id	sid	tid	token	lemma	pos
ejpam-5020	1	1	european	european	PROPN
ejpam-5020	1	2	journal	journal	PROPN
ejpam-5020	1	3	of	of	ADP
ejpam-5020	1	4	pure	pure	ADJ
ejpam-5020	1	5	and	and	CCONJ
ejpam-5020	1	6	applied	apply	VERB
ejpam-5020	1	7	mathematics	mathematic	NOUN
ejpam-5020	1	8	vol	vol	NOUN
ejpam-5020	1	9	.	.	PROPN
ejpam-5020	2	1	17	17	NUM
ejpam-5020	2	2	,	,	PUNCT
ejpam-5020	2	3	no	no	INTJ
ejpam-5020	2	4	.	.	NOUN
ejpam-5020	2	5	1	1	NUM
ejpam-5020	2	6	,	,	PUNCT
ejpam-5020	2	7	2024	2024	NUM
ejpam-5020	2	8	,	,	PUNCT
ejpam-5020	2	9	212	212	NUM
ejpam-5020	2	10	-	-	SYM
ejpam-5020	2	11	221	221	NUM
ejpam-5020	2	12	issn	issn	PROPN
ejpam-5020	2	13	1307	1307	NUM
ejpam-5020	2	14	-	-	SYM
ejpam-5020	2	15	5543	5543	NUM
ejpam-5020	2	16	–	–	PUNCT
ejpam-5020	2	17	ejpam.com	ejpam.com	X
ejpam-5020	2	18	published	publish	VERB
ejpam-5020	2	19	by	by	ADP
ejpam-5020	2	20	new	new	PROPN
ejpam-5020	2	21	york	york	PROPN
ejpam-5020	2	22	business	business	PROPN
ejpam-5020	2	23	global	global	PROPN
ejpam-5020	2	24	closeness	closeness	NOUN
ejpam-5020	2	25	energy	energy	NOUN
ejpam-5020	2	26	of	of	ADP
ejpam-5020	2	27	non	non	ADJ
ejpam-5020	2	28	-	-	ADJ
ejpam-5020	2	29	commuting	commuting	ADJ
ejpam-5020	2	30	graph	graph	NOUN
ejpam-5020	2	31	for	for	ADP
ejpam-5020	2	32	dihedral	dihedral	ADJ
ejpam-5020	2	33	groups	group	NOUN
ejpam-5020	2	34	mamika	mamika	PROPN
ejpam-5020	2	35	ujianita	ujianita	PROPN
ejpam-5020	2	36	romdhini1,∗	romdhini1,∗	PROPN
ejpam-5020	2	37	,	,	PUNCT
ejpam-5020	2	38	athirah	athirah	PROPN
ejpam-5020	2	39	nawawi2	nawawi2	PROPN
ejpam-5020	2	40	,	,	PUNCT
ejpam-5020	2	41	faisal	faisal	PROPN
ejpam-5020	2	42	al	al	PROPN
ejpam-5020	2	43	-	-	PUNCT
ejpam-5020	2	44	sharqi3	sharqi3	PROPN
ejpam-5020	2	45	,	,	PUNCT
ejpam-5020	2	46	ashraf	ashraf	PROPN
ejpam-5020	2	47	alquran4	alquran4	PROPN
ejpam-5020	2	48	1	1	NUM
ejpam-5020	2	49	department	department	NOUN
ejpam-5020	2	50	of	of	ADP
ejpam-5020	2	51	mathematics	mathematic	NOUN
ejpam-5020	2	52	,	,	PUNCT
ejpam-5020	2	53	faculty	faculty	NOUN
ejpam-5020	2	54	of	of	ADP
ejpam-5020	2	55	mathematics	mathematic	NOUN
ejpam-5020	2	56	and	and	CCONJ
ejpam-5020	2	57	natural	natural	ADJ
ejpam-5020	2	58	science	science	NOUN
ejpam-5020	2	59	,	,	PUNCT
ejpam-5020	2	60	universitas	universitas	PROPN
ejpam-5020	2	61	mataram	mataram	PROPN
ejpam-5020	2	62	,	,	PUNCT
ejpam-5020	2	63	mataram	mataram	PROPN
ejpam-5020	2	64	83125	83125	NUM
ejpam-5020	2	65	,	,	PUNCT
ejpam-5020	2	66	indonesia	indonesia	PROPN
ejpam-5020	2	67	2	2	NUM
ejpam-5020	2	68	department	department	NOUN
ejpam-5020	2	69	of	of	ADP
ejpam-5020	2	70	mathematics	mathematic	NOUN
ejpam-5020	2	71	and	and	CCONJ
ejpam-5020	2	72	statistics	statistic	NOUN
ejpam-5020	2	73	,	,	PUNCT
ejpam-5020	2	74	faculty	faculty	NOUN
ejpam-5020	2	75	of	of	ADP
ejpam-5020	2	76	science	science	NOUN
ejpam-5020	2	77	,	,	PUNCT
ejpam-5020	2	78	universiti	universiti	PROPN
ejpam-5020	2	79	putra	putra	PROPN
ejpam-5020	2	80	malaysia	malaysia	PROPN
ejpam-5020	2	81	,	,	PUNCT
ejpam-5020	2	82	43400	43400	NUM
ejpam-5020	2	83	serdang	serdang	PROPN
ejpam-5020	2	84	,	,	PUNCT
ejpam-5020	2	85	selangor	selangor	PROPN
ejpam-5020	2	86	,	,	PUNCT
ejpam-5020	2	87	malaysia	malaysia	PROPN
ejpam-5020	2	88	3	3	NUM
ejpam-5020	2	89	department	department	NOUN
ejpam-5020	2	90	of	of	ADP
ejpam-5020	2	91	mathematics	mathematic	NOUN
ejpam-5020	2	92	,	,	PUNCT
ejpam-5020	2	93	faculty	faculty	NOUN
ejpam-5020	2	94	of	of	ADP
ejpam-5020	2	95	education	education	NOUN
ejpam-5020	2	96	for	for	ADP
ejpam-5020	2	97	pure	pure	ADJ
ejpam-5020	2	98	sciences	science	NOUN
ejpam-5020	2	99	,	,	PUNCT
ejpam-5020	2	100	university	university	NOUN
ejpam-5020	2	101	of	of	ADP
ejpam-5020	2	102	anbar	anbar	PROPN
ejpam-5020	2	103	,	,	PUNCT
ejpam-5020	2	104	ramadi	ramadi	PROPN
ejpam-5020	2	105	,	,	PUNCT
ejpam-5020	2	106	anbar	anbar	NOUN
ejpam-5020	2	107	,	,	PUNCT
ejpam-5020	2	108	iraq	iraq	PROPN
ejpam-5020	2	109	4	4	NUM
ejpam-5020	2	110	basic	basic	ADJ
ejpam-5020	2	111	sciences	sciences	PROPN
ejpam-5020	2	112	department	department	NOUN
ejpam-5020	2	113	,	,	PUNCT
ejpam-5020	2	114	preparatory	preparatory	ADJ
ejpam-5020	2	115	year	year	NOUN
ejpam-5020	2	116	deanship	deanship	NOUN
ejpam-5020	2	117	,	,	PUNCT
ejpam-5020	2	118	king	king	NOUN
ejpam-5020	2	119	faisal	faisal	PROPN
ejpam-5020	2	120	university	university	PROPN
ejpam-5020	2	121	,	,	PUNCT
ejpam-5020	2	122	al	al	PROPN
ejpam-5020	2	123	-	-	PUNCT
ejpam-5020	2	124	ahsa	ahsa	PROPN
ejpam-5020	2	125	,	,	PUNCT
ejpam-5020	3	1	saudi	saudi	PROPN
ejpam-5020	3	2	arabia	arabia	PROPN
ejpam-5020	3	3	abstract	abstract	NOUN
ejpam-5020	3	4	.	.	PUNCT
ejpam-5020	4	1	this	this	DET
ejpam-5020	4	2	paper	paper	NOUN
ejpam-5020	4	3	focuses	focus	VERB
ejpam-5020	4	4	on	on	ADP
ejpam-5020	4	5	the	the	DET
ejpam-5020	4	6	non	non	ADJ
ejpam-5020	4	7	-	-	ADJ
ejpam-5020	4	8	commuting	commuting	ADJ
ejpam-5020	4	9	graph	graph	NOUN
ejpam-5020	4	10	for	for	ADP
ejpam-5020	4	11	dihedral	dihedral	ADJ
ejpam-5020	4	12	groups	group	NOUN
ejpam-5020	4	13	of	of	ADP
ejpam-5020	4	14	order	order	NOUN
ejpam-5020	4	15	2n	2n	NUM
ejpam-5020	4	16	,	,	PUNCT
ejpam-5020	4	17	d2n	d2n	PROPN
ejpam-5020	4	18	,	,	PUNCT
ejpam-5020	4	19	where	where	SCONJ
ejpam-5020	4	20	n	n	PRON
ejpam-5020	4	21	≥	≥	NOUN
ejpam-5020	4	22	3	3	X
ejpam-5020	4	23	.	.	PUNCT
ejpam-5020	5	1	we	we	PRON
ejpam-5020	5	2	show	show	VERB
ejpam-5020	5	3	the	the	DET
ejpam-5020	5	4	spectrum	spectrum	NOUN
ejpam-5020	5	5	and	and	CCONJ
ejpam-5020	5	6	energy	energy	NOUN
ejpam-5020	5	7	of	of	ADP
ejpam-5020	5	8	the	the	DET
ejpam-5020	5	9	graph	graph	NOUN
ejpam-5020	5	10	corresponding	correspond	VERB
ejpam-5020	5	11	to	to	ADP
ejpam-5020	5	12	the	the	DET
ejpam-5020	5	13	closeness	closeness	NOUN
ejpam-5020	5	14	matrix	matrix	NOUN
ejpam-5020	5	15	.	.	PUNCT
ejpam-5020	6	1	the	the	DET
ejpam-5020	6	2	result	result	NOUN
ejpam-5020	6	3	is	be	AUX
ejpam-5020	6	4	that	that	SCONJ
ejpam-5020	6	5	the	the	DET
ejpam-5020	6	6	obtained	obtain	VERB
ejpam-5020	6	7	energy	energy	NOUN
ejpam-5020	6	8	is	be	AUX
ejpam-5020	6	9	always	always	ADV
ejpam-5020	6	10	twice	twice	DET
ejpam-5020	6	11	its	its	PRON
ejpam-5020	6	12	spectral	spectral	ADJ
ejpam-5020	6	13	radius	radius	NOUN
ejpam-5020	6	14	and	and	CCONJ
ejpam-5020	6	15	is	be	AUX
ejpam-5020	6	16	never	never	ADV
ejpam-5020	6	17	an	an	DET
ejpam-5020	6	18	odd	odd	ADJ
ejpam-5020	6	19	integer	integer	NOUN
ejpam-5020	6	20	.	.	PUNCT
ejpam-5020	7	1	moreover	moreover	ADV
ejpam-5020	7	2	,	,	PUNCT
ejpam-5020	7	3	it	it	PRON
ejpam-5020	7	4	is	be	AUX
ejpam-5020	7	5	classified	classify	VERB
ejpam-5020	7	6	as	as	ADP
ejpam-5020	7	7	hypoenergetic	hypoenergetic	ADJ
ejpam-5020	7	8	.	.	PUNCT
ejpam-5020	8	1	2020	2020	NUM
ejpam-5020	8	2	mathematics	mathematic	NOUN
ejpam-5020	8	3	subject	subject	NOUN
ejpam-5020	8	4	classifications	classification	NOUN
ejpam-5020	8	5	:	:	PUNCT
ejpam-5020	8	6	05c25	05c25	NUM
ejpam-5020	8	7	,	,	PUNCT
ejpam-5020	8	8	05c50	05c50	NUM
ejpam-5020	8	9	,	,	PUNCT
ejpam-5020	8	10	15a18	15a18	NUM
ejpam-5020	8	11	,	,	PUNCT
ejpam-5020	8	12	20d99	20d99	NUM
ejpam-5020	8	13	key	key	ADJ
ejpam-5020	8	14	words	word	NOUN
ejpam-5020	8	15	and	and	CCONJ
ejpam-5020	8	16	phrases	phrase	NOUN
ejpam-5020	8	17	:	:	PUNCT
ejpam-5020	8	18	closeness	closeness	NOUN
ejpam-5020	8	19	matrix	matrix	NOUN
ejpam-5020	8	20	,	,	PUNCT
ejpam-5020	8	21	energy	energy	NOUN
ejpam-5020	8	22	of	of	ADP
ejpam-5020	8	23	a	a	DET
ejpam-5020	8	24	graph	graph	NOUN
ejpam-5020	8	25	,	,	PUNCT
ejpam-5020	8	26	non	non	ADJ
ejpam-5020	8	27	-	-	ADJ
ejpam-5020	8	28	commuting	commuting	ADJ
ejpam-5020	8	29	graph	graph	NOUN
ejpam-5020	8	30	,	,	PUNCT
ejpam-5020	8	31	dihedral	dihedral	ADJ
ejpam-5020	8	32	groups	group	NOUN
ejpam-5020	8	33	1	1	NUM
ejpam-5020	8	34	.	.	PUNCT
ejpam-5020	9	1	introduction	introduction	NOUN
ejpam-5020	9	2	let	let	VERB
ejpam-5020	9	3	g	g	NOUN
ejpam-5020	9	4	be	be	AUX
ejpam-5020	9	5	a	a	DET
ejpam-5020	9	6	group	group	NOUN
ejpam-5020	9	7	and	and	CCONJ
ejpam-5020	9	8	z(g	z(g	NOUN
ejpam-5020	9	9	)	)	PUNCT
ejpam-5020	9	10	be	be	VERB
ejpam-5020	9	11	a	a	DET
ejpam-5020	9	12	center	center	NOUN
ejpam-5020	9	13	of	of	ADP
ejpam-5020	9	14	g.	g.	PROPN
ejpam-5020	9	15	the	the	DET
ejpam-5020	9	16	non	non	ADJ
ejpam-5020	9	17	-	-	ADJ
ejpam-5020	9	18	commuting	commuting	ADJ
ejpam-5020	9	19	graph	graph	NOUN
ejpam-5020	9	20	of	of	ADP
ejpam-5020	9	21	g	g	NOUN
ejpam-5020	9	22	,	,	PUNCT
ejpam-5020	9	23	denoted	denote	VERB
ejpam-5020	9	24	as	as	ADP
ejpam-5020	9	25	γg	γg	ADV
ejpam-5020	9	26	,	,	PUNCT
ejpam-5020	9	27	has	have	VERB
ejpam-5020	9	28	vertex	vertex	NOUN
ejpam-5020	9	29	set	set	VERB
ejpam-5020	9	30	g\z(g	g\z(g	NOUN
ejpam-5020	9	31	)	)	PUNCT
ejpam-5020	9	32	and	and	CCONJ
ejpam-5020	9	33	two	two	NUM
ejpam-5020	9	34	distinct	distinct	ADJ
ejpam-5020	9	35	vertices	vertex	NOUN
ejpam-5020	9	36	vp	vp	NOUN
ejpam-5020	9	37	,	,	PUNCT
ejpam-5020	9	38	vq	vq	PROPN
ejpam-5020	9	39	in	in	ADP
ejpam-5020	9	40	γg	γg	ADV
ejpam-5020	9	41	are	be	AUX
ejpam-5020	9	42	connected	connect	VERB
ejpam-5020	9	43	by	by	ADP
ejpam-5020	9	44	an	an	DET
ejpam-5020	9	45	edge	edge	NOUN
ejpam-5020	9	46	whenever	whenever	SCONJ
ejpam-5020	9	47	vpvq	vpvq	PROPN
ejpam-5020	9	48	̸=	̸=	PROPN
ejpam-5020	9	49	vqvp	vqvp	NOUN
ejpam-5020	10	1	[	[	X
ejpam-5020	10	2	1	1	NUM
ejpam-5020	10	3	]	]	PUNCT
ejpam-5020	10	4	.	.	PUNCT
ejpam-5020	11	1	many	many	ADJ
ejpam-5020	11	2	authors	author	NOUN
ejpam-5020	11	3	have	have	AUX
ejpam-5020	11	4	studied	study	VERB
ejpam-5020	11	5	non	non	ADJ
ejpam-5020	11	6	-	-	ADJ
ejpam-5020	11	7	commuting	commuting	ADJ
ejpam-5020	11	8	graphs	graph	NOUN
ejpam-5020	11	9	for	for	ADP
ejpam-5020	11	10	various	various	ADJ
ejpam-5020	11	11	kinds	kind	NOUN
ejpam-5020	11	12	of	of	ADP
ejpam-5020	11	13	groups	group	NOUN
ejpam-5020	11	14	.	.	PUNCT
ejpam-5020	12	1	according	accord	VERB
ejpam-5020	12	2	to	to	ADP
ejpam-5020	12	3	abdollahi	abdollahi	NOUN
ejpam-5020	12	4	[	[	X
ejpam-5020	12	5	1	1	NUM
ejpam-5020	12	6	]	]	PUNCT
ejpam-5020	12	7	,	,	PUNCT
ejpam-5020	12	8	γg	γg	ADV
ejpam-5020	12	9	is	be	AUX
ejpam-5020	12	10	always	always	ADV
ejpam-5020	12	11	connected	connect	VERB
ejpam-5020	12	12	and	and	CCONJ
ejpam-5020	12	13	its	its	PRON
ejpam-5020	12	14	diameter	diameter	NOUN
ejpam-5020	12	15	is	be	AUX
ejpam-5020	12	16	always	always	ADV
ejpam-5020	12	17	2	2	NUM
ejpam-5020	12	18	.	.	PUNCT
ejpam-5020	12	19	accordingly	accordingly	ADV
ejpam-5020	12	20	,	,	PUNCT
ejpam-5020	12	21	(	(	PUNCT
ejpam-5020	12	22	dpq	dpq	PROPN
ejpam-5020	12	23	)	)	PUNCT
ejpam-5020	12	24	,	,	PUNCT
ejpam-5020	12	25	which	which	PRON
ejpam-5020	12	26	is	be	AUX
ejpam-5020	12	27	the	the	DET
ejpam-5020	12	28	shortest	short	ADJ
ejpam-5020	12	29	path	path	NOUN
ejpam-5020	12	30	between	between	ADP
ejpam-5020	12	31	vp	vp	PROPN
ejpam-5020	12	32	and	and	CCONJ
ejpam-5020	12	33	vq	vq	PROPN
ejpam-5020	12	34	,	,	PUNCT
ejpam-5020	12	35	is	be	AUX
ejpam-5020	12	36	well	well	ADV
ejpam-5020	12	37	defined	define	VERB
ejpam-5020	12	38	in	in	ADP
ejpam-5020	12	39	γg	γg	PROPN
ejpam-5020	12	40	.	.	PUNCT
ejpam-5020	13	1	this	this	DET
ejpam-5020	13	2	discussion	discussion	NOUN
ejpam-5020	13	3	continues	continue	VERB
ejpam-5020	13	4	by	by	ADP
ejpam-5020	13	5	examining	examine	VERB
ejpam-5020	13	6	the	the	DET
ejpam-5020	13	7	isomorphic	isomorphic	ADJ
ejpam-5020	13	8	properties	property	NOUN
ejpam-5020	13	9	of	of	ADP
ejpam-5020	13	10	two	two	NUM
ejpam-5020	13	11	non	non	ADJ
ejpam-5020	13	12	-	-	ADJ
ejpam-5020	13	13	commuting	commuting	ADJ
ejpam-5020	13	14	graphs	graph	NOUN
ejpam-5020	13	15	related	relate	VERB
ejpam-5020	13	16	to	to	ADP
ejpam-5020	13	17	the	the	DET
ejpam-5020	13	18	isomorphic	isomorphic	ADJ
ejpam-5020	13	19	properties	property	NOUN
ejpam-5020	13	20	of	of	ADP
ejpam-5020	13	21	the	the	DET
ejpam-5020	13	22	corresponding	corresponding	ADJ
ejpam-5020	13	23	groups	group	NOUN
ejpam-5020	13	24	.	.	PUNCT
ejpam-5020	14	1	∗corresponding	∗corresponde	VERB
ejpam-5020	14	2	author	author	NOUN
ejpam-5020	14	3	.	.	PUNCT
ejpam-5020	15	1	doi	doi	NOUN
ejpam-5020	15	2	:	:	PUNCT
ejpam-5020	15	3	https://doi.org/10.29020/nybg.ejpam.v17i1.5020	https://doi.org/10.29020/nybg.ejpam.v17i1.5020	ADP
ejpam-5020	15	4	email	email	NOUN
ejpam-5020	15	5	addresses	address	NOUN
ejpam-5020	15	6	:	:	PUNCT
ejpam-5020	15	7	mamika@unram.ac.id	mamika@unram.ac.id	NOUN
ejpam-5020	15	8	(	(	PUNCT
ejpam-5020	15	9	m.	m.	PROPN
ejpam-5020	15	10	u.	u.	PROPN
ejpam-5020	15	11	romdhini	romdhini	PROPN
ejpam-5020	15	12	)	)	PUNCT
ejpam-5020	15	13	,	,	PUNCT
ejpam-5020	15	14	athirah@upm.edu.my	athirah@upm.edu.my	PROPN
ejpam-5020	15	15	(	(	PUNCT
ejpam-5020	15	16	a.	a.	NOUN
ejpam-5020	15	17	nawawi	nawawi	PROPN
ejpam-5020	15	18	)	)	PUNCT
ejpam-5020	15	19	,	,	PUNCT
ejpam-5020	15	20	faisal.ghazi@uoanbar.edu.iq	faisal.ghazi@uoanbar.edu.iq	NOUN
ejpam-5020	15	21	(	(	PUNCT
ejpam-5020	15	22	f.	f.	PROPN
ejpam-5020	15	23	al	al	PROPN
ejpam-5020	15	24	-	-	PUNCT
ejpam-5020	15	25	sharqi	sharqi	NOUN
ejpam-5020	15	26	)	)	PUNCT
ejpam-5020	15	27	,	,	PUNCT
ejpam-5020	15	28	aalquran@kfu.edu.sa	aalquran@kfu.edu.sa	PROPN
ejpam-5020	15	29	(	(	PUNCT
ejpam-5020	15	30	a.	a.	PROPN
ejpam-5020	15	31	al	al	PROPN
ejpam-5020	15	32	-	-	PUNCT
ejpam-5020	15	33	quran	quran	PROPN
ejpam-5020	15	34	)	)	PUNCT
ejpam-5020	15	35	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5020	16	1	212	212	NUM
ejpam-5020	16	2	©	©	ADP
ejpam-5020	16	3	2024	2024	NUM
ejpam-5020	16	4	ejpam	ejpam	NOUN
ejpam-5020	16	5	all	all	DET
ejpam-5020	16	6	rights	right	NOUN
ejpam-5020	16	7	reserved	reserve	VERB
ejpam-5020	16	8	.	.	PUNCT
ejpam-5020	17	1	m.	m.	NOUN
ejpam-5020	17	2	u.	u.	PROPN
ejpam-5020	17	3	romdhini	romdhini	PROPN
ejpam-5020	17	4	et	et	PROPN
ejpam-5020	17	5	al	al	PROPN
ejpam-5020	17	6	.	.	PUNCT
ejpam-5020	17	7	/	/	SYM
ejpam-5020	17	8	eur	eur	PROPN
ejpam-5020	17	9	.	.	PUNCT
ejpam-5020	18	1	j.	j.	PROPN
ejpam-5020	18	2	pure	pure	PROPN
ejpam-5020	18	3	appl	appl	PROPN
ejpam-5020	18	4	.	.	PROPN
ejpam-5020	18	5	math	math	PROPN
ejpam-5020	18	6	,	,	PUNCT
ejpam-5020	18	7	17	17	NUM
ejpam-5020	18	8	(	(	PUNCT
ejpam-5020	18	9	1	1	NUM
ejpam-5020	18	10	)	)	PUNCT
ejpam-5020	18	11	(	(	PUNCT
ejpam-5020	18	12	2024	2024	NUM
ejpam-5020	18	13	)	)	PUNCT
ejpam-5020	18	14	,	,	PUNCT
ejpam-5020	18	15	212	212	NUM
ejpam-5020	18	16	-	-	SYM
ejpam-5020	18	17	221	221	NUM
ejpam-5020	18	18	213	213	NUM
ejpam-5020	18	19	the	the	DET
ejpam-5020	18	20	energy	energy	NOUN
ejpam-5020	18	21	of	of	ADP
ejpam-5020	18	22	γg	γg	ADV
ejpam-5020	18	23	,	,	PUNCT
ejpam-5020	18	24	e(γg	e(γg	PROPN
ejpam-5020	18	25	)	)	PUNCT
ejpam-5020	18	26	,	,	PUNCT
ejpam-5020	18	27	is	be	AUX
ejpam-5020	18	28	calculated	calculate	VERB
ejpam-5020	18	29	by	by	ADP
ejpam-5020	18	30	adding	add	VERB
ejpam-5020	18	31	all	all	DET
ejpam-5020	18	32	the	the	DET
ejpam-5020	18	33	absolute	absolute	ADJ
ejpam-5020	18	34	values	value	NOUN
ejpam-5020	18	35	of	of	ADP
ejpam-5020	18	36	its	its	PRON
ejpam-5020	18	37	eigenvalues	eigenvalue	NOUN
ejpam-5020	18	38	.	.	PUNCT
ejpam-5020	19	1	this	this	DET
ejpam-5020	19	2	definition	definition	NOUN
ejpam-5020	19	3	was	be	AUX
ejpam-5020	19	4	pioneered	pioneer	VERB
ejpam-5020	19	5	by	by	ADP
ejpam-5020	19	6	gutman	gutman	NOUN
ejpam-5020	19	7	[	[	X
ejpam-5020	19	8	6	6	NUM
ejpam-5020	19	9	]	]	PUNCT
ejpam-5020	19	10	.	.	PUNCT
ejpam-5020	20	1	there	there	PRON
ejpam-5020	20	2	is	be	VERB
ejpam-5020	20	3	a	a	DET
ejpam-5020	20	4	classification	classification	NOUN
ejpam-5020	20	5	of	of	ADP
ejpam-5020	20	6	graphs	graph	NOUN
ejpam-5020	20	7	based	base	VERB
ejpam-5020	20	8	on	on	ADP
ejpam-5020	20	9	energy	energy	NOUN
ejpam-5020	20	10	value	value	NOUN
ejpam-5020	20	11	[	[	X
ejpam-5020	20	12	11	11	NUM
ejpam-5020	20	13	]	]	PUNCT
ejpam-5020	20	14	.	.	PUNCT
ejpam-5020	21	1	also	also	ADV
ejpam-5020	21	2	,	,	PUNCT
ejpam-5020	21	3	sun	sun	PROPN
ejpam-5020	21	4	et	et	PROPN
ejpam-5020	21	5	al	al	PROPN
ejpam-5020	21	6	.	.	PROPN
ejpam-5020	21	7	have	have	AUX
ejpam-5020	21	8	shown	show	VERB
ejpam-5020	21	9	that	that	SCONJ
ejpam-5020	21	10	the	the	DET
ejpam-5020	21	11	clique	clique	NOUN
ejpam-5020	21	12	path	path	NOUN
ejpam-5020	21	13	has	have	VERB
ejpam-5020	21	14	the	the	DET
ejpam-5020	21	15	maximum	maximum	ADJ
ejpam-5020	21	16	distance	distance	NOUN
ejpam-5020	21	17	of	of	ADP
ejpam-5020	21	18	eigenvalues	eigenvalue	NOUN
ejpam-5020	21	19	and	and	CCONJ
ejpam-5020	21	20	energy	energy	NOUN
ejpam-5020	21	21	[	[	X
ejpam-5020	21	22	23	23	NUM
ejpam-5020	21	23	]	]	PUNCT
ejpam-5020	21	24	.	.	PUNCT
ejpam-5020	22	1	as	as	SCONJ
ejpam-5020	22	2	has	have	AUX
ejpam-5020	22	3	been	be	AUX
ejpam-5020	22	4	shown	show	VERB
ejpam-5020	22	5	in	in	ADP
ejpam-5020	22	6	the	the	DET
ejpam-5020	22	7	literature	literature	NOUN
ejpam-5020	22	8	,	,	PUNCT
ejpam-5020	22	9	the	the	DET
ejpam-5020	22	10	adjacency	adjacency	NOUN
ejpam-5020	22	11	energy	energy	NOUN
ejpam-5020	22	12	of	of	ADP
ejpam-5020	22	13	a	a	DET
ejpam-5020	22	14	graph	graph	NOUN
ejpam-5020	22	15	is	be	AUX
ejpam-5020	22	16	never	never	ADV
ejpam-5020	22	17	an	an	DET
ejpam-5020	22	18	odd	odd	ADJ
ejpam-5020	22	19	integer	integer	NOUN
ejpam-5020	22	20	and	and	CCONJ
ejpam-5020	22	21	it	it	PRON
ejpam-5020	22	22	is	be	AUX
ejpam-5020	22	23	never	never	ADV
ejpam-5020	22	24	its	its	PRON
ejpam-5020	22	25	square	square	ADJ
ejpam-5020	22	26	root	root	NOUN
ejpam-5020	22	27	either	either	CCONJ
ejpam-5020	22	28	[	[	X
ejpam-5020	22	29	4	4	NUM
ejpam-5020	22	30	,	,	PUNCT
ejpam-5020	22	31	12	12	NUM
ejpam-5020	22	32	]	]	PUNCT
ejpam-5020	22	33	.	.	PUNCT
ejpam-5020	23	1	a	a	DET
ejpam-5020	23	2	graph	graph	NOUN
ejpam-5020	23	3	matrix	matrix	NOUN
ejpam-5020	23	4	based	base	VERB
ejpam-5020	23	5	on	on	ADP
ejpam-5020	23	6	the	the	DET
ejpam-5020	23	7	distance	distance	NOUN
ejpam-5020	23	8	between	between	ADP
ejpam-5020	23	9	two	two	NUM
ejpam-5020	23	10	vertices	vertex	NOUN
ejpam-5020	23	11	was	be	AUX
ejpam-5020	23	12	introduced	introduce	VERB
ejpam-5020	23	13	by	by	ADP
ejpam-5020	23	14	indulal	indulal	NOUN
ejpam-5020	23	15	and	and	CCONJ
ejpam-5020	23	16	gutman	gutman	NOUN
ejpam-5020	23	17	[	[	X
ejpam-5020	23	18	7	7	NUM
ejpam-5020	23	19	]	]	PUNCT
ejpam-5020	23	20	.	.	PUNCT
ejpam-5020	24	1	readers	reader	NOUN
ejpam-5020	24	2	may	may	AUX
ejpam-5020	24	3	refer	refer	VERB
ejpam-5020	24	4	to	to	ADP
ejpam-5020	24	5	[	[	X
ejpam-5020	24	6	8	8	NUM
ejpam-5020	24	7	]	]	PUNCT
ejpam-5020	24	8	for	for	ADP
ejpam-5020	24	9	information	information	NOUN
ejpam-5020	24	10	regarding	regard	VERB
ejpam-5020	24	11	degree	degree	NOUN
ejpam-5020	24	12	product	product	NOUN
ejpam-5020	24	13	distance	distance	NOUN
ejpam-5020	24	14	energy	energy	NOUN
ejpam-5020	24	15	.	.	PUNCT
ejpam-5020	25	1	in	in	ADP
ejpam-5020	25	2	addition	addition	NOUN
ejpam-5020	25	3	,	,	PUNCT
ejpam-5020	25	4	jog	jog	ADJ
ejpam-5020	25	5	and	and	CCONJ
ejpam-5020	25	6	gurjar	gurjar	VERB
ejpam-5020	25	7	[	[	X
ejpam-5020	25	8	9	9	X
ejpam-5020	25	9	]	]	PUNCT
ejpam-5020	25	10	discusses	discuss	VERB
ejpam-5020	25	11	the	the	DET
ejpam-5020	25	12	degree	degree	NOUN
ejpam-5020	25	13	sum	sum	NOUN
ejpam-5020	25	14	exponent	exponent	NOUN
ejpam-5020	25	15	distance	distance	NOUN
ejpam-5020	25	16	of	of	ADP
ejpam-5020	25	17	graphs	graph	NOUN
ejpam-5020	25	18	.	.	PUNCT
ejpam-5020	26	1	accordingly	accordingly	ADV
ejpam-5020	26	2	,	,	PUNCT
ejpam-5020	26	3	romdhini	romdhini	VERB
ejpam-5020	26	4	et	et	PROPN
ejpam-5020	26	5	al	al	PROPN
ejpam-5020	26	6	.	.	PUNCT
ejpam-5020	27	1	[	[	X
ejpam-5020	27	2	16	16	NUM
