id	sid	tid	token	lemma	pos
ejpam-6600	1	1	european	european	PROPN
ejpam-6600	1	2	journal	journal	PROPN
ejpam-6600	1	3	of	of	ADP
ejpam-6600	1	4	pure	pure	ADJ
ejpam-6600	1	5	and	and	CCONJ
ejpam-6600	1	6	applied	applied	ADJ
ejpam-6600	1	7	mathematics	mathematic	NOUN
ejpam-6600	1	8	2025	2025	NUM
ejpam-6600	1	9	,	,	PUNCT
ejpam-6600	1	10	vol	vol	NOUN
ejpam-6600	1	11	.	.	PROPN
ejpam-6600	1	12	18	18	NUM
ejpam-6600	1	13	,	,	PUNCT
ejpam-6600	1	14	issue	issue	NOUN
ejpam-6600	1	15	4	4	NUM
ejpam-6600	1	16	,	,	PUNCT
ejpam-6600	1	17	article	article	NOUN
ejpam-6600	1	18	number	number	NOUN
ejpam-6600	1	19	6600	6600	NUM
ejpam-6600	1	20	issn	issn	PROPN
ejpam-6600	1	21	1307	1307	NUM
ejpam-6600	1	22	-	-	SYM
ejpam-6600	1	23	5543	5543	NUM
ejpam-6600	1	24	–	–	PUNCT
ejpam-6600	1	25	ejpam.com	ejpam.com	X
ejpam-6600	1	26	published	publish	VERB
ejpam-6600	1	27	by	by	ADP
ejpam-6600	1	28	new	new	PROPN
ejpam-6600	1	29	york	york	PROPN
ejpam-6600	1	30	business	business	PROPN
ejpam-6600	1	31	global	global	PROPN
ejpam-6600	1	32	paley	paley	PROPN
ejpam-6600	1	33	,	,	PUNCT
ejpam-6600	1	34	cubic	cubic	ADJ
ejpam-6600	1	35	paley	paley	NOUN
ejpam-6600	1	36	,	,	PUNCT
ejpam-6600	1	37	quadruple	quadruple	NOUN
ejpam-6600	1	38	paley	paley	NOUN
ejpam-6600	1	39	,	,	PUNCT
ejpam-6600	1	40	and	and	CCONJ
ejpam-6600	1	41	generalized	generalized	ADJ
ejpam-6600	1	42	paley	paley	ADJ
ejpam-6600	1	43	graphs	graph	NOUN
ejpam-6600	1	44	with	with	ADP
ejpam-6600	1	45	an	an	DET
ejpam-6600	1	46	edge	edge	NOUN
ejpam-6600	1	47	graceful	graceful	ADJ
ejpam-6600	1	48	labeling	labeling	NOUN
ejpam-6600	1	49	ahmed	ahmed	PROPN
ejpam-6600	1	50	n.	n.	PROPN
ejpam-6600	1	51	elsawy1,2,∗	elsawy1,2,∗	PROPN
ejpam-6600	1	52	,	,	PUNCT
ejpam-6600	1	53	reyoud	reyoud	NOUN
ejpam-6600	1	54	nasser	nasser	PROPN
ejpam-6600	1	55	almohammadi1	almohammadi1	PROPN
ejpam-6600	1	56	1	1	NUM
ejpam-6600	1	57	department	department	NOUN
ejpam-6600	1	58	of	of	ADP
ejpam-6600	1	59	mathematics	mathematic	NOUN
ejpam-6600	1	60	,	,	PUNCT
ejpam-6600	1	61	college	college	NOUN
ejpam-6600	1	62	of	of	ADP
ejpam-6600	1	63	science	science	PROPN
ejpam-6600	1	64	,	,	PUNCT
ejpam-6600	1	65	taibah	taibah	PROPN
ejpam-6600	1	66	university	university	PROPN
ejpam-6600	1	67	,	,	PUNCT
ejpam-6600	1	68	madina	madina	PROPN
ejpam-6600	1	69	,	,	PUNCT
ejpam-6600	1	70	saudi	saudi	PROPN
ejpam-6600	1	71	arabia	arabia	PROPN
ejpam-6600	1	72	2	2	NUM
ejpam-6600	1	73	department	department	NOUN
ejpam-6600	1	74	of	of	ADP
ejpam-6600	1	75	mathematics	mathematic	NOUN
ejpam-6600	1	76	,	,	PUNCT
ejpam-6600	1	77	faculty	faculty	NOUN
ejpam-6600	1	78	of	of	ADP
ejpam-6600	1	79	science	science	NOUN
ejpam-6600	1	80	,	,	PUNCT
ejpam-6600	1	81	al	al	PROPN
ejpam-6600	1	82	-	-	PUNCT
ejpam-6600	1	83	azhar	azhar	PROPN
ejpam-6600	1	84	university	university	PROPN
ejpam-6600	1	85	,	,	PUNCT
ejpam-6600	1	86	cairo	cairo	PROPN
ejpam-6600	1	87	,	,	PUNCT
ejpam-6600	1	88	egypt	egypt	PROPN
ejpam-6600	1	89	abstract	abstract	PROPN
ejpam-6600	1	90	.	.	PUNCT
ejpam-6600	2	1	the	the	DET
ejpam-6600	2	2	paley	paley	PROPN
ejpam-6600	2	3	graph	graph	NOUN
ejpam-6600	2	4	pq	pq	NOUN
ejpam-6600	2	5	is	be	AUX
ejpam-6600	2	6	a	a	DET
ejpam-6600	2	7	simple	simple	ADJ
ejpam-6600	2	8	,	,	PUNCT
ejpam-6600	2	9	connected	connected	ADJ
ejpam-6600	2	10	,	,	PUNCT
ejpam-6600	2	11	strongly	strongly	ADV
ejpam-6600	2	12	regular	regular	ADJ
ejpam-6600	2	13	graph	graph	NOUN
ejpam-6600	2	14	with	with	ADP
ejpam-6600	2	15	parameters	parameter	NOUN
ejpam-6600	2	16	(	(	PUNCT
ejpam-6600	2	17	q	q	X
ejpam-6600	2	18	,	,	PUNCT
ejpam-6600	2	19	q−1	q−1	PROPN
ejpam-6600	2	20	2	2	NUM
ejpam-6600	2	21	,	,	PUNCT
ejpam-6600	2	22	q−5	q−5	ADP
ejpam-6600	2	23	4	4	NUM
ejpam-6600	2	24	,	,	PUNCT
ejpam-6600	2	25	q−1	q−1	PROPN
ejpam-6600	2	26	4	4	NUM
ejpam-6600	2	27	)	)	PUNCT
ejpam-6600	2	28	,	,	PUNCT
ejpam-6600	2	29	where	where	SCONJ
ejpam-6600	2	30	v	v	NOUN
ejpam-6600	2	31	(	(	PUNCT
ejpam-6600	2	32	pq	pq	NOUN
ejpam-6600	2	33	)	)	PUNCT
ejpam-6600	2	34	is	be	AUX
ejpam-6600	2	35	the	the	DET
ejpam-6600	2	36	finite	finite	ADJ
ejpam-6600	2	37	field	field	NOUN
ejpam-6600	2	38	fq	fq	PROPN
ejpam-6600	2	39	of	of	ADP
ejpam-6600	2	40	order	order	NOUN
ejpam-6600	2	41	q	q	NOUN
ejpam-6600	2	42	=	=	SYM
ejpam-6600	2	43	pn	pn	NOUN
ejpam-6600	2	44	,	,	PUNCT
ejpam-6600	2	45	p	p	PRON
ejpam-6600	2	46	is	be	AUX
ejpam-6600	2	47	an	an	DET
ejpam-6600	2	48	odd	odd	ADJ
ejpam-6600	2	49	prime	prime	NOUN
ejpam-6600	2	50	,	,	PUNCT
ejpam-6600	2	51	n	n	PROPN
ejpam-6600	2	52	∈	∈	PROPN
ejpam-6600	2	53	n	n	CCONJ
ejpam-6600	2	54	,	,	PUNCT
ejpam-6600	2	55	and	and	CCONJ
ejpam-6600	2	56	q	q	PROPN
ejpam-6600	2	57	≡	≡	PROPN
ejpam-6600	2	58	1	1	NUM
ejpam-6600	2	59	(	(	PUNCT
ejpam-6600	2	60	mod	mod	NOUN
ejpam-6600	2	61	4	4	NUM
ejpam-6600	2	62	)	)	PUNCT
ejpam-6600	2	63	.	.	PUNCT
ejpam-6600	3	1	in	in	ADP
ejpam-6600	3	2	paley	paley	ADJ
ejpam-6600	3	3	graphs	graph	NOUN
ejpam-6600	3	4	,	,	PUNCT
ejpam-6600	3	5	two	two	NUM
ejpam-6600	3	6	vertices	vertex	NOUN
ejpam-6600	3	7	are	be	AUX
ejpam-6600	3	8	adjacent	adjacent	ADJ
ejpam-6600	3	9	if	if	SCONJ
ejpam-6600	3	10	their	their	PRON
ejpam-6600	3	11	difference	difference	NOUN
ejpam-6600	3	12	is	be	AUX
ejpam-6600	3	13	a	a	DET
ejpam-6600	3	14	quadratic	quadratic	ADJ
ejpam-6600	3	15	residue	residue	NOUN
ejpam-6600	3	16	(	(	PUNCT
ejpam-6600	3	17	mod	mod	PROPN
ejpam-6600	3	18	q	q	NOUN
ejpam-6600	3	19	)	)	PUNCT
ejpam-6600	3	20	.	.	PUNCT
ejpam-6600	4	1	the	the	DET
ejpam-6600	4	2	vertex	vertex	NOUN
ejpam-6600	4	3	set	set	NOUN
ejpam-6600	4	4	of	of	ADP
ejpam-6600	4	5	the	the	DET
ejpam-6600	4	6	generalized	generalize	VERB
ejpam-6600	4	7	paley	paley	NOUN
ejpam-6600	4	8	graph	graph	NOUN
ejpam-6600	4	9	m	m	VERB
ejpam-6600	4	10	−	−	PROPN
ejpam-6600	4	11	pq	pq	NOUN
ejpam-6600	4	12	,	,	PUNCT
ejpam-6600	4	13	where	where	SCONJ
ejpam-6600	4	14	m	m	PROPN
ejpam-6600	4	15	≥	≥	NUM
ejpam-6600	4	16	3	3	NUM
ejpam-6600	4	17	is	be	AUX
ejpam-6600	4	18	an	an	DET
ejpam-6600	4	19	odd	odd	ADJ
ejpam-6600	4	20	integer	integer	NOUN
ejpam-6600	4	21	,	,	PUNCT
ejpam-6600	4	22	is	be	AUX
ejpam-6600	4	23	v	v	NOUN
ejpam-6600	4	24	(	(	PUNCT
ejpam-6600	4	25	m	m	PROPN
ejpam-6600	4	26	−	−	PROPN
ejpam-6600	4	27	pq	pq	NOUN
ejpam-6600	4	28	)	)	PUNCT
ejpam-6600	4	29	=	=	SYM
ejpam-6600	4	30	fq	fq	PROPN
ejpam-6600	4	31	and	and	CCONJ
ejpam-6600	4	32	the	the	DET
ejpam-6600	4	33	set	set	NOUN
ejpam-6600	4	34	of	of	ADP
ejpam-6600	4	35	edges	edge	NOUN
ejpam-6600	4	36	is	be	AUX
ejpam-6600	4	37	e(m	e(m	PROPN
ejpam-6600	4	38	−	−	PROPN
ejpam-6600	4	39	pq	pq	NOUN
ejpam-6600	4	40	)	)	PUNCT
ejpam-6600	4	41	=	=	PRON
ejpam-6600	4	42	{	{	PUNCT
ejpam-6600	4	43	(	(	PUNCT
ejpam-6600	4	44	x	x	NOUN
ejpam-6600	4	45	,	,	PUNCT
ejpam-6600	4	46	y	y	PROPN
ejpam-6600	4	47	)	)	PUNCT
ejpam-6600	4	48	⇔	⇔	PROPN
ejpam-6600	4	49	x−	x−	PROPN
ejpam-6600	4	50	y	y	PROPN
ejpam-6600	4	51	∈	∈	PROPN
ejpam-6600	4	52	(	(	PUNCT
ejpam-6600	4	53	f	f	PROPN
ejpam-6600	4	54	∗	∗	X
ejpam-6600	4	55	q	q	PROPN
ejpam-6600	4	56	)	)	PUNCT
ejpam-6600	4	57	m	m	VERB
ejpam-6600	4	58	}	}	PUNCT
ejpam-6600	4	59	.	.	PUNCT
ejpam-6600	5	1	in	in	ADP
ejpam-6600	5	2	1985	1985	NUM
ejpam-6600	5	3	,	,	PUNCT
ejpam-6600	5	4	edge	edge	NOUN
ejpam-6600	5	5	-	-	PUNCT
ejpam-6600	5	6	graceful	graceful	NOUN
ejpam-6600	5	7	labeling	labeling	NOUN
ejpam-6600	5	8	was	be	AUX
ejpam-6600	5	9	first	first	ADV
ejpam-6600	5	10	introduced	introduce	VERB
ejpam-6600	5	11	by	by	ADP
ejpam-6600	5	12	lo	lo	PROPN
ejpam-6600	6	1	[	[	X
ejpam-6600	6	2	1	1	NUM
ejpam-6600	6	3	]	]	PUNCT
ejpam-6600	6	4	.	.	PUNCT
ejpam-6600	7	1	a	a	DET
ejpam-6600	7	2	graph	graph	NOUN
ejpam-6600	7	3	g	g	NOUN
ejpam-6600	7	4	with	with	ADP
ejpam-6600	7	5	order	order	NOUN
ejpam-6600	7	6	n	n	NOUN
ejpam-6600	7	7	and	and	CCONJ
ejpam-6600	7	8	size	size	NOUN
ejpam-6600	7	9	m	m	VERB
ejpam-6600	7	10	is	be	AUX
ejpam-6600	7	11	called	call	VERB
ejpam-6600	7	12	edge	edge	NOUN
ejpam-6600	7	13	-	-	PUNCT
ejpam-6600	7	14	graceful	graceful	NOUN
ejpam-6600	7	15	if	if	SCONJ
ejpam-6600	7	16	there	there	PRON
ejpam-6600	7	17	exists	exist	VERB
ejpam-6600	7	18	a	a	DET
ejpam-6600	7	19	bijective	bijective	ADJ
ejpam-6600	7	20	mapping	mapping	NOUN
ejpam-6600	7	21	f	f	NOUN
ejpam-6600	7	22	:	:	PUNCT
ejpam-6600	7	23	e(g	e(g	NOUN
ejpam-6600	7	24	)	)	PUNCT
ejpam-6600	8	1	−→	−→	NOUN
ejpam-6600	8	2	{	{	PUNCT
ejpam-6600	8	3	1	1	NUM
ejpam-6600	8	4	,	,	PUNCT
ejpam-6600	8	5	2	2	NUM
ejpam-6600	8	6	,	,	PUNCT
ejpam-6600	8	7	3	3	NUM
ejpam-6600	8	8	,	,	PUNCT
ejpam-6600	8	9	.	.	PUNCT
ejpam-6600	8	10	.	.	PUNCT
ejpam-6600	9	1	.	.	PUNCT
ejpam-6600	10	1	,	,	PUNCT
ejpam-6600	10	2	m	m	VERB
ejpam-6600	10	3	}	}	PUNCT
ejpam-6600	10	4	such	such	ADJ
ejpam-6600	10	5	that	that	SCONJ
ejpam-6600	10	6	the	the	DET
ejpam-6600	10	7	weights	weight	NOUN
ejpam-6600	10	8	map	map	NOUN
ejpam-6600	10	9	fw	fw	INTJ
ejpam-6600	10	10	:	:	PUNCT
ejpam-6600	10	11	v	v	NOUN
ejpam-6600	10	12	(	(	PUNCT
ejpam-6600	10	13	g	g	NOUN
ejpam-6600	10	14	)	)	PUNCT
ejpam-6600	10	15	−→	−→	NOUN
ejpam-6600	10	16	{	{	PUNCT
ejpam-6600	10	17	0	0	NUM
ejpam-6600	10	18	,	,	PUNCT
ejpam-6600	10	19	1	1	NUM
ejpam-6600	10	20	,	,	PUNCT
ejpam-6600	10	21	2	2	NUM
ejpam-6600	10	22	,	,	PUNCT
ejpam-6600	10	23	.	.	PUNCT
ejpam-6600	10	24	.	.	PUNCT
ejpam-6600	11	1	.	.	PUNCT
ejpam-6600	12	1	,	,	PUNCT
ejpam-6600	12	2	n−	n−	NOUN
ejpam-6600	12	3	1	1	NUM
ejpam-6600	12	4	}	}	PUNCT
ejpam-6600	12	5	,	,	PUNCT
ejpam-6600	12	6	given	give	VERB
ejpam-6600	12	7	by	by	ADP
ejpam-6600	12	8	fw(u	fw(u	NOUN
ejpam-6600	12	9	)	)	PUNCT
ejpam-6600	12	10	=	=	SYM
ejpam-6600	12	11	∑	∑	PUNCT
ejpam-6600	12	12	v∈n(u	v∈n(u	PROPN
ejpam-6600	12	13	)	)	PUNCT
ejpam-6600	12	14	f(uv	f(uv	NOUN
ejpam-6600	12	15	)	)	PUNCT
ejpam-6600	12	16	(	(	PUNCT
ejpam-6600	12	17	mod	mod	NOUN
ejpam-6600	12	18	n	n	CCONJ
ejpam-6600	12	19	)	)	PUNCT
ejpam-6600	12	20	,	,	PUNCT
ejpam-6600	12	21	is	be	AUX
ejpam-6600	12	22	one	one	NUM
ejpam-6600	12	23	-	-	PUNCT
ejpam-6600	12	24	to	to	ADP
ejpam-6600	12	25	-	-	PUNCT
ejpam-6600	12	26	one	one	NUM
ejpam-6600	12	27	and	and	CCONJ
ejpam-6600	12	28	onto	onto	ADP
ejpam-6600	12	29	.	.	PUNCT
ejpam-6600	13	1	in	in	ADP
ejpam-6600	13	2	this	this	DET
ejpam-6600	13	3	paper	paper	NOUN
ejpam-6600	13	4	,	,	PUNCT
ejpam-6600	13	5	we	we	PRON
ejpam-6600	13	6	prove	prove	VERB
ejpam-6600	13	7	that	that	SCONJ
ejpam-6600	13	8	paley	paley	ADJ
ejpam-6600	13	9	graphs	graph	NOUN
ejpam-6600	13	10	and	and	CCONJ
ejpam-6600	13	11	generalized	generalized	ADJ
ejpam-6600	13	12	paley	paley	ADJ
ejpam-6600	13	13	graphs	graph	NOUN
ejpam-6600	13	14	of	of	ADP
ejpam-6600	13	15	prime	prime	ADJ
ejpam-6600	13	16	order	order	NOUN
ejpam-6600	13	17	are	be	AUX
ejpam-6600	13	18	edge	edge	NOUN
ejpam-6600	13	19	graceful	graceful	ADJ
ejpam-6600	13	20	,	,	PUNCT
ejpam-6600	13	21	edge	edge	NOUN
ejpam-6600	13	22	-	-	PUNCT
ejpam-6600	13	23	even	even	ADV
ejpam-6600	13	24	graceful	graceful	ADJ
ejpam-6600	13	25	,	,	PUNCT
ejpam-6600	13	26	and	and	CCONJ
ejpam-6600	13	27	edge	edge	NOUN
ejpam-6600	13	28	-	-	PUNCT
ejpam-6600	13	29	odd	odd	ADJ
ejpam-6600	13	30	graceful	graceful	ADJ
ejpam-6600	13	31	graphs	graph	NOUN
ejpam-6600	13	32	.	.	PUNCT
ejpam-6600	14	1	2020	2020	NUM
ejpam-6600	14	2	mathematics	mathematic	NOUN
ejpam-6600	14	3	subject	subject	NOUN
ejpam-6600	14	4	classifications	classification	NOUN
ejpam-6600	14	5	:	:	PUNCT
ejpam-6600	14	6	05c25	05c25	NUM
ejpam-6600	14	7	,	,	PUNCT
ejpam-6600	14	8	05c78	05c78	NUM
ejpam-6600	14	9	key	key	ADJ
ejpam-6600	14	10	words	word	NOUN
ejpam-6600	14	11	and	and	CCONJ
ejpam-6600	14	12	phrases	phrase	NOUN
ejpam-6600	14	13	:	:	PUNCT
ejpam-6600	14	14	paley	paley	ADJ
ejpam-6600	14	15	graphs	graph	NOUN
ejpam-6600	14	16	,	,	PUNCT
ejpam-6600	14	17	cubic	cubic	ADJ
ejpam-6600	14	18	paley	paley	NOUN
ejpam-6600	14	19	graphs	graph	NOUN
ejpam-6600	14	20	,	,	PUNCT
ejpam-6600	14	21	quadruple	quadruple	NOUN
ejpam-6600	14	22	paley	paley	NOUN
ejpam-6600	14	23	graphs	graph	NOUN
ejpam-6600	14	24	,	,	PUNCT
ejpam-6600	14	25	generalized	generalized	ADJ
ejpam-6600	14	26	paley	paley	ADJ
ejpam-6600	14	27	graphs	graph	NOUN
ejpam-6600	14	28	,	,	PUNCT
ejpam-6600	14	29	edge	edge	NOUN
ejpam-6600	14	30	-	-	PUNCT
ejpam-6600	14	31	graceful	graceful	NOUN
ejpam-6600	14	32	labeling	labeling	NOUN
ejpam-6600	14	33	,	,	PUNCT
ejpam-6600	14	34	edge	edge	NOUN
ejpam-6600	14	35	-	-	PUNCT
ejpam-6600	14	36	even	even	ADV
ejpam-6600	14	37	graceful	graceful	ADJ
ejpam-6600	14	38	labeling	labeling	NOUN
ejpam-6600	14	39	,	,	PUNCT
ejpam-6600	14	40	edge	edge	NOUN
ejpam-6600	14	41	-	-	PUNCT
ejpam-6600	14	42	odd	odd	ADJ
ejpam-6600	14	43	graceful	graceful	ADJ
ejpam-6600	14	44	labeling	labeling	NOUN
ejpam-6600	14	45	1	1	NUM
ejpam-6600	14	46	.	.	PUNCT
ejpam-6600	14	47	introduction	introduction	NOUN
ejpam-6600	14	48	a	a	DET
ejpam-6600	14	49	finite	finite	ADJ
ejpam-6600	14	50	field	field	NOUN
ejpam-6600	14	51	fq	fq	NOUN
ejpam-6600	14	52	of	of	ADP
ejpam-6600	14	53	order	order	NOUN
ejpam-6600	14	54	q	q	NOUN
ejpam-6600	14	55	,	,	PUNCT
ejpam-6600	14	56	where	where	SCONJ
ejpam-6600	14	57	q	q	NOUN
ejpam-6600	14	58	is	be	AUX
ejpam-6600	14	59	a	a	DET
ejpam-6600	14	60	prime	prime	ADJ
ejpam-6600	14	61	power	power	NOUN
ejpam-6600	14	62	congruent	congruent	NOUN
ejpam-6600	14	63	to	to	ADP
ejpam-6600	14	64	1	1	NUM
ejpam-6600	14	65	modulo	modulo	NOUN
ejpam-6600	14	66	4	4	NUM
ejpam-6600	14	67	,	,	PUNCT
ejpam-6600	14	68	is	be	AUX
ejpam-6600	14	69	used	use	VERB
ejpam-6600	14	70	in	in	ADP
ejpam-6600	14	71	the	the	DET
ejpam-6600	14	72	construction	construction	NOUN
ejpam-6600	14	73	of	of	ADP
ejpam-6600	14	74	the	the	DET
ejpam-6600	14	75	paley	paley	ADJ
ejpam-6600	14	76	graph	graph	NOUN
ejpam-6600	14	77	as	as	ADP
ejpam-6600	14	78	its	its	PRON
ejpam-6600	14	79	vertex	vertex	NOUN
ejpam-6600	14	80	set	set	NOUN
ejpam-6600	14	81	.	.	PUNCT
ejpam-6600	15	1	two	two	NUM
ejpam-6600	15	2	vertices	vertex	NOUN
ejpam-6600	15	3	are	be	AUX
ejpam-6600	15	4	adjacent	adjacent	ADJ
ejpam-6600	15	5	if	if	SCONJ
ejpam-6600	15	6	and	and	CCONJ
ejpam-6600	15	7	only	only	ADV
ejpam-6600	15	8	if	if	SCONJ
ejpam-6600	15	9	their	their	PRON
ejpam-6600	15	10	difference	difference	NOUN
ejpam-6600	15	11	is	be	AUX
ejpam-6600	15	12	a	a	DET
ejpam-6600	15	13	non	non	ADJ
ejpam-6600	15	14	-	-	ADJ
ejpam-6600	15	15	zero	zero	NUM
ejpam-6600	15	16	square	square	NOUN
ejpam-6600	15	17	in	in	ADP
ejpam-6600	15	18	the	the	DET
ejpam-6600	15	19	field	field	NOUN
ejpam-6600	15	20	.	.	PUNCT
ejpam-6600	16	1	in	in	ADP
ejpam-6600	16	2	this	this	DET
ejpam-6600	16	3	paper	paper	NOUN
ejpam-6600	16	4	,	,	PUNCT
ejpam-6600	16	5	we	we	PRON
ejpam-6600	16	6	are	be	AUX
ejpam-6600	16	7	concerned	concerned	ADJ
ejpam-6600	16	8	with	with	ADP
ejpam-6600	16	9	the	the	DET
ejpam-6600	16	10	simple	simple	ADJ
ejpam-6600	16	11	form	form	NOUN
ejpam-6600	16	12	of	of	ADP
ejpam-6600	16	13	paley	paley	ADJ
ejpam-6600	16	14	graphs	graph	NOUN
ejpam-6600	16	15	where	where	SCONJ
ejpam-6600	16	16	fq	fq	PROPN
ejpam-6600	16	17	=	=	PROPN
ejpam-6600	16	18	zp	zp	PROPN
ejpam-6600	16	19	is	be	AUX
ejpam-6600	16	20	the	the	DET
ejpam-6600	16	21	field	field	NOUN
ejpam-6600	16	22	of	of	ADP
ejpam-6600	16	23	integers	integer	NOUN
ejpam-6600	16	24	(	(	PUNCT
ejpam-6600	16	25	mod	mod	NOUN
ejpam-6600	16	26	p	p	X
ejpam-6600	16	27	)	)	PUNCT
ejpam-6600	16	28	.	.	PUNCT
ejpam-6600	17	1	we	we	PRON
ejpam-6600	17	2	are	be	AUX
ejpam-6600	17	3	also	also	ADV
ejpam-6600	17	4	interested	interested	ADJ
ejpam-6600	17	5	in	in	ADP
ejpam-6600	17	6	the	the	DET
ejpam-6600	17	7	generalized	generalized	ADJ
ejpam-6600	17	8	paley	paley	NOUN
ejpam-6600	17	9	graph	graph	NOUN
ejpam-6600	17	10	m−pq	m−pq	NOUN
ejpam-6600	17	11	,	,	PUNCT
ejpam-6600	17	12	where	where	SCONJ
ejpam-6600	17	13	v	v	NOUN
ejpam-6600	17	14	(	(	PUNCT
ejpam-6600	17	15	m−pq	m−pq	NOUN
ejpam-6600	17	16	)	)	PUNCT
ejpam-6600	18	1	=	=	SYM
ejpam-6600	18	2	fq	fq	PROPN
ejpam-6600	18	3	is	be	AUX
ejpam-6600	18	4	the	the	DET
ejpam-6600	18	5	finite	finite	ADJ
ejpam-6600	18	6	field	field	NOUN
ejpam-6600	18	7	with	with	ADP
ejpam-6600	18	8	q	q	NOUN
ejpam-6600	18	9	=	=	PUNCT
ejpam-6600	18	10	pn	pn	NOUN
ejpam-6600	18	11	elements	element	NOUN
ejpam-6600	18	12	,	,	PUNCT
ejpam-6600	18	13	p	p	NOUN
ejpam-6600	18	14	is	be	AUX
ejpam-6600	18	15	an	an	DET
ejpam-6600	18	16	odd	odd	ADJ
ejpam-6600	18	17	prime	prime	NOUN
ejpam-6600	18	18	,	,	PUNCT
ejpam-6600	18	19	and	and	CCONJ
ejpam-6600	18	20	n	n	DET
ejpam-6600	18	21	∈	∈	PROPN
ejpam-6600	18	22	n.	n.	NOUN
ejpam-6600	18	23	the	the	DET
ejpam-6600	18	24	edge	edge	NOUN
ejpam-6600	18	25	set	set	NOUN
ejpam-6600	18	26	is	be	AUX
ejpam-6600	18	27	e(m	e(m	PROPN
ejpam-6600	18	28	−	−	PROPN
ejpam-6600	18	29	pq	pq	NOUN
ejpam-6600	18	30	)	)	PUNCT
ejpam-6600	18	31	=	=	PRON
ejpam-6600	18	32	{	{	PUNCT
ejpam-6600	18	33	(	(	PUNCT
ejpam-6600	18	34	x	x	NOUN
ejpam-6600	18	35	,	,	PUNCT
ejpam-6600	18	36	y	y	PROPN
ejpam-6600	18	37	)	)	PUNCT
ejpam-6600	18	38	⇔	⇔	PROPN
ejpam-6600	18	39	x−	x−	PROPN
ejpam-6600	18	40	y	y	PROPN
ejpam-6600	18	41	∈	∈	PROPN
ejpam-6600	18	42	(	(	PUNCT
ejpam-6600	18	43	f	f	PROPN
ejpam-6600	18	44	∗	∗	X
ejpam-6600	18	45	q	q	PROPN
ejpam-6600	18	46	)	)	PUNCT
ejpam-6600	18	47	m	m	VERB
ejpam-6600	18	48	}	}	PUNCT
ejpam-6600	18	49	,	,	PUNCT
ejpam-6600	18	50	where	where	SCONJ
ejpam-6600	18	51	m	m	PROPN
ejpam-6600	18	52	≥	≥	NUM
ejpam-6600	18	53	3	3	NUM
ejpam-6600	18	54	is	be	AUX
ejpam-6600	18	55	an	an	DET
ejpam-6600	18	56	odd	odd	ADJ
ejpam-6600	18	57	integer	integer	NOUN
ejpam-6600	18	58	.	.	PUNCT
ejpam-6600	19	1	paley	paley	ADJ
ejpam-6600	19	2	graphs	graph	NOUN
ejpam-6600	19	3	have	have	VERB
ejpam-6600	19	4	several	several	ADJ
ejpam-6600	19	5	applications	application	NOUN
ejpam-6600	19	6	,	,	PUNCT
ejpam-6600	19	7	for	for	ADP
ejpam-6600	19	8	instance	instance	NOUN
ejpam-6600	19	9	,	,	PUNCT
ejpam-6600	19	10	in	in	ADP
ejpam-6600	19	11	network	network	NOUN
ejpam-6600	19	12	design	design	NOUN
ejpam-6600	19	13	[	[	X
ejpam-6600	19	14	2	2	NUM
ejpam-6600	19	15	]	]	PUNCT
ejpam-6600	19	16	.	.	PUNCT
ejpam-6600	20	1	also	also	ADV
ejpam-6600	20	2	,	,	PUNCT
ejpam-6600	20	3	paley	paley	ADJ
ejpam-6600	20	4	graphs	graph	NOUN
ejpam-6600	20	5	form	form	VERB
ejpam-6600	20	6	an	an	DET
ejpam-6600	20	7	important	important	ADJ
ejpam-6600	20	8	family	family	NOUN
ejpam-6600	20	9	in	in	ADP
ejpam-6600	20	10	graph	graph	NOUN
ejpam-6600	20	11	theory	theory	NOUN
ejpam-6600	20	12	due	due	ADP
ejpam-6600	20	13	to	to	ADP
ejpam-6600	20	14	their	their	PRON
ejpam-6600	20	15	rich	rich	ADJ
ejpam-6600	20	16	structural	structural	ADJ
ejpam-6600	20	17	properties	property	NOUN
ejpam-6600	20	18	.	.	PUNCT
ejpam-6600	21	1	one	one	NUM
ejpam-6600	21	2	of	of	ADP
ejpam-6600	21	3	their	their	PRON
ejpam-6600	21	4	key	key	ADJ
ejpam-6600	21	5	features	feature	NOUN
ejpam-6600	21	6	is	be	AUX
ejpam-6600	21	7	that	that	SCONJ
ejpam-6600	21	8	paley	paley	ADJ
ejpam-6600	21	9	graphs	graph	NOUN
ejpam-6600	21	10	are	be	AUX
ejpam-6600	21	11	strongly	strongly	ADV
ejpam-6600	21	12	regular	regular	ADJ
ejpam-6600	21	13	with	with	ADP
ejpam-6600	21	14	parameters	parameter	NOUN
ejpam-6600	21	15	∗corresponding	∗corresponde	VERB
ejpam-6600	21	16	author	author	NOUN
ejpam-6600	21	17	.	.	PUNCT
ejpam-6600	22	1	doi	doi	NOUN
ejpam-6600	22	2	:	:	PUNCT
ejpam-6600	22	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6600	https://doi.org/10.29020/nybg.ejpam.v18i4.6600	ADP
ejpam-6600	22	4	email	email	NOUN
ejpam-6600	22	5	addresses	address	NOUN
ejpam-6600	22	6	:	:	PUNCT
ejpam-6600	22	7	asawy@taibahu.edu.sa	asawy@taibahu.edu.sa	PROPN
ejpam-6600	22	8	,	,	PUNCT
ejpam-6600	22	9	ahnoby@yahoo.com	ahnoby@yahoo.com	X
ejpam-6600	22	10	(	(	PUNCT
ejpam-6600	22	11	a.	a.	PROPN
ejpam-6600	22	12	n.	n.	PROPN
ejpam-6600	22	13	elsawy	elsawy	PROPN
ejpam-6600	22	14	)	)	PUNCT
ejpam-6600	22	15	,	,	PUNCT
ejpam-6600	22	16	reyoud55@gmail.com	reyoud55@gmail.com	PROPN
ejpam-6600	22	17	(	(	PUNCT
ejpam-6600	22	18	r.	r.	PROPN
ejpam-6600	22	19	n.	n.	PROPN
ejpam-6600	22	20	almohammadi	almohammadi	PROPN
ejpam-6600	22	21	)	)	PUNCT
ejpam-6600	22	22	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6600	23	1	1	1	NUM
ejpam-6600	23	2	copyright	copyright	NOUN
ejpam-6600	23	3	:	:	PUNCT
ejpam-6600	23	4	©	©	PROPN
ejpam-6600	23	5	2025	2025	NUM
ejpam-6600	23	6	the	the	DET
ejpam-6600	23	7	author(s	author(s	NOUN
ejpam-6600	23	8	)	)	PUNCT
ejpam-6600	23	9	.	.	PUNCT
ejpam-6600	24	1	(	(	PUNCT
ejpam-6600	24	2	cc	cc	NOUN
ejpam-6600	24	3	by	by	ADP
ejpam-6600	24	4	-	-	PUNCT
ejpam-6600	24	5	nc	nc	PROPN
ejpam-6600	24	6	4.0	4.0	NUM
ejpam-6600	24	7	)	)	PUNCT
ejpam-6600	24	8	a.	a.	NOUN
ejpam-6600	24	9	n.	n.	PROPN
ejpam-6600	24	10	elsawy	elsawy	PROPN
ejpam-6600	24	11	,	,	PUNCT
ejpam-6600	24	12	r.	r.	PROPN
ejpam-6600	24	13	n.	n.	PROPN
ejpam-6600	24	14	almohammadi	almohammadi	PROPN
ejpam-6600	24	15	/	/	SYM
ejpam-6600	24	16	eur	eur	PROPN
ejpam-6600	24	17	.	.	PUNCT
ejpam-6600	25	1	j.	j.	PROPN
ejpam-6600	25	2	pure	pure	PROPN
ejpam-6600	25	3	appl	appl	PROPN
ejpam-6600	25	4	.	.	PROPN
ejpam-6600	25	5	math	math	PROPN
ejpam-6600	25	6	,	,	PUNCT
ejpam-6600	25	7	18	18	NUM
ejpam-6600	25	8	(	(	PUNCT
ejpam-6600	25	9	4	4	NUM
ejpam-6600	25	10	)	)	PUNCT
ejpam-6600	25	11	(	(	PUNCT
ejpam-6600	25	12	2025	2025	NUM
ejpam-6600	25	13	)	)	PUNCT
ejpam-6600	25	14	,	,	PUNCT
ejpam-6600	25	15	6600	6600	NUM
ejpam-6600	25	16	2	2	NUM
ejpam-6600	25	17	of	of	ADP
ejpam-6600	25	18	26	26	NUM
ejpam-6600	25	19	(	(	PUNCT
ejpam-6600	25	20	q	q	NOUN
ejpam-6600	25	21	,	,	PUNCT
ejpam-6600	25	22	q−1	q−1	PROPN
ejpam-6600	25	23	2	2	NUM
ejpam-6600	25	24	,	,	PUNCT
ejpam-6600	25	25	q−5	q−5	ADP
ejpam-6600	25	26	4	4	NUM
ejpam-6600	25	27	,	,	PUNCT
ejpam-6600	25	28	q−1	q−1	PROPN
ejpam-6600	25	29	4	4	NUM
ejpam-6600	25	30	)	)	PUNCT
ejpam-6600	25	31	.	.	PUNCT
ejpam-6600	26	1	this	this	PRON
ejpam-6600	26	2	means	mean	VERB
ejpam-6600	26	3	that	that	SCONJ
ejpam-6600	26	4	the	the	DET
ejpam-6600	26	5	graph	graph	NOUN
ejpam-6600	26	6	has	have	VERB
ejpam-6600	26	7	order	order	NOUN
ejpam-6600	26	8	q	q	NOUN
ejpam-6600	26	9	,	,	PUNCT
ejpam-6600	26	10	is	be	AUX
ejpam-6600	26	11	q−1	q−1	PROPN
ejpam-6600	26	12	2	2	NUM
ejpam-6600	26	13	−regular	−regular	NOUN
ejpam-6600	26	14	,	,	PUNCT
ejpam-6600	26	15	each	each	DET
ejpam-6600	26	16	pair	pair	NOUN
ejpam-6600	26	17	of	of	ADP
ejpam-6600	26	18	adjacent	adjacent	ADJ
ejpam-6600	26	19	vertices	vertex	NOUN
ejpam-6600	26	20	has	have	VERB
ejpam-6600	26	21	q−5	q−5	PROPN
ejpam-6600	26	22	4	4	NUM
ejpam-6600	26	23	common	common	ADJ
ejpam-6600	26	24	neighbors	neighbor	NOUN
ejpam-6600	26	25	,	,	PUNCT
ejpam-6600	26	26	and	and	CCONJ
ejpam-6600	26	27	each	each	DET
ejpam-6600	26	28	pair	pair	NOUN
ejpam-6600	26	29	of	of	ADP
ejpam-6600	26	30	non	non	ADJ
ejpam-6600	26	31	-	-	ADJ
ejpam-6600	26	32	adjacent	adjacent	ADJ
ejpam-6600	26	33	vertices	vertex	NOUN
ejpam-6600	26	34	has	have	VERB
ejpam-6600	26	35	q−1	q−1	PROPN
ejpam-6600	26	36	4	4	NUM
ejpam-6600	26	37	common	common	ADJ
ejpam-6600	26	38	neighbors	neighbor	NOUN
ejpam-6600	26	39	.	.	PUNCT
ejpam-6600	27	1	furthermore	furthermore	ADV
ejpam-6600	27	2	,	,	PUNCT
ejpam-6600	27	3	paley	paley	ADJ
ejpam-6600	27	4	graphs	graph	NOUN
ejpam-6600	27	5	are	be	AUX
ejpam-6600	27	6	self	self	NOUN
ejpam-6600	27	7	-	-	PUNCT
ejpam-6600	27	8	complementary	complementary	ADJ
ejpam-6600	27	9	,	,	PUNCT
ejpam-6600	27	10	symmetric	symmetric	ADJ
ejpam-6600	27	11	,	,	PUNCT
ejpam-6600	27	12	and	and	CCONJ
ejpam-6600	27	13	hamiltonian	hamiltonian	ADJ
ejpam-6600	27	14	,	,	PUNCT
ejpam-6600	27	15	for	for	ADP
ejpam-6600	27	16	more	more	ADJ
ejpam-6600	27	17	details	detail	NOUN
ejpam-6600	27	18	(	(	PUNCT
ejpam-6600	27	19	see	see	VERB
ejpam-6600	27	20	[	[	X
ejpam-6600	27	21	3	3	NUM
ejpam-6600	27	22	]	]	PUNCT
ejpam-6600	27	23	,	,	PUNCT
ejpam-6600	27	24	[	[	X
ejpam-6600	27	25	4	4	NUM
ejpam-6600	27	26	]	]	NUM
ejpam-6600	27	27	)	)	PUNCT
ejpam-6600	27	28	.	.	PUNCT
ejpam-6600	28	1	paley	paley	ADJ
ejpam-6600	28	2	graphs	graph	NOUN
ejpam-6600	28	3	possess	possess	VERB
ejpam-6600	28	4	not	not	PART
ejpam-6600	28	5	only	only	ADV
ejpam-6600	28	6	a	a	DET
ejpam-6600	28	7	hamiltonian	hamiltonian	ADJ
ejpam-6600	28	8	property	property	NOUN
ejpam-6600	28	9	but	but	CCONJ
ejpam-6600	28	10	also	also	ADV
ejpam-6600	28	11	a	a	DET
ejpam-6600	28	12	hamiltonian	hamiltonian	ADJ
ejpam-6600	28	13	decomposition	decomposition	NOUN
ejpam-6600	28	14	;	;	PUNCT
ejpam-6600	28	15	that	that	PRON
ejpam-6600	28	16	is	is	ADV
ejpam-6600	28	17	,	,	PUNCT
ejpam-6600	28	18	the	the	DET
ejpam-6600	28	19	edge	edge	NOUN
ejpam-6600	28	20	set	set	NOUN
ejpam-6600	28	21	can	can	AUX
ejpam-6600	28	22	be	be	AUX
ejpam-6600	28	23	represented	represent	VERB
ejpam-6600	28	24	as	as	ADP
ejpam-6600	28	25	the	the	DET
ejpam-6600	28	26	union	union	NOUN
ejpam-6600	28	27	of	of	ADP
ejpam-6600	28	28	edge	edge	NOUN
ejpam-6600	28	29	-	-	PUNCT
ejpam-6600	28	30	disjoint	disjoint	NOUN
ejpam-6600	28	31	hamiltonian	hamiltonian	ADJ
ejpam-6600	28	32	cycles	cycle	NOUN
ejpam-6600	28	33	,	,	PUNCT
ejpam-6600	28	34	see	see	VERB
ejpam-6600	28	35	[	[	X
ejpam-6600	28	36	5	5	NUM
ejpam-6600	28	37	]	]	PUNCT
ejpam-6600	28	38	.	.	PUNCT
ejpam-6600	29	1	paley	paley	ADJ
ejpam-6600	29	2	graphs	graph	NOUN
ejpam-6600	29	3	provide	provide	VERB
ejpam-6600	29	4	intriguing	intriguing	ADJ
ejpam-6600	29	5	characteristics	characteristic	NOUN
ejpam-6600	29	6	that	that	PRON
ejpam-6600	29	7	make	make	VERB
ejpam-6600	29	8	them	they	PRON
ejpam-6600	29	9	valuable	valuable	ADJ
ejpam-6600	29	10	in	in	ADP
ejpam-6600	29	11	graph	graph	NOUN
ejpam-6600	29	12	theory	theory	NOUN
ejpam-6600	29	13	and	and	CCONJ
ejpam-6600	29	14	allow	allow	VERB
ejpam-6600	29	15	the	the	DET
ejpam-6600	29	16	application	application	NOUN
ejpam-6600	29	17	of	of	ADP
ejpam-6600	29	18	graph	graph	NOUN
ejpam-6600	29	19	-	-	PUNCT
ejpam-6600	29	20	theoretic	theoretic	NOUN
ejpam-6600	29	21	techniques	technique	NOUN
ejpam-6600	29	22	to	to	ADP
ejpam-6600	29	23	the	the	DET
ejpam-6600	29	24	number	number	NOUN
ejpam-6600	29	25	theory	theory	NOUN
ejpam-6600	29	26	involving	involve	VERB
ejpam-6600	29	27	quadratic	quadratic	ADJ
ejpam-6600	29	28	residues	residue	NOUN
ejpam-6600	29	29	(	(	PUNCT
ejpam-6600	29	30	see	see	VERB
ejpam-6600	29	31	[	[	X
ejpam-6600	29	32	6	6	NUM
ejpam-6600	29	33	]	]	PUNCT
ejpam-6600	29	34	,	,	PUNCT
ejpam-6600	29	35	[	[	X
ejpam-6600	29	36	7	7	NUM
ejpam-6600	29	37	]	]	PUNCT
ejpam-6600	29	38	,	,	PUNCT
ejpam-6600	29	39	[	[	X
ejpam-6600	29	40	8	8	NUM
ejpam-6600	29	41	]	]	PUNCT
ejpam-6600	29	42	,	,	PUNCT
ejpam-6600	29	43	[	[	X
ejpam-6600	29	44	9	9	NUM
ejpam-6600	29	45	]	]	NUM
ejpam-6600	29	46	)	)	PUNCT
ejpam-6600	29	47	.	.	PUNCT
ejpam-6600	30	1	another	another	DET
ejpam-6600	30	2	active	active	ADJ
ejpam-6600	30	3	area	area	NOUN
ejpam-6600	30	4	of	of	ADP
ejpam-6600	30	5	research	research	NOUN
ejpam-6600	30	6	in	in	ADP
ejpam-6600	30	7	graph	graph	NOUN
ejpam-6600	30	8	theory	theory	NOUN
ejpam-6600	30	9	concerns	concern	NOUN
ejpam-6600	30	10	graph	graph	NOUN
ejpam-6600	30	11	coloring	coloring	NOUN
ejpam-6600	30	12	and	and	CCONJ
ejpam-6600	30	13	the	the	DET
ejpam-6600	30	14	clique	clique	ADJ
ejpam-6600	30	15	number	number	NOUN
ejpam-6600	30	16	.	.	PUNCT
ejpam-6600	31	1	several	several	ADJ
ejpam-6600	31	2	papers	paper	NOUN
ejpam-6600	31	3	have	have	AUX
ejpam-6600	31	4	investigated	investigate	VERB
ejpam-6600	31	5	the	the	DET
ejpam-6600	31	6	clique	clique	ADJ
ejpam-6600	31	7	number	number	NOUN
ejpam-6600	31	8	of	of	ADP
ejpam-6600	31	9	paley	paley	ADJ
ejpam-6600	31	10	graphs	graph	NOUN
ejpam-6600	31	11	and	and	CCONJ
ejpam-6600	31	12	their	their	PRON
ejpam-6600	31	13	generalizations	generalization	NOUN
ejpam-6600	31	14	(	(	PUNCT
ejpam-6600	31	15	see	see	VERB
ejpam-6600	31	16	[	[	X
ejpam-6600	31	17	10	10	NUM
ejpam-6600	31	18	]	]	PUNCT
ejpam-6600	31	19	,	,	PUNCT
ejpam-6600	31	20	[	[	X
ejpam-6600	31	21	11	11	NUM
ejpam-6600	31	22	]	]	PUNCT
ejpam-6600	31	23	,	,	PUNCT
ejpam-6600	31	24	[	[	X
ejpam-6600	31	25	12	12	NUM
ejpam-6600	31	26	]	]	PUNCT
ejpam-6600	31	27	,	,	PUNCT
ejpam-6600	31	28	[	[	X
ejpam-6600	31	29	13	13	NUM
ejpam-6600	31	30	]	]	PUNCT
ejpam-6600	31	31	,	,	PUNCT
ejpam-6600	31	32	[	[	X
ejpam-6600	31	33	14	14	NUM
ejpam-6600	31	34	]	]	SYM
ejpam-6600	31	35	)	)	PUNCT
ejpam-6600	31	36	.	.	PUNCT
ejpam-6600	32	1	graph	graph	NOUN
ejpam-6600	32	2	labeling	labeling	NOUN
ejpam-6600	32	3	is	be	AUX
ejpam-6600	32	4	another	another	DET
ejpam-6600	32	5	important	important	ADJ
ejpam-6600	32	6	branch	branch	NOUN
ejpam-6600	32	7	of	of	ADP
ejpam-6600	32	8	graph	graph	NOUN
ejpam-6600	32	9	theory	theory	NOUN
ejpam-6600	32	10	,	,	PUNCT
ejpam-6600	32	11	in	in	ADP
ejpam-6600	32	12	which	which	PRON
ejpam-6600	32	13	labels	label	NOUN
ejpam-6600	32	14	are	be	AUX
ejpam-6600	32	15	assigned	assign	VERB
ejpam-6600	32	16	to	to	ADP
ejpam-6600	32	17	the	the	DET
ejpam-6600	32	18	vertices	vertex	NOUN
ejpam-6600	32	19	,	,	PUNCT
ejpam-6600	32	20	edges	edge	NOUN
ejpam-6600	32	21	,	,	PUNCT
ejpam-6600	32	22	or	or	CCONJ
ejpam-6600	32	23	both	both	PRON
ejpam-6600	32	24	,	,	PUNCT
ejpam-6600	32	25	under	under	ADP
ejpam-6600	32	26	certain	certain	ADJ
ejpam-6600	32	27	conditions	condition	NOUN
ejpam-6600	32	28	,	,	PUNCT
ejpam-6600	32	29	see	see	VERB
ejpam-6600	32	30	[	[	X
ejpam-6600	32	31	15	15	NUM
ejpam-6600	32	32	]	]	PUNCT
ejpam-6600	32	33	.	.	PUNCT
ejpam-6600	33	1	one	one	NUM
ejpam-6600	33	2	prominent	prominent	ADJ
ejpam-6600	33	3	type	type	NOUN
ejpam-6600	33	4	of	of	ADP
ejpam-6600	33	5	labeling	labeling	NOUN
ejpam-6600	33	6	that	that	PRON
ejpam-6600	33	7	has	have	AUX
ejpam-6600	33	8	attracted	attract	VERB
ejpam-6600	33	9	significant	significant	ADJ
ejpam-6600	33	10	attention	attention	NOUN
ejpam-6600	33	11	is	be	AUX
ejpam-6600	33	12	edge	edge	NOUN
ejpam-6600	33	13	-	-	PUNCT
ejpam-6600	33	14	graceful	graceful	NOUN
ejpam-6600	33	15	labeling	labeling	NOUN
ejpam-6600	33	16	,	,	PUNCT
ejpam-6600	33	17	which	which	PRON
ejpam-6600	33	18	has	have	VERB
ejpam-6600	33	19	important	important	ADJ
ejpam-6600	33	20	applications	application	NOUN
ejpam-6600	33	21	in	in	ADP
ejpam-6600	33	22	various	various	ADJ
ejpam-6600	33	23	areas	area	NOUN
ejpam-6600	33	24	,	,	PUNCT
ejpam-6600	33	25	including	include	VERB
ejpam-6600	33	26	computer	computer	NOUN
ejpam-6600	33	27	networks	network	NOUN
ejpam-6600	33	28	,	,	PUNCT
ejpam-6600	33	29	coding	code	VERB
ejpam-6600	33	30	theory	theory	NOUN
ejpam-6600	33	31	,	,	PUNCT
ejpam-6600	33	32	radar	radar	NOUN
ejpam-6600	33	33	,	,	PUNCT
ejpam-6600	33	34	circuit	circuit	NOUN
ejpam-6600	33	35	design	design	NOUN
ejpam-6600	33	36	,	,	PUNCT
ejpam-6600	33	37	and	and	CCONJ
ejpam-6600	33	38	communication	communication	NOUN
ejpam-6600	33	39	systems	system	NOUN
ejpam-6600	33	40	.	.	PUNCT
ejpam-6600	34	1	in	in	ADP
ejpam-6600	34	2	1967	1967	NUM
ejpam-6600	34	3	,	,	PUNCT
ejpam-6600	34	4	alexander	alexander	PROPN
ejpam-6600	34	5	rosa	rosa	PROPN
ejpam-6600	35	1	[	[	X
ejpam-6600	35	2	16	16	NUM
ejpam-6600	35	3	]	]	PUNCT
ejpam-6600	35	4	identified	identify	VERB
ejpam-6600	35	5	three	three	NUM
ejpam-6600	35	6	types	type	NOUN
ejpam-6600	35	7	of	of	ADP
ejpam-6600	35	8	labeling	labeling	NOUN
ejpam-6600	35	9	:	:	PUNCT
ejpam-6600	35	10	α	α	X
ejpam-6600	35	11	-	-	NOUN
ejpam-6600	35	12	labeling	labeling	NOUN
ejpam-6600	35	13	,	,	PUNCT
ejpam-6600	35	14	β	β	NOUN
ejpam-6600	35	15	-	-	NOUN
ejpam-6600	35	16	labeling	labeling	NOUN
ejpam-6600	35	17	,	,	PUNCT
ejpam-6600	35	18	and	and	CCONJ
ejpam-6600	35	19	ρ	ρ	NOUN
ejpam-6600	35	20	-	-	NOUN
ejpam-6600	35	21	labeling	labeling	NOUN
ejpam-6600	35	22	.	.	PUNCT
ejpam-6600	36	1	later	later	ADV
ejpam-6600	36	2	,	,	PUNCT
ejpam-6600	36	3	β	β	X
ejpam-6600	36	4	-	-	ADJ
ejpam-6600	36	5	labeling	labeling	NOUN
ejpam-6600	36	6	was	be	AUX
ejpam-6600	36	7	renamed	rename	VERB
ejpam-6600	36	8	graceful	graceful	ADJ
ejpam-6600	36	9	labeling	labeling	NOUN
ejpam-6600	36	10	by	by	ADP
ejpam-6600	36	11	solomon	solomon	PROPN
ejpam-6600	36	12	golomb	golomb	PROPN
ejpam-6600	37	1	[	[	X
ejpam-6600	37	2	17	17	NUM
ejpam-6600	37	3	]	]	PUNCT
ejpam-6600	37	4	.	.	PUNCT
ejpam-6600	38	1	in	in	ADP
ejpam-6600	38	2	an	an	DET
ejpam-6600	38	3	edge	edge	NOUN
ejpam-6600	38	4	-	-	PUNCT
ejpam-6600	38	5	graceful	graceful	NOUN
ejpam-6600	38	6	labeling	labeling	NOUN
ejpam-6600	38	7	of	of	ADP
ejpam-6600	38	8	a	a	DET
ejpam-6600	38	9	graph	graph	NOUN
ejpam-6600	38	10	g	g	ADP
ejpam-6600	38	11	distinct	distinct	ADJ
ejpam-6600	38	12	integers	integer	NOUN
ejpam-6600	38	13	are	be	AUX
ejpam-6600	38	14	assigned	assign	VERB
ejpam-6600	38	15	to	to	ADP
ejpam-6600	38	16	the	the	DET
ejpam-6600	38	17	edges	edge	NOUN
ejpam-6600	38	18	,	,	PUNCT
ejpam-6600	38	19	and	and	CCONJ
ejpam-6600	38	20	each	each	DET
ejpam-6600	38	21	vertex	vertex	NOUN
ejpam-6600	38	22	is	be	AUX
ejpam-6600	38	23	labeled	label	VERB
ejpam-6600	38	24	,	,	PUNCT
ejpam-6600	38	25	using	use	VERB
ejpam-6600	38	26	an	an	DET
ejpam-6600	38	27	injective	injective	ADJ
ejpam-6600	38	28	map	map	NOUN
ejpam-6600	38	29	,	,	PUNCT
ejpam-6600	38	30	by	by	ADP
ejpam-6600	38	31	the	the	DET
ejpam-6600	38	32	sum	sum	NOUN
ejpam-6600	38	33	of	of	ADP
ejpam-6600	38	34	the	the	DET
ejpam-6600	38	35	labels	label	NOUN
ejpam-6600	38	36	on	on	ADP
ejpam-6600	38	37	its	its	PRON
ejpam-6600	38	38	incident	incident	NOUN
ejpam-6600	38	39	edges	edge	VERB
ejpam-6600	38	40	modulo	modulo	NOUN
ejpam-6600	38	41	p.	p.	NOUN
ejpam-6600	38	42	for	for	ADP
ejpam-6600	38	43	more	more	ADJ
ejpam-6600	38	44	information	information	NOUN
ejpam-6600	38	45	about	about	ADP
ejpam-6600	38	46	different	different	ADJ
ejpam-6600	38	47	types	type	NOUN
ejpam-6600	38	48	of	of	ADP
ejpam-6600	38	49	labeling	labeling	NOUN
ejpam-6600	38	50	(	(	PUNCT
ejpam-6600	38	51	see	see	VERB
ejpam-6600	38	52	[	[	X
ejpam-6600	38	53	18	18	NUM
ejpam-6600	38	54	]	]	PUNCT
ejpam-6600	38	55	,	,	PUNCT
ejpam-6600	38	56	[	[	X
ejpam-6600	38	57	19	19	NUM
ejpam-6600	38	58	]	]	PUNCT
ejpam-6600	38	59	,	,	PUNCT
ejpam-6600	38	60	[	[	X
ejpam-6600	38	61	20	20	NUM
ejpam-6600	38	62	]	]	PUNCT
ejpam-6600	38	63	,	,	PUNCT
ejpam-6600	39	1	[	[	X
ejpam-6600	39	2	21],[22	21],[22	NOUN
ejpam-6600	39	3	]	]	X
ejpam-6600	39	4	)	)	PUNCT
ejpam-6600	39	5	.	.	PUNCT
ejpam-6600	40	1	in	in	ADP
ejpam-6600	40	2	this	this	DET
ejpam-6600	40	3	paper	paper	NOUN
ejpam-6600	40	4	,	,	PUNCT
ejpam-6600	40	5	we	we	PRON
ejpam-6600	40	6	prove	prove	VERB
ejpam-6600	40	7	that	that	SCONJ
ejpam-6600	40	8	paley	paley	ADJ
ejpam-6600	40	9	graphs	graph	NOUN
ejpam-6600	40	10	and	and	CCONJ
ejpam-6600	40	11	generalized	generalized	ADJ
ejpam-6600	40	12	paley	paley	ADJ
ejpam-6600	40	13	graphs	graph	NOUN
ejpam-6600	40	14	of	of	ADP
ejpam-6600	40	15	prime	prime	ADJ
ejpam-6600	40	16	order	order	NOUN
ejpam-6600	40	17	are	be	AUX
ejpam-6600	40	18	edge	edge	NOUN
ejpam-6600	40	19	-	-	PUNCT
ejpam-6600	40	20	graceful	graceful	NOUN
ejpam-6600	40	21	.	.	PUNCT
ejpam-6600	41	1	2	2	X
ejpam-6600	41	2	.	.	X
ejpam-6600	41	3	paley	paley	ADJ
ejpam-6600	41	4	graphs	graph	NOUN
ejpam-6600	41	5	paley	paley	NOUN
ejpam-6600	41	6	graphs	graph	NOUN
ejpam-6600	41	7	have	have	VERB
ejpam-6600	41	8	many	many	ADJ
ejpam-6600	41	9	important	important	ADJ
ejpam-6600	41	10	applications	application	NOUN
ejpam-6600	41	11	in	in	ADP
ejpam-6600	41	12	coding	code	VERB
ejpam-6600	41	13	theory	theory	NOUN
ejpam-6600	41	14	and	and	CCONJ
ejpam-6600	41	15	cryptography	cryptography	NOUN
ejpam-6600	41	16	.	.	PUNCT
ejpam-6600	42	1	for	for	ADP
ejpam-6600	42	2	example	example	NOUN
ejpam-6600	42	3	they	they	PRON
ejpam-6600	42	4	are	be	AUX
ejpam-6600	42	5	used	use	VERB
ejpam-6600	42	6	in	in	ADP
ejpam-6600	42	7	quantum	quantum	ADJ
ejpam-6600	42	8	secret	secret	ADJ
ejpam-6600	42	9	sharing	sharing	NOUN
ejpam-6600	42	10	domain	domain	NOUN
ejpam-6600	42	11	[	[	X
ejpam-6600	42	12	23	23	NUM
ejpam-6600	42	13	]	]	PUNCT
ejpam-6600	42	14	and	and	CCONJ
ejpam-6600	42	15	in	in	ADP
ejpam-6600	42	16	construction	construction	NOUN
ejpam-6600	42	17	of	of	ADP
ejpam-6600	42	18	codes	code	NOUN
ejpam-6600	42	19	from	from	ADP
ejpam-6600	42	20	their	their	PRON
ejpam-6600	42	21	incidence	incidence	NOUN
ejpam-6600	42	22	matrices	matrix	NOUN
ejpam-6600	42	23	and	and	CCONJ
ejpam-6600	42	24	line	line	NOUN
ejpam-6600	42	25	graphs	graph	NOUN
ejpam-6600	42	26	[	[	X
ejpam-6600	42	27	24	24	NUM
ejpam-6600	42	28	]	]	PUNCT
ejpam-6600	42	29	.	.	PUNCT
ejpam-6600	43	1	moreover	moreover	ADV
ejpam-6600	43	2	,	,	PUNCT
ejpam-6600	43	3	a	a	DET
ejpam-6600	43	4	new	new	ADJ
ejpam-6600	43	5	application	application	NOUN
ejpam-6600	43	6	of	of	ADP
ejpam-6600	43	7	these	these	DET
ejpam-6600	43	8	graphs	graph	NOUN
ejpam-6600	43	9	in	in	ADP
ejpam-6600	43	10	cryptography	cryptography	NOUN
ejpam-6600	43	11	was	be	AUX
ejpam-6600	43	12	proposed	propose	VERB
ejpam-6600	43	13	in	in	ADP
ejpam-6600	43	14	[	[	X
ejpam-6600	43	15	25	25	NUM
ejpam-6600	43	16	]	]	PUNCT
ejpam-6600	43	17	,	,	PUNCT
ejpam-6600	43	18	introducing	introduce	VERB
ejpam-6600	43	19	an	an	DET
ejpam-6600	43	20	efficient	efficient	ADJ
ejpam-6600	43	21	algorithm	algorithm	NOUN
ejpam-6600	43	22	for	for	ADP
ejpam-6600	43	23	the	the	DET
ejpam-6600	43	24	encryption	encryption	NOUN
ejpam-6600	43	25	and	and	CCONJ
ejpam-6600	43	26	decryption	decryption	NOUN
ejpam-6600	43	27	of	of	ADP
ejpam-6600	43	28	sensitive	sensitive	ADJ
ejpam-6600	43	29	messages	message	NOUN
ejpam-6600	43	30	by	by	ADP
ejpam-6600	43	31	converting	convert	VERB
ejpam-6600	43	32	them	they	PRON
ejpam-6600	43	33	into	into	ADP
ejpam-6600	43	34	binary	binary	ADJ
ejpam-6600	43	35	form	form	NOUN
ejpam-6600	43	36	using	use	VERB
ejpam-6600	43	37	paley	paley	ADJ
ejpam-6600	43	38	graphs	graph	NOUN
ejpam-6600	43	39	.	.	PUNCT
ejpam-6600	44	1	definition	definition	NOUN
ejpam-6600	44	2	1	1	NUM
ejpam-6600	44	3	.	.	PUNCT
ejpam-6600	45	1	let	let	VERB
ejpam-6600	45	2	q	q	NOUN
ejpam-6600	45	3	=	=	PUNCT
ejpam-6600	45	4	pn	pn	PART
ejpam-6600	45	5	be	be	AUX
ejpam-6600	45	6	a	a	DET
ejpam-6600	45	7	prime	prime	ADJ
ejpam-6600	45	8	power	power	NOUN
ejpam-6600	45	9	,	,	PUNCT
ejpam-6600	45	10	where	where	SCONJ
ejpam-6600	45	11	q	q	PROPN
ejpam-6600	45	12	≡	≡	PROPN
ejpam-6600	45	13	1	1	NUM
ejpam-6600	45	14	(	(	PUNCT
ejpam-6600	45	15	mod	mod	NOUN
ejpam-6600	45	16	4	4	NUM
ejpam-6600	45	17	)	)	PUNCT
ejpam-6600	45	18	.	.	PUNCT
ejpam-6600	46	1	a	a	DET
ejpam-6600	46	2	paley	paley	ADJ
ejpam-6600	46	3	graph	graph	NOUN
ejpam-6600	46	4	pq	pq	PROPN
ejpam-6600	46	5	of	of	ADP
ejpam-6600	46	6	order	order	NOUN
ejpam-6600	46	7	q	q	X
ejpam-6600	46	8	is	be	AUX
ejpam-6600	46	9	a	a	DET
ejpam-6600	46	10	graph	graph	NOUN
ejpam-6600	46	11	with	with	ADP
ejpam-6600	46	12	vertex	vertex	NOUN
ejpam-6600	46	13	set	set	VERB
ejpam-6600	46	14	v	v	NOUN
ejpam-6600	46	15	(	(	PUNCT
ejpam-6600	46	16	pq	pq	NOUN
ejpam-6600	46	17	)	)	PUNCT
ejpam-6600	46	18	=	=	SYM
ejpam-6600	46	19	fq	fq	PROPN
ejpam-6600	46	20	,	,	PUNCT
ejpam-6600	46	21	where	where	SCONJ
ejpam-6600	46	22	fq	fq	PROPN
ejpam-6600	46	23	is	be	AUX
ejpam-6600	46	24	the	the	DET
ejpam-6600	46	25	finite	finite	ADJ
ejpam-6600	46	26	field	field	NOUN
ejpam-6600	46	27	with	with	ADP
ejpam-6600	46	28	q	q	NOUN
ejpam-6600	46	29	elements	element	NOUN
ejpam-6600	46	30	,	,	PUNCT
ejpam-6600	46	31	and	and	CCONJ
ejpam-6600	46	32	edge	edge	VERB
ejpam-6600	46	33	set	set	VERB
ejpam-6600	46	34	e(pq	e(pq	PROPN
ejpam-6600	46	35	)	)	PUNCT
ejpam-6600	46	36	=	=	PRON
ejpam-6600	46	37	{	{	PUNCT
ejpam-6600	46	38	(	(	PUNCT
ejpam-6600	46	39	u	u	NOUN
ejpam-6600	46	40	,	,	PUNCT
ejpam-6600	46	41	v	v	NOUN
ejpam-6600	46	42	)	)	PUNCT
ejpam-6600	47	1	|	|	ADV
ejpam-6600	47	2	u−	u−	NUM
ejpam-6600	47	3	v	v	X
ejpam-6600	47	4	∈	∈	PROPN
ejpam-6600	47	5	(	(	PUNCT
ejpam-6600	47	6	f∗	f∗	NOUN
ejpam-6600	47	7	q	q	NOUN
ejpam-6600	47	8	)	)	PUNCT
ejpam-6600	47	9	2	2	NUM
ejpam-6600	47	10	}	}	PUNCT
ejpam-6600	47	11	.	.	PUNCT
ejpam-6600	48	1	note	note	VERB
ejpam-6600	48	2	that	that	SCONJ
ejpam-6600	48	3	the	the	DET
ejpam-6600	48	4	condition	condition	NOUN
ejpam-6600	48	5	q	q	X
ejpam-6600	48	6	≡	≡	PROPN
ejpam-6600	48	7	1	1	NUM
ejpam-6600	48	8	(	(	PUNCT
ejpam-6600	48	9	mod	mod	NOUN
ejpam-6600	48	10	4	4	NUM
ejpam-6600	48	11	)	)	PUNCT
ejpam-6600	48	12	is	be	AUX
ejpam-6600	48	13	necessary	necessary	ADJ
ejpam-6600	48	14	for	for	SCONJ
ejpam-6600	48	15	the	the	DET
ejpam-6600	48	16	graph	graph	NOUN
ejpam-6600	48	17	to	to	PART
ejpam-6600	48	18	be	be	AUX
ejpam-6600	48	19	undirected	undirected	ADJ
ejpam-6600	48	20	.	.	PUNCT
ejpam-6600	49	1	a	a	DET
ejpam-6600	49	2	simple	simple	ADJ
ejpam-6600	49	3	version	version	NOUN
ejpam-6600	49	4	of	of	ADP
ejpam-6600	49	5	the	the	DET
ejpam-6600	49	6	paley	paley	ADJ
ejpam-6600	49	7	graph	graph	NOUN
ejpam-6600	49	8	is	be	AUX
ejpam-6600	49	9	obtained	obtain	VERB
ejpam-6600	49	10	when	when	SCONJ
ejpam-6600	49	11	n	n	X
ejpam-6600	49	12	=	=	SYM
ejpam-6600	49	13	1	1	X
ejpam-6600	49	14	.	.	X
ejpam-6600	50	1	that	that	PRON
ejpam-6600	50	2	is	be	AUX
ejpam-6600	50	3	,	,	PUNCT
ejpam-6600	50	4	when	when	SCONJ
ejpam-6600	50	5	fq	fq	PROPN
ejpam-6600	50	6	=	=	PROPN
ejpam-6600	50	7	zp	zp	PROPN
ejpam-6600	50	8	,	,	PUNCT
ejpam-6600	50	9	the	the	DET
ejpam-6600	50	10	field	field	NOUN
ejpam-6600	50	11	of	of	ADP
ejpam-6600	50	12	integers	integer	NOUN
ejpam-6600	50	13	(	(	PUNCT
ejpam-6600	50	14	mod	mod	NOUN
ejpam-6600	50	15	p	p	X
ejpam-6600	50	16	)	)	PUNCT
ejpam-6600	50	17	.	.	PUNCT
ejpam-6600	51	1	example	example	NOUN
ejpam-6600	52	1	1	1	NUM
ejpam-6600	52	2	.	.	PUNCT
ejpam-6600	53	1	the	the	DET
ejpam-6600	53	2	paley	paley	ADJ
ejpam-6600	53	3	graph	graph	NOUN
ejpam-6600	53	4	p13	p13	NOUN
ejpam-6600	53	5	has	have	VERB
ejpam-6600	53	6	vertex	vertex	NOUN
ejpam-6600	53	7	set	set	VERB
ejpam-6600	53	8	v	v	NOUN
ejpam-6600	53	9	(	(	PUNCT
ejpam-6600	53	10	p13	p13	PROPN
ejpam-6600	53	11	)	)	PUNCT
ejpam-6600	53	12	=	=	SYM
ejpam-6600	53	13	z13	z13	NOUN
ejpam-6600	53	14	=	=	SYM
ejpam-6600	53	15	{	{	PUNCT
ejpam-6600	53	16	0	0	NUM
ejpam-6600	53	17	,	,	PUNCT
ejpam-6600	53	18	1	1	NUM
ejpam-6600	53	19	,	,	PUNCT
ejpam-6600	53	20	2	2	NUM
ejpam-6600	53	21	,	,	PUNCT
ejpam-6600	53	22	.	.	PUNCT
ejpam-6600	53	23	.	.	PUNCT
ejpam-6600	54	1	.	.	PUNCT
ejpam-6600	55	1	,	,	PUNCT
ejpam-6600	55	2	12	12	NUM
ejpam-6600	55	3	}	}	PUNCT
ejpam-6600	55	4	,	,	PUNCT
ejpam-6600	55	5	where	where	SCONJ
ejpam-6600	55	6	two	two	NUM
ejpam-6600	55	7	vertices	vertice	VERB
ejpam-6600	55	8	u	u	NOUN
ejpam-6600	55	9	,	,	PUNCT
ejpam-6600	55	10	v	v	PROPN
ejpam-6600	55	11	∈	∈	NOUN
ejpam-6600	55	12	z13	z13	NOUN
ejpam-6600	55	13	are	be	AUX
ejpam-6600	55	14	adjacent	adjacent	ADJ
ejpam-6600	55	15	if	if	SCONJ
ejpam-6600	55	16	u−	u−	PROPN
ejpam-6600	55	17	v	v	ADP
ejpam-6600	55	18	∈	∈	PROPN
ejpam-6600	55	19	{	{	PUNCT
ejpam-6600	55	20	1	1	NUM
ejpam-6600	55	21	,	,	PUNCT
ejpam-6600	55	22	3	3	NUM
ejpam-6600	55	23	,	,	PUNCT
ejpam-6600	55	24	4	4	NUM
ejpam-6600	55	25	,	,	PUNCT
ejpam-6600	55	26	9	9	NUM
ejpam-6600	55	27	,	,	PUNCT
ejpam-6600	55	28	10	10	NUM
ejpam-6600	55	29	,	,	PUNCT
ejpam-6600	55	30	12	12	NUM
ejpam-6600	55	31	}	}	PUNCT
ejpam-6600	55	32	.	.	PUNCT
ejpam-6600	56	1	a.	a.	PROPN
ejpam-6600	56	2	n.	n.	PROPN
ejpam-6600	56	3	elsawy	elsawy	PROPN
ejpam-6600	56	4	,	,	PUNCT
ejpam-6600	56	5	r.	r.	PROPN
ejpam-6600	56	6	n.	n.	PROPN
ejpam-6600	56	7	almohammadi	almohammadi	PROPN
ejpam-6600	56	8	/	/	SYM
ejpam-6600	56	9	eur	eur	PROPN
ejpam-6600	56	10	.	.	PUNCT
ejpam-6600	57	1	j.	j.	PROPN
ejpam-6600	57	2	pure	pure	PROPN
ejpam-6600	57	3	appl	appl	PROPN
ejpam-6600	57	4	.	.	PROPN
ejpam-6600	57	5	math	math	PROPN
ejpam-6600	57	6	,	,	PUNCT
ejpam-6600	57	7	18	18	NUM
ejpam-6600	57	8	(	(	PUNCT
ejpam-6600	57	9	4	4	NUM
ejpam-6600	57	10	)	)	PUNCT
ejpam-6600	57	11	(	(	PUNCT
ejpam-6600	57	12	2025	2025	NUM
ejpam-6600	57	13	)	)	PUNCT
ejpam-6600	57	14	,	,	PUNCT
ejpam-6600	57	15	6600	6600	NUM
ejpam-6600	57	16	3	3	NUM
ejpam-6600	57	17	of	of	ADP
ejpam-6600	57	18	26	26	NUM
ejpam-6600	57	19	figure	figure	NOUN
ejpam-6600	57	20	1	1	NUM
ejpam-6600	57	21	:	:	PUNCT
ejpam-6600	57	22	the	the	DET
ejpam-6600	57	23	paley	paley	ADJ
ejpam-6600	57	24	graph	graph	NOUN
ejpam-6600	57	25	p13	p13	NOUN
ejpam-6600	57	26	of	of	ADP
ejpam-6600	57	27	order	order	NOUN
ejpam-6600	57	28	13	13	NUM
ejpam-6600	57	29	.	.	PUNCT
ejpam-6600	57	30	example	example	NOUN
ejpam-6600	58	1	2	2	NUM
ejpam-6600	58	2	.	.	X
ejpam-6600	58	3	consider	consider	VERB
ejpam-6600	58	4	the	the	DET
ejpam-6600	58	5	paley	paley	ADJ
ejpam-6600	58	6	graph	graph	NOUN
ejpam-6600	58	7	p9	p9	PROPN
ejpam-6600	58	8	of	of	ADP
ejpam-6600	58	9	order	order	NOUN
ejpam-6600	58	10	9	9	NUM
ejpam-6600	58	11	,	,	PUNCT
ejpam-6600	58	12	then	then	ADV
ejpam-6600	58	13	v	v	X
ejpam-6600	58	14	(	(	PUNCT
ejpam-6600	58	15	p9	p9	PROPN
ejpam-6600	58	16	)	)	PUNCT
ejpam-6600	58	17	=	=	SYM
ejpam-6600	59	1	f9	f9	PROPN
ejpam-6600	59	2	=	=	PUNCT
ejpam-6600	59	3	z3[x]/(x	z3[x]/(x	NOUN
ejpam-6600	59	4	2	2	NUM
ejpam-6600	59	5	+	+	NOUN
ejpam-6600	59	6	1	1	NUM
ejpam-6600	59	7	)	)	PUNCT
ejpam-6600	59	8	=	=	PRON
ejpam-6600	59	9	{	{	PUNCT
ejpam-6600	59	10	0	0	NUM
ejpam-6600	59	11	,	,	PUNCT
ejpam-6600	59	12	1	1	NUM
ejpam-6600	59	13	,	,	PUNCT
ejpam-6600	59	14	2	2	NUM
ejpam-6600	59	15	,	,	PUNCT
ejpam-6600	59	16	a+	a+	PRON
ejpam-6600	59	17	2	2	NUM
ejpam-6600	59	18	,	,	PUNCT
ejpam-6600	59	19	a	a	PRON
ejpam-6600	59	20	,	,	PUNCT
ejpam-6600	59	21	a+	a+	PRON
ejpam-6600	59	22	1	1	NUM
ejpam-6600	59	23	,	,	PUNCT
ejpam-6600	59	24	2a+	2a+	NUM
ejpam-6600	59	25	1	1	NUM
ejpam-6600	59	26	,	,	PUNCT
ejpam-6600	59	27	2a+	2a+	NUM
ejpam-6600	59	28	2	2	NUM
ejpam-6600	59	29	,	,	PUNCT
ejpam-6600	59	30	2a	2a	NUM
ejpam-6600	59	31	}	}	PUNCT
ejpam-6600	59	32	.	.	PUNCT
ejpam-6600	60	1	therefore	therefore	ADV
ejpam-6600	60	2	,	,	PUNCT
ejpam-6600	60	3	(	(	PUNCT
ejpam-6600	60	4	f∗	f∗	NOUN
ejpam-6600	60	5	9	9	NUM
ejpam-6600	60	6	)	)	PUNCT
ejpam-6600	60	7	2	2	NUM
ejpam-6600	60	8	=	=	SYM
ejpam-6600	60	9	{	{	PUNCT
ejpam-6600	60	10	1	1	NUM
ejpam-6600	60	11	,	,	PUNCT
ejpam-6600	60	12	2	2	NUM
ejpam-6600	60	13	,	,	PUNCT
ejpam-6600	60	14	a	a	DET
ejpam-6600	60	15	,	,	PUNCT
ejpam-6600	60	16	2a	2a	NUM
ejpam-6600	60	17	}	}	PUNCT
ejpam-6600	60	18	,	,	PUNCT
ejpam-6600	60	19	meaning	mean	VERB
ejpam-6600	60	20	that	that	SCONJ
ejpam-6600	60	21	every	every	DET
ejpam-6600	60	22	vertex	vertex	NOUN
ejpam-6600	60	23	in	in	ADP
ejpam-6600	60	24	v	v	NUM
ejpam-6600	60	25	(	(	PUNCT
ejpam-6600	60	26	p9	p9	PROPN
ejpam-6600	60	27	)	)	PUNCT
ejpam-6600	60	28	is	be	AUX
ejpam-6600	60	29	adjacent	adjacent	ADJ
ejpam-6600	60	30	to	to	ADP
ejpam-6600	60	31	four	four	NUM
ejpam-6600	60	32	vertices	vertex	NOUN
ejpam-6600	60	33	.	.	PUNCT
ejpam-6600	61	1	hence	hence	ADV
ejpam-6600	61	2	,	,	PUNCT
ejpam-6600	61	3	e(p9	e(p9	ADV
ejpam-6600	61	4	)	)	PUNCT
ejpam-6600	61	5	=	=	PRON
