id	sid	tid	token	lemma	pos
ejpam-6319	1	1	european	european	PROPN
ejpam-6319	1	2	journal	journal	PROPN
ejpam-6319	1	3	of	of	ADP
ejpam-6319	1	4	pure	pure	ADJ
ejpam-6319	1	5	and	and	CCONJ
ejpam-6319	1	6	applied	applied	ADJ
ejpam-6319	1	7	mathematics	mathematic	NOUN
ejpam-6319	1	8	2025	2025	NUM
ejpam-6319	1	9	,	,	PUNCT
ejpam-6319	1	10	vol	vol	NOUN
ejpam-6319	1	11	.	.	PROPN
ejpam-6319	1	12	18	18	NUM
ejpam-6319	1	13	,	,	PUNCT
ejpam-6319	1	14	issue	issue	NOUN
ejpam-6319	1	15	3	3	NUM
ejpam-6319	1	16	,	,	PUNCT
ejpam-6319	1	17	article	article	NOUN
ejpam-6319	1	18	number	number	NOUN
ejpam-6319	1	19	6319	6319	NUM
ejpam-6319	1	20	issn	issn	VERB
ejpam-6319	1	21	1307	1307	NUM
ejpam-6319	1	22	-	-	SYM
ejpam-6319	1	23	5543	5543	NUM
ejpam-6319	1	24	–	–	PUNCT
ejpam-6319	1	25	ejpam.com	ejpam.com	X
ejpam-6319	1	26	published	publish	VERB
ejpam-6319	1	27	by	by	ADP
ejpam-6319	1	28	new	new	PROPN
ejpam-6319	1	29	york	york	PROPN
ejpam-6319	1	30	business	business	PROPN
ejpam-6319	1	31	global	global	ADJ
ejpam-6319	1	32	spectral	spectral	ADJ
ejpam-6319	1	33	properties	property	NOUN
ejpam-6319	1	34	of	of	ADP
ejpam-6319	1	35	coprime	coprime	NOUN
ejpam-6319	1	36	graphs	graph	NOUN
ejpam-6319	1	37	for	for	ADP
ejpam-6319	1	38	dihedral	dihedral	ADJ
ejpam-6319	1	39	groups	group	NOUN
ejpam-6319	1	40	mamika	mamika	PROPN
ejpam-6319	1	41	ujianita	ujianita	PROPN
ejpam-6319	1	42	romdhini1,∗	romdhini1,∗	PROPN
ejpam-6319	1	43	,	,	PUNCT
ejpam-6319	1	44	abdurahim1	abdurahim1	PROPN
ejpam-6319	1	45	,	,	PUNCT
ejpam-6319	1	46	andika	andika	PROPN
ejpam-6319	1	47	ellena	ellena	PROPN
ejpam-6319	1	48	saufika	saufika	PROPN
ejpam-6319	1	49	hakim	hakim	PROPN
ejpam-6319	1	50	maharani1	maharani1	PROPN
ejpam-6319	2	1	1	1	NUM
ejpam-6319	2	2	department	department	NOUN
ejpam-6319	2	3	of	of	ADP
ejpam-6319	2	4	mathematics	mathematic	NOUN
ejpam-6319	2	5	,	,	PUNCT
ejpam-6319	2	6	faculty	faculty	NOUN
ejpam-6319	2	7	of	of	ADP
ejpam-6319	2	8	mathematics	mathematic	NOUN
ejpam-6319	2	9	and	and	CCONJ
ejpam-6319	2	10	natural	natural	ADJ
ejpam-6319	2	11	sciences	science	NOUN
ejpam-6319	2	12	,	,	PUNCT
ejpam-6319	2	13	university	university	NOUN
ejpam-6319	2	14	of	of	ADP
ejpam-6319	2	15	mataram	mataram	PROPN
ejpam-6319	2	16	,	,	PUNCT
ejpam-6319	2	17	mataram	mataram	PROPN
ejpam-6319	2	18	83125	83125	NUM
ejpam-6319	2	19	,	,	PUNCT
ejpam-6319	2	20	indonesia	indonesia	PROPN
ejpam-6319	2	21	abstract	abstract	NOUN
ejpam-6319	2	22	.	.	PUNCT
ejpam-6319	3	1	for	for	ADP
ejpam-6319	3	2	a	a	DET
ejpam-6319	3	3	finite	finite	ADJ
ejpam-6319	3	4	group	group	NOUN
ejpam-6319	3	5	g	g	PROPN
ejpam-6319	3	6	,	,	PUNCT
ejpam-6319	3	7	the	the	DET
ejpam-6319	3	8	coprime	coprime	NOUN
ejpam-6319	3	9	graph	graph	NOUN
ejpam-6319	3	10	γg	γg	ADV
ejpam-6319	3	11	of	of	ADP
ejpam-6319	3	12	g	g	PROPN
ejpam-6319	3	13	is	be	AUX
ejpam-6319	3	14	defined	define	VERB
ejpam-6319	3	15	as	as	ADP
ejpam-6319	3	16	the	the	DET
ejpam-6319	3	17	graph	graph	NOUN
ejpam-6319	3	18	with	with	ADP
ejpam-6319	3	19	vertex	vertex	NOUN
ejpam-6319	3	20	set	set	VERB
ejpam-6319	3	21	g	g	PROPN
ejpam-6319	3	22	,	,	PUNCT
ejpam-6319	3	23	the	the	DET
ejpam-6319	3	24	group	group	NOUN
ejpam-6319	3	25	itself	itself	PRON
ejpam-6319	3	26	,	,	PUNCT
ejpam-6319	3	27	and	and	CCONJ
ejpam-6319	3	28	two	two	NUM
ejpam-6319	3	29	distinct	distinct	ADJ
ejpam-6319	3	30	vertices	vertex	NOUN
ejpam-6319	3	31	u	u	NOUN
ejpam-6319	3	32	,	,	PUNCT
ejpam-6319	3	33	v	v	NOUN
ejpam-6319	3	34	in	in	ADP
ejpam-6319	3	35	γg	γg	ADV
ejpam-6319	3	36	are	be	AUX
ejpam-6319	3	37	adjacent	adjacent	ADJ
ejpam-6319	3	38	if	if	SCONJ
ejpam-6319	3	39	and	and	CCONJ
ejpam-6319	3	40	only	only	ADV
ejpam-6319	3	41	if	if	SCONJ
ejpam-6319	3	42	gcd(|u|	gcd(|u|	ADJ
ejpam-6319	3	43	,	,	PUNCT
ejpam-6319	3	44	|v|	|v|	NOUN
ejpam-6319	3	45	)	)	PUNCT
ejpam-6319	3	46	=	=	SYM
ejpam-6319	3	47	1	1	NUM
ejpam-6319	3	48	,	,	PUNCT
ejpam-6319	3	49	where	where	SCONJ
ejpam-6319	3	50	|u|	|u|	PROPN
ejpam-6319	3	51	is	be	AUX
ejpam-6319	3	52	the	the	DET
ejpam-6319	3	53	order	order	NOUN
ejpam-6319	3	54	of	of	ADP
ejpam-6319	3	55	u.	u.	NOUN
ejpam-6319	3	56	this	this	DET
ejpam-6319	3	57	study	study	NOUN
ejpam-6319	3	58	analyzes	analyze	VERB
ejpam-6319	3	59	the	the	DET
ejpam-6319	3	60	characteristic	characteristic	ADJ
ejpam-6319	3	61	polynomial	polynomial	NOUN
ejpam-6319	3	62	of	of	ADP
ejpam-6319	3	63	matrices	matrix	NOUN
ejpam-6319	3	64	for	for	ADP
ejpam-6319	3	65	the	the	DET
ejpam-6319	3	66	dihedral	dihedral	ADJ
ejpam-6319	3	67	group	group	NOUN
ejpam-6319	3	68	of	of	ADP
ejpam-6319	3	69	order	order	NOUN
ejpam-6319	3	70	2n	2n	NUM
ejpam-6319	3	71	,	,	PUNCT
ejpam-6319	3	72	where	where	SCONJ
ejpam-6319	3	73	n	n	PRON
ejpam-6319	3	74	is	be	AUX
ejpam-6319	3	75	a	a	DET
ejpam-6319	3	76	power	power	NOUN
ejpam-6319	3	77	of	of	ADP
ejpam-6319	3	78	a	a	DET
ejpam-6319	3	79	prime	prime	ADJ
ejpam-6319	3	80	number	number	NOUN
ejpam-6319	3	81	.	.	PUNCT
ejpam-6319	4	1	in	in	ADP
ejpam-6319	4	2	addition	addition	NOUN
ejpam-6319	4	3	,	,	PUNCT
ejpam-6319	4	4	this	this	DET
ejpam-6319	4	5	paper	paper	NOUN
ejpam-6319	4	6	examines	examine	VERB
ejpam-6319	4	7	the	the	DET
ejpam-6319	4	8	characteristic	characteristic	ADJ
ejpam-6319	4	9	polynomial	polynomial	NOUN
ejpam-6319	4	10	of	of	ADP
ejpam-6319	4	11	the	the	DET
ejpam-6319	4	12	matrices	matrix	NOUN
ejpam-6319	4	13	for	for	ADP
ejpam-6319	4	14	a	a	DET
ejpam-6319	4	15	power	power	NOUN
ejpam-6319	4	16	of	of	ADP
ejpam-6319	4	17	a	a	DET
ejpam-6319	4	18	prime	prime	ADJ
ejpam-6319	4	19	number	number	NOUN
ejpam-6319	4	20	n.	n.	NOUN
ejpam-6319	4	21	the	the	DET
ejpam-6319	4	22	energy	energy	NOUN
ejpam-6319	4	23	of	of	ADP
ejpam-6319	4	24	the	the	DET
ejpam-6319	4	25	graph	graph	NOUN
ejpam-6319	4	26	is	be	AUX
ejpam-6319	4	27	also	also	ADV
ejpam-6319	4	28	obtained	obtain	VERB
ejpam-6319	4	29	.	.	PUNCT
ejpam-6319	5	1	2020	2020	NUM
ejpam-6319	5	2	mathematics	mathematic	NOUN
ejpam-6319	5	3	subject	subject	NOUN
ejpam-6319	5	4	classifications	classification	NOUN
ejpam-6319	5	5	:	:	PUNCT
ejpam-6319	5	6	05c25	05c25	NUM
ejpam-6319	5	7	,	,	PUNCT
ejpam-6319	5	8	15a18	15a18	NUM
ejpam-6319	5	9	key	key	ADJ
ejpam-6319	5	10	words	word	NOUN
ejpam-6319	5	11	and	and	CCONJ
ejpam-6319	5	12	phrases	phrase	NOUN
ejpam-6319	5	13	:	:	PUNCT
ejpam-6319	5	14	coprime	coprime	NOUN
ejpam-6319	5	15	graph	graph	NOUN
ejpam-6319	5	16	,	,	PUNCT
ejpam-6319	5	17	dihedral	dihedral	ADJ
ejpam-6319	5	18	group	group	NOUN
ejpam-6319	5	19	,	,	PUNCT
ejpam-6319	5	20	spectral	spectral	ADJ
ejpam-6319	5	21	radius	radius	NOUN
ejpam-6319	5	22	,	,	PUNCT
ejpam-6319	5	23	energy	energy	NOUN
ejpam-6319	5	24	of	of	ADP
ejpam-6319	5	25	a	a	DET
ejpam-6319	5	26	graph	graph	NOUN
ejpam-6319	5	27	1	1	NUM
ejpam-6319	5	28	.	.	PUNCT
ejpam-6319	5	29	introduction	introduction	NOUN
ejpam-6319	5	30	in	in	ADP
ejpam-6319	5	31	spectral	spectral	ADJ
ejpam-6319	5	32	graph	graph	NOUN
ejpam-6319	5	33	theory	theory	NOUN
ejpam-6319	5	34	,	,	PUNCT
ejpam-6319	5	35	specific	specific	ADJ
ejpam-6319	5	36	matrices	matrix	NOUN
ejpam-6319	5	37	provide	provide	VERB
ejpam-6319	5	38	information	information	NOUN
ejpam-6319	5	39	about	about	ADP
ejpam-6319	5	40	graphs	graph	NOUN
ejpam-6319	5	41	,	,	PUNCT
ejpam-6319	5	42	such	such	ADJ
ejpam-6319	5	43	as	as	ADP
ejpam-6319	5	44	adjacency	adjacency	NOUN
ejpam-6319	5	45	,	,	PUNCT
ejpam-6319	5	46	laplacian	laplacian	ADJ
ejpam-6319	5	47	,	,	PUNCT
ejpam-6319	5	48	or	or	CCONJ
ejpam-6319	5	49	signless	signless	ADJ
ejpam-6319	5	50	laplacian	laplacian	ADJ
ejpam-6319	5	51	matrices	matrix	NOUN
ejpam-6319	5	52	.	.	PUNCT
ejpam-6319	6	1	a	a	DET
ejpam-6319	6	2	graph	graph	NOUN
ejpam-6319	6	3	can	can	AUX
ejpam-6319	6	4	be	be	AUX
ejpam-6319	6	5	characterized	characterize	VERB
ejpam-6319	6	6	by	by	ADP
ejpam-6319	6	7	the	the	DET
ejpam-6319	6	8	spectrum	spectrum	NOUN
ejpam-6319	6	9	of	of	ADP
ejpam-6319	6	10	one	one	NUM
ejpam-6319	6	11	of	of	ADP
ejpam-6319	6	12	these	these	DET
ejpam-6319	6	13	matrices	matrix	NOUN
ejpam-6319	6	14	.	.	PUNCT
ejpam-6319	7	1	in	in	ADP
ejpam-6319	7	2	general	general	ADJ
ejpam-6319	7	3	,	,	PUNCT
ejpam-6319	7	4	the	the	DET
ejpam-6319	7	5	spectra	spectra	NOUN
ejpam-6319	7	6	of	of	ADP
ejpam-6319	7	7	these	these	DET
ejpam-6319	7	8	various	various	ADJ
ejpam-6319	7	9	matrices	matrix	NOUN
ejpam-6319	7	10	can	can	AUX
ejpam-6319	7	11	provide	provide	VERB
ejpam-6319	7	12	useful	useful	ADJ
ejpam-6319	7	13	information	information	NOUN
ejpam-6319	7	14	about	about	ADP
ejpam-6319	7	15	the	the	DET
ejpam-6319	7	16	graph	graph	NOUN
ejpam-6319	7	17	.	.	PUNCT
ejpam-6319	8	1	apart	apart	ADV
ejpam-6319	8	2	from	from	ADP
ejpam-6319	8	3	that	that	PRON
ejpam-6319	8	4	,	,	PUNCT
ejpam-6319	8	5	graphs	graph	NOUN
ejpam-6319	8	6	can	can	AUX
ejpam-6319	8	7	be	be	AUX
ejpam-6319	8	8	involved	involve	VERB
ejpam-6319	8	9	in	in	ADP
ejpam-6319	8	10	decision	decision	NOUN
ejpam-6319	8	11	-	-	PUNCT
ejpam-6319	8	12	making	make	VERB
ejpam-6319	8	13	theory	theory	NOUN
ejpam-6319	8	14	as	as	SCONJ
ejpam-6319	8	15	seen	see	VERB
ejpam-6319	8	16	in	in	ADP
ejpam-6319	8	17	[	[	X
ejpam-6319	8	18	1–3	1–3	NOUN
ejpam-6319	8	19	]	]	PUNCT
ejpam-6319	8	20	and	and	CCONJ
ejpam-6319	8	21	more	more	ADJ
ejpam-6319	8	22	terminologies	terminology	NOUN
ejpam-6319	8	23	in	in	ADP
ejpam-6319	8	24	[	[	X
ejpam-6319	8	25	4	4	NUM
ejpam-6319	8	26	,	,	PUNCT
ejpam-6319	8	27	5	5	NUM
ejpam-6319	8	28	]	]	PUNCT
ejpam-6319	8	29	.	.	PUNCT
ejpam-6319	9	1	therefore	therefore	ADV
ejpam-6319	9	2	,	,	PUNCT
ejpam-6319	9	3	in	in	ADP
ejpam-6319	9	4	this	this	DET
ejpam-6319	9	5	paper	paper	NOUN
ejpam-6319	9	6	,	,	PUNCT
ejpam-6319	9	7	we	we	PRON
ejpam-6319	9	8	discuss	discuss	VERB
ejpam-6319	9	9	a	a	DET
ejpam-6319	9	10	coprime	coprime	ADJ
ejpam-6319	9	11	graph	graph	NOUN
ejpam-6319	9	12	of	of	ADP
ejpam-6319	9	13	a	a	DET
ejpam-6319	9	14	finite	finite	ADJ
ejpam-6319	9	15	group	group	NOUN
ejpam-6319	9	16	.	.	PUNCT
ejpam-6319	10	1	definition	definition	NOUN
ejpam-6319	10	2	1	1	NUM
ejpam-6319	10	3	.	.	PUNCT
ejpam-6319	11	1	[	[	X
ejpam-6319	11	2	6	6	NUM
ejpam-6319	11	3	]	]	PUNCT
ejpam-6319	11	4	let	let	VERB
ejpam-6319	11	5	g	g	PRON
ejpam-6319	11	6	be	be	AUX
ejpam-6319	11	7	a	a	DET
ejpam-6319	11	8	finite	finite	ADJ
ejpam-6319	11	9	group	group	NOUN
ejpam-6319	11	10	.	.	PUNCT
ejpam-6319	12	1	coprime	coprime	NOUN
ejpam-6319	12	2	graph	graph	NOUN
ejpam-6319	12	3	of	of	ADP
ejpam-6319	12	4	g	g	PROPN
ejpam-6319	12	5	is	be	AUX
ejpam-6319	12	6	denoted	denote	VERB
ejpam-6319	12	7	by	by	ADP
ejpam-6319	12	8	γg	γg	PROPN
ejpam-6319	12	9	and	and	CCONJ
ejpam-6319	12	10	g	g	PROPN
ejpam-6319	12	11	as	as	ADP
ejpam-6319	12	12	the	the	DET
ejpam-6319	12	13	set	set	NOUN
ejpam-6319	12	14	of	of	ADP
ejpam-6319	12	15	vertices	vertex	NOUN
ejpam-6319	12	16	and	and	CCONJ
ejpam-6319	12	17	∀	∀	NOUN
ejpam-6319	12	18	a	a	PRON
ejpam-6319	12	19	,	,	PUNCT
ejpam-6319	12	20	b	b	X
ejpam-6319	12	21	∈	∈	PROPN
ejpam-6319	12	22	g	g	NOUN
ejpam-6319	12	23	adjacent	adjacent	ADJ
ejpam-6319	12	24	whenever	whenever	SCONJ
ejpam-6319	12	25	gcd(|a|	gcd(|a|	NOUN
ejpam-6319	12	26	,	,	PUNCT
ejpam-6319	12	27	|b|	|b|	PROPN
ejpam-6319	12	28	)	)	PUNCT
ejpam-6319	13	1	=	=	SYM
ejpam-6319	13	2	1	1	X
ejpam-6319	13	3	.	.	PUNCT
ejpam-6319	14	1	the	the	DET
ejpam-6319	14	2	dihedral	dihedral	ADJ
ejpam-6319	14	3	group	group	NOUN
ejpam-6319	14	4	is	be	AUX
ejpam-6319	14	5	denoted	denote	VERB
ejpam-6319	14	6	by	by	ADP
ejpam-6319	14	7	d2n	d2n	PROPN
ejpam-6319	15	1	=	=	PUNCT
ejpam-6319	15	2	〈	〈	PROPN
ejpam-6319	15	3	a	a	PRON
ejpam-6319	15	4	,	,	PUNCT
ejpam-6319	15	5	b	b	NOUN
ejpam-6319	15	6	:	:	PUNCT
ejpam-6319	15	7	an	an	DET
ejpam-6319	15	8	=	=	NOUN
ejpam-6319	15	9	b2	b2	NOUN
ejpam-6319	15	10	=	=	SYM
ejpam-6319	15	11	e	e	PROPN
ejpam-6319	15	12	,	,	PUNCT
ejpam-6319	15	13	bab	bab	PROPN
ejpam-6319	15	14	=	=	SYM
ejpam-6319	15	15	a−1	a−1	PROPN
ejpam-6319	15	16	〉	〉	NOUN
ejpam-6319	15	17	[	[	X
ejpam-6319	15	18	7	7	NUM
ejpam-6319	15	19	]	]	PUNCT
ejpam-6319	15	20	.	.	PUNCT
ejpam-6319	16	1	this	this	DET
ejpam-6319	16	2	research	research	NOUN
ejpam-6319	16	3	investigates	investigate	VERB
ejpam-6319	16	4	the	the	DET
ejpam-6319	16	5	coprime	coprime	NOUN
ejpam-6319	16	6	graph	graph	NOUN
ejpam-6319	16	7	for	for	ADP
ejpam-6319	16	8	the	the	DET
ejpam-6319	16	9	non	non	ADJ
ejpam-6319	16	10	-	-	ADJ
ejpam-6319	16	11	abelian	abelian	ADJ
ejpam-6319	16	12	d2n	d2n	PROPN
ejpam-6319	16	13	,	,	PUNCT
ejpam-6319	16	14	where	where	SCONJ
ejpam-6319	16	15	n	n	PRON
ejpam-6319	16	16	≥	≥	X
ejpam-6319	16	17	3	3	NUM
ejpam-6319	16	18	and	and	CCONJ
ejpam-6319	16	19	n	n	PRON
ejpam-6319	16	20	∈	∈	PROPN
ejpam-6319	16	21	n	n	CCONJ
ejpam-6319	16	22	,	,	PUNCT
ejpam-6319	16	23	denoted	denote	VERB
ejpam-6319	16	24	by	by	ADP
ejpam-6319	16	25	γd2n	γd2n	PROPN
ejpam-6319	16	26	.	.	PUNCT
ejpam-6319	17	1	∗corresponding	∗corresponde	VERB
ejpam-6319	17	2	author	author	NOUN
ejpam-6319	17	3	.	.	PUNCT
ejpam-6319	18	1	doi	doi	NOUN
ejpam-6319	18	2	:	:	PUNCT
ejpam-6319	18	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6319	https://doi.org/10.29020/nybg.ejpam.v18i3.6319	PRON
ejpam-6319	18	4	email	email	NOUN
ejpam-6319	18	5	addresses	address	VERB
ejpam-6319	18	6	:	:	PUNCT
ejpam-6319	18	7	mamika@unram.ac.id	mamika@unram.ac.id	NOUN
ejpam-6319	18	8	(	(	PUNCT
ejpam-6319	18	9	m.	m.	PROPN
ejpam-6319	18	10	u.	u.	PROPN
ejpam-6319	18	11	romdhini	romdhini	PROPN
ejpam-6319	18	12	)	)	PUNCT
ejpam-6319	18	13	,	,	PUNCT
ejpam-6319	18	14	abdurahim@staff.unram.ac.id	abdurahim@staff.unram.ac.id	PROPN
ejpam-6319	18	15	(	(	PUNCT
ejpam-6319	18	16	abdurahim	abdurahim	PROPN
ejpam-6319	18	17	)	)	PUNCT
ejpam-6319	18	18	,	,	PUNCT
ejpam-6319	18	19	a.ellena.saufika@staff.unram.ac.id	a.ellena.saufika@staff.unram.ac.id	NOUN
ejpam-6319	18	20	(	(	PUNCT
ejpam-6319	18	21	a.	a.	PROPN
ejpam-6319	18	22	e.	e.	PROPN
ejpam-6319	18	23	s.	s.	PROPN
ejpam-6319	18	24	h.	h.	PROPN
ejpam-6319	18	25	maharani	maharani	PROPN
ejpam-6319	18	26	)	)	PUNCT
ejpam-6319	18	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6319	19	1	1	1	NUM
ejpam-6319	19	2	copyright	copyright	NOUN
ejpam-6319	19	3	:	:	PUNCT
ejpam-6319	19	4	©	©	PROPN
ejpam-6319	19	5	2025	2025	NUM
ejpam-6319	19	6	the	the	DET
ejpam-6319	19	7	author(s	author(s	NOUN
ejpam-6319	19	8	)	)	PUNCT
ejpam-6319	19	9	.	.	PUNCT
ejpam-6319	20	1	(	(	PUNCT
ejpam-6319	20	2	cc	cc	NOUN
ejpam-6319	20	3	by	by	ADP
ejpam-6319	20	4	-	-	PUNCT
ejpam-6319	20	5	nc	nc	PROPN
ejpam-6319	20	6	4.0	4.0	NUM
ejpam-6319	20	7	)	)	PUNCT
ejpam-6319	20	8	m.	m.	NOUN
ejpam-6319	20	9	u.	u.	PROPN
ejpam-6319	20	10	romdhini	romdhini	PROPN
ejpam-6319	20	11	,	,	PUNCT
ejpam-6319	20	12	abdurahim	abdurahim	PRON
ejpam-6319	20	13	,	,	PUNCT
ejpam-6319	20	14	a.	a.	PROPN
ejpam-6319	20	15	e.	e.	PROPN
ejpam-6319	20	16	s.	s.	PROPN
ejpam-6319	20	17	h.	h.	PROPN
ejpam-6319	20	18	maharani	maharani	PROPN
ejpam-6319	20	19	/	/	SYM
ejpam-6319	20	20	eur	eur	PROPN
ejpam-6319	20	21	.	.	PUNCT
ejpam-6319	21	1	j.	j.	PROPN
ejpam-6319	21	2	pure	pure	PROPN
ejpam-6319	21	3	appl	appl	PROPN
ejpam-6319	21	4	.	.	PROPN
ejpam-6319	21	5	math	math	PROPN
ejpam-6319	21	6	,	,	PUNCT
ejpam-6319	21	7	18	18	NUM
ejpam-6319	21	8	(	(	PUNCT
ejpam-6319	21	9	3	3	NUM
ejpam-6319	21	10	)	)	PUNCT
ejpam-6319	21	11	(	(	PUNCT
ejpam-6319	21	12	2025	2025	NUM
ejpam-6319	21	13	)	)	PUNCT
ejpam-6319	21	14	,	,	PUNCT
ejpam-6319	21	15	6319	6319	NUM
ejpam-6319	21	16	2	2	NUM
ejpam-6319	21	17	of	of	ADP
ejpam-6319	21	18	13	13	NUM
ejpam-6319	21	19	the	the	DET
ejpam-6319	21	20	energy	energy	NOUN
ejpam-6319	21	21	of	of	ADP
ejpam-6319	21	22	γd2n	γd2n	PROPN
ejpam-6319	21	23	is	be	AUX
ejpam-6319	21	24	denoted	denote	VERB
ejpam-6319	21	25	by	by	ADP
ejpam-6319	21	26	e(γd2n	e(γd2n	NOUN
ejpam-6319	21	27	)	)	PUNCT
ejpam-6319	21	28	.	.	PUNCT
ejpam-6319	22	1	gutman	gutman	NOUN
ejpam-6319	22	2	[	[	X
ejpam-6319	22	3	8	8	NUM
ejpam-6319	22	4	]	]	PUNCT
ejpam-6319	22	5	first	first	ADV
ejpam-6319	22	6	defined	define	VERB
ejpam-6319	22	7	the	the	DET
ejpam-6319	22	8	graph	graph	NOUN
ejpam-6319	22	9	energy	energy	NOUN
ejpam-6319	22	10	in	in	ADP
ejpam-6319	22	11	1978	1978	NUM
ejpam-6319	22	12	.	.	PUNCT
ejpam-6319	23	1	the	the	DET
ejpam-6319	23	2	graphs	graph	NOUN
ejpam-6319	23	3	on	on	ADP
ejpam-6319	23	4	2n	2n	NUM
ejpam-6319	23	5	vertices	vertex	NOUN
ejpam-6319	23	6	with	with	ADP
ejpam-6319	23	7	e(γd2n	e(γd2n	NOUN
ejpam-6319	23	8	)	)	PUNCT
ejpam-6319	23	9	≥	≥	PRON
ejpam-6319	23	10	2n	2n	NUM
ejpam-6319	23	11	is	be	AUX
ejpam-6319	23	12	nonhypoenergetic	nonhypoenergetic	ADJ
ejpam-6319	23	13	,	,	PUNCT
ejpam-6319	23	14	while	while	SCONJ
ejpam-6319	23	15	if	if	SCONJ
ejpam-6319	23	16	e(γd2n	e(γd2n	VERB
ejpam-6319	23	17	)	)	PUNCT
ejpam-6319	23	18	<	<	X
ejpam-6319	24	1	2n−	2n−	PROPN
ejpam-6319	24	2	1	1	NUM
ejpam-6319	24	3	is	be	AUX
ejpam-6319	24	4	strongly	strongly	ADV
ejpam-6319	24	5	hypoenergetic	hypoenergetic	ADJ
ejpam-6319	24	6	[	[	X
ejpam-6319	24	7	9	9	NUM
ejpam-6319	24	8	]	]	PUNCT
ejpam-6319	24	9	.	.	PUNCT
ejpam-6319	25	1	in	in	ADP
ejpam-6319	25	2	recent	recent	ADJ
ejpam-6319	25	3	years	year	NOUN
ejpam-6319	25	4	,	,	PUNCT
ejpam-6319	25	5	numerous	numerous	ADJ
ejpam-6319	25	6	papers	paper	NOUN
ejpam-6319	25	7	on	on	ADP
ejpam-6319	25	8	spectral	spectral	ADJ
ejpam-6319	25	9	graph	graph	NOUN
ejpam-6319	25	10	theory	theory	NOUN
ejpam-6319	25	11	have	have	AUX
ejpam-6319	25	12	been	be	AUX
ejpam-6319	25	13	published	publish	VERB
ejpam-6319	25	14	.	.	PUNCT
ejpam-6319	26	1	romdhini	romdhini	PROPN
ejpam-6319	26	2	et	et	PROPN
ejpam-6319	26	3	al	al	PROPN
ejpam-6319	26	4	.	.	PROPN
ejpam-6319	26	5	obtained	obtain	VERB
ejpam-6319	26	6	the	the	DET
ejpam-6319	26	7	spectral	spectral	ADJ
ejpam-6319	26	8	properties	property	NOUN
ejpam-6319	26	9	of	of	ADP
ejpam-6319	26	10	the	the	DET
ejpam-6319	26	11	non	non	ADJ
ejpam-6319	26	12	-	-	ADJ
ejpam-6319	26	13	commuting	commuting	ADJ
ejpam-6319	26	14	graph	graph	NOUN
ejpam-6319	26	15	for	for	ADP
ejpam-6319	26	16	d2n	d2n	NOUN
ejpam-6319	26	17	corresponding	correspond	VERB
ejpam-6319	26	18	with	with	ADP
ejpam-6319	26	19	the	the	DET
ejpam-6319	26	20	sombor	sombor	NOUN
ejpam-6319	26	21	matrix	matrix	NOUN
ejpam-6319	26	22	[	[	X
ejpam-6319	26	23	10	10	NUM
ejpam-6319	26	24	]	]	PUNCT
ejpam-6319	26	25	and	and	CCONJ
ejpam-6319	26	26	wiener	wiener	NOUN
ejpam-6319	26	27	-	-	PUNCT
ejpam-6319	26	28	hosoya	hosoya	NOUN
ejpam-6319	26	29	matrix	matrix	NOUN
ejpam-6319	26	30	[	[	X
ejpam-6319	26	31	11	11	NUM
ejpam-6319	26	32	]	]	PUNCT
ejpam-6319	26	33	.	.	PUNCT
ejpam-6319	27	1	apart	apart	ADV
ejpam-6319	27	2	from	from	ADP
ejpam-6319	27	3	that	that	PRON
ejpam-6319	27	4	,	,	PUNCT
ejpam-6319	27	5	the	the	DET
ejpam-6319	27	6	spectral	spectral	ADJ
ejpam-6319	27	7	and	and	CCONJ
ejpam-6319	27	8	structural	structural	ADJ
ejpam-6319	27	9	properties	property	NOUN
ejpam-6319	27	10	of	of	ADP
ejpam-6319	27	11	the	the	DET
ejpam-6319	27	12	cubic	cubic	ADJ
ejpam-6319	27	13	power	power	NOUN
ejpam-6319	27	14	graph	graph	NOUN
ejpam-6319	27	15	for	for	ADP
ejpam-6319	27	16	d2n	d2n	PROPN
ejpam-6319	27	17	can	can	AUX
ejpam-6319	27	18	be	be	AUX
ejpam-6319	27	19	seen	see	VERB
ejpam-6319	27	20	in	in	ADP
ejpam-6319	27	21	[	[	X
ejpam-6319	27	22	12	12	NUM
ejpam-6319	27	23	,	,	PUNCT
ejpam-6319	27	24	13	13	NUM
ejpam-6319	27	25	]	]	PUNCT
ejpam-6319	27	26	,	,	PUNCT
ejpam-6319	27	27	the	the	DET
ejpam-6319	27	28	equal	equal	ADJ
ejpam-6319	27	29	-	-	PUNCT
ejpam-6319	27	30	square	square	ADJ
ejpam-6319	27	31	graph	graph	NOUN
ejpam-6319	27	32	is	be	AUX
ejpam-6319	27	33	presented	present	VERB
ejpam-6319	27	34	by	by	ADP
ejpam-6319	27	35	[	[	X
ejpam-6319	27	36	14	14	NUM
ejpam-6319	27	37	]	]	PUNCT
ejpam-6319	27	38	,	,	PUNCT
ejpam-6319	27	39	the	the	DET
ejpam-6319	27	40	prime	prime	ADJ
ejpam-6319	27	41	ideal	ideal	NOUN
ejpam-6319	27	42	graph	graph	NOUN
ejpam-6319	27	43	[	[	X
ejpam-6319	27	44	15	15	NUM
ejpam-6319	27	45	]	]	PUNCT
ejpam-6319	27	46	,	,	PUNCT
ejpam-6319	27	47	and	and	CCONJ
ejpam-6319	27	48	the	the	DET
ejpam-6319	27	49	prime	prime	ADJ
ejpam-6319	27	50	coprime	coprime	NOUN
ejpam-6319	27	51	graph	graph	NOUN
ejpam-6319	27	52	[	[	X
ejpam-6319	27	53	16	16	NUM
ejpam-6319	27	54	]	]	PUNCT
ejpam-6319	27	55	.	.	PUNCT
ejpam-6319	28	1	furthermore	furthermore	ADV
ejpam-6319	28	2	,	,	PUNCT
ejpam-6319	28	3	in	in	ADP
ejpam-6319	28	4	[	[	PUNCT
ejpam-6319	28	5	17	17	NUM
ejpam-6319	28	6	]	]	PUNCT
ejpam-6319	28	7	,	,	PUNCT
ejpam-6319	28	8	it	it	PRON
ejpam-6319	28	9	is	be	AUX
ejpam-6319	28	10	shown	show	VERB
ejpam-6319	28	11	that	that	SCONJ
ejpam-6319	28	12	a	a	DET
ejpam-6319	28	13	precise	precise	ADJ
ejpam-6319	28	14	formula	formula	NOUN
ejpam-6319	28	15	can	can	AUX
ejpam-6319	28	16	be	be	AUX
ejpam-6319	28	17	derived	derive	VERB
ejpam-6319	28	18	for	for	ADP
ejpam-6319	28	19	the	the	DET
ejpam-6319	28	20	calculation	calculation	NOUN
ejpam-6319	28	21	of	of	ADP
ejpam-6319	28	22	the	the	DET
ejpam-6319	28	23	degree	degree	NOUN
ejpam-6319	28	24	of	of	ADP
ejpam-6319	28	25	the	the	DET
ejpam-6319	28	26	vertex	vertex	NOUN
ejpam-6319	28	27	in	in	ADP
ejpam-6319	28	28	a	a	DET
ejpam-6319	28	29	coprime	coprime	NOUN
ejpam-6319	28	30	order	order	NOUN
ejpam-6319	28	31	graph	graph	NOUN
ejpam-6319	28	32	of	of	ADP
ejpam-6319	28	33	group	group	NOUN
ejpam-6319	28	34	d2n	d2n	PROPN
ejpam-6319	28	35	”	"	PUNCT
ejpam-6319	28	36	.	.	PUNCT
ejpam-6319	29	1	additional	additional	ADJ
ejpam-6319	29	2	terminology	terminology	NOUN
ejpam-6319	29	3	related	relate	VERB
ejpam-6319	29	4	to	to	ADP
ejpam-6319	29	5	this	this	DET
ejpam-6319	29	6	discussion	discussion	NOUN
ejpam-6319	29	7	can	can	AUX
ejpam-6319	29	8	be	be	AUX
ejpam-6319	29	9	found	find	VERB
ejpam-6319	29	10	in	in	ADP
ejpam-6319	29	11	[	[	X
ejpam-6319	29	12	18–21	18–21	NUM
ejpam-6319	29	13	]	]	PUNCT
ejpam-6319	29	14	.	.	PUNCT
ejpam-6319	30	1	they	they	PRON
ejpam-6319	30	2	worked	work	VERB
ejpam-6319	30	3	on	on	ADP
ejpam-6319	30	4	finite	finite	ADJ
ejpam-6319	30	5	groups	group	NOUN
ejpam-6319	30	6	,	,	PUNCT
ejpam-6319	30	7	and	and	CCONJ
ejpam-6319	30	8	the	the	DET
ejpam-6319	30	9	review	review	NOUN
ejpam-6319	30	10	on	on	ADP
ejpam-6319	30	11	graphs	graph	NOUN
ejpam-6319	30	12	on	on	ADP
ejpam-6319	30	13	groups	group	NOUN
ejpam-6319	30	14	can	can	AUX
ejpam-6319	30	15	be	be	AUX
ejpam-6319	30	16	seen	see	VERB
ejpam-6319	30	17	in	in	ADP
ejpam-6319	30	18	[	[	X
ejpam-6319	30	19	22	22	NUM
ejpam-6319	30	20	]	]	PUNCT
ejpam-6319	30	21	.	.	PUNCT
ejpam-6319	31	1	in	in	ADP
ejpam-6319	31	2	addition	addition	NOUN
ejpam-6319	31	3	,	,	PUNCT
ejpam-6319	31	4	the	the	DET
ejpam-6319	31	5	discussion	discussion	NOUN
ejpam-6319	31	6	on	on	ADP
ejpam-6319	31	7	the	the	DET
ejpam-6319	31	8	vertex	vertex	NOUN
ejpam-6319	31	9	degree	degree	NOUN
ejpam-6319	31	10	of	of	ADP
ejpam-6319	31	11	the	the	DET
ejpam-6319	31	12	coprime	coprime	NOUN
ejpam-6319	31	13	graph	graph	NOUN
ejpam-6319	31	14	for	for	ADP
ejpam-6319	31	15	dihedral	dihedral	ADJ
ejpam-6319	31	16	groups	group	NOUN
ejpam-6319	31	17	has	have	AUX
ejpam-6319	31	18	been	be	AUX
ejpam-6319	31	19	discussed	discuss	VERB
ejpam-6319	31	20	in	in	ADP
ejpam-6319	31	21	[	[	X
ejpam-6319	31	22	23	23	NUM
ejpam-6319	31	23	]	]	PUNCT
ejpam-6319	31	24	.	.	PUNCT
ejpam-6319	32	1	therefore	therefore	ADV
ejpam-6319	32	2	,	,	PUNCT
ejpam-6319	32	3	this	this	DET
ejpam-6319	32	4	paper	paper	NOUN
