id	sid	tid	token	lemma	pos
ejpam-5019	1	1	european	european	PROPN
ejpam-5019	1	2	journal	journal	PROPN
ejpam-5019	1	3	of	of	ADP
ejpam-5019	1	4	pure	pure	ADJ
ejpam-5019	1	5	and	and	CCONJ
ejpam-5019	1	6	applied	apply	VERB
ejpam-5019	1	7	mathematics	mathematic	NOUN
ejpam-5019	1	8	vol	vol	NOUN
ejpam-5019	1	9	.	.	PROPN
ejpam-5019	2	1	17	17	NUM
ejpam-5019	2	2	,	,	PUNCT
ejpam-5019	2	3	no	no	INTJ
ejpam-5019	2	4	.	.	NOUN
ejpam-5019	2	5	1	1	NUM
ejpam-5019	2	6	,	,	PUNCT
ejpam-5019	2	7	2024	2024	NUM
ejpam-5019	2	8	,	,	PUNCT
ejpam-5019	2	9	462	462	NUM
ejpam-5019	2	10	-	-	SYM
ejpam-5019	2	11	476	476	NUM
ejpam-5019	2	12	issn	issn	PROPN
ejpam-5019	2	13	1307	1307	NUM
ejpam-5019	2	14	-	-	SYM
ejpam-5019	2	15	5543	5543	NUM
ejpam-5019	2	16	–	–	PUNCT
ejpam-5019	3	1	ejpam.com	ejpam.com	X
ejpam-5019	3	2	published	publish	VERB
ejpam-5019	3	3	by	by	ADP
ejpam-5019	3	4	new	new	PROPN
ejpam-5019	3	5	york	york	PROPN
ejpam-5019	3	6	business	business	PROPN
ejpam-5019	3	7	global	global	ADJ
ejpam-5019	3	8	universal	universal	PROPN
ejpam-5019	3	9	distance	distance	NOUN
ejpam-5019	3	10	spectra	spectra	NOUN
ejpam-5019	3	11	of	of	ADP
ejpam-5019	3	12	join	join	NOUN
ejpam-5019	3	13	of	of	ADP
ejpam-5019	3	14	graphs	graph	NOUN
ejpam-5019	3	15	sakthidevi	sakthidevi	PROPN
ejpam-5019	3	16	kaliyaperumal1	kaliyaperumal1	PROPN
ejpam-5019	3	17	,	,	PUNCT
ejpam-5019	3	18	kalyani	kalyani	PROPN
ejpam-5019	3	19	desikan,∗1	desikan,∗1	PROPN
ejpam-5019	3	20	1	1	NUM
ejpam-5019	3	21	school	school	NOUN
ejpam-5019	3	22	of	of	ADP
ejpam-5019	3	23	advanced	advanced	ADJ
ejpam-5019	3	24	sciences	science	NOUN
ejpam-5019	3	25	,	,	PUNCT
ejpam-5019	3	26	division	division	NOUN
ejpam-5019	3	27	of	of	ADP
ejpam-5019	3	28	mathematics	mathematic	NOUN
ejpam-5019	3	29	,	,	PUNCT
ejpam-5019	3	30	vellore	vellore	PROPN
ejpam-5019	3	31	institute	institute	PROPN
ejpam-5019	3	32	of	of	ADP
ejpam-5019	3	33	technology	technology	PROPN
ejpam-5019	3	34	,	,	PUNCT
ejpam-5019	3	35	chennai	chennai	PROPN
ejpam-5019	3	36	,	,	PUNCT
ejpam-5019	3	37	tamilnadu	tamilnadu	NOUN
ejpam-5019	3	38	,	,	PUNCT
ejpam-5019	3	39	india	india	PROPN
ejpam-5019	3	40	abstract	abstract	NOUN
ejpam-5019	3	41	.	.	PUNCT
ejpam-5019	4	1	let	let	VERB
ejpam-5019	4	2	g	g	PRON
ejpam-5019	4	3	be	be	AUX
ejpam-5019	4	4	a	a	DET
ejpam-5019	4	5	simple	simple	ADJ
ejpam-5019	4	6	undirected	undirected	ADJ
ejpam-5019	4	7	graph	graph	NOUN
ejpam-5019	4	8	of	of	ADP
ejpam-5019	4	9	order	order	NOUN
ejpam-5019	4	10	n.	n.	NOUN
ejpam-5019	4	11	in	in	ADP
ejpam-5019	4	12	this	this	DET
ejpam-5019	4	13	paper	paper	NOUN
ejpam-5019	4	14	,	,	PUNCT
ejpam-5019	4	15	we	we	PRON
ejpam-5019	4	16	introduce	introduce	VERB
ejpam-5019	4	17	a	a	DET
ejpam-5019	4	18	new	new	ADJ
ejpam-5019	4	19	distance	distance	NOUN
ejpam-5019	4	20	matrix	matrix	NOUN
ejpam-5019	4	21	called	call	VERB
ejpam-5019	4	22	the	the	DET
ejpam-5019	4	23	universal	universal	ADJ
ejpam-5019	4	24	distance	distance	NOUN
ejpam-5019	4	25	matrix	matrix	NOUN
ejpam-5019	4	26	of	of	ADP
ejpam-5019	4	27	g	g	NOUN
ejpam-5019	4	28	,	,	PUNCT
ejpam-5019	4	29	denoted	denote	VERB
ejpam-5019	4	30	as	as	ADP
ejpam-5019	4	31	ud	ud	ADP
ejpam-5019	4	32	(	(	PUNCT
ejpam-5019	4	33	g	g	NOUN
ejpam-5019	4	34	)	)	PUNCT
ejpam-5019	4	35	and	and	CCONJ
ejpam-5019	4	36	it	it	PRON
ejpam-5019	4	37	is	be	AUX
ejpam-5019	4	38	defined	define	VERB
ejpam-5019	4	39	as	as	ADP
ejpam-5019	4	40	ud	ud	INTJ
ejpam-5019	4	41	(	(	PUNCT
ejpam-5019	4	42	g	g	NOUN
ejpam-5019	4	43	)	)	PUNCT
ejpam-5019	5	1	=	=	SYM
ejpam-5019	5	2	αtr	αtr	NOUN
ejpam-5019	5	3	(	(	PUNCT
ejpam-5019	5	4	g	g	NOUN
ejpam-5019	5	5	)	)	PUNCT
ejpam-5019	5	6	+	+	NUM
ejpam-5019	5	7	βd	βd	INTJ
ejpam-5019	5	8	(	(	PUNCT
ejpam-5019	5	9	g	g	NOUN
ejpam-5019	5	10	)	)	PUNCT
ejpam-5019	5	11	+	+	SYM
ejpam-5019	5	12	γj	γj	ADP
ejpam-5019	5	13	+	+	CCONJ
ejpam-5019	5	14	δi	δi	PROPN
ejpam-5019	5	15	,	,	PUNCT
ejpam-5019	5	16	where	where	SCONJ
ejpam-5019	5	17	tr	tr	X
ejpam-5019	5	18	(	(	PUNCT
ejpam-5019	5	19	g	g	NOUN
ejpam-5019	5	20	)	)	PUNCT
ejpam-5019	5	21	is	be	AUX
ejpam-5019	5	22	the	the	DET
ejpam-5019	5	23	diagonal	diagonal	ADJ
ejpam-5019	5	24	matrix	matrix	NOUN
ejpam-5019	5	25	whose	whose	DET
ejpam-5019	5	26	elements	element	NOUN
ejpam-5019	5	27	are	be	AUX
ejpam-5019	5	28	the	the	DET
ejpam-5019	5	29	vertex	vertex	NOUN
ejpam-5019	5	30	transmissions	transmission	NOUN
ejpam-5019	5	31	,	,	PUNCT
ejpam-5019	5	32	and	and	CCONJ
ejpam-5019	5	33	d	d	X
ejpam-5019	5	34	(	(	PUNCT
ejpam-5019	5	35	g	g	NOUN
ejpam-5019	5	36	)	)	PUNCT
ejpam-5019	5	37	is	be	AUX
ejpam-5019	5	38	the	the	DET
ejpam-5019	5	39	distance	distance	NOUN
ejpam-5019	5	40	matrix	matrix	NOUN
ejpam-5019	5	41	of	of	ADP
ejpam-5019	5	42	g.	g.	PROPN
ejpam-5019	5	43	here	here	ADV
ejpam-5019	5	44	j	j	PROPN
ejpam-5019	5	45	is	be	AUX
ejpam-5019	5	46	the	the	DET
ejpam-5019	5	47	all	all	DET
ejpam-5019	5	48	-	-	PUNCT
ejpam-5019	5	49	ones	one	NOUN
ejpam-5019	5	50	matrix	matrix	NOUN
ejpam-5019	5	51	,	,	PUNCT
ejpam-5019	5	52	and	and	CCONJ
ejpam-5019	5	53	i	i	PRON
ejpam-5019	5	54	is	be	AUX
ejpam-5019	5	55	the	the	DET
ejpam-5019	5	56	identity	identity	NOUN
ejpam-5019	5	57	matrix	matrix	NOUN
ejpam-5019	5	58	and	and	CCONJ
ejpam-5019	5	59	α	α	NOUN
ejpam-5019	5	60	,	,	PUNCT
ejpam-5019	5	61	β	β	X
ejpam-5019	5	62	,	,	PUNCT
ejpam-5019	5	63	γ	γ	PROPN
ejpam-5019	5	64	,	,	PUNCT
ejpam-5019	5	65	δ	δ	PROPN
ejpam-5019	5	66	∈	∈	PROPN
ejpam-5019	5	67	r	r	NOUN
ejpam-5019	5	68	and	and	CCONJ
ejpam-5019	5	69	β	β	ADJ
ejpam-5019	5	70	̸=	̸=	PROPN
ejpam-5019	5	71	0	0	NUM
ejpam-5019	5	72	.	.	PUNCT
ejpam-5019	6	1	this	this	DET
ejpam-5019	6	2	unified	unified	ADJ
ejpam-5019	6	3	definition	definition	NOUN
ejpam-5019	6	4	enables	enable	VERB
ejpam-5019	6	5	us	we	PRON
ejpam-5019	6	6	to	to	PART
ejpam-5019	6	7	derive	derive	VERB
ejpam-5019	6	8	the	the	DET
ejpam-5019	6	9	spectra	spectra	NOUN
ejpam-5019	6	10	of	of	ADP
ejpam-5019	6	11	different	different	ADJ
ejpam-5019	6	12	matrices	matrix	NOUN
ejpam-5019	6	13	associated	associate	VERB
ejpam-5019	6	14	with	with	ADP
ejpam-5019	6	15	the	the	DET
ejpam-5019	6	16	distance	distance	NOUN
ejpam-5019	6	17	matrix	matrix	NOUN
ejpam-5019	6	18	of	of	ADP
ejpam-5019	6	19	graphs	graph	NOUN
ejpam-5019	6	20	.	.	PUNCT
ejpam-5019	7	1	the	the	DET
ejpam-5019	7	2	set	set	NOUN
ejpam-5019	7	3	of	of	ADP
ejpam-5019	7	4	eigenvalues	eigenvalue	NOUN
ejpam-5019	7	5	of	of	ADP
ejpam-5019	7	6	the	the	DET
ejpam-5019	7	7	universal	universal	ADJ
ejpam-5019	7	8	distance	distance	NOUN
ejpam-5019	7	9	matrix	matrix	NOUN
ejpam-5019	7	10	namely	namely	ADV
ejpam-5019	7	11	,	,	PUNCT
ejpam-5019	7	12	{	{	PUNCT
ejpam-5019	7	13	ρ1	ρ1	NOUN
ejpam-5019	7	14	,	,	PUNCT
ejpam-5019	7	15	ρ2	ρ2	NOUN
ejpam-5019	7	16	,	,	PUNCT
ejpam-5019	7	17	.	.	PUNCT
ejpam-5019	7	18	.	.	PUNCT
ejpam-5019	7	19	.	.	PUNCT
ejpam-5019	8	1	,	,	PUNCT
ejpam-5019	8	2	ρn	ρn	CCONJ
ejpam-5019	8	3	}	}	PUNCT
ejpam-5019	8	4	is	be	AUX
ejpam-5019	8	5	known	know	VERB
ejpam-5019	8	6	as	as	ADP
ejpam-5019	8	7	the	the	DET
ejpam-5019	8	8	universal	universal	ADJ
ejpam-5019	8	9	distance	distance	NOUN
ejpam-5019	8	10	spectrum	spectrum	NOUN
ejpam-5019	8	11	of	of	ADP
ejpam-5019	8	12	g.	g.	PROPN
ejpam-5019	8	13	as	as	ADP
ejpam-5019	8	14	a	a	DET
ejpam-5019	8	15	consequence	consequence	NOUN
ejpam-5019	8	16	,	,	PUNCT
ejpam-5019	8	17	by	by	ADP
ejpam-5019	8	18	taking	take	VERB
ejpam-5019	8	19	appropriate	appropriate	ADJ
ejpam-5019	8	20	values	value	NOUN
ejpam-5019	8	21	for	for	ADP
ejpam-5019	8	22	α	α	NOUN
ejpam-5019	8	23	,	,	PUNCT
ejpam-5019	8	24	β	β	X
ejpam-5019	8	25	,	,	PUNCT
ejpam-5019	8	26	γ	γ	PROPN
ejpam-5019	8	27	,	,	PUNCT
ejpam-5019	8	28	δ	δ	PROPN
ejpam-5019	8	29	∈	∈	PROPN
ejpam-5019	8	30	r	r	NOUN
ejpam-5019	8	31	and	and	CCONJ
ejpam-5019	8	32	β	β	ADJ
ejpam-5019	8	33	̸=	̸=	PROPN
ejpam-5019	8	34	0	0	NUM
ejpam-5019	8	35	,	,	PUNCT
ejpam-5019	8	36	we	we	PRON
ejpam-5019	8	37	obtain	obtain	VERB
ejpam-5019	8	38	the	the	DET
ejpam-5019	8	39	eigenvalues	eigenvalue	NOUN
ejpam-5019	8	40	of	of	ADP
ejpam-5019	8	41	distance	distance	NOUN
ejpam-5019	8	42	matrix	matrix	NOUN
ejpam-5019	8	43	,	,	PUNCT
ejpam-5019	8	44	distance	distance	NOUN
ejpam-5019	8	45	laplacian	laplacian	ADJ
ejpam-5019	8	46	matrix	matrix	NOUN
ejpam-5019	8	47	,	,	PUNCT
ejpam-5019	8	48	distance	distance	NOUN
ejpam-5019	8	49	signless	signless	NOUN
ejpam-5019	8	50	laplacian	laplacian	ADJ
ejpam-5019	8	51	matrix	matrix	NOUN
ejpam-5019	8	52	,	,	PUNCT
ejpam-5019	8	53	generalized	generalized	ADJ
ejpam-5019	8	54	distance	distance	NOUN
ejpam-5019	8	55	matrix	matrix	NOUN
ejpam-5019	8	56	,	,	PUNCT
ejpam-5019	8	57	distance	distance	NOUN
ejpam-5019	8	58	seidal	seidal	NOUN
ejpam-5019	8	59	matrix	matrix	NOUN
ejpam-5019	8	60	and	and	CCONJ
ejpam-5019	8	61	distance	distance	NOUN
ejpam-5019	8	62	matrices	matrix	NOUN
ejpam-5019	8	63	of	of	ADP
ejpam-5019	8	64	graph	graph	NOUN
ejpam-5019	8	65	complements	complement	NOUN
ejpam-5019	8	66	.	.	PUNCT
ejpam-5019	9	1	in	in	ADP
ejpam-5019	9	2	this	this	DET
ejpam-5019	9	3	paper	paper	NOUN
ejpam-5019	9	4	,	,	PUNCT
ejpam-5019	9	5	we	we	PRON
ejpam-5019	9	6	obtain	obtain	VERB
ejpam-5019	9	7	the	the	DET
ejpam-5019	9	8	universal	universal	ADJ
ejpam-5019	9	9	distance	distance	NOUN
ejpam-5019	9	10	spectra	spectra	NOUN
ejpam-5019	9	11	of	of	ADP
ejpam-5019	9	12	regular	regular	ADJ
ejpam-5019	9	13	graph	graph	NOUN
ejpam-5019	9	14	,	,	PUNCT
ejpam-5019	9	15	join	join	NOUN
ejpam-5019	9	16	of	of	ADP
ejpam-5019	9	17	two	two	NUM
ejpam-5019	9	18	regular	regular	ADJ
ejpam-5019	9	19	graphs	graph	NOUN
ejpam-5019	9	20	,	,	PUNCT
ejpam-5019	9	21	joined	join	VERB
ejpam-5019	9	22	union	union	NOUN
ejpam-5019	9	23	of	of	ADP
ejpam-5019	9	24	three	three	NUM
ejpam-5019	9	25	regular	regular	ADJ
ejpam-5019	9	26	graphs	graph	NOUN
ejpam-5019	9	27	,	,	PUNCT
ejpam-5019	9	28	generalized	generalize	VERB
ejpam-5019	9	29	joined	join	VERB
ejpam-5019	9	30	union	union	NOUN
ejpam-5019	9	31	of	of	ADP
ejpam-5019	9	32	n	n	PRON
ejpam-5019	9	33	disjoint	disjoint	NOUN
ejpam-5019	9	34	graphs	graph	NOUN
ejpam-5019	9	35	with	with	ADP
ejpam-5019	9	36	one	one	NUM
ejpam-5019	9	37	arbitrary	arbitrary	ADJ
ejpam-5019	9	38	graph	graph	NOUN
ejpam-5019	9	39	h	h	NOUN
ejpam-5019	9	40	using	use	VERB
ejpam-5019	9	41	the	the	DET
ejpam-5019	9	42	schur	schur	NOUN
ejpam-5019	9	43	complement	complement	NOUN
ejpam-5019	9	44	of	of	ADP
ejpam-5019	9	45	a	a	DET
ejpam-5019	9	46	block	block	NOUN
ejpam-5019	9	47	matrix	matrix	NOUN
ejpam-5019	9	48	.	.	PUNCT
ejpam-5019	10	1	2020	2020	NUM
ejpam-5019	10	2	mathematics	mathematic	NOUN
ejpam-5019	10	3	subject	subject	NOUN
ejpam-5019	10	4	classifications	classification	NOUN
ejpam-5019	10	5	:	:	PUNCT
ejpam-5019	10	6	05c50	05c50	NUM
ejpam-5019	10	7	key	key	ADJ
ejpam-5019	10	8	words	word	NOUN
ejpam-5019	10	9	and	and	CCONJ
ejpam-5019	10	10	phrases	phrase	NOUN
ejpam-5019	10	11	:	:	PUNCT
ejpam-5019	10	12	universal	universal	ADJ
ejpam-5019	10	13	distance	distance	NOUN
ejpam-5019	10	14	spectrum	spectrum	NOUN
ejpam-5019	10	15	,	,	PUNCT
ejpam-5019	10	16	seidal	seidal	NOUN
ejpam-5019	10	17	matrix	matrix	NOUN
ejpam-5019	10	18	,	,	PUNCT
ejpam-5019	10	19	joined	join	VERB
ejpam-5019	10	20	union	union	NOUN
ejpam-5019	10	21	,	,	PUNCT
ejpam-5019	10	22	complete	complete	ADJ
ejpam-5019	10	23	split	split	NOUN
ejpam-5019	10	24	graph	graph	NOUN
ejpam-5019	10	25	.	.	PUNCT
ejpam-5019	11	1	1	1	X
ejpam-5019	11	2	.	.	X
ejpam-5019	11	3	introduction	introduction	NOUN
ejpam-5019	11	4	consider	consider	VERB
ejpam-5019	11	5	a	a	DET
ejpam-5019	11	6	graph	graph	NOUN
