id	sid	tid	token	lemma	pos
ejpam-6755	1	1	european	european	PROPN
ejpam-6755	1	2	journal	journal	PROPN
ejpam-6755	1	3	of	of	ADP
ejpam-6755	1	4	pure	pure	ADJ
ejpam-6755	1	5	and	and	CCONJ
ejpam-6755	1	6	applied	applied	ADJ
ejpam-6755	1	7	mathematics	mathematic	NOUN
ejpam-6755	1	8	2025	2025	NUM
ejpam-6755	1	9	,	,	PUNCT
ejpam-6755	1	10	vol	vol	NOUN
ejpam-6755	1	11	.	.	PROPN
ejpam-6755	1	12	18	18	NUM
ejpam-6755	1	13	,	,	PUNCT
ejpam-6755	1	14	issue	issue	NOUN
ejpam-6755	1	15	4	4	NUM
ejpam-6755	1	16	,	,	PUNCT
ejpam-6755	1	17	article	article	NOUN
ejpam-6755	1	18	number	number	NOUN
ejpam-6755	1	19	6755	6755	NUM
ejpam-6755	1	20	issn	issn	VERB
ejpam-6755	1	21	1307	1307	NUM
ejpam-6755	1	22	-	-	SYM
ejpam-6755	1	23	5543	5543	NUM
ejpam-6755	1	24	–	–	PUNCT
ejpam-6755	1	25	ejpam.com	ejpam.com	X
ejpam-6755	1	26	published	publish	VERB
ejpam-6755	1	27	by	by	ADP
ejpam-6755	1	28	new	new	PROPN
ejpam-6755	1	29	york	york	PROPN
ejpam-6755	1	30	business	business	PROPN
ejpam-6755	1	31	global	global	PROPN
ejpam-6755	1	32	on	on	ADP
ejpam-6755	1	33	(	(	PUNCT
ejpam-6755	1	34	h1	h1	PROPN
ejpam-6755	1	35	,	,	PUNCT
ejpam-6755	1	36	h2)-magic	h2)-magic	ADJ
ejpam-6755	1	37	generalized	generalize	VERB
ejpam-6755	1	38	total	total	ADJ
ejpam-6755	1	39	composition	composition	NOUN
ejpam-6755	1	40	tita	tita	PROPN
ejpam-6755	1	41	khalis	khalis	PROPN
ejpam-6755	1	42	maryati1,∗	maryati1,∗	PROPN
ejpam-6755	1	43	,	,	PUNCT
ejpam-6755	1	44	fawwaz	fawwaz	ADJ
ejpam-6755	1	45	fakhrurrozi	fakhrurrozi	ADJ
ejpam-6755	1	46	hadiputra2	hadiputra2	PROPN
ejpam-6755	1	47	,	,	PUNCT
ejpam-6755	1	48	martin	martin	PROPN
ejpam-6755	1	49	bača3	bača3	PROPN
ejpam-6755	1	50	,	,	PUNCT
ejpam-6755	1	51	andrea	andrea	PROPN
ejpam-6755	1	52	semaničová-feňovč́ıková3,4	semaničová-feňovč́ıková3,4	ADJ
ejpam-6755	1	53	1	1	NUM
ejpam-6755	1	54	department	department	NOUN
ejpam-6755	1	55	of	of	ADP
ejpam-6755	1	56	mathematics	mathematics	PROPN
ejpam-6755	1	57	education	education	NOUN
ejpam-6755	1	58	,	,	PUNCT
ejpam-6755	1	59	uin	uin	PROPN
ejpam-6755	1	60	syarif	syarif	PROPN
ejpam-6755	1	61	hidayatullah	hidayatullah	PROPN
ejpam-6755	1	62	jakarta	jakarta	PROPN
ejpam-6755	1	63	,	,	PUNCT
ejpam-6755	1	64	indonesia	indonesia	PROPN
ejpam-6755	1	65	2	2	NUM
ejpam-6755	1	66	school	school	NOUN
ejpam-6755	1	67	of	of	ADP
ejpam-6755	1	68	mathematics	mathematic	NOUN
ejpam-6755	1	69	and	and	CCONJ
ejpam-6755	1	70	statistics	statistic	NOUN
ejpam-6755	1	71	,	,	PUNCT
ejpam-6755	1	72	the	the	DET
ejpam-6755	1	73	university	university	NOUN
ejpam-6755	1	74	of	of	ADP
ejpam-6755	1	75	melbourne	melbourne	PROPN
ejpam-6755	1	76	,	,	PUNCT
ejpam-6755	1	77	parkville	parkville	PROPN
ejpam-6755	1	78	,	,	PUNCT
ejpam-6755	1	79	vic	vic	PROPN
ejpam-6755	1	80	3010	3010	NUM
ejpam-6755	1	81	,	,	PUNCT
ejpam-6755	1	82	australia	australia	PROPN
ejpam-6755	1	83	3	3	NUM
ejpam-6755	1	84	department	department	NOUN
ejpam-6755	1	85	of	of	ADP
ejpam-6755	1	86	applied	apply	VERB
ejpam-6755	1	87	mathematics	mathematic	NOUN
ejpam-6755	1	88	and	and	CCONJ
ejpam-6755	1	89	informatics	informatic	NOUN
ejpam-6755	1	90	,	,	PUNCT
ejpam-6755	1	91	technical	technical	ADJ
ejpam-6755	1	92	university	university	NOUN
ejpam-6755	1	93	,	,	PUNCT
ejpam-6755	1	94	košice	košice	PROPN
ejpam-6755	1	95	,	,	PUNCT
ejpam-6755	1	96	slovakia	slovakia	PROPN
ejpam-6755	1	97	4	4	NUM
ejpam-6755	1	98	division	division	NOUN
ejpam-6755	1	99	of	of	ADP
ejpam-6755	1	100	mathematics	mathematic	NOUN
ejpam-6755	1	101	,	,	PUNCT
ejpam-6755	1	102	saveetha	saveetha	PROPN
ejpam-6755	1	103	school	school	PROPN
ejpam-6755	1	104	of	of	ADP
ejpam-6755	1	105	engineering	engineering	NOUN
ejpam-6755	1	106	,	,	PUNCT
ejpam-6755	1	107	simats	simat	NOUN
ejpam-6755	1	108	,	,	PUNCT
ejpam-6755	1	109	chennai	chennai	PROPN
ejpam-6755	1	110	,	,	PUNCT
ejpam-6755	1	111	india	india	PROPN
ejpam-6755	1	112	abstract	abstract	NOUN
ejpam-6755	1	113	.	.	PUNCT
ejpam-6755	2	1	let	let	VERB
ejpam-6755	2	2	h1	h1	VERB
ejpam-6755	2	3	and	and	CCONJ
ejpam-6755	2	4	h2	h2	NOUN
ejpam-6755	2	5	be	be	AUX
ejpam-6755	2	6	two	two	NUM
ejpam-6755	2	7	non	non	ADJ
ejpam-6755	2	8	-	-	ADJ
ejpam-6755	2	9	isomorphic	isomorphic	ADJ
ejpam-6755	2	10	graphs	graph	NOUN
ejpam-6755	2	11	.	.	PUNCT
ejpam-6755	3	1	a	a	DET
ejpam-6755	3	2	graph	graph	NOUN
ejpam-6755	3	3	g	g	NOUN
ejpam-6755	3	4	is	be	AUX
ejpam-6755	3	5	said	say	VERB
ejpam-6755	3	6	to	to	PART
ejpam-6755	3	7	admit	admit	VERB
ejpam-6755	3	8	an	an	DET
ejpam-6755	3	9	(	(	PUNCT
ejpam-6755	3	10	h1	h1	PROPN
ejpam-6755	3	11	,	,	PUNCT
ejpam-6755	3	12	h2)covering	h2)covere	VERB
ejpam-6755	3	13	if	if	SCONJ
ejpam-6755	3	14	every	every	DET
ejpam-6755	3	15	edge	edge	NOUN
ejpam-6755	3	16	of	of	ADP
ejpam-6755	3	17	g	g	NOUN
ejpam-6755	3	18	is	be	AUX
ejpam-6755	3	19	contained	contain	VERB
ejpam-6755	3	20	in	in	ADP
ejpam-6755	3	21	either	either	CCONJ
ejpam-6755	3	22	a	a	DET
ejpam-6755	3	23	subgraph	subgraph	NOUN
ejpam-6755	3	24	of	of	ADP
ejpam-6755	3	25	g	g	PROPN
ejpam-6755	3	26	isomorphic	isomorphic	ADJ
ejpam-6755	3	27	to	to	PART
ejpam-6755	3	28	h1	h1	VERB
ejpam-6755	3	29	or	or	CCONJ
ejpam-6755	3	30	to	to	ADP
ejpam-6755	3	31	h2	h2	NOUN
ejpam-6755	3	32	.	.	PUNCT
ejpam-6755	4	1	we	we	PRON
ejpam-6755	4	2	say	say	VERB
ejpam-6755	4	3	that	that	SCONJ
ejpam-6755	4	4	a	a	DET
ejpam-6755	4	5	graph	graph	NOUN
ejpam-6755	4	6	g	g	NOUN
ejpam-6755	4	7	admitting	admit	VERB
ejpam-6755	4	8	an	an	DET
ejpam-6755	4	9	(	(	PUNCT
ejpam-6755	4	10	h1	h1	PROPN
ejpam-6755	4	11	,	,	PUNCT
ejpam-6755	4	12	h2)-covering	h2)-covere	VERB
ejpam-6755	4	13	is	be	AUX
ejpam-6755	4	14	(	(	PUNCT
ejpam-6755	4	15	h1	h1	PROPN
ejpam-6755	4	16	,	,	PUNCT
ejpam-6755	4	17	h2)-magic	h2)-magic	ADJ
ejpam-6755	4	18	if	if	SCONJ
ejpam-6755	4	19	there	there	PRON
ejpam-6755	4	20	exists	exist	VERB
ejpam-6755	4	21	a	a	DET
ejpam-6755	4	22	total	total	ADJ
ejpam-6755	4	23	labeling	labeling	NOUN
ejpam-6755	4	24	f	f	NOUN
ejpam-6755	4	25	:	:	PUNCT
ejpam-6755	4	26	v	v	X
ejpam-6755	4	27	(	(	PUNCT
ejpam-6755	4	28	g	g	NOUN
ejpam-6755	4	29	)	)	PUNCT
ejpam-6755	4	30	∪e(g	∪e(g	NOUN
ejpam-6755	4	31	)	)	PUNCT
ejpam-6755	4	32	→	→	PUNCT
ejpam-6755	5	1	[	[	X
ejpam-6755	5	2	1	1	NUM
ejpam-6755	5	3	,	,	PUNCT
ejpam-6755	5	4	|v	|v	X
ejpam-6755	5	5	(	(	PUNCT
ejpam-6755	5	6	g)|+	g)|+	PROPN
ejpam-6755	5	7	|e(g)|	|e(g)|	PROPN
ejpam-6755	5	8	]	]	PUNCT
ejpam-6755	5	9	such	such	ADJ
ejpam-6755	5	10	that	that	SCONJ
ejpam-6755	5	11	there	there	PRON
ejpam-6755	5	12	exist	exist	VERB
ejpam-6755	5	13	magic	magic	ADJ
ejpam-6755	5	14	constants	constant	NOUN
ejpam-6755	5	15	c1	c1	PROPN
ejpam-6755	5	16	and	and	CCONJ
ejpam-6755	5	17	c2	c2	PROPN
ejpam-6755	5	18	such	such	ADJ
ejpam-6755	5	19	that	that	SCONJ
ejpam-6755	5	20	the	the	DET
ejpam-6755	5	21	weight	weight	NOUN
ejpam-6755	5	22	of	of	ADP
ejpam-6755	5	23	every	every	DET
ejpam-6755	5	24	subgraph	subgraph	NOUN
ejpam-6755	5	25	h∗	h∗	PROPN
ejpam-6755	5	26	i	i	PROPN
ejpam-6755	5	27	of	of	ADP
ejpam-6755	5	28	g	g	PROPN
ejpam-6755	5	29	isomorphic	isomorphic	ADJ
ejpam-6755	5	30	to	to	PART
ejpam-6755	5	31	hi	hi	VERB
ejpam-6755	5	32	equals	equal	VERB
ejpam-6755	5	33	to	to	ADP
ejpam-6755	5	34	ci	ci	VERB
ejpam-6755	5	35	,	,	PUNCT
ejpam-6755	5	36	i	i	NOUN
ejpam-6755	5	37	=	=	NOUN
ejpam-6755	5	38	1	1	NUM
ejpam-6755	5	39	,	,	PUNCT
ejpam-6755	5	40	2	2	NUM
ejpam-6755	5	41	.	.	PUNCT
ejpam-6755	6	1	the	the	DET
ejpam-6755	6	2	weight	weight	NOUN
ejpam-6755	6	3	of	of	ADP
ejpam-6755	6	4	a	a	DET
ejpam-6755	6	5	subgraph	subgraph	NOUN
ejpam-6755	6	6	h	h	NOUN
ejpam-6755	6	7	is	be	AUX
ejpam-6755	6	8	defined	define	VERB
ejpam-6755	6	9	as	as	ADP
ejpam-6755	6	10	w(h	w(h	NOUN
ejpam-6755	6	11	)	)	PUNCT
ejpam-6755	7	1	=	=	PUNCT
ejpam-6755	7	2	∑	∑	PUNCT
ejpam-6755	7	3	v∈v	v∈v	PROPN
ejpam-6755	7	4	(	(	PUNCT
ejpam-6755	7	5	h	h	NOUN
ejpam-6755	7	6	)	)	PUNCT
ejpam-6755	7	7	f(v	f(v	NOUN
ejpam-6755	7	8	)	)	PUNCT
ejpam-6755	8	1	+	+	CCONJ
ejpam-6755	8	2	∑	∑	PUNCT
ejpam-6755	8	3	e∈e(h	e∈e(h	NOUN
ejpam-6755	8	4	)	)	PUNCT
ejpam-6755	8	5	f(e	f(e	NOUN
ejpam-6755	8	6	)	)	PUNCT
ejpam-6755	8	7	.	.	PUNCT
ejpam-6755	9	1	moreover	moreover	ADV
ejpam-6755	9	2	,	,	PUNCT
ejpam-6755	9	3	a	a	DET
ejpam-6755	9	4	graph	graph	NOUN
ejpam-6755	9	5	g	g	NOUN
ejpam-6755	9	6	is	be	AUX
ejpam-6755	9	7	called	call	VERB
ejpam-6755	9	8	(	(	PUNCT
ejpam-6755	9	9	h1	h1	PROPN
ejpam-6755	9	10	,	,	PUNCT
ejpam-6755	9	11	h2)-supermagic	h2)-supermagic	PROPN
ejpam-6755	9	12	if	if	SCONJ
ejpam-6755	9	13	the	the	DET
ejpam-6755	9	14	vertices	vertex	NOUN
ejpam-6755	9	15	are	be	AUX
ejpam-6755	9	16	labeled	label	VERB
ejpam-6755	9	17	with	with	ADP
ejpam-6755	9	18	the	the	DET
ejpam-6755	9	19	numbers	number	NOUN
ejpam-6755	9	20	from	from	ADP
ejpam-6755	9	21	1	1	NUM
ejpam-6755	9	22	up	up	ADP
ejpam-6755	9	23	to	to	ADP
ejpam-6755	9	24	|v	|v	PROPN
ejpam-6755	9	25	(	(	PUNCT
ejpam-6755	9	26	g)|	g)|	NOUN
ejpam-6755	9	27	.	.	PUNCT
ejpam-6755	10	1	in	in	ADP
ejpam-6755	10	2	this	this	DET
ejpam-6755	10	3	paper	paper	NOUN
ejpam-6755	10	4	,	,	PUNCT
ejpam-6755	10	5	we	we	PRON
ejpam-6755	10	6	present	present	VERB
ejpam-6755	10	7	some	some	DET
ejpam-6755	10	8	constructions	construction	NOUN
ejpam-6755	10	9	of	of	ADP
ejpam-6755	10	10	(	(	PUNCT
ejpam-6755	10	11	h1	h1	PROPN
ejpam-6755	10	12	,	,	PUNCT
ejpam-6755	10	13	h2)-magic	h2)-magic	ADJ
ejpam-6755	10	14	graphs	graph	NOUN
ejpam-6755	10	15	.	.	PUNCT
ejpam-6755	11	1	2020	2020	NUM
ejpam-6755	11	2	mathematics	mathematic	NOUN
ejpam-6755	11	3	subject	subject	NOUN
ejpam-6755	11	4	classifications	classification	NOUN
ejpam-6755	11	5	:	:	PUNCT
ejpam-6755	11	6	05c78	05c78	NUM
ejpam-6755	11	7	key	key	ADJ
ejpam-6755	11	8	words	word	NOUN
ejpam-6755	11	9	and	and	CCONJ
ejpam-6755	11	10	phrases	phrase	NOUN
ejpam-6755	11	11	:	:	PUNCT
ejpam-6755	11	12	magic	magic	ADJ
ejpam-6755	11	13	labeling	labeling	NOUN
ejpam-6755	11	14	,	,	PUNCT
ejpam-6755	11	15	magic	magic	ADJ
ejpam-6755	11	16	covering	covering	NOUN
ejpam-6755	11	17	,	,	PUNCT
ejpam-6755	11	18	generalized	generalize	VERB
ejpam-6755	11	19	total	total	ADJ
ejpam-6755	11	20	composition	composition	NOUN
ejpam-6755	11	21	,	,	PUNCT
ejpam-6755	11	22	amalgamation	amalgamation	NOUN
ejpam-6755	11	23	of	of	ADP
ejpam-6755	11	24	graphs	graph	NOUN
ejpam-6755	11	25	1	1	NUM
ejpam-6755	11	26	.	.	PUNCT
ejpam-6755	12	1	introduction	introduction	NOUN
ejpam-6755	12	2	let	let	VERB
ejpam-6755	12	3	g	g	PROPN
ejpam-6755	12	4	=	=	SYM
ejpam-6755	12	5	(	(	PUNCT
ejpam-6755	12	6	v	v	NOUN
ejpam-6755	12	7	,	,	PUNCT
ejpam-6755	12	8	e	e	NOUN
ejpam-6755	12	9	)	)	PUNCT
ejpam-6755	12	10	be	be	AUX
ejpam-6755	12	11	a	a	DET
ejpam-6755	12	12	finite	finite	NOUN
ejpam-6755	12	13	,	,	PUNCT
ejpam-6755	12	14	simple	simple	ADJ
ejpam-6755	12	15	,	,	PUNCT
ejpam-6755	12	16	and	and	CCONJ
ejpam-6755	12	17	undirected	undirected	ADJ
ejpam-6755	12	18	graph	graph	NOUN
ejpam-6755	12	19	.	.	PUNCT
ejpam-6755	13	1	for	for	ADP
ejpam-6755	13	2	two	two	NUM
ejpam-6755	13	3	integers	integer	NOUN
ejpam-6755	13	4	a	a	DET
ejpam-6755	13	5	<	<	X
ejpam-6755	13	6	b	b	NOUN
ejpam-6755	13	7	,	,	PUNCT
ejpam-6755	13	8	let	let	VERB
ejpam-6755	13	9	[	[	X
ejpam-6755	13	10	a	a	X
ejpam-6755	13	11	,	,	PUNCT
ejpam-6755	13	12	b	b	NOUN
ejpam-6755	13	13	]	]	X
ejpam-6755	13	14	=	=	SYM
ejpam-6755	13	15	{	{	PUNCT
ejpam-6755	13	16	k	k	PROPN
ejpam-6755	13	17	∈	∈	PROPN
ejpam-6755	13	18	z	z	NOUN
ejpam-6755	14	1	|	|	ADV
ejpam-6755	14	2	a	a	DET
ejpam-6755	14	3	≤	≤	NUM
ejpam-6755	14	4	k	k	NOUN
ejpam-6755	14	5	≤	≤	NUM
ejpam-6755	14	6	b	b	X
ejpam-6755	14	7	}	}	PUNCT
ejpam-6755	14	8	.	.	PUNCT
ejpam-6755	15	1	in	in	ADP
ejpam-6755	15	2	2005	2005	NUM
ejpam-6755	15	3	,	,	PUNCT
ejpam-6755	15	4	gutiérrez	gutiérrez	NOUN
ejpam-6755	15	5	and	and	CCONJ
ejpam-6755	15	6	lladó	lladó	X
ejpam-6755	15	7	[	[	X
ejpam-6755	15	8	1	1	X
ejpam-6755	15	9	]	]	PUNCT
ejpam-6755	15	10	introduced	introduce	VERB
ejpam-6755	15	11	a	a	DET
ejpam-6755	15	12	concept	concept	NOUN
ejpam-6755	15	13	of	of	ADP
ejpam-6755	15	14	h-(super)magic	h-(super)magic	ADJ
ejpam-6755	15	15	graphs	graph	NOUN
ejpam-6755	15	16	.	.	PUNCT
ejpam-6755	16	1	a	a	DET
ejpam-6755	16	2	graph	graph	NOUN
ejpam-6755	16	3	g	g	NOUN
ejpam-6755	16	4	is	be	AUX
ejpam-6755	16	5	said	say	VERB
ejpam-6755	16	6	to	to	PART
ejpam-6755	16	7	admit	admit	VERB
ejpam-6755	16	8	an	an	DET
ejpam-6755	16	9	h	h	NOUN
ejpam-6755	16	10	-	-	PUNCT
ejpam-6755	16	11	covering	covering	NOUN
ejpam-6755	16	12	if	if	SCONJ
ejpam-6755	16	13	every	every	DET
ejpam-6755	16	14	edge	edge	NOUN
ejpam-6755	16	15	e	e	X
ejpam-6755	16	16	∈	∈	PROPN
ejpam-6755	16	17	e(g	e(g	PROPN
ejpam-6755	16	18	)	)	PUNCT
ejpam-6755	16	19	is	be	AUX
ejpam-6755	16	20	contained	contain	VERB
ejpam-6755	16	21	in	in	ADP
ejpam-6755	16	22	some	some	DET
ejpam-6755	16	23	∗corresponding	∗corresponde	VERB
ejpam-6755	16	24	author	author	NOUN
ejpam-6755	16	25	.	.	PUNCT
ejpam-6755	17	1	doi	doi	NOUN
ejpam-6755	17	2	:	:	PUNCT
ejpam-6755	17	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6755	https://doi.org/10.29020/nybg.ejpam.v18i4.6755	PRON
ejpam-6755	17	4	email	email	NOUN
ejpam-6755	17	5	addresses	address	VERB
ejpam-6755	17	6	:	:	PUNCT
ejpam-6755	17	7	tita.khalis@uinjkt.ac.id	tita.khalis@uinjkt.ac.id	NUM
ejpam-6755	17	8	(	(	PUNCT
ejpam-6755	17	9	t.	t.	PROPN
ejpam-6755	17	10	k.	k.	PROPN
ejpam-6755	17	11	maryati	maryati	PROPN
ejpam-6755	17	12	)	)	PUNCT
ejpam-6755	17	13	,	,	PUNCT
ejpam-6755	17	14	fhadiputra@student.unimelb.edu.au	fhadiputra@student.unimelb.edu.au	PROPN
ejpam-6755	17	15	(	(	PUNCT
ejpam-6755	17	16	f.	f.	PROPN
ejpam-6755	17	17	f.	f.	PROPN
ejpam-6755	17	18	hadiputra	hadiputra	PROPN
ejpam-6755	17	19	)	)	PUNCT
ejpam-6755	17	20	,	,	PUNCT
ejpam-6755	17	21	martin.baca@tuke.sk	martin.baca@tuke.sk	NOUN
ejpam-6755	17	22	(	(	PUNCT
ejpam-6755	17	23	m.	m.	NOUN
ejpam-6755	17	24	bača	bača	PROPN
ejpam-6755	17	25	)	)	PUNCT
ejpam-6755	17	26	,	,	PUNCT
ejpam-6755	17	27	andrea.fenovcikova@tuke.sk	andrea.fenovcikova@tuke.sk	PROPN
ejpam-6755	17	28	(	(	PUNCT
ejpam-6755	17	29	a.	a.	NOUN
ejpam-6755	17	30	semaničová-feňovč́ıková	semaničová-feňovč́ıková	PROPN
ejpam-6755	17	31	)	)	PUNCT
ejpam-6755	17	32	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6755	17	33	1	1	NUM
ejpam-6755	17	34	copyright	copyright	NOUN
ejpam-6755	17	35	:	:	PUNCT
ejpam-6755	18	1	©	©	PROPN
ejpam-6755	18	2	2025	2025	NUM
ejpam-6755	18	3	the	the	DET
ejpam-6755	18	4	author(s	author(s	NOUN
ejpam-6755	18	5	)	)	PUNCT
ejpam-6755	18	6	.	.	PUNCT
ejpam-6755	19	1	(	(	PUNCT
ejpam-6755	19	2	cc	cc	NOUN
ejpam-6755	19	3	by	by	ADP
ejpam-6755	19	4	-	-	PUNCT
ejpam-6755	19	5	nc	nc	PROPN
ejpam-6755	19	6	4.0	4.0	NUM
ejpam-6755	19	7	)	)	PUNCT
ejpam-6755	19	8	t.	t.	PROPN
ejpam-6755	19	9	k.	k.	PROPN
ejpam-6755	19	10	maryati	maryati	PROPN
ejpam-6755	19	11	et	et	PROPN
ejpam-6755	19	12	al	al	PROPN
ejpam-6755	19	13	.	.	PUNCT
ejpam-6755	19	14	/	/	SYM
ejpam-6755	19	15	eur	eur	PROPN
ejpam-6755	19	16	.	.	PUNCT
ejpam-6755	20	1	j.	j.	PROPN
ejpam-6755	20	2	pure	pure	PROPN
ejpam-6755	20	3	appl	appl	PROPN
ejpam-6755	20	4	.	.	PROPN
ejpam-6755	20	5	math	math	PROPN
ejpam-6755	20	6	,	,	PUNCT
ejpam-6755	20	7	18	18	NUM
ejpam-6755	20	8	(	(	PUNCT
ejpam-6755	20	9	4	4	NUM
ejpam-6755	20	10	)	)	PUNCT
ejpam-6755	20	11	(	(	PUNCT
ejpam-6755	20	12	2025	2025	NUM
ejpam-6755	20	13	)	)	PUNCT
ejpam-6755	20	14	,	,	PUNCT
ejpam-6755	20	15	6755	6755	NUM
ejpam-6755	20	16	2	2	NUM
ejpam-6755	20	17	of	of	ADP
ejpam-6755	20	18	13	13	NUM
ejpam-6755	20	19	subgraph	subgraph	NOUN
ejpam-6755	20	20	of	of	ADP
ejpam-6755	20	21	g	g	PROPN
ejpam-6755	20	22	isomorphic	isomorphic	ADJ
ejpam-6755	20	23	to	to	ADP
ejpam-6755	20	24	h.	h.	PROPN
ejpam-6755	20	25	suppose	suppose	VERB
ejpam-6755	20	26	that	that	SCONJ
ejpam-6755	20	27	g	g	PROPN
ejpam-6755	20	28	=	=	SYM
ejpam-6755	20	29	(	(	PUNCT
ejpam-6755	20	30	v	v	NOUN
ejpam-6755	20	31	,	,	PUNCT
ejpam-6755	20	32	e	e	NOUN
ejpam-6755	20	33	)	)	PUNCT
ejpam-6755	20	34	admits	admit	VERB
ejpam-6755	20	35	an	an	DET
ejpam-6755	20	36	h	h	NOUN
ejpam-6755	20	37	-	-	PUNCT
ejpam-6755	20	38	covering	covering	NOUN
ejpam-6755	20	39	.	.	PUNCT
ejpam-6755	21	1	a	a	DET
ejpam-6755	21	2	bijective	bijective	ADJ
ejpam-6755	21	3	function	function	NOUN
ejpam-6755	21	4	f	f	NOUN
ejpam-6755	21	5	:	:	PUNCT
ejpam-6755	21	6	v	v	X
ejpam-6755	21	7	(	(	PUNCT
ejpam-6755	21	8	g	g	NOUN
ejpam-6755	21	9	)	)	PUNCT
ejpam-6755	21	10	∪	∪	ADP
ejpam-6755	21	11	e(g	e(g	PROPN
ejpam-6755	21	12	)	)	PUNCT
ejpam-6755	21	13	→	→	PUNCT
ejpam-6755	22	1	[	[	X
ejpam-6755	22	2	1	1	NUM
ejpam-6755	22	3	,	,	PUNCT
ejpam-6755	22	4	|v	|v	X
ejpam-6755	22	5	(	(	PUNCT
ejpam-6755	22	6	g)|	g)|	NOUN
ejpam-6755	22	7	+	+	X
ejpam-6755	22	8	|e(g)|	|e(g)|	PROPN
ejpam-6755	22	9	]	]	PUNCT
ejpam-6755	22	10	is	be	AUX
ejpam-6755	22	11	called	call	VERB
ejpam-6755	22	12	an	an	DET
ejpam-6755	22	13	h	h	ADJ
ejpam-6755	22	14	-	-	PUNCT
ejpam-6755	22	15	magic	magic	ADJ
ejpam-6755	22	16	labeling	labeling	NOUN
ejpam-6755	22	17	if	if	SCONJ
ejpam-6755	22	18	there	there	PRON
ejpam-6755	22	19	exists	exist	VERB
ejpam-6755	22	20	a	a	DET
ejpam-6755	22	21	positive	positive	ADJ
ejpam-6755	22	22	integer	integer	NOUN
ejpam-6755	22	23	c	c	PROPN
ejpam-6755	22	24	∈	∈	PROPN
ejpam-6755	22	25	n	n	CCONJ
ejpam-6755	22	26	,	,	PUNCT
ejpam-6755	22	27	called	call	VERB
ejpam-6755	22	28	a	a	DET
ejpam-6755	22	29	magic	magic	NOUN
ejpam-6755	22	30	constant	constant	ADJ
ejpam-6755	22	31	,	,	PUNCT
ejpam-6755	22	32	such	such	ADJ
ejpam-6755	22	33	that	that	SCONJ
ejpam-6755	22	34	the	the	DET
ejpam-6755	22	35	weight	weight	NOUN
ejpam-6755	22	36	w(h∗	w(h∗	NOUN
ejpam-6755	22	37	)	)	PUNCT
ejpam-6755	22	38	=	=	SYM
ejpam-6755	22	39	∑	∑	PUNCT
ejpam-6755	22	40	v∈v	v∈v	PROPN
ejpam-6755	22	41	(	(	PUNCT
ejpam-6755	22	42	h∗	h∗	PROPN
ejpam-6755	22	43	)	)	PUNCT
ejpam-6755	22	44	f(v	f(v	PROPN
ejpam-6755	22	45	)	)	PUNCT
ejpam-6755	23	1	+	+	CCONJ
ejpam-6755	23	2	∑	∑	PROPN
ejpam-6755	23	3	e∈e(h∗	e∈e(h∗	PROPN
ejpam-6755	23	4	)	)	PUNCT
ejpam-6755	23	5	f(e	f(e	NOUN
ejpam-6755	23	6	)	)	PUNCT
ejpam-6755	23	7	=	=	SYM
ejpam-6755	24	1	c	c	NOUN
ejpam-6755	24	2	for	for	ADP
ejpam-6755	24	3	every	every	DET
ejpam-6755	24	4	subgraph	subgraph	NOUN
ejpam-6755	24	5	h∗	h∗	NOUN
ejpam-6755	24	6	of	of	ADP
ejpam-6755	24	7	g	g	PROPN
ejpam-6755	24	8	isomorphic	isomorphic	ADJ
ejpam-6755	24	9	to	to	ADP
ejpam-6755	24	10	h.	h.	PROPN
ejpam-6755	24	11	in	in	ADP
ejpam-6755	24	12	addition	addition	NOUN
ejpam-6755	24	13	,	,	PUNCT
ejpam-6755	24	14	if	if	SCONJ
ejpam-6755	24	15	{	{	PUNCT
ejpam-6755	24	16	f(v	f(v	NOUN
ejpam-6755	24	17	)	)	PUNCT
ejpam-6755	24	18	|	|	ADV
ejpam-6755	24	19	v	v	ADP
ejpam-6755	24	20	∈	∈	PROPN
ejpam-6755	24	21	v	v	NOUN
ejpam-6755	24	22	(	(	PUNCT
ejpam-6755	24	23	g	g	NOUN
ejpam-6755	24	24	)	)	PUNCT
ejpam-6755	24	25	}	}	PUNCT
ejpam-6755	25	1	=	=	PUNCT
ejpam-6755	26	1	[	[	X
ejpam-6755	26	2	1	1	NUM
ejpam-6755	26	3	,	,	PUNCT
ejpam-6755	26	4	|v	|v	PROPN
ejpam-6755	26	5	(	(	PUNCT
ejpam-6755	26	6	g)|	g)|	PROPN
ejpam-6755	26	7	]	]	PUNCT
ejpam-6755	26	8	then	then	ADV
ejpam-6755	26	9	f	f	PROPN
ejpam-6755	26	10	is	be	AUX
ejpam-6755	26	11	called	call	VERB
ejpam-6755	26	12	an	an	DET
ejpam-6755	26	13	h	h	ADJ
ejpam-6755	26	14	-	-	PUNCT
ejpam-6755	26	15	supermagic	supermagic	ADJ
ejpam-6755	26	16	labeling	labeling	NOUN
ejpam-6755	26	17	.	.	PUNCT
ejpam-6755	27	1	a	a	DET
ejpam-6755	27	2	graph	graph	NOUN
ejpam-6755	27	3	which	which	PRON
ejpam-6755	27	4	admits	admit	VERB
ejpam-6755	27	5	an	an	DET
ejpam-6755	27	6	h-(super)magic	h-(super)magic	ADJ
ejpam-6755	27	7	labeling	labeling	NOUN
ejpam-6755	27	8	is	be	AUX
ejpam-6755	27	9	called	call	VERB
ejpam-6755	27	10	an	an	DET
ejpam-6755	27	11	h-(super)magic	h-(super)magic	ADJ
ejpam-6755	27	12	graph	graph	NOUN
ejpam-6755	27	13	.	.	PUNCT
ejpam-6755	28	1	to	to	ADP
ejpam-6755	28	2	date	date	NOUN
ejpam-6755	28	3	,	,	PUNCT
ejpam-6755	28	4	there	there	PRON
ejpam-6755	28	5	are	be	VERB
ejpam-6755	28	6	some	some	DET
ejpam-6755	28	7	results	result	NOUN
ejpam-6755	28	8	of	of	ADP
ejpam-6755	28	9	h	h	NOUN
ejpam-6755	28	10	-	-	PUNCT
ejpam-6755	28	11	supermagicness	supermagicness	NOUN
ejpam-6755	28	12	in	in	ADP
ejpam-6755	28	13	planar	planar	ADJ
ejpam-6755	28	14	graphs	graph	NOUN
ejpam-6755	28	15	[	[	X
ejpam-6755	28	16	2	2	NUM
ejpam-6755	28	17	]	]	PUNCT
ejpam-6755	28	18	,	,	PUNCT
ejpam-6755	28	19	grid	grid	NOUN
ejpam-6755	28	20	graphs	graph	NOUN
ejpam-6755	29	1	[	[	X
ejpam-6755	29	2	3	3	NUM
ejpam-6755	29	3	]	]	PUNCT
ejpam-6755	29	4	,	,	PUNCT
ejpam-6755	29	5	polygonal	polygonal	ADJ
ejpam-6755	29	6	snake	snake	NOUN
ejpam-6755	29	7	graphs	graph	NOUN
ejpam-6755	29	8	[	[	X
ejpam-6755	29	9	4	4	NUM
ejpam-6755	29	10	]	]	PUNCT
ejpam-6755	29	11	,	,	PUNCT
ejpam-6755	29	12	edge	edge	NOUN
ejpam-6755	29	13	coronation	coronation	NOUN
ejpam-6755	29	14	of	of	ADP
ejpam-6755	29	15	graphs	graph	NOUN
ejpam-6755	29	16	[	[	X
ejpam-6755	29	17	5	5	NUM
ejpam-6755	29	18	]	]	PUNCT
ejpam-6755	29	19	,	,	PUNCT
ejpam-6755	29	20	and	and	CCONJ
ejpam-6755	29	21	disjoint	disjoint	PROPN
ejpam-6755	29	22	union	union	NOUN
ejpam-6755	29	23	of	of	ADP
ejpam-6755	29	24	prisms	prism	NOUN
ejpam-6755	29	25	[	[	X
ejpam-6755	29	26	6	6	NUM
ejpam-6755	29	27	]	]	PUNCT
ejpam-6755	29	28	.	.	PUNCT
ejpam-6755	30	1	it	it	PRON
ejpam-6755	30	2	is	be	AUX
ejpam-6755	30	3	known	know	VERB
ejpam-6755	30	4	that	that	SCONJ
ejpam-6755	30	5	for	for	ADP
ejpam-6755	30	6	any	any	DET
ejpam-6755	30	7	graph	graph	NOUN
ejpam-6755	30	8	h	h	NOUN
ejpam-6755	30	9	other	other	ADJ
ejpam-6755	30	10	than	than	ADP
ejpam-6755	30	11	a	a	DET
ejpam-6755	30	12	k2	k2	NOUN
ejpam-6755	30	13	,	,	PUNCT
ejpam-6755	30	14	we	we	PRON
ejpam-6755	30	15	can	can	AUX
ejpam-6755	30	16	always	always	ADV
ejpam-6755	30	17	find	find	VERB
ejpam-6755	30	18	several	several	ADJ
ejpam-6755	30	19	graphs	graph	NOUN
ejpam-6755	30	20	which	which	PRON
ejpam-6755	30	21	are	be	AUX
ejpam-6755	30	22	not	not	PART
ejpam-6755	30	23	h	h	NOUN
ejpam-6755	30	24	-	-	PUNCT
ejpam-6755	30	25	magic	magic	ADJ
ejpam-6755	30	26	.	.	PUNCT
ejpam-6755	31	1	one	one	NUM
ejpam-6755	31	2	possible	possible	ADJ
ejpam-6755	31	3	way	way	NOUN
ejpam-6755	31	4	to	to	PART
ejpam-6755	31	5	do	do	VERB
ejpam-6755	31	6	this	this	PRON
ejpam-6755	31	7	is	be	AUX
ejpam-6755	31	8	by	by	ADP
ejpam-6755	31	9	considering	consider	VERB
ejpam-6755	31	10	graphs	graph	NOUN
ejpam-6755	31	11	which	which	PRON
ejpam-6755	31	12	did	do	AUX
ejpam-6755	31	13	not	not	PART
ejpam-6755	31	14	admit	admit	VERB
ejpam-6755	31	15	h	h	NOUN
ejpam-6755	31	16	-	-	PUNCT
ejpam-6755	31	17	covering	covering	NOUN
ejpam-6755	31	18	.	.	PUNCT
ejpam-6755	32	1	therefore	therefore	ADV
ejpam-6755	32	2	,	,	PUNCT
ejpam-6755	32	3	if	if	SCONJ
ejpam-6755	32	4	we	we	PRON
ejpam-6755	32	5	want	want	VERB
ejpam-6755	32	6	to	to	PART
ejpam-6755	32	7	have	have	VERB
ejpam-6755	32	8	similar	similar	ADJ
ejpam-6755	32	9	magicness	magicness	NOUN
ejpam-6755	32	10	property	property	NOUN
ejpam-6755	32	11	for	for	ADP
ejpam-6755	32	12	graphs	graph	NOUN
ejpam-6755	32	13	which	which	PRON
ejpam-6755	32	14	did	do	AUX
ejpam-6755	32	15	not	not	PART
ejpam-6755	32	16	admit	admit	VERB
ejpam-6755	32	17	h	h	NOUN
ejpam-6755	32	18	-	-	PUNCT
ejpam-6755	32	19	magic	magic	NOUN
ejpam-6755	32	20	,	,	PUNCT
ejpam-6755	32	21	we	we	PRON
ejpam-6755	32	22	can	can	AUX
ejpam-6755	32	23	consider	consider	VERB
ejpam-6755	32	24	a	a	DET
ejpam-6755	32	25	relaxation	relaxation	NOUN
ejpam-6755	32	26	of	of	ADP
ejpam-6755	32	27	h	h	NOUN
ejpam-6755	32	28	-	-	PUNCT
ejpam-6755	32	29	magicness	magicness	NOUN
ejpam-6755	32	30	.	.	PUNCT
ejpam-6755	33	1	recently	recently	ADV
ejpam-6755	33	2	,	,	PUNCT
ejpam-6755	33	3	ashari	ashari	PROPN
ejpam-6755	33	4	and	and	CCONJ
ejpam-6755	33	5	salman	salman	PROPN
ejpam-6755	34	1	[	[	X
ejpam-6755	34	2	7	7	X
ejpam-6755	34	3	]	]	PUNCT
ejpam-6755	34	4	introduced	introduce	VERB
ejpam-6755	34	5	a	a	DET
ejpam-6755	34	6	notion	notion	NOUN
ejpam-6755	34	7	of	of	ADP
ejpam-6755	34	8	a	a	DET
ejpam-6755	34	9	generalization	generalization	NOUN
ejpam-6755	34	10	ofh-(super)magic	ofh-(super)magic	ADJ
ejpam-6755	34	11	labeling	labeling	NOUN
ejpam-6755	34	12	,	,	PUNCT
ejpam-6755	34	13	namely	namely	ADV
ejpam-6755	34	14	an	an	DET
ejpam-6755	34	15	(	(	PUNCT
ejpam-6755	34	16	h1	h1	PROPN
ejpam-6755	34	17	,	,	PUNCT
ejpam-6755	34	18	h2)-(super)magic	h2)-(super)magic	PROPN
ejpam-6755	34	19	labeling	labeling	NOUN
ejpam-6755	34	20	.	.	PUNCT
ejpam-6755	35	1	let	let	VERB
ejpam-6755	35	2	h1	h1	VERB
ejpam-6755	35	3	and	and	CCONJ
ejpam-6755	35	4	h2	h2	NOUN
ejpam-6755	35	5	be	be	AUX
ejpam-6755	35	6	two	two	NUM
ejpam-6755	35	7	nonisomorphic	nonisomorphic	ADJ
ejpam-6755	35	8	graphs	graph	NOUN
ejpam-6755	35	9	.	.	PUNCT
ejpam-6755	36	1	a	a	DET
ejpam-6755	36	2	graphg	graphg	NOUN
ejpam-6755	36	3	is	be	AUX
ejpam-6755	36	4	said	say	VERB
ejpam-6755	36	5	to	to	PART
ejpam-6755	36	6	admit	admit	VERB
ejpam-6755	36	7	an	an	DET
ejpam-6755	36	8	(	(	PUNCT
ejpam-6755	36	9	h1	h1	PROPN
ejpam-6755	36	10	,	,	PUNCT
ejpam-6755	36	11	h2)-covering	h2)-covere	VERB
ejpam-6755	36	12	if	if	SCONJ
ejpam-6755	36	13	every	every	DET
ejpam-6755	36	14	edge	edge	NOUN
ejpam-6755	36	15	e	e	PROPN
ejpam-6755	36	16	∈	∈	PROPN
ejpam-6755	36	17	e(g	e(g	PROPN
ejpam-6755	36	18	)	)	PUNCT
ejpam-6755	36	19	is	be	AUX
ejpam-6755	36	20	contained	contain	VERB
ejpam-6755	36	21	in	in	ADP
ejpam-6755	36	22	either	either	CCONJ
ejpam-6755	36	23	a	a	DET
ejpam-6755	36	24	subgraph	subgraph	NOUN
ejpam-6755	36	25	of	of	ADP
ejpam-6755	36	26	g	g	PROPN
ejpam-6755	36	27	isomorphic	isomorphic	ADJ
ejpam-6755	36	28	to	to	PART
ejpam-6755	36	29	h1	h1	VERB
ejpam-6755	36	30	or	or	CCONJ
ejpam-6755	36	31	a	a	DET
ejpam-6755	36	32	subgraph	subgraph	NOUN
ejpam-6755	36	33	of	of	ADP
ejpam-6755	36	34	g	g	PROPN
ejpam-6755	36	35	isomorphic	isomorphic	ADJ
ejpam-6755	36	36	to	to	ADP
ejpam-6755	36	37	h2	h2	PROPN
ejpam-6755	36	38	.	.	PUNCT
ejpam-6755	37	1	let	let	VERB
ejpam-6755	37	2	g	g	PRON
ejpam-6755	37	3	admit	admit	VERB
ejpam-6755	37	4	an	an	DET
ejpam-6755	37	5	(	(	PUNCT
ejpam-6755	37	6	h1	h1	PROPN
ejpam-6755	37	7	,	,	PUNCT
ejpam-6755	37	8	h2)-covering	h2)-covere	VERB
ejpam-6755	37	9	.	.	PUNCT
ejpam-6755	38	1	a	a	DET
ejpam-6755	38	2	bijection	bijection	ADJ
ejpam-6755	38	3	f	f	X
ejpam-6755	38	4	:	:	PUNCT
ejpam-6755	38	5	v	v	PROPN
ejpam-6755	38	6	(	(	PUNCT
ejpam-6755	38	7	g)∪e(g	g)∪e(g	NOUN
ejpam-6755	38	8	)	)	PUNCT
ejpam-6755	38	9	→	→	PUNCT
ejpam-6755	39	1	[	[	X
ejpam-6755	39	2	1	1	NUM
