id	sid	tid	token	lemma	pos
ejpam-1929	1	1	compiles	compile	NOUN
ejpam-1929	1	2	/	/	SYM
ejpam-1929	1	3	be29784c162a00b0bbcf92378a8261cf	be29784c162a00b0bbcf92378a8261cf	NOUN
ejpam-1929	1	4	/	/	SYM
ejpam-1929	1	5	output.dvi	output.dvi	NOUN
ejpam-1929	1	6	european	european	ADJ
ejpam-1929	1	7	journal	journal	NOUN
ejpam-1929	1	8	of	of	ADP
ejpam-1929	1	9	pure	pure	ADJ
ejpam-1929	1	10	and	and	CCONJ
ejpam-1929	1	11	applied	apply	VERB
ejpam-1929	1	12	mathematics	mathematic	NOUN
ejpam-1929	1	13	vol	vol	NOUN
ejpam-1929	1	14	.	.	PROPN
ejpam-1929	2	1	6	6	NUM
ejpam-1929	2	2	,	,	PUNCT
ejpam-1929	2	3	no	no	INTJ
ejpam-1929	2	4	.	.	NOUN
ejpam-1929	2	5	2	2	NUM
ejpam-1929	2	6	,	,	PUNCT
ejpam-1929	2	7	2013	2013	NUM
ejpam-1929	2	8	,	,	PUNCT
ejpam-1929	2	9	189	189	NUM
ejpam-1929	2	10	-	-	SYM
ejpam-1929	2	11	210	210	NUM
ejpam-1929	2	12	issn	issn	PROPN
ejpam-1929	2	13	1307	1307	NUM
ejpam-1929	2	14	-	-	SYM
ejpam-1929	2	15	5543	5543	NUM
ejpam-1929	2	16	–	–	PUNCT
ejpam-1929	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1929	2	18	unitary	unitary	ADJ
ejpam-1929	2	19	addition	addition	NOUN
ejpam-1929	2	20	cayley	cayley	NOUN
ejpam-1929	2	21	signed	sign	VERB
ejpam-1929	2	22	graphs	graph	NOUN
ejpam-1929	2	23	deepa	deepa	PROPN
ejpam-1929	2	24	sinha	sinha	PROPN
ejpam-1929	2	25	1	1	NUM
ejpam-1929	2	26	,	,	PUNCT
ejpam-1929	2	27	ayushi	ayushi	NOUN
ejpam-1929	2	28	dhama	dhama	NOUN
ejpam-1929	2	29	2,∗	2,∗	NUM
ejpam-1929	2	30	,	,	PUNCT
ejpam-1929	2	31	b.d	b.d	PROPN
ejpam-1929	2	32	.	.	PROPN
ejpam-1929	2	33	acharya	acharya	PROPN
ejpam-1929	2	34	3	3	NUM
ejpam-1929	2	35	1	1	NUM
ejpam-1929	2	36	south	south	PROPN
ejpam-1929	2	37	asian	asian	PROPN
ejpam-1929	2	38	university	university	PROPN
ejpam-1929	2	39	,	,	PUNCT
ejpam-1929	2	40	akbar	akbar	PROPN
ejpam-1929	2	41	bhawan	bhawan	PROPN
ejpam-1929	2	42	,	,	PUNCT
ejpam-1929	2	43	chankyapuri	chankyapuri	PROPN
ejpam-1929	2	44	,	,	PUNCT
ejpam-1929	2	45	new	new	ADJ
ejpam-1929	2	46	delhi-110	delhi-110	NOUN
ejpam-1929	2	47	021	021	NUM
ejpam-1929	2	48	,	,	PUNCT
ejpam-1929	2	49	india	india	PROPN
ejpam-1929	2	50	2	2	NUM
ejpam-1929	2	51	centre	centre	NOUN
ejpam-1929	2	52	for	for	ADP
ejpam-1929	2	53	mathematical	mathematical	ADJ
ejpam-1929	2	54	sciences	science	NOUN
ejpam-1929	2	55	,	,	PUNCT
ejpam-1929	2	56	banasthali	banasthali	PROPN
ejpam-1929	2	57	university	university	NOUN
ejpam-1929	2	58	,	,	PUNCT
ejpam-1929	2	59	banasthali-304	banasthali-304	VERB
ejpam-1929	2	60	022	022	NUM
ejpam-1929	2	61	rajasthan	rajasthan	PROPN
ejpam-1929	2	62	,	,	PUNCT
ejpam-1929	2	63	india	india	PROPN
ejpam-1929	2	64	3	3	NUM
ejpam-1929	2	65	centre	centre	NOUN
ejpam-1929	2	66	for	for	ADP
ejpam-1929	2	67	excellence	excellence	NOUN
ejpam-1929	2	68	in	in	ADP
ejpam-1929	2	69	interdisciplinary	interdisciplinary	ADJ
ejpam-1929	2	70	mathematics	mathematic	NOUN
ejpam-1929	2	71	,	,	PUNCT
ejpam-1929	2	72	m.e.r.i.t	m.e.r.i.t	NOUN
ejpam-1929	2	73	.	.	PUNCT
ejpam-1929	2	74	,	,	PUNCT
ejpam-1929	2	75	a/9	a/9	ADV
ejpam-1929	2	76	,	,	PUNCT
ejpam-1929	2	77	uso	uso	NOUN
ejpam-1929	2	78	road	road	NOUN
ejpam-1929	2	79	,	,	PUNCT
ejpam-1929	2	80	shaheed	shaheed	NOUN
ejpam-1929	2	81	jit	jit	PROPN
ejpam-1929	2	82	singh	singh	PROPN
ejpam-1929	2	83	marg	marg	PROPN
ejpam-1929	2	84	,	,	PUNCT
ejpam-1929	2	85	qutab	qutab	PROPN
ejpam-1929	2	86	institutional	institutional	ADJ
ejpam-1929	2	87	area	area	NOUN
ejpam-1929	2	88	,	,	PUNCT
ejpam-1929	2	89	new	new	ADJ
ejpam-1929	2	90	delhi	delhi	PROPN
ejpam-1929	2	91	100	100	NUM
ejpam-1929	2	92	067	067	NUM
ejpam-1929	2	93	,	,	PUNCT
ejpam-1929	2	94	india	india	PROPN
ejpam-1929	2	95	.	.	PUNCT
ejpam-1929	3	1	abstract	abstract	PROPN
ejpam-1929	3	2	.	.	PUNCT
ejpam-1929	4	1	a	a	DET
ejpam-1929	4	2	signed	sign	VERB
ejpam-1929	4	3	graph	graph	NOUN
ejpam-1929	4	4	(	(	PUNCT
ejpam-1929	4	5	or	or	CCONJ
ejpam-1929	4	6	sigraph	sigraph	VERB
ejpam-1929	4	7	in	in	ADP
ejpam-1929	4	8	short	short	ADJ
ejpam-1929	4	9	)	)	PUNCT
ejpam-1929	4	10	is	be	AUX
ejpam-1929	4	11	an	an	DET
ejpam-1929	4	12	ordered	order	VERB
ejpam-1929	4	13	pair	pair	NOUN
ejpam-1929	4	14	s	s	PART
ejpam-1929	4	15	=	=	SYM
ejpam-1929	4	16	(	(	PUNCT
ejpam-1929	4	17	su	su	PROPN
ejpam-1929	4	18	,	,	PUNCT
ejpam-1929	4	19	σ	σ	PROPN
ejpam-1929	4	20	)	)	PUNCT
ejpam-1929	4	21	,	,	PUNCT
ejpam-1929	4	22	where	where	SCONJ
ejpam-1929	4	23	su	su	PROPN
ejpam-1929	4	24	is	be	AUX
ejpam-1929	4	25	a	a	DET
ejpam-1929	4	26	graph	graph	NOUN
ejpam-1929	4	27	g	g	NOUN
ejpam-1929	4	28	=	=	SYM
ejpam-1929	4	29	(	(	PUNCT
ejpam-1929	4	30	v	v	NOUN
ejpam-1929	4	31	,	,	PUNCT
ejpam-1929	4	32	e	e	NOUN
ejpam-1929	4	33	)	)	PUNCT
ejpam-1929	4	34	and	and	CCONJ
ejpam-1929	4	35	σ	σ	NUM
ejpam-1929	4	36	:	:	PUNCT
ejpam-1929	4	37	e→	e→	NOUN
ejpam-1929	4	38	{	{	PUNCT
ejpam-1929	4	39	+	+	ADJ
ejpam-1929	4	40	,	,	PUNCT
ejpam-1929	4	41	−	−	NOUN
ejpam-1929	4	42	}	}	PUNCT
ejpam-1929	4	43	is	be	AUX
ejpam-1929	4	44	a	a	DET
ejpam-1929	4	45	function	function	NOUN
ejpam-1929	4	46	from	from	ADP
ejpam-1929	4	47	the	the	DET
ejpam-1929	4	48	edge	edge	NOUN
ejpam-1929	4	49	set	set	VERB
ejpam-1929	4	50	e	e	PROPN
ejpam-1929	4	51	of	of	ADP
ejpam-1929	4	52	su	su	PROPN
ejpam-1929	4	53	into	into	ADP
ejpam-1929	4	54	the	the	DET
ejpam-1929	4	55	set	set	NOUN
ejpam-1929	4	56	{	{	PUNCT
ejpam-1929	4	57	+	+	NOUN
ejpam-1929	4	58	,	,	PUNCT
ejpam-1929	4	59	−	−	NOUN
ejpam-1929	4	60	}	}	PUNCT
ejpam-1929	4	61	.	.	PUNCT
ejpam-1929	5	1	for	for	ADP
ejpam-1929	5	2	a	a	DET
ejpam-1929	5	3	positive	positive	ADJ
ejpam-1929	5	4	integer	integer	NOUN
ejpam-1929	5	5	n	n	CCONJ
ejpam-1929	5	6	,	,	PUNCT
ejpam-1929	5	7	the	the	DET
ejpam-1929	5	8	unitary	unitary	ADJ
ejpam-1929	5	9	addition	addition	NOUN
ejpam-1929	5	10	cayley	cayley	NOUN
ejpam-1929	5	11	graph	graph	NOUN
ejpam-1929	5	12	gn	gn	PROPN
ejpam-1929	5	13	is	be	AUX
ejpam-1929	5	14	the	the	DET
ejpam-1929	5	15	graph	graph	NOUN
ejpam-1929	5	16	whose	whose	DET
ejpam-1929	5	17	vertex	vertex	NOUN
ejpam-1929	5	18	set	set	NOUN
ejpam-1929	5	19	is	be	AUX
ejpam-1929	5	20	zn	zn	PROPN
ejpam-1929	5	21	,	,	PUNCT
ejpam-1929	5	22	the	the	DET
ejpam-1929	5	23	ring	ring	NOUN
ejpam-1929	5	24	of	of	ADP
ejpam-1929	5	25	integers	integer	NOUN
ejpam-1929	5	26	modulo	modulo	VERB
ejpam-1929	5	27	n	n	NOUN
ejpam-1929	6	1	and	and	CCONJ
ejpam-1929	6	2	if	if	SCONJ
ejpam-1929	6	3	un	un	PROPN
ejpam-1929	6	4	denotes	denote	NOUN
ejpam-1929	6	5	set	set	VERB
ejpam-1929	6	6	of	of	ADP
ejpam-1929	6	7	all	all	DET
ejpam-1929	6	8	units	unit	NOUN
ejpam-1929	6	9	of	of	ADP
ejpam-1929	6	10	the	the	DET
ejpam-1929	6	11	ring	ring	NOUN
ejpam-1929	6	12	,	,	PUNCT
ejpam-1929	6	13	then	then	ADV
ejpam-1929	6	14	two	two	NUM
ejpam-1929	6	15	vertices	vertex	NOUN
ejpam-1929	6	16	a	a	PRON
ejpam-1929	6	17	and	and	CCONJ
ejpam-1929	6	18	b	b	NOUN
ejpam-1929	6	19	are	be	AUX
ejpam-1929	6	20	adjacent	adjacent	ADJ
ejpam-1929	6	21	if	if	SCONJ
ejpam-1929	6	22	and	and	CCONJ
ejpam-1929	6	23	only	only	ADV
ejpam-1929	6	24	if	if	SCONJ
ejpam-1929	6	25	a+	a+	PRON
ejpam-1929	6	26	b	b	PROPN
ejpam-1929	6	27	∈	∈	PROPN
ejpam-1929	6	28	un	un	PROPN
ejpam-1929	6	29	.	.	PROPN
ejpam-1929	6	30	for	for	ADP
ejpam-1929	6	31	a	a	DET
ejpam-1929	6	32	positive	positive	ADJ
ejpam-1929	6	33	integer	integer	NOUN
ejpam-1929	6	34	n	n	CCONJ
ejpam-1929	6	35	,	,	PUNCT
ejpam-1929	6	36	the	the	DET
ejpam-1929	6	37	unitary	unitary	ADJ
ejpam-1929	6	38	addition	addition	NOUN
ejpam-1929	6	39	cayley	cayley	NOUN
ejpam-1929	6	40	sigraph	sigraph	NOUN
ejpam-1929	6	41	σn	σn	NOUN
ejpam-1929	6	42	=	=	SYM
ejpam-1929	6	43	(	(	PUNCT
ejpam-1929	6	44	σ	σ	X
ejpam-1929	6	45	u	u	PROPN
ejpam-1929	6	46	n	n	PROPN
ejpam-1929	6	47	,	,	PUNCT
ejpam-1929	6	48	σ	σ	PROPN
ejpam-1929	6	49	)	)	PUNCT
ejpam-1929	6	50	is	be	AUX
ejpam-1929	6	51	defined	define	VERB
ejpam-1929	6	52	as	as	ADP
ejpam-1929	6	53	the	the	DET
ejpam-1929	6	54	sigraph	sigraph	NOUN
ejpam-1929	6	55	,	,	PUNCT
ejpam-1929	6	56	where	where	SCONJ
ejpam-1929	6	57	σu	σu	PROPN
ejpam-1929	6	58	n	n	ADV
ejpam-1929	6	59	is	be	AUX
ejpam-1929	6	60	the	the	DET
ejpam-1929	6	61	unitary	unitary	ADJ
ejpam-1929	6	62	addition	addition	NOUN
ejpam-1929	6	63	cayley	cayley	NOUN
ejpam-1929	6	64	graph	graph	NOUN
ejpam-1929	6	65	and	and	CCONJ
ejpam-1929	6	66	for	for	ADP
ejpam-1929	6	67	an	an	DET
ejpam-1929	6	68	edge	edge	NOUN
ejpam-1929	6	69	ab	ab	PROPN
ejpam-1929	6	70	of	of	ADP
ejpam-1929	6	71	σn	σn	PROPN
ejpam-1929	6	72	,	,	PUNCT
ejpam-1929	6	73	σ(ab	σ(ab	NOUN
ejpam-1929	6	74	)	)	PUNCT
ejpam-1929	6	75	=	=	SYM
ejpam-1929	7	1	¨	¨	NOUN
ejpam-1929	7	2	+	+	CCONJ
ejpam-1929	7	3	if	if	SCONJ
ejpam-1929	7	4	a	a	DET
ejpam-1929	7	5	∈	∈	PROPN
ejpam-1929	7	6	un	un	NOUN
ejpam-1929	7	7	or	or	CCONJ
ejpam-1929	7	8	b	b	PROPN
ejpam-1929	7	9	∈	∈	PROPN
ejpam-1929	7	10	un	un	PROPN
ejpam-1929	7	11	,	,	PUNCT
ejpam-1929	7	12	−	−	PROPN
ejpam-1929	7	13	otherwise	otherwise	ADV
ejpam-1929	7	14	.	.	PUNCT
ejpam-1929	8	1	in	in	ADP
ejpam-1929	8	2	this	this	DET
ejpam-1929	8	3	paper	paper	NOUN
ejpam-1929	8	4	,	,	PUNCT
ejpam-1929	8	5	we	we	PRON
ejpam-1929	8	6	have	have	AUX
ejpam-1929	8	7	obtained	obtain	VERB
ejpam-1929	8	8	a	a	DET
ejpam-1929	8	9	characterization	characterization	NOUN
ejpam-1929	8	10	of	of	ADP
ejpam-1929	8	11	balanced	balanced	ADJ
ejpam-1929	8	12	and	and	CCONJ
ejpam-1929	8	13	clusterable	clusterable	ADJ
ejpam-1929	8	14	unitary	unitary	ADJ
ejpam-1929	8	15	addition	addition	NOUN
ejpam-1929	8	16	cayley	cayley	NOUN
ejpam-1929	8	17	sigraphs	sigraph	VERB
ejpam-1929	8	18	.	.	PUNCT
ejpam-1929	9	1	further	far	ADV
ejpam-1929	9	2	,	,	PUNCT
ejpam-1929	9	3	we	we	PRON
ejpam-1929	9	4	have	have	AUX
ejpam-1929	9	5	established	establish	VERB
ejpam-1929	9	6	a	a	DET
ejpam-1929	9	7	characterization	characterization	NOUN
ejpam-1929	9	8	of	of	ADP
ejpam-1929	9	9	canonically	canonically	ADV
ejpam-1929	9	10	consistent	consistent	ADJ
ejpam-1929	9	11	unitary	unitary	ADJ
ejpam-1929	9	12	addition	addition	NOUN
ejpam-1929	9	13	cayley	cayley	NOUN
ejpam-1929	9	14	sigraphs	sigraph	VERB
ejpam-1929	9	15	σn	σn	ADP
ejpam-1929	9	16	,	,	PUNCT
ejpam-1929	9	17	where	where	SCONJ
ejpam-1929	9	18	n	n	PRON
ejpam-1929	9	19	has	have	VERB
ejpam-1929	9	20	at	at	ADP
ejpam-1929	9	21	most	most	ADV
ejpam-1929	9	22	two	two	NUM
ejpam-1929	9	23	distinct	distinct	ADJ
ejpam-1929	9	24	odd	odd	ADJ
ejpam-1929	9	25	prime	prime	ADJ
ejpam-1929	9	26	factors	factor	NOUN
ejpam-1929	9	27	.	.	PUNCT
ejpam-1929	10	1	2010	2010	NUM
ejpam-1929	10	2	mathematics	mathematic	NOUN
ejpam-1929	10	3	subject	subject	NOUN
ejpam-1929	10	4	classifications	classification	NOUN
ejpam-1929	10	5	:	:	PUNCT
ejpam-1929	10	6	05c22	05c22	NOUN
ejpam-1929	10	7	;	;	PUNCT
ejpam-1929	10	8	05c75	05c75	NUM
ejpam-1929	10	9	key	key	ADJ
ejpam-1929	10	10	words	word	NOUN
ejpam-1929	10	11	and	and	CCONJ
ejpam-1929	10	12	phrases	phrase	NOUN
ejpam-1929	10	13	:	:	PUNCT
ejpam-1929	10	14	sigraph	sigraph	NOUN
ejpam-1929	10	15	,	,	PUNCT
ejpam-1929	10	16	balance	balance	NOUN
ejpam-1929	10	17	,	,	PUNCT
ejpam-1929	10	18	clustering	clustering	NOUN
ejpam-1929	10	19	,	,	PUNCT
ejpam-1929	10	20	c−consistency	c−consistency	NOUN
ejpam-1929	10	21	,	,	PUNCT
ejpam-1929	10	22	unitary	unitary	ADJ
ejpam-1929	10	23	cayley	cayley	ADJ
ejpam-1929	10	24	sigraph	sigraph	NOUN
ejpam-1929	10	25	,	,	PUNCT
ejpam-1929	10	26	unitary	unitary	ADJ
ejpam-1929	10	27	addition	addition	NOUN
ejpam-1929	10	28	cayley	cayley	NOUN
ejpam-1929	10	29	graph	graph	NOUN
ejpam-1929	10	30	,	,	PUNCT
ejpam-1929	10	31	unitary	unitary	ADJ
ejpam-1929	10	32	addition	addition	NOUN
ejpam-1929	10	33	cayley	cayley	NOUN
ejpam-1929	10	34	sigraph	sigraph	NOUN
ejpam-1929	10	35	1	1	NUM
ejpam-1929	10	36	.	.	PUNCT
ejpam-1929	10	37	introduction	introduction	NOUN
ejpam-1929	10	38	for	for	ADP
ejpam-1929	10	39	standard	standard	ADJ
ejpam-1929	10	40	terminology	terminology	NOUN
ejpam-1929	10	41	and	and	CCONJ
ejpam-1929	10	42	notation	notation	NOUN
ejpam-1929	10	43	in	in	ADP
ejpam-1929	10	44	graph	graph	NOUN
ejpam-1929	10	45	theory	theory	NOUN
ejpam-1929	11	1	,	,	PUNCT
ejpam-1929	11	2	we	we	PRON
ejpam-1929	11	3	refer	refer	VERB
ejpam-1929	11	4	the	the	DET
ejpam-1929	11	5	reader	reader	NOUN
ejpam-1929	11	6	to	to	ADP
ejpam-1929	11	7	harary	harary	NOUN
ejpam-1929	11	8	[	[	X
ejpam-1929	11	9	30	30	NUM
ejpam-1929	11	10	]	]	PUNCT
ejpam-1929	11	11	and	and	CCONJ
ejpam-1929	11	12	west	west	NOUN
ejpam-1929	12	1	[	[	X
ejpam-1929	12	2	45	45	NUM
ejpam-1929	12	3	]	]	PUNCT
ejpam-1929	12	4	and	and	CCONJ
ejpam-1929	12	5	to	to	ADP
ejpam-1929	12	6	zaslavsky	zaslavsky	NOUN
ejpam-1929	13	1	[	[	X
ejpam-1929	13	2	46	46	NUM
ejpam-1929	13	3	,	,	PUNCT
ejpam-1929	13	4	47	47	NUM
ejpam-1929	13	5	]	]	PUNCT
ejpam-1929	13	6	for	for	ADP
ejpam-1929	13	7	sigraphs	sigraph	NOUN
ejpam-1929	13	8	.	.	PUNCT
ejpam-1929	14	1	throughout	throughout	ADP
ejpam-1929	14	2	the	the	DET
ejpam-1929	14	3	text	text	NOUN
ejpam-1929	14	4	,	,	PUNCT
ejpam-1929	14	5	we	we	PRON
ejpam-1929	14	6	consider	consider	VERB
ejpam-1929	14	7	finite	finite	ADJ
ejpam-1929	14	8	,	,	PUNCT
ejpam-1929	14	9	undirected	undirected	ADJ
ejpam-1929	14	10	graphs	graph	NOUN
ejpam-1929	14	11	with	with	ADP
ejpam-1929	14	12	no	no	DET
ejpam-1929	14	13	loops	loop	NOUN
ejpam-1929	14	14	or	or	CCONJ
ejpam-1929	14	15	multiple	multiple	ADJ
ejpam-1929	14	16	edges	edge	NOUN
ejpam-1929	14	17	.	.	PUNCT
ejpam-1929	15	1	∗corresponding	∗corresponde	VERB
ejpam-1929	15	2	author	author	NOUN
ejpam-1929	15	3	.	.	PUNCT
ejpam-1929	16	1	email	email	NOUN
ejpam-1929	16	2	addresses	address	NOUN
ejpam-1929	16	3	:	:	PUNCT
ejpam-1929	16	4	deepa_sinha2001@yahoo.com	deepa_sinha2001@yahoo.com	X
ejpam-1929	16	5	(	(	PUNCT
ejpam-1929	16	6	d.	d.	PROPN
ejpam-1929	16	7	sinha	sinha	PROPN
ejpam-1929	16	8	)	)	PUNCT
ejpam-1929	16	9	,	,	PUNCT
ejpam-1929	16	10	ayushi.dhama2@gmail.com	ayushi.dhama2@gmail.com	X
ejpam-1929	16	11	(	(	PUNCT
ejpam-1929	16	12	a.	a.	NOUN
ejpam-1929	16	13	dhama	dhama	PROPN
ejpam-1929	16	14	)	)	PUNCT
ejpam-1929	16	15	,	,	PUNCT
ejpam-1929	16	16	devadas.acharya@gmail.com	devadas.acharya@gmail.com	X
ejpam-1929	16	17	(	(	PUNCT
ejpam-1929	16	18	b.	b.	PROPN
ejpam-1929	16	19	acharya	acharya	PROPN
ejpam-1929	16	20	)	)	PUNCT
ejpam-1929	16	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1929	17	1	189	189	NUM
ejpam-1929	18	1	c	c	X
ejpam-1929	18	2	©	©	PROPN
ejpam-1929	18	3	2013	2013	NUM
ejpam-1929	18	4	ejpam	ejpam	NOUN
ejpam-1929	18	5	all	all	DET
ejpam-1929	18	6	rights	right	NOUN
ejpam-1929	18	7	reserved	reserve	VERB
ejpam-1929	18	8	.	.	PUNCT
ejpam-1929	19	1	d.	d.	PROPN
ejpam-1929	19	2	sinha	sinha	PROPN
ejpam-1929	19	3	,	,	PUNCT
ejpam-1929	19	4	a.	a.	NOUN
ejpam-1929	19	5	dhama	dhama	PROPN
ejpam-1929	19	6	,	,	PUNCT
ejpam-1929	19	7	b.	b.	PROPN
ejpam-1929	19	8	acharya	acharya	PROPN
ejpam-1929	19	9	/	/	SYM
ejpam-1929	19	10	eur	eur	PROPN
ejpam-1929	19	11	.	.	PUNCT
ejpam-1929	20	1	j.	j.	PROPN
ejpam-1929	20	2	pure	pure	PROPN
ejpam-1929	20	3	appl	appl	PROPN
ejpam-1929	20	4	.	.	PROPN
ejpam-1929	20	5	math	math	PROPN
ejpam-1929	20	6	,	,	PUNCT
ejpam-1929	20	7	6	6	NUM
ejpam-1929	20	8	(	(	PUNCT
ejpam-1929	20	9	2013	2013	NUM
ejpam-1929	20	10	)	)	PUNCT
ejpam-1929	20	11	,	,	PUNCT
ejpam-1929	20	12	189	189	NUM
ejpam-1929	20	13	-	-	SYM
ejpam-1929	20	14	210	210	NUM
ejpam-1929	20	15	190	190	NUM
ejpam-1929	20	16	1.1	1.1	NUM
ejpam-1929	20	17	.	.	PUNCT
ejpam-1929	21	1	sigraphs	sigraph	NOUN
ejpam-1929	21	2	and	and	CCONJ
ejpam-1929	21	3	some	some	DET
ejpam-1929	21	4	basic	basic	ADJ
ejpam-1929	21	5	notions	notion	NOUN
ejpam-1929	21	6	and	and	CCONJ
ejpam-1929	21	7	notations	notation	NOUN
ejpam-1929	21	8	a	a	DET
ejpam-1929	21	9	signed	sign	VERB
ejpam-1929	21	10	graph	graph	NOUN
ejpam-1929	21	11	(	(	PUNCT
ejpam-1929	21	12	or	or	CCONJ
ejpam-1929	21	13	,	,	PUNCT
ejpam-1929	21	14	sigraph	sigraph	VERB
ejpam-1929	21	15	in	in	ADP
ejpam-1929	21	16	short	short	ADJ
ejpam-1929	21	17	;	;	PUNCT
ejpam-1929	21	18	see	see	VERB
ejpam-1929	21	19	[	[	X
ejpam-1929	21	20	29	29	NUM
ejpam-1929	21	21	]	]	PUNCT
ejpam-1929	21	22	)	)	PUNCT
ejpam-1929	21	23	is	be	AUX
ejpam-1929	21	24	an	an	DET
ejpam-1929	21	25	ordered	order	VERB
ejpam-1929	21	26	pair	pair	NOUN
ejpam-1929	21	27	s	s	PART
ejpam-1929	21	28	=	=	SYM
ejpam-1929	21	29	(	(	PUNCT
ejpam-1929	21	30	su	su	PROPN
ejpam-1929	21	31	,	,	PUNCT
ejpam-1929	21	32	σ	σ	PROPN
ejpam-1929	21	33	)	)	PUNCT
ejpam-1929	21	34	,	,	PUNCT
ejpam-1929	21	35	where	where	SCONJ
ejpam-1929	21	36	su	su	PROPN
ejpam-1929	21	37	is	be	AUX
ejpam-1929	21	38	a	a	DET
ejpam-1929	21	39	graph	graph	NOUN
ejpam-1929	21	40	g	g	NOUN
ejpam-1929	21	41	=	=	SYM
ejpam-1929	21	42	(	(	PUNCT
ejpam-1929	21	43	v	v	NOUN
ejpam-1929	21	44	,	,	PUNCT
ejpam-1929	21	45	e	e	NOUN
ejpam-1929	21	46	)	)	PUNCT
ejpam-1929	21	47	,	,	PUNCT
ejpam-1929	21	48	called	call	VERB
ejpam-1929	21	49	the	the	DET
ejpam-1929	21	50	underlying	underlie	VERB
ejpam-1929	21	51	graph	graph	NOUN
ejpam-1929	21	52	of	of	ADP
ejpam-1929	21	53	s	s	PRON
ejpam-1929	21	54	and	and	CCONJ
ejpam-1929	21	55	σ	σ	NOUN
ejpam-1929	21	56	:	:	PUNCT
ejpam-1929	21	57	e	e	X
ejpam-1929	21	58	→	→	PUNCT
ejpam-1929	21	59	{	{	PUNCT
ejpam-1929	21	60	+	+	ADJ
ejpam-1929	21	61	,	,	PUNCT
ejpam-1929	21	62	−	−	NOUN
ejpam-1929	21	63	}	}	PUNCT
ejpam-1929	21	64	is	be	AUX
ejpam-1929	21	65	a	a	DET
ejpam-1929	21	66	function	function	NOUN
ejpam-1929	21	67	from	from	ADP
ejpam-1929	21	68	the	the	DET
ejpam-1929	21	69	edge	edge	NOUN
ejpam-1929	21	70	set	set	VERB
ejpam-1929	21	71	e	e	PROPN
ejpam-1929	21	72	of	of	ADP
ejpam-1929	21	73	su	su	PROPN
ejpam-1929	21	74	into	into	ADP
ejpam-1929	21	75	the	the	DET
ejpam-1929	21	76	set	set	NOUN
ejpam-1929	21	77	{	{	PUNCT
ejpam-1929	21	78	+	+	NOUN
ejpam-1929	21	79	,	,	PUNCT
ejpam-1929	21	80	−	−	PROPN
ejpam-1929	21	81	}	}	PUNCT
ejpam-1929	21	82	,	,	PUNCT
ejpam-1929	21	83	called	call	VERB
ejpam-1929	21	84	the	the	DET
ejpam-1929	21	85	signature	signature	NOUN
ejpam-1929	21	86	of	of	ADP
ejpam-1929	21	87	s.	s.	PROPN
ejpam-1929	21	88	let	let	VERB
ejpam-1929	21	89	e+(s	e+(s	PRON
ejpam-1929	21	90	)	)	PUNCT
ejpam-1929	22	1	=	=	PRON
ejpam-1929	22	2	{	{	PUNCT
ejpam-1929	22	3	e	e	PROPN
ejpam-1929	22	4	∈	∈	PROPN
ejpam-1929	22	5	e(g	e(g	PROPN
ejpam-1929	22	6	)	)	PUNCT
ejpam-1929	22	7	:	:	PUNCT
ejpam-1929	23	1	σ(e	σ(e	PROPN
ejpam-1929	23	2	)	)	PUNCT
ejpam-1929	23	3	=	=	PUNCT
ejpam-1929	24	1	+	+	ADJ
ejpam-1929	24	2	}	}	PUNCT
ejpam-1929	24	3	and	and	CCONJ
ejpam-1929	24	4	e−(s	e−(s	ADJ
ejpam-1929	24	5	)	)	PUNCT
ejpam-1929	24	6	=	=	PRON
ejpam-1929	24	7	{	{	PUNCT
ejpam-1929	24	8	e	e	PROPN
ejpam-1929	24	9	∈	∈	PROPN
ejpam-1929	24	10	e(g	e(g	PROPN
ejpam-1929	24	11	)	)	PUNCT
ejpam-1929	24	12	:	:	PUNCT
ejpam-1929	24	13	σ(e	σ(e	PROPN
ejpam-1929	24	14	)	)	PUNCT
ejpam-1929	25	1	=	=	SYM
ejpam-1929	25	2	−	−	NOUN
ejpam-1929	25	3	}	}	PUNCT
ejpam-1929	25	4	.	.	PUNCT
ejpam-1929	26	1	the	the	DET
ejpam-1929	26	2	elements	element	NOUN
ejpam-1929	26	3	of	of	ADP
ejpam-1929	26	4	e+(s	e+(s	NUM
ejpam-1929	26	5	)	)	PUNCT
ejpam-1929	26	6	and	and	CCONJ
ejpam-1929	26	7	e−(s	e−(	VERB
ejpam-1929	26	8	)	)	PUNCT
ejpam-1929	26	9	are	be	AUX
ejpam-1929	26	10	called	call	VERB
ejpam-1929	26	11	positive	positive	ADJ
ejpam-1929	26	12	and	and	CCONJ
ejpam-1929	26	13	negative	negative	ADJ
ejpam-1929	26	14	edges	edge	NOUN
ejpam-1929	26	15	of	of	ADP
ejpam-1929	26	16	s	s	NOUN
ejpam-1929	26	17	,	,	PUNCT
ejpam-1929	26	18	respectively	respectively	ADV
ejpam-1929	26	19	.	.	PUNCT
ejpam-1929	27	1	a	a	DET
ejpam-1929	27	2	sigraph	sigraph	NOUN
ejpam-1929	27	3	is	be	AUX
ejpam-1929	27	4	all	all	ADV
ejpam-1929	27	5	-	-	PUNCT
ejpam-1929	27	6	positive	positive	ADJ
ejpam-1929	27	7	(	(	PUNCT
ejpam-1929	27	8	all	all	ADV
ejpam-1929	27	9	-	-	PUNCT
ejpam-1929	27	10	negative	negative	ADJ
ejpam-1929	27	11	)	)	PUNCT
ejpam-1929	27	12	if	if	SCONJ
ejpam-1929	27	13	all	all	DET
ejpam-1929	27	14	its	its	PRON
ejpam-1929	27	15	edges	edge	NOUN
ejpam-1929	27	16	are	be	AUX
ejpam-1929	27	17	positive	positive	ADJ
ejpam-1929	27	18	(	(	PUNCT
ejpam-1929	27	19	negative	negative	ADJ
ejpam-1929	27	20	)	)	PUNCT
ejpam-1929	27	21	;	;	PUNCT
ejpam-1929	27	22	further	far	ADV
ejpam-1929	27	23	,	,	PUNCT
ejpam-1929	27	24	it	it	PRON
ejpam-1929	27	25	is	be	AUX
ejpam-1929	27	26	said	say	VERB
ejpam-1929	27	27	to	to	PART
ejpam-1929	27	28	be	be	AUX
ejpam-1929	27	29	homogeneous	homogeneous	ADJ
ejpam-1929	27	30	if	if	SCONJ
ejpam-1929	27	31	it	it	PRON
ejpam-1929	27	32	is	be	AUX
ejpam-1929	27	33	either	either	CCONJ
ejpam-1929	27	34	all	all	ADV
ejpam-1929	27	35	-	-	PUNCT
ejpam-1929	27	36	positive	positive	ADJ
ejpam-1929	27	37	or	or	CCONJ
ejpam-1929	27	38	all	all	ADV
ejpam-1929	27	39	-	-	PUNCT
ejpam-1929	27	40	negative	negative	ADJ
ejpam-1929	27	41	and	and	CCONJ
ejpam-1929	27	42	heterogeneous	heterogeneous	ADJ
ejpam-1929	27	43	otherwise	otherwise	ADV
ejpam-1929	27	44	.	.	PUNCT
ejpam-1929	28	1	the	the	DET
ejpam-1929	28	2	positive	positive	ADJ
ejpam-1929	28	3	(	(	PUNCT
ejpam-1929	28	4	negative	negative	ADJ
ejpam-1929	28	5	)	)	PUNCT
ejpam-1929	28	6	degree	degree	NOUN
ejpam-1929	28	7	of	of	ADP
ejpam-1929	28	8	a	a	DET
ejpam-1929	28	9	vertex	vertex	NOUN
ejpam-1929	28	10	v	v	ADP
ejpam-1929	28	11	∈	∈	NOUN
ejpam-1929	28	12	v	v	NOUN
ejpam-1929	28	13	(	(	PUNCT
ejpam-1929	28	14	s	s	NOUN
ejpam-1929	28	15	)	)	PUNCT
ejpam-1929	28	16	denoted	denote	VERB
ejpam-1929	28	17	by	by	ADP
ejpam-1929	28	18	d+(v)(d−(v	d+(v)(d−(v	NOUN
ejpam-1929	28	19	)	)	PUNCT
ejpam-1929	28	20	)	)	PUNCT
ejpam-1929	28	21	is	be	AUX
ejpam-1929	28	22	the	the	DET
ejpam-1929	28	23	number	number	NOUN
ejpam-1929	28	24	of	of	ADP
ejpam-1929	28	25	positive	positive	ADJ
ejpam-1929	28	26	(	(	PUNCT
ejpam-1929	28	27	negative	negative	ADJ
ejpam-1929	28	28	)	)	PUNCT
ejpam-1929	28	29	edges	edge	NOUN
ejpam-1929	28	30	incident	incident	NOUN
ejpam-1929	28	31	on	on	ADP
ejpam-1929	28	32	the	the	DET
ejpam-1929	28	33	vertex	vertex	NOUN
ejpam-1929	28	34	v	v	NOUN
ejpam-1929	28	35	and	and	CCONJ
ejpam-1929	28	36	d(v	d(v	ADJ
ejpam-1929	28	37	)	)	PUNCT
ejpam-1929	28	38	=	=	PROPN
ejpam-1929	28	39	d+(v)+	d+(v)+	NOUN
ejpam-1929	28	40	d−(v	d−(v	PROPN
ejpam-1929	28	41	)	)	PUNCT
ejpam-1929	28	42	.	.	PUNCT
ejpam-1929	29	1	the	the	DET
ejpam-1929	29	2	negation	negation	NOUN
ejpam-1929	29	3	η(s	η(s	PROPN
ejpam-1929	29	4	)	)	PUNCT
ejpam-1929	29	5	of	of	ADP
ejpam-1929	29	6	a	a	DET
ejpam-1929	29	7	sigraph	sigraph	NOUN
ejpam-1929	29	8	s	s	PART
ejpam-1929	29	9	is	be	AUX
ejpam-1929	29	10	a	a	DET
ejpam-1929	29	11	sigraph	sigraph	NOUN
ejpam-1929	29	12	obtained	obtain	VERB
ejpam-1929	29	13	from	from	ADP
ejpam-1929	29	14	s	s	PRON
ejpam-1929	29	15	by	by	ADP
ejpam-1929	29	16	negating	negate	VERB
ejpam-1929	29	17	the	the	DET
ejpam-1929	29	18	sign	sign	NOUN
ejpam-1929	29	19	of	of	ADP
ejpam-1929	29	20	every	every	DET
ejpam-1929	29	21	edge	edge	NOUN
ejpam-1929	29	22	of	of	ADP
ejpam-1929	29	23	s	s	NOUN
ejpam-1929	29	24	,	,	PUNCT
ejpam-1929	29	25	in	in	ADP
ejpam-1929	29	26	the	the	DET
ejpam-1929	29	27	sense	sense	NOUN
ejpam-1929	29	28	that	that	PRON
ejpam-1929	29	29	to	to	PART
ejpam-1929	29	30	find	find	VERB
ejpam-1929	29	31	η(s	η(	NOUN
ejpam-1929	29	32	)	)	PUNCT
ejpam-1929	29	33	we	we	PRON
ejpam-1929	29	34	change	change	VERB
ejpam-1929	29	35	the	the	DET
ejpam-1929	29	36	sign	sign	NOUN
ejpam-1929	29	37	of	of	ADP
ejpam-1929	29	38	every	every	DET
ejpam-1929	29	39	edge	edge	NOUN
ejpam-1929	29	40	to	to	ADP
ejpam-1929	29	41	its	its	PRON
ejpam-1929	29	42	opposite	opposite	NOUN
ejpam-1929	29	43	in	in	ADP
ejpam-1929	29	44	s.	s.	PROPN
ejpam-1929	29	45	a	a	DET
ejpam-1929	29	46	positive	positive	ADJ
ejpam-1929	29	47	(	(	PUNCT
ejpam-1929	29	48	negative	negative	ADJ
ejpam-1929	29	49	)	)	PUNCT
ejpam-1929	29	50	section	section	NOUN
ejpam-1929	29	51	of	of	ADP
ejpam-1929	29	52	a	a	DET
ejpam-1929	29	53	subsigraph	subsigraph	NOUN
ejpam-1929	29	54	s′	s′	ADJ
ejpam-1929	29	55	of	of	ADP
ejpam-1929	29	56	a	a	DET
ejpam-1929	29	57	sigraph	sigraph	NOUN
ejpam-1929	29	58	s	s	PART
ejpam-1929	29	59	is	be	AUX
ejpam-1929	29	60	a	a	DET
ejpam-1929	29	61	maximal	maximal	ADJ
ejpam-1929	29	62	edge	edge	NOUN
ejpam-1929	29	63	-	-	PUNCT
ejpam-1929	29	64	induced	induce	VERB
ejpam-1929	29	65	connected	connected	ADJ
ejpam-1929	29	66	subsigraph	subsigraph	NOUN
ejpam-1929	29	67	in	in	ADP
ejpam-1929	29	68	s	s	PRON
ejpam-1929	29	69	consisting	consist	VERB
ejpam-1929	29	70	of	of	ADP
ejpam-1929	29	71	only	only	ADV
ejpam-1929	29	72	the	the	DET
ejpam-1929	29	73	positive	positive	ADJ
ejpam-1929	29	74	(	(	PUNCT
ejpam-1929	29	75	negative	negative	ADJ
ejpam-1929	29	76	)	)	PUNCT
ejpam-1929	29	77	edges	edge	NOUN
ejpam-1929	29	78	of	of	ADP
ejpam-1929	29	79	s	s	NOUN
ejpam-1929	29	80	;	;	PUNCT
ejpam-1929	29	81	in	in	ADP
ejpam-1929	29	82	particular	particular	ADJ
ejpam-1929	29	83	,	,	PUNCT
ejpam-1929	29	84	a	a	DET
ejpam-1929	29	85	positive	positive	ADJ
ejpam-1929	29	86	(	(	PUNCT
ejpam-1929	29	87	negative	negative	ADJ
ejpam-1929	29	88	)	)	PUNCT
ejpam-1929	29	89	section	section	NOUN
ejpam-1929	29	90	in	in	ADP
ejpam-1929	29	91	a	a	DET
ejpam-1929	29	92	heterogeneous	heterogeneous	ADJ
ejpam-1929	29	93	cycle	cycle	NOUN
ejpam-1929	29	94	of	of	ADP
ejpam-1929	29	95	s	s	NOUN
ejpam-1929	29	96	is	be	AUX
ejpam-1929	29	97	essentially	essentially	ADV
ejpam-1929	29	98	a	a	DET
ejpam-1929	29	99	maximal	maximal	ADJ
ejpam-1929	29	100	all	all	ADV
ejpam-1929	29	101	-	-	PUNCT
ejpam-1929	29	102	positive	positive	ADJ
ejpam-1929	29	103	(	(	PUNCT
ejpam-1929	29	104	all	all	ADV
ejpam-1929	29	105	-	-	PUNCT
ejpam-1929	29	106	negative	negative	ADJ
ejpam-1929	29	107	)	)	PUNCT
ejpam-1929	29	108	path	path	NOUN
ejpam-1929	29	109	in	in	ADP
ejpam-1929	29	110	the	the	DET
ejpam-1929	29	111	cycle	cycle	NOUN
ejpam-1929	29	112	.	.	PUNCT
ejpam-1929	30	1	two	two	NUM
ejpam-1929	30	2	graphs	graph	NOUN
ejpam-1929	30	3	g1	g1	PROPN
ejpam-1929	30	4	=	=	SYM
ejpam-1929	30	5	(	(	PUNCT
ejpam-1929	30	6	v1	v1	PROPN
ejpam-1929	30	7	,	,	PUNCT
ejpam-1929	30	8	e1	e1	NOUN
ejpam-1929	30	9	)	)	PUNCT
ejpam-1929	30	10	and	and	CCONJ
ejpam-1929	30	11	g2	g2	PROPN
ejpam-1929	30	12	=	=	PUNCT
ejpam-1929	30	13	(	(	PUNCT
ejpam-1929	30	14	v2	v2	PROPN
ejpam-1929	30	15	,	,	PUNCT
ejpam-1929	30	16	e2	e2	PROPN
ejpam-1929	30	17	)	)	PUNCT
ejpam-1929	30	18	are	be	AUX
ejpam-1929	30	19	isomorphic	isomorphic	ADJ
ejpam-1929	30	20	if	if	SCONJ
ejpam-1929	30	21	there	there	PRON
ejpam-1929	30	22	is	be	VERB
ejpam-1929	30	23	a	a	DET
ejpam-1929	30	24	bijective	bijective	ADJ
ejpam-1929	30	25	function	function	NOUN
ejpam-1929	30	26	f	f	NOUN
ejpam-1929	30	27	:	:	PUNCT
ejpam-1929	30	28	v1	v1	VERB
ejpam-1929	30	29	→	→	SYM
ejpam-1929	30	30	v2	v2	VERB
ejpam-1929	30	31	such	such	ADJ
ejpam-1929	30	32	that	that	PRON
ejpam-1929	30	33	for	for	ADP
ejpam-1929	30	34	all	all	DET
ejpam-1929	30	35	v1	v1	NOUN
ejpam-1929	30	36	,	,	PUNCT
ejpam-1929	30	37	v2	v2	PROPN
ejpam-1929	30	38	∈	∈	PROPN
ejpam-1929	30	39	v	v	NOUN
ejpam-1929	30	40	:	:	PUNCT
ejpam-1929	30	41	v1v2	v1v2	X
ejpam-1929	30	42	∈	∈	PROPN
ejpam-1929	30	43	e1⇔	e1⇔	PROPN
ejpam-1929	30	44	f	f	PROPN
ejpam-1929	30	45	(	(	PUNCT
ejpam-1929	30	46	v1	v1	PROPN
ejpam-1929	30	47	)	)	PUNCT
ejpam-1929	30	48	f	f	NOUN
ejpam-1929	30	49	(	(	PUNCT
ejpam-1929	30	50	v2	v2	NOUN
ejpam-1929	30	51	)	)	PUNCT
ejpam-1929	30	52	∈	∈	PROPN
ejpam-1929	30	53	e2	e2	PROPN
ejpam-1929	30	54	.	.	PUNCT
ejpam-1929	31	1	two	two	NUM
ejpam-1929	31	2	sigraphs	sigraph	NOUN
ejpam-1929	31	3	s1	s1	NOUN
ejpam-1929	31	4	and	and	CCONJ
ejpam-1929	31	5	s2	s2	NOUN
ejpam-1929	31	6	are	be	AUX
ejpam-1929	31	7	isomorphic	isomorphic	ADJ
ejpam-1929	31	8	if	if	SCONJ
ejpam-1929	31	9	there	there	PRON
ejpam-1929	31	10	is	be	VERB
ejpam-1929	31	11	an	an	DET
ejpam-1929	31	12	isomorphism	isomorphism	NOUN
ejpam-1929	31	13	between	between	ADP
ejpam-1929	31	14	their	their	PRON
ejpam-1929	31	15	underlying	underlie	VERB
ejpam-1929	31	16	graphs	graph	NOUN
ejpam-1929	31	17	that	that	PRON
ejpam-1929	31	18	preserves	preserve	VERB
ejpam-1929	31	19	edge	edge	NOUN
ejpam-1929	31	20	signs	sign	NOUN
ejpam-1929	31	21	.	.	PUNCT
ejpam-1929	32	1	a	a	DET
ejpam-1929	32	2	cycle	cycle	NOUN
ejpam-1929	32	3	in	in	ADP
ejpam-1929	32	4	a	a	DET
ejpam-1929	32	5	sigraph	sigraph	NOUN
ejpam-1929	32	6	s	s	NOUN
ejpam-1929	32	7	is	be	AUX
ejpam-1929	32	8	said	say	VERB
ejpam-1929	32	9	to	to	PART
ejpam-1929	32	10	be	be	AUX
ejpam-1929	32	11	positive	positive	ADJ
ejpam-1929	32	12	if	if	SCONJ
ejpam-1929	32	13	it	it	PRON
ejpam-1929	32	14	contains	contain	VERB
ejpam-1929	32	15	an	an	DET
ejpam-1929	32	16	even	even	ADJ
ejpam-1929	32	17	number	number	NOUN
ejpam-1929	32	18	of	of	ADP
ejpam-1929	32	19	negative	negative	ADJ
ejpam-1929	32	20	edges	edge	NOUN
ejpam-1929	32	21	.	.	PUNCT
ejpam-1929	33	1	a	a	DET
ejpam-1929	33	2	given	give	VERB
ejpam-1929	33	3	sigraph	sigraph	NOUN
ejpam-1929	33	4	s	s	PART
ejpam-1929	33	5	is	be	AUX
ejpam-1929	33	6	said	say	VERB
ejpam-1929	33	7	to	to	PART
ejpam-1929	33	8	be	be	AUX
ejpam-1929	33	9	balanced	balance	VERB
ejpam-1929	33	10	if	if	SCONJ
ejpam-1929	33	11	every	every	DET
ejpam-1929	33	12	cycle	cycle	NOUN
ejpam-1929	33	13	in	in	ADP
ejpam-1929	33	14	s	s	PROPN
ejpam-1929	33	15	is	be	AUX
ejpam-1929	33	16	positive	positive	ADJ
ejpam-1929	33	17	(	(	PUNCT
ejpam-1929	33	18	see	see	VERB
ejpam-1929	33	19	[	[	X
ejpam-1929	33	20	29	29	NUM
ejpam-1929	33	21	]	]	NUM
ejpam-1929	33	22	)	)	PUNCT
ejpam-1929	33	23	;	;	PUNCT
ejpam-1929	33	24	balanced	balanced	ADJ
ejpam-1929	33	25	sigraphs	sigraph	NOUN
ejpam-1929	33	26	were	be	AUX
ejpam-1929	33	27	first	first	ADV
ejpam-1929	33	28	defined	define	VERB
ejpam-1929	33	29	and	and	CCONJ
ejpam-1929	33	30	characterized	characterize	VERB
ejpam-1929	33	31	by	by	ADP
ejpam-1929	33	32	harary	harary	NOUN
ejpam-1929	33	33	[	[	X
ejpam-1929	33	34	29	29	NUM
ejpam-1929	33	35	]	]	PUNCT
ejpam-1929	33	36	.	.	PUNCT
ejpam-1929	34	1	a	a	DET
ejpam-1929	34	2	spectral	spectral	ADJ
ejpam-1929	34	3	characterization	characterization	NOUN
ejpam-1929	34	4	of	of	ADP
ejpam-1929	34	5	balanced	balanced	ADJ
ejpam-1929	34	6	sigraphs	sigraph	NOUN
ejpam-1929	34	7	was	be	AUX
ejpam-1929	34	8	given	give	VERB
ejpam-1929	34	9	by	by	ADP
ejpam-1929	34	10	acharya	acharya	NOUN
ejpam-1929	34	11	[	[	X
ejpam-1929	34	12	1	1	NUM
ejpam-1929	34	13	]	]	PUNCT
ejpam-1929	34	14	.	.	PUNCT
ejpam-1929	35	1	harary	harary	NOUN
ejpam-1929	35	2	and	and	CCONJ
ejpam-1929	35	3	kabell	kabell	NOUN
ejpam-1929	36	1	[	[	X
ejpam-1929	36	2	31	31	NUM
ejpam-1929	36	3	,	,	PUNCT
ejpam-1929	36	4	32	32	NUM
ejpam-1929	36	5	]	]	PUNCT
ejpam-1929	36	6	developed	develop	VERB
ejpam-1929	36	7	a	a	DET
ejpam-1929	36	8	simple	simple	ADJ
ejpam-1929	36	9	algorithm	algorithm	NOUN
ejpam-1929	36	10	to	to	PART
ejpam-1929	36	11	detect	detect	VERB
ejpam-1929	36	12	balanced	balanced	ADJ
ejpam-1929	36	13	sigraphs	sigraph	NOUN
ejpam-1929	36	14	and	and	CCONJ
ejpam-1929	36	15	also	also	ADV
ejpam-1929	36	16	enumerated	enumerate	VERB
ejpam-1929	36	17	them	they	PRON
ejpam-1929	36	18	.	.	PUNCT
ejpam-1929	37	1	1.2	1.2	NUM
ejpam-1929	37	2	.	.	PUNCT
ejpam-1929	38	1	the	the	DET
ejpam-1929	38	2	notion	notion	NOUN
ejpam-1929	38	3	of	of	ADP
ejpam-1929	38	4	balance	balance	NOUN
ejpam-1929	38	5	in	in	ADP
ejpam-1929	38	6	a	a	DET
ejpam-1929	38	7	sigraph	sigraph	ADJ
ejpam-1929	38	8	harary	harary	NOUN
ejpam-1929	38	9	[	[	X
ejpam-1929	38	10	29	29	NUM
ejpam-1929	38	11	]	]	PUNCT
ejpam-1929	38	12	derived	derive	VERB
ejpam-1929	38	13	the	the	DET
ejpam-1929	38	14	following	follow	VERB
ejpam-1929	38	15	structural	structural	ADJ
ejpam-1929	38	16	criterion	criterion	NOUN
ejpam-1929	38	17	called	call	VERB
ejpam-1929	38	18	partition	partition	NOUN
ejpam-1929	38	19	criterion	criterion	NOUN
ejpam-1929	38	20	for	for	ADP
ejpam-1929	38	21	balance	balance	NOUN
ejpam-1929	38	22	in	in	ADP
ejpam-1929	38	23	sigraphs	sigraph	NOUN
ejpam-1929	38	24	.	.	PUNCT
ejpam-1929	39	1	theorem	theorem	ADJ
ejpam-1929	39	2	1	1	NUM
ejpam-1929	39	3	(	(	PUNCT
ejpam-1929	39	4	[	[	X
ejpam-1929	39	5	29	29	NUM
ejpam-1929	39	6	]	]	NUM
ejpam-1929	39	7	)	)	PUNCT
ejpam-1929	39	8	.	.	PUNCT
ejpam-1929	40	1	a	a	DET
ejpam-1929	40	2	sigraph	sigraph	NOUN
ejpam-1929	40	3	s	s	PART
ejpam-1929	40	4	is	be	AUX
ejpam-1929	40	5	balanced	balance	VERB
ejpam-1929	40	6	if	if	SCONJ
ejpam-1929	40	7	and	and	CCONJ
ejpam-1929	40	8	only	only	ADV
ejpam-1929	40	9	if	if	SCONJ
ejpam-1929	40	10	its	its	PRON
ejpam-1929	40	11	vertex	vertex	NOUN
ejpam-1929	40	12	set	set	VERB
ejpam-1929	40	13	v	v	NOUN
ejpam-1929	40	14	(	(	PUNCT
ejpam-1929	40	15	s	s	X
ejpam-1929	40	16	)	)	PUNCT
ejpam-1929	40	17	can	can	AUX
ejpam-1929	40	18	be	be	AUX
ejpam-1929	40	19	partitioned	partition	VERB
ejpam-1929	40	20	into	into	ADP
ejpam-1929	40	21	two	two	NUM
ejpam-1929	40	22	subsets	subset	NOUN
ejpam-1929	40	23	v1	v1	NOUN
ejpam-1929	40	24	and	and	CCONJ
ejpam-1929	40	25	v2	v2	NOUN
ejpam-1929	40	26	,	,	PUNCT
ejpam-1929	40	27	one	one	NUM
ejpam-1929	40	28	of	of	ADP
ejpam-1929	40	29	them	they	PRON
ejpam-1929	40	30	possibly	possibly	ADV
ejpam-1929	40	31	empty	empty	ADJ
ejpam-1929	40	32	,	,	PUNCT
ejpam-1929	40	33	such	such	ADJ
ejpam-1929	40	34	that	that	SCONJ
ejpam-1929	40	35	every	every	DET
ejpam-1929	40	36	positive	positive	ADJ
ejpam-1929	40	37	edge	edge	NOUN
ejpam-1929	40	38	joins	join	VERB
ejpam-1929	40	39	two	two	NUM
ejpam-1929	40	40	vertices	vertex	NOUN
ejpam-1929	40	41	in	in	ADP
ejpam-1929	40	42	the	the	DET
ejpam-1929	40	43	same	same	ADJ
ejpam-1929	40	44	subset	subset	NOUN
ejpam-1929	40	45	and	and	CCONJ
ejpam-1929	40	46	every	every	DET
ejpam-1929	40	47	negative	negative	ADJ
ejpam-1929	40	48	edge	edge	NOUN
ejpam-1929	40	49	joins	join	VERB
ejpam-1929	40	50	two	two	NUM
ejpam-1929	40	51	vertices	vertex	NOUN
ejpam-1929	40	52	from	from	ADP
ejpam-1929	40	53	different	different	ADJ
ejpam-1929	40	54	subsets	subset	NOUN
ejpam-1929	40	55	.	.	PUNCT
ejpam-1929	41	1	the	the	DET
ejpam-1929	41	2	following	follow	VERB
ejpam-1929	41	3	important	important	ADJ
ejpam-1929	41	4	lemma	lemma	PROPN
ejpam-1929	41	5	on	on	ADP
ejpam-1929	41	6	balanced	balanced	ADJ
ejpam-1929	41	7	sigraphs	sigraph	NOUN
ejpam-1929	41	8	is	be	AUX
ejpam-1929	41	9	given	give	VERB
ejpam-1929	41	10	by	by	ADP
ejpam-1929	41	11	zaslavsky	zaslavsky	PROPN
ejpam-1929	41	12	:	:	PUNCT
ejpam-1929	41	13	d.	d.	PROPN
ejpam-1929	41	14	sinha	sinha	PROPN
ejpam-1929	41	15	,	,	PUNCT
ejpam-1929	41	16	a.	a.	NOUN
ejpam-1929	41	17	dhama	dhama	PROPN
ejpam-1929	41	18	,	,	PUNCT
ejpam-1929	41	19	b.	b.	PROPN
ejpam-1929	41	20	acharya	acharya	PROPN
ejpam-1929	41	21	/	/	SYM
ejpam-1929	41	22	eur	eur	PROPN
ejpam-1929	41	23	.	.	PUNCT
ejpam-1929	42	1	j.	j.	PROPN
ejpam-1929	42	2	pure	pure	PROPN
ejpam-1929	42	3	appl	appl	PROPN
ejpam-1929	42	4	.	.	PROPN
ejpam-1929	42	5	math	math	PROPN
ejpam-1929	42	6	,	,	PUNCT
ejpam-1929	42	7	6	6	NUM
ejpam-1929	42	8	(	(	PUNCT
ejpam-1929	42	9	2013	2013	NUM
ejpam-1929	42	10	)	)	PUNCT
ejpam-1929	42	11	,	,	PUNCT
ejpam-1929	42	12	189	189	NUM
ejpam-1929	42	13	-	-	SYM
ejpam-1929	42	14	210	210	NUM
ejpam-1929	42	15	191	191	NUM
ejpam-1929	42	16	lemma	lemma	PROPN
ejpam-1929	42	17	1	1	NUM
ejpam-1929	42	18	(	(	PUNCT
ejpam-1929	42	19	[	[	X
ejpam-1929	42	20	48	48	NUM
ejpam-1929	42	21	]	]	PUNCT
ejpam-1929	42	22	)	)	PUNCT
ejpam-1929	42	23	.	.	PUNCT
ejpam-1929	43	1	a	a	DET
ejpam-1929	43	2	sigraph	sigraph	NOUN
ejpam-1929	43	3	in	in	ADP
ejpam-1929	43	4	which	which	PRON
ejpam-1929	43	5	every	every	DET
ejpam-1929	43	6	chordless	chordless	ADJ
ejpam-1929	43	7	cycle	cycle	NOUN
ejpam-1929	43	8	is	be	AUX
ejpam-1929	43	9	positive	positive	ADJ
ejpam-1929	43	10	,	,	PUNCT
ejpam-1929	43	11	is	be	AUX
ejpam-1929	43	12	balanced	balanced	ADJ
ejpam-1929	43	13	.	.	PUNCT
ejpam-1929	44	1	1.3	1.3	NUM
ejpam-1929	44	2	.	.	PUNCT
ejpam-1929	45	1	the	the	DET
ejpam-1929	45	2	notion	notion	NOUN
ejpam-1929	45	3	of	of	ADP
ejpam-1929	45	4	clustering	cluster	VERB
ejpam-1929	45	5	in	in	ADP
ejpam-1929	45	6	a	a	DET
ejpam-1929	45	7	sigraph	sigraph	NOUN
ejpam-1929	45	8	a	a	DET
ejpam-1929	45	9	signed	sign	VERB
ejpam-1929	45	10	graph	graph	NOUN
ejpam-1929	45	11	is	be	AUX
ejpam-1929	45	12	said	say	VERB
ejpam-1929	45	13	to	to	PART
ejpam-1929	45	14	be	be	AUX
ejpam-1929	45	15	clusterable	clusterable	ADJ
ejpam-1929	45	16	if	if	SCONJ
ejpam-1929	45	17	its	its	PRON
ejpam-1929	45	18	vertex	vertex	NOUN
ejpam-1929	45	19	set	set	NOUN
ejpam-1929	45	20	can	can	AUX
ejpam-1929	45	21	be	be	AUX
ejpam-1929	45	22	partitioned	partition	VERB
ejpam-1929	45	23	into	into	ADP
ejpam-1929	45	24	pairwise	pairwise	NOUN
ejpam-1929	45	25	disjoint	disjoint	NOUN
ejpam-1929	45	26	subsets	subset	NOUN
ejpam-1929	45	27	,	,	PUNCT
ejpam-1929	45	28	called	call	VERB
ejpam-1929	45	29	clusters	cluster	NOUN
ejpam-1929	45	30	,	,	PUNCT
ejpam-1929	45	31	such	such	ADJ
ejpam-1929	45	32	that	that	SCONJ
ejpam-1929	45	33	every	every	DET
ejpam-1929	45	34	negative	negative	ADJ
ejpam-1929	45	35	edge	edge	NOUN
ejpam-1929	45	36	joins	join	VERB
ejpam-1929	45	37	vertices	vertex	NOUN
ejpam-1929	45	38	in	in	ADP
ejpam-1929	45	39	different	different	ADJ
ejpam-1929	45	40	clusters	cluster	NOUN
ejpam-1929	45	41	and	and	CCONJ
ejpam-1929	45	42	every	every	DET
ejpam-1929	45	43	positive	positive	ADJ
ejpam-1929	45	44	edge	edge	NOUN
ejpam-1929	45	45	joins	join	VERB
ejpam-1929	45	46	vertices	vertex	NOUN
ejpam-1929	45	47	in	in	ADP
ejpam-1929	45	48	the	the	DET
ejpam-1929	45	49	same	same	ADJ
ejpam-1929	45	50	cluster	cluster	NOUN
ejpam-1929	45	51	;	;	PUNCT
ejpam-1929	45	52	we	we	PRON
ejpam-1929	45	53	shall	shall	AUX
ejpam-1929	45	54	call	call	VERB
ejpam-1929	45	55	such	such	DET
ejpam-1929	45	56	a	a	DET
ejpam-1929	45	57	partition	partition	NOUN
ejpam-1929	45	58	a	a	DET
ejpam-1929	45	59	davis	davis	PROPN
ejpam-1929	45	60	partition	partition	NOUN
ejpam-1929	45	61	,	,	PUNCT
ejpam-1929	45	62	after	after	ADP
ejpam-1929	45	63	its	its	PRON
ejpam-1929	45	64	originator	originator	NOUN
ejpam-1929	45	65	[	[	X
ejpam-1929	45	66	19	19	NUM
ejpam-1929	45	67	]	]	X
ejpam-1929	45	68	,	,	PUNCT
ejpam-1929	45	69	or	or	CCONJ
ejpam-1929	45	70	a	a	DET
ejpam-1929	45	71	clustering	clustering	NOUN
ejpam-1929	45	72	[	[	X
ejpam-1929	45	73	16	16	NUM
ejpam-1929	45	74	]	]	PUNCT
ejpam-1929	45	75	.	.	PUNCT
ejpam-1929	46	1	clearly	clearly	ADV
ejpam-1929	46	2	,	,	PUNCT
ejpam-1929	46	3	every	every	DET
ejpam-1929	46	4	graph	graph	NOUN
ejpam-1929	46	5	,	,	PUNCT
ejpam-1929	46	6	treated	treat	VERB
ejpam-1929	46	7	as	as	ADP
ejpam-1929	46	8	an	an	DET
ejpam-1929	46	9	allpositive	allpositive	ADJ
ejpam-1929	46	10	sigraph	sigraph	NOUN
ejpam-1929	46	11	,	,	PUNCT
ejpam-1929	46	12	is	be	AUX
ejpam-1929	46	13	clusterable	clusterable	ADJ
ejpam-1929	46	14	with	with	ADP
ejpam-1929	46	15	its	its	PRON
ejpam-1929	46	16	entire	entire	ADJ
ejpam-1929	46	17	vertex	vertex	NOUN
ejpam-1929	46	18	set	set	NOUN
ejpam-1929	46	19	forming	form	VERB
ejpam-1929	46	20	a	a	DET
ejpam-1929	46	21	single	single	ADJ
ejpam-1929	46	22	cluster	cluster	NOUN
ejpam-1929	46	23	.	.	PUNCT
ejpam-1929	47	1	next	next	ADV
ejpam-1929	47	2	,	,	PUNCT
ejpam-1929	47	3	every	every	DET
ejpam-1929	47	4	heterogeneous	heterogeneous	ADJ
ejpam-1929	47	5	sigraph	sigraph	NOUN
ejpam-1929	47	6	is	be	AUX
ejpam-1929	47	7	balanced	balance	VERB
ejpam-1929	47	8	if	if	SCONJ
ejpam-1929	47	9	and	and	CCONJ
ejpam-1929	47	10	only	only	ADV
ejpam-1929	47	11	if	if	SCONJ
ejpam-1929	47	12	it	it	PRON
ejpam-1929	47	13	is	be	AUX
ejpam-1929	47	14	clusterable	clusterable	ADJ
ejpam-1929	47	15	with	with	ADP
ejpam-1929	47	16	exactly	exactly	ADV
ejpam-1929	47	17	two	two	NUM
ejpam-1929	47	18	clusters	cluster	NOUN
ejpam-1929	47	19	[	[	X
ejpam-1929	47	20	29	29	NUM
ejpam-1929	47	21	]	]	X
ejpam-1929	47	22	;	;	PUNCT
ejpam-1929	47	23	this	this	DET
ejpam-1929	47	24	particular	particular	ADJ
ejpam-1929	47	25	davis	davis	PROPN
ejpam-1929	47	26	partition	partition	NOUN
ejpam-1929	47	27	is	be	AUX
ejpam-1929	47	28	known	know	VERB
ejpam-1929	47	29	as	as	ADP
ejpam-1929	47	30	harary	harary	NOUN
ejpam-1929	47	31	bipartition	bipartition	NOUN
ejpam-1929	47	32	[	[	X
ejpam-1929	47	33	46	46	NUM
ejpam-1929	47	34	]	]	PUNCT
ejpam-1929	47	35	.	.	PUNCT
ejpam-1929	48	1	davis	davis	PROPN
ejpam-1929	49	1	[	[	X
ejpam-1929	49	2	19	19	NUM
ejpam-1929	49	3	]	]	PUNCT
ejpam-1929	49	4	characterized	characterize	VERB
ejpam-1929	49	5	clusterable	clusterable	ADJ
ejpam-1929	49	6	signed	sign	VERB
ejpam-1929	49	7	graphs	graph	NOUN
ejpam-1929	49	8	as	as	ADP
ejpam-1929	49	9	precisely	precisely	ADV
ejpam-1929	49	10	those	those	PRON
ejpam-1929	49	11	in	in	ADP
ejpam-1929	49	12	which	which	PRON
ejpam-1929	49	13	no	no	DET
ejpam-1929	49	14	cycle	cycle	NOUN
ejpam-1929	49	15	has	have	VERB
ejpam-1929	49	16	exactly	exactly	ADV
ejpam-1929	49	17	one	one	NUM
ejpam-1929	49	18	negative	negative	ADJ
ejpam-1929	49	19	edge	edge	NOUN
ejpam-1929	49	20	(	(	PUNCT
ejpam-1929	49	21	also	also	ADV
ejpam-1929	49	22	,	,	PUNCT
ejpam-1929	49	23	see	see	VERB
ejpam-1929	49	24	[	[	X
ejpam-1929	49	25	16	16	NUM
ejpam-1929	49	26	]	]	SYM
ejpam-1929	49	27	)	)	PUNCT
ejpam-1929	49	28	.	.	PUNCT
ejpam-1929	50	1	theorem	theorem	ADJ
ejpam-1929	50	2	2	2	NUM
ejpam-1929	50	3	(	(	PUNCT
ejpam-1929	50	4	[	[	X
ejpam-1929	50	5	19	19	NUM
ejpam-1929	50	6	]	]	NUM
ejpam-1929	50	7	)	)	PUNCT
ejpam-1929	50	8	.	.	PUNCT
ejpam-1929	51	1	a	a	DET
ejpam-1929	51	2	siraph	siraph	NOUN
ejpam-1929	51	3	s	s	VERB
ejpam-1929	51	4	is	be	AUX
ejpam-1929	51	5	clusterable	clusterable	ADJ
ejpam-1929	51	6	if	if	SCONJ
ejpam-1929	51	7	and	and	CCONJ
ejpam-1929	51	8	only	only	ADV
ejpam-1929	51	9	if	if	SCONJ
ejpam-1929	51	10	s	s	NOUN
ejpam-1929	51	11	contains	contain	VERB
ejpam-1929	51	12	no	no	DET
ejpam-1929	51	13	cycle	cycle	NOUN
ejpam-1929	51	14	with	with	ADP
ejpam-1929	51	15	exactly	exactly	ADV
ejpam-1929	51	16	one	one	NUM
ejpam-1929	51	17	negative	negative	ADJ
ejpam-1929	51	18	edge	edge	NOUN
ejpam-1929	51	19	.	.	PUNCT
ejpam-1929	52	1	1.4	1.4	NUM
ejpam-1929	52	2	.	.	PUNCT
ejpam-1929	53	1	the	the	DET
ejpam-1929	53	2	notions	notion	NOUN
ejpam-1929	53	3	of	of	ADP
ejpam-1929	53	4	consistency	consistency	NOUN
ejpam-1929	53	5	and	and	CCONJ
ejpam-1929	53	6	sign	sign	NOUN
ejpam-1929	53	7	-	-	PUNCT
ejpam-1929	53	8	compatibility	compatibility	NOUN
ejpam-1929	53	9	in	in	ADP
ejpam-1929	53	10	a	a	DET
ejpam-1929	53	11	sigraph	sigraph	NOUN
ejpam-1929	53	12	a	a	DET
ejpam-1929	53	13	marked	mark	VERB
ejpam-1929	53	14	sigraph	sigraph	NOUN
ejpam-1929	53	15	is	be	AUX
ejpam-1929	53	16	an	an	DET
ejpam-1929	53	17	ordered	order	VERB
ejpam-1929	53	18	pair	pair	NOUN
ejpam-1929	53	19	sµ	sµ	NOUN
ejpam-1929	53	20	=	=	SYM
ejpam-1929	53	21	(	(	PUNCT
ejpam-1929	53	22	s,µ	s,µ	X
ejpam-1929	53	23	)	)	PUNCT
ejpam-1929	53	24	where	where	SCONJ
ejpam-1929	53	25	s	s	VERB
ejpam-1929	53	26	=	=	SYM
ejpam-1929	53	27	(	(	PUNCT
ejpam-1929	53	28	su	su	PROPN
ejpam-1929	53	29	,	,	PUNCT
ejpam-1929	53	30	σ	σ	PROPN
ejpam-1929	53	31	)	)	PUNCT
ejpam-1929	53	32	is	be	AUX
ejpam-1929	53	33	a	a	DET
ejpam-1929	53	34	sigraph	sigraph	NOUN
ejpam-1929	53	35	and	and	CCONJ
ejpam-1929	53	36	µ	µ	NOUN
ejpam-1929	53	37	:	:	PUNCT
ejpam-1929	53	38	v	v	NOUN
ejpam-1929	53	39	(	(	PUNCT
ejpam-1929	53	40	su)→	su)→	NOUN
ejpam-1929	53	41	{	{	PUNCT
ejpam-1929	53	42	+	+	NOUN
ejpam-1929	53	43	,	,	PUNCT
ejpam-1929	53	44	−	−	NOUN
ejpam-1929	53	45	}	}	PUNCT
ejpam-1929	53	46	is	be	AUX
ejpam-1929	53	47	a	a	DET
ejpam-1929	53	48	function	function	NOUN
ejpam-1929	53	49	from	from	ADP
ejpam-1929	53	50	the	the	DET
ejpam-1929	53	51	vertex	vertex	NOUN
ejpam-1929	53	52	set	set	VERB
ejpam-1929	53	53	v	v	NOUN
ejpam-1929	53	54	(	(	PUNCT
ejpam-1929	53	55	su	su	NOUN
ejpam-1929	53	56	)	)	PUNCT
ejpam-1929	53	57	of	of	ADP
ejpam-1929	53	58	su	su	PROPN
ejpam-1929	53	59	into	into	ADP
ejpam-1929	53	60	the	the	DET
ejpam-1929	53	61	set	set	NOUN
ejpam-1929	53	62	{	{	PUNCT
ejpam-1929	53	63	+	+	NOUN
ejpam-1929	53	64	,	,	PUNCT
ejpam-1929	53	65	−	−	PROPN
ejpam-1929	53	66	}	}	PUNCT
ejpam-1929	53	67	,	,	PUNCT
ejpam-1929	53	68	called	call	VERB
ejpam-1929	53	69	a	a	DET
ejpam-1929	53	70	marking	marking	NOUN
ejpam-1929	53	71	of	of	ADP
ejpam-1929	53	72	s.	s.	PROPN
ejpam-1929	53	73	a	a	DET
ejpam-1929	53	74	cycle	cycle	NOUN
ejpam-1929	53	75	z	z	NOUN
ejpam-1929	53	76	in	in	ADP
ejpam-1929	53	77	sµ	sµ	PROPN
ejpam-1929	53	78	is	be	AUX
ejpam-1929	53	79	said	say	VERB
ejpam-1929	53	80	to	to	PART
ejpam-1929	53	81	be	be	AUX
ejpam-1929	53	82	consistent	consistent	ADJ
ejpam-1929	53	83	if	if	SCONJ
ejpam-1929	53	84	it	it	PRON
ejpam-1929	53	85	contains	contain	VERB
ejpam-1929	53	86	an	an	DET
ejpam-1929	53	87	even	even	ADJ
ejpam-1929	53	88	number	number	NOUN
ejpam-1929	53	89	of	of	ADP
ejpam-1929	53	90	negative	negative	ADJ
ejpam-1929	53	91	vertices	vertex	NOUN
ejpam-1929	53	92	.	.	PUNCT
ejpam-1929	54	1	a	a	DET
ejpam-1929	54	2	given	give	VERB
ejpam-1929	54	3	sigraph	sigraph	NOUN
ejpam-1929	54	4	s	s	PART
ejpam-1929	54	5	is	be	AUX
ejpam-1929	54	6	said	say	VERB
ejpam-1929	54	7	to	to	PART
ejpam-1929	54	8	be	be	AUX
ejpam-1929	54	9	consistent	consistent	ADJ
ejpam-1929	54	10	if	if	SCONJ
ejpam-1929	54	11	every	every	DET
ejpam-1929	54	12	cycle	cycle	NOUN
ejpam-1929	54	13	in	in	ADP
ejpam-1929	54	14	it	it	PRON
ejpam-1929	54	15	is	be	AUX
ejpam-1929	54	16	consistent	consistent	ADJ
ejpam-1929	54	17	[	[	X
ejpam-1929	54	18	2	2	NUM
ejpam-1929	54	19	]	]	PUNCT
ejpam-1929	54	20	;	;	PUNCT
ejpam-1929	54	21	for	for	ADP
ejpam-1929	54	22	digraphs	digraph	NOUN
ejpam-1929	54	23	,	,	PUNCT
ejpam-1929	54	24	the	the	DET
ejpam-1929	54	25	notion	notion	NOUN
ejpam-1929	54	26	was	be	AUX
ejpam-1929	54	27	due	due	ADJ
ejpam-1929	54	28	to	to	PART
ejpam-1929	54	29	beineke	beineke	VERB
ejpam-1929	54	30	and	and	CCONJ
ejpam-1929	54	31	harary	harary	NOUN
ejpam-1929	54	32	[	[	X
ejpam-1929	54	33	11	11	NUM
ejpam-1929	54	34	,	,	PUNCT
ejpam-1929	54	35	12	12	NUM
ejpam-1929	54	36	]	]	PUNCT
ejpam-1929	54	37	.	.	PUNCT
ejpam-1929	55	1	in	in	ADP
ejpam-1929	55	2	particular	particular	ADJ
ejpam-1929	55	3	,	,	PUNCT
ejpam-1929	55	4	σ	σ	PROPN
ejpam-1929	55	5	induces	induce	VERB
ejpam-1929	55	6	a	a	DET
ejpam-1929	55	7	unique	unique	ADJ
ejpam-1929	55	8	marking	marking	NOUN
ejpam-1929	55	9	µσ	µσ	ADV
ejpam-1929	55	10	defined	define	VERB
ejpam-1929	55	11	by	by	ADP
ejpam-1929	55	12	µσ(v	µσ(v	NOUN
ejpam-1929	55	13	)	)	PUNCT
ejpam-1929	55	14	=	=	SYM
ejpam-1929	55	15	∏	∏	PROPN
ejpam-1929	55	16	e	e	PROPN
ejpam-1929	55	17	j∈ev	j∈ev	PROPN
