id	sid	tid	token	lemma	pos
ejpam-5036	1	1	european	european	PROPN
ejpam-5036	1	2	journal	journal	PROPN
ejpam-5036	1	3	of	of	ADP
ejpam-5036	1	4	pure	pure	ADJ
ejpam-5036	1	5	and	and	CCONJ
ejpam-5036	1	6	applied	apply	VERB
ejpam-5036	1	7	mathematics	mathematic	NOUN
ejpam-5036	1	8	vol	vol	NOUN
ejpam-5036	1	9	.	.	PROPN
ejpam-5036	2	1	17	17	NUM
ejpam-5036	2	2	,	,	PUNCT
ejpam-5036	2	3	no	no	INTJ
ejpam-5036	2	4	.	.	NOUN
ejpam-5036	2	5	2	2	NUM
ejpam-5036	2	6	,	,	PUNCT
ejpam-5036	2	7	2024	2024	NUM
ejpam-5036	2	8	,	,	PUNCT
ejpam-5036	2	9	591	591	NUM
ejpam-5036	2	10	-	-	SYM
ejpam-5036	2	11	603	603	NUM
ejpam-5036	2	12	issn	issn	PROPN
ejpam-5036	2	13	1307	1307	NUM
ejpam-5036	2	14	-	-	SYM
ejpam-5036	2	15	5543	5543	NUM
ejpam-5036	2	16	–	–	PUNCT
ejpam-5036	2	17	ejpam.com	ejpam.com	X
ejpam-5036	2	18	published	publish	VERB
ejpam-5036	2	19	by	by	ADP
ejpam-5036	2	20	new	new	PROPN
ejpam-5036	2	21	york	york	PROPN
ejpam-5036	2	22	business	business	PROPN
ejpam-5036	2	23	global	global	ADJ
ejpam-5036	2	24	spectral	spectral	ADJ
ejpam-5036	2	25	properties	property	NOUN
ejpam-5036	2	26	of	of	ADP
ejpam-5036	2	27	power	power	NOUN
ejpam-5036	2	28	graph	graph	NOUN
ejpam-5036	2	29	of	of	ADP
ejpam-5036	2	30	dihedral	dihedral	ADJ
ejpam-5036	2	31	groups	group	NOUN
ejpam-5036	2	32	mamika	mamika	PROPN
ejpam-5036	2	33	ujianita	ujianita	PROPN
ejpam-5036	2	34	romdhini1,∗	romdhini1,∗	PROPN
ejpam-5036	2	35	,	,	PUNCT
ejpam-5036	2	36	athirah	athirah	PROPN
ejpam-5036	2	37	nawawi2	nawawi2	PROPN
ejpam-5036	2	38	,	,	PUNCT
ejpam-5036	2	39	faisal	faisal	PROPN
ejpam-5036	2	40	al	al	PROPN
ejpam-5036	2	41	-	-	PUNCT
ejpam-5036	2	42	sharqi3,4	sharqi3,4	PROPN
ejpam-5036	2	43	,	,	PUNCT
ejpam-5036	2	44	ashraf	ashraf	PROPN
ejpam-5036	2	45	al	al	PROPN
ejpam-5036	2	46	-	-	PUNCT
ejpam-5036	2	47	quran5	quran5	PROPN
ejpam-5036	2	48	1	1	NUM
ejpam-5036	2	49	department	department	NOUN
ejpam-5036	2	50	of	of	ADP
ejpam-5036	2	51	mathematics	mathematic	NOUN
ejpam-5036	2	52	,	,	PUNCT
ejpam-5036	2	53	faculty	faculty	NOUN
ejpam-5036	2	54	of	of	ADP
ejpam-5036	2	55	mathematics	mathematic	NOUN
ejpam-5036	2	56	and	and	CCONJ
ejpam-5036	2	57	natural	natural	ADJ
ejpam-5036	2	58	science	science	NOUN
ejpam-5036	2	59	,	,	PUNCT
ejpam-5036	2	60	universitas	universitas	PROPN
ejpam-5036	2	61	mataram	mataram	PROPN
ejpam-5036	2	62	,	,	PUNCT
ejpam-5036	2	63	mataram	mataram	PROPN
ejpam-5036	2	64	83125	83125	NUM
ejpam-5036	2	65	,	,	PUNCT
ejpam-5036	2	66	indonesia	indonesia	PROPN
ejpam-5036	2	67	2	2	NUM
ejpam-5036	2	68	department	department	NOUN
ejpam-5036	2	69	of	of	ADP
ejpam-5036	2	70	mathematics	mathematic	NOUN
ejpam-5036	2	71	and	and	CCONJ
ejpam-5036	2	72	statistics	statistic	NOUN
ejpam-5036	2	73	,	,	PUNCT
ejpam-5036	2	74	faculty	faculty	NOUN
ejpam-5036	2	75	of	of	ADP
ejpam-5036	2	76	science	science	NOUN
ejpam-5036	2	77	,	,	PUNCT
ejpam-5036	2	78	universiti	universiti	PROPN
ejpam-5036	2	79	putra	putra	PROPN
ejpam-5036	2	80	malaysia	malaysia	PROPN
ejpam-5036	2	81	,	,	PUNCT
ejpam-5036	2	82	43400	43400	NUM
ejpam-5036	2	83	serdang	serdang	PROPN
ejpam-5036	2	84	,	,	PUNCT
ejpam-5036	2	85	selangor	selangor	PROPN
ejpam-5036	2	86	,	,	PUNCT
ejpam-5036	2	87	malaysia	malaysia	PROPN
ejpam-5036	2	88	3	3	NUM
ejpam-5036	2	89	department	department	NOUN
ejpam-5036	2	90	of	of	ADP
ejpam-5036	2	91	mathematics	mathematic	NOUN
ejpam-5036	2	92	,	,	PUNCT
ejpam-5036	2	93	faculty	faculty	NOUN
ejpam-5036	2	94	of	of	ADP
ejpam-5036	2	95	education	education	NOUN
ejpam-5036	2	96	for	for	ADP
ejpam-5036	2	97	pure	pure	ADJ
ejpam-5036	2	98	sciences	science	NOUN
ejpam-5036	2	99	,	,	PUNCT
ejpam-5036	2	100	university	university	NOUN
ejpam-5036	2	101	of	of	ADP
ejpam-5036	2	102	anbar	anbar	PROPN
ejpam-5036	2	103	,	,	PUNCT
ejpam-5036	2	104	ramadi	ramadi	PROPN
ejpam-5036	2	105	,	,	PUNCT
ejpam-5036	2	106	anbar	anbar	NOUN
ejpam-5036	2	107	,	,	PUNCT
ejpam-5036	2	108	iraq	iraq	PROPN
ejpam-5036	2	109	4	4	NUM
ejpam-5036	2	110	college	college	NOUN
ejpam-5036	2	111	of	of	ADP
ejpam-5036	2	112	engineering	engineering	NOUN
ejpam-5036	2	113	,	,	PUNCT
ejpam-5036	2	114	national	national	ADJ
ejpam-5036	2	115	university	university	PROPN
ejpam-5036	2	116	of	of	ADP
ejpam-5036	2	117	science	science	NOUN
ejpam-5036	2	118	and	and	CCONJ
ejpam-5036	2	119	technology	technology	NOUN
ejpam-5036	2	120	,	,	PUNCT
ejpam-5036	2	121	dhi	dhi	PROPN
ejpam-5036	2	122	qar	qar	PROPN
ejpam-5036	2	123	,	,	PUNCT
ejpam-5036	2	124	iraq	iraq	PROPN
ejpam-5036	2	125	5	5	NUM
ejpam-5036	2	126	basic	basic	ADJ
ejpam-5036	2	127	sciences	sciences	PROPN
ejpam-5036	2	128	department	department	NOUN
ejpam-5036	2	129	,	,	PUNCT
ejpam-5036	2	130	preparatory	preparatory	ADJ
ejpam-5036	2	131	year	year	NOUN
ejpam-5036	2	132	deanship	deanship	NOUN
ejpam-5036	2	133	,	,	PUNCT
ejpam-5036	2	134	king	king	NOUN
ejpam-5036	2	135	faisal	faisal	PROPN
ejpam-5036	2	136	university	university	PROPN
ejpam-5036	2	137	,	,	PUNCT
ejpam-5036	2	138	al	al	PROPN
ejpam-5036	2	139	-	-	PUNCT
ejpam-5036	2	140	ahsa	ahsa	PROPN
ejpam-5036	2	141	,	,	PUNCT
ejpam-5036	2	142	saudi	saudi	PROPN
ejpam-5036	2	143	arabia	arabia	PROPN
ejpam-5036	2	144	abstract	abstract	NOUN
ejpam-5036	2	145	.	.	PUNCT
ejpam-5036	3	1	this	this	DET
ejpam-5036	3	2	paper	paper	NOUN
ejpam-5036	3	3	focuses	focus	VERB
ejpam-5036	3	4	on	on	ADP
ejpam-5036	3	5	the	the	DET
ejpam-5036	3	6	power	power	NOUN
ejpam-5036	3	7	graph	graph	NOUN
ejpam-5036	3	8	of	of	ADP
ejpam-5036	3	9	dihedral	dihedral	ADJ
ejpam-5036	3	10	groups	group	NOUN
ejpam-5036	3	11	of	of	ADP
ejpam-5036	3	12	order	order	NOUN
ejpam-5036	3	13	2n	2n	NUM
ejpam-5036	3	14	,	,	PUNCT
ejpam-5036	3	15	d2n	d2n	PROPN
ejpam-5036	3	16	,	,	PUNCT
ejpam-5036	3	17	where	where	SCONJ
ejpam-5036	3	18	n	n	PRON
ejpam-5036	3	19	≥	≥	NOUN
ejpam-5036	3	20	3	3	X
ejpam-5036	3	21	.	.	PUNCT
ejpam-5036	4	1	we	we	PRON
ejpam-5036	4	2	show	show	VERB
ejpam-5036	4	3	the	the	DET
ejpam-5036	4	4	characteristic	characteristic	ADJ
ejpam-5036	4	5	polynomial	polynomial	NOUN
ejpam-5036	4	6	of	of	ADP
ejpam-5036	4	7	the	the	DET
ejpam-5036	4	8	power	power	NOUN
ejpam-5036	4	9	graph	graph	NOUN
ejpam-5036	4	10	corresponding	correspond	VERB
ejpam-5036	4	11	to	to	ADP
ejpam-5036	4	12	the	the	DET
ejpam-5036	4	13	adjacency	adjacency	NOUN
ejpam-5036	4	14	,	,	PUNCT
ejpam-5036	4	15	laplacian	laplacian	ADJ
ejpam-5036	4	16	,	,	PUNCT
ejpam-5036	4	17	signless	signless	PROPN
ejpam-5036	4	18	laplacian	laplacian	NOUN
ejpam-5036	4	19	,	,	PUNCT
ejpam-5036	4	20	and	and	CCONJ
ejpam-5036	4	21	normalized	normalize	VERB
ejpam-5036	4	22	form	form	NOUN
ejpam-5036	4	23	of	of	ADP
ejpam-5036	4	24	these	these	DET
ejpam-5036	4	25	matrices	matrix	NOUN
ejpam-5036	4	26	.	.	PUNCT
ejpam-5036	5	1	2020	2020	NUM
ejpam-5036	5	2	mathematics	mathematic	NOUN
ejpam-5036	5	3	subject	subject	NOUN
ejpam-5036	5	4	classifications	classification	NOUN
ejpam-5036	5	5	:	:	PUNCT
ejpam-5036	5	6	05c25	05c25	NUM
ejpam-5036	5	7	,	,	PUNCT
ejpam-5036	5	8	05c50	05c50	NUM
ejpam-5036	5	9	,	,	PUNCT
ejpam-5036	5	10	15a18	15a18	NUM
ejpam-5036	5	11	,	,	PUNCT
ejpam-5036	5	12	20d99	20d99	NUM
ejpam-5036	5	13	key	key	ADJ
ejpam-5036	5	14	words	word	NOUN
ejpam-5036	5	15	and	and	CCONJ
ejpam-5036	5	16	phrases	phrase	NOUN
ejpam-5036	5	17	:	:	PUNCT
ejpam-5036	5	18	characteristic	characteristic	ADJ
ejpam-5036	5	19	polynomial	polynomial	ADJ
ejpam-5036	5	20	,	,	PUNCT
ejpam-5036	5	21	power	power	NOUN
ejpam-5036	5	22	graph	graph	NOUN
ejpam-5036	5	23	,	,	PUNCT
ejpam-5036	5	24	dihedral	dihedral	ADJ
ejpam-5036	5	25	groups	group	NOUN
ejpam-5036	5	26	1	1	NUM
ejpam-5036	5	27	.	.	X
ejpam-5036	6	1	introduction	introduction	NOUN
ejpam-5036	6	2	spectral	spectral	ADJ
ejpam-5036	6	3	graph	graph	NOUN
ejpam-5036	6	4	theory	theory	NOUN
ejpam-5036	6	5	describes	describe	VERB
ejpam-5036	6	6	graphs	graph	NOUN
ejpam-5036	6	7	based	base	VERB
ejpam-5036	6	8	on	on	ADP
ejpam-5036	6	9	specific	specific	ADJ
ejpam-5036	6	10	matrices	matrix	NOUN
ejpam-5036	6	11	,	,	PUNCT
ejpam-5036	6	12	such	such	ADJ
ejpam-5036	6	13	as	as	ADP
ejpam-5036	6	14	adjacency	adjacency	NOUN
ejpam-5036	6	15	,	,	PUNCT
ejpam-5036	6	16	laplacian	laplacian	ADJ
ejpam-5036	6	17	,	,	PUNCT
ejpam-5036	6	18	or	or	CCONJ
ejpam-5036	6	19	signless	signless	ADJ
ejpam-5036	6	20	laplacian	laplacian	ADJ
ejpam-5036	6	21	matrices	matrix	NOUN
ejpam-5036	6	22	.	.	PUNCT
ejpam-5036	7	1	the	the	DET
ejpam-5036	7	2	spectrum	spectrum	NOUN
ejpam-5036	7	3	of	of	ADP
ejpam-5036	7	4	these	these	DET
ejpam-5036	7	5	matrices	matrix	NOUN
ejpam-5036	7	6	can	can	AUX
ejpam-5036	7	7	characterize	characterize	VERB
ejpam-5036	7	8	a	a	DET
ejpam-5036	7	9	graph	graph	NOUN
ejpam-5036	7	10	.	.	PUNCT
ejpam-5036	8	1	these	these	DET
ejpam-5036	8	2	various	various	ADJ
ejpam-5036	8	3	matrices	matrix	NOUN
ejpam-5036	8	4	,	,	PUNCT
ejpam-5036	8	5	in	in	ADP
ejpam-5036	8	6	general	general	ADJ
ejpam-5036	8	7	,	,	PUNCT
ejpam-5036	8	8	give	give	VERB
ejpam-5036	8	9	insight	insight	NOUN
ejpam-5036	8	10	into	into	ADP
ejpam-5036	8	11	the	the	DET
ejpam-5036	8	12	graph	graph	NOUN
ejpam-5036	8	13	based	base	VERB
ejpam-5036	8	14	on	on	ADP
ejpam-5036	8	15	their	their	PRON
ejpam-5036	8	16	spectrum	spectrum	NOUN
ejpam-5036	8	17	.	.	PUNCT
ejpam-5036	9	1	this	this	DET
ejpam-5036	9	2	paper	paper	NOUN
ejpam-5036	9	3	examines	examine	VERB
ejpam-5036	9	4	a	a	DET
ejpam-5036	9	5	power	power	NOUN
ejpam-5036	9	6	graph	graph	NOUN
ejpam-5036	9	7	,	,	PUNCT
ejpam-5036	9	8	one	one	NUM
ejpam-5036	9	9	of	of	ADP
ejpam-5036	9	10	the	the	DET
ejpam-5036	9	11	finite	finite	ADJ
ejpam-5036	9	12	groups	group	NOUN
ejpam-5036	9	13	that	that	PRON
ejpam-5036	9	14	can	can	AUX
ejpam-5036	9	15	be	be	AUX
ejpam-5036	9	16	represented	represent	VERB
ejpam-5036	9	17	by	by	ADP
ejpam-5036	9	18	graphs	graph	NOUN
ejpam-5036	9	19	.	.	PUNCT
ejpam-5036	10	1	a	a	DET
ejpam-5036	10	2	power	power	NOUN
ejpam-5036	10	3	graph	graph	NOUN
ejpam-5036	10	4	of	of	ADP
ejpam-5036	10	5	the	the	DET
ejpam-5036	10	6	group	group	NOUN
ejpam-5036	10	7	g	g	PROPN
ejpam-5036	10	8	is	be	AUX
ejpam-5036	10	9	denoted	denote	VERB
ejpam-5036	10	10	by	by	ADP
ejpam-5036	10	11	γg	γg	ADV
ejpam-5036	10	12	and	and	CCONJ
ejpam-5036	10	13	defined	define	VERB
ejpam-5036	10	14	as	as	ADP
ejpam-5036	10	15	a	a	DET
ejpam-5036	10	16	graph	graph	NOUN
ejpam-5036	10	17	whose	whose	DET
ejpam-5036	10	18	vertex	vertex	NOUN
ejpam-5036	10	19	set	set	NOUN
ejpam-5036	10	20	is	be	AUX
ejpam-5036	10	21	all	all	DET
ejpam-5036	10	22	the	the	DET
ejpam-5036	10	23	elements	element	NOUN
ejpam-5036	10	24	of	of	ADP
ejpam-5036	10	25	g	g	PROPN
ejpam-5036	10	26	and	and	CCONJ
ejpam-5036	10	27	two	two	NUM
ejpam-5036	10	28	distinct	distinct	ADJ
ejpam-5036	10	29	vertices	vertex	NOUN
ejpam-5036	10	30	vp	vp	PROPN
ejpam-5036	10	31	and	and	CCONJ
ejpam-5036	10	32	vq	vq	PROPN
ejpam-5036	10	33	are	be	AUX
ejpam-5036	10	34	adjacent	adjacent	ADJ
ejpam-5036	10	35	if	if	SCONJ
ejpam-5036	10	36	and	and	CCONJ
ejpam-5036	10	37	only	only	ADV
ejpam-5036	10	38	if	if	SCONJ
ejpam-5036	10	39	vxp	vxp	ADJ
ejpam-5036	10	40	=	=	SYM
ejpam-5036	10	41	vq	vq	NOUN
ejpam-5036	10	42	or	or	CCONJ
ejpam-5036	10	43	v	v	ADP
ejpam-5036	10	44	y	y	PROPN
ejpam-5036	10	45	q	q	PROPN
ejpam-5036	10	46	=	=	PUNCT
ejpam-5036	10	47	vp	vp	PROPN
ejpam-5036	10	48	for	for	ADP
ejpam-5036	10	49	positive	positive	ADJ
ejpam-5036	10	50	integers	integer	NOUN
ejpam-5036	10	51	x	x	PUNCT
ejpam-5036	10	52	and	and	CCONJ
ejpam-5036	10	53	y	y	PROPN
ejpam-5036	11	1	[	[	X
ejpam-5036	11	2	5	5	NUM
ejpam-5036	11	3	]	]	PUNCT
ejpam-5036	11	4	.	.	PUNCT
ejpam-5036	12	1	the	the	DET
ejpam-5036	12	2	vertex	vertex	NOUN
ejpam-5036	12	3	set	set	NOUN
ejpam-5036	12	4	for	for	ADP
ejpam-5036	12	5	γg	γg	ADV
ejpam-5036	12	6	is	be	AUX
ejpam-5036	12	7	the	the	DET
ejpam-5036	12	8	non	non	ADJ
ejpam-5036	12	9	-	-	ADJ
ejpam-5036	12	10	abelian	abelian	ADJ
ejpam-5036	12	11	dihedral	dihedral	ADJ
ejpam-5036	12	12	group	group	NOUN
ejpam-5036	12	13	of	of	ADP
ejpam-5036	12	14	order	order	NOUN
ejpam-5036	12	15	2n	2n	NUM
ejpam-5036	12	16	,	,	PUNCT
ejpam-5036	12	17	where	where	SCONJ
ejpam-5036	12	18	n	n	PRON
ejpam-5036	12	19	≥	≥	NOUN
ejpam-5036	12	20	3	3	NUM
ejpam-5036	12	21	,	,	PUNCT
ejpam-5036	12	22	denoted	denote	VERB
ejpam-5036	12	23	by	by	ADP
ejpam-5036	12	24	d2n	d2n	PROPN
ejpam-5036	12	25	=	=	PUNCT
ejpam-5036	12	26	〈	〈	PROPN
ejpam-5036	12	27	a	a	PRON
ejpam-5036	12	28	,	,	PUNCT
ejpam-5036	12	29	b	b	NOUN
ejpam-5036	12	30	:	:	PUNCT
ejpam-5036	12	31	an	an	DET
ejpam-5036	12	32	=	=	NOUN
ejpam-5036	12	33	b2	b2	NOUN
ejpam-5036	12	34	=	=	SYM
ejpam-5036	12	35	e	e	PROPN
ejpam-5036	12	36	,	,	PUNCT
ejpam-5036	12	37	bab	bab	PROPN
ejpam-5036	12	38	=	=	SYM
ejpam-5036	12	39	a−1	a−1	PROPN
ejpam-5036	12	40	〉	〉	NOUN
ejpam-5036	12	41	[	[	X
ejpam-5036	12	42	3	3	NUM
ejpam-5036	12	43	]	]	PUNCT
ejpam-5036	12	44	.	.	PUNCT
ejpam-5036	13	1	let	let	VERB
ejpam-5036	13	2	g1	g1	PROPN
ejpam-5036	13	3	=	=	PUNCT
ejpam-5036	13	4	{	{	PUNCT
ejpam-5036	13	5	e	e	NOUN
ejpam-5036	13	6	}	}	PUNCT
ejpam-5036	13	7	,	,	PUNCT
ejpam-5036	13	8	g2	g2	PROPN
ejpam-5036	13	9	=	=	PUNCT
ejpam-5036	13	10	{	{	PUNCT
ejpam-5036	13	11	ai	ai	INTJ
ejpam-5036	13	12	:	:	PUNCT
ejpam-5036	13	13	1	1	NUM
ejpam-5036	13	14	≤	≤	NUM
ejpam-5036	13	15	i	i	PRON
ejpam-5036	13	16	≤	≤	ADJ
ejpam-5036	13	17	n	n	CCONJ
ejpam-5036	13	18	−	−	PROPN
ejpam-5036	13	19	1	1	NUM
ejpam-5036	13	20	}	}	PUNCT
ejpam-5036	13	21	,	,	PUNCT
ejpam-5036	13	22	and	and	CCONJ
ejpam-5036	13	23	g3	g3	PROPN
ejpam-5036	13	24	=	=	SYM
ejpam-5036	13	25	{	{	PUNCT
ejpam-5036	13	26	aib	aib	PROPN
ejpam-5036	13	27	:	:	PUNCT
ejpam-5036	13	28	1	1	NUM
ejpam-5036	13	29	≤	≤	NUM
ejpam-5036	13	30	i	i	PRON
ejpam-5036	13	31	≤	≤	NOUN
ejpam-5036	13	32	n	n	CCONJ
ejpam-5036	13	33	}	}	PUNCT
ejpam-5036	13	34	.	.	PUNCT
ejpam-5036	14	1	note	note	VERB
ejpam-5036	14	2	that	that	SCONJ
ejpam-5036	14	3	∗corresponding	∗corresponde	VERB
ejpam-5036	14	4	author	author	NOUN
ejpam-5036	14	5	.	.	PUNCT
ejpam-5036	15	1	doi	doi	NOUN
ejpam-5036	15	2	:	:	PUNCT
ejpam-5036	15	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5036	https://doi.org/10.29020/nybg.ejpam.v17i2.5036	NOUN
ejpam-5036	15	4	email	email	NOUN
ejpam-5036	15	5	addresses	address	NOUN
ejpam-5036	15	6	:	:	PUNCT
ejpam-5036	15	7	mamika@unram.ac.id	mamika@unram.ac.id	NOUN
ejpam-5036	15	8	(	(	PUNCT
ejpam-5036	15	9	m.	m.	PROPN
ejpam-5036	15	10	u.	u.	PROPN
ejpam-5036	15	11	romdhini	romdhini	PROPN
ejpam-5036	15	12	)	)	PUNCT
ejpam-5036	15	13	,	,	PUNCT
ejpam-5036	15	14	athirah@upm.edu.my	athirah@upm.edu.my	PROPN
ejpam-5036	15	15	(	(	PUNCT
ejpam-5036	15	16	a.	a.	NOUN
ejpam-5036	15	17	nawawi	nawawi	PROPN
ejpam-5036	15	18	)	)	PUNCT
ejpam-5036	15	19	,	,	PUNCT
ejpam-5036	15	20	faisal.ghazi@uoanbar.edu.iq	faisal.ghazi@uoanbar.edu.iq	NOUN
ejpam-5036	15	21	(	(	PUNCT
ejpam-5036	15	22	f.	f.	PROPN
ejpam-5036	15	23	al	al	PROPN
ejpam-5036	15	24	-	-	PUNCT
ejpam-5036	15	25	sharqi	sharqi	NOUN
ejpam-5036	15	26	)	)	PUNCT
ejpam-5036	15	27	,	,	PUNCT
ejpam-5036	15	28	aalquran@kfu.edu.sa	aalquran@kfu.edu.sa	PROPN
ejpam-5036	15	29	(	(	PUNCT
ejpam-5036	15	30	a.	a.	PROPN
ejpam-5036	15	31	al	al	PROPN
ejpam-5036	15	32	-	-	PUNCT
ejpam-5036	15	33	quran	quran	PROPN
ejpam-5036	15	34	)	)	PUNCT
ejpam-5036	15	35	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5036	16	1	591	591	NUM
ejpam-5036	16	2	©	©	ADP
ejpam-5036	16	3	2024	2024	NUM
ejpam-5036	16	4	ejpam	ejpam	NOUN
ejpam-5036	16	5	all	all	DET
ejpam-5036	16	6	rights	right	NOUN
ejpam-5036	16	7	reserved	reserve	VERB
ejpam-5036	16	8	.	.	PUNCT
ejpam-5036	17	1	m.	m.	NOUN
ejpam-5036	17	2	u.	u.	PROPN
ejpam-5036	17	3	romdhini	romdhini	PROPN
ejpam-5036	17	4	et	et	PROPN
ejpam-5036	17	5	al	al	PROPN
ejpam-5036	17	6	.	.	PUNCT
ejpam-5036	17	7	/	/	SYM
ejpam-5036	17	8	eur	eur	PROPN
ejpam-5036	17	9	.	.	PUNCT
ejpam-5036	18	1	j.	j.	PROPN
ejpam-5036	18	2	pure	pure	PROPN
ejpam-5036	18	3	appl	appl	PROPN
ejpam-5036	18	4	.	.	PROPN
ejpam-5036	18	5	math	math	PROPN
ejpam-5036	18	6	,	,	PUNCT
ejpam-5036	18	7	17	17	NUM
ejpam-5036	18	8	(	(	PUNCT
ejpam-5036	18	9	2	2	NUM
ejpam-5036	18	10	)	)	PUNCT
ejpam-5036	18	11	(	(	PUNCT
ejpam-5036	18	12	2024	2024	NUM
ejpam-5036	18	13	)	)	PUNCT
ejpam-5036	18	14	,	,	PUNCT
ejpam-5036	18	15	591	591	NUM
ejpam-5036	18	16	-	-	SYM
ejpam-5036	18	17	603	603	NUM
ejpam-5036	18	18	592	592	NUM
ejpam-5036	18	19	d2n	d2n	NOUN
ejpam-5036	18	20	=	=	PUNCT
ejpam-5036	18	21	g1	g1	PROPN
ejpam-5036	18	22	∪	∪	ADP
ejpam-5036	18	23	g2	g2	PROPN
ejpam-5036	18	24	∪	∪	X
ejpam-5036	18	25	g3	g3	PROPN
ejpam-5036	18	26	.	.	PUNCT
ejpam-5036	19	1	throughout	throughout	ADP
ejpam-5036	19	2	this	this	DET
ejpam-5036	19	3	paper	paper	NOUN
ejpam-5036	19	4	,	,	PUNCT
ejpam-5036	19	5	the	the	DET
ejpam-5036	19	6	power	power	NOUN
ejpam-5036	19	7	graph	graph	NOUN
ejpam-5036	19	8	for	for	ADP
ejpam-5036	19	9	the	the	DET
ejpam-5036	19	10	dihedral	dihedral	ADJ
ejpam-5036	19	11	group	group	NOUN
ejpam-5036	19	12	is	be	AUX
ejpam-5036	19	13	denoted	denote	VERB
ejpam-5036	19	14	by	by	ADP
ejpam-5036	19	15	γd2n	γd2n	PROPN
ejpam-5036	19	16	.	.	PUNCT
ejpam-5036	20	1	it	it	PRON
ejpam-5036	20	2	is	be	AUX
ejpam-5036	20	3	clear	clear	ADJ
ejpam-5036	20	4	that	that	SCONJ
ejpam-5036	20	5	γd2n	γd2n	PROPN
ejpam-5036	20	6	is	be	AUX
ejpam-5036	20	7	a	a	DET
ejpam-5036	20	8	connected	connected	ADJ
ejpam-5036	20	9	graph	graph	NOUN
ejpam-5036	20	10	[	[	X
ejpam-5036	20	11	2	2	NUM
ejpam-5036	20	12	]	]	PUNCT
ejpam-5036	20	13	.	.	PUNCT
ejpam-5036	21	1	furthermore	furthermore	ADV
ejpam-5036	21	2	,	,	PUNCT
ejpam-5036	21	3	the	the	DET
ejpam-5036	21	4	discussion	discussion	NOUN
ejpam-5036	21	5	on	on	ADP
ejpam-5036	21	6	the	the	DET
ejpam-5036	21	7	degree	degree	NOUN
ejpam-5036	21	8	formula	formula	NOUN
ejpam-5036	21	9	of	of	ADP
ejpam-5036	21	10	the	the	DET
ejpam-5036	21	11	power	power	NOUN
ejpam-5036	21	12	graph	graph	NOUN
ejpam-5036	21	13	of	of	ADP
ejpam-5036	21	14	some	some	DET
ejpam-5036	21	15	finite	finite	ADJ
ejpam-5036	21	16	group	group	NOUN
ejpam-5036	21	17	can	can	AUX
ejpam-5036	21	18	be	be	AUX
ejpam-5036	21	19	found	find	VERB
ejpam-5036	21	20	in	in	ADP
ejpam-5036	21	21	[	[	X
ejpam-5036	21	22	14	14	NUM
ejpam-5036	21	23	]	]	PUNCT
ejpam-5036	21	24	.	.	PUNCT
ejpam-5036	22	1	later	later	ADV
ejpam-5036	22	2	,	,	PUNCT
ejpam-5036	22	3	takshak	takshak	ADV
ejpam-5036	22	4	,	,	PUNCT
ejpam-5036	22	5	et	et	PROPN
ejpam-5036	22	6	al	al	PROPN
ejpam-5036	22	7	.	.	PUNCT
ejpam-5036	23	1	[	[	X
ejpam-5036	23	2	15	15	NUM
ejpam-5036	23	3	]	]	PUNCT
ejpam-5036	23	4	showed	show	VERB
ejpam-5036	23	5	the	the	DET
ejpam-5036	23	6	new	new	ADJ
ejpam-5036	23	7	finding	finding	NOUN
ejpam-5036	23	8	that	that	SCONJ
ejpam-5036	23	9	if	if	SCONJ
ejpam-5036	23	10	γg	γg	ADV
ejpam-5036	23	11	is	be	AUX
ejpam-5036	23	12	a	a	DET
ejpam-5036	23	13	power	power	NOUN
ejpam-5036	23	14	graph	graph	NOUN
ejpam-5036	23	15	of	of	ADP
ejpam-5036	23	16	a	a	DET
ejpam-5036	23	17	finite	finite	ADJ
ejpam-5036	23	18	group	group	NOUN
ejpam-5036	23	19	g	g	PROPN
ejpam-5036	23	20	,	,	PUNCT
ejpam-5036	23	21	then	then	ADV
ejpam-5036	23	22	it	it	PRON
ejpam-5036	23	23	is	be	AUX
ejpam-5036	23	24	a	a	DET
ejpam-5036	23	25	divisor	divisor	NOUN
ejpam-5036	23	26	graph	graph	NOUN
ejpam-5036	23	27	.	.	PUNCT
ejpam-5036	24	1	kumar	kumar	PROPN
ejpam-5036	24	2	et	et	PROPN
ejpam-5036	24	3	al	al	PROPN
ejpam-5036	24	4	.	.	PUNCT
ejpam-5036	25	1	[	[	X
ejpam-5036	25	2	7	7	X
ejpam-5036	25	3	]	]	PUNCT
ejpam-5036	25	4	have	have	AUX
ejpam-5036	25	5	presented	present	VERB
ejpam-5036	25	6	a	a	DET
ejpam-5036	25	7	complete	complete	ADJ
ejpam-5036	25	8	and	and	CCONJ
ejpam-5036	25	9	excellent	excellent	ADJ
ejpam-5036	25	10	survey	survey	NOUN
ejpam-5036	25	11	of	of	ADP
ejpam-5036	25	12	the	the	DET
ejpam-5036	25	13	power	power	NOUN
ejpam-5036	25	14	graph	graph	NOUN
ejpam-5036	25	15	for	for	ADP
ejpam-5036	25	16	some	some	DET
ejpam-5036	25	17	finite	finite	ADJ
ejpam-5036	25	18	groups	group	NOUN
ejpam-5036	25	19	.	.	PUNCT
ejpam-5036	26	1	meanwhile	meanwhile	ADV
ejpam-5036	26	2	,	,	PUNCT
ejpam-5036	26	3	the	the	DET
ejpam-5036	26	4	degree	degree	NOUN
ejpam-5036	26	5	of	of	ADP
ejpam-5036	26	6	γd2n	γd2n	PROPN
ejpam-5036	26	7	has	have	AUX
ejpam-5036	26	8	been	be	AUX
ejpam-5036	26	9	presented	present	VERB
ejpam-5036	26	10	by	by	ADP
ejpam-5036	26	11	[	[	X
ejpam-5036	26	12	2	2	NUM
ejpam-5036	26	13	]	]	PUNCT
ejpam-5036	26	14	as	as	ADP
ejpam-5036	26	15	in	in	ADP
ejpam-5036	26	16	the	the	DET
ejpam-5036	26	17	following	following	NOUN
ejpam-5036	26	18	theorem	theorem	NOUN
ejpam-5036	26	19	:	:	PUNCT
ejpam-5036	26	20	theorem	theorem	NOUN
ejpam-5036	26	21	1	1	NUM
ejpam-5036	26	22	.	.	PUNCT
ejpam-5036	27	1	[	[	X
ejpam-5036	27	2	2	2	X
ejpam-5036	27	3	]	]	X
ejpam-5036	27	4	if	if	SCONJ
ejpam-5036	27	5	γd2n	γd2n	PROPN
ejpam-5036	27	6	is	be	AUX
ejpam-5036	27	7	the	the	DET
ejpam-5036	27	8	power	power	NOUN
ejpam-5036	27	9	graph	graph	NOUN
ejpam-5036	27	10	of	of	ADP
ejpam-5036	27	11	d2n	d2n	NOUN
ejpam-5036	27	12	,	,	PUNCT
ejpam-5036	27	13	then	then	ADV
ejpam-5036	27	14	(	(	PUNCT
ejpam-5036	27	15	i	i	NOUN
ejpam-5036	27	16	)	)	PUNCT
ejpam-5036	27	17	the	the	DET
ejpam-5036	27	18	degree	degree	NOUN
ejpam-5036	27	19	of	of	ADP
ejpam-5036	27	20	a	a	PRON
ejpam-5036	27	21	in	in	ADP
ejpam-5036	27	22	γd2n	γd2n	PROPN
ejpam-5036	27	23	is	be	AUX
ejpam-5036	27	24	de	de	X
ejpam-5036	27	25	=	=	PUNCT
ejpam-5036	27	26	2n−	2n−	PROPN
ejpam-5036	27	27	1	1	NUM
ejpam-5036	27	28	,	,	PUNCT
ejpam-5036	27	29	(	(	PUNCT
ejpam-5036	27	30	ii	ii	NOUN
ejpam-5036	27	31	)	)	PUNCT
ejpam-5036	27	32	the	the	DET
ejpam-5036	27	33	degree	degree	NOUN
ejpam-5036	27	34	of	of	ADP
ejpam-5036	27	35	ai	ai	NOUN
ejpam-5036	27	36	in	in	ADP
ejpam-5036	27	37	γd2n	γd2n	PROPN
ejpam-5036	27	38	is	be	AUX
ejpam-5036	27	39	dai	dai	PROPN
ejpam-5036	27	40	=	=	PUNCT
ejpam-5036	27	41	n−	n−	NOUN
ejpam-5036	27	42	1	1	NUM
ejpam-5036	27	43	,	,	PUNCT
ejpam-5036	27	44	(	(	PUNCT
ejpam-5036	27	45	iii	iii	X
ejpam-5036	27	46	)	)	PUNCT
ejpam-5036	27	47	the	the	DET
ejpam-5036	27	48	degree	degree	NOUN
ejpam-5036	27	49	of	of	ADP
ejpam-5036	27	50	aib	aib	PROPN
ejpam-5036	27	51	in	in	ADP
ejpam-5036	27	52	γd2n	γd2n	PROPN
ejpam-5036	27	53	is	be	AUX
ejpam-5036	27	54	daib	daib	NOUN
ejpam-5036	27	55	=	=	SYM
ejpam-5036	27	56	1	1	NUM
ejpam-5036	27	57	,	,	PUNCT
ejpam-5036	27	58	the	the	DET
ejpam-5036	27	59	above	above	ADJ
ejpam-5036	27	60	theorem	theorem	NOUN
ejpam-5036	27	61	gives	give	VERB
ejpam-5036	27	62	the	the	DET
ejpam-5036	27	63	information	information	NOUN
ejpam-5036	27	64	that	that	SCONJ
ejpam-5036	27	65	vertex	vertex	NOUN
ejpam-5036	27	66	e	e	NOUN
ejpam-5036	27	67	is	be	AUX