ejpam-5019	11	7	g	g	NOUN
ejpam-5019	11	8	consisting	consist	VERB
ejpam-5019	11	9	of	of	ADP
ejpam-5019	11	10	the	the	DET
ejpam-5019	11	11	vertex	vertex	NOUN
ejpam-5019	11	12	set	set	VERB
ejpam-5019	11	13	v	v	NOUN
ejpam-5019	11	14	(	(	PUNCT
ejpam-5019	11	15	g	g	NOUN
ejpam-5019	11	16	)	)	PUNCT
ejpam-5019	11	17	and	and	CCONJ
ejpam-5019	11	18	the	the	DET
ejpam-5019	11	19	edge	edge	NOUN
ejpam-5019	11	20	set	set	NOUN
ejpam-5019	11	21	e	e	X
ejpam-5019	11	22	(	(	PUNCT
ejpam-5019	11	23	g	g	NOUN
ejpam-5019	11	24	)	)	PUNCT
ejpam-5019	11	25	on	on	ADP
ejpam-5019	11	26	n	n	PRON
ejpam-5019	11	27	vertices	vertex	NOUN
ejpam-5019	11	28	.	.	PUNCT
ejpam-5019	12	1	degree	degree	NOUN
ejpam-5019	12	2	of	of	ADP
ejpam-5019	12	3	a	a	DET
ejpam-5019	12	4	vertex	vertex	NOUN
ejpam-5019	12	5	is	be	AUX
ejpam-5019	12	6	the	the	DET
ejpam-5019	12	7	number	number	NOUN
ejpam-5019	12	8	of	of	ADP
ejpam-5019	12	9	edges	edge	NOUN
ejpam-5019	12	10	incident	incident	NOUN
ejpam-5019	12	11	on	on	ADP
ejpam-5019	12	12	that	that	DET
ejpam-5019	12	13	vertex	vertex	NOUN
ejpam-5019	12	14	.	.	PUNCT
ejpam-5019	13	1	a	a	DET
ejpam-5019	13	2	graph	graph	NOUN
ejpam-5019	13	3	g	g	NOUN
ejpam-5019	13	4	is	be	AUX
ejpam-5019	13	5	regular	regular	ADJ
ejpam-5019	13	6	if	if	SCONJ
ejpam-5019	13	7	every	every	DET
ejpam-5019	13	8	vertex	vertex	NOUN
ejpam-5019	13	9	has	have	VERB
ejpam-5019	13	10	the	the	DET
ejpam-5019	13	11	same	same	ADJ
ejpam-5019	13	12	degree	degree	NOUN
ejpam-5019	13	13	.	.	PUNCT
ejpam-5019	14	1	the	the	DET
ejpam-5019	14	2	adjacency	adjacency	PROPN
ejpam-5019	14	3	matrix	matrix	NOUN
ejpam-5019	14	4	a	a	DET
ejpam-5019	14	5	(	(	PUNCT
ejpam-5019	14	6	g	g	NOUN
ejpam-5019	14	7	)	)	PUNCT
ejpam-5019	14	8	=	=	PUNCT
ejpam-5019	14	9	(	(	PUNCT
ejpam-5019	14	10	aij	aij	PROPN
ejpam-5019	14	11	)	)	PUNCT
ejpam-5019	14	12	of	of	ADP
ejpam-5019	14	13	g	g	PROPN
ejpam-5019	14	14	,	,	PUNCT
ejpam-5019	14	15	where	where	SCONJ
ejpam-5019	14	16	v	v	X
ejpam-5019	14	17	(	(	PUNCT
ejpam-5019	14	18	g	g	NOUN
ejpam-5019	14	19	)	)	PUNCT
ejpam-5019	14	20	=	=	SYM
ejpam-5019	14	21	{	{	PUNCT
ejpam-5019	14	22	v1	v1	PROPN
ejpam-5019	14	23	,	,	PUNCT
ejpam-5019	14	24	v2	v2	PROPN
ejpam-5019	14	25	,	,	PUNCT
ejpam-5019	14	26	.	.	PUNCT
ejpam-5019	14	27	.	.	PUNCT
ejpam-5019	14	28	.	.	PUNCT
ejpam-5019	15	1	,	,	PUNCT
ejpam-5019	15	2	vn	vn	PROPN
ejpam-5019	15	3	}	}	PUNCT
ejpam-5019	15	4	is	be	AUX
ejpam-5019	15	5	the	the	DET
ejpam-5019	15	6	n×	n×	PROPN
ejpam-5019	15	7	n	n	CCONJ
ejpam-5019	15	8	symmetric	symmetric	ADJ
ejpam-5019	15	9	matrix	matrix	NOUN
ejpam-5019	15	10	defined	define	VERB
ejpam-5019	15	11	by	by	ADP
ejpam-5019	15	12	aij	aij	PROPN
ejpam-5019	15	13	=	=	SYM
ejpam-5019	15	14	{	{	PUNCT
ejpam-5019	15	15	1	1	NUM
ejpam-5019	15	16	,	,	PUNCT
ejpam-5019	15	17	if	if	SCONJ
ejpam-5019	15	18	d	d	X
ejpam-5019	15	19	(	(	PUNCT
ejpam-5019	15	20	vi	vi	PROPN
ejpam-5019	15	21	,	,	PUNCT
ejpam-5019	15	22	vj	vj	ADJ
ejpam-5019	15	23	)	)	PUNCT
ejpam-5019	15	24	=	=	SYM
ejpam-5019	16	1	1	1	NUM
ejpam-5019	16	2	0	0	NUM
ejpam-5019	16	3	,	,	PUNCT
ejpam-5019	16	4	otherwise	otherwise	ADV
ejpam-5019	16	5	.	.	PUNCT
ejpam-5019	17	1	∗corresponding	∗corresponde	VERB
ejpam-5019	17	2	author	author	NOUN
ejpam-5019	17	3	.	.	PUNCT
ejpam-5019	18	1	doi	doi	NOUN
ejpam-5019	18	2	:	:	PUNCT
ejpam-5019	18	3	https://doi.org/10.29020/nybg.ejpam.v17i1.5019	https://doi.org/10.29020/nybg.ejpam.v17i1.5019	ADJ
ejpam-5019	18	4	email	email	NOUN
ejpam-5019	18	5	addresses	address	VERB
ejpam-5019	18	6	:	:	PUNCT
ejpam-5019	18	7	sakthidevi.k2019@vitstudent.ac.in	sakthidevi.k2019@vitstudent.ac.in	X
ejpam-5019	18	8	(	(	PUNCT
ejpam-5019	18	9	s.	s.	PROPN
ejpam-5019	18	10	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	18	11	)	)	PUNCT
ejpam-5019	18	12	,	,	PUNCT
ejpam-5019	18	13	kalyanidesikan@vit.ac.in	kalyanidesikan@vit.ac.in	NOUN
ejpam-5019	18	14	(	(	PUNCT
ejpam-5019	18	15	k.	k.	PROPN
ejpam-5019	18	16	desikan	desikan	PROPN
ejpam-5019	18	17	)	)	PUNCT
ejpam-5019	18	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5019	19	1	462	462	NUM
ejpam-5019	19	2	©	©	PROPN
ejpam-5019	19	3	2024	2024	NUM
ejpam-5019	19	4	ejpam	ejpam	NOUN
ejpam-5019	19	5	all	all	DET
ejpam-5019	19	6	rights	right	NOUN
ejpam-5019	19	7	reserved	reserve	VERB
ejpam-5019	19	8	.	.	PUNCT
ejpam-5019	20	1	s.	s.	PROPN
ejpam-5019	20	2	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	20	3	,	,	PUNCT
ejpam-5019	20	4	k.	k.	PROPN
ejpam-5019	20	5	desikan	desikan	PROPN
ejpam-5019	20	6	/	/	SYM
ejpam-5019	20	7	eur	eur	PROPN
ejpam-5019	20	8	.	.	PUNCT
ejpam-5019	21	1	j.	j.	PROPN
ejpam-5019	21	2	pure	pure	PROPN
ejpam-5019	21	3	appl	appl	PROPN
ejpam-5019	21	4	.	.	PROPN
ejpam-5019	21	5	math	math	PROPN
ejpam-5019	21	6	,	,	PUNCT
ejpam-5019	21	7	17	17	NUM
ejpam-5019	21	8	(	(	PUNCT
ejpam-5019	21	9	1	1	NUM
ejpam-5019	21	10	)	)	PUNCT
ejpam-5019	21	11	(	(	PUNCT
ejpam-5019	21	12	2024	2024	NUM
ejpam-5019	21	13	)	)	PUNCT
ejpam-5019	21	14	,	,	PUNCT
ejpam-5019	21	15	462	462	NUM
ejpam-5019	21	16	-	-	SYM
ejpam-5019	21	17	476	476	NUM
ejpam-5019	21	18	463	463	NUM
ejpam-5019	21	19	let	let	VERB
ejpam-5019	21	20	λ1	λ1	PROPN
ejpam-5019	21	21	≥	≥	NOUN
ejpam-5019	21	22	λ2	λ2	NOUN
ejpam-5019	21	23	≥	≥	NOUN
ejpam-5019	21	24	·	·	PUNCT
ejpam-5019	21	25	·	·	PUNCT
ejpam-5019	21	26	·	·	PUNCT
ejpam-5019	22	1	≥	≥	PRON
ejpam-5019	22	2	λn	λn	AUX
ejpam-5019	22	3	be	be	AUX
ejpam-5019	22	4	the	the	DET
ejpam-5019	22	5	eigenvalues	eigenvalue	NOUN
ejpam-5019	22	6	of	of	ADP
ejpam-5019	22	7	the	the	DET
ejpam-5019	22	8	adjacency	adjacency	NOUN
ejpam-5019	22	9	matrix	matrix	NOUN
ejpam-5019	22	10	of	of	ADP
ejpam-5019	22	11	g.	g.	PROPN
ejpam-5019	22	12	the	the	DET
ejpam-5019	22	13	diameter	diameter	NOUN
ejpam-5019	22	14	is	be	AUX
ejpam-5019	22	15	the	the	DET
ejpam-5019	22	16	maximum	maximum	ADJ
ejpam-5019	22	17	distance	distance	NOUN
ejpam-5019	22	18	between	between	ADP
ejpam-5019	22	19	all	all	DET
ejpam-5019	22	20	pairs	pair	NOUN
ejpam-5019	22	21	of	of	ADP
ejpam-5019	22	22	vertices	vertex	NOUN
ejpam-5019	22	23	of	of	ADP
ejpam-5019	22	24	a	a	DET
ejpam-5019	22	25	graph	graph	NOUN
ejpam-5019	22	26	g.	g.	NOUN
ejpam-5019	22	27	the	the	DET
ejpam-5019	22	28	complement	complement	NOUN
ejpam-5019	22	29	of	of	ADP
ejpam-5019	22	30	g	g	PROPN
ejpam-5019	22	31	is	be	AUX
ejpam-5019	22	32	denoted	denote	VERB
ejpam-5019	22	33	by	by	ADP
ejpam-5019	22	34	g	g	PROPN
ejpam-5019	22	35	and	and	CCONJ
ejpam-5019	22	36	is	be	AUX
ejpam-5019	22	37	the	the	DET
ejpam-5019	22	38	graph	graph	NOUN
ejpam-5019	22	39	whose	whose	DET
ejpam-5019	22	40	vertex	vertex	NOUN
ejpam-5019	22	41	set	set	NOUN
ejpam-5019	22	42	is	be	AUX
ejpam-5019	22	43	the	the	DET
ejpam-5019	22	44	same	same	ADJ
ejpam-5019	22	45	as	as	ADP
ejpam-5019	22	46	that	that	PRON
ejpam-5019	22	47	of	of	ADP
ejpam-5019	22	48	g	g	PROPN
ejpam-5019	22	49	and	and	CCONJ
ejpam-5019	22	50	two	two	NUM
ejpam-5019	22	51	vertices	vertex	NOUN
ejpam-5019	22	52	are	be	AUX
ejpam-5019	22	53	adjacent	adjacent	ADJ
ejpam-5019	22	54	in	in	ADP
ejpam-5019	22	55	g	g	PROPN
ejpam-5019	22	56	if	if	SCONJ
ejpam-5019	23	1	and	and	CCONJ
ejpam-5019	23	2	only	only	ADV
ejpam-5019	23	3	if	if	SCONJ
ejpam-5019	23	4	they	they	PRON
ejpam-5019	23	5	are	be	AUX
ejpam-5019	23	6	not	not	PART
ejpam-5019	23	7	adjacent	adjacent	ADJ
ejpam-5019	23	8	in	in	ADP
ejpam-5019	23	9	g.	g.	PROPN
ejpam-5019	23	10	the	the	DET
ejpam-5019	23	11	join	join	NOUN
ejpam-5019	23	12	of	of	ADP
ejpam-5019	23	13	two	two	NUM
ejpam-5019	23	14	graphs	graph	NOUN
ejpam-5019	23	15	g1	g1	NOUN
ejpam-5019	23	16	and	and	CCONJ
ejpam-5019	23	17	g2	g2	PROPN
ejpam-5019	23	18	,	,	PUNCT
ejpam-5019	23	19	denoted	denote	VERB
ejpam-5019	23	20	by	by	ADP
ejpam-5019	23	21	g1∇g2	g1∇g2	NUM
ejpam-5019	23	22	is	be	AUX
ejpam-5019	23	23	the	the	DET
ejpam-5019	23	24	graph	graph	NOUN
ejpam-5019	23	25	obtained	obtain	VERB
ejpam-5019	23	26	by	by	ADP
ejpam-5019	23	27	joining	join	VERB
ejpam-5019	23	28	every	every	DET
ejpam-5019	23	29	vertex	vertex	NOUN
ejpam-5019	23	30	of	of	ADP
ejpam-5019	23	31	g1	g1	NOUN
ejpam-5019	23	32	with	with	ADP
ejpam-5019	23	33	every	every	DET
ejpam-5019	23	34	vertex	vertex	NOUN
ejpam-5019	23	35	of	of	ADP
ejpam-5019	23	36	g2	g2	PROPN
ejpam-5019	23	37	.	.	PUNCT
ejpam-5019	24	1	the	the	DET
ejpam-5019	24	2	union	union	NOUN
ejpam-5019	24	3	of	of	ADP
ejpam-5019	24	4	two	two	NUM
ejpam-5019	24	5	graphs	graph	NOUN
ejpam-5019	24	6	g1	g1	NOUN
ejpam-5019	24	7	and	and	CCONJ
ejpam-5019	24	8	g2	g2	PROPN
ejpam-5019	24	9	,	,	PUNCT
ejpam-5019	24	10	denoted	denote	VERB
ejpam-5019	24	11	by	by	ADP
ejpam-5019	24	12	g1	g1	PROPN
ejpam-5019	24	13	∪g2	∪g2	PROPN
ejpam-5019	24	14	is	be	AUX
ejpam-5019	24	15	the	the	DET
ejpam-5019	24	16	graph	graph	NOUN
ejpam-5019	24	17	whose	whose	DET
ejpam-5019	24	18	vertex	vertex	NOUN
ejpam-5019	24	19	set	set	NOUN
ejpam-5019	24	20	is	be	AUX
ejpam-5019	24	21	v	v	NOUN
ejpam-5019	24	22	(	(	PUNCT
ejpam-5019	24	23	g1)∪	g1)∪	NOUN
ejpam-5019	24	24	v	v	X
ejpam-5019	24	25	(	(	PUNCT
ejpam-5019	24	26	g2	g2	PROPN
ejpam-5019	24	27	)	)	PUNCT
ejpam-5019	24	28	and	and	CCONJ
ejpam-5019	24	29	edge	edge	NOUN
ejpam-5019	24	30	set	set	NOUN
ejpam-5019	24	31	is	be	AUX
ejpam-5019	24	32	e	e	NOUN
ejpam-5019	24	33	(	(	PUNCT
ejpam-5019	24	34	g1)∪	g1)∪	NOUN
ejpam-5019	24	35	e	e	X
ejpam-5019	24	36	(	(	PUNCT
ejpam-5019	24	37	g2	g2	PROPN
ejpam-5019	24	38	)	)	PUNCT
ejpam-5019	24	39	.	.	PUNCT
ejpam-5019	25	1	as	as	ADP
ejpam-5019	25	2	usual	usual	ADJ
ejpam-5019	25	3	,	,	PUNCT
ejpam-5019	25	4	we	we	PRON
ejpam-5019	25	5	denote	denote	VERB
ejpam-5019	25	6	by	by	ADP
ejpam-5019	25	7	cn	cn	PROPN
ejpam-5019	25	8	,	,	PUNCT
ejpam-5019	25	9	the	the	DET
ejpam-5019	25	10	cycle	cycle	NOUN
ejpam-5019	25	11	graph	graph	NOUN
ejpam-5019	25	12	and	and	CCONJ
ejpam-5019	25	13	kn	kn	PROPN
ejpam-5019	25	14	,	,	PUNCT
ejpam-5019	25	15	the	the	DET
ejpam-5019	25	16	complete	complete	ADJ
ejpam-5019	25	17	graph	graph	NOUN
ejpam-5019	25	18	,	,	PUNCT
ejpam-5019	25	19	on	on	ADP
ejpam-5019	25	20	n	n	PRON
ejpam-5019	25	21	vertices	vertex	NOUN
ejpam-5019	25	22	.	.	PUNCT
ejpam-5019	26	1	the	the	DET
ejpam-5019	26	2	distance	distance	NOUN
ejpam-5019	26	3	matrix	matrix	NOUN
ejpam-5019	26	4	of	of	ADP
ejpam-5019	26	5	a	a	DET
ejpam-5019	26	6	connected	connected	ADJ
ejpam-5019	26	7	graph	graph	NOUN
ejpam-5019	26	8	g	g	NOUN
ejpam-5019	26	9	of	of	ADP
ejpam-5019	26	10	order	order	NOUN
ejpam-5019	26	11	n	n	CCONJ
ejpam-5019	26	12	,	,	PUNCT
ejpam-5019	26	13	denoted	denote	VERB
ejpam-5019	26	14	by	by	ADP
ejpam-5019	26	15	d	d	PROPN
ejpam-5019	26	16	(	(	PUNCT
ejpam-5019	26	17	g	g	NOUN
ejpam-5019	26	18	)	)	PUNCT
ejpam-5019	26	19	,	,	PUNCT
ejpam-5019	26	20	is	be	AUX
ejpam-5019	26	21	the	the	DET
ejpam-5019	26	22	symmetric	symmetric	ADJ
ejpam-5019	26	23	n×	n×	PROPN
ejpam-5019	26	24	n	n	NOUN
ejpam-5019	26	25	matrix	matrix	NOUN
ejpam-5019	26	26	(	(	PUNCT
ejpam-5019	26	27	bij	bij	NOUN
ejpam-5019	26	28	)	)	PUNCT
ejpam-5019	26	29	,	,	PUNCT
ejpam-5019	26	30	where	where	SCONJ
ejpam-5019	26	31	bi	bi	NOUN
ejpam-5019	26	32	,	,	PUNCT
ejpam-5019	26	33	j	j	PROPN
ejpam-5019	26	34	=	=	SYM
ejpam-5019	26	35	d	d	PROPN
ejpam-5019	26	36	(	(	PUNCT
ejpam-5019	26	37	vi	vi	PROPN
ejpam-5019	26	38	,	,	PUNCT
ejpam-5019	26	39	vj	vj	PROPN
ejpam-5019	26	40	)	)	PUNCT
ejpam-5019	26	41	(	(	PUNCT
ejpam-5019	26	42	the	the	DET
ejpam-5019	26	43	length	length	NOUN
ejpam-5019	26	44	of	of	ADP
ejpam-5019	26	45	a	a	DET
ejpam-5019	26	46	shortest	short	ADJ
ejpam-5019	26	47	path	path	NOUN
ejpam-5019	26	48	connecting	connect	VERB