ejpam-1929	55	18	σ(e	σ(e	PROPN
ejpam-1929	55	19	j	j	PROPN
ejpam-1929	55	20	)	)	PUNCT
ejpam-1929	55	21	,	,	PUNCT
ejpam-1929	55	22	v	v	X
ejpam-1929	55	23	∈	∈	PROPN
ejpam-1929	55	24	v	v	ADP
ejpam-1929	55	25	(	(	PUNCT
ejpam-1929	55	26	s	s	NOUN
ejpam-1929	55	27	)	)	PUNCT
ejpam-1929	55	28	,	,	PUNCT
ejpam-1929	55	29	is	be	AUX
ejpam-1929	55	30	called	call	VERB
ejpam-1929	55	31	the	the	DET
ejpam-1929	55	32	canonical	canonical	ADJ
ejpam-1929	55	33	marking	marking	NOUN
ejpam-1929	55	34	(	(	PUNCT
ejpam-1929	55	35	or	or	CCONJ
ejpam-1929	55	36	,	,	PUNCT
ejpam-1929	55	37	c	c	PROPN
ejpam-1929	55	38	-marking	-marke	VERB
ejpam-1929	55	39	in	in	ADP
ejpam-1929	55	40	short	short	ADJ
ejpam-1929	55	41	)	)	PUNCT
ejpam-1929	55	42	of	of	ADP
ejpam-1929	55	43	s	s	PROPN
ejpam-1929	55	44	,	,	PUNCT
ejpam-1929	55	45	where	where	SCONJ
ejpam-1929	55	46	ev	ev	PROPN
ejpam-1929	55	47	is	be	AUX
ejpam-1929	55	48	the	the	DET
ejpam-1929	55	49	set	set	NOUN
ejpam-1929	55	50	of	of	ADP
ejpam-1929	55	51	edges	edge	NOUN
ejpam-1929	55	52	e	e	PROPN
ejpam-1929	55	53	j	j	PROPN
ejpam-1929	55	54	incident	incident	NOUN
ejpam-1929	55	55	at	at	ADP
ejpam-1929	55	56	v	v	NUM
ejpam-1929	55	57	in	in	ADP
ejpam-1929	55	58	s	s	PRON
ejpam-1929	55	59	[	[	X
ejpam-1929	55	60	40	40	NUM
ejpam-1929	55	61	]	]	PUNCT
ejpam-1929	55	62	.	.	PUNCT
ejpam-1929	56	1	now	now	ADV
ejpam-1929	56	2	,	,	PUNCT
ejpam-1929	56	3	if	if	SCONJ
ejpam-1929	56	4	every	every	DET
ejpam-1929	56	5	vertex	vertex	NOUN
ejpam-1929	56	6	of	of	ADP
ejpam-1929	56	7	a	a	DET
ejpam-1929	56	8	given	give	VERB
ejpam-1929	56	9	sigraph	sigraph	NOUN
ejpam-1929	56	10	s	s	PART
ejpam-1929	56	11	is	be	AUX
ejpam-1929	56	12	canonically	canonically	ADV
ejpam-1929	56	13	marked	mark	VERB
ejpam-1929	56	14	,	,	PUNCT
ejpam-1929	56	15	then	then	ADV
ejpam-1929	56	16	a	a	DET
ejpam-1929	56	17	cycle	cycle	NOUN
ejpam-1929	56	18	z	z	NOUN
ejpam-1929	56	19	in	in	ADP
ejpam-1929	56	20	s	s	PROPN
ejpam-1929	56	21	is	be	AUX
ejpam-1929	56	22	said	say	VERB
ejpam-1929	56	23	to	to	PART
ejpam-1929	56	24	be	be	AUX
ejpam-1929	56	25	canonically	canonically	ADV
ejpam-1929	56	26	consistent	consistent	ADJ
ejpam-1929	56	27	(	(	PUNCT
ejpam-1929	56	28	c	c	NOUN
ejpam-1929	56	29	-consistent	-consistent	NOUN
ejpam-1929	56	30	)	)	PUNCT
ejpam-1929	56	31	if	if	SCONJ
ejpam-1929	56	32	it	it	PRON
ejpam-1929	56	33	contains	contain	VERB
ejpam-1929	56	34	an	an	DET
ejpam-1929	56	35	even	even	ADJ
ejpam-1929	56	36	number	number	NOUN
ejpam-1929	56	37	of	of	ADP
ejpam-1929	56	38	negative	negative	ADJ
ejpam-1929	56	39	vertices	vertex	NOUN
ejpam-1929	56	40	and	and	CCONJ
ejpam-1929	56	41	the	the	DET
ejpam-1929	56	42	given	give	VERB
ejpam-1929	56	43	sigraph	sigraph	NOUN
ejpam-1929	56	44	s	s	PART
ejpam-1929	56	45	is	be	AUX
ejpam-1929	56	46	said	say	VERB
ejpam-1929	56	47	be	be	AUX
ejpam-1929	56	48	c	c	NOUN
ejpam-1929	56	49	-consistent	-consistent	ADJ
ejpam-1929	56	50	if	if	SCONJ
ejpam-1929	56	51	every	every	DET
ejpam-1929	56	52	cycle	cycle	NOUN
ejpam-1929	56	53	in	in	ADP
ejpam-1929	56	54	it	it	PRON
ejpam-1929	56	55	is	be	AUX
ejpam-1929	56	56	c	c	NOUN
ejpam-1929	56	57	-consistent	-consistent	NOUN
ejpam-1929	56	58	.	.	PUNCT
ejpam-1929	57	1	thus	thus	ADV
ejpam-1929	57	2	,	,	PUNCT
ejpam-1929	57	3	the	the	DET
ejpam-1929	57	4	original	original	ADJ
ejpam-1929	57	5	notion	notion	NOUN
ejpam-1929	57	6	of	of	ADP
ejpam-1929	57	7	consistent	consistent	ADJ
ejpam-1929	57	8	graphs	graph	NOUN
ejpam-1929	57	9	due	due	ADJ
ejpam-1929	57	10	to	to	ADP
ejpam-1929	57	11	beineke	beineke	VERB
ejpam-1929	57	12	and	and	CCONJ
ejpam-1929	57	13	harary	harary	NOUN
ejpam-1929	57	14	[	[	X
ejpam-1929	57	15	11	11	NUM
ejpam-1929	57	16	,	,	PUNCT
ejpam-1929	57	17	12	12	NUM
ejpam-1929	57	18	]	]	PUNCT
ejpam-1929	57	19	reduces	reduce	VERB
ejpam-1929	57	20	to	to	ADP
ejpam-1929	57	21	that	that	PRON
ejpam-1929	57	22	of	of	ADP
ejpam-1929	57	23	trivial	trivial	ADJ
ejpam-1929	57	24	c	c	NOUN
ejpam-1929	57	25	-consistency	-consistency	NOUN
ejpam-1929	57	26	,	,	PUNCT
ejpam-1929	57	27	when	when	SCONJ
ejpam-1929	57	28	all	all	DET
ejpam-1929	57	29	the	the	DET
ejpam-1929	57	30	vertices	vertex	NOUN
ejpam-1929	57	31	receive	receive	VERB
ejpam-1929	57	32	‘	'	PUNCT
ejpam-1929	57	33	+	+	ADJ
ejpam-1929	57	34	’	'	PUNCT
ejpam-1929	57	35	.	.	PUNCT
ejpam-1929	58	1	although	although	SCONJ
ejpam-1929	58	2	consistent	consistent	ADJ
ejpam-1929	58	3	digraphs	digraph	NOUN
ejpam-1929	58	4	were	be	AUX
ejpam-1929	58	5	neatly	neatly	ADV
ejpam-1929	58	6	characterized	characterize	VERB
ejpam-1929	58	7	in	in	ADP
ejpam-1929	58	8	[	[	PUNCT
ejpam-1929	58	9	11	11	NUM
ejpam-1929	58	10	,	,	PUNCT
ejpam-1929	58	11	12	12	NUM
ejpam-1929	58	12	]	]	PUNCT
ejpam-1929	58	13	,	,	PUNCT
ejpam-1929	58	14	the	the	DET
ejpam-1929	58	15	problem	problem	NOUN
ejpam-1929	58	16	of	of	ADP
ejpam-1929	58	17	characterizing	characterize	VERB
ejpam-1929	58	18	consistent	consistent	ADJ
ejpam-1929	58	19	marked	mark	VERB
ejpam-1929	58	20	graphs	graph	NOUN
ejpam-1929	58	21	was	be	AUX
ejpam-1929	58	22	declared	declare	VERB
ejpam-1929	58	23	open	open	ADJ
ejpam-1929	58	24	by	by	ADP
ejpam-1929	58	25	beineke	beineke	ADJ
ejpam-1929	58	26	and	and	CCONJ
ejpam-1929	58	27	harary	harary	NOUN
ejpam-1929	59	1	[	[	X
ejpam-1929	59	2	11	11	NUM
ejpam-1929	59	3	]	]	X
ejpam-1929	59	4	;	;	PUNCT
ejpam-1929	59	5	subsequently	subsequently	ADV
ejpam-1929	59	6	,	,	PUNCT
ejpam-1929	59	7	it	it	PRON
ejpam-1929	59	8	was	be	AUX
ejpam-1929	59	9	solved	solve	VERB
ejpam-1929	59	10	successfully	successfully	ADV
ejpam-1929	59	11	by	by	ADP
ejpam-1929	59	12	many	many	ADJ
ejpam-1929	59	13	authors	author	NOUN
ejpam-1929	59	14	(	(	PUNCT
ejpam-1929	59	15	see	see	VERB
ejpam-1929	59	16	[	[	X
ejpam-1929	59	17	46	46	NUM
ejpam-1929	59	18	]	]	PUNCT
ejpam-1929	59	19	for	for	ADP
ejpam-1929	59	20	a	a	DET
ejpam-1929	59	21	comprehensive	comprehensive	ADJ
ejpam-1929	59	22	appraisal	appraisal	NOUN
ejpam-1929	59	23	)	)	PUNCT
ejpam-1929	59	24	.	.	PUNCT
ejpam-1929	60	1	however	however	ADV
ejpam-1929	60	2	,	,	PUNCT
ejpam-1929	60	3	characterization	characterization	NOUN
ejpam-1929	60	4	of	of	ADP
ejpam-1929	60	5	c	c	NOUN
ejpam-1929	60	6	-consistent	-consistent	PROPN
ejpam-1929	60	7	sigraphs	sigraph	NOUN
ejpam-1929	60	8	is	be	AUX
ejpam-1929	60	9	still	still	ADV
ejpam-1929	60	10	an	an	DET
ejpam-1929	60	11	open	open	ADJ
ejpam-1929	60	12	problem	problem	NOUN
ejpam-1929	60	13	.	.	PUNCT
ejpam-1929	61	1	d.	d.	PROPN
ejpam-1929	61	2	sinha	sinha	PROPN
ejpam-1929	61	3	,	,	PUNCT
ejpam-1929	61	4	a.	a.	NOUN
ejpam-1929	61	5	dhama	dhama	PROPN
ejpam-1929	61	6	,	,	PUNCT
ejpam-1929	61	7	b.	b.	PROPN
ejpam-1929	61	8	acharya	acharya	PROPN
ejpam-1929	61	9	/	/	SYM
ejpam-1929	61	10	eur	eur	PROPN
ejpam-1929	61	11	.	.	PUNCT
ejpam-1929	62	1	j.	j.	PROPN
ejpam-1929	62	2	pure	pure	PROPN
ejpam-1929	62	3	appl	appl	PROPN
ejpam-1929	62	4	.	.	PROPN
ejpam-1929	62	5	math	math	PROPN
ejpam-1929	62	6	,	,	PUNCT
ejpam-1929	62	7	6	6	NUM
ejpam-1929	62	8	(	(	PUNCT
ejpam-1929	62	9	2013	2013	NUM
ejpam-1929	62	10	)	)	PUNCT
ejpam-1929	62	11	,	,	PUNCT
ejpam-1929	62	12	189	189	NUM
ejpam-1929	62	13	-	-	SYM
ejpam-1929	62	14	210	210	NUM
ejpam-1929	62	15	192	192	NUM
ejpam-1929	62	16	a	a	DET
ejpam-1929	62	17	sigraph	sigraph	NOUN
ejpam-1929	62	18	s	s	PART
ejpam-1929	62	19	is	be	AUX
ejpam-1929	62	20	sign	sign	NOUN
ejpam-1929	62	21	-	-	PUNCT
ejpam-1929	62	22	compatible	compatible	ADJ
ejpam-1929	62	23	[	[	X
ejpam-1929	62	24	40	40	NUM
ejpam-1929	62	25	]	]	PUNCT
ejpam-1929	62	26	if	if	SCONJ
ejpam-1929	62	27	there	there	PRON
ejpam-1929	62	28	exists	exist	VERB
ejpam-1929	62	29	a	a	DET
ejpam-1929	62	30	marking	marking	NOUN
ejpam-1929	62	31	µ	µ	NOUN
ejpam-1929	62	32	of	of	ADP
ejpam-1929	62	33	its	its	PRON
ejpam-1929	62	34	vertices	vertex	NOUN
ejpam-1929	62	35	such	such	ADJ
ejpam-1929	62	36	that	that	SCONJ
ejpam-1929	62	37	the	the	DET
ejpam-1929	62	38	end	end	NOUN
ejpam-1929	62	39	vertices	vertex	NOUN
ejpam-1929	62	40	of	of	ADP
ejpam-1929	62	41	every	every	DET
ejpam-1929	62	42	negative	negative	ADJ
ejpam-1929	62	43	edge	edge	NOUN
ejpam-1929	62	44	receive	receive	VERB
ejpam-1929	62	45	‘	'	PUNCT
ejpam-1929	62	46	-1	-1	NOUN
ejpam-1929	62	47	’	'	PUNCT
ejpam-1929	62	48	marks	mark	NOUN
ejpam-1929	62	49	in	in	ADP
ejpam-1929	62	50	µ	µ	NOUN
ejpam-1929	62	51	and	and	CCONJ
ejpam-1929	62	52	no	no	DET
ejpam-1929	62	53	positive	positive	ADJ
ejpam-1929	62	54	edge	edge	NOUN
ejpam-1929	62	55	in	in	ADP
ejpam-1929	62	56	s	s	PROPN
ejpam-1929	62	57	has	have	AUX
ejpam-1929	62	58	both	both	PRON
ejpam-1929	62	59	of	of	ADP
ejpam-1929	62	60	its	its	PRON
ejpam-1929	62	61	ends	end	NOUN
ejpam-1929	62	62	assigned	assign	VERB
ejpam-1929	62	63	‘	'	PUNCT
ejpam-1929	62	64	-1	-1	NOUN
ejpam-1929	62	65	’	'	PUNCT
ejpam-1929	62	66	marks	mark	NOUN
ejpam-1929	62	67	in	in	ADP
ejpam-1929	62	68	µ.	µ.	NOUN
ejpam-1929	62	69	sign	sign	PROPN
ejpam-1929	62	70	-	-	PUNCT
ejpam-1929	62	71	incompatible	incompatible	ADJ
ejpam-1929	62	72	otherwise	otherwise	ADV
ejpam-1929	62	73	.	.	PUNCT
ejpam-1929	63	1	the	the	DET
ejpam-1929	63	2	notion	notion	NOUN
ejpam-1929	63	3	of	of	ADP
ejpam-1929	63	4	sign	sign	NOUN
ejpam-1929	63	5	-	-	PUNCT
ejpam-1929	63	6	compatibility	compatibility	NOUN
ejpam-1929	63	7	arises	arise	VERB
ejpam-1929	63	8	naturally	naturally	ADV
ejpam-1929	63	9	in	in	ADP
ejpam-1929	63	10	the	the	DET
ejpam-1929	63	11	characterization	characterization	NOUN
ejpam-1929	63	12	of	of	ADP
ejpam-1929	63	13	line	line	NOUN
ejpam-1929	63	14	sigraphs	sigraph	VERB
ejpam-1929	64	1	[	[	X
ejpam-1929	64	2	5	5	NUM
ejpam-1929	64	3	]	]	PUNCT
ejpam-1929	64	4	.	.	PUNCT
ejpam-1929	65	1	1.5	1.5	NUM
ejpam-1929	65	2	.	.	PUNCT
ejpam-1929	66	1	some	some	DET
ejpam-1929	66	2	notions	notion	NOUN
ejpam-1929	66	3	of	of	ADP
ejpam-1929	66	4	derived	derive	VERB
ejpam-1929	66	5	sigraphs	sigraph	NOUN
ejpam-1929	66	6	there	there	PRON
ejpam-1929	66	7	are	be	VERB
ejpam-1929	66	8	many	many	ADJ
ejpam-1929	66	9	notions	notion	NOUN
ejpam-1929	66	10	of	of	ADP
ejpam-1929	66	11	sigraphs	sigraph	NOUN
ejpam-1929	66	12	derived	derive	VERB
ejpam-1929	66	13	from	from	ADP
ejpam-1929	66	14	a	a	DET
ejpam-1929	66	15	given	give	VERB
ejpam-1929	66	16	sigraph	sigraph	NOUN
ejpam-1929	66	17	,	,	PUNCT
ejpam-1929	66	18	generically	generically	ADV
ejpam-1929	66	19	addressed	address	VERB
ejpam-1929	66	20	here	here	ADV
ejpam-1929	66	21	as	as	ADP
ejpam-1929	66	22	‘	'	PUNCT
ejpam-1929	66	23	derived	derived	ADJ
ejpam-1929	66	24	sigraphs	sigraph	NOUN
ejpam-1929	66	25	’	'	PUNCT
ejpam-1929	66	26	.	.	PUNCT
ejpam-1929	67	1	some	some	PRON
ejpam-1929	67	2	of	of	ADP
ejpam-1929	67	3	them	they	PRON
ejpam-1929	67	4	considered	consider	VERB
ejpam-1929	67	5	in	in	ADP
ejpam-1929	67	6	our	our	PRON
ejpam-1929	67	7	investigations	investigation	NOUN
ejpam-1929	67	8	include	include	VERB
ejpam-1929	67	9	the	the	DET
ejpam-1929	67	10	following	follow	VERB
ejpam-1929	67	11	ones	one	NOUN
ejpam-1929	67	12	.	.	PUNCT
ejpam-1929	68	1	for	for	ADP
ejpam-1929	68	2	a	a	DET
ejpam-1929	68	3	sigraph	sigraph	NOUN
ejpam-1929	68	4	s	s	PROPN
ejpam-1929	68	5	,	,	PUNCT
ejpam-1929	68	6	behzad	behzad	PROPN
ejpam-1929	68	7	and	and	CCONJ
ejpam-1929	68	8	chartrand	chartrand	NOUN
ejpam-1929	68	9	[	[	X
ejpam-1929	68	10	10	10	NUM
ejpam-1929	68	11	]	]	PUNCT
ejpam-1929	68	12	defined	define	VERB
ejpam-1929	68	13	its	its	PRON
ejpam-1929	68	14	line	line	NOUN
ejpam-1929	68	15	sigraph	sigraph	NOUN
ejpam-1929	68	16	,	,	PUNCT
ejpam-1929	68	17	l(s	l(s	PROPN
ejpam-1929	68	18	)	)	PUNCT
ejpam-1929	68	19	as	as	ADP
ejpam-1929	68	20	the	the	DET
ejpam-1929	68	21	sigraph	sigraph	NOUN
ejpam-1929	68	22	in	in	ADP
ejpam-1929	68	23	which	which	PRON
ejpam-1929	68	24	the	the	DET
ejpam-1929	68	25	edges	edge	NOUN
ejpam-1929	68	26	of	of	ADP
ejpam-1929	68	27	s	s	NOUN
ejpam-1929	68	28	are	be	AUX
ejpam-1929	68	29	represented	represent	VERB
ejpam-1929	68	30	as	as	ADP
ejpam-1929	68	31	vertices	vertex	NOUN
ejpam-1929	68	32	,	,	PUNCT
ejpam-1929	68	33	two	two	NUM
ejpam-1929	68	34	of	of	ADP
ejpam-1929	68	35	these	these	DET
ejpam-1929	68	36	vertices	vertex	NOUN
ejpam-1929	68	37	are	be	AUX
ejpam-1929	68	38	defined	define	VERB
ejpam-1929	68	39	adjacent	adjacent	ADJ
ejpam-1929	68	40	whenever	whenever	SCONJ
ejpam-1929	68	41	the	the	DET
ejpam-1929	68	42	corresponding	corresponding	ADJ
ejpam-1929	68	43	edges	edge	NOUN
ejpam-1929	68	44	in	in	ADP
ejpam-1929	68	45	s	s	NOUN
ejpam-1929	68	46	have	have	VERB
ejpam-1929	68	47	a	a	DET
ejpam-1929	68	48	vertex	vertex	NOUN
ejpam-1929	68	49	in	in	ADP
ejpam-1929	68	50	common	common	ADJ
ejpam-1929	68	51	,	,	PUNCT
ejpam-1929	68	52	any	any	DET
ejpam-1929	68	53	such	such	ADJ
ejpam-1929	68	54	edge	edge	NOUN
ejpam-1929	68	55	e	e	AUX
ejpam-1929	68	56	f	f	PROPN
ejpam-1929	68	57	is	be	AUX
ejpam-1929	68	58	defined	define	VERB
ejpam-1929	68	59	to	to	PART
ejpam-1929	68	60	be	be	AUX
ejpam-1929	68	61	negative	negative	ADJ
ejpam-1929	68	62	whenever	whenever	SCONJ
ejpam-1929	68	63	both	both	DET
ejpam-1929	68	64	e	e	NOUN
ejpam-1929	68	65	and	and	CCONJ
ejpam-1929	68	66	f	f	PROPN
ejpam-1929	68	67	are	be	AUX
ejpam-1929	68	68	negative	negative	ADJ
ejpam-1929	68	69	edges	edge	NOUN
ejpam-1929	68	70	in	in	ADP
ejpam-1929	68	71	s.	s.	PROPN
ejpam-1929	68	72	for	for	ADP
ejpam-1929	68	73	a	a	DET
ejpam-1929	68	74	sigraph	sigraph	NOUN
ejpam-1929	68	75	s	s	NOUN
ejpam-1929	68	76	,	,	PUNCT
ejpam-1929	68	77	gill	gill	PROPN
ejpam-1929	69	1	[	[	X
ejpam-1929	69	2	24	24	NUM
ejpam-1929	69	3	]	]	PUNCT
ejpam-1929	69	4	defined	define	VERB
ejpam-1929	69	5	its×-line	its×-line	ADJ
ejpam-1929	69	6	sigraph	sigraph	NOUN
ejpam-1929	69	7	l×(s	l×(s	PROPN
ejpam-1929	69	8	)	)	PUNCT
ejpam-1929	69	9	as	as	SCONJ
ejpam-1929	69	10	follows	follow	VERB
ejpam-1929	69	11	:	:	PUNCT
ejpam-1929	69	12	the	the	DET
ejpam-1929	69	13	l×(s	l×(s	NOUN
ejpam-1929	69	14	)	)	PUNCT
ejpam-1929	69	15	is	be	AUX
ejpam-1929	69	16	a	a	DET
ejpam-1929	69	17	sigraph	sigraph	NOUN
ejpam-1929	69	18	defined	define	VERB
ejpam-1929	69	19	on	on	ADP
ejpam-1929	69	20	the	the	DET
ejpam-1929	69	21	line	line	NOUN
ejpam-1929	69	22	graph	graph	NOUN
ejpam-1929	69	23	l(su	l(su	ADJ
ejpam-1929	69	24	)	)	PUNCT
ejpam-1929	69	25	of	of	ADP
ejpam-1929	69	26	the	the	DET
ejpam-1929	69	27	graph	graph	NOUN
ejpam-1929	69	28	su	su	INTJ
ejpam-1929	69	29	by	by	ADP
ejpam-1929	69	30	assigning	assign	VERB
ejpam-1929	69	31	to	to	ADP
ejpam-1929	69	32	each	each	DET
ejpam-1929	69	33	edge	edge	NOUN
ejpam-1929	69	34	e	e	NOUN
ejpam-1929	69	35	f	f	NOUN
ejpam-1929	69	36	of	of	ADP
ejpam-1929	69	37	l(su	l(su	PROPN
ejpam-1929	69	38	)	)	PUNCT
ejpam-1929	69	39	,	,	PUNCT
ejpam-1929	69	40	the	the	DET
ejpam-1929	69	41	product	product	NOUN
ejpam-1929	69	42	of	of	ADP
ejpam-1929	69	43	signs	sign	NOUN
ejpam-1929	69	44	of	of	ADP
ejpam-1929	69	45	the	the	DET
ejpam-1929	69	46	adjacent	adjacent	ADJ
ejpam-1929	69	47	edges	edge	NOUN
ejpam-1929	69	48	e	e	NOUN
ejpam-1929	69	49	and	and	CCONJ
ejpam-1929	69	50	f	f	PROPN
ejpam-1929	69	51	of	of	ADP
ejpam-1929	69	52	s.	s.	PROPN
ejpam-1929	69	53	for	for	ADP
ejpam-1929	69	54	a	a	DET
ejpam-1929	69	55	sigraph	sigraph	NOUN
ejpam-1929	69	56	s	s	PROPN
ejpam-1929	69	57	,	,	PUNCT
ejpam-1929	69	58	acharya	acharya	PROPN
ejpam-1929	69	59	and	and	CCONJ
ejpam-1929	69	60	sinha	sinha	NOUN
ejpam-1929	69	61	[	[	X
ejpam-1929	69	62	6	6	NUM
ejpam-1929	69	63	]	]	PUNCT
ejpam-1929	69	64	defined	define	VERB
ejpam-1929	69	65	its	its	PRON
ejpam-1929	69	66	common	common	ADJ
ejpam-1929	69	67	-	-	PUNCT
ejpam-1929	69	68	edge	edge	NOUN
ejpam-1929	69	69	sigraph	sigraph	NOUN
ejpam-1929	69	70	ce(s	ce(s	ADV
ejpam-1929	69	71	)	)	PUNCT
ejpam-1929	69	72	as	as	ADP
ejpam-1929	69	73	the	the	DET
ejpam-1929	69	74	sigraph	sigraph	NOUN
ejpam-1929	69	75	whose	whose	DET
ejpam-1929	69	76	vertex	vertex	NOUN
ejpam-1929	69	77	set	set	NOUN
ejpam-1929	69	78	is	be	AUX
ejpam-1929	69	79	the	the	DET
ejpam-1929	69	80	set	set	NOUN
ejpam-1929	69	81	of	of	ADP
ejpam-1929	69	82	pairs	pair	NOUN
ejpam-1929	69	83	of	of	ADP
ejpam-1929	69	84	adjacent	adjacent	ADJ
ejpam-1929	69	85	edges	edge	NOUN
ejpam-1929	69	86	in	in	ADP
ejpam-1929	69	87	s	s	PRON
ejpam-1929	69	88	and	and	CCONJ
ejpam-1929	69	89	two	two	NUM
ejpam-1929	69	90	vertices	vertex	NOUN
ejpam-1929	69	91	of	of	ADP
ejpam-1929	69	92	ce(s	ce(s	ADJ
ejpam-1929	69	93	)	)	PUNCT
ejpam-1929	69	94	are	be	AUX
ejpam-1929	69	95	adjacent	adjacent	ADJ
ejpam-1929	69	96	if	if	SCONJ
ejpam-1929	69	97	the	the	DET
ejpam-1929	69	98	corresponding	correspond	VERB
ejpam-1929	69	99	pairs	pair	NOUN
ejpam-1929	69	100	of	of	ADP
ejpam-1929	69	101	adjacent	adjacent	ADJ
ejpam-1929	69	102	edges	edge	NOUN
ejpam-1929	69	103	of	of	ADP
ejpam-1929	69	104	s	s	PRON
ejpam-1929	69	105	have	have	VERB
ejpam-1929	69	106	exactly	exactly	ADV
ejpam-1929	69	107	one	one	NUM
ejpam-1929	69	108	edge	edge	NOUN
ejpam-1929	69	109	in	in	ADP
ejpam-1929	69	110	common	common	ADJ
ejpam-1929	69	111	,	,	PUNCT
ejpam-1929	69	112	with	with	ADP
ejpam-1929	69	113	the	the	DET
ejpam-1929	69	114	sign	sign	NOUN
ejpam-1929	69	115	same	same	ADJ
ejpam-1929	69	116	as	as	ADP
ejpam-1929	69	117	that	that	PRON
ejpam-1929	69	118	of	of	ADP
ejpam-1929	69	119	their	their	PRON
ejpam-1929	69	120	common	common	ADJ
ejpam-1929	69	121	edge	edge	NOUN
ejpam-1929	69	122	.	.	PUNCT
ejpam-1929	70	1	the	the	DET
ejpam-1929	70	2	semi	semi	ADJ
ejpam-1929	70	3	-	-	ADJ
ejpam-1929	70	4	total	total	ADJ
ejpam-1929	70	5	line	line	NOUN
ejpam-1929	70	6	graph	graph	NOUN
ejpam-1929	70	7	t1(g	t1(g	PROPN
ejpam-1929	70	8	)	)	PUNCT
ejpam-1929	71	1	[	[	X
ejpam-1929	71	2	38	38	NUM
ejpam-1929	71	3	]	]	PUNCT
ejpam-1929	71	4	of	of	ADP
ejpam-1929	71	5	a	a	DET
ejpam-1929	71	6	graph	graph	NOUN
ejpam-1929	71	7	g	g	NOUN
ejpam-1929	71	8	is	be	AUX
ejpam-1929	71	9	the	the	DET
ejpam-1929	71	10	graph	graph	NOUN
ejpam-1929	71	11	whose	whose	DET
ejpam-1929	71	12	vertex	vertex	NOUN
ejpam-1929	71	13	set	set	NOUN
ejpam-1929	71	14	is	be	AUX
ejpam-1929	71	15	v	v	NOUN
ejpam-1929	71	16	(	(	PUNCT
ejpam-1929	71	17	g)∪	g)∪	VERB
ejpam-1929	71	18	e(g	e(g	PROPN
ejpam-1929	71	19	)	)	PUNCT
ejpam-1929	71	20	where	where	SCONJ
ejpam-1929	71	21	v	v	X
ejpam-1929	71	22	(	(	PUNCT
ejpam-1929	71	23	g	g	NOUN
ejpam-1929	71	24	)	)	PUNCT
ejpam-1929	71	25	and	and	CCONJ
ejpam-1929	71	26	e(g	e(g	PROPN
ejpam-1929	71	27	)	)	PUNCT
ejpam-1929	71	28	are	be	AUX
ejpam-1929	71	29	vertex	vertex	NOUN
ejpam-1929	71	30	set	set	NOUN
ejpam-1929	71	31	and	and	CCONJ
ejpam-1929	71	32	edge	edge	NOUN
ejpam-1929	71	33	set	set	NOUN
ejpam-1929	71	34	of	of	ADP
ejpam-1929	71	35	g	g	NOUN
ejpam-1929	71	36	,	,	PUNCT
ejpam-1929	71	37	respectively	respectively	ADV
ejpam-1929	71	38	and	and	CCONJ
ejpam-1929	71	39	in	in	ADP
ejpam-1929	71	40	t1(g	t1(g	PROPN
ejpam-1929	71	41	)	)	PUNCT
ejpam-1929	71	42	two	two	NUM
ejpam-1929	71	43	vertices	vertex	NOUN
ejpam-1929	71	44	are	be	AUX
ejpam-1929	71	45	adjacent	adjacent	ADJ
ejpam-1929	71	46	if	if	SCONJ
ejpam-1929	71	47	and	and	CCONJ
ejpam-1929	71	48	only	only	ADV
ejpam-1929	71	49	if	if	SCONJ
ejpam-1929	71	50	(	(	PUNCT
ejpam-1929	71	51	i	i	NOUN
ejpam-1929	71	52	)	)	PUNCT
ejpam-1929	71	53	they	they	PRON
ejpam-1929	71	54	are	be	AUX
ejpam-1929	71	55	adjacent	adjacent	ADJ
ejpam-1929	71	56	edges	edge	NOUN
ejpam-1929	71	57	in	in	ADP
ejpam-1929	71	58	g	g	NOUN
ejpam-1929	71	59	,	,	PUNCT
ejpam-1929	71	60	or	or	CCONJ
ejpam-1929	71	61	(	(	PUNCT
ejpam-1929	71	62	ii	ii	NOUN
ejpam-1929	71	63	)	)	PUNCT
ejpam-1929	71	64	one	one	NOUN
ejpam-1929	71	65	is	be	AUX
ejpam-1929	71	66	a	a	DET
ejpam-1929	71	67	vertex	vertex	NOUN
ejpam-1929	71	68	and	and	CCONJ
ejpam-1929	71	69	the	the	DET
ejpam-1929	71	70	other	other	ADJ
ejpam-1929	71	71	is	be	AUX
ejpam-1929	71	72	an	an	DET
ejpam-1929	71	73	edge	edge	NOUN
ejpam-1929	71	74	in	in	ADP
ejpam-1929	71	75	g	g	PROPN
ejpam-1929	71	76	incident	incident	NOUN
ejpam-1929	71	77	to	to	ADP
ejpam-1929	71	78	it	it	PRON
ejpam-1929	71	79	.	.	PUNCT
ejpam-1929	72	1	sinha	sinha	NOUN
ejpam-1929	72	2	et	et	PROPN
ejpam-1929	72	3	al	al	PROPN
ejpam-1929	72	4	.	.	PUNCT
ejpam-1929	73	1	[	[	X
ejpam-1929	73	2	44	44	NUM
ejpam-1929	73	3	]	]	PUNCT
ejpam-1929	73	4	extended	extend	VERB
ejpam-1929	73	5	this	this	DET
ejpam-1929	73	6	notion	notion	NOUN
ejpam-1929	73	7	of	of	ADP
ejpam-1929	73	8	semi	semi	ADJ
ejpam-1929	73	9	-	-	ADJ
ejpam-1929	73	10	total	total	ADJ
ejpam-1929	73	11	line	line	NOUN
ejpam-1929	73	12	graphs	graph	NOUN
ejpam-1929	73	13	to	to	ADP
ejpam-1929	73	14	the	the	DET
ejpam-1929	73	15	theory	theory	NOUN
ejpam-1929	73	16	of	of	ADP
ejpam-1929	73	17	sigraphs	sigraph	NOUN
ejpam-1929	73	18	as	as	SCONJ
ejpam-1929	73	19	follows	follow	VERB
ejpam-1929	73	20	:	:	PUNCT
ejpam-1929	73	21	let	let	VERB
ejpam-1929	73	22	s	s	VERB
ejpam-1929	73	23	=	=	PUNCT
ejpam-1929	73	24	(	(	PUNCT
ejpam-1929	73	25	v	v	NOUN
ejpam-1929	73	26	,	,	PUNCT
ejpam-1929	73	27	e	e	NOUN
ejpam-1929	73	28	,	,	PUNCT
ejpam-1929	73	29	σ	σ	PROPN
ejpam-1929	73	30	)	)	PUNCT
ejpam-1929	73	31	be	be	VERB
ejpam-1929	73	32	any	any	DET
ejpam-1929	73	33	sigraph	sigraph	NOUN
ejpam-1929	73	34	.	.	PUNCT
ejpam-1929	74	1	its	its	PRON
ejpam-1929	74	2	semi	semi	ADJ
ejpam-1929	74	3	-	-	ADJ
ejpam-1929	74	4	total	total	ADJ
ejpam-1929	74	5	line	line	NOUN
ejpam-1929	74	6	sigraph	sigraph	NOUN
ejpam-1929	74	7	t1(s	t1(s	PROPN
ejpam-1929	74	8	)	)	PUNCT
ejpam-1929	74	9	has	have	VERB
ejpam-1929	74	10	t1(s	t1(s	DET
ejpam-1929	74	11	u	u	NOUN
ejpam-1929	74	12	)	)	PUNCT
ejpam-1929	74	13	as	as	ADP
ejpam-1929	74	14	its	its	PRON
ejpam-1929	74	15	underlying	underlie	VERB
ejpam-1929	74	16	graph	graph	NOUN
ejpam-1929	74	17	and	and	CCONJ
ejpam-1929	74	18	for	for	ADP
ejpam-1929	74	19	any	any	DET
ejpam-1929	74	20	edge	edge	NOUN
ejpam-1929	74	21	uv	uv	NOUN
ejpam-1929	74	22	of	of	ADP
ejpam-1929	74	23	t1(s	t1(s	DET
ejpam-1929	74	24	u	u	NOUN
ejpam-1929	74	25	)	)	PUNCT
ejpam-1929	74	26	,	,	PUNCT
ejpam-1929	74	27	σt1	σt1	INTJ
ejpam-1929	74	28	(	(	PUNCT
ejpam-1929	74	29	uv	uv	NOUN
ejpam-1929	74	30	)	)	PUNCT
ejpam-1929	74	31	=	=	SYM
ejpam-1929	74	32	(	(	PUNCT
ejpam-1929	74	33	σ(u)σ(v	σ(u)σ(v	NOUN
ejpam-1929	74	34	)	)	PUNCT
ejpam-1929	74	35	if	if	SCONJ
ejpam-1929	74	36	u	u	NOUN
ejpam-1929	74	37	,	,	PUNCT
ejpam-1929	74	38	v	v	NOUN
ejpam-1929	74	39	∈	∈	NOUN
ejpam-1929	74	40	e	e	NOUN
ejpam-1929	74	41	,	,	PUNCT
ejpam-1929	74	42	σ(v	σ(v	NOUN
ejpam-1929	74	43	)	)	PUNCT
ejpam-1929	74	44	if	if	SCONJ
ejpam-1929	74	45	u	u	PROPN
ejpam-1929	74	46	∈	∈	PROPN
ejpam-1929	74	47	v	v	NOUN
ejpam-1929	74	48	and	and	CCONJ
ejpam-1929	74	49	v	v	ADP
ejpam-1929	74	50	∈	∈	PROPN
ejpam-1929	74	51	e.	e.	PROPN
ejpam-1929	74	52	1.6	1.6	NUM
ejpam-1929	74	53	.	.	PUNCT
ejpam-1929	75	1	unitary	unitary	ADJ
ejpam-1929	75	2	cayley	cayley	ADJ
ejpam-1929	75	3	graph	graph	NOUN
ejpam-1929	75	4	and	and	CCONJ
ejpam-1929	75	5	its	its	PRON
ejpam-1929	75	6	sigraph	sigraph	ADJ
ejpam-1929	75	7	varieties	variety	NOUN
ejpam-1929	75	8	let	let	VERB
ejpam-1929	75	9	γ	γ	NOUN
ejpam-1929	75	10	be	be	AUX
ejpam-1929	75	11	a	a	DET
ejpam-1929	75	12	group	group	NOUN
ejpam-1929	75	13	and	and	CCONJ
ejpam-1929	75	14	b	b	NOUN
ejpam-1929	75	15	be	be	AUX
ejpam-1929	75	16	a	a	DET
ejpam-1929	75	17	subset	subset	NOUN
ejpam-1929	75	18	of	of	ADP
ejpam-1929	75	19	γ	γ	NOUN
ejpam-1929	75	20	such	such	ADJ
ejpam-1929	75	21	that	that	PRON
ejpam-1929	75	22	b	b	NOUN
ejpam-1929	75	23	does	do	AUX
ejpam-1929	75	24	not	not	PART
ejpam-1929	75	25	contain	contain	VERB
ejpam-1929	75	26	the	the	DET
ejpam-1929	75	27	identity	identity	NOUN
ejpam-1929	75	28	of	of	ADP
ejpam-1929	75	29	γ	γ	PROPN
ejpam-1929	75	30	.	.	PROPN
ejpam-1929	75	31	assume	assume	VERB
ejpam-1929	76	1	b−1	b−1	PROPN
ejpam-1929	76	2	=	=	PRON
ejpam-1929	76	3	{	{	PUNCT
ejpam-1929	76	4	b−1	b−1	PROPN
ejpam-1929	76	5	:	:	PUNCT
ejpam-1929	76	6	b	b	X
ejpam-1929	76	7	∈	∈	ADJ
ejpam-1929	76	8	b	b	NOUN
ejpam-1929	76	9	}	}	PUNCT
ejpam-1929	76	10	=	=	SYM
ejpam-1929	76	11	b.	b.	PROPN
ejpam-1929	76	12	the	the	DET
ejpam-1929	76	13	cayley	cayley	ADJ
ejpam-1929	76	14	graph	graph	NOUN
ejpam-1929	76	15	x	x	PUNCT
ejpam-1929	76	16	′	′	NUM
ejpam-1929	76	17	=	=	PUNCT
ejpam-1929	76	18	ca	ca	AUX
ejpam-1929	76	19	y(γ	y(γ	PROPN
ejpam-1929	76	20	,	,	PUNCT
ejpam-1929	76	21	b	b	X
ejpam-1929	76	22	)	)	PUNCT
ejpam-1929	76	23	is	be	AUX
ejpam-1929	76	24	an	an	DET
ejpam-1929	76	25	undirected	undirected	ADJ
ejpam-1929	76	26	graph	graph	NOUN
ejpam-1929	76	27	d.	d.	PROPN
ejpam-1929	76	28	sinha	sinha	PROPN
ejpam-1929	76	29	,	,	PUNCT
ejpam-1929	76	30	a.	a.	NOUN
ejpam-1929	76	31	dhama	dhama	PROPN
ejpam-1929	76	32	,	,	PUNCT
ejpam-1929	76	33	b.	b.	PROPN
ejpam-1929	76	34	acharya	acharya	PROPN
ejpam-1929	76	35	/	/	SYM
ejpam-1929	76	36	eur	eur	PROPN
ejpam-1929	76	37	.	.	PUNCT
ejpam-1929	77	1	j.	j.	PROPN
ejpam-1929	77	2	pure	pure	PROPN
ejpam-1929	77	3	appl	appl	PROPN
ejpam-1929	77	4	.	.	PROPN
ejpam-1929	77	5	math	math	PROPN
ejpam-1929	77	6	,	,	PUNCT
ejpam-1929	77	7	6	6	NUM
ejpam-1929	77	8	(	(	PUNCT
ejpam-1929	77	9	2013	2013	NUM
ejpam-1929	77	10	)	)	PUNCT
ejpam-1929	77	11	,	,	PUNCT
ejpam-1929	77	12	189	189	NUM
ejpam-1929	77	13	-	-	SYM
ejpam-1929	77	14	210	210	NUM
ejpam-1929	77	15	193	193	NUM
ejpam-1929	77	16	having	have	VERB
ejpam-1929	77	17	vertex	vertex	NOUN
ejpam-1929	77	18	set	set	VERB
ejpam-1929	77	19	v	v	NOUN
ejpam-1929	77	20	(	(	PUNCT
ejpam-1929	77	21	x	x	NOUN
ejpam-1929	77	22	′	′	NUM
ejpam-1929	77	23	)	)	PUNCT
ejpam-1929	78	1	=	=	SYM
ejpam-1929	78	2	γ	γ	NOUN
ejpam-1929	78	3	and	and	CCONJ
ejpam-1929	78	4	edge	edge	VERB
ejpam-1929	78	5	set	set	VERB
ejpam-1929	78	6	e(x	e(x	NUM
ejpam-1929	78	7	′	′	NUM
ejpam-1929	78	8	)	)	PUNCT
ejpam-1929	78	9	=	=	PRON
ejpam-1929	79	1	{	{	PUNCT
ejpam-1929	79	2	ab	ab	NOUN
ejpam-1929	79	3	:	:	PUNCT
ejpam-1929	79	4	ab−1	ab−1	PROPN
ejpam-1929	79	5	∈	∈	PROPN
ejpam-1929	79	6	b	b	PROPN
ejpam-1929	79	7	}	}	PUNCT
ejpam-1929	79	8	,	,	PUNCT
ejpam-1929	79	9	where	where	SCONJ
ejpam-1929	79	10	a	a	X
ejpam-1929	79	11	,	,	PUNCT
ejpam-1929	79	12	b	b	PROPN
ejpam-1929	79	13	∈	∈	PROPN
ejpam-1929	79	14	γ	γ	X
ejpam-1929	79	15	.	.	PUNCT
ejpam-1929	79	16	the	the	DET
ejpam-1929	79	17	cayley	cayley	ADJ
ejpam-1929	79	18	graph	graph	NOUN
ejpam-1929	79	19	x	x	PUNCT
ejpam-1929	79	20	′	′	NOUN
ejpam-1929	79	21	is	be	AUX
ejpam-1929	79	22	a	a	DET
ejpam-1929	79	23	regular	regular	ADJ
ejpam-1929	79	24	graph	graph	NOUN
ejpam-1929	79	25	of	of	ADP
ejpam-1929	79	26	degree	degree	NOUN
ejpam-1929	79	27	|b|	|b|	PROPN
ejpam-1929	79	28	.	.	PUNCT
ejpam-1929	80	1	its	its	PRON
ejpam-1929	80	2	connected	connected	ADJ
ejpam-1929	80	3	components	component	NOUN
ejpam-1929	80	4	are	be	AUX
ejpam-1929	80	5	the	the	DET
ejpam-1929	80	6	right	right	ADJ
ejpam-1929	80	7	cosets	coset	NOUN
ejpam-1929	80	8	of	of	ADP
ejpam-1929	80	9	the	the	DET
ejpam-1929	80	10	subgroup	subgroup	NOUN
ejpam-1929	80	11	generated	generate	VERB
ejpam-1929	80	12	by	by	ADP
ejpam-1929	80	13	b.	b.	PROPN
ejpam-1929	80	14	therefore	therefore	ADV
ejpam-1929	80	15	,	,	PUNCT
ejpam-1929	80	16	if	if	SCONJ
ejpam-1929	80	17	b	b	PROPN
ejpam-1929	80	18	generates	generate	VERB
ejpam-1929	80	19	γ	γ	NOUN
ejpam-1929	80	20	,	,	PUNCT
ejpam-1929	80	21	then	then	ADV
ejpam-1929	80	22	x	x	SYM
ejpam-1929	80	23	′	′	NOUN
ejpam-1929	80	24	is	be	AUX
ejpam-1929	80	25	a	a	DET
ejpam-1929	80	26	connected	connected	ADJ
ejpam-1929	80	27	graph	graph	NOUN
ejpam-1929	80	28	.	.	PUNCT
ejpam-1929	81	1	the	the	DET
ejpam-1929	81	2	books	book	NOUN
ejpam-1929	81	3	on	on	ADP
ejpam-1929	81	4	algebraic	algebraic	ADJ
ejpam-1929	81	5	graph	graph	NOUN
ejpam-1929	81	6	theory	theory	NOUN
ejpam-1929	81	7	by	by	ADP
ejpam-1929	81	8	biggs	biggs	PROPN
ejpam-1929	81	9	[	[	X
ejpam-1929	81	10	14	14	NUM
ejpam-1929	81	11	]	]	PUNCT
ejpam-1929	81	12	and	and	CCONJ
ejpam-1929	81	13	by	by	ADP
ejpam-1929	81	14	godsil	godsil	NOUN
ejpam-1929	81	15	and	and	CCONJ
ejpam-1929	81	16	royle	royle	NOUN
ejpam-1929	81	17	[	[	X
ejpam-1929	81	18	25	25	NUM
ejpam-1929	81	19	]	]	PUNCT
ejpam-1929	81	20	provide	provide	VERB
ejpam-1929	81	21	many	many	ADJ
ejpam-1929	81	22	information	information	NOUN
ejpam-1929	81	23	regarding	regard	VERB
ejpam-1929	81	24	cayley	cayley	ADJ
ejpam-1929	81	25	graphs	graph	NOUN
ejpam-1929	81	26	.	.	PUNCT
ejpam-1929	82	1	for	for	ADP
ejpam-1929	82	2	a	a	DET
ejpam-1929	82	3	positive	positive	ADJ
ejpam-1929	82	4	integer	integer	NOUN
ejpam-1929	82	5	n	n	CCONJ
ejpam-1929	82	6	,	,	PUNCT
ejpam-1929	82	7	the	the	DET
ejpam-1929	82	8	unitary	unitary	ADJ
ejpam-1929	82	9	cayley	cayley	NOUN
ejpam-1929	82	10	graph	graph	NOUN
ejpam-1929	82	11	xn	xn	PROPN
ejpam-1929	82	12	is	be	AUX
ejpam-1929	82	13	the	the	DET
ejpam-1929	82	14	graph	graph	NOUN
ejpam-1929	82	15	whose	whose	DET
ejpam-1929	82	16	vertex	vertex	NOUN
ejpam-1929	82	17	set	set	NOUN
ejpam-1929	82	18	is	be	AUX
ejpam-1929	82	19	zn	zn	PROPN
ejpam-1929	82	20	,	,	PUNCT
ejpam-1929	82	21	the	the	DET
ejpam-1929	82	22	ring	ring	NOUN
ejpam-1929	82	23	of	of	ADP
ejpam-1929	82	24	integers	integer	NOUN
ejpam-1929	82	25	modulo	modulo	VERB
ejpam-1929	82	26	n	n	NOUN
ejpam-1929	83	1	and	and	CCONJ
ejpam-1929	83	2	if	if	SCONJ
ejpam-1929	83	3	un	un	PROPN
ejpam-1929	83	4	denotes	denote	NOUN
ejpam-1929	83	5	set	set	VERB
ejpam-1929	83	6	of	of	ADP
ejpam-1929	83	7	all	all	DET
ejpam-1929	83	8	its	its	PRON
ejpam-1929	83	9	units	unit	NOUN
ejpam-1929	83	10	then	then	ADV
ejpam-1929	83	11	two	two	NUM
ejpam-1929	83	12	vertices	vertex	NOUN
ejpam-1929	83	13	a	a	PRON
ejpam-1929	83	14	and	and	CCONJ
ejpam-1929	83	15	b	b	NOUN
ejpam-1929	83	16	are	be	AUX
ejpam-1929	83	17	adjacent	adjacent	ADJ
ejpam-1929	83	18	if	if	SCONJ
ejpam-1929	83	19	and	and	CCONJ
ejpam-1929	83	20	only	only	ADV
ejpam-1929	83	21	if	if	SCONJ
ejpam-1929	83	22	(	(	PUNCT
ejpam-1929	83	23	a	a	DET
ejpam-1929	83	24	−	−	PROPN
ejpam-1929	83	25	b	b	NOUN
ejpam-1929	83	26	)	)	PUNCT
ejpam-1929	83	27	∈	∈	PROPN
ejpam-1929	83	28	un	un	PROPN
ejpam-1929	83	29	.	.	PUNCT
ejpam-1929	84	1	the	the	DET
ejpam-1929	84	2	unitary	unitary	ADJ
ejpam-1929	84	3	cayley	cayley	NOUN
ejpam-1929	84	4	graph	graph	NOUN
ejpam-1929	84	5	xn	xn	PROPN
ejpam-1929	84	6	is	be	AUX
ejpam-1929	84	7	then	then	ADV
ejpam-1929	84	8	the	the	DET
ejpam-1929	84	9	same	same	ADJ
ejpam-1929	84	10	as	as	ADP
ejpam-1929	84	11	xn	xn	PROPN
ejpam-1929	84	12	=	=	SYM
ejpam-1929	84	13	ca	ca	NOUN
ejpam-1929	84	14	y(zn	y(zn	PROPN
ejpam-1929	84	15	,	,	PUNCT
ejpam-1929	84	16	un	un	PROPN
ejpam-1929	84	17	)	)	PUNCT
ejpam-1929	84	18	.	.	PUNCT
ejpam-1929	85	1	the	the	DET
ejpam-1929	85	2	structure	structure	NOUN
ejpam-1929	85	3	and	and	CCONJ
ejpam-1929	85	4	various	various	ADJ
ejpam-1929	85	5	properties	property	NOUN
ejpam-1929	85	6	of	of	ADP
ejpam-1929	85	7	unitary	unitary	ADJ
ejpam-1929	85	8	cayley	cayley	NOUN
ejpam-1929	85	9	graphs	graph	NOUN
ejpam-1929	85	10	have	have	AUX
ejpam-1929	85	11	been	be	AUX
ejpam-1929	85	12	studied	study	VERB
ejpam-1929	85	13	in	in	ADP
ejpam-1929	85	14	literature	literature	NOUN
ejpam-1929	85	15	(	(	PUNCT
ejpam-1929	85	16	see	see	VERB
ejpam-1929	85	17	[	[	X
ejpam-1929	85	18	7	7	NUM
ejpam-1929	85	19	,	,	PUNCT
ejpam-1929	85	20	9	9	NUM
ejpam-1929	85	21	,	,	PUNCT
ejpam-1929	85	22	13	13	NUM
ejpam-1929	85	23	,	,	PUNCT
ejpam-1929	85	24	15	15	NUM
ejpam-1929	85	25	,	,	PUNCT
ejpam-1929	85	26	20–23	20–23	PROPN
ejpam-1929	85	27	,	,	PUNCT
ejpam-1929	85	28	34	34	NUM
ejpam-1929	85	29	,	,	PUNCT
ejpam-1929	85	30	37	37	NUM
ejpam-1929	85	31	,	,	PUNCT
ejpam-1929	85	32	39	39	NUM
ejpam-1929	85	33	]	]	PUNCT
ejpam-1929	85	34	)	)	PUNCT
ejpam-1929	85	35	.	.	PUNCT
ejpam-1929	86	1	let	let	VERB
ejpam-1929	86	2	γ	γ	NOUN
ejpam-1929	86	3	be	be	AUX
ejpam-1929	86	4	an	an	DET
ejpam-1929	86	5	abelian	abelian	ADJ
ejpam-1929	86	6	group	group	NOUN
ejpam-1929	86	7	and	and	CCONJ
ejpam-1929	86	8	b	b	NOUN
ejpam-1929	86	9	be	be	AUX
ejpam-1929	86	10	a	a	DET
ejpam-1929	86	11	subset	subset	NOUN
ejpam-1929	86	12	of	of	ADP
ejpam-1929	86	13	γ	γ	PROPN
ejpam-1929	86	14	.	.	PUNCT
ejpam-1929	87	1	the	the	DET
ejpam-1929	87	2	addition	addition	NOUN
ejpam-1929	87	3	cayley	cayley	NOUN
ejpam-1929	87	4	graph	graph	NOUN
ejpam-1929	87	5	g′	g′	NOUN
ejpam-1929	87	6	=	=	PUNCT
ejpam-1929	87	7	ca	ca	PROPN
ejpam-1929	87	8	y+(γ	y+(γ	PROPN
ejpam-1929	87	9	,	,	PUNCT
ejpam-1929	87	10	b	b	NOUN
ejpam-1929	87	11	)	)	PUNCT
ejpam-1929	87	12	is	be	AUX
ejpam-1929	87	13	the	the	DET
ejpam-1929	87	14	graph	graph	NOUN
ejpam-1929	87	15	having	have	VERB
ejpam-1929	87	16	the	the	DET
ejpam-1929	87	17	vertex	vertex	NOUN
ejpam-1929	87	18	set	set	VERB
ejpam-1929	87	19	v	v	NOUN
ejpam-1929	87	20	(	(	PUNCT
ejpam-1929	87	21	g′	g′	NOUN
ejpam-1929	87	22	)	)	PUNCT
ejpam-1929	88	1	=	=	SYM
ejpam-1929	88	2	γ	γ	NOUN
ejpam-1929	88	3	and	and	CCONJ
ejpam-1929	88	4	the	the	DET
ejpam-1929	88	5	edge	edge	NOUN
ejpam-1929	88	6	set	set	VERB
ejpam-1929	88	7	e(g′	e(g′	PRON
ejpam-1929	88	8	)	)	PUNCT
ejpam-1929	89	1	=	=	SYM
ejpam-1929	89	2	{	{	PUNCT
ejpam-1929	89	3	ab	ab	NOUN
ejpam-1929	89	4	:	:	PUNCT
ejpam-1929	89	5	a+	a+	PUNCT
ejpam-1929	89	6	b	b	X
ejpam-1929	89	7	∈	∈	PROPN
ejpam-1929	89	8	b	b	NOUN
ejpam-1929	89	9	}	}	PUNCT
ejpam-1929	89	10	,	,	PUNCT
ejpam-1929	89	11	where	where	SCONJ
ejpam-1929	89	12	a	a	X
ejpam-1929	89	13	,	,	PUNCT
ejpam-1929	89	14	b	b	PROPN
ejpam-1929	89	15	∈	∈	PROPN
ejpam-1929	89	16	γ	γ	X
ejpam-1929	89	17	.	.	PUNCT
ejpam-1929	89	18	several	several	ADJ
ejpam-1929	89	19	properties	property	NOUN
ejpam-1929	89	20	of	of	ADP
ejpam-1929	89	21	addition	addition	NOUN
ejpam-1929	89	22	cayley	cayley	NOUN
ejpam-1929	89	23	graphs	graph	NOUN
ejpam-1929	89	24	have	have	AUX
ejpam-1929	89	25	been	be	AUX
ejpam-1929	89	26	discussed	discuss	VERB
ejpam-1929	89	27	in	in	ADP
ejpam-1929	89	28	literature	literature	NOUN
ejpam-1929	89	29	(	(	PUNCT
ejpam-1929	89	30	see	see	VERB
ejpam-1929	89	31	[	[	X
ejpam-1929	89	32	8	8	NUM
ejpam-1929	89	33	,	,	PUNCT
ejpam-1929	89	34	17	17	NUM
ejpam-1929	89	35	,	,	PUNCT
ejpam-1929	89	36	18	18	NUM
ejpam-1929	89	37	,	,	PUNCT
ejpam-1929	89	38	26–28	26–28	NUM
ejpam-1929	89	39	,	,	PUNCT
ejpam-1929	89	40	35	35	NUM
ejpam-1929	89	41	,	,	PUNCT
ejpam-1929	89	42	36	36	NUM
ejpam-1929	89	43	]	]	PUNCT
ejpam-1929	89	44	)	)	PUNCT
ejpam-1929	89	45	.	.	PUNCT
ejpam-1929	90	1	for	for	ADP
ejpam-1929	90	2	a	a	DET
ejpam-1929	90	3	positive	positive	ADJ
ejpam-1929	90	4	integer	integer	NOUN
ejpam-1929	90	5	n	n	CCONJ
ejpam-1929	90	6	,	,	PUNCT
ejpam-1929	90	7	the	the	DET
ejpam-1929	90	8	unitary	unitary	ADJ
ejpam-1929	90	9	addition	addition	NOUN
ejpam-1929	90	10	cayley	cayley	NOUN
ejpam-1929	90	11	graph	graph	NOUN
ejpam-1929	90	12	gn	gn	PROPN
ejpam-1929	90	13	is	be	AUX
ejpam-1929	90	14	the	the	DET
ejpam-1929	90	15	graph	graph	NOUN
ejpam-1929	90	16	whose	whose	DET
ejpam-1929	90	17	vertex	vertex	NOUN
ejpam-1929	90	18	set	set	NOUN
ejpam-1929	90	19	is	be	AUX
ejpam-1929	90	20	zn	zn	PROPN
ejpam-1929	90	21	,	,	PUNCT
ejpam-1929	90	22	the	the	DET
ejpam-1929	90	23	integers	integer	NOUN
ejpam-1929	90	24	modulo	modulo	VERB
ejpam-1929	90	25	n	n	NOUN
ejpam-1929	90	26	and	and	CCONJ
ejpam-1929	90	27	if	if	SCONJ
ejpam-1929	90	28	un	un	PROPN
ejpam-1929	90	29	denotes	denote	NOUN
ejpam-1929	90	30	set	set	VERB
ejpam-1929	90	31	of	of	ADP
ejpam-1929	90	32	all	all	DET
ejpam-1929	90	33	units	unit	NOUN
ejpam-1929	90	34	of	of	ADP
ejpam-1929	90	35	the	the	DET
ejpam-1929	90	36	ring	ring	NOUN
ejpam-1929	90	37	zn	zn	PROPN
ejpam-1929	90	38	,	,	PUNCT
ejpam-1929	90	39	then	then	ADV
ejpam-1929	90	40	two	two	NUM
ejpam-1929	90	41	vertices	vertex	NOUN
ejpam-1929	90	42	a	a	PRON
ejpam-1929	90	43	and	and	CCONJ
ejpam-1929	90	44	b	b	NOUN
ejpam-1929	90	45	are	be	AUX
ejpam-1929	90	46	adjacent	adjacent	ADJ
ejpam-1929	90	47	if	if	SCONJ
ejpam-1929	90	48	and	and	CCONJ
ejpam-1929	90	49	only	only	ADV
ejpam-1929	90	50	if	if	SCONJ
ejpam-1929	90	51	a+	a+	PRON
ejpam-1929	90	52	b	b	PROPN
ejpam-1929	90	53	∈	∈	PROPN
ejpam-1929	90	54	un	un	PROPN
ejpam-1929	90	55	.	.	PUNCT
ejpam-1929	91	1	the	the	DET
ejpam-1929	91	2	unitary	unitary	ADJ
ejpam-1929	91	3	addition	addition	NOUN
ejpam-1929	91	4	cayley	cayley	NOUN
ejpam-1929	91	5	graph	graph	NOUN
ejpam-1929	91	6	gn	gn	PROPN
ejpam-1929	91	7	may	may	AUX
ejpam-1929	91	8	also	also	ADV
ejpam-1929	91	9	be	be	AUX
ejpam-1929	91	10	defined	define	VERB
ejpam-1929	91	11	as	as	ADP
ejpam-1929	91	12	,	,	PUNCT
ejpam-1929	91	13	gn	gn	PROPN
ejpam-1929	91	14	=	=	PUNCT
ejpam-1929	91	15	ca	ca	PROPN
ejpam-1929	91	16	y+(zn	y+(zn	PROPN
ejpam-1929	91	17	,	,	PUNCT
ejpam-1929	91	18	un	un	PROPN
ejpam-1929	91	19	)	)	PUNCT
ejpam-1929	91	20	.	.	PUNCT
ejpam-1929	92	1	some	some	DET
ejpam-1929	92	2	properties	property	NOUN
ejpam-1929	92	3	of	of	ADP
ejpam-1929	92	4	unitary	unitary	ADJ
ejpam-1929	92	5	addition	addition	NOUN
ejpam-1929	92	6	cayley	cayley	NOUN
ejpam-1929	92	7	graphs	graph	NOUN
ejpam-1929	92	8	have	have	AUX
ejpam-1929	92	9	been	be	AUX
ejpam-1929	92	10	studied	study	VERB
ejpam-1929	92	11	in	in	ADP
ejpam-1929	92	12	literature	literature	NOUN
ejpam-1929	92	13	(	(	PUNCT
ejpam-1929	92	14	see	see	VERB
ejpam-1929	92	15	[	[	X
ejpam-1929	92	16	43	43	NUM
ejpam-1929	92	17	]	]	NUM
ejpam-1929	92	18	)	)	PUNCT
ejpam-1929	92	19	.	.	PUNCT
ejpam-1929	93	1	theorem	theorem	ADJ
ejpam-1929	93	2	3	3	NUM
ejpam-1929	93	3	(	(	PUNCT
ejpam-1929	93	4	[	[	X
ejpam-1929	93	5	43	43	NUM
ejpam-1929	93	6	]	]	NUM
ejpam-1929	93	7	)	)	PUNCT
ejpam-1929	93	8	.	.	PUNCT
ejpam-1929	94	1	the	the	DET
ejpam-1929	94	2	unitary	unitary	ADJ
ejpam-1929	94	3	addition	addition	NOUN
ejpam-1929	94	4	cayley	cayley	NOUN
ejpam-1929	94	5	graph	graph	NOUN
ejpam-1929	94	6	gn	gn	PROPN
ejpam-1929	94	7	is	be	AUX
ejpam-1929	94	8	isomorphic	isomorphic	ADJ
ejpam-1929	94	9	to	to	ADP
ejpam-1929	94	10	the	the	DET
ejpam-1929	94	11	unitary	unitary	ADJ
ejpam-1929	94	12	cayley	cayley	ADJ
ejpam-1929	94	13	graph	graph	NOUN
ejpam-1929	94	14	xn	xn	PUNCT
ejpam-1929	95	1	if	if	SCONJ
ejpam-1929	95	2	and	and	CCONJ
ejpam-1929	95	3	only	only	ADV
ejpam-1929	95	4	if	if	SCONJ
ejpam-1929	95	5	n	n	PRON
ejpam-1929	95	6	is	be	AUX
ejpam-1929	95	7	even	even	ADV
ejpam-1929	95	8	.	.	PUNCT
ejpam-1929	96	1	some	some	DET
ejpam-1929	96	2	examples	example	NOUN
ejpam-1929	96	3	of	of	ADP
ejpam-1929	96	4	unitary	unitary	ADJ
ejpam-1929	96	5	addition	addition	NOUN
ejpam-1929	96	6	cayley	cayley	NOUN
ejpam-1929	96	7	graphs	graph	NOUN
ejpam-1929	96	8	are	be	AUX
ejpam-1929	96	9	displayed	display	VERB
ejpam-1929	96	10	in	in	ADP
ejpam-1929	96	11	figure	figure	NOUN
ejpam-1929	96	12	1	1	NUM
ejpam-1929	96	13	.	.	PUNCT
ejpam-1929	97	1	our	our	PRON
ejpam-1929	97	2	aim	aim	NOUN
ejpam-1929	97	3	in	in	ADP
ejpam-1929	97	4	this	this	DET
ejpam-1929	97	5	paper	paper	NOUN
ejpam-1929	97	6	is	be	AUX
ejpam-1929	97	7	to	to	PART
ejpam-1929	97	8	introduce	introduce	VERB
ejpam-1929	97	9	an	an	DET
ejpam-1929	97	10	extension	extension	NOUN
ejpam-1929	97	11	of	of	ADP
ejpam-1929	97	12	the	the	DET
ejpam-1929	97	13	notion	notion	NOUN
ejpam-1929	97	14	of	of	ADP
ejpam-1929	97	15	unitary	unitary	ADJ
ejpam-1929	97	16	addition	addition	NOUN
ejpam-1929	97	17	cayley	cayley	NOUN
ejpam-1929	97	18	graphs	graph	NOUN
ejpam-1929	97	19	in	in	ADP
ejpam-1929	97	20	a	a	DET
ejpam-1929	97	21	natural	natural	ADJ
ejpam-1929	97	22	way	way	NOUN
ejpam-1929	97	23	to	to	ADP
ejpam-1929	97	24	the	the	DET
ejpam-1929	97	25	theory	theory	NOUN
ejpam-1929	97	26	of	of	ADP
ejpam-1929	97	27	sigraphs	sigraph	NOUN
ejpam-1929	97	28	and	and	CCONJ
ejpam-1929	97	29	study	study	VERB
ejpam-1929	97	30	their	their	PRON
ejpam-1929	97	31	fundamental	fundamental	ADJ
ejpam-1929	97	32	properties	property	NOUN
ejpam-1929	97	33	.	.	PUNCT
ejpam-1929	98	1	2	2	X
ejpam-1929	98	2	.	.	NOUN
ejpam-1929	98	3	unitary	unitary	ADJ
ejpam-1929	98	4	addition	addition	NOUN
ejpam-1929	98	5	cayley	cayley	NOUN
ejpam-1929	98	6	sigraphs	sigraph	VERB
ejpam-1929	98	7	we	we	PRON
ejpam-1929	98	8	introduce	introduce	VERB
ejpam-1929	98	9	the	the	DET
ejpam-1929	98	10	definition	definition	NOUN
ejpam-1929	98	11	of	of	ADP
ejpam-1929	98	12	a	a	DET
ejpam-1929	98	13	unitary	unitary	ADJ
ejpam-1929	98	14	addition	addition	NOUN
ejpam-1929	98	15	cayley	cayley	NOUN
ejpam-1929	98	16	sigraph	sigraph	NOUN
ejpam-1929	98	17	as	as	SCONJ
ejpam-1929	98	18	follows	follow	VERB
ejpam-1929	98	19	:	:	PUNCT
ejpam-1929	98	20	definition	definition	NOUN
ejpam-1929	98	21	1	1	NUM
ejpam-1929	98	22	.	.	PUNCT
ejpam-1929	99	1	for	for	ADP
ejpam-1929	99	2	a	a	DET
ejpam-1929	99	3	positive	positive	ADJ
ejpam-1929	99	4	integer	integer	NOUN
ejpam-1929	99	5	n	n	CCONJ
ejpam-1929	99	6	,	,	PUNCT
ejpam-1929	99	7	the	the	DET
ejpam-1929	99	8	unitary	unitary	ADJ
ejpam-1929	99	9	addition	addition	NOUN
ejpam-1929	99	10	cayley	cayley	NOUN
ejpam-1929	99	11	sigraph	sigraph	NOUN
ejpam-1929	99	12	σn	σn	NOUN
ejpam-1929	99	13	=	=	SYM
ejpam-1929	99	14	(	(	PUNCT
ejpam-1929	99	15	σ	σ	PROPN
ejpam-1929	99	16	u	u	PROPN
ejpam-1929	99	17	n	n	NUM
ejpam-1929	99	18	,	,	PUNCT
ejpam-1929	99	19	σ	σ	PROPN
ejpam-1929	99	20	)	)	PUNCT
ejpam-1929	99	21	is	be	AUX
ejpam-1929	99	22	defined	define	VERB
ejpam-1929	99	23	as	as	ADP
ejpam-1929	99	24	the	the	DET
ejpam-1929	99	25	sigraph	sigraph	NOUN
ejpam-1929	99	26	,	,	PUNCT
ejpam-1929	99	27	where	where	SCONJ
ejpam-1929	99	28	σu	σu	PROPN
ejpam-1929	99	29	n	n	ADV
ejpam-1929	99	30	is	be	AUX
ejpam-1929	99	31	the	the	DET
ejpam-1929	99	32	unitary	unitary	ADJ
ejpam-1929	99	33	addition	addition	NOUN
ejpam-1929	99	34	cayley	cayley	NOUN
ejpam-1929	99	35	graph	graph	NOUN
ejpam-1929	99	36	and	and	CCONJ
ejpam-1929	99	37	for	for	ADP
ejpam-1929	99	38	an	an	DET
ejpam-1929	99	39	edge	edge	NOUN
ejpam-1929	99	40	ab	ab	PROPN
ejpam-1929	99	41	of	of	ADP
ejpam-1929	99	42	σn	σn	PROPN
ejpam-1929	99	43	,	,	PUNCT
ejpam-1929	99	44	σ(ab	σ(ab	NOUN
ejpam-1929	99	45	)	)	PUNCT
ejpam-1929	99	46	=	=	SYM
ejpam-1929	100	1	(	(	PUNCT
ejpam-1929	100	2	+	+	CCONJ
ejpam-1929	100	3	if	if	SCONJ
ejpam-1929	100	4	a	a	DET
ejpam-1929	100	5	∈	∈	PROPN
ejpam-1929	100	6	un	un	NOUN
ejpam-1929	100	7	or	or	CCONJ
ejpam-1929	100	8	b	b	PROPN
ejpam-1929	100	9	∈	∈	PROPN
ejpam-1929	100	10	un	un	PROPN
ejpam-1929	100	11	,	,	PUNCT
ejpam-1929	100	12	−	−	PROPN
ejpam-1929	100	13	otherwise	otherwise	ADV
ejpam-1929	100	14	.	.	PUNCT
ejpam-1929	101	1	d.	d.	PROPN
ejpam-1929	101	2	sinha	sinha	PROPN
ejpam-1929	101	3	,	,	PUNCT
ejpam-1929	101	4	a.	a.	NOUN
ejpam-1929	101	5	dhama	dhama	PROPN
ejpam-1929	101	6	,	,	PUNCT
ejpam-1929	101	7	b.	b.	PROPN
ejpam-1929	101	8	acharya	acharya	PROPN
ejpam-1929	101	9	/	/	SYM
ejpam-1929	101	10	eur	eur	PROPN
ejpam-1929	101	11	.	.	PUNCT
ejpam-1929	102	1	j.	j.	PROPN
ejpam-1929	102	2	pure	pure	PROPN
ejpam-1929	102	3	appl	appl	PROPN
ejpam-1929	102	4	.	.	PROPN
ejpam-1929	102	5	math	math	PROPN
ejpam-1929	102	6	,	,	PUNCT
ejpam-1929	102	7	6	6	NUM
ejpam-1929	102	8	(	(	PUNCT
ejpam-1929	102	9	2013	2013	NUM
ejpam-1929	102	10	)	)	PUNCT
ejpam-1929	102	11	,	,	PUNCT
ejpam-1929	102	12	189	189	NUM
ejpam-1929	102	13	-	-	SYM
ejpam-1929	102	14	210	210	NUM
ejpam-1929	103	1	194	194	NUM
ejpam-1929	103	2	0	0	NUM
ejpam-1929	103	3	1	1	NUM
ejpam-1929	103	4	(	(	PUNCT
ejpam-1929	103	5	a	a	NOUN
ejpam-1929	103	6	)	)	PUNCT
ejpam-1929	103	7	g2	g2	PROPN
ejpam-1929	103	8	(	(	PUNCT
ejpam-1929	103	9	b	b	X
ejpam-1929	103	10	)	)	PUNCT
ejpam-1929	103	11	g3	g3	NOUN
ejpam-1929	103	12	0	0	NUM
ejpam-1929	103	13	1	1	NUM
ejpam-1929	103	14	23	23	NUM
ejpam-1929	103	15	(	(	PUNCT
ejpam-1929	103	16	c	c	NOUN
ejpam-1929	103	17	)	)	PUNCT
ejpam-1929	103	18	g4	g4	NOUN
ejpam-1929	103	19	0	0	NUM
ejpam-1929	103	20	1	1	NUM
ejpam-1929	103	21	2	2	NUM
ejpam-1929	103	22	3	3	NUM
ejpam-1929	103	23	4	4	NUM
ejpam-1929	103	24	(	(	PUNCT
ejpam-1929	103	25	d	d	NOUN
ejpam-1929	103	26	)	)	PUNCT
ejpam-1929	103	27	g5	g5	NOUN
ejpam-1929	103	28	0	0	NUM
ejpam-1929	103	29	1	1	NUM
ejpam-1929	103	30	2	2	NUM
ejpam-1929	103	31	3	3	NUM
ejpam-1929	103	32	45	45	NUM
ejpam-1929	103	33	(	(	PUNCT
ejpam-1929	103	34	e	e	NOUN
ejpam-1929	103	35	)	)	PUNCT
ejpam-1929	103	36	g6	g6	ADJ
ejpam-1929	103	37	0	0	NUM
ejpam-1929	103	38	1	1	NUM
ejpam-1929	103	39	2	2	NUM
ejpam-1929	103	40	3	3	NUM
ejpam-1929	103	41	4	4	NUM
ejpam-1929	103	42	5	5	NUM
ejpam-1929	103	43	6	6	NUM
ejpam-1929	103	44	(	(	PUNCT
ejpam-1929	103	45	f	f	X
ejpam-1929	103	46	)	)	PUNCT
ejpam-1929	103	47	g7	g7	PROPN
ejpam-1929	103	48	figure	figure	NOUN
ejpam-1929	103	49	1	1	NUM
ejpam-1929	103	50	:	:	PUNCT
ejpam-1929	103	51	some	some	DET
ejpam-1929	103	52	examples	example	NOUN
ejpam-1929	103	53	of	of	ADP
ejpam-1929	103	54	unitary	unitary	ADJ
ejpam-1929	103	55	addition	addition	NOUN
ejpam-1929	103	56	cayley	cayley	NOUN
ejpam-1929	103	57	graphs	graph	NOUN
ejpam-1929	103	58	0	0	NUM
ejpam-1929	103	59	2	2	NUM
ejpam-1929	103	60	3	3	NUM
ejpam-1929	103	61	4	4	NUM
ejpam-1929	103	62	1	1	NUM
ejpam-1929	103	63	(	(	PUNCT
ejpam-1929	103	64	a	a	X
ejpam-1929	103	65	)	)	PUNCT
ejpam-1929	103	66	σ5	σ5	NOUN
ejpam-1929	103	67	0	0	NUM
ejpam-1929	103	68	1	1	NUM
ejpam-1929	103	69	2	2	NUM
ejpam-1929	103	70	3	3	NUM
ejpam-1929	103	71	45	45	NUM
ejpam-1929	103	72	(	(	PUNCT
ejpam-1929	103	73	b	b	NOUN
ejpam-1929	103	74	)	)	PUNCT
ejpam-1929	103	75	σ6	σ6	NOUN
ejpam-1929	103	76	(	(	PUNCT
ejpam-1929	103	77	c	c	NOUN
ejpam-1929	103	78	)	)	PUNCT
ejpam-1929	103	79	σ10	σ10	ADJ
ejpam-1929	103	80	figure	figure	NOUN
ejpam-1929	103	81	2	2	NUM
ejpam-1929	103	82	:	:	PUNCT
ejpam-1929	103	83	some	some	DET
ejpam-1929	103	84	examples	example	NOUN
ejpam-1929	103	85	of	of	ADP
ejpam-1929	103	86	unitary	unitary	ADJ
ejpam-1929	103	87	addition	addition	NOUN
ejpam-1929	103	88	cayley	cayley	NOUN
ejpam-1929	103	89	sigraphs	sigraph	VERB
ejpam-1929	103	90	three	three	NUM
ejpam-1929	103	91	examples	example	NOUN
ejpam-1929	103	92	of	of	ADP
ejpam-1929	103	93	unitary	unitary	ADJ
ejpam-1929	103	94	addition	addition	NOUN
ejpam-1929	103	95	cayley	cayley	NOUN
ejpam-1929	103	96	sigraphs	sigraph	VERB
ejpam-1929	103	97	for	for	ADP
ejpam-1929	103	98	n	n	NOUN
ejpam-1929	103	99	=	=	SYM
ejpam-1929	103	100	5,6,10	5,6,10	NOUN
ejpam-1929	103	101	are	be	AUX
ejpam-1929	103	102	displayed	display	VERB
ejpam-1929	103	103	as	as	ADP
ejpam-1929	103	104	(	(	PUNCT
ejpam-1929	103	105	a	a	NOUN
ejpam-1929	103	106	)	)	PUNCT
ejpam-1929	103	107	,	,	PUNCT
ejpam-1929	103	108	(	(	PUNCT
ejpam-1929	103	109	b	b	X
ejpam-1929	103	110	)	)	PUNCT
ejpam-1929	103	111	and	and	CCONJ
ejpam-1929	103	112	(	(	PUNCT
ejpam-1929	103	113	c	c	NOUN