ejpam-6755	39	3	,	,	PUNCT
ejpam-6755	39	4	|v	|v	X
ejpam-6755	39	5	(	(	PUNCT
ejpam-6755	39	6	g)|+|e(g)|	g)|+|e(g)|	NOUN
ejpam-6755	39	7	]	]	PUNCT
ejpam-6755	39	8	is	be	AUX
ejpam-6755	39	9	called	call	VERB
ejpam-6755	39	10	an	an	DET
ejpam-6755	39	11	(	(	PUNCT
ejpam-6755	39	12	h1	h1	PROPN
ejpam-6755	39	13	,	,	PUNCT
ejpam-6755	39	14	h2)-magic	h2)-magic	ADJ
ejpam-6755	39	15	labeling	labeling	NOUN
ejpam-6755	39	16	if	if	SCONJ
ejpam-6755	39	17	there	there	PRON
ejpam-6755	39	18	exist	exist	VERB
ejpam-6755	39	19	two	two	NUM
ejpam-6755	39	20	positive	positive	ADJ
ejpam-6755	39	21	integers	integer	NOUN
ejpam-6755	39	22	c1	c1	PROPN
ejpam-6755	39	23	and	and	CCONJ
ejpam-6755	39	24	c2	c2	PROPN
ejpam-6755	39	25	,	,	PUNCT
ejpam-6755	39	26	called	call	VERB
ejpam-6755	39	27	magic	magic	ADJ
ejpam-6755	39	28	constants	constant	NOUN
ejpam-6755	39	29	,	,	PUNCT
ejpam-6755	39	30	such	such	ADJ
ejpam-6755	39	31	that	that	PRON
ejpam-6755	39	32	for	for	SCONJ
ejpam-6755	39	33	every	every	DET
ejpam-6755	39	34	subgraph	subgraph	NOUN
ejpam-6755	39	35	h∗	h∗	PROPN
ejpam-6755	39	36	1	1	NUM
ejpam-6755	39	37	of	of	ADP
ejpam-6755	39	38	g	g	NOUN
ejpam-6755	39	39	isomorphic	isomorphic	ADJ
ejpam-6755	39	40	to	to	PART
ejpam-6755	39	41	h1	h1	VERB
ejpam-6755	39	42	holds	hold	VERB
ejpam-6755	39	43	w(h1	w(h1	NOUN
ejpam-6755	39	44	)	)	PUNCT
ejpam-6755	40	1	=	=	SYM
ejpam-6755	40	2	∑	∑	PUNCT
ejpam-6755	40	3	v∈v	v∈v	PROPN
ejpam-6755	40	4	(	(	PUNCT
ejpam-6755	40	5	h1	h1	PROPN
ejpam-6755	40	6	)	)	PUNCT
ejpam-6755	40	7	f(v	f(v	NOUN
ejpam-6755	40	8	)	)	PUNCT
ejpam-6755	41	1	+	+	CCONJ
ejpam-6755	41	2	∑	∑	PUNCT
ejpam-6755	41	3	e∈e(h1	e∈e(h1	PROPN
ejpam-6755	41	4	)	)	PUNCT
ejpam-6755	41	5	f(e	f(e	NOUN
ejpam-6755	41	6	)	)	PUNCT
ejpam-6755	41	7	=	=	SYM
ejpam-6755	41	8	c1	c1	NOUN
ejpam-6755	41	9	and	and	CCONJ
ejpam-6755	41	10	for	for	ADP
ejpam-6755	41	11	every	every	DET
ejpam-6755	41	12	subgraph	subgraph	NOUN
ejpam-6755	41	13	h∗	h∗	PROPN
ejpam-6755	41	14	2	2	NUM
ejpam-6755	41	15	of	of	ADP
ejpam-6755	41	16	g	g	NOUN
ejpam-6755	41	17	isomorphic	isomorphic	ADJ
ejpam-6755	41	18	to	to	ADP
ejpam-6755	41	19	h2	h2	PROPN
ejpam-6755	41	20	holds	hold	VERB
ejpam-6755	41	21	w(h2	w(h2	NOUN
ejpam-6755	41	22	)	)	PUNCT
ejpam-6755	41	23	=	=	SYM
ejpam-6755	41	24	∑	∑	PUNCT
ejpam-6755	41	25	v∈v	v∈v	PROPN
ejpam-6755	41	26	(	(	PUNCT
ejpam-6755	41	27	h2	h2	NOUN
ejpam-6755	41	28	)	)	PUNCT
ejpam-6755	41	29	f(v	f(v	PROPN
ejpam-6755	41	30	)	)	PUNCT
ejpam-6755	42	1	+	+	CCONJ
ejpam-6755	42	2	∑	∑	PUNCT
ejpam-6755	42	3	e∈e(h2	e∈e(h2	NOUN
ejpam-6755	42	4	)	)	PUNCT
ejpam-6755	42	5	f(e	f(e	NOUN
ejpam-6755	42	6	)	)	PUNCT
ejpam-6755	42	7	=	=	SYM
ejpam-6755	42	8	c2	c2	PROPN
ejpam-6755	42	9	.	.	PUNCT
ejpam-6755	43	1	moreover	moreover	ADV
ejpam-6755	43	2	,	,	PUNCT
ejpam-6755	43	3	an	an	DET
ejpam-6755	43	4	(	(	PUNCT
ejpam-6755	43	5	h1	h1	PROPN
ejpam-6755	43	6	,	,	PUNCT
ejpam-6755	43	7	h2)-magic	h2)-magic	ADJ
ejpam-6755	43	8	labeling	labeling	NOUN
ejpam-6755	43	9	f	f	NOUN
ejpam-6755	43	10	is	be	AUX
ejpam-6755	43	11	called	call	VERB
ejpam-6755	43	12	(	(	PUNCT
ejpam-6755	43	13	h1	h1	PROPN
ejpam-6755	43	14	,	,	PUNCT
ejpam-6755	43	15	h2)-supermagic	h2)-supermagic	PROPN
ejpam-6755	43	16	if	if	SCONJ
ejpam-6755	43	17	the	the	DET
ejpam-6755	43	18	vertices	vertex	NOUN
ejpam-6755	43	19	are	be	AUX
ejpam-6755	43	20	labeled	label	VERB
ejpam-6755	43	21	with	with	ADP
ejpam-6755	43	22	the	the	DET
ejpam-6755	43	23	smallest	small	ADJ
ejpam-6755	43	24	possible	possible	ADJ
ejpam-6755	43	25	numbers	number	NOUN
ejpam-6755	43	26	,	,	PUNCT
ejpam-6755	43	27	i.e.	i.e.	X
ejpam-6755	43	28	,	,	PUNCT
ejpam-6755	43	29	{	{	PUNCT
ejpam-6755	43	30	f(v	f(v	NOUN
ejpam-6755	43	31	)	)	PUNCT
ejpam-6755	43	32	|	|	ADV
ejpam-6755	43	33	v	v	ADP
ejpam-6755	43	34	∈	∈	PROPN
ejpam-6755	43	35	v	v	NOUN
ejpam-6755	43	36	(	(	PUNCT
ejpam-6755	43	37	g	g	NOUN
ejpam-6755	43	38	)	)	PUNCT
ejpam-6755	43	39	}	}	PUNCT
ejpam-6755	44	1	=	=	PUNCT
ejpam-6755	45	1	[	[	X
ejpam-6755	45	2	1	1	NUM
ejpam-6755	45	3	,	,	PUNCT
ejpam-6755	45	4	|v	|v	PROPN
ejpam-6755	45	5	(	(	PUNCT
ejpam-6755	45	6	g)|	g)|	PROPN
ejpam-6755	45	7	]	]	PUNCT
ejpam-6755	45	8	.	.	PUNCT
ejpam-6755	46	1	a	a	DET
ejpam-6755	46	2	graph	graph	NOUN
ejpam-6755	46	3	g	g	PROPN
ejpam-6755	46	4	called	call	VERB
ejpam-6755	46	5	is	be	AUX
ejpam-6755	46	6	called	call	VERB
ejpam-6755	46	7	(	(	PUNCT
ejpam-6755	46	8	h1	h1	PROPN
ejpam-6755	46	9	,	,	PUNCT
ejpam-6755	46	10	h2)-(super)magic	h2)-(super)magic	PROPN
ejpam-6755	46	11	if	if	SCONJ
ejpam-6755	46	12	g	g	PROPN
ejpam-6755	46	13	admits	admit	VERB
ejpam-6755	46	14	an	an	DET
ejpam-6755	46	15	(	(	PUNCT
ejpam-6755	46	16	h1	h1	PROPN
ejpam-6755	46	17	,	,	PUNCT
ejpam-6755	46	18	h2)-(super)magic	h2)-(super)magic	PROPN
ejpam-6755	46	19	labeling	labeling	NOUN
ejpam-6755	46	20	.	.	PUNCT
ejpam-6755	47	1	some	some	DET
ejpam-6755	47	2	other	other	ADJ
ejpam-6755	47	3	variations	variation	NOUN
ejpam-6755	47	4	of	of	ADP
ejpam-6755	47	5	h-(super)magic	h-(super)magic	ADJ
ejpam-6755	47	6	valuations	valuation	NOUN
ejpam-6755	47	7	of	of	ADP
ejpam-6755	47	8	graphs	graph	NOUN
ejpam-6755	47	9	can	can	AUX
ejpam-6755	47	10	be	be	AUX
ejpam-6755	47	11	seen	see	VERB
ejpam-6755	47	12	in	in	ADP
ejpam-6755	47	13	[	[	X
ejpam-6755	47	14	8–11	8–11	NOUN
ejpam-6755	47	15	]	]	PUNCT
ejpam-6755	47	16	.	.	PUNCT
ejpam-6755	48	1	for	for	ADP
ejpam-6755	48	2	more	more	ADJ
ejpam-6755	48	3	insights	insight	NOUN
ejpam-6755	48	4	about	about	ADP
ejpam-6755	48	5	graph	graph	NOUN
ejpam-6755	48	6	labeling	labeling	NOUN
ejpam-6755	48	7	,	,	PUNCT
ejpam-6755	48	8	please	please	INTJ
ejpam-6755	48	9	see	see	VERB
ejpam-6755	48	10	[	[	X
ejpam-6755	48	11	12	12	NUM
ejpam-6755	48	12	]	]	PUNCT
ejpam-6755	48	13	.	.	PUNCT
ejpam-6755	49	1	furthermore	furthermore	ADV
ejpam-6755	49	2	,	,	PUNCT
ejpam-6755	49	3	there	there	PRON
ejpam-6755	49	4	are	be	VERB
ejpam-6755	49	5	several	several	ADJ
ejpam-6755	49	6	recent	recent	ADJ
ejpam-6755	49	7	applications	application	NOUN
ejpam-6755	49	8	of	of	ADP
ejpam-6755	49	9	graph	graph	NOUN
ejpam-6755	49	10	theory	theory	NOUN
ejpam-6755	49	11	which	which	PRON
ejpam-6755	49	12	can	can	AUX
ejpam-6755	49	13	be	be	AUX
ejpam-6755	49	14	seen	see	VERB
ejpam-6755	49	15	in	in	ADP
ejpam-6755	49	16	[	[	X
ejpam-6755	49	17	13	13	NUM
ejpam-6755	49	18	,	,	PUNCT
ejpam-6755	49	19	14	14	NUM
ejpam-6755	49	20	]	]	PUNCT
ejpam-6755	49	21	.	.	PUNCT
ejpam-6755	50	1	in	in	ADP
ejpam-6755	50	2	this	this	DET
ejpam-6755	50	3	paper	paper	NOUN
ejpam-6755	50	4	,	,	PUNCT
ejpam-6755	50	5	we	we	PRON
ejpam-6755	50	6	present	present	VERB
ejpam-6755	50	7	several	several	ADJ
ejpam-6755	50	8	new	new	ADJ
ejpam-6755	50	9	constructions	construction	NOUN
ejpam-6755	50	10	of	of	ADP
ejpam-6755	50	11	(	(	PUNCT
ejpam-6755	50	12	h1	h1	PROPN
ejpam-6755	50	13	,	,	PUNCT
ejpam-6755	50	14	h2)-magic	h2)-magic	ADJ
ejpam-6755	50	15	graphs	graph	NOUN
ejpam-6755	50	16	and	and	CCONJ
ejpam-6755	50	17	also	also	ADV
ejpam-6755	50	18	results	result	VERB
ejpam-6755	50	19	for	for	ADP
ejpam-6755	50	20	ph-(super)magicness	ph-(super)magicness	NOUN
ejpam-6755	50	21	of	of	ADP
ejpam-6755	50	22	copies	copy	NOUN
ejpam-6755	50	23	of	of	ADP
ejpam-6755	50	24	paths	path	NOUN
ejpam-6755	50	25	.	.	PUNCT
ejpam-6755	51	1	2	2	X
ejpam-6755	51	2	.	.	X
ejpam-6755	51	3	the	the	DET
ejpam-6755	51	4	(	(	PUNCT
ejpam-6755	51	5	k	k	NOUN
ejpam-6755	51	6	,	,	PUNCT
ejpam-6755	51	7	θ)-balanced	θ)-balanced	ADJ
ejpam-6755	51	8	multisets	multiset	NOUN
ejpam-6755	51	9	maryati	maryati	NOUN
ejpam-6755	51	10	et	et	NOUN
ejpam-6755	51	11	al	al	PROPN
ejpam-6755	51	12	.	.	PUNCT
ejpam-6755	52	1	[	[	X
ejpam-6755	52	2	15	15	NUM
ejpam-6755	52	3	]	]	PUNCT
ejpam-6755	52	4	presented	present	VERB
ejpam-6755	52	5	a	a	DET
ejpam-6755	52	6	characterization	characterization	NOUN
ejpam-6755	52	7	of	of	ADP
ejpam-6755	52	8	mg	mg	PROPN
ejpam-6755	52	9	being	be	AUX
ejpam-6755	52	10	g	g	NOUN
ejpam-6755	52	11	-	-	PUNCT
ejpam-6755	52	12	supermagic	supermagic	NOUN
ejpam-6755	52	13	.	.	PUNCT
ejpam-6755	53	1	theorem	theorem	NOUN
ejpam-6755	53	2	1	1	NUM
ejpam-6755	53	3	.	.	PUNCT
ejpam-6755	54	1	[	[	X
ejpam-6755	54	2	15	15	NUM
ejpam-6755	54	3	]	]	PUNCT
ejpam-6755	54	4	let	let	VERB
ejpam-6755	54	5	m	m	PRON
ejpam-6755	54	6	be	be	AUX
ejpam-6755	54	7	a	a	DET
ejpam-6755	54	8	positive	positive	ADJ
ejpam-6755	54	9	integer	integer	NOUN
ejpam-6755	54	10	and	and	CCONJ
ejpam-6755	54	11	let	let	VERB
ejpam-6755	54	12	g	g	PRON
ejpam-6755	54	13	be	be	AUX
ejpam-6755	54	14	a	a	DET
ejpam-6755	54	15	graph	graph	NOUN
ejpam-6755	54	16	such	such	ADJ
ejpam-6755	54	17	that	that	SCONJ
ejpam-6755	54	18	all	all	PRON
ejpam-6755	54	19	its	its	PRON
ejpam-6755	54	20	components	component	NOUN
ejpam-6755	54	21	have	have	VERB
ejpam-6755	54	22	at	at	ADV
ejpam-6755	54	23	least	least	ADJ
ejpam-6755	54	24	2	2	NUM
ejpam-6755	54	25	vertices	vertex	NOUN
ejpam-6755	54	26	.	.	PUNCT
ejpam-6755	55	1	then	then	ADV
ejpam-6755	55	2	mg	mg	PROPN
ejpam-6755	55	3	is	be	AUX
ejpam-6755	55	4	g	g	NOUN
ejpam-6755	55	5	-	-	PUNCT
ejpam-6755	55	6	magic	magic	NOUN
ejpam-6755	55	7	if	if	SCONJ
ejpam-6755	55	8	and	and	CCONJ
ejpam-6755	55	9	only	only	ADV
ejpam-6755	55	10	if	if	SCONJ
ejpam-6755	55	11	|v	|v	PROPN
ejpam-6755	55	12	(	(	PUNCT
ejpam-6755	55	13	g)|+	g)|+	PROPN
ejpam-6755	55	14	|e(g)|	|e(g)|	PROPN
ejpam-6755	55	15	is	be	AUX
ejpam-6755	55	16	even	even	ADV
ejpam-6755	55	17	or	or	CCONJ
ejpam-6755	55	18	m	m	VERB
ejpam-6755	55	19	is	be	AUX
ejpam-6755	55	20	odd	odd	ADJ
ejpam-6755	55	21	.	.	PUNCT
ejpam-6755	56	1	t.	t.	PROPN
ejpam-6755	56	2	k.	k.	PROPN
ejpam-6755	56	3	maryati	maryati	PROPN
ejpam-6755	56	4	et	et	PROPN
ejpam-6755	56	5	al	al	PROPN
ejpam-6755	56	6	.	.	PUNCT
ejpam-6755	56	7	/	/	SYM
ejpam-6755	56	8	eur	eur	PROPN
ejpam-6755	56	9	.	.	PUNCT
ejpam-6755	57	1	j.	j.	PROPN
ejpam-6755	57	2	pure	pure	PROPN
ejpam-6755	57	3	appl	appl	PROPN
ejpam-6755	57	4	.	.	PROPN
ejpam-6755	57	5	math	math	PROPN
ejpam-6755	57	6	,	,	PUNCT
ejpam-6755	57	7	18	18	NUM
ejpam-6755	57	8	(	(	PUNCT
ejpam-6755	57	9	4	4	NUM
ejpam-6755	57	10	)	)	PUNCT
ejpam-6755	57	11	(	(	PUNCT
ejpam-6755	57	12	2025	2025	NUM
ejpam-6755	57	13	)	)	PUNCT
ejpam-6755	57	14	,	,	PUNCT
ejpam-6755	57	15	6755	6755	NUM
ejpam-6755	57	16	3	3	NUM
ejpam-6755	57	17	of	of	ADP
ejpam-6755	57	18	13	13	NUM
ejpam-6755	57	19	the	the	DET
ejpam-6755	57	20	proof	proof	NOUN
ejpam-6755	57	21	of	of	ADP
ejpam-6755	57	22	this	this	DET
ejpam-6755	57	23	theorem	theorem	NOUN
ejpam-6755	57	24	is	be	AUX
ejpam-6755	57	25	based	base	VERB
ejpam-6755	57	26	on	on	ADP
ejpam-6755	57	27	a	a	DET
ejpam-6755	57	28	technique	technique	NOUN
ejpam-6755	57	29	called	call	VERB
ejpam-6755	57	30	(	(	PUNCT
ejpam-6755	57	31	k	k	NOUN
ejpam-6755	57	32	,	,	PUNCT
ejpam-6755	57	33	θ)-balanced	θ)-balanced	ADJ
ejpam-6755	57	34	multisets	multiset	NOUN
ejpam-6755	57	35	,	,	PUNCT
ejpam-6755	57	36	see	see	VERB
ejpam-6755	57	37	[	[	X
ejpam-6755	57	38	15	15	NUM
ejpam-6755	57	39	,	,	PUNCT
ejpam-6755	57	40	16	16	NUM
ejpam-6755	57	41	]	]	PUNCT
ejpam-6755	57	42	.	.	PUNCT
ejpam-6755	58	1	in	in	ADP
ejpam-6755	58	2	this	this	DET
ejpam-6755	58	3	paper	paper	NOUN
ejpam-6755	58	4	,	,	PUNCT
ejpam-6755	58	5	we	we	PRON
ejpam-6755	58	6	will	will	AUX
ejpam-6755	58	7	also	also	ADV
ejpam-6755	58	8	use	use	VERB
ejpam-6755	58	9	this	this	DET
ejpam-6755	58	10	method	method	NOUN
ejpam-6755	58	11	;	;	PUNCT
ejpam-6755	58	12	therefore	therefore	ADV
ejpam-6755	58	13	,	,	PUNCT
ejpam-6755	58	14	we	we	PRON
ejpam-6755	58	15	begin	begin	VERB
ejpam-6755	58	16	by	by	ADP
ejpam-6755	58	17	introducing	introduce	VERB
ejpam-6755	58	18	several	several	ADJ
ejpam-6755	58	19	definitions	definition	NOUN
ejpam-6755	58	20	and	and	CCONJ
ejpam-6755	58	21	basic	basic	ADJ
ejpam-6755	58	22	properties	property	NOUN
ejpam-6755	58	23	.	.	PUNCT
ejpam-6755	59	1	multiset	multiset	PROPN
ejpam-6755	59	2	is	be	AUX
ejpam-6755	59	3	a	a	DET
ejpam-6755	59	4	generalization	generalization	NOUN
ejpam-6755	59	5	of	of	ADP
ejpam-6755	59	6	a	a	DET
ejpam-6755	59	7	set	set	NOUN
ejpam-6755	59	8	,	,	PUNCT
ejpam-6755	59	9	where	where	SCONJ
ejpam-6755	59	10	multiple	multiple	ADJ
ejpam-6755	59	11	instances	instance	NOUN
ejpam-6755	59	12	of	of	ADP
ejpam-6755	59	13	each	each	DET
ejpam-6755	59	14	element	element	NOUN
ejpam-6755	59	15	in	in	ADP
ejpam-6755	59	16	a	a	DET
ejpam-6755	59	17	set	set	NOUN
ejpam-6755	59	18	is	be	AUX
ejpam-6755	59	19	allowed	allow	VERB
ejpam-6755	59	20	.	.	PUNCT
ejpam-6755	60	1	the	the	DET
ejpam-6755	60	2	notion	notion	NOUN
ejpam-6755	60	3	⊎	⊎	PUNCT
ejpam-6755	60	4	combines	combine	VERB
ejpam-6755	60	5	multisets	multiset	NOUN
ejpam-6755	60	6	with	with	ADP
ejpam-6755	60	7	counting	count	VERB
ejpam-6755	60	8	repeated	repeat	VERB
ejpam-6755	60	9	occurrences	occurrence	NOUN
ejpam-6755	60	10	of	of	ADP
ejpam-6755	60	11	elements	element	NOUN
ejpam-6755	60	12	from	from	ADP
ejpam-6755	60	13	each	each	DET
ejpam-6755	60	14	multisets	multiset	NOUN
ejpam-6755	60	15	,	,	PUNCT
ejpam-6755	60	16	i.e.	i.e.	X
ejpam-6755	60	17	,	,	PUNCT
ejpam-6755	60	18	{	{	PUNCT
ejpam-6755	60	19	a}⊎{a	a}⊎{a	PROPN
ejpam-6755	60	20	,	,	PUNCT
ejpam-6755	60	21	b	b	NOUN
ejpam-6755	60	22	}	}	PUNCT
ejpam-6755	60	23	=	=	SYM
ejpam-6755	60	24	{	{	PUNCT
ejpam-6755	60	25	a	a	X
ejpam-6755	60	26	,	,	PUNCT
ejpam-6755	60	27	a	a	DET
ejpam-6755	60	28	,	,	PUNCT
ejpam-6755	60	29	b	b	NOUN
ejpam-6755	60	30	}	}	PUNCT
ejpam-6755	60	31	.	.	PUNCT
ejpam-6755	61	1	let	let	VERB
ejpam-6755	61	2	k	k	NOUN
ejpam-6755	61	3	=	=	PUNCT
ejpam-6755	61	4	hθ	hθ	VERB
ejpam-6755	61	5	for	for	ADP
ejpam-6755	61	6	some	some	DET
ejpam-6755	61	7	positive	positive	ADJ
ejpam-6755	61	8	integers	integer	NOUN
ejpam-6755	61	9	h	h	NOUN
ejpam-6755	61	10	and	and	CCONJ
ejpam-6755	61	11	θ	θ	PROPN
ejpam-6755	61	12	.	.	PUNCT
ejpam-6755	62	1	let	let	VERB
ejpam-6755	62	2	y	y	PRON
ejpam-6755	62	3	be	be	AUX
ejpam-6755	62	4	a	a	DET
ejpam-6755	62	5	multiset	multiset	NOUN
ejpam-6755	62	6	containing	contain	VERB
ejpam-6755	62	7	positive	positive	ADJ
ejpam-6755	62	8	integers	integer	NOUN
ejpam-6755	62	9	.	.	PUNCT
ejpam-6755	63	1	the	the	DET
ejpam-6755	63	2	multiset	multiset	ADJ
ejpam-6755	63	3	y	y	PROPN
ejpam-6755	63	4	is	be	AUX
ejpam-6755	63	5	said	say	VERB
ejpam-6755	63	6	to	to	PART
ejpam-6755	63	7	be	be	AUX
ejpam-6755	63	8	(	(	PUNCT
ejpam-6755	63	9	k	k	NOUN
ejpam-6755	63	10	,	,	PUNCT
ejpam-6755	63	11	θ)-balanced	θ)-balance	VERB
ejpam-6755	63	12	if	if	SCONJ
ejpam-6755	63	13	there	there	PRON
ejpam-6755	63	14	exist	exist	VERB
ejpam-6755	63	15	k	k	PROPN
ejpam-6755	63	16	submultisets	submultiset	NOUN
ejpam-6755	63	17	of	of	ADP
ejpam-6755	63	18	y	y	PROPN
ejpam-6755	63	19	,	,	PUNCT
ejpam-6755	63	20	namely	namely	ADV
ejpam-6755	63	21	yi	yi	NOUN
ejpam-6755	63	22	for	for	ADP
ejpam-6755	63	23	i	i	PRON
ejpam-6755	63	24	∈	∈	PROPN
ejpam-6755	64	1	[	[	X
ejpam-6755	64	2	1	1	NUM
ejpam-6755	64	3	,	,	PUNCT
ejpam-6755	64	4	k	k	NOUN
ejpam-6755	64	5	]	]	X
ejpam-6755	64	6	,	,	PUNCT
ejpam-6755	64	7	and	and	CCONJ
ejpam-6755	64	8	there	there	PRON
ejpam-6755	64	9	exist	exist	VERB
ejpam-6755	64	10	θ	θ	PROPN
ejpam-6755	64	11	distinct	distinct	ADJ
ejpam-6755	64	12	integers	integer	NOUN
ejpam-6755	64	13	aj	aj	PROPN
ejpam-6755	64	14	for	for	ADP
ejpam-6755	64	15	j	j	PROPN
ejpam-6755	64	16	∈	∈	PROPN
ejpam-6755	65	1	[	[	X
ejpam-6755	65	2	1	1	NUM
ejpam-6755	65	3	,	,	PUNCT
ejpam-6755	65	4	θ	θ	PROPN
ejpam-6755	65	5	]	]	X
ejpam-6755	65	6	,	,	PUNCT
ejpam-6755	65	7	such	such	ADJ
ejpam-6755	65	8	that	that	SCONJ
ejpam-6755	65	9	(	(	PUNCT
ejpam-6755	65	10	i	i	NOUN
ejpam-6755	65	11	)	)	PUNCT
ejpam-6755	65	12	⊎k	⊎k	NOUN
ejpam-6755	65	13	i=1yi	i=1yi	VERB
ejpam-6755	65	14	=	=	SYM
ejpam-6755	65	15	y	y	PROPN
ejpam-6755	65	16	,	,	PUNCT
ejpam-6755	65	17	(	(	PUNCT
ejpam-6755	65	18	ii	ii	NOUN
ejpam-6755	65	19	)	)	PUNCT
ejpam-6755	65	20	|yi|	|yi|	NOUN
ejpam-6755	65	21	=	=	NOUN
ejpam-6755	65	22	|y	|y	NOUN
ejpam-6755	65	23	|	|	ADV
ejpam-6755	65	24	k	k	PROPN
ejpam-6755	65	25	for	for	ADP
ejpam-6755	65	26	every	every	DET
ejpam-6755	65	27	i	i	NOUN
ejpam-6755	65	28	∈	∈	PROPN
ejpam-6755	66	1	[	[	X
ejpam-6755	66	2	1	1	NUM
ejpam-6755	66	3	,	,	PUNCT
ejpam-6755	66	4	k	k	NOUN
ejpam-6755	66	5	]	]	X
ejpam-6755	66	6	,	,	PUNCT
ejpam-6755	66	7	(	(	PUNCT
ejpam-6755	66	8	iii	iii	NOUN
ejpam-6755	66	9	)	)	PUNCT
ejpam-6755	66	10	∑	∑	ADP
ejpam-6755	66	11	b∈yth+r	b∈yth+r	X
ejpam-6755	66	12	b	b	X
ejpam-6755	66	13	=	=	PUNCT
ejpam-6755	66	14	at+1	at+1	PROPN
ejpam-6755	66	15	for	for	ADP
ejpam-6755	66	16	t	t	PROPN
ejpam-6755	66	17	∈	∈	PROPN
ejpam-6755	67	1	[	[	X
ejpam-6755	67	2	0	0	NUM
ejpam-6755	67	3	,	,	PUNCT
ejpam-6755	67	4	θ	θ	PROPN
ejpam-6755	67	5	−	−	PROPN
ejpam-6755	67	6	1	1	NUM
ejpam-6755	67	7	]	]	PUNCT
ejpam-6755	67	8	and	and	CCONJ
ejpam-6755	67	9	r	r	NOUN
ejpam-6755	67	10	∈	∈	PROPN
ejpam-6755	68	1	[	[	X
ejpam-6755	68	2	1	1	NUM
ejpam-6755	68	3	,	,	PUNCT
ejpam-6755	68	4	h	h	NOUN
ejpam-6755	68	5	]	]	X
ejpam-6755	68	6	.	.	PUNCT
ejpam-6755	69	1	for	for	ADP
ejpam-6755	69	2	i	i	PRON
ejpam-6755	69	3	∈	∈	PROPN
ejpam-6755	70	1	[	[	X
ejpam-6755	70	2	1	1	NUM
ejpam-6755	70	3	,	,	PUNCT
ejpam-6755	70	4	k	k	NOUN
ejpam-6755	70	5	]	]	X
ejpam-6755	70	6	,	,	PUNCT
ejpam-6755	70	7	yi	yi	PROPN
ejpam-6755	70	8	is	be	AUX
ejpam-6755	70	9	called	call	VERB
ejpam-6755	70	10	a	a	DET
ejpam-6755	70	11	balanced	balanced	ADJ
ejpam-6755	70	12	submultiset	submultiset	NOUN
ejpam-6755	70	13	of	of	ADP
ejpam-6755	70	14	y	y	PROPN
ejpam-6755	70	15	.	.	PUNCT
ejpam-6755	71	1	particularly	particularly	ADV
ejpam-6755	71	2	,	,	PUNCT
ejpam-6755	71	3	a	a	DET
ejpam-6755	71	4	(	(	PUNCT
ejpam-6755	71	5	k	k	NOUN
ejpam-6755	71	6	,	,	PUNCT
ejpam-6755	71	7	1)-balanced	1)-balanced	PROPN
ejpam-6755	71	8	multiset	multiset	VERB
ejpam-6755	71	9	is	be	AUX
ejpam-6755	71	10	exactly	exactly	ADV
ejpam-6755	71	11	a	a	DET
ejpam-6755	71	12	k	k	ADV
ejpam-6755	71	13	-	-	PUNCT
ejpam-6755	71	14	balanced	balanced	ADJ
ejpam-6755	71	15	multiset	multiset	NOUN
ejpam-6755	71	16	.	.	PUNCT
ejpam-6755	72	1	this	this	DET
ejpam-6755	72	2	method	method	NOUN
ejpam-6755	72	3	can	can	AUX
ejpam-6755	72	4	also	also	ADV
ejpam-6755	72	5	be	be	AUX
ejpam-6755	72	6	applied	apply	VERB
ejpam-6755	72	7	to	to	PART
ejpam-6755	72	8	identify	identify	VERB
ejpam-6755	72	9	(	(	PUNCT
ejpam-6755	72	10	h1	h1	PROPN
ejpam-6755	72	11	,	,	PUNCT
ejpam-6755	72	12	h2)-magic	h2)-magic	ADJ
ejpam-6755	72	13	graphs	graph	NOUN
ejpam-6755	72	14	.	.	PUNCT
ejpam-6755	73	1	additionally	additionally	ADV
ejpam-6755	73	2	,	,	PUNCT
ejpam-6755	73	3	some	some	DET
ejpam-6755	73	4	established	establish	VERB
ejpam-6755	73	5	results	result	NOUN
ejpam-6755	73	6	concerning	concern	VERB
ejpam-6755	73	7	(	(	PUNCT
ejpam-6755	73	8	k	k	X
ejpam-6755	73	9	,	,	PUNCT
ejpam-6755	73	10	θ)-balanced	θ)-balanced	ADJ
ejpam-6755	73	11	multisets	multiset	NOUN
ejpam-6755	73	12	are	be	AUX
ejpam-6755	73	13	presented	present	VERB
ejpam-6755	73	14	below	below	ADV
ejpam-6755	73	15	.	.	PUNCT
ejpam-6755	74	1	lemma	lemma	PROPN
ejpam-6755	74	2	1	1	NUM
ejpam-6755	74	3	.	.	PUNCT
ejpam-6755	75	1	[	[	X
ejpam-6755	75	2	15	15	NUM
ejpam-6755	75	3	]	]	X
ejpam-6755	75	4	let	let	VERB
ejpam-6755	75	5	x	x	PRON
ejpam-6755	75	6	,	,	PUNCT
ejpam-6755	75	7	y	y	PROPN
ejpam-6755	75	8	,	,	PUNCT
ejpam-6755	75	9	z	z	PROPN
ejpam-6755	75	10	and	and	CCONJ
ejpam-6755	75	11	k	k	PROPN
ejpam-6755	75	12	be	be	AUX
ejpam-6755	75	13	non	non	ADJ
ejpam-6755	75	14	-	-	ADJ
ejpam-6755	75	15	negative	negative	ADJ
ejpam-6755	75	16	integers	integer	NOUN
ejpam-6755	75	17	and	and	CCONJ
ejpam-6755	75	18	y	y	NOUN
ejpam-6755	75	19	=	=	PUNCT
ejpam-6755	76	1	[	[	X
ejpam-6755	76	2	x+	x+	ADJ
ejpam-6755	76	3	1	1	NUM
ejpam-6755	76	4	,	,	PUNCT
ejpam-6755	76	5	x+	x+	X
ejpam-6755	76	6	k	k	X
ejpam-6755	76	7	]	]	X
ejpam-6755	76	8	⊎	⊎	X
ejpam-6755	76	9	[	[	X
ejpam-6755	76	10	y	y	X
ejpam-6755	76	11	+	+	NOUN
ejpam-6755	76	12	1	1	NUM
ejpam-6755	76	13	,	,	PUNCT
ejpam-6755	76	14	y	y	PROPN
ejpam-6755	76	15	+	+	CCONJ
ejpam-6755	76	16	k	k	X
ejpam-6755	76	17	]	]	X
ejpam-6755	76	18	⊎	⊎	X
ejpam-6755	77	1	[	[	X
ejpam-6755	77	2	z	z	X
ejpam-6755	77	3	+	+	NOUN
ejpam-6755	77	4	1	1	NUM
ejpam-6755	77	5	,	,	PUNCT
ejpam-6755	77	6	z	z	NOUN
ejpam-6755	78	1	+	+	CCONJ
ejpam-6755	78	2	k	k	X
ejpam-6755	78	3	]	]	X
ejpam-6755	78	4	be	be	AUX
ejpam-6755	78	5	a	a	DET
ejpam-6755	78	6	multiset	multiset	NOUN
ejpam-6755	78	7	.	.	PUNCT
ejpam-6755	79	1	then	then	ADV
ejpam-6755	79	2	(	(	PUNCT
ejpam-6755	79	3	1	1	X
ejpam-6755	79	4	)	)	PUNCT
ejpam-6755	79	5	for	for	ADP
ejpam-6755	79	6	even	even	ADV
ejpam-6755	79	7	k	k	PROPN
ejpam-6755	79	8	≥	≥	NUM
ejpam-6755	79	9	2	2	NUM
ejpam-6755	79	10	,	,	PUNCT
ejpam-6755	79	11	y	y	PROPN
ejpam-6755	79	12	is	be	AUX
ejpam-6755	79	13	(	(	PUNCT
ejpam-6755	79	14	k	k	NOUN
ejpam-6755	79	15	,	,	PUNCT
ejpam-6755	79	16	2)-balanced	2)-balanced	NUM
ejpam-6755	79	17	,	,	PUNCT
ejpam-6755	79	18	with	with	ADP
ejpam-6755	79	19	∑	∑	PART
ejpam-6755	79	20	b∈yi	b∈yi	PROPN
ejpam-6755	79	21	b	b	NOUN
ejpam-6755	79	22	=	=	PUNCT
ejpam-6755	79	23	{	{	PUNCT
ejpam-6755	79	24	x+	x+	PROPN
ejpam-6755	79	25	y	y	PROPN
ejpam-6755	79	26	+	+	NOUN
ejpam-6755	79	27	z	z	PROPN
ejpam-6755	80	1	+	+	NOUN
ejpam-6755	80	2	3k	3k	X
ejpam-6755	80	3	2	2	NUM
ejpam-6755	80	4	+	+	CCONJ
ejpam-6755	80	5	2	2	NUM
ejpam-6755	80	6	,	,	PUNCT
ejpam-6755	80	7	for	for	ADP
ejpam-6755	80	8	i	i	PRON
ejpam-6755	80	9	∈	∈	PROPN
ejpam-6755	81	1	[	[	X
ejpam-6755	81	2	1	1	NUM
ejpam-6755	81	3	,	,	PUNCT
ejpam-6755	81	4	k2	k2	NOUN
ejpam-6755	81	5	]	]	PUNCT
ejpam-6755	81	6	,	,	PUNCT
ejpam-6755	81	7	x+	x+	X
ejpam-6755	81	8	y	y	PROPN
ejpam-6755	82	1	+	+	NOUN
ejpam-6755	82	2	z	z	PROPN
ejpam-6755	83	1	+	+	NOUN
ejpam-6755	83	2	3k	3k	X
ejpam-6755	83	3	2	2	NUM
ejpam-6755	83	4	+	+	CCONJ
ejpam-6755	83	5	1	1	NUM
ejpam-6755	83	6	,	,	PUNCT
ejpam-6755	83	7	for	for	ADP
ejpam-6755	83	8	i	i	PRON
ejpam-6755	83	9	∈	∈	PROPN
ejpam-6755	84	1	[	[	X
ejpam-6755	84	2	k2	k2	NOUN
ejpam-6755	84	3	+	+	CCONJ
ejpam-6755	84	4	1	1	NUM
ejpam-6755	84	5	,	,	PUNCT
ejpam-6755	84	6	k	k	NOUN
ejpam-6755	84	7	]	]	X
ejpam-6755	84	8	,	,	PUNCT
ejpam-6755	84	9	(	(	PUNCT
ejpam-6755	84	10	2	2	X
ejpam-6755	84	11	)	)	PUNCT
ejpam-6755	84	12	for	for	ADP
ejpam-6755	84	13	odd	odd	ADJ
ejpam-6755	84	14	k	k	PROPN
ejpam-6755	84	15	≥	≥	NUM
ejpam-6755	84	16	3	3	NUM
ejpam-6755	84	17	,	,	PUNCT
ejpam-6755	84	18	y	y	PROPN
ejpam-6755	84	19	is	be	AUX
ejpam-6755	84	20	k	k	NOUN
ejpam-6755	84	21	-	-	ADJ
ejpam-6755	84	22	balanced	balanced	ADJ
ejpam-6755	84	23	,	,	PUNCT
ejpam-6755	84	24	with	with	ADP
ejpam-6755	84	25	∑	∑	PUNCT
ejpam-6755	84	26	b∈yi	b∈yi	PROPN
ejpam-6755	84	27	b	b	NOUN
ejpam-6755	84	28	=	=	SYM
ejpam-6755	84	29	x+	x+	PROPN
ejpam-6755	84	30	y	y	PROPN
ejpam-6755	85	1	+	+	NOUN
ejpam-6755	85	2	z	z	NOUN
ejpam-6755	86	1	+	+	CCONJ
ejpam-6755	86	2	3	3	NUM
ejpam-6755	86	3	2(k	2(k	NUM
ejpam-6755	86	4	+	+	CCONJ
ejpam-6755	86	5	1	1	NUM
ejpam-6755	86	6	)	)	PUNCT
ejpam-6755	86	7	.	.	PUNCT
ejpam-6755	87	1	3	3	X
ejpam-6755	87	2	.	.	X
ejpam-6755	87	3	the	the	DET
ejpam-6755	87	4	ph	ph	ADJ
ejpam-6755	87	5	-	-	ADJ
ejpam-6755	87	6	supermagic	supermagic	ADJ
ejpam-6755	87	7	graphs	graph	NOUN
ejpam-6755	87	8	gutiérrez	gutiérrez	NOUN
ejpam-6755	87	9	and	and	CCONJ
ejpam-6755	87	10	lladó	lladó	X
ejpam-6755	88	1	[	[	X
ejpam-6755	88	2	1	1	X
ejpam-6755	88	3	]	]	PUNCT
ejpam-6755	88	4	characterized	characterize	VERB
ejpam-6755	88	5	the	the	DET
ejpam-6755	88	6	path	path	NOUN
ejpam-6755	88	7	-	-	PUNCT
ejpam-6755	88	8	supermagicness	supermagicness	NOUN
ejpam-6755	88	9	of	of	ADP
ejpam-6755	88	10	the	the	DET
ejpam-6755	88	11	path	path	NOUN
ejpam-6755	88	12	pn	pn	PROPN
ejpam-6755	88	13	on	on	ADP
ejpam-6755	88	14	n	n	PRON
ejpam-6755	88	15	vertices	vertex	NOUN
ejpam-6755	88	16	.	.	PUNCT
ejpam-6755	89	1	theorem	theorem	NOUN
ejpam-6755	89	2	2	2	NUM
ejpam-6755	89	3	.	.	PUNCT
ejpam-6755	90	1	[	[	X
ejpam-6755	90	2	1	1	X
ejpam-6755	90	3	]	]	PUNCT
ejpam-6755	90	4	the	the	DET
ejpam-6755	90	5	path	path	NOUN
ejpam-6755	90	6	pn	pn	PROPN
ejpam-6755	90	7	is	be	AUX
ejpam-6755	90	8	ph	ph	ADJ
ejpam-6755	90	9	-	-	NOUN
ejpam-6755	90	10	supermagic	supermagic	NOUN
ejpam-6755	90	11	for	for	ADP
ejpam-6755	90	12	any	any	DET
ejpam-6755	90	13	integer	integer	NOUN
ejpam-6755	90	14	h	h	NOUN
ejpam-6755	90	15	∈	∈	PROPN
ejpam-6755	91	1	[	[	X
ejpam-6755	91	2	2	2	NUM
ejpam-6755	91	3	,	,	PUNCT
ejpam-6755	91	4	n	n	CCONJ
ejpam-6755	91	5	]	]	PUNCT
ejpam-6755	91	6	.	.	PUNCT
ejpam-6755	92	1	moreover	moreover	ADV
ejpam-6755	92	2	,	,	PUNCT
ejpam-6755	92	3	maryati	maryati	NOUN
ejpam-6755	92	4	et	et	PROPN
ejpam-6755	92	5	al	al	PROPN
ejpam-6755	92	6	.	.	PUNCT
ejpam-6755	93	1	[	[	X
ejpam-6755	93	2	17	17	NUM
ejpam-6755	93	3	]	]	PUNCT
ejpam-6755	93	4	showed	show	VERB
ejpam-6755	93	5	that	that	SCONJ
ejpam-6755	93	6	the	the	DET
ejpam-6755	93	7	odd	odd	ADJ
ejpam-6755	93	8	copies	copy	NOUN
ejpam-6755	93	9	of	of	ADP
ejpam-6755	93	10	paths	path	NOUN
ejpam-6755	93	11	with	with	ADP
ejpam-6755	93	12	at	at	ADV
ejpam-6755	93	13	least	least	ADJ
ejpam-6755	93	14	3	3	NUM
ejpam-6755	93	15	vertices	vertex	NOUN
ejpam-6755	93	16	is	be	AUX
ejpam-6755	93	17	also	also	ADV
ejpam-6755	93	18	ph	ph	ADJ
ejpam-6755	93	19	-	-	ADJ
ejpam-6755	93	20	supermagic	supermagic	ADJ
ejpam-6755	93	21	with	with	ADP
ejpam-6755	93	22	certain	certain	ADJ
ejpam-6755	93	23	restrictions	restriction	NOUN
ejpam-6755	93	24	on	on	ADP
ejpam-6755	93	25	h.	h.	PROPN
ejpam-6755	93	26	by	by	ADP
ejpam-6755	93	27	mg	mg	PROPN
ejpam-6755	93	28	we	we	PRON
ejpam-6755	93	29	denote	denote	VERB
ejpam-6755	93	30	the	the	DET
ejpam-6755	93	31	union	union	NOUN
ejpam-6755	93	32	of	of	ADP
ejpam-6755	93	33	disjoint	disjoint	PROPN
ejpam-6755	93	34	m	m	VERB
ejpam-6755	93	35	copies	copy	NOUN
ejpam-6755	93	36	of	of	ADP
ejpam-6755	93	37	a	a	DET
ejpam-6755	93	38	graph	graph	NOUN
ejpam-6755	94	1	g.	g.	PROPN
ejpam-6755	94	2	t.	t.	PROPN
ejpam-6755	94	3	k.	k.	PROPN
ejpam-6755	94	4	maryati	maryati	PROPN
ejpam-6755	94	5	et	et	PROPN
ejpam-6755	94	6	al	al	PROPN
ejpam-6755	94	7	.	.	PUNCT
ejpam-6755	94	8	/	/	SYM
ejpam-6755	94	9	eur	eur	PROPN
ejpam-6755	94	10	.	.	PUNCT
ejpam-6755	95	1	j.	j.	PROPN
ejpam-6755	95	2	pure	pure	PROPN
ejpam-6755	95	3	appl	appl	PROPN
ejpam-6755	95	4	.	.	PROPN
ejpam-6755	95	5	math	math	PROPN
ejpam-6755	95	6	,	,	PUNCT
ejpam-6755	95	7	18	18	NUM
ejpam-6755	95	8	(	(	PUNCT
ejpam-6755	95	9	4	4	NUM
ejpam-6755	95	10	)	)	PUNCT