ejpam-6600	62	1	{	{	PUNCT
ejpam-6600	62	2	(	(	PUNCT
ejpam-6600	62	3	xi	xi	PROPN
ejpam-6600	62	4	,	,	PUNCT
ejpam-6600	62	5	xi	xi	PROPN
ejpam-6600	62	6	+	+	CCONJ
ejpam-6600	62	7	xj	xj	NOUN
ejpam-6600	62	8	)	)	PUNCT
ejpam-6600	62	9	|	|	ADV
ejpam-6600	62	10	xi	xi	X
ejpam-6600	62	11	∈	∈	PROPN
ejpam-6600	62	12	f9	f9	PROPN
ejpam-6600	62	13	,	,	PUNCT
ejpam-6600	62	14	xj	xj	PROPN
ejpam-6600	62	15	∈	∈	PROPN
ejpam-6600	62	16	(	(	PUNCT
ejpam-6600	62	17	f∗	f∗	NOUN
ejpam-6600	62	18	9	9	NUM
ejpam-6600	62	19	)	)	PUNCT
ejpam-6600	62	20	2	2	NUM
ejpam-6600	62	21	}	}	PUNCT
ejpam-6600	62	22	.	.	PUNCT
ejpam-6600	63	1	figure	figure	NOUN
ejpam-6600	63	2	2	2	NUM
ejpam-6600	63	3	:	:	PUNCT
ejpam-6600	63	4	the	the	DET
ejpam-6600	63	5	paley	paley	ADJ
ejpam-6600	63	6	graph	graph	NOUN
ejpam-6600	63	7	p9	p9	PROPN
ejpam-6600	63	8	of	of	ADP
ejpam-6600	63	9	order	order	NOUN
ejpam-6600	63	10	9	9	NUM
ejpam-6600	63	11	.	.	PUNCT
ejpam-6600	64	1	graph	graph	NOUN
ejpam-6600	64	2	labeling	labeling	NOUN
ejpam-6600	64	3	is	be	AUX
ejpam-6600	64	4	one	one	NUM
ejpam-6600	64	5	of	of	ADP
ejpam-6600	64	6	the	the	DET
ejpam-6600	64	7	significant	significant	ADJ
ejpam-6600	64	8	fields	field	NOUN
ejpam-6600	64	9	in	in	ADP
ejpam-6600	64	10	graph	graph	NOUN
ejpam-6600	64	11	theory	theory	NOUN
ejpam-6600	64	12	.	.	PUNCT
ejpam-6600	65	1	it	it	PRON
ejpam-6600	65	2	has	have	VERB
ejpam-6600	65	3	many	many	ADJ
ejpam-6600	65	4	applications	application	NOUN
ejpam-6600	65	5	in	in	ADP
ejpam-6600	65	6	coding	code	VERB
ejpam-6600	65	7	theory	theory	NOUN
ejpam-6600	65	8	,	,	PUNCT
ejpam-6600	65	9	x	x	NOUN
ejpam-6600	65	10	-	-	NOUN
ejpam-6600	65	11	ray	ray	NOUN
ejpam-6600	65	12	crystallography	crystallography	NOUN
ejpam-6600	65	13	,	,	PUNCT
ejpam-6600	65	14	radar	radar	NOUN
ejpam-6600	65	15	,	,	PUNCT
ejpam-6600	65	16	astronomy	astronomy	NOUN
ejpam-6600	65	17	,	,	PUNCT
ejpam-6600	65	18	circuit	circuit	NOUN
ejpam-6600	65	19	design	design	NOUN
ejpam-6600	65	20	,	,	PUNCT
ejpam-6600	65	21	communication	communication	NOUN
ejpam-6600	65	22	network	network	NOUN
ejpam-6600	65	23	addressing	address	VERB
ejpam-6600	65	24	,	,	PUNCT
ejpam-6600	65	25	and	and	CCONJ
ejpam-6600	65	26	data	datum	NOUN
ejpam-6600	65	27	base	base	NOUN
ejpam-6600	65	28	management	management	NOUN
ejpam-6600	65	29	(	(	PUNCT
ejpam-6600	65	30	see	see	VERB
ejpam-6600	65	31	[	[	X
ejpam-6600	65	32	26	26	NUM
ejpam-6600	65	33	]	]	PUNCT
ejpam-6600	65	34	,	,	PUNCT
ejpam-6600	65	35	[	[	X
ejpam-6600	65	36	27	27	NUM
ejpam-6600	65	37	]	]	PUNCT
ejpam-6600	65	38	)	)	PUNCT
ejpam-6600	65	39	.	.	PUNCT
ejpam-6600	66	1	in	in	ADP
ejpam-6600	66	2	[	[	X
ejpam-6600	66	3	21	21	NUM
ejpam-6600	66	4	]	]	PUNCT
ejpam-6600	66	5	,	,	PUNCT
ejpam-6600	66	6	kamaraj	kamaraj	ADJ
ejpam-6600	66	7	and	and	CCONJ
ejpam-6600	66	8	thangakani	thangakani	NOUN
ejpam-6600	66	9	investigated	investigate	VERB
ejpam-6600	66	10	edge	edge	NOUN
ejpam-6600	66	11	-	-	PUNCT
ejpam-6600	66	12	even	even	ADJ
ejpam-6600	66	13	and	and	CCONJ
ejpam-6600	66	14	edge	edge	NOUN
ejpam-6600	66	15	-	-	PUNCT
ejpam-6600	66	16	odd	odd	ADJ
ejpam-6600	66	17	graceful	graceful	ADJ
ejpam-6600	66	18	labela	labela	NOUN
ejpam-6600	66	19	.	.	PUNCT
ejpam-6600	67	1	n.	n.	PROPN
ejpam-6600	67	2	elsawy	elsawy	PROPN
ejpam-6600	67	3	,	,	PUNCT
ejpam-6600	67	4	r.	r.	PROPN
ejpam-6600	67	5	n.	n.	PROPN
ejpam-6600	67	6	almohammadi	almohammadi	PROPN
ejpam-6600	67	7	/	/	SYM
ejpam-6600	67	8	eur	eur	PROPN
ejpam-6600	67	9	.	.	PUNCT
ejpam-6600	68	1	j.	j.	PROPN
ejpam-6600	68	2	pure	pure	PROPN
ejpam-6600	68	3	appl	appl	PROPN
ejpam-6600	68	4	.	.	PROPN
ejpam-6600	68	5	math	math	PROPN
ejpam-6600	68	6	,	,	PUNCT
ejpam-6600	68	7	18	18	NUM
ejpam-6600	68	8	(	(	PUNCT
ejpam-6600	68	9	4	4	NUM
ejpam-6600	68	10	)	)	PUNCT
ejpam-6600	68	11	(	(	PUNCT
ejpam-6600	68	12	2025	2025	NUM
ejpam-6600	68	13	)	)	PUNCT
ejpam-6600	68	14	,	,	PUNCT
ejpam-6600	68	15	6600	6600	NUM
ejpam-6600	68	16	4	4	NUM
ejpam-6600	68	17	of	of	ADP
ejpam-6600	68	18	26	26	NUM
ejpam-6600	68	19	ing	ing	NOUN
ejpam-6600	68	20	for	for	ADP
ejpam-6600	68	21	paley	paley	ADJ
ejpam-6600	68	22	graphs	graph	NOUN
ejpam-6600	68	23	of	of	ADP
ejpam-6600	68	24	prime	prime	ADJ
ejpam-6600	68	25	order	order	NOUN
ejpam-6600	68	26	.	.	PUNCT
ejpam-6600	69	1	an	an	DET
ejpam-6600	69	2	edge	edge	NOUN
ejpam-6600	69	3	even	even	ADV
ejpam-6600	69	4	-	-	PUNCT
ejpam-6600	69	5	graceful	graceful	ADJ
ejpam-6600	69	6	labeling	labeling	NOUN
ejpam-6600	69	7	assigns	assign	NOUN
ejpam-6600	69	8	distinct	distinct	ADJ
ejpam-6600	69	9	even	even	ADJ
ejpam-6600	69	10	numbers	number	NOUN
ejpam-6600	69	11	to	to	ADP
ejpam-6600	69	12	the	the	DET
ejpam-6600	69	13	edges	edge	NOUN
ejpam-6600	69	14	and	and	CCONJ
ejpam-6600	69	15	ensures	ensure	VERB
ejpam-6600	69	16	that	that	SCONJ
ejpam-6600	69	17	the	the	DET
ejpam-6600	69	18	sum	sum	NOUN
ejpam-6600	69	19	of	of	ADP
ejpam-6600	69	20	labels	label	NOUN
ejpam-6600	69	21	modulo	modulo	PROPN
ejpam-6600	69	22	2k	2k	NOUN
ejpam-6600	69	23	assigned	assign	VERB
ejpam-6600	69	24	to	to	ADP
ejpam-6600	69	25	each	each	DET
ejpam-6600	69	26	vertex	vertex	NOUN
ejpam-6600	69	27	is	be	AUX
ejpam-6600	69	28	unique	unique	ADJ
ejpam-6600	69	29	.	.	PUNCT
ejpam-6600	70	1	on	on	ADP
ejpam-6600	70	2	the	the	DET
ejpam-6600	70	3	other	other	ADJ
ejpam-6600	70	4	hand	hand	NOUN
ejpam-6600	70	5	,	,	PUNCT
ejpam-6600	70	6	an	an	DET
ejpam-6600	70	7	edge	edge	NOUN
ejpam-6600	70	8	-	-	PUNCT
ejpam-6600	70	9	odd	odd	ADJ
ejpam-6600	70	10	graceful	graceful	ADJ
ejpam-6600	70	11	labeling	labeling	NOUN
ejpam-6600	70	12	assigns	assign	NOUN
ejpam-6600	70	13	distinct	distinct	ADJ
ejpam-6600	70	14	odd	odd	ADJ
ejpam-6600	70	15	numbers	number	NOUN
ejpam-6600	70	16	to	to	ADP
ejpam-6600	70	17	the	the	DET
ejpam-6600	70	18	edges	edge	NOUN
ejpam-6600	70	19	and	and	CCONJ
ejpam-6600	70	20	ensures	ensure	VERB
ejpam-6600	70	21	that	that	SCONJ
ejpam-6600	70	22	the	the	DET
ejpam-6600	70	23	sum	sum	NOUN
ejpam-6600	70	24	of	of	ADP
ejpam-6600	70	25	labels	label	NOUN
ejpam-6600	70	26	modulo	modulo	VERB
ejpam-6600	70	27	2q	2q	NUM
ejpam-6600	70	28	assigned	assign	VERB
ejpam-6600	70	29	to	to	ADP
ejpam-6600	70	30	each	each	DET
ejpam-6600	70	31	vertex	vertex	NOUN
ejpam-6600	70	32	is	be	AUX
ejpam-6600	70	33	unique	unique	ADJ
ejpam-6600	70	34	.	.	PUNCT
ejpam-6600	71	1	kamaraj	kamaraj	ADJ
ejpam-6600	71	2	and	and	CCONJ
ejpam-6600	71	3	thangakani	thangakani	NOUN
ejpam-6600	71	4	proved	prove	VERB
ejpam-6600	71	5	the	the	DET
ejpam-6600	71	6	following	follow	VERB
ejpam-6600	71	7	theorem	theorem	NOUN
ejpam-6600	71	8	:	:	PUNCT
ejpam-6600	71	9	theorem	theorem	NOUN
ejpam-6600	71	10	1	1	NUM
ejpam-6600	71	11	.	.	PUNCT
ejpam-6600	72	1	every	every	DET
ejpam-6600	72	2	paley	paley	ADJ
ejpam-6600	72	3	graph	graph	NOUN
ejpam-6600	72	4	of	of	ADP
ejpam-6600	72	5	prime	prime	ADJ
ejpam-6600	72	6	order	order	NOUN
ejpam-6600	72	7	admits	admit	VERB
ejpam-6600	72	8	both	both	DET
ejpam-6600	72	9	an	an	DET
ejpam-6600	72	10	edge	edge	NOUN
ejpam-6600	72	11	-	-	PUNCT
ejpam-6600	72	12	even	even	ADV
ejpam-6600	72	13	and	and	CCONJ
ejpam-6600	72	14	an	an	DET
ejpam-6600	72	15	edge	edge	NOUN
ejpam-6600	72	16	-	-	PUNCT
ejpam-6600	72	17	odd	odd	ADJ
ejpam-6600	72	18	graceful	graceful	ADJ
ejpam-6600	72	19	labeling	labeling	NOUN
ejpam-6600	72	20	.	.	PUNCT
ejpam-6600	73	1	we	we	PRON
ejpam-6600	73	2	introduce	introduce	VERB
ejpam-6600	73	3	another	another	DET
ejpam-6600	73	4	lebeling	lebeling	NOUN
ejpam-6600	73	5	of	of	ADP
ejpam-6600	73	6	paley	paley	ADJ
ejpam-6600	73	7	graphs	graph	NOUN
ejpam-6600	73	8	of	of	ADP
ejpam-6600	73	9	prime	prime	ADJ
ejpam-6600	73	10	order	order	NOUN
ejpam-6600	73	11	,	,	PUNCT
ejpam-6600	73	12	which	which	PRON
ejpam-6600	73	13	is	be	AUX
ejpam-6600	73	14	called	call	VERB
ejpam-6600	73	15	edge	edge	NOUN
ejpam-6600	73	16	graceful	graceful	ADJ
ejpam-6600	73	17	labeling	labeling	NOUN
ejpam-6600	73	18	.	.	PUNCT
ejpam-6600	74	1	definition	definition	NOUN
ejpam-6600	74	2	2	2	NUM
ejpam-6600	74	3	.	.	PUNCT
ejpam-6600	74	4	accordung	accordung	VERB
ejpam-6600	74	5	to	to	ADP
ejpam-6600	74	6	[	[	X
ejpam-6600	74	7	1	1	NUM
ejpam-6600	74	8	]	]	PUNCT
ejpam-6600	74	9	,	,	PUNCT
ejpam-6600	74	10	a	a	DET
ejpam-6600	74	11	graph	graph	NOUN
ejpam-6600	74	12	g	g	NOUN
ejpam-6600	74	13	of	of	ADP
ejpam-6600	74	14	order	order	NOUN
ejpam-6600	74	15	n	n	NOUN
ejpam-6600	74	16	and	and	CCONJ
ejpam-6600	74	17	size	size	NOUN
ejpam-6600	74	18	m	m	VERB
ejpam-6600	74	19	is	be	AUX
ejpam-6600	74	20	called	call	VERB
ejpam-6600	74	21	edge	edge	NOUN
ejpam-6600	74	22	-	-	PUNCT
ejpam-6600	74	23	graceful	graceful	NOUN
ejpam-6600	74	24	if	if	SCONJ
ejpam-6600	74	25	there	there	PRON
ejpam-6600	74	26	exists	exist	VERB
ejpam-6600	74	27	a	a	DET
ejpam-6600	74	28	bijective	bijective	ADJ
ejpam-6600	74	29	mapping	mapping	NOUN
ejpam-6600	74	30	h	h	NOUN
ejpam-6600	74	31	:	:	PUNCT
ejpam-6600	74	32	e(g	e(g	NOUN
ejpam-6600	74	33	)	)	PUNCT
ejpam-6600	75	1	−→	−→	NOUN
ejpam-6600	75	2	{	{	PUNCT
ejpam-6600	75	3	1	1	NUM
ejpam-6600	75	4	,	,	PUNCT
ejpam-6600	75	5	2	2	NUM
ejpam-6600	75	6	,	,	PUNCT
ejpam-6600	75	7	3	3	NUM
ejpam-6600	75	8	,	,	PUNCT
ejpam-6600	75	9	.	.	PUNCT
ejpam-6600	75	10	.	.	PUNCT
ejpam-6600	76	1	.	.	PUNCT
ejpam-6600	77	1	,	,	PUNCT
ejpam-6600	77	2	m	m	VERB
ejpam-6600	77	3	}	}	PUNCT
ejpam-6600	77	4	such	such	ADJ
ejpam-6600	77	5	that	that	SCONJ
ejpam-6600	77	6	the	the	DET
ejpam-6600	77	7	weight	weight	NOUN
ejpam-6600	77	8	function	function	NOUN
ejpam-6600	77	9	hw	hw	INTJ
ejpam-6600	77	10	:	:	PUNCT
ejpam-6600	77	11	v	v	X
ejpam-6600	77	12	(	(	PUNCT
ejpam-6600	77	13	g	g	NOUN
ejpam-6600	77	14	)	)	PUNCT
ejpam-6600	77	15	−→	−→	NOUN
ejpam-6600	77	16	{	{	PUNCT
ejpam-6600	77	17	0	0	NUM
ejpam-6600	77	18	,	,	PUNCT
ejpam-6600	77	19	1	1	NUM
ejpam-6600	77	20	,	,	PUNCT
ejpam-6600	77	21	2	2	NUM
ejpam-6600	77	22	,	,	PUNCT
ejpam-6600	77	23	.	.	PUNCT
ejpam-6600	77	24	.	.	PUNCT
ejpam-6600	78	1	.	.	PUNCT
ejpam-6600	79	1	,	,	PUNCT
ejpam-6600	79	2	n−	n−	NOUN
ejpam-6600	79	3	1	1	NUM
ejpam-6600	79	4	}	}	PUNCT
ejpam-6600	79	5	,	,	PUNCT
ejpam-6600	79	6	given	give	VERB
ejpam-6600	79	7	by	by	ADP
ejpam-6600	79	8	hw(u	hw(u	NOUN
ejpam-6600	79	9	)	)	PUNCT
ejpam-6600	79	10	=	=	SYM
ejpam-6600	79	11	∑	∑	PUNCT
ejpam-6600	79	12	v∈n(u	v∈n(u	PROPN
ejpam-6600	79	13	)	)	PUNCT
ejpam-6600	79	14	h(uv	h(uv	NOUN
ejpam-6600	79	15	)	)	PUNCT
ejpam-6600	79	16	(	(	PUNCT
ejpam-6600	79	17	mod	mod	NOUN
ejpam-6600	79	18	n	n	CCONJ
ejpam-6600	79	19	)	)	PUNCT
ejpam-6600	79	20	,	,	PUNCT
ejpam-6600	79	21	is	be	AUX
ejpam-6600	79	22	one	one	NUM
ejpam-6600	79	23	-	-	PUNCT
ejpam-6600	79	24	to	to	ADP
ejpam-6600	79	25	-	-	PUNCT
ejpam-6600	79	26	one	one	NUM
ejpam-6600	79	27	and	and	CCONJ
ejpam-6600	79	28	onto	onto	ADP
ejpam-6600	79	29	.	.	PUNCT
ejpam-6600	80	1	for	for	ADP
ejpam-6600	80	2	example	example	NOUN
ejpam-6600	80	3	,	,	PUNCT
ejpam-6600	80	4	consider	consider	VERB
ejpam-6600	80	5	the	the	DET
ejpam-6600	80	6	paley	paley	ADJ
ejpam-6600	80	7	graph	graph	NOUN
ejpam-6600	80	8	p9	p9	PROPN
ejpam-6600	80	9	.	.	PUNCT
ejpam-6600	81	1	as	as	SCONJ
ejpam-6600	81	2	in	in	ADP
ejpam-6600	81	3	figure	figure	NOUN
ejpam-6600	81	4	3	3	NUM
ejpam-6600	81	5	,	,	PUNCT
ejpam-6600	81	6	we	we	PRON
ejpam-6600	81	7	can	can	AUX
ejpam-6600	81	8	define	define	VERB
ejpam-6600	81	9	an	an	DET
ejpam-6600	81	10	edgegraceful	edgegraceful	ADJ
ejpam-6600	81	11	labeling	labeling	NOUN
ejpam-6600	81	12	to	to	ADP
ejpam-6600	81	13	the	the	DET
ejpam-6600	81	14	paley	paley	ADJ
ejpam-6600	81	15	graph	graph	NOUN
ejpam-6600	81	16	p9	p9	PROPN
ejpam-6600	81	17	such	such	ADJ
ejpam-6600	81	18	that	that	DET
ejpam-6600	81	19	h	h	NOUN
ejpam-6600	81	20	:	:	PUNCT
ejpam-6600	81	21	e(p9	e(p9	ADJ
ejpam-6600	81	22	)	)	PUNCT
ejpam-6600	81	23	−→	−→	NOUN
ejpam-6600	81	24	{	{	PUNCT
ejpam-6600	81	25	1	1	NUM
ejpam-6600	81	26	,	,	PUNCT
ejpam-6600	81	27	2	2	NUM
ejpam-6600	81	28	,	,	PUNCT
ejpam-6600	81	29	3	3	NUM
ejpam-6600	81	30	,	,	PUNCT
ejpam-6600	81	31	.	.	PUNCT
ejpam-6600	81	32	.	.	PUNCT
ejpam-6600	82	1	.	.	PUNCT
ejpam-6600	83	1	,	,	PUNCT
ejpam-6600	83	2	18	18	NUM
ejpam-6600	83	3	}	}	PUNCT
ejpam-6600	83	4	and	and	CCONJ
ejpam-6600	83	5	hw	hw	PRON
ejpam-6600	83	6	:	:	PUNCT
ejpam-6600	83	7	v	v	X
ejpam-6600	83	8	(	(	PUNCT
ejpam-6600	83	9	p9	p9	PROPN
ejpam-6600	83	10	)	)	PUNCT
ejpam-6600	83	11	−→	−→	NOUN
ejpam-6600	83	12	{	{	PUNCT
ejpam-6600	83	13	0	0	NUM
ejpam-6600	83	14	,	,	PUNCT
ejpam-6600	83	15	1	1	NUM
ejpam-6600	83	16	,	,	PUNCT
ejpam-6600	83	17	2	2	NUM
ejpam-6600	83	18	,	,	PUNCT
ejpam-6600	83	19	.	.	PUNCT
ejpam-6600	83	20	.	.	PUNCT
ejpam-6600	83	21	.	.	PUNCT
ejpam-6600	84	1	,	,	PUNCT
ejpam-6600	84	2	8	8	X
ejpam-6600	84	3	}	}	PUNCT
ejpam-6600	84	4	are	be	AUX
ejpam-6600	84	5	bijections	bijection	NOUN
ejpam-6600	84	6	.	.	PUNCT
ejpam-6600	85	1	figure	figure	NOUN
ejpam-6600	85	2	3	3	NUM
ejpam-6600	85	3	:	:	PUNCT
ejpam-6600	85	4	an	an	DET
ejpam-6600	85	5	edge	edge	NOUN
ejpam-6600	85	6	-	-	PUNCT
ejpam-6600	85	7	graceful	graceful	NOUN
ejpam-6600	85	8	labeling	labeling	NOUN
ejpam-6600	85	9	for	for	ADP
ejpam-6600	85	10	p9	p9	PROPN
ejpam-6600	85	11	in	in	ADP
ejpam-6600	85	12	the	the	DET
ejpam-6600	85	13	following	following	NOUN
ejpam-6600	85	14	we	we	PRON
ejpam-6600	85	15	provide	provide	VERB
ejpam-6600	85	16	an	an	DET
ejpam-6600	85	17	algorithm	algorithm	NOUN
ejpam-6600	85	18	which	which	PRON
ejpam-6600	85	19	produces	produce	VERB
ejpam-6600	85	20	an	an	DET
ejpam-6600	85	21	edge	edge	NOUN
ejpam-6600	85	22	-	-	PUNCT
ejpam-6600	85	23	graceful	graceful	NOUN
ejpam-6600	85	24	labeling	labeling	NOUN
ejpam-6600	85	25	for	for	ADP
ejpam-6600	85	26	the	the	DET
ejpam-6600	85	27	prime	prime	ADJ
ejpam-6600	85	28	order	order	NOUN
ejpam-6600	85	29	paley	paley	NOUN
ejpam-6600	85	30	graphs	graph	NOUN
ejpam-6600	85	31	.	.	PUNCT
ejpam-6600	86	1	note	note	VERB
ejpam-6600	86	2	that	that	SCONJ
ejpam-6600	86	3	the	the	DET
ejpam-6600	86	4	case	case	NOUN
ejpam-6600	86	5	of	of	ADP
ejpam-6600	86	6	the	the	DET
ejpam-6600	86	7	prime	prime	ADJ
ejpam-6600	86	8	power	power	NOUN
ejpam-6600	86	9	order	order	NOUN
ejpam-6600	86	10	is	be	AUX
ejpam-6600	86	11	open	open	ADJ
ejpam-6600	86	12	.	.	PUNCT
ejpam-6600	87	1	2.1	2.1	NUM
ejpam-6600	87	2	.	.	PUNCT
ejpam-6600	87	3	edge	edge	NOUN
ejpam-6600	87	4	-	-	PUNCT
ejpam-6600	87	5	graceful	graceful	NOUN
ejpam-6600	87	6	labeling	labeling	NOUN
ejpam-6600	87	7	algorithm	algorithm	NOUN
ejpam-6600	87	8	for	for	ADP
ejpam-6600	87	9	paley	paley	ADJ
ejpam-6600	87	10	graph	graph	NOUN
ejpam-6600	87	11	of	of	ADP
ejpam-6600	87	12	prime	prime	ADJ
ejpam-6600	87	13	order	order	NOUN
ejpam-6600	87	14	input	input	NOUN
ejpam-6600	87	15	:	:	PUNCT
ejpam-6600	87	16	the	the	DET
ejpam-6600	87	17	paley	paley	ADJ
ejpam-6600	87	18	graph	graph	NOUN
ejpam-6600	87	19	pp	pp	ADJ
ejpam-6600	87	20	with	with	ADP
ejpam-6600	87	21	v	v	PROPN
ejpam-6600	87	22	(	(	PUNCT
ejpam-6600	87	23	pp	pp	ADJ
ejpam-6600	87	24	)	)	PUNCT
ejpam-6600	87	25	=	=	SYM
ejpam-6600	87	26	zp	zp	PROPN
ejpam-6600	87	27	and	and	CCONJ
ejpam-6600	87	28	e(3	e(3	PROPN
ejpam-6600	88	1	−	−	PROPN
ejpam-6600	88	2	pp	pp	ADJ
ejpam-6600	88	3	)	)	PUNCT
ejpam-6600	88	4	=	=	PRON
ejpam-6600	88	5	{	{	PUNCT
ejpam-6600	88	6	(	(	PUNCT
ejpam-6600	88	7	u	u	NOUN
ejpam-6600	88	8	,	,	PUNCT
ejpam-6600	88	9	v	v	NOUN
ejpam-6600	88	10	)	)	PUNCT
ejpam-6600	89	1	|	|	ADV
ejpam-6600	89	2	u	u	NOUN
ejpam-6600	90	1	−	−	PROPN
ejpam-6600	90	2	v	v	ADP
ejpam-6600	90	3	∈	∈	PROPN
ejpam-6600	90	4	(	(	PUNCT
ejpam-6600	90	5	z∗	z∗	NOUN
ejpam-6600	90	6	p	p	NOUN
ejpam-6600	90	7	)	)	PUNCT
ejpam-6600	90	8	2	2	NUM
ejpam-6600	90	9	}	}	PUNCT
ejpam-6600	90	10	,	,	PUNCT
ejpam-6600	90	11	where	where	SCONJ
ejpam-6600	90	12	p	p	PRON
ejpam-6600	90	13	≡	≡	PROPN
ejpam-6600	90	14	1	1	NUM
ejpam-6600	90	15	(	(	PUNCT
ejpam-6600	90	16	mod	mod	NOUN
ejpam-6600	90	17	4	4	NUM
ejpam-6600	90	18	)	)	PUNCT
ejpam-6600	90	19	a.	a.	NOUN
ejpam-6600	90	20	n.	n.	PROPN
ejpam-6600	90	21	elsawy	elsawy	PROPN
ejpam-6600	90	22	,	,	PUNCT
ejpam-6600	90	23	r.	r.	PROPN
ejpam-6600	90	24	n.	n.	PROPN
ejpam-6600	90	25	almohammadi	almohammadi	PROPN
ejpam-6600	90	26	/	/	SYM
ejpam-6600	90	27	eur	eur	PROPN
ejpam-6600	90	28	.	.	PUNCT
ejpam-6600	91	1	j.	j.	PROPN
ejpam-6600	91	2	pure	pure	PROPN
ejpam-6600	91	3	appl	appl	PROPN
ejpam-6600	91	4	.	.	PROPN
ejpam-6600	91	5	math	math	PROPN
ejpam-6600	91	6	,	,	PUNCT
ejpam-6600	91	7	18	18	NUM
ejpam-6600	91	8	(	(	PUNCT
ejpam-6600	91	9	4	4	NUM
ejpam-6600	91	10	)	)	PUNCT
ejpam-6600	91	11	(	(	PUNCT
ejpam-6600	91	12	2025	2025	NUM
ejpam-6600	91	13	)	)	PUNCT
ejpam-6600	91	14	,	,	PUNCT
ejpam-6600	91	15	6600	6600	NUM
ejpam-6600	91	16	5	5	NUM
ejpam-6600	91	17	of	of	ADP
ejpam-6600	91	18	26	26	NUM
ejpam-6600	91	19	(	(	PUNCT
ejpam-6600	91	20	1	1	NUM
ejpam-6600	91	21	)	)	PUNCT
ejpam-6600	91	22	rename	rename	VERB
ejpam-6600	91	23	the	the	DET
ejpam-6600	91	24	vertices	vertex	NOUN
ejpam-6600	91	25	of	of	ADP
ejpam-6600	91	26	the	the	DET
ejpam-6600	91	27	graph	graph	NOUN
ejpam-6600	91	28	as	as	ADP
ejpam-6600	91	29	0	0	NUM
ejpam-6600	91	30	:	:	PUNCT
ejpam-6600	91	31	=	=	SYM
ejpam-6600	91	32	vp	vp	NOUN
ejpam-6600	91	33	,	,	PUNCT
ejpam-6600	91	34	1	1	NUM
ejpam-6600	91	35	:	:	PUNCT
ejpam-6600	91	36	=	=	NOUN
ejpam-6600	91	37	v1	v1	NOUN
ejpam-6600	91	38	,	,	PUNCT
ejpam-6600	91	39	2	2	NUM
ejpam-6600	91	40	:	:	PUNCT
ejpam-6600	91	41	=	=	SYM
ejpam-6600	91	42	v2	v2	PROPN
ejpam-6600	91	43	,	,	PUNCT
ejpam-6600	91	44	.	.	PUNCT
ejpam-6600	91	45	.	.	PUNCT
ejpam-6600	91	46	.	.	PUNCT
ejpam-6600	92	1	,	,	PUNCT
ejpam-6600	92	2	p−	p−	NOUN
ejpam-6600	92	3	1	1	NUM
ejpam-6600	92	4	:	:	PUNCT
ejpam-6600	92	5	=	=	SYM
ejpam-6600	92	6	vp−1	vp−1	PROPN
ejpam-6600	92	7	.	.	PUNCT
ejpam-6600	93	1	(	(	PUNCT
ejpam-6600	93	2	2	2	X
ejpam-6600	93	3	)	)	PUNCT
ejpam-6600	93	4	set	set	NOUN
ejpam-6600	93	5	r	r	NOUN
ejpam-6600	93	6	=	=	SYM
ejpam-6600	93	7	p−1	p−1	PROPN
ejpam-6600	93	8	4	4	NUM
ejpam-6600	93	9	,	,	PUNCT
ejpam-6600	93	10	and	and	CCONJ
ejpam-6600	93	11	rewrite	rewrite	VERB
ejpam-6600	93	12	(	(	PUNCT
ejpam-6600	93	13	z∗	z∗	NOUN
ejpam-6600	93	14	p	p	NOUN
ejpam-6600	93	15	)	)	PUNCT
ejpam-6600	93	16	2	2	NUM
ejpam-6600	93	17	as	as	ADP
ejpam-6600	93	18	(	(	PUNCT
ejpam-6600	93	19	z∗	z∗	NOUN
ejpam-6600	93	20	p	p	NOUN
ejpam-6600	93	21	)	)	PUNCT
ejpam-6600	93	22	2	2	NUM
ejpam-6600	93	23	=	=	SYM
ejpam-6600	93	24	s	s	NOUN
ejpam-6600	93	25	=	=	PUNCT
ejpam-6600	93	26	{	{	PUNCT
ejpam-6600	93	27	s1	s1	NOUN
ejpam-6600	93	28	,	,	PUNCT
ejpam-6600	93	29	s2	s2	PROPN
ejpam-6600	93	30	,	,	PUNCT
ejpam-6600	93	31	s3	s3	PROPN
ejpam-6600	93	32	,	,	PUNCT
ejpam-6600	93	33	.	.	PUNCT
ejpam-6600	93	34	.	.	PUNCT
ejpam-6600	94	1	.	.	PUNCT
ejpam-6600	95	1	,	,	PUNCT
ejpam-6600	95	2	s2r	s2r	PROPN
ejpam-6600	95	3	:	:	PUNCT
ejpam-6600	95	4	s1	s1	NOUN
ejpam-6600	95	5	<	<	X
ejpam-6600	95	6	s2	s2	PROPN
ejpam-6600	95	7	<	<	X
ejpam-6600	95	8	s3	s3	PROPN
ejpam-6600	95	9	<	<	X
ejpam-6600	95	10	.	.	PUNCT
ejpam-6600	95	11	.	.	PUNCT
ejpam-6600	96	1	.	.	PUNCT
ejpam-6600	97	1	<	<	X
ejpam-6600	97	2	s2r	s2r	PROPN
ejpam-6600	97	3	}	}	PUNCT
ejpam-6600	97	4	.	.	PUNCT
ejpam-6600	98	1	(	(	PUNCT
ejpam-6600	98	2	3	3	X
ejpam-6600	98	3	)	)	PUNCT
ejpam-6600	98	4	partition	partition	NOUN
ejpam-6600	98	5	s	s	NOUN
ejpam-6600	98	6	into	into	ADP
ejpam-6600	98	7	two	two	NUM
ejpam-6600	98	8	sets	set	NOUN
ejpam-6600	98	9	.	.	PUNCT
ejpam-6600	99	1	let	let	VERB
ejpam-6600	99	2	s1	s1	PROPN
ejpam-6600	99	3	=	=	PUNCT
ejpam-6600	99	4	{	{	PUNCT
ejpam-6600	99	5	s1	s1	NOUN
ejpam-6600	99	6	,	,	PUNCT
ejpam-6600	99	7	s2	s2	PROPN
ejpam-6600	99	8	,	,	PUNCT
ejpam-6600	99	9	s3	s3	PROPN
ejpam-6600	99	10	,	,	PUNCT
ejpam-6600	99	11	.	.	PUNCT
ejpam-6600	99	12	.	.	PUNCT
ejpam-6600	100	1	.	.	PUNCT
ejpam-6600	101	1	,	,	PUNCT
ejpam-6600	101	2	sr	sr	PROPN
ejpam-6600	101	3	}	}	PUNCT
ejpam-6600	101	4	and	and	CCONJ
ejpam-6600	101	5	s2	s2	VERB
ejpam-6600	101	6	=	=	SYM
ejpam-6600	101	7	{	{	PUNCT
ejpam-6600	101	8	sr+1	sr+1	PROPN
ejpam-6600	101	9	,	,	PUNCT
ejpam-6600	101	10	sr+2	sr+2	NOUN
ejpam-6600	101	11	,	,	PUNCT
ejpam-6600	101	12	sr+3	sr+3	NOUN
ejpam-6600	101	13	,	,	PUNCT
ejpam-6600	101	14	.	.	PUNCT
ejpam-6600	101	15	.	.	PUNCT
ejpam-6600	102	1	.	.	PUNCT
ejpam-6600	103	1	,	,	PUNCT
ejpam-6600	103	2	s2r	s2r	PROPN
ejpam-6600	103	3	}	}	PUNCT
ejpam-6600	103	4	.	.	PUNCT
ejpam-6600	104	1	note	note	VERB
ejpam-6600	104	2	that	that	SCONJ
ejpam-6600	104	3	:	:	PUNCT
ejpam-6600	104	4	p−1	p−1	PROPN
ejpam-6600	104	5	is	be	AUX
ejpam-6600	104	6	divisible	divisible	ADJ
ejpam-6600	104	7	by	by	ADP
ejpam-6600	104	8	4	4	NUM
ejpam-6600	104	9	and	and	CCONJ
ejpam-6600	104	10	for	for	ADP
ejpam-6600	104	11	any	any	DET
ejpam-6600	104	12	vertex	vertex	NOUN
ejpam-6600	104	13	vi	vi	PROPN
ejpam-6600	104	14	∈	∈	PROPN
ejpam-6600	104	15	zp	zp	NOUN
ejpam-6600	104	16	the	the	DET
ejpam-6600	104	17	vertex	vertex	NOUN
ejpam-6600	104	18	vi+sj	vi+sj	PROPN
ejpam-6600	104	19	is	be	AUX
ejpam-6600	104	20	adjacent	adjacent	ADJ
ejpam-6600	104	21	to	to	PART
ejpam-6600	104	22	vi	vi	VERB
ejpam-6600	104	23	for	for	ADP
ejpam-6600	104	24	all	all	DET
ejpam-6600	104	25	sj	sj	PROPN
ejpam-6600	104	26	∈	∈	PROPN
ejpam-6600	104	27	s.	s.	PROPN
ejpam-6600	104	28	(	(	PUNCT
ejpam-6600	104	29	4	4	X
ejpam-6600	104	30	)	)	PUNCT
ejpam-6600	104	31	if	if	SCONJ
ejpam-6600	104	32	sj	sj	PROPN
ejpam-6600	104	33	∈	∈	PROPN
ejpam-6600	104	34	s1	s1	PROPN
ejpam-6600	104	35	,	,	PUNCT
ejpam-6600	104	36	the	the	DET
ejpam-6600	104	37	vertex	vertex	NOUN
ejpam-6600	104	38	vi+sj	vi+sj	PROPN
ejpam-6600	104	39	is	be	AUX
ejpam-6600	104	40	placed	place	VERB
ejpam-6600	104	41	in	in	ADP
ejpam-6600	104	42	clockwise	clockwise	NOUN
ejpam-6600	104	43	direction	direction	NOUN
ejpam-6600	104	44	of	of	ADP
ejpam-6600	104	45	vi	vi	NOUN
ejpam-6600	104	46	and	and	CCONJ
ejpam-6600	104	47	if	if	SCONJ
ejpam-6600	104	48	sj	sj	PROPN
ejpam-6600	104	49	∈	∈	PROPN
ejpam-6600	104	50	s2	s2	PROPN
ejpam-6600	104	51	,	,	PUNCT
ejpam-6600	104	52	the	the	DET
ejpam-6600	104	53	vertex	vertex	NOUN
ejpam-6600	104	54	vi+sj	vi+sj	PROPN
ejpam-6600	104	55	is	be	AUX
ejpam-6600	104	56	placed	place	VERB
ejpam-6600	104	57	in	in	ADP
ejpam-6600	104	58	anticlockwise	anticlockwise	NOUN
ejpam-6600	104	59	direction	direction	NOUN
ejpam-6600	104	60	of	of	ADP
ejpam-6600	104	61	vi	vi	PROPN
ejpam-6600	104	62	.	.	PUNCT
ejpam-6600	105	1	(	(	PUNCT
ejpam-6600	105	2	5	5	X
ejpam-6600	105	3	)	)	PUNCT
ejpam-6600	105	4	set	set	NOUN
ejpam-6600	105	5	f(vi	f(vi	PROPN
ejpam-6600	105	6	,	,	PUNCT
ejpam-6600	105	7	vi+sj	vi+sj	NUM
ejpam-6600	105	8	)	)	PUNCT
ejpam-6600	106	1	=	=	SYM
ejpam-6600	106	2	0	0	NUM
ejpam-6600	107	1	for	for	ADP
ejpam-6600	107	2	all	all	PRON
ejpam-6600	107	3	i	i	PRON
ejpam-6600	107	4	∈	∈	PROPN
ejpam-6600	107	5	{	{	PUNCT
ejpam-6600	107	6	1	1	NUM
ejpam-6600	107	7	,	,	PUNCT
ejpam-6600	107	8	2	2	NUM
ejpam-6600	107	9	,	,	PUNCT
ejpam-6600	107	10	3	3	NUM
ejpam-6600	107	11	,	,	PUNCT
ejpam-6600	107	12	·	·	PUNCT
ejpam-6600	107	13	·	·	PUNCT
ejpam-6600	107	14	·	·	PUNCT
ejpam-6600	107	15	,	,	PUNCT
ejpam-6600	107	16	p	p	X
ejpam-6600	107	17	}	}	PUNCT
ejpam-6600	107	18	,	,	PUNCT
ejpam-6600	107	19	j	j	PROPN
ejpam-6600	107	20	∈	∈	PROPN
ejpam-6600	107	21	{	{	PUNCT
ejpam-6600	107	22	1	1	NUM
ejpam-6600	107	23	,	,	PUNCT
ejpam-6600	107	24	2	2	NUM
ejpam-6600	107	25	,	,	PUNCT
ejpam-6600	107	26	3	3	NUM
ejpam-6600	107	27	,	,	PUNCT
ejpam-6600	107	28	·	·	PUNCT
ejpam-6600	107	29	·	·	PUNCT
ejpam-6600	107	30	·	·	PUNCT
ejpam-6600	107	31	,	,	PUNCT
ejpam-6600	107	32	2r	2r	NUM
ejpam-6600	107	33	}	}	PUNCT
ejpam-6600	107	34	.	.	PUNCT
ejpam-6600	108	1	(	(	PUNCT
ejpam-6600	108	2	6	6	X
ejpam-6600	108	3	)	)	PUNCT
ejpam-6600	108	4	set	set	NOUN
ejpam-6600	108	5	i	i	NOUN
ejpam-6600	108	6	=	=	NOUN
ejpam-6600	109	1	1	1	X
ejpam-6600	109	2	.	.	X
ejpam-6600	109	3	step	step	NOUN
ejpam-6600	109	4	1	1	NUM
ejpam-6600	109	5	:	:	PUNCT
ejpam-6600	109	6	if	if	SCONJ
ejpam-6600	109	7	i	i	PRON
ejpam-6600	109	8	≤	≤	VERB
ejpam-6600	109	9	p	p	NOUN
ejpam-6600	109	10	then	then	ADV
ejpam-6600	109	11	continue	continue	VERB
ejpam-6600	109	12	to	to	PART
ejpam-6600	109	13	step	step	VERB
ejpam-6600	109	14	2	2	NUM
ejpam-6600	109	15	.	.	PUNCT
ejpam-6600	109	16	else	else	ADV
ejpam-6600	109	17	jump	jump	VERB
ejpam-6600	109	18	to	to	PART
ejpam-6600	109	19	step	step	VERB
ejpam-6600	109	20	4	4	NUM
ejpam-6600	109	21	.	.	PUNCT
ejpam-6600	110	1	step	step	NOUN
ejpam-6600	110	2	2	2	NUM
ejpam-6600	110	3	:	:	PUNCT
ejpam-6600	110	4	for	for	ADP
ejpam-6600	110	5	each	each	DET
ejpam-6600	110	6	sj	sj	PROPN
ejpam-6600	110	7	∈	∈	PROPN
ejpam-6600	110	8	s1	s1	PROPN
ejpam-6600	110	9	,	,	PUNCT
ejpam-6600	110	10	f	f	PROPN
ejpam-6600	110	11	(	(	PUNCT
ejpam-6600	110	12	vi	vi	PROPN
ejpam-6600	110	13	,	,	PUNCT
ejpam-6600	110	14	vi+sj	vi+sj	NUM
ejpam-6600	110	15	)	)	PUNCT
ejpam-6600	111	1	=	=	PRON
ejpam-6600	112	1	(	(	PUNCT
ejpam-6600	112	2	j	j	NOUN
ejpam-6600	112	3	−	−	PROPN
ejpam-6600	112	4	1	1	NUM
ejpam-6600	112	5	)	)	PUNCT
ejpam-6600	112	6	p+	p+	VERB
ejpam-6600	112	7	i.	i.	NOUN
ejpam-6600	112	8	step	step	NOUN
ejpam-6600	112	9	3	3	NUM
ejpam-6600	112	10	:	:	PUNCT
ejpam-6600	112	11	i	i	PRON
ejpam-6600	112	12	=	=	PUNCT
ejpam-6600	112	13	i+	i+	PROPN
ejpam-6600	112	14	1	1	NUM
ejpam-6600	112	15	,	,	PUNCT
ejpam-6600	112	16	go	go	VERB
ejpam-6600	112	17	back	back	ADV
ejpam-6600	112	18	to	to	PART
ejpam-6600	112	19	step	step	NOUN
ejpam-6600	112	20	1	1	NUM
ejpam-6600	112	21	.	.	PUNCT
ejpam-6600	113	1	step	step	NOUN
ejpam-6600	113	2	4	4	NUM
ejpam-6600	113	3	:	:	PUNCT
ejpam-6600	113	4	for	for	ADP
ejpam-6600	113	5	each	each	PRON
ejpam-6600	113	6	k	k	NOUN
ejpam-6600	113	7	=	=	SYM
ejpam-6600	113	8	1	1	NUM
ejpam-6600	113	9	,	,	PUNCT
ejpam-6600	113	10	2	2	NUM
ejpam-6600	113	11	,	,	PUNCT
ejpam-6600	113	12	3	3	NUM
ejpam-6600	113	13	,	,	PUNCT
ejpam-6600	113	14	.	.	PUNCT
ejpam-6600	113	15	.	.	PUNCT
ejpam-6600	114	1	.	.	PUNCT
ejpam-6600	115	1	,	,	PUNCT
ejpam-6600	115	2	p	p	X
ejpam-6600	115	3	,	,	PUNCT
ejpam-6600	115	4	find	find	VERB
ejpam-6600	115	5	the	the	DET
ejpam-6600	115	6	weight	weight	NOUN
ejpam-6600	115	7	of	of	ADP
ejpam-6600	115	8	the	the	DET
ejpam-6600	115	9	vertex	vertex	NOUN
ejpam-6600	115	10	vk	vk	NOUN
ejpam-6600	115	11	using	use	VERB
ejpam-6600	115	12	the	the	DET
ejpam-6600	115	13	following	follow	VERB
ejpam-6600	115	14	mapping	mapping	NOUN
ejpam-6600	115	15	:	:	PUNCT
ejpam-6600	115	16	fw(vk	fw(vk	PROPN
ejpam-6600	115	17	)	)	PUNCT
ejpam-6600	116	1	=	=	PUNCT
ejpam-6600	117	1	∑2r	∑2r	NOUN
ejpam-6600	117	2	j=1	j=1	PROPN
ejpam-6600	117	3	f(vk	f(vk	PROPN
ejpam-6600	117	4	,	,	PUNCT
ejpam-6600	117	5	vk+sj	vk+sj	NOUN
ejpam-6600	117	6	)	)	PUNCT
ejpam-6600	118	1	=	=	PUNCT
ejpam-6600	119	1	∑r	∑r	PROPN
ejpam-6600	119	2	j=1	j=1	PROPN
ejpam-6600	119	3	2[(j−1)p+k]+(p−sj	2[(j−1)p+k]+(p−sj	NOUN
ejpam-6600	119	4	)	)	PUNCT
ejpam-6600	120	1	=	=	SYM
ejpam-6600	120	2	2kr−l	2kr−l	NUM
ejpam-6600	120	3	(	(	PUNCT
ejpam-6600	120	4	mod	mod	NOUN
ejpam-6600	120	5	p	p	NOUN
ejpam-6600	120	6	)	)	PUNCT
ejpam-6600	120	7	,	,	PUNCT
ejpam-6600	120	8	where	where	SCONJ
ejpam-6600	120	9	l	l	NOUN
ejpam-6600	120	10	=	=	PUNCT
ejpam-6600	121	1	∑r	∑r	PROPN
ejpam-6600	121	2	j=1	j=1	NOUN
ejpam-6600	121	3	sj	sj	INTJ
ejpam-6600	121	4	.	.	PUNCT
ejpam-6600	122	1	theorem	theorem	NOUN
ejpam-6600	122	2	2	2	NUM
ejpam-6600	122	3	.	.	PUNCT
ejpam-6600	123	1	every	every	DET
ejpam-6600	123	2	paley	paley	ADJ
ejpam-6600	123	3	graph	graph	NOUN
ejpam-6600	123	4	of	of	ADP
ejpam-6600	123	5	prime	prime	ADJ
ejpam-6600	123	6	order	order	NOUN
ejpam-6600	123	7	admits	admit	VERB
ejpam-6600	123	8	an	an	DET
ejpam-6600	123	9	edge	edge	NOUN
ejpam-6600	123	10	-	-	PUNCT
ejpam-6600	123	11	graceful	graceful	NOUN
ejpam-6600	123	12	labeling	labeling	NOUN
ejpam-6600	123	13	.	.	PUNCT
ejpam-6600	124	1	proof	proof	NOUN
ejpam-6600	124	2	.	.	PUNCT
ejpam-6600	125	1	to	to	PART
ejpam-6600	125	2	prove	prove	VERB
ejpam-6600	125	3	that	that	SCONJ
ejpam-6600	125	4	the	the	DET
ejpam-6600	125	5	algorithm	algorithm	NOUN
ejpam-6600	125	6	defines	define	VERB
ejpam-6600	125	7	an	an	DET
ejpam-6600	125	8	edge	edge	NOUN
ejpam-6600	125	9	-	-	PUNCT
ejpam-6600	125	10	graceful	graceful	NOUN
ejpam-6600	125	11	labeling	labeling	NOUN
ejpam-6600	125	12	,	,	PUNCT
ejpam-6600	125	13	we	we	PRON
ejpam-6600	125	14	need	need	VERB
ejpam-6600	125	15	to	to	PART
ejpam-6600	125	16	prove	prove	VERB
ejpam-6600	125	17	that	that	SCONJ
ejpam-6600	125	18	both	both	DET
ejpam-6600	125	19	functions	function	NOUN
ejpam-6600	125	20	f	f	PROPN
ejpam-6600	125	21	and	and	CCONJ
ejpam-6600	125	22	fw	fw	PROPN
ejpam-6600	125	23	are	be	AUX
ejpam-6600	125	24	bijections	bijection	NOUN
ejpam-6600	125	25	.	.	PUNCT
ejpam-6600	126	1	(	(	PUNCT
ejpam-6600	126	2	i	i	NOUN
ejpam-6600	126	3	)	)	PUNCT
ejpam-6600	126	4	consider	consider	VERB
ejpam-6600	126	5	the	the	DET
ejpam-6600	126	6	function	function	NOUN
ejpam-6600	126	7	fw	fw	INTJ
ejpam-6600	126	8	:	:	PUNCT
ejpam-6600	126	9	v	v	NOUN
ejpam-6600	126	10	(	(	PUNCT
ejpam-6600	126	11	pp	pp	ADJ
ejpam-6600	126	12	)	)	PUNCT
ejpam-6600	127	1	−→	−→	NOUN
ejpam-6600	127	2	zp	zp	NOUN
ejpam-6600	127	3	defined	define	VERB
ejpam-6600	127	4	by	by	ADP
ejpam-6600	127	5	fw(vk	fw(vk	PROPN
ejpam-6600	127	6	)	)	PUNCT
ejpam-6600	128	1	=	=	PUNCT
ejpam-6600	129	1	∑2r	∑2r	PROPN
ejpam-6600	129	2	j=1	j=1	PROPN
ejpam-6600	129	3	f(vk	f(vk	PROPN
ejpam-6600	129	4	,	,	PUNCT
ejpam-6600	129	5	vk+sj	vk+sj	NOUN
ejpam-6600	129	6	)	)	PUNCT
ejpam-6600	130	1	=	=	PUNCT
ejpam-6600	131	1	2kr	2kr	NOUN
ejpam-6600	131	2	−	−	NOUN
ejpam-6600	131	3	l	l	NOUN
ejpam-6600	131	4	(	(	PUNCT
ejpam-6600	131	5	mod	mod	PROPN
ejpam-6600	131	6	p	p	X
ejpam-6600	131	7	)	)	PUNCT
ejpam-6600	131	8	.	.	PUNCT
ejpam-6600	132	1	now	now	ADV
ejpam-6600	132	2	,	,	PUNCT
ejpam-6600	132	3	we	we	PRON
ejpam-6600	132	4	prove	prove	VERB
ejpam-6600	132	5	that	that	SCONJ
ejpam-6600	132	6	fw	fw	PROPN
ejpam-6600	132	7	is	be	AUX
ejpam-6600	132	8	one	one	NUM
ejpam-6600	132	9	-	-	PUNCT
ejpam-6600	132	10	to	to	ADP
ejpam-6600	132	11	-	-	PUNCT
ejpam-6600	132	12	one	one	NOUN
ejpam-6600	132	13	,	,	PUNCT
ejpam-6600	132	14	which	which	PRON
ejpam-6600	132	15	implies	imply	VERB
ejpam-6600	132	16	tat	tat	NOUN
ejpam-6600	132	17	it	it	PRON
ejpam-6600	132	18	is	be	AUX
ejpam-6600	132	19	a	a	DET
ejpam-6600	132	20	bijection	bijection	NOUN
ejpam-6600	132	21	.	.	PUNCT
ejpam-6600	133	1	let	let	VERB
ejpam-6600	133	2	vx	vx	PROPN
ejpam-6600	133	3	and	and	CCONJ
ejpam-6600	133	4	vy	vy	PRON
ejpam-6600	133	5	be	be	AUX
ejpam-6600	133	6	two	two	NUM
ejpam-6600	133	7	vertices	vertex	NOUN
ejpam-6600	133	8	in	in	ADP
ejpam-6600	133	9	v	v	ADP
ejpam-6600	133	10	(	(	PUNCT
ejpam-6600	133	11	pp	pp	ADJ
ejpam-6600	133	12	)	)	PUNCT
ejpam-6600	133	13	,	,	PUNCT
ejpam-6600	133	14	if	if	SCONJ
ejpam-6600	133	15	fw(vx	fw(vx	NOUN
ejpam-6600	133	16	)	)	PUNCT
ejpam-6600	133	17	=	=	SYM
ejpam-6600	134	1	fw(vy	fw(vy	PROPN
ejpam-6600	134	2	)	)	PUNCT
ejpam-6600	134	3	then	then	ADV
ejpam-6600	134	4	2xr−l	2xr−l	NUM
ejpam-6600	134	5	=	=	SYM
ejpam-6600	134	6	2yr	2yr	NOUN
ejpam-6600	134	7	−	−	PROPN
ejpam-6600	134	8	l	l	NOUN
ejpam-6600	134	9	(	(	PUNCT
ejpam-6600	134	10	mod	mod	PROPN
ejpam-6600	134	11	p	p	X
ejpam-6600	134	12	)	)	PUNCT
ejpam-6600	134	13	which	which	PRON
ejpam-6600	134	14	leads	lead	VERB
ejpam-6600	134	15	to	to	ADP
ejpam-6600	134	16	x	x	PROPN
ejpam-6600	134	17	=	=	PUNCT
ejpam-6600	134	18	y.	y.	PROPN
ejpam-6600	134	19	(	(	PUNCT
ejpam-6600	134	20	ii	ii	PROPN
ejpam-6600	134	21	)	)	PUNCT
ejpam-6600	134	22	the	the	DET
ejpam-6600	134	23	function	function	NOUN
ejpam-6600	134	24	f	f	NOUN
ejpam-6600	134	25	:	:	PUNCT
ejpam-6600	134	26	e(pp	e(pp	NOUN
ejpam-6600	134	27	)	)	PUNCT
ejpam-6600	134	28	−→	−→	NOUN
ejpam-6600	134	29	{	{	PUNCT
ejpam-6600	134	30	1	1	NUM
ejpam-6600	134	31	,	,	PUNCT
ejpam-6600	134	32	2	2	NUM
ejpam-6600	134	33	,	,	PUNCT
ejpam-6600	134	34	3	3	NUM
ejpam-6600	134	35	,	,	PUNCT
ejpam-6600	134	36	.	.	PUNCT
ejpam-6600	134	37	.	.	PUNCT
ejpam-6600	134	38	.	.	PUNCT
ejpam-6600	135	1	,	,	PUNCT
ejpam-6600	135	2	rp	rp	NOUN
ejpam-6600	135	3	}	}	PUNCT
ejpam-6600	135	4	is	be	AUX
ejpam-6600	135	5	defined	define	VERB
ejpam-6600	135	6	as	as	ADP
ejpam-6600	135	7	f(vx	f(vx	PROPN
ejpam-6600	135	8	,	,	PUNCT
ejpam-6600	135	9	vx+sj	vx+sj	ADJ
ejpam-6600	135	10	)	)	PUNCT
ejpam-6600	136	1	=	=	PUNCT
ejpam-6600	136	2	(	(	PUNCT
ejpam-6600	136	3	j−	j−	PROPN
ejpam-6600	136	4	1)p+	1)p+	NUM
ejpam-6600	136	5	x.	x.	NOUN
ejpam-6600	136	6	to	to	PART
ejpam-6600	136	7	prove	prove	VERB
ejpam-6600	136	8	that	that	SCONJ
ejpam-6600	136	9	f	f	PROPN
ejpam-6600	136	10	is	be	AUX
ejpam-6600	136	11	a	a	DET
ejpam-6600	136	12	bijection	bijection	NOUN
ejpam-6600	136	13	,	,	PUNCT
ejpam-6600	136	14	we	we	PRON
ejpam-6600	136	15	need	need	VERB
ejpam-6600	136	16	only	only	ADV
ejpam-6600	136	17	to	to	PART
ejpam-6600	136	18	prove	prove	VERB
ejpam-6600	136	19	the	the	DET
ejpam-6600	136	20	injectivity	injectivity	NOUN
ejpam-6600	136	21	of	of	ADP
ejpam-6600	136	22	f	f	PROPN
ejpam-6600	136	23	.	.	PUNCT
ejpam-6600	137	1	let	let	VERB
ejpam-6600	137	2	(	(	PUNCT
ejpam-6600	137	3	vx	vx	NOUN
ejpam-6600	137	4	,	,	PUNCT
ejpam-6600	137	5	vx+si	vx+si	NOUN
ejpam-6600	137	6	)	)	PUNCT
ejpam-6600	137	7	and	and	CCONJ
ejpam-6600	137	8	(	(	PUNCT
ejpam-6600	137	9	vy	vy	INTJ
ejpam-6600	137	10	,	,	PUNCT
ejpam-6600	137	11	vy+sj	vy+sj	PRON
ejpam-6600	137	12	)	)	PUNCT
ejpam-6600	137	13	be	be	AUX
ejpam-6600	137	14	two	two	NUM
ejpam-6600	137	15	edges	edge	NOUN
ejpam-6600	137	16	,	,	PUNCT
ejpam-6600	137	17	with	with	ADP
ejpam-6600	137	18	x	x	PRON
ejpam-6600	137	19	,	,	PUNCT
ejpam-6600	137	20	y	y	PROPN
ejpam-6600	137	21	∈	∈	PROPN
ejpam-6600	137	22	{	{	PUNCT
ejpam-6600	137	23	1	1	NUM
ejpam-6600	137	24	,	,	PUNCT
ejpam-6600	137	25	2	2	NUM
ejpam-6600	137	26	,	,	PUNCT
ejpam-6600	137	27	3	3	NUM
ejpam-6600	137	28	,	,	PUNCT
ejpam-6600	137	29	·	·	PUNCT
ejpam-6600	137	30	·	·	PUNCT
ejpam-6600	137	31	·	·	PUNCT
ejpam-6600	137	32	,	,	PUNCT
ejpam-6600	137	33	p	p	X
ejpam-6600	137	34	}	}	PUNCT
ejpam-6600	137	35	,	,	PUNCT
ejpam-6600	137	36	si	si	INTJ
ejpam-6600	137	37	,	,	PUNCT
ejpam-6600	137	38	sj	sj	PROPN
ejpam-6600	137	39	∈	∈	PROPN
ejpam-6600	137	40	s	s	PART
ejpam-6600	137	41	=	=	PUNCT
ejpam-6600	137	42	(	(	PUNCT
ejpam-6600	137	43	z∗	z∗	PROPN
ejpam-6600	137	44	p	p	NOUN
ejpam-6600	137	45	)	)	PUNCT
ejpam-6600	137	46	2	2	NUM
ejpam-6600	137	47	,	,	PUNCT
ejpam-6600	137	48	and	and	CCONJ
ejpam-6600	137	49	f(vx	f(vx	PROPN
ejpam-6600	137	50	,	,	PUNCT
ejpam-6600	137	51	vx+sj	vx+sj	ADJ
ejpam-6600	137	52	)	)	PUNCT
ejpam-6600	138	1	=	=	SYM
ejpam-6600	138	2	f(vy	f(vy	ADJ
ejpam-6600	138	3	,	,	PUNCT
ejpam-6600	138	4	vy+si	vy+si	NOUN
ejpam-6600	138	5	)	)	PUNCT
ejpam-6600	138	6	,	,	PUNCT
ejpam-6600	138	7	which	which	PRON
ejpam-6600	138	8	implies	imply	VERB
ejpam-6600	138	9	that	that	SCONJ
ejpam-6600	138	10	(	(	PUNCT
ejpam-6600	138	11	i−	i−	PROPN
ejpam-6600	138	12	1)p+x	1)p+x	NOUN
ejpam-6600	138	13	=	=	SYM
ejpam-6600	138	14	(	(	PUNCT
ejpam-6600	138	15	j−	j−	PROPN
ejpam-6600	138	16	1)p+	1)p+	NUM
ejpam-6600	138	17	y.	y.	NOUN
ejpam-6600	138	18	in	in	ADP
ejpam-6600	138	19	case	case	NOUN
ejpam-6600	138	20	of	of	ADP
ejpam-6600	138	21	i	i	PRON
ejpam-6600	138	22	=	=	SYM
ejpam-6600	138	23	j	j	PROPN
ejpam-6600	138	24	or	or	CCONJ
ejpam-6600	138	25	x	x	X
ejpam-6600	138	26	=	=	SYM
ejpam-6600	138	27	y	y	PROPN
ejpam-6600	138	28	the	the	DET
ejpam-6600	138	29	proof	proof	NOUN
ejpam-6600	138	30	is	be	AUX
ejpam-6600	138	31	trivial	trivial	ADJ
ejpam-6600	138	32	.	.	PUNCT
ejpam-6600	139	1	the	the	DET
ejpam-6600	139	2	last	last	ADJ
ejpam-6600	139	3	case	case	NOUN
ejpam-6600	139	4	if	if	SCONJ
ejpam-6600	139	5	x	x	PROPN
ejpam-6600	139	6	̸=	̸=	PROPN
ejpam-6600	139	7	y	y	PROPN
ejpam-6600	139	8	and	and	CCONJ
ejpam-6600	139	9	j	j	PROPN
ejpam-6600	139	10	̸=	̸=	PROPN
ejpam-6600	139	11	i	i	PRON
ejpam-6600	139	12	,	,	PUNCT
ejpam-6600	139	13	here	here	ADV
ejpam-6600	139	14	we	we	PRON
ejpam-6600	139	15	will	will	AUX
ejpam-6600	139	16	find	find	VERB
ejpam-6600	139	17	that	that	SCONJ
ejpam-6600	139	18	x−	x−	PROPN
ejpam-6600	139	19	y	y	PROPN
ejpam-6600	139	20	=	=	PUNCT
ejpam-6600	139	21	(	(	PUNCT
ejpam-6600	139	22	j−	j−	PROPN
ejpam-6600	139	23	i)p	i)p	ADV
ejpam-6600	139	24	but	but	CCONJ
ejpam-6600	139	25	|x−	|x−	NOUN
ejpam-6600	139	26	y|	y|	VERB
ejpam-6600	139	27	<	<	X
ejpam-6600	139	28	p	p	X
ejpam-6600	139	29	and	and	CCONJ
ejpam-6600	139	30	in	in	ADP
ejpam-6600	139	31	the	the	DET
ejpam-6600	139	32	same	same	ADJ
ejpam-6600	139	33	time	time	NOUN
ejpam-6600	139	34	|p(i−	|p(i−	NUM
ejpam-6600	139	35	j)|	j)|	NOUN
ejpam-6600	139	36	≥	≥	NOUN
ejpam-6600	139	37	p	p	NOUN
ejpam-6600	139	38	which	which	PRON
ejpam-6600	139	39	is	be	AUX
ejpam-6600	139	40	a	a	DET
ejpam-6600	139	41	contradiction	contradiction	NOUN
ejpam-6600	139	42	.	.	PUNCT
ejpam-6600	140	1	so	so	ADV
ejpam-6600	140	2	,	,	PUNCT
ejpam-6600	140	3	from	from	ADP
ejpam-6600	140	4	these	these	DET
ejpam-6600	140	5	three	three	NUM
ejpam-6600	140	6	cases	case	NOUN
ejpam-6600	140	7	,	,	PUNCT
ejpam-6600	140	8	we	we	PRON
ejpam-6600	140	9	can	can	AUX
ejpam-6600	140	10	be	be	AUX
ejpam-6600	140	11	sure	sure	ADJ
ejpam-6600	140	12	that	that	SCONJ
ejpam-6600	140	13	the	the	DET
ejpam-6600	140	14	function	function	NOUN
ejpam-6600	140	15	f	f	PROPN
ejpam-6600	140	16	is	be	AUX
ejpam-6600	140	17	a	a	DET
ejpam-6600	140	18	one	one	NUM
ejpam-6600	140	19	-	-	PUNCT
ejpam-6600	140	20	to	to	ADP
ejpam-6600	140	21	-	-	PUNCT
ejpam-6600	140	22	one	one	NUM
ejpam-6600	140	23	function	function	NOUN
ejpam-6600	140	24	.	.	PUNCT
ejpam-6600	141	1	□	□	PUNCT
ejpam-6600	141	2	example	example	NOUN
ejpam-6600	142	1	3	3	X
ejpam-6600	142	2	.	.	X
ejpam-6600	143	1	we	we	PRON
ejpam-6600	143	2	apply	apply	VERB
ejpam-6600	143	3	the	the	DET
ejpam-6600	143	4	previous	previous	ADJ
ejpam-6600	143	5	algorithm	algorithm	NOUN
ejpam-6600	143	6	to	to	PART
ejpam-6600	143	7	show	show	VERB
ejpam-6600	143	8	that	that	SCONJ
ejpam-6600	143	9	:	:	PUNCT
ejpam-6600	143	10	the	the	DET
ejpam-6600	143	11	paley	paley	ADJ
ejpam-6600	143	12	graph	graph	NOUN
ejpam-6600	143	13	p13	p13	NOUN
ejpam-6600	143	14	is	be	AUX
ejpam-6600	143	15	an	an	DET
ejpam-6600	143	16	edge	edge	NOUN
ejpam-6600	143	17	-	-	PUNCT
ejpam-6600	143	18	graceful	graceful	NOUN
ejpam-6600	143	19	graph	graph	NOUN
ejpam-6600	143	20	,	,	PUNCT
ejpam-6600	143	21	where	where	SCONJ
ejpam-6600	143	22	v	v	X
ejpam-6600	143	23	(	(	PUNCT
ejpam-6600	143	24	p13	p13	PROPN
ejpam-6600	143	25	)	)	PUNCT
ejpam-6600	143	26	=	=	NOUN
ejpam-6600	143	27	{	{	PUNCT
ejpam-6600	143	28	v1	v1	PROPN
ejpam-6600	143	29	,	,	PUNCT
ejpam-6600	143	30	v2	v2	PROPN
ejpam-6600	143	31	,	,	PUNCT
ejpam-6600	143	32	·	·	PUNCT
ejpam-6600	143	33	·	·	PUNCT
ejpam-6600	143	34	·	·	PUNCT
ejpam-6600	143	35	,	,	PUNCT
ejpam-6600	143	36	v13	v13	PROPN
ejpam-6600	143	37	}	}	PUNCT
ejpam-6600	143	38	and	and	CCONJ
ejpam-6600	143	39	|e(p13)|	|e(p13)|	NUM
ejpam-6600	143	40	=	=	SYM
ejpam-6600	143	41	13·12	13·12	NUM
ejpam-6600	143	42	4	4	NUM
ejpam-6600	143	43	=	=	SYM
ejpam-6600	143	44	39	39	NUM
ejpam-6600	143	45	.	.	PUNCT
ejpam-6600	144	1	figure	figure	NOUN
ejpam-6600	144	2	4	4	NUM
ejpam-6600	144	3	illustrates	illustrate	VERB
ejpam-6600	144	4	the	the	DET
ejpam-6600	144	5	edge	edge	NOUN
ejpam-6600	144	6	-	-	PUNCT
ejpam-6600	144	7	graceful	graceful	NOUN
ejpam-6600	144	8	labeling	labeling	NOUN
ejpam-6600	144	9	for	for	ADP
ejpam-6600	144	10	p13	p13	NOUN
ejpam-6600	144	11	.	.	PUNCT
ejpam-6600	144	12	a.	a.	PROPN
ejpam-6600	144	13	n.	n.	PROPN
ejpam-6600	144	14	elsawy	elsawy	PROPN
ejpam-6600	144	15	,	,	PUNCT
ejpam-6600	144	16	r.	r.	PROPN
ejpam-6600	144	17	n.	n.	PROPN
ejpam-6600	144	18	almohammadi	almohammadi	PROPN
ejpam-6600	144	19	/	/	SYM
ejpam-6600	144	20	eur	eur	PROPN
ejpam-6600	144	21	.	.	PUNCT
ejpam-6600	145	1	j.	j.	PROPN
ejpam-6600	145	2	pure	pure	PROPN
ejpam-6600	145	3	appl	appl	PROPN
ejpam-6600	145	4	.	.	PROPN
ejpam-6600	145	5	math	math	PROPN
ejpam-6600	145	6	,	,	PUNCT
ejpam-6600	145	7	18	18	NUM
ejpam-6600	145	8	(	(	PUNCT
ejpam-6600	145	9	4	4	NUM
ejpam-6600	145	10	)	)	PUNCT
ejpam-6600	145	11	(	(	PUNCT
ejpam-6600	145	12	2025	2025	NUM
ejpam-6600	145	13	)	)	PUNCT
ejpam-6600	145	14	,	,	PUNCT
ejpam-6600	145	15	6600	6600	NUM
ejpam-6600	145	16	6	6	NUM
ejpam-6600	145	17	of	of	ADP
ejpam-6600	145	18	26	26	NUM
ejpam-6600	145	19	figure	figure	NOUN
ejpam-6600	145	20	4	4	NUM
ejpam-6600	145	21	:	:	PUNCT
ejpam-6600	145	22	an	an	DET
ejpam-6600	145	23	edge	edge	NOUN
ejpam-6600	145	24	-	-	PUNCT
ejpam-6600	145	25	graceful	graceful	NOUN
ejpam-6600	145	26	labeling	labeling	NOUN
ejpam-6600	145	27	for	for	ADP
ejpam-6600	145	28	p13	p13	NOUN
ejpam-6600	145	29	input	input	NOUN
ejpam-6600	145	30	:	:	PUNCT
ejpam-6600	145	31	the	the	DET
ejpam-6600	145	32	graph	graph	NOUN
ejpam-6600	145	33	p13	p13	VERB
ejpam-6600	145	34	.	.	PUNCT
ejpam-6600	146	1	here	here	ADV
ejpam-6600	146	2	we	we	PRON
ejpam-6600	146	3	have	have	VERB
ejpam-6600	146	4	p	p	NOUN
ejpam-6600	146	5	=	=	NOUN
ejpam-6600	146	6	13	13	NUM
ejpam-6600	146	7	,	,	PUNCT
ejpam-6600	146	8	r	r	NOUN
ejpam-6600	146	9	=	=	SYM
ejpam-6600	146	10	3	3	NUM
ejpam-6600	146	11	,	,	PUNCT
ejpam-6600	146	12	and	and	CCONJ
ejpam-6600	146	13	(	(	PUNCT
ejpam-6600	146	14	z∗	z∗	NOUN
ejpam-6600	146	15	13	13	NUM
ejpam-6600	146	16	)	)	PUNCT
ejpam-6600	146	17	2	2	NUM
ejpam-6600	146	18	=	=	SYM
ejpam-6600	146	19	{	{	PUNCT
ejpam-6600	146	20	12	12	NUM
ejpam-6600	146	21	,	,	PUNCT
ejpam-6600	146	22	22	22	NUM
ejpam-6600	146	23	,	,	PUNCT
ejpam-6600	146	24	32	32	NUM
ejpam-6600	146	25	,	,	PUNCT
ejpam-6600	146	26	·	·	PUNCT
ejpam-6600	146	27	·	·	PUNCT
ejpam-6600	146	28	·	·	PUNCT
ejpam-6600	146	29	,	,	PUNCT
ejpam-6600	146	30	122	122	NUM
ejpam-6600	146	31	}	}	PUNCT
ejpam-6600	146	32	=	=	SYM
ejpam-6600	146	33	{	{	PUNCT
ejpam-6600	146	34	1	1	NUM
ejpam-6600	146	35	,	,	PUNCT
ejpam-6600	146	36	4	4	NUM
ejpam-6600	146	37	,	,	PUNCT
ejpam-6600	146	38	9	9	NUM
ejpam-6600	146	39	,	,	PUNCT
ejpam-6600	146	40	3	3	NUM
ejpam-6600	146	41	,	,	PUNCT
ejpam-6600	146	42	12	12	NUM
ejpam-6600	146	43	,	,	PUNCT
ejpam-6600	146	44	10	10	NUM
ejpam-6600	146	45	}	}	PUNCT
ejpam-6600	146	46	.	.	PUNCT
ejpam-6600	147	1	(	(	PUNCT
ejpam-6600	147	2	1	1	X
ejpam-6600	147	3	)	)	PUNCT
ejpam-6600	147	4	rename	rename	VERB
ejpam-6600	147	5	the	the	DET
ejpam-6600	147	6	vertices	vertex	NOUN
ejpam-6600	147	7	of	of	ADP
ejpam-6600	147	8	the	the	DET
ejpam-6600	147	9	graph	graph	NOUN
ejpam-6600	147	10	as	as	ADP
ejpam-6600	147	11	0	0	NUM
ejpam-6600	147	12	:	:	PUNCT
ejpam-6600	147	13	=	=	SYM
ejpam-6600	147	14	v13	v13	X
ejpam-6600	147	15	,	,	PUNCT
ejpam-6600	147	16	1	1	NUM
ejpam-6600	147	17	:	:	PUNCT
ejpam-6600	147	18	=	=	NOUN
ejpam-6600	147	19	v1	v1	NOUN
ejpam-6600	147	20	,	,	PUNCT
ejpam-6600	147	21	2	2	NUM
ejpam-6600	147	22	:	:	PUNCT
ejpam-6600	147	23	=	=	SYM
ejpam-6600	147	24	v2	v2	PROPN
ejpam-6600	147	25	,	,	PUNCT
ejpam-6600	147	26	.	.	PUNCT
ejpam-6600	147	27	.	.	PUNCT
ejpam-6600	148	1	.	.	PUNCT
ejpam-6600	149	1	,	,	PUNCT
ejpam-6600	149	2	12	12	NUM
ejpam-6600	149	3	:	:	PUNCT
ejpam-6600	149	4	=	=	SYM
ejpam-6600	149	5	v12	v12	VERB
ejpam-6600	149	6	.	.	PUNCT
ejpam-6600	150	1	(	(	PUNCT
ejpam-6600	150	2	2	2	X
ejpam-6600	150	3	)	)	PUNCT
ejpam-6600	150	4	rewrite	rewrite	NOUN
ejpam-6600	150	5	(	(	PUNCT
ejpam-6600	150	6	z∗	z∗	NOUN
ejpam-6600	150	7	13	13	NUM
ejpam-6600	150	8	)	)	PUNCT
ejpam-6600	150	9	2	2	NUM
ejpam-6600	150	10	as	as	ADP
ejpam-6600	150	11	(	(	PUNCT
ejpam-6600	150	12	z∗	z∗	NOUN
ejpam-6600	150	13	13	13	NUM
ejpam-6600	150	14	)	)	PUNCT
ejpam-6600	150	15	2	2	NUM
ejpam-6600	150	16	=	=	SYM
ejpam-6600	150	17	s	s	NOUN
ejpam-6600	150	18	=	=	PUNCT
ejpam-6600	150	19	{	{	PUNCT
ejpam-6600	150	20	s1	s1	NOUN
ejpam-6600	150	21	,	,	PUNCT
ejpam-6600	150	22	s2	s2	PROPN
ejpam-6600	150	23	,	,	PUNCT
ejpam-6600	150	24	s3	s3	PROPN
ejpam-6600	150	25	,	,	PUNCT
ejpam-6600	150	26	s4	s4	PROPN
ejpam-6600	150	27	,	,	PUNCT
ejpam-6600	150	28	s5	s5	PROPN
ejpam-6600	150	29	,	,	PUNCT
ejpam-6600	150	30	s6	s6	PROPN
ejpam-6600	150	31	:	:	PUNCT
ejpam-6600	150	32	s1	s1	PROPN
ejpam-6600	150	33	<	<	X
ejpam-6600	150	34	s2	s2	PROPN
ejpam-6600	150	35	<	<	X
ejpam-6600	150	36	s3	s3	PROPN
ejpam-6600	150	37	<	<	X
ejpam-6600	150	38	s4	s4	PROPN
ejpam-6600	150	39	<	<	X
ejpam-6600	150	40	s5	s5	PROPN
ejpam-6600	150	41	<	<	X
ejpam-6600	150	42	s6	s6	PROPN
ejpam-6600	150	43	}	}	PUNCT
ejpam-6600	150	44	=	=	PUNCT
ejpam-6600	150	45	{	{	PUNCT
ejpam-6600	150	46	1	1	NUM
ejpam-6600	150	47	,	,	PUNCT
ejpam-6600	150	48	3	3	NUM
ejpam-6600	150	49	,	,	PUNCT
ejpam-6600	150	50	4	4	NUM
ejpam-6600	150	51	,	,	PUNCT
ejpam-6600	150	52	9	9	NUM
ejpam-6600	150	53	,	,	PUNCT
ejpam-6600	150	54	10	10	NUM
ejpam-6600	150	55	,	,	PUNCT
ejpam-6600	150	56	12	12	NUM
ejpam-6600	150	57	}	}	PUNCT
ejpam-6600	150	58	.	.	PUNCT
ejpam-6600	151	1	(	(	PUNCT
ejpam-6600	151	2	3	3	X
ejpam-6600	151	3	)	)	PUNCT
ejpam-6600	151	4	partition	partition	NOUN
ejpam-6600	151	5	s	s	NOUN
ejpam-6600	151	6	into	into	ADP
ejpam-6600	151	7	two	two	NUM
ejpam-6600	151	8	sets	set	NOUN
ejpam-6600	151	9	.	.	PUNCT
ejpam-6600	152	1	let	let	VERB
ejpam-6600	152	2	s1	s1	PROPN
ejpam-6600	152	3	=	=	PUNCT
ejpam-6600	152	4	{	{	PUNCT
ejpam-6600	152	5	s1	s1	NOUN
ejpam-6600	152	6	,	,	PUNCT
ejpam-6600	152	7	s2	s2	PROPN
ejpam-6600	152	8	,	,	PUNCT
ejpam-6600	152	9	s3	s3	PROPN
ejpam-6600	152	10	}	}	PUNCT
ejpam-6600	152	11	=	=	PUNCT
ejpam-6600	152	12	{	{	PUNCT
ejpam-6600	152	13	1	1	NUM
ejpam-6600	152	14	,	,	PUNCT
ejpam-6600	152	15	3	3	NUM
ejpam-6600	152	16	,	,	PUNCT
ejpam-6600	152	17	4	4	NUM
ejpam-6600	152	18	}	}	PUNCT
ejpam-6600	152	19	and	and	CCONJ
ejpam-6600	152	20	s2	s2	VERB
ejpam-6600	152	21	=	=	SYM
ejpam-6600	152	22	{	{	PUNCT
ejpam-6600	152	23	s4	s4	PROPN
ejpam-6600	152	24	,	,	PUNCT
ejpam-6600	152	25	s5	s5	PROPN
ejpam-6600	152	26	,	,	PUNCT
ejpam-6600	152	27	s6	s6	PROPN
ejpam-6600	152	28	}	}	PUNCT
ejpam-6600	152	29	=	=	PUNCT
ejpam-6600	152	30	{	{	PUNCT
ejpam-6600	152	31	9	9	NUM
ejpam-6600	152	32	,	,	PUNCT
ejpam-6600	152	33	10	10	NUM
ejpam-6600	152	34	,	,	PUNCT
ejpam-6600	152	35	12	12	NUM
ejpam-6600	152	36	}	}	PUNCT
ejpam-6600	152	37	.	.	PUNCT
ejpam-6600	153	1	note	note	VERB
ejpam-6600	153	2	that	that	SCONJ
ejpam-6600	153	3	:	:	PUNCT
ejpam-6600	153	4	for	for	ADP
ejpam-6600	153	5	any	any	DET
ejpam-6600	153	6	vertex	vertex	NOUN
ejpam-6600	153	7	vi	vi	NOUN
ejpam-6600	153	8	∈	∈	PROPN
ejpam-6600	153	9	z13	z13	NOUN
ejpam-6600	153	10	the	the	DET
ejpam-6600	153	11	vertices	vertex	NOUN
ejpam-6600	153	12	vi+1	vi+1	ADV
ejpam-6600	153	13	,	,	PUNCT
ejpam-6600	153	14	vi+3	vi+3	X
ejpam-6600	153	15	,	,	PUNCT
ejpam-6600	153	16	vi+4	vi+4	X
ejpam-6600	153	17	,	,	PUNCT
ejpam-6600	153	18	vi+9	vi+9	X
ejpam-6600	153	19	,	,	PUNCT
ejpam-6600	153	20	vi+10	vi+10	NOUN