ejpam-5036	27	68	adjacent	adjacent	ADJ
ejpam-5036	27	69	to	to	ADP
ejpam-5036	27	70	all	all	DET
ejpam-5036	27	71	other	other	ADJ
ejpam-5036	27	72	vertices	vertex	NOUN
ejpam-5036	27	73	in	in	ADP
ejpam-5036	27	74	γd2n	γd2n	PROPN
ejpam-5036	27	75	.	.	PUNCT
ejpam-5036	28	1	every	every	DET
ejpam-5036	28	2	vertex	vertex	NOUN
ejpam-5036	28	3	in	in	ADP
ejpam-5036	28	4	g2	g2	PROPN
ejpam-5036	28	5	is	be	AUX
ejpam-5036	28	6	adjacent	adjacent	ADJ
ejpam-5036	28	7	to	to	ADP
ejpam-5036	28	8	e	e	NOUN
ejpam-5036	28	9	and	and	CCONJ
ejpam-5036	28	10	all	all	DET
ejpam-5036	28	11	other	other	ADJ
ejpam-5036	28	12	members	member	NOUN
ejpam-5036	28	13	in	in	ADP
ejpam-5036	28	14	g2	g2	PROPN
ejpam-5036	28	15	.	.	PUNCT
ejpam-5036	29	1	meanwhile	meanwhile	ADV
ejpam-5036	29	2	,	,	PUNCT
ejpam-5036	29	3	all	all	DET
ejpam-5036	29	4	vertices	vertex	NOUN
ejpam-5036	29	5	in	in	ADP
ejpam-5036	29	6	g3	g3	PROPN
ejpam-5036	29	7	are	be	AUX
ejpam-5036	29	8	only	only	ADV
ejpam-5036	29	9	adjacent	adjacent	ADJ
ejpam-5036	29	10	to	to	ADP
ejpam-5036	29	11	e	e	PROPN
ejpam-5036	29	12	[	[	X
ejpam-5036	29	13	2	2	NUM
ejpam-5036	29	14	]	]	PUNCT
ejpam-5036	29	15	.	.	PUNCT
ejpam-5036	30	1	several	several	ADJ
ejpam-5036	30	2	authors	author	NOUN
ejpam-5036	30	3	have	have	AUX
ejpam-5036	30	4	discussed	discuss	VERB
ejpam-5036	30	5	the	the	DET
ejpam-5036	30	6	graphs	graph	NOUN
ejpam-5036	30	7	that	that	PRON
ejpam-5036	30	8	are	be	AUX
ejpam-5036	30	9	defined	define	VERB
ejpam-5036	30	10	on	on	ADP
ejpam-5036	30	11	dihedral	dihedral	ADJ
ejpam-5036	30	12	groups	group	NOUN
ejpam-5036	30	13	.	.	PUNCT
ejpam-5036	31	1	they	they	PRON
ejpam-5036	31	2	worked	work	VERB
ejpam-5036	31	3	on	on	ADP
ejpam-5036	31	4	the	the	DET
ejpam-5036	31	5	spectral	spectral	ADJ
ejpam-5036	31	6	problem	problem	NOUN
ejpam-5036	31	7	of	of	ADP
ejpam-5036	31	8	the	the	DET
ejpam-5036	31	9	commuting	commuting	NOUN
ejpam-5036	31	10	and	and	CCONJ
ejpam-5036	31	11	non	non	ADJ
ejpam-5036	31	12	-	-	ADJ
ejpam-5036	31	13	commuting	commuting	ADJ
ejpam-5036	31	14	graphs	graph	NOUN
ejpam-5036	31	15	,	,	PUNCT
ejpam-5036	31	16	which	which	PRON
ejpam-5036	31	17	can	can	AUX
ejpam-5036	31	18	be	be	AUX
ejpam-5036	31	19	seen	see	VERB
ejpam-5036	31	20	in	in	ADP
ejpam-5036	31	21	[	[	X
ejpam-5036	31	22	9–13	9–13	NOUN
ejpam-5036	31	23	]	]	PUNCT
ejpam-5036	31	24	,	,	PUNCT
ejpam-5036	31	25	accordingly	accordingly	ADV
ejpam-5036	31	26	,	,	PUNCT
ejpam-5036	31	27	romdhini	romdhini	NOUN
ejpam-5036	31	28	et	et	PROPN
ejpam-5036	31	29	al	al	PROPN
ejpam-5036	31	30	.	.	PUNCT
ejpam-5036	32	1	[	[	X
ejpam-5036	32	2	8	8	NUM
ejpam-5036	32	3	]	]	PUNCT
ejpam-5036	32	4	investigated	investigate	VERB
ejpam-5036	32	5	signless	signless	PROPN
ejpam-5036	32	6	laplacian	laplacian	ADJ
ejpam-5036	32	7	spectral	spectral	NOUN
ejpam-5036	32	8	of	of	ADP
ejpam-5036	32	9	interval	interval	NOUN
ejpam-5036	32	10	-	-	PUNCT
ejpam-5036	32	11	valued	value	VERB
ejpam-5036	32	12	fuzzy	fuzzy	ADJ
ejpam-5036	32	13	graphs	graph	NOUN
ejpam-5036	32	14	.	.	PUNCT
ejpam-5036	33	1	moreover	moreover	ADV
ejpam-5036	33	2	,	,	PUNCT
ejpam-5036	33	3	an	an	DET
ejpam-5036	33	4	analysis	analysis	NOUN
ejpam-5036	33	5	of	of	ADP
ejpam-5036	33	6	the	the	DET
ejpam-5036	33	7	relationship	relationship	NOUN
ejpam-5036	33	8	between	between	ADP
ejpam-5036	33	9	graphs	graph	NOUN
ejpam-5036	33	10	and	and	CCONJ
ejpam-5036	33	11	unitary	unitary	ADJ
ejpam-5036	33	12	commutative	commutative	ADJ
ejpam-5036	33	13	rings	ring	NOUN
ejpam-5036	33	14	’	'	PUNCT
ejpam-5036	33	15	prime	prime	ADJ
ejpam-5036	33	16	spectrum	spectrum	NOUN
ejpam-5036	33	17	is	be	AUX
ejpam-5036	33	18	presented	present	VERB
ejpam-5036	33	19	by	by	ADP
ejpam-5036	33	20	[	[	X
ejpam-5036	33	21	1	1	NUM
ejpam-5036	33	22	]	]	PUNCT
ejpam-5036	33	23	.	.	PUNCT
ejpam-5036	34	1	motivated	motivate	VERB
ejpam-5036	34	2	by	by	ADP
ejpam-5036	34	3	this	this	PRON
ejpam-5036	34	4	,	,	PUNCT
ejpam-5036	34	5	this	this	DET
ejpam-5036	34	6	research	research	NOUN
ejpam-5036	34	7	aims	aim	VERB
ejpam-5036	34	8	to	to	PART
ejpam-5036	34	9	formulate	formulate	VERB
ejpam-5036	34	10	the	the	DET
ejpam-5036	34	11	characteristic	characteristic	ADJ
ejpam-5036	34	12	polynomial	polynomial	NOUN
ejpam-5036	34	13	of	of	ADP
ejpam-5036	34	14	the	the	DET
ejpam-5036	34	15	power	power	NOUN
ejpam-5036	34	16	graph	graph	NOUN
ejpam-5036	34	17	of	of	ADP
ejpam-5036	34	18	the	the	DET
ejpam-5036	34	19	dihedral	dihedral	ADJ
ejpam-5036	34	20	group	group	NOUN
ejpam-5036	34	21	associated	associate	VERB
ejpam-5036	34	22	with	with	ADP
ejpam-5036	34	23	the	the	DET
ejpam-5036	34	24	adjacency	adjacency	NOUN
ejpam-5036	34	25	,	,	PUNCT
ejpam-5036	34	26	laplacian	laplacian	ADJ
ejpam-5036	34	27	,	,	PUNCT
ejpam-5036	34	28	signless	signless	PROPN
ejpam-5036	34	29	laplacian	laplacian	NOUN
ejpam-5036	34	30	,	,	PUNCT
ejpam-5036	34	31	and	and	CCONJ
ejpam-5036	34	32	normalized	normalize	VERB
ejpam-5036	34	33	form	form	NOUN
ejpam-5036	34	34	of	of	ADP
ejpam-5036	34	35	these	these	DET
ejpam-5036	34	36	matrices	matrix	NOUN
ejpam-5036	34	37	.	.	PUNCT
ejpam-5036	35	1	the	the	DET
ejpam-5036	35	2	definition	definition	NOUN
ejpam-5036	35	3	of	of	ADP
ejpam-5036	35	4	the	the	DET
ejpam-5036	35	5	various	various	ADJ
ejpam-5036	35	6	matrices	matrix	NOUN
ejpam-5036	35	7	can	can	AUX
ejpam-5036	35	8	be	be	AUX
ejpam-5036	35	9	seen	see	VERB
ejpam-5036	35	10	in	in	ADP
ejpam-5036	35	11	the	the	DET
ejpam-5036	35	12	following	follow	VERB
ejpam-5036	35	13	definitions	definition	NOUN
ejpam-5036	35	14	.	.	PUNCT
ejpam-5036	36	1	definition	definition	NOUN
ejpam-5036	36	2	1	1	NUM
ejpam-5036	36	3	.	.	PUNCT
ejpam-5036	37	1	(	(	PUNCT
ejpam-5036	37	2	[	[	X
ejpam-5036	37	3	4	4	NUM
ejpam-5036	37	4	]	]	PUNCT
ejpam-5036	37	5	)	)	PUNCT
ejpam-5036	37	6	the	the	DET
ejpam-5036	37	7	adjacency	adjacency	NOUN
ejpam-5036	37	8	matrix	matrix	NOUN
ejpam-5036	37	9	of	of	ADP
ejpam-5036	37	10	order	order	NOUN
ejpam-5036	37	11	n×n	n×n	PROPN
ejpam-5036	37	12	associated	associate	VERB
ejpam-5036	37	13	with	with	ADP
ejpam-5036	37	14	γd2n	γd2n	PROPN
ejpam-5036	37	15	is	be	AUX
ejpam-5036	37	16	given	give	VERB
ejpam-5036	37	17	by	by	ADP
ejpam-5036	37	18	a(γd2n	a(γd2n	PUNCT
ejpam-5036	37	19	)	)	PUNCT
ejpam-5036	37	20	=	=	PUNCT
ejpam-5036	38	1	[	[	X
ejpam-5036	38	2	aij	aij	X
ejpam-5036	38	3	]	]	X
ejpam-5036	38	4	whose	whose	DET
ejpam-5036	38	5	(	(	PUNCT
ejpam-5036	38	6	i	i	NOUN
ejpam-5036	38	7	,	,	PUNCT
ejpam-5036	38	8	j)-th	j)-th	PROPN
ejpam-5036	38	9	entry	entry	NOUN
ejpam-5036	38	10	aij	aij	PROPN
ejpam-5036	38	11	=	=	SYM
ejpam-5036	38	12	{	{	PUNCT
ejpam-5036	38	13	1	1	NUM
ejpam-5036	38	14	,	,	PUNCT
ejpam-5036	38	15	if	if	SCONJ
ejpam-5036	38	16	vi	vi	PRON
ejpam-5036	38	17	̸=	̸=	PROPN
ejpam-5036	38	18	vj	vj	NOUN
ejpam-5036	38	19	and	and	CCONJ
ejpam-5036	38	20	they	they	PRON
ejpam-5036	38	21	are	be	AUX
ejpam-5036	38	22	adjacent	adjacent	ADJ
ejpam-5036	38	23	0	0	NUM
ejpam-5036	38	24	,	,	PUNCT
ejpam-5036	38	25	otherwise	otherwise	ADV
ejpam-5036	38	26	definition	definition	NOUN
ejpam-5036	38	27	2	2	NUM
ejpam-5036	38	28	.	.	PUNCT
ejpam-5036	39	1	(	(	PUNCT
ejpam-5036	39	2	[	[	X
ejpam-5036	39	3	4	4	NUM
ejpam-5036	39	4	]	]	PUNCT
ejpam-5036	39	5	)	)	PUNCT
ejpam-5036	39	6	the	the	DET
ejpam-5036	39	7	diagonal	diagonal	ADJ
ejpam-5036	39	8	degree	degree	NOUN
ejpam-5036	39	9	matrix	matrix	NOUN
ejpam-5036	39	10	of	of	ADP
ejpam-5036	39	11	order	order	NOUN
ejpam-5036	39	12	n	n	CCONJ
ejpam-5036	39	13	×	×	VERB
ejpam-5036	39	14	n	n	PRON
ejpam-5036	39	15	associated	associate	VERB
ejpam-5036	39	16	with	with	ADP
ejpam-5036	39	17	γd2n	γd2n	PROPN
ejpam-5036	39	18	is	be	AUX
ejpam-5036	39	19	given	give	VERB
ejpam-5036	39	20	by	by	ADP
ejpam-5036	39	21	d(γd2n	d(γd2n	PROPN
ejpam-5036	39	22	)	)	PUNCT
ejpam-5036	39	23	=	=	PUNCT
ejpam-5036	40	1	[	[	X
ejpam-5036	40	2	dij	dij	X
ejpam-5036	40	3	]	]	X
ejpam-5036	40	4	whose	whose	DET
ejpam-5036	40	5	(	(	PUNCT
ejpam-5036	40	6	i	i	NOUN
ejpam-5036	40	7	,	,	PUNCT
ejpam-5036	40	8	j)-th	j)-th	PROPN
ejpam-5036	40	9	entry	entry	NOUN
ejpam-5036	40	10	dij	dij	PROPN
ejpam-5036	41	1	=	=	SYM
ejpam-5036	41	2	{	{	PUNCT
ejpam-5036	41	3	dvi	dvi	NOUN
ejpam-5036	41	4	,	,	PUNCT
ejpam-5036	41	5	if	if	SCONJ
ejpam-5036	41	6	vi	vi	ADJ
ejpam-5036	41	7	=	=	SYM
ejpam-5036	41	8	vj	vj	NOUN
ejpam-5036	41	9	0	0	NUM
ejpam-5036	41	10	,	,	PUNCT
ejpam-5036	41	11	otherwise	otherwise	ADV
ejpam-5036	41	12	where	where	SCONJ
ejpam-5036	41	13	dvi	dvi	NOUN
ejpam-5036	41	14	is	be	AUX
ejpam-5036	41	15	the	the	DET
ejpam-5036	41	16	degree	degree	NOUN
ejpam-5036	41	17	of	of	ADP
ejpam-5036	41	18	vertex	vertex	NOUN
ejpam-5036	41	19	vi	vi	PROPN
ejpam-5036	41	20	,	,	PUNCT
ejpam-5036	41	21	a	a	DET
ejpam-5036	41	22	number	number	NOUN
ejpam-5036	41	23	of	of	ADP
ejpam-5036	41	24	vertices	vertex	NOUN
ejpam-5036	41	25	adjacent	adjacent	ADJ
ejpam-5036	41	26	to	to	ADP
ejpam-5036	41	27	vi	vi	VERB
ejpam-5036	41	28	in	in	ADP
ejpam-5036	41	29	γd2n	γd2n	PROPN
ejpam-5036	41	30	.	.	PUNCT
ejpam-5036	42	1	definition	definition	NOUN
ejpam-5036	42	2	3	3	NUM
ejpam-5036	42	3	.	.	PUNCT
ejpam-5036	43	1	(	(	PUNCT
ejpam-5036	43	2	[	[	X
ejpam-5036	43	3	4	4	NUM
ejpam-5036	43	4	]	]	PUNCT
ejpam-5036	43	5	)	)	PUNCT
ejpam-5036	43	6	the	the	DET
ejpam-5036	43	7	laplacian	laplacian	ADJ
ejpam-5036	43	8	matrix	matrix	NOUN
ejpam-5036	43	9	of	of	ADP
ejpam-5036	43	10	order	order	NOUN
ejpam-5036	43	11	n×n	n×n	PROPN
ejpam-5036	43	12	associated	associate	VERB
ejpam-5036	43	13	with	with	ADP
ejpam-5036	43	14	γd2n	γd2n	PROPN
ejpam-5036	43	15	is	be	AUX
ejpam-5036	43	16	given	give	VERB
ejpam-5036	43	17	by	by	ADP
ejpam-5036	43	18	l(γd2n	l(γd2n	PROPN
ejpam-5036	43	19	)	)	PUNCT
ejpam-5036	43	20	=	=	SYM
ejpam-5036	43	21	d(γd2n)−a(γd2n	d(γd2n)−a(γd2n	PROPN
ejpam-5036	43	22	)	)	PUNCT
ejpam-5036	43	23	.	.	PUNCT
ejpam-5036	44	1	definition	definition	NOUN
ejpam-5036	44	2	4	4	NUM
ejpam-5036	44	3	.	.	PUNCT
ejpam-5036	45	1	(	(	PUNCT
ejpam-5036	45	2	[	[	X
ejpam-5036	45	3	4	4	NUM
ejpam-5036	45	4	]	]	PUNCT
ejpam-5036	45	5	)	)	PUNCT
ejpam-5036	45	6	the	the	DET
ejpam-5036	45	7	signless	signless	ADJ
ejpam-5036	45	8	laplacian	laplacian	ADJ
ejpam-5036	45	9	matrix	matrix	NOUN
ejpam-5036	45	10	of	of	ADP
ejpam-5036	45	11	order	order	NOUN
ejpam-5036	45	12	n×	n×	PRON
ejpam-5036	45	13	n	n	PRON
ejpam-5036	45	14	associated	associate	VERB
ejpam-5036	45	15	with	with	ADP
ejpam-5036	45	16	γd2n	γd2n	PROPN
ejpam-5036	45	17	is	be	AUX
ejpam-5036	45	18	given	give	VERB
ejpam-5036	45	19	by	by	ADP
ejpam-5036	45	20	sl(γd2n	sl(γd2n	NOUN
ejpam-5036	45	21	)	)	PUNCT
ejpam-5036	45	22	=	=	SYM
ejpam-5036	46	1	d(γd2n	d(γd2n	X
ejpam-5036	46	2	)	)	PUNCT
ejpam-5036	47	1	+	+	NOUN
ejpam-5036	47	2	a(γd2n	a(γd2n	X
ejpam-5036	47	3	)	)	PUNCT
ejpam-5036	47	4	.	.	PUNCT
ejpam-5036	48	1	m.	m.	PROPN
ejpam-5036	48	2	u.	u.	PROPN
ejpam-5036	48	3	romdhini	romdhini	PROPN
ejpam-5036	48	4	et	et	PROPN
ejpam-5036	48	5	al	al	PROPN
ejpam-5036	48	6	.	.	PUNCT
ejpam-5036	48	7	/	/	SYM
ejpam-5036	48	8	eur	eur	PROPN
ejpam-5036	48	9	.	.	PUNCT
ejpam-5036	49	1	j.	j.	PROPN
ejpam-5036	49	2	pure	pure	PROPN
ejpam-5036	49	3	appl	appl	PROPN
ejpam-5036	49	4	.	.	PROPN
ejpam-5036	49	5	math	math	PROPN
ejpam-5036	49	6	,	,	PUNCT
ejpam-5036	49	7	17	17	NUM
ejpam-5036	49	8	(	(	PUNCT
ejpam-5036	49	9	2	2	NUM
ejpam-5036	49	10	)	)	PUNCT
ejpam-5036	49	11	(	(	PUNCT
ejpam-5036	49	12	2024	2024	NUM
ejpam-5036	49	13	)	)	PUNCT
ejpam-5036	49	14	,	,	PUNCT
ejpam-5036	49	15	591	591	NUM
ejpam-5036	49	16	-	-	SYM
ejpam-5036	49	17	603	603	NUM
ejpam-5036	49	18	593	593	NUM
ejpam-5036	49	19	definition	definition	NOUN
ejpam-5036	49	20	5	5	NUM
ejpam-5036	49	21	.	.	PUNCT
ejpam-5036	50	1	(	(	PUNCT
ejpam-5036	50	2	[	[	X
ejpam-5036	50	3	4	4	NUM
ejpam-5036	50	4	]	]	PUNCT
ejpam-5036	50	5	)	)	PUNCT
ejpam-5036	50	6	the	the	DET
ejpam-5036	50	7	normalized	normalize	VERB
ejpam-5036	50	8	adjacency	adjacency	NOUN
ejpam-5036	50	9	matrix	matrix	NOUN
ejpam-5036	50	10	of	of	ADP
ejpam-5036	50	11	order	order	NOUN
ejpam-5036	50	12	n×n	n×n	PROPN
ejpam-5036	50	13	associated	associate	VERB
ejpam-5036	50	14	with	with	ADP
ejpam-5036	50	15	γd2n	γd2n	PROPN
ejpam-5036	50	16	is	be	AUX
ejpam-5036	50	17	given	give	VERB
ejpam-5036	50	18	by	by	ADP
ejpam-5036	50	19	na(γd2n	na(γd2n	NOUN
ejpam-5036	50	20	)	)	PUNCT
ejpam-5036	50	21	=	=	SYM
ejpam-5036	50	22	√	√	NUM
ejpam-5036	50	23	d(γd2n	d(γd2n	NOUN
ejpam-5036	50	24	)	)	PUNCT
ejpam-5036	50	25	−1	−1	NOUN
ejpam-5036	50	26	a(γd2n	a(γd2n	NOUN
ejpam-5036	50	27	)	)	PUNCT
ejpam-5036	50	28	√	√	ADP
ejpam-5036	50	29	d(γd2n	d(γd2n	NOUN
ejpam-5036	50	30	)	)	PUNCT
ejpam-5036	50	31	−1	−1	NOUN
ejpam-5036	50	32	.	.	PUNCT
ejpam-5036	51	1	definition	definition	NOUN
ejpam-5036	51	2	6	6	NUM
ejpam-5036	51	3	.	.	PUNCT
ejpam-5036	52	1	(	(	PUNCT
ejpam-5036	52	2	[	[	X
ejpam-5036	52	3	4	4	NUM
ejpam-5036	52	4	]	]	PUNCT
ejpam-5036	52	5	)	)	PUNCT
ejpam-5036	52	6	the	the	DET
ejpam-5036	52	7	normalized	normalize	VERB
ejpam-5036	52	8	laplacian	laplacian	ADJ
ejpam-5036	52	9	(	(	PUNCT
ejpam-5036	52	10	nl	nl	NOUN
ejpam-5036	52	11	)	)	PUNCT
ejpam-5036	52	12	matrix	matrix	NOUN
ejpam-5036	52	13	of	of	ADP
ejpam-5036	52	14	order	order	NOUN
ejpam-5036	52	15	n×n	n×n	PROPN
ejpam-5036	52	16	associated	associate	VERB
ejpam-5036	52	17	with	with	ADP
ejpam-5036	52	18	γd2n	γd2n	PROPN
ejpam-5036	52	19	is	be	AUX
ejpam-5036	52	20	given	give	VERB
ejpam-5036	52	21	by	by	ADP
ejpam-5036	52	22	nl(γd2n	nl(γd2n	NOUN
ejpam-5036	52	23	)	)	PUNCT
ejpam-5036	52	24	=	=	SYM
ejpam-5036	53	1	√	√	NUM
ejpam-5036	53	2	d(γd2n	d(γd2n	NOUN
ejpam-5036	53	3	)	)	PUNCT
ejpam-5036	53	4	−1	−1	NOUN
ejpam-5036	53	5	l(γd2n	l(γd2n	PROPN
ejpam-5036	53	6	)	)	PUNCT
ejpam-5036	53	7	√	√	ADP
ejpam-5036	53	8	d(γd2n	d(γd2n	NOUN
ejpam-5036	53	9	)	)	PUNCT
ejpam-5036	53	10	−1	−1	NOUN
ejpam-5036	54	1	=	=	PUNCT
ejpam-5036	54	2	in	in	ADP
ejpam-5036	54	3	−na(γd2n	−na(γd2n	NUM
ejpam-5036	54	4	)	)	PUNCT
ejpam-5036	54	5	.	.	PUNCT
ejpam-5036	55	1	definition	definition	NOUN
ejpam-5036	55	2	7	7	NUM
ejpam-5036	55	3	.	.	PUNCT
ejpam-5036	56	1	(	(	PUNCT
ejpam-5036	56	2	[	[	X
ejpam-5036	56	3	4	4	NUM
ejpam-5036	56	4	]	]	PUNCT
ejpam-5036	56	5	)	)	PUNCT
ejpam-5036	56	6	the	the	DET
ejpam-5036	56	7	normalized	normalize	VERB
ejpam-5036	56	8	signless	signless	PROPN
ejpam-5036	56	9	laplacian	laplacian	X
ejpam-5036	56	10	(	(	PUNCT
ejpam-5036	56	11	nsl	nsl	NOUN
ejpam-5036	56	12	)	)	PUNCT
ejpam-5036	56	13	matrix	matrix	NOUN
ejpam-5036	56	14	of	of	ADP
ejpam-5036	56	15	order	order	NOUN
ejpam-5036	56	16	n	n	CCONJ
ejpam-5036	56	17	×	×	VERB
ejpam-5036	56	18	n	n	PRON
ejpam-5036	56	19	associated	associate	VERB
ejpam-5036	56	20	with	with	ADP
ejpam-5036	56	21	γd2n	γd2n	PROPN
ejpam-5036	56	22	is	be	AUX
ejpam-5036	56	23	given	give	VERB
ejpam-5036	56	24	by	by	ADP
ejpam-5036	56	25	nsl(γd2n	nsl(γd2n	NOUN
ejpam-5036	56	26	)	)	PUNCT
ejpam-5036	56	27	=	=	SYM
ejpam-5036	56	28	√	√	NUM
ejpam-5036	56	29	d(γd2n	d(γd2n	NOUN
ejpam-5036	56	30	)	)	PUNCT
ejpam-5036	56	31	−1	−1	NOUN
ejpam-5036	56	32	sl(γd2n	sl(γd2n	NOUN
ejpam-5036	56	33	√	√	NUM
ejpam-5036	56	34	d(γd2n	d(γd2n	NOUN
ejpam-5036	56	35	)	)	PUNCT
ejpam-5036	56	36	−1	−1	NOUN
ejpam-5036	56	37	=	=	NOUN
ejpam-5036	56	38	in	in	ADP
ejpam-5036	56	39	+	+	ADJ
ejpam-5036	56	40	na(γd2n	na(γd2n	NOUN
ejpam-5036	56	41	)	)	PUNCT
ejpam-5036	56	42	.	.	PUNCT
ejpam-5036	57	1	the	the	DET
ejpam-5036	57	2	characteristic	characteristic	ADJ
ejpam-5036	57	3	polynomial	polynomial	ADJ
ejpam-5036	57	4	ofa(γd2n	ofa(γd2n	NOUN
ejpam-5036	57	5	)	)	PUNCT
ejpam-5036	57	6	is	be	AUX
ejpam-5036	57	7	defined	define	VERB
ejpam-5036	57	8	by	by	ADP
ejpam-5036	57	9	pa(γd2n	pa(γd2n	NOUN
ejpam-5036	57	10	)	)	PUNCT
ejpam-5036	57	11	(	(	PUNCT
ejpam-5036	57	12	λ	λ	NOUN
ejpam-5036	57	13	)	)	PUNCT
ejpam-5036	57	14	=	=	SYM
ejpam-5036	57	15	det	det	NOUN
ejpam-5036	57	16	(	(	PUNCT
ejpam-5036	57	17	λi2n	λi2n	PROPN
ejpam-5036	57	18	−a(γd2n	−a(γd2n	PROPN
ejpam-5036	57	19	)	)	PUNCT
ejpam-5036	57	20	)	)	PUNCT
ejpam-5036	57	21	,	,	PUNCT
ejpam-5036	57	22	where	where	SCONJ
ejpam-5036	57	23	i2n	i2n	NOUN
ejpam-5036	57	24	is	be	AUX
ejpam-5036	57	25	an	an	DET
ejpam-5036	57	26	2n×2n	2n×2n	NUM
ejpam-5036	57	27	identity	identity	NOUN
ejpam-5036	57	28	matrix	matrix	NOUN
ejpam-5036	57	29	.	.	PUNCT
ejpam-5036	58	1	likewise	likewise	ADV
ejpam-5036	58	2	,	,	PUNCT
ejpam-5036	58	3	the	the	DET
ejpam-5036	58	4	notation	notation	NOUN
ejpam-5036	58	5	for	for	ADP
ejpam-5036	58	6	other	other	ADJ
ejpam-5036	58	7	matrices	matrix	NOUN
ejpam-5036	58	8	can	can	AUX
ejpam-5036	58	9	also	also	ADV
ejpam-5036	58	10	be	be	AUX
ejpam-5036	58	11	applied	apply	VERB
ejpam-5036	58	12	in	in	ADP
ejpam-5036	58	13	the	the	DET
ejpam-5036	58	14	same	same	ADJ
ejpam-5036	58	15	way	way	NOUN
ejpam-5036	58	16	.	.	PUNCT
ejpam-5036	59	1	to	to	PART
ejpam-5036	59	2	formulate	formulate	VERB
ejpam-5036	59	3	the	the	DET
ejpam-5036	59	4	characteristic	characteristic	ADJ
ejpam-5036	59	5	polynomial	polynomial	NOUN
ejpam-5036	59	6	of	of	ADP
ejpam-5036	59	7	γd2n	γd2n	PROPN
ejpam-5036	59	8	,	,	PUNCT
ejpam-5036	59	9	row	row	NOUN
ejpam-5036	59	10	and	and	CCONJ
ejpam-5036	59	11	column	column	NOUN
ejpam-5036	59	12	operations	operation	NOUN
ejpam-5036	59	13	need	need	VERB
ejpam-5036	59	14	to	to	PART
ejpam-5036	59	15	be	be	AUX
ejpam-5036	59	16	performed	perform	VERB
ejpam-5036	59	17	.	.	PUNCT
ejpam-5036	60	1	assume	assume	VERB
ejpam-5036	60	2	that	that	SCONJ
ejpam-5036	60	3	ri	ri	PROPN
ejpam-5036	60	4	and	and	CCONJ
ejpam-5036	60	5	ci	ci	PROPN
ejpam-5036	60	6	are	be	AUX
ejpam-5036	60	7	the	the	DET
ejpam-5036	60	8	i−th	i−th	PROPN
ejpam-5036	60	9	row	row	NOUN
ejpam-5036	60	10	and	and	CCONJ
ejpam-5036	60	11	column	column	NOUN
ejpam-5036	60	12	of	of	ADP
ejpam-5036	60	13	the	the	DET
ejpam-5036	60	14	matrix	matrix	NOUN
ejpam-5036	60	15	,	,	PUNCT
ejpam-5036	60	16	respectively	respectively	ADV
ejpam-5036	60	17	.	.	PUNCT
ejpam-5036	61	1	in	in	ADP
ejpam-5036	61	2	this	this	DET
ejpam-5036	61	3	case	case	NOUN
ejpam-5036	61	4	,	,	PUNCT
ejpam-5036	61	5	r′	r′	PROPN
ejpam-5036	61	6	i	i	PRON
ejpam-5036	61	7	and	and	CCONJ
ejpam-5036	61	8	c	c	NOUN
ejpam-5036	62	1	′	′	NOUN
ejpam-5036	63	1	i	i	PRON
ejpam-5036	63	2	will	will	AUX
ejpam-5036	63	3	be	be	AUX
ejpam-5036	63	4	the	the	DET
ejpam-5036	63	5	new	new	ADJ
ejpam-5036	63	6	i−th	i−th	PROPN
ejpam-5036	63	7	row	row	NOUN
ejpam-5036	63	8	and	and	CCONJ
ejpam-5036	63	9	column	column	NOUN
ejpam-5036	63	10	of	of	ADP
ejpam-5036	63	11	the	the	DET
ejpam-5036	63	12	matrix	matrix	NOUN
ejpam-5036	63	13	,	,	PUNCT
ejpam-5036	63	14	respectively	respectively	ADV
ejpam-5036	63	15	,	,	PUNCT
ejpam-5036	63	16	as	as	SCONJ
ejpam-5036	63	17	obtained	obtain	VERB
ejpam-5036	63	18	from	from	ADP
ejpam-5036	63	19	ri	ri	PROPN
ejpam-5036	63	20	and	and	CCONJ
ejpam-5036	63	21	ci	ci	PROPN
ejpam-5036	63	22	.	.	PUNCT
ejpam-5036	64	1	the	the	DET
ejpam-5036	64	2	following	follow	VERB
ejpam-5036	64	3	theorem	theorem	NOUN
ejpam-5036	64	4	is	be	AUX
ejpam-5036	64	5	a	a	DET
ejpam-5036	64	6	result	result	NOUN
ejpam-5036	64	7	of	of	ADP
ejpam-5036	64	8	[	[	X
ejpam-5036	64	9	6	6	NUM
ejpam-5036	64	10	]	]	PUNCT
ejpam-5036	64	11	as	as	ADP
ejpam-5036	64	12	our	our	PRON
ejpam-5036	64	13	guideline	guideline	NOUN
ejpam-5036	64	14	to	to	PART
ejpam-5036	64	15	simplify	simplify	VERB
ejpam-5036	64	16	the	the	DET
ejpam-5036	64	17	characteristic	characteristic	ADJ
ejpam-5036	64	18	polynomial	polynomial	NOUN
ejpam-5036	64	19	of	of	ADP
ejpam-5036	64	20	γd2n	γd2n	PROPN
ejpam-5036	64	21	.	.	PUNCT
ejpam-5036	65	1	theorem	theorem	ADJ
ejpam-5036	65	2	2	2	NUM
ejpam-5036	65	3	.	.	PUNCT
ejpam-5036	66	1	[	[	X
ejpam-5036	66	2	6	6	NUM
ejpam-5036	66	3	]	]	X
ejpam-5036	66	4	if	if	SCONJ
ejpam-5036	66	5	a	a	DET
ejpam-5036	66	6	square	square	ADJ
ejpam-5036	66	7	matrix	matrix	NOUN
ejpam-5036	66	8	m	m	VERB
ejpam-5036	66	9	can	can	AUX
ejpam-5036	66	10	be	be	AUX
ejpam-5036	66	11	partitioned	partition	VERB
ejpam-5036	66	12	into	into	ADP
ejpam-5036	66	13	four	four	NUM
ejpam-5036	66	14	blocks	block	NOUN
ejpam-5036	66	15	m	m	VERB
ejpam-5036	66	16	=	=	PUNCT
ejpam-5036	67	1	[	[	PUNCT
ejpam-5036	67	2	a	a	DET
ejpam-5036	67	3	b	b	NOUN
ejpam-5036	67	4	c	c	NOUN
ejpam-5036	67	5	d	d	X
ejpam-5036	67	6	]	]	X
ejpam-5036	67	7	,	,	PUNCT
ejpam-5036	67	8	where	where	SCONJ
ejpam-5036	67	9	a	a	PRON
ejpam-5036	67	10	is	be	AUX
ejpam-5036	67	11	a	a	DET
ejpam-5036	67	12	nonsingular	nonsingular	ADJ
ejpam-5036	67	13	,	,	PUNCT
ejpam-5036	67	14	then	then	ADV
ejpam-5036	67	15	|m	|m	NOUN
ejpam-5036	67	16	|	|	ADV
ejpam-5036	67	17	=	=	PUNCT
ejpam-5036	67	18	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5036	67	19	a	a	DET
ejpam-5036	67	20	b	b	NOUN
ejpam-5036	67	21	o	o	X
ejpam-5036	67	22	d	d	X
ejpam-5036	67	23	−	−	PROPN
ejpam-5036	67	24	ca−1b	ca−1b	PROPN
ejpam-5036	67	25	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5036	67	26	=	=	SYM
ejpam-5036	67	27	|a|	|a|	NOUN
ejpam-5036	67	28	∣∣d	∣∣d	NOUN
ejpam-5036	67	29	−	−	PROPN
ejpam-5036	67	30	ca−1b	ca−1b	NOUN
ejpam-5036	67	31	∣∣	∣∣	X
ejpam-5036	67	32	.	.	PUNCT
ejpam-5036	68	1	2	2	X
ejpam-5036	68	2	.	.	X
ejpam-5036	68	3	main	main	ADJ
ejpam-5036	68	4	results	result	NOUN
ejpam-5036	68	5	this	this	DET
ejpam-5036	68	6	section	section	NOUN
ejpam-5036	68	7	presents	present	VERB
ejpam-5036	68	8	the	the	DET
ejpam-5036	68	9	main	main	ADJ
ejpam-5036	68	10	results	result	NOUN
ejpam-5036	68	11	on	on	ADP
ejpam-5036	68	12	the	the	DET
ejpam-5036	68	13	characteristic	characteristic	ADJ
ejpam-5036	68	14	polynomial	polynomial	NOUN
ejpam-5036	68	15	of	of	ADP
ejpam-5036	68	16	γd2n	γd2n	PROPN
ejpam-5036	68	17	.	.	PUNCT
ejpam-5036	69	1	we	we	PRON
ejpam-5036	69	2	begin	begin	VERB
ejpam-5036	69	3	with	with	ADP
ejpam-5036	69	4	the	the	DET
ejpam-5036	69	5	adjacency	adjacency	NOUN
ejpam-5036	69	6	matrix	matrix	NOUN
ejpam-5036	69	7	as	as	ADP
ejpam-5036	69	8	the	the	DET
ejpam-5036	69	9	matrix	matrix	NOUN
ejpam-5036	69	10	representation	representation	NOUN
ejpam-5036	69	11	of	of	ADP
ejpam-5036	69	12	γd2n	γd2n	PROPN
ejpam-5036	69	13	.	.	PUNCT
ejpam-5036	70	1	theorem	theorem	ADJ
ejpam-5036	70	2	3	3	X
ejpam-5036	70	3	.	.	PUNCT
ejpam-5036	71	1	let	let	VERB
ejpam-5036	71	2	γd2n	γd2n	PROPN
ejpam-5036	71	3	be	be	AUX
ejpam-5036	71	4	the	the	DET
ejpam-5036	71	5	power	power	NOUN
ejpam-5036	71	6	graph	graph	NOUN
ejpam-5036	71	7	for	for	ADP
ejpam-5036	71	8	d2n	d2n	NOUN
ejpam-5036	71	9	,	,	PUNCT
ejpam-5036	71	10	then	then	ADV
ejpam-5036	71	11	the	the	DET
ejpam-5036	71	12	characteristic	characteristic	ADJ
ejpam-5036	71	13	polynomial	polynomial	NOUN
ejpam-5036	71	14	of	of	ADP
ejpam-5036	71	15	a(γd2n	a(γd2n	X