ejpam-6755	95	11	(	(	PUNCT
ejpam-6755	95	12	2025	2025	NUM
ejpam-6755	95	13	)	)	PUNCT
ejpam-6755	95	14	,	,	PUNCT
ejpam-6755	95	15	6755	6755	NUM
ejpam-6755	95	16	4	4	NUM
ejpam-6755	95	17	of	of	ADP
ejpam-6755	95	18	13	13	NUM
ejpam-6755	95	19	theorem	theorem	NOUN
ejpam-6755	95	20	3	3	NUM
ejpam-6755	95	21	.	.	PUNCT
ejpam-6755	96	1	[	[	X
ejpam-6755	96	2	17	17	NUM
ejpam-6755	96	3	]	]	PUNCT
ejpam-6755	96	4	let	let	VERB
ejpam-6755	96	5	m	m	PRON
ejpam-6755	96	6	be	be	AUX
ejpam-6755	96	7	odd	odd	ADJ
ejpam-6755	96	8	and	and	CCONJ
ejpam-6755	96	9	n	n	PRON
ejpam-6755	96	10	≥	≥	NOUN
ejpam-6755	96	11	3	3	NUM
ejpam-6755	96	12	.	.	PUNCT
ejpam-6755	97	1	then	then	ADV
ejpam-6755	97	2	mpn	mpn	PROPN
ejpam-6755	97	3	is	be	AUX
ejpam-6755	97	4	kph	kph	PROPN
ejpam-6755	97	5	-	-	PUNCT
ejpam-6755	97	6	supermagic	supermagic	NOUN
ejpam-6755	97	7	for	for	ADP
ejpam-6755	97	8	k	k	PROPN
ejpam-6755	97	9	∈	∈	PROPN
ejpam-6755	98	1	[	[	X
ejpam-6755	98	2	1,m	1,m	X
ejpam-6755	98	3	]	]	X
ejpam-6755	98	4	and	and	CCONJ
ejpam-6755	98	5	h	h	NOUN
ejpam-6755	98	6	∈	∈	PROPN
ejpam-6755	98	7	[	[	PUNCT
ejpam-6755	98	8	⌈n2	⌈n2	NOUN
ejpam-6755	98	9	⌉+	⌉+	X
ejpam-6755	98	10	1	1	NUM
ejpam-6755	98	11	,	,	PUNCT
ejpam-6755	98	12	n	n	CCONJ
ejpam-6755	98	13	]	]	PUNCT
ejpam-6755	98	14	.	.	PUNCT
ejpam-6755	99	1	they	they	PRON
ejpam-6755	99	2	also	also	ADV
ejpam-6755	99	3	proposed	propose	VERB
ejpam-6755	99	4	that	that	SCONJ
ejpam-6755	99	5	mpn	mpn	PROPN
ejpam-6755	99	6	is	be	AUX
ejpam-6755	99	7	kph	kph	PROPN
ejpam-6755	99	8	-	-	PUNCT
ejpam-6755	99	9	supermagic	supermagic	NOUN
ejpam-6755	99	10	also	also	ADV
ejpam-6755	99	11	for	for	ADP
ejpam-6755	99	12	h	h	PROPN
ejpam-6755	99	13	∈	∈	PROPN
ejpam-6755	99	14	[	[	PUNCT
ejpam-6755	99	15	2	2	NUM
ejpam-6755	99	16	,	,	PUNCT
ejpam-6755	99	17	⌈n2	⌈n2	NOUN
ejpam-6755	99	18	⌉	⌉	X
ejpam-6755	99	19	]	]	PUNCT
ejpam-6755	99	20	.	.	PUNCT
ejpam-6755	100	1	in	in	ADP
ejpam-6755	100	2	the	the	DET
ejpam-6755	100	3	following	following	NOUN
ejpam-6755	100	4	theorem	theorem	NOUN
ejpam-6755	100	5	,	,	PUNCT
ejpam-6755	100	6	we	we	PRON
ejpam-6755	100	7	present	present	VERB
ejpam-6755	100	8	a	a	DET
ejpam-6755	100	9	complete	complete	ADJ
ejpam-6755	100	10	characterization	characterization	NOUN
ejpam-6755	100	11	when	when	SCONJ
ejpam-6755	100	12	odd	odd	ADJ
ejpam-6755	100	13	copies	copy	NOUN
ejpam-6755	100	14	of	of	ADP
ejpam-6755	100	15	paths	path	NOUN
ejpam-6755	100	16	is	be	AUX
ejpam-6755	100	17	path	path	NOUN
ejpam-6755	100	18	-	-	PUNCT
ejpam-6755	100	19	supermagic	supermagic	NOUN
ejpam-6755	100	20	.	.	PUNCT
ejpam-6755	101	1	theorem	theorem	NOUN
ejpam-6755	101	2	4	4	NUM
ejpam-6755	101	3	.	.	PUNCT
ejpam-6755	102	1	let	let	VERB
ejpam-6755	102	2	n	n	PRON
ejpam-6755	102	3	≥	≥	NUM
ejpam-6755	102	4	5	5	NUM
ejpam-6755	102	5	be	be	AUX
ejpam-6755	102	6	a	a	DET
ejpam-6755	102	7	positive	positive	ADJ
ejpam-6755	102	8	integer	integer	NOUN
ejpam-6755	102	9	,	,	PUNCT
ejpam-6755	102	10	m	m	VERB
ejpam-6755	102	11	≥	≥	NUM
ejpam-6755	102	12	3	3	NUM
ejpam-6755	102	13	be	be	AUX
ejpam-6755	102	14	a	a	DET
ejpam-6755	102	15	positive	positive	ADJ
ejpam-6755	102	16	odd	odd	ADJ
ejpam-6755	102	17	integer	integer	NOUN
ejpam-6755	102	18	and	and	CCONJ
ejpam-6755	102	19	h	h	NOUN
ejpam-6755	102	20	∈	∈	PROPN
ejpam-6755	103	1	[	[	X
ejpam-6755	103	2	3	3	NUM
ejpam-6755	103	3	,	,	PUNCT
ejpam-6755	103	4	n	n	CCONJ
ejpam-6755	103	5	]	]	PUNCT
ejpam-6755	103	6	.	.	PUNCT
ejpam-6755	104	1	then	then	ADV
ejpam-6755	104	2	,	,	PUNCT
ejpam-6755	104	3	the	the	DET
ejpam-6755	104	4	disjoint	disjoint	PROPN
ejpam-6755	104	5	union	union	NOUN
ejpam-6755	104	6	of	of	ADP
ejpam-6755	104	7	paths	path	NOUN
ejpam-6755	104	8	mpn	mpn	NOUN
ejpam-6755	104	9	is	be	AUX
ejpam-6755	104	10	kph	kph	PROPN
ejpam-6755	104	11	-	-	PUNCT
ejpam-6755	104	12	supermagic	supermagic	NOUN
ejpam-6755	104	13	for	for	ADP
ejpam-6755	104	14	k	k	PROPN
ejpam-6755	104	15	∈	∈	PROPN
ejpam-6755	105	1	[	[	X
ejpam-6755	105	2	1,m⌊nh⌋	1,m⌊nh⌋	NUM
ejpam-6755	105	3	−	−	NUM
ejpam-6755	105	4	1	1	NUM
ejpam-6755	105	5	]	]	PUNCT
ejpam-6755	105	6	.	.	PUNCT
ejpam-6755	106	1	proof	proof	NOUN
ejpam-6755	106	2	.	.	PUNCT
ejpam-6755	107	1	let	let	VERB
ejpam-6755	107	2	mpn	mpn	NOUN
ejpam-6755	107	3	be	be	AUX
ejpam-6755	107	4	a	a	DET
ejpam-6755	107	5	graph	graph	NOUN
ejpam-6755	107	6	with	with	ADP
ejpam-6755	107	7	the	the	DET
ejpam-6755	107	8	vertex	vertex	NOUN
ejpam-6755	107	9	set	set	NOUN
ejpam-6755	107	10	and	and	CCONJ
ejpam-6755	107	11	the	the	DET
ejpam-6755	107	12	edge	edge	NOUN
ejpam-6755	107	13	set	set	VERB
ejpam-6755	107	14	v	v	NOUN
ejpam-6755	107	15	(	(	PUNCT
ejpam-6755	107	16	mpn	mpn	NOUN
ejpam-6755	107	17	)	)	PUNCT
ejpam-6755	107	18	=	=	PRON
ejpam-6755	107	19	{	{	PUNCT
ejpam-6755	107	20	vi	vi	PROPN
ejpam-6755	107	21	,	,	PUNCT
ejpam-6755	108	1	j	j	PROPN
ejpam-6755	109	1	|	|	ADV
ejpam-6755	109	2	i	i	PRON
ejpam-6755	109	3	∈	∈	VERB
ejpam-6755	110	1	[	[	X
ejpam-6755	110	2	1,m	1,m	X
ejpam-6755	110	3	]	]	X
ejpam-6755	110	4	,	,	PUNCT
ejpam-6755	110	5	j	j	PROPN
ejpam-6755	110	6	∈	∈	PROPN
ejpam-6755	111	1	[	[	X
ejpam-6755	111	2	1	1	NUM
ejpam-6755	111	3	,	,	PUNCT
ejpam-6755	111	4	n	n	CCONJ
ejpam-6755	111	5	]	]	PUNCT
ejpam-6755	111	6	}	}	PUNCT
ejpam-6755	111	7	,	,	PUNCT
ejpam-6755	111	8	e(mpn	e(mpn	NOUN
ejpam-6755	111	9	)	)	PUNCT
ejpam-6755	111	10	=	=	PRON
ejpam-6755	111	11	{	{	PUNCT
ejpam-6755	111	12	vi	vi	PROPN
ejpam-6755	111	13	,	,	PUNCT
ejpam-6755	111	14	jvi	jvi	ADV
ejpam-6755	111	15	,	,	PUNCT
ejpam-6755	111	16	j+1	j+1	PUNCT
ejpam-6755	112	1	|	|	NOUN
ejpam-6755	112	2	i	i	PRON
ejpam-6755	112	3	∈	∈	VERB
ejpam-6755	113	1	[	[	X
ejpam-6755	113	2	1,m	1,m	X
ejpam-6755	113	3	]	]	X
ejpam-6755	113	4	,	,	PUNCT
ejpam-6755	113	5	j	j	PROPN
ejpam-6755	113	6	∈	∈	PROPN
ejpam-6755	113	7	[	[	X
ejpam-6755	113	8	1	1	NUM
ejpam-6755	113	9	,	,	PUNCT
ejpam-6755	113	10	n−	n−	NOUN
ejpam-6755	113	11	1	1	NUM
ejpam-6755	113	12	]	]	PUNCT
ejpam-6755	113	13	}	}	PUNCT
ejpam-6755	113	14	.	.	PUNCT
ejpam-6755	114	1	let	let	VERB
ejpam-6755	114	2	p	p	NOUN
ejpam-6755	114	3	(	(	PUNCT
ejpam-6755	114	4	i	i	PROPN
ejpam-6755	114	5	,	,	PUNCT
ejpam-6755	114	6	l	l	NOUN
ejpam-6755	114	7	)	)	PUNCT
ejpam-6755	114	8	h	h	NOUN
ejpam-6755	114	9	,	,	PUNCT
ejpam-6755	114	10	i	i	PRON
ejpam-6755	114	11	∈	∈	VERB
ejpam-6755	115	1	[	[	X
ejpam-6755	115	2	1,m	1,m	X
ejpam-6755	115	3	]	]	X
ejpam-6755	115	4	,	,	PUNCT
ejpam-6755	115	5	l	l	PROPN
ejpam-6755	115	6	∈	∈	PROPN
ejpam-6755	116	1	[	[	X
ejpam-6755	116	2	1	1	NUM
ejpam-6755	116	3	,	,	PUNCT
ejpam-6755	116	4	n−	n−	NOUN
ejpam-6755	116	5	h+	h+	X
ejpam-6755	116	6	1	1	X
ejpam-6755	116	7	]	]	PUNCT
ejpam-6755	116	8	be	be	AUX
ejpam-6755	116	9	the	the	DET
ejpam-6755	116	10	subgraph	subgraph	NOUN
ejpam-6755	116	11	of	of	ADP
ejpam-6755	116	12	mpn	mpn	NOUN
ejpam-6755	116	13	such	such	ADJ
ejpam-6755	116	14	that	that	DET
ejpam-6755	116	15	v	v	NOUN
ejpam-6755	116	16	(	(	PUNCT
ejpam-6755	116	17	p	p	X
ejpam-6755	116	18	(	(	PUNCT
ejpam-6755	116	19	i	i	PROPN
ejpam-6755	116	20	,	,	PUNCT
ejpam-6755	116	21	l	l	NOUN
ejpam-6755	116	22	)	)	PUNCT
ejpam-6755	116	23	h	h	NOUN
ejpam-6755	116	24	)	)	PUNCT
ejpam-6755	117	1	=	=	PRON
ejpam-6755	117	2	{	{	PUNCT
ejpam-6755	117	3	vi	vi	PROPN
ejpam-6755	117	4	,	,	PUNCT
ejpam-6755	117	5	j	j	PROPN
ejpam-6755	118	1	|	|	ADV
ejpam-6755	118	2	j	j	PROPN
ejpam-6755	118	3	∈	∈	PROPN
ejpam-6755	119	1	[	[	X
ejpam-6755	119	2	l	l	NOUN
ejpam-6755	119	3	,	,	PUNCT
ejpam-6755	119	4	l	l	PROPN
ejpam-6755	120	1	+	+	CCONJ
ejpam-6755	120	2	h−	h−	PROPN
ejpam-6755	120	3	1	1	NUM
ejpam-6755	120	4	]	]	PUNCT
ejpam-6755	120	5	}	}	PUNCT
ejpam-6755	120	6	,	,	PUNCT
ejpam-6755	120	7	e(p	e(p	PROPN
ejpam-6755	120	8	(	(	PUNCT
ejpam-6755	120	9	i	i	PROPN
ejpam-6755	120	10	,	,	PUNCT
ejpam-6755	120	11	l	l	NOUN
ejpam-6755	120	12	)	)	PUNCT
ejpam-6755	120	13	h	h	NOUN
ejpam-6755	120	14	)	)	PUNCT
ejpam-6755	120	15	=	=	PRON
ejpam-6755	120	16	{	{	PUNCT
ejpam-6755	120	17	vi	vi	PROPN
ejpam-6755	120	18	,	,	PUNCT
ejpam-6755	120	19	jvi	jvi	ADV
ejpam-6755	120	20	,	,	PUNCT
ejpam-6755	120	21	j+1	j+1	PUNCT
ejpam-6755	120	22	|	|	NOUN
ejpam-6755	120	23	j	j	PROPN
ejpam-6755	120	24	∈	∈	PROPN
ejpam-6755	121	1	[	[	X
ejpam-6755	121	2	l	l	NOUN
ejpam-6755	121	3	,	,	PUNCT
ejpam-6755	121	4	l	l	PROPN
ejpam-6755	122	1	+	+	CCONJ
ejpam-6755	122	2	h−	h−	PROPN
ejpam-6755	122	3	2	2	NUM
ejpam-6755	122	4	]	]	PUNCT
ejpam-6755	122	5	}	}	PUNCT
ejpam-6755	122	6	.	.	PUNCT
ejpam-6755	123	1	according	accord	VERB
ejpam-6755	123	2	to	to	ADP
ejpam-6755	123	3	theorem	theorem	NOUN
ejpam-6755	123	4	2	2	NUM
ejpam-6755	123	5	,	,	PUNCT
ejpam-6755	123	6	there	there	PRON
ejpam-6755	123	7	exists	exist	VERB
ejpam-6755	123	8	a	a	DET
ejpam-6755	123	9	ph	ph	ADJ
ejpam-6755	123	10	-	-	ADJ
ejpam-6755	123	11	supermagic	supermagic	ADJ
ejpam-6755	123	12	labeling	labeling	NOUN
ejpam-6755	123	13	g	g	NOUN
ejpam-6755	123	14	of	of	ADP
ejpam-6755	123	15	pn	pn	PROPN
ejpam-6755	123	16	which	which	PRON
ejpam-6755	123	17	induces	induce	VERB
ejpam-6755	123	18	the	the	DET
ejpam-6755	123	19	magic	magic	ADJ
ejpam-6755	123	20	constant	constant	ADJ
ejpam-6755	123	21	c.	c.	NOUN
ejpam-6755	123	22	for	for	ADP
ejpam-6755	123	23	m	m	PRON
ejpam-6755	123	24	odd	odd	ADJ
ejpam-6755	123	25	,	,	PUNCT
ejpam-6755	123	26	define	define	VERB
ejpam-6755	123	27	a	a	DET
ejpam-6755	123	28	total	total	ADJ
ejpam-6755	123	29	labeling	labeling	NOUN
ejpam-6755	123	30	f	f	PROPN
ejpam-6755	123	31	of	of	ADP
ejpam-6755	123	32	mpn	mpn	PROPN
ejpam-6755	123	33	in	in	ADP
ejpam-6755	123	34	the	the	DET
ejpam-6755	123	35	following	following	ADJ
ejpam-6755	123	36	way	way	NOUN
ejpam-6755	123	37	f(vi	f(vi	PROPN
ejpam-6755	123	38	,	,	PUNCT
ejpam-6755	123	39	j	j	NOUN
ejpam-6755	123	40	)	)	PUNCT
ejpam-6755	123	41	=	=	PUNCT
ejpam-6755	124	1			VERB
ejpam-6755	124	2	m	m	VERB
ejpam-6755	124	3	·	·	PUNCT
ejpam-6755	124	4	(	(	PUNCT
ejpam-6755	124	5	g(vi	g(vi	X
ejpam-6755	124	6	,	,	PUNCT
ejpam-6755	124	7	j)−	j)−	PROPN
ejpam-6755	124	8	1	1	NUM
ejpam-6755	124	9	)	)	PUNCT
ejpam-6755	124	10	+	+	CCONJ
ejpam-6755	124	11	i+	i+	ADV
ejpam-6755	124	12	m+1	m+1	NUM
ejpam-6755	124	13	2	2	NUM
ejpam-6755	124	14	,	,	PUNCT
ejpam-6755	124	15	for	for	ADP
ejpam-6755	124	16	j	j	PROPN
ejpam-6755	124	17	≡	≡	PROPN
ejpam-6755	124	18	1	1	NUM
ejpam-6755	124	19	(	(	PUNCT
ejpam-6755	124	20	mod	mod	PROPN
ejpam-6755	124	21	h	h	PROPN
ejpam-6755	124	22	)	)	PUNCT
ejpam-6755	124	23	,	,	PUNCT
ejpam-6755	124	24	i	i	PRON
ejpam-6755	124	25	∈	∈	VERB
ejpam-6755	125	1	[	[	X
ejpam-6755	125	2	1	1	NUM
ejpam-6755	125	3	,	,	PUNCT
ejpam-6755	125	4	m−1	m−1	PROPN
ejpam-6755	125	5	2	2	NUM
ejpam-6755	125	6	]	]	PUNCT
ejpam-6755	125	7	,	,	PUNCT
ejpam-6755	125	8	m	m	VERB
ejpam-6755	125	9	·	·	PUNCT
ejpam-6755	125	10	(	(	PUNCT
ejpam-6755	125	11	g(vi	g(vi	X
ejpam-6755	125	12	,	,	PUNCT
ejpam-6755	125	13	j)−	j)−	PROPN
ejpam-6755	125	14	1	1	NUM
ejpam-6755	125	15	)	)	PUNCT
ejpam-6755	125	16	+	+	CCONJ
ejpam-6755	125	17	i−	i−	PROPN
ejpam-6755	125	18	m−1	m−1	PROPN
ejpam-6755	125	19	2	2	NUM
ejpam-6755	125	20	,	,	PUNCT
ejpam-6755	125	21	for	for	ADP
ejpam-6755	125	22	j	j	PROPN
ejpam-6755	125	23	≡	≡	PROPN
ejpam-6755	125	24	1	1	NUM
ejpam-6755	125	25	(	(	PUNCT
ejpam-6755	125	26	mod	mod	PROPN
ejpam-6755	125	27	h	h	PROPN
ejpam-6755	125	28	)	)	PUNCT
ejpam-6755	125	29	,	,	PUNCT
ejpam-6755	125	30	i	i	PRON
ejpam-6755	125	31	∈	∈	VERB
ejpam-6755	126	1	[	[	X
ejpam-6755	126	2	m+1	m+1	NUM
ejpam-6755	126	3	2	2	NUM
ejpam-6755	126	4	,	,	PUNCT
ejpam-6755	126	5	m	m	PROPN
ejpam-6755	126	6	]	]	X
ejpam-6755	126	7	,	,	PUNCT
ejpam-6755	126	8	m	m	VERB
ejpam-6755	126	9	·	·	PUNCT
ejpam-6755	126	10	(	(	PUNCT
ejpam-6755	126	11	g(vi	g(vi	X
ejpam-6755	126	12	,	,	PUNCT
ejpam-6755	126	13	j)−	j)−	PROPN
ejpam-6755	126	14	1	1	NUM
ejpam-6755	126	15	)	)	PUNCT
ejpam-6755	126	16	+	+	CCONJ
ejpam-6755	126	17	i	i	PROPN
ejpam-6755	126	18	,	,	PUNCT
ejpam-6755	126	19	for	for	ADP
ejpam-6755	126	20	j	j	PROPN
ejpam-6755	126	21	̸≡	̸≡	PROPN
ejpam-6755	126	22	1	1	NUM
ejpam-6755	126	23	(	(	PUNCT
ejpam-6755	126	24	mod	mod	PROPN
ejpam-6755	126	25	h	h	PROPN
ejpam-6755	126	26	)	)	PUNCT
ejpam-6755	126	27	,	,	PUNCT
ejpam-6755	126	28	i	i	PRON
ejpam-6755	126	29	∈	∈	VERB
ejpam-6755	127	1	[	[	X
ejpam-6755	127	2	1,m	1,m	X
ejpam-6755	127	3	]	]	X
ejpam-6755	127	4	,	,	PUNCT
ejpam-6755	127	5	f(vi	f(vi	NOUN
ejpam-6755	127	6	,	,	PUNCT
ejpam-6755	127	7	jvi	jvi	ADV
ejpam-6755	127	8	,	,	PUNCT
ejpam-6755	127	9	j+1	j+1	NOUN
ejpam-6755	127	10	)	)	PUNCT
ejpam-6755	127	11	=	=	PUNCT
ejpam-6755	128	1			VERB
ejpam-6755	128	2	m	m	VERB
ejpam-6755	128	3	·	·	PUNCT
ejpam-6755	128	4	g(vi	g(vi	NOUN
ejpam-6755	128	5	,	,	PUNCT
ejpam-6755	128	6	jvi	jvi	ADV
ejpam-6755	128	7	,	,	PUNCT
ejpam-6755	128	8	j+1)−	j+1)−	PROPN
ejpam-6755	128	9	2i+	2i+	NUM
ejpam-6755	128	10	1	1	NUM
ejpam-6755	128	11	,	,	PUNCT
ejpam-6755	128	12	for	for	ADP
ejpam-6755	128	13	j	j	PROPN
ejpam-6755	128	14	≡	≡	PROPN
ejpam-6755	128	15	0	0	PUNCT
ejpam-6755	129	1	(	(	PUNCT
ejpam-6755	129	2	mod	mod	PROPN
ejpam-6755	129	3	h−	h−	PROPN
ejpam-6755	129	4	1	1	NUM
ejpam-6755	129	5	)	)	PUNCT
ejpam-6755	129	6	,	,	PUNCT
ejpam-6755	129	7	i	i	PRON
ejpam-6755	129	8	∈	∈	VERB
ejpam-6755	130	1	[	[	X
ejpam-6755	130	2	1	1	NUM
ejpam-6755	130	3	,	,	PUNCT
ejpam-6755	130	4	m−1	m−1	PROPN
ejpam-6755	130	5	2	2	NUM
ejpam-6755	130	6	]	]	PUNCT
ejpam-6755	130	7	,	,	PUNCT
ejpam-6755	130	8	m	m	VERB
ejpam-6755	130	9	·	·	PUNCT
ejpam-6755	130	10	(	(	PUNCT
ejpam-6755	130	11	g(vi	g(vi	NOUN
ejpam-6755	130	12	,	,	PUNCT
ejpam-6755	130	13	jvi	jvi	ADV
ejpam-6755	130	14	,	,	PUNCT
ejpam-6755	130	15	j+1	j+1	NUM
ejpam-6755	130	16	)	)	PUNCT
ejpam-6755	130	17	+	+	PROPN
ejpam-6755	131	1	1)−	1)−	PROPN
ejpam-6755	131	2	2i+	2i+	NUM
ejpam-6755	131	3	1	1	NUM
ejpam-6755	131	4	,	,	PUNCT
ejpam-6755	131	5	for	for	ADP
ejpam-6755	131	6	j	j	PROPN
ejpam-6755	131	7	≡	≡	PROPN
ejpam-6755	131	8	0	0	PUNCT
ejpam-6755	132	1	(	(	PUNCT
ejpam-6755	132	2	mod	mod	PROPN
ejpam-6755	132	3	h−	h−	PROPN
ejpam-6755	132	4	1	1	NUM
ejpam-6755	132	5	)	)	PUNCT
ejpam-6755	132	6	,	,	PUNCT
ejpam-6755	132	7	i	i	PRON
ejpam-6755	132	8	∈	∈	VERB
ejpam-6755	133	1	[	[	X
ejpam-6755	133	2	m+1	m+1	NUM
ejpam-6755	133	3	2	2	NUM
ejpam-6755	133	4	,	,	PUNCT
ejpam-6755	133	5	m	m	PROPN
ejpam-6755	133	6	]	]	X
ejpam-6755	133	7	,	,	PUNCT
ejpam-6755	133	8	m	m	VERB
ejpam-6755	133	9	·	·	PUNCT
ejpam-6755	133	10	g(vi	g(vi	NOUN
ejpam-6755	133	11	,	,	PUNCT
ejpam-6755	133	12	jvi	jvi	ADV
ejpam-6755	133	13	,	,	PUNCT
ejpam-6755	133	14	j+1)−	j+1)−	PROPN
ejpam-6755	133	15	i+	i+	PROPN
ejpam-6755	133	16	1	1	NUM
ejpam-6755	133	17	,	,	PUNCT
ejpam-6755	133	18	for	for	ADP
ejpam-6755	133	19	j	j	PROPN
ejpam-6755	133	20	̸≡	̸≡	PROPN
ejpam-6755	133	21	0	0	PROPN
ejpam-6755	134	1	(	(	PUNCT
ejpam-6755	134	2	mod	mod	PROPN
ejpam-6755	134	3	h−	h−	PROPN
ejpam-6755	134	4	1	1	NUM
ejpam-6755	134	5	)	)	PUNCT
ejpam-6755	134	6	,	,	PUNCT
ejpam-6755	134	7	i	i	PRON
ejpam-6755	134	8	∈	∈	VERB
ejpam-6755	135	1	[	[	X
ejpam-6755	135	2	1,m	1,m	X
ejpam-6755	135	3	]	]	X
ejpam-6755	135	4	.	.	PUNCT
ejpam-6755	136	1	it	it	PRON
ejpam-6755	136	2	is	be	AUX
ejpam-6755	136	3	easy	easy	ADJ
ejpam-6755	136	4	to	to	PART
ejpam-6755	136	5	see	see	VERB
ejpam-6755	136	6	that	that	SCONJ
ejpam-6755	136	7	f	f	PROPN
ejpam-6755	136	8	is	be	AUX
ejpam-6755	136	9	a	a	DET
ejpam-6755	136	10	bijection	bijection	NOUN
ejpam-6755	136	11	and	and	CCONJ
ejpam-6755	136	12	the	the	DET
ejpam-6755	136	13	vertices	vertex	NOUN
ejpam-6755	136	14	are	be	AUX
ejpam-6755	136	15	labeled	label	VERB
ejpam-6755	136	16	with	with	ADP
ejpam-6755	136	17	numbers	number	NOUN
ejpam-6755	136	18	1	1	NUM
ejpam-6755	136	19	,	,	PUNCT
ejpam-6755	136	20	2	2	NUM
ejpam-6755	136	21	,	,	PUNCT
ejpam-6755	136	22	.	.	PUNCT
ejpam-6755	136	23	.	.	PUNCT
ejpam-6755	136	24	.	.	PUNCT
ejpam-6755	137	1	,	,	PUNCT
ejpam-6755	137	2	mn	mn	PROPN
ejpam-6755	137	3	.	.	PUNCT
ejpam-6755	138	1	moreover	moreover	ADV
ejpam-6755	138	2	,	,	PUNCT
ejpam-6755	138	3	for	for	ADP
ejpam-6755	138	4	the	the	DET
ejpam-6755	138	5	weight	weight	NOUN
ejpam-6755	138	6	of	of	ADP
ejpam-6755	138	7	a	a	DET
ejpam-6755	138	8	subgraph	subgraph	NOUN
ejpam-6755	138	9	p	p	X
ejpam-6755	138	10	(	(	PUNCT
ejpam-6755	138	11	i	i	PROPN
ejpam-6755	138	12	,	,	PUNCT
ejpam-6755	138	13	l	l	NOUN
ejpam-6755	138	14	)	)	PUNCT
ejpam-6755	138	15	h	h	NOUN
ejpam-6755	138	16	,	,	PUNCT
ejpam-6755	138	17	i	i	PRON
ejpam-6755	138	18	∈	∈	VERB
ejpam-6755	139	1	[	[	X
ejpam-6755	139	2	1,m	1,m	X
ejpam-6755	139	3	]	]	X
ejpam-6755	139	4	,	,	PUNCT
ejpam-6755	139	5	l	l	PROPN
ejpam-6755	139	6	∈	∈	PROPN
ejpam-6755	140	1	[	[	X
ejpam-6755	140	2	1	1	NUM
ejpam-6755	140	3	,	,	PUNCT
ejpam-6755	140	4	n−h+1	n−h+1	PROPN
ejpam-6755	140	5	]	]	PUNCT
ejpam-6755	140	6	under	under	ADP
ejpam-6755	140	7	the	the	DET
ejpam-6755	140	8	labeling	labeling	NOUN
ejpam-6755	140	9	f	f	NOUN
ejpam-6755	140	10	we	we	PRON
ejpam-6755	140	11	have	have	VERB
ejpam-6755	140	12	w(p	w(p	NOUN
ejpam-6755	140	13	(	(	PUNCT
ejpam-6755	140	14	i	i	PROPN
ejpam-6755	140	15	,	,	PUNCT
ejpam-6755	140	16	l	l	NOUN
ejpam-6755	140	17	)	)	PUNCT
ejpam-6755	140	18	h	h	NOUN
ejpam-6755	140	19	)	)	PUNCT
ejpam-6755	141	1	=	=	PUNCT
ejpam-6755	142	1	mc−	mc−	NUM
ejpam-6755	142	2	h(m−	h(m−	PROPN
ejpam-6755	142	3	1	1	NUM
ejpam-6755	142	4	)	)	PUNCT
ejpam-6755	142	5	+	+	CCONJ
ejpam-6755	143	1	m−1	m−1	PROPN
ejpam-6755	143	2	2	2	NUM
ejpam-6755	143	3	.	.	PUNCT
ejpam-6755	144	1	therefore	therefore	ADV
ejpam-6755	144	2	,	,	PUNCT
ejpam-6755	144	3	the	the	DET
ejpam-6755	144	4	weight	weight	NOUN
ejpam-6755	144	5	of	of	ADP
ejpam-6755	144	6	every	every	DET
ejpam-6755	144	7	subgraph	subgraph	NOUN
ejpam-6755	144	8	of	of	ADP
ejpam-6755	144	9	mpn	mpn	NOUN
ejpam-6755	144	10	which	which	PRON
ejpam-6755	144	11	is	be	AUX
ejpam-6755	144	12	isomorphic	isomorphic	ADJ
ejpam-6755	144	13	to	to	ADP
ejpam-6755	144	14	ph	ph	NOUN
ejpam-6755	144	15	is	be	AUX
ejpam-6755	144	16	constant	constant	ADJ
ejpam-6755	144	17	.	.	PUNCT
ejpam-6755	145	1	this	this	PRON
ejpam-6755	145	2	immediately	immediately	ADV
ejpam-6755	145	3	implies	imply	VERB
ejpam-6755	145	4	that	that	SCONJ
ejpam-6755	145	5	mpn	mpn	PROPN
ejpam-6755	145	6	is	be	AUX
ejpam-6755	145	7	kph	kph	PROPN
ejpam-6755	145	8	-	-	PUNCT
ejpam-6755	145	9	supermagic	supermagic	NOUN
ejpam-6755	145	10	for	for	ADP
ejpam-6755	145	11	k	k	PROPN
ejpam-6755	145	12	∈	∈	PROPN
ejpam-6755	146	1	[	[	X
ejpam-6755	146	2	1,m⌊nh⌋	1,m⌊nh⌋	NUM
ejpam-6755	146	3	−	−	NOUN
ejpam-6755	146	4	1	1	NUM
ejpam-6755	146	5	]	]	PUNCT
ejpam-6755	146	6	.	.	PUNCT
ejpam-6755	147	1	□	□	PUNCT
ejpam-6755	147	2	remark	remark	NOUN
ejpam-6755	147	3	1	1	NUM
ejpam-6755	147	4	.	.	PUNCT
ejpam-6755	148	1	it	it	PRON
ejpam-6755	148	2	is	be	AUX
ejpam-6755	148	3	also	also	ADV
ejpam-6755	148	4	possible	possible	ADJ
ejpam-6755	148	5	to	to	PART
ejpam-6755	148	6	show	show	VERB
ejpam-6755	148	7	that	that	SCONJ
ejpam-6755	148	8	mpn	mpn	PROPN
ejpam-6755	148	9	is	be	AUX
ejpam-6755	148	10	kph	kph	PROPN
ejpam-6755	148	11	-	-	PUNCT
ejpam-6755	148	12	supermagic	supermagic	NOUN
ejpam-6755	148	13	for	for	ADP
ejpam-6755	148	14	k	k	X
ejpam-6755	148	15	=	=	PUNCT
ejpam-6755	148	16	m⌊nh⌋	m⌊nh⌋	INTJ
ejpam-6755	148	17	whenever	whenever	SCONJ
ejpam-6755	148	18	h	h	NOUN
ejpam-6755	148	19	does	do	AUX
ejpam-6755	148	20	not	not	PART
ejpam-6755	148	21	divide	divide	VERB
ejpam-6755	148	22	n	n	ADP
ejpam-6755	148	23	using	use	VERB
ejpam-6755	148	24	the	the	DET
ejpam-6755	148	25	same	same	ADJ
ejpam-6755	148	26	labeling	labeling	NOUN
ejpam-6755	148	27	as	as	ADP
ejpam-6755	148	28	in	in	ADP
ejpam-6755	148	29	theorem	theorem	NOUN
ejpam-6755	148	30	2	2	NUM
ejpam-6755	148	31	.	.	PUNCT
ejpam-6755	148	32	figure	figure	NOUN
ejpam-6755	148	33	1	1	NUM
ejpam-6755	148	34	illustrates	illustrate	VERB
ejpam-6755	148	35	the	the	DET
ejpam-6755	148	36	p3	p3	ADJ
ejpam-6755	148	37	-	-	ADJ
ejpam-6755	148	38	supermagic	supermagic	ADJ
ejpam-6755	148	39	labeling	labeling	NOUN
ejpam-6755	148	40	of	of	ADP
ejpam-6755	148	41	5p7	5p7	NUM
ejpam-6755	148	42	obtained	obtain	VERB
ejpam-6755	148	43	from	from	ADP
ejpam-6755	148	44	the	the	DET
ejpam-6755	148	45	p3	p3	NOUN
ejpam-6755	148	46	-	-	ADJ
ejpam-6755	148	47	supermagic	supermagic	ADJ
ejpam-6755	148	48	labeling	labeling	NOUN
ejpam-6755	148	49	of	of	ADP
ejpam-6755	148	50	p7	p7	NOUN
ejpam-6755	148	51	by	by	ADP
ejpam-6755	148	52	the	the	DET
ejpam-6755	148	53	construction	construction	NOUN
ejpam-6755	148	54	described	describe	VERB
ejpam-6755	148	55	in	in	ADP
ejpam-6755	148	56	the	the	DET
ejpam-6755	148	57	proof	proof	NOUN
ejpam-6755	148	58	of	of	ADP
ejpam-6755	148	59	theorem	theorem	NOUN
ejpam-6755	148	60	2	2	NUM
ejpam-6755	148	61	.	.	PUNCT
ejpam-6755	148	62	t.	t.	PROPN
ejpam-6755	148	63	k.	k.	PROPN
ejpam-6755	148	64	maryati	maryati	PROPN
ejpam-6755	148	65	et	et	PROPN
ejpam-6755	148	66	al	al	PROPN
ejpam-6755	148	67	.	.	PUNCT
ejpam-6755	148	68	/	/	SYM
ejpam-6755	148	69	eur	eur	PROPN
ejpam-6755	148	70	.	.	PUNCT
ejpam-6755	149	1	j.	j.	PROPN
ejpam-6755	149	2	pure	pure	PROPN
ejpam-6755	149	3	appl	appl	PROPN
ejpam-6755	149	4	.	.	PROPN
ejpam-6755	149	5	math	math	PROPN
ejpam-6755	149	6	,	,	PUNCT
ejpam-6755	149	7	18	18	NUM
ejpam-6755	149	8	(	(	PUNCT
ejpam-6755	149	9	4	4	NUM
ejpam-6755	149	10	)	)	PUNCT
ejpam-6755	149	11	(	(	PUNCT
ejpam-6755	149	12	2025	2025	NUM
ejpam-6755	149	13	)	)	PUNCT
ejpam-6755	149	14	,	,	PUNCT
ejpam-6755	149	15	6755	6755	NUM
ejpam-6755	149	16	5	5	NUM
ejpam-6755	149	17	of	of	ADP
ejpam-6755	149	18	13	13	NUM
ejpam-6755	149	19	figure	figure	NOUN
ejpam-6755	149	20	1	1	NUM
ejpam-6755	149	21	:	:	PUNCT
ejpam-6755	149	22	a	a	DET
ejpam-6755	149	23	p3	p3	ADJ
ejpam-6755	149	24	-	-	ADJ
ejpam-6755	149	25	supermagic	supermagic	ADJ
ejpam-6755	149	26	labeling	labeling	NOUN
ejpam-6755	149	27	of	of	ADP
ejpam-6755	149	28	p7	p7	NOUN
ejpam-6755	149	29	and	and	CCONJ
ejpam-6755	149	30	the	the	DET
ejpam-6755	149	31	corresponding	correspond	VERB
ejpam-6755	149	32	p3	p3	PROPN
ejpam-6755	149	33	-	-	ADJ
ejpam-6755	149	34	supermagic	supermagic	ADJ
ejpam-6755	149	35	labeling	labeling	NOUN
ejpam-6755	149	36	of	of	ADP
ejpam-6755	149	37	5p7	5p7	NUM
ejpam-6755	149	38	.	.	PUNCT
ejpam-6755	150	1	4	4	X
ejpam-6755	150	2	.	.	X
ejpam-6755	151	1	the	the	DET
ejpam-6755	151	2	(	(	PUNCT
ejpam-6755	151	3	h1	h1	PROPN
ejpam-6755	151	4	,	,	PUNCT
ejpam-6755	151	5	h2)-magic	h2)-magic	ADJ
ejpam-6755	151	6	graphs	graph	NOUN
ejpam-6755	151	7	in	in	ADP
ejpam-6755	151	8	this	this	DET
ejpam-6755	151	9	section	section	NOUN
ejpam-6755	151	10	,	,	PUNCT
ejpam-6755	151	11	we	we	PRON
ejpam-6755	151	12	study	study	VERB
ejpam-6755	151	13	several	several	ADJ
ejpam-6755	151	14	graph	graph	NOUN
ejpam-6755	151	15	operations	operation	NOUN
ejpam-6755	151	16	and	and	CCONJ
ejpam-6755	151	17	related	related	ADJ
ejpam-6755	151	18	results	result	NOUN
ejpam-6755	151	19	on	on	ADP
ejpam-6755	151	20	the	the	DET
ejpam-6755	151	21	magicness	magicness	NOUN
ejpam-6755	151	22	of	of	ADP
ejpam-6755	151	23	the	the	DET
ejpam-6755	151	24	obtained	obtain	VERB
ejpam-6755	151	25	graphs	graph	NOUN
ejpam-6755	151	26	.	.	PUNCT
ejpam-6755	152	1	the	the	DET
ejpam-6755	152	2	first	first	ADJ
ejpam-6755	152	3	operation	operation	NOUN
ejpam-6755	152	4	is	be	AUX
ejpam-6755	152	5	a	a	DET
ejpam-6755	152	6	generalized	generalized	ADJ
ejpam-6755	152	7	total	total	ADJ
ejpam-6755	152	8	composition	composition	NOUN
ejpam-6755	152	9	graph	graph	NOUN
ejpam-6755	152	10	.	.	PUNCT
ejpam-6755	153	1	let	let	VERB
ejpam-6755	153	2	f	f	PROPN
ejpam-6755	153	3	and	and	CCONJ
ejpam-6755	153	4	g	g	PROPN
ejpam-6755	153	5	be	be	AUX
ejpam-6755	153	6	two	two	NUM
ejpam-6755	153	7	graphs	graph	NOUN
ejpam-6755	153	8	.	.	PUNCT
ejpam-6755	154	1	let	let	VERB
ejpam-6755	154	2	hi	hi	INTJ
ejpam-6755	154	3	,	,	PUNCT
ejpam-6755	154	4	i	i	PRON
ejpam-6755	154	5	∈	∈	VERB
ejpam-6755	155	1	[	[	X
ejpam-6755	155	2	1	1	NUM
ejpam-6755	155	3	,	,	PUNCT
ejpam-6755	155	4	n	n	CCONJ
ejpam-6755	155	5	]	]	PUNCT
ejpam-6755	155	6	,	,	PUNCT
ejpam-6755	155	7	be	be	AUX
ejpam-6755	155	8	a	a	DET
ejpam-6755	155	9	graph	graph	NOUN
ejpam-6755	155	10	which	which	PRON
ejpam-6755	155	11	contains	contain	VERB
ejpam-6755	155	12	2f	2f	NUM
ejpam-6755	155	13	as	as	ADP
ejpam-6755	155	14	a	a	DET
ejpam-6755	155	15	subgraph	subgraph	NOUN
ejpam-6755	155	16	.	.	PUNCT
ejpam-6755	156	1	let	let	VERB
ejpam-6755	156	2	h	h	NOUN
ejpam-6755	156	3	=	=	PUNCT
ejpam-6755	156	4	{	{	PUNCT
ejpam-6755	156	5	h1	h1	PROPN
ejpam-6755	156	6	,	,	PUNCT
ejpam-6755	156	7	h2	h2	PROPN
ejpam-6755	156	8	,	,	PUNCT
ejpam-6755	156	9	.	.	PUNCT
ejpam-6755	156	10	.	.	PUNCT
ejpam-6755	157	1	.	.	PUNCT
ejpam-6755	158	1	,	,	PUNCT
ejpam-6755	158	2	hn	hn	PROPN
ejpam-6755	158	3	}	}	PUNCT
ejpam-6755	158	4	.	.	PUNCT
ejpam-6755	159	1	a	a	DET
ejpam-6755	159	2	generalized	generalized	ADJ
ejpam-6755	159	3	total	total	ADJ
ejpam-6755	159	4	composition	composition	NOUN
ejpam-6755	159	5	g[f	g[f	NOUN
ejpam-6755	159	6	;	;	PUNCT
ejpam-6755	159	7	h	h	X
ejpam-6755	159	8	]	]	X
ejpam-6755	159	9	is	be	AUX
ejpam-6755	159	10	a	a	DET
ejpam-6755	159	11	graph	graph	NOUN
ejpam-6755	159	12	obtained	obtain	VERB
ejpam-6755	159	13	from	from	ADP
ejpam-6755	159	14	the	the	DET
ejpam-6755	159	15	graph	graph	NOUN
ejpam-6755	159	16	g	g	NOUN
ejpam-6755	159	17	by	by	ADP
ejpam-6755	159	18	replacing	replace	VERB
ejpam-6755	159	19	each	each	DET
ejpam-6755	159	20	vertex	vertex	NOUN
ejpam-6755	159	21	v	v	ADP
ejpam-6755	159	22	∈	∈	PROPN
ejpam-6755	159	23	v	v	NOUN
ejpam-6755	159	24	(	(	PUNCT
ejpam-6755	159	25	g	g	NOUN
ejpam-6755	159	26	)	)	PUNCT
ejpam-6755	159	27	with	with	ADP
ejpam-6755	159	28	the	the	DET
ejpam-6755	159	29	graph	graph	NOUN
ejpam-6755	159	30	f	f	NOUN
ejpam-6755	159	31	,	,	PUNCT
ejpam-6755	159	32	and	and	CCONJ
ejpam-6755	159	33	every	every	DET
ejpam-6755	159	34	edge	edge	NOUN
ejpam-6755	159	35	e	e	PROPN
ejpam-6755	159	36	∈	∈	PROPN
ejpam-6755	159	37	e(g	e(g	PROPN
ejpam-6755	159	38	)	)	PUNCT
ejpam-6755	159	39	with	with	ADP
ejpam-6755	159	40	any	any	DET
ejpam-6755	159	41	graph	graph	NOUN
ejpam-6755	159	42	from	from	ADP
ejpam-6755	159	43	h.	h.	PROPN
ejpam-6755	159	44	note	note	PROPN
ejpam-6755	159	45	that	that	SCONJ
ejpam-6755	159	46	there	there	PRON
ejpam-6755	159	47	are	be	VERB
ejpam-6755	159	48	many	many	ADJ
ejpam-6755	159	49	non	non	ADJ
ejpam-6755	159	50	-	-	ADJ
ejpam-6755	159	51	isomorphic	isomorphic	ADJ
ejpam-6755	159	52	graphs	graph	NOUN
ejpam-6755	159	53	g[f	g[f	X