ejpam-6600	153	21	,	,	PUNCT
ejpam-6600	153	22	vi+12	vi+12	PROPN
ejpam-6600	153	23	are	be	AUX
ejpam-6600	153	24	adjacent	adjacent	ADJ
ejpam-6600	153	25	to	to	ADP
ejpam-6600	153	26	vi	vi	PROPN
ejpam-6600	153	27	.	.	PUNCT
ejpam-6600	154	1	(	(	PUNCT
ejpam-6600	154	2	4	4	X
ejpam-6600	154	3	)	)	PUNCT
ejpam-6600	154	4	the	the	DET
ejpam-6600	154	5	vertices	vertex	NOUN
ejpam-6600	154	6	vi+1	vi+1	NOUN
ejpam-6600	154	7	,	,	PUNCT
ejpam-6600	154	8	vi+3	vi+3	X
ejpam-6600	154	9	,	,	PUNCT
ejpam-6600	154	10	vi+4	vi+4	X
ejpam-6600	154	11	are	be	AUX
ejpam-6600	154	12	placed	place	VERB
ejpam-6600	154	13	in	in	ADP
ejpam-6600	154	14	clockwise	clockwise	NOUN
ejpam-6600	154	15	direction	direction	NOUN
ejpam-6600	154	16	of	of	ADP
ejpam-6600	154	17	vi	vi	NOUN
ejpam-6600	154	18	and	and	CCONJ
ejpam-6600	154	19	the	the	DET
ejpam-6600	154	20	vertices	vertex	NOUN
ejpam-6600	154	21	vi+9	vi+9	NUM
ejpam-6600	154	22	,	,	PUNCT
ejpam-6600	154	23	vi+10	vi+10	NOUN
ejpam-6600	154	24	,	,	PUNCT
ejpam-6600	154	25	vi+12	vi+12	PRON
ejpam-6600	154	26	are	be	AUX
ejpam-6600	154	27	placed	place	VERB
ejpam-6600	154	28	in	in	ADP
ejpam-6600	154	29	anticlockwise	anticlockwise	NOUN
ejpam-6600	154	30	direction	direction	NOUN
ejpam-6600	154	31	of	of	ADP
ejpam-6600	154	32	vi	vi	PROPN
ejpam-6600	154	33	.	.	PUNCT
ejpam-6600	155	1	(	(	PUNCT
ejpam-6600	155	2	5	5	X
ejpam-6600	155	3	)	)	PUNCT
ejpam-6600	155	4	set	set	NOUN
ejpam-6600	155	5	f(vi	f(vi	PROPN
ejpam-6600	155	6	,	,	PUNCT
ejpam-6600	155	7	vi+sj	vi+sj	NUM
ejpam-6600	155	8	)	)	PUNCT
ejpam-6600	156	1	=	=	SYM
ejpam-6600	156	2	0	0	NUM
ejpam-6600	157	1	for	for	ADP
ejpam-6600	157	2	all	all	PRON
ejpam-6600	157	3	i	i	PRON
ejpam-6600	157	4	∈	∈	PROPN
ejpam-6600	157	5	{	{	PUNCT
ejpam-6600	157	6	1	1	NUM
ejpam-6600	157	7	,	,	PUNCT
ejpam-6600	157	8	2	2	NUM
ejpam-6600	157	9	,	,	PUNCT
ejpam-6600	157	10	3	3	NUM
ejpam-6600	157	11	,	,	PUNCT
ejpam-6600	157	12	.	.	PUNCT
ejpam-6600	157	13	.	.	PUNCT
ejpam-6600	157	14	.	.	PUNCT
ejpam-6600	158	1	,	,	PUNCT
ejpam-6600	158	2	13	13	NUM
ejpam-6600	158	3	}	}	PUNCT
ejpam-6600	158	4	,	,	PUNCT
ejpam-6600	158	5	j	j	PROPN
ejpam-6600	158	6	∈	∈	PROPN
ejpam-6600	158	7	{	{	PUNCT
ejpam-6600	158	8	1	1	NUM
ejpam-6600	158	9	,	,	PUNCT
ejpam-6600	158	10	2	2	NUM
ejpam-6600	158	11	,	,	PUNCT
ejpam-6600	158	12	3	3	NUM
ejpam-6600	158	13	,	,	PUNCT
ejpam-6600	158	14	.	.	PUNCT
ejpam-6600	158	15	.	.	PUNCT
ejpam-6600	158	16	.	.	PUNCT
ejpam-6600	159	1	,	,	PUNCT
ejpam-6600	159	2	6	6	NUM
ejpam-6600	159	3	}	}	PUNCT
ejpam-6600	159	4	.	.	PUNCT
ejpam-6600	160	1	(	(	PUNCT
ejpam-6600	160	2	6	6	X
ejpam-6600	160	3	)	)	PUNCT
ejpam-6600	160	4	set	set	NOUN
ejpam-6600	160	5	i	i	NOUN
ejpam-6600	160	6	=	=	NOUN
ejpam-6600	161	1	1	1	X
ejpam-6600	161	2	.	.	X
ejpam-6600	161	3	step	step	NOUN
ejpam-6600	161	4	1	1	NUM
ejpam-6600	161	5	:	:	PUNCT
ejpam-6600	161	6	i	i	NOUN
ejpam-6600	161	7	=	=	NOUN
ejpam-6600	161	8	1	1	NUM
ejpam-6600	161	9	≤	≤	NUM
ejpam-6600	161	10	13	13	NUM
ejpam-6600	161	11	,	,	PUNCT
ejpam-6600	161	12	then	then	ADV
ejpam-6600	161	13	continue	continue	VERB
ejpam-6600	161	14	to	to	PART
ejpam-6600	161	15	step	step	VERB
ejpam-6600	161	16	2	2	NUM
ejpam-6600	161	17	.	.	PUNCT
ejpam-6600	161	18	step	step	NOUN
ejpam-6600	161	19	2	2	NUM
ejpam-6600	161	20	:	:	PUNCT
ejpam-6600	161	21	for	for	ADP
ejpam-6600	161	22	each	each	DET
ejpam-6600	161	23	s1	s1	NOUN
ejpam-6600	161	24	,	,	PUNCT
ejpam-6600	161	25	s2	s2	PROPN
ejpam-6600	161	26	,	,	PUNCT
ejpam-6600	161	27	s3	s3	PROPN
ejpam-6600	161	28	∈	∈	PROPN
ejpam-6600	161	29	s1	s1	NOUN
ejpam-6600	161	30	,	,	PUNCT
ejpam-6600	161	31	f	f	PROPN
ejpam-6600	161	32	(	(	PUNCT
ejpam-6600	161	33	v1	v1	PROPN
ejpam-6600	161	34	,	,	PUNCT
ejpam-6600	161	35	v1+sj	v1+sj	NOUN
ejpam-6600	161	36	)	)	PUNCT
ejpam-6600	162	1	=	=	SYM
ejpam-6600	162	2	(	(	PUNCT
ejpam-6600	162	3	j	j	NOUN
ejpam-6600	162	4	−	−	PROPN
ejpam-6600	162	5	1	1	NUM
ejpam-6600	162	6	)	)	PUNCT
ejpam-6600	162	7	p+	p+	VERB
ejpam-6600	162	8	1	1	NUM
ejpam-6600	162	9	.	.	PUNCT
ejpam-6600	163	1	that	that	PRON
ejpam-6600	163	2	is	be	AUX
ejpam-6600	163	3	,	,	PUNCT
ejpam-6600	163	4	f(v1	f(v1	ADJ
ejpam-6600	163	5	,	,	PUNCT
ejpam-6600	163	6	v2	v2	NOUN
ejpam-6600	163	7	)	)	PUNCT
ejpam-6600	163	8	=	=	PUNCT
ejpam-6600	164	1	(	(	PUNCT
ejpam-6600	164	2	1	1	NUM
ejpam-6600	164	3	−	−	NOUN
ejpam-6600	164	4	1)13	1)13	NOUN
ejpam-6600	165	1	+	+	CCONJ
ejpam-6600	165	2	1	1	NUM
ejpam-6600	165	3	=	=	SYM
ejpam-6600	165	4	1	1	NUM
ejpam-6600	165	5	,	,	PUNCT
ejpam-6600	165	6	f(v1	f(v1	NOUN
ejpam-6600	165	7	,	,	PUNCT
ejpam-6600	165	8	v4	v4	NOUN
ejpam-6600	165	9	)	)	PUNCT
ejpam-6600	165	10	=	=	PUNCT
ejpam-6600	166	1	(	(	PUNCT
ejpam-6600	166	2	2	2	NUM
ejpam-6600	166	3	−	−	NOUN
ejpam-6600	166	4	1)13	1)13	NOUN
ejpam-6600	167	1	+	+	CCONJ
ejpam-6600	167	2	1	1	NUM
ejpam-6600	167	3	=	=	SYM
ejpam-6600	167	4	14	14	NUM
ejpam-6600	167	5	,	,	PUNCT
ejpam-6600	167	6	f(v1	f(v1	NOUN
ejpam-6600	167	7	,	,	PUNCT
ejpam-6600	167	8	v5	v5	NOUN
ejpam-6600	167	9	)	)	PUNCT
ejpam-6600	167	10	=	=	PUNCT
ejpam-6600	167	11	(	(	PUNCT
ejpam-6600	167	12	3−	3−	NUM
ejpam-6600	167	13	1)13	1)13	NUM
ejpam-6600	167	14	+	+	CCONJ
ejpam-6600	167	15	1	1	NUM
ejpam-6600	167	16	=	=	SYM
ejpam-6600	167	17	27	27	NUM
ejpam-6600	167	18	.	.	PUNCT
ejpam-6600	168	1	step	step	NOUN
ejpam-6600	168	2	3	3	NUM
ejpam-6600	168	3	:	:	PUNCT
ejpam-6600	168	4	i	i	NOUN
ejpam-6600	168	5	=	=	NOUN
ejpam-6600	168	6	1	1	NUM
ejpam-6600	169	1	+	+	SYM
ejpam-6600	169	2	1	1	NUM
ejpam-6600	169	3	=	=	SYM
ejpam-6600	169	4	2	2	NUM
ejpam-6600	169	5	,	,	PUNCT
ejpam-6600	169	6	go	go	VERB
ejpam-6600	169	7	back	back	ADV
ejpam-6600	169	8	to	to	PART
ejpam-6600	169	9	step	step	NOUN
ejpam-6600	169	10	1	1	NUM
ejpam-6600	169	11	.	.	PUNCT
ejpam-6600	170	1	step	step	NOUN
ejpam-6600	170	2	1	1	NUM
ejpam-6600	170	3	:	:	PUNCT
ejpam-6600	170	4	i	i	NOUN
ejpam-6600	170	5	=	=	NOUN
ejpam-6600	170	6	2	2	NUM
ejpam-6600	170	7	≤	≤	NUM
ejpam-6600	170	8	13	13	NUM
ejpam-6600	170	9	,	,	PUNCT
ejpam-6600	170	10	then	then	ADV
ejpam-6600	170	11	continue	continue	VERB
ejpam-6600	170	12	to	to	PART
ejpam-6600	170	13	step	step	VERB
ejpam-6600	170	14	2	2	NUM
ejpam-6600	170	15	.	.	PUNCT
ejpam-6600	170	16	a.	a.	PROPN
ejpam-6600	170	17	n.	n.	PROPN
ejpam-6600	170	18	elsawy	elsawy	PROPN
ejpam-6600	170	19	,	,	PUNCT
ejpam-6600	170	20	r.	r.	PROPN
ejpam-6600	170	21	n.	n.	PROPN
ejpam-6600	170	22	almohammadi	almohammadi	PROPN
ejpam-6600	170	23	/	/	SYM
ejpam-6600	170	24	eur	eur	PROPN
ejpam-6600	170	25	.	.	PUNCT
ejpam-6600	171	1	j.	j.	PROPN
ejpam-6600	171	2	pure	pure	PROPN
ejpam-6600	171	3	appl	appl	PROPN
ejpam-6600	171	4	.	.	PROPN
ejpam-6600	171	5	math	math	PROPN
ejpam-6600	171	6	,	,	PUNCT
ejpam-6600	171	7	18	18	NUM
ejpam-6600	171	8	(	(	PUNCT
ejpam-6600	171	9	4	4	NUM
ejpam-6600	171	10	)	)	PUNCT
ejpam-6600	171	11	(	(	PUNCT
ejpam-6600	171	12	2025	2025	NUM
ejpam-6600	171	13	)	)	PUNCT
ejpam-6600	171	14	,	,	PUNCT
ejpam-6600	171	15	6600	6600	NUM
ejpam-6600	171	16	7	7	NUM
ejpam-6600	171	17	of	of	ADP
ejpam-6600	171	18	26	26	NUM
ejpam-6600	171	19	step	step	NOUN
ejpam-6600	171	20	2	2	NUM
ejpam-6600	171	21	:	:	PUNCT
ejpam-6600	171	22	for	for	ADP
ejpam-6600	171	23	each	each	DET
ejpam-6600	171	24	s1	s1	NOUN
ejpam-6600	171	25	,	,	PUNCT
ejpam-6600	171	26	s2	s2	PROPN
ejpam-6600	171	27	,	,	PUNCT
ejpam-6600	171	28	s3	s3	PROPN
ejpam-6600	171	29	∈	∈	PROPN
ejpam-6600	171	30	s1	s1	NOUN
ejpam-6600	171	31	,	,	PUNCT
ejpam-6600	171	32	f	f	PROPN
ejpam-6600	171	33	(	(	PUNCT
ejpam-6600	171	34	v2	v2	PROPN
ejpam-6600	171	35	,	,	PUNCT
ejpam-6600	171	36	v2+sj	v2+sj	PROPN
ejpam-6600	171	37	)	)	PUNCT
ejpam-6600	172	1	=	=	PRON
ejpam-6600	172	2	(	(	PUNCT
ejpam-6600	172	3	j	j	NOUN
ejpam-6600	172	4	−	−	PROPN
ejpam-6600	172	5	1	1	NUM
ejpam-6600	172	6	)	)	PUNCT
ejpam-6600	172	7	p+	p+	NOUN
ejpam-6600	172	8	2	2	NUM
ejpam-6600	172	9	.	.	X
ejpam-6600	172	10	that	that	PRON
ejpam-6600	172	11	is	be	AUX
ejpam-6600	172	12	,	,	PUNCT
ejpam-6600	172	13	f(v2	f(v2	NOUN
ejpam-6600	172	14	,	,	PUNCT
ejpam-6600	172	15	v3	v3	PROPN
ejpam-6600	172	16	)	)	PUNCT
ejpam-6600	172	17	=	=	PUNCT
ejpam-6600	173	1	(	(	PUNCT
ejpam-6600	173	2	1	1	NUM
ejpam-6600	173	3	−	−	NOUN
ejpam-6600	173	4	1)13	1)13	NOUN
ejpam-6600	174	1	+	+	CCONJ
ejpam-6600	174	2	2	2	NUM
ejpam-6600	174	3	=	=	SYM
ejpam-6600	174	4	2	2	NUM
ejpam-6600	174	5	,	,	PUNCT
ejpam-6600	174	6	f(v2	f(v2	NOUN
ejpam-6600	174	7	,	,	PUNCT
ejpam-6600	174	8	v5	v5	NOUN
ejpam-6600	174	9	)	)	PUNCT
ejpam-6600	174	10	=	=	PUNCT
ejpam-6600	174	11	(	(	PUNCT
ejpam-6600	174	12	2	2	NUM
ejpam-6600	174	13	−	−	NOUN
ejpam-6600	174	14	1)13	1)13	NOUN
ejpam-6600	175	1	+	+	CCONJ
ejpam-6600	175	2	2	2	NUM
ejpam-6600	175	3	=	=	SYM
ejpam-6600	175	4	15	15	NUM
ejpam-6600	175	5	,	,	PUNCT
ejpam-6600	175	6	f(v2	f(v2	NOUN
ejpam-6600	175	7	,	,	PUNCT
ejpam-6600	175	8	v6	v6	NOUN
ejpam-6600	175	9	)	)	PUNCT
ejpam-6600	176	1	=	=	PUNCT
ejpam-6600	176	2	(	(	PUNCT
ejpam-6600	176	3	3−	3−	NUM
ejpam-6600	176	4	1)13	1)13	NUM
ejpam-6600	177	1	+	+	CCONJ
ejpam-6600	177	2	2	2	NUM
ejpam-6600	177	3	=	=	SYM
ejpam-6600	177	4	28	28	NUM
ejpam-6600	177	5	.	.	PUNCT
ejpam-6600	178	1	step	step	NOUN
ejpam-6600	178	2	3	3	NUM
ejpam-6600	178	3	:	:	PUNCT
ejpam-6600	178	4	i	i	NOUN
ejpam-6600	178	5	=	=	VERB
ejpam-6600	179	1	2	2	NUM
ejpam-6600	179	2	+	+	SYM
ejpam-6600	179	3	1	1	NUM
ejpam-6600	179	4	=	=	SYM
ejpam-6600	179	5	3	3	NUM
ejpam-6600	179	6	,	,	PUNCT
ejpam-6600	179	7	go	go	VERB
ejpam-6600	179	8	back	back	ADV
ejpam-6600	179	9	to	to	PART
ejpam-6600	179	10	step	step	NOUN
ejpam-6600	179	11	1	1	NUM
ejpam-6600	179	12	.	.	PUNCT
ejpam-6600	180	1	we	we	PRON
ejpam-6600	180	2	repeat	repeat	VERB
ejpam-6600	180	3	step1	step1	PROPN
ejpam-6600	180	4	,	,	PUNCT
ejpam-6600	180	5	step2	step2	PROPN
ejpam-6600	180	6	,	,	PUNCT
ejpam-6600	180	7	and	and	CCONJ
ejpam-6600	180	8	step3	step3	PROPN
ejpam-6600	180	9	and	and	CCONJ
ejpam-6600	180	10	get	get	VERB
ejpam-6600	180	11	:	:	PUNCT
ejpam-6600	180	12	f(v3	f(v3	ADJ
ejpam-6600	180	13	,	,	PUNCT
ejpam-6600	180	14	v4	v4	NOUN
ejpam-6600	180	15	)	)	PUNCT
ejpam-6600	180	16	=	=	SYM
ejpam-6600	180	17	3	3	NUM
ejpam-6600	180	18	,	,	PUNCT
ejpam-6600	180	19	f(v3	f(v3	NOUN
ejpam-6600	180	20	,	,	PUNCT
ejpam-6600	180	21	v6	v6	NOUN
ejpam-6600	180	22	)	)	PUNCT
ejpam-6600	181	1	=	=	SYM
ejpam-6600	181	2	16	16	NUM
ejpam-6600	181	3	,	,	PUNCT
ejpam-6600	181	4	f(v3	f(v3	NOUN
ejpam-6600	181	5	,	,	PUNCT
ejpam-6600	181	6	v7	v7	NUM
ejpam-6600	181	7	)	)	PUNCT
ejpam-6600	181	8	=	=	SYM
ejpam-6600	181	9	29	29	NUM
ejpam-6600	181	10	,	,	PUNCT
ejpam-6600	181	11	f(v4	f(v4	PRON
ejpam-6600	181	12	,	,	PUNCT
ejpam-6600	181	13	v5	v5	PROPN
ejpam-6600	181	14	)	)	PUNCT
ejpam-6600	181	15	=	=	SYM
ejpam-6600	181	16	4	4	NUM
ejpam-6600	181	17	,	,	PUNCT
ejpam-6600	181	18	f(v4	f(v4	PRON
ejpam-6600	181	19	,	,	PUNCT
ejpam-6600	181	20	v7	v7	NUM
ejpam-6600	181	21	)	)	PUNCT
ejpam-6600	181	22	=	=	SYM
ejpam-6600	181	23	17	17	NUM
ejpam-6600	181	24	,	,	PUNCT
ejpam-6600	181	25	f(v4	f(v4	PRON
ejpam-6600	181	26	,	,	PUNCT
ejpam-6600	181	27	v8	v8	PROPN
ejpam-6600	181	28	)	)	PUNCT
ejpam-6600	181	29	=	=	SYM
ejpam-6600	181	30	30	30	NUM
ejpam-6600	181	31	,	,	PUNCT
ejpam-6600	181	32	f(v5	f(v5	NOUN
ejpam-6600	181	33	,	,	PUNCT
ejpam-6600	181	34	v6	v6	NOUN
ejpam-6600	181	35	)	)	PUNCT
ejpam-6600	181	36	=	=	SYM
ejpam-6600	182	1	5	5	NUM
ejpam-6600	182	2	,	,	PUNCT
ejpam-6600	182	3	f(v5	f(v5	NOUN
ejpam-6600	182	4	,	,	PUNCT
ejpam-6600	182	5	v8	v8	PROPN
ejpam-6600	182	6	)	)	PUNCT
ejpam-6600	182	7	=	=	SYM
ejpam-6600	182	8	18	18	NUM
ejpam-6600	182	9	,	,	PUNCT
ejpam-6600	182	10	f(v5	f(v5	NOUN
ejpam-6600	182	11	,	,	PUNCT
ejpam-6600	182	12	v9	v9	NOUN
ejpam-6600	182	13	)	)	PUNCT
ejpam-6600	182	14	=	=	SYM
ejpam-6600	182	15	31	31	NUM
ejpam-6600	182	16	,	,	PUNCT
ejpam-6600	182	17	f(v6	f(v6	NOUN
ejpam-6600	182	18	,	,	PUNCT
ejpam-6600	182	19	v7	v7	NUM
ejpam-6600	182	20	)	)	PUNCT
ejpam-6600	182	21	=	=	SYM
ejpam-6600	182	22	6	6	NUM
ejpam-6600	182	23	,	,	PUNCT
ejpam-6600	182	24	f(v6	f(v6	NOUN
ejpam-6600	182	25	,	,	PUNCT
ejpam-6600	182	26	v9	v9	PROPN
ejpam-6600	182	27	)	)	PUNCT
ejpam-6600	182	28	=	=	SYM
ejpam-6600	182	29	19	19	NUM
ejpam-6600	182	30	,	,	PUNCT
ejpam-6600	182	31	f(v6	f(v6	NOUN
ejpam-6600	182	32	,	,	PUNCT
ejpam-6600	182	33	v10	v10	NOUN
ejpam-6600	182	34	)	)	PUNCT
ejpam-6600	182	35	=	=	SYM
ejpam-6600	182	36	32	32	NUM
ejpam-6600	182	37	,	,	PUNCT
ejpam-6600	182	38	f(v7	f(v7	NOUN
ejpam-6600	182	39	,	,	PUNCT
ejpam-6600	182	40	v8	v8	PROPN
ejpam-6600	182	41	)	)	PUNCT
ejpam-6600	182	42	=	=	SYM
ejpam-6600	183	1	7	7	NUM
ejpam-6600	183	2	,	,	PUNCT
ejpam-6600	183	3	f(v7	f(v7	NOUN
ejpam-6600	183	4	,	,	PUNCT
ejpam-6600	183	5	v10	v10	NOUN
ejpam-6600	183	6	)	)	PUNCT
ejpam-6600	183	7	=	=	SYM
ejpam-6600	183	8	20	20	NUM
ejpam-6600	183	9	,	,	PUNCT
ejpam-6600	183	10	f(v7	f(v7	NOUN
ejpam-6600	183	11	,	,	PUNCT
ejpam-6600	183	12	v11	v11	NOUN
ejpam-6600	183	13	)	)	PUNCT
ejpam-6600	183	14	=	=	SYM
ejpam-6600	183	15	33	33	NUM
ejpam-6600	183	16	,	,	PUNCT
ejpam-6600	183	17	f(v8	f(v8	NOUN
ejpam-6600	183	18	,	,	PUNCT
ejpam-6600	183	19	v9	v9	PROPN
ejpam-6600	183	20	)	)	PUNCT
ejpam-6600	183	21	=	=	SYM
ejpam-6600	183	22	8	8	NUM
ejpam-6600	183	23	,	,	PUNCT
ejpam-6600	183	24	f(v8	f(v8	NOUN
ejpam-6600	183	25	,	,	PUNCT
ejpam-6600	183	26	v11	v11	NOUN
ejpam-6600	183	27	)	)	PUNCT
ejpam-6600	183	28	=	=	SYM
ejpam-6600	183	29	21	21	NUM
ejpam-6600	183	30	,	,	PUNCT
ejpam-6600	183	31	f(v8	f(v8	NOUN
ejpam-6600	183	32	,	,	PUNCT
ejpam-6600	183	33	v12	v12	VERB
ejpam-6600	183	34	)	)	PUNCT
ejpam-6600	183	35	=	=	SYM
ejpam-6600	183	36	34	34	NUM
ejpam-6600	183	37	,	,	PUNCT
ejpam-6600	183	38	f(v9	f(v9	X
ejpam-6600	183	39	,	,	PUNCT
ejpam-6600	183	40	v10	v10	NOUN
ejpam-6600	183	41	)	)	PUNCT
ejpam-6600	183	42	=	=	SYM
ejpam-6600	183	43	9	9	NUM
ejpam-6600	183	44	,	,	PUNCT
ejpam-6600	183	45	f(v9	f(v9	NOUN
ejpam-6600	183	46	,	,	PUNCT
ejpam-6600	183	47	v12	v12	VERB
ejpam-6600	183	48	)	)	PUNCT
ejpam-6600	183	49	=	=	SYM
ejpam-6600	183	50	22	22	NUM
ejpam-6600	183	51	,	,	PUNCT
ejpam-6600	183	52	f(v9	f(v9	NOUN
ejpam-6600	183	53	,	,	PUNCT
ejpam-6600	183	54	v13	v13	X
ejpam-6600	183	55	)	)	PUNCT
ejpam-6600	183	56	=	=	SYM
ejpam-6600	183	57	35	35	NUM
ejpam-6600	183	58	,	,	PUNCT
ejpam-6600	183	59	f(v10	f(v10	NOUN
ejpam-6600	183	60	,	,	PUNCT
ejpam-6600	183	61	v11	v11	NOUN
ejpam-6600	183	62	)	)	PUNCT
ejpam-6600	183	63	=	=	SYM
ejpam-6600	183	64	10	10	NUM
ejpam-6600	183	65	,	,	PUNCT
ejpam-6600	183	66	f(v10	f(v10	NOUN
ejpam-6600	183	67	,	,	PUNCT
ejpam-6600	183	68	v13	v13	PROPN
ejpam-6600	183	69	)	)	PUNCT
ejpam-6600	183	70	=	=	SYM
ejpam-6600	183	71	23	23	NUM
ejpam-6600	183	72	,	,	PUNCT
ejpam-6600	183	73	f(v10	f(v10	NOUN
ejpam-6600	183	74	,	,	PUNCT
ejpam-6600	183	75	v1	v1	NOUN
ejpam-6600	183	76	)	)	PUNCT
ejpam-6600	183	77	=	=	SYM
ejpam-6600	183	78	36	36	NUM
ejpam-6600	183	79	,	,	PUNCT
ejpam-6600	183	80	f(v11	f(v11	ADJ
ejpam-6600	183	81	,	,	PUNCT
ejpam-6600	183	82	v12	v12	VERB
ejpam-6600	183	83	)	)	PUNCT
ejpam-6600	183	84	=	=	SYM
ejpam-6600	183	85	11	11	NUM
ejpam-6600	183	86	,	,	PUNCT
ejpam-6600	183	87	f(v11	f(v11	ADJ
ejpam-6600	183	88	,	,	PUNCT
ejpam-6600	183	89	v1	v1	NOUN
ejpam-6600	183	90	)	)	PUNCT
ejpam-6600	183	91	=	=	SYM
ejpam-6600	183	92	24	24	NUM
ejpam-6600	183	93	,	,	PUNCT
ejpam-6600	183	94	f(v11	f(v11	NOUN
ejpam-6600	183	95	,	,	PUNCT
ejpam-6600	183	96	v2	v2	PROPN
ejpam-6600	183	97	)	)	PUNCT
ejpam-6600	183	98	=	=	SYM
ejpam-6600	183	99	37	37	NUM
ejpam-6600	183	100	,	,	PUNCT
ejpam-6600	183	101	f(v12	f(v12	NUM
ejpam-6600	183	102	,	,	PUNCT
ejpam-6600	183	103	v13	v13	NOUN
ejpam-6600	183	104	)	)	PUNCT
ejpam-6600	183	105	=	=	SYM
ejpam-6600	183	106	12	12	NUM
ejpam-6600	183	107	,	,	PUNCT
ejpam-6600	183	108	f(v12	f(v12	NUM
ejpam-6600	183	109	,	,	PUNCT
ejpam-6600	183	110	v2	v2	NOUN
ejpam-6600	183	111	)	)	PUNCT
ejpam-6600	183	112	=	=	SYM
ejpam-6600	183	113	25	25	NUM
ejpam-6600	183	114	,	,	PUNCT
ejpam-6600	183	115	f(v12	f(v12	NUM
ejpam-6600	183	116	,	,	PUNCT
ejpam-6600	183	117	v3	v3	PROPN
ejpam-6600	183	118	)	)	PUNCT
ejpam-6600	183	119	=	=	SYM
ejpam-6600	183	120	38	38	NUM
ejpam-6600	183	121	,	,	PUNCT
ejpam-6600	183	122	f(v13	f(v13	NOUN
ejpam-6600	183	123	,	,	PUNCT
ejpam-6600	183	124	v1	v1	NOUN
ejpam-6600	183	125	)	)	PUNCT
ejpam-6600	183	126	=	=	SYM
ejpam-6600	183	127	13	13	NUM
ejpam-6600	183	128	,	,	PUNCT
ejpam-6600	183	129	f(v13	f(v13	NOUN
ejpam-6600	183	130	,	,	PUNCT
ejpam-6600	183	131	v3	v3	PROPN
ejpam-6600	183	132	)	)	PUNCT
ejpam-6600	183	133	=	=	SYM
ejpam-6600	183	134	26	26	NUM
ejpam-6600	183	135	,	,	PUNCT
ejpam-6600	183	136	f(v13	f(v13	NOUN
ejpam-6600	183	137	,	,	PUNCT
ejpam-6600	183	138	v4	v4	NOUN
ejpam-6600	183	139	)	)	PUNCT
ejpam-6600	183	140	=	=	SYM
ejpam-6600	184	1	39	39	NUM
ejpam-6600	184	2	.	.	PUNCT
ejpam-6600	185	1	step	step	NOUN
ejpam-6600	185	2	4	4	NUM
ejpam-6600	185	3	:	:	PUNCT
ejpam-6600	185	4	for	for	ADP
ejpam-6600	185	5	each	each	PRON
ejpam-6600	185	6	k	k	NOUN
ejpam-6600	185	7	=	=	SYM
ejpam-6600	185	8	1	1	NUM
ejpam-6600	185	9	,	,	PUNCT
ejpam-6600	185	10	2	2	NUM
ejpam-6600	185	11	,	,	PUNCT
ejpam-6600	185	12	3	3	NUM
ejpam-6600	185	13	,	,	PUNCT
ejpam-6600	185	14	.	.	PUNCT
ejpam-6600	185	15	.	.	PUNCT
ejpam-6600	186	1	.	.	PUNCT
ejpam-6600	187	1	,	,	PUNCT
ejpam-6600	187	2	13	13	NUM
ejpam-6600	187	3	,	,	PUNCT
ejpam-6600	187	4	the	the	DET
ejpam-6600	187	5	weight	weight	NOUN
ejpam-6600	187	6	of	of	ADP
ejpam-6600	187	7	the	the	DET
ejpam-6600	187	8	vertex	vertex	NOUN
ejpam-6600	187	9	vk	vk	NOUN
ejpam-6600	187	10	can	can	AUX
ejpam-6600	187	11	be	be	AUX
ejpam-6600	187	12	found	find	VERB
ejpam-6600	187	13	by	by	ADP
ejpam-6600	187	14	:	:	PUNCT
ejpam-6600	187	15	fw(vk	fw(vk	PROPN
ejpam-6600	187	16	)	)	PUNCT
ejpam-6600	188	1	=	=	SYM
ejpam-6600	188	2	∑6	∑6	PROPN
ejpam-6600	188	3	j=1	j=1	PROPN
ejpam-6600	188	4	f(vk	f(vk	PROPN
ejpam-6600	188	5	,	,	PUNCT
ejpam-6600	188	6	vk+sj	vk+sj	NOUN
ejpam-6600	188	7	)	)	PUNCT
ejpam-6600	189	1	=	=	PUNCT
ejpam-6600	190	1	6k−	6k−	NUM
ejpam-6600	190	2	∑3	∑3	PUNCT
ejpam-6600	190	3	j=1	j=1	ADJ
ejpam-6600	190	4	sj	sj	PROPN
ejpam-6600	190	5	=	=	SYM
ejpam-6600	190	6	6k−8	6k−8	PROPN
ejpam-6600	190	7	(	(	PUNCT
ejpam-6600	190	8	mod	mod	PROPN
ejpam-6600	190	9	p	p	NOUN
ejpam-6600	190	10	)	)	PUNCT
ejpam-6600	190	11	.	.	PUNCT
ejpam-6600	191	1	fw	fw	PROPN
ejpam-6600	191	2	(	(	PUNCT
ejpam-6600	191	3	v1	v1	NOUN
ejpam-6600	191	4	)	)	PUNCT
ejpam-6600	191	5	=	=	SYM
ejpam-6600	192	1	6·1−8	6·1−8	NUM
ejpam-6600	192	2	=	=	SYM
ejpam-6600	192	3	−2	−2	PROPN
ejpam-6600	192	4	≡	≡	PROPN
ejpam-6600	192	5	11	11	NUM
ejpam-6600	192	6	(	(	PUNCT
ejpam-6600	192	7	mod	mod	PROPN
ejpam-6600	192	8	13	13	NUM
ejpam-6600	192	9	)	)	PUNCT
ejpam-6600	192	10	.	.	PUNCT
ejpam-6600	193	1	equivalently	equivalently	ADV
ejpam-6600	193	2	,	,	PUNCT
ejpam-6600	193	3	fw	fw	PROPN
ejpam-6600	193	4	(	(	PUNCT
ejpam-6600	193	5	v1	v1	NOUN
ejpam-6600	193	6	)	)	PUNCT
ejpam-6600	193	7	=	=	SYM
ejpam-6600	193	8	f(v1	f(v1	NOUN
ejpam-6600	193	9	,	,	PUNCT
ejpam-6600	193	10	v2)+f(v1	v2)+f(v1	NOUN
ejpam-6600	193	11	,	,	PUNCT
ejpam-6600	193	12	v4)+f(v1	v4)+f(v1	NOUN
ejpam-6600	193	13	,	,	PUNCT
ejpam-6600	193	14	v5)+f(v10	v5)+f(v10	PROPN
ejpam-6600	193	15	,	,	PUNCT
ejpam-6600	193	16	v1)+f(v11	v1)+f(v11	PROPN
ejpam-6600	193	17	,	,	PUNCT
ejpam-6600	193	18	v1)+f(v13	v1)+f(v13	PROPN
ejpam-6600	193	19	,	,	PUNCT
ejpam-6600	193	20	v1	v1	NOUN
ejpam-6600	193	21	)	)	PUNCT
ejpam-6600	193	22	=	=	SYM
ejpam-6600	193	23	1	1	NUM
ejpam-6600	193	24	+	+	NUM
ejpam-6600	193	25	14	14	NUM
ejpam-6600	193	26	+	+	CCONJ
ejpam-6600	193	27	27	27	NUM
ejpam-6600	193	28	+	+	NUM
ejpam-6600	193	29	36	36	NUM
ejpam-6600	193	30	+	+	NUM
ejpam-6600	193	31	24	24	NUM
ejpam-6600	193	32	+	+	SYM
ejpam-6600	193	33	13	13	NUM
ejpam-6600	193	34	≡	≡	PROPN
ejpam-6600	193	35	11	11	NUM
ejpam-6600	193	36	(	(	PUNCT
ejpam-6600	193	37	mod	mod	PROPN
ejpam-6600	193	38	13	13	NUM
ejpam-6600	193	39	)	)	PUNCT
ejpam-6600	193	40	.	.	PUNCT
ejpam-6600	194	1	by	by	ADP
ejpam-6600	194	2	the	the	DET
ejpam-6600	194	3	same	same	ADJ
ejpam-6600	194	4	function	function	NOUN
ejpam-6600	194	5	modulo	modulo	VERB
ejpam-6600	194	6	13	13	NUM
ejpam-6600	194	7	,	,	PUNCT
ejpam-6600	194	8	we	we	PRON
ejpam-6600	194	9	get	get	VERB
ejpam-6600	194	10	:	:	PUNCT
ejpam-6600	194	11	fw(v2	fw(v2	NOUN
ejpam-6600	194	12	)	)	PUNCT
ejpam-6600	194	13	=	=	SYM
ejpam-6600	194	14	4	4	NUM
ejpam-6600	194	15	,	,	PUNCT
ejpam-6600	194	16	fw(v3	fw(v3	NOUN
ejpam-6600	194	17	)	)	PUNCT
ejpam-6600	194	18	=	=	SYM
ejpam-6600	194	19	10	10	NUM
ejpam-6600	194	20	,	,	PUNCT
ejpam-6600	194	21	fw(v4	fw(v4	PRON
ejpam-6600	194	22	)	)	PUNCT
ejpam-6600	194	23	=	=	SYM
ejpam-6600	194	24	3	3	NUM
ejpam-6600	194	25	,	,	PUNCT
ejpam-6600	194	26	fw(v5	fw(v5	NOUN
ejpam-6600	194	27	)	)	PUNCT
ejpam-6600	195	1	=	=	SYM
ejpam-6600	195	2	9	9	NUM
ejpam-6600	195	3	,	,	PUNCT
ejpam-6600	195	4	fw(v6	fw(v6	NOUN
ejpam-6600	195	5	)	)	PUNCT
ejpam-6600	195	6	=	=	SYM
ejpam-6600	195	7	2	2	NUM
ejpam-6600	195	8	,	,	PUNCT
ejpam-6600	195	9	fw(v7	fw(v7	NOUN
ejpam-6600	195	10	)	)	PUNCT
ejpam-6600	195	11	=	=	SYM
ejpam-6600	195	12	8	8	NUM
ejpam-6600	195	13	,	,	PUNCT
ejpam-6600	195	14	fw(v8	fw(v8	NOUN
ejpam-6600	195	15	)	)	PUNCT
ejpam-6600	195	16	=	=	SYM
ejpam-6600	196	1	1	1	NUM
ejpam-6600	196	2	,	,	PUNCT
ejpam-6600	196	3	fw(v9	fw(v9	NUM
ejpam-6600	196	4	)	)	PUNCT
ejpam-6600	196	5	=	=	SYM
ejpam-6600	196	6	7	7	NUM
ejpam-6600	196	7	,	,	PUNCT
ejpam-6600	196	8	fw(v10	fw(v10	NOUN
ejpam-6600	196	9	)	)	PUNCT
ejpam-6600	196	10	=	=	SYM
ejpam-6600	196	11	0	0	NUM
ejpam-6600	196	12	,	,	PUNCT
ejpam-6600	196	13	fw(v11	fw(v11	ADJ
ejpam-6600	196	14	)	)	PUNCT
ejpam-6600	196	15	=	=	SYM
ejpam-6600	196	16	6	6	NUM
ejpam-6600	196	17	,	,	PUNCT
ejpam-6600	196	18	fw(v12	fw(v12	PUNCT
ejpam-6600	196	19	)	)	PUNCT
ejpam-6600	196	20	=	=	SYM
ejpam-6600	196	21	12	12	NUM
ejpam-6600	196	22	,	,	PUNCT
ejpam-6600	196	23	fw(v13	fw(v13	NUM
ejpam-6600	196	24	)	)	PUNCT
ejpam-6600	196	25	=	=	SYM
ejpam-6600	197	1	5	5	NUM
ejpam-6600	197	2	.	.	NOUN
ejpam-6600	197	3	3	3	NUM
ejpam-6600	197	4	.	.	NOUN
ejpam-6600	197	5	cubic	cubic	PROPN
ejpam-6600	197	6	paley	paley	PROPN
ejpam-6600	197	7	graphs	graph	VERB
ejpam-6600	197	8	a	a	DET
ejpam-6600	197	9	natural	natural	ADJ
ejpam-6600	197	10	generalization	generalization	NOUN
ejpam-6600	197	11	of	of	ADP
ejpam-6600	197	12	paley	paley	ADJ
ejpam-6600	197	13	graph	graph	NOUN
ejpam-6600	197	14	is	be	AUX
ejpam-6600	197	15	the	the	DET
ejpam-6600	197	16	cubic	cubic	ADJ
ejpam-6600	197	17	paley	paley	NOUN
ejpam-6600	197	18	graph	graph	NOUN
ejpam-6600	197	19	,	,	PUNCT
ejpam-6600	197	20	which	which	PRON
ejpam-6600	197	21	has	have	VERB
ejpam-6600	197	22	the	the	DET
ejpam-6600	197	23	same	same	ADJ
ejpam-6600	197	24	vertex	vertex	NOUN
ejpam-6600	197	25	set	set	NOUN
ejpam-6600	197	26	,	,	PUNCT
ejpam-6600	197	27	and	and	CCONJ
ejpam-6600	197	28	two	two	NUM
ejpam-6600	197	29	vertices	vertex	NOUN
ejpam-6600	197	30	are	be	AUX
ejpam-6600	197	31	adjacent	adjacent	ADJ
ejpam-6600	197	32	if	if	SCONJ
ejpam-6600	197	33	their	their	PRON
ejpam-6600	197	34	difference	difference	NOUN
ejpam-6600	197	35	is	be	AUX
ejpam-6600	197	36	a	a	DET
ejpam-6600	197	37	cubic	cubic	ADJ
ejpam-6600	197	38	residue	residue	NOUN
ejpam-6600	197	39	in	in	ADP
ejpam-6600	197	40	fq	fq	PROPN
ejpam-6600	197	41	.	.	PROPN
ejpam-6600	197	42	definition	definition	NOUN
ejpam-6600	197	43	3	3	NUM
ejpam-6600	197	44	.	.	PUNCT
ejpam-6600	198	1	[	[	X
ejpam-6600	198	2	28	28	NUM
ejpam-6600	198	3	]	]	X
ejpam-6600	198	4	let	let	VERB
ejpam-6600	198	5	q	q	NOUN
ejpam-6600	198	6	=	=	SYM
ejpam-6600	198	7	pn	pn	NOUN
ejpam-6600	198	8	,	,	PUNCT
ejpam-6600	198	9	where	where	SCONJ
ejpam-6600	198	10	p	p	NOUN
ejpam-6600	198	11	is	be	AUX
ejpam-6600	198	12	an	an	DET
ejpam-6600	198	13	odd	odd	ADJ
ejpam-6600	198	14	prime	prime	NOUN
ejpam-6600	198	15	,	,	PUNCT
ejpam-6600	198	16	and	and	CCONJ
ejpam-6600	198	17	n	n	PRON
ejpam-6600	198	18	∈	∈	PROPN
ejpam-6600	198	19	n	n	CCONJ
ejpam-6600	198	20	,	,	PUNCT
ejpam-6600	198	21	such	such	ADJ
ejpam-6600	198	22	that	that	PRON
ejpam-6600	198	23	q	q	PROPN
ejpam-6600	198	24	≡	≡	PROPN
ejpam-6600	198	25	1	1	NUM
ejpam-6600	198	26	(	(	PUNCT
ejpam-6600	198	27	mod	mod	NOUN
ejpam-6600	198	28	3	3	NUM
ejpam-6600	198	29	)	)	PUNCT
ejpam-6600	198	30	.	.	PUNCT
ejpam-6600	199	1	the	the	DET
ejpam-6600	199	2	graph	graph	NOUN
ejpam-6600	199	3	3−pq	3−pq	NUM
ejpam-6600	199	4	,	,	PUNCT
ejpam-6600	199	5	with	with	ADP
ejpam-6600	199	6	v	v	PROPN
ejpam-6600	199	7	(	(	PUNCT
ejpam-6600	199	8	3−pq	3−pq	NUM
ejpam-6600	199	9	)	)	PUNCT
ejpam-6600	199	10	=	=	SYM
ejpam-6600	199	11	fq	fq	PROPN
ejpam-6600	199	12	and	and	CCONJ
ejpam-6600	199	13	e(3−pq	e(3−pq	PROPN
ejpam-6600	199	14	)	)	PUNCT
ejpam-6600	199	15	=	=	SYM
ejpam-6600	199	16	{	{	PUNCT
ejpam-6600	199	17	(	(	PUNCT
ejpam-6600	199	18	u	u	NOUN
ejpam-6600	199	19	,	,	PUNCT
ejpam-6600	199	20	v	v	NOUN
ejpam-6600	199	21	)	)	PUNCT
ejpam-6600	199	22	|	|	ADV
ejpam-6600	199	23	u−	u−	NUM
ejpam-6600	199	24	v	v	X
ejpam-6600	199	25	∈	∈	PROPN
ejpam-6600	199	26	(	(	PUNCT
ejpam-6600	199	27	f∗	f∗	NOUN
ejpam-6600	199	28	q	q	PROPN
ejpam-6600	199	29	)	)	PUNCT
ejpam-6600	199	30	3	3	NUM
ejpam-6600	199	31	}	}	PUNCT
ejpam-6600	199	32	is	be	AUX
ejpam-6600	199	33	called	call	VERB
ejpam-6600	199	34	the	the	DET
ejpam-6600	199	35	cubic	cubic	ADJ
ejpam-6600	199	36	paley	paley	NOUN
ejpam-6600	199	37	graph	graph	NOUN
ejpam-6600	199	38	of	of	ADP
ejpam-6600	199	39	order	order	NOUN
ejpam-6600	199	40	q.	q.	NOUN
ejpam-6600	199	41	note	note	VERB
ejpam-6600	199	42	that	that	SCONJ
ejpam-6600	199	43	:	:	PUNCT
ejpam-6600	199	44	w.	w.	PROPN
ejpam-6600	199	45	ananchuen	ananchuen	PROPN
ejpam-6600	199	46	and	and	CCONJ
ejpam-6600	199	47	l.	l.	PROPN
ejpam-6600	199	48	caccetta	caccetta	PROPN
ejpam-6600	199	49	,	,	PUNCT
ejpam-6600	199	50	in	in	ADP
ejpam-6600	199	51	[	[	PUNCT
ejpam-6600	199	52	28	28	NUM
ejpam-6600	199	53	]	]	PUNCT
ejpam-6600	199	54	,	,	PUNCT
ejpam-6600	199	55	stated	state	VERB
ejpam-6600	199	56	that	that	SCONJ
ejpam-6600	199	57	the	the	DET
ejpam-6600	199	58	condition	condition	NOUN
ejpam-6600	199	59	q	q	X
ejpam-6600	199	60	≡	≡	PROPN
ejpam-6600	199	61	1	1	NUM
ejpam-6600	199	62	(	(	PUNCT
ejpam-6600	199	63	mod	mod	NOUN
ejpam-6600	199	64	3	3	NUM
ejpam-6600	199	65	)	)	PUNCT
ejpam-6600	199	66	is	be	AUX
ejpam-6600	199	67	necessary	necessary	ADJ
ejpam-6600	199	68	to	to	PART
ejpam-6600	199	69	ensure	ensure	VERB
ejpam-6600	199	70	that	that	PRON
ejpam-6600	199	71	−1	−1	NOUN
ejpam-6600	199	72	is	be	AUX
ejpam-6600	199	73	a	a	DET
ejpam-6600	199	74	cubic	cubic	ADJ
ejpam-6600	199	75	residue	residue	NOUN
ejpam-6600	199	76	and	and	CCONJ
ejpam-6600	199	77	,	,	PUNCT
ejpam-6600	199	78	consequently	consequently	ADV
ejpam-6600	199	79	,	,	PUNCT
ejpam-6600	199	80	that	that	SCONJ
ejpam-6600	199	81	the	the	DET
ejpam-6600	199	82	graph	graph	NOUN
ejpam-6600	199	83	3	3	NUM
ejpam-6600	199	84	−	−	PROPN
ejpam-6600	199	85	pq	pq	NOUN
ejpam-6600	199	86	is	be	AUX
ejpam-6600	199	87	well	well	ADV
ejpam-6600	199	88	-	-	PUNCT
ejpam-6600	199	89	defined	define	VERB
ejpam-6600	199	90	.	.	PUNCT
ejpam-6600	200	1	however	however	ADV
ejpam-6600	200	2	,	,	PUNCT
ejpam-6600	200	3	we	we	PRON
ejpam-6600	200	4	disagree	disagree	VERB
ejpam-6600	200	5	with	with	ADP
ejpam-6600	200	6	this	this	DET
ejpam-6600	200	7	claim	claim	NOUN
ejpam-6600	200	8	,	,	PUNCT
ejpam-6600	200	9	since	since	SCONJ
ejpam-6600	200	10	(	(	PUNCT
ejpam-6600	200	11	−1)3	−1)3	NOUN
ejpam-6600	200	12	=	=	SYM
ejpam-6600	200	13	−1	−1	NOUN
ejpam-6600	200	14	in	in	ADP
ejpam-6600	200	15	any	any	DET
ejpam-6600	200	16	field	field	NOUN
ejpam-6600	200	17	with	with	ADP
ejpam-6600	200	18	any	any	DET
ejpam-6600	200	19	order	order	NOUN
ejpam-6600	200	20	,	,	PUNCT
ejpam-6600	200	21	implying	imply	VERB
ejpam-6600	200	22	that	that	DET
ejpam-6600	200	23	−1	−1	NOUN
ejpam-6600	200	24	is	be	AUX
ejpam-6600	200	25	always	always	ADV
ejpam-6600	200	26	a	a	DET
ejpam-6600	200	27	cubic	cubic	ADJ
ejpam-6600	200	28	residue	residue	NOUN
ejpam-6600	200	29	.	.	PUNCT
ejpam-6600	201	1	therefore	therefore	ADV
ejpam-6600	201	2	,	,	PUNCT
ejpam-6600	201	3	the	the	DET
ejpam-6600	201	4	graph	graph	NOUN
ejpam-6600	201	5	3−	3−	NUM
ejpam-6600	201	6	pq	pq	NOUN
ejpam-6600	201	7	is	be	AUX
ejpam-6600	201	8	well	well	ADV
ejpam-6600	201	9	-	-	PUNCT
ejpam-6600	201	10	defined	define	VERB
ejpam-6600	201	11	without	without	ADP
ejpam-6600	201	12	the	the	DET
ejpam-6600	201	13	condition	condition	NOUN
ejpam-6600	201	14	q	q	PROPN
ejpam-6600	201	15	≡	≡	PROPN
ejpam-6600	201	16	1	1	NUM
ejpam-6600	201	17	(	(	PUNCT
ejpam-6600	201	18	mod	mod	NOUN
ejpam-6600	201	19	3	3	NUM
ejpam-6600	201	20	)	)	PUNCT
ejpam-6600	201	21	.	.	PUNCT
ejpam-6600	202	1	example	example	NOUN
ejpam-6600	203	1	4	4	NUM
ejpam-6600	203	2	.	.	PUNCT
ejpam-6600	204	1	the	the	DET
ejpam-6600	204	2	cubic	cubic	ADJ
ejpam-6600	204	3	paley	paley	PROPN
ejpam-6600	204	4	graph	graph	NOUN
ejpam-6600	204	5	3	3	NUM
ejpam-6600	204	6	−	−	NOUN
ejpam-6600	204	7	p19	p19	NOUN
ejpam-6600	204	8	of	of	ADP
ejpam-6600	204	9	order	order	NOUN
ejpam-6600	204	10	19	19	NUM
ejpam-6600	204	11	has	have	VERB
ejpam-6600	204	12	v	v	NUM
ejpam-6600	204	13	(	(	PUNCT
ejpam-6600	204	14	3	3	NUM
ejpam-6600	204	15	−	−	NOUN
ejpam-6600	204	16	p19	p19	NOUN
ejpam-6600	204	17	)	)	PUNCT
ejpam-6600	204	18	=	=	SYM
ejpam-6600	204	19	z19	z19	NOUN
ejpam-6600	204	20	and	and	CCONJ
ejpam-6600	204	21	e(3−	e(3−	ADJ
ejpam-6600	204	22	p19	p19	PROPN
ejpam-6600	204	23	)	)	PUNCT
ejpam-6600	205	1	=	=	PRON
ejpam-6600	205	2	{	{	PUNCT
ejpam-6600	205	3	(	(	PUNCT
ejpam-6600	205	4	u	u	NOUN
ejpam-6600	205	5	,	,	PUNCT
ejpam-6600	205	6	v	v	NOUN
ejpam-6600	205	7	)	)	PUNCT
ejpam-6600	206	1	|	|	ADV
ejpam-6600	206	2	u−	u−	NUM
ejpam-6600	206	3	v	v	X
ejpam-6600	206	4	∈	∈	PROPN
ejpam-6600	206	5	{	{	PUNCT
ejpam-6600	206	6	1	1	NUM
ejpam-6600	206	7	,	,	PUNCT
ejpam-6600	206	8	7	7	NUM
ejpam-6600	206	9	,	,	PUNCT
ejpam-6600	206	10	8	8	NUM
ejpam-6600	206	11	,	,	PUNCT
ejpam-6600	206	12	11	11	NUM
ejpam-6600	206	13	,	,	PUNCT
ejpam-6600	206	14	12	12	NUM
ejpam-6600	206	15	,	,	PUNCT
ejpam-6600	206	16	18	18	NUM
ejpam-6600	206	17	}	}	PUNCT
ejpam-6600	206	18	}	}	PUNCT
ejpam-6600	206	19	.	.	PUNCT
ejpam-6600	207	1	see	see	VERB
ejpam-6600	207	2	figure	figure	NOUN
ejpam-6600	207	3	5	5	NUM
ejpam-6600	207	4	.	.	PUNCT
ejpam-6600	207	5	a.	a.	PROPN
ejpam-6600	207	6	n.	n.	PROPN
ejpam-6600	207	7	elsawy	elsawy	PROPN
ejpam-6600	207	8	,	,	PUNCT
ejpam-6600	207	9	r.	r.	PROPN
ejpam-6600	207	10	n.	n.	PROPN
ejpam-6600	207	11	almohammadi	almohammadi	PROPN
ejpam-6600	207	12	/	/	SYM
ejpam-6600	207	13	eur	eur	PROPN
ejpam-6600	207	14	.	.	PUNCT
ejpam-6600	208	1	j.	j.	PROPN
ejpam-6600	208	2	pure	pure	PROPN
ejpam-6600	208	3	appl	appl	PROPN
ejpam-6600	208	4	.	.	PROPN
ejpam-6600	208	5	math	math	PROPN
ejpam-6600	208	6	,	,	PUNCT
ejpam-6600	208	7	18	18	NUM
ejpam-6600	208	8	(	(	PUNCT
ejpam-6600	208	9	4	4	NUM
ejpam-6600	208	10	)	)	PUNCT
ejpam-6600	208	11	(	(	PUNCT
ejpam-6600	208	12	2025	2025	NUM
ejpam-6600	208	13	)	)	PUNCT
ejpam-6600	208	14	,	,	PUNCT
ejpam-6600	208	15	6600	6600	NUM
ejpam-6600	208	16	8	8	NUM
ejpam-6600	208	17	of	of	ADP
ejpam-6600	208	18	26	26	NUM
ejpam-6600	208	19	figure	figure	NOUN
ejpam-6600	208	20	5	5	NUM
ejpam-6600	208	21	:	:	PUNCT
ejpam-6600	208	22	the	the	DET
ejpam-6600	208	23	cubic	cubic	ADJ
ejpam-6600	208	24	paley	paley	PROPN
ejpam-6600	208	25	graph	graph	NOUN
ejpam-6600	208	26	3−	3−	NUM
ejpam-6600	208	27	p19	p19	NOUN
ejpam-6600	208	28	now	now	ADV
ejpam-6600	208	29	we	we	PRON
ejpam-6600	208	30	provide	provide	VERB
ejpam-6600	208	31	an	an	DET
ejpam-6600	208	32	algorithm	algorithm	NOUN
ejpam-6600	208	33	that	that	PRON
ejpam-6600	208	34	produces	produce	VERB
ejpam-6600	208	35	an	an	DET
ejpam-6600	208	36	edge	edge	NOUN
ejpam-6600	208	37	-	-	PUNCT
ejpam-6600	208	38	graceful	graceful	NOUN
ejpam-6600	208	39	labeling	labeling	NOUN
ejpam-6600	208	40	for	for	ADP
ejpam-6600	208	41	cubic	cubic	ADJ
ejpam-6600	208	42	paley	paley	ADJ
ejpam-6600	208	43	graphs	graph	NOUN
ejpam-6600	208	44	of	of	ADP
ejpam-6600	208	45	prime	prime	ADJ
ejpam-6600	208	46	order	order	NOUN
ejpam-6600	208	47	3.1	3.1	NUM
ejpam-6600	208	48	.	.	PUNCT
ejpam-6600	208	49	edge	edge	NOUN
ejpam-6600	208	50	-	-	PUNCT
ejpam-6600	208	51	graceful	graceful	NOUN
ejpam-6600	208	52	labeling	labeling	NOUN
ejpam-6600	208	53	algorithm	algorithm	NOUN
ejpam-6600	208	54	for	for	ADP
ejpam-6600	208	55	cubic	cubic	ADJ
ejpam-6600	208	56	paley	paley	ADJ
ejpam-6600	208	57	graphs	graph	NOUN
ejpam-6600	208	58	of	of	ADP
ejpam-6600	208	59	prime	prime	ADJ
ejpam-6600	208	60	order	order	NOUN
ejpam-6600	208	61	input	input	NOUN
ejpam-6600	208	62	:	:	PUNCT
ejpam-6600	208	63	the	the	DET
ejpam-6600	208	64	cubic	cubic	ADJ
ejpam-6600	208	65	paley	paley	PROPN
ejpam-6600	208	66	graph	graph	NOUN
ejpam-6600	208	67	3	3	NUM
ejpam-6600	208	68	−	−	NOUN
ejpam-6600	208	69	pp	pp	ADV
ejpam-6600	208	70	with	with	ADP
ejpam-6600	208	71	v	v	NOUN
ejpam-6600	208	72	(	(	PUNCT
ejpam-6600	208	73	3	3	NUM
ejpam-6600	208	74	−	−	NUM
ejpam-6600	208	75	pp	pp	NUM
ejpam-6600	208	76	)	)	PUNCT
ejpam-6600	208	77	=	=	SYM
ejpam-6600	208	78	zp	zp	PROPN
ejpam-6600	208	79	and	and	CCONJ
ejpam-6600	208	80	e(3	e(3	PROPN
ejpam-6600	208	81	−	−	PROPN
ejpam-6600	209	1	pp	pp	ADJ
ejpam-6600	209	2	)	)	PUNCT
ejpam-6600	209	3	=	=	PRON
ejpam-6600	209	4	{	{	PUNCT
ejpam-6600	209	5	(	(	PUNCT
ejpam-6600	209	6	u	u	NOUN
ejpam-6600	209	7	,	,	PUNCT
ejpam-6600	209	8	v	v	NOUN
ejpam-6600	209	9	)	)	PUNCT
ejpam-6600	210	1	|	|	ADV
ejpam-6600	210	2	u−	u−	NUM
ejpam-6600	210	3	v	v	X
ejpam-6600	210	4	∈	∈	PROPN
ejpam-6600	210	5	(	(	PUNCT
ejpam-6600	210	6	z∗	z∗	NOUN
ejpam-6600	210	7	p	p	NOUN
ejpam-6600	210	8	)	)	PUNCT
ejpam-6600	210	9	3	3	NUM
ejpam-6600	210	10	}	}	PUNCT
ejpam-6600	210	11	,	,	PUNCT
ejpam-6600	210	12	where	where	SCONJ
ejpam-6600	210	13	p	p	NOUN
ejpam-6600	210	14	is	be	AUX
ejpam-6600	210	15	any	any	DET
ejpam-6600	210	16	odd	odd	ADJ
ejpam-6600	210	17	prime	prime	NOUN
ejpam-6600	210	18	.	.	PUNCT
ejpam-6600	211	1	(	(	PUNCT
ejpam-6600	211	2	1	1	X
ejpam-6600	211	3	)	)	PUNCT
ejpam-6600	211	4	rename	rename	VERB
ejpam-6600	211	5	the	the	DET
ejpam-6600	211	6	vertices	vertex	NOUN
ejpam-6600	211	7	of	of	ADP
ejpam-6600	211	8	the	the	DET
ejpam-6600	211	9	graph	graph	NOUN
ejpam-6600	211	10	as	as	ADP
ejpam-6600	211	11	0	0	NUM
ejpam-6600	211	12	:	:	PUNCT
ejpam-6600	211	13	=	=	SYM
ejpam-6600	211	14	vp	vp	NOUN
ejpam-6600	211	15	,	,	PUNCT
ejpam-6600	211	16	1	1	NUM
ejpam-6600	211	17	:	:	PUNCT
ejpam-6600	211	18	=	=	NOUN
ejpam-6600	211	19	v1	v1	NOUN
ejpam-6600	211	20	,	,	PUNCT
ejpam-6600	211	21	2	2	NUM
ejpam-6600	211	22	:	:	PUNCT
ejpam-6600	211	23	=	=	SYM
ejpam-6600	211	24	v2	v2	PROPN
ejpam-6600	211	25	,	,	PUNCT
ejpam-6600	211	26	.	.	PUNCT
ejpam-6600	211	27	.	.	PUNCT
ejpam-6600	212	1	.	.	PUNCT
ejpam-6600	213	1	,	,	PUNCT
ejpam-6600	213	2	p−	p−	NOUN
ejpam-6600	213	3	1	1	NUM
ejpam-6600	213	4	:	:	PUNCT
ejpam-6600	213	5	=	=	SYM
ejpam-6600	213	6	vp−1	vp−1	PROPN
ejpam-6600	213	7	.	.	PUNCT
ejpam-6600	214	1	(	(	PUNCT
ejpam-6600	214	2	2	2	X
ejpam-6600	214	3	)	)	PUNCT
ejpam-6600	214	4	set	set	NOUN
ejpam-6600	214	5	r	r	NOUN
ejpam-6600	214	6	=	=	SYM
ejpam-6600	214	7	p−1	p−1	PROPN
ejpam-6600	214	8	2d	2d	NOUN
ejpam-6600	214	9	,	,	PUNCT
ejpam-6600	214	10	where	where	SCONJ
ejpam-6600	214	11	d	d	NOUN
ejpam-6600	214	12	=	=	SYM
ejpam-6600	214	13	gcd(3	gcd(3	NOUN
ejpam-6600	214	14	,	,	PUNCT
ejpam-6600	214	15	p−	p−	NOUN
ejpam-6600	214	16	1	1	NUM
ejpam-6600	214	17	)	)	PUNCT
ejpam-6600	214	18	,	,	PUNCT
ejpam-6600	214	19	and	and	CCONJ
ejpam-6600	214	20	rewrite	rewrite	VERB
ejpam-6600	214	21	(	(	PUNCT
ejpam-6600	214	22	z∗	z∗	NOUN
ejpam-6600	214	23	p	p	NOUN
ejpam-6600	214	24	)	)	PUNCT
ejpam-6600	214	25	3	3	NUM
ejpam-6600	214	26	as	as	ADP
ejpam-6600	214	27	(	(	PUNCT
ejpam-6600	214	28	z∗	z∗	NOUN
ejpam-6600	214	29	p	p	NOUN
ejpam-6600	214	30	)	)	PUNCT
ejpam-6600	214	31	3	3	NUM
ejpam-6600	214	32	=	=	SYM
ejpam-6600	214	33	s	s	NOUN
ejpam-6600	214	34	=	=	PUNCT
ejpam-6600	214	35	{	{	PUNCT
ejpam-6600	214	36	s1	s1	NOUN
ejpam-6600	214	37	,	,	PUNCT
ejpam-6600	214	38	s2	s2	PROPN
ejpam-6600	214	39	,	,	PUNCT
ejpam-6600	214	40	s3	s3	PROPN
ejpam-6600	214	41	,	,	PUNCT
ejpam-6600	214	42	.	.	PUNCT
ejpam-6600	214	43	.	.	PUNCT
ejpam-6600	214	44	.	.	PUNCT
ejpam-6600	215	1	,	,	PUNCT
ejpam-6600	215	2	s2r	s2r	PROPN
ejpam-6600	215	3	:	:	PUNCT
ejpam-6600	215	4	s1	s1	NOUN
ejpam-6600	215	5	<	<	X
ejpam-6600	215	6	s2	s2	PROPN
ejpam-6600	215	7	<	<	X
ejpam-6600	215	8	s3	s3	PROPN
ejpam-6600	215	9	<	<	X
ejpam-6600	215	10	.	.	PUNCT
ejpam-6600	215	11	.	.	PUNCT
ejpam-6600	216	1	.	.	PUNCT
ejpam-6600	217	1	<	<	X
ejpam-6600	217	2	s2r	s2r	PROPN
ejpam-6600	217	3	}	}	PUNCT
ejpam-6600	217	4	.	.	PUNCT
ejpam-6600	218	1	(	(	PUNCT
ejpam-6600	218	2	3	3	X
ejpam-6600	218	3	)	)	PUNCT
ejpam-6600	218	4	partition	partition	NOUN
ejpam-6600	218	5	s	s	NOUN
ejpam-6600	218	6	into	into	ADP
ejpam-6600	218	7	two	two	NUM
ejpam-6600	218	8	sets	set	NOUN
ejpam-6600	218	9	.	.	PUNCT
ejpam-6600	219	1	let	let	VERB
ejpam-6600	219	2	s1	s1	PROPN
ejpam-6600	219	3	=	=	PUNCT
ejpam-6600	219	4	{	{	PUNCT
ejpam-6600	219	5	s1	s1	NOUN
ejpam-6600	219	6	,	,	PUNCT
ejpam-6600	219	7	s2	s2	PROPN
ejpam-6600	219	8	,	,	PUNCT
ejpam-6600	219	9	s3	s3	PROPN
ejpam-6600	219	10	,	,	PUNCT
ejpam-6600	219	11	.	.	PUNCT
ejpam-6600	219	12	.	.	PUNCT
ejpam-6600	220	1	.	.	PUNCT
ejpam-6600	221	1	,	,	PUNCT
ejpam-6600	221	2	sr	sr	PROPN
ejpam-6600	221	3	}	}	PUNCT
ejpam-6600	221	4	and	and	CCONJ
ejpam-6600	221	5	s2	s2	VERB
ejpam-6600	221	6	=	=	SYM
ejpam-6600	221	7	{	{	PUNCT
ejpam-6600	221	8	sr+1	sr+1	PROPN
ejpam-6600	221	9	,	,	PUNCT
ejpam-6600	221	10	sr+2	sr+2	NOUN
ejpam-6600	221	11	,	,	PUNCT
ejpam-6600	221	12	sr+3	sr+3	NOUN
ejpam-6600	221	13	,	,	PUNCT
ejpam-6600	221	14	.	.	PUNCT
ejpam-6600	221	15	.	.	PUNCT
ejpam-6600	222	1	.	.	PUNCT
ejpam-6600	223	1	,	,	PUNCT
ejpam-6600	223	2	s2r	s2r	PROPN
ejpam-6600	223	3	}	}	PUNCT
ejpam-6600	223	4	.	.	PUNCT
ejpam-6600	224	1	note	note	VERB
ejpam-6600	224	2	that	that	SCONJ
ejpam-6600	224	3	:	:	PUNCT
ejpam-6600	224	4	p−1	p−1	PROPN
ejpam-6600	224	5	is	be	AUX
ejpam-6600	224	6	divisible	divisible	ADJ
ejpam-6600	224	7	by	by	ADP
ejpam-6600	224	8	2d	2d	NOUN
ejpam-6600	224	9	and	and	CCONJ
ejpam-6600	224	10	for	for	ADP
ejpam-6600	224	11	any	any	DET
ejpam-6600	224	12	vertex	vertex	NOUN
ejpam-6600	224	13	vi	vi	PROPN
ejpam-6600	224	14	∈	∈	PROPN
ejpam-6600	224	15	zp	zp	NOUN
ejpam-6600	224	16	the	the	DET
ejpam-6600	224	17	vertex	vertex	NOUN
ejpam-6600	224	18	vi+sj	vi+sj	PROPN
ejpam-6600	224	19	is	be	AUX
ejpam-6600	224	20	adjacent	adjacent	ADJ
ejpam-6600	224	21	to	to	PART
ejpam-6600	224	22	vi	vi	VERB
ejpam-6600	224	23	for	for	ADP
ejpam-6600	224	24	all	all	DET
ejpam-6600	224	25	sj	sj	PROPN
ejpam-6600	224	26	∈	∈	PROPN
ejpam-6600	224	27	s.	s.	PROPN
ejpam-6600	224	28	(	(	PUNCT
ejpam-6600	224	29	4	4	X
ejpam-6600	224	30	)	)	PUNCT
ejpam-6600	224	31	if	if	SCONJ
ejpam-6600	224	32	sj	sj	PROPN
ejpam-6600	224	33	∈	∈	PROPN
ejpam-6600	224	34	s1	s1	PROPN
ejpam-6600	224	35	,	,	PUNCT
ejpam-6600	224	36	the	the	DET
ejpam-6600	224	37	vertex	vertex	NOUN
ejpam-6600	224	38	vi+sj	vi+sj	PROPN
ejpam-6600	224	39	is	be	AUX
ejpam-6600	224	40	placed	place	VERB
ejpam-6600	224	41	in	in	ADP
ejpam-6600	224	42	clockwise	clockwise	NOUN
ejpam-6600	224	43	direction	direction	NOUN
ejpam-6600	224	44	of	of	ADP
ejpam-6600	224	45	vi	vi	NOUN
ejpam-6600	224	46	and	and	CCONJ
ejpam-6600	224	47	if	if	SCONJ
ejpam-6600	224	48	sj	sj	PROPN
ejpam-6600	224	49	∈	∈	PROPN
ejpam-6600	224	50	s2	s2	PROPN
ejpam-6600	224	51	,	,	PUNCT
ejpam-6600	224	52	the	the	DET
ejpam-6600	224	53	vertex	vertex	NOUN
ejpam-6600	224	54	vi+sj	vi+sj	PROPN
ejpam-6600	224	55	is	be	AUX
ejpam-6600	224	56	placed	place	VERB
ejpam-6600	224	57	in	in	ADP
ejpam-6600	224	58	anticlockwise	anticlockwise	NOUN
ejpam-6600	224	59	direction	direction	NOUN
ejpam-6600	224	60	of	of	ADP
ejpam-6600	224	61	vi	vi	PROPN
ejpam-6600	224	62	.	.	PUNCT
ejpam-6600	225	1	(	(	PUNCT
ejpam-6600	225	2	5	5	X
ejpam-6600	225	3	)	)	PUNCT
ejpam-6600	225	4	set	set	NOUN
ejpam-6600	225	5	f(vi	f(vi	PROPN
ejpam-6600	225	6	,	,	PUNCT
ejpam-6600	225	7	vi+sj	vi+sj	NUM
ejpam-6600	225	8	)	)	PUNCT
ejpam-6600	226	1	=	=	SYM
ejpam-6600	226	2	0	0	NUM
ejpam-6600	227	1	for	for	ADP
ejpam-6600	227	2	all	all	PRON
ejpam-6600	227	3	i	i	PRON
ejpam-6600	227	4	∈	∈	PROPN
ejpam-6600	227	5	{	{	PUNCT
ejpam-6600	227	6	1	1	NUM
ejpam-6600	227	7	,	,	PUNCT
ejpam-6600	227	8	2	2	NUM
ejpam-6600	227	9	,	,	PUNCT
ejpam-6600	227	10	3	3	NUM
ejpam-6600	227	11	,	,	PUNCT
ejpam-6600	227	12	·	·	PUNCT
ejpam-6600	227	13	·	·	PUNCT
ejpam-6600	227	14	·	·	PUNCT
ejpam-6600	227	15	,	,	PUNCT
ejpam-6600	227	16	p	p	X
ejpam-6600	227	17	}	}	PUNCT
ejpam-6600	227	18	,	,	PUNCT
ejpam-6600	227	19	j	j	PROPN
ejpam-6600	227	20	∈	∈	PROPN
ejpam-6600	227	21	{	{	PUNCT
ejpam-6600	227	22	1	1	NUM
ejpam-6600	227	23	,	,	PUNCT
ejpam-6600	227	24	2	2	NUM
ejpam-6600	227	25	,	,	PUNCT
ejpam-6600	227	26	3	3	NUM
ejpam-6600	227	27	,	,	PUNCT
ejpam-6600	227	28	·	·	PUNCT
ejpam-6600	227	29	·	·	PUNCT
ejpam-6600	227	30	·	·	PUNCT
ejpam-6600	227	31	,	,	PUNCT
ejpam-6600	227	32	2r	2r	NUM
ejpam-6600	227	33	}	}	PUNCT
ejpam-6600	227	34	.	.	PUNCT
ejpam-6600	228	1	(	(	PUNCT
ejpam-6600	228	2	6	6	X
ejpam-6600	228	3	)	)	PUNCT
ejpam-6600	228	4	set	set	NOUN
ejpam-6600	228	5	i	i	NOUN
ejpam-6600	228	6	=	=	NOUN
ejpam-6600	229	1	1	1	X
ejpam-6600	229	2	.	.	X
ejpam-6600	229	3	step	step	NOUN
ejpam-6600	229	4	1	1	NUM
ejpam-6600	229	5	:	:	PUNCT
ejpam-6600	229	6	if	if	SCONJ
ejpam-6600	229	7	i	i	PRON
ejpam-6600	229	8	≤	≤	VERB
ejpam-6600	229	9	p	p	NOUN
ejpam-6600	229	10	then	then	ADV
ejpam-6600	229	11	continue	continue	VERB
ejpam-6600	229	12	to	to	PART
ejpam-6600	229	13	step	step	VERB
ejpam-6600	229	14	2	2	NUM
ejpam-6600	229	15	.	.	PUNCT
ejpam-6600	229	16	else	else	ADV
ejpam-6600	229	17	jump	jump	VERB
ejpam-6600	229	18	to	to	PART
ejpam-6600	229	19	step	step	VERB
ejpam-6600	229	20	4	4	NUM
ejpam-6600	229	21	.	.	PUNCT
ejpam-6600	230	1	step	step	NOUN
ejpam-6600	230	2	2	2	NUM
ejpam-6600	230	3	:	:	PUNCT
ejpam-6600	230	4	for	for	ADP
ejpam-6600	230	5	each	each	DET
ejpam-6600	230	6	sj	sj	PROPN
ejpam-6600	230	7	∈	∈	PROPN
ejpam-6600	230	8	s1	s1	PROPN
ejpam-6600	230	9	,	,	PUNCT
ejpam-6600	230	10	f	f	PROPN
ejpam-6600	230	11	(	(	PUNCT
ejpam-6600	230	12	vi	vi	PROPN
ejpam-6600	230	13	,	,	PUNCT
ejpam-6600	230	14	vi+sj	vi+sj	NUM
ejpam-6600	230	15	)	)	PUNCT
ejpam-6600	231	1	=	=	PRON
ejpam-6600	232	1	(	(	PUNCT
ejpam-6600	232	2	j	j	NOUN
ejpam-6600	232	3	−	−	PROPN
ejpam-6600	232	4	1	1	NUM
ejpam-6600	232	5	)	)	PUNCT
ejpam-6600	232	6	p+	p+	PROPN
ejpam-6600	232	7	i.	i.	PROPN
ejpam-6600	232	8	a.	a.	PROPN
ejpam-6600	232	9	n.	n.	PROPN
ejpam-6600	232	10	elsawy	elsawy	PROPN
ejpam-6600	232	11	,	,	PUNCT
ejpam-6600	232	12	r.	r.	PROPN
ejpam-6600	232	13	n.	n.	PROPN
ejpam-6600	232	14	almohammadi	almohammadi	PROPN
ejpam-6600	232	15	/	/	SYM
ejpam-6600	232	16	eur	eur	PROPN
ejpam-6600	232	17	.	.	PUNCT
ejpam-6600	233	1	j.	j.	PROPN
ejpam-6600	233	2	pure	pure	PROPN
ejpam-6600	233	3	appl	appl	PROPN
ejpam-6600	233	4	.	.	PROPN
ejpam-6600	233	5	math	math	PROPN
ejpam-6600	233	6	,	,	PUNCT
ejpam-6600	233	7	18	18	NUM
ejpam-6600	233	8	(	(	PUNCT
ejpam-6600	233	9	4	4	NUM
ejpam-6600	233	10	)	)	PUNCT
ejpam-6600	233	11	(	(	PUNCT
ejpam-6600	233	12	2025	2025	NUM
ejpam-6600	233	13	)	)	PUNCT
ejpam-6600	233	14	,	,	PUNCT
ejpam-6600	233	15	6600	6600	NUM
ejpam-6600	233	16	9	9	NUM
ejpam-6600	233	17	of	of	ADP
ejpam-6600	233	18	26	26	NUM
ejpam-6600	233	19	step	step	NOUN
ejpam-6600	233	20	3	3	NUM
ejpam-6600	233	21	:	:	PUNCT
ejpam-6600	233	22	i	i	PRON
ejpam-6600	233	23	=	=	PUNCT
ejpam-6600	233	24	i+	i+	PROPN
ejpam-6600	233	25	1	1	NUM
ejpam-6600	233	26	,	,	PUNCT
ejpam-6600	233	27	go	go	VERB
ejpam-6600	233	28	back	back	ADV
ejpam-6600	233	29	to	to	PART
ejpam-6600	233	30	step	step	NOUN
ejpam-6600	233	31	1	1	NUM
ejpam-6600	233	32	.	.	PUNCT
ejpam-6600	234	1	step	step	NOUN
ejpam-6600	234	2	4	4	NUM
ejpam-6600	234	3	:	:	PUNCT
ejpam-6600	234	4	for	for	ADP
ejpam-6600	234	5	each	each	PRON
ejpam-6600	234	6	k	k	NOUN
ejpam-6600	234	7	=	=	SYM
ejpam-6600	234	8	1	1	NUM
ejpam-6600	234	9	,	,	PUNCT
ejpam-6600	234	10	2	2	NUM
ejpam-6600	234	11	,	,	PUNCT
ejpam-6600	234	12	3	3	NUM
ejpam-6600	234	13	,	,	PUNCT
ejpam-6600	234	14	.	.	PUNCT
ejpam-6600	234	15	.	.	PUNCT
ejpam-6600	235	1	.	.	PUNCT
ejpam-6600	236	1	,	,	PUNCT
ejpam-6600	236	2	p	p	X
ejpam-6600	236	3	,	,	PUNCT
ejpam-6600	236	4	find	find	VERB
ejpam-6600	236	5	the	the	DET
ejpam-6600	236	6	weight	weight	NOUN
ejpam-6600	236	7	of	of	ADP
ejpam-6600	236	8	the	the	DET
ejpam-6600	236	9	vertex	vertex	NOUN
ejpam-6600	236	10	vk	vk	NOUN
ejpam-6600	236	11	using	use	VERB
ejpam-6600	236	12	the	the	DET
ejpam-6600	236	13	following	follow	VERB
ejpam-6600	236	14	mapping	mapping	NOUN
ejpam-6600	236	15	:	:	PUNCT
ejpam-6600	236	16	fw(vk	fw(vk	PROPN
ejpam-6600	236	17	)	)	PUNCT
ejpam-6600	237	1	=	=	PUNCT
ejpam-6600	238	1	∑2r	∑2r	NOUN
ejpam-6600	238	2	j=1	j=1	PROPN
ejpam-6600	238	3	f(vk	f(vk	PROPN
ejpam-6600	238	4	,	,	PUNCT
ejpam-6600	238	5	vk+sj	vk+sj	NOUN
ejpam-6600	238	6	)	)	PUNCT
ejpam-6600	239	1	=	=	PUNCT
ejpam-6600	240	1	∑r	∑r	PROPN
ejpam-6600	240	2	j=1	j=1	PROPN
ejpam-6600	240	3	2[(j−1)p+k]+(p−sj	2[(j−1)p+k]+(p−sj	NOUN
ejpam-6600	240	4	)	)	PUNCT
ejpam-6600	241	1	=	=	SYM
ejpam-6600	241	2	2kr−l	2kr−l	NUM
ejpam-6600	241	3	(	(	PUNCT
ejpam-6600	241	4	mod	mod	NOUN
ejpam-6600	241	5	p	p	NOUN
ejpam-6600	241	6	)	)	PUNCT
ejpam-6600	241	7	,	,	PUNCT
ejpam-6600	241	8	where	where	SCONJ
ejpam-6600	241	9	l	l	NOUN
ejpam-6600	241	10	=	=	PUNCT
ejpam-6600	242	1	∑r	∑r	PROPN
ejpam-6600	242	2	j=1	j=1	NOUN
ejpam-6600	242	3	sj	sj	INTJ
ejpam-6600	242	4	.	.	PUNCT
ejpam-6600	243	1	theorem	theorem	NOUN
ejpam-6600	243	2	3	3	NUM
ejpam-6600	243	3	.	.	PUNCT
ejpam-6600	244	1	every	every	DET
ejpam-6600	244	2	cubic	cubic	ADJ
ejpam-6600	244	3	paley	paley	NOUN
ejpam-6600	244	4	graph	graph	NOUN
ejpam-6600	244	5	of	of	ADP
ejpam-6600	244	6	prime	prime	ADJ
ejpam-6600	244	7	order	order	NOUN
ejpam-6600	244	8	admits	admit	VERB
ejpam-6600	244	9	an	an	DET
ejpam-6600	244	10	edge	edge	NOUN
ejpam-6600	244	11	-	-	PUNCT
ejpam-6600	244	12	graceful	graceful	NOUN
ejpam-6600	244	13	labeling	labeling	NOUN
ejpam-6600	244	14	.	.	PUNCT
ejpam-6600	245	1	proof	proof	NOUN
ejpam-6600	245	2	.	.	PUNCT
ejpam-6600	246	1	see	see	VERB
ejpam-6600	246	2	theorem	theorem	NOUN
ejpam-6600	246	3	5	5	NUM
ejpam-6600	246	4	with	with	ADP
ejpam-6600	246	5	m	m	PROPN
ejpam-6600	246	6	=	=	SYM
ejpam-6600	246	7	3	3	NUM
ejpam-6600	246	8	.	.	NOUN
ejpam-6600	246	9	example	example	NOUN
ejpam-6600	247	1	5	5	NUM
ejpam-6600	247	2	.	.	PUNCT
