id	sid	tid	token	lemma	pos
ejpam-5375	1	1	european	european	PROPN
ejpam-5375	1	2	journal	journal	PROPN
ejpam-5375	1	3	of	of	ADP
ejpam-5375	1	4	pure	pure	ADJ
ejpam-5375	1	5	and	and	CCONJ
ejpam-5375	1	6	applied	apply	VERB
ejpam-5375	1	7	mathematics	mathematic	NOUN
ejpam-5375	1	8	vol	vol	NOUN
ejpam-5375	1	9	.	.	PROPN
ejpam-5375	2	1	17	17	NUM
ejpam-5375	2	2	,	,	PUNCT
ejpam-5375	2	3	no	no	INTJ
ejpam-5375	2	4	.	.	NOUN
ejpam-5375	2	5	4	4	NUM
ejpam-5375	2	6	,	,	PUNCT
ejpam-5375	2	7	2024	2024	NUM
ejpam-5375	2	8	,	,	PUNCT
ejpam-5375	2	9	2915	2915	NUM
ejpam-5375	2	10	-	-	SYM
ejpam-5375	2	11	2929	2929	NUM
ejpam-5375	2	12	issn	issn	VERB
ejpam-5375	2	13	1307	1307	NUM
ejpam-5375	2	14	-	-	SYM
ejpam-5375	2	15	5543	5543	NUM
ejpam-5375	2	16	–	–	PUNCT
ejpam-5375	2	17	ejpam.com	ejpam.com	X
ejpam-5375	2	18	published	publish	VERB
ejpam-5375	2	19	by	by	ADP
ejpam-5375	2	20	new	new	PROPN
ejpam-5375	2	21	york	york	PROPN
ejpam-5375	2	22	business	business	PROPN
ejpam-5375	2	23	global	global	PROPN
ejpam-5375	2	24	on	on	ADP
ejpam-5375	2	25	spectrum	spectrum	NOUN
ejpam-5375	2	26	and	and	CCONJ
ejpam-5375	2	27	energy	energy	NOUN
ejpam-5375	2	28	of	of	ADP
ejpam-5375	2	29	identity	identity	NOUN
ejpam-5375	2	30	graph	graph	NOUN
ejpam-5375	2	31	for	for	ADP
ejpam-5375	2	32	group	group	NOUN
ejpam-5375	2	33	of	of	ADP
ejpam-5375	2	34	integers	integer	NOUN
ejpam-5375	2	35	modulo	modulo	PROPN
ejpam-5375	2	36	n	n	PRON
ejpam-5375	2	37	,	,	PUNCT
ejpam-5375	2	38	zn	zn	PROPN
ejpam-5375	2	39	mamika	mamika	PROPN
ejpam-5375	2	40	ujianita	ujianita	PROPN
ejpam-5375	2	41	romdhini1,∗	romdhini1,∗	PROPN
ejpam-5375	2	42	,	,	PUNCT
ejpam-5375	2	43	athirah	athirah	PROPN
ejpam-5375	2	44	nawawi2	nawawi2	PROPN
ejpam-5375	2	45	,	,	PUNCT
ejpam-5375	2	46	faisal	faisal	PROPN
ejpam-5375	2	47	al	al	PROPN
ejpam-5375	2	48	-	-	PUNCT
ejpam-5375	2	49	sharqi3,4	sharqi3,4	PROPN
ejpam-5375	2	50	,	,	PUNCT
ejpam-5375	2	51	salwa1	salwa1	ADJ
ejpam-5375	2	52	1	1	NUM
ejpam-5375	2	53	department	department	NOUN
ejpam-5375	2	54	of	of	ADP
ejpam-5375	2	55	mathematics	mathematic	NOUN
ejpam-5375	2	56	,	,	PUNCT
ejpam-5375	2	57	faculty	faculty	NOUN
ejpam-5375	2	58	of	of	ADP
ejpam-5375	2	59	mathematics	mathematic	NOUN
ejpam-5375	2	60	and	and	CCONJ
ejpam-5375	2	61	natural	natural	ADJ
ejpam-5375	2	62	science	science	NOUN
ejpam-5375	2	63	,	,	PUNCT
ejpam-5375	2	64	university	university	NOUN
ejpam-5375	2	65	of	of	ADP
ejpam-5375	2	66	mataram	mataram	PROPN
ejpam-5375	2	67	,	,	PUNCT
ejpam-5375	2	68	mataram	mataram	PROPN
ejpam-5375	2	69	83125	83125	NUM
ejpam-5375	2	70	,	,	PUNCT
ejpam-5375	2	71	indonesia	indonesia	PROPN
ejpam-5375	2	72	2	2	NUM
ejpam-5375	2	73	department	department	NOUN
ejpam-5375	2	74	of	of	ADP
ejpam-5375	2	75	mathematics	mathematic	NOUN
ejpam-5375	2	76	and	and	CCONJ
ejpam-5375	2	77	statistics	statistic	NOUN
ejpam-5375	2	78	,	,	PUNCT
ejpam-5375	2	79	faculty	faculty	NOUN
ejpam-5375	2	80	of	of	ADP
ejpam-5375	2	81	science	science	NOUN
ejpam-5375	2	82	,	,	PUNCT
ejpam-5375	2	83	universiti	universiti	PROPN
ejpam-5375	2	84	putra	putra	PROPN
ejpam-5375	2	85	malaysia	malaysia	PROPN
ejpam-5375	2	86	,	,	PUNCT
ejpam-5375	2	87	43400	43400	NUM
ejpam-5375	2	88	serdang	serdang	PROPN
ejpam-5375	2	89	,	,	PUNCT
ejpam-5375	2	90	selangor	selangor	PROPN
ejpam-5375	2	91	,	,	PUNCT
ejpam-5375	2	92	malaysia	malaysia	PROPN
ejpam-5375	2	93	3	3	NUM
ejpam-5375	2	94	department	department	NOUN
ejpam-5375	2	95	of	of	ADP
ejpam-5375	2	96	mathematics	mathematic	NOUN
ejpam-5375	2	97	,	,	PUNCT
ejpam-5375	2	98	faculty	faculty	NOUN
ejpam-5375	2	99	of	of	ADP
ejpam-5375	2	100	education	education	NOUN
ejpam-5375	2	101	for	for	ADP
ejpam-5375	2	102	pure	pure	ADJ
ejpam-5375	2	103	sciences	science	NOUN
ejpam-5375	2	104	,	,	PUNCT
ejpam-5375	2	105	university	university	NOUN
ejpam-5375	2	106	of	of	ADP
ejpam-5375	2	107	anbar	anbar	PROPN
ejpam-5375	2	108	,	,	PUNCT
ejpam-5375	2	109	ramadi	ramadi	PROPN
ejpam-5375	2	110	,	,	PUNCT
ejpam-5375	2	111	anbar	anbar	NOUN
ejpam-5375	2	112	,	,	PUNCT
ejpam-5375	2	113	iraq	iraq	PROPN
ejpam-5375	2	114	4	4	NUM
ejpam-5375	2	115	college	college	NOUN
ejpam-5375	2	116	of	of	ADP
ejpam-5375	2	117	engineering	engineering	NOUN
ejpam-5375	2	118	,	,	PUNCT
ejpam-5375	2	119	national	national	ADJ
ejpam-5375	2	120	university	university	PROPN
ejpam-5375	2	121	of	of	ADP
ejpam-5375	2	122	science	science	NOUN
ejpam-5375	2	123	and	and	CCONJ
ejpam-5375	2	124	technology	technology	NOUN
ejpam-5375	2	125	,	,	PUNCT
ejpam-5375	2	126	dhi	dhi	PROPN
ejpam-5375	2	127	qar	qar	PROPN
ejpam-5375	2	128	,	,	PUNCT
ejpam-5375	2	129	iraq	iraq	PROPN
ejpam-5375	2	130	abstract	abstract	NOUN
ejpam-5375	2	131	.	.	PUNCT
ejpam-5375	3	1	groups	group	NOUN
ejpam-5375	3	2	and	and	CCONJ
ejpam-5375	3	3	graphs	graph	NOUN
ejpam-5375	3	4	are	be	AUX
ejpam-5375	3	5	two	two	NUM
ejpam-5375	3	6	concepts	concept	NOUN
ejpam-5375	3	7	of	of	ADP
ejpam-5375	3	8	algebraic	algebraic	ADJ
ejpam-5375	3	9	mathematics	mathematic	NOUN
ejpam-5375	3	10	.	.	PUNCT
ejpam-5375	4	1	this	this	DET
ejpam-5375	4	2	paper	paper	NOUN
ejpam-5375	4	3	focuses	focus	VERB
ejpam-5375	4	4	on	on	ADP
ejpam-5375	4	5	group	group	NOUN
ejpam-5375	4	6	structures	structure	NOUN
ejpam-5375	4	7	that	that	PRON
ejpam-5375	4	8	can	can	AUX
ejpam-5375	4	9	be	be	AUX
ejpam-5375	4	10	expressed	express	VERB
ejpam-5375	4	11	in	in	ADP
ejpam-5375	4	12	graphs	graph	NOUN
ejpam-5375	4	13	known	know	VERB
ejpam-5375	4	14	as	as	ADP
ejpam-5375	4	15	identity	identity	NOUN
ejpam-5375	4	16	graphs	graph	NOUN
ejpam-5375	4	17	.	.	PUNCT
ejpam-5375	5	1	we	we	PRON
ejpam-5375	5	2	investigate	investigate	VERB
ejpam-5375	5	3	the	the	DET
ejpam-5375	5	4	energy	energy	NOUN
ejpam-5375	5	5	of	of	ADP
ejpam-5375	5	6	the	the	DET
ejpam-5375	5	7	identity	identity	NOUN
ejpam-5375	5	8	graph	graph	NOUN
ejpam-5375	5	9	for	for	ADP
ejpam-5375	5	10	a	a	DET
ejpam-5375	5	11	group	group	NOUN
ejpam-5375	5	12	of	of	ADP
ejpam-5375	5	13	integers	integer	NOUN
ejpam-5375	5	14	modulo	modulo	PROPN
ejpam-5375	5	15	n	n	CCONJ
ejpam-5375	5	16	,	,	PUNCT
ejpam-5375	5	17	zn	zn	PROPN
ejpam-5375	5	18	,	,	PUNCT
ejpam-5375	5	19	for	for	ADP
ejpam-5375	5	20	odd	odd	ADJ
ejpam-5375	5	21	and	and	CCONJ
ejpam-5375	5	22	even	even	ADV
ejpam-5375	5	23	n	n	ADV
ejpam-5375	5	24	corresponding	correspond	VERB
ejpam-5375	5	25	to	to	ADP
ejpam-5375	5	26	adjacency	adjacency	NOUN
ejpam-5375	5	27	,	,	PUNCT
ejpam-5375	5	28	laplacian	laplacian	ADJ
ejpam-5375	5	29	,	,	PUNCT
ejpam-5375	5	30	and	and	CCONJ
ejpam-5375	5	31	signless	signless	ADJ
ejpam-5375	5	32	laplacian	laplacian	ADJ
ejpam-5375	5	33	matrices	matrix	NOUN
ejpam-5375	5	34	.	.	PUNCT
ejpam-5375	6	1	it	it	PRON
ejpam-5375	6	2	can	can	AUX
ejpam-5375	6	3	be	be	AUX
ejpam-5375	6	4	seen	see	VERB
ejpam-5375	6	5	that	that	SCONJ
ejpam-5375	6	6	the	the	DET
ejpam-5375	6	7	laplacian	laplacian	ADJ
ejpam-5375	6	8	and	and	CCONJ
ejpam-5375	6	9	signless	signless	ADJ
ejpam-5375	6	10	laplacian	laplacian	ADJ
ejpam-5375	6	11	energies	energy	NOUN
ejpam-5375	6	12	are	be	AUX
ejpam-5375	6	13	always	always	ADV
ejpam-5375	6	14	equal	equal	ADJ
ejpam-5375	6	15	and	and	CCONJ
ejpam-5375	6	16	are	be	AUX
ejpam-5375	6	17	always	always	ADV
ejpam-5375	6	18	an	an	DET
ejpam-5375	6	19	even	even	ADV
ejpam-5375	6	20	integer	integer	NOUN
ejpam-5375	6	21	.	.	PUNCT
ejpam-5375	7	1	meanwhile	meanwhile	ADV
ejpam-5375	7	2	,	,	PUNCT
ejpam-5375	7	3	the	the	DET
ejpam-5375	7	4	adjacency	adjacency	NOUN
ejpam-5375	7	5	energy	energy	NOUN
ejpam-5375	7	6	is	be	AUX
ejpam-5375	7	7	never	never	ADV
ejpam-5375	7	8	an	an	DET
ejpam-5375	7	9	odd	odd	ADJ
ejpam-5375	7	10	integer	integer	NOUN
ejpam-5375	7	11	for	for	ADP
ejpam-5375	7	12	n	n	X
ejpam-5375	7	13	is	be	AUX
ejpam-5375	7	14	odd	odd	ADJ
ejpam-5375	7	15	.	.	PUNCT
ejpam-5375	8	1	2020	2020	NUM
ejpam-5375	8	2	mathematics	mathematic	NOUN
ejpam-5375	8	3	subject	subject	NOUN
ejpam-5375	8	4	classifications	classification	NOUN
ejpam-5375	8	5	:	:	PUNCT
ejpam-5375	8	6	05c25	05c25	NUM
ejpam-5375	8	7	,	,	PUNCT
ejpam-5375	8	8	15a18	15a18	NUM
ejpam-5375	8	9	key	key	ADJ
ejpam-5375	8	10	words	word	NOUN
ejpam-5375	8	11	and	and	CCONJ
ejpam-5375	8	12	phrases	phrase	NOUN
ejpam-5375	8	13	:	:	PUNCT
ejpam-5375	8	14	energy	energy	NOUN
ejpam-5375	8	15	of	of	ADP
ejpam-5375	8	16	a	a	DET
ejpam-5375	8	17	graph	graph	NOUN
ejpam-5375	8	18	,	,	PUNCT
ejpam-5375	8	19	identity	identity	NOUN
ejpam-5375	8	20	graph	graph	NOUN
ejpam-5375	8	21	of	of	ADP
ejpam-5375	8	22	a	a	DET
ejpam-5375	8	23	group	group	NOUN
ejpam-5375	8	24	,	,	PUNCT
ejpam-5375	8	25	zn	zn	PROPN
ejpam-5375	8	26	1	1	NUM
ejpam-5375	8	27	.	.	PUNCT
ejpam-5375	8	28	introduction	introduction	NOUN
ejpam-5375	8	29	groups	group	NOUN
ejpam-5375	8	30	and	and	CCONJ
ejpam-5375	8	31	graphs	graph	NOUN
ejpam-5375	8	32	are	be	AUX
ejpam-5375	8	33	two	two	NUM
ejpam-5375	8	34	concepts	concept	NOUN
ejpam-5375	8	35	of	of	ADP
ejpam-5375	8	36	algebraic	algebraic	ADJ
ejpam-5375	8	37	mathematics	mathematic	NOUN
ejpam-5375	8	38	.	.	PUNCT
ejpam-5375	9	1	a	a	DET
ejpam-5375	9	2	group	group	NOUN
ejpam-5375	9	3	is	be	AUX
ejpam-5375	9	4	an	an	DET
ejpam-5375	9	5	algebraic	algebraic	ADJ
ejpam-5375	9	6	structure	structure	NOUN
ejpam-5375	9	7	from	from	ADP
ejpam-5375	9	8	a	a	DET
ejpam-5375	9	9	non	non	ADJ
ejpam-5375	9	10	-	-	ADJ
ejpam-5375	9	11	empty	empty	ADJ
ejpam-5375	9	12	set	set	NOUN
ejpam-5375	9	13	with	with	ADP
ejpam-5375	9	14	a	a	DET
ejpam-5375	9	15	binary	binary	ADJ
ejpam-5375	9	16	operation	operation	NOUN
ejpam-5375	9	17	and	and	CCONJ
ejpam-5375	9	18	satisfies	satisfie	NOUN
ejpam-5375	9	19	associative	associative	ADJ
ejpam-5375	9	20	property	property	NOUN
ejpam-5375	9	21	,	,	PUNCT
ejpam-5375	9	22	there	there	PRON
ejpam-5375	9	23	is	be	VERB
ejpam-5375	9	24	an	an	DET
ejpam-5375	9	25	identity	identity	NOUN
ejpam-5375	9	26	element	element	NOUN
ejpam-5375	9	27	and	and	CCONJ
ejpam-5375	9	28	each	each	DET
ejpam-5375	9	29	element	element	NOUN
ejpam-5375	9	30	has	have	VERB
ejpam-5375	9	31	an	an	DET
ejpam-5375	9	32	inverse	inverse	NOUN
ejpam-5375	9	33	.	.	PUNCT
ejpam-5375	10	1	furthermore	furthermore	ADV
ejpam-5375	10	2	,	,	PUNCT
ejpam-5375	10	3	graph	graph	NOUN
ejpam-5375	10	4	theory	theory	NOUN
ejpam-5375	10	5	is	be	AUX
ejpam-5375	10	6	a	a	DET
ejpam-5375	10	7	discrete	discrete	ADJ
ejpam-5375	10	8	mathematics	mathematics	NOUN
ejpam-5375	10	9	study	study	NOUN
ejpam-5375	10	10	that	that	PRON
ejpam-5375	10	11	discusses	discuss	VERB
ejpam-5375	10	12	vertices	vertex	NOUN
ejpam-5375	10	13	and	and	CCONJ
ejpam-5375	10	14	edges	edge	NOUN
ejpam-5375	10	15	.	.	PUNCT
ejpam-5375	11	1	in	in	ADP
ejpam-5375	11	2	this	this	DET
ejpam-5375	11	3	paper	paper	NOUN
ejpam-5375	11	4	,	,	PUNCT
ejpam-5375	11	5	we	we	PRON
ejpam-5375	11	6	discuss	discuss	VERB
ejpam-5375	11	7	group	group	NOUN
ejpam-5375	11	8	structures	structure	NOUN
ejpam-5375	11	9	that	that	PRON
ejpam-5375	11	10	can	can	AUX
ejpam-5375	11	11	be	be	AUX
ejpam-5375	11	12	expressed	express	VERB
ejpam-5375	11	13	in	in	ADP
ejpam-5375	11	14	graphs	graph	NOUN
ejpam-5375	11	15	,	,	PUNCT
ejpam-5375	11	16	the	the	DET
ejpam-5375	11	17	name	name	NOUN
ejpam-5375	11	18	is	be	AUX
ejpam-5375	11	19	identity	identity	NOUN
ejpam-5375	11	20	graph	graph	NOUN
ejpam-5375	11	21	.	.	PUNCT
ejpam-5375	11	22	kandasamy	kandasamy	NOUN
ejpam-5375	11	23	and	and	CCONJ
ejpam-5375	11	24	smarandache	smarandache	NOUN
ejpam-5375	11	25	in	in	ADP
ejpam-5375	11	26	2009	2009	NUM
ejpam-5375	11	27	[	[	X
ejpam-5375	11	28	5	5	NUM
ejpam-5375	11	29	]	]	PUNCT
ejpam-5375	11	30	described	describe	VERB
ejpam-5375	11	31	finite	finite	ADJ
ejpam-5375	11	32	groups	group	NOUN
ejpam-5375	11	33	as	as	ADP
ejpam-5375	11	34	graphs	graph	NOUN
ejpam-5375	11	35	.	.	PUNCT
ejpam-5375	12	1	they	they	PRON
ejpam-5375	12	2	call	call	VERB
ejpam-5375	12	3	this	this	PRON
ejpam-5375	12	4	the	the	DET
ejpam-5375	12	5	identity	identity	NOUN
ejpam-5375	12	6	graph	graph	NOUN
ejpam-5375	12	7	because	because	SCONJ
ejpam-5375	12	8	the	the	DET
ejpam-5375	12	9	main	main	ADJ
ejpam-5375	12	10	key	key	NOUN
ejpam-5375	12	11	in	in	ADP
ejpam-5375	12	12	constructing	construct	VERB
ejpam-5375	12	13	the	the	DET
ejpam-5375	12	14	graph	graph	NOUN
ejpam-5375	12	15	is	be	AUX
ejpam-5375	12	16	determined	determine	VERB
ejpam-5375	12	17	by	by	ADP
ejpam-5375	12	18	the	the	DET
ejpam-5375	12	19	group	group	NOUN
ejpam-5375	12	20	’s	’s	PART
ejpam-5375	12	21	identity	identity	NOUN
ejpam-5375	12	22	elements	element	NOUN
ejpam-5375	12	23	.	.	PUNCT
ejpam-5375	13	1	the	the	DET
ejpam-5375	13	2	discussion	discussion	NOUN
ejpam-5375	13	3	on	on	ADP
ejpam-5375	13	4	labeling	labeling	NOUN
ejpam-5375	13	5	of	of	ADP
ejpam-5375	13	6	the	the	DET
ejpam-5375	13	7	identity	identity	NOUN
ejpam-5375	13	8	graph	graph	NOUN
ejpam-5375	13	9	can	can	AUX
ejpam-5375	13	10	be	be	AUX
ejpam-5375	13	11	found	find	VERB
ejpam-5375	13	12	in	in	ADP
ejpam-5375	13	13	[	[	X
ejpam-5375	13	14	10	10	NUM
ejpam-5375	13	15	]	]	PUNCT
ejpam-5375	13	16	.	.	PUNCT
ejpam-5375	14	1	∗corresponding	∗corresponde	VERB
ejpam-5375	14	2	author	author	NOUN
ejpam-5375	14	3	.	.	PUNCT
ejpam-5375	15	1	doi	doi	NOUN
ejpam-5375	15	2	:	:	PUNCT
ejpam-5375	15	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5375	https://doi.org/10.29020/nybg.ejpam.v17i4.5375	PROPN
ejpam-5375	15	4	email	email	NOUN
ejpam-5375	15	5	addresses	address	NOUN
ejpam-5375	15	6	:	:	PUNCT
ejpam-5375	15	7	mamika@unram.ac.id	mamika@unram.ac.id	NOUN
ejpam-5375	15	8	(	(	PUNCT
ejpam-5375	15	9	m.	m.	PROPN
ejpam-5375	15	10	u.	u.	PROPN
ejpam-5375	15	11	romdhini	romdhini	PROPN
ejpam-5375	15	12	)	)	PUNCT
ejpam-5375	15	13	,	,	PUNCT
ejpam-5375	15	14	athirah@upm.edu.my	athirah@upm.edu.my	PROPN
ejpam-5375	15	15	(	(	PUNCT
ejpam-5375	15	16	a.	a.	NOUN
ejpam-5375	15	17	nawawi	nawawi	PROPN
ejpam-5375	15	18	)	)	PUNCT
ejpam-5375	15	19	,	,	PUNCT
ejpam-5375	15	20	faisal.ghazi@uoanbar.edu.iq	faisal.ghazi@uoanbar.edu.iq	NOUN
ejpam-5375	15	21	(	(	PUNCT
ejpam-5375	15	22	f.	f.	PROPN
ejpam-5375	15	23	al	al	PROPN
ejpam-5375	15	24	-	-	PUNCT
ejpam-5375	15	25	sharqi	sharqi	NOUN
ejpam-5375	15	26	)	)	PUNCT
ejpam-5375	15	27	,	,	PUNCT
ejpam-5375	15	28	salwa@unram.ac.id	salwa@unram.ac.id	PROPN
ejpam-5375	15	29	(	(	PUNCT
ejpam-5375	15	30	salwa	salwa	PROPN
ejpam-5375	15	31	)	)	PUNCT
ejpam-5375	15	32	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5375	15	33	2915	2915	NUM
ejpam-5375	16	1	copyright	copyright	NOUN
ejpam-5375	16	2	:	:	PUNCT
ejpam-5375	16	3	©	©	PROPN
ejpam-5375	16	4	2024	2024	NUM
ejpam-5375	16	5	the	the	DET
ejpam-5375	16	6	author(s	author(s	NOUN
ejpam-5375	16	7	)	)	PUNCT
ejpam-5375	16	8	.	.	PUNCT
ejpam-5375	17	1	(	(	PUNCT
ejpam-5375	17	2	cc	cc	NOUN
ejpam-5375	17	3	by	by	ADP
ejpam-5375	17	4	-	-	PUNCT
ejpam-5375	17	5	nc	nc	PROPN
ejpam-5375	17	6	4.0	4.0	NUM
ejpam-5375	17	7	)	)	PUNCT
ejpam-5375	17	8	m.	m.	NOUN
ejpam-5375	17	9	u.	u.	PROPN
ejpam-5375	17	10	romdhini	romdhini	PROPN
ejpam-5375	17	11	et	et	PROPN
ejpam-5375	17	12	al	al	PROPN
ejpam-5375	17	13	.	.	PUNCT
ejpam-5375	17	14	/	/	SYM
ejpam-5375	17	15	eur	eur	PROPN
ejpam-5375	17	16	.	.	PUNCT
ejpam-5375	18	1	j.	j.	PROPN
ejpam-5375	18	2	pure	pure	PROPN
ejpam-5375	18	3	appl	appl	PROPN
ejpam-5375	18	4	.	.	PROPN
ejpam-5375	18	5	math	math	PROPN
ejpam-5375	18	6	,	,	PUNCT
ejpam-5375	18	7	17	17	NUM
ejpam-5375	18	8	(	(	PUNCT
ejpam-5375	18	9	4	4	NUM
ejpam-5375	18	10	)	)	PUNCT
ejpam-5375	18	11	(	(	PUNCT
ejpam-5375	18	12	2024	2024	NUM
ejpam-5375	18	13	)	)	PUNCT
ejpam-5375	18	14	,	,	PUNCT
ejpam-5375	18	15	2915	2915	NUM
ejpam-5375	18	16	-	-	SYM
ejpam-5375	18	17	2929	2929	NUM
ejpam-5375	18	18	2916	2916	NUM
ejpam-5375	18	19	the	the	DET
ejpam-5375	18	20	graph	graph	NOUN
ejpam-5375	18	21	energy	energy	NOUN
ejpam-5375	18	22	concept	concept	NOUN
ejpam-5375	18	23	was	be	AUX
ejpam-5375	18	24	pioneered	pioneer	VERB
ejpam-5375	18	25	by	by	ADP
ejpam-5375	18	26	gutman	gutman	NOUN
ejpam-5375	18	27	in	in	ADP
ejpam-5375	18	28	1978	1978	NUM
ejpam-5375	18	29	[	[	X
ejpam-5375	18	30	4	4	NUM
ejpam-5375	18	31	]	]	PUNCT
ejpam-5375	18	32	.	.	PUNCT
ejpam-5375	19	1	it	it	PRON
ejpam-5375	19	2	should	should	AUX
ejpam-5375	19	3	be	be	AUX
ejpam-5375	19	4	noted	note	VERB
ejpam-5375	19	5	that	that	SCONJ
ejpam-5375	19	6	the	the	DET
ejpam-5375	19	7	graph	graph	NOUN
ejpam-5375	19	8	energy	energy	NOUN
ejpam-5375	19	9	is	be	AUX
ejpam-5375	19	10	never	never	ADV
ejpam-5375	19	11	an	an	DET
ejpam-5375	19	12	odd	odd	ADJ
ejpam-5375	19	13	integer	integer	NOUN
ejpam-5375	19	14	[	[	X
ejpam-5375	19	15	1	1	NUM
ejpam-5375	19	16	,	,	PUNCT
ejpam-5375	19	17	9	9	NUM
ejpam-5375	19	18	]	]	PUNCT
ejpam-5375	19	19	.	.	PUNCT
ejpam-5375	20	1	moreover	moreover	ADV
ejpam-5375	20	2	,	,	PUNCT
ejpam-5375	20	3	several	several	ADJ
ejpam-5375	20	4	results	result	NOUN
ejpam-5375	20	5	on	on	ADP
ejpam-5375	20	6	the	the	DET
ejpam-5375	20	7	energy	energy	NOUN
ejpam-5375	20	8	of	of	ADP
ejpam-5375	20	9	a	a	DET
ejpam-5375	20	10	graph	graph	NOUN
ejpam-5375	20	11	defined	define	VERB
ejpam-5375	20	12	on	on	ADP
ejpam-5375	20	13	groups	group	NOUN
ejpam-5375	20	14	can	can	AUX
ejpam-5375	20	15	be	be	AUX
ejpam-5375	20	16	found	find	VERB
ejpam-5375	20	17	in	in	ADP
ejpam-5375	20	18	[	[	X
ejpam-5375	20	19	11	11	NUM
ejpam-5375	20	20	,	,	PUNCT
ejpam-5375	20	21	13	13	NUM
ejpam-5375	20	22	,	,	PUNCT
ejpam-5375	20	23	15	15	NUM
ejpam-5375	20	24	]	]	PUNCT
ejpam-5375	20	25	.	.	PUNCT
ejpam-5375	21	1	they	they	PRON
ejpam-5375	21	2	worked	work	VERB
ejpam-5375	21	3	on	on	ADP
ejpam-5375	21	4	non	non	ADJ
ejpam-5375	21	5	-	-	ADJ
ejpam-5375	21	6	commuting	commuting	ADJ
ejpam-5375	21	7	graphs	graph	NOUN
ejpam-5375	21	8	with	with	ADP
ejpam-5375	21	9	wiener	wiener	NOUN
ejpam-5375	21	10	-	-	PUNCT
ejpam-5375	21	11	hosoya	hosoya	NOUN
ejpam-5375	21	12	,	,	PUNCT
ejpam-5375	21	13	closeness	closeness	NOUN
ejpam-5375	21	14	and	and	CCONJ
ejpam-5375	21	15	degree	degree	NOUN
ejpam-5375	21	16	subtraction	subtraction	NOUN
ejpam-5375	21	17	matrices	matrix	NOUN
ejpam-5375	21	18	.	.	PUNCT
ejpam-5375	22	1	meanwhile	meanwhile	ADV
ejpam-5375	22	2	,	,	PUNCT
ejpam-5375	22	3	for	for	ADP
ejpam-5375	22	4	sombor	sombor	NOUN
ejpam-5375	22	5	energy	energy	NOUN
ejpam-5375	22	6	can	can	AUX
ejpam-5375	22	7	be	be	AUX
ejpam-5375	22	8	seen	see	VERB
ejpam-5375	22	9	in	in	ADP
ejpam-5375	22	10	[	[	X
ejpam-5375	22	11	12	12	NUM
ejpam-5375	22	12	]	]	PUNCT
ejpam-5375	22	13	.	.	PUNCT
ejpam-5375	23	1	shi	shi	PROPN
ejpam-5375	23	2	et	et	PROPN
ejpam-5375	23	3	al	al	PROPN
ejpam-5375	24	1	[	[	X
ejpam-5375	24	2	17	17	NUM
ejpam-5375	24	3	]	]	PUNCT
ejpam-5375	24	4	found	find	VERB
ejpam-5375	24	5	the	the	DET
ejpam-5375	24	6	energy	energy	NOUN
ejpam-5375	24	7	of	of	ADP
ejpam-5375	24	8	picture	picture	NOUN
ejpam-5375	24	9	fuzzy	fuzzy	ADJ
ejpam-5375	24	10	graphs	graph	NOUN
ejpam-5375	24	11	,	,	PUNCT
ejpam-5375	24	12	in	in	ADP
ejpam-5375	24	13	line	line	NOUN
ejpam-5375	24	14	with	with	ADP
ejpam-5375	24	15	the	the	DET
ejpam-5375	24	16	signless	signless	NOUN
ejpam-5375	24	17	laplacian	laplacian	ADJ
ejpam-5375	24	18	energy	energy	NOUN
ejpam-5375	24	19	[	[	X
ejpam-5375	24	20	11	11	NUM
ejpam-5375	24	21	]	]	PUNCT
ejpam-5375	24	22	and	and	CCONJ
ejpam-5375	24	23	cayley	cayley	NOUN
ejpam-5375	24	24	of	of	ADP
ejpam-5375	24	25	interval	interval	NOUN
ejpam-5375	24	26	-	-	PUNCT
ejpam-5375	24	27	valued	value	VERB
ejpam-5375	24	28	fuzzy	fuzzy	ADJ
ejpam-5375	24	29	graphs	graph	NOUN
ejpam-5375	24	30	[	[	X
ejpam-5375	24	31	2	2	NUM
ejpam-5375	24	32	]	]	PUNCT
ejpam-5375	24	33	.	.	PUNCT
ejpam-5375	25	1	kumari	kumari	PROPN
ejpam-5375	25	2	et	et	PROPN
ejpam-5375	25	3	al	al	PROPN
ejpam-5375	25	4	.	.	PUNCT
ejpam-5375	26	1	[	[	X
ejpam-5375	26	2	6	6	NUM
ejpam-5375	26	3	]	]	PUNCT
ejpam-5375	26	4	presented	present	VERB
ejpam-5375	26	5	the	the	DET
ejpam-5375	26	6	quotient	quotient	NOUN
ejpam-5375	26	7	energy	energy	NOUN
ejpam-5375	26	8	of	of	ADP
ejpam-5375	26	9	the	the	DET
ejpam-5375	26	10	identity	identity	NOUN
ejpam-5375	26	11	graph	graph	NOUN
ejpam-5375	26	12	for	for	ADP
ejpam-5375	26	13	zp	zp	PROPN
ejpam-5375	26	14	,	,	PUNCT
ejpam-5375	26	15	for	for	ADP
ejpam-5375	26	16	prime	prime	ADJ
ejpam-5375	26	17	number	number	NOUN
ejpam-5375	26	18	p	p	NOUN
ejpam-5375	26	19	and	and	CCONJ
ejpam-5375	26	20	romdhini	romdhini	NOUN
ejpam-5375	26	21	et	et	PROPN
ejpam-5375	26	22	al	al	PROPN
ejpam-5375	26	23	.	.	PUNCT
ejpam-5375	27	1	[	[	X
ejpam-5375	27	2	14	14	NUM
ejpam-5375	27	3	]	]	PUNCT
ejpam-5375	27	4	showed	show	VERB
ejpam-5375	27	5	the	the	DET
ejpam-5375	27	6	spectral	spectral	ADJ
ejpam-5375	27	7	properties	property	NOUN
ejpam-5375	27	8	of	of	ADP
ejpam-5375	27	9	power	power	NOUN
ejpam-5375	27	10	graph	graph	NOUN
ejpam-5375	27	11	for	for	ADP
ejpam-5375	27	12	dihedral	dihedral	ADJ
ejpam-5375	27	13	groups	group	NOUN
ejpam-5375	27	14	.	.	PUNCT
ejpam-5375	28	1	meanwhile	meanwhile	ADV
ejpam-5375	28	2	,	,	PUNCT
ejpam-5375	28	3	the	the	DET
ejpam-5375	28	4	spectral	spectral	ADJ
ejpam-5375	28	5	discussion	discussion	NOUN
ejpam-5375	28	6	of	of	ADP
ejpam-5375	28	7	the	the	DET
ejpam-5375	28	8	square	square	ADJ
ejpam-5375	28	9	power	power	NOUN
ejpam-5375	28	10	graph	graph	NOUN
ejpam-5375	28	11	can	can	AUX
ejpam-5375	28	12	be	be	AUX
ejpam-5375	28	13	seen	see	VERB
ejpam-5375	28	14	in	in	ADP
ejpam-5375	28	15	[	[	X
ejpam-5375	28	16	18	18	NUM
ejpam-5375	28	17	]	]	PUNCT
ejpam-5375	28	18	.	.	PUNCT
ejpam-5375	29	1	in	in	ADP
ejpam-5375	29	2	addition	addition	NOUN
ejpam-5375	29	3	,	,	PUNCT
ejpam-5375	29	4	shanthakumari	shanthakumari	NOUN
ejpam-5375	29	5	et	et	NOUN
ejpam-5375	29	6	al	al	PROPN
ejpam-5375	29	7	.	.	PUNCT
ejpam-5375	30	1	[	[	X
ejpam-5375	30	2	16	16	NUM
ejpam-5375	30	3	]	]	PUNCT
ejpam-5375	30	4	described	describe	VERB
ejpam-5375	30	5	the	the	DET
ejpam-5375	30	6	euclidean	euclidean	ADJ
ejpam-5375	30	7	degree	degree	NOUN
ejpam-5375	30	8	energy	energy	NOUN
ejpam-5375	30	9	and	and	CCONJ
ejpam-5375	30	10	lokesha	lokesha	NOUN
ejpam-5375	30	11	et	et	PROPN
ejpam-5375	30	12	al	al	PROPN
ejpam-5375	30	13	.	.	PUNCT
ejpam-5375	31	1	[	[	X
ejpam-5375	31	2	8	8	NUM
ejpam-5375	31	3	]	]	PUNCT
ejpam-5375	31	4	investigated	investigate	VERB
ejpam-5375	31	5	the	the	DET
ejpam-5375	31	6	skew	skew	ADJ
ejpam-5375	31	7	energy	energy	NOUN
ejpam-5375	31	8	of	of	ADP
ejpam-5375	31	9	a	a	DET
ejpam-5375	31	10	graph	graph	NOUN
ejpam-5375	31	11	.	.	PUNCT
ejpam-5375	32	1	inspired	inspire	VERB
ejpam-5375	32	2	by	by	ADP
ejpam-5375	32	3	this	this	PRON
ejpam-5375	32	4	,	,	PUNCT
ejpam-5375	32	5	we	we	PRON
ejpam-5375	32	6	work	work	VERB
ejpam-5375	32	7	on	on	ADP
ejpam-5375	32	8	the	the	DET
ejpam-5375	32	9	identity	identity	NOUN
ejpam-5375	32	10	matrix	matrix	NOUN
ejpam-5375	32	11	.	.	PUNCT
ejpam-5375	33	1	our	our	PRON
ejpam-5375	33	2	focus	focus	NOUN
ejpam-5375	33	3	in	in	ADP
ejpam-5375	33	4	this	this	DET
ejpam-5375	33	5	paper	paper	NOUN
ejpam-5375	33	6	is	be	AUX
ejpam-5375	33	7	a	a	DET
ejpam-5375	33	8	group	group	NOUN
ejpam-5375	33	9	of	of	ADP
ejpam-5375	33	10	integers	integer	NOUN
ejpam-5375	33	11	modulo	modulo	PROPN
ejpam-5375	33	12	n	n	CCONJ
ejpam-5375	33	13	,	,	PUNCT
ejpam-5375	33	14	zn	zn	PROPN
ejpam-5375	33	15	=	=	SYM
ejpam-5375	33	16	{	{	PUNCT
ejpam-5375	33	17	0	0	NUM
ejpam-5375	33	18	,	,	PUNCT
ejpam-5375	33	19	1	1	NUM
ejpam-5375	33	20	,	,	PUNCT
ejpam-5375	33	21	2	2	NUM
ejpam-5375	33	22	,	,	PUNCT
ejpam-5375	33	23	.	.	PUNCT
ejpam-5375	33	24	.	.	PUNCT
ejpam-5375	34	1	.	.	PUNCT
ejpam-5375	35	1	,	,	PUNCT
ejpam-5375	35	2	n−	n−	NOUN
ejpam-5375	35	3	1	1	NUM
ejpam-5375	35	4	}	}	PUNCT
ejpam-5375	35	5	.	.	PUNCT
ejpam-5375	36	1	we	we	PRON
ejpam-5375	36	2	construct	construct	VERB
ejpam-5375	36	3	the	the	DET
ejpam-5375	36	4	identity	identity	NOUN
ejpam-5375	36	5	graph	graph	NOUN
ejpam-5375	36	6	based	base	VERB
ejpam-5375	36	7	on	on	ADP
ejpam-5375	36	8	the	the	DET
ejpam-5375	36	9	group	group	NOUN
ejpam-5375	36	10	elements	element	NOUN
ejpam-5375	36	11	as	as	ADP
ejpam-5375	36	12	vertices	vertex	NOUN
ejpam-5375	36	13	.	.	PUNCT
ejpam-5375	37	1	we	we	PRON
ejpam-5375	37	2	develop	develop	VERB
ejpam-5375	37	3	some	some	DET
ejpam-5375	37	4	graph	graph	NOUN
ejpam-5375	37	5	matrices	matrix	NOUN
ejpam-5375	37	6	corresponding	correspond	VERB
ejpam-5375	37	7	to	to	ADP
ejpam-5375	37	8	this	this	DET
ejpam-5375	37	9	graph	graph	NOUN
ejpam-5375	37	10	concerning	concern	VERB
ejpam-5375	37	11	the	the	DET
ejpam-5375	37	12	adjacency	adjacency	NOUN
ejpam-5375	37	13	,	,	PUNCT
ejpam-5375	37	14	laplacian	laplacian	NOUN
ejpam-5375	37	15	,	,	PUNCT
ejpam-5375	37	16	and	and	CCONJ
ejpam-5375	37	17	signless	signless	ADJ
ejpam-5375	37	18	laplacian	laplacian	ADJ
ejpam-5375	37	19	matrices	matrix	NOUN
ejpam-5375	37	20	.	.	PUNCT
ejpam-5375	38	1	we	we	PRON
ejpam-5375	38	2	formulate	formulate	VERB
ejpam-5375	38	3	the	the	DET
ejpam-5375	38	4	graph	graph	NOUN
ejpam-5375	38	5	’s	’s	PART
ejpam-5375	38	6	characteristic	characteristic	ADJ
ejpam-5375	38	7	polynomial	polynomial	ADJ
ejpam-5375	38	8	,	,	PUNCT
ejpam-5375	38	9	spectrum	spectrum	NOUN
ejpam-5375	38	10	,	,	PUNCT
ejpam-5375	38	11	and	and	CCONJ
ejpam-5375	38	12	energy	energy	NOUN
ejpam-5375	38	13	,	,	PUNCT
ejpam-5375	38	14	and	and	CCONJ
ejpam-5375	38	15	analyze	analyze	VERB
ejpam-5375	38	16	the	the	DET
ejpam-5375	38	17	relationship	relationship	NOUN
ejpam-5375	38	18	between	between	ADP
ejpam-5375	38	19	those	those	DET
ejpam-5375	38	20	energies	energy	NOUN
ejpam-5375	38	21	.	.	PUNCT
ejpam-5375	39	1	we	we	PRON
ejpam-5375	39	2	also	also	ADV
ejpam-5375	39	3	observe	observe	VERB
ejpam-5375	39	4	the	the	DET
ejpam-5375	39	5	energy	energy	NOUN
ejpam-5375	39	6	values	value	NOUN
ejpam-5375	39	7	to	to	PART
ejpam-5375	39	8	draw	draw	VERB
ejpam-5375	39	9	interesting	interesting	ADJ
ejpam-5375	39	10	conclusions	conclusion	NOUN
ejpam-5375	39	11	.	.	PUNCT
ejpam-5375	40	1	2	2	X
ejpam-5375	40	2	.	.	NUM
ejpam-5375	40	3	preliminaries	preliminary	NOUN
ejpam-5375	40	4	in	in	ADP
ejpam-5375	40	5	this	this	DET
ejpam-5375	40	6	part	part	NOUN
ejpam-5375	40	7	,	,	PUNCT
ejpam-5375	40	8	we	we	PRON
ejpam-5375	40	9	recall	recall	VERB
ejpam-5375	40	10	the	the	DET
ejpam-5375	40	11	fundamental	fundamental	ADJ
ejpam-5375	40	12	definition	definition	NOUN
ejpam-5375	40	13	and	and	CCONJ
ejpam-5375	40	14	theorem	theorem	NOUN
ejpam-5375	40	15	that	that	PRON
ejpam-5375	40	16	are	be	AUX
ejpam-5375	40	17	useful	useful	ADJ
ejpam-5375	40	18	for	for	ADP
ejpam-5375	40	19	our	our	PRON
ejpam-5375	40	20	main	main	ADJ
ejpam-5375	40	21	results	result	NOUN
ejpam-5375	40	22	.	.	PUNCT
ejpam-5375	41	1	we	we	PRON
ejpam-5375	41	2	start	start	VERB
ejpam-5375	41	3	with	with	ADP
ejpam-5375	41	4	the	the	DET
ejpam-5375	41	5	definition	definition	NOUN
ejpam-5375	41	6	of	of	ADP
ejpam-5375	41	7	the	the	DET
ejpam-5375	41	8	identity	identity	NOUN
ejpam-5375	41	9	graph	graph	NOUN
ejpam-5375	41	10	.	.	PUNCT
ejpam-5375	42	1	definition	definition	NOUN
ejpam-5375	42	2	1	1	NUM
ejpam-5375	42	3	.	.	PUNCT
ejpam-5375	43	1	[	[	X
ejpam-5375	43	2	5	5	X
ejpam-5375	43	3	]	]	PUNCT
ejpam-5375	43	4	the	the	DET
ejpam-5375	43	5	identity	identity	NOUN
ejpam-5375	43	6	graph	graph	NOUN
ejpam-5375	43	7	of	of	ADP
ejpam-5375	43	8	a	a	DET
ejpam-5375	43	9	group	group	NOUN