ejpam-5019	26	49	vertices	vertex	NOUN
ejpam-5019	26	50	vi	vi	PROPN
ejpam-5019	26	51	and	and	CCONJ
ejpam-5019	26	52	vj	vj	NOUN
ejpam-5019	26	53	)	)	PUNCT
ejpam-5019	26	54	.	.	PUNCT
ejpam-5019	27	1	the	the	DET
ejpam-5019	27	2	transmission	transmission	NOUN
ejpam-5019	27	3	of	of	ADP
ejpam-5019	27	4	a	a	DET
ejpam-5019	27	5	vertex	vertex	NOUN
ejpam-5019	27	6	v	v	NOUN
ejpam-5019	27	7	,	,	PUNCT
ejpam-5019	27	8	denoted	denote	VERB
ejpam-5019	27	9	by	by	ADP
ejpam-5019	27	10	trg	trg	PROPN
ejpam-5019	27	11	(	(	PUNCT
ejpam-5019	27	12	v	v	NOUN
ejpam-5019	27	13	)	)	PUNCT
ejpam-5019	27	14	is	be	AUX
ejpam-5019	27	15	defined	define	VERB
ejpam-5019	27	16	as	as	ADP
ejpam-5019	27	17	the	the	DET
ejpam-5019	27	18	sum	sum	NOUN
ejpam-5019	27	19	of	of	ADP
ejpam-5019	27	20	the	the	DET
ejpam-5019	27	21	distances	distance	NOUN
ejpam-5019	27	22	from	from	ADP
ejpam-5019	27	23	v	v	NUM
ejpam-5019	27	24	to	to	ADP
ejpam-5019	27	25	all	all	DET
ejpam-5019	27	26	other	other	ADJ
ejpam-5019	27	27	vertices	vertex	NOUN
ejpam-5019	27	28	in	in	ADP
ejpam-5019	27	29	g	g	NOUN
ejpam-5019	27	30	,	,	PUNCT
ejpam-5019	27	31	i.e.	i.e.	X
ejpam-5019	27	32	,	,	PUNCT
ejpam-5019	27	33	trg	trg	PROPN
ejpam-5019	27	34	(	(	PUNCT
ejpam-5019	27	35	v	v	NOUN
ejpam-5019	27	36	)	)	PUNCT
ejpam-5019	27	37	=	=	PUNCT
ejpam-5019	27	38	∑	∑	PUNCT
ejpam-5019	27	39	u∈v	u∈v	NOUN
ejpam-5019	27	40	d	d	PROPN
ejpam-5019	27	41	(	(	PUNCT
ejpam-5019	27	42	u	u	NOUN
ejpam-5019	27	43	,	,	PUNCT
ejpam-5019	27	44	v	v	NOUN
ejpam-5019	27	45	)	)	PUNCT
ejpam-5019	27	46	.	.	PUNCT
ejpam-5019	28	1	the	the	DET
ejpam-5019	28	2	matrix	matrix	NOUN
ejpam-5019	28	3	tr	tr	VERB
ejpam-5019	28	4	(	(	PUNCT
ejpam-5019	28	5	g	g	NOUN
ejpam-5019	28	6	)	)	PUNCT
ejpam-5019	28	7	is	be	AUX
ejpam-5019	28	8	a	a	DET
ejpam-5019	28	9	diagonal	diagonal	ADJ
ejpam-5019	28	10	matrix	matrix	NOUN
ejpam-5019	28	11	whose	whose	DET
ejpam-5019	28	12	entries	entry	NOUN
ejpam-5019	28	13	are	be	AUX
ejpam-5019	28	14	the	the	DET
ejpam-5019	28	15	transmissions	transmission	NOUN
ejpam-5019	28	16	of	of	ADP
ejpam-5019	28	17	vertices	vertex	NOUN
ejpam-5019	28	18	of	of	ADP
ejpam-5019	28	19	g.	g.	NOUN
ejpam-5019	28	20	for	for	ADP
ejpam-5019	28	21	a	a	DET
ejpam-5019	28	22	connected	connected	ADJ
ejpam-5019	28	23	graph	graph	NOUN
ejpam-5019	28	24	g	g	NOUN
ejpam-5019	28	25	,	,	PUNCT
ejpam-5019	28	26	the	the	DET
ejpam-5019	28	27	distance	distance	NOUN
ejpam-5019	28	28	laplacian	laplacian	ADJ
ejpam-5019	28	29	matrix	matrix	NOUN
ejpam-5019	28	30	of	of	ADP
ejpam-5019	28	31	g	g	PROPN
ejpam-5019	28	32	is	be	AUX
ejpam-5019	28	33	the	the	DET
ejpam-5019	28	34	matrix	matrix	NOUN
ejpam-5019	28	35	dl	dl	X
ejpam-5019	28	36	(	(	PUNCT
ejpam-5019	28	37	g	g	NOUN
ejpam-5019	28	38	)	)	PUNCT
ejpam-5019	28	39	=	=	PUNCT
ejpam-5019	28	40	tr	tr	VERB
ejpam-5019	28	41	(	(	PUNCT
ejpam-5019	28	42	g	g	NOUN
ejpam-5019	28	43	)	)	PUNCT
ejpam-5019	28	44	−d	−d	PROPN
ejpam-5019	28	45	(	(	PUNCT
ejpam-5019	28	46	g	g	NOUN
ejpam-5019	28	47	)	)	PUNCT
ejpam-5019	28	48	and	and	CCONJ
ejpam-5019	28	49	the	the	DET
ejpam-5019	28	50	distance	distance	NOUN
ejpam-5019	28	51	signless	signless	NOUN
ejpam-5019	28	52	laplacian	laplacian	ADJ
ejpam-5019	28	53	matrix	matrix	NOUN
ejpam-5019	28	54	of	of	ADP
ejpam-5019	28	55	g	g	PROPN
ejpam-5019	28	56	is	be	AUX
ejpam-5019	28	57	the	the	DET
ejpam-5019	28	58	matrix	matrix	NOUN
ejpam-5019	28	59	dq	dq	NOUN
ejpam-5019	28	60	(	(	PUNCT
ejpam-5019	28	61	g	g	NOUN
ejpam-5019	28	62	)	)	PUNCT
ejpam-5019	28	63	=	=	PUNCT
ejpam-5019	29	1	tr	tr	VERB
ejpam-5019	29	2	(	(	PUNCT
ejpam-5019	29	3	g)+d	g)+d	PROPN
ejpam-5019	29	4	(	(	PUNCT
ejpam-5019	29	5	g	g	NOUN
ejpam-5019	29	6	)	)	PUNCT
ejpam-5019	29	7	.	.	PUNCT
ejpam-5019	30	1	these	these	DET
ejpam-5019	30	2	two	two	NUM
ejpam-5019	30	3	matrices	matrix	NOUN
ejpam-5019	30	4	have	have	AUX
ejpam-5019	30	5	been	be	AUX
ejpam-5019	30	6	introduced	introduce	VERB
ejpam-5019	30	7	by	by	ADP
ejpam-5019	30	8	m.	m.	NOUN
ejpam-5019	30	9	aouchiche	aouchiche	NOUN
ejpam-5019	30	10	and	and	CCONJ
ejpam-5019	30	11	p.	p.	NOUN
ejpam-5019	30	12	hansen	hansen	PUNCT
ejpam-5019	31	1	[	[	X
ejpam-5019	31	2	2	2	NUM
ejpam-5019	31	3	]	]	PUNCT
ejpam-5019	31	4	.	.	PUNCT
ejpam-5019	32	1	in	in	ADP
ejpam-5019	32	2	[	[	X
ejpam-5019	32	3	13	13	NUM
ejpam-5019	32	4	]	]	PUNCT
ejpam-5019	32	5	,	,	PUNCT
ejpam-5019	32	6	haritha	haritha	PROPN
ejpam-5019	32	7	and	and	CCONJ
ejpam-5019	32	8	chithra	chithra	PROPN
ejpam-5019	32	9	defined	define	VERB
ejpam-5019	32	10	a	a	DET
ejpam-5019	32	11	matrix	matrix	NOUN
ejpam-5019	32	12	called	call	VERB
ejpam-5019	32	13	distance	distance	NOUN
ejpam-5019	32	14	seidal	seidal	NOUN
ejpam-5019	32	15	matrix	matrix	NOUN
ejpam-5019	32	16	.	.	PUNCT
ejpam-5019	33	1	the	the	DET
ejpam-5019	33	2	distance	distance	NOUN
ejpam-5019	33	3	seidal	seidal	NOUN
ejpam-5019	33	4	matrix	matrix	NOUN
ejpam-5019	33	5	of	of	ADP
ejpam-5019	33	6	g	g	PROPN
ejpam-5019	33	7	is	be	AUX
ejpam-5019	33	8	the	the	DET
ejpam-5019	33	9	matrix	matrix	NOUN
ejpam-5019	33	10	ds	ds	NOUN
ejpam-5019	33	11	(	(	PUNCT
ejpam-5019	33	12	g	g	NOUN
ejpam-5019	33	13	)	)	PUNCT
ejpam-5019	33	14	=	=	SYM
ejpam-5019	34	1	j	j	PROPN
ejpam-5019	34	2	−	−	NOUN
ejpam-5019	35	1	i	i	PRON
ejpam-5019	35	2	−	−	PROPN
ejpam-5019	35	3	2d	2d	NOUN
ejpam-5019	35	4	(	(	PUNCT
ejpam-5019	35	5	g	g	NOUN
ejpam-5019	35	6	)	)	PUNCT
ejpam-5019	35	7	.	.	PUNCT
ejpam-5019	36	1	for	for	ADP
ejpam-5019	36	2	a	a	DET
ejpam-5019	36	3	connected	connected	ADJ
ejpam-5019	36	4	graph	graph	NOUN
ejpam-5019	36	5	g	g	NOUN
ejpam-5019	36	6	,	,	PUNCT
ejpam-5019	36	7	cui	cui	VERB
ejpam-5019	36	8	et	et	PROPN
ejpam-5019	36	9	al.[8	al.[8	PROPN
ejpam-5019	36	10	]	]	PUNCT
ejpam-5019	36	11	have	have	AUX
ejpam-5019	36	12	introduced	introduce	VERB
ejpam-5019	36	13	the	the	DET
ejpam-5019	36	14	generalized	generalized	ADJ
ejpam-5019	36	15	distance	distance	NOUN
ejpam-5019	36	16	matrix	matrix	NOUN
ejpam-5019	36	17	,	,	PUNCT
ejpam-5019	36	18	and	and	CCONJ
ejpam-5019	36	19	it	it	PRON
ejpam-5019	36	20	is	be	AUX
ejpam-5019	36	21	denoted	denote	VERB
ejpam-5019	36	22	by	by	ADP
ejpam-5019	36	23	dα	dα	PROPN
ejpam-5019	36	24	(	(	PUNCT
ejpam-5019	36	25	g	g	NOUN
ejpam-5019	36	26	)	)	PUNCT
ejpam-5019	36	27	.	.	PUNCT
ejpam-5019	37	1	it	it	PRON
ejpam-5019	37	2	is	be	AUX
ejpam-5019	37	3	defined	define	VERB
ejpam-5019	37	4	as	as	ADP
ejpam-5019	37	5	the	the	DET
ejpam-5019	37	6	convex	convex	NOUN
ejpam-5019	37	7	combination	combination	NOUN
ejpam-5019	37	8	of	of	ADP
ejpam-5019	37	9	tr	tr	VERB
ejpam-5019	37	10	(	(	PUNCT
ejpam-5019	37	11	g	g	NOUN
ejpam-5019	37	12	)	)	PUNCT
ejpam-5019	37	13	and	and	CCONJ
ejpam-5019	37	14	d	d	X
ejpam-5019	37	15	(	(	PUNCT
ejpam-5019	37	16	g	g	NOUN
ejpam-5019	37	17	)	)	PUNCT
ejpam-5019	37	18	.	.	PUNCT
ejpam-5019	38	1	it	it	PRON
ejpam-5019	38	2	is	be	AUX
ejpam-5019	38	3	of	of	ADP
ejpam-5019	38	4	the	the	DET
ejpam-5019	38	5	form	form	NOUN
ejpam-5019	38	6	dα	dα	X
ejpam-5019	38	7	(	(	PUNCT
ejpam-5019	38	8	g	g	NOUN
ejpam-5019	38	9	)	)	PUNCT
ejpam-5019	39	1	=	=	SYM
ejpam-5019	39	2	αtr	αtr	NOUN
ejpam-5019	39	3	(	(	PUNCT
ejpam-5019	39	4	g	g	NOUN
ejpam-5019	39	5	)	)	PUNCT
ejpam-5019	39	6	+	+	CCONJ
ejpam-5019	39	7	(	(	PUNCT
ejpam-5019	39	8	1−	1−	NUM
ejpam-5019	39	9	α)d	α)d	X
ejpam-5019	39	10	(	(	PUNCT
ejpam-5019	39	11	g	g	NOUN
ejpam-5019	39	12	)	)	PUNCT
ejpam-5019	39	13	,	,	PUNCT
ejpam-5019	39	14	α	α	PROPN
ejpam-5019	39	15	∈	∈	PROPN
ejpam-5019	40	1	[	[	X
ejpam-5019	40	2	0	0	NUM
ejpam-5019	40	3	,	,	PUNCT
ejpam-5019	40	4	1	1	NUM
ejpam-5019	40	5	]	]	PUNCT
ejpam-5019	40	6	.	.	PUNCT
ejpam-5019	41	1	in	in	ADP
ejpam-5019	41	2	[	[	X
ejpam-5019	41	3	12	12	NUM
ejpam-5019	41	4	]	]	PUNCT
ejpam-5019	41	5	,	,	PUNCT
ejpam-5019	41	6	haemers	haemer	NOUN
ejpam-5019	41	7	et	et	PROPN
ejpam-5019	41	8	al	al	PROPN
ejpam-5019	41	9	.	.	PROPN
ejpam-5019	41	10	have	have	AUX
ejpam-5019	41	11	derived	derive	VERB
ejpam-5019	41	12	the	the	DET
ejpam-5019	41	13	characteristic	characteristic	ADJ
ejpam-5019	41	14	polynomials	polynomial	NOUN
ejpam-5019	41	15	of	of	ADP
ejpam-5019	41	16	various	various	ADJ
ejpam-5019	41	17	universal	universal	ADJ
ejpam-5019	41	18	adjacency	adjacency	NOUN
ejpam-5019	41	19	matrices	matrix	NOUN
ejpam-5019	41	20	in	in	ADP
ejpam-5019	41	21	terms	term	NOUN
ejpam-5019	41	22	of	of	ADP
ejpam-5019	41	23	the	the	DET
ejpam-5019	41	24	characteristic	characteristic	ADJ
ejpam-5019	41	25	polynomials	polynomial	NOUN
ejpam-5019	41	26	of	of	ADP
ejpam-5019	41	27	the	the	DET
ejpam-5019	41	28	adjacency	adjacency	NOUN
ejpam-5019	41	29	matrices	matrix	NOUN
ejpam-5019	41	30	of	of	ADP
ejpam-5019	41	31	the	the	DET
ejpam-5019	41	32	components	component	NOUN
ejpam-5019	41	33	of	of	ADP
ejpam-5019	41	34	g.	g.	PROPN
ejpam-5019	41	35	in	in	ADP
ejpam-5019	41	36	[	[	X
ejpam-5019	41	37	6	6	NUM
ejpam-5019	41	38	,	,	PUNCT
ejpam-5019	41	39	7	7	NUM
ejpam-5019	41	40	]	]	PUNCT
ejpam-5019	41	41	,	,	PUNCT
ejpam-5019	41	42	cardoso	cardoso	PROPN
ejpam-5019	41	43	et	et	PROPN
ejpam-5019	41	44	al	al	PROPN
ejpam-5019	41	45	.	.	PROPN
ejpam-5019	41	46	obtained	obtain	VERB
ejpam-5019	41	47	the	the	DET
ejpam-5019	41	48	generalization	generalization	NOUN
ejpam-5019	41	49	of	of	ADP
ejpam-5019	41	50	fiedler	fiedler	PROPN
ejpam-5019	41	51	’s	’s	PART
ejpam-5019	41	52	lemma	lemma	PROPN
ejpam-5019	41	53	which	which	PRON
ejpam-5019	41	54	can	can	AUX
ejpam-5019	41	55	be	be	AUX
ejpam-5019	41	56	applied	apply	VERB
ejpam-5019	41	57	to	to	ADP
ejpam-5019	41	58	the	the	DET
ejpam-5019	41	59	h−join	h−join	NOUN
ejpam-5019	41	60	of	of	ADP
ejpam-5019	41	61	regular	regular	ADJ
ejpam-5019	41	62	graphs	graph	NOUN
ejpam-5019	41	63	.	.	PUNCT
ejpam-5019	42	1	in	in	ADP
ejpam-5019	42	2	[	[	X
ejpam-5019	42	3	18	18	NUM
ejpam-5019	42	4	]	]	PUNCT
ejpam-5019	42	5	,	,	PUNCT
ejpam-5019	42	6	saravanan	saravanan	PROPN
ejpam-5019	42	7	et	et	PROPN
ejpam-5019	42	8	al	al	PROPN
ejpam-5019	42	9	.	.	PROPN
ejpam-5019	42	10	have	have	AUX
ejpam-5019	42	11	determined	determine	VERB
ejpam-5019	42	12	the	the	DET
ejpam-5019	42	13	universal	universal	ADJ
ejpam-5019	42	14	adjacency	adjacency	NOUN
ejpam-5019	42	15	spectra	spectra	NOUN
ejpam-5019	42	16	of	of	ADP
ejpam-5019	42	17	h−	h−	PROPN
ejpam-5019	42	18	join	join	NOUN
ejpam-5019	42	19	of	of	ADP
ejpam-5019	42	20	graphs	graph	NOUN
ejpam-5019	42	21	using	use	VERB
ejpam-5019	42	22	another	another	DET
ejpam-5019	42	23	generalization	generalization	NOUN
ejpam-5019	42	24	of	of	ADP
ejpam-5019	42	25	fiedler	fiedler	PROPN
ejpam-5019	42	26	’s	’s	PART
ejpam-5019	42	27	lemma	lemma	PROPN
ejpam-5019	42	28	.	.	PUNCT
ejpam-5019	43	1	several	several	ADJ
ejpam-5019	43	2	authors	author	NOUN
ejpam-5019	43	3	[	[	X
ejpam-5019	43	4	1	1	NUM
ejpam-5019	43	5	,	,	PUNCT
ejpam-5019	43	6	4	4	NUM
ejpam-5019	43	7	,	,	PUNCT
ejpam-5019	43	8	8	8	NUM
ejpam-5019	43	9	,	,	PUNCT
ejpam-5019	43	10	10	10	NUM
ejpam-5019	43	11	,	,	PUNCT
ejpam-5019	43	12	11	11	NUM
ejpam-5019	43	13	,	,	PUNCT
ejpam-5019	43	14	14	14	NUM
ejpam-5019	43	15	,	,	PUNCT
ejpam-5019	43	16	15	15	NUM
ejpam-5019	43	17	,	,	PUNCT
ejpam-5019	43	18	20	20	NUM
ejpam-5019	43	19	]	]	PUNCT
ejpam-5019	43	20	have	have	AUX
ejpam-5019	43	21	determined	determine	VERB
ejpam-5019	43	22	the	the	DET
ejpam-5019	43	23	distance	distance	NOUN
ejpam-5019	43	24	spectra	spectra	NOUN
ejpam-5019	43	25	of	of	ADP
ejpam-5019	43	26	graphs	graph	NOUN
ejpam-5019	43	27	that	that	PRON
ejpam-5019	43	28	are	be	AUX
ejpam-5019	43	29	obtained	obtain	VERB
ejpam-5019	43	30	by	by	ADP
ejpam-5019	43	31	applying	apply	VERB
ejpam-5019	43	32	different	different	ADJ