ejpam-6600	248	1	we	we	PRON
ejpam-6600	248	2	apply	apply	VERB
ejpam-6600	248	3	the	the	DET
ejpam-6600	248	4	algorithm	algorithm	NOUN
ejpam-6600	248	5	to	to	PART
ejpam-6600	248	6	show	show	VERB
ejpam-6600	248	7	that	that	SCONJ
ejpam-6600	248	8	the	the	DET
ejpam-6600	248	9	cubic	cubic	ADJ
ejpam-6600	248	10	paley	paley	PROPN
ejpam-6600	248	11	graph	graph	NOUN
ejpam-6600	248	12	3−	3−	NUM
ejpam-6600	248	13	p19	p19	NOUN
ejpam-6600	248	14	is	be	AUX
ejpam-6600	248	15	edgegraceful	edgegraceful	ADJ
ejpam-6600	248	16	with	with	ADP
ejpam-6600	248	17	v	v	PROPN
ejpam-6600	248	18	(	(	PUNCT
ejpam-6600	248	19	3−p19	3−p19	PROPN
ejpam-6600	248	20	)	)	PUNCT
ejpam-6600	248	21	=	=	SYM
ejpam-6600	248	22	{	{	PUNCT
ejpam-6600	248	23	v1	v1	PROPN
ejpam-6600	248	24	,	,	PUNCT
ejpam-6600	248	25	v2	v2	PROPN
ejpam-6600	248	26	,	,	PUNCT
ejpam-6600	248	27	·	·	PUNCT
ejpam-6600	248	28	·	·	PUNCT
ejpam-6600	248	29	·	·	PUNCT
ejpam-6600	248	30	,	,	PUNCT
ejpam-6600	248	31	v19	v19	PROPN
ejpam-6600	248	32	}	}	PUNCT
ejpam-6600	248	33	and	and	CCONJ
ejpam-6600	248	34	|e(3−	|e(3−	VERB
ejpam-6600	248	35	p19)|	p19)|	PROPN
ejpam-6600	248	36	=	=	SYM
ejpam-6600	248	37	19·18	19·18	NUM
ejpam-6600	248	38	6	6	NUM
ejpam-6600	248	39	=	=	SYM
ejpam-6600	248	40	57	57	NUM
ejpam-6600	248	41	.	.	PUNCT
ejpam-6600	249	1	figure	figure	NOUN
ejpam-6600	249	2	6	6	NUM
ejpam-6600	249	3	shows	show	VERB
ejpam-6600	249	4	the	the	DET
ejpam-6600	249	5	edge	edge	NOUN
ejpam-6600	249	6	-	-	PUNCT
ejpam-6600	249	7	graceful	graceful	NOUN
ejpam-6600	249	8	labeling	labeling	NOUN
ejpam-6600	249	9	for	for	ADP
ejpam-6600	249	10	the	the	DET
ejpam-6600	249	11	cubic	cubic	ADJ
ejpam-6600	249	12	paley	paley	PROPN
ejpam-6600	249	13	graph	graph	NOUN
ejpam-6600	249	14	3−	3−	NUM
ejpam-6600	249	15	p19	p19	NOUN
ejpam-6600	249	16	.	.	PUNCT
ejpam-6600	250	1	figure	figure	NOUN
ejpam-6600	250	2	6	6	NUM
ejpam-6600	250	3	:	:	PUNCT
ejpam-6600	250	4	an	an	DET
ejpam-6600	250	5	edge	edge	NOUN
ejpam-6600	250	6	-	-	PUNCT
ejpam-6600	250	7	graceful	graceful	NOUN
ejpam-6600	250	8	labeling	labeling	NOUN
ejpam-6600	250	9	of	of	ADP
ejpam-6600	250	10	3−	3−	NUM
ejpam-6600	250	11	p19	p19	NOUN
ejpam-6600	250	12	a.	a.	NOUN
ejpam-6600	250	13	n.	n.	PROPN
ejpam-6600	250	14	elsawy	elsawy	PROPN
ejpam-6600	250	15	,	,	PUNCT
ejpam-6600	250	16	r.	r.	PROPN
ejpam-6600	250	17	n.	n.	PROPN
ejpam-6600	250	18	almohammadi	almohammadi	PROPN
ejpam-6600	250	19	/	/	SYM
ejpam-6600	250	20	eur	eur	PROPN
ejpam-6600	250	21	.	.	PUNCT
ejpam-6600	251	1	j.	j.	PROPN
ejpam-6600	251	2	pure	pure	PROPN
ejpam-6600	251	3	appl	appl	PROPN
ejpam-6600	251	4	.	.	PROPN
ejpam-6600	251	5	math	math	PROPN
ejpam-6600	251	6	,	,	PUNCT
ejpam-6600	251	7	18	18	NUM
ejpam-6600	251	8	(	(	PUNCT
ejpam-6600	251	9	4	4	NUM
ejpam-6600	251	10	)	)	PUNCT
ejpam-6600	251	11	(	(	PUNCT
ejpam-6600	251	12	2025	2025	NUM
ejpam-6600	251	13	)	)	PUNCT
ejpam-6600	251	14	,	,	PUNCT
ejpam-6600	251	15	6600	6600	NUM
ejpam-6600	251	16	10	10	NUM
ejpam-6600	251	17	of	of	ADP
ejpam-6600	251	18	26	26	NUM
ejpam-6600	251	19	input	input	NOUN
ejpam-6600	251	20	:	:	PUNCT
ejpam-6600	251	21	the	the	DET
ejpam-6600	251	22	graph	graph	NOUN
ejpam-6600	251	23	3−	3−	NUM
ejpam-6600	251	24	p19	p19	NOUN
ejpam-6600	251	25	.	.	PUNCT
ejpam-6600	252	1	we	we	PRON
ejpam-6600	252	2	have	have	VERB
ejpam-6600	252	3	p	p	NOUN
ejpam-6600	252	4	=	=	SYM
ejpam-6600	252	5	19,m	19,m	X
ejpam-6600	253	1	=	=	SYM
ejpam-6600	253	2	3	3	NUM
ejpam-6600	253	3	,	,	PUNCT
ejpam-6600	253	4	d	d	NOUN
ejpam-6600	253	5	=	=	SYM
ejpam-6600	253	6	3	3	NUM
ejpam-6600	253	7	,	,	PUNCT
ejpam-6600	253	8	and	and	CCONJ
ejpam-6600	253	9	(	(	PUNCT
ejpam-6600	253	10	z∗	z∗	NOUN
ejpam-6600	253	11	19	19	NUM
ejpam-6600	253	12	)	)	PUNCT
ejpam-6600	253	13	3	3	NUM
ejpam-6600	253	14	=	=	SYM
ejpam-6600	253	15	{	{	PUNCT
ejpam-6600	253	16	13	13	NUM
ejpam-6600	253	17	,	,	PUNCT
ejpam-6600	253	18	23	23	NUM
ejpam-6600	253	19	,	,	PUNCT
ejpam-6600	253	20	·	·	PUNCT
ejpam-6600	253	21	·	·	PUNCT
ejpam-6600	253	22	·	·	PUNCT
ejpam-6600	253	23	,	,	PUNCT
ejpam-6600	253	24	183	183	NUM
ejpam-6600	253	25	}	}	PUNCT
ejpam-6600	253	26	=	=	SYM
ejpam-6600	253	27	{	{	PUNCT
ejpam-6600	253	28	1	1	NUM
ejpam-6600	253	29	,	,	PUNCT
ejpam-6600	253	30	8	8	NUM
ejpam-6600	253	31	,	,	PUNCT
ejpam-6600	253	32	7	7	NUM
ejpam-6600	253	33	,	,	PUNCT
ejpam-6600	253	34	11	11	NUM
ejpam-6600	253	35	,	,	PUNCT
ejpam-6600	253	36	18	18	NUM
ejpam-6600	253	37	,	,	PUNCT
ejpam-6600	253	38	12	12	NUM
ejpam-6600	253	39	}	}	PUNCT
ejpam-6600	253	40	.	.	PUNCT
ejpam-6600	254	1	(	(	PUNCT
ejpam-6600	254	2	1	1	X
ejpam-6600	254	3	)	)	PUNCT
ejpam-6600	254	4	rename	rename	VERB
ejpam-6600	254	5	the	the	DET
ejpam-6600	254	6	vertices	vertex	NOUN
ejpam-6600	254	7	of	of	ADP
ejpam-6600	254	8	the	the	DET
ejpam-6600	254	9	graph	graph	NOUN
ejpam-6600	254	10	as	as	ADP
ejpam-6600	254	11	0	0	NUM
ejpam-6600	254	12	:	:	PUNCT
ejpam-6600	254	13	=	=	SYM
ejpam-6600	254	14	v19	v19	PROPN
ejpam-6600	254	15	,	,	PUNCT
ejpam-6600	254	16	1	1	NUM
ejpam-6600	254	17	:	:	PUNCT
ejpam-6600	254	18	=	=	NOUN
ejpam-6600	254	19	v1	v1	NOUN
ejpam-6600	254	20	,	,	PUNCT
ejpam-6600	254	21	2	2	NUM
ejpam-6600	254	22	:	:	PUNCT
ejpam-6600	254	23	=	=	SYM
ejpam-6600	254	24	v2	v2	PROPN
ejpam-6600	254	25	,	,	PUNCT
ejpam-6600	254	26	.	.	PUNCT
ejpam-6600	254	27	.	.	PUNCT
ejpam-6600	255	1	.	.	PUNCT
ejpam-6600	256	1	,	,	PUNCT
ejpam-6600	256	2	18	18	NUM
ejpam-6600	256	3	:	:	PUNCT
ejpam-6600	256	4	=	=	NOUN
ejpam-6600	256	5	v18	v18	NOUN
ejpam-6600	256	6	.	.	PUNCT
ejpam-6600	257	1	(	(	PUNCT
ejpam-6600	257	2	2	2	X
ejpam-6600	257	3	)	)	PUNCT
ejpam-6600	257	4	rewrite	rewrite	NOUN
ejpam-6600	257	5	(	(	PUNCT
ejpam-6600	257	6	z∗	z∗	NOUN
ejpam-6600	257	7	19	19	NUM
ejpam-6600	257	8	)	)	PUNCT
ejpam-6600	257	9	3	3	NUM
ejpam-6600	257	10	as	as	ADP
ejpam-6600	257	11	(	(	PUNCT
ejpam-6600	257	12	z∗	z∗	NOUN
ejpam-6600	257	13	19	19	NUM
ejpam-6600	257	14	)	)	PUNCT
ejpam-6600	257	15	3	3	NUM
ejpam-6600	257	16	=	=	SYM
ejpam-6600	257	17	s	s	NOUN
ejpam-6600	257	18	=	=	PUNCT
ejpam-6600	257	19	{	{	PUNCT
ejpam-6600	257	20	s1	s1	NOUN
ejpam-6600	257	21	,	,	PUNCT
ejpam-6600	257	22	s2	s2	PROPN
ejpam-6600	257	23	,	,	PUNCT
ejpam-6600	257	24	s3	s3	PROPN
ejpam-6600	257	25	,	,	PUNCT
ejpam-6600	257	26	s4	s4	PROPN
ejpam-6600	257	27	,	,	PUNCT
ejpam-6600	257	28	s5	s5	PROPN
ejpam-6600	257	29	,	,	PUNCT
ejpam-6600	257	30	s6	s6	PROPN
ejpam-6600	257	31	:	:	PUNCT
ejpam-6600	257	32	s1	s1	PROPN
ejpam-6600	257	33	<	<	X
ejpam-6600	257	34	s2	s2	PROPN
ejpam-6600	257	35	<	<	X
ejpam-6600	257	36	s3	s3	PROPN
ejpam-6600	257	37	<	<	X
ejpam-6600	257	38	s4	s4	PROPN
ejpam-6600	257	39	<	<	X
ejpam-6600	257	40	s5	s5	PROPN
ejpam-6600	257	41	<	<	X
ejpam-6600	257	42	s6	s6	PROPN
ejpam-6600	257	43	}	}	PUNCT
ejpam-6600	257	44	=	=	PUNCT
ejpam-6600	257	45	{	{	PUNCT
ejpam-6600	257	46	1	1	NUM
ejpam-6600	257	47	,	,	PUNCT
ejpam-6600	257	48	7	7	NUM
ejpam-6600	257	49	,	,	PUNCT
ejpam-6600	257	50	8	8	NUM
ejpam-6600	257	51	,	,	PUNCT
ejpam-6600	257	52	11	11	NUM
ejpam-6600	257	53	,	,	PUNCT
ejpam-6600	257	54	12	12	NUM
ejpam-6600	257	55	,	,	PUNCT
ejpam-6600	257	56	18	18	NUM
ejpam-6600	257	57	}	}	PUNCT
ejpam-6600	257	58	(	(	PUNCT
ejpam-6600	257	59	3	3	X
ejpam-6600	257	60	)	)	PUNCT
ejpam-6600	257	61	partition	partition	NOUN
ejpam-6600	257	62	s	s	NOUN
ejpam-6600	257	63	into	into	ADP
ejpam-6600	257	64	two	two	NUM
ejpam-6600	257	65	sets	set	NOUN
ejpam-6600	257	66	.	.	PUNCT
ejpam-6600	258	1	let	let	VERB
ejpam-6600	258	2	s1	s1	PROPN
ejpam-6600	258	3	=	=	PUNCT
ejpam-6600	258	4	{	{	PUNCT
ejpam-6600	258	5	s1	s1	NOUN
ejpam-6600	258	6	,	,	PUNCT
ejpam-6600	258	7	s2	s2	PROPN
ejpam-6600	258	8	,	,	PUNCT
ejpam-6600	258	9	s3	s3	PROPN
ejpam-6600	258	10	}	}	PUNCT
ejpam-6600	258	11	=	=	PUNCT
ejpam-6600	258	12	{	{	PUNCT
ejpam-6600	258	13	1	1	NUM
ejpam-6600	258	14	,	,	PUNCT
ejpam-6600	258	15	7	7	NUM
ejpam-6600	258	16	,	,	PUNCT
ejpam-6600	258	17	8	8	NUM
ejpam-6600	258	18	}	}	PUNCT
ejpam-6600	258	19	and	and	CCONJ
ejpam-6600	258	20	s2	s2	VERB
ejpam-6600	258	21	=	=	SYM
ejpam-6600	258	22	{	{	PUNCT
ejpam-6600	258	23	s4	s4	PROPN
ejpam-6600	258	24	,	,	PUNCT
ejpam-6600	258	25	s5	s5	PROPN
ejpam-6600	258	26	,	,	PUNCT
ejpam-6600	258	27	s6	s6	PROPN
ejpam-6600	258	28	}	}	PUNCT
ejpam-6600	258	29	=	=	PUNCT
ejpam-6600	258	30	{	{	PUNCT
ejpam-6600	258	31	11	11	NUM
ejpam-6600	258	32	,	,	PUNCT
ejpam-6600	258	33	12	12	NUM
ejpam-6600	258	34	,	,	PUNCT
ejpam-6600	258	35	18	18	NUM
ejpam-6600	258	36	}	}	PUNCT
ejpam-6600	258	37	.	.	PUNCT
ejpam-6600	259	1	note	note	VERB
ejpam-6600	259	2	that	that	SCONJ
ejpam-6600	259	3	:	:	PUNCT
ejpam-6600	259	4	for	for	ADP
ejpam-6600	259	5	any	any	DET
ejpam-6600	259	6	vertex	vertex	NOUN
ejpam-6600	259	7	vi	vi	PROPN
ejpam-6600	259	8	∈	∈	PROPN
ejpam-6600	259	9	z19	z19	NOUN
ejpam-6600	259	10	the	the	DET
ejpam-6600	259	11	vertices	vertex	NOUN
ejpam-6600	259	12	vi+1	vi+1	ADJ
ejpam-6600	259	13	,	,	PUNCT
ejpam-6600	259	14	vi+7	vi+7	NUM
ejpam-6600	259	15	,	,	PUNCT
ejpam-6600	259	16	vi+8	vi+8	NOUN
ejpam-6600	259	17	,	,	PUNCT
ejpam-6600	259	18	vi+11	vi+11	PROPN
ejpam-6600	259	19	,	,	PUNCT
ejpam-6600	259	20	vi+12	vi+12	PROPN
ejpam-6600	259	21	,	,	PUNCT
ejpam-6600	259	22	vi+18	vi+18	PROPN
ejpam-6600	259	23	are	be	AUX
ejpam-6600	259	24	adjacent	adjacent	ADJ
ejpam-6600	259	25	to	to	ADP
ejpam-6600	259	26	vi	vi	PROPN
ejpam-6600	259	27	.	.	PUNCT
ejpam-6600	260	1	(	(	PUNCT
ejpam-6600	260	2	4	4	X
ejpam-6600	260	3	)	)	PUNCT
ejpam-6600	260	4	the	the	DET
ejpam-6600	260	5	vertices	vertex	NOUN
ejpam-6600	260	6	vi+1	vi+1	NOUN
ejpam-6600	260	7	,	,	PUNCT
ejpam-6600	260	8	vi+7	vi+7	NUM
ejpam-6600	260	9	,	,	PUNCT
ejpam-6600	260	10	vi+8	vi+8	PROPN
ejpam-6600	260	11	are	be	AUX
ejpam-6600	260	12	placed	place	VERB
ejpam-6600	260	13	in	in	ADP
ejpam-6600	260	14	clockwise	clockwise	NOUN
ejpam-6600	260	15	direction	direction	NOUN
ejpam-6600	260	16	of	of	ADP
ejpam-6600	260	17	vi	vi	NOUN
ejpam-6600	260	18	and	and	CCONJ
ejpam-6600	260	19	the	the	DET
ejpam-6600	260	20	vertices	vertex	NOUN
ejpam-6600	260	21	vi+11	vi+11	PROPN
ejpam-6600	260	22	,	,	PUNCT
ejpam-6600	260	23	vi+12	vi+12	PROPN
ejpam-6600	260	24	,	,	PUNCT
ejpam-6600	260	25	vi+18	vi+18	PROPN
ejpam-6600	260	26	are	be	AUX
ejpam-6600	260	27	placed	place	VERB
ejpam-6600	260	28	in	in	ADP
ejpam-6600	260	29	anticlockwise	anticlockwise	NOUN
ejpam-6600	260	30	direction	direction	NOUN
ejpam-6600	260	31	of	of	ADP
ejpam-6600	260	32	vi	vi	PROPN
ejpam-6600	260	33	.	.	PUNCT
ejpam-6600	261	1	(	(	PUNCT
ejpam-6600	261	2	5	5	X
ejpam-6600	261	3	)	)	PUNCT
ejpam-6600	261	4	set	set	NOUN
ejpam-6600	261	5	f(vi	f(vi	PROPN
ejpam-6600	261	6	,	,	PUNCT
ejpam-6600	261	7	vi+sj	vi+sj	NUM
ejpam-6600	261	8	)	)	PUNCT
ejpam-6600	262	1	=	=	SYM
ejpam-6600	262	2	0	0	NUM
ejpam-6600	263	1	for	for	ADP
ejpam-6600	263	2	all	all	PRON
ejpam-6600	263	3	i	i	PRON
ejpam-6600	263	4	∈	∈	PROPN
ejpam-6600	263	5	{	{	PUNCT
ejpam-6600	263	6	1	1	NUM
ejpam-6600	263	7	,	,	PUNCT
ejpam-6600	263	8	2	2	NUM
ejpam-6600	263	9	,	,	PUNCT
ejpam-6600	263	10	3	3	NUM
ejpam-6600	263	11	,	,	PUNCT
ejpam-6600	263	12	·	·	PUNCT
ejpam-6600	263	13	·	·	PUNCT
ejpam-6600	263	14	·	·	PUNCT
ejpam-6600	263	15	,	,	PUNCT
ejpam-6600	263	16	19	19	NUM
ejpam-6600	263	17	}	}	PUNCT
ejpam-6600	263	18	,	,	PUNCT
ejpam-6600	263	19	j	j	PROPN
ejpam-6600	263	20	∈	∈	PROPN
ejpam-6600	263	21	{	{	PUNCT
ejpam-6600	263	22	1	1	NUM
ejpam-6600	263	23	,	,	PUNCT
ejpam-6600	263	24	2	2	NUM
ejpam-6600	263	25	,	,	PUNCT
ejpam-6600	263	26	3	3	NUM
ejpam-6600	263	27	,	,	PUNCT
ejpam-6600	263	28	·	·	PUNCT
ejpam-6600	263	29	·	·	PUNCT
ejpam-6600	263	30	·	·	PUNCT
ejpam-6600	263	31	,	,	PUNCT
ejpam-6600	263	32	6	6	NUM
ejpam-6600	263	33	}	}	PUNCT
ejpam-6600	263	34	.	.	PUNCT
ejpam-6600	264	1	(	(	PUNCT
ejpam-6600	264	2	6	6	X
ejpam-6600	264	3	)	)	PUNCT
ejpam-6600	264	4	set	set	NOUN
ejpam-6600	264	5	i	i	NOUN
ejpam-6600	264	6	=	=	NOUN
ejpam-6600	265	1	1	1	X
ejpam-6600	265	2	.	.	X
ejpam-6600	265	3	step	step	NOUN
ejpam-6600	265	4	1	1	NUM
ejpam-6600	265	5	:	:	PUNCT
ejpam-6600	265	6	i	i	NOUN
ejpam-6600	265	7	=	=	NOUN
ejpam-6600	265	8	1	1	NUM
ejpam-6600	265	9	≤	≤	NUM
ejpam-6600	265	10	19	19	NUM
ejpam-6600	265	11	,	,	PUNCT
ejpam-6600	265	12	then	then	ADV
ejpam-6600	265	13	continue	continue	VERB
ejpam-6600	265	14	to	to	PART
ejpam-6600	265	15	step	step	VERB
ejpam-6600	265	16	2	2	NUM
ejpam-6600	265	17	.	.	PUNCT
ejpam-6600	265	18	step	step	NOUN
ejpam-6600	265	19	2	2	NUM
ejpam-6600	265	20	:	:	PUNCT
ejpam-6600	265	21	for	for	ADP
ejpam-6600	265	22	each	each	DET
ejpam-6600	265	23	s1	s1	NOUN
ejpam-6600	265	24	,	,	PUNCT
ejpam-6600	265	25	s2	s2	PROPN
ejpam-6600	265	26	,	,	PUNCT
ejpam-6600	265	27	s3	s3	PROPN
ejpam-6600	265	28	∈	∈	PROPN
ejpam-6600	265	29	s1	s1	NOUN
ejpam-6600	265	30	,	,	PUNCT
ejpam-6600	265	31	f	f	PROPN
ejpam-6600	265	32	(	(	PUNCT
ejpam-6600	265	33	v1	v1	PROPN
ejpam-6600	265	34	,	,	PUNCT
ejpam-6600	265	35	v1+sj	v1+sj	NOUN
ejpam-6600	265	36	)	)	PUNCT
ejpam-6600	266	1	=	=	SYM
ejpam-6600	266	2	(	(	PUNCT
ejpam-6600	266	3	j	j	NOUN
ejpam-6600	266	4	−	−	PROPN
ejpam-6600	266	5	1	1	NUM
ejpam-6600	266	6	)	)	PUNCT
ejpam-6600	266	7	p+	p+	VERB
ejpam-6600	266	8	1	1	NUM
ejpam-6600	266	9	.	.	PUNCT
ejpam-6600	267	1	that	that	PRON
ejpam-6600	267	2	is	be	AUX
ejpam-6600	267	3	,	,	PUNCT
ejpam-6600	267	4	f(v1	f(v1	ADJ
ejpam-6600	267	5	,	,	PUNCT
ejpam-6600	267	6	v2	v2	NOUN
ejpam-6600	267	7	)	)	PUNCT
ejpam-6600	267	8	=	=	PUNCT
ejpam-6600	268	1	(	(	PUNCT
ejpam-6600	268	2	1	1	NUM
ejpam-6600	268	3	−	−	NUM
ejpam-6600	268	4	1)19	1)19	NUM
ejpam-6600	268	5	+	+	CCONJ
ejpam-6600	268	6	1	1	NUM
ejpam-6600	268	7	=	=	SYM
ejpam-6600	268	8	1	1	NUM
ejpam-6600	268	9	,	,	PUNCT
ejpam-6600	268	10	f(v1	f(v1	NOUN
ejpam-6600	268	11	,	,	PUNCT
ejpam-6600	268	12	v8	v8	PROPN
ejpam-6600	268	13	)	)	PUNCT
ejpam-6600	268	14	=	=	PUNCT
ejpam-6600	269	1	(	(	PUNCT
ejpam-6600	269	2	2	2	NUM
ejpam-6600	269	3	−	−	NOUN
ejpam-6600	269	4	1)19	1)19	NUM
ejpam-6600	270	1	+	+	CCONJ
ejpam-6600	270	2	1	1	NUM
ejpam-6600	270	3	=	=	SYM
ejpam-6600	270	4	20	20	NUM
ejpam-6600	270	5	,	,	PUNCT
ejpam-6600	270	6	f(v1	f(v1	NOUN
ejpam-6600	270	7	,	,	PUNCT
ejpam-6600	270	8	v9	v9	PROPN
ejpam-6600	270	9	)	)	PUNCT
ejpam-6600	270	10	=	=	PUNCT
ejpam-6600	271	1	(	(	PUNCT
ejpam-6600	271	2	3−	3−	NUM
ejpam-6600	271	3	1)19	1)19	NUM
ejpam-6600	271	4	+	+	CCONJ
ejpam-6600	271	5	1	1	NUM
ejpam-6600	271	6	=	=	SYM
ejpam-6600	271	7	39	39	NUM
ejpam-6600	271	8	.	.	PUNCT
ejpam-6600	272	1	step	step	NOUN
ejpam-6600	272	2	3	3	NUM
ejpam-6600	272	3	:	:	PUNCT
ejpam-6600	272	4	i	i	NOUN
ejpam-6600	272	5	=	=	NOUN
ejpam-6600	272	6	1	1	NUM
ejpam-6600	273	1	+	+	SYM
ejpam-6600	273	2	1	1	NUM
ejpam-6600	273	3	=	=	SYM
ejpam-6600	273	4	2	2	NUM
ejpam-6600	273	5	,	,	PUNCT
ejpam-6600	273	6	go	go	VERB
ejpam-6600	273	7	back	back	ADV
ejpam-6600	273	8	to	to	PART
ejpam-6600	273	9	step	step	NOUN
ejpam-6600	273	10	1	1	NUM
ejpam-6600	273	11	.	.	PUNCT
ejpam-6600	274	1	step	step	NOUN
ejpam-6600	274	2	1	1	NUM
ejpam-6600	274	3	:	:	PUNCT
ejpam-6600	275	1	i	i	NOUN
ejpam-6600	275	2	=	=	NOUN
ejpam-6600	275	3	2	2	NUM
ejpam-6600	275	4	≤	≤	NUM
ejpam-6600	275	5	19	19	NUM
ejpam-6600	275	6	,	,	PUNCT
ejpam-6600	275	7	then	then	ADV
ejpam-6600	275	8	continue	continue	VERB
ejpam-6600	275	9	to	to	PART
ejpam-6600	275	10	step	step	VERB
ejpam-6600	275	11	2	2	NUM
ejpam-6600	275	12	.	.	PUNCT
ejpam-6600	275	13	step	step	NOUN
ejpam-6600	275	14	2	2	NUM
ejpam-6600	275	15	:	:	PUNCT
ejpam-6600	275	16	for	for	ADP
ejpam-6600	275	17	each	each	DET
ejpam-6600	275	18	s1	s1	NOUN
ejpam-6600	275	19	,	,	PUNCT
ejpam-6600	275	20	s2	s2	PROPN
ejpam-6600	275	21	,	,	PUNCT
ejpam-6600	275	22	s3	s3	PROPN
ejpam-6600	275	23	∈	∈	PROPN
ejpam-6600	275	24	s1	s1	NOUN
ejpam-6600	275	25	,	,	PUNCT
ejpam-6600	275	26	f	f	PROPN
ejpam-6600	275	27	(	(	PUNCT
ejpam-6600	275	28	v2	v2	PROPN
ejpam-6600	275	29	,	,	PUNCT
ejpam-6600	275	30	v2+sj	v2+sj	PROPN
ejpam-6600	275	31	)	)	PUNCT
ejpam-6600	276	1	=	=	PRON
ejpam-6600	276	2	(	(	PUNCT
ejpam-6600	276	3	j	j	NOUN
ejpam-6600	276	4	−	−	PROPN
ejpam-6600	276	5	1	1	NUM
ejpam-6600	276	6	)	)	PUNCT
ejpam-6600	276	7	p+	p+	NOUN
ejpam-6600	276	8	2	2	NUM
ejpam-6600	276	9	.	.	X
ejpam-6600	276	10	that	that	PRON
ejpam-6600	276	11	is	be	AUX
ejpam-6600	276	12	,	,	PUNCT
ejpam-6600	276	13	f(v2	f(v2	NOUN
ejpam-6600	276	14	,	,	PUNCT
ejpam-6600	276	15	v3	v3	PROPN
ejpam-6600	276	16	)	)	PUNCT
ejpam-6600	276	17	=	=	PUNCT
ejpam-6600	277	1	(	(	PUNCT
ejpam-6600	277	2	1	1	NUM
ejpam-6600	277	3	−	−	NUM
ejpam-6600	277	4	1)19	1)19	NUM
ejpam-6600	278	1	+	+	CCONJ
ejpam-6600	278	2	2	2	NUM
ejpam-6600	278	3	=	=	SYM
ejpam-6600	278	4	2	2	NUM
ejpam-6600	278	5	,	,	PUNCT
ejpam-6600	278	6	f(v2	f(v2	NOUN
ejpam-6600	278	7	,	,	PUNCT
ejpam-6600	278	8	v9	v9	NOUN
ejpam-6600	278	9	)	)	PUNCT
ejpam-6600	279	1	=	=	PUNCT
ejpam-6600	279	2	(	(	PUNCT
ejpam-6600	279	3	2	2	NUM
ejpam-6600	279	4	−	−	NOUN
ejpam-6600	279	5	1)19	1)19	NUM
ejpam-6600	280	1	+	+	CCONJ
ejpam-6600	280	2	2	2	NUM
ejpam-6600	280	3	=	=	SYM
ejpam-6600	280	4	21	21	NUM
ejpam-6600	280	5	,	,	PUNCT
ejpam-6600	280	6	f(v2	f(v2	NOUN
ejpam-6600	280	7	,	,	PUNCT
ejpam-6600	280	8	v10	v10	NOUN
ejpam-6600	280	9	)	)	PUNCT
ejpam-6600	280	10	=	=	PUNCT
ejpam-6600	280	11	(	(	PUNCT
ejpam-6600	280	12	3−	3−	NUM
ejpam-6600	280	13	1)19	1)19	NUM
ejpam-6600	280	14	+	+	CCONJ
ejpam-6600	280	15	2	2	NUM
ejpam-6600	280	16	=	=	SYM
ejpam-6600	280	17	40	40	NUM
ejpam-6600	280	18	.	.	PUNCT
ejpam-6600	281	1	step	step	NOUN
ejpam-6600	281	2	3	3	NUM
ejpam-6600	281	3	:	:	PUNCT
ejpam-6600	281	4	i	i	NOUN
ejpam-6600	281	5	=	=	NOUN
ejpam-6600	281	6	2	2	NUM
ejpam-6600	281	7	+	+	CCONJ
ejpam-6600	281	8	1	1	NUM
ejpam-6600	281	9	=	=	SYM
ejpam-6600	281	10	3	3	NUM
ejpam-6600	281	11	,	,	PUNCT
ejpam-6600	281	12	go	go	VERB
ejpam-6600	281	13	back	back	ADV
ejpam-6600	281	14	to	to	PART
ejpam-6600	281	15	step	step	NOUN
ejpam-6600	281	16	1	1	NUM
ejpam-6600	281	17	.	.	PUNCT
ejpam-6600	282	1	we	we	PRON
ejpam-6600	282	2	repeat	repeat	VERB
ejpam-6600	282	3	step1	step1	PROPN
ejpam-6600	282	4	,	,	PUNCT
ejpam-6600	282	5	step2	step2	PROPN
ejpam-6600	282	6	,	,	PUNCT
ejpam-6600	282	7	and	and	CCONJ
ejpam-6600	282	8	step3	step3	PROPN
ejpam-6600	282	9	and	and	CCONJ
ejpam-6600	282	10	get	get	VERB
ejpam-6600	282	11	:	:	PUNCT
ejpam-6600	282	12	f(v3	f(v3	ADJ
ejpam-6600	282	13	,	,	PUNCT
ejpam-6600	282	14	v4	v4	NOUN
ejpam-6600	282	15	)	)	PUNCT
ejpam-6600	282	16	=	=	SYM
ejpam-6600	282	17	3	3	NUM
ejpam-6600	282	18	,	,	PUNCT
ejpam-6600	282	19	f(v3	f(v3	NOUN
ejpam-6600	282	20	,	,	PUNCT
ejpam-6600	282	21	v10	v10	NOUN
ejpam-6600	282	22	)	)	PUNCT
ejpam-6600	282	23	=	=	SYM
ejpam-6600	282	24	22	22	NUM
ejpam-6600	282	25	,	,	PUNCT
ejpam-6600	282	26	f(v3	f(v3	NOUN
ejpam-6600	282	27	,	,	PUNCT
ejpam-6600	282	28	v11	v11	NOUN
ejpam-6600	282	29	)	)	PUNCT
ejpam-6600	282	30	=	=	SYM
ejpam-6600	282	31	41	41	NUM
ejpam-6600	282	32	,	,	PUNCT
ejpam-6600	282	33	f(v4	f(v4	PRON
ejpam-6600	282	34	,	,	PUNCT
ejpam-6600	282	35	v5	v5	PROPN
ejpam-6600	282	36	)	)	PUNCT
ejpam-6600	282	37	=	=	SYM
ejpam-6600	282	38	4	4	NUM
ejpam-6600	282	39	,	,	PUNCT
ejpam-6600	282	40	f(v4	f(v4	PRON
ejpam-6600	282	41	,	,	PUNCT
ejpam-6600	282	42	v11	v11	NOUN
ejpam-6600	282	43	)	)	PUNCT
ejpam-6600	282	44	=	=	SYM
ejpam-6600	282	45	23	23	NUM
ejpam-6600	282	46	,	,	PUNCT
ejpam-6600	282	47	f(v4	f(v4	PRON
ejpam-6600	282	48	,	,	PUNCT
ejpam-6600	282	49	v12	v12	VERB
ejpam-6600	282	50	)	)	PUNCT
ejpam-6600	282	51	=	=	SYM
ejpam-6600	282	52	42	42	NUM
ejpam-6600	282	53	,	,	PUNCT
ejpam-6600	282	54	f(v5	f(v5	NOUN
ejpam-6600	282	55	,	,	PUNCT
ejpam-6600	282	56	v6	v6	NOUN
ejpam-6600	282	57	)	)	PUNCT
ejpam-6600	282	58	=	=	SYM
ejpam-6600	282	59	5	5	NUM
ejpam-6600	282	60	,	,	PUNCT
ejpam-6600	282	61	f(v5	f(v5	NOUN
ejpam-6600	282	62	,	,	PUNCT
ejpam-6600	282	63	v12	v12	VERB
ejpam-6600	282	64	)	)	PUNCT
ejpam-6600	282	65	=	=	SYM
ejpam-6600	282	66	24	24	NUM
ejpam-6600	282	67	,	,	PUNCT
ejpam-6600	282	68	f(v5	f(v5	NOUN
ejpam-6600	282	69	,	,	PUNCT
ejpam-6600	282	70	v13	v13	PROPN
ejpam-6600	282	71	)	)	PUNCT
ejpam-6600	282	72	=	=	SYM
ejpam-6600	282	73	43	43	NUM
ejpam-6600	282	74	,	,	PUNCT
ejpam-6600	282	75	f(v6	f(v6	NOUN
ejpam-6600	282	76	,	,	PUNCT
ejpam-6600	282	77	v7	v7	NUM
ejpam-6600	282	78	)	)	PUNCT
ejpam-6600	282	79	=	=	SYM
ejpam-6600	282	80	6	6	NUM
ejpam-6600	282	81	,	,	PUNCT
ejpam-6600	282	82	f(v6	f(v6	NOUN
ejpam-6600	282	83	,	,	PUNCT
ejpam-6600	282	84	v13	v13	PROPN
ejpam-6600	282	85	)	)	PUNCT
ejpam-6600	282	86	=	=	SYM
ejpam-6600	282	87	25	25	NUM
ejpam-6600	282	88	,	,	PUNCT
ejpam-6600	282	89	f(v6	f(v6	NOUN
ejpam-6600	282	90	,	,	PUNCT
ejpam-6600	282	91	v14	v14	PROPN
ejpam-6600	282	92	)	)	PUNCT
ejpam-6600	282	93	=	=	SYM
ejpam-6600	282	94	44	44	NUM
ejpam-6600	282	95	,	,	PUNCT
ejpam-6600	282	96	f(v7	f(v7	NOUN
ejpam-6600	282	97	,	,	PUNCT
ejpam-6600	282	98	v8	v8	PROPN
ejpam-6600	282	99	)	)	PUNCT
ejpam-6600	282	100	=	=	SYM
ejpam-6600	282	101	7	7	NUM
ejpam-6600	282	102	,	,	PUNCT
ejpam-6600	282	103	f(v7	f(v7	NOUN
ejpam-6600	282	104	,	,	PUNCT
ejpam-6600	282	105	v14	v14	NOUN
ejpam-6600	282	106	)	)	PUNCT
ejpam-6600	282	107	=	=	SYM
ejpam-6600	282	108	26	26	NUM
ejpam-6600	282	109	,	,	PUNCT
ejpam-6600	282	110	f(v7	f(v7	NOUN
ejpam-6600	282	111	,	,	PUNCT
ejpam-6600	282	112	v15	v15	NOUN
ejpam-6600	282	113	)	)	PUNCT
ejpam-6600	282	114	=	=	SYM
ejpam-6600	282	115	45	45	NUM
ejpam-6600	282	116	,	,	PUNCT
ejpam-6600	282	117	f(v8	f(v8	NOUN
ejpam-6600	282	118	,	,	PUNCT
ejpam-6600	282	119	v9	v9	PROPN
ejpam-6600	282	120	)	)	PUNCT
ejpam-6600	282	121	=	=	SYM
ejpam-6600	282	122	8	8	NUM
ejpam-6600	282	123	,	,	PUNCT
ejpam-6600	282	124	f(v8	f(v8	NOUN
ejpam-6600	282	125	,	,	PUNCT
ejpam-6600	282	126	v15	v15	NOUN
ejpam-6600	282	127	)	)	PUNCT
ejpam-6600	282	128	=	=	SYM
ejpam-6600	282	129	27	27	NUM
ejpam-6600	282	130	,	,	PUNCT
ejpam-6600	282	131	f(v8	f(v8	NOUN
ejpam-6600	282	132	,	,	PUNCT
ejpam-6600	282	133	v16	v16	NOUN
ejpam-6600	282	134	)	)	PUNCT
ejpam-6600	282	135	=	=	SYM
ejpam-6600	282	136	46	46	NUM
ejpam-6600	282	137	,	,	PUNCT
ejpam-6600	282	138	f(v9	f(v9	NOUN
ejpam-6600	282	139	,	,	PUNCT
ejpam-6600	282	140	v10	v10	NOUN
ejpam-6600	282	141	)	)	PUNCT
ejpam-6600	282	142	=	=	SYM
ejpam-6600	282	143	9	9	NUM
ejpam-6600	282	144	,	,	PUNCT
ejpam-6600	282	145	f(v9	f(v9	NOUN
ejpam-6600	282	146	,	,	PUNCT
ejpam-6600	282	147	v16	v16	NOUN
ejpam-6600	282	148	)	)	PUNCT
ejpam-6600	282	149	=	=	SYM
ejpam-6600	283	1	28	28	NUM
ejpam-6600	283	2	,	,	PUNCT
ejpam-6600	283	3	f(v9	f(v9	NOUN
ejpam-6600	283	4	,	,	PUNCT
ejpam-6600	283	5	v17	v17	NOUN
ejpam-6600	283	6	)	)	PUNCT
ejpam-6600	283	7	=	=	SYM
ejpam-6600	284	1	47	47	NUM
ejpam-6600	284	2	,	,	PUNCT
ejpam-6600	284	3	f(v10	f(v10	NOUN
ejpam-6600	284	4	,	,	PUNCT
ejpam-6600	284	5	v11	v11	NOUN
ejpam-6600	284	6	)	)	PUNCT
ejpam-6600	284	7	=	=	SYM
ejpam-6600	284	8	10	10	NUM
ejpam-6600	284	9	,	,	PUNCT
ejpam-6600	284	10	f(v10	f(v10	NOUN
ejpam-6600	284	11	,	,	PUNCT
ejpam-6600	284	12	v17	v17	NOUN
ejpam-6600	284	13	)	)	PUNCT
ejpam-6600	284	14	=	=	SYM
ejpam-6600	284	15	29	29	NUM
ejpam-6600	284	16	,	,	PUNCT
ejpam-6600	284	17	f(v10	f(v10	NOUN
ejpam-6600	284	18	,	,	PUNCT
ejpam-6600	284	19	v18	v18	NOUN
ejpam-6600	284	20	)	)	PUNCT
ejpam-6600	284	21	=	=	SYM
ejpam-6600	284	22	48	48	NUM
ejpam-6600	284	23	,	,	PUNCT
ejpam-6600	284	24	f(v11	f(v11	NOUN
ejpam-6600	284	25	,	,	PUNCT
ejpam-6600	284	26	v12	v12	VERB
ejpam-6600	284	27	)	)	PUNCT
ejpam-6600	284	28	=	=	SYM
ejpam-6600	284	29	11	11	NUM
ejpam-6600	284	30	,	,	PUNCT
ejpam-6600	284	31	f(v11	f(v11	ADJ
ejpam-6600	284	32	,	,	PUNCT
ejpam-6600	284	33	v18	v18	NOUN
ejpam-6600	284	34	)	)	PUNCT
ejpam-6600	284	35	=	=	SYM
ejpam-6600	284	36	30	30	NUM
ejpam-6600	284	37	,	,	PUNCT
ejpam-6600	284	38	f(v11	f(v11	NOUN
ejpam-6600	284	39	,	,	PUNCT
ejpam-6600	284	40	v19	v19	PROPN
ejpam-6600	284	41	)	)	PUNCT
ejpam-6600	284	42	=	=	SYM
ejpam-6600	284	43	49	49	NUM
ejpam-6600	284	44	,	,	PUNCT
ejpam-6600	284	45	f(v12	f(v12	NUM
ejpam-6600	284	46	,	,	PUNCT
ejpam-6600	284	47	v13	v13	NOUN
ejpam-6600	284	48	)	)	PUNCT
ejpam-6600	284	49	=	=	SYM
ejpam-6600	284	50	12	12	NUM
ejpam-6600	284	51	,	,	PUNCT
ejpam-6600	284	52	f(v12	f(v12	NUM
ejpam-6600	284	53	,	,	PUNCT
ejpam-6600	284	54	v19	v19	PROPN
ejpam-6600	284	55	)	)	PUNCT
ejpam-6600	284	56	=	=	SYM
ejpam-6600	285	1	31	31	NUM
ejpam-6600	285	2	,	,	PUNCT
ejpam-6600	285	3	f(v12	f(v12	ADJ
ejpam-6600	285	4	,	,	PUNCT
ejpam-6600	285	5	v1	v1	NOUN
ejpam-6600	285	6	)	)	PUNCT
ejpam-6600	285	7	=	=	SYM
ejpam-6600	285	8	50	50	NUM
ejpam-6600	285	9	,	,	PUNCT
ejpam-6600	285	10	f(v13	f(v13	NOUN
ejpam-6600	285	11	,	,	PUNCT
ejpam-6600	285	12	v14	v14	NOUN
ejpam-6600	285	13	)	)	PUNCT
ejpam-6600	285	14	=	=	SYM
ejpam-6600	285	15	13	13	NUM
ejpam-6600	285	16	,	,	PUNCT
ejpam-6600	285	17	f(v13	f(v13	NOUN
ejpam-6600	285	18	,	,	PUNCT
ejpam-6600	285	19	v1	v1	NOUN
ejpam-6600	285	20	)	)	PUNCT
ejpam-6600	285	21	=	=	SYM
ejpam-6600	285	22	32	32	NUM
ejpam-6600	285	23	,	,	PUNCT
ejpam-6600	285	24	f(v13	f(v13	NOUN
ejpam-6600	285	25	,	,	PUNCT
ejpam-6600	285	26	v2	v2	NOUN
ejpam-6600	285	27	)	)	PUNCT
ejpam-6600	285	28	=	=	SYM
ejpam-6600	285	29	51	51	NUM
ejpam-6600	285	30	,	,	PUNCT
ejpam-6600	285	31	f(v14	f(v14	ADJ
ejpam-6600	285	32	,	,	PUNCT
ejpam-6600	285	33	v15	v15	NOUN
ejpam-6600	285	34	)	)	PUNCT
ejpam-6600	285	35	=	=	SYM
ejpam-6600	285	36	14	14	NUM
ejpam-6600	285	37	,	,	PUNCT
ejpam-6600	285	38	f(v14	f(v14	ADJ
ejpam-6600	285	39	,	,	PUNCT
ejpam-6600	285	40	v2	v2	NOUN
ejpam-6600	285	41	)	)	PUNCT
ejpam-6600	285	42	=	=	SYM
ejpam-6600	285	43	33	33	NUM
ejpam-6600	285	44	,	,	PUNCT
ejpam-6600	285	45	f(v14	f(v14	ADJ
ejpam-6600	285	46	,	,	PUNCT
ejpam-6600	285	47	v3	v3	PROPN
ejpam-6600	285	48	)	)	PUNCT
ejpam-6600	285	49	=	=	SYM
ejpam-6600	286	1	52	52	NUM
ejpam-6600	286	2	,	,	PUNCT
ejpam-6600	286	3	f(v15	f(v15	ADJ
ejpam-6600	286	4	,	,	PUNCT
ejpam-6600	286	5	v16	v16	NOUN
ejpam-6600	286	6	)	)	PUNCT
ejpam-6600	286	7	=	=	SYM
ejpam-6600	287	1	15	15	NUM
ejpam-6600	287	2	,	,	PUNCT
ejpam-6600	287	3	f(v15	f(v15	ADJ
ejpam-6600	287	4	,	,	PUNCT
ejpam-6600	287	5	v3	v3	PROPN
ejpam-6600	287	6	)	)	PUNCT
ejpam-6600	287	7	=	=	SYM
ejpam-6600	287	8	34	34	NUM
ejpam-6600	287	9	,	,	PUNCT
ejpam-6600	287	10	f(v15	f(v15	X
ejpam-6600	287	11	,	,	PUNCT
ejpam-6600	287	12	v4	v4	NOUN
ejpam-6600	287	13	)	)	PUNCT
ejpam-6600	287	14	=	=	SYM
ejpam-6600	287	15	53	53	NUM
ejpam-6600	287	16	,	,	PUNCT
ejpam-6600	287	17	f(v16	f(v16	NOUN
ejpam-6600	287	18	,	,	PUNCT
ejpam-6600	287	19	v17	v17	NOUN
ejpam-6600	287	20	)	)	PUNCT
ejpam-6600	287	21	=	=	SYM
ejpam-6600	287	22	16	16	NUM
ejpam-6600	287	23	,	,	PUNCT
ejpam-6600	287	24	f(v16	f(v16	NOUN
ejpam-6600	287	25	,	,	PUNCT
ejpam-6600	287	26	v4	v4	NOUN
ejpam-6600	287	27	)	)	PUNCT
ejpam-6600	287	28	=	=	SYM
ejpam-6600	287	29	35	35	NUM
ejpam-6600	287	30	,	,	PUNCT
ejpam-6600	287	31	f(v16	f(v16	NOUN
ejpam-6600	287	32	,	,	PUNCT
ejpam-6600	287	33	v5	v5	PROPN
ejpam-6600	287	34	)	)	PUNCT
ejpam-6600	287	35	=	=	SYM
ejpam-6600	287	36	54	54	NUM
ejpam-6600	287	37	,	,	PUNCT
ejpam-6600	287	38	f(v17	f(v17	NOUN
ejpam-6600	287	39	,	,	PUNCT
ejpam-6600	287	40	v18	v18	NOUN
ejpam-6600	287	41	)	)	PUNCT
ejpam-6600	287	42	=	=	SYM
ejpam-6600	287	43	17	17	NUM
ejpam-6600	287	44	,	,	PUNCT
ejpam-6600	287	45	f(v17	f(v17	NOUN
ejpam-6600	287	46	,	,	PUNCT
ejpam-6600	287	47	v5	v5	PROPN
ejpam-6600	287	48	)	)	PUNCT
ejpam-6600	287	49	=	=	SYM
ejpam-6600	287	50	36	36	NUM
ejpam-6600	287	51	,	,	PUNCT
ejpam-6600	287	52	f(v17	f(v17	NOUN
ejpam-6600	287	53	,	,	PUNCT
ejpam-6600	287	54	v6	v6	NOUN
ejpam-6600	287	55	)	)	PUNCT
ejpam-6600	287	56	=	=	SYM
ejpam-6600	288	1	55	55	NUM
ejpam-6600	288	2	,	,	PUNCT
ejpam-6600	288	3	f(v18	f(v18	NOUN
ejpam-6600	288	4	,	,	PUNCT
ejpam-6600	288	5	v19	v19	PROPN
ejpam-6600	288	6	)	)	PUNCT
ejpam-6600	288	7	=	=	SYM
ejpam-6600	288	8	18	18	NUM
ejpam-6600	288	9	,	,	PUNCT
ejpam-6600	288	10	f(v18	f(v18	NOUN
ejpam-6600	288	11	,	,	PUNCT
ejpam-6600	288	12	v6	v6	NOUN
ejpam-6600	288	13	)	)	PUNCT
ejpam-6600	289	1	=	=	SYM
ejpam-6600	289	2	37	37	NUM
ejpam-6600	289	3	,	,	PUNCT
ejpam-6600	289	4	f(v18	f(v18	NOUN
ejpam-6600	289	5	,	,	PUNCT
ejpam-6600	289	6	v7	v7	NOUN
ejpam-6600	289	7	)	)	PUNCT
ejpam-6600	289	8	=	=	SYM
ejpam-6600	289	9	56	56	NUM
ejpam-6600	289	10	,	,	PUNCT
ejpam-6600	289	11	f(v19	f(v19	ADJ
ejpam-6600	289	12	,	,	PUNCT
ejpam-6600	289	13	v1	v1	NOUN
ejpam-6600	289	14	)	)	PUNCT
ejpam-6600	289	15	=	=	SYM
ejpam-6600	289	16	19	19	NUM
ejpam-6600	289	17	,	,	PUNCT
ejpam-6600	289	18	f(v19	f(v19	ADJ
ejpam-6600	289	19	,	,	PUNCT
ejpam-6600	289	20	v7	v7	NUM
ejpam-6600	289	21	)	)	PUNCT
ejpam-6600	289	22	=	=	SYM
ejpam-6600	289	23	38	38	NUM
ejpam-6600	289	24	,	,	PUNCT
ejpam-6600	289	25	f(v19	f(v19	ADJ
ejpam-6600	289	26	,	,	PUNCT
ejpam-6600	289	27	v8	v8	PROPN
ejpam-6600	289	28	)	)	PUNCT
ejpam-6600	289	29	=	=	SYM
ejpam-6600	290	1	57	57	NUM
ejpam-6600	290	2	.	.	PUNCT
ejpam-6600	291	1	step	step	NOUN
ejpam-6600	291	2	4	4	NUM
ejpam-6600	291	3	:	:	PUNCT
ejpam-6600	291	4	for	for	ADP
ejpam-6600	291	5	each	each	PRON
ejpam-6600	291	6	k	k	NOUN
ejpam-6600	291	7	=	=	SYM
ejpam-6600	291	8	1	1	NUM
ejpam-6600	291	9	,	,	PUNCT
ejpam-6600	291	10	2	2	NUM
ejpam-6600	291	11	,	,	PUNCT
ejpam-6600	291	12	3	3	NUM
ejpam-6600	291	13	,	,	PUNCT
ejpam-6600	291	14	·	·	PUNCT
ejpam-6600	291	15	·	·	PUNCT
ejpam-6600	291	16	·	·	PUNCT
ejpam-6600	291	17	,	,	PUNCT
ejpam-6600	291	18	19	19	NUM
ejpam-6600	291	19	,	,	PUNCT
ejpam-6600	291	20	find	find	VERB
ejpam-6600	291	21	the	the	DET
ejpam-6600	291	22	weight	weight	NOUN
ejpam-6600	291	23	of	of	ADP
ejpam-6600	291	24	the	the	DET
ejpam-6600	291	25	vertex	vertex	NOUN
ejpam-6600	291	26	vk	vk	NOUN
ejpam-6600	291	27	using	use	VERB
ejpam-6600	291	28	the	the	DET
ejpam-6600	291	29	following	follow	VERB
ejpam-6600	291	30	mapping	mapping	NOUN
ejpam-6600	291	31	:	:	PUNCT
ejpam-6600	291	32	fw(vk	fw(vk	PROPN
ejpam-6600	291	33	)	)	PUNCT
ejpam-6600	292	1	=	=	SYM
ejpam-6600	292	2	∑6	∑6	PROPN
ejpam-6600	292	3	j=1	j=1	PROPN
ejpam-6600	292	4	f(vk	f(vk	PROPN
ejpam-6600	292	5	,	,	PUNCT
ejpam-6600	292	6	vk+sj	vk+sj	NOUN
ejpam-6600	292	7	)	)	PUNCT
ejpam-6600	293	1	=	=	SYM
ejpam-6600	294	1	6k	6k	NOUN
ejpam-6600	294	2	−	−	NOUN
ejpam-6600	295	1	∑3	∑3	NOUN
ejpam-6600	295	2	j=1	j=1	ADJ
ejpam-6600	295	3	sj	sj	PROPN
ejpam-6600	295	4	=	=	PUNCT
ejpam-6600	295	5	6k	6k	PROPN
ejpam-6600	295	6	−	−	PROPN
ejpam-6600	296	1	16	16	NUM
ejpam-6600	296	2	(	(	PUNCT
ejpam-6600	296	3	mod	mod	PROPN
ejpam-6600	296	4	p	p	NOUN
ejpam-6600	296	5	)	)	PUNCT
ejpam-6600	296	6	.	.	PUNCT
ejpam-6600	297	1	so	so	ADV
ejpam-6600	297	2	fw	fw	PROPN
ejpam-6600	297	3	(	(	PUNCT
ejpam-6600	297	4	v1	v1	NOUN
ejpam-6600	297	5	)	)	PUNCT
ejpam-6600	297	6	=	=	SYM
ejpam-6600	298	1	6	6	NUM
ejpam-6600	298	2	·	·	SYM
ejpam-6600	298	3	1−	1−	NUM
ejpam-6600	298	4	16	16	NUM
ejpam-6600	298	5	=	=	SYM
ejpam-6600	298	6	−10	−10	NUM
ejpam-6600	298	7	≡	≡	PROPN
ejpam-6600	298	8	9	9	NUM
ejpam-6600	298	9	(	(	PUNCT
ejpam-6600	298	10	mod	mod	PROPN
ejpam-6600	298	11	19	19	NUM
ejpam-6600	298	12	)	)	PUNCT
ejpam-6600	298	13	.	.	PUNCT
ejpam-6600	299	1	equivalently	equivalently	ADV
ejpam-6600	299	2	,	,	PUNCT
ejpam-6600	299	3	fw	fw	PROPN
ejpam-6600	299	4	(	(	PUNCT
ejpam-6600	299	5	v1	v1	NOUN
ejpam-6600	299	6	)	)	PUNCT
ejpam-6600	299	7	=	=	SYM
ejpam-6600	299	8	f(v1	f(v1	NOUN
ejpam-6600	299	9	,	,	PUNCT
ejpam-6600	299	10	v2)+f(v1	v2)+f(v1	X
ejpam-6600	299	11	,	,	PUNCT
ejpam-6600	299	12	v8)+f(v1	v8)+f(v1	NOUN
ejpam-6600	299	13	,	,	PUNCT
ejpam-6600	299	14	v9)+f(v12	v9)+f(v12	VERB
ejpam-6600	299	15	,	,	PUNCT
ejpam-6600	299	16	v1)+f(v13	v1)+f(v13	PROPN
ejpam-6600	299	17	,	,	PUNCT
ejpam-6600	299	18	v1)+f(v19	v1)+f(v19	NOUN
ejpam-6600	299	19	,	,	PUNCT
ejpam-6600	299	20	v1	v1	NOUN
ejpam-6600	299	21	)	)	PUNCT
ejpam-6600	299	22	=	=	SYM
ejpam-6600	299	23	1	1	NUM
ejpam-6600	299	24	+	+	NUM
ejpam-6600	299	25	20	20	NUM
ejpam-6600	299	26	+	+	NUM
ejpam-6600	299	27	39	39	NUM
ejpam-6600	299	28	+	+	NUM
ejpam-6600	299	29	50	50	NUM
ejpam-6600	299	30	+	+	NUM
ejpam-6600	299	31	32	32	NUM
ejpam-6600	299	32	+	+	SYM
ejpam-6600	299	33	19	19	NUM
ejpam-6600	299	34	≡	≡	PROPN
ejpam-6600	299	35	9	9	NUM
ejpam-6600	299	36	(	(	PUNCT
ejpam-6600	299	37	mod	mod	PROPN
ejpam-6600	299	38	19	19	NUM
ejpam-6600	299	39	)	)	PUNCT
ejpam-6600	299	40	.	.	PUNCT
ejpam-6600	300	1	by	by	ADP
ejpam-6600	300	2	the	the	DET
ejpam-6600	300	3	same	same	ADJ
ejpam-6600	300	4	function	function	NOUN
ejpam-6600	300	5	modulo	modulo	VERB
ejpam-6600	300	6	19	19	NUM
ejpam-6600	300	7	,	,	PUNCT
ejpam-6600	300	8	we	we	PRON
ejpam-6600	300	9	get	get	VERB
ejpam-6600	300	10	:	:	PUNCT
ejpam-6600	300	11	fw(v2	fw(v2	NOUN
ejpam-6600	300	12	)	)	PUNCT
ejpam-6600	300	13	=	=	SYM
ejpam-6600	300	14	15	15	NUM
ejpam-6600	300	15	,	,	PUNCT
ejpam-6600	300	16	fw(v3	fw(v3	NOUN
ejpam-6600	300	17	)	)	PUNCT
ejpam-6600	300	18	=	=	SYM
ejpam-6600	300	19	2	2	NUM
ejpam-6600	300	20	,	,	PUNCT
ejpam-6600	300	21	fw(v4	fw(v4	PRON
ejpam-6600	300	22	)	)	PUNCT
ejpam-6600	300	23	=	=	SYM
ejpam-6600	300	24	8	8	NUM
ejpam-6600	300	25	,	,	PUNCT
ejpam-6600	300	26	fw(v5	fw(v5	NOUN
ejpam-6600	300	27	)	)	PUNCT
ejpam-6600	301	1	=	=	SYM
ejpam-6600	301	2	14	14	NUM
ejpam-6600	301	3	,	,	PUNCT
ejpam-6600	301	4	fw(v6	fw(v6	NOUN
ejpam-6600	301	5	)	)	PUNCT
ejpam-6600	301	6	=	=	SYM
ejpam-6600	301	7	1	1	NUM
ejpam-6600	301	8	,	,	PUNCT
ejpam-6600	301	9	fw(v7	fw(v7	NOUN
ejpam-6600	301	10	)	)	PUNCT
ejpam-6600	301	11	=	=	SYM
ejpam-6600	301	12	7	7	NUM
ejpam-6600	301	13	,	,	PUNCT
ejpam-6600	301	14	fw(v8	fw(v8	NOUN
ejpam-6600	301	15	)	)	PUNCT
ejpam-6600	301	16	=	=	SYM
ejpam-6600	301	17	13	13	NUM
ejpam-6600	301	18	,	,	PUNCT
ejpam-6600	301	19	fw(v9	fw(v9	NUM
ejpam-6600	301	20	)	)	PUNCT
ejpam-6600	301	21	=	=	SYM
ejpam-6600	301	22	0	0	NUM
ejpam-6600	301	23	,	,	PUNCT
ejpam-6600	301	24	fw(v10	fw(v10	NOUN
ejpam-6600	301	25	)	)	PUNCT
ejpam-6600	301	26	=	=	SYM
ejpam-6600	301	27	6	6	NUM
ejpam-6600	301	28	,	,	PUNCT
ejpam-6600	301	29	fw(v11	fw(v11	ADJ
ejpam-6600	301	30	)	)	PUNCT
ejpam-6600	301	31	=	=	SYM
ejpam-6600	301	32	12	12	NUM
ejpam-6600	301	33	,	,	PUNCT
ejpam-6600	301	34	fw(v12	fw(v12	X
ejpam-6600	301	35	)	)	PUNCT
ejpam-6600	301	36	=	=	SYM
ejpam-6600	301	37	18	18	NUM
ejpam-6600	301	38	,	,	PUNCT
ejpam-6600	301	39	fw(v13	fw(v13	NUM
ejpam-6600	301	40	)	)	PUNCT
ejpam-6600	301	41	=	=	SYM
ejpam-6600	301	42	5	5	NUM
ejpam-6600	301	43	,	,	PUNCT
ejpam-6600	301	44	fw(v14	fw(v14	NOUN
ejpam-6600	301	45	)	)	PUNCT
ejpam-6600	301	46	=	=	SYM
ejpam-6600	301	47	11	11	NUM
ejpam-6600	301	48	,	,	PUNCT
ejpam-6600	301	49	fw(v15	fw(v15	X
ejpam-6600	301	50	)	)	PUNCT
ejpam-6600	301	51	=	=	SYM
ejpam-6600	301	52	17	17	NUM
ejpam-6600	301	53	,	,	PUNCT
ejpam-6600	301	54	fw(v16	fw(v16	NOUN
ejpam-6600	301	55	)	)	PUNCT
ejpam-6600	301	56	=	=	SYM
ejpam-6600	302	1	4	4	NUM
ejpam-6600	302	2	,	,	PUNCT
ejpam-6600	302	3	fw(v17	fw(v17	NOUN
ejpam-6600	302	4	)	)	PUNCT
ejpam-6600	302	5	=	=	SYM
ejpam-6600	302	6	10	10	NUM
ejpam-6600	302	7	,	,	PUNCT
ejpam-6600	302	8	fw(v18	fw(v18	NOUN
ejpam-6600	302	9	)	)	PUNCT
ejpam-6600	302	10	=	=	SYM
ejpam-6600	302	11	16	16	NUM
ejpam-6600	302	12	,	,	PUNCT
ejpam-6600	302	13	fw(v19	fw(v19	NOUN
ejpam-6600	302	14	)	)	PUNCT
ejpam-6600	302	15	=	=	SYM
ejpam-6600	303	1	3	3	X
ejpam-6600	303	2	.	.	PUNCT
ejpam-6600	303	3	a.	a.	PROPN
ejpam-6600	303	4	n.	n.	PROPN
ejpam-6600	303	5	elsawy	elsawy	PROPN
ejpam-6600	303	6	,	,	PUNCT
ejpam-6600	303	7	r.	r.	PROPN
ejpam-6600	303	8	n.	n.	PROPN
ejpam-6600	303	9	almohammadi	almohammadi	PROPN
ejpam-6600	303	10	/	/	SYM
ejpam-6600	303	11	eur	eur	PROPN
ejpam-6600	303	12	.	.	PUNCT
ejpam-6600	304	1	j.	j.	PROPN
ejpam-6600	304	2	pure	pure	PROPN
ejpam-6600	304	3	appl	appl	PROPN
ejpam-6600	304	4	.	.	PROPN
ejpam-6600	304	5	math	math	PROPN
ejpam-6600	304	6	,	,	PUNCT
ejpam-6600	304	7	18	18	NUM
ejpam-6600	304	8	(	(	PUNCT
ejpam-6600	304	9	4	4	NUM
ejpam-6600	304	10	)	)	PUNCT
ejpam-6600	304	11	(	(	PUNCT
ejpam-6600	304	12	2025	2025	NUM
ejpam-6600	304	13	)	)	PUNCT
ejpam-6600	304	14	,	,	PUNCT
ejpam-6600	304	15	6600	6600	NUM
ejpam-6600	304	16	11	11	NUM
ejpam-6600	304	17	of	of	ADP
ejpam-6600	304	18	26	26	NUM
ejpam-6600	304	19	4	4	NUM
ejpam-6600	304	20	.	.	PUNCT
ejpam-6600	304	21	quadruple	quadruple	PROPN
ejpam-6600	304	22	paley	paley	ADJ
ejpam-6600	304	23	graphs	graph	NOUN
ejpam-6600	304	24	similarly	similarly	ADV
ejpam-6600	304	25	like	like	ADP
ejpam-6600	304	26	cubic	cubic	ADJ
ejpam-6600	304	27	paley	paley	PROPN
ejpam-6600	304	28	graphs	graph	NOUN
ejpam-6600	304	29	,	,	PUNCT
ejpam-6600	304	30	quadruple	quadruple	PROPN
ejpam-6600	304	31	paley	paley	ADJ
ejpam-6600	304	32	graphs	graph	NOUN
ejpam-6600	304	33	are	be	AUX
ejpam-6600	304	34	defined	define	VERB
ejpam-6600	304	35	with	with	ADP
ejpam-6600	304	36	the	the	DET
ejpam-6600	304	37	same	same	ADJ
ejpam-6600	304	38	vertex	vertex	NOUN
ejpam-6600	304	39	set	set	NOUN
ejpam-6600	304	40	and	and	CCONJ
ejpam-6600	304	41	two	two	NUM
ejpam-6600	304	42	vertices	vertex	NOUN
ejpam-6600	304	43	are	be	AUX
ejpam-6600	304	44	adjacent	adjacent	ADJ
ejpam-6600	304	45	if	if	SCONJ
ejpam-6600	304	46	their	their	PRON
ejpam-6600	304	47	difference	difference	NOUN
ejpam-6600	304	48	is	be	AUX
ejpam-6600	304	49	a	a	DET
ejpam-6600	304	50	quadruple	quadruple	NOUN
ejpam-6600	304	51	residue	residue	NOUN
ejpam-6600	304	52	in	in	ADP
ejpam-6600	304	53	fq	fq	PROPN
ejpam-6600	304	54	.	.	PROPN
ejpam-6600	304	55	definition	definition	NOUN
ejpam-6600	304	56	4	4	NUM
ejpam-6600	304	57	.	.	PUNCT
ejpam-6600	305	1	[	[	X
ejpam-6600	305	2	28	28	NUM
ejpam-6600	305	3	]	]	X
ejpam-6600	305	4	let	let	VERB
ejpam-6600	305	5	q	q	NOUN
ejpam-6600	305	6	=	=	SYM
ejpam-6600	305	7	pn	pn	NOUN
ejpam-6600	305	8	,	,	PUNCT
ejpam-6600	305	9	where	where	SCONJ
ejpam-6600	305	10	p	p	NOUN
ejpam-6600	305	11	is	be	AUX
ejpam-6600	305	12	an	an	DET
ejpam-6600	305	13	odd	odd	ADJ
ejpam-6600	305	14	prime	prime	ADJ
ejpam-6600	305	15	number	number	NOUN
ejpam-6600	305	16	,	,	PUNCT
ejpam-6600	305	17	and	and	CCONJ
ejpam-6600	305	18	n	n	PRON
ejpam-6600	305	19	∈	∈	PROPN
ejpam-6600	305	20	n	n	CCONJ
ejpam-6600	305	21	,	,	PUNCT
ejpam-6600	305	22	such	such	ADJ
ejpam-6600	305	23	that	that	PRON
ejpam-6600	305	24	q	q	PROPN
ejpam-6600	305	25	≡	≡	PROPN
ejpam-6600	305	26	1	1	NUM
ejpam-6600	305	27	(	(	PUNCT
ejpam-6600	305	28	mod	mod	PROPN
ejpam-6600	305	29	8)	8)	NUM
ejpam-6600	305	30	.	.	PUNCT
ejpam-6600	306	1	the	the	DET
ejpam-6600	306	2	graph	graph	NOUN
ejpam-6600	306	3	4−pq	4−pq	X
ejpam-6600	306	4	,	,	PUNCT
ejpam-6600	306	5	with	with	ADP
ejpam-6600	306	6	v	v	NOUN
ejpam-6600	306	7	(	(	PUNCT
ejpam-6600	306	8	4−pq	4−pq	X
ejpam-6600	306	9	)	)	PUNCT
ejpam-6600	306	10	=	=	SYM
ejpam-6600	306	11	fq	fq	PROPN
ejpam-6600	306	12	and	and	CCONJ
ejpam-6600	306	13	e(4−pq	e(4−pq	PROPN
ejpam-6600	306	14	)	)	PUNCT
ejpam-6600	306	15	=	=	PRON
ejpam-6600	306	16	{	{	PUNCT
ejpam-6600	306	17	(	(	PUNCT
ejpam-6600	306	18	u	u	NOUN
ejpam-6600	306	19	,	,	PUNCT
ejpam-6600	306	20	v	v	NOUN
ejpam-6600	306	21	)	)	PUNCT
ejpam-6600	306	22	|	|	ADV
ejpam-6600	306	23	u−	u−	NUM
ejpam-6600	306	24	v	v	X
ejpam-6600	306	25	∈	∈	PROPN
ejpam-6600	306	26	(	(	PUNCT
ejpam-6600	306	27	f∗	f∗	NOUN
ejpam-6600	306	28	q	q	PROPN
ejpam-6600	306	29	)	)	PUNCT
ejpam-6600	306	30	4	4	NUM
ejpam-6600	306	31	}	}	PUNCT
ejpam-6600	306	32	,	,	PUNCT
ejpam-6600	306	33	is	be	AUX
ejpam-6600	306	34	called	call	VERB
ejpam-6600	306	35	the	the	DET
ejpam-6600	306	36	quadruple	quadruple	NOUN
ejpam-6600	306	37	paley	paley	NOUN
ejpam-6600	306	38	graph	graph	NOUN
ejpam-6600	306	39	of	of	ADP
ejpam-6600	306	40	order	order	NOUN
ejpam-6600	306	41	q.	q.	NOUN
ejpam-6600	306	42	note	note	VERB
ejpam-6600	306	43	that	that	SCONJ
ejpam-6600	306	44	:	:	PUNCT
ejpam-6600	306	45	the	the	DET
ejpam-6600	306	46	condition	condition	NOUN
ejpam-6600	306	47	q	q	X
ejpam-6600	306	48	≡	≡	PROPN
ejpam-6600	306	49	1	1	NUM
ejpam-6600	306	50	(	(	PUNCT
ejpam-6600	306	51	mod	mod	PROPN
ejpam-6600	306	52	8)	8)	NUM
ejpam-6600	306	53	is	be	AUX
ejpam-6600	306	54	necessary	necessary	ADJ
ejpam-6600	306	55	to	to	PART
ejpam-6600	306	56	ensure	ensure	VERB
ejpam-6600	306	57	that	that	PRON
ejpam-6600	306	58	−1	−1	NOUN
ejpam-6600	306	59	is	be	AUX
ejpam-6600	306	60	a	a	DET
ejpam-6600	306	61	quadruple	quadruple	NOUN
ejpam-6600	306	62	and	and	CCONJ
ejpam-6600	306	63	,	,	PUNCT
ejpam-6600	306	64	consequently	consequently	ADV
ejpam-6600	306	65	,	,	PUNCT
ejpam-6600	306	66	the	the	DET
ejpam-6600	306	67	graph	graph	NOUN
ejpam-6600	306	68	4−	4−	NUM
ejpam-6600	306	69	pq	pq	NOUN
ejpam-6600	306	70	is	be	AUX
ejpam-6600	306	71	well	well	ADV
ejpam-6600	306	72	-	-	PUNCT
ejpam-6600	306	73	defined	define	VERB
ejpam-6600	306	74	.	.	PUNCT
ejpam-6600	306	75	example	example	NOUN
ejpam-6600	307	1	6	6	NUM
ejpam-6600	307	2	.	.	PUNCT
ejpam-6600	308	1	the	the	DET
ejpam-6600	308	2	quadruple	quadruple	NOUN
ejpam-6600	308	3	paley	paley	PROPN
ejpam-6600	308	4	graph	graph	NOUN
ejpam-6600	308	5	4	4	NUM
ejpam-6600	308	6	−	−	NOUN
ejpam-6600	308	7	p17	p17	NOUN
ejpam-6600	308	8	of	of	ADP
ejpam-6600	308	9	order	order	NOUN
ejpam-6600	308	10	17	17	NUM
ejpam-6600	308	11	has	have	VERB
ejpam-6600	308	12	v	v	X
ejpam-6600	308	13	(	(	PUNCT
ejpam-6600	308	14	4	4	NUM
ejpam-6600	308	15	−	−	NOUN
ejpam-6600	308	16	p17	p17	NOUN
ejpam-6600	308	17	)	)	PUNCT
ejpam-6600	308	18	=	=	SYM
ejpam-6600	308	19	z17	z17	NOUN
ejpam-6600	308	20	and	and	CCONJ
ejpam-6600	308	21	e(4−	e(4−	NOUN
ejpam-6600	308	22	p17	p17	NOUN
ejpam-6600	308	23	)	)	PUNCT
ejpam-6600	308	24	=	=	SYM
ejpam-6600	308	25	{	{	PUNCT
ejpam-6600	308	26	(	(	PUNCT
ejpam-6600	308	27	u	u	NOUN
ejpam-6600	308	28	,	,	PUNCT
ejpam-6600	308	29	v	v	NOUN
ejpam-6600	308	30	)	)	PUNCT
ejpam-6600	309	1	|	|	ADV
ejpam-6600	309	2	u−	u−	NUM
ejpam-6600	309	3	v	v	X
ejpam-6600	309	4	∈	∈	PROPN
ejpam-6600	309	5	{	{	PUNCT
ejpam-6600	309	6	1	1	NUM
ejpam-6600	309	7	,	,	PUNCT
ejpam-6600	309	8	4	4	NUM
ejpam-6600	309	9	,	,	PUNCT
ejpam-6600	309	10	13	13	NUM
ejpam-6600	309	11	,	,	PUNCT
ejpam-6600	309	12	16	16	NUM
ejpam-6600	309	13	}	}	PUNCT
ejpam-6600	309	14	}	}	PUNCT
ejpam-6600	309	15	,	,	PUNCT
ejpam-6600	309	16	as	as	ADP
ejpam-6600	309	17	in	in	ADP
ejpam-6600	309	18	figure	figure	NOUN
ejpam-6600	309	19	7	7	NUM
ejpam-6600	309	20	.	.	PUNCT
ejpam-6600	309	21	figure	figure	VERB
ejpam-6600	309	22	7	7	NUM
ejpam-6600	309	23	:	:	PUNCT
ejpam-6600	309	24	the	the	DET
ejpam-6600	309	25	quadruple	quadruple	NOUN
ejpam-6600	309	26	paley	paley	PROPN
ejpam-6600	309	27	graph	graph	NOUN
ejpam-6600	309	28	4−	4−	NUM
ejpam-6600	309	29	p17	p17	NOUN
ejpam-6600	309	30	example	example	NOUN
ejpam-6600	309	31	7	7	NUM
ejpam-6600	309	32	.	.	PUNCT
ejpam-6600	310	1	the	the	DET
ejpam-6600	310	2	quadruple	quadruple	NOUN
ejpam-6600	310	3	paley	paley	PROPN
ejpam-6600	310	4	graph	graph	NOUN
ejpam-6600	310	5	4	4	NUM
ejpam-6600	310	6	−	−	NOUN
ejpam-6600	310	7	p9	p9	PROPN
ejpam-6600	310	8	with	with	ADP
ejpam-6600	310	9	vertex	vertex	NOUN
ejpam-6600	310	10	set	set	VERB
ejpam-6600	310	11	v	v	NOUN
ejpam-6600	310	12	(	(	PUNCT
ejpam-6600	310	13	4	4	NUM
ejpam-6600	310	14	−	−	PROPN
ejpam-6600	310	15	p9	p9	PROPN
ejpam-6600	310	16	)	)	PUNCT
ejpam-6600	310	17	=	=	SYM
ejpam-6600	310	18	f9	f9	PROPN
ejpam-6600	310	19	and	and	CCONJ
ejpam-6600	310	20	(	(	PUNCT
ejpam-6600	310	21	f∗	f∗	NOUN
ejpam-6600	310	22	9	9	NUM
ejpam-6600	310	23	)	)	PUNCT
ejpam-6600	310	24	4	4	NUM
ejpam-6600	310	25	=	=	SYM
ejpam-6600	310	26	{	{	PUNCT
ejpam-6600	310	27	1	1	NUM
ejpam-6600	310	28	,	,	PUNCT
ejpam-6600	310	29	2	2	NUM
ejpam-6600	310	30	}	}	PUNCT
ejpam-6600	310	31	so	so	ADV
ejpam-6600	310	32	the	the	DET
ejpam-6600	310	33	edge	edge	NOUN
ejpam-6600	310	34	set	set	VERB
ejpam-6600	310	35	e(4	e(4	PROPN
ejpam-6600	310	36	−	−	PROPN
ejpam-6600	310	37	p9	p9	PROPN
ejpam-6600	310	38	)	)	PUNCT
ejpam-6600	310	39	=	=	PRON
ejpam-6600	310	40	{	{	PUNCT
ejpam-6600	310	41	(	(	PUNCT
ejpam-6600	310	42	0	0	NUM
ejpam-6600	310	43	,	,	PUNCT
ejpam-6600	310	44	1	1	NUM
ejpam-6600	310	45	)	)	PUNCT
ejpam-6600	310	46	,	,	PUNCT
ejpam-6600	310	47	(	(	PUNCT
ejpam-6600	310	48	0	0	NUM
ejpam-6600	310	49	,	,	PUNCT
ejpam-6600	310	50	2	2	NUM
ejpam-6600	310	51	)	)	PUNCT
ejpam-6600	310	52	,	,	PUNCT
ejpam-6600	310	53	(	(	PUNCT
ejpam-6600	310	54	1	1	NUM
ejpam-6600	310	55	,	,	PUNCT
ejpam-6600	310	56	2	2	NUM
ejpam-6600	310	57	)	)	PUNCT
ejpam-6600	310	58	,	,	PUNCT
ejpam-6600	310	59	(	(	PUNCT
ejpam-6600	310	60	a	a	X
ejpam-6600	310	61	,	,	PUNCT
ejpam-6600	310	62	a	a	DET
ejpam-6600	310	63	+	+	NOUN
ejpam-6600	310	64	1	1	NUM
ejpam-6600	310	65	)	)	PUNCT
ejpam-6600	310	66	,	,	PUNCT
ejpam-6600	310	67	(	(	PUNCT
ejpam-6600	310	68	a	a	X
ejpam-6600	310	69	,	,	PUNCT
ejpam-6600	310	70	a	a	DET
ejpam-6600	310	71	+	+	NOUN
ejpam-6600	310	72	2	2	NUM
ejpam-6600	310	73	)	)	PUNCT
ejpam-6600	310	74	,	,	PUNCT
ejpam-6600	310	75	(	(	PUNCT
ejpam-6600	310	76	a	a	DET
ejpam-6600	310	77	+	+	NUM
ejpam-6600	310	78	1	1	NUM
ejpam-6600	310	79	,	,	PUNCT
ejpam-6600	310	80	a+	a+	PRON
ejpam-6600	310	81	2	2	NUM
ejpam-6600	310	82	)	)	PUNCT
ejpam-6600	310	83	,	,	PUNCT
ejpam-6600	310	84	(	(	PUNCT
ejpam-6600	310	85	2a	2a	NUM
ejpam-6600	310	86	,	,	PUNCT
ejpam-6600	310	87	2a+	2a+	NUM
ejpam-6600	310	88	1	1	NUM
ejpam-6600	310	89	)	)	PUNCT
ejpam-6600	310	90	,	,	PUNCT
ejpam-6600	310	91	(	(	PUNCT
ejpam-6600	310	92	2a	2a	NUM
ejpam-6600	310	93	,	,	PUNCT
ejpam-6600	310	94	2a+	2a+	NUM
ejpam-6600	310	95	2	2	NUM
ejpam-6600	310	96	)	)	PUNCT
ejpam-6600	310	97	,	,	PUNCT
ejpam-6600	310	98	(	(	PUNCT
ejpam-6600	310	99	2a+	2a+	NUM
ejpam-6600	310	100	1	1	NUM
ejpam-6600	310	101	,	,	PUNCT
ejpam-6600	310	102	2a+	2a+	NUM
ejpam-6600	310	103	2	2	NUM
ejpam-6600	310	104	)	)	PUNCT
ejpam-6600	310	105	}	}	PUNCT
ejpam-6600	310	106	.	.	PUNCT
ejpam-6600	311	1	a.	a.	PROPN
ejpam-6600	311	2	n.	n.	PROPN
ejpam-6600	311	3	elsawy	elsawy	PROPN
ejpam-6600	311	4	,	,	PUNCT
ejpam-6600	311	5	r.	r.	PROPN
ejpam-6600	311	6	n.	n.	PROPN
ejpam-6600	311	7	almohammadi	almohammadi	PROPN
ejpam-6600	311	8	/	/	SYM
ejpam-6600	311	9	eur	eur	PROPN
ejpam-6600	311	10	.	.	PUNCT
ejpam-6600	312	1	j.	j.	PROPN
ejpam-6600	312	2	pure	pure	PROPN
ejpam-6600	312	3	appl	appl	PROPN
ejpam-6600	312	4	.	.	PROPN
ejpam-6600	312	5	math	math	PROPN
ejpam-6600	312	6	,	,	PUNCT
ejpam-6600	312	7	18	18	NUM
ejpam-6600	312	8	(	(	PUNCT
ejpam-6600	312	9	4	4	NUM
ejpam-6600	312	10	)	)	PUNCT
ejpam-6600	312	11	(	(	PUNCT
ejpam-6600	312	12	2025	2025	NUM
ejpam-6600	312	13	)	)	PUNCT
ejpam-6600	312	14	,	,	PUNCT
ejpam-6600	312	15	6600	6600	NUM
ejpam-6600	312	16	12	12	NUM
ejpam-6600	312	17	of	of	ADP
ejpam-6600	312	18	26	26	NUM
ejpam-6600	312	19	figure	figure	NOUN
ejpam-6600	312	20	8	8	NUM
ejpam-6600	312	21	:	:	PUNCT
ejpam-6600	312	22	the	the	DET
ejpam-6600	312	23	quadruple	quadruple	NOUN
ejpam-6600	312	24	paley	paley	PROPN
ejpam-6600	312	25	graph	graph	NOUN