ejpam-5375	43	10	g	g	NOUN
ejpam-5375	43	11	,	,	PUNCT
ejpam-5375	43	12	denoted	denote	VERB
ejpam-5375	43	13	by	by	ADP
ejpam-5375	43	14	γg	γg	PROPN
ejpam-5375	43	15	,	,	PUNCT
ejpam-5375	43	16	is	be	AUX
ejpam-5375	43	17	a	a	DET
ejpam-5375	43	18	graph	graph	NOUN
ejpam-5375	43	19	whose	whose	DET
ejpam-5375	43	20	vertex	vertex	NOUN
ejpam-5375	43	21	set	set	NOUN
ejpam-5375	43	22	is	be	AUX
ejpam-5375	43	23	the	the	DET
ejpam-5375	43	24	elements	element	NOUN
ejpam-5375	43	25	of	of	ADP
ejpam-5375	43	26	the	the	DET
ejpam-5375	43	27	group	group	NOUN
ejpam-5375	43	28	and	and	CCONJ
ejpam-5375	43	29	two	two	NUM
ejpam-5375	43	30	distinct	distinct	ADJ
ejpam-5375	43	31	vertices	vertex	NOUN
ejpam-5375	43	32	u	u	NOUN
ejpam-5375	43	33	and	and	CCONJ
ejpam-5375	43	34	v	v	NOUN
ejpam-5375	43	35	will	will	AUX
ejpam-5375	43	36	be	be	AUX
ejpam-5375	43	37	connected	connect	VERB
ejpam-5375	43	38	by	by	ADP
ejpam-5375	43	39	an	an	DET
ejpam-5375	43	40	edge	edge	NOUN
ejpam-5375	43	41	if	if	SCONJ
ejpam-5375	43	42	uv	uv	NOUN
ejpam-5375	43	43	=	=	SYM
ejpam-5375	43	44	e	e	NOUN
ejpam-5375	43	45	with	with	ADP
ejpam-5375	43	46	every	every	DET
ejpam-5375	43	47	member	member	NOUN
ejpam-5375	43	48	of	of	ADP
ejpam-5375	43	49	g\{e	g\{e	PROPN
ejpam-5375	43	50	}	}	PUNCT
ejpam-5375	43	51	is	be	AUX
ejpam-5375	43	52	adjacent	adjacent	ADJ
ejpam-5375	43	53	to	to	ADP
ejpam-5375	43	54	e	e	NOUN
ejpam-5375	43	55	,	,	PUNCT
ejpam-5375	43	56	where	where	SCONJ
ejpam-5375	43	57	e	e	NOUN
ejpam-5375	43	58	is	be	AUX
ejpam-5375	43	59	the	the	DET
ejpam-5375	43	60	identity	identity	NOUN
ejpam-5375	43	61	element	element	NOUN
ejpam-5375	43	62	of	of	ADP
ejpam-5375	43	63	g.	g.	PROPN
ejpam-5375	43	64	throughout	throughout	ADP
ejpam-5375	43	65	this	this	DET
ejpam-5375	43	66	paper	paper	NOUN
ejpam-5375	43	67	,	,	PUNCT
ejpam-5375	43	68	we	we	PRON
ejpam-5375	43	69	denote	denote	VERB
ejpam-5375	43	70	the	the	DET
ejpam-5375	43	71	identity	identity	NOUN
ejpam-5375	43	72	graph	graph	NOUN
ejpam-5375	43	73	for	for	ADP
ejpam-5375	43	74	zn	zn	PROPN
ejpam-5375	43	75	as	as	ADP
ejpam-5375	43	76	γzn	γzn	PROPN
ejpam-5375	43	77	.	.	PUNCT
ejpam-5375	44	1	the	the	DET
ejpam-5375	44	2	next	next	ADJ
ejpam-5375	44	3	two	two	NUM
ejpam-5375	44	4	theorems	theorem	NOUN
ejpam-5375	44	5	are	be	AUX
ejpam-5375	44	6	the	the	DET
ejpam-5375	44	7	description	description	NOUN
ejpam-5375	44	8	of	of	ADP
ejpam-5375	44	9	γzn	γzn	PROPN
ejpam-5375	44	10	,	,	PUNCT
ejpam-5375	44	11	for	for	ADP
ejpam-5375	44	12	n	n	PRON
ejpam-5375	44	13	is	be	AUX
ejpam-5375	44	14	odd	odd	ADJ
ejpam-5375	44	15	and	and	CCONJ
ejpam-5375	44	16	even	even	ADV
ejpam-5375	44	17	.	.	PUNCT
ejpam-5375	45	1	theorem	theorem	NOUN
ejpam-5375	45	2	1	1	NUM
ejpam-5375	45	3	.	.	PUNCT
ejpam-5375	46	1	[	[	X
ejpam-5375	46	2	5	5	X
ejpam-5375	46	3	]	]	PUNCT
ejpam-5375	46	4	if	if	SCONJ
ejpam-5375	46	5	zn	zn	PROPN
ejpam-5375	46	6	=	=	SYM
ejpam-5375	46	7	{	{	PUNCT
ejpam-5375	46	8	0	0	NUM
ejpam-5375	46	9	,	,	PUNCT
ejpam-5375	46	10	1	1	NUM
ejpam-5375	46	11	,	,	PUNCT
ejpam-5375	46	12	2	2	NUM
ejpam-5375	46	13	,	,	PUNCT
ejpam-5375	46	14	...	...	PUNCT
ejpam-5375	46	15	,	,	PUNCT
ejpam-5375	46	16	n−	n−	NOUN
ejpam-5375	46	17	1	1	NUM
ejpam-5375	46	18	}	}	PUNCT
ejpam-5375	46	19	is	be	AUX
ejpam-5375	46	20	a	a	DET
ejpam-5375	46	21	group	group	NOUN
ejpam-5375	46	22	of	of	ADP
ejpam-5375	46	23	order	order	NOUN
ejpam-5375	46	24	n	n	CCONJ
ejpam-5375	46	25	,	,	PUNCT
ejpam-5375	46	26	n	n	X
ejpam-5375	46	27	≥	≥	NOUN
ejpam-5375	46	28	3	3	NUM
ejpam-5375	46	29	with	with	ADP
ejpam-5375	46	30	odd	odd	ADJ
ejpam-5375	46	31	n	n	CCONJ
ejpam-5375	46	32	,	,	PUNCT
ejpam-5375	46	33	then	then	ADV
ejpam-5375	46	34	the	the	DET
ejpam-5375	46	35	identity	identity	NOUN
ejpam-5375	46	36	graph	graph	NOUN
ejpam-5375	46	37	of	of	ADP
ejpam-5375	46	38	zn	zn	PROPN
ejpam-5375	46	39	contains	contain	VERB
ejpam-5375	46	40	n−1	n−1	PROPN
ejpam-5375	46	41	2	2	NUM
ejpam-5375	46	42	of	of	ADP
ejpam-5375	46	43	k3	k3	PROPN
ejpam-5375	46	44	.	.	PUNCT
ejpam-5375	47	1	theorem	theorem	NOUN
ejpam-5375	47	2	2	2	NUM
ejpam-5375	47	3	.	.	PUNCT
ejpam-5375	48	1	[	[	X
ejpam-5375	48	2	5	5	X
ejpam-5375	48	3	]	]	PUNCT
ejpam-5375	48	4	if	if	SCONJ
ejpam-5375	48	5	zn	zn	PROPN
ejpam-5375	48	6	=	=	SYM
ejpam-5375	48	7	{	{	PUNCT
ejpam-5375	48	8	0	0	NUM
ejpam-5375	48	9	,	,	PUNCT
ejpam-5375	48	10	1	1	NUM
ejpam-5375	48	11	,	,	PUNCT
ejpam-5375	48	12	2	2	NUM
ejpam-5375	48	13	,	,	PUNCT
ejpam-5375	48	14	...	...	PUNCT
ejpam-5375	48	15	,	,	PUNCT
ejpam-5375	48	16	n−	n−	NOUN
ejpam-5375	48	17	1	1	NUM
ejpam-5375	48	18	}	}	PUNCT
ejpam-5375	48	19	is	be	AUX
ejpam-5375	48	20	a	a	DET
ejpam-5375	48	21	group	group	NOUN
ejpam-5375	48	22	of	of	ADP
ejpam-5375	48	23	order	order	NOUN
ejpam-5375	48	24	n	n	CCONJ
ejpam-5375	48	25	,	,	PUNCT
ejpam-5375	48	26	n	n	PRON
ejpam-5375	48	27	≥	≥	NOUN
ejpam-5375	48	28	2	2	NUM
ejpam-5375	48	29	with	with	ADP
ejpam-5375	48	30	even	even	ADV
ejpam-5375	48	31	n	n	CCONJ
ejpam-5375	48	32	,	,	PUNCT
ejpam-5375	48	33	then	then	ADV
ejpam-5375	48	34	the	the	DET
ejpam-5375	48	35	identity	identity	NOUN
ejpam-5375	48	36	graph	graph	NOUN
ejpam-5375	48	37	of	of	ADP
ejpam-5375	48	38	zn	zn	PROPN
ejpam-5375	48	39	contains	contain	VERB
ejpam-5375	48	40	n−2	n−2	PROPN
ejpam-5375	48	41	2	2	NUM
ejpam-5375	48	42	of	of	ADP
ejpam-5375	48	43	k3	k3	NOUN
ejpam-5375	48	44	and	and	CCONJ
ejpam-5375	48	45	a	a	DET
ejpam-5375	48	46	k2	k2	NOUN
ejpam-5375	48	47	.	.	PUNCT
ejpam-5375	49	1	the	the	DET
ejpam-5375	49	2	construction	construction	NOUN
ejpam-5375	49	3	of	of	ADP
ejpam-5375	49	4	the	the	DET
ejpam-5375	49	5	graph	graph	NOUN
ejpam-5375	49	6	matrices	matrix	NOUN
ejpam-5375	49	7	of	of	ADP
ejpam-5375	49	8	γzn	γzn	PROPN
ejpam-5375	49	9	is	be	AUX
ejpam-5375	49	10	based	base	VERB
ejpam-5375	49	11	on	on	ADP
ejpam-5375	49	12	the	the	DET
ejpam-5375	49	13	definition	definition	NOUN
ejpam-5375	49	14	of	of	ADP
ejpam-5375	49	15	the	the	DET
ejpam-5375	49	16	adjacency	adjacency	NOUN
ejpam-5375	49	17	,	,	PUNCT
ejpam-5375	49	18	laplacian	laplacian	NOUN
ejpam-5375	49	19	,	,	PUNCT
ejpam-5375	49	20	and	and	CCONJ
ejpam-5375	49	21	signless	signless	ADJ
ejpam-5375	49	22	laplacian	laplacian	ADJ
ejpam-5375	49	23	matrices	matrix	NOUN
ejpam-5375	49	24	.	.	PUNCT
ejpam-5375	50	1	we	we	PRON
ejpam-5375	50	2	refer	refer	VERB
ejpam-5375	50	3	these	these	DET
ejpam-5375	50	4	definition	definition	NOUN
ejpam-5375	50	5	to	to	ADP
ejpam-5375	50	6	(	(	PUNCT
ejpam-5375	50	7	[	[	X
ejpam-5375	50	8	3	3	NUM
ejpam-5375	50	9	]	]	PUNCT
ejpam-5375	50	10	)	)	PUNCT
ejpam-5375	50	11	as	as	SCONJ
ejpam-5375	50	12	presented	present	VERB
ejpam-5375	50	13	below	below	ADV
ejpam-5375	50	14	:	:	PUNCT
ejpam-5375	50	15	definition	definition	NOUN
ejpam-5375	50	16	2	2	NUM
ejpam-5375	50	17	.	.	PUNCT
ejpam-5375	51	1	(	(	PUNCT
ejpam-5375	51	2	[	[	X
ejpam-5375	51	3	3	3	NUM
ejpam-5375	51	4	]	]	PUNCT
ejpam-5375	51	5	)	)	PUNCT
ejpam-5375	51	6	the	the	DET
ejpam-5375	51	7	adjacency	adjacency	NOUN
ejpam-5375	51	8	matrix	matrix	NOUN
ejpam-5375	51	9	of	of	ADP
ejpam-5375	51	10	order	order	NOUN
ejpam-5375	51	11	n×	n×	PRON
ejpam-5375	51	12	n	n	PRON
ejpam-5375	51	13	associated	associate	VERB
ejpam-5375	51	14	with	with	ADP
ejpam-5375	51	15	γzn	γzn	PROPN
ejpam-5375	51	16	is	be	AUX
ejpam-5375	51	17	given	give	VERB
ejpam-5375	51	18	by	by	ADP
ejpam-5375	51	19	a(γzn	a(γzn	PROPN
ejpam-5375	51	20	)	)	PUNCT
ejpam-5375	51	21	=	=	PUNCT
ejpam-5375	52	1	[	[	X
ejpam-5375	52	2	aij	aij	X
ejpam-5375	52	3	]	]	X
ejpam-5375	52	4	whose	whose	DET
ejpam-5375	52	5	(	(	PUNCT
ejpam-5375	52	6	i	i	NOUN
ejpam-5375	52	7	,	,	PUNCT
ejpam-5375	52	8	j)-th	j)-th	PROPN
ejpam-5375	52	9	entry	entry	NOUN
ejpam-5375	52	10	aij	aij	PROPN
ejpam-5375	52	11	=	=	SYM
ejpam-5375	52	12	{	{	PUNCT
ejpam-5375	52	13	1	1	NUM
ejpam-5375	52	14	,	,	PUNCT
ejpam-5375	52	15	if	if	SCONJ
ejpam-5375	52	16	vi	vi	PRON
ejpam-5375	52	17	̸=	̸=	PROPN
ejpam-5375	52	18	vj	vj	NOUN
ejpam-5375	52	19	and	and	CCONJ
ejpam-5375	52	20	they	they	PRON
ejpam-5375	52	21	are	be	AUX
ejpam-5375	52	22	adjacent	adjacent	ADJ
ejpam-5375	52	23	0	0	NUM
ejpam-5375	52	24	,	,	PUNCT
ejpam-5375	52	25	otherwise	otherwise	ADV
ejpam-5375	52	26	m.	m.	PROPN
ejpam-5375	52	27	u.	u.	PROPN
ejpam-5375	52	28	romdhini	romdhini	PROPN
ejpam-5375	52	29	et	et	PROPN
ejpam-5375	52	30	al	al	PROPN
ejpam-5375	52	31	.	.	PUNCT
ejpam-5375	52	32	/	/	SYM
ejpam-5375	52	33	eur	eur	PROPN
ejpam-5375	52	34	.	.	PUNCT
ejpam-5375	53	1	j.	j.	PROPN
ejpam-5375	53	2	pure	pure	PROPN
ejpam-5375	53	3	appl	appl	PROPN
ejpam-5375	53	4	.	.	PROPN
ejpam-5375	53	5	math	math	PROPN
ejpam-5375	53	6	,	,	PUNCT
ejpam-5375	53	7	17	17	NUM
ejpam-5375	53	8	(	(	PUNCT
ejpam-5375	53	9	4	4	NUM
ejpam-5375	53	10	)	)	PUNCT
ejpam-5375	53	11	(	(	PUNCT
ejpam-5375	53	12	2024	2024	NUM
ejpam-5375	53	13	)	)	PUNCT
ejpam-5375	53	14	,	,	PUNCT
ejpam-5375	53	15	2915	2915	NUM
ejpam-5375	53	16	-	-	SYM
ejpam-5375	53	17	2929	2929	NUM
ejpam-5375	53	18	2917	2917	NUM
ejpam-5375	53	19	definition	definition	NOUN
ejpam-5375	53	20	3	3	NUM
ejpam-5375	53	21	.	.	PUNCT
ejpam-5375	54	1	(	(	PUNCT
ejpam-5375	54	2	[	[	X
ejpam-5375	54	3	3	3	NUM
ejpam-5375	54	4	]	]	PUNCT
ejpam-5375	54	5	)	)	PUNCT
ejpam-5375	54	6	the	the	DET
ejpam-5375	54	7	n	n	NUM
ejpam-5375	54	8	×	×	NOUN
ejpam-5375	54	9	n	n	CCONJ
ejpam-5375	54	10	diagonal	diagonal	ADJ
ejpam-5375	54	11	degree	degree	NOUN
ejpam-5375	54	12	matrix	matrix	NOUN
ejpam-5375	54	13	of	of	ADP
ejpam-5375	54	14	γzn	γzn	PROPN
ejpam-5375	54	15	is	be	AUX
ejpam-5375	54	16	given	give	VERB
ejpam-5375	54	17	by	by	ADP
ejpam-5375	54	18	d(γzn	d(γzn	NOUN
ejpam-5375	54	19	)	)	PUNCT
ejpam-5375	54	20	=	=	PUNCT
ejpam-5375	55	1	[	[	X
ejpam-5375	55	2	dij	dij	X
ejpam-5375	55	3	]	]	X
ejpam-5375	55	4	whose	whose	DET
ejpam-5375	55	5	(	(	PUNCT
ejpam-5375	55	6	i	i	NOUN
ejpam-5375	55	7	,	,	PUNCT
ejpam-5375	55	8	j)-th	j)-th	PROPN
ejpam-5375	55	9	entry	entry	NOUN
ejpam-5375	55	10	dij	dij	PROPN
ejpam-5375	56	1	=	=	SYM
ejpam-5375	56	2	{	{	PUNCT
ejpam-5375	56	3	dvi	dvi	NOUN
ejpam-5375	56	4	,	,	PUNCT
ejpam-5375	56	5	if	if	SCONJ
ejpam-5375	56	6	vi	vi	ADJ
ejpam-5375	56	7	=	=	SYM
ejpam-5375	56	8	vj	vj	NOUN
ejpam-5375	56	9	0	0	NUM
ejpam-5375	56	10	,	,	PUNCT
ejpam-5375	56	11	otherwise	otherwise	ADV
ejpam-5375	56	12	where	where	SCONJ
ejpam-5375	56	13	dvi	dvi	NOUN
ejpam-5375	56	14	is	be	AUX
ejpam-5375	56	15	the	the	DET
ejpam-5375	56	16	vertex	vertex	NOUN
ejpam-5375	56	17	degree	degree	NOUN
ejpam-5375	56	18	of	of	ADP
ejpam-5375	56	19	vi	vi	PROPN
ejpam-5375	56	20	.	.	PUNCT
ejpam-5375	56	21	definition	definition	NOUN
ejpam-5375	56	22	4	4	NUM
ejpam-5375	56	23	.	.	PUNCT
ejpam-5375	57	1	(	(	PUNCT
ejpam-5375	57	2	[	[	X
ejpam-5375	57	3	3	3	NUM
ejpam-5375	57	4	]	]	PUNCT
ejpam-5375	57	5	)	)	PUNCT
ejpam-5375	57	6	the	the	DET
ejpam-5375	57	7	n×	n×	PROPN
ejpam-5375	57	8	n	n	CCONJ
ejpam-5375	57	9	laplacian	laplacian	ADJ
ejpam-5375	57	10	matrix	matrix	NOUN
ejpam-5375	57	11	of	of	ADP
ejpam-5375	57	12	γd2n	γd2n	PROPN
ejpam-5375	57	13	is	be	AUX
ejpam-5375	57	14	given	give	VERB
ejpam-5375	57	15	by	by	ADP
ejpam-5375	57	16	l(γzn	l(γzn	NOUN
ejpam-5375	57	17	)	)	PUNCT
ejpam-5375	57	18	=	=	PUNCT
ejpam-5375	57	19	d(γzn)−	d(γzn)−	PROPN
ejpam-5375	57	20	a(γzn	a(γzn	NOUN
ejpam-5375	57	21	)	)	PUNCT
ejpam-5375	57	22	.	.	PUNCT
ejpam-5375	58	1	definition	definition	NOUN
ejpam-5375	58	2	5	5	NUM
ejpam-5375	58	3	.	.	PUNCT
ejpam-5375	59	1	(	(	PUNCT
ejpam-5375	59	2	[	[	X
ejpam-5375	59	3	3	3	NUM
ejpam-5375	59	4	]	]	PUNCT
ejpam-5375	59	5	)	)	PUNCT
ejpam-5375	59	6	the	the	DET
ejpam-5375	59	7	n	n	NUM
ejpam-5375	59	8	×	×	NOUN
ejpam-5375	59	9	n	n	CCONJ
ejpam-5375	59	10	signless	signless	ADJ
ejpam-5375	59	11	laplacian	laplacian	ADJ
ejpam-5375	59	12	matrix	matrix	NOUN
ejpam-5375	59	13	of	of	ADP
ejpam-5375	59	14	γzn	γzn	PROPN
ejpam-5375	59	15	is	be	AUX
ejpam-5375	59	16	given	give	VERB
ejpam-5375	59	17	by	by	ADP
ejpam-5375	59	18	sl(γzn	sl(γzn	ADJ
ejpam-5375	59	19	)	)	PUNCT
ejpam-5375	59	20	=	=	PUNCT
ejpam-5375	59	21	d(γzn	d(γzn	VERB
ejpam-5375	59	22	)	)	PUNCT
ejpam-5375	60	1	+	+	NOUN
ejpam-5375	60	2	a(γzn	a(γzn	PROPN
ejpam-5375	60	3	)	)	PUNCT
ejpam-5375	60	4	.	.	PUNCT
ejpam-5375	61	1	the	the	DET
ejpam-5375	61	2	characteristic	characteristic	ADJ
ejpam-5375	61	3	polynomial	polynomial	NOUN
ejpam-5375	61	4	of	of	ADP
ejpam-5375	61	5	a(γzn	a(γzn	PROPN
ejpam-5375	61	6	)	)	PUNCT
ejpam-5375	61	7	is	be	AUX
ejpam-5375	61	8	defined	define	VERB
ejpam-5375	61	9	by	by	ADP
ejpam-5375	61	10	pa(γzn	pa(γzn	ADJ
ejpam-5375	61	11	)	)	PUNCT
ejpam-5375	61	12	(	(	PUNCT
ejpam-5375	61	13	λ	λ	X
ejpam-5375	61	14	)	)	PUNCT
ejpam-5375	61	15	=	=	SYM
ejpam-5375	61	16	|λin	|λin	PUNCT
ejpam-5375	61	17	−a(γzn)|	−a(γzn)|	PROPN
ejpam-5375	61	18	,	,	PUNCT
ejpam-5375	61	19	(	(	PUNCT
ejpam-5375	61	20	1	1	X
ejpam-5375	61	21	)	)	PUNCT
ejpam-5375	61	22	where	where	SCONJ
ejpam-5375	61	23	in	in	ADP
ejpam-5375	61	24	is	be	AUX
ejpam-5375	61	25	an	an	DET
ejpam-5375	61	26	n	n	NUM
ejpam-5375	61	27	×	×	NOUN
ejpam-5375	61	28	n	n	CCONJ
ejpam-5375	61	29	identity	identity	NOUN
ejpam-5375	61	30	matrix	matrix	NOUN
ejpam-5375	61	31	.	.	PUNCT
ejpam-5375	62	1	similarly	similarly	ADV
ejpam-5375	62	2	,	,	PUNCT
ejpam-5375	62	3	notation	notation	NOUN
ejpam-5375	62	4	for	for	ADP
ejpam-5375	62	5	other	other	ADJ
ejpam-5375	62	6	matrices	matrix	NOUN
ejpam-5375	62	7	can	can	AUX
ejpam-5375	62	8	be	be	AUX
ejpam-5375	62	9	used	use	VERB
ejpam-5375	62	10	in	in	ADP
ejpam-5375	62	11	the	the	DET
ejpam-5375	62	12	same	same	ADJ
ejpam-5375	62	13	manner	manner	NOUN
ejpam-5375	62	14	.	.	PUNCT
ejpam-5375	63	1	to	to	PART
ejpam-5375	63	2	formulate	formulate	VERB
ejpam-5375	63	3	the	the	DET
ejpam-5375	63	4	determinant	determinant	ADJ
ejpam-5375	63	5	in	in	ADP
ejpam-5375	63	6	equation	equation	NOUN
ejpam-5375	63	7	1	1	NUM
ejpam-5375	63	8	,	,	PUNCT
ejpam-5375	63	9	we	we	PRON
ejpam-5375	63	10	need	need	VERB
ejpam-5375	63	11	row	row	NOUN
ejpam-5375	63	12	and	and	CCONJ
ejpam-5375	63	13	column	column	NOUN
ejpam-5375	63	14	operations	operation	NOUN
ejpam-5375	63	15	to	to	PART
ejpam-5375	63	16	simplify	simplify	VERB
ejpam-5375	63	17	the	the	DET
ejpam-5375	63	18	process	process	NOUN
ejpam-5375	63	19	.	.	PUNCT
ejpam-5375	64	1	let	let	VERB
ejpam-5375	64	2	ri	ri	PRON
ejpam-5375	64	3	be	be	AUX
ejpam-5375	64	4	the	the	DET
ejpam-5375	64	5	i	i	PROPN
ejpam-5375	64	6	-	-	PUNCT
ejpam-5375	64	7	th	th	X
ejpam-5375	64	8	row	row	NOUN
ejpam-5375	64	9	and	and	CCONJ
ejpam-5375	64	10	ci	ci	NOUN
ejpam-5375	64	11	be	be	AUX
ejpam-5375	64	12	the	the	DET
ejpam-5375	64	13	i	i	PROPN
ejpam-5375	64	14	-	-	PUNCT
ejpam-5375	64	15	th	th	X
ejpam-5375	64	16	column	column	NOUN
ejpam-5375	64	17	of	of	ADP
ejpam-5375	64	18	pa(γzn	pa(γzn	ADJ
ejpam-5375	64	19	)	)	PUNCT
ejpam-5375	64	20	(	(	PUNCT
ejpam-5375	64	21	λ	λ	X
ejpam-5375	64	22	)	)	PUNCT
ejpam-5375	64	23	.	.	PUNCT
ejpam-5375	65	1	furthermore	furthermore	ADV
ejpam-5375	65	2	,	,	PUNCT
ejpam-5375	65	3	the	the	DET
ejpam-5375	65	4	roots	root	NOUN
ejpam-5375	65	5	of	of	ADP
ejpam-5375	65	6	pa(γzn	pa(γzn	ADJ
ejpam-5375	65	7	)	)	PUNCT
ejpam-5375	65	8	(	(	PUNCT
ejpam-5375	65	9	λ	λ	X
ejpam-5375	65	10	)	)	PUNCT
ejpam-5375	65	11	=	=	SYM
ejpam-5375	65	12	0	0	NUM
ejpam-5375	65	13	are	be	AUX
ejpam-5375	65	14	the	the	DET
ejpam-5375	65	15	eigenvalues	eigenvalue	NOUN
ejpam-5375	65	16	of	of	ADP
ejpam-5375	65	17	γzn	γzn	PROPN
ejpam-5375	65	18	.	.	PUNCT
ejpam-5375	66	1	the	the	DET
ejpam-5375	66	2	graph	graph	NOUN
ejpam-5375	66	3	energy	energy	NOUN
ejpam-5375	66	4	definition	definition	NOUN
ejpam-5375	66	5	is	be	AUX
ejpam-5375	66	6	based	base	VERB
ejpam-5375	66	7	on	on	ADP
ejpam-5375	66	8	the	the	DET
ejpam-5375	66	9	eigenvalues	eigenvalue	NOUN
ejpam-5375	66	10	of	of	ADP
ejpam-5375	66	11	γzn	γzn	PROPN
ejpam-5375	66	12	as	as	SCONJ
ejpam-5375	66	13	presented	present	VERB
ejpam-5375	66	14	below	below	ADV
ejpam-5375	66	15	.	.	PUNCT
ejpam-5375	67	1	definition	definition	NOUN
ejpam-5375	67	2	6	6	NUM
ejpam-5375	67	3	.	.	PUNCT
ejpam-5375	68	1	[	[	X
ejpam-5375	68	2	4	4	X
ejpam-5375	68	3	]	]	PUNCT
ejpam-5375	68	4	the	the	DET
ejpam-5375	68	5	adjacency	adjacency	PROPN
ejpam-5375	68	6	energy	energy	NOUN
ejpam-5375	68	7	of	of	ADP
ejpam-5375	68	8	γzn	γzn	PROPN
ejpam-5375	68	9	can	can	AUX
ejpam-5375	68	10	be	be	AUX
ejpam-5375	68	11	written	write	VERB
ejpam-5375	68	12	by	by	ADP
ejpam-5375	68	13	ea(γzn	ea(γzn	ADJ
ejpam-5375	68	14	)	)	PUNCT
ejpam-5375	69	1	=	=	PUNCT
ejpam-5375	69	2	n∑	n∑	NOUN
ejpam-5375	69	3	i=1	i=1	PROPN
ejpam-5375	69	4	|λi|	|λi|	PROPN
ejpam-5375	69	5	,	,	PUNCT
ejpam-5375	69	6	where	where	SCONJ
ejpam-5375	69	7	λ1	λ1	ADJ
ejpam-5375	69	8	,	,	PUNCT
ejpam-5375	69	9	λ2	λ2	NOUN
ejpam-5375	69	10	,	,	PUNCT
ejpam-5375	69	11	.	.	PUNCT
ejpam-5375	69	12	.	.	PUNCT
ejpam-5375	70	1	.	.	PUNCT
ejpam-5375	71	1	,	,	PUNCT
ejpam-5375	71	2	λn	λn	PROPN
ejpam-5375	71	3	are	be	AUX
ejpam-5375	71	4	eigenvalues	eigenvalue	NOUN
ejpam-5375	71	5	of	of	ADP
ejpam-5375	71	6	a(γzn	a(γzn	PROPN
ejpam-5375	71	7	)	)	PUNCT
ejpam-5375	71	8	.	.	PUNCT
ejpam-5375	72	1	the	the	DET
ejpam-5375	72	2	spectrum	spectrum	NOUN
ejpam-5375	72	3	of	of	ADP
ejpam-5375	72	4	γzn	γzn	PROPN
ejpam-5375	72	5	in	in	ADP
ejpam-5375	72	6	accordance	accordance	NOUN
ejpam-5375	72	7	with	with	ADP
ejpam-5375	72	8	the	the	DET
ejpam-5375	72	9	adjacency	adjacency	NOUN
ejpam-5375	72	10	matrix	matrix	NOUN
ejpam-5375	72	11	is	be	AUX
ejpam-5375	72	12	speca(γzn	speca(γzn	ADJ
ejpam-5375	72	13	)	)	PUNCT
ejpam-5375	72	14	=	=	SYM
ejpam-5375	72	15	{	{	PUNCT
ejpam-5375	72	16	(	(	PUNCT
ejpam-5375	72	17	λ1	λ1	ADJ
ejpam-5375	72	18	)	)	PUNCT
ejpam-5375	72	19	k1	k1	NOUN
ejpam-5375	72	20	,	,	PUNCT
ejpam-5375	72	21	(	(	PUNCT
ejpam-5375	72	22	λ2	λ2	NOUN
ejpam-5375	72	23	)	)	PUNCT
ejpam-5375	72	24	k2	k2	NOUN
ejpam-5375	72	25	,	,	PUNCT
ejpam-5375	72	26	.	.	PUNCT
ejpam-5375	72	27	.	.	PUNCT
ejpam-5375	72	28	.	.	PUNCT
ejpam-5375	73	1	,	,	PUNCT
ejpam-5375	73	2	(	(	PUNCT
ejpam-5375	73	3	λn	λn	NOUN
ejpam-5375	73	4	)	)	PUNCT
ejpam-5375	73	5	kn	kn	PROPN
ejpam-5375	73	6	}	}	PUNCT
ejpam-5375	73	7	,	,	PUNCT
ejpam-5375	73	8	where	where	SCONJ
ejpam-5375	73	9	k1	k1	NOUN
ejpam-5375	73	10	,	,	PUNCT
ejpam-5375	73	11	k2	k2	NOUN
ejpam-5375	73	12	,	,	PUNCT
ejpam-5375	73	13	.	.	PUNCT
ejpam-5375	73	14	.	.	PUNCT
ejpam-5375	73	15	.	.	PUNCT
ejpam-5375	74	1	,	,	PUNCT
ejpam-5375	74	2	kn	kn	PROPN
ejpam-5375	74	3	are	be	AUX
ejpam-5375	74	4	the	the	DET
ejpam-5375	74	5	respective	respective	ADJ
ejpam-5375	74	6	multiplicities	multiplicity	NOUN
ejpam-5375	74	7	of	of	ADP
ejpam-5375	74	8	eigenvalus	eigenvalus	NOUN
ejpam-5375	74	9	.	.	PUNCT
ejpam-5375	75	1	the	the	DET
ejpam-5375	75	2	spectral	spectral	ADJ
ejpam-5375	75	3	radius	radius	NOUN
ejpam-5375	75	4	of	of	ADP
ejpam-5375	75	5	γzn	γzn	PROPN
ejpam-5375	75	6	corresponding	correspond	VERB
ejpam-5375	75	7	with	with	ADP
ejpam-5375	75	8	the	the	DET
ejpam-5375	75	9	adjacency	adjacency	NOUN
ejpam-5375	75	10	matrix	matrix	NOUN
ejpam-5375	75	11	is	be	AUX
ejpam-5375	75	12	ρa(γzn	ρa(γzn	VERB
ejpam-5375	75	13	)	)	PUNCT
ejpam-5375	76	1	=	=	SYM
ejpam-5375	76	2	max{|λ|	max{|λ|	NOUN
ejpam-5375	76	3	:	:	PUNCT
ejpam-5375	77	1	λ	λ	X
ejpam-5375	77	2	∈	∈	PROPN
ejpam-5375	77	3	speca(γzn	speca(γzn	ADJ
ejpam-5375	77	4	)	)	PUNCT
ejpam-5375	77	5	}	}	PUNCT
ejpam-5375	77	6	.	.	PUNCT
ejpam-5375	78	1	the	the	DET
ejpam-5375	78	2	energy	energy	NOUN
ejpam-5375	78	3	value	value	NOUN
ejpam-5375	78	4	of	of	ADP
ejpam-5375	78	5	γzn	γzn	PROPN
ejpam-5375	78	6	is	be	AUX
ejpam-5375	78	7	classified	classify	VERB
ejpam-5375	78	8	as	as	ADP
ejpam-5375	78	9	hyperenergetic	hyperenergetic	ADJ
ejpam-5375	78	10	if	if	SCONJ
ejpam-5375	78	11	the	the	DET
ejpam-5375	78	12	energy	energy	NOUN
ejpam-5375	78	13	of	of	ADP
ejpam-5375	78	14	γzn	γzn	PROPN
ejpam-5375	78	15	is	be	AUX
ejpam-5375	78	16	greater	great	ADJ
ejpam-5375	78	17	than	than	ADP
ejpam-5375	78	18	2(n−	2(n−	NUM
ejpam-5375	78	19	1	1	NUM
ejpam-5375	78	20	)	)	PUNCT
ejpam-5375	79	1	[	[	X
ejpam-5375	79	2	7	7	NUM
ejpam-5375	79	3	]	]	PUNCT
ejpam-5375	79	4	.	.	PUNCT
ejpam-5375	80	1	m.	m.	PROPN
ejpam-5375	80	2	u.	u.	PROPN
ejpam-5375	80	3	romdhini	romdhini	PROPN
ejpam-5375	80	4	et	et	PROPN
ejpam-5375	80	5	al	al	PROPN
ejpam-5375	80	6	.	.	PUNCT
ejpam-5375	80	7	/	/	SYM
ejpam-5375	80	8	eur	eur	PROPN
ejpam-5375	80	9	.	.	PUNCT
ejpam-5375	81	1	j.	j.	PROPN
ejpam-5375	81	2	pure	pure	PROPN
ejpam-5375	81	3	appl	appl	PROPN
ejpam-5375	81	4	.	.	PROPN
ejpam-5375	81	5	math	math	PROPN
ejpam-5375	81	6	,	,	PUNCT
ejpam-5375	81	7	17	17	NUM
ejpam-5375	81	8	(	(	PUNCT
ejpam-5375	81	9	4	4	NUM
ejpam-5375	81	10	)	)	PUNCT
ejpam-5375	81	11	(	(	PUNCT
ejpam-5375	81	12	2024	2024	NUM
ejpam-5375	81	13	)	)	PUNCT
ejpam-5375	81	14	,	,	PUNCT
ejpam-5375	81	15	2915	2915	NUM
ejpam-5375	81	16	-	-	SYM
ejpam-5375	81	17	2929	2929	NUM
ejpam-5375	81	18	2918	2918	NUM
ejpam-5375	81	19	3	3	NUM
ejpam-5375	81	20	.	.	PUNCT
ejpam-5375	81	21	main	main	ADJ
ejpam-5375	81	22	results	result	NOUN
ejpam-5375	81	23	in	in	ADP
ejpam-5375	81	24	this	this	DET
ejpam-5375	81	25	section	section	NOUN
ejpam-5375	81	26	,	,	PUNCT
ejpam-5375	81	27	we	we	PRON
ejpam-5375	81	28	begin	begin	VERB
ejpam-5375	81	29	with	with	ADP
ejpam-5375	81	30	the	the	DET
ejpam-5375	81	31	analysis	analysis	NOUN
ejpam-5375	81	32	of	of	ADP
ejpam-5375	81	33	the	the	DET
ejpam-5375	81	34	degree	degree	NOUN
ejpam-5375	81	35	of	of	ADP
ejpam-5375	81	36	every	every	DET
ejpam-5375	81	37	vertex	vertex	NOUN
ejpam-5375	81	38	in	in	ADP
ejpam-5375	81	39	γzn	γzn	PROPN
ejpam-5375	81	40	.	.	PUNCT
ejpam-5375	82	1	we	we	PRON
ejpam-5375	82	2	need	need	VERB
ejpam-5375	82	3	this	this	DET
ejpam-5375	82	4	property	property	NOUN
ejpam-5375	82	5	for	for	ADP
ejpam-5375	82	6	constructing	construct	VERB
ejpam-5375	82	7	the	the	DET
ejpam-5375	82	8	matrices	matrix	NOUN
ejpam-5375	82	9	of	of	ADP
ejpam-5375	82	10	γzn	γzn	PROPN
ejpam-5375	82	11	.	.	PUNCT
ejpam-5375	83	1	theorem	theorem	VERB
ejpam-5375	83	2	3	3	X
ejpam-5375	83	3	.	.	PUNCT
ejpam-5375	84	1	let	let	VERB
ejpam-5375	84	2	γzn	γzn	PROPN
ejpam-5375	84	3	be	be	AUX
ejpam-5375	84	4	the	the	DET
ejpam-5375	84	5	identity	identity	NOUN
ejpam-5375	84	6	graph	graph	NOUN
ejpam-5375	84	7	on	on	ADP
ejpam-5375	84	8	zn	zn	PROPN
ejpam-5375	84	9	.	.	PUNCT
ejpam-5375	85	1	for	for	ADP
ejpam-5375	85	2	n	n	NUM
ejpam-5375	85	3	is	be	AUX
ejpam-5375	85	4	odd	odd	ADJ
ejpam-5375	85	5	,	,	PUNCT
ejpam-5375	85	6	then	then	ADV
ejpam-5375	85	7	(	(	PUNCT
ejpam-5375	85	8	i	i	NOUN
ejpam-5375	85	9	)	)	PUNCT
ejpam-5375	85	10	the	the	DET
ejpam-5375	85	11	degree	degree	NOUN
ejpam-5375	85	12	of	of	ADP
ejpam-5375	85	13	0	0	NUM
ejpam-5375	85	14	on	on	ADP
ejpam-5375	85	15	γzn	γzn	PROPN
ejpam-5375	85	16	is	be	AUX
ejpam-5375	85	17	deg(0	deg(0	NOUN
ejpam-5375	85	18	)	)	PUNCT
ejpam-5375	86	1	=	=	PUNCT
ejpam-5375	86	2	n−	n−	NOUN
ejpam-5375	86	3	1	1	NUM
ejpam-5375	86	4	,	,	PUNCT
ejpam-5375	86	5	and	and	CCONJ
ejpam-5375	86	6	(	(	PUNCT
ejpam-5375	86	7	ii	ii	NOUN
ejpam-5375	86	8	)	)	PUNCT
ejpam-5375	86	9	the	the	DET
ejpam-5375	86	10	degree	degree	NOUN
ejpam-5375	86	11	of	of	ADP
ejpam-5375	86	12	a	a	PRON
ejpam-5375	86	13	on	on	ADP
ejpam-5375	86	14	γzn	γzn	PROPN
ejpam-5375	86	15	is	be	AUX
ejpam-5375	86	16	deg(a	deg(a	PROPN
ejpam-5375	86	17	)	)	PUNCT
ejpam-5375	86	18	=	=	SYM
ejpam-5375	86	19	2	2	NUM
ejpam-5375	86	20	,	,	PUNCT
ejpam-5375	86	21	for	for	ADP
ejpam-5375	86	22	a	a	DET
ejpam-5375	86	23	̸=	̸=	PROPN
ejpam-5375	86	24	0	0	NUM
ejpam-5375	86	25	.	.	PUNCT
ejpam-5375	87	1	proof	proof	NOUN
ejpam-5375	87	2	.	.	PUNCT
ejpam-5375	88	1	from	from	ADP
ejpam-5375	88	2	theorem	theorem	NOUN
ejpam-5375	88	3	1	1	NUM
ejpam-5375	88	4	for	for	ADP
ejpam-5375	88	5	odd	odd	ADJ
ejpam-5375	88	6	n	n	CCONJ
ejpam-5375	88	7	,	,	PUNCT
ejpam-5375	88	8	the	the	DET
ejpam-5375	88	9	identity	identity	NOUN
ejpam-5375	88	10	graph	graph	NOUN
ejpam-5375	88	11	of	of	ADP
ejpam-5375	88	12	zn	zn	PROPN
ejpam-5375	88	13	contains	contain	VERB
ejpam-5375	88	14	n−1	n−1	PROPN
ejpam-5375	88	15	2	2	NUM
ejpam-5375	88	16	of	of	ADP
ejpam-5375	88	17	k3	k3	PROPN
ejpam-5375	88	18	.	.	PUNCT
ejpam-5375	89	1	since	since	SCONJ
ejpam-5375	89	2	the	the	DET
ejpam-5375	89	3	identity	identity	NOUN
ejpam-5375	89	4	of	of	ADP
ejpam-5375	89	5	zn	zn	PROPN
ejpam-5375	89	6	is	be	AUX
ejpam-5375	89	7	0	0	NUM
ejpam-5375	89	8	,	,	PUNCT
ejpam-5375	89	9	then	then	ADV
ejpam-5375	89	10	0	0	NUM
ejpam-5375	89	11	is	be	AUX
ejpam-5375	89	12	adjacent	adjacent	ADJ
ejpam-5375	89	13	to	to	ADP
ejpam-5375	89	14	all	all	DET
ejpam-5375	89	15	other	other	ADJ
ejpam-5375	89	16	vertices	vertex	NOUN
ejpam-5375	89	17	in	in	ADP
ejpam-5375	89	18	zn	zn	PROPN
ejpam-5375	89	19	.	.	PUNCT
ejpam-5375	90	1	this	this	PRON
ejpam-5375	90	2	means	mean	VERB
ejpam-5375	90	3	that	that	SCONJ
ejpam-5375	90	4	the	the	DET
ejpam-5375	90	5	degree	degree	NOUN
ejpam-5375	90	6	of	of	ADP
ejpam-5375	90	7	0	0	NUM
ejpam-5375	90	8	is	be	AUX
ejpam-5375	90	9	equal	equal	ADJ
ejpam-5375	90	10	to	to	ADP
ejpam-5375	90	11	n	n	PROPN
ejpam-5375	90	12	−	−	PROPN
ejpam-5375	90	13	1	1	NUM
ejpam-5375	90	14	.	.	PUNCT
ejpam-5375	91	1	meanwhile	meanwhile	ADV
ejpam-5375	91	2	,	,	PUNCT
ejpam-5375	91	3	for	for	ADP
ejpam-5375	91	4	a	a	PRON
ejpam-5375	91	5	,	,	PUNCT
ejpam-5375	91	6	where	where	SCONJ
ejpam-5375	91	7	a	a	DET
ejpam-5375	91	8	̸=	̸=	PROPN
ejpam-5375	91	9	0	0	NUM
ejpam-5375	91	10	,	,	PUNCT
ejpam-5375	91	11	we	we	PRON
ejpam-5375	91	12	know	know	VERB
ejpam-5375	91	13	that	that	SCONJ
ejpam-5375	91	14	the	the	DET
ejpam-5375	91	15	inverse	inverse	NOUN
ejpam-5375	91	16	of	of	ADP
ejpam-5375	91	17	a	a	PRON
ejpam-5375	91	18	is	be	AUX
ejpam-5375	91	19	n−	n−	NOUN
ejpam-5375	91	20	a	a	PRON
ejpam-5375	91	21	,	,	PUNCT
ejpam-5375	91	22	since	since	SCONJ
ejpam-5375	91	23	a+	a+	PRON
ejpam-5375	91	24	(	(	PUNCT
ejpam-5375	91	25	n−	n−	NOUN
ejpam-5375	91	26	a	a	X
ejpam-5375	91	27	)	)	PUNCT
ejpam-5375	92	1	=	=	SYM
ejpam-5375	92	2	0	0	X
ejpam-5375	92	3	.	.	PUNCT
ejpam-5375	93	1	this	this	PRON
ejpam-5375	93	2	implies	imply	VERB
ejpam-5375	93	3	that	that	SCONJ
ejpam-5375	93	4	a	a	PRON
ejpam-5375	93	5	and	and	CCONJ
ejpam-5375	93	6	n−	n−	PROPN
ejpam-5375	93	7	a	a	PRON
ejpam-5375	93	8	are	be	AUX
ejpam-5375	93	9	always	always	ADV
ejpam-5375	93	10	adjacent	adjacent	ADJ
ejpam-5375	93	11	.	.	PUNCT
ejpam-5375	94	1	therefore	therefore	ADV
ejpam-5375	94	2	,	,	PUNCT
ejpam-5375	94	3	the	the	DET
ejpam-5375	94	4	degree	degree	NOUN
ejpam-5375	94	5	of	of	ADP
ejpam-5375	94	6	a	a	PRON
ejpam-5375	94	7	is	be	AUX
ejpam-5375	94	8	2	2	NUM
ejpam-5375	94	9	.	.	PUNCT
ejpam-5375	94	10	theorem	theorem	NOUN
ejpam-5375	94	11	4	4	NUM
ejpam-5375	94	12	.	.	PUNCT
ejpam-5375	95	1	let	let	VERB
ejpam-5375	95	2	γzn	γzn	PROPN
ejpam-5375	95	3	be	be	AUX
ejpam-5375	95	4	the	the	DET
ejpam-5375	95	5	identity	identity	NOUN
ejpam-5375	95	6	graph	graph	NOUN
ejpam-5375	95	7	on	on	ADP
ejpam-5375	95	8	zn	zn	PROPN
ejpam-5375	95	9	.	.	PUNCT
ejpam-5375	96	1	for	for	ADP
ejpam-5375	96	2	n	n	NUM
ejpam-5375	96	3	is	be	AUX
ejpam-5375	96	4	even	even	ADV
ejpam-5375	96	5	,	,	PUNCT
ejpam-5375	96	6	then	then	ADV
ejpam-5375	96	7	(	(	PUNCT
ejpam-5375	96	8	i	i	NOUN
ejpam-5375	96	9	)	)	PUNCT
ejpam-5375	96	10	the	the	DET
ejpam-5375	96	11	degree	degree	NOUN