ejpam-6319	32	5	examines	examine	VERB
ejpam-6319	32	6	the	the	DET
ejpam-6319	32	7	characteristic	characteristic	ADJ
ejpam-6319	32	8	polynomial	polynomial	NOUN
ejpam-6319	32	9	of	of	ADP
ejpam-6319	32	10	a	a	DET
ejpam-6319	32	11	coprime	coprime	NOUN
ejpam-6319	32	12	graph	graph	NOUN
ejpam-6319	32	13	associated	associate	VERB
ejpam-6319	32	14	with	with	ADP
ejpam-6319	32	15	the	the	DET
ejpam-6319	32	16	adjacency	adjacency	NOUN
ejpam-6319	32	17	,	,	PUNCT
ejpam-6319	32	18	laplacian	laplacian	NOUN
ejpam-6319	32	19	,	,	PUNCT
ejpam-6319	32	20	and	and	CCONJ
ejpam-6319	32	21	signless	signless	ADJ
ejpam-6319	32	22	laplacian	laplacian	ADJ
ejpam-6319	32	23	matrices	matrix	NOUN
ejpam-6319	32	24	.	.	PUNCT
ejpam-6319	33	1	the	the	DET
ejpam-6319	33	2	definition	definition	NOUN
ejpam-6319	33	3	of	of	ADP
ejpam-6319	33	4	them	they	PRON
ejpam-6319	33	5	refers	refer	VERB
ejpam-6319	33	6	to	to	ADP
ejpam-6319	33	7	a	a	DET
ejpam-6319	33	8	book	book	NOUN
ejpam-6319	33	9	from	from	ADP
ejpam-6319	33	10	[	[	X
ejpam-6319	33	11	24	24	NUM
ejpam-6319	33	12	]	]	PUNCT
ejpam-6319	33	13	.	.	PUNCT
ejpam-6319	34	1	the	the	DET
ejpam-6319	34	2	basic	basic	ADJ
ejpam-6319	34	3	definitions	definition	NOUN
ejpam-6319	34	4	and	and	CCONJ
ejpam-6319	34	5	notational	notational	ADJ
ejpam-6319	34	6	conventions	convention	NOUN
ejpam-6319	34	7	relevant	relevant	ADJ
ejpam-6319	34	8	to	to	ADP
ejpam-6319	34	9	this	this	DET
ejpam-6319	34	10	research	research	NOUN
ejpam-6319	34	11	are	be	AUX
ejpam-6319	34	12	summarized	summarize	VERB
ejpam-6319	34	13	in	in	ADP
ejpam-6319	34	14	the	the	DET
ejpam-6319	34	15	following	follow	VERB
ejpam-6319	34	16	table	table	NOUN
ejpam-6319	34	17	.	.	PUNCT
ejpam-6319	35	1	definition	definition	NOUN
ejpam-6319	35	2	2	2	NUM
ejpam-6319	35	3	.	.	PUNCT
ejpam-6319	36	1	[	[	X
ejpam-6319	36	2	24	24	NUM
ejpam-6319	36	3	]	]	X
ejpam-6319	36	4	an	an	DET
ejpam-6319	36	5	n×n	n×n	PROPN
ejpam-6319	36	6	adjacency	adjacency	NOUN
ejpam-6319	36	7	(	(	PUNCT
ejpam-6319	36	8	a	a	DET
ejpam-6319	36	9	)	)	PUNCT
ejpam-6319	36	10	matrix	matrix	NOUN
ejpam-6319	36	11	of	of	ADP
ejpam-6319	36	12	γd2n	γd2n	PROPN
ejpam-6319	36	13	is	be	AUX
ejpam-6319	36	14	denoted	denote	VERB
ejpam-6319	36	15	by	by	ADP
ejpam-6319	36	16	a(γd2n	a(γd2n	PUNCT
ejpam-6319	36	17	)	)	PUNCT
ejpam-6319	36	18	=	=	PUNCT
ejpam-6319	37	1	[	[	X
ejpam-6319	37	2	aij	aij	X
ejpam-6319	37	3	]	]	X
ejpam-6319	37	4	,	,	PUNCT
ejpam-6319	37	5	where	where	SCONJ
ejpam-6319	37	6	aij	aij	PROPN
ejpam-6319	37	7	=	=	SYM
ejpam-6319	37	8	{	{	PUNCT
ejpam-6319	37	9	1	1	NUM
ejpam-6319	37	10	,	,	PUNCT
ejpam-6319	37	11	if	if	SCONJ
ejpam-6319	37	12	vi	vi	PRON
ejpam-6319	37	13	̸=	̸=	PROPN
ejpam-6319	37	14	vj	vj	NOUN
ejpam-6319	37	15	and	and	CCONJ
ejpam-6319	37	16	they	they	PRON
ejpam-6319	37	17	are	be	AUX
ejpam-6319	37	18	adjacent	adjacent	ADJ
ejpam-6319	37	19	0	0	NUM
ejpam-6319	37	20	,	,	PUNCT
ejpam-6319	37	21	otherwise	otherwise	ADV
ejpam-6319	37	22	.	.	PUNCT
ejpam-6319	38	1	definition	definition	NOUN
ejpam-6319	38	2	3	3	NUM
ejpam-6319	38	3	.	.	PUNCT
ejpam-6319	39	1	[	[	X
ejpam-6319	39	2	24	24	NUM
ejpam-6319	39	3	]	]	PUNCT
ejpam-6319	39	4	an	an	DET
ejpam-6319	39	5	n	n	NUM
ejpam-6319	39	6	×	×	NOUN
ejpam-6319	39	7	n	n	CCONJ
ejpam-6319	39	8	diagonal	diagonal	ADJ
ejpam-6319	39	9	degree	degree	NOUN
ejpam-6319	39	10	matrix	matrix	NOUN
ejpam-6319	39	11	of	of	ADP
ejpam-6319	39	12	γd2n	γd2n	PROPN
ejpam-6319	39	13	is	be	AUX
ejpam-6319	39	14	d(γd2n	d(γd2n	PROPN
ejpam-6319	39	15	)	)	PUNCT
ejpam-6319	39	16	=	=	PUNCT
ejpam-6319	40	1	[	[	X
ejpam-6319	40	2	dij	dij	X
ejpam-6319	40	3	]	]	X
ejpam-6319	40	4	whose	whose	DET
ejpam-6319	40	5	(	(	PUNCT
ejpam-6319	40	6	i	i	NOUN
ejpam-6319	40	7	,	,	PUNCT
ejpam-6319	40	8	j)-th	j)-th	PROPN
ejpam-6319	40	9	entry	entry	NOUN
ejpam-6319	40	10	dij	dij	PROPN
ejpam-6319	40	11	=	=	X
ejpam-6319	40	12	{	{	PUNCT
ejpam-6319	40	13	deg(vi	deg(vi	NOUN
ejpam-6319	40	14	)	)	PUNCT
ejpam-6319	40	15	,	,	PUNCT
ejpam-6319	40	16	if	if	SCONJ
ejpam-6319	40	17	vi	vi	ADJ
ejpam-6319	40	18	=	=	SYM
ejpam-6319	40	19	vj	vj	NOUN
ejpam-6319	40	20	0	0	NUM
ejpam-6319	40	21	,	,	PUNCT
ejpam-6319	40	22	otherwise	otherwise	ADV
ejpam-6319	40	23	,	,	PUNCT
ejpam-6319	40	24	where	where	SCONJ
ejpam-6319	40	25	deg(vi	deg(vi	NOUN
ejpam-6319	40	26	)	)	PUNCT
ejpam-6319	40	27	represent	represent	VERB
ejpam-6319	40	28	the	the	DET
ejpam-6319	40	29	degree	degree	NOUN
ejpam-6319	40	30	of	of	ADP
ejpam-6319	40	31	vi	vi	PROPN
ejpam-6319	40	32	.	.	PUNCT
ejpam-6319	40	33	definition	definition	NOUN
ejpam-6319	40	34	4	4	NUM
ejpam-6319	40	35	.	.	PUNCT
ejpam-6319	40	36	an	an	DET
ejpam-6319	40	37	n×	n×	PROPN
ejpam-6319	40	38	n	n	CCONJ
ejpam-6319	40	39	laplacian	laplacian	X
ejpam-6319	40	40	(	(	PUNCT
ejpam-6319	40	41	l	l	NOUN
ejpam-6319	40	42	)	)	PUNCT
ejpam-6319	40	43	matrix	matrix	NOUN
ejpam-6319	40	44	of	of	ADP
ejpam-6319	40	45	γd2n	γd2n	PROPN
ejpam-6319	40	46	is	be	AUX
ejpam-6319	40	47	l(γd2n	l(γd2n	PROPN
ejpam-6319	40	48	)	)	PUNCT
ejpam-6319	40	49	=	=	SYM
ejpam-6319	40	50	d(γd2n)−a(γd2n	d(γd2n)−a(γd2n	PROPN
ejpam-6319	40	51	)	)	PUNCT
ejpam-6319	40	52	.	.	PUNCT
ejpam-6319	41	1	definition	definition	NOUN
ejpam-6319	41	2	5	5	NUM
ejpam-6319	41	3	.	.	PUNCT
ejpam-6319	42	1	[	[	X
ejpam-6319	42	2	24	24	NUM
ejpam-6319	42	3	]	]	PUNCT
ejpam-6319	42	4	an	an	DET
ejpam-6319	42	5	n	n	NUM
ejpam-6319	42	6	×	×	NOUN
ejpam-6319	42	7	n	n	CCONJ
ejpam-6319	42	8	signless	signless	NOUN
ejpam-6319	42	9	laplacian	laplacian	X
ejpam-6319	42	10	(	(	PUNCT
ejpam-6319	42	11	sl	sl	NOUN
ejpam-6319	42	12	)	)	PUNCT
ejpam-6319	42	13	matrix	matrix	NOUN
ejpam-6319	42	14	of	of	ADP
ejpam-6319	42	15	γd2n	γd2n	PROPN
ejpam-6319	42	16	is	be	AUX
ejpam-6319	42	17	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	42	18	)	)	PUNCT
ejpam-6319	42	19	=	=	SYM
ejpam-6319	43	1	d(γd2n	d(γd2n	X
ejpam-6319	43	2	)	)	PUNCT
ejpam-6319	44	1	+	+	NOUN
ejpam-6319	44	2	a(γd2n	a(γd2n	X
ejpam-6319	44	3	)	)	PUNCT
ejpam-6319	44	4	.	.	PUNCT
ejpam-6319	45	1	the	the	DET
ejpam-6319	45	2	energy	energy	NOUN
ejpam-6319	45	3	of	of	ADP
ejpam-6319	45	4	γd2n	γd2n	PROPN
ejpam-6319	46	1	[	[	X
ejpam-6319	46	2	8	8	NUM
ejpam-6319	46	3	]	]	PUNCT
ejpam-6319	46	4	associated	associate	VERB
ejpam-6319	46	5	with	with	ADP
ejpam-6319	46	6	a(γd2n	a(γd2n	PROPN
ejpam-6319	46	7	)	)	PUNCT
ejpam-6319	46	8	is	be	AUX
ejpam-6319	46	9	defined	define	VERB
ejpam-6319	46	10	as	as	ADP
ejpam-6319	46	11	ea(γd2n	ea(γd2n	NOUN
ejpam-6319	46	12	)	)	PUNCT
ejpam-6319	47	1	=	=	PUNCT
ejpam-6319	47	2	σn	σn	X
ejpam-6319	47	3	i=1	i=1	PROPN
ejpam-6319	47	4	|λi|	|λi|	PROPN
ejpam-6319	47	5	,	,	PUNCT
ejpam-6319	47	6	and	and	CCONJ
ejpam-6319	47	7	a−spectral	a−spectral	ADJ
ejpam-6319	47	8	radius	radius	NOUN
ejpam-6319	47	9	of	of	ADP
ejpam-6319	47	10	γd2n	γd2n	PROPN
ejpam-6319	47	11	are	be	AUX
ejpam-6319	47	12	defined	define	VERB
ejpam-6319	47	13	as	as	ADP
ejpam-6319	47	14	ρa(γd2n	ρa(γd2n	NOUN
ejpam-6319	47	15	)	)	PUNCT
ejpam-6319	48	1	=	=	SYM
ejpam-6319	48	2	max{|λ|	max{|λ|	NOUN
ejpam-6319	48	3	:	:	PUNCT
ejpam-6319	49	1	λ	λ	X
ejpam-6319	49	2	∈	∈	PROPN
ejpam-6319	49	3	speca(γd2n	speca(γd2n	PROPN
ejpam-6319	49	4	)	)	PUNCT
ejpam-6319	49	5	}	}	PUNCT
ejpam-6319	49	6	,	,	PUNCT
ejpam-6319	49	7	where	where	SCONJ
ejpam-6319	49	8	λ1	λ1	ADJ
ejpam-6319	49	9	,	,	PUNCT
ejpam-6319	49	10	λ2	λ2	NOUN
ejpam-6319	49	11	,	,	PUNCT
ejpam-6319	49	12	.	.	PUNCT
ejpam-6319	49	13	.	.	PUNCT
ejpam-6319	49	14	.	.	PUNCT
ejpam-6319	50	1	,	,	PUNCT
ejpam-6319	50	2	λ2n	λ2n	NOUN
ejpam-6319	50	3	are	be	AUX
ejpam-6319	50	4	eigenvalues	eigenvalue	NOUN
ejpam-6319	50	5	of	of	ADP
ejpam-6319	50	6	a(γd2n	a(γd2n	X
ejpam-6319	50	7	)	)	PUNCT
ejpam-6319	50	8	as	as	ADP
ejpam-6319	50	9	the	the	DET
ejpam-6319	50	10	roots	root	NOUN
ejpam-6319	50	11	of	of	ADP
ejpam-6319	50	12	characteristic	characteristic	ADJ
ejpam-6319	50	13	polynomial	polynomial	ADJ
ejpam-6319	50	14	pa(γd2n	pa(γd2n	NOUN
ejpam-6319	50	15	)	)	PUNCT
ejpam-6319	50	16	(	(	PUNCT
ejpam-6319	50	17	λ	λ	X
ejpam-6319	50	18	)	)	PUNCT
ejpam-6319	50	19	=	=	SYM
ejpam-6319	50	20	|λi2n	|λi2n	X
ejpam-6319	50	21	−a(γd2n)|	−a(γd2n)|	X
ejpam-6319	50	22	=	=	SYM
ejpam-6319	50	23	0	0	NUM
ejpam-6319	50	24	,	,	PUNCT
ejpam-6319	50	25	and	and	CCONJ
ejpam-6319	50	26	speca(γd2n	speca(γd2n	PROPN
ejpam-6319	50	27	)	)	PUNCT
ejpam-6319	50	28	is	be	AUX
ejpam-6319	50	29	the	the	DET
ejpam-6319	50	30	spectrum	spectrum	NOUN
ejpam-6319	50	31	of	of	ADP
ejpam-6319	50	32	a(γd2n	a(γd2n	PROPN
ejpam-6319	50	33	)	)	PUNCT
ejpam-6319	50	34	.	.	PUNCT
ejpam-6319	51	1	these	these	DET
ejpam-6319	51	2	notations	notation	NOUN
ejpam-6319	51	3	also	also	ADV
ejpam-6319	51	4	apply	apply	VERB
ejpam-6319	51	5	for	for	ADP
ejpam-6319	51	6	l(γd2n	l(γd2n	PROPN
ejpam-6319	51	7	)	)	PUNCT
ejpam-6319	51	8	and	and	CCONJ
ejpam-6319	51	9	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	51	10	)	)	PUNCT
ejpam-6319	51	11	.	.	PUNCT
ejpam-6319	52	1	some	some	DET
ejpam-6319	52	2	previous	previous	ADJ
ejpam-6319	52	3	results	result	NOUN
ejpam-6319	52	4	on	on	ADP
ejpam-6319	52	5	the	the	DET
ejpam-6319	52	6	degree	degree	NOUN
ejpam-6319	52	7	of	of	ADP
ejpam-6319	52	8	a	a	DET
ejpam-6319	52	9	vertex	vertex	NOUN
ejpam-6319	52	10	in	in	ADP
ejpam-6319	52	11	γd2n	γd2n	PROPN
ejpam-6319	52	12	are	be	AUX
ejpam-6319	52	13	presented	present	VERB
ejpam-6319	52	14	as	as	SCONJ
ejpam-6319	52	15	follows	follow	VERB
ejpam-6319	52	16	.	.	PUNCT
ejpam-6319	53	1	m.	m.	NOUN
ejpam-6319	53	2	u.	u.	PROPN
ejpam-6319	53	3	romdhini	romdhini	PROPN
ejpam-6319	53	4	,	,	PUNCT
ejpam-6319	53	5	abdurahim	abdurahim	PRON
ejpam-6319	53	6	,	,	PUNCT
ejpam-6319	53	7	a.	a.	PROPN
ejpam-6319	53	8	e.	e.	PROPN
ejpam-6319	53	9	s.	s.	PROPN
ejpam-6319	53	10	h.	h.	PROPN
ejpam-6319	53	11	maharani	maharani	PROPN
ejpam-6319	53	12	/	/	SYM
ejpam-6319	53	13	eur	eur	PROPN
ejpam-6319	53	14	.	.	PUNCT
ejpam-6319	54	1	j.	j.	PROPN
ejpam-6319	54	2	pure	pure	PROPN
ejpam-6319	54	3	appl	appl	PROPN
ejpam-6319	54	4	.	.	PROPN
ejpam-6319	54	5	math	math	PROPN
ejpam-6319	54	6	,	,	PUNCT
ejpam-6319	54	7	18	18	NUM
ejpam-6319	54	8	(	(	PUNCT
ejpam-6319	54	9	3	3	NUM
ejpam-6319	54	10	)	)	PUNCT
ejpam-6319	54	11	(	(	PUNCT
ejpam-6319	54	12	2025	2025	NUM
ejpam-6319	54	13	)	)	PUNCT
ejpam-6319	54	14	,	,	PUNCT
ejpam-6319	54	15	6319	6319	NUM
ejpam-6319	54	16	3	3	NUM
ejpam-6319	54	17	of	of	ADP
ejpam-6319	54	18	13	13	NUM
ejpam-6319	54	19	table	table	NOUN
ejpam-6319	54	20	1	1	NUM
ejpam-6319	54	21	:	:	PUNCT
ejpam-6319	54	22	notation	notation	NOUN
ejpam-6319	54	23	and	and	CCONJ
ejpam-6319	54	24	its	its	PRON
ejpam-6319	54	25	definition	definition	NOUN
ejpam-6319	54	26	symbol	symbol	NOUN
ejpam-6319	54	27	definition	definition	NOUN
ejpam-6319	54	28	g	g	PROPN
ejpam-6319	54	29	group	group	NOUN
ejpam-6319	54	30	γg	γg	PROPN
ejpam-6319	54	31	coprime	coprime	NOUN
ejpam-6319	54	32	graph	graph	NOUN
ejpam-6319	54	33	of	of	ADP
ejpam-6319	54	34	g	g	PROPN
ejpam-6319	54	35	|u|	|u|	PROPN
ejpam-6319	54	36	order	order	NOUN
ejpam-6319	54	37	of	of	ADP
ejpam-6319	54	38	u	u	NOUN
ejpam-6319	54	39	in	in	ADP
ejpam-6319	54	40	g	g	PROPN
ejpam-6319	54	41	d2n	d2n	PROPN
ejpam-6319	54	42	dihedral	dihedral	PROPN
ejpam-6319	54	43	group	group	NOUN
ejpam-6319	54	44	of	of	ADP
ejpam-6319	54	45	order	order	NOUN
ejpam-6319	54	46	2n	2n	NUM
ejpam-6319	54	47	γd2n	γd2n	PROPN
ejpam-6319	54	48	coprime	coprime	NOUN
ejpam-6319	54	49	graph	graph	NOUN
ejpam-6319	54	50	for	for	ADP
ejpam-6319	54	51	d2n	d2n	PROPN
ejpam-6319	54	52	deg(u	deg(u	PROPN
ejpam-6319	54	53	)	)	PUNCT
ejpam-6319	54	54	degree	degree	NOUN
ejpam-6319	54	55	of	of	ADP
ejpam-6319	54	56	vertex	vertex	NOUN
ejpam-6319	54	57	u	u	NOUN
ejpam-6319	54	58	a(γd2n	a(γd2n	NOUN
ejpam-6319	54	59	)	)	PUNCT
ejpam-6319	54	60	adjacency	adjacency	NOUN
ejpam-6319	54	61	matrix	matrix	NOUN
ejpam-6319	54	62	of	of	ADP
ejpam-6319	54	63	γd2n	γd2n	PROPN
ejpam-6319	54	64	d(γd2n	d(γd2n	NOUN
ejpam-6319	54	65	)	)	PUNCT
ejpam-6319	54	66	diagonal	diagonal	ADJ
ejpam-6319	54	67	degree	degree	NOUN
ejpam-6319	54	68	matrix	matrix	NOUN
ejpam-6319	54	69	of	of	ADP
ejpam-6319	54	70	γd2n	γd2n	PROPN
ejpam-6319	54	71	l(γd2n	l(γd2n	PROPN
ejpam-6319	54	72	)	)	PUNCT
ejpam-6319	54	73	laplacian	laplacian	ADJ
ejpam-6319	54	74	matrix	matrix	NOUN
ejpam-6319	54	75	of	of	ADP
ejpam-6319	54	76	γd2n	γd2n	PROPN
ejpam-6319	54	77	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	54	78	)	)	PUNCT
ejpam-6319	54	79	signless	signless	PROPN
ejpam-6319	54	80	laplacian	laplacian	ADJ
ejpam-6319	54	81	matrix	matrix	NOUN
ejpam-6319	54	82	of	of	ADP
ejpam-6319	54	83	γd2n	γd2n	PROPN
ejpam-6319	54	84	pa(γd2n	pa(γd2n	NOUN
ejpam-6319	54	85	)	)	PUNCT
ejpam-6319	54	86	(	(	PUNCT
ejpam-6319	54	87	λ	λ	NOUN
ejpam-6319	54	88	)	)	PUNCT
ejpam-6319	54	89	characteristic	characteristic	ADJ
ejpam-6319	54	90	polynomial	polynomial	NOUN
ejpam-6319	54	91	of	of	ADP
ejpam-6319	54	92	a(γd2n	a(γd2n	NOUN
ejpam-6319	54	93	)	)	PUNCT
ejpam-6319	54	94	pl(γd2n	pl(γd2n	NOUN
ejpam-6319	54	95	)	)	PUNCT
ejpam-6319	54	96	(	(	PUNCT
ejpam-6319	54	97	λ	λ	NOUN
ejpam-6319	54	98	)	)	PUNCT
ejpam-6319	54	99	characteristic	characteristic	ADJ
ejpam-6319	54	100	polynomial	polynomial	NOUN
ejpam-6319	54	101	of	of	ADP
ejpam-6319	54	102	l(γd2n	l(γd2n	PROPN
ejpam-6319	54	103	)	)	PUNCT
ejpam-6319	54	104	psl(γd2n	psl(γd2n	NOUN
ejpam-6319	54	105	)	)	PUNCT
ejpam-6319	54	106	(	(	PUNCT
ejpam-6319	54	107	λ	λ	NOUN
ejpam-6319	54	108	)	)	PUNCT
ejpam-6319	54	109	characteristic	characteristic	ADJ
ejpam-6319	54	110	polynomial	polynomial	NOUN
ejpam-6319	54	111	of	of	ADP
ejpam-6319	54	112	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	54	113	)	)	PUNCT
ejpam-6319	54	114	λi	λi	ADP
ejpam-6319	54	115	eigenvalues	eigenvalue	NOUN
ejpam-6319	54	116	of	of	ADP
ejpam-6319	54	117	the	the	DET
ejpam-6319	54	118	matrix	matrix	NOUN
ejpam-6319	54	119	ea(γd2n	ea(γd2n	NOUN
ejpam-6319	54	120	)	)	PUNCT
ejpam-6319	54	121	adjacency	adjacency	PROPN
ejpam-6319	54	122	energy	energy	NOUN
ejpam-6319	54	123	of	of	ADP
ejpam-6319	54	124	γd2n	γd2n	PROPN
ejpam-6319	54	125	el(γd2n	el(γd2n	ADJ
ejpam-6319	54	126	)	)	PUNCT
ejpam-6319	54	127	laplacian	laplacian	ADJ
ejpam-6319	54	128	energy	energy	NOUN
ejpam-6319	54	129	of	of	ADP
ejpam-6319	54	130	γd2n	γd2n	PROPN
ejpam-6319	54	131	esl(γd2n	esl(γd2n	NOUN
ejpam-6319	54	132	)	)	PUNCT
ejpam-6319	54	133	signless	signless	PROPN
ejpam-6319	54	134	laplacian	laplacian	ADJ
ejpam-6319	54	135	energy	energy	NOUN
ejpam-6319	54	136	of	of	ADP
ejpam-6319	54	137	γd2n	γd2n	PROPN
ejpam-6319	54	138	speca(γd2n	speca(γd2n	PROPN
ejpam-6319	54	139	)	)	PUNCT
ejpam-6319	54	140	spectrum	spectrum	NOUN
ejpam-6319	54	141	of	of	ADP
ejpam-6319	54	142	a(γd2n	a(γd2n	X
ejpam-6319	54	143	)	)	PUNCT
ejpam-6319	54	144	ρa(γd2n	ρa(γd2n	NOUN
ejpam-6319	54	145	)	)	PUNCT
ejpam-6319	54	146	spectral	spectral	ADJ
ejpam-6319	54	147	radius	radius	NOUN
ejpam-6319	54	148	of	of	ADP
ejpam-6319	54	149	γd2n	γd2n	PROPN
ejpam-6319	54	150	associated	associate	VERB
ejpam-6319	54	151	with	with	ADP
ejpam-6319	54	152	a(γd2n	a(γd2n	PROPN
ejpam-6319	54	153	)	)	PUNCT
ejpam-6319	54	154	ρl(γd2n	ρl(γd2n	NOUN
ejpam-6319	54	155	)	)	PUNCT
ejpam-6319	54	156	spectral	spectral	ADJ
ejpam-6319	54	157	radius	radius	NOUN
ejpam-6319	54	158	of	of	ADP
ejpam-6319	54	159	γd2n	γd2n	PROPN
ejpam-6319	54	160	associated	associate	VERB
ejpam-6319	54	161	with	with	ADP
ejpam-6319	54	162	l(γd2n	l(γd2n	PROPN
ejpam-6319	54	163	)	)	PUNCT
ejpam-6319	54	164	ρsl(γd2n	ρsl(γd2n	NOUN
ejpam-6319	54	165	)	)	PUNCT
ejpam-6319	54	166	spectral	spectral	ADJ
ejpam-6319	54	167	radius	radius	NOUN
ejpam-6319	54	168	of	of	ADP
ejpam-6319	54	169	γd2n	γd2n	PROPN
ejpam-6319	54	170	associated	associate	VERB
ejpam-6319	54	171	with	with	ADP
ejpam-6319	54	172	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	54	173	)	)	PUNCT
ejpam-6319	54	174	ri	ri	PROPN
ejpam-6319	55	1	the	the	DET
ejpam-6319	55	2	i	i	PROPN
ejpam-6319	55	3	-	-	PUNCT
ejpam-6319	55	4	th	th	X
ejpam-6319	55	5	row	row	NOUN
ejpam-6319	55	6	of	of	ADP
ejpam-6319	55	7	the	the	DET
ejpam-6319	55	8	matrix	matrix	NOUN
ejpam-6319	55	9	ci	ci	NOUN
ejpam-6319	56	1	the	the	DET
ejpam-6319	56	2	i	i	PROPN
ejpam-6319	56	3	-	-	PUNCT
ejpam-6319	56	4	th	th	X
ejpam-6319	56	5	column	column	NOUN
ejpam-6319	56	6	of	of	ADP
ejpam-6319	56	7	the	the	DET
ejpam-6319	56	8	matrix	matrix	NOUN
ejpam-6319	56	9	theorem	theorem	VERB
ejpam-6319	56	10	1	1	NUM
ejpam-6319	56	11	.	.	PUNCT
ejpam-6319	57	1	[	[	X
ejpam-6319	57	2	23	23	NUM
ejpam-6319	57	3	]	]	PUNCT
ejpam-6319	57	4	let	let	VERB
ejpam-6319	57	5	d2n	d2n	NOUN
ejpam-6319	57	6	be	be	AUX
ejpam-6319	57	7	the	the	DET
ejpam-6319	57	8	dihedral	dihedral	ADJ
ejpam-6319	57	9	group	group	NOUN
ejpam-6319	57	10	with	with	ADP
ejpam-6319	57	11	n	n	PROPN
ejpam-6319	57	12	is	be	AUX
ejpam-6319	57	13	a	a	DET
ejpam-6319	57	14	prime	prime	ADJ
ejpam-6319	57	15	number	number	NOUN
ejpam-6319	57	16	or	or	CCONJ
ejpam-6319	57	17	n	n	NOUN
ejpam-6319	57	18	=	=	SYM
ejpam-6319	57	19	pk	pk	NOUN
ejpam-6319	57	20	,	,	PUNCT
ejpam-6319	57	21	p	p	PROPN
ejpam-6319	57	22	̸=	̸=	PROPN
ejpam-6319	57	23	2	2	NUM
ejpam-6319	57	24	for	for	ADP
ejpam-6319	57	25	k	k	PROPN
ejpam-6319	57	26	∈	∈	PROPN
ejpam-6319	57	27	n	n	CCONJ
ejpam-6319	57	28	,	,	PUNCT
ejpam-6319	57	29	then	then	ADV
ejpam-6319	57	30	γd2n	γd2n	PROPN
ejpam-6319	57	31	is	be	AUX
ejpam-6319	57	32	a	a	DET
ejpam-6319	57	33	complete	complete	ADJ
ejpam-6319	57	34	tripartite	tripartite	ADJ
ejpam-6319	57	35	graph	graph	NOUN
ejpam-6319	57	36	and	and	CCONJ
ejpam-6319	57	37	deg(e	deg(e	NOUN
ejpam-6319	57	38	)	)	PUNCT
ejpam-6319	57	39	=	=	PUNCT
ejpam-6319	58	1	2n−	2n−	NUM
ejpam-6319	58	2	1	1	NUM
ejpam-6319	58	3	,	,	PUNCT
ejpam-6319	58	4	deg(ai	deg(ai	NOUN
ejpam-6319	58	5	)	)	PUNCT
ejpam-6319	58	6	=	=	SYM
ejpam-6319	58	7	n+	n+	PUNCT
ejpam-6319	58	8	1	1	NUM
ejpam-6319	58	9	,	,	PUNCT
ejpam-6319	58	10	deg(aib	deg(aib	NOUN
ejpam-6319	58	11	)	)	PUNCT
ejpam-6319	58	12	=	=	SYM
ejpam-6319	58	13	n	n	PROPN
ejpam-6319	58	14	for	for	ADP
ejpam-6319	58	15	1	1	NUM
ejpam-6319	58	16	≤	≤	NUM
ejpam-6319	58	17	i	i	PRON
ejpam-6319	58	18	≤	≤	ADJ
ejpam-6319	58	19	n−	n−	NOUN
ejpam-6319	58	20	1	1	NUM
ejpam-6319	58	21	.	.	PUNCT
ejpam-6319	58	22	theorem	theorem	NOUN
ejpam-6319	58	23	2	2	NUM
ejpam-6319	58	24	.	.	PUNCT
ejpam-6319	59	1	[	[	X
ejpam-6319	59	2	23	23	NUM
ejpam-6319	59	3	]	]	PUNCT
ejpam-6319	59	4	let	let	VERB
ejpam-6319	59	5	d2n	d2n	NOUN
ejpam-6319	59	6	be	be	AUX
ejpam-6319	59	7	the	the	DET
ejpam-6319	59	8	dihedral	dihedral	ADJ
ejpam-6319	59	9	group	group	NOUN
ejpam-6319	59	10	with	with	ADP
ejpam-6319	59	11	n	n	NOUN
ejpam-6319	59	12	=	=	SYM
ejpam-6319	59	13	2k	2k	NUM
ejpam-6319	59	14	,	,	PUNCT
ejpam-6319	59	15	k	k	PROPN
ejpam-6319	59	16	∈	∈	PROPN
ejpam-6319	59	17	n	n	CCONJ
ejpam-6319	59	18	,	,	PUNCT
ejpam-6319	59	19	then	then	ADV
ejpam-6319	59	20	γd2n	γd2n	PROPN
ejpam-6319	59	21	is	be	AUX
ejpam-6319	59	22	a	a	DET
ejpam-6319	59	23	complete	complete	ADJ
ejpam-6319	59	24	bipartite	bipartite	NOUN
ejpam-6319	59	25	graph	graph	NOUN
ejpam-6319	59	26	and	and	CCONJ
ejpam-6319	59	27	deg(ai	deg(ai	NOUN
ejpam-6319	59	28	)	)	PUNCT
ejpam-6319	59	29	=	=	SYM
ejpam-6319	59	30	deg(aib	deg(aib	X
ejpam-6319	59	31	)	)	PUNCT
ejpam-6319	59	32	=	=	SYM
ejpam-6319	59	33	1	1	NUM
ejpam-6319	59	34	and	and	CCONJ
ejpam-6319	59	35	deg(e	deg(e	NOUN
ejpam-6319	59	36	)	)	PUNCT
ejpam-6319	59	37	=	=	PUNCT
ejpam-6319	60	1	2n−	2n−	NUM
ejpam-6319	60	2	1	1	NUM
ejpam-6319	60	3	.	.	PUNCT
ejpam-6319	61	1	moreover	moreover	ADV
ejpam-6319	61	2	,	,	PUNCT
ejpam-6319	61	3	the	the	DET
ejpam-6319	61	4	determinant	determinant	ADJ
ejpam-6319	61	5	properties	property	NOUN
ejpam-6319	61	6	of	of	ADP
ejpam-6319	61	7	a	a	DET
ejpam-6319	61	8	square	square	ADJ
ejpam-6319	61	9	matrix	matrix	NOUN
ejpam-6319	61	10	are	be	AUX
ejpam-6319	61	11	useful	useful	ADJ
ejpam-6319	61	12	to	to	PART
ejpam-6319	61	13	ease	ease	VERB
ejpam-6319	61	14	the	the	DET
ejpam-6319	61	15	characteristic	characteristic	ADJ
ejpam-6319	61	16	polynomial	polynomial	NOUN
ejpam-6319	61	17	of	of	ADP
ejpam-6319	61	18	γd2n	γd2n	PROPN
ejpam-6319	61	19	.	.	PUNCT
ejpam-6319	62	1	now	now	ADV
ejpam-6319	62	2	,	,	PUNCT
ejpam-6319	62	3	let	let	VERB
ejpam-6319	62	4	jm×n	jm×n	NOUN
ejpam-6319	62	5	be	be	AUX
ejpam-6319	62	6	an	an	DET
ejpam-6319	62	7	m	m	NOUN
ejpam-6319	62	8	×	×	NOUN
ejpam-6319	62	9	n	n	NOUN
ejpam-6319	62	10	matrix	matrix	NOUN
ejpam-6319	62	11	whose	whose	DET
ejpam-6319	62	12	entries	entry	NOUN
ejpam-6319	62	13	are	be	AUX
ejpam-6319	62	14	all	all	PRON
ejpam-6319	62	15	1	1	NUM
ejpam-6319	62	16	.	.	PUNCT
ejpam-6319	63	1	lemma	lemma	PROPN
ejpam-6319	63	2	1	1	NUM
ejpam-6319	63	3	.	.	PUNCT
ejpam-6319	64	1	[	[	X
ejpam-6319	64	2	25	25	NUM
ejpam-6319	64	3	]	]	PUNCT
ejpam-6319	64	4	for	for	ADP
ejpam-6319	64	5	real	real	ADJ
ejpam-6319	64	6	numbers	number	NOUN
ejpam-6319	64	7	a	a	DET
ejpam-6319	64	8	,	,	PUNCT
ejpam-6319	64	9	b	b	NOUN
ejpam-6319	64	10	,	,	PUNCT
ejpam-6319	64	11	c	c	NOUN
ejpam-6319	64	12	,	,	PUNCT
ejpam-6319	64	13	and	and	CCONJ
ejpam-6319	64	14	d	d	X
ejpam-6319	64	15	,	,	PUNCT
ejpam-6319	64	16	the	the	DET
ejpam-6319	64	17	determinant	determinant	ADJ
ejpam-6319	64	18	of∣∣∣∣(λ+	of∣∣∣∣(λ+	NOUN
ejpam-6319	64	19	a)in1	a)in1	ADP
ejpam-6319	64	20	−	−	PROPN
ejpam-6319	64	21	ajn1	ajn1	PROPN
ejpam-6319	64	22	−cjn1×n2	−cjn1×n2	VERB
ejpam-6319	64	23	−djn2×n1	−djn2×n1	NOUN
ejpam-6319	64	24	(	(	PUNCT
ejpam-6319	64	25	λ+	λ+	NUM
ejpam-6319	64	26	b)in2	b)in2	NUM
ejpam-6319	64	27	−	−	PROPN
ejpam-6319	64	28	bjn2	bjn2	PROPN
ejpam-6319	64	29	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6319	64	30	of	of	ADP
ejpam-6319	64	31	size	size	NOUN
ejpam-6319	64	32	n1	n1	PROPN
ejpam-6319	64	33	+	+	CCONJ
ejpam-6319	64	34	n2	n2	NOUN
ejpam-6319	64	35	can	can	AUX
ejpam-6319	64	36	be	be	AUX
ejpam-6319	64	37	simplified	simplify	VERB
ejpam-6319	64	38	as	as	ADP
ejpam-6319	64	39	(	(	PUNCT
ejpam-6319	64	40	λ+	λ+	PUNCT
ejpam-6319	64	41	a)n1−1(λ+	a)n1−1(λ+	NOUN
ejpam-6319	64	42	b)n2−1	b)n2−1	NOUN
ejpam-6319	64	43	(	(	PUNCT
ejpam-6319	64	44	(	(	PUNCT
ejpam-6319	64	45	λ−	λ−	PROPN
ejpam-6319	64	46	(	(	PUNCT
ejpam-6319	64	47	n1	n1	PROPN
ejpam-6319	64	48	−	−	PROPN
ejpam-6319	64	49	1)a)(λ−	1)a)(λ−	NUM
ejpam-6319	64	50	(	(	PUNCT
ejpam-6319	64	51	n2	n2	NOUN
ejpam-6319	64	52	−	−	PROPN
ejpam-6319	64	53	1)b)−	1)b)−	NUM
ejpam-6319	64	54	n1n2cd	n1n2cd	NOUN
ejpam-6319	64	55	)	)	PUNCT
ejpam-6319	64	56	.	.	PUNCT
ejpam-6319	65	1	m.	m.	NOUN
ejpam-6319	65	2	u.	u.	PROPN
ejpam-6319	65	3	romdhini	romdhini	PROPN
ejpam-6319	65	4	,	,	PUNCT
ejpam-6319	65	5	abdurahim	abdurahim	PRON
ejpam-6319	65	6	,	,	PUNCT
ejpam-6319	65	7	a.	a.	PROPN
ejpam-6319	65	8	e.	e.	PROPN
ejpam-6319	65	9	s.	s.	PROPN
ejpam-6319	65	10	h.	h.	PROPN
ejpam-6319	65	11	maharani	maharani	PROPN
ejpam-6319	65	12	/	/	SYM
ejpam-6319	65	13	eur	eur	PROPN
ejpam-6319	65	14	.	.	PUNCT
ejpam-6319	66	1	j.	j.	PROPN
ejpam-6319	66	2	pure	pure	PROPN
ejpam-6319	66	3	appl	appl	PROPN
ejpam-6319	66	4	.	.	PROPN
ejpam-6319	66	5	math	math	PROPN
ejpam-6319	66	6	,	,	PUNCT
ejpam-6319	66	7	18	18	NUM
ejpam-6319	66	8	(	(	PUNCT
ejpam-6319	66	9	3	3	NUM
ejpam-6319	66	10	)	)	PUNCT
ejpam-6319	66	11	(	(	PUNCT
ejpam-6319	66	12	2025	2025	NUM
ejpam-6319	66	13	)	)	PUNCT
ejpam-6319	66	14	,	,	PUNCT
ejpam-6319	66	15	6319	6319	NUM