ejpam-6600	312	26	4−	4−	NUM
ejpam-6600	312	27	p9	p9	NOUN
ejpam-6600	312	28	now	now	ADV
ejpam-6600	312	29	we	we	PRON
ejpam-6600	312	30	provide	provide	VERB
ejpam-6600	312	31	an	an	DET
ejpam-6600	312	32	algorithm	algorithm	NOUN
ejpam-6600	312	33	which	which	PRON
ejpam-6600	312	34	produces	produce	VERB
ejpam-6600	312	35	an	an	DET
ejpam-6600	312	36	edge	edge	NOUN
ejpam-6600	312	37	-	-	PUNCT
ejpam-6600	312	38	graceful	graceful	NOUN
ejpam-6600	312	39	labeling	labeling	NOUN
ejpam-6600	312	40	for	for	ADP
ejpam-6600	312	41	quadruple	quadruple	NOUN
ejpam-6600	312	42	paley	paley	ADJ
ejpam-6600	312	43	graphs	graph	NOUN
ejpam-6600	312	44	of	of	ADP
ejpam-6600	312	45	prime	prime	ADJ
ejpam-6600	312	46	order	order	NOUN
ejpam-6600	312	47	.	.	PUNCT
ejpam-6600	313	1	4.1	4.1	NUM
ejpam-6600	313	2	.	.	PUNCT
ejpam-6600	313	3	edge	edge	NOUN
ejpam-6600	313	4	-	-	PUNCT
ejpam-6600	313	5	graceful	graceful	NOUN
ejpam-6600	313	6	labeling	labeling	NOUN
ejpam-6600	313	7	algorithm	algorithm	NOUN
ejpam-6600	313	8	for	for	ADP
ejpam-6600	313	9	quadruple	quadruple	NOUN
ejpam-6600	313	10	paley	paley	ADJ
ejpam-6600	313	11	graphs	graph	NOUN
ejpam-6600	313	12	of	of	ADP
ejpam-6600	313	13	prime	prime	ADJ
ejpam-6600	313	14	order	order	NOUN
ejpam-6600	313	15	input	input	NOUN
ejpam-6600	313	16	:	:	PUNCT
ejpam-6600	313	17	the	the	DET
ejpam-6600	313	18	quadruple	quadruple	NOUN
ejpam-6600	313	19	paley	paley	NOUN
ejpam-6600	313	20	graph	graph	NOUN
ejpam-6600	313	21	4−pp	4−pp	NUM
ejpam-6600	313	22	with	with	ADP
ejpam-6600	313	23	v	v	NOUN
ejpam-6600	313	24	(	(	PUNCT
ejpam-6600	313	25	4−pp	4−pp	NUM
ejpam-6600	313	26	)	)	PUNCT
ejpam-6600	313	27	=	=	SYM
ejpam-6600	313	28	zp	zp	NOUN
ejpam-6600	313	29	and	and	CCONJ
ejpam-6600	313	30	e(4−pp	e(4−pp	PROPN
ejpam-6600	313	31	)	)	PUNCT
ejpam-6600	313	32	=	=	PRON
ejpam-6600	313	33	{	{	PUNCT
ejpam-6600	313	34	(	(	PUNCT
ejpam-6600	313	35	u	u	NOUN
ejpam-6600	313	36	,	,	PUNCT
ejpam-6600	313	37	v	v	NOUN
ejpam-6600	313	38	)	)	PUNCT
ejpam-6600	314	1	|	|	ADV
ejpam-6600	314	2	u−	u−	NUM
ejpam-6600	314	3	v	v	X
ejpam-6600	314	4	∈	∈	PROPN
ejpam-6600	314	5	(	(	PUNCT
ejpam-6600	314	6	z∗	z∗	NOUN
ejpam-6600	314	7	p	p	NOUN
ejpam-6600	314	8	)	)	PUNCT
ejpam-6600	314	9	4	4	NUM
ejpam-6600	314	10	}	}	PUNCT
ejpam-6600	314	11	,	,	PUNCT
ejpam-6600	314	12	where	where	SCONJ
ejpam-6600	314	13	p	p	PRON
ejpam-6600	314	14	≡	≡	PROPN
ejpam-6600	314	15	1	1	NUM
ejpam-6600	314	16	(	(	PUNCT
ejpam-6600	314	17	mod	mod	PROPN
ejpam-6600	314	18	8)	8)	NUM
ejpam-6600	314	19	(	(	PUNCT
ejpam-6600	314	20	1	1	NUM
ejpam-6600	314	21	)	)	PUNCT
ejpam-6600	314	22	rename	rename	VERB
ejpam-6600	314	23	the	the	DET
ejpam-6600	314	24	vertices	vertex	NOUN
ejpam-6600	314	25	of	of	ADP
ejpam-6600	314	26	the	the	DET
ejpam-6600	314	27	graph	graph	NOUN
ejpam-6600	314	28	as	as	ADP
ejpam-6600	314	29	0	0	NUM
ejpam-6600	314	30	:	:	PUNCT
ejpam-6600	314	31	=	=	SYM
ejpam-6600	314	32	vp	vp	NOUN
ejpam-6600	314	33	,	,	PUNCT
ejpam-6600	314	34	1	1	NUM
ejpam-6600	314	35	:	:	PUNCT
ejpam-6600	314	36	=	=	NOUN
ejpam-6600	314	37	v1	v1	NOUN
ejpam-6600	314	38	,	,	PUNCT
ejpam-6600	314	39	2	2	NUM
ejpam-6600	314	40	:	:	PUNCT
ejpam-6600	314	41	=	=	SYM
ejpam-6600	314	42	v2	v2	PROPN
ejpam-6600	314	43	,	,	PUNCT
ejpam-6600	314	44	.	.	PUNCT
ejpam-6600	314	45	.	.	PUNCT
ejpam-6600	314	46	.	.	PUNCT
ejpam-6600	315	1	,	,	PUNCT
ejpam-6600	315	2	p−	p−	NOUN
ejpam-6600	315	3	1	1	NUM
ejpam-6600	315	4	:	:	PUNCT
ejpam-6600	315	5	=	=	SYM
ejpam-6600	315	6	vp−1	vp−1	PROPN
ejpam-6600	315	7	.	.	PUNCT
ejpam-6600	316	1	(	(	PUNCT
ejpam-6600	316	2	2	2	X
ejpam-6600	316	3	)	)	PUNCT
ejpam-6600	316	4	set	set	NOUN
ejpam-6600	316	5	r	r	NOUN
ejpam-6600	316	6	=	=	SYM
ejpam-6600	316	7	p−1	p−1	PROPN
ejpam-6600	316	8	8	8	NUM
ejpam-6600	316	9	,	,	PUNCT
ejpam-6600	316	10	and	and	CCONJ
ejpam-6600	316	11	rewrite	rewrite	VERB
ejpam-6600	316	12	(	(	PUNCT
ejpam-6600	316	13	z∗	z∗	NOUN
ejpam-6600	316	14	p	p	NOUN
ejpam-6600	316	15	)	)	PUNCT
ejpam-6600	316	16	4	4	NUM
ejpam-6600	316	17	as	as	ADP
ejpam-6600	316	18	(	(	PUNCT
ejpam-6600	316	19	z∗	z∗	NOUN
ejpam-6600	316	20	p	p	NOUN
ejpam-6600	316	21	)	)	PUNCT
ejpam-6600	316	22	4	4	NUM
ejpam-6600	316	23	=	=	SYM
ejpam-6600	316	24	s	s	NOUN
ejpam-6600	316	25	=	=	PUNCT
ejpam-6600	316	26	{	{	PUNCT
ejpam-6600	316	27	s1	s1	NOUN
ejpam-6600	316	28	,	,	PUNCT
ejpam-6600	316	29	s2	s2	PROPN
ejpam-6600	316	30	,	,	PUNCT
ejpam-6600	316	31	s3	s3	PROPN
ejpam-6600	316	32	,	,	PUNCT
ejpam-6600	316	33	.	.	PUNCT
ejpam-6600	316	34	.	.	PUNCT
ejpam-6600	317	1	.	.	PUNCT
ejpam-6600	318	1	,	,	PUNCT
ejpam-6600	318	2	s2r	s2r	PROPN
ejpam-6600	318	3	:	:	PUNCT
ejpam-6600	318	4	s1	s1	NOUN
ejpam-6600	318	5	<	<	X
ejpam-6600	318	6	s2	s2	PROPN
ejpam-6600	318	7	<	<	X
ejpam-6600	318	8	s3	s3	PROPN
ejpam-6600	318	9	<	<	X
ejpam-6600	318	10	.	.	PUNCT
ejpam-6600	318	11	.	.	PUNCT
ejpam-6600	319	1	.	.	PUNCT
ejpam-6600	320	1	<	<	X
ejpam-6600	320	2	s2r	s2r	PROPN
ejpam-6600	320	3	}	}	PUNCT
ejpam-6600	320	4	.	.	PUNCT
ejpam-6600	321	1	(	(	PUNCT
ejpam-6600	321	2	3	3	X
ejpam-6600	321	3	)	)	PUNCT
ejpam-6600	321	4	partition	partition	NOUN
ejpam-6600	321	5	s	s	NOUN
ejpam-6600	321	6	into	into	ADP
ejpam-6600	321	7	two	two	NUM
ejpam-6600	321	8	sets	set	NOUN
ejpam-6600	321	9	.	.	PUNCT
ejpam-6600	322	1	let	let	VERB
ejpam-6600	322	2	s1	s1	PROPN
ejpam-6600	322	3	=	=	PUNCT
ejpam-6600	322	4	{	{	PUNCT
ejpam-6600	322	5	s1	s1	NOUN
ejpam-6600	322	6	,	,	PUNCT
ejpam-6600	322	7	s2	s2	PROPN
ejpam-6600	322	8	,	,	PUNCT
ejpam-6600	322	9	s3	s3	PROPN
ejpam-6600	322	10	,	,	PUNCT
ejpam-6600	322	11	.	.	PUNCT
ejpam-6600	322	12	.	.	PUNCT
ejpam-6600	323	1	.	.	PUNCT
ejpam-6600	324	1	,	,	PUNCT
ejpam-6600	324	2	sr	sr	PROPN
ejpam-6600	324	3	}	}	PUNCT
ejpam-6600	324	4	and	and	CCONJ
ejpam-6600	324	5	s2	s2	VERB
ejpam-6600	324	6	=	=	SYM
ejpam-6600	324	7	{	{	PUNCT
ejpam-6600	324	8	sr+1	sr+1	PROPN
ejpam-6600	324	9	,	,	PUNCT
ejpam-6600	324	10	sr+2	sr+2	NOUN
ejpam-6600	324	11	,	,	PUNCT
ejpam-6600	324	12	sr+3	sr+3	NOUN
ejpam-6600	324	13	,	,	PUNCT
ejpam-6600	324	14	.	.	PUNCT
ejpam-6600	324	15	.	.	PUNCT
ejpam-6600	325	1	.	.	PUNCT
ejpam-6600	326	1	,	,	PUNCT
ejpam-6600	326	2	s2r	s2r	PROPN
ejpam-6600	326	3	}	}	PUNCT
ejpam-6600	326	4	.	.	PUNCT
ejpam-6600	327	1	note	note	VERB
ejpam-6600	327	2	that	that	SCONJ
ejpam-6600	327	3	:	:	PUNCT
ejpam-6600	327	4	p	p	X
ejpam-6600	327	5	−	−	PROPN
ejpam-6600	327	6	1	1	NUM
ejpam-6600	327	7	is	be	AUX
ejpam-6600	327	8	divisible	divisible	ADJ
ejpam-6600	327	9	by	by	ADP
ejpam-6600	327	10	8	8	NUM
ejpam-6600	327	11	and	and	CCONJ
ejpam-6600	327	12	for	for	ADP
ejpam-6600	327	13	any	any	DET
ejpam-6600	327	14	vertex	vertex	NOUN
ejpam-6600	327	15	vi	vi	PROPN
ejpam-6600	327	16	∈	∈	PROPN
ejpam-6600	327	17	zp	zp	NOUN
ejpam-6600	327	18	the	the	DET
ejpam-6600	327	19	vertex	vertex	NOUN
ejpam-6600	327	20	vi+sj	vi+sj	PROPN
ejpam-6600	327	21	is	be	AUX
ejpam-6600	327	22	adjacent	adjacent	ADJ
ejpam-6600	327	23	to	to	PART
ejpam-6600	327	24	vi	vi	VERB
ejpam-6600	327	25	for	for	ADP
ejpam-6600	327	26	all	all	DET
ejpam-6600	327	27	sj	sj	PROPN
ejpam-6600	327	28	∈	∈	PROPN
ejpam-6600	327	29	s.	s.	PROPN
ejpam-6600	327	30	(	(	PUNCT
ejpam-6600	327	31	4	4	X
ejpam-6600	327	32	)	)	PUNCT
ejpam-6600	327	33	if	if	SCONJ
ejpam-6600	327	34	sj	sj	PROPN
ejpam-6600	327	35	∈	∈	PROPN
ejpam-6600	327	36	s1	s1	PROPN
ejpam-6600	327	37	,	,	PUNCT
ejpam-6600	327	38	the	the	DET
ejpam-6600	327	39	vertex	vertex	NOUN
ejpam-6600	327	40	vi+sj	vi+sj	PROPN
ejpam-6600	327	41	is	be	AUX
ejpam-6600	327	42	placed	place	VERB
ejpam-6600	327	43	in	in	ADP
ejpam-6600	327	44	clockwise	clockwise	NOUN
ejpam-6600	327	45	direction	direction	NOUN
ejpam-6600	327	46	of	of	ADP
ejpam-6600	327	47	vi	vi	NOUN
ejpam-6600	327	48	and	and	CCONJ
ejpam-6600	327	49	if	if	SCONJ
ejpam-6600	327	50	sj	sj	PROPN
ejpam-6600	327	51	∈	∈	PROPN
ejpam-6600	327	52	s2	s2	PROPN
ejpam-6600	327	53	,	,	PUNCT
ejpam-6600	327	54	the	the	DET
ejpam-6600	327	55	vertex	vertex	NOUN
ejpam-6600	327	56	vi+sj	vi+sj	PROPN
ejpam-6600	327	57	is	be	AUX
ejpam-6600	327	58	placed	place	VERB
ejpam-6600	327	59	in	in	ADP
ejpam-6600	327	60	anticlockwise	anticlockwise	NOUN
ejpam-6600	327	61	direction	direction	NOUN
ejpam-6600	327	62	of	of	ADP
ejpam-6600	327	63	vi	vi	PROPN
ejpam-6600	327	64	.	.	PUNCT
ejpam-6600	328	1	(	(	PUNCT
ejpam-6600	328	2	5	5	X
ejpam-6600	328	3	)	)	PUNCT
ejpam-6600	328	4	set	set	NOUN
ejpam-6600	328	5	f(vi	f(vi	PROPN
ejpam-6600	328	6	,	,	PUNCT
ejpam-6600	328	7	vi+sj	vi+sj	NUM
ejpam-6600	328	8	)	)	PUNCT
ejpam-6600	329	1	=	=	SYM
ejpam-6600	329	2	0	0	NUM
ejpam-6600	330	1	for	for	ADP
ejpam-6600	330	2	all	all	PRON
ejpam-6600	330	3	i	i	PRON
ejpam-6600	330	4	∈	∈	PROPN
ejpam-6600	330	5	{	{	PUNCT
ejpam-6600	330	6	1	1	NUM
ejpam-6600	330	7	,	,	PUNCT
ejpam-6600	330	8	2	2	NUM
ejpam-6600	330	9	,	,	PUNCT
ejpam-6600	330	10	3	3	NUM
ejpam-6600	330	11	,	,	PUNCT
ejpam-6600	330	12	·	·	PUNCT
ejpam-6600	330	13	·	·	PUNCT
ejpam-6600	330	14	·	·	PUNCT
ejpam-6600	330	15	,	,	PUNCT
ejpam-6600	330	16	p	p	X
ejpam-6600	330	17	}	}	PUNCT
ejpam-6600	330	18	,	,	PUNCT
ejpam-6600	330	19	j	j	PROPN
ejpam-6600	330	20	∈	∈	PROPN
ejpam-6600	330	21	{	{	PUNCT
ejpam-6600	330	22	1	1	NUM
ejpam-6600	330	23	,	,	PUNCT
ejpam-6600	330	24	2	2	NUM
ejpam-6600	330	25	,	,	PUNCT
ejpam-6600	330	26	3	3	NUM
ejpam-6600	330	27	,	,	PUNCT
ejpam-6600	330	28	·	·	PUNCT
ejpam-6600	330	29	·	·	PUNCT
ejpam-6600	330	30	·	·	PUNCT
ejpam-6600	330	31	,	,	PUNCT
ejpam-6600	330	32	2r	2r	NUM
ejpam-6600	330	33	}	}	PUNCT
ejpam-6600	330	34	.	.	PUNCT
ejpam-6600	331	1	(	(	PUNCT
ejpam-6600	331	2	6	6	X
ejpam-6600	331	3	)	)	PUNCT
ejpam-6600	331	4	set	set	NOUN
ejpam-6600	331	5	i	i	NOUN
ejpam-6600	331	6	=	=	NOUN
ejpam-6600	332	1	1	1	X
ejpam-6600	332	2	.	.	X
ejpam-6600	332	3	step	step	NOUN
ejpam-6600	332	4	1	1	NUM
ejpam-6600	332	5	:	:	PUNCT
ejpam-6600	332	6	if	if	SCONJ
ejpam-6600	332	7	i	i	PRON
ejpam-6600	332	8	≤	≤	VERB
ejpam-6600	332	9	p	p	NOUN
ejpam-6600	332	10	then	then	ADV
ejpam-6600	332	11	continue	continue	VERB
ejpam-6600	332	12	to	to	PART
ejpam-6600	332	13	step	step	VERB
ejpam-6600	332	14	2	2	NUM
ejpam-6600	332	15	.	.	PUNCT
ejpam-6600	332	16	else	else	ADV
ejpam-6600	332	17	jump	jump	VERB
ejpam-6600	332	18	to	to	PART
ejpam-6600	332	19	step	step	VERB
ejpam-6600	332	20	4	4	NUM
ejpam-6600	332	21	.	.	PUNCT
ejpam-6600	333	1	step	step	NOUN
ejpam-6600	333	2	2	2	NUM
ejpam-6600	333	3	:	:	PUNCT
ejpam-6600	333	4	for	for	ADP
ejpam-6600	333	5	each	each	DET
ejpam-6600	333	6	sj	sj	PROPN
ejpam-6600	333	7	∈	∈	PROPN
ejpam-6600	333	8	s1	s1	PROPN
ejpam-6600	333	9	,	,	PUNCT
ejpam-6600	333	10	f	f	PROPN
ejpam-6600	333	11	(	(	PUNCT
ejpam-6600	333	12	vi	vi	PROPN
ejpam-6600	333	13	,	,	PUNCT
ejpam-6600	333	14	vi+sj	vi+sj	NUM
ejpam-6600	333	15	)	)	PUNCT
ejpam-6600	334	1	=	=	PRON
ejpam-6600	335	1	(	(	PUNCT
ejpam-6600	335	2	j	j	NOUN
ejpam-6600	335	3	−	−	PROPN
ejpam-6600	335	4	1	1	NUM
ejpam-6600	335	5	)	)	PUNCT
ejpam-6600	335	6	p+	p+	VERB
ejpam-6600	335	7	i.	i.	NOUN
ejpam-6600	335	8	step	step	NOUN
ejpam-6600	335	9	3	3	NUM
ejpam-6600	335	10	:	:	PUNCT
ejpam-6600	335	11	i	i	PRON
ejpam-6600	335	12	=	=	PUNCT
ejpam-6600	335	13	i+	i+	PROPN
ejpam-6600	335	14	1	1	NUM
ejpam-6600	335	15	,	,	PUNCT
ejpam-6600	335	16	go	go	VERB
ejpam-6600	335	17	back	back	ADV
ejpam-6600	335	18	to	to	PART
ejpam-6600	335	19	step	step	NOUN
ejpam-6600	335	20	1	1	NUM
ejpam-6600	335	21	.	.	PUNCT
ejpam-6600	336	1	step	step	NOUN
ejpam-6600	336	2	4	4	NUM
ejpam-6600	336	3	:	:	PUNCT
ejpam-6600	336	4	for	for	ADP
ejpam-6600	336	5	each	each	PRON
ejpam-6600	336	6	k	k	NOUN
ejpam-6600	336	7	=	=	SYM
ejpam-6600	336	8	1	1	NUM
ejpam-6600	336	9	,	,	PUNCT
ejpam-6600	336	10	2	2	NUM
ejpam-6600	336	11	,	,	PUNCT
ejpam-6600	336	12	3	3	NUM
ejpam-6600	336	13	,	,	PUNCT
ejpam-6600	336	14	.	.	PUNCT
ejpam-6600	336	15	.	.	PUNCT
ejpam-6600	337	1	.	.	PUNCT
ejpam-6600	338	1	,	,	PUNCT
ejpam-6600	338	2	p	p	X
ejpam-6600	338	3	,	,	PUNCT
ejpam-6600	338	4	find	find	VERB
ejpam-6600	338	5	the	the	DET
ejpam-6600	338	6	weight	weight	NOUN
ejpam-6600	338	7	of	of	ADP
ejpam-6600	338	8	the	the	DET
ejpam-6600	338	9	vertex	vertex	NOUN
ejpam-6600	338	10	vk	vk	NOUN
ejpam-6600	338	11	using	use	VERB
ejpam-6600	338	12	the	the	DET
ejpam-6600	338	13	following	follow	VERB
ejpam-6600	338	14	mapping	mapping	NOUN
ejpam-6600	338	15	:	:	PUNCT
ejpam-6600	338	16	fw(vk	fw(vk	PROPN
ejpam-6600	338	17	)	)	PUNCT
ejpam-6600	339	1	=	=	PUNCT
ejpam-6600	340	1	∑2r	∑2r	NOUN
ejpam-6600	340	2	j=1	j=1	PROPN
ejpam-6600	340	3	f(vk	f(vk	PROPN
ejpam-6600	340	4	,	,	PUNCT
ejpam-6600	340	5	vk+sj	vk+sj	NOUN
ejpam-6600	340	6	)	)	PUNCT
ejpam-6600	341	1	=	=	PUNCT
ejpam-6600	342	1	∑r	∑r	PROPN
ejpam-6600	342	2	j=1	j=1	PROPN
ejpam-6600	342	3	2[(j−1)p+k]+(p−sj	2[(j−1)p+k]+(p−sj	NOUN
ejpam-6600	342	4	)	)	PUNCT
ejpam-6600	343	1	=	=	SYM
ejpam-6600	343	2	2kr−l	2kr−l	NUM
ejpam-6600	343	3	(	(	PUNCT
ejpam-6600	343	4	mod	mod	NOUN
ejpam-6600	343	5	p	p	NOUN
ejpam-6600	343	6	)	)	PUNCT
ejpam-6600	343	7	,	,	PUNCT
ejpam-6600	343	8	where	where	SCONJ
ejpam-6600	343	9	l	l	NOUN
ejpam-6600	343	10	=	=	PUNCT
ejpam-6600	344	1	∑r	∑r	PROPN
ejpam-6600	344	2	j=1	j=1	NOUN
ejpam-6600	344	3	sj	sj	INTJ
ejpam-6600	344	4	.	.	PUNCT
ejpam-6600	345	1	theorem	theorem	VERB
ejpam-6600	345	2	4	4	NUM
ejpam-6600	345	3	.	.	PUNCT
ejpam-6600	346	1	every	every	DET
ejpam-6600	346	2	quadruple	quadruple	NOUN
ejpam-6600	346	3	paley	paley	NOUN
ejpam-6600	346	4	graph	graph	NOUN
ejpam-6600	346	5	of	of	ADP
ejpam-6600	346	6	prime	prime	ADJ
ejpam-6600	346	7	order	order	NOUN
ejpam-6600	346	8	admits	admit	VERB
ejpam-6600	346	9	an	an	DET
ejpam-6600	346	10	edge	edge	NOUN
ejpam-6600	346	11	-	-	PUNCT
ejpam-6600	346	12	graceful	graceful	NOUN
ejpam-6600	346	13	labeling	labeling	NOUN
ejpam-6600	346	14	.	.	PUNCT
ejpam-6600	347	1	proof	proof	NOUN
ejpam-6600	347	2	.	.	PUNCT
ejpam-6600	348	1	see	see	VERB
ejpam-6600	348	2	theorem	theorem	NOUN
ejpam-6600	348	3	5	5	NUM
ejpam-6600	348	4	with	with	ADP
ejpam-6600	348	5	m	m	PROPN
ejpam-6600	348	6	=	=	SYM
ejpam-6600	348	7	4	4	NUM
ejpam-6600	348	8	.	.	PUNCT
ejpam-6600	348	9	a.	a.	PROPN
ejpam-6600	348	10	n.	n.	PROPN
ejpam-6600	348	11	elsawy	elsawy	PROPN
ejpam-6600	348	12	,	,	PUNCT
ejpam-6600	348	13	r.	r.	PROPN
ejpam-6600	348	14	n.	n.	PROPN
ejpam-6600	348	15	almohammadi	almohammadi	PROPN
ejpam-6600	348	16	/	/	SYM
ejpam-6600	348	17	eur	eur	PROPN
ejpam-6600	348	18	.	.	PUNCT
ejpam-6600	349	1	j.	j.	PROPN
ejpam-6600	349	2	pure	pure	PROPN
ejpam-6600	349	3	appl	appl	PROPN
ejpam-6600	349	4	.	.	PROPN
ejpam-6600	349	5	math	math	PROPN
ejpam-6600	349	6	,	,	PUNCT
ejpam-6600	349	7	18	18	NUM
ejpam-6600	349	8	(	(	PUNCT
ejpam-6600	349	9	4	4	NUM
ejpam-6600	349	10	)	)	PUNCT
ejpam-6600	349	11	(	(	PUNCT
ejpam-6600	349	12	2025	2025	NUM
ejpam-6600	349	13	)	)	PUNCT
ejpam-6600	349	14	,	,	PUNCT
ejpam-6600	349	15	6600	6600	NUM
ejpam-6600	349	16	13	13	NUM
ejpam-6600	349	17	of	of	ADP
ejpam-6600	349	18	26	26	NUM
ejpam-6600	349	19	figure	figure	NOUN
ejpam-6600	349	20	9	9	NUM
ejpam-6600	349	21	:	:	PUNCT
ejpam-6600	349	22	an	an	DET
ejpam-6600	349	23	edge	edge	NOUN
ejpam-6600	349	24	-	-	PUNCT
ejpam-6600	349	25	graceful	graceful	NOUN
ejpam-6600	349	26	labeling	labeling	NOUN
ejpam-6600	349	27	of	of	ADP
ejpam-6600	349	28	4−	4−	PROPN
ejpam-6600	349	29	p17	p17	NOUN
ejpam-6600	349	30	.	.	PUNCT
ejpam-6600	350	1	example	example	NOUN
ejpam-6600	350	2	8	8	NUM
ejpam-6600	350	3	.	.	PUNCT
ejpam-6600	351	1	we	we	PRON
ejpam-6600	351	2	apply	apply	VERB
ejpam-6600	351	3	the	the	DET
ejpam-6600	351	4	algorithm	algorithm	NOUN
ejpam-6600	351	5	to	to	PART
ejpam-6600	351	6	show	show	VERB
ejpam-6600	351	7	that	that	SCONJ
ejpam-6600	351	8	:	:	PUNCT
ejpam-6600	351	9	the	the	DET
ejpam-6600	351	10	quadruple	quadruple	NOUN
ejpam-6600	351	11	paley	paley	PROPN
ejpam-6600	351	12	graph	graph	NOUN
ejpam-6600	351	13	4−	4−	NOUN
ejpam-6600	351	14	p17	p17	NOUN
ejpam-6600	351	15	is	be	AUX
ejpam-6600	351	16	edge	edge	NOUN
ejpam-6600	351	17	-	-	PUNCT
ejpam-6600	351	18	graceful	graceful	NOUN
ejpam-6600	351	19	with	with	ADP
ejpam-6600	351	20	v	v	PROPN
ejpam-6600	351	21	(	(	PUNCT
ejpam-6600	351	22	4	4	NUM
ejpam-6600	351	23	−	−	NOUN
ejpam-6600	351	24	p17	p17	NOUN
ejpam-6600	351	25	)	)	PUNCT
ejpam-6600	351	26	=	=	SYM
ejpam-6600	351	27	{	{	PUNCT
ejpam-6600	351	28	v1	v1	PROPN
ejpam-6600	351	29	,	,	PUNCT
ejpam-6600	351	30	v2	v2	PROPN
ejpam-6600	351	31	,	,	PUNCT
ejpam-6600	351	32	·	·	PUNCT
ejpam-6600	351	33	·	·	PUNCT
ejpam-6600	351	34	·	·	PUNCT
ejpam-6600	351	35	,	,	PUNCT
ejpam-6600	351	36	v17	v17	NOUN
ejpam-6600	351	37	}	}	PUNCT
ejpam-6600	351	38	and	and	CCONJ
ejpam-6600	351	39	|e(4−	|e(4−	ADP
ejpam-6600	351	40	p17)|	p17)|	NOUN
ejpam-6600	351	41	=	=	PUNCT
ejpam-6600	351	42	17·16	17·16	NUM
ejpam-6600	351	43	8	8	NUM
ejpam-6600	351	44	=	=	SYM
ejpam-6600	351	45	34	34	NUM
ejpam-6600	351	46	.	.	PUNCT
ejpam-6600	352	1	here	here	ADV
ejpam-6600	352	2	,	,	PUNCT
ejpam-6600	352	3	p	p	X
ejpam-6600	352	4	=	=	NOUN
ejpam-6600	352	5	17	17	NUM
ejpam-6600	352	6	,	,	PUNCT
ejpam-6600	352	7	r	r	NOUN
ejpam-6600	352	8	=	=	SYM
ejpam-6600	352	9	2	2	NUM
ejpam-6600	352	10	,	,	PUNCT
ejpam-6600	352	11	and	and	CCONJ
ejpam-6600	352	12	s1	s1	PROPN
ejpam-6600	352	13	=	=	SYM
ejpam-6600	352	14	{	{	PUNCT
ejpam-6600	352	15	1	1	NUM
ejpam-6600	352	16	,	,	PUNCT
ejpam-6600	352	17	4	4	NUM
ejpam-6600	352	18	}	}	PUNCT
ejpam-6600	352	19	.	.	PUNCT
ejpam-6600	353	1	so	so	ADV
ejpam-6600	353	2	for	for	ADP
ejpam-6600	353	3	each	each	DET
ejpam-6600	353	4	sj	sj	PROPN
ejpam-6600	353	5	∈	∈	PROPN
ejpam-6600	353	6	s1	s1	PROPN
ejpam-6600	353	7	,	,	PUNCT
ejpam-6600	353	8	f	f	PROPN
ejpam-6600	353	9	(	(	PUNCT
ejpam-6600	353	10	vk	vk	PROPN
ejpam-6600	353	11	,	,	PUNCT
ejpam-6600	353	12	vk+sj	vk+sj	NOUN
ejpam-6600	353	13	)	)	PUNCT
ejpam-6600	353	14	=	=	PUNCT
ejpam-6600	354	1	(	(	PUNCT
ejpam-6600	354	2	j	j	PROPN
ejpam-6600	354	3	−	−	PROPN
ejpam-6600	354	4	1	1	NUM
ejpam-6600	354	5	)	)	PUNCT
ejpam-6600	354	6	17	17	NUM
ejpam-6600	355	1	+	+	CCONJ
ejpam-6600	355	2	k	k	X
ejpam-6600	355	3	,	,	PUNCT
ejpam-6600	355	4	and	and	CCONJ
ejpam-6600	355	5	fw(vk	fw(vk	PROPN
ejpam-6600	355	6	)	)	PUNCT
ejpam-6600	356	1	=	=	PUNCT
ejpam-6600	356	2	4k	4k	PRON
ejpam-6600	356	3	−	−	NOUN
ejpam-6600	357	1	∑2	∑2	NOUN
ejpam-6600	357	2	j=1	j=1	NOUN
ejpam-6600	357	3	sj	sj	X
ejpam-6600	357	4	=	=	PUNCT
ejpam-6600	357	5	4k	4k	NOUN
ejpam-6600	357	6	−	−	NOUN
ejpam-6600	357	7	5	5	NUM
ejpam-6600	357	8	(	(	PUNCT
ejpam-6600	357	9	mod	mod	PROPN
ejpam-6600	357	10	17	17	NUM
ejpam-6600	357	11	)	)	PUNCT
ejpam-6600	357	12	.	.	PUNCT
ejpam-6600	358	1	figure	figure	NOUN
ejpam-6600	358	2	9	9	NUM
ejpam-6600	358	3	shows	show	VERB
ejpam-6600	358	4	the	the	DET
ejpam-6600	358	5	edge	edge	NOUN
ejpam-6600	358	6	-	-	PUNCT
ejpam-6600	358	7	graceful	graceful	NOUN
ejpam-6600	358	8	labeling	labeling	NOUN
ejpam-6600	358	9	for	for	ADP
ejpam-6600	358	10	the	the	DET
ejpam-6600	358	11	cubic	cubic	ADJ
ejpam-6600	358	12	paley	paley	PROPN
ejpam-6600	358	13	graph	graph	NOUN
ejpam-6600	358	14	4−	4−	NUM
ejpam-6600	358	15	p17	p17	NOUN
ejpam-6600	358	16	.	.	PUNCT
ejpam-6600	359	1	5	5	NUM
ejpam-6600	359	2	.	.	NUM
ejpam-6600	359	3	generalized	generalize	VERB
ejpam-6600	359	4	paley	paley	ADJ
ejpam-6600	359	5	graphs	graph	NOUN
ejpam-6600	359	6	generalized	generalize	VERB
ejpam-6600	359	7	paley	paley	ADJ
ejpam-6600	359	8	graphs	graph	NOUN
ejpam-6600	359	9	were	be	AUX
ejpam-6600	359	10	first	first	ADV
ejpam-6600	359	11	introduced	introduce	VERB
ejpam-6600	359	12	by	by	ADP
ejpam-6600	359	13	cohen	cohen	PROPN
ejpam-6600	360	1	[	[	X
ejpam-6600	360	2	29	29	NUM
ejpam-6600	360	3	]	]	PUNCT
ejpam-6600	360	4	,	,	PUNCT
ejpam-6600	360	5	and	and	CCONJ
ejpam-6600	360	6	reintroduced	reintroduce	VERB
ejpam-6600	360	7	by	by	ADP
ejpam-6600	360	8	lim	lim	PROPN
ejpam-6600	360	9	and	and	CCONJ
ejpam-6600	360	10	praeger	praeger	NOUN
ejpam-6600	361	1	[	[	X
ejpam-6600	361	2	30	30	NUM
ejpam-6600	361	3	]	]	PUNCT
ejpam-6600	361	4	in	in	ADP
ejpam-6600	361	5	2009	2009	NUM
ejpam-6600	361	6	,	,	PUNCT
ejpam-6600	361	7	and	and	CCONJ
ejpam-6600	361	8	by	by	ADP
ejpam-6600	361	9	elsawy	elsawy	NOUN
ejpam-6600	361	10	[	[	X
ejpam-6600	361	11	3	3	X
ejpam-6600	361	12	]	]	PUNCT
ejpam-6600	361	13	in	in	ADP
ejpam-6600	361	14	2009	2009	NUM
ejpam-6600	361	15	.	.	PUNCT
ejpam-6600	362	1	the	the	DET
ejpam-6600	362	2	generalized	generalized	ADJ
ejpam-6600	362	3	paley	paley	NOUN
ejpam-6600	362	4	graph	graph	NOUN
ejpam-6600	362	5	extends	extend	VERB
ejpam-6600	362	6	the	the	DET
ejpam-6600	362	7	concept	concept	NOUN
ejpam-6600	362	8	of	of	ADP
ejpam-6600	362	9	the	the	DET
ejpam-6600	362	10	paley	paley	ADJ
ejpam-6600	362	11	graph	graph	NOUN
ejpam-6600	362	12	and	and	CCONJ
ejpam-6600	362	13	its	its	PRON
ejpam-6600	362	14	higher	high	ADJ
ejpam-6600	362	15	-	-	PUNCT
ejpam-6600	362	16	order	order	NOUN
ejpam-6600	362	17	variants	variant	NOUN
ejpam-6600	362	18	,	,	PUNCT
ejpam-6600	362	19	providing	provide	VERB
ejpam-6600	362	20	a	a	DET
ejpam-6600	362	21	broader	broad	ADJ
ejpam-6600	362	22	class	class	NOUN
ejpam-6600	362	23	of	of	ADP
ejpam-6600	362	24	graphs	graph	NOUN
ejpam-6600	362	25	based	base	VERB
ejpam-6600	362	26	on	on	ADP
ejpam-6600	362	27	higher	high	ADJ
ejpam-6600	362	28	power	power	NOUN
ejpam-6600	362	29	residues	residue	NOUN
ejpam-6600	362	30	in	in	ADP
ejpam-6600	362	31	finite	finite	ADJ
ejpam-6600	362	32	fields	field	NOUN
ejpam-6600	362	33	.	.	PUNCT
ejpam-6600	363	1	in	in	ADP
ejpam-6600	363	2	the	the	DET
ejpam-6600	363	3	following	following	NOUN
ejpam-6600	363	4	we	we	PRON
ejpam-6600	363	5	extend	extend	VERB
ejpam-6600	363	6	the	the	DET
ejpam-6600	363	7	results	result	NOUN
ejpam-6600	363	8	of	of	ADP
ejpam-6600	363	9	edge	edge	NOUN
ejpam-6600	363	10	-	-	PUNCT
ejpam-6600	363	11	graceful	graceful	NOUN
ejpam-6600	363	12	labeling	labeling	NOUN
ejpam-6600	363	13	on	on	ADP
ejpam-6600	363	14	paley	paley	ADJ
ejpam-6600	363	15	,	,	PUNCT
ejpam-6600	363	16	cubic	cubic	ADJ
ejpam-6600	363	17	paley	paley	NOUN
ejpam-6600	363	18	,	,	PUNCT
ejpam-6600	363	19	quadruple	quadruple	NOUN
ejpam-6600	363	20	paley	paley	NOUN
ejpam-6600	363	21	graphs	graph	NOUN
ejpam-6600	363	22	to	to	ADP
ejpam-6600	363	23	generalized	generalize	VERB
ejpam-6600	363	24	paley	paley	ADJ
ejpam-6600	363	25	graphs	graph	NOUN
ejpam-6600	363	26	definition	definition	NOUN
ejpam-6600	363	27	5	5	NUM
ejpam-6600	363	28	.	.	PUNCT
ejpam-6600	364	1	let	let	VERB
ejpam-6600	364	2	m	m	PRON
ejpam-6600	364	3	,	,	PUNCT
ejpam-6600	364	4	n	n	X
ejpam-6600	364	5	be	be	AUX
ejpam-6600	364	6	positive	positive	ADJ
ejpam-6600	364	7	integers	integer	NOUN
ejpam-6600	364	8	and	and	CCONJ
ejpam-6600	364	9	p	p	NOUN
ejpam-6600	364	10	be	be	AUX
ejpam-6600	364	11	an	an	DET
ejpam-6600	364	12	odd	odd	ADJ
ejpam-6600	364	13	prime	prime	NOUN
ejpam-6600	364	14	such	such	ADJ
ejpam-6600	364	15	that	that	SCONJ
ejpam-6600	364	16	:	:	PUNCT
ejpam-6600	364	17	”	"	PUNCT
ejpam-6600	364	18	if	if	SCONJ
ejpam-6600	364	19	m	m	NOUN
ejpam-6600	364	20	is	be	AUX
ejpam-6600	364	21	even	even	ADV
ejpam-6600	364	22	then	then	ADV
ejpam-6600	364	23	q	q	PROPN
ejpam-6600	364	24	≡	≡	PROPN
ejpam-6600	364	25	1	1	NUM
ejpam-6600	364	26	(	(	PUNCT
ejpam-6600	364	27	mod	mod	PROPN
ejpam-6600	364	28	2	2	NUM
ejpam-6600	364	29	m	m	NOUN
ejpam-6600	364	30	)	)	PUNCT
ejpam-6600	364	31	and	and	CCONJ
ejpam-6600	364	32	if	if	SCONJ
ejpam-6600	364	33	m	m	NOUN
ejpam-6600	364	34	is	be	AUX
ejpam-6600	364	35	odd	odd	ADJ
ejpam-6600	364	36	then	then	ADV
ejpam-6600	364	37	p	p	PRON
ejpam-6600	364	38	is	be	AUX
ejpam-6600	364	39	any	any	DET
ejpam-6600	364	40	odd	odd	ADJ
ejpam-6600	364	41	prime	prime	NOUN
ejpam-6600	364	42	”	"	PUNCT
ejpam-6600	364	43	.	.	PUNCT
ejpam-6600	365	1	the	the	DET
ejpam-6600	365	2	generalized	generalized	ADJ
ejpam-6600	365	3	paley	paley	NOUN
ejpam-6600	365	4	graph	graph	NOUN
ejpam-6600	365	5	m−pq	m−pq	NOUN
ejpam-6600	365	6	has	have	VERB
ejpam-6600	365	7	vertex	vertex	NOUN
ejpam-6600	365	8	set	set	VERB
ejpam-6600	365	9	v	v	NOUN
ejpam-6600	365	10	(	(	PUNCT
ejpam-6600	365	11	m−pq	m−pq	NOUN
ejpam-6600	365	12	)	)	PUNCT
ejpam-6600	365	13	=	=	SYM
ejpam-6600	365	14	fq	fq	PROPN
ejpam-6600	365	15	,	,	PUNCT
ejpam-6600	365	16	where	where	SCONJ
ejpam-6600	365	17	fq	fq	PROPN
ejpam-6600	365	18	is	be	AUX
ejpam-6600	365	19	the	the	DET
ejpam-6600	365	20	finite	finite	ADJ
ejpam-6600	365	21	field	field	NOUN
ejpam-6600	365	22	of	of	ADP
ejpam-6600	365	23	order	order	NOUN
ejpam-6600	365	24	q	q	NOUN
ejpam-6600	365	25	=	=	SYM
ejpam-6600	365	26	pn	pn	NOUN
ejpam-6600	365	27	,	,	PUNCT
ejpam-6600	365	28	and	and	CCONJ
ejpam-6600	365	29	two	two	NUM
ejpam-6600	365	30	vertices	vertex	NOUN
ejpam-6600	365	31	are	be	AUX
ejpam-6600	365	32	adjacent	adjacent	ADJ
ejpam-6600	365	33	if	if	SCONJ
ejpam-6600	365	34	their	their	PRON
ejpam-6600	365	35	difference	difference	NOUN
ejpam-6600	365	36	belongs	belong	VERB
ejpam-6600	365	37	to	to	ADP
ejpam-6600	365	38	(	(	PUNCT
ejpam-6600	365	39	f	f	PROPN
ejpam-6600	365	40	∗	∗	X
ejpam-6600	365	41	q	q	NOUN
ejpam-6600	365	42	)	)	PUNCT
ejpam-6600	365	43	m.	m.	NOUN
ejpam-6600	365	44	remark	remark	NOUN
ejpam-6600	365	45	1	1	NUM
ejpam-6600	365	46	.	.	PUNCT
ejpam-6600	366	1	the	the	DET
ejpam-6600	366	2	generalized	generalized	ADJ
ejpam-6600	366	3	paley	paley	ADJ
ejpam-6600	366	4	graphs	graph	NOUN
ejpam-6600	366	5	m−pq	m−pq	NOUN
ejpam-6600	366	6	are	be	AUX
ejpam-6600	366	7	non	non	ADJ
ejpam-6600	366	8	-	-	ADJ
ejpam-6600	366	9	directed	directed	ADJ
ejpam-6600	366	10	graphs	graph	NOUN
ejpam-6600	366	11	because	because	SCONJ
ejpam-6600	366	12	(	(	PUNCT
ejpam-6600	366	13	f	f	PROPN
ejpam-6600	366	14	∗	∗	X
ejpam-6600	366	15	q	q	PROPN
ejpam-6600	366	16	)	)	PUNCT
ejpam-6600	366	17	m	m	VERB
ejpam-6600	367	1	=	=	SYM
ejpam-6600	367	2	−(f	−(f	PROPN
ejpam-6600	367	3	∗	∗	X
ejpam-6600	367	4	q	q	PROPN
ejpam-6600	367	5	)	)	PUNCT
ejpam-6600	367	6	m	m	ADP
ejpam-6600	367	7	,	,	PUNCT
ejpam-6600	367	8	in	in	ADP
ejpam-6600	367	9	other	other	ADJ
ejpam-6600	367	10	words	word	NOUN
ejpam-6600	367	11	−1	−1	NOUN
ejpam-6600	367	12	∈	∈	NOUN
ejpam-6600	367	13	(	(	PUNCT
ejpam-6600	367	14	f	f	PROPN
ejpam-6600	367	15	∗	∗	X
ejpam-6600	367	16	q	q	NOUN
ejpam-6600	367	17	)	)	PUNCT
ejpam-6600	367	18	m.	m.	NOUN
ejpam-6600	367	19	remark	remark	NOUN
ejpam-6600	367	20	2	2	NUM
ejpam-6600	367	21	.	.	PUNCT
ejpam-6600	368	1	the	the	DET
ejpam-6600	368	2	generalized	generalize	VERB
ejpam-6600	368	3	paley	paley	ADJ
ejpam-6600	368	4	graphs	graph	NOUN
ejpam-6600	368	5	m	m	VERB
ejpam-6600	368	6	−	−	ADJ
ejpam-6600	368	7	pq	pq	NOUN
ejpam-6600	368	8	are	be	AUX
ejpam-6600	368	9	regular	regular	ADJ
ejpam-6600	368	10	of	of	ADP
ejpam-6600	368	11	degree	degree	NOUN
ejpam-6600	369	1	q−1	q−1	PROPN
ejpam-6600	369	2	d	d	NOUN
ejpam-6600	369	3	,	,	PUNCT
ejpam-6600	369	4	where	where	SCONJ
ejpam-6600	369	5	d	d	NOUN
ejpam-6600	369	6	is	be	AUX
ejpam-6600	369	7	the	the	DET
ejpam-6600	369	8	greatest	great	ADJ
ejpam-6600	369	9	common	common	ADJ
ejpam-6600	369	10	divisor	divisor	NOUN
ejpam-6600	369	11	of	of	ADP
ejpam-6600	369	12	m	m	PROPN
ejpam-6600	369	13	and	and	CCONJ
ejpam-6600	369	14	q	q	ADJ
ejpam-6600	369	15	−	−	PROPN
ejpam-6600	369	16	1	1	NUM
ejpam-6600	369	17	(	(	PUNCT
ejpam-6600	369	18	see	see	VERB
ejpam-6600	369	19	[	[	X
ejpam-6600	369	20	3	3	NUM
ejpam-6600	369	21	]	]	NUM
ejpam-6600	369	22	)	)	PUNCT
ejpam-6600	369	23	.	.	PUNCT
ejpam-6600	370	1	a.	a.	PROPN
ejpam-6600	370	2	n.	n.	PROPN
ejpam-6600	370	3	elsawy	elsawy	PROPN
ejpam-6600	370	4	,	,	PUNCT
ejpam-6600	370	5	r.	r.	PROPN
ejpam-6600	370	6	n.	n.	PROPN
ejpam-6600	370	7	almohammadi	almohammadi	PROPN
ejpam-6600	370	8	/	/	SYM
ejpam-6600	370	9	eur	eur	PROPN
ejpam-6600	370	10	.	.	PUNCT
ejpam-6600	371	1	j.	j.	PROPN
ejpam-6600	371	2	pure	pure	PROPN
ejpam-6600	371	3	appl	appl	PROPN
ejpam-6600	371	4	.	.	PROPN
ejpam-6600	371	5	math	math	PROPN
ejpam-6600	371	6	,	,	PUNCT
ejpam-6600	371	7	18	18	NUM
ejpam-6600	371	8	(	(	PUNCT
ejpam-6600	371	9	4	4	NUM
ejpam-6600	371	10	)	)	PUNCT
ejpam-6600	371	11	(	(	PUNCT
ejpam-6600	371	12	2025	2025	NUM
ejpam-6600	371	13	)	)	PUNCT
ejpam-6600	371	14	,	,	PUNCT
ejpam-6600	371	15	6600	6600	NUM
ejpam-6600	371	16	14	14	NUM
ejpam-6600	371	17	of	of	ADP
ejpam-6600	371	18	26	26	NUM
ejpam-6600	371	19	remark	remark	NOUN
ejpam-6600	371	20	3	3	NUM
ejpam-6600	371	21	.	.	PUNCT
ejpam-6600	372	1	the	the	DET
ejpam-6600	372	2	size	size	NOUN
ejpam-6600	372	3	of	of	ADP
ejpam-6600	372	4	m−	m−	PROPN
ejpam-6600	372	5	pq	pq	PROPN
ejpam-6600	372	6	is	be	AUX
ejpam-6600	372	7	q(q−1	q(q−1	NOUN
ejpam-6600	372	8	)	)	PUNCT
ejpam-6600	372	9	2d	2d	NOUN
ejpam-6600	372	10	,	,	PUNCT
ejpam-6600	372	11	and	and	CCONJ
ejpam-6600	372	12	the	the	DET
ejpam-6600	372	13	positive	positive	ADJ
ejpam-6600	372	14	integer	integer	NOUN
ejpam-6600	372	15	q−1	q−1	PROPN
ejpam-6600	373	1	d	d	NOUN
ejpam-6600	373	2	is	be	AUX
ejpam-6600	373	3	even	even	ADV
ejpam-6600	373	4	.	.	PUNCT
ejpam-6600	374	1	remark	remark	PROPN
ejpam-6600	374	2	4	4	NUM
ejpam-6600	374	3	.	.	PUNCT
ejpam-6600	375	1	for	for	ADP
ejpam-6600	375	2	m	m	PROPN
ejpam-6600	375	3	=	=	SYM
ejpam-6600	375	4	2	2	NUM
ejpam-6600	375	5	,	,	PUNCT
ejpam-6600	375	6	3	3	NUM
ejpam-6600	375	7	,	,	PUNCT
ejpam-6600	375	8	or	or	CCONJ
ejpam-6600	375	9	4	4	NUM
ejpam-6600	375	10	we	we	PRON
ejpam-6600	375	11	get	get	VERB
ejpam-6600	375	12	paley	paley	ADJ
ejpam-6600	375	13	,	,	PUNCT
ejpam-6600	375	14	cubic	cubic	ADJ
ejpam-6600	375	15	paley	paley	NOUN
ejpam-6600	375	16	,	,	PUNCT
ejpam-6600	375	17	or	or	CCONJ
ejpam-6600	375	18	quadruple	quadruple	NOUN
ejpam-6600	375	19	paley	paley	NOUN
ejpam-6600	375	20	graphs	graph	NOUN
ejpam-6600	375	21	respectively	respectively	ADV
ejpam-6600	375	22	.	.	PUNCT
ejpam-6600	376	1	now	now	ADV
ejpam-6600	376	2	,	,	PUNCT
ejpam-6600	376	3	we	we	PRON
ejpam-6600	376	4	provide	provide	VERB
ejpam-6600	376	5	an	an	DET
ejpam-6600	376	6	algorithm	algorithm	NOUN
ejpam-6600	376	7	which	which	PRON
ejpam-6600	376	8	produces	produce	VERB
ejpam-6600	376	9	an	an	DET
ejpam-6600	376	10	edge	edge	NOUN
ejpam-6600	376	11	-	-	PUNCT
ejpam-6600	376	12	graceful	graceful	NOUN
ejpam-6600	376	13	labeling	labeling	NOUN
ejpam-6600	376	14	for	for	ADP
ejpam-6600	376	15	the	the	DET
ejpam-6600	376	16	prime	prime	ADJ
ejpam-6600	376	17	order	order	NOUN
ejpam-6600	376	18	generalized	generalize	VERB
ejpam-6600	376	19	paley	paley	ADJ
ejpam-6600	376	20	graphs	graph	NOUN
ejpam-6600	376	21	5.1	5.1	NUM
ejpam-6600	376	22	.	.	PUNCT
ejpam-6600	377	1	edge	edge	NOUN
ejpam-6600	377	2	-	-	PUNCT
ejpam-6600	377	3	graceful	graceful	ADJ
ejpam-6600	377	4	labeling	labeling	NOUN
ejpam-6600	377	5	algorithm	algorithm	NOUN
ejpam-6600	377	6	for	for	ADP
ejpam-6600	377	7	generalized	generalized	ADJ
ejpam-6600	377	8	paley	paley	ADJ
ejpam-6600	377	9	graphs	graph	NOUN
ejpam-6600	377	10	of	of	ADP
ejpam-6600	377	11	prime	prime	ADJ
ejpam-6600	377	12	order	order	NOUN
ejpam-6600	377	13	input	input	NOUN
ejpam-6600	377	14	:	:	PUNCT
ejpam-6600	377	15	the	the	DET
ejpam-6600	377	16	generalized	generalized	ADJ
ejpam-6600	377	17	paley	paley	NOUN
ejpam-6600	377	18	graph	graph	NOUN
ejpam-6600	377	19	m	m	VERB
ejpam-6600	377	20	−	−	NOUN
ejpam-6600	377	21	pp	pp	ADV
ejpam-6600	377	22	has	have	VERB
ejpam-6600	377	23	v	v	NUM
ejpam-6600	377	24	(	(	PUNCT
ejpam-6600	377	25	m	m	NOUN
ejpam-6600	377	26	−	−	NOUN
ejpam-6600	377	27	pp	pp	ADJ
ejpam-6600	377	28	)	)	PUNCT
ejpam-6600	377	29	=	=	SYM
ejpam-6600	377	30	zp	zp	PROPN
ejpam-6600	377	31	and	and	CCONJ
ejpam-6600	377	32	e(m	e(m	PROPN
ejpam-6600	377	33	−	−	PROPN
ejpam-6600	378	1	pp	pp	ADJ
ejpam-6600	378	2	)	)	PUNCT
ejpam-6600	378	3	=	=	PRON
ejpam-6600	378	4	{	{	PUNCT
ejpam-6600	378	5	(	(	PUNCT
ejpam-6600	378	6	u	u	NOUN
ejpam-6600	378	7	,	,	PUNCT
ejpam-6600	378	8	v	v	NOUN
ejpam-6600	378	9	)	)	PUNCT
ejpam-6600	379	1	|	|	ADV
ejpam-6600	379	2	u	u	NOUN
ejpam-6600	380	1	−	−	PROPN
ejpam-6600	380	2	v	v	ADP
ejpam-6600	380	3	∈	∈	PROPN
ejpam-6600	380	4	(	(	PUNCT
ejpam-6600	380	5	z∗	z∗	NOUN
ejpam-6600	380	6	p	p	NOUN
ejpam-6600	380	7	)	)	PUNCT
ejpam-6600	380	8	m	m	VERB
ejpam-6600	380	9	}	}	PUNCT
ejpam-6600	380	10	,	,	PUNCT
ejpam-6600	380	11	such	such	ADJ
ejpam-6600	380	12	that	that	SCONJ
ejpam-6600	380	13	:	:	PUNCT
ejpam-6600	380	14	if	if	SCONJ
ejpam-6600	380	15	m	m	NOUN
ejpam-6600	380	16	is	be	AUX
ejpam-6600	380	17	even	even	ADV
ejpam-6600	380	18	then	then	ADV
ejpam-6600	380	19	p	p	PROPN
ejpam-6600	380	20	≡	≡	PROPN
ejpam-6600	380	21	1	1	NUM
ejpam-6600	380	22	(	(	PUNCT
ejpam-6600	380	23	mod	mod	PROPN
ejpam-6600	380	24	2	2	NUM
ejpam-6600	380	25	m	m	NOUN
ejpam-6600	380	26	)	)	PUNCT
ejpam-6600	380	27	and	and	CCONJ
ejpam-6600	380	28	if	if	SCONJ
ejpam-6600	380	29	m	m	NOUN
ejpam-6600	380	30	is	be	AUX
ejpam-6600	380	31	odd	odd	ADJ
ejpam-6600	380	32	then	then	ADV
ejpam-6600	380	33	p	p	PRON
ejpam-6600	380	34	is	be	AUX
ejpam-6600	380	35	any	any	DET
ejpam-6600	380	36	odd	odd	ADJ
ejpam-6600	380	37	prime	prime	NOUN
ejpam-6600	380	38	.	.	PUNCT
ejpam-6600	381	1	(	(	PUNCT
ejpam-6600	381	2	1	1	X
ejpam-6600	381	3	)	)	PUNCT
ejpam-6600	381	4	rename	rename	VERB
ejpam-6600	381	5	the	the	DET
ejpam-6600	381	6	vertices	vertex	NOUN
ejpam-6600	381	7	of	of	ADP
ejpam-6600	381	8	the	the	DET
ejpam-6600	381	9	graph	graph	NOUN
ejpam-6600	381	10	as	as	ADP
ejpam-6600	381	11	0	0	NUM
ejpam-6600	381	12	:	:	PUNCT
ejpam-6600	381	13	=	=	SYM
ejpam-6600	381	14	vp	vp	NOUN
ejpam-6600	381	15	,	,	PUNCT
ejpam-6600	381	16	1	1	NUM
ejpam-6600	381	17	:	:	PUNCT
ejpam-6600	381	18	=	=	NOUN
ejpam-6600	381	19	v1	v1	NOUN
ejpam-6600	381	20	,	,	PUNCT
ejpam-6600	381	21	2	2	NUM
ejpam-6600	381	22	:	:	PUNCT
ejpam-6600	381	23	=	=	SYM
ejpam-6600	381	24	v2	v2	PROPN
ejpam-6600	381	25	,	,	PUNCT
ejpam-6600	381	26	.	.	PUNCT
ejpam-6600	381	27	.	.	PUNCT
ejpam-6600	382	1	.	.	PUNCT
ejpam-6600	383	1	,	,	PUNCT
ejpam-6600	383	2	p−	p−	NOUN
ejpam-6600	383	3	1	1	NUM
ejpam-6600	383	4	:	:	PUNCT
ejpam-6600	383	5	=	=	SYM
ejpam-6600	383	6	vp−1	vp−1	PROPN
ejpam-6600	383	7	.	.	PUNCT
ejpam-6600	384	1	(	(	PUNCT
ejpam-6600	384	2	2	2	X
ejpam-6600	384	3	)	)	PUNCT
ejpam-6600	384	4	set	set	NOUN
ejpam-6600	384	5	r	r	NOUN
ejpam-6600	384	6	=	=	SYM
ejpam-6600	384	7	p−1	p−1	PROPN
ejpam-6600	384	8	2d	2d	NOUN
ejpam-6600	384	9	,	,	PUNCT
ejpam-6600	384	10	where	where	SCONJ
ejpam-6600	384	11	d	d	PROPN
ejpam-6600	384	12	=	=	SYM
ejpam-6600	384	13	gcd(m	gcd(m	PROPN
ejpam-6600	384	14	,	,	PUNCT
ejpam-6600	384	15	p−	p−	NOUN
ejpam-6600	384	16	1	1	NUM
ejpam-6600	384	17	)	)	PUNCT
ejpam-6600	384	18	,	,	PUNCT
ejpam-6600	384	19	and	and	CCONJ
ejpam-6600	384	20	rewrite	rewrite	VERB
ejpam-6600	384	21	(	(	PUNCT
ejpam-6600	384	22	z∗	z∗	NOUN
ejpam-6600	384	23	p	p	NOUN
ejpam-6600	384	24	)	)	PUNCT
ejpam-6600	384	25	m	m	VERB
ejpam-6600	384	26	as	as	ADP
ejpam-6600	384	27	(	(	PUNCT
ejpam-6600	384	28	z∗	z∗	NOUN
ejpam-6600	384	29	p	p	NOUN
ejpam-6600	384	30	)	)	PUNCT
ejpam-6600	384	31	m	m	PROPN
ejpam-6600	384	32	=	=	SYM
ejpam-6600	384	33	s	s	PART
ejpam-6600	384	34	=	=	PUNCT
ejpam-6600	384	35	{	{	PUNCT
ejpam-6600	384	36	s1	s1	NOUN
ejpam-6600	384	37	,	,	PUNCT
ejpam-6600	384	38	s2	s2	PROPN
ejpam-6600	384	39	,	,	PUNCT
ejpam-6600	384	40	s3	s3	PROPN
ejpam-6600	384	41	,	,	PUNCT
ejpam-6600	384	42	.	.	PUNCT
ejpam-6600	384	43	.	.	PUNCT
ejpam-6600	384	44	.	.	PUNCT
ejpam-6600	385	1	,	,	PUNCT
ejpam-6600	385	2	s2r	s2r	PROPN
ejpam-6600	385	3	:	:	PUNCT
ejpam-6600	385	4	s1	s1	NOUN
ejpam-6600	385	5	<	<	X
ejpam-6600	385	6	s2	s2	PROPN
ejpam-6600	385	7	<	<	X
ejpam-6600	385	8	s3	s3	PROPN
ejpam-6600	385	9	<	<	X
ejpam-6600	385	10	.	.	PUNCT
ejpam-6600	385	11	.	.	PUNCT
ejpam-6600	386	1	.	.	PUNCT
ejpam-6600	387	1	<	<	X
ejpam-6600	387	2	s2r	s2r	PROPN
ejpam-6600	387	3	}	}	PUNCT
ejpam-6600	387	4	.	.	PUNCT
ejpam-6600	388	1	(	(	PUNCT
ejpam-6600	388	2	3	3	X
ejpam-6600	388	3	)	)	PUNCT
ejpam-6600	388	4	partition	partition	NOUN
ejpam-6600	388	5	s	s	NOUN
ejpam-6600	388	6	into	into	ADP
ejpam-6600	388	7	two	two	NUM
ejpam-6600	388	8	sets	set	NOUN
ejpam-6600	388	9	.	.	PUNCT
ejpam-6600	389	1	let	let	VERB
ejpam-6600	389	2	s1	s1	PROPN
ejpam-6600	389	3	=	=	PUNCT
ejpam-6600	389	4	{	{	PUNCT
ejpam-6600	389	5	s1	s1	NOUN
ejpam-6600	389	6	,	,	PUNCT
ejpam-6600	389	7	s2	s2	PROPN
ejpam-6600	389	8	,	,	PUNCT
ejpam-6600	389	9	s3	s3	PROPN
ejpam-6600	389	10	,	,	PUNCT
ejpam-6600	389	11	.	.	PUNCT
ejpam-6600	389	12	.	.	PUNCT
ejpam-6600	390	1	.	.	PUNCT
ejpam-6600	391	1	,	,	PUNCT
ejpam-6600	391	2	sr	sr	PROPN
ejpam-6600	391	3	}	}	PUNCT
ejpam-6600	391	4	and	and	CCONJ
ejpam-6600	391	5	s2	s2	VERB
ejpam-6600	391	6	=	=	SYM
ejpam-6600	391	7	{	{	PUNCT
ejpam-6600	391	8	sr+1	sr+1	PROPN
ejpam-6600	391	9	,	,	PUNCT
ejpam-6600	391	10	sr+2	sr+2	NOUN
ejpam-6600	391	11	,	,	PUNCT
ejpam-6600	391	12	sr+3	sr+3	NOUN
ejpam-6600	391	13	,	,	PUNCT
ejpam-6600	391	14	.	.	PUNCT
ejpam-6600	391	15	.	.	PUNCT
ejpam-6600	392	1	.	.	PUNCT
ejpam-6600	393	1	,	,	PUNCT
ejpam-6600	393	2	s2r	s2r	PROPN
ejpam-6600	393	3	}	}	PUNCT
ejpam-6600	393	4	.	.	PUNCT
ejpam-6600	394	1	note	note	VERB
ejpam-6600	394	2	that	that	SCONJ
ejpam-6600	394	3	:	:	PUNCT
ejpam-6600	394	4	p−1	p−1	PROPN
ejpam-6600	394	5	is	be	AUX
ejpam-6600	394	6	divisible	divisible	ADJ
ejpam-6600	394	7	by	by	ADP
ejpam-6600	394	8	2d	2d	NOUN
ejpam-6600	394	9	and	and	CCONJ
ejpam-6600	394	10	for	for	ADP
ejpam-6600	394	11	any	any	DET
ejpam-6600	394	12	vertex	vertex	NOUN
ejpam-6600	394	13	vi	vi	PROPN
ejpam-6600	394	14	∈	∈	PROPN
ejpam-6600	394	15	zp	zp	NOUN
ejpam-6600	394	16	the	the	DET
ejpam-6600	394	17	vertex	vertex	NOUN
ejpam-6600	394	18	vi+sj	vi+sj	PROPN
ejpam-6600	394	19	is	be	AUX
ejpam-6600	394	20	adjacent	adjacent	ADJ
ejpam-6600	394	21	to	to	PART
ejpam-6600	394	22	vi	vi	VERB
ejpam-6600	394	23	for	for	ADP
ejpam-6600	394	24	all	all	DET
ejpam-6600	394	25	sj	sj	PROPN
ejpam-6600	394	26	∈	∈	PROPN
ejpam-6600	394	27	s.	s.	PROPN
ejpam-6600	394	28	(	(	PUNCT
ejpam-6600	394	29	4	4	X
ejpam-6600	394	30	)	)	PUNCT
ejpam-6600	394	31	if	if	SCONJ
ejpam-6600	394	32	sj	sj	PROPN
ejpam-6600	394	33	∈	∈	PROPN
ejpam-6600	394	34	s1	s1	PROPN
ejpam-6600	394	35	,	,	PUNCT
ejpam-6600	394	36	the	the	DET
ejpam-6600	394	37	vertex	vertex	NOUN
ejpam-6600	394	38	vi+sj	vi+sj	PROPN
ejpam-6600	394	39	is	be	AUX
ejpam-6600	394	40	placed	place	VERB
ejpam-6600	394	41	in	in	ADP
ejpam-6600	394	42	clockwise	clockwise	NOUN
ejpam-6600	394	43	direction	direction	NOUN
ejpam-6600	394	44	of	of	ADP
ejpam-6600	394	45	vi	vi	NOUN
ejpam-6600	394	46	and	and	CCONJ
ejpam-6600	394	47	if	if	SCONJ
ejpam-6600	394	48	sj	sj	PROPN
ejpam-6600	394	49	∈	∈	PROPN
ejpam-6600	394	50	s2	s2	PROPN
ejpam-6600	394	51	,	,	PUNCT
ejpam-6600	394	52	the	the	DET
ejpam-6600	394	53	vertex	vertex	NOUN
ejpam-6600	394	54	vi+sj	vi+sj	PROPN
ejpam-6600	394	55	is	be	AUX
ejpam-6600	394	56	placed	place	VERB
ejpam-6600	394	57	in	in	ADP
ejpam-6600	394	58	anticlockwise	anticlockwise	NOUN
ejpam-6600	394	59	direction	direction	NOUN
ejpam-6600	394	60	of	of	ADP
ejpam-6600	394	61	vi	vi	PROPN
ejpam-6600	394	62	.	.	PUNCT
ejpam-6600	395	1	(	(	PUNCT
ejpam-6600	395	2	5	5	X
ejpam-6600	395	3	)	)	PUNCT
ejpam-6600	395	4	set	set	NOUN
ejpam-6600	395	5	f(vi	f(vi	PROPN
ejpam-6600	395	6	,	,	PUNCT
ejpam-6600	395	7	vi+sj	vi+sj	NUM
ejpam-6600	395	8	)	)	PUNCT
ejpam-6600	396	1	=	=	SYM
ejpam-6600	396	2	0	0	NUM
ejpam-6600	397	1	for	for	ADP
ejpam-6600	397	2	all	all	PRON
ejpam-6600	397	3	i	i	PRON
ejpam-6600	397	4	∈	∈	PROPN
ejpam-6600	397	5	{	{	PUNCT
ejpam-6600	397	6	1	1	NUM
ejpam-6600	397	7	,	,	PUNCT
ejpam-6600	397	8	2	2	NUM
ejpam-6600	397	9	,	,	PUNCT
ejpam-6600	397	10	3	3	NUM
ejpam-6600	397	11	,	,	PUNCT
ejpam-6600	397	12	·	·	PUNCT
ejpam-6600	397	13	·	·	PUNCT
ejpam-6600	397	14	·	·	PUNCT
ejpam-6600	397	15	,	,	PUNCT
ejpam-6600	397	16	p	p	X
ejpam-6600	397	17	}	}	PUNCT
ejpam-6600	397	18	,	,	PUNCT
ejpam-6600	397	19	j	j	PROPN
ejpam-6600	397	20	∈	∈	PROPN
ejpam-6600	397	21	{	{	PUNCT
ejpam-6600	397	22	1	1	NUM
ejpam-6600	397	23	,	,	PUNCT
ejpam-6600	397	24	2	2	NUM
ejpam-6600	397	25	,	,	PUNCT
ejpam-6600	397	26	3	3	NUM
ejpam-6600	397	27	,	,	PUNCT
ejpam-6600	397	28	·	·	PUNCT
ejpam-6600	397	29	·	·	PUNCT
ejpam-6600	397	30	·	·	PUNCT
ejpam-6600	397	31	,	,	PUNCT
ejpam-6600	397	32	2r	2r	NUM
ejpam-6600	397	33	}	}	PUNCT
ejpam-6600	397	34	.	.	PUNCT
ejpam-6600	398	1	(	(	PUNCT
ejpam-6600	398	2	6	6	X
ejpam-6600	398	3	)	)	PUNCT
ejpam-6600	398	4	set	set	NOUN
ejpam-6600	398	5	i	i	NOUN
ejpam-6600	398	6	=	=	NOUN
ejpam-6600	399	1	1	1	X
ejpam-6600	399	2	.	.	X
ejpam-6600	399	3	step	step	NOUN
ejpam-6600	399	4	1	1	NUM
ejpam-6600	399	5	:	:	PUNCT
ejpam-6600	399	6	if	if	SCONJ
ejpam-6600	399	7	i	i	PRON
ejpam-6600	399	8	≤	≤	VERB
ejpam-6600	399	9	p	p	NOUN
ejpam-6600	399	10	then	then	ADV
ejpam-6600	399	11	continue	continue	VERB
ejpam-6600	399	12	to	to	PART
ejpam-6600	399	13	step	step	VERB
ejpam-6600	399	14	2	2	NUM
ejpam-6600	399	15	.	.	PUNCT
ejpam-6600	399	16	else	else	ADV
ejpam-6600	399	17	jump	jump	VERB
ejpam-6600	399	18	to	to	PART
ejpam-6600	399	19	step	step	VERB
ejpam-6600	399	20	4	4	NUM
ejpam-6600	399	21	.	.	PUNCT
ejpam-6600	400	1	step	step	NOUN
ejpam-6600	400	2	2	2	NUM
ejpam-6600	400	3	:	:	PUNCT
ejpam-6600	400	4	for	for	ADP
ejpam-6600	400	5	each	each	DET
ejpam-6600	400	6	sj	sj	PROPN
ejpam-6600	400	7	∈	∈	PROPN
ejpam-6600	400	8	s1	s1	PROPN
ejpam-6600	400	9	,	,	PUNCT
ejpam-6600	400	10	f	f	PROPN
ejpam-6600	400	11	(	(	PUNCT
ejpam-6600	400	12	vi	vi	PROPN
ejpam-6600	400	13	,	,	PUNCT
ejpam-6600	400	14	vi+sj	vi+sj	NUM
ejpam-6600	400	15	)	)	PUNCT
ejpam-6600	401	1	=	=	PRON
ejpam-6600	402	1	(	(	PUNCT
ejpam-6600	402	2	j	j	NOUN
ejpam-6600	402	3	−	−	PROPN
ejpam-6600	402	4	1	1	NUM
ejpam-6600	402	5	)	)	PUNCT
ejpam-6600	402	6	p+	p+	VERB
ejpam-6600	402	7	i.	i.	NOUN
ejpam-6600	402	8	step	step	NOUN
ejpam-6600	402	9	3	3	NUM
ejpam-6600	402	10	:	:	PUNCT
ejpam-6600	402	11	i	i	PRON
ejpam-6600	402	12	=	=	PUNCT
ejpam-6600	402	13	i+	i+	PROPN
ejpam-6600	402	14	1	1	NUM
ejpam-6600	402	15	,	,	PUNCT
ejpam-6600	402	16	go	go	VERB
ejpam-6600	402	17	back	back	ADV
ejpam-6600	402	18	to	to	PART
ejpam-6600	402	19	step	step	NOUN
ejpam-6600	402	20	1	1	NUM
ejpam-6600	402	21	.	.	PUNCT
ejpam-6600	403	1	step	step	NOUN
ejpam-6600	403	2	4	4	NUM
ejpam-6600	403	3	:	:	PUNCT
ejpam-6600	403	4	for	for	ADP
ejpam-6600	403	5	each	each	PRON
ejpam-6600	403	6	k	k	NOUN
ejpam-6600	403	7	=	=	SYM
ejpam-6600	403	8	1	1	NUM
ejpam-6600	403	9	,	,	PUNCT
ejpam-6600	403	10	2	2	NUM
ejpam-6600	403	11	,	,	PUNCT
ejpam-6600	403	12	3	3	NUM
ejpam-6600	403	13	,	,	PUNCT
ejpam-6600	403	14	.	.	PUNCT
ejpam-6600	403	15	.	.	PUNCT
ejpam-6600	404	1	.	.	PUNCT
ejpam-6600	405	1	,	,	PUNCT
ejpam-6600	405	2	p	p	X
ejpam-6600	405	3	,	,	PUNCT
ejpam-6600	405	4	find	find	VERB
ejpam-6600	405	5	the	the	DET
ejpam-6600	405	6	weight	weight	NOUN
ejpam-6600	405	7	of	of	ADP
ejpam-6600	405	8	the	the	DET
ejpam-6600	405	9	vertex	vertex	NOUN
ejpam-6600	405	10	vk	vk	NOUN
ejpam-6600	405	11	using	use	VERB
ejpam-6600	405	12	the	the	DET
ejpam-6600	405	13	following	follow	VERB
ejpam-6600	405	14	mapping	mapping	NOUN
ejpam-6600	405	15	:	:	PUNCT
ejpam-6600	405	16	fw(vk	fw(vk	PROPN
ejpam-6600	405	17	)	)	PUNCT
ejpam-6600	406	1	=	=	PUNCT
ejpam-6600	407	1	∑2r	∑2r	NOUN
ejpam-6600	407	2	j=1	j=1	PROPN
ejpam-6600	407	3	f(vk	f(vk	PROPN
ejpam-6600	407	4	,	,	PUNCT
ejpam-6600	407	5	vk+sj	vk+sj	NOUN
ejpam-6600	407	6	)	)	PUNCT
ejpam-6600	408	1	=	=	PUNCT
ejpam-6600	409	1	∑r	∑r	PROPN
ejpam-6600	409	2	j=1	j=1	PROPN
ejpam-6600	409	3	2[(j−1)p+k]+(p−sj	2[(j−1)p+k]+(p−sj	NOUN
ejpam-6600	409	4	)	)	PUNCT
ejpam-6600	410	1	=	=	SYM
ejpam-6600	410	2	2kr−l	2kr−l	NUM
ejpam-6600	410	3	(	(	PUNCT
ejpam-6600	410	4	mod	mod	NOUN
ejpam-6600	410	5	p	p	NOUN
ejpam-6600	410	6	)	)	PUNCT
ejpam-6600	410	7	,	,	PUNCT
ejpam-6600	410	8	where	where	SCONJ
ejpam-6600	410	9	l	l	NOUN
ejpam-6600	410	10	=	=	PUNCT
ejpam-6600	411	1	∑r	∑r	PROPN
ejpam-6600	411	2	j=1	j=1	NOUN
ejpam-6600	411	3	sj	sj	INTJ
ejpam-6600	411	4	.	.	PUNCT
ejpam-6600	412	1	theorem	theorem	ADJ
ejpam-6600	412	2	5	5	NUM
ejpam-6600	412	3	.	.	PUNCT
ejpam-6600	412	4	paley	paley	ADJ
ejpam-6600	412	5	graphs	graph	NOUN
ejpam-6600	412	6	and	and	CCONJ
ejpam-6600	412	7	their	their	PRON
ejpam-6600	412	8	generalizations	generalization	NOUN
ejpam-6600	412	9	of	of	ADP
ejpam-6600	412	10	prime	prime	ADJ
ejpam-6600	412	11	order	order	NOUN
ejpam-6600	412	12	are	be	AUX
ejpam-6600	412	13	edge	edge	NOUN
ejpam-6600	412	14	-	-	PUNCT
ejpam-6600	412	15	graceful	graceful	NOUN
ejpam-6600	412	16	graphs	graph	NOUN
ejpam-6600	412	17	.	.	PUNCT
ejpam-6600	413	1	proof	proof	NOUN
ejpam-6600	413	2	.	.	PUNCT
ejpam-6600	414	1	to	to	PART
ejpam-6600	414	2	prove	prove	VERB
ejpam-6600	414	3	that	that	SCONJ
ejpam-6600	414	4	the	the	DET
ejpam-6600	414	5	algorithm	algorithm	NOUN
ejpam-6600	414	6	defines	define	VERB
ejpam-6600	414	7	an	an	DET
ejpam-6600	414	8	edge	edge	NOUN
ejpam-6600	414	9	-	-	PUNCT
ejpam-6600	414	10	graceful	graceful	NOUN
ejpam-6600	414	11	labeling	labeling	NOUN
ejpam-6600	414	12	,	,	PUNCT
ejpam-6600	414	13	we	we	PRON
ejpam-6600	414	14	need	need	VERB
ejpam-6600	414	15	to	to	PART
ejpam-6600	414	16	prove	prove	VERB
ejpam-6600	414	17	that	that	SCONJ
ejpam-6600	414	18	both	both	DET
ejpam-6600	414	19	functions	function	NOUN
ejpam-6600	414	20	f	f	PROPN
ejpam-6600	414	21	and	and	CCONJ
ejpam-6600	414	22	fw	fw	PROPN
ejpam-6600	414	23	are	be	AUX
ejpam-6600	414	24	bijections	bijection	NOUN
ejpam-6600	414	25	.	.	PUNCT
ejpam-6600	415	1	(	(	PUNCT
ejpam-6600	415	2	i	i	NOUN
ejpam-6600	415	3	)	)	PUNCT
ejpam-6600	415	4	consider	consider	VERB
ejpam-6600	415	5	the	the	DET
ejpam-6600	415	6	function	function	NOUN
ejpam-6600	415	7	fw	fw	INTJ
ejpam-6600	415	8	:	:	PUNCT
ejpam-6600	415	9	v	v	NOUN
ejpam-6600	415	10	(	(	PUNCT
ejpam-6600	415	11	m−pp	m−pp	NOUN
ejpam-6600	415	12	)	)	PUNCT
ejpam-6600	416	1	−→	−→	NOUN
ejpam-6600	416	2	zp	zp	INTJ
ejpam-6600	416	3	such	such	ADJ
ejpam-6600	416	4	that	that	SCONJ
ejpam-6600	416	5	fw(vk	fw(vk	PROPN
ejpam-6600	416	6	)	)	PUNCT
ejpam-6600	417	1	=	=	PUNCT
ejpam-6600	418	1	∑2r	∑2r	PROPN
ejpam-6600	418	2	j=1	j=1	PROPN
ejpam-6600	418	3	f(vk	f(vk	PROPN
ejpam-6600	418	4	,	,	PUNCT
ejpam-6600	418	5	vk+sj	vk+sj	NOUN
ejpam-6600	418	6	)	)	PUNCT
ejpam-6600	419	1	=	=	PUNCT
ejpam-6600	420	1	2kr	2kr	NOUN
ejpam-6600	420	2	−	−	NOUN
ejpam-6600	420	3	l	l	NOUN
ejpam-6600	420	4	(	(	PUNCT
ejpam-6600	420	5	mod	mod	PROPN
ejpam-6600	420	6	p	p	X
ejpam-6600	420	7	)	)	PUNCT
ejpam-6600	420	8	.	.	PUNCT
ejpam-6600	421	1	now	now	ADV
ejpam-6600	421	2	,	,	PUNCT
ejpam-6600	421	3	we	we	PRON
ejpam-6600	421	4	prove	prove	VERB
ejpam-6600	421	5	that	that	SCONJ
ejpam-6600	421	6	fw	fw	PROPN
ejpam-6600	421	7	is	be	AUX
ejpam-6600	421	8	one	one	NUM
ejpam-6600	421	9	-	-	PUNCT
ejpam-6600	421	10	to	to	ADP
ejpam-6600	421	11	-	-	PUNCT
ejpam-6600	421	12	one	one	NOUN
ejpam-6600	421	13	,	,	PUNCT