ejpam-5375	96	12	of	of	ADP
ejpam-5375	96	13	0	0	NUM
ejpam-5375	96	14	on	on	ADP
ejpam-5375	96	15	γzn	γzn	PROPN
ejpam-5375	96	16	is	be	AUX
ejpam-5375	96	17	deg(0	deg(0	NOUN
ejpam-5375	96	18	)	)	PUNCT
ejpam-5375	97	1	=	=	PUNCT
ejpam-5375	97	2	n−	n−	NOUN
ejpam-5375	97	3	1	1	NUM
ejpam-5375	97	4	,	,	PUNCT
ejpam-5375	97	5	(	(	PUNCT
ejpam-5375	97	6	ii	ii	NOUN
ejpam-5375	97	7	)	)	PUNCT
ejpam-5375	97	8	the	the	DET
ejpam-5375	97	9	degree	degree	NOUN
ejpam-5375	97	10	of	of	ADP
ejpam-5375	97	11	n	n	ADV
ejpam-5375	97	12	2	2	NUM
ejpam-5375	97	13	on	on	ADP
ejpam-5375	97	14	γzn	γzn	PROPN
ejpam-5375	97	15	is	be	AUX
ejpam-5375	97	16	deg(n2	deg(n2	ADV
ejpam-5375	97	17	)	)	PUNCT
ejpam-5375	98	1	=	=	SYM
ejpam-5375	98	2	1	1	NUM
ejpam-5375	98	3	,	,	PUNCT
ejpam-5375	98	4	and	and	CCONJ
ejpam-5375	98	5	(	(	PUNCT
ejpam-5375	98	6	iii	iii	X
ejpam-5375	98	7	)	)	PUNCT
ejpam-5375	98	8	the	the	DET
ejpam-5375	98	9	degree	degree	NOUN
ejpam-5375	98	10	of	of	ADP
ejpam-5375	98	11	a	a	PRON
ejpam-5375	98	12	on	on	ADP
ejpam-5375	98	13	γzn	γzn	PROPN
ejpam-5375	98	14	is	be	AUX
ejpam-5375	98	15	deg(a	deg(a	PROPN
ejpam-5375	98	16	)	)	PUNCT
ejpam-5375	98	17	=	=	SYM
ejpam-5375	98	18	2	2	NUM
ejpam-5375	98	19	,	,	PUNCT
ejpam-5375	98	20	for	for	ADP
ejpam-5375	98	21	a	a	DET
ejpam-5375	98	22	̸=	̸=	PROPN
ejpam-5375	98	23	0	0	NUM
ejpam-5375	98	24	,	,	PUNCT
ejpam-5375	98	25	n2	n2	NOUN
ejpam-5375	98	26	.	.	PUNCT
ejpam-5375	99	1	proof	proof	NOUN
ejpam-5375	99	2	.	.	PUNCT
ejpam-5375	100	1	recall	recall	VERB
ejpam-5375	100	2	the	the	DET
ejpam-5375	100	3	fact	fact	NOUN
ejpam-5375	100	4	from	from	ADP
ejpam-5375	100	5	theorem	theorem	ADJ
ejpam-5375	100	6	2	2	NUM
ejpam-5375	100	7	that	that	SCONJ
ejpam-5375	100	8	the	the	DET
ejpam-5375	100	9	identity	identity	NOUN
ejpam-5375	100	10	graph	graph	NOUN
ejpam-5375	100	11	of	of	ADP
ejpam-5375	100	12	zn	zn	PROPN
ejpam-5375	100	13	contains	contain	VERB
ejpam-5375	100	14	n−2	n−2	PROPN
ejpam-5375	100	15	2	2	NUM
ejpam-5375	100	16	of	of	ADP
ejpam-5375	100	17	k3	k3	NOUN
ejpam-5375	100	18	and	and	CCONJ
ejpam-5375	100	19	a	a	DET
ejpam-5375	100	20	k2	k2	NOUN
ejpam-5375	100	21	for	for	ADP
ejpam-5375	100	22	even	even	ADV
ejpam-5375	100	23	n.	n.	NOUN
ejpam-5375	100	24	by	by	ADP
ejpam-5375	100	25	the	the	DET
ejpam-5375	100	26	same	same	ADJ
ejpam-5375	100	27	argument	argument	NOUN
ejpam-5375	100	28	with	with	ADP
ejpam-5375	100	29	the	the	DET
ejpam-5375	100	30	proofing	proof	VERB
ejpam-5375	100	31	part	part	NOUN
ejpam-5375	100	32	of	of	ADP
ejpam-5375	100	33	theorem	theorem	NOUN
ejpam-5375	100	34	3	3	NUM
ejpam-5375	100	35	that	that	DET
ejpam-5375	100	36	0	0	NUM
ejpam-5375	100	37	is	be	AUX
ejpam-5375	100	38	the	the	DET
ejpam-5375	100	39	identity	identity	NOUN
ejpam-5375	100	40	of	of	ADP
ejpam-5375	100	41	zn	zn	PROPN
ejpam-5375	100	42	,	,	PUNCT
ejpam-5375	100	43	then	then	ADV
ejpam-5375	100	44	the	the	DET
ejpam-5375	100	45	degree	degree	NOUN
ejpam-5375	100	46	of	of	ADP
ejpam-5375	100	47	0	0	NUM
ejpam-5375	100	48	is	be	AUX
ejpam-5375	100	49	n−	n−	NOUN
ejpam-5375	100	50	1	1	NUM
ejpam-5375	100	51	.	.	PUNCT
ejpam-5375	101	1	now	now	ADV
ejpam-5375	101	2	,	,	PUNCT
ejpam-5375	101	3	we	we	PRON
ejpam-5375	101	4	concern	concern	VERB
ejpam-5375	101	5	with	with	ADP
ejpam-5375	101	6	n	n	ADV
ejpam-5375	101	7	2	2	NUM
ejpam-5375	101	8	∈	∈	NOUN
ejpam-5375	101	9	zn	zn	X
ejpam-5375	101	10	.	.	PUNCT
ejpam-5375	102	1	since	since	SCONJ
ejpam-5375	102	2	the	the	DET
ejpam-5375	102	3	inverse	inverse	NOUN
ejpam-5375	102	4	of	of	ADP
ejpam-5375	102	5	n	n	DET
ejpam-5375	102	6	2	2	NUM
ejpam-5375	102	7	is	be	AUX
ejpam-5375	102	8	itself	itself	PRON
ejpam-5375	102	9	,	,	PUNCT
ejpam-5375	102	10	then	then	ADV
ejpam-5375	102	11	n	n	DET
ejpam-5375	102	12	2	2	NUM
ejpam-5375	102	13	is	be	AUX
ejpam-5375	102	14	only	only	ADV
ejpam-5375	102	15	adjacent	adjacent	ADJ
ejpam-5375	102	16	to	to	ADP
ejpam-5375	102	17	0	0	NUM
ejpam-5375	102	18	which	which	PRON
ejpam-5375	102	19	means	mean	VERB
ejpam-5375	102	20	the	the	DET
ejpam-5375	102	21	degree	degree	NOUN
ejpam-5375	102	22	of	of	ADP
ejpam-5375	102	23	n	n	DET
ejpam-5375	102	24	2	2	NUM
ejpam-5375	102	25	is	be	AUX
ejpam-5375	102	26	1	1	NUM
ejpam-5375	102	27	.	.	PUNCT
ejpam-5375	103	1	meanwhile	meanwhile	ADV
ejpam-5375	103	2	,	,	PUNCT
ejpam-5375	103	3	for	for	ADP
ejpam-5375	103	4	a	a	DET
ejpam-5375	103	5	̸=	̸=	PROPN
ejpam-5375	103	6	0	0	NUM
ejpam-5375	103	7	,	,	PUNCT
ejpam-5375	103	8	n2	n2	NOUN
ejpam-5375	103	9	,	,	PUNCT
ejpam-5375	103	10	we	we	PRON
ejpam-5375	103	11	have	have	VERB
ejpam-5375	103	12	a+	a+	PUNCT
ejpam-5375	103	13	(	(	PUNCT
ejpam-5375	103	14	n−	n−	NOUN
ejpam-5375	103	15	a	a	X
ejpam-5375	103	16	)	)	PUNCT
ejpam-5375	103	17	=	=	SYM
ejpam-5375	104	1	0	0	X
ejpam-5375	104	2	.	.	PUNCT
ejpam-5375	105	1	consequently	consequently	ADV
ejpam-5375	105	2	,	,	PUNCT
ejpam-5375	105	3	a	a	PRON
ejpam-5375	105	4	is	be	AUX
ejpam-5375	105	5	adjacent	adjacent	ADJ
ejpam-5375	105	6	to	to	ADP
ejpam-5375	105	7	n−	n−	VERB
ejpam-5375	105	8	a	a	PRON
ejpam-5375	105	9	and	and	CCONJ
ejpam-5375	105	10	also	also	ADV
ejpam-5375	105	11	to	to	ADP
ejpam-5375	105	12	0	0	NUM
ejpam-5375	105	13	which	which	PRON
ejpam-5375	105	14	we	we	PRON
ejpam-5375	105	15	mentioned	mention	VERB
ejpam-5375	105	16	earlier	early	ADV
ejpam-5375	105	17	.	.	PUNCT
ejpam-5375	106	1	therefore	therefore	ADV
ejpam-5375	106	2	,	,	PUNCT
ejpam-5375	106	3	the	the	DET
ejpam-5375	106	4	degree	degree	NOUN
ejpam-5375	106	5	of	of	ADP
ejpam-5375	106	6	a	a	PRON
ejpam-5375	106	7	is	be	AUX
ejpam-5375	106	8	2	2	NUM
ejpam-5375	106	9	.	.	PUNCT
ejpam-5375	106	10	theorem	theorem	NOUN
ejpam-5375	106	11	5	5	NUM
ejpam-5375	106	12	.	.	PUNCT
ejpam-5375	107	1	let	let	VERB
ejpam-5375	107	2	mn×n	mn×n	PROPN
ejpam-5375	107	3	be	be	AUX
ejpam-5375	107	4	the	the	DET
ejpam-5375	107	5	matrix	matrix	NOUN
ejpam-5375	107	6	as	as	SCONJ
ejpam-5375	107	7	follows	follow	VERB
ejpam-5375	107	8	:	:	PUNCT
ejpam-5375	107	9	m	m	VERB
ejpam-5375	107	10	=	=	VERB
ejpam-5375	107	11			PROPN
ejpam-5375	108	1	a	a	DET
ejpam-5375	108	2	c	c	NOUN
ejpam-5375	108	3	c	c	NOUN
ejpam-5375	108	4	.	.	PUNCT
ejpam-5375	108	5	.	.	PUNCT
ejpam-5375	108	6	.	.	PUNCT
ejpam-5375	109	1	c	c	NOUN
ejpam-5375	110	1	c	c	NOUN
ejpam-5375	110	2	c	c	PROPN
ejpam-5375	110	3	b	b	PROPN
ejpam-5375	110	4	0	0	NUM
ejpam-5375	110	5	.	.	PUNCT
ejpam-5375	110	6	.	.	PUNCT
ejpam-5375	111	1	.	.	PUNCT
ejpam-5375	112	1	0	0	PUNCT
ejpam-5375	113	1	c	c	NOUN
ejpam-5375	113	2	c	c	NOUN
ejpam-5375	113	3	0	0	NUM
ejpam-5375	113	4	b	b	PROPN
ejpam-5375	113	5	.	.	PUNCT
ejpam-5375	113	6	.	.	PUNCT
ejpam-5375	113	7	.	.	PUNCT
ejpam-5375	114	1	c	c	NOUN
ejpam-5375	114	2	0	0	NUM
ejpam-5375	114	3	...	...	PUNCT
ejpam-5375	114	4	...	...	PUNCT
ejpam-5375	114	5	...	...	PUNCT
ejpam-5375	114	6	.	.	PUNCT
ejpam-5375	114	7	.	.	PUNCT
ejpam-5375	114	8	.	.	PUNCT
ejpam-5375	115	1	...	...	PUNCT
ejpam-5375	115	2	...	...	PUNCT
ejpam-5375	116	1	c	c	X
ejpam-5375	116	2	0	0	PUNCT
ejpam-5375	117	1	c	c	NOUN
ejpam-5375	117	2	.	.	PUNCT
ejpam-5375	117	3	.	.	PUNCT
ejpam-5375	117	4	.	.	PUNCT
ejpam-5375	118	1	b	b	X
ejpam-5375	118	2	0	0	NUM
ejpam-5375	119	1	c	c	NOUN
ejpam-5375	119	2	c	c	NOUN
ejpam-5375	119	3	0	0	NUM
ejpam-5375	119	4	.	.	PUNCT
ejpam-5375	119	5	.	.	PUNCT
ejpam-5375	120	1	.	.	PUNCT
ejpam-5375	121	1	0	0	NUM
ejpam-5375	122	1	b	b	X
ejpam-5375	122	2			NOUN
ejpam-5375	122	3	,	,	PUNCT
ejpam-5375	122	4	where	where	SCONJ
ejpam-5375	122	5	n	n	PRON
ejpam-5375	122	6	is	be	AUX
ejpam-5375	122	7	odd	odd	ADJ
ejpam-5375	122	8	,	,	PUNCT
ejpam-5375	122	9	and	and	CCONJ
ejpam-5375	122	10	real	real	ADJ
ejpam-5375	122	11	numbers	number	NOUN
ejpam-5375	122	12	a	a	DET
ejpam-5375	122	13	,	,	PUNCT
ejpam-5375	122	14	b	b	NOUN
ejpam-5375	122	15	,	,	PUNCT
ejpam-5375	122	16	c.	c.	NOUN
ejpam-5375	122	17	the	the	DET
ejpam-5375	122	18	characteristic	characteristic	ADJ
ejpam-5375	122	19	polynomial	polynomial	NOUN
ejpam-5375	122	20	of	of	ADP
ejpam-5375	122	21	m	m	PROPN
ejpam-5375	122	22	is	be	AUX
ejpam-5375	122	23	pm	pm	NOUN
ejpam-5375	122	24	(	(	PUNCT
ejpam-5375	122	25	λ	λ	NOUN
ejpam-5375	122	26	)	)	PUNCT
ejpam-5375	122	27	=	=	SYM
ejpam-5375	122	28	(	(	PUNCT
ejpam-5375	122	29	λ2	λ2	NOUN
ejpam-5375	122	30	−	−	PROPN
ejpam-5375	122	31	(	(	PUNCT
ejpam-5375	122	32	a+	a+	X
ejpam-5375	122	33	b+	b+	X
ejpam-5375	122	34	c)λ+	c)λ+	X
ejpam-5375	122	35	a(b+	a(b+	PUNCT
ejpam-5375	122	36	c)−	c)−	PROPN
ejpam-5375	122	37	c2(n−	c2(n−	VERB
ejpam-5375	122	38	1	1	NUM
ejpam-5375	122	39	)	)	PUNCT
ejpam-5375	122	40	)	)	PUNCT
ejpam-5375	123	1	(	(	PUNCT
ejpam-5375	123	2	λ−	λ−	PROPN
ejpam-5375	123	3	b−	b−	PROPN
ejpam-5375	123	4	c	c	NOUN
ejpam-5375	123	5	)	)	PUNCT
ejpam-5375	123	6	n−3	n−3	PROPN
ejpam-5375	123	7	2	2	NUM
ejpam-5375	123	8	(	(	PUNCT
ejpam-5375	123	9	λ−	λ−	PROPN
ejpam-5375	123	10	b+	b+	X
ejpam-5375	123	11	c	c	NOUN
ejpam-5375	123	12	)	)	PUNCT
ejpam-5375	123	13	n−1	n−1	PROPN
ejpam-5375	123	14	2	2	NUM
ejpam-5375	123	15	.	.	PUNCT
ejpam-5375	123	16	m.	m.	PROPN
ejpam-5375	123	17	u.	u.	PROPN
ejpam-5375	123	18	romdhini	romdhini	PROPN
ejpam-5375	123	19	et	et	PROPN
ejpam-5375	123	20	al	al	PROPN
ejpam-5375	123	21	.	.	PUNCT
ejpam-5375	123	22	/	/	SYM
ejpam-5375	123	23	eur	eur	PROPN
ejpam-5375	123	24	.	.	PUNCT
ejpam-5375	124	1	j.	j.	PROPN
ejpam-5375	124	2	pure	pure	PROPN
ejpam-5375	124	3	appl	appl	PROPN
ejpam-5375	124	4	.	.	PROPN
ejpam-5375	124	5	math	math	PROPN
ejpam-5375	124	6	,	,	PUNCT
ejpam-5375	124	7	17	17	NUM
ejpam-5375	124	8	(	(	PUNCT
ejpam-5375	124	9	4	4	NUM
ejpam-5375	124	10	)	)	PUNCT
ejpam-5375	124	11	(	(	PUNCT
ejpam-5375	124	12	2024	2024	NUM
ejpam-5375	124	13	)	)	PUNCT
ejpam-5375	124	14	,	,	PUNCT
ejpam-5375	124	15	2915	2915	NUM
ejpam-5375	124	16	-	-	SYM
ejpam-5375	124	17	2929	2929	NUM
ejpam-5375	124	18	2919	2919	NUM
ejpam-5375	124	19	proof	proof	NOUN
ejpam-5375	124	20	.	.	PUNCT
ejpam-5375	125	1	let	let	VERB
ejpam-5375	125	2	n	n	PRON
ejpam-5375	125	3	be	be	AUX
ejpam-5375	125	4	an	an	DET
ejpam-5375	125	5	odd	odd	ADJ
ejpam-5375	125	6	number	number	NOUN
ejpam-5375	125	7	.	.	PUNCT
ejpam-5375	126	1	the	the	DET
ejpam-5375	126	2	characteristic	characteristic	ADJ
ejpam-5375	126	3	polynomial	polynomial	NOUN
ejpam-5375	126	4	of	of	ADP
ejpam-5375	126	5	m	m	PROPN
ejpam-5375	126	6	is	be	AUX
ejpam-5375	126	7	given	give	VERB
ejpam-5375	126	8	by	by	ADP
ejpam-5375	126	9	pm	pm	NOUN
ejpam-5375	126	10	(	(	PUNCT
ejpam-5375	126	11	λ	λ	NOUN
ejpam-5375	126	12	)	)	PUNCT
ejpam-5375	126	13	=	=	SYM
ejpam-5375	127	1	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	127	2	λ−	λ−	PROPN
ejpam-5375	127	3	a	a	DET
ejpam-5375	127	4	−c	−c	ADJ
ejpam-5375	127	5	−c	−c	NOUN
ejpam-5375	127	6	.	.	PUNCT
ejpam-5375	127	7	.	.	PUNCT
ejpam-5375	127	8	.	.	PUNCT
ejpam-5375	128	1	−c	−c	ADJ
ejpam-5375	128	2	−c	−c	NOUN
ejpam-5375	128	3	−c	−c	NOUN
ejpam-5375	128	4	λ−	λ−	PROPN
ejpam-5375	128	5	b	b	PROPN
ejpam-5375	128	6	0	0	NUM
ejpam-5375	128	7	.	.	PUNCT
ejpam-5375	128	8	.	.	PUNCT
ejpam-5375	129	1	.	.	PUNCT
ejpam-5375	129	2	0	0	NUM
ejpam-5375	130	1	−c	−c	ADJ
ejpam-5375	130	2	−c	−c	NOUN
ejpam-5375	130	3	0	0	PUNCT
ejpam-5375	131	1	λ−	λ−	PROPN
ejpam-5375	131	2	b	b	PROPN
ejpam-5375	131	3	.	.	PUNCT
ejpam-5375	131	4	.	.	PUNCT
ejpam-5375	131	5	.	.	PUNCT
ejpam-5375	132	1	−c	−c	NOUN
ejpam-5375	132	2	0	0	NUM
ejpam-5375	132	3	...	...	PUNCT
ejpam-5375	132	4	...	...	PUNCT
ejpam-5375	132	5	...	...	PUNCT
ejpam-5375	132	6	.	.	PUNCT
ejpam-5375	132	7	.	.	PUNCT
ejpam-5375	132	8	.	.	PUNCT
ejpam-5375	133	1	...	...	PUNCT
ejpam-5375	133	2	...	...	PUNCT
ejpam-5375	134	1	−c	−c	NOUN
ejpam-5375	134	2	0	0	NUM
ejpam-5375	134	3	−c	−c	NOUN
ejpam-5375	134	4	.	.	PUNCT
ejpam-5375	134	5	.	.	PUNCT
ejpam-5375	134	6	.	.	PUNCT
ejpam-5375	135	1	λ−	λ−	PROPN
ejpam-5375	135	2	b	b	PROPN
ejpam-5375	135	3	0	0	NUM
ejpam-5375	135	4	−c	−c	NOUN
ejpam-5375	135	5	−c	−c	NOUN
ejpam-5375	135	6	0	0	NUM
ejpam-5375	135	7	.	.	PUNCT
ejpam-5375	135	8	.	.	PUNCT
ejpam-5375	135	9	.	.	PUNCT
ejpam-5375	135	10	0	0	NUM
ejpam-5375	136	1	λ−	λ−	PROPN
ejpam-5375	136	2	b	b	PROPN
ejpam-5375	136	3	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	136	4	,	,	PUNCT
ejpam-5375	136	5	where	where	SCONJ
ejpam-5375	136	6	the	the	DET
ejpam-5375	136	7	numbers	number	NOUN
ejpam-5375	136	8	a	a	DET
ejpam-5375	136	9	,	,	PUNCT
ejpam-5375	136	10	b	b	NOUN
ejpam-5375	136	11	,	,	PUNCT
ejpam-5375	136	12	c	c	PROPN
ejpam-5375	136	13	are	be	AUX
ejpam-5375	136	14	real	real	ADJ
ejpam-5375	136	15	.	.	PUNCT
ejpam-5375	137	1	we	we	PRON
ejpam-5375	137	2	need	need	VERB
ejpam-5375	137	3	to	to	PART
ejpam-5375	137	4	simplify	simplify	VERB
ejpam-5375	137	5	the	the	DET
ejpam-5375	137	6	above	above	ADJ
ejpam-5375	137	7	determinant	determinant	ADJ
ejpam-5375	137	8	by	by	ADP
ejpam-5375	137	9	applying	apply	VERB
ejpam-5375	137	10	row	row	NOUN
ejpam-5375	137	11	and	and	CCONJ
ejpam-5375	137	12	column	column	NOUN
ejpam-5375	137	13	operations	operation	NOUN
ejpam-5375	137	14	.	.	PUNCT
ejpam-5375	138	1	(	(	PUNCT
ejpam-5375	138	2	i	i	NOUN
ejpam-5375	138	3	)	)	PUNCT
ejpam-5375	138	4	rn+1	rn+1	VERB
ejpam-5375	138	5	2	2	NUM
ejpam-5375	139	1	+	+	NOUN
ejpam-5375	139	2	i	i	PRON
ejpam-5375	139	3	−→	−→	ADJ
ejpam-5375	139	4	rn+1	rn+1	VERB
ejpam-5375	139	5	2	2	NUM
ejpam-5375	139	6	+	+	NOUN
ejpam-5375	139	7	i	i	PROPN
ejpam-5375	139	8	−rn+3	−rn+3	PROPN
ejpam-5375	139	9	2	2	NUM
ejpam-5375	139	10	−i	−i	NOUN
ejpam-5375	139	11	,	,	PUNCT
ejpam-5375	139	12	for	for	ADP
ejpam-5375	139	13	i	i	PROPN
ejpam-5375	139	14	=	=	SYM
ejpam-5375	139	15	1	1	NUM
ejpam-5375	139	16	,	,	PUNCT
ejpam-5375	139	17	2	2	NUM
ejpam-5375	139	18	,	,	PUNCT
ejpam-5375	139	19	.	.	PUNCT
ejpam-5375	139	20	.	.	PUNCT
ejpam-5375	139	21	.	.	PUNCT
ejpam-5375	140	1	,	,	PUNCT
ejpam-5375	140	2	n−1	n−1	PROPN
ejpam-5375	140	3	2	2	NUM
ejpam-5375	140	4	.	.	PUNCT
ejpam-5375	141	1	then	then	ADV
ejpam-5375	141	2	we	we	PRON
ejpam-5375	141	3	have	have	VERB
ejpam-5375	141	4	pm	pm	NOUN
ejpam-5375	141	5	(	(	PUNCT
ejpam-5375	141	6	λ	λ	NOUN
ejpam-5375	141	7	)	)	PUNCT
ejpam-5375	141	8	=	=	SYM
ejpam-5375	142	1	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	142	2	λ−	λ−	PROPN
ejpam-5375	142	3	a	a	DET
ejpam-5375	142	4	−c	−c	ADJ
ejpam-5375	142	5	−c	−c	NOUN
ejpam-5375	142	6	.	.	PUNCT
ejpam-5375	142	7	.	.	PUNCT
ejpam-5375	142	8	.	.	PUNCT
ejpam-5375	143	1	−c	−c	ADJ
ejpam-5375	143	2	−c	−c	NOUN
ejpam-5375	143	3	−c	−c	NOUN
ejpam-5375	143	4	λ−	λ−	PROPN
ejpam-5375	143	5	b	b	PROPN
ejpam-5375	143	6	0	0	NUM
ejpam-5375	143	7	.	.	PUNCT
ejpam-5375	143	8	.	.	PUNCT
ejpam-5375	144	1	.	.	PUNCT
ejpam-5375	144	2	0	0	NUM
ejpam-5375	145	1	−c	−c	ADJ
ejpam-5375	145	2	−c	−c	NOUN
ejpam-5375	145	3	0	0	PUNCT
ejpam-5375	146	1	λ−	λ−	PROPN
ejpam-5375	146	2	b	b	PROPN
ejpam-5375	146	3	.	.	PUNCT
ejpam-5375	146	4	.	.	PUNCT
ejpam-5375	146	5	.	.	PUNCT
ejpam-5375	147	1	−c	−c	NOUN
ejpam-5375	147	2	0	0	NUM
ejpam-5375	147	3	...	...	PUNCT
ejpam-5375	147	4	...	...	PUNCT
ejpam-5375	147	5	...	...	PUNCT
ejpam-5375	147	6	.	.	PUNCT
ejpam-5375	147	7	.	.	PUNCT
ejpam-5375	147	8	.	.	PUNCT
ejpam-5375	148	1	...	...	PUNCT
ejpam-5375	149	1	...	...	PUNCT
ejpam-5375	150	1	0	0	NUM
ejpam-5375	150	2	0	0	NUM
ejpam-5375	151	1	−λ+	−λ+	PROPN
ejpam-5375	151	2	b−	b−	PROPN
ejpam-5375	151	3	c	c	PROPN
ejpam-5375	151	4	.	.	PUNCT
ejpam-5375	151	5	.	.	PUNCT
ejpam-5375	151	6	.	.	PUNCT
ejpam-5375	152	1	λ−	λ−	PROPN
ejpam-5375	152	2	b+	b+	VERB
ejpam-5375	152	3	c	c	PROPN
ejpam-5375	152	4	0	0	NUM
ejpam-5375	152	5	0	0	NUM
ejpam-5375	152	6	−λ+	−λ+	PROPN
ejpam-5375	152	7	b−	b−	PROPN
ejpam-5375	152	8	c	c	PROPN
ejpam-5375	152	9	0	0	NUM
ejpam-5375	152	10	.	.	PUNCT
ejpam-5375	152	11	.	.	PUNCT
ejpam-5375	153	1	.	.	PUNCT
ejpam-5375	153	2	0	0	NUM
ejpam-5375	154	1	λ−	λ−	PROPN
ejpam-5375	154	2	b+	b+	ADP
ejpam-5375	154	3	c	c	PROPN
ejpam-5375	154	4	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	154	5	.	.	PUNCT
ejpam-5375	155	1	(	(	PUNCT
ejpam-5375	155	2	ii	ii	NOUN
ejpam-5375	155	3	)	)	PUNCT
ejpam-5375	155	4	cn+3	cn+3	PROPN
ejpam-5375	155	5	2	2	NUM
ejpam-5375	155	6	−i	−i	NOUN
ejpam-5375	155	7	−→	−→	NOUN
ejpam-5375	155	8	cn+3	cn+3	PROPN
ejpam-5375	155	9	2	2	NUM
ejpam-5375	155	10	−i	−i	NOUN
ejpam-5375	155	11	+	+	CCONJ
ejpam-5375	155	12	cn+1	cn+1	NUM
ejpam-5375	155	13	2	2	NUM
ejpam-5375	155	14	+	+	NOUN
ejpam-5375	155	15	i	i	PROPN
ejpam-5375	155	16	,	,	PUNCT
ejpam-5375	155	17	for	for	ADP
ejpam-5375	155	18	i	i	PROPN
ejpam-5375	155	19	=	=	SYM
ejpam-5375	155	20	1	1	NUM
ejpam-5375	155	21	,	,	PUNCT
ejpam-5375	155	22	2	2	NUM
ejpam-5375	155	23	,	,	PUNCT
ejpam-5375	155	24	.	.	PUNCT
ejpam-5375	155	25	.	.	PUNCT
ejpam-5375	155	26	.	.	PUNCT
ejpam-5375	156	1	,	,	PUNCT
ejpam-5375	156	2	n−1	n−1	PROPN
ejpam-5375	156	3	2	2	NUM
ejpam-5375	156	4	.	.	PUNCT
ejpam-5375	157	1	consequently	consequently	ADV
ejpam-5375	157	2	,	,	PUNCT
ejpam-5375	157	3	pm	pm	NOUN
ejpam-5375	157	4	(	(	PUNCT
ejpam-5375	157	5	λ	λ	NOUN
ejpam-5375	157	6	)	)	PUNCT
ejpam-5375	157	7	=	=	SYM
ejpam-5375	158	1	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	159	1	λ−	λ−	PROPN
ejpam-5375	160	1	a	a	DET
ejpam-5375	160	2	−2c	−2c	PROPN
ejpam-5375	160	3	−2c	−2c	PROPN
ejpam-5375	160	4	.	.	PUNCT
ejpam-5375	160	5	.	.	PUNCT
ejpam-5375	160	6	.	.	PUNCT
ejpam-5375	161	1	−c	−c	ADJ
ejpam-5375	161	2	−c	−c	NOUN
ejpam-5375	161	3	−c	−c	NOUN
ejpam-5375	161	4	λ−	λ−	PROPN
ejpam-5375	161	5	b−	b−	PROPN
ejpam-5375	161	6	c	c	NOUN
ejpam-5375	161	7	0	0	NUM
ejpam-5375	161	8	.	.	PUNCT
ejpam-5375	161	9	.	.	PUNCT
ejpam-5375	162	1	.	.	PUNCT
ejpam-5375	162	2	0	0	NUM
ejpam-5375	163	1	−c	−c	ADJ
ejpam-5375	163	2	−c	−c	NOUN
ejpam-5375	163	3	0	0	PUNCT
ejpam-5375	164	1	λ−	λ−	PROPN
ejpam-5375	164	2	b−	b−	PROPN
ejpam-5375	164	3	c	c	PROPN
ejpam-5375	164	4	.	.	PUNCT
ejpam-5375	164	5	.	.	PUNCT
ejpam-5375	164	6	.	.	PUNCT
ejpam-5375	165	1	−c	−c	NOUN
ejpam-5375	165	2	0	0	NUM
ejpam-5375	165	3	...	...	PUNCT
ejpam-5375	165	4	...	...	PUNCT
ejpam-5375	165	5	...	...	PUNCT
ejpam-5375	165	6	.	.	PUNCT
ejpam-5375	165	7	.	.	PUNCT
ejpam-5375	165	8	.	.	PUNCT
ejpam-5375	166	1	...	...	PUNCT
ejpam-5375	167	1	...	...	PUNCT
ejpam-5375	168	1	0	0	NUM
ejpam-5375	168	2	0	0	NUM
ejpam-5375	168	3	0	0	NUM
ejpam-5375	168	4	.	.	PUNCT
ejpam-5375	168	5	.	.	PUNCT
ejpam-5375	168	6	.	.	PUNCT
ejpam-5375	169	1	λ−	λ−	PROPN
ejpam-5375	169	2	b+	b+	VERB
ejpam-5375	169	3	c	c	NOUN
ejpam-5375	169	4	0	0	NUM
ejpam-5375	169	5	0	0	NUM
ejpam-5375	169	6	0	0	NUM
ejpam-5375	169	7	0	0	NUM
ejpam-5375	169	8	.	.	PUNCT
ejpam-5375	169	9	.	.	PUNCT
ejpam-5375	170	1	.	.	PUNCT
ejpam-5375	170	2	0	0	NUM
ejpam-5375	171	1	λ−	λ−	PROPN
ejpam-5375	171	2	b+	b+	ADP
ejpam-5375	171	3	c	c	PROPN
ejpam-5375	171	4	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	171	5	.	.	PUNCT
ejpam-5375	172	1	(	(	PUNCT
ejpam-5375	172	2	iii	iii	X
ejpam-5375	172	3	)	)	PUNCT
ejpam-5375	172	4	c1	c1	PROPN
ejpam-5375	172	5	−→	−→	PROPN
ejpam-5375	172	6	c1	c1	PROPN
ejpam-5375	172	7	+	+	CCONJ
ejpam-5375	172	8	c	c	X
ejpam-5375	172	9	λ−b−cc2	λ−b−cc2	X
ejpam-5375	172	10	+	+	CCONJ
ejpam-5375	172	11	c	c	NOUN
ejpam-5375	172	12	λ−b−cc3	λ−b−cc3	VERB
ejpam-5375	172	13	+	+	X
ejpam-5375	172	14	.	.	PUNCT
ejpam-5375	172	15	.	.	PUNCT
ejpam-5375	173	1	.+	.+	NOUN
ejpam-5375	174	1	c	c	X
ejpam-5375	174	2	λ−b−ccn+1	λ−b−ccn+1	PROPN
ejpam-5375	174	3	2	2	NUM
ejpam-5375	174	4	.	.	PUNCT
ejpam-5375	175	1	hence	hence	ADV
ejpam-5375	175	2	we	we	PRON
ejpam-5375	175	3	can	can	AUX
ejpam-5375	175	4	write	write	VERB
ejpam-5375	175	5	pm	pm	NOUN
ejpam-5375	175	6	(	(	PUNCT
ejpam-5375	175	7	λ	λ	NOUN
ejpam-5375	175	8	)	)	PUNCT
ejpam-5375	175	9	=	=	SYM
ejpam-5375	175	10	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	175	11	(	(	PUNCT
ejpam-5375	175	12	λ−a)(λ−b−c)−c2(n−1	λ−a)(λ−b−c)−c2(n−1	INTJ
ejpam-5375	175	13	)	)	PUNCT
ejpam-5375	175	14	λ−b−c	λ−b−c	ADP
ejpam-5375	175	15	−2c	−2c	PROPN
ejpam-5375	175	16	−2c	−2c	PROPN
ejpam-5375	175	17	.	.	PUNCT
ejpam-5375	175	18	.	.	PUNCT
ejpam-5375	175	19	.	.	PUNCT
ejpam-5375	176	1	−c	−c	ADJ
ejpam-5375	176	2	−c	−c	NOUN
ejpam-5375	176	3	0	0	PUNCT
ejpam-5375	177	1	λ−	λ−	PROPN
ejpam-5375	177	2	b−	b−	NOUN
ejpam-5375	177	3	c	c	NOUN
ejpam-5375	177	4	0	0	NUM
ejpam-5375	177	5	.	.	PUNCT
ejpam-5375	177	6	.	.	PUNCT
ejpam-5375	177	7	.	.	PUNCT
ejpam-5375	178	1	0	0	NUM
ejpam-5375	179	1	−c	−c	NOUN
ejpam-5375	179	2	0	0	NUM
ejpam-5375	179	3	0	0	NUM
ejpam-5375	180	1	λ−	λ−	PROPN
ejpam-5375	180	2	b−	b−	PROPN
ejpam-5375	180	3	c	c	PROPN
ejpam-5375	180	4	.	.	PUNCT
ejpam-5375	180	5	.	.	PUNCT
ejpam-5375	180	6	.	.	PUNCT
ejpam-5375	181	1	−c	−c	NOUN
ejpam-5375	181	2	0	0	NUM
ejpam-5375	181	3	...	...	PUNCT
ejpam-5375	181	4	...	...	PUNCT
ejpam-5375	181	5	...	...	PUNCT
ejpam-5375	181	6	.	.	PUNCT
ejpam-5375	181	7	.	.	PUNCT
ejpam-5375	181	8	.	.	PUNCT
ejpam-5375	182	1	...	...	PUNCT
ejpam-5375	183	1	...	...	PUNCT
ejpam-5375	184	1	0	0	NUM
ejpam-5375	184	2	0	0	NUM
ejpam-5375	184	3	0	0	NUM
ejpam-5375	184	4	.	.	PUNCT
ejpam-5375	184	5	.	.	PUNCT
ejpam-5375	184	6	.	.	PUNCT
ejpam-5375	185	1	λ−	λ−	PROPN
ejpam-5375	185	2	b+	b+	VERB
ejpam-5375	185	3	c	c	NOUN
ejpam-5375	185	4	0	0	NUM
ejpam-5375	185	5	0	0	NUM
ejpam-5375	185	6	0	0	NUM
ejpam-5375	185	7	0	0	NUM
ejpam-5375	185	8	.	.	PUNCT
ejpam-5375	185	9	.	.	PUNCT
ejpam-5375	186	1	.	.	PUNCT
ejpam-5375	186	2	0	0	NUM
ejpam-5375	187	1	λ−	λ−	PROPN
ejpam-5375	187	2	b+	b+	ADP
ejpam-5375	187	3	c	c	PROPN
ejpam-5375	187	4	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	187	5	.	.	PUNCT
ejpam-5375	188	1	m.	m.	PROPN
ejpam-5375	188	2	u.	u.	PROPN
ejpam-5375	188	3	romdhini	romdhini	PROPN
ejpam-5375	188	4	et	et	PROPN
ejpam-5375	188	5	al	al	PROPN
ejpam-5375	188	6	.	.	PUNCT
ejpam-5375	188	7	/	/	SYM
ejpam-5375	188	8	eur	eur	PROPN
ejpam-5375	188	9	.	.	PUNCT
ejpam-5375	189	1	j.	j.	PROPN
ejpam-5375	189	2	pure	pure	PROPN
ejpam-5375	189	3	appl	appl	PROPN
ejpam-5375	189	4	.	.	PROPN
ejpam-5375	189	5	math	math	PROPN
ejpam-5375	189	6	,	,	PUNCT
ejpam-5375	189	7	17	17	NUM
ejpam-5375	189	8	(	(	PUNCT
ejpam-5375	189	9	4	4	NUM
ejpam-5375	189	10	)	)	PUNCT
ejpam-5375	189	11	(	(	PUNCT
ejpam-5375	189	12	2024	2024	NUM
ejpam-5375	189	13	)	)	PUNCT
ejpam-5375	189	14	,	,	PUNCT
ejpam-5375	189	15	2915	2915	NUM
ejpam-5375	189	16	-	-	SYM
ejpam-5375	189	17	2929	2929	NUM
ejpam-5375	189	18	2920	2920	NUM
ejpam-5375	189	19	it	it	PRON
ejpam-5375	189	20	follows	follow	VERB
ejpam-5375	189	21	that	that	DET
ejpam-5375	189	22	pm	pm	NOUN
ejpam-5375	189	23	(	(	PUNCT
ejpam-5375	189	24	λ	λ	NOUN
ejpam-5375	189	25	)	)	PUNCT
ejpam-5375	189	26	=	=	SYM
ejpam-5375	189	27	(	(	PUNCT
ejpam-5375	189	28	λ2	λ2	NOUN
ejpam-5375	189	29	−	−	PROPN
ejpam-5375	189	30	(	(	PUNCT
ejpam-5375	189	31	a+	a+	X
ejpam-5375	189	32	b+	b+	X
ejpam-5375	189	33	c)λ+	c)λ+	X
ejpam-5375	189	34	a(b+	a(b+	PUNCT
ejpam-5375	189	35	c)−	c)−	PROPN
ejpam-5375	189	36	c2(n−	c2(n−	VERB
ejpam-5375	189	37	1	1	NUM
ejpam-5375	189	38	)	)	PUNCT
ejpam-5375	189	39	)	)	PUNCT
ejpam-5375	190	1	(	(	PUNCT
ejpam-5375	190	2	λ−	λ−	PROPN
ejpam-5375	190	3	b−	b−	PROPN
ejpam-5375	190	4	c	c	NOUN
ejpam-5375	190	5	)	)	PUNCT
ejpam-5375	190	6	n−3	n−3	PROPN
ejpam-5375	190	7	2	2	NUM
ejpam-5375	190	8	(	(	PUNCT
ejpam-5375	190	9	λ−	λ−	PROPN
ejpam-5375	190	10	b+	b+	X
ejpam-5375	190	11	c	c	NOUN
ejpam-5375	190	12	)	)	PUNCT
ejpam-5375	190	13	n−1	n−1	PROPN
ejpam-5375	190	14	2	2	NUM
ejpam-5375	190	15	,	,	PUNCT
ejpam-5375	190	16	due	due	ADP
ejpam-5375	190	17	to	to	ADP
ejpam-5375	190	18	it	it	PRON
ejpam-5375	190	19	is	be	AUX
ejpam-5375	190	20	an	an	DET
ejpam-5375	190	21	upper	upper	ADJ
ejpam-5375	190	22	triangular	triangular	NOUN
ejpam-5375	190	23	matrix	matrix	NOUN
ejpam-5375	190	24	.	.	PUNCT
ejpam-5375	191	1	theorem	theorem	VERB
ejpam-5375	191	2	6	6	NUM
ejpam-5375	191	3	.	.	PUNCT
ejpam-5375	192	1	let	let	VERB
ejpam-5375	192	2	n	n	PRON
ejpam-5375	192	3	is	be	AUX
ejpam-5375	192	4	even	even	ADV
ejpam-5375	192	5	and	and	CCONJ
ejpam-5375	192	6	mn×n	mn×n	ADJ
ejpam-5375	192	7	be	be	AUX
ejpam-5375	192	8	the	the	DET
ejpam-5375	192	9	matrix	matrix	NOUN
ejpam-5375	192	10	as	as	SCONJ
ejpam-5375	192	11	follows	follow	VERB
ejpam-5375	192	12	:	:	PUNCT
ejpam-5375	192	13	m	m	VERB
ejpam-5375	192	14	=	=	VERB
ejpam-5375	192	15			VERB
ejpam-5375	192	16	a	a	DET
ejpam-5375	192	17	d	d	X
ejpam-5375	192	18	d	d	PROPN
ejpam-5375	192	19	.	.	PUNCT
ejpam-5375	192	20	.	.	PUNCT
ejpam-5375	192	21	.	.	PUNCT
ejpam-5375	193	1	d	d	PUNCT
ejpam-5375	193	2	d	d	X
ejpam-5375	193	3	d	d	NOUN
ejpam-5375	193	4	.	.	PUNCT
ejpam-5375	193	5	.	.	PUNCT
ejpam-5375	193	6	.	.	PUNCT
ejpam-5375	194	1	d	d	X
ejpam-5375	195	1	d	d	X
ejpam-5375	195	2	d	d	X
ejpam-5375	195	3	b	b	PROPN
ejpam-5375	195	4	0	0	NUM
ejpam-5375	195	5	.	.	PUNCT
ejpam-5375	195	6	.	.	PUNCT
ejpam-5375	196	1	.	.	PUNCT
ejpam-5375	197	1	0	0	NUM
ejpam-5375	198	1	0	0	NUM
ejpam-5375	198	2	0	0	NUM
ejpam-5375	198	3	.	.	PUNCT
ejpam-5375	198	4	.	.	PUNCT
ejpam-5375	198	5	.	.	PUNCT
ejpam-5375	199	1	0	0	PUNCT
ejpam-5375	200	1	d	d	X
ejpam-5375	200	2	d	d	NOUN
ejpam-5375	200	3	0	0	NUM
ejpam-5375	200	4	b	b	PROPN
ejpam-5375	200	5	.	.	PUNCT
ejpam-5375	200	6	.	.	PUNCT
ejpam-5375	200	7	.	.	PUNCT
ejpam-5375	201	1	0	0	NUM
ejpam-5375	202	1	0	0	NUM
ejpam-5375	202	2	0	0	NUM
ejpam-5375	202	3	.	.	PUNCT
ejpam-5375	202	4	.	.	PUNCT
ejpam-5375	202	5	.	.	PUNCT
ejpam-5375	203	1	d	d	NOUN
ejpam-5375	203	2	0	0	NUM
ejpam-5375	203	3	...	...	PUNCT
ejpam-5375	203	4	...	...	PUNCT
ejpam-5375	203	5	...	...	PUNCT
ejpam-5375	203	6	.	.	PUNCT
ejpam-5375	203	7	.	.	PUNCT
ejpam-5375	203	8	.	.	PUNCT
ejpam-5375	204	1	...	...	PUNCT
ejpam-5375	204	2	...	...	PUNCT
ejpam-5375	205	1	...	...	PUNCT
ejpam-5375	205	2	...	...	PUNCT
ejpam-5375	205	3	...	...	PUNCT
ejpam-5375	206	1	...	...	PUNCT
ejpam-5375	207	1	d	d	X
ejpam-5375	207	2	0	0	NUM
ejpam-5375	207	3	0	0	NUM
ejpam-5375	207	4	.	.	PUNCT
ejpam-5375	207	5	.	.	PUNCT
ejpam-5375	207	6	.	.	PUNCT
ejpam-5375	208	1	b	b	X
ejpam-5375	208	2	0	0	NUM
ejpam-5375	208	3	d	d	NOUN
ejpam-5375	208	4	.	.	PUNCT
ejpam-5375	208	5	.	.	PUNCT
ejpam-5375	208	6	.	.	PUNCT
ejpam-5375	209	1	0	0	NUM
ejpam-5375	209	2	0	0	NUM
ejpam-5375	210	1	d	d	NOUN
ejpam-5375	210	2	0	0	NUM
ejpam-5375	210	3	0	0	NUM
ejpam-5375	210	4	.	.	PUNCT
ejpam-5375	210	5	.	.	PUNCT
ejpam-5375	210	6	.	.	PUNCT
ejpam-5375	211	1	0	0	PUNCT
ejpam-5375	212	1	c	c	NOUN
ejpam-5375	212	2	0	0	NUM
ejpam-5375	212	3	.	.	PUNCT
ejpam-5375	212	4	.	.	PUNCT
ejpam-5375	212	5	.	.	PUNCT
ejpam-5375	213	1	0	0	NUM
ejpam-5375	213	2	0	0	NUM
ejpam-5375	214	1	d	d	NOUN
ejpam-5375	214	2	0	0	NUM
ejpam-5375	214	3	0	0	NUM
ejpam-5375	214	4	.	.	PUNCT
ejpam-5375	214	5	.	.	PUNCT
ejpam-5375	214	6	.	.	PUNCT
ejpam-5375	215	1	d	d	NOUN
ejpam-5375	215	2	0	0	NUM
ejpam-5375	215	3	b	b	NOUN
ejpam-5375	215	4	.	.	PUNCT
ejpam-5375	215	5	.	.	PUNCT
ejpam-5375	215	6	.	.	PUNCT
ejpam-5375	216	1	0	0	NUM
ejpam-5375	216	2	0	0	NUM
ejpam-5375	216	3	...	...	PUNCT
ejpam-5375	216	4	...	...	PUNCT
ejpam-5375	216	5	...	...	PUNCT
ejpam-5375	216	6	.	.	PUNCT
ejpam-5375	216	7	.	.	PUNCT
ejpam-5375	216	8	.	.	PUNCT
ejpam-5375	217	1	...	...	PUNCT
ejpam-5375	217	2	...	...	PUNCT
ejpam-5375	218	1	...	...	PUNCT
ejpam-5375	218	2	...	...	PUNCT
ejpam-5375	218	3	...	...	PUNCT
ejpam-5375	219	1	...	...	PUNCT
ejpam-5375	220	1	d	d	X
ejpam-5375	220	2	0	0	NUM
ejpam-5375	221	1	d	d	NOUN
ejpam-5375	221	2	.	.	PUNCT