ejpam-5036	71	16	)	)	PUNCT
ejpam-5036	71	17	is	be	AUX
ejpam-5036	71	18	pa(γd2n	pa(γd2n	NOUN
ejpam-5036	71	19	)	)	PUNCT
ejpam-5036	71	20	(	(	PUNCT
ejpam-5036	71	21	λ	λ	X
ejpam-5036	71	22	)	)	PUNCT
ejpam-5036	71	23	=	=	PUNCT
ejpam-5036	72	1	λn−1(λ+	λn−1(λ+	NOUN
ejpam-5036	72	2	1)n−2	1)n−2	NUM
ejpam-5036	72	3	(	(	PUNCT
ejpam-5036	72	4	λ3	λ3	PROPN
ejpam-5036	72	5	−	−	PROPN
ejpam-5036	72	6	(	(	PUNCT
ejpam-5036	72	7	n−	n−	NOUN
ejpam-5036	72	8	2)λ2	2)λ2	NUM
ejpam-5036	72	9	+	+	CCONJ
ejpam-5036	72	10	(	(	PUNCT
ejpam-5036	72	11	1−	1−	NUM
ejpam-5036	72	12	2n)λ+	2n)λ+	NUM
ejpam-5036	72	13	n(n−	n(n−	NOUN
ejpam-5036	72	14	2	2	NUM
ejpam-5036	72	15	)	)	PUNCT
ejpam-5036	72	16	)	)	PUNCT
ejpam-5036	72	17	.	.	PUNCT
ejpam-5036	73	1	proof	proof	NOUN
ejpam-5036	73	2	.	.	PUNCT
ejpam-5036	74	1	from	from	ADP
ejpam-5036	74	2	theorem	theorem	NOUN
ejpam-5036	74	3	1	1	NUM
ejpam-5036	74	4	we	we	PRON
ejpam-5036	74	5	know	know	VERB
ejpam-5036	74	6	that	that	SCONJ
ejpam-5036	74	7	vertex	vertex	NOUN
ejpam-5036	74	8	e	e	NOUN
ejpam-5036	74	9	is	be	AUX
ejpam-5036	74	10	adjacent	adjacent	ADJ
ejpam-5036	74	11	to	to	ADP
ejpam-5036	74	12	all	all	DET
ejpam-5036	74	13	other	other	ADJ
ejpam-5036	74	14	vertices	vertex	NOUN
ejpam-5036	74	15	in	in	ADP
ejpam-5036	74	16	γd2n	γd2n	PROPN
ejpam-5036	74	17	and	and	CCONJ
ejpam-5036	74	18	vertices	vertex	NOUN
ejpam-5036	74	19	in	in	ADP
ejpam-5036	74	20	g3	g3	PROPN
ejpam-5036	74	21	are	be	AUX
ejpam-5036	74	22	only	only	ADV
ejpam-5036	74	23	adjacent	adjacent	ADJ
ejpam-5036	74	24	to	to	ADP
ejpam-5036	74	25	e.	e.	PROPN
ejpam-5036	74	26	meanwhile	meanwhile	ADV
ejpam-5036	74	27	,	,	PUNCT
ejpam-5036	74	28	every	every	DET
ejpam-5036	74	29	vertex	vertex	NOUN
ejpam-5036	74	30	in	in	ADP
ejpam-5036	74	31	g2	g2	PROPN
ejpam-5036	74	32	is	be	AUX
ejpam-5036	74	33	adjacent	adjacent	ADJ
ejpam-5036	74	34	to	to	ADP
ejpam-5036	74	35	e	e	NOUN
ejpam-5036	74	36	and	and	CCONJ
ejpam-5036	74	37	all	all	DET
ejpam-5036	74	38	other	other	ADJ
ejpam-5036	74	39	vertices	vertex	NOUN
ejpam-5036	74	40	in	in	ADP
ejpam-5036	74	41	g2	g2	PROPN
ejpam-5036	74	42	.	.	PUNCT
ejpam-5036	75	1	following	follow	VERB
ejpam-5036	75	2	definition	definition	NOUN
ejpam-5036	75	3	1	1	NUM
ejpam-5036	75	4	,	,	PUNCT
ejpam-5036	75	5	we	we	PRON
ejpam-5036	75	6	can	can	AUX
ejpam-5036	75	7	construct	construct	VERB
ejpam-5036	75	8	a(γd2n	a(γd2n	PUNCT
ejpam-5036	75	9	)	)	PUNCT
ejpam-5036	75	10	of	of	ADP
ejpam-5036	75	11	the	the	DET
ejpam-5036	75	12	size	size	NOUN
ejpam-5036	75	13	m.	m.	PROPN
ejpam-5036	75	14	u.	u.	PROPN
ejpam-5036	75	15	romdhini	romdhini	PROPN
ejpam-5036	75	16	et	et	PROPN
ejpam-5036	75	17	al	al	PROPN
ejpam-5036	75	18	.	.	PUNCT
ejpam-5036	75	19	/	/	SYM
ejpam-5036	75	20	eur	eur	PROPN
ejpam-5036	75	21	.	.	PUNCT
ejpam-5036	76	1	j.	j.	PROPN
ejpam-5036	76	2	pure	pure	PROPN
ejpam-5036	76	3	appl	appl	PROPN
ejpam-5036	76	4	.	.	PROPN
ejpam-5036	76	5	math	math	PROPN
ejpam-5036	76	6	,	,	PUNCT
ejpam-5036	76	7	17	17	NUM
ejpam-5036	76	8	(	(	PUNCT
ejpam-5036	76	9	2	2	NUM
ejpam-5036	76	10	)	)	PUNCT
ejpam-5036	76	11	(	(	PUNCT
ejpam-5036	76	12	2024	2024	NUM
ejpam-5036	76	13	)	)	PUNCT
ejpam-5036	76	14	,	,	PUNCT
ejpam-5036	76	15	591	591	NUM
ejpam-5036	76	16	-	-	SYM
ejpam-5036	76	17	603	603	NUM
ejpam-5036	76	18	594	594	NUM
ejpam-5036	76	19	2n×	2n×	NUM
ejpam-5036	76	20	2n	2n	NUM
ejpam-5036	76	21	:	:	PUNCT
ejpam-5036	76	22	a(γd2n	a(γd2n	X
ejpam-5036	76	23	)	)	PUNCT
ejpam-5036	76	24	=	=	PUNCT
ejpam-5036	77	1	e	e	X
ejpam-5036	77	2	a	a	DET
ejpam-5036	77	3	a2	a2	PROPN
ejpam-5036	77	4	.	.	PUNCT
ejpam-5036	77	5	.	.	PUNCT
ejpam-5036	77	6	.	.	PUNCT
ejpam-5036	78	1	an−1	an−1	PROPN
ejpam-5036	78	2	b	b	PROPN
ejpam-5036	78	3	ab	ab	PROPN
ejpam-5036	78	4	.	.	PUNCT
ejpam-5036	78	5	.	.	PUNCT
ejpam-5036	78	6	.	.	PUNCT
ejpam-5036	79	1	an−1b	an−1b	PRON
ejpam-5036	79	2			NOUN
ejpam-5036	79	3	e	e	NOUN
ejpam-5036	79	4	0	0	NUM
ejpam-5036	79	5	1	1	NUM
ejpam-5036	79	6	1	1	NUM
ejpam-5036	79	7	.	.	PUNCT
ejpam-5036	79	8	.	.	PUNCT
ejpam-5036	79	9	.	.	PUNCT
ejpam-5036	80	1	1	1	NUM
ejpam-5036	80	2	1	1	NUM
ejpam-5036	80	3	1	1	NUM
ejpam-5036	80	4	.	.	PUNCT
ejpam-5036	80	5	.	.	PUNCT
ejpam-5036	80	6	.	.	PUNCT
ejpam-5036	81	1	1	1	NUM
ejpam-5036	81	2	a	a	DET
ejpam-5036	81	3	1	1	NUM
ejpam-5036	81	4	0	0	NUM
ejpam-5036	81	5	1	1	NUM
ejpam-5036	81	6	.	.	PUNCT
ejpam-5036	81	7	.	.	PUNCT
ejpam-5036	81	8	.	.	PUNCT
ejpam-5036	82	1	1	1	NUM
ejpam-5036	82	2	0	0	NUM
ejpam-5036	82	3	0	0	NUM
ejpam-5036	82	4	.	.	PUNCT
ejpam-5036	82	5	.	.	PUNCT
ejpam-5036	82	6	.	.	PUNCT
ejpam-5036	83	1	0	0	NUM
ejpam-5036	83	2	a2	a2	PROPN
ejpam-5036	83	3	1	1	NUM
ejpam-5036	83	4	1	1	NUM
ejpam-5036	83	5	0	0	NUM
ejpam-5036	83	6	.	.	PUNCT
ejpam-5036	83	7	.	.	PUNCT
ejpam-5036	83	8	.	.	PUNCT
ejpam-5036	84	1	1	1	NUM
ejpam-5036	84	2	0	0	NUM
ejpam-5036	84	3	0	0	NUM
ejpam-5036	84	4	.	.	PUNCT
ejpam-5036	84	5	.	.	PUNCT
ejpam-5036	84	6	.	.	PUNCT
ejpam-5036	85	1	0	0	NUM
ejpam-5036	85	2	...	...	PUNCT
ejpam-5036	85	3	...	...	PUNCT
ejpam-5036	85	4	...	...	PUNCT
ejpam-5036	85	5	...	...	PUNCT
ejpam-5036	85	6	.	.	PUNCT
ejpam-5036	85	7	.	.	PUNCT
ejpam-5036	86	1	.	.	PUNCT
ejpam-5036	86	2	...	...	PUNCT
ejpam-5036	87	1	...	...	PUNCT
ejpam-5036	87	2	...	...	PUNCT
ejpam-5036	87	3	.	.	PUNCT
ejpam-5036	87	4	.	.	PUNCT
ejpam-5036	88	1	.	.	PUNCT
ejpam-5036	89	1	...	...	PUNCT
ejpam-5036	90	1	an−1	an−1	ADJ
ejpam-5036	90	2	1	1	NUM
ejpam-5036	90	3	1	1	NUM
ejpam-5036	90	4	1	1	NUM
ejpam-5036	90	5	.	.	PUNCT
ejpam-5036	90	6	.	.	PUNCT
ejpam-5036	90	7	.	.	PUNCT
ejpam-5036	91	1	0	0	NUM
ejpam-5036	92	1	0	0	NUM
ejpam-5036	92	2	0	0	NUM
ejpam-5036	92	3	.	.	PUNCT
ejpam-5036	92	4	.	.	PUNCT
ejpam-5036	92	5	.	.	PUNCT
ejpam-5036	93	1	0	0	NUM
ejpam-5036	94	1	b	b	X
ejpam-5036	94	2	1	1	NUM
ejpam-5036	94	3	0	0	NUM
ejpam-5036	94	4	0	0	NUM
ejpam-5036	94	5	.	.	PUNCT
ejpam-5036	94	6	.	.	PUNCT
ejpam-5036	94	7	.	.	PUNCT
ejpam-5036	95	1	0	0	NUM
ejpam-5036	96	1	0	0	NUM
ejpam-5036	96	2	0	0	NUM
ejpam-5036	96	3	.	.	PUNCT
ejpam-5036	96	4	.	.	PUNCT
ejpam-5036	97	1	.	.	PUNCT
ejpam-5036	97	2	0	0	PUNCT
ejpam-5036	98	1	ab	ab	PROPN
ejpam-5036	98	2	1	1	NUM
ejpam-5036	98	3	0	0	NUM
ejpam-5036	98	4	0	0	NUM
ejpam-5036	98	5	.	.	PUNCT
ejpam-5036	98	6	.	.	PUNCT
ejpam-5036	98	7	.	.	PUNCT
ejpam-5036	99	1	0	0	NUM
ejpam-5036	100	1	0	0	NUM
ejpam-5036	100	2	0	0	NUM
ejpam-5036	100	3	.	.	PUNCT
ejpam-5036	100	4	.	.	PUNCT
ejpam-5036	101	1	.	.	PUNCT
ejpam-5036	102	1	0	0	NUM
ejpam-5036	102	2	...	...	PUNCT
ejpam-5036	102	3	...	...	PUNCT
ejpam-5036	102	4	...	...	PUNCT
ejpam-5036	102	5	...	...	PUNCT
ejpam-5036	102	6	.	.	PUNCT
ejpam-5036	102	7	.	.	PUNCT
ejpam-5036	103	1	.	.	PUNCT
ejpam-5036	103	2	...	...	PUNCT
ejpam-5036	104	1	...	...	PUNCT
ejpam-5036	104	2	...	...	PUNCT
ejpam-5036	104	3	.	.	PUNCT
ejpam-5036	104	4	.	.	PUNCT
ejpam-5036	104	5	.	.	PUNCT
ejpam-5036	105	1	...	...	PUNCT
ejpam-5036	106	1	an−1b	an−1b	PUNCT
ejpam-5036	107	1	1	1	NUM
ejpam-5036	107	2	0	0	NUM
ejpam-5036	107	3	0	0	NUM
ejpam-5036	107	4	.	.	PUNCT
ejpam-5036	107	5	.	.	PUNCT
ejpam-5036	107	6	.	.	PUNCT
ejpam-5036	108	1	0	0	NUM
ejpam-5036	109	1	0	0	NUM
ejpam-5036	109	2	0	0	NUM
ejpam-5036	109	3	.	.	PUNCT
ejpam-5036	109	4	.	.	PUNCT
ejpam-5036	110	1	.	.	PUNCT
ejpam-5036	110	2	0	0	PUNCT
ejpam-5036	111	1	.	.	PUNCT
ejpam-5036	112	1	(	(	PUNCT
ejpam-5036	112	2	1	1	X
ejpam-5036	112	3	)	)	PUNCT
ejpam-5036	112	4	matrix	matrix	NOUN
ejpam-5036	112	5	a(γd2n	a(γd2n	PUNCT
ejpam-5036	112	6	)	)	PUNCT
ejpam-5036	112	7	can	can	AUX
ejpam-5036	112	8	be	be	AUX
ejpam-5036	112	9	partitioned	partition	VERB
ejpam-5036	112	10	into	into	ADP
ejpam-5036	112	11	nine	nine	NUM
ejpam-5036	112	12	block	block	NOUN
ejpam-5036	112	13	matrices	matrix	NOUN
ejpam-5036	112	14	as	as	SCONJ
ejpam-5036	112	15	follows	follow	VERB
ejpam-5036	112	16	:	:	PUNCT
ejpam-5036	112	17	a(γd2n	a(γd2n	X
ejpam-5036	112	18	)	)	PUNCT
ejpam-5036	112	19	=	=	PUNCT
ejpam-5036	112	20			NOUN
ejpam-5036	112	21	0	0	NUM
ejpam-5036	112	22	j1×(n−1	j1×(n−1	PROPN
ejpam-5036	112	23	)	)	PUNCT
ejpam-5036	112	24	j1×n	j1×n	ADJ
ejpam-5036	112	25	j(n−1)×1	j(n−1)×1	INTJ
ejpam-5036	112	26	(	(	PUNCT
ejpam-5036	112	27	j	j	PROPN
ejpam-5036	112	28	−	−	PROPN
ejpam-5036	112	29	i)n−1	i)n−1	PROPN
ejpam-5036	112	30	0(n−1)×n	0(n−1)×n	NUM
ejpam-5036	112	31	jn×1	jn×1	VERB
ejpam-5036	112	32	0n×(n−1	0n×(n−1	NUM
ejpam-5036	112	33	)	)	PUNCT
ejpam-5036	112	34	0n	0n	NOUN
ejpam-5036	112	35			NOUN
ejpam-5036	112	36	.	.	PUNCT
ejpam-5036	113	1	the	the	DET
ejpam-5036	113	2	characteristic	characteristic	ADJ
ejpam-5036	113	3	polynomial	polynomial	NOUN
ejpam-5036	113	4	of	of	ADP
ejpam-5036	113	5	a(γd2n	a(γd2n	X
ejpam-5036	113	6	)	)	PUNCT
ejpam-5036	113	7	is	be	AUX
ejpam-5036	113	8	pa(γd2n	pa(γd2n	NOUN
ejpam-5036	113	9	)	)	PUNCT
ejpam-5036	113	10	(	(	PUNCT
ejpam-5036	113	11	λ	λ	X
ejpam-5036	113	12	)	)	PUNCT
ejpam-5036	113	13	=	=	SYM
ejpam-5036	114	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5036	114	2	λ	λ	PROPN
ejpam-5036	114	3	−j1×(n−1	−j1×(n−1	PROPN
ejpam-5036	114	4	)	)	PUNCT
ejpam-5036	114	5	−j1×n	−j1×n	PUNCT
ejpam-5036	115	1	−j(n−1)×1	−j(n−1)×1	PROPN
ejpam-5036	115	2	(	(	PUNCT
ejpam-5036	115	3	λ+	λ+	PUNCT
ejpam-5036	115	4	1)in−1	1)in−1	NUM
ejpam-5036	115	5	−	−	PROPN
ejpam-5036	115	6	jn−1	jn−1	PROPN
ejpam-5036	115	7	0(n−1)×n	0(n−1)×n	PROPN
ejpam-5036	115	8	−jn×1	−jn×1	PUNCT
ejpam-5036	115	9	0n×(n−1	0n×(n−1	PROPN
ejpam-5036	115	10	)	)	PUNCT
ejpam-5036	115	11	λin	λin	NOUN
ejpam-5036	115	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADV
ejpam-5036	115	13	.	.	PUNCT
ejpam-5036	116	1	(	(	PUNCT
ejpam-5036	116	2	2	2	X
ejpam-5036	116	3	)	)	PUNCT
ejpam-5036	116	4	we	we	PRON
ejpam-5036	116	5	apply	apply	VERB
ejpam-5036	116	6	the	the	DET
ejpam-5036	116	7	following	follow	VERB
ejpam-5036	116	8	steps	step	NOUN
ejpam-5036	116	9	to	to	PART
ejpam-5036	116	10	simplify	simplify	VERB
ejpam-5036	116	11	the	the	DET
ejpam-5036	116	12	determinant	determinant	ADJ
ejpam-5036	116	13	in	in	ADP
ejpam-5036	116	14	equation	equation	NOUN
ejpam-5036	116	15	2	2	NUM
ejpam-5036	116	16	:	:	PUNCT
ejpam-5036	116	17	(	(	PUNCT
ejpam-5036	116	18	i	i	NOUN
ejpam-5036	116	19	)	)	PUNCT
ejpam-5036	116	20	rn+1+i	rn+1+i	NOUN
ejpam-5036	116	21	−→	−→	ADJ
ejpam-5036	116	22	rn+1+i	rn+1+i	NOUN
ejpam-5036	116	23	−rn+1	−rn+1	VERB
ejpam-5036	116	24	,	,	PUNCT
ejpam-5036	116	25	for	for	ADP
ejpam-5036	116	26	i	i	PROPN
ejpam-5036	116	27	=	=	SYM
ejpam-5036	116	28	1	1	NUM
ejpam-5036	116	29	,	,	PUNCT
ejpam-5036	116	30	2	2	NUM
ejpam-5036	116	31	,	,	PUNCT
ejpam-5036	116	32	.	.	PUNCT
ejpam-5036	116	33	.	.	PUNCT
ejpam-5036	117	1	.	.	PUNCT
ejpam-5036	118	1	,	,	PUNCT
ejpam-5036	118	2	n−	n−	NOUN
ejpam-5036	118	3	1	1	NUM
ejpam-5036	118	4	.	.	PUNCT
ejpam-5036	118	5	(	(	PUNCT
ejpam-5036	118	6	ii	ii	NOUN
ejpam-5036	118	7	)	)	PUNCT
ejpam-5036	118	8	cn+1	cn+1	VERB
ejpam-5036	118	9	−→	−→	NOUN
ejpam-5036	118	10	cn+1	cn+1	NOUN
ejpam-5036	118	11	+	+	CCONJ
ejpam-5036	118	12	cn+2	cn+2	PRON
ejpam-5036	119	1	+	+	CCONJ
ejpam-5036	119	2	.	.	PUNCT
ejpam-5036	119	3	.	.	PUNCT
ejpam-5036	120	1	.+	.+	NOUN
ejpam-5036	120	2	c2n	c2n	NOUN
ejpam-5036	120	3	.	.	PUNCT
ejpam-5036	121	1	(	(	PUNCT
ejpam-5036	121	2	iii	iii	X
ejpam-5036	121	3	)	)	PUNCT
ejpam-5036	121	4	c1	c1	PROPN
ejpam-5036	121	5	−→	−→	PROPN
ejpam-5036	121	6	c1	c1	PROPN
ejpam-5036	121	7	+	+	CCONJ
ejpam-5036	121	8	1	1	NUM
ejpam-5036	121	9	λcn+1	λcn+1	ADJ
ejpam-5036	121	10	.	.	PUNCT
ejpam-5036	122	1	(	(	PUNCT
ejpam-5036	122	2	iv	iv	X
ejpam-5036	122	3	)	)	PUNCT
ejpam-5036	122	4	r2+i	r2+i	PROPN
ejpam-5036	122	5	−→	−→	NOUN
ejpam-5036	122	6	r2+i	r2+i	PROPN
ejpam-5036	122	7	−r2	−r2	PROPN
ejpam-5036	122	8	,	,	PUNCT
ejpam-5036	122	9	for	for	ADP
ejpam-5036	122	10	i	i	PROPN
ejpam-5036	122	11	=	=	SYM
ejpam-5036	122	12	1	1	NUM
ejpam-5036	122	13	,	,	PUNCT
ejpam-5036	122	14	2	2	NUM
ejpam-5036	122	15	,	,	PUNCT
ejpam-5036	122	16	.	.	PUNCT
ejpam-5036	122	17	.	.	PUNCT
ejpam-5036	123	1	.	.	PUNCT
ejpam-5036	124	1	,	,	PUNCT
ejpam-5036	124	2	n−	n−	NOUN
ejpam-5036	124	3	2	2	NUM
ejpam-5036	124	4	.	.	PUNCT
ejpam-5036	125	1	(	(	PUNCT
ejpam-5036	125	2	v	v	NOUN
ejpam-5036	125	3	)	)	PUNCT
ejpam-5036	125	4	c2	c2	PROPN
ejpam-5036	125	5	−→	−→	PROPN
ejpam-5036	125	6	c2	c2	PROPN
ejpam-5036	125	7	+	+	CCONJ
ejpam-5036	125	8	c3	c3	PROPN
ejpam-5036	125	9	+	+	X
ejpam-5036	125	10	.	.	PUNCT
ejpam-5036	125	11	.	.	PUNCT
ejpam-5036	126	1	.+	.+	NOUN
ejpam-5036	127	1	cn	cn	PROPN
ejpam-5036	127	2	.	.	PUNCT
ejpam-5036	128	1	then	then	ADV
ejpam-5036	128	2	we	we	PRON
ejpam-5036	128	3	get	get	VERB
ejpam-5036	128	4	pa(γd2n	pa(γd2n	NOUN
ejpam-5036	128	5	)	)	PUNCT
ejpam-5036	128	6	(	(	PUNCT
ejpam-5036	128	7	λ	λ	X
ejpam-5036	128	8	)	)	PUNCT
ejpam-5036	128	9	=	=	PUNCT
ejpam-5036	129	1	∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣	NUM
ejpam-5036	129	2	λ2+n	λ2+n	VERB
ejpam-5036	129	3	λ	λ	PROPN
ejpam-5036	129	4	1−	1−	NUM
ejpam-5036	129	5	n	n	PRON
ejpam-5036	129	6	−j1×(n−2	−j1×(n−2	NUM
ejpam-5036	129	7	)	)	PUNCT
ejpam-5036	129	8	−n	−n	ADV
ejpam-5036	129	9	−j1×n	−j1×n	ADP
ejpam-5036	129	10	−1	−1	ADV
ejpam-5036	129	11	λ−	λ−	PROPN
ejpam-5036	129	12	(	(	PUNCT
ejpam-5036	129	13	n−	n−	NOUN
ejpam-5036	129	14	2	2	NUM
ejpam-5036	129	15	)	)	PUNCT
ejpam-5036	129	16	−j1×(n−2	−j1×(n−2	NUM
ejpam-5036	129	17	)	)	PUNCT
ejpam-5036	129	18	0	0	NUM
ejpam-5036	129	19	01×(n−1	01×(n−1	NUM
ejpam-5036	129	20	)	)	PUNCT
ejpam-5036	129	21	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	129	22	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	129	23	(	(	PUNCT
ejpam-5036	129	24	λ+	λ+	NUM
ejpam-5036	129	25	1)in−2	1)in−2	NUM
ejpam-5036	129	26	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	129	27	0(n−2)×(n−1	0(n−2)×(n−1	NUM
ejpam-5036	129	28	)	)	PUNCT
ejpam-5036	129	29	0	0	NUM
ejpam-5036	129	30	0	0	NUM
ejpam-5036	129	31	01×(n−2	01×(n−2	X
ejpam-5036	129	32	)	)	PUNCT
ejpam-5036	129	33	λ	λ	NOUN
ejpam-5036	129	34	01×(n−1	01×(n−1	NUM
ejpam-5036	129	35	)	)	PUNCT
ejpam-5036	129	36	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	129	37	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	130	1	0n−1	0n−1	NUM
ejpam-5036	130	2	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	131	1	λin−1	λin−1	PROPN
ejpam-5036	131	2	∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5036	131	3	.	.	PUNCT
ejpam-5036	132	1	m.	m.	PROPN
ejpam-5036	132	2	u.	u.	PROPN
ejpam-5036	132	3	romdhini	romdhini	PROPN
ejpam-5036	132	4	et	et	PROPN
ejpam-5036	132	5	al	al	PROPN
ejpam-5036	132	6	.	.	PUNCT
ejpam-5036	132	7	/	/	SYM
ejpam-5036	132	8	eur	eur	PROPN
ejpam-5036	132	9	.	.	PUNCT
ejpam-5036	133	1	j.	j.	PROPN
ejpam-5036	133	2	pure	pure	PROPN
ejpam-5036	133	3	appl	appl	PROPN
ejpam-5036	133	4	.	.	PROPN
ejpam-5036	133	5	math	math	PROPN
ejpam-5036	133	6	,	,	PUNCT
ejpam-5036	133	7	17	17	NUM
ejpam-5036	133	8	(	(	PUNCT
ejpam-5036	133	9	2	2	NUM
ejpam-5036	133	10	)	)	PUNCT
ejpam-5036	133	11	(	(	PUNCT
ejpam-5036	133	12	2024	2024	NUM
ejpam-5036	133	13	)	)	PUNCT
ejpam-5036	133	14	,	,	PUNCT
ejpam-5036	133	15	591	591	NUM
ejpam-5036	133	16	-	-	SYM
ejpam-5036	133	17	603	603	NUM
ejpam-5036	133	18	595	595	NUM
ejpam-5036	133	19	consequently	consequently	ADV
ejpam-5036	133	20	,	,	PUNCT
ejpam-5036	133	21	by	by	ADP
ejpam-5036	133	22	theorem	theorem	NOUN
ejpam-5036	133	23	2	2	NUM
ejpam-5036	133	24	,	,	PUNCT
ejpam-5036	133	25	we	we	PRON
ejpam-5036	133	26	can	can	AUX
ejpam-5036	133	27	obtain	obtain	VERB
ejpam-5036	133	28	the	the	DET
ejpam-5036	133	29	characteristic	characteristic	ADJ
ejpam-5036	133	30	polynomial	polynomial	NOUN
ejpam-5036	133	31	of	of	ADP
ejpam-5036	133	32	a(γd2n	a(γd2n	PROPN
ejpam-5036	133	33	)	)	PUNCT
ejpam-5036	133	34	as	as	SCONJ
ejpam-5036	133	35	follows	follow	VERB
ejpam-5036	133	36	:	:	PUNCT
ejpam-5036	133	37	pa(γd2n	pa(γd2n	NOUN
ejpam-5036	133	38	)	)	PUNCT
ejpam-5036	133	39	(	(	PUNCT
ejpam-5036	133	40	λ	λ	X
ejpam-5036	133	41	)	)	PUNCT
ejpam-5036	133	42	=	=	PUNCT
ejpam-5036	133	43	λn−1(λ+	λn−1(λ+	NOUN
ejpam-5036	133	44	1)n−2	1)n−2	NUM
ejpam-5036	133	45	(	(	PUNCT
ejpam-5036	133	46	λ3	λ3	PROPN
ejpam-5036	133	47	−	−	PROPN
ejpam-5036	133	48	(	(	PUNCT
ejpam-5036	133	49	n−	n−	NOUN
ejpam-5036	133	50	2)λ2	2)λ2	NUM
ejpam-5036	133	51	+	+	CCONJ
ejpam-5036	133	52	(	(	PUNCT
ejpam-5036	133	53	1−	1−	NUM
ejpam-5036	133	54	2n)λ+	2n)λ+	NUM
ejpam-5036	133	55	n(n−	n(n−	NOUN
ejpam-5036	133	56	2	2	NUM
ejpam-5036	133	57	)	)	PUNCT
ejpam-5036	133	58	)	)	PUNCT
ejpam-5036	133	59	.	.	PUNCT
ejpam-5036	134	1	the	the	DET
ejpam-5036	134	2	previous	previous	ADJ
ejpam-5036	134	3	theorem	theorem	NOUN
ejpam-5036	134	4	is	be	AUX
ejpam-5036	134	5	devoted	devote	VERB
ejpam-5036	134	6	to	to	ADP
ejpam-5036	134	7	the	the	DET
ejpam-5036	134	8	adjacency	adjacency	NOUN
ejpam-5036	134	9	matrix	matrix	NOUN
ejpam-5036	134	10	.	.	PUNCT
ejpam-5036	135	1	now	now	ADV
ejpam-5036	135	2	we	we	PRON
ejpam-5036	135	3	are	be	AUX
ejpam-5036	135	4	moving	move	VERB
ejpam-5036	135	5	to	to	ADP
ejpam-5036	135	6	the	the	DET
ejpam-5036	135	7	laplacian	laplacian	ADJ
ejpam-5036	135	8	matrix	matrix	NOUN
ejpam-5036	135	9	as	as	ADP
ejpam-5036	135	10	the	the	DET
ejpam-5036	135	11	representation	representation	NOUN
ejpam-5036	135	12	of	of	ADP
ejpam-5036	135	13	γd2n	γd2n	PROPN
ejpam-5036	135	14	.	.	PUNCT
ejpam-5036	136	1	theorem	theorem	ADJ
ejpam-5036	136	2	4	4	NUM
ejpam-5036	136	3	.	.	PUNCT
ejpam-5036	137	1	let	let	VERB
ejpam-5036	137	2	γd2n	γd2n	PROPN
ejpam-5036	137	3	be	be	AUX
ejpam-5036	137	4	the	the	DET
ejpam-5036	137	5	power	power	NOUN
ejpam-5036	137	6	graph	graph	NOUN
ejpam-5036	137	7	for	for	ADP
ejpam-5036	137	8	d2n	d2n	NOUN
ejpam-5036	137	9	,	,	PUNCT
ejpam-5036	137	10	then	then	ADV
ejpam-5036	137	11	the	the	DET
ejpam-5036	137	12	characteristic	characteristic	ADJ
ejpam-5036	137	13	polynomial	polynomial	NOUN
ejpam-5036	137	14	of	of	ADP
ejpam-5036	137	15	l(γd2n	l(γd2n	PROPN
ejpam-5036	137	16	)	)	PUNCT
ejpam-5036	137	17	is	be	AUX
ejpam-5036	137	18	pl(γd2n	pl(γd2n	ADJ
ejpam-5036	137	19	)	)	PUNCT
ejpam-5036	137	20	(	(	PUNCT
ejpam-5036	137	21	λ	λ	X
ejpam-5036	137	22	)	)	PUNCT
ejpam-5036	137	23	=	=	SYM
ejpam-5036	137	24	λ(λ−	λ(λ−	PROPN
ejpam-5036	137	25	2n)(λ−	2n)(λ−	NUM
ejpam-5036	137	26	n)n−2(λ−	n)n−2(λ−	PROPN
ejpam-5036	137	27	1)n	1)n	NUM
ejpam-5036	137	28	.	.	PUNCT
ejpam-5036	138	1	proof	proof	NOUN
ejpam-5036	138	2	.	.	PUNCT
ejpam-5036	139	1	the	the	DET
ejpam-5036	139	2	laplacian	laplacian	ADJ
ejpam-5036	139	3	matrix	matrix	NOUN
ejpam-5036	139	4	of	of	ADP
ejpam-5036	139	5	γd2n	γd2n	PROPN
ejpam-5036	139	6	construction	construction	NOUN
ejpam-5036	139	7	depends	depend	VERB
ejpam-5036	139	8	on	on	ADP
ejpam-5036	139	9	the	the	DET
ejpam-5036	139	10	degree	degree	NOUN
ejpam-5036	139	11	and	and	CCONJ
ejpam-5036	139	12	adjacency	adjacency	NOUN
ejpam-5036	139	13	matrices	matrix	NOUN
ejpam-5036	139	14	of	of	ADP
ejpam-5036	139	15	γd2n	γd2n	PROPN
ejpam-5036	139	16	.	.	PUNCT
ejpam-5036	140	1	now	now	ADV
ejpam-5036	140	2	we	we	PRON
ejpam-5036	140	3	need	need	VERB
ejpam-5036	140	4	to	to	PART
ejpam-5036	140	5	construct	construct	VERB
ejpam-5036	140	6	a	a	DET
ejpam-5036	140	7	2n×	2n×	NUM
ejpam-5036	140	8	2n	2n	NUM
ejpam-5036	140	9	degree	degree	NOUN
ejpam-5036	140	10	matrix	matrix	NOUN
ejpam-5036	140	11	of	of	ADP
ejpam-5036	140	12	γd2n	γd2n	PROPN
ejpam-5036	140	13	as	as	SCONJ
ejpam-5036	140	14	follows	follow	VERB
ejpam-5036	140	15	:	:	PUNCT
ejpam-5036	140	16	d(γd2n	d(γd2n	X
ejpam-5036	140	17	)	)	PUNCT
ejpam-5036	140	18	=	=	PUNCT
ejpam-5036	141	1	e	e	X
ejpam-5036	141	2	a	a	DET
ejpam-5036	141	3	a2	a2	PROPN
ejpam-5036	141	4	.	.	PUNCT
ejpam-5036	141	5	.	.	PUNCT
ejpam-5036	141	6	.	.	PUNCT
ejpam-5036	142	1	an−1	an−1	PROPN
ejpam-5036	142	2	b	b	PROPN
ejpam-5036	142	3	ab	ab	PROPN
ejpam-5036	142	4	.	.	PUNCT
ejpam-5036	142	5	.	.	PUNCT
ejpam-5036	142	6	.	.	PUNCT
ejpam-5036	143	1	an−1b	an−1b	PRON
ejpam-5036	143	2			NOUN
ejpam-5036	143	3	e	e	NOUN
ejpam-5036	143	4	2n−	2n−	NUM
ejpam-5036	143	5	1	1	NUM
ejpam-5036	143	6	0	0	NUM
ejpam-5036	143	7	0	0	NUM
ejpam-5036	143	8	.	.	PUNCT
ejpam-5036	143	9	.	.	PUNCT
ejpam-5036	143	10	.	.	PUNCT
ejpam-5036	144	1	0	0	NUM
ejpam-5036	145	1	0	0	NUM
ejpam-5036	145	2	0	0	NUM
ejpam-5036	145	3	.	.	PUNCT
ejpam-5036	145	4	.	.	PUNCT
ejpam-5036	146	1	.	.	PUNCT
ejpam-5036	146	2	0	0	PUNCT
ejpam-5036	147	1	a	a	DET
ejpam-5036	147	2	0	0	NUM
ejpam-5036	147	3	n−	n−	NOUN
ejpam-5036	147	4	1	1	NUM
ejpam-5036	147	5	0	0	NUM
ejpam-5036	147	6	.	.	PUNCT
ejpam-5036	147	7	.	.	PUNCT
ejpam-5036	147	8	.	.	PUNCT
ejpam-5036	148	1	0	0	NUM
ejpam-5036	149	1	0	0	NUM
ejpam-5036	149	2	0	0	NUM
ejpam-5036	149	3	.	.	PUNCT
ejpam-5036	149	4	.	.	PUNCT
ejpam-5036	150	1	.	.	PUNCT
ejpam-5036	151	1	0	0	NUM
ejpam-5036	151	2	a2	a2	PROPN
ejpam-5036	151	3	0	0	NUM
ejpam-5036	151	4	0	0	NUM
ejpam-5036	151	5	n−	n−	NOUN
ejpam-5036	151	6	1	1	NUM
ejpam-5036	151	7	.	.	PUNCT
ejpam-5036	151	8	.	.	PUNCT
ejpam-5036	151	9	.	.	PUNCT
ejpam-5036	152	1	0	0	NUM
ejpam-5036	153	1	0	0	NUM
ejpam-5036	153	2	0	0	NUM
ejpam-5036	153	3	.	.	PUNCT
ejpam-5036	153	4	.	.	PUNCT
ejpam-5036	154	1	.	.	PUNCT
ejpam-5036	155	1	0	0	NUM
ejpam-5036	155	2	...	...	PUNCT
ejpam-5036	155	3	...	...	PUNCT
ejpam-5036	155	4	...	...	PUNCT
ejpam-5036	155	5	...	...	PUNCT
ejpam-5036	155	6	.	.	PUNCT
ejpam-5036	155	7	.	.	PUNCT
ejpam-5036	156	1	.	.	PUNCT
ejpam-5036	156	2	...	...	PUNCT
ejpam-5036	157	1	...	...	PUNCT
ejpam-5036	157	2	...	...	PUNCT
ejpam-5036	157	3	.	.	PUNCT
ejpam-5036	157	4	.	.	PUNCT
ejpam-5036	158	1	.	.	PUNCT
ejpam-5036	159	1	...	...	PUNCT
ejpam-5036	160	1	an−1	an−1	ADV
ejpam-5036	160	2	0	0	NUM
ejpam-5036	160	3	0	0	NUM
ejpam-5036	160	4	0	0	NUM
ejpam-5036	160	5	.	.	PUNCT
ejpam-5036	160	6	.	.	PUNCT
ejpam-5036	160	7	.	.	PUNCT
ejpam-5036	161	1	n−	n−	NOUN
ejpam-5036	161	2	1	1	NUM
ejpam-5036	161	3	0	0	NUM
ejpam-5036	161	4	0	0	NUM
ejpam-5036	161	5	.	.	PUNCT
ejpam-5036	161	6	.	.	PUNCT
ejpam-5036	162	1	.	.	PUNCT
ejpam-5036	163	1	0	0	NUM
ejpam-5036	164	1	b	b	X
ejpam-5036	164	2	0	0	NUM
ejpam-5036	164	3	0	0	NUM
ejpam-5036	164	4	0	0	NUM
ejpam-5036	164	5	.	.	PUNCT
ejpam-5036	164	6	.	.	PUNCT
ejpam-5036	164	7	.	.	PUNCT
ejpam-5036	165	1	0	0	NUM
ejpam-5036	166	1	1	1	NUM
ejpam-5036	166	2	0	0	NUM
ejpam-5036	166	3	.	.	PUNCT
ejpam-5036	166	4	.	.	PUNCT
ejpam-5036	167	1	.	.	PUNCT
ejpam-5036	167	2	0	0	PUNCT
ejpam-5036	168	1	ab	ab	NOUN
ejpam-5036	168	2	0	0	NUM
ejpam-5036	168	3	0	0	NUM
ejpam-5036	168	4	0	0	NUM
ejpam-5036	168	5	.	.	PUNCT
ejpam-5036	168	6	.	.	PUNCT
ejpam-5036	168	7	.	.	PUNCT
ejpam-5036	169	1	0	0	NUM
ejpam-5036	169	2	0	0	NUM
ejpam-5036	169	3	1	1	NUM
ejpam-5036	169	4	.	.	PUNCT
ejpam-5036	169	5	.	.	PUNCT
ejpam-5036	170	1	.	.	PUNCT
ejpam-5036	171	1	0	0	NUM