ejpam-6600	421	14	which	which	PRON
ejpam-6600	421	15	implies	imply	VERB
ejpam-6600	421	16	tat	tat	NOUN
ejpam-6600	421	17	it	it	PRON
ejpam-6600	421	18	is	be	AUX
ejpam-6600	421	19	a	a	DET
ejpam-6600	421	20	bijection	bijection	NOUN
ejpam-6600	421	21	.	.	PUNCT
ejpam-6600	422	1	let	let	VERB
ejpam-6600	422	2	vx	vx	PROPN
ejpam-6600	422	3	and	and	CCONJ
ejpam-6600	422	4	vy	vy	PRON
ejpam-6600	422	5	be	be	AUX
ejpam-6600	422	6	two	two	NUM
ejpam-6600	422	7	vertices	vertex	NOUN
ejpam-6600	422	8	in	in	ADP
ejpam-6600	422	9	v	v	NOUN
ejpam-6600	422	10	(	(	PUNCT
ejpam-6600	422	11	m	m	NOUN
ejpam-6600	422	12	−	−	NOUN
ejpam-6600	422	13	pp	pp	ADJ
ejpam-6600	422	14	)	)	PUNCT
ejpam-6600	422	15	,	,	PUNCT
ejpam-6600	422	16	if	if	SCONJ
ejpam-6600	422	17	fw(vx	fw(vx	NOUN
ejpam-6600	422	18	)	)	PUNCT
ejpam-6600	422	19	=	=	SYM
ejpam-6600	423	1	fw(vy	fw(vy	PROPN
ejpam-6600	423	2	)	)	PUNCT
ejpam-6600	423	3	then	then	ADV
ejpam-6600	423	4	2xr	2xr	ADJ
ejpam-6600	423	5	−	−	PROPN
ejpam-6600	423	6	l	l	NOUN
ejpam-6600	423	7	=	=	PUNCT
ejpam-6600	423	8	2yr	2yr	NOUN
ejpam-6600	424	1	−	−	PROPN
ejpam-6600	424	2	l	l	NOUN
ejpam-6600	424	3	(	(	PUNCT
ejpam-6600	424	4	mod	mod	PROPN
ejpam-6600	424	5	p	p	X
ejpam-6600	424	6	)	)	PUNCT
ejpam-6600	424	7	which	which	PRON
ejpam-6600	424	8	leads	lead	VERB
ejpam-6600	424	9	to	to	ADP
ejpam-6600	424	10	x	x	X
ejpam-6600	424	11	=	=	PUNCT
ejpam-6600	424	12	y.	y.	PROPN
ejpam-6600	424	13	a.	a.	PROPN
ejpam-6600	424	14	n.	n.	PROPN
ejpam-6600	424	15	elsawy	elsawy	PROPN
ejpam-6600	424	16	,	,	PUNCT
ejpam-6600	424	17	r.	r.	PROPN
ejpam-6600	424	18	n.	n.	PROPN
ejpam-6600	424	19	almohammadi	almohammadi	PROPN
ejpam-6600	424	20	/	/	SYM
ejpam-6600	424	21	eur	eur	PROPN
ejpam-6600	424	22	.	.	PUNCT
ejpam-6600	425	1	j.	j.	PROPN
ejpam-6600	425	2	pure	pure	PROPN
ejpam-6600	425	3	appl	appl	PROPN
ejpam-6600	425	4	.	.	PROPN
ejpam-6600	425	5	math	math	PROPN
ejpam-6600	425	6	,	,	PUNCT
ejpam-6600	425	7	18	18	NUM
ejpam-6600	425	8	(	(	PUNCT
ejpam-6600	425	9	4	4	NUM
ejpam-6600	425	10	)	)	PUNCT
ejpam-6600	425	11	(	(	PUNCT
ejpam-6600	425	12	2025	2025	NUM
ejpam-6600	425	13	)	)	PUNCT
ejpam-6600	425	14	,	,	PUNCT
ejpam-6600	425	15	6600	6600	NUM
ejpam-6600	425	16	15	15	NUM
ejpam-6600	425	17	of	of	ADP
ejpam-6600	425	18	26	26	NUM
ejpam-6600	425	19	(	(	PUNCT
ejpam-6600	425	20	ii	ii	NOUN
ejpam-6600	425	21	)	)	PUNCT
ejpam-6600	425	22	the	the	DET
ejpam-6600	425	23	function	function	NOUN
ejpam-6600	425	24	f	f	NOUN
ejpam-6600	425	25	:	:	PUNCT
ejpam-6600	425	26	e(m	e(m	PROPN
ejpam-6600	425	27	−	−	PROPN
ejpam-6600	425	28	pp	pp	ADJ
ejpam-6600	425	29	)	)	PUNCT
ejpam-6600	425	30	−→	−→	NOUN
ejpam-6600	425	31	{	{	PUNCT
ejpam-6600	425	32	1	1	NUM
ejpam-6600	425	33	,	,	PUNCT
ejpam-6600	425	34	2	2	NUM
ejpam-6600	425	35	,	,	PUNCT
ejpam-6600	425	36	3	3	NUM
ejpam-6600	425	37	,	,	PUNCT
ejpam-6600	425	38	.	.	PUNCT
ejpam-6600	425	39	.	.	PUNCT
ejpam-6600	426	1	.	.	PUNCT
ejpam-6600	427	1	,	,	PUNCT
ejpam-6600	427	2	rp	rp	NOUN
ejpam-6600	427	3	}	}	PUNCT
ejpam-6600	427	4	is	be	AUX
ejpam-6600	427	5	defined	define	VERB
ejpam-6600	427	6	as	as	ADP
ejpam-6600	427	7	f(vx	f(vx	PROPN
ejpam-6600	427	8	,	,	PUNCT
ejpam-6600	427	9	vx+sj	vx+sj	ADJ
ejpam-6600	427	10	)	)	PUNCT
ejpam-6600	428	1	=	=	SYM
ejpam-6600	428	2	(	(	PUNCT
ejpam-6600	428	3	j	j	PROPN
ejpam-6600	428	4	−	−	PROPN
ejpam-6600	428	5	1)p+	1)p+	NUM
ejpam-6600	428	6	x.	x.	NOUN
ejpam-6600	428	7	to	to	PART
ejpam-6600	428	8	prove	prove	VERB
ejpam-6600	428	9	that	that	SCONJ
ejpam-6600	428	10	f	f	PROPN
ejpam-6600	428	11	is	be	AUX
ejpam-6600	428	12	a	a	DET
ejpam-6600	428	13	bijection	bijection	NOUN
ejpam-6600	428	14	,	,	PUNCT
ejpam-6600	428	15	we	we	PRON
ejpam-6600	428	16	need	need	VERB
ejpam-6600	428	17	only	only	ADV
ejpam-6600	428	18	to	to	PART
ejpam-6600	428	19	prove	prove	VERB
ejpam-6600	428	20	that	that	SCONJ
ejpam-6600	428	21	it	it	PRON
ejpam-6600	428	22	is	be	AUX
ejpam-6600	428	23	one	one	NUM
ejpam-6600	428	24	-	-	PUNCT
ejpam-6600	428	25	to	to	ADP
ejpam-6600	428	26	-	-	PUNCT
ejpam-6600	428	27	one	one	NUM
ejpam-6600	428	28	.	.	PUNCT
ejpam-6600	429	1	let	let	VERB
ejpam-6600	429	2	(	(	PUNCT
ejpam-6600	429	3	vx	vx	NOUN
ejpam-6600	429	4	,	,	PUNCT
ejpam-6600	429	5	vx+si	vx+si	NOUN
ejpam-6600	429	6	)	)	PUNCT
ejpam-6600	429	7	and	and	CCONJ
ejpam-6600	429	8	(	(	PUNCT
ejpam-6600	429	9	vy	vy	INTJ
ejpam-6600	429	10	,	,	PUNCT
ejpam-6600	429	11	vy+sj	vy+sj	PRON
ejpam-6600	429	12	)	)	PUNCT
ejpam-6600	429	13	be	be	AUX
ejpam-6600	429	14	two	two	NUM
ejpam-6600	429	15	edges	edge	NOUN
ejpam-6600	429	16	,	,	PUNCT
ejpam-6600	429	17	with	with	ADP
ejpam-6600	429	18	x	x	PRON
ejpam-6600	429	19	,	,	PUNCT
ejpam-6600	429	20	y	y	PROPN
ejpam-6600	429	21	∈	∈	PROPN
ejpam-6600	429	22	{	{	PUNCT
ejpam-6600	429	23	1	1	NUM
ejpam-6600	429	24	,	,	PUNCT
ejpam-6600	429	25	2	2	NUM
ejpam-6600	429	26	,	,	PUNCT
ejpam-6600	429	27	3	3	NUM
ejpam-6600	429	28	,	,	PUNCT
ejpam-6600	429	29	·	·	PUNCT
ejpam-6600	429	30	·	·	PUNCT
ejpam-6600	429	31	·	·	PUNCT
ejpam-6600	429	32	,	,	PUNCT
ejpam-6600	429	33	p	p	X
ejpam-6600	429	34	}	}	PUNCT
ejpam-6600	429	35	,	,	PUNCT
ejpam-6600	429	36	si	si	INTJ
ejpam-6600	429	37	,	,	PUNCT
ejpam-6600	429	38	sj	sj	PROPN
ejpam-6600	429	39	∈	∈	PROPN
ejpam-6600	429	40	s	s	PART
ejpam-6600	429	41	=	=	PUNCT
ejpam-6600	429	42	(	(	PUNCT
ejpam-6600	429	43	z∗	z∗	PROPN
ejpam-6600	429	44	p	p	NOUN
ejpam-6600	429	45	)	)	PUNCT
ejpam-6600	429	46	m	m	PROPN
ejpam-6600	429	47	,	,	PUNCT
ejpam-6600	429	48	and	and	CCONJ
ejpam-6600	429	49	f(vx	f(vx	PROPN
ejpam-6600	429	50	,	,	PUNCT
ejpam-6600	429	51	vx+sj	vx+sj	ADJ
ejpam-6600	429	52	)	)	PUNCT
ejpam-6600	429	53	=	=	SYM
ejpam-6600	430	1	f(vy	f(vy	ADJ
ejpam-6600	430	2	,	,	PUNCT
ejpam-6600	430	3	vy+si	vy+si	NOUN
ejpam-6600	430	4	)	)	PUNCT
ejpam-6600	430	5	,	,	PUNCT
ejpam-6600	430	6	which	which	PRON
ejpam-6600	430	7	implies	imply	VERB
ejpam-6600	430	8	that	that	SCONJ
ejpam-6600	430	9	(	(	PUNCT
ejpam-6600	430	10	i−1)p+x	i−1)p+x	NOUN
ejpam-6600	430	11	=	=	SYM
ejpam-6600	430	12	(	(	PUNCT
ejpam-6600	430	13	j−1)p+y	j−1)p+y	PROPN
ejpam-6600	430	14	.	.	PUNCT
ejpam-6600	431	1	in	in	ADP
ejpam-6600	431	2	case	case	NOUN
ejpam-6600	431	3	of	of	ADP
ejpam-6600	431	4	i	i	PRON
ejpam-6600	431	5	=	=	SYM
ejpam-6600	431	6	j	j	PROPN
ejpam-6600	431	7	or	or	CCONJ
ejpam-6600	431	8	x	x	X
ejpam-6600	431	9	=	=	SYM
ejpam-6600	431	10	y	y	PROPN
ejpam-6600	431	11	the	the	DET
ejpam-6600	431	12	proof	proof	NOUN
ejpam-6600	431	13	is	be	AUX
ejpam-6600	431	14	trivial	trivial	ADJ
ejpam-6600	431	15	.	.	PUNCT
ejpam-6600	432	1	the	the	DET
ejpam-6600	432	2	last	last	ADJ
ejpam-6600	432	3	case	case	NOUN
ejpam-6600	432	4	if	if	SCONJ
ejpam-6600	432	5	x	x	PROPN
ejpam-6600	432	6	̸=	̸=	PROPN
ejpam-6600	432	7	y	y	PROPN
ejpam-6600	432	8	and	and	CCONJ
ejpam-6600	432	9	j	j	PROPN
ejpam-6600	432	10	̸=	̸=	PROPN
ejpam-6600	432	11	i	i	PRON
ejpam-6600	432	12	,	,	PUNCT
ejpam-6600	432	13	here	here	ADV
ejpam-6600	432	14	we	we	PRON
ejpam-6600	432	15	will	will	AUX
ejpam-6600	432	16	find	find	VERB
ejpam-6600	432	17	that	that	SCONJ
ejpam-6600	432	18	x−	x−	PROPN
ejpam-6600	432	19	y	y	PROPN
ejpam-6600	432	20	=	=	PUNCT
ejpam-6600	432	21	(	(	PUNCT
ejpam-6600	432	22	j−	j−	PROPN
ejpam-6600	432	23	i)p	i)p	ADV
ejpam-6600	432	24	but	but	CCONJ
ejpam-6600	432	25	|x−	|x−	NOUN
ejpam-6600	432	26	y|	y|	VERB
ejpam-6600	432	27	<	<	X
ejpam-6600	432	28	p	p	X
ejpam-6600	432	29	and	and	CCONJ
ejpam-6600	432	30	in	in	ADP
ejpam-6600	432	31	the	the	DET
ejpam-6600	432	32	same	same	ADJ
ejpam-6600	432	33	time	time	NOUN
ejpam-6600	432	34	|p(i−	|p(i−	NUM
ejpam-6600	432	35	j)|	j)|	NOUN
ejpam-6600	432	36	≥	≥	NOUN
ejpam-6600	432	37	p	p	NOUN
ejpam-6600	432	38	which	which	PRON
ejpam-6600	432	39	is	be	AUX
ejpam-6600	432	40	a	a	DET
ejpam-6600	432	41	contradiction	contradiction	NOUN
ejpam-6600	432	42	.	.	PUNCT
ejpam-6600	433	1	so	so	ADV
ejpam-6600	433	2	,	,	PUNCT
ejpam-6600	433	3	from	from	ADP
ejpam-6600	433	4	these	these	DET
ejpam-6600	433	5	three	three	NUM
ejpam-6600	433	6	cases	case	NOUN
ejpam-6600	433	7	,	,	PUNCT
ejpam-6600	433	8	we	we	PRON
ejpam-6600	433	9	can	can	AUX
ejpam-6600	433	10	be	be	AUX
ejpam-6600	433	11	sure	sure	ADJ
ejpam-6600	433	12	that	that	SCONJ
ejpam-6600	433	13	the	the	DET
ejpam-6600	433	14	function	function	NOUN
ejpam-6600	433	15	f	f	PROPN
ejpam-6600	433	16	is	be	AUX
ejpam-6600	433	17	a	a	DET
ejpam-6600	433	18	one	one	NUM
ejpam-6600	433	19	-	-	PUNCT
ejpam-6600	433	20	to	to	ADP
ejpam-6600	433	21	-	-	PUNCT
ejpam-6600	433	22	one	one	NUM
ejpam-6600	433	23	function	function	NOUN
ejpam-6600	433	24	.	.	PUNCT
ejpam-6600	434	1	□	□	PUNCT
ejpam-6600	434	2	example	example	NOUN
ejpam-6600	434	3	9	9	NUM
ejpam-6600	434	4	.	.	X
ejpam-6600	434	5	consider	consider	VERB
ejpam-6600	434	6	the	the	DET
ejpam-6600	434	7	cubic	cubic	ADJ
ejpam-6600	434	8	paley	paley	NOUN
ejpam-6600	434	9	graph	graph	NOUN
ejpam-6600	434	10	3−	3−	NUM
ejpam-6600	434	11	p13	p13	NOUN
ejpam-6600	434	12	.	.	PUNCT
ejpam-6600	435	1	here	here	ADV
ejpam-6600	435	2	,	,	PUNCT
ejpam-6600	435	3	p	p	X
ejpam-6600	435	4	=	=	SYM
ejpam-6600	435	5	13,m	13,m	NUM
ejpam-6600	435	6	=	=	SYM
ejpam-6600	435	7	3	3	NUM
ejpam-6600	435	8	,	,	PUNCT
ejpam-6600	435	9	d	d	NOUN
ejpam-6600	435	10	=	=	SYM
ejpam-6600	435	11	3	3	NUM
ejpam-6600	435	12	,	,	PUNCT
ejpam-6600	435	13	r	r	NOUN
ejpam-6600	435	14	=	=	SYM
ejpam-6600	435	15	2	2	NUM
ejpam-6600	435	16	,	,	PUNCT
ejpam-6600	435	17	and	and	CCONJ
ejpam-6600	435	18	s1	s1	PROPN
ejpam-6600	435	19	=	=	SYM
ejpam-6600	435	20	{	{	PUNCT
ejpam-6600	435	21	1	1	NUM
ejpam-6600	435	22	,	,	PUNCT
ejpam-6600	435	23	5	5	NUM
ejpam-6600	435	24	}	}	PUNCT
ejpam-6600	435	25	.	.	PUNCT
ejpam-6600	436	1	so	so	ADV
ejpam-6600	436	2	for	for	ADP
ejpam-6600	436	3	each	each	DET
ejpam-6600	436	4	sj	sj	PROPN
ejpam-6600	436	5	∈	∈	PROPN
ejpam-6600	436	6	s1	s1	PROPN
ejpam-6600	436	7	,	,	PUNCT
ejpam-6600	436	8	f	f	PROPN
ejpam-6600	436	9	(	(	PUNCT
ejpam-6600	436	10	vk	vk	PROPN
ejpam-6600	436	11	,	,	PUNCT
ejpam-6600	436	12	vk+sj	vk+sj	NOUN
ejpam-6600	436	13	)	)	PUNCT
ejpam-6600	436	14	=	=	PUNCT
ejpam-6600	437	1	(	(	PUNCT
ejpam-6600	437	2	j	j	NOUN
ejpam-6600	437	3	−	−	PROPN
ejpam-6600	437	4	1	1	NUM
ejpam-6600	437	5	)	)	PUNCT
ejpam-6600	437	6	13	13	NUM
ejpam-6600	438	1	+	+	CCONJ
ejpam-6600	438	2	k	k	NOUN
ejpam-6600	438	3	,	,	PUNCT
ejpam-6600	438	4	and	and	CCONJ
ejpam-6600	438	5	fw(vk	fw(vk	PROPN
ejpam-6600	438	6	)	)	PUNCT
ejpam-6600	439	1	=	=	PUNCT
ejpam-6600	440	1	4k−	4k−	PROPN
ejpam-6600	440	2	∑2	∑2	NOUN
ejpam-6600	440	3	j=1	j=1	NOUN
ejpam-6600	440	4	sj	sj	PROPN
ejpam-6600	440	5	=	=	SYM
ejpam-6600	440	6	4k−	4k−	PROPN
ejpam-6600	440	7	6	6	NUM
ejpam-6600	440	8	(	(	PUNCT
ejpam-6600	440	9	mod	mod	PROPN
ejpam-6600	440	10	13	13	NUM
ejpam-6600	440	11	)	)	PUNCT
ejpam-6600	440	12	.	.	PUNCT
ejpam-6600	441	1	the	the	DET
ejpam-6600	441	2	edge	edge	NOUN
ejpam-6600	441	3	-	-	PUNCT
ejpam-6600	441	4	graceful	graceful	NOUN
ejpam-6600	441	5	labeling	labeling	NOUN
ejpam-6600	441	6	of	of	ADP
ejpam-6600	441	7	the	the	DET
ejpam-6600	441	8	graph	graph	NOUN
ejpam-6600	441	9	3−p13	3−p13	PROPN
ejpam-6600	441	10	is	be	AUX
ejpam-6600	441	11	shown	show	VERB
ejpam-6600	441	12	in	in	ADP
ejpam-6600	441	13	figure	figure	NOUN
ejpam-6600	441	14	10	10	NUM
ejpam-6600	441	15	.	.	PUNCT
ejpam-6600	442	1	figure	figure	VERB
ejpam-6600	442	2	10	10	NUM
ejpam-6600	442	3	:	:	PUNCT
ejpam-6600	442	4	an	an	DET
ejpam-6600	442	5	edge	edge	NOUN
ejpam-6600	442	6	-	-	PUNCT
ejpam-6600	442	7	graceful	graceful	NOUN
ejpam-6600	442	8	labeling	labeling	NOUN
ejpam-6600	442	9	of	of	ADP
ejpam-6600	442	10	3−	3−	NUM
ejpam-6600	442	11	p13	p13	NOUN
ejpam-6600	442	12	.	.	PUNCT
ejpam-6600	442	13	example	example	NOUN
ejpam-6600	442	14	10	10	NUM
ejpam-6600	442	15	.	.	PUNCT
ejpam-6600	443	1	consider	consider	VERB
ejpam-6600	443	2	the	the	DET
ejpam-6600	443	3	generalized	generalized	ADJ
ejpam-6600	443	4	paley	paley	NOUN
ejpam-6600	443	5	graph	graph	NOUN
ejpam-6600	443	6	5−p7	5−p7	NUM
ejpam-6600	443	7	.	.	PUNCT
ejpam-6600	444	1	here	here	ADV
ejpam-6600	444	2	,	,	PUNCT
ejpam-6600	444	3	p	p	X
ejpam-6600	444	4	=	=	PUNCT
ejpam-6600	444	5	7,m	7,m	VERB
ejpam-6600	444	6	=	=	SYM
ejpam-6600	444	7	5	5	NUM
ejpam-6600	444	8	,	,	PUNCT
ejpam-6600	444	9	7	7	NUM
ejpam-6600	444	10	,	,	PUNCT
ejpam-6600	444	11	or	or	CCONJ
ejpam-6600	444	12	11	11	NUM
ejpam-6600	444	13	,	,	PUNCT
ejpam-6600	444	14	d	d	NOUN
ejpam-6600	444	15	=	=	SYM
ejpam-6600	444	16	1	1	NUM
ejpam-6600	444	17	,	,	PUNCT
ejpam-6600	444	18	r	r	NOUN
ejpam-6600	444	19	=	=	SYM
ejpam-6600	444	20	3	3	NUM
ejpam-6600	444	21	,	,	PUNCT
ejpam-6600	444	22	and	and	CCONJ
ejpam-6600	444	23	s1	s1	PROPN
ejpam-6600	444	24	=	=	SYM
ejpam-6600	444	25	{	{	PUNCT
ejpam-6600	444	26	1	1	NUM
ejpam-6600	444	27	,	,	PUNCT
ejpam-6600	444	28	2	2	NUM
ejpam-6600	444	29	,	,	PUNCT
ejpam-6600	444	30	3	3	NUM
ejpam-6600	444	31	}	}	PUNCT
ejpam-6600	444	32	.	.	PUNCT
ejpam-6600	445	1	so	so	ADV
ejpam-6600	445	2	for	for	ADP
ejpam-6600	445	3	each	each	DET
ejpam-6600	445	4	sj	sj	PROPN
ejpam-6600	445	5	∈	∈	PROPN
ejpam-6600	445	6	s1	s1	PROPN
ejpam-6600	445	7	,	,	PUNCT
ejpam-6600	445	8	f	f	PROPN
ejpam-6600	445	9	(	(	PUNCT
ejpam-6600	445	10	vk	vk	PROPN
ejpam-6600	445	11	,	,	PUNCT
ejpam-6600	445	12	vk+sj	vk+sj	NOUN
ejpam-6600	445	13	)	)	PUNCT
ejpam-6600	445	14	=	=	PUNCT
ejpam-6600	446	1	(	(	PUNCT
ejpam-6600	446	2	j	j	NOUN
ejpam-6600	446	3	−	−	PROPN
ejpam-6600	446	4	1	1	NUM
ejpam-6600	446	5	)	)	PUNCT
ejpam-6600	446	6	7	7	NUM
ejpam-6600	447	1	+	+	CCONJ
ejpam-6600	447	2	k	k	NOUN
ejpam-6600	447	3	,	,	PUNCT
ejpam-6600	447	4	and	and	CCONJ
ejpam-6600	447	5	fw(vk	fw(vk	PROPN
ejpam-6600	447	6	)	)	PUNCT
ejpam-6600	448	1	=	=	SYM
ejpam-6600	448	2	6k	6k	NOUN
ejpam-6600	448	3	−	−	NOUN
ejpam-6600	449	1	∑3	∑3	NOUN
ejpam-6600	449	2	j=1	j=1	ADJ
ejpam-6600	449	3	sj	sj	PROPN
ejpam-6600	449	4	=	=	PUNCT
ejpam-6600	449	5	6k	6k	PROPN
ejpam-6600	449	6	−	−	NOUN
ejpam-6600	449	7	6	6	NUM
ejpam-6600	449	8	(	(	PUNCT
ejpam-6600	449	9	mod	mod	PROPN
ejpam-6600	449	10	7	7	NUM
ejpam-6600	449	11	)	)	PUNCT
ejpam-6600	449	12	.	.	PUNCT
ejpam-6600	450	1	the	the	DET
ejpam-6600	450	2	edge	edge	NOUN
ejpam-6600	450	3	-	-	PUNCT
ejpam-6600	450	4	graceful	graceful	NOUN
ejpam-6600	450	5	labeling	labeling	NOUN
ejpam-6600	450	6	of	of	ADP
ejpam-6600	450	7	the	the	DET
ejpam-6600	450	8	graph	graph	NOUN
ejpam-6600	450	9	5	5	NUM
ejpam-6600	450	10	−	−	NOUN
ejpam-6600	450	11	p7	p7	NOUN
ejpam-6600	450	12	is	be	AUX
ejpam-6600	450	13	shown	show	VERB
ejpam-6600	450	14	in	in	ADP
ejpam-6600	450	15	figure	figure	NOUN
ejpam-6600	450	16	11	11	NUM
ejpam-6600	450	17	.	.	PUNCT
ejpam-6600	450	18	a.	a.	PROPN
ejpam-6600	450	19	n.	n.	PROPN
ejpam-6600	450	20	elsawy	elsawy	PROPN
ejpam-6600	450	21	,	,	PUNCT
ejpam-6600	450	22	r.	r.	PROPN
ejpam-6600	450	23	n.	n.	PROPN
ejpam-6600	450	24	almohammadi	almohammadi	PROPN
ejpam-6600	450	25	/	/	SYM
ejpam-6600	450	26	eur	eur	PROPN
ejpam-6600	450	27	.	.	PUNCT
ejpam-6600	451	1	j.	j.	PROPN
ejpam-6600	451	2	pure	pure	PROPN
ejpam-6600	451	3	appl	appl	PROPN
ejpam-6600	451	4	.	.	PROPN
ejpam-6600	451	5	math	math	PROPN
ejpam-6600	451	6	,	,	PUNCT
ejpam-6600	451	7	18	18	NUM
ejpam-6600	451	8	(	(	PUNCT
ejpam-6600	451	9	4	4	NUM
ejpam-6600	451	10	)	)	PUNCT
ejpam-6600	451	11	(	(	PUNCT
ejpam-6600	451	12	2025	2025	NUM
ejpam-6600	451	13	)	)	PUNCT
ejpam-6600	451	14	,	,	PUNCT
ejpam-6600	451	15	6600	6600	NUM
ejpam-6600	451	16	16	16	NUM
ejpam-6600	451	17	of	of	ADP
ejpam-6600	451	18	26	26	NUM
ejpam-6600	451	19	figure	figure	NOUN
ejpam-6600	451	20	11	11	NUM
ejpam-6600	451	21	:	:	PUNCT
ejpam-6600	451	22	an	an	DET
ejpam-6600	451	23	edge	edge	NOUN
ejpam-6600	451	24	-	-	PUNCT
ejpam-6600	451	25	graceful	graceful	NOUN
ejpam-6600	451	26	labeling	labeling	NOUN
ejpam-6600	451	27	of	of	ADP
ejpam-6600	451	28	5−	5−	NUM
ejpam-6600	451	29	p7	p7	NOUN
ejpam-6600	451	30	,	,	PUNCT
ejpam-6600	451	31	7−	7−	NUM
ejpam-6600	451	32	p7	p7	NOUN
ejpam-6600	451	33	,	,	PUNCT
ejpam-6600	451	34	11−	11−	NUM
ejpam-6600	451	35	p7	p7	NOUN
ejpam-6600	451	36	.	.	PUNCT
ejpam-6600	451	37	example	example	NOUN
ejpam-6600	452	1	11	11	NUM
ejpam-6600	452	2	.	.	PUNCT
ejpam-6600	453	1	consider	consider	VERB
ejpam-6600	453	2	the	the	DET
ejpam-6600	453	3	paley	paley	ADJ
ejpam-6600	453	4	graph	graph	NOUN
ejpam-6600	453	5	p17	p17	NOUN
ejpam-6600	453	6	.	.	PUNCT
ejpam-6600	454	1	here	here	ADV
ejpam-6600	454	2	,	,	PUNCT
ejpam-6600	454	3	p	p	X
ejpam-6600	454	4	=	=	X
ejpam-6600	454	5	17,m	17,m	NUM
ejpam-6600	454	6	=	=	SYM
ejpam-6600	454	7	d	d	NOUN
ejpam-6600	454	8	=	=	SYM
ejpam-6600	454	9	2	2	NUM
ejpam-6600	454	10	,	,	PUNCT
ejpam-6600	454	11	r	r	NOUN
ejpam-6600	454	12	=	=	SYM
ejpam-6600	454	13	4	4	NUM
ejpam-6600	454	14	,	,	PUNCT
ejpam-6600	454	15	and	and	CCONJ
ejpam-6600	454	16	s1	s1	PROPN
ejpam-6600	454	17	=	=	SYM
ejpam-6600	454	18	{	{	PUNCT
ejpam-6600	454	19	1	1	NUM
ejpam-6600	454	20	,	,	PUNCT
ejpam-6600	454	21	2	2	NUM
ejpam-6600	454	22	,	,	PUNCT
ejpam-6600	454	23	4	4	NUM
ejpam-6600	454	24	,	,	PUNCT
ejpam-6600	454	25	8	8	NUM
ejpam-6600	454	26	}	}	PUNCT
ejpam-6600	454	27	.	.	PUNCT
ejpam-6600	455	1	so	so	ADV
ejpam-6600	455	2	for	for	ADP
ejpam-6600	455	3	each	each	DET
ejpam-6600	455	4	sj	sj	PROPN
ejpam-6600	455	5	∈	∈	PROPN
ejpam-6600	455	6	s1	s1	PROPN
ejpam-6600	455	7	,	,	PUNCT
ejpam-6600	455	8	f	f	PROPN
ejpam-6600	455	9	(	(	PUNCT
ejpam-6600	455	10	vk	vk	PROPN
ejpam-6600	455	11	,	,	PUNCT
ejpam-6600	455	12	vk+sj	vk+sj	NOUN
ejpam-6600	455	13	)	)	PUNCT
ejpam-6600	455	14	=	=	PUNCT
ejpam-6600	456	1	(	(	PUNCT
ejpam-6600	456	2	j	j	PROPN
ejpam-6600	456	3	−	−	PROPN
ejpam-6600	456	4	1	1	NUM
ejpam-6600	456	5	)	)	PUNCT
ejpam-6600	456	6	17	17	NUM
ejpam-6600	457	1	+	+	CCONJ
ejpam-6600	457	2	k	k	X
ejpam-6600	457	3	,	,	PUNCT
ejpam-6600	457	4	and	and	CCONJ
ejpam-6600	457	5	fw(vk	fw(vk	PROPN
ejpam-6600	457	6	)	)	PUNCT
ejpam-6600	458	1	=	=	PUNCT
ejpam-6600	459	1	8k−	8k−	NUM
ejpam-6600	459	2	∑4	∑4	INTJ
ejpam-6600	460	1	j=1	j=1	NOUN
ejpam-6600	460	2	sj	sj	PROPN
ejpam-6600	460	3	=	=	SYM
ejpam-6600	460	4	8k−	8k−	PROPN
ejpam-6600	460	5	15	15	NUM
ejpam-6600	460	6	(	(	PUNCT
ejpam-6600	460	7	mod	mod	PROPN
ejpam-6600	460	8	17	17	NUM
ejpam-6600	460	9	)	)	PUNCT
ejpam-6600	460	10	.	.	PUNCT
ejpam-6600	461	1	the	the	DET
ejpam-6600	461	2	edge	edge	NOUN
ejpam-6600	461	3	-	-	PUNCT
ejpam-6600	461	4	graceful	graceful	NOUN
ejpam-6600	461	5	labeling	labeling	NOUN
ejpam-6600	461	6	of	of	ADP
ejpam-6600	461	7	the	the	DET
ejpam-6600	461	8	graph	graph	NOUN
ejpam-6600	461	9	p17	p17	NOUN
ejpam-6600	461	10	is	be	AUX
ejpam-6600	461	11	shown	show	VERB
ejpam-6600	461	12	in	in	ADP
ejpam-6600	461	13	figure	figure	NOUN
ejpam-6600	461	14	12	12	NUM
ejpam-6600	461	15	.	.	PUNCT
ejpam-6600	462	1	figure	figure	NOUN
ejpam-6600	462	2	12	12	NUM
ejpam-6600	462	3	:	:	PUNCT
ejpam-6600	462	4	an	an	DET
ejpam-6600	462	5	edge	edge	NOUN
ejpam-6600	462	6	-	-	PUNCT
ejpam-6600	462	7	graceful	graceful	NOUN
ejpam-6600	462	8	labeling	labeling	NOUN
ejpam-6600	462	9	of	of	ADP
ejpam-6600	462	10	p17	p17	NOUN
ejpam-6600	462	11	.	.	PUNCT
ejpam-6600	462	12	a.	a.	PROPN
ejpam-6600	462	13	n.	n.	PROPN
ejpam-6600	462	14	elsawy	elsawy	PROPN
ejpam-6600	462	15	,	,	PUNCT
ejpam-6600	462	16	r.	r.	PROPN
ejpam-6600	462	17	n.	n.	PROPN
ejpam-6600	462	18	almohammadi	almohammadi	PROPN
ejpam-6600	462	19	/	/	SYM
ejpam-6600	462	20	eur	eur	PROPN
ejpam-6600	462	21	.	.	PUNCT
ejpam-6600	463	1	j.	j.	PROPN
ejpam-6600	463	2	pure	pure	PROPN
ejpam-6600	463	3	appl	appl	PROPN
ejpam-6600	463	4	.	.	PROPN
ejpam-6600	463	5	math	math	PROPN
ejpam-6600	463	6	,	,	PUNCT
ejpam-6600	463	7	18	18	NUM
ejpam-6600	463	8	(	(	PUNCT
ejpam-6600	463	9	4	4	NUM
ejpam-6600	463	10	)	)	PUNCT
ejpam-6600	463	11	(	(	PUNCT
ejpam-6600	463	12	2025	2025	NUM
ejpam-6600	463	13	)	)	PUNCT
ejpam-6600	463	14	,	,	PUNCT
ejpam-6600	463	15	6600	6600	NUM
ejpam-6600	463	16	17	17	NUM
ejpam-6600	463	17	of	of	ADP
ejpam-6600	463	18	26	26	NUM
ejpam-6600	463	19	example	example	NOUN
ejpam-6600	463	20	12	12	NUM
ejpam-6600	463	21	.	.	PUNCT
ejpam-6600	464	1	consider	consider	VERB
ejpam-6600	464	2	the	the	DET
ejpam-6600	464	3	generalized	generalized	ADJ
ejpam-6600	464	4	paley	paley	NOUN
ejpam-6600	464	5	graph	graph	NOUN
ejpam-6600	464	6	7	7	NUM
ejpam-6600	464	7	−	−	NOUN
ejpam-6600	464	8	p29	p29	NOUN
ejpam-6600	464	9	.	.	PUNCT
ejpam-6600	465	1	here	here	ADV
ejpam-6600	465	2	,	,	PUNCT
ejpam-6600	465	3	p	p	NOUN
ejpam-6600	465	4	=	=	SYM
ejpam-6600	465	5	29,m	29,m	NUM
ejpam-6600	465	6	=	=	SYM
ejpam-6600	465	7	7	7	NUM
ejpam-6600	465	8	,	,	PUNCT
ejpam-6600	465	9	d	d	NOUN
ejpam-6600	465	10	=	=	SYM
ejpam-6600	465	11	7	7	NUM
ejpam-6600	465	12	,	,	PUNCT
ejpam-6600	465	13	r	r	NOUN
ejpam-6600	465	14	=	=	SYM
ejpam-6600	465	15	2	2	NUM
ejpam-6600	465	16	,	,	PUNCT
ejpam-6600	465	17	and	and	CCONJ
ejpam-6600	465	18	s1	s1	PROPN
ejpam-6600	465	19	=	=	SYM
ejpam-6600	465	20	{	{	PUNCT
ejpam-6600	465	21	1	1	NUM
ejpam-6600	465	22	,	,	PUNCT
ejpam-6600	465	23	12	12	NUM
ejpam-6600	465	24	}	}	PUNCT
ejpam-6600	465	25	.	.	PUNCT
ejpam-6600	466	1	so	so	ADV
ejpam-6600	466	2	for	for	ADP
ejpam-6600	466	3	each	each	DET
ejpam-6600	466	4	sj	sj	PROPN
ejpam-6600	466	5	∈	∈	PROPN
ejpam-6600	466	6	s1	s1	PROPN
ejpam-6600	466	7	,	,	PUNCT
ejpam-6600	466	8	f	f	PROPN
ejpam-6600	466	9	(	(	PUNCT
ejpam-6600	466	10	vk	vk	PROPN
ejpam-6600	466	11	,	,	PUNCT
ejpam-6600	466	12	vk+sj	vk+sj	NOUN
ejpam-6600	466	13	)	)	PUNCT
ejpam-6600	466	14	=	=	PUNCT
ejpam-6600	467	1	(	(	PUNCT
ejpam-6600	467	2	j	j	NOUN
ejpam-6600	467	3	−	−	PROPN
ejpam-6600	467	4	1	1	NUM
ejpam-6600	467	5	)	)	PUNCT
ejpam-6600	467	6	29	29	NUM
ejpam-6600	468	1	+	+	CCONJ
ejpam-6600	468	2	k	k	NOUN
ejpam-6600	468	3	,	,	PUNCT
ejpam-6600	468	4	and	and	CCONJ
ejpam-6600	468	5	fw(vk	fw(vk	PROPN
ejpam-6600	468	6	)	)	PUNCT
ejpam-6600	469	1	=	=	PUNCT
ejpam-6600	470	1	4k−	4k−	PROPN
ejpam-6600	470	2	∑2	∑2	NOUN
ejpam-6600	470	3	j=1	j=1	NOUN
ejpam-6600	470	4	sj	sj	PROPN
ejpam-6600	470	5	=	=	SYM
ejpam-6600	470	6	4k−13	4k−13	X
ejpam-6600	470	7	(	(	PUNCT
ejpam-6600	470	8	mod	mod	PROPN
ejpam-6600	470	9	29	29	NUM
ejpam-6600	470	10	)	)	PUNCT
ejpam-6600	470	11	.	.	PUNCT
ejpam-6600	471	1	the	the	DET
ejpam-6600	471	2	edge	edge	NOUN
ejpam-6600	471	3	-	-	PUNCT
ejpam-6600	471	4	graceful	graceful	NOUN
ejpam-6600	471	5	labeling	labeling	NOUN
ejpam-6600	471	6	of	of	ADP
ejpam-6600	471	7	the	the	DET
ejpam-6600	471	8	graph	graph	NOUN
ejpam-6600	471	9	7−p29	7−p29	PROPN
ejpam-6600	471	10	is	be	AUX
ejpam-6600	471	11	shown	show	VERB
ejpam-6600	471	12	in	in	ADP
ejpam-6600	471	13	figure	figure	NOUN
ejpam-6600	471	14	13	13	NUM
ejpam-6600	471	15	.	.	PUNCT
ejpam-6600	472	1	figure	figure	VERB
ejpam-6600	472	2	13	13	NUM
ejpam-6600	472	3	:	:	PUNCT
ejpam-6600	472	4	an	an	DET
ejpam-6600	472	5	edge	edge	NOUN
ejpam-6600	472	6	-	-	PUNCT
ejpam-6600	472	7	graceful	graceful	NOUN
ejpam-6600	472	8	labeling	labeling	NOUN
ejpam-6600	472	9	of	of	ADP
ejpam-6600	472	10	7−	7−	NUM
ejpam-6600	472	11	p29	p29	NOUN
ejpam-6600	472	12	.	.	PUNCT
ejpam-6600	473	1	example	example	NOUN
ejpam-6600	473	2	13	13	NUM
ejpam-6600	473	3	.	.	PUNCT
ejpam-6600	474	1	consider	consider	VERB
ejpam-6600	474	2	the	the	DET
ejpam-6600	474	3	generalized	generalized	ADJ
ejpam-6600	474	4	paley	paley	NOUN
ejpam-6600	474	5	graph	graph	NOUN
ejpam-6600	474	6	9	9	NUM
ejpam-6600	474	7	−	−	NOUN
ejpam-6600	474	8	p31	p31	NOUN
ejpam-6600	474	9	.	.	PUNCT
ejpam-6600	475	1	here	here	ADV
ejpam-6600	475	2	,	,	PUNCT
ejpam-6600	475	3	p	p	NOUN
ejpam-6600	475	4	=	=	NOUN
ejpam-6600	475	5	31,m	31,m	NUM
ejpam-6600	475	6	=	=	SYM
ejpam-6600	475	7	9	9	NUM
ejpam-6600	475	8	,	,	PUNCT
ejpam-6600	475	9	d	d	NOUN
ejpam-6600	475	10	=	=	SYM
ejpam-6600	475	11	3	3	NUM
ejpam-6600	475	12	,	,	PUNCT
ejpam-6600	475	13	r	r	NOUN
ejpam-6600	475	14	=	=	SYM
ejpam-6600	475	15	5	5	NUM
ejpam-6600	475	16	,	,	PUNCT
ejpam-6600	475	17	and	and	CCONJ
ejpam-6600	475	18	s1	s1	PROPN
ejpam-6600	475	19	=	=	SYM
ejpam-6600	475	20	{	{	PUNCT
ejpam-6600	475	21	1	1	NUM
ejpam-6600	475	22	,	,	PUNCT
ejpam-6600	475	23	2	2	NUM
ejpam-6600	475	24	,	,	PUNCT
ejpam-6600	475	25	4	4	NUM
ejpam-6600	475	26	,	,	PUNCT
ejpam-6600	475	27	8	8	NUM
ejpam-6600	475	28	,	,	PUNCT
ejpam-6600	475	29	15	15	NUM
ejpam-6600	475	30	}	}	PUNCT
ejpam-6600	475	31	.	.	PUNCT
ejpam-6600	476	1	so	so	ADV
ejpam-6600	476	2	for	for	ADP
ejpam-6600	476	3	each	each	DET
ejpam-6600	476	4	sj	sj	PROPN
ejpam-6600	476	5	∈	∈	PROPN
ejpam-6600	476	6	s1	s1	PROPN
ejpam-6600	476	7	,	,	PUNCT
ejpam-6600	476	8	f	f	PROPN
ejpam-6600	476	9	(	(	PUNCT
ejpam-6600	476	10	vk	vk	PROPN
ejpam-6600	476	11	,	,	PUNCT
ejpam-6600	476	12	vk+sj	vk+sj	NOUN
ejpam-6600	476	13	)	)	PUNCT
ejpam-6600	476	14	=	=	PUNCT
ejpam-6600	477	1	(	(	PUNCT
ejpam-6600	477	2	j	j	PROPN
ejpam-6600	477	3	−	−	PROPN
ejpam-6600	477	4	1	1	NUM
ejpam-6600	477	5	)	)	PUNCT
ejpam-6600	477	6	31	31	NUM
ejpam-6600	478	1	+	+	CCONJ
ejpam-6600	478	2	k	k	X
ejpam-6600	478	3	,	,	PUNCT
ejpam-6600	478	4	and	and	CCONJ
ejpam-6600	478	5	fw(vk	fw(vk	PROPN
ejpam-6600	478	6	)	)	PUNCT
ejpam-6600	479	1	=	=	SYM
ejpam-6600	480	1	10k−	10k−	NUM
ejpam-6600	480	2	∑5	∑5	X
ejpam-6600	481	1	j=1	j=1	NOUN
ejpam-6600	481	2	sj	sj	PROPN
ejpam-6600	481	3	=	=	NOUN
ejpam-6600	481	4	10k−	10k−	NUM
ejpam-6600	481	5	30	30	NUM
ejpam-6600	481	6	(	(	PUNCT
ejpam-6600	481	7	mod	mod	PROPN
ejpam-6600	481	8	31	31	NUM
ejpam-6600	481	9	)	)	PUNCT
ejpam-6600	481	10	.	.	PUNCT
ejpam-6600	482	1	the	the	DET
ejpam-6600	482	2	edge	edge	NOUN
ejpam-6600	482	3	-	-	PUNCT
ejpam-6600	482	4	graceful	graceful	NOUN
ejpam-6600	482	5	labeling	labeling	NOUN
ejpam-6600	482	6	of	of	ADP
ejpam-6600	482	7	the	the	DET
ejpam-6600	482	8	graph	graph	NOUN
ejpam-6600	482	9	9−	9−	NUM
ejpam-6600	482	10	p31	p31	NOUN
ejpam-6600	482	11	is	be	AUX
ejpam-6600	482	12	shown	show	VERB
ejpam-6600	482	13	in	in	ADP
ejpam-6600	482	14	figure	figure	NOUN
ejpam-6600	482	15	14	14	NUM
ejpam-6600	482	16	.	.	PUNCT
ejpam-6600	482	17	a.	a.	PROPN
ejpam-6600	482	18	n.	n.	PROPN
ejpam-6600	482	19	elsawy	elsawy	PROPN
ejpam-6600	482	20	,	,	PUNCT
ejpam-6600	482	21	r.	r.	PROPN
ejpam-6600	482	22	n.	n.	PROPN
ejpam-6600	482	23	almohammadi	almohammadi	PROPN
ejpam-6600	482	24	/	/	SYM
ejpam-6600	482	25	eur	eur	PROPN
ejpam-6600	482	26	.	.	PUNCT
ejpam-6600	483	1	j.	j.	PROPN
ejpam-6600	483	2	pure	pure	PROPN
ejpam-6600	483	3	appl	appl	PROPN
ejpam-6600	483	4	.	.	PROPN
ejpam-6600	483	5	math	math	PROPN
ejpam-6600	483	6	,	,	PUNCT
ejpam-6600	483	7	18	18	NUM
ejpam-6600	483	8	(	(	PUNCT
ejpam-6600	483	9	4	4	NUM
ejpam-6600	483	10	)	)	PUNCT
ejpam-6600	483	11	(	(	PUNCT
ejpam-6600	483	12	2025	2025	NUM
ejpam-6600	483	13	)	)	PUNCT
ejpam-6600	483	14	,	,	PUNCT
ejpam-6600	483	15	6600	6600	NUM
ejpam-6600	483	16	18	18	NUM
ejpam-6600	483	17	of	of	ADP
ejpam-6600	483	18	26	26	NUM
ejpam-6600	483	19	figure	figure	NOUN
ejpam-6600	483	20	14	14	NUM
ejpam-6600	483	21	:	:	PUNCT
ejpam-6600	483	22	an	an	DET
ejpam-6600	483	23	edge	edge	NOUN
ejpam-6600	483	24	-	-	PUNCT
ejpam-6600	483	25	graceful	graceful	NOUN
ejpam-6600	483	26	labeling	labeling	NOUN
ejpam-6600	483	27	of	of	ADP
ejpam-6600	483	28	9−	9−	NUM
ejpam-6600	483	29	p31	p31	NOUN
ejpam-6600	483	30	.	.	PUNCT
ejpam-6600	484	1	6	6	NUM
ejpam-6600	484	2	.	.	X
ejpam-6600	484	3	edge	edge	VERB
ejpam-6600	484	4	even	even	ADV
ejpam-6600	484	5	graceful	graceful	ADJ
ejpam-6600	484	6	labeling	labeling	NOUN
ejpam-6600	484	7	of	of	ADP
ejpam-6600	484	8	generalized	generalized	ADJ
ejpam-6600	484	9	paley	paley	ADJ
ejpam-6600	484	10	graphs	graph	NOUN
ejpam-6600	484	11	definition	definition	NOUN
ejpam-6600	484	12	6	6	NUM
ejpam-6600	484	13	.	.	PUNCT
ejpam-6600	485	1	a	a	DET
ejpam-6600	485	2	graph	graph	NOUN
ejpam-6600	485	3	g	g	NOUN
ejpam-6600	485	4	of	of	ADP
ejpam-6600	485	5	order	order	NOUN
ejpam-6600	485	6	n	n	NOUN
ejpam-6600	485	7	and	and	CCONJ
ejpam-6600	485	8	size	size	NOUN
ejpam-6600	485	9	m	m	VERB
ejpam-6600	485	10	is	be	AUX
ejpam-6600	485	11	said	say	VERB
ejpam-6600	485	12	to	to	PART
ejpam-6600	485	13	be	be	AUX
ejpam-6600	485	14	edge	edge	NOUN
ejpam-6600	485	15	-	-	PUNCT
ejpam-6600	485	16	even	even	ADV
ejpam-6600	485	17	graceful	graceful	ADJ
ejpam-6600	485	18	if	if	SCONJ
ejpam-6600	485	19	there	there	PRON
ejpam-6600	485	20	exists	exist	VERB
ejpam-6600	485	21	a	a	DET
ejpam-6600	485	22	bijection	bijection	ADJ
ejpam-6600	485	23	f	f	X
ejpam-6600	485	24	:	:	PUNCT
ejpam-6600	485	25	e(g	e(g	NOUN
ejpam-6600	485	26	)	)	PUNCT
ejpam-6600	486	1	−→	−→	NOUN
ejpam-6600	486	2	{	{	PUNCT
ejpam-6600	486	3	2	2	NUM
ejpam-6600	486	4	,	,	PUNCT
ejpam-6600	486	5	4	4	NUM
ejpam-6600	486	6	,	,	PUNCT
ejpam-6600	486	7	6	6	NUM
ejpam-6600	486	8	,	,	PUNCT
ejpam-6600	486	9	.	.	PUNCT
ejpam-6600	486	10	.	.	PUNCT
ejpam-6600	487	1	.	.	PUNCT
ejpam-6600	488	1	,	,	PUNCT
ejpam-6600	488	2	2	2	NUM
ejpam-6600	488	3	m	m	VERB
ejpam-6600	488	4	}	}	PUNCT
ejpam-6600	488	5	such	such	ADJ
ejpam-6600	488	6	that	that	SCONJ
ejpam-6600	488	7	the	the	DET
ejpam-6600	488	8	function	function	NOUN
ejpam-6600	488	9	fw	fw	INTJ
ejpam-6600	488	10	:	:	PUNCT
ejpam-6600	488	11	v	v	NOUN
ejpam-6600	488	12	(	(	PUNCT
ejpam-6600	488	13	g	g	NOUN
ejpam-6600	488	14	)	)	PUNCT
ejpam-6600	488	15	−→	−→	NOUN
ejpam-6600	488	16	{	{	PUNCT
ejpam-6600	488	17	0	0	NUM
ejpam-6600	488	18	,	,	PUNCT
ejpam-6600	488	19	2	2	NUM
ejpam-6600	488	20	,	,	PUNCT
ejpam-6600	488	21	4	4	NUM
ejpam-6600	488	22	,	,	PUNCT
ejpam-6600	488	23	.	.	PUNCT
ejpam-6600	488	24	.	.	PUNCT
ejpam-6600	489	1	.	.	PUNCT
ejpam-6600	490	1	,	,	PUNCT
ejpam-6600	490	2	2k	2k	NOUN
ejpam-6600	490	3	−	−	NOUN
ejpam-6600	490	4	2	2	NUM
ejpam-6600	490	5	}	}	PUNCT
ejpam-6600	490	6	,	,	PUNCT
ejpam-6600	490	7	k	k	PROPN
ejpam-6600	490	8	=	=	SYM
ejpam-6600	490	9	max(n	max(n	PROPN
ejpam-6600	490	10	,	,	PUNCT
ejpam-6600	490	11	m	m	NOUN
ejpam-6600	490	12	)	)	PUNCT
ejpam-6600	490	13	given	give	VERB
ejpam-6600	490	14	by	by	ADP
ejpam-6600	490	15	fw(u	fw(u	NOUN
ejpam-6600	490	16	)	)	PUNCT
ejpam-6600	490	17	=	=	SYM
ejpam-6600	490	18	∑	∑	PUNCT
ejpam-6600	490	19	uv∈n(u	uv∈n(u	NUM
ejpam-6600	490	20	)	)	PUNCT
ejpam-6600	490	21	f(uv	f(uv	NOUN
ejpam-6600	490	22	)	)	PUNCT
ejpam-6600	490	23	(	(	PUNCT
ejpam-6600	490	24	mod	mod	PROPN
ejpam-6600	490	25	2k	2k	NUM
ejpam-6600	490	26	)	)	PUNCT
ejpam-6600	490	27	is	be	AUX
ejpam-6600	490	28	an	an	DET
ejpam-6600	490	29	injection	injection	NOUN
ejpam-6600	490	30	.	.	PUNCT
ejpam-6600	491	1	using	use	VERB
ejpam-6600	491	2	the	the	DET
ejpam-6600	491	3	following	follow	VERB
ejpam-6600	491	4	algorithm	algorithm	NOUN
ejpam-6600	491	5	,	,	PUNCT
ejpam-6600	491	6	we	we	PRON
ejpam-6600	491	7	show	show	VERB
ejpam-6600	491	8	that	that	SCONJ
ejpam-6600	491	9	the	the	DET
ejpam-6600	491	10	generalized	generalized	ADJ
ejpam-6600	491	11	paley	paley	ADJ
ejpam-6600	491	12	graphs	graph	NOUN
ejpam-6600	491	13	m	m	VERB
ejpam-6600	491	14	−	−	NOUN
ejpam-6600	491	15	pp	pp	ADV
ejpam-6600	491	16	of	of	ADP
ejpam-6600	491	17	prime	prime	ADJ
ejpam-6600	491	18	order	order	NOUN
ejpam-6600	491	19	are	be	AUX
ejpam-6600	491	20	edge	edge	NOUN
ejpam-6600	491	21	-	-	PUNCT
ejpam-6600	491	22	even	even	ADV
ejpam-6600	491	23	graceful	graceful	ADJ
ejpam-6600	491	24	.	.	PUNCT
ejpam-6600	492	1	6.1	6.1	NUM
ejpam-6600	492	2	.	.	PUNCT
ejpam-6600	492	3	edge	edge	NOUN
ejpam-6600	492	4	-	-	PUNCT
ejpam-6600	492	5	even	even	ADV
ejpam-6600	492	6	graceful	graceful	ADJ
ejpam-6600	492	7	labeling	labeling	NOUN
ejpam-6600	492	8	algorithm	algorithm	NOUN
ejpam-6600	492	9	for	for	ADP
ejpam-6600	492	10	generalized	generalized	ADJ
ejpam-6600	492	11	paley	paley	ADJ
ejpam-6600	492	12	graph	graph	NOUN
ejpam-6600	492	13	of	of	ADP
ejpam-6600	492	14	prime	prime	ADJ
ejpam-6600	492	15	order	order	NOUN
ejpam-6600	492	16	input	input	NOUN
ejpam-6600	492	17	:	:	PUNCT
ejpam-6600	492	18	the	the	DET
ejpam-6600	492	19	generalized	generalized	ADJ
ejpam-6600	492	20	paley	paley	NOUN
ejpam-6600	492	21	graph	graph	NOUN
ejpam-6600	492	22	m	m	VERB
ejpam-6600	492	23	−	−	NOUN
ejpam-6600	492	24	pp	pp	ADJ
ejpam-6600	492	25	with	with	ADP
ejpam-6600	492	26	zp	zp	PROPN
ejpam-6600	492	27	as	as	ADP
ejpam-6600	492	28	its	its	PRON
ejpam-6600	492	29	vertices	vertex	NOUN
ejpam-6600	492	30	and	and	CCONJ
ejpam-6600	492	31	two	two	NUM
ejpam-6600	492	32	vertices	vertex	NOUN
ejpam-6600	492	33	are	be	AUX
ejpam-6600	492	34	joined	join	VERB
ejpam-6600	492	35	by	by	ADP
ejpam-6600	492	36	an	an	DET
ejpam-6600	492	37	edge	edge	NOUN
ejpam-6600	492	38	if	if	SCONJ
ejpam-6600	492	39	their	their	PRON
ejpam-6600	492	40	difference	difference	NOUN
ejpam-6600	492	41	belongs	belong	VERB
ejpam-6600	492	42	to	to	ADP
ejpam-6600	492	43	(	(	PUNCT
ejpam-6600	492	44	z∗	z∗	PROPN
ejpam-6600	492	45	p	p	NOUN
ejpam-6600	492	46	)	)	PUNCT
ejpam-6600	492	47	m	m	VERB
ejpam-6600	492	48	such	such	ADJ
ejpam-6600	492	49	that	that	SCONJ
ejpam-6600	492	50	:	:	PUNCT
ejpam-6600	492	51	if	if	SCONJ
ejpam-6600	492	52	m	m	NOUN
ejpam-6600	492	53	is	be	AUX
ejpam-6600	492	54	even	even	ADV
ejpam-6600	492	55	then	then	ADV
ejpam-6600	492	56	p	p	PROPN
ejpam-6600	492	57	≡	≡	PROPN
ejpam-6600	492	58	1	1	NUM
ejpam-6600	492	59	a.	a.	NOUN
ejpam-6600	492	60	n.	n.	NOUN
ejpam-6600	492	61	elsawy	elsawy	PROPN
ejpam-6600	492	62	,	,	PUNCT
ejpam-6600	492	63	r.	r.	PROPN
ejpam-6600	492	64	n.	n.	PROPN
ejpam-6600	492	65	almohammadi	almohammadi	PROPN
ejpam-6600	492	66	/	/	SYM
ejpam-6600	492	67	eur	eur	PROPN
ejpam-6600	492	68	.	.	PUNCT
ejpam-6600	493	1	j.	j.	PROPN
ejpam-6600	493	2	pure	pure	PROPN
ejpam-6600	493	3	appl	appl	PROPN
ejpam-6600	493	4	.	.	PROPN
ejpam-6600	493	5	math	math	PROPN
ejpam-6600	493	6	,	,	PUNCT
ejpam-6600	493	7	18	18	NUM
ejpam-6600	493	8	(	(	PUNCT
ejpam-6600	493	9	4	4	NUM
ejpam-6600	493	10	)	)	PUNCT
ejpam-6600	493	11	(	(	PUNCT
ejpam-6600	493	12	2025	2025	NUM
ejpam-6600	493	13	)	)	PUNCT
ejpam-6600	493	14	,	,	PUNCT
ejpam-6600	493	15	6600	6600	NUM
ejpam-6600	493	16	19	19	NUM
ejpam-6600	493	17	of	of	ADP
ejpam-6600	493	18	26	26	NUM
ejpam-6600	493	19	(	(	PUNCT
ejpam-6600	493	20	mod	mod	PROPN
ejpam-6600	493	21	2	2	NUM
ejpam-6600	493	22	m	m	NOUN
ejpam-6600	493	23	)	)	PUNCT
ejpam-6600	493	24	and	and	CCONJ
ejpam-6600	493	25	if	if	SCONJ
ejpam-6600	493	26	m	m	NOUN
ejpam-6600	493	27	is	be	AUX
ejpam-6600	493	28	odd	odd	ADJ
ejpam-6600	493	29	then	then	ADV
ejpam-6600	493	30	p	p	PRON
ejpam-6600	493	31	is	be	AUX
ejpam-6600	493	32	any	any	DET
ejpam-6600	493	33	odd	odd	ADJ
ejpam-6600	493	34	prime	prime	NOUN
ejpam-6600	493	35	.	.	PUNCT
ejpam-6600	494	1	(	(	PUNCT
ejpam-6600	494	2	1	1	X
ejpam-6600	494	3	)	)	PUNCT
ejpam-6600	494	4	rename	rename	VERB
ejpam-6600	494	5	the	the	DET
ejpam-6600	494	6	vertices	vertex	NOUN
ejpam-6600	494	7	of	of	ADP
ejpam-6600	494	8	the	the	DET
ejpam-6600	494	9	graph	graph	NOUN
ejpam-6600	494	10	as	as	ADP
ejpam-6600	494	11	0	0	NUM
ejpam-6600	494	12	:	:	PUNCT
ejpam-6600	494	13	=	=	SYM
ejpam-6600	494	14	vp	vp	NOUN
ejpam-6600	494	15	,	,	PUNCT
ejpam-6600	494	16	1	1	NUM
ejpam-6600	494	17	:	:	PUNCT
ejpam-6600	494	18	=	=	NOUN
ejpam-6600	494	19	v1	v1	NOUN
ejpam-6600	494	20	,	,	PUNCT
ejpam-6600	494	21	2	2	NUM
ejpam-6600	494	22	:	:	PUNCT
ejpam-6600	494	23	=	=	SYM
ejpam-6600	494	24	v2	v2	PROPN
ejpam-6600	494	25	,	,	PUNCT
ejpam-6600	494	26	.	.	PUNCT
ejpam-6600	494	27	.	.	PUNCT
ejpam-6600	495	1	.	.	PUNCT
ejpam-6600	496	1	,	,	PUNCT
ejpam-6600	496	2	p−	p−	NOUN
ejpam-6600	496	3	1	1	NUM
ejpam-6600	496	4	:	:	PUNCT
ejpam-6600	496	5	=	=	SYM
ejpam-6600	496	6	vp−1	vp−1	PROPN
ejpam-6600	496	7	.	.	PUNCT
ejpam-6600	497	1	(	(	PUNCT
ejpam-6600	497	2	2	2	X
ejpam-6600	497	3	)	)	PUNCT
ejpam-6600	497	4	set	set	NOUN
ejpam-6600	497	5	r	r	NOUN
ejpam-6600	497	6	=	=	SYM
ejpam-6600	497	7	p−1	p−1	PROPN
ejpam-6600	497	8	2d	2d	NUM
ejpam-6600	498	1	where	where	SCONJ
ejpam-6600	498	2	d	d	PROPN
ejpam-6600	498	3	=	=	SYM
ejpam-6600	498	4	gcd(m	gcd(m	PROPN
ejpam-6600	498	5	,	,	PUNCT
ejpam-6600	498	6	p−	p−	NOUN
ejpam-6600	498	7	1	1	NUM
ejpam-6600	498	8	)	)	PUNCT
ejpam-6600	498	9	,	,	PUNCT
ejpam-6600	498	10	and	and	CCONJ
ejpam-6600	498	11	rewrite	rewrite	VERB
ejpam-6600	498	12	(	(	PUNCT
ejpam-6600	498	13	z∗	z∗	NOUN
ejpam-6600	498	14	p	p	NOUN
ejpam-6600	498	15	)	)	PUNCT
ejpam-6600	498	16	m	m	VERB
ejpam-6600	498	17	as	as	ADP
ejpam-6600	498	18	(	(	PUNCT
ejpam-6600	498	19	z∗	z∗	NOUN
ejpam-6600	498	20	p	p	NOUN
ejpam-6600	498	21	)	)	PUNCT
ejpam-6600	498	22	m	m	PROPN
ejpam-6600	498	23	=	=	SYM
ejpam-6600	498	24	s	s	PART
ejpam-6600	498	25	=	=	PUNCT
ejpam-6600	498	26	{	{	PUNCT
ejpam-6600	498	27	s1	s1	NOUN
ejpam-6600	498	28	,	,	PUNCT
ejpam-6600	498	29	s2	s2	PROPN
ejpam-6600	498	30	,	,	PUNCT
ejpam-6600	498	31	s3	s3	PROPN
ejpam-6600	498	32	,	,	PUNCT
ejpam-6600	498	33	.	.	PUNCT
ejpam-6600	498	34	.	.	PUNCT
ejpam-6600	498	35	.	.	PUNCT
ejpam-6600	499	1	,	,	PUNCT
ejpam-6600	499	2	s2r	s2r	PROPN
ejpam-6600	499	3	:	:	PUNCT
ejpam-6600	499	4	s1	s1	PROPN
ejpam-6600	499	5	>	>	X
ejpam-6600	499	6	s2	s2	PROPN
ejpam-6600	499	7	>	>	X
ejpam-6600	499	8	s3	s3	PROPN
ejpam-6600	499	9	>	>	X
ejpam-6600	499	10	.	.	PUNCT
ejpam-6600	499	11	.	.	PUNCT
ejpam-6600	499	12	.	.	PUNCT
ejpam-6600	500	1	>	>	X
ejpam-6600	500	2	s2r	s2r	PROPN
ejpam-6600	500	3	}	}	PUNCT
ejpam-6600	500	4	.	.	PUNCT
ejpam-6600	501	1	(	(	PUNCT
ejpam-6600	501	2	3	3	X
ejpam-6600	501	3	)	)	PUNCT
ejpam-6600	501	4	partition	partition	NOUN
ejpam-6600	501	5	s	s	NOUN
ejpam-6600	501	6	into	into	ADP
ejpam-6600	501	7	two	two	NUM
ejpam-6600	501	8	sets	set	NOUN
ejpam-6600	501	9	.	.	PUNCT
ejpam-6600	502	1	let	let	VERB
ejpam-6600	502	2	s1	s1	PROPN
ejpam-6600	502	3	=	=	PUNCT
ejpam-6600	502	4	{	{	PUNCT
ejpam-6600	502	5	s1	s1	NOUN
ejpam-6600	502	6	,	,	PUNCT
ejpam-6600	502	7	s2	s2	PROPN
ejpam-6600	502	8	,	,	PUNCT
ejpam-6600	502	9	s3	s3	PROPN
ejpam-6600	502	10	,	,	PUNCT
ejpam-6600	502	11	.	.	PUNCT
ejpam-6600	502	12	.	.	PUNCT
ejpam-6600	503	1	.	.	PUNCT
ejpam-6600	504	1	,	,	PUNCT
ejpam-6600	504	2	sr	sr	PROPN
ejpam-6600	504	3	}	}	PUNCT
ejpam-6600	504	4	and	and	CCONJ
ejpam-6600	504	5	s2	s2	VERB
ejpam-6600	504	6	=	=	SYM
ejpam-6600	504	7	{	{	PUNCT
ejpam-6600	504	8	sr+1	sr+1	PROPN
ejpam-6600	504	9	,	,	PUNCT
ejpam-6600	504	10	sr+2	sr+2	NOUN
ejpam-6600	504	11	,	,	PUNCT
ejpam-6600	504	12	sr+3	sr+3	NOUN
ejpam-6600	504	13	,	,	PUNCT
ejpam-6600	504	14	.	.	PUNCT
ejpam-6600	504	15	.	.	PUNCT
ejpam-6600	505	1	.	.	PUNCT
ejpam-6600	506	1	,	,	PUNCT
ejpam-6600	506	2	s2r	s2r	PROPN
ejpam-6600	506	3	}	}	PUNCT
ejpam-6600	506	4	.	.	PUNCT
ejpam-6600	507	1	(	(	PUNCT
ejpam-6600	507	2	4	4	X
ejpam-6600	507	3	)	)	PUNCT
ejpam-6600	507	4	if	if	SCONJ
ejpam-6600	507	5	sj	sj	PROPN
ejpam-6600	507	6	∈	∈	PROPN
ejpam-6600	507	7	s1	s1	PROPN
ejpam-6600	507	8	,	,	PUNCT
ejpam-6600	507	9	the	the	DET
ejpam-6600	507	10	vertex	vertex	NOUN
ejpam-6600	507	11	vi+sj	vi+sj	PROPN
ejpam-6600	507	12	is	be	AUX
ejpam-6600	507	13	placed	place	VERB
ejpam-6600	507	14	in	in	ADP
ejpam-6600	507	15	anticlockwise	anticlockwise	NOUN
ejpam-6600	507	16	direction	direction	NOUN
ejpam-6600	507	17	of	of	ADP
ejpam-6600	507	18	vi	vi	NOUN
ejpam-6600	507	19	and	and	CCONJ
ejpam-6600	507	20	if	if	SCONJ
ejpam-6600	507	21	sj	sj	PROPN
ejpam-6600	507	22	∈	∈	PROPN
ejpam-6600	507	23	s2	s2	PROPN
ejpam-6600	507	24	,	,	PUNCT
ejpam-6600	507	25	the	the	DET
ejpam-6600	507	26	vertex	vertex	NOUN
ejpam-6600	507	27	vi+sj	vi+sj	PROPN
ejpam-6600	507	28	is	be	AUX
ejpam-6600	507	29	placed	place	VERB
ejpam-6600	507	30	in	in	ADP
ejpam-6600	507	31	clockwise	clockwise	NOUN
ejpam-6600	507	32	direction	direction	NOUN
ejpam-6600	507	33	of	of	ADP
ejpam-6600	507	34	vi	vi	PROPN
ejpam-6600	507	35	.	.	PUNCT
ejpam-6600	508	1	(	(	PUNCT
ejpam-6600	508	2	5	5	X
ejpam-6600	508	3	)	)	PUNCT
ejpam-6600	508	4	set	set	NOUN
ejpam-6600	508	5	f(vi	f(vi	PROPN
ejpam-6600	508	6	,	,	PUNCT
ejpam-6600	508	7	vi+sj	vi+sj	NUM
ejpam-6600	508	8	)	)	PUNCT
ejpam-6600	509	1	=	=	SYM
ejpam-6600	509	2	0	0	NUM
ejpam-6600	510	1	for	for	ADP
ejpam-6600	510	2	all	all	PRON
ejpam-6600	510	3	i	i	PRON
ejpam-6600	510	4	∈	∈	PROPN
ejpam-6600	510	5	{	{	PUNCT
ejpam-6600	510	6	1	1	NUM
ejpam-6600	510	7	,	,	PUNCT
ejpam-6600	510	8	2	2	NUM
ejpam-6600	510	9	,	,	PUNCT
ejpam-6600	510	10	3	3	NUM
ejpam-6600	510	11	,	,	PUNCT
ejpam-6600	510	12	.	.	PUNCT
ejpam-6600	510	13	.	.	PUNCT
ejpam-6600	510	14	.	.	PUNCT
ejpam-6600	511	1	,	,	PUNCT
ejpam-6600	511	2	p	p	X
ejpam-6600	511	3	}	}	PUNCT
ejpam-6600	511	4	,	,	PUNCT
ejpam-6600	511	5	j	j	PROPN
ejpam-6600	511	6	∈	∈	PROPN
ejpam-6600	511	7	{	{	PUNCT
ejpam-6600	511	8	1	1	NUM
ejpam-6600	511	9	,	,	PUNCT
ejpam-6600	511	10	2	2	NUM
ejpam-6600	511	11	,	,	PUNCT
ejpam-6600	511	12	3	3	NUM
ejpam-6600	511	13	,	,	PUNCT
ejpam-6600	511	14	.	.	PUNCT
ejpam-6600	511	15	.	.	PUNCT
ejpam-6600	511	16	.	.	PUNCT
ejpam-6600	512	1	,	,	PUNCT
ejpam-6600	512	2	2r	2r	NUM
ejpam-6600	512	3	}	}	PUNCT
ejpam-6600	512	4	.	.	PUNCT
ejpam-6600	513	1	(	(	PUNCT
ejpam-6600	513	2	6	6	X
ejpam-6600	513	3	)	)	PUNCT
ejpam-6600	513	4	set	set	NOUN
ejpam-6600	513	5	i	i	NOUN
ejpam-6600	513	6	=	=	NOUN
ejpam-6600	514	1	1	1	X
ejpam-6600	514	2	.	.	X
ejpam-6600	514	3	step	step	NOUN
ejpam-6600	514	4	1	1	NUM
ejpam-6600	514	5	:	:	PUNCT
ejpam-6600	514	6	if	if	SCONJ
ejpam-6600	514	7	i	i	PRON
ejpam-6600	514	8	≤	≤	VERB
ejpam-6600	514	9	p	p	NOUN
ejpam-6600	514	10	then	then	ADV
ejpam-6600	514	11	continue	continue	VERB
ejpam-6600	514	12	to	to	PART
ejpam-6600	514	13	step	step	VERB
ejpam-6600	514	14	2	2	NUM
ejpam-6600	514	15	.	.	PUNCT
ejpam-6600	514	16	else	else	ADV
ejpam-6600	514	17	jump	jump	VERB
ejpam-6600	514	18	to	to	PART
ejpam-6600	514	19	step	step	VERB
ejpam-6600	514	20	4	4	NUM
ejpam-6600	514	21	.	.	PUNCT
ejpam-6600	515	1	step	step	NOUN
ejpam-6600	515	2	2	2	NUM
ejpam-6600	515	3	:	:	PUNCT
ejpam-6600	515	4	for	for	ADP
ejpam-6600	515	5	each	each	DET
ejpam-6600	515	6	sj	sj	PROPN
ejpam-6600	515	7	∈	∈	PROPN
ejpam-6600	515	8	s1	s1	PROPN
ejpam-6600	515	9	,	,	PUNCT
ejpam-6600	515	10	f	f	PROPN
ejpam-6600	515	11	(	(	PUNCT
ejpam-6600	515	12	vi	vi	PROPN
ejpam-6600	515	13	,	,	PUNCT
ejpam-6600	515	14	vi+sj	vi+sj	NUM
ejpam-6600	515	15	)	)	PUNCT
ejpam-6600	516	1	=	=	PUNCT
ejpam-6600	517	1	2[(j	2[(j	NUM
ejpam-6600	517	2	−	−	NUM
ejpam-6600	517	3	1	1	NUM
ejpam-6600	517	4	)	)	PUNCT
ejpam-6600	517	5	p+	p+	VERB
ejpam-6600	517	6	i	i	PRON
ejpam-6600	517	7	]	]	PUNCT
ejpam-6600	517	8	.	.	PUNCT
ejpam-6600	518	1	step	step	NOUN
ejpam-6600	518	2	3	3	NUM
ejpam-6600	518	3	:	:	PUNCT
ejpam-6600	518	4	i	i	PRON
ejpam-6600	518	5	=	=	PUNCT
ejpam-6600	518	6	i+	i+	PROPN
ejpam-6600	518	7	1	1	NUM
ejpam-6600	518	8	,	,	PUNCT
ejpam-6600	518	9	go	go	VERB
ejpam-6600	518	10	back	back	ADV
ejpam-6600	518	11	to	to	PART
ejpam-6600	518	12	step	step	NOUN
ejpam-6600	518	13	1	1	NUM
ejpam-6600	518	14	.	.	PUNCT
ejpam-6600	519	1	step	step	NOUN
ejpam-6600	519	2	4	4	NUM
ejpam-6600	519	3	:	:	PUNCT
ejpam-6600	519	4	for	for	ADP
ejpam-6600	519	5	each	each	PRON
ejpam-6600	519	6	k	k	NOUN
ejpam-6600	519	7	=	=	SYM
ejpam-6600	519	8	1	1	NUM
ejpam-6600	519	9	,	,	PUNCT
ejpam-6600	519	10	2	2	NUM
ejpam-6600	519	11	,	,	PUNCT
ejpam-6600	519	12	3	3	NUM
ejpam-6600	519	13	,	,	PUNCT
ejpam-6600	519	14	.	.	PUNCT
ejpam-6600	519	15	.	.	PUNCT
ejpam-6600	520	1	.	.	PUNCT
ejpam-6600	521	1	,	,	PUNCT
ejpam-6600	521	2	p	p	X
ejpam-6600	521	3	,	,	PUNCT
ejpam-6600	521	4	find	find	VERB
ejpam-6600	521	5	the	the	DET
ejpam-6600	521	6	weight	weight	NOUN
ejpam-6600	521	7	of	of	ADP
ejpam-6600	521	8	the	the	DET
ejpam-6600	521	9	vertex	vertex	NOUN
ejpam-6600	521	10	vk	vk	NOUN
ejpam-6600	521	11	using	use	VERB
ejpam-6600	521	12	the	the	DET
ejpam-6600	521	13	following	follow	VERB
ejpam-6600	521	14	mapping	mapping	NOUN
ejpam-6600	521	15	:	:	PUNCT
ejpam-6600	521	16	fw(vk	fw(vk	PROPN
ejpam-6600	521	17	)	)	PUNCT
ejpam-6600	522	1	=	=	PUNCT
ejpam-6600	523	1	∑2r	∑2r	NOUN
ejpam-6600	523	2	j=1	j=1	PROPN
ejpam-6600	523	3	f(vk	f(vk	PROPN
ejpam-6600	523	4	,	,	PUNCT
ejpam-6600	523	5	vk+sj	vk+sj	PROPN
ejpam-6600	523	6	)	)	PUNCT
ejpam-6600	523	7	(	(	PUNCT
ejpam-6600	523	8	mod	mod	PROPN
ejpam-6600	523	9	2	2	NUM
ejpam-6600	523	10	t	t	NOUN
ejpam-6600	523	11	)	)	PUNCT
ejpam-6600	523	12	,	,	PUNCT
ejpam-6600	523	13	where	where	SCONJ
ejpam-6600	523	14	t	t	NOUN
ejpam-6600	523	15	=	=	SYM
ejpam-6600	523	16	max(p	max(p	PROPN
ejpam-6600	523	17	,	,	PUNCT
ejpam-6600	523	18	pr	pr	NOUN
ejpam-6600	523	19	)	)	PUNCT
ejpam-6600	523	20	.	.	PUNCT
ejpam-6600	524	1	take	take	VERB
ejpam-6600	524	2	m	m	NOUN
ejpam-6600	524	3	=	=	PUNCT
ejpam-6600	525	1	∑r	∑r	PROPN
ejpam-6600	525	2	j=1	j=1	NOUN
ejpam-6600	525	3	sj	sj	INTJ
ejpam-6600	525	4	,	,	PUNCT
ejpam-6600	525	5	then	then	ADV
ejpam-6600	525	6	fw(vk	fw(vk	PROPN
ejpam-6600	525	7	)	)	PUNCT
ejpam-6600	526	1	=	=	PUNCT
ejpam-6600	527	1	∑r	∑r	NOUN
ejpam-6600	527	2	j=1	j=1	NOUN
ejpam-6600	528	1	4[(j	4[(j	NOUN
ejpam-6600	529	1	−	−	NOUN
ejpam-6600	529	2	1	1	NUM
ejpam-6600	529	3	)	)	PUNCT
ejpam-6600	529	4	p+	p+	NOUN
ejpam-6600	529	5	k	k	X
ejpam-6600	529	6	]	]	X
ejpam-6600	529	7	+	+	CCONJ
ejpam-6600	529	8	2(p−	2(p−	NUM
ejpam-6600	529	9	sj	sj	NOUN
ejpam-6600	529	10	)	)	PUNCT
ejpam-6600	529	11	=	=	SYM
ejpam-6600	529	12	4rk	4rk	NOUN
ejpam-6600	529	13	−	−	NOUN
ejpam-6600	530	1	2	2	NUM
ejpam-6600	530	2	m	m	NOUN
ejpam-6600	530	3	(	(	PUNCT
ejpam-6600	530	4	mod	mod	ADJ
ejpam-6600	530	5	2rp	2rp	NOUN
ejpam-6600	530	6	)	)	PUNCT
ejpam-6600	530	7	.	.	PUNCT
ejpam-6600	531	1	theorem	theorem	VERB
ejpam-6600	531	2	6	6	NUM
ejpam-6600	531	3	.	.	PUNCT
ejpam-6600	531	4	paley	paley	ADJ
ejpam-6600	531	5	graphs	graph	NOUN
ejpam-6600	531	6	and	and	CCONJ
ejpam-6600	531	7	their	their	PRON
ejpam-6600	531	8	generalizations	generalization	NOUN
ejpam-6600	531	9	of	of	ADP
ejpam-6600	531	10	prime	prime	ADJ
ejpam-6600	531	11	order	order	NOUN
ejpam-6600	531	12	are	be	AUX
ejpam-6600	531	13	edge	edge	NOUN
ejpam-6600	531	14	-	-	PUNCT
ejpam-6600	531	15	even	even	ADV
ejpam-6600	531	16	graceful	graceful	ADJ
ejpam-6600	531	17	graphs	graph	NOUN
ejpam-6600	531	18	.	.	PUNCT
ejpam-6600	532	1	proof	proof	NOUN
ejpam-6600	532	2	.	.	PUNCT
ejpam-6600	533	1	to	to	PART
ejpam-6600	533	2	prove	prove	VERB
ejpam-6600	533	3	that	that	SCONJ
ejpam-6600	533	4	the	the	DET
ejpam-6600	533	5	algorithm	algorithm	NOUN
ejpam-6600	533	6	defines	define	VERB
ejpam-6600	533	7	an	an	DET
ejpam-6600	533	8	edge	edge	NOUN
ejpam-6600	533	9	-	-	PUNCT
ejpam-6600	533	10	even	even	ADV
ejpam-6600	533	11	graceful	graceful	ADJ
ejpam-6600	533	12	labeling	labeling	NOUN
ejpam-6600	533	13	,	,	PUNCT
ejpam-6600	533	14	we	we	PRON
ejpam-6600	533	15	need	need	VERB
ejpam-6600	533	16	to	to	PART
ejpam-6600	533	17	prove	prove	VERB
ejpam-6600	533	18	that	that	SCONJ
ejpam-6600	533	19	both	both	DET
ejpam-6600	533	20	functions	function	NOUN
ejpam-6600	533	21	f	f	PROPN
ejpam-6600	533	22	and	and	CCONJ
ejpam-6600	533	23	fw	fw	PROPN
ejpam-6600	533	24	are	be	AUX
ejpam-6600	533	25	injection	injection	NOUN