ejpam-5019	43	33	graph	graph	NOUN
ejpam-5019	43	34	operations	operation	NOUN
ejpam-5019	43	35	,	,	PUNCT
ejpam-5019	43	36	as	as	ADV
ejpam-5019	43	37	well	well	ADV
ejpam-5019	43	38	as	as	ADP
ejpam-5019	43	39	the	the	DET
ejpam-5019	43	40	distance	distance	NOUN
ejpam-5019	43	41	spectra	spectra	NOUN
ejpam-5019	43	42	that	that	PRON
ejpam-5019	43	43	characterize	characterize	VERB
ejpam-5019	43	44	the	the	DET
ejpam-5019	43	45	graphs	graph	NOUN
ejpam-5019	43	46	from	from	ADP
ejpam-5019	43	47	an	an	DET
ejpam-5019	43	48	application	application	NOUN
ejpam-5019	43	49	perspective	perspective	NOUN
ejpam-5019	43	50	.	.	PUNCT
ejpam-5019	44	1	recently	recently	ADV
ejpam-5019	44	2	,	,	PUNCT
ejpam-5019	44	3	in	in	ADP
ejpam-5019	44	4	[	[	PUNCT
ejpam-5019	44	5	3	3	NUM
ejpam-5019	44	6	,	,	PUNCT
ejpam-5019	44	7	16	16	NUM
ejpam-5019	44	8	,	,	PUNCT
ejpam-5019	44	9	17	17	NUM
ejpam-5019	44	10	]	]	PUNCT
ejpam-5019	44	11	,	,	PUNCT
ejpam-5019	44	12	the	the	DET
ejpam-5019	44	13	authors	author	NOUN
ejpam-5019	44	14	have	have	AUX
ejpam-5019	44	15	determined	determine	VERB
ejpam-5019	44	16	the	the	DET
ejpam-5019	44	17	upper	upper	ADJ
ejpam-5019	44	18	bounds	bound	NOUN
ejpam-5019	44	19	for	for	ADP
ejpam-5019	44	20	the	the	DET
ejpam-5019	44	21	extremal	extremal	ADJ
ejpam-5019	44	22	graphs	graph	NOUN
ejpam-5019	44	23	related	relate	VERB
ejpam-5019	44	24	to	to	ADP
ejpam-5019	44	25	reciprocal	reciprocal	ADJ
ejpam-5019	44	26	distance	distance	NOUN
ejpam-5019	44	27	laplacian	laplacian	ADJ
ejpam-5019	44	28	spectral	spectral	ADJ
ejpam-5019	44	29	radius	radius	NOUN
ejpam-5019	44	30	.	.	PUNCT
ejpam-5019	45	1	the	the	DET
ejpam-5019	45	2	books	book	NOUN
ejpam-5019	45	3	[	[	X
ejpam-5019	45	4	5	5	NUM
ejpam-5019	45	5	,	,	PUNCT
ejpam-5019	45	6	9	9	NUM
ejpam-5019	45	7	]	]	PUNCT
ejpam-5019	45	8	are	be	AUX
ejpam-5019	45	9	excellent	excellent	ADJ
ejpam-5019	45	10	resources	resource	NOUN
ejpam-5019	45	11	on	on	ADP
ejpam-5019	45	12	spectra	spectra	NOUN
ejpam-5019	45	13	of	of	ADP
ejpam-5019	45	14	graphs	graph	NOUN
ejpam-5019	45	15	for	for	ADP
ejpam-5019	45	16	interested	interested	ADJ
ejpam-5019	45	17	readers	reader	NOUN
ejpam-5019	45	18	.	.	PUNCT
ejpam-5019	46	1	motivated	motivate	VERB
ejpam-5019	46	2	by	by	ADP
ejpam-5019	46	3	these	these	PRON
ejpam-5019	46	4	,	,	PUNCT
ejpam-5019	46	5	we	we	PRON
ejpam-5019	46	6	define	define	VERB
ejpam-5019	46	7	a	a	DET
ejpam-5019	46	8	new	new	ADJ
ejpam-5019	46	9	distance	distance	NOUN
ejpam-5019	46	10	matrix	matrix	NOUN
ejpam-5019	46	11	is	be	AUX
ejpam-5019	46	12	called	call	VERB
ejpam-5019	46	13	the	the	DET
ejpam-5019	46	14	universal	universal	ADJ
ejpam-5019	46	15	distance	distance	NOUN
ejpam-5019	46	16	matrix	matrix	NOUN
ejpam-5019	46	17	of	of	ADP
ejpam-5019	46	18	g.	g.	PROPN
ejpam-5019	46	19	for	for	ADP
ejpam-5019	46	20	α	α	PROPN
ejpam-5019	46	21	,	,	PUNCT
ejpam-5019	46	22	β	β	X
ejpam-5019	46	23	,	,	PUNCT
ejpam-5019	46	24	γ	γ	PROPN
ejpam-5019	46	25	,	,	PUNCT
ejpam-5019	46	26	δ	δ	PROPN
ejpam-5019	46	27	∈	∈	PROPN
ejpam-5019	46	28	r	r	NOUN
ejpam-5019	46	29	and	and	CCONJ
ejpam-5019	46	30	β	β	ADJ
ejpam-5019	46	31	̸=	̸=	PROPN
ejpam-5019	46	32	0	0	NUM
ejpam-5019	46	33	,	,	PUNCT
ejpam-5019	46	34	the	the	DET
ejpam-5019	46	35	universal	universal	ADJ
ejpam-5019	46	36	distance	distance	NOUN
ejpam-5019	46	37	matrix	matrix	NOUN
ejpam-5019	46	38	ud	ud	INTJ
ejpam-5019	46	39	(	(	PUNCT
ejpam-5019	46	40	g	g	NOUN
ejpam-5019	46	41	)	)	PUNCT
ejpam-5019	46	42	is	be	AUX
ejpam-5019	46	43	defined	define	VERB
ejpam-5019	46	44	as	as	ADP
ejpam-5019	46	45	ud	ud	INTJ
ejpam-5019	46	46	(	(	PUNCT
ejpam-5019	46	47	g	g	NOUN
ejpam-5019	46	48	)	)	PUNCT
ejpam-5019	47	1	=	=	SYM
ejpam-5019	47	2	αtr	αtr	NOUN
ejpam-5019	47	3	(	(	PUNCT
ejpam-5019	47	4	g	g	NOUN
ejpam-5019	47	5	)	)	PUNCT
ejpam-5019	47	6	+	+	NUM
ejpam-5019	47	7	βd	βd	INTJ
ejpam-5019	47	8	(	(	PUNCT
ejpam-5019	47	9	g	g	NOUN
ejpam-5019	47	10	)	)	PUNCT
ejpam-5019	47	11	+	+	SYM
ejpam-5019	47	12	γj	γj	ADP
ejpam-5019	47	13	+	+	CCONJ
ejpam-5019	47	14	δi	δi	PROPN
ejpam-5019	47	15	,	,	PUNCT
ejpam-5019	47	16	where	where	SCONJ
ejpam-5019	47	17	tr	tr	X
ejpam-5019	47	18	(	(	PUNCT
ejpam-5019	47	19	g	g	NOUN
ejpam-5019	47	20	)	)	PUNCT
ejpam-5019	47	21	is	be	AUX
ejpam-5019	47	22	the	the	DET
ejpam-5019	47	23	diagonal	diagonal	ADJ
ejpam-5019	47	24	matrix	matrix	NOUN
ejpam-5019	47	25	whose	whose	DET
ejpam-5019	47	26	s.	s.	PROPN
ejpam-5019	47	27	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	47	28	,	,	PUNCT
ejpam-5019	47	29	k.	k.	PROPN
ejpam-5019	47	30	desikan	desikan	PROPN
ejpam-5019	47	31	/	/	SYM
ejpam-5019	47	32	eur	eur	PROPN
ejpam-5019	47	33	.	.	PUNCT
ejpam-5019	48	1	j.	j.	PROPN
ejpam-5019	48	2	pure	pure	PROPN
ejpam-5019	48	3	appl	appl	PROPN
ejpam-5019	48	4	.	.	PROPN
ejpam-5019	48	5	math	math	PROPN
ejpam-5019	48	6	,	,	PUNCT
ejpam-5019	48	7	17	17	NUM
ejpam-5019	48	8	(	(	PUNCT
ejpam-5019	48	9	1	1	NUM
ejpam-5019	48	10	)	)	PUNCT
ejpam-5019	48	11	(	(	PUNCT
ejpam-5019	48	12	2024	2024	NUM
ejpam-5019	48	13	)	)	PUNCT
ejpam-5019	48	14	,	,	PUNCT
ejpam-5019	48	15	462	462	NUM
ejpam-5019	48	16	-	-	SYM
ejpam-5019	48	17	476	476	NUM
ejpam-5019	48	18	464	464	NUM
ejpam-5019	48	19	elements	element	NOUN
ejpam-5019	48	20	are	be	AUX
ejpam-5019	48	21	the	the	DET
ejpam-5019	48	22	vertex	vertex	NOUN
ejpam-5019	48	23	transmissions	transmission	NOUN
ejpam-5019	48	24	,	,	PUNCT
ejpam-5019	48	25	and	and	CCONJ
ejpam-5019	48	26	d	d	X
ejpam-5019	48	27	(	(	PUNCT
ejpam-5019	48	28	g	g	NOUN
ejpam-5019	48	29	)	)	PUNCT
ejpam-5019	48	30	is	be	AUX
ejpam-5019	48	31	the	the	DET
ejpam-5019	48	32	distance	distance	NOUN
ejpam-5019	48	33	matrix	matrix	NOUN
ejpam-5019	48	34	of	of	ADP
ejpam-5019	48	35	g.	g.	PROPN
ejpam-5019	48	36	here	here	ADV
ejpam-5019	48	37	j	j	PROPN
ejpam-5019	48	38	is	be	AUX
ejpam-5019	48	39	the	the	DET
ejpam-5019	48	40	all	all	DET
ejpam-5019	48	41	-	-	PUNCT
ejpam-5019	48	42	ones	one	NOUN
ejpam-5019	48	43	matrix	matrix	NOUN
ejpam-5019	48	44	,	,	PUNCT
ejpam-5019	48	45	and	and	CCONJ
ejpam-5019	48	46	i	i	PRON
ejpam-5019	48	47	is	be	AUX
ejpam-5019	48	48	the	the	DET
ejpam-5019	48	49	identity	identity	NOUN
ejpam-5019	48	50	matrix	matrix	NOUN
ejpam-5019	48	51	.	.	PUNCT
ejpam-5019	49	1	the	the	DET
ejpam-5019	49	2	set	set	NOUN
ejpam-5019	49	3	of	of	ADP
ejpam-5019	49	4	eigenvalues	eigenvalue	NOUN
ejpam-5019	49	5	of	of	ADP
ejpam-5019	49	6	the	the	DET
ejpam-5019	49	7	universal	universal	ADJ
ejpam-5019	49	8	distance	distance	NOUN
ejpam-5019	49	9	matrix	matrix	NOUN
ejpam-5019	49	10	namely	namely	ADV
ejpam-5019	49	11	,	,	PUNCT
ejpam-5019	49	12	{	{	PUNCT
ejpam-5019	49	13	ρ1	ρ1	NOUN
ejpam-5019	49	14	,	,	PUNCT
ejpam-5019	49	15	ρ2	ρ2	NOUN
ejpam-5019	49	16	,	,	PUNCT
ejpam-5019	49	17	.	.	PUNCT
ejpam-5019	49	18	.	.	PUNCT
ejpam-5019	49	19	.	.	PUNCT
ejpam-5019	50	1	,	,	PUNCT
ejpam-5019	50	2	ρn	ρn	CCONJ
ejpam-5019	50	3	}	}	PUNCT
ejpam-5019	50	4	is	be	AUX
ejpam-5019	50	5	known	know	VERB
ejpam-5019	50	6	as	as	ADP
ejpam-5019	50	7	the	the	DET
ejpam-5019	50	8	universal	universal	ADJ
ejpam-5019	50	9	distance	distance	NOUN
ejpam-5019	50	10	spectrum	spectrum	NOUN
ejpam-5019	50	11	of	of	ADP
ejpam-5019	50	12	g.	g.	PROPN
ejpam-5019	50	13	by	by	ADP
ejpam-5019	50	14	taking	take	VERB
ejpam-5019	50	15	appropriate	appropriate	ADJ
ejpam-5019	50	16	values	value	NOUN
ejpam-5019	50	17	for	for	ADP
ejpam-5019	50	18	α	α	NOUN
ejpam-5019	50	19	,	,	PUNCT
ejpam-5019	50	20	β	β	X
ejpam-5019	50	21	,	,	PUNCT
ejpam-5019	50	22	γ	γ	X
ejpam-5019	50	23	,	,	PUNCT
ejpam-5019	50	24	and	and	CCONJ
ejpam-5019	50	25	δ	δ	PROPN
ejpam-5019	50	26	,	,	PUNCT
ejpam-5019	50	27	we	we	PRON
ejpam-5019	50	28	obtain	obtain	VERB
ejpam-5019	50	29	the	the	DET
ejpam-5019	50	30	eigenvalues	eigenvalue	NOUN
ejpam-5019	50	31	for	for	ADP
ejpam-5019	50	32	the	the	DET
ejpam-5019	50	33	universal	universal	ADJ
ejpam-5019	50	34	distance	distance	NOUN
ejpam-5019	50	35	matrix	matrix	NOUN
ejpam-5019	50	36	and	and	CCONJ
ejpam-5019	50	37	various	various	ADJ
ejpam-5019	50	38	matrices	matrix	NOUN
ejpam-5019	50	39	related	relate	VERB
ejpam-5019	50	40	to	to	ADP
ejpam-5019	50	41	distance	distance	NOUN
ejpam-5019	50	42	.	.	PUNCT
ejpam-5019	51	1	consequently	consequently	ADV
ejpam-5019	51	2	,	,	PUNCT
ejpam-5019	51	3	we	we	PRON
ejpam-5019	51	4	also	also	ADV
ejpam-5019	51	5	determine	determine	VERB
ejpam-5019	51	6	the	the	DET
ejpam-5019	51	7	spectrum	spectrum	NOUN
ejpam-5019	51	8	of	of	ADP
ejpam-5019	51	9	universal	universal	ADJ
ejpam-5019	51	10	distance	distance	NOUN
ejpam-5019	51	11	matrix	matrix	NOUN
ejpam-5019	51	12	of	of	ADP
ejpam-5019	51	13	the	the	DET
ejpam-5019	51	14	graph	graph	NOUN
ejpam-5019	51	15	complement	complement	NOUN
ejpam-5019	51	16	of	of	ADP
ejpam-5019	51	17	g.	g.	PROPN
ejpam-5019	51	18	here	here	ADV
ejpam-5019	51	19	we	we	PRON
ejpam-5019	51	20	determine	determine	VERB
ejpam-5019	51	21	the	the	DET
ejpam-5019	51	22	universal	universal	ADJ
ejpam-5019	51	23	distance	distance	NOUN
ejpam-5019	51	24	spectra	spectra	NOUN
ejpam-5019	51	25	of	of	ADP
ejpam-5019	51	26	regular	regular	ADJ
ejpam-5019	51	27	graphs	graph	NOUN
ejpam-5019	51	28	and	and	CCONJ
ejpam-5019	51	29	graphs	graph	NOUN
ejpam-5019	51	30	obtained	obtain	VERB
ejpam-5019	51	31	using	use	VERB
ejpam-5019	51	32	graph	graph	NOUN
ejpam-5019	51	33	operations	operation	NOUN
ejpam-5019	51	34	such	such	ADJ
ejpam-5019	51	35	as	as	ADP
ejpam-5019	51	36	join	join	NOUN
ejpam-5019	51	37	,	,	PUNCT
ejpam-5019	51	38	joined	join	VERB
ejpam-5019	51	39	union	union	NOUN
ejpam-5019	51	40	,	,	PUNCT
ejpam-5019	51	41	generalized	generalize	VERB
ejpam-5019	51	42	joined	join	VERB
ejpam-5019	51	43	union	union	NOUN
ejpam-5019	51	44	of	of	ADP
ejpam-5019	51	45	regular	regular	ADJ
ejpam-5019	51	46	graphs	graph	NOUN
ejpam-5019	51	47	of	of	ADP
ejpam-5019	51	48	diameter	diameter	NOUN
ejpam-5019	51	49	two	two	NUM
ejpam-5019	51	50	.	.	PUNCT
ejpam-5019	52	1	2	2	X
ejpam-5019	52	2	.	.	X
ejpam-5019	52	3	main	main	ADJ
ejpam-5019	52	4	results	result	NOUN
ejpam-5019	52	5	in	in	ADP
ejpam-5019	52	6	this	this	DET
ejpam-5019	52	7	section	section	NOUN
ejpam-5019	52	8	,	,	PUNCT
ejpam-5019	52	9	we	we	PRON
ejpam-5019	52	10	discuss	discuss	VERB
ejpam-5019	52	11	the	the	DET
ejpam-5019	52	12	universal	universal	ADJ
ejpam-5019	52	13	distance	distance	NOUN
ejpam-5019	52	14	spectra	spectra	NOUN
ejpam-5019	52	15	of	of	ADP
ejpam-5019	52	16	r−regular	r−regular	ADJ
ejpam-5019	52	17	graph	graph	NOUN
ejpam-5019	52	18	,	,	PUNCT
ejpam-5019	52	19	join	join	NOUN
ejpam-5019	52	20	of	of	ADP
ejpam-5019	52	21	two	two	NUM
ejpam-5019	52	22	regular	regular	ADJ
ejpam-5019	52	23	graphs	graph	NOUN
ejpam-5019	52	24	and	and	CCONJ
ejpam-5019	52	25	joined	join	VERB
ejpam-5019	52	26	union	union	NOUN
ejpam-5019	52	27	of	of	ADP
ejpam-5019	52	28	graphs	graph	NOUN
ejpam-5019	52	29	.	.	PUNCT
ejpam-5019	53	1	also	also	ADV
ejpam-5019	53	2	,	,	PUNCT
ejpam-5019	53	3	we	we	PRON
ejpam-5019	53	4	obtain	obtain	VERB
ejpam-5019	53	5	the	the	DET
ejpam-5019	53	6	universal	universal	ADJ
ejpam-5019	53	7	distance	distance	NOUN
ejpam-5019	53	8	spectrum	spectrum	NOUN
ejpam-5019	53	9	of	of	ADP
ejpam-5019	53	10	petersen	petersen	PROPN
ejpam-5019	53	11	graph	graph	NOUN
ejpam-5019	53	12	,	,	PUNCT
ejpam-5019	53	13	complete	complete	ADJ
ejpam-5019	53	14	bipartite	bipartite	NOUN
ejpam-5019	53	15	graph	graph	NOUN
ejpam-5019	53	16	,	,	PUNCT
ejpam-5019	53	17	wheel	wheel	NOUN
ejpam-5019	53	18	graph	graph	NOUN
ejpam-5019	53	19	,	,	PUNCT
ejpam-5019	53	20	complete	complete	ADJ