ejpam-6755	159	54	;	;	PUNCT
ejpam-6755	159	55	h	h	NOUN
ejpam-6755	159	56	]	]	X
ejpam-6755	159	57	.	.	PUNCT
ejpam-6755	160	1	for	for	ADP
ejpam-6755	160	2	convenience	convenience	NOUN
ejpam-6755	160	3	,	,	PUNCT
ejpam-6755	160	4	if	if	SCONJ
ejpam-6755	160	5	h	h	NOUN
ejpam-6755	160	6	=	=	PRON
ejpam-6755	160	7	{	{	PUNCT
ejpam-6755	160	8	h1	h1	PROPN
ejpam-6755	160	9	,	,	PUNCT
ejpam-6755	160	10	h2	h2	PROPN
ejpam-6755	160	11	}	}	PUNCT
ejpam-6755	160	12	,	,	PUNCT
ejpam-6755	160	13	then	then	ADV
ejpam-6755	160	14	g[f	g[f	X
ejpam-6755	160	15	;	;	PUNCT
ejpam-6755	160	16	h	h	X
ejpam-6755	160	17	]	]	X
ejpam-6755	160	18	=	=	SYM
ejpam-6755	160	19	g[f	g[f	PROPN
ejpam-6755	160	20	;	;	PUNCT
ejpam-6755	160	21	h1	h1	PROPN
ejpam-6755	160	22	,	,	PUNCT
ejpam-6755	160	23	h2	h2	PROPN
ejpam-6755	160	24	]	]	PUNCT
ejpam-6755	160	25	.	.	PUNCT
ejpam-6755	161	1	for	for	ADP
ejpam-6755	161	2	any	any	DET
ejpam-6755	161	3	graph	graph	NOUN
ejpam-6755	161	4	γ	γ	NOUN
ejpam-6755	161	5	,	,	PUNCT
ejpam-6755	161	6	let	let	VERB
ejpam-6755	161	7	tγ	tγ	NOUN
ejpam-6755	161	8	=	=	PRON
ejpam-6755	161	9	|v	|v	X
ejpam-6755	161	10	(	(	PUNCT
ejpam-6755	161	11	γ)|+	γ)|+	NUM
ejpam-6755	161	12	|e(γ)|	|e(γ)|	NOUN
ejpam-6755	161	13	.	.	PROPN
ejpam-6755	161	14	in	in	ADP
ejpam-6755	161	15	the	the	DET
ejpam-6755	161	16	next	next	ADJ
ejpam-6755	161	17	theorem	theorem	NOUN
ejpam-6755	161	18	we	we	PRON
ejpam-6755	161	19	give	give	VERB
ejpam-6755	161	20	a	a	DET
ejpam-6755	161	21	sufficient	sufficient	ADJ
ejpam-6755	161	22	condition	condition	NOUN
ejpam-6755	161	23	when	when	SCONJ
ejpam-6755	161	24	a	a	DET
ejpam-6755	161	25	generalized	generalized	ADJ
ejpam-6755	161	26	total	total	ADJ
ejpam-6755	161	27	composition	composition	NOUN
ejpam-6755	161	28	g[f	g[f	NOUN
ejpam-6755	161	29	;	;	PUNCT
ejpam-6755	161	30	h1	h1	PROPN
ejpam-6755	161	31	,	,	PUNCT
ejpam-6755	161	32	h2	h2	PROPN
ejpam-6755	161	33	]	]	PUNCT
ejpam-6755	161	34	is	be	AUX
ejpam-6755	161	35	(	(	PUNCT
ejpam-6755	161	36	h1	h1	PROPN
ejpam-6755	161	37	,	,	PUNCT
ejpam-6755	161	38	h2)-magic	h2)-magic	ADJ
ejpam-6755	162	1	.	.	PUNCT
ejpam-6755	162	2	theorem	theorem	NOUN
ejpam-6755	162	3	5	5	NUM
ejpam-6755	162	4	.	.	PUNCT
ejpam-6755	163	1	let	let	VERB
ejpam-6755	163	2	g	g	NOUN
ejpam-6755	163	3	and	and	CCONJ
ejpam-6755	163	4	f	f	PROPN
ejpam-6755	163	5	be	be	AUX
ejpam-6755	163	6	connected	connect	VERB
ejpam-6755	163	7	nontrivial	nontrivial	ADJ
ejpam-6755	163	8	graphs	graph	NOUN
ejpam-6755	163	9	.	.	PUNCT
ejpam-6755	164	1	let	let	VERB
ejpam-6755	164	2	h1	h1	VERB
ejpam-6755	164	3	and	and	CCONJ
ejpam-6755	164	4	h2	h2	PROPN
ejpam-6755	164	5	be	be	AUX
ejpam-6755	164	6	nonisomorphic	nonisomorphic	ADV
ejpam-6755	164	7	connected	connected	ADJ
ejpam-6755	164	8	graphs	graph	NOUN
ejpam-6755	164	9	which	which	PRON
ejpam-6755	164	10	have	have	VERB
ejpam-6755	164	11	size	size	NOUN
ejpam-6755	164	12	at	at	ADP
ejpam-6755	164	13	least	least	ADJ
ejpam-6755	164	14	2|e(f	2|e(f	NUM
ejpam-6755	164	15	)	)	PUNCT
ejpam-6755	165	1	|	|	ADV
ejpam-6755	165	2	+	+	CCONJ
ejpam-6755	165	3	2	2	NUM
ejpam-6755	165	4	and	and	CCONJ
ejpam-6755	165	5	contain	contain	VERB
ejpam-6755	165	6	2f	2f	NUM
ejpam-6755	165	7	as	as	ADP
ejpam-6755	165	8	a	a	DET
ejpam-6755	165	9	subgraph	subgraph	NOUN
ejpam-6755	165	10	.	.	PUNCT
ejpam-6755	166	1	let	let	VERB
ejpam-6755	166	2	si	si	INTJ
ejpam-6755	166	3	be	be	AUX
ejpam-6755	166	4	the	the	DET
ejpam-6755	166	5	number	number	NOUN
ejpam-6755	166	6	of	of	ADP
ejpam-6755	166	7	subgraphs	subgraph	NOUN
ejpam-6755	166	8	of	of	ADP
ejpam-6755	166	9	g[f	g[f	PROPN
ejpam-6755	166	10	;	;	PUNCT
ejpam-6755	166	11	h1	h1	PROPN
ejpam-6755	166	12	,	,	PUNCT
ejpam-6755	166	13	h2	h2	PROPN
ejpam-6755	166	14	]	]	PUNCT
ejpam-6755	166	15	isomorphic	isomorphic	ADJ
ejpam-6755	166	16	to	to	PART
ejpam-6755	166	17	hi	hi	VERB
ejpam-6755	166	18	,	,	PUNCT
ejpam-6755	166	19	i	i	PRON
ejpam-6755	166	20	=	=	NOUN
ejpam-6755	166	21	1	1	NUM
ejpam-6755	166	22	,	,	PUNCT
ejpam-6755	166	23	2	2	NUM
ejpam-6755	166	24	.	.	X
ejpam-6755	167	1	let	let	VERB
ejpam-6755	168	1	s1	s1	NOUN
ejpam-6755	168	2	+	+	CCONJ
ejpam-6755	168	3	s2	s2	NOUN
ejpam-6755	168	4	=	=	SYM
ejpam-6755	168	5	|e(g)|	|e(g)|	PROPN
ejpam-6755	168	6	.	.	PUNCT
ejpam-6755	168	7	let	let	VERB
ejpam-6755	168	8	|v	|v	PROPN
ejpam-6755	168	9	(	(	PUNCT
ejpam-6755	168	10	f	f	NOUN
ejpam-6755	168	11	)	)	PUNCT
ejpam-6755	169	1	|	|	ADV
ejpam-6755	169	2	+	+	SYM
ejpam-6755	169	3	|e(f	|e(f	PROPN
ejpam-6755	169	4	)	)	PUNCT
ejpam-6755	169	5	|	|	ADV
ejpam-6755	169	6	be	be	AUX
ejpam-6755	169	7	even	even	ADV
ejpam-6755	169	8	or	or	CCONJ
ejpam-6755	169	9	|v	|v	PROPN
ejpam-6755	169	10	(	(	PUNCT
ejpam-6755	169	11	g)|	g)|	PROPN
ejpam-6755	169	12	be	be	AUX
ejpam-6755	169	13	odd	odd	ADJ
ejpam-6755	169	14	.	.	PUNCT
ejpam-6755	170	1	if	if	SCONJ
ejpam-6755	170	2	both	both	PRON
ejpam-6755	170	3	th1(s1	th1(s1	PUNCT
ejpam-6755	170	4	−	−	PROPN
ejpam-6755	170	5	1	1	NUM
ejpam-6755	170	6	)	)	PUNCT
ejpam-6755	170	7	and	and	CCONJ
ejpam-6755	170	8	th2(s2	th2(s2	NOUN
ejpam-6755	170	9	−	−	NOUN
ejpam-6755	170	10	1	1	NUM
ejpam-6755	170	11	)	)	PUNCT
ejpam-6755	170	12	are	be	AUX
ejpam-6755	170	13	even	even	ADV
ejpam-6755	170	14	then	then	ADV
ejpam-6755	170	15	the	the	DET
ejpam-6755	170	16	graph	graph	NOUN
ejpam-6755	170	17	g[f	g[f	PROPN
ejpam-6755	170	18	;	;	PUNCT
ejpam-6755	170	19	h1	h1	PROPN
ejpam-6755	170	20	,	,	PUNCT
ejpam-6755	170	21	h2	h2	PROPN
ejpam-6755	170	22	]	]	PUNCT
ejpam-6755	170	23	is	be	AUX
ejpam-6755	170	24	(	(	PUNCT
ejpam-6755	170	25	h1	h1	PROPN
ejpam-6755	170	26	,	,	PUNCT
ejpam-6755	170	27	h2)-magic	h2)-magic	ADJ
ejpam-6755	170	28	.	.	PUNCT
ejpam-6755	171	1	proof	proof	NOUN
ejpam-6755	171	2	.	.	PUNCT
ejpam-6755	172	1	let	let	VERB
ejpam-6755	172	2	g	g	PRON
ejpam-6755	172	3	be	be	AUX
ejpam-6755	172	4	a	a	DET
ejpam-6755	172	5	connected	connected	ADJ
ejpam-6755	172	6	graph	graph	NOUN
ejpam-6755	172	7	of	of	ADP
ejpam-6755	172	8	order	order	NOUN
ejpam-6755	172	9	n.	n.	VERB
ejpam-6755	172	10	the	the	DET
ejpam-6755	172	11	idea	idea	NOUN
ejpam-6755	172	12	of	of	ADP
ejpam-6755	172	13	the	the	DET
ejpam-6755	172	14	proof	proof	NOUN
ejpam-6755	172	15	is	be	AUX
ejpam-6755	172	16	to	to	PART
ejpam-6755	172	17	label	label	VERB
ejpam-6755	172	18	the	the	DET
ejpam-6755	172	19	vertices	vertex	NOUN
ejpam-6755	172	20	and	and	CCONJ
ejpam-6755	172	21	edges	edge	NOUN
ejpam-6755	172	22	of	of	ADP
ejpam-6755	172	23	g[f	g[f	PROPN
ejpam-6755	172	24	;	;	PUNCT
ejpam-6755	172	25	h1	h1	PROPN
ejpam-6755	172	26	,	,	PUNCT
ejpam-6755	172	27	h2	h2	PROPN
ejpam-6755	172	28	]	]	PUNCT
ejpam-6755	172	29	such	such	ADJ
ejpam-6755	172	30	that	that	SCONJ
ejpam-6755	172	31	its	its	PRON
ejpam-6755	172	32	every	every	DET
ejpam-6755	172	33	subgraph	subgraph	NOUN
ejpam-6755	172	34	isomorphic	isomorphic	ADJ
ejpam-6755	172	35	to	to	ADP
ejpam-6755	172	36	f	f	PROPN
ejpam-6755	172	37	(	(	PUNCT
ejpam-6755	172	38	which	which	PRON
ejpam-6755	172	39	is	be	AUX
ejpam-6755	172	40	obtained	obtain	VERB
ejpam-6755	172	41	by	by	ADP
ejpam-6755	172	42	replacing	replace	VERB
ejpam-6755	172	43	a	a	DET
ejpam-6755	172	44	vertex	vertex	NOUN
ejpam-6755	172	45	of	of	ADP
ejpam-6755	172	46	g	g	NOUN
ejpam-6755	172	47	)	)	PUNCT
ejpam-6755	172	48	has	have	VERB
ejpam-6755	172	49	constant	constant	ADJ
ejpam-6755	172	50	sum	sum	NOUN
ejpam-6755	172	51	of	of	ADP
ejpam-6755	172	52	labels	label	NOUN
ejpam-6755	172	53	,	,	PUNCT
ejpam-6755	172	54	and	and	CCONJ
ejpam-6755	172	55	then	then	ADV
ejpam-6755	172	56	ensure	ensure	VERB
ejpam-6755	172	57	that	that	SCONJ
ejpam-6755	172	58	every	every	DET
ejpam-6755	172	59	pair	pair	NOUN
ejpam-6755	172	60	of	of	ADP
ejpam-6755	172	61	vertices	vertex	NOUN
ejpam-6755	172	62	or	or	CCONJ
ejpam-6755	172	63	edges	edge	NOUN
ejpam-6755	172	64	in	in	ADP
ejpam-6755	172	65	the	the	DET
ejpam-6755	172	66	same	same	ADJ
ejpam-6755	172	67	’	'	PUNCT
ejpam-6755	172	68	component	component	NOUN
ejpam-6755	172	69	’	'	PUNCT
ejpam-6755	172	70	have	have	VERB
ejpam-6755	172	71	the	the	DET
ejpam-6755	172	72	constant	constant	ADJ
ejpam-6755	172	73	sums	sum	NOUN
ejpam-6755	172	74	.	.	PUNCT
ejpam-6755	173	1	suppose	suppose	VERB
ejpam-6755	173	2	that	that	SCONJ
ejpam-6755	173	3	either	either	CCONJ
ejpam-6755	173	4	tf	tf	X
ejpam-6755	173	5	is	be	AUX
ejpam-6755	173	6	even	even	ADV
ejpam-6755	173	7	or	or	CCONJ
ejpam-6755	173	8	n	n	PRON
ejpam-6755	173	9	is	be	AUX
ejpam-6755	173	10	odd	odd	ADJ
ejpam-6755	173	11	.	.	PUNCT
ejpam-6755	174	1	then	then	ADV
ejpam-6755	174	2	nf	nf	PROPN
ejpam-6755	174	3	is	be	AUX
ejpam-6755	174	4	f	f	PROPN
ejpam-6755	174	5	-magic	-magic	PROPN
ejpam-6755	174	6	due	due	ADJ
ejpam-6755	174	7	to	to	ADP
ejpam-6755	174	8	theorem	theorem	NOUN
ejpam-6755	174	9	1	1	NUM
ejpam-6755	174	10	.	.	PUNCT
ejpam-6755	175	1	let	let	VERB
ejpam-6755	175	2	g	g	NOUN
ejpam-6755	175	3	:	:	PUNCT
ejpam-6755	175	4	v	v	NOUN
ejpam-6755	175	5	(	(	PUNCT
ejpam-6755	175	6	nf	nf	INTJ
ejpam-6755	175	7	)	)	PUNCT
ejpam-6755	175	8	∪	∪	ADP
ejpam-6755	175	9	e(nf	e(nf	PROPN
ejpam-6755	175	10	)	)	PUNCT
ejpam-6755	175	11	→	→	PUNCT
ejpam-6755	176	1	[	[	X
ejpam-6755	176	2	1	1	NUM
ejpam-6755	176	3	,	,	PUNCT
ejpam-6755	176	4	ntf	ntf	PROPN
ejpam-6755	176	5	]	]	PUNCT
ejpam-6755	176	6	be	be	AUX
ejpam-6755	176	7	a	a	DET
ejpam-6755	176	8	f	f	PROPN
ejpam-6755	176	9	-magic	-magic	NOUN
ejpam-6755	176	10	labeling	labeling	NOUN
ejpam-6755	176	11	of	of	ADP
ejpam-6755	176	12	nf	nf	NOUN
ejpam-6755	176	13	with	with	ADP
ejpam-6755	176	14	the	the	DET
ejpam-6755	176	15	magic	magic	ADJ
ejpam-6755	176	16	constant	constant	ADJ
ejpam-6755	176	17	c	c	NOUN
ejpam-6755	176	18	,	,	PUNCT
ejpam-6755	176	19	i.e.	i.e.	X
ejpam-6755	176	20	,	,	PUNCT
ejpam-6755	176	21	the	the	DET
ejpam-6755	176	22	weights	weight	NOUN
ejpam-6755	176	23	of	of	ADP
ejpam-6755	176	24	subgraphs	subgraph	NOUN
ejpam-6755	176	25	f	f	PROPN
ejpam-6755	176	26	corresponding	correspond	VERB
ejpam-6755	176	27	to	to	ADP
ejpam-6755	176	28	the	the	DET
ejpam-6755	176	29	vertices	vertex	NOUN
ejpam-6755	176	30	of	of	ADP
ejpam-6755	176	31	g	g	NOUN
ejpam-6755	176	32	are	be	AUX
ejpam-6755	176	33	wg(f	wg(f	NOUN
ejpam-6755	176	34	)	)	PUNCT
ejpam-6755	176	35	=	=	SYM
ejpam-6755	176	36	c.	c.	PROPN
ejpam-6755	176	37	let	let	VERB
ejpam-6755	176	38	si	si	PROPN
ejpam-6755	176	39	denote	denote	VERB
ejpam-6755	176	40	the	the	DET
ejpam-6755	176	41	number	number	NOUN
ejpam-6755	176	42	of	of	ADP
ejpam-6755	176	43	subgraphs	subgraph	NOUN
ejpam-6755	176	44	of	of	ADP
ejpam-6755	176	45	g[f	g[f	PROPN
ejpam-6755	176	46	;	;	PUNCT
ejpam-6755	176	47	h1	h1	PROPN
ejpam-6755	176	48	,	,	PUNCT
ejpam-6755	176	49	h2	h2	PROPN
ejpam-6755	176	50	]	]	PUNCT
ejpam-6755	176	51	isomorphic	isomorphic	ADJ
ejpam-6755	176	52	to	to	PART
ejpam-6755	176	53	hi	hi	VERB
ejpam-6755	176	54	,	,	PUNCT
ejpam-6755	176	55	i	i	PRON
ejpam-6755	176	56	=	=	NOUN
ejpam-6755	176	57	1	1	NUM
ejpam-6755	176	58	,	,	PUNCT
ejpam-6755	176	59	2	2	NUM
ejpam-6755	176	60	,	,	PUNCT
ejpam-6755	176	61	and	and	CCONJ
ejpam-6755	176	62	let	let	VERB
ejpam-6755	177	1	s1	s1	NOUN
ejpam-6755	177	2	+	+	CCONJ
ejpam-6755	177	3	s2	s2	NOUN
ejpam-6755	177	4	=	=	SYM
ejpam-6755	177	5	|e(g)|	|e(g)|	PROPN
ejpam-6755	177	6	.	.	PUNCT
ejpam-6755	177	7	now	now	ADV
ejpam-6755	177	8	suppose	suppose	VERB
ejpam-6755	177	9	that	that	SCONJ
ejpam-6755	177	10	th1(s1	th1(s1	PUNCT
ejpam-6755	177	11	−	−	NUM
ejpam-6755	177	12	1	1	NUM
ejpam-6755	177	13	)	)	PUNCT
ejpam-6755	177	14	is	be	AUX
ejpam-6755	177	15	even	even	ADV
ejpam-6755	177	16	.	.	PUNCT
ejpam-6755	178	1	consider	consider	VERB
ejpam-6755	178	2	the	the	DET
ejpam-6755	178	3	following	follow	VERB
ejpam-6755	178	4	two	two	NUM
ejpam-6755	178	5	cases	case	NOUN
ejpam-6755	178	6	.	.	PUNCT
ejpam-6755	179	1	case	case	NOUN
ejpam-6755	179	2	1	1	NUM
ejpam-6755	179	3	.	.	PUNCT
ejpam-6755	179	4	when	when	SCONJ
ejpam-6755	179	5	th1	th1	PROPN
ejpam-6755	179	6	is	be	AUX
ejpam-6755	179	7	even	even	ADV
ejpam-6755	179	8	.	.	PUNCT
ejpam-6755	180	1	let	let	VERB
ejpam-6755	180	2	x1	x1	NOUN
ejpam-6755	180	3	=	=	PUNCT
ejpam-6755	181	1	[	[	X
ejpam-6755	181	2	ntf	ntf	PROPN
ejpam-6755	181	3	+1	+1	PROPN
ejpam-6755	181	4	,	,	PUNCT
ejpam-6755	181	5	s1(th1	s1(th1	PROPN
ejpam-6755	181	6	−	−	PROPN
ejpam-6755	181	7	2tf	2tf	NOUN
ejpam-6755	181	8	)	)	PUNCT
ejpam-6755	182	1	+	+	NOUN
ejpam-6755	182	2	ntf	ntf	PROPN
ejpam-6755	182	3	]	]	X
ejpam-6755	182	4	.	.	PUNCT
ejpam-6755	183	1	create	create	VERB
ejpam-6755	183	2	a	a	DET
ejpam-6755	183	3	partition	partition	NOUN
ejpam-6755	183	4	of	of	ADP
ejpam-6755	183	5	x1	x1	NUM
ejpam-6755	183	6	into	into	ADP
ejpam-6755	183	7	2	2	NUM
ejpam-6755	183	8	-	-	PUNCT
ejpam-6755	183	9	sets	set	NOUN
ejpam-6755	183	10	,	,	PUNCT
ejpam-6755	183	11	x1	x1	PROPN
ejpam-6755	183	12	j	j	PROPN
ejpam-6755	183	13	for	for	ADP
ejpam-6755	183	14	j	j	PROPN
ejpam-6755	183	15	∈	∈	PROPN
ejpam-6755	184	1	[	[	X
ejpam-6755	184	2	1	1	NUM
ejpam-6755	184	3	,	,	PUNCT
ejpam-6755	184	4	12(s1(th1	12(s1(th1	NUM
ejpam-6755	184	5	−	−	PROPN
ejpam-6755	184	6	2tf	2tf	NOUN
ejpam-6755	184	7	)	)	PUNCT
ejpam-6755	184	8	)	)	PUNCT
ejpam-6755	184	9	]	]	PUNCT
ejpam-6755	184	10	such	such	ADJ
ejpam-6755	184	11	that∑	that∑	NOUN
ejpam-6755	184	12	a∈x1	a∈x1	VERB
ejpam-6755	184	13	j	j	PROPN
ejpam-6755	184	14	a	a	X
ejpam-6755	184	15	=	=	X
ejpam-6755	184	16	s1(th1	s1(th1	PROPN
ejpam-6755	184	17	−	−	PROPN
ejpam-6755	184	18	2tf	2tf	NOUN
ejpam-6755	184	19	)	)	PUNCT
ejpam-6755	185	1	+	+	CCONJ
ejpam-6755	186	1	2ntf	2ntf	NUM
ejpam-6755	186	2	+	+	CCONJ
ejpam-6755	186	3	1	1	NUM
ejpam-6755	186	4	t.	t.	PROPN
ejpam-6755	186	5	k.	k.	PROPN
ejpam-6755	186	6	maryati	maryati	PROPN
ejpam-6755	186	7	et	et	PROPN
ejpam-6755	186	8	al	al	PROPN
ejpam-6755	186	9	.	.	PUNCT
ejpam-6755	186	10	/	/	SYM
ejpam-6755	186	11	eur	eur	PROPN
ejpam-6755	186	12	.	.	PUNCT
ejpam-6755	187	1	j.	j.	PROPN
ejpam-6755	187	2	pure	pure	PROPN
ejpam-6755	187	3	appl	appl	PROPN
ejpam-6755	187	4	.	.	PROPN
ejpam-6755	187	5	math	math	PROPN
ejpam-6755	187	6	,	,	PUNCT
ejpam-6755	187	7	18	18	NUM
ejpam-6755	187	8	(	(	PUNCT
ejpam-6755	187	9	4	4	NUM
ejpam-6755	187	10	)	)	PUNCT
ejpam-6755	187	11	(	(	PUNCT
ejpam-6755	187	12	2025	2025	NUM
ejpam-6755	187	13	)	)	PUNCT
ejpam-6755	187	14	,	,	PUNCT
ejpam-6755	187	15	6755	6755	NUM
ejpam-6755	187	16	6	6	NUM
ejpam-6755	187	17	of	of	ADP
ejpam-6755	187	18	13	13	NUM
ejpam-6755	187	19	and	and	CCONJ
ejpam-6755	187	20	put	put	VERB
ejpam-6755	187	21	s1(th1	s1(th1	PROPN
ejpam-6755	187	22	−	−	PROPN
ejpam-6755	187	23	2tf	2tf	NOUN
ejpam-6755	187	24	)	)	PUNCT
ejpam-6755	188	1	+	+	CCONJ
ejpam-6755	189	1	2ntf	2ntf	NUM
ejpam-6755	189	2	+	+	CCONJ
ejpam-6755	189	3	1	1	NUM
ejpam-6755	189	4	=	=	SYM
ejpam-6755	189	5	x1	x1	PROPN
ejpam-6755	189	6	.	.	PUNCT
ejpam-6755	189	7	case	case	NOUN
ejpam-6755	189	8	2	2	NUM
ejpam-6755	189	9	.	.	X
ejpam-6755	189	10	when	when	SCONJ
ejpam-6755	189	11	both	both	DET
ejpam-6755	189	12	s1	s1	NOUN
ejpam-6755	189	13	and	and	CCONJ
ejpam-6755	189	14	th1	th1	NOUN
ejpam-6755	189	15	are	be	AUX
ejpam-6755	189	16	odd	odd	ADJ
ejpam-6755	189	17	.	.	PUNCT
ejpam-6755	190	1	let	let	VERB
ejpam-6755	190	2	y	y	PROPN
ejpam-6755	190	3	1	1	NUM
ejpam-6755	190	4	=	=	SYM
ejpam-6755	191	1	[	[	X
ejpam-6755	191	2	ntf	ntf	PROPN
ejpam-6755	191	3	+	+	PROPN
ejpam-6755	191	4	1	1	NUM
ejpam-6755	191	5	,	,	PUNCT
ejpam-6755	191	6	s1(th1	s1(th1	PROPN
ejpam-6755	191	7	−	−	PROPN
ejpam-6755	191	8	2tf	2tf	NOUN
ejpam-6755	191	9	−	−	NOUN
ejpam-6755	191	10	3	3	NUM
ejpam-6755	191	11	)	)	PUNCT
ejpam-6755	191	12	+	+	CCONJ
ejpam-6755	191	13	ntf	ntf	PROPN
ejpam-6755	191	14	]	]	X
ejpam-6755	191	15	.	.	PUNCT
ejpam-6755	192	1	similarly	similarly	ADV
ejpam-6755	192	2	,	,	PUNCT
ejpam-6755	192	3	create	create	VERB
ejpam-6755	192	4	a	a	DET
ejpam-6755	192	5	partition	partition	NOUN
ejpam-6755	192	6	of	of	ADP
ejpam-6755	192	7	y	y	NOUN
ejpam-6755	192	8	1	1	NUM
ejpam-6755	192	9	into	into	ADP
ejpam-6755	192	10	2	2	NUM
ejpam-6755	192	11	-	-	PUNCT
ejpam-6755	192	12	sets	set	NOUN
ejpam-6755	192	13	,	,	PUNCT
ejpam-6755	192	14	y	y	PROPN
ejpam-6755	192	15	1	1	NUM
ejpam-6755	192	16	k	k	PROPN
ejpam-6755	192	17	for	for	ADP
ejpam-6755	192	18	k	k	PROPN
ejpam-6755	192	19	∈	∈	PROPN
ejpam-6755	193	1	[	[	X
ejpam-6755	193	2	1	1	NUM
ejpam-6755	193	3	,	,	PUNCT
ejpam-6755	193	4	12(s1(th1	12(s1(th1	NUM
ejpam-6755	193	5	−2tf	−2tf	X
ejpam-6755	193	6	−3	−3	PROPN
ejpam-6755	193	7	)	)	PUNCT
ejpam-6755	193	8	)	)	PUNCT
ejpam-6755	193	9	]	]	PUNCT
ejpam-6755	193	10	such	such	ADJ
ejpam-6755	193	11	that∑	that∑	NOUN
ejpam-6755	193	12	a∈y	a∈y	VERB
ejpam-6755	193	13	1	1	NUM
ejpam-6755	193	14	k	k	PROPN
ejpam-6755	193	15	a	a	X
ejpam-6755	193	16	=	=	X
ejpam-6755	193	17	s1(th1	s1(th1	PROPN
ejpam-6755	193	18	−	−	PROPN
ejpam-6755	193	19	2tf	2tf	NOUN
ejpam-6755	193	20	−	−	NOUN
ejpam-6755	193	21	3	3	NUM
ejpam-6755	193	22	)	)	PUNCT
ejpam-6755	193	23	+	+	CCONJ
ejpam-6755	194	1	2ntf	2ntf	NUM
ejpam-6755	194	2	+	+	NUM
ejpam-6755	194	3	1	1	NUM
ejpam-6755	194	4	,	,	PUNCT
ejpam-6755	194	5	and	and	CCONJ
ejpam-6755	194	6	denote	denote	VERB
ejpam-6755	194	7	s1(th1	s1(th1	PROPN
ejpam-6755	194	8	−	−	PROPN
ejpam-6755	194	9	2tf	2tf	NOUN
ejpam-6755	194	10	−	−	NOUN
ejpam-6755	194	11	3	3	NUM
ejpam-6755	194	12	)	)	PUNCT
ejpam-6755	194	13	+	+	CCONJ
ejpam-6755	195	1	2ntf	2ntf	NUM
ejpam-6755	195	2	+	+	CCONJ
ejpam-6755	195	3	1	1	NUM
ejpam-6755	195	4	=	=	SYM
ejpam-6755	195	5	y	y	PROPN
ejpam-6755	195	6	1	1	NUM
ejpam-6755	195	7	.	.	PUNCT
ejpam-6755	196	1	next	next	ADV
ejpam-6755	196	2	,	,	PUNCT
ejpam-6755	196	3	let	let	VERB
ejpam-6755	196	4	z1	z1	X
ejpam-6755	196	5	=	=	PUNCT
ejpam-6755	197	1	[	[	X
ejpam-6755	197	2	s1(th1	s1(th1	X
ejpam-6755	197	3	−	−	PROPN
ejpam-6755	197	4	2tf	2tf	NOUN
ejpam-6755	197	5	−	−	NOUN
ejpam-6755	197	6	3	3	NUM
ejpam-6755	197	7	)	)	PUNCT
ejpam-6755	197	8	+	+	CCONJ
ejpam-6755	197	9	ntf	ntf	PROPN
ejpam-6755	198	1	+	+	CCONJ
ejpam-6755	198	2	1	1	NUM
ejpam-6755	198	3	,	,	PUNCT
ejpam-6755	198	4	s1(th1	s1(th1	PROPN
ejpam-6755	198	5	−	−	PROPN
ejpam-6755	198	6	2tf	2tf	NOUN
ejpam-6755	198	7	)	)	PUNCT
ejpam-6755	199	1	+	+	CCONJ
ejpam-6755	200	1	ntf	ntf	PROPN
ejpam-6755	200	2	]	]	PUNCT
ejpam-6755	200	3	and	and	CCONJ
ejpam-6755	200	4	consider	consider	VERB
ejpam-6755	200	5	x	x	X
ejpam-6755	200	6	=	=	PRON
ejpam-6755	200	7	s1(th1	s1(th1	PROPN
ejpam-6755	200	8	−	−	PROPN
ejpam-6755	200	9	2tf	2tf	NOUN
ejpam-6755	200	10	−	−	NOUN
ejpam-6755	200	11	3	3	NUM
ejpam-6755	200	12	)	)	PUNCT
ejpam-6755	200	13	+	+	CCONJ
ejpam-6755	200	14	ntf	ntf	PROPN
ejpam-6755	200	15	,	,	PUNCT
ejpam-6755	200	16	y	y	PROPN
ejpam-6755	200	17	=	=	PUNCT
ejpam-6755	200	18	x	x	PROPN
ejpam-6755	200	19	+	+	NUM
ejpam-6755	200	20	s1	s1	NOUN
ejpam-6755	200	21	,	,	PUNCT
ejpam-6755	200	22	z	z	NOUN
ejpam-6755	200	23	=	=	SYM
ejpam-6755	200	24	x	x	SYM
ejpam-6755	200	25	+	+	NUM
ejpam-6755	200	26	2s1	2s1	NUM
ejpam-6755	200	27	.	.	PUNCT
ejpam-6755	201	1	by	by	ADP
ejpam-6755	201	2	lemma	lemma	PROPN
ejpam-6755	201	3	1	1	NUM
ejpam-6755	201	4	,	,	PUNCT
ejpam-6755	201	5	z1	z1	PROPN
ejpam-6755	201	6	is	be	AUX
ejpam-6755	201	7	s1	s1	NOUN
ejpam-6755	201	8	-	-	PUNCT
ejpam-6755	201	9	balanced	balanced	ADJ
ejpam-6755	201	10	.	.	PUNCT
ejpam-6755	202	1	let	let	VERB
ejpam-6755	202	2	zl	zl	PRON
ejpam-6755	202	3	be	be	AUX
ejpam-6755	202	4	a	a	DET
ejpam-6755	202	5	balanced	balanced	ADJ
ejpam-6755	202	6	multisets	multiset	NOUN
ejpam-6755	202	7	of	of	ADP
ejpam-6755	202	8	z1	z1	NOUN
ejpam-6755	202	9	for	for	ADP
ejpam-6755	202	10	l	l	NOUN
ejpam-6755	202	11	∈	∈	PROPN
ejpam-6755	203	1	[	[	X
ejpam-6755	203	2	1	1	NUM
ejpam-6755	203	3	,	,	PUNCT
ejpam-6755	203	4	s1	s1	NOUN
ejpam-6755	203	5	]	]	PUNCT
ejpam-6755	203	6	.	.	PUNCT
ejpam-6755	204	1	hence∑	hence∑	PROPN
ejpam-6755	204	2	a∈z1	a∈z1	PROPN
ejpam-6755	204	3	l	l	NOUN
ejpam-6755	205	1	a	a	PRON
ejpam-6755	205	2	=	=	SYM
ejpam-6755	205	3	3(s1(th1	3(s1(th1	NUM
ejpam-6755	205	4	−	−	NOUN
ejpam-6755	205	5	2tf	2tf	NOUN
ejpam-6755	205	6	−	−	NOUN
ejpam-6755	205	7	2	2	NUM
ejpam-6755	205	8	)	)	PUNCT
ejpam-6755	205	9	+	+	CCONJ
ejpam-6755	205	10	ntf	ntf	PROPN
ejpam-6755	205	11	+	+	CCONJ
ejpam-6755	205	12	1	1	NUM
ejpam-6755	205	13	2(s1	2(s1	NUM
ejpam-6755	205	14	+	+	CCONJ
ejpam-6755	205	15	1	1	NUM
ejpam-6755	205	16	)	)	PUNCT
ejpam-6755	205	17	)	)	PUNCT
ejpam-6755	205	18	,	,	PUNCT
ejpam-6755	205	19	let	let	VERB
ejpam-6755	205	20	3(s1(th1	3(s1(th1	NUM
ejpam-6755	205	21	−	−	NOUN
ejpam-6755	205	22	2tf	2tf	NOUN
ejpam-6755	205	23	−	−	NOUN
ejpam-6755	205	24	2	2	NUM
ejpam-6755	205	25	)	)	PUNCT
ejpam-6755	205	26	+	+	CCONJ
ejpam-6755	206	1	ntf	ntf	PROPN
ejpam-6755	206	2	+	+	CCONJ
ejpam-6755	206	3	1	1	NUM
ejpam-6755	206	4	2(s1	2(s1	NUM
ejpam-6755	206	5	+	+	CCONJ
ejpam-6755	206	6	1	1	NUM
ejpam-6755	206	7	)	)	PUNCT
ejpam-6755	206	8	)	)	PUNCT
ejpam-6755	207	1	=	=	SYM
ejpam-6755	207	2	z1	z1	PROPN
ejpam-6755	207	3	.	.	PUNCT
ejpam-6755	208	1	furthermore	furthermore	ADV
ejpam-6755	208	2	,	,	PUNCT
ejpam-6755	208	3	let	let	VERB
ejpam-6755	208	4	x2	x2	PROPN
ejpam-6755	208	5	=	=	PUNCT
ejpam-6755	209	1	[	[	X
ejpam-6755	209	2	s1(th1	s1(th1	X
ejpam-6755	209	3	−	−	PROPN
ejpam-6755	209	4	2tf	2tf	NOUN
ejpam-6755	209	5	)	)	PUNCT
ejpam-6755	210	1	+	+	CCONJ
ejpam-6755	210	2	ntf	ntf	PROPN
ejpam-6755	210	3	+	+	CCONJ
ejpam-6755	210	4	1	1	NUM
ejpam-6755	210	5	,	,	PUNCT
ejpam-6755	210	6	s1(th1	s1(th1	PROPN
ejpam-6755	210	7	−	−	PROPN
ejpam-6755	210	8	2tf	2tf	NOUN
ejpam-6755	210	9	)	)	PUNCT
ejpam-6755	211	1	+	+	CCONJ
ejpam-6755	211	2	s2(th2	s2(th2	X
ejpam-6755	211	3	−	−	PROPN
ejpam-6755	211	4	2tf	2tf	NOUN
ejpam-6755	211	5	)	)	PUNCT
ejpam-6755	212	1	+	+	CCONJ
ejpam-6755	212	2	ntf	ntf	PROPN
ejpam-6755	212	3	]	]	X
ejpam-6755	212	4	,	,	PUNCT
ejpam-6755	212	5	y	y	PROPN
ejpam-6755	212	6	2	2	NUM
ejpam-6755	212	7	=	=	SYM
ejpam-6755	213	1	[	[	X
ejpam-6755	213	2	s1(th1	s1(th1	X
ejpam-6755	213	3	−	−	PROPN
ejpam-6755	213	4	2tf	2tf	NOUN
ejpam-6755	213	5	)	)	PUNCT
ejpam-6755	214	1	+	+	CCONJ
ejpam-6755	214	2	ntf	ntf	PROPN
ejpam-6755	214	3	+	+	CCONJ
ejpam-6755	214	4	1	1	NUM
ejpam-6755	214	5	,	,	PUNCT
ejpam-6755	214	6	s1(th1	s1(th1	PROPN
ejpam-6755	214	7	−	−	PROPN
ejpam-6755	214	8	2tf	2tf	NOUN
ejpam-6755	214	9	)	)	PUNCT
ejpam-6755	215	1	+	+	CCONJ
ejpam-6755	215	2	s2(th2	s2(th2	X
ejpam-6755	215	3	−	−	PROPN
ejpam-6755	215	4	2tf	2tf	NOUN
ejpam-6755	215	5	−	−	NOUN
ejpam-6755	215	6	3	3	NUM
ejpam-6755	215	7	)	)	PUNCT
ejpam-6755	215	8	+	+	CCONJ
ejpam-6755	215	9	ntf	ntf	PROPN
ejpam-6755	216	1	]	]	X
ejpam-6755	216	2	,	,	PUNCT
ejpam-6755	216	3	z2	z2	PROPN
ejpam-6755	216	4	=	=	PUNCT
ejpam-6755	217	1	[	[	X
ejpam-6755	217	2	s1(th1	s1(th1	X
ejpam-6755	217	3	−	−	PROPN
ejpam-6755	217	4	2tf	2tf	NOUN
ejpam-6755	217	5	)	)	PUNCT
ejpam-6755	218	1	+	+	CCONJ
ejpam-6755	218	2	s2(th2	s2(th2	X
ejpam-6755	218	3	−	−	PROPN
ejpam-6755	218	4	2tf	2tf	NOUN
ejpam-6755	218	5	−	−	NOUN
ejpam-6755	218	6	3	3	NUM
ejpam-6755	218	7	)	)	PUNCT
ejpam-6755	218	8	+	+	CCONJ
ejpam-6755	219	1	ntf	ntf	PROPN
ejpam-6755	219	2	+	+	CCONJ
ejpam-6755	219	3	1	1	NUM
ejpam-6755	219	4	,	,	PUNCT
ejpam-6755	219	5	s1(th1	s1(th1	PROPN
ejpam-6755	219	6	−	−	PROPN
ejpam-6755	219	7	2tf	2tf	NOUN
ejpam-6755	219	8	)	)	PUNCT
ejpam-6755	220	1	+	+	CCONJ
ejpam-6755	220	2	s2(th2	s2(th2	X
ejpam-6755	220	3	−	−	PROPN
ejpam-6755	220	4	2tf	2tf	NOUN
ejpam-6755	220	5	)	)	PUNCT
ejpam-6755	221	1	+	+	CCONJ
ejpam-6755	221	2	ntf	ntf	PROPN
ejpam-6755	221	3	]	]	PUNCT
ejpam-6755	221	4	.	.	PUNCT
ejpam-6755	222	1	by	by	ADP
ejpam-6755	222	2	a	a	DET
ejpam-6755	222	3	similar	similar	ADJ
ejpam-6755	222	4	approach	approach	NOUN
ejpam-6755	222	5	,	,	PUNCT
ejpam-6755	222	6	when	when	SCONJ
ejpam-6755	222	7	th2(s2−1	th2(s2−1	VERB
ejpam-6755	222	8	)	)	PUNCT
ejpam-6755	222	9	is	be	AUX
ejpam-6755	222	10	even	even	ADV
ejpam-6755	222	11	,	,	PUNCT
ejpam-6755	222	12	we	we	PRON
ejpam-6755	222	13	obtain	obtain	VERB
ejpam-6755	222	14	balanced	balanced	ADJ
ejpam-6755	222	15	multisets	multiset	NOUN
ejpam-6755	223	1	x2	x2	PROPN
ejpam-6755	223	2	j	j	PROPN
ejpam-6755	223	3	,	,	PUNCT
ejpam-6755	223	4	y	y	PROPN
ejpam-6755	223	5	2	2	NUM
ejpam-6755	223	6	k	k	NOUN
ejpam-6755	223	7	and	and	CCONJ
ejpam-6755	223	8	z2	z2	PROPN
ejpam-6755	223	9	l	l	NOUN
ejpam-6755	223	10	such	such	ADJ
ejpam-6755	223	11	that	that	SCONJ
ejpam-6755	223	12	∑	∑	PUNCT
ejpam-6755	223	13	a∈xj	a∈xj	VERB
ejpam-6755	223	14	a	a	DET
ejpam-6755	223	15	=	=	SYM
ejpam-6755	223	16	2s1(th1	2s1(th1	NUM
ejpam-6755	223	17	−	−	PROPN
ejpam-6755	223	18	2tf	2tf	NOUN
ejpam-6755	223	19	)	)	PUNCT
ejpam-6755	224	1	+	+	CCONJ
ejpam-6755	224	2	s2(th2	s2(th2	X
ejpam-6755	224	3	−	−	PROPN
ejpam-6755	224	4	2tf	2tf	NOUN
ejpam-6755	224	5	)	)	PUNCT
ejpam-6755	225	1	+	+	CCONJ
ejpam-6755	226	1	2ntf	2ntf	NUM
ejpam-6755	226	2	+	+	CCONJ
ejpam-6755	226	3	1	1	NUM
ejpam-6755	226	4	=	=	SYM
ejpam-6755	226	5	x2	x2	PROPN
ejpam-6755	226	6	,	,	PUNCT
ejpam-6755	226	7	∑	∑	PUNCT
ejpam-6755	226	8	a∈yk	a∈yk	VERB
ejpam-6755	226	9	a	a	DET
ejpam-6755	226	10	=	=	SYM
ejpam-6755	226	11	2s1(th1	2s1(th1	NUM
ejpam-6755	226	12	−	−	PROPN
ejpam-6755	226	13	2tf	2tf	NOUN
ejpam-6755	226	14	)	)	PUNCT
ejpam-6755	227	1	+	+	CCONJ
ejpam-6755	227	2	s2(th2	s2(th2	X
ejpam-6755	227	3	−	−	PROPN
ejpam-6755	227	4	2tf	2tf	NOUN
ejpam-6755	227	5	−	−	NOUN
ejpam-6755	227	6	3	3	NUM
ejpam-6755	227	7	)	)	PUNCT
ejpam-6755	227	8	+	+	CCONJ
ejpam-6755	228	1	2ntf	2ntf	NUM
ejpam-6755	228	2	+	+	CCONJ
ejpam-6755	228	3	1	1	NUM
ejpam-6755	228	4	=	=	SYM
ejpam-6755	228	5	y	y	PROPN
ejpam-6755	228	6	2	2	NUM
ejpam-6755	228	7	,	,	PUNCT
ejpam-6755	228	8	∑	∑	PUNCT
ejpam-6755	228	9	a∈zl	a∈zl	VERB
ejpam-6755	228	10	a	a	DET
ejpam-6755	228	11	=	=	SYM
ejpam-6755	228	12	2s1(th1	2s1(th1	NUM
ejpam-6755	228	13	−	−	PROPN
ejpam-6755	228	14	2tf	2tf	NOUN
ejpam-6755	228	15	)	)	PUNCT
ejpam-6755	229	1	+	+	CCONJ
ejpam-6755	229	2	s2(2th2	s2(2th2	CCONJ
ejpam-6755	229	3	−	−	PROPN
ejpam-6755	229	4	4tf	4tf	ADJ
ejpam-6755	229	5	−	−	PROPN
ejpam-6755	229	6	3	3	NUM
ejpam-6755	229	7	)	)	PUNCT
ejpam-6755	229	8	+	+	CCONJ
ejpam-6755	230	1	2ntf	2ntf	NUM
ejpam-6755	230	2	+	+	CCONJ
ejpam-6755	230	3	1	1	NUM
ejpam-6755	230	4	=	=	SYM
ejpam-6755	230	5	z2	z2	PROPN
ejpam-6755	230	6	.	.	PUNCT
ejpam-6755	231	1	now	now	ADV
ejpam-6755	231	2	,	,	PUNCT
ejpam-6755	231	3	define	define	VERB
ejpam-6755	231	4	a	a	DET
ejpam-6755	231	5	total	total	ADJ
ejpam-6755	231	6	labeling	labeling	NOUN
ejpam-6755	231	7	f	f	PROPN
ejpam-6755	231	8	of	of	ADP