ejpam-1929	103	114	)	)	PUNCT
ejpam-1929	103	115	respectively	respectively	ADV
ejpam-1929	103	116	in	in	ADP
ejpam-1929	103	117	figure	figure	NOUN
ejpam-1929	103	118	2	2	NUM
ejpam-1929	103	119	.	.	PUNCT
ejpam-1929	104	1	throughout	throughout	ADP
ejpam-1929	104	2	the	the	DET
ejpam-1929	104	3	text	text	NOUN
ejpam-1929	104	4	,	,	PUNCT
ejpam-1929	104	5	we	we	PRON
ejpam-1929	104	6	consider	consider	VERB
ejpam-1929	104	7	n≥	n≥	NOUN
ejpam-1929	104	8	2	2	NUM
ejpam-1929	104	9	.	.	X
ejpam-1929	104	10	d.	d.	PROPN
ejpam-1929	104	11	sinha	sinha	PROPN
ejpam-1929	104	12	,	,	PUNCT
ejpam-1929	104	13	a.	a.	NOUN
ejpam-1929	104	14	dhama	dhama	PROPN
ejpam-1929	104	15	,	,	PUNCT
ejpam-1929	104	16	b.	b.	PROPN
ejpam-1929	104	17	acharya	acharya	PROPN
ejpam-1929	104	18	/	/	SYM
ejpam-1929	104	19	eur	eur	PROPN
ejpam-1929	104	20	.	.	PUNCT
ejpam-1929	105	1	j.	j.	PROPN
ejpam-1929	105	2	pure	pure	PROPN
ejpam-1929	105	3	appl	appl	PROPN
ejpam-1929	105	4	.	.	PROPN
ejpam-1929	105	5	math	math	PROPN
ejpam-1929	105	6	,	,	PUNCT
ejpam-1929	105	7	6	6	NUM
ejpam-1929	105	8	(	(	PUNCT
ejpam-1929	105	9	2013	2013	NUM
ejpam-1929	105	10	)	)	PUNCT
ejpam-1929	105	11	,	,	PUNCT
ejpam-1929	105	12	189	189	NUM
ejpam-1929	105	13	-	-	SYM
ejpam-1929	105	14	210	210	NUM
ejpam-1929	105	15	195	195	NUM
ejpam-1929	105	16	theorem	theorem	NOUN
ejpam-1929	105	17	4	4	NUM
ejpam-1929	105	18	(	(	PUNCT
ejpam-1929	105	19	[	[	X
ejpam-1929	105	20	43	43	NUM
ejpam-1929	105	21	]	]	PUNCT
ejpam-1929	105	22	)	)	PUNCT
ejpam-1929	105	23	.	.	PUNCT
ejpam-1929	106	1	let	let	VERB
ejpam-1929	106	2	m	m	PRON
ejpam-1929	106	3	be	be	AUX
ejpam-1929	106	4	any	any	DET
ejpam-1929	106	5	vertex	vertex	NOUN
ejpam-1929	106	6	of	of	ADP
ejpam-1929	106	7	the	the	DET
ejpam-1929	106	8	unitary	unitary	ADJ
ejpam-1929	106	9	addition	addition	NOUN
ejpam-1929	106	10	cayley	cayley	NOUN
ejpam-1929	106	11	graph	graph	NOUN
ejpam-1929	106	12	gn	gn	PROPN
ejpam-1929	106	13	.	.	PUNCT
ejpam-1929	107	1	then	then	ADV
ejpam-1929	107	2	,	,	PUNCT
ejpam-1929	107	3	d(m	d(m	PROPN
ejpam-1929	107	4	)	)	PUNCT
ejpam-1929	107	5	=	=	PUNCT
ejpam-1929	108	1	(	(	PUNCT
ejpam-1929	108	2	φ(n)−	φ(n)−	X
ejpam-1929	108	3	1	1	NUM
ejpam-1929	108	4	if	if	SCONJ
ejpam-1929	108	5	n	n	NOUN
ejpam-1929	108	6	is	be	AUX
ejpam-1929	108	7	odd	odd	ADJ
ejpam-1929	108	8	and	and	CCONJ
ejpam-1929	108	9	(	(	PUNCT
ejpam-1929	108	10	m	m	PROPN
ejpam-1929	108	11	,	,	PUNCT
ejpam-1929	108	12	n	n	CCONJ
ejpam-1929	108	13	)	)	PUNCT
ejpam-1929	108	14	=	=	SYM
ejpam-1929	108	15	1	1	X
ejpam-1929	108	16	.	.	PUNCT
ejpam-1929	108	17	φ(n	φ(n	NOUN
ejpam-1929	108	18	)	)	PUNCT
ejpam-1929	108	19	otherwise	otherwise	ADV
ejpam-1929	108	20	.	.	PUNCT
ejpam-1929	109	1	where	where	SCONJ
ejpam-1929	109	2	φ(n	φ(n	NOUN
ejpam-1929	109	3	)	)	PUNCT
ejpam-1929	109	4	denotes	denote	VERB
ejpam-1929	109	5	the	the	DET
ejpam-1929	109	6	euler	euler	PROPN
ejpam-1929	109	7	totient	totient	PROPN
ejpam-1929	109	8	function	function	NOUN
ejpam-1929	109	9	that	that	PRON
ejpam-1929	109	10	gives	give	VERB
ejpam-1929	109	11	the	the	DET
ejpam-1929	109	12	number	number	NOUN
ejpam-1929	109	13	of	of	ADP
ejpam-1929	109	14	primes	prime	NOUN
ejpam-1929	109	15	not	not	PART
ejpam-1929	109	16	exceeding	exceed	VERB
ejpam-1929	109	17	n.	n.	PROPN
ejpam-1929	109	18	lemma	lemma	PROPN
ejpam-1929	109	19	2	2	NUM
ejpam-1929	109	20	.	.	PUNCT
ejpam-1929	109	21	for	for	ADP
ejpam-1929	109	22	an	an	DET
ejpam-1929	109	23	integer	integer	NOUN
ejpam-1929	109	24	n	n	CCONJ
ejpam-1929	109	25	,	,	PUNCT
ejpam-1929	109	26	if	if	SCONJ
ejpam-1929	109	27	i	i	PRON
ejpam-1929	109	28	∈	∈	PROPN
ejpam-1929	109	29	un	un	PROPN
ejpam-1929	109	30	then	then	ADV
ejpam-1929	109	31	(	(	PUNCT
ejpam-1929	109	32	n−	n−	NOUN
ejpam-1929	109	33	i	i	NOUN
ejpam-1929	109	34	)	)	PUNCT
ejpam-1929	109	35	∈	∈	PROPN
ejpam-1929	109	36	un	un	PROPN
ejpam-1929	110	1	and	and	CCONJ
ejpam-1929	110	2	if	if	SCONJ
ejpam-1929	110	3	i	i	PRON
ejpam-1929	110	4	6∈	6∈	PROPN
ejpam-1929	110	5	un	un	PROPN
ejpam-1929	110	6	then	then	ADV
ejpam-1929	110	7	(	(	PUNCT
ejpam-1929	110	8	n−	n−	NOUN
ejpam-1929	110	9	i	i	NOUN
ejpam-1929	110	10	)	)	PUNCT
ejpam-1929	110	11	6∈	6∈	PROPN
ejpam-1929	110	12	un	un	PROPN
ejpam-1929	111	1	.	.	PROPN
ejpam-1929	111	2	proof	proof	NOUN
ejpam-1929	111	3	.	.	PUNCT
ejpam-1929	112	1	suppose	suppose	VERB
ejpam-1929	112	2	n	n	PRON
ejpam-1929	112	3	is	be	AUX
ejpam-1929	112	4	any	any	DET
ejpam-1929	112	5	integer	integer	NOUN
ejpam-1929	112	6	.	.	PUNCT
ejpam-1929	113	1	then	then	ADV
ejpam-1929	113	2	,	,	PUNCT
ejpam-1929	113	3	i	i	PROPN
ejpam-1929	113	4	∈	∈	PROPN
ejpam-1929	113	5	un	un	PROPN
ejpam-1929	113	6	⇒	⇒	PROPN
ejpam-1929	113	7	(	(	PUNCT
ejpam-1929	113	8	n	n	CCONJ
ejpam-1929	113	9	,	,	PUNCT
ejpam-1929	113	10	i	i	NOUN
ejpam-1929	113	11	)	)	PUNCT
ejpam-1929	113	12	=	=	PUNCT
ejpam-1929	113	13	1	1	NUM
ejpam-1929	113	14	,	,	PUNCT
ejpam-1929	113	15	where	where	SCONJ
ejpam-1929	113	16	(	(	PUNCT
ejpam-1929	113	17	n	n	X
ejpam-1929	113	18	,	,	PUNCT
ejpam-1929	113	19	i	i	NOUN
ejpam-1929	113	20	)	)	PUNCT
ejpam-1929	113	21	is	be	AUX
ejpam-1929	113	22	gcd(n	gcd(n	NOUN
ejpam-1929	113	23	,	,	PUNCT
ejpam-1929	113	24	i	i	NOUN
ejpam-1929	113	25	)	)	PUNCT
ejpam-1929	113	26	.	.	PUNCT
ejpam-1929	114	1	we	we	PRON
ejpam-1929	114	2	want	want	VERB
ejpam-1929	114	3	to	to	PART
ejpam-1929	114	4	show	show	VERB
ejpam-1929	114	5	that	that	SCONJ
ejpam-1929	114	6	(	(	PUNCT
ejpam-1929	114	7	n−	n−	NOUN
ejpam-1929	114	8	i	i	NOUN
ejpam-1929	114	9	)	)	PUNCT
ejpam-1929	114	10	∈	∈	PROPN
ejpam-1929	114	11	un	un	PROPN
ejpam-1929	114	12	.	.	PROPN
ejpam-1929	114	13	suppose	suppose	VERB
ejpam-1929	114	14	,	,	PUNCT
ejpam-1929	114	15	on	on	ADP
ejpam-1929	114	16	the	the	DET
ejpam-1929	114	17	contrary	contrary	NOUN
ejpam-1929	114	18	,	,	PUNCT
ejpam-1929	114	19	(	(	PUNCT
ejpam-1929	114	20	n−	n−	NOUN
ejpam-1929	114	21	i	i	NOUN
ejpam-1929	114	22	)	)	PUNCT
ejpam-1929	114	23	6∈	6∈	PROPN
ejpam-1929	114	24	un	un	PROPN
ejpam-1929	114	25	.	.	PROPN
ejpam-1929	115	1	then	then	ADV
ejpam-1929	115	2	,	,	PUNCT
ejpam-1929	115	3	(	(	PUNCT
ejpam-1929	115	4	n	n	CCONJ
ejpam-1929	115	5	,	,	PUNCT
ejpam-1929	115	6	n−	n−	PROPN
ejpam-1929	115	7	i	i	NOUN
ejpam-1929	115	8	)	)	PUNCT
ejpam-1929	115	9	=	=	SYM
ejpam-1929	115	10	k	k	PROPN
ejpam-1929	115	11	⇒	⇒	PROPN
ejpam-1929	116	1	k	k	PROPN
ejpam-1929	117	1	|	|	ADV
ejpam-1929	117	2	n	n	PROPN
ejpam-1929	118	1	and	and	CCONJ
ejpam-1929	118	2	k	k	PROPN
ejpam-1929	119	1	|	|	ADV
ejpam-1929	119	2	(	(	PUNCT
ejpam-1929	119	3	n−	n−	NOUN
ejpam-1929	119	4	i	i	NOUN
ejpam-1929	119	5	)	)	PUNCT
ejpam-1929	119	6	,	,	PUNCT
ejpam-1929	119	7	whence	whence	NOUN
ejpam-1929	119	8	n	n	NOUN
ejpam-1929	119	9	=	=	SYM
ejpam-1929	119	10	αk	αk	NOUN
ejpam-1929	120	1	and	and	CCONJ
ejpam-1929	120	2	(	(	PUNCT
ejpam-1929	120	3	n−	n−	NOUN
ejpam-1929	120	4	i	i	NOUN
ejpam-1929	120	5	)	)	PUNCT
ejpam-1929	121	1	=	=	PUNCT
ejpam-1929	121	2	βk	βk	PROPN
ejpam-1929	121	3	.	.	PUNCT
ejpam-1929	122	1	but	but	CCONJ
ejpam-1929	122	2	,	,	PUNCT
ejpam-1929	122	3	n	n	NOUN
ejpam-1929	122	4	=	=	PRON
ejpam-1929	122	5	αk	αk	NOUN
ejpam-1929	122	6	gives	give	VERB
ejpam-1929	122	7	αk−	αk−	PUNCT
ejpam-1929	123	1	i	i	PRON
ejpam-1929	123	2	=	=	VERB
ejpam-1929	123	3	βk⇒	βk⇒	PROPN
ejpam-1929	123	4	(	(	PUNCT
ejpam-1929	123	5	α−	α−	X
ejpam-1929	123	6	β)k	β)k	PUNCT
ejpam-1929	124	1	=	=	PUNCT
ejpam-1929	124	2	i	i	PRON
ejpam-1929	124	3	⇒	⇒	VERB
ejpam-1929	124	4	k	k	PROPN
ejpam-1929	124	5	|	|	ADV
ejpam-1929	124	6	i.	i.	PROPN
ejpam-1929	124	7	thus	thus	ADV
ejpam-1929	124	8	,	,	PUNCT
ejpam-1929	124	9	k	k	PROPN
ejpam-1929	125	1	|	|	ADV
ejpam-1929	125	2	i	i	PRON
ejpam-1929	125	3	and	and	CCONJ
ejpam-1929	125	4	k	k	NOUN
ejpam-1929	126	1	|	|	ADV
ejpam-1929	126	2	n	n	ADV
ejpam-1929	126	3	imply	imply	VERB
ejpam-1929	126	4	(	(	PUNCT
ejpam-1929	126	5	n	n	X
ejpam-1929	126	6	,	,	PUNCT
ejpam-1929	126	7	i	i	NOUN
ejpam-1929	126	8	)	)	PUNCT
ejpam-1929	126	9	6=	6=	ADP
ejpam-1929	126	10	1	1	NUM
ejpam-1929	126	11	,	,	PUNCT
ejpam-1929	126	12	a	a	DET
ejpam-1929	126	13	contradiction	contradiction	NOUN
ejpam-1929	126	14	to	to	ADP
ejpam-1929	126	15	our	our	PRON
ejpam-1929	126	16	hypothesis	hypothesis	NOUN
ejpam-1929	126	17	.	.	PUNCT
ejpam-1929	127	1	hence	hence	ADV
ejpam-1929	127	2	,	,	PUNCT
ejpam-1929	127	3	if	if	SCONJ
ejpam-1929	127	4	i	i	PRON
ejpam-1929	127	5	∈	∈	PROPN
ejpam-1929	127	6	un	un	PROPN
ejpam-1929	127	7	then	then	ADV
ejpam-1929	127	8	(	(	PUNCT
ejpam-1929	127	9	n−	n−	NOUN
ejpam-1929	127	10	i	i	NOUN
ejpam-1929	127	11	)	)	PUNCT
ejpam-1929	127	12	∈	∈	PROPN
ejpam-1929	127	13	un	un	PROPN
ejpam-1929	127	14	.	.	PROPN
ejpam-1929	128	1	next	next	ADV
ejpam-1929	128	2	,	,	PUNCT
ejpam-1929	128	3	suppose	suppose	VERB
ejpam-1929	128	4	i	i	PRON
ejpam-1929	128	5	6∈	6∈	PROPN
ejpam-1929	128	6	un	un	PROPN
ejpam-1929	128	7	.	.	PROPN
ejpam-1929	129	1	then	then	ADV
ejpam-1929	129	2	,	,	PUNCT
ejpam-1929	129	3	(	(	PUNCT
ejpam-1929	129	4	n−	n−	NOUN
ejpam-1929	129	5	i	i	NOUN
ejpam-1929	129	6	)	)	PUNCT
ejpam-1929	129	7	∈	∈	PROPN
ejpam-1929	129	8	un⇒	un⇒	NOUN
ejpam-1929	129	9	(	(	PUNCT
ejpam-1929	129	10	n	n	CCONJ
ejpam-1929	129	11	,	,	PUNCT
ejpam-1929	129	12	(	(	PUNCT
ejpam-1929	129	13	n−	n−	NOUN
ejpam-1929	129	14	i	i	NOUN
ejpam-1929	129	15	)	)	PUNCT
ejpam-1929	129	16	)	)	PUNCT
ejpam-1929	130	1	=	=	PUNCT
ejpam-1929	130	2	1	1	X
ejpam-1929	130	3	.	.	X
ejpam-1929	131	1	as	as	SCONJ
ejpam-1929	131	2	i	i	PRON
ejpam-1929	131	3	6∈	6∈	NOUN
ejpam-1929	131	4	un⇒	un⇒	NOUN
ejpam-1929	131	5	1	1	NUM
ejpam-1929	131	6	6=	6=	NUM
ejpam-1929	131	7	(	(	PUNCT
ejpam-1929	131	8	n	n	CCONJ
ejpam-1929	131	9	,	,	PUNCT
ejpam-1929	131	10	i	i	NOUN
ejpam-1929	131	11	)	)	PUNCT
ejpam-1929	132	1	=	=	SYM
ejpam-1929	132	2	l	l	NOUN
ejpam-1929	132	3	⇒	⇒	X
ejpam-1929	132	4	l	l	NOUN
ejpam-1929	133	1	|	|	ADV
ejpam-1929	133	2	n	n	PROPN
ejpam-1929	133	3	and	and	CCONJ
ejpam-1929	133	4	l	l	NOUN
ejpam-1929	134	1	|	|	ADV
ejpam-1929	134	2	i	i	PRON
ejpam-1929	134	3	⇒	⇒	VERB
ejpam-1929	134	4	n	n	NOUN
ejpam-1929	134	5	=	=	SYM
ejpam-1929	134	6	αl	αl	PROPN
ejpam-1929	135	1	and	and	CCONJ
ejpam-1929	135	2	i	i	PRON
ejpam-1929	135	3	=	=	PUNCT
ejpam-1929	135	4	β	β	PROPN
ejpam-1929	135	5	l.	l.	PROPN
ejpam-1929	136	1	this	this	PRON
ejpam-1929	136	2	shows	show	VERB
ejpam-1929	136	3	that	that	SCONJ
ejpam-1929	136	4	n−	n−	NOUN
ejpam-1929	136	5	i	i	NOUN
ejpam-1929	136	6	=	=	PUNCT
ejpam-1929	136	7	αl	αl	ADP
ejpam-1929	136	8	−	−	PROPN
ejpam-1929	136	9	β	β	SYM
ejpam-1929	136	10	l	l	NOUN
ejpam-1929	136	11	⇒	⇒	NOUN
ejpam-1929	136	12	(	(	PUNCT
ejpam-1929	136	13	α−	α−	X
ejpam-1929	136	14	β)l	β)l	PUNCT
ejpam-1929	136	15	⇒	⇒	NOUN
ejpam-1929	137	1	l	l	NOUN
ejpam-1929	138	1	|	|	ADV
ejpam-1929	138	2	(	(	PUNCT
ejpam-1929	138	3	n−	n−	NOUN
ejpam-1929	138	4	i	i	NOUN
ejpam-1929	138	5	)	)	PUNCT
ejpam-1929	138	6	.	.	PUNCT
ejpam-1929	139	1	thus	thus	ADV
ejpam-1929	139	2	,	,	PUNCT
ejpam-1929	139	3	l	l	PROPN
ejpam-1929	139	4	|	|	NOUN
ejpam-1929	139	5	n	n	PROPN
ejpam-1929	139	6	and	and	CCONJ
ejpam-1929	139	7	l	l	NOUN
ejpam-1929	139	8	|	|	ADV
ejpam-1929	139	9	(	(	PUNCT
ejpam-1929	139	10	n−	n−	NOUN
ejpam-1929	139	11	i	i	NOUN
ejpam-1929	139	12	)	)	PUNCT
ejpam-1929	139	13	imply	imply	VERB
ejpam-1929	139	14	(	(	PUNCT
ejpam-1929	139	15	n	n	CCONJ
ejpam-1929	139	16	,	,	PUNCT
ejpam-1929	139	17	(	(	PUNCT
ejpam-1929	139	18	n−	n−	NOUN
ejpam-1929	139	19	i	i	NOUN
ejpam-1929	139	20	)	)	PUNCT
ejpam-1929	139	21	)	)	PUNCT
ejpam-1929	140	1	6=	6=	ADP
ejpam-1929	140	2	1	1	NUM
ejpam-1929	140	3	,	,	PUNCT
ejpam-1929	140	4	a	a	DET
ejpam-1929	140	5	contradiction	contradiction	NOUN
ejpam-1929	140	6	to	to	ADP
ejpam-1929	140	7	the	the	DET
ejpam-1929	140	8	hypothesis	hypothesis	NOUN
ejpam-1929	140	9	.	.	PUNCT
ejpam-1929	141	1	hence	hence	ADV
ejpam-1929	141	2	,	,	PUNCT
ejpam-1929	141	3	by	by	ADP
ejpam-1929	141	4	contraposition	contraposition	NOUN
ejpam-1929	141	5	,	,	PUNCT
ejpam-1929	141	6	if	if	SCONJ
ejpam-1929	141	7	i	i	PRON
ejpam-1929	141	8	6∈	6∈	PROPN
ejpam-1929	141	9	un	un	PROPN
ejpam-1929	141	10	then	then	ADV
ejpam-1929	141	11	(	(	PUNCT
ejpam-1929	141	12	n−	n−	NOUN
ejpam-1929	141	13	i	i	NOUN
ejpam-1929	141	14	)	)	PUNCT
ejpam-1929	141	15	6∈	6∈	PROPN
ejpam-1929	141	16	un	un	PROPN
ejpam-1929	141	17	.	.	PUNCT
ejpam-1929	142	1	thus	thus	ADV
ejpam-1929	142	2	,	,	PUNCT
ejpam-1929	142	3	the	the	DET
ejpam-1929	142	4	result	result	NOUN
ejpam-1929	142	5	follows	follow	VERB
ejpam-1929	142	6	.	.	PUNCT
ejpam-1929	143	1	theorem	theorem	ADJ
ejpam-1929	143	2	5	5	NUM
ejpam-1929	143	3	.	.	PUNCT
ejpam-1929	144	1	the	the	DET
ejpam-1929	144	2	unitary	unitary	ADJ
ejpam-1929	144	3	addition	addition	NOUN
ejpam-1929	144	4	cayley	cayley	NOUN
ejpam-1929	144	5	sigraph	sigraph	NOUN
ejpam-1929	144	6	σn	σn	NOUN
ejpam-1929	144	7	=	=	SYM
ejpam-1929	144	8	(	(	PUNCT
ejpam-1929	144	9	σ	σ	PROPN
ejpam-1929	144	10	u	u	PROPN
ejpam-1929	144	11	n	n	CCONJ
ejpam-1929	144	12	,	,	PUNCT
ejpam-1929	144	13	σ1	σ1	PROPN
ejpam-1929	144	14	)	)	PUNCT
ejpam-1929	144	15	is	be	AUX
ejpam-1929	144	16	isomorphic	isomorphic	ADJ
ejpam-1929	144	17	to	to	ADP
ejpam-1929	144	18	the	the	DET
ejpam-1929	144	19	unitary	unitary	ADJ
ejpam-1929	144	20	cayley	cayley	NOUN
ejpam-1929	144	21	sigraph	sigraph	NOUN
ejpam-1929	144	22	sn	sn	NOUN
ejpam-1929	144	23	=	=	PUNCT
ejpam-1929	145	1	(	(	PUNCT
ejpam-1929	145	2	s	s	NOUN
ejpam-1929	145	3	u	u	NOUN
ejpam-1929	145	4	n	n	NOUN
ejpam-1929	145	5	,	,	PUNCT
ejpam-1929	145	6	σ2	σ2	NOUN
ejpam-1929	145	7	)	)	PUNCT
ejpam-1929	145	8	if	if	SCONJ
ejpam-1929	145	9	and	and	CCONJ
ejpam-1929	145	10	only	only	ADV
ejpam-1929	145	11	if	if	SCONJ
ejpam-1929	145	12	n	n	PRON
ejpam-1929	145	13	is	be	AUX
ejpam-1929	145	14	even	even	ADV
ejpam-1929	145	15	.	.	PUNCT
ejpam-1929	146	1	proof	proof	NOUN
ejpam-1929	146	2	.	.	PUNCT
ejpam-1929	147	1	necessity	necessity	NOUN
ejpam-1929	147	2	:	:	PUNCT
ejpam-1929	147	3	suppose	suppose	VERB
ejpam-1929	147	4	σn	σn	PRON
ejpam-1929	147	5	∼=	∼=	PROPN
ejpam-1929	147	6	sn	sn	NOUN
ejpam-1929	147	7	.	.	PUNCT
ejpam-1929	148	1	then	then	ADV
ejpam-1929	148	2	,	,	PUNCT
ejpam-1929	148	3	σu	σu	PROPN
ejpam-1929	148	4	n	n	PRON
ejpam-1929	148	5	∼=	∼=	PROPN
ejpam-1929	148	6	su	su	PROPN
ejpam-1929	148	7	n	n	CCONJ
ejpam-1929	148	8	,	,	PUNCT
ejpam-1929	148	9	whence	whence	SCONJ
ejpam-1929	148	10	the	the	DET
ejpam-1929	148	11	proof	proof	NOUN
ejpam-1929	148	12	follows	follow	VERB
ejpam-1929	148	13	by	by	ADP
ejpam-1929	148	14	theorem	theorem	NOUN
ejpam-1929	148	15	3	3	NUM
ejpam-1929	148	16	.	.	PUNCT
ejpam-1929	148	17	sufficiency	sufficiency	NOUN
ejpam-1929	148	18	:	:	PUNCT
ejpam-1929	148	19	suppose	suppose	VERB
ejpam-1929	148	20	n	n	PRON
ejpam-1929	148	21	is	be	AUX
ejpam-1929	148	22	even	even	ADV
ejpam-1929	148	23	.	.	PUNCT
ejpam-1929	149	1	then	then	ADV
ejpam-1929	149	2	,	,	PUNCT
ejpam-1929	149	3	by	by	ADP
ejpam-1929	149	4	theorem	theorem	NOUN
ejpam-1929	149	5	3	3	NUM
ejpam-1929	149	6	,	,	PUNCT
ejpam-1929	149	7	we	we	PRON
ejpam-1929	149	8	get	get	VERB
ejpam-1929	149	9	σu	σu	ADP
ejpam-1929	149	10	n	n	PRON
ejpam-1929	149	11	∼=	∼=	PROPN
ejpam-1929	149	12	su	su	NOUN
ejpam-1929	149	13	n.	n.	PROPN
ejpam-1929	149	14	now	now	ADV
ejpam-1929	149	15	,	,	PUNCT
ejpam-1929	149	16	consider	consider	VERB
ejpam-1929	149	17	a	a	DET
ejpam-1929	149	18	function	function	NOUN
ejpam-1929	150	1	f	f	NOUN
ejpam-1929	150	2	:	:	PUNCT
ejpam-1929	150	3	v	v	X
ejpam-1929	150	4	(	(	PUNCT
ejpam-1929	150	5	gn)→	gn)→	NOUN
ejpam-1929	150	6	v	v	NOUN
ejpam-1929	150	7	(	(	PUNCT
ejpam-1929	150	8	xn	xn	PROPN
ejpam-1929	150	9	)	)	PUNCT
ejpam-1929	150	10	such	such	ADJ
ejpam-1929	150	11	that	that	SCONJ
ejpam-1929	150	12	f	f	PROPN
ejpam-1929	150	13	(	(	PUNCT
ejpam-1929	150	14	m	m	PROPN
ejpam-1929	150	15	)	)	PUNCT
ejpam-1929	150	16	=	=	SYM
ejpam-1929	151	1	(	(	PUNCT
ejpam-1929	151	2	m	m	VERB
ejpam-1929	151	3	if	if	SCONJ
ejpam-1929	151	4	m	m	ADJ
ejpam-1929	151	5	is	be	AUX
ejpam-1929	151	6	even	even	ADV
ejpam-1929	151	7	n−m	n−m	ADJ
ejpam-1929	151	8	if	if	SCONJ
ejpam-1929	151	9	m	m	PROPN
ejpam-1929	151	10	is	be	AUX
ejpam-1929	151	11	odd	odd	ADJ
ejpam-1929	151	12	.	.	PUNCT
ejpam-1929	152	1	let	let	VERB
ejpam-1929	152	2	un	un	PROPN
ejpam-1929	152	3	=	=	PROPN
ejpam-1929	152	4	{	{	PUNCT
ejpam-1929	152	5	a1	a1	PROPN
ejpam-1929	152	6	,	,	PUNCT
ejpam-1929	152	7	a2	a2	PROPN
ejpam-1929	152	8	,	,	PUNCT
ejpam-1929	152	9	.	.	PUNCT
ejpam-1929	152	10	.	.	PUNCT
ejpam-1929	153	1	.	.	PUNCT
ejpam-1929	154	1	,	,	PUNCT
ejpam-1929	155	1	aφ(n	aφ(n	PUNCT
ejpam-1929	155	2	)	)	PUNCT
ejpam-1929	155	3	}	}	PUNCT
ejpam-1929	155	4	.	.	PUNCT
ejpam-1929	156	1	since	since	SCONJ
ejpam-1929	156	2	the	the	DET
ejpam-1929	156	3	vertex	vertex	NOUN
ejpam-1929	156	4	m	m	NOUN
ejpam-1929	156	5	is	be	AUX
ejpam-1929	156	6	adjacent	adjacent	ADJ
ejpam-1929	156	7	to	to	ADP
ejpam-1929	156	8	the	the	DET
ejpam-1929	156	9	vertices	vertex	NOUN
ejpam-1929	156	10	of	of	ADP
ejpam-1929	156	11	type	type	NOUN
ejpam-1929	156	12	ar	ar	PROPN
ejpam-1929	156	13	−	−	PROPN
ejpam-1929	156	14	m	m	PROPN
ejpam-1929	156	15	,	,	PUNCT
ejpam-1929	156	16	consider	consider	VERB
ejpam-1929	156	17	a	a	DET
ejpam-1929	156	18	set	set	ADJ
ejpam-1929	156	19	a=	a=	NOUN
ejpam-1929	156	20	{	{	PUNCT
ejpam-1929	156	21	a1−m	a1−m	PROPN
ejpam-1929	156	22	,	,	PUNCT
ejpam-1929	156	23	a2−m	a2−m	PROPN
ejpam-1929	156	24	,	,	PUNCT
ejpam-1929	156	25	.	.	PUNCT
ejpam-1929	156	26	.	.	PUNCT
ejpam-1929	157	1	.	.	PUNCT
ejpam-1929	158	1	,	,	PUNCT
ejpam-1929	158	2	aφ(n)−m	aφ(n)−m	NOUN
ejpam-1929	158	3	}	}	PUNCT
ejpam-1929	158	4	.	.	PUNCT
ejpam-1929	159	1	suppose	suppose	VERB
ejpam-1929	159	2	two	two	NUM
ejpam-1929	159	3	vertices	vertex	NOUN
ejpam-1929	159	4	i	i	PRON
ejpam-1929	159	5	and	and	CCONJ
ejpam-1929	159	6	j	j	PROPN
ejpam-1929	159	7	are	be	AUX
ejpam-1929	159	8	adjacent	adjacent	ADJ
ejpam-1929	159	9	in	in	ADP
ejpam-1929	159	10	gn	gn	PROPN
ejpam-1929	159	11	,	,	PUNCT
ejpam-1929	159	12	then	then	ADV
ejpam-1929	159	13	j	j	PROPN
ejpam-1929	159	14	is	be	AUX
ejpam-1929	159	15	of	of	ADP
ejpam-1929	159	16	the	the	DET
ejpam-1929	159	17	form	form	NOUN
ejpam-1929	159	18	ar	ar	PROPN
ejpam-1929	159	19	−	−	PROPN
ejpam-1929	160	1	i	i	PRON
ejpam-1929	160	2	,	,	PUNCT
ejpam-1929	160	3	where	where	SCONJ
ejpam-1929	160	4	ar	ar	PROPN
ejpam-1929	160	5	∈	∈	PROPN
ejpam-1929	160	6	un	un	PROPN
ejpam-1929	160	7	.	.	PROPN
ejpam-1929	160	8	case	case	NOUN
ejpam-1929	161	1	i	i	PRON
ejpam-1929	161	2	:	:	PUNCT
ejpam-1929	161	3	if	if	SCONJ
ejpam-1929	161	4	i	i	PRON
ejpam-1929	161	5	is	be	AUX
ejpam-1929	161	6	even	even	ADV
ejpam-1929	161	7	,	,	PUNCT
ejpam-1929	161	8	then	then	ADV
ejpam-1929	161	9	j	j	PROPN
ejpam-1929	161	10	=	=	PROPN
ejpam-1929	161	11	ar	ar	PROPN
ejpam-1929	162	1	−	−	PROPN
ejpam-1929	163	1	i	i	PRON
ejpam-1929	163	2	is	be	AUX
ejpam-1929	163	3	odd	odd	ADJ
ejpam-1929	163	4	.	.	PUNCT
ejpam-1929	164	1	this	this	PRON
ejpam-1929	164	2	implies	imply	VERB
ejpam-1929	164	3	that	that	SCONJ
ejpam-1929	164	4	f	f	PROPN
ejpam-1929	164	5	(	(	PUNCT
ejpam-1929	164	6	i	i	NOUN
ejpam-1929	164	7	)	)	PUNCT
ejpam-1929	165	1	=	=	VERB
ejpam-1929	165	2	i	i	PRON
ejpam-1929	165	3	and	and	CCONJ
ejpam-1929	165	4	f	f	PROPN
ejpam-1929	165	5	(	(	PUNCT
ejpam-1929	165	6	j	j	NOUN
ejpam-1929	165	7	)	)	PUNCT
ejpam-1929	165	8	=	=	PUNCT
ejpam-1929	166	1	n−	n−	NOUN
ejpam-1929	166	2	j	j	NOUN
ejpam-1929	166	3	=	=	SYM
ejpam-1929	166	4	n−	n−	PROPN
ejpam-1929	166	5	(	(	PUNCT
ejpam-1929	166	6	ar	ar	NOUN
ejpam-1929	166	7	−	−	PROPN
ejpam-1929	166	8	i	i	PROPN
ejpam-1929	166	9	)	)	PUNCT
ejpam-1929	166	10	.	.	PUNCT
ejpam-1929	167	1	now	now	ADV
ejpam-1929	167	2	,	,	PUNCT
ejpam-1929	167	3	by	by	ADP
ejpam-1929	167	4	theorem	theorem	NOUN
ejpam-1929	167	5	3	3	NUM
ejpam-1929	167	6	,	,	PUNCT
ejpam-1929	167	7	we	we	PRON
ejpam-1929	167	8	can	can	AUX
ejpam-1929	167	9	see	see	VERB
ejpam-1929	167	10	that	that	SCONJ
ejpam-1929	167	11	f	f	PROPN
ejpam-1929	167	12	(	(	PUNCT
ejpam-1929	167	13	i	i	NOUN
ejpam-1929	167	14	)	)	PUNCT
ejpam-1929	167	15	and	and	CCONJ
ejpam-1929	167	16	f	f	PROPN
ejpam-1929	167	17	(	(	PUNCT
ejpam-1929	167	18	j	j	NOUN
ejpam-1929	167	19	)	)	PUNCT
ejpam-1929	167	20	are	be	AUX
ejpam-1929	167	21	adjacent	adjacent	ADJ
ejpam-1929	167	22	in	in	ADP
ejpam-1929	167	23	xn	xn	PROPN
ejpam-1929	167	24	.	.	PUNCT
ejpam-1929	168	1	it	it	PRON
ejpam-1929	168	2	is	be	AUX
ejpam-1929	168	3	clear	clear	ADJ
ejpam-1929	168	4	that	that	SCONJ
ejpam-1929	168	5	i	i	PRON
ejpam-1929	168	6	6∈	6∈	PROPN
ejpam-1929	168	7	un	un	VERB
ejpam-1929	168	8	.	.	PUNCT
ejpam-1929	169	1	now	now	ADV
ejpam-1929	169	2	,	,	PUNCT
ejpam-1929	169	3	either	either	CCONJ
ejpam-1929	169	4	j	j	PROPN
ejpam-1929	169	5	∈	∈	PROPN
ejpam-1929	169	6	un	un	PROPN
ejpam-1929	169	7	or	or	CCONJ
ejpam-1929	169	8	j	j	PROPN
ejpam-1929	169	9	6∈	6∈	PROPN
ejpam-1929	169	10	un	un	PROPN
ejpam-1929	169	11	.	.	PROPN
ejpam-1929	170	1	if	if	SCONJ
ejpam-1929	170	2	j	j	PROPN
ejpam-1929	170	3	∈	∈	PROPN
ejpam-1929	170	4	un	un	PROPN
ejpam-1929	170	5	,	,	PUNCT
ejpam-1929	170	6	then	then	ADV
ejpam-1929	170	7	by	by	ADP
ejpam-1929	170	8	lemma	lemma	PROPN
ejpam-1929	170	9	2	2	NUM
ejpam-1929	170	10	,	,	PUNCT
ejpam-1929	170	11	n−	n−	PROPN
ejpam-1929	170	12	j	j	PROPN
ejpam-1929	170	13	∈	∈	PROPN
ejpam-1929	170	14	un	un	PROPN
ejpam-1929	170	15	.	.	PROPN
ejpam-1929	171	1	then	then	ADV
ejpam-1929	171	2	,	,	PUNCT
ejpam-1929	171	3	by	by	ADP
ejpam-1929	171	4	the	the	DET
ejpam-1929	171	5	definition	definition	NOUN
ejpam-1929	171	6	of	of	ADP
ejpam-1929	171	7	unitary	unitary	ADJ
ejpam-1929	171	8	cayley	cayley	NOUN
ejpam-1929	171	9	sigraph	sigraph	NOUN
ejpam-1929	171	10	σ2(i	σ2(i	PROPN
ejpam-1929	171	11	j	j	NOUN
ejpam-1929	171	12	)	)	PUNCT
ejpam-1929	171	13	=	=	PUNCT
ejpam-1929	171	14	+	+	X
ejpam-1929	171	15	.	.	PUNCT
ejpam-1929	171	16	now	now	ADV
ejpam-1929	171	17	,	,	PUNCT
ejpam-1929	171	18	f	f	PROPN
ejpam-1929	171	19	(	(	PUNCT
ejpam-1929	171	20	i	i	NOUN
ejpam-1929	171	21	)	)	PUNCT
ejpam-1929	171	22	6∈	6∈	PROPN
ejpam-1929	171	23	un	un	PROPN
ejpam-1929	171	24	as	as	ADP
ejpam-1929	171	25	f	f	PROPN
ejpam-1929	171	26	(	(	PUNCT
ejpam-1929	171	27	i	i	NOUN
ejpam-1929	171	28	)	)	PUNCT
ejpam-1929	171	29	is	be	AUX
ejpam-1929	171	30	even	even	ADV
ejpam-1929	171	31	and	and	CCONJ
ejpam-1929	171	32	f	f	PROPN
ejpam-1929	171	33	(	(	PUNCT
ejpam-1929	171	34	j	j	PROPN
ejpam-1929	171	35	)	)	PUNCT
ejpam-1929	171	36	∈	∈	PROPN
ejpam-1929	171	37	un	un	PROPN
ejpam-1929	171	38	as	as	ADP
ejpam-1929	171	39	f	f	PROPN
ejpam-1929	171	40	(	(	PUNCT
ejpam-1929	171	41	j	j	NOUN
ejpam-1929	171	42	)	)	PUNCT
ejpam-1929	172	1	=	=	PUNCT
ejpam-1929	172	2	n−	n−	NOUN
ejpam-1929	172	3	j	j	PROPN
ejpam-1929	172	4	∈	∈	PROPN
ejpam-1929	172	5	un	un	PROPN
ejpam-1929	172	6	.	.	PUNCT
ejpam-1929	173	1	so	so	ADV
ejpam-1929	173	2	,	,	PUNCT
ejpam-1929	173	3	by	by	ADP
ejpam-1929	173	4	the	the	DET
ejpam-1929	173	5	definition	definition	NOUN
ejpam-1929	173	6	of	of	ADP
ejpam-1929	173	7	unitary	unitary	ADJ
ejpam-1929	173	8	addition	addition	NOUN
ejpam-1929	173	9	cayley	cayley	NOUN
ejpam-1929	173	10	sigraph	sigraph	PROPN
ejpam-1929	173	11	σ1	σ1	PROPN
ejpam-1929	173	12	(	(	PUNCT
ejpam-1929	173	13	f	f	PROPN
ejpam-1929	173	14	(	(	PUNCT
ejpam-1929	173	15	i	i	NOUN
ejpam-1929	173	16	)	)	PUNCT
ejpam-1929	173	17	f	f	PROPN
ejpam-1929	173	18	(	(	PUNCT
ejpam-1929	173	19	j	j	NOUN
ejpam-1929	173	20	)	)	PUNCT
ejpam-1929	173	21	)	)	PUNCT
ejpam-1929	174	1	=	=	PUNCT
ejpam-1929	175	1	+	+	X
ejpam-1929	175	2	.	.	PROPN
ejpam-1929	175	3	d.	d.	PROPN
ejpam-1929	175	4	sinha	sinha	PROPN
ejpam-1929	175	5	,	,	PUNCT
ejpam-1929	175	6	a.	a.	NOUN
ejpam-1929	175	7	dhama	dhama	PROPN
ejpam-1929	175	8	,	,	PUNCT
ejpam-1929	175	9	b.	b.	PROPN
ejpam-1929	175	10	acharya	acharya	PROPN
ejpam-1929	175	11	/	/	SYM
ejpam-1929	175	12	eur	eur	PROPN
ejpam-1929	175	13	.	.	PUNCT
ejpam-1929	176	1	j.	j.	PROPN
ejpam-1929	176	2	pure	pure	PROPN
ejpam-1929	176	3	appl	appl	PROPN
ejpam-1929	176	4	.	.	PROPN
ejpam-1929	176	5	math	math	PROPN
ejpam-1929	176	6	,	,	PUNCT
ejpam-1929	176	7	6	6	NUM
ejpam-1929	176	8	(	(	PUNCT
ejpam-1929	176	9	2013	2013	NUM
ejpam-1929	176	10	)	)	PUNCT
ejpam-1929	176	11	,	,	PUNCT
ejpam-1929	176	12	189	189	NUM
ejpam-1929	176	13	-	-	SYM
ejpam-1929	176	14	210	210	NUM
ejpam-1929	176	15	196	196	NUM
ejpam-1929	176	16	if	if	SCONJ
ejpam-1929	176	17	j	j	PROPN
ejpam-1929	176	18	6∈	6∈	PROPN
ejpam-1929	176	19	un	un	PROPN
ejpam-1929	176	20	,	,	PUNCT
ejpam-1929	176	21	then	then	ADV
ejpam-1929	176	22	by	by	ADP
ejpam-1929	176	23	lemma	lemma	PROPN
ejpam-1929	176	24	2	2	NUM
ejpam-1929	176	25	n	n	NUM
ejpam-1929	176	26	−	−	PROPN
ejpam-1929	176	27	j	j	PROPN
ejpam-1929	176	28	6∈	6∈	PROPN
ejpam-1929	176	29	un	un	PROPN
ejpam-1929	176	30	.	.	PROPN
ejpam-1929	177	1	then	then	ADV
ejpam-1929	177	2	,	,	PUNCT
ejpam-1929	177	3	by	by	ADP
ejpam-1929	177	4	the	the	DET
ejpam-1929	177	5	definition	definition	NOUN
ejpam-1929	177	6	of	of	ADP
ejpam-1929	177	7	unitary	unitary	ADJ
ejpam-1929	177	8	cayley	cayley	NOUN
ejpam-1929	177	9	sigraph	sigraph	NOUN
ejpam-1929	177	10	σ2(i	σ2(i	PROPN
ejpam-1929	177	11	j	j	NOUN
ejpam-1929	177	12	)	)	PUNCT
ejpam-1929	177	13	=	=	NOUN
ejpam-1929	177	14	−	−	PROPN
ejpam-1929	177	15	and	and	CCONJ
ejpam-1929	177	16	as	as	ADP
ejpam-1929	177	17	in	in	ADP
ejpam-1929	177	18	the	the	DET
ejpam-1929	177	19	above	above	ADJ
ejpam-1929	177	20	argument	argument	NOUN
ejpam-1929	177	21	σ1	σ1	PROPN
ejpam-1929	177	22	(	(	PUNCT
ejpam-1929	177	23	f	f	PROPN
ejpam-1929	177	24	(	(	PUNCT
ejpam-1929	177	25	i	i	NOUN
ejpam-1929	177	26	)	)	PUNCT
ejpam-1929	177	27	f	f	PROPN
ejpam-1929	177	28	(	(	PUNCT
ejpam-1929	177	29	j	j	NOUN
ejpam-1929	177	30	)	)	PUNCT
ejpam-1929	177	31	)	)	PUNCT
ejpam-1929	178	1	=	=	PUNCT
ejpam-1929	179	1	−.	−.	ADV
ejpam-1929	179	2	thus	thus	ADV
ejpam-1929	179	3	,	,	PUNCT
ejpam-1929	179	4	we	we	PRON
ejpam-1929	179	5	have	have	VERB
ejpam-1929	179	6	σ1	σ1	PROPN
ejpam-1929	179	7	(	(	PUNCT
ejpam-1929	179	8	f	f	PROPN
ejpam-1929	179	9	(	(	PUNCT
ejpam-1929	179	10	i	i	NOUN
ejpam-1929	179	11	)	)	PUNCT
ejpam-1929	179	12	f	f	PROPN
ejpam-1929	179	13	(	(	PUNCT
ejpam-1929	179	14	j	j	NOUN
ejpam-1929	179	15	)	)	PUNCT
ejpam-1929	179	16	)	)	PUNCT
ejpam-1929	180	1	=	=	PUNCT
ejpam-1929	181	1	σ2(i	σ2(i	PROPN
ejpam-1929	181	2	j	j	NOUN
ejpam-1929	181	3	)	)	PUNCT
ejpam-1929	181	4	.	.	PUNCT
ejpam-1929	182	1	case	case	NOUN
ejpam-1929	182	2	ii	ii	NOUN
ejpam-1929	182	3	:	:	PUNCT
ejpam-1929	182	4	if	if	SCONJ
ejpam-1929	182	5	i	i	PRON
ejpam-1929	182	6	is	be	AUX
ejpam-1929	182	7	odd	odd	ADJ
ejpam-1929	182	8	,	,	PUNCT
ejpam-1929	182	9	then	then	ADV
ejpam-1929	182	10	j	j	PROPN
ejpam-1929	182	11	=	=	PROPN
ejpam-1929	182	12	ar	ar	PROPN
ejpam-1929	183	1	−	−	PROPN
ejpam-1929	183	2	i	i	PRON
ejpam-1929	183	3	is	be	AUX
ejpam-1929	183	4	even	even	ADV
ejpam-1929	183	5	.	.	PUNCT
ejpam-1929	184	1	thus	thus	ADV
ejpam-1929	184	2	,	,	PUNCT
ejpam-1929	184	3	j	j	PROPN
ejpam-1929	184	4	6∈	6∈	PROPN
ejpam-1929	184	5	un	un	PROPN
ejpam-1929	184	6	.	.	PROPN
ejpam-1929	184	7	again	again	ADV
ejpam-1929	184	8	,	,	PUNCT
ejpam-1929	184	9	either	either	CCONJ
ejpam-1929	184	10	i	i	PROPN
ejpam-1929	184	11	∈	∈	PROPN
ejpam-1929	184	12	un	un	PROPN
ejpam-1929	184	13	or	or	CCONJ
ejpam-1929	184	14	i	i	PRON
ejpam-1929	184	15	6∈	6∈	PROPN
ejpam-1929	184	16	un	un	PROPN
ejpam-1929	184	17	.	.	PROPN
ejpam-1929	185	1	if	if	SCONJ
ejpam-1929	185	2	i	i	PRON
ejpam-1929	185	3	∈	∈	PROPN
ejpam-1929	185	4	un	un	PROPN
ejpam-1929	185	5	,	,	PUNCT
ejpam-1929	185	6	then	then	ADV
ejpam-1929	185	7	n−	n−	VERB
ejpam-1929	185	8	i	i	PROPN
ejpam-1929	185	9	∈	∈	PROPN
ejpam-1929	185	10	un	un	PROPN
ejpam-1929	185	11	and	and	CCONJ
ejpam-1929	185	12	σ2(i	σ2(i	PROPN
ejpam-1929	185	13	j	j	PROPN
ejpam-1929	185	14	)	)	PUNCT
ejpam-1929	186	1	=	=	PUNCT
ejpam-1929	187	1	+	+	CCONJ
ejpam-1929	187	2	and	and	CCONJ
ejpam-1929	187	3	as	as	ADP
ejpam-1929	187	4	in	in	ADP
ejpam-1929	187	5	the	the	DET
ejpam-1929	187	6	above	above	ADJ
ejpam-1929	187	7	argument	argument	NOUN
ejpam-1929	187	8	,	,	PUNCT
ejpam-1929	187	9	σ1	σ1	PROPN
ejpam-1929	187	10	(	(	PUNCT
ejpam-1929	187	11	f	f	PROPN
ejpam-1929	187	12	(	(	PUNCT
ejpam-1929	187	13	i	i	NOUN
ejpam-1929	187	14	)	)	PUNCT
ejpam-1929	187	15	f	f	PROPN
ejpam-1929	187	16	(	(	PUNCT
ejpam-1929	187	17	j	j	NOUN
ejpam-1929	187	18	)	)	PUNCT
ejpam-1929	187	19	)	)	PUNCT
ejpam-1929	188	1	=	=	PUNCT
ejpam-1929	189	1	+	+	ADJ
ejpam-1929	189	2	.	.	PUNCT
ejpam-1929	190	1	if	if	SCONJ
ejpam-1929	190	2	i	i	PRON
ejpam-1929	190	3	6∈	6∈	PROPN
ejpam-1929	190	4	un	un	VERB
ejpam-1929	190	5	,	,	PUNCT
ejpam-1929	190	6	then	then	ADV
ejpam-1929	190	7	n−	n−	PROPN
ejpam-1929	190	8	i	i	PRON
ejpam-1929	190	9	6∈	6∈	PROPN
ejpam-1929	190	10	un	un	VERB
ejpam-1929	190	11	.	.	PROPN
ejpam-1929	190	12	hence	hence	ADV
ejpam-1929	190	13	,	,	PUNCT
ejpam-1929	190	14	by	by	ADP
ejpam-1929	190	15	the	the	DET
ejpam-1929	190	16	same	same	ADJ
ejpam-1929	190	17	argument	argument	NOUN
ejpam-1929	190	18	,	,	PUNCT
ejpam-1929	190	19	σ2(i	σ2(i	PROPN
ejpam-1929	190	20	j	j	NOUN
ejpam-1929	190	21	)	)	PUNCT
ejpam-1929	190	22	=	=	SYM
ejpam-1929	190	23	−	−	PROPN
ejpam-1929	190	24	and	and	CCONJ
ejpam-1929	190	25	σ1	σ1	PROPN
ejpam-1929	190	26	(	(	PUNCT
ejpam-1929	190	27	f	f	PROPN
ejpam-1929	190	28	(	(	PUNCT
ejpam-1929	190	29	i	i	NOUN
ejpam-1929	190	30	)	)	PUNCT
ejpam-1929	190	31	f	f	PROPN
ejpam-1929	190	32	(	(	PUNCT
ejpam-1929	190	33	j	j	NOUN
ejpam-1929	190	34	)	)	PUNCT
ejpam-1929	190	35	)	)	PUNCT
ejpam-1929	191	1	=	=	PUNCT
ejpam-1929	192	1	−.	−.	ADV
ejpam-1929	192	2	now	now	ADV
ejpam-1929	192	3	,	,	PUNCT
ejpam-1929	192	4	one	one	PRON
ejpam-1929	192	5	can	can	AUX
ejpam-1929	192	6	easily	easily	ADV
ejpam-1929	192	7	verify	verify	VERB
ejpam-1929	192	8	that	that	SCONJ
ejpam-1929	192	9	f	f	PROPN
ejpam-1929	192	10	is	be	AUX
ejpam-1929	192	11	one	one	NUM
ejpam-1929	192	12	-	-	PUNCT
ejpam-1929	192	13	to	to	ADP
ejpam-1929	192	14	-	-	PUNCT
ejpam-1929	192	15	one	one	NUM
ejpam-1929	192	16	and	and	CCONJ
ejpam-1929	192	17	onto	onto	ADP
ejpam-1929	192	18	function	function	NOUN
ejpam-1929	192	19	that	that	PRON
ejpam-1929	192	20	preserves	preserve	VERB
ejpam-1929	192	21	adjacency	adjacency	NOUN
ejpam-1929	192	22	as	as	ADV
ejpam-1929	192	23	well	well	ADV
ejpam-1929	192	24	as	as	ADP
ejpam-1929	192	25	sign	sign	NOUN
ejpam-1929	192	26	of	of	ADP
ejpam-1929	192	27	the	the	DET
ejpam-1929	192	28	edges	edge	NOUN
ejpam-1929	192	29	.	.	PUNCT
ejpam-1929	193	1	hence	hence	ADV
ejpam-1929	193	2	,	,	PUNCT
ejpam-1929	193	3	σn	σn	PRON
ejpam-1929	193	4	∼=	∼=	PROPN
ejpam-1929	193	5	sn	sn	NOUN
ejpam-1929	193	6	.	.	PROPN
ejpam-1929	194	1	3	3	X
ejpam-1929	194	2	.	.	X
ejpam-1929	194	3	balance	balance	NOUN
ejpam-1929	194	4	in	in	ADP
ejpam-1929	194	5	σn	σn	NOUN
ejpam-1929	194	6	in	in	ADP
ejpam-1929	194	7	this	this	DET
ejpam-1929	194	8	section	section	NOUN
ejpam-1929	194	9	,	,	PUNCT
ejpam-1929	194	10	we	we	PRON
ejpam-1929	194	11	establish	establish	VERB
ejpam-1929	194	12	a	a	DET
ejpam-1929	194	13	characterization	characterization	NOUN
ejpam-1929	194	14	of	of	ADP
ejpam-1929	194	15	balanced	balanced	ADJ
ejpam-1929	194	16	unitary	unitary	ADJ
ejpam-1929	194	17	addition	addition	NOUN
ejpam-1929	194	18	cayley	cayley	NOUN
ejpam-1929	194	19	sigraphs	sigraph	VERB
ejpam-1929	194	20	.	.	PUNCT
ejpam-1929	195	1	we	we	PRON
ejpam-1929	195	2	recall	recall	VERB
ejpam-1929	195	3	a	a	DET
ejpam-1929	195	4	known	know	VERB
ejpam-1929	195	5	result	result	NOUN
ejpam-1929	195	6	first	first	ADV
ejpam-1929	195	7	.	.	PUNCT
ejpam-1929	196	1	theorem	theorem	VERB
ejpam-1929	196	2	6	6	NUM
ejpam-1929	196	3	(	(	PUNCT
ejpam-1929	196	4	[	[	X
ejpam-1929	196	5	43	43	NUM
ejpam-1929	196	6	]	]	NUM
ejpam-1929	196	7	)	)	PUNCT
ejpam-1929	196	8	.	.	PUNCT
ejpam-1929	197	1	the	the	DET
ejpam-1929	197	2	unitary	unitary	ADJ
ejpam-1929	197	3	addition	addition	NOUN
ejpam-1929	197	4	cayley	cayley	NOUN
ejpam-1929	197	5	graph	graph	NOUN
ejpam-1929	197	6	gn	gn	PROPN
ejpam-1929	197	7	,	,	PUNCT
ejpam-1929	197	8	n	n	PRON
ejpam-1929	197	9	≥	≥	NOUN
ejpam-1929	197	10	2	2	NUM
ejpam-1929	197	11	,	,	PUNCT
ejpam-1929	197	12	is	be	AUX
ejpam-1929	197	13	bipartite	bipartite	ADJ
ejpam-1929	197	14	if	if	SCONJ
ejpam-1929	197	15	and	and	CCONJ
ejpam-1929	197	16	only	only	ADV
ejpam-1929	197	17	if	if	SCONJ
ejpam-1929	197	18	either	either	CCONJ
ejpam-1929	197	19	n=	n=	ADJ
ejpam-1929	197	20	3	3	NUM
ejpam-1929	197	21	or	or	CCONJ
ejpam-1929	197	22	n	n	NOUN
ejpam-1929	197	23	is	be	AUX
ejpam-1929	197	24	even	even	ADV
ejpam-1929	197	25	.	.	PUNCT
ejpam-1929	198	1	lemma	lemma	PROPN
ejpam-1929	198	2	3	3	NUM
ejpam-1929	198	3	.	.	X
ejpam-1929	199	1	for	for	ADP
ejpam-1929	199	2	the	the	DET
ejpam-1929	199	3	unitary	unitary	ADJ
ejpam-1929	199	4	addition	addition	NOUN
ejpam-1929	199	5	cayley	cayley	NOUN
ejpam-1929	199	6	sigraph	sigraph	NOUN
ejpam-1929	199	7	σn	σn	NOUN
ejpam-1929	199	8	=	=	SYM
ejpam-1929	199	9	(	(	PUNCT
ejpam-1929	199	10	σ	σ	PROPN
ejpam-1929	199	11	u	u	PROPN
ejpam-1929	199	12	n	n	NUM
ejpam-1929	199	13	,	,	PUNCT
ejpam-1929	199	14	σ	σ	PROPN
ejpam-1929	199	15	)	)	PUNCT
ejpam-1929	199	16	,	,	PUNCT
ejpam-1929	199	17	if	if	SCONJ
ejpam-1929	199	18	n	n	PROPN
ejpam-1929	199	19	=	=	SYM
ejpam-1929	199	20	pa	pa	PROPN
ejpam-1929	199	21	,	,	PUNCT
ejpam-1929	199	22	where	where	SCONJ
ejpam-1929	199	23	p	p	NOUN
ejpam-1929	199	24	is	be	AUX
ejpam-1929	199	25	a	a	DET
ejpam-1929	199	26	prime	prime	ADJ
ejpam-1929	199	27	number	number	NOUN
ejpam-1929	199	28	,	,	PUNCT
ejpam-1929	199	29	then	then	ADV
ejpam-1929	199	30	σn	σn	PROPN
ejpam-1929	199	31	is	be	AUX
ejpam-1929	199	32	an	an	DET
ejpam-1929	199	33	all	all	ADV
ejpam-1929	199	34	-	-	PUNCT
ejpam-1929	199	35	positive	positive	ADJ
ejpam-1929	199	36	sigraph	sigraph	NOUN
ejpam-1929	199	37	.	.	PUNCT
ejpam-1929	200	1	proof	proof	NOUN
ejpam-1929	200	2	.	.	PUNCT
ejpam-1929	201	1	for	for	ADP
ejpam-1929	201	2	the	the	DET
ejpam-1929	201	3	unitary	unitary	ADJ
ejpam-1929	201	4	addition	addition	NOUN
ejpam-1929	201	5	cayley	cayley	NOUN
ejpam-1929	201	6	sigraph	sigraph	NOUN
ejpam-1929	201	7	σn	σn	NOUN
ejpam-1929	201	8	,	,	PUNCT
ejpam-1929	201	9	if	if	SCONJ
ejpam-1929	201	10	n	n	PROPN
ejpam-1929	201	11	=	=	SYM
ejpam-1929	201	12	pa	pa	PROPN
ejpam-1929	201	13	,	,	PUNCT
ejpam-1929	201	14	then	then	ADV
ejpam-1929	201	15	un	un	PROPN
ejpam-1929	201	16	consists	consist	VERB
ejpam-1929	201	17	of	of	ADP
ejpam-1929	201	18	all	all	DET
ejpam-1929	201	19	the	the	DET
ejpam-1929	201	20	numbers	number	NOUN
ejpam-1929	201	21	less	less	ADJ
ejpam-1929	201	22	than	than	ADP
ejpam-1929	201	23	n	n	CCONJ
ejpam-1929	201	24	,	,	PUNCT
ejpam-1929	201	25	which	which	PRON
ejpam-1929	201	26	are	be	AUX
ejpam-1929	201	27	not	not	PART
ejpam-1929	201	28	multiples	multiple	NOUN
ejpam-1929	201	29	of	of	ADP
ejpam-1929	201	30	p.	p.	NOUN
ejpam-1929	201	31	suppose	suppose	VERB
ejpam-1929	201	32	αp	αp	NOUN
ejpam-1929	201	33	and	and	CCONJ
ejpam-1929	201	34	βp	βp	NUM
ejpam-1929	201	35	are	be	AUX
ejpam-1929	201	36	two	two	NUM
ejpam-1929	201	37	numbers	number	NOUN
ejpam-1929	201	38	less	less	ADJ
ejpam-1929	201	39	than	than	ADP
ejpam-1929	201	40	n	n	NOUN
ejpam-1929	201	41	and	and	CCONJ
ejpam-1929	201	42	multiples	multiple	NOUN
ejpam-1929	201	43	of	of	ADP
ejpam-1929	201	44	p.	p.	NOUN
ejpam-1929	201	45	then	then	ADV
ejpam-1929	201	46	,	,	PUNCT
ejpam-1929	201	47	by	by	ADP
ejpam-1929	201	48	the	the	DET
ejpam-1929	201	49	definition	definition	NOUN
ejpam-1929	201	50	of	of	ADP
ejpam-1929	201	51	the	the	DET
ejpam-1929	201	52	unitary	unitary	ADJ
ejpam-1929	201	53	addition	addition	NOUN
ejpam-1929	201	54	cayley	cayley	PROPN
ejpam-1929	201	55	sigraph	sigraph	NOUN
ejpam-1929	201	56	,	,	PUNCT
ejpam-1929	201	57	we	we	PRON
ejpam-1929	201	58	have	have	VERB
ejpam-1929	201	59	a	a	DET
ejpam-1929	201	60	negative	negative	ADJ
ejpam-1929	201	61	edge	edge	NOUN
ejpam-1929	201	62	only	only	ADV
ejpam-1929	201	63	when	when	SCONJ
ejpam-1929	201	64	αp	αp	NOUN
ejpam-1929	201	65	is	be	AUX
ejpam-1929	201	66	adjacent	adjacent	ADJ
ejpam-1929	201	67	to	to	ADP
ejpam-1929	201	68	βp	βp	PROPN
ejpam-1929	201	69	.	.	PUNCT
ejpam-1929	202	1	now	now	ADV
ejpam-1929	202	2	,	,	PUNCT
ejpam-1929	202	3	we	we	PRON
ejpam-1929	202	4	have	have	VERB
ejpam-1929	202	5	three	three	NUM
ejpam-1929	202	6	possibilities	possibility	NOUN
ejpam-1929	202	7	,	,	PUNCT
ejpam-1929	202	8	viz	viz	PROPN
ejpam-1929	202	9	.	.	PROPN
ejpam-1929	202	10	,	,	PUNCT
ejpam-1929	202	11	αp+	αp+	NOUN
ejpam-1929	202	12	βp	βp	NOUN
ejpam-1929	202	13	<	<	X
ejpam-1929	202	14	n	n	CCONJ
ejpam-1929	202	15	,	,	PUNCT
ejpam-1929	202	16	αp+	αp+	NOUN
ejpam-1929	202	17	βp	βp	NOUN
ejpam-1929	203	1	=	=	PUNCT
ejpam-1929	203	2	n	n	NOUN
ejpam-1929	203	3	or	or	CCONJ
ejpam-1929	203	4	αp+	αp+	VERB
ejpam-1929	204	1	βp	βp	INTJ
ejpam-1929	204	2	>	>	X
ejpam-1929	204	3	n.	n.	PROPN
ejpam-1929	204	4	when	when	SCONJ
ejpam-1929	204	5	,	,	PUNCT
ejpam-1929	204	6	αp+	αp+	NOUN
ejpam-1929	204	7	βp	βp	NOUN
ejpam-1929	204	8	<	<	X
ejpam-1929	204	9	n	n	CCONJ
ejpam-1929	204	10	,	,	PUNCT
ejpam-1929	204	11	we	we	PRON
ejpam-1929	204	12	see	see	VERB
ejpam-1929	204	13	that	that	DET
ejpam-1929	204	14	αp+	αp+	NOUN
ejpam-1929	204	15	βp	βp	PROPN
ejpam-1929	204	16	/∈	/∈	PROPN
ejpam-1929	204	17	un	un	PROPN
ejpam-1929	204	18	as	as	SCONJ
ejpam-1929	204	19	it	it	PRON
ejpam-1929	204	20	is	be	AUX
ejpam-1929	204	21	a	a	DET
ejpam-1929	204	22	number	number	NOUN
ejpam-1929	204	23	less	less	ADJ
ejpam-1929	204	24	than	than	ADP
ejpam-1929	204	25	n	n	ADV
ejpam-1929	204	26	and	and	CCONJ
ejpam-1929	204	27	a	a	DET
ejpam-1929	204	28	multiple	multiple	NOUN
ejpam-1929	204	29	of	of	ADP
ejpam-1929	204	30	p.	p.	NOUN
ejpam-1929	204	31	secondly	secondly	ADV
ejpam-1929	204	32	,	,	PUNCT
ejpam-1929	204	33	when	when	SCONJ
ejpam-1929	204	34	αp	αp	NOUN
ejpam-1929	204	35	+	+	CCONJ
ejpam-1929	204	36	βp	βp	NOUN
ejpam-1929	204	37	=	=	SYM
ejpam-1929	204	38	n	n	CCONJ
ejpam-1929	204	39	,	,	PUNCT
ejpam-1929	204	40	we	we	PRON
ejpam-1929	204	41	get	get	VERB
ejpam-1929	204	42	αp+βp	αp+βp	NOUN
ejpam-1929	204	43	=	=	SYM
ejpam-1929	204	44	0	0	NUM
ejpam-1929	204	45	/∈	/∈	NUM
ejpam-1929	204	46	un	un	PROPN
ejpam-1929	204	47	.	.	PROPN
ejpam-1929	205	1	when	when	SCONJ
ejpam-1929	205	2	αp+βp	αp+βp	AUX
ejpam-1929	205	3	>	>	X
ejpam-1929	205	4	n	n	CCONJ
ejpam-1929	205	5	,	,	PUNCT
ejpam-1929	205	6	there	there	PRON
ejpam-1929	205	7	exists	exist	VERB
ejpam-1929	205	8	an	an	DET
ejpam-1929	205	9	integer	integer	NOUN
ejpam-1929	205	10	k	k	PROPN
ejpam-1929	205	11	such	such	ADJ
ejpam-1929	205	12	that	that	SCONJ
ejpam-1929	205	13	αp+βp	αp+βp	NUM
ejpam-1929	205	14	=	=	SYM
ejpam-1929	205	15	n+k	n+k	PROPN
ejpam-1929	205	16	=	=	SYM
ejpam-1929	205	17	k	k	NOUN
ejpam-1929	205	18	,	,	PUNCT
ejpam-1929	205	19	which	which	PRON
ejpam-1929	205	20	is	be	AUX
ejpam-1929	205	21	again	again	ADV
ejpam-1929	205	22	a	a	DET
ejpam-1929	205	23	number	number	NOUN
ejpam-1929	205	24	less	less	ADJ
ejpam-1929	205	25	than	than	ADP
ejpam-1929	205	26	n	n	ADV
ejpam-1929	205	27	and	and	CCONJ
ejpam-1929	205	28	a	a	DET
ejpam-1929	205	29	multiple	multiple	NOUN
ejpam-1929	205	30	of	of	ADP
ejpam-1929	205	31	p.	p.	NOUN
ejpam-1929	205	32	this	this	PRON
ejpam-1929	205	33	implies	imply	VERB
ejpam-1929	205	34	αp	αp	NOUN
ejpam-1929	206	1	+	+	CCONJ
ejpam-1929	206	2	βp	βp	PROPN
ejpam-1929	206	3	/∈	/∈	INTJ
ejpam-1929	206	4	un	un	PROPN
ejpam-1929	206	5	.	.	PROPN
ejpam-1929	207	1	thus	thus	ADV
ejpam-1929	207	2	,	,	PUNCT
ejpam-1929	207	3	in	in	ADP
ejpam-1929	207	4	each	each	DET
ejpam-1929	207	5	case	case	NOUN
ejpam-1929	207	6	αp	αp	NOUN
ejpam-1929	207	7	is	be	AUX
ejpam-1929	207	8	not	not	PART
ejpam-1929	207	9	adjacent	adjacent	ADJ
ejpam-1929	207	10	with	with	ADP
ejpam-1929	207	11	βp	βp	NOUN
ejpam-1929	207	12	since	since	SCONJ
ejpam-1929	207	13	their	their	PRON
ejpam-1929	207	14	addition	addition	NOUN
ejpam-1929	207	15	αp	αp	NOUN
ejpam-1929	208	1	+	+	CCONJ
ejpam-1929	208	2	βp	βp	PROPN
ejpam-1929	208	3	/∈	/∈	INTJ
ejpam-1929	208	4	un	un	PROPN
ejpam-1929	208	5	.	.	PROPN
ejpam-1929	209	1	thus	thus	ADV
ejpam-1929	209	2	,	,	PUNCT
ejpam-1929	209	3	σn	σn	PROPN
ejpam-1929	209	4	is	be	AUX
ejpam-1929	209	5	an	an	DET
ejpam-1929	209	6	all	all	ADV
ejpam-1929	209	7	-	-	PUNCT
ejpam-1929	209	8	positive	positive	ADJ
ejpam-1929	209	9	sigraph	sigraph	NOUN
ejpam-1929	209	10	.	.	PUNCT
ejpam-1929	210	1	we	we	PRON
ejpam-1929	210	2	shall	shall	AUX
ejpam-1929	210	3	now	now	ADV
ejpam-1929	210	4	establish	establish	VERB
ejpam-1929	210	5	the	the	DET
ejpam-1929	210	6	following	follow	VERB
ejpam-1929	210	7	characterization	characterization	NOUN
ejpam-1929	210	8	of	of	ADP
ejpam-1929	210	9	balanced	balanced	ADJ
ejpam-1929	210	10	unitary	unitary	ADJ
ejpam-1929	210	11	addition	addition	NOUN
ejpam-1929	210	12	cayley	cayley	NOUN
ejpam-1929	210	13	sigraphs	sigraph	VERB
ejpam-1929	210	14	.	.	PUNCT
ejpam-1929	211	1	theorem	theorem	ADJ
ejpam-1929	211	2	7	7	NUM
ejpam-1929	211	3	.	.	PUNCT
ejpam-1929	212	1	the	the	DET
ejpam-1929	212	2	unitary	unitary	ADJ
ejpam-1929	212	3	addition	addition	NOUN
ejpam-1929	212	4	cayley	cayley	NOUN
ejpam-1929	212	5	sigraph	sigraph	NOUN
ejpam-1929	212	6	σn	σn	NOUN
ejpam-1929	212	7	=	=	SYM
ejpam-1929	212	8	(	(	PUNCT
ejpam-1929	212	9	σ	σ	PROPN
ejpam-1929	212	10	u	u	PROPN
ejpam-1929	212	11	n	n	NUM
ejpam-1929	212	12	,	,	PUNCT
ejpam-1929	212	13	σ	σ	PROPN
ejpam-1929	212	14	)	)	PUNCT
ejpam-1929	212	15	is	be	AUX
ejpam-1929	212	16	balanced	balance	VERB
ejpam-1929	212	17	if	if	SCONJ
ejpam-1929	212	18	and	and	CCONJ
ejpam-1929	212	19	only	only	ADV
ejpam-1929	212	20	if	if	SCONJ
ejpam-1929	212	21	either	either	PRON
ejpam-1929	212	22	n	n	ADV
ejpam-1929	212	23	is	be	AUX
ejpam-1929	212	24	even	even	ADV
ejpam-1929	212	25	or	or	CCONJ
ejpam-1929	212	26	it	it	PRON
ejpam-1929	212	27	does	do	AUX
ejpam-1929	212	28	not	not	PART
ejpam-1929	212	29	have	have	VERB
ejpam-1929	212	30	more	more	ADJ
ejpam-1929	212	31	than	than	ADP
ejpam-1929	212	32	one	one	NUM
ejpam-1929	212	33	distinct	distinct	ADJ
ejpam-1929	212	34	prime	prime	ADJ
ejpam-1929	212	35	factors	factor	NOUN
ejpam-1929	212	36	.	.	PUNCT
ejpam-1929	213	1	proof	proof	NOUN
ejpam-1929	213	2	.	.	PUNCT
ejpam-1929	214	1	necessity	necessity	NOUN
ejpam-1929	214	2	:	:	PUNCT
ejpam-1929	214	3	suppose	suppose	VERB
ejpam-1929	214	4	the	the	DET
ejpam-1929	214	5	unitary	unitary	ADJ
ejpam-1929	214	6	addition	addition	NOUN
ejpam-1929	214	7	cayley	cayley	NOUN
ejpam-1929	214	8	sigraph	sigraph	NOUN
ejpam-1929	214	9	σn	σn	NOUN
ejpam-1929	214	10	=	=	SYM
ejpam-1929	214	11	(	(	PUNCT
ejpam-1929	214	12	σ	σ	PROPN
ejpam-1929	214	13	u	u	PROPN
ejpam-1929	214	14	n	n	NUM
ejpam-1929	214	15	,	,	PUNCT
ejpam-1929	214	16	σ	σ	PROPN
ejpam-1929	214	17	)	)	PUNCT
ejpam-1929	214	18	is	be	AUX
ejpam-1929	214	19	balanced	balanced	ADJ
ejpam-1929	214	20	.	.	PUNCT
ejpam-1929	215	1	assume	assume	VERB
ejpam-1929	215	2	that	that	SCONJ
ejpam-1929	215	3	the	the	DET
ejpam-1929	215	4	conclusion	conclusion	NOUN
ejpam-1929	215	5	is	be	AUX
ejpam-1929	215	6	false	false	ADJ
ejpam-1929	215	7	.	.	PUNCT
ejpam-1929	216	1	suppose	suppose	VERB
ejpam-1929	216	2	n	n	PRON
ejpam-1929	216	3	is	be	AUX
ejpam-1929	216	4	odd	odd	ADJ
ejpam-1929	216	5	and	and	CCONJ
ejpam-1929	216	6	it	it	PRON
ejpam-1929	216	7	has	have	VERB
ejpam-1929	216	8	at	at	ADV
ejpam-1929	216	9	least	least	ADJ
ejpam-1929	216	10	two	two	NUM
ejpam-1929	216	11	distinct	distinct	ADJ
ejpam-1929	216	12	prime	prime	ADJ
ejpam-1929	216	13	factors	factor	NOUN
ejpam-1929	216	14	.	.	PUNCT
ejpam-1929	217	1	so	so	ADV
ejpam-1929	217	2	,	,	PUNCT
ejpam-1929	217	3	let	let	VERB
ejpam-1929	217	4	n	n	NOUN
ejpam-1929	217	5	=	=	SYM
ejpam-1929	217	6	p	p	NOUN
ejpam-1929	217	7	a1	a1	NOUN
ejpam-1929	217	8	1	1	NUM
ejpam-1929	217	9	p	p	NOUN
ejpam-1929	217	10	a2	a2	PROPN
ejpam-1929	217	11	2	2	NUM
ejpam-1929	217	12	.	.	PUNCT
ejpam-1929	217	13	.	.	PUNCT
ejpam-1929	217	14	.	.	PUNCT
ejpam-1929	218	1	p	p	PROPN
ejpam-1929	218	2	am	be	AUX
ejpam-1929	218	3	m	m	PRON
ejpam-1929	218	4	,	,	PUNCT
ejpam-1929	218	5	where	where	SCONJ
ejpam-1929	218	6	all	all	DET
ejpam-1929	218	7	p1	p1	NOUN
ejpam-1929	218	8	,	,	PUNCT
ejpam-1929	218	9	p2	p2	NOUN
ejpam-1929	218	10	,	,	PUNCT
ejpam-1929	218	11	.	.	PUNCT
ejpam-1929	218	12	.	.	PUNCT
ejpam-1929	219	1	.	.	PUNCT
ejpam-1929	220	1	,	,	PUNCT
ejpam-1929	220	2	pm	pm	NOUN
ejpam-1929	220	3	are	be	AUX
ejpam-1929	220	4	distinct	distinct	ADJ
ejpam-1929	220	5	primes	prime	NOUN
ejpam-1929	220	6	,	,	PUNCT
ejpam-1929	220	7	p1	p1	NOUN
ejpam-1929	220	8	6=	6=	ADP
ejpam-1929	220	9	2	2	NUM
ejpam-1929	220	10	and	and	CCONJ
ejpam-1929	220	11	d.	d.	PROPN
ejpam-1929	220	12	sinha	sinha	PROPN
ejpam-1929	220	13	,	,	PUNCT
ejpam-1929	220	14	a.	a.	NOUN
ejpam-1929	220	15	dhama	dhama	PROPN
ejpam-1929	220	16	,	,	PUNCT
ejpam-1929	220	17	b.	b.	PROPN
ejpam-1929	220	18	acharya	acharya	PROPN
ejpam-1929	220	19	/	/	SYM
ejpam-1929	220	20	eur	eur	PROPN
ejpam-1929	220	21	.	.	PUNCT
ejpam-1929	221	1	j.	j.	PROPN
ejpam-1929	221	2	pure	pure	PROPN
ejpam-1929	221	3	appl	appl	PROPN
ejpam-1929	221	4	.	.	PROPN
ejpam-1929	221	5	math	math	PROPN
ejpam-1929	221	6	,	,	PUNCT
ejpam-1929	221	7	6	6	NUM
ejpam-1929	221	8	(	(	PUNCT
ejpam-1929	221	9	2013	2013	NUM
ejpam-1929	221	10	)	)	PUNCT
ejpam-1929	221	11	,	,	PUNCT
ejpam-1929	221	12	189	189	NUM
ejpam-1929	221	13	-	-	SYM
ejpam-1929	221	14	210	210	NUM
ejpam-1929	221	15	197	197	NUM
ejpam-1929	221	16	p1	p1	NOUN
ejpam-1929	221	17	<	<	X
ejpam-1929	221	18	p2	p2	X
ejpam-1929	221	19	<	<	X
ejpam-1929	221	20	·	·	PUNCT
ejpam-1929	221	21	·	·	PUNCT
ejpam-1929	221	22	·	·	PUNCT
ejpam-1929	221	23	<	<	X
ejpam-1929	221	24	pm	pm	NOUN
ejpam-1929	221	25	.	.	PUNCT
ejpam-1929	222	1	in	in	ADP
ejpam-1929	222	2	the	the	DET
ejpam-1929	222	3	unitary	unitary	ADJ
ejpam-1929	222	4	addition	addition	NOUN
ejpam-1929	222	5	cayley	cayley	NOUN
ejpam-1929	222	6	graph	graph	NOUN
ejpam-1929	222	7	σu	σu	ADP
ejpam-1929	222	8	n	n	CCONJ
ejpam-1929	222	9	,	,	PUNCT
ejpam-1929	222	10	p1	p1	PROPN
ejpam-1929	222	11	is	be	AUX
ejpam-1929	222	12	adjacent	adjacent	ADJ
ejpam-1929	222	13	with	with	ADP
ejpam-1929	222	14	1	1	NUM
ejpam-1929	222	15	as	as	ADP
ejpam-1929	222	16	p1	p1	NOUN
ejpam-1929	222	17	+	+	CCONJ
ejpam-1929	222	18	1	1	NUM
ejpam-1929	222	19	is	be	AUX
ejpam-1929	222	20	not	not	PART
ejpam-1929	222	21	a	a	DET
ejpam-1929	222	22	multiple	multiple	NOUN