ejpam-5375	221	3	.	.	PUNCT
ejpam-5375	221	4	.	.	PUNCT
ejpam-5375	222	1	0	0	NUM
ejpam-5375	223	1	0	0	NUM
ejpam-5375	223	2	0	0	NUM
ejpam-5375	223	3	.	.	PUNCT
ejpam-5375	223	4	.	.	PUNCT
ejpam-5375	223	5	.	.	PUNCT
ejpam-5375	224	1	b	b	X
ejpam-5375	224	2	0	0	PUNCT
ejpam-5375	224	3	d	d	PROPN
ejpam-5375	224	4	d	d	PROPN
ejpam-5375	224	5	0	0	PROPN
ejpam-5375	224	6	.	.	PUNCT
ejpam-5375	224	7	.	.	PUNCT
ejpam-5375	224	8	.	.	PUNCT
ejpam-5375	225	1	0	0	NUM
ejpam-5375	226	1	0	0	NUM
ejpam-5375	226	2	0	0	NUM
ejpam-5375	226	3	.	.	PUNCT
ejpam-5375	226	4	.	.	PUNCT
ejpam-5375	226	5	.	.	PUNCT
ejpam-5375	227	1	0	0	NUM
ejpam-5375	228	1	b	b	X
ejpam-5375	228	2			NUM
ejpam-5375	228	3	,	,	PUNCT
ejpam-5375	228	4	where	where	SCONJ
ejpam-5375	228	5	a	a	DET
ejpam-5375	228	6	,	,	PUNCT
ejpam-5375	228	7	b	b	NOUN
ejpam-5375	228	8	,	,	PUNCT
ejpam-5375	228	9	c	c	NOUN
ejpam-5375	228	10	,	,	PUNCT
ejpam-5375	228	11	d	d	X
ejpam-5375	228	12	are	be	AUX
ejpam-5375	228	13	real	real	ADJ
ejpam-5375	228	14	numbers	number	NOUN
ejpam-5375	228	15	.	.	PUNCT
ejpam-5375	229	1	the	the	DET
ejpam-5375	229	2	characteristic	characteristic	ADJ
ejpam-5375	229	3	polynomial	polynomial	NOUN
ejpam-5375	229	4	of	of	ADP
ejpam-5375	229	5	m	m	PROPN
ejpam-5375	229	6	is	be	AUX
ejpam-5375	229	7	pm	pm	NOUN
ejpam-5375	229	8	(	(	PUNCT
ejpam-5375	229	9	λ	λ	NOUN
ejpam-5375	229	10	)	)	PUNCT
ejpam-5375	229	11	=	=	SYM
ejpam-5375	230	1	(	(	PUNCT
ejpam-5375	230	2	λ3	λ3	PROPN
ejpam-5375	230	3	−	−	PROPN
ejpam-5375	230	4	(	(	PUNCT
ejpam-5375	230	5	a+	a+	X
ejpam-5375	230	6	b+	b+	X
ejpam-5375	230	7	c+	c+	VERB
ejpam-5375	230	8	d)λ2	d)λ2	VERB
ejpam-5375	230	9	+	+	CCONJ
ejpam-5375	230	10	(	(	PUNCT
ejpam-5375	230	11	(	(	PUNCT
ejpam-5375	230	12	a+	a+	X
ejpam-5375	230	13	c)(b+	c)(b+	NOUN
ejpam-5375	230	14	d	d	X
ejpam-5375	230	15	)	)	PUNCT
ejpam-5375	231	1	+	+	NUM
ejpam-5375	231	2	ac−	ac−	NUM
ejpam-5375	231	3	d2(n−	d2(n−	ADJ
ejpam-5375	231	4	1))λ+	1))λ+	NUM
ejpam-5375	231	5	(	(	PUNCT
ejpam-5375	231	6	b+	b+	NUM
ejpam-5375	231	7	d)(d2	d)(d2	PROPN
ejpam-5375	231	8	−	−	NUM
ejpam-5375	231	9	ac	ac	PROPN
ejpam-5375	231	10	)	)	PUNCT
ejpam-5375	232	1	+	+	CCONJ
ejpam-5375	232	2	cd2(n−	cd2(n−	VERB
ejpam-5375	232	3	2	2	NUM
ejpam-5375	232	4	)	)	PUNCT
ejpam-5375	232	5	)	)	PUNCT
ejpam-5375	233	1	(	(	PUNCT
ejpam-5375	233	2	λ−	λ−	PROPN
ejpam-5375	233	3	b−	b−	PROPN
ejpam-5375	233	4	d	d	PROPN
ejpam-5375	233	5	)	)	PUNCT
ejpam-5375	233	6	n	n	PRON
ejpam-5375	233	7	2	2	NUM
ejpam-5375	233	8	−2(λ−	−2(λ−	PROPN
ejpam-5375	233	9	b+	b+	X
ejpam-5375	233	10	d	d	NOUN
ejpam-5375	233	11	)	)	PUNCT
ejpam-5375	233	12	n	n	DET
ejpam-5375	233	13	2	2	NUM
ejpam-5375	233	14	−1	−1	NOUN
ejpam-5375	233	15	..	..	PUNCT
ejpam-5375	234	1	proof	proof	NOUN
ejpam-5375	234	2	.	.	PUNCT
ejpam-5375	235	1	let	let	VERB
ejpam-5375	235	2	n	n	PRON
ejpam-5375	235	3	is	be	AUX
ejpam-5375	235	4	even	even	ADV
ejpam-5375	235	5	,	,	PUNCT
ejpam-5375	235	6	and	and	CCONJ
ejpam-5375	235	7	a	a	DET
ejpam-5375	235	8	,	,	PUNCT
ejpam-5375	235	9	b	b	NOUN
ejpam-5375	235	10	,	,	PUNCT
ejpam-5375	235	11	c	c	NOUN
ejpam-5375	235	12	,	,	PUNCT
ejpam-5375	235	13	d	d	X
ejpam-5375	235	14	are	be	AUX
ejpam-5375	235	15	real	real	ADJ
ejpam-5375	235	16	numbers	number	NOUN
ejpam-5375	235	17	.	.	PUNCT
ejpam-5375	236	1	the	the	DET
ejpam-5375	236	2	characteristic	characteristic	ADJ
ejpam-5375	236	3	polynomial	polynomial	NOUN
ejpam-5375	236	4	of	of	ADP
ejpam-5375	236	5	m	m	PROPN
ejpam-5375	236	6	is	be	AUX
ejpam-5375	236	7	given	give	VERB
ejpam-5375	236	8	by	by	ADP
ejpam-5375	236	9	pm	pm	NOUN
ejpam-5375	236	10	(	(	PUNCT
ejpam-5375	236	11	λ	λ	NOUN
ejpam-5375	236	12	)	)	PUNCT
ejpam-5375	236	13	=	=	SYM
ejpam-5375	237	1	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	237	2	λ−	λ−	PROPN
ejpam-5375	237	3	a	a	DET
ejpam-5375	237	4	−d	−d	PROPN
ejpam-5375	237	5	−d	−d	PROPN
ejpam-5375	237	6	.	.	PUNCT
ejpam-5375	237	7	.	.	PUNCT
ejpam-5375	237	8	.	.	PUNCT
ejpam-5375	238	1	−d	−d	PROPN
ejpam-5375	238	2	−d	−d	PROPN
ejpam-5375	238	3	−d	−d	PROPN
ejpam-5375	238	4	.	.	PUNCT
ejpam-5375	238	5	.	.	PUNCT
ejpam-5375	239	1	.	.	PUNCT
ejpam-5375	240	1	−d	−d	PROPN
ejpam-5375	240	2	−d	−d	PROPN
ejpam-5375	240	3	−d	−d	VERB
ejpam-5375	240	4	λ−	λ−	PROPN
ejpam-5375	240	5	b	b	PROPN
ejpam-5375	240	6	0	0	NUM
ejpam-5375	240	7	.	.	PUNCT
ejpam-5375	240	8	.	.	PUNCT
ejpam-5375	241	1	.	.	PUNCT
ejpam-5375	242	1	0	0	NUM
ejpam-5375	243	1	0	0	NUM
ejpam-5375	243	2	0	0	NUM
ejpam-5375	243	3	.	.	PUNCT
ejpam-5375	243	4	.	.	PUNCT
ejpam-5375	244	1	.	.	PUNCT
ejpam-5375	244	2	0	0	NUM
ejpam-5375	245	1	−d	−d	PROPN
ejpam-5375	245	2	−d	−d	PROPN
ejpam-5375	245	3	0	0	PUNCT
ejpam-5375	246	1	λ−	λ−	PROPN
ejpam-5375	246	2	b	b	PROPN
ejpam-5375	246	3	.	.	PUNCT
ejpam-5375	246	4	.	.	PUNCT
ejpam-5375	246	5	.	.	PUNCT
ejpam-5375	247	1	0	0	NUM
ejpam-5375	248	1	0	0	NUM
ejpam-5375	248	2	0	0	NUM
ejpam-5375	248	3	.	.	PUNCT
ejpam-5375	248	4	.	.	PUNCT
ejpam-5375	248	5	.	.	PUNCT
ejpam-5375	249	1	−d	−d	PROPN
ejpam-5375	249	2	0	0	NUM
ejpam-5375	249	3	...	...	PUNCT
ejpam-5375	249	4	...	...	PUNCT
ejpam-5375	249	5	...	...	PUNCT
ejpam-5375	249	6	.	.	PUNCT
ejpam-5375	249	7	.	.	PUNCT
ejpam-5375	249	8	.	.	PUNCT
ejpam-5375	250	1	...	...	PUNCT
ejpam-5375	250	2	...	...	PUNCT
ejpam-5375	250	3	...	...	PUNCT
ejpam-5375	250	4	.	.	PUNCT
ejpam-5375	250	5	.	.	PUNCT
ejpam-5375	251	1	.	.	PUNCT
ejpam-5375	252	1	...	...	PUNCT
ejpam-5375	253	1	...	...	PUNCT
ejpam-5375	254	1	−d	−d	ADJ
ejpam-5375	254	2	0	0	NUM
ejpam-5375	254	3	0	0	NUM
ejpam-5375	254	4	.	.	PUNCT
ejpam-5375	254	5	.	.	PUNCT
ejpam-5375	254	6	.	.	PUNCT
ejpam-5375	255	1	λ−	λ−	PROPN
ejpam-5375	255	2	b	b	PROPN
ejpam-5375	255	3	0	0	PROPN
ejpam-5375	255	4	−d	−d	PROPN
ejpam-5375	255	5	.	.	PUNCT
ejpam-5375	255	6	.	.	PUNCT
ejpam-5375	256	1	.	.	PUNCT
ejpam-5375	257	1	0	0	NUM
ejpam-5375	257	2	0	0	NUM
ejpam-5375	257	3	−d	−d	ADJ
ejpam-5375	257	4	0	0	NUM
ejpam-5375	257	5	0	0	NUM
ejpam-5375	257	6	.	.	PUNCT
ejpam-5375	257	7	.	.	PUNCT
ejpam-5375	258	1	.	.	PUNCT
ejpam-5375	258	2	0	0	PUNCT
ejpam-5375	259	1	λ−	λ−	PROPN
ejpam-5375	259	2	c	c	NOUN
ejpam-5375	259	3	0	0	NUM
ejpam-5375	259	4	.	.	PUNCT
ejpam-5375	259	5	.	.	PUNCT
ejpam-5375	259	6	.	.	PUNCT
ejpam-5375	260	1	0	0	NUM
ejpam-5375	260	2	0	0	NUM
ejpam-5375	260	3	−d	−d	ADJ
ejpam-5375	260	4	0	0	NUM
ejpam-5375	260	5	0	0	NUM
ejpam-5375	260	6	.	.	PUNCT
ejpam-5375	260	7	.	.	PUNCT
ejpam-5375	260	8	.	.	PUNCT
ejpam-5375	261	1	−d	−d	PROPN
ejpam-5375	261	2	0	0	NUM
ejpam-5375	262	1	λ−	λ−	PROPN
ejpam-5375	262	2	b	b	PROPN
ejpam-5375	262	3	.	.	PUNCT
ejpam-5375	262	4	.	.	PUNCT
ejpam-5375	262	5	.	.	PUNCT
ejpam-5375	263	1	0	0	NUM
ejpam-5375	263	2	0	0	NUM
ejpam-5375	263	3	...	...	PUNCT
ejpam-5375	263	4	...	...	PUNCT
ejpam-5375	263	5	...	...	PUNCT
ejpam-5375	263	6	.	.	PUNCT
ejpam-5375	263	7	.	.	PUNCT
ejpam-5375	263	8	.	.	PUNCT
ejpam-5375	264	1	...	...	PUNCT
ejpam-5375	264	2	...	...	PUNCT
ejpam-5375	264	3	...	...	PUNCT
ejpam-5375	264	4	.	.	PUNCT
ejpam-5375	264	5	.	.	PUNCT
ejpam-5375	265	1	.	.	PUNCT
ejpam-5375	265	2	...	...	PUNCT
ejpam-5375	266	1	...	...	PUNCT
ejpam-5375	267	1	−d	−d	PROPN
ejpam-5375	267	2	0	0	PUNCT
ejpam-5375	267	3	−d	−d	PROPN
ejpam-5375	267	4	.	.	PUNCT
ejpam-5375	267	5	.	.	PUNCT
ejpam-5375	267	6	.	.	PUNCT
ejpam-5375	268	1	0	0	NUM
ejpam-5375	269	1	0	0	NUM
ejpam-5375	269	2	0	0	NUM
ejpam-5375	269	3	.	.	PUNCT
ejpam-5375	269	4	.	.	PUNCT
ejpam-5375	269	5	.	.	PUNCT
ejpam-5375	270	1	λ−	λ−	PROPN
ejpam-5375	270	2	b	b	PROPN
ejpam-5375	270	3	0	0	PROPN
ejpam-5375	270	4	−d	−d	PROPN
ejpam-5375	270	5	−d	−d	PROPN
ejpam-5375	270	6	0	0	PUNCT
ejpam-5375	270	7	.	.	PUNCT
ejpam-5375	270	8	.	.	PUNCT
ejpam-5375	270	9	.	.	PUNCT
ejpam-5375	271	1	0	0	NUM
ejpam-5375	272	1	0	0	NUM
ejpam-5375	272	2	0	0	NUM
ejpam-5375	272	3	.	.	PUNCT
ejpam-5375	272	4	.	.	PUNCT
ejpam-5375	273	1	.	.	PUNCT
ejpam-5375	273	2	0	0	NUM
ejpam-5375	274	1	λ−	λ−	PROPN
ejpam-5375	274	2	b	b	PROPN
ejpam-5375	274	3	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	274	4	.	.	PUNCT
ejpam-5375	275	1	we	we	PRON
ejpam-5375	275	2	need	need	VERB
ejpam-5375	275	3	to	to	PART
ejpam-5375	275	4	simplify	simplify	VERB
ejpam-5375	275	5	the	the	DET
ejpam-5375	275	6	above	above	ADJ
ejpam-5375	275	7	determinant	determinant	ADJ
ejpam-5375	275	8	by	by	ADP
ejpam-5375	275	9	applying	apply	VERB
ejpam-5375	275	10	row	row	NOUN
ejpam-5375	275	11	and	and	CCONJ
ejpam-5375	275	12	column	column	NOUN
ejpam-5375	275	13	operations	operation	NOUN
ejpam-5375	275	14	.	.	PUNCT
ejpam-5375	276	1	(	(	PUNCT
ejpam-5375	276	2	i	i	NOUN
ejpam-5375	276	3	)	)	PUNCT
ejpam-5375	276	4	rn	rn	PROPN
ejpam-5375	276	5	2	2	NUM
ejpam-5375	276	6	+1+i	+1+i	NOUN
ejpam-5375	276	7	−→	−→	NOUN
ejpam-5375	276	8	rn	rn	PROPN
ejpam-5375	276	9	2	2	NUM
ejpam-5375	276	10	+1+i	+1+i	NOUN
ejpam-5375	276	11	−rn	−rn	NUM
ejpam-5375	276	12	2	2	NUM
ejpam-5375	276	13	+1−i	+1−i	NOUN
ejpam-5375	276	14	,	,	PUNCT
ejpam-5375	276	15	for	for	ADP
ejpam-5375	276	16	i	i	PROPN
ejpam-5375	276	17	=	=	SYM
ejpam-5375	276	18	1	1	NUM
ejpam-5375	276	19	,	,	PUNCT
ejpam-5375	276	20	2	2	NUM
ejpam-5375	276	21	,	,	PUNCT
ejpam-5375	276	22	.	.	PUNCT
ejpam-5375	276	23	.	.	PUNCT
ejpam-5375	276	24	.	.	PUNCT
ejpam-5375	277	1	,	,	PUNCT
ejpam-5375	277	2	n2	n2	ADJ
ejpam-5375	277	3	−	−	PROPN
ejpam-5375	277	4	1	1	X
ejpam-5375	277	5	.	.	PUNCT
ejpam-5375	277	6	m.	m.	PROPN
ejpam-5375	277	7	u.	u.	PROPN
ejpam-5375	277	8	romdhini	romdhini	PROPN
ejpam-5375	277	9	et	et	PROPN
ejpam-5375	277	10	al	al	PROPN
ejpam-5375	277	11	.	.	PUNCT
ejpam-5375	277	12	/	/	SYM
ejpam-5375	277	13	eur	eur	PROPN
ejpam-5375	277	14	.	.	PUNCT
ejpam-5375	278	1	j.	j.	PROPN
ejpam-5375	278	2	pure	pure	PROPN
ejpam-5375	278	3	appl	appl	PROPN
ejpam-5375	278	4	.	.	PROPN
ejpam-5375	278	5	math	math	PROPN
ejpam-5375	278	6	,	,	PUNCT
ejpam-5375	278	7	17	17	NUM
ejpam-5375	278	8	(	(	PUNCT
ejpam-5375	278	9	4	4	NUM
ejpam-5375	278	10	)	)	PUNCT
ejpam-5375	278	11	(	(	PUNCT
ejpam-5375	278	12	2024	2024	NUM
ejpam-5375	278	13	)	)	PUNCT
ejpam-5375	278	14	,	,	PUNCT
ejpam-5375	278	15	2915	2915	NUM
ejpam-5375	278	16	-	-	SYM
ejpam-5375	278	17	2929	2929	NUM
ejpam-5375	278	18	2921	2921	NUM
ejpam-5375	278	19	then	then	ADV
ejpam-5375	278	20	we	we	PRON
ejpam-5375	278	21	obtain	obtain	VERB
ejpam-5375	278	22	pm	pm	NOUN
ejpam-5375	278	23	(	(	PUNCT
ejpam-5375	278	24	λ	λ	NOUN
ejpam-5375	278	25	)	)	PUNCT
ejpam-5375	278	26	=	=	PUNCT
ejpam-5375	279	1	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	ADP
ejpam-5375	279	2	λ−	λ−	PROPN
ejpam-5375	279	3	a	a	DET
ejpam-5375	279	4	−d	−d	PROPN
ejpam-5375	279	5	−d	−d	PROPN
ejpam-5375	279	6	.	.	PUNCT
ejpam-5375	279	7	.	.	PUNCT
ejpam-5375	280	1	.	.	PUNCT
ejpam-5375	281	1	−d	−d	PROPN
ejpam-5375	281	2	−d	−d	PROPN
ejpam-5375	281	3	−d	−d	PROPN
ejpam-5375	281	4	.	.	PUNCT
ejpam-5375	281	5	.	.	PUNCT
ejpam-5375	282	1	.	.	PUNCT
ejpam-5375	283	1	−d	−d	PROPN
ejpam-5375	283	2	−d	−d	PROPN
ejpam-5375	283	3	−d	−d	VERB
ejpam-5375	283	4	λ−	λ−	PROPN
ejpam-5375	283	5	b	b	PROPN
ejpam-5375	283	6	0	0	NUM
ejpam-5375	283	7	.	.	PUNCT
ejpam-5375	283	8	.	.	PUNCT
ejpam-5375	284	1	.	.	PUNCT
ejpam-5375	285	1	0	0	NUM
ejpam-5375	286	1	0	0	NUM
ejpam-5375	286	2	0	0	NUM
ejpam-5375	286	3	.	.	PUNCT
ejpam-5375	286	4	.	.	PUNCT
ejpam-5375	287	1	.	.	PUNCT
ejpam-5375	287	2	0	0	NUM
ejpam-5375	288	1	−d	−d	PROPN
ejpam-5375	288	2	−d	−d	PROPN
ejpam-5375	288	3	0	0	PUNCT
ejpam-5375	289	1	λ−	λ−	PROPN
ejpam-5375	289	2	b	b	PROPN
ejpam-5375	289	3	.	.	PUNCT
ejpam-5375	289	4	.	.	PUNCT
ejpam-5375	289	5	.	.	PUNCT
ejpam-5375	290	1	0	0	NUM
ejpam-5375	291	1	0	0	NUM
ejpam-5375	291	2	0	0	NUM
ejpam-5375	291	3	.	.	PUNCT
ejpam-5375	291	4	.	.	PUNCT
ejpam-5375	291	5	.	.	PUNCT
ejpam-5375	292	1	−d	−d	PROPN
ejpam-5375	292	2	0	0	NUM
ejpam-5375	292	3	...	...	PUNCT
ejpam-5375	292	4	...	...	PUNCT
ejpam-5375	292	5	...	...	PUNCT
ejpam-5375	292	6	.	.	PUNCT
ejpam-5375	292	7	.	.	PUNCT
ejpam-5375	292	8	.	.	PUNCT
ejpam-5375	293	1	...	...	PUNCT
ejpam-5375	293	2	...	...	PUNCT
ejpam-5375	293	3	...	...	PUNCT
ejpam-5375	293	4	.	.	PUNCT
ejpam-5375	293	5	.	.	PUNCT
ejpam-5375	294	1	.	.	PUNCT
ejpam-5375	295	1	...	...	PUNCT
ejpam-5375	296	1	...	...	PUNCT
ejpam-5375	297	1	−d	−d	ADJ
ejpam-5375	297	2	0	0	NUM
ejpam-5375	297	3	0	0	NUM
ejpam-5375	297	4	.	.	PUNCT
ejpam-5375	297	5	.	.	PUNCT
ejpam-5375	297	6	.	.	PUNCT
ejpam-5375	298	1	λ−	λ−	PROPN
ejpam-5375	298	2	b	b	PROPN
ejpam-5375	298	3	0	0	PROPN
ejpam-5375	298	4	−d	−d	PROPN
ejpam-5375	298	5	.	.	PUNCT
ejpam-5375	298	6	.	.	PUNCT
ejpam-5375	299	1	.	.	PUNCT
ejpam-5375	300	1	0	0	NUM
ejpam-5375	300	2	0	0	NUM
ejpam-5375	300	3	−d	−d	ADJ
ejpam-5375	300	4	0	0	NUM
ejpam-5375	300	5	0	0	NUM
ejpam-5375	300	6	.	.	PUNCT
ejpam-5375	300	7	.	.	PUNCT
ejpam-5375	301	1	.	.	PUNCT
ejpam-5375	301	2	0	0	PUNCT
ejpam-5375	302	1	λ−	λ−	PROPN
ejpam-5375	302	2	c	c	NOUN
ejpam-5375	302	3	0	0	NUM
ejpam-5375	302	4	.	.	PUNCT
ejpam-5375	302	5	.	.	PUNCT
ejpam-5375	302	6	.	.	PUNCT
ejpam-5375	303	1	0	0	NUM
ejpam-5375	304	1	0	0	NUM
ejpam-5375	304	2	0	0	NUM
ejpam-5375	304	3	0	0	NUM
ejpam-5375	304	4	0	0	NUM
ejpam-5375	304	5	.	.	PUNCT
ejpam-5375	304	6	.	.	PUNCT
ejpam-5375	304	7	.	.	PUNCT
ejpam-5375	305	1	−λ+	−λ+	PROPN
ejpam-5375	306	1	b−	b−	PROPN
ejpam-5375	307	1	d	d	PROPN
ejpam-5375	307	2	0	0	PUNCT
ejpam-5375	307	3	λ−	λ−	PROPN
ejpam-5375	307	4	b+	b+	X
ejpam-5375	307	5	d	d	X
ejpam-5375	307	6	.	.	PUNCT
ejpam-5375	307	7	.	.	PUNCT
ejpam-5375	308	1	.	.	PUNCT
ejpam-5375	309	1	0	0	NUM
ejpam-5375	309	2	0	0	NUM
ejpam-5375	309	3	...	...	PUNCT
ejpam-5375	309	4	...	...	PUNCT
ejpam-5375	309	5	...	...	PUNCT
ejpam-5375	309	6	.	.	PUNCT
ejpam-5375	309	7	.	.	PUNCT
ejpam-5375	309	8	.	.	PUNCT
ejpam-5375	310	1	...	...	PUNCT
ejpam-5375	310	2	...	...	PUNCT
ejpam-5375	310	3	...	...	PUNCT
ejpam-5375	310	4	.	.	PUNCT
ejpam-5375	310	5	.	.	PUNCT
ejpam-5375	311	1	.	.	PUNCT
ejpam-5375	312	1	...	...	PUNCT
ejpam-5375	313	1	...	...	PUNCT
ejpam-5375	314	1	0	0	NUM
ejpam-5375	314	2	0	0	NUM
ejpam-5375	315	1	−λ+	−λ+	PROPN
ejpam-5375	315	2	b−	b−	PROPN
ejpam-5375	315	3	d	d	PROPN
ejpam-5375	315	4	.	.	PUNCT
ejpam-5375	315	5	.	.	PUNCT
ejpam-5375	315	6	.	.	PUNCT
ejpam-5375	316	1	0	0	NUM
ejpam-5375	317	1	0	0	NUM
ejpam-5375	317	2	0	0	NUM
ejpam-5375	317	3	.	.	PUNCT
ejpam-5375	317	4	.	.	PUNCT
ejpam-5375	317	5	.	.	PUNCT
ejpam-5375	318	1	λ−	λ−	PROPN
ejpam-5375	318	2	b+	b+	VERB
ejpam-5375	318	3	d	d	X
ejpam-5375	318	4	0	0	NUM
ejpam-5375	318	5	0	0	NUM
ejpam-5375	318	6	−λ+	−λ+	PROPN
ejpam-5375	318	7	b−	b−	PROPN
ejpam-5375	318	8	d	d	PROPN
ejpam-5375	318	9	0	0	PROPN
ejpam-5375	318	10	.	.	PUNCT
ejpam-5375	318	11	.	.	PUNCT
ejpam-5375	319	1	.	.	PUNCT
ejpam-5375	320	1	0	0	NUM
ejpam-5375	321	1	0	0	NUM
ejpam-5375	321	2	0	0	NUM
ejpam-5375	321	3	.	.	PUNCT
ejpam-5375	321	4	.	.	PUNCT
ejpam-5375	322	1	.	.	PUNCT
ejpam-5375	322	2	0	0	NUM
ejpam-5375	323	1	λ−	λ−	PROPN
ejpam-5375	323	2	b+	b+	ADP
ejpam-5375	323	3	d	d	PROPN
ejpam-5375	323	4	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	323	5	.	.	PUNCT
ejpam-5375	324	1	(	(	PUNCT
ejpam-5375	324	2	ii	ii	X
ejpam-5375	324	3	)	)	PUNCT
ejpam-5375	324	4	cn	cn	NOUN
ejpam-5375	324	5	2	2	NUM
ejpam-5375	324	6	+1−i	+1−i	NOUN
ejpam-5375	324	7	−→	−→	ADJ
ejpam-5375	324	8	cn	cn	PROPN
ejpam-5375	324	9	2	2	NUM
ejpam-5375	324	10	+1−i	+1−i	NOUN
ejpam-5375	324	11	+	+	CCONJ
ejpam-5375	324	12	cn	cn	PROPN
ejpam-5375	324	13	2	2	NUM
ejpam-5375	324	14	+1+i	+1+i	PROPN
ejpam-5375	324	15	,	,	PUNCT
ejpam-5375	324	16	for	for	ADP
ejpam-5375	324	17	i	i	PROPN
ejpam-5375	324	18	=	=	SYM
ejpam-5375	324	19	1	1	NUM
ejpam-5375	324	20	,	,	PUNCT
ejpam-5375	324	21	2	2	NUM
ejpam-5375	324	22	,	,	PUNCT
ejpam-5375	324	23	.	.	PUNCT
ejpam-5375	324	24	.	.	PUNCT
ejpam-5375	324	25	.	.	PUNCT
ejpam-5375	325	1	,	,	PUNCT
ejpam-5375	325	2	n2	n2	ADJ
ejpam-5375	325	3	−	−	PROPN
ejpam-5375	325	4	1	1	X
ejpam-5375	325	5	.	.	PUNCT
ejpam-5375	326	1	consequently	consequently	ADV
ejpam-5375	326	2	,	,	PUNCT
ejpam-5375	326	3	we	we	PRON
ejpam-5375	326	4	have	have	VERB
ejpam-5375	326	5	pm	pm	NOUN
ejpam-5375	326	6	(	(	PUNCT
ejpam-5375	326	7	λ	λ	NOUN
ejpam-5375	326	8	)	)	PUNCT
ejpam-5375	326	9	=	=	PUNCT
ejpam-5375	326	10	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	ADP
ejpam-5375	326	11	λ−	λ−	PROPN
ejpam-5375	326	12	a	a	DET
ejpam-5375	326	13	−2d	−2d	PROPN
ejpam-5375	326	14	−2d	−2d	PROPN
ejpam-5375	326	15	.	.	PUNCT
ejpam-5375	326	16	.	.	PUNCT
ejpam-5375	326	17	.	.	PUNCT
ejpam-5375	327	1	−2d	−2d	PROPN
ejpam-5375	327	2	−d	−d	PROPN
ejpam-5375	327	3	−d	−d	PROPN
ejpam-5375	327	4	.	.	PUNCT
ejpam-5375	327	5	.	.	PUNCT
ejpam-5375	327	6	.	.	PUNCT
ejpam-5375	328	1	−d	−d	PROPN
ejpam-5375	328	2	−d	−d	PROPN
ejpam-5375	328	3	−d	−d	PROPN
ejpam-5375	328	4	λ−	λ−	PROPN
ejpam-5375	328	5	b−	b−	PROPN
ejpam-5375	328	6	d	d	PROPN
ejpam-5375	328	7	0	0	PROPN
ejpam-5375	328	8	.	.	PUNCT
ejpam-5375	328	9	.	.	PUNCT
ejpam-5375	329	1	.	.	PUNCT
ejpam-5375	330	1	0	0	NUM
ejpam-5375	331	1	0	0	NUM
ejpam-5375	331	2	0	0	NUM
ejpam-5375	331	3	.	.	PUNCT
ejpam-5375	331	4	.	.	PUNCT
ejpam-5375	332	1	.	.	PUNCT
ejpam-5375	332	2	0	0	NUM
ejpam-5375	333	1	−d	−d	PROPN
ejpam-5375	333	2	−d	−d	PROPN
ejpam-5375	333	3	0	0	PUNCT
ejpam-5375	334	1	λ−	λ−	PROPN
ejpam-5375	334	2	b−	b−	PROPN
ejpam-5375	334	3	d	d	PROPN
ejpam-5375	334	4	.	.	PUNCT
ejpam-5375	334	5	.	.	PUNCT
ejpam-5375	334	6	.	.	PUNCT
ejpam-5375	335	1	0	0	NUM
ejpam-5375	336	1	0	0	NUM
ejpam-5375	336	2	0	0	NUM
ejpam-5375	336	3	.	.	PUNCT
ejpam-5375	336	4	.	.	PUNCT
ejpam-5375	336	5	.	.	PUNCT
ejpam-5375	337	1	−d	−d	PROPN
ejpam-5375	337	2	0	0	NUM
ejpam-5375	337	3	...	...	PUNCT
ejpam-5375	337	4	...	...	PUNCT
ejpam-5375	337	5	...	...	PUNCT
ejpam-5375	337	6	.	.	PUNCT
ejpam-5375	337	7	.	.	PUNCT
ejpam-5375	337	8	.	.	PUNCT
ejpam-5375	338	1	...	...	PUNCT
ejpam-5375	338	2	...	...	PUNCT
ejpam-5375	338	3	...	...	PUNCT
ejpam-5375	338	4	.	.	PUNCT
ejpam-5375	338	5	.	.	PUNCT
ejpam-5375	339	1	.	.	PUNCT
ejpam-5375	340	1	...	...	PUNCT
ejpam-5375	341	1	...	...	PUNCT
ejpam-5375	342	1	−d	−d	ADJ
ejpam-5375	342	2	0	0	NUM
ejpam-5375	342	3	0	0	NUM
ejpam-5375	342	4	.	.	PUNCT
ejpam-5375	342	5	.	.	PUNCT
ejpam-5375	342	6	.	.	PUNCT
ejpam-5375	343	1	λ−	λ−	PROPN
ejpam-5375	343	2	b−	b−	PROPN
ejpam-5375	344	1	d	d	PROPN
ejpam-5375	344	2	0	0	PUNCT
ejpam-5375	344	3	−d	−d	PROPN
ejpam-5375	344	4	.	.	PUNCT
ejpam-5375	344	5	.	.	PUNCT
ejpam-5375	345	1	.	.	PUNCT
ejpam-5375	346	1	0	0	NUM
ejpam-5375	346	2	0	0	NUM
ejpam-5375	346	3	−d	−d	ADJ
ejpam-5375	346	4	0	0	NUM
ejpam-5375	346	5	0	0	NUM
ejpam-5375	346	6	.	.	PUNCT
ejpam-5375	346	7	.	.	PUNCT
ejpam-5375	347	1	.	.	PUNCT
ejpam-5375	347	2	0	0	PUNCT
ejpam-5375	348	1	λ−	λ−	PROPN
ejpam-5375	348	2	c	c	NOUN
ejpam-5375	348	3	0	0	NUM
ejpam-5375	348	4	.	.	PUNCT
ejpam-5375	348	5	.	.	PUNCT
ejpam-5375	348	6	.	.	PUNCT
ejpam-5375	349	1	0	0	NUM
ejpam-5375	350	1	0	0	NUM
ejpam-5375	350	2	0	0	NUM
ejpam-5375	350	3	0	0	NUM
ejpam-5375	350	4	0	0	NUM
ejpam-5375	350	5	.	.	PUNCT
ejpam-5375	350	6	.	.	PUNCT
ejpam-5375	350	7	.	.	PUNCT
ejpam-5375	351	1	0	0	NUM
ejpam-5375	351	2	0	0	X
ejpam-5375	352	1	λ−	λ−	PROPN
ejpam-5375	352	2	b+	b+	X
ejpam-5375	352	3	d	d	X
ejpam-5375	352	4	.	.	PUNCT
ejpam-5375	352	5	.	.	PUNCT
ejpam-5375	353	1	.	.	PUNCT
ejpam-5375	354	1	0	0	NUM
ejpam-5375	354	2	0	0	NUM
ejpam-5375	354	3	...	...	PUNCT
ejpam-5375	354	4	...	...	PUNCT
ejpam-5375	354	5	...	...	PUNCT
ejpam-5375	354	6	.	.	PUNCT
ejpam-5375	354	7	.	.	PUNCT
ejpam-5375	354	8	.	.	PUNCT
ejpam-5375	355	1	...	...	PUNCT
ejpam-5375	355	2	...	...	PUNCT
ejpam-5375	355	3	...	...	PUNCT
ejpam-5375	355	4	.	.	PUNCT
ejpam-5375	355	5	.	.	PUNCT
ejpam-5375	356	1	.	.	PUNCT
ejpam-5375	357	1	...	...	PUNCT
ejpam-5375	358	1	...	...	PUNCT
ejpam-5375	359	1	0	0	NUM
ejpam-5375	359	2	0	0	NUM
ejpam-5375	359	3	0	0	NUM
ejpam-5375	359	4	.	.	PUNCT
ejpam-5375	359	5	.	.	PUNCT
ejpam-5375	359	6	.	.	PUNCT
ejpam-5375	360	1	0	0	NUM
ejpam-5375	361	1	0	0	NUM
ejpam-5375	361	2	0	0	NUM
ejpam-5375	361	3	.	.	PUNCT
ejpam-5375	361	4	.	.	PUNCT
ejpam-5375	361	5	.	.	PUNCT
ejpam-5375	362	1	λ−	λ−	PROPN
ejpam-5375	362	2	b+	b+	VERB
ejpam-5375	362	3	d	d	X
ejpam-5375	362	4	0	0	NUM
ejpam-5375	362	5	0	0	NUM
ejpam-5375	362	6	0	0	NUM
ejpam-5375	362	7	0	0	NUM
ejpam-5375	362	8	.	.	PUNCT
ejpam-5375	362	9	.	.	PUNCT
ejpam-5375	363	1	.	.	PUNCT
ejpam-5375	364	1	0	0	NUM
ejpam-5375	365	1	0	0	NUM
ejpam-5375	365	2	0	0	NUM
ejpam-5375	365	3	.	.	PUNCT
ejpam-5375	365	4	.	.	PUNCT
ejpam-5375	366	1	.	.	PUNCT
ejpam-5375	366	2	0	0	NUM
ejpam-5375	367	1	λ−	λ−	PROPN
ejpam-5375	367	2	b+	b+	ADP
ejpam-5375	367	3	d	d	PROPN
ejpam-5375	367	4	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	367	5	.	.	PUNCT
ejpam-5375	368	1	(	(	PUNCT
ejpam-5375	368	2	iii	iii	X
ejpam-5375	368	3	)	)	PUNCT
ejpam-5375	368	4	c1	c1	PROPN
ejpam-5375	368	5	−→	−→	NOUN
ejpam-5375	368	6	c1	c1	PROPN
ejpam-5375	368	7	+	+	CCONJ
ejpam-5375	369	1	d	d	X
ejpam-5375	369	2	λ−b−dc2	λ−b−dc2	NOUN
ejpam-5375	370	1	+	+	CCONJ
ejpam-5375	370	2	d	d	NOUN
ejpam-5375	370	3	λ−b−dc3	λ−b−dc3	NOUN
ejpam-5375	371	1	+	+	X
ejpam-5375	371	2	.	.	PUNCT
ejpam-5375	371	3	.	.	PUNCT
ejpam-5375	372	1	.+	.+	NOUN
ejpam-5375	373	1	d	d	PRON
ejpam-5375	373	2	λ−b−dcn	λ−b−dcn	NOUN
ejpam-5375	373	3	2	2	NUM
ejpam-5375	373	4	−1	−1	NOUN
ejpam-5375	374	1	+	+	CCONJ
ejpam-5375	375	1	d	d	NOUN
ejpam-5375	375	2	λ−b−dcn	λ−b−dcn	NOUN
ejpam-5375	375	3	2	2	NUM
ejpam-5375	375	4	.	.	PUNCT
ejpam-5375	376	1	then	then	ADV
ejpam-5375	376	2	,	,	PUNCT
ejpam-5375	376	3	we	we	PRON
ejpam-5375	376	4	can	can	AUX
ejpam-5375	376	5	state	state	VERB
ejpam-5375	376	6	that	that	DET
ejpam-5375	376	7	pm	pm	NOUN
ejpam-5375	376	8	(	(	PUNCT
ejpam-5375	376	9	λ	λ	NOUN
ejpam-5375	376	10	)	)	PUNCT
ejpam-5375	376	11	is∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	is∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-5375	376	12	(	(	PUNCT
ejpam-5375	376	13	λ−a)(λ−b−d)−d2(n−2	λ−a)(λ−b−d)−d2(n−2	PROPN
ejpam-5375	376	14	)	)	PUNCT
ejpam-5375	376	15	λ−b−d	λ−b−d	NOUN
ejpam-5375	376	16	−2d	−2d	PROPN
ejpam-5375	376	17	−2d	−2d	PROPN
ejpam-5375	376	18	.	.	PUNCT
ejpam-5375	376	19	.	.	PUNCT
ejpam-5375	376	20	.	.	PUNCT
ejpam-5375	377	1	−2d	−2d	PROPN
ejpam-5375	377	2	0	0	NUM
ejpam-5375	377	3	−d	−d	PROPN
ejpam-5375	377	4	.	.	PUNCT
ejpam-5375	377	5	.	.	PUNCT
ejpam-5375	377	6	.	.	PUNCT
ejpam-5375	378	1	−d	−d	PROPN
ejpam-5375	378	2	−d	−d	PROPN
ejpam-5375	378	3	0	0	PUNCT
ejpam-5375	379	1	λ−	λ−	PROPN
ejpam-5375	379	2	b−	b−	PROPN
ejpam-5375	379	3	d	d	NOUN
ejpam-5375	379	4	0	0	PROPN
ejpam-5375	379	5	.	.	PUNCT
ejpam-5375	379	6	.	.	PUNCT
ejpam-5375	380	1	.	.	PUNCT
ejpam-5375	381	1	0	0	NUM
ejpam-5375	382	1	0	0	NUM
ejpam-5375	382	2	0	0	NUM
ejpam-5375	382	3	.	.	PUNCT
ejpam-5375	382	4	.	.	PUNCT
ejpam-5375	383	1	.	.	PUNCT
ejpam-5375	383	2	0	0	PUNCT
ejpam-5375	384	1	−d	−d	ADJ
ejpam-5375	384	2	0	0	NUM
ejpam-5375	384	3	0	0	NUM
ejpam-5375	385	1	λ−	λ−	PROPN
ejpam-5375	385	2	b−	b−	PROPN
ejpam-5375	385	3	d	d	PROPN
ejpam-5375	385	4	.	.	PUNCT
ejpam-5375	385	5	.	.	PUNCT
ejpam-5375	385	6	.	.	PUNCT
ejpam-5375	386	1	0	0	NUM
ejpam-5375	387	1	0	0	NUM
ejpam-5375	387	2	0	0	NUM
ejpam-5375	387	3	.	.	PUNCT
ejpam-5375	387	4	.	.	PUNCT
ejpam-5375	387	5	.	.	PUNCT
ejpam-5375	388	1	−d	−d	PROPN
ejpam-5375	388	2	0	0	NUM
ejpam-5375	388	3	...	...	PUNCT
ejpam-5375	388	4	...	...	PUNCT
ejpam-5375	388	5	...	...	PUNCT
ejpam-5375	388	6	.	.	PUNCT
ejpam-5375	388	7	.	.	PUNCT
ejpam-5375	388	8	.	.	PUNCT
ejpam-5375	389	1	...	...	PUNCT
ejpam-5375	389	2	...	...	PUNCT
ejpam-5375	389	3	...	...	PUNCT
ejpam-5375	389	4	.	.	PUNCT
ejpam-5375	389	5	.	.	PUNCT
ejpam-5375	390	1	.	.	PUNCT
ejpam-5375	391	1	...	...	PUNCT
ejpam-5375	392	1	...	...	PUNCT
ejpam-5375	393	1	0	0	NUM
ejpam-5375	393	2	0	0	NUM
ejpam-5375	393	3	0	0	NUM
ejpam-5375	393	4	.	.	PUNCT
ejpam-5375	393	5	.	.	PUNCT
ejpam-5375	393	6	.	.	PUNCT
ejpam-5375	394	1	λ−	λ−	PROPN
ejpam-5375	394	2	b−	b−	PROPN
ejpam-5375	395	1	d	d	PROPN
ejpam-5375	395	2	0	0	PUNCT
ejpam-5375	395	3	−d	−d	PROPN
ejpam-5375	395	4	.	.	PUNCT
ejpam-5375	395	5	.	.	PUNCT
ejpam-5375	396	1	.	.	PUNCT
ejpam-5375	397	1	0	0	NUM
ejpam-5375	397	2	0	0	NUM
ejpam-5375	397	3	−d	−d	ADJ
ejpam-5375	397	4	0	0	NUM
ejpam-5375	397	5	0	0	NUM
ejpam-5375	397	6	.	.	PUNCT
ejpam-5375	397	7	.	.	PUNCT
ejpam-5375	398	1	.	.	PUNCT
ejpam-5375	398	2	0	0	PUNCT
ejpam-5375	399	1	λ−	λ−	PROPN
ejpam-5375	399	2	c	c	NOUN
ejpam-5375	399	3	0	0	NUM
ejpam-5375	399	4	.	.	PUNCT
ejpam-5375	399	5	.	.	PUNCT
ejpam-5375	399	6	.	.	PUNCT
ejpam-5375	400	1	0	0	NUM
ejpam-5375	401	1	0	0	NUM
ejpam-5375	401	2	0	0	NUM
ejpam-5375	401	3	0	0	NUM
ejpam-5375	401	4	0	0	NUM
ejpam-5375	401	5	.	.	PUNCT
ejpam-5375	401	6	.	.	PUNCT
ejpam-5375	401	7	.	.	PUNCT
ejpam-5375	402	1	0	0	NUM
ejpam-5375	402	2	0	0	X
ejpam-5375	403	1	λ−	λ−	PROPN
ejpam-5375	403	2	b+	b+	X
ejpam-5375	403	3	d	d	X
ejpam-5375	403	4	.	.	PUNCT
ejpam-5375	403	5	.	.	PUNCT
ejpam-5375	404	1	.	.	PUNCT
ejpam-5375	405	1	0	0	NUM
ejpam-5375	405	2	0	0	NUM
ejpam-5375	405	3	...	...	PUNCT
ejpam-5375	405	4	...	...	PUNCT
ejpam-5375	405	5	...	...	PUNCT
ejpam-5375	405	6	.	.	PUNCT
ejpam-5375	405	7	.	.	PUNCT
ejpam-5375	405	8	.	.	PUNCT
ejpam-5375	406	1	...	...	PUNCT
ejpam-5375	406	2	...	...	PUNCT
ejpam-5375	406	3	...	...	PUNCT
ejpam-5375	406	4	.	.	PUNCT
ejpam-5375	406	5	.	.	PUNCT
ejpam-5375	407	1	.	.	PUNCT
ejpam-5375	408	1	...	...	PUNCT
ejpam-5375	409	1	...	...	PUNCT
ejpam-5375	410	1	0	0	NUM
ejpam-5375	410	2	0	0	NUM
ejpam-5375	410	3	0	0	NUM
ejpam-5375	410	4	.	.	PUNCT
ejpam-5375	410	5	.	.	PUNCT
ejpam-5375	410	6	.	.	PUNCT
ejpam-5375	411	1	0	0	NUM
ejpam-5375	412	1	0	0	NUM
ejpam-5375	412	2	0	0	NUM
ejpam-5375	412	3	.	.	PUNCT
ejpam-5375	412	4	.	.	PUNCT
ejpam-5375	412	5	.	.	PUNCT
ejpam-5375	413	1	λ−	λ−	PROPN
ejpam-5375	413	2	b+	b+	VERB
ejpam-5375	413	3	d	d	X
ejpam-5375	413	4	0	0	NUM
ejpam-5375	413	5	0	0	NUM
ejpam-5375	413	6	0	0	NUM
ejpam-5375	413	7	0	0	NUM
ejpam-5375	413	8	.	.	PUNCT
ejpam-5375	413	9	.	.	PUNCT
ejpam-5375	414	1	.	.	PUNCT
ejpam-5375	415	1	0	0	NUM
ejpam-5375	416	1	0	0	NUM
ejpam-5375	416	2	0	0	NUM
ejpam-5375	416	3	.	.	PUNCT
ejpam-5375	416	4	.	.	PUNCT
ejpam-5375	417	1	.	.	PUNCT
ejpam-5375	417	2	0	0	NUM
ejpam-5375	418	1	λ−	λ−	PROPN
ejpam-5375	418	2	b+	b+	VERB
ejpam-5375	418	3	d	d	NOUN
ejpam-5375	418	4	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	418	5	.	.	PUNCT
ejpam-5375	419	1	(	(	PUNCT
ejpam-5375	419	2	iv	iv	X
ejpam-5375	419	3	)	)	PUNCT
ejpam-5375	419	4	c1	c1	PROPN
ejpam-5375	419	5	−→	−→	PROPN
ejpam-5375	419	6	c1	c1	PROPN
ejpam-5375	420	1	+	+	CCONJ
ejpam-5375	420	2	d	d	X
ejpam-5375	420	3	λ−ccn	λ−ccn	NOUN
ejpam-5375	420	4	2	2	NUM
ejpam-5375	420	5	+1	+1	PROPN
ejpam-5375	420	6	.	.	PUNCT
ejpam-5375	421	1	it	it	PRON
ejpam-5375	421	2	follows	follow	VERB
ejpam-5375	421	3	that	that	DET
ejpam-5375	421	4	pm	pm	NOUN
ejpam-5375	421	5	(	(	PUNCT
ejpam-5375	421	6	λ	λ	X
ejpam-5375	421	7	)	)	PUNCT
ejpam-5375	421	8	is	be	AUX
ejpam-5375	421	9	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	ADJ
ejpam-5375	421	10	(	(	PUNCT
ejpam-5375	421	11	λ−a)(λ−c)(λ−b−d)−d2((n−2)(n−c)+(λ−b−d	λ−a)(λ−c)(λ−b−d)−d2((n−2)(n−c)+(λ−b−d	NOUN
ejpam-5375	421	12	)	)	PUNCT
ejpam-5375	421	13	(	(	PUNCT
ejpam-5375	421	14	λ−b−d)(λ−c	λ−b−d)(λ−c	PROPN
ejpam-5375	421	15	)	)	PUNCT
ejpam-5375	421	16	−2d	−2d	PROPN
ejpam-5375	421	17	−2d	−2d	PROPN
ejpam-5375	421	18	.	.	PUNCT