ejpam-5020	27	3	]	]	PUNCT
ejpam-5020	27	4	investigated	investigate	VERB
ejpam-5020	27	5	signless	signless	NOUN
ejpam-5020	27	6	laplacian	laplacian	ADJ
ejpam-5020	27	7	energies	energy	NOUN
ejpam-5020	27	8	of	of	ADP
ejpam-5020	27	9	interval	interval	NOUN
ejpam-5020	27	10	-	-	PUNCT
ejpam-5020	27	11	valued	value	VERB
ejpam-5020	27	12	fuzzy	fuzzy	ADJ
ejpam-5020	27	13	graphs	graph	NOUN
ejpam-5020	27	14	.	.	PUNCT
ejpam-5020	28	1	in	in	ADP
ejpam-5020	28	2	addition	addition	NOUN
ejpam-5020	28	3	,	,	PUNCT
ejpam-5020	28	4	zheng	zheng	PROPN
ejpam-5020	28	5	and	and	CCONJ
ejpam-5020	28	6	zhou	zhou	PROPN
ejpam-5020	29	1	[	[	X
ejpam-5020	29	2	24	24	NUM
ejpam-5020	29	3	]	]	PUNCT
ejpam-5020	29	4	presented	present	VERB
ejpam-5020	29	5	the	the	DET
ejpam-5020	29	6	closeness	closeness	NOUN
ejpam-5020	29	7	eigenvalues	eigenvalue	VERB
ejpam-5020	29	8	of	of	ADP
ejpam-5020	29	9	graphs	graph	NOUN
ejpam-5020	29	10	.	.	PUNCT
ejpam-5020	30	1	throughout	throughout	ADP
ejpam-5020	30	2	this	this	DET
ejpam-5020	30	3	work	work	NOUN
ejpam-5020	30	4	,	,	PUNCT
ejpam-5020	30	5	the	the	DET
ejpam-5020	30	6	vertex	vertex	NOUN
ejpam-5020	30	7	set	set	NOUN
ejpam-5020	30	8	for	for	ADP
ejpam-5020	30	9	γg	γg	ADV
ejpam-5020	30	10	is	be	AUX
ejpam-5020	30	11	the	the	DET
ejpam-5020	30	12	non	non	ADJ
ejpam-5020	30	13	-	-	ADJ
ejpam-5020	30	14	abelian	abelian	ADJ
ejpam-5020	30	15	dihedral	dihedral	ADJ
ejpam-5020	30	16	group	group	NOUN
ejpam-5020	30	17	of	of	ADP
ejpam-5020	30	18	order	order	NOUN
ejpam-5020	30	19	2n	2n	NUM
ejpam-5020	30	20	,	,	PUNCT
ejpam-5020	30	21	where	where	SCONJ
ejpam-5020	30	22	n	n	PRON
ejpam-5020	30	23	≥	≥	NOUN
ejpam-5020	30	24	3	3	NUM
ejpam-5020	30	25	,	,	PUNCT
ejpam-5020	30	26	denoted	denote	VERB
ejpam-5020	30	27	by	by	ADP
ejpam-5020	30	28	d2n	d2n	PROPN
ejpam-5020	31	1	=	=	PUNCT
ejpam-5020	31	2	〈	〈	PROPN
ejpam-5020	31	3	a	a	PRON
ejpam-5020	31	4	,	,	PUNCT
ejpam-5020	31	5	b	b	NOUN
ejpam-5020	31	6	:	:	PUNCT
ejpam-5020	31	7	an	an	DET
ejpam-5020	31	8	=	=	NOUN
ejpam-5020	31	9	b2	b2	NOUN
ejpam-5020	31	10	=	=	SYM
ejpam-5020	31	11	e	e	PROPN
ejpam-5020	31	12	,	,	PUNCT
ejpam-5020	31	13	bab	bab	PROPN
ejpam-5020	31	14	=	=	SYM
ejpam-5020	31	15	a−1	a−1	PROPN
ejpam-5020	31	16	〉	〉	NOUN
ejpam-5020	32	1	[	[	X
ejpam-5020	32	2	3	3	NUM
ejpam-5020	32	3	]	]	PUNCT
ejpam-5020	32	4	.	.	PUNCT
ejpam-5020	33	1	the	the	DET
ejpam-5020	33	2	center	center	NOUN
ejpam-5020	33	3	of	of	ADP
ejpam-5020	33	4	d2n	d2n	PROPN
ejpam-5020	33	5	is	be	AUX
ejpam-5020	33	6	either	either	DET
ejpam-5020	33	7	z	z	PROPN
ejpam-5020	33	8	(	(	PUNCT
ejpam-5020	33	9	d2n	d2n	X
ejpam-5020	33	10	)	)	PUNCT
ejpam-5020	33	11	=	=	PRON
ejpam-5020	34	1	{	{	PUNCT
ejpam-5020	34	2	e	e	NOUN
ejpam-5020	34	3	}	}	PUNCT
ejpam-5020	34	4	for	for	ADP
ejpam-5020	34	5	n	n	NUM
ejpam-5020	34	6	is	be	AUX
ejpam-5020	34	7	odd	odd	ADJ
ejpam-5020	34	8	,	,	PUNCT
ejpam-5020	34	9	or	or	CCONJ
ejpam-5020	34	10	{	{	PUNCT
ejpam-5020	34	11	e	e	NOUN
ejpam-5020	34	12	,	,	PUNCT
ejpam-5020	34	13	a	a	DET
ejpam-5020	34	14	n	n	NOUN
ejpam-5020	34	15	2	2	NUM
ejpam-5020	34	16	}	}	PUNCT
ejpam-5020	34	17	for	for	ADP
ejpam-5020	34	18	n	n	X
ejpam-5020	34	19	is	be	AUX
ejpam-5020	34	20	even	even	ADV
ejpam-5020	34	21	.	.	PUNCT
ejpam-5020	35	1	the	the	DET
ejpam-5020	35	2	centralizer	centralizer	NOUN
ejpam-5020	35	3	of	of	ADP
ejpam-5020	35	4	the	the	DET
ejpam-5020	35	5	element	element	NOUN
ejpam-5020	35	6	ai	ai	VERB
ejpam-5020	35	7	in	in	ADP
ejpam-5020	35	8	d2n	d2n	PROPN
ejpam-5020	35	9	is	be	AUX
ejpam-5020	35	10	cd2n(a	cd2n(a	PROPN
ejpam-5020	35	11	i	i	NOUN
ejpam-5020	35	12	)	)	PUNCT
ejpam-5020	35	13	=	=	PUNCT
ejpam-5020	35	14	{	{	PUNCT
ejpam-5020	35	15	aj	aj	PROPN
ejpam-5020	35	16	:	:	PUNCT
ejpam-5020	35	17	1	1	NUM
ejpam-5020	35	18	≤	≤	NUM
ejpam-5020	35	19	j	j	PROPN
ejpam-5020	35	20	≤	≤	NUM
ejpam-5020	35	21	n	n	CCONJ
ejpam-5020	35	22	}	}	PUNCT
ejpam-5020	35	23	and	and	CCONJ
ejpam-5020	35	24	for	for	ADP
ejpam-5020	35	25	the	the	DET
ejpam-5020	35	26	element	element	NOUN
ejpam-5020	35	27	aib	aib	PROPN
ejpam-5020	35	28	is	be	AUX
ejpam-5020	35	29	either	either	CCONJ
ejpam-5020	35	30	cd2n(a	cd2n(a	ADV
ejpam-5020	35	31	ib	ib	NOUN
ejpam-5020	35	32	)	)	PUNCT
ejpam-5020	35	33	=	=	SYM
ejpam-5020	35	34	{	{	PUNCT
ejpam-5020	35	35	e	e	PROPN
ejpam-5020	35	36	,	,	PUNCT
ejpam-5020	35	37	aib	aib	PROPN
ejpam-5020	35	38	}	}	PUNCT
ejpam-5020	35	39	,	,	PUNCT
ejpam-5020	35	40	if	if	SCONJ
ejpam-5020	35	41	n	n	PRON
ejpam-5020	35	42	is	be	AUX
ejpam-5020	35	43	odd	odd	ADJ
ejpam-5020	35	44	or	or	CCONJ
ejpam-5020	35	45	cd2n(a	cd2n(a	ADV
ejpam-5020	35	46	ib	ib	NOUN
ejpam-5020	35	47	)	)	PUNCT
ejpam-5020	35	48	=	=	SYM
ejpam-5020	35	49	{	{	PUNCT
ejpam-5020	35	50	e	e	NOUN
ejpam-5020	35	51	,	,	PUNCT
ejpam-5020	35	52	a	a	DET
ejpam-5020	35	53	n	n	PRON
ejpam-5020	35	54	2	2	NUM
ejpam-5020	35	55	,	,	PUNCT
ejpam-5020	35	56	aib	aib	PROPN
ejpam-5020	35	57	,	,	PUNCT
ejpam-5020	35	58	a	a	DET
ejpam-5020	35	59	n	n	PRON
ejpam-5020	35	60	2	2	NUM
ejpam-5020	35	61	+	+	NOUN
ejpam-5020	35	62	ib	ib	X
ejpam-5020	35	63	}	}	PUNCT
ejpam-5020	35	64	,	,	PUNCT
ejpam-5020	35	65	if	if	SCONJ
ejpam-5020	35	66	n	n	PRON
ejpam-5020	35	67	is	be	AUX
ejpam-5020	35	68	even	even	ADV
ejpam-5020	35	69	.	.	PUNCT
ejpam-5020	36	1	several	several	ADJ
ejpam-5020	36	2	authors	author	NOUN
ejpam-5020	36	3	have	have	AUX
ejpam-5020	36	4	examined	examine	VERB
ejpam-5020	36	5	the	the	DET
ejpam-5020	36	6	energy	energy	NOUN
ejpam-5020	36	7	of	of	ADP
ejpam-5020	36	8	commuting	commuting	NOUN
ejpam-5020	36	9	and	and	CCONJ
ejpam-5020	36	10	non	non	ADJ
ejpam-5020	36	11	-	-	ADJ
ejpam-5020	36	12	commuting	commuting	ADJ
ejpam-5020	36	13	graphs	graph	NOUN
ejpam-5020	36	14	involving	involve	VERB
ejpam-5020	36	15	d2n	d2n	PROPN
ejpam-5020	36	16	as	as	ADP
ejpam-5020	36	17	the	the	DET
ejpam-5020	36	18	set	set	NOUN
ejpam-5020	36	19	of	of	ADP
ejpam-5020	36	20	vertex	vertex	NOUN
ejpam-5020	36	21	.	.	PUNCT
ejpam-5020	37	1	by	by	ADP
ejpam-5020	37	2	considering	consider	VERB
ejpam-5020	37	3	the	the	DET
ejpam-5020	37	4	eigenvalues	eigenvalue	NOUN
ejpam-5020	37	5	of	of	ADP
ejpam-5020	37	6	the	the	DET
ejpam-5020	37	7	degree	degree	NOUN
ejpam-5020	37	8	sum	sum	NOUN
ejpam-5020	37	9	and	and	CCONJ
ejpam-5020	37	10	degree	degree	NOUN
ejpam-5020	37	11	subtraction	subtraction	NOUN
ejpam-5020	37	12	matrices	matrix	NOUN
ejpam-5020	37	13	,	,	PUNCT
ejpam-5020	37	14	romdhini	romdhini	NOUN
ejpam-5020	37	15	and	and	CCONJ
ejpam-5020	37	16	nawawi	nawawi	VERB
ejpam-5020	37	17	[	[	X
ejpam-5020	37	18	17	17	NUM
ejpam-5020	37	19	,	,	PUNCT
ejpam-5020	37	20	19	19	NUM
ejpam-5020	37	21	]	]	PUNCT
ejpam-5020	37	22	and	and	CCONJ
ejpam-5020	37	23	romdhini	romdhini	PROPN
ejpam-5020	37	24	et	et	PROPN
ejpam-5020	37	25	al	al	PROPN
ejpam-5020	37	26	.	.	PUNCT
ejpam-5020	38	1	[	[	X
ejpam-5020	38	2	22	22	NUM
ejpam-5020	38	3	]	]	PUNCT
ejpam-5020	38	4	formulated	formulate	VERB
ejpam-5020	38	5	the	the	DET
ejpam-5020	38	6	energy	energy	NOUN
ejpam-5020	38	7	.	.	PUNCT
ejpam-5020	39	1	in	in	ADP
ejpam-5020	39	2	[	[	X
ejpam-5020	39	3	18	18	NUM
ejpam-5020	39	4	,	,	PUNCT
ejpam-5020	39	5	21	21	NUM
ejpam-5020	39	6	]	]	PUNCT
ejpam-5020	39	7	,	,	PUNCT
ejpam-5020	39	8	the	the	DET
ejpam-5020	39	9	sum	sum	NOUN
ejpam-5020	39	10	of	of	ADP
ejpam-5020	39	11	the	the	DET
ejpam-5020	39	12	degree	degree	NOUN
ejpam-5020	39	13	exponent	exponent	NOUN
ejpam-5020	39	14	and	and	CCONJ
ejpam-5020	39	15	the	the	DET
ejpam-5020	39	16	maximum	maximum	ADJ
ejpam-5020	39	17	and	and	CCONJ
ejpam-5020	39	18	minimum	minimum	NOUN
ejpam-5020	39	19	degree	degree	NOUN
ejpam-5020	39	20	energies	energy	NOUN
ejpam-5020	39	21	were	be	AUX
ejpam-5020	39	22	presented	present	VERB
ejpam-5020	39	23	for	for	ADP
ejpam-5020	39	24	d2n	d2n	PROPN
ejpam-5020	39	25	.	.	PUNCT
ejpam-5020	40	1	therefore	therefore	ADV
ejpam-5020	40	2	,	,	PUNCT
ejpam-5020	40	3	the	the	DET
ejpam-5020	40	4	purpose	purpose	NOUN
ejpam-5020	40	5	of	of	ADP
ejpam-5020	40	6	this	this	DET
ejpam-5020	40	7	paper	paper	NOUN
ejpam-5020	40	8	is	be	AUX
ejpam-5020	40	9	to	to	PART
ejpam-5020	40	10	formulate	formulate	VERB
ejpam-5020	40	11	the	the	DET
ejpam-5020	40	12	energy	energy	NOUN
ejpam-5020	40	13	based	base	VERB
ejpam-5020	40	14	on	on	ADP
ejpam-5020	40	15	the	the	DET
ejpam-5020	40	16	closeness	closeness	NOUN
ejpam-5020	40	17	matrix	matrix	NOUN
ejpam-5020	40	18	for	for	ADP
ejpam-5020	40	19	γg	γg	ADV
ejpam-5020	40	20	on	on	ADP
ejpam-5020	40	21	d2n	d2n	NOUN
ejpam-5020	40	22	.	.	PUNCT
ejpam-5020	41	1	2	2	X
ejpam-5020	41	2	.	.	X
ejpam-5020	41	3	preliminaries	preliminary	NOUN
ejpam-5020	41	4	in	in	ADP
ejpam-5020	41	5	this	this	DET
ejpam-5020	41	6	part	part	NOUN
ejpam-5020	41	7	,	,	PUNCT
ejpam-5020	41	8	we	we	PRON
ejpam-5020	41	9	begin	begin	VERB
ejpam-5020	41	10	with	with	ADP
ejpam-5020	41	11	the	the	DET
ejpam-5020	41	12	definition	definition	NOUN
ejpam-5020	41	13	of	of	ADP
ejpam-5020	41	14	the	the	DET
ejpam-5020	41	15	closeness	closeness	NOUN
ejpam-5020	41	16	matrix	matrix	NOUN
ejpam-5020	41	17	of	of	ADP
ejpam-5020	41	18	a	a	DET
ejpam-5020	41	19	graph	graph	NOUN
ejpam-5020	41	20	.	.	PUNCT
ejpam-5020	42	1	definition	definition	NOUN
ejpam-5020	42	2	1	1	NUM
ejpam-5020	42	3	.	.	PUNCT
ejpam-5020	43	1	[	[	X
ejpam-5020	43	2	24	24	NUM
ejpam-5020	43	3	]	]	PUNCT
ejpam-5020	43	4	let	let	VERB
ejpam-5020	43	5	dpq	dpq	VERB
ejpam-5020	43	6	be	be	AUX
ejpam-5020	43	7	the	the	DET
ejpam-5020	43	8	distance	distance	NOUN
ejpam-5020	43	9	between	between	ADP
ejpam-5020	43	10	vertex	vertex	NOUN
ejpam-5020	43	11	vp	vp	PROPN
ejpam-5020	43	12	and	and	CCONJ
ejpam-5020	43	13	vq	vq	PROPN
ejpam-5020	43	14	.	.	PUNCT
ejpam-5020	44	1	the	the	DET
ejpam-5020	44	2	closeness	closeness	NOUN
ejpam-5020	44	3	matrix	matrix	NOUN
ejpam-5020	44	4	of	of	ADP
ejpam-5020	44	5	order	order	NOUN
ejpam-5020	44	6	n×	n×	PRON
ejpam-5020	44	7	n	n	PRON
ejpam-5020	44	8	associated	associate	VERB
ejpam-5020	44	9	with	with	ADP
ejpam-5020	44	10	γg	γg	ADV
ejpam-5020	44	11	is	be	AUX
ejpam-5020	44	12	given	give	VERB
ejpam-5020	44	13	by	by	ADP
ejpam-5020	44	14	c(γg	c(γg	NOUN
ejpam-5020	44	15	)	)	PUNCT
ejpam-5020	44	16	=	=	PUNCT
ejpam-5020	45	1	[	[	X
ejpam-5020	45	2	cpq	cpq	X
ejpam-5020	45	3	]	]	X
ejpam-5020	45	4	whose	whose	DET
ejpam-5020	45	5	(	(	PUNCT
ejpam-5020	45	6	p	p	NOUN
ejpam-5020	45	7	,	,	PUNCT
ejpam-5020	45	8	q)-th	q)-th	NOUN
ejpam-5020	45	9	entry	entry	NOUN
ejpam-5020	45	10	is	be	AUX
ejpam-5020	45	11	cpq	cpq	PROPN
ejpam-5020	45	12	=	=	PUNCT
ejpam-5020	45	13	{	{	PUNCT
ejpam-5020	45	14	2−dpq	2−dpq	NOUN
ejpam-5020	45	15	,	,	PUNCT
ejpam-5020	45	16	if	if	SCONJ
ejpam-5020	45	17	vp	vp	PROPN
ejpam-5020	45	18	̸=	̸=	PROPN
ejpam-5020	45	19	vq	vq	PROPN
ejpam-5020	45	20	0	0	NUM
ejpam-5020	45	21	,	,	PUNCT
ejpam-5020	45	22	if	if	SCONJ
ejpam-5020	45	23	vp	vp	PROPN
ejpam-5020	45	24	=	=	SYM
ejpam-5020	45	25	vq	vq	PROPN
ejpam-5020	45	26	.	.	PUNCT
ejpam-5020	46	1	the	the	DET
ejpam-5020	46	2	closeness	closeness	NOUN
ejpam-5020	46	3	energy	energy	NOUN
ejpam-5020	46	4	of	of	ADP
ejpam-5020	46	5	γg	γg	ADV
ejpam-5020	46	6	can	can	AUX
ejpam-5020	46	7	be	be	AUX
ejpam-5020	46	8	written	write	VERB
ejpam-5020	46	9	by	by	ADP
ejpam-5020	46	10	ec(γg	ec(γg	PROPN
ejpam-5020	46	11	)	)	PUNCT
ejpam-5020	47	1	=	=	SYM
ejpam-5020	47	2	n∑	n∑	NOUN
ejpam-5020	47	3	i=1	i=1	PROPN
ejpam-5020	47	4	|λi|	|λi|	PROPN
ejpam-5020	47	5	,	,	PUNCT
ejpam-5020	47	6	where	where	SCONJ
ejpam-5020	47	7	λ1	λ1	ADJ
ejpam-5020	47	8	,	,	PUNCT
ejpam-5020	47	9	λ2	λ2	NOUN
ejpam-5020	47	10	,	,	PUNCT
ejpam-5020	47	11	.	.	PUNCT
ejpam-5020	47	12	.	.	PUNCT
ejpam-5020	48	1	.	.	PUNCT
ejpam-5020	49	1	,	,	PUNCT
ejpam-5020	49	2	λn	λn	PROPN
ejpam-5020	49	3	are	be	AUX
ejpam-5020	49	4	eigenvalues	eigenvalue	NOUN
ejpam-5020	49	5	of	of	ADP
ejpam-5020	49	6	c(γg	c(γg	NOUN
ejpam-5020	49	7	)	)	PUNCT
ejpam-5020	49	8	.	.	PUNCT
ejpam-5020	50	1	the	the	DET
ejpam-5020	50	2	spectral	spectral	ADJ
ejpam-5020	50	3	radius	radius	NOUN
ejpam-5020	50	4	of	of	ADP
ejpam-5020	50	5	γg	γg	PROPN
ejpam-5020	50	6	corresponding	corresponding	NOUN
ejpam-5020	50	7	with	with	ADP
ejpam-5020	50	8	closeness	closeness	NOUN
ejpam-5020	50	9	matrix	matrix	NOUN
ejpam-5020	50	10	is	be	AUX
ejpam-5020	50	11	ρc(γg	ρc(γg	NOUN
ejpam-5020	50	12	)	)	PUNCT
ejpam-5020	51	1	=	=	SYM
ejpam-5020	51	2	max{|λ|	max{|λ|	NOUN
ejpam-5020	51	3	:	:	PUNCT
ejpam-5020	51	4	λ	λ	PROPN
ejpam-5020	51	5	∈	∈	NOUN
ejpam-5020	51	6	specc(γg	specc(γg	NOUN
ejpam-5020	51	7	)	)	PUNCT
ejpam-5020	51	8	}	}	PUNCT
ejpam-5020	51	9	.	.	PUNCT
ejpam-5020	52	1	m.	m.	NOUN
ejpam-5020	52	2	u.	u.	PROPN
ejpam-5020	52	3	romdhini	romdhini	PROPN
ejpam-5020	52	4	et	et	PROPN
ejpam-5020	52	5	al	al	PROPN
ejpam-5020	52	6	.	.	PUNCT
ejpam-5020	52	7	/	/	SYM
ejpam-5020	52	8	eur	eur	PROPN
ejpam-5020	52	9	.	.	PUNCT
ejpam-5020	53	1	j.	j.	PROPN
ejpam-5020	53	2	pure	pure	PROPN
ejpam-5020	53	3	appl	appl	PROPN
ejpam-5020	53	4	.	.	PROPN
ejpam-5020	53	5	math	math	PROPN
ejpam-5020	53	6	,	,	PUNCT
ejpam-5020	53	7	17	17	NUM
ejpam-5020	53	8	(	(	PUNCT
ejpam-5020	53	9	1	1	NUM
ejpam-5020	53	10	)	)	PUNCT
ejpam-5020	53	11	(	(	PUNCT
ejpam-5020	53	12	2024	2024	NUM
ejpam-5020	53	13	)	)	PUNCT
ejpam-5020	53	14	,	,	PUNCT
ejpam-5020	53	15	212	212	NUM
ejpam-5020	53	16	-	-	SYM
ejpam-5020	53	17	221	221	NUM
ejpam-5020	53	18	214	214	NUM
ejpam-5020	53	19	we	we	PRON
ejpam-5020	53	20	know	know	VERB
ejpam-5020	53	21	that	that	SCONJ
ejpam-5020	53	22	γg	γg	ADV
ejpam-5020	53	23	has	have	VERB
ejpam-5020	53	24	2n	2n	NUM
ejpam-5020	53	25	−	−	ADP
ejpam-5020	53	26	1	1	NUM
ejpam-5020	53	27	and	and	CCONJ
ejpam-5020	53	28	2n	2n	NUM
ejpam-5020	53	29	−	−	ADP
ejpam-5020	53	30	2	2	NUM
ejpam-5020	53	31	vertices	vertex	NOUN
ejpam-5020	53	32	for	for	ADP
ejpam-5020	53	33	odd	odd	ADJ
ejpam-5020	53	34	and	and	CCONJ
ejpam-5020	53	35	even	even	ADV
ejpam-5020	53	36	n	n	CCONJ
ejpam-5020	53	37	,	,	PUNCT
ejpam-5020	53	38	respectively	respectively	ADV
ejpam-5020	53	39	,	,	PUNCT
ejpam-5020	53	40	then	then	ADV
ejpam-5020	53	41	γg	γg	ADV
ejpam-5020	53	42	corresponding	correspond	VERB
ejpam-5020	53	43	to	to	ADP
ejpam-5020	53	44	the	the	DET
ejpam-5020	53	45	c−matrix	c−matrix	NOUN
ejpam-5020	53	46	can	can	AUX
ejpam-5020	53	47	be	be	AUX
ejpam-5020	53	48	classified	classify	VERB
ejpam-5020	53	49	as	as	ADP
ejpam-5020	53	50	hypoenergetic	hypoenergetic	ADJ
ejpam-5020	53	51	graph	graph	NOUN
ejpam-5020	53	52	if	if	SCONJ
ejpam-5020	53	53	the	the	DET
ejpam-5020	53	54	c−energy	c−energy	X
ejpam-5020	53	55	complies	comply	VERB
ejpam-5020	53	56	with	with	ADP
ejpam-5020	53	57	the	the	DET
ejpam-5020	53	58	statement	statement	NOUN
ejpam-5020	53	59	below	below	ADV
ejpam-5020	53	60	:	:	PUNCT
ejpam-5020	54	1	[	[	X
ejpam-5020	54	2	11]ec(γg	11]ec(γg	NUM
ejpam-5020	54	3	)	)	PUNCT
ejpam-5020	54	4	<	<	X
ejpam-5020	54	5	{	{	PUNCT
ejpam-5020	54	6	2n−	2n−	PROPN
ejpam-5020	54	7	1	1	NUM
ejpam-5020	54	8	,	,	PUNCT
ejpam-5020	54	9	for	for	ADP
ejpam-5020	54	10	odd	odd	ADJ
ejpam-5020	54	11	n	n	NOUN
ejpam-5020	54	12	2n−	2n−	PROPN
ejpam-5020	54	13	2	2	NUM
ejpam-5020	54	14	,	,	PUNCT
ejpam-5020	54	15	for	for	ADP
ejpam-5020	54	16	even	even	ADV
ejpam-5020	54	17	n	n	CCONJ
ejpam-5020	54	18	,	,	PUNCT
ejpam-5020	54	19	the	the	DET
ejpam-5020	54	20	following	follow	VERB
ejpam-5020	54	21	theorem	theorem	NOUN
ejpam-5020	54	22	is	be	AUX
ejpam-5020	54	23	useful	useful	ADJ
ejpam-5020	54	24	to	to	PART
ejpam-5020	54	25	construct	construct	VERB
ejpam-5020	54	26	the	the	DET
ejpam-5020	54	27	closeness	closeness	NOUN
ejpam-5020	54	28	matrix	matrix	NOUN
ejpam-5020	54	29	of	of	ADP
ejpam-5020	54	30	γg	γg	PROPN
ejpam-5020	54	31	.	.	PUNCT
ejpam-5020	55	1	we	we	PRON
ejpam-5020	55	2	define	define	VERB
ejpam-5020	55	3	g1	g1	PROPN
ejpam-5020	55	4	=	=	PUNCT
ejpam-5020	55	5	{	{	PUNCT
ejpam-5020	55	6	ai	ai	VERB
ejpam-5020	55	7	:	:	PUNCT
ejpam-5020	55	8	1	1	NUM
ejpam-5020	55	9	≤	≤	NUM
ejpam-5020	55	10	i	i	PRON
ejpam-5020	55	11	≤	≤	NUM
ejpam-5020	55	12	n}\z	n}\z	VERB
ejpam-5020	55	13	(	(	PUNCT
ejpam-5020	55	14	d2n	d2n	PROPN
ejpam-5020	55	15	)	)	PUNCT
ejpam-5020	55	16	and	and	CCONJ
ejpam-5020	55	17	g2	g2	PROPN
ejpam-5020	55	18	=	=	SYM
ejpam-5020	55	19	{	{	PUNCT
ejpam-5020	55	20	aib	aib	PROPN
ejpam-5020	55	21	:	:	PUNCT
ejpam-5020	55	22	1	1	NUM
ejpam-5020	55	23	≤	≤	NUM
ejpam-5020	55	24	i	i	PRON
ejpam-5020	55	25	≤	≤	NOUN
ejpam-5020	55	26	n	n	CCONJ
ejpam-5020	55	27	}	}	PUNCT
ejpam-5020	55	28	.	.	PUNCT
ejpam-5020	56	1	theorem	theorem	NOUN
ejpam-5020	56	2	1	1	NUM
ejpam-5020	56	3	.	.	PUNCT
ejpam-5020	57	1	[	[	X
ejpam-5020	57	2	10	10	NUM
ejpam-5020	57	3	]	]	PUNCT
ejpam-5020	57	4	for	for	ADP
ejpam-5020	57	5	a	a	DET
ejpam-5020	57	6	non	non	ADJ
ejpam-5020	57	7	-	-	ADJ
ejpam-5020	57	8	commuting	commuting	ADJ
ejpam-5020	57	9	graph	graph	NOUN
ejpam-5020	57	10	for	for	ADP
ejpam-5020	57	11	g	g	NOUN
ejpam-5020	57	12	,	,	PUNCT
ejpam-5020	57	13	γg	γg	ADV
ejpam-5020	57	14	,	,	PUNCT
ejpam-5020	57	15	(	(	PUNCT
ejpam-5020	57	16	i	i	NOUN
ejpam-5020	57	17	)	)	PUNCT
ejpam-5020	57	18	if	if	SCONJ
ejpam-5020	57	19	g	g	PROPN
ejpam-5020	57	20	=	=	SYM
ejpam-5020	57	21	g1	g1	PROPN
ejpam-5020	57	22	,	,	PUNCT
ejpam-5020	57	23	then	then	ADV
ejpam-5020	57	24	γg	γg	PROPN
ejpam-5020	57	25	∼=	∼=	PROPN
ejpam-5020	57	26	k̄m	k̄m	PROPN
ejpam-5020	57	27	,	,	PUNCT
ejpam-5020	57	28	where	where	SCONJ
ejpam-5020	57	29	m	m	NOUN
ejpam-5020	57	30	=	=	VERB
ejpam-5020	57	31	|g1|	|g1|	NOUN
ejpam-5020	57	32	,	,	PUNCT
ejpam-5020	57	33	(	(	PUNCT
ejpam-5020	57	34	ii	ii	NOUN
ejpam-5020	57	35	)	)	PUNCT
ejpam-5020	57	36	if	if	SCONJ
ejpam-5020	57	37	g	g	PROPN
ejpam-5020	57	38	=	=	PROPN
ejpam-5020	57	39	g2	g2	PROPN
ejpam-5020	57	40	,	,	PUNCT
ejpam-5020	57	41	then	then	ADV
ejpam-5020	57	42	γg	γg	ADV
ejpam-5020	57	43	∼=	∼=	PROPN
ejpam-5020	57	44	{	{	PUNCT
ejpam-5020	57	45	kn	kn	NOUN
ejpam-5020	57	46	,	,	PUNCT
ejpam-5020	57	47	if	if	SCONJ
ejpam-5020	57	48	n	n	PRON
ejpam-5020	57	49	is	be	AUX
ejpam-5020	57	50	odd	odd	ADJ
ejpam-5020	57	51	kn	kn	PROPN
ejpam-5020	57	52	−	−	PROPN
ejpam-5020	57	53	n	n	PRON
ejpam-5020	57	54	2k2	2k2	NUM
ejpam-5020	57	55	,	,	PUNCT
ejpam-5020	57	56	if	if	SCONJ
ejpam-5020	57	57	n	n	PRON
ejpam-5020	57	58	is	be	AUX
ejpam-5020	57	59	even	even	ADV
ejpam-5020	57	60	.	.	PUNCT
ejpam-5020	58	1	where	where	SCONJ
ejpam-5020	58	2	n	n	NUM
ejpam-5020	58	3	2k2	2k2	NUM
ejpam-5020	58	4	denotes	denote	NOUN
ejpam-5020	58	5	n	n	X
ejpam-5020	58	6	2	2	NUM
ejpam-5020	58	7	copies	copy	NOUN
ejpam-5020	58	8	of	of	ADP
ejpam-5020	58	9	k2	k2	PROPN
ejpam-5020	58	10	.	.	PUNCT
ejpam-5020	59	1	lemma	lemma	PROPN
ejpam-5020	59	2	1	1	NUM
ejpam-5020	59	3	.	.	PUNCT
ejpam-5020	60	1	[	[	X
ejpam-5020	60	2	5	5	X
ejpam-5020	60	3	]	]	PUNCT
ejpam-5020	60	4	the	the	DET
ejpam-5020	60	5	adjacency	adjacency	PROPN
ejpam-5020	60	6	spectrum	spectrum	NOUN
ejpam-5020	60	7	of	of	ADP
ejpam-5020	60	8	kn	kn	PROPN
ejpam-5020	60	9	is	be	AUX
ejpam-5020	60	10	{	{	PUNCT
ejpam-5020	60	11	(	(	PUNCT
ejpam-5020	60	12	n−	n−	NOUN
ejpam-5020	60	13	1)(1	1)(1	NUM
ejpam-5020	60	14	)	)	PUNCT
ejpam-5020	60	15	,	,	PUNCT
ejpam-5020	60	16	(	(	PUNCT
ejpam-5020	60	17	−1)(n−1	−1)(n−1	X
ejpam-5020	60	18	)	)	PUNCT
ejpam-5020	60	19	}	}	PUNCT
ejpam-5020	60	20	.	.	PUNCT
ejpam-5020	61	1	in	in	ADP
ejpam-5020	61	2	order	order	NOUN
ejpam-5020	61	3	to	to	PART
ejpam-5020	61	4	simplify	simplify	VERB
ejpam-5020	61	5	the	the	DET
ejpam-5020	61	6	determinant	determinant	NOUN
ejpam-5020	61	7	in	in	ADP
ejpam-5020	61	8	the	the	DET
ejpam-5020	61	9	characteristic	characteristic	ADJ
ejpam-5020	61	10	polynomial	polynomial	NOUN