ejpam-5019	53	21	split	split	NOUN
ejpam-5019	53	22	graph	graph	NOUN
ejpam-5019	53	23	and	and	CCONJ
ejpam-5019	53	24	joined	join	VERB
ejpam-5019	53	25	union	union	NOUN
ejpam-5019	53	26	of	of	ADP
ejpam-5019	53	27	graphs	graph	NOUN
ejpam-5019	53	28	related	relate	VERB
ejpam-5019	53	29	to	to	ADP
ejpam-5019	53	30	complete	complete	ADJ
ejpam-5019	53	31	graph	graph	NOUN
ejpam-5019	53	32	.	.	PUNCT
ejpam-5019	54	1	2.1	2.1	NUM
ejpam-5019	54	2	.	.	PUNCT
ejpam-5019	55	1	universal	universal	ADJ
ejpam-5019	55	2	distance	distance	NOUN
ejpam-5019	55	3	spectrum	spectrum	NOUN
ejpam-5019	55	4	of	of	ADP
ejpam-5019	55	5	r−	r−	PROPN
ejpam-5019	55	6	regular	regular	ADJ
ejpam-5019	55	7	graph	graph	NOUN
ejpam-5019	55	8	in	in	ADP
ejpam-5019	55	9	this	this	DET
ejpam-5019	55	10	subsection	subsection	NOUN
ejpam-5019	55	11	,	,	PUNCT
ejpam-5019	55	12	we	we	PRON
ejpam-5019	55	13	describe	describe	VERB
ejpam-5019	55	14	the	the	DET
ejpam-5019	55	15	universal	universal	ADJ
ejpam-5019	55	16	distance	distance	NOUN
ejpam-5019	55	17	spectrum	spectrum	NOUN
ejpam-5019	55	18	of	of	ADP
ejpam-5019	55	19	r−	r−	PROPN
ejpam-5019	55	20	regular	regular	ADJ
ejpam-5019	55	21	graph	graph	NOUN
ejpam-5019	55	22	and	and	CCONJ
ejpam-5019	55	23	obtain	obtain	VERB
ejpam-5019	55	24	the	the	DET
ejpam-5019	55	25	universal	universal	ADJ
ejpam-5019	55	26	distance	distance	NOUN
ejpam-5019	55	27	spectrum	spectrum	NOUN
ejpam-5019	55	28	of	of	ADP
ejpam-5019	55	29	r−	r−	PROPN
ejpam-5019	55	30	regular	regular	ADJ
ejpam-5019	55	31	graph	graph	NOUN
ejpam-5019	55	32	.	.	PUNCT
ejpam-5019	56	1	in	in	ADP
ejpam-5019	56	2	particular	particular	ADJ
ejpam-5019	56	3	,	,	PUNCT
ejpam-5019	56	4	we	we	PRON
ejpam-5019	56	5	obtain	obtain	VERB
ejpam-5019	56	6	the	the	DET
ejpam-5019	56	7	universal	universal	ADJ
ejpam-5019	56	8	distance	distance	NOUN
ejpam-5019	56	9	spectrum	spectrum	NOUN
ejpam-5019	56	10	of	of	ADP
ejpam-5019	56	11	petersen	petersen	PROPN
ejpam-5019	56	12	graph	graph	NOUN
ejpam-5019	56	13	.	.	PUNCT
ejpam-5019	57	1	theorem	theorem	NOUN
ejpam-5019	57	2	1	1	NUM
ejpam-5019	57	3	.	.	PUNCT
ejpam-5019	58	1	let	let	VERB
ejpam-5019	58	2	g	g	PRON
ejpam-5019	58	3	be	be	AUX
ejpam-5019	58	4	a	a	DET
ejpam-5019	58	5	r−regular	r−regular	ADJ
ejpam-5019	58	6	graph	graph	NOUN
ejpam-5019	58	7	of	of	ADP
ejpam-5019	58	8	order	order	NOUN
ejpam-5019	58	9	n	n	PRON
ejpam-5019	58	10	with	with	ADP
ejpam-5019	58	11	diameter	diameter	NOUN
ejpam-5019	58	12	at	at	ADP
ejpam-5019	58	13	most	most	ADV
ejpam-5019	58	14	two	two	NUM
ejpam-5019	58	15	.	.	PUNCT
ejpam-5019	59	1	the	the	DET
ejpam-5019	59	2	adjacency	adjacency	PROPN
ejpam-5019	59	3	eigenvalues	eigenvalue	VERB
ejpam-5019	59	4	of	of	ADP
ejpam-5019	59	5	g	g	PROPN
ejpam-5019	59	6	are	be	AUX
ejpam-5019	59	7	denoted	denote	VERB
ejpam-5019	59	8	by	by	ADP
ejpam-5019	59	9	r	r	NOUN
ejpam-5019	59	10	=	=	SYM
ejpam-5019	59	11	λ1	λ1	ADJ
ejpam-5019	59	12	,	,	PUNCT
ejpam-5019	59	13	λ2	λ2	NOUN
ejpam-5019	59	14	,	,	PUNCT
ejpam-5019	59	15	.	.	PUNCT
ejpam-5019	59	16	.	.	PUNCT
ejpam-5019	60	1	.	.	PUNCT
ejpam-5019	61	1	,	,	PUNCT
ejpam-5019	61	2	λn	λn	NOUN
ejpam-5019	61	3	.	.	PUNCT
ejpam-5019	62	1	the	the	DET
ejpam-5019	62	2	eigenvalues	eigenvalue	NOUN
ejpam-5019	62	3	of	of	ADP
ejpam-5019	62	4	the	the	DET
ejpam-5019	62	5	universal	universal	ADJ
ejpam-5019	62	6	distance	distance	NOUN
ejpam-5019	62	7	matrix	matrix	NOUN
ejpam-5019	62	8	of	of	ADP
ejpam-5019	62	9	g	g	PROPN
ejpam-5019	62	10	are	be	AUX
ejpam-5019	62	11	{	{	PUNCT
ejpam-5019	62	12	(	(	PUNCT
ejpam-5019	62	13	α+	α+	X
ejpam-5019	62	14	β	β	X
ejpam-5019	62	15	)	)	PUNCT
ejpam-5019	62	16	(	(	PUNCT
ejpam-5019	63	1	2n−	2n−	NUM
ejpam-5019	63	2	r	r	NOUN
ejpam-5019	63	3	−	−	NOUN
ejpam-5019	63	4	2	2	NUM
ejpam-5019	63	5	)	)	PUNCT
ejpam-5019	63	6	+	+	CCONJ
ejpam-5019	63	7	γn+	γn+	ADJ
ejpam-5019	63	8	δ	δ	PROPN
ejpam-5019	63	9	,	,	PUNCT
ejpam-5019	63	10	α	α	PROPN
ejpam-5019	63	11	(	(	PUNCT
ejpam-5019	63	12	2n−	2n−	PROPN
ejpam-5019	63	13	r	r	NOUN
ejpam-5019	63	14	−	−	NOUN
ejpam-5019	63	15	2	2	NUM
ejpam-5019	63	16	)	)	PUNCT
ejpam-5019	63	17	+	+	CCONJ
ejpam-5019	63	18	(	(	PUNCT
ejpam-5019	63	19	−2−	−2−	NUM
ejpam-5019	63	20	λi)β	λi)β	PROPN
ejpam-5019	63	21	+	+	NUM
ejpam-5019	63	22	δ	δ	PROPN
ejpam-5019	63	23	,	,	PUNCT
ejpam-5019	63	24	i	i	NOUN
ejpam-5019	63	25	=	=	NOUN
ejpam-5019	63	26	2	2	NUM
ejpam-5019	63	27	,	,	PUNCT
ejpam-5019	63	28	3	3	NUM
ejpam-5019	63	29	,	,	PUNCT
ejpam-5019	63	30	.	.	PUNCT
ejpam-5019	63	31	.	.	PUNCT
ejpam-5019	63	32	.	.	PUNCT
ejpam-5019	63	33	,	,	PUNCT
ejpam-5019	63	34	n	n	CCONJ
ejpam-5019	63	35	}	}	PUNCT
ejpam-5019	63	36	proof	proof	NOUN
ejpam-5019	63	37	.	.	PUNCT
ejpam-5019	64	1	let	let	VERB
ejpam-5019	64	2	g	g	PROPN
ejpam-5019	64	3	represent	represent	VERB
ejpam-5019	64	4	a	a	DET
ejpam-5019	64	5	r−	r−	PROPN
ejpam-5019	64	6	regular	regular	ADJ
ejpam-5019	64	7	graph	graph	NOUN
ejpam-5019	64	8	of	of	ADP
ejpam-5019	64	9	order	order	NOUN
ejpam-5019	64	10	n	n	PRON
ejpam-5019	64	11	with	with	ADP
ejpam-5019	64	12	diameter	diameter	NOUN
ejpam-5019	64	13	at	at	ADP
ejpam-5019	64	14	most	most	ADV
ejpam-5019	64	15	two	two	NUM
ejpam-5019	64	16	.	.	PUNCT
ejpam-5019	65	1	let	let	VERB
ejpam-5019	65	2	v	v	X
ejpam-5019	65	3	(	(	PUNCT
ejpam-5019	65	4	g	g	NOUN
ejpam-5019	65	5	)	)	PUNCT
ejpam-5019	65	6	=	=	SYM
ejpam-5019	65	7	{	{	PUNCT
ejpam-5019	65	8	v1	v1	PROPN
ejpam-5019	65	9	,	,	PUNCT
ejpam-5019	65	10	v2	v2	PROPN
ejpam-5019	65	11	,	,	PUNCT
ejpam-5019	65	12	.	.	PUNCT
ejpam-5019	65	13	.	.	PUNCT
ejpam-5019	66	1	.	.	PUNCT
ejpam-5019	67	1	,	,	PUNCT
ejpam-5019	67	2	vn	vn	AUX
ejpam-5019	67	3	}	}	PUNCT
ejpam-5019	67	4	be	be	AUX
ejpam-5019	67	5	the	the	DET
ejpam-5019	67	6	vertex	vertex	NOUN
ejpam-5019	67	7	set	set	NOUN
ejpam-5019	67	8	of	of	ADP
ejpam-5019	67	9	the	the	DET
ejpam-5019	67	10	graph	graph	NOUN
ejpam-5019	67	11	g.	g.	NOUN
ejpam-5019	67	12	in	in	ADP
ejpam-5019	67	13	g	g	PROPN
ejpam-5019	67	14	,	,	PUNCT
ejpam-5019	67	15	for	for	ADP
ejpam-5019	67	16	all	all	PRON
ejpam-5019	67	17	v	v	ADP
ejpam-5019	67	18	∈	∈	NUM
ejpam-5019	67	19	v	v	NOUN
ejpam-5019	67	20	(	(	PUNCT
ejpam-5019	67	21	g	g	NOUN
ejpam-5019	67	22	)	)	PUNCT
ejpam-5019	67	23	,	,	PUNCT
ejpam-5019	67	24	we	we	PRON
ejpam-5019	67	25	have	have	AUX
ejpam-5019	67	26	tr	tr	VERB
ejpam-5019	67	27	(	(	PUNCT
ejpam-5019	67	28	v	v	NOUN
ejpam-5019	67	29	)	)	PUNCT
ejpam-5019	67	30	=	=	SYM
ejpam-5019	68	1	r	r	NOUN
ejpam-5019	68	2	+	+	NUM
ejpam-5019	68	3	2	2	NUM
ejpam-5019	68	4	(	(	PUNCT
ejpam-5019	68	5	n−	n−	NOUN
ejpam-5019	68	6	r	r	NOUN
ejpam-5019	68	7	−	−	NOUN
ejpam-5019	68	8	1	1	NUM
ejpam-5019	68	9	)	)	PUNCT
ejpam-5019	68	10	=	=	PUNCT
ejpam-5019	69	1	2n−	2n−	NUM
ejpam-5019	69	2	r	r	NOUN
ejpam-5019	69	3	−	−	NOUN
ejpam-5019	69	4	2	2	NUM
ejpam-5019	69	5	.	.	PUNCT
ejpam-5019	70	1	the	the	DET
ejpam-5019	70	2	universal	universal	ADJ
ejpam-5019	70	3	distance	distance	NOUN
ejpam-5019	70	4	matrix	matrix	NOUN
ejpam-5019	70	5	of	of	ADP
ejpam-5019	70	6	g	g	NOUN
ejpam-5019	70	7	can	can	AUX
ejpam-5019	70	8	be	be	AUX
ejpam-5019	70	9	written	write	VERB
ejpam-5019	70	10	as	as	ADP
ejpam-5019	70	11	ud	ud	PROPN
ejpam-5019	70	12	(	(	PUNCT
ejpam-5019	70	13	g	g	NOUN
ejpam-5019	70	14	)	)	PUNCT
ejpam-5019	71	1	=	=	SYM
ejpam-5019	71	2	αtr	αtr	NOUN
ejpam-5019	71	3	(	(	PUNCT
ejpam-5019	71	4	g	g	NOUN
ejpam-5019	71	5	)	)	PUNCT
ejpam-5019	71	6	+	+	NUM
ejpam-5019	71	7	βd	βd	INTJ
ejpam-5019	71	8	(	(	PUNCT
ejpam-5019	71	9	g	g	NOUN
ejpam-5019	71	10	)	)	PUNCT
ejpam-5019	71	11	+	+	NUM
ejpam-5019	71	12	γjn	γjn	NOUN
ejpam-5019	71	13	+	+	CCONJ
ejpam-5019	71	14	δin	δin	NOUN
ejpam-5019	71	15	,	,	PUNCT
ejpam-5019	71	16	for	for	ADP
ejpam-5019	71	17	α	α	NOUN
ejpam-5019	71	18	,	,	PUNCT
ejpam-5019	71	19	β	β	X
ejpam-5019	71	20	,	,	PUNCT
ejpam-5019	71	21	γ	γ	PROPN
ejpam-5019	71	22	,	,	PUNCT
ejpam-5019	71	23	δ	δ	PROPN
ejpam-5019	71	24	∈	∈	PROPN
ejpam-5019	71	25	r	r	NOUN
ejpam-5019	71	26	,	,	PUNCT
ejpam-5019	71	27	β	β	X
ejpam-5019	71	28	̸=	̸=	PROPN
ejpam-5019	71	29	0	0	NUM
ejpam-5019	71	30	.	.	PUNCT
ejpam-5019	72	1	=	=	SYM
ejpam-5019	72	2	α	α	PRON
ejpam-5019	72	3	(	(	PUNCT
ejpam-5019	72	4	2n−	2n−	PROPN
ejpam-5019	72	5	r	r	NOUN
ejpam-5019	72	6	−	−	NOUN
ejpam-5019	72	7	2	2	NUM
ejpam-5019	72	8	)	)	PUNCT
ejpam-5019	72	9	in	in	ADP
ejpam-5019	72	10	+	+	ADJ
ejpam-5019	72	11	β	β	X
ejpam-5019	72	12	[	[	PUNCT
ejpam-5019	72	13	a	a	DET
ejpam-5019	72	14	(	(	PUNCT
ejpam-5019	72	15	g	g	NOUN
ejpam-5019	72	16	)	)	PUNCT
ejpam-5019	72	17	+	+	NUM
ejpam-5019	72	18	2a	2a	NUM
ejpam-5019	72	19	(	(	PUNCT
ejpam-5019	72	20	g	g	NOUN
ejpam-5019	72	21	)	)	PUNCT
ejpam-5019	72	22	]	]	PUNCT
ejpam-5019	73	1	+	+	CCONJ
ejpam-5019	73	2	γjn	γjn	NOUN
ejpam-5019	73	3	+	+	CCONJ
ejpam-5019	73	4	δin	δin	NOUN
ejpam-5019	73	5	=	=	SYM
ejpam-5019	73	6	α	α	PROPN
ejpam-5019	73	7	(	(	PUNCT
ejpam-5019	73	8	2n−	2n−	PROPN
ejpam-5019	73	9	r	r	NOUN
ejpam-5019	73	10	−	−	NOUN
ejpam-5019	73	11	2	2	NUM
ejpam-5019	73	12	)	)	PUNCT
ejpam-5019	73	13	in	in	ADP
ejpam-5019	73	14	+	+	ADJ
ejpam-5019	73	15	β	β	X
ejpam-5019	73	16	(	(	PUNCT
ejpam-5019	73	17	2jn	2jn	NOUN
ejpam-5019	73	18	−	−	NOUN
ejpam-5019	73	19	2	2	NUM
ejpam-5019	73	20	in	in	ADP
ejpam-5019	73	21	−a	−a	ADJ
ejpam-5019	73	22	(	(	PUNCT
ejpam-5019	73	23	g	g	NOUN
ejpam-5019	73	24	)	)	PUNCT
ejpam-5019	73	25	)	)	PUNCT
ejpam-5019	74	1	+	+	CCONJ
ejpam-5019	74	2	γjn	γjn	NOUN
ejpam-5019	74	3	+	+	X
ejpam-5019	74	4	δin	δin	NOUN
ejpam-5019	74	5	where	where	SCONJ
ejpam-5019	74	6	jn	jn	PROPN
ejpam-5019	74	7	is	be	AUX
ejpam-5019	74	8	an	an	DET
ejpam-5019	74	9	all	all	DET
ejpam-5019	74	10	ones	one	NOUN
ejpam-5019	74	11	matrix	matrix	NOUN
ejpam-5019	74	12	of	of	ADP
ejpam-5019	74	13	order	order	NOUN
ejpam-5019	74	14	n	n	NOUN
ejpam-5019	74	15	and	and	CCONJ
ejpam-5019	74	16	in	in	ADP
ejpam-5019	74	17	is	be	AUX
ejpam-5019	74	18	the	the	DET
ejpam-5019	74	19	identity	identity	NOUN
ejpam-5019	74	20	matrix	matrix	NOUN
ejpam-5019	74	21	of	of	ADP
ejpam-5019	74	22	order	order	NOUN
ejpam-5019	74	23	n.	n.	PROPN
ejpam-5019	74	24	s.	s.	PROPN
ejpam-5019	74	25	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	74	26	,	,	PUNCT
ejpam-5019	74	27	k.	k.	PROPN
ejpam-5019	74	28	desikan	desikan	PROPN
ejpam-5019	74	29	/	/	SYM
ejpam-5019	74	30	eur	eur	PROPN
ejpam-5019	74	31	.	.	PUNCT
ejpam-5019	75	1	j.	j.	PROPN
ejpam-5019	75	2	pure	pure	PROPN
ejpam-5019	75	3	appl	appl	PROPN
ejpam-5019	75	4	.	.	PROPN
ejpam-5019	75	5	math	math	PROPN
ejpam-5019	75	6	,	,	PUNCT
ejpam-5019	75	7	17	17	NUM
ejpam-5019	75	8	(	(	PUNCT
ejpam-5019	75	9	1	1	NUM
ejpam-5019	75	10	)	)	PUNCT
ejpam-5019	75	11	(	(	PUNCT
ejpam-5019	75	12	2024	2024	NUM
ejpam-5019	75	13	)	)	PUNCT
ejpam-5019	75	14	,	,	PUNCT
ejpam-5019	75	15	462	462	NUM
ejpam-5019	75	16	-	-	SYM
ejpam-5019	75	17	476	476	NUM
ejpam-5019	75	18	465	465	NUM
ejpam-5019	75	19	letx	letx	NOUN
ejpam-5019	75	20	=	=	PUNCT
ejpam-5019	75	21	(	(	PUNCT
ejpam-5019	75	22	1	1	NUM
ejpam-5019	75	23	1	1	NUM
ejpam-5019	75	24	1	1	NUM
ejpam-5019	75	25	.	.	PUNCT
ejpam-5019	75	26	.	.	PUNCT
ejpam-5019	75	27	.	.	PUNCT
ejpam-5019	76	1	1)t	1)t	PROPN
ejpam-5019	76	2	be	be	AUX
ejpam-5019	76	3	the	the	DET
ejpam-5019	76	4	all	all	DET
ejpam-5019	76	5	ones	one	NOUN
ejpam-5019	76	6	vector	vector	NOUN
ejpam-5019	76	7	of	of	ADP
ejpam-5019	76	8	order	order	NOUN
ejpam-5019	76	9	n.	n.	NOUN
ejpam-5019	76	10	sinceg	sinceg	PROPN
ejpam-5019	76	11	is	be	AUX
ejpam-5019	76	12	a	a	DET
ejpam-5019	76	13	r−regular	r−regular	ADJ
ejpam-5019	76	14	graph	graph	NOUN
ejpam-5019	76	15	,	,	PUNCT
ejpam-5019	76	16	it	it	PRON