ejpam-5375	421	19	.	.	PUNCT
ejpam-5375	421	20	.	.	PUNCT
ejpam-5375	422	1	−2d	−2d	PROPN
ejpam-5375	422	2	0	0	NUM
ejpam-5375	422	3	−d	−d	PROPN
ejpam-5375	422	4	.	.	PUNCT
ejpam-5375	422	5	.	.	PUNCT
ejpam-5375	422	6	.	.	PUNCT
ejpam-5375	423	1	−d	−d	PROPN
ejpam-5375	423	2	−d	−d	PROPN
ejpam-5375	423	3	0	0	PUNCT
ejpam-5375	424	1	λ	λ	NOUN
ejpam-5375	424	2	−	−	PROPN
ejpam-5375	424	3	b	b	NOUN
ejpam-5375	424	4	−	−	PROPN
ejpam-5375	424	5	d	d	NOUN
ejpam-5375	424	6	0	0	NUM
ejpam-5375	424	7	.	.	PUNCT
ejpam-5375	424	8	.	.	PUNCT
ejpam-5375	425	1	.	.	PUNCT
ejpam-5375	426	1	0	0	NUM
ejpam-5375	427	1	0	0	NUM
ejpam-5375	427	2	0	0	NUM
ejpam-5375	427	3	.	.	PUNCT
ejpam-5375	427	4	.	.	PUNCT
ejpam-5375	428	1	.	.	PUNCT
ejpam-5375	428	2	0	0	PUNCT
ejpam-5375	429	1	−d	−d	ADJ
ejpam-5375	429	2	0	0	NUM
ejpam-5375	429	3	0	0	NUM
ejpam-5375	430	1	λ	λ	NOUN
ejpam-5375	430	2	−	−	PROPN
ejpam-5375	430	3	b	b	PROPN
ejpam-5375	430	4	−	−	PROPN
ejpam-5375	430	5	d	d	NOUN
ejpam-5375	430	6	.	.	PUNCT
ejpam-5375	430	7	.	.	PUNCT
ejpam-5375	430	8	.	.	PUNCT
ejpam-5375	431	1	0	0	NUM
ejpam-5375	432	1	0	0	NUM
ejpam-5375	432	2	0	0	NUM
ejpam-5375	432	3	.	.	PUNCT
ejpam-5375	432	4	.	.	PUNCT
ejpam-5375	432	5	.	.	PUNCT
ejpam-5375	433	1	−d	−d	PROPN
ejpam-5375	433	2	0	0	PUNCT
ejpam-5375	433	3	.	.	PUNCT
ejpam-5375	433	4	.	.	PUNCT
ejpam-5375	433	5	.	.	PUNCT
ejpam-5375	433	6	.	.	PUNCT
ejpam-5375	433	7	.	.	PUNCT
ejpam-5375	433	8	.	.	PUNCT
ejpam-5375	433	9	.	.	PUNCT
ejpam-5375	433	10	.	.	PUNCT
ejpam-5375	433	11	.	.	PUNCT
ejpam-5375	433	12	.	.	PUNCT
ejpam-5375	433	13	.	.	PUNCT
ejpam-5375	433	14	.	.	PUNCT
ejpam-5375	433	15	.	.	PUNCT
ejpam-5375	433	16	.	.	PUNCT
ejpam-5375	433	17	.	.	PUNCT
ejpam-5375	433	18	.	.	PUNCT
ejpam-5375	433	19	.	.	PUNCT
ejpam-5375	433	20	.	.	PUNCT
ejpam-5375	433	21	.	.	PUNCT
ejpam-5375	433	22	.	.	PUNCT
ejpam-5375	433	23	.	.	PUNCT
ejpam-5375	433	24	.	.	PUNCT
ejpam-5375	433	25	.	.	PUNCT
ejpam-5375	433	26	.	.	PUNCT
ejpam-5375	433	27	.	.	PUNCT
ejpam-5375	433	28	.	.	PUNCT
ejpam-5375	433	29	.	.	PUNCT
ejpam-5375	433	30	.	.	PUNCT
ejpam-5375	433	31	.	.	PUNCT
ejpam-5375	434	1	.	.	PUNCT
ejpam-5375	435	1	0	0	NUM
ejpam-5375	436	1	0	0	NUM
ejpam-5375	436	2	0	0	NUM
ejpam-5375	436	3	.	.	PUNCT
ejpam-5375	436	4	.	.	PUNCT
ejpam-5375	436	5	.	.	PUNCT
ejpam-5375	437	1	λ	λ	X
ejpam-5375	438	1	−	−	NOUN
ejpam-5375	438	2	b	b	PROPN
ejpam-5375	438	3	−	−	PROPN
ejpam-5375	438	4	d	d	SYM
ejpam-5375	438	5	0	0	PROPN
ejpam-5375	438	6	−d	−d	PROPN
ejpam-5375	438	7	.	.	PUNCT
ejpam-5375	438	8	.	.	PUNCT
ejpam-5375	438	9	.	.	PUNCT
ejpam-5375	439	1	0	0	NUM
ejpam-5375	440	1	0	0	NUM
ejpam-5375	440	2	0	0	NUM
ejpam-5375	440	3	0	0	NUM
ejpam-5375	440	4	0	0	NUM
ejpam-5375	440	5	.	.	PUNCT
ejpam-5375	440	6	.	.	PUNCT
ejpam-5375	440	7	.	.	PUNCT
ejpam-5375	441	1	0	0	PUNCT
ejpam-5375	442	1	λ	λ	INTJ
ejpam-5375	442	2	−	−	NOUN
ejpam-5375	442	3	c	c	NOUN
ejpam-5375	442	4	0	0	NUM
ejpam-5375	442	5	.	.	PUNCT
ejpam-5375	442	6	.	.	PUNCT
ejpam-5375	443	1	.	.	PUNCT
ejpam-5375	444	1	0	0	NUM
ejpam-5375	445	1	0	0	NUM
ejpam-5375	445	2	0	0	NUM
ejpam-5375	445	3	0	0	NUM
ejpam-5375	445	4	0	0	NUM
ejpam-5375	445	5	.	.	PUNCT
ejpam-5375	445	6	.	.	PUNCT
ejpam-5375	445	7	.	.	PUNCT
ejpam-5375	446	1	0	0	NUM
ejpam-5375	446	2	0	0	NUM
ejpam-5375	447	1	λ	λ	NOUN
ejpam-5375	447	2	−	−	PROPN
ejpam-5375	447	3	b	b	PROPN
ejpam-5375	448	1	+	+	CCONJ
ejpam-5375	448	2	d	d	NOUN
ejpam-5375	448	3	.	.	PUNCT
ejpam-5375	448	4	.	.	PUNCT
ejpam-5375	448	5	.	.	PUNCT
ejpam-5375	449	1	0	0	NUM
ejpam-5375	449	2	0	0	NUM
ejpam-5375	449	3	.	.	PUNCT
ejpam-5375	449	4	.	.	PUNCT
ejpam-5375	449	5	.	.	PUNCT
ejpam-5375	449	6	.	.	PUNCT
ejpam-5375	449	7	.	.	PUNCT
ejpam-5375	449	8	.	.	PUNCT
ejpam-5375	449	9	.	.	PUNCT
ejpam-5375	449	10	.	.	PUNCT
ejpam-5375	449	11	.	.	PUNCT
ejpam-5375	449	12	.	.	PUNCT
ejpam-5375	449	13	.	.	PUNCT
ejpam-5375	449	14	.	.	PUNCT
ejpam-5375	449	15	.	.	PUNCT
ejpam-5375	449	16	.	.	PUNCT
ejpam-5375	449	17	.	.	PUNCT
ejpam-5375	449	18	.	.	PUNCT
ejpam-5375	449	19	.	.	PUNCT
ejpam-5375	449	20	.	.	PUNCT
ejpam-5375	449	21	.	.	PUNCT
ejpam-5375	449	22	.	.	PUNCT
ejpam-5375	449	23	.	.	PUNCT
ejpam-5375	449	24	.	.	PUNCT
ejpam-5375	449	25	.	.	PUNCT
ejpam-5375	449	26	.	.	PUNCT
ejpam-5375	449	27	.	.	PUNCT
ejpam-5375	449	28	.	.	PUNCT
ejpam-5375	449	29	.	.	PUNCT
ejpam-5375	449	30	.	.	PUNCT
ejpam-5375	449	31	.	.	PUNCT
ejpam-5375	450	1	.	.	PUNCT
ejpam-5375	451	1	0	0	NUM
ejpam-5375	452	1	0	0	NUM
ejpam-5375	452	2	0	0	NUM
ejpam-5375	452	3	.	.	PUNCT
ejpam-5375	452	4	.	.	PUNCT
ejpam-5375	452	5	.	.	PUNCT
ejpam-5375	453	1	0	0	NUM
ejpam-5375	454	1	0	0	NUM
ejpam-5375	454	2	0	0	NUM
ejpam-5375	454	3	.	.	PUNCT
ejpam-5375	454	4	.	.	PUNCT
ejpam-5375	454	5	.	.	PUNCT
ejpam-5375	455	1	λ	λ	X
ejpam-5375	456	1	−	−	NOUN
ejpam-5375	456	2	b	b	PROPN
ejpam-5375	457	1	+	+	CCONJ
ejpam-5375	457	2	d	d	NOUN
ejpam-5375	457	3	0	0	NUM
ejpam-5375	457	4	0	0	NUM
ejpam-5375	457	5	0	0	NUM
ejpam-5375	457	6	0	0	NUM
ejpam-5375	457	7	.	.	PUNCT
ejpam-5375	457	8	.	.	PUNCT
ejpam-5375	457	9	.	.	PUNCT
ejpam-5375	458	1	0	0	NUM
ejpam-5375	459	1	0	0	NUM
ejpam-5375	459	2	0	0	NUM
ejpam-5375	459	3	.	.	PUNCT
ejpam-5375	459	4	.	.	PUNCT
ejpam-5375	460	1	.	.	PUNCT
ejpam-5375	461	1	0	0	PUNCT
ejpam-5375	462	1	λ	λ	INTJ
ejpam-5375	462	2	−	−	PROPN
ejpam-5375	462	3	b	b	PROPN
ejpam-5375	462	4	+	+	CCONJ
ejpam-5375	462	5	d	d	PROPN
ejpam-5375	462	6	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5375	462	7	.	.	PUNCT
ejpam-5375	463	1	m.	m.	PROPN
ejpam-5375	463	2	u.	u.	PROPN
ejpam-5375	463	3	romdhini	romdhini	PROPN
ejpam-5375	463	4	et	et	PROPN
ejpam-5375	463	5	al	al	PROPN
ejpam-5375	463	6	.	.	PUNCT
ejpam-5375	463	7	/	/	SYM
ejpam-5375	463	8	eur	eur	PROPN
ejpam-5375	463	9	.	.	PUNCT
ejpam-5375	464	1	j.	j.	PROPN
ejpam-5375	464	2	pure	pure	PROPN
ejpam-5375	464	3	appl	appl	PROPN
ejpam-5375	464	4	.	.	PROPN
ejpam-5375	464	5	math	math	PROPN
ejpam-5375	464	6	,	,	PUNCT
ejpam-5375	464	7	17	17	NUM
ejpam-5375	464	8	(	(	PUNCT
ejpam-5375	464	9	4	4	NUM
ejpam-5375	464	10	)	)	PUNCT
ejpam-5375	464	11	(	(	PUNCT
ejpam-5375	464	12	2024	2024	NUM
ejpam-5375	464	13	)	)	PUNCT
ejpam-5375	464	14	,	,	PUNCT
ejpam-5375	464	15	2915	2915	NUM
ejpam-5375	464	16	-	-	SYM
ejpam-5375	464	17	2929	2929	NUM
ejpam-5375	464	18	2922	2922	NUM
ejpam-5375	464	19	the	the	DET
ejpam-5375	464	20	matrix	matrix	NOUN
ejpam-5375	464	21	form	form	NOUN
ejpam-5375	464	22	is	be	AUX
ejpam-5375	464	23	upper	upper	ADJ
ejpam-5375	464	24	triangular	triangular	NOUN
ejpam-5375	464	25	,	,	PUNCT
ejpam-5375	464	26	consequently	consequently	ADV
ejpam-5375	464	27	,	,	PUNCT
ejpam-5375	464	28	we	we	PRON
ejpam-5375	464	29	derive	derive	VERB
ejpam-5375	464	30	the	the	DET
ejpam-5375	464	31	following	follow	VERB
ejpam-5375	464	32	formula	formula	NOUN
ejpam-5375	464	33	:	:	PUNCT
ejpam-5375	464	34	pm	pm	NOUN
ejpam-5375	464	35	(	(	PUNCT
ejpam-5375	464	36	λ	λ	NOUN
ejpam-5375	464	37	)	)	PUNCT
ejpam-5375	464	38	=	=	SYM
ejpam-5375	464	39	(	(	PUNCT
ejpam-5375	464	40	λ3	λ3	PROPN
ejpam-5375	464	41	−	−	PROPN
ejpam-5375	464	42	(	(	PUNCT
ejpam-5375	464	43	a+	a+	X
ejpam-5375	464	44	b+	b+	X
ejpam-5375	464	45	c+	c+	VERB
ejpam-5375	464	46	d)λ2	d)λ2	VERB
ejpam-5375	464	47	+	+	CCONJ
ejpam-5375	464	48	(	(	PUNCT
ejpam-5375	464	49	(	(	PUNCT
ejpam-5375	464	50	a+	a+	X
ejpam-5375	464	51	c)(b+	c)(b+	NOUN
ejpam-5375	464	52	d	d	X
ejpam-5375	464	53	)	)	PUNCT
ejpam-5375	465	1	+	+	NUM
ejpam-5375	465	2	ac−	ac−	NUM
ejpam-5375	465	3	d2(n−	d2(n−	ADJ
ejpam-5375	465	4	1))λ+	1))λ+	NUM
ejpam-5375	465	5	(	(	PUNCT
ejpam-5375	465	6	b+	b+	NUM
ejpam-5375	465	7	d)(d2	d)(d2	PROPN
ejpam-5375	465	8	−	−	NUM
ejpam-5375	465	9	ac	ac	PROPN
ejpam-5375	465	10	)	)	PUNCT
ejpam-5375	466	1	+	+	CCONJ
ejpam-5375	466	2	cd2(n−	cd2(n−	VERB
ejpam-5375	466	3	2	2	NUM
ejpam-5375	466	4	)	)	PUNCT
ejpam-5375	466	5	)	)	PUNCT
ejpam-5375	467	1	(	(	PUNCT
ejpam-5375	467	2	λ−	λ−	PROPN
ejpam-5375	467	3	b−	b−	PROPN
ejpam-5375	467	4	d	d	PROPN
ejpam-5375	467	5	)	)	PUNCT
ejpam-5375	467	6	n	n	PRON
ejpam-5375	467	7	2	2	NUM
ejpam-5375	467	8	−2(λ−	−2(λ−	PROPN
ejpam-5375	467	9	b+	b+	X
ejpam-5375	467	10	d	d	NOUN
ejpam-5375	467	11	)	)	PUNCT
ejpam-5375	467	12	n	n	PRON
ejpam-5375	467	13	2	2	NUM
ejpam-5375	467	14	−1	−1	NOUN
ejpam-5375	467	15	.	.	PUNCT
ejpam-5375	468	1	3.1	3.1	NUM
ejpam-5375	468	2	.	.	PUNCT
ejpam-5375	468	3	adjacency	adjacency	PROPN
ejpam-5375	468	4	matrix	matrix	NOUN
ejpam-5375	468	5	in	in	ADP
ejpam-5375	468	6	this	this	DET
ejpam-5375	468	7	part	part	NOUN
ejpam-5375	468	8	,	,	PUNCT
ejpam-5375	468	9	the	the	DET
ejpam-5375	468	10	goal	goal	NOUN
ejpam-5375	468	11	is	be	AUX
ejpam-5375	468	12	to	to	PART
ejpam-5375	468	13	provide	provide	VERB
ejpam-5375	468	14	the	the	DET
ejpam-5375	468	15	energy	energy	NOUN
ejpam-5375	468	16	formula	formula	NOUN
ejpam-5375	468	17	of	of	ADP
ejpam-5375	468	18	γzn	γzn	PROPN
ejpam-5375	468	19	associated	associate	VERB
ejpam-5375	468	20	with	with	ADP
ejpam-5375	468	21	the	the	DET
ejpam-5375	468	22	adjacency	adjacency	NOUN
ejpam-5375	468	23	matrix	matrix	NOUN
ejpam-5375	468	24	.	.	PUNCT
ejpam-5375	469	1	we	we	PRON
ejpam-5375	469	2	begin	begin	VERB
ejpam-5375	469	3	with	with	ADP
ejpam-5375	469	4	the	the	DET
ejpam-5375	469	5	case	case	NOUN
ejpam-5375	469	6	for	for	ADP
ejpam-5375	469	7	n	n	NUM
ejpam-5375	469	8	is	be	AUX
ejpam-5375	469	9	odd	odd	ADJ
ejpam-5375	469	10	.	.	PUNCT
ejpam-5375	470	1	theorem	theorem	ADJ
ejpam-5375	470	2	7	7	NUM
ejpam-5375	470	3	.	.	PUNCT
ejpam-5375	471	1	let	let	VERB
ejpam-5375	471	2	γzn	γzn	PROPN
ejpam-5375	471	3	be	be	AUX
ejpam-5375	471	4	the	the	DET
ejpam-5375	471	5	identity	identity	NOUN
ejpam-5375	471	6	graph	graph	NOUN
ejpam-5375	471	7	on	on	ADP
ejpam-5375	471	8	zn	zn	PROPN
ejpam-5375	471	9	.	.	PUNCT
ejpam-5375	472	1	the	the	DET
ejpam-5375	472	2	adjacency	adjacency	PROPN
ejpam-5375	472	3	energy	energy	NOUN
ejpam-5375	472	4	of	of	ADP
ejpam-5375	472	5	γzn	γzn	PROPN
ejpam-5375	472	6	for	for	ADP
ejpam-5375	472	7	odd	odd	ADJ
ejpam-5375	472	8	n	n	X
ejpam-5375	472	9	is	be	AUX
ejpam-5375	472	10	ea(γzn	ea(γzn	VERB
ejpam-5375	472	11	)	)	PUNCT
ejpam-5375	473	1	=	=	PUNCT
ejpam-5375	473	2	n−	n−	NOUN
ejpam-5375	473	3	2	2	NUM
ejpam-5375	473	4	+	+	CCONJ
ejpam-5375	473	5	√	√	ADV
ejpam-5375	474	1	4n−	4n−	NUM
ejpam-5375	474	2	3	3	NUM
ejpam-5375	474	3	.	.	PUNCT
ejpam-5375	474	4	proof	proof	NOUN
ejpam-5375	474	5	.	.	PUNCT
ejpam-5375	475	1	according	accord	VERB
ejpam-5375	475	2	to	to	ADP
ejpam-5375	475	3	theorems	theorems	PROPN
ejpam-5375	475	4	1	1	NUM
ejpam-5375	475	5	and	and	CCONJ
ejpam-5375	475	6	3	3	NUM
ejpam-5375	475	7	,	,	PUNCT
ejpam-5375	475	8	we	we	PRON
ejpam-5375	475	9	can	can	AUX
ejpam-5375	475	10	construct	construct	VERB
ejpam-5375	475	11	an	an	DET
ejpam-5375	475	12	n	n	NUM
ejpam-5375	475	13	×	×	NOUN
ejpam-5375	475	14	n	n	CCONJ
ejpam-5375	475	15	adjacency	adjacency	NOUN
ejpam-5375	475	16	matrix	matrix	NOUN
ejpam-5375	475	17	of	of	ADP
ejpam-5375	475	18	γzn	γzn	PROPN
ejpam-5375	475	19	as	as	SCONJ
ejpam-5375	475	20	follows	follow	VERB
ejpam-5375	475	21	:	:	PUNCT
ejpam-5375	475	22	a(γzn	a(γzn	X
ejpam-5375	475	23	)	)	PUNCT
ejpam-5375	475	24	=	=	SYM
ejpam-5375	475	25	0	0	NUM
ejpam-5375	475	26	1	1	NUM
ejpam-5375	475	27	2	2	NUM
ejpam-5375	475	28	.	.	PUNCT
ejpam-5375	475	29	.	.	PUNCT
ejpam-5375	475	30	.	.	PUNCT
ejpam-5375	476	1	n−	n−	NOUN
ejpam-5375	476	2	2	2	NUM
ejpam-5375	476	3	n−	n−	NOUN
ejpam-5375	476	4	1	1	NUM
ejpam-5375	476	5			NOUN
ejpam-5375	476	6	0	0	NUM
ejpam-5375	476	7	0	0	NUM
ejpam-5375	476	8	1	1	NUM
ejpam-5375	476	9	1	1	NUM
ejpam-5375	476	10	.	.	PUNCT
ejpam-5375	476	11	.	.	PUNCT
ejpam-5375	477	1	.	.	PUNCT
ejpam-5375	478	1	1	1	NUM
ejpam-5375	478	2	1	1	NUM
ejpam-5375	478	3	1	1	NUM
ejpam-5375	478	4	1	1	NUM
ejpam-5375	478	5	0	0	NUM
ejpam-5375	478	6	0	0	NUM
ejpam-5375	478	7	.	.	PUNCT
ejpam-5375	478	8	.	.	PUNCT
ejpam-5375	479	1	.	.	PUNCT
ejpam-5375	480	1	0	0	NUM
ejpam-5375	481	1	1	1	NUM
ejpam-5375	481	2	2	2	NUM
ejpam-5375	481	3	1	1	NUM
ejpam-5375	481	4	0	0	NUM
ejpam-5375	481	5	0	0	NUM
ejpam-5375	481	6	.	.	PUNCT
ejpam-5375	481	7	.	.	PUNCT
ejpam-5375	482	1	.	.	PUNCT
ejpam-5375	483	1	1	1	NUM
ejpam-5375	483	2	0	0	NUM
ejpam-5375	483	3	...	...	PUNCT
ejpam-5375	483	4	...	...	PUNCT
ejpam-5375	483	5	...	...	PUNCT
ejpam-5375	483	6	...	...	PUNCT
ejpam-5375	483	7	.	.	PUNCT
ejpam-5375	483	8	.	.	PUNCT
ejpam-5375	483	9	.	.	PUNCT
ejpam-5375	483	10	...	...	PUNCT
ejpam-5375	484	1	...	...	PUNCT
ejpam-5375	485	1	n−	n−	NOUN
ejpam-5375	485	2	2	2	NUM
ejpam-5375	485	3	1	1	NUM
ejpam-5375	485	4	0	0	NUM
ejpam-5375	485	5	1	1	NUM
ejpam-5375	485	6	.	.	PUNCT
ejpam-5375	485	7	.	.	PUNCT
ejpam-5375	485	8	.	.	PUNCT
ejpam-5375	486	1	0	0	NUM
ejpam-5375	486	2	0	0	NUM
ejpam-5375	487	1	n−	n−	NOUN
ejpam-5375	487	2	1	1	NUM
ejpam-5375	487	3	1	1	NUM
ejpam-5375	487	4	1	1	NUM
ejpam-5375	487	5	0	0	NUM
ejpam-5375	487	6	.	.	PUNCT
ejpam-5375	487	7	.	.	PUNCT
ejpam-5375	487	8	.	.	PUNCT
ejpam-5375	488	1	0	0	NUM
ejpam-5375	488	2	0	0	NUM
ejpam-5375	489	1	(	(	PUNCT
ejpam-5375	489	2	2	2	NUM
ejpam-5375	489	3	)	)	PUNCT
ejpam-5375	489	4	following	follow	VERB
ejpam-5375	489	5	the	the	DET
ejpam-5375	489	6	principle	principle	NOUN
ejpam-5375	489	7	of	of	ADP
ejpam-5375	489	8	theorem	theorem	NOUN
ejpam-5375	489	9	5	5	NUM
ejpam-5375	489	10	with	with	ADP
ejpam-5375	489	11	a	a	DET
ejpam-5375	489	12	=	=	SYM
ejpam-5375	489	13	b	b	NOUN
ejpam-5375	489	14	=	=	SYM
ejpam-5375	489	15	0	0	PROPN
ejpam-5375	489	16	and	and	CCONJ
ejpam-5375	489	17	c	c	NOUN
ejpam-5375	489	18	=	=	SYM
ejpam-5375	489	19	1	1	NUM
ejpam-5375	489	20	,	,	PUNCT
ejpam-5375	489	21	then	then	ADV
ejpam-5375	489	22	we	we	PRON
ejpam-5375	489	23	derive	derive	VERB
ejpam-5375	489	24	pa(γzn	pa(γzn	NOUN
ejpam-5375	489	25	)	)	PUNCT
ejpam-5375	489	26	(	(	PUNCT
ejpam-5375	489	27	λ	λ	X
ejpam-5375	489	28	)	)	PUNCT
ejpam-5375	489	29	=	=	SYM
ejpam-5375	489	30	(	(	PUNCT
ejpam-5375	489	31	λ2	λ2	PROPN
ejpam-5375	489	32	−	−	PROPN
ejpam-5375	489	33	λ−	λ−	PROPN
ejpam-5375	489	34	(	(	PUNCT
ejpam-5375	489	35	n−	n−	NOUN
ejpam-5375	489	36	1	1	NUM
ejpam-5375	489	37	)	)	PUNCT
ejpam-5375	489	38	)	)	PUNCT
ejpam-5375	490	1	(	(	PUNCT
ejpam-5375	490	2	λ−	λ−	PROPN
ejpam-5375	490	3	1	1	NUM
ejpam-5375	490	4	)	)	PUNCT
ejpam-5375	490	5	n−3	n−3	PROPN
ejpam-5375	490	6	2	2	NUM
ejpam-5375	490	7	(	(	PUNCT
ejpam-5375	490	8	λ+	λ+	NUM
ejpam-5375	490	9	1	1	X
ejpam-5375	490	10	)	)	PUNCT
ejpam-5375	490	11	n−1	n−1	PROPN
ejpam-5375	490	12	2	2	NUM
ejpam-5375	490	13	.	.	PUNCT
ejpam-5375	491	1	the	the	DET
ejpam-5375	491	2	roots	root	NOUN
ejpam-5375	491	3	of	of	ADP
ejpam-5375	491	4	pa(γzn	pa(γzn	ADJ
ejpam-5375	491	5	)	)	PUNCT
ejpam-5375	491	6	(	(	PUNCT
ejpam-5375	491	7	λ	λ	X
ejpam-5375	491	8	)	)	PUNCT
ejpam-5375	491	9	=	=	SYM
ejpam-5375	491	10	0	0	NUM
ejpam-5375	491	11	are	be	AUX
ejpam-5375	491	12	λ1	λ1	ADJ
ejpam-5375	491	13	=	=	SYM
ejpam-5375	491	14	1	1	NUM
ejpam-5375	491	15	of	of	ADP
ejpam-5375	491	16	multiplicity	multiplicity	NOUN
ejpam-5375	491	17	n−3	n−3	PROPN
ejpam-5375	491	18	2	2	NUM
ejpam-5375	491	19	,	,	PUNCT
ejpam-5375	491	20	λ2	λ2	NOUN
ejpam-5375	491	21	=	=	SYM
ejpam-5375	491	22	−1	−1	NOUN
ejpam-5375	491	23	of	of	ADP
ejpam-5375	491	24	multiplicity	multiplicity	NOUN
ejpam-5375	491	25	n−1	n−1	PROPN
ejpam-5375	491	26	2	2	NUM
ejpam-5375	491	27	,	,	PUNCT
ejpam-5375	491	28	and	and	CCONJ
ejpam-5375	491	29	λ3,4	λ3,4	NOUN
ejpam-5375	491	30	=	=	SYM
ejpam-5375	491	31	1	1	NUM
ejpam-5375	491	32	2	2	NUM
ejpam-5375	491	33	±	±	NUM
ejpam-5375	491	34	√	√	NOUN
ejpam-5375	491	35	4n−3	4n−3	NUM
ejpam-5375	491	36	2	2	NUM
ejpam-5375	491	37	of	of	ADP
ejpam-5375	491	38	multiplicity	multiplicity	NOUN
ejpam-5375	491	39	1	1	NUM
ejpam-5375	491	40	,	,	PUNCT
ejpam-5375	491	41	respectively	respectively	ADV
ejpam-5375	491	42	.	.	PUNCT
ejpam-5375	492	1	consequently	consequently	ADV
ejpam-5375	492	2	,	,	PUNCT
ejpam-5375	492	3	the	the	DET
ejpam-5375	492	4	spectrum	spectrum	NOUN
ejpam-5375	492	5	of	of	ADP
ejpam-5375	492	6	γzn	γzn	PROPN
ejpam-5375	492	7	is	be	AUX
ejpam-5375	492	8	speca(γzn	speca(γzn	ADJ
ejpam-5375	492	9	)	)	PUNCT
ejpam-5375	493	1	=	=	PRON
ejpam-5375	493	2	{	{	PUNCT
ejpam-5375	493	3	(	(	PUNCT
ejpam-5375	493	4	1	1	NUM
ejpam-5375	493	5	2	2	NUM
ejpam-5375	493	6	+	+	CCONJ
ejpam-5375	493	7	√	√	ADV
ejpam-5375	494	1	4n−	4n−	NUM
ejpam-5375	494	2	3	3	NUM
ejpam-5375	494	3	2	2	NUM
ejpam-5375	494	4	)	)	PUNCT
ejpam-5375	494	5	1	1	NUM
ejpam-5375	494	6	,	,	PUNCT
ejpam-5375	494	7	(	(	PUNCT
ejpam-5375	494	8	1	1	X
ejpam-5375	494	9	)	)	PUNCT
ejpam-5375	494	10	n−3	n−3	PROPN
ejpam-5375	494	11	2	2	NUM
ejpam-5375	494	12	,	,	PUNCT
ejpam-5375	494	13	(	(	PUNCT
ejpam-5375	494	14	−1	−1	NOUN
ejpam-5375	494	15	)	)	PUNCT
ejpam-5375	494	16	n−1	n−1	PROPN
ejpam-5375	494	17	2	2	NUM
ejpam-5375	494	18	,	,	PUNCT
ejpam-5375	494	19	(	(	PUNCT
ejpam-5375	494	20	1	1	NUM
ejpam-5375	494	21	2	2	NUM
ejpam-5375	494	22	−	−	NOUN
ejpam-5375	494	23	√	√	NOUN
ejpam-5375	495	1	4n−	4n−	NUM
ejpam-5375	495	2	3	3	NUM
ejpam-5375	495	3	2	2	NUM
ejpam-5375	495	4	)	)	PUNCT
ejpam-5375	495	5	1	1	NUM
ejpam-5375	495	6	}	}	PUNCT
ejpam-5375	495	7	.	.	PUNCT
ejpam-5375	496	1	it	it	PRON
ejpam-5375	496	2	is	be	AUX
ejpam-5375	496	3	clear	clear	ADJ
ejpam-5375	496	4	that	that	SCONJ
ejpam-5375	496	5	the	the	DET
ejpam-5375	496	6	spectral	spectral	ADJ
ejpam-5375	496	7	radius	radius	NOUN
ejpam-5375	496	8	of	of	ADP
ejpam-5375	496	9	γzn	γzn	PROPN
ejpam-5375	496	10	is	be	AUX
ejpam-5375	496	11	ρa(γzn	ρa(γzn	VERB
ejpam-5375	496	12	)	)	PUNCT
ejpam-5375	496	13	=	=	SYM
ejpam-5375	496	14	1	1	NUM
ejpam-5375	496	15	2	2	NUM
ejpam-5375	496	16	+	+	CCONJ
ejpam-5375	496	17	√	√	ADV
ejpam-5375	497	1	4n−	4n−	NUM
ejpam-5375	497	2	3	3	NUM
ejpam-5375	497	3	2	2	NUM
ejpam-5375	497	4	.	.	PUNCT
ejpam-5375	498	1	therefore	therefore	ADV
ejpam-5375	498	2	,	,	PUNCT
ejpam-5375	498	3	the	the	DET
ejpam-5375	498	4	adjacency	adjacency	PROPN
ejpam-5375	498	5	energy	energy	NOUN
ejpam-5375	498	6	of	of	ADP
ejpam-5375	498	7	γzn	γzn	PROPN
ejpam-5375	498	8	is	be	AUX
ejpam-5375	498	9	as	as	SCONJ
ejpam-5375	498	10	follows	follow	VERB
ejpam-5375	498	11	:	:	PUNCT
ejpam-5375	498	12	ea(γzn	ea(γzn	ADJ
ejpam-5375	498	13	)	)	PUNCT
ejpam-5375	499	1	=	=	PUNCT
ejpam-5375	499	2	(	(	PUNCT
ejpam-5375	499	3	n−	n−	NOUN
ejpam-5375	499	4	3	3	NUM
ejpam-5375	499	5	2	2	NUM
ejpam-5375	499	6	)	)	PUNCT
ejpam-5375	499	7	|1|+	|1|+	PUNCT
ejpam-5375	500	1	(	(	PUNCT
ejpam-5375	500	2	n−	n−	NOUN
ejpam-5375	500	3	1	1	NUM
ejpam-5375	500	4	2	2	NUM
ejpam-5375	500	5	)	)	PUNCT
ejpam-5375	500	6	|	|	ADV
ejpam-5375	500	7	−	−	PROPN
ejpam-5375	500	8	1|+	1|+	NUM
ejpam-5375	500	9	∣∣∣∣12	∣∣∣∣12	ADJ
ejpam-5375	500	10	±	±	NOUN
ejpam-5375	500	11	√	√	NOUN
ejpam-5375	501	1	4n−	4n−	NUM
ejpam-5375	501	2	3	3	NUM
ejpam-5375	501	3	2	2	NUM
ejpam-5375	501	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5375	501	5	=	=	SYM
ejpam-5375	501	6	n−	n−	NOUN
ejpam-5375	501	7	2	2	NUM
ejpam-5375	501	8	+	+	CCONJ
ejpam-5375	501	9	√	√	ADV
ejpam-5375	501	10	4n−	4n−	NUM
ejpam-5375	501	11	3	3	NUM
ejpam-5375	501	12	.	.	PUNCT
ejpam-5375	501	13	m.	m.	PROPN
ejpam-5375	501	14	u.	u.	PROPN
ejpam-5375	501	15	romdhini	romdhini	PROPN
ejpam-5375	501	16	et	et	PROPN
ejpam-5375	501	17	al	al	PROPN
ejpam-5375	501	18	.	.	PUNCT
ejpam-5375	501	19	/	/	SYM
ejpam-5375	501	20	eur	eur	PROPN
ejpam-5375	501	21	.	.	PUNCT
ejpam-5375	502	1	j.	j.	PROPN
ejpam-5375	502	2	pure	pure	PROPN
ejpam-5375	502	3	appl	appl	PROPN
ejpam-5375	502	4	.	.	PROPN
ejpam-5375	502	5	math	math	PROPN
ejpam-5375	502	6	,	,	PUNCT
ejpam-5375	502	7	17	17	NUM
ejpam-5375	502	8	(	(	PUNCT
ejpam-5375	502	9	4	4	NUM
ejpam-5375	502	10	)	)	PUNCT
ejpam-5375	502	11	(	(	PUNCT
ejpam-5375	502	12	2024	2024	NUM
ejpam-5375	502	13	)	)	PUNCT
ejpam-5375	502	14	,	,	PUNCT
ejpam-5375	502	15	2915	2915	NUM
ejpam-5375	502	16	-	-	SYM
ejpam-5375	502	17	2929	2929	NUM
ejpam-5375	502	18	2923	2923	NUM
ejpam-5375	502	19	theorem	theorem	VERB
ejpam-5375	502	20	8	8	NUM
ejpam-5375	502	21	.	.	PUNCT
ejpam-5375	503	1	let	let	VERB
ejpam-5375	503	2	γzn	γzn	PROPN
ejpam-5375	503	3	be	be	AUX
ejpam-5375	503	4	the	the	DET
ejpam-5375	503	5	identity	identity	NOUN
ejpam-5375	503	6	graph	graph	NOUN
ejpam-5375	503	7	on	on	ADP
ejpam-5375	503	8	zn	zn	PROPN
ejpam-5375	503	9	.	.	PUNCT
ejpam-5375	504	1	the	the	DET
ejpam-5375	504	2	characteristic	characteristic	ADJ
ejpam-5375	504	3	polynomial	polynomial	NOUN
ejpam-5375	504	4	of	of	ADP
ejpam-5375	504	5	a(γzn	a(γzn	PROPN
ejpam-5375	504	6	)	)	PUNCT
ejpam-5375	504	7	for	for	ADP
ejpam-5375	504	8	even	even	ADV
ejpam-5375	504	9	n	n	NUM
ejpam-5375	504	10	is	be	AUX
ejpam-5375	504	11	pa(γzn	pa(γzn	ADJ
ejpam-5375	504	12	)	)	PUNCT
ejpam-5375	504	13	(	(	PUNCT
ejpam-5375	504	14	λ	λ	X
ejpam-5375	504	15	)	)	PUNCT
ejpam-5375	504	16	=	=	SYM
ejpam-5375	505	1	(	(	PUNCT
ejpam-5375	505	2	λ3	λ3	PROPN
ejpam-5375	505	3	−	−	PROPN
ejpam-5375	505	4	λ2	λ2	PROPN
ejpam-5375	505	5	−	−	PROPN
ejpam-5375	506	1	(	(	PUNCT
ejpam-5375	506	2	n−	n−	NOUN
ejpam-5375	506	3	1)λ+	1)λ+	NUM
ejpam-5375	506	4	1	1	NUM
ejpam-5375	506	5	)	)	PUNCT
ejpam-5375	506	6	(	(	PUNCT
ejpam-5375	506	7	λ−	λ−	PROPN
ejpam-5375	506	8	1	1	NUM
ejpam-5375	506	9	)	)	PUNCT
ejpam-5375	506	10	n	n	PRON
ejpam-5375	506	11	2	2	NUM
ejpam-5375	506	12	−2(λ+	−2(λ+	NUM
ejpam-5375	506	13	1	1	NUM
ejpam-5375	506	14	)	)	PUNCT
ejpam-5375	506	15	n	n	PRON
ejpam-5375	506	16	2	2	NUM
ejpam-5375	506	17	−1	−1	NOUN
ejpam-5375	506	18	.	.	PUNCT
ejpam-5375	507	1	proof	proof	NOUN
ejpam-5375	507	2	.	.	PUNCT
ejpam-5375	508	1	according	accord	VERB
ejpam-5375	508	2	to	to	ADP
ejpam-5375	508	3	theorems	theorems	PROPN
ejpam-5375	508	4	2	2	NUM
ejpam-5375	508	5	and	and	CCONJ
ejpam-5375	508	6	4	4	NUM
ejpam-5375	508	7	,	,	PUNCT
ejpam-5375	508	8	we	we	PRON
ejpam-5375	508	9	can	can	AUX
ejpam-5375	508	10	construct	construct	VERB
ejpam-5375	508	11	an	an	DET
ejpam-5375	508	12	n	n	NUM
ejpam-5375	508	13	×	×	NOUN
ejpam-5375	508	14	n	n	CCONJ
ejpam-5375	508	15	adjacency	adjacency	NOUN
ejpam-5375	508	16	matrix	matrix	NOUN
ejpam-5375	508	17	of	of	ADP
ejpam-5375	508	18	γzn	γzn	PROPN
ejpam-5375	508	19	as	as	SCONJ
ejpam-5375	508	20	follows	follow	VERB
ejpam-5375	508	21	:	:	PUNCT
ejpam-5375	508	22	a(γzn	a(γzn	X
ejpam-5375	508	23	)	)	PUNCT
ejpam-5375	508	24	=	=	SYM
ejpam-5375	508	25	0	0	NUM
ejpam-5375	508	26	1	1	NUM
ejpam-5375	508	27	2	2	NUM
ejpam-5375	508	28	.	.	PUNCT
ejpam-5375	508	29	.	.	PUNCT
ejpam-5375	508	30	.	.	PUNCT
ejpam-5375	509	1	n	n	CCONJ
ejpam-5375	509	2	2	2	NUM
ejpam-5375	509	3	−	−	NUM
ejpam-5375	509	4	1	1	NUM
ejpam-5375	509	5	n	n	SYM
ejpam-5375	509	6	2	2	NUM
ejpam-5375	509	7	n	n	NUM
ejpam-5375	509	8	2	2	NUM
ejpam-5375	509	9	+	+	CCONJ
ejpam-5375	509	10	1	1	NUM
ejpam-5375	509	11	.	.	PUNCT
ejpam-5375	509	12	.	.	PUNCT
ejpam-5375	509	13	.	.	PUNCT
ejpam-5375	510	1	n−	n−	NOUN
ejpam-5375	510	2	2	2	NUM
ejpam-5375	510	3	n−	n−	NOUN
ejpam-5375	510	4	1	1	NUM
ejpam-5375	510	5			NOUN
ejpam-5375	510	6	0	0	NUM
ejpam-5375	510	7	0	0	NUM
ejpam-5375	510	8	1	1	NUM
ejpam-5375	510	9	1	1	NUM
ejpam-5375	510	10	.	.	PUNCT
ejpam-5375	510	11	.	.	PUNCT
ejpam-5375	511	1	.	.	PUNCT
ejpam-5375	512	1	1	1	NUM
ejpam-5375	512	2	1	1	NUM
ejpam-5375	512	3	1	1	NUM
ejpam-5375	512	4	.	.	PUNCT
ejpam-5375	512	5	.	.	PUNCT
ejpam-5375	512	6	.	.	PUNCT
ejpam-5375	513	1	1	1	NUM
ejpam-5375	513	2	1	1	NUM
ejpam-5375	513	3	1	1	NUM
ejpam-5375	513	4	1	1	NUM
ejpam-5375	513	5	0	0	NUM
ejpam-5375	513	6	0	0	NUM
ejpam-5375	513	7	.	.	PUNCT
ejpam-5375	513	8	.	.	PUNCT
ejpam-5375	514	1	.	.	PUNCT
ejpam-5375	515	1	0	0	NUM
ejpam-5375	516	1	0	0	NUM
ejpam-5375	516	2	0	0	NUM
ejpam-5375	516	3	.	.	PUNCT
ejpam-5375	516	4	.	.	PUNCT
ejpam-5375	517	1	.	.	PUNCT
ejpam-5375	518	1	0	0	NUM
ejpam-5375	519	1	1	1	NUM
ejpam-5375	519	2	2	2	NUM
ejpam-5375	519	3	1	1	NUM
ejpam-5375	519	4	0	0	NUM
ejpam-5375	519	5	0	0	NUM
ejpam-5375	519	6	.	.	PUNCT
ejpam-5375	519	7	.	.	PUNCT
ejpam-5375	520	1	.	.	PUNCT
ejpam-5375	521	1	0	0	NUM
ejpam-5375	522	1	0	0	NUM
ejpam-5375	522	2	0	0	NUM
ejpam-5375	522	3	.	.	PUNCT
ejpam-5375	522	4	.	.	PUNCT
ejpam-5375	522	5	.	.	PUNCT
ejpam-5375	523	1	1	1	NUM
ejpam-5375	523	2	0	0	NUM
ejpam-5375	523	3	...	...	PUNCT
ejpam-5375	523	4	...	...	PUNCT
ejpam-5375	523	5	...	...	PUNCT
ejpam-5375	523	6	...	...	PUNCT
ejpam-5375	523	7	.	.	PUNCT
ejpam-5375	523	8	.	.	PUNCT
ejpam-5375	523	9	.	.	PUNCT
ejpam-5375	523	10	...	...	PUNCT
ejpam-5375	523	11	...	...	PUNCT
ejpam-5375	523	12	...	...	PUNCT
ejpam-5375	523	13	...	...	PUNCT
ejpam-5375	523	14	...	...	PUNCT
ejpam-5375	523	15	...	...	PUNCT
ejpam-5375	524	1	n	n	X
ejpam-5375	524	2	2	2	NUM
ejpam-5375	524	3	−	−	NOUN
ejpam-5375	524	4	1	1	NUM
ejpam-5375	524	5	1	1	NUM
ejpam-5375	524	6	0	0	NUM
ejpam-5375	524	7	0	0	NUM
ejpam-5375	524	8	.	.	PUNCT
ejpam-5375	524	9	.	.	PUNCT
ejpam-5375	524	10	.	.	PUNCT
ejpam-5375	525	1	0	0	NUM
ejpam-5375	525	2	0	0	NUM
ejpam-5375	525	3	1	1	NUM
ejpam-5375	525	4	.	.	PUNCT
ejpam-5375	525	5	.	.	PUNCT
ejpam-5375	525	6	.	.	PUNCT
ejpam-5375	526	1	0	0	NUM
ejpam-5375	526	2	0	0	NUM
ejpam-5375	527	1	n	n	CCONJ
ejpam-5375	527	2	2	2	NUM
ejpam-5375	527	3	1	1	NUM
ejpam-5375	527	4	0	0	NUM
ejpam-5375	527	5	0	0	NUM
ejpam-5375	527	6	.	.	PUNCT
ejpam-5375	527	7	.	.	PUNCT
ejpam-5375	528	1	.	.	PUNCT
ejpam-5375	529	1	0	0	NUM
ejpam-5375	530	1	0	0	NUM
ejpam-5375	530	2	0	0	NUM
ejpam-5375	530	3	.	.	PUNCT
ejpam-5375	530	4	.	.	PUNCT
ejpam-5375	531	1	.	.	PUNCT
ejpam-5375	532	1	0	0	NUM
ejpam-5375	532	2	0	0	NUM
ejpam-5375	533	1	n	n	NUM
ejpam-5375	533	2	2	2	NUM
ejpam-5375	533	3	+	+	CCONJ
ejpam-5375	533	4	1	1	NUM
ejpam-5375	533	5	1	1	NUM
ejpam-5375	533	6	0	0	NUM
ejpam-5375	533	7	0	0	NUM
ejpam-5375	533	8	.	.	PUNCT
ejpam-5375	533	9	.	.	PUNCT
ejpam-5375	533	10	.	.	PUNCT
ejpam-5375	534	1	1	1	NUM
ejpam-5375	534	2	0	0	NUM
ejpam-5375	534	3	0	0	NUM
ejpam-5375	534	4	.	.	PUNCT
ejpam-5375	534	5	.	.	PUNCT
ejpam-5375	534	6	.	.	PUNCT
ejpam-5375	535	1	0	0	NUM
ejpam-5375	535	2	0	0	NUM
ejpam-5375	535	3	...	...	PUNCT
ejpam-5375	535	4	...	...	PUNCT
ejpam-5375	535	5	...	...	PUNCT
ejpam-5375	535	6	...	...	PUNCT
ejpam-5375	535	7	.	.	PUNCT
ejpam-5375	535	8	.	.	PUNCT
ejpam-5375	535	9	.	.	PUNCT
ejpam-5375	536	1	...	...	PUNCT
ejpam-5375	536	2	...	...	PUNCT
ejpam-5375	537	1	...	...	PUNCT
ejpam-5375	537	2	...	...	PUNCT
ejpam-5375	537	3	...	...	PUNCT
ejpam-5375	537	4	...	...	PUNCT
ejpam-5375	538	1	n−	n−	NOUN
ejpam-5375	538	2	2	2	NUM
ejpam-5375	538	3	1	1	NUM
ejpam-5375	538	4	0	0	NUM
ejpam-5375	538	5	1	1	NUM
ejpam-5375	538	6	.	.	PUNCT
ejpam-5375	538	7	.	.	PUNCT
ejpam-5375	538	8	.	.	PUNCT
ejpam-5375	539	1	0	0	NUM
ejpam-5375	540	1	0	0	NUM
ejpam-5375	540	2	0	0	NUM
ejpam-5375	540	3	.	.	PUNCT
ejpam-5375	540	4	.	.	PUNCT
ejpam-5375	541	1	.	.	PUNCT
ejpam-5375	542	1	0	0	NUM
ejpam-5375	542	2	0	0	NUM
ejpam-5375	543	1	n−	n−	NOUN
ejpam-5375	543	2	1	1	NUM
ejpam-5375	543	3	1	1	NUM
ejpam-5375	543	4	1	1	NUM
ejpam-5375	543	5	0	0	NUM
ejpam-5375	543	6	.	.	PUNCT
ejpam-5375	543	7	.	.	PUNCT
ejpam-5375	543	8	.	.	PUNCT
ejpam-5375	544	1	0	0	NUM
ejpam-5375	545	1	0	0	NUM
ejpam-5375	545	2	0	0	NUM
ejpam-5375	545	3	.	.	PUNCT
ejpam-5375	545	4	.	.	PUNCT
ejpam-5375	545	5	.	.	PUNCT
ejpam-5375	546	1	0	0	NUM
ejpam-5375	546	2	0	0	NUM
ejpam-5375	546	3	.	.	PUNCT
ejpam-5375	547	1	(	(	PUNCT
ejpam-5375	547	2	3	3	X
ejpam-5375	547	3	)	)	PUNCT
ejpam-5375	547	4	according	accord	VERB