ejpam-5036	171	2	...	...	PUNCT
ejpam-5036	171	3	...	...	PUNCT
ejpam-5036	171	4	...	...	PUNCT
ejpam-5036	171	5	...	...	PUNCT
ejpam-5036	171	6	.	.	PUNCT
ejpam-5036	171	7	.	.	PUNCT
ejpam-5036	172	1	.	.	PUNCT
ejpam-5036	172	2	...	...	PUNCT
ejpam-5036	173	1	...	...	PUNCT
ejpam-5036	173	2	...	...	PUNCT
ejpam-5036	173	3	.	.	PUNCT
ejpam-5036	173	4	.	.	PUNCT
ejpam-5036	173	5	.	.	PUNCT
ejpam-5036	174	1	...	...	PUNCT
ejpam-5036	175	1	an−1b	an−1b	PUNCT
ejpam-5036	176	1	0	0	NUM
ejpam-5036	176	2	0	0	NUM
ejpam-5036	176	3	0	0	NUM
ejpam-5036	176	4	.	.	PUNCT
ejpam-5036	176	5	.	.	PUNCT
ejpam-5036	176	6	.	.	PUNCT
ejpam-5036	177	1	0	0	NUM
ejpam-5036	178	1	0	0	NUM
ejpam-5036	178	2	0	0	NUM
ejpam-5036	178	3	.	.	PUNCT
ejpam-5036	178	4	.	.	PUNCT
ejpam-5036	178	5	.	.	PUNCT
ejpam-5036	179	1	1	1	X
ejpam-5036	179	2	.	.	PUNCT
ejpam-5036	180	1	(	(	PUNCT
ejpam-5036	180	2	3	3	X
ejpam-5036	180	3	)	)	PUNCT
ejpam-5036	180	4	based	base	VERB
ejpam-5036	180	5	on	on	ADP
ejpam-5036	180	6	definition	definition	NOUN
ejpam-5036	180	7	3	3	NUM
ejpam-5036	180	8	,	,	PUNCT
ejpam-5036	180	9	the	the	DET
ejpam-5036	180	10	laplacian	laplacian	ADJ
ejpam-5036	180	11	matrix	matrix	NOUN
ejpam-5036	180	12	of	of	ADP
ejpam-5036	180	13	γd2n	γd2n	PROPN
ejpam-5036	180	14	is	be	AUX
ejpam-5036	180	15	l(γd2n	l(γd2n	X
ejpam-5036	180	16	)	)	PUNCT
ejpam-5036	181	1	=	=	SYM
ejpam-5036	181	2	d(γd2n)−a(γd2n	d(γd2n)−a(γd2n	PROPN
ejpam-5036	181	3	)	)	PUNCT
ejpam-5036	182	1	=	=	PUNCT
ejpam-5036	182	2	e	e	X
ejpam-5036	182	3	a	a	DET
ejpam-5036	182	4	a2	a2	PROPN
ejpam-5036	182	5	.	.	PUNCT
ejpam-5036	182	6	.	.	PUNCT
ejpam-5036	182	7	.	.	PUNCT
ejpam-5036	183	1	an−1	an−1	PROPN
ejpam-5036	183	2	b	b	PROPN
ejpam-5036	183	3	ab	ab	PROPN
ejpam-5036	183	4	.	.	PUNCT
ejpam-5036	183	5	.	.	PUNCT
ejpam-5036	183	6	.	.	PUNCT
ejpam-5036	184	1	an−1b	an−1b	PRON
ejpam-5036	185	1			NOUN
ejpam-5036	185	2	e	e	PROPN
ejpam-5036	185	3	2n−	2n−	NUM
ejpam-5036	185	4	1	1	NUM
ejpam-5036	185	5	−1	−1	NOUN
ejpam-5036	185	6	−1	−1	NOUN
ejpam-5036	185	7	.	.	PUNCT
ejpam-5036	185	8	.	.	PUNCT
ejpam-5036	185	9	.	.	PUNCT
ejpam-5036	186	1	−1	−1	NOUN
ejpam-5036	186	2	−1	−1	NOUN
ejpam-5036	186	3	−1	−1	NOUN
ejpam-5036	186	4	.	.	PUNCT
ejpam-5036	186	5	.	.	PUNCT
ejpam-5036	186	6	.	.	PUNCT
ejpam-5036	187	1	−1	−1	NOUN
ejpam-5036	187	2	a	a	DET
ejpam-5036	187	3	−1	−1	NOUN
ejpam-5036	187	4	n−	n−	NOUN
ejpam-5036	187	5	1	1	NUM
ejpam-5036	187	6	−1	−1	NOUN
ejpam-5036	187	7	.	.	PUNCT
ejpam-5036	187	8	.	.	PUNCT
ejpam-5036	187	9	.	.	PUNCT
ejpam-5036	188	1	−1	−1	NOUN
ejpam-5036	188	2	0	0	NUM
ejpam-5036	188	3	0	0	NUM
ejpam-5036	188	4	.	.	PUNCT
ejpam-5036	188	5	.	.	PUNCT
ejpam-5036	189	1	.	.	PUNCT
ejpam-5036	190	1	0	0	NUM
ejpam-5036	191	1	a2	a2	PROPN
ejpam-5036	191	2	−1	−1	NOUN
ejpam-5036	191	3	−1	−1	NOUN
ejpam-5036	191	4	n−	n−	NOUN
ejpam-5036	191	5	1	1	NUM
ejpam-5036	191	6	.	.	PUNCT
ejpam-5036	191	7	.	.	PUNCT
ejpam-5036	191	8	.	.	PUNCT
ejpam-5036	192	1	−1	−1	NOUN
ejpam-5036	192	2	0	0	NUM
ejpam-5036	192	3	0	0	NUM
ejpam-5036	192	4	.	.	PUNCT
ejpam-5036	192	5	.	.	PUNCT
ejpam-5036	193	1	.	.	PUNCT
ejpam-5036	194	1	0	0	NUM
ejpam-5036	194	2	...	...	PUNCT
ejpam-5036	194	3	...	...	PUNCT
ejpam-5036	194	4	...	...	PUNCT
ejpam-5036	194	5	...	...	PUNCT
ejpam-5036	194	6	.	.	PUNCT
ejpam-5036	194	7	.	.	PUNCT
ejpam-5036	195	1	.	.	PUNCT
ejpam-5036	195	2	...	...	PUNCT
ejpam-5036	196	1	...	...	PUNCT
ejpam-5036	196	2	...	...	PUNCT
ejpam-5036	196	3	.	.	PUNCT
ejpam-5036	196	4	.	.	PUNCT
ejpam-5036	197	1	.	.	PUNCT
ejpam-5036	198	1	...	...	PUNCT
ejpam-5036	199	1	an−1	an−1	ADV
ejpam-5036	199	2	−1	−1	NOUN
ejpam-5036	199	3	−1	−1	NOUN
ejpam-5036	199	4	−1	−1	NOUN
ejpam-5036	199	5	.	.	PUNCT
ejpam-5036	199	6	.	.	PUNCT
ejpam-5036	199	7	.	.	PUNCT
ejpam-5036	200	1	n−	n−	NOUN
ejpam-5036	200	2	1	1	NUM
ejpam-5036	200	3	0	0	NUM
ejpam-5036	200	4	0	0	NUM
ejpam-5036	200	5	.	.	PUNCT
ejpam-5036	200	6	.	.	PUNCT
ejpam-5036	201	1	.	.	PUNCT
ejpam-5036	202	1	0	0	NUM
ejpam-5036	203	1	b	b	X
ejpam-5036	203	2	−1	−1	NOUN
ejpam-5036	203	3	0	0	NUM
ejpam-5036	203	4	0	0	NUM
ejpam-5036	203	5	.	.	PUNCT
ejpam-5036	203	6	.	.	PUNCT
ejpam-5036	203	7	.	.	PUNCT
ejpam-5036	204	1	0	0	NUM
ejpam-5036	205	1	1	1	NUM
ejpam-5036	205	2	0	0	NUM
ejpam-5036	205	3	.	.	PUNCT
ejpam-5036	205	4	.	.	PUNCT
ejpam-5036	206	1	.	.	PUNCT
ejpam-5036	206	2	0	0	NUM
ejpam-5036	207	1	ab	ab	PROPN
ejpam-5036	207	2	−1	−1	NOUN
ejpam-5036	207	3	0	0	NUM
ejpam-5036	207	4	0	0	NUM
ejpam-5036	207	5	.	.	PUNCT
ejpam-5036	207	6	.	.	PUNCT
ejpam-5036	207	7	.	.	PUNCT
ejpam-5036	208	1	0	0	NUM
ejpam-5036	208	2	0	0	NUM
ejpam-5036	208	3	1	1	NUM
ejpam-5036	208	4	.	.	PUNCT
ejpam-5036	208	5	.	.	PUNCT
ejpam-5036	209	1	.	.	PUNCT
ejpam-5036	210	1	0	0	NUM
ejpam-5036	210	2	...	...	PUNCT
ejpam-5036	210	3	...	...	PUNCT
ejpam-5036	210	4	...	...	PUNCT
ejpam-5036	210	5	...	...	PUNCT
ejpam-5036	210	6	.	.	PUNCT
ejpam-5036	210	7	.	.	PUNCT
ejpam-5036	211	1	.	.	PUNCT
ejpam-5036	211	2	...	...	PUNCT
ejpam-5036	212	1	...	...	PUNCT
ejpam-5036	212	2	...	...	PUNCT
ejpam-5036	212	3	.	.	PUNCT
ejpam-5036	212	4	.	.	PUNCT
ejpam-5036	212	5	.	.	PUNCT
ejpam-5036	213	1	...	...	PUNCT
ejpam-5036	214	1	an−1b	an−1b	PUNCT
ejpam-5036	214	2	−1	−1	NOUN
ejpam-5036	214	3	0	0	NUM
ejpam-5036	214	4	0	0	NUM
ejpam-5036	214	5	.	.	PUNCT
ejpam-5036	214	6	.	.	PUNCT
ejpam-5036	214	7	.	.	PUNCT
ejpam-5036	215	1	0	0	NUM
ejpam-5036	216	1	0	0	NUM
ejpam-5036	216	2	0	0	NUM
ejpam-5036	216	3	.	.	PUNCT
ejpam-5036	216	4	.	.	PUNCT
ejpam-5036	216	5	.	.	PUNCT
ejpam-5036	217	1	1	1	X
ejpam-5036	217	2	.	.	PUNCT
ejpam-5036	217	3	m.	m.	PROPN
ejpam-5036	217	4	u.	u.	PROPN
ejpam-5036	217	5	romdhini	romdhini	PROPN
ejpam-5036	217	6	et	et	PROPN
ejpam-5036	217	7	al	al	PROPN
ejpam-5036	217	8	.	.	PUNCT
ejpam-5036	217	9	/	/	SYM
ejpam-5036	217	10	eur	eur	PROPN
ejpam-5036	217	11	.	.	PUNCT
ejpam-5036	218	1	j.	j.	PROPN
ejpam-5036	218	2	pure	pure	PROPN
ejpam-5036	218	3	appl	appl	PROPN
ejpam-5036	218	4	.	.	PROPN
ejpam-5036	218	5	math	math	PROPN
ejpam-5036	218	6	,	,	PUNCT
ejpam-5036	218	7	17	17	NUM
ejpam-5036	218	8	(	(	PUNCT
ejpam-5036	218	9	2	2	NUM
ejpam-5036	218	10	)	)	PUNCT
ejpam-5036	218	11	(	(	PUNCT
ejpam-5036	218	12	2024	2024	NUM
ejpam-5036	218	13	)	)	PUNCT
ejpam-5036	218	14	,	,	PUNCT
ejpam-5036	218	15	591	591	NUM
ejpam-5036	218	16	-	-	SYM
ejpam-5036	218	17	603	603	NUM
ejpam-5036	218	18	596	596	NUM
ejpam-5036	218	19	moreover	moreover	ADV
ejpam-5036	218	20	,	,	PUNCT
ejpam-5036	218	21	l(γd2n	l(γd2n	PROPN
ejpam-5036	218	22	)	)	PUNCT
ejpam-5036	218	23	can	can	AUX
ejpam-5036	218	24	be	be	AUX
ejpam-5036	218	25	partitioned	partition	VERB
ejpam-5036	218	26	into	into	ADP
ejpam-5036	218	27	six	six	NUM
ejpam-5036	218	28	block	block	NOUN
ejpam-5036	218	29	matrices	matrix	NOUN
ejpam-5036	218	30	as	as	ADP
ejpam-5036	218	31	given	give	VERB
ejpam-5036	218	32	below	below	ADV
ejpam-5036	218	33	:	:	PUNCT
ejpam-5036	218	34	l(γd2n	l(γd2n	X
ejpam-5036	218	35	)	)	PUNCT
ejpam-5036	218	36	=	=	PUNCT
ejpam-5036	219	1			PROPN
ejpam-5036	219	2	2n−	2n−	PROPN
ejpam-5036	219	3	1	1	NUM
ejpam-5036	219	4	−j1×(n−1	−j1×(n−1	NUM
ejpam-5036	219	5	)	)	PUNCT
ejpam-5036	219	6	−j1×n	−j1×n	PUNCT
ejpam-5036	220	1	−j(n−1)×1	−j(n−1)×1	PROPN
ejpam-5036	220	2	nin−1	nin−1	PROPN
ejpam-5036	220	3	−	−	PROPN
ejpam-5036	220	4	jn−1	jn−1	PROPN
ejpam-5036	220	5	0(n−1)×n	0(n−1)×n	NUM
ejpam-5036	220	6	−jn×1	−jn×1	PUNCT
ejpam-5036	220	7	0n×(n−1	0n×(n−1	PROPN
ejpam-5036	220	8	)	)	PUNCT
ejpam-5036	220	9	in	in	ADP
ejpam-5036	220	10			PROPN
ejpam-5036	220	11	.	.	PUNCT
ejpam-5036	221	1	the	the	DET
ejpam-5036	221	2	characteristic	characteristic	ADJ
ejpam-5036	221	3	polynomial	polynomial	NOUN
ejpam-5036	221	4	of	of	ADP
ejpam-5036	221	5	l(γd2n	l(γd2n	PROPN
ejpam-5036	221	6	)	)	PUNCT
ejpam-5036	221	7	can	can	AUX
ejpam-5036	221	8	be	be	AUX
ejpam-5036	221	9	obtained	obtain	VERB
ejpam-5036	221	10	from	from	ADP
ejpam-5036	221	11	the	the	DET
ejpam-5036	221	12	following	follow	VERB
ejpam-5036	221	13	determinant	determinant	ADJ
ejpam-5036	221	14	:	:	PUNCT
ejpam-5036	221	15	pl(γd2n	pl(γd2n	ADJ
ejpam-5036	221	16	)	)	PUNCT
ejpam-5036	221	17	(	(	PUNCT
ejpam-5036	221	18	λ	λ	NOUN
ejpam-5036	221	19	)	)	PUNCT
ejpam-5036	221	20	=	=	SYM
ejpam-5036	222	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5036	222	2	λ−	λ−	PROPN
ejpam-5036	222	3	(	(	PUNCT
ejpam-5036	222	4	2n−	2n−	PROPN
ejpam-5036	222	5	1	1	NUM
ejpam-5036	222	6	)	)	PUNCT
ejpam-5036	222	7	j1×(n−1	j1×(n−1	PROPN
ejpam-5036	222	8	)	)	PUNCT
ejpam-5036	223	1	j1×n	j1×n	ADJ
ejpam-5036	223	2	j(n−1)×1	j(n−1)×1	NOUN
ejpam-5036	223	3	(	(	PUNCT
ejpam-5036	223	4	λ−	λ−	PROPN
ejpam-5036	223	5	(	(	PUNCT
ejpam-5036	223	6	n−	n−	NOUN
ejpam-5036	223	7	2))in−1	2))in−1	NUM
ejpam-5036	223	8	−	−	PROPN
ejpam-5036	224	1	jn−1	jn−1	PROPN
ejpam-5036	224	2	0(n−1)×n	0(n−1)×n	PROPN
ejpam-5036	224	3	jn×1	jn×1	VERB
ejpam-5036	224	4	0n×(n−1	0n×(n−1	PROPN
ejpam-5036	224	5	)	)	PUNCT
ejpam-5036	224	6	(	(	PUNCT
ejpam-5036	224	7	λ−	λ−	PROPN
ejpam-5036	224	8	1)in	1)in	PROPN
ejpam-5036	224	9	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5036	224	10	.	.	PUNCT
ejpam-5036	225	1	(	(	PUNCT
ejpam-5036	225	2	4	4	X
ejpam-5036	225	3	)	)	PUNCT
ejpam-5036	225	4	we	we	PRON
ejpam-5036	225	5	apply	apply	VERB
ejpam-5036	225	6	the	the	DET
ejpam-5036	225	7	following	follow	VERB
ejpam-5036	225	8	steps	step	NOUN
ejpam-5036	225	9	to	to	ADP
ejpam-5036	225	10	equation	equation	NOUN
ejpam-5036	225	11	4	4	NUM
ejpam-5036	225	12	:	:	PUNCT
ejpam-5036	225	13	(	(	PUNCT
ejpam-5036	225	14	i	i	NOUN
ejpam-5036	225	15	)	)	PUNCT
ejpam-5036	225	16	rn+1+i	rn+1+i	NOUN
ejpam-5036	225	17	−→	−→	ADJ
ejpam-5036	225	18	rn+1+i	rn+1+i	NOUN
ejpam-5036	225	19	−rn+1	−rn+1	VERB
ejpam-5036	225	20	,	,	PUNCT
ejpam-5036	225	21	for	for	ADP
ejpam-5036	225	22	i	i	PROPN
ejpam-5036	225	23	=	=	SYM
ejpam-5036	225	24	1	1	NUM
ejpam-5036	225	25	,	,	PUNCT
ejpam-5036	225	26	2	2	NUM
ejpam-5036	225	27	,	,	PUNCT
ejpam-5036	225	28	.	.	PUNCT
ejpam-5036	225	29	.	.	PUNCT
ejpam-5036	226	1	.	.	PUNCT
ejpam-5036	227	1	,	,	PUNCT
ejpam-5036	227	2	n−	n−	NOUN
ejpam-5036	227	3	1	1	NUM
ejpam-5036	227	4	.	.	PUNCT
ejpam-5036	227	5	(	(	PUNCT
ejpam-5036	227	6	ii	ii	NOUN
ejpam-5036	227	7	)	)	PUNCT
ejpam-5036	227	8	cn+1	cn+1	VERB
ejpam-5036	227	9	−→	−→	NOUN
ejpam-5036	227	10	cn+1	cn+1	NOUN
ejpam-5036	227	11	+	+	CCONJ
ejpam-5036	227	12	cn+2	cn+2	PRON
ejpam-5036	228	1	+	+	CCONJ
ejpam-5036	228	2	.	.	PUNCT
ejpam-5036	228	3	.	.	PUNCT
ejpam-5036	229	1	.+	.+	NOUN
ejpam-5036	229	2	c2n	c2n	NOUN
ejpam-5036	229	3	.	.	PUNCT
ejpam-5036	230	1	(	(	PUNCT
ejpam-5036	230	2	iii	iii	X
ejpam-5036	230	3	)	)	PUNCT
ejpam-5036	230	4	c1	c1	PROPN
ejpam-5036	230	5	−→	−→	PROPN
ejpam-5036	230	6	c1	c1	PROPN
ejpam-5036	230	7	−	−	PROPN
ejpam-5036	230	8	1	1	NUM
ejpam-5036	230	9	λ−1cn+1	λ−1cn+1	NOUN
ejpam-5036	230	10	.	.	PUNCT
ejpam-5036	231	1	(	(	PUNCT
ejpam-5036	231	2	iv	iv	X
ejpam-5036	231	3	)	)	PUNCT
ejpam-5036	231	4	r2+i	r2+i	PROPN
ejpam-5036	231	5	−→	−→	NOUN
ejpam-5036	231	6	r2+i	r2+i	PROPN
ejpam-5036	231	7	−r2	−r2	PROPN
ejpam-5036	231	8	,	,	PUNCT
ejpam-5036	231	9	for	for	ADP
ejpam-5036	231	10	i	i	PROPN
ejpam-5036	231	11	=	=	SYM
ejpam-5036	231	12	1	1	NUM
ejpam-5036	231	13	,	,	PUNCT
ejpam-5036	231	14	2	2	NUM
ejpam-5036	231	15	,	,	PUNCT
ejpam-5036	231	16	.	.	PUNCT
ejpam-5036	231	17	.	.	PUNCT
ejpam-5036	232	1	.	.	PUNCT
ejpam-5036	233	1	,	,	PUNCT
ejpam-5036	233	2	n−	n−	NOUN
ejpam-5036	233	3	2	2	NUM
ejpam-5036	233	4	.	.	PUNCT
ejpam-5036	234	1	(	(	PUNCT
ejpam-5036	234	2	v	v	NOUN
ejpam-5036	234	3	)	)	PUNCT
ejpam-5036	234	4	c2	c2	PROPN
ejpam-5036	234	5	−→	−→	PROPN
ejpam-5036	234	6	c2	c2	PROPN
ejpam-5036	234	7	+	+	CCONJ
ejpam-5036	234	8	c2	c2	PROPN
ejpam-5036	234	9	+	+	PROPN
ejpam-5036	234	10	1	1	NUM
ejpam-5036	234	11	+	+	NUM
ejpam-5036	234	12	.	.	PUNCT
ejpam-5036	234	13	.	.	PUNCT
ejpam-5036	235	1	.+	.+	NOUN
ejpam-5036	235	2	cn	cn	PROPN
ejpam-5036	235	3	,	,	PUNCT
ejpam-5036	235	4	then	then	ADV
ejpam-5036	235	5	we	we	PRON
ejpam-5036	235	6	get	get	VERB
ejpam-5036	235	7	pl(γd2n	pl(γd2n	ADJ
ejpam-5036	235	8	)	)	PUNCT
ejpam-5036	235	9	(	(	PUNCT
ejpam-5036	235	10	λ	λ	NOUN
ejpam-5036	235	11	)	)	PUNCT
ejpam-5036	235	12	=	=	PUNCT
ejpam-5036	235	13	∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-5036	235	14	λ2−2nλ+n−1	λ2−2nλ+n−1	X
ejpam-5036	236	1	λ−1	λ−1	PROPN
ejpam-5036	236	2	n−	n−	PROPN
ejpam-5036	236	3	1	1	NUM
ejpam-5036	236	4	j1×(n−2	j1×(n−2	NOUN
ejpam-5036	236	5	)	)	PUNCT
ejpam-5036	236	6	n	n	X
ejpam-5036	236	7	j1×(n−1	j1×(n−1	ADJ
ejpam-5036	236	8	)	)	PUNCT
ejpam-5036	236	9	1	1	NUM
ejpam-5036	236	10	λ−	λ−	PROPN
ejpam-5036	236	11	1	1	NUM
ejpam-5036	236	12	j1×(n−2	j1×(n−2	NOUN
ejpam-5036	236	13	)	)	PUNCT
ejpam-5036	236	14	0	0	NUM
ejpam-5036	237	1	01×(n−1	01×(n−1	NUM
ejpam-5036	237	2	)	)	PUNCT
ejpam-5036	237	3	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	237	4	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	238	1	(	(	PUNCT
ejpam-5036	238	2	λ−	λ−	PROPN
ejpam-5036	238	3	n)in−2	n)in−2	PROPN
ejpam-5036	238	4	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	238	5	0(n−2)×(n−1	0(n−2)×(n−1	NUM
ejpam-5036	238	6	)	)	PUNCT
ejpam-5036	238	7	0	0	NUM
ejpam-5036	238	8	0	0	NUM
ejpam-5036	238	9	01×(n−2	01×(n−2	X
ejpam-5036	238	10	)	)	PUNCT
ejpam-5036	238	11	λ−	λ−	PROPN
ejpam-5036	238	12	1	1	NUM
ejpam-5036	238	13	01×(n−1	01×(n−1	NUM
ejpam-5036	238	14	)	)	PUNCT
ejpam-5036	238	15	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	238	16	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	239	1	0n−1	0n−1	NUM
ejpam-5036	239	2	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	240	1	(	(	PUNCT
ejpam-5036	240	2	λ−	λ−	PROPN
ejpam-5036	240	3	1)in−1	1)in−1	PROPN
ejpam-5036	240	4	∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5036	240	5	.	.	PUNCT
ejpam-5036	241	1	following	follow	VERB
ejpam-5036	241	2	theorem	theorem	NOUN
ejpam-5036	241	3	2	2	NUM
ejpam-5036	241	4	,	,	PUNCT
ejpam-5036	241	5	we	we	PRON
ejpam-5036	241	6	then	then	ADV
ejpam-5036	241	7	can	can	AUX
ejpam-5036	241	8	obtain	obtain	VERB
ejpam-5036	241	9	pl(γd2n	pl(γd2n	NOUN
ejpam-5036	241	10	)	)	PUNCT
ejpam-5036	241	11	(	(	PUNCT
ejpam-5036	241	12	λ	λ	X
ejpam-5036	241	13	)	)	PUNCT
ejpam-5036	241	14	=	=	SYM
ejpam-5036	241	15	λ(λ−	λ(λ−	PROPN
ejpam-5036	241	16	2n)(λ−	2n)(λ−	NUM
ejpam-5036	241	17	n)n−2(λ−	n)n−2(λ−	PROPN
ejpam-5036	241	18	1)n	1)n	NUM
ejpam-5036	241	19	.	.	PUNCT
ejpam-5036	242	1	the	the	DET
ejpam-5036	242	2	next	next	ADJ
ejpam-5036	242	3	theorem	theorem	NOUN
ejpam-5036	242	4	presents	present	VERB
ejpam-5036	242	5	the	the	DET
ejpam-5036	242	6	characteristic	characteristic	ADJ
ejpam-5036	242	7	polynomial	polynomial	NOUN
ejpam-5036	242	8	of	of	ADP
ejpam-5036	242	9	γd2n	γd2n	PROPN
ejpam-5036	242	10	associated	associate	VERB
ejpam-5036	242	11	with	with	ADP
ejpam-5036	242	12	the	the	DET
ejpam-5036	242	13	signless	signless	ADJ
ejpam-5036	242	14	laplacian	laplacian	ADJ
ejpam-5036	242	15	matrix	matrix	NOUN
ejpam-5036	242	16	.	.	PUNCT
ejpam-5036	243	1	theorem	theorem	NOUN
ejpam-5036	243	2	5	5	NUM
ejpam-5036	243	3	.	.	PUNCT
ejpam-5036	244	1	let	let	VERB
ejpam-5036	244	2	γd2n	γd2n	PROPN
ejpam-5036	244	3	be	be	AUX
ejpam-5036	244	4	the	the	DET
ejpam-5036	244	5	power	power	NOUN
ejpam-5036	244	6	graph	graph	NOUN
ejpam-5036	244	7	for	for	ADP
ejpam-5036	244	8	d2n	d2n	NOUN
ejpam-5036	244	9	,	,	PUNCT
ejpam-5036	244	10	then	then	ADV
ejpam-5036	244	11	the	the	DET
ejpam-5036	244	12	characteristic	characteristic	ADJ
ejpam-5036	244	13	polynomial	polynomial	NOUN
ejpam-5036	244	14	of	of	ADP
ejpam-5036	244	15	sl(γd2n	sl(γd2n	NOUN
ejpam-5036	244	16	)	)	PUNCT
ejpam-5036	244	17	is	be	AUX
ejpam-5036	244	18	psl(γd2n	psl(γd2n	NOUN
ejpam-5036	244	19	)	)	PUNCT
ejpam-5036	244	20	(	(	PUNCT
ejpam-5036	244	21	λ	λ	NOUN
ejpam-5036	244	22	)	)	PUNCT
ejpam-5036	244	23	=	=	SYM
ejpam-5036	244	24	(	(	PUNCT
ejpam-5036	244	25	λ−1)n−1(λ−n+2)n−2	λ−1)n−1(λ−n+2)n−2	PROPN
ejpam-5036	244	26	(	(	PUNCT
ejpam-5036	244	27	λ3	λ3	PROPN
ejpam-5036	244	28	+	+	PROPN
ejpam-5036	244	29	(	(	PUNCT
ejpam-5036	244	30	3−	3−	NUM
ejpam-5036	244	31	4n)λ2	4n)λ2	NUM
ejpam-5036	245	1	+	+	CCONJ
ejpam-5036	245	2	2n(2n−	2n(2n−	NUM
ejpam-5036	245	3	3)λ−	3)λ−	NUM
ejpam-5036	245	4	2(n−	2(n−	NUM
ejpam-5036	245	5	1)(n−	1)(n−	NUM
ejpam-5036	245	6	2	2	NUM
ejpam-5036	245	7	)	)	PUNCT
ejpam-5036	245	8	)	)	PUNCT
ejpam-5036	245	9	.	.	PUNCT
ejpam-5036	246	1	proof	proof	NOUN
ejpam-5036	246	2	.	.	PUNCT
ejpam-5036	247	1	by	by	ADP
ejpam-5036	247	2	equations	equation	NOUN
ejpam-5036	247	3	1	1	NUM
ejpam-5036	247	4	and	and	CCONJ
ejpam-5036	247	5	4	4	NUM
ejpam-5036	247	6	,	,	PUNCT
ejpam-5036	247	7	and	and	CCONJ
ejpam-5036	247	8	definition	definition	NOUN
ejpam-5036	247	9	4	4	NUM
ejpam-5036	247	10	,	,	PUNCT
ejpam-5036	247	11	the	the	DET
ejpam-5036	247	12	signless	signless	ADJ
ejpam-5036	247	13	laplacian	laplacian	ADJ
ejpam-5036	247	14	matrix	matrix	NOUN
ejpam-5036	247	15	of	of	ADP
ejpam-5036	247	16	γd2n	γd2n	PROPN
ejpam-5036	247	17	is	be	AUX
ejpam-5036	247	18	sl(γd2n	sl(γd2n	NOUN
ejpam-5036	247	19	)	)	PUNCT
ejpam-5036	248	1	=	=	SYM
ejpam-5036	248	2	d(γd2n	d(γd2n	X
ejpam-5036	248	3	)	)	PUNCT
ejpam-5036	248	4	+	+	NOUN
ejpam-5036	248	5	a(γd2n	a(γd2n	X
ejpam-5036	248	6	)	)	PUNCT
ejpam-5036	248	7	m.	m.	NOUN
ejpam-5036	248	8	u.	u.	PROPN
ejpam-5036	248	9	romdhini	romdhini	PROPN
ejpam-5036	248	10	et	et	PROPN
ejpam-5036	248	11	al	al	PROPN
ejpam-5036	248	12	.	.	PUNCT
ejpam-5036	248	13	/	/	SYM
ejpam-5036	248	14	eur	eur	PROPN
ejpam-5036	248	15	.	.	PUNCT
ejpam-5036	249	1	j.	j.	PROPN
ejpam-5036	249	2	pure	pure	PROPN
ejpam-5036	249	3	appl	appl	PROPN
ejpam-5036	249	4	.	.	PROPN
ejpam-5036	249	5	math	math	PROPN
ejpam-5036	249	6	,	,	PUNCT
ejpam-5036	249	7	17	17	NUM
ejpam-5036	249	8	(	(	PUNCT
ejpam-5036	249	9	2	2	NUM
ejpam-5036	249	10	)	)	PUNCT
ejpam-5036	249	11	(	(	PUNCT
ejpam-5036	249	12	2024	2024	NUM
ejpam-5036	249	13	)	)	PUNCT
ejpam-5036	249	14	,	,	PUNCT
ejpam-5036	249	15	591	591	NUM
ejpam-5036	249	16	-	-	SYM
ejpam-5036	249	17	603	603	NUM
ejpam-5036	249	18	597	597	NUM
ejpam-5036	249	19	=	=	SYM
ejpam-5036	249	20	e	e	X
ejpam-5036	249	21	a	a	DET
ejpam-5036	249	22	a2	a2	PROPN
ejpam-5036	249	23	.	.	PUNCT
ejpam-5036	249	24	.	.	PUNCT
ejpam-5036	249	25	.	.	PUNCT
ejpam-5036	250	1	an−1	an−1	PROPN
ejpam-5036	250	2	b	b	PROPN
ejpam-5036	250	3	ab	ab	PROPN
ejpam-5036	250	4	.	.	PUNCT
ejpam-5036	250	5	.	.	PUNCT
ejpam-5036	250	6	.	.	PUNCT
ejpam-5036	251	1	an−1b	an−1b	PRON
ejpam-5036	252	1			NOUN
ejpam-5036	252	2	e	e	PROPN
ejpam-5036	252	3	2n−	2n−	NUM
ejpam-5036	252	4	1	1	NUM
ejpam-5036	252	5	1	1	NUM
ejpam-5036	252	6	1	1	NUM
ejpam-5036	252	7	.	.	PUNCT
ejpam-5036	252	8	.	.	PUNCT
ejpam-5036	253	1	.	.	PUNCT
ejpam-5036	254	1	1	1	NUM
ejpam-5036	254	2	1	1	NUM
ejpam-5036	254	3	1	1	NUM
ejpam-5036	254	4	.	.	PUNCT
ejpam-5036	254	5	.	.	PUNCT
ejpam-5036	254	6	.	.	PUNCT
ejpam-5036	255	1	1	1	NUM
ejpam-5036	255	2	a	a	DET
ejpam-5036	255	3	1	1	NUM
ejpam-5036	255	4	n−	n−	NOUN
ejpam-5036	255	5	1	1	NUM
ejpam-5036	255	6	1	1	NUM
ejpam-5036	255	7	.	.	PUNCT
ejpam-5036	255	8	.	.	PUNCT
ejpam-5036	255	9	.	.	PUNCT
ejpam-5036	256	1	1	1	NUM
ejpam-5036	256	2	0	0	NUM
ejpam-5036	256	3	0	0	NUM
ejpam-5036	256	4	.	.	PUNCT
ejpam-5036	256	5	.	.	PUNCT
ejpam-5036	256	6	.	.	PUNCT
ejpam-5036	257	1	0	0	NUM
ejpam-5036	257	2	a2	a2	PROPN
ejpam-5036	257	3	1	1	NUM
ejpam-5036	257	4	1	1	NUM
ejpam-5036	257	5	n−	n−	NOUN
ejpam-5036	257	6	1	1	NUM
ejpam-5036	257	7	.	.	PUNCT
ejpam-5036	257	8	.	.	PUNCT
ejpam-5036	257	9	.	.	PUNCT
ejpam-5036	258	1	1	1	NUM
ejpam-5036	258	2	0	0	NUM
ejpam-5036	258	3	0	0	NUM
ejpam-5036	258	4	.	.	PUNCT
ejpam-5036	258	5	.	.	PUNCT
ejpam-5036	258	6	.	.	PUNCT
ejpam-5036	259	1	0	0	NUM
ejpam-5036	259	2	...	...	PUNCT
ejpam-5036	259	3	...	...	PUNCT
ejpam-5036	259	4	...	...	PUNCT
ejpam-5036	259	5	...	...	PUNCT
ejpam-5036	259	6	.	.	PUNCT
ejpam-5036	259	7	.	.	PUNCT
ejpam-5036	260	1	.	.	PUNCT
ejpam-5036	260	2	...	...	PUNCT
ejpam-5036	261	1	...	...	PUNCT
ejpam-5036	261	2	...	...	PUNCT
ejpam-5036	261	3	.	.	PUNCT
ejpam-5036	261	4	.	.	PUNCT
ejpam-5036	262	1	.	.	PUNCT
ejpam-5036	263	1	...	...	PUNCT
ejpam-5036	264	1	an−1	an−1	ADJ
ejpam-5036	264	2	1	1	NUM
ejpam-5036	264	3	1	1	NUM
ejpam-5036	264	4	1	1	NUM
ejpam-5036	264	5	.	.	PUNCT
ejpam-5036	264	6	.	.	PUNCT
ejpam-5036	264	7	.	.	PUNCT
ejpam-5036	265	1	n−	n−	NOUN
ejpam-5036	265	2	1	1	NUM
ejpam-5036	265	3	0	0	NUM
ejpam-5036	265	4	0	0	NUM
ejpam-5036	265	5	.	.	PUNCT
ejpam-5036	265	6	.	.	PUNCT
ejpam-5036	266	1	.	.	PUNCT
ejpam-5036	267	1	0	0	NUM
ejpam-5036	268	1	b	b	X
ejpam-5036	268	2	1	1	NUM
ejpam-5036	268	3	0	0	NUM
ejpam-5036	268	4	0	0	NUM
ejpam-5036	268	5	.	.	PUNCT
ejpam-5036	268	6	.	.	PUNCT
ejpam-5036	268	7	.	.	PUNCT
ejpam-5036	269	1	0	0	NUM
ejpam-5036	270	1	1	1	NUM
ejpam-5036	270	2	0	0	NUM
ejpam-5036	270	3	.	.	PUNCT
ejpam-5036	270	4	.	.	PUNCT
ejpam-5036	271	1	.	.	PUNCT
ejpam-5036	271	2	0	0	PUNCT
ejpam-5036	272	1	ab	ab	PROPN
ejpam-5036	272	2	1	1	NUM
ejpam-5036	272	3	0	0	NUM
ejpam-5036	272	4	0	0	NUM
ejpam-5036	272	5	.	.	PUNCT
ejpam-5036	272	6	.	.	PUNCT
ejpam-5036	272	7	.	.	PUNCT
ejpam-5036	273	1	0	0	NUM
ejpam-5036	273	2	0	0	NUM
ejpam-5036	273	3	1	1	NUM
ejpam-5036	273	4	.	.	PUNCT
ejpam-5036	273	5	.	.	PUNCT
ejpam-5036	274	1	.	.	PUNCT
ejpam-5036	275	1	0	0	NUM
ejpam-5036	275	2	...	...	PUNCT
ejpam-5036	275	3	...	...	PUNCT
ejpam-5036	275	4	...	...	PUNCT
ejpam-5036	275	5	...	...	PUNCT
ejpam-5036	275	6	.	.	PUNCT
ejpam-5036	275	7	.	.	PUNCT
ejpam-5036	276	1	.	.	PUNCT
ejpam-5036	276	2	...	...	PUNCT
ejpam-5036	277	1	...	...	PUNCT
ejpam-5036	277	2	...	...	PUNCT
ejpam-5036	277	3	.	.	PUNCT
ejpam-5036	277	4	.	.	PUNCT
ejpam-5036	277	5	.	.	PUNCT
ejpam-5036	278	1	...	...	PUNCT
ejpam-5036	279	1	an−1b	an−1b	PUNCT
ejpam-5036	280	1	1	1	NUM
ejpam-5036	280	2	0	0	NUM
ejpam-5036	280	3	0	0	NUM
ejpam-5036	280	4	.	.	PUNCT
ejpam-5036	280	5	.	.	PUNCT
ejpam-5036	280	6	.	.	PUNCT
ejpam-5036	281	1	0	0	NUM
ejpam-5036	282	1	0	0	NUM
ejpam-5036	282	2	0	0	NUM
ejpam-5036	282	3	.	.	PUNCT
ejpam-5036	282	4	.	.	PUNCT
ejpam-5036	282	5	.	.	PUNCT
ejpam-5036	283	1	1	1	X
ejpam-5036	283	2	.	.	PUNCT
ejpam-5036	284	1	moreover	moreover	ADV
ejpam-5036	284	2	,	,	PUNCT
ejpam-5036	284	3	sl(γd2n	sl(γd2n	NOUN
ejpam-5036	284	4	)	)	PUNCT
ejpam-5036	284	5	can	can	AUX
ejpam-5036	284	6	be	be	AUX
ejpam-5036	284	7	partitioned	partition	VERB
ejpam-5036	284	8	into	into	ADP
ejpam-5036	284	9	nine	nine	NUM
ejpam-5036	284	10	block	block	NOUN
ejpam-5036	284	11	matrices	matrix	NOUN
ejpam-5036	284	12	as	as	SCONJ
ejpam-5036	284	13	given	give	VERB
ejpam-5036	284	14	below	below	ADV
ejpam-5036	284	15	:	:	PUNCT
ejpam-5036	284	16	sl(γd2n	sl(γd2n	NOUN