ejpam-5020	61	11	of	of	ADP
ejpam-5020	61	12	γg	γg	PROPN
ejpam-5020	61	13	,	,	PUNCT
ejpam-5020	61	14	we	we	PRON
ejpam-5020	61	15	need	need	VERB
ejpam-5020	61	16	the	the	DET
ejpam-5020	61	17	following	follow	VERB
ejpam-5020	61	18	three	three	NUM
ejpam-5020	61	19	results	result	NOUN
ejpam-5020	61	20	.	.	PUNCT
ejpam-5020	62	1	lemma	lemma	PROPN
ejpam-5020	62	2	2	2	NUM
ejpam-5020	62	3	.	.	PUNCT
ejpam-5020	63	1	[	[	X
ejpam-5020	63	2	13	13	NUM
ejpam-5020	63	3	]	]	X
ejpam-5020	63	4	if	if	SCONJ
ejpam-5020	63	5	a	a	DET
ejpam-5020	63	6	,	,	PUNCT
ejpam-5020	63	7	b	b	NOUN
ejpam-5020	63	8	,	,	PUNCT
ejpam-5020	63	9	c	c	PROPN
ejpam-5020	63	10	and	and	CCONJ
ejpam-5020	63	11	d	d	PROPN
ejpam-5020	63	12	are	be	AUX
ejpam-5020	63	13	real	real	ADJ
ejpam-5020	63	14	numbers	number	NOUN
ejpam-5020	63	15	,	,	PUNCT
ejpam-5020	63	16	then	then	ADV
ejpam-5020	63	17	the	the	DET
ejpam-5020	63	18	determinant	determinant	NOUN
ejpam-5020	63	19	of	of	ADP
ejpam-5020	63	20	the	the	DET
ejpam-5020	63	21	(	(	PUNCT
ejpam-5020	63	22	n1	n1	PROPN
ejpam-5020	63	23	+	+	CCONJ
ejpam-5020	63	24	n2)×	n2)×	X
ejpam-5020	63	25	(	(	PUNCT
ejpam-5020	63	26	n1	n1	NOUN
ejpam-5020	63	27	+	+	CCONJ
ejpam-5020	63	28	n2	n2	ADJ
ejpam-5020	63	29	)	)	PUNCT
ejpam-5020	63	30	matrix	matrix	NOUN
ejpam-5020	63	31	of	of	ADP
ejpam-5020	63	32	the	the	DET
ejpam-5020	63	33	form∣∣∣∣	form∣∣∣∣	PROPN
ejpam-5020	63	34	(	(	PUNCT
ejpam-5020	63	35	λ+	λ+	PUNCT
ejpam-5020	63	36	a)in1	a)in1	ADV
ejpam-5020	63	37	−	−	PROPN
ejpam-5020	63	38	ajn1	ajn1	PROPN
ejpam-5020	63	39	−cjn1×n2	−cjn1×n2	VERB
ejpam-5020	63	40	−djn2×n1	−djn2×n1	NOUN
ejpam-5020	63	41	(	(	PUNCT
ejpam-5020	63	42	λ+	λ+	NUM
ejpam-5020	63	43	b)in2	b)in2	NUM
ejpam-5020	63	44	−	−	PROPN
ejpam-5020	63	45	bjn2	bjn2	PROPN
ejpam-5020	63	46	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5020	63	47	can	can	AUX
ejpam-5020	63	48	be	be	AUX
ejpam-5020	63	49	simplified	simplify	VERB
ejpam-5020	63	50	in	in	ADP
ejpam-5020	63	51	an	an	DET
ejpam-5020	63	52	expression	expression	NOUN
ejpam-5020	63	53	as	as	ADP
ejpam-5020	63	54	(	(	PUNCT
ejpam-5020	63	55	λ+	λ+	PUNCT
ejpam-5020	63	56	a)n1−1(λ+	a)n1−1(λ+	NOUN
ejpam-5020	63	57	b)n2−1	b)n2−1	NOUN
ejpam-5020	63	58	(	(	PUNCT
ejpam-5020	63	59	(	(	PUNCT
ejpam-5020	63	60	λ−	λ−	PROPN
ejpam-5020	63	61	(	(	PUNCT
ejpam-5020	63	62	n1	n1	PROPN
ejpam-5020	63	63	−	−	PROPN
ejpam-5020	63	64	1	1	NUM
ejpam-5020	63	65	)	)	PUNCT
ejpam-5020	63	66	a	a	NOUN
ejpam-5020	63	67	)	)	PUNCT
ejpam-5020	63	68	(	(	PUNCT
ejpam-5020	63	69	λ−	λ−	PROPN
ejpam-5020	63	70	(	(	PUNCT
ejpam-5020	63	71	n2	n2	ADJ
ejpam-5020	63	72	−	−	PROPN
ejpam-5020	63	73	1	1	X
ejpam-5020	63	74	)	)	PUNCT
ejpam-5020	63	75	b)−	b)−	PROPN
ejpam-5020	63	76	n1n2cd	n1n2cd	NOUN
ejpam-5020	63	77	)	)	PUNCT
ejpam-5020	63	78	,	,	PUNCT
ejpam-5020	63	79	where	where	SCONJ
ejpam-5020	63	80	1	1	NUM
ejpam-5020	63	81	≤	≤	NUM
ejpam-5020	63	82	n1	n1	NOUN
ejpam-5020	63	83	,	,	PUNCT
ejpam-5020	63	84	n2	n2	ADJ
ejpam-5020	63	85	≤	≤	NOUN
ejpam-5020	63	86	n	n	CCONJ
ejpam-5020	63	87	and	and	CCONJ
ejpam-5020	63	88	n1	n1	PROPN
ejpam-5020	63	89	+	+	CCONJ
ejpam-5020	63	90	n2	n2	ADJ
ejpam-5020	63	91	=	=	PROPN
ejpam-5020	63	92	n.	n.	NOUN
ejpam-5020	63	93	theorem	theorem	NOUN
ejpam-5020	63	94	2	2	NUM
ejpam-5020	63	95	.	.	PUNCT
ejpam-5020	64	1	[	[	X
ejpam-5020	64	2	20	20	NUM
ejpam-5020	64	3	]	]	X
ejpam-5020	64	4	if	if	SCONJ
ejpam-5020	64	5	s	s	PROPN
ejpam-5020	64	6	,	,	PUNCT
ejpam-5020	64	7	t	t	PROPN
ejpam-5020	64	8	are	be	AUX
ejpam-5020	64	9	real	real	ADJ
ejpam-5020	64	10	numbers	number	NOUN
ejpam-5020	64	11	,	,	PUNCT
ejpam-5020	64	12	then	then	ADV
ejpam-5020	64	13	the	the	DET
ejpam-5020	64	14	characteristic	characteristic	ADJ
ejpam-5020	64	15	polynomial	polynomial	NOUN
ejpam-5020	64	16	of	of	ADP
ejpam-5020	64	17	an	an	DET
ejpam-5020	64	18	n×	n×	NOUN
ejpam-5020	64	19	n	n	NOUN
ejpam-5020	64	20	matrix	matrix	NOUN
ejpam-5020	64	21	m	m	VERB
ejpam-5020	64	22	=	=	PUNCT
ejpam-5020	65	1	[	[	PUNCT
ejpam-5020	65	2	t(j	t(j	PROPN
ejpam-5020	65	3	−	−	PROPN
ejpam-5020	65	4	i)n	i)n	NOUN
ejpam-5020	65	5	2	2	NUM
ejpam-5020	65	6	t(j	t(j	PROPN
ejpam-5020	65	7	−	−	NOUN
ejpam-5020	65	8	i)n	i)n	NOUN
ejpam-5020	65	9	2	2	NUM
ejpam-5020	65	10	+	+	CCONJ
ejpam-5020	65	11	sin	sin	NOUN
ejpam-5020	65	12	2	2	NUM
ejpam-5020	65	13	t(j	t(j	PROPN
ejpam-5020	65	14	−	−	NOUN
ejpam-5020	65	15	i)n	i)n	NOUN
ejpam-5020	65	16	2	2	NUM
ejpam-5020	65	17	+	+	CCONJ
ejpam-5020	65	18	sin	sin	NOUN
ejpam-5020	65	19	2	2	NUM
ejpam-5020	65	20	t(j	t(j	PROPN
ejpam-5020	65	21	−	−	NOUN
ejpam-5020	65	22	i)n	i)n	NOUN
ejpam-5020	65	23	2	2	NUM
ejpam-5020	65	24	]	]	PUNCT
ejpam-5020	65	25	is	be	AUX
ejpam-5020	65	26	pm	pm	NOUN
ejpam-5020	65	27	(	(	PUNCT
ejpam-5020	65	28	λ	λ	NOUN
ejpam-5020	65	29	)	)	PUNCT
ejpam-5020	65	30	=	=	SYM
ejpam-5020	66	1	(	(	PUNCT
ejpam-5020	66	2	λ−	λ−	PROPN
ejpam-5020	66	3	s+	s+	PUNCT
ejpam-5020	66	4	2	2	NUM
ejpam-5020	66	5	t	t	NOUN
ejpam-5020	66	6	)	)	PUNCT
ejpam-5020	66	7	n	n	PRON
ejpam-5020	66	8	2	2	NUM
ejpam-5020	66	9	−1	−1	NOUN
ejpam-5020	66	10	(	(	PUNCT
ejpam-5020	66	11	λ−	λ−	PROPN
ejpam-5020	66	12	s−	s−	PROPN
ejpam-5020	66	13	(	(	PUNCT
ejpam-5020	66	14	n−	n−	NOUN
ejpam-5020	66	15	2	2	NUM
ejpam-5020	66	16	)	)	PUNCT
ejpam-5020	66	17	t	t	PROPN
ejpam-5020	66	18	)	)	PUNCT
ejpam-5020	66	19	(	(	PUNCT
ejpam-5020	66	20	λ+	λ+	X
ejpam-5020	66	21	s	s	X
ejpam-5020	66	22	)	)	PUNCT
ejpam-5020	66	23	n	n	DET
ejpam-5020	66	24	2	2	NUM
ejpam-5020	66	25	.	.	PUNCT
ejpam-5020	66	26	theorem	theorem	NOUN
ejpam-5020	66	27	3	3	NUM
ejpam-5020	66	28	.	.	PUNCT
ejpam-5020	67	1	[	[	X
ejpam-5020	67	2	20	20	NUM
ejpam-5020	67	3	]	]	PUNCT
ejpam-5020	67	4	if	if	SCONJ
ejpam-5020	67	5	r	r	NOUN
ejpam-5020	67	6	,	,	PUNCT
ejpam-5020	67	7	s	s	PROPN
ejpam-5020	67	8	,	,	PUNCT
ejpam-5020	67	9	t	t	PROPN
ejpam-5020	67	10	,	,	PUNCT
ejpam-5020	67	11	u	u	PROPN
ejpam-5020	67	12	are	be	AUX
ejpam-5020	67	13	real	real	ADJ
ejpam-5020	67	14	numbers	number	NOUN
ejpam-5020	67	15	,	,	PUNCT
ejpam-5020	67	16	then	then	ADV
ejpam-5020	67	17	the	the	DET
ejpam-5020	67	18	characteristic	characteristic	ADJ
ejpam-5020	67	19	polynomial	polynomial	NOUN
ejpam-5020	67	20	of	of	ADP
ejpam-5020	67	21	an	an	DET
ejpam-5020	67	22	(	(	PUNCT
ejpam-5020	67	23	2n−	2n−	PROPN
ejpam-5020	67	24	2)×	2)×	NUM
ejpam-5020	67	25	(	(	PUNCT
ejpam-5020	67	26	2n−	2n−	PROPN
ejpam-5020	67	27	2	2	NUM
ejpam-5020	67	28	)	)	PUNCT
ejpam-5020	67	29	matrix	matrix	NOUN
ejpam-5020	67	30	m	m	NOUN
ejpam-5020	67	31	=	=	ADJ
ejpam-5020	67	32			NUM
ejpam-5020	67	33	r(j	r(j	PROPN
ejpam-5020	67	34	−	−	PROPN
ejpam-5020	67	35	i)n−2	i)n−2	PROPN
ejpam-5020	67	36	tj(n−2)×n	tj(n−2)×n	NOUN
ejpam-5020	67	37	2	2	NUM
ejpam-5020	67	38	tj(n−2)×n	tj(n−2)×n	NUM
ejpam-5020	67	39	2	2	NUM
ejpam-5020	67	40	tjn	tjn	NOUN
ejpam-5020	67	41	2	2	NUM
ejpam-5020	67	42	×(n−2	×(n−2	NOUN
ejpam-5020	67	43	)	)	PUNCT
ejpam-5020	67	44	u(j	u(j	PROPN
ejpam-5020	67	45	−	−	PROPN
ejpam-5020	67	46	i)n	i)n	PUNCT
ejpam-5020	67	47	2	2	NUM
ejpam-5020	67	48	u(j	u(j	NOUN
ejpam-5020	67	49	−	−	NOUN
ejpam-5020	67	50	i)n	i)n	NOUN
ejpam-5020	67	51	2	2	NUM
ejpam-5020	67	52	+	+	CCONJ
ejpam-5020	67	53	sin	sin	NOUN
ejpam-5020	67	54	2	2	NUM
ejpam-5020	67	55	tjn	tjn	NOUN
ejpam-5020	67	56	2	2	NUM
ejpam-5020	67	57	×(n−2	×(n−2	NOUN
ejpam-5020	67	58	)	)	PUNCT
ejpam-5020	67	59	u(j	u(j	PROPN
ejpam-5020	67	60	−	−	PROPN
ejpam-5020	67	61	i)n	i)n	NOUN
ejpam-5020	67	62	2	2	NUM
ejpam-5020	67	63	+	+	CCONJ
ejpam-5020	67	64	sin	sin	NOUN
ejpam-5020	67	65	2	2	NUM
ejpam-5020	67	66	u(j	u(j	NOUN
ejpam-5020	67	67	−	−	NOUN
ejpam-5020	67	68	i)n	i)n	NOUN
ejpam-5020	67	69	2	2	NUM
ejpam-5020	67	70			NOUN
ejpam-5020	67	71	is	be	AUX
ejpam-5020	67	72	pm	pm	NOUN
ejpam-5020	67	73	(	(	PUNCT
ejpam-5020	67	74	λ	λ	NOUN
ejpam-5020	67	75	)	)	PUNCT
ejpam-5020	67	76	=	=	SYM
ejpam-5020	67	77	(	(	PUNCT
ejpam-5020	67	78	λ+	λ+	NUM
ejpam-5020	67	79	r)n−3	r)n−3	NOUN
ejpam-5020	67	80	(	(	PUNCT
ejpam-5020	67	81	λ−	λ−	PROPN
ejpam-5020	67	82	s+	s+	PUNCT
ejpam-5020	67	83	2u	2u	PROPN
ejpam-5020	67	84	)	)	PUNCT
ejpam-5020	67	85	n	n	PRON
ejpam-5020	67	86	2	2	NUM
ejpam-5020	67	87	−1	−1	NOUN
ejpam-5020	67	88	(	(	PUNCT
ejpam-5020	67	89	λ+	λ+	NOUN
ejpam-5020	67	90	s	s	NOUN
ejpam-5020	67	91	)	)	PUNCT
ejpam-5020	67	92	n	n	PRON
ejpam-5020	67	93	2	2	NUM
ejpam-5020	67	94	(	(	PUNCT
ejpam-5020	67	95	λ2	λ2	NOUN
ejpam-5020	67	96	−	−	PROPN
ejpam-5020	67	97	(	(	PUNCT
ejpam-5020	67	98	s+	s+	X
ejpam-5020	67	99	(	(	PUNCT
ejpam-5020	67	100	n−	n−	NOUN
ejpam-5020	67	101	2)u+	2)u+	NUM
ejpam-5020	67	102	r(n−	r(n−	NOUN
ejpam-5020	67	103	3))λ+	3))λ+	NUM
ejpam-5020	67	104	r(n−	r(n−	NOUN
ejpam-5020	67	105	3	3	NUM
ejpam-5020	67	106	)	)	PUNCT
ejpam-5020	67	107	(	(	PUNCT
ejpam-5020	67	108	s+	s+	X
ejpam-5020	67	109	(	(	PUNCT
ejpam-5020	67	110	n−	n−	NOUN
ejpam-5020	67	111	2)u)−	2)u)−	NUM
ejpam-5020	67	112	n(n−	n(n−	NOUN
ejpam-5020	67	113	2)t2	2)t2	NUM
ejpam-5020	67	114	)	)	PUNCT
ejpam-5020	67	115	.	.	PUNCT
ejpam-5020	68	1	m.	m.	PROPN
ejpam-5020	68	2	u.	u.	PROPN
ejpam-5020	68	3	romdhini	romdhini	PROPN
ejpam-5020	68	4	et	et	PROPN
ejpam-5020	68	5	al	al	PROPN
ejpam-5020	68	6	.	.	PUNCT
ejpam-5020	68	7	/	/	SYM
ejpam-5020	68	8	eur	eur	PROPN
ejpam-5020	68	9	.	.	PUNCT
ejpam-5020	69	1	j.	j.	PROPN
ejpam-5020	69	2	pure	pure	PROPN
ejpam-5020	69	3	appl	appl	PROPN
ejpam-5020	69	4	.	.	PROPN
ejpam-5020	69	5	math	math	PROPN
ejpam-5020	69	6	,	,	PUNCT
ejpam-5020	69	7	17	17	NUM
ejpam-5020	69	8	(	(	PUNCT
ejpam-5020	69	9	1	1	NUM
ejpam-5020	69	10	)	)	PUNCT
ejpam-5020	69	11	(	(	PUNCT
ejpam-5020	69	12	2024	2024	NUM
ejpam-5020	69	13	)	)	PUNCT
ejpam-5020	69	14	,	,	PUNCT
ejpam-5020	69	15	212	212	NUM
ejpam-5020	69	16	-	-	SYM
ejpam-5020	69	17	221	221	NUM
ejpam-5020	69	18	215	215	NUM
ejpam-5020	69	19	3	3	NUM
ejpam-5020	69	20	.	.	PUNCT
ejpam-5020	69	21	main	main	ADJ
ejpam-5020	69	22	results	result	NOUN
ejpam-5020	69	23	in	in	ADP
ejpam-5020	69	24	this	this	DET
ejpam-5020	69	25	section	section	NOUN
ejpam-5020	69	26	,	,	PUNCT
ejpam-5020	69	27	we	we	PRON
ejpam-5020	69	28	begin	begin	VERB
ejpam-5020	69	29	with	with	ADP
ejpam-5020	69	30	the	the	DET
ejpam-5020	69	31	distance	distance	NOUN
ejpam-5020	69	32	between	between	ADP
ejpam-5020	69	33	two	two	NUM
ejpam-5020	69	34	distinct	distinct	ADJ
ejpam-5020	69	35	vertices	vertex	NOUN
ejpam-5020	69	36	in	in	ADP
ejpam-5020	69	37	γg	γg	PROPN
ejpam-5020	69	38	.	.	PUNCT
ejpam-5020	69	39	theorem	theorem	NOUN
ejpam-5020	69	40	4	4	NUM
ejpam-5020	69	41	.	.	PUNCT
ejpam-5020	70	1	let	let	AUX
ejpam-5020	70	2	γg	γg	ADV
ejpam-5020	70	3	be	be	AUX
ejpam-5020	70	4	the	the	DET
ejpam-5020	70	5	non	non	ADJ
ejpam-5020	70	6	-	-	ADJ
ejpam-5020	70	7	commuting	commuting	ADJ
ejpam-5020	70	8	graph	graph	NOUN
ejpam-5020	70	9	on	on	ADP
ejpam-5020	70	10	g	g	PROPN
ejpam-5020	70	11	=	=	PUNCT
ejpam-5020	70	12	g1	g1	PROPN
ejpam-5020	70	13	∪	∪	ADP
ejpam-5020	70	14	g2	g2	PROPN
ejpam-5020	70	15	.	.	PUNCT
ejpam-5020	71	1	for	for	ADP
ejpam-5020	71	2	two	two	NUM
ejpam-5020	71	3	distinct	distinct	ADJ
ejpam-5020	71	4	vertices	vertex	NOUN
ejpam-5020	71	5	vp	vp	NOUN
ejpam-5020	71	6	,	,	PUNCT
ejpam-5020	71	7	vq	vq	PROPN
ejpam-5020	71	8	∈	∈	PROPN
ejpam-5020	71	9	v	v	ADP
ejpam-5020	71	10	(	(	PUNCT
ejpam-5020	71	11	γg	γg	ADJ
ejpam-5020	71	12	)	)	PUNCT
ejpam-5020	71	13	,	,	PUNCT
ejpam-5020	71	14	then	then	ADV
ejpam-5020	71	15	the	the	DET
ejpam-5020	71	16	distance	distance	NOUN
ejpam-5020	71	17	between	between	ADP
ejpam-5020	71	18	vp	vp	PROPN
ejpam-5020	71	19	and	and	CCONJ
ejpam-5020	71	20	vq	vq	PROPN
ejpam-5020	71	21	(	(	PUNCT
ejpam-5020	71	22	i	i	NOUN
ejpam-5020	71	23	)	)	PUNCT
ejpam-5020	71	24	for	for	ADP
ejpam-5020	71	25	the	the	DET
ejpam-5020	71	26	odd	odd	ADJ
ejpam-5020	71	27	n	n	NOUN
ejpam-5020	71	28	,	,	PUNCT
ejpam-5020	71	29	dpq	dpq	VERB
ejpam-5020	71	30	=	=	PUNCT
ejpam-5020	71	31	{	{	PUNCT
ejpam-5020	71	32	2	2	NUM
ejpam-5020	71	33	,	,	PUNCT
ejpam-5020	71	34	if	if	SCONJ
ejpam-5020	71	35	vp	vp	PROPN
ejpam-5020	71	36	,	,	PUNCT
ejpam-5020	71	37	vq	vq	PROPN
ejpam-5020	71	38	∈	∈	PROPN
ejpam-5020	71	39	g1	g1	PROPN
ejpam-5020	71	40	1	1	NUM
ejpam-5020	71	41	,	,	PUNCT
ejpam-5020	71	42	otherwise	otherwise	ADV
ejpam-5020	71	43	,	,	PUNCT
ejpam-5020	71	44	,	,	PUNCT
ejpam-5020	71	45	and	and	CCONJ
ejpam-5020	71	46	(	(	PUNCT
ejpam-5020	71	47	ii	ii	NOUN
ejpam-5020	71	48	)	)	PUNCT
ejpam-5020	71	49	for	for	ADP
ejpam-5020	71	50	the	the	DET
ejpam-5020	71	51	even	even	ADJ
ejpam-5020	71	52	n	n	CCONJ
ejpam-5020	71	53	,	,	PUNCT
ejpam-5020	71	54	dpq	dpq	VERB
ejpam-5020	71	55	=	=	SYM
ejpam-5020	71	56			NOUN
ejpam-5020	71	57	2	2	NUM
ejpam-5020	71	58	,	,	PUNCT
ejpam-5020	71	59	if	if	SCONJ
ejpam-5020	71	60	vp	vp	PROPN
ejpam-5020	71	61	,	,	PUNCT
ejpam-5020	71	62	vq	vq	PROPN
ejpam-5020	71	63	∈	∈	PROPN
ejpam-5020	71	64	g1	g1	PROPN
ejpam-5020	71	65	2	2	NUM
ejpam-5020	71	66	,	,	PUNCT
ejpam-5020	71	67	vp	vp	PROPN
ejpam-5020	71	68	∈	∈	PROPN
ejpam-5020	71	69	g2	g2	PROPN
ejpam-5020	71	70	,	,	PUNCT
ejpam-5020	71	71	vq	vq	PROPN
ejpam-5020	71	72	∈	∈	PROPN
ejpam-5020	71	73	{	{	PUNCT
ejpam-5020	71	74	a	a	DET
ejpam-5020	71	75	n	n	PRON
ejpam-5020	71	76	2	2	NUM
ejpam-5020	71	77	+	+	NOUN
ejpam-5020	71	78	ib	ib	NOUN
ejpam-5020	71	79	}	}	PUNCT
ejpam-5020	71	80	1	1	NUM
ejpam-5020	71	81	,	,	PUNCT
ejpam-5020	71	82	otherwise	otherwise	ADV
ejpam-5020	71	83	.	.	PUNCT
ejpam-5020	72	1	proof	proof	NOUN
ejpam-5020	72	2	.	.	PUNCT
ejpam-5020	73	1	for	for	ADP
ejpam-5020	73	2	odd	odd	ADJ
ejpam-5020	73	3	n	n	PRON
ejpam-5020	73	4	case	case	NOUN
ejpam-5020	73	5	,	,	PUNCT
ejpam-5020	73	6	since	since	SCONJ
ejpam-5020	73	7	cd2n(a	cd2n(a	PROPN
ejpam-5020	73	8	i	i	NOUN
ejpam-5020	73	9	)	)	PUNCT
ejpam-5020	73	10	=	=	PUNCT
ejpam-5020	73	11	{	{	PUNCT
ejpam-5020	73	12	aj	aj	PROPN
ejpam-5020	73	13	:	:	PUNCT
ejpam-5020	73	14	1	1	NUM
ejpam-5020	73	15	≤	≤	NUM
ejpam-5020	73	16	j	j	PROPN
ejpam-5020	73	17	≤	≤	NUM
ejpam-5020	73	18	n	n	CCONJ
ejpam-5020	73	19	}	}	PUNCT
ejpam-5020	73	20	,	,	PUNCT
ejpam-5020	73	21	then	then	ADV
ejpam-5020	73	22	the	the	DET
ejpam-5020	73	23	vertex	vertex	NOUN
ejpam-5020	73	24	ai	ai	VERB
ejpam-5020	73	25	,	,	PUNCT
ejpam-5020	73	26	for	for	ADP
ejpam-5020	73	27	1	1	NUM
ejpam-5020	73	28	,	,	PUNCT
ejpam-5020	73	29	2	2	NUM
ejpam-5020	73	30	,	,	PUNCT
ejpam-5020	73	31	.	.	PUNCT
ejpam-5020	73	32	.	.	PUNCT
ejpam-5020	74	1	.	.	PUNCT
ejpam-5020	75	1	,	,	PUNCT
ejpam-5020	76	1	n	n	CCONJ
ejpam-5020	76	2	−	−	PROPN
ejpam-5020	76	3	1	1	NUM
ejpam-5020	76	4	,	,	PUNCT
ejpam-5020	76	5	is	be	AUX
ejpam-5020	76	6	not	not	PART
ejpam-5020	76	7	adjacent	adjacent	ADJ
ejpam-5020	76	8	to	to	ADP
ejpam-5020	76	9	all	all	DET
ejpam-5020	76	10	vertices	vertex	NOUN
ejpam-5020	76	11	of	of	ADP
ejpam-5020	76	12	g1	g1	NOUN
ejpam-5020	76	13	,	,	PUNCT
ejpam-5020	76	14	however	however	ADV
ejpam-5020	76	15	,	,	PUNCT
ejpam-5020	76	16	it	it	PRON
ejpam-5020	76	17	always	always	ADV
ejpam-5020	76	18	has	have	VERB
ejpam-5020	76	19	an	an	DET
ejpam-5020	76	20	edge	edge	NOUN
ejpam-5020	76	21	with	with	ADP
ejpam-5020	76	22	all	all	DET
ejpam-5020	76	23	members	member	NOUN
ejpam-5020	76	24	of	of	ADP
ejpam-5020	76	25	g2	g2	PROPN
ejpam-5020	76	26	.	.	PUNCT
ejpam-5020	77	1	thus	thus	ADV
ejpam-5020	77	2	,	,	PUNCT
ejpam-5020	77	3	it	it	PRON
ejpam-5020	77	4	is	be	AUX
ejpam-5020	77	5	proven	prove	VERB
ejpam-5020	77	6	that	that	SCONJ
ejpam-5020	77	7	dpq	dpq	NOUN
ejpam-5020	77	8	=	=	SYM
ejpam-5020	77	9	1	1	NUM
ejpam-5020	77	10	,	,	PUNCT
ejpam-5020	77	11	where	where	SCONJ
ejpam-5020	77	12	vp	vp	PROPN
ejpam-5020	77	13	belongs	belong	VERB
ejpam-5020	77	14	to	to	ADP
ejpam-5020	77	15	g1	g1	PROPN
ejpam-5020	77	16	and	and	CCONJ
ejpam-5020	77	17	vq	vq	PROPN
ejpam-5020	77	18	∈	∈	PROPN
ejpam-5020	77	19	g2	g2	PROPN
ejpam-5020	77	20	,	,	PUNCT
ejpam-5020	77	21	or	or	CCONJ
ejpam-5020	77	22	vice	vice	NOUN
ejpam-5020	77	23	versa	versa	ADV
ejpam-5020	77	24	.	.	PUNCT
ejpam-5020	78	1	suppose	suppose	VERB
ejpam-5020	78	2	now	now	ADV
ejpam-5020	78	3	two	two	NUM
ejpam-5020	78	4	distinct	distinct	ADJ
ejpam-5020	78	5	vertices	vertex	NOUN
ejpam-5020	78	6	ap	ap	PROPN
ejpam-5020	78	7	,	,	PUNCT
ejpam-5020	78	8	aq	aq	PROPN
ejpam-5020	78	9	∈	∈	PROPN
ejpam-5020	78	10	g1	g1	NOUN
ejpam-5020	78	11	with	with	ADP
ejpam-5020	78	12	p	p	PROPN
ejpam-5020	78	13	̸=	̸=	PROPN
ejpam-5020	78	14	q	q	NOUN
ejpam-5020	78	15	,	,	PUNCT
ejpam-5020	78	16	meaning	mean	VERB
ejpam-5020	78	17	from	from	ADP
ejpam-5020	78	18	ap	ap	PROPN
ejpam-5020	78	19	there	there	PRON
ejpam-5020	78	20	are	be	VERB
ejpam-5020	78	21	two	two	NUM
ejpam-5020	78	22	vertices	vertex	NOUN
ejpam-5020	78	23	that	that	PRON
ejpam-5020	78	24	must	must	AUX
ejpam-5020	78	25	be	be	AUX
ejpam-5020	78	26	passed	pass	VERB
ejpam-5020	78	27	to	to	PART
ejpam-5020	78	28	arrive	arrive	VERB
ejpam-5020	78	29	at	at	ADP
ejpam-5020	78	30	the	the	DET
ejpam-5020	78	31	terminal	terminal	ADJ
ejpam-5020	78	32	vertex	vertex	NOUN
ejpam-5020	78	33	vq	vq	NOUN
ejpam-5020	78	34	,	,	PUNCT
ejpam-5020	78	35	they	they	PRON
ejpam-5020	78	36	are	be	AUX
ejpam-5020	78	37	one	one	NUM
ejpam-5020	78	38	of	of	ADP
ejpam-5020	78	39	aib	aib	PROPN
ejpam-5020	78	40	and	and	CCONJ
ejpam-5020	78	41	vq	vq	ADP
ejpam-5020	78	42	itself	itself	PRON
ejpam-5020	78	43	.	.	PUNCT
ejpam-5020	79	1	from	from	ADP
ejpam-5020	79	2	this	this	DET
ejpam-5020	79	3	fact	fact	NOUN
ejpam-5020	79	4	,	,	PUNCT
ejpam-5020	79	5	we	we	PRON
ejpam-5020	79	6	then	then	ADV
ejpam-5020	79	7	get	get	VERB
ejpam-5020	79	8	dpq	dpq	ADJ
ejpam-5020	79	9	=	=	SYM
ejpam-5020	80	1	2	2	X
ejpam-5020	80	2	.	.	PUNCT
ejpam-5020	80	3	while	while	SCONJ
ejpam-5020	80	4	for	for	ADP
ejpam-5020	80	5	the	the	DET
ejpam-5020	80	6	even	even	ADJ
ejpam-5020	80	7	n	n	PRON
ejpam-5020	80	8	case	case	NOUN
ejpam-5020	80	9	,	,	PUNCT
ejpam-5020	80	10	the	the	DET
ejpam-5020	80	11	centralizer	centralizer	NOUN
ejpam-5020	80	12	of	of	ADP
ejpam-5020	80	13	aib	aib	PROPN
ejpam-5020	80	14	in	in	ADP
ejpam-5020	80	15	d2n	d2n	PROPN
ejpam-5020	80	16	is	be	AUX
ejpam-5020	80	17	{	{	PUNCT
ejpam-5020	80	18	e	e	NOUN
ejpam-5020	80	19	,	,	PUNCT
ejpam-5020	80	20	aib	aib	PROPN
ejpam-5020	80	21	}	}	PUNCT
ejpam-5020	80	22	implies	imply	VERB
ejpam-5020	80	23	that	that	SCONJ
ejpam-5020	80	24	for	for	ADP
ejpam-5020	80	25	1	1	NUM
ejpam-5020	80	26	≤	≤	NUM
ejpam-5020	80	27	i	i	PRON
ejpam-5020	80	28	≤	≤	PROPN
ejpam-5020	80	29	n	n	CCONJ
ejpam-5020	80	30	,	,	PUNCT
ejpam-5020	80	31	vertex	vertex	PROPN
ejpam-5020	80	32	aib	aib	PROPN
ejpam-5020	80	33	is	be	AUX
ejpam-5020	80	34	connected	connect	VERB
ejpam-5020	80	35	with	with	ADP
ejpam-5020	80	36	all	all	DET
ejpam-5020	80	37	other	other	ADJ
ejpam-5020	80	38	elements	element	NOUN
ejpam-5020	80	39	of	of	ADP
ejpam-5020	80	40	g1	g1	PROPN
ejpam-5020	80	41	∪	∪	ADP
ejpam-5020	80	42	g2	g2	PROPN
ejpam-5020	80	43	.	.	PUNCT
ejpam-5020	81	1	therefore	therefore	ADV
ejpam-5020	81	2	,	,	PUNCT
ejpam-5020	81	3	for	for	ADP
ejpam-5020	81	4	vp	vp	PROPN
ejpam-5020	81	5	,	,	PUNCT
ejpam-5020	81	6	vq	vq	PROPN
ejpam-5020	81	7	∈	∈	PROPN
ejpam-5020	81	8	g2	g2	PROPN
ejpam-5020	81	9	,	,	PUNCT
ejpam-5020	81	10	it	it	PRON
ejpam-5020	81	11	is	be	AUX
ejpam-5020	81	12	shown	show	VERB
ejpam-5020	81	13	that	that	SCONJ
ejpam-5020	81	14	dpq	dpq	NOUN
ejpam-5020	81	15	=	=	SYM
ejpam-5020	81	16	1	1	X
ejpam-5020	81	17	.	.	PUNCT
ejpam-5020	82	1	now	now	ADV
ejpam-5020	82	2	when	when	SCONJ
ejpam-5020	82	3	n	n	PRON
ejpam-5020	82	4	is	be	AUX
ejpam-5020	82	5	even	even	ADV
ejpam-5020	82	6	,	,	PUNCT
ejpam-5020	82	7	as	as	ADP
ejpam-5020	82	8	a	a	DET
ejpam-5020	82	9	result	result	NOUN