ejpam-5375	547	5	to	to	ADP
ejpam-5375	547	6	theorem	theorem	NOUN
ejpam-5375	547	7	6	6	NUM
ejpam-5375	547	8	with	with	ADP
ejpam-5375	547	9	a	a	DET
ejpam-5375	547	10	=	=	SYM
ejpam-5375	547	11	b	b	NOUN
ejpam-5375	547	12	=	=	SYM
ejpam-5375	547	13	c	c	NOUN
ejpam-5375	547	14	=	=	SYM
ejpam-5375	547	15	0	0	PROPN
ejpam-5375	547	16	,	,	PUNCT
ejpam-5375	547	17	d	d	NOUN
ejpam-5375	547	18	=	=	SYM
ejpam-5375	547	19	1	1	NUM
ejpam-5375	547	20	,	,	PUNCT
ejpam-5375	547	21	consequently	consequently	ADV
ejpam-5375	547	22	,	,	PUNCT
ejpam-5375	547	23	we	we	PRON
ejpam-5375	547	24	derive	derive	VERB
ejpam-5375	547	25	the	the	DET
ejpam-5375	547	26	following	follow	VERB
ejpam-5375	547	27	formula	formula	NOUN
ejpam-5375	547	28	:	:	PUNCT
ejpam-5375	547	29	pa(γzn	pa(γzn	ADJ
ejpam-5375	547	30	)	)	PUNCT
ejpam-5375	547	31	(	(	PUNCT
ejpam-5375	547	32	λ	λ	X
ejpam-5375	547	33	)	)	PUNCT
ejpam-5375	547	34	=	=	SYM
ejpam-5375	547	35	(	(	PUNCT
ejpam-5375	547	36	λ3	λ3	PROPN
ejpam-5375	547	37	−	−	PROPN
ejpam-5375	547	38	λ2	λ2	PROPN
ejpam-5375	547	39	−	−	PROPN
ejpam-5375	547	40	(	(	PUNCT
ejpam-5375	547	41	n−	n−	NOUN
ejpam-5375	547	42	1)λ+	1)λ+	NUM
ejpam-5375	547	43	1	1	NUM
ejpam-5375	547	44	)	)	PUNCT
ejpam-5375	547	45	(	(	PUNCT
ejpam-5375	547	46	λ−	λ−	PROPN
ejpam-5375	547	47	1	1	NUM
ejpam-5375	547	48	)	)	PUNCT
ejpam-5375	547	49	n	n	PRON
ejpam-5375	547	50	2	2	NUM
ejpam-5375	547	51	−2(λ+	−2(λ+	NUM
ejpam-5375	547	52	1	1	NUM
ejpam-5375	547	53	)	)	PUNCT
ejpam-5375	547	54	n	n	PRON
ejpam-5375	547	55	2	2	NUM
ejpam-5375	547	56	−1	−1	NOUN
ejpam-5375	547	57	.	.	PUNCT
ejpam-5375	548	1	3.2	3.2	NUM
ejpam-5375	548	2	.	.	PUNCT
ejpam-5375	549	1	laplacian	laplacian	ADJ
ejpam-5375	549	2	matrix	matrix	NOUN
ejpam-5375	549	3	this	this	DET
ejpam-5375	549	4	part	part	NOUN
ejpam-5375	549	5	focuses	focus	VERB
ejpam-5375	549	6	on	on	ADP
ejpam-5375	549	7	the	the	DET
ejpam-5375	549	8	laplacian	laplacian	ADJ
ejpam-5375	549	9	matrix	matrix	NOUN
ejpam-5375	549	10	of	of	ADP
ejpam-5375	549	11	γzn	γzn	PROPN
ejpam-5375	549	12	,	,	PUNCT
ejpam-5375	549	13	for	for	ADP
ejpam-5375	549	14	odd	odd	ADJ
ejpam-5375	549	15	and	and	CCONJ
ejpam-5375	549	16	even	even	ADV
ejpam-5375	549	17	n	n	CCONJ
ejpam-5375	549	18	,	,	PUNCT
ejpam-5375	549	19	followed	follow	VERB
ejpam-5375	549	20	by	by	ADP
ejpam-5375	549	21	calculating	calculate	VERB
ejpam-5375	549	22	the	the	DET
ejpam-5375	549	23	energy	energy	NOUN
ejpam-5375	549	24	.	.	PUNCT
ejpam-5375	550	1	theorem	theorem	NOUN
ejpam-5375	550	2	9	9	NUM
ejpam-5375	550	3	.	.	PUNCT
ejpam-5375	551	1	let	let	VERB
ejpam-5375	551	2	γzn	γzn	PROPN
ejpam-5375	551	3	be	be	AUX
ejpam-5375	551	4	the	the	DET
ejpam-5375	551	5	identity	identity	NOUN
ejpam-5375	551	6	graph	graph	NOUN
ejpam-5375	551	7	on	on	ADP
ejpam-5375	551	8	zn	zn	PROPN
ejpam-5375	551	9	.	.	PUNCT
ejpam-5375	552	1	the	the	DET
ejpam-5375	552	2	laplacian	laplacian	ADJ
ejpam-5375	552	3	energy	energy	NOUN
ejpam-5375	552	4	of	of	ADP
ejpam-5375	552	5	γzn	γzn	PROPN
ejpam-5375	552	6	for	for	ADP
ejpam-5375	552	7	odd	odd	ADJ
ejpam-5375	552	8	n	n	NOUN
ejpam-5375	552	9	is	be	AUX
ejpam-5375	552	10	el(γzn	el(γzn	ADJ
ejpam-5375	552	11	)	)	PUNCT
ejpam-5375	553	1	=	=	PUNCT
ejpam-5375	553	2	3(n−	3(n−	NUM
ejpam-5375	553	3	1	1	NUM
ejpam-5375	553	4	)	)	PUNCT
ejpam-5375	553	5	.	.	PUNCT
ejpam-5375	554	1	proof	proof	NOUN
ejpam-5375	554	2	.	.	PUNCT
ejpam-5375	555	1	based	base	VERB
ejpam-5375	555	2	on	on	ADP
ejpam-5375	555	3	theorem	theorem	NOUN
ejpam-5375	555	4	3	3	NUM
ejpam-5375	555	5	,	,	PUNCT
ejpam-5375	555	6	we	we	PRON
ejpam-5375	555	7	have	have	VERB
ejpam-5375	555	8	n	n	NUM
ejpam-5375	555	9	×	×	NOUN
ejpam-5375	555	10	n	n	CCONJ
ejpam-5375	555	11	degree	degree	NOUN
ejpam-5375	555	12	matrix	matrix	NOUN
ejpam-5375	555	13	of	of	ADP
ejpam-5375	555	14	γzn	γzn	PROPN
ejpam-5375	555	15	as	as	ADP
ejpam-5375	555	16	diag(n	diag(n	NOUN
ejpam-5375	555	17	−	−	PROPN
ejpam-5375	555	18	1	1	NUM
ejpam-5375	555	19	,	,	PUNCT
ejpam-5375	555	20	2	2	NUM
ejpam-5375	555	21	,	,	PUNCT
ejpam-5375	555	22	2	2	NUM
ejpam-5375	555	23	,	,	PUNCT
ejpam-5375	555	24	...	...	PUNCT
ejpam-5375	555	25	,	,	PUNCT
ejpam-5375	555	26	2	2	NUM
ejpam-5375	555	27	,	,	PUNCT
ejpam-5375	555	28	2	2	NUM
ejpam-5375	555	29	)	)	PUNCT
ejpam-5375	555	30	.	.	PUNCT
ejpam-5375	556	1	according	accord	VERB
ejpam-5375	556	2	to	to	ADP
ejpam-5375	556	3	definition	definition	NOUN
ejpam-5375	556	4	4	4	NUM
ejpam-5375	556	5	and	and	CCONJ
ejpam-5375	556	6	equation	equation	NOUN
ejpam-5375	556	7	2	2	NUM
ejpam-5375	556	8	,	,	PUNCT
ejpam-5375	556	9	we	we	PRON
ejpam-5375	556	10	can	can	AUX
ejpam-5375	556	11	construct	construct	VERB
ejpam-5375	556	12	an	an	DET
ejpam-5375	556	13	n	n	NUM
ejpam-5375	556	14	×	×	NOUN
ejpam-5375	556	15	n	n	CCONJ
ejpam-5375	556	16	laplacian	laplacian	ADJ
ejpam-5375	556	17	matrix	matrix	NOUN
ejpam-5375	556	18	of	of	ADP
ejpam-5375	556	19	γzn	γzn	PROPN
ejpam-5375	556	20	as	as	SCONJ
ejpam-5375	556	21	follows	follow	VERB
ejpam-5375	556	22	:	:	PUNCT
ejpam-5375	556	23	l(γzn	l(γzn	VERB
ejpam-5375	556	24	)	)	PUNCT
ejpam-5375	556	25	=	=	SYM
ejpam-5375	556	26	d(γzn)−a(γzn	d(γzn)−a(γzn	PROPN
ejpam-5375	556	27	)	)	PUNCT
ejpam-5375	556	28	(	(	PUNCT
ejpam-5375	556	29	4	4	X
ejpam-5375	556	30	)	)	PUNCT
ejpam-5375	556	31	m.	m.	NOUN
ejpam-5375	556	32	u.	u.	PROPN
ejpam-5375	556	33	romdhini	romdhini	PROPN
ejpam-5375	556	34	et	et	PROPN
ejpam-5375	556	35	al	al	PROPN
ejpam-5375	556	36	.	.	PUNCT
ejpam-5375	556	37	/	/	SYM
ejpam-5375	556	38	eur	eur	PROPN
ejpam-5375	556	39	.	.	PUNCT
ejpam-5375	557	1	j.	j.	PROPN
ejpam-5375	557	2	pure	pure	PROPN
ejpam-5375	557	3	appl	appl	PROPN
ejpam-5375	557	4	.	.	PROPN
ejpam-5375	557	5	math	math	PROPN
ejpam-5375	557	6	,	,	PUNCT
ejpam-5375	557	7	17	17	NUM
ejpam-5375	557	8	(	(	PUNCT
ejpam-5375	557	9	4	4	NUM
ejpam-5375	557	10	)	)	PUNCT
ejpam-5375	557	11	(	(	PUNCT
ejpam-5375	557	12	2024	2024	NUM
ejpam-5375	557	13	)	)	PUNCT
ejpam-5375	557	14	,	,	PUNCT
ejpam-5375	557	15	2915	2915	NUM
ejpam-5375	557	16	-	-	SYM
ejpam-5375	557	17	2929	2929	NUM
ejpam-5375	557	18	2924	2924	NUM
ejpam-5375	557	19	=	=	SYM
ejpam-5375	557	20	0	0	NUM
ejpam-5375	557	21	1	1	NUM
ejpam-5375	557	22	2	2	NUM
ejpam-5375	557	23	.	.	PUNCT
ejpam-5375	557	24	.	.	PUNCT
ejpam-5375	557	25	.	.	PUNCT
ejpam-5375	558	1	n−	n−	NOUN
ejpam-5375	558	2	2	2	NUM
ejpam-5375	558	3	n−	n−	NOUN
ejpam-5375	558	4	1	1	NUM
ejpam-5375	558	5			NOUN
ejpam-5375	558	6	0	0	NUM
ejpam-5375	558	7	n−	n−	NOUN
ejpam-5375	558	8	1	1	NUM
ejpam-5375	558	9	−1	−1	NOUN
ejpam-5375	558	10	−1	−1	NOUN
ejpam-5375	558	11	.	.	PUNCT
ejpam-5375	558	12	.	.	PUNCT
ejpam-5375	558	13	.	.	PUNCT
ejpam-5375	559	1	−1	−1	NOUN
ejpam-5375	559	2	−1	−1	NOUN
ejpam-5375	559	3	1	1	NUM
ejpam-5375	559	4	−1	−1	NOUN
ejpam-5375	559	5	2	2	NUM
ejpam-5375	559	6	0	0	NUM
ejpam-5375	559	7	.	.	PUNCT
ejpam-5375	559	8	.	.	PUNCT
ejpam-5375	560	1	.	.	PUNCT
ejpam-5375	561	1	0	0	NUM
ejpam-5375	562	1	−1	−1	NOUN
ejpam-5375	562	2	2	2	NUM
ejpam-5375	562	3	−1	−1	NOUN
ejpam-5375	562	4	0	0	NUM
ejpam-5375	562	5	2	2	NUM
ejpam-5375	562	6	.	.	PUNCT
ejpam-5375	562	7	.	.	PUNCT
ejpam-5375	562	8	.	.	PUNCT
ejpam-5375	563	1	−1	−1	NOUN
ejpam-5375	563	2	0	0	NUM
ejpam-5375	563	3	...	...	PUNCT
ejpam-5375	563	4	...	...	PUNCT
ejpam-5375	563	5	...	...	PUNCT
ejpam-5375	563	6	...	...	PUNCT
ejpam-5375	563	7	.	.	PUNCT
ejpam-5375	563	8	.	.	PUNCT
ejpam-5375	563	9	.	.	PUNCT
ejpam-5375	564	1	...	...	PUNCT
ejpam-5375	564	2	...	...	PUNCT
ejpam-5375	565	1	n−	n−	NOUN
ejpam-5375	565	2	2	2	NUM
ejpam-5375	565	3	−1	−1	NOUN
ejpam-5375	565	4	0	0	NUM
ejpam-5375	565	5	−1	−1	NOUN
ejpam-5375	565	6	.	.	PUNCT
ejpam-5375	565	7	.	.	PUNCT
ejpam-5375	566	1	.	.	PUNCT
ejpam-5375	567	1	2	2	NUM
ejpam-5375	567	2	0	0	NUM
ejpam-5375	567	3	n−	n−	NOUN
ejpam-5375	567	4	1	1	NUM
ejpam-5375	567	5	−1	−1	NOUN
ejpam-5375	567	6	−1	−1	NOUN
ejpam-5375	567	7	0	0	NUM
ejpam-5375	567	8	.	.	PUNCT
ejpam-5375	567	9	.	.	PUNCT
ejpam-5375	567	10	.	.	PUNCT
ejpam-5375	568	1	0	0	NUM
ejpam-5375	568	2	2	2	NUM
ejpam-5375	568	3	.	.	PUNCT
ejpam-5375	569	1	(	(	PUNCT
ejpam-5375	569	2	5	5	NUM
ejpam-5375	569	3	)	)	PUNCT
ejpam-5375	569	4	according	accord	VERB
ejpam-5375	569	5	to	to	ADP
ejpam-5375	569	6	theorem	theorem	NOUN
ejpam-5375	569	7	5	5	NUM
ejpam-5375	569	8	with	with	ADP
ejpam-5375	569	9	a	a	DET
ejpam-5375	569	10	=	=	ADJ
ejpam-5375	569	11	n−	n−	NOUN
ejpam-5375	569	12	1	1	NUM
ejpam-5375	569	13	,	,	PUNCT
ejpam-5375	569	14	b	b	NOUN
ejpam-5375	569	15	=	=	SYM
ejpam-5375	569	16	2	2	NUM
ejpam-5375	569	17	,	,	PUNCT
ejpam-5375	569	18	and	and	CCONJ
ejpam-5375	569	19	c	c	X
ejpam-5375	569	20	=	=	SYM
ejpam-5375	569	21	−1	−1	NOUN
ejpam-5375	569	22	,	,	PUNCT
ejpam-5375	569	23	then	then	ADV
ejpam-5375	569	24	we	we	PRON
ejpam-5375	569	25	obtain	obtain	VERB
ejpam-5375	569	26	pl(γzn	pl(γzn	NOUN
ejpam-5375	569	27	)	)	PUNCT
ejpam-5375	569	28	(	(	PUNCT
ejpam-5375	569	29	λ	λ	X
ejpam-5375	569	30	)	)	PUNCT
ejpam-5375	569	31	=	=	SYM
ejpam-5375	569	32	λ(λ−	λ(λ−	PROPN
ejpam-5375	569	33	n)(λ−	n)(λ−	ADJ
ejpam-5375	569	34	1	1	X
ejpam-5375	569	35	)	)	PUNCT
ejpam-5375	569	36	n−3	n−3	PROPN
ejpam-5375	569	37	2	2	NUM
ejpam-5375	569	38	(	(	PUNCT
ejpam-5375	569	39	λ−	λ−	PROPN
ejpam-5375	569	40	3	3	NUM
ejpam-5375	569	41	)	)	PUNCT
ejpam-5375	569	42	n−1	n−1	PROPN
ejpam-5375	569	43	2	2	NUM
ejpam-5375	569	44	.	.	PUNCT
ejpam-5375	570	1	the	the	DET
ejpam-5375	570	2	roots	root	NOUN
ejpam-5375	570	3	of	of	ADP
ejpam-5375	570	4	pl(γzn	pl(γzn	NOUN
ejpam-5375	570	5	)	)	PUNCT
ejpam-5375	570	6	(	(	PUNCT
ejpam-5375	570	7	λ	λ	X
ejpam-5375	570	8	)	)	PUNCT
ejpam-5375	570	9	=	=	SYM
ejpam-5375	570	10	0	0	NUM
ejpam-5375	570	11	are	be	AUX
ejpam-5375	570	12	λ1	λ1	ADJ
ejpam-5375	570	13	=	=	SYM
ejpam-5375	570	14	0	0	NUM
ejpam-5375	570	15	of	of	ADP
ejpam-5375	570	16	multiplicity	multiplicity	NOUN
ejpam-5375	570	17	1	1	NUM
ejpam-5375	570	18	,	,	PUNCT
ejpam-5375	570	19	λ2	λ2	NOUN
ejpam-5375	570	20	=	=	SYM
ejpam-5375	570	21	n	n	NOUN
ejpam-5375	570	22	of	of	ADP
ejpam-5375	570	23	multiplicity	multiplicity	NOUN
ejpam-5375	570	24	1	1	NUM
ejpam-5375	570	25	,	,	PUNCT
ejpam-5375	570	26	λ3	λ3	PROPN
ejpam-5375	570	27	=	=	NOUN
ejpam-5375	570	28	1	1	NUM
ejpam-5375	570	29	of	of	ADP
ejpam-5375	570	30	multiplicity	multiplicity	NOUN
ejpam-5375	570	31	n−3	n−3	PROPN
ejpam-5375	570	32	2	2	NUM
ejpam-5375	570	33	,	,	PUNCT
ejpam-5375	570	34	and	and	CCONJ
ejpam-5375	570	35	λ4	λ4	PROPN
ejpam-5375	570	36	=	=	SYM
ejpam-5375	570	37	3	3	NUM
ejpam-5375	570	38	of	of	ADP
ejpam-5375	570	39	multiplicity	multiplicity	NOUN
ejpam-5375	570	40	n−1	n−1	PROPN
ejpam-5375	570	41	2	2	NUM
ejpam-5375	570	42	.	.	PUNCT
ejpam-5375	571	1	consequently	consequently	ADV
ejpam-5375	571	2	,	,	PUNCT
ejpam-5375	571	3	the	the	DET
ejpam-5375	571	4	spectrum	spectrum	NOUN
ejpam-5375	571	5	of	of	ADP
ejpam-5375	571	6	γzn	γzn	PROPN
ejpam-5375	571	7	is	be	AUX
ejpam-5375	571	8	specl(γzn	specl(γzn	ADJ
ejpam-5375	571	9	)	)	PUNCT
ejpam-5375	572	1	=	=	PRON
ejpam-5375	572	2	{	{	PUNCT
ejpam-5375	572	3	(	(	PUNCT
ejpam-5375	572	4	n)1	n)1	NOUN
ejpam-5375	572	5	,	,	PUNCT
ejpam-5375	572	6	(	(	PUNCT
ejpam-5375	572	7	1	1	X
ejpam-5375	572	8	)	)	PUNCT
ejpam-5375	572	9	n−3	n−3	PROPN
ejpam-5375	572	10	2	2	NUM
ejpam-5375	572	11	,	,	PUNCT
ejpam-5375	572	12	(	(	PUNCT
ejpam-5375	572	13	3	3	X
ejpam-5375	572	14	)	)	PUNCT
ejpam-5375	572	15	n−1	n−1	PROPN
ejpam-5375	572	16	2	2	NUM
ejpam-5375	572	17	,	,	PUNCT
ejpam-5375	572	18	(	(	PUNCT
ejpam-5375	572	19	0)1	0)1	PROPN
ejpam-5375	572	20	}	}	PUNCT
ejpam-5375	572	21	.	.	PUNCT
ejpam-5375	573	1	it	it	PRON
ejpam-5375	573	2	is	be	AUX
ejpam-5375	573	3	clear	clear	ADJ
ejpam-5375	573	4	that	that	SCONJ
ejpam-5375	573	5	the	the	DET
ejpam-5375	573	6	spectral	spectral	ADJ
ejpam-5375	573	7	radius	radius	NOUN
ejpam-5375	573	8	of	of	ADP
ejpam-5375	573	9	γzn	γzn	PROPN
ejpam-5375	573	10	is	be	AUX
ejpam-5375	573	11	ρl(γzn	ρl(γzn	ADJ
ejpam-5375	573	12	)	)	PUNCT
ejpam-5375	574	1	=	=	SYM
ejpam-5375	574	2	n.	n.	NOUN
ejpam-5375	574	3	therefore	therefore	ADV
ejpam-5375	574	4	,	,	PUNCT
ejpam-5375	574	5	the	the	DET
ejpam-5375	574	6	laplacian	laplacian	ADJ
ejpam-5375	574	7	energy	energy	NOUN
ejpam-5375	574	8	of	of	ADP
ejpam-5375	574	9	γzn	γzn	PROPN
ejpam-5375	574	10	is	be	AUX
ejpam-5375	574	11	as	as	SCONJ
ejpam-5375	574	12	follows	follow	VERB
ejpam-5375	574	13	:	:	PUNCT
ejpam-5375	574	14	el(γzn	el(γzn	X
ejpam-5375	574	15	)	)	PUNCT
ejpam-5375	575	1	=	=	SYM
ejpam-5375	575	2	(	(	PUNCT
ejpam-5375	575	3	1	1	X
ejpam-5375	575	4	)	)	PUNCT
ejpam-5375	575	5	|n|+	|n|+	PROPN
ejpam-5375	575	6	(	(	PUNCT
ejpam-5375	575	7	n−	n−	NOUN
ejpam-5375	575	8	1	1	NUM
ejpam-5375	575	9	2	2	NUM
ejpam-5375	575	10	)	)	PUNCT
ejpam-5375	576	1	|3|+	|3|+	PROPN
ejpam-5375	576	2	(	(	PUNCT
ejpam-5375	576	3	n−	n−	NOUN
ejpam-5375	576	4	3	3	NUM
ejpam-5375	576	5	2	2	NUM
ejpam-5375	576	6	)	)	PUNCT
ejpam-5375	576	7	|1|+	|1|+	PUNCT
ejpam-5375	576	8	(	(	PUNCT
ejpam-5375	576	9	1	1	X
ejpam-5375	576	10	)	)	PUNCT
ejpam-5375	576	11	|0|	|0|	NOUN
ejpam-5375	577	1	=	=	PUNCT
ejpam-5375	577	2	3(n−	3(n−	NUM
ejpam-5375	577	3	1	1	NUM
ejpam-5375	577	4	)	)	PUNCT
ejpam-5375	577	5	.	.	PUNCT
ejpam-5375	578	1	theorem	theorem	ADJ
ejpam-5375	578	2	10	10	NUM
ejpam-5375	578	3	.	.	PUNCT
ejpam-5375	579	1	let	let	VERB
ejpam-5375	579	2	γzn	γzn	PROPN
ejpam-5375	579	3	be	be	AUX
ejpam-5375	579	4	the	the	DET
ejpam-5375	579	5	identity	identity	NOUN
ejpam-5375	579	6	graph	graph	NOUN
ejpam-5375	579	7	on	on	ADP
ejpam-5375	579	8	zn	zn	PROPN
ejpam-5375	579	9	.	.	PUNCT
ejpam-5375	580	1	the	the	DET
ejpam-5375	580	2	laplacian	laplacian	ADJ
ejpam-5375	580	3	energy	energy	NOUN
ejpam-5375	580	4	of	of	ADP
ejpam-5375	580	5	γzn	γzn	PROPN
ejpam-5375	580	6	for	for	ADP
ejpam-5375	580	7	even	even	ADV
ejpam-5375	580	8	n	n	NUM
ejpam-5375	580	9	is	be	AUX
ejpam-5375	580	10	el(γzn	el(γzn	ADJ
ejpam-5375	580	11	)	)	PUNCT
ejpam-5375	581	1	=	=	SYM
ejpam-5375	582	1	3n−	3n−	NUM
ejpam-5375	582	2	4	4	NUM
ejpam-5375	582	3	.	.	PUNCT
ejpam-5375	583	1	proof	proof	NOUN
ejpam-5375	583	2	.	.	PUNCT
ejpam-5375	584	1	from	from	ADP
ejpam-5375	584	2	theorem	theorem	NOUN
ejpam-5375	584	3	2	2	NUM
ejpam-5375	584	4	,	,	PUNCT
ejpam-5375	584	5	we	we	PRON
ejpam-5375	584	6	have	have	VERB
ejpam-5375	584	7	the	the	DET
ejpam-5375	584	8	degree	degree	NOUN
ejpam-5375	584	9	of	of	ADP
ejpam-5375	584	10	every	every	DET
ejpam-5375	584	11	vertex	vertex	NOUN
ejpam-5375	584	12	in	in	ADP
ejpam-5375	584	13	γzn	γzn	PROPN
ejpam-5375	584	14	for	for	ADP
ejpam-5375	584	15	even	even	ADV
ejpam-5375	584	16	n.	n.	PROPN
ejpam-5375	584	17	then	then	ADV
ejpam-5375	584	18	the	the	DET
ejpam-5375	584	19	diagonal	diagonal	ADJ
ejpam-5375	584	20	matrix	matrix	NOUN
ejpam-5375	584	21	of	of	ADP
ejpam-5375	584	22	γzn	γzn	PROPN
ejpam-5375	584	23	is	be	AUX
ejpam-5375	584	24	d(γzn	d(γzn	VERB
ejpam-5375	584	25	)	)	PUNCT
ejpam-5375	585	1	=	=	SYM
ejpam-5375	585	2	diag(n	diag(n	NOUN
ejpam-5375	585	3	−	−	NOUN
ejpam-5375	585	4	1	1	NUM
ejpam-5375	585	5	,	,	PUNCT
ejpam-5375	585	6	2	2	NUM
ejpam-5375	585	7	,	,	PUNCT
ejpam-5375	585	8	2	2	NUM
ejpam-5375	585	9	,	,	PUNCT
ejpam-5375	585	10	...	...	PUNCT
ejpam-5375	585	11	,	,	PUNCT
ejpam-5375	585	12	2	2	NUM
ejpam-5375	585	13	,	,	PUNCT
ejpam-5375	585	14	1	1	NUM
ejpam-5375	585	15	,	,	PUNCT
ejpam-5375	585	16	2	2	NUM
ejpam-5375	585	17	,	,	PUNCT
ejpam-5375	585	18	...	...	PUNCT
ejpam-5375	585	19	,	,	PUNCT
ejpam-5375	585	20	2	2	NUM
ejpam-5375	585	21	)	)	PUNCT
ejpam-5375	585	22	.	.	PUNCT
ejpam-5375	586	1	based	base	VERB
ejpam-5375	586	2	on	on	ADP
ejpam-5375	586	3	definition	definition	NOUN
ejpam-5375	586	4	4	4	NUM
ejpam-5375	586	5	and	and	CCONJ
ejpam-5375	586	6	equation	equation	NOUN
ejpam-5375	586	7	3	3	NUM
ejpam-5375	586	8	,	,	PUNCT
ejpam-5375	586	9	we	we	PRON
ejpam-5375	586	10	can	can	AUX
ejpam-5375	586	11	construct	construct	VERB
ejpam-5375	586	12	an	an	DET
ejpam-5375	586	13	n×	n×	PROPN
ejpam-5375	586	14	n	n	CCONJ
ejpam-5375	586	15	laplacian	laplacian	ADJ
ejpam-5375	586	16	matrix	matrix	NOUN
ejpam-5375	586	17	of	of	ADP
ejpam-5375	586	18	γzn	γzn	PROPN
ejpam-5375	586	19	as	as	SCONJ
ejpam-5375	586	20	follows	follow	VERB
ejpam-5375	586	21	:	:	PUNCT
ejpam-5375	586	22	l(γzn	l(γzn	PROPN
ejpam-5375	586	23	)	)	PUNCT
ejpam-5375	587	1	=	=	VERB
ejpam-5375	587	2	d(γzn	d(γzn	ADJ
ejpam-5375	587	3	)	)	PUNCT
ejpam-5375	587	4	−a(γzn	−a(γzn	PROPN
ejpam-5375	587	5	)	)	PUNCT
ejpam-5375	587	6	(	(	PUNCT
ejpam-5375	587	7	6	6	X
ejpam-5375	587	8	)	)	PUNCT
ejpam-5375	587	9	m.	m.	NOUN
ejpam-5375	587	10	u.	u.	PROPN
ejpam-5375	587	11	romdhini	romdhini	PROPN
ejpam-5375	587	12	et	et	PROPN
ejpam-5375	587	13	al	al	PROPN
ejpam-5375	587	14	.	.	PUNCT
ejpam-5375	587	15	/	/	SYM
ejpam-5375	587	16	eur	eur	PROPN
ejpam-5375	587	17	.	.	PUNCT
ejpam-5375	588	1	j.	j.	PROPN
ejpam-5375	588	2	pure	pure	PROPN
ejpam-5375	588	3	appl	appl	PROPN
ejpam-5375	588	4	.	.	PROPN
ejpam-5375	588	5	math	math	PROPN
ejpam-5375	588	6	,	,	PUNCT
ejpam-5375	588	7	17	17	NUM
ejpam-5375	588	8	(	(	PUNCT
ejpam-5375	588	9	4	4	NUM
ejpam-5375	588	10	)	)	PUNCT
ejpam-5375	588	11	(	(	PUNCT
ejpam-5375	588	12	2024	2024	NUM
ejpam-5375	588	13	)	)	PUNCT
ejpam-5375	588	14	,	,	PUNCT
ejpam-5375	588	15	2915	2915	NUM
ejpam-5375	588	16	-	-	SYM
ejpam-5375	588	17	2929	2929	NUM
ejpam-5375	588	18	2925	2925	NUM
ejpam-5375	588	19	=	=	SYM
ejpam-5375	588	20	0	0	NUM
ejpam-5375	588	21	1	1	NUM
ejpam-5375	588	22	2	2	NUM
ejpam-5375	588	23	.	.	PUNCT
ejpam-5375	588	24	.	.	PUNCT
ejpam-5375	588	25	.	.	PUNCT
ejpam-5375	589	1	n	n	CCONJ
ejpam-5375	589	2	2	2	NUM
ejpam-5375	589	3	−	−	NUM
ejpam-5375	589	4	1	1	NUM
ejpam-5375	589	5	n	n	SYM
ejpam-5375	589	6	2	2	NUM
ejpam-5375	589	7	n	n	NUM
ejpam-5375	589	8	2	2	NUM
ejpam-5375	589	9	+	+	CCONJ
ejpam-5375	589	10	1	1	NUM
ejpam-5375	589	11	.	.	PUNCT
ejpam-5375	589	12	.	.	PUNCT
ejpam-5375	589	13	.	.	PUNCT
ejpam-5375	590	1	n−	n−	NOUN
ejpam-5375	590	2	2	2	NUM
ejpam-5375	590	3	n−	n−	NOUN
ejpam-5375	590	4	1	1	NUM
ejpam-5375	590	5			X
ejpam-5375	590	6	0	0	NUM
ejpam-5375	590	7	n−	n−	NOUN
ejpam-5375	590	8	1	1	NUM
ejpam-5375	590	9	−1	−1	NOUN
ejpam-5375	590	10	−1	−1	NOUN
ejpam-5375	590	11	.	.	PUNCT
ejpam-5375	590	12	.	.	PUNCT
ejpam-5375	590	13	.	.	PUNCT
ejpam-5375	591	1	−1	−1	NOUN
ejpam-5375	591	2	−1	−1	NOUN
ejpam-5375	591	3	−1	−1	NOUN
ejpam-5375	591	4	.	.	PUNCT
ejpam-5375	591	5	.	.	PUNCT
ejpam-5375	591	6	.	.	PUNCT
ejpam-5375	592	1	−1	−1	NOUN
ejpam-5375	592	2	−1	−1	NOUN
ejpam-5375	592	3	1	1	NUM
ejpam-5375	592	4	−1	−1	NOUN
ejpam-5375	592	5	2	2	NUM
ejpam-5375	592	6	0	0	NUM
ejpam-5375	592	7	.	.	PUNCT
ejpam-5375	592	8	.	.	PUNCT
ejpam-5375	592	9	.	.	PUNCT
ejpam-5375	593	1	0	0	NUM
ejpam-5375	594	1	0	0	NUM
ejpam-5375	594	2	0	0	NUM
ejpam-5375	594	3	.	.	PUNCT
ejpam-5375	594	4	.	.	PUNCT
ejpam-5375	595	1	.	.	PUNCT
ejpam-5375	596	1	0	0	NUM
ejpam-5375	597	1	−1	−1	NOUN
ejpam-5375	597	2	2	2	NUM
ejpam-5375	597	3	−1	−1	NOUN
ejpam-5375	597	4	0	0	NUM
ejpam-5375	597	5	2	2	NUM
ejpam-5375	597	6	.	.	PUNCT
ejpam-5375	597	7	.	.	PUNCT
ejpam-5375	597	8	.	.	PUNCT
ejpam-5375	598	1	0	0	NUM
ejpam-5375	599	1	0	0	NUM
ejpam-5375	599	2	0	0	NUM
ejpam-5375	599	3	.	.	PUNCT
ejpam-5375	599	4	.	.	PUNCT
ejpam-5375	599	5	.	.	PUNCT
ejpam-5375	600	1	−1	−1	NOUN
ejpam-5375	600	2	0	0	NUM
ejpam-5375	600	3	...	...	PUNCT
ejpam-5375	600	4	...	...	PUNCT
ejpam-5375	600	5	...	...	PUNCT
ejpam-5375	600	6	...	...	PUNCT
ejpam-5375	600	7	.	.	PUNCT
ejpam-5375	600	8	.	.	PUNCT
ejpam-5375	600	9	.	.	PUNCT
ejpam-5375	601	1	...	...	PUNCT
ejpam-5375	601	2	...	...	PUNCT
ejpam-5375	602	1	...	...	PUNCT
ejpam-5375	602	2	...	...	PUNCT
ejpam-5375	602	3	...	...	PUNCT
ejpam-5375	602	4	...	...	PUNCT
ejpam-5375	603	1	n	n	X
ejpam-5375	603	2	2	2	NUM
ejpam-5375	603	3	−	−	NUM
ejpam-5375	603	4	1	1	NUM
ejpam-5375	603	5	−1	−1	NOUN
ejpam-5375	603	6	0	0	NUM
ejpam-5375	603	7	0	0	NUM
ejpam-5375	603	8	.	.	PUNCT
ejpam-5375	603	9	.	.	PUNCT
ejpam-5375	603	10	.	.	PUNCT
ejpam-5375	604	1	2	2	NUM
ejpam-5375	604	2	0	0	NUM
ejpam-5375	604	3	−1	−1	NOUN
ejpam-5375	604	4	.	.	PUNCT
ejpam-5375	604	5	.	.	PUNCT
ejpam-5375	605	1	.	.	PUNCT
ejpam-5375	606	1	0	0	NUM
ejpam-5375	606	2	0	0	NUM
ejpam-5375	607	1	n	n	NUM
ejpam-5375	607	2	2	2	NUM
ejpam-5375	607	3	−1	−1	NOUN
ejpam-5375	607	4	0	0	NUM
ejpam-5375	607	5	0	0	NUM
ejpam-5375	607	6	.	.	PUNCT
ejpam-5375	607	7	.	.	PUNCT
ejpam-5375	607	8	.	.	PUNCT
ejpam-5375	608	1	0	0	NUM
ejpam-5375	609	1	1	1	NUM
ejpam-5375	609	2	0	0	NUM
ejpam-5375	609	3	.	.	PUNCT
ejpam-5375	609	4	.	.	PUNCT
ejpam-5375	609	5	.	.	PUNCT
ejpam-5375	610	1	0	0	NUM
ejpam-5375	610	2	0	0	NUM
ejpam-5375	611	1	n	n	NUM
ejpam-5375	611	2	2	2	NUM
ejpam-5375	611	3	+	+	CCONJ
ejpam-5375	611	4	1	1	NUM
ejpam-5375	611	5	−1	−1	NOUN
ejpam-5375	611	6	0	0	NUM
ejpam-5375	611	7	0	0	NUM
ejpam-5375	611	8	.	.	PUNCT
ejpam-5375	611	9	.	.	PUNCT
ejpam-5375	611	10	.	.	PUNCT
ejpam-5375	612	1	−1	−1	NOUN
ejpam-5375	612	2	0	0	NUM
ejpam-5375	612	3	2	2	NUM
ejpam-5375	612	4	.	.	PUNCT
ejpam-5375	612	5	.	.	PUNCT
ejpam-5375	613	1	.	.	PUNCT
ejpam-5375	614	1	0	0	NUM
ejpam-5375	614	2	0	0	NUM
ejpam-5375	614	3	...	...	PUNCT
ejpam-5375	614	4	...	...	PUNCT
ejpam-5375	614	5	...	...	PUNCT
ejpam-5375	614	6	...	...	PUNCT
ejpam-5375	614	7	.	.	PUNCT
ejpam-5375	614	8	.	.	PUNCT
ejpam-5375	614	9	.	.	PUNCT
ejpam-5375	615	1	...	...	PUNCT
ejpam-5375	615	2	...	...	PUNCT
ejpam-5375	616	1	...	...	PUNCT
ejpam-5375	616	2	...	...	PUNCT
ejpam-5375	616	3	...	...	PUNCT
ejpam-5375	616	4	...	...	PUNCT
ejpam-5375	617	1	n−	n−	NOUN
ejpam-5375	617	2	2	2	NUM
ejpam-5375	617	3	−1	−1	NOUN
ejpam-5375	617	4	0	0	NUM
ejpam-5375	617	5	−1	−1	NOUN
ejpam-5375	617	6	.	.	PUNCT
ejpam-5375	617	7	.	.	PUNCT
ejpam-5375	617	8	.	.	PUNCT
ejpam-5375	618	1	0	0	NUM
ejpam-5375	619	1	0	0	NUM
ejpam-5375	619	2	0	0	NUM
ejpam-5375	619	3	.	.	PUNCT
ejpam-5375	619	4	.	.	PUNCT
ejpam-5375	619	5	.	.	PUNCT
ejpam-5375	620	1	2	2	NUM
ejpam-5375	620	2	0	0	NUM
ejpam-5375	620	3	n−	n−	NOUN
ejpam-5375	620	4	1	1	NUM
ejpam-5375	620	5	−1	−1	NOUN
ejpam-5375	620	6	−1	−1	NOUN
ejpam-5375	620	7	0	0	NUM
ejpam-5375	620	8	.	.	PUNCT
ejpam-5375	620	9	.	.	PUNCT
ejpam-5375	620	10	.	.	PUNCT
ejpam-5375	621	1	0	0	NUM
ejpam-5375	622	1	0	0	NUM
ejpam-5375	622	2	0	0	NUM
ejpam-5375	622	3	.	.	PUNCT
ejpam-5375	622	4	.	.	PUNCT
ejpam-5375	623	1	.	.	PUNCT
ejpam-5375	624	1	0	0	NUM
ejpam-5375	624	2	2	2	NUM
ejpam-5375	624	3	.	.	PUNCT
ejpam-5375	625	1	(	(	PUNCT
ejpam-5375	625	2	7	7	X
ejpam-5375	625	3	)	)	PUNCT
ejpam-5375	625	4	following	follow	VERB
ejpam-5375	625	5	the	the	DET
ejpam-5375	625	6	guideline	guideline	NOUN
ejpam-5375	625	7	in	in	ADP
ejpam-5375	625	8	theorem	theorem	NOUN
ejpam-5375	625	9	6	6	NUM
ejpam-5375	625	10	with	with	ADP
ejpam-5375	625	11	a	a	DET
ejpam-5375	625	12	=	=	ADJ
ejpam-5375	625	13	n−	n−	NOUN
ejpam-5375	625	14	1	1	NUM
ejpam-5375	625	15	,	,	PUNCT
ejpam-5375	625	16	b	b	NOUN
ejpam-5375	625	17	=	=	SYM
ejpam-5375	625	18	2	2	NUM
ejpam-5375	625	19	,	,	PUNCT
ejpam-5375	625	20	c	c	NOUN
ejpam-5375	625	21	=	=	SYM
ejpam-5375	625	22	1	1	NUM
ejpam-5375	625	23	,	,	PUNCT
ejpam-5375	625	24	and	and	CCONJ
ejpam-5375	625	25	d	d	NOUN
ejpam-5375	625	26	=	=	SYM
ejpam-5375	625	27	−1	−1	NOUN
ejpam-5375	625	28	,	,	PUNCT
ejpam-5375	625	29	then	then	ADV
ejpam-5375	625	30	we	we	PRON
ejpam-5375	625	31	can	can	AUX
ejpam-5375	625	32	write	write	VERB
ejpam-5375	625	33	the	the	DET
ejpam-5375	625	34	following	follow	VERB
ejpam-5375	625	35	expression	expression	NOUN
ejpam-5375	625	36	:	:	PUNCT
ejpam-5375	625	37	pl(γzn	pl(γzn	ADJ
ejpam-5375	625	38	)	)	PUNCT
ejpam-5375	625	39	(	(	PUNCT
ejpam-5375	625	40	λ	λ	X
ejpam-5375	625	41	)	)	PUNCT
ejpam-5375	625	42	=	=	SYM
ejpam-5375	625	43	λ(λ−	λ(λ−	PROPN
ejpam-5375	625	44	n)(λ−	n)(λ−	ADJ
ejpam-5375	625	45	1	1	NUM
ejpam-5375	625	46	)	)	PUNCT
ejpam-5375	625	47	n	n	PRON
ejpam-5375	625	48	2	2	NUM
ejpam-5375	625	49	−1(λ−	−1(λ−	ADJ
ejpam-5375	625	50	3	3	NUM
ejpam-5375	625	51	)	)	PUNCT
ejpam-5375	625	52	n	n	PRON
ejpam-5375	625	53	2	2	NUM
ejpam-5375	625	54	−1	−1	NOUN
ejpam-5375	625	55	.	.	PUNCT
ejpam-5375	626	1	the	the	DET
ejpam-5375	626	2	roots	root	NOUN
ejpam-5375	626	3	of	of	ADP
ejpam-5375	626	4	pl(γzn	pl(γzn	NOUN
ejpam-5375	626	5	)	)	PUNCT
ejpam-5375	626	6	(	(	PUNCT
ejpam-5375	626	7	λ	λ	X
ejpam-5375	626	8	)	)	PUNCT
ejpam-5375	626	9	=	=	SYM
ejpam-5375	626	10	0	0	NUM
ejpam-5375	626	11	are	be	AUX
ejpam-5375	626	12	λ1	λ1	ADJ
ejpam-5375	626	13	=	=	SYM
ejpam-5375	626	14	0	0	NUM
ejpam-5375	626	15	of	of	ADP
ejpam-5375	626	16	multiplicity	multiplicity	NOUN
ejpam-5375	626	17	1	1	NUM
ejpam-5375	626	18	,	,	PUNCT
ejpam-5375	626	19	λ2	λ2	NOUN
ejpam-5375	626	20	=	=	SYM
ejpam-5375	626	21	n	n	NOUN
ejpam-5375	626	22	of	of	ADP
ejpam-5375	626	23	multiplicity	multiplicity	NOUN
ejpam-5375	626	24	1	1	NUM
ejpam-5375	626	25	,	,	PUNCT
ejpam-5375	626	26	λ3	λ3	PROPN
ejpam-5375	626	27	=	=	NOUN
ejpam-5375	626	28	1	1	NUM
ejpam-5375	626	29	of	of	ADP
ejpam-5375	626	30	multiplicity	multiplicity	NOUN
ejpam-5375	626	31	n	n	CCONJ
ejpam-5375	626	32	2	2	NUM
ejpam-5375	626	33	−	−	NUM
ejpam-5375	626	34	1	1	NUM
ejpam-5375	626	35	,	,	PUNCT
ejpam-5375	626	36	and	and	CCONJ
ejpam-5375	626	37	λ4	λ4	PROPN
ejpam-5375	626	38	=	=	SYM
ejpam-5375	626	39	3	3	NUM
ejpam-5375	626	40	of	of	ADP
ejpam-5375	626	41	multiplicity	multiplicity	NOUN
ejpam-5375	626	42	n	n	CCONJ
ejpam-5375	626	43	2	2	NUM
ejpam-5375	626	44	−	−	NUM
ejpam-5375	626	45	1	1	NUM
ejpam-5375	626	46	.	.	PUNCT
ejpam-5375	627	1	consequently	consequently	ADV
ejpam-5375	627	2	,	,	PUNCT
ejpam-5375	627	3	the	the	DET
ejpam-5375	627	4	spectrum	spectrum	NOUN
ejpam-5375	627	5	of	of	ADP
ejpam-5375	627	6	γzn	γzn	PROPN
ejpam-5375	627	7	is	be	AUX
ejpam-5375	627	8	specl(γzn	specl(γzn	ADJ
ejpam-5375	627	9	)	)	PUNCT
ejpam-5375	628	1	=	=	PRON
ejpam-5375	628	2	{	{	PUNCT
ejpam-5375	628	3	(	(	PUNCT
ejpam-5375	628	4	n)1	n)1	NOUN
ejpam-5375	628	5	,	,	PUNCT
ejpam-5375	628	6	(	(	PUNCT
ejpam-5375	628	7	3	3	X
ejpam-5375	628	8	)	)	PUNCT
ejpam-5375	628	9	n	n	PRON
ejpam-5375	628	10	2	2	NUM
ejpam-5375	628	11	−1	−1	NOUN
ejpam-5375	628	12	,	,	PUNCT
ejpam-5375	628	13	(	(	PUNCT
ejpam-5375	628	14	1	1	X
ejpam-5375	628	15	)	)	PUNCT
ejpam-5375	628	16	n	n	PRON
ejpam-5375	628	17	2	2	NUM
ejpam-5375	628	18	−1	−1	NOUN
ejpam-5375	628	19	,	,	PUNCT
ejpam-5375	628	20	(	(	PUNCT
ejpam-5375	628	21	0)1	0)1	PROPN
ejpam-5375	628	22	}	}	PUNCT
ejpam-5375	628	23	.	.	PUNCT
ejpam-5375	629	1	it	it	PRON
ejpam-5375	629	2	is	be	AUX
ejpam-5375	629	3	clear	clear	ADJ
ejpam-5375	629	4	that	that	SCONJ
ejpam-5375	629	5	the	the	DET
ejpam-5375	629	6	spectral	spectral	ADJ
ejpam-5375	629	7	radius	radius	NOUN
ejpam-5375	629	8	of	of	ADP
ejpam-5375	629	9	γzn	γzn	PROPN
ejpam-5375	629	10	is	be	AUX
ejpam-5375	629	11	ρl(γzn	ρl(γzn	ADJ
ejpam-5375	629	12	)	)	PUNCT
ejpam-5375	630	1	=	=	SYM
ejpam-5375	630	2	n.	n.	NOUN
ejpam-5375	630	3	therefore	therefore	ADV
ejpam-5375	630	4	,	,	PUNCT
ejpam-5375	630	5	the	the	DET
ejpam-5375	630	6	laplacian	laplacian	ADJ
ejpam-5375	630	7	energy	energy	NOUN
ejpam-5375	630	8	of	of	ADP
ejpam-5375	630	9	γzn	γzn	PROPN
ejpam-5375	630	10	is	be	AUX
ejpam-5375	630	11	as	as	SCONJ
ejpam-5375	630	12	follows	follow	VERB
ejpam-5375	630	13	:	:	PUNCT
ejpam-5375	630	14	el(γzn	el(γzn	X
ejpam-5375	630	15	)	)	PUNCT
ejpam-5375	631	1	=	=	SYM