ejpam-5019	76	17	follows	follow	VERB
ejpam-5019	76	18	thatx	thatx	NOUN
ejpam-5019	76	19	is	be	AUX
ejpam-5019	76	20	the	the	DET
ejpam-5019	76	21	perron	perron	PROPN
ejpam-5019	76	22	vector	vector	NOUN
ejpam-5019	76	23	corresponding	correspond	VERB
ejpam-5019	76	24	to	to	ADP
ejpam-5019	76	25	ρ1	ρ1	NOUN
ejpam-5019	76	26	(	(	PUNCT
ejpam-5019	76	27	g	g	NOUN
ejpam-5019	76	28	)	)	PUNCT
ejpam-5019	76	29	=	=	SYM
ejpam-5019	76	30	(	(	PUNCT
ejpam-5019	76	31	α+	α+	X
ejpam-5019	76	32	β	β	X
ejpam-5019	76	33	)	)	PUNCT
ejpam-5019	76	34	(	(	PUNCT
ejpam-5019	76	35	2n−	2n−	NUM
ejpam-5019	76	36	r	r	NOUN
ejpam-5019	76	37	−	−	NOUN
ejpam-5019	76	38	2)+γn+δ	2)+γn+δ	X
ejpam-5019	76	39	.	.	PUNCT
ejpam-5019	76	40	note	note	VERB
ejpam-5019	76	41	that	that	SCONJ
ejpam-5019	76	42	since	since	SCONJ
ejpam-5019	76	43	g	g	PROPN
ejpam-5019	76	44	is	be	AUX
ejpam-5019	76	45	r−regular	r−regular	NUM
ejpam-5019	76	46	,	,	PUNCT
ejpam-5019	76	47	a	a	DET
ejpam-5019	76	48	(	(	PUNCT
ejpam-5019	76	49	g	g	NOUN
ejpam-5019	76	50	)	)	PUNCT
ejpam-5019	76	51	is	be	AUX
ejpam-5019	76	52	(	(	PUNCT
ejpam-5019	76	53	n−	n−	NOUN
ejpam-5019	76	54	1−	1−	NUM
ejpam-5019	76	55	r)−	r)−	ADV
ejpam-5019	76	56	regular	regular	ADV
ejpam-5019	76	57	and	and	CCONJ
ejpam-5019	76	58	x	x	SYM
ejpam-5019	76	59	=	=	SYM
ejpam-5019	76	60	(	(	PUNCT
ejpam-5019	76	61	1	1	NUM
ejpam-5019	76	62	1	1	NUM
ejpam-5019	76	63	1	1	NUM
ejpam-5019	76	64	.	.	PUNCT
ejpam-5019	76	65	.	.	PUNCT
ejpam-5019	76	66	.	.	PUNCT
ejpam-5019	77	1	1)t	1)t	PROPN
ejpam-5019	77	2	is	be	AUX
ejpam-5019	77	3	also	also	ADV
ejpam-5019	77	4	an	an	DET
ejpam-5019	77	5	eigenvector	eigenvector	NOUN
ejpam-5019	77	6	corresponding	correspond	VERB
ejpam-5019	77	7	to	to	ADP
ejpam-5019	77	8	λ1	λ1	PROPN
ejpam-5019	77	9	(	(	PUNCT
ejpam-5019	77	10	a	a	PRON
ejpam-5019	77	11	(	(	PUNCT
ejpam-5019	77	12	g	g	NOUN
ejpam-5019	77	13	)	)	PUNCT
ejpam-5019	77	14	)	)	PUNCT
ejpam-5019	77	15	.	.	PUNCT
ejpam-5019	78	1	for	for	ADP
ejpam-5019	78	2	each	each	DET
ejpam-5019	78	3	i	i	PRON
ejpam-5019	78	4	∈	∈	PROPN
ejpam-5019	78	5	{	{	PUNCT
ejpam-5019	78	6	2	2	NUM
ejpam-5019	78	7	,	,	PUNCT
ejpam-5019	78	8	3	3	NUM
ejpam-5019	78	9	,	,	PUNCT
ejpam-5019	78	10	.	.	PUNCT
ejpam-5019	78	11	.	.	PUNCT
ejpam-5019	78	12	.	.	PUNCT
ejpam-5019	78	13	,	,	PUNCT
ejpam-5019	78	14	n	n	CCONJ
ejpam-5019	78	15	}	}	PUNCT
ejpam-5019	78	16	,	,	PUNCT
ejpam-5019	78	17	let	let	VERB
ejpam-5019	78	18	λi	λi	INTJ
ejpam-5019	78	19	and	and	CCONJ
ejpam-5019	78	20	xi	xi	AUX
ejpam-5019	78	21	be	be	AUX
ejpam-5019	78	22	an	an	DET
ejpam-5019	78	23	eigenvalue	eigenvalue	NOUN
ejpam-5019	78	24	and	and	CCONJ
ejpam-5019	78	25	the	the	DET
ejpam-5019	78	26	corresponding	corresponding	ADJ
ejpam-5019	78	27	eigenvector	eigenvector	NOUN
ejpam-5019	78	28	of	of	ADP
ejpam-5019	78	29	λi	λi	NOUN
ejpam-5019	78	30	,	,	PUNCT
ejpam-5019	78	31	respectively	respectively	ADV
ejpam-5019	78	32	,	,	PUNCT
ejpam-5019	78	33	of	of	ADP
ejpam-5019	78	34	a	a	DET
ejpam-5019	78	35	(	(	PUNCT
ejpam-5019	78	36	g	g	NOUN
ejpam-5019	78	37	)	)	PUNCT
ejpam-5019	78	38	.	.	PUNCT
ejpam-5019	79	1	then	then	ADV
ejpam-5019	79	2	xtxi	xtxi	PROPN
ejpam-5019	80	1	=	=	PUNCT
ejpam-5019	80	2	0	0	PUNCT
ejpam-5019	81	1	and	and	CCONJ
ejpam-5019	81	2	ud	ud	INTJ
ejpam-5019	81	3	(	(	PUNCT
ejpam-5019	81	4	g)xi	g)xi	NOUN
ejpam-5019	81	5	=	=	SYM
ejpam-5019	81	6	[	[	PUNCT
ejpam-5019	81	7	α	α	X
ejpam-5019	81	8	(	(	PUNCT
ejpam-5019	81	9	2n−	2n−	PROPN
ejpam-5019	81	10	r	r	NOUN
ejpam-5019	81	11	−	−	NOUN
ejpam-5019	81	12	2	2	NUM
ejpam-5019	81	13	)	)	PUNCT
ejpam-5019	81	14	in	in	ADP
ejpam-5019	81	15	+	+	ADJ
ejpam-5019	81	16	β	β	X
ejpam-5019	81	17	(	(	PUNCT
ejpam-5019	81	18	2jn	2jn	NOUN
ejpam-5019	81	19	−	−	NOUN
ejpam-5019	81	20	2	2	NUM
ejpam-5019	81	21	in	in	ADP
ejpam-5019	81	22	−a	−a	ADJ
ejpam-5019	81	23	(	(	PUNCT
ejpam-5019	81	24	g	g	NOUN
ejpam-5019	81	25	)	)	PUNCT
ejpam-5019	81	26	)	)	PUNCT
ejpam-5019	82	1	+	+	CCONJ
ejpam-5019	82	2	γjn	γjn	NOUN
ejpam-5019	82	3	+	+	X
ejpam-5019	82	4	δin	δin	NOUN
ejpam-5019	82	5	]	]	PUNCT
ejpam-5019	82	6	xi	xi	X
ejpam-5019	83	1	=	=	PUNCT
ejpam-5019	83	2	[	[	PUNCT
ejpam-5019	83	3	α	α	X
ejpam-5019	83	4	(	(	PUNCT
ejpam-5019	83	5	2n−	2n−	PROPN
ejpam-5019	83	6	r	r	NOUN
ejpam-5019	83	7	−	−	NOUN
ejpam-5019	83	8	2	2	NUM
ejpam-5019	83	9	)	)	PUNCT
ejpam-5019	83	10	+	+	CCONJ
ejpam-5019	84	1	(	(	PUNCT
ejpam-5019	84	2	−2−	−2−	NUM
ejpam-5019	84	3	λi)β	λi)β	PROPN
ejpam-5019	84	4	+	+	NUM
ejpam-5019	84	5	δ	δ	X
ejpam-5019	84	6	]	]	PUNCT
ejpam-5019	84	7	xi	xi	PROPN
ejpam-5019	84	8	,	,	PUNCT
ejpam-5019	84	9	i	i	PRON
ejpam-5019	84	10	=	=	NOUN
ejpam-5019	84	11	2	2	NUM
ejpam-5019	84	12	,	,	PUNCT
ejpam-5019	84	13	3	3	NUM
ejpam-5019	84	14	,	,	PUNCT
ejpam-5019	84	15	.	.	PUNCT
ejpam-5019	84	16	.	.	PUNCT
ejpam-5019	84	17	.	.	PUNCT
ejpam-5019	85	1	,	,	PUNCT
ejpam-5019	85	2	n.	n.	PROPN
ejpam-5019	85	3	this	this	PRON
ejpam-5019	85	4	completes	complete	VERB
ejpam-5019	85	5	the	the	DET
ejpam-5019	85	6	proof	proof	NOUN
ejpam-5019	85	7	.	.	PUNCT
ejpam-5019	86	1	corollary	corollary	ADJ
ejpam-5019	86	2	1	1	NUM
ejpam-5019	86	3	.	.	PUNCT
ejpam-5019	87	1	the	the	DET
ejpam-5019	87	2	universal	universal	ADJ
ejpam-5019	87	3	distance	distance	NOUN
ejpam-5019	87	4	spectrum	spectrum	NOUN
ejpam-5019	87	5	of	of	ADP
ejpam-5019	87	6	petersen	petersen	PROPN
ejpam-5019	87	7	graph	graph	NOUN
ejpam-5019	87	8	consists	consist	VERB
ejpam-5019	87	9	precisely	precisely	ADV
ejpam-5019	87	10	of	of	ADP
ejpam-5019	87	11	15	15	NUM
ejpam-5019	87	12	(	(	PUNCT
ejpam-5019	87	13	α+	α+	X
ejpam-5019	87	14	β)+10γ+δ	β)+10γ+δ	ADP
ejpam-5019	87	15	,	,	PUNCT
ejpam-5019	87	16	15α−3β+δ	15α−3β+δ	NUM
ejpam-5019	87	17	with	with	ADP
ejpam-5019	87	18	algebraic	algebraic	ADJ
ejpam-5019	87	19	multiplicity	multiplicity	NOUN
ejpam-5019	87	20	5	5	NUM
ejpam-5019	87	21	and	and	CCONJ
ejpam-5019	87	22	15α+δ	15α+δ	NUM
ejpam-5019	87	23	with	with	ADP
ejpam-5019	87	24	algebraic	algebraic	ADJ
ejpam-5019	87	25	multiplicity	multiplicity	NOUN
ejpam-5019	87	26	4	4	NUM
ejpam-5019	87	27	.	.	X
ejpam-5019	87	28	2.2	2.2	NUM
ejpam-5019	87	29	.	.	PUNCT
ejpam-5019	88	1	eigenvalues	eigenvalue	NOUN
ejpam-5019	88	2	of	of	ADP
ejpam-5019	88	3	universal	universal	ADJ
ejpam-5019	88	4	distance	distance	NOUN
ejpam-5019	88	5	matrix	matrix	NOUN
ejpam-5019	88	6	of	of	ADP
ejpam-5019	88	7	join	join	NOUN
ejpam-5019	88	8	of	of	ADP
ejpam-5019	88	9	graphs	graph	NOUN
ejpam-5019	88	10	in	in	ADP
ejpam-5019	88	11	this	this	DET
ejpam-5019	88	12	subsection	subsection	NOUN
ejpam-5019	88	13	,	,	PUNCT
ejpam-5019	88	14	we	we	PRON
ejpam-5019	88	15	describe	describe	VERB
ejpam-5019	88	16	the	the	DET
ejpam-5019	88	17	universal	universal	ADJ
ejpam-5019	88	18	distance	distance	NOUN
ejpam-5019	88	19	spectrum	spectrum	NOUN
ejpam-5019	88	20	of	of	ADP
ejpam-5019	88	21	join	join	NOUN
ejpam-5019	88	22	of	of	ADP
ejpam-5019	88	23	two	two	NUM
ejpam-5019	88	24	regular	regular	ADJ
ejpam-5019	88	25	graphs	graph	NOUN
ejpam-5019	88	26	and	and	CCONJ
ejpam-5019	88	27	obtain	obtain	VERB
ejpam-5019	88	28	the	the	DET
ejpam-5019	88	29	universal	universal	ADJ
ejpam-5019	88	30	distance	distance	NOUN
ejpam-5019	88	31	spectrum	spectrum	NOUN
ejpam-5019	88	32	of	of	ADP
ejpam-5019	88	33	this	this	DET
ejpam-5019	88	34	graph	graph	NOUN
ejpam-5019	88	35	.	.	PUNCT
ejpam-5019	89	1	also	also	ADV
ejpam-5019	89	2	,	,	PUNCT
ejpam-5019	89	3	we	we	PRON
ejpam-5019	89	4	obtain	obtain	VERB
ejpam-5019	89	5	the	the	DET
ejpam-5019	89	6	universal	universal	ADJ
ejpam-5019	89	7	distance	distance	NOUN
ejpam-5019	89	8	spectra	spectra	NOUN
ejpam-5019	89	9	of	of	ADP
ejpam-5019	89	10	complete	complete	ADJ
ejpam-5019	89	11	bipartite	bipartite	NOUN
ejpam-5019	89	12	graph	graph	NOUN
ejpam-5019	89	13	,	,	PUNCT
ejpam-5019	89	14	wheel	wheel	NOUN
ejpam-5019	89	15	graph	graph	NOUN
ejpam-5019	89	16	and	and	CCONJ
ejpam-5019	89	17	complete	complete	ADJ
ejpam-5019	89	18	split	split	NOUN
ejpam-5019	89	19	graph	graph	NOUN
ejpam-5019	89	20	.	.	PUNCT
ejpam-5019	90	1	theorem	theorem	NOUN
ejpam-5019	90	2	2	2	NUM
ejpam-5019	90	3	.	.	X
ejpam-5019	91	1	for	for	ADP
ejpam-5019	91	2	i	i	PROPN
ejpam-5019	91	3	∈	∈	PROPN
ejpam-5019	91	4	{	{	PUNCT
ejpam-5019	91	5	1	1	NUM
ejpam-5019	91	6	,	,	PUNCT
ejpam-5019	91	7	2	2	NUM
ejpam-5019	91	8	}	}	PUNCT
ejpam-5019	91	9	,	,	PUNCT
ejpam-5019	91	10	let	let	VERB
ejpam-5019	91	11	gi	gi	PART
ejpam-5019	91	12	be	be	AUX
ejpam-5019	91	13	an	an	DET
ejpam-5019	91	14	ri−regular	ri−regular	ADJ
ejpam-5019	91	15	graph	graph	NOUN
ejpam-5019	91	16	of	of	ADP
ejpam-5019	91	17	order	order	NOUN
ejpam-5019	91	18	ni	ni	PROPN
ejpam-5019	91	19	and	and	CCONJ
ejpam-5019	91	20	let	let	VERB
ejpam-5019	91	21	ri	ri	NOUN
ejpam-5019	91	22	=	=	PUNCT
ejpam-5019	91	23	λi	λi	ADP
ejpam-5019	91	24	1	1	NUM
ejpam-5019	91	25	,	,	PUNCT
ejpam-5019	91	26	λ	λ	VERB
ejpam-5019	91	27	i	i	PRON
ejpam-5019	91	28	2	2	NUM
ejpam-5019	91	29	,	,	PUNCT
ejpam-5019	91	30	.	.	PUNCT
ejpam-5019	91	31	.	.	PUNCT
ejpam-5019	92	1	.	.	PUNCT
ejpam-5019	93	1	,	,	PUNCT
ejpam-5019	93	2	λ	λ	INTJ
ejpam-5019	93	3	i	i	PRON
ejpam-5019	93	4	ni	ni	VERB
ejpam-5019	93	5	be	be	VERB
ejpam-5019	93	6	the	the	DET
ejpam-5019	93	7	eigenvalues	eigenvalue	NOUN
ejpam-5019	93	8	of	of	ADP
ejpam-5019	93	9	a	a	DET
ejpam-5019	93	10	(	(	PUNCT
ejpam-5019	93	11	gi	gi	NOUN
ejpam-5019	93	12	)	)	PUNCT
ejpam-5019	93	13	.	.	PUNCT
ejpam-5019	94	1	the	the	DET
ejpam-5019	94	2	characteristic	characteristic	ADJ
ejpam-5019	94	3	polynomial	polynomial	NOUN
ejpam-5019	94	4	of	of	ADP
ejpam-5019	94	5	g	g	PROPN
ejpam-5019	94	6	=	=	SYM
ejpam-5019	94	7	g1∇g2	g1∇g2	NOUN
ejpam-5019	94	8	,	,	PUNCT
ejpam-5019	94	9	denoted	denote	VERB
ejpam-5019	94	10	by	by	ADP
ejpam-5019	94	11	p	p	PROPN
ejpam-5019	94	12	(	(	PUNCT
ejpam-5019	94	13	g	g	NOUN
ejpam-5019	94	14	:	:	PUNCT
ejpam-5019	94	15	x	x	X
ejpam-5019	94	16	)	)	PUNCT
ejpam-5019	94	17	,	,	PUNCT
ejpam-5019	94	18	is	be	AUX
ejpam-5019	94	19	given	give	VERB
ejpam-5019	94	20	by	by	ADP
ejpam-5019	94	21	p	p	X
ejpam-5019	94	22	(	(	PUNCT
ejpam-5019	94	23	g	g	NOUN
ejpam-5019	94	24	:	:	PUNCT
ejpam-5019	94	25	x	x	X
ejpam-5019	94	26	)	)	PUNCT
ejpam-5019	94	27	=	=	NOUN
ejpam-5019	95	1	[	[	PUNCT
ejpam-5019	95	2	x2−(s1	x2−(s1	PROPN
ejpam-5019	95	3	+	+	CCONJ
ejpam-5019	95	4	s2)x+	s2)x+	NOUN
ejpam-5019	95	5	[	[	PUNCT
ejpam-5019	95	6	s1s2−(β	s1s2−(β	NOUN
ejpam-5019	95	7	+	+	X
ejpam-5019	95	8	γ)2	γ)2	PROPN
ejpam-5019	95	9	n1n2	n1n2	NUM
ejpam-5019	95	10	]	]	PUNCT
ejpam-5019	95	11	]	]	X
ejpam-5019	95	12	∏n1	∏n1	ADJ
ejpam-5019	95	13	s=2	s=2	X
ejpam-5019	95	14	[	[	PUNCT
ejpam-5019	95	15	x−	x−	PROPN
ejpam-5019	95	16	[	[	PUNCT
ejpam-5019	95	17	α	α	X
ejpam-5019	95	18	(	(	PUNCT
ejpam-5019	95	19	2n1	2n1	NUM
ejpam-5019	95	20	−	−	PROPN
ejpam-5019	95	21	r1	r1	PROPN
ejpam-5019	95	22	+	+	CCONJ
ejpam-5019	95	23	n2	n2	ADJ
ejpam-5019	95	24	−	−	PROPN
ejpam-5019	95	25	2	2	NUM
ejpam-5019	95	26	)	)	PUNCT
ejpam-5019	95	27	]	]	PUNCT
ejpam-5019	96	1	+	+	CCONJ
ejpam-5019	96	2	β	β	X
ejpam-5019	96	3	(	(	PUNCT
ejpam-5019	96	4	−λ1	−λ1	PROPN
ejpam-5019	96	5	s	s	PART
ejpam-5019	96	6	)	)	PUNCT
ejpam-5019	96	7	+	+	CCONJ
ejpam-5019	96	8	δ	δ	X
ejpam-5019	96	9	]	]	PUNCT
ejpam-5019	96	10	∏n2	∏n2	X
ejpam-5019	96	11	j=2	j=2	X
ejpam-5019	96	12	[	[	PUNCT
ejpam-5019	96	13	x−	x−	PROPN
ejpam-5019	96	14	[	[	PUNCT
ejpam-5019	96	15	α	α	X
ejpam-5019	96	16	(	(	PUNCT
ejpam-5019	96	17	2n2	2n2	NUM
ejpam-5019	96	18	−	−	ADP
ejpam-5019	96	19	r2	r2	NOUN
ejpam-5019	96	20	+	+	CCONJ
ejpam-5019	96	21	n1	n1	NOUN
ejpam-5019	96	22	−	−	NOUN
ejpam-5019	96	23	2	2	NUM
ejpam-5019	96	24	)	)	PUNCT