ejpam-6319	66	16	4	4	NUM
ejpam-6319	66	17	of	of	ADP
ejpam-6319	66	18	13	13	NUM
ejpam-6319	66	19	additionally	additionally	ADV
ejpam-6319	66	20	,	,	PUNCT
ejpam-6319	66	21	we	we	PRON
ejpam-6319	66	22	require	require	VERB
ejpam-6319	66	23	some	some	DET
ejpam-6319	66	24	row	row	NOUN
ejpam-6319	66	25	and	and	CCONJ
ejpam-6319	66	26	column	column	NOUN
ejpam-6319	66	27	operations	operation	NOUN
ejpam-6319	66	28	in	in	ADP
ejpam-6319	66	29	our	our	PRON
ejpam-6319	66	30	proof	proof	NOUN
ejpam-6319	66	31	.	.	PUNCT
ejpam-6319	67	1	we	we	PRON
ejpam-6319	67	2	shall	shall	AUX
ejpam-6319	67	3	introduce	introduce	VERB
ejpam-6319	67	4	the	the	DET
ejpam-6319	67	5	i−th	i−th	PROPN
ejpam-6319	67	6	row	row	NOUN
ejpam-6319	67	7	of	of	ADP
ejpam-6319	67	8	a	a	DET
ejpam-6319	67	9	matrix	matrix	NOUN
ejpam-6319	67	10	,	,	PUNCT
ejpam-6319	67	11	ri	ri	NOUN
ejpam-6319	67	12	,	,	PUNCT
ejpam-6319	67	13	and	and	CCONJ
ejpam-6319	67	14	the	the	DET
ejpam-6319	67	15	i−th	i−th	PROPN
ejpam-6319	67	16	column	column	PROPN
ejpam-6319	67	17	,	,	PUNCT
ejpam-6319	67	18	ci	ci	PROPN
ejpam-6319	67	19	.	.	PROPN
ejpam-6319	67	20	2	2	NUM
ejpam-6319	67	21	.	.	X
ejpam-6319	67	22	main	main	ADJ
ejpam-6319	67	23	results	result	NOUN
ejpam-6319	67	24	in	in	ADP
ejpam-6319	67	25	this	this	DET
ejpam-6319	67	26	part	part	NOUN
ejpam-6319	67	27	,	,	PUNCT
ejpam-6319	67	28	we	we	PRON
ejpam-6319	67	29	discuss	discuss	VERB
ejpam-6319	67	30	the	the	DET
ejpam-6319	67	31	spectral	spectral	ADJ
ejpam-6319	67	32	radius	radius	NOUN
ejpam-6319	67	33	of	of	ADP
ejpam-6319	67	34	the	the	DET
ejpam-6319	67	35	coprime	coprime	NOUN
ejpam-6319	67	36	graph	graph	NOUN
ejpam-6319	67	37	for	for	ADP
ejpam-6319	67	38	the	the	DET
ejpam-6319	67	39	dihedral	dihedral	ADJ
ejpam-6319	67	40	group	group	NOUN
ejpam-6319	67	41	,	,	PUNCT
ejpam-6319	67	42	d2n	d2n	PROPN
ejpam-6319	67	43	,	,	PUNCT
ejpam-6319	67	44	with	with	ADP
ejpam-6319	67	45	n	n	PRON
ejpam-6319	67	46	as	as	ADP
ejpam-6319	67	47	a	a	DET
ejpam-6319	67	48	prime	prime	ADJ
ejpam-6319	67	49	number	number	NOUN
ejpam-6319	67	50	or	or	CCONJ
ejpam-6319	67	51	n	n	NOUN
ejpam-6319	67	52	=	=	SYM
ejpam-6319	67	53	2k	2k	PROPN
ejpam-6319	67	54	or	or	CCONJ
ejpam-6319	67	55	n	n	NOUN
ejpam-6319	67	56	=	=	SYM
ejpam-6319	67	57	pk	pk	NOUN
ejpam-6319	67	58	,	,	PUNCT
ejpam-6319	67	59	where	where	SCONJ
ejpam-6319	67	60	p	p	PROPN
ejpam-6319	67	61	̸=	̸=	PROPN
ejpam-6319	67	62	2	2	NUM
ejpam-6319	67	63	,	,	PUNCT
ejpam-6319	67	64	p	p	X
ejpam-6319	67	65	,	,	PUNCT
ejpam-6319	67	66	k	k	PROPN
ejpam-6319	67	67	∈	∈	PROPN
ejpam-6319	67	68	n	n	NOUN
ejpam-6319	67	69	corresponding	correspond	VERB
ejpam-6319	67	70	with	with	ADP
ejpam-6319	67	71	a(γd2n	a(γd2n	PROPN
ejpam-6319	67	72	)	)	PUNCT
ejpam-6319	67	73	,	,	PUNCT
ejpam-6319	67	74	l(γd2n	l(γd2n	PROPN
ejpam-6319	67	75	)	)	PUNCT
ejpam-6319	67	76	,	,	PUNCT
ejpam-6319	67	77	and	and	CCONJ
ejpam-6319	67	78	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	67	79	)	)	PUNCT
ejpam-6319	67	80	.	.	PUNCT
ejpam-6319	68	1	2.1	2.1	NUM
ejpam-6319	68	2	.	.	PUNCT
ejpam-6319	69	1	adjacency	adjacency	PROPN
ejpam-6319	69	2	energy	energy	NOUN
ejpam-6319	69	3	we	we	PRON
ejpam-6319	69	4	first	first	ADV
ejpam-6319	69	5	prove	prove	VERB
ejpam-6319	69	6	the	the	DET
ejpam-6319	69	7	adjacency	adjacency	NOUN
ejpam-6319	69	8	matrix	matrix	NOUN
ejpam-6319	69	9	of	of	ADP
ejpam-6319	69	10	the	the	DET
ejpam-6319	69	11	coprime	coprime	NOUN
ejpam-6319	69	12	graph	graph	NOUN
ejpam-6319	69	13	for	for	ADP
ejpam-6319	69	14	d2n	d2n	PROPN
ejpam-6319	69	15	.	.	PUNCT
ejpam-6319	70	1	theorem	theorem	NOUN
ejpam-6319	70	2	3	3	X
ejpam-6319	70	3	.	.	PUNCT
ejpam-6319	71	1	let	let	VERB
ejpam-6319	71	2	γd2n	γd2n	PROPN
ejpam-6319	71	3	be	be	AUX
ejpam-6319	71	4	the	the	DET
ejpam-6319	71	5	coprime	coprime	ADJ
ejpam-6319	71	6	graph	graph	NOUN
ejpam-6319	71	7	for	for	ADP
ejpam-6319	71	8	d2n	d2n	PROPN
ejpam-6319	71	9	with	with	ADP
ejpam-6319	71	10	n	n	PROPN
ejpam-6319	71	11	is	be	AUX
ejpam-6319	71	12	a	a	DET
ejpam-6319	71	13	prime	prime	ADJ
ejpam-6319	71	14	number	number	NOUN
ejpam-6319	71	15	or	or	CCONJ
ejpam-6319	71	16	n	n	NOUN
ejpam-6319	71	17	=	=	SYM
ejpam-6319	71	18	pk	pk	NOUN
ejpam-6319	71	19	,	,	PUNCT
ejpam-6319	71	20	p	p	PROPN
ejpam-6319	71	21	̸=	̸=	PROPN
ejpam-6319	71	22	2	2	NUM
ejpam-6319	71	23	for	for	ADP
ejpam-6319	71	24	a	a	DET
ejpam-6319	71	25	k	k	PROPN
ejpam-6319	71	26	∈	∈	PROPN
ejpam-6319	71	27	n	n	CCONJ
ejpam-6319	71	28	,	,	PUNCT
ejpam-6319	71	29	then	then	ADV
ejpam-6319	71	30	pa(γd2n	pa(γd2n	NOUN
ejpam-6319	71	31	)	)	PUNCT
ejpam-6319	71	32	(	(	PUNCT
ejpam-6319	71	33	λ	λ	X
ejpam-6319	71	34	)	)	PUNCT
ejpam-6319	71	35	=	=	SYM
ejpam-6319	72	1	λ2n−3	λ2n−3	PROPN
ejpam-6319	72	2	(	(	PUNCT
ejpam-6319	72	3	λ3	λ3	PROPN
ejpam-6319	72	4	−	−	PROPN
ejpam-6319	72	5	(	(	PUNCT
ejpam-6319	72	6	n2	n2	NOUN
ejpam-6319	72	7	+	+	CCONJ
ejpam-6319	72	8	n−	n−	NOUN
ejpam-6319	72	9	1	1	NUM
ejpam-6319	72	10	)	)	PUNCT
ejpam-6319	72	11	λ+	λ+	PUNCT
ejpam-6319	72	12	2n(n−	2n(n−	NUM
ejpam-6319	72	13	1	1	NUM
ejpam-6319	72	14	)	)	PUNCT
ejpam-6319	72	15	)	)	PUNCT
ejpam-6319	72	16	.	.	PUNCT
ejpam-6319	73	1	proof	proof	NOUN
ejpam-6319	73	2	.	.	PUNCT
ejpam-6319	74	1	from	from	ADP
ejpam-6319	74	2	theorem	theorem	NOUN
ejpam-6319	74	3	1	1	NUM
ejpam-6319	74	4	,	,	PUNCT
ejpam-6319	74	5	γd2n	γd2n	PROPN
ejpam-6319	74	6	,	,	PUNCT
ejpam-6319	74	7	for	for	ADP
ejpam-6319	74	8	d2n	d2n	PROPN
ejpam-6319	74	9	with	with	ADP
ejpam-6319	74	10	n	n	PROPN
ejpam-6319	74	11	is	be	AUX
ejpam-6319	74	12	a	a	DET
ejpam-6319	74	13	prime	prime	ADJ
ejpam-6319	74	14	number	number	NOUN
ejpam-6319	74	15	or	or	CCONJ
ejpam-6319	74	16	n	n	NOUN
ejpam-6319	74	17	=	=	SYM
ejpam-6319	74	18	pk	pk	NOUN
ejpam-6319	74	19	,	,	PUNCT
ejpam-6319	74	20	p	p	PROPN
ejpam-6319	74	21	̸=	̸=	PROPN
ejpam-6319	74	22	2	2	NUM
ejpam-6319	74	23	for	for	ADP
ejpam-6319	74	24	a	a	DET
ejpam-6319	74	25	k	k	PROPN
ejpam-6319	74	26	∈	∈	PROPN
ejpam-6319	74	27	n	n	CCONJ
ejpam-6319	74	28	,	,	PUNCT
ejpam-6319	74	29	is	be	AUX
ejpam-6319	74	30	a	a	DET
ejpam-6319	74	31	complete	complete	ADJ
ejpam-6319	74	32	tripartite	tripartite	ADJ
ejpam-6319	74	33	graph	graph	NOUN
ejpam-6319	74	34	,	,	PUNCT
ejpam-6319	74	35	then	then	ADV
ejpam-6319	74	36	we	we	PRON
ejpam-6319	74	37	have	have	VERB
ejpam-6319	74	38	a	a	DET
ejpam-6319	74	39	2n×	2n×	NUM
ejpam-6319	74	40	2n	2n	NUM
ejpam-6319	74	41	adjacency	adjacency	NOUN
ejpam-6319	74	42	matrix	matrix	NOUN
ejpam-6319	74	43	of	of	ADP
ejpam-6319	74	44	γd2n	γd2n	PROPN
ejpam-6319	74	45	,	,	PUNCT
ejpam-6319	74	46	a(γd2n	a(γd2n	X
ejpam-6319	74	47	)	)	PUNCT
ejpam-6319	74	48	=	=	PUNCT
ejpam-6319	75	1	e	e	X
ejpam-6319	75	2	a	a	DET
ejpam-6319	75	3	a2	a2	PROPN
ejpam-6319	75	4	.	.	PUNCT
ejpam-6319	75	5	.	.	PUNCT
ejpam-6319	75	6	.	.	PUNCT
ejpam-6319	76	1	an−1	an−1	PROPN
ejpam-6319	76	2	b	b	PROPN
ejpam-6319	76	3	ab	ab	PROPN
ejpam-6319	76	4	.	.	PUNCT
ejpam-6319	76	5	.	.	PUNCT
ejpam-6319	76	6	.	.	PUNCT
ejpam-6319	77	1	an−1b	an−1b	PRON
ejpam-6319	77	2			NOUN
ejpam-6319	77	3	e	e	NOUN
ejpam-6319	77	4	0	0	NUM
ejpam-6319	77	5	1	1	NUM
ejpam-6319	77	6	1	1	NUM
ejpam-6319	77	7	.	.	PUNCT
ejpam-6319	77	8	.	.	PUNCT
ejpam-6319	77	9	.	.	PUNCT
ejpam-6319	78	1	1	1	NUM
ejpam-6319	78	2	1	1	NUM
ejpam-6319	78	3	1	1	NUM
ejpam-6319	78	4	.	.	PUNCT
ejpam-6319	78	5	.	.	PUNCT
ejpam-6319	78	6	.	.	PUNCT
ejpam-6319	79	1	1	1	NUM
ejpam-6319	79	2	a	a	DET
ejpam-6319	79	3	1	1	NUM
ejpam-6319	79	4	0	0	NUM
ejpam-6319	79	5	0	0	NUM
ejpam-6319	79	6	.	.	PUNCT
ejpam-6319	79	7	.	.	PUNCT
ejpam-6319	80	1	.	.	PUNCT
ejpam-6319	81	1	0	0	NUM
ejpam-6319	81	2	1	1	NUM
ejpam-6319	81	3	1	1	NUM
ejpam-6319	81	4	.	.	PUNCT
ejpam-6319	81	5	.	.	PUNCT
ejpam-6319	81	6	.	.	PUNCT
ejpam-6319	82	1	1	1	NUM
ejpam-6319	82	2	a2	a2	PROPN
ejpam-6319	82	3	1	1	NUM
ejpam-6319	82	4	0	0	NUM
ejpam-6319	82	5	0	0	NUM
ejpam-6319	82	6	.	.	PUNCT
ejpam-6319	82	7	.	.	PUNCT
ejpam-6319	82	8	.	.	PUNCT
ejpam-6319	83	1	0	0	NUM
ejpam-6319	83	2	1	1	NUM
ejpam-6319	83	3	1	1	NUM
ejpam-6319	83	4	.	.	PUNCT
ejpam-6319	83	5	.	.	PUNCT
ejpam-6319	83	6	.	.	PUNCT
ejpam-6319	84	1	1	1	NUM
ejpam-6319	84	2	...	...	PUNCT
ejpam-6319	84	3	...	...	PUNCT
ejpam-6319	84	4	...	...	PUNCT
ejpam-6319	84	5	...	...	PUNCT
ejpam-6319	84	6	.	.	PUNCT
ejpam-6319	84	7	.	.	PUNCT
ejpam-6319	84	8	.	.	PUNCT
ejpam-6319	85	1	...	...	PUNCT
ejpam-6319	85	2	...	...	PUNCT
ejpam-6319	85	3	...	...	PUNCT
ejpam-6319	85	4	.	.	PUNCT
ejpam-6319	85	5	.	.	PUNCT
ejpam-6319	86	1	.	.	PUNCT
ejpam-6319	87	1	...	...	PUNCT
ejpam-6319	88	1	an−1	an−1	ADV
ejpam-6319	88	2	1	1	NUM
ejpam-6319	88	3	0	0	NUM
ejpam-6319	88	4	0	0	NUM
ejpam-6319	88	5	.	.	PUNCT
ejpam-6319	88	6	.	.	PUNCT
ejpam-6319	89	1	.	.	PUNCT
ejpam-6319	90	1	0	0	NUM
ejpam-6319	90	2	1	1	NUM
ejpam-6319	90	3	1	1	NUM
ejpam-6319	90	4	.	.	PUNCT
ejpam-6319	90	5	.	.	PUNCT
ejpam-6319	90	6	.	.	PUNCT
ejpam-6319	91	1	1	1	NUM
ejpam-6319	91	2	b	b	SYM
ejpam-6319	91	3	1	1	NUM
ejpam-6319	91	4	1	1	NUM
ejpam-6319	91	5	1	1	NUM
ejpam-6319	91	6	.	.	PUNCT
ejpam-6319	91	7	.	.	PUNCT
ejpam-6319	91	8	.	.	PUNCT
ejpam-6319	92	1	1	1	NUM
ejpam-6319	92	2	0	0	NUM
ejpam-6319	92	3	0	0	NUM
ejpam-6319	92	4	.	.	PUNCT
ejpam-6319	92	5	.	.	PUNCT
ejpam-6319	92	6	.	.	PUNCT
ejpam-6319	92	7	0	0	PUNCT
ejpam-6319	93	1	ab	ab	NOUN
ejpam-6319	93	2	1	1	NUM
ejpam-6319	93	3	1	1	NUM
ejpam-6319	93	4	1	1	NUM
ejpam-6319	93	5	.	.	PUNCT
ejpam-6319	93	6	.	.	PUNCT
ejpam-6319	93	7	.	.	PUNCT
ejpam-6319	94	1	1	1	NUM
ejpam-6319	94	2	0	0	NUM
ejpam-6319	94	3	0	0	NUM
ejpam-6319	94	4	.	.	PUNCT
ejpam-6319	94	5	.	.	PUNCT
ejpam-6319	94	6	.	.	PUNCT
ejpam-6319	95	1	0	0	NUM
ejpam-6319	95	2	...	...	PUNCT
ejpam-6319	95	3	...	...	PUNCT
ejpam-6319	95	4	...	...	PUNCT
ejpam-6319	95	5	...	...	PUNCT
ejpam-6319	95	6	.	.	PUNCT
ejpam-6319	95	7	.	.	PUNCT
ejpam-6319	96	1	.	.	PUNCT
ejpam-6319	96	2	...	...	PUNCT
ejpam-6319	97	1	...	...	PUNCT
ejpam-6319	97	2	...	...	PUNCT
ejpam-6319	97	3	.	.	PUNCT
ejpam-6319	97	4	.	.	PUNCT
ejpam-6319	97	5	.	.	PUNCT
ejpam-6319	98	1	...	...	PUNCT
ejpam-6319	99	1	an−1b	an−1b	PUNCT
ejpam-6319	99	2	1	1	NUM
ejpam-6319	99	3	1	1	NUM
ejpam-6319	99	4	1	1	NUM
ejpam-6319	99	5	.	.	PUNCT
ejpam-6319	99	6	.	.	PUNCT
ejpam-6319	99	7	.	.	PUNCT
ejpam-6319	100	1	1	1	NUM
ejpam-6319	100	2	0	0	NUM
ejpam-6319	100	3	0	0	NUM
ejpam-6319	100	4	.	.	PUNCT
ejpam-6319	100	5	.	.	PUNCT
ejpam-6319	100	6	.	.	PUNCT
ejpam-6319	100	7	0	0	PUNCT
ejpam-6319	100	8	.	.	PUNCT
ejpam-6319	101	1	(	(	PUNCT
ejpam-6319	101	2	1	1	X
ejpam-6319	101	3	)	)	PUNCT
ejpam-6319	101	4	moreover	moreover	ADV
ejpam-6319	101	5	,	,	PUNCT
ejpam-6319	101	6	a(γd2n	a(γd2n	X
ejpam-6319	101	7	)	)	PUNCT
ejpam-6319	101	8	can	can	AUX
ejpam-6319	101	9	be	be	AUX
ejpam-6319	101	10	mentioned	mention	VERB
ejpam-6319	101	11	as	as	ADP
ejpam-6319	101	12	a(γd2n	a(γd2n	X
ejpam-6319	101	13	)	)	PUNCT
ejpam-6319	102	1	=	=	SYM
ejpam-6319	102	2			PROPN
ejpam-6319	102	3	0	0	NUM
ejpam-6319	102	4	j1×(n−1	j1×(n−1	PROPN
ejpam-6319	102	5	)	)	PUNCT
ejpam-6319	102	6	j1×n	j1×n	ADJ
ejpam-6319	102	7	j(n−1)×1	j(n−1)×1	NOUN
ejpam-6319	102	8	0n−1	0n−1	PROPN
ejpam-6319	102	9	j(n−1)×n	j(n−1)×n	PROPN
ejpam-6319	102	10	jn×1	jn×1	PROPN
ejpam-6319	102	11	jn×(n−1	jn×(n−1	PROPN
ejpam-6319	102	12	)	)	PUNCT
ejpam-6319	102	13	0n	0n	NOUN
ejpam-6319	102	14			PROPN
ejpam-6319	102	15	.	.	PUNCT
ejpam-6319	103	1	the	the	DET
ejpam-6319	103	2	characteristic	characteristic	ADJ
ejpam-6319	103	3	formula	formula	NOUN
ejpam-6319	103	4	of	of	ADP
ejpam-6319	103	5	a(γd2n	a(γd2n	X
ejpam-6319	103	6	)	)	PUNCT
ejpam-6319	103	7	is	be	AUX
ejpam-6319	103	8	given	give	VERB
ejpam-6319	103	9	in	in	ADP
ejpam-6319	103	10	the	the	DET
ejpam-6319	103	11	following	follow	VERB
ejpam-6319	103	12	pa(γd2n	pa(γd2n	NOUN
ejpam-6319	103	13	)	)	PUNCT
ejpam-6319	103	14	(	(	PUNCT
ejpam-6319	103	15	λ	λ	X
ejpam-6319	103	16	)	)	PUNCT
ejpam-6319	103	17	=	=	SYM
ejpam-6319	103	18	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6319	103	19	λ	λ	PROPN
ejpam-6319	103	20	−j1×(n−1	−j1×(n−1	PROPN
ejpam-6319	103	21	)	)	PUNCT
ejpam-6319	103	22	−j1×n	−j1×n	PUNCT
ejpam-6319	104	1	−j(n−1)×1	−j(n−1)×1	PROPN
ejpam-6319	104	2	λin−1	λin−1	PROPN
ejpam-6319	104	3	−j(n−1)×n	−j(n−1)×n	PROPN
ejpam-6319	104	4	−jn×1	−jn×1	PUNCT
ejpam-6319	104	5	−jn×(n−1	−jn×(n−1	PROPN
ejpam-6319	104	6	)	)	PUNCT
ejpam-6319	104	7	λin	λin	NOUN
ejpam-6319	104	8	∣∣∣∣∣∣	∣∣∣∣∣∣	ADV
ejpam-6319	104	9	.	.	PUNCT
ejpam-6319	105	1	the	the	DET
ejpam-6319	105	2	proof	proof	NOUN
ejpam-6319	105	3	follows	follow	VERB
ejpam-6319	105	4	from	from	ADP
ejpam-6319	105	5	the	the	DET
ejpam-6319	105	6	following	follow	VERB
ejpam-6319	105	7	sequential	sequential	ADJ
ejpam-6319	105	8	steps	step	NOUN
ejpam-6319	105	9	:	:	PUNCT
ejpam-6319	105	10	m.	m.	NOUN
ejpam-6319	105	11	u.	u.	PROPN
ejpam-6319	105	12	romdhini	romdhini	PROPN
ejpam-6319	105	13	,	,	PUNCT
ejpam-6319	105	14	abdurahim	abdurahim	PRON
ejpam-6319	105	15	,	,	PUNCT
ejpam-6319	105	16	a.	a.	PROPN
ejpam-6319	105	17	e.	e.	PROPN
ejpam-6319	105	18	s.	s.	PROPN
ejpam-6319	105	19	h.	h.	PROPN
ejpam-6319	105	20	maharani	maharani	PROPN
ejpam-6319	105	21	/	/	SYM
ejpam-6319	105	22	eur	eur	PROPN
ejpam-6319	105	23	.	.	PUNCT
ejpam-6319	106	1	j.	j.	PROPN
ejpam-6319	106	2	pure	pure	PROPN
ejpam-6319	106	3	appl	appl	PROPN
ejpam-6319	106	4	.	.	PROPN
ejpam-6319	106	5	math	math	PROPN
ejpam-6319	106	6	,	,	PUNCT
ejpam-6319	106	7	18	18	NUM
ejpam-6319	106	8	(	(	PUNCT
ejpam-6319	106	9	3	3	NUM
ejpam-6319	106	10	)	)	PUNCT
ejpam-6319	106	11	(	(	PUNCT
ejpam-6319	106	12	2025	2025	NUM
ejpam-6319	106	13	)	)	PUNCT
ejpam-6319	106	14	,	,	PUNCT
ejpam-6319	106	15	6319	6319	NUM
ejpam-6319	106	16	5	5	NUM
ejpam-6319	106	17	of	of	ADP
ejpam-6319	106	18	13	13	NUM
ejpam-6319	106	19	(	(	PUNCT
ejpam-6319	106	20	i	i	NOUN
ejpam-6319	106	21	)	)	PUNCT
ejpam-6319	106	22	for	for	ADP
ejpam-6319	106	23	i	i	PROPN
ejpam-6319	106	24	=	=	SYM
ejpam-6319	106	25	1	1	NUM
ejpam-6319	106	26	,	,	PUNCT
ejpam-6319	106	27	2	2	NUM
ejpam-6319	106	28	,	,	PUNCT
ejpam-6319	106	29	.	.	PUNCT
ejpam-6319	106	30	.	.	PUNCT
ejpam-6319	107	1	.	.	PUNCT
ejpam-6319	108	1	,	,	PUNCT
ejpam-6319	108	2	n	n	CCONJ
ejpam-6319	108	3	−	−	PROPN
ejpam-6319	108	4	1	1	NUM
ejpam-6319	108	5	,	,	PUNCT
ejpam-6319	108	6	we	we	PRON
ejpam-6319	108	7	replace	replace	VERB
ejpam-6319	108	8	elements	element	NOUN
ejpam-6319	108	9	in	in	ADP
ejpam-6319	108	10	the	the	DET
ejpam-6319	108	11	n	n	NOUN
ejpam-6319	108	12	+	+	CCONJ
ejpam-6319	108	13	1	1	NUM
ejpam-6319	108	14	+	+	CCONJ
ejpam-6319	108	15	i	i	PROPN
ejpam-6319	108	16	-	-	PUNCT
ejpam-6319	108	17	th	th	VERB
ejpam-6319	108	18	row	row	NOUN
ejpam-6319	108	19	by	by	ADP
ejpam-6319	108	20	subtracting	subtract	VERB
ejpam-6319	108	21	the	the	DET
ejpam-6319	108	22	corresponding	corresponding	ADJ
ejpam-6319	108	23	element	element	NOUN
ejpam-6319	108	24	of	of	ADP
ejpam-6319	108	25	the	the	PRON
ejpam-6319	108	26	n+	n+	NUM
ejpam-6319	108	27	1	1	NUM
ejpam-6319	108	28	+	+	CCONJ
ejpam-6319	108	29	i	i	PROPN
ejpam-6319	108	30	-	-	PUNCT
ejpam-6319	108	31	th	th	VERB
ejpam-6319	108	32	row	row	NOUN
ejpam-6319	108	33	from	from	ADP
ejpam-6319	108	34	the	the	DET
ejpam-6319	108	35	element	element	NOUN
ejpam-6319	108	36	in	in	ADP
ejpam-6319	108	37	the	the	DET
ejpam-6319	108	38	n+	n+	NUM
ejpam-6319	108	39	1	1	NUM
ejpam-6319	108	40	-	-	PUNCT
ejpam-6319	108	41	th	th	NUM
ejpam-6319	108	42	row	row	NOUN
ejpam-6319	108	43	,	,	PUNCT
ejpam-6319	108	44	or	or	CCONJ
ejpam-6319	108	45	in	in	ADP
ejpam-6319	108	46	other	other	ADJ
ejpam-6319	108	47	words	word	NOUN
ejpam-6319	108	48	,	,	PUNCT
ejpam-6319	108	49	rn+1+i	rn+1+i	NOUN
ejpam-6319	108	50	−→	−→	NOUN
ejpam-6319	108	51	rn+1+i	rn+1+i	NOUN
ejpam-6319	108	52	−rn+1	−rn+1	PROPN
ejpam-6319	108	53	.	.	PUNCT
ejpam-6319	109	1	(	(	PUNCT
ejpam-6319	109	2	ii	ii	NOUN
ejpam-6319	109	3	)	)	PUNCT
ejpam-6319	109	4	we	we	PRON
ejpam-6319	109	5	replace	replace	VERB
ejpam-6319	109	6	the	the	DET
ejpam-6319	109	7	elements	element	NOUN
ejpam-6319	109	8	of	of	ADP
ejpam-6319	109	9	the	the	DET
ejpam-6319	109	10	n+	n+	SYM
ejpam-6319	109	11	1	1	NUM
ejpam-6319	109	12	-	-	PUNCT
ejpam-6319	109	13	th	th	VERB
ejpam-6319	109	14	column	column	NOUN
ejpam-6319	109	15	with	with	ADP
ejpam-6319	109	16	the	the	DET
ejpam-6319	109	17	sum	sum	NOUN
ejpam-6319	109	18	of	of	ADP
ejpam-6319	109	19	the	the	DET
ejpam-6319	109	20	corresponding	corresponding	ADJ
ejpam-6319	109	21	elements	element	NOUN
ejpam-6319	109	22	in	in	ADP
ejpam-6319	109	23	columns	column	NOUN
ejpam-6319	109	24	numbered	number	VERB
ejpam-6319	109	25	n	n	PROPN
ejpam-6319	109	26	+	+	NUM
ejpam-6319	109	27	1	1	NUM
ejpam-6319	109	28	,	,	PUNCT
ejpam-6319	109	29	n	n	PROPN
ejpam-6319	109	30	+	+	NOUN
ejpam-6319	109	31	2	2	NUM
ejpam-6319	109	32	,	,	PUNCT
ejpam-6319	109	33	...	...	PUNCT
ejpam-6319	109	34	,	,	PUNCT
ejpam-6319	109	35	and	and	CCONJ
ejpam-6319	109	36	2n	2n	NUM
ejpam-6319	109	37	.	.	PUNCT
ejpam-6319	110	1	it	it	PRON
ejpam-6319	110	2	is	be	AUX
ejpam-6319	110	3	written	write	VERB
ejpam-6319	110	4	by	by	ADP
ejpam-6319	110	5	cn+1	cn+1	NUM
ejpam-6319	110	6	−→	−→	NOUN
ejpam-6319	110	7	cn+1	cn+1	NOUN
ejpam-6319	110	8	+	+	CCONJ
ejpam-6319	110	9	cn+2	cn+2	PRON
ejpam-6319	110	10	+	+	CCONJ
ejpam-6319	110	11	.	.	PUNCT
ejpam-6319	110	12	.	.	PUNCT
ejpam-6319	111	1	.+	.+	NOUN
ejpam-6319	111	2	c2n	c2n	NOUN
ejpam-6319	111	3	.	.	PUNCT
ejpam-6319	112	1	(	(	PUNCT
ejpam-6319	112	2	iii	iii	X
ejpam-6319	112	3	)	)	PUNCT
ejpam-6319	112	4	we	we	PRON
ejpam-6319	112	5	replace	replace	VERB
ejpam-6319	112	6	elements	element	NOUN
ejpam-6319	112	7	in	in	ADP
ejpam-6319	112	8	the	the	DET
ejpam-6319	112	9	n+1	n+1	NOUN
ejpam-6319	112	10	-	-	PUNCT
ejpam-6319	112	11	th	th	VERB
ejpam-6319	112	12	row	row	NOUN
ejpam-6319	112	13	by	by	ADP
ejpam-6319	112	14	subtraction	subtraction	NOUN
ejpam-6319	112	15	between	between	ADP
ejpam-6319	112	16	those	those	DET
ejpam-6319	112	17	elements	element	NOUN
ejpam-6319	112	18	and	and	CCONJ
ejpam-6319	112	19	the	the	DET
ejpam-6319	112	20	elements	element	NOUN
ejpam-6319	112	21	in	in	ADP
ejpam-6319	112	22	the	the	DET
ejpam-6319	112	23	first	first	ADJ
ejpam-6319	112	24	row	row	NOUN
ejpam-6319	112	25	,	,	PUNCT
ejpam-6319	112	26	or	or	CCONJ
ejpam-6319	112	27	equivalently	equivalently	ADV
ejpam-6319	112	28	,	,	PUNCT
ejpam-6319	112	29	rn+1	rn+1	VERB
ejpam-6319	112	30	−→	−→	NOUN
ejpam-6319	112	31	rn+1	rn+1	X
ejpam-6319	112	32	−r1	−r1	PROPN
ejpam-6319	112	33	.	.	PUNCT
ejpam-6319	113	1	(	(	PUNCT
ejpam-6319	113	2	iv	iv	X
ejpam-6319	113	3	)	)	PUNCT
ejpam-6319	113	4	we	we	PRON
ejpam-6319	113	5	replace	replace	VERB
ejpam-6319	113	6	the	the	DET
ejpam-6319	113	7	first	first	ADJ
ejpam-6319	113	8	column	column	NOUN
ejpam-6319	113	9	by	by	ADP
ejpam-6319	113	10	adding	add	VERB
ejpam-6319	113	11	its	its	PRON
ejpam-6319	113	12	own	own	ADJ
ejpam-6319	113	13	elements	element	NOUN
ejpam-6319	113	14	and	and	CCONJ
ejpam-6319	113	15	λ+1	λ+1	X
ejpam-6319	113	16	λ+n	λ+n	PROPN
ejpam-6319	113	17	times	time	NOUN
ejpam-6319	113	18	the	the	DET
ejpam-6319	113	19	elements	element	NOUN
ejpam-6319	113	20	of	of	ADP
ejpam-6319	113	21	the	the	DET
ejpam-6319	113	22	n+	n+	SYM
ejpam-6319	113	23	1	1	NUM
ejpam-6319	113	24	-	-	PUNCT
ejpam-6319	113	25	th	th	X
ejpam-6319	113	26	column	column	NOUN
ejpam-6319	113	27	,	,	PUNCT
ejpam-6319	113	28	or	or	CCONJ
ejpam-6319	113	29	in	in	ADP
ejpam-6319	113	30	other	other	ADJ
ejpam-6319	113	31	words	word	NOUN
ejpam-6319	113	32	,	,	PUNCT
ejpam-6319	113	33	c1	c1	PROPN
ejpam-6319	113	34	−→	−→	NOUN
ejpam-6319	113	35	c1	c1	PROPN
ejpam-6319	113	36	+	+	CCONJ
ejpam-6319	113	37	(	(	PUNCT
ejpam-6319	113	38	λ+1	λ+1	NUM
ejpam-6319	113	39	λ+n	λ+n	X
ejpam-6319	113	40	)	)	PUNCT
ejpam-6319	113	41	cn+1	cn+1	VERB
ejpam-6319	113	42	.	.	PUNCT
ejpam-6319	114	1	(	(	PUNCT
ejpam-6319	114	2	v	v	NOUN
ejpam-6319	114	3	)	)	PUNCT
ejpam-6319	114	4	for	for	ADP
ejpam-6319	114	5	i	i	PROPN
ejpam-6319	114	6	=	=	SYM
ejpam-6319	114	7	1	1	NUM
ejpam-6319	114	8	,	,	PUNCT
ejpam-6319	114	9	2	2	NUM
ejpam-6319	114	10	,	,	PUNCT
ejpam-6319	114	11	.	.	PUNCT
ejpam-6319	114	12	.	.	PUNCT
ejpam-6319	115	1	.	.	PUNCT
ejpam-6319	116	1	,	,	PUNCT
ejpam-6319	116	2	n−2	n−2	PROPN
ejpam-6319	116	3	,	,	PUNCT
ejpam-6319	116	4	the	the	DET
ejpam-6319	116	5	2+i	2+i	PROPN
ejpam-6319	116	6	-	-	PUNCT
ejpam-6319	116	7	th	th	VERB
ejpam-6319	116	8	row	row	NOUN
ejpam-6319	116	9	is	be	AUX
ejpam-6319	116	10	replaced	replace	VERB
ejpam-6319	116	11	by	by	ADP
ejpam-6319	116	12	subtraction	subtraction	NOUN
ejpam-6319	116	13	between	between	ADP
ejpam-6319	116	14	the	the	DET
ejpam-6319	116	15	elements	element	NOUN
ejpam-6319	116	16	of	of	ADP
ejpam-6319	116	17	the	the	DET
ejpam-6319	116	18	2	2	NUM
ejpam-6319	116	19	+	+	NUM
ejpam-6319	116	20	ith	ith	NOUN
ejpam-6319	116	21	row	row	NOUN
ejpam-6319	116	22	and	and	CCONJ
ejpam-6319	116	23	the	the	DET
ejpam-6319	116	24	second	second	ADJ
ejpam-6319	116	25	row	row	NOUN
ejpam-6319	116	26	,	,	PUNCT
ejpam-6319	116	27	and	and	CCONJ
ejpam-6319	116	28	is	be	AUX
ejpam-6319	116	29	expressed	express	VERB
ejpam-6319	116	30	as	as	ADP
ejpam-6319	116	31	r2+i	r2+i	PROPN
ejpam-6319	116	32	−→	−→	NOUN
ejpam-6319	116	33	r2+i	r2+i	PROPN
ejpam-6319	116	34	−r2	−r2	PROPN
ejpam-6319	116	35	.	.	PROPN
ejpam-6319	117	1	(	(	PUNCT
ejpam-6319	117	2	vi	vi	X
ejpam-6319	117	3	)	)	PUNCT
ejpam-6319	117	4	the	the	DET
ejpam-6319	117	5	second	second	ADJ
ejpam-6319	117	6	column	column	NOUN
ejpam-6319	117	7	is	be	AUX
ejpam-6319	117	8	replaced	replace	VERB
ejpam-6319	117	9	by	by	ADP
ejpam-6319	117	10	the	the	DET
ejpam-6319	117	11	sum	sum	NOUN
ejpam-6319	117	12	of	of	ADP
ejpam-6319	117	13	the	the	DET
ejpam-6319	117	14	second	second	ADJ
ejpam-6319	117	15	,	,	PUNCT
ejpam-6319	117	16	third	third	ADJ
ejpam-6319	117	17	,	,	PUNCT
ejpam-6319	117	18	fourth	fourth	ADJ
ejpam-6319	117	19	,	,	PUNCT
ejpam-6319	117	20	...	...	PUNCT
ejpam-6319	117	21	,	,	PUNCT
ejpam-6319	117	22	and	and	CCONJ
ejpam-6319	117	23	n	n	CCONJ
ejpam-6319	117	24	-	-	PUNCT
ejpam-6319	117	25	th	th	VERB
ejpam-6319	117	26	columns	column	NOUN
ejpam-6319	117	27	,	,	PUNCT
ejpam-6319	117	28	and	and	CCONJ
ejpam-6319	117	29	is	be	AUX
ejpam-6319	117	30	stated	state	VERB
ejpam-6319	117	31	as	as	ADP
ejpam-6319	117	32	c2	c2	PROPN
ejpam-6319	117	33	−→	−→	PROPN
ejpam-6319	117	34	c2	c2	PROPN
ejpam-6319	117	35	+	+	CCONJ
ejpam-6319	117	36	c3	c3	PROPN
ejpam-6319	117	37	+	+	X
ejpam-6319	117	38	.	.	PUNCT
ejpam-6319	117	39	.	.	PUNCT
ejpam-6319	118	1	.+	.+	NOUN
ejpam-6319	119	1	cn	cn	PROPN
ejpam-6319	119	2	.	.	PUNCT
ejpam-6319	120	1	hence	hence	ADV
ejpam-6319	120	2	,	,	PUNCT
ejpam-6319	120	3	pa(γd2n	pa(γd2n	NOUN
ejpam-6319	120	4	)	)	PUNCT
ejpam-6319	120	5	(	(	PUNCT
ejpam-6319	120	6	λ	λ	X
ejpam-6319	120	7	)	)	PUNCT
ejpam-6319	120	8	=	=	SYM
ejpam-6319	121	1	λ2n−3	λ2n−3	PROPN
ejpam-6319	121	2	(	(	PUNCT
ejpam-6319	121	3	λ3	λ3	PROPN
ejpam-6319	121	4	−	−	PROPN
ejpam-6319	121	5	(	(	PUNCT
ejpam-6319	121	6	n2	n2	NOUN
ejpam-6319	121	7	+	+	CCONJ
ejpam-6319	121	8	n−	n−	NOUN
ejpam-6319	121	9	1	1	NUM
ejpam-6319	121	10	)	)	PUNCT
ejpam-6319	121	11	λ+	λ+	PUNCT
ejpam-6319	121	12	2n(n−	2n(n−	NUM
ejpam-6319	121	13	1	1	NUM
ejpam-6319	121	14	)	)	PUNCT
ejpam-6319	121	15	)	)	PUNCT
ejpam-6319	121	16	.	.	PUNCT
ejpam-6319	122	1	theorem	theorem	ADJ
ejpam-6319	122	2	4	4	NUM
ejpam-6319	122	3	.	.	PUNCT
ejpam-6319	123	1	let	let	VERB