ejpam-5020	82	10	of	of	ADP
ejpam-5020	82	11	cd2n(a	cd2n(a	NOUN
ejpam-5020	82	12	ib	ib	NOUN
ejpam-5020	82	13	)	)	PUNCT
ejpam-5020	82	14	=	=	SYM
ejpam-5020	82	15	{	{	PUNCT
ejpam-5020	82	16	e	e	NOUN
ejpam-5020	82	17	,	,	PUNCT
ejpam-5020	82	18	a	a	DET
ejpam-5020	82	19	n	n	PRON
ejpam-5020	82	20	2	2	NUM
ejpam-5020	82	21	,	,	PUNCT
ejpam-5020	82	22	aib	aib	PROPN
ejpam-5020	82	23	,	,	PUNCT
ejpam-5020	82	24	a	a	DET
ejpam-5020	82	25	n	n	PRON
ejpam-5020	82	26	2	2	NUM
ejpam-5020	82	27	+	+	NOUN
ejpam-5020	82	28	ib	ib	X
ejpam-5020	82	29	}	}	PUNCT
ejpam-5020	82	30	for	for	ADP
ejpam-5020	82	31	all	all	DET
ejpam-5020	82	32	1	1	NUM
ejpam-5020	82	33	≤	≤	NUM
ejpam-5020	82	34	i	i	PRON
ejpam-5020	82	35	≤	≤	PROPN
ejpam-5020	82	36	n	n	CCONJ
ejpam-5020	82	37	,	,	PUNCT
ejpam-5020	82	38	then	then	ADV
ejpam-5020	82	39	vertices	vertice	VERB
ejpam-5020	82	40	aib	aib	PROPN
ejpam-5020	82	41	and	and	CCONJ
ejpam-5020	82	42	a	a	DET
ejpam-5020	82	43	n	n	NOUN
ejpam-5020	82	44	2	2	NUM
ejpam-5020	82	45	+1b	+1b	NUM
ejpam-5020	82	46	are	be	AUX
ejpam-5020	82	47	always	always	ADV
ejpam-5020	82	48	disconnected	disconnected	ADJ
ejpam-5020	82	49	in	in	ADP
ejpam-5020	82	50	γg	γg	PROPN
ejpam-5020	82	51	.	.	PUNCT
ejpam-5020	83	1	hence	hence	ADV
ejpam-5020	83	2	,	,	PUNCT
ejpam-5020	83	3	for	for	ADP
ejpam-5020	83	4	vp	vp	PROPN
ejpam-5020	83	5	∈	∈	PROPN
ejpam-5020	83	6	g2	g2	PROPN
ejpam-5020	83	7	and	and	CCONJ
ejpam-5020	83	8	vq	vq	PROPN
ejpam-5020	83	9	∈	∈	PROPN
ejpam-5020	83	10	{	{	PUNCT
ejpam-5020	83	11	a	a	DET
ejpam-5020	83	12	n	n	PRON
ejpam-5020	83	13	2	2	NUM
ejpam-5020	83	14	+	+	NOUN
ejpam-5020	83	15	ib	ib	X
ejpam-5020	83	16	}	}	PUNCT
ejpam-5020	83	17	,	,	PUNCT
ejpam-5020	83	18	dpq	dpq	ADJ
ejpam-5020	83	19	=	=	SYM
ejpam-5020	84	1	2	2	X
ejpam-5020	84	2	.	.	PUNCT
ejpam-5020	84	3	this	this	PRON
ejpam-5020	84	4	also	also	ADV
ejpam-5020	84	5	applies	apply	VERB
ejpam-5020	84	6	vice	vice	NOUN
ejpam-5020	84	7	versa	versa	ADV
ejpam-5020	84	8	when	when	SCONJ
ejpam-5020	84	9	vq	vq	PROPN
ejpam-5020	84	10	∈	∈	PROPN
ejpam-5020	84	11	g2	g2	PROPN
ejpam-5020	84	12	and	and	CCONJ
ejpam-5020	84	13	vp	vp	PROPN
ejpam-5020	84	14	∈	∈	PROPN
ejpam-5020	84	15	{	{	PUNCT
ejpam-5020	84	16	a	a	DET
ejpam-5020	84	17	n	n	DET
ejpam-5020	84	18	2	2	NUM
ejpam-5020	84	19	+	+	NOUN
ejpam-5020	84	20	ib	ib	X
ejpam-5020	84	21	}	}	PUNCT
ejpam-5020	84	22	.	.	PUNCT
ejpam-5020	85	1	however	however	ADV
ejpam-5020	85	2	,	,	PUNCT
ejpam-5020	85	3	when	when	SCONJ
ejpam-5020	85	4	one	one	NUM
ejpam-5020	85	5	of	of	ADP
ejpam-5020	85	6	vp	vp	PROPN
ejpam-5020	85	7	and	and	CCONJ
ejpam-5020	85	8	vq	vq	PROPN
ejpam-5020	85	9	is	be	AUX
ejpam-5020	85	10	not	not	PART
ejpam-5020	85	11	in	in	ADP
ejpam-5020	85	12	{	{	PUNCT
ejpam-5020	85	13	a	a	DET
ejpam-5020	85	14	n	n	PRON
ejpam-5020	85	15	2	2	NUM
ejpam-5020	85	16	+	+	NOUN
ejpam-5020	85	17	ib	ib	X
ejpam-5020	85	18	}	}	PUNCT
ejpam-5020	85	19	,	,	PUNCT
ejpam-5020	85	20	then	then	ADV
ejpam-5020	85	21	dpq	dpq	VERB
ejpam-5020	85	22	=	=	SYM
ejpam-5020	85	23	1	1	X
ejpam-5020	85	24	.	.	PUNCT
ejpam-5020	86	1	the	the	DET
ejpam-5020	86	2	closeness	closeness	NOUN
ejpam-5020	86	3	energy	energy	NOUN
ejpam-5020	86	4	of	of	ADP
ejpam-5020	86	5	the	the	DET
ejpam-5020	86	6	non	non	ADJ
ejpam-5020	86	7	-	-	ADJ
ejpam-5020	86	8	commuting	commuting	ADJ
ejpam-5020	86	9	graph	graph	NOUN
ejpam-5020	86	10	on	on	ADP
ejpam-5020	86	11	g	g	NOUN
ejpam-5020	86	12	,	,	PUNCT
ejpam-5020	86	13	for	for	ADP
ejpam-5020	86	14	g	g	PROPN
ejpam-5020	86	15	=	=	SYM
ejpam-5020	86	16	g1	g1	PROPN
ejpam-5020	86	17	or	or	CCONJ
ejpam-5020	86	18	g	g	PROPN
ejpam-5020	86	19	=	=	PROPN
ejpam-5020	86	20	g2	g2	PROPN
ejpam-5020	86	21	is	be	AUX
ejpam-5020	86	22	presented	present	VERB
ejpam-5020	86	23	in	in	ADP
ejpam-5020	86	24	the	the	DET
ejpam-5020	86	25	theorem	theorem	NOUN
ejpam-5020	86	26	below	below	ADV
ejpam-5020	86	27	:	:	PUNCT
ejpam-5020	86	28	theorem	theorem	NOUN
ejpam-5020	86	29	5	5	NUM
ejpam-5020	86	30	.	.	PUNCT
ejpam-5020	87	1	let	let	AUX
ejpam-5020	87	2	γg	γg	ADV
ejpam-5020	87	3	be	be	AUX
ejpam-5020	87	4	the	the	DET
ejpam-5020	87	5	non	non	ADJ
ejpam-5020	87	6	-	-	ADJ
ejpam-5020	87	7	commuting	commuting	ADJ
ejpam-5020	87	8	graph	graph	NOUN
ejpam-5020	87	9	on	on	ADP
ejpam-5020	87	10	g.	g.	PROPN
ejpam-5020	87	11	(	(	PUNCT
ejpam-5020	87	12	i	i	NOUN
ejpam-5020	87	13	)	)	PUNCT
ejpam-5020	87	14	if	if	SCONJ
ejpam-5020	87	15	g	g	PROPN
ejpam-5020	87	16	=	=	SYM
ejpam-5020	87	17	g1	g1	PROPN
ejpam-5020	87	18	,	,	PUNCT
ejpam-5020	87	19	then	then	ADV
ejpam-5020	87	20	ec(γg	ec(γg	PROPN
ejpam-5020	87	21	)	)	PUNCT
ejpam-5020	87	22	is	be	AUX
ejpam-5020	87	23	undefined	undefined	ADJ
ejpam-5020	87	24	,	,	PUNCT
ejpam-5020	87	25	and	and	CCONJ
ejpam-5020	87	26	(	(	PUNCT
ejpam-5020	87	27	ii	ii	NOUN
ejpam-5020	87	28	)	)	PUNCT
ejpam-5020	87	29	if	if	SCONJ
ejpam-5020	87	30	g	g	PROPN
ejpam-5020	87	31	=	=	PROPN
ejpam-5020	87	32	g2	g2	PROPN
ejpam-5020	87	33	,	,	PUNCT
ejpam-5020	87	34	then	then	ADV
ejpam-5020	87	35	ec(γg	ec(γg	PROPN
ejpam-5020	87	36	)	)	PUNCT
ejpam-5020	88	1	=	=	PRON
ejpam-5020	88	2	{	{	PUNCT
ejpam-5020	88	3	n−	n−	NOUN
ejpam-5020	88	4	1	1	NUM
ejpam-5020	88	5	,	,	PUNCT
ejpam-5020	88	6	if	if	SCONJ
ejpam-5020	88	7	n	n	PRON
ejpam-5020	88	8	is	be	AUX
ejpam-5020	88	9	odd	odd	ADJ
ejpam-5020	88	10	n−	n−	NOUN
ejpam-5020	88	11	3	3	NUM
ejpam-5020	88	12	2	2	NUM
ejpam-5020	88	13	,	,	PUNCT
ejpam-5020	88	14	if	if	SCONJ
ejpam-5020	88	15	n	n	PRON
ejpam-5020	88	16	is	be	AUX
ejpam-5020	88	17	even	even	ADV
ejpam-5020	88	18	.	.	PUNCT
ejpam-5020	88	19	.	.	PUNCT
ejpam-5020	89	1	proof	proof	NOUN
ejpam-5020	89	2	.	.	PUNCT
ejpam-5020	90	1	(	(	PUNCT
ejpam-5020	90	2	i	i	NOUN
ejpam-5020	90	3	)	)	PUNCT
ejpam-5020	90	4	for	for	ADP
ejpam-5020	90	5	g	g	PROPN
ejpam-5020	90	6	=	=	PUNCT
ejpam-5020	90	7	g1	g1	PROPN
ejpam-5020	90	8	case	case	NOUN
ejpam-5020	90	9	,	,	PUNCT
ejpam-5020	90	10	by	by	ADP
ejpam-5020	90	11	theorem	theorem	NOUN
ejpam-5020	90	12	1	1	NUM
ejpam-5020	90	13	(	(	PUNCT
ejpam-5020	90	14	1	1	NUM
ejpam-5020	90	15	)	)	PUNCT
ejpam-5020	90	16	,	,	PUNCT
ejpam-5020	90	17	γg	γg	PROPN
ejpam-5020	90	18	∼=	∼=	PROPN
ejpam-5020	90	19	k̄m	k̄m	PROPN
ejpam-5020	90	20	,	,	PUNCT
ejpam-5020	90	21	where	where	SCONJ
ejpam-5020	90	22	m	m	NOUN
ejpam-5020	90	23	=	=	ADJ
ejpam-5020	90	24	|g1|	|g1|	PROPN
ejpam-5020	90	25	.	.	PUNCT
ejpam-5020	91	1	then	then	ADV
ejpam-5020	91	2	γg	γg	ADV
ejpam-5020	91	3	consists	consist	VERB
ejpam-5020	91	4	of	of	ADP
ejpam-5020	91	5	m	m	VERB
ejpam-5020	91	6	isolated	isolate	VERB
ejpam-5020	91	7	vertices	vertex	NOUN
ejpam-5020	91	8	which	which	PRON
ejpam-5020	91	9	implies	imply	VERB
ejpam-5020	91	10	the	the	DET
ejpam-5020	91	11	distance	distance	NOUN
ejpam-5020	91	12	of	of	ADP
ejpam-5020	91	13	every	every	DET
ejpam-5020	91	14	pair	pair	NOUN
ejpam-5020	91	15	vertices	vertex	NOUN
ejpam-5020	91	16	of	of	ADP
ejpam-5020	91	17	g1	g1	PROPN
ejpam-5020	91	18	is	be	AUX
ejpam-5020	91	19	undefined	undefined	ADJ
ejpam-5020	91	20	.	.	PUNCT
ejpam-5020	92	1	(	(	PUNCT
ejpam-5020	92	2	ii	ii	NOUN
ejpam-5020	92	3	)	)	PUNCT
ejpam-5020	92	4	for	for	ADP
ejpam-5020	92	5	the	the	DET
ejpam-5020	92	6	second	second	ADJ
ejpam-5020	92	7	case	case	NOUN
ejpam-5020	92	8	when	when	SCONJ
ejpam-5020	92	9	g	g	PROPN
ejpam-5020	92	10	=	=	PROPN
ejpam-5020	92	11	g2	g2	PROPN
ejpam-5020	92	12	,	,	PUNCT
ejpam-5020	92	13	we	we	PRON
ejpam-5020	92	14	first	first	ADV
ejpam-5020	92	15	proceed	proceed	VERB
ejpam-5020	92	16	if	if	SCONJ
ejpam-5020	92	17	n	n	PRON
ejpam-5020	92	18	is	be	AUX
ejpam-5020	92	19	odd	odd	ADJ
ejpam-5020	92	20	.	.	PUNCT
ejpam-5020	93	1	again	again	ADV
ejpam-5020	93	2	,	,	PUNCT
ejpam-5020	93	3	by	by	ADP
ejpam-5020	93	4	theorem	theorem	NOUN
ejpam-5020	93	5	1	1	NUM
ejpam-5020	93	6	(	(	PUNCT
ejpam-5020	93	7	2	2	NUM
ejpam-5020	93	8	)	)	PUNCT
ejpam-5020	93	9	,	,	PUNCT
ejpam-5020	93	10	γg	γg	PROPN
ejpam-5020	93	11	∼=	∼=	PROPN
ejpam-5020	93	12	kn	kn	PROPN
ejpam-5020	93	13	.	.	PUNCT
ejpam-5020	94	1	then	then	ADV
ejpam-5020	94	2	every	every	DET
ejpam-5020	94	3	pair	pair	NOUN
ejpam-5020	94	4	of	of	ADP
ejpam-5020	94	5	vertices	vertex	NOUN
ejpam-5020	94	6	are	be	AUX
ejpam-5020	94	7	at	at	ADP
ejpam-5020	94	8	distance	distance	NOUN
ejpam-5020	94	9	1	1	NUM
ejpam-5020	94	10	.	.	PUNCT
ejpam-5020	95	1	now	now	ADV
ejpam-5020	95	2	the	the	DET
ejpam-5020	95	3	closeness	closeness	NOUN
ejpam-5020	95	4	m.	m.	PROPN
ejpam-5020	95	5	u.	u.	PROPN
ejpam-5020	95	6	romdhini	romdhini	PROPN
ejpam-5020	95	7	et	et	PROPN
ejpam-5020	95	8	al	al	PROPN
ejpam-5020	95	9	.	.	PUNCT
ejpam-5020	95	10	/	/	SYM
ejpam-5020	95	11	eur	eur	PROPN
ejpam-5020	95	12	.	.	PUNCT
ejpam-5020	96	1	j.	j.	PROPN
ejpam-5020	96	2	pure	pure	PROPN
ejpam-5020	96	3	appl	appl	PROPN
ejpam-5020	96	4	.	.	PROPN
ejpam-5020	96	5	math	math	PROPN
ejpam-5020	96	6	,	,	PUNCT
ejpam-5020	96	7	17	17	NUM
ejpam-5020	96	8	(	(	PUNCT
ejpam-5020	96	9	1	1	NUM
ejpam-5020	96	10	)	)	PUNCT
ejpam-5020	96	11	(	(	PUNCT
ejpam-5020	96	12	2024	2024	NUM
ejpam-5020	96	13	)	)	PUNCT
ejpam-5020	96	14	,	,	PUNCT
ejpam-5020	96	15	212	212	NUM
ejpam-5020	96	16	-	-	SYM
ejpam-5020	96	17	221	221	NUM
ejpam-5020	96	18	216	216	NUM
ejpam-5020	96	19	matrix	matrix	NOUN
ejpam-5020	96	20	of	of	ADP
ejpam-5020	96	21	γg	γg	ADV
ejpam-5020	96	22	is	be	AUX
ejpam-5020	96	23	c(γg	c(γg	NOUN
ejpam-5020	96	24	)	)	PUNCT
ejpam-5020	96	25	=	=	SYM
ejpam-5020	96	26	cpq	cpq	PROPN
ejpam-5020	96	27	,	,	PUNCT
ejpam-5020	96	28	with	with	ADP
ejpam-5020	96	29	(	(	PUNCT
ejpam-5020	96	30	p	p	X
ejpam-5020	96	31	,	,	PUNCT
ejpam-5020	96	32	q)−entry	q)−entry	NOUN
ejpam-5020	96	33	if	if	SCONJ
ejpam-5020	96	34	vp	vp	PROPN
ejpam-5020	96	35	̸=	̸=	PROPN
ejpam-5020	96	36	vq	vq	NOUN
ejpam-5020	96	37	is	be	AUX
ejpam-5020	96	38	2−1	2−1	NUM
ejpam-5020	96	39	,	,	PUNCT
ejpam-5020	96	40	and	and	CCONJ
ejpam-5020	96	41	zero	zero	NUM
ejpam-5020	96	42	if	if	SCONJ
ejpam-5020	96	43	vp	vp	PROPN
ejpam-5020	96	44	=	=	SYM
ejpam-5020	96	45	vq	vq	PROPN
ejpam-5020	96	46	.	.	PROPN
ejpam-5020	96	47	hence	hence	ADV
ejpam-5020	96	48	,	,	PUNCT
ejpam-5020	96	49	c(γg	c(γg	NOUN
ejpam-5020	96	50	)	)	PUNCT
ejpam-5020	96	51	=	=	PRON
ejpam-5020	96	52			VERB
ejpam-5020	97	1	0	0	NUM
ejpam-5020	97	2	1	1	NUM
ejpam-5020	97	3	2	2	NUM
ejpam-5020	97	4	1	1	NUM
ejpam-5020	97	5	2	2	NUM
ejpam-5020	97	6	.	.	PUNCT
ejpam-5020	97	7	.	.	PUNCT
ejpam-5020	97	8	.	.	PUNCT
ejpam-5020	98	1	1	1	NUM
ejpam-5020	98	2	2	2	NUM
ejpam-5020	98	3	1	1	NUM
ejpam-5020	98	4	2	2	NUM
ejpam-5020	98	5	0	0	NUM
ejpam-5020	98	6	1	1	NUM
ejpam-5020	98	7	2	2	NUM
ejpam-5020	98	8	.	.	PUNCT
ejpam-5020	98	9	.	.	PUNCT
ejpam-5020	98	10	.	.	PUNCT
ejpam-5020	99	1	1	1	NUM
ejpam-5020	99	2	2	2	NUM
ejpam-5020	99	3	1	1	NUM
ejpam-5020	99	4	2	2	NUM
ejpam-5020	99	5	1	1	NUM
ejpam-5020	99	6	2	2	NUM
ejpam-5020	99	7	0	0	NUM
ejpam-5020	99	8	.	.	PUNCT
ejpam-5020	99	9	.	.	PUNCT
ejpam-5020	99	10	.	.	PUNCT
ejpam-5020	100	1	1	1	NUM
ejpam-5020	100	2	2	2	NUM
ejpam-5020	100	3	...	...	PUNCT
ejpam-5020	100	4	...	...	PUNCT
ejpam-5020	100	5	...	...	PUNCT
ejpam-5020	100	6	.	.	PUNCT
ejpam-5020	100	7	.	.	PUNCT
ejpam-5020	100	8	.	.	PUNCT
ejpam-5020	101	1	...	...	PUNCT
ejpam-5020	102	1	1	1	NUM
ejpam-5020	102	2	2	2	NUM
ejpam-5020	102	3	1	1	NUM
ejpam-5020	102	4	2	2	NUM
ejpam-5020	102	5	1	1	NUM
ejpam-5020	102	6	2	2	NUM
ejpam-5020	102	7	.	.	PUNCT
ejpam-5020	102	8	.	.	PUNCT
ejpam-5020	102	9	.	.	PUNCT
ejpam-5020	103	1	0	0	NUM
ejpam-5020	104	1			NOUN
ejpam-5020	104	2	=	=	SYM
ejpam-5020	104	3	1	1	NUM
ejpam-5020	104	4	2	2	NUM
ejpam-5020	104	5	a(kn	a(kn	PROPN
ejpam-5020	104	6	)	)	PUNCT
ejpam-5020	104	7	.	.	PUNCT
ejpam-5020	105	1	in	in	ADP
ejpam-5020	105	2	other	other	ADJ
ejpam-5020	105	3	words	word	NOUN
ejpam-5020	105	4	,	,	PUNCT
ejpam-5020	105	5	c(γg	c(γg	NOUN
ejpam-5020	105	6	)	)	PUNCT
ejpam-5020	105	7	is	be	AUX
ejpam-5020	105	8	the	the	DET
ejpam-5020	105	9	product	product	NOUN
ejpam-5020	105	10	of	of	ADP
ejpam-5020	105	11	1	1	NUM
ejpam-5020	105	12	2	2	NUM
ejpam-5020	105	13	and	and	CCONJ
ejpam-5020	105	14	the	the	DET
ejpam-5020	105	15	adjacency	adjacency	NOUN
ejpam-5020	105	16	matrix	matrix	NOUN
ejpam-5020	105	17	ofkn	ofkn	NOUN
ejpam-5020	105	18	.	.	PUNCT
ejpam-5020	106	1	therefore	therefore	ADV
ejpam-5020	106	2	,	,	PUNCT
ejpam-5020	106	3	from	from	ADP
ejpam-5020	106	4	lemma	lemma	PROPN
ejpam-5020	106	5	1	1	NUM
ejpam-5020	106	6	,	,	PUNCT
ejpam-5020	106	7	the	the	DET
ejpam-5020	106	8	closeness	closeness	NOUN
ejpam-5020	106	9	energy	energy	NOUN
ejpam-5020	106	10	of	of	ADP
ejpam-5020	106	11	γg	γg	ADV
ejpam-5020	106	12	will	will	AUX
ejpam-5020	106	13	be	be	AUX
ejpam-5020	106	14	n−	n−	NOUN
ejpam-5020	106	15	1	1	NUM
ejpam-5020	106	16	.	.	PUNCT
ejpam-5020	107	1	meanwhile	meanwhile	ADV
ejpam-5020	107	2	for	for	ADP
ejpam-5020	107	3	the	the	DET
ejpam-5020	107	4	even	even	ADJ
ejpam-5020	107	5	n	n	CCONJ
ejpam-5020	107	6	,	,	PUNCT
ejpam-5020	107	7	by	by	ADP
ejpam-5020	107	8	theorem	theorem	NOUN
ejpam-5020	107	9	1	1	NUM
ejpam-5020	107	10	,	,	PUNCT
ejpam-5020	108	1	γg	γg	ADV
ejpam-5020	108	2	∼=	∼=	PROPN
ejpam-5020	108	3	kn−	kn−	PROPN
ejpam-5020	108	4	n	n	PRON
ejpam-5020	108	5	2k2	2k2	NUM
ejpam-5020	108	6	,	,	PUNCT
ejpam-5020	108	7	then	then	ADV
ejpam-5020	108	8	the	the	DET
ejpam-5020	108	9	distance	distance	NOUN
ejpam-5020	108	10	between	between	ADP
ejpam-5020	108	11	every	every	DET
ejpam-5020	108	12	pair	pair	NOUN
ejpam-5020	108	13	aib	aib	PROPN
ejpam-5020	108	14	and	and	CCONJ
ejpam-5020	108	15	a	a	DET
ejpam-5020	108	16	n	n	NOUN
ejpam-5020	108	17	2	2	NUM
ejpam-5020	108	18	+	+	NOUN
ejpam-5020	108	19	i	i	PRON
ejpam-5020	108	20	for	for	ADP
ejpam-5020	108	21	all	all	DET
ejpam-5020	108	22	1	1	NUM
ejpam-5020	108	23	≤	≤	NUM
ejpam-5020	108	24	i	i	PRON
ejpam-5020	109	1	≤	≤	NOUN
ejpam-5020	110	1	n	n	PRON
ejpam-5020	110	2	is	be	AUX
ejpam-5020	110	3	2	2	NUM
ejpam-5020	110	4	,	,	PUNCT
ejpam-5020	110	5	and	and	CCONJ
ejpam-5020	110	6	1	1	NUM
ejpam-5020	110	7	,	,	PUNCT
ejpam-5020	110	8	otherwise	otherwise	ADV
ejpam-5020	110	9	.	.	PUNCT
ejpam-5020	111	1	thus	thus	ADV
ejpam-5020	111	2	,	,	PUNCT
ejpam-5020	111	3	c(γg	c(γg	NOUN
ejpam-5020	111	4	)	)	PUNCT
ejpam-5020	111	5	=	=	SYM
ejpam-5020	111	6	cpq	cpq	PROPN
ejpam-5020	111	7	and	and	CCONJ
ejpam-5020	111	8	for	for	ADP
ejpam-5020	111	9	vp	vp	PROPN
ejpam-5020	111	10	̸=	̸=	PROPN
ejpam-5020	111	11	vq	vq	PROPN
ejpam-5020	111	12	,	,	PUNCT
ejpam-5020	111	13	cij	cij	PROPN
ejpam-5020	111	14	=	=	PUNCT
ejpam-5020	111	15			PROPN
ejpam-5020	111	16	1	1	NUM
ejpam-5020	111	17	4	4	NUM
ejpam-5020	111	18	,	,	PUNCT
ejpam-5020	111	19	if	if	SCONJ
ejpam-5020	111	20	vp	vp	PROPN
ejpam-5020	111	21	=	=	SYM
ejpam-5020	111	22	aib	aib	PROPN
ejpam-5020	111	23	,	,	PUNCT
ejpam-5020	111	24	vq	vq	NOUN
ejpam-5020	111	25	=	=	PUNCT
ejpam-5020	112	1	a	a	DET
ejpam-5020	112	2	n	n	PRON
ejpam-5020	112	3	2	2	NUM
ejpam-5020	112	4	+	+	NOUN
ejpam-5020	112	5	ib	ib	NOUN
ejpam-5020	112	6	,	,	PUNCT
ejpam-5020	112	7	1	1	NUM
ejpam-5020	112	8	≤	≤	NUM
ejpam-5020	112	9	i	i	PRON
ejpam-5020	112	10	≤	≤	NOUN
ejpam-5020	112	11	n	n	CCONJ
ejpam-5020	112	12	1	1	NUM
ejpam-5020	112	13	2	2	NUM
ejpam-5020	112	14	,	,	PUNCT
ejpam-5020	112	15	if	if	SCONJ
ejpam-5020	112	16	vp	vp	PROPN
ejpam-5020	112	17	=	=	SYM
ejpam-5020	112	18	aib	aib	PROPN
ejpam-5020	112	19	,	,	PUNCT
ejpam-5020	112	20	vq	vq	ADP
ejpam-5020	112	21	̸=	̸=	PROPN
ejpam-5020	112	22	a	a	DET
ejpam-5020	112	23	n	n	PRON
ejpam-5020	112	24	2	2	NUM
ejpam-5020	112	25	+	+	NOUN
ejpam-5020	112	26	ib	ib	NOUN
ejpam-5020	112	27	,	,	PUNCT
ejpam-5020	112	28	1	1	NUM
ejpam-5020	112	29	≤	≤	NUM
ejpam-5020	112	30	i	i	PRON
ejpam-5020	112	31	≤	≤	NOUN
ejpam-5020	112	32	n	n	PRON
ejpam-5020	112	33	0	0	NUM
ejpam-5020	112	34	,	,	PUNCT
ejpam-5020	112	35	otherwise	otherwise	ADV
ejpam-5020	112	36	.	.	PUNCT
ejpam-5020	113	1	now	now	ADV
ejpam-5020	113	2	we	we	PRON
ejpam-5020	113	3	can	can	AUX
ejpam-5020	113	4	construct	construct	VERB
ejpam-5020	113	5	c(γg	c(γg	NOUN
ejpam-5020	113	6	)	)	PUNCT
ejpam-5020	113	7	as	as	SCONJ
ejpam-5020	113	8	follows	follow	VERB
ejpam-5020	113	9	:	:	PUNCT
ejpam-5020	113	10	c(γg	c(γg	NOUN
ejpam-5020	113	11	)	)	PUNCT
ejpam-5020	114	1	=	=	SYM
ejpam-5020	114	2			NOUN
ejpam-5020	114	3	0	0	PUNCT
ejpam-5020	114	4	.	.	PUNCT
ejpam-5020	114	5	.	.	PUNCT
ejpam-5020	115	1	.	.	PUNCT
ejpam-5020	116	1	1	1	NUM
ejpam-5020	116	2	2	2	NUM
ejpam-5020	116	3	1	1	NUM
ejpam-5020	116	4	4	4	NUM
ejpam-5020	116	5	.	.	PUNCT
ejpam-5020	116	6	.	.	PUNCT
ejpam-5020	116	7	.	.	PUNCT
ejpam-5020	117	1	1	1	NUM
ejpam-5020	117	2	2	2	NUM
ejpam-5020	117	3	...	...	PUNCT
ejpam-5020	117	4	...	...	PUNCT
ejpam-5020	117	5	...	...	PUNCT
ejpam-5020	117	6	...	...	PUNCT
ejpam-5020	117	7	.	.	PUNCT
ejpam-5020	117	8	.	.	PUNCT
ejpam-5020	117	9	.	.	PUNCT
ejpam-5020	118	1	...	...	PUNCT
ejpam-5020	119	1	1	1	NUM
ejpam-5020	119	2	2	2	NUM
ejpam-5020	119	3	.	.	PUNCT
ejpam-5020	119	4	.	.	PUNCT
ejpam-5020	119	5	.	.	PUNCT
ejpam-5020	120	1	0	0	NUM
ejpam-5020	120	2	1	1	NUM
ejpam-5020	120	3	2	2	NUM
ejpam-5020	120	4	.	.	PUNCT
ejpam-5020	120	5	.	.	PUNCT
ejpam-5020	120	6	.	.	PUNCT
ejpam-5020	121	1	1	1	NUM
ejpam-5020	121	2	4	4	NUM
ejpam-5020	121	3	1	1	NUM
ejpam-5020	121	4	4	4	NUM
ejpam-5020	121	5	.	.	PUNCT
ejpam-5020	121	6	.	.	PUNCT
ejpam-5020	121	7	.	.	PUNCT
ejpam-5020	122	1	1	1	NUM
ejpam-5020	122	2	2	2	NUM
ejpam-5020	122	3	0	0	NUM
ejpam-5020	122	4	.	.	PUNCT
ejpam-5020	122	5	.	.	PUNCT
ejpam-5020	122	6	.	.	PUNCT
ejpam-5020	123	1	1	1	NUM
ejpam-5020	123	2	2	2	NUM
ejpam-5020	123	3	...	...	PUNCT
ejpam-5020	123	4	...	...	PUNCT
ejpam-5020	123	5	...	...	PUNCT
ejpam-5020	123	6	...	...	PUNCT
ejpam-5020	123	7	.	.	PUNCT
ejpam-5020	123	8	.	.	PUNCT
ejpam-5020	123	9	.	.	PUNCT
ejpam-5020	124	1	...	...	PUNCT
ejpam-5020	125	1	1	1	NUM
ejpam-5020	125	2	2	2	NUM
ejpam-5020	125	3	.	.	PUNCT
ejpam-5020	125	4	.	.	PUNCT
ejpam-5020	125	5	.	.	PUNCT
ejpam-5020	126	1	1	1	NUM
ejpam-5020	126	2	4	4	NUM
ejpam-5020	126	3	1	1	NUM
ejpam-5020	126	4	2	2	NUM
ejpam-5020	126	5	.	.	PUNCT
ejpam-5020	126	6	.	.	PUNCT
ejpam-5020	126	7	.	.	PUNCT
ejpam-5020	127	1	0	0	PUNCT
ejpam-5020	128	1			NUM
ejpam-5020	128	2	=	=	SYM
ejpam-5020	128	3	[	[	PUNCT
ejpam-5020	128	4	1	1	NUM
ejpam-5020	128	5	2(j	2(j	NUM
ejpam-5020	128	6	−	−	NOUN
ejpam-5020	128	7	i)n	i)n	NOUN
ejpam-5020	128	8	2	2	NUM
ejpam-5020	128	9	1	1	NUM
ejpam-5020	128	10	4(j	4(j	NUM
ejpam-5020	128	11	−	−	NOUN
ejpam-5020	128	12	i)n	i)n	NOUN
ejpam-5020	128	13	2	2	NUM
ejpam-5020	128	14	+	+	CCONJ
ejpam-5020	128	15	1	1	NUM
ejpam-5020	128	16	4	4	NUM
ejpam-5020	128	17	in	in	ADP
ejpam-5020	128	18	2	2	NUM
ejpam-5020	128	19	1	1	NUM
ejpam-5020	128	20	4(j	4(j	NUM
ejpam-5020	128	21	−	−	NOUN
ejpam-5020	128	22	i)n	i)n	NOUN
ejpam-5020	128	23	2	2	NUM
ejpam-5020	128	24	+	+	CCONJ
ejpam-5020	128	25	1	1	NUM
ejpam-5020	128	26	4	4	NUM
ejpam-5020	128	27	in	in	ADP
ejpam-5020	128	28	2	2	NUM
ejpam-5020	128	29	1	1	NUM
ejpam-5020	128	30	2(j	2(j	NUM
ejpam-5020	128	31	−	−	NOUN
ejpam-5020	128	32	i)n	i)n	NOUN
ejpam-5020	128	33	2	2	NUM
ejpam-5020	128	34	]	]	PUNCT
ejpam-5020	128	35	.	.	PUNCT
ejpam-5020	129	1	in	in	ADP
ejpam-5020	129	2	this	this	DET
ejpam-5020	129	3	case	case	NOUN
ejpam-5020	129	4	,	,	PUNCT
ejpam-5020	129	5	we	we	PRON
ejpam-5020	129	6	have	have	VERB
ejpam-5020	129	7	four	four	NUM
ejpam-5020	129	8	block	block	NOUN
ejpam-5020	129	9	matrices	matrix	NOUN
ejpam-5020	129	10	of	of	ADP
ejpam-5020	129	11	c(γg	c(γg	NOUN
ejpam-5020	129	12	):	):	PUNCT
ejpam-5020	129	13	c(γg	c(γg	NOUN
ejpam-5020	129	14	)	)	PUNCT
ejpam-5020	129	15	=	=	PUNCT
ejpam-5020	130	1	[	[	PUNCT