ejpam-1929	222	23	of	of	ADP
ejpam-1929	222	24	any	any	DET
ejpam-1929	222	25	pi	pi	NOUN
ejpam-1929	222	26	’s	’s	ADV
ejpam-1929	222	27	for	for	ADP
ejpam-1929	222	28	i	i	PROPN
ejpam-1929	222	29	=	=	SYM
ejpam-1929	222	30	1,2	1,2	NUM
ejpam-1929	222	31	,	,	PUNCT
ejpam-1929	222	32	.	.	PUNCT
ejpam-1929	222	33	.	.	PUNCT
ejpam-1929	223	1	.	.	PUNCT
ejpam-1929	224	1	,	,	PUNCT
ejpam-1929	224	2	m	m	VERB
ejpam-1929	224	3	i.e.	i.e.	X
ejpam-1929	224	4	,	,	PUNCT
ejpam-1929	224	5	p1	p1	NOUN
ejpam-1929	224	6	+	+	CCONJ
ejpam-1929	224	7	1	1	NUM
ejpam-1929	224	8	∈	∈	PROPN
ejpam-1929	224	9	un	un	NOUN
ejpam-1929	224	10	.	.	PUNCT
ejpam-1929	225	1	now	now	ADV
ejpam-1929	225	2	,	,	PUNCT
ejpam-1929	225	3	we	we	PRON
ejpam-1929	225	4	claim	claim	VERB
ejpam-1929	225	5	that	that	SCONJ
ejpam-1929	225	6	p1	p1	NOUN
ejpam-1929	225	7	and	and	CCONJ
ejpam-1929	225	8	p2	p2	PROPN
ejpam-1929	225	9	are	be	AUX
ejpam-1929	225	10	also	also	ADV
ejpam-1929	225	11	adjacent	adjacent	ADJ
ejpam-1929	225	12	in	in	ADP
ejpam-1929	225	13	σu	σu	PROPN
ejpam-1929	225	14	n.	n.	NOUN
ejpam-1929	225	15	if	if	SCONJ
ejpam-1929	225	16	possible	possible	ADJ
ejpam-1929	225	17	,	,	PUNCT
ejpam-1929	225	18	suppose	suppose	VERB
ejpam-1929	225	19	p1	p1	NOUN
ejpam-1929	225	20	and	and	CCONJ
ejpam-1929	225	21	p2	p2	PROPN
ejpam-1929	225	22	are	be	AUX
ejpam-1929	225	23	not	not	PART
ejpam-1929	225	24	adjacent	adjacent	ADJ
ejpam-1929	225	25	in	in	ADP
ejpam-1929	225	26	σu	σu	PROPN
ejpam-1929	225	27	n.	n.	PROPN
ejpam-1929	225	28	this	this	DET
ejpam-1929	225	29	shows	show	NOUN
ejpam-1929	225	30	,	,	PUNCT
ejpam-1929	225	31	p1	p1	NOUN
ejpam-1929	225	32	+	+	CCONJ
ejpam-1929	225	33	p2	p2	PROPN
ejpam-1929	225	34	/∈	/∈	PUNCT
ejpam-1929	226	1	un	un	PROPN
ejpam-1929	226	2	.	.	PROPN
ejpam-1929	227	1	then	then	ADV
ejpam-1929	227	2	,	,	PUNCT
ejpam-1929	227	3	p1	p1	PROPN
ejpam-1929	227	4	+	+	CCONJ
ejpam-1929	227	5	p2	p2	PROPN
ejpam-1929	227	6	is	be	AUX
ejpam-1929	227	7	a	a	DET
ejpam-1929	227	8	multiple	multiple	NOUN
ejpam-1929	227	9	of	of	ADP
ejpam-1929	227	10	some	some	DET
ejpam-1929	227	11	pi	pi	NOUN
ejpam-1929	227	12	’s	’s	ADV
ejpam-1929	227	13	for	for	ADP
ejpam-1929	227	14	i	i	PROPN
ejpam-1929	227	15	=	=	SYM
ejpam-1929	227	16	1,2	1,2	NUM
ejpam-1929	227	17	,	,	PUNCT
ejpam-1929	227	18	.	.	PUNCT
ejpam-1929	227	19	.	.	PUNCT
ejpam-1929	228	1	.	.	PUNCT
ejpam-1929	229	1	,	,	PUNCT
ejpam-1929	229	2	m.	m.	NOUN
ejpam-1929	229	3	suppose	suppose	VERB
ejpam-1929	229	4	p1	p1	PROPN
ejpam-1929	229	5	+	+	CCONJ
ejpam-1929	229	6	p2	p2	PROPN
ejpam-1929	229	7	is	be	AUX
ejpam-1929	229	8	a	a	DET
ejpam-1929	229	9	multiple	multiple	NOUN
ejpam-1929	229	10	of	of	ADP
ejpam-1929	229	11	p1	p1	PROPN
ejpam-1929	229	12	.	.	PUNCT
ejpam-1929	230	1	then	then	ADV
ejpam-1929	230	2	,	,	PUNCT
ejpam-1929	230	3	p1	p1	PROPN
ejpam-1929	230	4	+	+	CCONJ
ejpam-1929	230	5	p2	p2	X
ejpam-1929	230	6	=	=	SYM
ejpam-1929	230	7	αp1	αp1	ADJ
ejpam-1929	230	8	p2	p2	NOUN
ejpam-1929	230	9	=	=	SYM
ejpam-1929	230	10	αp1−	αp1−	NOUN
ejpam-1929	230	11	p1	p1	NOUN
ejpam-1929	230	12	=	=	SYM
ejpam-1929	230	13	(	(	PUNCT
ejpam-1929	230	14	α−	α−	ADP
ejpam-1929	230	15	1)p1	1)p1	NUM
ejpam-1929	230	16	for	for	ADP
ejpam-1929	230	17	some	some	DET
ejpam-1929	230	18	positive	positive	ADJ
ejpam-1929	230	19	integer	integer	NOUN
ejpam-1929	230	20	α	α	NOUN
ejpam-1929	230	21	,	,	PUNCT
ejpam-1929	230	22	which	which	PRON
ejpam-1929	230	23	is	be	AUX
ejpam-1929	230	24	not	not	PART
ejpam-1929	230	25	possible	possible	ADJ
ejpam-1929	230	26	.	.	PUNCT
ejpam-1929	231	1	similarly	similarly	ADV
ejpam-1929	231	2	,	,	PUNCT
ejpam-1929	231	3	we	we	PRON
ejpam-1929	231	4	can	can	AUX
ejpam-1929	231	5	see	see	VERB
ejpam-1929	231	6	that	that	DET
ejpam-1929	231	7	p1	p1	NOUN
ejpam-1929	231	8	+	+	CCONJ
ejpam-1929	231	9	p2	p2	PROPN
ejpam-1929	231	10	is	be	AUX
ejpam-1929	231	11	not	not	PART
ejpam-1929	231	12	a	a	DET
ejpam-1929	231	13	multiple	multiple	NOUN
ejpam-1929	231	14	of	of	ADP
ejpam-1929	231	15	p2	p2	NOUN
ejpam-1929	231	16	.	.	PUNCT
ejpam-1929	232	1	now	now	ADV
ejpam-1929	232	2	,	,	PUNCT
ejpam-1929	232	3	the	the	DET
ejpam-1929	232	4	possibilities	possibility	NOUN
ejpam-1929	232	5	are	be	AUX
ejpam-1929	232	6	i	i	NOUN
ejpam-1929	232	7	=	=	NOUN
ejpam-1929	232	8	3,4	3,4	NUM
ejpam-1929	232	9	,	,	PUNCT
ejpam-1929	232	10	.	.	PUNCT
ejpam-1929	232	11	.	.	PUNCT
ejpam-1929	232	12	.	.	PUNCT
ejpam-1929	233	1	,	,	PUNCT
ejpam-1929	233	2	m.	m.	NOUN
ejpam-1929	233	3	suppose	suppose	VERB
ejpam-1929	233	4	p1	p1	PROPN
ejpam-1929	233	5	+	+	CCONJ
ejpam-1929	233	6	p2	p2	X
ejpam-1929	233	7	=	=	SYM
ejpam-1929	233	8	αpi	αpi	NOUN
ejpam-1929	233	9	for	for	ADP
ejpam-1929	233	10	i	i	PRON
ejpam-1929	233	11	=	=	NOUN
ejpam-1929	233	12	3,4	3,4	NUM
ejpam-1929	233	13	,	,	PUNCT
ejpam-1929	233	14	.	.	PUNCT
ejpam-1929	233	15	.	.	PUNCT
ejpam-1929	234	1	.	.	PUNCT
ejpam-1929	235	1	,	,	PUNCT
ejpam-1929	235	2	m.	m.	NOUN
ejpam-1929	235	3	since	since	SCONJ
ejpam-1929	235	4	p1	p1	PROPN
ejpam-1929	235	5	+	+	CCONJ
ejpam-1929	235	6	p2	p2	PROPN
ejpam-1929	235	7	is	be	AUX
ejpam-1929	235	8	even	even	ADV
ejpam-1929	235	9	,	,	PUNCT
ejpam-1929	235	10	α	α	PRON
ejpam-1929	235	11	is	be	AUX
ejpam-1929	235	12	even	even	ADV
ejpam-1929	235	13	and	and	CCONJ
ejpam-1929	235	14	is	be	AUX
ejpam-1929	235	15	at	at	ADV
ejpam-1929	235	16	least	least	ADJ
ejpam-1929	235	17	2	2	NUM
ejpam-1929	235	18	,	,	PUNCT
ejpam-1929	235	19	for	for	ADP
ejpam-1929	235	20	any	any	DET
ejpam-1929	235	21	positive	positive	ADJ
ejpam-1929	235	22	integer	integer	NOUN
ejpam-1929	235	23	α	α	NOUN
ejpam-1929	235	24	.	.	PUNCT
ejpam-1929	236	1	but	but	CCONJ
ejpam-1929	236	2	as	as	SCONJ
ejpam-1929	236	3	p1	p1	PROPN
ejpam-1929	236	4	<	<	X
ejpam-1929	236	5	p2	p2	PROPN
ejpam-1929	236	6	<	<	X
ejpam-1929	236	7	pi	pi	NOUN
ejpam-1929	236	8	,	,	PUNCT
ejpam-1929	236	9	p1	p1	NOUN
ejpam-1929	236	10	+	+	CCONJ
ejpam-1929	236	11	p2	p2	PROPN
ejpam-1929	236	12	is	be	AUX
ejpam-1929	236	13	always	always	ADV
ejpam-1929	236	14	less	less	ADJ
ejpam-1929	236	15	than	than	ADP
ejpam-1929	236	16	any	any	DET
ejpam-1929	236	17	multiple	multiple	NOUN
ejpam-1929	236	18	of	of	ADP
ejpam-1929	236	19	pi	pi	NOUN
ejpam-1929	236	20	for	for	ADP
ejpam-1929	236	21	i	i	PRON
ejpam-1929	236	22	=	=	NOUN
ejpam-1929	236	23	3,4	3,4	NUM
ejpam-1929	236	24	,	,	PUNCT
ejpam-1929	236	25	.	.	PUNCT
ejpam-1929	236	26	.	.	PUNCT
ejpam-1929	237	1	.	.	PUNCT
ejpam-1929	238	1	,	,	PUNCT
ejpam-1929	238	2	m.	m.	NOUN
ejpam-1929	238	3	thus	thus	ADV
ejpam-1929	238	4	,	,	PUNCT
ejpam-1929	238	5	p1	p1	NOUN
ejpam-1929	238	6	+	+	CCONJ
ejpam-1929	238	7	p2	p2	PROPN
ejpam-1929	238	8	is	be	AUX
ejpam-1929	238	9	not	not	PART
ejpam-1929	238	10	a	a	DET
ejpam-1929	238	11	multiple	multiple	NOUN
ejpam-1929	238	12	of	of	ADP
ejpam-1929	238	13	any	any	DET
ejpam-1929	238	14	pi	pi	NOUN
ejpam-1929	238	15	’s	’s	ADV
ejpam-1929	238	16	for	for	ADP
ejpam-1929	238	17	i	i	PROPN
ejpam-1929	238	18	=	=	SYM
ejpam-1929	238	19	1,2	1,2	NUM
ejpam-1929	238	20	,	,	PUNCT
ejpam-1929	238	21	.	.	PUNCT
ejpam-1929	238	22	.	.	PUNCT
ejpam-1929	239	1	.	.	PUNCT
ejpam-1929	240	1	,	,	PUNCT
ejpam-1929	240	2	m.	m.	NOUN
ejpam-1929	240	3	so	so	ADV
ejpam-1929	240	4	p1	p1	PROPN
ejpam-1929	240	5	+	+	CCONJ
ejpam-1929	240	6	p2	p2	PROPN
ejpam-1929	240	7	∈	∈	PROPN
ejpam-1929	240	8	un	un	NOUN
ejpam-1929	240	9	.	.	PUNCT
ejpam-1929	241	1	this	this	PRON
ejpam-1929	241	2	shows	show	VERB
ejpam-1929	241	3	that	that	SCONJ
ejpam-1929	241	4	p1	p1	NOUN
ejpam-1929	241	5	and	and	CCONJ
ejpam-1929	241	6	p2	p2	PROPN
ejpam-1929	241	7	are	be	AUX
ejpam-1929	241	8	adjacent	adjacent	ADJ
ejpam-1929	241	9	in	in	ADP
ejpam-1929	241	10	σu	σu	PROPN
ejpam-1929	241	11	n.	n.	PROPN
ejpam-1929	241	12	now	now	ADV
ejpam-1929	241	13	,	,	PUNCT
ejpam-1929	241	14	if	if	SCONJ
ejpam-1929	241	15	p2	p2	PROPN
ejpam-1929	241	16	is	be	AUX
ejpam-1929	241	17	adjacent	adjacent	ADJ
ejpam-1929	241	18	with	with	ADP
ejpam-1929	241	19	1	1	NUM
ejpam-1929	241	20	in	in	ADP
ejpam-1929	241	21	σu	σu	NUM
ejpam-1929	241	22	n	n	CCONJ
ejpam-1929	241	23	,	,	PUNCT
ejpam-1929	241	24	then	then	ADV
ejpam-1929	241	25	we	we	PRON
ejpam-1929	241	26	have	have	VERB
ejpam-1929	241	27	a	a	DET
ejpam-1929	241	28	cycle	cycle	NOUN
ejpam-1929	241	29	z	z	NOUN
ejpam-1929	241	30	=	=	SYM
ejpam-1929	241	31	(	(	PUNCT
ejpam-1929	241	32	p1	p1	PROPN
ejpam-1929	241	33	,	,	PUNCT
ejpam-1929	241	34	p2	p2	NOUN
ejpam-1929	241	35	,	,	PUNCT
ejpam-1929	241	36	1	1	NUM
ejpam-1929	241	37	,	,	PUNCT
ejpam-1929	241	38	p1	p1	NOUN
ejpam-1929	241	39	)	)	PUNCT
ejpam-1929	241	40	in	in	ADP
ejpam-1929	241	41	σn	σn	PROPN
ejpam-1929	241	42	.	.	PUNCT
ejpam-1929	242	1	clearly	clearly	ADV
ejpam-1929	242	2	,	,	PUNCT
ejpam-1929	242	3	p1	p1	NOUN
ejpam-1929	242	4	and	and	CCONJ
ejpam-1929	242	5	p2	p2	PROPN
ejpam-1929	242	6	do	do	AUX
ejpam-1929	242	7	not	not	PART
ejpam-1929	242	8	belong	belong	VERB
ejpam-1929	242	9	to	to	ADP
ejpam-1929	242	10	un	un	PROPN
ejpam-1929	242	11	and	and	CCONJ
ejpam-1929	242	12	1	1	NUM
ejpam-1929	242	13	∈	∈	PROPN
ejpam-1929	242	14	un	un	NOUN
ejpam-1929	242	15	.	.	PROPN
ejpam-1929	243	1	then	then	ADV
ejpam-1929	243	2	,	,	PUNCT
ejpam-1929	243	3	by	by	ADP
ejpam-1929	243	4	the	the	DET
ejpam-1929	243	5	definition	definition	NOUN
ejpam-1929	243	6	of	of	ADP
ejpam-1929	243	7	σn	σn	PROPN
ejpam-1929	243	8	,	,	PUNCT
ejpam-1929	243	9	z	z	PROPN
ejpam-1929	243	10	has	have	VERB
ejpam-1929	243	11	exactly	exactly	ADV
ejpam-1929	243	12	one	one	NUM
ejpam-1929	243	13	negative	negative	ADJ
ejpam-1929	243	14	edge	edge	NOUN
ejpam-1929	243	15	p1p2	p1p2	PROPN
ejpam-1929	243	16	.	.	PUNCT
ejpam-1929	244	1	thus	thus	ADV
ejpam-1929	244	2	,	,	PUNCT
ejpam-1929	244	3	z	z	PROPN
ejpam-1929	244	4	is	be	AUX
ejpam-1929	244	5	a	a	DET
ejpam-1929	244	6	negative	negative	ADJ
ejpam-1929	244	7	cycle	cycle	NOUN
ejpam-1929	244	8	in	in	ADP
ejpam-1929	244	9	σn	σn	PROPN
ejpam-1929	244	10	.	.	PUNCT
ejpam-1929	245	1	this	this	PRON
ejpam-1929	245	2	implies	imply	VERB
ejpam-1929	245	3	that	that	SCONJ
ejpam-1929	245	4	σn	σn	NOUN
ejpam-1929	245	5	is	be	AUX
ejpam-1929	245	6	not	not	PART
ejpam-1929	245	7	balanced	balanced	ADJ
ejpam-1929	245	8	.	.	PUNCT
ejpam-1929	246	1	now	now	ADV
ejpam-1929	246	2	,	,	PUNCT
ejpam-1929	246	3	suppose	suppose	VERB
ejpam-1929	246	4	p2	p2	PROPN
ejpam-1929	246	5	is	be	AUX
ejpam-1929	246	6	not	not	PART
ejpam-1929	246	7	adjacent	adjacent	ADJ
ejpam-1929	246	8	with	with	ADP
ejpam-1929	246	9	1	1	NUM
ejpam-1929	246	10	in	in	ADP
ejpam-1929	246	11	σu	σu	NOUN
ejpam-1929	246	12	n	n	CCONJ
ejpam-1929	246	13	,	,	PUNCT
ejpam-1929	246	14	i.e.	i.e.	X
ejpam-1929	246	15	,	,	PUNCT
ejpam-1929	246	16	p2	p2	X
ejpam-1929	246	17	+	+	SYM
ejpam-1929	246	18	1	1	NUM
ejpam-1929	246	19	6	6	NUM
ejpam-1929	246	20	inun	inun	NOUN
ejpam-1929	246	21	.	.	PUNCT
ejpam-1929	247	1	then	then	ADV
ejpam-1929	247	2	,	,	PUNCT
ejpam-1929	247	3	p2	p2	PROPN
ejpam-1929	247	4	+	+	SYM
ejpam-1929	247	5	1	1	NUM
ejpam-1929	247	6	is	be	AUX
ejpam-1929	247	7	multiple	multiple	ADJ
ejpam-1929	247	8	of	of	ADP
ejpam-1929	247	9	one	one	NUM
ejpam-1929	247	10	of	of	ADP
ejpam-1929	247	11	the	the	DET
ejpam-1929	247	12	pi	pi	NOUN
ejpam-1929	247	13	’s	’s	ADV
ejpam-1929	247	14	for	for	ADP
ejpam-1929	247	15	i	i	PROPN
ejpam-1929	247	16	=	=	SYM
ejpam-1929	247	17	1,2	1,2	NUM
ejpam-1929	247	18	,	,	PUNCT
ejpam-1929	247	19	.	.	PUNCT
ejpam-1929	247	20	.	.	PUNCT
ejpam-1929	248	1	.	.	PUNCT
ejpam-1929	249	1	,	,	PUNCT
ejpam-1929	249	2	m.	m.	NOUN
ejpam-1929	249	3	clearly	clearly	ADV
ejpam-1929	249	4	,	,	PUNCT
ejpam-1929	249	5	i	i	PRON
ejpam-1929	249	6	can	can	AUX
ejpam-1929	249	7	not	not	PART
ejpam-1929	249	8	exceed	exceed	VERB
ejpam-1929	249	9	1	1	NUM
ejpam-1929	249	10	,	,	PUNCT
ejpam-1929	249	11	as	as	ADP
ejpam-1929	249	12	p2	p2	PROPN
ejpam-1929	249	13	<	<	X
ejpam-1929	249	14	p3	p3	PROPN
ejpam-1929	249	15	·	·	PUNCT
ejpam-1929	249	16	·	·	PUNCT
ejpam-1929	249	17	·	·	PUNCT
ejpam-1929	250	1	<	<	X
ejpam-1929	250	2	pm	pm	NOUN
ejpam-1929	250	3	.	.	PUNCT
ejpam-1929	251	1	so	so	ADV
ejpam-1929	251	2	,	,	PUNCT
ejpam-1929	251	3	the	the	DET
ejpam-1929	251	4	only	only	ADJ
ejpam-1929	251	5	possibility	possibility	NOUN
ejpam-1929	251	6	is	be	AUX
ejpam-1929	251	7	i	i	NOUN
ejpam-1929	251	8	=	=	NOUN
ejpam-1929	251	9	1	1	NUM
ejpam-1929	251	10	,	,	PUNCT
ejpam-1929	251	11	whence	whence	NOUN
ejpam-1929	251	12	p2	p2	NOUN
ejpam-1929	251	13	+	+	SYM
ejpam-1929	251	14	1	1	NUM
ejpam-1929	251	15	is	be	AUX
ejpam-1929	251	16	a	a	DET
ejpam-1929	251	17	multiple	multiple	NOUN
ejpam-1929	251	18	of	of	ADP
ejpam-1929	251	19	p1	p1	PROPN
ejpam-1929	251	20	.	.	PUNCT
ejpam-1929	252	1	then	then	ADV
ejpam-1929	252	2	,	,	PUNCT
ejpam-1929	252	3	p2	p2	X
ejpam-1929	252	4	+	+	SYM
ejpam-1929	252	5	1=	1=	NUM
ejpam-1929	252	6	αp1	αp1	PROPN
ejpam-1929	252	7	(	(	PUNCT
ejpam-1929	252	8	1	1	NUM
ejpam-1929	252	9	)	)	PUNCT
ejpam-1929	252	10	for	for	ADP
ejpam-1929	252	11	some	some	DET
ejpam-1929	252	12	positive	positive	ADJ
ejpam-1929	252	13	integer	integer	NOUN
ejpam-1929	252	14	α	α	NOUN
ejpam-1929	252	15	.	.	PUNCT
ejpam-1929	252	16	by	by	ADP
ejpam-1929	252	17	lemma	lemma	PROPN
ejpam-1929	252	18	2	2	NUM
ejpam-1929	252	19	,	,	PUNCT
ejpam-1929	252	20	it	it	PRON
ejpam-1929	252	21	is	be	AUX
ejpam-1929	252	22	clear	clear	ADJ
ejpam-1929	252	23	that	that	SCONJ
ejpam-1929	252	24	n	n	CCONJ
ejpam-1929	252	25	−	−	PROPN
ejpam-1929	252	26	p2	p2	PROPN
ejpam-1929	252	27	6∈	6∈	PROPN
ejpam-1929	252	28	un	un	PROPN
ejpam-1929	252	29	.	.	PUNCT
ejpam-1929	253	1	now	now	ADV
ejpam-1929	253	2	,	,	PUNCT
ejpam-1929	253	3	we	we	PRON
ejpam-1929	253	4	claim	claim	VERB
ejpam-1929	253	5	n	n	PRON
ejpam-1929	253	6	−	−	PROPN
ejpam-1929	253	7	p2	p2	PROPN
ejpam-1929	253	8	is	be	AUX
ejpam-1929	253	9	adjacent	adjacent	ADJ
ejpam-1929	253	10	with	with	ADP
ejpam-1929	253	11	1	1	NUM
ejpam-1929	253	12	i.e.	i.e.	X
ejpam-1929	253	13	,	,	PUNCT
ejpam-1929	253	14	n−	n−	NOUN
ejpam-1929	253	15	p2	p2	VERB
ejpam-1929	253	16	+	+	NOUN
ejpam-1929	253	17	1=	1=	NUM
ejpam-1929	253	18	n−(p2−1	n−(p2−1	NOUN
ejpam-1929	253	19	)	)	PUNCT
ejpam-1929	253	20	∈	∈	PROPN
ejpam-1929	253	21	un	un	PROPN
ejpam-1929	253	22	.	.	PROPN
ejpam-1929	254	1	if	if	SCONJ
ejpam-1929	254	2	p2−1	p2−1	PROPN
ejpam-1929	254	3	∈	∈	PROPN
ejpam-1929	254	4	un	un	NOUN
ejpam-1929	254	5	,	,	PUNCT
ejpam-1929	254	6	then	then	ADV
ejpam-1929	254	7	by	by	ADP
ejpam-1929	254	8	lemma	lemma	PROPN
ejpam-1929	254	9	2	2	NUM
ejpam-1929	254	10	,	,	PUNCT
ejpam-1929	254	11	n−	n−	NOUN
ejpam-1929	254	12	p2	p2	VERB
ejpam-1929	254	13	+	+	NOUN
ejpam-1929	254	14	1=	1=	X
ejpam-1929	254	15	n−(p2	n−(p2	X
ejpam-1929	254	16	+	+	ADJ
ejpam-1929	254	17	1	1	NUM
ejpam-1929	254	18	)	)	PUNCT
ejpam-1929	254	19	∈	∈	PROPN
ejpam-1929	254	20	un	un	PROPN
ejpam-1929	254	21	.	.	PROPN
ejpam-1929	254	22	suppose	suppose	VERB
ejpam-1929	254	23	p2−1	p2−1	ADP
ejpam-1929	254	24	6∈	6∈	PROPN
ejpam-1929	254	25	un	un	PROPN
ejpam-1929	254	26	.	.	PROPN
ejpam-1929	255	1	then	then	ADV
ejpam-1929	255	2	,	,	PUNCT
ejpam-1929	255	3	p2−1	p2−1	NOUN
ejpam-1929	255	4	is	be	AUX
ejpam-1929	255	5	a	a	DET
ejpam-1929	255	6	multiple	multiple	NOUN
ejpam-1929	255	7	of	of	ADP
ejpam-1929	255	8	one	one	NUM
ejpam-1929	255	9	of	of	ADP
ejpam-1929	255	10	the	the	DET
ejpam-1929	255	11	pi	pi	NOUN
ejpam-1929	255	12	’s	’s	ADV
ejpam-1929	255	13	for	for	ADP
ejpam-1929	255	14	i	i	PROPN
ejpam-1929	255	15	=	=	SYM
ejpam-1929	255	16	1,2	1,2	NUM
ejpam-1929	255	17	,	,	PUNCT
ejpam-1929	255	18	.	.	PUNCT
ejpam-1929	255	19	.	.	PUNCT
ejpam-1929	256	1	.	.	PUNCT
ejpam-1929	257	1	,	,	PUNCT
ejpam-1929	257	2	m	m	VERB
ejpam-1929	257	3	and	and	CCONJ
ejpam-1929	257	4	by	by	ADP
ejpam-1929	257	5	the	the	DET
ejpam-1929	257	6	same	same	ADJ
ejpam-1929	257	7	argument	argument	NOUN
ejpam-1929	257	8	as	as	ADP
ejpam-1929	257	9	above	above	ADP
ejpam-1929	257	10	i	i	PRON
ejpam-1929	257	11	=	=	NOUN
ejpam-1929	257	12	1	1	NUM
ejpam-1929	257	13	,	,	PUNCT
ejpam-1929	257	14	whence	whence	NOUN
ejpam-1929	257	15	p2	p2	PROPN
ejpam-1929	257	16	−	−	PROPN
ejpam-1929	257	17	1	1	NUM
ejpam-1929	257	18	is	be	AUX
ejpam-1929	257	19	a	a	DET
ejpam-1929	257	20	multiple	multiple	NOUN
ejpam-1929	257	21	of	of	ADP
ejpam-1929	257	22	p1	p1	PROPN
ejpam-1929	257	23	.	.	PUNCT
ejpam-1929	258	1	then	then	ADV
ejpam-1929	258	2	,	,	PUNCT
ejpam-1929	258	3	p2	p2	PROPN
ejpam-1929	258	4	−	−	PROPN
ejpam-1929	258	5	1	1	NUM
ejpam-1929	258	6	=	=	SYM
ejpam-1929	258	7	βp1	βp1	NOUN
ejpam-1929	258	8	.	.	PUNCT
ejpam-1929	259	1	but	but	CCONJ
ejpam-1929	259	2	,	,	PUNCT
ejpam-1929	259	3	from	from	ADP
ejpam-1929	259	4	equation	equation	NOUN
ejpam-1929	259	5	1	1	NUM
ejpam-1929	259	6	,	,	PUNCT
ejpam-1929	259	7	p2	p2	PROPN
ejpam-1929	259	8	=	=	SYM
ejpam-1929	259	9	αp1−	αp1−	NOUN
ejpam-1929	259	10	1	1	NUM
ejpam-1929	259	11	.	.	PUNCT
ejpam-1929	260	1	this	this	PRON
ejpam-1929	260	2	implies	imply	VERB
ejpam-1929	260	3	,	,	PUNCT
ejpam-1929	260	4	p2−	p2−	NOUN
ejpam-1929	260	5	1=	1=	NOUN
ejpam-1929	260	6	βp1	βp1	NOUN
ejpam-1929	260	7	αp1−	αp1−	NOUN
ejpam-1929	260	8	1−	1−	NUM
ejpam-1929	260	9	1=	1=	NUM
ejpam-1929	260	10	βp1	βp1	NOUN
ejpam-1929	260	11	αp1−	αp1−	NOUN
ejpam-1929	260	12	2=	2=	NUM
ejpam-1929	260	13	βp1	βp1	NOUN
ejpam-1929	260	14	αp1−	αp1−	NOUN
ejpam-1929	260	15	βp1	βp1	NOUN
ejpam-1929	260	16	=	=	SYM
ejpam-1929	260	17	2	2	NUM
ejpam-1929	260	18	(	(	PUNCT
ejpam-1929	260	19	α−	α−	ADP
ejpam-1929	260	20	β)p1	β)p1	PROPN
ejpam-1929	260	21	=	=	PUNCT
ejpam-1929	261	1	2	2	X
ejpam-1929	261	2	.	.	PUNCT
ejpam-1929	262	1	this	this	PRON
ejpam-1929	262	2	is	be	AUX
ejpam-1929	262	3	not	not	PART
ejpam-1929	262	4	possible	possible	ADJ
ejpam-1929	262	5	as	as	SCONJ
ejpam-1929	262	6	p1	p1	NOUN
ejpam-1929	262	7	is	be	AUX
ejpam-1929	262	8	at	at	ADV
ejpam-1929	262	9	least	least	ADJ
ejpam-1929	262	10	3	3	NUM
ejpam-1929	262	11	.	.	PUNCT
ejpam-1929	263	1	thus	thus	ADV
ejpam-1929	263	2	,	,	PUNCT
ejpam-1929	263	3	p2−1	p2−1	NOUN
ejpam-1929	263	4	is	be	AUX
ejpam-1929	263	5	not	not	PART
ejpam-1929	263	6	a	a	DET
ejpam-1929	263	7	multiple	multiple	NOUN
ejpam-1929	263	8	of	of	ADP
ejpam-1929	263	9	any	any	PRON
ejpam-1929	263	10	of	of	ADP
ejpam-1929	263	11	the	the	DET
ejpam-1929	263	12	pi	pi	NOUN
ejpam-1929	263	13	’s	’s	ADV
ejpam-1929	263	14	,	,	PUNCT
ejpam-1929	263	15	whence	whence	NOUN
ejpam-1929	263	16	p2	p2	PROPN
ejpam-1929	263	17	−	−	PROPN
ejpam-1929	263	18	1	1	NUM
ejpam-1929	263	19	∈	∈	PROPN
ejpam-1929	263	20	un	un	NOUN
ejpam-1929	263	21	.	.	PROPN
ejpam-1929	264	1	hence	hence	ADV
ejpam-1929	264	2	,	,	PUNCT
ejpam-1929	264	3	n−	n−	NOUN
ejpam-1929	264	4	p2	p2	VERB
ejpam-1929	264	5	+	+	CCONJ
ejpam-1929	264	6	1	1	NUM
ejpam-1929	264	7	=	=	SYM
ejpam-1929	264	8	n−	n−	PROPN
ejpam-1929	264	9	(	(	PUNCT
ejpam-1929	264	10	p2	p2	PROPN
ejpam-1929	264	11	−	−	NOUN
ejpam-1929	264	12	1	1	X
ejpam-1929	264	13	)	)	PUNCT
ejpam-1929	264	14	∈	∈	PROPN
ejpam-1929	264	15	un	un	NOUN
ejpam-1929	264	16	,	,	PUNCT
ejpam-1929	264	17	whence	whence	ADP
ejpam-1929	264	18	n−	n−	PROPN
ejpam-1929	264	19	p2	p2	PROPN
ejpam-1929	264	20	is	be	AUX
ejpam-1929	264	21	adjacent	adjacent	ADJ
ejpam-1929	264	22	with	with	ADP
ejpam-1929	264	23	1	1	NUM
ejpam-1929	264	24	in	in	ADP
ejpam-1929	264	25	σu	σu	PROPN
ejpam-1929	264	26	n.	n.	PROPN
ejpam-1929	264	27	d.	d.	PROPN
ejpam-1929	264	28	sinha	sinha	PROPN
ejpam-1929	264	29	,	,	PUNCT
ejpam-1929	264	30	a.	a.	NOUN
ejpam-1929	264	31	dhama	dhama	PROPN
ejpam-1929	264	32	,	,	PUNCT
ejpam-1929	264	33	b.	b.	PROPN
ejpam-1929	264	34	acharya	acharya	PROPN
ejpam-1929	264	35	/	/	SYM
ejpam-1929	264	36	eur	eur	PROPN
ejpam-1929	264	37	.	.	PUNCT
ejpam-1929	265	1	j.	j.	PROPN
ejpam-1929	265	2	pure	pure	PROPN
ejpam-1929	265	3	appl	appl	PROPN
ejpam-1929	265	4	.	.	PROPN
ejpam-1929	265	5	math	math	PROPN
ejpam-1929	265	6	,	,	PUNCT
ejpam-1929	265	7	6	6	NUM
ejpam-1929	265	8	(	(	PUNCT
ejpam-1929	265	9	2013	2013	NUM
ejpam-1929	265	10	)	)	PUNCT
ejpam-1929	265	11	,	,	PUNCT
ejpam-1929	265	12	189	189	NUM
ejpam-1929	265	13	-	-	SYM
ejpam-1929	265	14	210	210	NUM
ejpam-1929	265	15	198	198	NUM
ejpam-1929	265	16	now	now	ADV
ejpam-1929	265	17	,	,	PUNCT
ejpam-1929	265	18	n−	n−	NOUN
ejpam-1929	265	19	p2	p2	X
ejpam-1929	265	20	+	+	CCONJ
ejpam-1929	265	21	p1	p1	PROPN
ejpam-1929	265	22	=	=	SYM
ejpam-1929	265	23	n−	n−	PROPN
ejpam-1929	265	24	(	(	PUNCT
ejpam-1929	265	25	p2	p2	PROPN
ejpam-1929	265	26	−	−	PROPN
ejpam-1929	265	27	p1	p1	PROPN
ejpam-1929	265	28	)	)	PUNCT
ejpam-1929	265	29	.	.	PUNCT
ejpam-1929	266	1	since	since	SCONJ
ejpam-1929	266	2	p1	p1	PROPN
ejpam-1929	266	3	<	<	X
ejpam-1929	266	4	p2	p2	X
ejpam-1929	266	5	<	<	X
ejpam-1929	266	6	·	·	PUNCT
ejpam-1929	266	7	·	·	PUNCT
ejpam-1929	266	8	·	·	PUNCT
ejpam-1929	266	9	pm	pm	NOUN
ejpam-1929	266	10	,	,	PUNCT
ejpam-1929	266	11	p2	p2	PROPN
ejpam-1929	266	12	−	−	PROPN
ejpam-1929	266	13	p1	p1	NOUN
ejpam-1929	266	14	is	be	AUX
ejpam-1929	266	15	not	not	PART
ejpam-1929	266	16	a	a	DET
ejpam-1929	266	17	multiple	multiple	NOUN
ejpam-1929	266	18	of	of	ADP
ejpam-1929	266	19	any	any	PRON
ejpam-1929	266	20	of	of	ADP
ejpam-1929	266	21	the	the	DET
ejpam-1929	266	22	pi	pi	NOUN
ejpam-1929	266	23	’s	’s	ADV
ejpam-1929	266	24	for	for	ADP
ejpam-1929	266	25	i	i	PROPN
ejpam-1929	266	26	=	=	NOUN
ejpam-1929	266	27	2,3	2,3	NUM
ejpam-1929	266	28	,	,	PUNCT
ejpam-1929	266	29	.	.	PUNCT
ejpam-1929	266	30	.	.	PUNCT
ejpam-1929	266	31	.	.	PUNCT
ejpam-1929	267	1	m.	m.	NOUN
ejpam-1929	267	2	also	also	ADV
ejpam-1929	267	3	,	,	PUNCT
ejpam-1929	267	4	p2	p2	PROPN
ejpam-1929	267	5	−	−	PROPN
ejpam-1929	267	6	p1	p1	NOUN
ejpam-1929	267	7	is	be	AUX
ejpam-1929	267	8	not	not	PART
ejpam-1929	267	9	a	a	DET
ejpam-1929	267	10	multiple	multiple	NOUN
ejpam-1929	267	11	of	of	ADP
ejpam-1929	267	12	p1	p1	NOUN
ejpam-1929	267	13	.	.	PUNCT
ejpam-1929	268	1	this	this	PRON
ejpam-1929	268	2	shows	show	VERB
ejpam-1929	268	3	that	that	SCONJ
ejpam-1929	268	4	p2	p2	PROPN
ejpam-1929	268	5	−	−	PROPN
ejpam-1929	268	6	p1	p1	PROPN
ejpam-1929	268	7	∈	∈	PROPN
ejpam-1929	268	8	un	un	PROPN
ejpam-1929	268	9	and	and	CCONJ
ejpam-1929	268	10	by	by	ADP
ejpam-1929	268	11	lemma	lemma	PROPN
ejpam-1929	268	12	2	2	NUM
ejpam-1929	268	13	,	,	PUNCT
ejpam-1929	268	14	n−	n−	PROPN
ejpam-1929	268	15	(	(	PUNCT
ejpam-1929	268	16	p2	p2	PROPN
ejpam-1929	268	17	−	−	PROPN
ejpam-1929	268	18	p1	p1	PROPN
ejpam-1929	268	19	)	)	PUNCT
ejpam-1929	268	20	∈	∈	PROPN
ejpam-1929	268	21	un	un	PROPN
ejpam-1929	268	22	.	.	PUNCT
ejpam-1929	269	1	this	this	PRON
ejpam-1929	269	2	shows	show	VERB
ejpam-1929	269	3	that	that	SCONJ
ejpam-1929	269	4	n−	n−	NOUN
ejpam-1929	269	5	p2	p2	PROPN
ejpam-1929	269	6	is	be	AUX
ejpam-1929	269	7	adjacent	adjacent	ADJ
ejpam-1929	269	8	with	with	ADP
ejpam-1929	269	9	p1	p1	PROPN
ejpam-1929	269	10	in	in	ADP
ejpam-1929	269	11	σn	σn	PROPN
ejpam-1929	269	12	.	.	PUNCT
ejpam-1929	270	1	thus	thus	ADV
ejpam-1929	270	2	,	,	PUNCT
ejpam-1929	270	3	we	we	PRON
ejpam-1929	270	4	have	have	VERB
ejpam-1929	270	5	a	a	DET
ejpam-1929	270	6	cycle	cycle	NOUN
ejpam-1929	270	7	z	z	NOUN
ejpam-1929	270	8	′	′	NUM
ejpam-1929	271	1	=	=	SYM
ejpam-1929	272	1	(	(	PUNCT
ejpam-1929	272	2	p1	p1	PROPN
ejpam-1929	272	3	,	,	PUNCT
ejpam-1929	272	4	n−	n−	NOUN
ejpam-1929	272	5	p2	p2	NOUN
ejpam-1929	272	6	,	,	PUNCT
ejpam-1929	272	7	1	1	NUM
ejpam-1929	272	8	,	,	PUNCT
ejpam-1929	272	9	p1	p1	NOUN
ejpam-1929	272	10	)	)	PUNCT
ejpam-1929	272	11	in	in	ADP
ejpam-1929	272	12	σn	σn	PROPN
ejpam-1929	272	13	.	.	PUNCT
ejpam-1929	273	1	clearly	clearly	ADV
ejpam-1929	273	2	,	,	PUNCT
ejpam-1929	273	3	p1	p1	PROPN
ejpam-1929	273	4	and	and	CCONJ
ejpam-1929	273	5	n−	n−	PROPN
ejpam-1929	273	6	p2	p2	NOUN
ejpam-1929	273	7	do	do	AUX
ejpam-1929	273	8	not	not	PART
ejpam-1929	273	9	belong	belong	VERB
ejpam-1929	273	10	to	to	ADP
ejpam-1929	273	11	un	un	PROPN
ejpam-1929	273	12	and	and	CCONJ
ejpam-1929	273	13	1	1	NUM
ejpam-1929	273	14	∈	∈	PROPN
ejpam-1929	273	15	un	un	NOUN
ejpam-1929	273	16	.	.	PROPN
ejpam-1929	274	1	then	then	ADV
ejpam-1929	274	2	,	,	PUNCT
ejpam-1929	274	3	by	by	ADP
ejpam-1929	274	4	the	the	DET
ejpam-1929	274	5	definition	definition	NOUN
ejpam-1929	274	6	of	of	ADP
ejpam-1929	274	7	σn	σn	NOUN
ejpam-1929	274	8	,	,	PUNCT
ejpam-1929	274	9	z	z	NOUN
ejpam-1929	274	10	′	′	NOUN
ejpam-1929	274	11	has	have	VERB
ejpam-1929	274	12	exactly	exactly	ADV
ejpam-1929	274	13	one	one	NUM
ejpam-1929	274	14	negative	negative	ADJ
ejpam-1929	274	15	edge	edge	NOUN
ejpam-1929	274	16	p1(n−	p1(n−	VERB
ejpam-1929	274	17	p2	p2	NOUN
ejpam-1929	274	18	)	)	PUNCT
ejpam-1929	274	19	.	.	PUNCT
ejpam-1929	275	1	thus	thus	ADV
ejpam-1929	275	2	,	,	PUNCT
ejpam-1929	275	3	z	z	NOUN
ejpam-1929	275	4	′	′	NOUN
ejpam-1929	275	5	is	be	AUX
ejpam-1929	275	6	a	a	DET
ejpam-1929	275	7	negative	negative	ADJ
ejpam-1929	275	8	cycle	cycle	NOUN
ejpam-1929	275	9	in	in	ADP
ejpam-1929	275	10	σn	σn	PROPN
ejpam-1929	275	11	.	.	PUNCT
ejpam-1929	276	1	this	this	PRON
ejpam-1929	276	2	implies	imply	VERB
ejpam-1929	276	3	that	that	SCONJ
ejpam-1929	276	4	σn	σn	NOUN
ejpam-1929	276	5	is	be	AUX
ejpam-1929	276	6	not	not	PART
ejpam-1929	276	7	balanced	balanced	ADJ
ejpam-1929	276	8	,	,	PUNCT
ejpam-1929	276	9	a	a	DET
ejpam-1929	276	10	contradiction	contradiction	NOUN
ejpam-1929	276	11	to	to	ADP
ejpam-1929	276	12	the	the	DET
ejpam-1929	276	13	hypothesis	hypothesis	NOUN
ejpam-1929	276	14	.	.	PUNCT
ejpam-1929	277	1	so	so	ADV
ejpam-1929	277	2	,	,	PUNCT
ejpam-1929	277	3	by	by	ADP
ejpam-1929	277	4	contraposition	contraposition	NOUN
ejpam-1929	277	5	,	,	PUNCT
ejpam-1929	277	6	the	the	DET
ejpam-1929	277	7	conditions	condition	NOUN
ejpam-1929	277	8	are	be	AUX
ejpam-1929	277	9	satisfied	satisfied	ADJ
ejpam-1929	277	10	.	.	PUNCT
ejpam-1929	278	1	sufficiency	sufficiency	NOUN
ejpam-1929	278	2	:	:	PUNCT
ejpam-1929	278	3	suppose	suppose	VERB
ejpam-1929	278	4	n	n	PRON
ejpam-1929	278	5	is	be	AUX
ejpam-1929	278	6	even	even	ADV
ejpam-1929	278	7	.	.	PUNCT
ejpam-1929	279	1	then	then	ADV
ejpam-1929	279	2	,	,	PUNCT
ejpam-1929	279	3	un	un	PROPN
ejpam-1929	279	4	does	do	AUX
ejpam-1929	279	5	not	not	PART
ejpam-1929	279	6	contain	contain	VERB
ejpam-1929	279	7	any	any	DET
ejpam-1929	279	8	multiple	multiple	NOUN
ejpam-1929	279	9	of	of	ADP
ejpam-1929	279	10	2	2	NUM
ejpam-1929	279	11	.	.	PUNCT
ejpam-1929	280	1	then	then	ADV
ejpam-1929	280	2	,	,	PUNCT
ejpam-1929	280	3	by	by	ADP
ejpam-1929	280	4	theorem	theorem	NOUN
ejpam-1929	280	5	6	6	NUM
ejpam-1929	280	6	,	,	PUNCT
ejpam-1929	280	7	σn	σn	PROPN
ejpam-1929	280	8	is	be	AUX
ejpam-1929	280	9	bipartite	bipartite	ADJ
ejpam-1929	280	10	,	,	PUNCT
ejpam-1929	280	11	whence	whence	SCONJ
ejpam-1929	280	12	all	all	DET
ejpam-1929	280	13	its	its	PRON
ejpam-1929	280	14	cycles	cycle	NOUN
ejpam-1929	280	15	are	be	AUX
ejpam-1929	280	16	even	even	ADV
ejpam-1929	280	17	.	.	PUNCT
ejpam-1929	281	1	therefore	therefore	ADV
ejpam-1929	281	2	,	,	PUNCT
ejpam-1929	281	3	every	every	DET
ejpam-1929	281	4	cycle	cycle	NOUN
ejpam-1929	281	5	inσn	inσn	NOUN
ejpam-1929	281	6	contains	contain	VERB
ejpam-1929	281	7	alternately	alternately	ADV
ejpam-1929	281	8	either	either	CCONJ
ejpam-1929	281	9	even	even	ADV
ejpam-1929	281	10	-	-	PUNCT
ejpam-1929	281	11	odd	odd	ADJ
ejpam-1929	281	12	or	or	CCONJ
ejpam-1929	281	13	odd	odd	ADV
ejpam-1929	281	14	-	-	PUNCT
ejpam-1929	281	15	even	even	ADV
ejpam-1929	281	16	labeled	label	VERB
ejpam-1929	281	17	vertices	vertex	NOUN
ejpam-1929	281	18	.	.	PUNCT
ejpam-1929	282	1	without	without	ADP
ejpam-1929	282	2	loss	loss	NOUN
ejpam-1929	282	3	of	of	ADP
ejpam-1929	282	4	generality	generality	NOUN
ejpam-1929	282	5	,	,	PUNCT
ejpam-1929	282	6	let	let	VERB
ejpam-1929	282	7	z	z	PRON
ejpam-1929	282	8	′′	′′	PROPN
ejpam-1929	282	9	=	=	SYM
ejpam-1929	282	10	(	(	PUNCT
ejpam-1929	282	11	e1	e1	PROPN
ejpam-1929	282	12	,	,	PUNCT
ejpam-1929	282	13	o1	o1	NOUN
ejpam-1929	282	14	,	,	PUNCT
ejpam-1929	282	15	e2	e2	PROPN
ejpam-1929	282	16	,	,	PUNCT
ejpam-1929	282	17	o2	o2	PROPN
ejpam-1929	282	18	,	,	PUNCT
ejpam-1929	282	19	.	.	PUNCT
ejpam-1929	282	20	.	.	PUNCT
ejpam-1929	283	1	.	.	PUNCT
ejpam-1929	284	1	,	,	PUNCT
ejpam-1929	284	2	em	em	PRON
ejpam-1929	284	3	,	,	PUNCT
ejpam-1929	284	4	om	om	PROPN
ejpam-1929	284	5	,	,	PUNCT
ejpam-1929	284	6	e1	e1	PROPN
ejpam-1929	284	7	)	)	PUNCT
ejpam-1929	284	8	be	be	VERB
ejpam-1929	284	9	a	a	DET
ejpam-1929	284	10	cycle	cycle	NOUN
ejpam-1929	284	11	of	of	ADP
ejpam-1929	284	12	even	even	ADV
ejpam-1929	284	13	length	length	NOUN
ejpam-1929	284	14	in	in	ADP
ejpam-1929	284	15	σn	σn	PROPN
ejpam-1929	284	16	.	.	PUNCT
ejpam-1929	285	1	clearly	clearly	ADV
ejpam-1929	285	2	,	,	PUNCT
ejpam-1929	285	3	ei	ei	INTJ
ejpam-1929	285	4	/∈	/∈	PUNCT
ejpam-1929	285	5	un∀i	un∀i	NUM
ejpam-1929	285	6	=	=	SYM
ejpam-1929	285	7	1,2	1,2	NUM
ejpam-1929	285	8	,	,	PUNCT
ejpam-1929	285	9	.	.	PUNCT
ejpam-1929	285	10	.	.	PUNCT
ejpam-1929	286	1	.	.	PUNCT
ejpam-1929	287	1	,	,	PUNCT
ejpam-1929	287	2	m.	m.	NOUN
ejpam-1929	287	3	case(i	case(i	PROPN
ejpam-1929	287	4	):	):	PUNCT
ejpam-1929	287	5	suppose	suppose	VERB
ejpam-1929	287	6	o	o	X
ejpam-1929	287	7	j	j	PROPN
ejpam-1929	287	8	∈	∈	PROPN
ejpam-1929	287	9	un∀	un∀	PROPN
ejpam-1929	287	10	j	j	X
ejpam-1929	287	11	=	=	SYM
ejpam-1929	287	12	1,2	1,2	NUM
ejpam-1929	287	13	,	,	PUNCT
ejpam-1929	287	14	.	.	PUNCT
ejpam-1929	287	15	.	.	PUNCT
ejpam-1929	288	1	.	.	PUNCT
ejpam-1929	289	1	,	,	PUNCT
ejpam-1929	289	2	m.	m.	NOUN
ejpam-1929	289	3	then	then	ADV
ejpam-1929	289	4	,	,	PUNCT
ejpam-1929	289	5	all	all	DET
ejpam-1929	289	6	the	the	DET
ejpam-1929	289	7	edges	edge	NOUN
ejpam-1929	289	8	in	in	ADP
ejpam-1929	289	9	z	z	NOUN
ejpam-1929	289	10	′′	′′	PROPN
ejpam-1929	289	11	are	be	AUX
ejpam-1929	289	12	positive	positive	ADJ
ejpam-1929	289	13	.	.	PUNCT
ejpam-1929	290	1	case(ii	case(ii	ADJ
ejpam-1929	290	2	):	):	PUNCT
ejpam-1929	290	3	suppose	suppose	VERB
ejpam-1929	290	4	o	o	X
ejpam-1929	290	5	j	j	PROPN
ejpam-1929	290	6	/∈	/∈	PROPN
ejpam-1929	290	7	un	un	PROPN
ejpam-1929	290	8	for	for	ADP
ejpam-1929	290	9	some	some	PRON
ejpam-1929	290	10	j	j	NOUN
ejpam-1929	290	11	=	=	SYM
ejpam-1929	290	12	1,2	1,2	NUM
ejpam-1929	290	13	,	,	PUNCT
ejpam-1929	290	14	.	.	PUNCT
ejpam-1929	290	15	.	.	PUNCT
ejpam-1929	291	1	.	.	PUNCT
ejpam-1929	292	1	,	,	PUNCT
ejpam-1929	292	2	m.	m.	NOUN
ejpam-1929	292	3	then	then	ADV
ejpam-1929	292	4	,	,	PUNCT
ejpam-1929	292	5	z	z	PROPN
ejpam-1929	292	6	′′	′′	PROPN
ejpam-1929	292	7	contains	contain	VERB
ejpam-1929	292	8	two	two	NUM
ejpam-1929	292	9	negative	negative	ADJ
ejpam-1929	292	10	edges	edge	NOUN
ejpam-1929	292	11	e	e	NOUN
ejpam-1929	292	12	jo	jo	PROPN
ejpam-1929	292	13	j	j	PROPN
ejpam-1929	292	14	and	and	CCONJ
ejpam-1929	292	15	o	o	PROPN
ejpam-1929	292	16	je	je	X
ejpam-1929	292	17	j+1	j+1	ADJ
ejpam-1929	292	18	with	with	ADP
ejpam-1929	292	19	respect	respect	NOUN
ejpam-1929	292	20	to	to	ADP
ejpam-1929	292	21	each	each	DET
ejpam-1929	292	22	o	o	NOUN
ejpam-1929	292	23	j	j	PROPN
ejpam-1929	292	24	/∈	/∈	PUNCT
ejpam-1929	292	25	un	un	PROPN
ejpam-1929	292	26	.	.	PROPN
ejpam-1929	292	27	thus	thus	ADV
ejpam-1929	292	28	,	,	PUNCT
ejpam-1929	292	29	z	z	PROPN
ejpam-1929	292	30	′′	′′	PROPN
ejpam-1929	292	31	contains	contain	VERB
ejpam-1929	292	32	an	an	DET
ejpam-1929	292	33	even	even	ADJ
ejpam-1929	292	34	number	number	NOUN
ejpam-1929	292	35	of	of	ADP
ejpam-1929	292	36	negative	negative	ADJ
ejpam-1929	292	37	edges	edge	NOUN
ejpam-1929	292	38	.	.	PUNCT
ejpam-1929	293	1	since	since	SCONJ
ejpam-1929	293	2	z	z	PROPN
ejpam-1929	293	3	′′	′′	PROPN
ejpam-1929	293	4	is	be	AUX
ejpam-1929	293	5	an	an	DET
ejpam-1929	293	6	arbitrary	arbitrary	ADJ
ejpam-1929	293	7	cycle	cycle	NOUN
ejpam-1929	293	8	in	in	ADP
ejpam-1929	293	9	σn	σn	NOUN
ejpam-1929	293	10	,	,	PUNCT
ejpam-1929	293	11	using	use	VERB
ejpam-1929	293	12	lemma	lemma	PROPN
ejpam-1929	293	13	1	1	NUM
ejpam-1929	293	14	,	,	PUNCT
ejpam-1929	293	15	we	we	PRON
ejpam-1929	293	16	conclude	conclude	VERB
ejpam-1929	293	17	σn	σn	NOUN
ejpam-1929	293	18	is	be	AUX
ejpam-1929	293	19	balanced	balanced	ADJ
ejpam-1929	293	20	.	.	PUNCT
ejpam-1929	294	1	next	next	ADV
ejpam-1929	294	2	,	,	PUNCT
ejpam-1929	294	3	suppose	suppose	VERB
ejpam-1929	294	4	n	n	PRON
ejpam-1929	294	5	is	be	AUX
ejpam-1929	294	6	odd	odd	ADJ
ejpam-1929	294	7	and	and	CCONJ
ejpam-1929	294	8	it	it	PRON
ejpam-1929	294	9	does	do	AUX
ejpam-1929	294	10	not	not	PART
ejpam-1929	294	11	have	have	VERB
ejpam-1929	294	12	more	more	ADJ
ejpam-1929	294	13	than	than	ADP
ejpam-1929	294	14	one	one	NUM
ejpam-1929	294	15	distinct	distinct	ADJ
ejpam-1929	294	16	prime	prime	ADJ
ejpam-1929	294	17	factors	factor	NOUN
ejpam-1929	294	18	.	.	PUNCT
ejpam-1929	295	1	that	that	PRON
ejpam-1929	295	2	means	mean	VERB
ejpam-1929	295	3	,	,	PUNCT
ejpam-1929	295	4	n	n	PROPN
ejpam-1929	295	5	=	=	PROPN
ejpam-1929	295	6	pa	pa	PROPN
ejpam-1929	295	7	.	.	PUNCT
ejpam-1929	296	1	now	now	ADV
ejpam-1929	296	2	,	,	PUNCT
ejpam-1929	296	3	using	use	VERB
ejpam-1929	296	4	lemma	lemma	PROPN
ejpam-1929	296	5	3	3	NUM
ejpam-1929	296	6	,	,	PUNCT
ejpam-1929	296	7	σn	σn	PROPN
ejpam-1929	296	8	is	be	AUX
ejpam-1929	296	9	an	an	DET
ejpam-1929	296	10	all	all	ADV
ejpam-1929	296	11	-	-	PUNCT
ejpam-1929	296	12	positive	positive	ADJ
ejpam-1929	296	13	sigraph	sigraph	NOUN
ejpam-1929	296	14	which	which	PRON
ejpam-1929	296	15	is	be	AUX
ejpam-1929	296	16	trivially	trivially	ADV
ejpam-1929	296	17	balanced	balanced	ADJ
ejpam-1929	296	18	.	.	PUNCT
ejpam-1929	297	1	hence	hence	ADV
ejpam-1929	297	2	the	the	DET
ejpam-1929	297	3	theorem	theorem	NOUN
ejpam-1929	297	4	.	.	PROPN
ejpam-1929	298	1	11	11	NUM
ejpam-1929	298	2	0	0	NUM
ejpam-1929	298	3	1	1	NUM
ejpam-1929	298	4	2	2	NUM
ejpam-1929	298	5	3	3	NUM
ejpam-1929	298	6	4	4	NUM
ejpam-1929	298	7	5	5	NUM
ejpam-1929	298	8	6	6	NUM
ejpam-1929	298	9	78	78	NUM
ejpam-1929	298	10	9	9	NUM
ejpam-1929	298	11	10	10	NUM
ejpam-1929	298	12	12	12	NUM
ejpam-1929	298	13	13	13	NUM
ejpam-1929	298	14	14	14	NUM
ejpam-1929	298	15	figure	figure	NOUN
ejpam-1929	298	16	3	3	NUM
ejpam-1929	298	17	:	:	PUNCT
ejpam-1929	298	18	smallest	small	ADJ
ejpam-1929	298	19	unbalanced	unbalanced	ADJ
ejpam-1929	298	20	unitary	unitary	ADJ
ejpam-1929	298	21	addition	addition	NOUN
ejpam-1929	298	22	cayley	cayley	NOUN
ejpam-1929	298	23	sigraph	sigraph	PROPN
ejpam-1929	298	24	d.	d.	PROPN
ejpam-1929	298	25	sinha	sinha	PROPN
ejpam-1929	298	26	,	,	PUNCT
ejpam-1929	298	27	a.	a.	NOUN
ejpam-1929	298	28	dhama	dhama	PROPN
ejpam-1929	298	29	,	,	PUNCT
ejpam-1929	298	30	b.	b.	PROPN
ejpam-1929	298	31	acharya	acharya	PROPN
ejpam-1929	298	32	/	/	SYM
ejpam-1929	298	33	eur	eur	PROPN
ejpam-1929	298	34	.	.	PUNCT
ejpam-1929	299	1	j.	j.	PROPN
ejpam-1929	299	2	pure	pure	PROPN
ejpam-1929	299	3	appl	appl	PROPN
ejpam-1929	299	4	.	.	PROPN
ejpam-1929	299	5	math	math	PROPN
ejpam-1929	299	6	,	,	PUNCT
ejpam-1929	299	7	6	6	NUM
ejpam-1929	299	8	(	(	PUNCT
ejpam-1929	299	9	2013	2013	NUM
ejpam-1929	299	10	)	)	PUNCT
ejpam-1929	299	11	,	,	PUNCT
ejpam-1929	299	12	189	189	NUM
ejpam-1929	299	13	-	-	SYM
ejpam-1929	299	14	210	210	NUM
ejpam-1929	299	15	199	199	NUM
ejpam-1929	299	16	the	the	DET
ejpam-1929	299	17	smallest	small	ADJ
ejpam-1929	299	18	heterogeneous	heterogeneous	ADJ
ejpam-1929	299	19	unbalanced	unbalanced	ADJ
ejpam-1929	299	20	unitary	unitary	ADJ
ejpam-1929	299	21	addition	addition	NOUN
ejpam-1929	299	22	sigraph	sigraph	NOUN
ejpam-1929	299	23	is	be	AUX
ejpam-1929	299	24	σ15	σ15	PROPN
ejpam-1929	299	25	,	,	PUNCT
ejpam-1929	299	26	which	which	PRON
ejpam-1929	299	27	is	be	AUX
ejpam-1929	299	28	shown	show	VERB
ejpam-1929	299	29	in	in	ADP
ejpam-1929	299	30	figure	figure	NOUN
ejpam-1929	299	31	3	3	NUM
ejpam-1929	299	32	.	.	NOUN
ejpam-1929	299	33	4	4	NUM
ejpam-1929	299	34	.	.	X
ejpam-1929	300	1	clusterability	clusterability	NOUN
ejpam-1929	300	2	of	of	ADP
ejpam-1929	300	3	σn	σn	NOUN
ejpam-1929	300	4	in	in	ADP
ejpam-1929	300	5	this	this	DET
ejpam-1929	300	6	section	section	NOUN
ejpam-1929	300	7	,	,	PUNCT
ejpam-1929	300	8	we	we	PRON
ejpam-1929	300	9	discuss	discuss	VERB
ejpam-1929	300	10	clusterability	clusterability	NOUN
ejpam-1929	300	11	of	of	ADP
ejpam-1929	300	12	unitary	unitary	ADJ
ejpam-1929	300	13	addition	addition	NOUN
ejpam-1929	300	14	cayley	cayley	NOUN
ejpam-1929	300	15	sigraphs	sigraph	VERB
ejpam-1929	300	16	and	and	CCONJ
ejpam-1929	300	17	obtain	obtain	VERB
ejpam-1929	300	18	the	the	DET
ejpam-1929	300	19	following	follow	VERB
ejpam-1929	300	20	somewhat	somewhat	ADV
ejpam-1929	300	21	surprising	surprising	ADJ
ejpam-1929	300	22	result	result	NOUN
ejpam-1929	300	23	.	.	PUNCT
ejpam-1929	301	1	theorem	theorem	ADJ
ejpam-1929	301	2	8	8	NUM
ejpam-1929	301	3	.	.	PUNCT
ejpam-1929	302	1	a	a	DET
ejpam-1929	302	2	unitary	unitary	ADJ
ejpam-1929	302	3	addition	addition	NOUN
ejpam-1929	302	4	cayley	cayley	NOUN
ejpam-1929	302	5	sigraph	sigraph	NOUN
ejpam-1929	302	6	σn	σn	NOUN
ejpam-1929	302	7	=	=	SYM
ejpam-1929	302	8	(	(	PUNCT
ejpam-1929	302	9	σ	σ	PROPN
ejpam-1929	302	10	u	u	PROPN
ejpam-1929	302	11	n	n	NUM
ejpam-1929	302	12	,	,	PUNCT
ejpam-1929	302	13	σ	σ	PROPN
ejpam-1929	302	14	)	)	PUNCT
ejpam-1929	302	15	is	be	AUX
ejpam-1929	302	16	clusterable	clusterable	ADJ
ejpam-1929	302	17	if	if	SCONJ
ejpam-1929	302	18	and	and	CCONJ
ejpam-1929	302	19	only	only	ADV
ejpam-1929	302	20	if	if	SCONJ
ejpam-1929	302	21	it	it	PRON
ejpam-1929	302	22	is	be	AUX
ejpam-1929	302	23	balanced	balanced	ADJ
ejpam-1929	302	24	.	.	PUNCT
ejpam-1929	303	1	proof	proof	NOUN
ejpam-1929	303	2	.	.	PUNCT
ejpam-1929	304	1	sufficiency	sufficiency	NOUN
ejpam-1929	304	2	:	:	PUNCT
ejpam-1929	304	3	suppose	suppose	VERB
ejpam-1929	304	4	the	the	DET
ejpam-1929	304	5	unitary	unitary	ADJ
ejpam-1929	304	6	addition	addition	NOUN
ejpam-1929	304	7	cayley	cayley	NOUN
ejpam-1929	304	8	sigraph	sigraph	NOUN
ejpam-1929	304	9	σn	σn	NOUN
ejpam-1929	304	10	=	=	SYM
ejpam-1929	304	11	(	(	PUNCT
ejpam-1929	304	12	σ	σ	PROPN
ejpam-1929	304	13	u	u	PROPN
ejpam-1929	304	14	n	n	NUM
ejpam-1929	304	15	,	,	PUNCT
ejpam-1929	304	16	σ	σ	PROPN
ejpam-1929	304	17	)	)	PUNCT
ejpam-1929	304	18	is	be	AUX
ejpam-1929	304	19	balanced	balanced	ADJ
ejpam-1929	304	20	.	.	PUNCT
ejpam-1929	305	1	then	then	ADV
ejpam-1929	305	2	,	,	PUNCT
ejpam-1929	305	3	by	by	ADP
ejpam-1929	305	4	the	the	DET
ejpam-1929	305	5	definition	definition	NOUN
ejpam-1929	305	6	of	of	ADP
ejpam-1929	305	7	clusterability	clusterability	NOUN
ejpam-1929	305	8	,	,	PUNCT
ejpam-1929	305	9	σn	σn	PROPN
ejpam-1929	305	10	is	be	AUX
ejpam-1929	305	11	clusterable	clusterable	ADJ
ejpam-1929	305	12	with	with	ADP
ejpam-1929	305	13	two	two	NUM
ejpam-1929	305	14	clusters	cluster	NOUN
ejpam-1929	305	15	.	.	PUNCT
ejpam-1929	306	1	necessity	necessity	NOUN
ejpam-1929	306	2	:	:	PUNCT
ejpam-1929	306	3	suppose	suppose	VERB
ejpam-1929	306	4	unitary	unitary	ADJ
ejpam-1929	306	5	addition	addition	NOUN
ejpam-1929	306	6	cayley	cayley	NOUN
ejpam-1929	306	7	sigraph	sigraph	NOUN
ejpam-1929	306	8	σn	σn	NOUN
ejpam-1929	306	9	=	=	SYM
ejpam-1929	306	10	(	(	PUNCT
ejpam-1929	306	11	σ	σ	PROPN
ejpam-1929	306	12	u	u	PROPN
ejpam-1929	306	13	n	n	NUM
ejpam-1929	306	14	,	,	PUNCT
ejpam-1929	306	15	σ	σ	PROPN
ejpam-1929	306	16	)	)	PUNCT
ejpam-1929	306	17	is	be	AUX
ejpam-1929	306	18	clusterable	clusterable	ADJ
ejpam-1929	306	19	.	.	PUNCT
ejpam-1929	307	1	if	if	SCONJ
ejpam-1929	307	2	possible	possible	ADJ
ejpam-1929	307	3	,	,	PUNCT
ejpam-1929	307	4	suppose	suppose	VERB
ejpam-1929	307	5	σn	σn	NOUN
ejpam-1929	307	6	is	be	AUX
ejpam-1929	307	7	not	not	PART
ejpam-1929	307	8	balanced	balanced	ADJ
ejpam-1929	307	9	.	.	PUNCT
ejpam-1929	308	1	then	then	ADV
ejpam-1929	308	2	,	,	PUNCT
ejpam-1929	308	3	by	by	ADP
ejpam-1929	308	4	theorem	theorem	NOUN
ejpam-1929	308	5	7	7	NUM
ejpam-1929	308	6	,	,	PUNCT
ejpam-1929	308	7	n	n	X
ejpam-1929	308	8	is	be	AUX
ejpam-1929	308	9	odd	odd	ADJ
ejpam-1929	308	10	with	with	ADP
ejpam-1929	308	11	at	at	ADV
ejpam-1929	308	12	least	least	ADV
ejpam-1929	308	13	two	two	NUM
ejpam-1929	308	14	distinct	distinct	ADJ
ejpam-1929	308	15	prime	prime	ADJ
ejpam-1929	308	16	factors	factor	NOUN
ejpam-1929	308	17	.	.	PUNCT
ejpam-1929	309	1	so	so	ADV
ejpam-1929	309	2	,	,	PUNCT
ejpam-1929	309	3	let	let	VERB
ejpam-1929	309	4	n	n	NOUN
ejpam-1929	309	5	=	=	SYM
ejpam-1929	309	6	p	p	NOUN
ejpam-1929	309	7	a1	a1	NOUN
ejpam-1929	309	8	1	1	NUM
ejpam-1929	309	9	p	p	NOUN
ejpam-1929	309	10	a2	a2	PROPN
ejpam-1929	309	11	2	2	NUM
ejpam-1929	309	12	.	.	PUNCT
ejpam-1929	309	13	.	.	PUNCT
ejpam-1929	309	14	.	.	PUNCT
ejpam-1929	310	1	p	p	PROPN
ejpam-1929	310	2	am	be	AUX
ejpam-1929	310	3	m	m	PRON
ejpam-1929	310	4	,	,	PUNCT
ejpam-1929	310	5	where	where	SCONJ
ejpam-1929	310	6	all	all	PRON
ejpam-1929	310	7	of	of	ADP
ejpam-1929	310	8	p1	p1	NOUN
ejpam-1929	310	9	,	,	PUNCT
ejpam-1929	310	10	p2	p2	NOUN
ejpam-1929	310	11	,	,	PUNCT
ejpam-1929	310	12	.	.	PUNCT
ejpam-1929	310	13	.	.	PUNCT
ejpam-1929	311	1	.	.	PUNCT
ejpam-1929	312	1	,	,	PUNCT
ejpam-1929	312	2	pm	pm	NOUN
ejpam-1929	312	3	are	be	AUX
ejpam-1929	312	4	distinct	distinct	ADJ
ejpam-1929	312	5	primes	prime	NOUN
ejpam-1929	312	6	,	,	PUNCT
ejpam-1929	312	7	p1	p1	NOUN
ejpam-1929	312	8	6=	6=	NUM
ejpam-1929	312	9	2	2	NUM
ejpam-1929	312	10	and	and	CCONJ
ejpam-1929	312	11	p1	p1	PROPN
ejpam-1929	312	12	<	<	X
ejpam-1929	312	13	p2	p2	X
ejpam-1929	312	14	<	<	X
ejpam-1929	312	15	·	·	PUNCT
ejpam-1929	312	16	·	·	PUNCT
ejpam-1929	312	17	·	·	PUNCT
ejpam-1929	313	1	<	<	X
ejpam-1929	313	2	pm	pm	NOUN
ejpam-1929	313	3	.	.	PUNCT
ejpam-1929	314	1	now	now	ADV
ejpam-1929	314	2	,	,	PUNCT
ejpam-1929	314	3	as	as	ADP
ejpam-1929	314	4	in	in	ADP
ejpam-1929	314	5	the	the	DET
ejpam-1929	314	6	proof	proof	NOUN
ejpam-1929	314	7	of	of	ADP
ejpam-1929	314	8	theorem	theorem	NOUN
ejpam-1929	314	9	7	7	NUM
ejpam-1929	314	10	,	,	PUNCT
ejpam-1929	314	11	we	we	PRON
ejpam-1929	314	12	have	have	VERB
ejpam-1929	314	13	at	at	ADV
ejpam-1929	314	14	least	least	ADJ
ejpam-1929	314	15	one	one	NUM
ejpam-1929	314	16	of	of	ADP
ejpam-1929	314	17	the	the	DET
ejpam-1929	314	18	cycles	cycle	NOUN
ejpam-1929	314	19	z	z	NOUN
ejpam-1929	314	20	=	=	SYM
ejpam-1929	314	21	(	(	PUNCT
ejpam-1929	314	22	p1	p1	PROPN
ejpam-1929	314	23	,	,	PUNCT
ejpam-1929	314	24	p2	p2	NOUN
ejpam-1929	314	25	,	,	PUNCT
ejpam-1929	314	26	1	1	NUM
ejpam-1929	314	27	,	,	PUNCT
ejpam-1929	314	28	p1	p1	NOUN
ejpam-1929	314	29	)	)	PUNCT
ejpam-1929	314	30	and	and	CCONJ
ejpam-1929	314	31	z	z	NOUN
ejpam-1929	314	32	′	′	NUM
ejpam-1929	315	1	=	=	SYM
ejpam-1929	315	2	(	(	PUNCT
ejpam-1929	315	3	p1	p1	PROPN
ejpam-1929	315	4	,	,	PUNCT
ejpam-1929	315	5	n−	n−	NOUN
ejpam-1929	315	6	p2	p2	NOUN
ejpam-1929	315	7	,	,	PUNCT
ejpam-1929	315	8	1	1	NUM
ejpam-1929	315	9	,	,	PUNCT
ejpam-1929	315	10	p1	p1	NOUN
ejpam-1929	315	11	)	)	PUNCT
ejpam-1929	315	12	in	in	ADP
ejpam-1929	315	13	σn	σn	PROPN
ejpam-1929	315	14	.	.	PUNCT
ejpam-1929	316	1	clearly	clearly	ADV
ejpam-1929	316	2	,	,	PUNCT
ejpam-1929	316	3	p1	p1	NOUN
ejpam-1929	316	4	and	and	CCONJ
ejpam-1929	316	5	p2	p2	PROPN
ejpam-1929	316	6	do	do	AUX
ejpam-1929	316	7	not	not	PART
ejpam-1929	316	8	belong	belong	VERB
ejpam-1929	316	9	to	to	ADP
ejpam-1929	316	10	un	un	PROPN
ejpam-1929	316	11	and	and	CCONJ
ejpam-1929	316	12	1	1	NUM
ejpam-1929	316	13	∈	∈	PROPN
ejpam-1929	316	14	un	un	NOUN
ejpam-1929	316	15	.	.	PROPN
ejpam-1929	317	1	then	then	ADV
ejpam-1929	317	2	,	,	PUNCT
ejpam-1929	317	3	by	by	ADP
ejpam-1929	317	4	the	the	DET
ejpam-1929	317	5	definition	definition	NOUN
ejpam-1929	317	6	of	of	ADP
ejpam-1929	317	7	σn	σn	PROPN
ejpam-1929	317	8	,	,	PUNCT
ejpam-1929	317	9	z	z	PROPN
ejpam-1929	317	10	has	have	VERB
ejpam-1929	317	11	exactly	exactly	ADV
ejpam-1929	317	12	one	one	NUM
ejpam-1929	317	13	negative	negative	ADJ
ejpam-1929	317	14	edge	edge	NOUN
ejpam-1929	317	15	p1p2	p1p2	PROPN
ejpam-1929	317	16	.	.	PUNCT
ejpam-1929	318	1	also	also	ADV
ejpam-1929	318	2	,	,	PUNCT
ejpam-1929	318	3	p1	p1	PROPN
ejpam-1929	318	4	and	and	CCONJ
ejpam-1929	318	5	n−	n−	PROPN
ejpam-1929	318	6	p2	p2	NOUN
ejpam-1929	318	7	do	do	AUX
ejpam-1929	318	8	not	not	PART
ejpam-1929	318	9	belong	belong	VERB
ejpam-1929	318	10	to	to	ADP
ejpam-1929	318	11	un	un	PROPN
ejpam-1929	318	12	and	and	CCONJ
ejpam-1929	318	13	1	1	NUM
ejpam-1929	318	14	∈	∈	PROPN
ejpam-1929	318	15	un	un	NOUN
ejpam-1929	318	16	.	.	PROPN
ejpam-1929	319	1	then	then	ADV
ejpam-1929	319	2	,	,	PUNCT
ejpam-1929	319	3	again	again	ADV
ejpam-1929	319	4	by	by	ADP
ejpam-1929	319	5	the	the	DET
ejpam-1929	319	6	definition	definition	NOUN
ejpam-1929	319	7	of	of	ADP
ejpam-1929	319	8	σn	σn	NOUN
ejpam-1929	319	9	,	,	PUNCT
ejpam-1929	319	10	z	z	NOUN
ejpam-1929	319	11	′	′	NOUN
ejpam-1929	319	12	has	have	VERB
ejpam-1929	319	13	exactly	exactly	ADV
ejpam-1929	319	14	one	one	NUM
ejpam-1929	319	15	negative	negative	ADJ
ejpam-1929	319	16	edge	edge	NOUN
ejpam-1929	319	17	p1(n−	p1(n−	VERB
ejpam-1929	319	18	p2	p2	NOUN
ejpam-1929	319	19	)	)	PUNCT
ejpam-1929	319	20	.	.	PUNCT
ejpam-1929	320	1	thus	thus	ADV
ejpam-1929	320	2	,	,	PUNCT
ejpam-1929	320	3	in	in	ADP
ejpam-1929	320	4	each	each	DET
ejpam-1929	320	5	case	case	NOUN
ejpam-1929	320	6	we	we	PRON
ejpam-1929	320	7	have	have	VERB
ejpam-1929	320	8	a	a	DET
ejpam-1929	320	9	cycle	cycle	NOUN
ejpam-1929	320	10	with	with	ADP
ejpam-1929	320	11	exactly	exactly	ADV
ejpam-1929	320	12	one	one	NUM
ejpam-1929	320	13	negative	negative	ADJ
ejpam-1929	320	14	edge	edge	NOUN
ejpam-1929	320	15	.	.	PUNCT
ejpam-1929	321	1	this	this	PRON
ejpam-1929	321	2	shows	show	VERB
ejpam-1929	321	3	that	that	SCONJ
ejpam-1929	321	4	σn	σn	NOUN
ejpam-1929	321	5	is	be	AUX
ejpam-1929	321	6	not	not	PART
ejpam-1929	321	7	clusterable	clusterable	ADJ
ejpam-1929	321	8	,	,	PUNCT
ejpam-1929	321	9	a	a	DET
ejpam-1929	321	10	contradiction	contradiction	NOUN
ejpam-1929	321	11	to	to	ADP
ejpam-1929	321	12	the	the	DET
ejpam-1929	321	13	hypothesis	hypothesis	NOUN
ejpam-1929	321	14	.	.	PUNCT
ejpam-1929	322	1	thus	thus	ADV
ejpam-1929	322	2	,	,	PUNCT
ejpam-1929	322	3	σn	σn	PROPN
ejpam-1929	322	4	is	be	AUX
ejpam-1929	322	5	balanced	balanced	ADJ
ejpam-1929	322	6	.	.	PUNCT
ejpam-1929	323	1	hence	hence	ADV
ejpam-1929	323	2	,	,	PUNCT
ejpam-1929	323	3	the	the	DET
ejpam-1929	323	4	theorem	theorem	NOUN
ejpam-1929	323	5	.	.	PROPN
ejpam-1929	323	6	5	5	NUM
ejpam-1929	323	7	.	.	X
ejpam-1929	323	8	sign	sign	NOUN
ejpam-1929	323	9	-	-	PUNCT
ejpam-1929	323	10	compatibility	compatibility	NOUN