ejpam-5036	284	17	)	)	PUNCT
ejpam-5036	284	18	=	=	PUNCT
ejpam-5036	285	1			PROPN
ejpam-5036	285	2	2n−	2n−	PROPN
ejpam-5036	285	3	1	1	NUM
ejpam-5036	285	4	j1×(n−1	j1×(n−1	NOUN
ejpam-5036	285	5	)	)	PUNCT
ejpam-5036	285	6	j1×n	j1×n	ADJ
ejpam-5036	285	7	j(n−1)×1	j(n−1)×1	INTJ
ejpam-5036	285	8	(	(	PUNCT
ejpam-5036	285	9	n−	n−	NOUN
ejpam-5036	285	10	2)in−1	2)in−1	PROPN
ejpam-5036	285	11	+	+	CCONJ
ejpam-5036	285	12	jn−1	jn−1	PROPN
ejpam-5036	285	13	0(n−1)×n	0(n−1)×n	PROPN
ejpam-5036	285	14	jn×1	jn×1	VERB
ejpam-5036	285	15	0n×(n−1	0n×(n−1	NUM
ejpam-5036	285	16	)	)	PUNCT
ejpam-5036	285	17	in	in	ADP
ejpam-5036	285	18			PROPN
ejpam-5036	285	19	.	.	PUNCT
ejpam-5036	286	1	the	the	DET
ejpam-5036	286	2	characteristic	characteristic	ADJ
ejpam-5036	286	3	polynomial	polynomial	NOUN
ejpam-5036	286	4	of	of	ADP
ejpam-5036	286	5	sl(γd2n	sl(γd2n	NOUN
ejpam-5036	286	6	)	)	PUNCT
ejpam-5036	286	7	can	can	AUX
ejpam-5036	286	8	be	be	AUX
ejpam-5036	286	9	obtained	obtain	VERB
ejpam-5036	286	10	from	from	ADP
ejpam-5036	286	11	the	the	DET
ejpam-5036	286	12	following	follow	VERB
ejpam-5036	286	13	determinant	determinant	ADJ
ejpam-5036	286	14	:	:	PUNCT
ejpam-5036	286	15	psl(γd2n	psl(γd2n	NOUN
ejpam-5036	286	16	)	)	PUNCT
ejpam-5036	286	17	(	(	PUNCT
ejpam-5036	286	18	λ	λ	NOUN
ejpam-5036	286	19	)	)	PUNCT
ejpam-5036	286	20	=	=	SYM
ejpam-5036	287	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5036	287	2	λ−	λ−	PROPN
ejpam-5036	287	3	(	(	PUNCT
ejpam-5036	287	4	2n−	2n−	PROPN
ejpam-5036	287	5	1	1	NUM
ejpam-5036	287	6	)	)	PUNCT
ejpam-5036	287	7	−j1×(n−1	−j1×(n−1	NUM
ejpam-5036	287	8	)	)	PUNCT
ejpam-5036	287	9	−j1×n	−j1×n	PUNCT
ejpam-5036	288	1	−j(n−1)×1	−j(n−1)×1	PROPN
ejpam-5036	288	2	(	(	PUNCT
ejpam-5036	288	3	λ−	λ−	PROPN
ejpam-5036	288	4	(	(	PUNCT
ejpam-5036	288	5	n−	n−	NOUN
ejpam-5036	288	6	2))in−1	2))in−1	NUM
ejpam-5036	288	7	−	−	PROPN
ejpam-5036	288	8	jn−1	jn−1	PROPN
ejpam-5036	288	9	0(n−1)×n	0(n−1)×n	PROPN
ejpam-5036	288	10	−jn×1	−jn×1	VERB
ejpam-5036	288	11	0n×(n−1	0n×(n−1	PROPN
ejpam-5036	288	12	)	)	PUNCT
ejpam-5036	288	13	(	(	PUNCT
ejpam-5036	288	14	λ−	λ−	PROPN
ejpam-5036	288	15	1)in	1)in	PROPN
ejpam-5036	288	16	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5036	288	17	.	.	PUNCT
ejpam-5036	289	1	(	(	PUNCT
ejpam-5036	289	2	5	5	X
ejpam-5036	289	3	)	)	PUNCT
ejpam-5036	289	4	we	we	PRON
ejpam-5036	289	5	apply	apply	VERB
ejpam-5036	289	6	the	the	DET
ejpam-5036	289	7	following	follow	VERB
ejpam-5036	289	8	steps	step	NOUN
ejpam-5036	289	9	into	into	ADP
ejpam-5036	289	10	equation	equation	NOUN
ejpam-5036	289	11	5	5	NUM
ejpam-5036	289	12	:	:	PUNCT
ejpam-5036	289	13	(	(	PUNCT
ejpam-5036	289	14	i	i	NOUN
ejpam-5036	289	15	)	)	PUNCT
ejpam-5036	289	16	rn+1+i	rn+1+i	NOUN
ejpam-5036	289	17	−→	−→	ADJ
ejpam-5036	289	18	rn+1+i	rn+1+i	NOUN
ejpam-5036	289	19	−rn+1	−rn+1	VERB
ejpam-5036	289	20	,	,	PUNCT
ejpam-5036	289	21	for	for	ADP
ejpam-5036	289	22	i	i	PROPN
ejpam-5036	289	23	=	=	SYM
ejpam-5036	289	24	1	1	NUM
ejpam-5036	289	25	,	,	PUNCT
ejpam-5036	289	26	2	2	NUM
ejpam-5036	289	27	,	,	PUNCT
ejpam-5036	289	28	.	.	PUNCT
ejpam-5036	289	29	.	.	PUNCT
ejpam-5036	290	1	.	.	PUNCT
ejpam-5036	291	1	,	,	PUNCT
ejpam-5036	291	2	n−	n−	NOUN
ejpam-5036	291	3	1	1	NUM
ejpam-5036	291	4	.	.	PUNCT
ejpam-5036	291	5	(	(	PUNCT
ejpam-5036	291	6	ii	ii	NOUN
ejpam-5036	291	7	)	)	PUNCT
ejpam-5036	291	8	cn+1	cn+1	VERB
ejpam-5036	291	9	−→	−→	NOUN
ejpam-5036	291	10	cn+1	cn+1	NOUN
ejpam-5036	291	11	+	+	CCONJ
ejpam-5036	291	12	cn+2	cn+2	PRON
ejpam-5036	292	1	+	+	CCONJ
ejpam-5036	292	2	.	.	PUNCT
ejpam-5036	292	3	.	.	PUNCT
ejpam-5036	293	1	.+	.+	NOUN
ejpam-5036	293	2	c2n	c2n	NOUN
ejpam-5036	293	3	.	.	PUNCT
ejpam-5036	294	1	(	(	PUNCT
ejpam-5036	294	2	iii	iii	X
ejpam-5036	294	3	)	)	PUNCT
ejpam-5036	294	4	c1	c1	PROPN
ejpam-5036	294	5	−→	−→	PROPN
ejpam-5036	294	6	c1	c1	PROPN
ejpam-5036	294	7	+	+	CCONJ
ejpam-5036	294	8	(	(	PUNCT
ejpam-5036	294	9	1	1	NUM
ejpam-5036	294	10	λ−1	λ−1	PROPN
ejpam-5036	294	11	)	)	PUNCT
ejpam-5036	294	12	cn+1	cn+1	VERB
ejpam-5036	294	13	.	.	PUNCT
ejpam-5036	295	1	(	(	PUNCT
ejpam-5036	295	2	iv	iv	X
ejpam-5036	295	3	)	)	PUNCT
ejpam-5036	295	4	r2+i	r2+i	PROPN
ejpam-5036	295	5	−→	−→	NOUN
ejpam-5036	295	6	r2+i	r2+i	PROPN
ejpam-5036	295	7	−r2	−r2	PROPN
ejpam-5036	295	8	,	,	PUNCT
ejpam-5036	295	9	for	for	ADP
ejpam-5036	295	10	i	i	PROPN
ejpam-5036	295	11	=	=	SYM
ejpam-5036	295	12	1	1	NUM
ejpam-5036	295	13	,	,	PUNCT
ejpam-5036	295	14	2	2	NUM
ejpam-5036	295	15	,	,	PUNCT
ejpam-5036	295	16	.	.	PUNCT
ejpam-5036	295	17	.	.	PUNCT
ejpam-5036	296	1	.	.	PUNCT
ejpam-5036	297	1	,	,	PUNCT
ejpam-5036	297	2	n−	n−	NOUN
ejpam-5036	297	3	2	2	NUM
ejpam-5036	297	4	.	.	PUNCT
ejpam-5036	298	1	(	(	PUNCT
ejpam-5036	298	2	v	v	NOUN
ejpam-5036	298	3	)	)	PUNCT
ejpam-5036	298	4	c2	c2	PROPN
ejpam-5036	298	5	−→	−→	PROPN
ejpam-5036	298	6	c2	c2	PROPN
ejpam-5036	298	7	+	+	CCONJ
ejpam-5036	298	8	c2	c2	PROPN
ejpam-5036	298	9	+	+	PROPN
ejpam-5036	298	10	1	1	NUM
ejpam-5036	298	11	+	+	NUM
ejpam-5036	298	12	.	.	PUNCT
ejpam-5036	298	13	.	.	PUNCT
ejpam-5036	299	1	.+	.+	NOUN
ejpam-5036	299	2	cn	cn	PROPN
ejpam-5036	299	3	,	,	PUNCT
ejpam-5036	299	4	then	then	ADV
ejpam-5036	299	5	we	we	PRON
ejpam-5036	299	6	get	get	VERB
ejpam-5036	299	7	psl(γd2n	psl(γd2n	NOUN
ejpam-5036	299	8	)	)	PUNCT
ejpam-5036	299	9	(	(	PUNCT
ejpam-5036	299	10	λ	λ	X
ejpam-5036	299	11	)	)	PUNCT
ejpam-5036	299	12	=	=	PUNCT
ejpam-5036	299	13	∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-5036	299	14	λ2−2nλ+n−1	λ2−2nλ+n−1	X
ejpam-5036	300	1	λ−1	λ−1	PROPN
ejpam-5036	300	2	1−	1−	NUM
ejpam-5036	300	3	n	n	PRON
ejpam-5036	300	4	−j1×(n−2	−j1×(n−2	NUM
ejpam-5036	300	5	)	)	PUNCT
ejpam-5036	300	6	−n	−n	ADV
ejpam-5036	300	7	−j1×(n−1	−j1×(n−1	PROPN
ejpam-5036	300	8	)	)	PUNCT
ejpam-5036	300	9	−1	−1	NOUN
ejpam-5036	300	10	λ−	λ−	PROPN
ejpam-5036	300	11	2n+	2n+	NUM
ejpam-5036	300	12	3	3	NUM
ejpam-5036	300	13	−j1×(n−2	−j1×(n−2	NUM
ejpam-5036	300	14	)	)	PUNCT
ejpam-5036	300	15	0	0	NUM
ejpam-5036	300	16	01×(n−1	01×(n−1	NUM
ejpam-5036	300	17	)	)	PUNCT
ejpam-5036	300	18	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	300	19	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	301	1	(	(	PUNCT
ejpam-5036	301	2	λ−	λ−	PROPN
ejpam-5036	301	3	n+	n+	PROPN
ejpam-5036	301	4	2)in−2	2)in−2	PROPN
ejpam-5036	301	5	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	301	6	0(n−2)×(n−1	0(n−2)×(n−1	NUM
ejpam-5036	301	7	)	)	PUNCT
ejpam-5036	301	8	0	0	NUM
ejpam-5036	301	9	0	0	NUM
ejpam-5036	301	10	01×(n−2	01×(n−2	X
ejpam-5036	301	11	)	)	PUNCT
ejpam-5036	301	12	λ−	λ−	PROPN
ejpam-5036	301	13	1	1	NUM
ejpam-5036	301	14	01×(n−1	01×(n−1	NUM
ejpam-5036	301	15	)	)	PUNCT
ejpam-5036	301	16	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	301	17	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	302	1	0n−1	0n−1	NUM
ejpam-5036	302	2	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	303	1	(	(	PUNCT
ejpam-5036	303	2	λ−	λ−	PROPN
ejpam-5036	303	3	1)in−1	1)in−1	PROPN
ejpam-5036	303	4	∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5036	303	5	.	.	PUNCT
ejpam-5036	304	1	m.	m.	PROPN
ejpam-5036	304	2	u.	u.	PROPN
ejpam-5036	304	3	romdhini	romdhini	PROPN
ejpam-5036	304	4	et	et	PROPN
ejpam-5036	304	5	al	al	PROPN
ejpam-5036	304	6	.	.	PUNCT
ejpam-5036	304	7	/	/	SYM
ejpam-5036	304	8	eur	eur	PROPN
ejpam-5036	304	9	.	.	PUNCT
ejpam-5036	305	1	j.	j.	PROPN
ejpam-5036	305	2	pure	pure	PROPN
ejpam-5036	305	3	appl	appl	PROPN
ejpam-5036	305	4	.	.	PROPN
ejpam-5036	305	5	math	math	PROPN
ejpam-5036	305	6	,	,	PUNCT
ejpam-5036	305	7	17	17	NUM
ejpam-5036	305	8	(	(	PUNCT
ejpam-5036	305	9	2	2	NUM
ejpam-5036	305	10	)	)	PUNCT
ejpam-5036	305	11	(	(	PUNCT
ejpam-5036	305	12	2024	2024	NUM
ejpam-5036	305	13	)	)	PUNCT
ejpam-5036	305	14	,	,	PUNCT
ejpam-5036	305	15	591	591	NUM
ejpam-5036	305	16	-	-	SYM
ejpam-5036	305	17	603	603	NUM
ejpam-5036	305	18	598	598	NUM
ejpam-5036	305	19	from	from	ADP
ejpam-5036	305	20	theorem	theorem	ADJ
ejpam-5036	305	21	2	2	NUM
ejpam-5036	305	22	,	,	PUNCT
ejpam-5036	305	23	we	we	PRON
ejpam-5036	305	24	derive	derive	VERB
ejpam-5036	305	25	the	the	DET
ejpam-5036	305	26	characteristic	characteristic	ADJ
ejpam-5036	305	27	polynomial	polynomial	NOUN
ejpam-5036	305	28	of	of	ADP
ejpam-5036	305	29	sl(γd2n	sl(γd2n	NOUN
ejpam-5036	305	30	)	)	PUNCT
ejpam-5036	305	31	as	as	SCONJ
ejpam-5036	305	32	follows	follow	VERB
ejpam-5036	305	33	:	:	PUNCT
ejpam-5036	305	34	psl(γd2n	psl(γd2n	NOUN
ejpam-5036	305	35	)	)	PUNCT
ejpam-5036	305	36	(	(	PUNCT
ejpam-5036	305	37	λ	λ	NOUN
ejpam-5036	305	38	)	)	PUNCT
ejpam-5036	305	39	=	=	SYM
ejpam-5036	305	40	(	(	PUNCT
ejpam-5036	305	41	λ−	λ−	PROPN
ejpam-5036	305	42	1)n−1(λ−	1)n−1(λ−	NUM
ejpam-5036	305	43	n+	n+	PUNCT
ejpam-5036	305	44	2)n−2	2)n−2	NUM
ejpam-5036	305	45	(	(	PUNCT
ejpam-5036	305	46	λ3	λ3	PROPN
ejpam-5036	305	47	+	+	PROPN
ejpam-5036	305	48	(	(	PUNCT
ejpam-5036	305	49	3−	3−	NUM
ejpam-5036	305	50	4n)λ2	4n)λ2	NUM
ejpam-5036	305	51	+	+	CCONJ
ejpam-5036	305	52	2n(2n−	2n(2n−	NUM
ejpam-5036	305	53	3)λ−	3)λ−	NUM
ejpam-5036	305	54	2(n−	2(n−	NUM
ejpam-5036	305	55	1)(n−	1)(n−	NUM
ejpam-5036	305	56	2	2	NUM
ejpam-5036	305	57	)	)	PUNCT
ejpam-5036	305	58	)	)	PUNCT
ejpam-5036	305	59	.	.	PUNCT
ejpam-5036	306	1	the	the	DET
ejpam-5036	306	2	normalized	normalize	VERB
ejpam-5036	306	3	form	form	NOUN
ejpam-5036	306	4	of	of	ADP
ejpam-5036	306	5	the	the	DET
ejpam-5036	306	6	adjacency	adjacency	NOUN
ejpam-5036	306	7	,	,	PUNCT
ejpam-5036	306	8	laplacian	laplacian	NOUN
ejpam-5036	306	9	,	,	PUNCT
ejpam-5036	306	10	and	and	CCONJ
ejpam-5036	306	11	signless	signless	ADJ
ejpam-5036	306	12	laplacian	laplacian	ADJ
ejpam-5036	306	13	matrices	matrix	NOUN
ejpam-5036	306	14	of	of	ADP
ejpam-5036	306	15	γd2n	γd2n	PROPN
ejpam-5036	306	16	are	be	AUX
ejpam-5036	306	17	presented	present	VERB
ejpam-5036	306	18	in	in	ADP
ejpam-5036	306	19	the	the	DET
ejpam-5036	306	20	following	follow	VERB
ejpam-5036	306	21	three	three	NUM
ejpam-5036	306	22	theorems	theorem	NOUN
ejpam-5036	306	23	.	.	PUNCT
ejpam-5036	307	1	theorem	theorem	NOUN
ejpam-5036	307	2	6	6	NUM
ejpam-5036	307	3	.	.	PUNCT
ejpam-5036	308	1	let	let	VERB
ejpam-5036	308	2	γd2n	γd2n	PROPN
ejpam-5036	308	3	be	be	AUX
ejpam-5036	308	4	the	the	DET
ejpam-5036	308	5	power	power	NOUN
ejpam-5036	308	6	graph	graph	NOUN
ejpam-5036	308	7	for	for	ADP
ejpam-5036	308	8	d2n	d2n	NOUN
ejpam-5036	308	9	,	,	PUNCT
ejpam-5036	308	10	then	then	ADV
ejpam-5036	308	11	the	the	DET
ejpam-5036	308	12	characteristic	characteristic	ADJ
ejpam-5036	308	13	polynomial	polynomial	NOUN
ejpam-5036	308	14	of	of	ADP
ejpam-5036	308	15	na(γd2n	na(γd2n	NOUN
ejpam-5036	308	16	)	)	PUNCT
ejpam-5036	308	17	is	be	AUX
ejpam-5036	308	18	pna(γd2n	pna(γd2n	ADJ
ejpam-5036	308	19	)	)	PUNCT
ejpam-5036	308	20	(	(	PUNCT
ejpam-5036	308	21	λ	λ	X
ejpam-5036	308	22	)	)	PUNCT
ejpam-5036	308	23	=	=	SYM
ejpam-5036	309	1	λn−1	λn−1	PROPN
ejpam-5036	309	2	(	(	PUNCT
ejpam-5036	309	3	λ+	λ+	NUM
ejpam-5036	309	4	1	1	NUM
ejpam-5036	309	5	n−	n−	NOUN
ejpam-5036	309	6	1	1	NUM
ejpam-5036	309	7	)	)	PUNCT
ejpam-5036	309	8	n−2	n−2	PROPN
ejpam-5036	309	9	(	(	PUNCT
ejpam-5036	309	10	λ3	λ3	PROPN
ejpam-5036	309	11	−	−	PROPN
ejpam-5036	309	12	(	(	PUNCT
ejpam-5036	309	13	n−	n−	NOUN
ejpam-5036	309	14	2	2	NUM
ejpam-5036	309	15	)	)	PUNCT
ejpam-5036	309	16	n−	n−	NOUN
ejpam-5036	309	17	1	1	NUM
ejpam-5036	309	18	λ2	λ2	NOUN
ejpam-5036	309	19	−	−	NOUN
ejpam-5036	309	20	n+	n+	NOUN
ejpam-5036	309	21	1	1	NUM
ejpam-5036	309	22	2n−	2n−	NUM
ejpam-5036	309	23	1	1	NUM
ejpam-5036	309	24	λ+	λ+	PUNCT
ejpam-5036	309	25	n(n−	n(n−	NOUN
ejpam-5036	309	26	2	2	NUM
ejpam-5036	309	27	)	)	PUNCT
ejpam-5036	309	28	(	(	PUNCT
ejpam-5036	309	29	n−	n−	NOUN
ejpam-5036	309	30	1)(2n−	1)(2n−	NUM
ejpam-5036	309	31	1	1	NUM
ejpam-5036	309	32	)	)	PUNCT
ejpam-5036	309	33	)	)	PUNCT
ejpam-5036	309	34	.	.	PUNCT
ejpam-5036	310	1	proof	proof	NOUN
ejpam-5036	310	2	.	.	PUNCT
ejpam-5036	311	1	by	by	ADP
ejpam-5036	311	2	definition	definition	NOUN
ejpam-5036	311	3	5	5	NUM
ejpam-5036	311	4	,	,	PUNCT
ejpam-5036	311	5	we	we	PRON
ejpam-5036	311	6	need	need	VERB
ejpam-5036	311	7	to	to	PART
ejpam-5036	311	8	construct	construct	VERB
ejpam-5036	311	9	(	(	PUNCT
ejpam-5036	311	10	√	√	NUM
ejpam-5036	311	11	d)−1(γd2n	d)−1(γd2n	NOUN
ejpam-5036	311	12	)	)	PUNCT
ejpam-5036	311	13	.	.	PUNCT
ejpam-5036	312	1	using	use	VERB
ejpam-5036	312	2	equation	equation	NOUN
ejpam-5036	312	3	3	3	NUM
ejpam-5036	312	4	,	,	PUNCT
ejpam-5036	312	5	we	we	PRON
ejpam-5036	312	6	can	can	AUX
ejpam-5036	312	7	construct	construct	VERB
ejpam-5036	312	8	(	(	PUNCT
ejpam-5036	312	9	√	√	NUM
ejpam-5036	312	10	d)−1(γd2n	d)−1(γd2n	NOUN
ejpam-5036	312	11	)	)	PUNCT
ejpam-5036	312	12	as	as	SCONJ
ejpam-5036	312	13	follows	follow	VERB
ejpam-5036	312	14	:	:	PUNCT
ejpam-5036	312	15	(	(	PUNCT
ejpam-5036	312	16	√	√	ADP
ejpam-5036	312	17	d)−1(γd2n	d)−1(γd2n	NOUN
ejpam-5036	312	18	)	)	PUNCT
ejpam-5036	312	19	=	=	PUNCT
ejpam-5036	313	1	e	e	X
ejpam-5036	313	2	a	a	DET
ejpam-5036	313	3	a2	a2	PROPN
ejpam-5036	313	4	.	.	PUNCT
ejpam-5036	313	5	.	.	PUNCT
ejpam-5036	313	6	.	.	PUNCT
ejpam-5036	314	1	an−1	an−1	PROPN
ejpam-5036	314	2	b	b	PROPN
ejpam-5036	314	3	ab	ab	PROPN
ejpam-5036	314	4	.	.	PUNCT
ejpam-5036	314	5	.	.	PUNCT
ejpam-5036	314	6	.	.	PUNCT
ejpam-5036	315	1	an−1b	an−1b	PROPN
ejpam-5036	315	2			X
ejpam-5036	316	1	e	e	X
ejpam-5036	316	2	1√	1√	PROPN
ejpam-5036	316	3	2n−1	2n−1	NUM
ejpam-5036	316	4	0	0	NUM
ejpam-5036	316	5	0	0	NUM
ejpam-5036	316	6	.	.	PUNCT
ejpam-5036	316	7	.	.	PUNCT
ejpam-5036	317	1	.	.	PUNCT
ejpam-5036	318	1	0	0	NUM
ejpam-5036	319	1	0	0	NUM
ejpam-5036	319	2	0	0	NUM
ejpam-5036	319	3	.	.	PUNCT
ejpam-5036	319	4	.	.	PUNCT
ejpam-5036	320	1	.	.	PUNCT
ejpam-5036	320	2	0	0	PUNCT
ejpam-5036	321	1	a	a	DET
ejpam-5036	321	2	0	0	NUM
ejpam-5036	321	3	1√	1√	PROPN
ejpam-5036	321	4	n−1	n−1	PROPN
ejpam-5036	321	5	0	0	NUM
ejpam-5036	321	6	.	.	PUNCT
ejpam-5036	321	7	.	.	PUNCT
ejpam-5036	321	8	.	.	PUNCT
ejpam-5036	322	1	0	0	NUM
ejpam-5036	323	1	0	0	NUM
ejpam-5036	323	2	0	0	NUM
ejpam-5036	323	3	.	.	PUNCT
ejpam-5036	323	4	.	.	PUNCT
ejpam-5036	324	1	.	.	PUNCT
ejpam-5036	325	1	0	0	NUM
ejpam-5036	325	2	a2	a2	PROPN
ejpam-5036	325	3	0	0	NUM
ejpam-5036	325	4	0	0	NUM
ejpam-5036	325	5	1√	1√	PROPN
ejpam-5036	325	6	n−1	n−1	PROPN
ejpam-5036	325	7	.	.	PUNCT
ejpam-5036	325	8	.	.	PUNCT
ejpam-5036	325	9	.	.	PUNCT
ejpam-5036	326	1	0	0	NUM
ejpam-5036	327	1	0	0	NUM
ejpam-5036	327	2	0	0	NUM
ejpam-5036	327	3	.	.	PUNCT
ejpam-5036	327	4	.	.	PUNCT
ejpam-5036	328	1	.	.	PUNCT
ejpam-5036	329	1	0	0	NUM
ejpam-5036	329	2	...	...	PUNCT
ejpam-5036	329	3	...	...	PUNCT
ejpam-5036	329	4	...	...	PUNCT
ejpam-5036	329	5	...	...	PUNCT
ejpam-5036	329	6	.	.	PUNCT
ejpam-5036	329	7	.	.	PUNCT
ejpam-5036	330	1	.	.	PUNCT
ejpam-5036	330	2	...	...	PUNCT
ejpam-5036	331	1	...	...	PUNCT
ejpam-5036	331	2	...	...	PUNCT
ejpam-5036	331	3	.	.	PUNCT
ejpam-5036	331	4	.	.	PUNCT
ejpam-5036	332	1	.	.	PUNCT
ejpam-5036	333	1	...	...	PUNCT
ejpam-5036	334	1	an−1	an−1	ADV
ejpam-5036	334	2	0	0	NUM
ejpam-5036	334	3	0	0	NUM
ejpam-5036	334	4	0	0	NUM
ejpam-5036	334	5	.	.	PUNCT
ejpam-5036	334	6	.	.	PUNCT
ejpam-5036	334	7	.	.	PUNCT
ejpam-5036	335	1	1√	1√	PROPN
ejpam-5036	335	2	n−1	n−1	PROPN
ejpam-5036	335	3	0	0	NUM
ejpam-5036	335	4	0	0	NUM
ejpam-5036	335	5	.	.	PUNCT
ejpam-5036	335	6	.	.	PUNCT
ejpam-5036	335	7	.	.	PUNCT
ejpam-5036	336	1	0	0	NUM
ejpam-5036	337	1	b	b	X
ejpam-5036	337	2	0	0	NUM
ejpam-5036	337	3	0	0	NUM
ejpam-5036	337	4	0	0	NUM
ejpam-5036	337	5	.	.	PUNCT
ejpam-5036	337	6	.	.	PUNCT
ejpam-5036	337	7	.	.	PUNCT
ejpam-5036	338	1	0	0	NUM
ejpam-5036	339	1	1	1	NUM
ejpam-5036	339	2	0	0	NUM
ejpam-5036	339	3	.	.	PUNCT
ejpam-5036	339	4	.	.	PUNCT
ejpam-5036	340	1	.	.	PUNCT
ejpam-5036	340	2	0	0	PUNCT
ejpam-5036	341	1	ab	ab	NOUN
ejpam-5036	341	2	0	0	NUM
ejpam-5036	341	3	0	0	NUM
ejpam-5036	341	4	0	0	NUM
ejpam-5036	341	5	.	.	PUNCT
ejpam-5036	341	6	.	.	PUNCT
ejpam-5036	341	7	.	.	PUNCT
ejpam-5036	342	1	0	0	NUM
ejpam-5036	342	2	0	0	NUM
ejpam-5036	342	3	1	1	NUM
ejpam-5036	342	4	.	.	PUNCT
ejpam-5036	342	5	.	.	PUNCT
ejpam-5036	343	1	.	.	PUNCT
ejpam-5036	344	1	0	0	NUM
ejpam-5036	344	2	...	...	PUNCT
ejpam-5036	344	3	...	...	PUNCT
ejpam-5036	344	4	...	...	PUNCT
ejpam-5036	344	5	...	...	PUNCT
ejpam-5036	344	6	.	.	PUNCT
ejpam-5036	344	7	.	.	PUNCT
ejpam-5036	345	1	.	.	PUNCT
ejpam-5036	345	2	...	...	PUNCT
ejpam-5036	346	1	...	...	PUNCT
ejpam-5036	346	2	...	...	PUNCT
ejpam-5036	346	3	.	.	PUNCT
ejpam-5036	346	4	.	.	PUNCT
ejpam-5036	346	5	.	.	PUNCT
ejpam-5036	347	1	...	...	PUNCT
ejpam-5036	348	1	an−1b	an−1b	PUNCT
ejpam-5036	349	1	0	0	NUM
ejpam-5036	349	2	0	0	NUM
ejpam-5036	349	3	0	0	NUM
ejpam-5036	349	4	.	.	PUNCT
ejpam-5036	349	5	.	.	PUNCT
ejpam-5036	349	6	.	.	PUNCT
ejpam-5036	350	1	0	0	NUM
ejpam-5036	351	1	0	0	NUM
ejpam-5036	351	2	0	0	NUM
ejpam-5036	351	3	.	.	PUNCT
ejpam-5036	351	4	.	.	PUNCT
ejpam-5036	351	5	.	.	PUNCT
ejpam-5036	352	1	1	1	X
ejpam-5036	352	2	.	.	PUNCT
ejpam-5036	353	1	(	(	PUNCT
ejpam-5036	353	2	6	6	NUM
ejpam-5036	353	3	)	)	PUNCT
ejpam-5036	353	4	based	base	VERB
ejpam-5036	353	5	on	on	ADP
ejpam-5036	353	6	definition	definition	NOUN
ejpam-5036	353	7	5	5	NUM
ejpam-5036	353	8	,	,	PUNCT
ejpam-5036	353	9	na(γd2n	na(γd2n	NOUN
ejpam-5036	353	10	)	)	PUNCT
ejpam-5036	353	11	is	be	AUX
ejpam-5036	353	12	a	a	DET
ejpam-5036	353	13	2n×	2n×	NUM
ejpam-5036	353	14	2n	2n	NUM
ejpam-5036	353	15	matrix	matrix	NOUN
ejpam-5036	353	16	as	as	SCONJ
ejpam-5036	353	17	given	give	VERB
ejpam-5036	353	18	below	below	ADV
ejpam-5036	353	19	:	:	PUNCT
ejpam-5036	353	20	e	e	PROPN
ejpam-5036	353	21	a	a	DET
ejpam-5036	353	22	a2	a2	PROPN
ejpam-5036	353	23	.	.	PUNCT
ejpam-5036	353	24	.	.	PUNCT
ejpam-5036	354	1	.	.	PUNCT
ejpam-5036	355	1	an−1	an−1	PROPN
ejpam-5036	355	2	b	b	PROPN
ejpam-5036	355	3	ab	ab	PROPN
ejpam-5036	355	4	.	.	PUNCT
ejpam-5036	355	5	.	.	PUNCT
ejpam-5036	355	6	.	.	PUNCT
ejpam-5036	356	1	an−1b	an−1b	NOUN
ejpam-5036	356	2			PROPN
ejpam-5036	356	3	e	e	PROPN
ejpam-5036	356	4	0	0	NUM
ejpam-5036	356	5	1√	1√	PROPN
ejpam-5036	356	6	(	(	PUNCT
ejpam-5036	356	7	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	356	8	)	)	PUNCT
ejpam-5036	356	9	1√	1√	NOUN
ejpam-5036	356	10	(	(	PUNCT
ejpam-5036	356	11	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	356	12	)	)	PUNCT
ejpam-5036	356	13	.	.	PUNCT
ejpam-5036	356	14	.	.	PUNCT
ejpam-5036	357	1	.	.	PUNCT
ejpam-5036	358	1	1√	1√	NOUN
ejpam-5036	358	2	(	(	PUNCT
ejpam-5036	358	3	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	358	4	)	)	PUNCT
ejpam-5036	358	5	1√	1√	NOUN
ejpam-5036	358	6	2n−1	2n−1	NUM
ejpam-5036	358	7	1√	1√	PROPN
ejpam-5036	358	8	2n−1	2n−1	NUM
ejpam-5036	358	9	.	.	PUNCT
ejpam-5036	358	10	.	.	PUNCT
ejpam-5036	358	11	.	.	PUNCT
ejpam-5036	359	1	1√	1√	NOUN
ejpam-5036	359	2	2n−1	2n−1	NUM
ejpam-5036	359	3	a	a	DET
ejpam-5036	359	4	1√	1√	PROPN
ejpam-5036	359	5	(	(	PUNCT
ejpam-5036	359	6	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	359	7	)	)	PUNCT
ejpam-5036	359	8	0	0	NUM
ejpam-5036	360	1	1	1	NUM
ejpam-5036	360	2	n−1	n−1	PROPN
ejpam-5036	360	3	.	.	PUNCT
ejpam-5036	360	4	.	.	PUNCT
ejpam-5036	361	1	.	.	PUNCT
ejpam-5036	362	1	1	1	NUM
ejpam-5036	362	2	n−1	n−1	PROPN
ejpam-5036	362	3	0	0	NUM
ejpam-5036	362	4	0	0	NUM
ejpam-5036	362	5	.	.	PUNCT
ejpam-5036	362	6	.	.	PUNCT
ejpam-5036	362	7	.	.	PUNCT
ejpam-5036	363	1	0	0	NUM
ejpam-5036	364	1	a2	a2	PROPN
ejpam-5036	364	2	1√	1√	PROPN
ejpam-5036	364	3	(	(	PUNCT
ejpam-5036	364	4	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	364	5	)	)	PUNCT
ejpam-5036	364	6	1	1	NUM
ejpam-5036	364	7	n−1	n−1	PROPN
ejpam-5036	364	8	0	0	NUM
ejpam-5036	364	9	.	.	PUNCT
ejpam-5036	364	10	.	.	PUNCT
ejpam-5036	364	11	.	.	PUNCT
ejpam-5036	365	1	1	1	NUM
ejpam-5036	365	2	n−1	n−1	PROPN
ejpam-5036	365	3	0	0	NUM
ejpam-5036	365	4	0	0	NUM
ejpam-5036	365	5	.	.	PUNCT
ejpam-5036	365	6	.	.	PUNCT
ejpam-5036	365	7	.	.	PUNCT
ejpam-5036	366	1	0	0	NUM
ejpam-5036	366	2	...	...	PUNCT
ejpam-5036	366	3	...	...	PUNCT
ejpam-5036	366	4	...	...	PUNCT
ejpam-5036	366	5	...	...	PUNCT
ejpam-5036	366	6	.	.	PUNCT
ejpam-5036	366	7	.	.	PUNCT
ejpam-5036	367	1	.	.	PUNCT
ejpam-5036	367	2	...	...	PUNCT
ejpam-5036	368	1	...	...	PUNCT
ejpam-5036	368	2	...	...	PUNCT
ejpam-5036	368	3	.	.	PUNCT
ejpam-5036	368	4	.	.	PUNCT
ejpam-5036	369	1	.	.	PUNCT
ejpam-5036	370	1	...	...	PUNCT
ejpam-5036	371	1	an−1	an−1	PROPN
ejpam-5036	371	2	1√	1√	PROPN
ejpam-5036	371	3	(	(	PUNCT
ejpam-5036	371	4	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	371	5	)	)	PUNCT
ejpam-5036	371	6	1	1	NUM
ejpam-5036	371	7	n−1	n−1	PROPN
ejpam-5036	371	8	1	1	NUM
ejpam-5036	371	9	n−1	n−1	PROPN
ejpam-5036	371	10	.	.	PUNCT
ejpam-5036	371	11	.	.	PUNCT
ejpam-5036	371	12	.	.	PUNCT
ejpam-5036	372	1	0	0	NUM
ejpam-5036	373	1	0	0	NUM
ejpam-5036	373	2	0	0	NUM
ejpam-5036	373	3	.	.	PUNCT
ejpam-5036	373	4	.	.	PUNCT
ejpam-5036	373	5	.	.	PUNCT
ejpam-5036	374	1	0	0	NUM
ejpam-5036	375	1	b	b	X
ejpam-5036	375	2	1√	1√	NUM
ejpam-5036	375	3	2n−1	2n−1	NUM
ejpam-5036	375	4	0	0	NUM
ejpam-5036	375	5	0	0	NUM
ejpam-5036	375	6	.	.	PUNCT
ejpam-5036	375	7	.	.	PUNCT
ejpam-5036	375	8	.	.	PUNCT
ejpam-5036	376	1	0	0	NUM
ejpam-5036	377	1	0	0	NUM
ejpam-5036	377	2	0	0	NUM
ejpam-5036	377	3	.	.	PUNCT
ejpam-5036	377	4	.	.	PUNCT
ejpam-5036	378	1	.	.	PUNCT
ejpam-5036	378	2	0	0	NUM
ejpam-5036	379	1	ab	ab	PROPN
ejpam-5036	379	2	1√	1√	PROPN
ejpam-5036	379	3	2n−1	2n−1	NUM
ejpam-5036	379	4	0	0	NUM
ejpam-5036	379	5	0	0	NUM
ejpam-5036	379	6	.	.	PUNCT
ejpam-5036	379	7	.	.	PUNCT
ejpam-5036	380	1	.	.	PUNCT
ejpam-5036	381	1	0	0	NUM
ejpam-5036	382	1	0	0	NUM
ejpam-5036	382	2	0	0	NUM
ejpam-5036	382	3	.	.	PUNCT
ejpam-5036	382	4	.	.	PUNCT
ejpam-5036	383	1	.	.	PUNCT
ejpam-5036	384	1	0	0	NUM
ejpam-5036	384	2	...	...	PUNCT
ejpam-5036	384	3	...	...	PUNCT
ejpam-5036	384	4	...	...	PUNCT
ejpam-5036	384	5	...	...	PUNCT
ejpam-5036	384	6	.	.	PUNCT
ejpam-5036	384	7	.	.	PUNCT
ejpam-5036	385	1	.	.	PUNCT
ejpam-5036	385	2	...	...	PUNCT
ejpam-5036	386	1	...	...	PUNCT
ejpam-5036	386	2	...	...	PUNCT
ejpam-5036	386	3	.	.	PUNCT
ejpam-5036	386	4	.	.	PUNCT
ejpam-5036	387	1	.	.	PUNCT
ejpam-5036	388	1	...	...	PUNCT
ejpam-5036	389	1	an−1b	an−1b	PUNCT
ejpam-5036	389	2	1√	1√	NOUN
ejpam-5036	389	3	2n−1	2n−1	NUM
ejpam-5036	389	4	0	0	NUM
ejpam-5036	389	5	0	0	NUM
ejpam-5036	389	6	.	.	PUNCT
ejpam-5036	389	7	.	.	PUNCT
ejpam-5036	389	8	.	.	PUNCT
ejpam-5036	390	1	0	0	NUM
ejpam-5036	391	1	0	0	NUM
ejpam-5036	391	2	0	0	NUM
ejpam-5036	391	3	.	.	PUNCT
ejpam-5036	391	4	.	.	PUNCT
ejpam-5036	392	1	.	.	PUNCT
ejpam-5036	392	2	0	0	PUNCT