ejpam-5020	130	2	a	a	DET
ejpam-5020	130	3	b	b	PROPN
ejpam-5020	130	4	b	b	PROPN
ejpam-5020	130	5	a	a	NOUN
ejpam-5020	130	6	]	]	PUNCT
ejpam-5020	130	7	,	,	PUNCT
ejpam-5020	130	8	where	where	SCONJ
ejpam-5020	130	9	a	a	PRON
ejpam-5020	130	10	is	be	AUX
ejpam-5020	130	11	a	a	DET
ejpam-5020	130	12	matrix	matrix	NOUN
ejpam-5020	130	13	of	of	ADP
ejpam-5020	130	14	order	order	NOUN
ejpam-5020	130	15	n	n	PRON
ejpam-5020	130	16	2	2	NUM
ejpam-5020	130	17	with	with	ADP
ejpam-5020	130	18	zero	zero	NUM
ejpam-5020	130	19	diagonal	diagonal	ADJ
ejpam-5020	130	20	entries	entry	NOUN
ejpam-5020	130	21	and	and	CCONJ
ejpam-5020	130	22	all	all	PRON
ejpam-5020	130	23	of	of	ADP
ejpam-5020	130	24	the	the	DET
ejpam-5020	130	25	non	non	ADJ
ejpam-5020	130	26	-	-	ADJ
ejpam-5020	130	27	diagonal	diagonal	ADJ
ejpam-5020	130	28	entries	entry	NOUN
ejpam-5020	130	29	as	as	ADP
ejpam-5020	130	30	1	1	NUM
ejpam-5020	130	31	2	2	NUM
ejpam-5020	130	32	and	and	CCONJ
ejpam-5020	130	33	b	b	NOUN
ejpam-5020	130	34	is	be	AUX
ejpam-5020	130	35	the	the	DET
ejpam-5020	130	36	matrix	matrix	NOUN
ejpam-5020	130	37	of	of	ADP
ejpam-5020	130	38	order	order	NOUN
ejpam-5020	130	39	n	n	PRON
ejpam-5020	130	40	2	2	NUM
ejpam-5020	130	41	with	with	ADP
ejpam-5020	130	42	diagonal	diagonal	ADJ
ejpam-5020	130	43	entries	entry	NOUN
ejpam-5020	130	44	are	be	AUX
ejpam-5020	130	45	1	1	NUM
ejpam-5020	130	46	4	4	NUM
ejpam-5020	130	47	and	and	CCONJ
ejpam-5020	130	48	the	the	DET
ejpam-5020	130	49	non	non	ADJ
ejpam-5020	130	50	-	-	ADJ
ejpam-5020	130	51	diagonal	diagonal	ADJ
ejpam-5020	130	52	entries	entry	NOUN
ejpam-5020	130	53	are	be	AUX
ejpam-5020	130	54	1	1	NUM
ejpam-5020	130	55	2	2	NUM
ejpam-5020	130	56	.	.	PUNCT
ejpam-5020	131	1	by	by	ADP
ejpam-5020	131	2	theorem	theorem	NOUN
ejpam-5020	131	3	2	2	NUM
ejpam-5020	131	4	with	with	ADP
ejpam-5020	131	5	s	s	NOUN
ejpam-5020	131	6	=	=	SYM
ejpam-5020	131	7	1	1	NUM
ejpam-5020	131	8	4	4	NUM
ejpam-5020	131	9	and	and	CCONJ
ejpam-5020	131	10	t	t	NOUN
ejpam-5020	131	11	=	=	SYM
ejpam-5020	131	12	1	1	NUM
ejpam-5020	131	13	2	2	NUM
ejpam-5020	131	14	,	,	PUNCT
ejpam-5020	131	15	equation	equation	NOUN
ejpam-5020	131	16	2	2	NUM
ejpam-5020	131	17	is	be	AUX
ejpam-5020	131	18	pc(γg)(λ	pc(γg)(λ	NOUN
ejpam-5020	131	19	)	)	PUNCT
ejpam-5020	132	1	=	=	PUNCT
ejpam-5020	132	2	(	(	PUNCT
ejpam-5020	132	3	λ+	λ+	PUNCT
ejpam-5020	132	4	3	3	NUM
ejpam-5020	132	5	4	4	NUM
ejpam-5020	132	6	)	)	PUNCT
ejpam-5020	132	7	n	n	PRON
ejpam-5020	132	8	2	2	NUM
ejpam-5020	132	9	−1	−1	NOUN
ejpam-5020	132	10	(	(	PUNCT
ejpam-5020	132	11	λ+	λ+	PUNCT
ejpam-5020	132	12	3	3	NUM
ejpam-5020	132	13	4	4	NUM
ejpam-5020	132	14	−	−	NUM
ejpam-5020	132	15	1	1	NUM
ejpam-5020	132	16	2	2	NUM
ejpam-5020	132	17	n	n	NOUN
ejpam-5020	132	18	)	)	PUNCT
ejpam-5020	132	19	(	(	PUNCT
ejpam-5020	132	20	λ+	λ+	PUNCT
ejpam-5020	132	21	1	1	NUM
ejpam-5020	132	22	4	4	NUM
ejpam-5020	132	23	)	)	PUNCT
ejpam-5020	132	24	n	n	PRON
ejpam-5020	132	25	2	2	NUM
ejpam-5020	132	26	.	.	PUNCT
ejpam-5020	133	1	therefore	therefore	ADV
ejpam-5020	133	2	,	,	PUNCT
ejpam-5020	133	3	using	use	VERB
ejpam-5020	133	4	the	the	DET
ejpam-5020	133	5	roots	root	NOUN
ejpam-5020	133	6	of	of	ADP
ejpam-5020	133	7	equation	equation	NOUN
ejpam-5020	133	8	2	2	NUM
ejpam-5020	133	9	,	,	PUNCT
ejpam-5020	133	10	the	the	DET
ejpam-5020	133	11	closeness	closeness	NOUN
ejpam-5020	133	12	energy	energy	NOUN
ejpam-5020	133	13	of	of	ADP
ejpam-5020	133	14	γg	γg	ADV
ejpam-5020	133	15	is	be	AUX
ejpam-5020	133	16	ec(γg	ec(γg	PROPN
ejpam-5020	133	17	)	)	PUNCT
ejpam-5020	134	1	=	=	PUNCT
ejpam-5020	134	2	(	(	PUNCT
ejpam-5020	134	3	n	n	NOUN
ejpam-5020	134	4	2	2	NUM
ejpam-5020	134	5	)	)	PUNCT
ejpam-5020	134	6	∣∣∣∣−1	∣∣∣∣−1	ADP
ejpam-5020	134	7	4	4	NUM
ejpam-5020	134	8	∣∣∣∣+	∣∣∣∣+	NOUN
ejpam-5020	134	9	(	(	PUNCT
ejpam-5020	134	10	n	n	ADV
ejpam-5020	134	11	2	2	NUM
ejpam-5020	134	12	−	−	NOUN
ejpam-5020	134	13	1	1	NUM
ejpam-5020	134	14	)	)	PUNCT
ejpam-5020	134	15	∣∣∣∣−3	∣∣∣∣−3	PROPN
ejpam-5020	134	16	4	4	NUM
ejpam-5020	134	17	∣∣∣∣+	∣∣∣∣+	NOUN
ejpam-5020	134	18	∣∣∣∣12n−	∣∣∣∣12n−	VERB
ejpam-5020	134	19	3	3	NUM
ejpam-5020	134	20	4	4	NUM
ejpam-5020	134	21	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5020	134	22	=	=	SYM
ejpam-5020	134	23	n−	n−	NOUN
ejpam-5020	134	24	3	3	NUM
ejpam-5020	134	25	2	2	NUM
ejpam-5020	134	26	.	.	PUNCT
ejpam-5020	135	1	m.	m.	PROPN
ejpam-5020	135	2	u.	u.	PROPN
ejpam-5020	135	3	romdhini	romdhini	PROPN
ejpam-5020	135	4	et	et	PROPN
ejpam-5020	135	5	al	al	PROPN
ejpam-5020	135	6	.	.	PUNCT
ejpam-5020	135	7	/	/	SYM
ejpam-5020	135	8	eur	eur	PROPN
ejpam-5020	135	9	.	.	PUNCT
ejpam-5020	136	1	j.	j.	PROPN
ejpam-5020	136	2	pure	pure	PROPN
ejpam-5020	136	3	appl	appl	PROPN
ejpam-5020	136	4	.	.	PROPN
ejpam-5020	136	5	math	math	PROPN
ejpam-5020	136	6	,	,	PUNCT
ejpam-5020	136	7	17	17	NUM
ejpam-5020	136	8	(	(	PUNCT
ejpam-5020	136	9	1	1	NUM
ejpam-5020	136	10	)	)	PUNCT
ejpam-5020	136	11	(	(	PUNCT
ejpam-5020	136	12	2024	2024	NUM
ejpam-5020	136	13	)	)	PUNCT
ejpam-5020	136	14	,	,	PUNCT
ejpam-5020	136	15	212	212	NUM
ejpam-5020	136	16	-	-	SYM
ejpam-5020	136	17	221	221	NUM
ejpam-5020	136	18	217	217	NUM
ejpam-5020	136	19	theorem	theorem	NOUN
ejpam-5020	136	20	6	6	NUM
ejpam-5020	136	21	.	.	PUNCT
ejpam-5020	137	1	the	the	DET
ejpam-5020	137	2	characteristic	characteristic	ADJ
ejpam-5020	137	3	polynomial	polynomial	NOUN
ejpam-5020	137	4	of	of	ADP
ejpam-5020	137	5	γg	γg	ADV
ejpam-5020	137	6	,	,	PUNCT
ejpam-5020	137	7	where	where	SCONJ
ejpam-5020	137	8	g	g	PROPN
ejpam-5020	137	9	=	=	PUNCT
ejpam-5020	137	10	g1	g1	PROPN
ejpam-5020	137	11	∪g2	∪g2	PROPN
ejpam-5020	137	12	,	,	PUNCT
ejpam-5020	137	13	is	be	AUX
ejpam-5020	137	14	(	(	PUNCT
ejpam-5020	137	15	i	i	NOUN
ejpam-5020	137	16	)	)	PUNCT
ejpam-5020	137	17	for	for	ADP
ejpam-5020	137	18	n	n	X
ejpam-5020	137	19	is	be	AUX
ejpam-5020	137	20	odd	odd	ADJ
ejpam-5020	137	21	:	:	PUNCT
ejpam-5020	137	22	pc(γg)(λ	pc(γg)(λ	NOUN
ejpam-5020	137	23	)	)	PUNCT
ejpam-5020	137	24	=	=	PUNCT
ejpam-5020	138	1	(	(	PUNCT
ejpam-5020	138	2	λ+	λ+	NUM
ejpam-5020	138	3	2)n−2	2)n−2	NUM
ejpam-5020	138	4	(	(	PUNCT
ejpam-5020	138	5	λ+	λ+	NUM
ejpam-5020	138	6	1)n−1	1)n−1	NUM
ejpam-5020	138	7	(	(	PUNCT
ejpam-5020	138	8	λ2	λ2	NOUN
ejpam-5020	138	9	−	−	PROPN
ejpam-5020	138	10	(	(	PUNCT
ejpam-5020	138	11	3n−	3n−	PROPN
ejpam-5020	138	12	5)λ+	5)λ+	NUM
ejpam-5020	138	13	(	(	PUNCT
ejpam-5020	138	14	n−	n−	NOUN
ejpam-5020	138	15	1)(n−	1)(n−	NUM
ejpam-5020	138	16	4	4	NUM
ejpam-5020	138	17	)	)	PUNCT
ejpam-5020	138	18	)	)	PUNCT
ejpam-5020	138	19	,	,	PUNCT
ejpam-5020	138	20	(	(	PUNCT
ejpam-5020	138	21	ii	ii	NOUN
ejpam-5020	138	22	)	)	PUNCT
ejpam-5020	138	23	for	for	ADP
ejpam-5020	138	24	n	n	NUM
ejpam-5020	138	25	is	be	AUX
ejpam-5020	138	26	even	even	ADV
ejpam-5020	138	27	:	:	PUNCT
ejpam-5020	138	28	pd(γg)(λ	pd(γg)(λ	NOUN
ejpam-5020	138	29	)	)	PUNCT
ejpam-5020	138	30	=	=	SYM
ejpam-5020	139	1	λ	λ	NOUN
ejpam-5020	139	2	n	n	CCONJ
ejpam-5020	139	3	2	2	NUM
ejpam-5020	139	4	−1	−1	NOUN
ejpam-5020	139	5	(	(	PUNCT
ejpam-5020	139	6	λ+	λ+	PUNCT
ejpam-5020	139	7	2)n−3+n	2)n−3+n	PROPN
ejpam-5020	139	8	2	2	NUM
ejpam-5020	139	9	(	(	PUNCT
ejpam-5020	139	10	λ2	λ2	NOUN
ejpam-5020	139	11	−	−	PROPN
ejpam-5020	139	12	3	3	NUM
ejpam-5020	139	13	(	(	PUNCT
ejpam-5020	139	14	n−	n−	NOUN
ejpam-5020	139	15	2)λ+	2)λ+	NUM
ejpam-5020	139	16	n(n−	n(n−	NOUN
ejpam-5020	139	17	4	4	NUM
ejpam-5020	139	18	)	)	PUNCT
ejpam-5020	139	19	)	)	PUNCT
ejpam-5020	139	20	.	.	PUNCT
ejpam-5020	140	1	proof	proof	NOUN
ejpam-5020	140	2	.	.	PUNCT
ejpam-5020	141	1	(	(	PUNCT
ejpam-5020	141	2	i	i	NOUN
ejpam-5020	141	3	)	)	PUNCT
ejpam-5020	141	4	when	when	SCONJ
ejpam-5020	141	5	n	n	X
ejpam-5020	141	6	is	be	AUX
ejpam-5020	141	7	odd	odd	ADJ
ejpam-5020	141	8	and	and	CCONJ
ejpam-5020	141	9	g	g	PROPN
ejpam-5020	141	10	=	=	PROPN
ejpam-5020	141	11	g1	g1	PROPN
ejpam-5020	141	12	∪g2	∪g2	PROPN
ejpam-5020	141	13	,	,	PUNCT
ejpam-5020	141	14	by	by	ADP
ejpam-5020	141	15	theorem	theorem	NOUN
ejpam-5020	141	16	4	4	NUM
ejpam-5020	141	17	,	,	PUNCT
ejpam-5020	141	18	we	we	PRON
ejpam-5020	141	19	have	have	VERB
ejpam-5020	141	20	the	the	DET
ejpam-5020	141	21	distance	distance	NOUN
ejpam-5020	141	22	of	of	ADP
ejpam-5020	141	23	every	every	DET
ejpam-5020	141	24	pair	pair	NOUN
ejpam-5020	141	25	of	of	ADP
ejpam-5020	141	26	vertices	vertex	NOUN
ejpam-5020	141	27	.	.	PUNCT
ejpam-5020	142	1	since	since	SCONJ
ejpam-5020	142	2	z(d2n	z(d2n	NUM
ejpam-5020	142	3	)	)	PUNCT
ejpam-5020	142	4	=	=	PUNCT
ejpam-5020	142	5	{	{	PUNCT
ejpam-5020	142	6	e	e	NOUN
ejpam-5020	142	7	}	}	PUNCT
ejpam-5020	142	8	,	,	PUNCT
ejpam-5020	142	9	consequently	consequently	ADV
ejpam-5020	142	10	,	,	PUNCT
ejpam-5020	142	11	γg	γg	ADV
ejpam-5020	142	12	has	have	VERB
ejpam-5020	142	13	2n	2n	NUM
ejpam-5020	142	14	−	−	ADP
ejpam-5020	142	15	1	1	NUM
ejpam-5020	142	16	vertices	vertex	NOUN
ejpam-5020	142	17	.	.	PUNCT
ejpam-5020	143	1	they	they	PRON
ejpam-5020	143	2	are	be	AUX
ejpam-5020	143	3	n−	n−	NOUN
ejpam-5020	143	4	1	1	NUM
ejpam-5020	143	5	vertices	vertex	NOUN
ejpam-5020	143	6	of	of	ADP
ejpam-5020	143	7	ai	ai	NOUN
ejpam-5020	143	8	,	,	PUNCT
ejpam-5020	143	9	for	for	ADP
ejpam-5020	143	10	1	1	NUM
ejpam-5020	143	11	≤	≤	NUM
ejpam-5020	143	12	i	i	PRON
ejpam-5020	143	13	≤	≤	ADJ
ejpam-5020	143	14	n−	n−	PROPN
ejpam-5020	143	15	1	1	NUM
ejpam-5020	143	16	,	,	PUNCT
ejpam-5020	143	17	and	and	CCONJ
ejpam-5020	143	18	n	n	DET
ejpam-5020	143	19	vertices	vertex	NOUN
ejpam-5020	143	20	of	of	ADP
ejpam-5020	143	21	aib	aib	PROPN
ejpam-5020	143	22	,	,	PUNCT
ejpam-5020	143	23	1	1	NUM
ejpam-5020	143	24	≤	≤	NUM
ejpam-5020	143	25	i	i	PRON
ejpam-5020	143	26	≤	≤	ADJ
ejpam-5020	143	27	n.	n.	NOUN
ejpam-5020	143	28	hence	hence	ADV
ejpam-5020	143	29	,	,	PUNCT
ejpam-5020	143	30	from	from	ADP
ejpam-5020	143	31	definition	definition	NOUN
ejpam-5020	143	32	1	1	NUM
ejpam-5020	143	33	,	,	PUNCT
ejpam-5020	143	34	c(γg	c(γg	NOUN
ejpam-5020	143	35	)	)	PUNCT
ejpam-5020	143	36	is	be	AUX
ejpam-5020	143	37	a	a	DET
ejpam-5020	143	38	(	(	PUNCT
ejpam-5020	143	39	2n−	2n−	PROPN
ejpam-5020	143	40	1)×	1)×	NUM
ejpam-5020	143	41	(	(	PUNCT
ejpam-5020	143	42	2n−	2n−	PROPN
ejpam-5020	143	43	1	1	NUM
ejpam-5020	143	44	)	)	PUNCT
ejpam-5020	143	45	matrix	matrix	NOUN
ejpam-5020	143	46	as	as	ADP
ejpam-5020	143	47	the	the	DET
ejpam-5020	143	48	following	following	NOUN
ejpam-5020	143	49	:	:	PUNCT
ejpam-5020	143	50	c(γg	c(γg	NOUN
ejpam-5020	143	51	)	)	PUNCT
ejpam-5020	144	1	=	=	SYM
ejpam-5020	144	2			NOUN
ejpam-5020	144	3	0	0	PUNCT
ejpam-5020	144	4	.	.	PUNCT
ejpam-5020	144	5	.	.	PUNCT
ejpam-5020	145	1	.	.	PUNCT
ejpam-5020	146	1	1	1	NUM
ejpam-5020	146	2	4	4	NUM
ejpam-5020	146	3	1	1	NUM
ejpam-5020	146	4	2	2	NUM
ejpam-5020	146	5	.	.	PUNCT
ejpam-5020	146	6	.	.	PUNCT
ejpam-5020	146	7	.	.	PUNCT
ejpam-5020	147	1	1	1	NUM
ejpam-5020	147	2	2	2	NUM
ejpam-5020	147	3	...	...	PUNCT
ejpam-5020	147	4	.	.	PUNCT
ejpam-5020	147	5	.	.	PUNCT
ejpam-5020	147	6	.	.	PUNCT
ejpam-5020	147	7	...	...	PUNCT
ejpam-5020	147	8	...	...	PUNCT
ejpam-5020	147	9	.	.	PUNCT
ejpam-5020	147	10	.	.	PUNCT
ejpam-5020	147	11	.	.	PUNCT
ejpam-5020	148	1	...	...	PUNCT
ejpam-5020	149	1	1	1	NUM
ejpam-5020	149	2	4	4	NUM
ejpam-5020	149	3	.	.	PUNCT
ejpam-5020	149	4	.	.	PUNCT
ejpam-5020	149	5	.	.	PUNCT
ejpam-5020	150	1	0	0	NUM
ejpam-5020	150	2	1	1	NUM
ejpam-5020	150	3	2	2	NUM
ejpam-5020	150	4	.	.	PUNCT
ejpam-5020	150	5	.	.	PUNCT
ejpam-5020	150	6	.	.	PUNCT
ejpam-5020	151	1	1	1	NUM
ejpam-5020	151	2	2	2	NUM
ejpam-5020	151	3	1	1	NUM
ejpam-5020	151	4	2	2	NUM
ejpam-5020	151	5	.	.	PUNCT
ejpam-5020	151	6	.	.	PUNCT
ejpam-5020	151	7	.	.	PUNCT
ejpam-5020	152	1	1	1	NUM
ejpam-5020	152	2	2	2	NUM
ejpam-5020	152	3	0	0	NUM
ejpam-5020	152	4	.	.	PUNCT
ejpam-5020	152	5	.	.	PUNCT
ejpam-5020	152	6	.	.	PUNCT
ejpam-5020	153	1	1	1	NUM
ejpam-5020	153	2	2	2	NUM
ejpam-5020	153	3	...	...	PUNCT
ejpam-5020	153	4	.	.	PUNCT
ejpam-5020	153	5	.	.	PUNCT
ejpam-5020	153	6	.	.	PUNCT
ejpam-5020	153	7	...	...	PUNCT
ejpam-5020	153	8	...	...	PUNCT
ejpam-5020	153	9	.	.	PUNCT
ejpam-5020	153	10	.	.	PUNCT
ejpam-5020	153	11	.	.	PUNCT
ejpam-5020	154	1	...	...	PUNCT
ejpam-5020	155	1	1	1	NUM
ejpam-5020	155	2	2	2	NUM
ejpam-5020	155	3	.	.	PUNCT
ejpam-5020	155	4	.	.	PUNCT
ejpam-5020	155	5	.	.	PUNCT
ejpam-5020	156	1	1	1	NUM
ejpam-5020	156	2	2	2	NUM
ejpam-5020	156	3	1	1	NUM
ejpam-5020	156	4	2	2	NUM
ejpam-5020	156	5	.	.	PUNCT
ejpam-5020	156	6	.	.	PUNCT
ejpam-5020	156	7	.	.	PUNCT
ejpam-5020	157	1	0	0	PUNCT
ejpam-5020	158	1			NUM
ejpam-5020	158	2	=	=	SYM
ejpam-5020	158	3	[	[	PUNCT
ejpam-5020	158	4	1	1	NUM
ejpam-5020	158	5	4(j	4(j	NUM
ejpam-5020	158	6	−	−	NOUN
ejpam-5020	158	7	i)n−1	i)n−1	ADJ
ejpam-5020	158	8	1	1	NUM
ejpam-5020	158	9	2j(n−1)×n	2j(n−1)×n	NUM
ejpam-5020	158	10	1	1	NUM
ejpam-5020	158	11	2j(n−1)×n	2j(n−1)×n	NUM
ejpam-5020	158	12	1	1	NUM
ejpam-5020	158	13	2(j	2(j	NUM
ejpam-5020	158	14	−	−	NOUN
ejpam-5020	158	15	i)n	i)n	PROPN
ejpam-5020	158	16	]	]	PUNCT
ejpam-5020	158	17	.	.	PUNCT
ejpam-5020	159	1	now	now	ADV
ejpam-5020	159	2	the	the	DET
ejpam-5020	159	3	characteristic	characteristic	ADJ
ejpam-5020	159	4	polynomial	polynomial	NOUN
ejpam-5020	159	5	of	of	ADP
ejpam-5020	159	6	equation	equation	NOUN
ejpam-5020	159	7	1	1	NUM
ejpam-5020	159	8	is	be	AUX
ejpam-5020	159	9	pc(γg)(λ	pc(γg)(λ	NOUN
ejpam-5020	159	10	)	)	PUNCT
ejpam-5020	160	1	=	=	SYM
ejpam-5020	161	1	|λi2n−1	|λi2n−1	PROPN
ejpam-5020	161	2	−	−	NUM
ejpam-5020	161	3	c(γg)|	c(γg)|	NOUN
ejpam-5020	161	4	=	=	PUNCT
ejpam-5020	161	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5020	161	6	(	(	PUNCT
ejpam-5020	161	7	λ+	λ+	PUNCT
ejpam-5020	161	8	2)in−1	2)in−1	NUM
ejpam-5020	161	9	−	−	NUM
ejpam-5020	161	10	2jn−1	2jn−1	NUM
ejpam-5020	161	11	−j(n−1)×n	−j(n−1)×n	VERB
ejpam-5020	161	12	−jn×(n−1	−jn×(n−1	PROPN
ejpam-5020	161	13	)	)	PUNCT
ejpam-5020	161	14	(	(	PUNCT
ejpam-5020	161	15	λ+	λ+	PUNCT
ejpam-5020	161	16	1)in	1)in	NUM
ejpam-5020	161	17	−	−	PROPN
ejpam-5020	161	18	jn	jn	PROPN
ejpam-5020	161	19	)	)	PUNCT
ejpam-5020	161	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5020	161	21	.	.	PUNCT
ejpam-5020	162	1	using	use	VERB
ejpam-5020	162	2	lemma	lemma	PROPN
ejpam-5020	162	3	2	2	NUM
ejpam-5020	162	4	,	,	PUNCT
ejpam-5020	162	5	with	with	ADP
ejpam-5020	162	6	a	a	PRON
ejpam-5020	162	7	=	=	SYM
ejpam-5020	162	8	1	1	NUM
ejpam-5020	162	9	4	4	NUM
ejpam-5020	162	10	,	,	PUNCT
ejpam-5020	162	11	b	b	X
ejpam-5020	162	12	=	=	SYM
ejpam-5020	162	13	1	1	NUM
ejpam-5020	162	14	2	2	NUM
ejpam-5020	162	15	,	,	PUNCT
ejpam-5020	162	16	c	c	NOUN
ejpam-5020	162	17	=	=	SYM
ejpam-5020	162	18	d	d	NOUN
ejpam-5020	162	19	=	=	SYM
ejpam-5020	162	20	1	1	NUM
ejpam-5020	162	21	2	2	NUM
ejpam-5020	162	22	,	,	PUNCT
ejpam-5020	162	23	and	and	CCONJ
ejpam-5020	162	24	n1	n1	PROPN
ejpam-5020	162	25	=	=	SYM
ejpam-5020	162	26	n	n	CCONJ
ejpam-5020	162	27	−	−	NUM
ejpam-5020	162	28	1	1	NUM
ejpam-5020	162	29	,	,	PUNCT
ejpam-5020	162	30	n2	n2	NOUN
ejpam-5020	162	31	=	=	PUNCT
ejpam-5020	162	32	n	n	CCONJ
ejpam-5020	162	33	,	,	PUNCT
ejpam-5020	162	34	then	then	ADV
ejpam-5020	162	35	we	we	PRON
ejpam-5020	162	36	obtain	obtain	VERB
ejpam-5020	162	37	the	the	DET
ejpam-5020	162	38	formula	formula	NOUN
ejpam-5020	162	39	of	of	ADP
ejpam-5020	162	40	pc(γg)(λ	pc(γg)(λ	NOUN
ejpam-5020	162	41	)	)	PUNCT
ejpam-5020	162	42	,	,	PUNCT
ejpam-5020	162	43	pc(γg)(λ	pc(γg)(λ	NOUN
ejpam-5020	162	44	)	)	PUNCT
ejpam-5020	162	45	=	=	PUNCT
ejpam-5020	163	1	(	(	PUNCT
ejpam-5020	163	2	λ+	λ+	NUM
ejpam-5020	163	3	1	1	NUM
ejpam-5020	163	4	4	4	NUM
ejpam-5020	163	5	)	)	PUNCT
ejpam-5020	163	6	n−2	n−2	PROPN
ejpam-5020	163	7	(	(	PUNCT
ejpam-5020	163	8	λ+	λ+	NUM
ejpam-5020	163	9	1	1	NUM
ejpam-5020	163	10	2	2	NUM
ejpam-5020	163	11	)	)	PUNCT
ejpam-5020	163	12	n−1	n−1	PROPN
ejpam-5020	163	13	(	(	PUNCT
ejpam-5020	163	14	λ2	λ2	NOUN
ejpam-5020	163	15	+	+	CCONJ
ejpam-5020	163	16	1−	1−	NUM
ejpam-5020	163	17	(	(	PUNCT
ejpam-5020	163	18	3	3	NUM
ejpam-5020	163	19	4	4	NUM
ejpam-5020	163	20	n	n	NOUN
ejpam-5020	163	21	)	)	PUNCT
ejpam-5020	163	22	λ−	λ−	PROPN
ejpam-5020	163	23	1	1	NUM
ejpam-5020	163	24	8	8	NUM
ejpam-5020	163	25	(	(	PUNCT
ejpam-5020	163	26	n+	n+	NUM
ejpam-5020	163	27	2)(n−	2)(n−	NUM
ejpam-5020	163	28	1	1	NUM
ejpam-5020	163	29	)	)	PUNCT
ejpam-5020	163	30	)	)	PUNCT
ejpam-5020	163	31	(	(	PUNCT
ejpam-5020	163	32	ii	ii	NOUN
ejpam-5020	163	33	)	)	PUNCT
ejpam-5020	163	34	now	now	ADV
ejpam-5020	163	35	for	for	ADP
ejpam-5020	163	36	the	the	DET
ejpam-5020	163	37	even	even	ADJ
ejpam-5020	163	38	n	n	PRON
ejpam-5020	163	39	case	case	NOUN
ejpam-5020	163	40	and	and	CCONJ
ejpam-5020	163	41	g	g	NOUN
ejpam-5020	163	42	=	=	PROPN
ejpam-5020	163	43	g1	g1	PROPN
ejpam-5020	163	44	∪g2	∪g2	PROPN
ejpam-5020	163	45	,	,	PUNCT
ejpam-5020	163	46	we	we	PRON
ejpam-5020	163	47	know	know	VERB
ejpam-5020	163	48	that	that	SCONJ
ejpam-5020	163	49	z(d2n	z(d2n	NOUN
ejpam-5020	163	50	)	)	PUNCT
ejpam-5020	163	51	=	=	PUNCT
ejpam-5020	163	52	{	{	PUNCT
ejpam-5020	163	53	e	e	NOUN
ejpam-5020	163	54	,	,	PUNCT
ejpam-5020	163	55	a	a	DET
ejpam-5020	163	56	n	n	NOUN
ejpam-5020	163	57	2	2	NUM
ejpam-5020	163	58	}	}	PUNCT
ejpam-5020	163	59	.	.	PUNCT
ejpam-5020	164	1	then	then	ADV
ejpam-5020	164	2	,	,	PUNCT
ejpam-5020	164	3	the	the	DET
ejpam-5020	164	4	cardinality	cardinality	NOUN
ejpam-5020	164	5	of	of	ADP
ejpam-5020	164	6	the	the	DET
ejpam-5020	164	7	vertex	vertex	NOUN
ejpam-5020	164	8	set	set	NOUN
ejpam-5020	164	9	of	of	ADP
ejpam-5020	164	10	γg	γg	ADV
ejpam-5020	164	11	is	be	AUX
ejpam-5020	164	12	2n−	2n−	PROPN
ejpam-5020	164	13	2	2	NUM
ejpam-5020	164	14	with	with	ADP
ejpam-5020	164	15	detail	detail	NOUN
ejpam-5020	164	16	n−	n−	NOUN
ejpam-5020	164	17	2	2	NUM
ejpam-5020	164	18	vertices	vertex	NOUN
ejpam-5020	164	19	of	of	ADP
ejpam-5020	164	20	ai	ai	NOUN
ejpam-5020	164	21	,	,	PUNCT
ejpam-5020	164	22	for	for	ADP
ejpam-5020	164	23	1	1	NUM
ejpam-5020	164	24	≤	≤	NUM
ejpam-5020	165	1	i	i	PRON
ejpam-5020	165	2	<	<	X
ejpam-5020	165	3	n	n	PROPN
ejpam-5020	165	4	2	2	NUM
ejpam-5020	165	5	,	,	PUNCT
ejpam-5020	165	6	n	n	ADV
ejpam-5020	165	7	2	2	NUM
ejpam-5020	165	8	<	<	X
ejpam-5020	165	9	i	i	PRON
ejpam-5020	165	10	<	<	X
ejpam-5020	165	11	n	n	CCONJ
ejpam-5020	165	12	,	,	PUNCT
ejpam-5020	165	13	and	and	CCONJ
ejpam-5020	165	14	n	n	DET
ejpam-5020	165	15	vertices	vertex	NOUN
ejpam-5020	165	16	of	of	ADP
ejpam-5020	165	17	aib	aib	PROPN
ejpam-5020	165	18	,	,	PUNCT
ejpam-5020	165	19	for	for	ADP
ejpam-5020	165	20	1	1	NUM
ejpam-5020	165	21	≤	≤	NUM
ejpam-5020	165	22	i	i	PRON
ejpam-5020	165	23	≤	≤	ADJ
ejpam-5020	165	24	n.	n.	NOUN
ejpam-5020	165	25	following	follow	VERB
ejpam-5020	165	26	the	the	DET
ejpam-5020	165	27	result	result	NOUN
ejpam-5020	165	28	of	of	ADP
ejpam-5020	165	29	theorem	theorem	NOUN
ejpam-5020	165	30	4	4	NUM
ejpam-5020	165	31	and	and	CCONJ
ejpam-5020	165	32	by	by	ADP
ejpam-5020	165	33	definition	definition	NOUN
ejpam-5020	165	34	1	1	NUM
ejpam-5020	165	35	,	,	PUNCT
ejpam-5020	165	36	then	then	ADV
ejpam-5020	165	37	c(γg	c(γg	NOUN
ejpam-5020	165	38	)	)	PUNCT
ejpam-5020	165	39	is	be	AUX
ejpam-5020	165	40	a	a	DET
ejpam-5020	165	41	(	(	PUNCT
ejpam-5020	165	42	2n	2n	NUM
ejpam-5020	165	43	−	−	NOUN
ejpam-5020	165	44	2	2	X
ejpam-5020	165	45	)	)	PUNCT
ejpam-5020	165	46	×	×	NOUN
ejpam-5020	165	47	(	(	PUNCT
ejpam-5020	165	48	2n	2n	NUM
ejpam-5020	165	49	−	−	NOUN
ejpam-5020	165	50	2	2	NUM
ejpam-5020	165	51	)	)	PUNCT
ejpam-5020	165	52	matrix	matrix	NOUN
ejpam-5020	165	53	as	as	ADP
ejpam-5020	165	54	the	the	DET