ejpam-6319	123	2	γd2n	γd2n	PROPN
ejpam-6319	123	3	be	be	AUX
ejpam-6319	123	4	the	the	DET
ejpam-6319	123	5	coprime	coprime	ADJ
ejpam-6319	123	6	graph	graph	NOUN
ejpam-6319	123	7	for	for	ADP
ejpam-6319	123	8	d2n	d2n	PROPN
ejpam-6319	123	9	with	with	ADP
ejpam-6319	123	10	n	n	NOUN
ejpam-6319	123	11	=	=	SYM
ejpam-6319	123	12	2k	2k	NUM
ejpam-6319	123	13	,	,	PUNCT
ejpam-6319	123	14	k	k	PROPN
ejpam-6319	123	15	∈	∈	PROPN
ejpam-6319	123	16	n	n	CCONJ
ejpam-6319	123	17	,	,	PUNCT
ejpam-6319	123	18	then	then	ADV
ejpam-6319	123	19	pa(γd2n	pa(γd2n	NOUN
ejpam-6319	123	20	)	)	PUNCT
ejpam-6319	123	21	(	(	PUNCT
ejpam-6319	123	22	λ	λ	X
ejpam-6319	123	23	)	)	PUNCT
ejpam-6319	123	24	=	=	SYM
ejpam-6319	124	1	λ2n−2	λ2n−2	PROPN
ejpam-6319	124	2	(	(	PUNCT
ejpam-6319	124	3	λ−	λ−	PROPN
ejpam-6319	124	4	√	√	PROPN
ejpam-6319	125	1	2n−	2n−	NUM
ejpam-6319	125	2	1	1	NUM
ejpam-6319	125	3	)	)	PUNCT
ejpam-6319	125	4	(	(	PUNCT
ejpam-6319	125	5	λ+	λ+	NUM
ejpam-6319	125	6	√	√	INTJ
ejpam-6319	125	7	2n−	2n−	NUM
ejpam-6319	125	8	1	1	NUM
ejpam-6319	125	9	)	)	PUNCT
ejpam-6319	125	10	.	.	PUNCT
ejpam-6319	126	1	proof	proof	NOUN
ejpam-6319	126	2	.	.	PUNCT
ejpam-6319	127	1	according	accord	VERB
ejpam-6319	127	2	to	to	ADP
ejpam-6319	127	3	theorem	theorem	NOUN
ejpam-6319	127	4	2	2	NUM
ejpam-6319	127	5	,	,	PUNCT
ejpam-6319	127	6	γd2n	γd2n	PROPN
ejpam-6319	127	7	,	,	PUNCT
ejpam-6319	127	8	for	for	ADP
ejpam-6319	127	9	d2n	d2n	PROPN
ejpam-6319	127	10	with	with	ADP
ejpam-6319	127	11	n	n	NOUN
ejpam-6319	127	12	=	=	SYM
ejpam-6319	127	13	2k	2k	NUM
ejpam-6319	127	14	,	,	PUNCT
ejpam-6319	127	15	k	k	PROPN
ejpam-6319	127	16	∈	∈	PROPN
ejpam-6319	127	17	n	n	CCONJ
ejpam-6319	127	18	,	,	PUNCT
ejpam-6319	127	19	is	be	AUX
ejpam-6319	127	20	a	a	DET
ejpam-6319	127	21	complete	complete	ADJ
ejpam-6319	127	22	bipartite	bipartite	NOUN
ejpam-6319	127	23	graph	graph	NOUN
ejpam-6319	127	24	,	,	PUNCT
ejpam-6319	127	25	then	then	ADV
ejpam-6319	127	26	we	we	PRON
ejpam-6319	127	27	provide	provide	VERB
ejpam-6319	127	28	a	a	DET
ejpam-6319	127	29	2n×	2n×	NUM
ejpam-6319	127	30	2n	2n	NUM
ejpam-6319	127	31	adjacency	adjacency	NOUN
ejpam-6319	127	32	matrix	matrix	NOUN
ejpam-6319	127	33	of	of	ADP
ejpam-6319	127	34	γd2n	γd2n	PROPN
ejpam-6319	127	35	.	.	PUNCT
ejpam-6319	128	1	a(γd2n	a(γd2n	PUNCT
ejpam-6319	128	2	)	)	PUNCT
ejpam-6319	128	3	=	=	PUNCT
ejpam-6319	128	4			NOUN
ejpam-6319	128	5	0	0	NUM
ejpam-6319	128	6	1	1	NUM
ejpam-6319	128	7	1	1	NUM
ejpam-6319	128	8	.	.	PUNCT
ejpam-6319	128	9	.	.	PUNCT
ejpam-6319	128	10	.	.	PUNCT
ejpam-6319	129	1	1	1	NUM
ejpam-6319	129	2	1	1	NUM
ejpam-6319	129	3	1	1	NUM
ejpam-6319	129	4	.	.	PUNCT
ejpam-6319	129	5	.	.	PUNCT
ejpam-6319	129	6	.	.	PUNCT
ejpam-6319	130	1	1	1	NUM
ejpam-6319	130	2	1	1	NUM
ejpam-6319	130	3	0	0	NUM
ejpam-6319	130	4	0	0	NUM
ejpam-6319	130	5	.	.	PUNCT
ejpam-6319	130	6	.	.	PUNCT
ejpam-6319	130	7	.	.	PUNCT
ejpam-6319	131	1	0	0	NUM
ejpam-6319	132	1	0	0	NUM
ejpam-6319	132	2	0	0	NUM
ejpam-6319	132	3	.	.	PUNCT
ejpam-6319	132	4	.	.	PUNCT
ejpam-6319	132	5	.	.	PUNCT
ejpam-6319	133	1	0	0	NUM
ejpam-6319	134	1	1	1	NUM
ejpam-6319	134	2	0	0	NUM
ejpam-6319	134	3	0	0	NUM
ejpam-6319	134	4	.	.	PUNCT
ejpam-6319	134	5	.	.	PUNCT
ejpam-6319	134	6	.	.	PUNCT
ejpam-6319	135	1	0	0	NUM
ejpam-6319	136	1	0	0	NUM
ejpam-6319	136	2	0	0	NUM
ejpam-6319	136	3	.	.	PUNCT
ejpam-6319	136	4	.	.	PUNCT
ejpam-6319	137	1	.	.	PUNCT
ejpam-6319	138	1	0	0	NUM
ejpam-6319	138	2	...	...	PUNCT
ejpam-6319	138	3	...	...	PUNCT
ejpam-6319	138	4	...	...	PUNCT
ejpam-6319	138	5	.	.	PUNCT
ejpam-6319	138	6	.	.	PUNCT
ejpam-6319	139	1	.	.	PUNCT
ejpam-6319	139	2	...	...	PUNCT
ejpam-6319	140	1	...	...	PUNCT
ejpam-6319	140	2	...	...	PUNCT
ejpam-6319	140	3	.	.	PUNCT
ejpam-6319	140	4	.	.	PUNCT
ejpam-6319	141	1	.	.	PUNCT
ejpam-6319	142	1	...	...	PUNCT
ejpam-6319	143	1	1	1	NUM
ejpam-6319	143	2	0	0	NUM
ejpam-6319	143	3	0	0	NUM
ejpam-6319	143	4	.	.	PUNCT
ejpam-6319	143	5	.	.	PUNCT
ejpam-6319	143	6	.	.	PUNCT
ejpam-6319	144	1	0	0	NUM
ejpam-6319	145	1	0	0	NUM
ejpam-6319	145	2	0	0	NUM
ejpam-6319	145	3	.	.	PUNCT
ejpam-6319	145	4	.	.	PUNCT
ejpam-6319	145	5	.	.	PUNCT
ejpam-6319	146	1	0	0	NUM
ejpam-6319	147	1	1	1	NUM
ejpam-6319	147	2	0	0	NUM
ejpam-6319	147	3	0	0	NUM
ejpam-6319	147	4	.	.	PUNCT
ejpam-6319	147	5	.	.	PUNCT
ejpam-6319	147	6	.	.	PUNCT
ejpam-6319	148	1	0	0	NUM
ejpam-6319	149	1	0	0	NUM
ejpam-6319	149	2	0	0	NUM
ejpam-6319	149	3	.	.	PUNCT
ejpam-6319	149	4	.	.	PUNCT
ejpam-6319	149	5	.	.	PUNCT
ejpam-6319	150	1	0	0	NUM
ejpam-6319	151	1	1	1	NUM
ejpam-6319	151	2	0	0	NUM
ejpam-6319	151	3	0	0	NUM
ejpam-6319	151	4	.	.	PUNCT
ejpam-6319	151	5	.	.	PUNCT
ejpam-6319	151	6	.	.	PUNCT
ejpam-6319	152	1	0	0	NUM
ejpam-6319	153	1	0	0	NUM
ejpam-6319	153	2	0	0	NUM
ejpam-6319	153	3	.	.	PUNCT
ejpam-6319	153	4	.	.	PUNCT
ejpam-6319	154	1	.	.	PUNCT
ejpam-6319	155	1	0	0	NUM
ejpam-6319	155	2	...	...	PUNCT
ejpam-6319	155	3	...	...	PUNCT
ejpam-6319	155	4	...	...	PUNCT
ejpam-6319	155	5	.	.	PUNCT
ejpam-6319	155	6	.	.	PUNCT
ejpam-6319	156	1	.	.	PUNCT
ejpam-6319	156	2	...	...	PUNCT
ejpam-6319	157	1	...	...	PUNCT
ejpam-6319	157	2	...	...	PUNCT
ejpam-6319	157	3	.	.	PUNCT
ejpam-6319	157	4	.	.	PUNCT
ejpam-6319	158	1	.	.	PUNCT
ejpam-6319	159	1	...	...	PUNCT
ejpam-6319	160	1	1	1	NUM
ejpam-6319	160	2	0	0	NUM
ejpam-6319	160	3	0	0	NUM
ejpam-6319	160	4	.	.	PUNCT
ejpam-6319	160	5	.	.	PUNCT
ejpam-6319	160	6	.	.	PUNCT
ejpam-6319	161	1	0	0	NUM
ejpam-6319	162	1	0	0	NUM
ejpam-6319	162	2	0	0	NUM
ejpam-6319	162	3	.	.	PUNCT
ejpam-6319	162	4	.	.	PUNCT
ejpam-6319	162	5	.	.	PUNCT
ejpam-6319	163	1	0	0	PUNCT
ejpam-6319	164	1			PROPN
ejpam-6319	164	2	.	.	PUNCT
ejpam-6319	165	1	observe	observe	VERB
ejpam-6319	165	2	that	that	SCONJ
ejpam-6319	165	3	a(γd2n	a(γd2n	PUNCT
ejpam-6319	165	4	)	)	PUNCT
ejpam-6319	165	5	is	be	AUX
ejpam-6319	165	6	a(γd2n	a(γd2n	PRON
ejpam-6319	165	7	)	)	PUNCT
ejpam-6319	165	8	=	=	SYM
ejpam-6319	166	1	(	(	PUNCT
ejpam-6319	166	2	0	0	NUM
ejpam-6319	166	3	j1×(2n−1	j1×(2n−1	ADJ
ejpam-6319	166	4	)	)	PUNCT
ejpam-6319	166	5	j(2n−1)×1	j(2n−1)×1	NOUN
ejpam-6319	166	6	02n−1	02n−1	ADJ
ejpam-6319	166	7	)	)	PUNCT
ejpam-6319	166	8	.	.	PUNCT
ejpam-6319	167	1	m.	m.	PROPN
ejpam-6319	167	2	u.	u.	PROPN
ejpam-6319	167	3	romdhini	romdhini	PROPN
ejpam-6319	167	4	,	,	PUNCT
ejpam-6319	167	5	abdurahim	abdurahim	PRON
ejpam-6319	167	6	,	,	PUNCT
ejpam-6319	167	7	a.	a.	PROPN
ejpam-6319	167	8	e.	e.	PROPN
ejpam-6319	167	9	s.	s.	PROPN
ejpam-6319	167	10	h.	h.	PROPN
ejpam-6319	167	11	maharani	maharani	PROPN
ejpam-6319	167	12	/	/	SYM
ejpam-6319	167	13	eur	eur	PROPN
ejpam-6319	167	14	.	.	PUNCT
ejpam-6319	168	1	j.	j.	PROPN
ejpam-6319	168	2	pure	pure	PROPN
ejpam-6319	168	3	appl	appl	PROPN
ejpam-6319	168	4	.	.	PROPN
ejpam-6319	168	5	math	math	PROPN
ejpam-6319	168	6	,	,	PUNCT
ejpam-6319	168	7	18	18	NUM
ejpam-6319	168	8	(	(	PUNCT
ejpam-6319	168	9	3	3	NUM
ejpam-6319	168	10	)	)	PUNCT
ejpam-6319	168	11	(	(	PUNCT
ejpam-6319	168	12	2025	2025	NUM
ejpam-6319	168	13	)	)	PUNCT
ejpam-6319	168	14	,	,	PUNCT
ejpam-6319	168	15	6319	6319	NUM
ejpam-6319	168	16	6	6	NUM
ejpam-6319	168	17	of	of	ADP
ejpam-6319	168	18	13	13	NUM
ejpam-6319	168	19	it	it	PRON
ejpam-6319	168	20	can	can	AUX
ejpam-6319	168	21	be	be	AUX
ejpam-6319	168	22	seen	see	VERB
ejpam-6319	168	23	that	that	DET
ejpam-6319	168	24	pa(γd2n	pa(γd2n	NOUN
ejpam-6319	168	25	)	)	PUNCT
ejpam-6319	168	26	(	(	PUNCT
ejpam-6319	168	27	λ	λ	NOUN
ejpam-6319	168	28	)	)	PUNCT
ejpam-6319	168	29	=	=	SYM
ejpam-6319	168	30	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6319	168	31	λ	λ	NOUN
ejpam-6319	168	32	−j1×(2n−1	−j1×(2n−1	NUM
ejpam-6319	168	33	)	)	PUNCT
ejpam-6319	169	1	−j(2n−1)×1	−j(2n−1)×1	X
ejpam-6319	169	2	λi2n−1	λi2n−1	X
ejpam-6319	169	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6319	169	4	.	.	PUNCT
ejpam-6319	170	1	based	base	VERB
ejpam-6319	170	2	on	on	ADP
ejpam-6319	170	3	lemma	lemma	PROPN
ejpam-6319	170	4	1	1	NUM
ejpam-6319	170	5	with	with	ADP
ejpam-6319	170	6	a	a	DET
ejpam-6319	170	7	=	=	SYM
ejpam-6319	170	8	b	b	NOUN
ejpam-6319	170	9	=	=	SYM
ejpam-6319	170	10	0	0	NUM
ejpam-6319	170	11	,	,	PUNCT
ejpam-6319	170	12	c	c	NOUN
ejpam-6319	170	13	=	=	SYM
ejpam-6319	170	14	d	d	NOUN
ejpam-6319	170	15	=	=	SYM
ejpam-6319	170	16	1	1	NUM
ejpam-6319	170	17	,	,	PUNCT
ejpam-6319	170	18	n1	n1	NOUN
ejpam-6319	170	19	=	=	SYM
ejpam-6319	170	20	1	1	NUM
ejpam-6319	170	21	,	,	PUNCT
ejpam-6319	170	22	and	and	CCONJ
ejpam-6319	170	23	n2	n2	ADJ
ejpam-6319	170	24	=	=	PUNCT
ejpam-6319	171	1	2n−	2n−	NUM
ejpam-6319	171	2	1	1	NUM
ejpam-6319	171	3	,	,	PUNCT
ejpam-6319	171	4	then	then	ADV
ejpam-6319	171	5	we	we	PRON
ejpam-6319	171	6	obtain	obtain	VERB
ejpam-6319	171	7	pa(γd2n	pa(γd2n	NOUN
ejpam-6319	171	8	)	)	PUNCT
ejpam-6319	171	9	(	(	PUNCT
ejpam-6319	171	10	λ	λ	X
ejpam-6319	171	11	)	)	PUNCT
ejpam-6319	171	12	=	=	SYM
ejpam-6319	172	1	λ2n−2	λ2n−2	PROPN
ejpam-6319	172	2	(	(	PUNCT
ejpam-6319	172	3	λ−	λ−	PROPN
ejpam-6319	172	4	√	√	PROPN
ejpam-6319	173	1	2n−	2n−	NUM
ejpam-6319	173	2	1	1	NUM
ejpam-6319	173	3	)	)	PUNCT
ejpam-6319	173	4	(	(	PUNCT
ejpam-6319	173	5	λ+	λ+	NUM
ejpam-6319	173	6	√	√	INTJ
ejpam-6319	173	7	2n−	2n−	NUM
ejpam-6319	173	8	1	1	NUM
ejpam-6319	173	9	)	)	PUNCT
ejpam-6319	173	10	.	.	PUNCT
ejpam-6319	174	1	2.2	2.2	NUM
ejpam-6319	174	2	.	.	PUNCT
ejpam-6319	175	1	laplacian	laplacian	ADJ
ejpam-6319	175	2	energy	energy	NOUN
ejpam-6319	175	3	in	in	ADP
ejpam-6319	175	4	the	the	DET
ejpam-6319	175	5	next	next	ADJ
ejpam-6319	175	6	two	two	NUM
ejpam-6319	175	7	theorems	theorem	NOUN
ejpam-6319	175	8	,	,	PUNCT
ejpam-6319	175	9	we	we	PRON
ejpam-6319	175	10	focus	focus	VERB
ejpam-6319	175	11	on	on	ADP
ejpam-6319	175	12	the	the	DET
ejpam-6319	175	13	laplacian	laplacian	ADJ
ejpam-6319	175	14	matrix	matrix	NOUN
ejpam-6319	175	15	of	of	ADP
ejpam-6319	175	16	γd2n	γd2n	PROPN
ejpam-6319	175	17	.	.	PUNCT
ejpam-6319	176	1	theorem	theorem	ADJ
ejpam-6319	176	2	5	5	NUM
ejpam-6319	176	3	.	.	PUNCT
ejpam-6319	177	1	let	let	VERB
ejpam-6319	177	2	γd2n	γd2n	PROPN
ejpam-6319	177	3	be	be	AUX
ejpam-6319	177	4	the	the	DET
ejpam-6319	177	5	coprime	coprime	ADJ
ejpam-6319	177	6	graph	graph	NOUN
ejpam-6319	177	7	for	for	ADP
ejpam-6319	177	8	d2n	d2n	PROPN
ejpam-6319	177	9	with	with	ADP
ejpam-6319	177	10	n	n	PROPN
ejpam-6319	177	11	is	be	AUX
ejpam-6319	177	12	a	a	DET
ejpam-6319	177	13	prime	prime	ADJ
ejpam-6319	177	14	number	number	NOUN
ejpam-6319	177	15	or	or	CCONJ
ejpam-6319	177	16	n	n	NOUN
ejpam-6319	177	17	=	=	SYM
ejpam-6319	177	18	pk	pk	NOUN
ejpam-6319	177	19	,	,	PUNCT
ejpam-6319	177	20	p	p	PROPN
ejpam-6319	177	21	̸=	̸=	PROPN
ejpam-6319	177	22	2	2	NUM
ejpam-6319	177	23	for	for	ADP
ejpam-6319	177	24	a	a	DET
ejpam-6319	177	25	k	k	PROPN
ejpam-6319	177	26	∈	∈	PROPN
ejpam-6319	177	27	n	n	CCONJ
ejpam-6319	177	28	,	,	PUNCT
ejpam-6319	177	29	then	then	ADV
ejpam-6319	177	30	pl(γd2n	pl(γd2n	ADJ
ejpam-6319	177	31	)	)	PUNCT
ejpam-6319	177	32	(	(	PUNCT
ejpam-6319	177	33	λ	λ	X
ejpam-6319	177	34	)	)	PUNCT
ejpam-6319	177	35	=	=	SYM
ejpam-6319	178	1	λ(λ−	λ(λ−	PROPN
ejpam-6319	178	2	n)n−1(λ−	n)n−1(λ−	NOUN
ejpam-6319	178	3	2n)(λ−	2n)(λ−	NUM
ejpam-6319	178	4	(	(	PUNCT
ejpam-6319	178	5	n+	n+	NUM
ejpam-6319	178	6	1))n−2	1))n−2	PROPN
ejpam-6319	178	7	(	(	PUNCT
ejpam-6319	178	8	λ−	λ−	PROPN
ejpam-6319	178	9	2n	2n	NUM
ejpam-6319	178	10	)	)	PUNCT
ejpam-6319	178	11	.	.	PUNCT
ejpam-6319	179	1	proof	proof	NOUN
ejpam-6319	179	2	.	.	PUNCT
ejpam-6319	180	1	since	since	SCONJ
ejpam-6319	180	2	γd2n	γd2n	PROPN
ejpam-6319	180	3	,	,	PUNCT
ejpam-6319	180	4	for	for	ADP
ejpam-6319	180	5	d2n	d2n	PROPN
ejpam-6319	180	6	with	with	ADP
ejpam-6319	180	7	n	n	PROPN
ejpam-6319	180	8	is	be	AUX
ejpam-6319	180	9	a	a	DET
ejpam-6319	180	10	prime	prime	ADJ
ejpam-6319	180	11	number	number	NOUN
ejpam-6319	180	12	or	or	CCONJ
ejpam-6319	180	13	n	n	NOUN
ejpam-6319	180	14	=	=	SYM
ejpam-6319	180	15	pk	pk	NOUN
ejpam-6319	180	16	,	,	PUNCT
ejpam-6319	180	17	p	p	PROPN
ejpam-6319	180	18	̸=	̸=	PROPN
ejpam-6319	180	19	2	2	NUM
ejpam-6319	180	20	for	for	ADP
ejpam-6319	180	21	a	a	DET
ejpam-6319	180	22	k	k	PROPN
ejpam-6319	180	23	∈	∈	PROPN
ejpam-6319	180	24	n	n	CCONJ
ejpam-6319	180	25	,	,	PUNCT
ejpam-6319	180	26	has	have	AUX
ejpam-6319	180	27	deg(e	deg(e	NOUN
ejpam-6319	180	28	)	)	PUNCT
ejpam-6319	180	29	=	=	PUNCT
ejpam-6319	181	1	2n−	2n−	NUM
ejpam-6319	181	2	1	1	NUM
ejpam-6319	181	3	,	,	PUNCT
ejpam-6319	181	4	deg(ai	deg(ai	NOUN
ejpam-6319	181	5	)	)	PUNCT
ejpam-6319	181	6	=	=	SYM
ejpam-6319	181	7	n+	n+	PUNCT
ejpam-6319	181	8	1	1	NUM
ejpam-6319	181	9	,	,	PUNCT
ejpam-6319	181	10	and	and	CCONJ
ejpam-6319	181	11	deg(aib	deg(aib	PROPN
ejpam-6319	181	12	)	)	PUNCT
ejpam-6319	181	13	=	=	SYM
ejpam-6319	182	1	n	n	NOUN
ejpam-6319	182	2	corforming	corforme	VERB
ejpam-6319	182	3	from	from	ADP
ejpam-6319	182	4	theorem	theorem	ADJ
ejpam-6319	182	5	1	1	NUM
ejpam-6319	182	6	,	,	PUNCT
ejpam-6319	182	7	then	then	ADV
ejpam-6319	182	8	we	we	PRON
ejpam-6319	182	9	have	have	VERB
ejpam-6319	182	10	d(γd2n	d(γd2n	NOUN
ejpam-6319	182	11	)	)	PUNCT
ejpam-6319	182	12	=	=	SYM
ejpam-6319	183	1			NOUN
ejpam-6319	184	1	2n−	2n−	NUM
ejpam-6319	184	2	1	1	NUM
ejpam-6319	184	3	0	0	NUM
ejpam-6319	184	4	0	0	NUM
ejpam-6319	184	5	.	.	PUNCT
ejpam-6319	184	6	.	.	PUNCT
ejpam-6319	184	7	.	.	PUNCT
ejpam-6319	185	1	0	0	NUM
ejpam-6319	186	1	0	0	NUM
ejpam-6319	186	2	0	0	NUM
ejpam-6319	186	3	.	.	PUNCT
ejpam-6319	186	4	.	.	PUNCT
ejpam-6319	186	5	.	.	PUNCT
ejpam-6319	187	1	0	0	NUM
ejpam-6319	187	2	0	0	NUM
ejpam-6319	188	1	n+	n+	NUM
ejpam-6319	188	2	1	1	NUM
ejpam-6319	188	3	0	0	NUM
ejpam-6319	188	4	.	.	PUNCT
ejpam-6319	188	5	.	.	PUNCT
ejpam-6319	189	1	.	.	PUNCT
ejpam-6319	190	1	0	0	NUM
ejpam-6319	191	1	0	0	NUM
ejpam-6319	191	2	0	0	NUM
ejpam-6319	191	3	.	.	PUNCT
ejpam-6319	191	4	.	.	PUNCT
ejpam-6319	191	5	.	.	PUNCT
ejpam-6319	192	1	0	0	NUM
ejpam-6319	192	2	0	0	NUM
ejpam-6319	192	3	0	0	NUM
ejpam-6319	192	4	n+	n+	NUM
ejpam-6319	192	5	1	1	NUM
ejpam-6319	192	6	.	.	PUNCT
ejpam-6319	192	7	.	.	PUNCT
ejpam-6319	192	8	.	.	PUNCT
ejpam-6319	193	1	0	0	NUM
ejpam-6319	194	1	0	0	NUM
ejpam-6319	194	2	0	0	NUM
ejpam-6319	194	3	.	.	PUNCT
ejpam-6319	194	4	.	.	PUNCT
ejpam-6319	195	1	.	.	PUNCT
ejpam-6319	196	1	0	0	NUM
ejpam-6319	196	2	...	...	PUNCT
ejpam-6319	196	3	...	...	PUNCT
ejpam-6319	196	4	...	...	PUNCT
ejpam-6319	196	5	.	.	PUNCT
ejpam-6319	196	6	.	.	PUNCT
ejpam-6319	197	1	.	.	PUNCT
ejpam-6319	197	2	...	...	PUNCT
ejpam-6319	198	1	...	...	PUNCT
ejpam-6319	198	2	...	...	PUNCT
ejpam-6319	198	3	.	.	PUNCT
ejpam-6319	198	4	.	.	PUNCT
ejpam-6319	199	1	.	.	PUNCT
ejpam-6319	200	1	...	...	PUNCT
ejpam-6319	201	1	0	0	NUM
ejpam-6319	201	2	0	0	NUM
ejpam-6319	201	3	0	0	NUM
ejpam-6319	201	4	.	.	PUNCT
ejpam-6319	201	5	.	.	PUNCT
ejpam-6319	201	6	.	.	PUNCT
ejpam-6319	202	1	n+	n+	PUNCT
ejpam-6319	202	2	1	1	NUM
ejpam-6319	202	3	0	0	NUM
ejpam-6319	202	4	0	0	NUM
ejpam-6319	202	5	.	.	PUNCT
ejpam-6319	202	6	.	.	PUNCT
ejpam-6319	203	1	.	.	PUNCT
ejpam-6319	204	1	0	0	NUM
ejpam-6319	205	1	0	0	NUM
ejpam-6319	205	2	0	0	NUM
ejpam-6319	205	3	0	0	NUM
ejpam-6319	205	4	.	.	PUNCT
ejpam-6319	205	5	.	.	PUNCT
ejpam-6319	206	1	.	.	PUNCT
ejpam-6319	207	1	0	0	NUM
ejpam-6319	208	1	n	n	CCONJ
ejpam-6319	208	2	0	0	NUM
ejpam-6319	208	3	.	.	PUNCT
ejpam-6319	208	4	.	.	PUNCT
ejpam-6319	208	5	.	.	PUNCT
ejpam-6319	209	1	0	0	NUM
ejpam-6319	210	1	0	0	NUM
ejpam-6319	210	2	0	0	NUM
ejpam-6319	210	3	0	0	NUM
ejpam-6319	210	4	.	.	PUNCT
ejpam-6319	210	5	.	.	PUNCT
ejpam-6319	210	6	.	.	PUNCT
ejpam-6319	211	1	0	0	NUM
ejpam-6319	211	2	0	0	NUM
ejpam-6319	212	1	n	n	PROPN
ejpam-6319	212	2	.	.	PUNCT
ejpam-6319	212	3	.	.	PUNCT
ejpam-6319	213	1	.	.	PUNCT
ejpam-6319	214	1	0	0	NUM
ejpam-6319	214	2	...	...	PUNCT
ejpam-6319	214	3	...	...	PUNCT
ejpam-6319	214	4	...	...	PUNCT
ejpam-6319	214	5	.	.	PUNCT
ejpam-6319	214	6	.	.	PUNCT
ejpam-6319	215	1	.	.	PUNCT
ejpam-6319	215	2	...	...	PUNCT
ejpam-6319	216	1	...	...	PUNCT
ejpam-6319	216	2	...	...	PUNCT
ejpam-6319	216	3	.	.	PUNCT
ejpam-6319	216	4	.	.	PUNCT
ejpam-6319	217	1	.	.	PUNCT
ejpam-6319	218	1	...	...	PUNCT
ejpam-6319	219	1	0	0	NUM
ejpam-6319	219	2	0	0	NUM
ejpam-6319	219	3	0	0	NUM
ejpam-6319	219	4	.	.	PUNCT
ejpam-6319	219	5	.	.	PUNCT
ejpam-6319	219	6	.	.	PUNCT
ejpam-6319	220	1	0	0	NUM
ejpam-6319	221	1	0	0	NUM
ejpam-6319	221	2	0	0	NUM
ejpam-6319	221	3	.	.	PUNCT
ejpam-6319	221	4	.	.	PUNCT
ejpam-6319	221	5	.	.	PUNCT
ejpam-6319	222	1	n	n	X
ejpam-6319	223	1			PROPN
ejpam-6319	223	2	.	.	PUNCT
ejpam-6319	224	1	(	(	PUNCT
ejpam-6319	224	2	2	2	X
ejpam-6319	224	3	)	)	PUNCT
ejpam-6319	224	4	according	accord	VERB
ejpam-6319	224	5	to	to	ADP
ejpam-6319	224	6	equation	equation	NOUN
ejpam-6319	224	7	1	1	NUM
ejpam-6319	224	8	and	and	CCONJ
ejpam-6319	224	9	following	follow	VERB
ejpam-6319	224	10	definition	definition	NOUN
ejpam-6319	224	11	4	4	NUM
ejpam-6319	224	12	,	,	PUNCT
ejpam-6319	224	13	then	then	ADV
ejpam-6319	224	14	we	we	PRON
ejpam-6319	224	15	obtain	obtain	VERB
ejpam-6319	224	16	l(γd2n	l(γd2n	NOUN
ejpam-6319	224	17	)	)	PUNCT
ejpam-6319	225	1	=	=	SYM
ejpam-6319	225	2	d(γd2n)−a(γd2n	d(γd2n)−a(γd2n	PROPN
ejpam-6319	225	3	)	)	PUNCT
ejpam-6319	225	4	=	=	PUNCT
ejpam-6319	225	5			NOUN
ejpam-6319	225	6	2n−	2n−	NUM
ejpam-6319	225	7	1	1	NUM
ejpam-6319	225	8	−1	−1	NOUN
ejpam-6319	225	9	−1	−1	NOUN
ejpam-6319	225	10	.	.	PUNCT
ejpam-6319	225	11	.	.	PUNCT
ejpam-6319	226	1	.	.	PUNCT
ejpam-6319	227	1	−1	−1	NOUN
ejpam-6319	227	2	−1	−1	NOUN
ejpam-6319	227	3	−1	−1	NOUN
ejpam-6319	227	4	.	.	PUNCT
ejpam-6319	227	5	.	.	PUNCT
ejpam-6319	227	6	.	.	PUNCT
ejpam-6319	228	1	−1	−1	NOUN
ejpam-6319	228	2	−1	−1	NOUN
ejpam-6319	228	3	n+	n+	ADP
ejpam-6319	228	4	1	1	NUM
ejpam-6319	228	5	0	0	NUM
ejpam-6319	228	6	.	.	PUNCT
ejpam-6319	228	7	.	.	PUNCT
ejpam-6319	229	1	.	.	PUNCT
ejpam-6319	230	1	0	0	NUM
ejpam-6319	231	1	−1	−1	NOUN
ejpam-6319	231	2	−1	−1	NOUN
ejpam-6319	231	3	.	.	PUNCT
ejpam-6319	231	4	.	.	PUNCT
ejpam-6319	231	5	.	.	PUNCT
ejpam-6319	232	1	−1	−1	NOUN
ejpam-6319	232	2	−1	−1	NOUN
ejpam-6319	232	3	0	0	PUNCT
ejpam-6319	232	4	n+	n+	SYM
ejpam-6319	232	5	1	1	NUM
ejpam-6319	232	6	.	.	PUNCT
ejpam-6319	232	7	.	.	PUNCT
ejpam-6319	233	1	.	.	PUNCT
ejpam-6319	234	1	0	0	NUM
ejpam-6319	235	1	−1	−1	NOUN
ejpam-6319	235	2	−1	−1	NOUN
ejpam-6319	235	3	.	.	PUNCT
ejpam-6319	235	4	.	.	PUNCT
ejpam-6319	235	5	.	.	PUNCT
ejpam-6319	236	1	−1	−1	NOUN
ejpam-6319	236	2	...	...	PUNCT
ejpam-6319	236	3	...	...	PUNCT
ejpam-6319	236	4	...	...	PUNCT
ejpam-6319	236	5	.	.	PUNCT
ejpam-6319	236	6	.	.	PUNCT
ejpam-6319	236	7	.	.	PUNCT
ejpam-6319	237	1	...	...	PUNCT
ejpam-6319	237	2	...	...	PUNCT
ejpam-6319	237	3	...	...	PUNCT
ejpam-6319	237	4	.	.	PUNCT
ejpam-6319	237	5	.	.	PUNCT
ejpam-6319	238	1	.	.	PUNCT
ejpam-6319	239	1	...	...	PUNCT
ejpam-6319	240	1	−1	−1	NOUN
ejpam-6319	240	2	0	0	NUM
ejpam-6319	240	3	0	0	NUM
ejpam-6319	240	4	.	.	PUNCT
ejpam-6319	240	5	.	.	PUNCT
ejpam-6319	240	6	.	.	PUNCT
ejpam-6319	241	1	n+	n+	ADV
ejpam-6319	242	1	1	1	NUM
ejpam-6319	242	2	−1	−1	NOUN
ejpam-6319	242	3	−1	−1	NOUN
ejpam-6319	242	4	.	.	PUNCT
ejpam-6319	242	5	.	.	PUNCT
ejpam-6319	242	6	.	.	PUNCT
ejpam-6319	243	1	−1	−1	NOUN
ejpam-6319	243	2	−1	−1	NOUN
ejpam-6319	243	3	−1	−1	NOUN
ejpam-6319	243	4	−1	−1	NOUN
ejpam-6319	243	5	.	.	PUNCT
ejpam-6319	243	6	.	.	PUNCT
ejpam-6319	243	7	.	.	PUNCT
ejpam-6319	244	1	−1	−1	NOUN
ejpam-6319	244	2	n	n	ADV
ejpam-6319	244	3	0	0	NUM
ejpam-6319	244	4	.	.	PUNCT
ejpam-6319	244	5	.	.	PUNCT
ejpam-6319	245	1	.	.	PUNCT
ejpam-6319	246	1	0	0	NUM
ejpam-6319	247	1	−1	−1	NOUN
ejpam-6319	247	2	−1	−1	NOUN
ejpam-6319	247	3	−1	−1	NOUN
ejpam-6319	247	4	.	.	PUNCT
ejpam-6319	247	5	.	.	PUNCT
ejpam-6319	247	6	.	.	PUNCT
ejpam-6319	248	1	−1	−1	NOUN
ejpam-6319	248	2	0	0	NUM
ejpam-6319	249	1	n	n	PROPN
ejpam-6319	249	2	.	.	PUNCT
ejpam-6319	249	3	.	.	PUNCT
ejpam-6319	250	1	.	.	PUNCT
ejpam-6319	251	1	0	0	NUM
ejpam-6319	251	2	...	...	PUNCT
ejpam-6319	251	3	...	...	PUNCT
ejpam-6319	251	4	...	...	PUNCT
ejpam-6319	251	5	.	.	PUNCT
ejpam-6319	251	6	.	.	PUNCT
ejpam-6319	252	1	.	.	PUNCT
ejpam-6319	252	2	...	...	PUNCT
ejpam-6319	253	1	...	...	PUNCT
ejpam-6319	253	2	...	...	PUNCT
ejpam-6319	253	3	.	.	PUNCT
ejpam-6319	253	4	.	.	PUNCT
ejpam-6319	254	1	.	.	PUNCT
ejpam-6319	254	2	...	...	PUNCT
ejpam-6319	255	1	−1	−1	NOUN
ejpam-6319	255	2	−1	−1	NOUN
ejpam-6319	255	3	−1	−1	NOUN
ejpam-6319	255	4	.	.	PUNCT
ejpam-6319	255	5	.	.	PUNCT
ejpam-6319	255	6	.	.	PUNCT
ejpam-6319	256	1	−1	−1	NOUN
ejpam-6319	256	2	0	0	NUM
ejpam-6319	256	3	0	0	NUM
ejpam-6319	256	4	.	.	PUNCT
ejpam-6319	256	5	.	.	PUNCT
ejpam-6319	256	6	.	.	PUNCT
ejpam-6319	257	1	n	n	PROPN
ejpam-6319	258	1			PROPN
ejpam-6319	258	2	.	.	PUNCT
ejpam-6319	258	3	m.	m.	PROPN
ejpam-6319	258	4	u.	u.	PROPN
ejpam-6319	258	5	romdhini	romdhini	PROPN
ejpam-6319	258	6	,	,	PUNCT
ejpam-6319	258	7	abdurahim	abdurahim	PRON
ejpam-6319	258	8	,	,	PUNCT
ejpam-6319	258	9	a.	a.	PROPN
ejpam-6319	258	10	e.	e.	PROPN
ejpam-6319	258	11	s.	s.	PROPN
ejpam-6319	258	12	h.	h.	PROPN
ejpam-6319	258	13	maharani	maharani	PROPN
ejpam-6319	258	14	/	/	SYM
ejpam-6319	258	15	eur	eur	PROPN
ejpam-6319	258	16	.	.	PUNCT
ejpam-6319	259	1	j.	j.	PROPN
ejpam-6319	259	2	pure	pure	PROPN
ejpam-6319	259	3	appl	appl	PROPN
ejpam-6319	259	4	.	.	PROPN
ejpam-6319	259	5	math	math	PROPN
ejpam-6319	259	6	,	,	PUNCT
ejpam-6319	259	7	18	18	NUM
ejpam-6319	259	8	(	(	PUNCT
ejpam-6319	259	9	3	3	NUM
ejpam-6319	259	10	)	)	PUNCT
ejpam-6319	259	11	(	(	PUNCT
ejpam-6319	259	12	2025	2025	NUM
ejpam-6319	259	13	)	)	PUNCT
ejpam-6319	259	14	,	,	PUNCT
ejpam-6319	259	15	6319	6319	NUM
ejpam-6319	259	16	7	7	NUM
ejpam-6319	259	17	of	of	ADP
ejpam-6319	259	18	13	13	NUM
ejpam-6319	259	19	hence	hence	ADV
ejpam-6319	259	20	,	,	PUNCT
ejpam-6319	259	21	it	it	PRON
ejpam-6319	259	22	is	be	AUX
ejpam-6319	259	23	l(γd2n	l(γd2n	PROPN
ejpam-6319	259	24	)	)	PUNCT
ejpam-6319	259	25	=	=	PUNCT
ejpam-6319	260	1			PROPN
ejpam-6319	260	2	2n−	2n−	PROPN
ejpam-6319	260	3	1	1	NUM
ejpam-6319	260	4	−j1×(n−1	−j1×(n−1	NUM
ejpam-6319	260	5	)	)	PUNCT
ejpam-6319	260	6	−j1×n	−j1×n	PUNCT
ejpam-6319	261	1	−j(n−1)×1	−j(n−1)×1	PROPN
ejpam-6319	261	2	(	(	PUNCT
ejpam-6319	261	3	n+	n+	PROPN
ejpam-6319	261	4	1)in−1	1)in−1	NUM
ejpam-6319	261	5	−j(n−1)×n	−j(n−1)×n	DET
ejpam-6319	261	6	−jn×1	−jn×1	PUNCT
ejpam-6319	261	7	−jn×(n−1	−jn×(n−1	PROPN
ejpam-6319	261	8	)	)	PUNCT
ejpam-6319	261	9	nin	nin	PROPN
ejpam-6319	261	10			PROPN
ejpam-6319	261	11	.	.	PUNCT
ejpam-6319	262	1	the	the	DET
ejpam-6319	262	2	characteristic	characteristic	ADJ
ejpam-6319	262	3	equation	equation	NOUN
ejpam-6319	262	4	of	of	ADP
ejpam-6319	262	5	l(γd2n	l(γd2n	PROPN
ejpam-6319	262	6	)	)	PUNCT
ejpam-6319	262	7	is	be	AUX
ejpam-6319	262	8	given	give	VERB
ejpam-6319	262	9	below	below	ADP
ejpam-6319	262	10	pl(γd2n	pl(γd2n	NOUN
ejpam-6319	262	11	)	)	PUNCT
ejpam-6319	262	12	(	(	PUNCT
ejpam-6319	262	13	λ	λ	NOUN
ejpam-6319	262	14	)	)	PUNCT
ejpam-6319	262	15	=	=	SYM
ejpam-6319	263	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6319	263	2	λ−	λ−	PROPN
ejpam-6319	263	3	(	(	PUNCT
ejpam-6319	263	4	2n−	2n−	PROPN
ejpam-6319	263	5	1	1	NUM
ejpam-6319	263	6	)	)	PUNCT
ejpam-6319	263	7	j1×(n−1	j1×(n−1	PROPN
ejpam-6319	263	8	)	)	PUNCT
ejpam-6319	264	1	j1×n	j1×n	ADJ
ejpam-6319	264	2	j(n−1)×1	j(n−1)×1	NOUN
ejpam-6319	264	3	(	(	PUNCT