ejpam-5036	393	1	.	.	PUNCT
ejpam-5036	394	1	(	(	PUNCT
ejpam-5036	394	2	7	7	X
ejpam-5036	394	3	)	)	PUNCT
ejpam-5036	394	4	m.	m.	NOUN
ejpam-5036	394	5	u.	u.	PROPN
ejpam-5036	394	6	romdhini	romdhini	PROPN
ejpam-5036	394	7	et	et	PROPN
ejpam-5036	394	8	al	al	PROPN
ejpam-5036	394	9	.	.	PUNCT
ejpam-5036	394	10	/	/	SYM
ejpam-5036	394	11	eur	eur	PROPN
ejpam-5036	394	12	.	.	PUNCT
ejpam-5036	395	1	j.	j.	PROPN
ejpam-5036	395	2	pure	pure	PROPN
ejpam-5036	395	3	appl	appl	PROPN
ejpam-5036	395	4	.	.	PROPN
ejpam-5036	395	5	math	math	PROPN
ejpam-5036	395	6	,	,	PUNCT
ejpam-5036	395	7	17	17	NUM
ejpam-5036	395	8	(	(	PUNCT
ejpam-5036	395	9	2	2	NUM
ejpam-5036	395	10	)	)	PUNCT
ejpam-5036	395	11	(	(	PUNCT
ejpam-5036	395	12	2024	2024	NUM
ejpam-5036	395	13	)	)	PUNCT
ejpam-5036	395	14	,	,	PUNCT
ejpam-5036	395	15	591	591	NUM
ejpam-5036	395	16	-	-	SYM
ejpam-5036	395	17	603	603	NUM
ejpam-5036	395	18	599	599	NUM
ejpam-5036	395	19	in	in	ADP
ejpam-5036	395	20	other	other	ADJ
ejpam-5036	395	21	words	word	NOUN
ejpam-5036	395	22	,	,	PUNCT
ejpam-5036	395	23	na(γd2n	na(γd2n	NOUN
ejpam-5036	395	24	)	)	PUNCT
ejpam-5036	395	25	can	can	AUX
ejpam-5036	395	26	be	be	AUX
ejpam-5036	395	27	partitioned	partition	VERB
ejpam-5036	395	28	into	into	ADP
ejpam-5036	395	29	nine	nine	NUM
ejpam-5036	395	30	block	block	NOUN
ejpam-5036	395	31	matrices	matrix	NOUN
ejpam-5036	395	32	as	as	SCONJ
ejpam-5036	395	33	follows	follow	VERB
ejpam-5036	395	34	:	:	PUNCT
ejpam-5036	395	35	na(γd2n	na(γd2n	NOUN
ejpam-5036	395	36	)	)	PUNCT
ejpam-5036	396	1	=	=	SYM
ejpam-5036	396	2			NOUN
ejpam-5036	396	3	0	0	NUM
ejpam-5036	396	4	1√	1√	PROPN
ejpam-5036	396	5	(	(	PUNCT
ejpam-5036	396	6	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	396	7	)	)	PUNCT
ejpam-5036	396	8	j1×(n−1	j1×(n−1	PROPN
ejpam-5036	396	9	)	)	PUNCT
ejpam-5036	396	10	1√	1√	PROPN
ejpam-5036	396	11	2n−1	2n−1	NUM
ejpam-5036	397	1	j1×n	j1×n	PROPN
ejpam-5036	397	2	1√	1√	PROPN
ejpam-5036	397	3	(	(	PUNCT
ejpam-5036	397	4	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	397	5	)	)	PUNCT
ejpam-5036	397	6	j(n−1)×1	j(n−1)×1	NOUN
ejpam-5036	397	7	1	1	NUM
ejpam-5036	397	8	n−1(j	n−1(j	NOUN
ejpam-5036	398	1	−	−	PROPN
ejpam-5036	398	2	i)n−1	i)n−1	PROPN
ejpam-5036	399	1	0(n−1)×n	0(n−1)×n	NUM
ejpam-5036	399	2	1√	1√	PROPN
ejpam-5036	399	3	2n−1	2n−1	NUM
ejpam-5036	399	4	jn×1	jn×1	VERB
ejpam-5036	399	5	0n×(n−1	0n×(n−1	NUM
ejpam-5036	399	6	)	)	PUNCT
ejpam-5036	399	7	0n	0n	NOUN
ejpam-5036	399	8			NOUN
ejpam-5036	399	9	.	.	PUNCT
ejpam-5036	400	1	the	the	DET
ejpam-5036	400	2	characteristic	characteristic	ADJ
ejpam-5036	400	3	polynomial	polynomial	NOUN
ejpam-5036	400	4	of	of	ADP
ejpam-5036	400	5	na(γd2n	na(γd2n	NOUN
ejpam-5036	400	6	)	)	PUNCT
ejpam-5036	400	7	is	be	AUX
ejpam-5036	400	8	pna(γd2n	pna(γd2n	ADJ
ejpam-5036	400	9	)	)	PUNCT
ejpam-5036	400	10	(	(	PUNCT
ejpam-5036	400	11	λ	λ	NOUN
ejpam-5036	400	12	)	)	PUNCT
ejpam-5036	400	13	=	=	PUNCT
ejpam-5036	401	1	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-5036	401	2	λ	λ	PROPN
ejpam-5036	401	3	−	−	PROPN
ejpam-5036	401	4	1√	1√	PROPN
ejpam-5036	401	5	(	(	PUNCT
ejpam-5036	401	6	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	401	7	)	)	PUNCT
ejpam-5036	401	8	j1×(n−1	j1×(n−1	PROPN
ejpam-5036	401	9	)	)	PUNCT
ejpam-5036	401	10	−	−	PROPN
ejpam-5036	401	11	1√	1√	PROPN
ejpam-5036	401	12	2n−1	2n−1	NUM
ejpam-5036	402	1	j1×n	j1×n	ADJ
ejpam-5036	402	2	−	−	PROPN
ejpam-5036	402	3	1√	1√	PROPN
ejpam-5036	402	4	(	(	PUNCT
ejpam-5036	402	5	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	402	6	)	)	PUNCT
ejpam-5036	402	7	j(n−1)×1	j(n−1)×1	NOUN
ejpam-5036	402	8	(	(	PUNCT
ejpam-5036	402	9	λ+	λ+	PUNCT
ejpam-5036	402	10	1	1	NUM
ejpam-5036	402	11	n−1	n−1	PROPN
ejpam-5036	402	12	)	)	PUNCT
ejpam-5036	402	13	in−1	in−1	ADJ
ejpam-5036	402	14	−	−	PROPN
ejpam-5036	402	15	1	1	NUM
ejpam-5036	402	16	n−1jn−1	n−1jn−1	NOUN
ejpam-5036	403	1	0(n−1)×n	0(n−1)×n	NUM
ejpam-5036	404	1	−	−	PROPN
ejpam-5036	404	2	1√	1√	PROPN
ejpam-5036	404	3	2n−1	2n−1	NUM
ejpam-5036	404	4	jn×1	jn×1	VERB
ejpam-5036	404	5	0n×(n−1	0n×(n−1	NOUN
ejpam-5036	404	6	)	)	PUNCT
ejpam-5036	404	7	λin	λin	NOUN
ejpam-5036	404	8	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-5036	404	9	.	.	PUNCT
ejpam-5036	405	1	(	(	PUNCT
ejpam-5036	405	2	8)	8)	NUM
ejpam-5036	405	3	we	we	PRON
ejpam-5036	405	4	apply	apply	VERB
ejpam-5036	405	5	the	the	DET
ejpam-5036	405	6	following	follow	VERB
ejpam-5036	405	7	steps	step	NOUN
ejpam-5036	405	8	into	into	ADP
ejpam-5036	405	9	equation	equation	NOUN
ejpam-5036	405	10	8	8	NUM
ejpam-5036	405	11	:	:	PUNCT
ejpam-5036	405	12	(	(	PUNCT
ejpam-5036	405	13	i	i	NOUN
ejpam-5036	405	14	)	)	PUNCT
ejpam-5036	405	15	rn+1+i	rn+1+i	NOUN
ejpam-5036	405	16	−→	−→	ADJ
ejpam-5036	405	17	rn+1+i	rn+1+i	NOUN
ejpam-5036	405	18	−rn+1	−rn+1	VERB
ejpam-5036	405	19	,	,	PUNCT
ejpam-5036	405	20	for	for	ADP
ejpam-5036	405	21	i	i	PROPN
ejpam-5036	405	22	=	=	SYM
ejpam-5036	405	23	1	1	NUM
ejpam-5036	405	24	,	,	PUNCT
ejpam-5036	405	25	2	2	NUM
ejpam-5036	405	26	,	,	PUNCT
ejpam-5036	405	27	.	.	PUNCT
ejpam-5036	405	28	.	.	PUNCT
ejpam-5036	406	1	.	.	PUNCT
ejpam-5036	407	1	,	,	PUNCT
ejpam-5036	407	2	n−	n−	NOUN
ejpam-5036	407	3	1	1	NUM
ejpam-5036	407	4	.	.	PUNCT
ejpam-5036	407	5	(	(	PUNCT
ejpam-5036	407	6	ii	ii	NOUN
ejpam-5036	407	7	)	)	PUNCT
ejpam-5036	407	8	cn+1	cn+1	VERB
ejpam-5036	407	9	−→	−→	NOUN
ejpam-5036	407	10	cn+1	cn+1	NOUN
ejpam-5036	407	11	+	+	CCONJ
ejpam-5036	407	12	cn+2	cn+2	PRON
ejpam-5036	408	1	+	+	CCONJ
ejpam-5036	408	2	.	.	PUNCT
ejpam-5036	408	3	.	.	PUNCT
ejpam-5036	409	1	.+	.+	NOUN
ejpam-5036	409	2	c2n	c2n	NOUN
ejpam-5036	409	3	.	.	PUNCT
ejpam-5036	410	1	(	(	PUNCT
ejpam-5036	410	2	iii	iii	X
ejpam-5036	410	3	)	)	PUNCT
ejpam-5036	410	4	c1	c1	PROPN
ejpam-5036	410	5	−→	−→	PROPN
ejpam-5036	410	6	c1	c1	PROPN
ejpam-5036	410	7	+	+	CCONJ
ejpam-5036	410	8	1	1	NUM
ejpam-5036	410	9	λ	λ	NOUN
ejpam-5036	410	10	√	√	PROPN
ejpam-5036	410	11	2n−1	2n−1	NUM
ejpam-5036	410	12	cn+1	cn+1	NOUN
ejpam-5036	410	13	.	.	PUNCT
ejpam-5036	411	1	(	(	PUNCT
ejpam-5036	411	2	iv	iv	X
ejpam-5036	411	3	)	)	PUNCT
ejpam-5036	411	4	r2+i	r2+i	PROPN
ejpam-5036	411	5	−→	−→	NOUN
ejpam-5036	411	6	r2+i	r2+i	PROPN
ejpam-5036	411	7	−r2	−r2	PROPN
ejpam-5036	411	8	,	,	PUNCT
ejpam-5036	411	9	for	for	ADP
ejpam-5036	411	10	i	i	PROPN
ejpam-5036	411	11	=	=	SYM
ejpam-5036	411	12	1	1	NUM
ejpam-5036	411	13	,	,	PUNCT
ejpam-5036	411	14	2	2	NUM
ejpam-5036	411	15	,	,	PUNCT
ejpam-5036	411	16	.	.	PUNCT
ejpam-5036	411	17	.	.	PUNCT
ejpam-5036	412	1	.	.	PUNCT
ejpam-5036	413	1	,	,	PUNCT
ejpam-5036	413	2	n−	n−	NOUN
ejpam-5036	413	3	2	2	NUM
ejpam-5036	413	4	.	.	PUNCT
ejpam-5036	414	1	(	(	PUNCT
ejpam-5036	414	2	v	v	NOUN
ejpam-5036	414	3	)	)	PUNCT
ejpam-5036	414	4	c2	c2	PROPN
ejpam-5036	414	5	−→	−→	PROPN
ejpam-5036	414	6	c2	c2	PROPN
ejpam-5036	414	7	+	+	CCONJ
ejpam-5036	414	8	c2	c2	PROPN
ejpam-5036	414	9	+	+	PROPN
ejpam-5036	414	10	1	1	NUM
ejpam-5036	414	11	+	+	NUM
ejpam-5036	414	12	.	.	PUNCT
ejpam-5036	414	13	.	.	PUNCT
ejpam-5036	415	1	.+	.+	NOUN
ejpam-5036	415	2	cn	cn	PROPN
ejpam-5036	415	3	,	,	PUNCT
ejpam-5036	415	4	then	then	ADV
ejpam-5036	415	5	we	we	PRON
ejpam-5036	415	6	get	get	VERB
ejpam-5036	415	7	pna(γd2n	pna(γd2n	ADJ
ejpam-5036	415	8	)	)	PUNCT
ejpam-5036	415	9	(	(	PUNCT
ejpam-5036	415	10	λ	λ	NOUN
ejpam-5036	415	11	)	)	PUNCT
ejpam-5036	415	12	=	=	SYM
ejpam-5036	415	13	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5036	415	14	(	(	PUNCT
ejpam-5036	415	15	2n−1)λ2−n	2n−1)λ2−n	NUM
ejpam-5036	415	16	(	(	PUNCT
ejpam-5036	415	17	2n−1)λ	2n−1)λ	NUM
ejpam-5036	415	18	−	−	PROPN
ejpam-5036	415	19	n−1√	n−1√	SYM
ejpam-5036	415	20	(	(	PUNCT
ejpam-5036	415	21	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	415	22	)	)	PUNCT
ejpam-5036	415	23	−	−	PROPN
ejpam-5036	415	24	1√	1√	PROPN
ejpam-5036	415	25	(	(	PUNCT
ejpam-5036	415	26	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	415	27	)	)	PUNCT
ejpam-5036	415	28	j1×(n−2	j1×(n−2	NOUN
ejpam-5036	415	29	)	)	PUNCT
ejpam-5036	415	30	−	−	ADP
ejpam-5036	416	1	n√	n√	PRON
ejpam-5036	416	2	2n−1	2n−1	NUM
ejpam-5036	416	3	−	−	PROPN
ejpam-5036	416	4	1√	1√	PROPN
ejpam-5036	416	5	2n−1	2n−1	NUM
ejpam-5036	417	1	j1×n	j1×n	ADJ
ejpam-5036	417	2	−	−	PROPN
ejpam-5036	417	3	1√	1√	PROPN
ejpam-5036	417	4	(	(	PUNCT
ejpam-5036	417	5	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	417	6	)	)	PUNCT
ejpam-5036	417	7	λ−	λ−	PROPN
ejpam-5036	417	8	(	(	PUNCT
ejpam-5036	417	9	n−2	n−2	PROPN
ejpam-5036	417	10	)	)	PUNCT
ejpam-5036	417	11	n−1	n−1	PROPN
ejpam-5036	417	12	−	−	PROPN
ejpam-5036	417	13	1	1	NUM
ejpam-5036	417	14	n−1j1×(n−2	n−1j1×(n−2	PROPN
ejpam-5036	417	15	)	)	PUNCT
ejpam-5036	417	16	0	0	NUM
ejpam-5036	417	17	01×(n−1	01×(n−1	NUM
ejpam-5036	417	18	)	)	PUNCT
ejpam-5036	417	19	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	417	20	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	417	21	(	(	PUNCT
ejpam-5036	417	22	λ+	λ+	PUNCT
ejpam-5036	417	23	1	1	NUM
ejpam-5036	417	24	n−1	n−1	PROPN
ejpam-5036	417	25	)	)	PUNCT
ejpam-5036	418	1	in−2	in−2	NOUN
ejpam-5036	418	2	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	418	3	0(n−2)×(n−1	0(n−2)×(n−1	NUM
ejpam-5036	418	4	)	)	PUNCT
ejpam-5036	418	5	0	0	NUM
ejpam-5036	418	6	0	0	NUM
ejpam-5036	418	7	01×(n−2	01×(n−2	X
ejpam-5036	418	8	)	)	PUNCT
ejpam-5036	418	9	λ	λ	NOUN
ejpam-5036	418	10	01×(n−1	01×(n−1	NUM
ejpam-5036	418	11	)	)	PUNCT
ejpam-5036	418	12	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	418	13	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	419	1	0n−1	0n−1	NUM
ejpam-5036	419	2	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	420	1	λin−1	λin−1	PROPN
ejpam-5036	420	2	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5036	420	3	.	.	PUNCT
ejpam-5036	421	1	(	(	PUNCT
ejpam-5036	421	2	9	9	NUM
ejpam-5036	421	3	)	)	PUNCT
ejpam-5036	421	4	by	by	ADP
ejpam-5036	421	5	theorem	theorem	NOUN
ejpam-5036	421	6	2	2	NUM
ejpam-5036	421	7	,	,	PUNCT
ejpam-5036	421	8	we	we	PRON
ejpam-5036	421	9	can	can	AUX
ejpam-5036	421	10	obtain	obtain	VERB
ejpam-5036	421	11	pna(γd2n	pna(γd2n	NOUN
ejpam-5036	421	12	)	)	PUNCT
ejpam-5036	421	13	(	(	PUNCT
ejpam-5036	421	14	λ	λ	X
ejpam-5036	421	15	)	)	PUNCT
ejpam-5036	421	16	as	as	SCONJ
ejpam-5036	421	17	follows	follow	VERB
ejpam-5036	421	18	:	:	PUNCT
ejpam-5036	421	19	pna(γd2n	pna(γd2n	NOUN
ejpam-5036	421	20	)	)	PUNCT
ejpam-5036	421	21	(	(	PUNCT
ejpam-5036	421	22	λ	λ	NOUN
ejpam-5036	421	23	)	)	PUNCT
ejpam-5036	421	24	=	=	SYM
ejpam-5036	422	1	λn−1	λn−1	PROPN
ejpam-5036	422	2	(	(	PUNCT
ejpam-5036	422	3	λ+	λ+	NUM
ejpam-5036	422	4	1	1	NUM
ejpam-5036	422	5	n−	n−	NOUN
ejpam-5036	422	6	1	1	NUM
ejpam-5036	422	7	)	)	PUNCT
ejpam-5036	422	8	n−2	n−2	PROPN
ejpam-5036	422	9	(	(	PUNCT
ejpam-5036	422	10	λ3	λ3	PROPN
ejpam-5036	422	11	−	−	PROPN
ejpam-5036	422	12	(	(	PUNCT
ejpam-5036	422	13	n−	n−	NOUN
ejpam-5036	422	14	2	2	NUM
ejpam-5036	422	15	)	)	PUNCT
ejpam-5036	422	16	n−	n−	NOUN
ejpam-5036	422	17	1	1	NUM
ejpam-5036	422	18	λ2	λ2	NOUN
ejpam-5036	422	19	−	−	NOUN
ejpam-5036	422	20	n+	n+	NOUN
ejpam-5036	422	21	1	1	NUM
ejpam-5036	422	22	2n−	2n−	NUM
ejpam-5036	422	23	1	1	NUM
ejpam-5036	422	24	λ+	λ+	PUNCT
ejpam-5036	422	25	n(n−	n(n−	NOUN
ejpam-5036	422	26	2	2	NUM
ejpam-5036	422	27	)	)	PUNCT
ejpam-5036	422	28	(	(	PUNCT
ejpam-5036	422	29	n−	n−	NOUN
ejpam-5036	422	30	1)(2n−	1)(2n−	NUM
ejpam-5036	422	31	1	1	NUM
ejpam-5036	422	32	)	)	PUNCT
ejpam-5036	422	33	)	)	PUNCT
ejpam-5036	422	34	.	.	PUNCT
ejpam-5036	423	1	theorem	theorem	ADJ
ejpam-5036	423	2	7	7	NUM
ejpam-5036	423	3	.	.	PUNCT
ejpam-5036	424	1	let	let	VERB
ejpam-5036	424	2	γd2n	γd2n	PROPN
ejpam-5036	424	3	be	be	AUX
ejpam-5036	424	4	the	the	DET
ejpam-5036	424	5	power	power	NOUN
ejpam-5036	424	6	graph	graph	NOUN
ejpam-5036	424	7	for	for	ADP
ejpam-5036	424	8	d2n	d2n	NOUN
ejpam-5036	424	9	,	,	PUNCT
ejpam-5036	424	10	then	then	ADV
ejpam-5036	424	11	the	the	DET
ejpam-5036	424	12	characteristic	characteristic	ADJ
ejpam-5036	424	13	polynomial	polynomial	NOUN
ejpam-5036	424	14	of	of	ADP
ejpam-5036	424	15	nl(γd2n	nl(γd2n	NOUN
ejpam-5036	424	16	)	)	PUNCT
ejpam-5036	424	17	is	be	AUX
ejpam-5036	424	18	pnl(γd2n	pnl(γd2n	NOUN
ejpam-5036	424	19	)	)	PUNCT
ejpam-5036	424	20	(	(	PUNCT
ejpam-5036	424	21	λ	λ	X
ejpam-5036	424	22	)	)	PUNCT
ejpam-5036	424	23	=	=	SYM
ejpam-5036	424	24	λ(λ−	λ(λ−	PROPN
ejpam-5036	424	25	1)n−1	1)n−1	NUM
ejpam-5036	424	26	(	(	PUNCT
ejpam-5036	424	27	λ−	λ−	PROPN
ejpam-5036	424	28	1−	1−	NUM
ejpam-5036	424	29	1	1	NUM
ejpam-5036	424	30	n−	n−	NOUN
ejpam-5036	424	31	1	1	NUM
ejpam-5036	424	32	)	)	PUNCT
ejpam-5036	425	1	n−2	n−2	PROPN
ejpam-5036	425	2	(	(	PUNCT
ejpam-5036	425	3	λ2	λ2	NOUN
ejpam-5036	425	4	+	+	CCONJ
ejpam-5036	425	5	(	(	PUNCT
ejpam-5036	425	6	1−	1−	NUM
ejpam-5036	425	7	2n	2n	NUM
ejpam-5036	425	8	)	)	PUNCT
ejpam-5036	425	9	n−	n−	NOUN
ejpam-5036	425	10	1	1	NUM
ejpam-5036	425	11	λ+	λ+	PUNCT
ejpam-5036	425	12	n(n+	n(n+	NUM
ejpam-5036	425	13	1	1	NUM
ejpam-5036	425	14	)	)	PUNCT
ejpam-5036	425	15	(	(	PUNCT
ejpam-5036	425	16	2n−	2n−	PROPN
ejpam-5036	425	17	1)(n−	1)(n−	NUM
ejpam-5036	425	18	1	1	NUM
ejpam-5036	425	19	)	)	PUNCT
ejpam-5036	425	20	)	)	PUNCT
ejpam-5036	425	21	.	.	PUNCT
ejpam-5036	426	1	m.	m.	NOUN
ejpam-5036	426	2	u.	u.	PROPN
ejpam-5036	426	3	romdhini	romdhini	PROPN
ejpam-5036	426	4	et	et	PROPN
ejpam-5036	426	5	al	al	PROPN
ejpam-5036	426	6	.	.	PUNCT
ejpam-5036	426	7	/	/	SYM
ejpam-5036	426	8	eur	eur	PROPN
ejpam-5036	426	9	.	.	PUNCT
ejpam-5036	427	1	j.	j.	PROPN
ejpam-5036	427	2	pure	pure	PROPN
ejpam-5036	427	3	appl	appl	PROPN
ejpam-5036	427	4	.	.	PROPN
ejpam-5036	427	5	math	math	PROPN
ejpam-5036	427	6	,	,	PUNCT
ejpam-5036	427	7	17	17	NUM
ejpam-5036	427	8	(	(	PUNCT
ejpam-5036	427	9	2	2	NUM
ejpam-5036	427	10	)	)	PUNCT
ejpam-5036	427	11	(	(	PUNCT
ejpam-5036	427	12	2024	2024	NUM
ejpam-5036	427	13	)	)	PUNCT
ejpam-5036	427	14	,	,	PUNCT
ejpam-5036	427	15	591	591	NUM
ejpam-5036	427	16	-	-	SYM
ejpam-5036	427	17	603	603	NUM
ejpam-5036	427	18	600	600	NUM
ejpam-5036	427	19	proof	proof	NOUN
ejpam-5036	427	20	.	.	PUNCT
ejpam-5036	428	1	by	by	ADP
ejpam-5036	428	2	definition	definition	NOUN
ejpam-5036	428	3	6	6	NUM
ejpam-5036	428	4	,	,	PUNCT
ejpam-5036	428	5	and	and	CCONJ
ejpam-5036	428	6	equations	equation	NOUN
ejpam-5036	428	7	6	6	NUM
ejpam-5036	428	8	and	and	CCONJ
ejpam-5036	428	9	7	7	NUM
ejpam-5036	428	10	,	,	PUNCT
ejpam-5036	428	11	we	we	PRON
ejpam-5036	428	12	can	can	AUX
ejpam-5036	428	13	construct	construct	VERB
ejpam-5036	428	14	nl(γd2n	nl(γd2n	NOUN
ejpam-5036	428	15	)	)	PUNCT
ejpam-5036	428	16	of	of	ADP
ejpam-5036	428	17	the	the	DET
ejpam-5036	428	18	size	size	NOUN
ejpam-5036	428	19	2n×	2n×	NOUN
ejpam-5036	428	20	2n	2n	NUM
ejpam-5036	428	21	as	as	SCONJ
ejpam-5036	428	22	follows	follow	VERB
ejpam-5036	428	23	:	:	PUNCT
ejpam-5036	428	24	e	e	X
ejpam-5036	428	25	a	a	DET
ejpam-5036	428	26	a2	a2	PROPN
ejpam-5036	428	27	.	.	PUNCT
ejpam-5036	428	28	.	.	PUNCT
ejpam-5036	428	29	.	.	PUNCT
ejpam-5036	429	1	an−1	an−1	PROPN
ejpam-5036	429	2	b	b	PROPN
ejpam-5036	429	3	ab	ab	PROPN
ejpam-5036	429	4	.	.	PUNCT
ejpam-5036	429	5	.	.	PUNCT
ejpam-5036	429	6	.	.	PUNCT
ejpam-5036	430	1	an−1b	an−1b	NOUN
ejpam-5036	430	2			PROPN
ejpam-5036	430	3	e	e	PROPN
ejpam-5036	430	4	1	1	NUM
ejpam-5036	430	5	−	−	PROPN
ejpam-5036	430	6	1√	1√	PROPN
ejpam-5036	430	7	(	(	PUNCT
ejpam-5036	430	8	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	430	9	)	)	PUNCT
ejpam-5036	430	10	−	−	PROPN
ejpam-5036	430	11	1√	1√	PROPN
ejpam-5036	430	12	(	(	PUNCT
ejpam-5036	430	13	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	430	14	)	)	PUNCT
ejpam-5036	430	15	.	.	PUNCT
ejpam-5036	430	16	.	.	PUNCT
ejpam-5036	430	17	.	.	PUNCT
ejpam-5036	431	1	−	−	PROPN
ejpam-5036	431	2	1√	1√	PROPN
ejpam-5036	431	3	(	(	PUNCT
ejpam-5036	431	4	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	431	5	)	)	PUNCT
ejpam-5036	431	6	−	−	PROPN
ejpam-5036	431	7	1√	1√	PROPN
ejpam-5036	431	8	2n−1	2n−1	NUM
ejpam-5036	431	9	−	−	NUM
ejpam-5036	431	10	1√	1√	PROPN
ejpam-5036	431	11	2n−1	2n−1	PROPN
ejpam-5036	431	12	.	.	PUNCT
ejpam-5036	431	13	.	.	PUNCT
ejpam-5036	431	14	.	.	PUNCT
ejpam-5036	432	1	−	−	PROPN
ejpam-5036	433	1	1√	1√	PROPN
ejpam-5036	433	2	2n−1	2n−1	NUM
ejpam-5036	433	3	a	a	DET
ejpam-5036	433	4	−	−	PROPN
ejpam-5036	433	5	1√	1√	PROPN
ejpam-5036	433	6	(	(	PUNCT
ejpam-5036	433	7	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	433	8	)	)	PUNCT
ejpam-5036	433	9	1	1	NUM
ejpam-5036	433	10	−	−	PROPN
ejpam-5036	433	11	1	1	NUM
ejpam-5036	433	12	n−1	n−1	PROPN
ejpam-5036	433	13	.	.	PUNCT
ejpam-5036	433	14	.	.	PUNCT
ejpam-5036	433	15	.	.	PUNCT
ejpam-5036	434	1	−	−	NOUN
ejpam-5036	434	2	1	1	NUM
ejpam-5036	434	3	n−1	n−1	PROPN
ejpam-5036	434	4	0	0	NUM
ejpam-5036	434	5	0	0	NUM
ejpam-5036	434	6	.	.	PUNCT
ejpam-5036	434	7	.	.	PUNCT
ejpam-5036	435	1	.	.	PUNCT
ejpam-5036	436	1	0	0	NUM
ejpam-5036	437	1	a2	a2	PROPN
ejpam-5036	437	2	−	−	PROPN
ejpam-5036	437	3	1√	1√	PROPN
ejpam-5036	437	4	(	(	PUNCT
ejpam-5036	437	5	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	437	6	)	)	PUNCT
ejpam-5036	437	7	−	−	PROPN
ejpam-5036	437	8	1	1	NUM
ejpam-5036	437	9	n−1	n−1	PROPN
ejpam-5036	437	10	1	1	NUM
ejpam-5036	437	11	.	.	PUNCT
ejpam-5036	437	12	.	.	PUNCT
ejpam-5036	437	13	.	.	PUNCT
ejpam-5036	438	1	−	−	NOUN
ejpam-5036	438	2	1	1	NUM
ejpam-5036	438	3	n−1	n−1	PROPN
ejpam-5036	438	4	0	0	NUM
ejpam-5036	438	5	0	0	NUM
ejpam-5036	438	6	.	.	PUNCT
ejpam-5036	438	7	.	.	PUNCT
ejpam-5036	439	1	.	.	PUNCT
ejpam-5036	440	1	0	0	NUM
ejpam-5036	440	2	...	...	PUNCT
ejpam-5036	440	3	...	...	PUNCT
ejpam-5036	440	4	...	...	PUNCT
ejpam-5036	440	5	...	...	PUNCT
ejpam-5036	440	6	.	.	PUNCT
ejpam-5036	440	7	.	.	PUNCT
ejpam-5036	441	1	.	.	PUNCT
ejpam-5036	441	2	...	...	PUNCT
ejpam-5036	442	1	...	...	PUNCT
ejpam-5036	442	2	...	...	PUNCT
ejpam-5036	442	3	.	.	PUNCT
ejpam-5036	442	4	.	.	PUNCT
ejpam-5036	443	1	.	.	PUNCT
ejpam-5036	444	1	...	...	PUNCT
ejpam-5036	445	1	an−1	an−1	ADJ
ejpam-5036	445	2	−	−	PROPN
ejpam-5036	445	3	1√	1√	PROPN
ejpam-5036	445	4	(	(	PUNCT
ejpam-5036	445	5	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	445	6	)	)	PUNCT
ejpam-5036	445	7	−	−	PROPN
ejpam-5036	445	8	1	1	NUM
ejpam-5036	445	9	n−1	n−1	PROPN
ejpam-5036	445	10	−	−	PROPN
ejpam-5036	445	11	1	1	NUM
ejpam-5036	445	12	n−1	n−1	PROPN
ejpam-5036	445	13	.	.	PUNCT
ejpam-5036	445	14	.	.	PUNCT
ejpam-5036	445	15	.	.	PUNCT
ejpam-5036	446	1	1	1	NUM
ejpam-5036	446	2	0	0	NUM
ejpam-5036	446	3	0	0	NUM
ejpam-5036	446	4	.	.	PUNCT
ejpam-5036	446	5	.	.	PUNCT
ejpam-5036	446	6	.	.	PUNCT
ejpam-5036	447	1	0	0	NUM
ejpam-5036	448	1	b	b	X
ejpam-5036	448	2	−	−	PROPN
ejpam-5036	448	3	1√	1√	PROPN
ejpam-5036	448	4	2n−1	2n−1	NUM
ejpam-5036	448	5	0	0	NUM
ejpam-5036	448	6	0	0	NUM
ejpam-5036	448	7	.	.	PUNCT
ejpam-5036	448	8	.	.	PUNCT
ejpam-5036	448	9	.	.	PUNCT
ejpam-5036	449	1	0	0	NUM
ejpam-5036	450	1	1	1	NUM
ejpam-5036	450	2	0	0	NUM
ejpam-5036	450	3	.	.	PUNCT
ejpam-5036	450	4	.	.	PUNCT
ejpam-5036	451	1	.	.	PUNCT
ejpam-5036	451	2	0	0	NUM
ejpam-5036	452	1	ab	ab	PROPN
ejpam-5036	452	2	−	−	PROPN
ejpam-5036	452	3	1√	1√	PROPN
ejpam-5036	452	4	2n−1	2n−1	NUM
ejpam-5036	452	5	0	0	NUM
ejpam-5036	452	6	0	0	NUM
ejpam-5036	452	7	.	.	PUNCT
ejpam-5036	452	8	.	.	PUNCT
ejpam-5036	453	1	.	.	PUNCT
ejpam-5036	454	1	0	0	NUM
ejpam-5036	454	2	0	0	NUM
ejpam-5036	454	3	1	1	NUM
ejpam-5036	454	4	.	.	PUNCT
ejpam-5036	454	5	.	.	PUNCT
ejpam-5036	455	1	.	.	PUNCT
ejpam-5036	456	1	0	0	NUM
ejpam-5036	456	2	...	...	PUNCT
ejpam-5036	456	3	...	...	PUNCT
ejpam-5036	456	4	...	...	PUNCT
ejpam-5036	456	5	...	...	PUNCT
ejpam-5036	456	6	.	.	PUNCT
ejpam-5036	456	7	.	.	PUNCT
ejpam-5036	457	1	.	.	PUNCT
ejpam-5036	457	2	...	...	PUNCT
ejpam-5036	458	1	...	...	PUNCT
ejpam-5036	458	2	...	...	PUNCT
ejpam-5036	458	3	.	.	PUNCT
ejpam-5036	458	4	.	.	PUNCT
ejpam-5036	458	5	.	.	PUNCT
ejpam-5036	459	1	...	...	PUNCT
ejpam-5036	460	1	an−1b	an−1b	PUNCT
ejpam-5036	461	1	−	−	PROPN
ejpam-5036	461	2	1√	1√	PROPN
ejpam-5036	461	3	2n−1	2n−1	NUM
ejpam-5036	461	4	0	0	NUM
ejpam-5036	461	5	0	0	NUM
ejpam-5036	461	6	.	.	PUNCT
ejpam-5036	461	7	.	.	PUNCT
ejpam-5036	461	8	.	.	PUNCT
ejpam-5036	462	1	0	0	NUM
ejpam-5036	463	1	0	0	NUM
ejpam-5036	463	2	0	0	NUM
ejpam-5036	463	3	.	.	PUNCT
ejpam-5036	463	4	.	.	PUNCT
ejpam-5036	463	5	.	.	PUNCT
ejpam-5036	464	1	1	1	X
ejpam-5036	464	2	.	.	PUNCT
ejpam-5036	465	1	nl(γd2n	nl(γd2n	NOUN
ejpam-5036	465	2	)	)	PUNCT
ejpam-5036	465	3	can	can	AUX
ejpam-5036	465	4	be	be	AUX
ejpam-5036	465	5	partitioned	partition	VERB
ejpam-5036	465	6	into	into	ADP
ejpam-5036	465	7	nine	nine	NUM
ejpam-5036	465	8	block	block	NOUN
ejpam-5036	465	9	matrices	matrix	NOUN
ejpam-5036	465	10	as	as	SCONJ
ejpam-5036	465	11	follows	follow	VERB
ejpam-5036	465	12	:	:	PUNCT
ejpam-5036	465	13	nl(γd2n	nl(γd2n	NOUN
ejpam-5036	465	14	)	)	PUNCT
ejpam-5036	466	1	=	=	SYM
ejpam-5036	466	2			NOUN
ejpam-5036	467	1	1	1	NUM
ejpam-5036	467	2	−	−	PROPN
ejpam-5036	467	3	1√	1√	PROPN
ejpam-5036	467	4	(	(	PUNCT
ejpam-5036	467	5	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	467	6	)	)	PUNCT
ejpam-5036	467	7	j1×(n−1	j1×(n−1	PROPN
ejpam-5036	467	8	)	)	PUNCT
ejpam-5036	467	9	−	−	PROPN
ejpam-5036	467	10	1√	1√	PROPN
ejpam-5036	467	11	2n−1	2n−1	NUM
ejpam-5036	468	1	j1×n	j1×n	ADJ
ejpam-5036	468	2	−	−	PROPN
ejpam-5036	468	3	1√	1√	PROPN
ejpam-5036	468	4	(	(	PUNCT
ejpam-5036	468	5	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	468	6	)	)	PUNCT
ejpam-5036	468	7	j(n−1)×1	j(n−1)×1	NOUN
ejpam-5036	468	8	(	(	PUNCT
ejpam-5036	468	9	1	1	NUM
ejpam-5036	468	10	+	+	SYM
ejpam-5036	468	11	1	1	NUM
ejpam-5036	468	12	n−1	n−1	PROPN
ejpam-5036	468	13	)	)	PUNCT
ejpam-5036	468	14	in−1	in−1	ADJ
ejpam-5036	468	15	−	−	PROPN
ejpam-5036	468	16	1	1	NUM
ejpam-5036	468	17	n−1jn−1	n−1jn−1	NOUN
ejpam-5036	469	1	0(n−1)×n	0(n−1)×n	NUM
ejpam-5036	470	1	−	−	PROPN
ejpam-5036	470	2	1√	1√	PROPN
ejpam-5036	470	3	2n−1	2n−1	NUM
ejpam-5036	470	4	jn×1	jn×1	NOUN
ejpam-5036	470	5	0n×(n−1	0n×(n−1	NUM
ejpam-5036	470	6	)	)	PUNCT
ejpam-5036	470	7	in	in	ADP
ejpam-5036	470	8			NOUN
ejpam-5036	470	9	.	.	PUNCT
ejpam-5036	471	1	the	the	DET
ejpam-5036	471	2	characteristic	characteristic	ADJ
ejpam-5036	471	3	polynomial	polynomial	NOUN
ejpam-5036	471	4	of	of	ADP
ejpam-5036	471	5	nl(γd2n	nl(γd2n	NOUN
ejpam-5036	471	6	)	)	PUNCT
ejpam-5036	471	7	is	be	AUX
ejpam-5036	471	8	pnl(γd2n	pnl(γd2n	NOUN
ejpam-5036	471	9	)	)	PUNCT
ejpam-5036	471	10	(	(	PUNCT
ejpam-5036	471	11	λ	λ	X
ejpam-5036	471	12	)	)	PUNCT
ejpam-5036	471	13	=	=	PUNCT