ejpam-6755	231	9	g[f	g[f	PROPN
ejpam-6755	231	10	;	;	PUNCT
ejpam-6755	231	11	h1	h1	PROPN
ejpam-6755	231	12	,	,	PUNCT
ejpam-6755	231	13	h2	h2	PROPN
ejpam-6755	231	14	]	]	PUNCT
ejpam-6755	231	15	as	as	SCONJ
ejpam-6755	231	16	follows	follow	VERB
ejpam-6755	231	17	.	.	PUNCT
ejpam-6755	232	1	•	•	NOUN
ejpam-6755	232	2	for	for	ADP
ejpam-6755	232	3	v	v	NOUN
ejpam-6755	232	4	∈	∈	NOUN
ejpam-6755	232	5	v	v	NOUN
ejpam-6755	232	6	(	(	PUNCT
ejpam-6755	232	7	nf	nf	INTJ
ejpam-6755	232	8	)	)	PUNCT
ejpam-6755	232	9	put	put	VERB
ejpam-6755	232	10	f(v	f(v	NOUN
ejpam-6755	232	11	)	)	PUNCT
ejpam-6755	233	1	=	=	SYM
ejpam-6755	233	2	g(v	g(v	X
ejpam-6755	233	3	)	)	PUNCT
ejpam-6755	233	4	.	.	PUNCT
ejpam-6755	234	1	•	•	NUM
ejpam-6755	234	2	assign	assign	VERB
ejpam-6755	234	3	the	the	DET
ejpam-6755	234	4	elements	element	NOUN
ejpam-6755	234	5	of	of	ADP
ejpam-6755	234	6	x1	x1	PROPN
ejpam-6755	234	7	j	j	PROPN
ejpam-6755	234	8	,	,	PUNCT
ejpam-6755	234	9	y	y	PROPN
ejpam-6755	234	10	1	1	NUM
ejpam-6755	234	11	k	k	NOUN
ejpam-6755	234	12	or	or	CCONJ
ejpam-6755	234	13	z1	z1	ADJ
ejpam-6755	234	14	l	l	NOUN
ejpam-6755	234	15	to	to	PART
ejpam-6755	234	16	label	label	VERB
ejpam-6755	234	17	unlabeled	unlabele	VERB
ejpam-6755	234	18	vertices	vertex	NOUN
ejpam-6755	234	19	and	and	CCONJ
ejpam-6755	234	20	unlabeled	unlabele	VERB
ejpam-6755	234	21	edges	edge	NOUN
ejpam-6755	234	22	of	of	ADP
ejpam-6755	234	23	a	a	DET
ejpam-6755	234	24	subgraph	subgraph	NOUN
ejpam-6755	234	25	isomorphic	isomorphic	ADJ
ejpam-6755	234	26	to	to	ADP
ejpam-6755	234	27	h1	h1	PROPN
ejpam-6755	234	28	.	.	PUNCT
ejpam-6755	235	1	•	•	NUM
ejpam-6755	235	2	likewise	likewise	ADV
ejpam-6755	235	3	,	,	PUNCT
ejpam-6755	235	4	use	use	VERB
ejpam-6755	235	5	the	the	DET
ejpam-6755	235	6	elements	element	NOUN
ejpam-6755	235	7	of	of	ADP
ejpam-6755	235	8	x2	x2	PROPN
ejpam-6755	235	9	j	j	PROPN
ejpam-6755	235	10	,	,	PUNCT
ejpam-6755	235	11	y	y	PROPN
ejpam-6755	235	12	2	2	NUM
ejpam-6755	235	13	k	k	NOUN
ejpam-6755	235	14	,	,	PUNCT
ejpam-6755	235	15	z	z	NOUN
ejpam-6755	235	16	2	2	NUM
ejpam-6755	235	17	l	l	NOUN
ejpam-6755	235	18	to	to	PART
ejpam-6755	235	19	label	label	VERB
ejpam-6755	235	20	unlabeled	unlabele	VERB
ejpam-6755	235	21	vertices	vertex	NOUN
ejpam-6755	235	22	and	and	CCONJ
ejpam-6755	235	23	unlabeled	unlabele	VERB
ejpam-6755	235	24	edges	edge	NOUN
ejpam-6755	235	25	of	of	ADP
ejpam-6755	235	26	subgraph	subgraph	NOUN
ejpam-6755	235	27	isomorphic	isomorphic	ADJ
ejpam-6755	235	28	to	to	ADP
ejpam-6755	235	29	h2	h2	NOUN
ejpam-6755	235	30	.	.	PUNCT
ejpam-6755	236	1	t.	t.	PROPN
ejpam-6755	236	2	k.	k.	PROPN
ejpam-6755	236	3	maryati	maryati	PROPN
ejpam-6755	236	4	et	et	PROPN
ejpam-6755	236	5	al	al	PROPN
ejpam-6755	236	6	.	.	PUNCT
ejpam-6755	236	7	/	/	SYM
ejpam-6755	236	8	eur	eur	PROPN
ejpam-6755	236	9	.	.	PUNCT
ejpam-6755	237	1	j.	j.	PROPN
ejpam-6755	237	2	pure	pure	PROPN
ejpam-6755	237	3	appl	appl	PROPN
ejpam-6755	237	4	.	.	PROPN
ejpam-6755	237	5	math	math	PROPN
ejpam-6755	237	6	,	,	PUNCT
ejpam-6755	237	7	18	18	NUM
ejpam-6755	237	8	(	(	PUNCT
ejpam-6755	237	9	4	4	NUM
ejpam-6755	237	10	)	)	PUNCT
ejpam-6755	237	11	(	(	PUNCT
ejpam-6755	237	12	2025	2025	NUM
ejpam-6755	237	13	)	)	PUNCT
ejpam-6755	237	14	,	,	PUNCT
ejpam-6755	237	15	6755	6755	NUM
ejpam-6755	237	16	7	7	NUM
ejpam-6755	237	17	of	of	ADP
ejpam-6755	237	18	13	13	NUM
ejpam-6755	237	19	it	it	PRON
ejpam-6755	237	20	is	be	AUX
ejpam-6755	237	21	a	a	DET
ejpam-6755	237	22	routine	routine	NOUN
ejpam-6755	237	23	to	to	PART
ejpam-6755	237	24	check	check	VERB
ejpam-6755	237	25	that	that	SCONJ
ejpam-6755	237	26	f	f	PROPN
ejpam-6755	237	27	is	be	AUX
ejpam-6755	237	28	a	a	DET
ejpam-6755	237	29	bijection	bijection	NOUN
ejpam-6755	237	30	.	.	PUNCT
ejpam-6755	238	1	to	to	PART
ejpam-6755	238	2	prove	prove	VERB
ejpam-6755	238	3	that	that	SCONJ
ejpam-6755	238	4	g[f	g[f	PROPN
ejpam-6755	238	5	;	;	PUNCT
ejpam-6755	238	6	h1	h1	PROPN
ejpam-6755	238	7	,	,	PUNCT
ejpam-6755	238	8	h2	h2	PROPN
ejpam-6755	238	9	]	]	PUNCT
ejpam-6755	238	10	is	be	AUX
ejpam-6755	238	11	(	(	PUNCT
ejpam-6755	238	12	h1	h1	PROPN
ejpam-6755	238	13	,	,	PUNCT
ejpam-6755	238	14	h2)magic	h2)magic	PROPN
ejpam-6755	238	15	,	,	PUNCT
ejpam-6755	238	16	consider	consider	VERB
ejpam-6755	238	17	a	a	DET
ejpam-6755	238	18	subgraph	subgraph	NOUN
ejpam-6755	238	19	h∗	h∗	NOUN
ejpam-6755	238	20	1	1	NUM
ejpam-6755	238	21	of	of	ADP
ejpam-6755	238	22	g[f	g[f	PROPN
ejpam-6755	238	23	;	;	PUNCT
ejpam-6755	238	24	h1	h1	PROPN
ejpam-6755	238	25	,	,	PUNCT
ejpam-6755	238	26	h2	h2	PROPN
ejpam-6755	238	27	]	]	PUNCT
ejpam-6755	238	28	isomorphic	isomorphic	ADJ
ejpam-6755	238	29	to	to	AUX
ejpam-6755	238	30	h1	h1	VERB
ejpam-6755	238	31	.	.	PUNCT
ejpam-6755	239	1	we	we	PRON
ejpam-6755	239	2	get	get	VERB
ejpam-6755	239	3	that	that	DET
ejpam-6755	239	4	wf	wf	PROPN
ejpam-6755	239	5	(	(	PUNCT
ejpam-6755	239	6	h	h	NOUN
ejpam-6755	239	7	∗	∗	NOUN
ejpam-6755	239	8	1	1	NUM
ejpam-6755	239	9	)	)	PUNCT
ejpam-6755	239	10	=	=	VERB
ejpam-6755	239	11	{	{	PUNCT
ejpam-6755	239	12	2c+	2c+	NUM
ejpam-6755	239	13	1	1	NUM
ejpam-6755	239	14	2x	2x	NUM
ejpam-6755	239	15	1(th1	1(th1	NUM
ejpam-6755	239	16	−	−	NOUN
ejpam-6755	239	17	2tf	2tf	NOUN
ejpam-6755	239	18	)	)	PUNCT
ejpam-6755	239	19	,	,	PUNCT
ejpam-6755	239	20	if	if	SCONJ
ejpam-6755	239	21	s1	s1	NOUN
ejpam-6755	239	22	is	be	AUX
ejpam-6755	239	23	even	even	ADV
ejpam-6755	239	24	,	,	PUNCT
ejpam-6755	239	25	2c+	2c+	NUM
ejpam-6755	239	26	1	1	NUM
ejpam-6755	239	27	2y	2y	NUM
ejpam-6755	239	28	1(th1	1(th1	NOUN
ejpam-6755	239	29	−	−	NOUN
ejpam-6755	239	30	2tf	2tf	NOUN
ejpam-6755	239	31	−	−	NOUN
ejpam-6755	239	32	3	3	NUM
ejpam-6755	239	33	)	)	PUNCT
ejpam-6755	239	34	+	+	CCONJ
ejpam-6755	239	35	z1	z1	VERB
ejpam-6755	239	36	,	,	PUNCT
ejpam-6755	239	37	if	if	SCONJ
ejpam-6755	239	38	s1	s1	PROPN
ejpam-6755	239	39	and	and	CCONJ
ejpam-6755	239	40	th1	th1	NOUN
ejpam-6755	239	41	are	be	AUX
ejpam-6755	239	42	odd	odd	ADJ
ejpam-6755	239	43	.	.	PUNCT
ejpam-6755	240	1	moreover	moreover	ADV
ejpam-6755	240	2	,	,	PUNCT
ejpam-6755	240	3	for	for	ADP
ejpam-6755	240	4	a	a	DET
ejpam-6755	240	5	subgraph	subgraph	NOUN
ejpam-6755	240	6	h∗	h∗	NOUN
ejpam-6755	240	7	2	2	NUM
ejpam-6755	240	8	of	of	ADP
ejpam-6755	240	9	g[f	g[f	PROPN
ejpam-6755	240	10	;	;	PUNCT
ejpam-6755	240	11	h1	h1	PROPN
ejpam-6755	240	12	,	,	PUNCT
ejpam-6755	240	13	h2	h2	PROPN
ejpam-6755	240	14	]	]	PUNCT
ejpam-6755	240	15	isomorphic	isomorphic	ADJ
ejpam-6755	240	16	to	to	ADP
ejpam-6755	240	17	h2	h2	NOUN
ejpam-6755	240	18	,	,	PUNCT
ejpam-6755	240	19	we	we	PRON
ejpam-6755	240	20	have	have	VERB
ejpam-6755	240	21	wf	wf	PROPN
ejpam-6755	240	22	(	(	PUNCT
ejpam-6755	240	23	h	h	NOUN
ejpam-6755	240	24	∗	∗	NOUN
ejpam-6755	240	25	2	2	NUM
ejpam-6755	240	26	)	)	PUNCT
ejpam-6755	240	27	=	=	VERB
ejpam-6755	240	28	{	{	PUNCT
ejpam-6755	240	29	2c+	2c+	NUM
ejpam-6755	240	30	1	1	NUM
ejpam-6755	240	31	2x	2x	NUM
ejpam-6755	240	32	2(th2	2(th2	NUM
ejpam-6755	240	33	−	−	NOUN
ejpam-6755	240	34	2tf	2tf	NOUN
ejpam-6755	240	35	)	)	PUNCT
ejpam-6755	240	36	,	,	PUNCT
ejpam-6755	240	37	if	if	SCONJ
ejpam-6755	240	38	s2	s2	NOUN
ejpam-6755	240	39	is	be	AUX
ejpam-6755	240	40	even	even	ADV
ejpam-6755	240	41	,	,	PUNCT
ejpam-6755	240	42	2c+	2c+	NUM
ejpam-6755	240	43	1	1	NUM
ejpam-6755	240	44	2y	2y	NUM
ejpam-6755	241	1	2(th2	2(th2	NUM
ejpam-6755	241	2	−	−	PROPN
ejpam-6755	241	3	2tf	2tf	NOUN
ejpam-6755	241	4	−	−	NOUN
ejpam-6755	241	5	3	3	NUM
ejpam-6755	241	6	)	)	PUNCT
ejpam-6755	242	1	+	+	NOUN
ejpam-6755	242	2	z2	z2	NOUN
ejpam-6755	242	3	,	,	PUNCT
ejpam-6755	242	4	if	if	SCONJ
ejpam-6755	242	5	s2	s2	PROPN
ejpam-6755	242	6	and	and	CCONJ
ejpam-6755	242	7	th2	th2	PROPN
ejpam-6755	242	8	are	be	AUX
ejpam-6755	242	9	odd	odd	ADJ
ejpam-6755	242	10	.	.	PUNCT
ejpam-6755	243	1	thus	thus	ADV
ejpam-6755	243	2	it	it	PRON
ejpam-6755	243	3	may	may	AUX
ejpam-6755	243	4	be	be	AUX
ejpam-6755	243	5	concluded	conclude	VERB
ejpam-6755	243	6	that	that	SCONJ
ejpam-6755	243	7	g[f	g[f	PROPN
ejpam-6755	243	8	;	;	PUNCT
ejpam-6755	243	9	h1	h1	PROPN
ejpam-6755	243	10	,	,	PUNCT
ejpam-6755	243	11	h2	h2	PROPN
ejpam-6755	243	12	]	]	PUNCT
ejpam-6755	243	13	is	be	AUX
ejpam-6755	243	14	(	(	PUNCT
ejpam-6755	243	15	h1	h1	PROPN
ejpam-6755	243	16	,	,	PUNCT
ejpam-6755	243	17	h2)-magic	h2)-magic	ADJ
ejpam-6755	243	18	.	.	PUNCT
ejpam-6755	244	1	□	□	PUNCT
ejpam-6755	244	2	an	an	DET
ejpam-6755	244	3	illustration	illustration	NOUN
ejpam-6755	244	4	of	of	ADP
ejpam-6755	244	5	a	a	DET
ejpam-6755	244	6	construction	construction	NOUN
ejpam-6755	244	7	described	describe	VERB
ejpam-6755	244	8	in	in	ADP
ejpam-6755	244	9	the	the	DET
ejpam-6755	244	10	proof	proof	NOUN
ejpam-6755	244	11	of	of	ADP
ejpam-6755	244	12	theorem	theorem	ADJ
ejpam-6755	244	13	5	5	NUM
ejpam-6755	244	14	is	be	AUX
ejpam-6755	244	15	given	give	VERB
ejpam-6755	244	16	in	in	ADP
ejpam-6755	244	17	figure	figure	NOUN
ejpam-6755	244	18	2	2	NUM
ejpam-6755	244	19	.	.	PUNCT
ejpam-6755	244	20	figure	figure	NOUN
ejpam-6755	244	21	2	2	NUM
ejpam-6755	244	22	:	:	PUNCT
ejpam-6755	244	23	the	the	DET
ejpam-6755	244	24	p7[k2;h1	p7[k2;h1	NOUN
ejpam-6755	244	25	,	,	PUNCT
ejpam-6755	244	26	h2	h2	PROPN
ejpam-6755	244	27	]	]	PUNCT
ejpam-6755	244	28	is	be	AUX
ejpam-6755	244	29	(	(	PUNCT
ejpam-6755	244	30	h1	h1	PROPN
ejpam-6755	244	31	,	,	PUNCT
ejpam-6755	244	32	h2)-magic	h2)-magic	ADJ
ejpam-6755	244	33	,	,	PUNCT
ejpam-6755	244	34	where	where	SCONJ
ejpam-6755	244	35	h1	h1	PROPN
ejpam-6755	244	36	is	be	AUX
ejpam-6755	244	37	a	a	DET
ejpam-6755	244	38	cycle	cycle	NOUN
ejpam-6755	244	39	on	on	ADP
ejpam-6755	244	40	6	6	NUM
ejpam-6755	244	41	vertices	vertex	NOUN
ejpam-6755	244	42	with	with	ADP
ejpam-6755	244	43	a	a	DET
ejpam-6755	244	44	subdivided	subdivided	ADJ
ejpam-6755	244	45	chord	chord	NOUN
ejpam-6755	244	46	and	and	CCONJ
ejpam-6755	244	47	h2	h2	NOUN
ejpam-6755	244	48	is	be	AUX
ejpam-6755	244	49	a	a	DET
ejpam-6755	244	50	cycle	cycle	NOUN
ejpam-6755	244	51	on	on	ADP
ejpam-6755	244	52	5	5	NUM
ejpam-6755	244	53	vertices	vertex	NOUN
ejpam-6755	244	54	with	with	ADP
ejpam-6755	244	55	a	a	DET
ejpam-6755	244	56	subdivided	subdivided	ADJ
ejpam-6755	244	57	chord	chord	NOUN
ejpam-6755	244	58	.	.	PUNCT
ejpam-6755	245	1	in	in	ADP
ejpam-6755	245	2	the	the	DET
ejpam-6755	245	3	next	next	ADJ
ejpam-6755	245	4	part	part	NOUN
ejpam-6755	245	5	we	we	PRON
ejpam-6755	245	6	present	present	VERB
ejpam-6755	245	7	another	another	DET
ejpam-6755	245	8	method	method	NOUN
ejpam-6755	245	9	of	of	ADP
ejpam-6755	245	10	generating	generate	VERB
ejpam-6755	245	11	(	(	PUNCT
ejpam-6755	245	12	h1	h1	PROPN
ejpam-6755	245	13	,	,	PUNCT
ejpam-6755	245	14	h2)-magic	h2)-magic	ADJ
ejpam-6755	245	15	graphs	graph	NOUN
ejpam-6755	245	16	.	.	PUNCT
ejpam-6755	246	1	let	let	VERB
ejpam-6755	246	2	f1	f1	PROPN
ejpam-6755	246	3	and	and	CCONJ
ejpam-6755	246	4	f2	f2	PROPN
ejpam-6755	246	5	be	be	VERB
ejpam-6755	246	6	finite	finite	ADJ
ejpam-6755	246	7	graphs	graph	NOUN
ejpam-6755	246	8	containing	contain	VERB
ejpam-6755	246	9	a	a	DET
ejpam-6755	246	10	graph	graph	NOUN
ejpam-6755	246	11	a	a	PRON
ejpam-6755	246	12	as	as	ADP
ejpam-6755	246	13	a	a	DET
ejpam-6755	246	14	subgraph	subgraph	NOUN
ejpam-6755	246	15	.	.	PUNCT
ejpam-6755	247	1	we	we	PRON
ejpam-6755	247	2	call	call	VERB
ejpam-6755	247	3	a	a	PRON
ejpam-6755	247	4	as	as	ADP
ejpam-6755	247	5	a	a	DET
ejpam-6755	247	6	connector	connector	NOUN
ejpam-6755	247	7	.	.	PUNCT
ejpam-6755	248	1	an	an	DET
ejpam-6755	248	2	a	a	DET
ejpam-6755	248	3	-	-	PUNCT
ejpam-6755	248	4	amalgamation	amalgamation	NOUN
ejpam-6755	248	5	of	of	ADP
ejpam-6755	248	6	graphs	graph	NOUN
ejpam-6755	248	7	f1	f1	PROPN
ejpam-6755	248	8	and	and	CCONJ
ejpam-6755	248	9	f2	f2	PROPN
ejpam-6755	248	10	,	,	PUNCT
ejpam-6755	248	11	denoted	denote	VERB
ejpam-6755	248	12	by	by	ADP
ejpam-6755	248	13	amal(f1	amal(f1	NOUN
ejpam-6755	248	14	,	,	PUNCT
ejpam-6755	248	15	f2;a	f2;a	NOUN
ejpam-6755	248	16	)	)	PUNCT
ejpam-6755	248	17	,	,	PUNCT
ejpam-6755	248	18	is	be	AUX
ejpam-6755	248	19	a	a	DET
ejpam-6755	248	20	graph	graph	NOUN
ejpam-6755	248	21	obtained	obtain	VERB
ejpam-6755	248	22	by	by	ADP
ejpam-6755	248	23	taking	take	VERB
ejpam-6755	248	24	f1	f1	NOUN
ejpam-6755	248	25	and	and	CCONJ
ejpam-6755	248	26	f2	f2	PROPN
ejpam-6755	248	27	and	and	CCONJ
ejpam-6755	248	28	identifying	identify	VERB
ejpam-6755	248	29	their	their	PRON
ejpam-6755	248	30	connectors	connector	NOUN
ejpam-6755	248	31	a.	a.	NOUN
ejpam-6755	248	32	let	let	VERB
ejpam-6755	248	33	h1	h1	PRON
ejpam-6755	248	34	be	be	AUX
ejpam-6755	248	35	a	a	DET
ejpam-6755	248	36	connected	connected	ADJ
ejpam-6755	248	37	graph	graph	NOUN
ejpam-6755	248	38	which	which	PRON
ejpam-6755	248	39	contains	contain	VERB
ejpam-6755	248	40	amal(f1	amal(f1	NOUN
ejpam-6755	248	41	,	,	PUNCT
ejpam-6755	248	42	f2;a	f2;a	NOUN
ejpam-6755	248	43	)	)	PUNCT
ejpam-6755	248	44	as	as	ADP
ejpam-6755	248	45	a	a	DET
ejpam-6755	248	46	proper	proper	ADJ
ejpam-6755	248	47	subgraph	subgraph	NOUN
ejpam-6755	248	48	and	and	CCONJ
ejpam-6755	248	49	let	let	VERB
ejpam-6755	248	50	h2	h2	PROPN
ejpam-6755	248	51	be	be	AUX
ejpam-6755	248	52	a	a	DET
ejpam-6755	248	53	connected	connected	ADJ
ejpam-6755	248	54	graph	graph	NOUN
ejpam-6755	248	55	which	which	PRON
ejpam-6755	248	56	contains	contain	VERB
ejpam-6755	248	57	f1	f1	NOUN
ejpam-6755	248	58	∪	∪	NOUN
ejpam-6755	248	59	f2	f2	PROPN
ejpam-6755	248	60	as	as	ADP
ejpam-6755	248	61	a	a	DET
ejpam-6755	248	62	proper	proper	ADJ
ejpam-6755	248	63	subgraph	subgraph	NOUN
ejpam-6755	248	64	.	.	PUNCT
ejpam-6755	249	1	the	the	DET
ejpam-6755	249	2	graph	graph	NOUN
ejpam-6755	249	3	pn[h1;h2	pn[h1;h2	PROPN
ejpam-6755	249	4	]	]	PUNCT
ejpam-6755	249	5	is	be	AUX
ejpam-6755	249	6	constructed	construct	VERB
ejpam-6755	249	7	as	as	ADP
ejpam-6755	249	8	an	an	DET
ejpam-6755	249	9	alternating	alternate	VERB
ejpam-6755	249	10	sequence	sequence	NOUN
ejpam-6755	249	11	of	of	ADP
ejpam-6755	249	12	⌈n/2⌉	⌈n/2⌉	NOUN
ejpam-6755	249	13	copies	copy	NOUN
ejpam-6755	249	14	of	of	ADP
ejpam-6755	249	15	the	the	DET
ejpam-6755	249	16	graph	graph	NOUN
ejpam-6755	249	17	h1	h1	PROPN
ejpam-6755	249	18	and	and	CCONJ
ejpam-6755	249	19	⌊n/2⌋	⌊n/2⌋	X
ejpam-6755	249	20	copies	copy	NOUN
ejpam-6755	249	21	of	of	ADP
ejpam-6755	249	22	the	the	DET
ejpam-6755	249	23	graph	graph	NOUN
ejpam-6755	249	24	h2	h2	NOUN
ejpam-6755	249	25	.	.	PUNCT
ejpam-6755	250	1	for	for	ADP
ejpam-6755	250	2	i	i	PRON
ejpam-6755	250	3	=	=	NOUN
ejpam-6755	250	4	1	1	NUM
ejpam-6755	250	5	,	,	PUNCT
ejpam-6755	250	6	2	2	NUM
ejpam-6755	250	7	,	,	PUNCT
ejpam-6755	250	8	.	.	PUNCT
ejpam-6755	250	9	.	.	PUNCT
ejpam-6755	251	1	.	.	PUNCT
ejpam-6755	252	1	,	,	PUNCT
ejpam-6755	252	2	⌈n/2⌉	⌈n/2⌉	NOUN
ejpam-6755	252	3	−	−	PROPN
ejpam-6755	252	4	1	1	NUM
ejpam-6755	252	5	,	,	PUNCT
ejpam-6755	252	6	the	the	DET
ejpam-6755	252	7	ith	ith	PROPN
ejpam-6755	252	8	copy	copy	NOUN
ejpam-6755	252	9	of	of	ADP
ejpam-6755	252	10	h1	h1	PROPN
ejpam-6755	252	11	is	be	AUX
ejpam-6755	252	12	connected	connect	VERB
ejpam-6755	252	13	to	to	ADP
ejpam-6755	252	14	the	the	DET
ejpam-6755	252	15	ith	ith	PROPN
ejpam-6755	252	16	copy	copy	NOUN
ejpam-6755	252	17	of	of	ADP
ejpam-6755	252	18	h2	h2	NOUN
ejpam-6755	252	19	by	by	ADP
ejpam-6755	252	20	identifying	identify	VERB
ejpam-6755	252	21	the	the	DET
ejpam-6755	252	22	connector	connector	NOUN
ejpam-6755	252	23	f2	f2	PROPN
ejpam-6755	252	24	,	,	PUNCT
ejpam-6755	252	25	and	and	CCONJ
ejpam-6755	252	26	the	the	DET
ejpam-6755	252	27	ith	ith	PROPN
ejpam-6755	252	28	copy	copy	NOUN
ejpam-6755	252	29	of	of	ADP
ejpam-6755	252	30	h2	h2	PROPN
ejpam-6755	252	31	is	be	AUX
ejpam-6755	252	32	connected	connect	VERB
ejpam-6755	252	33	to	to	ADP
ejpam-6755	252	34	the	the	DET
ejpam-6755	252	35	(	(	PUNCT
ejpam-6755	252	36	i	i	PRON
ejpam-6755	252	37	+	+	CCONJ
ejpam-6755	252	38	1)th	1)th	NUM
ejpam-6755	252	39	copy	copy	NOUN
ejpam-6755	252	40	of	of	ADP
ejpam-6755	252	41	h1	h1	NOUN
ejpam-6755	252	42	by	by	ADP
ejpam-6755	252	43	identifying	identify	VERB
ejpam-6755	252	44	the	the	DET
ejpam-6755	252	45	connector	connector	NOUN
ejpam-6755	252	46	f1	f1	NOUN
ejpam-6755	252	47	.	.	PUNCT
ejpam-6755	253	1	to	to	PART
ejpam-6755	253	2	aid	aid	VERB
ejpam-6755	253	3	visualization	visualization	NOUN
ejpam-6755	253	4	,	,	PUNCT
ejpam-6755	253	5	a	a	DET
ejpam-6755	253	6	diagram	diagram	NOUN
ejpam-6755	253	7	of	of	ADP
ejpam-6755	253	8	p3[h1;h2	p3[h1;h2	PROPN
ejpam-6755	253	9	]	]	PUNCT
ejpam-6755	253	10	is	be	AUX
ejpam-6755	253	11	provided	provide	VERB
ejpam-6755	253	12	in	in	ADP
ejpam-6755	253	13	figure	figure	NOUN
ejpam-6755	253	14	3	3	NUM
ejpam-6755	253	15	.	.	PUNCT
ejpam-6755	254	1	let	let	VERB
ejpam-6755	254	2	h	h	PRON
ejpam-6755	254	3	be	be	AUX
ejpam-6755	254	4	a	a	DET
ejpam-6755	254	5	subgraph	subgraph	NOUN
ejpam-6755	254	6	of	of	ADP
ejpam-6755	254	7	g.	g.	PROPN
ejpam-6755	254	8	for	for	ADP
ejpam-6755	254	9	the	the	DET
ejpam-6755	254	10	sake	sake	NOUN
ejpam-6755	254	11	of	of	ADP
ejpam-6755	254	12	clarity	clarity	NOUN
ejpam-6755	254	13	we	we	PRON
ejpam-6755	254	14	use	use	VERB
ejpam-6755	254	15	the	the	DET
ejpam-6755	254	16	notation	notation	NOUN
ejpam-6755	254	17	tg−h	tg−h	NOUN
ejpam-6755	254	18	=	=	PUNCT
ejpam-6755	254	19	tg−	tg−	NUM
ejpam-6755	254	20	th	th	X
ejpam-6755	254	21	.	.	PUNCT
ejpam-6755	255	1	theorem	theorem	VERB
ejpam-6755	255	2	6	6	NUM
ejpam-6755	255	3	.	.	PUNCT
ejpam-6755	256	1	let	let	VERB
ejpam-6755	256	2	f1	f1	PROPN
ejpam-6755	256	3	and	and	CCONJ
ejpam-6755	256	4	f2	f2	PROPN
ejpam-6755	256	5	be	be	AUX
ejpam-6755	256	6	connected	connect	VERB
ejpam-6755	256	7	graphs	graph	NOUN
ejpam-6755	256	8	containing	contain	VERB
ejpam-6755	256	9	a	a	DET
ejpam-6755	256	10	graph	graph	NOUN
ejpam-6755	256	11	a	a	PRON
ejpam-6755	256	12	as	as	ADP
ejpam-6755	256	13	a	a	DET
ejpam-6755	256	14	proper	proper	ADJ
ejpam-6755	256	15	subgraph	subgraph	NOUN
ejpam-6755	256	16	and	and	CCONJ
ejpam-6755	256	17	let	let	VERB
ejpam-6755	256	18	f	f	PROPN
ejpam-6755	256	19	∗	∗	NOUN
ejpam-6755	256	20	=	=	SYM
ejpam-6755	256	21	amal(f1	amal(f1	NOUN
ejpam-6755	256	22	,	,	PUNCT
ejpam-6755	256	23	f2;a	f2;a	NOUN
ejpam-6755	256	24	)	)	PUNCT
ejpam-6755	256	25	contain	contain	VERB
ejpam-6755	256	26	exactly	exactly	ADV
ejpam-6755	256	27	one	one	NUM
ejpam-6755	256	28	subgraph	subgraph	NOUN
ejpam-6755	256	29	isomorphic	isomorphic	ADJ
ejpam-6755	256	30	to	to	ADP
ejpam-6755	256	31	fi	fi	NOUN
ejpam-6755	256	32	,	,	PUNCT
ejpam-6755	256	33	i	i	NOUN
ejpam-6755	256	34	=	=	NOUN
ejpam-6755	256	35	1	1	NUM
ejpam-6755	256	36	,	,	PUNCT
ejpam-6755	256	37	2	2	NUM
ejpam-6755	256	38	.	.	X
ejpam-6755	257	1	let	let	VERB
ejpam-6755	257	2	h1	h1	PROPN
ejpam-6755	257	3	be	be	AUX
ejpam-6755	257	4	a	a	DET
ejpam-6755	257	5	connected	connected	ADJ
ejpam-6755	257	6	graph	graph	NOUN
ejpam-6755	257	7	containing	contain	VERB
ejpam-6755	257	8	f	f	PROPN
ejpam-6755	257	9	∗	∗	NOUN
ejpam-6755	257	10	as	as	ADP
ejpam-6755	257	11	a	a	DET
ejpam-6755	257	12	proper	proper	ADJ
ejpam-6755	257	13	subgraph	subgraph	NOUN
ejpam-6755	257	14	and	and	CCONJ
ejpam-6755	257	15	let	let	VERB
ejpam-6755	257	16	h2	h2	PROPN
ejpam-6755	257	17	be	be	AUX
ejpam-6755	257	18	a	a	DET
ejpam-6755	257	19	connected	connected	ADJ
ejpam-6755	257	20	graph	graph	NOUN
ejpam-6755	257	21	containing	contain	VERB
ejpam-6755	257	22	f1∪f2	f1∪f2	NOUN
ejpam-6755	257	23	as	as	ADP
ejpam-6755	257	24	a	a	DET
ejpam-6755	257	25	proper	proper	ADJ
ejpam-6755	257	26	subgraph	subgraph	NOUN
ejpam-6755	257	27	.	.	PUNCT
ejpam-6755	258	1	let	let	VERB
ejpam-6755	258	2	each	each	PRON
ejpam-6755	258	3	of	of	ADP
ejpam-6755	258	4	tf1−(f1∩f2)+tf2−(f1∩f2	tf1−(f1∩f2)+tf2−(f1∩f2	PROPN
ejpam-6755	258	5	)	)	PUNCT
ejpam-6755	258	6	,	,	PUNCT
ejpam-6755	258	7	th2−(f1∪f2	th2−(f1∪f2	NOUN
ejpam-6755	258	8	)	)	PUNCT
ejpam-6755	258	9	,	,	PUNCT
ejpam-6755	258	10	and	and	CCONJ
ejpam-6755	258	11	tf1∩f2+th1−f	tf1∩f2+th1−f	NOUN
ejpam-6755	258	12	∗	∗	NOUN
ejpam-6755	258	13	be	be	VERB
ejpam-6755	258	14	an	an	DET
ejpam-6755	258	15	even	even	ADJ
ejpam-6755	258	16	number	number	NOUN
ejpam-6755	258	17	.	.	PUNCT
ejpam-6755	259	1	if	if	SCONJ
ejpam-6755	259	2	there	there	PRON
ejpam-6755	259	3	are	be	VERB
ejpam-6755	259	4	exactly	exactly	ADV
ejpam-6755	259	5	n+1−i	n+1−i	ADJ
ejpam-6755	259	6	subgraphs	subgraph	NOUN
ejpam-6755	259	7	in	in	ADP
ejpam-6755	259	8	pn[h1;h2	pn[h1;h2	NOUN
ejpam-6755	259	9	]	]	PUNCT
ejpam-6755	259	10	isomorphic	isomorphic	ADJ
ejpam-6755	259	11	to	to	PART
ejpam-6755	259	12	hi	hi	VERB
ejpam-6755	259	13	,	,	PUNCT
ejpam-6755	259	14	i	i	PRON
ejpam-6755	259	15	=	=	NOUN
ejpam-6755	259	16	1	1	NUM
ejpam-6755	259	17	,	,	PUNCT
ejpam-6755	259	18	2	2	NUM
ejpam-6755	259	19	,	,	PUNCT
ejpam-6755	259	20	then	then	ADV
ejpam-6755	259	21	the	the	DET
ejpam-6755	259	22	graph	graph	NOUN
ejpam-6755	259	23	pn[h1;h2	pn[h1;h2	PROPN
ejpam-6755	259	24	]	]	X
ejpam-6755	259	25	is	be	AUX
ejpam-6755	259	26	(	(	PUNCT
ejpam-6755	259	27	h1	h1	PROPN
ejpam-6755	259	28	,	,	PUNCT
ejpam-6755	259	29	h2)-magic	h2)-magic	ADJ
ejpam-6755	259	30	for	for	ADP
ejpam-6755	259	31	n	n	X
ejpam-6755	259	32	≥	≥	NOUN
ejpam-6755	259	33	2	2	NUM
ejpam-6755	259	34	.	.	PUNCT
ejpam-6755	260	1	t.	t.	PROPN
ejpam-6755	260	2	k.	k.	PROPN
ejpam-6755	260	3	maryati	maryati	PROPN
ejpam-6755	260	4	et	et	PROPN
ejpam-6755	260	5	al	al	PROPN
ejpam-6755	260	6	.	.	PUNCT
ejpam-6755	260	7	/	/	SYM
ejpam-6755	260	8	eur	eur	PROPN
ejpam-6755	260	9	.	.	PUNCT
ejpam-6755	261	1	j.	j.	PROPN
ejpam-6755	261	2	pure	pure	PROPN
ejpam-6755	261	3	appl	appl	PROPN
ejpam-6755	261	4	.	.	PROPN
ejpam-6755	261	5	math	math	PROPN
ejpam-6755	261	6	,	,	PUNCT
ejpam-6755	261	7	18	18	NUM
ejpam-6755	261	8	(	(	PUNCT
ejpam-6755	261	9	4	4	NUM
ejpam-6755	261	10	)	)	PUNCT
ejpam-6755	261	11	(	(	PUNCT
ejpam-6755	261	12	2025	2025	NUM
ejpam-6755	261	13	)	)	PUNCT
ejpam-6755	261	14	,	,	PUNCT
ejpam-6755	261	15	6755	6755	NUM
ejpam-6755	261	16	8	8	NUM
ejpam-6755	261	17	of	of	ADP
ejpam-6755	261	18	13	13	NUM
ejpam-6755	261	19	figure	figure	NOUN
ejpam-6755	261	20	3	3	NUM
ejpam-6755	261	21	:	:	PUNCT
ejpam-6755	261	22	visualization	visualization	NOUN
ejpam-6755	261	23	of	of	ADP
ejpam-6755	261	24	p3[h1;h2	p3[h1;h2	PROPN
ejpam-6755	261	25	]	]	PUNCT
ejpam-6755	261	26	.	.	PUNCT
ejpam-6755	262	1	proof	proof	NOUN
ejpam-6755	262	2	.	.	PUNCT
ejpam-6755	263	1	the	the	DET
ejpam-6755	263	2	idea	idea	NOUN
ejpam-6755	263	3	of	of	ADP
ejpam-6755	263	4	the	the	DET
ejpam-6755	263	5	proof	proof	NOUN
ejpam-6755	263	6	is	be	AUX
ejpam-6755	263	7	similar	similar	ADJ
ejpam-6755	263	8	to	to	ADP
ejpam-6755	263	9	the	the	DET
ejpam-6755	263	10	proof	proof	NOUN
ejpam-6755	263	11	of	of	ADP
ejpam-6755	263	12	theorem	theorem	NOUN
ejpam-6755	263	13	5	5	NUM
ejpam-6755	263	14	.	.	PUNCT
ejpam-6755	264	1	let	let	VERB
ejpam-6755	264	2	v	v	X
ejpam-6755	264	3	(	(	PUNCT
ejpam-6755	264	4	pn	pn	NOUN
ejpam-6755	264	5	)	)	PUNCT
ejpam-6755	264	6	=	=	SYM
ejpam-6755	264	7	{	{	PUNCT
ejpam-6755	264	8	v1	v1	PROPN
ejpam-6755	264	9	,	,	PUNCT
ejpam-6755	264	10	v2	v2	PROPN
ejpam-6755	264	11	,	,	PUNCT
ejpam-6755	264	12	.	.	PUNCT
ejpam-6755	264	13	.	.	PUNCT
ejpam-6755	265	1	.	.	PUNCT
ejpam-6755	266	1	,	,	PUNCT
ejpam-6755	266	2	vn	vn	VERB
ejpam-6755	266	3	}	}	PUNCT
ejpam-6755	266	4	in	in	ADP
ejpam-6755	266	5	a	a	DET
ejpam-6755	266	6	natural	natural	ADJ
ejpam-6755	266	7	way	way	NOUN
ejpam-6755	266	8	.	.	PUNCT
ejpam-6755	267	1	for	for	ADP
ejpam-6755	267	2	every	every	DET
ejpam-6755	267	3	γ	γ	PROPN
ejpam-6755	267	4	∈	∈	PROPN
ejpam-6755	267	5	{	{	PUNCT
ejpam-6755	267	6	f1	f1	NOUN
ejpam-6755	267	7	,	,	PUNCT
ejpam-6755	267	8	f2	f2	PROPN
ejpam-6755	267	9	,	,	PUNCT
ejpam-6755	267	10	f1	f1	NOUN
ejpam-6755	267	11	∩	∩	NOUN
ejpam-6755	267	12	f2	f2	PROPN
ejpam-6755	267	13	,	,	PUNCT
ejpam-6755	267	14	h1	h1	NOUN
ejpam-6755	267	15	−	−	PROPN
ejpam-6755	267	16	f	f	PROPN
ejpam-6755	267	17	∗	∗	PROPN
ejpam-6755	267	18	}	}	PUNCT
ejpam-6755	267	19	,	,	PUNCT
ejpam-6755	267	20	where	where	SCONJ
ejpam-6755	267	21	f	f	PROPN
ejpam-6755	267	22	∗	∗	NOUN
ejpam-6755	267	23	=	=	SYM
ejpam-6755	267	24	amal(f1	amal(f1	NOUN
ejpam-6755	267	25	,	,	PUNCT
ejpam-6755	267	26	f2;a	f2;a	NOUN
ejpam-6755	267	27	)	)	PUNCT
ejpam-6755	267	28	,	,	PUNCT
ejpam-6755	267	29	let	let	VERB
ejpam-6755	267	30	γ(i	γ(i	NOUN
ejpam-6755	267	31	)	)	PUNCT
ejpam-6755	267	32	be	be	AUX
ejpam-6755	267	33	a	a	DET
ejpam-6755	267	34	subgraph	subgraph	NOUN
ejpam-6755	267	35	isomorphic	isomorphic	ADJ
ejpam-6755	267	36	to	to	ADP
ejpam-6755	267	37	γ	γ	PROPN
ejpam-6755	267	38	which	which	PRON
ejpam-6755	267	39	is	be	AUX
ejpam-6755	267	40	originated	originate	VERB
ejpam-6755	267	41	from	from	ADP
ejpam-6755	267	42	vi	vi	PROPN
ejpam-6755	267	43	∈	∈	PROPN
ejpam-6755	267	44	v	v	NOUN
ejpam-6755	267	45	(	(	PUNCT
ejpam-6755	267	46	pn	pn	NOUN
ejpam-6755	267	47	)	)	PUNCT
ejpam-6755	267	48	.	.	PUNCT
ejpam-6755	268	1	first	first	ADV
ejpam-6755	268	2	,	,	PUNCT
ejpam-6755	268	3	let	let	VERB
ejpam-6755	268	4	z	z	NOUN
ejpam-6755	268	5	=	=	PUNCT
ejpam-6755	269	1	[	[	X
ejpam-6755	269	2	n(th1	n(th1	NOUN
ejpam-6755	269	3	)	)	PUNCT
ejpam-6755	269	4	+	+	NOUN
ejpam-6755	269	5	1	1	NUM
ejpam-6755	269	6	,	,	PUNCT
ejpam-6755	270	1	n(th1	n(th1	NOUN
ejpam-6755	270	2	+	+	NUM
ejpam-6755	270	3	th2−(f1∪f2	th2−(f1∪f2	NOUN
ejpam-6755	270	4	)	)	PUNCT
ejpam-6755	270	5	)	)	PUNCT
ejpam-6755	271	1	]	]	PUNCT
ejpam-6755	271	2	.	.	PUNCT
ejpam-6755	272	1	create	create	VERB
ejpam-6755	272	2	a	a	DET
ejpam-6755	272	3	partition	partition	NOUN
ejpam-6755	272	4	of	of	ADP
ejpam-6755	272	5	z	z	NOUN
ejpam-6755	272	6	into	into	ADP
ejpam-6755	272	7	2	2	NUM
ejpam-6755	272	8	-	-	PUNCT
ejpam-6755	272	9	sets	set	NOUN
ejpam-6755	272	10	,	,	PUNCT
ejpam-6755	272	11	zk	zk	PROPN
ejpam-6755	272	12	for	for	ADP
ejpam-6755	272	13	k	k	PROPN
ejpam-6755	272	14	∈	∈	PROPN
ejpam-6755	273	1	[	[	X
ejpam-6755	273	2	1	1	NUM
ejpam-6755	273	3	,	,	PUNCT
ejpam-6755	273	4	12n(th2−(f1∪f2	12n(th2−(f1∪f2	NUM
ejpam-6755	273	5	)	)	PUNCT
ejpam-6755	273	6	)	)	PUNCT
ejpam-6755	273	7	]	]	PUNCT
ejpam-6755	273	8	such	such	ADJ
ejpam-6755	273	9	that∑	that∑	NOUN
ejpam-6755	273	10	a∈zk	a∈zk	VERB
ejpam-6755	273	11	a	a	DET
ejpam-6755	273	12	=	=	X
ejpam-6755	273	13	n(2th1	n(2th1	PROPN
ejpam-6755	273	14	+	+	CCONJ
ejpam-6755	273	15	th2−(f1∪f2	th2−(f1∪f2	NOUN
ejpam-6755	273	16	)	)	PUNCT
ejpam-6755	273	17	)	)	PUNCT
ejpam-6755	274	1	+	+	CCONJ