ejpam-5019	96	25	]	]	PUNCT
ejpam-5019	97	1	+	+	CCONJ
ejpam-5019	97	2	β	β	X
ejpam-5019	97	3	(	(	PUNCT
ejpam-5019	97	4	−λ2	−λ2	PROPN
ejpam-5019	97	5	j	j	PROPN
ejpam-5019	97	6	)	)	PUNCT
ejpam-5019	98	1	+	+	CCONJ
ejpam-5019	98	2	δ	δ	X
ejpam-5019	98	3	]	]	X
ejpam-5019	98	4	;	;	PUNCT
ejpam-5019	98	5	where	where	SCONJ
ejpam-5019	98	6	s1	s1	NOUN
ejpam-5019	98	7	=	=	PROPN
ejpam-5019	98	8	α	α	PROPN
ejpam-5019	98	9	(	(	PUNCT
ejpam-5019	98	10	2n1	2n1	NUM
ejpam-5019	98	11	−	−	PROPN
ejpam-5019	98	12	r1	r1	PROPN
ejpam-5019	98	13	+	+	CCONJ
ejpam-5019	98	14	n2	n2	ADJ
ejpam-5019	98	15	−	−	PROPN
ejpam-5019	98	16	2	2	NUM
ejpam-5019	98	17	)	)	PUNCT
ejpam-5019	98	18	+	+	NUM
ejpam-5019	98	19	β	β	X
ejpam-5019	98	20	(	(	PUNCT
ejpam-5019	98	21	2−	2−	NUM
ejpam-5019	98	22	r1	r1	NOUN
ejpam-5019	98	23	)	)	PUNCT
ejpam-5019	99	1	+	+	SYM
ejpam-5019	99	2	γn1	γn1	X
ejpam-5019	99	3	+	+	CCONJ
ejpam-5019	99	4	δ	δ	PROPN
ejpam-5019	99	5	,	,	PUNCT
ejpam-5019	99	6	s2	s2	NOUN
ejpam-5019	99	7	=	=	PUNCT
ejpam-5019	99	8	α	α	PROPN
ejpam-5019	99	9	(	(	PUNCT
ejpam-5019	99	10	2n2	2n2	NUM
ejpam-5019	99	11	−	−	ADP
ejpam-5019	99	12	r2	r2	NOUN
ejpam-5019	99	13	+	+	CCONJ
ejpam-5019	99	14	n1	n1	NOUN
ejpam-5019	99	15	−	−	NOUN
ejpam-5019	99	16	2	2	NUM
ejpam-5019	99	17	)	)	PUNCT
ejpam-5019	99	18	+	+	NUM
ejpam-5019	99	19	β	β	X
ejpam-5019	99	20	(	(	PUNCT
ejpam-5019	99	21	2−	2−	NUM
ejpam-5019	99	22	r2	r2	NOUN
ejpam-5019	99	23	)	)	PUNCT
ejpam-5019	99	24	+	+	CCONJ
ejpam-5019	99	25	γn2	γn2	NOUN
ejpam-5019	99	26	+	+	CCONJ
ejpam-5019	99	27	δ	δ	PROPN
ejpam-5019	99	28	.	.	PUNCT
ejpam-5019	99	29	proof	proof	NOUN
ejpam-5019	99	30	.	.	PUNCT
ejpam-5019	100	1	let	let	VERB
ejpam-5019	100	2	g1	g1	PROPN
ejpam-5019	100	3	and	and	CCONJ
ejpam-5019	100	4	g2	g2	PROPN
ejpam-5019	100	5	be	be	AUX
ejpam-5019	100	6	r1−	r1−	NOUN
ejpam-5019	100	7	and	and	CCONJ
ejpam-5019	100	8	r2−	r2−	VERB
ejpam-5019	100	9	regular	regular	ADJ
ejpam-5019	100	10	graphs	graph	NOUN
ejpam-5019	100	11	of	of	ADP
ejpam-5019	100	12	orders	order	NOUN
ejpam-5019	100	13	n1	n1	PROPN
ejpam-5019	100	14	and	and	CCONJ
ejpam-5019	100	15	n2	n2	ADJ
ejpam-5019	100	16	,	,	PUNCT
ejpam-5019	100	17	respectively	respectively	ADV
ejpam-5019	100	18	.	.	PUNCT
ejpam-5019	101	1	consider	consider	VERB
ejpam-5019	101	2	the	the	DET
ejpam-5019	101	3	vertex	vertex	NOUN
ejpam-5019	101	4	sets	set	NOUN
ejpam-5019	101	5	of	of	ADP
ejpam-5019	101	6	g1	g1	NOUN
ejpam-5019	101	7	and	and	CCONJ
ejpam-5019	101	8	g2	g2	PROPN
ejpam-5019	101	9	with	with	ADP
ejpam-5019	101	10	,	,	PUNCT
ejpam-5019	101	11	v	v	PROPN
ejpam-5019	101	12	(	(	PUNCT
ejpam-5019	101	13	g1	g1	PROPN
ejpam-5019	101	14	)	)	PUNCT
ejpam-5019	101	15	and	and	CCONJ
ejpam-5019	101	16	v	v	NOUN
ejpam-5019	101	17	(	(	PUNCT
ejpam-5019	101	18	g2	g2	PROPN
ejpam-5019	101	19	)	)	PUNCT
ejpam-5019	101	20	,	,	PUNCT
ejpam-5019	101	21	respectively	respectively	ADV
ejpam-5019	101	22	.	.	PUNCT
ejpam-5019	102	1	clearly	clearly	ADV
ejpam-5019	102	2	,	,	PUNCT
ejpam-5019	102	3	the	the	DET
ejpam-5019	102	4	graph	graph	NOUN
ejpam-5019	102	5	g	g	NOUN
ejpam-5019	102	6	has	have	VERB
ejpam-5019	102	7	diameter	diameter	NOUN
ejpam-5019	102	8	at	at	ADP
ejpam-5019	102	9	most	most	ADV
ejpam-5019	102	10	two	two	NUM
ejpam-5019	102	11	with	with	ADP
ejpam-5019	102	12	the	the	DET
ejpam-5019	102	13	vertex	vertex	NOUN
ejpam-5019	102	14	set	set	VERB
ejpam-5019	102	15	v	v	NOUN
ejpam-5019	102	16	(	(	PUNCT
ejpam-5019	102	17	g1	g1	PROPN
ejpam-5019	102	18	)	)	PUNCT
ejpam-5019	102	19	∪	∪	NOUN
ejpam-5019	102	20	v	v	PROPN
ejpam-5019	102	21	(	(	PUNCT
ejpam-5019	102	22	g2	g2	PROPN
ejpam-5019	102	23	)	)	PUNCT
ejpam-5019	102	24	.	.	PUNCT
ejpam-5019	103	1	in	in	ADP
ejpam-5019	103	2	g1	g1	PROPN
ejpam-5019	103	3	,	,	PUNCT
ejpam-5019	103	4	we	we	PRON
ejpam-5019	103	5	have	have	AUX
ejpam-5019	103	6	trg1	trg1	VERB
ejpam-5019	103	7	(	(	PUNCT
ejpam-5019	103	8	v	v	NOUN
ejpam-5019	103	9	)	)	PUNCT
ejpam-5019	103	10	=	=	SYM
ejpam-5019	103	11	2	2	NUM
ejpam-5019	103	12	(	(	PUNCT
ejpam-5019	103	13	n1	n1	NOUN
ejpam-5019	103	14	−	−	PROPN
ejpam-5019	103	15	r1	r1	NOUN
ejpam-5019	103	16	−	−	PROPN
ejpam-5019	103	17	1	1	NUM
ejpam-5019	103	18	)	)	PUNCT
ejpam-5019	103	19	+	+	CCONJ
ejpam-5019	103	20	r1	r1	PROPN
ejpam-5019	103	21	+	+	CCONJ
ejpam-5019	103	22	n2	n2	ADJ
ejpam-5019	103	23	,	,	PUNCT
ejpam-5019	103	24	for	for	ADP
ejpam-5019	103	25	all	all	DET
ejpam-5019	103	26	v	v	ADP
ejpam-5019	103	27	∈	∈	NOUN
ejpam-5019	103	28	v	v	NOUN
ejpam-5019	103	29	(	(	PUNCT
ejpam-5019	103	30	g1	g1	PROPN
ejpam-5019	103	31	)	)	PUNCT
ejpam-5019	103	32	.	.	PUNCT
ejpam-5019	104	1	in	in	ADP
ejpam-5019	104	2	g2	g2	PROPN
ejpam-5019	104	3	,	,	PUNCT
ejpam-5019	104	4	we	we	PRON
ejpam-5019	104	5	have	have	AUX
ejpam-5019	104	6	trg2	trg2	VERB
ejpam-5019	104	7	(	(	PUNCT
ejpam-5019	104	8	v	v	NOUN
ejpam-5019	104	9	)	)	PUNCT
ejpam-5019	104	10	=	=	SYM
ejpam-5019	104	11	2	2	NUM
ejpam-5019	104	12	(	(	PUNCT
ejpam-5019	104	13	n2	n2	ADJ
ejpam-5019	104	14	−	−	PROPN
ejpam-5019	104	15	r2	r2	NOUN
ejpam-5019	104	16	−	−	PROPN
ejpam-5019	104	17	1	1	NUM
ejpam-5019	104	18	)	)	PUNCT
ejpam-5019	105	1	+	+	CCONJ
ejpam-5019	105	2	r2	r2	NOUN
ejpam-5019	105	3	+	+	CCONJ
ejpam-5019	105	4	n1	n1	NOUN
ejpam-5019	105	5	,	,	PUNCT
ejpam-5019	105	6	for	for	ADP
ejpam-5019	105	7	all	all	PRON
ejpam-5019	105	8	v	v	ADP
ejpam-5019	105	9	∈	∈	NUM
ejpam-5019	105	10	v	v	NOUN
ejpam-5019	105	11	(	(	PUNCT
ejpam-5019	105	12	g2	g2	PROPN
ejpam-5019	105	13	)	)	PUNCT
ejpam-5019	105	14	.	.	PUNCT
ejpam-5019	106	1	label	label	VERB
ejpam-5019	106	2	the	the	DET
ejpam-5019	106	3	vertices	vertex	NOUN
ejpam-5019	106	4	of	of	ADP
ejpam-5019	106	5	the	the	DET
ejpam-5019	106	6	graph	graph	NOUN
ejpam-5019	106	7	g	g	ADP
ejpam-5019	106	8	such	such	ADJ
ejpam-5019	106	9	that	that	SCONJ
ejpam-5019	106	10	the	the	DET
ejpam-5019	106	11	first	first	ADJ
ejpam-5019	106	12	n1	n1	ADJ
ejpam-5019	106	13	vertices	vertex	NOUN
ejpam-5019	106	14	are	be	AUX
ejpam-5019	106	15	from	from	ADP
ejpam-5019	106	16	g1	g1	PROPN
ejpam-5019	106	17	and	and	CCONJ
ejpam-5019	106	18	the	the	DET
ejpam-5019	106	19	s.	s.	PROPN
ejpam-5019	106	20	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	106	21	,	,	PUNCT
ejpam-5019	106	22	k.	k.	PROPN
ejpam-5019	106	23	desikan	desikan	PROPN
ejpam-5019	106	24	/	/	SYM
ejpam-5019	106	25	eur	eur	PROPN
ejpam-5019	106	26	.	.	PUNCT
ejpam-5019	107	1	j.	j.	PROPN
ejpam-5019	107	2	pure	pure	PROPN
ejpam-5019	107	3	appl	appl	PROPN
ejpam-5019	107	4	.	.	PROPN
ejpam-5019	107	5	math	math	PROPN
ejpam-5019	107	6	,	,	PUNCT
ejpam-5019	107	7	17	17	NUM
ejpam-5019	107	8	(	(	PUNCT
ejpam-5019	107	9	1	1	NUM
ejpam-5019	107	10	)	)	PUNCT
ejpam-5019	107	11	(	(	PUNCT
ejpam-5019	107	12	2024	2024	NUM
ejpam-5019	107	13	)	)	PUNCT
ejpam-5019	107	14	,	,	PUNCT
ejpam-5019	107	15	462	462	NUM
ejpam-5019	107	16	-	-	SYM
ejpam-5019	107	17	476	476	NUM
ejpam-5019	107	18	466	466	NUM
ejpam-5019	107	19	next	next	ADJ
ejpam-5019	107	20	n2	n2	ADJ
ejpam-5019	107	21	vertices	vertex	NOUN
ejpam-5019	107	22	are	be	AUX
ejpam-5019	107	23	from	from	ADP
ejpam-5019	107	24	g2	g2	PROPN
ejpam-5019	107	25	.	.	PUNCT
ejpam-5019	108	1	the	the	DET
ejpam-5019	108	2	universal	universal	ADJ
ejpam-5019	108	3	distance	distance	NOUN
ejpam-5019	108	4	matrix	matrix	NOUN
ejpam-5019	108	5	of	of	ADP
ejpam-5019	108	6	g	g	NOUN
ejpam-5019	108	7	can	can	AUX
ejpam-5019	108	8	be	be	AUX
ejpam-5019	108	9	written	write	VERB
ejpam-5019	108	10	as	as	ADP
ejpam-5019	108	11	ud	ud	PROPN
ejpam-5019	108	12	(	(	PUNCT
ejpam-5019	108	13	g	g	NOUN
ejpam-5019	108	14	)	)	PUNCT
ejpam-5019	108	15	=	=	SYM
ejpam-5019	108	16	(	(	PUNCT
ejpam-5019	108	17	u	u	X
ejpam-5019	108	18	(	(	PUNCT
ejpam-5019	108	19	g1	g1	PROPN
ejpam-5019	108	20	)	)	PUNCT
ejpam-5019	108	21	(	(	PUNCT
ejpam-5019	108	22	β	β	X
ejpam-5019	108	23	+	+	CCONJ
ejpam-5019	108	24	γ	γ	X
ejpam-5019	108	25	)	)	PUNCT
ejpam-5019	108	26	jn1×n2	jn1×n2	NOUN
ejpam-5019	108	27	(	(	PUNCT
ejpam-5019	108	28	β	β	X
ejpam-5019	108	29	+	+	CCONJ
ejpam-5019	108	30	γ	γ	X
ejpam-5019	108	31	)	)	PUNCT
ejpam-5019	108	32	jn2×n1	jn2×n1	PROPN
ejpam-5019	108	33	u	u	NOUN
ejpam-5019	108	34	(	(	PUNCT
ejpam-5019	108	35	g2	g2	PROPN
ejpam-5019	108	36	)	)	PUNCT
ejpam-5019	108	37	)	)	PUNCT
ejpam-5019	109	1	where	where	SCONJ
ejpam-5019	109	2	ud	ud	INTJ
ejpam-5019	109	3	(	(	PUNCT
ejpam-5019	109	4	g1	g1	PROPN
ejpam-5019	109	5	)	)	PUNCT
ejpam-5019	109	6	=	=	SYM
ejpam-5019	109	7	α	α	PROPN
ejpam-5019	109	8	(	(	PUNCT
ejpam-5019	109	9	2n1	2n1	NUM
ejpam-5019	109	10	−	−	PROPN
ejpam-5019	109	11	r1	r1	PROPN
ejpam-5019	109	12	+	+	CCONJ
ejpam-5019	109	13	n2	n2	ADJ
ejpam-5019	109	14	−	−	PROPN
ejpam-5019	109	15	2	2	NUM
ejpam-5019	109	16	)	)	PUNCT
ejpam-5019	109	17	in1	in1	NOUN
ejpam-5019	110	1	+	+	CCONJ
ejpam-5019	110	2	β	β	X
ejpam-5019	110	3	(	(	PUNCT
ejpam-5019	110	4	2in1	2in1	NUM
ejpam-5019	110	5	−a	−a	NOUN
ejpam-5019	110	6	(	(	PUNCT
ejpam-5019	110	7	g1	g1	PROPN
ejpam-5019	110	8	)	)	PUNCT
ejpam-5019	110	9	)	)	PUNCT
ejpam-5019	111	1	+	+	CCONJ
ejpam-5019	111	2	γjn1	γjn1	NOUN
ejpam-5019	111	3	+	+	CCONJ
ejpam-5019	111	4	δin1	δin1	PROPN
ejpam-5019	111	5	ud	ud	INTJ
ejpam-5019	111	6	(	(	PUNCT
ejpam-5019	111	7	g2	g2	PROPN
ejpam-5019	111	8	)	)	PUNCT
ejpam-5019	111	9	=	=	SYM
ejpam-5019	111	10	α	α	PROPN
ejpam-5019	111	11	(	(	PUNCT
ejpam-5019	111	12	2n2	2n2	NUM
ejpam-5019	111	13	−	−	ADP
ejpam-5019	111	14	r2	r2	NOUN
ejpam-5019	111	15	+	+	CCONJ
ejpam-5019	111	16	n1	n1	NOUN
ejpam-5019	111	17	−	−	NOUN
ejpam-5019	111	18	2	2	NUM
ejpam-5019	111	19	)	)	PUNCT
ejpam-5019	111	20	in2	in2	PROPN
ejpam-5019	112	1	+	+	X
ejpam-5019	112	2	β	β	X
ejpam-5019	112	3	(	(	PUNCT
ejpam-5019	112	4	2in2	2in2	NUM
ejpam-5019	112	5	−a	−a	NOUN
ejpam-5019	112	6	(	(	PUNCT
ejpam-5019	112	7	g2	g2	PROPN
ejpam-5019	112	8	)	)	PUNCT
ejpam-5019	112	9	)	)	PUNCT
ejpam-5019	113	1	+	+	CCONJ
ejpam-5019	113	2	γjn2	γjn2	NOUN
ejpam-5019	113	3	+	+	NUM
ejpam-5019	113	4	δin2	δin2	NOUN
ejpam-5019	113	5	let	let	VERB
ejpam-5019	113	6	1n	1n	NUM
ejpam-5019	113	7	=	=	SYM
ejpam-5019	113	8	(	(	PUNCT
ejpam-5019	113	9	1	1	NUM
ejpam-5019	113	10	1	1	NUM
ejpam-5019	113	11	1	1	NUM
ejpam-5019	113	12	.	.	PUNCT
ejpam-5019	113	13	.	.	PUNCT
ejpam-5019	113	14	.	.	PUNCT
ejpam-5019	114	1	1)t	1)t	PROPN
ejpam-5019	114	2	be	be	AUX
ejpam-5019	114	3	an	an	DET
ejpam-5019	114	4	all	all	DET
ejpam-5019	114	5	ones	one	NOUN
ejpam-5019	114	6	vector	vector	NOUN
ejpam-5019	114	7	of	of	ADP
ejpam-5019	114	8	order	order	NOUN
ejpam-5019	114	9	n.	n.	NOUN
ejpam-5019	114	10	since	since	SCONJ
ejpam-5019	114	11	g1	g1	PROPN
ejpam-5019	114	12	is	be	AUX
ejpam-5019	114	13	a	a	DET
ejpam-5019	114	14	r1−	r1−	NUM
ejpam-5019	114	15	regular	regular	ADJ
ejpam-5019	114	16	graph	graph	NOUN
ejpam-5019	114	17	,	,	PUNCT
ejpam-5019	114	18	1n1	1n1	NUM
ejpam-5019	114	19	is	be	AUX
ejpam-5019	114	20	the	the	DET
ejpam-5019	114	21	eigenvector	eigenvector	NOUN
ejpam-5019	114	22	corresponding	corresponding	NOUN
ejpam-5019	114	23	to	to	ADP
ejpam-5019	114	24	the	the	DET
ejpam-5019	114	25	eigenvalue	eigenvalue	ADJ
ejpam-5019	114	26	r1	r1	NOUN
ejpam-5019	114	27	of	of	ADP
ejpam-5019	114	28	a	a	DET
ejpam-5019	114	29	(	(	PUNCT
ejpam-5019	114	30	g1	g1	PROPN
ejpam-5019	114	31	)	)	PUNCT
ejpam-5019	114	32	.	.	PUNCT
ejpam-5019	115	1	similarly	similarly	ADV
ejpam-5019	115	2	,	,	PUNCT
ejpam-5019	115	3	g2	g2	PROPN
ejpam-5019	115	4	is	be	AUX
ejpam-5019	115	5	a	a	DET
ejpam-5019	115	6	r2−	r2−	ADJ
ejpam-5019	115	7	regular	regular	ADJ
ejpam-5019	115	8	graph	graph	NOUN
ejpam-5019	115	9	,	,	PUNCT
ejpam-5019	115	10	1n2	1n2	NUM