ejpam-5020	165	55	following	following	NOUN
ejpam-5020	165	56	:	:	PUNCT
ejpam-5020	165	57	c(γg	c(γg	NOUN
ejpam-5020	165	58	)	)	PUNCT
ejpam-5020	165	59	=	=	SYM
ejpam-5020	165	60			NOUN
ejpam-5020	165	61	0	0	NUM
ejpam-5020	165	62	.	.	PUNCT
ejpam-5020	165	63	.	.	PUNCT
ejpam-5020	166	1	.	.	PUNCT
ejpam-5020	167	1	1	1	NUM
ejpam-5020	167	2	4	4	NUM
ejpam-5020	167	3	1	1	NUM
ejpam-5020	167	4	2	2	NUM
ejpam-5020	167	5	.	.	PUNCT
ejpam-5020	167	6	.	.	PUNCT
ejpam-5020	167	7	.	.	PUNCT
ejpam-5020	168	1	1	1	NUM
ejpam-5020	168	2	2	2	NUM
ejpam-5020	168	3	1	1	NUM
ejpam-5020	168	4	2	2	NUM
ejpam-5020	168	5	.	.	PUNCT
ejpam-5020	168	6	.	.	PUNCT
ejpam-5020	168	7	.	.	PUNCT
ejpam-5020	169	1	1	1	NUM
ejpam-5020	169	2	2	2	NUM
ejpam-5020	169	3	...	...	PUNCT
ejpam-5020	169	4	.	.	PUNCT
ejpam-5020	169	5	.	.	PUNCT
ejpam-5020	169	6	.	.	PUNCT
ejpam-5020	169	7	...	...	PUNCT
ejpam-5020	169	8	...	...	PUNCT
ejpam-5020	169	9	.	.	PUNCT
ejpam-5020	169	10	.	.	PUNCT
ejpam-5020	169	11	.	.	PUNCT
ejpam-5020	169	12	...	...	PUNCT
ejpam-5020	169	13	...	...	PUNCT
ejpam-5020	169	14	.	.	PUNCT
ejpam-5020	169	15	.	.	PUNCT
ejpam-5020	169	16	.	.	PUNCT
ejpam-5020	170	1	...	...	PUNCT
ejpam-5020	171	1	1	1	NUM
ejpam-5020	171	2	4	4	NUM
ejpam-5020	171	3	.	.	PUNCT
ejpam-5020	171	4	.	.	PUNCT
ejpam-5020	171	5	.	.	PUNCT
ejpam-5020	172	1	0	0	NUM
ejpam-5020	172	2	1	1	NUM
ejpam-5020	172	3	2	2	NUM
ejpam-5020	172	4	.	.	PUNCT
ejpam-5020	172	5	.	.	PUNCT
ejpam-5020	172	6	.	.	PUNCT
ejpam-5020	173	1	1	1	NUM
ejpam-5020	173	2	2	2	NUM
ejpam-5020	173	3	1	1	NUM
ejpam-5020	173	4	2	2	NUM
ejpam-5020	173	5	.	.	PUNCT
ejpam-5020	173	6	.	.	PUNCT
ejpam-5020	173	7	.	.	PUNCT
ejpam-5020	174	1	1	1	NUM
ejpam-5020	174	2	2	2	NUM
ejpam-5020	174	3	1	1	NUM
ejpam-5020	174	4	2	2	NUM
ejpam-5020	174	5	.	.	PUNCT
ejpam-5020	174	6	.	.	PUNCT
ejpam-5020	174	7	.	.	PUNCT
ejpam-5020	175	1	1	1	NUM
ejpam-5020	175	2	2	2	NUM
ejpam-5020	175	3	0	0	NUM
ejpam-5020	175	4	.	.	PUNCT
ejpam-5020	175	5	.	.	PUNCT
ejpam-5020	175	6	.	.	PUNCT
ejpam-5020	176	1	1	1	NUM
ejpam-5020	176	2	2	2	NUM
ejpam-5020	176	3	1	1	NUM
ejpam-5020	176	4	4	4	NUM
ejpam-5020	176	5	.	.	PUNCT
ejpam-5020	176	6	.	.	PUNCT
ejpam-5020	176	7	.	.	PUNCT
ejpam-5020	177	1	1	1	NUM
ejpam-5020	177	2	2	2	NUM
ejpam-5020	177	3	...	...	PUNCT
ejpam-5020	177	4	.	.	PUNCT
ejpam-5020	177	5	.	.	PUNCT
ejpam-5020	177	6	.	.	PUNCT
ejpam-5020	177	7	...	...	PUNCT
ejpam-5020	177	8	...	...	PUNCT
ejpam-5020	177	9	.	.	PUNCT
ejpam-5020	177	10	.	.	PUNCT
ejpam-5020	177	11	.	.	PUNCT
ejpam-5020	177	12	...	...	PUNCT
ejpam-5020	177	13	...	...	PUNCT
ejpam-5020	177	14	.	.	PUNCT
ejpam-5020	177	15	.	.	PUNCT
ejpam-5020	177	16	.	.	PUNCT
ejpam-5020	178	1	...	...	PUNCT
ejpam-5020	179	1	1	1	NUM
ejpam-5020	179	2	2	2	NUM
ejpam-5020	179	3	.	.	PUNCT
ejpam-5020	179	4	.	.	PUNCT
ejpam-5020	179	5	.	.	PUNCT
ejpam-5020	180	1	1	1	NUM
ejpam-5020	180	2	2	2	NUM
ejpam-5020	180	3	1	1	NUM
ejpam-5020	180	4	2	2	NUM
ejpam-5020	180	5	.	.	PUNCT
ejpam-5020	180	6	.	.	PUNCT
ejpam-5020	180	7	.	.	PUNCT
ejpam-5020	181	1	0	0	NUM
ejpam-5020	181	2	1	1	NUM
ejpam-5020	181	3	2	2	NUM
ejpam-5020	181	4	.	.	PUNCT
ejpam-5020	181	5	.	.	PUNCT
ejpam-5020	181	6	.	.	PUNCT
ejpam-5020	182	1	1	1	NUM
ejpam-5020	182	2	4	4	NUM
ejpam-5020	182	3	1	1	NUM
ejpam-5020	182	4	2	2	NUM
ejpam-5020	182	5	.	.	PUNCT
ejpam-5020	182	6	.	.	PUNCT
ejpam-5020	182	7	.	.	PUNCT
ejpam-5020	183	1	1	1	NUM
ejpam-5020	183	2	2	2	NUM
ejpam-5020	183	3	1	1	NUM
ejpam-5020	183	4	4	4	NUM
ejpam-5020	183	5	.	.	PUNCT
ejpam-5020	183	6	.	.	PUNCT
ejpam-5020	183	7	.	.	PUNCT
ejpam-5020	184	1	1	1	NUM
ejpam-5020	184	2	2	2	NUM
ejpam-5020	184	3	0	0	NUM
ejpam-5020	184	4	.	.	PUNCT
ejpam-5020	184	5	.	.	PUNCT
ejpam-5020	184	6	.	.	PUNCT
ejpam-5020	185	1	1	1	NUM
ejpam-5020	185	2	2	2	NUM
ejpam-5020	185	3	...	...	PUNCT
ejpam-5020	185	4	.	.	PUNCT
ejpam-5020	185	5	.	.	PUNCT
ejpam-5020	185	6	.	.	PUNCT
ejpam-5020	185	7	...	...	PUNCT
ejpam-5020	185	8	...	...	PUNCT
ejpam-5020	185	9	.	.	PUNCT
ejpam-5020	185	10	.	.	PUNCT
ejpam-5020	185	11	.	.	PUNCT
ejpam-5020	185	12	...	...	PUNCT
ejpam-5020	185	13	...	...	PUNCT
ejpam-5020	185	14	.	.	PUNCT
ejpam-5020	185	15	.	.	PUNCT
ejpam-5020	185	16	.	.	PUNCT
ejpam-5020	186	1	...	...	PUNCT
ejpam-5020	187	1	1	1	NUM
ejpam-5020	187	2	2	2	NUM
ejpam-5020	187	3	.	.	PUNCT
ejpam-5020	187	4	.	.	PUNCT
ejpam-5020	187	5	.	.	PUNCT
ejpam-5020	188	1	1	1	NUM
ejpam-5020	188	2	2	2	NUM
ejpam-5020	188	3	1	1	NUM
ejpam-5020	188	4	2	2	NUM
ejpam-5020	188	5	.	.	PUNCT
ejpam-5020	188	6	.	.	PUNCT
ejpam-5020	188	7	.	.	PUNCT
ejpam-5020	189	1	1	1	NUM
ejpam-5020	189	2	4	4	NUM
ejpam-5020	189	3	1	1	NUM
ejpam-5020	189	4	2	2	NUM
ejpam-5020	189	5	.	.	PUNCT
ejpam-5020	189	6	.	.	PUNCT
ejpam-5020	189	7	.	.	PUNCT
ejpam-5020	190	1	0	0	NUM
ejpam-5020	190	2			NUM
ejpam-5020	190	3	m.	m.	NOUN
ejpam-5020	190	4	u.	u.	PROPN
ejpam-5020	190	5	romdhini	romdhini	PROPN
ejpam-5020	190	6	et	et	PROPN
ejpam-5020	190	7	al	al	PROPN
ejpam-5020	190	8	.	.	PUNCT
ejpam-5020	190	9	/	/	SYM
ejpam-5020	190	10	eur	eur	PROPN
ejpam-5020	190	11	.	.	PUNCT
ejpam-5020	191	1	j.	j.	PROPN
ejpam-5020	191	2	pure	pure	PROPN
ejpam-5020	191	3	appl	appl	PROPN
ejpam-5020	191	4	.	.	PROPN
ejpam-5020	191	5	math	math	PROPN
ejpam-5020	191	6	,	,	PUNCT
ejpam-5020	191	7	17	17	NUM
ejpam-5020	191	8	(	(	PUNCT
ejpam-5020	191	9	1	1	NUM
ejpam-5020	191	10	)	)	PUNCT
ejpam-5020	191	11	(	(	PUNCT
ejpam-5020	191	12	2024	2024	NUM
ejpam-5020	191	13	)	)	PUNCT
ejpam-5020	191	14	,	,	PUNCT
ejpam-5020	191	15	212	212	NUM
ejpam-5020	191	16	-	-	SYM
ejpam-5020	191	17	221	221	NUM
ejpam-5020	191	18	218	218	NUM
ejpam-5020	191	19	now	now	ADV
ejpam-5020	191	20	we	we	PRON
ejpam-5020	191	21	provide	provide	VERB
ejpam-5020	191	22	nine	nine	NUM
ejpam-5020	191	23	block	block	NOUN
ejpam-5020	191	24	matrices	matrix	NOUN
ejpam-5020	191	25	of	of	ADP
ejpam-5020	191	26	c(γg	c(γg	NOUN
ejpam-5020	191	27	)	)	PUNCT
ejpam-5020	191	28	as	as	SCONJ
ejpam-5020	191	29	follows	follow	VERB
ejpam-5020	191	30	:	:	PUNCT
ejpam-5020	191	31	c(γg	c(γg	NOUN
ejpam-5020	191	32	)	)	PUNCT
ejpam-5020	192	1	=	=	PUNCT
ejpam-5020	192	2			NOUN
ejpam-5020	193	1	1	1	NUM
ejpam-5020	193	2	4(j	4(j	NUM
ejpam-5020	193	3	−	−	PROPN
ejpam-5020	193	4	i)n−2	i)n−2	PROPN
ejpam-5020	193	5	1	1	NUM
ejpam-5020	193	6	2j(n−2)×n	2j(n−2)×n	NUM
ejpam-5020	193	7	2	2	NUM
ejpam-5020	193	8	1	1	NUM
ejpam-5020	193	9	2j(n−2)×n	2j(n−2)×n	NUM
ejpam-5020	193	10	2	2	NUM
ejpam-5020	193	11	1	1	NUM
ejpam-5020	193	12	2jn	2jn	NOUN
ejpam-5020	193	13	2	2	NUM
ejpam-5020	193	14	×(n−2	×(n−2	NOUN
ejpam-5020	193	15	)	)	PUNCT
ejpam-5020	193	16	1	1	NUM
ejpam-5020	193	17	2(j	2(j	NUM
ejpam-5020	193	18	−	−	NOUN
ejpam-5020	193	19	i)n	i)n	NOUN
ejpam-5020	193	20	2	2	NUM
ejpam-5020	193	21	1	1	NUM
ejpam-5020	193	22	2(j	2(j	NUM
ejpam-5020	193	23	−	−	NOUN
ejpam-5020	193	24	i)n	i)n	NOUN
ejpam-5020	193	25	2	2	NUM
ejpam-5020	193	26	+	+	CCONJ
ejpam-5020	193	27	1	1	NUM
ejpam-5020	193	28	4	4	NUM
ejpam-5020	193	29	in	in	ADP
ejpam-5020	193	30	2	2	NUM
ejpam-5020	193	31	1	1	NUM
ejpam-5020	193	32	2jn	2jn	NOUN
ejpam-5020	193	33	2	2	NUM
ejpam-5020	193	34	×(n−2	×(n−2	NOUN
ejpam-5020	193	35	)	)	PUNCT
ejpam-5020	193	36	1	1	NUM
ejpam-5020	193	37	2(j	2(j	NUM
ejpam-5020	193	38	−	−	NOUN
ejpam-5020	193	39	i)n	i)n	NOUN
ejpam-5020	193	40	2	2	NUM
ejpam-5020	193	41	+	+	CCONJ
ejpam-5020	193	42	1	1	NUM
ejpam-5020	193	43	4	4	NUM
ejpam-5020	193	44	in	in	ADP
ejpam-5020	193	45	2	2	NUM
ejpam-5020	193	46	1	1	NUM
ejpam-5020	193	47	2(j	2(j	NUM
ejpam-5020	193	48	−	−	NOUN
ejpam-5020	193	49	i)n	i)n	NOUN
ejpam-5020	193	50	2	2	NUM
ejpam-5020	193	51			NUM
ejpam-5020	193	52	.	.	PUNCT
ejpam-5020	194	1	by	by	ADP
ejpam-5020	194	2	theorem	theorem	NOUN
ejpam-5020	194	3	3	3	NUM
ejpam-5020	194	4	with	with	ADP
ejpam-5020	194	5	r	r	NOUN
ejpam-5020	194	6	=	=	SYM
ejpam-5020	194	7	s	s	NOUN
ejpam-5020	194	8	=	=	SYM
ejpam-5020	194	9	1	1	NUM
ejpam-5020	194	10	4	4	NUM
ejpam-5020	194	11	and	and	CCONJ
ejpam-5020	194	12	t	t	NOUN
ejpam-5020	194	13	=	=	SYM
ejpam-5020	194	14	u	u	NOUN
ejpam-5020	194	15	=	=	NOUN
ejpam-5020	194	16	1	1	NUM
ejpam-5020	194	17	2	2	NUM
ejpam-5020	194	18	,	,	PUNCT
ejpam-5020	194	19	we	we	PRON
ejpam-5020	194	20	then	then	ADV
ejpam-5020	194	21	obtain	obtain	VERB
ejpam-5020	194	22	pc(γg)(λ	pc(γg)(λ	NOUN
ejpam-5020	194	23	)	)	PUNCT
ejpam-5020	195	1	=	=	PUNCT
ejpam-5020	195	2	(	(	PUNCT
ejpam-5020	195	3	λ+	λ+	NUM
ejpam-5020	195	4	1	1	NUM
ejpam-5020	195	5	4	4	NUM
ejpam-5020	195	6	)	)	PUNCT
ejpam-5020	195	7	3n−6	3n−6	NUM
ejpam-5020	195	8	2	2	NUM
ejpam-5020	195	9	(	(	PUNCT
ejpam-5020	195	10	λ+	λ+	PUNCT
ejpam-5020	195	11	3	3	NUM
ejpam-5020	195	12	4	4	NUM
ejpam-5020	195	13	)	)	PUNCT
ejpam-5020	195	14	n	n	PRON
ejpam-5020	195	15	2	2	NUM
ejpam-5020	195	16	−1	−1	NOUN
ejpam-5020	195	17	(	(	PUNCT
ejpam-5020	195	18	λ2	λ2	NOUN
ejpam-5020	195	19	−	−	PROPN
ejpam-5020	195	20	3	3	NUM
ejpam-5020	195	21	4	4	NUM
ejpam-5020	195	22	(	(	PUNCT
ejpam-5020	195	23	n−	n−	NOUN
ejpam-5020	195	24	2)λ−	2)λ−	NUM
ejpam-5020	195	25	1	1	NUM
ejpam-5020	195	26	16	16	NUM
ejpam-5020	195	27	(	(	PUNCT
ejpam-5020	195	28	2n2	2n2	NUM
ejpam-5020	195	29	+	+	CCONJ
ejpam-5020	195	30	n−	n−	NOUN
ejpam-5020	195	31	9	9	NUM
ejpam-5020	195	32	)	)	PUNCT
ejpam-5020	195	33	)	)	PUNCT
ejpam-5020	195	34	.	.	PUNCT
ejpam-5020	196	1	theorem	theorem	VERB
ejpam-5020	196	2	7	7	NUM
ejpam-5020	196	3	.	.	PUNCT
ejpam-5020	197	1	the	the	DET
ejpam-5020	197	2	c−spectral	c−spectral	ADJ
ejpam-5020	197	3	radius	radius	NOUN
ejpam-5020	197	4	for	for	ADP
ejpam-5020	197	5	γg	γg	ADV
ejpam-5020	197	6	,	,	PUNCT
ejpam-5020	197	7	where	where	SCONJ
ejpam-5020	197	8	g	g	PROPN
ejpam-5020	197	9	=	=	PUNCT
ejpam-5020	197	10	g1	g1	PROPN
ejpam-5020	197	11	∪g2	∪g2	PROPN
ejpam-5020	197	12	,	,	PUNCT
ejpam-5020	197	13	is	be	AUX
ejpam-5020	197	14	(	(	PUNCT
ejpam-5020	197	15	i	i	NOUN
ejpam-5020	197	16	)	)	PUNCT
ejpam-5020	197	17	for	for	ADP
ejpam-5020	197	18	n	n	X
ejpam-5020	197	19	is	be	AUX
ejpam-5020	197	20	odd	odd	ADJ
ejpam-5020	197	21	:	:	PUNCT
ejpam-5020	197	22	ρc(γg	ρc(γg	NUM
ejpam-5020	197	23	)	)	PUNCT
ejpam-5020	197	24	=	=	SYM
ejpam-5020	198	1	1	1	NUM
ejpam-5020	198	2	8	8	NUM
ejpam-5020	198	3	(	(	PUNCT
ejpam-5020	198	4	3n−	3n−	NUM
ejpam-5020	198	5	4	4	NUM
ejpam-5020	198	6	+	+	CCONJ
ejpam-5020	198	7	√	√	NOUN
ejpam-5020	198	8	n(17n−	n(17n−	VERB
ejpam-5020	198	9	16	16	NUM
ejpam-5020	198	10	)	)	PUNCT
ejpam-5020	198	11	)	)	PUNCT
ejpam-5020	198	12	,	,	PUNCT
ejpam-5020	198	13	(	(	PUNCT
ejpam-5020	198	14	ii	ii	NOUN
ejpam-5020	198	15	)	)	PUNCT
ejpam-5020	198	16	for	for	ADP
ejpam-5020	198	17	n	n	NUM
ejpam-5020	198	18	is	be	AUX
ejpam-5020	198	19	even	even	ADV
ejpam-5020	198	20	:	:	PUNCT
ejpam-5020	198	21	ρc(γg	ρc(γg	NUM
ejpam-5020	198	22	)	)	PUNCT
ejpam-5020	198	23	=	=	SYM
ejpam-5020	198	24	1	1	NUM
ejpam-5020	198	25	8	8	NUM
ejpam-5020	198	26	(	(	PUNCT
ejpam-5020	198	27	3n−	3n−	NUM
ejpam-5020	198	28	6	6	NUM
ejpam-5020	198	29	+	+	CCONJ
ejpam-5020	198	30	√	√	NOUN
ejpam-5020	198	31	n(17n−	n(17n−	VERB
ejpam-5020	198	32	32	32	NUM
ejpam-5020	198	33	)	)	PUNCT
ejpam-5020	198	34	)	)	PUNCT
ejpam-5020	198	35	.	.	PUNCT
ejpam-5020	199	1	proof	proof	NOUN
ejpam-5020	199	2	.	.	PUNCT
ejpam-5020	200	1	(	(	PUNCT
ejpam-5020	200	2	i	i	NOUN
ejpam-5020	200	3	)	)	PUNCT
ejpam-5020	200	4	according	accord	VERB
ejpam-5020	200	5	to	to	ADP
ejpam-5020	200	6	theorem	theorem	ADJ
ejpam-5020	200	7	6	6	NUM
ejpam-5020	200	8	(	(	PUNCT
ejpam-5020	200	9	1	1	NUM
ejpam-5020	200	10	)	)	PUNCT
ejpam-5020	200	11	,	,	PUNCT
ejpam-5020	200	12	for	for	ADP
ejpam-5020	200	13	the	the	DET
ejpam-5020	200	14	odd	odd	ADJ
ejpam-5020	200	15	n	n	PRON
ejpam-5020	200	16	case	case	NOUN
ejpam-5020	200	17	gives	give	VERB
ejpam-5020	200	18	four	four	NUM
ejpam-5020	200	19	eigenvalues	eigenvalue	NOUN
ejpam-5020	200	20	.	.	PUNCT
ejpam-5020	201	1	they	they	PRON
ejpam-5020	201	2	are	be	AUX
ejpam-5020	201	3	λ1	λ1	ADJ
ejpam-5020	201	4	=	=	SYM
ejpam-5020	201	5	−1	−1	NOUN
ejpam-5020	201	6	4	4	NUM
ejpam-5020	201	7	of	of	ADP
ejpam-5020	201	8	multiplicity	multiplicity	NOUN
ejpam-5020	201	9	(	(	PUNCT
ejpam-5020	201	10	n	n	CCONJ
ejpam-5020	201	11	−	−	PROPN
ejpam-5020	201	12	2	2	NUM
ejpam-5020	201	13	)	)	PUNCT
ejpam-5020	201	14	,	,	PUNCT
ejpam-5020	201	15	λ2	λ2	NOUN
ejpam-5020	201	16	=	=	SYM
ejpam-5020	201	17	−1	−1	NOUN
ejpam-5020	201	18	2	2	NUM
ejpam-5020	201	19	of	of	ADP
ejpam-5020	201	20	multiplicity	multiplicity	NOUN
ejpam-5020	201	21	(	(	PUNCT
ejpam-5020	201	22	n	n	CCONJ
ejpam-5020	201	23	−	−	PROPN
ejpam-5020	201	24	1	1	NUM
ejpam-5020	201	25	)	)	PUNCT
ejpam-5020	201	26	,	,	PUNCT
ejpam-5020	201	27	and	and	CCONJ
ejpam-5020	201	28	λ3,4	λ3,4	NOUN
ejpam-5020	201	29	=	=	NOUN
ejpam-5020	201	30	1	1	NUM
ejpam-5020	201	31	8	8	NUM
ejpam-5020	201	32	(	(	PUNCT
ejpam-5020	201	33	3n−	3n−	NUM
ejpam-5020	201	34	4±	4±	PRON
ejpam-5020	201	35	√	√	NUM
ejpam-5020	201	36	n(17n−	n(17n−	VERB
ejpam-5020	201	37	16	16	NUM
ejpam-5020	201	38	)	)	PUNCT
ejpam-5020	201	39	)	)	PUNCT
ejpam-5020	201	40	.	.	PUNCT
ejpam-5020	202	1	hence	hence	ADV
ejpam-5020	202	2	,	,	PUNCT
ejpam-5020	202	3	the	the	DET
ejpam-5020	202	4	spectrum	spectrum	NOUN
ejpam-5020	202	5	of	of	ADP
ejpam-5020	202	6	γg	γg	ADV
ejpam-5020	202	7	as	as	ADP
ejpam-5020	202	8	the	the	DET
ejpam-5020	202	9	following	follow	VERB
ejpam-5020	202	10	:	:	PUNCT
ejpam-5020	202	11	specc(γg	specc(γg	NOUN
ejpam-5020	202	12	)	)	PUNCT
ejpam-5020	202	13	=	=	SYM
ejpam-5020	202	14	{	{	PUNCT
ejpam-5020	202	15	(	(	PUNCT
ejpam-5020	202	16	1	1	NUM
ejpam-5020	202	17	8	8	NUM
ejpam-5020	202	18	(	(	PUNCT
ejpam-5020	202	19	3n−	3n−	NUM
ejpam-5020	202	20	4	4	NUM
ejpam-5020	202	21	+	+	CCONJ
ejpam-5020	202	22	√	√	NOUN
ejpam-5020	202	23	n(17n−	n(17n−	VERB
ejpam-5020	202	24	16	16	NUM
ejpam-5020	202	25	)	)	PUNCT
ejpam-5020	202	26	)	)	PUNCT
ejpam-5020	202	27	)	)	PUNCT
ejpam-5020	202	28	1	1	NUM
ejpam-5020	202	29	,	,	PUNCT
ejpam-5020	202	30	(	(	PUNCT
ejpam-5020	202	31	−1	−1	NOUN
ejpam-5020	202	32	4	4	NUM
ejpam-5020	202	33	)	)	PUNCT
ejpam-5020	202	34	n−2	n−2	PROPN
ejpam-5020	202	35	,	,	PUNCT
ejpam-5020	202	36	(	(	PUNCT
ejpam-5020	202	37	−1	−1	NOUN
ejpam-5020	202	38	2	2	NUM
ejpam-5020	202	39	)	)	PUNCT
ejpam-5020	202	40	n−1	n−1	PROPN
ejpam-5020	202	41	,	,	PUNCT
ejpam-5020	202	42	(	(	PUNCT
ejpam-5020	202	43	1	1	NUM
ejpam-5020	202	44	8	8	NUM
ejpam-5020	202	45	(	(	PUNCT
ejpam-5020	202	46	3n−	3n−	PROPN
ejpam-5020	202	47	4−	4−	NOUN
ejpam-5020	202	48	√	√	NOUN
ejpam-5020	202	49	n(17n−	n(17n−	VERB
ejpam-5020	202	50	16	16	NUM
ejpam-5020	202	51	)	)	PUNCT
ejpam-5020	202	52	)	)	PUNCT
ejpam-5020	202	53	)	)	PUNCT
ejpam-5020	202	54	1	1	X
ejpam-5020	202	55	}	}	PUNCT
ejpam-5020	202	56	.	.	PUNCT
ejpam-5020	203	1	we	we	PRON
ejpam-5020	203	2	take	take	VERB
ejpam-5020	203	3	the	the	DET
ejpam-5020	203	4	maximum	maximum	ADJ
ejpam-5020	203	5	absolute	absolute	ADJ
ejpam-5020	203	6	eigenvalues	eigenvalue	NOUN
ejpam-5020	203	7	and	and	CCONJ
ejpam-5020	203	8	get	get	VERB
ejpam-5020	203	9	the	the	DET
ejpam-5020	203	10	spectral	spectral	ADJ
ejpam-5020	203	11	radius	radius	NOUN
ejpam-5020	203	12	of	of	ADP
ejpam-5020	203	13	γg	γg	ADV
ejpam-5020	203	14	as	as	ADP
ejpam-5020	203	15	the	the	DET
ejpam-5020	203	16	desired	desire	VERB
ejpam-5020	203	17	result	result	NOUN
ejpam-5020	203	18	.	.	PUNCT
ejpam-5020	204	1	(	(	PUNCT
ejpam-5020	204	2	ii	ii	NOUN
ejpam-5020	204	3	)	)	PUNCT
ejpam-5020	204	4	for	for	ADP
ejpam-5020	204	5	n	n	CCONJ
ejpam-5020	204	6	is	be	AUX
ejpam-5020	204	7	even	even	ADV
ejpam-5020	204	8	and	and	CCONJ
ejpam-5020	204	9	following	follow	VERB
ejpam-5020	204	10	theorem	theorem	NOUN
ejpam-5020	204	11	6	6	NUM
ejpam-5020	204	12	(	(	PUNCT
ejpam-5020	204	13	2	2	NUM
ejpam-5020	204	14	)	)	PUNCT
ejpam-5020	204	15	implies	imply	VERB
ejpam-5020	204	16	that	that	SCONJ
ejpam-5020	204	17	γg	γg	ADV
ejpam-5020	204	18	has	have	VERB
ejpam-5020	204	19	four	four	NUM
ejpam-5020	204	20	eigenvalues	eigenvalue	NOUN
ejpam-5020	204	21	.	.	PUNCT
ejpam-5020	205	1	they	they	PRON
ejpam-5020	205	2	are	be	AUX
ejpam-5020	205	3	λ1	λ1	ADJ
ejpam-5020	205	4	=	=	SYM
ejpam-5020	205	5	−1	−1	NOUN
ejpam-5020	205	6	4	4	NUM
ejpam-5020	205	7	of	of	ADP
ejpam-5020	205	8	multiplicity	multiplicity	NOUN
ejpam-5020	205	9	n	n	CCONJ
ejpam-5020	205	10	−	−	PROPN
ejpam-5020	205	11	3	3	NUM
ejpam-5020	205	12	+	+	CCONJ
ejpam-5020	205	13	n	n	NUM
ejpam-5020	205	14	2	2	NUM
ejpam-5020	205	15	,	,	PUNCT
ejpam-5020	205	16	λ2	λ2	NOUN
ejpam-5020	205	17	=	=	SYM
ejpam-5020	205	18	−3	−3	NOUN
ejpam-5020	205	19	4	4	NUM
ejpam-5020	205	20	of	of	ADP
ejpam-5020	205	21	multiplicity	multiplicity	NOUN
ejpam-5020	205	22	n	n	CCONJ
ejpam-5020	205	23	2	2	NUM
ejpam-5020	205	24	−	−	NUM
ejpam-5020	205	25	1	1	NUM
ejpam-5020	205	26	and	and	CCONJ
ejpam-5020	205	27	λ3,4	λ3,4	NOUN
ejpam-5020	205	28	=	=	NOUN
ejpam-5020	205	29	1	1	NUM
ejpam-5020	205	30	8	8	NUM
ejpam-5020	205	31	(	(	PUNCT
ejpam-5020	205	32	3n−	3n−	PROPN
ejpam-5020	205	33	6±	6±	NUM
ejpam-5020	205	34	√	√	NUM
ejpam-5020	205	35	n(17n−	n(17n−	VERB
ejpam-5020	205	36	32	32	NUM
ejpam-5020	205	37	)	)	PUNCT
ejpam-5020	205	38	)	)	PUNCT
ejpam-5020	205	39	.	.	PUNCT
ejpam-5020	206	1	hence	hence	ADV
ejpam-5020	206	2	,	,	PUNCT
ejpam-5020	206	3	the	the	DET
ejpam-5020	206	4	spectrum	spectrum	NOUN
ejpam-5020	206	5	of	of	ADP
ejpam-5020	206	6	γg	γg	ADV
ejpam-5020	206	7	as	as	ADP
ejpam-5020	206	8	the	the	DET
ejpam-5020	206	9	following	follow	VERB
ejpam-5020	206	10	:	:	PUNCT
ejpam-5020	206	11	specc(γg	specc(γg	NOUN
ejpam-5020	206	12	)	)	PUNCT
ejpam-5020	206	13	=	=	SYM
ejpam-5020	206	14	{	{	PUNCT
ejpam-5020	206	15	(	(	PUNCT
ejpam-5020	206	16	1	1	NUM
ejpam-5020	206	17	8	8	NUM
ejpam-5020	206	18	(	(	PUNCT
ejpam-5020	206	19	3n−	3n−	NUM
ejpam-5020	206	20	6	6	NUM
ejpam-5020	206	21	+	+	CCONJ
ejpam-5020	206	22	√	√	NOUN
ejpam-5020	206	23	n(17n−	n(17n−	VERB
ejpam-5020	206	24	32	32	NUM
ejpam-5020	206	25	)	)	PUNCT
ejpam-5020	206	26	)	)	PUNCT
ejpam-5020	206	27	)	)	PUNCT
ejpam-5020	206	28	1	1	NUM
ejpam-5020	206	29	,	,	PUNCT
ejpam-5020	206	30	(	(	PUNCT
ejpam-5020	206	31	−1	−1	NOUN
ejpam-5020	206	32	4	4	NUM
ejpam-5020	206	33	)	)	PUNCT
ejpam-5020	206	34	n−3+n	n−3+n	NOUN
ejpam-5020	206	35	2	2	NUM
ejpam-5020	206	36	,	,	PUNCT
ejpam-5020	206	37	(	(	PUNCT
ejpam-5020	206	38	−3	−3	NOUN
ejpam-5020	206	39	4	4	NUM
ejpam-5020	206	40	)	)	PUNCT
ejpam-5020	206	41	n	n	PRON
ejpam-5020	206	42	2	2	NUM
ejpam-5020	206	43	−1	−1	NOUN
ejpam-5020	206	44	,	,	PUNCT
ejpam-5020	206	45	(	(	PUNCT
ejpam-5020	206	46	1	1	NUM
ejpam-5020	206	47	8	8	NUM
ejpam-5020	206	48	(	(	PUNCT
ejpam-5020	206	49	3n−	3n−	NUM
ejpam-5020	206	50	6−	6−	NUM
ejpam-5020	206	51	√	√	NUM
ejpam-5020	206	52	n(17n−	n(17n−	VERB
ejpam-5020	206	53	32	32	NUM
ejpam-5020	206	54	)	)	PUNCT
ejpam-5020	206	55	)	)	PUNCT
ejpam-5020	206	56	)	)	PUNCT
ejpam-5020	206	57	1	1	X
ejpam-5020	206	58	}	}	PUNCT
ejpam-5020	206	59	.	.	PUNCT
ejpam-5020	207	1	the	the	DET
ejpam-5020	207	2	maximum	maximum	NOUN
ejpam-5020	207	3	of	of	ADP
ejpam-5020	207	4	|λi|	|λi|	NOUN
ejpam-5020	207	5	,	,	PUNCT
ejpam-5020	207	6	i	i	PRON
ejpam-5020	207	7	=	=	NOUN
ejpam-5020	207	8	1	1	NUM
ejpam-5020	207	9	,	,	PUNCT
ejpam-5020	207	10	2	2	NUM
ejpam-5020	207	11	,	,	PUNCT
ejpam-5020	207	12	3	3	NUM
ejpam-5020	207	13	,	,	PUNCT
ejpam-5020	207	14	4	4	NUM
ejpam-5020	207	15	is	be	AUX
ejpam-5020	207	16	the	the	DET
ejpam-5020	207	17	c−spectral	c−spectral	ADJ
ejpam-5020	207	18	radius	radius	NOUN
ejpam-5020	207	19	of	of	ADP
ejpam-5020	207	20	γg	γg	PROPN
ejpam-5020	207	21	,	,	PUNCT
ejpam-5020	207	22	and	and	CCONJ
ejpam-5020	207	23	we	we	PRON
ejpam-5020	207	24	complete	complete	VERB