ejpam-6755	274	2	1	1	NUM
ejpam-6755	274	3	,	,	PUNCT
ejpam-6755	274	4	and	and	CCONJ
ejpam-6755	274	5	put	put	VERB
ejpam-6755	274	6	n(2th1	n(2th1	NOUN
ejpam-6755	274	7	+	+	CCONJ
ejpam-6755	274	8	th2−(f1∪f2))+1	th2−(f1∪f2))+1	NOUN
ejpam-6755	274	9	=	=	PUNCT
ejpam-6755	274	10	z.	z.	PROPN
ejpam-6755	274	11	now	now	ADV
ejpam-6755	274	12	,	,	PUNCT
ejpam-6755	274	13	we	we	PRON
ejpam-6755	274	14	consider	consider	VERB
ejpam-6755	274	15	several	several	ADJ
ejpam-6755	274	16	cases	case	NOUN
ejpam-6755	274	17	based	base	VERB
ejpam-6755	274	18	on	on	ADP
ejpam-6755	274	19	the	the	DET
ejpam-6755	274	20	parity	parity	NOUN
ejpam-6755	274	21	of	of	ADP
ejpam-6755	274	22	tf1	tf1	NOUN
ejpam-6755	274	23	and	and	CCONJ
ejpam-6755	274	24	tf2	tf2	NOUN
ejpam-6755	274	25	.	.	PUNCT
ejpam-6755	275	1	since	since	SCONJ
ejpam-6755	275	2	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	275	3	)	)	PUNCT
ejpam-6755	275	4	+	+	SYM
ejpam-6755	275	5	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	275	6	)	)	PUNCT
ejpam-6755	275	7	is	be	AUX
ejpam-6755	275	8	even	even	ADV
ejpam-6755	275	9	,	,	PUNCT
ejpam-6755	275	10	then	then	ADV
ejpam-6755	275	11	both	both	PRON
ejpam-6755	275	12	of	of	ADP
ejpam-6755	275	13	them	they	PRON
ejpam-6755	275	14	have	have	VERB
ejpam-6755	275	15	the	the	DET
ejpam-6755	275	16	same	same	ADJ
ejpam-6755	275	17	parity	parity	NOUN
ejpam-6755	275	18	.	.	PUNCT
ejpam-6755	276	1	case	case	NOUN
ejpam-6755	276	2	1.1	1.1	NUM
ejpam-6755	276	3	.	.	PUNCT
ejpam-6755	277	1	when	when	SCONJ
ejpam-6755	277	2	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	277	3	)	)	PUNCT
ejpam-6755	277	4	and	and	CCONJ
ejpam-6755	277	5	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	277	6	)	)	PUNCT
ejpam-6755	277	7	are	be	AUX
ejpam-6755	277	8	even	even	ADV
ejpam-6755	277	9	.	.	PUNCT
ejpam-6755	278	1	let	let	VERB
ejpam-6755	278	2	x1	x1	NOUN
ejpam-6755	278	3	=	=	PUNCT
ejpam-6755	279	1	[	[	X
ejpam-6755	279	2	1	1	NUM
ejpam-6755	279	3	,	,	PUNCT
ejpam-6755	279	4	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	279	5	)	)	PUNCT
ejpam-6755	279	6	)	)	PUNCT
ejpam-6755	279	7	]	]	PUNCT
ejpam-6755	279	8	.	.	PUNCT
ejpam-6755	280	1	create	create	VERB
ejpam-6755	280	2	a	a	DET
ejpam-6755	280	3	partition	partition	NOUN
ejpam-6755	280	4	x1	x1	ADJ
ejpam-6755	280	5	into	into	ADP
ejpam-6755	280	6	2	2	NUM
ejpam-6755	280	7	-	-	PUNCT
ejpam-6755	280	8	sets	set	NOUN
ejpam-6755	280	9	,	,	PUNCT
ejpam-6755	280	10	x1	x1	PROPN
ejpam-6755	280	11	i	i	PROPN
ejpam-6755	280	12	for	for	ADP
ejpam-6755	280	13	i	i	PRON
ejpam-6755	280	14	∈	∈	PROPN
ejpam-6755	281	1	[	[	X
ejpam-6755	281	2	1	1	NUM
ejpam-6755	281	3	,	,	PUNCT
ejpam-6755	281	4	12n(tf1−(f1∩f2	12n(tf1−(f1∩f2	NUM
ejpam-6755	281	5	)	)	PUNCT
ejpam-6755	281	6	)	)	PUNCT
ejpam-6755	281	7	]	]	PUNCT
ejpam-6755	281	8	such	such	ADJ
ejpam-6755	281	9	that∑	that∑	NOUN
ejpam-6755	281	10	a∈x1	a∈x1	VERB
ejpam-6755	281	11	i	i	PRON
ejpam-6755	281	12	a	a	DET
ejpam-6755	281	13	=	=	PUNCT
ejpam-6755	281	14	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	281	15	)	)	PUNCT
ejpam-6755	281	16	)	)	PUNCT
ejpam-6755	282	1	+	+	CCONJ
ejpam-6755	282	2	1	1	NUM
ejpam-6755	282	3	,	,	PUNCT
ejpam-6755	282	4	and	and	CCONJ
ejpam-6755	282	5	denote	denote	VERB
ejpam-6755	282	6	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	282	7	)	)	PUNCT
ejpam-6755	282	8	)	)	PUNCT
ejpam-6755	283	1	+	+	CCONJ
ejpam-6755	283	2	1	1	NUM
ejpam-6755	283	3	=	=	SYM
ejpam-6755	283	4	x1	x1	PROPN
ejpam-6755	283	5	.	.	PUNCT
ejpam-6755	284	1	likewise	likewise	ADV
ejpam-6755	284	2	,	,	PUNCT
ejpam-6755	284	3	let	let	VERB
ejpam-6755	284	4	y	y	PROPN
ejpam-6755	284	5	1	1	NUM
ejpam-6755	284	6	=	=	SYM
ejpam-6755	284	7	[	[	X
ejpam-6755	284	8	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	284	9	)	)	PUNCT
ejpam-6755	284	10	)	)	PUNCT
ejpam-6755	285	1	+	+	CCONJ
ejpam-6755	285	2	1	1	NUM
ejpam-6755	285	3	,	,	PUNCT
ejpam-6755	285	4	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	285	5	)	)	PUNCT
ejpam-6755	285	6	+	+	SYM
ejpam-6755	285	7	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	285	8	)	)	PUNCT
ejpam-6755	285	9	)	)	PUNCT
ejpam-6755	285	10	]	]	PUNCT
ejpam-6755	285	11	and	and	CCONJ
ejpam-6755	285	12	create	create	VERB
ejpam-6755	285	13	a	a	DET
ejpam-6755	285	14	partition	partition	NOUN
ejpam-6755	285	15	of	of	ADP
ejpam-6755	285	16	y	y	NOUN
ejpam-6755	285	17	1	1	NUM
ejpam-6755	285	18	into	into	ADP
ejpam-6755	285	19	2	2	NUM
ejpam-6755	285	20	-	-	PUNCT
ejpam-6755	285	21	sets	set	NOUN
ejpam-6755	285	22	,	,	PUNCT
ejpam-6755	285	23	y	y	PROPN
ejpam-6755	285	24	1	1	NUM
ejpam-6755	285	25	i	i	PRON
ejpam-6755	285	26	for	for	ADP
ejpam-6755	285	27	i	i	PRON
ejpam-6755	285	28	∈	∈	PROPN
ejpam-6755	286	1	[	[	X
ejpam-6755	286	2	1	1	NUM
ejpam-6755	286	3	,	,	PUNCT
ejpam-6755	286	4	12n(tf2−(f1∩f2	12n(tf2−(f1∩f2	NUM
ejpam-6755	286	5	)	)	PUNCT
ejpam-6755	286	6	)	)	PUNCT
ejpam-6755	286	7	]	]	PUNCT
ejpam-6755	286	8	such	such	ADJ
ejpam-6755	286	9	that∑	that∑	NOUN
ejpam-6755	286	10	a∈y	a∈y	VERB
ejpam-6755	286	11	1	1	NUM
ejpam-6755	286	12	i	i	PRON
ejpam-6755	286	13	a	a	PRON
ejpam-6755	286	14	=	=	SYM
ejpam-6755	286	15	n(2(tf1−(f1∩f2	n(2(tf1−(f1∩f2	PROPN
ejpam-6755	286	16	)	)	PUNCT
ejpam-6755	286	17	)	)	PUNCT
ejpam-6755	287	1	+	+	CCONJ
ejpam-6755	287	2	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	287	3	)	)	PUNCT
ejpam-6755	287	4	)	)	PUNCT
ejpam-6755	288	1	+	+	CCONJ
ejpam-6755	288	2	1	1	NUM
ejpam-6755	288	3	,	,	PUNCT
ejpam-6755	288	4	and	and	CCONJ
ejpam-6755	288	5	put	put	VERB
ejpam-6755	288	6	n(2(tf1−(f1∩f2	n(2(tf1−(f1∩f2	PROPN
ejpam-6755	288	7	)	)	PUNCT
ejpam-6755	288	8	)	)	PUNCT
ejpam-6755	289	1	+	+	CCONJ
ejpam-6755	289	2	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	289	3	)	)	PUNCT
ejpam-6755	289	4	)	)	PUNCT
ejpam-6755	290	1	+	+	CCONJ
ejpam-6755	290	2	1	1	NUM
ejpam-6755	290	3	=	=	SYM
ejpam-6755	290	4	y	y	PROPN
ejpam-6755	290	5	1	1	NUM
ejpam-6755	290	6	.	.	PUNCT
ejpam-6755	290	7	case	case	NOUN
ejpam-6755	290	8	1.2	1.2	NUM
ejpam-6755	290	9	.	.	PUNCT
ejpam-6755	291	1	when	when	SCONJ
ejpam-6755	291	2	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	291	3	)	)	PUNCT
ejpam-6755	291	4	and	and	CCONJ
ejpam-6755	291	5	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	291	6	)	)	PUNCT
ejpam-6755	291	7	are	be	AUX
ejpam-6755	291	8	odd	odd	ADJ
ejpam-6755	291	9	.	.	PUNCT
ejpam-6755	292	1	let	let	VERB
ejpam-6755	292	2	x2	x2	NOUN
ejpam-6755	293	1	=	=	PUNCT
ejpam-6755	294	1	[	[	X
ejpam-6755	294	2	1	1	NUM
ejpam-6755	294	3	,	,	PUNCT
ejpam-6755	294	4	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	294	5	)	)	PUNCT
ejpam-6755	294	6	−	−	ADP
ejpam-6755	295	1	1	1	NUM
ejpam-6755	295	2	)	)	PUNCT
ejpam-6755	295	3	]	]	PUNCT
ejpam-6755	295	4	.	.	PUNCT
ejpam-6755	296	1	create	create	VERB
ejpam-6755	296	2	a	a	DET
ejpam-6755	296	3	partition	partition	NOUN
ejpam-6755	296	4	x2	x2	NOUN
ejpam-6755	296	5	into	into	ADP
ejpam-6755	296	6	2	2	NUM
ejpam-6755	296	7	-	-	PUNCT
ejpam-6755	296	8	sets	set	NOUN
ejpam-6755	296	9	,	,	PUNCT
ejpam-6755	296	10	x2	x2	PROPN
ejpam-6755	296	11	i	i	PROPN
ejpam-6755	296	12	for	for	ADP
ejpam-6755	296	13	i	i	PRON
ejpam-6755	296	14	∈	∈	PROPN
ejpam-6755	297	1	[	[	X
ejpam-6755	297	2	1	1	NUM
ejpam-6755	297	3	,	,	PUNCT
ejpam-6755	297	4	12n(tf1−(f1∩f2	12n(tf1−(f1∩f2	NUM
ejpam-6755	297	5	)	)	PUNCT
ejpam-6755	297	6	−	−	ADP
ejpam-6755	297	7	1	1	NUM
ejpam-6755	297	8	)	)	PUNCT
ejpam-6755	297	9	]	]	PUNCT
ejpam-6755	297	10	such	such	ADJ
ejpam-6755	297	11	that∑	that∑	NOUN
ejpam-6755	297	12	a∈x2	a∈x2	NOUN
ejpam-6755	297	13	i	i	PRON
ejpam-6755	297	14	a	a	DET
ejpam-6755	297	15	=	=	PUNCT
ejpam-6755	297	16	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	297	17	)	)	PUNCT
ejpam-6755	297	18	−	−	ADP
ejpam-6755	297	19	1	1	X
ejpam-6755	297	20	)	)	PUNCT
ejpam-6755	297	21	+	+	NUM
ejpam-6755	297	22	1	1	NUM
ejpam-6755	297	23	,	,	PUNCT
ejpam-6755	297	24	and	and	CCONJ
ejpam-6755	297	25	let	let	VERB
ejpam-6755	297	26	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NOUN
ejpam-6755	297	27	)	)	PUNCT
ejpam-6755	297	28	−	−	ADP
ejpam-6755	297	29	1	1	X
ejpam-6755	297	30	)	)	PUNCT
ejpam-6755	297	31	+	+	CCONJ
ejpam-6755	297	32	1	1	NUM
ejpam-6755	297	33	=	=	SYM
ejpam-6755	297	34	x2	x2	PROPN
ejpam-6755	297	35	.	.	PUNCT
ejpam-6755	298	1	again	again	ADV
ejpam-6755	298	2	,	,	PUNCT
ejpam-6755	298	3	let	let	VERB
ejpam-6755	298	4	y	y	PROPN
ejpam-6755	298	5	2	2	NUM
ejpam-6755	298	6	=	=	SYM
ejpam-6755	298	7	[	[	X
ejpam-6755	298	8	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	298	9	)	)	PUNCT
ejpam-6755	298	10	)	)	PUNCT
ejpam-6755	299	1	+	+	CCONJ
ejpam-6755	299	2	1	1	NUM
ejpam-6755	299	3	,	,	PUNCT
ejpam-6755	299	4	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	299	5	)	)	PUNCT
ejpam-6755	299	6	+	+	SYM
ejpam-6755	299	7	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	299	8	)	)	PUNCT
ejpam-6755	299	9	−	−	NOUN
ejpam-6755	299	10	1	1	NUM
ejpam-6755	299	11	)	)	PUNCT
ejpam-6755	299	12	]	]	PUNCT
ejpam-6755	300	1	t.	t.	PROPN
ejpam-6755	300	2	k.	k.	PROPN
ejpam-6755	300	3	maryati	maryati	PROPN
ejpam-6755	300	4	et	et	PROPN
ejpam-6755	300	5	al	al	PROPN
ejpam-6755	300	6	.	.	PUNCT
ejpam-6755	300	7	/	/	SYM
ejpam-6755	300	8	eur	eur	PROPN
ejpam-6755	300	9	.	.	PUNCT
ejpam-6755	301	1	j.	j.	PROPN
ejpam-6755	301	2	pure	pure	PROPN
ejpam-6755	301	3	appl	appl	PROPN
ejpam-6755	301	4	.	.	PROPN
ejpam-6755	301	5	math	math	PROPN
ejpam-6755	301	6	,	,	PUNCT
ejpam-6755	301	7	18	18	NUM
ejpam-6755	301	8	(	(	PUNCT
ejpam-6755	301	9	4	4	NUM
ejpam-6755	301	10	)	)	PUNCT
ejpam-6755	301	11	(	(	PUNCT
ejpam-6755	301	12	2025	2025	NUM
ejpam-6755	301	13	)	)	PUNCT
ejpam-6755	301	14	,	,	PUNCT
ejpam-6755	301	15	6755	6755	NUM
ejpam-6755	301	16	9	9	NUM
ejpam-6755	301	17	of	of	ADP
ejpam-6755	301	18	13	13	NUM
ejpam-6755	301	19	and	and	CCONJ
ejpam-6755	301	20	create	create	VERB
ejpam-6755	301	21	a	a	DET
ejpam-6755	301	22	partition	partition	NOUN
ejpam-6755	301	23	of	of	ADP
ejpam-6755	301	24	y	y	PROPN
ejpam-6755	301	25	2	2	NUM
ejpam-6755	301	26	into	into	ADP
ejpam-6755	301	27	2	2	NUM
ejpam-6755	301	28	-	-	PUNCT
ejpam-6755	301	29	sets	set	NOUN
ejpam-6755	301	30	,	,	PUNCT
ejpam-6755	301	31	y	y	PROPN
ejpam-6755	301	32	2	2	NUM
ejpam-6755	301	33	i	i	PRON
ejpam-6755	301	34	for	for	ADP
ejpam-6755	301	35	i	i	PRON
ejpam-6755	301	36	∈	∈	PROPN
ejpam-6755	302	1	[	[	X
ejpam-6755	302	2	1	1	NUM
ejpam-6755	302	3	,	,	PUNCT
ejpam-6755	302	4	12n(tf2−(f1∩f2	12n(tf2−(f1∩f2	NUM
ejpam-6755	302	5	)	)	PUNCT
ejpam-6755	302	6	−	−	PROPN
ejpam-6755	302	7	1	1	NUM
ejpam-6755	302	8	)	)	PUNCT
ejpam-6755	302	9	]	]	PUNCT
ejpam-6755	302	10	such	such	ADJ
ejpam-6755	302	11	that∑	that∑	NOUN
ejpam-6755	302	12	a∈y	a∈y	VERB
ejpam-6755	302	13	2	2	NUM
ejpam-6755	302	14	i	i	PRON
ejpam-6755	302	15	a	a	DET
ejpam-6755	302	16	=	=	SYM
ejpam-6755	302	17	n(2(tf1−(f1∩f2	n(2(tf1−(f1∩f2	PROPN
ejpam-6755	302	18	)	)	PUNCT
ejpam-6755	302	19	)	)	PUNCT
ejpam-6755	303	1	+	+	CCONJ
ejpam-6755	303	2	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	303	3	)	)	PUNCT
ejpam-6755	303	4	−	−	NOUN
ejpam-6755	303	5	1	1	NUM
ejpam-6755	303	6	)	)	PUNCT
ejpam-6755	303	7	+	+	NUM
ejpam-6755	303	8	1	1	NUM
ejpam-6755	303	9	,	,	PUNCT
ejpam-6755	303	10	and	and	CCONJ
ejpam-6755	303	11	denote	denote	VERB
ejpam-6755	303	12	n(2(tf1−(f1∩f2	n(2(tf1−(f1∩f2	PROPN
ejpam-6755	303	13	)	)	PUNCT
ejpam-6755	303	14	)	)	PUNCT
ejpam-6755	304	1	+	+	CCONJ
ejpam-6755	304	2	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	304	3	)	)	PUNCT
ejpam-6755	304	4	−	−	NOUN
ejpam-6755	304	5	1	1	NUM
ejpam-6755	304	6	)	)	PUNCT
ejpam-6755	304	7	+	+	CCONJ
ejpam-6755	304	8	1	1	NUM
ejpam-6755	304	9	=	=	SYM
ejpam-6755	304	10	y	y	PROPN
ejpam-6755	304	11	2	2	NUM
ejpam-6755	304	12	.	.	PUNCT
ejpam-6755	305	1	next	next	ADV
ejpam-6755	305	2	,	,	PUNCT
ejpam-6755	305	3	we	we	PRON
ejpam-6755	305	4	consider	consider	VERB
ejpam-6755	305	5	the	the	DET
ejpam-6755	305	6	parity	parity	NOUN
ejpam-6755	305	7	of	of	ADP
ejpam-6755	305	8	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	305	9	and	and	CCONJ
ejpam-6755	305	10	th1−f	th1−f	NOUN
ejpam-6755	305	11	∗	∗	VERB
ejpam-6755	305	12	in	in	ADP
ejpam-6755	305	13	a	a	DET
ejpam-6755	305	14	similar	similar	ADJ
ejpam-6755	305	15	manner	manner	NOUN
ejpam-6755	305	16	.	.	PUNCT
ejpam-6755	306	1	case	case	NOUN
ejpam-6755	306	2	2.1	2.1	NUM
ejpam-6755	306	3	.	.	PUNCT
ejpam-6755	307	1	when	when	SCONJ
ejpam-6755	307	2	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	307	3	and	and	CCONJ
ejpam-6755	307	4	th1−f	th1−f	NOUN
ejpam-6755	307	5	∗	∗	NOUN
ejpam-6755	307	6	are	be	AUX
ejpam-6755	307	7	even	even	ADV
ejpam-6755	307	8	.	.	PUNCT
ejpam-6755	308	1	let	let	VERB
ejpam-6755	308	2	u1	u1	NOUN
ejpam-6755	308	3	=	=	PUNCT
ejpam-6755	309	1	[	[	X
ejpam-6755	309	2	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	309	3	)	)	PUNCT
ejpam-6755	309	4	+	+	SYM
ejpam-6755	309	5	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	309	6	)	)	PUNCT
ejpam-6755	309	7	)	)	PUNCT
ejpam-6755	310	1	+	+	CCONJ
ejpam-6755	310	2	1	1	NUM
ejpam-6755	310	3	,	,	PUNCT
ejpam-6755	310	4	n(tf	n(tf	NOUN
ejpam-6755	310	5	∗	∗	NOUN
ejpam-6755	310	6	)	)	PUNCT
ejpam-6755	310	7	]	]	PUNCT
ejpam-6755	310	8	.	.	PUNCT
ejpam-6755	311	1	create	create	VERB
ejpam-6755	311	2	a	a	DET
ejpam-6755	311	3	partition	partition	NOUN
ejpam-6755	311	4	of	of	ADP
ejpam-6755	311	5	u1	u1	NOUN
ejpam-6755	311	6	into	into	ADP
ejpam-6755	311	7	2	2	NUM
ejpam-6755	311	8	-	-	PUNCT
ejpam-6755	311	9	sets	set	NOUN
ejpam-6755	311	10	,	,	PUNCT
ejpam-6755	311	11	u1	u1	PROPN
ejpam-6755	311	12	j	j	PROPN
ejpam-6755	311	13	for	for	ADP
ejpam-6755	311	14	j	j	PROPN
ejpam-6755	311	15	∈	∈	PROPN
ejpam-6755	312	1	[	[	X
ejpam-6755	312	2	1	1	NUM
ejpam-6755	312	3	,	,	PUNCT
ejpam-6755	312	4	12n(tf1∩f2	12n(tf1∩f2	PROPN
ejpam-6755	312	5	)	)	PUNCT
ejpam-6755	312	6	]	]	PUNCT
ejpam-6755	312	7	such	such	ADJ
ejpam-6755	312	8	that∑	that∑	NOUN
ejpam-6755	312	9	a∈u1	a∈u1	VERB
ejpam-6755	312	10	j	j	PROPN
ejpam-6755	312	11	a	a	DET
ejpam-6755	312	12	=	=	PUNCT
ejpam-6755	312	13	n(tf1−(f1∩f2	n(tf1−(f1∩f2	PROPN
ejpam-6755	312	14	)	)	PUNCT
ejpam-6755	312	15	+	+	SYM
ejpam-6755	312	16	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	312	17	)	)	PUNCT
ejpam-6755	313	1	+	+	CCONJ
ejpam-6755	313	2	tf	tf	NUM
ejpam-6755	313	3	∗	∗	NOUN
ejpam-6755	313	4	)	)	PUNCT
ejpam-6755	314	1	+	+	CCONJ
ejpam-6755	314	2	1	1	NUM
ejpam-6755	314	3	=	=	SYM
ejpam-6755	314	4	u1	u1	NOUN
ejpam-6755	314	5	.	.	PUNCT
ejpam-6755	315	1	similarly	similarly	ADV
ejpam-6755	315	2	,	,	PUNCT
ejpam-6755	315	3	let	let	VERB
ejpam-6755	315	4	w	w	NOUN
ejpam-6755	315	5	1	1	NUM
ejpam-6755	315	6	=	=	SYM
ejpam-6755	316	1	[	[	X
ejpam-6755	316	2	n(tf	n(tf	PRON
ejpam-6755	316	3	∗	∗	NOUN
ejpam-6755	316	4	)	)	PUNCT
ejpam-6755	317	1	+	+	CCONJ
ejpam-6755	317	2	1	1	NUM
ejpam-6755	317	3	,	,	PUNCT
ejpam-6755	317	4	n(th1	n(th1	NOUN
ejpam-6755	317	5	)	)	PUNCT
ejpam-6755	317	6	]	]	PUNCT
ejpam-6755	317	7	and	and	CCONJ
ejpam-6755	317	8	create	create	VERB
ejpam-6755	317	9	a	a	DET
ejpam-6755	317	10	partition	partition	NOUN
ejpam-6755	317	11	of	of	ADP
ejpam-6755	317	12	w	w	NOUN
ejpam-6755	317	13	1	1	NUM
ejpam-6755	317	14	into	into	ADP
ejpam-6755	317	15	2	2	NUM
ejpam-6755	317	16	-	-	PUNCT
ejpam-6755	317	17	sets	set	NOUN
ejpam-6755	317	18	,	,	PUNCT
ejpam-6755	317	19	w	w	PROPN
ejpam-6755	317	20	1	1	NUM
ejpam-6755	317	21	j	j	PROPN
ejpam-6755	317	22	for	for	ADP
ejpam-6755	317	23	j	j	PROPN
ejpam-6755	317	24	∈	∈	PROPN
ejpam-6755	318	1	[	[	X
ejpam-6755	318	2	1	1	NUM
ejpam-6755	318	3	,	,	PUNCT
ejpam-6755	318	4	12n(th1−f	12n(th1−f	NUM
ejpam-6755	318	5	∗	∗	NOUN
ejpam-6755	318	6	)	)	PUNCT
ejpam-6755	318	7	]	]	PUNCT
ejpam-6755	318	8	such	such	ADJ
ejpam-6755	318	9	that∑	that∑	NOUN
ejpam-6755	318	10	a∈w	a∈w	ADJ
ejpam-6755	318	11	1	1	NUM
ejpam-6755	318	12	j	j	NOUN
ejpam-6755	318	13	a	a	X
ejpam-6755	318	14	=	=	X
ejpam-6755	318	15	n(th1	n(th1	NOUN
ejpam-6755	319	1	+	+	CCONJ
ejpam-6755	319	2	tf	tf	NUM
ejpam-6755	319	3	∗	∗	NOUN
ejpam-6755	319	4	)	)	PUNCT
ejpam-6755	320	1	+	+	CCONJ
ejpam-6755	320	2	1	1	NUM
ejpam-6755	320	3	=	=	SYM
ejpam-6755	320	4	w	w	PROPN
ejpam-6755	320	5	1	1	NUM
ejpam-6755	320	6	.	.	PUNCT
ejpam-6755	320	7	case	case	NOUN
ejpam-6755	320	8	2.2	2.2	NUM
ejpam-6755	320	9	.	.	PUNCT
ejpam-6755	321	1	when	when	SCONJ
ejpam-6755	321	2	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	321	3	and	and	CCONJ
ejpam-6755	321	4	th1−f	th1−f	NOUN
ejpam-6755	321	5	∗	∗	NOUN
ejpam-6755	321	6	are	be	AUX
ejpam-6755	321	7	odd	odd	ADJ
ejpam-6755	321	8	.	.	PUNCT
ejpam-6755	322	1	let	let	VERB
ejpam-6755	322	2	u2	u2	NOUN
ejpam-6755	322	3	=	=	PUNCT
ejpam-6755	322	4	[	[	X
ejpam-6755	322	5	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	322	6	)	)	PUNCT
ejpam-6755	322	7	+	+	SYM
ejpam-6755	322	8	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	322	9	)	)	PUNCT
ejpam-6755	322	10	)	)	PUNCT
ejpam-6755	323	1	+	+	CCONJ
ejpam-6755	323	2	1	1	NUM
ejpam-6755	323	3	,	,	PUNCT
ejpam-6755	323	4	n(tf	n(tf	PRON
ejpam-6755	323	5	∗	∗	VERB
ejpam-6755	323	6	−	−	PROPN
ejpam-6755	323	7	1	1	NUM
ejpam-6755	323	8	)	)	PUNCT
ejpam-6755	323	9	]	]	PUNCT
ejpam-6755	323	10	.	.	PUNCT
ejpam-6755	324	1	create	create	VERB
ejpam-6755	324	2	a	a	DET
ejpam-6755	324	3	partition	partition	NOUN
ejpam-6755	324	4	of	of	ADP
ejpam-6755	324	5	u2	u2	NOUN
ejpam-6755	324	6	into	into	ADP
ejpam-6755	324	7	2	2	NUM
ejpam-6755	324	8	-	-	PUNCT
ejpam-6755	324	9	sets	set	NOUN
ejpam-6755	324	10	,	,	PUNCT
ejpam-6755	324	11	u2	u2	PROPN
ejpam-6755	324	12	j	j	PROPN
ejpam-6755	324	13	for	for	ADP
ejpam-6755	324	14	j	j	PROPN
ejpam-6755	324	15	∈	∈	PROPN
ejpam-6755	325	1	[	[	X
ejpam-6755	325	2	1	1	NUM
ejpam-6755	325	3	,	,	PUNCT
ejpam-6755	325	4	12n(tf1∩f2	12n(tf1∩f2	PROPN
ejpam-6755	325	5	−	−	PROPN
ejpam-6755	325	6	1	1	NUM
ejpam-6755	325	7	)	)	PUNCT
ejpam-6755	325	8	]	]	PUNCT
ejpam-6755	325	9	such	such	ADJ
ejpam-6755	325	10	that∑	that∑	VERB
ejpam-6755	325	11	a∈u2	a∈u2	NOUN
ejpam-6755	325	12	j	j	PROPN
ejpam-6755	325	13	a	a	DET
ejpam-6755	325	14	=	=	PUNCT
ejpam-6755	325	15	n(tf1−(f1∩f2	n(tf1−(f1∩f2	PROPN
ejpam-6755	325	16	)	)	PUNCT
ejpam-6755	325	17	+	+	SYM
ejpam-6755	325	18	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	325	19	)	)	PUNCT
ejpam-6755	326	1	+	+	CCONJ
ejpam-6755	326	2	tf	tf	PROPN
ejpam-6755	326	3	∗	∗	NOUN
ejpam-6755	326	4	−	−	PROPN
ejpam-6755	326	5	1	1	NUM
ejpam-6755	326	6	)	)	PUNCT
ejpam-6755	326	7	+	+	CCONJ
ejpam-6755	326	8	1	1	NUM
ejpam-6755	326	9	=	=	SYM
ejpam-6755	326	10	u2	u2	PROPN
ejpam-6755	326	11	.	.	PROPN
ejpam-6755	327	1	similarly	similarly	ADV
ejpam-6755	327	2	,	,	PUNCT
ejpam-6755	327	3	let	let	VERB
ejpam-6755	327	4	w	w	NOUN
ejpam-6755	327	5	2	2	NUM
ejpam-6755	327	6	=	=	SYM
ejpam-6755	328	1	[	[	X
ejpam-6755	328	2	n(tf	n(tf	PRON
ejpam-6755	328	3	∗	∗	NOUN
ejpam-6755	328	4	)	)	PUNCT
ejpam-6755	329	1	+	+	NOUN
ejpam-6755	329	2	1	1	NUM
ejpam-6755	329	3	,	,	PUNCT
ejpam-6755	329	4	n(th1	n(th1	NOUN
ejpam-6755	329	5	−	−	PROPN
ejpam-6755	329	6	1	1	NUM
ejpam-6755	329	7	)	)	PUNCT
ejpam-6755	329	8	]	]	PUNCT
ejpam-6755	329	9	and	and	CCONJ
ejpam-6755	329	10	create	create	VERB
ejpam-6755	329	11	a	a	DET
ejpam-6755	329	12	partition	partition	NOUN
ejpam-6755	329	13	of	of	ADP
ejpam-6755	329	14	w	w	NOUN
ejpam-6755	329	15	2	2	NUM
ejpam-6755	329	16	into	into	ADP
ejpam-6755	329	17	2	2	NUM
ejpam-6755	329	18	-	-	PUNCT
ejpam-6755	329	19	sets	set	NOUN
ejpam-6755	329	20	,	,	PUNCT
ejpam-6755	329	21	w	w	PROPN
ejpam-6755	329	22	2	2	NUM
ejpam-6755	329	23	j	j	NOUN
ejpam-6755	329	24	for	for	ADP
ejpam-6755	329	25	j	j	PROPN
ejpam-6755	329	26	∈	∈	PROPN
ejpam-6755	330	1	[	[	X
ejpam-6755	330	2	1	1	NUM
ejpam-6755	330	3	,	,	PUNCT
ejpam-6755	330	4	12n(th1−f	12n(th1−f	NUM
ejpam-6755	330	5	∗	∗	NOUN
ejpam-6755	330	6	−	−	NOUN
ejpam-6755	330	7	1	1	NUM
ejpam-6755	330	8	)	)	PUNCT
ejpam-6755	330	9	]	]	PUNCT
ejpam-6755	330	10	such	such	ADJ
ejpam-6755	330	11	that∑	that∑	NOUN
ejpam-6755	330	12	a∈w	a∈w	ADJ
ejpam-6755	330	13	2	2	NUM
ejpam-6755	330	14	j	j	NOUN
ejpam-6755	330	15	a	a	X
ejpam-6755	330	16	=	=	X
ejpam-6755	330	17	n(th1	n(th1	NOUN
ejpam-6755	331	1	+	+	CCONJ
ejpam-6755	331	2	tf	tf	PROPN
ejpam-6755	331	3	∗	∗	NOUN
ejpam-6755	331	4	−	−	PROPN
ejpam-6755	331	5	1	1	NUM
ejpam-6755	331	6	)	)	PUNCT
ejpam-6755	331	7	+	+	CCONJ
ejpam-6755	331	8	1	1	NUM
ejpam-6755	331	9	=	=	SYM
ejpam-6755	331	10	w	w	PROPN
ejpam-6755	331	11	2	2	NUM
ejpam-6755	331	12	.	.	PUNCT
ejpam-6755	331	13	now	now	ADV
ejpam-6755	331	14	construct	construct	VERB
ejpam-6755	331	15	a	a	DET
ejpam-6755	331	16	total	total	ADJ
ejpam-6755	331	17	labeling	labeling	NOUN
ejpam-6755	331	18	f	f	PROPN
ejpam-6755	331	19	of	of	ADP
ejpam-6755	331	20	pn[h1;h2	pn[h1;h2	PROPN
ejpam-6755	331	21	]	]	PUNCT
ejpam-6755	331	22	as	as	SCONJ
ejpam-6755	331	23	follows	follow	VERB
ejpam-6755	331	24	.	.	PUNCT
ejpam-6755	332	1	•	•	NUM
ejpam-6755	332	2	according	accord	VERB
ejpam-6755	332	3	to	to	ADP
ejpam-6755	332	4	the	the	DET
ejpam-6755	332	5	parity	parity	NOUN
ejpam-6755	332	6	of	of	ADP
ejpam-6755	332	7	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	332	8	use	use	VERB
ejpam-6755	332	9	either	either	CCONJ
ejpam-6755	332	10	the	the	DET
ejpam-6755	332	11	elements	element	NOUN
ejpam-6755	332	12	of	of	ADP
ejpam-6755	332	13	u1	u1	PROPN
ejpam-6755	332	14	j	j	PROPN
ejpam-6755	332	15	or	or	CCONJ
ejpam-6755	332	16	the	the	DET
ejpam-6755	332	17	elements	element	NOUN
ejpam-6755	332	18	of	of	ADP
ejpam-6755	332	19	u2	u2	PROPN
ejpam-6755	332	20	j	j	PROPN
ejpam-6755	332	21	to	to	PART
ejpam-6755	332	22	label	label	NOUN
ejpam-6755	332	23	vertices	vertex	NOUN
ejpam-6755	332	24	and	and	CCONJ
ejpam-6755	332	25	edges	edge	NOUN
ejpam-6755	332	26	of	of	ADP
ejpam-6755	332	27	(	(	PUNCT
ejpam-6755	332	28	f1	f1	PROPN
ejpam-6755	332	29	∩	∩	NOUN
ejpam-6755	332	30	f2	f2	PROPN
ejpam-6755	332	31	)	)	PUNCT
ejpam-6755	332	32	(	(	PUNCT
ejpam-6755	332	33	j	j	NOUN
ejpam-6755	332	34	)	)	PUNCT
ejpam-6755	332	35	.	.	PUNCT
ejpam-6755	333	1	moreover	moreover	ADV
ejpam-6755	333	2	,	,	PUNCT
ejpam-6755	333	3	if	if	SCONJ
ejpam-6755	333	4	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	333	5	is	be	AUX
ejpam-6755	333	6	odd	odd	ADJ
ejpam-6755	333	7	,	,	PUNCT
ejpam-6755	333	8	label	label	VERB
ejpam-6755	333	9	the	the	DET
ejpam-6755	333	10	unlabeled	unlabeled	ADJ
ejpam-6755	333	11	vertex	vertex	NOUN
ejpam-6755	333	12	or	or	CCONJ
ejpam-6755	333	13	unlabeled	unlabeled	ADJ
ejpam-6755	333	14	edge	edge	NOUN
ejpam-6755	333	15	in	in	ADP
ejpam-6755	333	16	(	(	PUNCT
ejpam-6755	333	17	f1	f1	NOUN
ejpam-6755	333	18	∩	∩	NOUN
ejpam-6755	333	19	f2	f2	PROPN
ejpam-6755	333	20	)	)	PUNCT
ejpam-6755	333	21	(	(	PUNCT
ejpam-6755	333	22	j	j	NOUN
ejpam-6755	333	23	)	)	PUNCT
ejpam-6755	333	24	with	with	ADP
ejpam-6755	333	25	n(tf	n(tf	PRON
ejpam-6755	333	26	∗	∗	NOUN
ejpam-6755	333	27	−	−	PROPN
ejpam-6755	333	28	1	1	NUM
ejpam-6755	333	29	)	)	PUNCT
ejpam-6755	333	30	+	+	CCONJ
ejpam-6755	333	31	j.	j.	PROPN
ejpam-6755	333	32	•	•	NOUN
ejpam-6755	333	33	according	accord	VERB
ejpam-6755	333	34	to	to	ADP
ejpam-6755	333	35	the	the	DET
ejpam-6755	333	36	parity	parity	NOUN
ejpam-6755	333	37	of	of	ADP
ejpam-6755	333	38	th1−f	th1−f	NOUN
ejpam-6755	333	39	∗	∗	NOUN
ejpam-6755	333	40	use	use	VERB
ejpam-6755	333	41	either	either	CCONJ
ejpam-6755	333	42	the	the	DET
ejpam-6755	333	43	elements	element	NOUN
ejpam-6755	333	44	of	of	ADP
ejpam-6755	333	45	w	w	PROPN
ejpam-6755	333	46	1	1	NUM
ejpam-6755	333	47	j	j	NOUN
ejpam-6755	333	48	or	or	CCONJ
ejpam-6755	333	49	w	w	PROPN
ejpam-6755	333	50	2	2	NUM
ejpam-6755	333	51	j	j	NOUN
ejpam-6755	333	52	to	to	PART
ejpam-6755	333	53	label	label	NOUN
ejpam-6755	333	54	vertices	vertex	NOUN
ejpam-6755	333	55	and	and	CCONJ
ejpam-6755	333	56	edges	edge	NOUN
ejpam-6755	333	57	of	of	ADP
ejpam-6755	333	58	(	(	PUNCT
ejpam-6755	333	59	h1	h1	PROPN
ejpam-6755	333	60	−	−	PROPN
ejpam-6755	333	61	f	f	PROPN
ejpam-6755	333	62	∗)(j	∗)(j	PROPN
ejpam-6755	333	63	)	)	PUNCT
ejpam-6755	333	64	.	.	PUNCT
ejpam-6755	334	1	moreover	moreover	ADV
ejpam-6755	334	2	,	,	PUNCT
ejpam-6755	334	3	if	if	SCONJ
ejpam-6755	334	4	th1−f	th1−f	NOUN
ejpam-6755	334	5	∗	∗	NOUN
ejpam-6755	334	6	is	be	AUX
ejpam-6755	334	7	odd	odd	ADJ
ejpam-6755	334	8	,	,	PUNCT
ejpam-6755	334	9	label	label	VERB
ejpam-6755	334	10	the	the	DET
ejpam-6755	334	11	unlabeled	unlabeled	ADJ
ejpam-6755	334	12	vertex	vertex	NOUN
ejpam-6755	334	13	or	or	CCONJ
ejpam-6755	334	14	unlabeled	unlabeled	ADJ
ejpam-6755	334	15	edge	edge	NOUN
ejpam-6755	334	16	in	in	ADP
ejpam-6755	334	17	(	(	PUNCT
ejpam-6755	334	18	h1	h1	PROPN
ejpam-6755	334	19	−	−	PROPN
ejpam-6755	334	20	f	f	SYM
ejpam-6755	334	21	∗)(j	∗)(j	PROPN
ejpam-6755	334	22	)	)	PUNCT
ejpam-6755	334	23	with	with	ADP
ejpam-6755	334	24	n(th1)−	n(th1)−	PROPN
ejpam-6755	334	25	j	j	PROPN
ejpam-6755	335	1	+	+	NOUN
ejpam-6755	335	2	1	1	X
ejpam-6755	335	3	.	.	PUNCT
ejpam-6755	335	4	t.	t.	PROPN
ejpam-6755	335	5	k.	k.	PROPN
ejpam-6755	335	6	maryati	maryati	PROPN
ejpam-6755	336	1	et	et	PROPN
ejpam-6755	336	2	al	al	PROPN
ejpam-6755	336	3	.	.	PUNCT
ejpam-6755	336	4	/	/	SYM
ejpam-6755	336	5	eur	eur	PROPN
ejpam-6755	336	6	.	.	PUNCT
ejpam-6755	337	1	j.	j.	PROPN
ejpam-6755	337	2	pure	pure	PROPN
ejpam-6755	337	3	appl	appl	PROPN
ejpam-6755	337	4	.	.	PROPN
ejpam-6755	337	5	math	math	PROPN
ejpam-6755	337	6	,	,	PUNCT
ejpam-6755	337	7	18	18	NUM
ejpam-6755	337	8	(	(	PUNCT
ejpam-6755	337	9	4	4	NUM
ejpam-6755	337	10	)	)	PUNCT
ejpam-6755	337	11	(	(	PUNCT
ejpam-6755	337	12	2025	2025	NUM
ejpam-6755	337	13	)	)	PUNCT
ejpam-6755	337	14	,	,	PUNCT
ejpam-6755	337	15	6755	6755	NUM
ejpam-6755	337	16	10	10	NUM
ejpam-6755	337	17	of	of	ADP
ejpam-6755	337	18	13	13	NUM
ejpam-6755	337	19	•	•	NUM
ejpam-6755	337	20	according	accord	VERB
ejpam-6755	337	21	to	to	ADP
ejpam-6755	337	22	the	the	DET
ejpam-6755	337	23	parity	parity	NOUN
ejpam-6755	337	24	of	of	ADP
ejpam-6755	337	25	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	337	26	)	)	PUNCT
ejpam-6755	337	27	assign	assign	VERB
ejpam-6755	337	28	the	the	DET
ejpam-6755	337	29	elements	element	NOUN
ejpam-6755	337	30	of	of	ADP
ejpam-6755	337	31	x1	x1	PROPN
ejpam-6755	337	32	i	i	PRON
ejpam-6755	337	33	or	or	CCONJ
ejpam-6755	337	34	x2	x2	PRON
ejpam-6755	337	35	i	i	PRON
ejpam-6755	337	36	to	to	ADP
ejpam-6755	337	37	unlabeled	unlabele	VERB
ejpam-6755	337	38	vertices	vertex	NOUN