ejpam-5375	631	2	(	(	PUNCT
ejpam-5375	631	3	1	1	X
ejpam-5375	631	4	)	)	PUNCT
ejpam-5375	631	5	|n|+	|n|+	PROPN
ejpam-5375	631	6	(	(	PUNCT
ejpam-5375	631	7	n	n	ADV
ejpam-5375	631	8	2	2	NUM
ejpam-5375	631	9	−	−	NOUN
ejpam-5375	631	10	1	1	NUM
ejpam-5375	631	11	)	)	PUNCT
ejpam-5375	632	1	|3|+	|3|+	PROPN
ejpam-5375	632	2	(	(	PUNCT
ejpam-5375	632	3	n	n	NOUN
ejpam-5375	632	4	2	2	NUM
ejpam-5375	632	5	−	−	NOUN
ejpam-5375	632	6	1	1	NUM
ejpam-5375	632	7	)	)	PUNCT
ejpam-5375	632	8	|1|+	|1|+	NOUN
ejpam-5375	632	9	(	(	PUNCT
ejpam-5375	632	10	1	1	X
ejpam-5375	632	11	)	)	PUNCT
ejpam-5375	632	12	|0|	|0|	NOUN
ejpam-5375	633	1	=	=	PUNCT
ejpam-5375	633	2	3n−	3n−	NUM
ejpam-5375	633	3	4	4	NUM
ejpam-5375	633	4	.	.	NOUN
ejpam-5375	633	5	3.3	3.3	NUM
ejpam-5375	633	6	.	.	PUNCT
ejpam-5375	634	1	signless	signless	ADJ
ejpam-5375	634	2	laplacian	laplacian	ADJ
ejpam-5375	634	3	matrix	matrix	NOUN
ejpam-5375	634	4	next	next	ADV
ejpam-5375	634	5	,	,	PUNCT
ejpam-5375	634	6	we	we	PRON
ejpam-5375	634	7	show	show	VERB
ejpam-5375	634	8	the	the	DET
ejpam-5375	634	9	energy	energy	NOUN
ejpam-5375	634	10	of	of	ADP
ejpam-5375	634	11	γzn	γzn	PROPN
ejpam-5375	634	12	with	with	ADP
ejpam-5375	634	13	respect	respect	NOUN
ejpam-5375	634	14	to	to	ADP
ejpam-5375	634	15	the	the	DET
ejpam-5375	634	16	signless	signless	ADJ
ejpam-5375	634	17	laplacian	laplacian	ADJ
ejpam-5375	634	18	matrix	matrix	NOUN
ejpam-5375	634	19	,	,	PUNCT
ejpam-5375	634	20	for	for	ADP
ejpam-5375	634	21	odd	odd	ADJ
ejpam-5375	634	22	and	and	CCONJ
ejpam-5375	634	23	even	even	ADV
ejpam-5375	634	24	n.	n.	NOUN
ejpam-5375	634	25	theorem	theorem	NOUN
ejpam-5375	634	26	11	11	NUM
ejpam-5375	634	27	.	.	PUNCT
ejpam-5375	635	1	let	let	VERB
ejpam-5375	635	2	γzn	γzn	PROPN
ejpam-5375	635	3	be	be	AUX
ejpam-5375	635	4	the	the	DET
ejpam-5375	635	5	identity	identity	NOUN
ejpam-5375	635	6	graph	graph	NOUN
ejpam-5375	635	7	on	on	ADP
ejpam-5375	635	8	zn	zn	PROPN
ejpam-5375	635	9	.	.	PUNCT
ejpam-5375	636	1	the	the	DET
ejpam-5375	636	2	signless	signless	PROPN
ejpam-5375	636	3	laplacian	laplacian	ADJ
ejpam-5375	636	4	energy	energy	NOUN
ejpam-5375	636	5	of	of	ADP
ejpam-5375	636	6	γzn	γzn	PROPN
ejpam-5375	636	7	for	for	ADP
ejpam-5375	636	8	odd	odd	ADJ
ejpam-5375	636	9	n	n	X
ejpam-5375	636	10	is	be	AUX
ejpam-5375	636	11	esl(γzn	esl(γzn	PRON
ejpam-5375	636	12	)	)	PUNCT
ejpam-5375	637	1	=	=	SYM
ejpam-5375	637	2	3(n−	3(n−	NUM
ejpam-5375	637	3	1	1	NUM
ejpam-5375	637	4	)	)	PUNCT
ejpam-5375	637	5	.	.	PUNCT
ejpam-5375	638	1	m.	m.	PROPN
ejpam-5375	638	2	u.	u.	PROPN
ejpam-5375	638	3	romdhini	romdhini	PROPN
ejpam-5375	638	4	et	et	PROPN
ejpam-5375	638	5	al	al	PROPN
ejpam-5375	638	6	.	.	PUNCT
ejpam-5375	638	7	/	/	SYM
ejpam-5375	638	8	eur	eur	PROPN
ejpam-5375	638	9	.	.	PUNCT
ejpam-5375	639	1	j.	j.	PROPN
ejpam-5375	639	2	pure	pure	PROPN
ejpam-5375	639	3	appl	appl	PROPN
ejpam-5375	639	4	.	.	PROPN
ejpam-5375	639	5	math	math	PROPN
ejpam-5375	639	6	,	,	PUNCT
ejpam-5375	639	7	17	17	NUM
ejpam-5375	639	8	(	(	PUNCT
ejpam-5375	639	9	4	4	NUM
ejpam-5375	639	10	)	)	PUNCT
ejpam-5375	639	11	(	(	PUNCT
ejpam-5375	639	12	2024	2024	NUM
ejpam-5375	639	13	)	)	PUNCT
ejpam-5375	639	14	,	,	PUNCT
ejpam-5375	639	15	2915	2915	NUM
ejpam-5375	639	16	-	-	SYM
ejpam-5375	639	17	2929	2929	NUM
ejpam-5375	639	18	2926	2926	NUM
ejpam-5375	639	19	proof	proof	NOUN
ejpam-5375	639	20	.	.	PUNCT
ejpam-5375	640	1	based	base	VERB
ejpam-5375	640	2	on	on	ADP
ejpam-5375	640	3	theorem	theorem	NOUN
ejpam-5375	640	4	3	3	NUM
ejpam-5375	640	5	,	,	PUNCT
ejpam-5375	640	6	we	we	PRON
ejpam-5375	640	7	have	have	VERB
ejpam-5375	640	8	n	n	NUM
ejpam-5375	640	9	×	×	NOUN
ejpam-5375	640	10	n	n	CCONJ
ejpam-5375	640	11	degree	degree	NOUN
ejpam-5375	640	12	matrix	matrix	NOUN
ejpam-5375	640	13	of	of	ADP
ejpam-5375	640	14	γzn	γzn	PROPN
ejpam-5375	640	15	as	as	ADP
ejpam-5375	640	16	diag(n	diag(n	NOUN
ejpam-5375	640	17	−	−	PROPN
ejpam-5375	640	18	1	1	NUM
ejpam-5375	640	19	,	,	PUNCT
ejpam-5375	640	20	2	2	NUM
ejpam-5375	640	21	,	,	PUNCT
ejpam-5375	640	22	2	2	NUM
ejpam-5375	640	23	,	,	PUNCT
ejpam-5375	640	24	...	...	PUNCT
ejpam-5375	640	25	,	,	PUNCT
ejpam-5375	640	26	2	2	NUM
ejpam-5375	640	27	,	,	PUNCT
ejpam-5375	640	28	2	2	NUM
ejpam-5375	640	29	)	)	PUNCT
ejpam-5375	640	30	.	.	PUNCT
ejpam-5375	641	1	according	accord	VERB
ejpam-5375	641	2	to	to	ADP
ejpam-5375	641	3	definition	definition	NOUN
ejpam-5375	641	4	5	5	NUM
ejpam-5375	641	5	and	and	CCONJ
ejpam-5375	641	6	equation	equation	NOUN
ejpam-5375	641	7	2	2	NUM
ejpam-5375	641	8	,	,	PUNCT
ejpam-5375	641	9	we	we	PRON
ejpam-5375	641	10	can	can	AUX
ejpam-5375	641	11	construct	construct	VERB
ejpam-5375	641	12	an	an	DET
ejpam-5375	641	13	n	n	NUM
ejpam-5375	641	14	×	×	NOUN
ejpam-5375	641	15	n	n	CCONJ
ejpam-5375	641	16	signless	signless	ADJ
ejpam-5375	641	17	laplacian	laplacian	ADJ
ejpam-5375	641	18	matrix	matrix	NOUN
ejpam-5375	641	19	of	of	ADP
ejpam-5375	641	20	γzn	γzn	PROPN
ejpam-5375	641	21	as	as	SCONJ
ejpam-5375	641	22	follows	follow	VERB
ejpam-5375	641	23	:	:	PUNCT
ejpam-5375	641	24	sl(γzn	sl(γzn	X
ejpam-5375	641	25	)	)	PUNCT
ejpam-5375	641	26	=	=	PRON
ejpam-5375	641	27	d(γzn	d(γzn	VERB
ejpam-5375	641	28	)	)	PUNCT
ejpam-5375	642	1	+	+	NOUN
ejpam-5375	642	2	a(γzn	a(γzn	X
ejpam-5375	642	3	)	)	PUNCT
ejpam-5375	642	4	(	(	PUNCT
ejpam-5375	642	5	8)	8)	NUM
ejpam-5375	642	6	=	=	SYM
ejpam-5375	642	7	0	0	NUM
ejpam-5375	642	8	1	1	NUM
ejpam-5375	642	9	2	2	NUM
ejpam-5375	642	10	.	.	PUNCT
ejpam-5375	642	11	.	.	PUNCT
ejpam-5375	643	1	.	.	PUNCT
ejpam-5375	644	1	n−	n−	NOUN
ejpam-5375	644	2	2	2	NUM
ejpam-5375	644	3	n−	n−	NOUN
ejpam-5375	644	4	1	1	NUM
ejpam-5375	644	5			NOUN
ejpam-5375	644	6	0	0	NUM
ejpam-5375	644	7	n−	n−	NOUN
ejpam-5375	644	8	1	1	NUM
ejpam-5375	644	9	1	1	NUM
ejpam-5375	644	10	1	1	NUM
ejpam-5375	644	11	.	.	PUNCT
ejpam-5375	644	12	.	.	PUNCT
ejpam-5375	645	1	.	.	PUNCT
ejpam-5375	646	1	1	1	NUM
ejpam-5375	646	2	1	1	NUM
ejpam-5375	646	3	1	1	NUM
ejpam-5375	646	4	1	1	NUM
ejpam-5375	646	5	2	2	NUM
ejpam-5375	646	6	0	0	NUM
ejpam-5375	646	7	.	.	PUNCT
ejpam-5375	646	8	.	.	PUNCT
ejpam-5375	647	1	.	.	PUNCT
ejpam-5375	648	1	0	0	NUM
ejpam-5375	648	2	1	1	NUM
ejpam-5375	648	3	2	2	NUM
ejpam-5375	648	4	1	1	NUM
ejpam-5375	648	5	0	0	NUM
ejpam-5375	648	6	2	2	NUM
ejpam-5375	648	7	.	.	PUNCT
ejpam-5375	648	8	.	.	PUNCT
ejpam-5375	648	9	.	.	PUNCT
ejpam-5375	649	1	1	1	NUM
ejpam-5375	649	2	0	0	NUM
ejpam-5375	649	3	...	...	PUNCT
ejpam-5375	649	4	...	...	PUNCT
ejpam-5375	649	5	...	...	PUNCT
ejpam-5375	649	6	...	...	PUNCT
ejpam-5375	649	7	.	.	PUNCT
ejpam-5375	649	8	.	.	PUNCT
ejpam-5375	649	9	.	.	PUNCT
ejpam-5375	649	10	...	...	PUNCT
ejpam-5375	650	1	...	...	PUNCT
ejpam-5375	651	1	n−	n−	NOUN
ejpam-5375	651	2	2	2	NUM
ejpam-5375	651	3	1	1	NUM
ejpam-5375	651	4	0	0	NUM
ejpam-5375	651	5	1	1	NUM
ejpam-5375	651	6	.	.	PUNCT
ejpam-5375	651	7	.	.	PUNCT
ejpam-5375	651	8	.	.	PUNCT
ejpam-5375	652	1	2	2	NUM
ejpam-5375	652	2	0	0	NUM
ejpam-5375	652	3	n−	n−	NOUN
ejpam-5375	652	4	1	1	NUM
ejpam-5375	652	5	1	1	NUM
ejpam-5375	652	6	1	1	NUM
ejpam-5375	652	7	0	0	NUM
ejpam-5375	652	8	.	.	PUNCT
ejpam-5375	652	9	.	.	PUNCT
ejpam-5375	652	10	.	.	PUNCT
ejpam-5375	653	1	0	0	NUM
ejpam-5375	653	2	2	2	NUM
ejpam-5375	653	3	(	(	PUNCT
ejpam-5375	653	4	9	9	NUM
ejpam-5375	653	5	)	)	PUNCT
ejpam-5375	653	6	from	from	ADP
ejpam-5375	653	7	theorem	theorem	NOUN
ejpam-5375	653	8	5	5	NUM
ejpam-5375	653	9	with	with	ADP
ejpam-5375	653	10	a	a	DET
ejpam-5375	653	11	=	=	ADJ
ejpam-5375	653	12	n−	n−	NOUN
ejpam-5375	653	13	1	1	NUM
ejpam-5375	653	14	,	,	PUNCT
ejpam-5375	653	15	b	b	X
ejpam-5375	653	16	=	=	SYM
ejpam-5375	653	17	2	2	NUM
ejpam-5375	653	18	and	and	CCONJ
ejpam-5375	653	19	c	c	NOUN
ejpam-5375	653	20	=	=	SYM
ejpam-5375	653	21	1	1	NUM
ejpam-5375	653	22	,	,	PUNCT
ejpam-5375	653	23	we	we	PRON
ejpam-5375	653	24	can	can	AUX
ejpam-5375	653	25	simplify	simplify	VERB
ejpam-5375	653	26	psl(γzn	psl(γzn	NOUN
ejpam-5375	653	27	)	)	PUNCT
ejpam-5375	654	1	(	(	PUNCT
ejpam-5375	654	2	λ	λ	X
ejpam-5375	654	3	)	)	PUNCT
ejpam-5375	654	4	as	as	SCONJ
ejpam-5375	654	5	follows	follow	VERB
ejpam-5375	654	6	:	:	PUNCT
ejpam-5375	654	7	psl(γzn	psl(γzn	NOUN
ejpam-5375	654	8	)	)	PUNCT
ejpam-5375	655	1	(	(	PUNCT
ejpam-5375	655	2	λ	λ	X
ejpam-5375	655	3	)	)	PUNCT
ejpam-5375	655	4	=	=	SYM
ejpam-5375	655	5	(	(	PUNCT
ejpam-5375	655	6	λ2	λ2	NOUN
ejpam-5375	655	7	−	−	PROPN
ejpam-5375	655	8	(	(	PUNCT
ejpam-5375	655	9	2	2	NUM
ejpam-5375	655	10	+	+	NUM
ejpam-5375	655	11	n)λ+	n)λ+	PROPN
ejpam-5375	655	12	2(n−	2(n−	NUM
ejpam-5375	655	13	1))(λ−	1))(λ−	NUM
ejpam-5375	655	14	3	3	NUM
ejpam-5375	655	15	)	)	PUNCT
ejpam-5375	655	16	n−3	n−3	PROPN
ejpam-5375	655	17	2	2	NUM
ejpam-5375	655	18	(	(	PUNCT
ejpam-5375	655	19	λ−	λ−	PROPN
ejpam-5375	655	20	1	1	NUM
ejpam-5375	655	21	)	)	PUNCT
ejpam-5375	655	22	n−1	n−1	PROPN
ejpam-5375	655	23	2	2	NUM
ejpam-5375	655	24	.	.	PUNCT
ejpam-5375	656	1	the	the	DET
ejpam-5375	656	2	roots	root	NOUN
ejpam-5375	656	3	of	of	ADP
ejpam-5375	656	4	psl(γzn	psl(γzn	NOUN
ejpam-5375	656	5	)	)	PUNCT
ejpam-5375	657	1	(	(	PUNCT
ejpam-5375	657	2	λ	λ	X
ejpam-5375	657	3	)	)	PUNCT
ejpam-5375	657	4	=	=	SYM
ejpam-5375	657	5	0	0	NUM
ejpam-5375	657	6	are	be	AUX
ejpam-5375	657	7	λ1	λ1	ADJ
ejpam-5375	657	8	=	=	SYM
ejpam-5375	657	9	3	3	NUM
ejpam-5375	657	10	of	of	ADP
ejpam-5375	657	11	multiplicity	multiplicity	NOUN
ejpam-5375	657	12	n−3	n−3	PROPN
ejpam-5375	657	13	2	2	NUM
ejpam-5375	657	14	,	,	PUNCT
ejpam-5375	657	15	λ2	λ2	NOUN
ejpam-5375	657	16	=	=	SYM
ejpam-5375	657	17	1	1	NUM
ejpam-5375	657	18	of	of	ADP
ejpam-5375	657	19	multiplicity	multiplicity	NOUN
ejpam-5375	657	20	n−1	n−1	PROPN
ejpam-5375	657	21	2	2	NUM
ejpam-5375	657	22	,	,	PUNCT
ejpam-5375	657	23	λ3,4	λ3,4	NOUN
ejpam-5375	657	24	=	=	X
ejpam-5375	657	25	2+n	2+n	NUM
ejpam-5375	657	26	2	2	NUM
ejpam-5375	657	27	±	±	NUM
ejpam-5375	657	28	√	√	PROPN
ejpam-5375	657	29	n2−4n+12	n2−4n+12	NOUN
ejpam-5375	657	30	2	2	NUM
ejpam-5375	657	31	of	of	ADP
ejpam-5375	657	32	multiplicity	multiplicity	NOUN
ejpam-5375	657	33	1	1	NUM
ejpam-5375	657	34	,	,	PUNCT
ejpam-5375	657	35	respectively	respectively	ADV
ejpam-5375	657	36	.	.	PUNCT
ejpam-5375	658	1	consequently	consequently	ADV
ejpam-5375	658	2	,	,	PUNCT
ejpam-5375	658	3	the	the	DET
ejpam-5375	658	4	spectrum	spectrum	NOUN
ejpam-5375	658	5	of	of	ADP
ejpam-5375	658	6	γzn	γzn	PROPN
ejpam-5375	658	7	is	be	AUX
ejpam-5375	658	8	specsl(γzn	specsl(γzn	ADJ
ejpam-5375	658	9	)	)	PUNCT
ejpam-5375	658	10	=	=	PUNCT
ejpam-5375	659	1			PUNCT
ejpam-5375	659	2	(	(	PUNCT
ejpam-5375	659	3	2	2	NUM
ejpam-5375	659	4	+	+	CCONJ
ejpam-5375	659	5	n	n	PRON
ejpam-5375	659	6	2	2	NUM
ejpam-5375	659	7	+	+	CCONJ
ejpam-5375	659	8	√	√	ADJ
ejpam-5375	659	9	n2	n2	NOUN
ejpam-5375	659	10	−	−	PROPN
ejpam-5375	659	11	4n+	4n+	NUM
ejpam-5375	659	12	12	12	NUM
ejpam-5375	659	13	2	2	NUM
ejpam-5375	659	14	)	)	PUNCT
ejpam-5375	659	15	1	1	NUM
ejpam-5375	659	16	,	,	PUNCT
ejpam-5375	659	17	(	(	PUNCT
ejpam-5375	659	18	3	3	X
ejpam-5375	659	19	)	)	PUNCT
ejpam-5375	659	20	n−3	n−3	PROPN
ejpam-5375	659	21	2	2	NUM
ejpam-5375	659	22	,	,	PUNCT
ejpam-5375	659	23	(	(	PUNCT
ejpam-5375	659	24	1	1	X
ejpam-5375	659	25	)	)	PUNCT
ejpam-5375	659	26	n−1	n−1	PROPN
ejpam-5375	659	27	2	2	NUM
ejpam-5375	659	28	,	,	PUNCT
ejpam-5375	659	29	(	(	PUNCT
ejpam-5375	659	30	2	2	NUM
ejpam-5375	659	31	+	+	SYM
ejpam-5375	659	32	n	n	PRON
ejpam-5375	659	33	2	2	NUM
ejpam-5375	659	34	−	−	NOUN
ejpam-5375	659	35	√	√	NOUN
ejpam-5375	659	36	n2	n2	NOUN
ejpam-5375	659	37	−	−	PROPN
ejpam-5375	659	38	4n+	4n+	NUM
ejpam-5375	659	39	12	12	NUM
ejpam-5375	659	40	2	2	NUM
ejpam-5375	659	41	)	)	SYM
ejpam-5375	659	42	1	1	NUM
ejpam-5375	659	43			NOUN
ejpam-5375	659	44	.	.	PUNCT
ejpam-5375	660	1	it	it	PRON
ejpam-5375	660	2	is	be	AUX
ejpam-5375	660	3	clear	clear	ADJ
ejpam-5375	660	4	that	that	SCONJ
ejpam-5375	660	5	the	the	DET
ejpam-5375	660	6	spectral	spectral	ADJ
ejpam-5375	660	7	radius	radius	NOUN
ejpam-5375	660	8	of	of	ADP
ejpam-5375	660	9	γzn	γzn	PROPN
ejpam-5375	660	10	is	be	AUX
ejpam-5375	660	11	ρsl(γzn	ρsl(γzn	PRON
ejpam-5375	660	12	)	)	PUNCT
ejpam-5375	661	1	=	=	SYM
ejpam-5375	661	2	2	2	NUM
ejpam-5375	661	3	+	+	CCONJ
ejpam-5375	661	4	n	n	DET
ejpam-5375	661	5	2	2	NUM
ejpam-5375	661	6	+	+	CCONJ
ejpam-5375	661	7	√	√	ADJ
ejpam-5375	661	8	n2	n2	NOUN
ejpam-5375	661	9	−	−	PROPN
ejpam-5375	661	10	4n+	4n+	NUM
ejpam-5375	661	11	12	12	NUM
ejpam-5375	661	12	2	2	NUM
ejpam-5375	661	13	.	.	PUNCT
ejpam-5375	662	1	therefore	therefore	ADV
ejpam-5375	662	2	,	,	PUNCT
ejpam-5375	662	3	the	the	DET
ejpam-5375	662	4	signless	signless	PROPN
ejpam-5375	662	5	laplacian	laplacian	ADJ
ejpam-5375	662	6	energy	energy	NOUN
ejpam-5375	662	7	of	of	ADP
ejpam-5375	662	8	γzn	γzn	PROPN
ejpam-5375	662	9	is	be	AUX
ejpam-5375	662	10	as	as	SCONJ
ejpam-5375	662	11	follows	follow	VERB
ejpam-5375	662	12	:	:	PUNCT
ejpam-5375	662	13	esl(γzn	esl(γzn	ADV
ejpam-5375	662	14	)	)	PUNCT
ejpam-5375	663	1	=	=	PRON
ejpam-5375	663	2	(	(	PUNCT
ejpam-5375	663	3	n−	n−	NOUN
ejpam-5375	663	4	3	3	NUM
ejpam-5375	663	5	2	2	NUM
ejpam-5375	663	6	)	)	PUNCT
ejpam-5375	663	7	|3|+	|3|+	PROPN
ejpam-5375	663	8	(	(	PUNCT
ejpam-5375	663	9	n−	n−	NOUN
ejpam-5375	663	10	1	1	NUM
ejpam-5375	663	11	2	2	NUM
ejpam-5375	663	12	)	)	PUNCT
ejpam-5375	664	1	|1|+	|1|+	ADP
ejpam-5375	664	2	∣∣∣∣∣2	∣∣∣∣∣2	ADV
ejpam-5375	664	3	+	+	CCONJ
ejpam-5375	664	4	n	n	CCONJ
ejpam-5375	664	5	2	2	NUM
ejpam-5375	664	6	±	±	NUM
ejpam-5375	664	7	√	√	PROPN
ejpam-5375	664	8	n2	n2	NOUN
ejpam-5375	664	9	−	−	PROPN
ejpam-5375	664	10	4n+	4n+	NUM
ejpam-5375	664	11	12	12	NUM
ejpam-5375	664	12	2	2	NUM
ejpam-5375	664	13	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5375	664	14	=	=	SYM
ejpam-5375	665	1	3(n−	3(n−	NUM
ejpam-5375	665	2	1	1	NUM
ejpam-5375	665	3	)	)	PUNCT
ejpam-5375	665	4	.	.	PUNCT
ejpam-5375	666	1	theorem	theorem	NOUN
ejpam-5375	666	2	12	12	NUM
ejpam-5375	666	3	.	.	PUNCT
ejpam-5375	667	1	let	let	VERB
ejpam-5375	667	2	γzn	γzn	PROPN
ejpam-5375	667	3	be	be	AUX
ejpam-5375	667	4	the	the	DET
ejpam-5375	667	5	identity	identity	NOUN
ejpam-5375	667	6	graph	graph	NOUN
ejpam-5375	667	7	on	on	ADP
ejpam-5375	667	8	zn	zn	PROPN
ejpam-5375	667	9	.	.	PUNCT
ejpam-5375	668	1	the	the	DET
ejpam-5375	668	2	signless	signless	PROPN
ejpam-5375	668	3	laplacian	laplacian	ADJ
ejpam-5375	668	4	energy	energy	NOUN
ejpam-5375	668	5	of	of	ADP
ejpam-5375	668	6	γzn	γzn	PROPN
ejpam-5375	668	7	for	for	ADP
ejpam-5375	668	8	even	even	ADV
ejpam-5375	668	9	n	n	PROPN
ejpam-5375	668	10	is	be	AUX
ejpam-5375	668	11	esl(γzn	esl(γzn	PRON
ejpam-5375	668	12	)	)	PUNCT
ejpam-5375	669	1	=	=	SYM
ejpam-5375	670	1	3n−	3n−	NUM
ejpam-5375	670	2	4	4	NUM
ejpam-5375	670	3	.	.	PUNCT
ejpam-5375	671	1	proof	proof	NOUN
ejpam-5375	671	2	.	.	PUNCT
ejpam-5375	672	1	since	since	SCONJ
ejpam-5375	672	2	the	the	DET
ejpam-5375	672	3	diagonal	diagonal	ADJ
ejpam-5375	672	4	matrix	matrix	NOUN
ejpam-5375	672	5	of	of	ADP
ejpam-5375	672	6	γzn	γzn	PROPN
ejpam-5375	672	7	is	be	AUX
ejpam-5375	672	8	d(γzn	d(γzn	VERB
ejpam-5375	672	9	)	)	PUNCT
ejpam-5375	673	1	=	=	SYM
ejpam-5375	673	2	diag(n	diag(n	NOUN
ejpam-5375	673	3	−	−	NOUN
ejpam-5375	673	4	1	1	NUM
ejpam-5375	673	5	,	,	PUNCT
ejpam-5375	673	6	2	2	NUM
ejpam-5375	673	7	,	,	PUNCT
ejpam-5375	673	8	2	2	NUM
ejpam-5375	673	9	,	,	PUNCT
ejpam-5375	673	10	...	...	PUNCT
ejpam-5375	673	11	,	,	PUNCT
ejpam-5375	673	12	2	2	NUM
ejpam-5375	673	13	,	,	PUNCT
ejpam-5375	673	14	1	1	NUM
ejpam-5375	673	15	,	,	PUNCT
ejpam-5375	673	16	2	2	NUM
ejpam-5375	673	17	,	,	PUNCT
ejpam-5375	673	18	...	...	PUNCT
ejpam-5375	673	19	,	,	PUNCT
ejpam-5375	673	20	2	2	NUM
ejpam-5375	673	21	)	)	PUNCT
ejpam-5375	673	22	.	.	PUNCT
ejpam-5375	674	1	based	base	VERB
ejpam-5375	674	2	on	on	ADP
ejpam-5375	674	3	definition	definition	NOUN
ejpam-5375	674	4	5	5	NUM
ejpam-5375	674	5	and	and	CCONJ
ejpam-5375	674	6	equation	equation	NOUN
ejpam-5375	674	7	3	3	NUM
ejpam-5375	674	8	,	,	PUNCT
ejpam-5375	674	9	we	we	PRON
ejpam-5375	674	10	can	can	AUX
ejpam-5375	674	11	construct	construct	VERB
ejpam-5375	674	12	an	an	DET
ejpam-5375	674	13	n×n	n×n	PROPN
ejpam-5375	674	14	signless	signless	NOUN
ejpam-5375	674	15	laplacian	laplacian	ADJ
ejpam-5375	674	16	matrix	matrix	NOUN
ejpam-5375	674	17	of	of	ADP
ejpam-5375	674	18	γzn	γzn	PROPN
ejpam-5375	674	19	as	as	SCONJ
ejpam-5375	674	20	follows	follow	VERB
ejpam-5375	674	21	:	:	PUNCT
ejpam-5375	674	22	m.	m.	PROPN
ejpam-5375	674	23	u.	u.	PROPN
ejpam-5375	674	24	romdhini	romdhini	PROPN
ejpam-5375	674	25	et	et	PROPN
ejpam-5375	674	26	al	al	PROPN
ejpam-5375	674	27	.	.	PUNCT
ejpam-5375	674	28	/	/	SYM
ejpam-5375	674	29	eur	eur	PROPN
ejpam-5375	674	30	.	.	PUNCT
ejpam-5375	675	1	j.	j.	PROPN
ejpam-5375	675	2	pure	pure	PROPN
ejpam-5375	675	3	appl	appl	PROPN
ejpam-5375	675	4	.	.	PROPN
ejpam-5375	675	5	math	math	PROPN
ejpam-5375	675	6	,	,	PUNCT
ejpam-5375	675	7	17	17	NUM
ejpam-5375	675	8	(	(	PUNCT
ejpam-5375	675	9	4	4	NUM
ejpam-5375	675	10	)	)	PUNCT
ejpam-5375	675	11	(	(	PUNCT
ejpam-5375	675	12	2024	2024	NUM
ejpam-5375	675	13	)	)	PUNCT
ejpam-5375	675	14	,	,	PUNCT
ejpam-5375	675	15	2915	2915	NUM
ejpam-5375	675	16	-	-	SYM
ejpam-5375	675	17	2929	2929	NUM
ejpam-5375	675	18	2927	2927	NUM
ejpam-5375	675	19	sl(γzn	sl(γzn	NUM
ejpam-5375	675	20	)	)	PUNCT
ejpam-5375	675	21	=	=	PRON
ejpam-5375	675	22	d(γzn	d(γzn	VERB
ejpam-5375	675	23	)	)	PUNCT
ejpam-5375	676	1	+	+	NOUN
ejpam-5375	676	2	a(γzn	a(γzn	X
ejpam-5375	676	3	)	)	PUNCT
ejpam-5375	676	4	(	(	PUNCT
ejpam-5375	676	5	10	10	NUM
ejpam-5375	676	6	)	)	PUNCT
ejpam-5375	676	7	=	=	SYM
ejpam-5375	676	8	0	0	NUM
ejpam-5375	676	9	1	1	NUM
ejpam-5375	676	10	2	2	NUM
ejpam-5375	676	11	.	.	PUNCT
ejpam-5375	676	12	.	.	PUNCT
ejpam-5375	676	13	.	.	PUNCT
ejpam-5375	677	1	n	n	CCONJ
ejpam-5375	677	2	2	2	NUM
ejpam-5375	677	3	−	−	NUM
ejpam-5375	677	4	1	1	NUM
ejpam-5375	677	5	n	n	SYM
ejpam-5375	677	6	2	2	NUM
ejpam-5375	677	7	n	n	NUM
ejpam-5375	677	8	2	2	NUM
ejpam-5375	677	9	+	+	CCONJ
ejpam-5375	677	10	1	1	NUM
ejpam-5375	677	11	.	.	PUNCT
ejpam-5375	677	12	.	.	PUNCT
ejpam-5375	677	13	.	.	PUNCT
ejpam-5375	678	1	n−	n−	NOUN
ejpam-5375	678	2	2	2	NUM
ejpam-5375	678	3	n−	n−	NOUN
ejpam-5375	678	4	1	1	NUM
ejpam-5375	678	5			X
ejpam-5375	678	6	0	0	NUM
ejpam-5375	678	7	n−	n−	NOUN
ejpam-5375	678	8	1	1	NUM
ejpam-5375	678	9	1	1	NUM
ejpam-5375	678	10	1	1	NUM
ejpam-5375	678	11	.	.	PUNCT
ejpam-5375	678	12	.	.	PUNCT
ejpam-5375	679	1	.	.	PUNCT
ejpam-5375	680	1	1	1	NUM
ejpam-5375	680	2	1	1	NUM
ejpam-5375	680	3	1	1	NUM
ejpam-5375	680	4	.	.	PUNCT
ejpam-5375	680	5	.	.	PUNCT
ejpam-5375	680	6	.	.	PUNCT
ejpam-5375	681	1	1	1	NUM
ejpam-5375	681	2	1	1	NUM
ejpam-5375	681	3	1	1	NUM
ejpam-5375	681	4	1	1	NUM
ejpam-5375	681	5	2	2	NUM
ejpam-5375	681	6	0	0	NUM
ejpam-5375	681	7	.	.	PUNCT
ejpam-5375	681	8	.	.	PUNCT
ejpam-5375	682	1	.	.	PUNCT
ejpam-5375	683	1	0	0	NUM
ejpam-5375	684	1	0	0	NUM
ejpam-5375	684	2	0	0	NUM
ejpam-5375	684	3	.	.	PUNCT
ejpam-5375	684	4	.	.	PUNCT
ejpam-5375	685	1	.	.	PUNCT
ejpam-5375	686	1	0	0	NUM
ejpam-5375	686	2	1	1	NUM
ejpam-5375	686	3	2	2	NUM
ejpam-5375	686	4	1	1	NUM
ejpam-5375	686	5	0	0	NUM
ejpam-5375	686	6	2	2	NUM
ejpam-5375	686	7	.	.	PUNCT
ejpam-5375	686	8	.	.	PUNCT
ejpam-5375	686	9	.	.	PUNCT
ejpam-5375	687	1	0	0	NUM
ejpam-5375	688	1	0	0	NUM
ejpam-5375	688	2	0	0	NUM
ejpam-5375	688	3	.	.	PUNCT
ejpam-5375	688	4	.	.	PUNCT
ejpam-5375	688	5	.	.	PUNCT
ejpam-5375	689	1	1	1	NUM
ejpam-5375	689	2	0	0	NUM
ejpam-5375	689	3	...	...	PUNCT
ejpam-5375	689	4	...	...	PUNCT
ejpam-5375	689	5	...	...	PUNCT
ejpam-5375	689	6	...	...	PUNCT
ejpam-5375	689	7	.	.	PUNCT
ejpam-5375	689	8	.	.	PUNCT
ejpam-5375	689	9	.	.	PUNCT
ejpam-5375	689	10	...	...	PUNCT
ejpam-5375	689	11	...	...	PUNCT
ejpam-5375	689	12	...	...	PUNCT
ejpam-5375	689	13	...	...	PUNCT
ejpam-5375	689	14	...	...	PUNCT
ejpam-5375	689	15	...	...	PUNCT
ejpam-5375	690	1	n	n	X
ejpam-5375	690	2	2	2	NUM
ejpam-5375	690	3	−	−	NOUN
ejpam-5375	690	4	1	1	NUM
ejpam-5375	690	5	1	1	NUM
ejpam-5375	690	6	0	0	NUM
ejpam-5375	690	7	0	0	NUM
ejpam-5375	690	8	.	.	PUNCT
ejpam-5375	690	9	.	.	PUNCT
ejpam-5375	690	10	.	.	PUNCT
ejpam-5375	691	1	2	2	NUM
ejpam-5375	691	2	0	0	NUM
ejpam-5375	691	3	1	1	NUM
ejpam-5375	691	4	.	.	PUNCT
ejpam-5375	691	5	.	.	PUNCT
ejpam-5375	691	6	.	.	PUNCT
ejpam-5375	692	1	0	0	NUM
ejpam-5375	692	2	0	0	NUM
ejpam-5375	693	1	n	n	CCONJ
ejpam-5375	693	2	2	2	NUM
ejpam-5375	693	3	1	1	NUM
ejpam-5375	693	4	0	0	NUM
ejpam-5375	693	5	0	0	NUM
ejpam-5375	693	6	.	.	PUNCT
ejpam-5375	693	7	.	.	PUNCT
ejpam-5375	694	1	.	.	PUNCT
ejpam-5375	695	1	0	0	NUM
ejpam-5375	696	1	1	1	NUM
ejpam-5375	696	2	0	0	NUM
ejpam-5375	696	3	.	.	PUNCT
ejpam-5375	696	4	.	.	PUNCT
ejpam-5375	696	5	.	.	PUNCT
ejpam-5375	697	1	0	0	NUM
ejpam-5375	697	2	0	0	NUM
ejpam-5375	698	1	n	n	NUM
ejpam-5375	698	2	2	2	NUM
ejpam-5375	698	3	+	+	CCONJ
ejpam-5375	698	4	1	1	NUM
ejpam-5375	698	5	1	1	NUM
ejpam-5375	698	6	0	0	NUM
ejpam-5375	698	7	0	0	NUM
ejpam-5375	698	8	.	.	PUNCT
ejpam-5375	698	9	.	.	PUNCT
ejpam-5375	698	10	.	.	PUNCT
ejpam-5375	699	1	1	1	NUM
ejpam-5375	699	2	0	0	NUM
ejpam-5375	699	3	2	2	NUM
ejpam-5375	699	4	.	.	PUNCT
ejpam-5375	699	5	.	.	PUNCT
ejpam-5375	699	6	.	.	PUNCT
ejpam-5375	700	1	0	0	NUM
ejpam-5375	700	2	0	0	NUM
ejpam-5375	700	3	...	...	PUNCT
ejpam-5375	700	4	...	...	PUNCT
ejpam-5375	700	5	...	...	PUNCT
ejpam-5375	700	6	...	...	PUNCT
ejpam-5375	700	7	.	.	PUNCT
ejpam-5375	700	8	.	.	PUNCT
ejpam-5375	700	9	.	.	PUNCT
ejpam-5375	701	1	...	...	PUNCT
ejpam-5375	701	2	...	...	PUNCT
ejpam-5375	702	1	...	...	PUNCT
ejpam-5375	702	2	...	...	PUNCT
ejpam-5375	702	3	...	...	PUNCT
ejpam-5375	702	4	...	...	PUNCT
ejpam-5375	703	1	n−	n−	NOUN
ejpam-5375	703	2	2	2	NUM
ejpam-5375	703	3	1	1	NUM
ejpam-5375	703	4	0	0	NUM
ejpam-5375	703	5	1	1	NUM
ejpam-5375	703	6	.	.	PUNCT
ejpam-5375	703	7	.	.	PUNCT
ejpam-5375	703	8	.	.	PUNCT
ejpam-5375	704	1	0	0	NUM
ejpam-5375	705	1	0	0	NUM
ejpam-5375	705	2	0	0	NUM
ejpam-5375	705	3	.	.	PUNCT
ejpam-5375	705	4	.	.	PUNCT
ejpam-5375	705	5	.	.	PUNCT
ejpam-5375	706	1	2	2	NUM
ejpam-5375	706	2	0	0	NUM
ejpam-5375	706	3	n−	n−	NOUN
ejpam-5375	706	4	1	1	NUM
ejpam-5375	706	5	1	1	NUM
ejpam-5375	706	6	1	1	NUM
ejpam-5375	706	7	0	0	NUM
ejpam-5375	706	8	.	.	PUNCT
ejpam-5375	706	9	.	.	PUNCT
ejpam-5375	706	10	.	.	PUNCT
ejpam-5375	707	1	0	0	NUM
ejpam-5375	708	1	0	0	NUM
ejpam-5375	708	2	0	0	NUM
ejpam-5375	708	3	.	.	PUNCT
ejpam-5375	708	4	.	.	PUNCT
ejpam-5375	709	1	.	.	PUNCT
ejpam-5375	710	1	0	0	NUM
ejpam-5375	710	2	2	2	NUM
ejpam-5375	710	3	.	.	PUNCT
ejpam-5375	711	1	(	(	PUNCT
ejpam-5375	711	2	11	11	NUM
ejpam-5375	711	3	)	)	PUNCT
ejpam-5375	711	4	again	again	ADV
ejpam-5375	711	5	,	,	PUNCT
ejpam-5375	711	6	by	by	ADP
ejpam-5375	711	7	theorem	theorem	NOUN
ejpam-5375	711	8	6	6	NUM
ejpam-5375	711	9	with	with	ADP
ejpam-5375	711	10	a	a	DET
ejpam-5375	711	11	=	=	ADJ
ejpam-5375	711	12	n−	n−	NOUN
ejpam-5375	711	13	1	1	NUM
ejpam-5375	711	14	,	,	PUNCT
ejpam-5375	711	15	b	b	NOUN
ejpam-5375	711	16	=	=	SYM
ejpam-5375	711	17	2	2	NUM
ejpam-5375	711	18	,	,	PUNCT
ejpam-5375	711	19	c	c	NOUN
ejpam-5375	711	20	=	=	SYM
ejpam-5375	711	21	1	1	NUM
ejpam-5375	711	22	,	,	PUNCT
ejpam-5375	711	23	and	and	CCONJ
ejpam-5375	711	24	d	d	NOUN
ejpam-5375	711	25	=	=	SYM
ejpam-5375	711	26	1	1	NUM
ejpam-5375	711	27	,	,	PUNCT
ejpam-5375	711	28	we	we	PRON
ejpam-5375	711	29	have	have	AUX
ejpam-5375	711	30	psl(γzn	psl(γzn	VERB
ejpam-5375	711	31	)	)	PUNCT
ejpam-5375	712	1	(	(	PUNCT
ejpam-5375	712	2	λ	λ	NOUN
ejpam-5375	712	3	)	)	PUNCT
ejpam-5375	712	4	=(	=(	NOUN
ejpam-5375	712	5	λ3	λ3	PROPN
ejpam-5375	712	6	−	−	PROPN
ejpam-5375	712	7	(	(	PUNCT
ejpam-5375	712	8	n+	n+	NUM
ejpam-5375	712	9	3)λ2	3)λ2	NUM
ejpam-5375	712	10	+	+	CCONJ
ejpam-5375	712	11	3nλ−	3nλ−	NUM
ejpam-5375	712	12	2(n−	2(n−	NUM
ejpam-5375	712	13	2))(λ−	2))(λ−	NUM
ejpam-5375	712	14	3	3	NUM
ejpam-5375	712	15	)	)	PUNCT
ejpam-5375	712	16	n	n	PRON
ejpam-5375	712	17	2	2	NUM
ejpam-5375	712	18	−2(λ−	−2(λ−	PROPN
ejpam-5375	712	19	1	1	NUM
ejpam-5375	712	20	)	)	PUNCT
ejpam-5375	712	21	n	n	PRON
ejpam-5375	712	22	2	2	NUM
ejpam-5375	712	23	−1	−1	NOUN
ejpam-5375	712	24	=(	=(	NOUN
ejpam-5375	712	25	λ−	λ−	PROPN
ejpam-5375	712	26	2)(λ2	2)(λ2	NUM
ejpam-5375	713	1	−	−	PROPN
ejpam-5375	713	2	(	(	PUNCT
ejpam-5375	713	3	n+	n+	NUM
ejpam-5375	713	4	1)λ+	1)λ+	NUM
ejpam-5375	713	5	n−	n−	NOUN
ejpam-5375	713	6	2)(λ−	2)(λ−	NUM
ejpam-5375	713	7	3	3	NUM
ejpam-5375	713	8	)	)	PUNCT
ejpam-5375	713	9	n	n	PRON
ejpam-5375	713	10	2	2	NUM
ejpam-5375	713	11	−2(λ−	−2(λ−	PROPN
ejpam-5375	713	12	1	1	NUM
ejpam-5375	713	13	)	)	PUNCT
ejpam-5375	713	14	n	n	PRON
ejpam-5375	713	15	2	2	NUM
ejpam-5375	713	16	−1	−1	NOUN
ejpam-5375	713	17	.	.	PUNCT
ejpam-5375	714	1	the	the	DET
ejpam-5375	714	2	roots	root	NOUN
ejpam-5375	714	3	of	of	ADP
ejpam-5375	714	4	psl(γzn	psl(γzn	NOUN
ejpam-5375	714	5	)	)	PUNCT
ejpam-5375	714	6	(	(	PUNCT
ejpam-5375	714	7	λ	λ	X
ejpam-5375	714	8	)	)	PUNCT
ejpam-5375	714	9	=	=	SYM
ejpam-5375	714	10	0	0	NUM
ejpam-5375	714	11	are	be	AUX
ejpam-5375	714	12	λ1	λ1	ADJ
ejpam-5375	714	13	=	=	SYM
ejpam-5375	714	14	2	2	NUM
ejpam-5375	714	15	of	of	ADP
ejpam-5375	714	16	multiplicity	multiplicity	NOUN
ejpam-5375	714	17	1	1	NUM
ejpam-5375	714	18	,	,	PUNCT
ejpam-5375	714	19	λ2	λ2	NOUN
ejpam-5375	714	20	=	=	SYM
ejpam-5375	714	21	3	3	NUM
ejpam-5375	714	22	of	of	ADP
ejpam-5375	714	23	multiplicity	multiplicity	NOUN
ejpam-5375	714	24	n	n	CCONJ
ejpam-5375	714	25	2	2	NUM
ejpam-5375	714	26	−	−	NUM
ejpam-5375	714	27	2	2	NUM
ejpam-5375	714	28	,	,	PUNCT
ejpam-5375	714	29	λ3	λ3	PROPN
ejpam-5375	714	30	=	=	NOUN
ejpam-5375	714	31	1	1	NUM
ejpam-5375	714	32	of	of	ADP
ejpam-5375	714	33	multiplicity	multiplicity	NOUN
ejpam-5375	714	34	n	n	CCONJ
ejpam-5375	714	35	2	2	NUM
ejpam-5375	714	36	−	−	NUM
ejpam-5375	714	37	1	1	NUM
ejpam-5375	714	38	,	,	PUNCT
ejpam-5375	714	39	and	and	CCONJ
ejpam-5375	714	40	λ4,5	λ4,5	NOUN
ejpam-5375	714	41	=	=	SYM
ejpam-5375	714	42	n+1	n+1	PROPN
ejpam-5375	714	43	2	2	NUM
ejpam-5375	714	44	±	±	NUM
ejpam-5375	714	45	√	√	NUM
ejpam-5375	714	46	n2−2n+9	n2−2n+9	NOUN
ejpam-5375	714	47	2	2	NUM
ejpam-5375	714	48	of	of	ADP
ejpam-5375	714	49	multiplicity	multiplicity	NOUN
ejpam-5375	714	50	1	1	NUM
ejpam-5375	714	51	,	,	PUNCT
ejpam-5375	714	52	respectively	respectively	ADV
ejpam-5375	714	53	.	.	PUNCT
ejpam-5375	715	1	consequently	consequently	ADV
ejpam-5375	715	2	,	,	PUNCT
ejpam-5375	715	3	the	the	DET
ejpam-5375	715	4	spectrum	spectrum	NOUN
ejpam-5375	715	5	of	of	ADP
ejpam-5375	715	6	γzn	γzn	PROPN
ejpam-5375	715	7	is	be	AUX
ejpam-5375	715	8	specsl(γzn	specsl(γzn	VERB
ejpam-5375	715	9	)	)	PUNCT
ejpam-5375	715	10	=	=	PUNCT
ejpam-5375	716	1			PUNCT
ejpam-5375	716	2	(	(	PUNCT
ejpam-5375	716	3	n+	n+	NUM
ejpam-5375	716	4	1	1	NUM
ejpam-5375	716	5	2	2	NUM
ejpam-5375	716	6	+	+	CCONJ
ejpam-5375	716	7	√	√	ADJ
ejpam-5375	716	8	n2	n2	NOUN
ejpam-5375	716	9	−	−	PROPN
ejpam-5375	716	10	2n+	2n+	NUM
ejpam-5375	716	11	9	9	NUM
ejpam-5375	716	12	2	2	NUM
ejpam-5375	716	13	)	)	PUNCT
ejpam-5375	716	14	1	1	NUM
ejpam-5375	716	15	,	,	PUNCT
ejpam-5375	716	16	(	(	PUNCT
ejpam-5375	716	17	3	3	X
ejpam-5375	716	18	)	)	PUNCT
ejpam-5375	716	19	n	n	PRON
ejpam-5375	716	20	2	2	NUM