ejpam-1929	323	11	of	of	ADP
ejpam-1929	323	12	σn	σn	NOUN
ejpam-1929	323	13	theorem	theorem	ADJ
ejpam-1929	323	14	9	9	NUM
ejpam-1929	323	15	(	(	PUNCT
ejpam-1929	323	16	[	[	X
ejpam-1929	323	17	41	41	NUM
ejpam-1929	323	18	]	]	NUM
ejpam-1929	323	19	)	)	PUNCT
ejpam-1929	323	20	.	.	PUNCT
ejpam-1929	324	1	a	a	DET
ejpam-1929	324	2	sigraph	sigraph	NOUN
ejpam-1929	324	3	s	s	PART
ejpam-1929	324	4	is	be	AUX
ejpam-1929	324	5	sign	sign	NOUN
ejpam-1929	324	6	-	-	PUNCT
ejpam-1929	324	7	compatible	compatible	ADJ
ejpam-1929	324	8	if	if	SCONJ
ejpam-1929	324	9	and	and	CCONJ
ejpam-1929	324	10	only	only	ADV
ejpam-1929	324	11	if	if	SCONJ
ejpam-1929	324	12	s	s	NOUN
ejpam-1929	324	13	does	do	AUX
ejpam-1929	324	14	not	not	PART
ejpam-1929	324	15	contain	contain	VERB
ejpam-1929	324	16	a	a	DET
ejpam-1929	324	17	subsigraph	subsigraph	NOUN
ejpam-1929	324	18	isomorphic	isomorphic	ADJ
ejpam-1929	324	19	to	to	ADP
ejpam-1929	324	20	either	either	PRON
ejpam-1929	324	21	of	of	ADP
ejpam-1929	324	22	the	the	DET
ejpam-1929	324	23	two	two	NUM
ejpam-1929	324	24	sigraphs	sigraph	NOUN
ejpam-1929	324	25	,	,	PUNCT
ejpam-1929	324	26	s1	s1	PROPN
ejpam-1929	324	27	formed	form	VERB
ejpam-1929	324	28	by	by	ADP
ejpam-1929	324	29	taking	take	VERB
ejpam-1929	324	30	the	the	DET
ejpam-1929	324	31	path	path	NOUN
ejpam-1929	324	32	p4	p4	NOUN
ejpam-1929	324	33	=	=	PUNCT
ejpam-1929	324	34	(	(	PUNCT
ejpam-1929	324	35	x	x	INTJ
ejpam-1929	324	36	,	,	PUNCT
ejpam-1929	324	37	u	u	NOUN
ejpam-1929	324	38	,	,	PUNCT
ejpam-1929	324	39	v	v	NOUN
ejpam-1929	324	40	,	,	PUNCT
ejpam-1929	324	41	y	y	NOUN
ejpam-1929	324	42	)	)	PUNCT
ejpam-1929	324	43	with	with	ADP
ejpam-1929	324	44	both	both	CCONJ
ejpam-1929	324	45	the	the	DET
ejpam-1929	324	46	edges	edge	NOUN
ejpam-1929	325	1	xu	xu	PROPN
ejpam-1929	325	2	and	and	CCONJ
ejpam-1929	325	3	v	v	ADP
ejpam-1929	325	4	y	y	PROPN
ejpam-1929	325	5	negative	negative	ADJ
ejpam-1929	325	6	and	and	CCONJ
ejpam-1929	325	7	the	the	DET
ejpam-1929	325	8	edge	edge	NOUN
ejpam-1929	325	9	uv	uv	INTJ
ejpam-1929	325	10	positive	positive	ADJ
ejpam-1929	325	11	and	and	CCONJ
ejpam-1929	325	12	s2	s2	PROPN
ejpam-1929	325	13	formed	form	VERB
ejpam-1929	325	14	by	by	ADP
ejpam-1929	325	15	taking	take	VERB
ejpam-1929	325	16	s1	s1	NOUN
ejpam-1929	325	17	and	and	CCONJ
ejpam-1929	325	18	identifying	identify	VERB
ejpam-1929	325	19	the	the	DET
ejpam-1929	325	20	vertices	vertex	NOUN
ejpam-1929	325	21	x	x	PUNCT
ejpam-1929	325	22	and	and	CCONJ
ejpam-1929	325	23	y	y	PROPN
ejpam-1929	325	24	(	(	PUNCT
ejpam-1929	325	25	figure	figure	NOUN
ejpam-1929	325	26	4	4	NUM
ejpam-1929	325	27	)	)	PUNCT
ejpam-1929	325	28	.	.	PUNCT
ejpam-1929	326	1	x	x	PUNCT
ejpam-1929	326	2	u	u	NOUN
ejpam-1929	326	3	v	v	X
ejpam-1929	326	4	y	y	PROPN
ejpam-1929	326	5	(	(	PUNCT
ejpam-1929	326	6	a	a	NOUN
ejpam-1929	326	7	)	)	PUNCT
ejpam-1929	326	8	s1	s1	NOUN
ejpam-1929	326	9	x	x	PUNCT
ejpam-1929	326	10	=	=	PUNCT
ejpam-1929	326	11	y	y	PROPN
ejpam-1929	326	12	u	u	NOUN
ejpam-1929	326	13	v	v	X
ejpam-1929	326	14	(	(	PUNCT
ejpam-1929	326	15	b	b	NOUN
ejpam-1929	326	16	)	)	PUNCT
ejpam-1929	326	17	s2	s2	NOUN
ejpam-1929	326	18	figure	figure	NOUN
ejpam-1929	326	19	4	4	NUM
ejpam-1929	326	20	:	:	PUNCT
ejpam-1929	326	21	two	two	NUM
ejpam-1929	326	22	forbidden	forbid	VERB
ejpam-1929	326	23	subsigraphs	subsigraph	NOUN
ejpam-1929	326	24	for	for	ADP
ejpam-1929	326	25	a	a	DET
ejpam-1929	326	26	sign	sign	NOUN
ejpam-1929	326	27	-	-	PUNCT
ejpam-1929	326	28	compatible	compatible	ADJ
ejpam-1929	326	29	sigraph	sigraph	NOUN
ejpam-1929	326	30	[	[	X
ejpam-1929	326	31	40	40	NUM
ejpam-1929	326	32	]	]	PUNCT
ejpam-1929	326	33	d.	d.	PROPN
ejpam-1929	326	34	sinha	sinha	PROPN
ejpam-1929	326	35	,	,	PUNCT
ejpam-1929	326	36	a.	a.	NOUN
ejpam-1929	326	37	dhama	dhama	PROPN
ejpam-1929	326	38	,	,	PUNCT
ejpam-1929	326	39	b.	b.	PROPN
ejpam-1929	326	40	acharya	acharya	PROPN
ejpam-1929	326	41	/	/	SYM
ejpam-1929	326	42	eur	eur	PROPN
ejpam-1929	326	43	.	.	PUNCT
ejpam-1929	327	1	j.	j.	PROPN
ejpam-1929	327	2	pure	pure	PROPN
ejpam-1929	327	3	appl	appl	PROPN
ejpam-1929	327	4	.	.	PROPN
ejpam-1929	327	5	math	math	PROPN
ejpam-1929	327	6	,	,	PUNCT
ejpam-1929	327	7	6	6	NUM
ejpam-1929	327	8	(	(	PUNCT
ejpam-1929	327	9	2013	2013	NUM
ejpam-1929	327	10	)	)	PUNCT
ejpam-1929	327	11	,	,	PUNCT
ejpam-1929	327	12	189	189	NUM
ejpam-1929	327	13	-	-	SYM
ejpam-1929	327	14	210	210	NUM
ejpam-1929	327	15	200	200	NUM
ejpam-1929	327	16	theorem	theorem	VERB
ejpam-1929	327	17	10	10	NUM
ejpam-1929	327	18	.	.	PUNCT
ejpam-1929	328	1	every	every	DET
ejpam-1929	328	2	unitary	unitary	ADJ
ejpam-1929	328	3	addition	addition	NOUN
ejpam-1929	328	4	cayley	cayley	NOUN
ejpam-1929	328	5	sigraph	sigraph	NOUN
ejpam-1929	328	6	σn	σn	NOUN
ejpam-1929	328	7	is	be	AUX
ejpam-1929	328	8	sign	sign	NOUN
ejpam-1929	328	9	-	-	PUNCT
ejpam-1929	328	10	compatible	compatible	ADJ
ejpam-1929	328	11	.	.	PUNCT
ejpam-1929	329	1	proof	proof	NOUN
ejpam-1929	329	2	.	.	PUNCT
ejpam-1929	330	1	suppose	suppose	VERB
ejpam-1929	330	2	that	that	SCONJ
ejpam-1929	330	3	the	the	DET
ejpam-1929	330	4	unitary	unitary	ADJ
ejpam-1929	330	5	addition	addition	NOUN
ejpam-1929	330	6	cayley	cayley	NOUN
ejpam-1929	330	7	sigraph	sigraph	NOUN
ejpam-1929	330	8	σn	σn	NOUN
ejpam-1929	330	9	is	be	AUX
ejpam-1929	330	10	not	not	PART
ejpam-1929	330	11	sign	sign	NOUN
ejpam-1929	330	12	-	-	PUNCT
ejpam-1929	330	13	compatible	compatible	ADJ
ejpam-1929	330	14	.	.	PUNCT
ejpam-1929	331	1	then	then	ADV
ejpam-1929	331	2	,	,	PUNCT
ejpam-1929	331	3	by	by	ADP
ejpam-1929	331	4	theorem	theorem	NOUN
ejpam-1929	331	5	9	9	NUM
ejpam-1929	331	6	,	,	PUNCT
ejpam-1929	331	7	there	there	PRON
ejpam-1929	331	8	is	be	VERB
ejpam-1929	331	9	at	at	ADV
ejpam-1929	331	10	least	least	ADJ
ejpam-1929	331	11	one	one	NUM
ejpam-1929	331	12	positive	positive	ADJ
ejpam-1929	331	13	edge	edge	NOUN
ejpam-1929	331	14	,	,	PUNCT
ejpam-1929	331	15	say	say	VERB
ejpam-1929	331	16	vi	vi	PROPN
ejpam-1929	331	17	v	v	PROPN
ejpam-1929	331	18	j	j	PROPN
ejpam-1929	331	19	in	in	ADP
ejpam-1929	331	20	σn	σn	PRON
ejpam-1929	331	21	such	such	ADJ
ejpam-1929	331	22	that	that	SCONJ
ejpam-1929	331	23	there	there	PRON
ejpam-1929	331	24	are	be	VERB
ejpam-1929	331	25	negative	negative	ADJ
ejpam-1929	331	26	edges	edge	NOUN
ejpam-1929	331	27	on	on	ADP
ejpam-1929	331	28	both	both	CCONJ
ejpam-1929	331	29	the	the	DET
ejpam-1929	331	30	vertices	vertex	NOUN
ejpam-1929	331	31	,	,	PUNCT
ejpam-1929	331	32	vi	vi	NOUN
ejpam-1929	331	33	and	and	CCONJ
ejpam-1929	331	34	v	v	ADP
ejpam-1929	331	35	j	j	NOUN
ejpam-1929	331	36	in	in	ADV
ejpam-1929	331	37	.	.	PUNCT
ejpam-1929	332	1	since	since	SCONJ
ejpam-1929	332	2	vi	vi	PROPN
ejpam-1929	332	3	v	v	PROPN
ejpam-1929	332	4	j	j	PROPN
ejpam-1929	332	5	is	be	AUX
ejpam-1929	332	6	a	a	DET
ejpam-1929	332	7	positive	positive	ADJ
ejpam-1929	332	8	edge	edge	NOUN
ejpam-1929	332	9	in	in	ADP
ejpam-1929	332	10	σn	σn	NOUN
ejpam-1929	332	11	,	,	PUNCT
ejpam-1929	332	12	by	by	ADP
ejpam-1929	332	13	the	the	DET
ejpam-1929	332	14	definition	definition	NOUN
ejpam-1929	332	15	of	of	ADP
ejpam-1929	332	16	σn	σn	NOUN
ejpam-1929	332	17	,	,	PUNCT
ejpam-1929	332	18	at	at	ADP
ejpam-1929	332	19	least	least	ADJ
ejpam-1929	332	20	one	one	NUM
ejpam-1929	332	21	of	of	ADP
ejpam-1929	332	22	vi	vi	PROPN
ejpam-1929	332	23	,	,	PUNCT
ejpam-1929	332	24	v	v	PROPN
ejpam-1929	332	25	j	j	PROPN
ejpam-1929	332	26	∈	∈	PROPN
ejpam-1929	332	27	un	un	PROPN
ejpam-1929	332	28	.	.	PROPN
ejpam-1929	333	1	as	as	ADP
ejpam-1929	333	2	at	at	ADV
ejpam-1929	333	3	least	least	ADV
ejpam-1929	333	4	one	one	NUM
ejpam-1929	333	5	of	of	ADP
ejpam-1929	333	6	vi	vi	PROPN
ejpam-1929	333	7	,	,	PUNCT
ejpam-1929	333	8	v	v	PROPN
ejpam-1929	333	9	j	j	PROPN
ejpam-1929	333	10	∈	∈	PROPN
ejpam-1929	333	11	un	un	PROPN
ejpam-1929	333	12	,	,	PUNCT
ejpam-1929	333	13	again	again	ADV
ejpam-1929	333	14	by	by	ADP
ejpam-1929	333	15	the	the	DET
ejpam-1929	333	16	definition	definition	NOUN
ejpam-1929	333	17	of	of	ADP
ejpam-1929	333	18	σn	σn	NOUN
ejpam-1929	333	19	,	,	PUNCT
ejpam-1929	333	20	there	there	PRON
ejpam-1929	333	21	is	be	VERB
ejpam-1929	333	22	no	no	DET
ejpam-1929	333	23	negative	negative	ADJ
ejpam-1929	333	24	edge	edge	NOUN
ejpam-1929	333	25	on	on	ADP
ejpam-1929	333	26	at	at	ADV
ejpam-1929	333	27	least	least	ADV
ejpam-1929	333	28	one	one	NUM
ejpam-1929	333	29	vertex	vertex	NOUN
ejpam-1929	333	30	,	,	PUNCT
ejpam-1929	333	31	a	a	DET
ejpam-1929	333	32	contradiction	contradiction	NOUN
ejpam-1929	333	33	to	to	ADP
ejpam-1929	333	34	the	the	DET
ejpam-1929	333	35	hypothesis	hypothesis	NOUN
ejpam-1929	333	36	.	.	PUNCT
ejpam-1929	334	1	hence	hence	ADV
ejpam-1929	334	2	,	,	PUNCT
ejpam-1929	334	3	σn	σn	PROPN
ejpam-1929	334	4	is	be	AUX
ejpam-1929	334	5	sign	sign	NOUN
ejpam-1929	334	6	-	-	PUNCT
ejpam-1929	334	7	compatible	compatible	ADJ
ejpam-1929	334	8	.	.	PUNCT
ejpam-1929	335	1	it	it	PRON
ejpam-1929	335	2	has	have	AUX
ejpam-1929	335	3	been	be	AUX
ejpam-1929	335	4	shown	show	VERB
ejpam-1929	335	5	elsewhere	elsewhere	ADV
ejpam-1929	335	6	that	that	SCONJ
ejpam-1929	335	7	all	all	DET
ejpam-1929	335	8	line	line	NOUN
ejpam-1929	335	9	sigraphs	sigraph	NOUN
ejpam-1929	335	10	are	be	AUX
ejpam-1929	335	11	sign	sign	NOUN
ejpam-1929	335	12	-	-	PUNCT
ejpam-1929	335	13	compatible	compatible	ADJ
ejpam-1929	335	14	[	[	X
ejpam-1929	335	15	5	5	NUM
ejpam-1929	335	16	]	]	PUNCT
ejpam-1929	335	17	.	.	PUNCT
ejpam-1929	336	1	hence	hence	ADV
ejpam-1929	336	2	,	,	PUNCT
ejpam-1929	336	3	in	in	ADP
ejpam-1929	336	4	view	view	NOUN
ejpam-1929	336	5	of	of	ADP
ejpam-1929	336	6	theorem	theorem	NOUN
ejpam-1929	336	7	10	10	NUM
ejpam-1929	336	8	the	the	DET
ejpam-1929	336	9	question	question	NOUN
ejpam-1929	336	10	arises	arise	VERB
ejpam-1929	336	11	whether	whether	SCONJ
ejpam-1929	336	12	any	any	DET
ejpam-1929	336	13	unitary	unitary	ADJ
ejpam-1929	336	14	addition	addition	NOUN
ejpam-1929	336	15	cayley	cayley	NOUN
ejpam-1929	336	16	sigraph	sigraph	NOUN
ejpam-1929	336	17	is	be	AUX
ejpam-1929	336	18	a	a	DET
ejpam-1929	336	19	line	line	NOUN
ejpam-1929	336	20	sigraph	sigraph	NOUN
ejpam-1929	336	21	.	.	PUNCT
ejpam-1929	337	1	the	the	DET
ejpam-1929	337	2	answer	answer	NOUN
ejpam-1929	337	3	of	of	ADP
ejpam-1929	337	4	this	this	DET
ejpam-1929	337	5	question	question	NOUN
ejpam-1929	337	6	is	be	AUX
ejpam-1929	337	7	given	give	VERB
ejpam-1929	337	8	in	in	ADP
ejpam-1929	337	9	theorem	theorem	ADJ
ejpam-1929	337	10	12	12	NUM
ejpam-1929	337	11	.	.	PUNCT
ejpam-1929	338	1	theorem	theorem	VERB
ejpam-1929	338	2	11	11	NUM
ejpam-1929	338	3	.	.	PUNCT
ejpam-1929	339	1	unitary	unitary	ADJ
ejpam-1929	339	2	addition	addition	NOUN
ejpam-1929	339	3	cayley	cayley	NOUN
ejpam-1929	339	4	graph	graph	NOUN
ejpam-1929	339	5	gn	gn	PROPN
ejpam-1929	339	6	is	be	AUX
ejpam-1929	339	7	a	a	DET
ejpam-1929	339	8	line	line	NOUN
ejpam-1929	339	9	graph	graph	NOUN
ejpam-1929	339	10	if	if	SCONJ
ejpam-1929	340	1	and	and	CCONJ
ejpam-1929	340	2	only	only	ADV
ejpam-1929	340	3	if	if	SCONJ
ejpam-1929	340	4	n	n	PRON
ejpam-1929	340	5	∈	∈	PROPN
ejpam-1929	340	6	{	{	PUNCT
ejpam-1929	340	7	2,3,4,6	2,3,4,6	NUM
ejpam-1929	340	8	}	}	PUNCT
ejpam-1929	340	9	.	.	PUNCT
ejpam-1929	341	1	proof	proof	NOUN
ejpam-1929	341	2	.	.	PUNCT
ejpam-1929	342	1	necessity	necessity	NOUN
ejpam-1929	342	2	:	:	PUNCT
ejpam-1929	342	3	suppose	suppose	VERB
ejpam-1929	342	4	unitary	unitary	ADJ
ejpam-1929	342	5	addition	addition	NOUN
ejpam-1929	342	6	cayley	cayley	NOUN
ejpam-1929	342	7	graph	graph	NOUN
ejpam-1929	342	8	gn	gn	PROPN
ejpam-1929	342	9	is	be	AUX
ejpam-1929	342	10	a	a	DET
ejpam-1929	342	11	line	line	NOUN
ejpam-1929	342	12	graph	graph	NOUN
ejpam-1929	342	13	.	.	PUNCT
ejpam-1929	343	1	if	if	SCONJ
ejpam-1929	343	2	possible	possible	ADJ
ejpam-1929	343	3	,	,	PUNCT
ejpam-1929	343	4	suppose	suppose	VERB
ejpam-1929	343	5	n	n	ADV
ejpam-1929	343	6	/∈	/∈	PUNCT
ejpam-1929	343	7	{	{	PUNCT
ejpam-1929	343	8	2,3,4,6	2,3,4,6	NUM
ejpam-1929	343	9	}	}	PUNCT
ejpam-1929	343	10	.	.	PUNCT
ejpam-1929	344	1	case	case	NOUN
ejpam-1929	345	1	i	i	PRON
ejpam-1929	345	2	:	:	PUNCT
ejpam-1929	345	3	suppose	suppose	VERB
ejpam-1929	345	4	n	n	PRON
ejpam-1929	345	5	is	be	AUX
ejpam-1929	345	6	a	a	DET
ejpam-1929	345	7	prime	prime	ADJ
ejpam-1929	345	8	number	number	NOUN
ejpam-1929	345	9	.	.	PUNCT
ejpam-1929	346	1	clearly	clearly	ADV
ejpam-1929	346	2	,	,	PUNCT
ejpam-1929	346	3	in	in	ADP
ejpam-1929	346	4	this	this	DET
ejpam-1929	346	5	case	case	NOUN
ejpam-1929	346	6	n≥	n≥	NOUN
ejpam-1929	346	7	5	5	NUM
ejpam-1929	346	8	.	.	PUNCT
ejpam-1929	346	9	since	since	SCONJ
ejpam-1929	346	10	n	n	NUM
ejpam-1929	346	11	is	be	AUX
ejpam-1929	346	12	prime	prime	ADJ
ejpam-1929	346	13	,	,	PUNCT
ejpam-1929	346	14	un	un	PROPN
ejpam-1929	346	15	contains	contain	VERB
ejpam-1929	346	16	all	all	DET
ejpam-1929	346	17	numbers	number	NOUN
ejpam-1929	346	18	from	from	ADP
ejpam-1929	346	19	1	1	NUM
ejpam-1929	346	20	to	to	PART
ejpam-1929	346	21	(	(	PUNCT
ejpam-1929	346	22	n−	n−	NOUN
ejpam-1929	346	23	1	1	NUM
ejpam-1929	346	24	)	)	PUNCT
ejpam-1929	346	25	.	.	PUNCT
ejpam-1929	347	1	now	now	ADV
ejpam-1929	347	2	,	,	PUNCT
ejpam-1929	347	3	0	0	NUM
ejpam-1929	347	4	is	be	AUX
ejpam-1929	347	5	adjacent	adjacent	ADJ
ejpam-1929	347	6	with	with	ADP
ejpam-1929	347	7	all	all	DET
ejpam-1929	347	8	the	the	DET
ejpam-1929	347	9	vertices	vertex	NOUN
ejpam-1929	347	10	of	of	ADP
ejpam-1929	347	11	gn	gn	PROPN
ejpam-1929	347	12	.	.	PUNCT
ejpam-1929	348	1	also	also	ADV
ejpam-1929	348	2	,	,	PUNCT
ejpam-1929	348	3	for	for	ADP
ejpam-1929	348	4	any	any	DET
ejpam-1929	348	5	other	other	ADJ
ejpam-1929	348	6	vertex	vertex	NOUN
ejpam-1929	348	7	i	i	PRON
ejpam-1929	348	8	in	in	ADP
ejpam-1929	348	9	gn	gn	PROPN
ejpam-1929	348	10	,	,	PUNCT
ejpam-1929	348	11	i	i	PRON
ejpam-1929	348	12	is	be	AUX
ejpam-1929	348	13	not	not	PART
ejpam-1929	348	14	adjacent	adjacent	ADJ
ejpam-1929	348	15	only	only	ADV
ejpam-1929	348	16	with	with	ADP
ejpam-1929	348	17	(	(	PUNCT
ejpam-1929	348	18	n−	n−	NOUN
ejpam-1929	348	19	i	i	NOUN
ejpam-1929	348	20	)	)	PUNCT
ejpam-1929	348	21	as	as	ADP
ejpam-1929	348	22	i	i	PRON
ejpam-1929	348	23	+	+	X
ejpam-1929	348	24	(	(	PUNCT
ejpam-1929	348	25	n−	n−	NOUN
ejpam-1929	348	26	i	i	NOUN
ejpam-1929	348	27	)	)	PUNCT
ejpam-1929	349	1	=	=	PUNCT
ejpam-1929	349	2	n	n	NOUN
ejpam-1929	349	3	=	=	SYM
ejpam-1929	349	4	0	0	PROPN
ejpam-1929	349	5	6=	6=	NUM
ejpam-1929	349	6	un	un	PROPN
ejpam-1929	349	7	.	.	PROPN
ejpam-1929	350	1	thus	thus	ADV
ejpam-1929	350	2	,	,	PUNCT
ejpam-1929	350	3	for	for	ADP
ejpam-1929	350	4	any	any	DET
ejpam-1929	350	5	two	two	NUM
ejpam-1929	350	6	vertices	vertex	NOUN
ejpam-1929	350	7	i	i	PRON
ejpam-1929	350	8	and	and	CCONJ
ejpam-1929	350	9	j	j	PROPN
ejpam-1929	350	10	in	in	ADP
ejpam-1929	350	11	gn	gn	PROPN
ejpam-1929	351	1	such	such	ADJ
ejpam-1929	351	2	that	that	SCONJ
ejpam-1929	351	3	i	i	PRON
ejpam-1929	351	4	6=	6=	PROPN
ejpam-1929	351	5	j	j	PROPN
ejpam-1929	351	6	6=	6=	ADP
ejpam-1929	351	7	0	0	NUM
ejpam-1929	351	8	,	,	PUNCT
ejpam-1929	351	9	we	we	PRON
ejpam-1929	351	10	have	have	VERB
ejpam-1929	351	11	an	an	DET
ejpam-1929	351	12	induced	induced	ADJ
ejpam-1929	351	13	subgraph	subgraph	NOUN
ejpam-1929	351	14	in	in	ADP
ejpam-1929	351	15	gn	gn	PROPN
ejpam-1929	351	16	,	,	PUNCT
ejpam-1929	351	17	which	which	PRON
ejpam-1929	351	18	is	be	AUX
ejpam-1929	351	19	shown	show	VERB
ejpam-1929	351	20	in	in	ADP
ejpam-1929	351	21	figure	figure	NOUN
ejpam-1929	351	22	5	5	NUM
ejpam-1929	351	23	.	.	NOUN
ejpam-1929	351	24	0	0	PUNCT
ejpam-1929	352	1	i	i	PRON
ejpam-1929	352	2	j	j	PROPN
ejpam-1929	352	3	n	n	CCONJ
ejpam-1929	352	4	-	-	PUNCT
ejpam-1929	352	5	i	i	PROPN
ejpam-1929	352	6	n	n	CCONJ
ejpam-1929	352	7	-	-	PUNCT
ejpam-1929	352	8	j	j	PROPN
ejpam-1929	352	9	figure	figure	NOUN
ejpam-1929	352	10	5	5	NUM
ejpam-1929	352	11	:	:	PUNCT
ejpam-1929	352	12	showing	show	VERB
ejpam-1929	352	13	an	an	DET
ejpam-1929	352	14	induced	induced	ADJ
ejpam-1929	352	15	subgraph	subgraph	NOUN
ejpam-1929	352	16	of	of	ADP
ejpam-1929	352	17	gn	gn	PROPN
ejpam-1929	352	18	,	,	PUNCT
ejpam-1929	352	19	which	which	PRON
ejpam-1929	352	20	is	be	AUX
ejpam-1929	352	21	forbidden	forbid	VERB
ejpam-1929	352	22	for	for	SCONJ
ejpam-1929	352	23	gn	gn	PROPN
ejpam-1929	352	24	to	to	PART
ejpam-1929	352	25	be	be	AUX
ejpam-1929	352	26	a	a	DET
ejpam-1929	352	27	line	line	NOUN
ejpam-1929	352	28	graph	graph	NOUN
ejpam-1929	352	29	.	.	PUNCT
ejpam-1929	353	1	this	this	PRON
ejpam-1929	353	2	is	be	AUX
ejpam-1929	353	3	one	one	NUM
ejpam-1929	353	4	of	of	ADP
ejpam-1929	353	5	the	the	DET
ejpam-1929	353	6	beineke	beineke	NOUN
ejpam-1929	353	7	’s	’s	PART
ejpam-1929	353	8	nine	nine	NUM
ejpam-1929	353	9	forbidden	forbidden	ADJ
ejpam-1929	353	10	subgraphs	subgraph	NOUN
ejpam-1929	353	11	for	for	ADP
ejpam-1929	353	12	line	line	NOUN
ejpam-1929	353	13	graph	graph	NOUN
ejpam-1929	353	14	[	[	X
ejpam-1929	353	15	30	30	NUM
ejpam-1929	353	16	]	]	PUNCT
ejpam-1929	353	17	.	.	PUNCT
ejpam-1929	354	1	this	this	PRON
ejpam-1929	354	2	shows	show	VERB
ejpam-1929	354	3	that	that	SCONJ
ejpam-1929	354	4	gn	gn	PROPN
ejpam-1929	354	5	is	be	AUX
ejpam-1929	354	6	not	not	PART
ejpam-1929	354	7	a	a	DET
ejpam-1929	354	8	line	line	NOUN
ejpam-1929	354	9	graph	graph	NOUN
ejpam-1929	354	10	,	,	PUNCT
ejpam-1929	354	11	a	a	DET
ejpam-1929	354	12	contradiction	contradiction	NOUN
ejpam-1929	354	13	to	to	ADP
ejpam-1929	354	14	the	the	DET
ejpam-1929	354	15	hypothesis	hypothesis	NOUN
ejpam-1929	354	16	.	.	PUNCT
ejpam-1929	355	1	case	case	NOUN
ejpam-1929	355	2	ii	ii	PROPN
ejpam-1929	355	3	:	:	PUNCT
ejpam-1929	355	4	suppose	suppose	VERB
ejpam-1929	355	5	n	n	PRON
ejpam-1929	355	6	is	be	AUX
ejpam-1929	355	7	not	not	PART
ejpam-1929	355	8	a	a	DET
ejpam-1929	355	9	prime	prime	ADJ
ejpam-1929	355	10	number	number	NOUN
ejpam-1929	355	11	.	.	PUNCT
ejpam-1929	356	1	clearly	clearly	ADV
ejpam-1929	356	2	,	,	PUNCT
ejpam-1929	356	3	1	1	NUM
ejpam-1929	356	4	is	be	AUX
ejpam-1929	356	5	(	(	PUNCT
ejpam-1929	356	6	always	always	ADV
ejpam-1929	356	7	)	)	PUNCT
ejpam-1929	356	8	adjacent	adjacent	ADJ
ejpam-1929	356	9	with	with	ADP
ejpam-1929	356	10	0	0	NUM
ejpam-1929	356	11	in	in	ADP
ejpam-1929	356	12	gn	gn	PROPN
ejpam-1929	356	13	.	.	PUNCT
ejpam-1929	357	1	also	also	ADV
ejpam-1929	357	2	,	,	PUNCT
ejpam-1929	357	3	1	1	NUM
ejpam-1929	357	4	is	be	AUX
ejpam-1929	357	5	adjacent	adjacent	ADJ
ejpam-1929	357	6	with	with	ADP
ejpam-1929	357	7	p1	p1	NOUN
ejpam-1929	357	8	,	,	PUNCT
ejpam-1929	357	9	as	as	SCONJ
ejpam-1929	357	10	p1	p1	NOUN
ejpam-1929	357	11	+	+	CCONJ
ejpam-1929	357	12	1	1	NUM
ejpam-1929	357	13	∈	∈	NOUN
ejpam-1929	357	14	un	un	NOUN
ejpam-1929	357	15	,	,	PUNCT
ejpam-1929	357	16	where	where	SCONJ
ejpam-1929	357	17	p1	p1	PROPN
ejpam-1929	357	18	is	be	AUX
ejpam-1929	357	19	the	the	DET
ejpam-1929	357	20	smallest	small	ADJ
ejpam-1929	357	21	multiple	multiple	NOUN
ejpam-1929	357	22	of	of	ADP
ejpam-1929	357	23	n.	n.	NOUN
ejpam-1929	357	24	suppose	suppose	VERB
ejpam-1929	357	25	a	a	PRON
ejpam-1929	357	26	is	be	AUX
ejpam-1929	357	27	some	some	DET
ejpam-1929	357	28	number	number	NOUN
ejpam-1929	357	29	such	such	ADJ
ejpam-1929	357	30	that	that	DET
ejpam-1929	357	31	ap1	ap1	PROPN
ejpam-1929	357	32	=	=	PROPN
ejpam-1929	357	33	n.	n.	PROPN
ejpam-1929	357	34	now	now	ADV
ejpam-1929	357	35	,	,	PUNCT
ejpam-1929	357	36	1	1	NUM
ejpam-1929	357	37	+	+	CCONJ
ejpam-1929	357	38	(	(	PUNCT
ejpam-1929	357	39	a−	a−	PROPN
ejpam-1929	357	40	1)p1	1)p1	NUM
ejpam-1929	357	41	=	=	SYM
ejpam-1929	357	42	1	1	NUM
ejpam-1929	357	43	+	+	CCONJ
ejpam-1929	357	44	ap1−	ap1−	X
ejpam-1929	357	45	p1	p1	NOUN
ejpam-1929	357	46	=	=	SYM
ejpam-1929	358	1	1	1	NUM
ejpam-1929	358	2	+	+	NUM
ejpam-1929	358	3	n−	n−	PROPN
ejpam-1929	358	4	p1	p1	NOUN
ejpam-1929	358	5	=	=	SYM
ejpam-1929	358	6	n−	n−	PROPN
ejpam-1929	358	7	(	(	PUNCT
ejpam-1929	358	8	p1−	p1−	PROPN
ejpam-1929	358	9	1	1	NUM
ejpam-1929	358	10	)	)	PUNCT
ejpam-1929	358	11	.	.	PUNCT
ejpam-1929	359	1	d.	d.	PROPN
ejpam-1929	359	2	sinha	sinha	PROPN
ejpam-1929	359	3	,	,	PUNCT
ejpam-1929	359	4	a.	a.	NOUN
ejpam-1929	359	5	dhama	dhama	PROPN
ejpam-1929	359	6	,	,	PUNCT
ejpam-1929	359	7	b.	b.	PROPN
ejpam-1929	359	8	acharya	acharya	PROPN
ejpam-1929	359	9	/	/	SYM
ejpam-1929	359	10	eur	eur	PROPN
ejpam-1929	359	11	.	.	PUNCT
ejpam-1929	360	1	j.	j.	PROPN
ejpam-1929	360	2	pure	pure	PROPN
ejpam-1929	360	3	appl	appl	PROPN
ejpam-1929	360	4	.	.	PROPN
ejpam-1929	360	5	math	math	PROPN
ejpam-1929	360	6	,	,	PUNCT
ejpam-1929	360	7	6	6	NUM
ejpam-1929	360	8	(	(	PUNCT
ejpam-1929	360	9	2013	2013	NUM
ejpam-1929	360	10	)	)	PUNCT
ejpam-1929	360	11	,	,	PUNCT
ejpam-1929	360	12	189	189	NUM
ejpam-1929	360	13	-	-	SYM
ejpam-1929	360	14	210	210	NUM
ejpam-1929	360	15	201	201	NUM
ejpam-1929	360	16	since	since	SCONJ
ejpam-1929	360	17	p1	p1	NOUN
ejpam-1929	360	18	−	−	PROPN
ejpam-1929	360	19	1	1	NUM
ejpam-1929	360	20	∈	∈	PROPN
ejpam-1929	360	21	un	un	NOUN
ejpam-1929	360	22	,	,	PUNCT
ejpam-1929	360	23	by	by	ADP
ejpam-1929	360	24	lemma	lemma	PROPN
ejpam-1929	360	25	2	2	NUM
ejpam-1929	360	26	,	,	PUNCT
ejpam-1929	360	27	n−	n−	PROPN
ejpam-1929	360	28	(	(	PUNCT
ejpam-1929	360	29	p1	p1	NOUN
ejpam-1929	360	30	−	−	PROPN
ejpam-1929	360	31	1	1	NUM
ejpam-1929	360	32	)	)	PUNCT
ejpam-1929	360	33	∈	∈	PROPN
ejpam-1929	360	34	un	un	PROPN
ejpam-1929	360	35	.	.	PUNCT
ejpam-1929	361	1	thus	thus	ADV
ejpam-1929	361	2	,	,	PUNCT
ejpam-1929	361	3	1	1	NUM
ejpam-1929	361	4	and	and	CCONJ
ejpam-1929	361	5	(	(	PUNCT
ejpam-1929	361	6	a−	a−	PROPN
ejpam-1929	361	7	1)p1	1)p1	PROPN
ejpam-1929	361	8	are	be	AUX
ejpam-1929	361	9	adjacent	adjacent	ADJ
ejpam-1929	361	10	in	in	ADP
ejpam-1929	361	11	gn	gn	PROPN
ejpam-1929	361	12	.	.	PUNCT
ejpam-1929	361	13	also	also	ADV
ejpam-1929	361	14	,	,	PUNCT
ejpam-1929	361	15	0	0	NUM
ejpam-1929	361	16	is	be	AUX
ejpam-1929	361	17	not	not	PART
ejpam-1929	361	18	adjacent	adjacent	ADJ
ejpam-1929	361	19	with	with	ADP
ejpam-1929	361	20	p1	p1	PROPN
ejpam-1929	361	21	and	and	CCONJ
ejpam-1929	361	22	(	(	PUNCT
ejpam-1929	361	23	a−1)p1	a−1)p1	PROPN
ejpam-1929	361	24	as	as	SCONJ
ejpam-1929	361	25	their	their	PRON
ejpam-1929	361	26	addition	addition	NOUN
ejpam-1929	361	27	is	be	AUX
ejpam-1929	361	28	a	a	DET
ejpam-1929	361	29	multiple	multiple	NOUN
ejpam-1929	361	30	of	of	ADP
ejpam-1929	361	31	p1	p1	PROPN
ejpam-1929	361	32	.	.	PUNCT
ejpam-1929	362	1	similarly	similarly	ADV
ejpam-1929	362	2	,	,	PUNCT
ejpam-1929	362	3	p1	p1	PROPN
ejpam-1929	362	4	and	and	CCONJ
ejpam-1929	362	5	(	(	PUNCT
ejpam-1929	362	6	a−	a−	PROPN
ejpam-1929	362	7	1)p1	1)p1	PROPN
ejpam-1929	362	8	are	be	AUX
ejpam-1929	362	9	not	not	PART
ejpam-1929	362	10	adjacent	adjacent	ADJ
ejpam-1929	362	11	in	in	ADP
ejpam-1929	362	12	gn	gn	PROPN
ejpam-1929	362	13	as	as	SCONJ
ejpam-1929	362	14	their	their	PRON
ejpam-1929	362	15	addition	addition	NOUN
ejpam-1929	362	16	is	be	AUX
ejpam-1929	362	17	a	a	DET
ejpam-1929	362	18	multiple	multiple	NOUN
ejpam-1929	362	19	of	of	ADP
ejpam-1929	362	20	p1	p1	NOUN
ejpam-1929	362	21	.	.	PUNCT
ejpam-1929	363	1	thus	thus	ADV
ejpam-1929	363	2	,	,	PUNCT
ejpam-1929	363	3	we	we	PRON
ejpam-1929	363	4	have	have	VERB
ejpam-1929	363	5	an	an	DET
ejpam-1929	363	6	induced	induced	ADJ
ejpam-1929	363	7	subgraph	subgraph	NOUN
ejpam-1929	363	8	in	in	ADP
ejpam-1929	363	9	gn	gn	PROPN
ejpam-1929	363	10	,	,	PUNCT
ejpam-1929	363	11	which	which	PRON
ejpam-1929	363	12	is	be	AUX
ejpam-1929	363	13	shown	show	VERB
ejpam-1929	363	14	in	in	ADP
ejpam-1929	363	15	figure	figure	NOUN
ejpam-1929	363	16	6	6	NUM
ejpam-1929	363	17	.	.	PUNCT
ejpam-1929	364	1	again	again	ADV
ejpam-1929	364	2	,	,	PUNCT
ejpam-1929	364	3	we	we	PRON
ejpam-1929	364	4	have	have	VERB
ejpam-1929	364	5	a	a	DET
ejpam-1929	364	6	forbidden	forbid	VERB
ejpam-1929	364	7	subgraph	subgraph	NOUN
ejpam-1929	364	8	k1,3	k1,3	NOUN
ejpam-1929	364	9	for	for	ADP
ejpam-1929	364	10	a	a	DET
ejpam-1929	364	11	line	line	NOUN
ejpam-1929	364	12	graph	graph	NOUN
ejpam-1929	364	13	showing	show	VERB
ejpam-1929	364	14	that	that	SCONJ
ejpam-1929	364	15	gn	gn	PROPN
ejpam-1929	364	16	is	be	AUX
ejpam-1929	364	17	not	not	PART
ejpam-1929	364	18	a	a	DET
ejpam-1929	364	19	line	line	NOUN
ejpam-1929	364	20	graph	graph	NOUN
ejpam-1929	364	21	,	,	PUNCT
ejpam-1929	364	22	a	a	DET
ejpam-1929	364	23	contradiction	contradiction	NOUN
ejpam-1929	364	24	to	to	ADP
ejpam-1929	364	25	the	the	DET
ejpam-1929	364	26	hypothesis	hypothesis	NOUN
ejpam-1929	364	27	.	.	PUNCT
ejpam-1929	365	1	hence	hence	ADV
ejpam-1929	365	2	,	,	PUNCT
ejpam-1929	365	3	the	the	DET
ejpam-1929	365	4	condition	condition	NOUN
ejpam-1929	365	5	is	be	AUX
ejpam-1929	365	6	satisfied	satisfied	ADJ
ejpam-1929	365	7	.	.	PUNCT
ejpam-1929	366	1	0	0	NUM
ejpam-1929	366	2	1	1	NUM
ejpam-1929	366	3	p1	p1	NOUN
ejpam-1929	366	4	(	(	PUNCT
ejpam-1929	366	5	a-1)p1	a-1)p1	NOUN
ejpam-1929	366	6	figure	figure	NOUN
ejpam-1929	366	7	6	6	NUM
ejpam-1929	366	8	:	:	PUNCT
ejpam-1929	366	9	showing	show	VERB
ejpam-1929	366	10	k1,3	k1,3	PROPN
ejpam-1929	366	11	as	as	ADP
ejpam-1929	366	12	an	an	DET
ejpam-1929	366	13	induced	induced	ADJ
ejpam-1929	366	14	subgraph	subgraph	NOUN
ejpam-1929	366	15	of	of	ADP
ejpam-1929	366	16	gn	gn	PROPN
ejpam-1929	366	17	,	,	PUNCT
ejpam-1929	366	18	which	which	PRON
ejpam-1929	366	19	is	be	AUX
ejpam-1929	366	20	forbidden	forbid	VERB
ejpam-1929	366	21	for	for	SCONJ
ejpam-1929	366	22	gn	gn	PROPN
ejpam-1929	366	23	to	to	PART
ejpam-1929	366	24	be	be	AUX
ejpam-1929	366	25	a	a	DET
ejpam-1929	366	26	line	line	NOUN
ejpam-1929	366	27	graph	graph	NOUN
ejpam-1929	366	28	.	.	PUNCT
ejpam-1929	367	1	sufficiency	sufficiency	NOUN
ejpam-1929	367	2	:	:	PUNCT
ejpam-1929	367	3	suppose	suppose	VERB
ejpam-1929	367	4	n=	n=	ADJ
ejpam-1929	367	5	2,3,4	2,3,4	NUM
ejpam-1929	367	6	or	or	CCONJ
ejpam-1929	367	7	6	6	NUM
ejpam-1929	367	8	.	.	PUNCT
ejpam-1929	368	1	the	the	DET
ejpam-1929	368	2	corresponding	correspond	VERB
ejpam-1929	368	3	graphs	graph	NOUN
ejpam-1929	368	4	are	be	AUX
ejpam-1929	368	5	shown	show	VERB
ejpam-1929	368	6	in	in	ADP
ejpam-1929	368	7	figure	figure	NOUN
ejpam-1929	368	8	7	7	NUM
ejpam-1929	368	9	,	,	PUNCT
ejpam-1929	368	10	which	which	PRON
ejpam-1929	368	11	are	be	AUX
ejpam-1929	368	12	line	line	NOUN
ejpam-1929	368	13	graphs	graph	NOUN
ejpam-1929	368	14	of	of	ADP
ejpam-1929	368	15	p3	p3	PROPN
ejpam-1929	368	16	,	,	PUNCT
ejpam-1929	368	17	p4	p4	ADJ
ejpam-1929	368	18	,	,	PUNCT
ejpam-1929	368	19	c4	c4	NOUN
ejpam-1929	368	20	and	and	CCONJ
ejpam-1929	368	21	c6	c6	PROPN
ejpam-1929	368	22	,	,	PUNCT
ejpam-1929	368	23	respectively	respectively	ADV
ejpam-1929	368	24	.	.	PUNCT
ejpam-1929	369	1	hence	hence	ADV
ejpam-1929	369	2	,	,	PUNCT
ejpam-1929	369	3	the	the	DET
ejpam-1929	369	4	result	result	NOUN
ejpam-1929	369	5	.	.	PUNCT
ejpam-1929	370	1	0	0	NUM
ejpam-1929	370	2	1	1	NUM
ejpam-1929	370	3	(	(	PUNCT
ejpam-1929	370	4	a	a	NOUN
ejpam-1929	370	5	)	)	PUNCT
ejpam-1929	370	6	g2	g2	PROPN
ejpam-1929	370	7	0	0	NUM
ejpam-1929	370	8	1	1	NUM
ejpam-1929	370	9	2	2	NUM
ejpam-1929	370	10	(	(	PUNCT
ejpam-1929	370	11	b	b	NOUN
ejpam-1929	370	12	)	)	PUNCT
ejpam-1929	370	13	g3	g3	NOUN
ejpam-1929	370	14	0	0	NUM
ejpam-1929	370	15	1	1	NUM
ejpam-1929	370	16	23	23	NUM
ejpam-1929	370	17	(	(	PUNCT
ejpam-1929	370	18	c	c	NOUN
ejpam-1929	370	19	)	)	PUNCT
ejpam-1929	370	20	g4	g4	NOUN
ejpam-1929	370	21	0	0	NUM
ejpam-1929	370	22	1	1	NUM
ejpam-1929	370	23	2	2	NUM
ejpam-1929	370	24	4	4	NUM
ejpam-1929	370	25	3	3	NUM
ejpam-1929	370	26	5	5	NUM
ejpam-1929	370	27	(	(	PUNCT
ejpam-1929	370	28	d	d	NOUN
ejpam-1929	370	29	)	)	PUNCT
ejpam-1929	370	30	g6	g6	ADJ
ejpam-1929	370	31	figure	figure	NOUN
ejpam-1929	370	32	7	7	NUM
ejpam-1929	370	33	:	:	PUNCT
ejpam-1929	370	34	showing	show	VERB
ejpam-1929	370	35	g2	g2	PROPN
ejpam-1929	370	36	,	,	PUNCT
ejpam-1929	370	37	g3	g3	NOUN
ejpam-1929	370	38	,	,	PUNCT
ejpam-1929	370	39	g4	g4	NOUN
ejpam-1929	370	40	and	and	CCONJ
ejpam-1929	370	41	g6	g6	ADJ
ejpam-1929	370	42	theorem	theorem	NOUN
ejpam-1929	370	43	12	12	NUM
ejpam-1929	370	44	.	.	PUNCT
ejpam-1929	371	1	unitary	unitary	ADJ
ejpam-1929	371	2	addition	addition	NOUN
ejpam-1929	371	3	cayley	cayley	NOUN
ejpam-1929	371	4	sigraph	sigraph	NOUN
ejpam-1929	371	5	σn	σn	NOUN
ejpam-1929	371	6	is	be	AUX
ejpam-1929	371	7	a	a	DET
ejpam-1929	371	8	line	line	NOUN
ejpam-1929	371	9	sigraph	sigraph	NOUN
ejpam-1929	371	10	if	if	SCONJ
ejpam-1929	371	11	and	and	CCONJ
ejpam-1929	371	12	only	only	ADV
ejpam-1929	371	13	if	if	SCONJ
ejpam-1929	371	14	n	n	PRON
ejpam-1929	371	15	∈	∈	PROPN
ejpam-1929	371	16	{	{	PUNCT
ejpam-1929	371	17	2,3,4,6	2,3,4,6	NUM
ejpam-1929	371	18	}	}	PUNCT
ejpam-1929	371	19	.	.	PUNCT
ejpam-1929	372	1	proof	proof	NOUN
ejpam-1929	372	2	.	.	PUNCT
ejpam-1929	373	1	necessity	necessity	NOUN
ejpam-1929	373	2	:	:	PUNCT
ejpam-1929	373	3	suppose	suppose	VERB
ejpam-1929	373	4	the	the	DET
ejpam-1929	373	5	unitary	unitary	ADJ
ejpam-1929	373	6	addition	addition	NOUN
ejpam-1929	373	7	cayley	cayley	NOUN
ejpam-1929	373	8	sigraph	sigraph	NOUN
ejpam-1929	373	9	σn	σn	NOUN
ejpam-1929	373	10	is	be	AUX
ejpam-1929	373	11	a	a	DET
ejpam-1929	373	12	line	line	NOUN
ejpam-1929	373	13	sigraph	sigraph	NOUN
ejpam-1929	373	14	.	.	PUNCT
ejpam-1929	374	1	if	if	SCONJ
ejpam-1929	374	2	possible	possible	ADJ
ejpam-1929	374	3	,	,	PUNCT
ejpam-1929	374	4	suppose	suppose	VERB
ejpam-1929	374	5	n	n	ADV
ejpam-1929	374	6	/∈	/∈	PUNCT
ejpam-1929	374	7	{	{	PUNCT
ejpam-1929	374	8	2,3,4,6	2,3,4,6	NUM
ejpam-1929	374	9	}	}	PUNCT
ejpam-1929	374	10	.	.	PUNCT
ejpam-1929	375	1	then	then	ADV
ejpam-1929	375	2	,	,	PUNCT
ejpam-1929	375	3	by	by	ADP
ejpam-1929	375	4	theorem	theorem	NOUN
ejpam-1929	375	5	11	11	NUM
ejpam-1929	375	6	,	,	PUNCT
ejpam-1929	375	7	σu	σu	PROPN
ejpam-1929	375	8	n	n	ADV
ejpam-1929	375	9	is	be	AUX
ejpam-1929	375	10	not	not	PART
ejpam-1929	375	11	a	a	DET
ejpam-1929	375	12	line	line	NOUN
ejpam-1929	375	13	graph	graph	NOUN
ejpam-1929	375	14	,	,	PUNCT
ejpam-1929	375	15	a	a	DET
ejpam-1929	375	16	contradiction	contradiction	NOUN
ejpam-1929	375	17	to	to	ADP
ejpam-1929	375	18	the	the	DET
ejpam-1929	375	19	hypothesis	hypothesis	NOUN
ejpam-1929	375	20	.	.	PUNCT
ejpam-1929	376	1	hence	hence	ADV
ejpam-1929	376	2	,	,	PUNCT
ejpam-1929	376	3	n	n	PROPN
ejpam-1929	376	4	∈	∈	PROPN
ejpam-1929	376	5	{	{	PUNCT
ejpam-1929	376	6	2,3,4,6	2,3,4,6	NUM
ejpam-1929	376	7	}	}	PUNCT
ejpam-1929	376	8	.	.	PUNCT
ejpam-1929	377	1	d.	d.	PROPN
ejpam-1929	377	2	sinha	sinha	PROPN
ejpam-1929	377	3	,	,	PUNCT
ejpam-1929	377	4	a.	a.	NOUN
ejpam-1929	377	5	dhama	dhama	PROPN
ejpam-1929	377	6	,	,	PUNCT
ejpam-1929	377	7	b.	b.	PROPN
ejpam-1929	377	8	acharya	acharya	PROPN
ejpam-1929	377	9	/	/	SYM
ejpam-1929	377	10	eur	eur	PROPN
ejpam-1929	377	11	.	.	PUNCT
ejpam-1929	378	1	j.	j.	PROPN
ejpam-1929	378	2	pure	pure	PROPN
ejpam-1929	378	3	appl	appl	PROPN
ejpam-1929	378	4	.	.	PROPN
ejpam-1929	378	5	math	math	PROPN
ejpam-1929	378	6	,	,	PUNCT
ejpam-1929	378	7	6	6	NUM
ejpam-1929	378	8	(	(	PUNCT
ejpam-1929	378	9	2013	2013	NUM
ejpam-1929	378	10	)	)	PUNCT
ejpam-1929	378	11	,	,	PUNCT
ejpam-1929	378	12	189	189	NUM
ejpam-1929	378	13	-	-	SYM
ejpam-1929	378	14	210	210	NUM
ejpam-1929	378	15	202	202	NUM
ejpam-1929	378	16	sufficiency	sufficiency	NOUN
ejpam-1929	378	17	:	:	PUNCT
ejpam-1929	378	18	now	now	ADV
ejpam-1929	378	19	,	,	PUNCT
ejpam-1929	378	20	suppose	suppose	VERB
ejpam-1929	378	21	n	n	PRON
ejpam-1929	378	22	∈	∈	PROPN
ejpam-1929	378	23	{	{	PUNCT
ejpam-1929	378	24	2,3,4,6	2,3,4,6	NUM
ejpam-1929	378	25	}	}	PUNCT
ejpam-1929	378	26	.	.	PUNCT
ejpam-1929	379	1	the	the	DET
ejpam-1929	379	2	corresponding	corresponding	ADJ
ejpam-1929	379	3	sigraphs	sigraph	NOUN
ejpam-1929	379	4	σ2,σ3,σ4	σ2,σ3,σ4	PROPN
ejpam-1929	379	5	and	and	CCONJ
ejpam-1929	379	6	σ6	σ6	NOUN
ejpam-1929	379	7	and	and	CCONJ
ejpam-1929	379	8	the	the	DET
ejpam-1929	379	9	sigraphs	sigraph	NOUN
ejpam-1929	379	10	whose	whose	DET
ejpam-1929	379	11	line	line	NOUN
ejpam-1929	379	12	sigraphs	sigraph	VERB
ejpam-1929	379	13	are	be	AUX
ejpam-1929	379	14	these	these	DET
ejpam-1929	379	15	sigraphs	sigraph	NOUN
ejpam-1929	379	16	are	be	AUX
ejpam-1929	379	17	shown	show	VERB
ejpam-1929	379	18	in	in	ADP
ejpam-1929	379	19	figure	figure	NOUN
ejpam-1929	379	20	8	8	NUM
ejpam-1929	379	21	.	.	PUNCT
ejpam-1929	380	1	hence	hence	ADV
ejpam-1929	380	2	,	,	PUNCT
ejpam-1929	380	3	σn	σn	PROPN
ejpam-1929	380	4	is	be	AUX
ejpam-1929	380	5	a	a	DET
ejpam-1929	380	6	line	line	NOUN
ejpam-1929	380	7	sigraph	sigraph	NOUN
ejpam-1929	380	8	for	for	ADP
ejpam-1929	380	9	n	n	DET
ejpam-1929	380	10	∈	∈	NOUN
ejpam-1929	380	11	{	{	PUNCT
ejpam-1929	380	12	2,3,4,6	2,3,4,6	NUM
ejpam-1929	380	13	}	}	PUNCT
ejpam-1929	380	14	.	.	PUNCT
ejpam-1929	381	1	0	0	NUM
ejpam-1929	381	2	1	1	NUM
ejpam-1929	381	3	(	(	PUNCT
ejpam-1929	381	4	a	a	NOUN
ejpam-1929	381	5	)	)	PUNCT
ejpam-1929	381	6	σ2	σ2	NOUN
ejpam-1929	381	7	0	0	NUM
ejpam-1929	381	8	1	1	NUM
ejpam-1929	381	9	2	2	NUM
ejpam-1929	381	10	(	(	PUNCT
ejpam-1929	381	11	b	b	NOUN
ejpam-1929	381	12	)	)	PUNCT
ejpam-1929	381	13	σ3	σ3	NOUN
ejpam-1929	381	14	0	0	NUM
ejpam-1929	381	15	1	1	NUM
ejpam-1929	381	16	23	23	NUM
ejpam-1929	381	17	(	(	PUNCT
ejpam-1929	381	18	c	c	NOUN
ejpam-1929	381	19	)	)	PUNCT
ejpam-1929	381	20	σ4	σ4	NOUN
ejpam-1929	381	21	0	0	NUM
ejpam-1929	381	22	1	1	NUM
ejpam-1929	381	23	2	2	NUM
ejpam-1929	381	24	4	4	NUM
ejpam-1929	381	25	3	3	NUM
ejpam-1929	381	26	5	5	NUM
ejpam-1929	381	27	(	(	PUNCT
ejpam-1929	381	28	d	d	NOUN
ejpam-1929	381	29	)	)	PUNCT
ejpam-1929	381	30	σ6	σ6	NOUN
ejpam-1929	381	31	(	(	PUNCT
ejpam-1929	381	32	e	e	NOUN
ejpam-1929	381	33	)	)	PUNCT
ejpam-1929	381	34	(	(	PUNCT
ejpam-1929	381	35	f	f	X
ejpam-1929	381	36	)	)	PUNCT
ejpam-1929	381	37	(	(	PUNCT
ejpam-1929	381	38	g	g	NOUN
ejpam-1929	381	39	)	)	PUNCT
ejpam-1929	381	40	(	(	PUNCT
ejpam-1929	381	41	h	h	NOUN
ejpam-1929	381	42	)	)	PUNCT
ejpam-1929	381	43	figure	figure	NOUN
ejpam-1929	381	44	8	8	NUM
ejpam-1929	381	45	:	:	PUNCT
ejpam-1929	381	46	showing	show	VERB
ejpam-1929	381	47	σ2	σ2	NOUN
ejpam-1929	381	48	,	,	PUNCT
ejpam-1929	381	49	σ3	σ3	PROPN
ejpam-1929	381	50	,	,	PUNCT
ejpam-1929	381	51	σ4	σ4	NOUN
ejpam-1929	381	52	and	and	CCONJ
ejpam-1929	381	53	σ6	σ6	NOUN
ejpam-1929	381	54	and	and	CCONJ
ejpam-1929	381	55	the	the	DET
ejpam-1929	381	56	sigraphs	sigraph	NOUN
ejpam-1929	381	57	whose	whose	DET
ejpam-1929	381	58	line	line	NOUN
ejpam-1929	381	59	sigraphs	sigraph	VERB
ejpam-1929	381	60	are	be	AUX
ejpam-1929	381	61	these	these	DET
ejpam-1929	381	62	sigraphs	sigraphs	ADJ
ejpam-1929	381	63	remark	remark	NOUN
ejpam-1929	381	64	1	1	NUM
ejpam-1929	381	65	.	.	PUNCT
ejpam-1929	381	66	unitary	unitary	ADJ
ejpam-1929	381	67	addition	addition	NOUN
ejpam-1929	381	68	cayley	cayley	NOUN
ejpam-1929	381	69	sigraph	sigraph	NOUN
ejpam-1929	381	70	σn	σn	NOUN
ejpam-1929	381	71	is	be	AUX
ejpam-1929	381	72	a	a	DET
ejpam-1929	381	73	product	product	NOUN
ejpam-1929	381	74	line	line	NOUN
ejpam-1929	381	75	sigraph	sigraph	NOUN
ejpam-1929	381	76	if	if	SCONJ
ejpam-1929	382	1	and	and	CCONJ
ejpam-1929	382	2	only	only	ADV
ejpam-1929	382	3	if	if	SCONJ
ejpam-1929	382	4	n	n	PRON
ejpam-1929	382	5	∈	∈	PROPN
ejpam-1929	382	6	{	{	PUNCT
ejpam-1929	382	7	2,3,4,6	2,3,4,6	NUM
ejpam-1929	382	8	}	}	PUNCT
ejpam-1929	382	9	.	.	PUNCT
ejpam-1929	383	1	proof	proof	NOUN
ejpam-1929	383	2	.	.	PUNCT
ejpam-1929	384	1	suppose	suppose	VERB
ejpam-1929	384	2	the	the	DET
ejpam-1929	384	3	unitary	unitary	ADJ
ejpam-1929	384	4	addition	addition	NOUN
ejpam-1929	384	5	cayley	cayley	NOUN
ejpam-1929	384	6	sigraph	sigraph	NOUN
ejpam-1929	384	7	σn	σn	NOUN
ejpam-1929	384	8	is	be	AUX
ejpam-1929	384	9	a	a	DET
ejpam-1929	384	10	product	product	NOUN
ejpam-1929	384	11	line	line	NOUN
ejpam-1929	384	12	sigraph	sigraph	NOUN
ejpam-1929	384	13	.	.	PUNCT
ejpam-1929	385	1	since	since	SCONJ
ejpam-1929	385	2	,	,	PUNCT
ejpam-1929	385	3	for	for	ADP
ejpam-1929	385	4	any	any	DET
ejpam-1929	385	5	given	give	VERB
ejpam-1929	385	6	sigraph	sigraph	PROPN
ejpam-1929	385	7	s	s	PROPN
ejpam-1929	385	8	,	,	PUNCT
ejpam-1929	385	9	the	the	DET
ejpam-1929	385	10	underlying	underlie	VERB
ejpam-1929	385	11	graphs	graph	NOUN
ejpam-1929	385	12	of	of	ADP
ejpam-1929	385	13	the	the	DET
ejpam-1929	385	14	line	line	NOUN
ejpam-1929	385	15	sigraph	sigraph	NOUN
ejpam-1929	385	16	l(s	l(s	PROPN
ejpam-1929	385	17	)	)	PUNCT
ejpam-1929	385	18	and	and	CCONJ
ejpam-1929	385	19	the	the	DET
ejpam-1929	385	20	product	product	NOUN
ejpam-1929	385	21	line	line	NOUN
ejpam-1929	385	22	sigraph	sigraph	PROPN
ejpam-1929	385	23	l×(s	l×(s	PROPN
ejpam-1929	385	24	)	)	PUNCT
ejpam-1929	385	25	are	be	AUX
ejpam-1929	385	26	the	the	DET
ejpam-1929	385	27	same	same	ADJ
ejpam-1929	385	28	,	,	PUNCT
ejpam-1929	385	29	the	the	DET
ejpam-1929	385	30	condition	condition	NOUN
ejpam-1929	385	31	follows	follow	VERB
ejpam-1929	385	32	from	from	ADP
ejpam-1929	385	33	theorem	theorem	ADJ
ejpam-1929	385	34	11	11	NUM
ejpam-1929	385	35	.	.	PUNCT
ejpam-1929	386	1	conversely	conversely	ADV
ejpam-1929	386	2	,	,	PUNCT
ejpam-1929	386	3	suppose	suppose	VERB
ejpam-1929	386	4	n	n	PRON
ejpam-1929	386	5	∈	∈	PROPN
ejpam-1929	386	6	{	{	PUNCT
ejpam-1929	386	7	2,3,4,6	2,3,4,6	NUM
ejpam-1929	386	8	}	}	PUNCT
ejpam-1929	386	9	.	.	PUNCT
ejpam-1929	387	1	by	by	ADP
ejpam-1929	387	2	theorem	theorem	NOUN
ejpam-1929	387	3	7	7	NUM
ejpam-1929	387	4	for	for	ADP
ejpam-1929	387	5	these	these	DET
ejpam-1929	387	6	values	value	NOUN
ejpam-1929	387	7	of	of	ADP
ejpam-1929	387	8	n	n	CCONJ
ejpam-1929	387	9	,	,	PUNCT
ejpam-1929	387	10	σn	σn	PROPN
ejpam-1929	387	11	is	be	AUX
ejpam-1929	387	12	balanced	balanced	ADJ
ejpam-1929	387	13	.	.	PUNCT
ejpam-1929	388	1	since	since	SCONJ
ejpam-1929	388	2	the	the	DET
ejpam-1929	388	3	product	product	NOUN
ejpam-1929	388	4	line	line	NOUN
ejpam-1929	388	5	sigraph	sigraph	NOUN
ejpam-1929	388	6	of	of	ADP
ejpam-1929	388	7	any	any	DET
ejpam-1929	388	8	sigraph	sigraph	NOUN
ejpam-1929	388	9	is	be	AUX
ejpam-1929	388	10	always	always	ADV
ejpam-1929	388	11	balanced	balanced	ADJ
ejpam-1929	388	12	and	and	CCONJ
ejpam-1929	388	13	its	its	PRON
ejpam-1929	388	14	underlying	underlie	VERB
ejpam-1929	388	15	structure	structure	NOUN
ejpam-1929	388	16	is	be	AUX
ejpam-1929	388	17	the	the	DET
ejpam-1929	388	18	line	line	NOUN
ejpam-1929	388	19	graph	graph	NOUN
ejpam-1929	388	20	(	(	PUNCT
ejpam-1929	388	21	see	see	VERB
ejpam-1929	388	22	[	[	X
ejpam-1929	388	23	3	3	NUM
ejpam-1929	388	24	]	]	NUM
ejpam-1929	388	25	)	)	PUNCT
ejpam-1929	388	26	,	,	PUNCT
ejpam-1929	388	27	the	the	DET
ejpam-1929	388	28	result	result	NOUN
ejpam-1929	388	29	follows	follow	VERB
ejpam-1929	388	30	from	from	ADP
ejpam-1929	388	31	theorem	theorem	ADJ
ejpam-1929	388	32	7	7	NUM
ejpam-1929	388	33	and	and	CCONJ
ejpam-1929	388	34	theorem	theorem	VERB
ejpam-1929	388	35	11	11	NUM
ejpam-1929	388	36	.	.	PUNCT
ejpam-1929	389	1	unitary	unitary	ADJ
ejpam-1929	389	2	addition	addition	NOUN
ejpam-1929	389	3	cayley	cayley	NOUN
ejpam-1929	389	4	sigraphs	sigraph	VERB
ejpam-1929	389	5	σ2,σ3,σ4	σ2,σ3,σ4	NOUN
ejpam-1929	389	6	and	and	CCONJ
ejpam-1929	389	7	σ6	σ6	NOUN
ejpam-1929	389	8	and	and	CCONJ
ejpam-1929	389	9	the	the	DET
ejpam-1929	389	10	sigraphs	sigraph	NOUN
ejpam-1929	389	11	whose	whose	DET
ejpam-1929	389	12	product	product	NOUN
ejpam-1929	389	13	line	line	NOUN
ejpam-1929	389	14	sigraphs	sigraph	NOUN
ejpam-1929	389	15	are	be	AUX
ejpam-1929	389	16	these	these	DET
ejpam-1929	389	17	sigraph	sigraph	NOUN
ejpam-1929	389	18	are	be	AUX
ejpam-1929	389	19	shown	show	VERB
ejpam-1929	389	20	in	in	ADP
ejpam-1929	389	21	figure	figure	NOUN
ejpam-1929	389	22	9	9	NUM
ejpam-1929	389	23	.	.	NOUN
ejpam-1929	389	24	6	6	NUM
ejpam-1929	389	25	.	.	PUNCT
ejpam-1929	390	1	c	c	NOUN
ejpam-1929	390	2	-consistency	-consistency	NOUN
ejpam-1929	390	3	of	of	ADP
ejpam-1929	390	4	σn	σn	PRON
ejpam-1929	390	5	now	now	ADV
ejpam-1929	390	6	,	,	PUNCT
ejpam-1929	390	7	we	we	PRON
ejpam-1929	390	8	present	present	VERB
ejpam-1929	390	9	a	a	DET
ejpam-1929	390	10	characterization	characterization	NOUN
ejpam-1929	390	11	of	of	ADP
ejpam-1929	390	12	c	c	NOUN
ejpam-1929	390	13	-consistent	-consistent	PROPN
ejpam-1929	390	14	unitary	unitary	ADJ
ejpam-1929	390	15	addition	addition	NOUN
ejpam-1929	390	16	cayley	cayley	NOUN
ejpam-1929	390	17	sigraphs	sigraph	VERB
ejpam-1929	390	18	.	.	PUNCT
ejpam-1929	391	1	theorem	theorem	ADJ
ejpam-1929	391	2	13	13	NUM
ejpam-1929	391	3	(	(	PUNCT
ejpam-1929	391	4	[	[	X
ejpam-1929	391	5	33	33	NUM
ejpam-1929	391	6	]	]	PUNCT
ejpam-1929	391	7	)	)	PUNCT
ejpam-1929	391	8	.	.	PUNCT
ejpam-1929	392	1	let	let	VERB
ejpam-1929	392	2	g	g	PRON
ejpam-1929	392	3	be	be	AUX
ejpam-1929	392	4	a	a	DET
ejpam-1929	392	5	marked	mark	VERB
ejpam-1929	392	6	graph	graph	NOUN
ejpam-1929	392	7	and	and	CCONJ
ejpam-1929	392	8	t	t	PROPN
ejpam-1929	392	9	be	be	AUX
ejpam-1929	392	10	a	a	DET
ejpam-1929	392	11	spanning	span	VERB
ejpam-1929	392	12	tree	tree	NOUN
ejpam-1929	392	13	of	of	ADP
ejpam-1929	392	14	g.	g.	PROPN
ejpam-1929	392	15	then	then	ADV
ejpam-1929	392	16	,	,	PUNCT
ejpam-1929	392	17	g	g	PROPN
ejpam-1929	392	18	is	be	AUX
ejpam-1929	392	19	consistent	consistent	ADJ
ejpam-1929	392	20	if	if	SCONJ
ejpam-1929	392	21	and	and	CCONJ
ejpam-1929	392	22	only	only	ADV
ejpam-1929	392	23	if	if	SCONJ
ejpam-1929	392	24	g	g	PROPN
ejpam-1929	392	25	satisfies	satisfy	VERB
ejpam-1929	392	26	the	the	DET
ejpam-1929	392	27	following	follow	VERB
ejpam-1929	392	28	two	two	NUM
ejpam-1929	392	29	conditions	condition	NOUN
ejpam-1929	392	30	:	:	PUNCT
ejpam-1929	392	31	(	(	PUNCT
ejpam-1929	392	32	i	i	NOUN
ejpam-1929	392	33	)	)	PUNCT
ejpam-1929	392	34	each	each	DET
ejpam-1929	392	35	fundamental	fundamental	ADJ
ejpam-1929	392	36	cycle	cycle	NOUN
ejpam-1929	392	37	relative	relative	ADJ
ejpam-1929	392	38	to	to	ADP
ejpam-1929	392	39	t	t	PROPN
ejpam-1929	392	40	is	be	AUX
ejpam-1929	392	41	positive	positive	ADJ
ejpam-1929	392	42	,	,	PUNCT
ejpam-1929	392	43	and	and	CCONJ
ejpam-1929	392	44	d.	d.	PROPN
ejpam-1929	392	45	sinha	sinha	PROPN
ejpam-1929	392	46	,	,	PUNCT
ejpam-1929	392	47	a.	a.	NOUN
ejpam-1929	392	48	dhama	dhama	PROPN
ejpam-1929	392	49	,	,	PUNCT
ejpam-1929	392	50	b.	b.	PROPN
ejpam-1929	392	51	acharya	acharya	PROPN
ejpam-1929	392	52	/	/	SYM
ejpam-1929	392	53	eur	eur	PROPN
ejpam-1929	392	54	.	.	PUNCT
ejpam-1929	393	1	j.	j.	PROPN
ejpam-1929	393	2	pure	pure	PROPN
ejpam-1929	393	3	appl	appl	PROPN
ejpam-1929	393	4	.	.	PROPN
ejpam-1929	393	5	math	math	PROPN
ejpam-1929	393	6	,	,	PUNCT
ejpam-1929	393	7	6	6	NUM
ejpam-1929	393	8	(	(	PUNCT
ejpam-1929	393	9	2013	2013	NUM
ejpam-1929	393	10	)	)	PUNCT
ejpam-1929	393	11	,	,	PUNCT
ejpam-1929	393	12	189	189	NUM
ejpam-1929	393	13	-	-	SYM
ejpam-1929	393	14	210	210	NUM
ejpam-1929	393	15	203	203	NUM
ejpam-1929	393	16	(	(	PUNCT
ejpam-1929	393	17	ii	ii	NOUN
ejpam-1929	393	18	)	)	PUNCT
ejpam-1929	393	19	the	the	DET
ejpam-1929	393	20	two	two	NUM
ejpam-1929	393	21	end	end	NOUN
ejpam-1929	393	22	vertices	vertex	NOUN
ejpam-1929	393	23	of	of	ADP
ejpam-1929	393	24	any	any	DET
ejpam-1929	393	25	common	common	ADJ
ejpam-1929	393	26	path	path	NOUN
ejpam-1929	393	27	between	between	ADP
ejpam-1929	393	28	each	each	DET
ejpam-1929	393	29	pair	pair	NOUN
ejpam-1929	393	30	of	of	ADP
ejpam-1929	393	31	fundamental	fundamental	ADJ
ejpam-1929	393	32	cycles	cycle	NOUN
ejpam-1929	393	33	relative	relative	ADJ
ejpam-1929	393	34	to	to	ADP
ejpam-1929	393	35	t	t	PROPN
ejpam-1929	393	36	have	have	VERB
ejpam-1929	393	37	the	the	DET
ejpam-1929	393	38	same	same	ADJ
ejpam-1929	393	39	mark	mark	NOUN
ejpam-1929	393	40	.	.	PUNCT
ejpam-1929	394	1	0	0	NUM
ejpam-1929	394	2	1	1	NUM
ejpam-1929	394	3	(	(	PUNCT
ejpam-1929	394	4	a	a	NOUN
ejpam-1929	394	5	)	)	PUNCT
ejpam-1929	394	6	σ2	σ2	NOUN
ejpam-1929	394	7	0	0	NUM
ejpam-1929	394	8	1	1	NUM
ejpam-1929	394	9	2	2	NUM
ejpam-1929	394	10	(	(	PUNCT
ejpam-1929	394	11	b	b	NOUN
ejpam-1929	394	12	)	)	PUNCT
ejpam-1929	394	13	σ3	σ3	NOUN
ejpam-1929	394	14	0	0	NUM
ejpam-1929	394	15	1	1	NUM
ejpam-1929	394	16	23	23	NUM
ejpam-1929	394	17	(	(	PUNCT
ejpam-1929	394	18	c	c	NOUN
ejpam-1929	394	19	)	)	PUNCT
ejpam-1929	394	20	σ4	σ4	NOUN
ejpam-1929	394	21	0	0	NUM
ejpam-1929	394	22	1	1	NUM
ejpam-1929	394	23	2	2	NUM
ejpam-1929	394	24	4	4	NUM
ejpam-1929	394	25	3	3	NUM
ejpam-1929	394	26	5	5	NUM
ejpam-1929	394	27	(	(	PUNCT
ejpam-1929	394	28	d	d	NOUN
ejpam-1929	394	29	)	)	PUNCT
ejpam-1929	394	30	σ6	σ6	NOUN
ejpam-1929	394	31	(	(	PUNCT
ejpam-1929	394	32	e	e	NOUN
ejpam-1929	394	33	)	)	PUNCT
ejpam-1929	394	34	(	(	PUNCT
ejpam-1929	394	35	f	f	X
ejpam-1929	394	36	)	)	PUNCT
ejpam-1929	394	37	(	(	PUNCT
ejpam-1929	394	38	g	g	NOUN
ejpam-1929	394	39	)	)	PUNCT
ejpam-1929	394	40	(	(	PUNCT
ejpam-1929	394	41	h	h	NOUN
ejpam-1929	394	42	)	)	PUNCT
ejpam-1929	394	43	figure	figure	NOUN
ejpam-1929	394	44	9	9	NUM
ejpam-1929	394	45	:	:	PUNCT
ejpam-1929	394	46	showing	show	VERB
ejpam-1929	394	47	σ2	σ2	NOUN
ejpam-1929	394	48	,	,	PUNCT
ejpam-1929	394	49	σ3	σ3	PROPN
ejpam-1929	394	50	,	,	PUNCT
ejpam-1929	394	51	σ4	σ4	NOUN
ejpam-1929	394	52	and	and	CCONJ
ejpam-1929	394	53	σ6	σ6	NOUN
ejpam-1929	394	54	and	and	CCONJ
ejpam-1929	394	55	the	the	DET
ejpam-1929	394	56	sigraphs	sigraph	NOUN
ejpam-1929	394	57	whose	whose	DET
ejpam-1929	394	58	product	product	NOUN
ejpam-1929	394	59	line	line	NOUN
ejpam-1929	394	60	sigraphs	sigraph	NOUN
ejpam-1929	394	61	are	be	AUX
ejpam-1929	394	62	these	these	DET
ejpam-1929	394	63	sigraphs	sigraph	NOUN
ejpam-1929	394	64	theorem	theorem	VERB
ejpam-1929	394	65	14	14	NUM
ejpam-1929	394	66	(	(	PUNCT
ejpam-1929	394	67	[	[	X
ejpam-1929	394	68	42	42	NUM
ejpam-1929	394	69	]	]	PUNCT
ejpam-1929	394	70	)	)	PUNCT
ejpam-1929	394	71	.	.	PUNCT
ejpam-1929	395	1	the	the	DET
ejpam-1929	395	2	unitary	unitary	ADJ
ejpam-1929	395	3	cayley	cayley	NOUN
ejpam-1929	395	4	sigraph	sigraph	NOUN
ejpam-1929	395	5	sn	sn	NOUN
ejpam-1929	395	6	=	=	PUNCT
ejpam-1929	395	7	(	(	PUNCT
ejpam-1929	395	8	s	s	NOUN
ejpam-1929	395	9	u	u	NOUN
ejpam-1929	395	10	n	n	X
ejpam-1929	395	11	,	,	PUNCT
ejpam-1929	395	12	σ	σ	PROPN
ejpam-1929	395	13	)	)	PUNCT
ejpam-1929	395	14	,	,	PUNCT
ejpam-1929	395	15	where	where	SCONJ
ejpam-1929	395	16	n	n	PRON
ejpam-1929	395	17	has	have	VERB
ejpam-1929	395	18	at	at	ADP