ejpam-5036	472	1	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-5036	472	2	λ−	λ−	PROPN
ejpam-5036	472	3	1	1	NUM
ejpam-5036	472	4	1√	1√	PROPN
ejpam-5036	472	5	(	(	PUNCT
ejpam-5036	472	6	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	472	7	)	)	PUNCT
ejpam-5036	472	8	j1×(n−1	j1×(n−1	PROPN
ejpam-5036	472	9	)	)	PUNCT
ejpam-5036	472	10	1√	1√	PROPN
ejpam-5036	472	11	2n−1	2n−1	NUM
ejpam-5036	472	12	j1×n	j1×n	PROPN
ejpam-5036	472	13	1√	1√	PROPN
ejpam-5036	472	14	(	(	PUNCT
ejpam-5036	472	15	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	472	16	)	)	PUNCT
ejpam-5036	472	17	j(n−1)×1	j(n−1)×1	NOUN
ejpam-5036	472	18	(	(	PUNCT
ejpam-5036	472	19	λ−	λ−	PROPN
ejpam-5036	472	20	1−	1−	NUM
ejpam-5036	472	21	1	1	NUM
ejpam-5036	472	22	n−1	n−1	PROPN
ejpam-5036	472	23	)	)	PUNCT
ejpam-5036	472	24	in−1	in−1	PROPN
ejpam-5036	473	1	+	+	CCONJ
ejpam-5036	473	2	1	1	NUM
ejpam-5036	473	3	n−1jn−1	n−1jn−1	NOUN
ejpam-5036	473	4	0(n−1)×n	0(n−1)×n	NUM
ejpam-5036	473	5	1√	1√	PROPN
ejpam-5036	473	6	2n−1	2n−1	NUM
ejpam-5036	473	7	jn×1	jn×1	VERB
ejpam-5036	473	8	0n×(n−1	0n×(n−1	NUM
ejpam-5036	473	9	)	)	PUNCT
ejpam-5036	473	10	(	(	PUNCT
ejpam-5036	473	11	λ−	λ−	PROPN
ejpam-5036	473	12	1)in	1)in	PROPN
ejpam-5036	473	13	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-5036	473	14	.	.	PUNCT
ejpam-5036	474	1	(	(	PUNCT
ejpam-5036	474	2	10	10	NUM
ejpam-5036	474	3	)	)	PUNCT
ejpam-5036	474	4	by	by	ADP
ejpam-5036	474	5	applying	apply	VERB
ejpam-5036	474	6	row	row	NOUN
ejpam-5036	474	7	and	and	CCONJ
ejpam-5036	474	8	column	column	NOUN
ejpam-5036	474	9	operations	operation	NOUN
ejpam-5036	474	10	into	into	ADP
ejpam-5036	474	11	equation	equation	NOUN
ejpam-5036	474	12	10	10	NUM
ejpam-5036	474	13	:	:	PUNCT
ejpam-5036	474	14	(	(	PUNCT
ejpam-5036	474	15	i	i	NOUN
ejpam-5036	474	16	)	)	PUNCT
ejpam-5036	474	17	rn+1+i	rn+1+i	NOUN
ejpam-5036	474	18	−→	−→	ADJ
ejpam-5036	474	19	rn+1+i	rn+1+i	NOUN
ejpam-5036	474	20	−rn+1	−rn+1	VERB
ejpam-5036	474	21	,	,	PUNCT
ejpam-5036	474	22	for	for	ADP
ejpam-5036	474	23	i	i	PROPN
ejpam-5036	474	24	=	=	SYM
ejpam-5036	474	25	1	1	NUM
ejpam-5036	474	26	,	,	PUNCT
ejpam-5036	474	27	2	2	NUM
ejpam-5036	474	28	,	,	PUNCT
ejpam-5036	474	29	.	.	PUNCT
ejpam-5036	474	30	.	.	PUNCT
ejpam-5036	475	1	.	.	PUNCT
ejpam-5036	476	1	,	,	PUNCT
ejpam-5036	476	2	n−	n−	NOUN
ejpam-5036	476	3	1	1	NUM
ejpam-5036	476	4	.	.	PUNCT
ejpam-5036	476	5	(	(	PUNCT
ejpam-5036	476	6	ii	ii	NOUN
ejpam-5036	476	7	)	)	PUNCT
ejpam-5036	476	8	cn+1	cn+1	VERB
ejpam-5036	476	9	−→	−→	NOUN
ejpam-5036	476	10	cn+1	cn+1	NOUN
ejpam-5036	476	11	+	+	CCONJ
ejpam-5036	476	12	cn+2	cn+2	PRON
ejpam-5036	477	1	+	+	CCONJ
ejpam-5036	477	2	.	.	PUNCT
ejpam-5036	477	3	.	.	PUNCT
ejpam-5036	478	1	.+	.+	NOUN
ejpam-5036	478	2	c2n	c2n	NOUN
ejpam-5036	478	3	.	.	PUNCT
ejpam-5036	479	1	(	(	PUNCT
ejpam-5036	479	2	iii	iii	X
ejpam-5036	479	3	)	)	PUNCT
ejpam-5036	479	4	c1	c1	PROPN
ejpam-5036	479	5	−→	−→	PROPN
ejpam-5036	479	6	c1	c1	PROPN
ejpam-5036	479	7	−	−	PROPN
ejpam-5036	479	8	1	1	NUM
ejpam-5036	479	9	(	(	PUNCT
ejpam-5036	479	10	λ−1	λ−1	PROPN
ejpam-5036	479	11	)	)	PUNCT
ejpam-5036	479	12	√	√	ADP
ejpam-5036	479	13	2n−1	2n−1	NUM
ejpam-5036	479	14	cn+1	cn+1	NOUN
ejpam-5036	479	15	.	.	PUNCT
ejpam-5036	480	1	(	(	PUNCT
ejpam-5036	480	2	iv	iv	X
ejpam-5036	480	3	)	)	PUNCT
ejpam-5036	480	4	r2+i	r2+i	PROPN
ejpam-5036	480	5	−→	−→	NOUN
ejpam-5036	480	6	r2+i	r2+i	PROPN
ejpam-5036	480	7	−r2	−r2	PROPN
ejpam-5036	480	8	,	,	PUNCT
ejpam-5036	480	9	for	for	ADP
ejpam-5036	480	10	i	i	PROPN
ejpam-5036	480	11	=	=	SYM
ejpam-5036	480	12	1	1	NUM
ejpam-5036	480	13	,	,	PUNCT
ejpam-5036	480	14	2	2	NUM
ejpam-5036	480	15	,	,	PUNCT
ejpam-5036	480	16	.	.	PUNCT
ejpam-5036	480	17	.	.	PUNCT
ejpam-5036	481	1	.	.	PUNCT
ejpam-5036	482	1	,	,	PUNCT
ejpam-5036	482	2	n−	n−	NOUN
ejpam-5036	482	3	2	2	NUM
ejpam-5036	482	4	.	.	PUNCT
ejpam-5036	483	1	(	(	PUNCT
ejpam-5036	483	2	v	v	NOUN
ejpam-5036	483	3	)	)	PUNCT
ejpam-5036	483	4	c2	c2	PROPN
ejpam-5036	483	5	−→	−→	PROPN
ejpam-5036	483	6	c2	c2	PROPN
ejpam-5036	483	7	+	+	CCONJ
ejpam-5036	483	8	c2	c2	PROPN
ejpam-5036	483	9	+	+	PROPN
ejpam-5036	483	10	1	1	NUM
ejpam-5036	483	11	+	+	NUM
ejpam-5036	483	12	.	.	PUNCT
ejpam-5036	483	13	.	.	PUNCT
ejpam-5036	484	1	.+	.+	NOUN
ejpam-5036	484	2	cn	cn	PROPN
ejpam-5036	484	3	,	,	PUNCT
ejpam-5036	484	4	then	then	ADV
ejpam-5036	484	5	we	we	PRON
ejpam-5036	484	6	get	get	VERB
ejpam-5036	484	7	pnl(γd2n	pnl(γd2n	NOUN
ejpam-5036	484	8	)	)	PUNCT
ejpam-5036	484	9	(	(	PUNCT
ejpam-5036	484	10	λ	λ	NOUN
ejpam-5036	484	11	)	)	PUNCT
ejpam-5036	484	12	=	=	SYM
ejpam-5036	484	13	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	ADJ
ejpam-5036	484	14	−n	−n	ADJ
ejpam-5036	484	15	(	(	PUNCT
ejpam-5036	484	16	λ−1)(2n−1	λ−1)(2n−1	PROPN
ejpam-5036	484	17	)	)	PUNCT
ejpam-5036	484	18	+	+	CCONJ
ejpam-5036	484	19	λ−	λ−	PROPN
ejpam-5036	484	20	1	1	NUM
ejpam-5036	484	21	n−1√	n−1√	NOUN
ejpam-5036	484	22	(	(	PUNCT
ejpam-5036	484	23	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	484	24	)	)	PUNCT
ejpam-5036	484	25	1√	1√	NOUN
ejpam-5036	484	26	(	(	PUNCT
ejpam-5036	484	27	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	484	28	)	)	PUNCT
ejpam-5036	484	29	j1×(n−2	j1×(n−2	NOUN
ejpam-5036	484	30	)	)	PUNCT
ejpam-5036	484	31	n√	n√	PROPN
ejpam-5036	484	32	2n−1	2n−1	NUM
ejpam-5036	484	33	1√	1√	PROPN
ejpam-5036	484	34	2n−1	2n−1	NUM
ejpam-5036	485	1	j1×n	j1×n	PROPN
ejpam-5036	485	2	1√	1√	PROPN
ejpam-5036	485	3	(	(	PUNCT
ejpam-5036	485	4	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	485	5	)	)	PUNCT
ejpam-5036	485	6	λ−	λ−	PROPN
ejpam-5036	485	7	1	1	NUM
ejpam-5036	485	8	+	+	CCONJ
ejpam-5036	485	9	(	(	PUNCT
ejpam-5036	485	10	n−2	n−2	PROPN
ejpam-5036	485	11	)	)	PUNCT
ejpam-5036	485	12	n−1	n−1	PROPN
ejpam-5036	485	13	1	1	NUM
ejpam-5036	485	14	n−1j1×(n−2	n−1j1×(n−2	PROPN
ejpam-5036	485	15	)	)	PUNCT
ejpam-5036	485	16	0	0	NUM
ejpam-5036	485	17	01×(n−1	01×(n−1	NUM
ejpam-5036	485	18	)	)	PUNCT
ejpam-5036	485	19	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	485	20	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	486	1	(	(	PUNCT
ejpam-5036	486	2	λ−	λ−	PROPN
ejpam-5036	486	3	1−	1−	NUM
ejpam-5036	486	4	1	1	NUM
ejpam-5036	486	5	n−1	n−1	PROPN
ejpam-5036	486	6	)	)	PUNCT
ejpam-5036	486	7	in−2	in−2	NOUN
ejpam-5036	486	8	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	486	9	0(n−2)×(n−1	0(n−2)×(n−1	NUM
ejpam-5036	486	10	)	)	PUNCT
ejpam-5036	486	11	0	0	NUM
ejpam-5036	486	12	0	0	NUM
ejpam-5036	486	13	01×(n−2	01×(n−2	X
ejpam-5036	486	14	)	)	PUNCT
ejpam-5036	486	15	λ−	λ−	PROPN
ejpam-5036	486	16	1	1	NUM
ejpam-5036	486	17	01×(n−1	01×(n−1	NUM
ejpam-5036	486	18	)	)	PUNCT
ejpam-5036	486	19	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	486	20	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	487	1	0n−1	0n−1	NUM
ejpam-5036	487	2	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	488	1	(	(	PUNCT
ejpam-5036	488	2	λ−	λ−	PROPN
ejpam-5036	488	3	1)in−1	1)in−1	PROPN
ejpam-5036	488	4	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5036	488	5	.	.	PUNCT
ejpam-5036	489	1	(	(	PUNCT
ejpam-5036	489	2	11	11	NUM
ejpam-5036	489	3	)	)	PUNCT
ejpam-5036	489	4	m.	m.	NOUN
ejpam-5036	489	5	u.	u.	PROPN
ejpam-5036	489	6	romdhini	romdhini	PROPN
ejpam-5036	489	7	et	et	PROPN
ejpam-5036	489	8	al	al	PROPN
ejpam-5036	489	9	.	.	PUNCT
ejpam-5036	489	10	/	/	SYM
ejpam-5036	489	11	eur	eur	PROPN
ejpam-5036	489	12	.	.	PUNCT
ejpam-5036	490	1	j.	j.	PROPN
ejpam-5036	490	2	pure	pure	PROPN
ejpam-5036	490	3	appl	appl	PROPN
ejpam-5036	490	4	.	.	PROPN
ejpam-5036	490	5	math	math	PROPN
ejpam-5036	490	6	,	,	PUNCT
ejpam-5036	490	7	17	17	NUM
ejpam-5036	490	8	(	(	PUNCT
ejpam-5036	490	9	2	2	NUM
ejpam-5036	490	10	)	)	PUNCT
ejpam-5036	490	11	(	(	PUNCT
ejpam-5036	490	12	2024	2024	NUM
ejpam-5036	490	13	)	)	PUNCT
ejpam-5036	490	14	,	,	PUNCT
ejpam-5036	490	15	591	591	NUM
ejpam-5036	490	16	-	-	SYM
ejpam-5036	490	17	603	603	NUM
ejpam-5036	490	18	601	601	NUM
ejpam-5036	490	19	consequently	consequently	ADV
ejpam-5036	490	20	,	,	PUNCT
ejpam-5036	490	21	based	base	VERB
ejpam-5036	490	22	on	on	ADP
ejpam-5036	490	23	theorem	theorem	NOUN
ejpam-5036	490	24	2	2	NUM
ejpam-5036	490	25	,	,	PUNCT
ejpam-5036	490	26	we	we	PRON
ejpam-5036	490	27	can	can	AUX
ejpam-5036	490	28	obtain	obtain	VERB
ejpam-5036	490	29	pnl(γd2n	pnl(γd2n	NOUN
ejpam-5036	490	30	)	)	PUNCT
ejpam-5036	490	31	(	(	PUNCT
ejpam-5036	490	32	λ	λ	X
ejpam-5036	490	33	)	)	PUNCT
ejpam-5036	490	34	as	as	SCONJ
ejpam-5036	490	35	follows	follow	VERB
ejpam-5036	490	36	:	:	PUNCT
ejpam-5036	490	37	pnl(γd2n	pnl(γd2n	NOUN
ejpam-5036	490	38	)	)	PUNCT
ejpam-5036	490	39	(	(	PUNCT
ejpam-5036	490	40	λ	λ	X
ejpam-5036	490	41	)	)	PUNCT
ejpam-5036	490	42	=	=	SYM
ejpam-5036	490	43	λ(λ−	λ(λ−	PROPN
ejpam-5036	490	44	1)n−1	1)n−1	NUM
ejpam-5036	490	45	(	(	PUNCT
ejpam-5036	490	46	λ−	λ−	PROPN
ejpam-5036	490	47	1−	1−	NUM
ejpam-5036	490	48	1	1	NUM
ejpam-5036	490	49	n−	n−	NOUN
ejpam-5036	490	50	1	1	NUM
ejpam-5036	490	51	)	)	PUNCT
ejpam-5036	491	1	n−2	n−2	PROPN
ejpam-5036	491	2	(	(	PUNCT
ejpam-5036	491	3	λ2	λ2	NOUN
ejpam-5036	491	4	+	+	CCONJ
ejpam-5036	491	5	(	(	PUNCT
ejpam-5036	491	6	1−	1−	NUM
ejpam-5036	491	7	2n	2n	NUM
ejpam-5036	491	8	)	)	PUNCT
ejpam-5036	491	9	n−	n−	NOUN
ejpam-5036	491	10	1	1	NUM
ejpam-5036	491	11	λ+	λ+	PUNCT
ejpam-5036	491	12	n(n+	n(n+	NUM
ejpam-5036	491	13	1	1	NUM
ejpam-5036	491	14	)	)	PUNCT
ejpam-5036	491	15	(	(	PUNCT
ejpam-5036	491	16	2n−	2n−	PROPN
ejpam-5036	491	17	1)(n−	1)(n−	NUM
ejpam-5036	491	18	1	1	NUM
ejpam-5036	491	19	)	)	PUNCT
ejpam-5036	491	20	)	)	PUNCT
ejpam-5036	491	21	.	.	PUNCT
ejpam-5036	492	1	theorem	theorem	ADJ
ejpam-5036	492	2	8	8	NUM
ejpam-5036	492	3	.	.	PUNCT
ejpam-5036	493	1	let	let	VERB
ejpam-5036	493	2	γd2n	γd2n	PROPN
ejpam-5036	493	3	be	be	AUX
ejpam-5036	493	4	the	the	DET
ejpam-5036	493	5	power	power	NOUN
ejpam-5036	493	6	graph	graph	NOUN
ejpam-5036	493	7	for	for	ADP
ejpam-5036	493	8	d2n	d2n	NOUN
ejpam-5036	493	9	,	,	PUNCT
ejpam-5036	493	10	then	then	ADV
ejpam-5036	493	11	the	the	DET
ejpam-5036	493	12	characteristic	characteristic	ADJ
ejpam-5036	493	13	polynomial	polynomial	NOUN
ejpam-5036	493	14	of	of	ADP
ejpam-5036	493	15	nsl(γd2n	nsl(γd2n	NOUN
ejpam-5036	493	16	)	)	PUNCT
ejpam-5036	493	17	is	be	AUX
ejpam-5036	493	18	pnsl(γd2n	pnsl(γd2n	NOUN
ejpam-5036	493	19	)	)	PUNCT
ejpam-5036	493	20	(	(	PUNCT
ejpam-5036	493	21	λ	λ	NOUN
ejpam-5036	493	22	)	)	PUNCT
ejpam-5036	493	23	=	=	SYM
ejpam-5036	494	1	(	(	PUNCT
ejpam-5036	494	2	λ−1)n−1	λ−1)n−1	PROPN
ejpam-5036	494	3	(	(	PUNCT
ejpam-5036	494	4	λ−	λ−	PROPN
ejpam-5036	494	5	1	1	NUM
ejpam-5036	494	6	+	+	SYM
ejpam-5036	494	7	1	1	NUM
ejpam-5036	494	8	n−	n−	NOUN
ejpam-5036	494	9	1	1	NUM
ejpam-5036	494	10	)	)	PUNCT
ejpam-5036	494	11	n−2	n−2	PROPN
ejpam-5036	494	12	(	(	PUNCT
ejpam-5036	494	13	λ3	λ3	PROPN
ejpam-5036	494	14	+	+	PROPN
ejpam-5036	494	15	(	(	PUNCT
ejpam-5036	494	16	5−	5−	NUM
ejpam-5036	494	17	4n	4n	NOUN
ejpam-5036	494	18	)	)	PUNCT
ejpam-5036	494	19	n−	n−	NOUN
ejpam-5036	494	20	1	1	NUM
ejpam-5036	494	21	λ2	λ2	NOUN
ejpam-5036	494	22	+	+	CCONJ
ejpam-5036	494	23	(	(	PUNCT
ejpam-5036	494	24	9n2	9n2	NUM
ejpam-5036	494	25	−	−	PROPN
ejpam-5036	494	26	19n+	19n+	NUM
ejpam-5036	494	27	8)	8)	NUM
ejpam-5036	494	28	(	(	PUNCT
ejpam-5036	494	29	2n−	2n−	PROPN
ejpam-5036	494	30	1)(n−	1)(n−	NUM
ejpam-5036	494	31	1	1	NUM
ejpam-5036	494	32	)	)	PUNCT
ejpam-5036	494	33	λ−	λ−	PROPN
ejpam-5036	494	34	2(n−	2(n−	NUM
ejpam-5036	494	35	2	2	NUM
ejpam-5036	494	36	)	)	PUNCT
ejpam-5036	494	37	2n−	2n−	PROPN
ejpam-5036	494	38	1	1	NUM
ejpam-5036	494	39	)	)	PUNCT
ejpam-5036	494	40	.	.	PUNCT
ejpam-5036	495	1	proof	proof	NOUN
ejpam-5036	495	2	.	.	PUNCT
ejpam-5036	496	1	by	by	ADP
ejpam-5036	496	2	definition	definition	NOUN
ejpam-5036	496	3	7	7	NUM
ejpam-5036	496	4	,	,	PUNCT
ejpam-5036	496	5	and	and	CCONJ
ejpam-5036	496	6	equations	equation	NOUN
ejpam-5036	496	7	6	6	NUM
ejpam-5036	496	8	and	and	CCONJ
ejpam-5036	496	9	7	7	NUM
ejpam-5036	496	10	,	,	PUNCT
ejpam-5036	496	11	we	we	PRON
ejpam-5036	496	12	can	can	AUX
ejpam-5036	496	13	construct	construct	VERB
ejpam-5036	496	14	nsl(γd2n	nsl(γd2n	NOUN
ejpam-5036	496	15	)	)	PUNCT
ejpam-5036	496	16	of	of	ADP
ejpam-5036	496	17	the	the	DET
ejpam-5036	496	18	size	size	NOUN
ejpam-5036	496	19	2n×	2n×	NOUN
ejpam-5036	496	20	2n	2n	NUM
ejpam-5036	496	21	as	as	SCONJ
ejpam-5036	496	22	given	give	VERB
ejpam-5036	496	23	below	below	ADV
ejpam-5036	496	24	:	:	PUNCT
ejpam-5036	496	25	e	e	PROPN
ejpam-5036	496	26	a	a	DET
ejpam-5036	496	27	a2	a2	PROPN
ejpam-5036	496	28	.	.	PUNCT
ejpam-5036	496	29	.	.	PUNCT
ejpam-5036	496	30	.	.	PUNCT
ejpam-5036	497	1	an−1	an−1	PROPN
ejpam-5036	497	2	b	b	PROPN
ejpam-5036	497	3	ab	ab	PROPN
ejpam-5036	497	4	.	.	PUNCT
ejpam-5036	497	5	.	.	PUNCT
ejpam-5036	497	6	.	.	PUNCT
ejpam-5036	498	1	an−1b	an−1b	PROPN
ejpam-5036	498	2			NOUN
ejpam-5036	498	3	e	e	NOUN
ejpam-5036	498	4	1	1	NUM
ejpam-5036	498	5	1√	1√	PROPN
ejpam-5036	498	6	(	(	PUNCT
ejpam-5036	498	7	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	498	8	)	)	PUNCT
ejpam-5036	498	9	1√	1√	NOUN
ejpam-5036	498	10	(	(	PUNCT
ejpam-5036	498	11	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	498	12	)	)	PUNCT
ejpam-5036	498	13	.	.	PUNCT
ejpam-5036	498	14	.	.	PUNCT
ejpam-5036	499	1	.	.	PUNCT
ejpam-5036	500	1	1√	1√	NOUN
ejpam-5036	500	2	(	(	PUNCT
ejpam-5036	500	3	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	500	4	)	)	PUNCT
ejpam-5036	500	5	1√	1√	NOUN
ejpam-5036	500	6	2n−1	2n−1	NUM
ejpam-5036	500	7	1√	1√	PROPN
ejpam-5036	500	8	2n−1	2n−1	NUM
ejpam-5036	500	9	.	.	PUNCT
ejpam-5036	500	10	.	.	PUNCT
ejpam-5036	500	11	.	.	PUNCT
ejpam-5036	501	1	1√	1√	NOUN
ejpam-5036	501	2	2n−1	2n−1	NUM
ejpam-5036	501	3	a	a	DET
ejpam-5036	501	4	1√	1√	PROPN
ejpam-5036	501	5	(	(	PUNCT
ejpam-5036	501	6	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	501	7	)	)	PUNCT
ejpam-5036	501	8	1	1	NUM
ejpam-5036	501	9	1	1	NUM
ejpam-5036	501	10	n−1	n−1	PROPN
ejpam-5036	501	11	.	.	PUNCT
ejpam-5036	501	12	.	.	PUNCT
ejpam-5036	502	1	.	.	PUNCT
ejpam-5036	503	1	1	1	NUM
ejpam-5036	503	2	n−1	n−1	PROPN
ejpam-5036	503	3	0	0	NUM
ejpam-5036	503	4	0	0	NUM
ejpam-5036	503	5	.	.	PUNCT
ejpam-5036	503	6	.	.	PUNCT
ejpam-5036	503	7	.	.	PUNCT
ejpam-5036	504	1	0	0	NUM
ejpam-5036	505	1	a2	a2	PROPN
ejpam-5036	505	2	1√	1√	PROPN
ejpam-5036	505	3	(	(	PUNCT
ejpam-5036	505	4	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	505	5	)	)	PUNCT
ejpam-5036	505	6	1	1	NUM
ejpam-5036	505	7	n−1	n−1	PROPN
ejpam-5036	505	8	1	1	NUM
ejpam-5036	505	9	.	.	PUNCT
ejpam-5036	505	10	.	.	PUNCT
ejpam-5036	505	11	.	.	PUNCT
ejpam-5036	506	1	1	1	NUM
ejpam-5036	506	2	n−1	n−1	PROPN
ejpam-5036	506	3	0	0	NUM
ejpam-5036	506	4	0	0	NUM
ejpam-5036	506	5	.	.	PUNCT
ejpam-5036	506	6	.	.	PUNCT
ejpam-5036	506	7	.	.	PUNCT
ejpam-5036	507	1	0	0	NUM
ejpam-5036	507	2	...	...	PUNCT
ejpam-5036	507	3	...	...	PUNCT
ejpam-5036	507	4	...	...	PUNCT
ejpam-5036	507	5	...	...	PUNCT
ejpam-5036	507	6	.	.	PUNCT
ejpam-5036	507	7	.	.	PUNCT
ejpam-5036	508	1	.	.	PUNCT
ejpam-5036	508	2	...	...	PUNCT
ejpam-5036	509	1	...	...	PUNCT
ejpam-5036	509	2	...	...	PUNCT
ejpam-5036	509	3	.	.	PUNCT
ejpam-5036	509	4	.	.	PUNCT
ejpam-5036	510	1	.	.	PUNCT
ejpam-5036	511	1	...	...	PUNCT
ejpam-5036	512	1	an−1	an−1	PROPN
ejpam-5036	512	2	1√	1√	PROPN
ejpam-5036	512	3	(	(	PUNCT
ejpam-5036	512	4	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	512	5	)	)	PUNCT
ejpam-5036	512	6	1	1	NUM
ejpam-5036	512	7	n−1	n−1	PROPN
ejpam-5036	512	8	1	1	NUM
ejpam-5036	512	9	n−1	n−1	PROPN
ejpam-5036	512	10	.	.	PUNCT
ejpam-5036	512	11	.	.	PUNCT
ejpam-5036	512	12	.	.	PUNCT
ejpam-5036	513	1	1	1	NUM
ejpam-5036	513	2	0	0	NUM
ejpam-5036	513	3	0	0	NUM
ejpam-5036	513	4	.	.	PUNCT
ejpam-5036	513	5	.	.	PUNCT
ejpam-5036	513	6	.	.	PUNCT
ejpam-5036	514	1	0	0	NUM
ejpam-5036	515	1	b	b	X
ejpam-5036	515	2	1√	1√	NUM
ejpam-5036	515	3	2n−1	2n−1	NUM
ejpam-5036	515	4	0	0	NUM
ejpam-5036	515	5	0	0	NUM
ejpam-5036	515	6	.	.	PUNCT
ejpam-5036	515	7	.	.	PUNCT
ejpam-5036	515	8	.	.	PUNCT
ejpam-5036	516	1	0	0	NUM
ejpam-5036	517	1	1	1	NUM
ejpam-5036	517	2	0	0	NUM
ejpam-5036	517	3	.	.	PUNCT
ejpam-5036	517	4	.	.	PUNCT
ejpam-5036	518	1	.	.	PUNCT
ejpam-5036	518	2	0	0	NUM
ejpam-5036	519	1	ab	ab	PROPN
ejpam-5036	519	2	1√	1√	PROPN
ejpam-5036	519	3	2n−1	2n−1	NUM
ejpam-5036	519	4	0	0	NUM
ejpam-5036	519	5	0	0	NUM
ejpam-5036	519	6	.	.	PUNCT
ejpam-5036	519	7	.	.	PUNCT
ejpam-5036	520	1	.	.	PUNCT
ejpam-5036	521	1	0	0	NUM
ejpam-5036	521	2	0	0	NUM
ejpam-5036	521	3	1	1	NUM
ejpam-5036	521	4	.	.	PUNCT
ejpam-5036	521	5	.	.	PUNCT
ejpam-5036	522	1	.	.	PUNCT
ejpam-5036	523	1	0	0	NUM
ejpam-5036	523	2	...	...	PUNCT
ejpam-5036	523	3	...	...	PUNCT
ejpam-5036	523	4	...	...	PUNCT
ejpam-5036	523	5	...	...	PUNCT
ejpam-5036	523	6	.	.	PUNCT
ejpam-5036	523	7	.	.	PUNCT
ejpam-5036	524	1	.	.	PUNCT
ejpam-5036	524	2	...	...	PUNCT
ejpam-5036	525	1	...	...	PUNCT
ejpam-5036	525	2	...	...	PUNCT
ejpam-5036	525	3	.	.	PUNCT
ejpam-5036	525	4	.	.	PUNCT
ejpam-5036	526	1	.	.	PUNCT
ejpam-5036	527	1	...	...	PUNCT
ejpam-5036	528	1	an−1b	an−1b	PUNCT
ejpam-5036	528	2	1√	1√	NOUN
ejpam-5036	528	3	2n−1	2n−1	NUM
ejpam-5036	528	4	0	0	NUM
ejpam-5036	528	5	0	0	NUM
ejpam-5036	528	6	.	.	PUNCT
ejpam-5036	528	7	.	.	PUNCT
ejpam-5036	528	8	.	.	PUNCT
ejpam-5036	529	1	0	0	NUM
ejpam-5036	530	1	0	0	NUM
ejpam-5036	530	2	0	0	NUM
ejpam-5036	530	3	.	.	PUNCT
ejpam-5036	530	4	.	.	PUNCT
ejpam-5036	530	5	.	.	PUNCT
ejpam-5036	531	1	1	1	X
ejpam-5036	531	2	.	.	PUNCT
ejpam-5036	532	1	in	in	ADP
ejpam-5036	532	2	other	other	ADJ
ejpam-5036	532	3	words	word	NOUN
ejpam-5036	532	4	,	,	PUNCT
ejpam-5036	532	5	nsl(γd2n	nsl(γd2n	NOUN
ejpam-5036	532	6	)	)	PUNCT
ejpam-5036	532	7	can	can	AUX
ejpam-5036	532	8	be	be	AUX
ejpam-5036	532	9	partitioned	partition	VERB
ejpam-5036	532	10	into	into	ADP
ejpam-5036	532	11	nine	nine	NUM
ejpam-5036	532	12	block	block	NOUN
ejpam-5036	532	13	matrices	matrix	NOUN
ejpam-5036	532	14	as	as	SCONJ
ejpam-5036	532	15	follows	follow	VERB
ejpam-5036	532	16	:	:	PUNCT
ejpam-5036	532	17	nsl(γd2n	nsl(γd2n	NOUN
ejpam-5036	532	18	)	)	PUNCT
ejpam-5036	533	1	=	=	SYM
ejpam-5036	533	2			NOUN
ejpam-5036	533	3	1	1	NUM
ejpam-5036	533	4	1√	1√	PROPN
ejpam-5036	533	5	(	(	PUNCT
ejpam-5036	533	6	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	533	7	)	)	PUNCT
ejpam-5036	533	8	j1×(n−1	j1×(n−1	PROPN
ejpam-5036	533	9	)	)	PUNCT
ejpam-5036	533	10	1√	1√	PROPN
ejpam-5036	533	11	2n−1	2n−1	NUM
ejpam-5036	534	1	j1×n	j1×n	PROPN
ejpam-5036	534	2	1√	1√	PROPN
ejpam-5036	534	3	(	(	PUNCT
ejpam-5036	534	4	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	534	5	)	)	PUNCT
ejpam-5036	534	6	j(n−1)×1	j(n−1)×1	NOUN
ejpam-5036	534	7	(	(	PUNCT
ejpam-5036	534	8	1−	1−	NUM
ejpam-5036	534	9	1	1	NUM
ejpam-5036	534	10	n−1	n−1	PROPN
ejpam-5036	534	11	)	)	PUNCT
ejpam-5036	534	12	in−1	in−1	PROPN
ejpam-5036	535	1	+	+	CCONJ
ejpam-5036	535	2	1	1	NUM
ejpam-5036	535	3	n−1jn−1	n−1jn−1	NOUN
ejpam-5036	535	4	0(n−1)×n	0(n−1)×n	NUM
ejpam-5036	535	5	1√	1√	PROPN
ejpam-5036	535	6	2n−1	2n−1	NUM
ejpam-5036	535	7	jn×1	jn×1	VERB
ejpam-5036	535	8	0n×(n−1	0n×(n−1	NUM
ejpam-5036	535	9	)	)	PUNCT
ejpam-5036	535	10	in	in	ADP
ejpam-5036	535	11			NOUN
ejpam-5036	535	12	.	.	PUNCT
ejpam-5036	536	1	the	the	DET
ejpam-5036	536	2	characteristic	characteristic	ADJ
ejpam-5036	536	3	polynomial	polynomial	NOUN
ejpam-5036	536	4	of	of	ADP
ejpam-5036	536	5	nsl(γd2n	nsl(γd2n	NOUN
ejpam-5036	536	6	)	)	PUNCT
ejpam-5036	536	7	is	be	AUX
ejpam-5036	536	8	pnsl(γd2n	pnsl(γd2n	NOUN
ejpam-5036	536	9	)	)	PUNCT
ejpam-5036	536	10	(	(	PUNCT
ejpam-5036	536	11	λ	λ	X
ejpam-5036	536	12	)	)	PUNCT
ejpam-5036	536	13	=	=	PUNCT
ejpam-5036	537	1	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-5036	537	2	λ−	λ−	PROPN
ejpam-5036	537	3	1	1	NUM
ejpam-5036	538	1	−	−	PROPN
ejpam-5036	538	2	1√	1√	PROPN
ejpam-5036	538	3	(	(	PUNCT
ejpam-5036	538	4	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	538	5	)	)	PUNCT
ejpam-5036	538	6	j1×(n−1	j1×(n−1	PROPN
ejpam-5036	538	7	)	)	PUNCT
ejpam-5036	538	8	−	−	PROPN
ejpam-5036	538	9	1√	1√	PROPN
ejpam-5036	538	10	2n−1	2n−1	NUM
ejpam-5036	539	1	j1×n	j1×n	ADJ
ejpam-5036	539	2	−	−	PROPN
ejpam-5036	539	3	1√	1√	PROPN
ejpam-5036	539	4	(	(	PUNCT
ejpam-5036	539	5	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	539	6	)	)	PUNCT
ejpam-5036	539	7	j(n−1)×1	j(n−1)×1	NOUN
ejpam-5036	539	8	(	(	PUNCT
ejpam-5036	539	9	λ−	λ−	PROPN
ejpam-5036	539	10	1	1	NUM
ejpam-5036	539	11	+	+	SYM
ejpam-5036	539	12	1	1	NUM
ejpam-5036	539	13	n−1	n−1	PROPN
ejpam-5036	539	14	)	)	PUNCT
ejpam-5036	539	15	in−1	in−1	ADJ
ejpam-5036	539	16	−	−	PROPN
ejpam-5036	539	17	1	1	NUM
ejpam-5036	539	18	n−1jn−1	n−1jn−1	NOUN
ejpam-5036	540	1	0(n−1)×n	0(n−1)×n	NUM
ejpam-5036	541	1	−	−	PROPN
ejpam-5036	541	2	1√	1√	PROPN
ejpam-5036	541	3	2n−1	2n−1	NUM
ejpam-5036	541	4	jn×1	jn×1	NOUN
ejpam-5036	541	5	0n×(n−1	0n×(n−1	NUM
ejpam-5036	541	6	)	)	PUNCT
ejpam-5036	541	7	(	(	PUNCT
ejpam-5036	541	8	λ−	λ−	PROPN
ejpam-5036	541	9	1)in	1)in	PROPN
ejpam-5036	541	10	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-5036	541	11	.	.	PUNCT
ejpam-5036	542	1	(	(	PUNCT
ejpam-5036	542	2	12	12	NUM
ejpam-5036	542	3	)	)	PUNCT
ejpam-5036	542	4	we	we	PRON
ejpam-5036	542	5	apply	apply	VERB
ejpam-5036	542	6	the	the	DET
ejpam-5036	542	7	row	row	NOUN
ejpam-5036	542	8	and	and	CCONJ
ejpam-5036	542	9	column	column	NOUN
ejpam-5036	542	10	operations	operation	NOUN
ejpam-5036	542	11	to	to	PART
ejpam-5036	542	12	equation	equation	NOUN
ejpam-5036	542	13	12	12	NUM
ejpam-5036	542	14	:	:	PUNCT
ejpam-5036	542	15	(	(	PUNCT
ejpam-5036	542	16	i	i	NOUN
ejpam-5036	542	17	)	)	PUNCT
ejpam-5036	542	18	rn+1+i	rn+1+i	NOUN
ejpam-5036	542	19	−→	−→	ADJ
ejpam-5036	542	20	rn+1+i	rn+1+i	NOUN
ejpam-5036	542	21	−rn+1	−rn+1	VERB
ejpam-5036	542	22	,	,	PUNCT
ejpam-5036	542	23	for	for	ADP
ejpam-5036	542	24	i	i	PROPN
ejpam-5036	542	25	=	=	SYM
ejpam-5036	542	26	1	1	NUM
ejpam-5036	542	27	,	,	PUNCT
ejpam-5036	542	28	2	2	NUM
ejpam-5036	542	29	,	,	PUNCT
ejpam-5036	542	30	.	.	PUNCT
ejpam-5036	542	31	.	.	PUNCT
ejpam-5036	543	1	.	.	PUNCT
ejpam-5036	544	1	,	,	PUNCT
ejpam-5036	544	2	n−	n−	NOUN
ejpam-5036	544	3	1	1	NUM
ejpam-5036	544	4	.	.	PUNCT
ejpam-5036	545	1	references	reference	NOUN
ejpam-5036	545	2	602	602	NUM
ejpam-5036	545	3	(	(	PUNCT
ejpam-5036	545	4	ii	ii	NOUN
ejpam-5036	545	5	)	)	PUNCT
ejpam-5036	545	6	cn+1	cn+1	VERB
ejpam-5036	545	7	−→	−→	NOUN
ejpam-5036	545	8	cn+1	cn+1	NOUN
ejpam-5036	545	9	+	+	CCONJ
ejpam-5036	545	10	cn+2	cn+2	PRON
ejpam-5036	546	1	+	+	CCONJ
ejpam-5036	546	2	.	.	PUNCT
ejpam-5036	546	3	.	.	PUNCT