ejpam-6755	337	39	and	and	CCONJ
ejpam-6755	337	40	unlabeled	unlabele	VERB
ejpam-6755	337	41	edges	edge	NOUN
ejpam-6755	337	42	of	of	ADP
ejpam-6755	337	43	f	f	PROPN
ejpam-6755	337	44	(	(	PUNCT
ejpam-6755	337	45	i	i	NOUN
ejpam-6755	337	46	)	)	PUNCT
ejpam-6755	337	47	1	1	X
ejpam-6755	337	48	.	.	PUNCT
ejpam-6755	338	1	in	in	ADP
ejpam-6755	338	2	addition	addition	NOUN
ejpam-6755	338	3	,	,	PUNCT
ejpam-6755	338	4	if	if	SCONJ
ejpam-6755	338	5	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	338	6	)	)	PUNCT
ejpam-6755	338	7	is	be	AUX
ejpam-6755	338	8	odd	odd	ADJ
ejpam-6755	338	9	,	,	PUNCT
ejpam-6755	338	10	label	label	VERB
ejpam-6755	338	11	the	the	DET
ejpam-6755	338	12	unlabeled	unlabeled	ADJ
ejpam-6755	338	13	vertex	vertex	NOUN
ejpam-6755	338	14	or	or	CCONJ
ejpam-6755	338	15	unlabeled	unlabele	VERB
ejpam-6755	338	16	edge	edge	NOUN
ejpam-6755	338	17	in	in	ADP
ejpam-6755	338	18	f	f	PROPN
ejpam-6755	338	19	(	(	PUNCT
ejpam-6755	338	20	i	i	NOUN
ejpam-6755	338	21	)	)	PUNCT
ejpam-6755	338	22	1	1	NUM
ejpam-6755	338	23	with	with	ADP
ejpam-6755	338	24	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	338	25	)	)	PUNCT
ejpam-6755	338	26	−	−	ADP
ejpam-6755	339	1	1	1	X
ejpam-6755	339	2	)	)	PUNCT
ejpam-6755	339	3	+	+	CCONJ
ejpam-6755	339	4	i.	i.	NOUN
ejpam-6755	339	5	•	•	NOUN
ejpam-6755	339	6	according	accord	VERB
ejpam-6755	339	7	to	to	ADP
ejpam-6755	339	8	the	the	DET
ejpam-6755	339	9	parity	parity	NOUN
ejpam-6755	339	10	of	of	ADP
ejpam-6755	339	11	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	339	12	)	)	PUNCT
ejpam-6755	339	13	assign	assign	VERB
ejpam-6755	339	14	the	the	DET
ejpam-6755	339	15	elements	element	NOUN
ejpam-6755	339	16	of	of	ADP
ejpam-6755	339	17	y	y	PROPN
ejpam-6755	339	18	1	1	NUM
ejpam-6755	339	19	i	i	NOUN
ejpam-6755	339	20	or	or	CCONJ
ejpam-6755	339	21	y	y	PROPN
ejpam-6755	339	22	2	2	NUM
ejpam-6755	339	23	i	i	PRON
ejpam-6755	339	24	to	to	ADP
ejpam-6755	339	25	unlabeled	unlabele	VERB
ejpam-6755	339	26	vertices	vertex	NOUN
ejpam-6755	339	27	and	and	CCONJ
ejpam-6755	339	28	unlabeled	unlabele	VERB
ejpam-6755	339	29	edges	edge	NOUN
ejpam-6755	339	30	of	of	ADP
ejpam-6755	339	31	f	f	PROPN
ejpam-6755	339	32	(	(	PUNCT
ejpam-6755	339	33	i	i	NOUN
ejpam-6755	339	34	)	)	PUNCT
ejpam-6755	339	35	2	2	NUM
ejpam-6755	339	36	.	.	PUNCT
ejpam-6755	340	1	similarly	similarly	ADV
ejpam-6755	340	2	,	,	PUNCT
ejpam-6755	340	3	if	if	SCONJ
ejpam-6755	340	4	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	340	5	)	)	PUNCT
ejpam-6755	340	6	is	be	AUX
ejpam-6755	340	7	odd	odd	ADJ
ejpam-6755	340	8	,	,	PUNCT
ejpam-6755	340	9	label	label	VERB
ejpam-6755	340	10	the	the	DET
ejpam-6755	340	11	unlabeled	unlabeled	ADJ
ejpam-6755	340	12	vertex	vertex	NOUN
ejpam-6755	340	13	or	or	CCONJ
ejpam-6755	340	14	unlabeled	unlabele	VERB
ejpam-6755	340	15	edge	edge	NOUN
ejpam-6755	340	16	in	in	ADP
ejpam-6755	340	17	f	f	PROPN
ejpam-6755	340	18	(	(	PUNCT
ejpam-6755	340	19	i	i	NOUN
ejpam-6755	340	20	)	)	PUNCT
ejpam-6755	340	21	2	2	NUM
ejpam-6755	340	22	with	with	ADP
ejpam-6755	340	23	n(tf1−(f1∩f2	n(tf1−(f1∩f2	NUM
ejpam-6755	340	24	)	)	PUNCT
ejpam-6755	341	1	+	+	CCONJ
ejpam-6755	341	2	tf2−(f1∩f2))−	tf2−(f1∩f2))−	ADJ
ejpam-6755	341	3	i+	i+	PRON
ejpam-6755	342	1	1	1	NUM
ejpam-6755	342	2	.	.	NUM
ejpam-6755	342	3	•	•	ADV
ejpam-6755	342	4	lastly	lastly	ADV
ejpam-6755	342	5	,	,	PUNCT
ejpam-6755	342	6	use	use	VERB
ejpam-6755	342	7	the	the	DET
ejpam-6755	342	8	elements	element	NOUN
ejpam-6755	342	9	of	of	ADP
ejpam-6755	342	10	z	z	NOUN
ejpam-6755	342	11	to	to	PART
ejpam-6755	342	12	label	label	VERB
ejpam-6755	342	13	unlabeled	unlabele	VERB
ejpam-6755	342	14	vertices	vertex	NOUN
ejpam-6755	342	15	and	and	CCONJ
ejpam-6755	342	16	unlabeled	unlabele	VERB
ejpam-6755	342	17	edges	edge	NOUN
ejpam-6755	342	18	of	of	ADP
ejpam-6755	342	19	a	a	DET
ejpam-6755	342	20	subgraph	subgraph	NOUN
ejpam-6755	342	21	isomorphic	isomorphic	ADJ
ejpam-6755	342	22	to	to	ADP
ejpam-6755	342	23	h2	h2	NOUN
ejpam-6755	342	24	.	.	PUNCT
ejpam-6755	343	1	it	it	PRON
ejpam-6755	343	2	can	can	AUX
ejpam-6755	343	3	be	be	AUX
ejpam-6755	343	4	shown	show	VERB
ejpam-6755	343	5	that	that	SCONJ
ejpam-6755	343	6	f	f	PROPN
ejpam-6755	343	7	is	be	AUX
ejpam-6755	343	8	a	a	DET
ejpam-6755	343	9	bijection	bijection	NOUN
ejpam-6755	343	10	.	.	PUNCT
ejpam-6755	344	1	to	to	PART
ejpam-6755	344	2	show	show	VERB
ejpam-6755	344	3	that	that	SCONJ
ejpam-6755	344	4	pn[h1;h2	pn[h1;h2	PROPN
ejpam-6755	344	5	]	]	X
ejpam-6755	344	6	is	be	AUX
ejpam-6755	344	7	(	(	PUNCT
ejpam-6755	344	8	h1	h1	PROPN
ejpam-6755	344	9	,	,	PUNCT
ejpam-6755	344	10	h2)-magic	h2)-magic	ADJ
ejpam-6755	344	11	,	,	PUNCT
ejpam-6755	344	12	consider	consider	VERB
ejpam-6755	344	13	a	a	DET
ejpam-6755	344	14	subgraph	subgraph	NOUN
ejpam-6755	344	15	h	h	NOUN
ejpam-6755	344	16	(	(	PUNCT
ejpam-6755	344	17	i	i	NOUN
ejpam-6755	344	18	)	)	PUNCT
ejpam-6755	344	19	1	1	NUM
ejpam-6755	344	20	of	of	ADP
ejpam-6755	344	21	pn[h1;h2	pn[h1;h2	PROPN
ejpam-6755	344	22	]	]	PUNCT
ejpam-6755	344	23	isomorphic	isomorphic	ADJ
ejpam-6755	344	24	to	to	AUX
ejpam-6755	344	25	h1	h1	PROPN
ejpam-6755	344	26	.	.	PUNCT
ejpam-6755	345	1	if	if	SCONJ
ejpam-6755	345	2	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	345	3	)	)	PUNCT
ejpam-6755	345	4	and	and	CCONJ
ejpam-6755	345	5	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	345	6	are	be	AUX
ejpam-6755	345	7	even	even	ADV
ejpam-6755	345	8	we	we	PRON
ejpam-6755	345	9	get	get	VERB
ejpam-6755	345	10	that	that	SCONJ
ejpam-6755	345	11	w(h	w(h	PROPN
ejpam-6755	345	12	(	(	PUNCT
ejpam-6755	345	13	i	i	NOUN
ejpam-6755	345	14	)	)	PUNCT
ejpam-6755	345	15	1	1	NUM
ejpam-6755	345	16	)	)	PUNCT
ejpam-6755	345	17	=	=	SYM
ejpam-6755	345	18	1	1	NUM
ejpam-6755	345	19	2x	2x	NUM
ejpam-6755	345	20	1tf1−(f1∩f2	1tf1−(f1∩f2	NUM
ejpam-6755	345	21	)	)	PUNCT
ejpam-6755	345	22	+	+	CCONJ
ejpam-6755	345	23	1	1	NUM
ejpam-6755	345	24	2y	2y	NUM
ejpam-6755	345	25	1tf2−(f1∩f2	1tf2−(f1∩f2	NUM
ejpam-6755	345	26	)	)	PUNCT
ejpam-6755	345	27	+	+	CCONJ
ejpam-6755	345	28	1	1	NUM
ejpam-6755	345	29	2u	2u	NOUN
ejpam-6755	345	30	1tf1∩f2	1tf1∩f2	NUM
ejpam-6755	345	31	+	+	CCONJ
ejpam-6755	345	32	1	1	NUM
ejpam-6755	345	33	2w	2w	NUM
ejpam-6755	345	34	1th1−f	1th1−f	NUM
ejpam-6755	345	35	∗	∗	NOUN
ejpam-6755	345	36	.	.	PUNCT
ejpam-6755	346	1	if	if	SCONJ
ejpam-6755	346	2	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	346	3	)	)	PUNCT
ejpam-6755	346	4	is	be	AUX
ejpam-6755	346	5	odd	odd	ADJ
ejpam-6755	346	6	but	but	CCONJ
ejpam-6755	346	7	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	346	8	is	be	AUX
ejpam-6755	346	9	even	even	ADV
ejpam-6755	346	10	,	,	PUNCT
ejpam-6755	346	11	then	then	ADV
ejpam-6755	346	12	w(h	w(h	PROPN
ejpam-6755	346	13	(	(	PUNCT
ejpam-6755	346	14	i	i	NOUN
ejpam-6755	346	15	)	)	PUNCT
ejpam-6755	346	16	1	1	NUM
ejpam-6755	346	17	)	)	PUNCT
ejpam-6755	346	18	=	=	SYM
ejpam-6755	347	1	1	1	NUM
ejpam-6755	347	2	2x	2x	NUM
ejpam-6755	347	3	2(tf1−(f1∩f2	2(tf1−(f1∩f2	NUM
ejpam-6755	347	4	)	)	PUNCT
ejpam-6755	347	5	−	−	ADP
ejpam-6755	347	6	1	1	X
ejpam-6755	347	7	)	)	PUNCT
ejpam-6755	347	8	+	+	CCONJ
ejpam-6755	347	9	1	1	NUM
ejpam-6755	347	10	2y	2y	NUM
ejpam-6755	347	11	2(tf2−(f1∩f2	2(tf2−(f1∩f2	NUM
ejpam-6755	347	12	)	)	PUNCT
ejpam-6755	348	1	−	−	NUM
ejpam-6755	348	2	1	1	NUM
ejpam-6755	348	3	)	)	PUNCT
ejpam-6755	348	4	+	+	CCONJ
ejpam-6755	348	5	1	1	NUM
ejpam-6755	348	6	2u	2u	NOUN
ejpam-6755	348	7	1tf1∩f2	1tf1∩f2	NUM
ejpam-6755	348	8	+	+	CCONJ
ejpam-6755	348	9	1	1	NUM
ejpam-6755	348	10	2w	2w	NUM
ejpam-6755	348	11	1th1−f	1th1−f	NUM
ejpam-6755	348	12	∗	∗	NOUN
ejpam-6755	348	13	+	+	X
ejpam-6755	348	14	n(2tf1−(f1∩f2	n(2tf1−(f1∩f2	PROPN
ejpam-6755	348	15	)	)	PUNCT
ejpam-6755	349	1	+	+	SYM
ejpam-6755	349	2	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	349	3	)	)	PUNCT
ejpam-6755	349	4	−	−	NOUN
ejpam-6755	349	5	1	1	NUM
ejpam-6755	349	6	)	)	PUNCT
ejpam-6755	349	7	+	+	NOUN
ejpam-6755	349	8	1	1	X
ejpam-6755	349	9	.	.	X
ejpam-6755	349	10	if	if	SCONJ
ejpam-6755	349	11	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	349	12	)	)	PUNCT
ejpam-6755	349	13	is	be	AUX
ejpam-6755	349	14	even	even	ADV
ejpam-6755	349	15	but	but	CCONJ
ejpam-6755	349	16	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	349	17	is	be	AUX
ejpam-6755	349	18	odd	odd	ADJ
ejpam-6755	349	19	,	,	PUNCT
ejpam-6755	349	20	we	we	PRON
ejpam-6755	349	21	have	have	VERB
ejpam-6755	349	22	w(h	w(h	PROPN
ejpam-6755	349	23	(	(	PUNCT
ejpam-6755	349	24	i	i	NOUN
ejpam-6755	349	25	)	)	PUNCT
ejpam-6755	349	26	1	1	NUM
ejpam-6755	349	27	)	)	PUNCT
ejpam-6755	349	28	=	=	SYM
ejpam-6755	349	29	1	1	NUM
ejpam-6755	349	30	2x	2x	NUM
ejpam-6755	349	31	1tf1−(f1∩f2	1tf1−(f1∩f2	NUM
ejpam-6755	349	32	)	)	PUNCT
ejpam-6755	350	1	+	+	CCONJ
ejpam-6755	350	2	1	1	NUM
ejpam-6755	350	3	2y	2y	NUM
ejpam-6755	350	4	1tf2−(f1∩f2	1tf2−(f1∩f2	NUM
ejpam-6755	350	5	)	)	PUNCT
ejpam-6755	350	6	+	+	CCONJ
ejpam-6755	350	7	1	1	NUM
ejpam-6755	350	8	2u	2u	NOUN
ejpam-6755	350	9	2(tf1∩f2	2(tf1∩f2	NUM
ejpam-6755	350	10	−	−	NOUN
ejpam-6755	350	11	1	1	NUM
ejpam-6755	350	12	)	)	PUNCT
ejpam-6755	350	13	+	+	CCONJ
ejpam-6755	350	14	1	1	NUM
ejpam-6755	350	15	2w	2w	NUM
ejpam-6755	350	16	2(th1−f	2(th1−f	NUM
ejpam-6755	350	17	∗	∗	NOUN
ejpam-6755	350	18	−	−	NOUN
ejpam-6755	350	19	1	1	NUM
ejpam-6755	350	20	)	)	PUNCT
ejpam-6755	350	21	+	+	NUM
ejpam-6755	350	22	n(2tf	n(2tf	NOUN
ejpam-6755	350	23	∗	∗	NOUN
ejpam-6755	350	24	+	+	CCONJ
ejpam-6755	350	25	th1−f	th1−f	NOUN
ejpam-6755	350	26	∗	∗	NOUN
ejpam-6755	350	27	−	−	PROPN
ejpam-6755	350	28	1	1	NUM
ejpam-6755	350	29	)	)	PUNCT
ejpam-6755	350	30	+	+	NOUN
ejpam-6755	350	31	1	1	X
ejpam-6755	350	32	.	.	X
ejpam-6755	350	33	if	if	SCONJ
ejpam-6755	350	34	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	350	35	)	)	PUNCT
ejpam-6755	350	36	and	and	CCONJ
ejpam-6755	350	37	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	350	38	are	be	AUX
ejpam-6755	350	39	odd	odd	ADJ
ejpam-6755	350	40	,	,	PUNCT
ejpam-6755	350	41	it	it	PRON
ejpam-6755	350	42	follows	follow	VERB
ejpam-6755	350	43	that	that	SCONJ
ejpam-6755	350	44	w(h	w(h	PROPN
ejpam-6755	350	45	(	(	PUNCT
ejpam-6755	350	46	i	i	NOUN
ejpam-6755	350	47	)	)	PUNCT
ejpam-6755	350	48	1	1	NUM
ejpam-6755	350	49	)	)	PUNCT
ejpam-6755	350	50	=	=	SYM
ejpam-6755	351	1	1	1	NUM
ejpam-6755	351	2	2x	2x	NUM
ejpam-6755	351	3	2(tf1−(f1∩f2	2(tf1−(f1∩f2	NUM
ejpam-6755	351	4	)	)	PUNCT
ejpam-6755	351	5	−	−	ADP
ejpam-6755	351	6	1	1	X
ejpam-6755	351	7	)	)	PUNCT
ejpam-6755	351	8	+	+	CCONJ
ejpam-6755	351	9	1	1	NUM
ejpam-6755	351	10	2y	2y	NUM
ejpam-6755	351	11	2(tf2−(f1∩f2	2(tf2−(f1∩f2	NUM
ejpam-6755	351	12	)	)	PUNCT
ejpam-6755	352	1	−	−	NUM
ejpam-6755	352	2	1	1	NUM
ejpam-6755	352	3	)	)	PUNCT
ejpam-6755	352	4	+	+	CCONJ
ejpam-6755	352	5	1	1	NUM
ejpam-6755	352	6	2u	2u	NOUN
ejpam-6755	352	7	2(tf1∩f2	2(tf1∩f2	NUM
ejpam-6755	352	8	−	−	NOUN
ejpam-6755	352	9	1	1	NUM
ejpam-6755	352	10	)	)	PUNCT
ejpam-6755	352	11	+	+	CCONJ
ejpam-6755	352	12	1	1	NUM
ejpam-6755	352	13	2w	2w	NUM
ejpam-6755	352	14	2(th1−f	2(th1−f	NUM
ejpam-6755	352	15	∗	∗	NOUN
ejpam-6755	352	16	−	−	NOUN
ejpam-6755	352	17	1	1	NUM
ejpam-6755	352	18	)	)	PUNCT
ejpam-6755	352	19	+	+	CCONJ
ejpam-6755	352	20	n(2tf1−(f1∩f2	n(2tf1−(f1∩f2	PROPN
ejpam-6755	352	21	)	)	PUNCT
ejpam-6755	353	1	+	+	SYM
ejpam-6755	353	2	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	353	3	)	)	PUNCT
ejpam-6755	353	4	−	−	NOUN
ejpam-6755	353	5	1	1	NUM
ejpam-6755	353	6	)	)	PUNCT
ejpam-6755	353	7	+	+	NUM
ejpam-6755	353	8	n(2tf	n(2tf	NOUN
ejpam-6755	353	9	∗	∗	NOUN
ejpam-6755	353	10	+	+	CCONJ
ejpam-6755	353	11	th1−f	th1−f	NOUN
ejpam-6755	353	12	∗	∗	NOUN
ejpam-6755	353	13	−	−	PROPN
ejpam-6755	353	14	1	1	NUM
ejpam-6755	353	15	)	)	PUNCT
ejpam-6755	353	16	+	+	CCONJ
ejpam-6755	353	17	2	2	X
ejpam-6755	353	18	.	.	X
ejpam-6755	353	19	furthermore	furthermore	ADV
ejpam-6755	353	20	,	,	PUNCT
ejpam-6755	353	21	consider	consider	VERB
ejpam-6755	353	22	h	h	NOUN
ejpam-6755	353	23	(	(	PUNCT
ejpam-6755	353	24	i	i	NOUN
ejpam-6755	353	25	)	)	PUNCT
ejpam-6755	353	26	2	2	NUM
ejpam-6755	353	27	∼=	∼=	PROPN
ejpam-6755	353	28	h2	h2	NOUN
ejpam-6755	353	29	.	.	PUNCT
ejpam-6755	354	1	if	if	SCONJ
ejpam-6755	354	2	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	354	3	)	)	PUNCT
ejpam-6755	354	4	and	and	CCONJ
ejpam-6755	354	5	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	354	6	are	be	AUX
ejpam-6755	354	7	even	even	ADV
ejpam-6755	354	8	,	,	PUNCT
ejpam-6755	354	9	then	then	ADV
ejpam-6755	354	10	w(h	w(h	PROPN
ejpam-6755	354	11	(	(	PUNCT
ejpam-6755	354	12	i	i	NOUN
ejpam-6755	354	13	)	)	PUNCT
ejpam-6755	354	14	2	2	NUM
ejpam-6755	354	15	)	)	PUNCT
ejpam-6755	354	16	=	=	SYM
ejpam-6755	354	17	1	1	NUM
ejpam-6755	354	18	2zth2−(f1∪f2	2zth2−(f1∪f2	NUM
ejpam-6755	354	19	)	)	PUNCT
ejpam-6755	355	1	+	+	CCONJ
ejpam-6755	355	2	1	1	NUM
ejpam-6755	355	3	2x	2x	NUM
ejpam-6755	355	4	1tf1−(f1∩f2	1tf1−(f1∩f2	NUM
ejpam-6755	355	5	)	)	PUNCT
ejpam-6755	355	6	+	+	CCONJ
ejpam-6755	355	7	1	1	NUM
ejpam-6755	355	8	2y	2y	NUM
ejpam-6755	355	9	1tf2−(f1∩f2	1tf2−(f1∩f2	NUM
ejpam-6755	355	10	)	)	PUNCT
ejpam-6755	355	11	+	+	CCONJ
ejpam-6755	355	12	u1tf1∩f2	u1tf1∩f2	NOUN
ejpam-6755	355	13	.	.	PUNCT
ejpam-6755	356	1	if	if	SCONJ
ejpam-6755	356	2	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	356	3	)	)	PUNCT
ejpam-6755	356	4	is	be	AUX
ejpam-6755	356	5	odd	odd	ADJ
ejpam-6755	356	6	but	but	CCONJ
ejpam-6755	356	7	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	356	8	is	be	AUX
ejpam-6755	356	9	even	even	ADV
ejpam-6755	356	10	,	,	PUNCT
ejpam-6755	356	11	we	we	PRON
ejpam-6755	356	12	have	have	VERB
ejpam-6755	356	13	w(h	w(h	PROPN
ejpam-6755	356	14	(	(	PUNCT
ejpam-6755	356	15	i	i	NOUN
ejpam-6755	356	16	)	)	PUNCT
ejpam-6755	356	17	2	2	NUM
ejpam-6755	356	18	)	)	PUNCT
ejpam-6755	356	19	=	=	SYM
ejpam-6755	356	20	1	1	NUM
ejpam-6755	356	21	2zth2−(f1∪f2	2zth2−(f1∪f2	NUM
ejpam-6755	356	22	)	)	PUNCT
ejpam-6755	357	1	+	+	CCONJ
ejpam-6755	357	2	1	1	NUM
ejpam-6755	357	3	2x	2x	NUM
ejpam-6755	357	4	2(tf1−(f1∩f2	2(tf1−(f1∩f2	NUM
ejpam-6755	357	5	)	)	PUNCT
ejpam-6755	357	6	−	−	ADP
ejpam-6755	357	7	1	1	X
ejpam-6755	357	8	)	)	PUNCT
ejpam-6755	357	9	+	+	CCONJ
ejpam-6755	357	10	1	1	NUM
ejpam-6755	357	11	2y	2y	NUM
ejpam-6755	357	12	2(tf2−(f1∩f2	2(tf2−(f1∩f2	NUM
ejpam-6755	357	13	)	)	PUNCT
ejpam-6755	357	14	−	−	NUM
ejpam-6755	357	15	1	1	NUM
ejpam-6755	357	16	)	)	PUNCT
ejpam-6755	358	1	+	+	CCONJ
ejpam-6755	358	2	u1tf1∩f2	u1tf1∩f2	X
ejpam-6755	358	3	+	+	ADJ
ejpam-6755	358	4	n(2tf1−(f1∩f2	n(2tf1−(f1∩f2	PROPN
ejpam-6755	358	5	)	)	PUNCT
ejpam-6755	359	1	+	+	SYM
ejpam-6755	359	2	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	359	3	)	)	PUNCT
ejpam-6755	359	4	−	−	NOUN
ejpam-6755	359	5	1	1	NUM
ejpam-6755	359	6	)	)	PUNCT
ejpam-6755	359	7	+	+	NOUN
ejpam-6755	359	8	1	1	X
ejpam-6755	359	9	.	.	PUNCT
ejpam-6755	359	10	t.	t.	PROPN
ejpam-6755	359	11	k.	k.	PROPN
ejpam-6755	359	12	maryati	maryati	PROPN
ejpam-6755	359	13	et	et	PROPN
ejpam-6755	359	14	al	al	PROPN
ejpam-6755	359	15	.	.	PUNCT
ejpam-6755	359	16	/	/	SYM
ejpam-6755	359	17	eur	eur	PROPN
ejpam-6755	359	18	.	.	PUNCT
ejpam-6755	360	1	j.	j.	PROPN
ejpam-6755	360	2	pure	pure	PROPN
ejpam-6755	360	3	appl	appl	PROPN
ejpam-6755	360	4	.	.	PROPN
ejpam-6755	360	5	math	math	PROPN
ejpam-6755	360	6	,	,	PUNCT
ejpam-6755	360	7	18	18	NUM
ejpam-6755	360	8	(	(	PUNCT
ejpam-6755	360	9	4	4	NUM
ejpam-6755	360	10	)	)	PUNCT
ejpam-6755	360	11	(	(	PUNCT
ejpam-6755	360	12	2025	2025	NUM
ejpam-6755	360	13	)	)	PUNCT
ejpam-6755	360	14	,	,	PUNCT
ejpam-6755	360	15	6755	6755	NUM
ejpam-6755	360	16	11	11	NUM
ejpam-6755	360	17	of	of	ADP
ejpam-6755	360	18	13	13	NUM
ejpam-6755	360	19	if	if	SCONJ
ejpam-6755	360	20	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	360	21	)	)	PUNCT
ejpam-6755	360	22	is	be	AUX
ejpam-6755	360	23	even	even	ADV
ejpam-6755	360	24	but	but	CCONJ
ejpam-6755	360	25	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	360	26	is	be	AUX
ejpam-6755	360	27	odd	odd	ADJ
ejpam-6755	360	28	,	,	PUNCT
ejpam-6755	360	29	it	it	PRON
ejpam-6755	360	30	follows	follow	VERB
ejpam-6755	360	31	that	that	SCONJ
ejpam-6755	360	32	w(h	w(h	PROPN
ejpam-6755	360	33	(	(	PUNCT
ejpam-6755	360	34	i	i	NOUN
ejpam-6755	360	35	)	)	PUNCT
ejpam-6755	360	36	2	2	NUM
ejpam-6755	360	37	)	)	PUNCT
ejpam-6755	360	38	=	=	SYM
ejpam-6755	360	39	1	1	NUM
ejpam-6755	360	40	2zth2−(f1∪f2	2zth2−(f1∪f2	NUM
ejpam-6755	360	41	)	)	PUNCT
ejpam-6755	360	42	+	+	CCONJ
ejpam-6755	360	43	1	1	NUM
ejpam-6755	360	44	2x	2x	NUM
ejpam-6755	360	45	1tf1−(f1∩f2	1tf1−(f1∩f2	NUM
ejpam-6755	360	46	)	)	PUNCT
ejpam-6755	361	1	+	+	CCONJ
ejpam-6755	361	2	1	1	NUM
ejpam-6755	361	3	2y	2y	NUM
ejpam-6755	361	4	1tf2−(f1∩f2	1tf2−(f1∩f2	NUM
ejpam-6755	361	5	)	)	PUNCT
ejpam-6755	362	1	+	+	CCONJ
ejpam-6755	362	2	u2(tf1∩f2	u2(tf1∩f2	NOUN
ejpam-6755	362	3	−	−	PROPN
ejpam-6755	362	4	1	1	NUM
ejpam-6755	362	5	)	)	PUNCT
ejpam-6755	363	1	+	+	NUM
ejpam-6755	363	2	n(2tf	n(2tf	NOUN
ejpam-6755	363	3	∗	∗	NOUN
ejpam-6755	363	4	+	+	CCONJ
ejpam-6755	363	5	th1−f	th1−f	NOUN
ejpam-6755	363	6	∗	∗	NOUN
ejpam-6755	363	7	−	−	PROPN
ejpam-6755	363	8	1	1	NUM
ejpam-6755	363	9	)	)	PUNCT
ejpam-6755	363	10	+	+	NOUN
ejpam-6755	363	11	1	1	X
ejpam-6755	363	12	.	.	X
ejpam-6755	363	13	if	if	SCONJ
ejpam-6755	363	14	tf1−(f1∩f2	tf1−(f1∩f2	NOUN
ejpam-6755	363	15	)	)	PUNCT
ejpam-6755	363	16	and	and	CCONJ
ejpam-6755	363	17	tf1∩f2	tf1∩f2	PROPN
ejpam-6755	363	18	are	be	AUX
ejpam-6755	363	19	odd	odd	ADJ
ejpam-6755	363	20	,	,	PUNCT
ejpam-6755	363	21	it	it	PRON
ejpam-6755	363	22	holds	hold	VERB
ejpam-6755	363	23	that	that	SCONJ
ejpam-6755	363	24	w(h	w(h	PROPN
ejpam-6755	363	25	(	(	PUNCT
ejpam-6755	363	26	i	i	NOUN
ejpam-6755	363	27	)	)	PUNCT
ejpam-6755	363	28	2	2	NUM
ejpam-6755	363	29	)	)	PUNCT
ejpam-6755	363	30	=	=	SYM
ejpam-6755	363	31	1	1	NUM
ejpam-6755	363	32	2zth2−(f1∪f2	2zth2−(f1∪f2	NUM
ejpam-6755	363	33	)	)	PUNCT
ejpam-6755	363	34	+	+	CCONJ
ejpam-6755	363	35	1	1	NUM
ejpam-6755	363	36	2x	2x	NUM
ejpam-6755	363	37	2(tf1−(f1∩f2	2(tf1−(f1∩f2	NUM
ejpam-6755	363	38	)	)	PUNCT
ejpam-6755	363	39	−	−	ADP
ejpam-6755	363	40	1	1	X
ejpam-6755	363	41	)	)	PUNCT
ejpam-6755	363	42	+	+	CCONJ
ejpam-6755	363	43	1	1	NUM
ejpam-6755	363	44	2y	2y	NUM
ejpam-6755	363	45	2(tf2−(f1∩f2	2(tf2−(f1∩f2	NUM
ejpam-6755	363	46	)	)	PUNCT
ejpam-6755	363	47	−	−	NUM
ejpam-6755	363	48	1	1	NUM
ejpam-6755	363	49	)	)	PUNCT
ejpam-6755	363	50	+	+	NOUN
ejpam-6755	363	51	u2(tf1∩f2	u2(tf1∩f2	NOUN
ejpam-6755	363	52	−	−	PROPN
ejpam-6755	363	53	1	1	NUM
ejpam-6755	363	54	)	)	PUNCT
ejpam-6755	363	55	+	+	CCONJ
ejpam-6755	363	56	n(2tf1−(f1∩f2	n(2tf1−(f1∩f2	PROPN
ejpam-6755	363	57	)	)	PUNCT
ejpam-6755	363	58	+	+	SYM
ejpam-6755	363	59	tf2−(f1∩f2	tf2−(f1∩f2	NOUN
ejpam-6755	363	60	)	)	PUNCT
ejpam-6755	363	61	−	−	NOUN
ejpam-6755	363	62	1	1	NUM
ejpam-6755	363	63	)	)	PUNCT
ejpam-6755	363	64	+	+	NUM
ejpam-6755	363	65	n(2tf	n(2tf	NOUN
ejpam-6755	363	66	∗	∗	NOUN
ejpam-6755	363	67	+	+	CCONJ
ejpam-6755	363	68	th1−f	th1−f	NOUN
ejpam-6755	363	69	∗	∗	NOUN
ejpam-6755	363	70	−	−	PROPN
ejpam-6755	363	71	1	1	NUM
ejpam-6755	363	72	)	)	PUNCT
ejpam-6755	363	73	+	+	CCONJ
ejpam-6755	364	1	2	2	X
ejpam-6755	364	2	.	.	X
ejpam-6755	364	3	therefore	therefore	ADV
ejpam-6755	364	4	,	,	PUNCT
ejpam-6755	364	5	pn[h1;h2	pn[h1;h2	X
ejpam-6755	364	6	]	]	PUNCT
ejpam-6755	364	7	is	be	AUX
ejpam-6755	364	8	(	(	PUNCT
ejpam-6755	364	9	h1	h1	PROPN
ejpam-6755	364	10	,	,	PUNCT
ejpam-6755	364	11	h2)-magic	h2)-magic	ADJ
ejpam-6755	364	12	.	.	PUNCT
ejpam-6755	365	1	□	□	PUNCT
ejpam-6755	365	2	for	for	ADP
ejpam-6755	365	3	instance	instance	NOUN
ejpam-6755	365	4	,	,	PUNCT
ejpam-6755	365	5	we	we	PRON
ejpam-6755	365	6	present	present	VERB
ejpam-6755	365	7	an	an	DET
ejpam-6755	365	8	example	example	NOUN
ejpam-6755	365	9	of	of	ADP
ejpam-6755	365	10	p3[h1;h2	p3[h1;h2	PROPN
ejpam-6755	365	11	]	]	PUNCT
ejpam-6755	365	12	which	which	PRON
ejpam-6755	365	13	is	be	AUX
ejpam-6755	365	14	(	(	PUNCT
ejpam-6755	365	15	h1	h1	PROPN
ejpam-6755	365	16	,	,	PUNCT
ejpam-6755	365	17	h2)-magic	h2)-magic	ADJ
ejpam-6755	365	18	,	,	PUNCT
ejpam-6755	365	19	see	see	VERB
ejpam-6755	365	20	figure	figure	NOUN
ejpam-6755	365	21	4	4	NUM
ejpam-6755	365	22	.	.	PUNCT
ejpam-6755	365	23	figure	figure	VERB
ejpam-6755	365	24	4	4	NUM
ejpam-6755	365	25	:	:	PUNCT
ejpam-6755	365	26	the	the	DET
ejpam-6755	365	27	graphs	graph	NOUN
ejpam-6755	365	28	(	(	PUNCT
ejpam-6755	365	29	a	a	DET
ejpam-6755	365	30	)	)	PUNCT
ejpam-6755	365	31	f1	f1	NOUN
ejpam-6755	365	32	,	,	PUNCT
ejpam-6755	365	33	(	(	PUNCT
ejpam-6755	365	34	b	b	X
ejpam-6755	365	35	)	)	PUNCT
ejpam-6755	365	36	f2	f2	PROPN
ejpam-6755	365	37	,	,	PUNCT
ejpam-6755	365	38	(	(	PUNCT
ejpam-6755	365	39	c	c	X
ejpam-6755	365	40	)	)	PUNCT
ejpam-6755	365	41	h1	h1	NOUN
ejpam-6755	365	42	,	,	PUNCT
ejpam-6755	365	43	(	(	PUNCT
ejpam-6755	365	44	d	d	X
ejpam-6755	365	45	)	)	PUNCT
ejpam-6755	365	46	h2	h2	NOUN
ejpam-6755	365	47	,	,	PUNCT
ejpam-6755	365	48	(	(	PUNCT
ejpam-6755	365	49	e	e	NOUN
ejpam-6755	365	50	)	)	PUNCT
ejpam-6755	365	51	(	(	PUNCT
ejpam-6755	365	52	h1	h1	PROPN
ejpam-6755	365	53	,	,	PUNCT
ejpam-6755	365	54	h2)-magic	h2)-magic	ADJ
ejpam-6755	365	55	labeling	labeling	NOUN
ejpam-6755	365	56	of	of	ADP
ejpam-6755	365	57	p3[h1;h2	p3[h1;h2	PROPN
ejpam-6755	365	58	]	]	PUNCT
ejpam-6755	365	59	.	.	PUNCT
ejpam-6755	366	1	in	in	ADP
ejpam-6755	366	2	addition	addition	NOUN
ejpam-6755	366	3	,	,	PUNCT
ejpam-6755	366	4	vertices	vertex	NOUN
ejpam-6755	366	5	and	and	CCONJ
ejpam-6755	366	6	edges	edge	NOUN
ejpam-6755	366	7	of	of	ADP
ejpam-6755	366	8	f1	f1	NOUN
ejpam-6755	366	9	∩	∩	NOUN
ejpam-6755	366	10	f2	f2	NOUN
ejpam-6755	366	11	are	be	AUX
ejpam-6755	366	12	outlined	outline	VERB
ejpam-6755	366	13	in	in	ADP
ejpam-6755	366	14	red	red	PROPN
ejpam-6755	366	15	.	.	PROPN
ejpam-6755	367	1	5	5	NUM
ejpam-6755	367	2	.	.	X
ejpam-6755	367	3	conclusion	conclusion	NOUN
ejpam-6755	367	4	in	in	ADP
ejpam-6755	367	5	this	this	DET
ejpam-6755	367	6	paper	paper	NOUN
ejpam-6755	367	7	,	,	PUNCT
ejpam-6755	367	8	we	we	PRON
ejpam-6755	367	9	have	have	AUX
ejpam-6755	367	10	presented	present	VERB
ejpam-6755	367	11	a	a	DET
ejpam-6755	367	12	path	path	NOUN
ejpam-6755	367	13	-	-	PUNCT
ejpam-6755	367	14	magic	magic	NOUN
ejpam-6755	367	15	family	family	NOUN
ejpam-6755	367	16	of	of	ADP
ejpam-6755	367	17	disjoint	disjoint	PROPN
ejpam-6755	367	18	union	union	PROPN
ejpam-6755	367	19	of	of	ADP
ejpam-6755	367	20	paths	path	NOUN
ejpam-6755	367	21	and	and	CCONJ
ejpam-6755	367	22	two	two	NUM
ejpam-6755	367	23	general	general	ADJ
ejpam-6755	367	24	constructions	construction	NOUN
ejpam-6755	367	25	of	of	ADP
ejpam-6755	367	26	(	(	PUNCT
ejpam-6755	367	27	h1	h1	PROPN
ejpam-6755	367	28	,	,	PUNCT
ejpam-6755	367	29	h2)-magic	h2)-magic	ADJ
ejpam-6755	367	30	graphs	graph	NOUN
ejpam-6755	367	31	.	.	PUNCT
ejpam-6755	368	1	our	our	PRON
ejpam-6755	368	2	findings	finding	NOUN
ejpam-6755	368	3	partially	partially	ADV
ejpam-6755	368	4	address	address	VERB
ejpam-6755	368	5	the	the	DET
ejpam-6755	368	6	gaps	gap	NOUN
ejpam-6755	368	7	in	in	ADP
ejpam-6755	368	8	the	the	DET
ejpam-6755	368	9	existing	exist	VERB
ejpam-6755	368	10	knowledge	knowledge	NOUN
ejpam-6755	368	11	on	on	ADP
ejpam-6755	368	12	this	this	DET
ejpam-6755	368	13	emerging	emerge	VERB
ejpam-6755	368	14	topic	topic	NOUN
ejpam-6755	368	15	.	.	PUNCT
ejpam-6755	369	1	a	a	DET
ejpam-6755	369	2	potential	potential	ADJ
ejpam-6755	369	3	application	application	NOUN
ejpam-6755	369	4	of	of	ADP
ejpam-6755	369	5	(	(	PUNCT
ejpam-6755	369	6	h1	h1	PROPN
ejpam-6755	369	7	,	,	PUNCT
ejpam-6755	369	8	h2)-magic	h2)-magic	ADJ
ejpam-6755	369	9	graphs	graph	NOUN
ejpam-6755	369	10	is	be	AUX
ejpam-6755	369	11	in	in	ADP
ejpam-6755	369	12	the	the	DET
ejpam-6755	369	13	foundational	foundational	ADJ
ejpam-6755	369	14	design	design	NOUN
ejpam-6755	369	15	of	of	ADP
ejpam-6755	369	16	structured	structured	ADJ
ejpam-6755	369	17	networks	network	NOUN
ejpam-6755	369	18	,	,	PUNCT
ejpam-6755	369	19	where	where	SCONJ
ejpam-6755	369	20	they	they	PRON
ejpam-6755	369	21	help	help	VERB
ejpam-6755	369	22	enforce	enforce	VERB
ejpam-6755	369	23	a	a	DET
ejpam-6755	369	24	hidden	hide	VERB
ejpam-6755	369	25	uniformity	uniformity	NOUN
ejpam-6755	369	26	.	.	PUNCT
ejpam-6755	370	1	by	by	ADP
ejpam-6755	370	2	ensuring	ensure	VERB
ejpam-6755	370	3	that	that	SCONJ
ejpam-6755	370	4	specific	specific	ADJ
ejpam-6755	370	5	,	,	PUNCT
ejpam-6755	370	6	critical	critical	ADJ
ejpam-6755	370	7	patterns	pattern	NOUN
ejpam-6755	370	8	within	within	ADP
ejpam-6755	370	9	the	the	DET
ejpam-6755	370	10	larger	large	ADJ
ejpam-6755	370	11	system	system	NOUN
ejpam-6755	370	12	all	all	PRON
ejpam-6755	370	13	share	share	VERB
ejpam-6755	370	14	an	an	DET
ejpam-6755	370	15	identical	identical	ADJ
ejpam-6755	370	16	cumulative	cumulative	ADJ
ejpam-6755	370	17	property	property	NOUN
ejpam-6755	370	18	,	,	PUNCT
ejpam-6755	370	19	these	these	DET
ejpam-6755	370	20	t.	t.	PROPN
ejpam-6755	370	21	k.	k.	PROPN
ejpam-6755	370	22	maryati	maryati	PROPN
ejpam-6755	370	23	et	et	PROPN
ejpam-6755	370	24	al	al	PROPN
ejpam-6755	370	25	.	.	PUNCT
ejpam-6755	370	26	/	/	SYM
ejpam-6755	370	27	eur	eur	PROPN
ejpam-6755	370	28	.	.	PUNCT
ejpam-6755	371	1	j.	j.	PROPN
ejpam-6755	371	2	pure	pure	PROPN
ejpam-6755	371	3	appl	appl	PROPN
ejpam-6755	371	4	.	.	PROPN
ejpam-6755	371	5	math	math	PROPN
ejpam-6755	371	6	,	,	PUNCT
ejpam-6755	371	7	18	18	NUM
ejpam-6755	371	8	(	(	PUNCT
ejpam-6755	371	9	4	4	NUM
ejpam-6755	371	10	)	)	PUNCT
ejpam-6755	371	11	(	(	PUNCT
ejpam-6755	371	12	2025	2025	NUM
ejpam-6755	371	13	)	)	PUNCT
ejpam-6755	371	14	,	,	PUNCT
ejpam-6755	371	15	6755	6755	NUM
ejpam-6755	371	16	12	12	NUM
ejpam-6755	371	17	of	of	ADP
ejpam-6755	371	18	13	13	NUM
ejpam-6755	371	19	graphs	graph	NOUN
ejpam-6755	371	20	enable	enable	VERB
ejpam-6755	371	21	a	a	DET
ejpam-6755	371	22	built	build	VERB
ejpam-6755	371	23	-	-	PUNCT
ejpam-6755	371	24	in	in	ADP
ejpam-6755	371	25	balance	balance	NOUN
ejpam-6755	371	26	and	and	CCONJ
ejpam-6755	371	27	symmetry	symmetry	NOUN
ejpam-6755	371	28	.	.	PUNCT
ejpam-6755	372	1	this	this	DET
ejpam-6755	372	2	inherent	inherent	ADJ
ejpam-6755	372	3	harmony	harmony	NOUN
ejpam-6755	372	4	simplifies	simplifie	NOUN
ejpam-6755	372	5	systemwide	systemwide	NOUN