ejpam-6319	264	4	λ−	λ−	PROPN
ejpam-6319	264	5	(	(	PUNCT
ejpam-6319	264	6	n+	n+	NUM
ejpam-6319	264	7	1))in−1	1))in−1	PROPN
ejpam-6319	264	8	j(n−1)×n	j(n−1)×n	PROPN
ejpam-6319	264	9	jn×1	jn×1	PROPN
ejpam-6319	264	10	jn×(n−1	jn×(n−1	PROPN
ejpam-6319	264	11	)	)	PUNCT
ejpam-6319	264	12	(	(	PUNCT
ejpam-6319	264	13	λ−	λ−	PROPN
ejpam-6319	264	14	n)in	n)in	PROPN
ejpam-6319	264	15	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-6319	264	16	.	.	PUNCT
ejpam-6319	265	1	we	we	PRON
ejpam-6319	265	2	follow	follow	VERB
ejpam-6319	265	3	the	the	DET
ejpam-6319	265	4	following	follow	VERB
ejpam-6319	265	5	operational	operational	ADJ
ejpam-6319	265	6	steps	step	NOUN
ejpam-6319	265	7	in	in	ADP
ejpam-6319	265	8	the	the	DET
ejpam-6319	265	9	same	same	ADJ
ejpam-6319	265	10	manner	manner	NOUN
ejpam-6319	265	11	as	as	ADP
ejpam-6319	265	12	the	the	DET
ejpam-6319	265	13	proof	proof	NOUN
ejpam-6319	265	14	of	of	ADP
ejpam-6319	265	15	theorem	theorem	ADJ
ejpam-6319	265	16	3	3	NUM
ejpam-6319	265	17	:	:	PUNCT
ejpam-6319	265	18	(	(	PUNCT
ejpam-6319	265	19	i	i	NOUN
ejpam-6319	265	20	)	)	PUNCT
ejpam-6319	265	21	rn+1+i	rn+1+i	NOUN
ejpam-6319	265	22	−→	−→	ADJ
ejpam-6319	265	23	rn+1+i	rn+1+i	NOUN
ejpam-6319	265	24	−rn+1	−rn+1	VERB
ejpam-6319	265	25	,	,	PUNCT
ejpam-6319	265	26	for	for	ADP
ejpam-6319	265	27	i	i	PROPN
ejpam-6319	265	28	=	=	SYM
ejpam-6319	265	29	1	1	NUM
ejpam-6319	265	30	,	,	PUNCT
ejpam-6319	265	31	2	2	NUM
ejpam-6319	265	32	,	,	PUNCT
ejpam-6319	265	33	.	.	PUNCT
ejpam-6319	265	34	.	.	PUNCT
ejpam-6319	266	1	.	.	PUNCT
ejpam-6319	267	1	,	,	PUNCT
ejpam-6319	267	2	n−	n−	NOUN
ejpam-6319	267	3	1	1	NUM
ejpam-6319	267	4	.	.	PUNCT
ejpam-6319	267	5	(	(	PUNCT
ejpam-6319	267	6	ii	ii	NOUN
ejpam-6319	267	7	)	)	PUNCT
ejpam-6319	267	8	cn+1	cn+1	VERB
ejpam-6319	267	9	−→	−→	NOUN
ejpam-6319	267	10	cn+1	cn+1	NOUN
ejpam-6319	267	11	+	+	CCONJ
ejpam-6319	267	12	cn+2	cn+2	PRON
ejpam-6319	268	1	+	+	CCONJ
ejpam-6319	268	2	.	.	PUNCT
ejpam-6319	268	3	.	.	PUNCT
ejpam-6319	269	1	.+	.+	NOUN
ejpam-6319	269	2	c2n	c2n	NOUN
ejpam-6319	269	3	.	.	PUNCT
ejpam-6319	270	1	(	(	PUNCT
ejpam-6319	270	2	iii	iii	NOUN
ejpam-6319	270	3	)	)	PUNCT
ejpam-6319	270	4	rn+1	rn+1	VERB
ejpam-6319	270	5	−→	−→	NOUN
ejpam-6319	270	6	rn+1	rn+1	X
ejpam-6319	270	7	−r1	−r1	PROPN
ejpam-6319	270	8	.	.	PUNCT
ejpam-6319	271	1	(	(	PUNCT
ejpam-6319	271	2	iv	iv	X
ejpam-6319	271	3	)	)	PUNCT
ejpam-6319	271	4	c1	c1	PROPN
ejpam-6319	271	5	−→	−→	PROPN
ejpam-6319	271	6	c1	c1	PROPN
ejpam-6319	271	7	+	+	CCONJ
ejpam-6319	271	8	cn+1	cn+1	PROPN
ejpam-6319	271	9	.	.	PUNCT
ejpam-6319	272	1	(	(	PUNCT
ejpam-6319	272	2	v	v	NOUN
ejpam-6319	272	3	)	)	PUNCT
ejpam-6319	272	4	for	for	ADP
ejpam-6319	272	5	i	i	PROPN
ejpam-6319	272	6	=	=	SYM
ejpam-6319	272	7	1	1	NUM
ejpam-6319	272	8	,	,	PUNCT
ejpam-6319	272	9	2	2	NUM
ejpam-6319	272	10	,	,	PUNCT
ejpam-6319	272	11	.	.	PUNCT
ejpam-6319	272	12	.	.	PUNCT
ejpam-6319	273	1	.	.	PUNCT
ejpam-6319	274	1	,	,	PUNCT
ejpam-6319	274	2	n−	n−	NOUN
ejpam-6319	274	3	2	2	NUM
ejpam-6319	274	4	,	,	PUNCT
ejpam-6319	274	5	r2+i	r2+i	VERB
ejpam-6319	274	6	−→	−→	NOUN
ejpam-6319	274	7	r2+i	r2+i	PROPN
ejpam-6319	274	8	−r2	−r2	PROPN
ejpam-6319	274	9	.	.	PROPN
ejpam-6319	274	10	(	(	PUNCT
ejpam-6319	274	11	vi	vi	NOUN
ejpam-6319	274	12	)	)	PUNCT
ejpam-6319	274	13	c2	c2	PROPN
ejpam-6319	274	14	−→	−→	PROPN
ejpam-6319	274	15	c2	c2	PROPN
ejpam-6319	274	16	+	+	CCONJ
ejpam-6319	274	17	c2	c2	PROPN
ejpam-6319	274	18	+	+	PROPN
ejpam-6319	274	19	1	1	NUM
ejpam-6319	274	20	+	+	NUM
ejpam-6319	274	21	.	.	PUNCT
ejpam-6319	274	22	.	.	PUNCT
ejpam-6319	275	1	.+	.+	NOUN
ejpam-6319	276	1	cn	cn	PROPN
ejpam-6319	276	2	.	.	PUNCT
ejpam-6319	277	1	therefore	therefore	ADV
ejpam-6319	277	2	,	,	PUNCT
ejpam-6319	277	3	pl(γd2n	pl(γd2n	ADJ
ejpam-6319	277	4	)	)	PUNCT
ejpam-6319	277	5	(	(	PUNCT
ejpam-6319	277	6	λ	λ	X
ejpam-6319	277	7	)	)	PUNCT
ejpam-6319	277	8	=	=	SYM
ejpam-6319	278	1	λ(λ−	λ(λ−	PROPN
ejpam-6319	279	1	n)n−1(λ−	n)n−1(λ−	NOUN
ejpam-6319	279	2	2n)(λ−	2n)(λ−	NUM
ejpam-6319	279	3	(	(	PUNCT
ejpam-6319	279	4	n+	n+	NUM
ejpam-6319	279	5	1))n−2	1))n−2	PROPN
ejpam-6319	279	6	(	(	PUNCT
ejpam-6319	279	7	λ−	λ−	PROPN
ejpam-6319	279	8	2n	2n	NUM
ejpam-6319	279	9	)	)	PUNCT
ejpam-6319	279	10	.	.	PUNCT
ejpam-6319	280	1	theorem	theorem	ADJ
ejpam-6319	280	2	6	6	NUM
ejpam-6319	280	3	.	.	PUNCT
ejpam-6319	281	1	let	let	VERB
ejpam-6319	281	2	γd2n	γd2n	PROPN
ejpam-6319	281	3	be	be	AUX
ejpam-6319	281	4	the	the	DET
ejpam-6319	281	5	coprime	coprime	ADJ
ejpam-6319	281	6	graph	graph	NOUN
ejpam-6319	281	7	for	for	ADP
ejpam-6319	281	8	d2n	d2n	PROPN
ejpam-6319	281	9	with	with	ADP
ejpam-6319	281	10	n	n	NOUN
ejpam-6319	281	11	=	=	SYM
ejpam-6319	281	12	2k	2k	NUM
ejpam-6319	281	13	,	,	PUNCT
ejpam-6319	281	14	k	k	PROPN
ejpam-6319	281	15	∈	∈	PROPN
ejpam-6319	281	16	n	n	CCONJ
ejpam-6319	281	17	,	,	PUNCT
ejpam-6319	281	18	then	then	ADV
ejpam-6319	281	19	pl(γd2n	pl(γd2n	ADJ
ejpam-6319	281	20	)	)	PUNCT
ejpam-6319	281	21	(	(	PUNCT
ejpam-6319	281	22	λ	λ	NOUN
ejpam-6319	281	23	)	)	PUNCT
ejpam-6319	281	24	=	=	SYM
ejpam-6319	281	25	(	(	PUNCT
ejpam-6319	281	26	λ−	λ−	PROPN
ejpam-6319	281	27	1)2n−2	1)2n−2	NUM
ejpam-6319	281	28	(	(	PUNCT
ejpam-6319	281	29	λ+	λ+	NUM
ejpam-6319	281	30	1	1	NUM
ejpam-6319	281	31	)	)	PUNCT
ejpam-6319	281	32	(	(	PUNCT
ejpam-6319	281	33	λ−	λ−	PROPN
ejpam-6319	281	34	(	(	PUNCT
ejpam-6319	281	35	2n−	2n−	PROPN
ejpam-6319	281	36	1	1	NUM
ejpam-6319	281	37	)	)	PUNCT
ejpam-6319	281	38	)	)	PUNCT
ejpam-6319	281	39	.	.	PUNCT
ejpam-6319	282	1	proof	proof	NOUN
ejpam-6319	282	2	.	.	PUNCT
ejpam-6319	283	1	based	base	VERB
ejpam-6319	283	2	on	on	ADP
ejpam-6319	283	3	theorem	theorem	NOUN
ejpam-6319	283	4	2	2	NUM
ejpam-6319	283	5	,	,	PUNCT
ejpam-6319	283	6	γd2n	γd2n	PROPN
ejpam-6319	283	7	,	,	PUNCT
ejpam-6319	283	8	for	for	ADP
ejpam-6319	283	9	d2n	d2n	PROPN
ejpam-6319	283	10	with	with	ADP
ejpam-6319	283	11	n	n	NOUN
ejpam-6319	283	12	=	=	SYM
ejpam-6319	283	13	2k	2k	NUM
ejpam-6319	283	14	,	,	PUNCT
ejpam-6319	283	15	k	k	PROPN
ejpam-6319	283	16	∈	∈	PROPN
ejpam-6319	283	17	n	n	CCONJ
ejpam-6319	283	18	,	,	PUNCT
ejpam-6319	283	19	has	have	VERB
ejpam-6319	283	20	deg(ai	deg(ai	PRON
ejpam-6319	283	21	)	)	PUNCT
ejpam-6319	283	22	=	=	SYM
ejpam-6319	283	23	deg(aib	deg(aib	X
ejpam-6319	283	24	)	)	PUNCT
ejpam-6319	284	1	=	=	SYM
ejpam-6319	284	2	1	1	NUM
ejpam-6319	284	3	and	and	CCONJ
ejpam-6319	284	4	deg(e	deg(e	NOUN
ejpam-6319	284	5	)	)	PUNCT
ejpam-6319	284	6	=	=	SYM
ejpam-6319	284	7	2n	2n	NUM
ejpam-6319	284	8	−	−	NOUN
ejpam-6319	284	9	1	1	NUM
ejpam-6319	284	10	,	,	PUNCT
ejpam-6319	284	11	then	then	ADV
ejpam-6319	284	12	we	we	PRON
ejpam-6319	284	13	can	can	AUX
ejpam-6319	284	14	provide	provide	VERB
ejpam-6319	284	15	a	a	DET
ejpam-6319	284	16	2n	2n	NUM
ejpam-6319	284	17	×	×	PROPN
ejpam-6319	284	18	2n	2n	NUM
ejpam-6319	284	19	degree	degree	NOUN
ejpam-6319	284	20	matrix	matrix	NOUN
ejpam-6319	284	21	of	of	ADP
ejpam-6319	284	22	γd2n	γd2n	PROPN
ejpam-6319	284	23	.	.	PUNCT
ejpam-6319	285	1	d(γd2n	d(γd2n	X
ejpam-6319	285	2	)	)	PUNCT
ejpam-6319	286	1	=	=	PUNCT
ejpam-6319	286	2			NOUN
ejpam-6319	287	1	2n−	2n−	NUM
ejpam-6319	287	2	1	1	NUM
ejpam-6319	287	3	0	0	NUM
ejpam-6319	287	4	0	0	NUM
ejpam-6319	287	5	.	.	PUNCT
ejpam-6319	287	6	.	.	PUNCT
ejpam-6319	287	7	.	.	PUNCT
ejpam-6319	288	1	0	0	NUM
ejpam-6319	289	1	0	0	NUM
ejpam-6319	289	2	0	0	NUM
ejpam-6319	289	3	.	.	PUNCT
ejpam-6319	289	4	.	.	PUNCT
ejpam-6319	289	5	.	.	PUNCT
ejpam-6319	290	1	0	0	NUM
ejpam-6319	291	1	0	0	NUM
ejpam-6319	291	2	1	1	NUM
ejpam-6319	291	3	0	0	NUM
ejpam-6319	291	4	.	.	PUNCT
ejpam-6319	291	5	.	.	PUNCT
ejpam-6319	291	6	.	.	PUNCT
ejpam-6319	292	1	0	0	NUM
ejpam-6319	293	1	0	0	NUM
ejpam-6319	293	2	0	0	NUM
ejpam-6319	293	3	.	.	PUNCT
ejpam-6319	293	4	.	.	PUNCT
ejpam-6319	293	5	.	.	PUNCT
ejpam-6319	294	1	0	0	NUM
ejpam-6319	294	2	0	0	NUM
ejpam-6319	294	3	0	0	NUM
ejpam-6319	294	4	1	1	NUM
ejpam-6319	294	5	.	.	PUNCT
ejpam-6319	294	6	.	.	PUNCT
ejpam-6319	294	7	.	.	PUNCT
ejpam-6319	295	1	0	0	NUM
ejpam-6319	296	1	0	0	NUM
ejpam-6319	296	2	0	0	NUM
ejpam-6319	296	3	.	.	PUNCT
ejpam-6319	296	4	.	.	PUNCT
ejpam-6319	297	1	.	.	PUNCT
ejpam-6319	298	1	0	0	NUM
ejpam-6319	298	2	...	...	PUNCT
ejpam-6319	298	3	...	...	PUNCT
ejpam-6319	298	4	...	...	PUNCT
ejpam-6319	298	5	.	.	PUNCT
ejpam-6319	298	6	.	.	PUNCT
ejpam-6319	299	1	.	.	PUNCT
ejpam-6319	299	2	...	...	PUNCT
ejpam-6319	300	1	...	...	PUNCT
ejpam-6319	300	2	...	...	PUNCT
ejpam-6319	300	3	.	.	PUNCT
ejpam-6319	300	4	.	.	PUNCT
ejpam-6319	301	1	.	.	PUNCT
ejpam-6319	302	1	...	...	PUNCT
ejpam-6319	303	1	0	0	NUM
ejpam-6319	303	2	0	0	NUM
ejpam-6319	303	3	0	0	NUM
ejpam-6319	303	4	.	.	PUNCT
ejpam-6319	303	5	.	.	PUNCT
ejpam-6319	303	6	.	.	PUNCT
ejpam-6319	304	1	1	1	NUM
ejpam-6319	304	2	0	0	NUM
ejpam-6319	304	3	0	0	NUM
ejpam-6319	304	4	.	.	PUNCT
ejpam-6319	304	5	.	.	PUNCT
ejpam-6319	304	6	.	.	PUNCT
ejpam-6319	305	1	0	0	NUM
ejpam-6319	306	1	0	0	NUM
ejpam-6319	306	2	0	0	NUM
ejpam-6319	306	3	0	0	NUM
ejpam-6319	306	4	.	.	PUNCT
ejpam-6319	306	5	.	.	PUNCT
ejpam-6319	306	6	.	.	PUNCT
ejpam-6319	307	1	0	0	NUM
ejpam-6319	308	1	1	1	NUM
ejpam-6319	308	2	0	0	NUM
ejpam-6319	308	3	.	.	PUNCT
ejpam-6319	308	4	.	.	PUNCT
ejpam-6319	308	5	.	.	PUNCT
ejpam-6319	309	1	0	0	NUM
ejpam-6319	310	1	0	0	NUM
ejpam-6319	310	2	0	0	NUM
ejpam-6319	310	3	0	0	NUM
ejpam-6319	310	4	.	.	PUNCT
ejpam-6319	310	5	.	.	PUNCT
ejpam-6319	310	6	.	.	PUNCT
ejpam-6319	311	1	0	0	NUM
ejpam-6319	311	2	0	0	NUM
ejpam-6319	311	3	1	1	NUM
ejpam-6319	311	4	.	.	PUNCT
ejpam-6319	311	5	.	.	PUNCT
ejpam-6319	312	1	.	.	PUNCT
ejpam-6319	313	1	0	0	NUM
ejpam-6319	313	2	...	...	PUNCT
ejpam-6319	313	3	...	...	PUNCT
ejpam-6319	313	4	...	...	PUNCT
ejpam-6319	313	5	.	.	PUNCT
ejpam-6319	313	6	.	.	PUNCT
ejpam-6319	314	1	.	.	PUNCT
ejpam-6319	314	2	...	...	PUNCT
ejpam-6319	315	1	...	...	PUNCT
ejpam-6319	315	2	...	...	PUNCT
ejpam-6319	315	3	.	.	PUNCT
ejpam-6319	315	4	.	.	PUNCT
ejpam-6319	316	1	.	.	PUNCT
ejpam-6319	317	1	...	...	PUNCT
ejpam-6319	318	1	0	0	NUM
ejpam-6319	318	2	0	0	NUM
ejpam-6319	318	3	0	0	NUM
ejpam-6319	318	4	.	.	PUNCT
ejpam-6319	318	5	.	.	PUNCT
ejpam-6319	318	6	.	.	PUNCT
ejpam-6319	319	1	0	0	NUM
ejpam-6319	320	1	0	0	NUM
ejpam-6319	320	2	0	0	NUM
ejpam-6319	320	3	.	.	PUNCT
ejpam-6319	320	4	.	.	PUNCT
ejpam-6319	320	5	.	.	PUNCT
ejpam-6319	321	1	1	1	NUM
ejpam-6319	321	2			NOUN
ejpam-6319	321	3	.	.	PUNCT
ejpam-6319	322	1	(	(	PUNCT
ejpam-6319	322	2	3	3	X
ejpam-6319	322	3	)	)	PUNCT
ejpam-6319	322	4	m.	m.	NOUN
ejpam-6319	322	5	u.	u.	PROPN
ejpam-6319	322	6	romdhini	romdhini	PROPN
ejpam-6319	322	7	,	,	PUNCT
ejpam-6319	322	8	abdurahim	abdurahim	PRON
ejpam-6319	322	9	,	,	PUNCT
ejpam-6319	322	10	a.	a.	PROPN
ejpam-6319	322	11	e.	e.	PROPN
ejpam-6319	322	12	s.	s.	PROPN
ejpam-6319	322	13	h.	h.	PROPN
ejpam-6319	322	14	maharani	maharani	PROPN
ejpam-6319	322	15	/	/	SYM
ejpam-6319	322	16	eur	eur	PROPN
ejpam-6319	322	17	.	.	PUNCT
ejpam-6319	323	1	j.	j.	PROPN
ejpam-6319	323	2	pure	pure	PROPN
ejpam-6319	323	3	appl	appl	PROPN
ejpam-6319	323	4	.	.	PROPN
ejpam-6319	323	5	math	math	PROPN
ejpam-6319	323	6	,	,	PUNCT
ejpam-6319	323	7	18	18	NUM
ejpam-6319	323	8	(	(	PUNCT
ejpam-6319	323	9	3	3	NUM
ejpam-6319	323	10	)	)	PUNCT
ejpam-6319	323	11	(	(	PUNCT
ejpam-6319	323	12	2025	2025	NUM
ejpam-6319	323	13	)	)	PUNCT
ejpam-6319	323	14	,	,	PUNCT
ejpam-6319	323	15	6319	6319	NUM
ejpam-6319	323	16	8	8	NUM
ejpam-6319	323	17	of	of	ADP
ejpam-6319	323	18	13	13	NUM
ejpam-6319	323	19	based	base	VERB
ejpam-6319	323	20	on	on	ADP
ejpam-6319	323	21	equation	equation	NOUN
ejpam-6319	323	22	1	1	NUM
ejpam-6319	323	23	and	and	CCONJ
ejpam-6319	323	24	by	by	ADP
ejpam-6319	323	25	definition	definition	NOUN
ejpam-6319	323	26	4	4	NUM
ejpam-6319	323	27	,	,	PUNCT
ejpam-6319	323	28	then	then	ADV
ejpam-6319	323	29	l(γd2n	l(γd2n	X
ejpam-6319	323	30	)	)	PUNCT
ejpam-6319	323	31	=	=	SYM
ejpam-6319	323	32	d(γd2n)−a(γd2n	d(γd2n)−a(γd2n	PROPN
ejpam-6319	323	33	)	)	PUNCT
ejpam-6319	323	34	=	=	PUNCT
ejpam-6319	324	1			NOUN
ejpam-6319	324	2	2n−	2n−	NUM
ejpam-6319	324	3	1	1	NUM
ejpam-6319	324	4	−1	−1	NOUN
ejpam-6319	324	5	−1	−1	NOUN
ejpam-6319	324	6	.	.	PUNCT
ejpam-6319	324	7	.	.	PUNCT
ejpam-6319	324	8	.	.	PUNCT
ejpam-6319	325	1	−1	−1	NOUN
ejpam-6319	325	2	−1	−1	NOUN
ejpam-6319	325	3	−1	−1	NOUN
ejpam-6319	325	4	.	.	PUNCT
ejpam-6319	325	5	.	.	PUNCT
ejpam-6319	325	6	.	.	PUNCT
ejpam-6319	326	1	−1	−1	NOUN
ejpam-6319	326	2	−1	−1	NOUN
ejpam-6319	326	3	1	1	NUM
ejpam-6319	326	4	0	0	NUM
ejpam-6319	326	5	.	.	PUNCT
ejpam-6319	326	6	.	.	PUNCT
ejpam-6319	326	7	.	.	PUNCT
ejpam-6319	327	1	0	0	NUM
ejpam-6319	328	1	0	0	NUM
ejpam-6319	328	2	0	0	NUM
ejpam-6319	328	3	.	.	PUNCT
ejpam-6319	328	4	.	.	PUNCT
ejpam-6319	329	1	.	.	PUNCT
ejpam-6319	330	1	0	0	NUM
ejpam-6319	330	2	−1	−1	NOUN
ejpam-6319	330	3	0	0	NUM
ejpam-6319	330	4	1	1	NUM
ejpam-6319	330	5	.	.	PUNCT
ejpam-6319	330	6	.	.	PUNCT
ejpam-6319	330	7	.	.	PUNCT
ejpam-6319	331	1	0	0	NUM
ejpam-6319	332	1	0	0	NUM
ejpam-6319	332	2	0	0	NUM
ejpam-6319	332	3	.	.	PUNCT
ejpam-6319	332	4	.	.	PUNCT
ejpam-6319	333	1	.	.	PUNCT
ejpam-6319	334	1	0	0	NUM
ejpam-6319	334	2	...	...	PUNCT
ejpam-6319	334	3	...	...	PUNCT
ejpam-6319	334	4	...	...	PUNCT
ejpam-6319	334	5	.	.	PUNCT
ejpam-6319	334	6	.	.	PUNCT
ejpam-6319	335	1	.	.	PUNCT
ejpam-6319	335	2	...	...	PUNCT
ejpam-6319	336	1	...	...	PUNCT
ejpam-6319	336	2	...	...	PUNCT
ejpam-6319	336	3	.	.	PUNCT
ejpam-6319	336	4	.	.	PUNCT
ejpam-6319	337	1	.	.	PUNCT
ejpam-6319	338	1	...	...	PUNCT
ejpam-6319	339	1	−1	−1	NOUN
ejpam-6319	339	2	0	0	NUM
ejpam-6319	339	3	0	0	NUM
ejpam-6319	339	4	.	.	PUNCT
ejpam-6319	339	5	.	.	PUNCT
ejpam-6319	339	6	.	.	PUNCT
ejpam-6319	340	1	1	1	NUM
ejpam-6319	340	2	0	0	NUM
ejpam-6319	340	3	0	0	NUM
ejpam-6319	340	4	.	.	PUNCT
ejpam-6319	340	5	.	.	PUNCT
ejpam-6319	340	6	.	.	PUNCT
ejpam-6319	341	1	0	0	NUM
ejpam-6319	341	2	−1	−1	NOUN
ejpam-6319	341	3	0	0	NUM
ejpam-6319	341	4	0	0	NUM
ejpam-6319	341	5	.	.	PUNCT
ejpam-6319	341	6	.	.	PUNCT
ejpam-6319	342	1	.	.	PUNCT
ejpam-6319	343	1	0	0	NUM
ejpam-6319	344	1	1	1	NUM
ejpam-6319	344	2	0	0	NUM
ejpam-6319	344	3	.	.	PUNCT
ejpam-6319	344	4	.	.	PUNCT
ejpam-6319	344	5	.	.	PUNCT
ejpam-6319	345	1	0	0	NUM
ejpam-6319	345	2	−1	−1	NOUN
ejpam-6319	345	3	0	0	NUM
ejpam-6319	345	4	0	0	NUM
ejpam-6319	345	5	.	.	PUNCT
ejpam-6319	345	6	.	.	PUNCT
ejpam-6319	346	1	.	.	PUNCT
ejpam-6319	347	1	0	0	NUM
ejpam-6319	347	2	0	0	NUM
ejpam-6319	347	3	1	1	NUM
ejpam-6319	347	4	.	.	PUNCT
ejpam-6319	347	5	.	.	PUNCT
ejpam-6319	348	1	.	.	PUNCT
ejpam-6319	349	1	0	0	NUM
ejpam-6319	349	2	...	...	PUNCT
ejpam-6319	349	3	...	...	PUNCT
ejpam-6319	349	4	...	...	PUNCT
ejpam-6319	349	5	.	.	PUNCT
ejpam-6319	349	6	.	.	PUNCT
ejpam-6319	350	1	.	.	PUNCT
ejpam-6319	350	2	...	...	PUNCT
ejpam-6319	351	1	...	...	PUNCT
ejpam-6319	351	2	...	...	PUNCT
ejpam-6319	351	3	.	.	PUNCT
ejpam-6319	351	4	.	.	PUNCT
ejpam-6319	352	1	.	.	PUNCT
ejpam-6319	353	1	...	...	PUNCT
ejpam-6319	354	1	−1	−1	NOUN
ejpam-6319	354	2	0	0	NUM
ejpam-6319	354	3	0	0	NUM
ejpam-6319	354	4	.	.	PUNCT
ejpam-6319	354	5	.	.	PUNCT
ejpam-6319	355	1	.	.	PUNCT
ejpam-6319	356	1	0	0	NUM
ejpam-6319	357	1	0	0	NUM
ejpam-6319	357	2	0	0	NUM
ejpam-6319	357	3	.	.	PUNCT
ejpam-6319	357	4	.	.	PUNCT
ejpam-6319	357	5	.	.	PUNCT
ejpam-6319	358	1	1	1	NUM
ejpam-6319	358	2			NOUN
ejpam-6319	358	3	.	.	PUNCT
ejpam-6319	359	1	hence	hence	ADV
ejpam-6319	359	2	,	,	PUNCT
ejpam-6319	359	3	we	we	PRON
ejpam-6319	359	4	have	have	VERB
ejpam-6319	359	5	l(γd2n	l(γd2n	X
ejpam-6319	359	6	)	)	PUNCT
ejpam-6319	360	1	=	=	NOUN
ejpam-6319	361	1	(	(	PUNCT
ejpam-6319	361	2	2n−	2n−	NUM
ejpam-6319	361	3	1	1	NUM
ejpam-6319	361	4	−j1×(2n−1	−j1×(2n−1	NUM
ejpam-6319	361	5	)	)	PUNCT
ejpam-6319	361	6	−j(2n−1)×1	−j(2n−1)×1	PRON
ejpam-6319	361	7	i2n−1	i2n−1	PROPN
ejpam-6319	361	8	)	)	PUNCT
ejpam-6319	361	9	.	.	PUNCT
ejpam-6319	362	1	furthermore	furthermore	ADV
ejpam-6319	362	2	,	,	PUNCT
ejpam-6319	362	3	as	as	ADP
ejpam-6319	362	4	pl(γd2n	pl(γd2n	ADJ
ejpam-6319	362	5	)	)	PUNCT
ejpam-6319	362	6	(	(	PUNCT
ejpam-6319	362	7	λ	λ	NOUN
ejpam-6319	362	8	)	)	PUNCT
ejpam-6319	362	9	=	=	SYM
ejpam-6319	362	10	|l(γd2n)−	|l(γd2n)−	NOUN
ejpam-6319	362	11	λi2n|	λi2n|	ADP
ejpam-6319	362	12	,	,	PUNCT
ejpam-6319	362	13	then	then	ADV
ejpam-6319	362	14	pl(γd2n	pl(γd2n	ADJ
ejpam-6319	362	15	)	)	PUNCT
ejpam-6319	362	16	(	(	PUNCT
ejpam-6319	362	17	λ	λ	NOUN
ejpam-6319	362	18	)	)	PUNCT
ejpam-6319	362	19	=	=	SYM
ejpam-6319	362	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6319	362	21	λ−	λ−	PROPN
ejpam-6319	362	22	(	(	PUNCT
ejpam-6319	362	23	2n−	2n−	PROPN
ejpam-6319	362	24	1	1	NUM
ejpam-6319	362	25	)	)	PUNCT
ejpam-6319	362	26	j1×(2n−1	j1×(2n−1	PROPN
ejpam-6319	362	27	)	)	PUNCT
ejpam-6319	362	28	j(2n−1)×1	j(2n−1)×1	NOUN
ejpam-6319	362	29	(	(	PUNCT
ejpam-6319	362	30	λ−	λ−	PROPN
ejpam-6319	362	31	1)i2n−1	1)i2n−1	NUM
ejpam-6319	362	32	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6319	362	33	.	.	PUNCT
ejpam-6319	363	1	we	we	PRON
ejpam-6319	363	2	follow	follow	VERB
ejpam-6319	363	3	the	the	DET
ejpam-6319	363	4	following	follow	VERB
ejpam-6319	363	5	operational	operational	ADJ
ejpam-6319	363	6	steps	step	NOUN
ejpam-6319	363	7	(	(	PUNCT
ejpam-6319	363	8	i	i	NOUN
ejpam-6319	363	9	)	)	PUNCT
ejpam-6319	364	1	r2+i	r2+i	VERB
ejpam-6319	364	2	−→	−→	NOUN
ejpam-6319	364	3	r2+i	r2+i	PROPN
ejpam-6319	364	4	−r2	−r2	PROPN
ejpam-6319	364	5	,	,	PUNCT
ejpam-6319	364	6	for	for	ADP
ejpam-6319	364	7	i	i	PROPN
ejpam-6319	364	8	=	=	SYM
ejpam-6319	364	9	1	1	NUM
ejpam-6319	364	10	,	,	PUNCT
ejpam-6319	364	11	2	2	NUM
ejpam-6319	364	12	,	,	PUNCT
ejpam-6319	364	13	.	.	PUNCT
ejpam-6319	364	14	.	.	PUNCT
ejpam-6319	365	1	.	.	PUNCT
ejpam-6319	366	1	,	,	PUNCT
ejpam-6319	367	1	2n−	2n−	PROPN
ejpam-6319	367	2	2	2	NUM
ejpam-6319	367	3	.	.	PUNCT
ejpam-6319	367	4	(	(	PUNCT
ejpam-6319	367	5	ii	ii	NOUN
ejpam-6319	367	6	)	)	PUNCT
ejpam-6319	367	7	c2	c2	PROPN
ejpam-6319	367	8	−→	−→	PROPN
ejpam-6319	367	9	c2	c2	PROPN
ejpam-6319	367	10	+	+	CCONJ
ejpam-6319	367	11	c3	c3	PROPN
ejpam-6319	367	12	+	+	X
ejpam-6319	367	13	.	.	PUNCT
ejpam-6319	367	14	.	.	PUNCT
ejpam-6319	368	1	.+	.+	NOUN
ejpam-6319	368	2	c2n	c2n	NOUN
ejpam-6319	368	3	.	.	PUNCT
ejpam-6319	369	1	therefore	therefore	ADV
ejpam-6319	369	2	,	,	PUNCT
ejpam-6319	369	3	pl(γd2n	pl(γd2n	ADJ
ejpam-6319	369	4	)	)	PUNCT
ejpam-6319	369	5	(	(	PUNCT
ejpam-6319	369	6	λ	λ	X
ejpam-6319	369	7	)	)	PUNCT
ejpam-6319	369	8	=	=	SYM
ejpam-6319	369	9	λ(λ−	λ(λ−	PROPN
ejpam-6319	369	10	1)2n−2	1)2n−2	NUM
ejpam-6319	369	11	(	(	PUNCT
ejpam-6319	369	12	λ−	λ−	PROPN
ejpam-6319	369	13	2n	2n	NUM
ejpam-6319	369	14	)	)	PUNCT
ejpam-6319	369	15	.	.	PUNCT
ejpam-6319	370	1	2.3	2.3	NUM
ejpam-6319	370	2	.	.	PUNCT
ejpam-6319	370	3	signless	signless	PROPN
ejpam-6319	370	4	laplacian	laplacian	ADJ
ejpam-6319	370	5	energy	energy	NOUN
ejpam-6319	370	6	the	the	DET
ejpam-6319	370	7	next	next	ADJ
ejpam-6319	370	8	theorems	theorem	NOUN
ejpam-6319	370	9	are	be	AUX
ejpam-6319	370	10	the	the	DET
ejpam-6319	370	11	results	result	NOUN
ejpam-6319	370	12	of	of	ADP
ejpam-6319	370	13	the	the	DET
ejpam-6319	370	14	signless	signless	ADJ
ejpam-6319	370	15	laplacian	laplacian	ADJ
ejpam-6319	370	16	matrix	matrix	NOUN
ejpam-6319	370	17	of	of	ADP
ejpam-6319	370	18	γd2n	γd2n	PROPN
ejpam-6319	370	19	.	.	PUNCT
ejpam-6319	371	1	theorem	theorem	VERB
ejpam-6319	371	2	7	7	NUM
ejpam-6319	371	3	.	.	PUNCT
ejpam-6319	372	1	let	let	VERB
ejpam-6319	372	2	γd2n	γd2n	PROPN
ejpam-6319	372	3	be	be	AUX
ejpam-6319	372	4	the	the	DET
ejpam-6319	372	5	coprime	coprime	ADJ
ejpam-6319	372	6	graph	graph	NOUN
ejpam-6319	372	7	for	for	ADP
ejpam-6319	372	8	d2n	d2n	PROPN
ejpam-6319	372	9	with	with	ADP
ejpam-6319	372	10	n	n	PROPN
ejpam-6319	372	11	is	be	AUX
ejpam-6319	372	12	a	a	DET
ejpam-6319	372	13	prime	prime	ADJ
ejpam-6319	372	14	number	number	NOUN
ejpam-6319	372	15	or	or	CCONJ
ejpam-6319	372	16	n	n	NOUN
ejpam-6319	372	17	=	=	SYM
ejpam-6319	372	18	pk	pk	NOUN
ejpam-6319	372	19	,	,	PUNCT
ejpam-6319	372	20	p	p	PROPN
ejpam-6319	372	21	̸=	̸=	PROPN
ejpam-6319	372	22	2	2	NUM
ejpam-6319	372	23	for	for	ADP
ejpam-6319	372	24	a	a	DET
ejpam-6319	372	25	k	k	PROPN
ejpam-6319	372	26	∈	∈	PROPN
ejpam-6319	372	27	n	n	CCONJ
ejpam-6319	372	28	,	,	PUNCT
ejpam-6319	372	29	then	then	ADV
ejpam-6319	372	30	psl(γd2n	psl(γd2n	VERB
ejpam-6319	372	31	)	)	PUNCT
ejpam-6319	372	32	(	(	PUNCT
ejpam-6319	372	33	λ	λ	NOUN
ejpam-6319	372	34	)	)	PUNCT
ejpam-6319	372	35	=(	=(	NOUN
ejpam-6319	372	36	λ−	λ−	PROPN
ejpam-6319	372	37	n)n−1(λ−	n)n−1(λ−	PROPN
ejpam-6319	372	38	(	(	PUNCT
ejpam-6319	372	39	n+	n+	NUM
ejpam-6319	372	40	1))n−2	1))n−2	NUM
ejpam-6319	373	1	(	(	PUNCT
ejpam-6319	373	2	λ3	λ3	PROPN
ejpam-6319	373	3	−	−	PROPN
ejpam-6319	373	4	4nλ2	4nλ2	NUM
ejpam-6319	374	1	+	+	CCONJ
ejpam-6319	374	2	4n2λ−	4n2λ−	NUM
ejpam-6319	374	3	4n(n−	4n(n−	NUM
ejpam-6319	374	4	1	1	NUM
ejpam-6319	374	5	)	)	PUNCT
ejpam-6319	374	6	)	)	PUNCT
ejpam-6319	374	7	.	.	PUNCT
ejpam-6319	375	1	m.	m.	NOUN
ejpam-6319	375	2	u.	u.	PROPN
ejpam-6319	375	3	romdhini	romdhini	PROPN
ejpam-6319	375	4	,	,	PUNCT
ejpam-6319	375	5	abdurahim	abdurahim	PRON
ejpam-6319	375	6	,	,	PUNCT
ejpam-6319	375	7	a.	a.	PROPN
ejpam-6319	375	8	e.	e.	PROPN
ejpam-6319	375	9	s.	s.	PROPN
ejpam-6319	375	10	h.	h.	PROPN
ejpam-6319	375	11	maharani	maharani	PROPN
ejpam-6319	375	12	/	/	SYM
ejpam-6319	375	13	eur	eur	PROPN
ejpam-6319	375	14	.	.	PUNCT
ejpam-6319	376	1	j.	j.	PROPN
ejpam-6319	376	2	pure	pure	PROPN
ejpam-6319	376	3	appl	appl	PROPN
ejpam-6319	376	4	.	.	PROPN
ejpam-6319	376	5	math	math	PROPN
ejpam-6319	376	6	,	,	PUNCT
ejpam-6319	376	7	18	18	NUM
ejpam-6319	376	8	(	(	PUNCT
ejpam-6319	376	9	3	3	NUM
ejpam-6319	376	10	)	)	PUNCT
ejpam-6319	376	11	(	(	PUNCT
ejpam-6319	376	12	2025	2025	NUM
ejpam-6319	376	13	)	)	PUNCT
ejpam-6319	376	14	,	,	PUNCT
ejpam-6319	376	15	6319	6319	NUM
ejpam-6319	376	16	9	9	NUM
ejpam-6319	376	17	of	of	ADP
ejpam-6319	376	18	13	13	NUM
ejpam-6319	376	19	proof	proof	NOUN
ejpam-6319	376	20	.	.	PUNCT
ejpam-6319	377	1	as	as	ADP
ejpam-6319	377	2	the	the	DET
ejpam-6319	377	3	same	same	ADJ
ejpam-6319	377	4	argument	argument	NOUN
ejpam-6319	377	5	with	with	ADP
ejpam-6319	377	6	theorem	theorem	NOUN
ejpam-6319	377	7	5	5	NUM
ejpam-6319	377	8	and	and	CCONJ
ejpam-6319	377	9	according	accord	VERB
ejpam-6319	377	10	to	to	ADP
ejpam-6319	377	11	equation	equation	NOUN
ejpam-6319	377	12	2	2	NUM
ejpam-6319	377	13	and	and	CCONJ
ejpam-6319	377	14	definition	definition	NOUN
ejpam-6319	377	15	5	5	NUM
ejpam-6319	377	16	,	,	PUNCT
ejpam-6319	377	17	then	then	ADV
ejpam-6319	377	18	sl	sl	NOUN
ejpam-6319	377	19	-	-	PUNCT
ejpam-6319	377	20	matrix	matrix	NOUN
ejpam-6319	377	21	of	of	ADP
ejpam-6319	377	22	γd2n	γd2n	PROPN
ejpam-6319	377	23	is	be	AUX
ejpam-6319	377	24	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	377	25	)	)	PUNCT
ejpam-6319	378	1	=	=	SYM
ejpam-6319	378	2	d(γd2n	d(γd2n	X
ejpam-6319	378	3	)	)	PUNCT
ejpam-6319	378	4	+	+	NOUN
ejpam-6319	378	5	a(γd2n	a(γd2n	X
ejpam-6319	378	6	)	)	PUNCT
ejpam-6319	379	1	=	=	SYM
ejpam-6319	379	2			NOUN
ejpam-6319	380	1	2n−	2n−	NUM
ejpam-6319	380	2	1	1	NUM
ejpam-6319	380	3	1	1	NUM
ejpam-6319	380	4	1	1	NUM
ejpam-6319	380	5	.	.	PUNCT
ejpam-6319	380	6	.	.	PUNCT
ejpam-6319	380	7	.	.	PUNCT