ejpam-1929	395	19	most	most	ADV
ejpam-1929	395	20	two	two	NUM
ejpam-1929	395	21	distinct	distinct	ADJ
ejpam-1929	395	22	odd	odd	ADJ
ejpam-1929	395	23	prime	prime	ADJ
ejpam-1929	395	24	factors	factor	NOUN
ejpam-1929	395	25	,	,	PUNCT
ejpam-1929	395	26	is	be	AUX
ejpam-1929	395	27	c	c	NOUN
ejpam-1929	395	28	-consistent	-consistent	ADJ
ejpam-1929	395	29	if	if	SCONJ
ejpam-1929	396	1	and	and	CCONJ
ejpam-1929	396	2	only	only	ADV
ejpam-1929	396	3	if	if	SCONJ
ejpam-1929	396	4	n	n	PRON
ejpam-1929	396	5	is	be	AUX
ejpam-1929	396	6	either	either	CCONJ
ejpam-1929	396	7	odd	odd	ADJ
ejpam-1929	396	8	or	or	CCONJ
ejpam-1929	396	9	n	n	PRON
ejpam-1929	396	10	is	be	AUX
ejpam-1929	396	11	2	2	NUM
ejpam-1929	396	12	,	,	PUNCT
ejpam-1929	396	13	6	6	NUM
ejpam-1929	396	14	or	or	CCONJ
ejpam-1929	396	15	a	a	DET
ejpam-1929	396	16	multiple	multiple	NOUN
ejpam-1929	396	17	of	of	ADP
ejpam-1929	396	18	4	4	NUM
ejpam-1929	396	19	.	.	PUNCT
ejpam-1929	397	1	lemma	lemma	PROPN
ejpam-1929	397	2	4	4	X
ejpam-1929	397	3	.	.	PUNCT
ejpam-1929	398	1	in	in	ADP
ejpam-1929	398	2	the	the	DET
ejpam-1929	398	3	unitary	unitary	ADJ
ejpam-1929	398	4	addition	addition	NOUN
ejpam-1929	398	5	cayley	cayley	NOUN
ejpam-1929	398	6	sigraph	sigraph	NOUN
ejpam-1929	398	7	σn	σn	NOUN
ejpam-1929	398	8	,	,	PUNCT
ejpam-1929	398	9	if	if	SCONJ
ejpam-1929	398	10	n	n	NOUN
ejpam-1929	398	11	=	=	SYM
ejpam-1929	398	12	2p	2p	NUM
ejpam-1929	398	13	a1	a1	NOUN
ejpam-1929	398	14	1	1	NUM
ejpam-1929	398	15	,	,	PUNCT
ejpam-1929	398	16	where	where	SCONJ
ejpam-1929	398	17	p1	p1	NOUN
ejpam-1929	398	18	is	be	AUX
ejpam-1929	398	19	an	an	DET
ejpam-1929	398	20	odd	odd	ADJ
ejpam-1929	398	21	prime	prime	NOUN
ejpam-1929	398	22	,	,	PUNCT
ejpam-1929	398	23	then	then	ADV
ejpam-1929	398	24	the	the	DET
ejpam-1929	398	25	negative	negative	ADJ
ejpam-1929	398	26	degree	degree	NOUN
ejpam-1929	398	27	of	of	ADP
ejpam-1929	398	28	the	the	DET
ejpam-1929	398	29	vertex	vertex	NOUN
ejpam-1929	398	30	2	2	NUM
ejpam-1929	398	31	of	of	ADP
ejpam-1929	398	32	σn	σn	NOUN
ejpam-1929	398	33	is	be	AUX
ejpam-1929	398	34	odd	odd	ADJ
ejpam-1929	398	35	.	.	PUNCT
ejpam-1929	399	1	proof	proof	NOUN
ejpam-1929	399	2	.	.	PUNCT
ejpam-1929	400	1	suppose	suppose	VERB
ejpam-1929	401	1	n	n	PROPN
ejpam-1929	401	2	=	=	SYM
ejpam-1929	401	3	2p	2p	NUM
ejpam-1929	401	4	a1	a1	NOUN
ejpam-1929	401	5	1	1	NUM
ejpam-1929	401	6	in	in	ADP
ejpam-1929	401	7	σn	σn	NOUN
ejpam-1929	401	8	,	,	PUNCT
ejpam-1929	401	9	where	where	SCONJ
ejpam-1929	401	10	p1	p1	PROPN
ejpam-1929	401	11	is	be	AUX
ejpam-1929	401	12	an	an	DET
ejpam-1929	401	13	odd	odd	ADJ
ejpam-1929	401	14	prime	prime	NOUN
ejpam-1929	401	15	.	.	PUNCT
ejpam-1929	402	1	by	by	ADP
ejpam-1929	402	2	the	the	DET
ejpam-1929	402	3	definition	definition	NOUN
ejpam-1929	402	4	of	of	ADP
ejpam-1929	402	5	σn	σn	PROPN
ejpam-1929	402	6	,	,	PUNCT
ejpam-1929	402	7	negative	negative	ADJ
ejpam-1929	402	8	edges	edge	NOUN
ejpam-1929	402	9	are	be	AUX
ejpam-1929	402	10	incident	incident	NOUN
ejpam-1929	402	11	at	at	ADP
ejpam-1929	402	12	the	the	DET
ejpam-1929	402	13	vertex	vertex	NOUN
ejpam-1929	402	14	2	2	NUM
ejpam-1929	402	15	of	of	ADP
ejpam-1929	402	16	σn	σn	NOUN
ejpam-1929	402	17	only	only	ADV
ejpam-1929	402	18	when	when	SCONJ
ejpam-1929	402	19	2	2	NUM
ejpam-1929	402	20	is	be	AUX
ejpam-1929	402	21	adjacent	adjacent	ADJ
ejpam-1929	402	22	to	to	ADP
ejpam-1929	402	23	multiples	multiple	NOUN
ejpam-1929	402	24	of	of	ADP
ejpam-1929	402	25	p1	p1	NOUN
ejpam-1929	402	26	.	.	PUNCT
ejpam-1929	403	1	since	since	SCONJ
ejpam-1929	403	2	addition	addition	NOUN
ejpam-1929	403	3	of	of	ADP
ejpam-1929	403	4	2	2	NUM
ejpam-1929	403	5	and	and	CCONJ
ejpam-1929	403	6	any	any	DET
ejpam-1929	403	7	even	even	ADV
ejpam-1929	403	8	multiple	multiple	NOUN
ejpam-1929	403	9	of	of	ADP
ejpam-1929	403	10	p1	p1	NOUN
ejpam-1929	403	11	is	be	AUX
ejpam-1929	403	12	an	an	DET
ejpam-1929	403	13	even	even	ADJ
ejpam-1929	403	14	number	number	NOUN
ejpam-1929	403	15	and	and	CCONJ
ejpam-1929	403	16	un	un	PROPN
ejpam-1929	403	17	does	do	AUX
ejpam-1929	403	18	not	not	PART
ejpam-1929	403	19	contain	contain	VERB
ejpam-1929	403	20	an	an	DET
ejpam-1929	403	21	even	even	ADJ
ejpam-1929	403	22	number	number	NOUN
ejpam-1929	403	23	,	,	PUNCT
ejpam-1929	403	24	the	the	DET
ejpam-1929	403	25	vertex	vertex	NOUN
ejpam-1929	403	26	2	2	NUM
ejpam-1929	403	27	is	be	AUX
ejpam-1929	403	28	not	not	PART
ejpam-1929	403	29	adjacent	adjacent	ADJ
ejpam-1929	403	30	to	to	ADP
ejpam-1929	403	31	any	any	DET
ejpam-1929	403	32	even	even	ADJ
ejpam-1929	403	33	multiple	multiple	NOUN
ejpam-1929	403	34	of	of	ADP
ejpam-1929	403	35	p1	p1	PROPN
ejpam-1929	403	36	.	.	PUNCT
ejpam-1929	404	1	now	now	ADV
ejpam-1929	404	2	,	,	PUNCT
ejpam-1929	404	3	the	the	DET
ejpam-1929	404	4	number	number	NOUN
ejpam-1929	404	5	of	of	ADP
ejpam-1929	404	6	odd	odd	ADJ
ejpam-1929	404	7	multiples	multiple	NOUN
ejpam-1929	404	8	of	of	ADP
ejpam-1929	404	9	p1	p1	NOUN
ejpam-1929	404	10	are	be	AUX
ejpam-1929	404	11	p	p	X
ejpam-1929	404	12	a1−1	a1−1	NUM
ejpam-1929	404	13	1	1	NUM
ejpam-1929	404	14	.	.	PUNCT
ejpam-1929	405	1	now	now	ADV
ejpam-1929	405	2	,	,	PUNCT
ejpam-1929	405	3	2	2	NUM
ejpam-1929	405	4	is	be	AUX
ejpam-1929	405	5	adjacent	adjacent	ADJ
ejpam-1929	405	6	with	with	ADP
ejpam-1929	405	7	all	all	DET
ejpam-1929	405	8	the	the	DET
ejpam-1929	405	9	odd	odd	ADJ
ejpam-1929	405	10	multiples	multiple	NOUN
ejpam-1929	405	11	of	of	ADP
ejpam-1929	405	12	p1	p1	NOUN
ejpam-1929	405	13	as	as	ADP
ejpam-1929	405	14	their	their	PRON
ejpam-1929	405	15	addition	addition	NOUN
ejpam-1929	405	16	with	with	ADP
ejpam-1929	405	17	2	2	NUM
ejpam-1929	405	18	is	be	AUX
ejpam-1929	405	19	neither	neither	CCONJ
ejpam-1929	405	20	a	a	DET
ejpam-1929	405	21	multiple	multiple	NOUN
ejpam-1929	405	22	of	of	ADP
ejpam-1929	405	23	2	2	NUM
ejpam-1929	405	24	nor	nor	CCONJ
ejpam-1929	405	25	a	a	DET
ejpam-1929	405	26	multiple	multiple	NOUN
ejpam-1929	405	27	of	of	ADP
ejpam-1929	405	28	p1	p1	NOUN
ejpam-1929	405	29	.	.	PROPN
ejpam-1929	405	30	2	2	NUM
ejpam-1929	405	31	is	be	AUX
ejpam-1929	405	32	negatively	negatively	ADV
ejpam-1929	405	33	adjacent	adjacent	ADJ
ejpam-1929	405	34	with	with	ADP
ejpam-1929	405	35	p	p	X
ejpam-1929	405	36	a1−1	a1−1	PROPN
ejpam-1929	405	37	1	1	NUM
ejpam-1929	405	38	.	.	PUNCT
ejpam-1929	406	1	since	since	SCONJ
ejpam-1929	406	2	p1	p1	PROPN
ejpam-1929	406	3	is	be	AUX
ejpam-1929	406	4	an	an	DET
ejpam-1929	406	5	odd	odd	ADJ
ejpam-1929	406	6	prime	prime	NOUN
ejpam-1929	406	7	,	,	PUNCT
ejpam-1929	406	8	d−(2	d−(2	PROPN
ejpam-1929	406	9	)	)	PUNCT
ejpam-1929	406	10	is	be	AUX
ejpam-1929	406	11	odd	odd	ADJ
ejpam-1929	406	12	.	.	PUNCT
ejpam-1929	407	1	lemma	lemma	PROPN
ejpam-1929	407	2	5	5	NUM
ejpam-1929	407	3	(	(	PUNCT
ejpam-1929	407	4	[	[	X
ejpam-1929	407	5	42	42	NUM
ejpam-1929	407	6	]	]	PUNCT
ejpam-1929	407	7	)	)	PUNCT
ejpam-1929	407	8	.	.	PUNCT
ejpam-1929	408	1	in	in	ADP
ejpam-1929	408	2	the	the	DET
ejpam-1929	408	3	unitary	unitary	ADJ
ejpam-1929	408	4	cayley	cayley	NOUN
ejpam-1929	408	5	sigraph	sigraph	NOUN
ejpam-1929	408	6	sn	sn	INTJ
ejpam-1929	408	7	,	,	PUNCT
ejpam-1929	408	8	if	if	SCONJ
ejpam-1929	408	9	n=	n=	ADJ
ejpam-1929	408	10	2p	2p	NUM
ejpam-1929	408	11	a1	a1	NOUN
ejpam-1929	408	12	1	1	NUM
ejpam-1929	408	13	p	p	NOUN
ejpam-1929	408	14	a2	a2	PROPN
ejpam-1929	408	15	2	2	NUM
ejpam-1929	408	16	,	,	PUNCT
ejpam-1929	408	17	where	where	SCONJ
ejpam-1929	408	18	p1	p1	NOUN
ejpam-1929	408	19	and	and	CCONJ
ejpam-1929	408	20	p2	p2	PROPN
ejpam-1929	408	21	are	be	AUX
ejpam-1929	408	22	distinct	distinct	ADJ
ejpam-1929	408	23	odd	odd	ADJ
ejpam-1929	408	24	primes	prime	NOUN
ejpam-1929	408	25	,	,	PUNCT
ejpam-1929	408	26	then	then	ADV
ejpam-1929	408	27	the	the	DET
ejpam-1929	408	28	negative	negative	ADJ
ejpam-1929	408	29	degree	degree	NOUN
ejpam-1929	408	30	of	of	ADP
ejpam-1929	408	31	the	the	DET
ejpam-1929	408	32	vertex	vertex	NOUN
ejpam-1929	408	33	2	2	NUM
ejpam-1929	408	34	of	of	ADP
ejpam-1929	408	35	sn	sn	PROPN
ejpam-1929	408	36	is	be	AUX
ejpam-1929	408	37	odd	odd	ADJ
ejpam-1929	408	38	.	.	PUNCT
ejpam-1929	409	1	lemma	lemma	PROPN
ejpam-1929	409	2	6	6	NUM
ejpam-1929	409	3	.	.	PUNCT
ejpam-1929	410	1	in	in	ADP
ejpam-1929	410	2	the	the	DET
ejpam-1929	410	3	unitary	unitary	ADJ
ejpam-1929	410	4	addition	addition	NOUN
ejpam-1929	410	5	cayley	cayley	NOUN
ejpam-1929	410	6	sigraph	sigraph	NOUN
ejpam-1929	410	7	σn	σn	NOUN
ejpam-1929	410	8	,	,	PUNCT
ejpam-1929	410	9	if	if	SCONJ
ejpam-1929	410	10	n	n	NOUN
ejpam-1929	410	11	=	=	SYM
ejpam-1929	410	12	2p	2p	NUM
ejpam-1929	410	13	a1	a1	NOUN
ejpam-1929	410	14	1	1	NUM
ejpam-1929	410	15	p	p	NOUN
ejpam-1929	410	16	a2	a2	PROPN
ejpam-1929	410	17	2	2	NUM
ejpam-1929	410	18	,	,	PUNCT
ejpam-1929	410	19	where	where	SCONJ
ejpam-1929	410	20	p1	p1	NOUN
ejpam-1929	410	21	and	and	CCONJ
ejpam-1929	410	22	p2	p2	PROPN
ejpam-1929	410	23	are	be	AUX
ejpam-1929	410	24	distinct	distinct	ADJ
ejpam-1929	410	25	odd	odd	ADJ
ejpam-1929	410	26	primes	prime	NOUN
ejpam-1929	410	27	,	,	PUNCT
ejpam-1929	410	28	then	then	ADV
ejpam-1929	410	29	the	the	DET
ejpam-1929	410	30	negative	negative	ADJ
ejpam-1929	410	31	degree	degree	NOUN
ejpam-1929	410	32	of	of	ADP
ejpam-1929	410	33	the	the	DET
ejpam-1929	410	34	vertex	vertex	NOUN
ejpam-1929	410	35	2	2	NUM
ejpam-1929	410	36	of	of	ADP
ejpam-1929	410	37	σn	σn	NOUN
ejpam-1929	410	38	is	be	AUX
ejpam-1929	410	39	odd	odd	ADJ
ejpam-1929	410	40	.	.	PUNCT
ejpam-1929	411	1	proof	proof	NOUN
ejpam-1929	411	2	.	.	PUNCT
ejpam-1929	412	1	given	give	VERB
ejpam-1929	412	2	that	that	DET
ejpam-1929	412	3	n	n	NOUN
ejpam-1929	412	4	=	=	SYM
ejpam-1929	412	5	2p	2p	NUM
ejpam-1929	412	6	a1	a1	NOUN
ejpam-1929	412	7	1	1	NUM
ejpam-1929	412	8	p	p	NOUN
ejpam-1929	412	9	a2	a2	PROPN
ejpam-1929	412	10	2	2	NUM
ejpam-1929	412	11	,	,	PUNCT
ejpam-1929	412	12	where	where	SCONJ
ejpam-1929	412	13	p1	p1	NOUN
ejpam-1929	412	14	and	and	CCONJ
ejpam-1929	412	15	p2	p2	PROPN
ejpam-1929	412	16	are	be	AUX
ejpam-1929	412	17	distinct	distinct	ADJ
ejpam-1929	412	18	odd	odd	ADJ
ejpam-1929	412	19	primes	prime	NOUN
ejpam-1929	412	20	,	,	PUNCT
ejpam-1929	412	21	since	since	SCONJ
ejpam-1929	412	22	n	n	NUM
ejpam-1929	412	23	is	be	AUX
ejpam-1929	412	24	even	even	ADV
ejpam-1929	412	25	,	,	PUNCT
ejpam-1929	412	26	σn	σn	PRON
ejpam-1929	412	27	∼=	∼=	PROPN
ejpam-1929	412	28	sn	sn	NOUN
ejpam-1929	412	29	by	by	ADP
ejpam-1929	412	30	theorem	theorem	NOUN
ejpam-1929	412	31	5	5	NUM
ejpam-1929	412	32	.	.	PUNCT
ejpam-1929	413	1	since	since	SCONJ
ejpam-1929	413	2	2	2	NUM
ejpam-1929	413	3	is	be	AUX
ejpam-1929	413	4	an	an	DET
ejpam-1929	413	5	even	even	ADJ
ejpam-1929	413	6	number	number	NOUN
ejpam-1929	413	7	,	,	PUNCT
ejpam-1929	413	8	by	by	ADP
ejpam-1929	413	9	the	the	DET
ejpam-1929	413	10	consideration	consideration	NOUN
ejpam-1929	413	11	of	of	ADP
ejpam-1929	413	12	mapping	mapping	NOUN
ejpam-1929	413	13	in	in	ADP
ejpam-1929	413	14	theorem	theorem	ADJ
ejpam-1929	413	15	5	5	NUM
ejpam-1929	413	16	,	,	PUNCT
ejpam-1929	413	17	vertex	vertex	NOUN
ejpam-1929	413	18	2	2	NUM
ejpam-1929	413	19	of	of	ADP
ejpam-1929	413	20	sn	sn	PROPN
ejpam-1929	413	21	is	be	AUX
ejpam-1929	413	22	mapped	map	VERB
ejpam-1929	413	23	to	to	ADP
ejpam-1929	413	24	the	the	DET
ejpam-1929	413	25	vertex	vertex	NOUN
ejpam-1929	413	26	2	2	NUM
ejpam-1929	413	27	in	in	ADP
ejpam-1929	413	28	σn	σn	NOUN
ejpam-1929	413	29	and	and	CCONJ
ejpam-1929	413	30	by	by	ADP
ejpam-1929	413	31	lemma	lemma	PROPN
ejpam-1929	413	32	5	5	NUM
ejpam-1929	413	33	,	,	PUNCT
ejpam-1929	413	34	negative	negative	ADJ
ejpam-1929	413	35	degree	degree	NOUN
ejpam-1929	413	36	of	of	ADP
ejpam-1929	413	37	the	the	DET
ejpam-1929	413	38	vertex	vertex	NOUN
ejpam-1929	413	39	2	2	NUM
ejpam-1929	413	40	in	in	ADP
ejpam-1929	413	41	σn	σn	NOUN
ejpam-1929	413	42	is	be	AUX
ejpam-1929	413	43	odd	odd	ADJ
ejpam-1929	413	44	.	.	PUNCT
ejpam-1929	414	1	d.	d.	PROPN
ejpam-1929	414	2	sinha	sinha	PROPN
ejpam-1929	414	3	,	,	PUNCT
ejpam-1929	414	4	a.	a.	NOUN
ejpam-1929	414	5	dhama	dhama	PROPN
ejpam-1929	414	6	,	,	PUNCT
ejpam-1929	414	7	b.	b.	PROPN
ejpam-1929	414	8	acharya	acharya	PROPN
ejpam-1929	414	9	/	/	SYM
ejpam-1929	414	10	eur	eur	PROPN
ejpam-1929	414	11	.	.	PUNCT
ejpam-1929	415	1	j.	j.	PROPN
ejpam-1929	415	2	pure	pure	PROPN
ejpam-1929	415	3	appl	appl	PROPN
ejpam-1929	415	4	.	.	PROPN
ejpam-1929	415	5	math	math	PROPN
ejpam-1929	415	6	,	,	PUNCT
ejpam-1929	415	7	6	6	NUM
ejpam-1929	415	8	(	(	PUNCT
ejpam-1929	415	9	2013	2013	NUM
ejpam-1929	415	10	)	)	PUNCT
ejpam-1929	415	11	,	,	PUNCT
ejpam-1929	415	12	189	189	NUM
ejpam-1929	415	13	-	-	SYM
ejpam-1929	415	14	210	210	NUM
ejpam-1929	415	15	204	204	NUM
ejpam-1929	415	16	lemma	lemma	PROPN
ejpam-1929	415	17	7	7	NUM
ejpam-1929	415	18	.	.	PUNCT
ejpam-1929	416	1	in	in	ADP
ejpam-1929	416	2	the	the	DET
ejpam-1929	416	3	unitary	unitary	ADJ
ejpam-1929	416	4	addition	addition	NOUN
ejpam-1929	416	5	cayley	cayley	NOUN
ejpam-1929	416	6	sigraph	sigraph	NOUN
ejpam-1929	416	7	σn	σn	NOUN
ejpam-1929	416	8	,	,	PUNCT
ejpam-1929	416	9	if	if	SCONJ
ejpam-1929	416	10	n	n	ADV
ejpam-1929	416	11	=	=	SYM
ejpam-1929	416	12	p	p	NOUN
ejpam-1929	416	13	a1	a1	NOUN
ejpam-1929	416	14	1	1	NUM
ejpam-1929	416	15	p	p	NOUN
ejpam-1929	416	16	a2	a2	PROPN
ejpam-1929	416	17	2	2	NUM
ejpam-1929	416	18	,	,	PUNCT
ejpam-1929	416	19	where	where	SCONJ
ejpam-1929	416	20	n	n	PRON
ejpam-1929	416	21	is	be	AUX
ejpam-1929	416	22	odd	odd	ADJ
ejpam-1929	416	23	,	,	PUNCT
ejpam-1929	416	24	then	then	ADV
ejpam-1929	416	25	the	the	DET
ejpam-1929	416	26	negative	negative	ADJ
ejpam-1929	416	27	degree	degree	NOUN
ejpam-1929	416	28	of	of	ADP
ejpam-1929	416	29	the	the	DET
ejpam-1929	416	30	vertices	vertex	NOUN
ejpam-1929	416	31	of	of	ADP
ejpam-1929	416	32	σn	σn	PRON
ejpam-1929	416	33	that	that	PRON
ejpam-1929	416	34	are	be	AUX
ejpam-1929	416	35	multiples	multiple	NOUN
ejpam-1929	416	36	of	of	ADP
ejpam-1929	416	37	p1	p1	NOUN
ejpam-1929	416	38	or	or	CCONJ
ejpam-1929	416	39	p2	p2	PROPN
ejpam-1929	416	40	is	be	AUX
ejpam-1929	416	41	even	even	ADV
ejpam-1929	416	42	.	.	PUNCT
ejpam-1929	417	1	proof	proof	NOUN
ejpam-1929	417	2	.	.	PUNCT
ejpam-1929	418	1	given	give	VERB
ejpam-1929	418	2	that	that	DET
ejpam-1929	418	3	n	n	NOUN
ejpam-1929	418	4	=	=	SYM
ejpam-1929	418	5	p	p	NOUN
ejpam-1929	418	6	a1	a1	NOUN
ejpam-1929	418	7	1	1	NUM
ejpam-1929	418	8	p	p	NOUN
ejpam-1929	418	9	a2	a2	PROPN
ejpam-1929	418	10	2	2	NUM
ejpam-1929	418	11	,	,	PUNCT
ejpam-1929	418	12	where	where	SCONJ
ejpam-1929	418	13	n	n	PRON
ejpam-1929	418	14	is	be	AUX
ejpam-1929	418	15	odd	odd	ADJ
ejpam-1929	418	16	,	,	PUNCT
ejpam-1929	418	17	and	and	CCONJ
ejpam-1929	418	18	p1	p1	NOUN
ejpam-1929	418	19	and	and	CCONJ
ejpam-1929	418	20	p2	p2	PROPN
ejpam-1929	418	21	are	be	AUX
ejpam-1929	418	22	distinct	distinct	ADJ
ejpam-1929	418	23	odd	odd	ADJ
ejpam-1929	418	24	primes	prime	NOUN
ejpam-1929	418	25	it	it	PRON
ejpam-1929	418	26	follows	follow	VERB
ejpam-1929	418	27	from	from	ADP
ejpam-1929	418	28	the	the	DET
ejpam-1929	418	29	definition	definition	NOUN
ejpam-1929	418	30	of	of	ADP
ejpam-1929	418	31	σn	σn	NOUN
ejpam-1929	418	32	,	,	PUNCT
ejpam-1929	418	33	that	that	SCONJ
ejpam-1929	418	34	the	the	DET
ejpam-1929	418	35	negative	negative	ADJ
ejpam-1929	418	36	edges	edge	NOUN
ejpam-1929	418	37	are	be	AUX
ejpam-1929	418	38	incident	incident	NOUN
ejpam-1929	418	39	at	at	ADP
ejpam-1929	418	40	the	the	DET
ejpam-1929	418	41	vertex	vertex	NOUN
ejpam-1929	418	42	p1	p1	NOUN
ejpam-1929	418	43	when	when	SCONJ
ejpam-1929	418	44	p1	p1	PROPN
ejpam-1929	418	45	is	be	AUX
ejpam-1929	418	46	adjacent	adjacent	ADJ
ejpam-1929	418	47	to	to	ADP
ejpam-1929	418	48	multiples	multiple	NOUN
ejpam-1929	418	49	of	of	ADP
ejpam-1929	418	50	p2	p2	PROPN
ejpam-1929	418	51	which	which	PRON
ejpam-1929	418	52	do	do	AUX
ejpam-1929	418	53	not	not	PART
ejpam-1929	418	54	have	have	VERB
ejpam-1929	418	55	p1	p1	NOUN
ejpam-1929	418	56	as	as	ADP
ejpam-1929	418	57	the	the	DET
ejpam-1929	418	58	factor	factor	NOUN
ejpam-1929	418	59	.	.	PUNCT
ejpam-1929	419	1	every	every	DET
ejpam-1929	419	2	multiple	multiple	NOUN
ejpam-1929	419	3	of	of	ADP
ejpam-1929	419	4	p2	p2	NOUN
ejpam-1929	419	5	,	,	PUNCT
ejpam-1929	419	6	which	which	PRON
ejpam-1929	419	7	does	do	AUX
ejpam-1929	419	8	not	not	PART
ejpam-1929	419	9	contain	contain	VERB
ejpam-1929	419	10	any	any	DET
ejpam-1929	419	11	multiple	multiple	NOUN
ejpam-1929	419	12	of	of	ADP
ejpam-1929	419	13	p1	p1	NOUN
ejpam-1929	419	14	,	,	PUNCT
ejpam-1929	419	15	is	be	AUX
ejpam-1929	419	16	adjacent	adjacent	ADJ
ejpam-1929	419	17	with	with	ADP
ejpam-1929	419	18	p1	p1	PROPN
ejpam-1929	419	19	as	as	ADP
ejpam-1929	419	20	its	its	PRON
ejpam-1929	419	21	addition	addition	NOUN
ejpam-1929	419	22	is	be	AUX
ejpam-1929	419	23	neither	neither	CCONJ
ejpam-1929	419	24	a	a	DET
ejpam-1929	419	25	multiple	multiple	NOUN
ejpam-1929	419	26	of	of	ADP
ejpam-1929	419	27	p1	p1	NOUN
ejpam-1929	419	28	nor	nor	CCONJ
ejpam-1929	419	29	a	a	DET
ejpam-1929	419	30	multiple	multiple	NOUN
ejpam-1929	419	31	of	of	ADP
ejpam-1929	419	32	p2	p2	NOUN
ejpam-1929	419	33	.	.	PUNCT
ejpam-1929	420	1	thus	thus	ADV
ejpam-1929	420	2	,	,	PUNCT
ejpam-1929	420	3	d−(p1	d−(p1	VERB
ejpam-1929	420	4	)	)	PUNCT
ejpam-1929	420	5	=	=	SYM
ejpam-1929	421	1	p	p	NOUN
ejpam-1929	421	2	a1	a1	NOUN
ejpam-1929	421	3	1	1	NUM
ejpam-1929	421	4	p	p	NOUN
ejpam-1929	421	5	a2−1	a2−1	NOUN
ejpam-1929	421	6	2	2	NUM
ejpam-1929	421	7	−	−	NOUN
ejpam-1929	421	8	p	p	NOUN
ejpam-1929	421	9	a1−1	a1−1	PROPN
ejpam-1929	421	10	1	1	NUM
ejpam-1929	421	11	p	p	NOUN
ejpam-1929	421	12	a2−1	a2−1	NOUN
ejpam-1929	421	13	2	2	NUM
ejpam-1929	421	14	=	=	SYM
ejpam-1929	421	15	p	p	NOUN
ejpam-1929	421	16	a1−1	a1−1	NOUN
ejpam-1929	421	17	1	1	NUM
ejpam-1929	421	18	p	p	NOUN
ejpam-1929	421	19	a2−1	a2−1	NOUN
ejpam-1929	421	20	2	2	NUM
ejpam-1929	421	21	(	(	PUNCT
ejpam-1929	421	22	p1−	p1−	PROPN
ejpam-1929	421	23	1	1	NUM
ejpam-1929	421	24	)	)	PUNCT
ejpam-1929	421	25	.	.	PUNCT
ejpam-1929	422	1	since	since	SCONJ
ejpam-1929	422	2	p1	p1	NOUN
ejpam-1929	422	3	and	and	CCONJ
ejpam-1929	422	4	p2	p2	PROPN
ejpam-1929	422	5	are	be	AUX
ejpam-1929	422	6	odd	odd	ADJ
ejpam-1929	422	7	,	,	PUNCT
ejpam-1929	422	8	d−(p1	d−(p1	NOUN
ejpam-1929	422	9	)	)	PUNCT
ejpam-1929	422	10	is	be	AUX
ejpam-1929	422	11	even	even	ADV
ejpam-1929	422	12	.	.	PUNCT
ejpam-1929	423	1	this	this	DET
ejpam-1929	423	2	formula	formula	NOUN
ejpam-1929	423	3	works	work	VERB
ejpam-1929	423	4	for	for	ADP
ejpam-1929	423	5	any	any	DET
ejpam-1929	423	6	multiple	multiple	NOUN
ejpam-1929	423	7	of	of	ADP
ejpam-1929	423	8	p1	p1	NOUN
ejpam-1929	423	9	except	except	SCONJ
ejpam-1929	423	10	those	those	PRON
ejpam-1929	423	11	which	which	PRON
ejpam-1929	423	12	have	have	VERB
ejpam-1929	423	13	p2	p2	NOUN
ejpam-1929	423	14	as	as	ADP
ejpam-1929	423	15	a	a	DET
ejpam-1929	423	16	factor	factor	NOUN
ejpam-1929	423	17	.	.	PUNCT
ejpam-1929	424	1	similarly	similarly	ADV
ejpam-1929	424	2	,	,	PUNCT
ejpam-1929	424	3	d−(p2	d−(p2	X
ejpam-1929	424	4	)	)	PUNCT
ejpam-1929	425	1	=	=	SYM
ejpam-1929	426	1	p	p	X
ejpam-1929	426	2	a1−1	a1−1	NOUN
ejpam-1929	426	3	1	1	NUM
ejpam-1929	426	4	p	p	NOUN
ejpam-1929	426	5	a2	a2	PROPN
ejpam-1929	426	6	2	2	NUM
ejpam-1929	426	7	−	−	NOUN
ejpam-1929	427	1	p	p	NOUN
ejpam-1929	427	2	a1−1	a1−1	PROPN
ejpam-1929	427	3	1	1	NUM
ejpam-1929	427	4	p	p	NOUN
ejpam-1929	427	5	a2−1	a2−1	NOUN
ejpam-1929	427	6	2	2	NUM
ejpam-1929	427	7	.	.	PUNCT
ejpam-1929	428	1	=	=	PUNCT
ejpam-1929	429	1	p	p	X
ejpam-1929	429	2	a1−1	a1−1	NOUN
ejpam-1929	429	3	1	1	NUM
ejpam-1929	429	4	p	p	NOUN
ejpam-1929	429	5	a2−1	a2−1	NOUN
ejpam-1929	429	6	2	2	NUM
ejpam-1929	429	7	(	(	PUNCT
ejpam-1929	429	8	p2−	p2−	NOUN
ejpam-1929	429	9	1	1	NUM
ejpam-1929	429	10	)	)	PUNCT
ejpam-1929	429	11	.	.	PUNCT
ejpam-1929	430	1	since	since	SCONJ
ejpam-1929	430	2	p1	p1	NOUN
ejpam-1929	430	3	and	and	CCONJ
ejpam-1929	430	4	p2	p2	PROPN
ejpam-1929	430	5	are	be	AUX
ejpam-1929	430	6	odd	odd	ADJ
ejpam-1929	430	7	,	,	PUNCT
ejpam-1929	430	8	d−(p2	d−(p2	PRON
ejpam-1929	430	9	)	)	PUNCT
ejpam-1929	430	10	is	be	AUX
ejpam-1929	430	11	even	even	ADV
ejpam-1929	430	12	.	.	PUNCT
ejpam-1929	431	1	this	this	DET
ejpam-1929	431	2	formula	formula	NOUN
ejpam-1929	431	3	works	work	VERB
ejpam-1929	431	4	for	for	ADP
ejpam-1929	431	5	any	any	DET
ejpam-1929	431	6	multiple	multiple	NOUN
ejpam-1929	431	7	of	of	ADP
ejpam-1929	431	8	p2	p2	PROPN
ejpam-1929	431	9	except	except	SCONJ
ejpam-1929	431	10	those	those	PRON
ejpam-1929	431	11	which	which	PRON
ejpam-1929	431	12	have	have	VERB
ejpam-1929	431	13	p1	p1	NOUN
ejpam-1929	431	14	as	as	ADP
ejpam-1929	431	15	a	a	DET
ejpam-1929	431	16	factor	factor	NOUN
ejpam-1929	431	17	.	.	PUNCT
ejpam-1929	432	1	and	and	CCONJ
ejpam-1929	432	2	the	the	DET
ejpam-1929	432	3	negative	negative	ADJ
ejpam-1929	432	4	degree	degree	NOUN
ejpam-1929	432	5	of	of	ADP
ejpam-1929	432	6	the	the	DET
ejpam-1929	432	7	vertices	vertex	NOUN
ejpam-1929	432	8	of	of	ADP
ejpam-1929	432	9	σn	σn	PRON
ejpam-1929	432	10	that	that	PRON
ejpam-1929	432	11	are	be	AUX
ejpam-1929	432	12	multiples	multiple	NOUN
ejpam-1929	432	13	of	of	ADP
ejpam-1929	432	14	p1p2	p1p2	PROPN
ejpam-1929	432	15	is	be	AUX
ejpam-1929	432	16	zero	zero	NUM
ejpam-1929	432	17	.	.	PUNCT
ejpam-1929	433	1	thus	thus	ADV
ejpam-1929	433	2	,	,	PUNCT
ejpam-1929	433	3	the	the	DET
ejpam-1929	433	4	negative	negative	ADJ
ejpam-1929	433	5	degree	degree	NOUN
ejpam-1929	433	6	of	of	ADP
ejpam-1929	433	7	the	the	DET
ejpam-1929	433	8	vertices	vertex	NOUN
ejpam-1929	433	9	of	of	ADP
ejpam-1929	433	10	σn	σn	PRON
ejpam-1929	433	11	that	that	PRON
ejpam-1929	433	12	are	be	AUX
ejpam-1929	433	13	multiples	multiple	NOUN
ejpam-1929	433	14	of	of	ADP
ejpam-1929	433	15	p1	p1	NOUN
ejpam-1929	433	16	or	or	CCONJ
ejpam-1929	433	17	p2	p2	PROPN
ejpam-1929	433	18	is	be	AUX
ejpam-1929	433	19	even	even	ADV
ejpam-1929	433	20	.	.	PUNCT
ejpam-1929	434	1	theorem	theorem	ADJ
ejpam-1929	434	2	15	15	NUM
ejpam-1929	434	3	.	.	PUNCT
ejpam-1929	435	1	the	the	DET
ejpam-1929	435	2	unitary	unitary	ADJ
ejpam-1929	435	3	addition	addition	NOUN
ejpam-1929	435	4	cayley	cayley	NOUN
ejpam-1929	435	5	sigraph	sigraph	NOUN
ejpam-1929	435	6	σn	σn	NOUN
ejpam-1929	435	7	=	=	SYM
ejpam-1929	435	8	(	(	PUNCT
ejpam-1929	435	9	σ	σ	PROPN
ejpam-1929	435	10	u	u	PROPN
ejpam-1929	435	11	n	n	NUM
ejpam-1929	435	12	,	,	PUNCT
ejpam-1929	435	13	σ	σ	PROPN
ejpam-1929	435	14	)	)	PUNCT
ejpam-1929	435	15	,	,	PUNCT
ejpam-1929	435	16	where	where	SCONJ
ejpam-1929	435	17	n	n	PRON
ejpam-1929	435	18	has	have	VERB
ejpam-1929	435	19	at	at	ADP
ejpam-1929	435	20	most	most	ADV
ejpam-1929	435	21	two	two	NUM
ejpam-1929	435	22	distinct	distinct	ADJ
ejpam-1929	435	23	odd	odd	ADJ
ejpam-1929	435	24	prime	prime	ADJ
ejpam-1929	435	25	factors	factor	NOUN
ejpam-1929	435	26	,	,	PUNCT
ejpam-1929	435	27	is	be	AUX
ejpam-1929	435	28	c	c	NOUN
ejpam-1929	435	29	-consistent	-consistent	ADJ
ejpam-1929	435	30	if	if	SCONJ
ejpam-1929	436	1	and	and	CCONJ
ejpam-1929	436	2	only	only	ADV
ejpam-1929	436	3	if	if	SCONJ
ejpam-1929	436	4	n	n	PRON
ejpam-1929	436	5	is	be	AUX
ejpam-1929	436	6	either	either	CCONJ
ejpam-1929	436	7	odd	odd	ADJ
ejpam-1929	436	8	,	,	PUNCT
ejpam-1929	436	9	or	or	CCONJ
ejpam-1929	436	10	n	n	PRON
ejpam-1929	436	11	is	be	AUX
ejpam-1929	436	12	2	2	NUM
ejpam-1929	436	13	,	,	PUNCT
ejpam-1929	436	14	6	6	NUM
ejpam-1929	436	15	or	or	CCONJ
ejpam-1929	436	16	a	a	DET
ejpam-1929	436	17	multiple	multiple	NOUN
ejpam-1929	436	18	of	of	ADP
ejpam-1929	436	19	4	4	NUM
ejpam-1929	436	20	.	.	PUNCT
ejpam-1929	437	1	proof	proof	NOUN
ejpam-1929	437	2	.	.	PUNCT
ejpam-1929	438	1	necessity	necessity	NOUN
ejpam-1929	438	2	:	:	PUNCT
ejpam-1929	438	3	suppose	suppose	VERB
ejpam-1929	438	4	the	the	DET
ejpam-1929	438	5	unitary	unitary	ADJ
ejpam-1929	438	6	addition	addition	NOUN
ejpam-1929	438	7	cayley	cayley	NOUN
ejpam-1929	438	8	sigraphσn	sigraphσn	VERB
ejpam-1929	438	9	=	=	SYM
ejpam-1929	438	10	(	(	PUNCT
ejpam-1929	438	11	σ	σ	NUM
ejpam-1929	438	12	u	u	PROPN
ejpam-1929	438	13	n	n	NUM
ejpam-1929	438	14	,	,	PUNCT
ejpam-1929	438	15	σ	σ	PROPN
ejpam-1929	438	16	)	)	PUNCT
ejpam-1929	438	17	isc	isc	PROPN
ejpam-1929	438	18	-consistent	-consistent	PROPN
ejpam-1929	438	19	.	.	PUNCT
ejpam-1929	439	1	let	let	VERB
ejpam-1929	439	2	,	,	PUNCT
ejpam-1929	439	3	on	on	ADP
ejpam-1929	439	4	contrary	contrary	ADJ
ejpam-1929	439	5	,	,	PUNCT
ejpam-1929	439	6	n	n	CCONJ
ejpam-1929	439	7	≡	≡	PROPN
ejpam-1929	439	8	2	2	NUM
ejpam-1929	439	9	(	(	PUNCT
ejpam-1929	439	10	mod	mod	NOUN
ejpam-1929	439	11	4	4	NUM
ejpam-1929	439	12	)	)	PUNCT
ejpam-1929	439	13	with	with	ADP
ejpam-1929	439	14	n	n	PROPN
ejpam-1929	439	15	6=	6=	NUM
ejpam-1929	439	16	2	2	NUM
ejpam-1929	439	17	and	and	CCONJ
ejpam-1929	439	18	n	n	NOUN
ejpam-1929	439	19	6=	6=	PROPN
ejpam-1929	439	20	6	6	NUM
ejpam-1929	439	21	.	.	PUNCT
ejpam-1929	440	1	then	then	ADV
ejpam-1929	440	2	,	,	PUNCT
ejpam-1929	440	3	either	either	CCONJ
ejpam-1929	440	4	n	n	PROPN
ejpam-1929	440	5	=	=	SYM
ejpam-1929	440	6	2p	2p	NUM
ejpam-1929	440	7	a1	a1	NOUN
ejpam-1929	440	8	1	1	NUM
ejpam-1929	440	9	or	or	CCONJ
ejpam-1929	440	10	n	n	NOUN
ejpam-1929	440	11	=	=	SYM
ejpam-1929	440	12	2p	2p	NUM
ejpam-1929	440	13	a1	a1	NOUN
ejpam-1929	440	14	1	1	NUM
ejpam-1929	440	15	p	p	NOUN
ejpam-1929	440	16	a2	a2	PROPN
ejpam-1929	440	17	2	2	NUM
ejpam-1929	440	18	,	,	PUNCT
ejpam-1929	440	19	where	where	SCONJ
ejpam-1929	440	20	p1	p1	NOUN
ejpam-1929	440	21	and	and	CCONJ
ejpam-1929	440	22	p2	p2	PROPN
ejpam-1929	440	23	are	be	AUX
ejpam-1929	440	24	distinct	distinct	ADJ
ejpam-1929	440	25	odd	odd	ADJ
ejpam-1929	440	26	primes	prime	NOUN
ejpam-1929	440	27	.	.	PUNCT
ejpam-1929	441	1	case(i	case(i	PROPN
ejpam-1929	441	2	):	):	PUNCT
ejpam-1929	441	3	suppose	suppose	VERB
ejpam-1929	441	4	n≡	n≡	ADP
ejpam-1929	441	5	0	0	NUM
ejpam-1929	442	1	(	(	PUNCT
ejpam-1929	442	2	mod	mod	PROPN
ejpam-1929	442	3	3	3	NUM
ejpam-1929	442	4	)	)	PUNCT
ejpam-1929	442	5	.	.	PUNCT
ejpam-1929	443	1	then	then	ADV
ejpam-1929	443	2	,	,	PUNCT
ejpam-1929	443	3	either	either	CCONJ
ejpam-1929	443	4	n=	n=	ADJ
ejpam-1929	443	5	2×3a1	2×3a1	PROPN
ejpam-1929	443	6	or	or	CCONJ
ejpam-1929	443	7	n=	n=	ADJ
ejpam-1929	443	8	2×3a1	2×3a1	PROPN
ejpam-1929	443	9	×	×	NOUN
ejpam-1929	443	10	p	p	PROPN
ejpam-1929	443	11	a2	a2	PROPN
ejpam-1929	443	12	2	2	NUM
ejpam-1929	443	13	.	.	PUNCT
ejpam-1929	444	1	first	first	ADV
ejpam-1929	444	2	,	,	PUNCT
ejpam-1929	444	3	suppose	suppose	VERB
ejpam-1929	444	4	p2	p2	PROPN
ejpam-1929	444	5	6=	6=	ADP
ejpam-1929	444	6	5	5	NUM
ejpam-1929	444	7	and	and	CCONJ
ejpam-1929	444	8	p2	p2	PROPN
ejpam-1929	444	9	6=	6=	ADP
ejpam-1929	444	10	7	7	NUM
ejpam-1929	444	11	.	.	PUNCT
ejpam-1929	445	1	then	then	ADV
ejpam-1929	445	2	,	,	PUNCT
ejpam-1929	445	3	due	due	ADP
ejpam-1929	445	4	to	to	ADP
ejpam-1929	445	5	lemma	lemma	PROPN
ejpam-1929	445	6	4	4	NUM
ejpam-1929	445	7	and	and	CCONJ
ejpam-1929	445	8	lemma	lemma	PROPN
ejpam-1929	445	9	6	6	NUM
ejpam-1929	445	10	,	,	PUNCT
ejpam-1929	445	11	µσ(2	µσ(2	NUM
ejpam-1929	445	12	)	)	PUNCT
ejpam-1929	445	13	=	=	PUNCT
ejpam-1929	446	1	−.	−.	ADV
ejpam-1929	446	2	since	since	SCONJ
ejpam-1929	446	3	the	the	DET
ejpam-1929	446	4	vertex	vertex	NOUN
ejpam-1929	446	5	5	5	NUM
ejpam-1929	446	6	∈	∈	PROPN
ejpam-1929	446	7	un	un	NOUN
ejpam-1929	446	8	,	,	PUNCT
ejpam-1929	446	9	by	by	ADP
ejpam-1929	446	10	the	the	DET
ejpam-1929	446	11	definition	definition	NOUN
ejpam-1929	446	12	of	of	ADP
ejpam-1929	446	13	σn	σn	PROPN
ejpam-1929	446	14	,	,	PUNCT
ejpam-1929	446	15	d−(5	d−(5	PROPN
ejpam-1929	446	16	)	)	PUNCT
ejpam-1929	446	17	=	=	SYM
ejpam-1929	447	1	0	0	X
ejpam-1929	447	2	.	.	PUNCT
ejpam-1929	448	1	it	it	PRON
ejpam-1929	448	2	follows	follow	VERB
ejpam-1929	448	3	,	,	PUNCT
ejpam-1929	448	4	µσ(5	µσ(5	NOUN
ejpam-1929	448	5	)	)	PUNCT
ejpam-1929	448	6	=	=	PUNCT
ejpam-1929	449	1	+	+	X
ejpam-1929	449	2	.	.	PUNCT
ejpam-1929	449	3	now	now	ADV
ejpam-1929	449	4	,	,	PUNCT
ejpam-1929	449	5	the	the	DET
ejpam-1929	449	6	vertex	vertex	NOUN
ejpam-1929	449	7	5	5	NUM
ejpam-1929	449	8	is	be	AUX
ejpam-1929	449	9	adjacent	adjacent	ADJ
ejpam-1929	449	10	to	to	ADP
ejpam-1929	449	11	the	the	DET
ejpam-1929	449	12	vertex	vertex	NOUN
ejpam-1929	449	13	2	2	NUM
ejpam-1929	449	14	since	since	SCONJ
ejpam-1929	449	15	5	5	NUM
ejpam-1929	449	16	+	+	NOUN
ejpam-1929	449	17	2=	2=	NUM
ejpam-1929	449	18	7	7	NUM
ejpam-1929	449	19	∈	∈	PROPN
ejpam-1929	449	20	un	un	NOUN
ejpam-1929	449	21	.	.	PROPN
ejpam-1929	450	1	since	since	SCONJ
ejpam-1929	450	2	(	(	PUNCT
ejpam-1929	450	3	n	n	CCONJ
ejpam-1929	450	4	−	−	PROPN
ejpam-1929	450	5	4	4	NUM
ejpam-1929	450	6	)	)	PUNCT
ejpam-1929	450	7	+	+	CCONJ
ejpam-1929	451	1	(	(	PUNCT
ejpam-1929	451	2	n	n	CCONJ
ejpam-1929	451	3	−	−	PROPN
ejpam-1929	451	4	3	3	NUM
ejpam-1929	451	5	)	)	PUNCT
ejpam-1929	451	6	=	=	SYM
ejpam-1929	451	7	n	n	PROPN
ejpam-1929	451	8	+	+	CCONJ
ejpam-1929	451	9	(	(	PUNCT
ejpam-1929	451	10	n−	n−	NOUN
ejpam-1929	451	11	7	7	NUM
ejpam-1929	451	12	)	)	PUNCT
ejpam-1929	451	13	=	=	SYM
ejpam-1929	452	1	n	n	CCONJ
ejpam-1929	452	2	−	−	PROPN
ejpam-1929	452	3	7	7	NUM
ejpam-1929	452	4	∈	∈	PROPN
ejpam-1929	452	5	un	un	NOUN
ejpam-1929	452	6	as	as	ADP
ejpam-1929	452	7	7	7	NUM
ejpam-1929	452	8	∈	∈	PROPN
ejpam-1929	452	9	un	un	NOUN
ejpam-1929	452	10	,	,	PUNCT
ejpam-1929	452	11	(	(	PUNCT
ejpam-1929	452	12	n	n	CCONJ
ejpam-1929	452	13	−	−	PROPN
ejpam-1929	452	14	4	4	NUM
ejpam-1929	452	15	)	)	PUNCT
ejpam-1929	452	16	and	and	CCONJ
ejpam-1929	452	17	(	(	PUNCT
ejpam-1929	452	18	n	n	CCONJ
ejpam-1929	452	19	−	−	PROPN
ejpam-1929	452	20	3	3	NUM
ejpam-1929	452	21	)	)	PUNCT
ejpam-1929	452	22	are	be	AUX
ejpam-1929	452	23	adjacent	adjacent	ADJ
ejpam-1929	452	24	in	in	ADP
ejpam-1929	452	25	σu	σu	PROPN
ejpam-1929	452	26	n	n	PROPN
ejpam-1929	453	1	and	and	CCONJ
ejpam-1929	453	2	(	(	PUNCT
ejpam-1929	453	3	n	n	CCONJ
ejpam-1929	453	4	−	−	PROPN
ejpam-1929	453	5	3	3	NUM
ejpam-1929	453	6	)	)	PUNCT
ejpam-1929	453	7	+	+	CCONJ
ejpam-1929	454	1	2	2	NUM
ejpam-1929	454	2	=	=	SYM
ejpam-1929	454	3	n	n	CCONJ
ejpam-1929	454	4	−	−	PROPN
ejpam-1929	454	5	1	1	NUM
ejpam-1929	454	6	∈	∈	PROPN
ejpam-1929	454	7	un	un	NOUN
ejpam-1929	454	8	.	.	PUNCT
ejpam-1929	455	1	this	this	PRON
ejpam-1929	455	2	implies	imply	VERB
ejpam-1929	455	3	(	(	PUNCT
ejpam-1929	455	4	n	n	CCONJ
ejpam-1929	455	5	−	−	PROPN
ejpam-1929	455	6	3	3	NUM
ejpam-1929	455	7	)	)	PUNCT
ejpam-1929	455	8	and	and	CCONJ
ejpam-1929	455	9	2	2	NUM
ejpam-1929	455	10	are	be	AUX
ejpam-1929	455	11	also	also	ADV
ejpam-1929	455	12	adjacent	adjacent	ADJ
ejpam-1929	455	13	in	in	ADP
ejpam-1929	455	14	σu	σu	PROPN
ejpam-1929	455	15	n.	n.	PROPN
ejpam-1929	455	16	similarly	similarly	ADV
ejpam-1929	455	17	,	,	PUNCT
ejpam-1929	455	18	(	(	PUNCT
ejpam-1929	455	19	n−4)+5=	n−4)+5=	INTJ
ejpam-1929	455	20	n+1=	n+1=	PROPN
ejpam-1929	455	21	1	1	NUM
ejpam-1929	455	22	∈	∈	PROPN
ejpam-1929	455	23	un	un	NOUN
ejpam-1929	455	24	.	.	PUNCT
ejpam-1929	456	1	this	this	PRON
ejpam-1929	456	2	implies	imply	VERB
ejpam-1929	456	3	5	5	NUM
ejpam-1929	456	4	and	and	CCONJ
ejpam-1929	456	5	(	(	PUNCT
ejpam-1929	456	6	n−4	n−4	NOUN
ejpam-1929	456	7	)	)	PUNCT
ejpam-1929	456	8	are	be	AUX
ejpam-1929	456	9	adjacent	adjacent	ADJ
ejpam-1929	456	10	in	in	ADP
ejpam-1929	456	11	σu	σu	PROPN
ejpam-1929	456	12	n.	n.	PROPN
ejpam-1929	456	13	consider	consider	VERB
ejpam-1929	456	14	the	the	DET
ejpam-1929	456	15	two	two	NUM
ejpam-1929	456	16	cycles	cycle	NOUN
ejpam-1929	456	17	,	,	PUNCT
ejpam-1929	456	18	z1	z1	PROPN
ejpam-1929	456	19	=	=	SYM
ejpam-1929	456	20	(	(	PUNCT
ejpam-1929	456	21	2,5,0,1,4,3,2	2,5,0,1,4,3,2	NOUN
ejpam-1929	456	22	)	)	PUNCT
ejpam-1929	456	23	and	and	CCONJ
ejpam-1929	456	24	z2	z2	PROPN
ejpam-1929	456	25	=	=	SYM
ejpam-1929	456	26	(	(	PUNCT
ejpam-1929	456	27	2,5	2,5	NUM
ejpam-1929	456	28	,	,	PUNCT
ejpam-1929	456	29	(	(	PUNCT
ejpam-1929	456	30	n−	n−	NOUN
ejpam-1929	456	31	4	4	NUM
ejpam-1929	456	32	)	)	PUNCT
ejpam-1929	456	33	,	,	PUNCT
ejpam-1929	456	34	(	(	PUNCT
ejpam-1929	456	35	n−	n−	NOUN
ejpam-1929	456	36	3	3	NUM
ejpam-1929	456	37	)	)	PUNCT
ejpam-1929	456	38	,	,	PUNCT
ejpam-1929	456	39	2	2	X
ejpam-1929	456	40	)	)	PUNCT
ejpam-1929	456	41	in	in	ADP
ejpam-1929	456	42	σn	σn	PROPN
ejpam-1929	456	43	.	.	PUNCT
ejpam-1929	457	1	clearly	clearly	ADV
ejpam-1929	457	2	,	,	PUNCT
ejpam-1929	457	3	the	the	DET
ejpam-1929	457	4	d.	d.	PROPN
ejpam-1929	457	5	sinha	sinha	PROPN
ejpam-1929	457	6	,	,	PUNCT
ejpam-1929	457	7	a.	a.	NOUN
ejpam-1929	457	8	dhama	dhama	PROPN
ejpam-1929	457	9	,	,	PUNCT
ejpam-1929	457	10	b.	b.	PROPN
ejpam-1929	457	11	acharya	acharya	PROPN
ejpam-1929	457	12	/	/	SYM
ejpam-1929	457	13	eur	eur	PROPN
ejpam-1929	457	14	.	.	PUNCT
ejpam-1929	458	1	j.	j.	PROPN
ejpam-1929	458	2	pure	pure	PROPN
ejpam-1929	458	3	appl	appl	PROPN
ejpam-1929	458	4	.	.	PROPN
ejpam-1929	458	5	math	math	PROPN
ejpam-1929	458	6	,	,	PUNCT
ejpam-1929	458	7	6	6	NUM
ejpam-1929	458	8	(	(	PUNCT
ejpam-1929	458	9	2013	2013	NUM
ejpam-1929	458	10	)	)	PUNCT
ejpam-1929	458	11	,	,	PUNCT
ejpam-1929	458	12	189	189	NUM
ejpam-1929	458	13	-	-	SYM
ejpam-1929	458	14	210	210	NUM
ejpam-1929	458	15	205	205	NUM
ejpam-1929	458	16	cycles	cycle	NOUN
ejpam-1929	458	17	z1	z1	NOUN
ejpam-1929	458	18	and	and	CCONJ
ejpam-1929	458	19	z2	z2	PROPN
ejpam-1929	458	20	share	share	VERB
ejpam-1929	458	21	the	the	DET
ejpam-1929	458	22	chord	chord	NOUN
ejpam-1929	458	23	whose	whose	DET
ejpam-1929	458	24	end	end	NOUN
ejpam-1929	458	25	vertices	vertex	NOUN
ejpam-1929	458	26	are	be	AUX
ejpam-1929	458	27	2	2	NUM
ejpam-1929	458	28	and	and	CCONJ
ejpam-1929	458	29	5	5	NUM
ejpam-1929	458	30	.	.	PUNCT
ejpam-1929	459	1	now	now	ADV
ejpam-1929	459	2	,	,	PUNCT
ejpam-1929	459	3	if	if	SCONJ
ejpam-1929	459	4	either	either	CCONJ
ejpam-1929	459	5	z1	z1	PROPN
ejpam-1929	459	6	or	or	CCONJ
ejpam-1929	459	7	z2	z2	NOUN
ejpam-1929	459	8	is	be	AUX
ejpam-1929	459	9	c	c	NOUN
ejpam-1929	459	10	-inconsistent	-inconsistent	ADJ
ejpam-1929	459	11	cycle	cycle	NOUN
ejpam-1929	459	12	,	,	PUNCT
ejpam-1929	459	13	then	then	ADV
ejpam-1929	459	14	we	we	PRON
ejpam-1929	459	15	have	have	VERB
ejpam-1929	459	16	a	a	DET
ejpam-1929	459	17	contradiction	contradiction	NOUN
ejpam-1929	459	18	to	to	ADP
ejpam-1929	459	19	the	the	DET
ejpam-1929	459	20	hypothesis	hypothesis	NOUN
ejpam-1929	459	21	.	.	PUNCT
ejpam-1929	460	1	therefore	therefore	ADV
ejpam-1929	460	2	,	,	PUNCT
ejpam-1929	460	3	z1	z1	PROPN
ejpam-1929	460	4	and	and	CCONJ
ejpam-1929	460	5	z2	z2	NOUN
ejpam-1929	460	6	are	be	AUX
ejpam-1929	460	7	both	both	PRON
ejpam-1929	460	8	c	c	NOUN
ejpam-1929	460	9	-consistent	-consistent	PROPN
ejpam-1929	460	10	cycles	cycle	NOUN
ejpam-1929	460	11	.	.	PUNCT
ejpam-1929	461	1	however	however	ADV
ejpam-1929	461	2	,	,	PUNCT
ejpam-1929	461	3	the	the	DET
ejpam-1929	461	4	end	end	NOUN
ejpam-1929	461	5	vertices	vertice	VERB
ejpam-1929	461	6	2	2	NUM
ejpam-1929	461	7	and	and	CCONJ
ejpam-1929	461	8	5	5	NUM
ejpam-1929	461	9	of	of	ADP
ejpam-1929	461	10	their	their	PRON
ejpam-1929	461	11	common	common	ADJ
ejpam-1929	461	12	chord	chord	NOUN
ejpam-1929	461	13	are	be	AUX
ejpam-1929	461	14	marked	mark	VERB
ejpam-1929	461	15	oppositely	oppositely	ADV
ejpam-1929	461	16	under	under	ADP
ejpam-1929	461	17	the	the	DET
ejpam-1929	461	18	canonical	canonical	ADJ
ejpam-1929	461	19	marking	marking	NOUN
ejpam-1929	461	20	and	and	CCONJ
ejpam-1929	461	21	this	this	PRON
ejpam-1929	461	22	contradicts	contradict	VERB
ejpam-1929	461	23	theorem	theorem	ADJ
ejpam-1929	461	24	13	13	NUM
ejpam-1929	461	25	.	.	PUNCT
ejpam-1929	462	1	now	now	ADV
ejpam-1929	462	2	,	,	PUNCT
ejpam-1929	462	3	if	if	SCONJ
ejpam-1929	462	4	n=	n=	ADJ
ejpam-1929	462	5	2×3a1	2×3a1	PROPN
ejpam-1929	462	6	×	×	NOUN
ejpam-1929	462	7	p	p	PROPN
ejpam-1929	462	8	a2	a2	PROPN
ejpam-1929	462	9	2	2	NUM
ejpam-1929	462	10	,	,	PUNCT
ejpam-1929	462	11	where	where	SCONJ
ejpam-1929	462	12	either	either	CCONJ
ejpam-1929	462	13	p2	p2	X
ejpam-1929	462	14	=	=	SYM
ejpam-1929	462	15	5	5	NUM
ejpam-1929	462	16	or	or	CCONJ
ejpam-1929	462	17	p2	p2	X
ejpam-1929	462	18	=	=	SYM
ejpam-1929	462	19	7	7	NUM
ejpam-1929	462	20	,	,	PUNCT
ejpam-1929	462	21	then	then	ADV
ejpam-1929	462	22	since	since	SCONJ
ejpam-1929	462	23	the	the	DET
ejpam-1929	462	24	vertex	vertex	NOUN
ejpam-1929	462	25	11	11	NUM
ejpam-1929	462	26	∈	∈	PROPN
ejpam-1929	462	27	un	un	NOUN
ejpam-1929	462	28	,	,	PUNCT
ejpam-1929	462	29	by	by	ADP
ejpam-1929	462	30	the	the	DET
ejpam-1929	462	31	definition	definition	NOUN
ejpam-1929	462	32	of	of	ADP
ejpam-1929	462	33	σn	σn	PROPN
ejpam-1929	462	34	,	,	PUNCT
ejpam-1929	462	35	d−(11	d−(11	NOUN
ejpam-1929	462	36	)	)	PUNCT
ejpam-1929	462	37	=	=	SYM
ejpam-1929	463	1	0	0	X
ejpam-1929	463	2	.	.	PUNCT
ejpam-1929	464	1	it	it	PRON
ejpam-1929	464	2	follows	follow	VERB
ejpam-1929	464	3	,	,	PUNCT
ejpam-1929	464	4	µσ(11	µσ(11	PROPN
ejpam-1929	464	5	)	)	PUNCT
ejpam-1929	464	6	=	=	PUNCT
ejpam-1929	465	1	+	+	X
ejpam-1929	465	2	.	.	PUNCT
ejpam-1929	465	3	now	now	ADV
ejpam-1929	465	4	,	,	PUNCT
ejpam-1929	465	5	the	the	DET
ejpam-1929	465	6	vertex	vertex	NOUN
ejpam-1929	465	7	11	11	NUM
ejpam-1929	465	8	is	be	AUX
ejpam-1929	465	9	adjacent	adjacent	ADJ
ejpam-1929	465	10	to	to	ADP
ejpam-1929	465	11	the	the	DET
ejpam-1929	465	12	vertex	vertex	NOUN
ejpam-1929	465	13	2	2	NUM
ejpam-1929	465	14	since	since	SCONJ
ejpam-1929	465	15	11	11	NUM
ejpam-1929	465	16	+	+	NOUN
ejpam-1929	465	17	2=	2=	NUM
ejpam-1929	465	18	13	13	NUM
ejpam-1929	465	19	∈	∈	PROPN
ejpam-1929	465	20	un	un	NOUN
ejpam-1929	465	21	.	.	PROPN
ejpam-1929	466	1	since	since	SCONJ
ejpam-1929	466	2	(	(	PUNCT
ejpam-1929	466	3	n−12)+(n−1	n−12)+(n−1	ADJ
ejpam-1929	466	4	)	)	PUNCT
ejpam-1929	466	5	=	=	SYM
ejpam-1929	466	6	n+(n−13	n+(n−13	X
ejpam-1929	466	7	)	)	PUNCT
ejpam-1929	466	8	∈	∈	PROPN
ejpam-1929	466	9	un	un	PROPN
ejpam-1929	466	10	as	as	ADP
ejpam-1929	466	11	13	13	NUM
ejpam-1929	466	12	∈	∈	PROPN
ejpam-1929	466	13	un	un	NOUN
ejpam-1929	466	14	,	,	PUNCT
ejpam-1929	466	15	(	(	PUNCT
ejpam-1929	466	16	n−12	n−12	NOUN
ejpam-1929	466	17	)	)	PUNCT
ejpam-1929	466	18	and	and	CCONJ
ejpam-1929	466	19	(	(	PUNCT
ejpam-1929	466	20	n−1	n−1	PROPN
ejpam-1929	466	21	)	)	PUNCT
ejpam-1929	466	22	are	be	AUX
ejpam-1929	466	23	adjacent	adjacent	ADJ
ejpam-1929	466	24	in	in	ADP
ejpam-1929	466	25	σu	σu	PROPN
ejpam-1929	466	26	n	n	PROPN
ejpam-1929	467	1	and	and	CCONJ
ejpam-1929	467	2	(	(	PUNCT
ejpam-1929	467	3	n−	n−	NOUN
ejpam-1929	467	4	1	1	NUM
ejpam-1929	467	5	)	)	PUNCT
ejpam-1929	467	6	+	+	CCONJ
ejpam-1929	467	7	2	2	NUM
ejpam-1929	467	8	=	=	SYM
ejpam-1929	467	9	n+	n+	X
ejpam-1929	467	10	1	1	NUM
ejpam-1929	467	11	=	=	SYM
ejpam-1929	467	12	1	1	NUM
ejpam-1929	467	13	∈	∈	PROPN
ejpam-1929	467	14	un	un	NOUN
ejpam-1929	467	15	.	.	PUNCT
ejpam-1929	468	1	this	this	PRON
ejpam-1929	468	2	implies	imply	VERB
ejpam-1929	468	3	,	,	PUNCT
ejpam-1929	468	4	(	(	PUNCT
ejpam-1929	468	5	n−	n−	NOUN
ejpam-1929	468	6	1	1	NUM
ejpam-1929	468	7	)	)	PUNCT
ejpam-1929	468	8	and	and	CCONJ
ejpam-1929	468	9	2	2	NUM
ejpam-1929	468	10	are	be	AUX
ejpam-1929	468	11	also	also	ADV
ejpam-1929	468	12	adjacent	adjacent	ADJ
ejpam-1929	468	13	in	in	ADP
ejpam-1929	468	14	σu	σu	PROPN
ejpam-1929	468	15	n.	n.	PROPN
ejpam-1929	468	16	similarly	similarly	ADV
ejpam-1929	468	17	,	,	PUNCT
ejpam-1929	468	18	(	(	PUNCT
ejpam-1929	468	19	n−	n−	NOUN
ejpam-1929	468	20	12	12	NUM
ejpam-1929	468	21	)	)	PUNCT
ejpam-1929	469	1	+	+	CCONJ
ejpam-1929	469	2	11=	11=	NUM
ejpam-1929	469	3	n−	n−	NOUN
ejpam-1929	469	4	1	1	NUM
ejpam-1929	469	5	∈	∈	PROPN
ejpam-1929	469	6	un	un	NOUN
ejpam-1929	469	7	,	,	PUNCT
ejpam-1929	469	8	which	which	PRON
ejpam-1929	469	9	implies	imply	VERB
ejpam-1929	469	10	11	11	NUM
ejpam-1929	469	11	and	and	CCONJ
ejpam-1929	469	12	(	(	PUNCT
ejpam-1929	469	13	n−	n−	NOUN
ejpam-1929	469	14	12	12	NUM
ejpam-1929	469	15	)	)	PUNCT
ejpam-1929	469	16	are	be	AUX
ejpam-1929	469	17	adjacent	adjacent	ADJ
ejpam-1929	469	18	in	in	ADP
ejpam-1929	469	19	σu	σu	PROPN
ejpam-1929	469	20	n.	n.	PROPN
ejpam-1929	469	21	now	now	ADV
ejpam-1929	469	22	,	,	PUNCT
ejpam-1929	469	23	consider	consider	VERB
ejpam-1929	469	24	the	the	DET
ejpam-1929	469	25	two	two	NUM
ejpam-1929	469	26	cycles	cycle	NOUN
ejpam-1929	469	27	,	,	PUNCT
ejpam-1929	469	28	z3	z3	PROPN
ejpam-1929	469	29	=	=	SYM
ejpam-1929	469	30	(	(	PUNCT
ejpam-1929	469	31	11,2,9,4,7,6,11	11,2,9,4,7,6,11	NUM
ejpam-1929	469	32	)	)	PUNCT
ejpam-1929	469	33	and	and	CCONJ
ejpam-1929	469	34	z4	z4	PROPN
ejpam-1929	469	35	=	=	SYM
ejpam-1929	469	36	(	(	PUNCT
ejpam-1929	469	37	2,11	2,11	NUM
ejpam-1929	469	38	,	,	PUNCT
ejpam-1929	469	39	(	(	PUNCT
ejpam-1929	469	40	n−	n−	NOUN
ejpam-1929	469	41	12	12	NUM
ejpam-1929	469	42	)	)	PUNCT
ejpam-1929	469	43	,	,	PUNCT
ejpam-1929	469	44	(	(	PUNCT
ejpam-1929	469	45	n−	n−	NOUN
ejpam-1929	469	46	1	1	NUM
ejpam-1929	469	47	)	)	PUNCT
ejpam-1929	469	48	,	,	PUNCT
ejpam-1929	469	49	2	2	X
ejpam-1929	469	50	)	)	PUNCT
ejpam-1929	469	51	in	in	ADP
ejpam-1929	469	52	σn	σn	PROPN
ejpam-1929	469	53	.	.	PUNCT
ejpam-1929	470	1	clearly	clearly	ADV
ejpam-1929	470	2	,	,	PUNCT
ejpam-1929	470	3	the	the	DET
ejpam-1929	470	4	cycles	cycle	NOUN
ejpam-1929	470	5	z3	z3	PROPN
ejpam-1929	470	6	and	and	CCONJ
ejpam-1929	470	7	z4	z4	PROPN
ejpam-1929	470	8	share	share	VERB
ejpam-1929	470	9	the	the	DET
ejpam-1929	470	10	chord	chord	NOUN
ejpam-1929	470	11	whose	whose	DET
ejpam-1929	470	12	end	end	NOUN
ejpam-1929	470	13	vertices	vertex	NOUN
ejpam-1929	470	14	are	be	AUX
ejpam-1929	470	15	2	2	NUM
ejpam-1929	470	16	and	and	CCONJ
ejpam-1929	470	17	11	11	NUM
ejpam-1929	470	18	.	.	PUNCT
ejpam-1929	471	1	as	as	SCONJ
ejpam-1929	471	2	argued	argue	VERB
ejpam-1929	471	3	above	above	ADV
ejpam-1929	471	4	,	,	PUNCT
ejpam-1929	471	5	z3	z3	PROPN
ejpam-1929	471	6	and	and	CCONJ
ejpam-1929	471	7	z4	z4	PROPN
ejpam-1929	471	8	are	be	AUX
ejpam-1929	471	9	both	both	PRON
ejpam-1929	471	10	c	c	NOUN
ejpam-1929	471	11	-consistent	-consistent	PROPN
ejpam-1929	471	12	cycles	cycle	NOUN
ejpam-1929	471	13	.	.	PUNCT
ejpam-1929	472	1	however	however	ADV
ejpam-1929	472	2	,	,	PUNCT
ejpam-1929	472	3	the	the	DET
ejpam-1929	472	4	end	end	NOUN
ejpam-1929	472	5	vertices	vertice	VERB
ejpam-1929	472	6	2	2	NUM
ejpam-1929	472	7	and	and	CCONJ
ejpam-1929	472	8	11	11	NUM
ejpam-1929	472	9	of	of	ADP
ejpam-1929	472	10	their	their	PRON
ejpam-1929	472	11	common	common	ADJ
ejpam-1929	472	12	chord	chord	NOUN
ejpam-1929	472	13	are	be	AUX
ejpam-1929	472	14	marked	mark	VERB
ejpam-1929	472	15	oppositely	oppositely	ADV
ejpam-1929	472	16	under	under	ADP
ejpam-1929	472	17	the	the	DET
ejpam-1929	472	18	canonical	canonical	ADJ
ejpam-1929	472	19	marking	marking	NOUN
ejpam-1929	472	20	,	,	PUNCT
ejpam-1929	472	21	a	a	DET
ejpam-1929	472	22	contradiction	contradiction	NOUN
ejpam-1929	472	23	to	to	PART
ejpam-1929	472	24	theorem	theorem	VERB
ejpam-1929	472	25	13	13	NUM
ejpam-1929	472	26	.	.	PUNCT
ejpam-1929	473	1	case(ii	case(ii	ADJ
ejpam-1929	473	2	):	):	PUNCT
ejpam-1929	473	3	suppose	suppose	VERB
ejpam-1929	473	4	either	either	CCONJ
ejpam-1929	473	5	n	n	PRON
ejpam-1929	473	6	≡	≡	PROPN
ejpam-1929	473	7	1	1	NUM
ejpam-1929	473	8	(	(	PUNCT
ejpam-1929	473	9	mod	mod	NOUN
ejpam-1929	473	10	3	3	NUM
ejpam-1929	473	11	)	)	PUNCT
ejpam-1929	473	12	or	or	CCONJ
ejpam-1929	473	13	n	n	PRON
ejpam-1929	473	14	≡	≡	PROPN
ejpam-1929	473	15	2	2	NUM
ejpam-1929	473	16	(	(	PUNCT
ejpam-1929	473	17	mod	mod	NOUN
ejpam-1929	473	18	3	3	NUM
ejpam-1929	473	19	)	)	PUNCT
ejpam-1929	473	20	.	.	PUNCT
ejpam-1929	474	1	that	that	PRON
ejpam-1929	474	2	means	mean	VERB
ejpam-1929	474	3	,	,	PUNCT
ejpam-1929	474	4	3	3	NUM
ejpam-1929	474	5	does	do	AUX
ejpam-1929	474	6	not	not	PART
ejpam-1929	474	7	divide	divide	VERB
ejpam-1929	474	8	n	n	CCONJ
ejpam-1929	474	9	,	,	PUNCT
ejpam-1929	474	10	which	which	PRON
ejpam-1929	474	11	implies	imply	VERB
ejpam-1929	474	12	that	that	SCONJ
ejpam-1929	474	13	the	the	DET
ejpam-1929	474	14	vertex	vertex	NOUN
ejpam-1929	474	15	3	3	NUM
ejpam-1929	474	16	∈	∈	PROPN
ejpam-1929	474	17	un	un	PROPN
ejpam-1929	474	18	.	.	PUNCT
ejpam-1929	475	1	now	now	ADV
ejpam-1929	475	2	,	,	PUNCT
ejpam-1929	475	3	consider	consider	VERB
ejpam-1929	475	4	a	a	DET
ejpam-1929	475	5	cycle	cycle	NOUN
ejpam-1929	475	6	z	z	NOUN
ejpam-1929	475	7	=	=	SYM
ejpam-1929	476	1	(	(	PUNCT
ejpam-1929	476	2	0,1,2	0,1,2	NUM
ejpam-1929	476	3	,	,	PUNCT
ejpam-1929	476	4	(	(	PUNCT
ejpam-1929	476	5	n−	n−	NOUN
ejpam-1929	476	6	1	1	NUM
ejpam-1929	476	7	)	)	PUNCT
ejpam-1929	476	8	,	,	PUNCT
ejpam-1929	476	9	0	0	NUM
ejpam-1929	476	10	)	)	PUNCT
ejpam-1929	476	11	in	in	ADP
ejpam-1929	476	12	σn	σn	PROPN
ejpam-1929	476	13	.	.	PUNCT
ejpam-1929	477	1	since	since	SCONJ
ejpam-1929	477	2	1	1	NUM
ejpam-1929	477	3	∈	∈	PROPN
ejpam-1929	477	4	un	un	PROPN
ejpam-1929	477	5	and	and	CCONJ
ejpam-1929	477	6	(	(	PUNCT
ejpam-1929	477	7	n−	n−	NOUN
ejpam-1929	477	8	1	1	NUM
ejpam-1929	477	9	)	)	PUNCT
ejpam-1929	477	10	∈	∈	PROPN
ejpam-1929	477	11	un	un	NOUN
ejpam-1929	477	12	,	,	PUNCT
ejpam-1929	477	13	by	by	ADP
ejpam-1929	477	14	the	the	DET
ejpam-1929	477	15	definition	definition	NOUN
ejpam-1929	477	16	of	of	ADP
ejpam-1929	477	17	σn	σn	NOUN
ejpam-1929	477	18	,	,	PUNCT
ejpam-1929	477	19	d−(1	d−(1	NOUN
ejpam-1929	477	20	)	)	PUNCT
ejpam-1929	477	21	=	=	PUNCT
ejpam-1929	477	22	d−(n−	d−(n−	PROPN
ejpam-1929	477	23	1	1	NUM
ejpam-1929	477	24	)	)	PUNCT
ejpam-1929	477	25	=	=	SYM
ejpam-1929	477	26	0	0	X
ejpam-1929	477	27	.	.	PUNCT
ejpam-1929	478	1	it	it	PRON
ejpam-1929	478	2	follows	follow	VERB
ejpam-1929	478	3	that	that	SCONJ
ejpam-1929	478	4	in	in	ADP
ejpam-1929	478	5	the	the	DET
ejpam-1929	478	6	cycle	cycle	NOUN
ejpam-1929	478	7	z	z	NOUN
ejpam-1929	478	8	,	,	PUNCT
ejpam-1929	478	9	µσ(1	µσ(1	NOUN
ejpam-1929	478	10	)	)	PUNCT
ejpam-1929	478	11	=	=	SYM
ejpam-1929	478	12	µσ(n−	µσ(n−	VERB
ejpam-1929	478	13	1	1	X
ejpam-1929	478	14	)	)	PUNCT
ejpam-1929	478	15	=	=	PUNCT
ejpam-1929	479	1	+	+	PROPN
ejpam-1929	479	2	.	.	NOUN
ejpam-1929	480	1	since	since	SCONJ
ejpam-1929	480	2	the	the	DET
ejpam-1929	480	3	vertex	vertex	NOUN
ejpam-1929	480	4	0	0	PUNCT
ejpam-1929	480	5	is	be	AUX
ejpam-1929	480	6	adjacent	adjacent	ADJ
ejpam-1929	480	7	to	to	ADP
ejpam-1929	480	8	those	those	DET