ejpam-6600	533	26	.	.	PUNCT
ejpam-6600	534	1	(	(	PUNCT
ejpam-6600	534	2	i	i	NOUN
ejpam-6600	534	3	)	)	PUNCT
ejpam-6600	534	4	consider	consider	VERB
ejpam-6600	534	5	the	the	DET
ejpam-6600	534	6	function	function	NOUN
ejpam-6600	534	7	fw	fw	INTJ
ejpam-6600	534	8	:	:	PUNCT
ejpam-6600	534	9	v	v	NOUN
ejpam-6600	534	10	(	(	PUNCT
ejpam-6600	534	11	m−pp	m−pp	NOUN
ejpam-6600	534	12	)	)	PUNCT
ejpam-6600	534	13	−→	−→	NOUN
ejpam-6600	534	14	{	{	PUNCT
ejpam-6600	534	15	0	0	NUM
ejpam-6600	534	16	,	,	PUNCT
ejpam-6600	534	17	2	2	NUM
ejpam-6600	534	18	,	,	PUNCT
ejpam-6600	534	19	4	4	NUM
ejpam-6600	534	20	,	,	PUNCT
ejpam-6600	534	21	.	.	PUNCT
ejpam-6600	534	22	.	.	PUNCT
ejpam-6600	535	1	.	.	PUNCT
ejpam-6600	536	1	,	,	PUNCT
ejpam-6600	536	2	2rp−	2rp−	NUM
ejpam-6600	536	3	2	2	NUM
ejpam-6600	536	4	}	}	PUNCT
ejpam-6600	536	5	defined	define	VERB
ejpam-6600	536	6	by	by	ADP
ejpam-6600	536	7	fw(vk	fw(vk	PROPN
ejpam-6600	536	8	)	)	PUNCT
ejpam-6600	537	1	=	=	X
ejpam-6600	537	2	∑2r	∑2r	PROPN
ejpam-6600	537	3	j=1	j=1	PROPN
ejpam-6600	537	4	f(vk	f(vk	PROPN
ejpam-6600	537	5	,	,	PUNCT
ejpam-6600	537	6	vk+sj	vk+sj	NOUN
ejpam-6600	537	7	)	)	PUNCT
ejpam-6600	537	8	=	=	PUNCT
ejpam-6600	538	1	4kr	4kr	NOUN
ejpam-6600	538	2	−	−	NOUN
ejpam-6600	538	3	2	2	NUM
ejpam-6600	538	4	m	m	NOUN
ejpam-6600	538	5	(	(	PUNCT
ejpam-6600	538	6	mod	mod	ADJ
ejpam-6600	538	7	2rp	2rp	NOUN
ejpam-6600	538	8	)	)	PUNCT
ejpam-6600	538	9	.	.	PUNCT
ejpam-6600	539	1	let	let	VERB
ejpam-6600	540	1	vx	vx	PROPN
ejpam-6600	540	2	and	and	CCONJ
ejpam-6600	540	3	vy	vy	PRON
ejpam-6600	540	4	be	be	AUX
ejpam-6600	540	5	two	two	NUM
ejpam-6600	540	6	vertices	vertex	NOUN
ejpam-6600	540	7	in	in	ADP
ejpam-6600	540	8	v	v	NOUN
ejpam-6600	540	9	(	(	PUNCT
ejpam-6600	540	10	m−	m−	PROPN
ejpam-6600	540	11	pp	pp	PROPN
ejpam-6600	540	12	)	)	PUNCT
ejpam-6600	540	13	,	,	PUNCT
ejpam-6600	540	14	if	if	SCONJ
ejpam-6600	540	15	fw(vx	fw(vx	NOUN
ejpam-6600	540	16	)	)	PUNCT
ejpam-6600	541	1	=	=	SYM
ejpam-6600	541	2	fw(vy	fw(vy	PROPN
ejpam-6600	541	3	)	)	PUNCT
ejpam-6600	541	4	then	then	ADV
ejpam-6600	541	5	4xr−2	4xr−2	NOUN
ejpam-6600	541	6	m	m	NOUN
ejpam-6600	541	7	=	=	NOUN
ejpam-6600	541	8	4yr−2	4yr−2	PROPN
ejpam-6600	541	9	m	m	VERB
ejpam-6600	541	10	(	(	PUNCT
ejpam-6600	541	11	mod	mod	PROPN
ejpam-6600	541	12	2rp	2rp	NOUN
ejpam-6600	541	13	)	)	PUNCT
ejpam-6600	541	14	which	which	PRON
ejpam-6600	541	15	leads	lead	VERB
ejpam-6600	541	16	to	to	ADP
ejpam-6600	541	17	x	x	PROPN
ejpam-6600	541	18	=	=	PUNCT
ejpam-6600	541	19	y.	y.	PROPN
ejpam-6600	541	20	(	(	PUNCT
ejpam-6600	541	21	ii	ii	PROPN
ejpam-6600	541	22	)	)	PUNCT
ejpam-6600	541	23	the	the	DET
ejpam-6600	541	24	function	function	NOUN
ejpam-6600	541	25	f	f	PROPN
ejpam-6600	541	26	:	:	PUNCT
ejpam-6600	541	27	e(m−pp	e(m−pp	X
ejpam-6600	541	28	)	)	PUNCT
ejpam-6600	541	29	−→	−→	NOUN
ejpam-6600	541	30	{	{	PUNCT
ejpam-6600	541	31	2	2	NUM
ejpam-6600	541	32	,	,	PUNCT
ejpam-6600	541	33	4	4	NUM
ejpam-6600	541	34	,	,	PUNCT
ejpam-6600	541	35	6	6	NUM
ejpam-6600	541	36	,	,	PUNCT
ejpam-6600	541	37	.	.	PUNCT
ejpam-6600	541	38	.	.	PUNCT
ejpam-6600	542	1	.	.	PUNCT
ejpam-6600	543	1	,	,	PUNCT
ejpam-6600	543	2	2rp	2rp	ADJ
ejpam-6600	543	3	}	}	PUNCT
ejpam-6600	543	4	is	be	AUX
ejpam-6600	543	5	defined	define	VERB
ejpam-6600	543	6	as	as	ADP
ejpam-6600	543	7	f(vx	f(vx	PROPN
ejpam-6600	543	8	,	,	PUNCT
ejpam-6600	543	9	vx+sj	vx+sj	ADJ
ejpam-6600	543	10	)	)	PUNCT
ejpam-6600	544	1	=	=	PUNCT
ejpam-6600	545	1	2[(j	2[(j	NUM
ejpam-6600	546	1	−	−	NUM
ejpam-6600	546	2	1)p+	1)p+	NUM
ejpam-6600	546	3	x	x	NOUN
ejpam-6600	546	4	]	]	X
ejpam-6600	546	5	.	.	PUNCT
ejpam-6600	547	1	to	to	PART
ejpam-6600	547	2	prove	prove	VERB
ejpam-6600	547	3	that	that	SCONJ
ejpam-6600	547	4	f	f	PROPN
ejpam-6600	547	5	is	be	AUX
ejpam-6600	547	6	a	a	DET
ejpam-6600	547	7	bijection	bijection	NOUN
ejpam-6600	547	8	,	,	PUNCT
ejpam-6600	547	9	we	we	PRON
ejpam-6600	547	10	need	need	VERB
ejpam-6600	547	11	only	only	ADV
ejpam-6600	547	12	to	to	PART
ejpam-6600	547	13	prove	prove	VERB
ejpam-6600	547	14	that	that	SCONJ
ejpam-6600	547	15	it	it	PRON
ejpam-6600	547	16	is	be	AUX
ejpam-6600	547	17	one	one	NUM
ejpam-6600	547	18	-	-	PUNCT
ejpam-6600	547	19	to	to	ADP
ejpam-6600	547	20	-	-	PUNCT
ejpam-6600	547	21	one	one	NUM
ejpam-6600	547	22	.	.	PUNCT
ejpam-6600	548	1	let	let	VERB
ejpam-6600	548	2	(	(	PUNCT
ejpam-6600	548	3	vx	vx	NOUN
ejpam-6600	548	4	,	,	PUNCT
ejpam-6600	548	5	vx+si	vx+si	NOUN
ejpam-6600	548	6	)	)	PUNCT
ejpam-6600	548	7	and	and	CCONJ
ejpam-6600	548	8	(	(	PUNCT
ejpam-6600	548	9	vy	vy	INTJ
ejpam-6600	548	10	,	,	PUNCT
ejpam-6600	548	11	vy+sj	vy+sj	PRON
ejpam-6600	548	12	)	)	PUNCT
ejpam-6600	548	13	be	be	AUX
ejpam-6600	548	14	two	two	NUM
ejpam-6600	548	15	edges	edge	NOUN
ejpam-6600	548	16	,	,	PUNCT
ejpam-6600	548	17	with	with	ADP
ejpam-6600	548	18	x	x	PRON
ejpam-6600	548	19	,	,	PUNCT
ejpam-6600	548	20	y	y	PROPN
ejpam-6600	548	21	∈	∈	PROPN
ejpam-6600	548	22	{	{	PUNCT
ejpam-6600	548	23	1	1	NUM
ejpam-6600	548	24	,	,	PUNCT
ejpam-6600	548	25	2	2	NUM
ejpam-6600	548	26	,	,	PUNCT
ejpam-6600	548	27	3	3	NUM
ejpam-6600	548	28	,	,	PUNCT
ejpam-6600	548	29	·	·	PUNCT
ejpam-6600	548	30	·	·	PUNCT
ejpam-6600	548	31	·	·	PUNCT
ejpam-6600	548	32	,	,	PUNCT
ejpam-6600	548	33	p	p	X
ejpam-6600	548	34	}	}	PUNCT
ejpam-6600	548	35	,	,	PUNCT
ejpam-6600	548	36	si	si	INTJ
ejpam-6600	548	37	,	,	PUNCT
ejpam-6600	548	38	sj	sj	PROPN
ejpam-6600	548	39	∈	∈	PROPN
ejpam-6600	548	40	s1	s1	NOUN
ejpam-6600	548	41	,	,	PUNCT
ejpam-6600	548	42	and	and	CCONJ
ejpam-6600	548	43	f(vx	f(vx	PROPN
ejpam-6600	548	44	,	,	PUNCT
ejpam-6600	548	45	vx+sj	vx+sj	ADJ
ejpam-6600	548	46	)	)	PUNCT
ejpam-6600	548	47	=	=	SYM
ejpam-6600	549	1	f(vy	f(vy	ADJ
ejpam-6600	549	2	,	,	PUNCT
ejpam-6600	549	3	vy+si	vy+si	NOUN
ejpam-6600	549	4	)	)	PUNCT
ejpam-6600	549	5	,	,	PUNCT
ejpam-6600	549	6	which	which	PRON
ejpam-6600	549	7	implies	imply	VERB
ejpam-6600	549	8	that	that	SCONJ
ejpam-6600	549	9	2[(i−	2[(i−	NUM
ejpam-6600	549	10	1)p+	1)p+	NUM
ejpam-6600	549	11	x	x	SYM
ejpam-6600	549	12	]	]	X
ejpam-6600	549	13	=	=	PUNCT
ejpam-6600	550	1	2[(j	2[(j	NUM
ejpam-6600	551	1	−	−	NUM
ejpam-6600	551	2	1)p+	1)p+	NUM
ejpam-6600	551	3	y	y	NOUN
ejpam-6600	551	4	]	]	PUNCT
ejpam-6600	551	5	.	.	PUNCT
ejpam-6600	552	1	in	in	ADP
ejpam-6600	552	2	case	case	NOUN
ejpam-6600	552	3	of	of	ADP
ejpam-6600	552	4	i	i	PRON
ejpam-6600	552	5	=	=	SYM
ejpam-6600	552	6	j	j	PROPN
ejpam-6600	552	7	or	or	CCONJ
ejpam-6600	552	8	x	x	X
ejpam-6600	552	9	=	=	SYM
ejpam-6600	552	10	y	y	PROPN
ejpam-6600	552	11	the	the	DET
ejpam-6600	552	12	proof	proof	NOUN
ejpam-6600	552	13	is	be	AUX
ejpam-6600	552	14	trivial	trivial	ADJ
ejpam-6600	552	15	.	.	PUNCT
ejpam-6600	553	1	the	the	DET
ejpam-6600	553	2	last	last	ADJ
ejpam-6600	553	3	case	case	NOUN
ejpam-6600	553	4	if	if	SCONJ
ejpam-6600	553	5	x	x	PROPN
ejpam-6600	553	6	̸=	̸=	PROPN
ejpam-6600	553	7	y	y	PROPN
ejpam-6600	553	8	and	and	CCONJ
ejpam-6600	553	9	j	j	PROPN
ejpam-6600	553	10	̸=	̸=	PROPN
ejpam-6600	553	11	i	i	PRON
ejpam-6600	553	12	,	,	PUNCT
ejpam-6600	553	13	here	here	ADV
ejpam-6600	553	14	we	we	PRON
ejpam-6600	553	15	will	will	AUX
ejpam-6600	553	16	find	find	VERB
ejpam-6600	553	17	that	that	SCONJ
ejpam-6600	553	18	x−	x−	PROPN
ejpam-6600	553	19	y	y	PROPN
ejpam-6600	553	20	=	=	PUNCT
ejpam-6600	553	21	(	(	PUNCT
ejpam-6600	553	22	j−	j−	PROPN
ejpam-6600	553	23	i)p	i)p	ADV
ejpam-6600	553	24	but	but	CCONJ
ejpam-6600	553	25	|x−	|x−	NOUN
ejpam-6600	553	26	y|	y|	VERB
ejpam-6600	553	27	<	<	X
ejpam-6600	553	28	p	p	X
ejpam-6600	553	29	and	and	CCONJ
ejpam-6600	553	30	in	in	ADP
ejpam-6600	553	31	the	the	DET
ejpam-6600	553	32	same	same	ADJ
ejpam-6600	553	33	time	time	NOUN
ejpam-6600	553	34	|p(i−	|p(i−	NUM
ejpam-6600	553	35	j)|	j)|	NOUN
ejpam-6600	553	36	≥	≥	NOUN
ejpam-6600	553	37	p	p	NOUN
ejpam-6600	553	38	which	which	PRON
ejpam-6600	553	39	is	be	AUX
ejpam-6600	553	40	a	a	DET
ejpam-6600	553	41	contradiction	contradiction	NOUN
ejpam-6600	553	42	.	.	PUNCT
ejpam-6600	554	1	so	so	ADV
ejpam-6600	554	2	,	,	PUNCT
ejpam-6600	554	3	from	from	ADP
ejpam-6600	554	4	these	these	DET
ejpam-6600	554	5	three	three	NUM
ejpam-6600	554	6	cases	case	NOUN
ejpam-6600	554	7	,	,	PUNCT
ejpam-6600	554	8	we	we	PRON
ejpam-6600	554	9	can	can	AUX
ejpam-6600	554	10	be	be	AUX
ejpam-6600	554	11	sure	sure	ADJ
ejpam-6600	554	12	that	that	SCONJ
ejpam-6600	554	13	the	the	DET
ejpam-6600	554	14	function	function	NOUN
ejpam-6600	554	15	f	f	PROPN
ejpam-6600	554	16	is	be	AUX
ejpam-6600	554	17	a	a	DET
ejpam-6600	554	18	one	one	NUM
ejpam-6600	554	19	-	-	PUNCT
ejpam-6600	554	20	to	to	ADP
ejpam-6600	554	21	-	-	PUNCT
ejpam-6600	554	22	one	one	NUM
ejpam-6600	554	23	function	function	NOUN
ejpam-6600	554	24	and	and	CCONJ
ejpam-6600	554	25	because	because	SCONJ
ejpam-6600	554	26	|e(m−	|e(m−	PROPN
ejpam-6600	554	27	pp)|	pp)|	PROPN
ejpam-6600	554	28	=	=	PUNCT
ejpam-6600	554	29	rp	rp	NOUN
ejpam-6600	554	30	,	,	PUNCT
ejpam-6600	554	31	f	f	PROPN
ejpam-6600	554	32	is	be	AUX
ejpam-6600	554	33	a	a	DET
ejpam-6600	554	34	bijection	bijection	NOUN
ejpam-6600	554	35	.	.	PUNCT
ejpam-6600	555	1	□	□	PUNCT
ejpam-6600	555	2	example	example	NOUN
ejpam-6600	555	3	14	14	NUM
ejpam-6600	555	4	.	.	PUNCT
ejpam-6600	555	5	consider	consider	VERB
ejpam-6600	555	6	the	the	DET
ejpam-6600	555	7	quadruple	quadruple	NOUN
ejpam-6600	555	8	paley	paley	PROPN
ejpam-6600	555	9	graph	graph	NOUN
ejpam-6600	555	10	4	4	NUM
ejpam-6600	555	11	−	−	NOUN
ejpam-6600	555	12	p17	p17	NOUN
ejpam-6600	555	13	.	.	PUNCT
ejpam-6600	556	1	here	here	ADV
ejpam-6600	556	2	,	,	PUNCT
ejpam-6600	556	3	p	p	X
ejpam-6600	556	4	=	=	X
ejpam-6600	556	5	17,m	17,m	NUM
ejpam-6600	556	6	=	=	SYM
ejpam-6600	556	7	4	4	NUM
ejpam-6600	556	8	,	,	PUNCT
ejpam-6600	556	9	d	d	NOUN
ejpam-6600	556	10	=	=	SYM
ejpam-6600	556	11	4	4	NUM
ejpam-6600	556	12	,	,	PUNCT
ejpam-6600	556	13	r	r	NOUN
ejpam-6600	556	14	=	=	SYM
ejpam-6600	556	15	2	2	NUM
ejpam-6600	556	16	,	,	PUNCT
ejpam-6600	556	17	and	and	CCONJ
ejpam-6600	556	18	s1	s1	PROPN
ejpam-6600	556	19	=	=	SYM
ejpam-6600	556	20	{	{	PUNCT
ejpam-6600	556	21	16	16	NUM
ejpam-6600	556	22	,	,	PUNCT
ejpam-6600	556	23	13	13	NUM
ejpam-6600	556	24	}	}	PUNCT
ejpam-6600	556	25	.	.	PUNCT
ejpam-6600	557	1	so	so	ADV
ejpam-6600	557	2	for	for	ADP
ejpam-6600	557	3	each	each	DET
ejpam-6600	557	4	sj	sj	PROPN
ejpam-6600	557	5	∈	∈	PROPN
ejpam-6600	557	6	s1	s1	PROPN
ejpam-6600	557	7	,	,	PUNCT
ejpam-6600	557	8	f	f	PROPN
ejpam-6600	557	9	(	(	PUNCT
ejpam-6600	557	10	vk	vk	PROPN
ejpam-6600	557	11	,	,	PUNCT
ejpam-6600	557	12	vk+sj	vk+sj	NOUN
ejpam-6600	557	13	)	)	PUNCT
ejpam-6600	558	1	=	=	PUNCT
ejpam-6600	559	1	2[(j	2[(j	NUM
ejpam-6600	559	2	−	−	NOUN
ejpam-6600	559	3	1	1	NUM
ejpam-6600	559	4	)	)	PUNCT
ejpam-6600	559	5	17	17	NUM
ejpam-6600	560	1	+	+	CCONJ
ejpam-6600	560	2	k	k	X
ejpam-6600	560	3	]	]	X
ejpam-6600	560	4	,	,	PUNCT
ejpam-6600	560	5	and	and	CCONJ
ejpam-6600	560	6	fw(vk	fw(vk	PROPN
ejpam-6600	560	7	)	)	PUNCT
ejpam-6600	561	1	=	=	PUNCT
ejpam-6600	561	2	8k−	8k−	NUM
ejpam-6600	561	3	2	2	NUM
ejpam-6600	561	4	∑2	∑2	NOUN
ejpam-6600	561	5	j=1	j=1	NOUN
ejpam-6600	561	6	sj	sj	PROPN
ejpam-6600	561	7	=	=	SYM
ejpam-6600	561	8	8k−	8k−	PROPN
ejpam-6600	561	9	58	58	NUM
ejpam-6600	561	10	(	(	PUNCT
ejpam-6600	561	11	mod	mod	PROPN
ejpam-6600	561	12	68	68	NUM
ejpam-6600	561	13	)	)	PUNCT
ejpam-6600	561	14	.	.	PUNCT
ejpam-6600	562	1	the	the	DET
ejpam-6600	562	2	edge	edge	NOUN
ejpam-6600	562	3	-	-	PUNCT
ejpam-6600	562	4	even	even	ADV
ejpam-6600	562	5	graceful	graceful	ADJ
ejpam-6600	562	6	labeling	labeling	NOUN
ejpam-6600	562	7	of	of	ADP
ejpam-6600	562	8	the	the	DET
ejpam-6600	562	9	graph	graph	NOUN
ejpam-6600	562	10	4−	4−	NOUN
ejpam-6600	562	11	p17	p17	NOUN
ejpam-6600	562	12	is	be	AUX
ejpam-6600	562	13	shown	show	VERB
ejpam-6600	562	14	in	in	ADP
ejpam-6600	562	15	figure	figure	NOUN
ejpam-6600	562	16	15	15	NUM
ejpam-6600	562	17	.	.	PUNCT
ejpam-6600	562	18	a.	a.	PROPN
ejpam-6600	562	19	n.	n.	PROPN
ejpam-6600	562	20	elsawy	elsawy	PROPN
ejpam-6600	562	21	,	,	PUNCT
ejpam-6600	562	22	r.	r.	PROPN
ejpam-6600	562	23	n.	n.	PROPN
ejpam-6600	562	24	almohammadi	almohammadi	PROPN
ejpam-6600	562	25	/	/	SYM
ejpam-6600	562	26	eur	eur	PROPN
ejpam-6600	562	27	.	.	PUNCT
ejpam-6600	563	1	j.	j.	PROPN
ejpam-6600	563	2	pure	pure	PROPN
ejpam-6600	563	3	appl	appl	PROPN
ejpam-6600	563	4	.	.	PROPN
ejpam-6600	563	5	math	math	PROPN
ejpam-6600	563	6	,	,	PUNCT
ejpam-6600	563	7	18	18	NUM
ejpam-6600	563	8	(	(	PUNCT
ejpam-6600	563	9	4	4	NUM
ejpam-6600	563	10	)	)	PUNCT
ejpam-6600	563	11	(	(	PUNCT
ejpam-6600	563	12	2025	2025	NUM
ejpam-6600	563	13	)	)	PUNCT
ejpam-6600	563	14	,	,	PUNCT
ejpam-6600	563	15	6600	6600	NUM
ejpam-6600	563	16	20	20	NUM
ejpam-6600	563	17	of	of	ADP
ejpam-6600	563	18	26	26	NUM
ejpam-6600	563	19	figure	figure	NOUN
ejpam-6600	563	20	15	15	NUM
ejpam-6600	563	21	:	:	PUNCT
ejpam-6600	563	22	an	an	DET
ejpam-6600	563	23	edge	edge	NOUN
ejpam-6600	563	24	-	-	PUNCT
ejpam-6600	563	25	even	even	ADV
ejpam-6600	563	26	graceful	graceful	ADJ
ejpam-6600	563	27	labeling	labeling	NOUN
ejpam-6600	563	28	of	of	ADP
ejpam-6600	563	29	4−	4−	PROPN
ejpam-6600	563	30	p17	p17	NOUN
ejpam-6600	563	31	.	.	PUNCT
ejpam-6600	564	1	example	example	NOUN
ejpam-6600	564	2	15	15	NUM
ejpam-6600	564	3	.	.	PUNCT
ejpam-6600	565	1	consider	consider	VERB
ejpam-6600	565	2	the	the	DET
ejpam-6600	565	3	generalized	generalized	ADJ
ejpam-6600	565	4	paley	paley	NOUN
ejpam-6600	565	5	graph	graph	NOUN
ejpam-6600	565	6	5	5	NUM
ejpam-6600	565	7	−	−	NOUN
ejpam-6600	565	8	p7	p7	NOUN
ejpam-6600	565	9	.	.	PUNCT
ejpam-6600	566	1	here	here	ADV
ejpam-6600	566	2	,	,	PUNCT
ejpam-6600	566	3	p	p	X
ejpam-6600	566	4	=	=	PUNCT
ejpam-6600	566	5	7,m	7,m	VERB
ejpam-6600	566	6	=	=	SYM
ejpam-6600	566	7	5	5	NUM
ejpam-6600	566	8	,	,	PUNCT
ejpam-6600	566	9	d	d	NOUN
ejpam-6600	566	10	=	=	SYM
ejpam-6600	566	11	1	1	NUM
ejpam-6600	566	12	,	,	PUNCT
ejpam-6600	566	13	r	r	NOUN
ejpam-6600	566	14	=	=	SYM
ejpam-6600	566	15	3	3	NUM
ejpam-6600	566	16	,	,	PUNCT
ejpam-6600	566	17	and	and	CCONJ
ejpam-6600	566	18	s1	s1	PROPN
ejpam-6600	566	19	=	=	SYM
ejpam-6600	566	20	{	{	PUNCT
ejpam-6600	566	21	6	6	NUM
ejpam-6600	566	22	,	,	PUNCT
ejpam-6600	566	23	5	5	NUM
ejpam-6600	566	24	,	,	PUNCT
ejpam-6600	566	25	4	4	NUM
ejpam-6600	566	26	}	}	PUNCT
ejpam-6600	566	27	.	.	PUNCT
ejpam-6600	567	1	so	so	ADV
ejpam-6600	567	2	for	for	ADP
ejpam-6600	567	3	each	each	DET
ejpam-6600	567	4	sj	sj	PROPN
ejpam-6600	567	5	∈	∈	PROPN
ejpam-6600	567	6	s1	s1	PROPN
ejpam-6600	567	7	,	,	PUNCT
ejpam-6600	567	8	f	f	PROPN
ejpam-6600	567	9	(	(	PUNCT
ejpam-6600	567	10	vk	vk	PROPN
ejpam-6600	567	11	,	,	PUNCT
ejpam-6600	567	12	vk+sj	vk+sj	NOUN
ejpam-6600	567	13	)	)	PUNCT
ejpam-6600	568	1	=	=	PUNCT
ejpam-6600	569	1	2[(j	2[(j	NUM
ejpam-6600	569	2	−	−	NOUN
ejpam-6600	569	3	1	1	NUM
ejpam-6600	569	4	)	)	PUNCT
ejpam-6600	569	5	7	7	NUM
ejpam-6600	570	1	+	+	CCONJ
ejpam-6600	570	2	k	k	X
ejpam-6600	570	3	]	]	X
ejpam-6600	570	4	,	,	PUNCT
ejpam-6600	570	5	and	and	CCONJ
ejpam-6600	570	6	fw(vk	fw(vk	PROPN
ejpam-6600	570	7	)	)	PUNCT
ejpam-6600	570	8	=	=	SYM
ejpam-6600	570	9	12k	12k	PROPN
ejpam-6600	570	10	−	−	NUM
ejpam-6600	570	11	2	2	NUM
ejpam-6600	570	12	∑2	∑2	NOUN
ejpam-6600	570	13	j=1	j=1	NOUN
ejpam-6600	570	14	sj	sj	PROPN
ejpam-6600	570	15	=	=	PROPN
ejpam-6600	570	16	12k	12k	PROPN
ejpam-6600	570	17	−	−	PROPN
ejpam-6600	570	18	30	30	NUM
ejpam-6600	570	19	(	(	PUNCT
ejpam-6600	570	20	mod	mod	PROPN
ejpam-6600	570	21	42	42	NUM
ejpam-6600	570	22	)	)	PUNCT
ejpam-6600	570	23	.	.	PUNCT
ejpam-6600	571	1	the	the	DET
ejpam-6600	571	2	edge	edge	NOUN
ejpam-6600	571	3	-	-	PUNCT
ejpam-6600	571	4	even	even	ADV
ejpam-6600	571	5	graceful	graceful	ADJ
ejpam-6600	571	6	labeling	labeling	NOUN
ejpam-6600	571	7	of	of	ADP
ejpam-6600	571	8	the	the	DET
ejpam-6600	571	9	graph	graph	NOUN
ejpam-6600	571	10	5−	5−	NUM
ejpam-6600	571	11	p7	p7	NOUN
ejpam-6600	571	12	is	be	AUX
ejpam-6600	571	13	shown	show	VERB
ejpam-6600	571	14	in	in	ADP
ejpam-6600	571	15	figure	figure	NOUN
ejpam-6600	571	16	16	16	NUM
ejpam-6600	571	17	.	.	PUNCT
ejpam-6600	572	1	figure	figure	VERB
ejpam-6600	572	2	16	16	NUM
ejpam-6600	572	3	:	:	PUNCT
ejpam-6600	572	4	an	an	DET
ejpam-6600	572	5	edge	edge	NOUN
ejpam-6600	572	6	-	-	PUNCT
ejpam-6600	572	7	even	even	ADV
ejpam-6600	572	8	graceful	graceful	ADJ
ejpam-6600	572	9	labeling	labeling	NOUN
ejpam-6600	572	10	of	of	ADP
ejpam-6600	572	11	7−	7−	NUM
ejpam-6600	572	12	p7	p7	ADJ
ejpam-6600	572	13	,	,	PUNCT
ejpam-6600	572	14	5−	5−	NUM
ejpam-6600	572	15	p7	p7	NOUN
ejpam-6600	572	16	,	,	PUNCT
ejpam-6600	572	17	11−	11−	NUM
ejpam-6600	572	18	p7	p7	NOUN
ejpam-6600	572	19	.	.	PUNCT
ejpam-6600	572	20	example	example	NOUN
ejpam-6600	573	1	16	16	NUM
ejpam-6600	573	2	.	.	PUNCT
ejpam-6600	574	1	consider	consider	VERB
ejpam-6600	574	2	the	the	DET
ejpam-6600	574	3	cubic	cubic	ADJ
ejpam-6600	574	4	paley	paley	PROPN
ejpam-6600	574	5	graph	graph	NOUN
ejpam-6600	574	6	3−p19	3−p19	PROPN
ejpam-6600	574	7	.	.	PUNCT
ejpam-6600	575	1	here	here	ADV
ejpam-6600	575	2	,	,	PUNCT
ejpam-6600	575	3	p	p	NOUN
ejpam-6600	575	4	=	=	SYM
ejpam-6600	575	5	19,m	19,m	X
ejpam-6600	575	6	=	=	SYM
ejpam-6600	575	7	3	3	NUM
ejpam-6600	575	8	,	,	PUNCT
ejpam-6600	575	9	d	d	PROPN
ejpam-6600	575	10	=	=	SYM
ejpam-6600	575	11	3	3	NUM
ejpam-6600	575	12	,	,	PUNCT
ejpam-6600	575	13	r	r	NOUN
ejpam-6600	575	14	=	=	SYM
ejpam-6600	575	15	3	3	NUM
ejpam-6600	575	16	,	,	PUNCT
ejpam-6600	575	17	and	and	CCONJ
ejpam-6600	575	18	s1	s1	PROPN
ejpam-6600	575	19	=	=	SYM
ejpam-6600	575	20	{	{	PUNCT
ejpam-6600	575	21	18	18	NUM
ejpam-6600	575	22	,	,	PUNCT
ejpam-6600	575	23	12	12	NUM
ejpam-6600	575	24	,	,	PUNCT
ejpam-6600	575	25	11	11	NUM
ejpam-6600	575	26	}	}	PUNCT
ejpam-6600	575	27	.	.	PUNCT
ejpam-6600	576	1	so	so	ADV
ejpam-6600	576	2	for	for	ADP
ejpam-6600	576	3	each	each	DET
ejpam-6600	576	4	sj	sj	PROPN
ejpam-6600	576	5	∈	∈	PROPN
ejpam-6600	576	6	s1	s1	PROPN
ejpam-6600	576	7	,	,	PUNCT
ejpam-6600	576	8	f	f	PROPN
ejpam-6600	576	9	(	(	PUNCT
ejpam-6600	576	10	vk	vk	PROPN
ejpam-6600	576	11	,	,	PUNCT
ejpam-6600	576	12	vk+sj	vk+sj	NOUN
ejpam-6600	576	13	)	)	PUNCT
ejpam-6600	577	1	=	=	PUNCT
ejpam-6600	578	1	2[(j	2[(j	NUM
ejpam-6600	578	2	−	−	NOUN
ejpam-6600	578	3	1	1	NUM
ejpam-6600	578	4	)	)	PUNCT
ejpam-6600	578	5	19	19	NUM
ejpam-6600	578	6	+	+	NUM
ejpam-6600	578	7	k	k	X
ejpam-6600	578	8	]	]	X
ejpam-6600	578	9	,	,	PUNCT
ejpam-6600	578	10	and	and	CCONJ
ejpam-6600	578	11	fw(vk	fw(vk	PROPN
ejpam-6600	578	12	)	)	PUNCT
ejpam-6600	579	1	=	=	SYM
ejpam-6600	580	1	12k−2	12k−2	PROPN
ejpam-6600	580	2	∑2	∑2	NOUN
ejpam-6600	580	3	j=1	j=1	NOUN
ejpam-6600	580	4	sj	sj	PROPN
ejpam-6600	580	5	=	=	SYM
ejpam-6600	580	6	12k−82	12k−82	PROPN
ejpam-6600	580	7	(	(	PUNCT
ejpam-6600	580	8	mod	mod	PROPN
ejpam-6600	580	9	114	114	NUM
ejpam-6600	580	10	)	)	PUNCT
ejpam-6600	580	11	.	.	PUNCT
ejpam-6600	581	1	the	the	DET
ejpam-6600	581	2	edge	edge	NOUN
ejpam-6600	581	3	-	-	PUNCT
ejpam-6600	581	4	even	even	ADV
ejpam-6600	581	5	graceful	graceful	ADJ
ejpam-6600	581	6	labeling	labeling	NOUN
ejpam-6600	581	7	of	of	ADP
ejpam-6600	581	8	the	the	DET
ejpam-6600	581	9	graph	graph	NOUN
ejpam-6600	581	10	3−p19	3−p19	PROPN
ejpam-6600	581	11	is	be	AUX
ejpam-6600	581	12	shown	show	VERB
ejpam-6600	581	13	in	in	ADP
ejpam-6600	581	14	figure	figure	NOUN
ejpam-6600	581	15	17	17	NUM
ejpam-6600	581	16	.	.	PUNCT
ejpam-6600	581	17	a.	a.	PROPN
ejpam-6600	581	18	n.	n.	PROPN
ejpam-6600	581	19	elsawy	elsawy	PROPN
ejpam-6600	581	20	,	,	PUNCT
ejpam-6600	581	21	r.	r.	PROPN
ejpam-6600	581	22	n.	n.	PROPN
ejpam-6600	581	23	almohammadi	almohammadi	PROPN
ejpam-6600	581	24	/	/	SYM
ejpam-6600	581	25	eur	eur	PROPN
ejpam-6600	581	26	.	.	PUNCT
ejpam-6600	582	1	j.	j.	PROPN
ejpam-6600	582	2	pure	pure	PROPN
ejpam-6600	582	3	appl	appl	PROPN
ejpam-6600	582	4	.	.	PROPN
ejpam-6600	582	5	math	math	PROPN
ejpam-6600	582	6	,	,	PUNCT
ejpam-6600	582	7	18	18	NUM
ejpam-6600	582	8	(	(	PUNCT
ejpam-6600	582	9	4	4	NUM
ejpam-6600	582	10	)	)	PUNCT
ejpam-6600	582	11	(	(	PUNCT
ejpam-6600	582	12	2025	2025	NUM
ejpam-6600	582	13	)	)	PUNCT
ejpam-6600	582	14	,	,	PUNCT
ejpam-6600	582	15	6600	6600	NUM
ejpam-6600	582	16	21	21	NUM
ejpam-6600	582	17	of	of	ADP
ejpam-6600	582	18	26	26	NUM
ejpam-6600	582	19	figure	figure	NOUN
ejpam-6600	582	20	17	17	NUM
ejpam-6600	582	21	:	:	PUNCT
ejpam-6600	582	22	an	an	DET
ejpam-6600	582	23	edge	edge	NOUN
ejpam-6600	582	24	-	-	PUNCT
ejpam-6600	582	25	even	even	ADV
ejpam-6600	582	26	graceful	graceful	ADJ
ejpam-6600	582	27	labeling	labeling	NOUN
ejpam-6600	582	28	of	of	ADP
ejpam-6600	582	29	3−	3−	NUM
ejpam-6600	582	30	p19	p19	NOUN
ejpam-6600	582	31	.	.	PUNCT
ejpam-6600	583	1	7	7	X
ejpam-6600	583	2	.	.	X
ejpam-6600	583	3	edge	edge	VERB
ejpam-6600	583	4	odd	odd	ADJ
ejpam-6600	583	5	graceful	graceful	ADJ
ejpam-6600	583	6	labeling	labeling	NOUN
ejpam-6600	583	7	of	of	ADP
ejpam-6600	583	8	generalized	generalized	ADJ
ejpam-6600	583	9	paley	paley	ADJ
ejpam-6600	583	10	graphs	graph	NOUN
ejpam-6600	583	11	definition	definition	NOUN
ejpam-6600	583	12	7	7	NUM
ejpam-6600	583	13	.	.	PUNCT
ejpam-6600	584	1	a	a	DET
ejpam-6600	584	2	graph	graph	NOUN
ejpam-6600	584	3	g	g	NOUN
ejpam-6600	584	4	of	of	ADP
ejpam-6600	584	5	order	order	NOUN
ejpam-6600	584	6	n	n	NOUN
ejpam-6600	584	7	and	and	CCONJ
ejpam-6600	584	8	size	size	NOUN
ejpam-6600	584	9	m	m	VERB
ejpam-6600	584	10	is	be	AUX
ejpam-6600	584	11	said	say	VERB
ejpam-6600	584	12	to	to	PART
ejpam-6600	584	13	be	be	AUX
ejpam-6600	584	14	edge	edge	NOUN
ejpam-6600	584	15	-	-	PUNCT
ejpam-6600	584	16	odd	odd	ADJ
ejpam-6600	584	17	graceful	graceful	NOUN
ejpam-6600	584	18	if	if	SCONJ
ejpam-6600	584	19	there	there	PRON
ejpam-6600	584	20	exists	exist	VERB
ejpam-6600	584	21	a	a	DET
ejpam-6600	584	22	bijection	bijection	ADJ
ejpam-6600	584	23	f	f	X
ejpam-6600	584	24	:	:	PUNCT
ejpam-6600	584	25	e(g	e(g	NOUN
ejpam-6600	584	26	)	)	PUNCT
ejpam-6600	585	1	−→	−→	NOUN
ejpam-6600	585	2	{	{	PUNCT
ejpam-6600	585	3	1	1	NUM
ejpam-6600	585	4	,	,	PUNCT
ejpam-6600	585	5	3	3	NUM
ejpam-6600	585	6	,	,	PUNCT
ejpam-6600	585	7	5	5	NUM
ejpam-6600	585	8	,	,	PUNCT
ejpam-6600	585	9	.	.	PUNCT
ejpam-6600	585	10	.	.	PUNCT
ejpam-6600	586	1	.	.	PUNCT
ejpam-6600	587	1	,	,	PUNCT
ejpam-6600	587	2	2m−	2m−	NOUN
ejpam-6600	587	3	1	1	NUM
ejpam-6600	587	4	}	}	PUNCT
ejpam-6600	587	5	such	such	ADJ
ejpam-6600	587	6	that	that	SCONJ
ejpam-6600	587	7	the	the	DET
ejpam-6600	587	8	function	function	NOUN
ejpam-6600	587	9	fw	fw	INTJ
ejpam-6600	587	10	:	:	PUNCT
ejpam-6600	587	11	v	v	NOUN
ejpam-6600	587	12	(	(	PUNCT
ejpam-6600	587	13	g	g	NOUN
ejpam-6600	587	14	)	)	PUNCT
ejpam-6600	587	15	−→	−→	NOUN
ejpam-6600	587	16	{	{	PUNCT
ejpam-6600	587	17	0	0	NUM
ejpam-6600	587	18	,	,	PUNCT
ejpam-6600	587	19	1	1	NUM
ejpam-6600	587	20	,	,	PUNCT
ejpam-6600	587	21	2	2	NUM
ejpam-6600	587	22	,	,	PUNCT
ejpam-6600	587	23	.	.	PUNCT
ejpam-6600	587	24	.	.	PUNCT
ejpam-6600	587	25	.	.	PUNCT
ejpam-6600	588	1	,	,	PUNCT
ejpam-6600	588	2	2m−	2m−	PROPN
ejpam-6600	588	3	1	1	NUM
ejpam-6600	588	4	}	}	PUNCT
ejpam-6600	588	5	,	,	PUNCT
ejpam-6600	588	6	given	give	VERB
ejpam-6600	588	7	by	by	ADP
ejpam-6600	588	8	fw(u	fw(u	NOUN
ejpam-6600	588	9	)	)	PUNCT
ejpam-6600	588	10	=	=	SYM
ejpam-6600	588	11	∑	∑	PUNCT
ejpam-6600	588	12	uv∈n(u	uv∈n(u	NUM
ejpam-6600	588	13	)	)	PUNCT
ejpam-6600	588	14	f(uv	f(uv	NOUN
ejpam-6600	588	15	)	)	PUNCT
ejpam-6600	588	16	(	(	PUNCT
ejpam-6600	588	17	mod	mod	PROPN
ejpam-6600	588	18	2	2	NUM
ejpam-6600	588	19	m	m	NOUN
ejpam-6600	588	20	)	)	PUNCT
ejpam-6600	588	21	is	be	AUX
ejpam-6600	588	22	an	an	DET
ejpam-6600	588	23	injection	injection	NOUN
ejpam-6600	588	24	.	.	PUNCT
ejpam-6600	589	1	7.1	7.1	NUM
ejpam-6600	589	2	.	.	PUNCT
ejpam-6600	590	1	edge	edge	NOUN
ejpam-6600	590	2	-	-	PUNCT
ejpam-6600	590	3	odd	odd	ADJ
ejpam-6600	590	4	graceful	graceful	ADJ
ejpam-6600	590	5	labeling	labeling	NOUN
ejpam-6600	590	6	algorithm	algorithm	NOUN
ejpam-6600	590	7	for	for	ADP
ejpam-6600	590	8	generalized	generalized	ADJ
ejpam-6600	590	9	paley	paley	ADJ
ejpam-6600	590	10	graph	graph	NOUN
ejpam-6600	590	11	of	of	ADP
ejpam-6600	590	12	prime	prime	ADJ
ejpam-6600	590	13	order	order	NOUN
ejpam-6600	590	14	input	input	NOUN
ejpam-6600	590	15	:	:	PUNCT
ejpam-6600	590	16	the	the	DET
ejpam-6600	590	17	generalized	generalized	ADJ
ejpam-6600	590	18	paley	paley	NOUN
ejpam-6600	590	19	graph	graph	NOUN
ejpam-6600	590	20	m	m	VERB
ejpam-6600	590	21	−	−	NOUN
ejpam-6600	590	22	pp	pp	ADJ
ejpam-6600	590	23	with	with	ADP
ejpam-6600	590	24	zp	zp	PROPN
ejpam-6600	590	25	as	as	ADP
ejpam-6600	590	26	its	its	PRON
ejpam-6600	590	27	vertices	vertex	NOUN
ejpam-6600	590	28	and	and	CCONJ
ejpam-6600	590	29	two	two	NUM
ejpam-6600	590	30	vertices	vertex	NOUN
ejpam-6600	590	31	are	be	AUX
ejpam-6600	590	32	joined	join	VERB
ejpam-6600	590	33	by	by	ADP
ejpam-6600	590	34	an	an	DET
ejpam-6600	590	35	edge	edge	NOUN
ejpam-6600	590	36	if	if	SCONJ
ejpam-6600	590	37	their	their	PRON
ejpam-6600	590	38	difference	difference	NOUN
ejpam-6600	590	39	belongs	belong	VERB
ejpam-6600	590	40	to	to	ADP
ejpam-6600	590	41	(	(	PUNCT
ejpam-6600	590	42	z∗	z∗	PROPN
ejpam-6600	590	43	p	p	NOUN
ejpam-6600	590	44	)	)	PUNCT
ejpam-6600	590	45	m	m	VERB
ejpam-6600	590	46	such	such	ADJ
ejpam-6600	590	47	that	that	SCONJ
ejpam-6600	590	48	:	:	PUNCT
ejpam-6600	590	49	if	if	SCONJ
ejpam-6600	590	50	m	m	NOUN
ejpam-6600	590	51	is	be	AUX
ejpam-6600	590	52	even	even	ADV
ejpam-6600	590	53	then	then	ADV
ejpam-6600	590	54	p	p	PROPN
ejpam-6600	590	55	≡	≡	PROPN
ejpam-6600	590	56	1	1	NUM
ejpam-6600	590	57	(	(	PUNCT
ejpam-6600	590	58	mod	mod	PROPN
ejpam-6600	590	59	2	2	NUM
ejpam-6600	590	60	m	m	NOUN
ejpam-6600	590	61	)	)	PUNCT
ejpam-6600	590	62	and	and	CCONJ
ejpam-6600	590	63	if	if	SCONJ
ejpam-6600	590	64	m	m	NOUN
ejpam-6600	590	65	is	be	AUX
ejpam-6600	590	66	odd	odd	ADJ
ejpam-6600	590	67	then	then	ADV
ejpam-6600	590	68	p	p	PRON
ejpam-6600	590	69	is	be	AUX
ejpam-6600	590	70	any	any	DET
ejpam-6600	590	71	odd	odd	ADJ
ejpam-6600	590	72	prime	prime	NOUN
ejpam-6600	590	73	.	.	PUNCT
ejpam-6600	591	1	(	(	PUNCT
ejpam-6600	591	2	1	1	X
ejpam-6600	591	3	)	)	PUNCT
ejpam-6600	591	4	rename	rename	VERB
ejpam-6600	591	5	the	the	DET
ejpam-6600	591	6	vertices	vertex	NOUN
ejpam-6600	591	7	of	of	ADP
ejpam-6600	591	8	the	the	DET
ejpam-6600	591	9	graph	graph	NOUN
ejpam-6600	591	10	as	as	ADP
ejpam-6600	591	11	0	0	NUM
ejpam-6600	591	12	:	:	PUNCT
ejpam-6600	591	13	=	=	SYM
ejpam-6600	591	14	vp	vp	NOUN
ejpam-6600	591	15	,	,	PUNCT
ejpam-6600	591	16	1	1	NUM
ejpam-6600	591	17	:	:	PUNCT
ejpam-6600	591	18	=	=	NOUN
ejpam-6600	591	19	v1	v1	NOUN
ejpam-6600	591	20	,	,	PUNCT
ejpam-6600	591	21	2	2	NUM
ejpam-6600	591	22	:	:	PUNCT
ejpam-6600	591	23	=	=	SYM
ejpam-6600	591	24	v2	v2	PROPN
ejpam-6600	591	25	,	,	PUNCT
ejpam-6600	591	26	.	.	PUNCT
ejpam-6600	591	27	.	.	PUNCT
ejpam-6600	592	1	.	.	PUNCT
ejpam-6600	593	1	,	,	PUNCT
ejpam-6600	593	2	p−	p−	NOUN
ejpam-6600	593	3	1	1	NUM
ejpam-6600	593	4	:	:	PUNCT
ejpam-6600	593	5	=	=	SYM
ejpam-6600	593	6	vp−1	vp−1	PROPN
ejpam-6600	593	7	.	.	PUNCT
ejpam-6600	594	1	(	(	PUNCT
ejpam-6600	594	2	2	2	X
ejpam-6600	594	3	)	)	PUNCT
ejpam-6600	594	4	set	set	NOUN
ejpam-6600	594	5	r	r	NOUN
ejpam-6600	594	6	=	=	SYM
ejpam-6600	594	7	p−1	p−1	PROPN
ejpam-6600	594	8	2d	2d	NUM
ejpam-6600	595	1	where	where	SCONJ
ejpam-6600	595	2	d	d	PROPN
ejpam-6600	595	3	=	=	SYM
ejpam-6600	595	4	gcd(m	gcd(m	PROPN
ejpam-6600	595	5	,	,	PUNCT
ejpam-6600	595	6	p−	p−	NOUN
ejpam-6600	595	7	1	1	NUM
ejpam-6600	595	8	)	)	PUNCT
ejpam-6600	595	9	,	,	PUNCT
ejpam-6600	595	10	and	and	CCONJ
ejpam-6600	595	11	rewrite	rewrite	VERB
ejpam-6600	595	12	(	(	PUNCT
ejpam-6600	595	13	z∗	z∗	NOUN
ejpam-6600	595	14	p	p	NOUN
ejpam-6600	595	15	)	)	PUNCT
ejpam-6600	595	16	m	m	VERB
ejpam-6600	595	17	as	as	ADP
ejpam-6600	595	18	(	(	PUNCT
ejpam-6600	595	19	z∗	z∗	NOUN
ejpam-6600	595	20	p	p	NOUN
ejpam-6600	595	21	)	)	PUNCT
ejpam-6600	595	22	m	m	PROPN
ejpam-6600	595	23	=	=	SYM
ejpam-6600	595	24	s	s	PART
ejpam-6600	595	25	=	=	PUNCT
ejpam-6600	595	26	{	{	PUNCT
ejpam-6600	595	27	s1	s1	NOUN
ejpam-6600	595	28	,	,	PUNCT
ejpam-6600	595	29	s2	s2	PROPN
ejpam-6600	595	30	,	,	PUNCT
ejpam-6600	595	31	s3	s3	PROPN
ejpam-6600	595	32	,	,	PUNCT
ejpam-6600	595	33	.	.	PUNCT
ejpam-6600	595	34	.	.	PUNCT
ejpam-6600	595	35	.	.	PUNCT
ejpam-6600	596	1	,	,	PUNCT
ejpam-6600	596	2	s2r	s2r	PROPN
ejpam-6600	596	3	:	:	PUNCT
ejpam-6600	596	4	s1	s1	PROPN
ejpam-6600	596	5	>	>	X
ejpam-6600	596	6	s2	s2	PROPN
ejpam-6600	596	7	>	>	X
ejpam-6600	596	8	s3	s3	PROPN
ejpam-6600	596	9	>	>	X
ejpam-6600	596	10	.	.	PUNCT
ejpam-6600	596	11	.	.	PUNCT
ejpam-6600	596	12	.	.	PUNCT
ejpam-6600	597	1	>	>	X
ejpam-6600	597	2	s2r	s2r	PROPN
ejpam-6600	597	3	}	}	PUNCT
ejpam-6600	597	4	.	.	PUNCT
ejpam-6600	598	1	(	(	PUNCT
ejpam-6600	598	2	3	3	X
ejpam-6600	598	3	)	)	PUNCT
ejpam-6600	598	4	partition	partition	NOUN
ejpam-6600	598	5	s	s	NOUN
ejpam-6600	598	6	into	into	ADP
ejpam-6600	598	7	two	two	NUM
ejpam-6600	598	8	sets	set	NOUN
ejpam-6600	598	9	.	.	PUNCT
ejpam-6600	599	1	let	let	VERB
ejpam-6600	599	2	s1	s1	PROPN
ejpam-6600	599	3	=	=	PUNCT
ejpam-6600	599	4	{	{	PUNCT
ejpam-6600	599	5	s1	s1	NOUN
ejpam-6600	599	6	,	,	PUNCT
ejpam-6600	599	7	s2	s2	PROPN
ejpam-6600	599	8	,	,	PUNCT
ejpam-6600	599	9	s3	s3	PROPN
ejpam-6600	599	10	,	,	PUNCT
ejpam-6600	599	11	.	.	PUNCT
ejpam-6600	599	12	.	.	PUNCT
ejpam-6600	600	1	.	.	PUNCT
ejpam-6600	601	1	,	,	PUNCT
ejpam-6600	601	2	sr	sr	PROPN
ejpam-6600	601	3	}	}	PUNCT
ejpam-6600	601	4	and	and	CCONJ
ejpam-6600	601	5	s2	s2	VERB
ejpam-6600	601	6	=	=	SYM
ejpam-6600	601	7	{	{	PUNCT
ejpam-6600	601	8	sr+1	sr+1	PROPN
ejpam-6600	601	9	,	,	PUNCT
ejpam-6600	601	10	sr+2	sr+2	NOUN
ejpam-6600	601	11	,	,	PUNCT
ejpam-6600	601	12	sr+3	sr+3	NOUN
ejpam-6600	601	13	,	,	PUNCT
ejpam-6600	601	14	.	.	PUNCT
ejpam-6600	601	15	.	.	PUNCT
ejpam-6600	602	1	.	.	PUNCT
ejpam-6600	603	1	,	,	PUNCT
ejpam-6600	603	2	s2r	s2r	PROPN
ejpam-6600	603	3	}	}	PUNCT
ejpam-6600	603	4	.	.	PUNCT
ejpam-6600	604	1	a.	a.	PROPN
ejpam-6600	604	2	n.	n.	PROPN
ejpam-6600	604	3	elsawy	elsawy	PROPN
ejpam-6600	604	4	,	,	PUNCT
ejpam-6600	604	5	r.	r.	PROPN
ejpam-6600	604	6	n.	n.	PROPN
ejpam-6600	604	7	almohammadi	almohammadi	PROPN
ejpam-6600	604	8	/	/	SYM
ejpam-6600	604	9	eur	eur	PROPN
ejpam-6600	604	10	.	.	PUNCT
ejpam-6600	605	1	j.	j.	PROPN
ejpam-6600	605	2	pure	pure	PROPN
ejpam-6600	605	3	appl	appl	PROPN
ejpam-6600	605	4	.	.	PROPN
ejpam-6600	605	5	math	math	PROPN
ejpam-6600	605	6	,	,	PUNCT
ejpam-6600	605	7	18	18	NUM
ejpam-6600	605	8	(	(	PUNCT
ejpam-6600	605	9	4	4	NUM
ejpam-6600	605	10	)	)	PUNCT
ejpam-6600	605	11	(	(	PUNCT
ejpam-6600	605	12	2025	2025	NUM
ejpam-6600	605	13	)	)	PUNCT
ejpam-6600	605	14	,	,	PUNCT
ejpam-6600	605	15	6600	6600	NUM
ejpam-6600	605	16	22	22	NUM
ejpam-6600	605	17	of	of	ADP
ejpam-6600	605	18	26	26	NUM
ejpam-6600	605	19	(	(	PUNCT
ejpam-6600	605	20	4	4	NUM
ejpam-6600	605	21	)	)	PUNCT
ejpam-6600	605	22	if	if	SCONJ
ejpam-6600	605	23	sj	sj	PROPN
ejpam-6600	605	24	∈	∈	PROPN
ejpam-6600	605	25	s1	s1	PROPN
ejpam-6600	605	26	,	,	PUNCT
ejpam-6600	605	27	the	the	DET
ejpam-6600	605	28	vertex	vertex	NOUN
ejpam-6600	605	29	vi+sj	vi+sj	PROPN
ejpam-6600	605	30	is	be	AUX
ejpam-6600	605	31	placed	place	VERB
ejpam-6600	605	32	in	in	ADP
ejpam-6600	605	33	anticlockwise	anticlockwise	NOUN
ejpam-6600	605	34	direction	direction	NOUN
ejpam-6600	605	35	of	of	ADP
ejpam-6600	605	36	vi	vi	NOUN
ejpam-6600	605	37	and	and	CCONJ
ejpam-6600	605	38	if	if	SCONJ
ejpam-6600	605	39	sj	sj	PROPN
ejpam-6600	605	40	∈	∈	PROPN
ejpam-6600	605	41	s2	s2	PROPN
ejpam-6600	605	42	,	,	PUNCT
ejpam-6600	605	43	the	the	DET
ejpam-6600	605	44	vertex	vertex	NOUN
ejpam-6600	605	45	vi+sj	vi+sj	PROPN
ejpam-6600	605	46	is	be	AUX
ejpam-6600	605	47	placed	place	VERB
ejpam-6600	605	48	in	in	ADP
ejpam-6600	605	49	clockwise	clockwise	NOUN
ejpam-6600	605	50	direction	direction	NOUN
ejpam-6600	605	51	of	of	ADP
ejpam-6600	605	52	vi	vi	PROPN
ejpam-6600	605	53	.	.	PUNCT
ejpam-6600	606	1	(	(	PUNCT
ejpam-6600	606	2	5	5	X
ejpam-6600	606	3	)	)	PUNCT
ejpam-6600	606	4	set	set	NOUN
ejpam-6600	606	5	f(vi	f(vi	PROPN
ejpam-6600	606	6	,	,	PUNCT
ejpam-6600	606	7	vi+sj	vi+sj	NUM
ejpam-6600	606	8	)	)	PUNCT
ejpam-6600	607	1	=	=	SYM
ejpam-6600	607	2	0	0	NUM
ejpam-6600	608	1	for	for	ADP
ejpam-6600	608	2	all	all	PRON
ejpam-6600	608	3	i	i	PRON
ejpam-6600	608	4	∈	∈	PROPN
ejpam-6600	608	5	{	{	PUNCT
ejpam-6600	608	6	1	1	NUM
ejpam-6600	608	7	,	,	PUNCT
ejpam-6600	608	8	2	2	NUM
ejpam-6600	608	9	,	,	PUNCT
ejpam-6600	608	10	3	3	NUM
ejpam-6600	608	11	,	,	PUNCT
ejpam-6600	608	12	.	.	PUNCT
ejpam-6600	608	13	.	.	PUNCT
ejpam-6600	608	14	.	.	PUNCT
ejpam-6600	609	1	,	,	PUNCT
ejpam-6600	609	2	p	p	X
ejpam-6600	609	3	}	}	PUNCT
ejpam-6600	609	4	,	,	PUNCT
ejpam-6600	609	5	j	j	PROPN
ejpam-6600	609	6	∈	∈	PROPN
ejpam-6600	609	7	{	{	PUNCT
ejpam-6600	609	8	1	1	NUM
ejpam-6600	609	9	,	,	PUNCT
ejpam-6600	609	10	2	2	NUM
ejpam-6600	609	11	,	,	PUNCT
ejpam-6600	609	12	3	3	NUM
ejpam-6600	609	13	,	,	PUNCT
ejpam-6600	609	14	.	.	PUNCT
ejpam-6600	609	15	.	.	PUNCT
ejpam-6600	609	16	.	.	PUNCT
ejpam-6600	610	1	,	,	PUNCT
ejpam-6600	610	2	2r	2r	NUM
ejpam-6600	610	3	}	}	PUNCT
ejpam-6600	610	4	.	.	PUNCT
ejpam-6600	611	1	(	(	PUNCT
ejpam-6600	611	2	6	6	X
ejpam-6600	611	3	)	)	PUNCT
ejpam-6600	611	4	set	set	NOUN
ejpam-6600	611	5	i	i	NOUN
ejpam-6600	611	6	=	=	NOUN
ejpam-6600	612	1	1	1	X
ejpam-6600	612	2	.	.	X
ejpam-6600	612	3	step	step	NOUN
ejpam-6600	612	4	1	1	NUM
ejpam-6600	612	5	:	:	PUNCT
ejpam-6600	612	6	if	if	SCONJ
ejpam-6600	612	7	i	i	PRON
ejpam-6600	612	8	≤	≤	VERB
ejpam-6600	612	9	p	p	NOUN
ejpam-6600	612	10	then	then	ADV
ejpam-6600	612	11	continue	continue	VERB
ejpam-6600	612	12	to	to	PART
ejpam-6600	612	13	step	step	VERB
ejpam-6600	612	14	2	2	NUM
ejpam-6600	612	15	.	.	PUNCT
ejpam-6600	612	16	else	else	ADV
ejpam-6600	612	17	jump	jump	VERB
ejpam-6600	612	18	to	to	PART
ejpam-6600	612	19	step	step	VERB
ejpam-6600	612	20	4	4	NUM
ejpam-6600	612	21	.	.	PUNCT
ejpam-6600	613	1	step	step	NOUN
ejpam-6600	613	2	2	2	NUM
ejpam-6600	613	3	:	:	PUNCT
ejpam-6600	613	4	for	for	ADP
ejpam-6600	613	5	each	each	DET
ejpam-6600	613	6	sj	sj	PROPN
ejpam-6600	613	7	∈	∈	PROPN
ejpam-6600	613	8	s1	s1	PROPN
ejpam-6600	613	9	,	,	PUNCT
ejpam-6600	613	10	f	f	PROPN
ejpam-6600	613	11	(	(	PUNCT
ejpam-6600	613	12	vi	vi	PROPN
ejpam-6600	613	13	,	,	PUNCT
ejpam-6600	613	14	vi+sj	vi+sj	NUM
ejpam-6600	613	15	)	)	PUNCT
ejpam-6600	614	1	=	=	PUNCT
ejpam-6600	615	1	2[(j	2[(j	NUM
ejpam-6600	615	2	−	−	NUM
ejpam-6600	615	3	1	1	NUM
ejpam-6600	615	4	)	)	PUNCT
ejpam-6600	615	5	p+	p+	VERB
ejpam-6600	615	6	i]−	i]−	PROPN
ejpam-6600	615	7	1	1	NUM
ejpam-6600	615	8	.	.	PUNCT
ejpam-6600	616	1	step	step	NOUN
ejpam-6600	616	2	3	3	NUM
ejpam-6600	616	3	:	:	PUNCT
ejpam-6600	616	4	i	i	PRON
ejpam-6600	616	5	=	=	PUNCT
ejpam-6600	616	6	i+	i+	PROPN
ejpam-6600	616	7	1	1	NUM
ejpam-6600	616	8	,	,	PUNCT
ejpam-6600	616	9	go	go	VERB
ejpam-6600	616	10	back	back	ADV
ejpam-6600	616	11	to	to	PART
ejpam-6600	616	12	step	step	NOUN
ejpam-6600	616	13	1	1	NUM
ejpam-6600	616	14	.	.	PUNCT
ejpam-6600	617	1	step	step	NOUN
ejpam-6600	617	2	4	4	NUM
ejpam-6600	617	3	:	:	PUNCT
ejpam-6600	617	4	for	for	ADP
ejpam-6600	617	5	each	each	PRON
ejpam-6600	617	6	k	k	NOUN
ejpam-6600	617	7	=	=	SYM
ejpam-6600	617	8	1	1	NUM
ejpam-6600	617	9	,	,	PUNCT
ejpam-6600	617	10	2	2	NUM
ejpam-6600	617	11	,	,	PUNCT
ejpam-6600	617	12	3	3	NUM
ejpam-6600	617	13	,	,	PUNCT
ejpam-6600	617	14	.	.	PUNCT
ejpam-6600	617	15	.	.	PUNCT
ejpam-6600	618	1	.	.	PUNCT
ejpam-6600	619	1	,	,	PUNCT
ejpam-6600	619	2	p	p	X
ejpam-6600	619	3	,	,	PUNCT
ejpam-6600	619	4	find	find	VERB
ejpam-6600	619	5	the	the	DET
ejpam-6600	619	6	weight	weight	NOUN
ejpam-6600	619	7	of	of	ADP
ejpam-6600	619	8	the	the	DET
ejpam-6600	619	9	vertex	vertex	NOUN
ejpam-6600	619	10	vk	vk	NOUN
ejpam-6600	619	11	using	use	VERB
ejpam-6600	619	12	the	the	DET
ejpam-6600	619	13	following	follow	VERB
ejpam-6600	619	14	mapping	mapping	NOUN
ejpam-6600	619	15	:	:	PUNCT
ejpam-6600	619	16	fw(vk	fw(vk	PROPN
ejpam-6600	619	17	)	)	PUNCT
ejpam-6600	620	1	=	=	PUNCT
ejpam-6600	621	1	∑2r	∑2r	NOUN
ejpam-6600	621	2	j=1	j=1	PROPN
ejpam-6600	621	3	f(vk	f(vk	PROPN
ejpam-6600	621	4	,	,	PUNCT
ejpam-6600	621	5	vk+sj	vk+sj	PROPN
ejpam-6600	621	6	)	)	PUNCT
ejpam-6600	621	7	(	(	PUNCT
ejpam-6600	621	8	mod	mod	PROPN
ejpam-6600	621	9	2rp	2rp	NOUN
ejpam-6600	621	10	)	)	PUNCT
ejpam-6600	621	11	.	.	PUNCT
ejpam-6600	622	1	take	take	VERB
ejpam-6600	622	2	m	m	NOUN
ejpam-6600	622	3	=	=	PUNCT
ejpam-6600	623	1	∑r	∑r	PROPN
ejpam-6600	623	2	j=1	j=1	NOUN
ejpam-6600	623	3	sj	sj	INTJ
ejpam-6600	623	4	,	,	PUNCT
ejpam-6600	623	5	then	then	ADV
ejpam-6600	623	6	fw(vk	fw(vk	PROPN
ejpam-6600	623	7	)	)	PUNCT
ejpam-6600	624	1	=	=	PUNCT
ejpam-6600	625	1	∑r	∑r	NOUN
ejpam-6600	625	2	j=1	j=1	NOUN
ejpam-6600	626	1	4[(j	4[(j	NOUN
ejpam-6600	627	1	−	−	NOUN
ejpam-6600	627	2	1	1	NUM
ejpam-6600	627	3	)	)	PUNCT
ejpam-6600	627	4	p+	p+	PROPN
ejpam-6600	627	5	k]−	k]−	NOUN
ejpam-6600	627	6	2	2	NUM
ejpam-6600	627	7	+	+	SYM
ejpam-6600	627	8	2(p−	2(p−	NUM
ejpam-6600	627	9	sj	sj	NOUN
ejpam-6600	627	10	)	)	PUNCT
ejpam-6600	627	11	=	=	SYM
ejpam-6600	627	12	4rk	4rk	NOUN
ejpam-6600	627	13	−	−	NOUN
ejpam-6600	627	14	2(m	2(m	NUM
ejpam-6600	628	1	+	+	CCONJ
ejpam-6600	628	2	r	r	X
ejpam-6600	628	3	)	)	PUNCT
ejpam-6600	628	4	(	(	PUNCT
ejpam-6600	628	5	mod	mod	PROPN
ejpam-6600	628	6	2rp	2rp	NOUN
ejpam-6600	628	7	)	)	PUNCT
ejpam-6600	628	8	.	.	PUNCT
ejpam-6600	629	1	theorem	theorem	VERB
ejpam-6600	629	2	7	7	NUM
ejpam-6600	629	3	.	.	PUNCT
ejpam-6600	629	4	paley	paley	ADJ
ejpam-6600	629	5	graphs	graph	NOUN
ejpam-6600	629	6	and	and	CCONJ
ejpam-6600	629	7	their	their	PRON
ejpam-6600	629	8	generalizations	generalization	NOUN
ejpam-6600	629	9	of	of	ADP
ejpam-6600	629	10	prime	prime	ADJ
ejpam-6600	629	11	order	order	NOUN
ejpam-6600	629	12	are	be	AUX
ejpam-6600	629	13	edge	edge	NOUN
ejpam-6600	629	14	-	-	PUNCT
ejpam-6600	629	15	odd	odd	ADJ
ejpam-6600	629	16	graceful	graceful	ADJ
ejpam-6600	629	17	graphs	graph	NOUN
ejpam-6600	629	18	.	.	PUNCT
ejpam-6600	630	1	proof	proof	NOUN
ejpam-6600	630	2	.	.	PUNCT
ejpam-6600	631	1	following	follow	VERB
ejpam-6600	631	2	the	the	DET
ejpam-6600	631	3	same	same	ADJ
ejpam-6600	631	4	steps	step	NOUN
ejpam-6600	631	5	in	in	ADP
ejpam-6600	631	6	the	the	DET
ejpam-6600	631	7	previews	preview	NOUN
ejpam-6600	631	8	theorem	theorem	VERB
ejpam-6600	631	9	we	we	PRON
ejpam-6600	631	10	can	can	AUX
ejpam-6600	631	11	easily	easily	ADV
ejpam-6600	631	12	prove	prove	VERB
ejpam-6600	631	13	that	that	SCONJ
ejpam-6600	631	14	the	the	DET
ejpam-6600	631	15	algorithm	algorithm	NOUN
ejpam-6600	631	16	defines	define	VERB
ejpam-6600	631	17	an	an	DET
ejpam-6600	631	18	edge	edge	NOUN
ejpam-6600	631	19	-	-	PUNCT
ejpam-6600	631	20	odd	odd	ADJ
ejpam-6600	631	21	graceful	graceful	ADJ
ejpam-6600	631	22	labeling	labeling	NOUN
ejpam-6600	631	23	.	.	PUNCT
ejpam-6600	632	1	□	□	PUNCT
ejpam-6600	632	2	example	example	NOUN
ejpam-6600	632	3	17	17	NUM
ejpam-6600	632	4	.	.	PUNCT
ejpam-6600	633	1	consider	consider	VERB
ejpam-6600	633	2	the	the	DET
ejpam-6600	633	3	cubic	cubic	ADJ
ejpam-6600	633	4	paley	paley	PROPN
ejpam-6600	633	5	graph	graph	NOUN
ejpam-6600	633	6	3−p13	3−p13	PROPN
ejpam-6600	633	7	.	.	PUNCT
ejpam-6600	634	1	here	here	ADV
ejpam-6600	634	2	,	,	PUNCT
ejpam-6600	634	3	p	p	X
ejpam-6600	634	4	=	=	SYM
ejpam-6600	634	5	13,m	13,m	NUM
ejpam-6600	634	6	=	=	SYM
ejpam-6600	634	7	3	3	NUM
ejpam-6600	634	8	,	,	PUNCT
ejpam-6600	634	9	d	d	NOUN
ejpam-6600	634	10	=	=	SYM
ejpam-6600	634	11	3	3	NUM
ejpam-6600	634	12	,	,	PUNCT
ejpam-6600	634	13	r	r	NOUN
ejpam-6600	634	14	=	=	SYM
ejpam-6600	634	15	2	2	NUM
ejpam-6600	634	16	,	,	PUNCT
ejpam-6600	634	17	and	and	CCONJ
ejpam-6600	634	18	s1	s1	PROPN
ejpam-6600	634	19	=	=	PUNCT
ejpam-6600	634	20	{	{	PUNCT
ejpam-6600	634	21	12	12	NUM
ejpam-6600	634	22	,	,	PUNCT
ejpam-6600	634	23	8	8	NUM
ejpam-6600	634	24	}	}	PUNCT
ejpam-6600	634	25	.	.	PUNCT
ejpam-6600	635	1	so	so	ADV
ejpam-6600	635	2	for	for	ADP
ejpam-6600	635	3	each	each	DET
ejpam-6600	635	4	sj	sj	PROPN
ejpam-6600	635	5	∈	∈	PROPN
ejpam-6600	635	6	s1	s1	PROPN
ejpam-6600	635	7	,	,	PUNCT
ejpam-6600	635	8	f	f	PROPN
ejpam-6600	635	9	(	(	PUNCT
ejpam-6600	635	10	vk	vk	PROPN
ejpam-6600	635	11	,	,	PUNCT
ejpam-6600	635	12	vk+sj	vk+sj	NOUN
ejpam-6600	635	13	)	)	PUNCT
ejpam-6600	636	1	=	=	PUNCT
ejpam-6600	637	1	2[(j	2[(j	NUM
ejpam-6600	637	2	−	−	NOUN
ejpam-6600	637	3	1	1	NUM
ejpam-6600	637	4	)	)	PUNCT
ejpam-6600	637	5	13	13	NUM
ejpam-6600	638	1	+	+	CCONJ
ejpam-6600	638	2	k]−	k]−	PROPN
ejpam-6600	638	3	1	1	NUM
ejpam-6600	638	4	,	,	PUNCT
ejpam-6600	638	5	and	and	CCONJ
ejpam-6600	638	6	fw(vk	fw(vk	PROPN
ejpam-6600	638	7	)	)	PUNCT
ejpam-6600	639	1	=	=	SYM
ejpam-6600	639	2	8k−2r−2	8k−2r−2	NUM
ejpam-6600	639	3	∑2	∑2	NOUN
ejpam-6600	639	4	j=1	j=1	NOUN
ejpam-6600	639	5	sj	sj	X
ejpam-6600	639	6	=	=	SYM
ejpam-6600	639	7	8k−44	8k−44	PROPN
ejpam-6600	639	8	(	(	PUNCT
ejpam-6600	639	9	mod	mod	PROPN
ejpam-6600	639	10	52	52	NUM
ejpam-6600	639	11	)	)	PUNCT
ejpam-6600	639	12	.	.	PUNCT
ejpam-6600	640	1	the	the	DET
ejpam-6600	640	2	edge	edge	NOUN
ejpam-6600	640	3	-	-	PUNCT
ejpam-6600	640	4	odd	odd	ADJ
ejpam-6600	640	5	graceful	graceful	ADJ
ejpam-6600	640	6	labeling	labeling	NOUN
ejpam-6600	640	7	of	of	ADP
ejpam-6600	640	8	the	the	DET
ejpam-6600	640	9	graph	graph	NOUN
ejpam-6600	640	10	3−p13	3−p13	PROPN
ejpam-6600	640	11	is	be	AUX
ejpam-6600	640	12	shown	show	VERB
ejpam-6600	640	13	in	in	ADP
ejpam-6600	640	14	figure	figure	NOUN
ejpam-6600	640	15	18	18	NUM
ejpam-6600	640	16	.	.	PUNCT
ejpam-6600	641	1	figure	figure	NOUN
ejpam-6600	641	2	18	18	NUM
ejpam-6600	641	3	:	:	PUNCT
ejpam-6600	641	4	an	an	DET
ejpam-6600	641	5	edge	edge	NOUN
ejpam-6600	641	6	-	-	PUNCT
ejpam-6600	641	7	odd	odd	ADJ
ejpam-6600	641	8	graceful	graceful	ADJ
ejpam-6600	641	9	labeling	labeling	NOUN
ejpam-6600	641	10	of	of	ADP
ejpam-6600	641	11	3−	3−	NUM
ejpam-6600	641	12	p13	p13	NOUN
ejpam-6600	641	13	.	.	PUNCT
ejpam-6600	641	14	example	example	NOUN
ejpam-6600	641	15	18	18	NUM
ejpam-6600	641	16	.	.	PUNCT
ejpam-6600	642	1	consider	consider	VERB
ejpam-6600	642	2	the	the	DET
ejpam-6600	642	3	quadruple	quadruple	NOUN
ejpam-6600	642	4	paley	paley	PROPN
ejpam-6600	642	5	graph	graph	NOUN
ejpam-6600	642	6	4	4	NUM
ejpam-6600	642	7	−	−	NOUN
ejpam-6600	642	8	p17	p17	NOUN
ejpam-6600	642	9	.	.	PUNCT
ejpam-6600	643	1	here	here	ADV
ejpam-6600	643	2	,	,	PUNCT
ejpam-6600	643	3	p	p	X
ejpam-6600	643	4	=	=	X
ejpam-6600	643	5	17,m	17,m	NUM
ejpam-6600	643	6	=	=	SYM
ejpam-6600	643	7	4	4	NUM
ejpam-6600	643	8	,	,	PUNCT
ejpam-6600	643	9	d	d	NOUN
ejpam-6600	643	10	=	=	SYM
ejpam-6600	643	11	4	4	NUM
ejpam-6600	643	12	,	,	PUNCT
ejpam-6600	643	13	r	r	NOUN
ejpam-6600	643	14	=	=	SYM
ejpam-6600	643	15	2	2	NUM
ejpam-6600	643	16	,	,	PUNCT
ejpam-6600	643	17	and	and	CCONJ
ejpam-6600	643	18	s1	s1	PROPN
ejpam-6600	643	19	=	=	SYM
ejpam-6600	643	20	{	{	PUNCT
ejpam-6600	643	21	16	16	NUM
ejpam-6600	643	22	,	,	PUNCT
ejpam-6600	643	23	13	13	NUM
ejpam-6600	643	24	}	}	PUNCT
ejpam-6600	643	25	.	.	PUNCT
ejpam-6600	644	1	so	so	ADV
ejpam-6600	644	2	for	for	ADP
ejpam-6600	644	3	each	each	DET
ejpam-6600	644	4	sj	sj	PROPN
ejpam-6600	644	5	∈	∈	PROPN
ejpam-6600	644	6	s1	s1	PROPN
ejpam-6600	644	7	,	,	PUNCT
ejpam-6600	644	8	f	f	PROPN
ejpam-6600	644	9	(	(	PUNCT
ejpam-6600	644	10	vk	vk	PROPN
ejpam-6600	644	11	,	,	PUNCT
ejpam-6600	644	12	vk+sj	vk+sj	NOUN
ejpam-6600	644	13	)	)	PUNCT
ejpam-6600	645	1	=	=	PUNCT
ejpam-6600	646	1	2[(j	2[(j	NUM
ejpam-6600	647	1	−	−	NOUN
ejpam-6600	647	2	1	1	NUM
ejpam-6600	647	3	)	)	PUNCT
ejpam-6600	647	4	17	17	NUM
ejpam-6600	648	1	+	+	CCONJ
ejpam-6600	648	2	k]−	k]−	PROPN
ejpam-6600	648	3	1	1	NUM
ejpam-6600	648	4	,	,	PUNCT
ejpam-6600	648	5	and	and	CCONJ
ejpam-6600	648	6	fw(vk	fw(vk	PROPN
ejpam-6600	648	7	)	)	PUNCT
ejpam-6600	649	1	=	=	SYM
ejpam-6600	650	1	8k	8k	PROPN
ejpam-6600	650	2	−	−	PROPN
ejpam-6600	651	1	2r	2r	NUM
ejpam-6600	651	2	−	−	NOUN
ejpam-6600	651	3	2	2	NUM
ejpam-6600	651	4	∑2	∑2	NOUN
ejpam-6600	651	5	j=1	j=1	NOUN
ejpam-6600	651	6	sj	sj	PROPN
ejpam-6600	651	7	=	=	SYM
ejpam-6600	651	8	8k	8k	PROPN
ejpam-6600	651	9	−	−	PROPN
ejpam-6600	652	1	62	62	NUM
ejpam-6600	652	2	(	(	PUNCT
ejpam-6600	652	3	mod	mod	PROPN
ejpam-6600	652	4	68	68	NUM
ejpam-6600	652	5	)	)	PUNCT
ejpam-6600	652	6	.	.	PUNCT
ejpam-6600	653	1	the	the	DET
ejpam-6600	653	2	edge	edge	NOUN
ejpam-6600	653	3	-	-	PUNCT
ejpam-6600	653	4	odd	odd	ADJ
ejpam-6600	653	5	graceful	graceful	ADJ
ejpam-6600	653	6	labeling	labeling	NOUN
ejpam-6600	653	7	of	of	ADP
ejpam-6600	653	8	the	the	DET
ejpam-6600	653	9	graph	graph	NOUN
ejpam-6600	653	10	4−	4−	NOUN
ejpam-6600	653	11	p17	p17	NOUN
ejpam-6600	653	12	is	be	AUX
ejpam-6600	653	13	shown	show	VERB
ejpam-6600	653	14	in	in	ADP
ejpam-6600	653	15	figure	figure	NOUN
ejpam-6600	653	16	19	19	NUM
ejpam-6600	653	17	.	.	PUNCT
ejpam-6600	653	18	a.	a.	PROPN
ejpam-6600	653	19	n.	n.	PROPN
ejpam-6600	653	20	elsawy	elsawy	PROPN
ejpam-6600	653	21	,	,	PUNCT
ejpam-6600	653	22	r.	r.	PROPN
ejpam-6600	653	23	n.	n.	PROPN
ejpam-6600	653	24	almohammadi	almohammadi	PROPN
ejpam-6600	653	25	/	/	SYM
ejpam-6600	653	26	eur	eur	PROPN
ejpam-6600	653	27	.	.	PUNCT
ejpam-6600	654	1	j.	j.	PROPN
ejpam-6600	654	2	pure	pure	PROPN
ejpam-6600	654	3	appl	appl	PROPN
ejpam-6600	654	4	.	.	PROPN
ejpam-6600	654	5	math	math	PROPN
ejpam-6600	654	6	,	,	PUNCT
ejpam-6600	654	7	18	18	NUM
ejpam-6600	654	8	(	(	PUNCT
ejpam-6600	654	9	4	4	NUM
ejpam-6600	654	10	)	)	PUNCT
ejpam-6600	654	11	(	(	PUNCT
ejpam-6600	654	12	2025	2025	NUM
ejpam-6600	654	13	)	)	PUNCT
ejpam-6600	654	14	,	,	PUNCT
ejpam-6600	654	15	6600	6600	NUM
ejpam-6600	654	16	23	23	NUM
ejpam-6600	654	17	of	of	ADP
ejpam-6600	654	18	26	26	NUM
ejpam-6600	654	19	figure	figure	NOUN
ejpam-6600	654	20	19	19	NUM
ejpam-6600	654	21	:	:	PUNCT
ejpam-6600	654	22	an	an	DET
ejpam-6600	654	23	edge	edge	NOUN
ejpam-6600	654	24	-	-	PUNCT
ejpam-6600	654	25	odd	odd	ADJ
ejpam-6600	654	26	graceful	graceful	ADJ
ejpam-6600	654	27	labeling	labeling	NOUN
ejpam-6600	654	28	of	of	ADP
ejpam-6600	654	29	4−	4−	PROPN
ejpam-6600	654	30	p17	p17	NOUN
ejpam-6600	654	31	.	.	PUNCT
ejpam-6600	655	1	8	8	NUM
ejpam-6600	655	2	.	.	X
ejpam-6600	655	3	paley	paley	ADJ
ejpam-6600	655	4	graph	graph	NOUN
ejpam-6600	655	5	of	of	ADP
ejpam-6600	655	6	prime	prime	ADJ
ejpam-6600	655	7	power	power	NOUN
ejpam-6600	655	8	order	order	NOUN
ejpam-6600	655	9	an	an	DET
ejpam-6600	655	10	edge	edge	NOUN