ejpam-6319	381	1	1	1	NUM
ejpam-6319	381	2	1	1	NUM
ejpam-6319	381	3	1	1	NUM
ejpam-6319	381	4	.	.	PUNCT
ejpam-6319	381	5	.	.	PUNCT
ejpam-6319	381	6	.	.	PUNCT
ejpam-6319	382	1	1	1	NUM
ejpam-6319	382	2	1	1	NUM
ejpam-6319	382	3	n+	n+	ADP
ejpam-6319	382	4	1	1	NUM
ejpam-6319	382	5	0	0	NUM
ejpam-6319	382	6	.	.	PUNCT
ejpam-6319	382	7	.	.	PUNCT
ejpam-6319	382	8	.	.	PUNCT
ejpam-6319	383	1	0	0	NUM
ejpam-6319	383	2	1	1	NUM
ejpam-6319	383	3	1	1	NUM
ejpam-6319	383	4	.	.	PUNCT
ejpam-6319	383	5	.	.	PUNCT
ejpam-6319	383	6	.	.	PUNCT
ejpam-6319	384	1	1	1	NUM
ejpam-6319	384	2	1	1	NUM
ejpam-6319	384	3	0	0	NUM
ejpam-6319	384	4	n+	n+	NUM
ejpam-6319	384	5	1	1	NUM
ejpam-6319	384	6	.	.	PUNCT
ejpam-6319	384	7	.	.	PUNCT
ejpam-6319	384	8	.	.	PUNCT
ejpam-6319	385	1	0	0	NUM
ejpam-6319	385	2	1	1	NUM
ejpam-6319	385	3	1	1	NUM
ejpam-6319	385	4	.	.	PUNCT
ejpam-6319	385	5	.	.	PUNCT
ejpam-6319	385	6	.	.	PUNCT
ejpam-6319	386	1	1	1	NUM
ejpam-6319	386	2	...	...	PUNCT
ejpam-6319	386	3	...	...	PUNCT
ejpam-6319	386	4	...	...	PUNCT
ejpam-6319	386	5	.	.	PUNCT
ejpam-6319	386	6	.	.	PUNCT
ejpam-6319	386	7	.	.	PUNCT
ejpam-6319	387	1	...	...	PUNCT
ejpam-6319	387	2	...	...	PUNCT
ejpam-6319	387	3	...	...	PUNCT
ejpam-6319	387	4	.	.	PUNCT
ejpam-6319	387	5	.	.	PUNCT
ejpam-6319	388	1	.	.	PUNCT
ejpam-6319	389	1	...	...	PUNCT
ejpam-6319	390	1	1	1	NUM
ejpam-6319	390	2	0	0	NUM
ejpam-6319	390	3	0	0	NUM
ejpam-6319	390	4	.	.	PUNCT
ejpam-6319	390	5	.	.	PUNCT
ejpam-6319	390	6	.	.	PUNCT
ejpam-6319	391	1	n+	n+	NUM
ejpam-6319	391	2	1	1	NUM
ejpam-6319	391	3	1	1	NUM
ejpam-6319	391	4	1	1	NUM
ejpam-6319	391	5	.	.	PUNCT
ejpam-6319	391	6	.	.	PUNCT
ejpam-6319	391	7	.	.	PUNCT
ejpam-6319	392	1	1	1	NUM
ejpam-6319	392	2	1	1	NUM
ejpam-6319	392	3	1	1	NUM
ejpam-6319	392	4	1	1	NUM
ejpam-6319	392	5	.	.	PUNCT
ejpam-6319	392	6	.	.	PUNCT
ejpam-6319	392	7	.	.	PUNCT
ejpam-6319	393	1	1	1	NUM
ejpam-6319	393	2	n	n	NUM
ejpam-6319	393	3	0	0	NUM
ejpam-6319	393	4	.	.	PUNCT
ejpam-6319	393	5	.	.	PUNCT
ejpam-6319	393	6	.	.	PUNCT
ejpam-6319	394	1	0	0	NUM
ejpam-6319	394	2	1	1	NUM
ejpam-6319	394	3	1	1	NUM
ejpam-6319	394	4	1	1	NUM
ejpam-6319	394	5	.	.	PUNCT
ejpam-6319	394	6	.	.	PUNCT
ejpam-6319	394	7	.	.	PUNCT
ejpam-6319	395	1	1	1	NUM
ejpam-6319	395	2	0	0	NUM
ejpam-6319	395	3	n	n	NOUN
ejpam-6319	395	4	.	.	PUNCT
ejpam-6319	395	5	.	.	PUNCT
ejpam-6319	395	6	.	.	PUNCT
ejpam-6319	396	1	0	0	NUM
ejpam-6319	396	2	...	...	PUNCT
ejpam-6319	396	3	...	...	PUNCT
ejpam-6319	396	4	...	...	PUNCT
ejpam-6319	396	5	.	.	PUNCT
ejpam-6319	396	6	.	.	PUNCT
ejpam-6319	397	1	.	.	PUNCT
ejpam-6319	397	2	...	...	PUNCT
ejpam-6319	398	1	...	...	PUNCT
ejpam-6319	398	2	...	...	PUNCT
ejpam-6319	398	3	.	.	PUNCT
ejpam-6319	398	4	.	.	PUNCT
ejpam-6319	399	1	.	.	PUNCT
ejpam-6319	400	1	...	...	PUNCT
ejpam-6319	401	1	1	1	NUM
ejpam-6319	401	2	1	1	NUM
ejpam-6319	401	3	1	1	NUM
ejpam-6319	401	4	.	.	PUNCT
ejpam-6319	401	5	.	.	PUNCT
ejpam-6319	401	6	.	.	PUNCT
ejpam-6319	402	1	1	1	NUM
ejpam-6319	402	2	0	0	NUM
ejpam-6319	402	3	0	0	NUM
ejpam-6319	402	4	.	.	PUNCT
ejpam-6319	402	5	.	.	PUNCT
ejpam-6319	402	6	.	.	PUNCT
ejpam-6319	403	1	n	n	PROPN
ejpam-6319	404	1			PROPN
ejpam-6319	404	2	.	.	PUNCT
ejpam-6319	405	1	thus	thus	ADV
ejpam-6319	405	2	,	,	PUNCT
ejpam-6319	405	3	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	405	4	)	)	PUNCT
ejpam-6319	405	5	is	be	AUX
ejpam-6319	405	6	a	a	DET
ejpam-6319	405	7	partitioned	partition	VERB
ejpam-6319	405	8	matrix	matrix	NOUN
ejpam-6319	405	9	,	,	PUNCT
ejpam-6319	405	10	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	405	11	)	)	PUNCT
ejpam-6319	405	12	=	=	PUNCT
ejpam-6319	406	1			PROPN
ejpam-6319	406	2	2n−	2n−	PROPN
ejpam-6319	406	3	1	1	NUM
ejpam-6319	406	4	j1×(n−1	j1×(n−1	NOUN
ejpam-6319	406	5	)	)	PUNCT
ejpam-6319	406	6	j1×n	j1×n	ADJ
ejpam-6319	406	7	j(n−1)×1	j(n−1)×1	NOUN
ejpam-6319	406	8	(	(	PUNCT
ejpam-6319	406	9	n+	n+	NUM
ejpam-6319	406	10	1)in−1	1)in−1	NUM
ejpam-6319	406	11	j(n−1)×n	j(n−1)×n	PROPN
ejpam-6319	406	12	jn×1	jn×1	PROPN
ejpam-6319	406	13	jn×(n−1	jn×(n−1	PROPN
ejpam-6319	406	14	)	)	PUNCT
ejpam-6319	406	15	nin	nin	PROPN
ejpam-6319	406	16			PROPN
ejpam-6319	406	17	.	.	PUNCT
ejpam-6319	407	1	since	since	SCONJ
ejpam-6319	407	2	psl(γd2n	psl(γd2n	NOUN
ejpam-6319	407	3	)	)	PUNCT
ejpam-6319	407	4	(	(	PUNCT
ejpam-6319	407	5	λ	λ	NOUN
ejpam-6319	407	6	)	)	PUNCT
ejpam-6319	407	7	=	=	NOUN
ejpam-6319	407	8	|sl(γd2n)−	|sl(γd2n)−	NOUN
ejpam-6319	407	9	λi2n|	λi2n|	ADP
ejpam-6319	407	10	,	,	PUNCT
ejpam-6319	407	11	then	then	ADV
ejpam-6319	407	12	psl(γd2n	psl(γd2n	NOUN
ejpam-6319	407	13	)	)	PUNCT
ejpam-6319	407	14	(	(	PUNCT
ejpam-6319	407	15	λ	λ	NOUN
ejpam-6319	407	16	)	)	PUNCT
ejpam-6319	407	17	=	=	SYM
ejpam-6319	407	18	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6319	407	19	λ−	λ−	PROPN
ejpam-6319	407	20	(	(	PUNCT
ejpam-6319	407	21	2n−	2n−	PROPN
ejpam-6319	407	22	1	1	NUM
ejpam-6319	407	23	)	)	PUNCT
ejpam-6319	407	24	−j1×(n−1	−j1×(n−1	NUM
ejpam-6319	407	25	)	)	PUNCT
ejpam-6319	407	26	−j1×n	−j1×n	PUNCT
ejpam-6319	407	27	−j(n−1)×1	−j(n−1)×1	PROPN
ejpam-6319	407	28	(	(	PUNCT
ejpam-6319	407	29	λ−	λ−	PROPN
ejpam-6319	407	30	(	(	PUNCT
ejpam-6319	407	31	n+	n+	NUM
ejpam-6319	407	32	1))in−1	1))in−1	NUM
ejpam-6319	407	33	−j(n−1)×n	−j(n−1)×n	PRON
ejpam-6319	407	34	−jn×1	−jn×1	PUNCT
ejpam-6319	407	35	−jn×(n−1	−jn×(n−1	PROPN
ejpam-6319	407	36	)	)	PUNCT
ejpam-6319	407	37	(	(	PUNCT
ejpam-6319	407	38	λ−	λ−	PROPN
ejpam-6319	407	39	n)in	n)in	PROPN
ejpam-6319	407	40	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-6319	407	41	.	.	PUNCT
ejpam-6319	408	1	by	by	ADP
ejpam-6319	408	2	the	the	DET
ejpam-6319	408	3	same	same	ADJ
ejpam-6319	408	4	argument	argument	NOUN
ejpam-6319	408	5	of	of	ADP
ejpam-6319	408	6	the	the	DET
ejpam-6319	408	7	proof	proof	NOUN
ejpam-6319	408	8	of	of	ADP
ejpam-6319	408	9	theorem	theorem	NOUN
ejpam-6319	408	10	3	3	NUM
ejpam-6319	408	11	,	,	PUNCT
ejpam-6319	408	12	we	we	PRON
ejpam-6319	408	13	apply	apply	VERB
ejpam-6319	408	14	the	the	DET
ejpam-6319	408	15	following	follow	VERB
ejpam-6319	408	16	steps	step	NOUN
ejpam-6319	408	17	:	:	PUNCT
ejpam-6319	408	18	(	(	PUNCT
ejpam-6319	408	19	i	i	NOUN
ejpam-6319	408	20	)	)	PUNCT
ejpam-6319	408	21	rn+1+i	rn+1+i	NOUN
ejpam-6319	408	22	−→	−→	ADJ
ejpam-6319	408	23	rn+1+i	rn+1+i	NOUN
ejpam-6319	408	24	−rn+1	−rn+1	VERB
ejpam-6319	408	25	,	,	PUNCT
ejpam-6319	408	26	for	for	ADP
ejpam-6319	408	27	i	i	PROPN
ejpam-6319	408	28	=	=	SYM
ejpam-6319	408	29	1	1	NUM
ejpam-6319	408	30	,	,	PUNCT
ejpam-6319	408	31	2	2	NUM
ejpam-6319	408	32	,	,	PUNCT
ejpam-6319	408	33	.	.	PUNCT
ejpam-6319	408	34	.	.	PUNCT
ejpam-6319	409	1	.	.	PUNCT
ejpam-6319	410	1	,	,	PUNCT
ejpam-6319	410	2	n−	n−	NOUN
ejpam-6319	410	3	1	1	NUM
ejpam-6319	410	4	.	.	PUNCT
ejpam-6319	410	5	(	(	PUNCT
ejpam-6319	410	6	ii	ii	NOUN
ejpam-6319	410	7	)	)	PUNCT
ejpam-6319	410	8	cn+1	cn+1	VERB
ejpam-6319	410	9	−→	−→	NOUN
ejpam-6319	410	10	cn+1	cn+1	NOUN
ejpam-6319	410	11	+	+	CCONJ
ejpam-6319	410	12	cn+2	cn+2	PRON
ejpam-6319	411	1	+	+	CCONJ
ejpam-6319	411	2	.	.	PUNCT
ejpam-6319	411	3	.	.	PUNCT
ejpam-6319	412	1	.+	.+	NOUN
ejpam-6319	412	2	c2n	c2n	NOUN
ejpam-6319	412	3	.	.	PUNCT
ejpam-6319	413	1	(	(	PUNCT
ejpam-6319	413	2	iii	iii	NOUN
ejpam-6319	413	3	)	)	PUNCT
ejpam-6319	413	4	rn+1	rn+1	VERB
ejpam-6319	413	5	−→	−→	NOUN
ejpam-6319	413	6	rn+1	rn+1	X
ejpam-6319	413	7	−r1	−r1	PROPN
ejpam-6319	413	8	.	.	PUNCT
ejpam-6319	414	1	(	(	PUNCT
ejpam-6319	414	2	iv	iv	X
ejpam-6319	414	3	)	)	PUNCT
ejpam-6319	414	4	c1	c1	PROPN
ejpam-6319	414	5	−→	−→	PROPN
ejpam-6319	414	6	c1	c1	PROPN
ejpam-6319	414	7	+	+	CCONJ
ejpam-6319	414	8	(	(	PUNCT
ejpam-6319	414	9	λ−2(n−1	λ−2(n−1	ADJ
ejpam-6319	414	10	)	)	PUNCT
ejpam-6319	414	11	λ	λ	NOUN
ejpam-6319	414	12	)	)	PUNCT
ejpam-6319	414	13	cn+1	cn+1	VERB
ejpam-6319	414	14	.	.	PUNCT
ejpam-6319	415	1	(	(	PUNCT
ejpam-6319	415	2	v	v	NOUN
ejpam-6319	415	3	)	)	PUNCT
ejpam-6319	415	4	for	for	ADP
ejpam-6319	415	5	i	i	PROPN
ejpam-6319	415	6	=	=	SYM
ejpam-6319	415	7	1	1	NUM
ejpam-6319	415	8	,	,	PUNCT
ejpam-6319	415	9	2	2	NUM
ejpam-6319	415	10	,	,	PUNCT
ejpam-6319	415	11	.	.	PUNCT
ejpam-6319	415	12	.	.	PUNCT
ejpam-6319	416	1	.	.	PUNCT
ejpam-6319	417	1	,	,	PUNCT
ejpam-6319	417	2	n−	n−	NOUN
ejpam-6319	417	3	2	2	NUM
ejpam-6319	417	4	,	,	PUNCT
ejpam-6319	417	5	r2+i	r2+i	VERB
ejpam-6319	417	6	−→	−→	NOUN
ejpam-6319	417	7	r2+i	r2+i	PROPN
ejpam-6319	417	8	−r2	−r2	PROPN
ejpam-6319	417	9	.	.	PROPN
ejpam-6319	417	10	(	(	PUNCT
ejpam-6319	417	11	vi	vi	NOUN
ejpam-6319	417	12	)	)	PUNCT
ejpam-6319	417	13	c2	c2	PROPN
ejpam-6319	417	14	−→	−→	PROPN
ejpam-6319	417	15	c2	c2	PROPN
ejpam-6319	417	16	+	+	CCONJ
ejpam-6319	417	17	c2	c2	PROPN
ejpam-6319	417	18	+	+	PROPN
ejpam-6319	417	19	1	1	NUM
ejpam-6319	417	20	+	+	NUM
ejpam-6319	417	21	.	.	PUNCT
ejpam-6319	417	22	.	.	PUNCT
ejpam-6319	418	1	.+	.+	NOUN
ejpam-6319	419	1	cn	cn	PROPN
ejpam-6319	419	2	.	.	PUNCT
ejpam-6319	420	1	hence	hence	ADV
ejpam-6319	420	2	,	,	PUNCT
ejpam-6319	420	3	we	we	PRON
ejpam-6319	420	4	obtain	obtain	VERB
ejpam-6319	420	5	psl(γd2n	psl(γd2n	NOUN
ejpam-6319	420	6	)	)	PUNCT
ejpam-6319	420	7	(	(	PUNCT
ejpam-6319	420	8	λ	λ	NOUN
ejpam-6319	420	9	)	)	PUNCT
ejpam-6319	420	10	=(	=(	NOUN
ejpam-6319	420	11	λ−	λ−	PROPN
ejpam-6319	420	12	n)n−1(λ−	n)n−1(λ−	PROPN
ejpam-6319	420	13	(	(	PUNCT
ejpam-6319	420	14	n+	n+	NUM
ejpam-6319	420	15	1))n−2	1))n−2	NUM
ejpam-6319	420	16	(	(	PUNCT
ejpam-6319	420	17	λ3	λ3	PROPN
ejpam-6319	420	18	−	−	PROPN
ejpam-6319	420	19	4nλ2	4nλ2	NUM
ejpam-6319	421	1	+	+	CCONJ
ejpam-6319	421	2	4n2λ−	4n2λ−	NUM
ejpam-6319	421	3	4n(n−	4n(n−	NUM
ejpam-6319	421	4	1	1	NUM
ejpam-6319	421	5	)	)	PUNCT
ejpam-6319	421	6	)	)	PUNCT
ejpam-6319	421	7	.	.	PUNCT
ejpam-6319	422	1	m.	m.	NOUN
ejpam-6319	422	2	u.	u.	PROPN
ejpam-6319	422	3	romdhini	romdhini	PROPN
ejpam-6319	422	4	,	,	PUNCT
ejpam-6319	422	5	abdurahim	abdurahim	PRON
ejpam-6319	422	6	,	,	PUNCT
ejpam-6319	422	7	a.	a.	PROPN
ejpam-6319	422	8	e.	e.	PROPN
ejpam-6319	422	9	s.	s.	PROPN
ejpam-6319	422	10	h.	h.	PROPN
ejpam-6319	422	11	maharani	maharani	PROPN
ejpam-6319	422	12	/	/	SYM
ejpam-6319	422	13	eur	eur	PROPN
ejpam-6319	422	14	.	.	PUNCT
ejpam-6319	423	1	j.	j.	PROPN
ejpam-6319	423	2	pure	pure	PROPN
ejpam-6319	423	3	appl	appl	PROPN
ejpam-6319	423	4	.	.	PROPN
ejpam-6319	423	5	math	math	PROPN
ejpam-6319	423	6	,	,	PUNCT
ejpam-6319	423	7	18	18	NUM
ejpam-6319	423	8	(	(	PUNCT
ejpam-6319	423	9	3	3	NUM
ejpam-6319	423	10	)	)	PUNCT
ejpam-6319	423	11	(	(	PUNCT
ejpam-6319	423	12	2025	2025	NUM
ejpam-6319	423	13	)	)	PUNCT
ejpam-6319	423	14	,	,	PUNCT
ejpam-6319	423	15	6319	6319	NUM
ejpam-6319	423	16	10	10	NUM
ejpam-6319	423	17	of	of	ADP
ejpam-6319	423	18	13	13	NUM
ejpam-6319	423	19	theorem	theorem	NOUN
ejpam-6319	423	20	8	8	NUM
ejpam-6319	423	21	.	.	PUNCT
ejpam-6319	424	1	let	let	VERB
ejpam-6319	424	2	γd2n	γd2n	PROPN
ejpam-6319	424	3	be	be	AUX
ejpam-6319	424	4	the	the	DET
ejpam-6319	424	5	coprime	coprime	ADJ
ejpam-6319	424	6	graph	graph	NOUN
ejpam-6319	424	7	for	for	ADP
ejpam-6319	424	8	d2n	d2n	PROPN
ejpam-6319	424	9	with	with	ADP
ejpam-6319	424	10	n	n	NOUN
ejpam-6319	424	11	=	=	SYM
ejpam-6319	424	12	2k	2k	NUM
ejpam-6319	424	13	,	,	PUNCT
ejpam-6319	424	14	k	k	PROPN
ejpam-6319	424	15	∈	∈	PROPN
ejpam-6319	424	16	n	n	CCONJ
ejpam-6319	424	17	,	,	PUNCT
ejpam-6319	424	18	then	then	ADV
ejpam-6319	424	19	psl(γd2n	psl(γd2n	VERB
ejpam-6319	424	20	)	)	PUNCT
ejpam-6319	424	21	(	(	PUNCT
ejpam-6319	424	22	λ	λ	NOUN
ejpam-6319	424	23	)	)	PUNCT
ejpam-6319	424	24	=	=	SYM
ejpam-6319	424	25	(	(	PUNCT
ejpam-6319	424	26	λ−	λ−	PROPN
ejpam-6319	424	27	1)2n−2	1)2n−2	NUM
ejpam-6319	424	28	(	(	PUNCT
ejpam-6319	424	29	λ+	λ+	NUM
ejpam-6319	424	30	1	1	NUM
ejpam-6319	424	31	)	)	PUNCT
ejpam-6319	424	32	(	(	PUNCT
ejpam-6319	424	33	λ−	λ−	PROPN
ejpam-6319	424	34	(	(	PUNCT
ejpam-6319	424	35	2n−	2n−	PROPN
ejpam-6319	424	36	1	1	NUM
ejpam-6319	424	37	)	)	PUNCT
ejpam-6319	424	38	)	)	PUNCT
ejpam-6319	424	39	.	.	PUNCT
ejpam-6319	425	1	proof	proof	NOUN
ejpam-6319	425	2	.	.	PUNCT
ejpam-6319	426	1	based	base	VERB
ejpam-6319	426	2	on	on	ADP
ejpam-6319	426	3	the	the	DET
ejpam-6319	426	4	adjacency	adjacency	NOUN
ejpam-6319	426	5	matrix	matrix	NOUN
ejpam-6319	426	6	in	in	ADP
ejpam-6319	426	7	equation	equation	NOUN
ejpam-6319	426	8	1	1	NUM
ejpam-6319	426	9	,	,	PUNCT
ejpam-6319	426	10	the	the	DET
ejpam-6319	426	11	degree	degree	NOUN
ejpam-6319	426	12	matrix	matrix	NOUN
ejpam-6319	426	13	in	in	ADP
ejpam-6319	426	14	equation	equation	NOUN
ejpam-6319	426	15	3	3	NUM
ejpam-6319	426	16	,	,	PUNCT
ejpam-6319	426	17	and	and	CCONJ
ejpam-6319	426	18	definition	definition	NOUN
ejpam-6319	426	19	5	5	NUM
ejpam-6319	426	20	,	,	PUNCT
ejpam-6319	426	21	then	then	ADV
ejpam-6319	426	22	we	we	PRON
ejpam-6319	426	23	can	can	AUX
ejpam-6319	426	24	produce	produce	VERB
ejpam-6319	426	25	a	a	DET
ejpam-6319	426	26	2n×	2n×	PROPN
ejpam-6319	426	27	2n	2n	NUM
ejpam-6319	426	28	signless	signless	NOUN
ejpam-6319	426	29	laplacian	laplacian	ADJ
ejpam-6319	426	30	matrix	matrix	NOUN
ejpam-6319	426	31	of	of	ADP
ejpam-6319	426	32	γd2n	γd2n	PROPN
ejpam-6319	426	33	,	,	PUNCT
ejpam-6319	426	34	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	426	35	)	)	PUNCT
ejpam-6319	427	1	=	=	SYM
ejpam-6319	427	2	d(γd2n	d(γd2n	X
ejpam-6319	427	3	)	)	PUNCT
ejpam-6319	427	4	+	+	NOUN
ejpam-6319	427	5	a(γd2n	a(γd2n	X
ejpam-6319	427	6	)	)	PUNCT
ejpam-6319	428	1	=	=	SYM
ejpam-6319	428	2			NOUN
ejpam-6319	429	1	2n−	2n−	NUM
ejpam-6319	429	2	1	1	NUM
ejpam-6319	429	3	1	1	NUM
ejpam-6319	429	4	1	1	NUM
ejpam-6319	429	5	.	.	PUNCT
ejpam-6319	429	6	.	.	PUNCT
ejpam-6319	429	7	.	.	PUNCT
ejpam-6319	430	1	1	1	NUM
ejpam-6319	430	2	1	1	NUM
ejpam-6319	430	3	1	1	NUM
ejpam-6319	430	4	.	.	PUNCT
ejpam-6319	430	5	.	.	PUNCT
ejpam-6319	430	6	.	.	PUNCT
ejpam-6319	431	1	1	1	NUM
ejpam-6319	431	2	1	1	NUM
ejpam-6319	431	3	1	1	NUM
ejpam-6319	431	4	0	0	NUM
ejpam-6319	431	5	.	.	PUNCT
ejpam-6319	431	6	.	.	PUNCT
ejpam-6319	431	7	.	.	PUNCT
ejpam-6319	432	1	0	0	NUM
ejpam-6319	433	1	0	0	NUM
ejpam-6319	433	2	0	0	NUM
ejpam-6319	433	3	.	.	PUNCT
ejpam-6319	433	4	.	.	PUNCT
ejpam-6319	434	1	.	.	PUNCT
ejpam-6319	435	1	0	0	NUM
ejpam-6319	435	2	1	1	NUM
ejpam-6319	435	3	0	0	NUM
ejpam-6319	435	4	1	1	NUM
ejpam-6319	435	5	.	.	PUNCT
ejpam-6319	435	6	.	.	PUNCT
ejpam-6319	435	7	.	.	PUNCT
ejpam-6319	436	1	0	0	NUM
ejpam-6319	437	1	0	0	NUM
ejpam-6319	437	2	0	0	NUM
ejpam-6319	437	3	.	.	PUNCT
ejpam-6319	437	4	.	.	PUNCT
ejpam-6319	438	1	.	.	PUNCT
ejpam-6319	439	1	0	0	NUM
ejpam-6319	439	2	...	...	PUNCT
ejpam-6319	439	3	...	...	PUNCT
ejpam-6319	439	4	...	...	PUNCT
ejpam-6319	439	5	.	.	PUNCT
ejpam-6319	439	6	.	.	PUNCT
ejpam-6319	440	1	.	.	PUNCT
ejpam-6319	440	2	...	...	PUNCT
ejpam-6319	441	1	...	...	PUNCT
ejpam-6319	441	2	...	...	PUNCT
ejpam-6319	441	3	.	.	PUNCT
ejpam-6319	441	4	.	.	PUNCT
ejpam-6319	442	1	.	.	PUNCT
ejpam-6319	443	1	...	...	PUNCT
ejpam-6319	444	1	1	1	NUM
ejpam-6319	444	2	0	0	NUM
ejpam-6319	444	3	0	0	NUM
ejpam-6319	444	4	.	.	PUNCT
ejpam-6319	444	5	.	.	PUNCT
ejpam-6319	444	6	.	.	PUNCT
ejpam-6319	445	1	1	1	NUM
ejpam-6319	445	2	0	0	NUM
ejpam-6319	445	3	0	0	NUM
ejpam-6319	445	4	.	.	PUNCT
ejpam-6319	445	5	.	.	PUNCT
ejpam-6319	445	6	.	.	PUNCT
ejpam-6319	446	1	0	0	NUM
ejpam-6319	447	1	1	1	NUM
ejpam-6319	447	2	0	0	NUM
ejpam-6319	447	3	0	0	NUM
ejpam-6319	447	4	.	.	PUNCT
ejpam-6319	447	5	.	.	PUNCT
ejpam-6319	447	6	.	.	PUNCT
ejpam-6319	448	1	0	0	NUM
ejpam-6319	449	1	1	1	NUM
ejpam-6319	449	2	0	0	NUM
ejpam-6319	449	3	.	.	PUNCT
ejpam-6319	449	4	.	.	PUNCT
ejpam-6319	449	5	.	.	PUNCT
ejpam-6319	450	1	0	0	NUM
ejpam-6319	451	1	1	1	NUM
ejpam-6319	451	2	0	0	NUM
ejpam-6319	451	3	0	0	NUM
ejpam-6319	451	4	.	.	PUNCT
ejpam-6319	451	5	.	.	PUNCT
ejpam-6319	451	6	.	.	PUNCT
ejpam-6319	452	1	0	0	NUM
ejpam-6319	452	2	0	0	NUM
ejpam-6319	452	3	1	1	NUM
ejpam-6319	452	4	.	.	PUNCT
ejpam-6319	452	5	.	.	PUNCT
ejpam-6319	453	1	.	.	PUNCT
ejpam-6319	454	1	0	0	NUM
ejpam-6319	454	2	...	...	PUNCT
ejpam-6319	454	3	...	...	PUNCT
ejpam-6319	454	4	...	...	PUNCT
ejpam-6319	454	5	.	.	PUNCT
ejpam-6319	454	6	.	.	PUNCT
ejpam-6319	455	1	.	.	PUNCT
ejpam-6319	455	2	...	...	PUNCT
ejpam-6319	456	1	...	...	PUNCT
ejpam-6319	456	2	...	...	PUNCT
ejpam-6319	456	3	.	.	PUNCT
ejpam-6319	456	4	.	.	PUNCT
ejpam-6319	457	1	.	.	PUNCT
ejpam-6319	458	1	...	...	PUNCT
ejpam-6319	459	1	1	1	NUM
ejpam-6319	459	2	0	0	NUM
ejpam-6319	459	3	0	0	NUM
ejpam-6319	459	4	.	.	PUNCT
ejpam-6319	459	5	.	.	PUNCT
ejpam-6319	459	6	.	.	PUNCT
ejpam-6319	460	1	0	0	NUM
ejpam-6319	461	1	0	0	NUM
ejpam-6319	461	2	0	0	NUM
ejpam-6319	461	3	.	.	PUNCT
ejpam-6319	461	4	.	.	PUNCT
ejpam-6319	461	5	.	.	PUNCT
ejpam-6319	462	1	1	1	NUM
ejpam-6319	462	2			NOUN
ejpam-6319	462	3	.	.	PUNCT
ejpam-6319	463	1	in	in	ADP
ejpam-6319	463	2	this	this	DET
ejpam-6319	463	3	case	case	NOUN
ejpam-6319	463	4	,	,	PUNCT
ejpam-6319	463	5	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	463	6	)	)	PUNCT
ejpam-6319	463	7	is	be	AUX
ejpam-6319	463	8	sl(γd2n	sl(γd2n	NOUN
ejpam-6319	463	9	)	)	PUNCT
ejpam-6319	463	10	=	=	PUNCT
ejpam-6319	464	1	(	(	PUNCT
ejpam-6319	464	2	2n−	2n−	NUM
ejpam-6319	464	3	1	1	NUM
ejpam-6319	464	4	j1×(2n−1	j1×(2n−1	NOUN
ejpam-6319	464	5	)	)	PUNCT
ejpam-6319	464	6	j(2n−1)×1	j(2n−1)×1	NOUN
ejpam-6319	464	7	i2n−1	i2n−1	PROPN
ejpam-6319	464	8	)	)	PUNCT
ejpam-6319	464	9	.	.	PUNCT
ejpam-6319	465	1	hence	hence	ADV
ejpam-6319	465	2	,	,	PUNCT
ejpam-6319	465	3	using	use	VERB
ejpam-6319	465	4	|sl(γd2n)−	|sl(γd2n)−	NOUN
ejpam-6319	465	5	λi2n|	λi2n|	NOUN
ejpam-6319	465	6	,	,	PUNCT
ejpam-6319	465	7	we	we	PRON
ejpam-6319	465	8	have	have	VERB
ejpam-6319	465	9	psl(γd2n	psl(γd2n	NOUN
ejpam-6319	465	10	)	)	PUNCT
ejpam-6319	465	11	(	(	PUNCT
ejpam-6319	465	12	λ	λ	NOUN
ejpam-6319	465	13	)	)	PUNCT
ejpam-6319	465	14	=	=	SYM
ejpam-6319	465	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6319	465	16	λ−	λ−	PROPN
ejpam-6319	465	17	(	(	PUNCT
ejpam-6319	465	18	2n−	2n−	PROPN
ejpam-6319	465	19	1	1	NUM
ejpam-6319	465	20	)	)	PUNCT
ejpam-6319	465	21	−j1×(2n−1	−j1×(2n−1	NUM
ejpam-6319	465	22	)	)	PUNCT
ejpam-6319	465	23	−j(2n−1)×1	−j(2n−1)×1	PRON
ejpam-6319	465	24	(	(	PUNCT
ejpam-6319	465	25	λ−	λ−	PROPN
ejpam-6319	465	26	1)i2n−1	1)i2n−1	NUM
ejpam-6319	465	27	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6319	465	28	.	.	PUNCT
ejpam-6319	466	1	we	we	PRON
ejpam-6319	466	2	follow	follow	VERB
ejpam-6319	466	3	the	the	DET
ejpam-6319	466	4	following	follow	VERB
ejpam-6319	466	5	operational	operational	ADJ
ejpam-6319	466	6	steps	step	NOUN
ejpam-6319	466	7	(	(	PUNCT
ejpam-6319	466	8	i	i	NOUN
ejpam-6319	466	9	)	)	PUNCT
ejpam-6319	467	1	r2+i	r2+i	VERB
ejpam-6319	467	2	−→	−→	NOUN
ejpam-6319	467	3	r2+i	r2+i	PROPN
ejpam-6319	467	4	−r2	−r2	PROPN
ejpam-6319	467	5	,	,	PUNCT
ejpam-6319	467	6	for	for	ADP
ejpam-6319	467	7	i	i	PROPN
ejpam-6319	467	8	=	=	SYM
ejpam-6319	467	9	1	1	NUM
ejpam-6319	467	10	,	,	PUNCT
ejpam-6319	467	11	2	2	NUM
ejpam-6319	467	12	,	,	PUNCT
ejpam-6319	467	13	.	.	PUNCT
ejpam-6319	467	14	.	.	PUNCT
ejpam-6319	468	1	.	.	PUNCT
ejpam-6319	469	1	,	,	PUNCT
ejpam-6319	470	1	2n−	2n−	PROPN
ejpam-6319	470	2	2	2	NUM
ejpam-6319	470	3	.	.	PUNCT
ejpam-6319	470	4	(	(	PUNCT
ejpam-6319	470	5	ii	ii	NOUN
ejpam-6319	470	6	)	)	PUNCT
ejpam-6319	470	7	c2	c2	PROPN
ejpam-6319	470	8	−→	−→	PROPN
ejpam-6319	470	9	c2	c2	PROPN
ejpam-6319	470	10	+	+	CCONJ
ejpam-6319	470	11	c3	c3	PROPN
ejpam-6319	470	12	+	+	X
ejpam-6319	470	13	.	.	PUNCT
ejpam-6319	470	14	.	.	PUNCT
ejpam-6319	471	1	.+	.+	NOUN
ejpam-6319	471	2	c2n	c2n	NOUN
ejpam-6319	471	3	.	.	PUNCT
ejpam-6319	472	1	then	then	ADV
ejpam-6319	472	2	we	we	PRON
ejpam-6319	472	3	obtain	obtain	VERB
ejpam-6319	472	4	psl(γd2n	psl(γd2n	NOUN
ejpam-6319	472	5	)	)	PUNCT
ejpam-6319	472	6	(	(	PUNCT
ejpam-6319	472	7	λ	λ	X
ejpam-6319	472	8	)	)	PUNCT
ejpam-6319	472	9	=	=	SYM
ejpam-6319	472	10	λ(λ−	λ(λ−	PROPN
ejpam-6319	472	11	1)2n−2	1)2n−2	NUM
ejpam-6319	472	12	(	(	PUNCT
ejpam-6319	472	13	λ−	λ−	PROPN
ejpam-6319	472	14	2n	2n	NUM
ejpam-6319	472	15	)	)	PUNCT
ejpam-6319	472	16	.	.	PUNCT
ejpam-6319	473	1	3	3	X
ejpam-6319	473	2	.	.	X
ejpam-6319	473	3	further	further	ADJ
ejpam-6319	473	4	discussions	discussion	NOUN
ejpam-6319	473	5	in	in	ADP
ejpam-6319	473	6	comparing	compare	VERB
ejpam-6319	473	7	the	the	DET
ejpam-6319	473	8	result	result	NOUN
ejpam-6319	473	9	from	from	ADP
ejpam-6319	473	10	theorems	theorem	NOUN
ejpam-6319	473	11	6	6	NUM
ejpam-6319	473	12	and	and	CCONJ
ejpam-6319	473	13	8	8	NUM
ejpam-6319	473	14	,	,	PUNCT
ejpam-6319	473	15	we	we	PRON
ejpam-6319	473	16	derive	derive	VERB
ejpam-6319	473	17	the	the	DET
ejpam-6319	473	18	following	follow	VERB
ejpam-6319	473	19	fact	fact	NOUN
ejpam-6319	473	20	:	:	PUNCT
ejpam-6319	473	21	corollary	corollary	ADJ
ejpam-6319	473	22	1	1	X
ejpam-6319	473	23	.	.	PUNCT
ejpam-6319	474	1	let	let	VERB
ejpam-6319	474	2	γd2n	γd2n	PROPN
ejpam-6319	474	3	be	be	AUX
ejpam-6319	474	4	the	the	DET
ejpam-6319	474	5	coprime	coprime	ADJ
ejpam-6319	474	6	graph	graph	NOUN
ejpam-6319	474	7	for	for	ADP
ejpam-6319	474	8	d2n	d2n	PROPN
ejpam-6319	474	9	with	with	ADP
ejpam-6319	474	10	n	n	NOUN
ejpam-6319	474	11	=	=	SYM
ejpam-6319	474	12	2k	2k	NUM
ejpam-6319	474	13	,	,	PUNCT
ejpam-6319	474	14	k	k	PROPN
ejpam-6319	474	15	∈	∈	PROPN
ejpam-6319	474	16	n	n	CCONJ
ejpam-6319	474	17	,	,	PUNCT
ejpam-6319	474	18	then	then	ADV
ejpam-6319	474	19	pl(γd2n	pl(γd2n	ADJ
ejpam-6319	474	20	)	)	PUNCT
ejpam-6319	474	21	(	(	PUNCT
ejpam-6319	474	22	λ	λ	NOUN
ejpam-6319	474	23	)	)	PUNCT
ejpam-6319	474	24	=	=	SYM
ejpam-6319	474	25	psl(γd2n	psl(γd2n	NOUN
ejpam-6319	474	26	)	)	PUNCT
ejpam-6319	474	27	(	(	PUNCT
ejpam-6319	474	28	λ	λ	NOUN
ejpam-6319	474	29	)	)	PUNCT
ejpam-6319	474	30	.	.	PUNCT
ejpam-6319	475	1	m.	m.	PROPN
ejpam-6319	475	2	u.	u.	PROPN
ejpam-6319	475	3	romdhini	romdhini	PROPN
ejpam-6319	475	4	,	,	PUNCT
ejpam-6319	475	5	abdurahim	abdurahim	PRON
ejpam-6319	475	6	,	,	PUNCT
ejpam-6319	475	7	a.	a.	PROPN
ejpam-6319	475	8	e.	e.	PROPN
ejpam-6319	475	9	s.	s.	PROPN
ejpam-6319	475	10	h.	h.	PROPN
ejpam-6319	475	11	maharani	maharani	PROPN
ejpam-6319	475	12	/	/	SYM
ejpam-6319	475	13	eur	eur	PROPN
ejpam-6319	475	14	.	.	PUNCT
ejpam-6319	476	1	j.	j.	PROPN
ejpam-6319	476	2	pure	pure	PROPN
ejpam-6319	476	3	appl	appl	PROPN
ejpam-6319	476	4	.	.	PROPN
ejpam-6319	476	5	math	math	PROPN
ejpam-6319	476	6	,	,	PUNCT
ejpam-6319	476	7	18	18	NUM
ejpam-6319	476	8	(	(	PUNCT
ejpam-6319	476	9	3	3	NUM
ejpam-6319	476	10	)	)	PUNCT
ejpam-6319	476	11	(	(	PUNCT
ejpam-6319	476	12	2025	2025	NUM
ejpam-6319	476	13	)	)	PUNCT
ejpam-6319	476	14	,	,	PUNCT
ejpam-6319	476	15	6319	6319	NUM
ejpam-6319	476	16	11	11	NUM
ejpam-6319	476	17	of	of	ADP
ejpam-6319	476	18	13	13	NUM
ejpam-6319	476	19	according	accord	VERB
ejpam-6319	476	20	to	to	ADP
ejpam-6319	476	21	theorems	theorem	NOUN
ejpam-6319	476	22	4	4	NUM
ejpam-6319	476	23	,	,	PUNCT
ejpam-6319	476	24	6	6	NUM
ejpam-6319	476	25	,	,	PUNCT
ejpam-6319	476	26	and	and	CCONJ
ejpam-6319	476	27	8	8	NUM
ejpam-6319	477	1	,	,	PUNCT
ejpam-6319	477	2	we	we	PRON
ejpam-6319	477	3	can	can	AUX
ejpam-6319	477	4	determine	determine	VERB
ejpam-6319	477	5	the	the	DET
ejpam-6319	477	6	energy	energy	NOUN
ejpam-6319	477	7	of	of	ADP
ejpam-6319	477	8	γd2n	γd2n	PROPN
ejpam-6319	477	9	as	as	SCONJ