ejpam-1929	480	9	vertices	vertex	NOUN
ejpam-1929	480	10	which	which	PRON
ejpam-1929	480	11	belong	belong	VERB
ejpam-1929	480	12	to	to	ADP
ejpam-1929	480	13	un	un	PROPN
ejpam-1929	480	14	,	,	PUNCT
ejpam-1929	480	15	d−(0	d−(0	NOUN
ejpam-1929	480	16	)	)	PUNCT
ejpam-1929	480	17	=	=	SYM
ejpam-1929	480	18	0	0	X
ejpam-1929	480	19	.	.	PUNCT
ejpam-1929	481	1	that	that	PRON
ejpam-1929	481	2	means	mean	VERB
ejpam-1929	481	3	,	,	PUNCT
ejpam-1929	481	4	µσ(0	µσ(0	NOUN
ejpam-1929	481	5	)	)	PUNCT
ejpam-1929	481	6	=	=	PUNCT
ejpam-1929	482	1	+	+	X
ejpam-1929	482	2	.	.	PUNCT
ejpam-1929	482	3	now	now	ADV
ejpam-1929	482	4	,	,	PUNCT
ejpam-1929	482	5	due	due	ADP
ejpam-1929	482	6	to	to	ADP
ejpam-1929	482	7	lemma	lemma	PROPN
ejpam-1929	482	8	4	4	NUM
ejpam-1929	482	9	and	and	CCONJ
ejpam-1929	482	10	lemma	lemma	PROPN
ejpam-1929	482	11	6	6	NUM
ejpam-1929	482	12	,	,	PUNCT
ejpam-1929	482	13	µσ(2	µσ(2	NUM
ejpam-1929	482	14	)	)	PUNCT
ejpam-1929	482	15	=	=	PUNCT
ejpam-1929	483	1	−.	−.	ADV
ejpam-1929	483	2	thus	thus	ADV
ejpam-1929	483	3	,	,	PUNCT
ejpam-1929	483	4	the	the	DET
ejpam-1929	483	5	cycle	cycle	NOUN
ejpam-1929	483	6	z	z	NOUN
ejpam-1929	483	7	is	be	AUX
ejpam-1929	483	8	c	c	NOUN
ejpam-1929	483	9	-inconsistent	-inconsistent	NOUN
ejpam-1929	483	10	,	,	PUNCT
ejpam-1929	483	11	whence	whence	ADP
ejpam-1929	483	12	σn	σn	NOUN
ejpam-1929	483	13	is	be	AUX
ejpam-1929	483	14	not	not	PART
ejpam-1929	483	15	c	c	NOUN
ejpam-1929	483	16	-consistent	-consistent	NOUN
ejpam-1929	483	17	,	,	PUNCT
ejpam-1929	483	18	a	a	DET
ejpam-1929	483	19	contradiction	contradiction	NOUN
ejpam-1929	483	20	to	to	ADP
ejpam-1929	483	21	the	the	DET
ejpam-1929	483	22	hypothesis	hypothesis	NOUN
ejpam-1929	483	23	.	.	PUNCT
ejpam-1929	484	1	thus	thus	ADV
ejpam-1929	484	2	,	,	PUNCT
ejpam-1929	484	3	this	this	DET
ejpam-1929	484	4	part	part	NOUN
ejpam-1929	484	5	of	of	ADP
ejpam-1929	484	6	the	the	DET
ejpam-1929	484	7	proof	proof	NOUN
ejpam-1929	484	8	is	be	AUX
ejpam-1929	484	9	complete	complete	ADJ
ejpam-1929	484	10	.	.	PUNCT
ejpam-1929	485	1	sufficiency	sufficiency	NOUN
ejpam-1929	485	2	:	:	PUNCT
ejpam-1929	485	3	next	next	ADV
ejpam-1929	485	4	,	,	PUNCT
ejpam-1929	485	5	suppose	suppose	VERB
ejpam-1929	485	6	n	n	PRON
ejpam-1929	485	7	is	be	AUX
ejpam-1929	485	8	odd	odd	ADJ
ejpam-1929	485	9	,	,	PUNCT
ejpam-1929	485	10	2	2	NUM
ejpam-1929	485	11	,	,	PUNCT
ejpam-1929	485	12	6	6	NUM
ejpam-1929	485	13	or	or	CCONJ
ejpam-1929	485	14	a	a	DET
ejpam-1929	485	15	multiple	multiple	NOUN
ejpam-1929	485	16	of	of	ADP
ejpam-1929	485	17	4	4	NUM
ejpam-1929	485	18	.	.	PUNCT
ejpam-1929	486	1	case(i	case(i	PROPN
ejpam-1929	486	2	):	):	PUNCT
ejpam-1929	486	3	let	let	VERB
ejpam-1929	486	4	n	n	PRON
ejpam-1929	486	5	be	be	AUX
ejpam-1929	486	6	odd	odd	ADJ
ejpam-1929	486	7	,	,	PUNCT
ejpam-1929	486	8	and	and	CCONJ
ejpam-1929	486	9	n	n	CCONJ
ejpam-1929	486	10	=	=	SYM
ejpam-1929	486	11	p	p	NOUN
ejpam-1929	486	12	a1	a1	NOUN
ejpam-1929	486	13	1	1	NUM
ejpam-1929	486	14	p	p	NOUN
ejpam-1929	486	15	a2	a2	PROPN
ejpam-1929	486	16	2	2	NUM
ejpam-1929	486	17	,	,	PUNCT
ejpam-1929	486	18	where	where	SCONJ
ejpam-1929	486	19	p1	p1	NOUN
ejpam-1929	486	20	and	and	CCONJ
ejpam-1929	486	21	p2	p2	PROPN
ejpam-1929	486	22	are	be	AUX
ejpam-1929	486	23	distinct	distinct	ADJ
ejpam-1929	486	24	odd	odd	ADJ
ejpam-1929	486	25	primes	prime	NOUN
ejpam-1929	486	26	.	.	PUNCT
ejpam-1929	487	1	using	use	VERB
ejpam-1929	487	2	lemma	lemma	PROPN
ejpam-1929	487	3	7	7	NUM
ejpam-1929	487	4	one	one	NOUN
ejpam-1929	487	5	can	can	AUX
ejpam-1929	487	6	easily	easily	ADV
ejpam-1929	487	7	see	see	VERB
ejpam-1929	487	8	that	that	SCONJ
ejpam-1929	487	9	all	all	DET
ejpam-1929	487	10	the	the	DET
ejpam-1929	487	11	vertices	vertex	NOUN
ejpam-1929	487	12	in	in	ADP
ejpam-1929	487	13	σn	σn	NOUN
ejpam-1929	487	14	which	which	PRON
ejpam-1929	487	15	are	be	AUX
ejpam-1929	487	16	multiples	multiple	NOUN
ejpam-1929	487	17	of	of	ADP
ejpam-1929	487	18	p1	p1	NOUN
ejpam-1929	487	19	and	and	CCONJ
ejpam-1929	487	20	p2	p2	PROPN
ejpam-1929	487	21	are	be	AUX
ejpam-1929	487	22	even	even	ADV
ejpam-1929	487	23	and	and	CCONJ
ejpam-1929	487	24	all	all	DET
ejpam-1929	487	25	other	other	ADJ
ejpam-1929	487	26	vertices	vertex	NOUN
ejpam-1929	487	27	belong	belong	VERB
ejpam-1929	487	28	to	to	ADP
ejpam-1929	487	29	un	un	PROPN
ejpam-1929	487	30	.	.	PUNCT
ejpam-1929	488	1	so	so	ADV
ejpam-1929	488	2	,	,	PUNCT
ejpam-1929	488	3	their	their	PRON
ejpam-1929	488	4	negative	negative	ADJ
ejpam-1929	488	5	degrees	degree	NOUN
ejpam-1929	488	6	are	be	AUX
ejpam-1929	488	7	zero	zero	NUM
ejpam-1929	488	8	.	.	PUNCT
ejpam-1929	489	1	hence	hence	ADV
ejpam-1929	489	2	,	,	PUNCT
ejpam-1929	489	3	all	all	DET
ejpam-1929	489	4	the	the	DET
ejpam-1929	489	5	vertices	vertex	NOUN
ejpam-1929	489	6	of	of	ADP
ejpam-1929	489	7	σn	σn	NOUN
ejpam-1929	489	8	are	be	AUX
ejpam-1929	489	9	marked	mark	VERB
ejpam-1929	489	10	positively	positively	ADV
ejpam-1929	489	11	under	under	ADP
ejpam-1929	489	12	the	the	DET
ejpam-1929	489	13	canonical	canonical	ADJ
ejpam-1929	489	14	marking	marking	NOUN
ejpam-1929	489	15	.	.	PUNCT
ejpam-1929	490	1	hence	hence	ADV
ejpam-1929	490	2	,	,	PUNCT
ejpam-1929	490	3	σn	σn	PROPN
ejpam-1929	490	4	is	be	AUX
ejpam-1929	490	5	c	c	NOUN
ejpam-1929	490	6	-consistent	-consistent	NOUN
ejpam-1929	490	7	.	.	PUNCT
ejpam-1929	491	1	case(ii	case(ii	ADJ
ejpam-1929	491	2	):	):	PUNCT
ejpam-1929	491	3	suppose	suppose	VERB
ejpam-1929	491	4	n=	n=	ADJ
ejpam-1929	491	5	2,6	2,6	NUM
ejpam-1929	491	6	in	in	ADP
ejpam-1929	491	7	σn	σn	PROPN
ejpam-1929	491	8	.	.	PUNCT
ejpam-1929	492	1	then	then	ADV
ejpam-1929	492	2	,	,	PUNCT
ejpam-1929	492	3	we	we	PRON
ejpam-1929	492	4	can	can	AUX
ejpam-1929	492	5	easily	easily	ADV
ejpam-1929	492	6	verify	verify	VERB
ejpam-1929	492	7	that	that	PRON
ejpam-1929	492	8	σ2	σ2	NOUN
ejpam-1929	492	9	and	and	CCONJ
ejpam-1929	492	10	σ6	σ6	NOUN
ejpam-1929	492	11	are	be	AUX
ejpam-1929	492	12	c	c	NOUN
ejpam-1929	492	13	-consistent	-consistent	NOUN
ejpam-1929	492	14	.	.	PUNCT
ejpam-1929	493	1	case(iii	case(iii	PROPN
ejpam-1929	493	2	):	):	PUNCT
ejpam-1929	493	3	suppose	suppose	VERB
ejpam-1929	493	4	n	n	PRON
ejpam-1929	493	5	is	be	AUX
ejpam-1929	493	6	a	a	DET
ejpam-1929	493	7	multiple	multiple	NOUN
ejpam-1929	493	8	of	of	ADP
ejpam-1929	493	9	4	4	NUM
ejpam-1929	493	10	.	.	PUNCT
ejpam-1929	494	1	here	here	ADV
ejpam-1929	494	2	n	n	AUX
ejpam-1929	494	3	is	be	AUX
ejpam-1929	494	4	even	even	ADV
ejpam-1929	494	5	and	and	CCONJ
ejpam-1929	494	6	by	by	ADP
ejpam-1929	494	7	theorem	theorem	NOUN
ejpam-1929	494	8	5	5	NUM
ejpam-1929	494	9	σn	σn	NOUN
ejpam-1929	494	10	∼=	∼=	NOUN
ejpam-1929	494	11	sn	sn	NOUN
ejpam-1929	494	12	and	and	CCONJ
ejpam-1929	494	13	by	by	ADP
ejpam-1929	494	14	theorem	theorem	NOUN
ejpam-1929	494	15	14	14	NUM
ejpam-1929	494	16	,	,	PUNCT
ejpam-1929	494	17	σn	σn	PROPN
ejpam-1929	494	18	is	be	AUX
ejpam-1929	494	19	c−consistent	c−consistent	PROPN
ejpam-1929	494	20	.	.	PUNCT
ejpam-1929	495	1	d.	d.	PROPN
ejpam-1929	495	2	sinha	sinha	PROPN
ejpam-1929	495	3	,	,	PUNCT
ejpam-1929	495	4	a.	a.	NOUN
ejpam-1929	495	5	dhama	dhama	PROPN
ejpam-1929	495	6	,	,	PUNCT
ejpam-1929	495	7	b.	b.	PROPN
ejpam-1929	495	8	acharya	acharya	PROPN
ejpam-1929	495	9	/	/	SYM
ejpam-1929	495	10	eur	eur	PROPN
ejpam-1929	495	11	.	.	PUNCT
ejpam-1929	496	1	j.	j.	PROPN
ejpam-1929	496	2	pure	pure	PROPN
ejpam-1929	496	3	appl	appl	PROPN
ejpam-1929	496	4	.	.	PROPN
ejpam-1929	496	5	math	math	PROPN
ejpam-1929	496	6	,	,	PUNCT
ejpam-1929	496	7	6	6	NUM
ejpam-1929	496	8	(	(	PUNCT
ejpam-1929	496	9	2013	2013	NUM
ejpam-1929	496	10	)	)	PUNCT
ejpam-1929	496	11	,	,	PUNCT
ejpam-1929	496	12	189	189	NUM
ejpam-1929	496	13	-	-	SYM
ejpam-1929	496	14	210	210	NUM
ejpam-1929	496	15	206	206	NUM
ejpam-1929	496	16	7	7	NUM
ejpam-1929	496	17	.	.	PUNCT
ejpam-1929	497	1	balance	balance	NOUN
ejpam-1929	497	2	in	in	ADP
ejpam-1929	497	3	certain	certain	ADJ
ejpam-1929	497	4	derived	derive	VERB
ejpam-1929	497	5	sigraphs	sigraph	NOUN
ejpam-1929	497	6	in	in	ADP
ejpam-1929	497	7	this	this	DET
ejpam-1929	497	8	section	section	NOUN
ejpam-1929	497	9	,	,	PUNCT
ejpam-1929	497	10	we	we	PRON
ejpam-1929	497	11	consider	consider	VERB
ejpam-1929	497	12	the	the	DET
ejpam-1929	497	13	conditions	condition	NOUN
ejpam-1929	497	14	that	that	PRON
ejpam-1929	497	15	a	a	DET
ejpam-1929	497	16	given	give	VERB
ejpam-1929	497	17	sigraph	sigraph	NOUN
ejpam-1929	497	18	must	must	AUX
ejpam-1929	497	19	satisfy	satisfy	VERB
ejpam-1929	497	20	in	in	ADP
ejpam-1929	497	21	order	order	NOUN
ejpam-1929	497	22	that	that	SCONJ
ejpam-1929	497	23	its	its	PRON
ejpam-1929	497	24	certain	certain	ADJ
ejpam-1929	497	25	derived	derive	VERB
ejpam-1929	497	26	sigraphs	sigraph	NOUN
ejpam-1929	497	27	are	be	AUX
ejpam-1929	497	28	balanced	balanced	ADJ
ejpam-1929	497	29	.	.	PUNCT
ejpam-1929	498	1	corollary	corollary	ADJ
ejpam-1929	498	2	1	1	NUM
ejpam-1929	498	3	.	.	PUNCT
ejpam-1929	499	1	for	for	ADP
ejpam-1929	499	2	the	the	DET
ejpam-1929	499	3	unitary	unitary	ADJ
ejpam-1929	499	4	addition	addition	NOUN
ejpam-1929	499	5	cayley	cayley	NOUN
ejpam-1929	499	6	sigraph	sigraph	NOUN
ejpam-1929	499	7	σn	σn	NOUN
ejpam-1929	499	8	=	=	SYM
ejpam-1929	499	9	(	(	PUNCT
ejpam-1929	499	10	σ	σ	PROPN
ejpam-1929	499	11	u	u	PROPN
ejpam-1929	499	12	n	n	NUM
ejpam-1929	499	13	,	,	PUNCT
ejpam-1929	499	14	σ	σ	PROPN
ejpam-1929	499	15	)	)	PUNCT
ejpam-1929	499	16	,	,	PUNCT
ejpam-1929	499	17	its	its	PRON
ejpam-1929	499	18	negation	negation	NOUN
ejpam-1929	499	19	sigraph	sigraph	NOUN
ejpam-1929	499	20	η(σn	η(σn	PROPN
ejpam-1929	499	21	)	)	PUNCT
ejpam-1929	499	22	is	be	AUX
ejpam-1929	499	23	balanced	balance	VERB
ejpam-1929	499	24	if	if	SCONJ
ejpam-1929	499	25	and	and	CCONJ
ejpam-1929	499	26	only	only	ADV
ejpam-1929	499	27	if	if	SCONJ
ejpam-1929	499	28	either	either	CCONJ
ejpam-1929	499	29	n=	n=	ADJ
ejpam-1929	499	30	3	3	NUM
ejpam-1929	499	31	or	or	CCONJ
ejpam-1929	499	32	n	n	NOUN
ejpam-1929	499	33	is	be	AUX
ejpam-1929	499	34	even	even	ADV
ejpam-1929	499	35	.	.	PUNCT
ejpam-1929	500	1	proof	proof	NOUN
ejpam-1929	500	2	.	.	PUNCT
ejpam-1929	501	1	first	first	ADV
ejpam-1929	501	2	,	,	PUNCT
ejpam-1929	501	3	suppose	suppose	VERB
ejpam-1929	501	4	η(σn	η(σn	NOUN
ejpam-1929	501	5	)	)	PUNCT
ejpam-1929	501	6	is	be	AUX
ejpam-1929	501	7	balanced	balanced	ADJ
ejpam-1929	501	8	.	.	PUNCT
ejpam-1929	502	1	assume	assume	VERB
ejpam-1929	502	2	that	that	SCONJ
ejpam-1929	502	3	the	the	DET
ejpam-1929	502	4	conclusion	conclusion	NOUN
ejpam-1929	502	5	is	be	AUX
ejpam-1929	502	6	false	false	ADJ
ejpam-1929	502	7	.	.	PUNCT
ejpam-1929	503	1	suppose	suppose	VERB
ejpam-1929	503	2	n	n	PRON
ejpam-1929	503	3	is	be	AUX
ejpam-1929	503	4	odd	odd	ADJ
ejpam-1929	503	5	and	and	CCONJ
ejpam-1929	503	6	not	not	PART
ejpam-1929	503	7	equal	equal	ADJ
ejpam-1929	503	8	to	to	ADP
ejpam-1929	503	9	3	3	NUM
ejpam-1929	503	10	.	.	PUNCT
ejpam-1929	504	1	then	then	ADV
ejpam-1929	504	2	,	,	PUNCT
ejpam-1929	504	3	2	2	NUM
ejpam-1929	504	4	∈	∈	PROPN
ejpam-1929	504	5	un	un	NOUN
ejpam-1929	504	6	.	.	PROPN
ejpam-1929	505	1	since	since	SCONJ
ejpam-1929	505	2	0	0	NUM
ejpam-1929	505	3	+	+	SYM
ejpam-1929	505	4	2	2	NUM
ejpam-1929	505	5	=	=	SYM
ejpam-1929	505	6	2	2	NUM
ejpam-1929	505	7	∈	∈	NOUN
ejpam-1929	505	8	un	un	NOUN
ejpam-1929	505	9	,	,	PUNCT
ejpam-1929	505	10	0	0	NUM
ejpam-1929	505	11	and	and	CCONJ
ejpam-1929	505	12	2	2	NUM
ejpam-1929	505	13	are	be	AUX
ejpam-1929	505	14	adjacent	adjacent	ADJ
ejpam-1929	505	15	in	in	ADP
ejpam-1929	505	16	σu	σu	PROPN
ejpam-1929	505	17	n	n	PROPN
ejpam-1929	505	18	and	and	CCONJ
ejpam-1929	505	19	2	2	NUM
ejpam-1929	505	20	+	+	NUM
ejpam-1929	505	21	(	(	PUNCT
ejpam-1929	505	22	n−	n−	NOUN
ejpam-1929	505	23	1	1	NUM
ejpam-1929	505	24	)	)	PUNCT
ejpam-1929	505	25	=	=	SYM
ejpam-1929	505	26	n+	n+	PUNCT
ejpam-1929	505	27	1	1	NUM
ejpam-1929	505	28	=	=	SYM
ejpam-1929	505	29	1	1	NUM
ejpam-1929	505	30	∈	∈	PROPN
ejpam-1929	505	31	un	un	NOUN
ejpam-1929	505	32	.	.	PUNCT
ejpam-1929	506	1	this	this	PRON
ejpam-1929	506	2	implies	imply	VERB
ejpam-1929	506	3	,	,	PUNCT
ejpam-1929	506	4	2	2	NUM
ejpam-1929	506	5	and	and	CCONJ
ejpam-1929	506	6	n−	n−	NOUN
ejpam-1929	506	7	1	1	NUM
ejpam-1929	506	8	are	be	AUX
ejpam-1929	506	9	adjacent	adjacent	ADJ
ejpam-1929	506	10	in	in	ADP
ejpam-1929	506	11	σu	σu	PROPN
ejpam-1929	506	12	n.	n.	PROPN
ejpam-1929	506	13	thus	thus	ADV
ejpam-1929	506	14	,	,	PUNCT
ejpam-1929	506	15	we	we	PRON
ejpam-1929	506	16	can	can	AUX
ejpam-1929	506	17	consider	consider	VERB
ejpam-1929	506	18	a	a	DET
ejpam-1929	506	19	triangle	triangle	NOUN
ejpam-1929	506	20	t	t	NOUN
ejpam-1929	506	21	:	:	PUNCT
ejpam-1929	506	22	(	(	PUNCT
ejpam-1929	506	23	0,2	0,2	NUM
ejpam-1929	506	24	,	,	PUNCT
ejpam-1929	506	25	n−1,0	n−1,0	NUM
ejpam-1929	506	26	)	)	PUNCT
ejpam-1929	506	27	in	in	ADP
ejpam-1929	506	28	σn	σn	PROPN
ejpam-1929	506	29	.	.	PUNCT
ejpam-1929	507	1	since	since	SCONJ
ejpam-1929	507	2	2	2	NUM
ejpam-1929	507	3	,	,	PUNCT
ejpam-1929	507	4	n−1	n−1	PROPN
ejpam-1929	507	5	∈	∈	PROPN
ejpam-1929	507	6	un	un	NOUN
ejpam-1929	507	7	,	,	PUNCT
ejpam-1929	507	8	by	by	ADP
ejpam-1929	507	9	the	the	DET
ejpam-1929	507	10	definition	definition	NOUN
ejpam-1929	507	11	of	of	ADP
ejpam-1929	507	12	σn	σn	PRON
ejpam-1929	507	13	all	all	DET
ejpam-1929	507	14	the	the	DET
ejpam-1929	507	15	edges	edge	NOUN
ejpam-1929	507	16	of	of	ADP
ejpam-1929	507	17	t	t	PROPN
ejpam-1929	507	18	are	be	AUX
ejpam-1929	507	19	positive	positive	ADJ
ejpam-1929	507	20	.	.	PUNCT
ejpam-1929	508	1	that	that	PRON
ejpam-1929	508	2	means	mean	VERB
ejpam-1929	508	3	,	,	PUNCT
ejpam-1929	508	4	all	all	DET
ejpam-1929	508	5	the	the	DET
ejpam-1929	508	6	edges	edge	NOUN
ejpam-1929	508	7	of	of	ADP
ejpam-1929	508	8	the	the	DET
ejpam-1929	508	9	triangle	triangle	NOUN
ejpam-1929	508	10	t	t	NOUN
ejpam-1929	508	11	are	be	AUX
ejpam-1929	508	12	negative	negative	ADJ
ejpam-1929	508	13	in	in	ADP
ejpam-1929	508	14	η(σn	η(σn	NOUN
ejpam-1929	508	15	)	)	PUNCT
ejpam-1929	508	16	.	.	PUNCT
ejpam-1929	509	1	thus	thus	ADV
ejpam-1929	509	2	,	,	PUNCT
ejpam-1929	509	3	η(σn	η(σn	NOUN
ejpam-1929	509	4	)	)	PUNCT
ejpam-1929	509	5	is	be	AUX
ejpam-1929	509	6	unbalanced	unbalanced	ADJ
ejpam-1929	509	7	,	,	PUNCT
ejpam-1929	509	8	which	which	PRON
ejpam-1929	509	9	contradicts	contradict	VERB
ejpam-1929	509	10	the	the	DET
ejpam-1929	509	11	hypothesis	hypothesis	NOUN
ejpam-1929	509	12	.	.	PUNCT
ejpam-1929	510	1	conversely	conversely	ADV
ejpam-1929	510	2	,	,	PUNCT
ejpam-1929	510	3	suppose	suppose	VERB
ejpam-1929	510	4	n	n	PRON
ejpam-1929	510	5	is	be	AUX
ejpam-1929	510	6	even	even	ADV
ejpam-1929	510	7	or	or	CCONJ
ejpam-1929	510	8	n	n	CCONJ
ejpam-1929	510	9	=	=	SYM
ejpam-1929	510	10	3	3	X
ejpam-1929	510	11	.	.	PUNCT
ejpam-1929	511	1	now	now	ADV
ejpam-1929	511	2	,	,	PUNCT
ejpam-1929	511	3	due	due	ADP
ejpam-1929	511	4	to	to	ADP
ejpam-1929	511	5	theorem	theorem	VERB
ejpam-1929	511	6	6	6	NUM
ejpam-1929	511	7	,	,	PUNCT
ejpam-1929	511	8	su	su	PROPN
ejpam-1929	511	9	n	n	PROPN
ejpam-1929	511	10	is	be	AUX
ejpam-1929	511	11	bipartite	bipartite	ADJ
ejpam-1929	511	12	and	and	CCONJ
ejpam-1929	511	13	due	due	ADJ
ejpam-1929	511	14	to	to	ADP
ejpam-1929	511	15	theorem	theorem	NOUN
ejpam-1929	511	16	7	7	NUM
ejpam-1929	511	17	,	,	PUNCT
ejpam-1929	511	18	σn	σn	PROPN
ejpam-1929	511	19	is	be	AUX
ejpam-1929	511	20	balanced	balanced	ADJ
ejpam-1929	511	21	.	.	PUNCT
ejpam-1929	512	1	thus	thus	ADV
ejpam-1929	512	2	,	,	PUNCT
ejpam-1929	512	3	η(σn	η(σn	NOUN
ejpam-1929	512	4	)	)	PUNCT
ejpam-1929	512	5	is	be	AUX
ejpam-1929	512	6	balanced	balance	VERB
ejpam-1929	512	7	.	.	PUNCT
ejpam-1929	513	1	theorem	theorem	VERB
ejpam-1929	513	2	16	16	NUM
ejpam-1929	513	3	(	(	PUNCT
ejpam-1929	513	4	[	[	X
ejpam-1929	513	5	4	4	NUM
ejpam-1929	513	6	]	]	NUM
ejpam-1929	513	7	)	)	PUNCT
ejpam-1929	513	8	.	.	PUNCT
ejpam-1929	514	1	for	for	ADP
ejpam-1929	514	2	a	a	DET
ejpam-1929	514	3	sigraph	sigraph	NOUN
ejpam-1929	514	4	s	s	NOUN
ejpam-1929	514	5	,	,	PUNCT
ejpam-1929	514	6	its	its	PRON
ejpam-1929	514	7	line	line	NOUN
ejpam-1929	514	8	sigraph	sigraph	NOUN
ejpam-1929	514	9	l(s	l(s	PROPN
ejpam-1929	514	10	)	)	PUNCT
ejpam-1929	514	11	is	be	AUX
ejpam-1929	514	12	balanced	balance	VERB
ejpam-1929	514	13	if	if	SCONJ
ejpam-1929	514	14	and	and	CCONJ
ejpam-1929	514	15	only	only	ADV
ejpam-1929	514	16	if	if	SCONJ
ejpam-1929	514	17	the	the	DET
ejpam-1929	514	18	following	follow	VERB
ejpam-1929	514	19	conditions	condition	NOUN
ejpam-1929	514	20	hold	hold	VERB
ejpam-1929	514	21	:	:	PUNCT
ejpam-1929	514	22	(	(	PUNCT
ejpam-1929	514	23	i	i	NOUN
ejpam-1929	514	24	)	)	PUNCT
ejpam-1929	514	25	for	for	ADP
ejpam-1929	514	26	any	any	DET
ejpam-1929	514	27	cycle	cycle	NOUN
ejpam-1929	514	28	z	z	NOUN
ejpam-1929	514	29	in	in	ADP
ejpam-1929	514	30	s	s	PROPN
ejpam-1929	514	31	,	,	PUNCT
ejpam-1929	514	32	(	(	PUNCT
ejpam-1929	514	33	a	a	X
ejpam-1929	514	34	)	)	PUNCT
ejpam-1929	514	35	if	if	SCONJ
ejpam-1929	514	36	z	z	NOUN
ejpam-1929	514	37	is	be	AUX
ejpam-1929	514	38	all	all	ADV
ejpam-1929	514	39	-	-	PUNCT
ejpam-1929	514	40	negative	negative	ADJ
ejpam-1929	514	41	,	,	PUNCT
ejpam-1929	514	42	then	then	ADV
ejpam-1929	514	43	z	z	PROPN
ejpam-1929	514	44	has	have	AUX
ejpam-1929	514	45	even	even	ADV
ejpam-1929	514	46	length	length	NOUN
ejpam-1929	514	47	,	,	PUNCT
ejpam-1929	514	48	(	(	PUNCT
ejpam-1929	514	49	b	b	X
ejpam-1929	514	50	)	)	PUNCT
ejpam-1929	514	51	if	if	SCONJ
ejpam-1929	514	52	z	z	NOUN
ejpam-1929	514	53	is	be	AUX
ejpam-1929	514	54	heterogeneous	heterogeneous	ADJ
ejpam-1929	514	55	,	,	PUNCT
ejpam-1929	514	56	then	then	ADV
ejpam-1929	514	57	z	z	PROPN
ejpam-1929	514	58	has	have	VERB
ejpam-1929	514	59	an	an	DET
ejpam-1929	514	60	even	even	ADJ
ejpam-1929	514	61	number	number	NOUN
ejpam-1929	514	62	of	of	ADP
ejpam-1929	514	63	negative	negative	ADJ
ejpam-1929	514	64	sections	section	NOUN
ejpam-1929	514	65	with	with	ADP
ejpam-1929	514	66	even	even	ADV
ejpam-1929	514	67	length	length	NOUN
ejpam-1929	514	68	,	,	PUNCT
ejpam-1929	514	69	and	and	CCONJ
ejpam-1929	514	70	(	(	PUNCT
ejpam-1929	514	71	ii	ii	NOUN
ejpam-1929	514	72	)	)	PUNCT
ejpam-1929	514	73	for	for	ADP
ejpam-1929	514	74	v	v	NUM
ejpam-1929	514	75	∈	∈	PROPN
ejpam-1929	514	76	s	s	NOUN
ejpam-1929	514	77	,	,	PUNCT
ejpam-1929	514	78	if	if	SCONJ
ejpam-1929	514	79	d(v	d(v	PROPN
ejpam-1929	514	80	)	)	PUNCT
ejpam-1929	514	81	>	>	X
ejpam-1929	514	82	2	2	NUM
ejpam-1929	514	83	,	,	PUNCT
ejpam-1929	514	84	then	then	ADV
ejpam-1929	514	85	there	there	PRON
ejpam-1929	514	86	is	be	VERB
ejpam-1929	514	87	at	at	ADP
ejpam-1929	514	88	most	most	ADV
ejpam-1929	514	89	one	one	NUM
ejpam-1929	514	90	negative	negative	ADJ
ejpam-1929	514	91	edge	edge	NOUN
ejpam-1929	514	92	incident	incident	NOUN
ejpam-1929	514	93	at	at	ADP
ejpam-1929	514	94	v	v	NOUN
ejpam-1929	514	95	in	in	ADP
ejpam-1929	514	96	s.	s.	PROPN
ejpam-1929	514	97	corollary	corollary	PROPN
ejpam-1929	514	98	2	2	PROPN
ejpam-1929	514	99	.	.	PUNCT
ejpam-1929	515	1	for	for	ADP
ejpam-1929	515	2	the	the	DET
ejpam-1929	515	3	unitary	unitary	ADJ
ejpam-1929	515	4	addition	addition	NOUN
ejpam-1929	515	5	cayley	cayley	NOUN
ejpam-1929	515	6	sigraph	sigraph	NOUN
ejpam-1929	515	7	σn	σn	NOUN
ejpam-1929	515	8	,	,	PUNCT
ejpam-1929	515	9	its	its	PRON
ejpam-1929	515	10	line	line	NOUN
ejpam-1929	515	11	sigraph	sigraph	PROPN
ejpam-1929	515	12	l(σn	l(σn	NOUN
ejpam-1929	515	13	)	)	PUNCT
ejpam-1929	515	14	is	be	AUX
ejpam-1929	515	15	balanced	balance	VERB
ejpam-1929	515	16	if	if	SCONJ
ejpam-1929	515	17	and	and	CCONJ
ejpam-1929	515	18	only	only	ADV
ejpam-1929	515	19	if	if	SCONJ
ejpam-1929	515	20	n=	n=	ADJ
ejpam-1929	515	21	pa	pa	PROPN
ejpam-1929	515	22	,	,	PUNCT
ejpam-1929	515	23	where	where	SCONJ
ejpam-1929	515	24	p	p	NOUN
ejpam-1929	515	25	is	be	AUX
ejpam-1929	515	26	a	a	DET
ejpam-1929	515	27	prime	prime	ADJ
ejpam-1929	515	28	number	number	NOUN
ejpam-1929	515	29	.	.	PUNCT
ejpam-1929	516	1	proof	proof	NOUN
ejpam-1929	516	2	.	.	PUNCT
ejpam-1929	517	1	suppose	suppose	VERB
ejpam-1929	517	2	l(σn	l(σn	NOUN
ejpam-1929	517	3	)	)	PUNCT
ejpam-1929	517	4	is	be	AUX
ejpam-1929	517	5	balanced	balance	VERB
ejpam-1929	517	6	for	for	ADP
ejpam-1929	517	7	the	the	DET
ejpam-1929	517	8	unitary	unitary	ADJ
ejpam-1929	517	9	addition	addition	NOUN
ejpam-1929	517	10	cayley	cayley	NOUN
ejpam-1929	517	11	sigraph	sigraph	NOUN
ejpam-1929	517	12	σn	σn	PROPN
ejpam-1929	517	13	.	.	PUNCT
ejpam-1929	517	14	assume	assume	VERB
ejpam-1929	517	15	that	that	SCONJ
ejpam-1929	517	16	the	the	DET
ejpam-1929	517	17	conclusion	conclusion	NOUN
ejpam-1929	517	18	is	be	AUX
ejpam-1929	517	19	false	false	ADJ
ejpam-1929	517	20	.	.	PUNCT
ejpam-1929	518	1	let	let	VERB
ejpam-1929	518	2	n	n	PRON
ejpam-1929	518	3	have	have	VERB
ejpam-1929	518	4	at	at	ADV
ejpam-1929	518	5	least	least	ADV
ejpam-1929	518	6	two	two	NUM
ejpam-1929	518	7	distinct	distinct	ADJ
ejpam-1929	518	8	prime	prime	ADJ
ejpam-1929	518	9	factors	factor	NOUN
ejpam-1929	518	10	.	.	PUNCT
ejpam-1929	519	1	suppose	suppose	VERB
ejpam-1929	519	2	p1	p1	NOUN
ejpam-1929	519	3	and	and	CCONJ
ejpam-1929	519	4	p2	p2	PROPN
ejpam-1929	519	5	are	be	AUX
ejpam-1929	519	6	two	two	NUM
ejpam-1929	519	7	smallest	small	ADJ
ejpam-1929	519	8	prime	prime	ADJ
ejpam-1929	519	9	factors	factor	NOUN
ejpam-1929	519	10	of	of	ADP
ejpam-1929	519	11	n	n	PRON
ejpam-1929	519	12	such	such	ADJ
ejpam-1929	519	13	that	that	DET
ejpam-1929	519	14	p1	p1	PROPN
ejpam-1929	519	15	<	<	X
ejpam-1929	519	16	p2	p2	PROPN
ejpam-1929	519	17	.	.	PUNCT
ejpam-1929	520	1	it	it	PRON
ejpam-1929	520	2	is	be	AUX
ejpam-1929	520	3	shown	show	VERB
ejpam-1929	520	4	in	in	ADP
ejpam-1929	520	5	the	the	DET
ejpam-1929	520	6	proof	proof	NOUN
ejpam-1929	520	7	of	of	ADP
ejpam-1929	520	8	theorem	theorem	ADJ
ejpam-1929	520	9	7	7	NUM
ejpam-1929	520	10	,	,	PUNCT
ejpam-1929	520	11	p1	p1	NOUN
ejpam-1929	520	12	is	be	AUX
ejpam-1929	520	13	adjacent	adjacent	ADJ
ejpam-1929	520	14	with	with	ADP
ejpam-1929	520	15	1	1	NUM
ejpam-1929	520	16	and	and	CCONJ
ejpam-1929	520	17	p2	p2	NOUN
ejpam-1929	520	18	.	.	PUNCT
ejpam-1929	521	1	suppose	suppose	VERB
ejpam-1929	521	2	αp2	αp2	ADJ
ejpam-1929	521	3	=	=	NOUN
ejpam-1929	521	4	n	n	NOUN
ejpam-1929	521	5	for	for	ADP
ejpam-1929	521	6	any	any	DET
ejpam-1929	521	7	positive	positive	ADJ
ejpam-1929	521	8	integer	integer	NOUN
ejpam-1929	521	9	α	α	NOUN
ejpam-1929	521	10	.	.	PUNCT
ejpam-1929	522	1	now	now	ADV
ejpam-1929	522	2	,	,	PUNCT
ejpam-1929	522	3	(	(	PUNCT
ejpam-1929	522	4	α−	α−	ADP
ejpam-1929	522	5	1)p2	1)p2	NUM
ejpam-1929	522	6	+	+	NOUN
ejpam-1929	522	7	p1	p1	NOUN
ejpam-1929	522	8	=	=	SYM
ejpam-1929	522	9	αp2−	αp2−	VERB
ejpam-1929	522	10	p2	p2	NOUN
ejpam-1929	522	11	+	+	CCONJ
ejpam-1929	522	12	p1	p1	NOUN
ejpam-1929	522	13	=	=	SYM
ejpam-1929	522	14	n−	n−	NOUN
ejpam-1929	522	15	p2	p2	NOUN
ejpam-1929	522	16	+	+	CCONJ
ejpam-1929	522	17	p1	p1	NOUN
ejpam-1929	522	18	=	=	SYM
ejpam-1929	522	19	n−	n−	PROPN
ejpam-1929	522	20	(	(	PUNCT
ejpam-1929	522	21	p2−	p2−	NUM
ejpam-1929	522	22	p1	p1	NOUN
ejpam-1929	522	23	)	)	PUNCT
ejpam-1929	522	24	since	since	SCONJ
ejpam-1929	522	25	p2−	p2−	NUM
ejpam-1929	522	26	p1	p1	PROPN
ejpam-1929	522	27	∈	∈	PROPN
ejpam-1929	522	28	un	un	NOUN
ejpam-1929	522	29	,	,	PUNCT
ejpam-1929	522	30	by	by	ADP
ejpam-1929	522	31	lemma	lemma	PROPN
ejpam-1929	522	32	2	2	NUM
ejpam-1929	522	33	n−	n−	PROPN
ejpam-1929	522	34	(	(	PUNCT
ejpam-1929	522	35	p2−	p2−	NUM
ejpam-1929	522	36	p1	p1	NOUN
ejpam-1929	522	37	)	)	PUNCT
ejpam-1929	522	38	∈	∈	PROPN
ejpam-1929	522	39	un	un	PROPN
ejpam-1929	522	40	,	,	PUNCT
ejpam-1929	522	41	whence	whence	X
ejpam-1929	522	42	(	(	PUNCT
ejpam-1929	522	43	α−	α−	ADP
ejpam-1929	522	44	1)p2	1)p2	NUM
ejpam-1929	522	45	+	+	CCONJ
ejpam-1929	522	46	p1	p1	PROPN
ejpam-1929	522	47	∈	∈	PROPN
ejpam-1929	522	48	un	un	PROPN
ejpam-1929	522	49	.	.	PUNCT
ejpam-1929	523	1	this	this	PRON
ejpam-1929	523	2	shows	show	VERB
ejpam-1929	523	3	that	that	SCONJ
ejpam-1929	523	4	(	(	PUNCT
ejpam-1929	523	5	α−	α−	ADP
ejpam-1929	523	6	1)p2	1)p2	PROPN
ejpam-1929	523	7	is	be	AUX
ejpam-1929	523	8	adjacent	adjacent	ADJ
ejpam-1929	523	9	with	with	ADP
ejpam-1929	523	10	p1	p1	PROPN
ejpam-1929	523	11	.	.	PUNCT
ejpam-1929	524	1	clearly	clearly	ADV
ejpam-1929	524	2	,	,	PUNCT
ejpam-1929	524	3	the	the	DET
ejpam-1929	524	4	vertex	vertex	NOUN
ejpam-1929	524	5	p2	p2	NOUN
ejpam-1929	524	6	and	and	CCONJ
ejpam-1929	524	7	(	(	PUNCT
ejpam-1929	524	8	α−	α−	ADP
ejpam-1929	524	9	1)p2	1)p2	NUM
ejpam-1929	524	10	are	be	AUX
ejpam-1929	524	11	adjacent	adjacent	ADJ
ejpam-1929	524	12	to	to	ADP
ejpam-1929	524	13	the	the	DET
ejpam-1929	524	14	vertex	vertex	NOUN
ejpam-1929	524	15	p1	p1	NOUN
ejpam-1929	524	16	with	with	ADP
ejpam-1929	524	17	negative	negative	ADJ
ejpam-1929	524	18	edges	edge	NOUN
ejpam-1929	524	19	in	in	ADP
ejpam-1929	524	20	σn	σn	NOUN
ejpam-1929	524	21	.	.	PUNCT
ejpam-1929	525	1	that	that	PRON
ejpam-1929	525	2	means	mean	VERB
ejpam-1929	525	3	,	,	PUNCT
ejpam-1929	525	4	d−(p1	d−(p1	NOUN
ejpam-1929	525	5	)	)	PUNCT
ejpam-1929	525	6	≥	≥	NOUN
ejpam-1929	525	7	2	2	NUM
ejpam-1929	525	8	and	and	CCONJ
ejpam-1929	525	9	clearly	clearly	ADV
ejpam-1929	525	10	d(p1	d(p1	VERB
ejpam-1929	525	11	)	)	PUNCT
ejpam-1929	525	12	>	>	X
ejpam-1929	525	13	2	2	NUM
ejpam-1929	525	14	except	except	SCONJ
ejpam-1929	525	15	n	n	NOUN
ejpam-1929	525	16	=	=	NUM
ejpam-1929	525	17	6	6	NUM
ejpam-1929	525	18	in	in	ADP
ejpam-1929	525	19	σn	σn	NOUN
ejpam-1929	525	20	.	.	PUNCT
ejpam-1929	526	1	thus	thus	ADV
ejpam-1929	526	2	,	,	PUNCT
ejpam-1929	526	3	condition	condition	NOUN
ejpam-1929	526	4	(	(	PUNCT
ejpam-1929	526	5	ii	ii	NOUN
ejpam-1929	526	6	)	)	PUNCT
ejpam-1929	526	7	of	of	ADP
ejpam-1929	526	8	theorem	theorem	NOUN
ejpam-1929	526	9	16	16	NUM
ejpam-1929	526	10	does	do	AUX
ejpam-1929	526	11	not	not	PART
ejpam-1929	526	12	hold	hold	VERB
ejpam-1929	526	13	for	for	ADP
ejpam-1929	526	14	σn	σn	NOUN
ejpam-1929	526	15	and	and	CCONJ
ejpam-1929	526	16	when	when	SCONJ
ejpam-1929	526	17	n	n	X
ejpam-1929	526	18	=	=	SYM
ejpam-1929	526	19	6	6	NUM
ejpam-1929	526	20	it	it	PRON
ejpam-1929	526	21	is	be	AUX
ejpam-1929	526	22	easy	easy	ADJ
ejpam-1929	526	23	to	to	PART
ejpam-1929	526	24	see	see	VERB
ejpam-1929	526	25	that	that	DET
ejpam-1929	526	26	condition	condition	NOUN
ejpam-1929	526	27	(	(	PUNCT
ejpam-1929	526	28	i)(b	i)(b	NUM
ejpam-1929	526	29	)	)	PUNCT
ejpam-1929	526	30	does	do	AUX
ejpam-1929	526	31	not	not	PART
ejpam-1929	526	32	hold	hold	VERB
ejpam-1929	526	33	,	,	PUNCT
ejpam-1929	526	34	which	which	PRON
ejpam-1929	526	35	implies	imply	VERB
ejpam-1929	526	36	that	that	SCONJ
ejpam-1929	526	37	l(σn	l(σn	NOUN
ejpam-1929	526	38	)	)	PUNCT
ejpam-1929	526	39	is	be	AUX
ejpam-1929	526	40	unbalanced	unbalanced	ADJ
ejpam-1929	526	41	,	,	PUNCT
ejpam-1929	526	42	a	a	DET
ejpam-1929	526	43	contradiction	contradiction	NOUN
ejpam-1929	526	44	to	to	ADP
ejpam-1929	526	45	the	the	DET
ejpam-1929	526	46	hypothesis	hypothesis	NOUN
ejpam-1929	526	47	.	.	PUNCT
ejpam-1929	527	1	hence	hence	ADV
ejpam-1929	527	2	n=	n=	PROPN
ejpam-1929	527	3	pa	pa	PROPN
ejpam-1929	527	4	,	,	PUNCT
ejpam-1929	527	5	where	where	SCONJ
ejpam-1929	527	6	p	p	NOUN
ejpam-1929	527	7	is	be	AUX
ejpam-1929	527	8	a	a	DET
ejpam-1929	527	9	prime	prime	ADJ
ejpam-1929	527	10	number	number	NOUN
ejpam-1929	527	11	.	.	PUNCT
ejpam-1929	528	1	converse	converse	NOUN
ejpam-1929	528	2	part	part	NOUN
ejpam-1929	528	3	can	can	AUX
ejpam-1929	528	4	be	be	AUX
ejpam-1929	528	5	proved	prove	VERB
ejpam-1929	528	6	easily	easily	ADV
ejpam-1929	528	7	by	by	ADP
ejpam-1929	528	8	using	use	VERB
ejpam-1929	528	9	lemma	lemma	PROPN
ejpam-1929	528	10	3	3	NUM
ejpam-1929	528	11	.	.	PUNCT
ejpam-1929	528	12	d.	d.	PROPN
ejpam-1929	528	13	sinha	sinha	PROPN
ejpam-1929	528	14	,	,	PUNCT
ejpam-1929	528	15	a.	a.	NOUN
ejpam-1929	528	16	dhama	dhama	PROPN
ejpam-1929	528	17	,	,	PUNCT
ejpam-1929	528	18	b.	b.	PROPN
ejpam-1929	528	19	acharya	acharya	PROPN
ejpam-1929	528	20	/	/	SYM
ejpam-1929	528	21	eur	eur	PROPN
ejpam-1929	528	22	.	.	PUNCT
ejpam-1929	529	1	j.	j.	PROPN
ejpam-1929	529	2	pure	pure	PROPN
ejpam-1929	529	3	appl	appl	PROPN
ejpam-1929	529	4	.	.	PROPN
ejpam-1929	529	5	math	math	PROPN
ejpam-1929	529	6	,	,	PUNCT
ejpam-1929	529	7	6	6	NUM
ejpam-1929	529	8	(	(	PUNCT
ejpam-1929	529	9	2013	2013	NUM
ejpam-1929	529	10	)	)	PUNCT
ejpam-1929	529	11	,	,	PUNCT
ejpam-1929	529	12	189	189	NUM
ejpam-1929	529	13	-	-	SYM
ejpam-1929	529	14	210	210	NUM
ejpam-1929	529	15	207	207	NUM
ejpam-1929	529	16	theorem	theorem	VERB
ejpam-1929	529	17	17	17	NUM
ejpam-1929	529	18	(	(	PUNCT
ejpam-1929	529	19	[	[	X
ejpam-1929	529	20	6	6	NUM
ejpam-1929	529	21	]	]	NUM
ejpam-1929	529	22	)	)	PUNCT
ejpam-1929	529	23	.	.	PUNCT
ejpam-1929	530	1	for	for	ADP
ejpam-1929	530	2	any	any	DET
ejpam-1929	530	3	sigraph	sigraph	NOUN
ejpam-1929	530	4	s	s	NOUN
ejpam-1929	530	5	,	,	PUNCT
ejpam-1929	530	6	ce(s	ce(s	ADJ
ejpam-1929	530	7	)	)	PUNCT
ejpam-1929	530	8	is	be	AUX
ejpam-1929	530	9	balanced	balance	VERB
ejpam-1929	530	10	if	if	SCONJ
ejpam-1929	530	11	and	and	CCONJ
ejpam-1929	530	12	only	only	ADV
ejpam-1929	530	13	if	if	SCONJ
ejpam-1929	530	14	s	s	NOUN
ejpam-1929	530	15	is	be	AUX
ejpam-1929	530	16	a	a	DET
ejpam-1929	530	17	balanced	balanced	ADJ
ejpam-1929	530	18	sigraph	sigraph	NOUN
ejpam-1929	530	19	such	such	ADJ
ejpam-1929	530	20	that	that	PRON
ejpam-1929	530	21	for	for	ADP
ejpam-1929	530	22	every	every	DET
ejpam-1929	530	23	vertex	vertex	NOUN
ejpam-1929	530	24	v	v	ADP
ejpam-1929	530	25	∈	∈	PROPN
ejpam-1929	530	26	v	v	NOUN
ejpam-1929	530	27	(	(	PUNCT
ejpam-1929	530	28	s	s	NOUN
ejpam-1929	530	29	)	)	PUNCT
ejpam-1929	530	30	with	with	ADP
ejpam-1929	530	31	d(v)≥	d(v)≥	ADJ
ejpam-1929	530	32	3	3	NUM
ejpam-1929	530	33	(	(	PUNCT
ejpam-1929	530	34	i	i	NOUN
ejpam-1929	530	35	)	)	PUNCT
ejpam-1929	530	36	if	if	SCONJ
ejpam-1929	530	37	d(v	d(v	PROPN
ejpam-1929	530	38	)	)	PUNCT
ejpam-1929	530	39	>	>	X
ejpam-1929	530	40	3	3	NUM
ejpam-1929	530	41	then	then	ADV
ejpam-1929	530	42	d−(v	d−(v	PROPN
ejpam-1929	530	43	)	)	PUNCT
ejpam-1929	531	1	=	=	SYM
ejpam-1929	531	2	0	0	NUM
ejpam-1929	531	3	(	(	PUNCT
ejpam-1929	531	4	ii	ii	NOUN
ejpam-1929	531	5	)	)	PUNCT
ejpam-1929	531	6	if	if	SCONJ
ejpam-1929	531	7	d(v	d(v	ADJ
ejpam-1929	531	8	)	)	PUNCT
ejpam-1929	531	9	=	=	SYM
ejpam-1929	531	10	3	3	NUM
ejpam-1929	531	11	then	then	ADV
ejpam-1929	531	12	d−(v	d−(v	PROPN
ejpam-1929	531	13	)	)	PUNCT
ejpam-1929	531	14	=	=	SYM
ejpam-1929	531	15	0	0	NUM
ejpam-1929	531	16	or	or	CCONJ
ejpam-1929	531	17	d−(v	d−(v	PROPN
ejpam-1929	531	18	)	)	PUNCT
ejpam-1929	531	19	=	=	SYM
ejpam-1929	531	20	2	2	NUM
ejpam-1929	531	21	(	(	PUNCT
ejpam-1929	531	22	iii	iii	NOUN
ejpam-1929	531	23	)	)	PUNCT
ejpam-1929	531	24	for	for	ADP
ejpam-1929	531	25	every	every	DET
ejpam-1929	531	26	x	x	PROPN
ejpam-1929	531	27	-	-	ADJ
ejpam-1929	531	28	y	y	ADJ
ejpam-1929	531	29	path	path	NOUN
ejpam-1929	531	30	p4	p4	NOUN
ejpam-1929	531	31	=	=	PUNCT
ejpam-1929	531	32	(	(	PUNCT
ejpam-1929	531	33	x	x	INTJ
ejpam-1929	531	34	,	,	PUNCT
ejpam-1929	531	35	v	v	NOUN
ejpam-1929	531	36	,	,	PUNCT
ejpam-1929	531	37	w	w	PROPN
ejpam-1929	531	38	,	,	PUNCT
ejpam-1929	531	39	y	y	NOUN
ejpam-1929	531	40	)	)	PUNCT
ejpam-1929	531	41	of	of	ADP
ejpam-1929	531	42	length	length	NOUN
ejpam-1929	531	43	three	three	NUM
ejpam-1929	531	44	,	,	PUNCT
ejpam-1929	531	45	vw	vw	PROPN
ejpam-1929	531	46	is	be	AUX
ejpam-1929	531	47	a	a	DET
ejpam-1929	531	48	positive	positive	ADJ
ejpam-1929	531	49	edge	edge	NOUN
ejpam-1929	531	50	in	in	ADP
ejpam-1929	531	51	s.	s.	PROPN
ejpam-1929	531	52	theorem	theorem	VERB
ejpam-1929	531	53	18	18	NUM
ejpam-1929	531	54	.	.	PUNCT
ejpam-1929	532	1	for	for	ADP
ejpam-1929	532	2	the	the	DET
ejpam-1929	532	3	unitary	unitary	ADJ
ejpam-1929	532	4	addition	addition	NOUN
ejpam-1929	532	5	cayley	cayley	NOUN
ejpam-1929	532	6	sigraph	sigraph	NOUN
ejpam-1929	532	7	σn	σn	NOUN
ejpam-1929	532	8	=	=	SYM
ejpam-1929	532	9	(	(	PUNCT
ejpam-1929	532	10	σ	σ	PROPN
ejpam-1929	532	11	u	u	PROPN
ejpam-1929	532	12	n	n	NUM
ejpam-1929	532	13	,	,	PUNCT
ejpam-1929	532	14	σ	σ	PROPN
ejpam-1929	532	15	)	)	PUNCT
ejpam-1929	532	16	,	,	PUNCT
ejpam-1929	532	17	its	its	PRON
ejpam-1929	532	18	ce(σn	ce(σn	NOUN
ejpam-1929	532	19	)	)	PUNCT
ejpam-1929	532	20	is	be	AUX
ejpam-1929	532	21	balanced	balance	VERB
ejpam-1929	532	22	if	if	SCONJ
ejpam-1929	532	23	and	and	CCONJ
ejpam-1929	532	24	only	only	ADV
ejpam-1929	532	25	if	if	SCONJ
ejpam-1929	532	26	n=	n=	ADJ
ejpam-1929	532	27	pa	pa	PROPN
ejpam-1929	532	28	or	or	CCONJ
ejpam-1929	532	29	n=	n=	ADJ
ejpam-1929	532	30	6	6	NUM
ejpam-1929	532	31	,	,	PUNCT
ejpam-1929	532	32	where	where	SCONJ
ejpam-1929	532	33	p	p	NOUN
ejpam-1929	532	34	is	be	AUX
ejpam-1929	532	35	a	a	DET
ejpam-1929	532	36	prime	prime	ADJ
ejpam-1929	532	37	number	number	NOUN
ejpam-1929	532	38	.	.	PUNCT
ejpam-1929	533	1	proof	proof	NOUN
ejpam-1929	533	2	.	.	PUNCT
ejpam-1929	534	1	suppose	suppose	VERB
ejpam-1929	534	2	ce(σn	ce(σn	PROPN
ejpam-1929	534	3	)	)	PUNCT
ejpam-1929	534	4	is	be	AUX
ejpam-1929	534	5	balanced	balance	VERB
ejpam-1929	534	6	for	for	ADP
ejpam-1929	534	7	the	the	DET
ejpam-1929	534	8	unitary	unitary	ADJ
ejpam-1929	534	9	addition	addition	NOUN
ejpam-1929	534	10	cayley	cayley	NOUN
ejpam-1929	534	11	sigraph	sigraph	NOUN
ejpam-1929	534	12	σn	σn	PROPN
ejpam-1929	534	13	.	.	PUNCT
ejpam-1929	534	14	assume	assume	VERB
ejpam-1929	534	15	that	that	SCONJ
ejpam-1929	534	16	the	the	DET
ejpam-1929	534	17	conclusion	conclusion	NOUN
ejpam-1929	534	18	is	be	AUX
ejpam-1929	534	19	false	false	ADJ
ejpam-1929	534	20	.	.	PUNCT
ejpam-1929	535	1	let	let	VERB
ejpam-1929	535	2	n	n	PRON
ejpam-1929	535	3	6=	6=	NUM
ejpam-1929	535	4	6	6	NUM
ejpam-1929	535	5	and	and	CCONJ
ejpam-1929	535	6	have	have	VERB
ejpam-1929	535	7	at	at	ADV
ejpam-1929	535	8	least	least	ADV
ejpam-1929	535	9	two	two	NUM
ejpam-1929	535	10	distinct	distinct	ADJ
ejpam-1929	535	11	prime	prime	ADJ
ejpam-1929	535	12	factors	factor	NOUN
ejpam-1929	535	13	.	.	PUNCT
ejpam-1929	536	1	so	so	ADV
ejpam-1929	536	2	,	,	PUNCT
ejpam-1929	536	3	let	let	VERB
ejpam-1929	536	4	n=	n=	ADJ
ejpam-1929	536	5	p	p	ADJ
ejpam-1929	536	6	a1	a1	NOUN
ejpam-1929	536	7	1	1	NUM
ejpam-1929	536	8	p	p	NOUN
ejpam-1929	536	9	a2	a2	PROPN
ejpam-1929	536	10	2	2	NUM
ejpam-1929	536	11	.	.	PUNCT
ejpam-1929	536	12	.	.	PUNCT
ejpam-1929	536	13	.	.	PUNCT
ejpam-1929	537	1	p	p	PROPN
ejpam-1929	537	2	am	be	AUX
ejpam-1929	537	3	m	m	PRON
ejpam-1929	537	4	,	,	PUNCT
ejpam-1929	537	5	where	where	SCONJ
ejpam-1929	537	6	all	all	PRON
ejpam-1929	537	7	of	of	ADP
ejpam-1929	537	8	p1	p1	NOUN
ejpam-1929	537	9	,	,	PUNCT
ejpam-1929	537	10	p2	p2	NOUN
ejpam-1929	537	11	,	,	PUNCT
ejpam-1929	537	12	.	.	PUNCT
ejpam-1929	537	13	.	.	PUNCT
ejpam-1929	538	1	.	.	PUNCT
ejpam-1929	539	1	,	,	PUNCT
ejpam-1929	539	2	pm	pm	NOUN
ejpam-1929	539	3	are	be	AUX
ejpam-1929	539	4	distinct	distinct	ADJ
ejpam-1929	539	5	primes	prime	NOUN
ejpam-1929	539	6	and	and	CCONJ
ejpam-1929	539	7	p1	p1	NOUN
ejpam-1929	539	8	<	<	X
ejpam-1929	539	9	p2	p2	X
ejpam-1929	539	10	<	<	X
ejpam-1929	539	11	·	·	PUNCT
ejpam-1929	539	12	·	·	PUNCT
ejpam-1929	540	1	·	·	PUNCT
ejpam-1929	540	2	<	<	X
ejpam-1929	540	3	pm	pm	NOUN
ejpam-1929	540	4	.	.	PUNCT
ejpam-1929	540	5	case	case	NOUN
ejpam-1929	541	1	i	i	PRON
ejpam-1929	541	2	:	:	PUNCT
ejpam-1929	541	3	suppose	suppose	VERB
ejpam-1929	541	4	n	n	PRON
ejpam-1929	541	5	is	be	AUX
ejpam-1929	541	6	even	even	ADV
ejpam-1929	541	7	.	.	PUNCT
ejpam-1929	542	1	clearly	clearly	ADV
ejpam-1929	542	2	,	,	PUNCT
ejpam-1929	542	3	p1	p1	PROPN
ejpam-1929	542	4	=	=	SYM
ejpam-1929	542	5	2	2	NUM
ejpam-1929	542	6	/∈	/∈	SYM
ejpam-1929	542	7	un	un	PROPN
ejpam-1929	542	8	.	.	PROPN
ejpam-1929	542	9	p2	p2	PROPN
ejpam-1929	542	10	can	can	AUX
ejpam-1929	542	11	never	never	ADV
ejpam-1929	542	12	be	be	AUX
ejpam-1929	542	13	adjacent	adjacent	ADJ
ejpam-1929	542	14	with	with	ADP
ejpam-1929	542	15	any	any	DET
ejpam-1929	542	16	number	number	NOUN
ejpam-1929	542	17	in	in	ADP
ejpam-1929	542	18	un	un	PROPN
ejpam-1929	542	19	because	because	SCONJ
ejpam-1929	542	20	un	un	PROPN
ejpam-1929	542	21	contains	contain	VERB
ejpam-1929	542	22	only	only	ADV
ejpam-1929	542	23	odd	odd	ADJ
ejpam-1929	542	24	numbers	number	NOUN
ejpam-1929	542	25	as	as	ADP
ejpam-1929	542	26	n	n	NUM
ejpam-1929	542	27	is	be	AUX
ejpam-1929	542	28	even	even	ADV
ejpam-1929	542	29	and	and	CCONJ
ejpam-1929	542	30	then	then	ADV
ejpam-1929	542	31	sum	sum	NOUN
ejpam-1929	542	32	of	of	ADP
ejpam-1929	542	33	these	these	DET
ejpam-1929	542	34	two	two	NUM
ejpam-1929	542	35	elements	element	NOUN
ejpam-1929	542	36	will	will	AUX
ejpam-1929	542	37	be	be	AUX
ejpam-1929	542	38	always	always	ADV
ejpam-1929	542	39	even	even	ADV
ejpam-1929	542	40	and	and	CCONJ
ejpam-1929	542	41	does	do	AUX
ejpam-1929	542	42	not	not	PART
ejpam-1929	542	43	belong	belong	VERB
ejpam-1929	542	44	to	to	ADP
ejpam-1929	542	45	un	un	PROPN
ejpam-1929	542	46	.	.	PROPN
ejpam-1929	542	47	since	since	SCONJ
ejpam-1929	542	48	p2	p2	PROPN
ejpam-1929	542	49	/∈	/∈	PUNCT
ejpam-1929	542	50	un	un	PROPN
ejpam-1929	542	51	,	,	PUNCT
ejpam-1929	542	52	by	by	ADP
ejpam-1929	542	53	theorem	theorem	NOUN
ejpam-1929	542	54	4	4	NUM
ejpam-1929	542	55	,	,	PUNCT
ejpam-1929	542	56	we	we	PRON
ejpam-1929	542	57	have	have	AUX
ejpam-1929	542	58	d(p2	d(p2	ADJ
ejpam-1929	542	59	)	)	PUNCT
ejpam-1929	542	60	=	=	SYM
ejpam-1929	542	61	φ(n	φ(n	NOUN
ejpam-1929	542	62	)	)	PUNCT
ejpam-1929	542	63	.	.	PUNCT
ejpam-1929	543	1	so	so	ADV
ejpam-1929	543	2	all	all	DET
ejpam-1929	543	3	the	the	DET
ejpam-1929	543	4	degrees	degree	NOUN
ejpam-1929	543	5	of	of	ADP
ejpam-1929	543	6	p2	p2	PROPN
ejpam-1929	543	7	are	be	AUX
ejpam-1929	543	8	negative	negative	ADJ
ejpam-1929	543	9	and	and	CCONJ
ejpam-1929	543	10	greater	great	ADJ
ejpam-1929	543	11	than	than	ADP
ejpam-1929	543	12	3	3	NUM
ejpam-1929	543	13	.	.	PUNCT
ejpam-1929	544	1	thus	thus	ADV
ejpam-1929	544	2	,	,	PUNCT
ejpam-1929	544	3	the	the	DET
ejpam-1929	544	4	condition	condition	NOUN
ejpam-1929	544	5	(	(	PUNCT
ejpam-1929	544	6	i	i	NOUN
ejpam-1929	544	7	)	)	PUNCT
ejpam-1929	544	8	of	of	ADP
ejpam-1929	544	9	theorem	theorem	NOUN
ejpam-1929	544	10	17	17	NUM
ejpam-1929	544	11	does	do	AUX
ejpam-1929	544	12	not	not	PART
ejpam-1929	544	13	hold	hold	VERB
ejpam-1929	544	14	for	for	ADP
ejpam-1929	544	15	σn	σn	NOUN
ejpam-1929	544	16	,	,	PUNCT
ejpam-1929	544	17	which	which	PRON
ejpam-1929	544	18	implies	imply	VERB
ejpam-1929	544	19	that	that	SCONJ
ejpam-1929	544	20	ce(σ	ce(σ	NOUN
ejpam-1929	544	21	)	)	PUNCT
ejpam-1929	544	22	is	be	AUX
ejpam-1929	544	23	unbalanced	unbalanced	ADJ
ejpam-1929	544	24	,	,	PUNCT
ejpam-1929	544	25	a	a	DET
ejpam-1929	544	26	contradiction	contradiction	NOUN
ejpam-1929	544	27	to	to	ADP
ejpam-1929	544	28	the	the	DET
ejpam-1929	544	29	hypothesis	hypothesis	NOUN
ejpam-1929	544	30	.	.	PUNCT
ejpam-1929	545	1	case	case	NOUN
ejpam-1929	545	2	ii	ii	PROPN
ejpam-1929	545	3	:	:	PUNCT
ejpam-1929	545	4	now	now	ADV
ejpam-1929	545	5	,	,	PUNCT
ejpam-1929	545	6	suppose	suppose	VERB
ejpam-1929	545	7	n	n	PRON
ejpam-1929	545	8	is	be	AUX
ejpam-1929	545	9	odd	odd	ADJ
ejpam-1929	545	10	.	.	PUNCT
ejpam-1929	546	1	we	we	PRON
ejpam-1929	546	2	have	have	AUX
ejpam-1929	546	3	already	already	ADV
ejpam-1929	546	4	shown	show	VERB
ejpam-1929	546	5	that	that	SCONJ
ejpam-1929	546	6	p1	p1	NOUN
ejpam-1929	546	7	is	be	AUX
ejpam-1929	546	8	adjacent	adjacent	ADJ
ejpam-1929	546	9	p2	p2	NOUN
ejpam-1929	546	10	.	.	PUNCT
ejpam-1929	547	1	clearly	clearly	ADV
ejpam-1929	547	2	,	,	PUNCT
ejpam-1929	547	3	d(p1	d(p1	NOUN
ejpam-1929	547	4	)	)	PUNCT
ejpam-1929	547	5	>	>	X
ejpam-1929	548	1	3	3	NUM
ejpam-1929	548	2	and	and	CCONJ
ejpam-1929	548	3	d−(p1	d−(p1	PROPN
ejpam-1929	548	4	)	)	PUNCT
ejpam-1929	548	5	≥	≥	NOUN
ejpam-1929	548	6	1	1	NUM
ejpam-1929	548	7	.	.	PUNCT
ejpam-1929	549	1	thus	thus	ADV
ejpam-1929	549	2	,	,	PUNCT
ejpam-1929	549	3	condition	condition	NOUN
ejpam-1929	549	4	(	(	PUNCT
ejpam-1929	549	5	i	i	NOUN
ejpam-1929	549	6	)	)	PUNCT
ejpam-1929	549	7	of	of	ADP
ejpam-1929	549	8	theorem	theorem	NOUN
ejpam-1929	549	9	17	17	NUM
ejpam-1929	549	10	does	do	AUX
ejpam-1929	549	11	not	not	PART
ejpam-1929	549	12	hold	hold	VERB
ejpam-1929	549	13	for	for	ADP
ejpam-1929	549	14	σn	σn	NOUN
ejpam-1929	549	15	,	,	PUNCT
ejpam-1929	549	16	which	which	PRON
ejpam-1929	549	17	implies	imply	VERB
ejpam-1929	549	18	that	that	SCONJ
ejpam-1929	549	19	ce(σ	ce(σ	NOUN
ejpam-1929	549	20	)	)	PUNCT
ejpam-1929	549	21	is	be	AUX
ejpam-1929	549	22	unbalanced	unbalanced	ADJ
ejpam-1929	549	23	,	,	PUNCT
ejpam-1929	549	24	a	a	DET
ejpam-1929	549	25	contradiction	contradiction	NOUN
ejpam-1929	549	26	to	to	ADP
ejpam-1929	549	27	the	the	DET
ejpam-1929	549	28	hypothesis	hypothesis	NOUN
ejpam-1929	549	29	.	.	PUNCT
ejpam-1929	550	1	hence	hence	ADV
ejpam-1929	550	2	n	n	NOUN
ejpam-1929	550	3	=	=	SYM
ejpam-1929	550	4	pa	pa	PROPN
ejpam-1929	550	5	or	or	CCONJ
ejpam-1929	550	6	n	n	CCONJ
ejpam-1929	550	7	=	=	NUM
ejpam-1929	550	8	6	6	NUM
ejpam-1929	550	9	,	,	PUNCT
ejpam-1929	550	10	where	where	SCONJ
ejpam-1929	550	11	p	p	NOUN
ejpam-1929	550	12	is	be	AUX
ejpam-1929	550	13	a	a	DET
ejpam-1929	550	14	prime	prime	ADJ
ejpam-1929	550	15	number	number	NOUN
ejpam-1929	550	16	.	.	PUNCT
ejpam-1929	551	1	converse	converse	NOUN
ejpam-1929	551	2	part	part	NOUN
ejpam-1929	551	3	can	can	AUX
ejpam-1929	551	4	be	be	AUX
ejpam-1929	551	5	proved	prove	VERB
ejpam-1929	551	6	easily	easily	ADV
ejpam-1929	551	7	by	by	ADP
ejpam-1929	551	8	using	use	VERB
ejpam-1929	551	9	lemma	lemma	PROPN
ejpam-1929	551	10	3	3	NUM
ejpam-1929	551	11	.	.	PUNCT
ejpam-1929	551	12	theorem	theorem	VERB
ejpam-1929	551	13	19	19	NUM
ejpam-1929	551	14	(	(	PUNCT
ejpam-1929	551	15	[	[	X
ejpam-1929	551	16	3	3	NUM
ejpam-1929	551	17	]	]	NUM
ejpam-1929	551	18	)	)	PUNCT
ejpam-1929	551	19	.	.	PUNCT
ejpam-1929	552	1	the	the	DET
ejpam-1929	552	2	×-line	×-line	NOUN
ejpam-1929	552	3	sigraph	sigraph	PROPN
ejpam-1929	552	4	l×(s	l×(s	PROPN
ejpam-1929	552	5	)	)	PUNCT
ejpam-1929	552	6	of	of	ADP
ejpam-1929	552	7	a	a	DET
ejpam-1929	552	8	sigraph	sigraph	NOUN
ejpam-1929	552	9	s	s	PART
ejpam-1929	552	10	is	be	AUX
ejpam-1929	552	11	a	a	DET
ejpam-1929	552	12	balanced	balanced	ADJ
ejpam-1929	552	13	sigraph	sigraph	NOUN
ejpam-1929	552	14	.	.	PUNCT
ejpam-1929	553	1	theorem	theorem	PROPN
ejpam-1929	553	2	20	20	NUM
ejpam-1929	553	3	.	.	PUNCT
ejpam-1929	554	1	for	for	ADP
ejpam-1929	554	2	the	the	DET
ejpam-1929	554	3	unitary	unitary	ADJ
ejpam-1929	554	4	addition	addition	NOUN
ejpam-1929	554	5	cayley	cayley	NOUN
ejpam-1929	554	6	sigraph	sigraph	NOUN
ejpam-1929	554	7	σn	σn	NOUN
ejpam-1929	554	8	,	,	PUNCT
ejpam-1929	554	9	its	its	PRON
ejpam-1929	554	10	×-line	×-line	NOUN
ejpam-1929	554	11	sigraph	sigraph	NOUN
ejpam-1929	554	12	l×(σn	l×(σn	PROPN
ejpam-1929	554	13	)	)	PUNCT
ejpam-1929	554	14	is	be	AUX
ejpam-1929	554	15	balanced	balanced	ADJ
ejpam-1929	554	16	.	.	PUNCT
ejpam-1929	555	1	proof	proof	NOUN
ejpam-1929	555	2	.	.	PUNCT
ejpam-1929	556	1	result	result	NOUN
ejpam-1929	556	2	follows	follow	VERB
ejpam-1929	556	3	from	from	ADP
ejpam-1929	556	4	theorem	theorem	ADJ
ejpam-1929	556	5	19	19	NUM
ejpam-1929	556	6	.	.	PUNCT
ejpam-1929	557	1	theorem	theorem	NOUN
ejpam-1929	557	2	21	21	NUM
ejpam-1929	557	3	(	(	PUNCT
ejpam-1929	557	4	[	[	X
ejpam-1929	557	5	44	44	NUM
ejpam-1929	557	6	]	]	NUM
ejpam-1929	557	7	)	)	PUNCT
ejpam-1929	557	8	.	.	PUNCT
ejpam-1929	558	1	the	the	DET
ejpam-1929	558	2	semi	semi	ADJ
ejpam-1929	558	3	-	-	ADJ
ejpam-1929	558	4	total	total	ADJ
ejpam-1929	558	5	line	line	NOUN
ejpam-1929	558	6	sigraph	sigraph	NOUN
ejpam-1929	558	7	t1(s	t1(s	PROPN
ejpam-1929	558	8	)	)	PUNCT
ejpam-1929	558	9	of	of	ADP
ejpam-1929	558	10	a	a	DET
ejpam-1929	558	11	sigraph	sigraph	NOUN
ejpam-1929	558	12	s	s	PART
ejpam-1929	558	13	is	be	AUX
ejpam-1929	558	14	a	a	DET
ejpam-1929	558	15	balanced	balanced	ADJ
ejpam-1929	558	16	sigraph	sigraph	NOUN
ejpam-1929	558	17	.	.	PUNCT
ejpam-1929	559	1	theorem	theorem	PROPN
ejpam-1929	559	2	22	22	NUM
ejpam-1929	559	3	.	.	PUNCT
ejpam-1929	560	1	for	for	ADP
ejpam-1929	560	2	the	the	DET
ejpam-1929	560	3	unitary	unitary	ADJ
ejpam-1929	560	4	addition	addition	NOUN
ejpam-1929	560	5	cayley	cayley	NOUN
ejpam-1929	560	6	sigraph	sigraph	NOUN
ejpam-1929	560	7	σn	σn	NOUN
ejpam-1929	560	8	,	,	PUNCT
ejpam-1929	560	9	its	its	PRON
ejpam-1929	560	10	semi	semi	ADJ
ejpam-1929	560	11	-	-	ADJ
ejpam-1929	560	12	total	total	ADJ
ejpam-1929	560	13	line	line	NOUN
ejpam-1929	560	14	sigraph	sigraph	NOUN
ejpam-1929	560	15	t1(σn	t1(σn	PROPN
ejpam-1929	560	16	)	)	PUNCT
ejpam-1929	560	17	is	be	AUX
ejpam-1929	560	18	balanced	balanced	ADJ
ejpam-1929	560	19	.	.	PUNCT
ejpam-1929	561	1	proof	proof	NOUN
ejpam-1929	561	2	.	.	PUNCT
ejpam-1929	562	1	result	result	NOUN
ejpam-1929	562	2	follows	follow	VERB
ejpam-1929	562	3	from	from	ADP
ejpam-1929	562	4	theorem	theorem	ADJ
ejpam-1929	562	5	21	21	NUM
ejpam-1929	562	6	.	.	PUNCT
ejpam-1929	563	1	acknowledgements	acknowledgement	NOUN
ejpam-1929	563	2	this	this	DET
ejpam-1929	563	3	research	research	NOUN
ejpam-1929	563	4	is	be	AUX
ejpam-1929	563	5	supported	support	VERB
ejpam-1929	563	6	by	by	ADP
ejpam-1929	563	7	the	the	DET
ejpam-1929	563	8	department	department	PROPN
ejpam-1929	563	9	of	of	ADP
ejpam-1929	563	10	science	science	NOUN
ejpam-1929	563	11	and	and	CCONJ
ejpam-1929	563	12	technology	technology	NOUN
ejpam-1929	563	13	(	(	PUNCT
ejpam-1929	563	14	govt	govt	PROPN
ejpam-1929	563	15	.	.	PUNCT
ejpam-1929	564	1	of	of	ADP
ejpam-1929	564	2	india	india	PROPN
ejpam-1929	564	3	)	)	PUNCT
ejpam-1929	564	4	,	,	PUNCT
ejpam-1929	564	5	new	new	PROPN
ejpam-1929	564	6	delhi	delhi	PROPN
ejpam-1929	564	7	,	,	PUNCT
ejpam-1929	564	8	india	india	PROPN
ejpam-1929	564	9	under	under	ADP
ejpam-1929	564	10	the	the	DET
ejpam-1929	564	11	project	project	NOUN
ejpam-1929	564	12	sr	sr	PROPN
ejpam-1929	564	13	/	/	SYM
ejpam-1929	564	14	s4	s4	PROPN
ejpam-1929	564	15	/	/	SYM
ejpam-1929	564	16	ms	ms	NOUN
ejpam-1929	564	17	:	:	PUNCT
ejpam-1929	564	18	409/06	409/06	NUM
ejpam-1929	564	19	.	.	PUNCT
ejpam-1929	565	1	references	reference	NOUN
ejpam-1929	565	2	208	208	NUM
ejpam-1929	565	3	references	reference	NOUN