ejpam-5375	716	21	−2	−2	NOUN
ejpam-5375	716	22	,	,	PUNCT
ejpam-5375	716	23	(	(	PUNCT
ejpam-5375	716	24	2)1	2)1	NUM
ejpam-5375	716	25	,	,	PUNCT
ejpam-5375	716	26	(	(	PUNCT
ejpam-5375	716	27	1	1	X
ejpam-5375	716	28	)	)	PUNCT
ejpam-5375	716	29	n	n	PRON
ejpam-5375	716	30	2	2	NUM
ejpam-5375	716	31	−1	−1	NOUN
ejpam-5375	716	32	,	,	PUNCT
ejpam-5375	716	33	(	(	PUNCT
ejpam-5375	716	34	n+	n+	ADP
ejpam-5375	716	35	1	1	NUM
ejpam-5375	716	36	2	2	NUM
ejpam-5375	716	37	−	−	NOUN
ejpam-5375	716	38	√	√	PROPN
ejpam-5375	716	39	n2	n2	NOUN
ejpam-5375	716	40	−	−	PROPN
ejpam-5375	716	41	2n+	2n+	NUM
ejpam-5375	716	42	9	9	NUM
ejpam-5375	716	43	2	2	NUM
ejpam-5375	716	44	)	)	PUNCT
ejpam-5375	716	45	1	1	NUM
ejpam-5375	716	46			NOUN
ejpam-5375	716	47	.	.	PUNCT
ejpam-5375	717	1	it	it	PRON
ejpam-5375	717	2	is	be	AUX
ejpam-5375	717	3	clear	clear	ADJ
ejpam-5375	717	4	that	that	SCONJ
ejpam-5375	717	5	the	the	DET
ejpam-5375	717	6	spectral	spectral	ADJ
ejpam-5375	717	7	radius	radius	NOUN
ejpam-5375	717	8	of	of	ADP
ejpam-5375	717	9	γzn	γzn	PROPN
ejpam-5375	717	10	is	be	AUX
ejpam-5375	717	11	ρsl(γzn	ρsl(γzn	PRON
ejpam-5375	717	12	)	)	PUNCT
ejpam-5375	718	1	=	=	PRON
ejpam-5375	718	2	n+	n+	PUNCT
ejpam-5375	718	3	1	1	NUM
ejpam-5375	718	4	2	2	NUM
ejpam-5375	718	5	+	+	CCONJ
ejpam-5375	718	6	√	√	ADJ
ejpam-5375	718	7	n2	n2	NOUN
ejpam-5375	718	8	−	−	PROPN
ejpam-5375	718	9	2n+	2n+	NUM
ejpam-5375	718	10	9	9	NUM
ejpam-5375	718	11	2	2	NUM
ejpam-5375	718	12	.	.	PUNCT
ejpam-5375	719	1	therefore	therefore	ADV
ejpam-5375	719	2	,	,	PUNCT
ejpam-5375	719	3	the	the	DET
ejpam-5375	719	4	signless	signless	PROPN
ejpam-5375	719	5	laplacian	laplacian	ADJ
ejpam-5375	719	6	energy	energy	NOUN
ejpam-5375	719	7	of	of	ADP
ejpam-5375	719	8	γzn	γzn	PROPN
ejpam-5375	719	9	is	be	AUX
ejpam-5375	719	10	as	as	SCONJ
ejpam-5375	719	11	follows	follow	VERB
ejpam-5375	719	12	:	:	PUNCT
ejpam-5375	719	13	esl(γzn	esl(γzn	ADV
ejpam-5375	719	14	)	)	PUNCT
ejpam-5375	720	1	=	=	PUNCT
ejpam-5375	720	2	(	(	PUNCT
ejpam-5375	720	3	n	n	ADV
ejpam-5375	720	4	2	2	NUM
ejpam-5375	720	5	−	−	NOUN
ejpam-5375	720	6	2	2	NUM
ejpam-5375	720	7	)	)	PUNCT
ejpam-5375	720	8	|3|+	|3|+	PROPN
ejpam-5375	720	9	(	(	PUNCT
ejpam-5375	720	10	1	1	X
ejpam-5375	720	11	)	)	PUNCT
ejpam-5375	721	1	|2|+	|2|+	PROPN
ejpam-5375	721	2	(	(	PUNCT
ejpam-5375	721	3	n	n	NOUN
ejpam-5375	721	4	2	2	NUM
ejpam-5375	721	5	−	−	NOUN
ejpam-5375	721	6	1	1	NUM
ejpam-5375	721	7	)	)	PUNCT
ejpam-5375	721	8	|1|+	|1|+	PUNCT
ejpam-5375	722	1	∣∣∣∣∣n+	∣∣∣∣∣n+	NUM
ejpam-5375	722	2	1	1	NUM
ejpam-5375	722	3	2	2	NUM
ejpam-5375	722	4	±	±	NUM
ejpam-5375	722	5	√	√	PROPN
ejpam-5375	722	6	n2	n2	NOUN
ejpam-5375	722	7	−	−	PROPN
ejpam-5375	722	8	2n+	2n+	NUM
ejpam-5375	722	9	9	9	NUM
ejpam-5375	722	10	2	2	NUM
ejpam-5375	722	11	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-5375	722	12	=	=	SYM
ejpam-5375	723	1	3n−	3n−	NUM
ejpam-5375	723	2	4	4	NUM
ejpam-5375	723	3	.	.	NOUN
ejpam-5375	723	4	4	4	NUM
ejpam-5375	723	5	.	.	X
ejpam-5375	723	6	discussion	discussion	NOUN
ejpam-5375	723	7	from	from	ADP
ejpam-5375	723	8	the	the	DET
ejpam-5375	723	9	results	result	NOUN
ejpam-5375	723	10	of	of	ADP
ejpam-5375	723	11	the	the	DET
ejpam-5375	723	12	previous	previous	ADJ
ejpam-5375	723	13	section	section	NOUN
ejpam-5375	723	14	,	,	PUNCT
ejpam-5375	723	15	we	we	PRON
ejpam-5375	723	16	can	can	AUX
ejpam-5375	723	17	conclude	conclude	VERB
ejpam-5375	723	18	several	several	ADJ
ejpam-5375	723	19	interesting	interesting	ADJ
ejpam-5375	723	20	statements	statement	NOUN
ejpam-5375	723	21	.	.	PUNCT
ejpam-5375	724	1	references	reference	NOUN
ejpam-5375	724	2	2928	2928	NUM
ejpam-5375	724	3	corollary	corollary	ADJ
ejpam-5375	724	4	1	1	NUM
ejpam-5375	724	5	.	.	PUNCT
ejpam-5375	725	1	the	the	DET
ejpam-5375	725	2	laplacian	laplacian	ADJ
ejpam-5375	725	3	energy	energy	NOUN
ejpam-5375	725	4	of	of	ADP
ejpam-5375	725	5	γzn	γzn	PROPN
ejpam-5375	725	6	is	be	AUX
ejpam-5375	725	7	always	always	ADV
ejpam-5375	725	8	similar	similar	ADJ
ejpam-5375	725	9	to	to	ADP
ejpam-5375	725	10	the	the	DET
ejpam-5375	725	11	signless	signless	NOUN
ejpam-5375	725	12	laplacian	laplacian	ADJ
ejpam-5375	725	13	energy	energy	NOUN
ejpam-5375	725	14	of	of	ADP
ejpam-5375	725	15	γzn	γzn	PROPN
ejpam-5375	725	16	.	.	PUNCT
ejpam-5375	726	1	corollary	corollary	ADJ
ejpam-5375	726	2	2	2	NUM
ejpam-5375	726	3	.	.	PUNCT
ejpam-5375	727	1	the	the	DET
ejpam-5375	727	2	energy	energy	NOUN
ejpam-5375	727	3	of	of	ADP
ejpam-5375	727	4	γzn	γzn	PROPN
ejpam-5375	727	5	is	be	AUX
ejpam-5375	727	6	always	always	ADV
ejpam-5375	727	7	an	an	DET
ejpam-5375	727	8	even	even	ADV
ejpam-5375	727	9	integer	integer	NOUN
ejpam-5375	727	10	associated	associate	VERB
ejpam-5375	727	11	with	with	ADP
ejpam-5375	727	12	the	the	DET
ejpam-5375	727	13	laplacian	laplacian	ADJ
ejpam-5375	727	14	and	and	CCONJ
ejpam-5375	727	15	signless	signless	ADJ
ejpam-5375	727	16	laplacian	laplacian	ADJ
ejpam-5375	727	17	matrices	matrix	NOUN
ejpam-5375	727	18	.	.	PUNCT
ejpam-5375	728	1	corollary	corollary	ADJ
ejpam-5375	728	2	3	3	NUM
ejpam-5375	728	3	.	.	PUNCT
ejpam-5375	729	1	the	the	DET
ejpam-5375	729	2	energy	energy	NOUN
ejpam-5375	729	3	of	of	ADP
ejpam-5375	729	4	γzn	γzn	PROPN
ejpam-5375	729	5	for	for	ADP
ejpam-5375	729	6	odd	odd	ADJ
ejpam-5375	729	7	n	n	NOUN
ejpam-5375	729	8	is	be	AUX
ejpam-5375	729	9	never	never	ADV
ejpam-5375	729	10	an	an	DET
ejpam-5375	729	11	odd	odd	ADJ
ejpam-5375	729	12	integer	integer	NOUN
ejpam-5375	729	13	associated	associate	VERB
ejpam-5375	729	14	with	with	ADP
ejpam-5375	729	15	the	the	DET
ejpam-5375	729	16	adjacency	adjacency	NOUN
ejpam-5375	729	17	matrix	matrix	NOUN
ejpam-5375	729	18	.	.	PUNCT
ejpam-5375	730	1	corollary	corollary	ADJ
ejpam-5375	730	2	4	4	NUM
ejpam-5375	730	3	.	.	PUNCT
ejpam-5375	730	4	γzn	γzn	PROPN
ejpam-5375	730	5	is	be	AUX
ejpam-5375	730	6	hyperenergetic	hyperenergetic	ADJ
ejpam-5375	730	7	associated	associate	VERB
ejpam-5375	730	8	with	with	ADP
ejpam-5375	730	9	the	the	DET
ejpam-5375	730	10	laplacian	laplacian	ADJ
ejpam-5375	730	11	and	and	CCONJ
ejpam-5375	730	12	signless	signless	ADJ
ejpam-5375	730	13	laplacian	laplacian	ADJ
ejpam-5375	730	14	matrices	matrix	NOUN
ejpam-5375	730	15	.	.	PUNCT
ejpam-5375	731	1	acknowledgements	acknowledgement	NOUN
ejpam-5375	731	2	we	we	PRON
ejpam-5375	731	3	wish	wish	VERB
ejpam-5375	731	4	to	to	PART
ejpam-5375	731	5	express	express	VERB
ejpam-5375	731	6	our	our	PRON
ejpam-5375	731	7	gratitude	gratitude	NOUN
ejpam-5375	731	8	to	to	ADP
ejpam-5375	731	9	university	university	PROPN
ejpam-5375	731	10	of	of	ADP
ejpam-5375	731	11	mataram	mataram	PROPN
ejpam-5375	731	12	,	,	PUNCT
ejpam-5375	731	13	indonesia	indonesia	PROPN
ejpam-5375	731	14	,	,	PUNCT
ejpam-5375	731	15	for	for	ADP
ejpam-5375	731	16	providing	provide	VERB
ejpam-5375	731	17	partial	partial	ADJ
ejpam-5375	731	18	funding	funding	NOUN
ejpam-5375	731	19	assistance	assistance	NOUN
ejpam-5375	731	20	.	.	PUNCT
ejpam-5375	732	1	references	reference	NOUN
ejpam-5375	732	2	[	[	X
ejpam-5375	732	3	1	1	NUM
ejpam-5375	732	4	]	]	X
ejpam-5375	732	5	r	r	NOUN
ejpam-5375	732	6	b	b	X
ejpam-5375	732	7	bapat	bapat	PROPN
ejpam-5375	732	8	and	and	CCONJ
ejpam-5375	732	9	s	s	NOUN
ejpam-5375	732	10	pati	pati	NOUN
ejpam-5375	732	11	.	.	PUNCT
ejpam-5375	733	1	energy	energy	NOUN
ejpam-5375	733	2	of	of	ADP
ejpam-5375	733	3	a	a	DET
ejpam-5375	733	4	graph	graph	NOUN
ejpam-5375	733	5	is	be	AUX
ejpam-5375	733	6	never	never	ADV
ejpam-5375	733	7	an	an	DET
ejpam-5375	733	8	odd	odd	ADJ
ejpam-5375	733	9	integer	integer	NOUN
ejpam-5375	733	10	.	.	PUNCT
ejpam-5375	734	1	bulletin	bulletin	NOUN
ejpam-5375	734	2	of	of	ADP
ejpam-5375	734	3	kerala	kerala	PROPN
ejpam-5375	734	4	mathematics	mathematics	PROPN
ejpam-5375	734	5	association	association	PROPN
ejpam-5375	734	6	,	,	PUNCT
ejpam-5375	734	7	1:129–132	1:129–132	NUM
ejpam-5375	734	8	,	,	PUNCT
ejpam-5375	734	9	2004	2004	NUM
ejpam-5375	734	10	.	.	PUNCT
ejpam-5375	735	1	[	[	X
ejpam-5375	735	2	2	2	NUM
ejpam-5375	735	3	]	]	X
ejpam-5375	735	4	r	r	NOUN
ejpam-5375	735	5	a	a	DET
ejpam-5375	735	6	borzooei	borzooei	NOUN
ejpam-5375	735	7	and	and	CCONJ
ejpam-5375	735	8	h	h	PROPN
ejpam-5375	735	9	rashmanlou	rashmanlou	NOUN
ejpam-5375	735	10	.	.	PUNCT
ejpam-5375	736	1	cayley	cayley	ADJ
ejpam-5375	736	2	interval	interval	NOUN
ejpam-5375	736	3	-	-	PUNCT
ejpam-5375	736	4	valued	value	VERB
ejpam-5375	736	5	fuzzy	fuzzy	ADJ
ejpam-5375	736	6	graphs	graph	NOUN
ejpam-5375	736	7	.	.	PUNCT
ejpam-5375	737	1	upb	upb	ADJ
ejpam-5375	737	2	scientific	scientific	ADJ
ejpam-5375	737	3	bulletin	bulletin	NOUN
ejpam-5375	737	4	,	,	PUNCT
ejpam-5375	737	5	series	series	PROPN
ejpam-5375	737	6	a	a	PRON
ejpam-5375	737	7	:	:	PUNCT
ejpam-5375	737	8	applied	apply	VERB
ejpam-5375	737	9	mathematics	mathematic	NOUN
ejpam-5375	737	10	and	and	CCONJ
ejpam-5375	737	11	physics	physic	NOUN
ejpam-5375	737	12	,	,	PUNCT
ejpam-5375	737	13	78(3):83–94	78(3):83–94	NUM
ejpam-5375	737	14	,	,	PUNCT
ejpam-5375	737	15	2016	2016	NUM
ejpam-5375	737	16	.	.	PUNCT
ejpam-5375	738	1	[	[	X
ejpam-5375	738	2	3	3	X
ejpam-5375	738	3	]	]	PUNCT
ejpam-5375	738	4	a	a	DET
ejpam-5375	738	5	e	e	X
ejpam-5375	738	6	brouwer	brouwer	PROPN
ejpam-5375	738	7	and	and	CCONJ
ejpam-5375	738	8	w	w	NOUN
ejpam-5375	738	9	h	h	NOUN
ejpam-5375	738	10	haemers	haemer	NOUN
ejpam-5375	738	11	.	.	PUNCT
ejpam-5375	739	1	spectra	spectra	NOUN
ejpam-5375	739	2	of	of	ADP
ejpam-5375	739	3	graphs	graph	NOUN
ejpam-5375	739	4	.	.	PUNCT
ejpam-5375	740	1	springer	springer	NOUN
ejpam-5375	740	2	,	,	PUNCT
ejpam-5375	740	3	new	new	PROPN
ejpam-5375	740	4	york	york	PROPN
ejpam-5375	740	5	,	,	PUNCT
ejpam-5375	740	6	2011	2011	NUM
ejpam-5375	740	7	.	.	PUNCT
ejpam-5375	741	1	[	[	X
ejpam-5375	741	2	4	4	X
ejpam-5375	741	3	]	]	X
ejpam-5375	741	4	i	i	PROPN
ejpam-5375	741	5	gutman	gutman	PROPN
ejpam-5375	741	6	.	.	PUNCT
ejpam-5375	742	1	the	the	DET
ejpam-5375	742	2	energy	energy	NOUN
ejpam-5375	742	3	of	of	ADP
ejpam-5375	742	4	graph	graph	NOUN
ejpam-5375	742	5	.	.	PUNCT
ejpam-5375	743	1	ber	ber	NOUN
ejpam-5375	743	2	.	.	PUNCT
ejpam-5375	743	3	math.-stat	math.-stat	PROPN
ejpam-5375	743	4	.	.	PROPN
ejpam-5375	743	5	sekt	sekt	PROPN
ejpam-5375	743	6	.	.	PUNCT
ejpam-5375	744	1	forschungsz	forschungsz	PROPN
ejpam-5375	744	2	.	.	PUNCT
ejpam-5375	745	1	graz	graz	PROPN
ejpam-5375	745	2	,	,	PUNCT
ejpam-5375	745	3	103:1–2	103:1–2	NUM
ejpam-5375	745	4	,	,	PUNCT
ejpam-5375	745	5	1978	1978	NUM
ejpam-5375	745	6	.	.	PUNCT
ejpam-5375	746	1	[	[	X
ejpam-5375	746	2	5	5	NUM
ejpam-5375	746	3	]	]	PUNCT
ejpam-5375	746	4	w	w	PROPN
ejpam-5375	746	5	b	b	PROPN
ejpam-5375	746	6	v	v	ADP
ejpam-5375	746	7	kandasamy	kandasamy	NOUN
ejpam-5375	746	8	and	and	CCONJ
ejpam-5375	746	9	f	f	PROPN
ejpam-5375	746	10	smarandache	smarandache	NOUN
ejpam-5375	746	11	.	.	PUNCT
ejpam-5375	747	1	groups	group	NOUN
ejpam-5375	747	2	as	as	ADP
ejpam-5375	747	3	graphs	graph	NOUN
ejpam-5375	747	4	.	.	PUNCT
ejpam-5375	748	1	editura	editura	PROPN
ejpam-5375	748	2	cuart	cuart	NOUN
ejpam-5375	748	3	,	,	PUNCT
ejpam-5375	748	4	romania	romania	PROPN
ejpam-5375	748	5	,	,	PUNCT
ejpam-5375	748	6	2009	2009	NUM
ejpam-5375	748	7	.	.	PUNCT
ejpam-5375	749	1	[	[	X
ejpam-5375	749	2	6	6	NUM
ejpam-5375	749	3	]	]	PUNCT
ejpam-5375	749	4	l	l	NOUN
ejpam-5375	749	5	m	m	VERB
ejpam-5375	749	6	kumari	kumari	X
ejpam-5375	749	7	,	,	PUNCT
ejpam-5375	749	8	l	l	PROPN
ejpam-5375	749	9	pandiselvi	pandiselvi	ADJ
ejpam-5375	749	10	,	,	PUNCT
ejpam-5375	749	11	and	and	CCONJ
ejpam-5375	749	12	k	k	PROPN
ejpam-5375	749	13	palani	palani	PROPN
ejpam-5375	749	14	.	.	PUNCT
ejpam-5375	750	1	quotient	quotient	VERB
ejpam-5375	750	2	energy	energy	NOUN
ejpam-5375	750	3	of	of	ADP
ejpam-5375	750	4	zero	zero	NUM
ejpam-5375	750	5	divisor	divisor	NOUN
ejpam-5375	750	6	graphs	graph	NOUN
ejpam-5375	750	7	and	and	CCONJ
ejpam-5375	750	8	identity	identity	NOUN
ejpam-5375	750	9	graph	graph	NOUN
ejpam-5375	750	10	.	.	PUNCT
ejpam-5375	751	1	baghdad	baghdad	PROPN
ejpam-5375	751	2	sci	sci	PROPN
ejpam-5375	751	3	.	.	PUNCT
ejpam-5375	752	1	j.	j.	PROPN
ejpam-5375	752	2	,	,	PUNCT
ejpam-5375	752	3	20(1(si)):277–282	20(1(si)):277–282	NUM
ejpam-5375	752	4	,	,	PUNCT
ejpam-5375	752	5	2023	2023	NUM
ejpam-5375	752	6	.	.	PUNCT
ejpam-5375	753	1	[	[	X
ejpam-5375	753	2	7	7	NUM
ejpam-5375	753	3	]	]	X
ejpam-5375	753	4	x	x	X
ejpam-5375	753	5	li	li	PROPN
ejpam-5375	753	6	,	,	PUNCT
ejpam-5375	753	7	y	y	PROPN
ejpam-5375	753	8	shi	shi	PROPN
ejpam-5375	753	9	,	,	PUNCT
ejpam-5375	753	10	and	and	CCONJ
ejpam-5375	753	11	i	i	PROPN
ejpam-5375	753	12	gutman	gutman	NOUN
ejpam-5375	753	13	.	.	PUNCT
ejpam-5375	754	1	graph	graph	NOUN
ejpam-5375	754	2	energy	energy	NOUN
ejpam-5375	754	3	.	.	PUNCT
ejpam-5375	755	1	springer	springer	NOUN
ejpam-5375	755	2	,	,	PUNCT
ejpam-5375	755	3	new	new	PROPN
ejpam-5375	755	4	york	york	PROPN
ejpam-5375	755	5	,	,	PUNCT
ejpam-5375	755	6	2012	2012	NUM
ejpam-5375	755	7	.	.	PUNCT
ejpam-5375	756	1	[	[	X
ejpam-5375	756	2	8	8	NUM
ejpam-5375	756	3	]	]	SYM
ejpam-5375	756	4	v	v	ADP
ejpam-5375	756	5	lokesha	lokesha	NOUN
ejpam-5375	756	6	,	,	PUNCT
ejpam-5375	756	7	,	,	PUNCT
ejpam-5375	756	8	y	y	PROPN
ejpam-5375	756	9	shanthakumari	shanthakumari	NOUN
ejpam-5375	756	10	,	,	PUNCT
ejpam-5375	756	11	and	and	CCONJ
ejpam-5375	756	12	y	y	PROPN
ejpam-5375	756	13	zeba	zeba	PROPN
ejpam-5375	756	14	.	.	PUNCT
ejpam-5375	756	15	energy	energy	NOUN
ejpam-5375	756	16	and	and	CCONJ
ejpam-5375	756	17	skew	skew	ADJ
ejpam-5375	756	18	energy	energy	NOUN
ejpam-5375	756	19	of	of	ADP
ejpam-5375	756	20	a	a	DET
ejpam-5375	756	21	modified	modify	VERB
ejpam-5375	756	22	graph	graph	NOUN
ejpam-5375	756	23	.	.	PUNCT
ejpam-5375	757	1	creat	creat	PROPN
ejpam-5375	757	2	.	.	PUNCT
ejpam-5375	757	3	math	math	PROPN
ejpam-5375	757	4	.	.	PUNCT
ejpam-5375	758	1	inform	inform	NOUN
ejpam-5375	758	2	.	.	PUNCT
ejpam-5375	758	3	,	,	PUNCT
ejpam-5375	758	4	30(1):41–48	30(1):41–48	NUM
ejpam-5375	758	5	,	,	PUNCT
ejpam-5375	758	6	2021	2021	NUM
ejpam-5375	758	7	.	.	PUNCT
ejpam-5375	759	1	[	[	X
ejpam-5375	759	2	9	9	NUM
ejpam-5375	759	3	]	]	SYM
ejpam-5375	759	4	s	s	PART
ejpam-5375	759	5	pirzada	pirzada	NOUN
ejpam-5375	759	6	and	and	CCONJ
ejpam-5375	759	7	i	i	PROPN
ejpam-5375	759	8	gutman	gutman	PROPN
ejpam-5375	759	9	.	.	PUNCT
ejpam-5375	760	1	energy	energy	NOUN
ejpam-5375	760	2	of	of	ADP
ejpam-5375	760	3	a	a	DET
ejpam-5375	760	4	graph	graph	NOUN
ejpam-5375	760	5	is	be	AUX
ejpam-5375	760	6	never	never	ADV
ejpam-5375	760	7	the	the	DET
ejpam-5375	760	8	square	square	ADJ
ejpam-5375	760	9	root	root	NOUN
ejpam-5375	760	10	of	of	ADP
ejpam-5375	760	11	an	an	DET
ejpam-5375	760	12	odd	odd	ADJ
ejpam-5375	760	13	integer	integer	NOUN
ejpam-5375	760	14	.	.	PUNCT
ejpam-5375	761	1	applicable	applicable	ADJ
ejpam-5375	761	2	analysis	analysis	NOUN
ejpam-5375	761	3	and	and	CCONJ
ejpam-5375	761	4	discrete	discrete	ADJ
ejpam-5375	761	5	mathematics	mathematic	NOUN
ejpam-5375	761	6	,	,	PUNCT
ejpam-5375	761	7	2:118–121	2:118–121	NUM
ejpam-5375	761	8	,	,	PUNCT
ejpam-5375	761	9	2008	2008	NUM
ejpam-5375	761	10	.	.	PUNCT
ejpam-5375	762	1	[	[	X
ejpam-5375	762	2	10	10	NUM
ejpam-5375	762	3	]	]	X
ejpam-5375	762	4	n	n	PRON
ejpam-5375	762	5	m	m	NOUN
ejpam-5375	762	6	rilwan	rilwan	NOUN
ejpam-5375	762	7	and	and	CCONJ
ejpam-5375	762	8	a	a	DET
ejpam-5375	762	9	s	s	NOUN
ejpam-5375	762	10	hussain	hussain	NOUN
ejpam-5375	762	11	.	.	PUNCT
ejpam-5375	763	1	different	different	ADJ
ejpam-5375	763	2	kinds	kind	NOUN
ejpam-5375	763	3	of	of	ADP
ejpam-5375	763	4	cordial	cordial	ADJ
ejpam-5375	763	5	labeling	labeling	NOUN
ejpam-5375	763	6	on	on	ADP
ejpam-5375	763	7	identity	identity	NOUN
ejpam-5375	763	8	graphs	graph	NOUN
ejpam-5375	763	9	.	.	PUNCT
ejpam-5375	764	1	eur	eur	ADJ
ejpam-5375	764	2	.	.	PUNCT
ejpam-5375	764	3	chem	chem	PROPN
ejpam-5375	764	4	.	.	PUNCT
ejpam-5375	765	1	bull	bull	PROPN
ejpam-5375	765	2	.	.	PUNCT
ejpam-5375	765	3	,	,	PUNCT
ejpam-5375	765	4	12(10):12374–12381	12(10):12374–12381	NUM
ejpam-5375	765	5	,	,	PUNCT
ejpam-5375	765	6	2023	2023	NUM
ejpam-5375	765	7	.	.	PUNCT
ejpam-5375	766	1	references	reference	NOUN
ejpam-5375	766	2	2929	2929	NUM
ejpam-5375	767	1	[	[	X
ejpam-5375	767	2	11	11	NUM
ejpam-5375	767	3	]	]	SYM
ejpam-5375	767	4	m	m	VERB
ejpam-5375	767	5	u	u	NOUN
ejpam-5375	767	6	romdhini	romdhini	NOUN
ejpam-5375	767	7	and	and	CCONJ
ejpam-5375	767	8	a	a	DET
ejpam-5375	767	9	nawawi	nawawi	ADJ
ejpam-5375	767	10	.	.	PUNCT
ejpam-5375	767	11	degree	degree	NOUN
ejpam-5375	767	12	subtraction	subtraction	NOUN
ejpam-5375	767	13	energy	energy	NOUN
ejpam-5375	767	14	of	of	ADP
ejpam-5375	767	15	commuting	commute	VERB
ejpam-5375	767	16	and	and	CCONJ
ejpam-5375	767	17	noncommuting	noncommute	VERB
ejpam-5375	767	18	graphs	graph	NOUN
ejpam-5375	767	19	for	for	ADP
ejpam-5375	767	20	dihedral	dihedral	ADJ
ejpam-5375	767	21	groups	group	NOUN
ejpam-5375	767	22	.	.	PUNCT
ejpam-5375	768	1	international	international	ADJ
ejpam-5375	768	2	journal	journal	PROPN
ejpam-5375	768	3	of	of	ADP
ejpam-5375	768	4	mathematics	mathematic	NOUN
ejpam-5375	768	5	and	and	CCONJ
ejpam-5375	768	6	computer	computer	NOUN
ejpam-5375	768	7	science	science	NOUN
ejpam-5375	768	8	,	,	PUNCT
ejpam-5375	768	9	18(3):497–508	18(3):497–508	NUM
ejpam-5375	768	10	,	,	PUNCT
ejpam-5375	768	11	2023	2023	NUM
ejpam-5375	768	12	.	.	PUNCT
ejpam-5375	769	1	[	[	X
ejpam-5375	769	2	12	12	NUM
ejpam-5375	769	3	]	]	X
ejpam-5375	769	4	m	m	VERB
ejpam-5375	769	5	u	u	NOUN
ejpam-5375	769	6	romdhini	romdhini	NOUN
ejpam-5375	769	7	and	and	CCONJ
ejpam-5375	769	8	a.	a.	PROPN
ejpam-5375	769	9	nawawi	nawawi	PROPN
ejpam-5375	769	10	.	.	PUNCT
ejpam-5375	770	1	on	on	ADP
ejpam-5375	770	2	the	the	DET
ejpam-5375	770	3	spectral	spectral	ADJ
ejpam-5375	770	4	radius	radius	NOUN
ejpam-5375	770	5	and	and	CCONJ
ejpam-5375	770	6	sombor	sombor	NOUN
ejpam-5375	770	7	energy	energy	NOUN
ejpam-5375	770	8	of	of	ADP
ejpam-5375	770	9	the	the	DET
ejpam-5375	770	10	non	non	ADJ
ejpam-5375	770	11	-	-	ADJ
ejpam-5375	770	12	commuting	commuting	ADJ
ejpam-5375	770	13	graph	graph	NOUN
ejpam-5375	770	14	for	for	ADP
ejpam-5375	770	15	dihedral	dihedral	ADJ
ejpam-5375	770	16	groups	group	NOUN
ejpam-5375	770	17	.	.	PUNCT
ejpam-5375	771	1	mal	mal	ADJ
ejpam-5375	771	2	.	.	PUNCT
ejpam-5375	771	3	j.	j.	PROPN
ejpam-5375	771	4	fund	fund	PROPN
ejpam-5375	771	5	.	.	PUNCT
ejpam-5375	772	1	appl	appl	PROPN
ejpam-5375	772	2	.	.	PUNCT
ejpam-5375	773	1	sci	sci	PROPN
ejpam-5375	773	2	.	.	PROPN
ejpam-5375	773	3	,	,	PUNCT
ejpam-5375	773	4	20(1):65–73	20(1):65–73	NUM
ejpam-5375	773	5	,	,	PUNCT
ejpam-5375	773	6	2024	2024	NUM
ejpam-5375	773	7	.	.	PUNCT
ejpam-5375	774	1	[	[	X
ejpam-5375	774	2	13	13	NUM
ejpam-5375	774	3	]	]	SYM
ejpam-5375	774	4	m	m	VERB
ejpam-5375	774	5	u	u	NOUN
ejpam-5375	774	6	romdhini	romdhini	NOUN
ejpam-5375	774	7	,	,	PUNCT
ejpam-5375	774	8	a.	a.	PROPN
ejpam-5375	774	9	nawawi	nawawi	PROPN
ejpam-5375	774	10	,	,	PUNCT
ejpam-5375	774	11	f	f	PROPN
ejpam-5375	774	12	al	al	PROPN
ejpam-5375	774	13	-	-	PUNCT
ejpam-5375	774	14	sharqi	sharqi	PROPN
ejpam-5375	774	15	,	,	PUNCT
ejpam-5375	774	16	and	and	CCONJ
ejpam-5375	774	17	a	a	DET
ejpam-5375	774	18	al	al	PROPN
ejpam-5375	774	19	-	-	PUNCT
ejpam-5375	774	20	quran	quran	PROPN
ejpam-5375	774	21	.	.	PUNCT
ejpam-5375	775	1	closeness	closeness	NOUN
ejpam-5375	775	2	energy	energy	NOUN
ejpam-5375	775	3	of	of	ADP
ejpam-5375	775	4	non	non	ADJ
ejpam-5375	775	5	-	-	ADJ
ejpam-5375	775	6	commuting	commuting	ADJ
ejpam-5375	775	7	graph	graph	NOUN
ejpam-5375	775	8	for	for	ADP
ejpam-5375	775	9	dihedral	dihedral	ADJ
ejpam-5375	775	10	groups	group	NOUN
ejpam-5375	775	11	.	.	PUNCT
ejpam-5375	776	1	eur	eur	PROPN
ejpam-5375	776	2	.	.	PUNCT
ejpam-5375	777	1	j.	j.	PROPN
ejpam-5375	777	2	pure	pure	PROPN
ejpam-5375	777	3	appl	appl	PROPN
ejpam-5375	777	4	.	.	PUNCT
ejpam-5375	777	5	math	math	PROPN
ejpam-5375	777	6	.	.	PUNCT
ejpam-5375	777	7	,	,	PUNCT
ejpam-5375	777	8	17(1):212–221	17(1):212–221	NUM
ejpam-5375	777	9	,	,	PUNCT
ejpam-5375	777	10	2024	2024	NUM
ejpam-5375	777	11	.	.	PUNCT
ejpam-5375	778	1	[	[	X
ejpam-5375	778	2	14	14	NUM
ejpam-5375	778	3	]	]	X
ejpam-5375	778	4	m	m	VERB
ejpam-5375	778	5	u	u	NOUN
ejpam-5375	778	6	romdhini	romdhini	NOUN
ejpam-5375	778	7	,	,	PUNCT
ejpam-5375	778	8	a.	a.	PROPN
ejpam-5375	778	9	nawawi	nawawi	PROPN
ejpam-5375	778	10	,	,	PUNCT
ejpam-5375	778	11	f	f	PROPN
ejpam-5375	778	12	al	al	PROPN
ejpam-5375	778	13	-	-	PUNCT
ejpam-5375	778	14	sharqi	sharqi	PROPN
ejpam-5375	778	15	,	,	PUNCT
ejpam-5375	778	16	and	and	CCONJ
ejpam-5375	778	17	a	a	DET
ejpam-5375	778	18	al	al	PROPN
ejpam-5375	778	19	-	-	PUNCT
ejpam-5375	778	20	quran	quran	PROPN
ejpam-5375	778	21	.	.	PUNCT
ejpam-5375	779	1	spectral	spectral	ADJ
ejpam-5375	779	2	properties	property	NOUN
ejpam-5375	779	3	of	of	ADP
ejpam-5375	779	4	power	power	NOUN
ejpam-5375	779	5	graph	graph	NOUN
ejpam-5375	779	6	of	of	ADP
ejpam-5375	779	7	dihedral	dihedral	ADJ
ejpam-5375	779	8	groups	group	NOUN
ejpam-5375	779	9	.	.	PUNCT
ejpam-5375	780	1	eur	eur	PROPN
ejpam-5375	780	2	.	.	PUNCT
ejpam-5375	781	1	j.	j.	PROPN
ejpam-5375	781	2	pure	pure	PROPN
ejpam-5375	781	3	appl	appl	PROPN
ejpam-5375	781	4	.	.	PUNCT
ejpam-5375	781	5	math	math	PROPN
ejpam-5375	781	6	.	.	PUNCT
ejpam-5375	781	7	,	,	PUNCT
ejpam-5375	781	8	17(2):591–603	17(2):591–603	NUM
ejpam-5375	781	9	,	,	PUNCT
ejpam-5375	781	10	2024	2024	NUM
ejpam-5375	781	11	.	.	PUNCT
ejpam-5375	782	1	[	[	X
ejpam-5375	782	2	15	15	NUM
ejpam-5375	782	3	]	]	X
ejpam-5375	782	4	m	m	VERB
ejpam-5375	782	5	u	u	NOUN
ejpam-5375	782	6	romdhini	romdhini	NOUN
ejpam-5375	782	7	,	,	PUNCT
ejpam-5375	782	8	a.	a.	PROPN
ejpam-5375	782	9	nawawi	nawawi	PROPN
ejpam-5375	782	10	,	,	PUNCT
ejpam-5375	782	11	f	f	PROPN
ejpam-5375	782	12	al	al	PROPN
ejpam-5375	782	13	-	-	PUNCT
ejpam-5375	782	14	sharqi	sharqi	PROPN
ejpam-5375	782	15	,	,	PUNCT
ejpam-5375	782	16	a	a	DET
ejpam-5375	782	17	al	al	PROPN
ejpam-5375	782	18	-	-	PUNCT
ejpam-5375	782	19	quran	quran	PROPN
ejpam-5375	782	20	,	,	PUNCT
ejpam-5375	782	21	and	and	CCONJ
ejpam-5375	782	22	s	s	NOUN
ejpam-5375	782	23	r	r	NOUN
ejpam-5375	782	24	kamali	kamali	X
ejpam-5375	782	25	.	.	PUNCT
ejpam-5375	783	1	wienerhosoya	wienerhosoya	PROPN
ejpam-5375	783	2	energy	energy	NOUN
ejpam-5375	783	3	of	of	ADP
ejpam-5375	783	4	non	non	ADJ
ejpam-5375	783	5	-	-	ADJ
ejpam-5375	783	6	commuting	commuting	ADJ
ejpam-5375	783	7	graph	graph	NOUN
ejpam-5375	783	8	for	for	ADP
ejpam-5375	783	9	dihedral	dihedral	ADJ
ejpam-5375	783	10	groups	group	NOUN
ejpam-5375	783	11	.	.	PUNCT
ejpam-5375	784	1	asia	asia	PROPN
ejpam-5375	784	2	pac	pac	PROPN
ejpam-5375	784	3	.	.	PUNCT
ejpam-5375	785	1	j.	j.	PROPN
ejpam-5375	785	2	math	math	PROPN
ejpam-5375	785	3	.	.	PUNCT
ejpam-5375	785	4	,	,	PUNCT
ejpam-5375	785	5	11(9):1–9	11(9):1–9	NUM
ejpam-5375	785	6	,	,	PUNCT
ejpam-5375	785	7	2024	2024	NUM
ejpam-5375	785	8	.	.	PUNCT
ejpam-5375	786	1	[	[	X
ejpam-5375	786	2	16	16	NUM
ejpam-5375	786	3	]	]	X
ejpam-5375	786	4	y	y	PROPN
ejpam-5375	786	5	shanthakumari	shanthakumari	PROPN
ejpam-5375	786	6	,	,	PUNCT
ejpam-5375	786	7	m	m	PROPN
ejpam-5375	786	8	smitha	smitha	PROPN
ejpam-5375	786	9	,	,	PUNCT
ejpam-5375	786	10	and	and	CCONJ
ejpam-5375	786	11	v	v	ADP
ejpam-5375	786	12	lokesha	lokesha	NOUN
ejpam-5375	786	13	.	.	PUNCT
ejpam-5375	787	1	euclidean	euclidean	PROPN
ejpam-5375	787	2	degree	degree	NOUN
ejpam-5375	787	3	energy	energy	NOUN
ejpam-5375	787	4	graphs	graph	NOUN
ejpam-5375	787	5	.	.	PUNCT
ejpam-5375	788	1	montes	montes	PROPN
ejpam-5375	788	2	taurus	taurus	PROPN
ejpam-5375	788	3	j.	j.	PROPN
ejpam-5375	788	4	pure	pure	PROPN
ejpam-5375	788	5	appl	appl	PROPN
ejpam-5375	788	6	.	.	PUNCT
ejpam-5375	788	7	math	math	PROPN
ejpam-5375	788	8	.	.	PUNCT
ejpam-5375	788	9	,	,	PUNCT
ejpam-5375	788	10	3(1):89–105	3(1):89–105	NOUN
ejpam-5375	788	11	,	,	PUNCT
ejpam-5375	788	12	2021	2021	NUM
ejpam-5375	788	13	.	.	PUNCT
ejpam-5375	789	1	[	[	X
ejpam-5375	789	2	17	17	NUM
ejpam-5375	789	3	]	]	X
ejpam-5375	789	4	x	x	X
ejpam-5375	789	5	shi	shi	PROPN
ejpam-5375	789	6	,	,	PUNCT
ejpam-5375	789	7	s	s	PART
ejpam-5375	789	8	kosari	kosari	X
ejpam-5375	789	9	,	,	PUNCT
ejpam-5375	789	10	a	a	DET
ejpam-5375	789	11	a	a	DET
ejpam-5375	789	12	talebi	talebi	ADJ
ejpam-5375	789	13	,	,	PUNCT
ejpam-5375	789	14	s	s	NOUN
ejpam-5375	789	15	h	h	NOUN
ejpam-5375	789	16	sadati	sadati	NOUN
ejpam-5375	789	17	,	,	PUNCT
ejpam-5375	789	18	and	and	CCONJ
ejpam-5375	789	19	h	h	PROPN
ejpam-5375	789	20	rashmanlou	rashmanlou	NOUN
ejpam-5375	789	21	.	.	PUNCT
ejpam-5375	790	1	investigation	investigation	NOUN
ejpam-5375	790	2	of	of	ADP
ejpam-5375	790	3	the	the	DET
ejpam-5375	790	4	main	main	ADJ
ejpam-5375	790	5	energies	energy	NOUN
ejpam-5375	790	6	of	of	ADP
ejpam-5375	790	7	picture	picture	NOUN
ejpam-5375	790	8	fuzzy	fuzzy	ADJ
ejpam-5375	790	9	graph	graph	NOUN
ejpam-5375	790	10	and	and	CCONJ
ejpam-5375	790	11	its	its	PRON
ejpam-5375	790	12	applications	application	NOUN
ejpam-5375	790	13	.	.	PUNCT
ejpam-5375	791	1	int	int	NOUN
ejpam-5375	791	2	.	.	PUNCT
ejpam-5375	792	1	j.	j.	PROPN
ejpam-5375	792	2	comput	comput	PROPN
ejpam-5375	792	3	.	.	PUNCT
ejpam-5375	793	1	intell	intell	PROPN
ejpam-5375	793	2	.	.	PUNCT
ejpam-5375	794	1	syst	syst	PROPN
ejpam-5375	794	2	.	.	PROPN
ejpam-5375	794	3	,	,	PUNCT
ejpam-5375	794	4	15(1):31	15(1):31	NUM
ejpam-5375	794	5	,	,	PUNCT
ejpam-5375	794	6	2022	2022	NUM
ejpam-5375	794	7	.	.	PUNCT
ejpam-5375	795	1	[	[	X
ejpam-5375	795	2	18	18	NUM
ejpam-5375	795	3	]	]	PUNCT
ejpam-5375	795	4	a	a	DET
ejpam-5375	795	5	siwach	siwach	NOUN
ejpam-5375	795	6	,	,	PUNCT
ejpam-5375	795	7	v	v	PROPN
ejpam-5375	795	8	bhatia	bhatia	PROPN
ejpam-5375	795	9	,	,	PUNCT
ejpam-5375	795	10	a	a	DET
ejpam-5375	795	11	sehgal	sehgal	NOUN
ejpam-5375	795	12	,	,	PUNCT
ejpam-5375	795	13	and	and	CCONJ
ejpam-5375	795	14	p	p	PROPN
ejpam-5375	795	15	rana	rana	PROPN
ejpam-5375	795	16	.	.	PUNCT
ejpam-5375	796	1	characteristic	characteristic	ADJ
ejpam-5375	796	2	polynomial	polynomial	NOUN
ejpam-5375	796	3	of	of	ADP
ejpam-5375	796	4	maximum	maximum	ADJ
ejpam-5375	796	5	and	and	CCONJ
ejpam-5375	796	6	minimum	minimum	ADJ
ejpam-5375	796	7	matrix	matrix	NOUN
ejpam-5375	796	8	of	of	ADP
ejpam-5375	796	9	square	square	ADJ
ejpam-5375	796	10	power	power	NOUN
ejpam-5375	796	11	graph	graph	NOUN
ejpam-5375	796	12	of	of	ADP
ejpam-5375	796	13	dihedral	dihedral	ADJ
ejpam-5375	796	14	group	group	NOUN
ejpam-5375	796	15	of	of	ADP
ejpam-5375	796	16	order	order	NOUN
ejpam-5375	796	17	2n	2n	NUM
ejpam-5375	796	18	with	with	ADP
ejpam-5375	796	19	odd	odd	ADJ
ejpam-5375	796	20	natural	natural	ADJ
ejpam-5375	796	21	number	number	NOUN
ejpam-5375	796	22	n.	n.	NOUN
ejpam-5375	796	23	int	int	PROPN
ejpam-5375	796	24	.	.	PUNCT
ejpam-5375	797	1	j.	j.	PROPN
ejpam-5375	797	2	stat	stat	PROPN
ejpam-5375	797	3	.	.	PUNCT
ejpam-5375	798	1	appl	appl	PROPN
ejpam-5375	798	2	.	.	PROPN
ejpam-5375	798	3	math	math	PROPN
ejpam-5375	798	4	.	.	PUNCT
ejpam-5375	798	5	,	,	PUNCT
ejpam-5375	798	6	9(3):57–64	9(3):57–64	NUM
ejpam-5375	798	7	,	,	PUNCT
ejpam-5375	798	8	2024	2024	NUM
ejpam-5375	798	9	.	.	PUNCT