ejpam-6319	477	10	presented	present	VERB
ejpam-6319	477	11	in	in	ADP
ejpam-6319	477	12	theorems	theorem	NOUN
ejpam-6319	477	13	9	9	NUM
ejpam-6319	477	14	and	and	CCONJ
ejpam-6319	477	15	10	10	NUM
ejpam-6319	477	16	.	.	PUNCT
ejpam-6319	478	1	theorem	theorem	NOUN
ejpam-6319	478	2	9	9	NUM
ejpam-6319	478	3	.	.	PUNCT
ejpam-6319	479	1	let	let	VERB
ejpam-6319	479	2	γd2n	γd2n	PROPN
ejpam-6319	479	3	be	be	AUX
ejpam-6319	479	4	the	the	DET
ejpam-6319	479	5	coprime	coprime	ADJ
ejpam-6319	479	6	graph	graph	NOUN
ejpam-6319	479	7	for	for	ADP
ejpam-6319	479	8	d2n	d2n	PROPN
ejpam-6319	479	9	with	with	ADP
ejpam-6319	479	10	n	n	NOUN
ejpam-6319	479	11	=	=	SYM
ejpam-6319	479	12	2k	2k	NUM
ejpam-6319	479	13	,	,	PUNCT
ejpam-6319	479	14	k	k	PROPN
ejpam-6319	479	15	∈	∈	PROPN
ejpam-6319	479	16	n	n	CCONJ
ejpam-6319	479	17	,	,	PUNCT
ejpam-6319	479	18	then	then	ADV
ejpam-6319	479	19	ea(γd2n	ea(γd2n	NOUN
ejpam-6319	479	20	)	)	PUNCT
ejpam-6319	479	21	=	=	SYM
ejpam-6319	480	1	2	2	NUM
ejpam-6319	480	2	√	√	NOUN
ejpam-6319	480	3	2n−	2n−	NUM
ejpam-6319	480	4	1	1	NUM
ejpam-6319	480	5	=	=	SYM
ejpam-6319	480	6	2ρa(γd2n	2ρa(γd2n	NUM
ejpam-6319	480	7	)	)	PUNCT
ejpam-6319	480	8	.	.	PUNCT
ejpam-6319	481	1	proof	proof	NOUN
ejpam-6319	481	2	.	.	PUNCT
ejpam-6319	482	1	theorem	theorem	NOUN
ejpam-6319	482	2	4	4	NUM
ejpam-6319	482	3	gives	give	VERB
ejpam-6319	482	4	the	the	DET
ejpam-6319	482	5	formula	formula	NOUN
ejpam-6319	482	6	of	of	ADP
ejpam-6319	482	7	pa(γd2n	pa(γd2n	NOUN
ejpam-6319	482	8	)	)	PUNCT
ejpam-6319	482	9	(	(	PUNCT
ejpam-6319	482	10	λ	λ	X
ejpam-6319	482	11	)	)	PUNCT
ejpam-6319	482	12	.	.	PUNCT
ejpam-6319	483	1	the	the	DET
ejpam-6319	483	2	roots	root	NOUN
ejpam-6319	483	3	of	of	ADP
ejpam-6319	483	4	this	this	DET
ejpam-6319	483	5	polynomial	polynomial	NOUN
ejpam-6319	483	6	are	be	AUX
ejpam-6319	483	7	λ1	λ1	ADJ
ejpam-6319	483	8	=	=	SYM
ejpam-6319	483	9	0	0	NUM
ejpam-6319	483	10	with	with	ADP
ejpam-6319	483	11	multiplicity	multiplicity	NOUN
ejpam-6319	483	12	2n	2n	NUM
ejpam-6319	483	13	−	−	ADP
ejpam-6319	483	14	2	2	NUM
ejpam-6319	483	15	,	,	PUNCT
ejpam-6319	483	16	and	and	CCONJ
ejpam-6319	483	17	λ2,3	λ2,3	ADJ
ejpam-6319	483	18	=	=	SYM
ejpam-6319	483	19	±	±	NUM
ejpam-6319	483	20	√	√	NOUN
ejpam-6319	484	1	2n−	2n−	NUM
ejpam-6319	484	2	1	1	NUM
ejpam-6319	484	3	.	.	PUNCT
ejpam-6319	485	1	thus	thus	ADV
ejpam-6319	485	2	,	,	PUNCT
ejpam-6319	485	3	the	the	DET
ejpam-6319	485	4	spectral	spectral	ADJ
ejpam-6319	485	5	radius	radius	NOUN
ejpam-6319	485	6	and	and	CCONJ
ejpam-6319	485	7	energy	energy	NOUN
ejpam-6319	485	8	of	of	ADP
ejpam-6319	485	9	γd2n	γd2n	PROPN
ejpam-6319	485	10	corresponds	correspond	VERB
ejpam-6319	485	11	with	with	ADP
ejpam-6319	485	12	adjacency	adjacency	NOUN
ejpam-6319	485	13	matrix	matrix	NOUN
ejpam-6319	485	14	is	be	AUX
ejpam-6319	485	15	ρa(γd2n	ρa(γd2n	NOUN
ejpam-6319	485	16	)	)	PUNCT
ejpam-6319	485	17	=	=	PUNCT
ejpam-6319	486	1	√	√	PROPN
ejpam-6319	486	2	2n−	2n−	NUM
ejpam-6319	486	3	1	1	NUM
ejpam-6319	486	4	,	,	PUNCT
ejpam-6319	486	5	ea(γd2n	ea(γd2n	NOUN
ejpam-6319	486	6	)	)	PUNCT
ejpam-6319	486	7	=	=	PUNCT
ejpam-6319	487	1	(	(	PUNCT
ejpam-6319	487	2	2n−	2n−	NUM
ejpam-6319	487	3	2)|0|+	2)|0|+	PROPN
ejpam-6319	487	4	∣∣±√	∣∣±√	NOUN
ejpam-6319	487	5	2n−	2n−	PROPN
ejpam-6319	487	6	1	1	NUM
ejpam-6319	487	7	∣∣	∣∣	NOUN
ejpam-6319	487	8	=	=	SYM
ejpam-6319	487	9	2	2	NUM
ejpam-6319	487	10	√	√	PROPN
ejpam-6319	487	11	2n−	2n−	NUM
ejpam-6319	487	12	1	1	NUM
ejpam-6319	487	13	.	.	PUNCT
ejpam-6319	488	1	theorem	theorem	NOUN
ejpam-6319	488	2	10	10	NUM
ejpam-6319	488	3	.	.	PUNCT
ejpam-6319	489	1	let	let	VERB
ejpam-6319	489	2	γd2n	γd2n	PROPN
ejpam-6319	489	3	be	be	AUX
ejpam-6319	489	4	the	the	DET
ejpam-6319	489	5	coprime	coprime	ADJ
ejpam-6319	489	6	graph	graph	NOUN
ejpam-6319	489	7	for	for	ADP
ejpam-6319	489	8	d2n	d2n	PROPN
ejpam-6319	489	9	with	with	ADP
ejpam-6319	489	10	n	n	NOUN
ejpam-6319	489	11	=	=	SYM
ejpam-6319	489	12	2k	2k	NUM
ejpam-6319	489	13	,	,	PUNCT
ejpam-6319	489	14	k	k	PROPN
ejpam-6319	489	15	∈	∈	PROPN
ejpam-6319	489	16	n	n	CCONJ
ejpam-6319	489	17	,	,	PUNCT
ejpam-6319	489	18	then	then	ADV
ejpam-6319	489	19	el(γd2n	el(γd2n	ADJ
ejpam-6319	489	20	)	)	PUNCT
ejpam-6319	489	21	=	=	SYM
ejpam-6319	489	22	esl(γd2n	esl(γd2n	NOUN
ejpam-6319	489	23	)	)	PUNCT
ejpam-6319	489	24	=	=	PUNCT
ejpam-6319	490	1	2(2n−	2(2n−	NUM
ejpam-6319	490	2	1	1	NUM
ejpam-6319	490	3	)	)	PUNCT
ejpam-6319	490	4	=	=	SYM
ejpam-6319	490	5	2ρl(γd2n	2ρl(γd2n	NUM
ejpam-6319	490	6	)	)	PUNCT
ejpam-6319	490	7	=	=	SYM
ejpam-6319	491	1	2ρsl(γd2n	2ρsl(γd2n	NUM
ejpam-6319	491	2	)	)	PUNCT
ejpam-6319	491	3	.	.	PUNCT
ejpam-6319	492	1	proof	proof	NOUN
ejpam-6319	492	2	.	.	PUNCT
ejpam-6319	493	1	theorem	theorem	NOUN
ejpam-6319	493	2	1	1	NUM
ejpam-6319	493	3	gives	give	VERB
ejpam-6319	493	4	pl(γd2n	pl(γd2n	NOUN
ejpam-6319	493	5	)	)	PUNCT
ejpam-6319	493	6	(	(	PUNCT
ejpam-6319	493	7	λ	λ	NOUN
ejpam-6319	493	8	)	)	PUNCT
ejpam-6319	493	9	=	=	SYM
ejpam-6319	493	10	psl(γd2n	psl(γd2n	NOUN
ejpam-6319	493	11	)	)	PUNCT
ejpam-6319	493	12	(	(	PUNCT
ejpam-6319	493	13	λ	λ	NOUN
ejpam-6319	493	14	)	)	PUNCT
ejpam-6319	493	15	.	.	PUNCT
ejpam-6319	494	1	the	the	DET
ejpam-6319	494	2	roots	root	NOUN
ejpam-6319	494	3	of	of	ADP
ejpam-6319	494	4	this	this	DET
ejpam-6319	494	5	polynomial	polynomial	NOUN
ejpam-6319	494	6	are	be	AUX
ejpam-6319	494	7	λ1	λ1	ADJ
ejpam-6319	494	8	=	=	SYM
ejpam-6319	494	9	1	1	NUM
ejpam-6319	494	10	with	with	ADP
ejpam-6319	494	11	multiplicity	multiplicity	NOUN
ejpam-6319	494	12	2n	2n	NUM
ejpam-6319	494	13	−	−	ADP
ejpam-6319	494	14	2	2	NUM
ejpam-6319	494	15	,	,	PUNCT
ejpam-6319	494	16	and	and	CCONJ
ejpam-6319	494	17	a	a	DET
ejpam-6319	494	18	single	single	ADJ
ejpam-6319	494	19	λ2	λ2	NOUN
ejpam-6319	494	20	=	=	SYM
ejpam-6319	494	21	0	0	NUM
ejpam-6319	494	22	,	,	PUNCT
ejpam-6319	494	23	λ3	λ3	PROPN
ejpam-6319	494	24	=	=	SYM
ejpam-6319	494	25	2n	2n	NUM
ejpam-6319	494	26	.	.	PUNCT
ejpam-6319	495	1	therefore	therefore	ADV
ejpam-6319	495	2	,	,	PUNCT
ejpam-6319	495	3	the	the	DET
ejpam-6319	495	4	spectral	spectral	ADJ
ejpam-6319	495	5	radius	radius	NOUN
ejpam-6319	495	6	and	and	CCONJ
ejpam-6319	495	7	the	the	DET
ejpam-6319	495	8	energy	energy	NOUN
ejpam-6319	495	9	of	of	ADP
ejpam-6319	495	10	γd2n	γd2n	PROPN
ejpam-6319	495	11	corresponds	correspond	VERB
ejpam-6319	495	12	with	with	ADP
ejpam-6319	495	13	laplacian	laplacian	ADJ
ejpam-6319	495	14	and	and	CCONJ
ejpam-6319	495	15	signless	signless	ADJ
ejpam-6319	495	16	laplacian	laplacian	ADJ
ejpam-6319	495	17	matrices	matrix	NOUN
ejpam-6319	495	18	is	be	AUX
ejpam-6319	495	19	ρl(γd2n	ρl(γd2n	NOUN
ejpam-6319	495	20	)	)	PUNCT
ejpam-6319	496	1	=	=	SYM
ejpam-6319	496	2	ρsl(γd2n	ρsl(γd2n	NOUN
ejpam-6319	496	3	)	)	PUNCT
ejpam-6319	496	4	=	=	SYM
ejpam-6319	496	5	2n	2n	NUM
ejpam-6319	496	6	,	,	PUNCT
ejpam-6319	496	7	el(γd2n	el(γd2n	NOUN
ejpam-6319	496	8	)	)	PUNCT
ejpam-6319	496	9	=	=	SYM
ejpam-6319	496	10	esl(γd2n	esl(γd2n	NOUN
ejpam-6319	496	11	)	)	PUNCT
ejpam-6319	496	12	=	=	PUNCT
ejpam-6319	497	1	(	(	PUNCT
ejpam-6319	497	2	2n−	2n−	NUM
ejpam-6319	497	3	2)|1|+	2)|1|+	PROPN
ejpam-6319	497	4	(	(	PUNCT
ejpam-6319	497	5	1)|0|+	1)|0|+	NUM
ejpam-6319	497	6	(	(	PUNCT
ejpam-6319	497	7	1)|2n|	1)|2n|	NUM
ejpam-6319	497	8	=	=	SYM
ejpam-6319	497	9	2(2n−	2(2n−	NUM
ejpam-6319	497	10	1	1	NUM
ejpam-6319	497	11	)	)	PUNCT
ejpam-6319	497	12	.	.	PUNCT
ejpam-6319	498	1	according	accord	VERB
ejpam-6319	498	2	to	to	ADP
ejpam-6319	498	3	the	the	DET
ejpam-6319	498	4	two	two	NUM
ejpam-6319	498	5	previous	previous	ADJ
ejpam-6319	498	6	theorems	theorem	NOUN
ejpam-6319	498	7	,	,	PUNCT
ejpam-6319	498	8	we	we	PRON
ejpam-6319	498	9	can	can	AUX
ejpam-6319	498	10	conclude	conclude	VERB
ejpam-6319	498	11	that	that	SCONJ
ejpam-6319	498	12	γd2n	γd2n	PROPN
ejpam-6319	498	13	with	with	ADP
ejpam-6319	498	14	n	n	NOUN
ejpam-6319	498	15	=	=	SYM
ejpam-6319	498	16	2k	2k	NUM
ejpam-6319	498	17	,	,	PUNCT
ejpam-6319	498	18	k	k	PROPN
ejpam-6319	498	19	∈	∈	PROPN
ejpam-6319	498	20	n	n	PRON
ejpam-6319	498	21	is	be	AUX
ejpam-6319	498	22	always	always	ADV
ejpam-6319	498	23	twice	twice	DET
ejpam-6319	498	24	their	their	PRON
ejpam-6319	498	25	spectral	spectral	ADJ
ejpam-6319	498	26	radius	radius	NOUN
ejpam-6319	498	27	.	.	PUNCT
ejpam-6319	499	1	moreover	moreover	ADV
ejpam-6319	499	2	,	,	PUNCT
ejpam-6319	499	3	it	it	PRON
ejpam-6319	499	4	is	be	AUX
ejpam-6319	499	5	shown	show	VERB
ejpam-6319	499	6	that	that	SCONJ
ejpam-6319	499	7	the	the	DET
ejpam-6319	499	8	energy	energy	NOUN
ejpam-6319	499	9	of	of	ADP
ejpam-6319	499	10	γd2n	γd2n	PROPN
ejpam-6319	499	11	is	be	AUX
ejpam-6319	499	12	never	never	ADV
ejpam-6319	499	13	an	an	DET
ejpam-6319	499	14	odd	odd	ADJ
ejpam-6319	499	15	integer	integer	NOUN
ejpam-6319	499	16	and	and	CCONJ
ejpam-6319	499	17	strongly	strongly	ADV
ejpam-6319	499	18	hypoenergetic	hypoenergetic	ADJ
ejpam-6319	499	19	,	,	PUNCT
ejpam-6319	499	20	meanwhile	meanwhile	ADV
ejpam-6319	499	21	the	the	DET
ejpam-6319	499	22	l	l	NOUN
ejpam-6319	499	23	and	and	CCONJ
ejpam-6319	499	24	sl	sl	NOUN
ejpam-6319	499	25	-	-	PUNCT
ejpam-6319	499	26	energies	energy	NOUN
ejpam-6319	499	27	are	be	AUX
ejpam-6319	499	28	always	always	ADV
ejpam-6319	499	29	even	even	ADV
ejpam-6319	499	30	integers	integer	NOUN
ejpam-6319	499	31	and	and	CCONJ
ejpam-6319	499	32	are	be	AUX
ejpam-6319	499	33	nonhypoenergetic	nonhypoenergetic	ADJ
ejpam-6319	499	34	.	.	PUNCT
ejpam-6319	500	1	these	these	DET
ejpam-6319	500	2	results	result	NOUN
ejpam-6319	500	3	are	be	AUX
ejpam-6319	500	4	consistent	consistent	ADJ
ejpam-6319	500	5	with	with	ADP
ejpam-6319	500	6	the	the	DET
ejpam-6319	500	7	previous	previous	ADJ
ejpam-6319	500	8	results	result	NOUN
ejpam-6319	500	9	of	of	ADP
ejpam-6319	500	10	bapat	bapat	NOUN
ejpam-6319	500	11	and	and	CCONJ
ejpam-6319	500	12	pati	pati	NOUN
ejpam-6319	501	1	[	[	X
ejpam-6319	501	2	26	26	NUM
ejpam-6319	501	3	]	]	PUNCT
ejpam-6319	501	4	.	.	PUNCT
ejpam-6319	502	1	4	4	X
ejpam-6319	502	2	.	.	X
ejpam-6319	502	3	conclusion	conclusion	NOUN
ejpam-6319	502	4	this	this	DET
ejpam-6319	502	5	paper	paper	NOUN
ejpam-6319	502	6	presented	present	VERB
ejpam-6319	502	7	the	the	DET
ejpam-6319	502	8	spectral	spectral	ADJ
ejpam-6319	502	9	properties	property	NOUN
ejpam-6319	502	10	of	of	ADP
ejpam-6319	502	11	the	the	DET
ejpam-6319	502	12	coprime	coprime	NOUN
ejpam-6319	502	13	graph	graph	NOUN
ejpam-6319	502	14	for	for	ADP
ejpam-6319	502	15	dihedral	dihedral	ADJ
ejpam-6319	502	16	groups	group	NOUN
ejpam-6319	502	17	.	.	PUNCT
ejpam-6319	503	1	the	the	DET
ejpam-6319	503	2	spectral	spectral	ADJ
ejpam-6319	503	3	radius	radius	NOUN
ejpam-6319	503	4	and	and	CCONJ
ejpam-6319	503	5	the	the	DET
ejpam-6319	503	6	energy	energy	NOUN
ejpam-6319	503	7	of	of	ADP
ejpam-6319	503	8	γd2n	γd2n	PROPN
ejpam-6319	503	9	have	have	AUX
ejpam-6319	503	10	been	be	AUX
ejpam-6319	503	11	studied	study	VERB
ejpam-6319	503	12	.	.	PUNCT
ejpam-6319	504	1	we	we	PRON
ejpam-6319	504	2	also	also	ADV
ejpam-6319	504	3	found	find	VERB
ejpam-6319	504	4	a	a	DET
ejpam-6319	504	5	correlation	correlation	NOUN
ejpam-6319	504	6	between	between	ADP
ejpam-6319	504	7	them	they	PRON
ejpam-6319	504	8	and	and	CCONJ
ejpam-6319	504	9	the	the	DET
ejpam-6319	504	10	graph	graph	NOUN
ejpam-6319	504	11	classification	classification	NOUN
ejpam-6319	504	12	based	base	VERB
ejpam-6319	504	13	on	on	ADP
ejpam-6319	504	14	the	the	DET
ejpam-6319	504	15	obtained	obtain	VERB
ejpam-6319	504	16	energies	energy	NOUN
ejpam-6319	504	17	.	.	PUNCT
ejpam-6319	505	1	acknowledgements	acknowledgement	VERB
ejpam-6319	505	2	the	the	DET
ejpam-6319	505	3	authors	author	NOUN
ejpam-6319	505	4	thank	thank	VERB
ejpam-6319	505	5	the	the	DET
ejpam-6319	505	6	referees	referee	NOUN
ejpam-6319	505	7	for	for	ADP
ejpam-6319	505	8	their	their	PRON
ejpam-6319	505	9	helpful	helpful	ADJ
ejpam-6319	505	10	comments	comment	NOUN
ejpam-6319	505	11	and	and	CCONJ
ejpam-6319	505	12	recommendations	recommendation	NOUN
ejpam-6319	505	13	on	on	ADP
ejpam-6319	505	14	this	this	DET
ejpam-6319	505	15	article	article	NOUN
ejpam-6319	505	16	.	.	PUNCT
ejpam-6319	506	1	we	we	PRON
ejpam-6319	506	2	also	also	ADV
ejpam-6319	506	3	thank	thank	VERB
ejpam-6319	506	4	the	the	DET
ejpam-6319	506	5	university	university	PROPN
ejpam-6319	506	6	of	of	ADP
ejpam-6319	506	7	mataram	mataram	PROPN
ejpam-6319	506	8	,	,	PUNCT
ejpam-6319	506	9	indonesia	indonesia	PROPN
ejpam-6319	506	10	,	,	PUNCT
ejpam-6319	506	11	for	for	ADP
ejpam-6319	506	12	partial	partial	ADJ
ejpam-6319	506	13	funding	funding	NOUN
ejpam-6319	506	14	assistance	assistance	NOUN
ejpam-6319	506	15	.	.	PUNCT
ejpam-6319	507	1	m.	m.	NOUN
ejpam-6319	507	2	u.	u.	PROPN
ejpam-6319	507	3	romdhini	romdhini	PROPN
ejpam-6319	507	4	,	,	PUNCT
ejpam-6319	507	5	abdurahim	abdurahim	PRON
ejpam-6319	507	6	,	,	PUNCT
ejpam-6319	507	7	a.	a.	PROPN
ejpam-6319	507	8	e.	e.	PROPN
ejpam-6319	507	9	s.	s.	PROPN
ejpam-6319	507	10	h.	h.	PROPN
ejpam-6319	507	11	maharani	maharani	PROPN
ejpam-6319	507	12	/	/	SYM
ejpam-6319	507	13	eur	eur	PROPN
ejpam-6319	507	14	.	.	PUNCT
ejpam-6319	508	1	j.	j.	PROPN
ejpam-6319	508	2	pure	pure	PROPN
ejpam-6319	508	3	appl	appl	PROPN
ejpam-6319	508	4	.	.	PROPN
ejpam-6319	508	5	math	math	PROPN
ejpam-6319	508	6	,	,	PUNCT
ejpam-6319	508	7	18	18	NUM
ejpam-6319	508	8	(	(	PUNCT
ejpam-6319	508	9	3	3	NUM
ejpam-6319	508	10	)	)	PUNCT
ejpam-6319	508	11	(	(	PUNCT
ejpam-6319	508	12	2025	2025	NUM
ejpam-6319	508	13	)	)	PUNCT
ejpam-6319	508	14	,	,	PUNCT
ejpam-6319	508	15	6319	6319	NUM
ejpam-6319	508	16	12	12	NUM
ejpam-6319	508	17	of	of	ADP
ejpam-6319	508	18	13	13	NUM
ejpam-6319	508	19	references	reference	NOUN
ejpam-6319	508	20	[	[	X
ejpam-6319	508	21	1	1	NUM
ejpam-6319	508	22	]	]	X
ejpam-6319	508	23	s	s	VERB
ejpam-6319	508	24	kosari	kosari	X
ejpam-6319	508	25	,	,	PUNCT
ejpam-6319	508	26	x	x	PROPN
ejpam-6319	508	27	qiang	qiang	PROPN
ejpam-6319	508	28	,	,	PUNCT
ejpam-6319	508	29	j	j	PROPN
ejpam-6319	508	30	kacprzyk	kacprzyk	PROPN
ejpam-6319	508	31	,	,	PUNCT
ejpam-6319	508	32	q	q	PROPN
ejpam-6319	508	33	t	t	X
ejpam-6319	508	34	ain	ain	PROPN
ejpam-6319	508	35	,	,	PUNCT
ejpam-6319	508	36	and	and	CCONJ
ejpam-6319	508	37	h	h	PROPN
ejpam-6319	508	38	rashmanlou	rashmanlou	NOUN
ejpam-6319	508	39	.	.	PUNCT
ejpam-6319	509	1	a	a	DET
ejpam-6319	509	2	study	study	NOUN
ejpam-6319	509	3	on	on	ADP
ejpam-6319	509	4	topological	topological	ADJ
ejpam-6319	509	5	indices	index	NOUN
ejpam-6319	509	6	in	in	ADP
ejpam-6319	509	7	fuzzy	fuzzy	ADJ
ejpam-6319	509	8	graphs	graph	NOUN
ejpam-6319	509	9	with	with	ADP
ejpam-6319	509	10	application	application	NOUN
ejpam-6319	509	11	in	in	ADP
ejpam-6319	509	12	decision	decision	NOUN
ejpam-6319	509	13	making	make	VERB
ejpam-6319	509	14	problems	problem	NOUN
ejpam-6319	509	15	.	.	PUNCT
ejpam-6319	510	1	journal	journal	NOUN
ejpam-6319	510	2	of	of	ADP
ejpam-6319	510	3	multiple	multiple	ADV
ejpam-6319	510	4	-	-	PUNCT
ejpam-6319	510	5	valued	value	VERB
ejpam-6319	510	6	logic	logic	NOUN
ejpam-6319	510	7	&	&	CCONJ
ejpam-6319	510	8	soft	soft	ADJ
ejpam-6319	510	9	computing	computing	NOUN
ejpam-6319	510	10	,	,	PUNCT
ejpam-6319	510	11	42(5	42(5	NUM
ejpam-6319	510	12	-	-	PUNCT
ejpam-6319	510	13	6):567–589	6):567–589	NUM
ejpam-6319	510	14	,	,	PUNCT
ejpam-6319	510	15	2024	2024	NUM
ejpam-6319	510	16	.	.	PUNCT
ejpam-6319	511	1	[	[	X
ejpam-6319	511	2	2	2	NUM
ejpam-6319	511	3	]	]	X
ejpam-6319	511	4	y	y	PROPN
ejpam-6319	511	5	rao	rao	PROPN
ejpam-6319	511	6	,	,	PUNCT
ejpam-6319	511	7	s	s	VERB
ejpam-6319	511	8	kosari	kosari	X
ejpam-6319	511	9	,	,	PUNCT
ejpam-6319	511	10	s	s	NOUN
ejpam-6319	511	11	hameed	hameed	NOUN
ejpam-6319	511	12	,	,	PUNCT
ejpam-6319	511	13	and	and	CCONJ
ejpam-6319	511	14	z	z	PROPN
ejpam-6319	511	15	yousaf	yousaf	PROPN
ejpam-6319	511	16	.	.	PUNCT
ejpam-6319	511	17	multi	multi	ADJ
ejpam-6319	511	18	-	-	ADJ
ejpam-6319	511	19	attribute	attribute	NOUN
ejpam-6319	511	20	decision	decision	NOUN
ejpam-6319	511	21	-	-	PUNCT
ejpam-6319	511	22	making	making	NOUN
ejpam-6319	511	23	using	use	VERB
ejpam-6319	511	24	q	q	ADJ
ejpam-6319	511	25	-	-	PUNCT
ejpam-6319	511	26	rung	rung	ADJ
ejpam-6319	511	27	orthopair	orthopair	ADJ
ejpam-6319	511	28	fuzzy	fuzzy	ADJ
ejpam-6319	511	29	zagreb	zagreb	PROPN
ejpam-6319	511	30	index	index	PROPN
ejpam-6319	511	31	.	.	PUNCT
ejpam-6319	512	1	artificial	artificial	ADJ
ejpam-6319	512	2	intelligence	intelligence	NOUN
ejpam-6319	512	3	review	review	NOUN
ejpam-6319	512	4	,	,	PUNCT
ejpam-6319	512	5	58(153):1–31	58(153):1–31	PROPN
ejpam-6319	512	6	,	,	PUNCT
ejpam-6319	512	7	2025	2025	NUM
ejpam-6319	512	8	.	.	PUNCT
ejpam-6319	513	1	[	[	X
ejpam-6319	513	2	3	3	NUM
ejpam-6319	513	3	]	]	X
ejpam-6319	513	4	s	s	VERB
ejpam-6319	513	5	kosari	kosari	X
ejpam-6319	513	6	,	,	PUNCT
ejpam-6319	513	7	x	x	PROPN
ejpam-6319	513	8	shi	shi	PROPN
ejpam-6319	513	9	,	,	PUNCT
ejpam-6319	513	10	j	j	PROPN
ejpam-6319	513	11	kacprzyk	kacprzyk	PROPN
ejpam-6319	513	12	,	,	PUNCT
ejpam-6319	513	13	z	z	PROPN
ejpam-6319	513	14	chen	chen	PROPN
ejpam-6319	513	15	,	,	PUNCT
ejpam-6319	513	16	and	and	CCONJ
ejpam-6319	513	17	h	h	PROPN
ejpam-6319	513	18	rashmanlou	rashmanlou	NOUN
ejpam-6319	513	19	.	.	PUNCT
ejpam-6319	514	1	a	a	DET
ejpam-6319	514	2	novel	novel	ADJ
ejpam-6319	514	3	description	description	NOUN
ejpam-6319	514	4	of	of	ADP
ejpam-6319	514	5	perfectly	perfectly	ADV
ejpam-6319	514	6	regular	regular	ADJ
ejpam-6319	514	7	fuzzy	fuzzy	ADJ
ejpam-6319	514	8	graphs	graph	NOUN
ejpam-6319	514	9	with	with	ADP
ejpam-6319	514	10	application	application	NOUN
ejpam-6319	514	11	in	in	ADP
ejpam-6319	514	12	psychological	psychological	ADJ
ejpam-6319	514	13	sciences	science	NOUN
ejpam-6319	514	14	.	.	PUNCT
ejpam-6319	515	1	journal	journal	NOUN
ejpam-6319	515	2	of	of	ADP
ejpam-6319	515	3	multiple	multiple	ADV
ejpam-6319	515	4	-	-	PUNCT
ejpam-6319	515	5	valued	value	VERB
ejpam-6319	515	6	logic	logic	NOUN
ejpam-6319	515	7	&	&	CCONJ
ejpam-6319	515	8	soft	soft	ADJ
ejpam-6319	515	9	computing	computing	NOUN
ejpam-6319	515	10	,	,	PUNCT
ejpam-6319	515	11	42(5	42(5	PROPN
ejpam-6319	515	12	-	-	SYM
ejpam-6319	515	13	6):405–424	6):405–424	NUM
ejpam-6319	515	14	,	,	PUNCT
ejpam-6319	515	15	2024	2024	NUM
ejpam-6319	515	16	.	.	PUNCT
ejpam-6319	516	1	[	[	X
ejpam-6319	516	2	4	4	NUM
ejpam-6319	516	3	]	]	PUNCT
ejpam-6319	516	4	x	x	X
ejpam-6319	516	5	shi	shi	PROPN
ejpam-6319	516	6	,	,	PUNCT
ejpam-6319	516	7	s	s	VERB
ejpam-6319	516	8	kosari	kosari	X
ejpam-6319	516	9	,	,	PUNCT
ejpam-6319	516	10	p	p	NOUN
ejpam-6319	516	11	rangasamy	rangasamy	NOUN
ejpam-6319	516	12	,	,	PUNCT
ejpam-6319	516	13	r	r	NOUN
ejpam-6319	516	14	k	k	PROPN
ejpam-6319	516	15	nivedhaa	nivedhaa	PROPN
ejpam-6319	516	16	,	,	PUNCT
ejpam-6319	516	17	and	and	CCONJ
ejpam-6319	516	18	h	h	PROPN
ejpam-6319	516	19	rashmanlou	rashmanlou	NOUN
ejpam-6319	516	20	.	.	PUNCT
ejpam-6319	516	21	scaled	scale	VERB
ejpam-6319	516	22	aggregation	aggregation	NOUN
ejpam-6319	516	23	operations	operation	NOUN
ejpam-6319	516	24	over	over	ADP
ejpam-6319	516	25	three	three	NUM
ejpam-6319	516	26	-	-	PUNCT
ejpam-6319	516	27	dimensional	dimensional	ADJ
ejpam-6319	516	28	extended	extended	ADJ
ejpam-6319	516	29	intuitionistic	intuitionistic	ADJ
ejpam-6319	516	30	fuzzy	fuzzy	ADJ
ejpam-6319	516	31	index	index	NOUN
ejpam-6319	516	32	matrices	matrix	NOUN
ejpam-6319	516	33	.	.	PUNCT
ejpam-6319	517	1	journal	journal	NOUN
ejpam-6319	517	2	of	of	ADP
ejpam-6319	517	3	intelligent	intelligent	ADJ
ejpam-6319	517	4	&	&	CCONJ
ejpam-6319	517	5	fuzzy	fuzzy	ADJ
ejpam-6319	517	6	systems	system	NOUN
ejpam-6319	517	7	,	,	PUNCT
ejpam-6319	517	8	48(1	48(1	NOUN
ejpam-6319	517	9	-	-	NOUN
ejpam-6319	517	10	2):123–139	2):123–139	NUM
ejpam-6319	517	11	,	,	PUNCT
ejpam-6319	517	12	2025	2025	NUM
ejpam-6319	517	13	.	.	PUNCT
ejpam-6319	518	1	[	[	X
ejpam-6319	518	2	5	5	NUM
ejpam-6319	518	3	]	]	X
ejpam-6319	518	4	z	z	PROPN
ejpam-6319	518	5	shao	shao	PROPN
ejpam-6319	518	6	,	,	PUNCT
ejpam-6319	518	7	s	s	VERB
ejpam-6319	518	8	kosari	kosari	X
ejpam-6319	518	9	,	,	PUNCT
ejpam-6319	518	10	s	s	NOUN
ejpam-6319	518	11	raman	raman	NOUN
ejpam-6319	518	12	,	,	PUNCT
ejpam-6319	518	13	and	and	CCONJ
ejpam-6319	518	14	b	b	PROPN
ejpam-6319	518	15	ganesan	ganesan	PROPN
ejpam-6319	518	16	.	.	PUNCT
ejpam-6319	519	1	a	a	DET
ejpam-6319	519	2	study	study	NOUN
ejpam-6319	519	3	on	on	ADP
ejpam-6319	519	4	strong	strong	ADJ
ejpam-6319	519	5	and	and	CCONJ
ejpam-6319	519	6	geodetic	geodetic	ADJ
ejpam-6319	519	7	domination	domination	NOUN
ejpam-6319	519	8	integrity	integrity	NOUN
ejpam-6319	519	9	sets	set	VERB
ejpam-6319	519	10	in	in	ADP
ejpam-6319	519	11	graphs	graph	NOUN
ejpam-6319	519	12	.	.	PUNCT
ejpam-6319	520	1	communications	communication	NOUN
ejpam-6319	520	2	in	in	ADP
ejpam-6319	520	3	combinatorics	combinatoric	NOUN
ejpam-6319	520	4	and	and	CCONJ
ejpam-6319	520	5	optimization	optimization	NOUN
ejpam-6319	520	6	,	,	PUNCT
ejpam-6319	520	7	in	in	ADP
ejpam-6319	520	8	press:1–19	press:1–19	PROPN
ejpam-6319	520	9	,	,	PUNCT
ejpam-6319	520	10	2025	2025	NUM
ejpam-6319	520	11	.	.	PUNCT
ejpam-6319	521	1	[	[	X
ejpam-6319	521	2	6	6	NUM
ejpam-6319	521	3	]	]	PUNCT
ejpam-6319	521	4	x	x	X
ejpam-6319	521	5	ma	ma	PROPN
ejpam-6319	521	6	,	,	PUNCT
ejpam-6319	521	7	h	h	PROPN
ejpam-6319	521	8	wei	wei	PROPN
ejpam-6319	521	9	,	,	PUNCT
ejpam-6319	521	10	and	and	CCONJ
ejpam-6319	521	11	l	l	PROPN
ejpam-6319	521	12	yang	yang	PROPN
ejpam-6319	521	13	.	.	PUNCT
ejpam-6319	522	1	the	the	DET
ejpam-6319	522	2	coprime	coprime	ADJ
ejpam-6319	522	3	graph	graph	NOUN
ejpam-6319	522	4	of	of	ADP
ejpam-6319	522	5	a	a	DET
ejpam-6319	522	6	group	group	NOUN
ejpam-6319	522	7	.	.	PUNCT
ejpam-6319	523	1	international	international	ADJ
ejpam-6319	523	2	journal	journal	PROPN
ejpam-6319	523	3	of	of	ADP
ejpam-6319	523	4	group	group	PROPN
ejpam-6319	523	5	theory	theory	NOUN
ejpam-6319	523	6	,	,	PUNCT
ejpam-6319	523	7	3(3):13–23	3(3):13–23	NUM
ejpam-6319	523	8	,	,	PUNCT
ejpam-6319	523	9	2014	2014	NUM
ejpam-6319	523	10	.	.	PUNCT
ejpam-6319	524	1	[	[	X
ejpam-6319	524	2	7	7	X
ejpam-6319	524	3	]	]	X
ejpam-6319	524	4	m	m	NOUN
ejpam-6319	524	5	aschbacher	aschbacher	NOUN
ejpam-6319	524	6	.	.	PUNCT
ejpam-6319	525	1	finite	finite	PROPN
ejpam-6319	525	2	group	group	PROPN
ejpam-6319	525	3	theory	theory	PROPN
ejpam-6319	525	4	.	.	PUNCT
ejpam-6319	526	1	cambridge	cambridge	PROPN
ejpam-6319	526	2	university	university	PROPN
ejpam-6319	526	3	press	press	PROPN
ejpam-6319	526	4	,	,	PUNCT
ejpam-6319	526	5	cambridge	cambridge	PROPN
ejpam-6319	526	6	,	,	PUNCT
ejpam-6319	526	7	2000	2000	NUM
ejpam-6319	526	8	.	.	PUNCT
ejpam-6319	527	1	[	[	X
ejpam-6319	527	2	8	8	NUM
ejpam-6319	527	3	]	]	X
ejpam-6319	527	4	i	i	PROPN
ejpam-6319	527	5	gutman	gutman	PROPN
ejpam-6319	527	6	.	.	PUNCT
ejpam-6319	528	1	the	the	DET
ejpam-6319	528	2	energy	energy	NOUN
ejpam-6319	528	3	of	of	ADP
ejpam-6319	528	4	graph	graph	NOUN
ejpam-6319	528	5	.	.	PUNCT
ejpam-6319	529	1	ber	ber	NOUN
ejpam-6319	529	2	.	.	PUNCT
ejpam-6319	529	3	math.-stat	math.-stat	PROPN
ejpam-6319	529	4	.	.	PROPN
ejpam-6319	529	5	sekt	sekt	PROPN
ejpam-6319	529	6	.	.	PUNCT
ejpam-6319	530	1	forschungsz	forschungsz	PROPN
ejpam-6319	530	2	.	.	PUNCT
ejpam-6319	531	1	graz	graz	PROPN