ejpam-1929	565	4	[	[	X
ejpam-1929	565	5	1	1	NUM
ejpam-1929	565	6	]	]	X
ejpam-1929	565	7	b.d	b.d	PROPN
ejpam-1929	565	8	.	.	PROPN
ejpam-1929	565	9	acharya	acharya	PROPN
ejpam-1929	565	10	,	,	PUNCT
ejpam-1929	565	11	a	a	DET
ejpam-1929	565	12	spectral	spectral	ADJ
ejpam-1929	565	13	criterion	criterion	NOUN
ejpam-1929	565	14	for	for	ADP
ejpam-1929	565	15	cycle	cycle	NOUN
ejpam-1929	565	16	balance	balance	NOUN
ejpam-1929	565	17	in	in	ADP
ejpam-1929	565	18	networks	network	NOUN
ejpam-1929	565	19	,	,	PUNCT
ejpam-1929	565	20	journal	journal	NOUN
ejpam-1929	565	21	of	of	ADP
ejpam-1929	565	22	graph	graph	NOUN
ejpam-1929	565	23	theory	theory	NOUN
ejpam-1929	565	24	,	,	PUNCT
ejpam-1929	565	25	4(1	4(1	NOUN
ejpam-1929	565	26	)	)	PUNCT
ejpam-1929	565	27	,	,	PUNCT
ejpam-1929	565	28	1	1	NUM
ejpam-1929	565	29	-	-	SYM
ejpam-1929	565	30	11	11	NUM
ejpam-1929	565	31	.	.	PUNCT
ejpam-1929	565	32	1980	1980	NUM
ejpam-1929	565	33	.	.	PUNCT
ejpam-1929	566	1	[	[	X
ejpam-1929	566	2	2	2	NUM
ejpam-1929	566	3	]	]	X
ejpam-1929	566	4	b.d	b.d	PROPN
ejpam-1929	566	5	.	.	PROPN
ejpam-1929	566	6	acharya	acharya	PROPN
ejpam-1929	566	7	,	,	PUNCT
ejpam-1929	566	8	a	a	DET
ejpam-1929	566	9	characterization	characterization	NOUN
ejpam-1929	566	10	of	of	ADP
ejpam-1929	566	11	consistent	consistent	ADJ
ejpam-1929	566	12	marked	mark	VERB
ejpam-1929	566	13	graphs	graph	NOUN
ejpam-1929	566	14	,	,	PUNCT
ejpam-1929	566	15	national	national	PROPN
ejpam-1929	566	16	academy	academy	PROPN
ejpam-1929	566	17	of	of	ADP
ejpam-1929	566	18	science	science	NOUN
ejpam-1929	566	19	letters	letter	NOUN
ejpam-1929	566	20	,	,	PUNCT
ejpam-1929	566	21	6	6	NUM
ejpam-1929	566	22	,	,	PUNCT
ejpam-1929	566	23	431	431	NUM
ejpam-1929	566	24	-	-	SYM
ejpam-1929	566	25	440	440	NUM
ejpam-1929	566	26	.	.	PUNCT
ejpam-1929	566	27	1983	1983	NUM
ejpam-1929	567	1	[	[	X
ejpam-1929	567	2	3	3	NUM
ejpam-1929	567	3	]	]	PUNCT
ejpam-1929	567	4	m.	m.	NOUN
ejpam-1929	567	5	acharya,×-line	acharya,×-line	PROPN
ejpam-1929	567	6	sigraph	sigraph	NOUN
ejpam-1929	567	7	of	of	ADP
ejpam-1929	567	8	a	a	DET
ejpam-1929	567	9	sigraph	sigraph	NOUN
ejpam-1929	567	10	,	,	PUNCT
ejpam-1929	567	11	journal	journal	NOUN
ejpam-1929	567	12	of	of	ADP
ejpam-1929	567	13	combinatorial	combinatorial	ADJ
ejpam-1929	567	14	mathematics	mathematic	NOUN
ejpam-1929	567	15	and	and	CCONJ
ejpam-1929	567	16	combinatorial	combinatorial	ADJ
ejpam-1929	567	17	computing	computing	NOUN
ejpam-1929	567	18	,	,	PUNCT
ejpam-1929	567	19	69	69	NUM
ejpam-1929	567	20	,	,	PUNCT
ejpam-1929	567	21	103	103	NUM
ejpam-1929	567	22	-	-	SYM
ejpam-1929	567	23	111	111	NUM
ejpam-1929	567	24	.	.	PUNCT
ejpam-1929	567	25	2009	2009	NUM
ejpam-1929	567	26	.	.	PUNCT
ejpam-1929	568	1	[	[	X
ejpam-1929	568	2	4	4	NUM
ejpam-1929	568	3	]	]	PUNCT
ejpam-1929	568	4	m.	m.	NOUN
ejpam-1929	568	5	acharya	acharya	PROPN
ejpam-1929	568	6	and	and	CCONJ
ejpam-1929	568	7	d.	d.	PROPN
ejpam-1929	568	8	sinha	sinha	PROPN
ejpam-1929	568	9	,	,	PUNCT
ejpam-1929	568	10	a	a	DET
ejpam-1929	568	11	characterization	characterization	NOUN
ejpam-1929	568	12	of	of	ADP
ejpam-1929	568	13	sigraphs	sigraph	NOUN
ejpam-1929	568	14	whose	whose	DET
ejpam-1929	568	15	line	line	NOUN
ejpam-1929	568	16	sigraphs	sigraph	VERB
ejpam-1929	568	17	and	and	CCONJ
ejpam-1929	568	18	jump	jump	NOUN
ejpam-1929	568	19	sigraphs	sigraph	NOUN
ejpam-1929	568	20	are	be	AUX
ejpam-1929	568	21	switching	switch	VERB
ejpam-1929	568	22	equivalent	equivalent	ADJ
ejpam-1929	568	23	,	,	PUNCT
ejpam-1929	568	24	graph	graph	NOUN
ejpam-1929	568	25	theory	theory	NOUN
ejpam-1929	568	26	notes	note	VERB
ejpam-1929	568	27	n.	n.	PROPN
ejpam-1929	568	28	y.	y.	PROPN
ejpam-1929	568	29	,	,	PUNCT
ejpam-1929	568	30	xliv	xliv	PROPN
ejpam-1929	568	31	,	,	PUNCT
ejpam-1929	568	32	30	30	NUM
ejpam-1929	568	33	-	-	SYM
ejpam-1929	568	34	34	34	NUM
ejpam-1929	568	35	.	.	PUNCT
ejpam-1929	568	36	2003	2003	NUM
ejpam-1929	568	37	.	.	PUNCT
ejpam-1929	569	1	[	[	X
ejpam-1929	569	2	5	5	NUM
ejpam-1929	569	3	]	]	PUNCT
ejpam-1929	569	4	m.	m.	NOUN
ejpam-1929	569	5	acharya	acharya	PROPN
ejpam-1929	569	6	and	and	CCONJ
ejpam-1929	569	7	d.	d.	PROPN
ejpam-1929	569	8	sinha	sinha	PROPN
ejpam-1929	569	9	,	,	PUNCT
ejpam-1929	569	10	characterizations	characterization	NOUN
ejpam-1929	569	11	of	of	ADP
ejpam-1929	569	12	line	line	NOUN
ejpam-1929	569	13	sigraphs	sigraph	NOUN
ejpam-1929	569	14	,	,	PUNCT
ejpam-1929	569	15	national	national	PROPN
ejpam-1929	569	16	academy	academy	PROPN
ejpam-1929	569	17	of	of	ADP
ejpam-1929	569	18	science	science	PROPN
ejpam-1929	569	19	letters	letter	NOUN
ejpam-1929	569	20	,	,	PUNCT
ejpam-1929	569	21	28(1	28(1	NUM
ejpam-1929	569	22	&	&	CCONJ
ejpam-1929	569	23	2	2	NUM
ejpam-1929	569	24	)	)	PUNCT
ejpam-1929	569	25	,	,	PUNCT
ejpam-1929	569	26	31	31	NUM
ejpam-1929	569	27	-	-	SYM
ejpam-1929	569	28	34	34	NUM
ejpam-1929	569	29	.	.	PUNCT
ejpam-1929	569	30	2005	2005	NUM
ejpam-1929	569	31	.	.	PUNCT
ejpam-1929	570	1	[	[	X
ejpam-1929	570	2	6	6	NUM
ejpam-1929	570	3	]	]	PUNCT
ejpam-1929	570	4	m.	m.	NOUN
ejpam-1929	570	5	acharya	acharya	PROPN
ejpam-1929	570	6	and	and	CCONJ
ejpam-1929	570	7	d.	d.	PROPN
ejpam-1929	570	8	sinha	sinha	PROPN
ejpam-1929	570	9	,	,	PUNCT
ejpam-1929	570	10	common	common	ADJ
ejpam-1929	570	11	-	-	PUNCT
ejpam-1929	570	12	edge	edge	NOUN
ejpam-1929	570	13	sigraphs	sigraph	NOUN
ejpam-1929	570	14	,	,	PUNCT
ejpam-1929	570	15	akce	akce	PROPN
ejpam-1929	570	16	international	international	ADJ
ejpam-1929	570	17	journal	journal	NOUN
ejpam-1929	570	18	of	of	ADP
ejpam-1929	570	19	graphs	graph	NOUN
ejpam-1929	570	20	and	and	CCONJ
ejpam-1929	570	21	combinatorics	combinatoric	NOUN
ejpam-1929	570	22	,	,	PUNCT
ejpam-1929	570	23	3(2	3(2	NUM
ejpam-1929	570	24	)	)	PUNCT
ejpam-1929	570	25	,	,	PUNCT
ejpam-1929	570	26	115	115	NUM
ejpam-1929	570	27	-	-	SYM
ejpam-1929	570	28	130	130	NUM
ejpam-1929	570	29	.	.	PUNCT
ejpam-1929	570	30	2006	2006	NUM
ejpam-1929	570	31	.	.	PUNCT
ejpam-1929	571	1	[	[	X
ejpam-1929	571	2	7	7	X
ejpam-1929	571	3	]	]	X
ejpam-1929	571	4	r.	r.	PROPN
ejpam-1929	571	5	akhtar	akhtar	PROPN
ejpam-1929	571	6	,	,	PUNCT
ejpam-1929	571	7	m.	m.	PROPN
ejpam-1929	571	8	boggess	boggess	PROPN
ejpam-1929	571	9	,	,	PUNCT
ejpam-1929	571	10	t.	t.	PROPN
ejpam-1929	571	11	jackson	jackson	PROPN
ejpam-1929	571	12	-	-	PUNCT
ejpam-1929	571	13	henderson	henderson	PROPN
ejpam-1929	571	14	,	,	PUNCT
ejpam-1929	571	15	i.	i.	PROPN
ejpam-1929	571	16	jiménez	jiménez	PROPN
ejpam-1929	571	17	,	,	PUNCT
ejpam-1929	571	18	r.	r.	PROPN
ejpam-1929	571	19	karpman	karpman	PROPN
ejpam-1929	571	20	,	,	PUNCT
ejpam-1929	571	21	a.	a.	NOUN
ejpam-1929	571	22	kinzel	kinzel	PROPN
ejpam-1929	571	23	and	and	CCONJ
ejpam-1929	571	24	d.	d.	PROPN
ejpam-1929	571	25	pritikin	pritikin	PROPN
ejpam-1929	571	26	,	,	PUNCT
ejpam-1929	571	27	on	on	ADP
ejpam-1929	571	28	the	the	DET
ejpam-1929	571	29	unitary	unitary	ADJ
ejpam-1929	571	30	cayley	cayley	ADJ
ejpam-1929	571	31	graph	graph	NOUN
ejpam-1929	571	32	of	of	ADP
ejpam-1929	571	33	a	a	DET
ejpam-1929	571	34	finite	finite	ADJ
ejpam-1929	571	35	ring	ring	NOUN
ejpam-1929	571	36	,	,	PUNCT
ejpam-1929	571	37	electronic	electronic	ADJ
ejpam-1929	571	38	journal	journal	NOUN
ejpam-1929	571	39	of	of	ADP
ejpam-1929	571	40	combinatorics	combinatoric	NOUN
ejpam-1929	571	41	,	,	PUNCT
ejpam-1929	571	42	16(1)(2009	16(1)(2009	NUM
ejpam-1929	571	43	)	)	PUNCT
ejpam-1929	571	44	,	,	PUNCT
ejpam-1929	571	45	#	#	SYM
ejpam-1929	571	46	r117	r117	NUM
ejpam-1929	571	47	.	.	PUNCT
ejpam-1929	572	1	[	[	X
ejpam-1929	572	2	8	8	NUM
ejpam-1929	572	3	]	]	X
ejpam-1929	572	4	n.	n.	PROPN
ejpam-1929	572	5	alon	alon	PROPN
ejpam-1929	572	6	,	,	PUNCT
ejpam-1929	572	7	large	large	ADJ
ejpam-1929	572	8	sets	set	NOUN
ejpam-1929	572	9	in	in	ADP
ejpam-1929	572	10	finite	finite	ADJ
ejpam-1929	572	11	fields	field	NOUN
ejpam-1929	572	12	are	be	AUX
ejpam-1929	572	13	sumsets	sumset	NOUN
ejpam-1929	572	14	,	,	PUNCT
ejpam-1929	572	15	journal	journal	NOUN
ejpam-1929	572	16	of	of	ADP
ejpam-1929	572	17	number	number	NOUN
ejpam-1929	572	18	theory	theory	NOUN
ejpam-1929	572	19	,	,	PUNCT
ejpam-1929	572	20	126(1)(2007	126(1)(2007	PROPN
ejpam-1929	572	21	)	)	PUNCT
ejpam-1929	572	22	,	,	PUNCT
ejpam-1929	572	23	110	110	NUM
ejpam-1929	572	24	-	-	SYM
ejpam-1929	572	25	118	118	NUM
ejpam-1929	572	26	.	.	PUNCT
ejpam-1929	573	1	[	[	X
ejpam-1929	573	2	9	9	NUM
ejpam-1929	573	3	]	]	X
ejpam-1929	573	4	n.d	n.d	PROPN
ejpam-1929	573	5	.	.	PROPN
ejpam-1929	573	6	beaudrap	beaudrap	PROPN
ejpam-1929	573	7	,	,	PUNCT
ejpam-1929	573	8	on	on	ADP
ejpam-1929	573	9	restricted	restrict	VERB
ejpam-1929	573	10	unitary	unitary	ADJ
ejpam-1929	573	11	cayley	cayley	ADJ
ejpam-1929	573	12	graphs	graph	NOUN
ejpam-1929	573	13	and	and	CCONJ
ejpam-1929	573	14	symplectic	symplectic	ADJ
ejpam-1929	573	15	transformations	transformation	NOUN
ejpam-1929	573	16	modulo	modulo	NOUN
ejpam-1929	573	17	n	n	CCONJ
ejpam-1929	573	18	,	,	PUNCT
ejpam-1929	573	19	electronic	electronic	ADJ
ejpam-1929	573	20	journal	journal	NOUN
ejpam-1929	573	21	of	of	ADP
ejpam-1929	573	22	combinatorics	combinatoric	NOUN
ejpam-1929	573	23	,	,	PUNCT
ejpam-1929	573	24	17(2010	17(2010	NUM
ejpam-1929	573	25	)	)	PUNCT
ejpam-1929	573	26	,	,	PUNCT
ejpam-1929	573	27	#	#	SYM
ejpam-1929	573	28	r69	r69	NOUN
ejpam-1929	573	29	.	.	PUNCT
ejpam-1929	574	1	[	[	X
ejpam-1929	574	2	10	10	NUM
ejpam-1929	574	3	]	]	X
ejpam-1929	574	4	m.	m.	PROPN
ejpam-1929	574	5	behzad	behzad	PROPN
ejpam-1929	574	6	and	and	CCONJ
ejpam-1929	574	7	g.t	g.t	PROPN
ejpam-1929	574	8	.	.	PROPN
ejpam-1929	574	9	chartrand	chartrand	PROPN
ejpam-1929	574	10	,	,	PUNCT
ejpam-1929	574	11	line	line	NOUN
ejpam-1929	574	12	coloring	coloring	NOUN
ejpam-1929	574	13	of	of	ADP
ejpam-1929	574	14	signed	sign	VERB
ejpam-1929	574	15	graphs	graph	NOUN
ejpam-1929	574	16	,	,	PUNCT
ejpam-1929	574	17	elemente	elemente	PROPN
ejpam-1929	574	18	der	der	PROPN
ejpam-1929	574	19	mathematik	mathematik	PROPN
ejpam-1929	574	20	,	,	PUNCT
ejpam-1929	574	21	24(3	24(3	NUM
ejpam-1929	574	22	)	)	PUNCT
ejpam-1929	574	23	(	(	PUNCT
ejpam-1929	574	24	1969	1969	NUM
ejpam-1929	574	25	)	)	PUNCT
ejpam-1929	574	26	,	,	PUNCT
ejpam-1929	574	27	49	49	NUM
ejpam-1929	574	28	-	-	SYM
ejpam-1929	574	29	52	52	NUM
ejpam-1929	574	30	.	.	PUNCT
ejpam-1929	575	1	[	[	X
ejpam-1929	575	2	11	11	NUM
ejpam-1929	575	3	]	]	X
ejpam-1929	575	4	l.w	l.w	PROPN
ejpam-1929	575	5	.	.	PROPN
ejpam-1929	575	6	beineke	beineke	PROPN
ejpam-1929	575	7	and	and	CCONJ
ejpam-1929	575	8	f.	f.	PROPN
ejpam-1929	575	9	harary	harary	PROPN
ejpam-1929	575	10	,	,	PUNCT
ejpam-1929	575	11	consistency	consistency	NOUN
ejpam-1929	575	12	in	in	ADP
ejpam-1929	575	13	marked	mark	VERB
ejpam-1929	575	14	graphs	graph	NOUN
ejpam-1929	575	15	,	,	PUNCT
ejpam-1929	575	16	journal	journal	NOUN
ejpam-1929	575	17	of	of	ADP
ejpam-1929	575	18	mathematical	mathematical	ADJ
ejpam-1929	575	19	psychology	psychology	NOUN
ejpam-1929	575	20	,	,	PUNCT
ejpam-1929	575	21	18(3)(1978	18(3)(1978	NUM
ejpam-1929	575	22	)	)	PUNCT
ejpam-1929	575	23	,	,	PUNCT
ejpam-1929	575	24	260	260	NUM
ejpam-1929	575	25	-	-	SYM
ejpam-1929	575	26	269	269	NUM
ejpam-1929	575	27	.	.	PUNCT
ejpam-1929	576	1	[	[	X
ejpam-1929	576	2	12	12	NUM
ejpam-1929	576	3	]	]	X
ejpam-1929	576	4	l.w	l.w	PROPN
ejpam-1929	576	5	.	.	PROPN
ejpam-1929	576	6	beineke	beineke	PROPN
ejpam-1929	576	7	and	and	CCONJ
ejpam-1929	576	8	f.	f.	PROPN
ejpam-1929	576	9	harary	harary	PROPN
ejpam-1929	576	10	,	,	PUNCT
ejpam-1929	576	11	consistent	consistent	ADJ
ejpam-1929	576	12	graphs	graph	NOUN
ejpam-1929	576	13	with	with	ADP
ejpam-1929	576	14	signed	sign	VERB
ejpam-1929	576	15	points	point	NOUN
ejpam-1929	576	16	,	,	PUNCT
ejpam-1929	576	17	rivista	rivista	PROPN
ejpam-1929	576	18	di	di	X
ejpam-1929	576	19	matematica	matematica	PROPN
ejpam-1929	576	20	per	per	ADP
ejpam-1929	576	21	le	le	X
ejpam-1929	576	22	scienze	scienze	PROPN
ejpam-1929	576	23	economiche	economiche	PROPN
ejpam-1929	576	24	e	e	PROPN
ejpam-1929	576	25	sociali	sociali	PROPN
ejpam-1929	576	26	,	,	PUNCT
ejpam-1929	576	27	1(1978	1(1978	NUM
ejpam-1929	576	28	)	)	PUNCT
ejpam-1929	576	29	,	,	PUNCT
ejpam-1929	576	30	81	81	NUM
ejpam-1929	576	31	-	-	SYM
ejpam-1929	576	32	88	88	NUM
ejpam-1929	576	33	.	.	PUNCT
ejpam-1929	577	1	[	[	X
ejpam-1929	577	2	13	13	NUM
ejpam-1929	577	3	]	]	PUNCT
ejpam-1929	577	4	p.	p.	NOUN
ejpam-1929	577	5	berrizbeitia	berrizbeitia	PROPN
ejpam-1929	577	6	and	and	CCONJ
ejpam-1929	577	7	r.e	r.e	PROPN
ejpam-1929	577	8	.	.	PROPN
ejpam-1929	577	9	giudici	giudici	PROPN
ejpam-1929	577	10	,	,	PUNCT
ejpam-1929	577	11	on	on	ADP
ejpam-1929	577	12	cycles	cycle	NOUN
ejpam-1929	577	13	in	in	ADP
ejpam-1929	577	14	the	the	DET
ejpam-1929	577	15	sequence	sequence	NOUN
ejpam-1929	577	16	of	of	ADP
ejpam-1929	577	17	unitary	unitary	ADJ
ejpam-1929	577	18	cayley	cayley	ADJ
ejpam-1929	577	19	graphs	graph	NOUN
ejpam-1929	577	20	,	,	PUNCT
ejpam-1929	577	21	discrete	discrete	ADJ
ejpam-1929	577	22	mathematics	mathematic	NOUN
ejpam-1929	577	23	,	,	PUNCT
ejpam-1929	577	24	282(1	282(1	NUM
ejpam-1929	577	25	-	-	SYM
ejpam-1929	577	26	3)(2004	3)(2004	NUM
ejpam-1929	577	27	)	)	PUNCT
ejpam-1929	577	28	,	,	PUNCT
ejpam-1929	577	29	239	239	NUM
ejpam-1929	577	30	-	-	SYM
ejpam-1929	577	31	243	243	NUM
ejpam-1929	577	32	.	.	PUNCT
ejpam-1929	578	1	[	[	X
ejpam-1929	578	2	14	14	NUM
ejpam-1929	578	3	]	]	X
ejpam-1929	578	4	n.	n.	PROPN
ejpam-1929	578	5	biggs	biggs	PROPN
ejpam-1929	578	6	,	,	PUNCT
ejpam-1929	578	7	algebraic	algebraic	ADJ
ejpam-1929	578	8	graph	graph	NOUN
ejpam-1929	578	9	theory	theory	NOUN
ejpam-1929	578	10	,	,	PUNCT
ejpam-1929	578	11	second	second	ADJ
ejpam-1929	578	12	edition	edition	NOUN
ejpam-1929	578	13	,	,	PUNCT
ejpam-1929	578	14	cambridge	cambridge	PROPN
ejpam-1929	578	15	mathematical	mathematical	PROPN
ejpam-1929	578	16	library	library	PROPN
ejpam-1929	578	17	,	,	PUNCT
ejpam-1929	578	18	cambridge	cambridge	PROPN
ejpam-1929	578	19	university	university	PROPN
ejpam-1929	578	20	press	press	NOUN
ejpam-1929	578	21	,	,	PUNCT
ejpam-1929	578	22	1993	1993	NUM
ejpam-1929	578	23	.	.	PUNCT
ejpam-1929	579	1	[	[	X
ejpam-1929	579	2	15	15	NUM
ejpam-1929	579	3	]	]	X
ejpam-1929	579	4	m.	m.	NOUN
ejpam-1929	579	5	boggess	boggess	PROPN
ejpam-1929	579	6	,	,	PUNCT
ejpam-1929	579	7	t.	t.	PROPN
ejpam-1929	579	8	jackson	jackson	PROPN
ejpam-1929	579	9	-	-	PUNCT
ejpam-1929	579	10	henderson	henderson	PROPN
ejpam-1929	579	11	,	,	PUNCT
ejpam-1929	579	12	i.	i.	PROPN
ejpam-1929	579	13	jiménez	jiménez	PROPN
ejpam-1929	579	14	and	and	CCONJ
ejpam-1929	579	15	r.	r.	PROPN
ejpam-1929	579	16	karpman	karpman	PROPN
ejpam-1929	579	17	,	,	PUNCT
ejpam-1929	579	18	the	the	DET
ejpam-1929	579	19	structure	structure	NOUN
ejpam-1929	579	20	of	of	ADP
ejpam-1929	579	21	unitary	unitary	ADJ
ejpam-1929	579	22	cayley	cayley	ADJ
ejpam-1929	579	23	graphs	graph	NOUN
ejpam-1929	579	24	,	,	PUNCT
ejpam-1929	579	25	sumsri	sumsri	PROPN
ejpam-1929	579	26	journal	journal	NOUN
ejpam-1929	579	27	,	,	PUNCT
ejpam-1929	579	28	(	(	PUNCT
ejpam-1929	579	29	2008	2008	NUM
ejpam-1929	579	30	)	)	PUNCT
ejpam-1929	579	31	,	,	PUNCT
ejpam-1929	579	32	1	1	NUM
ejpam-1929	579	33	-	-	SYM
ejpam-1929	579	34	23	23	NUM
ejpam-1929	579	35	.	.	PUNCT
ejpam-1929	580	1	references	reference	NOUN
ejpam-1929	580	2	209	209	NUM
ejpam-1929	581	1	[	[	X
ejpam-1929	581	2	16	16	NUM
ejpam-1929	581	3	]	]	X
ejpam-1929	581	4	g.t	g.t	PROPN
ejpam-1929	581	5	.	.	PROPN
ejpam-1929	581	6	chartrand	chartrand	PROPN
ejpam-1929	581	7	,	,	PUNCT
ejpam-1929	581	8	graphs	graph	VERB
ejpam-1929	581	9	as	as	ADP
ejpam-1929	581	10	mathematical	mathematical	ADJ
ejpam-1929	581	11	models	model	NOUN
ejpam-1929	581	12	,	,	PUNCT
ejpam-1929	581	13	prindle	prindle	NOUN
ejpam-1929	581	14	,	,	PUNCT
ejpam-1929	581	15	weber	weber	PROPN
ejpam-1929	581	16	and	and	CCONJ
ejpam-1929	581	17	schmidt	schmidt	PROPN
ejpam-1929	581	18	.	.	PROPN
ejpam-1929	581	19	inc	inc	PROPN
ejpam-1929	581	20	.	.	PROPN
ejpam-1929	581	21	,	,	PUNCT
ejpam-1929	581	22	boston	boston	PROPN
ejpam-1929	581	23	,	,	PUNCT
ejpam-1929	581	24	massachusetts	massachusetts	PROPN
ejpam-1929	581	25	,	,	PUNCT
ejpam-1929	581	26	1977	1977	NUM
ejpam-1929	581	27	.	.	PUNCT
ejpam-1929	582	1	[	[	X
ejpam-1929	582	2	17	17	NUM
ejpam-1929	582	3	]	]	X
ejpam-1929	582	4	b.	b.	PROPN
ejpam-1929	582	5	cheyne	cheyne	PROPN
ejpam-1929	582	6	,	,	PUNCT
ejpam-1929	582	7	v.	v.	PROPN
ejpam-1929	582	8	gupta	gupta	PROPN
ejpam-1929	582	9	and	and	CCONJ
ejpam-1929	582	10	c.	c.	PROPN
ejpam-1929	582	11	wheeler	wheeler	NOUN
ejpam-1929	582	12	,	,	PUNCT
ejpam-1929	582	13	hamilton	hamilton	PROPN
ejpam-1929	582	14	cycles	cycle	NOUN
ejpam-1929	582	15	in	in	ADP
ejpam-1929	582	16	addition	addition	NOUN
ejpam-1929	582	17	graphs	graph	NOUN
ejpam-1929	582	18	,	,	PUNCT
ejpam-1929	582	19	rose	rose	NOUN
ejpam-1929	582	20	-	-	PUNCT
ejpam-1929	582	21	hulman	hulman	NOUN
ejpam-1929	582	22	undergraduate	undergraduate	PROPN
ejpam-1929	582	23	math	math	PROPN
ejpam-1929	582	24	journal	journal	PROPN
ejpam-1929	582	25	,	,	PUNCT
ejpam-1929	582	26	4(1)(2003	4(1)(2003	NUM
ejpam-1929	582	27	)	)	PUNCT
ejpam-1929	582	28	,	,	PUNCT
ejpam-1929	582	29	1	1	NUM
ejpam-1929	582	30	-	-	SYM
ejpam-1929	582	31	17	17	NUM
ejpam-1929	582	32	.	.	PUNCT
ejpam-1929	583	1	[	[	X
ejpam-1929	583	2	18	18	NUM
ejpam-1929	583	3	]	]	X
ejpam-1929	583	4	f.r.k	f.r.k	PROPN
ejpam-1929	583	5	.	.	PUNCT
ejpam-1929	583	6	chung	chung	PROPN
ejpam-1929	583	7	,	,	PUNCT
ejpam-1929	583	8	diameters	diameter	NOUN
ejpam-1929	583	9	and	and	CCONJ
ejpam-1929	583	10	eigenvalues	eigenvalue	NOUN
ejpam-1929	583	11	,	,	PUNCT
ejpam-1929	583	12	journal	journal	NOUN
ejpam-1929	583	13	of	of	ADP
ejpam-1929	583	14	the	the	DET
ejpam-1929	583	15	american	american	PROPN
ejpam-1929	583	16	mathematical	mathematical	PROPN
ejpam-1929	583	17	society	society	NOUN
ejpam-1929	583	18	,	,	PUNCT
ejpam-1929	583	19	2(2)(1989	2(2)(1989	NUM
ejpam-1929	583	20	)	)	PUNCT
ejpam-1929	583	21	,	,	PUNCT
ejpam-1929	583	22	187	187	NUM
ejpam-1929	583	23	-	-	SYM
ejpam-1929	583	24	196	196	NUM
ejpam-1929	583	25	.	.	PUNCT
ejpam-1929	584	1	[	[	X
ejpam-1929	584	2	19	19	NUM
ejpam-1929	584	3	]	]	X
ejpam-1929	584	4	j.a	j.a	PROPN
ejpam-1929	584	5	.	.	PROPN
ejpam-1929	584	6	davis	davis	PROPN
ejpam-1929	584	7	,	,	PUNCT
ejpam-1929	584	8	clustering	clustering	NOUN
ejpam-1929	584	9	and	and	CCONJ
ejpam-1929	584	10	structural	structural	ADJ
ejpam-1929	584	11	balance	balance	NOUN
ejpam-1929	584	12	in	in	ADP
ejpam-1929	584	13	graphs	graph	NOUN
ejpam-1929	584	14	,	,	PUNCT
ejpam-1929	584	15	human	human	ADJ
ejpam-1929	584	16	relations	relation	NOUN
ejpam-1929	584	17	,	,	PUNCT
ejpam-1929	584	18	20(1967	20(1967	NOUN
ejpam-1929	584	19	)	)	PUNCT
ejpam-1929	584	20	,	,	PUNCT
ejpam-1929	584	21	181187	181187	NUM
ejpam-1929	584	22	.	.	PUNCT
ejpam-1929	585	1	[	[	X
ejpam-1929	585	2	20	20	NUM
ejpam-1929	585	3	]	]	X
ejpam-1929	585	4	i.j	i.j	PROPN
ejpam-1929	585	5	.	.	PROPN
ejpam-1929	585	6	dejter	dejter	PROPN
ejpam-1929	585	7	and	and	CCONJ
ejpam-1929	585	8	r.e	r.e	PROPN
ejpam-1929	585	9	.	.	PROPN
ejpam-1929	585	10	giudici	giudici	PROPN
ejpam-1929	585	11	,	,	PUNCT
ejpam-1929	585	12	on	on	ADP
ejpam-1929	585	13	unitary	unitary	ADJ
ejpam-1929	585	14	cayley	cayley	ADJ
ejpam-1929	585	15	graphs	graph	NOUN
ejpam-1929	585	16	,	,	PUNCT
ejpam-1929	585	17	journal	journal	NOUN
ejpam-1929	585	18	of	of	ADP
ejpam-1929	585	19	combinatorial	combinatorial	ADJ
ejpam-1929	585	20	mathematics	mathematic	NOUN
ejpam-1929	585	21	and	and	CCONJ
ejpam-1929	585	22	combinatorial	combinatorial	ADJ
ejpam-1929	585	23	computing	computing	NOUN
ejpam-1929	585	24	,	,	PUNCT
ejpam-1929	585	25	18(1995	18(1995	NUM
ejpam-1929	585	26	)	)	PUNCT
ejpam-1929	585	27	,	,	PUNCT
ejpam-1929	585	28	121	121	NUM
ejpam-1929	585	29	-	-	SYM
ejpam-1929	585	30	124	124	NUM
ejpam-1929	585	31	.	.	PUNCT
ejpam-1929	586	1	[	[	X
ejpam-1929	586	2	21	21	NUM
ejpam-1929	586	3	]	]	PUNCT
ejpam-1929	586	4	a.	a.	NOUN
ejpam-1929	586	5	droll	droll	NOUN
ejpam-1929	586	6	,	,	PUNCT
ejpam-1929	586	7	a	a	DET
ejpam-1929	586	8	classification	classification	NOUN
ejpam-1929	586	9	of	of	ADP
ejpam-1929	586	10	ramanujan	ramanujan	NOUN
ejpam-1929	586	11	unitary	unitary	ADJ
ejpam-1929	586	12	cayley	cayley	ADJ
ejpam-1929	586	13	graphs	graph	NOUN
ejpam-1929	586	14	,	,	PUNCT
ejpam-1929	586	15	electronic	electronic	ADJ
ejpam-1929	586	16	journal	journal	NOUN
ejpam-1929	586	17	of	of	ADP
ejpam-1929	586	18	combinatorics	combinatoric	NOUN
ejpam-1929	586	19	,	,	PUNCT
ejpam-1929	586	20	17(2010	17(2010	NUM
ejpam-1929	586	21	)	)	PUNCT
ejpam-1929	586	22	,	,	PUNCT
ejpam-1929	586	23	#	#	NOUN
ejpam-1929	586	24	n29	n29	NOUN
ejpam-1929	586	25	.	.	PUNCT
ejpam-1929	587	1	[	[	X
ejpam-1929	587	2	22	22	NUM
ejpam-1929	587	3	]	]	X
ejpam-1929	587	4	e.d	e.d	PROPN
ejpam-1929	587	5	.	.	PROPN
ejpam-1929	587	6	fuchs	fuchs	PROPN
ejpam-1929	587	7	and	and	CCONJ
ejpam-1929	587	8	j.	j.	PROPN
ejpam-1929	587	9	sinz	sinz	PROPN
ejpam-1929	587	10	,	,	PUNCT
ejpam-1929	587	11	longest	long	ADV
ejpam-1929	587	12	induced	induce	VERB
ejpam-1929	587	13	cycles	cycle	NOUN
ejpam-1929	587	14	in	in	ADP
ejpam-1929	587	15	cayley	cayley	ADJ
ejpam-1929	587	16	graphs	graph	NOUN
ejpam-1929	587	17	,	,	PUNCT
ejpam-1929	587	18	eprint	eprint	NOUN
ejpam-1929	587	19	arxiv	arxiv	PROPN
ejpam-1929	587	20	:	:	PUNCT
ejpam-1929	587	21	math/0410308v2	math/0410308v2	NOUN
ejpam-1929	587	22	(	(	PUNCT
ejpam-1929	587	23	2004	2004	NUM
ejpam-1929	587	24	)	)	PUNCT
ejpam-1929	587	25	,	,	PUNCT
ejpam-1929	587	26	1	1	NUM
ejpam-1929	587	27	-	-	SYM
ejpam-1929	587	28	16	16	NUM
ejpam-1929	587	29	.	.	PUNCT
ejpam-1929	588	1	[	[	X
ejpam-1929	588	2	23	23	NUM
ejpam-1929	588	3	]	]	X
ejpam-1929	588	4	e.d	e.d	PROPN
ejpam-1929	588	5	.	.	PROPN
ejpam-1929	588	6	fuchs	fuchs	PROPN
ejpam-1929	588	7	,	,	PUNCT
ejpam-1929	588	8	longest	long	ADV
ejpam-1929	588	9	induced	induce	VERB
ejpam-1929	588	10	cycles	cycle	NOUN
ejpam-1929	588	11	in	in	ADP
ejpam-1929	588	12	circulant	circulant	ADJ
ejpam-1929	588	13	graphs	graph	NOUN
ejpam-1929	588	14	,	,	PUNCT
ejpam-1929	588	15	electronic	electronic	ADJ
ejpam-1929	588	16	journal	journal	NOUN
ejpam-1929	588	17	of	of	ADP
ejpam-1929	588	18	combinatorics	combinatoric	NOUN
ejpam-1929	588	19	,	,	PUNCT
ejpam-1929	588	20	12(2005	12(2005	NUM
ejpam-1929	588	21	)	)	PUNCT
ejpam-1929	588	22	,	,	PUNCT
ejpam-1929	588	23	1	1	NUM
ejpam-1929	588	24	-	-	SYM
ejpam-1929	588	25	12	12	NUM
ejpam-1929	588	26	.	.	PUNCT
ejpam-1929	589	1	[	[	X
ejpam-1929	589	2	24	24	NUM
ejpam-1929	589	3	]	]	X
ejpam-1929	589	4	m.k	m.k	PROPN
ejpam-1929	589	5	.	.	PUNCT
ejpam-1929	589	6	gill	gill	PROPN
ejpam-1929	589	7	,	,	PUNCT
ejpam-1929	589	8	contribution	contribution	NOUN
ejpam-1929	589	9	to	to	ADP
ejpam-1929	589	10	some	some	DET
ejpam-1929	589	11	topics	topic	NOUN
ejpam-1929	589	12	in	in	ADP
ejpam-1929	589	13	graph	graph	NOUN
ejpam-1929	589	14	theory	theory	NOUN
ejpam-1929	589	15	and	and	CCONJ
ejpam-1929	589	16	its	its	PRON
ejpam-1929	589	17	applications	application	NOUN
ejpam-1929	589	18	,	,	PUNCT
ejpam-1929	589	19	ph.d	ph.d	PROPN
ejpam-1929	589	20	.	.	PUNCT
ejpam-1929	590	1	thesis	thesis	PROPN
ejpam-1929	590	2	,	,	PUNCT
ejpam-1929	590	3	indian	indian	PROPN
ejpam-1929	590	4	institute	institute	PROPN
ejpam-1929	590	5	of	of	ADP
ejpam-1929	590	6	technology	technology	PROPN
ejpam-1929	590	7	,	,	PUNCT
ejpam-1929	590	8	bombay	bombay	PROPN
ejpam-1929	590	9	,	,	PUNCT
ejpam-1929	590	10	1983	1983	NUM
ejpam-1929	590	11	.	.	PUNCT
ejpam-1929	591	1	[	[	X
ejpam-1929	591	2	25	25	NUM
ejpam-1929	591	3	]	]	X
ejpam-1929	591	4	c.	c.	NOUN
ejpam-1929	591	5	godsil	godsil	PROPN
ejpam-1929	591	6	and	and	CCONJ
ejpam-1929	591	7	g.	g.	PROPN
ejpam-1929	591	8	royle	royle	PROPN
ejpam-1929	591	9	,	,	PUNCT
ejpam-1929	591	10	algebraic	algebraic	ADJ
ejpam-1929	591	11	graph	graph	NOUN
ejpam-1929	591	12	theory	theory	NOUN
ejpam-1929	591	13	,	,	PUNCT
ejpam-1929	591	14	graduate	graduate	NOUN
ejpam-1929	591	15	texts	text	NOUN
ejpam-1929	591	16	in	in	ADP
ejpam-1929	591	17	mathematics	mathematic	NOUN
ejpam-1929	591	18	,	,	PUNCT
ejpam-1929	591	19	springer	springer	NOUN
ejpam-1929	591	20	,	,	PUNCT
ejpam-1929	591	21	207	207	NUM
ejpam-1929	591	22	,	,	PUNCT
ejpam-1929	591	23	2001	2001	NUM
ejpam-1929	591	24	.	.	PUNCT
ejpam-1929	592	1	[	[	X
ejpam-1929	592	2	26	26	NUM
ejpam-1929	592	3	]	]	X
ejpam-1929	592	4	b.j	b.j	PROPN
ejpam-1929	592	5	.	.	PROPN
ejpam-1929	592	6	green	green	PROPN
ejpam-1929	592	7	,	,	PUNCT
ejpam-1929	592	8	counting	count	VERB
ejpam-1929	592	9	sets	set	NOUN
ejpam-1929	592	10	with	with	ADP
ejpam-1929	592	11	small	small	ADJ
ejpam-1929	592	12	sumset	sumset	NOUN
ejpam-1929	592	13	,	,	PUNCT
ejpam-1929	592	14	and	and	CCONJ
ejpam-1929	592	15	the	the	DET
ejpam-1929	592	16	clique	clique	ADJ
ejpam-1929	592	17	number	number	NOUN
ejpam-1929	592	18	of	of	ADP
ejpam-1929	592	19	random	random	ADJ
ejpam-1929	592	20	cayley	cayley	NOUN
ejpam-1929	592	21	graphs	graph	NOUN
ejpam-1929	592	22	,	,	PUNCT
ejpam-1929	592	23	combinatorica	combinatorica	PROPN
ejpam-1929	592	24	,	,	PUNCT
ejpam-1929	592	25	25(2005	25(2005	NUM
ejpam-1929	592	26	)	)	PUNCT
ejpam-1929	592	27	,	,	PUNCT
ejpam-1929	592	28	307	307	NUM
ejpam-1929	592	29	-	-	SYM
ejpam-1929	592	30	326	326	NUM
ejpam-1929	592	31	.	.	PUNCT
ejpam-1929	593	1	[	[	X
ejpam-1929	593	2	27	27	NUM
ejpam-1929	593	3	]	]	X
ejpam-1929	593	4	d.	d.	PROPN
ejpam-1929	593	5	grynkiewicz	grynkiewicz	PROPN
ejpam-1929	593	6	,	,	PUNCT
ejpam-1929	593	7	v.f	v.f	PROPN
ejpam-1929	593	8	.	.	PROPN
ejpam-1929	593	9	lev	lev	PROPN
ejpam-1929	593	10	and	and	CCONJ
ejpam-1929	593	11	o.	o.	PROPN
ejpam-1929	593	12	serra	serra	PROPN
ejpam-1929	593	13	,	,	PUNCT
ejpam-1929	593	14	the	the	DET
ejpam-1929	593	15	connectivity	connectivity	NOUN
ejpam-1929	593	16	of	of	ADP
ejpam-1929	593	17	addition	addition	NOUN
ejpam-1929	593	18	cayley	cayley	NOUN
ejpam-1929	593	19	graphs	graph	NOUN
ejpam-1929	593	20	,	,	PUNCT
ejpam-1929	593	21	electronic	electronic	ADJ
ejpam-1929	593	22	notes	note	NOUN
ejpam-1929	593	23	in	in	ADP
ejpam-1929	593	24	discrete	discrete	ADJ
ejpam-1929	593	25	mathematics	mathematic	NOUN
ejpam-1929	593	26	,	,	PUNCT
ejpam-1929	593	27	29(2007	29(2007	NUM
ejpam-1929	593	28	)	)	PUNCT
ejpam-1929	593	29	,	,	PUNCT
ejpam-1929	593	30	135	135	NUM
ejpam-1929	593	31	-	-	SYM
ejpam-1929	593	32	139	139	NUM
ejpam-1929	593	33	.	.	PUNCT
ejpam-1929	594	1	[	[	X
ejpam-1929	594	2	28	28	NUM
ejpam-1929	594	3	]	]	X
ejpam-1929	594	4	d.	d.	PROPN
ejpam-1929	594	5	grynkiewicz	grynkiewicz	PROPN
ejpam-1929	594	6	,	,	PUNCT
ejpam-1929	594	7	v.f	v.f	PROPN
ejpam-1929	594	8	.	.	PROPN
ejpam-1929	594	9	lev	lev	PROPN
ejpam-1929	594	10	and	and	CCONJ
ejpam-1929	594	11	o.	o.	PROPN
ejpam-1929	594	12	serra	serra	PROPN
ejpam-1929	594	13	,	,	PUNCT
ejpam-1929	594	14	connectivity	connectivity	NOUN
ejpam-1929	594	15	of	of	ADP
ejpam-1929	594	16	addition	addition	NOUN
ejpam-1929	594	17	cayley	cayley	NOUN
ejpam-1929	594	18	graphs	graph	NOUN
ejpam-1929	594	19	,	,	PUNCT
ejpam-1929	594	20	journal	journal	NOUN
ejpam-1929	594	21	of	of	ADP
ejpam-1929	594	22	combinatorial	combinatorial	ADJ
ejpam-1929	594	23	theory	theory	NOUN
ejpam-1929	594	24	,	,	PUNCT
ejpam-1929	594	25	series	series	PROPN
ejpam-1929	594	26	b	b	PROPN
ejpam-1929	594	27	,	,	PUNCT
ejpam-1929	594	28	99(1)(2009	99(1)(2009	NUM
ejpam-1929	594	29	)	)	PUNCT
ejpam-1929	594	30	,	,	PUNCT
ejpam-1929	594	31	202	202	NUM
ejpam-1929	594	32	-	-	SYM
ejpam-1929	594	33	217	217	NUM
ejpam-1929	594	34	.	.	PUNCT
ejpam-1929	595	1	[	[	X
ejpam-1929	595	2	29	29	NUM
ejpam-1929	595	3	]	]	X
ejpam-1929	595	4	f.	f.	PROPN
ejpam-1929	595	5	harary	harary	PROPN
ejpam-1929	595	6	,	,	PUNCT
ejpam-1929	595	7	on	on	ADP
ejpam-1929	595	8	the	the	DET
ejpam-1929	595	9	notion	notion	NOUN
ejpam-1929	595	10	of	of	ADP
ejpam-1929	595	11	balance	balance	NOUN
ejpam-1929	595	12	of	of	ADP
ejpam-1929	595	13	a	a	DET
ejpam-1929	595	14	signed	sign	VERB
ejpam-1929	595	15	graph	graph	NOUN
ejpam-1929	595	16	,	,	PUNCT
ejpam-1929	595	17	michigan	michigan	PROPN
ejpam-1929	595	18	mathematical	mathematical	PROPN
ejpam-1929	595	19	journal	journal	PROPN
ejpam-1929	595	20	,	,	PUNCT
ejpam-1929	595	21	2(1953	2(1953	NUM
ejpam-1929	595	22	)	)	PUNCT
ejpam-1929	595	23	,	,	PUNCT
ejpam-1929	595	24	143	143	NUM
ejpam-1929	595	25	-	-	SYM
ejpam-1929	595	26	146	146	NUM
ejpam-1929	595	27	.	.	PUNCT
ejpam-1929	596	1	[	[	X
ejpam-1929	596	2	30	30	NUM
ejpam-1929	596	3	]	]	X
ejpam-1929	596	4	f.	f.	PROPN
ejpam-1929	596	5	harary	harary	PROPN
ejpam-1929	596	6	,	,	PUNCT
ejpam-1929	596	7	graph	graph	NOUN
ejpam-1929	596	8	theory	theory	NOUN
ejpam-1929	596	9	,	,	PUNCT
ejpam-1929	596	10	addison	addison	PROPN
ejpam-1929	596	11	-	-	PUNCT
ejpam-1929	596	12	wesley	wesley	PROPN
ejpam-1929	596	13	publishing	publishing	PROPN
ejpam-1929	596	14	company	company	NOUN
ejpam-1929	596	15	,	,	PUNCT
ejpam-1929	596	16	reading	reading	NOUN
ejpam-1929	596	17	,	,	PUNCT
ejpam-1929	596	18	massachusetts	massachusetts	PROPN
ejpam-1929	596	19	,	,	PUNCT
ejpam-1929	596	20	1969	1969	NUM
ejpam-1929	596	21	.	.	PUNCT
ejpam-1929	597	1	[	[	X
ejpam-1929	597	2	31	31	NUM
ejpam-1929	597	3	]	]	X
ejpam-1929	597	4	f.	f.	PROPN
ejpam-1929	597	5	harary	harary	PROPN
ejpam-1929	597	6	and	and	CCONJ
ejpam-1929	597	7	j.a	j.a	PROPN
ejpam-1929	597	8	.	.	PROPN
ejpam-1929	597	9	kabell	kabell	PROPN
ejpam-1929	597	10	,	,	PUNCT
ejpam-1929	597	11	a	a	DET
ejpam-1929	597	12	simple	simple	ADJ
ejpam-1929	597	13	algorithm	algorithm	NOUN
ejpam-1929	597	14	to	to	PART
ejpam-1929	597	15	detect	detect	VERB
ejpam-1929	597	16	balance	balance	NOUN
ejpam-1929	597	17	in	in	ADP
ejpam-1929	597	18	signed	sign	VERB
ejpam-1929	597	19	graphs	graph	NOUN
ejpam-1929	597	20	,	,	PUNCT
ejpam-1929	597	21	mathematical	mathematical	ADJ
ejpam-1929	597	22	social	social	ADJ
ejpam-1929	597	23	sciences	science	NOUN
ejpam-1929	597	24	,	,	PUNCT
ejpam-1929	597	25	1(1980	1(1980	NUM
ejpam-1929	597	26	-	-	SYM
ejpam-1929	597	27	81	81	NUM
ejpam-1929	597	28	)	)	PUNCT
ejpam-1929	597	29	,	,	PUNCT
ejpam-1929	597	30	131	131	NUM
ejpam-1929	597	31	-	-	SYM
ejpam-1929	597	32	136	136	NUM
ejpam-1929	597	33	.	.	PUNCT
ejpam-1929	598	1	references	reference	NOUN
ejpam-1929	598	2	210	210	NUM
ejpam-1929	599	1	[	[	X
ejpam-1929	599	2	32	32	NUM
ejpam-1929	599	3	]	]	PUNCT
ejpam-1929	599	4	f.	f.	PROPN
ejpam-1929	599	5	harary	harary	PROPN
ejpam-1929	599	6	and	and	CCONJ
ejpam-1929	599	7	j.a	j.a	PROPN
ejpam-1929	599	8	.	.	PROPN
ejpam-1929	599	9	kabell	kabell	PROPN
ejpam-1929	599	10	,	,	PUNCT
ejpam-1929	599	11	counting	count	VERB
ejpam-1929	599	12	balanced	balance	VERB
ejpam-1929	599	13	signed	sign	VERB
ejpam-1929	599	14	graphs	graph	NOUN
ejpam-1929	599	15	using	use	VERB
ejpam-1929	599	16	marked	mark	VERB
ejpam-1929	599	17	graphs	graph	NOUN
ejpam-1929	599	18	,	,	PUNCT
ejpam-1929	599	19	proceedings	proceeding	NOUN
ejpam-1929	599	20	of	of	ADP
ejpam-1929	599	21	the	the	DET
ejpam-1929	599	22	edinburgh	edinburgh	PROPN
ejpam-1929	599	23	mathematical	mathematical	PROPN
ejpam-1929	599	24	society	society	PROPN
ejpam-1929	599	25	,	,	PUNCT
ejpam-1929	599	26	24(2)(1981	24(2)(1981	NUM
ejpam-1929	599	27	)	)	PUNCT
ejpam-1929	599	28	,	,	PUNCT
ejpam-1929	599	29	99	99	NUM
ejpam-1929	599	30	-	-	SYM
ejpam-1929	599	31	104	104	NUM
ejpam-1929	599	32	.	.	PUNCT
ejpam-1929	600	1	[	[	X
ejpam-1929	600	2	33	33	NUM
ejpam-1929	600	3	]	]	PUNCT
ejpam-1929	600	4	c.	c.	PROPN
ejpam-1929	600	5	hoede	hoede	PROPN
ejpam-1929	600	6	,	,	PUNCT
ejpam-1929	600	7	a	a	DET
ejpam-1929	600	8	characterization	characterization	NOUN
ejpam-1929	600	9	of	of	ADP
ejpam-1929	600	10	consistent	consistent	ADJ
ejpam-1929	600	11	marked	mark	VERB
ejpam-1929	600	12	graphs	graph	NOUN
ejpam-1929	600	13	,	,	PUNCT
ejpam-1929	600	14	journal	journal	NOUN
ejpam-1929	600	15	of	of	ADP
ejpam-1929	600	16	graph	graph	NOUN
ejpam-1929	600	17	theory	theory	NOUN
ejpam-1929	600	18	,	,	PUNCT
ejpam-1929	600	19	16(1)(1992	16(1)(1992	NUM
ejpam-1929	600	20	)	)	PUNCT
ejpam-1929	600	21	,	,	PUNCT
ejpam-1929	600	22	17	17	NUM
ejpam-1929	600	23	-	-	SYM
ejpam-1929	600	24	23	23	NUM
ejpam-1929	600	25	.	.	PUNCT
ejpam-1929	601	1	[	[	X
ejpam-1929	601	2	34	34	NUM
ejpam-1929	601	3	]	]	X
ejpam-1929	601	4	w.	w.	PROPN
ejpam-1929	601	5	klotz	klotz	PROPN
ejpam-1929	601	6	and	and	CCONJ
ejpam-1929	601	7	t.	t.	PROPN
ejpam-1929	601	8	sander	sander	NOUN
ejpam-1929	601	9	,	,	PUNCT
ejpam-1929	601	10	some	some	DET
ejpam-1929	601	11	properties	property	NOUN
ejpam-1929	601	12	of	of	ADP
ejpam-1929	601	13	unitary	unitary	ADJ
ejpam-1929	601	14	cayley	cayley	ADJ
ejpam-1929	601	15	graphs	graph	NOUN
ejpam-1929	601	16	,	,	PUNCT
ejpam-1929	601	17	electronic	electronic	ADJ
ejpam-1929	601	18	journal	journal	NOUN
ejpam-1929	601	19	of	of	ADP
ejpam-1929	601	20	combinatorics	combinatoric	NOUN
ejpam-1929	601	21	,	,	PUNCT
ejpam-1929	601	22	14(2007	14(2007	NUM
ejpam-1929	601	23	)	)	PUNCT
ejpam-1929	601	24	,	,	PUNCT
ejpam-1929	601	25	#	#	NOUN
ejpam-1929	601	26	r45	r45	NOUN
ejpam-1929	601	27	.	.	PUNCT
ejpam-1929	602	1	[	[	X
ejpam-1929	602	2	35	35	NUM
ejpam-1929	602	3	]	]	X
ejpam-1929	602	4	v.f	v.f	PROPN
ejpam-1929	602	5	.	.	PROPN
ejpam-1929	602	6	lev	lev	PROPN
ejpam-1929	602	7	,	,	PUNCT
ejpam-1929	602	8	sums	sum	NOUN
ejpam-1929	602	9	and	and	CCONJ
ejpam-1929	602	10	differences	difference	NOUN
ejpam-1929	602	11	along	along	ADP
ejpam-1929	602	12	hamiltonian	hamiltonian	ADJ
ejpam-1929	602	13	cycles	cycle	NOUN
ejpam-1929	602	14	,	,	PUNCT
ejpam-1929	602	15	electronic	electronic	ADJ
ejpam-1929	602	16	notes	note	NOUN
ejpam-1929	602	17	in	in	ADP
ejpam-1929	602	18	discrete	discrete	ADJ
ejpam-1929	602	19	mathematics	mathematic	NOUN
ejpam-1929	602	20	,	,	PUNCT
ejpam-1929	602	21	28(2007	28(2007	NUM
ejpam-1929	602	22	)	)	PUNCT
ejpam-1929	602	23	,	,	PUNCT
ejpam-1929	602	24	25	25	NUM
ejpam-1929	602	25	-	-	SYM
ejpam-1929	602	26	31	31	NUM
ejpam-1929	602	27	.	.	PUNCT
ejpam-1929	603	1	[	[	X
ejpam-1929	603	2	36	36	NUM
ejpam-1929	603	3	]	]	X
ejpam-1929	603	4	v.f	v.f	PROPN
ejpam-1929	603	5	.	.	PROPN
ejpam-1929	603	6	lev	lev	PROPN
ejpam-1929	603	7	,	,	PUNCT
ejpam-1929	603	8	sums	sum	NOUN
ejpam-1929	603	9	and	and	CCONJ
ejpam-1929	603	10	differences	difference	NOUN
ejpam-1929	603	11	along	along	ADP
ejpam-1929	603	12	hamiltonian	hamiltonian	ADJ
ejpam-1929	603	13	cycles	cycle	NOUN
ejpam-1929	603	14	,	,	PUNCT
ejpam-1929	603	15	discrete	discrete	ADJ
ejpam-1929	603	16	mathematics	mathematic	NOUN
ejpam-1929	603	17	,	,	PUNCT
ejpam-1929	603	18	310(3)(2010	310(3)(2010	NOUN
ejpam-1929	603	19	)	)	PUNCT
ejpam-1929	603	20	,	,	PUNCT
ejpam-1929	603	21	575	575	NUM
ejpam-1929	603	22	-	-	SYM
ejpam-1929	603	23	584	584	NUM
ejpam-1929	603	24	.	.	PUNCT
ejpam-1929	604	1	[	[	X
ejpam-1929	604	2	37	37	NUM
ejpam-1929	604	3	]	]	X
ejpam-1929	604	4	h.n	h.n	PROPN
ejpam-1929	604	5	.	.	PROPN
ejpam-1929	604	6	ramaswamy	ramaswamy	PROPN
ejpam-1929	604	7	and	and	CCONJ
ejpam-1929	604	8	c.r	c.r	PROPN
ejpam-1929	604	9	.	.	PROPN
ejpam-1929	604	10	veena	veena	PROPN
ejpam-1929	604	11	,	,	PUNCT
ejpam-1929	604	12	on	on	ADP
ejpam-1929	604	13	the	the	DET
ejpam-1929	604	14	energy	energy	NOUN
ejpam-1929	604	15	of	of	ADP
ejpam-1929	604	16	unitary	unitary	ADJ
ejpam-1929	604	17	cayley	cayley	ADJ
ejpam-1929	604	18	graphs	graph	NOUN
ejpam-1929	604	19	,	,	PUNCT
ejpam-1929	604	20	electronic	electronic	ADJ
ejpam-1929	604	21	journal	journal	NOUN
ejpam-1929	604	22	of	of	ADP
ejpam-1929	604	23	combinatorics	combinatoric	NOUN
ejpam-1929	604	24	,	,	PUNCT
ejpam-1929	604	25	16(2009	16(2009	NUM
ejpam-1929	604	26	)	)	PUNCT
ejpam-1929	604	27	,	,	PUNCT
ejpam-1929	604	28	#	#	NOUN
ejpam-1929	604	29	n24	n24	NOUN
ejpam-1929	604	30	.	.	PUNCT
ejpam-1929	605	1	[	[	X
ejpam-1929	605	2	38	38	NUM
ejpam-1929	605	3	]	]	PUNCT
ejpam-1929	605	4	e.	e.	PROPN
ejpam-1929	605	5	sampathkumar	sampathkumar	PROPN
ejpam-1929	605	6	and	and	CCONJ
ejpam-1929	605	7	s.b	s.b	PROPN
ejpam-1929	605	8	.	.	PROPN
ejpam-1929	605	9	chikkodimath	chikkodimath	PROPN
ejpam-1929	605	10	,	,	PUNCT
ejpam-1929	605	11	semitotal	semitotal	ADJ
ejpam-1929	605	12	graphs	graph	NOUN
ejpam-1929	605	13	of	of	ADP
ejpam-1929	605	14	a	a	DET
ejpam-1929	605	15	graph	graph	NOUN
ejpam-1929	605	16	-	-	PUNCT
ejpam-1929	605	17	i	i	PROPN
ejpam-1929	605	18	,	,	PUNCT
ejpam-1929	605	19	journal	journal	NOUN
ejpam-1929	605	20	of	of	ADP
ejpam-1929	605	21	karnatak	karnatak	PROPN
ejpam-1929	605	22	university	university	PROPN
ejpam-1929	605	23	science	science	NOUN
ejpam-1929	605	24	,	,	PUNCT
ejpam-1929	605	25	18(1973	18(1973	NUM
ejpam-1929	605	26	)	)	PUNCT
ejpam-1929	605	27	,	,	PUNCT
ejpam-1929	605	28	274	274	NUM
ejpam-1929	605	29	-	-	SYM
ejpam-1929	605	30	280	280	NUM
ejpam-1929	605	31	.	.	PUNCT
ejpam-1929	606	1	[	[	X
ejpam-1929	606	2	39	39	NUM
ejpam-1929	606	3	]	]	PUNCT
ejpam-1929	606	4	t.	t.	NOUN
ejpam-1929	606	5	sander	sander	NOUN
ejpam-1929	606	6	,	,	PUNCT
ejpam-1929	606	7	eigenspaces	eigenspace	NOUN
ejpam-1929	606	8	of	of	ADP
ejpam-1929	606	9	hamming	hamming	NOUN
ejpam-1929	606	10	graphs	graph	NOUN
ejpam-1929	606	11	and	and	CCONJ
ejpam-1929	606	12	unitary	unitary	ADJ
ejpam-1929	606	13	cayley	cayley	ADJ
ejpam-1929	606	14	graphs	graph	NOUN
ejpam-1929	606	15	,	,	PUNCT
ejpam-1929	606	16	ars	ar	VERB
ejpam-1929	606	17	mathematica	mathematica	PROPN
ejpam-1929	606	18	contemporanea	contemporanea	PROPN
ejpam-1929	606	19	,	,	PUNCT
ejpam-1929	606	20	3(2010	3(2010	NUM
ejpam-1929	606	21	)	)	PUNCT
ejpam-1929	606	22	,	,	PUNCT
ejpam-1929	606	23	13	13	NUM
ejpam-1929	606	24	-	-	SYM
ejpam-1929	606	25	19	19	NUM
ejpam-1929	606	26	.	.	PUNCT
ejpam-1929	607	1	[	[	X
ejpam-1929	607	2	40	40	NUM
ejpam-1929	607	3	]	]	X
ejpam-1929	607	4	d.	d.	PROPN
ejpam-1929	607	5	sinha	sinha	PROPN
ejpam-1929	607	6	,	,	PUNCT
ejpam-1929	607	7	new	new	ADJ
ejpam-1929	607	8	frontiers	frontier	NOUN
ejpam-1929	607	9	in	in	ADP
ejpam-1929	607	10	the	the	DET
ejpam-1929	607	11	theory	theory	NOUN
ejpam-1929	607	12	of	of	ADP
ejpam-1929	607	13	signed	sign	VERB
ejpam-1929	607	14	graphs	graph	NOUN
ejpam-1929	607	15	,	,	PUNCT
ejpam-1929	607	16	ph.d	ph.d	PROPN
ejpam-1929	607	17	.	.	PUNCT
ejpam-1929	608	1	thesis	thesis	NOUN
ejpam-1929	608	2	,	,	PUNCT
ejpam-1929	608	3	university	university	NOUN
ejpam-1929	608	4	of	of	ADP
ejpam-1929	608	5	delhi	delhi	PROPN
ejpam-1929	608	6	,	,	PUNCT
ejpam-1929	608	7	2005	2005	NUM
ejpam-1929	608	8	.	.	PUNCT
ejpam-1929	609	1	[	[	X
ejpam-1929	609	2	41	41	NUM
ejpam-1929	609	3	]	]	X
ejpam-1929	609	4	d.	d.	PROPN
ejpam-1929	609	5	sinha	sinha	PROPN
ejpam-1929	609	6	and	and	CCONJ
ejpam-1929	609	7	a.	a.	NOUN
ejpam-1929	609	8	dhama	dhama	PROPN
ejpam-1929	609	9	,	,	PUNCT
ejpam-1929	609	10	sign	sign	NOUN
ejpam-1929	609	11	-	-	PUNCT
ejpam-1929	609	12	compatibility	compatibility	NOUN
ejpam-1929	609	13	of	of	ADP
ejpam-1929	609	14	some	some	DET
ejpam-1929	609	15	derived	derive	VERB
ejpam-1929	609	16	signed	sign	VERB
ejpam-1929	609	17	graphs	graph	NOUN
ejpam-1929	609	18	,	,	PUNCT
ejpam-1929	609	19	indian	indian	ADJ
ejpam-1929	609	20	journal	journal	NOUN
ejpam-1929	609	21	of	of	ADP
ejpam-1929	609	22	mathematics	mathematic	NOUN
ejpam-1929	609	23	,	,	PUNCT
ejpam-1929	609	24	55(1	55(1	NOUN
ejpam-1929	609	25	)	)	PUNCT
ejpam-1929	609	26	,	,	PUNCT
ejpam-1929	609	27	2013	2013	NUM
ejpam-1929	609	28	.	.	PUNCT
ejpam-1929	610	1	[	[	X
ejpam-1929	610	2	42	42	NUM
ejpam-1929	610	3	]	]	X
ejpam-1929	610	4	d.	d.	PROPN
ejpam-1929	610	5	sinha	sinha	PROPN
ejpam-1929	610	6	and	and	CCONJ
ejpam-1929	610	7	p.	p.	PROPN
ejpam-1929	610	8	garg	garg	NOUN
ejpam-1929	610	9	,	,	PUNCT
ejpam-1929	610	10	on	on	ADP
ejpam-1929	610	11	the	the	DET
ejpam-1929	610	12	unitary	unitary	ADJ
ejpam-1929	610	13	cayley	cayley	NOUN
ejpam-1929	610	14	signed	sign	VERB
ejpam-1929	610	15	graphs	graph	NOUN
ejpam-1929	610	16	,	,	PUNCT
ejpam-1929	610	17	electronic	electronic	ADJ
ejpam-1929	610	18	journal	journal	NOUN
ejpam-1929	610	19	of	of	ADP
ejpam-1929	610	20	combinatorics	combinatoric	NOUN
ejpam-1929	610	21	,	,	PUNCT
ejpam-1929	610	22	18(2011	18(2011	NUM
ejpam-1929	610	23	)	)	PUNCT
ejpam-1929	610	24	,	,	PUNCT
ejpam-1929	610	25	#	#	SYM
ejpam-1929	610	26	p229	p229	PROPN
ejpam-1929	610	27	.	.	PUNCT
ejpam-1929	611	1	[	[	X
ejpam-1929	611	2	43	43	NUM
ejpam-1929	611	3	]	]	X
ejpam-1929	611	4	d.	d.	PROPN
ejpam-1929	611	5	sinha	sinha	PROPN
ejpam-1929	611	6	,	,	PUNCT
ejpam-1929	611	7	p.	p.	NOUN
ejpam-1929	611	8	garg	garg	PROPN
ejpam-1929	611	9	and	and	CCONJ
ejpam-1929	611	10	a.	a.	PROPN
ejpam-1929	611	11	singh	singh	PROPN
ejpam-1929	611	12	,	,	PUNCT
ejpam-1929	611	13	some	some	DET
ejpam-1929	611	14	properties	property	NOUN
ejpam-1929	611	15	of	of	ADP
ejpam-1929	611	16	unitary	unitary	ADJ
ejpam-1929	611	17	addition	addition	NOUN
ejpam-1929	611	18	cayley	cayley	NOUN
ejpam-1929	611	19	graphs	graph	NOUN
ejpam-1929	611	20	,	,	PUNCT
ejpam-1929	611	21	notes	note	NOUN
ejpam-1929	611	22	on	on	ADP
ejpam-1929	611	23	number	number	NOUN
ejpam-1929	611	24	theory	theory	NOUN
ejpam-1929	611	25	and	and	CCONJ
ejpam-1929	611	26	discrete	discrete	ADJ
ejpam-1929	611	27	mathematics	mathematic	NOUN
ejpam-1929	611	28	,	,	PUNCT
ejpam-1929	611	29	17(3)(2011	17(3)(2011	NUM
ejpam-1929	611	30	)	)	PUNCT
ejpam-1929	611	31	,	,	PUNCT
ejpam-1929	611	32	49	49	NUM
ejpam-1929	611	33	-	-	SYM
ejpam-1929	611	34	59	59	NUM
ejpam-1929	611	35	.	.	PUNCT
ejpam-1929	612	1	[	[	X
ejpam-1929	612	2	44	44	NUM
ejpam-1929	612	3	]	]	PUNCT
ejpam-1929	612	4	d.	d.	PROPN
ejpam-1929	612	5	sinha	sinha	PROPN
ejpam-1929	612	6	and	and	CCONJ
ejpam-1929	612	7	p.	p.	PROPN
ejpam-1929	612	8	garg	garg	NOUN
ejpam-1929	612	9	,	,	PUNCT
ejpam-1929	612	10	some	some	DET
ejpam-1929	612	11	results	result	NOUN
ejpam-1929	612	12	on	on	ADP
ejpam-1929	612	13	semi	semi	ADJ
ejpam-1929	612	14	-	-	ADJ
ejpam-1929	612	15	total	total	ADJ
ejpam-1929	612	16	signed	sign	VERB
ejpam-1929	612	17	graphs	graph	NOUN
ejpam-1929	612	18	,	,	PUNCT
ejpam-1929	612	19	discussiones	discussione	NOUN
ejpam-1929	612	20	mathematicae	mathematicae	VERB
ejpam-1929	612	21	.	.	PUNCT
ejpam-1929	613	1	graph	graph	NOUN
ejpam-1929	613	2	theory	theory	NOUN
ejpam-1929	613	3	,	,	PUNCT
ejpam-1929	613	4	31(4)(2011b	31(4)(2011b	NUM
ejpam-1929	613	5	)	)	PUNCT
ejpam-1929	613	6	,	,	PUNCT
ejpam-1929	613	7	625	625	NUM
ejpam-1929	613	8	-	-	SYM
ejpam-1929	613	9	638	638	NUM
ejpam-1929	613	10	.	.	PUNCT
ejpam-1929	614	1	[	[	X
ejpam-1929	614	2	45	45	NUM
ejpam-1929	614	3	]	]	SYM
ejpam-1929	614	4	d.b	d.b	PROPN
ejpam-1929	614	5	.	.	PROPN
ejpam-1929	614	6	west	west	PROPN
ejpam-1929	614	7	,	,	PUNCT
ejpam-1929	614	8	introduction	introduction	NOUN
ejpam-1929	614	9	to	to	AUX
ejpam-1929	614	10	graph	graph	NOUN
ejpam-1929	614	11	theory	theory	NOUN
ejpam-1929	614	12	,	,	PUNCT
ejpam-1929	614	13	prentice	prentice	NOUN
ejpam-1929	614	14	-	-	PUNCT
ejpam-1929	614	15	hall	hall	NOUN
ejpam-1929	614	16	of	of	ADP
ejpam-1929	614	17	india	india	PROPN
ejpam-1929	614	18	pvt	pvt	PROPN
ejpam-1929	614	19	.	.	PROPN
ejpam-1929	614	20	ltd	ltd	PROPN
ejpam-1929	614	21	.	.	PROPN
ejpam-1929	614	22	,	,	PUNCT
ejpam-1929	614	23	1996	1996	NUM
ejpam-1929	614	24	.	.	PUNCT
ejpam-1929	615	1	[	[	X
ejpam-1929	615	2	46	46	NUM
ejpam-1929	615	3	]	]	PUNCT
ejpam-1929	615	4	t.	t.	NOUN
ejpam-1929	615	5	zaslavsky	zaslavsky	NOUN
ejpam-1929	615	6	,	,	PUNCT
ejpam-1929	615	7	glossary	glossary	NOUN
ejpam-1929	615	8	of	of	ADP
ejpam-1929	615	9	signed	sign	VERB
ejpam-1929	615	10	and	and	CCONJ
ejpam-1929	615	11	gain	gain	VERB
ejpam-1929	615	12	graphs	graph	NOUN
ejpam-1929	615	13	and	and	CCONJ
ejpam-1929	615	14	allied	allied	ADJ
ejpam-1929	615	15	areas	area	NOUN
ejpam-1929	615	16	,	,	PUNCT
ejpam-1929	615	17	ii	ii	PROPN
ejpam-1929	615	18	edition	edition	NOUN
ejpam-1929	615	19	,	,	PUNCT
ejpam-1929	615	20	electronic	electronic	ADJ
ejpam-1929	615	21	journal	journal	NOUN
ejpam-1929	615	22	of	of	ADP
ejpam-1929	615	23	combinatorics	combinatoric	NOUN
ejpam-1929	615	24	,	,	PUNCT
ejpam-1929	615	25	#	#	SYM
ejpam-1929	615	26	ds8(1998	ds8(1998	NUM
ejpam-1929	615	27	)	)	PUNCT
ejpam-1929	615	28	.	.	PUNCT
ejpam-1929	616	1	[	[	X
ejpam-1929	616	2	47	47	NUM
ejpam-1929	616	3	]	]	PUNCT
ejpam-1929	616	4	t.	t.	NOUN
ejpam-1929	616	5	zaslavsky	zaslavsky	PROPN
ejpam-1929	616	6	,	,	PUNCT
ejpam-1929	616	7	a	a	DET
ejpam-1929	616	8	mathematical	mathematical	ADJ
ejpam-1929	616	9	bibliography	bibliography	NOUN
ejpam-1929	616	10	of	of	ADP
ejpam-1929	616	11	signed	sign	VERB
ejpam-1929	616	12	and	and	CCONJ
ejpam-1929	616	13	gain	gain	VERB
ejpam-1929	616	14	graphs	graph	NOUN
ejpam-1929	616	15	and	and	CCONJ
ejpam-1929	616	16	allied	allied	ADJ
ejpam-1929	616	17	areas	area	NOUN
ejpam-1929	616	18	,	,	PUNCT
ejpam-1929	616	19	vii	vii	PROPN
ejpam-1929	616	20	edition	edition	PROPN
ejpam-1929	616	21	,	,	PUNCT
ejpam-1929	616	22	electronic	electronic	ADJ
ejpam-1929	616	23	journal	journal	NOUN
ejpam-1929	616	24	of	of	ADP
ejpam-1929	616	25	combinatorics	combinatoric	NOUN
ejpam-1929	616	26	,	,	PUNCT
ejpam-1929	616	27	#	#	SYM
ejpam-1929	616	28	ds8(1998	ds8(1998	NUM
ejpam-1929	616	29	)	)	PUNCT
ejpam-1929	616	30	.	.	PUNCT
ejpam-1929	617	1	(	(	PUNCT
ejpam-1929	617	2	latest	late	ADJ
ejpam-1929	617	3	update	update	NOUN
ejpam-1929	617	4	:	:	PUNCT
ejpam-1929	617	5	8th	8th	ADJ
ejpam-1929	617	6	edition	edition	NOUN
ejpam-1929	617	7	,	,	PUNCT
ejpam-1929	617	8	september	september	PROPN
ejpam-1929	617	9	2012	2012	NUM
ejpam-1929	617	10	)	)	PUNCT
ejpam-1929	617	11	.	.	PUNCT
ejpam-1929	618	1	[	[	X
ejpam-1929	618	2	48	48	NUM
ejpam-1929	618	3	]	]	PUNCT
ejpam-1929	618	4	t.	t.	NOUN
ejpam-1929	618	5	zaslavsky	zaslavsky	PROPN
ejpam-1929	618	6	,	,	PUNCT
ejpam-1929	618	7	signed	sign	VERB
ejpam-1929	618	8	analogs	analog	NOUN
ejpam-1929	618	9	of	of	ADP
ejpam-1929	618	10	bipartite	bipartite	NOUN
ejpam-1929	618	11	graphs	graph	NOUN
ejpam-1929	618	12	,	,	PUNCT
ejpam-1929	618	13	discrete	discrete	ADJ
ejpam-1929	618	14	mathematics	mathematic	NOUN
ejpam-1929	618	15	,	,	PUNCT
ejpam-1929	618	16	179(1998	179(1998	NUM
ejpam-1929	618	17	)	)	PUNCT
ejpam-1929	618	18	,	,	PUNCT
ejpam-1929	618	19	205216	205216	NUM
ejpam-1929	618	20	,	,	PUNCT
ejpam-1929	618	21	(	(	PUNCT
ejpam-1929	618	22	1998	1998	NUM
ejpam-1929	618	23	)	)	PUNCT
ejpam-1929	618	24	.	.	PUNCT