ejpam-6600	655	11	-	-	PUNCT
ejpam-6600	655	12	graceful	graceful	ADJ
ejpam-6600	655	13	,	,	PUNCT
ejpam-6600	655	14	edge	edge	NOUN
ejpam-6600	655	15	-	-	PUNCT
ejpam-6600	655	16	even	even	ADV
ejpam-6600	655	17	graceful	graceful	ADJ
ejpam-6600	655	18	,	,	PUNCT
ejpam-6600	655	19	and	and	CCONJ
ejpam-6600	655	20	edge	edge	NOUN
ejpam-6600	655	21	-	-	PUNCT
ejpam-6600	655	22	odd	odd	ADJ
ejpam-6600	655	23	graceful	graceful	ADJ
ejpam-6600	655	24	labelling	labelling	NOUN
ejpam-6600	655	25	for	for	ADP
ejpam-6600	655	26	paley	paley	ADJ
ejpam-6600	655	27	graph	graph	NOUN
ejpam-6600	655	28	of	of	ADP
ejpam-6600	655	29	order	order	NOUN
ejpam-6600	655	30	q	q	NOUN
ejpam-6600	656	1	=	=	SYM
ejpam-6600	656	2	pn	pn	NOUN
ejpam-6600	656	3	,	,	PUNCT
ejpam-6600	656	4	where	where	SCONJ
ejpam-6600	656	5	n	n	X
ejpam-6600	656	6	>	>	X
ejpam-6600	656	7	1	1	NUM
ejpam-6600	656	8	,	,	PUNCT
ejpam-6600	656	9	remains	remain	VERB
ejpam-6600	656	10	an	an	DET
ejpam-6600	656	11	open	open	ADJ
ejpam-6600	656	12	challenge	challenge	NOUN
ejpam-6600	656	13	.	.	PUNCT
ejpam-6600	657	1	the	the	DET
ejpam-6600	657	2	paley	paley	PROPN
ejpam-6600	657	3	graph	graph	NOUN
ejpam-6600	657	4	pq	pq	PROPN
ejpam-6600	657	5	of	of	ADP
ejpam-6600	657	6	order	order	NOUN
ejpam-6600	657	7	q	q	NOUN
ejpam-6600	658	1	=	=	SYM
ejpam-6600	658	2	pn	pn	NOUN
ejpam-6600	658	3	,	,	PUNCT
ejpam-6600	658	4	where	where	SCONJ
ejpam-6600	658	5	n	n	X
ejpam-6600	658	6	>	>	X
ejpam-6600	658	7	1	1	NUM
ejpam-6600	658	8	,	,	PUNCT
ejpam-6600	658	9	has	have	VERB
ejpam-6600	658	10	the	the	DET
ejpam-6600	658	11	vertex	vertex	NOUN
ejpam-6600	658	12	set	set	VERB
ejpam-6600	658	13	v	v	NOUN
ejpam-6600	658	14	(	(	PUNCT
ejpam-6600	658	15	pq	pq	NOUN
ejpam-6600	658	16	)	)	PUNCT
ejpam-6600	659	1	=	=	SYM
ejpam-6600	659	2	fq	fq	PROPN
ejpam-6600	659	3	.	.	PUNCT
ejpam-6600	659	4	here	here	ADV
ejpam-6600	659	5	,	,	PUNCT
ejpam-6600	659	6	fq	fq	PROPN
ejpam-6600	659	7	̸=	̸=	PROPN
ejpam-6600	659	8	{	{	PUNCT
ejpam-6600	659	9	0	0	NUM
ejpam-6600	659	10	,	,	PUNCT
ejpam-6600	659	11	1	1	NUM
ejpam-6600	659	12	,	,	PUNCT
ejpam-6600	659	13	2	2	NUM
ejpam-6600	659	14	,	,	PUNCT
ejpam-6600	659	15	.	.	PUNCT
ejpam-6600	659	16	.	.	PUNCT
ejpam-6600	659	17	.	.	PUNCT
ejpam-6600	660	1	,	,	PUNCT
ejpam-6600	660	2	q	q	X
ejpam-6600	660	3	}	}	PUNCT
ejpam-6600	660	4	,	,	PUNCT
ejpam-6600	660	5	and	and	CCONJ
ejpam-6600	660	6	so	so	ADV
ejpam-6600	660	7	the	the	DET
ejpam-6600	660	8	algorithms	algorithm	NOUN
ejpam-6600	660	9	introduced	introduce	VERB
ejpam-6600	660	10	in	in	ADP
ejpam-6600	660	11	this	this	DET
ejpam-6600	660	12	paper	paper	NOUN
ejpam-6600	660	13	are	be	AUX
ejpam-6600	660	14	not	not	PART
ejpam-6600	660	15	applicable	applicable	ADJ
ejpam-6600	660	16	for	for	ADP
ejpam-6600	660	17	this	this	DET
ejpam-6600	660	18	case	case	NOUN
ejpam-6600	660	19	.	.	PUNCT
ejpam-6600	661	1	for	for	ADP
ejpam-6600	661	2	example	example	NOUN
ejpam-6600	661	3	,	,	PUNCT
ejpam-6600	661	4	if	if	SCONJ
ejpam-6600	661	5	p	p	NOUN
ejpam-6600	661	6	=	=	SYM
ejpam-6600	661	7	5	5	NUM
ejpam-6600	661	8	,	,	PUNCT
ejpam-6600	661	9	n	n	NOUN
ejpam-6600	661	10	=	=	SYM
ejpam-6600	661	11	2	2	NUM
ejpam-6600	661	12	,	,	PUNCT
ejpam-6600	661	13	we	we	PRON
ejpam-6600	661	14	get	get	VERB
ejpam-6600	661	15	the	the	DET
ejpam-6600	661	16	smallest	small	ADJ
ejpam-6600	661	17	case	case	NOUN
ejpam-6600	661	18	without	without	ADP
ejpam-6600	661	19	edge	edge	NOUN
ejpam-6600	661	20	-	-	PUNCT
ejpam-6600	661	21	graceful	graceful	ADJ
ejpam-6600	661	22	,	,	PUNCT
ejpam-6600	661	23	edge	edge	NOUN
ejpam-6600	661	24	-	-	PUNCT
ejpam-6600	661	25	even	even	ADV
ejpam-6600	661	26	graceful	graceful	ADJ
ejpam-6600	661	27	,	,	PUNCT
ejpam-6600	661	28	and	and	CCONJ
ejpam-6600	661	29	edge	edge	NOUN
ejpam-6600	661	30	-	-	PUNCT
ejpam-6600	661	31	odd	odd	ADJ
ejpam-6600	661	32	graceful	graceful	ADJ
ejpam-6600	661	33	labelling	labelling	NOUN
ejpam-6600	661	34	,	,	PUNCT
ejpam-6600	661	35	where	where	SCONJ
ejpam-6600	661	36	v	v	X
ejpam-6600	661	37	(	(	PUNCT
ejpam-6600	661	38	p25	p25	PROPN
ejpam-6600	661	39	)	)	PUNCT
ejpam-6600	661	40	=	=	SYM
ejpam-6600	662	1	f25	f25	NOUN
ejpam-6600	662	2	=	=	PUNCT
ejpam-6600	662	3	{	{	PUNCT
ejpam-6600	662	4	0	0	NUM
ejpam-6600	662	5	,	,	PUNCT
ejpam-6600	662	6	1	1	NUM
ejpam-6600	662	7	,	,	PUNCT
ejpam-6600	662	8	2	2	NUM
ejpam-6600	662	9	,	,	PUNCT
ejpam-6600	662	10	3	3	NUM
ejpam-6600	662	11	,	,	PUNCT
ejpam-6600	662	12	4	4	NUM
ejpam-6600	662	13	,	,	PUNCT
ejpam-6600	662	14	a	a	PRON
ejpam-6600	662	15	,	,	PUNCT
ejpam-6600	662	16	2a	2a	NUM
ejpam-6600	662	17	,	,	PUNCT
ejpam-6600	662	18	3a	3a	NUM
ejpam-6600	662	19	,	,	PUNCT
ejpam-6600	662	20	4a	4a	NUM
ejpam-6600	662	21	,	,	PUNCT
ejpam-6600	662	22	a	a	DET
ejpam-6600	662	23	+	+	NUM
ejpam-6600	662	24	1	1	NUM
ejpam-6600	662	25	,	,	PUNCT
ejpam-6600	662	26	a	a	DET
ejpam-6600	662	27	+	+	ADJ
ejpam-6600	662	28	2	2	NUM
ejpam-6600	662	29	,	,	PUNCT
ejpam-6600	662	30	a	a	DET
ejpam-6600	662	31	+	+	NUM
ejpam-6600	662	32	3	3	NUM
ejpam-6600	662	33	,	,	PUNCT
ejpam-6600	662	34	a	a	DET
ejpam-6600	662	35	+	+	NUM
ejpam-6600	662	36	4	4	NUM
ejpam-6600	662	37	,	,	PUNCT
ejpam-6600	662	38	2a	2a	NUM
ejpam-6600	662	39	+	+	CCONJ
ejpam-6600	662	40	1	1	NUM
ejpam-6600	662	41	,	,	PUNCT
ejpam-6600	662	42	2a	2a	NUM
ejpam-6600	662	43	+	+	CCONJ
ejpam-6600	662	44	2	2	NUM
ejpam-6600	662	45	,	,	PUNCT
ejpam-6600	662	46	2a	2a	NUM
ejpam-6600	662	47	+	+	CCONJ
ejpam-6600	662	48	3	3	NUM
ejpam-6600	662	49	,	,	PUNCT
ejpam-6600	662	50	2a	2a	NUM
ejpam-6600	662	51	+	+	CCONJ
ejpam-6600	662	52	4	4	NUM
ejpam-6600	662	53	,	,	PUNCT
ejpam-6600	662	54	3a	3a	NUM
ejpam-6600	662	55	+	+	X
ejpam-6600	662	56	1	1	NUM
ejpam-6600	662	57	,	,	PUNCT
ejpam-6600	662	58	3a	3a	NUM
ejpam-6600	662	59	+	+	X
ejpam-6600	662	60	2	2	NUM
ejpam-6600	662	61	,	,	PUNCT
ejpam-6600	662	62	3a	3a	NUM
ejpam-6600	662	63	+	+	CCONJ
ejpam-6600	662	64	3	3	NUM
ejpam-6600	662	65	,	,	PUNCT
ejpam-6600	662	66	3a	3a	NUM
ejpam-6600	662	67	+	+	CCONJ
ejpam-6600	662	68	4	4	NUM
ejpam-6600	662	69	,	,	PUNCT
ejpam-6600	662	70	4a	4a	NOUN
ejpam-6600	662	71	+	+	CCONJ
ejpam-6600	662	72	1	1	NUM
ejpam-6600	662	73	,	,	PUNCT
ejpam-6600	662	74	4a	4a	NOUN
ejpam-6600	662	75	+	+	CCONJ
ejpam-6600	662	76	2	2	NUM
ejpam-6600	662	77	,	,	PUNCT
ejpam-6600	662	78	4a	4a	NOUN
ejpam-6600	662	79	+	+	CCONJ
ejpam-6600	662	80	3	3	NUM
ejpam-6600	662	81	,	,	PUNCT
ejpam-6600	662	82	4a	4a	NOUN
ejpam-6600	662	83	+	+	CCONJ
ejpam-6600	662	84	4	4	NUM
ejpam-6600	662	85	}	}	PUNCT
ejpam-6600	662	86	=	=	NOUN
ejpam-6600	662	87	z5[x]/(x	z5[x]/(x	NOUN
ejpam-6600	662	88	2	2	NUM
ejpam-6600	662	89	+	+	CCONJ
ejpam-6600	662	90	2	2	NUM
ejpam-6600	662	91	)	)	PUNCT
ejpam-6600	662	92	.	.	PUNCT
ejpam-6600	663	1	and	and	CCONJ
ejpam-6600	663	2	(	(	PUNCT
ejpam-6600	663	3	f∗	f∗	NOUN
ejpam-6600	663	4	25	25	NUM
ejpam-6600	663	5	)	)	PUNCT
ejpam-6600	663	6	2	2	NUM
ejpam-6600	663	7	=	=	SYM
ejpam-6600	663	8	{	{	PUNCT
ejpam-6600	663	9	1	1	NUM
ejpam-6600	663	10	,	,	PUNCT
ejpam-6600	663	11	2	2	NUM
ejpam-6600	663	12	,	,	PUNCT
ejpam-6600	663	13	3	3	NUM
ejpam-6600	663	14	,	,	PUNCT
ejpam-6600	663	15	4	4	NUM
ejpam-6600	663	16	,	,	PUNCT
ejpam-6600	663	17	a+2	a+2	PROPN
ejpam-6600	663	18	,	,	PUNCT
ejpam-6600	663	19	a+3	a+3	ADV
ejpam-6600	663	20	,	,	PUNCT
ejpam-6600	663	21	2a+1	2a+1	PROPN
ejpam-6600	663	22	,	,	PUNCT
ejpam-6600	663	23	2a+4	2a+4	PROPN
ejpam-6600	663	24	,	,	PUNCT
ejpam-6600	663	25	3a+1	3a+1	PROPN
ejpam-6600	663	26	,	,	PUNCT
ejpam-6600	663	27	3a+4	3a+4	PROPN
ejpam-6600	663	28	,	,	PUNCT
ejpam-6600	663	29	4a+2	4a+2	PROPN
ejpam-6600	663	30	,	,	PUNCT
ejpam-6600	663	31	4a+3	4a+3	NOUN
ejpam-6600	663	32	}	}	PUNCT
ejpam-6600	663	33	,	,	PUNCT
ejpam-6600	663	34	so	so	SCONJ
ejpam-6600	663	35	e(p25	e(p25	NOUN
ejpam-6600	663	36	)	)	PUNCT
ejpam-6600	664	1	=	=	PRON
ejpam-6600	664	2	{	{	PUNCT
ejpam-6600	664	3	(	(	PUNCT
ejpam-6600	664	4	xi	xi	PROPN
ejpam-6600	664	5	,	,	PUNCT
ejpam-6600	664	6	xi	xi	PROPN
ejpam-6600	664	7	+	+	CCONJ
ejpam-6600	664	8	xj	xj	PROPN
ejpam-6600	664	9	)	)	PUNCT
ejpam-6600	664	10	∀xi	∀xi	PROPN
ejpam-6600	664	11	∈	∈	PROPN
ejpam-6600	664	12	f25	f25	NOUN
ejpam-6600	664	13	and	and	CCONJ
ejpam-6600	664	14	∀xj	∀xj	NOUN
ejpam-6600	664	15	∈	∈	PROPN
ejpam-6600	664	16	(	(	PUNCT
ejpam-6600	664	17	f∗	f∗	NOUN
ejpam-6600	664	18	25	25	NUM
ejpam-6600	664	19	)	)	PUNCT
ejpam-6600	664	20	2	2	NUM
ejpam-6600	664	21	}	}	PUNCT
ejpam-6600	664	22	.	.	PUNCT
ejpam-6600	665	1	(	(	PUNCT
ejpam-6600	665	2	see	see	VERB
ejpam-6600	665	3	figure	figure	NOUN
ejpam-6600	665	4	20	20	NUM
ejpam-6600	665	5	)	)	PUNCT
ejpam-6600	665	6	.	.	PUNCT
ejpam-6600	666	1	the	the	DET
ejpam-6600	666	2	case	case	NOUN
ejpam-6600	666	3	of	of	ADP
ejpam-6600	666	4	p9	p9	PROPN
ejpam-6600	666	5	is	be	AUX
ejpam-6600	666	6	shown	show	VERB
ejpam-6600	666	7	in	in	ADP
ejpam-6600	666	8	figure	figure	NOUN
ejpam-6600	666	9	3	3	NUM
ejpam-6600	666	10	.	.	PUNCT
ejpam-6600	666	11	a.	a.	PROPN
ejpam-6600	666	12	n.	n.	PROPN
ejpam-6600	666	13	elsawy	elsawy	PROPN
ejpam-6600	666	14	,	,	PUNCT
ejpam-6600	666	15	r.	r.	PROPN
ejpam-6600	666	16	n.	n.	PROPN
ejpam-6600	666	17	almohammadi	almohammadi	PROPN
ejpam-6600	666	18	/	/	SYM
ejpam-6600	666	19	eur	eur	PROPN
ejpam-6600	666	20	.	.	PUNCT
ejpam-6600	667	1	j.	j.	PROPN
ejpam-6600	667	2	pure	pure	PROPN
ejpam-6600	667	3	appl	appl	PROPN
ejpam-6600	667	4	.	.	PROPN
ejpam-6600	667	5	math	math	PROPN
ejpam-6600	667	6	,	,	PUNCT
ejpam-6600	667	7	18	18	NUM
ejpam-6600	667	8	(	(	PUNCT
ejpam-6600	667	9	4	4	NUM
ejpam-6600	667	10	)	)	PUNCT
ejpam-6600	667	11	(	(	PUNCT
ejpam-6600	667	12	2025	2025	NUM
ejpam-6600	667	13	)	)	PUNCT
ejpam-6600	667	14	,	,	PUNCT
ejpam-6600	667	15	6600	6600	NUM
ejpam-6600	667	16	24	24	NUM
ejpam-6600	667	17	of	of	ADP
ejpam-6600	667	18	26	26	NUM
ejpam-6600	667	19	figure	figure	NOUN
ejpam-6600	667	20	20	20	NUM
ejpam-6600	667	21	:	:	PUNCT
ejpam-6600	667	22	the	the	DET
ejpam-6600	667	23	paley	paley	ADJ
ejpam-6600	667	24	graph	graph	NOUN
ejpam-6600	667	25	p25	p25	NOUN
ejpam-6600	667	26	.	.	PUNCT
ejpam-6600	668	1	the	the	DET
ejpam-6600	668	2	structure	structure	NOUN
ejpam-6600	668	3	of	of	ADP
ejpam-6600	668	4	this	this	DET
ejpam-6600	668	5	field	field	NOUN
ejpam-6600	668	6	is	be	AUX
ejpam-6600	668	7	more	more	ADV
ejpam-6600	668	8	complex	complex	ADJ
ejpam-6600	668	9	,	,	PUNCT
ejpam-6600	668	10	and	and	CCONJ
ejpam-6600	668	11	the	the	DET
ejpam-6600	668	12	simple	simple	ADJ
ejpam-6600	668	13	modular	modular	ADJ
ejpam-6600	668	14	arithmetic	arithmetic	NOUN
ejpam-6600	668	15	used	use	VERB
ejpam-6600	668	16	in	in	ADP
ejpam-6600	668	17	the	the	DET
ejpam-6600	668	18	proof	proof	NOUN
ejpam-6600	668	19	for	for	SCONJ
ejpam-6600	668	20	no	no	ADV
ejpam-6600	668	21	longer	long	ADV
ejpam-6600	668	22	holds	hold	VERB
ejpam-6600	668	23	directly	directly	ADV
ejpam-6600	668	24	.	.	PUNCT
ejpam-6600	669	1	therefore	therefore	ADV
ejpam-6600	669	2	,	,	PUNCT
ejpam-6600	669	3	we	we	PRON
ejpam-6600	669	4	need	need	VERB
ejpam-6600	669	5	to	to	PART
ejpam-6600	669	6	understand	understand	VERB
ejpam-6600	669	7	the	the	DET
ejpam-6600	669	8	structure	structure	NOUN
ejpam-6600	669	9	of	of	ADP
ejpam-6600	669	10	the	the	DET
ejpam-6600	669	11	field	field	NOUN
ejpam-6600	669	12	deeply	deeply	ADV
ejpam-6600	669	13	to	to	PART
ejpam-6600	669	14	construct	construct	VERB
ejpam-6600	669	15	an	an	DET
ejpam-6600	669	16	edge	edge	NOUN
ejpam-6600	669	17	-	-	PUNCT
ejpam-6600	669	18	graceful	graceful	ADJ
ejpam-6600	669	19	,	,	PUNCT
ejpam-6600	669	20	edge	edge	NOUN
ejpam-6600	669	21	-	-	PUNCT
ejpam-6600	669	22	even	even	ADV
ejpam-6600	669	23	graceful	graceful	ADJ
ejpam-6600	669	24	,	,	PUNCT
ejpam-6600	669	25	and	and	CCONJ
ejpam-6600	669	26	edge	edge	NOUN
ejpam-6600	669	27	-	-	PUNCT
ejpam-6600	669	28	odd	odd	ADJ
ejpam-6600	669	29	graceful	graceful	ADJ
ejpam-6600	669	30	labelling	labelling	NOUN
ejpam-6600	669	31	algorithm	algorithm	NOUN
ejpam-6600	669	32	.	.	PUNCT
ejpam-6600	670	1	for	for	ADP
ejpam-6600	670	2	more	more	ADJ
ejpam-6600	670	3	information	information	NOUN
ejpam-6600	670	4	about	about	ADP
ejpam-6600	670	5	the	the	DET
ejpam-6600	670	6	structure	structure	NOUN
ejpam-6600	670	7	of	of	ADP
ejpam-6600	670	8	the	the	DET
ejpam-6600	670	9	field	field	NOUN
ejpam-6600	670	10	,	,	PUNCT
ejpam-6600	670	11	see	see	VERB
ejpam-6600	670	12	[	[	X
ejpam-6600	670	13	3	3	NUM
ejpam-6600	670	14	]	]	PUNCT
ejpam-6600	670	15	.	.	PUNCT
ejpam-6600	671	1	also	also	ADV
ejpam-6600	671	2	,	,	PUNCT
ejpam-6600	671	3	an	an	DET
ejpam-6600	671	4	other	other	ADJ
ejpam-6600	671	5	challenge	challenge	NOUN
ejpam-6600	671	6	is	be	AUX
ejpam-6600	671	7	to	to	PART
ejpam-6600	671	8	find	find	VERB
ejpam-6600	671	9	different	different	ADJ
ejpam-6600	671	10	types	type	NOUN
ejpam-6600	671	11	of	of	ADP
ejpam-6600	671	12	labellings	labelling	NOUN
ejpam-6600	671	13	for	for	ADP
ejpam-6600	671	14	paley	paley	ADJ
ejpam-6600	671	15	graph	graph	NOUN
ejpam-6600	671	16	and	and	CCONJ
ejpam-6600	671	17	its	its	PRON
ejpam-6600	671	18	generalizations	generalization	NOUN
ejpam-6600	671	19	.	.	PUNCT
ejpam-6600	672	1	9	9	X
ejpam-6600	672	2	.	.	X
ejpam-6600	672	3	conclusions	conclusion	NOUN
ejpam-6600	672	4	we	we	PRON
ejpam-6600	672	5	introduced	introduce	VERB
ejpam-6600	672	6	three	three	NUM
ejpam-6600	672	7	algorithms	algorithm	NOUN
ejpam-6600	672	8	which	which	PRON
ejpam-6600	672	9	produce	produce	VERB
ejpam-6600	672	10	an	an	DET
ejpam-6600	672	11	edge	edge	NOUN
ejpam-6600	672	12	-	-	PUNCT
ejpam-6600	672	13	graceful	graceful	ADJ
ejpam-6600	672	14	,	,	PUNCT
ejpam-6600	672	15	edge	edge	NOUN
ejpam-6600	672	16	-	-	PUNCT
ejpam-6600	672	17	even	even	ADV
ejpam-6600	672	18	graceful	graceful	ADJ
ejpam-6600	672	19	,	,	PUNCT
ejpam-6600	672	20	and	and	CCONJ
ejpam-6600	672	21	edge	edge	NOUN
ejpam-6600	672	22	-	-	PUNCT
ejpam-6600	672	23	odd	odd	ADJ
ejpam-6600	672	24	graceful	graceful	ADJ
ejpam-6600	672	25	labelling	labelling	NOUN
ejpam-6600	672	26	for	for	ADP
ejpam-6600	672	27	paley	paley	ADJ
ejpam-6600	672	28	graphs	graph	NOUN
ejpam-6600	672	29	and	and	CCONJ
ejpam-6600	672	30	their	their	PRON
ejpam-6600	672	31	generalizations	generalization	NOUN
ejpam-6600	672	32	.	.	PUNCT
ejpam-6600	673	1	we	we	PRON
ejpam-6600	673	2	proved	prove	VERB
ejpam-6600	673	3	that	that	DET
ejpam-6600	673	4	paley	paley	ADJ
ejpam-6600	673	5	graphs	graph	NOUN
ejpam-6600	673	6	and	and	CCONJ
ejpam-6600	673	7	their	their	PRON
ejpam-6600	673	8	generalizations	generalization	NOUN
ejpam-6600	673	9	including	include	VERB
ejpam-6600	673	10	cubic	cubic	ADJ
ejpam-6600	673	11	and	and	CCONJ
ejpam-6600	673	12	quadruple	quadruple	NOUN
ejpam-6600	673	13	paley	paley	ADJ
ejpam-6600	673	14	graphs	graph	NOUN
ejpam-6600	673	15	of	of	ADP
ejpam-6600	673	16	prime	prime	ADJ
ejpam-6600	673	17	order	order	NOUN
ejpam-6600	673	18	are	be	AUX
ejpam-6600	673	19	edge	edge	NOUN
ejpam-6600	673	20	-	-	PUNCT
ejpam-6600	673	21	graceful	graceful	ADJ
ejpam-6600	673	22	,	,	PUNCT
ejpam-6600	673	23	edge	edge	NOUN
ejpam-6600	673	24	-	-	PUNCT
ejpam-6600	673	25	even	even	ADV
ejpam-6600	673	26	graceful	graceful	ADJ
ejpam-6600	673	27	,	,	PUNCT
ejpam-6600	673	28	and	and	CCONJ
ejpam-6600	673	29	edge	edge	NOUN
ejpam-6600	673	30	-	-	PUNCT
ejpam-6600	673	31	odd	odd	ADJ
ejpam-6600	673	32	graceful	graceful	ADJ
ejpam-6600	673	33	graphs	graph	NOUN
ejpam-6600	673	34	.	.	PUNCT
ejpam-6600	674	1	acknowledgements	acknowledgement	NOUN
ejpam-6600	674	2	the	the	DET
ejpam-6600	674	3	authors	author	NOUN
ejpam-6600	674	4	are	be	AUX
ejpam-6600	674	5	so	so	ADV
ejpam-6600	674	6	grateful	grateful	ADJ
ejpam-6600	674	7	to	to	ADP
ejpam-6600	674	8	the	the	DET
ejpam-6600	674	9	reviewers	reviewer	NOUN
ejpam-6600	674	10	and	and	CCONJ
ejpam-6600	674	11	the	the	DET
ejpam-6600	674	12	editor	editor	NOUN
ejpam-6600	674	13	of	of	ADP
ejpam-6600	674	14	european	european	PROPN
ejpam-6600	674	15	journal	journal	PROPN
ejpam-6600	674	16	of	of	ADP
ejpam-6600	674	17	pure	pure	ADJ
ejpam-6600	674	18	and	and	CCONJ
ejpam-6600	674	19	applied	applied	ADJ
ejpam-6600	674	20	mathematics	mathematic	NOUN
ejpam-6600	674	21	,	,	PUNCT
ejpam-6600	674	22	for	for	ADP
ejpam-6600	674	23	their	their	PRON
ejpam-6600	674	24	valuable	valuable	ADJ
ejpam-6600	674	25	suggestions	suggestion	NOUN
ejpam-6600	674	26	and	and	CCONJ
ejpam-6600	674	27	comments	comment	NOUN
ejpam-6600	674	28	that	that	PRON
ejpam-6600	674	29	significantly	significantly	ADV
ejpam-6600	674	30	a.	a.	PROPN
ejpam-6600	674	31	n.	n.	PROPN
ejpam-6600	674	32	elsawy	elsawy	PROPN
ejpam-6600	674	33	,	,	PUNCT
ejpam-6600	674	34	r.	r.	PROPN
ejpam-6600	674	35	n.	n.	PROPN
ejpam-6600	674	36	almohammadi	almohammadi	PROPN
ejpam-6600	674	37	/	/	SYM
ejpam-6600	674	38	eur	eur	PROPN
ejpam-6600	674	39	.	.	PUNCT
ejpam-6600	675	1	j.	j.	PROPN
ejpam-6600	675	2	pure	pure	PROPN
ejpam-6600	675	3	appl	appl	PROPN
ejpam-6600	675	4	.	.	PROPN
ejpam-6600	675	5	math	math	PROPN
ejpam-6600	675	6	,	,	PUNCT
ejpam-6600	675	7	18	18	NUM
ejpam-6600	675	8	(	(	PUNCT
ejpam-6600	675	9	4	4	NUM
ejpam-6600	675	10	)	)	PUNCT
ejpam-6600	675	11	(	(	PUNCT
ejpam-6600	675	12	2025	2025	NUM
ejpam-6600	675	13	)	)	PUNCT
ejpam-6600	675	14	,	,	PUNCT
ejpam-6600	675	15	6600	6600	NUM
ejpam-6600	675	16	25	25	NUM
ejpam-6600	675	17	of	of	ADP
ejpam-6600	675	18	26	26	NUM
ejpam-6600	675	19	improved	improve	VERB
ejpam-6600	675	20	the	the	DET
ejpam-6600	675	21	paper	paper	NOUN
ejpam-6600	675	22	.	.	PUNCT
ejpam-6600	676	1	references	reference	NOUN
ejpam-6600	676	2	[	[	X
ejpam-6600	676	3	1	1	X
ejpam-6600	676	4	]	]	PUNCT
ejpam-6600	676	5	s.	s.	PROPN
ejpam-6600	676	6	p.	p.	PROPN
ejpam-6600	676	7	lo	lo	PROPN
ejpam-6600	676	8	.	.	PUNCT
ejpam-6600	677	1	on	on	ADP
ejpam-6600	677	2	edge	edge	NOUN
ejpam-6600	677	3	-	-	PUNCT
ejpam-6600	677	4	graceful	graceful	NOUN
ejpam-6600	677	5	labelings	labeling	NOUN
ejpam-6600	677	6	of	of	ADP
ejpam-6600	677	7	graphs	graph	NOUN
ejpam-6600	677	8	.	.	PUNCT
ejpam-6600	678	1	congressus	congressus	PROPN
ejpam-6600	678	2	numerantium	numerantium	PROPN
ejpam-6600	678	3	,	,	PUNCT
ejpam-6600	678	4	50:231–241	50:231–241	PROPN
ejpam-6600	678	5	,	,	PUNCT
ejpam-6600	678	6	1985	1985	NUM
ejpam-6600	678	7	.	.	PUNCT
ejpam-6600	679	1	[	[	X
ejpam-6600	679	2	2	2	NUM
ejpam-6600	679	3	]	]	PUNCT
ejpam-6600	679	4	w	w	NOUN
ejpam-6600	679	5	ananchuen	ananchuen	NOUN
ejpam-6600	679	6	and	and	CCONJ
ejpam-6600	679	7	l	l	PROPN
ejpam-6600	679	8	caccetta	caccetta	NOUN
ejpam-6600	679	9	.	.	PUNCT
ejpam-6600	680	1	on	on	ADP
ejpam-6600	680	2	the	the	DET
ejpam-6600	680	3	adjacency	adjacency	NOUN
ejpam-6600	680	4	properties	property	NOUN
ejpam-6600	680	5	of	of	ADP
ejpam-6600	680	6	paley	paley	ADJ
ejpam-6600	680	7	graphs	graph	NOUN
ejpam-6600	680	8	.	.	PUNCT
ejpam-6600	681	1	networks	network	NOUN
ejpam-6600	681	2	,	,	PUNCT
ejpam-6600	681	3	23(4):227–236	23(4):227–236	PROPN
ejpam-6600	681	4	,	,	PUNCT
ejpam-6600	681	5	1993	1993	NUM
ejpam-6600	681	6	.	.	PUNCT
ejpam-6600	682	1	[	[	X
ejpam-6600	682	2	3	3	NUM
ejpam-6600	682	3	]	]	PUNCT
ejpam-6600	682	4	a.	a.	NOUN
ejpam-6600	682	5	n.	n.	PROPN
ejpam-6600	682	6	elsawy	elsawy	PROPN
ejpam-6600	682	7	.	.	PUNCT
ejpam-6600	683	1	paley	paley	ADJ
ejpam-6600	683	2	graphs	graph	NOUN
ejpam-6600	683	3	and	and	CCONJ
ejpam-6600	683	4	their	their	PRON
ejpam-6600	683	5	generalizations	generalization	NOUN
ejpam-6600	683	6	.	.	PUNCT
ejpam-6600	684	1	lap	lap	NOUN
ejpam-6600	684	2	publishing	publishing	PROPN
ejpam-6600	684	3	,	,	PUNCT
ejpam-6600	684	4	germany	germany	PROPN
ejpam-6600	684	5	,	,	PUNCT
ejpam-6600	684	6	2009	2009	NUM
ejpam-6600	684	7	.	.	PUNCT
ejpam-6600	685	1	master	master	NOUN
ejpam-6600	685	2	’s	’s	PART
ejpam-6600	685	3	thesis	thesis	NOUN
ejpam-6600	685	4	.	.	PUNCT
ejpam-6600	686	1	[	[	X
ejpam-6600	686	2	4	4	NUM
ejpam-6600	686	3	]	]	PUNCT
ejpam-6600	686	4	a.	a.	NOUN
ejpam-6600	686	5	haritha	haritha	NOUN
ejpam-6600	686	6	and	and	CCONJ
ejpam-6600	686	7	j.	j.	PROPN
ejpam-6600	686	8	chithra	chithra	PROPN
ejpam-6600	686	9	.	.	PUNCT
ejpam-6600	687	1	some	some	DET
ejpam-6600	687	2	new	new	ADJ
ejpam-6600	687	3	results	result	NOUN
ejpam-6600	687	4	on	on	ADP
ejpam-6600	687	5	paley	paley	ADJ
ejpam-6600	687	6	graphs	graph	NOUN
ejpam-6600	687	7	.	.	PUNCT
ejpam-6600	688	1	advances	advance	NOUN
ejpam-6600	688	2	and	and	CCONJ
ejpam-6600	688	3	applications	application	NOUN
ejpam-6600	688	4	in	in	ADP
ejpam-6600	688	5	mathematical	mathematical	ADJ
ejpam-6600	688	6	sciences	science	NOUN
ejpam-6600	688	7	,	,	PUNCT
ejpam-6600	688	8	22:1765–1770	22:1765–1770	PROPN
ejpam-6600	688	9	,	,	PUNCT
ejpam-6600	688	10	2023	2023	NUM
ejpam-6600	688	11	.	.	PUNCT
ejpam-6600	689	1	[	[	X
ejpam-6600	689	2	5	5	NUM
ejpam-6600	689	3	]	]	PUNCT
ejpam-6600	689	4	a.	a.	PROPN
ejpam-6600	689	5	thomason	thomason	PROPN
ejpam-6600	689	6	.	.	PUNCT
ejpam-6600	690	1	a	a	DET
ejpam-6600	690	2	paley	paley	ADJ
ejpam-6600	690	3	-	-	PUNCT
ejpam-6600	690	4	like	like	ADJ
ejpam-6600	690	5	graph	graph	NOUN
ejpam-6600	690	6	in	in	ADP
ejpam-6600	690	7	characteristic	characteristic	ADJ
ejpam-6600	690	8	two	two	NUM
ejpam-6600	690	9	.	.	PUNCT
ejpam-6600	691	1	arxiv	arxiv	PROPN
ejpam-6600	691	2	preprint	preprint	NOUN
ejpam-6600	691	3	,	,	PUNCT
ejpam-6600	691	4	2015	2015	NUM
ejpam-6600	691	5	.	.	PUNCT
ejpam-6600	692	1	[	[	X
ejpam-6600	692	2	6	6	NUM
ejpam-6600	692	3	]	]	X
ejpam-6600	692	4	g.	g.	PROPN
ejpam-6600	692	5	a.	a.	PROPN
ejpam-6600	692	6	jones	jones	PROPN
ejpam-6600	692	7	.	.	PROPN
ejpam-6600	692	8	paley	paley	PROPN
ejpam-6600	692	9	and	and	CCONJ
ejpam-6600	692	10	the	the	DET
ejpam-6600	692	11	paley	paley	ADJ
ejpam-6600	692	12	graphs	graph	NOUN
ejpam-6600	692	13	.	.	PUNCT
ejpam-6600	693	1	in	in	ADP
ejpam-6600	693	2	international	international	ADJ
ejpam-6600	693	3	workshop	workshop	NOUN
ejpam-6600	693	4	on	on	ADP
ejpam-6600	693	5	isomorphisms	isomorphism	NOUN
ejpam-6600	693	6	,	,	PUNCT
ejpam-6600	693	7	symmetry	symmetry	NOUN
ejpam-6600	693	8	and	and	CCONJ
ejpam-6600	693	9	computations	computation	NOUN
ejpam-6600	693	10	in	in	ADP
ejpam-6600	693	11	algebraic	algebraic	ADJ
ejpam-6600	693	12	graph	graph	NOUN
ejpam-6600	693	13	theory	theory	NOUN
ejpam-6600	693	14	,	,	PUNCT
ejpam-6600	693	15	pages	page	NOUN
ejpam-6600	693	16	155–183	155–183	NUM
ejpam-6600	693	17	.	.	PUNCT
ejpam-6600	693	18	springer	springer	NOUN
ejpam-6600	693	19	,	,	PUNCT
ejpam-6600	693	20	2020	2020	NUM
ejpam-6600	693	21	.	.	PUNCT
ejpam-6600	694	1	[	[	X
ejpam-6600	694	2	7	7	X
ejpam-6600	694	3	]	]	X
ejpam-6600	694	4	j.	j.	PROPN
ejpam-6600	694	5	minač	minač	PROPN
ejpam-6600	694	6	,	,	PUNCT
ejpam-6600	694	7	l.	l.	PROPN
ejpam-6600	694	8	muller	muller	PROPN
ejpam-6600	694	9	,	,	PUNCT
ejpam-6600	694	10	t.	t.	PROPN
ejpam-6600	694	11	t.	t.	PROPN
ejpam-6600	694	12	nguyen	nguyen	PROPN
ejpam-6600	694	13	,	,	PUNCT
ejpam-6600	694	14	and	and	CCONJ
ejpam-6600	694	15	n.	n.	PROPN
ejpam-6600	694	16	d.	d.	PROPN
ejpam-6600	694	17	tan	tan	PROPN
ejpam-6600	694	18	.	.	PUNCT
ejpam-6600	695	1	on	on	ADP
ejpam-6600	695	2	the	the	DET
ejpam-6600	695	3	paley	paley	ADJ
ejpam-6600	695	4	graph	graph	NOUN
ejpam-6600	695	5	of	of	ADP
ejpam-6600	695	6	a	a	DET
ejpam-6600	695	7	quadratic	quadratic	ADJ
ejpam-6600	695	8	character	character	NOUN
ejpam-6600	695	9	.	.	PUNCT
ejpam-6600	696	1	arxiv	arxiv	PROPN
ejpam-6600	696	2	preprint	preprint	PROPN
ejpam-6600	696	3	,	,	PUNCT
ejpam-6600	696	4	2023	2023	NUM
ejpam-6600	696	5	.	.	PUNCT
ejpam-6600	697	1	[	[	X
ejpam-6600	697	2	8	8	X
ejpam-6600	697	3	]	]	X
ejpam-6600	697	4	j.	j.	PROPN
ejpam-6600	697	5	minač	minač	PROPN
ejpam-6600	697	6	,	,	PUNCT
ejpam-6600	697	7	t.	t.	PROPN
ejpam-6600	697	8	t.	t.	PROPN
ejpam-6600	697	9	nguyen	nguyen	PROPN
ejpam-6600	697	10	,	,	PUNCT
ejpam-6600	697	11	and	and	CCONJ
ejpam-6600	697	12	n.	n.	PROPN
ejpam-6600	697	13	d.	d.	PROPN
ejpam-6600	697	14	tan	tan	PROPN
ejpam-6600	697	15	.	.	PUNCT
ejpam-6600	698	1	fekete	fekete	PROPN
ejpam-6600	698	2	polynomials	polynomial	NOUN
ejpam-6600	698	3	,	,	PUNCT
ejpam-6600	698	4	quadratic	quadratic	ADJ
ejpam-6600	698	5	residues	residue	NOUN
ejpam-6600	698	6	,	,	PUNCT
ejpam-6600	698	7	and	and	CCONJ
ejpam-6600	698	8	arithmetic	arithmetic	ADJ
ejpam-6600	698	9	.	.	PUNCT
ejpam-6600	699	1	journal	journal	PROPN
ejpam-6600	699	2	of	of	ADP
ejpam-6600	699	3	number	number	NOUN
ejpam-6600	699	4	theory	theory	NOUN
ejpam-6600	699	5	,	,	PUNCT
ejpam-6600	699	6	242:532–575	242:532–575	NUM
ejpam-6600	699	7	,	,	PUNCT
ejpam-6600	699	8	2023	2023	NUM
ejpam-6600	699	9	.	.	PUNCT
ejpam-6600	700	1	[	[	X
ejpam-6600	700	2	9	9	NUM
ejpam-6600	700	3	]	]	X
ejpam-6600	700	4	y.	y.	PROPN
ejpam-6600	700	5	nishimura	nishimura	PROPN
ejpam-6600	700	6	.	.	PUNCT
ejpam-6600	701	1	a	a	DET
ejpam-6600	701	2	new	new	ADJ
ejpam-6600	701	3	approach	approach	NOUN
ejpam-6600	701	4	to	to	ADP
ejpam-6600	701	5	pancyclicity	pancyclicity	NOUN
ejpam-6600	701	6	of	of	ADP
ejpam-6600	701	7	paley	paley	PROPN
ejpam-6600	701	8	graphs	graph	NOUN
ejpam-6600	701	9	i.	i.	PROPN
ejpam-6600	701	10	arxiv	arxiv	PROPN
ejpam-6600	701	11	preprint	preprint	NOUN
ejpam-6600	701	12	,	,	PUNCT
ejpam-6600	701	13	2023	2023	NUM
ejpam-6600	701	14	.	.	PUNCT
ejpam-6600	702	1	[	[	X
ejpam-6600	702	2	10	10	NUM
ejpam-6600	702	3	]	]	X
ejpam-6600	702	4	s.	s.	PROPN
ejpam-6600	702	5	goryainov	goryainov	PROPN
ejpam-6600	702	6	,	,	PUNCT
ejpam-6600	702	7	l.	l.	PROPN
ejpam-6600	702	8	shalaginov	shalaginov	PROPN
ejpam-6600	702	9	,	,	PUNCT
ejpam-6600	702	10	and	and	CCONJ
ejpam-6600	702	11	c.	c.	PROPN
ejpam-6600	702	12	h.	h.	PROPN
ejpam-6600	702	13	yip	yip	PROPN
ejpam-6600	702	14	.	.	PUNCT
ejpam-6600	703	1	on	on	ADP
ejpam-6600	703	2	eigenfunctions	eigenfunction	NOUN
ejpam-6600	703	3	and	and	CCONJ
ejpam-6600	703	4	maximal	maximal	ADJ
ejpam-6600	703	5	cliques	clique	NOUN
ejpam-6600	703	6	of	of	ADP
ejpam-6600	703	7	generalised	generalise	VERB
ejpam-6600	703	8	paley	paley	ADJ
ejpam-6600	703	9	graphs	graph	NOUN
ejpam-6600	703	10	of	of	ADP
ejpam-6600	703	11	square	square	ADJ
ejpam-6600	703	12	order	order	NOUN
ejpam-6600	703	13	.	.	PUNCT
ejpam-6600	704	1	finite	finite	PROPN
ejpam-6600	704	2	fields	field	NOUN
ejpam-6600	704	3	and	and	CCONJ
ejpam-6600	704	4	their	their	PRON
ejpam-6600	704	5	applications	application	NOUN
ejpam-6600	704	6	,	,	PUNCT
ejpam-6600	704	7	87	87	NUM
ejpam-6600	704	8	,	,	PUNCT
ejpam-6600	704	9	2023	2023	NUM
ejpam-6600	704	10	.	.	PUNCT
ejpam-6600	705	1	[	[	X
ejpam-6600	705	2	11	11	NUM
ejpam-6600	705	3	]	]	X
ejpam-6600	705	4	y.	y.	PROPN
ejpam-6600	705	5	kuswardi	kuswardi	PROPN
ejpam-6600	705	6	,	,	PUNCT
ejpam-6600	705	7	l.	l.	PROPN
ejpam-6600	705	8	almira	almira	PROPN
ejpam-6600	705	9	,	,	PUNCT
ejpam-6600	705	10	n.	n.	PROPN
ejpam-6600	705	11	nurussakbana	nurussakbana	PROPN
ejpam-6600	705	12	,	,	PUNCT
ejpam-6600	705	13	and	and	CCONJ
ejpam-6600	705	14	a.	a.	PROPN
ejpam-6600	705	15	c.	c.	PROPN
ejpam-6600	705	16	pinilih	pinilih	VERB
ejpam-6600	705	17	.	.	PUNCT
ejpam-6600	706	1	chromatic	chromatic	ADJ
ejpam-6600	706	2	number	number	NOUN
ejpam-6600	706	3	of	of	ADP
ejpam-6600	706	4	amalgamation	amalgamation	NOUN
ejpam-6600	706	5	of	of	ADP
ejpam-6600	706	6	wheel	wheel	NOUN
ejpam-6600	706	7	graph	graph	NOUN
ejpam-6600	706	8	-	-	PUNCT
ejpam-6600	706	9	star	star	NOUN
ejpam-6600	706	10	graph	graph	NOUN
ejpam-6600	706	11	and	and	CCONJ
ejpam-6600	706	12	amalgamation	amalgamation	NOUN
ejpam-6600	706	13	of	of	ADP
ejpam-6600	706	14	wheel	wheel	NOUN
ejpam-6600	706	15	graph	graph	NOUN
ejpam-6600	706	16	-	-	PUNCT
ejpam-6600	706	17	sikel	sikel	NOUN
ejpam-6600	706	18	graph	graph	NOUN
ejpam-6600	706	19	.	.	PUNCT
ejpam-6600	707	1	journal	journal	PROPN
ejpam-6600	707	2	of	of	ADP
ejpam-6600	707	3	mathematics	mathematics	PROPN
ejpam-6600	707	4	and	and	CCONJ
ejpam-6600	707	5	mathematics	mathematic	NOUN
ejpam-6600	707	6	education	education	NOUN
ejpam-6600	707	7	,	,	PUNCT
ejpam-6600	707	8	12(2):132–146	12(2):132–146	PROPN
ejpam-6600	707	9	,	,	PUNCT
ejpam-6600	707	10	2022	2022	NUM
ejpam-6600	707	11	.	.	PUNCT
ejpam-6600	708	1	[	[	X
ejpam-6600	708	2	12	12	NUM
ejpam-6600	708	3	]	]	X
ejpam-6600	708	4	c.	c.	PROPN
ejpam-6600	708	5	h.	h.	PROPN
ejpam-6600	708	6	yip	yip	PROPN
ejpam-6600	708	7	.	.	PUNCT
ejpam-6600	709	1	on	on	ADP
ejpam-6600	709	2	the	the	DET
ejpam-6600	709	3	directions	direction	NOUN
ejpam-6600	709	4	determined	determine	VERB
ejpam-6600	709	5	by	by	ADP
ejpam-6600	709	6	cartesian	cartesian	ADJ
ejpam-6600	709	7	products	product	NOUN
ejpam-6600	709	8	and	and	CCONJ
ejpam-6600	709	9	the	the	DET
ejpam-6600	709	10	clique	clique	ADJ
ejpam-6600	709	11	number	number	NOUN
ejpam-6600	709	12	of	of	ADP
ejpam-6600	709	13	generalized	generalized	ADJ
ejpam-6600	709	14	paley	paley	ADJ
ejpam-6600	709	15	graphs	graph	NOUN
ejpam-6600	709	16	.	.	PUNCT
ejpam-6600	710	1	arxiv	arxiv	PROPN
ejpam-6600	710	2	preprint	preprint	PROPN
ejpam-6600	710	3	,	,	PUNCT
ejpam-6600	710	4	2020	2020	NUM
ejpam-6600	710	5	.	.	PUNCT
ejpam-6600	711	1	[	[	X
ejpam-6600	711	2	13	13	NUM
ejpam-6600	711	3	]	]	X
ejpam-6600	711	4	c.	c.	PROPN
ejpam-6600	711	5	h.	h.	PROPN
ejpam-6600	711	6	yip	yip	PROPN
ejpam-6600	711	7	.	.	PUNCT
ejpam-6600	712	1	on	on	ADP
ejpam-6600	712	2	the	the	DET
ejpam-6600	712	3	clique	clique	ADJ
ejpam-6600	712	4	number	number	NOUN
ejpam-6600	712	5	of	of	ADP
ejpam-6600	712	6	paley	paley	ADJ
ejpam-6600	712	7	graphs	graph	NOUN
ejpam-6600	712	8	of	of	ADP
ejpam-6600	712	9	prime	prime	ADJ
ejpam-6600	712	10	power	power	NOUN
ejpam-6600	712	11	order	order	NOUN
ejpam-6600	712	12	.	.	PUNCT
ejpam-6600	713	1	finite	finite	PROPN
ejpam-6600	713	2	fields	field	NOUN
ejpam-6600	713	3	and	and	CCONJ
ejpam-6600	713	4	their	their	PRON
ejpam-6600	713	5	applications	application	NOUN
ejpam-6600	713	6	,	,	PUNCT
ejpam-6600	713	7	77	77	NUM
ejpam-6600	713	8	,	,	PUNCT
ejpam-6600	713	9	2022	2022	NUM
ejpam-6600	713	10	.	.	PUNCT
ejpam-6600	714	1	[	[	X
ejpam-6600	714	2	14	14	NUM
ejpam-6600	714	3	]	]	X
ejpam-6600	714	4	c.	c.	PROPN
ejpam-6600	714	5	h.	h.	PROPN
ejpam-6600	714	6	yip	yip	PROPN
ejpam-6600	714	7	.	.	PUNCT
ejpam-6600	715	1	refined	refined	ADJ
ejpam-6600	715	2	estimates	estimate	NOUN
ejpam-6600	715	3	on	on	ADP
ejpam-6600	715	4	the	the	DET
ejpam-6600	715	5	clique	clique	ADJ
ejpam-6600	715	6	number	number	NOUN
ejpam-6600	715	7	of	of	ADP
ejpam-6600	715	8	generalized	generalized	ADJ
ejpam-6600	715	9	paley	paley	ADJ
ejpam-6600	715	10	graphs	graph	NOUN
ejpam-6600	715	11	.	.	PUNCT
ejpam-6600	716	1	arxiv	arxiv	PROPN
ejpam-6600	716	2	preprint	preprint	NOUN
ejpam-6600	716	3	,	,	PUNCT
ejpam-6600	716	4	2023	2023	NUM
ejpam-6600	716	5	.	.	PUNCT
ejpam-6600	717	1	[	[	X
ejpam-6600	717	2	15	15	NUM
ejpam-6600	717	3	]	]	X
ejpam-6600	717	4	j.	j.	PROPN
ejpam-6600	717	5	a.	a.	PROPN
ejpam-6600	717	6	gallian	gallian	PROPN
ejpam-6600	717	7	.	.	PUNCT
ejpam-6600	718	1	a	a	DET
ejpam-6600	718	2	dynamic	dynamic	ADJ
ejpam-6600	718	3	survey	survey	NOUN
ejpam-6600	718	4	of	of	ADP
ejpam-6600	718	5	graph	graph	NOUN
ejpam-6600	718	6	labelling	labelling	NOUN
ejpam-6600	718	7	.	.	PUNCT
ejpam-6600	719	1	the	the	DET
ejpam-6600	719	2	electronic	electronic	ADJ
ejpam-6600	719	3	journal	journal	NOUN
ejpam-6600	719	4	of	of	ADP
ejpam-6600	719	5	combinatorics	combinatoric	NOUN
ejpam-6600	719	6	,	,	PUNCT
ejpam-6600	719	7	17:205–255	17:205–255	PROPN
ejpam-6600	719	8	,	,	PUNCT
ejpam-6600	719	9	2015	2015	NUM
ejpam-6600	719	10	.	.	PUNCT
ejpam-6600	720	1	[	[	X
ejpam-6600	720	2	16	16	NUM
ejpam-6600	720	3	]	]	PUNCT
ejpam-6600	720	4	a.	a.	PROPN
ejpam-6600	720	5	rosa	rosa	PROPN
ejpam-6600	720	6	.	.	PUNCT
ejpam-6600	721	1	on	on	ADP
ejpam-6600	721	2	certain	certain	ADJ
ejpam-6600	721	3	valuations	valuation	NOUN
ejpam-6600	721	4	of	of	ADP
ejpam-6600	721	5	the	the	DET
ejpam-6600	721	6	vertices	vertex	NOUN
ejpam-6600	721	7	of	of	ADP
ejpam-6600	721	8	a	a	DET
ejpam-6600	721	9	graph	graph	NOUN
ejpam-6600	721	10	.	.	PUNCT
ejpam-6600	722	1	in	in	ADP
ejpam-6600	722	2	theory	theory	NOUN
ejpam-6600	722	3	of	of	ADP
ejpam-6600	722	4	graphs	graph	NOUN
ejpam-6600	722	5	.	.	PUNCT
ejpam-6600	723	1	internat	internat	PROPN
ejpam-6600	723	2	.	.	PUNCT
ejpam-6600	724	1	symposium	symposium	PROPN
ejpam-6600	724	2	,	,	PUNCT
ejpam-6600	724	3	rome	rome	PROPN
ejpam-6600	724	4	,	,	PUNCT
ejpam-6600	724	5	1966	1966	NUM
ejpam-6600	724	6	.	.	PUNCT
ejpam-6600	725	1	[	[	X
ejpam-6600	725	2	17	17	NUM
ejpam-6600	725	3	]	]	PUNCT
ejpam-6600	725	4	s.	s.	PROPN
ejpam-6600	725	5	w.	w.	PROPN
ejpam-6600	725	6	golomb	golomb	PROPN
ejpam-6600	725	7	.	.	PUNCT
ejpam-6600	726	1	how	how	SCONJ
ejpam-6600	726	2	to	to	PART
ejpam-6600	726	3	number	number	VERB
ejpam-6600	726	4	a	a	DET
ejpam-6600	726	5	graph	graph	NOUN
ejpam-6600	726	6	.	.	PUNCT
ejpam-6600	727	1	in	in	ADP
ejpam-6600	727	2	graph	graph	NOUN
ejpam-6600	727	3	theory	theory	NOUN
ejpam-6600	727	4	and	and	CCONJ
ejpam-6600	727	5	computing	computing	NOUN
ejpam-6600	727	6	,	,	PUNCT
ejpam-6600	727	7	pages	page	NOUN
ejpam-6600	727	8	23–37	23–37	VERB
ejpam-6600	727	9	.	.	PUNCT
ejpam-6600	728	1	academic	academic	ADJ
ejpam-6600	728	2	press	press	NOUN
ejpam-6600	728	3	,	,	PUNCT
ejpam-6600	728	4	1972	1972	NUM
ejpam-6600	728	5	.	.	PUNCT
ejpam-6600	729	1	[	[	X
ejpam-6600	729	2	18	18	NUM
ejpam-6600	729	3	]	]	PUNCT
ejpam-6600	729	4	m	m	VERB
ejpam-6600	729	5	aljohani	aljohani	ADJ
ejpam-6600	729	6	and	and	CCONJ
ejpam-6600	729	7	s.	s.	PROPN
ejpam-6600	729	8	n.	n.	PROPN
ejpam-6600	729	9	daoud	daoud	PROPN
ejpam-6600	729	10	.	.	PROPN
ejpam-6600	729	11	edge	edge	PROPN
ejpam-6600	729	12	odd	odd	ADJ
ejpam-6600	729	13	graceful	graceful	ADJ
ejpam-6600	729	14	labeling	labeling	NOUN
ejpam-6600	729	15	in	in	ADP
ejpam-6600	729	16	some	some	DET
ejpam-6600	729	17	wheel	wheel	NOUN
ejpam-6600	729	18	-	-	PUNCT
ejpam-6600	729	19	related	relate	VERB
ejpam-6600	729	20	graphs	graph	NOUN
ejpam-6600	729	21	.	.	PUNCT
ejpam-6600	730	1	mathematics	mathematic	NOUN
ejpam-6600	730	2	,	,	PUNCT
ejpam-6600	730	3	12(1203):1–23	12(1203):1–23	PROPN
ejpam-6600	730	4	,	,	PUNCT
ejpam-6600	730	5	2024	2024	NUM
ejpam-6600	730	6	.	.	PUNCT
ejpam-6600	730	7	a.	a.	PROPN
ejpam-6600	730	8	n.	n.	PROPN
ejpam-6600	730	9	elsawy	elsawy	PROPN
ejpam-6600	730	10	,	,	PUNCT
ejpam-6600	730	11	r.	r.	PROPN
ejpam-6600	730	12	n.	n.	PROPN
ejpam-6600	730	13	almohammadi	almohammadi	PROPN
ejpam-6600	730	14	/	/	SYM
ejpam-6600	730	15	eur	eur	PROPN
ejpam-6600	730	16	.	.	PUNCT
ejpam-6600	731	1	j.	j.	PROPN
ejpam-6600	731	2	pure	pure	PROPN
ejpam-6600	731	3	appl	appl	PROPN
ejpam-6600	731	4	.	.	PROPN
ejpam-6600	731	5	math	math	PROPN
ejpam-6600	731	6	,	,	PUNCT
ejpam-6600	731	7	18	18	NUM
ejpam-6600	731	8	(	(	PUNCT
ejpam-6600	731	9	4	4	NUM
ejpam-6600	731	10	)	)	PUNCT
ejpam-6600	731	11	(	(	PUNCT
ejpam-6600	731	12	2025	2025	NUM
ejpam-6600	731	13	)	)	PUNCT
ejpam-6600	731	14	,	,	PUNCT
ejpam-6600	731	15	6600	6600	NUM
ejpam-6600	731	16	26	26	NUM
ejpam-6600	731	17	of	of	ADP
ejpam-6600	731	18	26	26	NUM
ejpam-6600	731	19	[	[	SYM
ejpam-6600	731	20	19	19	NUM
ejpam-6600	731	21	]	]	PUNCT
ejpam-6600	731	22	s.	s.	PROPN
ejpam-6600	731	23	n.	n.	PROPN
ejpam-6600	731	24	daoud	daoud	PROPN
ejpam-6600	731	25	.	.	PROPN
ejpam-6600	731	26	edge	edge	VERB
ejpam-6600	731	27	even	even	ADV
ejpam-6600	731	28	graceful	graceful	ADJ
ejpam-6600	731	29	labeling	labeling	NOUN
ejpam-6600	731	30	of	of	ADP
ejpam-6600	731	31	polar	polar	ADJ
ejpam-6600	731	32	grid	grid	NOUN
ejpam-6600	731	33	graphs	graph	NOUN
ejpam-6600	731	34	.	.	PUNCT
ejpam-6600	732	1	symmetry	symmetry	NOUN
ejpam-6600	732	2	,	,	PUNCT
ejpam-6600	732	3	11(1):1–26	11(1):1–26	NUM
ejpam-6600	732	4	,	,	PUNCT
ejpam-6600	732	5	2019	2019	NUM
ejpam-6600	732	6	.	.	PUNCT
ejpam-6600	733	1	[	[	X
ejpam-6600	733	2	20	20	NUM
ejpam-6600	733	3	]	]	PUNCT
ejpam-6600	733	4	a.	a.	NOUN
ejpam-6600	733	5	elsonbaty	elsonbaty	NOUN
ejpam-6600	733	6	and	and	CCONJ
ejpam-6600	733	7	s.	s.	PROPN
ejpam-6600	733	8	n.	n.	PROPN
ejpam-6600	733	9	daoud	daoud	PROPN
ejpam-6600	733	10	.	.	PROPN
ejpam-6600	733	11	edge	edge	VERB
ejpam-6600	733	12	even	even	ADV
ejpam-6600	733	13	graceful	graceful	ADJ
ejpam-6600	733	14	labeling	labeling	NOUN
ejpam-6600	733	15	of	of	ADP
ejpam-6600	733	16	some	some	DET
ejpam-6600	733	17	path	path	NOUN
ejpam-6600	733	18	and	and	CCONJ
ejpam-6600	733	19	cycle	cycle	NOUN
ejpam-6600	733	20	related	relate	VERB
ejpam-6600	733	21	graphs	graph	NOUN
ejpam-6600	733	22	.	.	PUNCT
ejpam-6600	734	1	ars	ars	PROPN
ejpam-6600	734	2	combinatoria	combinatoria	PROPN
ejpam-6600	734	3	,	,	PUNCT
ejpam-6600	734	4	130:79–96	130:79–96	NUM
ejpam-6600	734	5	,	,	PUNCT
ejpam-6600	734	6	2017	2017	NUM
ejpam-6600	734	7	.	.	PUNCT
ejpam-6600	735	1	[	[	X
ejpam-6600	735	2	21	21	NUM
ejpam-6600	735	3	]	]	X
ejpam-6600	735	4	t.	t.	NOUN
ejpam-6600	735	5	kamaraj	kamaraj	PROPN
ejpam-6600	735	6	and	and	CCONJ
ejpam-6600	735	7	j.	j.	PROPN
ejpam-6600	735	8	thangakani	thangakani	PROPN
ejpam-6600	735	9	.	.	PUNCT
ejpam-6600	736	1	edge	edge	VERB
ejpam-6600	736	2	even	even	ADV
ejpam-6600	736	3	and	and	CCONJ
ejpam-6600	736	4	edge	edge	VERB
ejpam-6600	736	5	odd	odd	ADJ
ejpam-6600	736	6	graceful	graceful	ADJ
ejpam-6600	736	7	labelings	labeling	NOUN
ejpam-6600	736	8	of	of	ADP
ejpam-6600	736	9	paley	paley	ADJ
ejpam-6600	736	10	graphs	graph	NOUN
ejpam-6600	736	11	.	.	PUNCT
ejpam-6600	737	1	in	in	ADP
ejpam-6600	737	2	journal	journal	PROPN
ejpam-6600	737	3	of	of	ADP
ejpam-6600	737	4	physics	physics	PROPN
ejpam-6600	737	5	:	:	PUNCT
ejpam-6600	737	6	conference	conference	NOUN
ejpam-6600	737	7	series	series	NOUN
ejpam-6600	737	8	,	,	PUNCT
ejpam-6600	737	9	volume	volume	NOUN
ejpam-6600	737	10	1770	1770	NUM
ejpam-6600	737	11	,	,	PUNCT
ejpam-6600	737	12	page	page	NOUN
ejpam-6600	737	13	012068	012068	NUM
ejpam-6600	737	14	.	.	PUNCT
ejpam-6600	738	1	top	top	ADJ
ejpam-6600	738	2	publishing	publishing	NOUN
ejpam-6600	738	3	,	,	PUNCT
ejpam-6600	738	4	2021	2021	NUM
ejpam-6600	738	5	.	.	PUNCT
ejpam-6600	739	1	[	[	X
ejpam-6600	739	2	22	22	NUM
ejpam-6600	739	3	]	]	PUNCT
ejpam-6600	739	4	a.	a.	NOUN
ejpam-6600	739	5	solairaju	solairaju	NOUN
ejpam-6600	739	6	and	and	CCONJ
ejpam-6600	739	7	k.	k.	PROPN
ejpam-6600	739	8	chithra	chithra	PROPN
ejpam-6600	739	9	.	.	PUNCT
ejpam-6600	740	1	edge	edge	PROPN
ejpam-6600	740	2	-	-	PUNCT
ejpam-6600	740	3	odd	odd	ADJ
ejpam-6600	740	4	graceful	graceful	ADJ
ejpam-6600	740	5	graphs	graph	NOUN
ejpam-6600	740	6	.	.	PUNCT
ejpam-6600	741	1	electronic	electronic	ADJ
ejpam-6600	741	2	notes	note	NOUN
ejpam-6600	741	3	in	in	ADP
ejpam-6600	741	4	discrete	discrete	ADJ
ejpam-6600	741	5	mathematics	mathematic	NOUN
ejpam-6600	741	6	,	,	PUNCT
ejpam-6600	741	7	33:15–20	33:15–20	NUM
ejpam-6600	741	8	,	,	PUNCT
ejpam-6600	741	9	2009	2009	NUM
ejpam-6600	741	10	.	.	PUNCT
ejpam-6600	742	1	[	[	X
ejpam-6600	742	2	23	23	NUM
ejpam-6600	742	3	]	]	PUNCT
ejpam-6600	742	4	j.	j.	PROPN
ejpam-6600	742	5	javelle	javelle	PROPN
ejpam-6600	742	6	.	.	PUNCT
ejpam-6600	743	1	cryptographie	cryptographie	PROPN
ejpam-6600	743	2	quantique	quantique	ADJ
ejpam-6600	743	3	:	:	PUNCT
ejpam-6600	743	4	protocoles	protocole	NOUN
ejpam-6600	743	5	et	et	NOUN
ejpam-6600	743	6	graphes	graphes	PROPN
ejpam-6600	743	7	.	.	PUNCT
ejpam-6600	744	1	algèbres	algèbre	VERB
ejpam-6600	744	2	quantiques	quantique	NOUN
ejpam-6600	744	3	[	[	X
ejpam-6600	744	4	math.qa	math.qa	X
ejpam-6600	744	5	]	]	PUNCT
ejpam-6600	744	6	.	.	PUNCT
ejpam-6600	745	1	phd	phd	NOUN
ejpam-6600	745	2	thesis	thesis	PROPN
ejpam-6600	745	3	,	,	PUNCT
ejpam-6600	745	4	université	université	PROPN
ejpam-6600	745	5	de	de	X
ejpam-6600	745	6	grenoble	grenoble	PROPN
ejpam-6600	745	7	,	,	PUNCT
ejpam-6600	745	8	2014	2014	NUM
ejpam-6600	745	9	.	.	PUNCT
ejpam-6600	746	1	[	[	X
ejpam-6600	746	2	24	24	NUM
ejpam-6600	746	3	]	]	X
ejpam-6600	746	4	d.	d.	PROPN
ejpam-6600	746	5	ghinelli	ghinelli	PROPN
ejpam-6600	746	6	and	and	CCONJ
ejpam-6600	746	7	jennifer	jennifer	PROPN
ejpam-6600	746	8	d.	d.	PROPN
ejpam-6600	746	9	key	key	PROPN
ejpam-6600	746	10	.	.	PUNCT
ejpam-6600	747	1	codes	code	NOUN
ejpam-6600	747	2	from	from	ADP
ejpam-6600	747	3	incidence	incidence	ADJ
ejpam-6600	747	4	matrices	matrix	NOUN
ejpam-6600	747	5	and	and	CCONJ
ejpam-6600	747	6	line	line	NOUN
ejpam-6600	747	7	graphs	graph	NOUN
ejpam-6600	747	8	of	of	ADP
ejpam-6600	747	9	paley	paley	ADJ
ejpam-6600	747	10	graphs	graph	NOUN
ejpam-6600	747	11	.	.	PUNCT
ejpam-6600	748	1	advances	advance	NOUN
ejpam-6600	748	2	in	in	ADP
ejpam-6600	748	3	mathematics	mathematic	NOUN
ejpam-6600	748	4	of	of	ADP
ejpam-6600	748	5	communications	communication	NOUN
ejpam-6600	748	6	,	,	PUNCT
ejpam-6600	748	7	5:93–108	5:93–108	NUM
ejpam-6600	748	8	,	,	PUNCT
ejpam-6600	748	9	2011	2011	NUM
ejpam-6600	748	10	.	.	PUNCT
ejpam-6600	749	1	[	[	X
ejpam-6600	749	2	25	25	NUM
ejpam-6600	749	3	]	]	PUNCT
ejpam-6600	749	4	zhour	zhour	PROPN
ejpam-6600	749	5	oumazouz	oumazouz	NOUN
ejpam-6600	749	6	and	and	CCONJ
ejpam-6600	749	7	driss	driss	PROPN
ejpam-6600	749	8	karim	karim	PROPN
ejpam-6600	749	9	.	.	PUNCT
ejpam-6600	750	1	a	a	DET
ejpam-6600	750	2	new	new	ADJ
ejpam-6600	750	3	symmetric	symmetric	ADJ
ejpam-6600	750	4	key	key	ADJ
ejpam-6600	750	5	cryptographic	cryptographic	ADJ
ejpam-6600	750	6	algorithm	algorithm	NOUN
ejpam-6600	750	7	using	use	VERB
ejpam-6600	750	8	paley	paley	ADJ
ejpam-6600	750	9	graphs	graph	NOUN
ejpam-6600	750	10	and	and	CCONJ
ejpam-6600	750	11	ascii	ascii	ADJ
ejpam-6600	750	12	values	value	NOUN
ejpam-6600	750	13	.	.	PUNCT
ejpam-6600	751	1	e3s	e3s	PROPN
ejpam-6600	751	2	web	web	NOUN
ejpam-6600	751	3	of	of	ADP
ejpam-6600	751	4	conferences	conference	NOUN
ejpam-6600	751	5	,	,	PUNCT
ejpam-6600	751	6	297:01046	297:01046	NUM
ejpam-6600	751	7	,	,	PUNCT
ejpam-6600	751	8	2021	2021	NUM
ejpam-6600	751	9	.	.	PUNCT
ejpam-6600	752	1	[	[	X
ejpam-6600	752	2	26	26	NUM
ejpam-6600	752	3	]	]	X
ejpam-6600	752	4	n.	n.	PROPN
ejpam-6600	752	5	lakshmi	lakshmi	PROPN
ejpam-6600	752	6	prasanna	prasanna	PROPN
ejpam-6600	752	7	,	,	PUNCT
ejpam-6600	752	8	k.	k.	PROPN
ejpam-6600	752	9	sravanthi	sravanthi	PROPN
ejpam-6600	752	10	,	,	PUNCT
ejpam-6600	752	11	and	and	CCONJ
ejpam-6600	752	12	n.	n.	PROPN
ejpam-6600	752	13	sudhakar	sudhakar	PROPN
ejpam-6600	752	14	.	.	PUNCT
ejpam-6600	753	1	applications	application	NOUN
ejpam-6600	753	2	of	of	ADP
ejpam-6600	753	3	graph	graph	NOUN
ejpam-6600	753	4	labeling	labeling	NOUN
ejpam-6600	753	5	in	in	ADP
ejpam-6600	753	6	communication	communication	NOUN
ejpam-6600	753	7	networks	network	NOUN
ejpam-6600	753	8	.	.	PUNCT
ejpam-6600	754	1	oriental	oriental	ADJ
ejpam-6600	754	2	journal	journal	PROPN
ejpam-6600	754	3	of	of	ADP
ejpam-6600	754	4	computer	computer	NOUN
ejpam-6600	754	5	science	science	NOUN
ejpam-6600	754	6	and	and	CCONJ
ejpam-6600	754	7	technology	technology	NOUN
ejpam-6600	754	8	,	,	PUNCT
ejpam-6600	754	9	7(1):139–145	7(1):139–145	NUM
ejpam-6600	754	10	,	,	PUNCT
ejpam-6600	754	11	2014	2014	NUM
ejpam-6600	754	12	.	.	PUNCT
ejpam-6600	755	1	[	[	X
ejpam-6600	755	2	27	27	NUM
ejpam-6600	755	3	]	]	PUNCT
ejpam-6600	755	4	m.	m.	NOUN
ejpam-6600	755	5	s.	s.	PROPN
ejpam-6600	755	6	vinutha	vinutha	PROPN
ejpam-6600	755	7	and	and	CCONJ
ejpam-6600	755	8	p.	p.	PROPN
ejpam-6600	755	9	arathi	arathi	PROPN
ejpam-6600	755	10	.	.	PUNCT
ejpam-6600	756	1	applications	application	NOUN
ejpam-6600	756	2	of	of	ADP
ejpam-6600	756	3	graph	graph	NOUN
ejpam-6600	756	4	coloring	coloring	NOUN
ejpam-6600	756	5	and	and	CCONJ
ejpam-6600	756	6	labeling	labeling	NOUN
ejpam-6600	756	7	in	in	ADP
ejpam-6600	756	8	computer	computer	NOUN
ejpam-6600	756	9	science	science	NOUN
ejpam-6600	756	10	.	.	PUNCT
ejpam-6600	757	1	international	international	ADJ
ejpam-6600	757	2	journal	journal	PROPN
ejpam-6600	757	3	on	on	ADP
ejpam-6600	757	4	future	future	ADJ
ejpam-6600	757	5	revolution	revolution	NOUN
ejpam-6600	757	6	in	in	ADP
ejpam-6600	757	7	computer	computer	NOUN
ejpam-6600	757	8	science	science	NOUN
ejpam-6600	757	9	and	and	CCONJ
ejpam-6600	757	10	communication	communication	NOUN
ejpam-6600	757	11	engineering	engineering	NOUN
ejpam-6600	757	12	,	,	PUNCT
ejpam-6600	757	13	3(8):14–16	3(8):14–16	NUM
ejpam-6600	757	14	,	,	PUNCT
ejpam-6600	757	15	2017	2017	NUM
ejpam-6600	757	16	.	.	PUNCT
ejpam-6600	758	1	[	[	X
ejpam-6600	758	2	28	28	NUM
ejpam-6600	758	3	]	]	X
ejpam-6600	758	4	w.	w.	PROPN
ejpam-6600	758	5	ananchuen	ananchuen	PROPN
ejpam-6600	758	6	and	and	CCONJ
ejpam-6600	758	7	l.	l.	PROPN
ejpam-6600	758	8	caccetta	caccetta	PROPN
ejpam-6600	758	9	.	.	PUNCT
ejpam-6600	759	1	cubic	cubic	ADJ
ejpam-6600	759	2	and	and	CCONJ
ejpam-6600	759	3	quadruple	quadruple	NOUN
ejpam-6600	759	4	paley	paley	NOUN
ejpam-6600	759	5	graphs	graph	NOUN
ejpam-6600	759	6	with	with	ADP
ejpam-6600	759	7	the	the	DET
ejpam-6600	759	8	ne	ne	PROPN
ejpam-6600	759	9	.	.	PUNCT
ejpam-6600	760	1	c.	c.	PROPN
ejpam-6600	760	2	property	property	PROPN
ejpam-6600	760	3	.	.	PUNCT
ejpam-6600	761	1	discrete	discrete	ADJ
ejpam-6600	761	2	mathematics	mathematic	NOUN
ejpam-6600	761	3	,	,	PUNCT
ejpam-6600	761	4	306(22):2954–2961	306(22):2954–2961	NUM
ejpam-6600	761	5	,	,	PUNCT
ejpam-6600	761	6	2006	2006	NUM
ejpam-6600	761	7	.	.	PUNCT
ejpam-6600	762	1	[	[	X
ejpam-6600	762	2	29	29	NUM
ejpam-6600	762	3	]	]	PUNCT
ejpam-6600	762	4	s.	s.	PROPN
ejpam-6600	762	5	d.	d.	PROPN
ejpam-6600	762	6	cohen	cohen	PROPN
ejpam-6600	762	7	.	.	PUNCT
ejpam-6600	763	1	clique	clique	ADJ
ejpam-6600	763	2	numbers	number	NOUN
ejpam-6600	763	3	of	of	ADP
ejpam-6600	763	4	paley	paley	ADJ
ejpam-6600	763	5	graphs	graph	NOUN
ejpam-6600	763	6	.	.	PUNCT
ejpam-6600	764	1	quaestiones	quaestione	NOUN
ejpam-6600	764	2	mathematicae	mathematicae	PROPN
ejpam-6600	764	3	,	,	PUNCT
ejpam-6600	764	4	11(2):225	11(2):225	NUM
ejpam-6600	764	5	–	–	PUNCT
ejpam-6600	764	6	231	231	NUM
ejpam-6600	764	7	,	,	PUNCT
ejpam-6600	764	8	1988	1988	NUM
ejpam-6600	764	9	.	.	PUNCT
ejpam-6600	765	1	[	[	X
ejpam-6600	765	2	30	30	NUM
ejpam-6600	765	3	]	]	PUNCT
ejpam-6600	765	4	t.	t.	PROPN
ejpam-6600	765	5	k.	k.	PROPN
ejpam-6600	765	6	lim	lim	PROPN
ejpam-6600	765	7	and	and	CCONJ
ejpam-6600	765	8	c.	c.	PROPN
ejpam-6600	765	9	e.	e.	PROPN
ejpam-6600	765	10	praeger	praeger	PROPN
ejpam-6600	765	11	.	.	PUNCT
ejpam-6600	766	1	on	on	ADP
ejpam-6600	766	2	generalised	generalise	VERB
ejpam-6600	766	3	paley	paley	ADJ
ejpam-6600	766	4	graphs	graph	NOUN
ejpam-6600	766	5	and	and	CCONJ
ejpam-6600	766	6	their	their	PRON
ejpam-6600	766	7	automorphism	automorphism	NOUN
ejpam-6600	766	8	groups	group	NOUN
ejpam-6600	766	9	.	.	PUNCT
ejpam-6600	767	1	michigan	michigan	PROPN
ejpam-6600	767	2	mathematical	mathematical	PROPN
ejpam-6600	767	3	journal	journal	PROPN
ejpam-6600	767	4	,	,	PUNCT
ejpam-6600	767	5	58(1):293–308	58(1):293–308	PROPN
ejpam-6600	767	6	,	,	PUNCT
ejpam-6600	767	7	2009	2009	NUM
ejpam-6600	767	8	.	.	PUNCT