ejpam-6319	531	2	,	,	PUNCT
ejpam-6319	531	3	103:1–2	103:1–2	NUM
ejpam-6319	531	4	,	,	PUNCT
ejpam-6319	531	5	1978	1978	NUM
ejpam-6319	531	6	.	.	PUNCT
ejpam-6319	532	1	[	[	X
ejpam-6319	532	2	9	9	NUM
ejpam-6319	532	3	]	]	SYM
ejpam-6319	532	4	x	x	X
ejpam-6319	532	5	li	li	PROPN
ejpam-6319	532	6	,	,	PUNCT
ejpam-6319	532	7	y	y	PROPN
ejpam-6319	532	8	shi	shi	PROPN
ejpam-6319	532	9	,	,	PUNCT
ejpam-6319	532	10	and	and	CCONJ
ejpam-6319	532	11	i	i	PROPN
ejpam-6319	532	12	gutman	gutman	NOUN
ejpam-6319	532	13	.	.	PUNCT
ejpam-6319	533	1	graph	graph	NOUN
ejpam-6319	533	2	energy	energy	NOUN
ejpam-6319	533	3	.	.	PUNCT
ejpam-6319	534	1	springer	springer	NOUN
ejpam-6319	534	2	,	,	PUNCT
ejpam-6319	534	3	new	new	PROPN
ejpam-6319	534	4	york	york	PROPN
ejpam-6319	534	5	,	,	PUNCT
ejpam-6319	534	6	2012	2012	NUM
ejpam-6319	534	7	.	.	PUNCT
ejpam-6319	535	1	[	[	X
ejpam-6319	535	2	10	10	NUM
ejpam-6319	535	3	]	]	X
ejpam-6319	535	4	m	m	VERB
ejpam-6319	535	5	u	u	NOUN
ejpam-6319	535	6	romdhini	romdhini	NOUN
ejpam-6319	535	7	,	,	PUNCT
ejpam-6319	535	8	a	a	DET
ejpam-6319	535	9	nawawi	nawawi	NOUN
ejpam-6319	535	10	,	,	PUNCT
ejpam-6319	535	11	f	f	PROPN
ejpam-6319	535	12	al	al	PROPN
ejpam-6319	535	13	-	-	PUNCT
ejpam-6319	535	14	sharqi	sharqi	PROPN
ejpam-6319	535	15	,	,	PUNCT
ejpam-6319	535	16	a	a	DET
ejpam-6319	535	17	al	al	PROPN
ejpam-6319	535	18	-	-	PUNCT
ejpam-6319	535	19	quran	quran	PROPN
ejpam-6319	535	20	,	,	PUNCT
ejpam-6319	535	21	and	and	CCONJ
ejpam-6319	535	22	s	s	NOUN
ejpam-6319	535	23	r	r	NOUN
ejpam-6319	535	24	kamali	kamali	X
ejpam-6319	535	25	.	.	PUNCT
ejpam-6319	536	1	wienerhosoya	wienerhosoya	PROPN
ejpam-6319	536	2	energy	energy	NOUN
ejpam-6319	536	3	of	of	ADP
ejpam-6319	536	4	non	non	ADJ
ejpam-6319	536	5	-	-	ADJ
ejpam-6319	536	6	commuting	commuting	ADJ
ejpam-6319	536	7	graph	graph	NOUN
ejpam-6319	536	8	for	for	ADP
ejpam-6319	536	9	dihedral	dihedral	ADJ
ejpam-6319	536	10	groups	group	NOUN
ejpam-6319	536	11	.	.	PUNCT
ejpam-6319	537	1	asia	asia	PROPN
ejpam-6319	537	2	pacific	pacific	PROPN
ejpam-6319	537	3	journal	journal	PROPN
ejpam-6319	537	4	of	of	ADP
ejpam-6319	537	5	mathematics	mathematic	NOUN
ejpam-6319	537	6	,	,	PUNCT
ejpam-6319	537	7	11(9):1–9	11(9):1–9	NUM
ejpam-6319	537	8	,	,	PUNCT
ejpam-6319	537	9	2024	2024	NUM
ejpam-6319	537	10	.	.	PUNCT
ejpam-6319	538	1	[	[	X
ejpam-6319	538	2	11	11	NUM
ejpam-6319	538	3	]	]	SYM
ejpam-6319	538	4	m	m	VERB
ejpam-6319	538	5	u	u	NOUN
ejpam-6319	538	6	romdhini	romdhini	NOUN
ejpam-6319	538	7	and	and	CCONJ
ejpam-6319	538	8	a	a	DET
ejpam-6319	538	9	nawawi	nawawi	NOUN
ejpam-6319	538	10	.	.	PUNCT
ejpam-6319	539	1	on	on	ADP
ejpam-6319	539	2	the	the	DET
ejpam-6319	539	3	spectral	spectral	ADJ
ejpam-6319	539	4	radius	radius	NOUN
ejpam-6319	539	5	and	and	CCONJ
ejpam-6319	539	6	sombor	sombor	NOUN
ejpam-6319	539	7	energy	energy	NOUN
ejpam-6319	539	8	of	of	ADP
ejpam-6319	539	9	the	the	DET
ejpam-6319	539	10	non	non	ADJ
ejpam-6319	539	11	-	-	ADJ
ejpam-6319	539	12	commuting	commuting	ADJ
ejpam-6319	539	13	graph	graph	NOUN
ejpam-6319	539	14	for	for	ADP
ejpam-6319	539	15	dihedral	dihedral	ADJ
ejpam-6319	539	16	groups	group	NOUN
ejpam-6319	539	17	.	.	PUNCT
ejpam-6319	540	1	malaysian	malaysian	ADJ
ejpam-6319	540	2	journal	journal	PROPN
ejpam-6319	540	3	of	of	ADP
ejpam-6319	540	4	fundamental	fundamental	ADJ
ejpam-6319	540	5	and	and	CCONJ
ejpam-6319	540	6	applied	applied	ADJ
ejpam-6319	540	7	sciences	science	NOUN
ejpam-6319	540	8	,	,	PUNCT
ejpam-6319	540	9	20:65–73	20:65–73	NUM
ejpam-6319	540	10	,	,	PUNCT
ejpam-6319	540	11	2024	2024	NUM
ejpam-6319	540	12	.	.	PUNCT
ejpam-6319	541	1	[	[	X
ejpam-6319	541	2	12	12	NUM
ejpam-6319	541	3	]	]	X
ejpam-6319	541	4	m	m	VERB
ejpam-6319	541	5	u	u	NOUN
ejpam-6319	541	6	romdhini	romdhini	NOUN
ejpam-6319	541	7	,	,	PUNCT
ejpam-6319	541	8	p	p	PROPN
ejpam-6319	541	9	rana	rana	PROPN
ejpam-6319	541	10	,	,	PUNCT
ejpam-6319	541	11	a	a	DET
ejpam-6319	541	12	sehgal	sehgal	NOUN
ejpam-6319	541	13	,	,	PUNCT
ejpam-6319	541	14	and	and	CCONJ
ejpam-6319	541	15	p	p	PROPN
ejpam-6319	541	16	bhatia	bhatia	PROPN
ejpam-6319	541	17	.	.	PUNCT
ejpam-6319	542	1	structural	structural	ADJ
ejpam-6319	542	2	properties	property	NOUN
ejpam-6319	542	3	and	and	CCONJ
ejpam-6319	542	4	characteristic	characteristic	ADJ
ejpam-6319	542	5	polynomials	polynomial	NOUN
ejpam-6319	542	6	of	of	ADP
ejpam-6319	542	7	cubic	cubic	ADJ
ejpam-6319	542	8	power	power	NOUN
ejpam-6319	542	9	graph	graph	NOUN
ejpam-6319	542	10	of	of	ADP
ejpam-6319	542	11	dihedral	dihedral	ADJ
ejpam-6319	542	12	group	group	NOUN
ejpam-6319	542	13	.	.	PUNCT
ejpam-6319	543	1	mathematics	mathematic	NOUN
ejpam-6319	543	2	and	and	CCONJ
ejpam-6319	543	3	statistics	statistic	NOUN
ejpam-6319	543	4	,	,	PUNCT
ejpam-6319	543	5	13(2):97–104	13(2):97–104	PROPN
ejpam-6319	543	6	,	,	PUNCT
ejpam-6319	543	7	2025	2025	NUM
ejpam-6319	543	8	.	.	PUNCT
ejpam-6319	544	1	[	[	X
ejpam-6319	544	2	13	13	NUM
ejpam-6319	544	3	]	]	X
ejpam-6319	544	4	p	p	X
ejpam-6319	544	5	rana	rana	PROPN
ejpam-6319	544	6	,	,	PUNCT
ejpam-6319	544	7	a	a	DET
ejpam-6319	544	8	sehgal	sehgal	PROPN
ejpam-6319	544	9	,	,	PUNCT
ejpam-6319	544	10	p	p	PROPN
ejpam-6319	544	11	bhatia	bhatia	PROPN
ejpam-6319	544	12	,	,	PUNCT
ejpam-6319	544	13	and	and	CCONJ
ejpam-6319	544	14	p	p	PROPN
ejpam-6319	544	15	kumar	kumar	PROPN
ejpam-6319	544	16	.	.	PUNCT
ejpam-6319	545	1	topological	topological	ADJ
ejpam-6319	545	2	indices	index	NOUN
ejpam-6319	545	3	and	and	CCONJ
ejpam-6319	545	4	structural	structural	ADJ
ejpam-6319	545	5	properties	property	NOUN
ejpam-6319	545	6	of	of	ADP
ejpam-6319	545	7	cubic	cubic	ADJ
ejpam-6319	545	8	power	power	NOUN
ejpam-6319	545	9	graph	graph	NOUN
ejpam-6319	545	10	of	of	ADP
ejpam-6319	545	11	dihedral	dihedral	ADJ
ejpam-6319	545	12	group	group	NOUN
ejpam-6319	545	13	.	.	PUNCT
ejpam-6319	546	1	contemporary	contemporary	ADJ
ejpam-6319	546	2	mathematics	mathematics	PROPN
ejpam-6319	546	3	,	,	PUNCT
ejpam-6319	546	4	5(1):761–779	5(1):761–779	NUM
ejpam-6319	546	5	,	,	PUNCT
ejpam-6319	546	6	2024	2024	NUM
ejpam-6319	546	7	.	.	PUNCT
ejpam-6319	547	1	[	[	X
ejpam-6319	547	2	14	14	NUM
ejpam-6319	547	3	]	]	X
ejpam-6319	547	4	p	p	X
ejpam-6319	547	5	rana	rana	PROPN
ejpam-6319	547	6	,	,	PUNCT
ejpam-6319	547	7	s	s	PART
ejpam-6319	547	8	aggarwal	aggarwal	NOUN
ejpam-6319	547	9	,	,	PUNCT
ejpam-6319	547	10	a	a	DET
ejpam-6319	547	11	sehgal	sehgal	NOUN
ejpam-6319	547	12	,	,	PUNCT
ejpam-6319	547	13	and	and	CCONJ
ejpam-6319	547	14	p	p	PROPN
ejpam-6319	547	15	bhatia	bhatia	PROPN
ejpam-6319	547	16	.	.	PUNCT
ejpam-6319	548	1	structural	structural	ADJ
ejpam-6319	548	2	properties	property	NOUN
ejpam-6319	548	3	and	and	CCONJ
ejpam-6319	548	4	laplacian	laplacian	ADJ
ejpam-6319	548	5	spectrum	spectrum	NOUN
ejpam-6319	548	6	of	of	ADP
ejpam-6319	548	7	equal	equal	ADJ
ejpam-6319	548	8	-	-	PUNCT
ejpam-6319	548	9	square	square	ADJ
ejpam-6319	548	10	graph	graph	NOUN
ejpam-6319	548	11	of	of	ADP
ejpam-6319	548	12	finite	finite	ADJ
ejpam-6319	548	13	groups	group	NOUN
ejpam-6319	548	14	.	.	PUNCT
ejpam-6319	549	1	palestine	palestine	PROPN
ejpam-6319	549	2	journal	journal	PROPN
ejpam-6319	549	3	of	of	ADP
ejpam-6319	549	4	mathematics	mathematics	PROPN
ejpam-6319	549	5	,	,	PUNCT
ejpam-6319	549	6	13(sp.issue	13(sp.issue	NOUN
ejpam-6319	549	7	iii):154–161	iii):154–161	ADJ
ejpam-6319	549	8	,	,	PUNCT
ejpam-6319	549	9	2024	2024	NUM
ejpam-6319	549	10	.	.	PUNCT
ejpam-6319	550	1	[	[	X
ejpam-6319	550	2	15	15	NUM
ejpam-6319	550	3	]	]	X
ejpam-6319	550	4	m	m	VERB
ejpam-6319	550	5	u	u	NOUN
ejpam-6319	550	6	romdhini	romdhini	NOUN
ejpam-6319	550	7	,	,	PUNCT
ejpam-6319	550	8	a	a	DET
ejpam-6319	550	9	nawawi	nawawi	NOUN
ejpam-6319	550	10	,	,	PUNCT
ejpam-6319	550	11	s	s	PART
ejpam-6319	550	12	k	k	PROPN
ejpam-6319	550	13	s	s	PROPN
ejpam-6319	550	14	husain	husain	NOUN
ejpam-6319	550	15	,	,	PUNCT
ejpam-6319	550	16	f	f	PROPN
ejpam-6319	550	17	al	al	PROPN
ejpam-6319	550	18	-	-	PUNCT
ejpam-6319	550	19	sharqi	sharqi	PROPN
ejpam-6319	550	20	,	,	PUNCT
ejpam-6319	550	21	and	and	CCONJ
ejpam-6319	550	22	n	n	DET
ejpam-6319	550	23	a	a	DET
ejpam-6319	550	24	purnamasari	purnamasari	NOUN
ejpam-6319	550	25	.	.	PUNCT
ejpam-6319	551	1	on	on	ADP
ejpam-6319	551	2	energy	energy	NOUN
ejpam-6319	551	3	of	of	ADP
ejpam-6319	551	4	prime	prime	ADJ
ejpam-6319	551	5	ideal	ideal	ADJ
ejpam-6319	551	6	graph	graph	NOUN
ejpam-6319	551	7	of	of	ADP
ejpam-6319	551	8	a	a	DET
ejpam-6319	551	9	commutative	commutative	ADJ
ejpam-6319	551	10	ring	ring	NOUN
ejpam-6319	551	11	associated	associate	VERB
ejpam-6319	551	12	with	with	ADP
ejpam-6319	551	13	transmissionbased	transmissionbase	VERB
ejpam-6319	551	14	matrices	matrix	NOUN
ejpam-6319	551	15	.	.	PUNCT
ejpam-6319	552	1	malaysian	malaysian	ADJ
ejpam-6319	552	2	journal	journal	PROPN
ejpam-6319	552	3	of	of	ADP
ejpam-6319	552	4	mathematical	mathematical	ADJ
ejpam-6319	552	5	sciences	science	NOUN
ejpam-6319	552	6	,	,	PUNCT
ejpam-6319	552	7	18(3):663–674	18(3):663–674	NUM
ejpam-6319	552	8	,	,	PUNCT
ejpam-6319	552	9	2024	2024	NUM
ejpam-6319	552	10	.	.	PUNCT
ejpam-6319	553	1	[	[	X
ejpam-6319	553	2	16	16	NUM
ejpam-6319	553	3	]	]	X
ejpam-6319	553	4	abdurahim	abdurahim	PROPN
ejpam-6319	553	5	,	,	PUNCT
ejpam-6319	553	6	m	m	VERB
ejpam-6319	553	7	u	u	NOUN
ejpam-6319	553	8	romdhini	romdhini	NOUN
ejpam-6319	553	9	,	,	PUNCT
ejpam-6319	553	10	f	f	PROPN
ejpam-6319	553	11	al	al	PROPN
ejpam-6319	553	12	-	-	PUNCT
ejpam-6319	553	13	sharqi	sharqi	PROPN
ejpam-6319	553	14	,	,	PUNCT
ejpam-6319	553	15	and	and	CCONJ
ejpam-6319	553	16	n	n	DET
ejpam-6319	553	17	a	a	DET
ejpam-6319	553	18	robbaniyyah	robbaniyyah	NOUN
ejpam-6319	553	19	.	.	PUNCT
ejpam-6319	554	1	relative	relative	ADJ
ejpam-6319	554	2	prime	prime	PROPN
ejpam-6319	554	3	coprime	coprime	NOUN
ejpam-6319	554	4	graph	graph	NOUN
ejpam-6319	554	5	of	of	ADP
ejpam-6319	554	6	integers	integer	NOUN
ejpam-6319	554	7	modulo	modulo	PROPN
ejpam-6319	554	8	group	group	NOUN
ejpam-6319	554	9	and	and	CCONJ
ejpam-6319	554	10	its	its	PRON
ejpam-6319	554	11	reverse	reverse	ADJ
ejpam-6319	554	12	topological	topological	ADJ
ejpam-6319	554	13	indices	index	NOUN
ejpam-6319	554	14	.	.	PUNCT
ejpam-6319	555	1	panm	panm	NOUN
ejpam-6319	555	2	.	.	PUNCT
ejpam-6319	556	1	u.	u.	PROPN
ejpam-6319	556	2	romdhini	romdhini	PROPN
ejpam-6319	556	3	,	,	PUNCT
ejpam-6319	556	4	abdurahim	abdurahim	PRON
ejpam-6319	556	5	,	,	PUNCT
ejpam-6319	556	6	a.	a.	PROPN
ejpam-6319	556	7	e.	e.	PROPN
ejpam-6319	556	8	s.	s.	PROPN
ejpam-6319	556	9	h.	h.	PROPN
ejpam-6319	556	10	maharani	maharani	PROPN
ejpam-6319	556	11	/	/	SYM
ejpam-6319	556	12	eur	eur	PROPN
ejpam-6319	556	13	.	.	PUNCT
ejpam-6319	557	1	j.	j.	PROPN
ejpam-6319	557	2	pure	pure	PROPN
ejpam-6319	557	3	appl	appl	PROPN
ejpam-6319	557	4	.	.	PROPN
ejpam-6319	557	5	math	math	PROPN
ejpam-6319	557	6	,	,	PUNCT
ejpam-6319	557	7	18	18	NUM
ejpam-6319	557	8	(	(	PUNCT
ejpam-6319	557	9	3	3	NUM
ejpam-6319	557	10	)	)	PUNCT
ejpam-6319	557	11	(	(	PUNCT
ejpam-6319	557	12	2025	2025	NUM
ejpam-6319	557	13	)	)	PUNCT
ejpam-6319	557	14	,	,	PUNCT
ejpam-6319	557	15	6319	6319	NUM
ejpam-6319	557	16	13	13	NUM
ejpam-6319	557	17	of	of	ADP
ejpam-6319	557	18	13	13	NUM
ejpam-6319	557	19	american	american	ADJ
ejpam-6319	557	20	journal	journal	PROPN
ejpam-6319	557	21	of	of	ADP
ejpam-6319	557	22	mathematics	mathematic	NOUN
ejpam-6319	557	23	,	,	PUNCT
ejpam-6319	557	24	4(10):1–9	4(10):1–9	NOUN
ejpam-6319	557	25	,	,	PUNCT
ejpam-6319	557	26	2025	2025	NUM
ejpam-6319	557	27	.	.	PUNCT
ejpam-6319	558	1	[	[	X
ejpam-6319	558	2	17	17	NUM
ejpam-6319	558	3	]	]	X
ejpam-6319	558	4	a	a	DET
ejpam-6319	558	5	sehgal	sehgal	ADJ
ejpam-6319	558	6	,	,	PUNCT
ejpam-6319	558	7	manjeet	manjeet	ADJ
ejpam-6319	558	8	,	,	PUNCT
ejpam-6319	558	9	and	and	CCONJ
ejpam-6319	558	10	d	d	ADP
ejpam-6319	558	11	singh	singh	PROPN
ejpam-6319	558	12	.	.	PUNCT
ejpam-6319	559	1	co	co	ADJ
ejpam-6319	559	2	-	-	ADJ
ejpam-6319	559	3	prime	prime	ADJ
ejpam-6319	559	4	order	order	NOUN
ejpam-6319	559	5	graphs	graph	NOUN
ejpam-6319	559	6	of	of	ADP
ejpam-6319	559	7	finite	finite	ADJ
ejpam-6319	559	8	abelian	abelian	ADJ
ejpam-6319	559	9	groups	group	NOUN
ejpam-6319	559	10	and	and	CCONJ
ejpam-6319	559	11	dihedral	dihedral	ADJ
ejpam-6319	559	12	groups	group	NOUN
ejpam-6319	559	13	.	.	PUNCT
ejpam-6319	560	1	journal	journal	NOUN
ejpam-6319	560	2	of	of	ADP
ejpam-6319	560	3	mathematics	mathematic	NOUN
ejpam-6319	560	4	and	and	CCONJ
ejpam-6319	560	5	computer	computer	NOUN
ejpam-6319	560	6	science	science	NOUN
ejpam-6319	560	7	,	,	PUNCT
ejpam-6319	560	8	23:196–202	23:196–202	PROPN
ejpam-6319	560	9	,	,	PUNCT
ejpam-6319	560	10	2021	2021	NUM
ejpam-6319	560	11	.	.	PUNCT
ejpam-6319	561	1	[	[	X
ejpam-6319	561	2	18	18	NUM
ejpam-6319	561	3	]	]	X
ejpam-6319	561	4	s	s	PROPN
ejpam-6319	561	5	hao	hao	PROPN
ejpam-6319	561	6	,	,	PUNCT
ejpam-6319	561	7	g	g	PROPN
ejpam-6319	561	8	zhong	zhong	PROPN
ejpam-6319	561	9	,	,	PUNCT
ejpam-6319	561	10	and	and	CCONJ
ejpam-6319	561	11	x	x	PROPN
ejpam-6319	561	12	ma	ma	PROPN
ejpam-6319	561	13	.	.	PROPN
ejpam-6319	561	14	notes	note	NOUN
ejpam-6319	561	15	on	on	ADP
ejpam-6319	561	16	the	the	DET
ejpam-6319	561	17	coprime	coprime	NOUN
ejpam-6319	561	18	order	order	NOUN
ejpam-6319	561	19	graph	graph	NOUN
ejpam-6319	561	20	of	of	ADP
ejpam-6319	561	21	a	a	DET
ejpam-6319	561	22	group	group	NOUN
ejpam-6319	561	23	.	.	PUNCT
ejpam-6319	562	1	in	in	ADP
ejpam-6319	562	2	proceedings	proceeding	NOUN
ejpam-6319	562	3	of	of	ADP
ejpam-6319	562	4	the	the	DET
ejpam-6319	562	5	bulgarian	bulgarian	PROPN
ejpam-6319	562	6	academy	academy	PROPN
ejpam-6319	562	7	of	of	ADP
ejpam-6319	562	8	sciences	sciences	PROPN
ejpam-6319	562	9	,	,	PUNCT
ejpam-6319	562	10	75(3):340–348	75(3):340–348	PROPN
ejpam-6319	562	11	,	,	PUNCT
ejpam-6319	562	12	2022	2022	NUM
ejpam-6319	562	13	.	.	PUNCT
ejpam-6319	563	1	[	[	X
ejpam-6319	563	2	19	19	NUM
ejpam-6319	563	3	]	]	X
ejpam-6319	563	4	h	h	NOUN
ejpam-6319	563	5	li	li	PROPN
ejpam-6319	563	6	,	,	PUNCT
ejpam-6319	563	7	g	g	PROPN
ejpam-6319	563	8	zhong	zhong	PROPN
ejpam-6319	563	9	,	,	PUNCT
ejpam-6319	563	10	and	and	CCONJ
ejpam-6319	563	11	x	x	PROPN
ejpam-6319	563	12	ma	ma	PROPN
ejpam-6319	563	13	.	.	PROPN
ejpam-6319	563	14	finite	finite	PROPN
ejpam-6319	563	15	groups	group	NOUN
ejpam-6319	563	16	whose	whose	DET
ejpam-6319	563	17	co	co	NOUN
ejpam-6319	563	18	-	-	ADJ
ejpam-6319	563	19	prime	prime	ADJ
ejpam-6319	563	20	order	order	NOUN
ejpam-6319	563	21	graphs	graph	NOUN
ejpam-6319	563	22	have	have	VERB
ejpam-6319	563	23	positive	positive	ADJ
ejpam-6319	563	24	genus	genus	NOUN
ejpam-6319	563	25	.	.	PUNCT
ejpam-6319	564	1	in	in	ADP
ejpam-6319	564	2	proceedings	proceeding	NOUN
ejpam-6319	564	3	of	of	ADP
ejpam-6319	564	4	the	the	DET
ejpam-6319	564	5	bulgarian	bulgarian	PROPN
ejpam-6319	564	6	academy	academy	PROPN
ejpam-6319	564	7	of	of	ADP
ejpam-6319	564	8	sciences	sciences	PROPN
ejpam-6319	564	9	,	,	PUNCT
ejpam-6319	564	10	75(9):1270	75(9):1270	NUM
ejpam-6319	564	11	–	–	PUNCT
ejpam-6319	564	12	1278	1278	NUM
ejpam-6319	564	13	,	,	PUNCT
ejpam-6319	564	14	2022	2022	NUM
ejpam-6319	564	15	.	.	PUNCT
ejpam-6319	565	1	[	[	X
ejpam-6319	565	2	20	20	NUM
ejpam-6319	565	3	]	]	X
ejpam-6319	565	4	m	m	PROPN
ejpam-6319	565	5	saini	saini	PROPN
ejpam-6319	565	6	,	,	PUNCT
ejpam-6319	565	7	g	g	PROPN
ejpam-6319	565	8	singh	singh	PROPN
ejpam-6319	565	9	,	,	PUNCT
ejpam-6319	565	10	a	a	DET
ejpam-6319	565	11	sehgal	sehgal	ADJ
ejpam-6319	565	12	,	,	PUNCT
ejpam-6319	565	13	and	and	CCONJ
ejpam-6319	565	14	d	d	ADP
ejpam-6319	565	15	singh	singh	PROPN
ejpam-6319	565	16	.	.	PUNCT
ejpam-6319	566	1	on	on	ADP
ejpam-6319	566	2	divisor	divisor	NOUN
ejpam-6319	566	3	labeling	labeling	NOUN
ejpam-6319	566	4	of	of	ADP
ejpam-6319	566	5	co	co	ADJ
ejpam-6319	566	6	-	-	ADJ
ejpam-6319	566	7	prime	prime	ADJ
ejpam-6319	566	8	order	order	NOUN
ejpam-6319	566	9	graphs	graph	NOUN
ejpam-6319	566	10	of	of	ADP
ejpam-6319	566	11	finite	finite	ADJ
ejpam-6319	566	12	groups	group	NOUN
ejpam-6319	566	13	.	.	PUNCT
ejpam-6319	567	1	italian	italian	ADJ
ejpam-6319	567	2	journal	journal	NOUN
ejpam-6319	567	3	of	of	ADP
ejpam-6319	567	4	pure	pure	ADJ
ejpam-6319	567	5	and	and	CCONJ
ejpam-6319	567	6	applied	applied	ADJ
ejpam-6319	567	7	mathematics	mathematic	NOUN
ejpam-6319	567	8	,	,	PUNCT
ejpam-6319	567	9	51:443–451	51:443–451	NUM
ejpam-6319	567	10	,	,	PUNCT
ejpam-6319	567	11	2024	2024	NUM
ejpam-6319	567	12	.	.	PUNCT
ejpam-6319	568	1	[	[	X
ejpam-6319	568	2	21	21	NUM
ejpam-6319	568	3	]	]	X
ejpam-6319	568	4	m	m	PROPN
ejpam-6319	568	5	saini	saini	PROPN
ejpam-6319	568	6	,	,	PUNCT
ejpam-6319	568	7	s	s	PART
ejpam-6319	568	8	m	m	PROPN
ejpam-6319	568	9	s	s	PROPN
ejpam-6319	568	10	khasraw	khasraw	PROPN
ejpam-6319	568	11	,	,	PUNCT
ejpam-6319	568	12	a	a	DET
ejpam-6319	568	13	sehgal	sehgal	ADJ
ejpam-6319	568	14	,	,	PUNCT
ejpam-6319	568	15	and	and	CCONJ
ejpam-6319	568	16	d	d	ADP
ejpam-6319	568	17	singh	singh	PROPN
ejpam-6319	568	18	.	.	PUNCT
ejpam-6319	569	1	on	on	ADP
ejpam-6319	569	2	co	co	ADJ
ejpam-6319	569	3	-	-	ADJ
ejpam-6319	569	4	prime	prime	ADJ
ejpam-6319	569	5	order	order	NOUN
ejpam-6319	569	6	graphs	graph	NOUN
ejpam-6319	569	7	of	of	ADP
ejpam-6319	569	8	finite	finite	ADJ
ejpam-6319	569	9	abelian	abelian	PROPN
ejpam-6319	569	10	p	p	PROPN
ejpam-6319	569	11	-	-	PUNCT
ejpam-6319	569	12	groups	group	NOUN
ejpam-6319	569	13	.	.	PUNCT
ejpam-6319	570	1	journal	journal	PROPN
ejpam-6319	570	2	of	of	ADP
ejpam-6319	570	3	mathematical	mathematical	ADJ
ejpam-6319	570	4	and	and	CCONJ
ejpam-6319	570	5	computational	computational	ADJ
ejpam-6319	570	6	science	science	NOUN
ejpam-6319	570	7	,	,	PUNCT
ejpam-6319	570	8	11(6):7052	11(6):7052	NUM
ejpam-6319	570	9	–	–	PUNCT
ejpam-6319	570	10	7061	7061	NUM
ejpam-6319	570	11	,	,	PUNCT
ejpam-6319	570	12	2021	2021	NUM
ejpam-6319	570	13	.	.	PUNCT
ejpam-6319	571	1	[	[	X
ejpam-6319	571	2	22	22	NUM
ejpam-6319	571	3	]	]	X
ejpam-6319	571	4	s	s	PART
ejpam-6319	571	5	madhumitha	madhumitha	NOUN
ejpam-6319	571	6	and	and	CCONJ
ejpam-6319	571	7	s	s	VERB
ejpam-6319	571	8	naduvath	naduvath	NOUN
ejpam-6319	571	9	.	.	PUNCT
ejpam-6319	572	1	graphs	graph	NOUN
ejpam-6319	572	2	on	on	ADP
ejpam-6319	572	3	groups	group	NOUN
ejpam-6319	572	4	in	in	ADP
ejpam-6319	572	5	terms	term	NOUN
ejpam-6319	572	6	of	of	ADP
ejpam-6319	572	7	the	the	DET
ejpam-6319	572	8	order	order	NOUN
ejpam-6319	572	9	of	of	ADP
ejpam-6319	572	10	elements	element	NOUN
ejpam-6319	572	11	:	:	PUNCT
ejpam-6319	572	12	a	a	DET
ejpam-6319	572	13	review	review	NOUN
ejpam-6319	572	14	.	.	PUNCT
ejpam-6319	573	1	discrete	discrete	ADJ
ejpam-6319	573	2	mathematics	mathematic	NOUN
ejpam-6319	573	3	,	,	PUNCT
ejpam-6319	573	4	algorithms	algorithms	NOUN
ejpam-6319	573	5	&	&	CCONJ
ejpam-6319	573	6	applications	application	NOUN
ejpam-6319	573	7	,	,	PUNCT
ejpam-6319	573	8	16(3):2330003	16(3):2330003	NUM
ejpam-6319	573	9	,	,	PUNCT
ejpam-6319	573	10	2024	2024	NUM
ejpam-6319	573	11	.	.	PUNCT
ejpam-6319	574	1	[	[	X
ejpam-6319	574	2	23	23	NUM
ejpam-6319	574	3	]	]	PUNCT
ejpam-6319	574	4	a	a	DET
ejpam-6319	574	5	s	s	X
ejpam-6319	574	6	gazir	gazir	NOUN
ejpam-6319	574	7	,	,	PUNCT
ejpam-6319	574	8	i	i	PRON
ejpam-6319	574	9	g	g	VERB
ejpam-6319	574	10	a	a	DET
ejpam-6319	574	11	w	w	NOUN
ejpam-6319	574	12	wardhana	wardhana	NOUN
ejpam-6319	574	13	,	,	PUNCT
ejpam-6319	574	14	and	and	CCONJ
ejpam-6319	574	15	n	n	PRON
ejpam-6319	574	16	w	w	PROPN
ejpam-6319	574	17	switrayni	switrayni	PROPN
ejpam-6319	574	18	.	.	PUNCT
ejpam-6319	575	1	the	the	DET
ejpam-6319	575	2	degree	degree	NOUN
ejpam-6319	575	3	,	,	PUNCT
ejpam-6319	575	4	radius	radius	NOUN
ejpam-6319	575	5	,	,	PUNCT
ejpam-6319	575	6	and	and	CCONJ
ejpam-6319	575	7	diameter	diameter	NOUN
ejpam-6319	575	8	of	of	ADP
ejpam-6319	575	9	coprime	coprime	ADJ
ejpam-6319	575	10	graph	graph	NOUN
ejpam-6319	575	11	of	of	ADP
ejpam-6319	575	12	dihedral	dihedral	ADJ
ejpam-6319	575	13	group	group	NOUN
ejpam-6319	575	14	.	.	PUNCT
ejpam-6319	576	1	proc	proc	PROPN
ejpam-6319	576	2	.	.	PUNCT
ejpam-6319	577	1	of	of	ADP
ejpam-6319	577	2	international	international	ADJ
ejpam-6319	577	3	conference	conference	NOUN
ejpam-6319	577	4	on	on	ADP
ejpam-6319	577	5	science	science	NOUN
ejpam-6319	577	6	and	and	CCONJ
ejpam-6319	577	7	technology	technology	NOUN
ejpam-6319	577	8	,	,	PUNCT
ejpam-6319	577	9	1:149–154	1:149–154	NUM
ejpam-6319	577	10	,	,	PUNCT
ejpam-6319	577	11	2020	2020	NUM
ejpam-6319	577	12	.	.	PUNCT
ejpam-6319	578	1	[	[	X
ejpam-6319	578	2	24	24	NUM
ejpam-6319	578	3	]	]	PUNCT
ejpam-6319	578	4	a	a	DET
ejpam-6319	578	5	e	e	X
ejpam-6319	578	6	brouwer	brouwer	PROPN
ejpam-6319	578	7	and	and	CCONJ
ejpam-6319	578	8	w	w	NOUN
ejpam-6319	578	9	h	h	NOUN
ejpam-6319	578	10	haemers	haemer	NOUN
ejpam-6319	578	11	.	.	PUNCT
ejpam-6319	579	1	spectra	spectra	NOUN
ejpam-6319	579	2	of	of	ADP
ejpam-6319	579	3	graphs	graph	NOUN
ejpam-6319	579	4	.	.	PUNCT
ejpam-6319	580	1	springer	springer	NOUN
ejpam-6319	580	2	,	,	PUNCT
ejpam-6319	580	3	new	new	PROPN
ejpam-6319	580	4	york	york	PROPN
ejpam-6319	580	5	,	,	PUNCT
ejpam-6319	580	6	2011	2011	NUM
ejpam-6319	580	7	.	.	PUNCT
ejpam-6319	581	1	[	[	X
ejpam-6319	581	2	25	25	NUM
ejpam-6319	581	3	]	]	X
ejpam-6319	581	4	h	h	PROPN
ejpam-6319	581	5	s	s	PROPN
ejpam-6319	581	6	ramane	ramane	NOUN
ejpam-6319	581	7	and	and	CCONJ
ejpam-6319	581	8	s	s	NOUN
ejpam-6319	581	9	s	s	NOUN
ejpam-6319	581	10	shinde	shinde	PROPN
ejpam-6319	581	11	.	.	PUNCT
ejpam-6319	581	12	degree	degree	NOUN
ejpam-6319	581	13	exponent	exponent	NOUN
ejpam-6319	581	14	polynomial	polynomial	NOUN
ejpam-6319	581	15	of	of	ADP
ejpam-6319	581	16	graphs	graph	NOUN
ejpam-6319	581	17	obtained	obtain	VERB
ejpam-6319	581	18	by	by	ADP
ejpam-6319	581	19	some	some	DET
ejpam-6319	581	20	graph	graph	NOUN
ejpam-6319	581	21	operations	operation	NOUN
ejpam-6319	581	22	.	.	PUNCT
ejpam-6319	582	1	electronic	electronic	ADJ
ejpam-6319	582	2	journal	journal	NOUN
ejpam-6319	582	3	of	of	ADP
ejpam-6319	582	4	graph	graph	NOUN
ejpam-6319	582	5	theory	theory	NOUN
ejpam-6319	582	6	and	and	CCONJ
ejpam-6319	582	7	application	application	NOUN
ejpam-6319	582	8	,	,	PUNCT
ejpam-6319	582	9	63:161–168	63:161–168	PROPN
ejpam-6319	582	10	,	,	PUNCT
ejpam-6319	582	11	2017	2017	NUM
ejpam-6319	582	12	.	.	PUNCT
ejpam-6319	583	1	[	[	X
ejpam-6319	583	2	26	26	NUM
ejpam-6319	583	3	]	]	X
ejpam-6319	583	4	r	r	NOUN
ejpam-6319	583	5	b	b	X
ejpam-6319	583	6	bapat	bapat	PROPN
ejpam-6319	583	7	and	and	CCONJ
ejpam-6319	583	8	s	s	NOUN
ejpam-6319	583	9	pati	pati	NOUN
ejpam-6319	583	10	.	.	PUNCT
ejpam-6319	584	1	energy	energy	NOUN
ejpam-6319	584	2	of	of	ADP
ejpam-6319	584	3	a	a	DET
ejpam-6319	584	4	graph	graph	NOUN
ejpam-6319	584	5	is	be	AUX
ejpam-6319	584	6	never	never	ADV
ejpam-6319	584	7	an	an	DET
ejpam-6319	584	8	odd	odd	ADJ
ejpam-6319	584	9	integer	integer	NOUN
ejpam-6319	584	10	.	.	PUNCT
ejpam-6319	585	1	bulletin	bulletin	NOUN
ejpam-6319	585	2	of	of	ADP
ejpam-6319	585	3	kerala	kerala	PROPN
ejpam-6319	585	4	mathematics	mathematics	PROPN
ejpam-6319	585	5	association	association	PROPN
ejpam-6319	585	6	,	,	PUNCT
ejpam-6319	585	7	1:129–132	1:129–132	NUM
ejpam-6319	585	8	,	,	PUNCT
ejpam-6319	585	9	2004	2004	NUM
ejpam-6319	585	10	.	.	PUNCT