ejpam-5020	207	25	the	the	DET
ejpam-5020	207	26	proof	proof	NOUN
ejpam-5020	207	27	.	.	PUNCT
ejpam-5020	208	1	m.	m.	NOUN
ejpam-5020	208	2	u.	u.	PROPN
ejpam-5020	208	3	romdhini	romdhini	PROPN
ejpam-5020	208	4	et	et	PROPN
ejpam-5020	208	5	al	al	PROPN
ejpam-5020	208	6	.	.	PUNCT
ejpam-5020	208	7	/	/	SYM
ejpam-5020	208	8	eur	eur	PROPN
ejpam-5020	208	9	.	.	PUNCT
ejpam-5020	209	1	j.	j.	PROPN
ejpam-5020	209	2	pure	pure	PROPN
ejpam-5020	209	3	appl	appl	PROPN
ejpam-5020	209	4	.	.	PROPN
ejpam-5020	209	5	math	math	PROPN
ejpam-5020	209	6	,	,	PUNCT
ejpam-5020	209	7	17	17	NUM
ejpam-5020	209	8	(	(	PUNCT
ejpam-5020	209	9	1	1	NUM
ejpam-5020	209	10	)	)	PUNCT
ejpam-5020	209	11	(	(	PUNCT
ejpam-5020	209	12	2024	2024	NUM
ejpam-5020	209	13	)	)	PUNCT
ejpam-5020	209	14	,	,	PUNCT
ejpam-5020	209	15	212	212	NUM
ejpam-5020	209	16	-	-	SYM
ejpam-5020	209	17	221	221	NUM
ejpam-5020	209	18	219	219	NUM
ejpam-5020	209	19	theorem	theorem	NOUN
ejpam-5020	209	20	8	8	NUM
ejpam-5020	209	21	.	.	PUNCT
ejpam-5020	210	1	the	the	DET
ejpam-5020	210	2	c−energy	c−energy	PROPN
ejpam-5020	210	3	for	for	ADP
ejpam-5020	210	4	γg	γg	ADV
ejpam-5020	210	5	,	,	PUNCT
ejpam-5020	210	6	where	where	SCONJ
ejpam-5020	210	7	g	g	PROPN
ejpam-5020	210	8	=	=	PUNCT
ejpam-5020	210	9	g1	g1	PROPN
ejpam-5020	210	10	∪g2	∪g2	PROPN
ejpam-5020	210	11	,	,	PUNCT
ejpam-5020	210	12	is	be	AUX
ejpam-5020	210	13	(	(	PUNCT
ejpam-5020	210	14	i	i	NOUN
ejpam-5020	210	15	)	)	PUNCT
ejpam-5020	210	16	for	for	ADP
ejpam-5020	210	17	n	n	X
ejpam-5020	210	18	is	be	AUX
ejpam-5020	210	19	odd	odd	ADJ
ejpam-5020	210	20	:	:	PUNCT
ejpam-5020	210	21	ec(γg	ec(γg	PROPN
ejpam-5020	210	22	)	)	PUNCT
ejpam-5020	210	23	=	=	SYM
ejpam-5020	211	1	1	1	NUM
ejpam-5020	211	2	4	4	NUM
ejpam-5020	211	3	(	(	PUNCT
ejpam-5020	211	4	3n−	3n−	NUM
ejpam-5020	211	5	4	4	NUM
ejpam-5020	211	6	+	+	CCONJ
ejpam-5020	211	7	√	√	NOUN
ejpam-5020	211	8	n(17n−	n(17n−	VERB
ejpam-5020	211	9	16	16	NUM
ejpam-5020	211	10	)	)	PUNCT
ejpam-5020	211	11	)	)	PUNCT
ejpam-5020	211	12	(	(	PUNCT
ejpam-5020	211	13	ii	ii	NOUN
ejpam-5020	211	14	)	)	PUNCT
ejpam-5020	211	15	for	for	ADP
ejpam-5020	211	16	n	n	NUM
ejpam-5020	211	17	is	be	AUX
ejpam-5020	211	18	even	even	ADV
ejpam-5020	211	19	:	:	PUNCT
ejpam-5020	211	20	ec(γg	ec(γg	PROPN
ejpam-5020	211	21	)	)	PUNCT
ejpam-5020	211	22	=	=	SYM
ejpam-5020	211	23	1	1	NUM
ejpam-5020	211	24	4	4	NUM
ejpam-5020	211	25	(	(	PUNCT
ejpam-5020	211	26	3n−	3n−	NUM
ejpam-5020	211	27	6	6	NUM
ejpam-5020	211	28	+	+	CCONJ
ejpam-5020	211	29	√	√	NOUN
ejpam-5020	211	30	n(17n−	n(17n−	VERB
ejpam-5020	211	31	32	32	NUM
ejpam-5020	211	32	)	)	PUNCT
ejpam-5020	211	33	)	)	PUNCT
ejpam-5020	211	34	.	.	PUNCT
ejpam-5020	212	1	proof	proof	NOUN
ejpam-5020	212	2	.	.	PUNCT
ejpam-5020	213	1	(	(	PUNCT
ejpam-5020	213	2	i	i	NOUN
ejpam-5020	213	3	)	)	PUNCT
ejpam-5020	213	4	by	by	ADP
ejpam-5020	213	5	theorem	theorem	VERB
ejpam-5020	213	6	7	7	NUM
ejpam-5020	213	7	(	(	PUNCT
ejpam-5020	213	8	1	1	NUM
ejpam-5020	213	9	)	)	PUNCT
ejpam-5020	213	10	,	,	PUNCT
ejpam-5020	213	11	for	for	ADP
ejpam-5020	213	12	the	the	DET
ejpam-5020	213	13	odd	odd	ADJ
ejpam-5020	213	14	n	n	CCONJ
ejpam-5020	213	15	,	,	PUNCT
ejpam-5020	213	16	the	the	DET
ejpam-5020	213	17	c−energy	c−energy	NUM
ejpam-5020	213	18	of	of	ADP
ejpam-5020	213	19	γg	γg	ADV
ejpam-5020	213	20	can	can	AUX
ejpam-5020	213	21	be	be	AUX
ejpam-5020	213	22	calculated	calculate	VERB
ejpam-5020	213	23	as	as	SCONJ
ejpam-5020	213	24	follows	follow	VERB
ejpam-5020	213	25	:	:	PUNCT
ejpam-5020	213	26	ec(γg	ec(γg	NUM
ejpam-5020	213	27	)	)	PUNCT
ejpam-5020	214	1	=	=	PUNCT
ejpam-5020	214	2	(	(	PUNCT
ejpam-5020	214	3	n−	n−	NOUN
ejpam-5020	214	4	2	2	NUM
ejpam-5020	214	5	)	)	PUNCT
ejpam-5020	214	6	∣∣∣∣−1	∣∣∣∣−1	NUM
ejpam-5020	214	7	4	4	NUM
ejpam-5020	214	8	∣∣∣∣+	∣∣∣∣+	NOUN
ejpam-5020	214	9	(	(	PUNCT
ejpam-5020	214	10	n−	n−	NOUN
ejpam-5020	214	11	1	1	NUM
ejpam-5020	214	12	)	)	PUNCT
ejpam-5020	214	13	∣∣∣∣−1	∣∣∣∣−1	SYM
ejpam-5020	214	14	2	2	NUM
ejpam-5020	214	15	∣∣∣∣+	∣∣∣∣+	NOUN
ejpam-5020	214	16	∣∣∣∣18	∣∣∣∣18	NOUN
ejpam-5020	214	17	(	(	PUNCT
ejpam-5020	214	18	3n−	3n−	PROPN
ejpam-5020	214	19	4±	4±	PROPN
ejpam-5020	214	20	√	√	NUM
ejpam-5020	214	21	n(17n−	n(17n−	VERB
ejpam-5020	214	22	16	16	NUM
ejpam-5020	214	23	)	)	PUNCT
ejpam-5020	214	24	)	)	PUNCT
ejpam-5020	215	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5020	215	2	=	=	SYM
ejpam-5020	215	3	1	1	NUM
ejpam-5020	215	4	4	4	NUM
ejpam-5020	215	5	(	(	PUNCT
ejpam-5020	215	6	3n−	3n−	NUM
ejpam-5020	215	7	4	4	NUM
ejpam-5020	215	8	+	+	CCONJ
ejpam-5020	215	9	√	√	NOUN
ejpam-5020	215	10	n(17n−	n(17n−	VERB
ejpam-5020	215	11	16	16	NUM
ejpam-5020	215	12	)	)	PUNCT
ejpam-5020	215	13	)	)	PUNCT
ejpam-5020	215	14	.	.	PUNCT
ejpam-5020	216	1	(	(	PUNCT
ejpam-5020	216	2	ii	ii	NOUN
ejpam-5020	216	3	)	)	PUNCT
ejpam-5020	216	4	for	for	ADP
ejpam-5020	216	5	even	even	ADV
ejpam-5020	216	6	n	n	CCONJ
ejpam-5020	216	7	,	,	PUNCT
ejpam-5020	216	8	by	by	ADP
ejpam-5020	216	9	theorem	theorem	NOUN
ejpam-5020	216	10	7	7	NUM
ejpam-5020	216	11	(	(	PUNCT
ejpam-5020	216	12	2	2	NUM
ejpam-5020	216	13	)	)	PUNCT
ejpam-5020	216	14	,	,	PUNCT
ejpam-5020	216	15	then	then	ADV
ejpam-5020	216	16	the	the	DET
ejpam-5020	216	17	c−energy	c−energy	NOUN
ejpam-5020	216	18	of	of	ADP
ejpam-5020	216	19	γg	γg	ADV
ejpam-5020	216	20	is	be	AUX
ejpam-5020	216	21	ec(γg	ec(γg	PROPN
ejpam-5020	216	22	)	)	PUNCT
ejpam-5020	217	1	=	=	NOUN
ejpam-5020	217	2	(	(	PUNCT
ejpam-5020	217	3	3n−	3n−	NUM
ejpam-5020	217	4	6	6	NUM
ejpam-5020	217	5	2	2	NUM
ejpam-5020	217	6	)	)	PUNCT
ejpam-5020	217	7	∣∣∣∣−1	∣∣∣∣−1	ADP
ejpam-5020	217	8	4	4	NUM
ejpam-5020	217	9	∣∣∣∣+	∣∣∣∣+	NOUN
ejpam-5020	217	10	(	(	PUNCT
ejpam-5020	217	11	n	n	ADV
ejpam-5020	217	12	2	2	NUM
ejpam-5020	217	13	−	−	NOUN
ejpam-5020	217	14	1	1	NUM
ejpam-5020	217	15	)	)	PUNCT
ejpam-5020	217	16	∣∣∣∣−3	∣∣∣∣−3	PROPN
ejpam-5020	217	17	4	4	NUM
ejpam-5020	217	18	∣∣∣∣+	∣∣∣∣+	NOUN
ejpam-5020	217	19	∣∣∣∣18	∣∣∣∣18	NOUN
ejpam-5020	217	20	(	(	PUNCT
ejpam-5020	217	21	3n−	3n−	PROPN
ejpam-5020	217	22	6±	6±	NUM
ejpam-5020	217	23	√	√	NUM
ejpam-5020	217	24	n(17n−	n(17n−	VERB
ejpam-5020	217	25	32	32	NUM
ejpam-5020	217	26	)	)	PUNCT
ejpam-5020	217	27	)	)	PUNCT
ejpam-5020	218	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5020	218	2	=	=	SYM
ejpam-5020	218	3	1	1	NUM
ejpam-5020	218	4	4	4	NUM
ejpam-5020	218	5	(	(	PUNCT
ejpam-5020	218	6	3n−	3n−	NUM
ejpam-5020	218	7	6	6	NUM
ejpam-5020	218	8	+	+	CCONJ
ejpam-5020	218	9	√	√	NOUN
ejpam-5020	218	10	n(17n−	n(17n−	VERB
ejpam-5020	218	11	32	32	NUM
ejpam-5020	218	12	)	)	PUNCT
ejpam-5020	218	13	)	)	PUNCT
ejpam-5020	218	14	.	.	PUNCT
ejpam-5020	219	1	as	as	ADP
ejpam-5020	219	2	a	a	DET
ejpam-5020	219	3	result	result	NOUN
ejpam-5020	219	4	of	of	ADP
ejpam-5020	219	5	theorem	theorem	NOUN
ejpam-5020	219	6	8	8	NUM
ejpam-5020	219	7	,	,	PUNCT
ejpam-5020	219	8	in	in	ADP
ejpam-5020	219	9	the	the	DET
ejpam-5020	219	10	following	following	NOUN
ejpam-5020	219	11	,	,	PUNCT
ejpam-5020	219	12	we	we	PRON
ejpam-5020	219	13	obtain	obtain	VERB
ejpam-5020	219	14	the	the	DET
ejpam-5020	219	15	classification	classification	NOUN
ejpam-5020	219	16	of	of	ADP
ejpam-5020	219	17	the	the	DET
ejpam-5020	219	18	closeness	closeness	NOUN
ejpam-5020	219	19	energy	energy	NOUN
ejpam-5020	219	20	of	of	ADP
ejpam-5020	219	21	γg	γg	PROPN
ejpam-5020	219	22	for	for	ADP
ejpam-5020	219	23	d2n	d2n	NOUN
ejpam-5020	219	24	,	,	PUNCT
ejpam-5020	219	25	where	where	SCONJ
ejpam-5020	219	26	g	g	PROPN
ejpam-5020	219	27	=	=	PUNCT
ejpam-5020	219	28	g1	g1	PROPN
ejpam-5020	219	29	∪g2	∪g2	PROPN
ejpam-5020	219	30	.	.	PUNCT
ejpam-5020	220	1	corollary	corollary	ADJ
ejpam-5020	220	2	1	1	NUM
ejpam-5020	220	3	.	.	PUNCT
ejpam-5020	221	1	γg	γg	ADV
ejpam-5020	221	2	associated	associate	VERB
ejpam-5020	221	3	with	with	ADP
ejpam-5020	221	4	the	the	DET
ejpam-5020	221	5	closeness	closeness	NOUN
ejpam-5020	221	6	matrix	matrix	NOUN
ejpam-5020	221	7	is	be	AUX
ejpam-5020	221	8	hypoenergetic	hypoenergetic	ADJ
ejpam-5020	221	9	.	.	PUNCT
ejpam-5020	222	1	moreover	moreover	ADV
ejpam-5020	222	2	,	,	PUNCT
ejpam-5020	222	3	based	base	VERB
ejpam-5020	222	4	on	on	ADP
ejpam-5020	222	5	the	the	DET
ejpam-5020	222	6	energies	energy	NOUN
ejpam-5020	222	7	in	in	ADP
ejpam-5020	222	8	theorem	theorem	NOUN
ejpam-5020	222	9	8	8	NUM
ejpam-5020	222	10	,	,	PUNCT
ejpam-5020	222	11	we	we	PRON
ejpam-5020	222	12	can	can	AUX
ejpam-5020	222	13	conclude	conclude	VERB
ejpam-5020	222	14	the	the	DET
ejpam-5020	222	15	following	following	ADJ
ejpam-5020	222	16	fact	fact	NOUN
ejpam-5020	222	17	:	:	PUNCT
ejpam-5020	222	18	corollary	corollary	ADJ
ejpam-5020	222	19	2	2	NUM
ejpam-5020	222	20	.	.	NUM
ejpam-5020	222	21	c−energy	c−energy	X
ejpam-5020	223	1	for	for	ADP
ejpam-5020	223	2	γg	γg	ADV
ejpam-5020	223	3	is	be	AUX
ejpam-5020	223	4	never	never	ADV
ejpam-5020	223	5	an	an	DET
ejpam-5020	223	6	odd	odd	ADJ
ejpam-5020	223	7	integer	integer	NOUN
ejpam-5020	223	8	.	.	PUNCT
ejpam-5020	224	1	the	the	DET
ejpam-5020	224	2	statements	statement	NOUN
ejpam-5020	224	3	in	in	ADP
ejpam-5020	224	4	corollary	corollary	ADJ
ejpam-5020	224	5	2	2	NUM
ejpam-5020	224	6	comply	comply	NOUN
ejpam-5020	224	7	with	with	ADP
ejpam-5020	224	8	the	the	DET
ejpam-5020	224	9	well	well	ADV
ejpam-5020	224	10	-	-	PUNCT
ejpam-5020	224	11	known	know	VERB
ejpam-5020	224	12	facts	fact	NOUN
ejpam-5020	224	13	from	from	ADP
ejpam-5020	224	14	[	[	X
ejpam-5020	224	15	4	4	NUM
ejpam-5020	224	16	]	]	PUNCT
ejpam-5020	224	17	and	and	CCONJ
ejpam-5020	224	18	[	[	X
ejpam-5020	224	19	12	12	NUM
ejpam-5020	224	20	]	]	PUNCT
ejpam-5020	224	21	.	.	PUNCT
ejpam-5020	225	1	furthermore	furthermore	ADV
ejpam-5020	225	2	,	,	PUNCT
ejpam-5020	225	3	the	the	DET
ejpam-5020	225	4	comparison	comparison	NOUN
ejpam-5020	225	5	between	between	ADP
ejpam-5020	225	6	energy	energy	NOUN
ejpam-5020	225	7	in	in	ADP
ejpam-5020	225	8	theorem	theorem	ADJ
ejpam-5020	225	9	8	8	NUM
ejpam-5020	225	10	and	and	CCONJ
ejpam-5020	225	11	its	its	PRON
ejpam-5020	225	12	spectral	spectral	ADJ
ejpam-5020	225	13	radius	radius	NOUN
ejpam-5020	225	14	in	in	ADP
ejpam-5020	225	15	theorem	theorem	NOUN
ejpam-5020	225	16	7	7	NUM
ejpam-5020	225	17	can	can	AUX
ejpam-5020	225	18	be	be	AUX
ejpam-5020	225	19	determined	determine	VERB
ejpam-5020	225	20	in	in	ADP
ejpam-5020	225	21	the	the	DET
ejpam-5020	225	22	following	follow	VERB
ejpam-5020	225	23	statement	statement	NOUN
ejpam-5020	225	24	:	:	PUNCT
ejpam-5020	225	25	corollary	corollary	ADJ
ejpam-5020	225	26	3	3	NUM
ejpam-5020	225	27	.	.	NUM
ejpam-5020	225	28	c−energy	c−energy	X
ejpam-5020	226	1	for	for	ADP
ejpam-5020	226	2	γg	γg	ADV
ejpam-5020	226	3	is	be	AUX
ejpam-5020	226	4	always	always	ADV
ejpam-5020	226	5	twice	twice	DET
ejpam-5020	226	6	its	its	PRON
ejpam-5020	226	7	spectral	spectral	ADJ
ejpam-5020	226	8	radius	radius	NOUN
ejpam-5020	226	9	.	.	PUNCT
ejpam-5020	227	1	as	as	ADP
ejpam-5020	227	2	a	a	DET
ejpam-5020	227	3	future	future	ADJ
ejpam-5020	227	4	view	view	NOUN
ejpam-5020	227	5	of	of	ADP
ejpam-5020	227	6	this	this	DET
ejpam-5020	227	7	research	research	NOUN
ejpam-5020	227	8	,	,	PUNCT
ejpam-5020	227	9	we	we	PRON
ejpam-5020	227	10	recommend	recommend	VERB
ejpam-5020	227	11	combining	combine	VERB
ejpam-5020	227	12	them	they	PRON
ejpam-5020	227	13	with	with	ADP
ejpam-5020	227	14	[	[	X
ejpam-5020	227	15	2	2	NUM
ejpam-5020	227	16	]	]	PUNCT
ejpam-5020	227	17	,	,	PUNCT
ejpam-5020	227	18	which	which	PRON
ejpam-5020	227	19	is	be	AUX
ejpam-5020	227	20	essentially	essentially	ADV
ejpam-5020	227	21	an	an	DET
ejpam-5020	227	22	extension	extension	NOUN
ejpam-5020	227	23	of	of	ADP
ejpam-5020	227	24	the	the	DET
ejpam-5020	227	25	graph	graph	NOUN
ejpam-5020	227	26	matrix	matrix	NOUN
ejpam-5020	227	27	based	base	VERB
ejpam-5020	227	28	on	on	ADP
ejpam-5020	227	29	q	q	ADJ
ejpam-5020	227	30	-	-	PUNCT
ejpam-5020	227	31	nss	nss	NOUN
ejpam-5020	227	32	matrix	matrix	NOUN
ejpam-5020	227	33	.	.	PUNCT
ejpam-5020	228	1	in	in	ADP
ejpam-5020	228	2	addition	addition	NOUN
ejpam-5020	228	3	,	,	PUNCT
ejpam-5020	228	4	this	this	DET
ejpam-5020	228	5	work	work	NOUN
ejpam-5020	228	6	can	can	AUX
ejpam-5020	228	7	be	be	AUX
ejpam-5020	228	8	extended	extend	VERB
ejpam-5020	228	9	to	to	ADP
ejpam-5020	228	10	the	the	DET
ejpam-5020	228	11	neutrosophic	neutrosophic	ADJ
ejpam-5020	228	12	soft	soft	ADJ
ejpam-5020	228	13	rings	ring	NOUN
ejpam-5020	228	14	and	and	CCONJ
ejpam-5020	228	15	neutrosophic	neutrosophic	ADJ
ejpam-5020	228	16	soft	soft	ADJ
ejpam-5020	228	17	field	field	NOUN
ejpam-5020	229	1	[	[	X
ejpam-5020	229	2	14	14	NUM
ejpam-5020	229	3	,	,	PUNCT
ejpam-5020	229	4	15	15	NUM
ejpam-5020	229	5	]	]	PUNCT
ejpam-5020	229	6	.	.	PUNCT
ejpam-5020	230	1	acknowledgements	acknowledgement	NOUN
ejpam-5020	230	2	we	we	PRON
ejpam-5020	230	3	wish	wish	VERB
ejpam-5020	230	4	to	to	PART
ejpam-5020	230	5	express	express	VERB
ejpam-5020	230	6	our	our	PRON
ejpam-5020	230	7	gratitude	gratitude	NOUN
ejpam-5020	230	8	to	to	ADP
ejpam-5020	230	9	universitas	universitas	PROPN
ejpam-5020	230	10	mataram	mataram	PROPN
ejpam-5020	230	11	,	,	PUNCT
ejpam-5020	230	12	indonesia	indonesia	PROPN
ejpam-5020	230	13	,	,	PUNCT
ejpam-5020	230	14	for	for	ADP
ejpam-5020	230	15	providing	provide	VERB
ejpam-5020	230	16	partial	partial	ADJ
ejpam-5020	230	17	funding	funding	NOUN
ejpam-5020	230	18	assistance	assistance	NOUN
ejpam-5020	230	19	.	.	PUNCT
ejpam-5020	231	1	references	reference	NOUN
ejpam-5020	231	2	220	220	NUM
ejpam-5020	231	3	references	reference	NOUN
ejpam-5020	231	4	[	[	X
ejpam-5020	231	5	1	1	X
ejpam-5020	231	6	]	]	PUNCT
ejpam-5020	231	7	a	a	DET
ejpam-5020	231	8	abdollahi	abdollahi	NOUN
ejpam-5020	231	9	,	,	PUNCT
ejpam-5020	231	10	s	s	NOUN
ejpam-5020	231	11	akbari	akbari	PROPN
ejpam-5020	231	12	,	,	PUNCT
ejpam-5020	231	13	and	and	CCONJ
ejpam-5020	231	14	h	h	NOUN
ejpam-5020	231	15	r	r	NOUN
ejpam-5020	231	16	maimani	maimani	NOUN
ejpam-5020	231	17	.	.	PUNCT
ejpam-5020	232	1	non	non	ADJ
ejpam-5020	232	2	-	-	ADJ
ejpam-5020	232	3	commuting	commuting	ADJ
ejpam-5020	232	4	graph	graph	NOUN
ejpam-5020	232	5	of	of	ADP
ejpam-5020	232	6	a	a	DET
ejpam-5020	232	7	group	group	NOUN
ejpam-5020	232	8	.	.	PUNCT
ejpam-5020	233	1	journal	journal	PROPN
ejpam-5020	233	2	of	of	ADP
ejpam-5020	233	3	algebra	algebra	PROPN
ejpam-5020	233	4	,	,	PUNCT
ejpam-5020	233	5	298(2):468–492	298(2):468–492	NUM
ejpam-5020	233	6	,	,	PUNCT
ejpam-5020	233	7	2006	2006	NUM
ejpam-5020	233	8	.	.	PUNCT
ejpam-5020	234	1	[	[	X
ejpam-5020	234	2	2	2	NUM
ejpam-5020	234	3	]	]	X
ejpam-5020	234	4	f	f	PROPN
ejpam-5020	234	5	al	al	PROPN
ejpam-5020	234	6	-	-	PUNCT
ejpam-5020	234	7	sharqi	sharqi	PROPN
ejpam-5020	234	8	,	,	PUNCT
ejpam-5020	234	9	m	m	VERB
ejpam-5020	234	10	u	u	NOUN
ejpam-5020	234	11	romdhini	romdhini	NOUN
ejpam-5020	234	12	,	,	PUNCT
ejpam-5020	234	13	and	and	CCONJ
ejpam-5020	234	14	a	a	DET
ejpam-5020	234	15	alquran	alquran	NOUN
ejpam-5020	234	16	.	.	PUNCT
ejpam-5020	235	1	group	group	NOUN
ejpam-5020	235	2	decision	decision	NOUN
ejpam-5020	235	3	-	-	PUNCT
ejpam-5020	235	4	making	making	NOUN
ejpam-5020	235	5	based	base	VERB
ejpam-5020	235	6	on	on	ADP
ejpam-5020	235	7	aggregation	aggregation	NOUN
ejpam-5020	235	8	operator	operator	NOUN
ejpam-5020	235	9	and	and	CCONJ
ejpam-5020	235	10	score	score	NOUN
ejpam-5020	235	11	function	function	NOUN
ejpam-5020	235	12	of	of	ADP
ejpam-5020	235	13	q	q	ADJ
ejpam-5020	235	14	-	-	ADJ
ejpam-5020	235	15	neutrosophic	neutrosophic	ADJ
ejpam-5020	235	16	soft	soft	ADJ
ejpam-5020	235	17	matrix	matrix	NOUN
ejpam-5020	235	18	.	.	PUNCT
ejpam-5020	236	1	journal	journal	NOUN
ejpam-5020	236	2	of	of	ADP
ejpam-5020	236	3	intelligent	intelligent	ADJ
ejpam-5020	236	4	and	and	CCONJ
ejpam-5020	236	5	fuzzy	fuzzy	ADJ
ejpam-5020	236	6	systems	system	NOUN
ejpam-5020	236	7	,	,	PUNCT
ejpam-5020	236	8	45:305–321	45:305–321	PROPN
ejpam-5020	236	9	,	,	PUNCT
ejpam-5020	236	10	2023	2023	NUM
ejpam-5020	236	11	.	.	PUNCT
ejpam-5020	237	1	[	[	X
ejpam-5020	237	2	3	3	X
ejpam-5020	237	3	]	]	X
ejpam-5020	237	4	m	m	NOUN
ejpam-5020	237	5	aschbacher	aschbacher	NOUN
ejpam-5020	237	6	.	.	PUNCT
ejpam-5020	238	1	finite	finite	PROPN
ejpam-5020	238	2	group	group	PROPN
ejpam-5020	238	3	theory	theory	PROPN
ejpam-5020	238	4	.	.	PUNCT
ejpam-5020	239	1	cambridge	cambridge	PROPN
ejpam-5020	239	2	university	university	PROPN
ejpam-5020	239	3	press	press	PROPN
ejpam-5020	239	4	,	,	PUNCT
ejpam-5020	239	5	cambridge	cambridge	PROPN
ejpam-5020	239	6	,	,	PUNCT
ejpam-5020	239	7	2000	2000	NUM
ejpam-5020	239	8	.	.	PUNCT
ejpam-5020	240	1	[	[	X
ejpam-5020	240	2	4	4	NUM
ejpam-5020	240	3	]	]	X
ejpam-5020	240	4	r	r	NOUN
ejpam-5020	240	5	b	b	X
ejpam-5020	240	6	bapat	bapat	PROPN
ejpam-5020	240	7	and	and	CCONJ
ejpam-5020	240	8	s	s	NOUN
ejpam-5020	240	9	pati	pati	NOUN
ejpam-5020	240	10	.	.	PUNCT
ejpam-5020	241	1	energy	energy	NOUN
ejpam-5020	241	2	of	of	ADP
ejpam-5020	241	3	a	a	DET
ejpam-5020	241	4	graph	graph	NOUN
ejpam-5020	241	5	is	be	AUX
ejpam-5020	241	6	never	never	ADV
ejpam-5020	241	7	an	an	DET
ejpam-5020	241	8	odd	odd	ADJ
ejpam-5020	241	9	integer	integer	NOUN
ejpam-5020	241	10	.	.	PUNCT
ejpam-5020	242	1	bulletin	bulletin	NOUN
ejpam-5020	242	2	of	of	ADP
ejpam-5020	242	3	kerala	kerala	PROPN
ejpam-5020	242	4	mathematics	mathematics	PROPN
ejpam-5020	242	5	association	association	PROPN
ejpam-5020	242	6	,	,	PUNCT
ejpam-5020	242	7	1:129–132	1:129–132	NUM
ejpam-5020	242	8	,	,	PUNCT
ejpam-5020	242	9	2004	2004	NUM
ejpam-5020	242	10	.	.	PUNCT
ejpam-5020	243	1	[	[	X
ejpam-5020	243	2	5	5	NUM
ejpam-5020	243	3	]	]	PUNCT
ejpam-5020	243	4	a	a	DET
ejpam-5020	243	5	e	e	X
ejpam-5020	243	6	brouwer	brouwer	PROPN
ejpam-5020	243	7	and	and	CCONJ
ejpam-5020	243	8	w	w	NOUN
ejpam-5020	243	9	h	h	NOUN
ejpam-5020	243	10	haemers	haemer	NOUN
ejpam-5020	243	11	.	.	PUNCT
ejpam-5020	244	1	spectra	spectra	NOUN
ejpam-5020	244	2	of	of	ADP
ejpam-5020	244	3	graphs	graph	NOUN
ejpam-5020	244	4	.	.	PUNCT
ejpam-5020	245	1	springer	springer	NOUN
ejpam-5020	245	2	,	,	PUNCT
ejpam-5020	245	3	new	new	PROPN
ejpam-5020	245	4	york	york	PROPN
ejpam-5020	245	5	,	,	PUNCT
ejpam-5020	245	6	2011	2011	NUM
ejpam-5020	245	7	.	.	PUNCT
ejpam-5020	246	1	[	[	X
ejpam-5020	246	2	6	6	NUM
ejpam-5020	246	3	]	]	PUNCT
ejpam-5020	246	4	i	i	PROPN
ejpam-5020	246	5	gutman	gutman	PROPN
ejpam-5020	246	6	.	.	PUNCT
ejpam-5020	247	1	the	the	DET
ejpam-5020	247	2	energy	energy	NOUN
ejpam-5020	247	3	of	of	ADP
ejpam-5020	247	4	graph	graph	NOUN
ejpam-5020	247	5	.	.	PUNCT
ejpam-5020	248	1	ber	ber	NOUN
ejpam-5020	248	2	.	.	PUNCT
ejpam-5020	248	3	math.-stat	math.-stat	PROPN
ejpam-5020	248	4	.	.	PROPN
ejpam-5020	248	5	sekt	sekt	PROPN
ejpam-5020	248	6	.	.	PUNCT
ejpam-5020	249	1	forschungsz	forschungsz	PROPN
ejpam-5020	249	2	.	.	PUNCT
ejpam-5020	250	1	graz	graz	PROPN
ejpam-5020	250	2	,	,	PUNCT
ejpam-5020	250	3	103:1–2	103:1–2	NUM
ejpam-5020	250	4	,	,	PUNCT
ejpam-5020	250	5	1978	1978	NUM
ejpam-5020	250	6	.	.	PUNCT
ejpam-5020	251	1	[	[	X
ejpam-5020	251	2	7	7	X
ejpam-5020	251	3	]	]	SYM
ejpam-5020	251	4	g	g	NOUN
ejpam-5020	251	5	indulal	indulal	ADV
ejpam-5020	251	6	,	,	PUNCT
ejpam-5020	251	7	i	i	PRON
ejpam-5020	251	8	gutman	gutman	NOUN
ejpam-5020	251	9	,	,	PUNCT
ejpam-5020	251	10	and	and	CCONJ
ejpam-5020	251	11	a	a	DET
ejpam-5020	251	12	vijayakumar	vijayakumar	NOUN
ejpam-5020	251	13	.	.	PUNCT
ejpam-5020	252	1	on	on	ADP
ejpam-5020	252	2	distance	distance	NOUN
ejpam-5020	252	3	energy	energy	NOUN
ejpam-5020	252	4	of	of	ADP