ejpam-6755	372	6	management	management	NOUN
ejpam-6755	372	7	,	,	PUNCT
ejpam-6755	372	8	promotes	promote	VERB
ejpam-6755	372	9	fault	fault	VERB
ejpam-6755	372	10	tolerance	tolerance	NOUN
ejpam-6755	372	11	by	by	ADP
ejpam-6755	372	12	making	make	VERB
ejpam-6755	372	13	key	key	ADJ
ejpam-6755	372	14	components	component	NOUN
ejpam-6755	372	15	interchangeable	interchangeable	ADJ
ejpam-6755	372	16	,	,	PUNCT
ejpam-6755	372	17	and	and	CCONJ
ejpam-6755	372	18	provides	provide	VERB
ejpam-6755	372	19	a	a	DET
ejpam-6755	372	20	robust	robust	ADJ
ejpam-6755	372	21	mathematical	mathematical	ADJ
ejpam-6755	372	22	framework	framework	NOUN
ejpam-6755	372	23	.	.	PUNCT
ejpam-6755	373	1	the	the	DET
ejpam-6755	373	2	next	next	ADJ
ejpam-6755	373	3	research	research	NOUN
ejpam-6755	373	4	direction	direction	NOUN
ejpam-6755	373	5	in	in	ADP
ejpam-6755	373	6	this	this	DET
ejpam-6755	373	7	topic	topic	NOUN
ejpam-6755	373	8	is	be	AUX
ejpam-6755	373	9	to	to	PART
ejpam-6755	373	10	systematically	systematically	ADV
ejpam-6755	373	11	investigate	investigate	VERB
ejpam-6755	373	12	the	the	DET
ejpam-6755	373	13	(	(	PUNCT
ejpam-6755	373	14	h1	h1	PROPN
ejpam-6755	373	15	,	,	PUNCT
ejpam-6755	373	16	h2)magic	h2)magic	ADJ
ejpam-6755	373	17	properties	property	NOUN
ejpam-6755	373	18	of	of	ADP
ejpam-6755	373	19	graphs	graph	NOUN
ejpam-6755	373	20	formed	form	VERB
ejpam-6755	373	21	by	by	ADP
ejpam-6755	373	22	a	a	DET
ejpam-6755	373	23	graph	graph	NOUN
ejpam-6755	373	24	operation	operation	NOUN
ejpam-6755	373	25	,	,	PUNCT
ejpam-6755	373	26	such	such	ADJ
ejpam-6755	373	27	as	as	ADP
ejpam-6755	373	28	the	the	DET
ejpam-6755	373	29	cartesian	cartesian	ADJ
ejpam-6755	373	30	product	product	NOUN
ejpam-6755	373	31	or	or	CCONJ
ejpam-6755	373	32	strong	strong	ADJ
ejpam-6755	373	33	product	product	NOUN
ejpam-6755	373	34	.	.	PUNCT
ejpam-6755	374	1	while	while	SCONJ
ejpam-6755	374	2	some	some	DET
ejpam-6755	374	3	specific	specific	ADJ
ejpam-6755	374	4	cases	case	NOUN
ejpam-6755	374	5	are	be	AUX
ejpam-6755	374	6	not	not	PART
ejpam-6755	374	7	that	that	ADV
ejpam-6755	374	8	hard	hard	ADJ
ejpam-6755	374	9	to	to	PART
ejpam-6755	374	10	be	be	AUX
ejpam-6755	374	11	determined	determine	VERB
ejpam-6755	374	12	,	,	PUNCT
ejpam-6755	374	13	a	a	DET
ejpam-6755	374	14	general	general	ADJ
ejpam-6755	374	15	theory	theory	NOUN
ejpam-6755	374	16	is	be	AUX
ejpam-6755	374	17	lacking	lack	VERB
ejpam-6755	374	18	.	.	PUNCT
ejpam-6755	375	1	establishing	establish	VERB
ejpam-6755	375	2	necessary	necessary	ADJ
ejpam-6755	375	3	and	and	CCONJ
ejpam-6755	375	4	sufficient	sufficient	ADJ
ejpam-6755	375	5	conditions	condition	NOUN
ejpam-6755	375	6	when	when	SCONJ
ejpam-6755	375	7	a	a	DET
ejpam-6755	375	8	graph	graph	NOUN
ejpam-6755	375	9	is	be	AUX
ejpam-6755	375	10	(	(	PUNCT
ejpam-6755	375	11	h1	h1	PROPN
ejpam-6755	375	12	,	,	PUNCT
ejpam-6755	375	13	h2)-magic	h2)-magic	ADJ
ejpam-6755	375	14	would	would	AUX
ejpam-6755	375	15	represent	represent	VERB
ejpam-6755	375	16	a	a	DET
ejpam-6755	375	17	significant	significant	ADJ
ejpam-6755	375	18	advancement	advancement	NOUN
ejpam-6755	375	19	.	.	PUNCT
ejpam-6755	376	1	acknowledgements	acknowledgement	NOUN
ejpam-6755	376	2	this	this	DET
ejpam-6755	376	3	work	work	NOUN
ejpam-6755	376	4	was	be	AUX
ejpam-6755	376	5	supported	support	VERB
ejpam-6755	376	6	by	by	ADP
ejpam-6755	376	7	lp2	lp2	PROPN
ejpam-6755	376	8	m	m	PROPN
ejpam-6755	376	9	uin	uin	PROPN
ejpam-6755	376	10	syarif	syarif	PROPN
ejpam-6755	376	11	hidayatullah	hidayatullah	PROPN
ejpam-6755	376	12	jakarta	jakarta	PROPN
ejpam-6755	376	13	research	research	PROPN
ejpam-6755	376	14	fellowship	fellowship	NOUN
ejpam-6755	376	15	program	program	NOUN
ejpam-6755	376	16	2023	2023	NUM
ejpam-6755	376	17	and	and	CCONJ
ejpam-6755	376	18	the	the	DET
ejpam-6755	376	19	slovak	slovak	ADJ
ejpam-6755	376	20	research	research	NOUN
ejpam-6755	376	21	and	and	CCONJ
ejpam-6755	376	22	development	development	NOUN
ejpam-6755	376	23	agency	agency	NOUN
ejpam-6755	376	24	under	under	ADP
ejpam-6755	376	25	the	the	DET
ejpam-6755	376	26	contract	contract	NOUN
ejpam-6755	376	27	no	no	INTJ
ejpam-6755	376	28	.	.	PUNCT
ejpam-6755	377	1	apvv-23	apvv-23	NOUN
ejpam-6755	377	2	-	-	PUNCT
ejpam-6755	377	3	0191	0191	NUM
ejpam-6755	377	4	and	and	CCONJ
ejpam-6755	377	5	by	by	ADP
ejpam-6755	377	6	vega	vega	PROPN
ejpam-6755	377	7	1/0243/23	1/0243/23	NUM
ejpam-6755	377	8	.	.	PUNCT
ejpam-6755	378	1	references	reference	NOUN
ejpam-6755	378	2	[	[	X
ejpam-6755	378	3	1	1	NUM
ejpam-6755	378	4	]	]	PUNCT
ejpam-6755	378	5	a.	a.	NOUN
ejpam-6755	378	6	gutiérrez	gutiérrez	PROPN
ejpam-6755	378	7	and	and	CCONJ
ejpam-6755	378	8	a.	a.	NOUN
ejpam-6755	378	9	lladó.	lladó.	PROPN
ejpam-6755	378	10	magic	magic	ADJ
ejpam-6755	378	11	covering	covering	NOUN
ejpam-6755	378	12	.	.	PUNCT
ejpam-6755	379	1	journal	journal	NOUN
ejpam-6755	379	2	of	of	ADP
ejpam-6755	379	3	combinatorial	combinatorial	ADJ
ejpam-6755	379	4	mathematics	mathematic	NOUN
ejpam-6755	379	5	and	and	CCONJ
ejpam-6755	379	6	combinatorial	combinatorial	ADJ
ejpam-6755	379	7	computing	computing	NOUN
ejpam-6755	379	8	,	,	PUNCT
ejpam-6755	379	9	55:43–56	55:43–56	NUM
ejpam-6755	379	10	,	,	PUNCT
ejpam-6755	379	11	2005	2005	NUM
ejpam-6755	379	12	.	.	PUNCT
ejpam-6755	380	1	[	[	X
ejpam-6755	380	2	2	2	NUM
ejpam-6755	380	3	]	]	PUNCT
ejpam-6755	380	4	b.	b.	PROPN
ejpam-6755	380	5	yang	yang	PROPN
ejpam-6755	380	6	,	,	PUNCT
ejpam-6755	380	7	m.	m.	PROPN
ejpam-6755	380	8	a.	a.	PROPN
ejpam-6755	380	9	rashid	rashid	PROPN
ejpam-6755	380	10	,	,	PUNCT
ejpam-6755	380	11	s.	s.	PROPN
ejpam-6755	380	12	ahmad	ahmad	PROPN
ejpam-6755	380	13	,	,	PUNCT
ejpam-6755	380	14	m.	m.	PROPN
ejpam-6755	380	15	f.	f.	PROPN
ejpam-6755	380	16	nadeem	nadeem	PROPN
ejpam-6755	380	17	,	,	PUNCT
ejpam-6755	380	18	and	and	CCONJ
ejpam-6755	380	19	m.	m.	PROPN
ejpam-6755	380	20	k.	k.	PROPN
ejpam-6755	380	21	siddiqui	siddiqui	PROPN
ejpam-6755	380	22	.	.	PUNCT
ejpam-6755	381	1	cycle	cycle	NOUN
ejpam-6755	381	2	super	super	ADJ
ejpam-6755	381	3	magic	magic	ADJ
ejpam-6755	381	4	labeling	labeling	NOUN
ejpam-6755	381	5	of	of	ADP
ejpam-6755	381	6	planar	planar	ADJ
ejpam-6755	381	7	graphs	graph	NOUN
ejpam-6755	381	8	.	.	PUNCT
ejpam-6755	382	1	international	international	ADJ
ejpam-6755	382	2	journal	journal	NOUN
ejpam-6755	382	3	of	of	ADP
ejpam-6755	382	4	applied	apply	VERB
ejpam-6755	382	5	mathematics	mathematic	NOUN
ejpam-6755	382	6	,	,	PUNCT
ejpam-6755	382	7	32(6):945–957	32(6):945–957	PROPN
ejpam-6755	382	8	,	,	PUNCT
ejpam-6755	382	9	2019	2019	NUM
ejpam-6755	382	10	.	.	PUNCT
ejpam-6755	383	1	[	[	X
ejpam-6755	383	2	3	3	X
ejpam-6755	383	3	]	]	X
ejpam-6755	383	4	m.	m.	NOUN
ejpam-6755	383	5	asif	asif	PROPN
ejpam-6755	383	6	,	,	PUNCT
ejpam-6755	383	7	g.	g.	PROPN
ejpam-6755	383	8	ali	ali	PROPN
ejpam-6755	383	9	,	,	PUNCT
ejpam-6755	383	10	m.	m.	PROPN
ejpam-6755	383	11	numan	numan	PROPN
ejpam-6755	383	12	,	,	PUNCT
ejpam-6755	383	13	and	and	CCONJ
ejpam-6755	383	14	a.	a.	NOUN
ejpam-6755	383	15	semaničová-feňovč́ıková.	semaničová-feňovč́ıková.	NOUN
ejpam-6755	383	16	cycle	cycle	NOUN
ejpam-6755	383	17	-	-	PUNCT
ejpam-6755	383	18	supermagic	supermagic	NOUN
ejpam-6755	383	19	labeling	labeling	NOUN
ejpam-6755	383	20	for	for	ADP
ejpam-6755	383	21	some	some	DET
ejpam-6755	383	22	families	family	NOUN
ejpam-6755	383	23	of	of	ADP
ejpam-6755	383	24	graphs	graph	NOUN
ejpam-6755	383	25	.	.	PUNCT
ejpam-6755	384	1	utilitas	utilitas	PROPN
ejpam-6755	384	2	mathematica	mathematica	PROPN
ejpam-6755	384	3	,	,	PUNCT
ejpam-6755	384	4	103:51–59	103:51–59	NUM
ejpam-6755	384	5	,	,	PUNCT
ejpam-6755	384	6	2017	2017	NUM
ejpam-6755	384	7	.	.	PUNCT
ejpam-6755	385	1	[	[	X
ejpam-6755	385	2	4	4	X
ejpam-6755	385	3	]	]	PUNCT
ejpam-6755	385	4	t.	t.	NOUN
ejpam-6755	385	5	öner	öner	NOUN
ejpam-6755	385	6	,	,	PUNCT
ejpam-6755	385	7	m.	m.	NOUN
ejpam-6755	385	8	hussain	hussain	PROPN
ejpam-6755	385	9	,	,	PUNCT
ejpam-6755	385	10	and	and	CCONJ
ejpam-6755	385	11	s.	s.	PROPN
ejpam-6755	385	12	baranas	baranas	PROPN
ejpam-6755	385	13	.	.	PUNCT
ejpam-6755	386	1	cn	cn	ADJ
ejpam-6755	386	2	-	-	ADJ
ejpam-6755	386	3	supermagic	supermagic	ADJ
ejpam-6755	386	4	labeling	labeling	NOUN
ejpam-6755	386	5	of	of	ADP
ejpam-6755	386	6	polygonal	polygonal	ADJ
ejpam-6755	386	7	snake	snake	NOUN
ejpam-6755	386	8	graphs	graph	NOUN
ejpam-6755	386	9	.	.	PUNCT
ejpam-6755	387	1	journal	journal	NOUN
ejpam-6755	387	2	of	of	ADP
ejpam-6755	387	3	mathematics	mathematic	NOUN
ejpam-6755	387	4	and	and	CCONJ
ejpam-6755	387	5	computer	computer	NOUN
ejpam-6755	387	6	science	science	NOUN
ejpam-6755	387	7	,	,	PUNCT
ejpam-6755	387	8	20(3):189–195	20(3):189–195	PROPN
ejpam-6755	387	9	,	,	PUNCT
ejpam-6755	387	10	2019	2019	NUM
ejpam-6755	387	11	.	.	PUNCT
ejpam-6755	388	1	[	[	X
ejpam-6755	388	2	5	5	X
ejpam-6755	388	3	]	]	PUNCT
ejpam-6755	388	4	h.	h.	PROPN
ejpam-6755	388	5	sandariria	sandariria	PROPN
ejpam-6755	388	6	and	and	CCONJ
ejpam-6755	388	7	y.	y.	PROPN
ejpam-6755	388	8	susanti	susanti	PROPN
ejpam-6755	388	9	.	.	PUNCT
ejpam-6755	389	1	h	h	NOUN
ejpam-6755	389	2	-	-	PUNCT
ejpam-6755	389	3	supermagic	supermagic	ADJ
ejpam-6755	389	4	labeling	labeling	NOUN
ejpam-6755	389	5	on	on	ADP
ejpam-6755	389	6	edge	edge	NOUN
ejpam-6755	389	7	coronation	coronation	NOUN
ejpam-6755	389	8	of	of	ADP
ejpam-6755	389	9	some	some	DET
ejpam-6755	389	10	graphs	graph	NOUN
ejpam-6755	389	11	with	with	ADP
ejpam-6755	389	12	a	a	DET
ejpam-6755	389	13	cycle	cycle	NOUN
ejpam-6755	389	14	.	.	PUNCT
ejpam-6755	390	1	in	in	ADP
ejpam-6755	390	2	aip	aip	PROPN
ejpam-6755	390	3	conference	conference	NOUN
ejpam-6755	390	4	proceedings	proceeding	NOUN
ejpam-6755	390	5	,	,	PUNCT
ejpam-6755	390	6	volume	volume	NOUN
ejpam-6755	390	7	2192	2192	NUM
ejpam-6755	390	8	,	,	PUNCT
ejpam-6755	390	9	page	page	NOUN
ejpam-6755	390	10	040014	040014	NUM
ejpam-6755	390	11	,	,	PUNCT
ejpam-6755	390	12	2019	2019	NUM
ejpam-6755	390	13	.	.	PUNCT
ejpam-6755	391	1	[	[	X
ejpam-6755	391	2	6	6	NUM
ejpam-6755	391	3	]	]	PUNCT
ejpam-6755	391	4	k.	k.	PROPN
ejpam-6755	391	5	ali	ali	PROPN
ejpam-6755	391	6	,	,	PUNCT
ejpam-6755	391	7	s.	s.	PROPN
ejpam-6755	391	8	t.	t.	PROPN
ejpam-6755	391	9	r.	r.	PROPN
ejpam-6755	391	10	rizvi	rizvi	PROPN
ejpam-6755	391	11	,	,	PUNCT
ejpam-6755	391	12	and	and	CCONJ
ejpam-6755	391	13	a.	a.	NOUN
ejpam-6755	391	14	semaničová-feňovč́ıková.	semaničová-feňovč́ıková.	PROPN
ejpam-6755	391	15	c4	c4	NOUN
ejpam-6755	391	16	-	-	PUNCT
ejpam-6755	391	17	supermagic	supermagic	ADJ
ejpam-6755	391	18	labelings	labeling	NOUN
ejpam-6755	391	19	of	of	ADP
ejpam-6755	391	20	disjoint	disjoint	PROPN
ejpam-6755	391	21	union	union	NOUN
ejpam-6755	391	22	of	of	ADP
ejpam-6755	391	23	prisms	prism	NOUN
ejpam-6755	391	24	.	.	PUNCT
ejpam-6755	392	1	mathematical	mathematical	ADJ
ejpam-6755	392	2	reports	report	NOUN
ejpam-6755	392	3	,	,	PUNCT
ejpam-6755	392	4	18(3):315–320	18(3):315–320	PROPN
ejpam-6755	392	5	,	,	PUNCT
ejpam-6755	392	6	2016	2016	NUM
ejpam-6755	392	7	.	.	PUNCT
ejpam-6755	393	1	[	[	X
ejpam-6755	393	2	7	7	X
ejpam-6755	393	3	]	]	X
ejpam-6755	393	4	y.	y.	PROPN
ejpam-6755	393	5	f.	f.	PROPN
ejpam-6755	393	6	ashari	ashari	PROPN
ejpam-6755	393	7	and	and	CCONJ
ejpam-6755	393	8	a.	a.	PROPN
ejpam-6755	393	9	n.	n.	PROPN
ejpam-6755	393	10	m.	m.	PROPN
ejpam-6755	393	11	salman	salman	PROPN
ejpam-6755	393	12	.	.	PUNCT
ejpam-6755	394	1	on	on	ADP
ejpam-6755	394	2	(	(	PUNCT
ejpam-6755	394	3	h1	h1	PROPN
ejpam-6755	394	4	,	,	PUNCT
ejpam-6755	394	5	h2)-supermagic	h2)-supermagic	ADJ
ejpam-6755	394	6	labeling	labeling	NOUN
ejpam-6755	394	7	of	of	ADP
ejpam-6755	394	8	some	some	DET
ejpam-6755	394	9	graph	graph	NOUN
ejpam-6755	394	10	operation	operation	NOUN
ejpam-6755	394	11	.	.	PUNCT
ejpam-6755	395	1	electronic	electronic	ADJ
ejpam-6755	395	2	journal	journal	NOUN
ejpam-6755	395	3	of	of	ADP
ejpam-6755	395	4	graph	graph	NOUN
ejpam-6755	395	5	theory	theory	NOUN
ejpam-6755	395	6	and	and	CCONJ
ejpam-6755	395	7	applications	application	NOUN
ejpam-6755	395	8	,	,	PUNCT
ejpam-6755	395	9	2025	2025	NUM
ejpam-6755	395	10	.	.	PUNCT
ejpam-6755	395	11	submitted	submit	VERB
ejpam-6755	395	12	.	.	PUNCT
ejpam-6755	396	1	[	[	X
ejpam-6755	396	2	8	8	NUM
ejpam-6755	396	3	]	]	PUNCT
ejpam-6755	396	4	m.	m.	NOUN
ejpam-6755	396	5	bača	bača	PROPN
ejpam-6755	396	6	,	,	PUNCT
ejpam-6755	396	7	p.	p.	NOUN
ejpam-6755	396	8	jeyanthi	jeyanthi	PROPN
ejpam-6755	396	9	,	,	PUNCT
ejpam-6755	396	10	n.	n.	PROPN
ejpam-6755	396	11	t.	t.	PROPN
ejpam-6755	396	12	muthuraja	muthuraja	PROPN
ejpam-6755	396	13	,	,	PUNCT
ejpam-6755	396	14	p.	p.	PROPN
ejpam-6755	396	15	n.	n.	PROPN
ejpam-6755	396	16	selvagopal	selvagopal	PROPN
ejpam-6755	396	17	,	,	PUNCT
ejpam-6755	396	18	and	and	CCONJ
ejpam-6755	396	19	a.	a.	PROPN
ejpam-6755	396	20	semaničováfeňovč́ıková.	semaničováfeňovč́ıková.	PROPN
ejpam-6755	396	21	ladders	ladder	NOUN
ejpam-6755	396	22	and	and	CCONJ
ejpam-6755	396	23	fan	fan	NOUN
ejpam-6755	396	24	graphs	graph	NOUN
ejpam-6755	396	25	are	be	AUX
ejpam-6755	396	26	cycle	cycle	NOUN
ejpam-6755	396	27	-	-	PUNCT
ejpam-6755	396	28	antimagic	antimagic	NOUN
ejpam-6755	396	29	.	.	PUNCT
ejpam-6755	397	1	hacettepe	hacettepe	PROPN
ejpam-6755	397	2	journal	journal	PROPN
ejpam-6755	397	3	of	of	ADP
ejpam-6755	397	4	mathematics	mathematic	NOUN
ejpam-6755	397	5	and	and	CCONJ
ejpam-6755	397	6	statistics	statistic	NOUN
ejpam-6755	397	7	,	,	PUNCT
ejpam-6755	397	8	49(3):1093–1106	49(3):1093–1106	PROPN
ejpam-6755	397	9	,	,	PUNCT
ejpam-6755	397	10	2020	2020	NUM
ejpam-6755	397	11	.	.	PUNCT
ejpam-6755	398	1	[	[	X
ejpam-6755	398	2	9	9	NUM
ejpam-6755	398	3	]	]	X
ejpam-6755	398	4	c.	c.	PROPN
ejpam-6755	398	5	chithra	chithra	PROPN
ejpam-6755	398	6	,	,	PUNCT
ejpam-6755	398	7	g.	g.	PROPN
ejpam-6755	398	8	marimuthu	marimuthu	PROPN
ejpam-6755	398	9	,	,	PUNCT
ejpam-6755	398	10	and	and	CCONJ
ejpam-6755	398	11	g.	g.	PROPN
ejpam-6755	398	12	kumar	kumar	PROPN
ejpam-6755	398	13	.	.	PUNCT
ejpam-6755	399	1	cm	cm	PROPN
ejpam-6755	399	2	-	-	PUNCT
ejpam-6755	399	3	e	e	NOUN
ejpam-6755	399	4	-	-	ADJ
ejpam-6755	399	5	supermagic	supermagic	ADJ
ejpam-6755	399	6	labelings	labeling	NOUN
ejpam-6755	399	7	of	of	ADP
ejpam-6755	399	8	graphs	graph	NOUN
ejpam-6755	399	9	,	,	PUNCT
ejpam-6755	399	10	journal	journal	NOUN
ejpam-6755	399	11	=	=	SYM
ejpam-6755	399	12	akce	akce	PROPN
ejpam-6755	399	13	international	international	PROPN
ejpam-6755	399	14	journal	journal	NOUN
ejpam-6755	399	15	of	of	ADP
ejpam-6755	399	16	graphs	graph	NOUN
ejpam-6755	399	17	and	and	CCONJ
ejpam-6755	399	18	combinatorics	combinatoric	NOUN
ejpam-6755	399	19	.	.	PUNCT
ejpam-6755	400	1	17(1):510–518	17(1):510–518	NUM
ejpam-6755	400	2	,	,	PUNCT
ejpam-6755	400	3	2020	2020	NUM
ejpam-6755	400	4	.	.	PUNCT
ejpam-6755	401	1	[	[	X
ejpam-6755	401	2	10	10	NUM
ejpam-6755	401	3	]	]	PUNCT
ejpam-6755	401	4	x.	x.	PROPN
ejpam-6755	401	5	ma	ma	PROPN
ejpam-6755	401	6	,	,	PUNCT
ejpam-6755	401	7	m.	m.	PROPN
ejpam-6755	401	8	a.	a.	PROPN
ejpam-6755	401	9	umar	umar	PROPN
ejpam-6755	401	10	,	,	PUNCT
ejpam-6755	401	11	s.	s.	PROPN
ejpam-6755	401	12	nazeer	nazeer	PROPN
ejpam-6755	401	13	,	,	PUNCT
ejpam-6755	401	14	y.	y.	PROPN
ejpam-6755	401	15	chu	chu	PROPN
ejpam-6755	401	16	,	,	PUNCT
ejpam-6755	401	17	and	and	CCONJ
ejpam-6755	401	18	y.	y.	PROPN
ejpam-6755	401	19	liu	liu	PROPN
ejpam-6755	401	20	.	.	PUNCT
ejpam-6755	402	1	stacked	stack	VERB
ejpam-6755	402	2	book	book	NOUN
ejpam-6755	402	3	graphs	graph	NOUN
ejpam-6755	402	4	are	be	AUX
ejpam-6755	402	5	cycleantimagic	cycleantimagic	ADJ
ejpam-6755	402	6	.	.	PUNCT
ejpam-6755	403	1	aims	aim	VERB
ejpam-6755	403	2	mathematics	mathematic	NOUN
ejpam-6755	403	3	,	,	PUNCT
ejpam-6755	403	4	5(6):6043–6050	5(6):6043–6050	NUM
ejpam-6755	403	5	,	,	PUNCT
ejpam-6755	403	6	2020	2020	NUM
ejpam-6755	403	7	.	.	PUNCT
ejpam-6755	404	1	[	[	X
ejpam-6755	404	2	11	11	NUM
ejpam-6755	404	3	]	]	PUNCT
ejpam-6755	404	4	t.	t.	PROPN
ejpam-6755	404	5	k.	k.	PROPN
ejpam-6755	404	6	maryati	maryati	PROPN
ejpam-6755	404	7	,	,	PUNCT
ejpam-6755	404	8	f.	f.	PROPN
ejpam-6755	404	9	f.	f.	PROPN
ejpam-6755	404	10	hadiputra	hadiputra	PROPN
ejpam-6755	404	11	,	,	PUNCT
ejpam-6755	404	12	and	and	CCONJ
ejpam-6755	404	13	a.	a.	PROPN
ejpam-6755	404	14	n.	n.	PROPN
ejpam-6755	404	15	m.	m.	PROPN
ejpam-6755	404	16	salman	salman	PROPN
ejpam-6755	404	17	.	.	PUNCT
ejpam-6755	405	1	forbidden	forbid	VERB
ejpam-6755	405	2	family	family	NOUN
ejpam-6755	405	3	of	of	ADP
ejpam-6755	405	4	ph	ph	ADJ
ejpam-6755	405	5	-	-	ADJ
ejpam-6755	405	6	magic	magic	ADJ
ejpam-6755	405	7	graphs	graph	NOUN
ejpam-6755	405	8	.	.	PUNCT
ejpam-6755	406	1	electronic	electronic	ADJ
ejpam-6755	406	2	journal	journal	NOUN
ejpam-6755	406	3	of	of	ADP
ejpam-6755	406	4	graph	graph	NOUN
ejpam-6755	406	5	theory	theory	NOUN
ejpam-6755	406	6	and	and	CCONJ
ejpam-6755	406	7	applications	application	NOUN
ejpam-6755	406	8	,	,	PUNCT
ejpam-6755	406	9	12(1):43–54	12(1):43–54	NUM
ejpam-6755	406	10	,	,	PUNCT
ejpam-6755	406	11	2024	2024	NUM
ejpam-6755	406	12	.	.	PUNCT
ejpam-6755	407	1	t.	t.	PROPN
ejpam-6755	407	2	k.	k.	PROPN
ejpam-6755	407	3	maryati	maryati	PROPN
ejpam-6755	407	4	et	et	PROPN
ejpam-6755	407	5	al	al	PROPN
ejpam-6755	407	6	.	.	PUNCT
ejpam-6755	407	7	/	/	SYM
ejpam-6755	407	8	eur	eur	PROPN
ejpam-6755	407	9	.	.	PUNCT
ejpam-6755	408	1	j.	j.	PROPN
ejpam-6755	408	2	pure	pure	PROPN
ejpam-6755	408	3	appl	appl	PROPN
ejpam-6755	408	4	.	.	PROPN
ejpam-6755	408	5	math	math	PROPN
ejpam-6755	408	6	,	,	PUNCT
ejpam-6755	408	7	18	18	NUM
ejpam-6755	408	8	(	(	PUNCT
ejpam-6755	408	9	4	4	NUM
ejpam-6755	408	10	)	)	PUNCT
ejpam-6755	408	11	(	(	PUNCT
ejpam-6755	408	12	2025	2025	NUM
ejpam-6755	408	13	)	)	PUNCT
ejpam-6755	408	14	,	,	PUNCT
ejpam-6755	408	15	6755	6755	NUM
ejpam-6755	408	16	13	13	NUM
ejpam-6755	408	17	of	of	ADP
ejpam-6755	408	18	13	13	NUM
ejpam-6755	409	1	[	[	X
ejpam-6755	409	2	12	12	NUM
ejpam-6755	409	3	]	]	PUNCT
ejpam-6755	409	4	j.	j.	PROPN
ejpam-6755	409	5	a.	a.	PROPN
ejpam-6755	409	6	gallian	gallian	PROPN
ejpam-6755	409	7	.	.	PUNCT
ejpam-6755	410	1	a	a	DET
ejpam-6755	410	2	dynamic	dynamic	ADJ
ejpam-6755	410	3	survey	survey	NOUN
ejpam-6755	410	4	of	of	ADP
ejpam-6755	410	5	graph	graph	NOUN
ejpam-6755	410	6	labelings	labeling	NOUN
ejpam-6755	410	7	,	,	PUNCT
ejpam-6755	410	8	2024	2024	NUM
ejpam-6755	410	9	.	.	PUNCT
ejpam-6755	411	1	[	[	X
ejpam-6755	411	2	13	13	NUM
ejpam-6755	411	3	]	]	X
ejpam-6755	411	4	d.	d.	PROPN
ejpam-6755	411	5	i.	i.	PROPN
ejpam-6755	411	6	lanlege	lanlege	PROPN
ejpam-6755	411	7	,	,	PUNCT
ejpam-6755	411	8	s.	s.	PROPN
ejpam-6755	411	9	e.	e.	PROPN
ejpam-6755	411	10	fadugba	fadugba	PROPN
ejpam-6755	411	11	,	,	PUNCT
ejpam-6755	411	12	n.	n.	PROPN
ejpam-6755	411	13	ali	ali	PROPN
ejpam-6755	411	14	,	,	PUNCT
ejpam-6755	411	15	a.	a.	PROPN
ejpam-6755	411	16	l.	l.	PROPN
ejpam-6755	411	17	ozioko	ozioko	PROPN
ejpam-6755	411	18	,	,	PUNCT
ejpam-6755	411	19	n.	n.	PROPN
ejpam-6755	411	20	alam	alam	PROPN
ejpam-6755	411	21	,	,	PUNCT
ejpam-6755	411	22	s.	s.	PROPN
ejpam-6755	411	23	ahmad	ahmad	PROPN
ejpam-6755	411	24	,	,	PUNCT
ejpam-6755	411	25	n.	n.	PROPN
ejpam-6755	411	26	jeeva	jeeva	PROPN
ejpam-6755	411	27	,	,	PUNCT
ejpam-6755	411	28	and	and	CCONJ
ejpam-6755	411	29	m.	m.	PROPN
ejpam-6755	411	30	z.	z.	PROPN
ejpam-6755	411	31	sayed	say	VERB
ejpam-6755	411	32	-	-	PUNCT
ejpam-6755	411	33	ahmed	ahme	VERB
ejpam-6755	411	34	.	.	PUNCT
ejpam-6755	411	35	mathematical	mathematical	ADJ
ejpam-6755	411	36	model	model	NOUN
ejpam-6755	411	37	of	of	ADP
ejpam-6755	411	38	the	the	DET
ejpam-6755	411	39	social	social	ADJ
ejpam-6755	411	40	pathogen	pathogen	NOUN
ejpam-6755	411	41	of	of	ADP
ejpam-6755	411	42	hiv	hiv	PROPN
ejpam-6755	411	43	/	/	SYM
ejpam-6755	411	44	aids	aids	PROPN
ejpam-6755	411	45	stigma	stigma	NOUN
ejpam-6755	411	46	.	.	PUNCT
ejpam-6755	412	1	communications	communication	NOUN
ejpam-6755	412	2	in	in	ADP
ejpam-6755	412	3	mathematical	mathematical	ADJ
ejpam-6755	412	4	biology	biology	NOUN
ejpam-6755	412	5	and	and	CCONJ
ejpam-6755	412	6	neuroscience	neuroscience	NOUN
ejpam-6755	412	7	,	,	PUNCT
ejpam-6755	412	8	page	page	NOUN
ejpam-6755	412	9	article	article	NOUN
ejpam-6755	412	10	i	i	PROPN
ejpam-6755	412	11	d	d	PROPN
ejpam-6755	412	12	6	6	NUM
ejpam-6755	412	13	,	,	PUNCT
ejpam-6755	412	14	2025	2025	NUM
ejpam-6755	412	15	.	.	PUNCT
ejpam-6755	413	1	[	[	X
ejpam-6755	413	2	14	14	NUM
ejpam-6755	413	3	]	]	PUNCT
ejpam-6755	413	4	s.	s.	PROPN
ejpam-6755	413	5	n.	n.	PROPN
ejpam-6755	413	6	saleh	saleh	PROPN
ejpam-6755	413	7	,	,	PUNCT
ejpam-6755	413	8	m.	m.	PROPN
ejpam-6755	413	9	k.	k.	PROPN
ejpam-6755	413	10	naseer	naseer	PROPN
ejpam-6755	413	11	,	,	PUNCT
ejpam-6755	413	12	n.	n.	PROPN
ejpam-6755	413	13	ali	ali	PROPN
ejpam-6755	413	14	,	,	PUNCT
ejpam-6755	413	15	ü.	ü.	PROPN
ejpam-6755	413	16	karabiyik	karabiyik	NOUN
ejpam-6755	413	17	,	,	PUNCT
ejpam-6755	413	18	m.	m.	NOUN
ejpam-6755	413	19	s.	s.	PROPN
ejpam-6755	413	20	zakir	zakir	PROPN
ejpam-6755	413	21	,	,	PUNCT
ejpam-6755	413	22	and	and	CCONJ
ejpam-6755	413	23	m.	m.	PROPN
ejpam-6755	413	24	arshad	arshad	PROPN
ejpam-6755	413	25	.	.	PUNCT
ejpam-6755	414	1	graphtheoretical	graphtheoretical	ADJ
ejpam-6755	414	2	approaches	approach	NOUN
ejpam-6755	414	3	to	to	AUX
ejpam-6755	414	4	entropy	entropy	VERB
ejpam-6755	414	5	in	in	ADP
ejpam-6755	414	6	cu2o	cu2o	PROPN
ejpam-6755	414	7	crystalline	crystalline	ADJ
ejpam-6755	414	8	structures	structure	NOUN
ejpam-6755	414	9	:	:	PUNCT
ejpam-6755	414	10	implications	implication	NOUN
ejpam-6755	414	11	for	for	ADP
ejpam-6755	414	12	biomedical	biomedical	ADJ
ejpam-6755	414	13	and	and	CCONJ
ejpam-6755	414	14	energy	energy	NOUN
ejpam-6755	414	15	applications	application	NOUN
ejpam-6755	414	16	.	.	PUNCT
ejpam-6755	415	1	communications	communication	NOUN
ejpam-6755	415	2	in	in	ADP
ejpam-6755	415	3	mathematical	mathematical	ADJ
ejpam-6755	415	4	biology	biology	NOUN
ejpam-6755	415	5	and	and	CCONJ
ejpam-6755	415	6	neuroscience	neuroscience	NOUN
ejpam-6755	415	7	,	,	PUNCT
ejpam-6755	415	8	page	page	NOUN
ejpam-6755	415	9	article	article	NOUN
ejpam-6755	415	10	i	i	PROPN
ejpam-6755	415	11	d	d	PROPN
ejpam-6755	415	12	64	64	NUM
ejpam-6755	415	13	,	,	PUNCT
ejpam-6755	415	14	2025	2025	NUM
ejpam-6755	415	15	.	.	PUNCT
ejpam-6755	416	1	[	[	X
ejpam-6755	416	2	15	15	NUM
ejpam-6755	416	3	]	]	PUNCT
ejpam-6755	416	4	t.	t.	PROPN
ejpam-6755	416	5	k.	k.	PROPN
ejpam-6755	416	6	maryati	maryati	PROPN
ejpam-6755	416	7	,	,	PUNCT
ejpam-6755	416	8	a.	a.	PROPN
ejpam-6755	416	9	n.	n.	PROPN
ejpam-6755	416	10	m.	m.	PROPN
ejpam-6755	416	11	salman	salman	PROPN
ejpam-6755	416	12	,	,	PUNCT
ejpam-6755	416	13	and	and	CCONJ
ejpam-6755	416	14	e.	e.	PROPN
ejpam-6755	416	15	t.	t.	PROPN
ejpam-6755	416	16	baskoro	baskoro	PROPN
ejpam-6755	416	17	.	.	PUNCT
ejpam-6755	417	1	supermagic	supermagic	ADJ
ejpam-6755	417	2	coverings	covering	NOUN
ejpam-6755	417	3	of	of	ADP
ejpam-6755	417	4	the	the	DET
ejpam-6755	417	5	disjoint	disjoint	PROPN
ejpam-6755	417	6	union	union	NOUN
ejpam-6755	417	7	of	of	ADP
ejpam-6755	417	8	graphs	graph	NOUN
ejpam-6755	417	9	and	and	CCONJ
ejpam-6755	417	10	amalgamations	amalgamation	NOUN
ejpam-6755	417	11	.	.	PUNCT
ejpam-6755	418	1	discrete	discrete	ADJ
ejpam-6755	418	2	mathematics	mathematic	NOUN
ejpam-6755	418	3	,	,	PUNCT
ejpam-6755	418	4	313:397–405	313:397–405	NUM
ejpam-6755	418	5	,	,	PUNCT
ejpam-6755	418	6	2013	2013	NUM
ejpam-6755	418	7	.	.	PUNCT
ejpam-6755	419	1	[	[	X
ejpam-6755	419	2	16	16	NUM
ejpam-6755	419	3	]	]	PUNCT
ejpam-6755	419	4	t.	t.	PROPN
ejpam-6755	419	5	k.	k.	PROPN
ejpam-6755	419	6	maryati	maryati	PROPN
ejpam-6755	419	7	,	,	PUNCT
ejpam-6755	419	8	a.	a.	PROPN
ejpam-6755	419	9	n.	n.	PROPN
ejpam-6755	419	10	m.	m.	PROPN
ejpam-6755	419	11	salman	salman	PROPN
ejpam-6755	419	12	,	,	PUNCT
ejpam-6755	419	13	e.	e.	PROPN
ejpam-6755	419	14	t.	t.	PROPN
ejpam-6755	419	15	baskoro	baskoro	PROPN
ejpam-6755	419	16	,	,	PUNCT
ejpam-6755	419	17	j.	j.	PROPN
ejpam-6755	419	18	ryan	ryan	PROPN
ejpam-6755	419	19	,	,	PUNCT
ejpam-6755	419	20	and	and	CCONJ
ejpam-6755	419	21	m.	m.	PROPN
ejpam-6755	419	22	miller	miller	PROPN
ejpam-6755	419	23	.	.	PUNCT
ejpam-6755	420	1	on	on	ADP
ejpam-6755	420	2	hsupermagic	hsupermagic	ADJ
ejpam-6755	420	3	labelings	labeling	NOUN
ejpam-6755	420	4	for	for	ADP
ejpam-6755	420	5	certain	certain	ADJ
ejpam-6755	420	6	shackles	shackle	NOUN
ejpam-6755	420	7	and	and	CCONJ
ejpam-6755	420	8	amalgamations	amalgamation	NOUN
ejpam-6755	420	9	of	of	ADP
ejpam-6755	420	10	a	a	DET
ejpam-6755	420	11	connected	connected	ADJ
ejpam-6755	420	12	graph	graph	NOUN
ejpam-6755	420	13	.	.	PUNCT
ejpam-6755	421	1	utilitas	utilitas	PROPN
ejpam-6755	421	2	mathematica	mathematica	PROPN
ejpam-6755	421	3	,	,	PUNCT
ejpam-6755	421	4	83:333–342	83:333–342	PROPN
ejpam-6755	421	5	,	,	PUNCT
ejpam-6755	421	6	2010	2010	NUM
ejpam-6755	421	7	.	.	PUNCT
ejpam-6755	422	1	[	[	X
ejpam-6755	422	2	17	17	NUM
ejpam-6755	422	3	]	]	PUNCT
ejpam-6755	422	4	t.	t.	PROPN
ejpam-6755	422	5	k.	k.	PROPN
ejpam-6755	422	6	maryati	maryati	PROPN
ejpam-6755	422	7	,	,	PUNCT
ejpam-6755	422	8	a.	a.	PROPN
ejpam-6755	422	9	n.	n.	PROPN
ejpam-6755	422	10	m.	m.	PROPN
ejpam-6755	422	11	salman	salman	PROPN
ejpam-6755	422	12	,	,	PUNCT
ejpam-6755	422	13	e.	e.	PROPN
ejpam-6755	422	14	t.	t.	PROPN
ejpam-6755	422	15	baskoro	baskoro	PROPN
ejpam-6755	422	16	,	,	PUNCT
ejpam-6755	422	17	and	and	CCONJ
ejpam-6755	422	18	irawati	irawati	NOUN
ejpam-6755	422	19	.	.	PUNCT
ejpam-6755	423	1	on	on	ADP
ejpam-6755	423	2	ph	ph	ADJ
ejpam-6755	423	3	-	-	ADJ
ejpam-6755	423	4	supermagic	supermagic	ADJ
ejpam-6755	423	5	labelings	labeling	NOUN
ejpam-6755	423	6	of	of	ADP
ejpam-6755	423	7	cpn	cpn	NOUN
ejpam-6755	423	8	,	,	PUNCT
ejpam-6755	423	9	booktitle	booktitle	NOUN
ejpam-6755	423	10	=	=	SYM
ejpam-6755	423	11	proceedings	proceeding	NOUN
ejpam-6755	423	12	of	of	ADP
ejpam-6755	423	13	the	the	DET
ejpam-6755	423	14	14th	14th	ADJ
ejpam-6755	423	15	national	national	ADJ
ejpam-6755	423	16	conference	conference	NOUN
ejpam-6755	423	17	of	of	ADP
ejpam-6755	423	18	mathematics	mathematic	NOUN
ejpam-6755	423	19	,	,	PUNCT
ejpam-6755	423	20	pages	page	NOUN
ejpam-6755	423	21	=	=	SYM
ejpam-6755	423	22	281–285	281–285	NUM
ejpam-6755	423	23	,	,	PUNCT
ejpam-6755	423	24	year	year	NOUN
ejpam-6755	423	25	=	=	SYM
ejpam-6755	423	26	2009	2009	NUM
ejpam-6755	423	27	.	.	PUNCT