ejpam-5036	547	1	.+	.+	NOUN
ejpam-5036	547	2	c2n	c2n	NOUN
ejpam-5036	547	3	.	.	PUNCT
ejpam-5036	548	1	(	(	PUNCT
ejpam-5036	548	2	iii	iii	X
ejpam-5036	548	3	)	)	PUNCT
ejpam-5036	548	4	c1	c1	PROPN
ejpam-5036	548	5	−→	−→	PROPN
ejpam-5036	548	6	c1	c1	PROPN
ejpam-5036	548	7	+	+	CCONJ
ejpam-5036	548	8	1	1	NUM
ejpam-5036	548	9	(	(	PUNCT
ejpam-5036	548	10	λ−1	λ−1	PROPN
ejpam-5036	548	11	)	)	PUNCT
ejpam-5036	548	12	√	√	ADP
ejpam-5036	548	13	2n−1	2n−1	NUM
ejpam-5036	548	14	cn+1	cn+1	NOUN
ejpam-5036	548	15	.	.	PUNCT
ejpam-5036	549	1	(	(	PUNCT
ejpam-5036	549	2	iv	iv	X
ejpam-5036	549	3	)	)	PUNCT
ejpam-5036	549	4	r2+i	r2+i	PROPN
ejpam-5036	549	5	−→	−→	NOUN
ejpam-5036	549	6	r2+i	r2+i	PROPN
ejpam-5036	549	7	−r2	−r2	PROPN
ejpam-5036	549	8	,	,	PUNCT
ejpam-5036	549	9	for	for	ADP
ejpam-5036	549	10	i	i	PROPN
ejpam-5036	549	11	=	=	SYM
ejpam-5036	549	12	1	1	NUM
ejpam-5036	549	13	,	,	PUNCT
ejpam-5036	549	14	2	2	NUM
ejpam-5036	549	15	,	,	PUNCT
ejpam-5036	549	16	.	.	PUNCT
ejpam-5036	549	17	.	.	PUNCT
ejpam-5036	550	1	.	.	PUNCT
ejpam-5036	551	1	,	,	PUNCT
ejpam-5036	551	2	n−	n−	NOUN
ejpam-5036	551	3	2	2	NUM
ejpam-5036	551	4	.	.	PUNCT
ejpam-5036	552	1	(	(	PUNCT
ejpam-5036	552	2	v	v	NOUN
ejpam-5036	552	3	)	)	PUNCT
ejpam-5036	552	4	c2	c2	PROPN
ejpam-5036	552	5	−→	−→	PROPN
ejpam-5036	552	6	c2	c2	PROPN
ejpam-5036	552	7	+	+	CCONJ
ejpam-5036	552	8	c2	c2	PROPN
ejpam-5036	552	9	+	+	PROPN
ejpam-5036	552	10	1	1	NUM
ejpam-5036	552	11	+	+	NUM
ejpam-5036	552	12	.	.	PUNCT
ejpam-5036	552	13	.	.	PUNCT
ejpam-5036	553	1	.+	.+	NOUN
ejpam-5036	553	2	cn	cn	PROPN
ejpam-5036	553	3	,	,	PUNCT
ejpam-5036	553	4	consequently	consequently	ADV
ejpam-5036	553	5	we	we	PRON
ejpam-5036	553	6	have	have	VERB
ejpam-5036	553	7	pnsl(γd2n	pnsl(γd2n	NOUN
ejpam-5036	553	8	)	)	PUNCT
ejpam-5036	553	9	(	(	PUNCT
ejpam-5036	553	10	λ	λ	NOUN
ejpam-5036	553	11	)	)	PUNCT
ejpam-5036	553	12	=	=	SYM
ejpam-5036	553	13	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	ADJ
ejpam-5036	553	14	−n	−n	ADJ
ejpam-5036	553	15	(	(	PUNCT
ejpam-5036	553	16	λ−1)(2n−1	λ−1)(2n−1	PROPN
ejpam-5036	553	17	)	)	PUNCT
ejpam-5036	553	18	+	+	CCONJ
ejpam-5036	553	19	λ−	λ−	PROPN
ejpam-5036	553	20	1	1	NUM
ejpam-5036	553	21	−	−	NOUN
ejpam-5036	553	22	n−1√	n−1√	SYM
ejpam-5036	553	23	(	(	PUNCT
ejpam-5036	553	24	2n−1)(n−1	2n−1)(n−1	NUM
ejpam-5036	553	25	)	)	PUNCT
ejpam-5036	553	26	−	−	PROPN
ejpam-5036	553	27	1√	1√	PROPN
ejpam-5036	553	28	(	(	PUNCT
ejpam-5036	553	29	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	553	30	)	)	PUNCT
ejpam-5036	553	31	j1×(n−2	j1×(n−2	NOUN
ejpam-5036	553	32	)	)	PUNCT
ejpam-5036	553	33	−	−	ADP
ejpam-5036	554	1	n√	n√	PRON
ejpam-5036	554	2	2n−1	2n−1	NUM
ejpam-5036	554	3	−	−	PROPN
ejpam-5036	554	4	1√	1√	PROPN
ejpam-5036	554	5	2n−1	2n−1	NUM
ejpam-5036	555	1	j1×n	j1×n	ADJ
ejpam-5036	555	2	−	−	PROPN
ejpam-5036	555	3	1√	1√	PROPN
ejpam-5036	555	4	(	(	PUNCT
ejpam-5036	555	5	2n−1)(n−1	2n−1)(n−1	PROPN
ejpam-5036	555	6	)	)	PUNCT
ejpam-5036	555	7	λ−	λ−	PROPN
ejpam-5036	555	8	1−	1−	NUM
ejpam-5036	555	9	(	(	PUNCT
ejpam-5036	555	10	n−2	n−2	PROPN
ejpam-5036	555	11	)	)	PUNCT
ejpam-5036	555	12	n−1	n−1	PROPN
ejpam-5036	555	13	−	−	PROPN
ejpam-5036	555	14	1	1	NUM
ejpam-5036	555	15	n−1	n−1	PROPN
ejpam-5036	555	16	j1×(n−2	j1×(n−2	NOUN
ejpam-5036	555	17	)	)	PUNCT
ejpam-5036	555	18	0	0	NUM
ejpam-5036	555	19	01×(n−1	01×(n−1	NUM
ejpam-5036	555	20	)	)	PUNCT
ejpam-5036	555	21	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	555	22	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	556	1	(	(	PUNCT
ejpam-5036	556	2	λ−	λ−	PROPN
ejpam-5036	556	3	1	1	NUM
ejpam-5036	556	4	+	+	NUM
ejpam-5036	556	5	1	1	NUM
ejpam-5036	556	6	n−1	n−1	PROPN
ejpam-5036	556	7	)	)	PUNCT
ejpam-5036	556	8	in−2	in−2	NOUN
ejpam-5036	556	9	0(n−2)×1	0(n−2)×1	NUM
ejpam-5036	556	10	0(n−2)×(n−1	0(n−2)×(n−1	NUM
ejpam-5036	556	11	)	)	PUNCT
ejpam-5036	556	12	0	0	NUM
ejpam-5036	556	13	0	0	NUM
ejpam-5036	556	14	01×(n−2	01×(n−2	X
ejpam-5036	556	15	)	)	PUNCT
ejpam-5036	556	16	λ−	λ−	PROPN
ejpam-5036	556	17	1	1	NUM
ejpam-5036	556	18	01×(n−1	01×(n−1	NUM
ejpam-5036	556	19	)	)	PUNCT
ejpam-5036	556	20	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	556	21	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	557	1	0n−1	0n−1	NUM
ejpam-5036	557	2	0(n−1)×1	0(n−1)×1	NUM
ejpam-5036	558	1	(	(	PUNCT
ejpam-5036	558	2	λ−	λ−	PROPN
ejpam-5036	558	3	1)in−1	1)in−1	PROPN
ejpam-5036	558	4	∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5036	558	5	.	.	PUNCT
ejpam-5036	559	1	according	accord	VERB
ejpam-5036	559	2	to	to	ADP
ejpam-5036	559	3	theorem	theorem	NOUN
ejpam-5036	559	4	2	2	NUM
ejpam-5036	559	5	,	,	PUNCT
ejpam-5036	559	6	we	we	PRON
ejpam-5036	559	7	can	can	AUX
ejpam-5036	559	8	obtain	obtain	VERB
ejpam-5036	559	9	pnsl(γd2n	pnsl(γd2n	NOUN
ejpam-5036	559	10	)	)	PUNCT
ejpam-5036	559	11	(	(	PUNCT
ejpam-5036	559	12	λ	λ	X
ejpam-5036	559	13	)	)	PUNCT
ejpam-5036	559	14	as	as	SCONJ
ejpam-5036	559	15	follows	follow	VERB
ejpam-5036	559	16	:	:	PUNCT
ejpam-5036	559	17	pnsl(γd2n	pnsl(γd2n	NOUN
ejpam-5036	559	18	)	)	PUNCT
ejpam-5036	559	19	(	(	PUNCT
ejpam-5036	559	20	λ	λ	NOUN
ejpam-5036	559	21	)	)	PUNCT
ejpam-5036	559	22	=	=	SYM
ejpam-5036	560	1	(	(	PUNCT
ejpam-5036	560	2	λ−1)n−1	λ−1)n−1	PROPN
ejpam-5036	560	3	(	(	PUNCT
ejpam-5036	560	4	λ−	λ−	PROPN
ejpam-5036	560	5	1	1	NUM
ejpam-5036	560	6	+	+	SYM
ejpam-5036	560	7	1	1	NUM
ejpam-5036	560	8	n−	n−	NOUN
ejpam-5036	560	9	1	1	NUM
ejpam-5036	560	10	)	)	PUNCT
ejpam-5036	560	11	n−2	n−2	PROPN
ejpam-5036	560	12	(	(	PUNCT
ejpam-5036	560	13	λ3	λ3	PROPN
ejpam-5036	560	14	+	+	PROPN
ejpam-5036	560	15	(	(	PUNCT
ejpam-5036	560	16	5−	5−	NUM
ejpam-5036	560	17	4n	4n	NOUN
ejpam-5036	560	18	)	)	PUNCT
ejpam-5036	560	19	n−	n−	NOUN
ejpam-5036	560	20	1	1	NUM
ejpam-5036	560	21	λ2	λ2	NOUN
ejpam-5036	560	22	+	+	CCONJ
ejpam-5036	560	23	(	(	PUNCT
ejpam-5036	560	24	9n2	9n2	NUM
ejpam-5036	560	25	−	−	PROPN
ejpam-5036	560	26	19n+	19n+	NUM
ejpam-5036	560	27	8)	8)	NUM
ejpam-5036	560	28	(	(	PUNCT
ejpam-5036	560	29	2n−	2n−	PROPN
ejpam-5036	560	30	1)(n−	1)(n−	NUM
ejpam-5036	560	31	1	1	NUM
ejpam-5036	560	32	)	)	PUNCT
ejpam-5036	560	33	λ−	λ−	PROPN
ejpam-5036	560	34	2(n−	2(n−	NUM
ejpam-5036	560	35	2	2	NUM
ejpam-5036	560	36	)	)	PUNCT
ejpam-5036	560	37	2n−	2n−	PROPN
ejpam-5036	560	38	1	1	NUM
ejpam-5036	560	39	)	)	PUNCT
ejpam-5036	560	40	.	.	PUNCT
ejpam-5036	561	1	acknowledgements	acknowledgement	NOUN
ejpam-5036	561	2	we	we	PRON
ejpam-5036	561	3	wish	wish	VERB
ejpam-5036	561	4	to	to	PART
ejpam-5036	561	5	express	express	VERB
ejpam-5036	561	6	our	our	PRON
ejpam-5036	561	7	gratitude	gratitude	NOUN
ejpam-5036	561	8	to	to	ADP
ejpam-5036	561	9	universitas	universitas	PROPN
ejpam-5036	561	10	mataram	mataram	PROPN
ejpam-5036	561	11	,	,	PUNCT
ejpam-5036	561	12	indonesia	indonesia	PROPN
ejpam-5036	561	13	,	,	PUNCT
ejpam-5036	561	14	for	for	ADP
ejpam-5036	561	15	providing	provide	VERB
ejpam-5036	561	16	partial	partial	ADJ
ejpam-5036	561	17	funding	funding	NOUN
ejpam-5036	561	18	assistance	assistance	NOUN
ejpam-5036	561	19	.	.	PUNCT
ejpam-5036	562	1	references	reference	NOUN
ejpam-5036	562	2	[	[	X
ejpam-5036	562	3	1	1	NUM
ejpam-5036	562	4	]	]	SYM
ejpam-5036	562	5	b	b	NOUN
ejpam-5036	562	6	alharbi	alharbi	NOUN
ejpam-5036	562	7	.	.	PUNCT
ejpam-5036	563	1	graphs	graph	NOUN
ejpam-5036	563	2	and	and	CCONJ
ejpam-5036	563	3	the	the	DET
ejpam-5036	563	4	prime	prime	ADJ
ejpam-5036	563	5	spectrum	spectrum	NOUN
ejpam-5036	563	6	of	of	ADP
ejpam-5036	563	7	unitary	unitary	ADJ
ejpam-5036	563	8	commutative	commutative	ADJ
ejpam-5036	563	9	rings	ring	NOUN
ejpam-5036	563	10	.	.	PUNCT
ejpam-5036	564	1	european	european	PROPN
ejpam-5036	564	2	journal	journal	PROPN
ejpam-5036	564	3	of	of	ADP
ejpam-5036	564	4	pure	pure	ADJ
ejpam-5036	564	5	and	and	CCONJ
ejpam-5036	564	6	applied	applied	ADJ
ejpam-5036	564	7	mathematics	mathematic	NOUN
ejpam-5036	564	8	,	,	PUNCT
ejpam-5036	564	9	16(1):314–318	16(1):314–318	NUM
ejpam-5036	564	10	,	,	PUNCT
ejpam-5036	564	11	2023	2023	NUM
ejpam-5036	564	12	.	.	PUNCT
ejpam-5036	565	1	[	[	X
ejpam-5036	565	2	2	2	NUM
ejpam-5036	565	3	]	]	X
ejpam-5036	565	4	f	f	PROPN
ejpam-5036	565	5	ali	ali	PROPN
ejpam-5036	565	6	,	,	PUNCT
ejpam-5036	565	7	s	s	PROPN
ejpam-5036	565	8	fatima	fatima	PROPN
ejpam-5036	565	9	,	,	PUNCT
ejpam-5036	565	10	and	and	CCONJ
ejpam-5036	565	11	w	w	PROPN
ejpam-5036	565	12	wang	wang	PROPN
ejpam-5036	565	13	.	.	PUNCT
ejpam-5036	566	1	on	on	ADP
ejpam-5036	566	2	the	the	DET
ejpam-5036	566	3	power	power	NOUN
ejpam-5036	566	4	graphs	graph	NOUN
ejpam-5036	566	5	of	of	ADP
ejpam-5036	566	6	certain	certain	ADJ
ejpam-5036	566	7	finite	finite	ADJ
ejpam-5036	566	8	groups	group	NOUN
ejpam-5036	566	9	.	.	PUNCT
ejpam-5036	567	1	linear	linear	ADJ
ejpam-5036	567	2	and	and	CCONJ
ejpam-5036	567	3	multilinear	multilinear	PROPN
ejpam-5036	567	4	algebra	algebra	PROPN
ejpam-5036	567	5	,	,	PUNCT
ejpam-5036	567	6	pages	page	NOUN
ejpam-5036	567	7	1–15	1–15	NUM
ejpam-5036	567	8	,	,	PUNCT
ejpam-5036	567	9	2020	2020	NUM
ejpam-5036	567	10	.	.	PUNCT
ejpam-5036	568	1	[	[	X
ejpam-5036	568	2	3	3	X
ejpam-5036	568	3	]	]	X
ejpam-5036	568	4	m	m	NOUN
ejpam-5036	568	5	aschbacher	aschbacher	NOUN
ejpam-5036	568	6	.	.	PUNCT
ejpam-5036	569	1	finite	finite	PROPN
ejpam-5036	569	2	group	group	PROPN
ejpam-5036	569	3	theory	theory	PROPN
ejpam-5036	569	4	.	.	PUNCT
ejpam-5036	570	1	cambridge	cambridge	PROPN
ejpam-5036	570	2	university	university	PROPN
ejpam-5036	570	3	press	press	PROPN
ejpam-5036	570	4	,	,	PUNCT
ejpam-5036	570	5	cambridge	cambridge	PROPN
ejpam-5036	570	6	,	,	PUNCT
ejpam-5036	570	7	2000	2000	NUM
ejpam-5036	570	8	.	.	PUNCT
ejpam-5036	571	1	[	[	X
ejpam-5036	571	2	4	4	X
ejpam-5036	571	3	]	]	PUNCT
ejpam-5036	571	4	a	a	DET
ejpam-5036	571	5	e	e	X
ejpam-5036	571	6	brouwer	brouwer	PROPN
ejpam-5036	571	7	and	and	CCONJ
ejpam-5036	571	8	w	w	NOUN
ejpam-5036	571	9	h	h	NOUN
ejpam-5036	571	10	haemers	haemer	NOUN
ejpam-5036	571	11	.	.	PUNCT
ejpam-5036	572	1	spectra	spectra	NOUN
ejpam-5036	572	2	of	of	ADP
ejpam-5036	572	3	graphs	graph	NOUN
ejpam-5036	572	4	.	.	PUNCT
ejpam-5036	573	1	springer	springer	NOUN
ejpam-5036	573	2	,	,	PUNCT
ejpam-5036	573	3	new	new	PROPN
ejpam-5036	573	4	york	york	PROPN
ejpam-5036	573	5	,	,	PUNCT
ejpam-5036	573	6	2011	2011	NUM
ejpam-5036	573	7	.	.	PUNCT
ejpam-5036	574	1	[	[	X
ejpam-5036	574	2	5	5	NUM
ejpam-5036	574	3	]	]	PUNCT
ejpam-5036	574	4	t	t	PROPN
ejpam-5036	574	5	t	t	PROPN
ejpam-5036	574	6	chelvam	chelvam	VERB
ejpam-5036	574	7	and	and	CCONJ
ejpam-5036	574	8	m	m	VERB
ejpam-5036	574	9	sattanathan	sattanathan	ADJ
ejpam-5036	574	10	.	.	PUNCT
ejpam-5036	575	1	power	power	NOUN
ejpam-5036	575	2	graph	graph	NOUN
ejpam-5036	575	3	of	of	ADP
ejpam-5036	575	4	finite	finite	ADJ
ejpam-5036	575	5	abelian	abelian	ADJ
ejpam-5036	575	6	groups	group	NOUN
ejpam-5036	575	7	.	.	PUNCT
ejpam-5036	576	1	algebra	algebra	NOUN
ejpam-5036	576	2	and	and	CCONJ
ejpam-5036	576	3	discrete	discrete	ADJ
ejpam-5036	576	4	mathematics	mathematic	NOUN
ejpam-5036	576	5	,	,	PUNCT
ejpam-5036	576	6	16(1):33–41	16(1):33–41	NUM
ejpam-5036	576	7	,	,	PUNCT
ejpam-5036	576	8	2013	2013	NUM
ejpam-5036	576	9	.	.	PUNCT
ejpam-5036	577	1	[	[	X
ejpam-5036	577	2	6	6	NUM
ejpam-5036	577	3	]	]	SYM
ejpam-5036	577	4	f	f	NOUN
ejpam-5036	577	5	r	r	NOUN
ejpam-5036	577	6	gantmacher	gantmacher	ADV
ejpam-5036	577	7	.	.	PUNCT
ejpam-5036	578	1	the	the	DET
ejpam-5036	578	2	theory	theory	NOUN
ejpam-5036	578	3	of	of	ADP
ejpam-5036	578	4	matrices	matrix	NOUN
ejpam-5036	578	5	.	.	PUNCT
ejpam-5036	579	1	chelsea	chelsea	PROPN
ejpam-5036	579	2	publishing	publishing	PROPN
ejpam-5036	579	3	company	company	NOUN
ejpam-5036	579	4	,	,	PUNCT
ejpam-5036	579	5	new	new	PROPN
ejpam-5036	579	6	york	york	PROPN
ejpam-5036	579	7	,	,	PUNCT
ejpam-5036	579	8	1959	1959	NUM
ejpam-5036	579	9	.	.	PUNCT
ejpam-5036	580	1	[	[	X
ejpam-5036	580	2	7	7	X
ejpam-5036	580	3	]	]	PUNCT
ejpam-5036	580	4	a	a	DET
ejpam-5036	580	5	kumar	kumar	PROPN
ejpam-5036	580	6	,	,	PUNCT
ejpam-5036	580	7	l	l	PROPN
ejpam-5036	580	8	selvaganesh	selvaganesh	NOUN
ejpam-5036	580	9	,	,	PUNCT
ejpam-5036	580	10	p	p	PROPN
ejpam-5036	580	11	j	j	PROPN
ejpam-5036	580	12	cameron	cameron	PROPN
ejpam-5036	580	13	,	,	PUNCT
ejpam-5036	580	14	and	and	CCONJ
ejpam-5036	580	15	t	t	PROPN
ejpam-5036	580	16	chelvam	chelvam	VERB
ejpam-5036	580	17	.	.	PUNCT
ejpam-5036	581	1	recent	recent	ADJ
ejpam-5036	581	2	developments	development	NOUN
ejpam-5036	581	3	on	on	ADP
ejpam-5036	581	4	the	the	DET
ejpam-5036	581	5	power	power	NOUN
ejpam-5036	581	6	graph	graph	NOUN
ejpam-5036	581	7	of	of	ADP
ejpam-5036	581	8	finite	finite	ADJ
ejpam-5036	581	9	groups	group	NOUN
ejpam-5036	581	10	–	–	PUNCT
ejpam-5036	581	11	a	a	DET
ejpam-5036	581	12	survey	survey	NOUN
ejpam-5036	581	13	.	.	PUNCT
ejpam-5036	582	1	akce	akce	PROPN
ejpam-5036	582	2	international	international	PROPN
ejpam-5036	582	3	journal	journal	NOUN
ejpam-5036	582	4	of	of	ADP
ejpam-5036	582	5	graphs	graph	NOUN
ejpam-5036	582	6	and	and	CCONJ
ejpam-5036	582	7	combinatorics	combinatoric	NOUN
ejpam-5036	582	8	,	,	PUNCT
ejpam-5036	582	9	18(2):65–94	18(2):65–94	NUM
ejpam-5036	582	10	,	,	PUNCT
ejpam-5036	582	11	2021	2021	NUM
ejpam-5036	582	12	.	.	PUNCT
ejpam-5036	583	1	references	reference	NOUN
ejpam-5036	583	2	603	603	NUM
ejpam-5036	584	1	[	[	X
ejpam-5036	584	2	8	8	NUM
ejpam-5036	584	3	]	]	SYM
ejpam-5036	584	4	m	m	VERB
ejpam-5036	584	5	u	u	NOUN
ejpam-5036	584	6	romdhini	romdhini	NOUN
ejpam-5036	584	7	,	,	PUNCT
ejpam-5036	584	8	f	f	PROPN
ejpam-5036	584	9	al	al	PROPN
ejpam-5036	584	10	-	-	PUNCT
ejpam-5036	584	11	sharqi	sharqi	PROPN
ejpam-5036	584	12	,	,	PUNCT
ejpam-5036	584	13	a	a	DET
ejpam-5036	584	14	nawawi	nawawi	NOUN
ejpam-5036	584	15	,	,	PUNCT
ejpam-5036	584	16	a	a	DET
ejpam-5036	584	17	al	al	PROPN
ejpam-5036	584	18	-	-	PUNCT
ejpam-5036	584	19	quran	quran	PROPN
ejpam-5036	584	20	,	,	PUNCT
ejpam-5036	584	21	and	and	CCONJ
ejpam-5036	584	22	h	h	PROPN
ejpam-5036	584	23	rashmanlou	rashmanlou	NOUN
ejpam-5036	584	24	.	.	PUNCT
ejpam-5036	585	1	signless	signless	PROPN
ejpam-5036	585	2	laplacian	laplacian	ADJ
ejpam-5036	585	3	energy	energy	NOUN
ejpam-5036	585	4	of	of	ADP
ejpam-5036	585	5	interval	interval	NOUN
ejpam-5036	585	6	-	-	PUNCT
ejpam-5036	585	7	valued	value	VERB
ejpam-5036	585	8	fuzzy	fuzzy	ADJ
ejpam-5036	585	9	graph	graph	NOUN
ejpam-5036	585	10	and	and	CCONJ
ejpam-5036	585	11	its	its	PRON
ejpam-5036	585	12	applications	application	NOUN
ejpam-5036	585	13	.	.	PUNCT
ejpam-5036	586	1	sains	sain	NOUN
ejpam-5036	586	2	malaysiana	malaysiana	PROPN
ejpam-5036	586	3	,	,	PUNCT
ejpam-5036	586	4	52(7):2127–2137	52(7):2127–2137	NUM
ejpam-5036	586	5	,	,	PUNCT
ejpam-5036	586	6	2023	2023	NUM
ejpam-5036	586	7	.	.	PUNCT
ejpam-5036	587	1	[	[	X
ejpam-5036	587	2	9	9	NUM
ejpam-5036	587	3	]	]	SYM
ejpam-5036	587	4	m	m	VERB
ejpam-5036	587	5	u	u	NOUN
ejpam-5036	587	6	romdhini	romdhini	NOUN
ejpam-5036	587	7	and	and	CCONJ
ejpam-5036	587	8	a	a	DET
ejpam-5036	587	9	nawawi	nawawi	ADJ
ejpam-5036	587	10	.	.	PUNCT
ejpam-5036	587	11	degree	degree	NOUN
ejpam-5036	587	12	sum	sum	NOUN
ejpam-5036	587	13	energy	energy	NOUN
ejpam-5036	587	14	of	of	ADP
ejpam-5036	587	15	non	non	ADJ
ejpam-5036	587	16	-	-	ADJ
ejpam-5036	587	17	commuting	commuting	ADJ
ejpam-5036	587	18	graph	graph	NOUN
ejpam-5036	587	19	for	for	ADP
ejpam-5036	587	20	dihedral	dihedral	ADJ
ejpam-5036	587	21	groups	group	NOUN
ejpam-5036	587	22	.	.	PUNCT
ejpam-5036	588	1	malaysian	malaysian	ADJ
ejpam-5036	588	2	journal	journal	PROPN
ejpam-5036	588	3	of	of	ADP
ejpam-5036	588	4	science	science	PROPN
ejpam-5036	588	5	,	,	PUNCT
ejpam-5036	588	6	41(sp1):34–39	41(sp1):34–39	PRON
ejpam-5036	588	7	,	,	PUNCT
ejpam-5036	588	8	2022	2022	NUM
ejpam-5036	588	9	.	.	PUNCT
ejpam-5036	589	1	[	[	X
ejpam-5036	589	2	10	10	NUM
ejpam-5036	589	3	]	]	X
ejpam-5036	589	4	m	m	VERB
ejpam-5036	589	5	u	u	NOUN
ejpam-5036	589	6	romdhini	romdhini	NOUN
ejpam-5036	589	7	and	and	CCONJ
ejpam-5036	589	8	a	a	DET
ejpam-5036	589	9	nawawi	nawawi	NOUN
ejpam-5036	589	10	.	.	PUNCT
ejpam-5036	590	1	maximum	maximum	ADJ
ejpam-5036	590	2	and	and	CCONJ
ejpam-5036	590	3	minimum	minimum	NOUN
ejpam-5036	590	4	degree	degree	NOUN
ejpam-5036	590	5	energy	energy	NOUN
ejpam-5036	590	6	of	of	ADP
ejpam-5036	590	7	commuting	commuting	NOUN
ejpam-5036	590	8	graph	graph	NOUN
ejpam-5036	590	9	for	for	ADP
ejpam-5036	590	10	dihedral	dihedral	ADJ
ejpam-5036	590	11	groups	group	NOUN
ejpam-5036	590	12	.	.	PUNCT
ejpam-5036	591	1	sains	sain	NOUN
ejpam-5036	591	2	malaysiana	malaysiana	PROPN
ejpam-5036	591	3	,	,	PUNCT
ejpam-5036	591	4	51(12):4145–4151	51(12):4145–4151	NUM
ejpam-5036	591	5	,	,	PUNCT
ejpam-5036	591	6	2022	2022	NUM
ejpam-5036	591	7	.	.	PUNCT
ejpam-5036	592	1	[	[	X
ejpam-5036	592	2	11	11	NUM
ejpam-5036	592	3	]	]	SYM
ejpam-5036	592	4	m	m	VERB
ejpam-5036	592	5	u	u	NOUN
ejpam-5036	592	6	romdhini	romdhini	NOUN
ejpam-5036	592	7	and	and	CCONJ
ejpam-5036	592	8	a	a	DET
ejpam-5036	592	9	nawawi	nawawi	ADJ
ejpam-5036	592	10	.	.	PUNCT
ejpam-5036	592	11	degree	degree	NOUN
ejpam-5036	592	12	subtraction	subtraction	NOUN
ejpam-5036	592	13	energy	energy	NOUN
ejpam-5036	592	14	of	of	ADP
ejpam-5036	592	15	commuting	commute	VERB
ejpam-5036	592	16	and	and	CCONJ
ejpam-5036	592	17	noncommuting	noncommute	VERB
ejpam-5036	592	18	graphs	graph	NOUN
ejpam-5036	592	19	for	for	ADP
ejpam-5036	592	20	dihedral	dihedral	ADJ
ejpam-5036	592	21	groups	group	NOUN
ejpam-5036	592	22	.	.	PUNCT
ejpam-5036	593	1	journal	journal	PROPN
ejpam-5036	593	2	of	of	ADP
ejpam-5036	593	3	mathematical	mathematical	ADJ
ejpam-5036	593	4	and	and	CCONJ
ejpam-5036	593	5	computational	computational	ADJ
ejpam-5036	593	6	science	science	NOUN
ejpam-5036	593	7	,	,	PUNCT
ejpam-5036	593	8	18(3):497–508	18(3):497–508	NUM
ejpam-5036	593	9	,	,	PUNCT
ejpam-5036	593	10	2023	2023	NUM
ejpam-5036	593	11	.	.	PUNCT
ejpam-5036	594	1	[	[	X
ejpam-5036	594	2	12	12	NUM
ejpam-5036	594	3	]	]	X
ejpam-5036	594	4	m	m	VERB
ejpam-5036	594	5	u	u	NOUN
ejpam-5036	594	6	romdhini	romdhini	NOUN
ejpam-5036	594	7	,	,	PUNCT
ejpam-5036	594	8	a	a	DET
ejpam-5036	594	9	nawawi	nawawi	NOUN
ejpam-5036	594	10	,	,	PUNCT
ejpam-5036	594	11	and	and	CCONJ
ejpam-5036	594	12	c	c	PROPN
ejpam-5036	594	13	y	y	PROPN
ejpam-5036	594	14	chen	chen	PROPN
ejpam-5036	594	15	.	.	PUNCT
ejpam-5036	594	16	degree	degree	PROPN
ejpam-5036	594	17	exponent	exponent	NOUN
ejpam-5036	594	18	sum	sum	NOUN
ejpam-5036	594	19	energy	energy	NOUN
ejpam-5036	594	20	of	of	ADP
ejpam-5036	594	21	commuting	commuting	NOUN
ejpam-5036	594	22	graph	graph	NOUN
ejpam-5036	594	23	for	for	ADP
ejpam-5036	594	24	dihedral	dihedral	ADJ
ejpam-5036	594	25	groups	group	NOUN
ejpam-5036	594	26	.	.	PUNCT
ejpam-5036	595	1	malaysian	malaysian	ADJ
ejpam-5036	595	2	journal	journal	PROPN
ejpam-5036	595	3	of	of	ADP
ejpam-5036	595	4	science	science	NOUN
ejpam-5036	595	5	,	,	PUNCT
ejpam-5036	595	6	41(sp1):40–46	41(sp1):40–46	NUM
ejpam-5036	595	7	,	,	PUNCT
ejpam-5036	595	8	2022	2022	NUM
ejpam-5036	595	9	.	.	PUNCT
ejpam-5036	596	1	[	[	X
ejpam-5036	596	2	13	13	NUM
ejpam-5036	596	3	]	]	SYM
ejpam-5036	596	4	m	m	VERB
ejpam-5036	596	5	u	u	NOUN
ejpam-5036	596	6	romdhini	romdhini	NOUN
ejpam-5036	596	7	,	,	PUNCT
ejpam-5036	596	8	a	a	DET
ejpam-5036	596	9	nawawi	nawawi	NOUN
ejpam-5036	596	10	,	,	PUNCT
ejpam-5036	596	11	and	and	CCONJ
ejpam-5036	596	12	c	c	PROPN
ejpam-5036	596	13	y	y	PROPN
ejpam-5036	596	14	chen	chen	PROPN
ejpam-5036	596	15	.	.	PUNCT
ejpam-5036	597	1	neighbors	neighbor	NOUN
ejpam-5036	597	2	degree	degree	VERB
ejpam-5036	597	3	sum	sum	NOUN
ejpam-5036	597	4	energy	energy	NOUN
ejpam-5036	597	5	of	of	ADP
ejpam-5036	597	6	commuting	commuting	NOUN
ejpam-5036	597	7	and	and	CCONJ
ejpam-5036	597	8	non	non	ADJ
ejpam-5036	597	9	-	-	ADJ
ejpam-5036	597	10	commuting	commuting	ADJ
ejpam-5036	597	11	graphs	graph	NOUN
ejpam-5036	597	12	for	for	ADP
ejpam-5036	597	13	dihedral	dihedral	ADJ
ejpam-5036	597	14	groups	group	NOUN
ejpam-5036	597	15	.	.	PUNCT
ejpam-5036	598	1	malaysian	malaysian	ADJ
ejpam-5036	598	2	journal	journal	PROPN
ejpam-5036	598	3	of	of	ADP
ejpam-5036	598	4	mathematical	mathematical	ADJ
ejpam-5036	598	5	sciences	science	NOUN
ejpam-5036	598	6	,	,	PUNCT
ejpam-5036	598	7	17(1):53–65	17(1):53–65	NUM
ejpam-5036	598	8	,	,	PUNCT
ejpam-5036	598	9	2023	2023	NUM
ejpam-5036	598	10	.	.	PUNCT
ejpam-5036	599	1	[	[	X
ejpam-5036	599	2	14	14	NUM
ejpam-5036	599	3	]	]	X
ejpam-5036	599	4	a	a	DET
ejpam-5036	599	5	sehgal	sehgal	ADJ
ejpam-5036	599	6	and	and	CCONJ
ejpam-5036	599	7	s	s	NOUN
ejpam-5036	599	8	n	n	PRON
ejpam-5036	599	9	singh	singh	NOUN
ejpam-5036	599	10	.	.	PUNCT
ejpam-5036	600	1	the	the	DET
ejpam-5036	600	2	degree	degree	NOUN
ejpam-5036	600	3	of	of	ADP
ejpam-5036	600	4	a	a	DET
ejpam-5036	600	5	vertex	vertex	NOUN
ejpam-5036	600	6	in	in	ADP
ejpam-5036	600	7	the	the	DET
ejpam-5036	600	8	power	power	NOUN
ejpam-5036	600	9	graph	graph	NOUN
ejpam-5036	600	10	of	of	ADP
ejpam-5036	600	11	a	a	DET
ejpam-5036	600	12	finite	finite	ADJ
ejpam-5036	600	13	abelian	abelian	PROPN
ejpam-5036	600	14	group	group	NOUN
ejpam-5036	600	15	.	.	PUNCT
ejpam-5036	601	1	southeast	southeast	ADJ
ejpam-5036	601	2	asian	asian	ADJ
ejpam-5036	601	3	bulletin	bulletin	NOUN
ejpam-5036	601	4	of	of	ADP
ejpam-5036	601	5	mathematics	mathematic	NOUN
ejpam-5036	601	6	,	,	PUNCT
ejpam-5036	601	7	47:89–296	47:89–296	NUM
ejpam-5036	601	8	,	,	PUNCT
ejpam-5036	601	9	2023	2023	NUM
ejpam-5036	601	10	.	.	PUNCT
ejpam-5036	602	1	[	[	X
ejpam-5036	602	2	15	15	NUM
ejpam-5036	602	3	]	]	X
ejpam-5036	602	4	n	n	CCONJ
ejpam-5036	602	5	takshak	takshak	ADV
ejpam-5036	602	6	and	and	CCONJ
ejpam-5036	602	7	a	a	DET
ejpam-5036	602	8	sehgal	sehgal	PROPN
ejpam-5036	602	9	a	a	DET
ejpam-5036	602	10	malik	malik	PROPN
ejpam-5036	602	11	.	.	PUNCT
ejpam-5036	603	1	power	power	NOUN
ejpam-5036	603	2	graph	graph	NOUN
ejpam-5036	603	3	of	of	ADP
ejpam-5036	603	4	a	a	DET
ejpam-5036	603	5	finite	finite	ADJ
ejpam-5036	603	6	group	group	NOUN
ejpam-5036	603	7	is	be	AUX
ejpam-5036	603	8	always	always	ADV
ejpam-5036	603	9	divisor	divisor	NOUN
ejpam-5036	603	10	graph	graph	NOUN
ejpam-5036	603	11	.	.	PUNCT
ejpam-5036	604	1	asian	asian	ADJ
ejpam-5036	604	2	-	-	PUNCT
ejpam-5036	604	3	european	european	ADJ
ejpam-5036	604	4	journal	journal	NOUN
ejpam-5036	604	5	of	of	ADP
ejpam-5036	604	6	mathematics	mathematic	NOUN
ejpam-5036	604	7	,	,	PUNCT
ejpam-5036	604	8	16(1):2250236	16(1):2250236	NUM
ejpam-5036	604	9	,	,	PUNCT
ejpam-5036	604	10	2023	2023	NUM
ejpam-5036	604	11	.	.	PUNCT