ejpam-5020	252	5	graphs	graph	NOUN
ejpam-5020	252	6	.	.	PUNCT
ejpam-5020	253	1	match	match	VERB
ejpam-5020	253	2	communications	communication	NOUN
ejpam-5020	253	3	in	in	ADP
ejpam-5020	253	4	mathematical	mathematical	ADJ
ejpam-5020	253	5	and	and	CCONJ
ejpam-5020	253	6	in	in	ADP
ejpam-5020	253	7	computer	computer	NOUN
ejpam-5020	253	8	chemistry	chemistry	NOUN
ejpam-5020	253	9	,	,	PUNCT
ejpam-5020	253	10	60:461–472	60:461–472	PROPN
ejpam-5020	253	11	,	,	PUNCT
ejpam-5020	253	12	2008	2008	NUM
ejpam-5020	253	13	.	.	PUNCT
ejpam-5020	254	1	[	[	X
ejpam-5020	254	2	8	8	NUM
ejpam-5020	254	3	]	]	SYM
ejpam-5020	254	4	s	s	NOUN
ejpam-5020	254	5	r	r	NOUN
ejpam-5020	254	6	jog	jog	NOUN
ejpam-5020	254	7	and	and	CCONJ
ejpam-5020	254	8	j	j	PROPN
ejpam-5020	254	9	r	r	NOUN
ejpam-5020	254	10	gurjar	gurjar	NOUN
ejpam-5020	254	11	.	.	PUNCT
ejpam-5020	254	12	degree	degree	NOUN
ejpam-5020	254	13	product	product	NOUN
ejpam-5020	254	14	distance	distance	NOUN
ejpam-5020	254	15	energy	energy	NOUN
ejpam-5020	254	16	of	of	ADP
ejpam-5020	254	17	some	some	DET
ejpam-5020	254	18	graphs	graph	NOUN
ejpam-5020	254	19	.	.	PUNCT
ejpam-5020	255	1	asian	asian	ADJ
ejpam-5020	255	2	journal	journal	PROPN
ejpam-5020	255	3	of	of	ADP
ejpam-5020	255	4	mathematics	mathematic	NOUN
ejpam-5020	255	5	,	,	PUNCT
ejpam-5020	255	6	24(1):42–49	24(1):42–49	NUM
ejpam-5020	255	7	,	,	PUNCT
ejpam-5020	255	8	2018	2018	NUM
ejpam-5020	255	9	.	.	PUNCT
ejpam-5020	256	1	[	[	X
ejpam-5020	256	2	9	9	NUM
ejpam-5020	256	3	]	]	SYM
ejpam-5020	256	4	s	s	NOUN
ejpam-5020	256	5	r	r	NOUN
ejpam-5020	256	6	jog	jog	NOUN
ejpam-5020	256	7	and	and	CCONJ
ejpam-5020	256	8	j	j	PROPN
ejpam-5020	256	9	r	r	NOUN
ejpam-5020	256	10	gurjar	gurjar	NOUN
ejpam-5020	256	11	.	.	PUNCT
ejpam-5020	256	12	degree	degree	NOUN
ejpam-5020	256	13	sum	sum	NOUN
ejpam-5020	256	14	exponent	exponent	NOUN
ejpam-5020	256	15	distance	distance	NOUN
ejpam-5020	256	16	energy	energy	NOUN
ejpam-5020	256	17	of	of	ADP
ejpam-5020	256	18	some	some	DET
ejpam-5020	256	19	graphs	graph	NOUN
ejpam-5020	256	20	.	.	PUNCT
ejpam-5020	257	1	journal	journal	NOUN
ejpam-5020	257	2	of	of	ADP
ejpam-5020	257	3	the	the	DET
ejpam-5020	257	4	indonesian	indonesian	PROPN
ejpam-5020	257	5	mathematical	mathematical	ADJ
ejpam-5020	257	6	society	society	NOUN
ejpam-5020	257	7	,	,	PUNCT
ejpam-5020	257	8	27(1):67–74	27(1):67–74	NUM
ejpam-5020	257	9	,	,	PUNCT
ejpam-5020	257	10	2021	2021	NUM
ejpam-5020	257	11	.	.	PUNCT
ejpam-5020	258	1	[	[	X
ejpam-5020	258	2	10	10	NUM
ejpam-5020	258	3	]	]	X
ejpam-5020	258	4	s	s	VERB
ejpam-5020	258	5	m	m	PROPN
ejpam-5020	258	6	s	s	PROPN
ejpam-5020	258	7	khasraw	khasraw	PROPN
ejpam-5020	258	8	,	,	PUNCT
ejpam-5020	258	9	i	i	PROPN
ejpam-5020	258	10	d	d	PROPN
ejpam-5020	258	11	ali	ali	PROPN
ejpam-5020	258	12	,	,	PUNCT
ejpam-5020	258	13	and	and	CCONJ
ejpam-5020	258	14	r	r	NOUN
ejpam-5020	258	15	r	r	NOUN
ejpam-5020	258	16	haji	haji	PROPN
ejpam-5020	258	17	.	.	PUNCT
ejpam-5020	259	1	on	on	ADP
ejpam-5020	259	2	the	the	DET
ejpam-5020	259	3	non	non	ADJ
ejpam-5020	259	4	-	-	ADJ
ejpam-5020	259	5	commuting	commuting	ADJ
ejpam-5020	259	6	graph	graph	NOUN
ejpam-5020	259	7	of	of	ADP
ejpam-5020	259	8	dihedral	dihedral	ADJ
ejpam-5020	259	9	group	group	NOUN
ejpam-5020	259	10	.	.	PUNCT
ejpam-5020	260	1	electronic	electronic	ADJ
ejpam-5020	260	2	journal	journal	NOUN
ejpam-5020	260	3	of	of	ADP
ejpam-5020	260	4	graph	graph	NOUN
ejpam-5020	260	5	theory	theory	NOUN
ejpam-5020	260	6	and	and	CCONJ
ejpam-5020	260	7	application	application	NOUN
ejpam-5020	260	8	,	,	PUNCT
ejpam-5020	260	9	8(2):233–239	8(2):233–239	NUM
ejpam-5020	260	10	,	,	PUNCT
ejpam-5020	260	11	2020	2020	NUM
ejpam-5020	260	12	.	.	PUNCT
ejpam-5020	261	1	[	[	X
ejpam-5020	261	2	11	11	NUM
ejpam-5020	261	3	]	]	X
ejpam-5020	261	4	x	x	X
ejpam-5020	261	5	li	li	PROPN
ejpam-5020	261	6	,	,	PUNCT
ejpam-5020	261	7	y	y	PROPN
ejpam-5020	261	8	shi	shi	PROPN
ejpam-5020	261	9	,	,	PUNCT
ejpam-5020	261	10	and	and	CCONJ
ejpam-5020	261	11	i	i	PROPN
ejpam-5020	261	12	gutman	gutman	NOUN
ejpam-5020	261	13	.	.	PUNCT
ejpam-5020	262	1	graph	graph	NOUN
ejpam-5020	262	2	energy	energy	NOUN
ejpam-5020	262	3	.	.	PUNCT
ejpam-5020	263	1	springer	springer	NOUN
ejpam-5020	263	2	,	,	PUNCT
ejpam-5020	263	3	new	new	PROPN
ejpam-5020	263	4	york	york	PROPN
ejpam-5020	263	5	,	,	PUNCT
ejpam-5020	263	6	2012	2012	NUM
ejpam-5020	263	7	.	.	PUNCT
ejpam-5020	264	1	[	[	X
ejpam-5020	264	2	12	12	NUM
ejpam-5020	264	3	]	]	X
ejpam-5020	264	4	s	s	X
ejpam-5020	264	5	pirzada	pirzada	NOUN
ejpam-5020	264	6	and	and	CCONJ
ejpam-5020	264	7	i	i	PROPN
ejpam-5020	264	8	gutman	gutman	PROPN
ejpam-5020	264	9	.	.	PUNCT
ejpam-5020	265	1	energy	energy	NOUN
ejpam-5020	265	2	of	of	ADP
ejpam-5020	265	3	a	a	DET
ejpam-5020	265	4	graph	graph	NOUN
ejpam-5020	265	5	is	be	AUX
ejpam-5020	265	6	never	never	ADV
ejpam-5020	265	7	the	the	DET
ejpam-5020	265	8	square	square	ADJ
ejpam-5020	265	9	root	root	NOUN
ejpam-5020	265	10	of	of	ADP
ejpam-5020	265	11	an	an	DET
ejpam-5020	265	12	odd	odd	ADJ
ejpam-5020	265	13	integer	integer	NOUN
ejpam-5020	265	14	.	.	PUNCT
ejpam-5020	266	1	applicable	applicable	ADJ
ejpam-5020	266	2	analysis	analysis	NOUN
ejpam-5020	266	3	and	and	CCONJ
ejpam-5020	266	4	discrete	discrete	ADJ
ejpam-5020	266	5	mathematics	mathematic	NOUN
ejpam-5020	266	6	,	,	PUNCT
ejpam-5020	266	7	2:118–121	2:118–121	NUM
ejpam-5020	266	8	,	,	PUNCT
ejpam-5020	266	9	2008	2008	NUM
ejpam-5020	266	10	.	.	PUNCT
ejpam-5020	267	1	[	[	X
ejpam-5020	267	2	13	13	NUM
ejpam-5020	267	3	]	]	X
ejpam-5020	267	4	h	h	NOUN
ejpam-5020	267	5	s	s	PROPN
ejpam-5020	267	6	ramane	ramane	NOUN
ejpam-5020	267	7	and	and	CCONJ
ejpam-5020	267	8	s	s	NOUN
ejpam-5020	267	9	s	s	NOUN
ejpam-5020	267	10	shinde	shinde	PROPN
ejpam-5020	267	11	.	.	PUNCT
ejpam-5020	267	12	degree	degree	NOUN
ejpam-5020	267	13	exponent	exponent	NOUN
ejpam-5020	267	14	polynomial	polynomial	NOUN
ejpam-5020	267	15	of	of	ADP
ejpam-5020	267	16	graphs	graph	NOUN
ejpam-5020	267	17	obtained	obtain	VERB
ejpam-5020	267	18	by	by	ADP
ejpam-5020	267	19	some	some	DET
ejpam-5020	267	20	graph	graph	NOUN
ejpam-5020	267	21	operations	operation	NOUN
ejpam-5020	267	22	.	.	PUNCT
ejpam-5020	268	1	electronic	electronic	ADJ
ejpam-5020	268	2	journal	journal	NOUN
ejpam-5020	268	3	of	of	ADP
ejpam-5020	268	4	graph	graph	NOUN
ejpam-5020	268	5	theory	theory	NOUN
ejpam-5020	268	6	and	and	CCONJ
ejpam-5020	268	7	application	application	NOUN
ejpam-5020	268	8	,	,	PUNCT
ejpam-5020	268	9	63:161–168	63:161–168	PROPN
ejpam-5020	268	10	,	,	PUNCT
ejpam-5020	268	11	2017	2017	NUM
ejpam-5020	268	12	.	.	PUNCT
ejpam-5020	269	1	[	[	X
ejpam-5020	269	2	14	14	NUM
ejpam-5020	269	3	]	]	X
ejpam-5020	269	4	m	m	VERB
ejpam-5020	269	5	u	u	NOUN
ejpam-5020	269	6	romdhini	romdhini	NOUN
ejpam-5020	269	7	,	,	PUNCT
ejpam-5020	269	8	a	a	DET
ejpam-5020	269	9	al	al	PROPN
ejpam-5020	269	10	-	-	PUNCT
ejpam-5020	269	11	quran	quran	PROPN
ejpam-5020	269	12	,	,	PUNCT
ejpam-5020	269	13	f	f	PROPN
ejpam-5020	269	14	al	al	PROPN
ejpam-5020	269	15	-	-	PUNCT
ejpam-5020	269	16	sharqi	sharqi	PROPN
ejpam-5020	269	17	,	,	PUNCT
ejpam-5020	269	18	h	h	NOUN
ejpam-5020	269	19	hashim	hashim	PROPN
ejpam-5020	269	20	,	,	PUNCT
ejpam-5020	269	21	and	and	CCONJ
ejpam-5020	269	22	a	a	DET
ejpam-5020	269	23	lutfi	lutfi	NOUN
ejpam-5020	269	24	.	.	PUNCT
ejpam-5020	269	25	unveiling	unveil	VERB
ejpam-5020	269	26	an	an	DET
ejpam-5020	269	27	innovative	innovative	ADJ
ejpam-5020	269	28	approach	approach	NOUN
ejpam-5020	269	29	to	to	ADP
ejpam-5020	269	30	q	q	ADJ
ejpam-5020	269	31	-	-	PUNCT
ejpam-5020	269	32	complex	complex	ADJ
ejpam-5020	269	33	neutrosophic	neutrosophic	ADJ
ejpam-5020	269	34	soft	soft	ADJ
ejpam-5020	269	35	rings	ring	NOUN
ejpam-5020	269	36	.	.	PUNCT
ejpam-5020	270	1	international	international	ADJ
ejpam-5020	270	2	journal	journal	PROPN
ejpam-5020	270	3	of	of	ADP
ejpam-5020	270	4	neutrosophic	neutrosophic	ADJ
ejpam-5020	270	5	science	science	NOUN
ejpam-5020	270	6	,	,	PUNCT
ejpam-5020	270	7	22(04):20–35	22(04):20–35	NUM
ejpam-5020	270	8	,	,	PUNCT
ejpam-5020	270	9	2023	2023	NUM
ejpam-5020	270	10	.	.	PUNCT
ejpam-5020	271	1	[	[	X
ejpam-5020	271	2	15	15	NUM
ejpam-5020	271	3	]	]	X
ejpam-5020	271	4	m	m	VERB
ejpam-5020	271	5	u	u	NOUN
ejpam-5020	271	6	romdhini	romdhini	NOUN
ejpam-5020	271	7	,	,	PUNCT
ejpam-5020	271	8	a	a	DET
ejpam-5020	271	9	al	al	PROPN
ejpam-5020	271	10	-	-	PUNCT
ejpam-5020	271	11	quran	quran	PROPN
ejpam-5020	271	12	,	,	PUNCT
ejpam-5020	271	13	f	f	PROPN
ejpam-5020	271	14	al	al	PROPN
ejpam-5020	271	15	-	-	PUNCT
ejpam-5020	271	16	sharqi	sharqi	PROPN
ejpam-5020	271	17	,	,	PUNCT
ejpam-5020	271	18	m	m	VERB
ejpam-5020	271	19	k	k	NOUN
ejpam-5020	271	20	tahat	tahat	PROPN
ejpam-5020	271	21	,	,	PUNCT
ejpam-5020	271	22	and	and	CCONJ
ejpam-5020	271	23	a	a	DET
ejpam-5020	271	24	lutfi	lutfi	NOUN
ejpam-5020	271	25	.	.	PUNCT
ejpam-5020	272	1	exploring	explore	VERB
ejpam-5020	272	2	the	the	DET
ejpam-5020	272	3	algebraic	algebraic	ADJ
ejpam-5020	272	4	structures	structure	NOUN
ejpam-5020	272	5	of	of	ADP
ejpam-5020	272	6	q	q	ADJ
ejpam-5020	272	7	-	-	PUNCT
ejpam-5020	272	8	complex	complex	ADJ
ejpam-5020	272	9	neutrosophic	neutrosophic	ADJ
ejpam-5020	272	10	softfields	softfield	NOUN
ejpam-5020	272	11	.	.	PUNCT
ejpam-5020	273	1	international	international	ADJ
ejpam-5020	273	2	journal	journal	PROPN
ejpam-5020	273	3	of	of	ADP
ejpam-5020	273	4	neutrosophic	neutrosophic	ADJ
ejpam-5020	273	5	science	science	NOUN
ejpam-5020	273	6	,	,	PUNCT
ejpam-5020	273	7	22(04):93–105	22(04):93–105	PROPN
ejpam-5020	273	8	,	,	PUNCT
ejpam-5020	273	9	2023	2023	NUM
ejpam-5020	273	10	.	.	PUNCT
ejpam-5020	274	1	references	reference	NOUN
ejpam-5020	274	2	221	221	NUM
ejpam-5020	275	1	[	[	X
ejpam-5020	275	2	16	16	NUM
ejpam-5020	275	3	]	]	X
ejpam-5020	275	4	m	m	VERB
ejpam-5020	275	5	u	u	NOUN
ejpam-5020	275	6	romdhini	romdhini	NOUN
ejpam-5020	275	7	,	,	PUNCT
ejpam-5020	275	8	f	f	PROPN
ejpam-5020	275	9	al	al	PROPN
ejpam-5020	275	10	-	-	PUNCT
ejpam-5020	275	11	sharqi	sharqi	PROPN
ejpam-5020	275	12	,	,	PUNCT
ejpam-5020	275	13	a	a	DET
ejpam-5020	275	14	nawawi	nawawi	NOUN
ejpam-5020	275	15	,	,	PUNCT
ejpam-5020	275	16	a	a	DET
ejpam-5020	275	17	al	al	PROPN
ejpam-5020	275	18	-	-	PUNCT
ejpam-5020	275	19	quran	quran	PROPN
ejpam-5020	275	20	,	,	PUNCT
ejpam-5020	275	21	and	and	CCONJ
ejpam-5020	275	22	h	h	PROPN
ejpam-5020	275	23	rashmanlou	rashmanlou	NOUN
ejpam-5020	275	24	.	.	PUNCT
ejpam-5020	276	1	signless	signless	PROPN
ejpam-5020	276	2	laplacian	laplacian	ADJ
ejpam-5020	276	3	energy	energy	NOUN
ejpam-5020	276	4	of	of	ADP
ejpam-5020	276	5	interval	interval	NOUN
ejpam-5020	276	6	-	-	PUNCT
ejpam-5020	276	7	valued	value	VERB
ejpam-5020	276	8	fuzzy	fuzzy	ADJ
ejpam-5020	276	9	graph	graph	NOUN
ejpam-5020	276	10	and	and	CCONJ
ejpam-5020	276	11	its	its	PRON
ejpam-5020	276	12	applications	application	NOUN
ejpam-5020	276	13	.	.	PUNCT
ejpam-5020	277	1	sains	sain	NOUN
ejpam-5020	277	2	malaysiana	malaysiana	PROPN
ejpam-5020	277	3	,	,	PUNCT
ejpam-5020	277	4	52(7):2127–2137	52(7):2127–2137	NUM
ejpam-5020	277	5	,	,	PUNCT
ejpam-5020	277	6	2023	2023	NUM
ejpam-5020	277	7	.	.	PUNCT
ejpam-5020	278	1	[	[	X
ejpam-5020	278	2	17	17	NUM
ejpam-5020	278	3	]	]	X
ejpam-5020	278	4	m	m	VERB
ejpam-5020	278	5	u	u	NOUN
ejpam-5020	278	6	romdhini	romdhini	NOUN
ejpam-5020	278	7	and	and	CCONJ
ejpam-5020	278	8	a	a	DET
ejpam-5020	278	9	nawawi	nawawi	ADJ
ejpam-5020	278	10	.	.	PUNCT
ejpam-5020	278	11	degree	degree	NOUN
ejpam-5020	278	12	sum	sum	NOUN
ejpam-5020	278	13	energy	energy	NOUN
ejpam-5020	278	14	of	of	ADP
ejpam-5020	278	15	non	non	ADJ
ejpam-5020	278	16	-	-	ADJ
ejpam-5020	278	17	commuting	commuting	ADJ
ejpam-5020	278	18	graph	graph	NOUN
ejpam-5020	278	19	for	for	ADP
ejpam-5020	278	20	dihedral	dihedral	ADJ
ejpam-5020	278	21	groups	group	NOUN
ejpam-5020	278	22	.	.	PUNCT
ejpam-5020	279	1	malaysian	malaysian	ADJ
ejpam-5020	279	2	journal	journal	PROPN
ejpam-5020	279	3	of	of	ADP
ejpam-5020	279	4	science	science	PROPN
ejpam-5020	279	5	,	,	PUNCT
ejpam-5020	279	6	41(sp1):34–39	41(sp1):34–39	PRON
ejpam-5020	279	7	,	,	PUNCT
ejpam-5020	279	8	2022	2022	NUM
ejpam-5020	279	9	.	.	PUNCT
ejpam-5020	280	1	[	[	X
ejpam-5020	280	2	18	18	NUM
ejpam-5020	280	3	]	]	X
ejpam-5020	280	4	m	m	VERB
ejpam-5020	280	5	u	u	NOUN
ejpam-5020	280	6	romdhini	romdhini	NOUN
ejpam-5020	280	7	and	and	CCONJ
ejpam-5020	280	8	a	a	DET
ejpam-5020	280	9	nawawi	nawawi	NOUN
ejpam-5020	280	10	.	.	PUNCT
ejpam-5020	281	1	maximum	maximum	ADJ
ejpam-5020	281	2	and	and	CCONJ
ejpam-5020	281	3	minimum	minimum	NOUN
ejpam-5020	281	4	degree	degree	NOUN
ejpam-5020	281	5	energy	energy	NOUN
ejpam-5020	281	6	of	of	ADP
ejpam-5020	281	7	commuting	commuting	NOUN
ejpam-5020	281	8	graph	graph	NOUN
ejpam-5020	281	9	for	for	ADP
ejpam-5020	281	10	dihedral	dihedral	ADJ
ejpam-5020	281	11	groups	group	NOUN
ejpam-5020	281	12	.	.	PUNCT
ejpam-5020	282	1	sains	sain	NOUN
ejpam-5020	282	2	malaysiana	malaysiana	PROPN
ejpam-5020	282	3	,	,	PUNCT
ejpam-5020	282	4	51(12):4145–4151	51(12):4145–4151	NUM
ejpam-5020	282	5	,	,	PUNCT
ejpam-5020	282	6	2022	2022	NUM
ejpam-5020	282	7	.	.	PUNCT
ejpam-5020	283	1	[	[	X
ejpam-5020	283	2	19	19	NUM
ejpam-5020	283	3	]	]	SYM
ejpam-5020	283	4	m	m	VERB
ejpam-5020	283	5	u	u	NOUN
ejpam-5020	283	6	romdhini	romdhini	NOUN
ejpam-5020	283	7	and	and	CCONJ
ejpam-5020	283	8	a	a	DET
ejpam-5020	283	9	nawawi	nawawi	ADJ
ejpam-5020	283	10	.	.	PUNCT
ejpam-5020	283	11	degree	degree	NOUN
ejpam-5020	283	12	subtraction	subtraction	NOUN
ejpam-5020	283	13	energy	energy	NOUN
ejpam-5020	283	14	of	of	ADP
ejpam-5020	283	15	commuting	commute	VERB
ejpam-5020	283	16	and	and	CCONJ
ejpam-5020	283	17	noncommuting	noncommute	VERB
ejpam-5020	283	18	graphs	graph	NOUN
ejpam-5020	283	19	for	for	ADP
ejpam-5020	283	20	dihedral	dihedral	ADJ
ejpam-5020	283	21	groups	group	NOUN
ejpam-5020	283	22	.	.	PUNCT
ejpam-5020	284	1	journal	journal	PROPN
ejpam-5020	284	2	of	of	ADP
ejpam-5020	284	3	mathematical	mathematical	ADJ
ejpam-5020	284	4	and	and	CCONJ
ejpam-5020	284	5	computational	computational	ADJ
ejpam-5020	284	6	science	science	NOUN
ejpam-5020	284	7	,	,	PUNCT
ejpam-5020	284	8	18(3):497–508	18(3):497–508	NUM
ejpam-5020	284	9	,	,	PUNCT
ejpam-5020	284	10	2023	2023	NUM
ejpam-5020	284	11	.	.	PUNCT
ejpam-5020	285	1	[	[	X
ejpam-5020	285	2	20	20	NUM
ejpam-5020	285	3	]	]	SYM
ejpam-5020	285	4	m	m	VERB
ejpam-5020	285	5	u	u	NOUN
ejpam-5020	285	6	romdhini	romdhini	NOUN
ejpam-5020	285	7	and	and	CCONJ
ejpam-5020	285	8	a	a	DET
ejpam-5020	285	9	nawawi	nawawi	NOUN
ejpam-5020	285	10	.	.	PUNCT
ejpam-5020	286	1	distance	distance	NOUN
ejpam-5020	286	2	energy	energy	NOUN
ejpam-5020	286	3	of	of	ADP
ejpam-5020	286	4	non	non	ADJ
ejpam-5020	286	5	-	-	ADJ
ejpam-5020	286	6	commuting	commuting	ADJ
ejpam-5020	286	7	graphs	graph	NOUN
ejpam-5020	286	8	for	for	ADP
ejpam-5020	286	9	dihedral	dihedral	ADJ
ejpam-5020	286	10	groups	group	NOUN
ejpam-5020	286	11	.	.	PUNCT
ejpam-5020	287	1	jordan	jordan	PROPN
ejpam-5020	287	2	journal	journal	PROPN
ejpam-5020	287	3	of	of	ADP
ejpam-5020	287	4	mathematics	mathematic	NOUN
ejpam-5020	287	5	and	and	CCONJ
ejpam-5020	287	6	statestics	statestic	NOUN
ejpam-5020	287	7	,	,	PUNCT
ejpam-5020	287	8	page	page	NOUN
ejpam-5020	287	9	submitted	submit	VERB
ejpam-5020	287	10	,	,	PUNCT
ejpam-5020	287	11	2023	2023	NUM
ejpam-5020	287	12	.	.	PUNCT
ejpam-5020	288	1	[	[	X
ejpam-5020	288	2	21	21	NUM
ejpam-5020	288	3	]	]	X
ejpam-5020	288	4	m	m	VERB
ejpam-5020	288	5	u	u	NOUN
ejpam-5020	288	6	romdhini	romdhini	NOUN
ejpam-5020	288	7	,	,	PUNCT
ejpam-5020	288	8	a	a	DET
ejpam-5020	288	9	nawawi	nawawi	NOUN
ejpam-5020	288	10	,	,	PUNCT
ejpam-5020	288	11	and	and	CCONJ
ejpam-5020	288	12	c	c	PROPN
ejpam-5020	288	13	y	y	PROPN
ejpam-5020	288	14	chen	chen	PROPN
ejpam-5020	288	15	.	.	PUNCT
ejpam-5020	288	16	degree	degree	PROPN
ejpam-5020	288	17	exponent	exponent	NOUN
ejpam-5020	288	18	sum	sum	NOUN
ejpam-5020	288	19	energy	energy	NOUN
ejpam-5020	288	20	of	of	ADP
ejpam-5020	288	21	commuting	commuting	NOUN
ejpam-5020	288	22	graph	graph	NOUN
ejpam-5020	288	23	for	for	ADP
ejpam-5020	288	24	dihedral	dihedral	ADJ
ejpam-5020	288	25	groups	group	NOUN
ejpam-5020	288	26	.	.	PUNCT
ejpam-5020	289	1	malaysian	malaysian	ADJ
ejpam-5020	289	2	journal	journal	PROPN
ejpam-5020	289	3	of	of	ADP
ejpam-5020	289	4	science	science	NOUN
ejpam-5020	289	5	,	,	PUNCT
ejpam-5020	289	6	41(sp1):40–46	41(sp1):40–46	NUM
ejpam-5020	289	7	,	,	PUNCT
ejpam-5020	289	8	2022	2022	NUM
ejpam-5020	289	9	.	.	PUNCT
ejpam-5020	290	1	[	[	X
ejpam-5020	290	2	22	22	NUM
ejpam-5020	290	3	]	]	X
ejpam-5020	290	4	m	m	VERB
ejpam-5020	290	5	u	u	NOUN
ejpam-5020	290	6	romdhini	romdhini	NOUN
ejpam-5020	290	7	,	,	PUNCT
ejpam-5020	290	8	a	a	DET
ejpam-5020	290	9	nawawi	nawawi	NOUN
ejpam-5020	290	10	,	,	PUNCT
ejpam-5020	290	11	and	and	CCONJ
ejpam-5020	290	12	c	c	PROPN
ejpam-5020	290	13	y	y	PROPN
ejpam-5020	290	14	chen	chen	PROPN
ejpam-5020	290	15	.	.	PUNCT
ejpam-5020	291	1	neighbors	neighbor	NOUN
ejpam-5020	291	2	degree	degree	VERB
ejpam-5020	291	3	sum	sum	NOUN
ejpam-5020	291	4	energy	energy	NOUN
ejpam-5020	291	5	of	of	ADP
ejpam-5020	291	6	commuting	commuting	NOUN
ejpam-5020	291	7	and	and	CCONJ
ejpam-5020	291	8	non	non	ADJ
ejpam-5020	291	9	-	-	ADJ
ejpam-5020	291	10	commuting	commuting	ADJ
ejpam-5020	291	11	graphs	graph	NOUN
ejpam-5020	291	12	for	for	ADP
ejpam-5020	291	13	dihedral	dihedral	ADJ
ejpam-5020	291	14	groups	group	NOUN
ejpam-5020	291	15	.	.	PUNCT
ejpam-5020	292	1	malaysian	malaysian	ADJ
ejpam-5020	292	2	journal	journal	PROPN
ejpam-5020	292	3	of	of	ADP
ejpam-5020	292	4	mathematical	mathematical	ADJ
ejpam-5020	292	5	sciences	science	NOUN
ejpam-5020	292	6	,	,	PUNCT
ejpam-5020	292	7	17(1):53–65	17(1):53–65	NUM
ejpam-5020	292	8	,	,	PUNCT
ejpam-5020	292	9	2023	2023	NUM
ejpam-5020	292	10	.	.	PUNCT
ejpam-5020	293	1	[	[	X
ejpam-5020	293	2	23	23	NUM
ejpam-5020	293	3	]	]	X
ejpam-5020	293	4	s	s	VERB
ejpam-5020	293	5	sun	sun	NOUN
ejpam-5020	293	6	,	,	PUNCT
ejpam-5020	293	7	k	k	PROPN
ejpam-5020	293	8	c	c	PROPN
ejpam-5020	293	9	das	das	PROPN
ejpam-5020	293	10	,	,	PUNCT
ejpam-5020	293	11	and	and	CCONJ
ejpam-5020	293	12	y	y	PROPN
ejpam-5020	293	13	shang	shang	PROPN
ejpam-5020	293	14	.	.	PUNCT
ejpam-5020	294	1	on	on	ADP
ejpam-5020	294	2	maximal	maximal	ADJ
ejpam-5020	294	3	energy	energy	NOUN
ejpam-5020	294	4	distance	distance	NOUN
ejpam-5020	294	5	.	.	PUNCT
ejpam-5020	295	1	mathematics	mathematic	NOUN
ejpam-5020	295	2	,	,	PUNCT
ejpam-5020	295	3	9(360):1	9(360):1	PROPN
ejpam-5020	295	4	–	–	PUNCT
ejpam-5020	295	5	7	7	NUM
ejpam-5020	295	6	,	,	PUNCT
ejpam-5020	295	7	2021	2021	NUM
ejpam-5020	295	8	.	.	PUNCT
ejpam-5020	296	1	[	[	X
ejpam-5020	296	2	24	24	NUM
ejpam-5020	296	3	]	]	X
ejpam-5020	296	4	l	l	X
ejpam-5020	296	5	zheng	zheng	PROPN
ejpam-5020	296	6	and	and	CCONJ
ejpam-5020	296	7	b	b	PROPN
ejpam-5020	296	8	zhou	zhou	PROPN
ejpam-5020	296	9	.	.	PUNCT
ejpam-5020	297	1	the	the	DET
ejpam-5020	297	2	closeness	closeness	NOUN
ejpam-5020	297	3	eigenvalues	eigenvalue	VERB
ejpam-5020	297	4	of	of	ADP
ejpam-5020	297	5	graphs	graph	NOUN
ejpam-5020	297	6	.	.	PUNCT
ejpam-5020	298	1	journal	journal	NOUN
ejpam-5020	298	2	of	of	ADP
ejpam-5020	298	3	algebraic	algebraic	PROPN
ejpam-5020	298	4	combinatorics	combinatoric	NOUN
ejpam-5020	298	5	,	,	PUNCT
ejpam-5020	298	6	58:741–760	58:741–760	PROPN
ejpam-5020	298	7	,	,	PUNCT
ejpam-5020	298	8	2023	2023	NUM
ejpam-5020	298	9	.	.	PUNCT