ejpam-5019	115	11	is	be	AUX
ejpam-5019	115	12	the	the	DET
ejpam-5019	115	13	eigenvector	eigenvector	NOUN
ejpam-5019	115	14	corresponding	correspond	VERB
ejpam-5019	115	15	to	to	ADP
ejpam-5019	115	16	the	the	DET
ejpam-5019	115	17	eigenvalue	eigenvalue	ADJ
ejpam-5019	115	18	r2	r2	NOUN
ejpam-5019	115	19	of	of	ADP
ejpam-5019	115	20	a	a	DET
ejpam-5019	115	21	(	(	PUNCT
ejpam-5019	115	22	g2	g2	PROPN
ejpam-5019	115	23	)	)	PUNCT
ejpam-5019	115	24	.	.	PUNCT
ejpam-5019	116	1	let	let	VERB
ejpam-5019	116	2	w	w	NOUN
ejpam-5019	116	3	be	be	AUX
ejpam-5019	116	4	an	an	DET
ejpam-5019	116	5	orthogonal	orthogonal	ADJ
ejpam-5019	116	6	vector	vector	NOUN
ejpam-5019	116	7	to	to	ADP
ejpam-5019	116	8	1n1	1n1	NUM
ejpam-5019	116	9	,	,	PUNCT
ejpam-5019	116	10	and	and	CCONJ
ejpam-5019	116	11	a	a	DET
ejpam-5019	116	12	(	(	PUNCT
ejpam-5019	116	13	g1)1n1	g1)1n1	NOUN
ejpam-5019	116	14	=	=	SYM
ejpam-5019	116	15	λ1	λ1	PROPN
ejpam-5019	116	16	1w	1w	NOUN
ejpam-5019	116	17	.	.	PUNCT
ejpam-5019	117	1	we	we	PRON
ejpam-5019	117	2	take	take	VERB
ejpam-5019	117	3	w	w	NOUN
ejpam-5019	117	4	=	=	PUNCT
ejpam-5019	117	5	(	(	PUNCT
ejpam-5019	117	6	w	w	NOUN
ejpam-5019	117	7	0	0	NUM
ejpam-5019	117	8	)	)	PUNCT
ejpam-5019	117	9	t	t	NOUN
ejpam-5019	117	10	and	and	CCONJ
ejpam-5019	117	11	since	since	SCONJ
ejpam-5019	117	12	jt	jt	PROPN
ejpam-5019	117	13	n1×n2	n1×n2	PROPN
ejpam-5019	117	14	w	w	PROPN
ejpam-5019	117	15	=	=	SYM
ejpam-5019	117	16	0	0	NUM
ejpam-5019	117	17	,	,	PUNCT
ejpam-5019	117	18	we	we	PRON
ejpam-5019	117	19	get	get	VERB
ejpam-5019	117	20	ud	ud	INTJ
ejpam-5019	117	21	(	(	PUNCT
ejpam-5019	117	22	g)w	g)w	X
ejpam-5019	118	1	=	=	PUNCT
ejpam-5019	118	2	[	[	PUNCT
ejpam-5019	118	3	(	(	PUNCT
ejpam-5019	118	4	2n1	2n1	NUM
ejpam-5019	118	5	−	−	PROPN
ejpam-5019	118	6	r1	r1	PROPN
ejpam-5019	118	7	+	+	CCONJ
ejpam-5019	118	8	n2	n2	ADJ
ejpam-5019	118	9	−	−	PROPN
ejpam-5019	118	10	2)α+	2)α+	NUM
ejpam-5019	118	11	(	(	PUNCT
ejpam-5019	118	12	−λ1	−λ1	PROPN
ejpam-5019	118	13	s	s	PART
ejpam-5019	118	14	)	)	PUNCT
ejpam-5019	118	15	β	β	PROPN
ejpam-5019	118	16	+	+	CCONJ
ejpam-5019	118	17	δ	δ	X
ejpam-5019	118	18	]	]	X
ejpam-5019	118	19	w	w	PROPN
ejpam-5019	118	20	;	;	PUNCT
ejpam-5019	118	21	s	s	X
ejpam-5019	118	22	=	=	SYM
ejpam-5019	118	23	2	2	NUM
ejpam-5019	118	24	,	,	PUNCT
ejpam-5019	118	25	3	3	NUM
ejpam-5019	118	26	,	,	PUNCT
ejpam-5019	118	27	.	.	PUNCT
ejpam-5019	118	28	.	.	PUNCT
ejpam-5019	118	29	.	.	PUNCT
ejpam-5019	119	1	,	,	PUNCT
ejpam-5019	119	2	n1	n1	PROPN
ejpam-5019	119	3	.	.	PUNCT
ejpam-5019	120	1	this	this	PRON
ejpam-5019	120	2	shows	show	VERB
ejpam-5019	120	3	that	that	SCONJ
ejpam-5019	120	4	(	(	PUNCT
ejpam-5019	120	5	2n1	2n1	NUM
ejpam-5019	120	6	−	−	PROPN
ejpam-5019	120	7	r1	r1	PROPN
ejpam-5019	120	8	+	+	CCONJ
ejpam-5019	120	9	n2	n2	PROPN
ejpam-5019	120	10	−	−	PROPN
ejpam-5019	120	11	2)α	2)α	NUM
ejpam-5019	121	1	+	+	CCONJ
ejpam-5019	121	2	(	(	PUNCT
ejpam-5019	121	3	−λ1	−λ1	NOUN
ejpam-5019	121	4	s	s	PART
ejpam-5019	121	5	)	)	PUNCT
ejpam-5019	121	6	β	β	PROPN
ejpam-5019	121	7	+	+	CCONJ
ejpam-5019	121	8	δ	δ	PROPN
ejpam-5019	121	9	is	be	AUX
ejpam-5019	121	10	an	an	DET
ejpam-5019	121	11	eigenvalue	eigenvalue	NOUN
ejpam-5019	121	12	of	of	ADP
ejpam-5019	121	13	ud	ud	INTJ
ejpam-5019	121	14	(	(	PUNCT
ejpam-5019	121	15	g	g	NOUN
ejpam-5019	121	16	)	)	PUNCT
ejpam-5019	121	17	and	and	CCONJ
ejpam-5019	121	18	w	w	NOUN
ejpam-5019	121	19	=	=	SYM
ejpam-5019	121	20	(	(	PUNCT
ejpam-5019	121	21	w	w	NOUN
ejpam-5019	121	22	0	0	NUM
ejpam-5019	121	23	)	)	PUNCT
ejpam-5019	121	24	t	t	PROPN
ejpam-5019	121	25	is	be	AUX
ejpam-5019	121	26	the	the	DET
ejpam-5019	121	27	corresponding	corresponding	ADJ
ejpam-5019	121	28	eigenvector	eigenvector	NOUN
ejpam-5019	121	29	.	.	PUNCT
ejpam-5019	122	1	similarly	similarly	ADV
ejpam-5019	122	2	,	,	PUNCT
ejpam-5019	122	3	let	let	VERB
ejpam-5019	122	4	x	x	PRON
ejpam-5019	122	5	be	be	AUX
ejpam-5019	122	6	an	an	DET
ejpam-5019	122	7	orthogonal	orthogonal	ADJ
ejpam-5019	122	8	vector	vector	NOUN
ejpam-5019	122	9	to	to	ADP
ejpam-5019	122	10	1n2	1n2	NUM
ejpam-5019	122	11	,	,	PUNCT
ejpam-5019	122	12	and	and	CCONJ
ejpam-5019	122	13	a	a	DET
ejpam-5019	122	14	(	(	PUNCT
ejpam-5019	122	15	g2)1n2	g2)1n2	NOUN
ejpam-5019	122	16	=	=	SYM
ejpam-5019	122	17	λ2	λ2	NOUN
ejpam-5019	122	18	1x	1x	NUM
ejpam-5019	122	19	.	.	PUNCT
ejpam-5019	123	1	we	we	PRON
ejpam-5019	123	2	take	take	VERB
ejpam-5019	123	3	x	x	X
ejpam-5019	123	4	=(	=(	NOUN
ejpam-5019	123	5	0	0	NUM
ejpam-5019	123	6	x	x	X
ejpam-5019	123	7	)	)	PUNCT
ejpam-5019	123	8	t	t	PROPN
ejpam-5019	123	9	and	and	CCONJ
ejpam-5019	123	10	since	since	SCONJ
ejpam-5019	123	11	jt	jt	PROPN
ejpam-5019	123	12	n2×n1	n2×n1	PROPN
ejpam-5019	123	13	x	x	PUNCT
ejpam-5019	124	1	=	=	SYM
ejpam-5019	124	2	0	0	NUM
ejpam-5019	124	3	,	,	PUNCT
ejpam-5019	124	4	we	we	PRON
ejpam-5019	124	5	get	get	VERB
ejpam-5019	124	6	ud	ud	INTJ
ejpam-5019	124	7	(	(	PUNCT
ejpam-5019	124	8	g)x	g)x	NOUN
ejpam-5019	124	9	=	=	PUNCT
ejpam-5019	125	1	[	[	PUNCT
ejpam-5019	125	2	(	(	PUNCT
ejpam-5019	125	3	2n2	2n2	NUM
ejpam-5019	125	4	−	−	NOUN
ejpam-5019	125	5	r2	r2	NOUN
ejpam-5019	125	6	+	+	CCONJ
ejpam-5019	125	7	n1	n1	PROPN
ejpam-5019	125	8	−	−	PROPN
ejpam-5019	125	9	2)α+	2)α+	NUM
ejpam-5019	125	10	(	(	PUNCT
ejpam-5019	125	11	−λ2	−λ2	NOUN
ejpam-5019	125	12	j	j	PROPN
ejpam-5019	125	13	)	)	PUNCT
ejpam-5019	125	14	β	β	PROPN
ejpam-5019	126	1	+	+	CCONJ
ejpam-5019	126	2	δ	δ	X
ejpam-5019	126	3	]	]	X
ejpam-5019	127	1	x	x	X
ejpam-5019	127	2	;	;	PUNCT
ejpam-5019	127	3	j	j	PROPN
ejpam-5019	127	4	=	=	SYM
ejpam-5019	127	5	2	2	NUM
ejpam-5019	127	6	,	,	PUNCT
ejpam-5019	127	7	3	3	NUM
ejpam-5019	127	8	,	,	PUNCT
ejpam-5019	127	9	.	.	PUNCT
ejpam-5019	127	10	.	.	PUNCT
ejpam-5019	128	1	.	.	PUNCT
ejpam-5019	129	1	,	,	PUNCT
ejpam-5019	129	2	n2	n2	PROPN
ejpam-5019	129	3	.	.	PUNCT
ejpam-5019	130	1	this	this	PRON
ejpam-5019	130	2	shows	show	VERB
ejpam-5019	130	3	that	that	SCONJ
ejpam-5019	130	4	(	(	PUNCT
ejpam-5019	130	5	2n2	2n2	NUM
ejpam-5019	130	6	−	−	NOUN
ejpam-5019	130	7	r2	r2	NOUN
ejpam-5019	130	8	+	+	CCONJ
ejpam-5019	130	9	n1	n1	PROPN
ejpam-5019	130	10	−	−	PROPN
ejpam-5019	130	11	2)α	2)α	NUM
ejpam-5019	130	12	+	+	CCONJ
ejpam-5019	131	1	(	(	PUNCT
ejpam-5019	131	2	−λ2	−λ2	PROPN
ejpam-5019	131	3	j	j	PROPN
ejpam-5019	131	4	)	)	PUNCT
ejpam-5019	131	5	β	β	PROPN
ejpam-5019	132	1	+	+	CCONJ
ejpam-5019	132	2	δ	δ	PROPN
ejpam-5019	132	3	is	be	AUX
ejpam-5019	132	4	an	an	DET
ejpam-5019	132	5	eigenvalue	eigenvalue	NOUN
ejpam-5019	132	6	of	of	ADP
ejpam-5019	132	7	ud	ud	INTJ
ejpam-5019	132	8	(	(	PUNCT
ejpam-5019	132	9	g	g	NOUN
ejpam-5019	132	10	)	)	PUNCT
ejpam-5019	132	11	and	and	CCONJ
ejpam-5019	132	12	x	x	X
ejpam-5019	132	13	=	=	PUNCT
ejpam-5019	132	14	(	(	PUNCT
ejpam-5019	132	15	0	0	NUM
ejpam-5019	132	16	x	x	X
ejpam-5019	132	17	)	)	PUNCT
ejpam-5019	132	18	t	t	PROPN
ejpam-5019	132	19	is	be	AUX
ejpam-5019	132	20	the	the	DET
ejpam-5019	132	21	corresponding	corresponding	ADJ
ejpam-5019	132	22	eigenvector	eigenvector	NOUN
ejpam-5019	132	23	.	.	PUNCT
ejpam-5019	133	1	totally	totally	ADV
ejpam-5019	133	2	,	,	PUNCT
ejpam-5019	133	3	we	we	PRON
ejpam-5019	133	4	have	have	VERB
ejpam-5019	133	5	n1	n1	NOUN
ejpam-5019	133	6	+	+	SYM
ejpam-5019	133	7	n2	n2	ADJ
ejpam-5019	133	8	−	−	PROPN
ejpam-5019	133	9	2	2	NUM
ejpam-5019	133	10	eigenvalues	eigenvalue	NOUN
ejpam-5019	133	11	of	of	ADP
ejpam-5019	133	12	ud	ud	INTJ
ejpam-5019	133	13	(	(	PUNCT
ejpam-5019	133	14	g	g	NOUN
ejpam-5019	133	15	)	)	PUNCT
ejpam-5019	133	16	.	.	PUNCT
ejpam-5019	134	1	then	then	ADV
ejpam-5019	134	2	the	the	DET
ejpam-5019	134	3	other	other	ADJ
ejpam-5019	134	4	two	two	NUM
ejpam-5019	134	5	eigenvalues	eigenvalue	NOUN
ejpam-5019	134	6	of	of	ADP
ejpam-5019	134	7	ud	ud	INTJ
ejpam-5019	134	8	(	(	PUNCT
ejpam-5019	134	9	g	g	NOUN
ejpam-5019	134	10	)	)	PUNCT
ejpam-5019	134	11	are	be	AUX
ejpam-5019	134	12	derived	derive	VERB
ejpam-5019	134	13	from	from	ADP
ejpam-5019	134	14	the	the	DET
ejpam-5019	134	15	quotient	quotient	NOUN
ejpam-5019	134	16	matrix	matrix	NOUN
ejpam-5019	134	17	s	s	PART
ejpam-5019	134	18	=	=	PUNCT
ejpam-5019	134	19	(	(	PUNCT
ejpam-5019	134	20	s1	s1	PROPN
ejpam-5019	134	21	(	(	PUNCT
ejpam-5019	134	22	β	β	X
ejpam-5019	134	23	+	+	X
ejpam-5019	134	24	γ)n2	γ)n2	PROPN
ejpam-5019	134	25	(	(	PUNCT
ejpam-5019	134	26	β	β	X
ejpam-5019	134	27	+	+	CCONJ
ejpam-5019	134	28	γ)n1	γ)n1	PROPN
ejpam-5019	134	29	s2	s2	PROPN
ejpam-5019	134	30	)	)	PUNCT
ejpam-5019	134	31	where	where	SCONJ
ejpam-5019	134	32	s1	s1	NOUN
ejpam-5019	134	33	=	=	PROPN
ejpam-5019	134	34	α	α	PROPN
ejpam-5019	134	35	(	(	PUNCT
ejpam-5019	134	36	2n1	2n1	NUM
ejpam-5019	134	37	−	−	PROPN
ejpam-5019	134	38	r1	r1	PROPN
ejpam-5019	134	39	+	+	CCONJ
ejpam-5019	134	40	n2	n2	ADJ
ejpam-5019	134	41	−	−	PROPN
ejpam-5019	134	42	2	2	NUM
ejpam-5019	134	43	)	)	PUNCT
ejpam-5019	134	44	+	+	NUM
ejpam-5019	134	45	β	β	X
ejpam-5019	134	46	(	(	PUNCT
ejpam-5019	134	47	2−	2−	NUM
ejpam-5019	134	48	r1	r1	NOUN
ejpam-5019	134	49	)	)	PUNCT
ejpam-5019	134	50	+	+	SYM
ejpam-5019	134	51	γn1	γn1	X
ejpam-5019	134	52	+	+	CCONJ
ejpam-5019	134	53	δ	δ	PROPN
ejpam-5019	134	54	s.	s.	PROPN
ejpam-5019	134	55	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	134	56	,	,	PUNCT
ejpam-5019	134	57	k.	k.	PROPN
ejpam-5019	134	58	desikan	desikan	PROPN
ejpam-5019	134	59	/	/	SYM
ejpam-5019	134	60	eur	eur	PROPN
ejpam-5019	134	61	.	.	PUNCT
ejpam-5019	135	1	j.	j.	PROPN
ejpam-5019	135	2	pure	pure	PROPN
ejpam-5019	135	3	appl	appl	PROPN
ejpam-5019	135	4	.	.	PROPN
ejpam-5019	135	5	math	math	PROPN
ejpam-5019	135	6	,	,	PUNCT
ejpam-5019	135	7	17	17	NUM
ejpam-5019	135	8	(	(	PUNCT
ejpam-5019	135	9	1	1	NUM
ejpam-5019	135	10	)	)	PUNCT
ejpam-5019	135	11	(	(	PUNCT
ejpam-5019	135	12	2024	2024	NUM
ejpam-5019	135	13	)	)	PUNCT
ejpam-5019	135	14	,	,	PUNCT
ejpam-5019	135	15	462	462	NUM
ejpam-5019	135	16	-	-	SYM
ejpam-5019	135	17	476	476	NUM
ejpam-5019	135	18	467	467	NUM
ejpam-5019	135	19	s2	s2	NOUN
ejpam-5019	135	20	=	=	PUNCT
ejpam-5019	135	21	α	α	PROPN
ejpam-5019	135	22	(	(	PUNCT
ejpam-5019	135	23	2n2	2n2	NUM
ejpam-5019	135	24	−	−	ADP
ejpam-5019	135	25	r2	r2	NOUN
ejpam-5019	135	26	+	+	CCONJ
ejpam-5019	135	27	n1	n1	NOUN
ejpam-5019	135	28	−	−	NOUN
ejpam-5019	135	29	2	2	NUM
ejpam-5019	135	30	)	)	PUNCT
ejpam-5019	136	1	+	+	NUM
ejpam-5019	136	2	β	β	X
ejpam-5019	136	3	(	(	PUNCT
ejpam-5019	136	4	2−	2−	NUM
ejpam-5019	136	5	r2	r2	NOUN
ejpam-5019	136	6	)	)	PUNCT
ejpam-5019	137	1	+	+	CCONJ
ejpam-5019	137	2	γn2	γn2	NOUN
ejpam-5019	137	3	+	+	CCONJ
ejpam-5019	137	4	δ	δ	X
ejpam-5019	137	5	the	the	DET
ejpam-5019	137	6	characteristic	characteristic	ADJ
ejpam-5019	137	7	equation	equation	NOUN
ejpam-5019	137	8	of	of	ADP
ejpam-5019	137	9	s	s	PROPN
ejpam-5019	137	10	is	be	AUX
ejpam-5019	137	11	x2−	x2−	PROPN
ejpam-5019	137	12	(	(	PUNCT
ejpam-5019	137	13	s1	s1	NOUN
ejpam-5019	137	14	+	+	CCONJ
ejpam-5019	137	15	s2)x+	s2)x+	PROPN
ejpam-5019	137	16	[	[	PUNCT
ejpam-5019	137	17	s1	s1	NOUN
ejpam-5019	137	18	+	+	X
ejpam-5019	137	19	s2−	s2−	PROPN
ejpam-5019	137	20	(	(	PUNCT
ejpam-5019	137	21	β	β	X
ejpam-5019	137	22	+	+	X
ejpam-5019	137	23	γ)2	γ)2	PROPN
ejpam-5019	137	24	n1n2	n1n2	NUM
ejpam-5019	137	25	]	]	PUNCT
ejpam-5019	137	26	=	=	SYM
ejpam-5019	137	27	0	0	PUNCT
ejpam-5019	137	28	and	and	CCONJ
ejpam-5019	137	29	its	its	PRON
ejpam-5019	137	30	roots	root	NOUN
ejpam-5019	137	31	are	be	AUX
ejpam-5019	137	32	the	the	DET
ejpam-5019	137	33	eigenvalues	eigenvalue	NOUN
ejpam-5019	137	34	of	of	ADP
ejpam-5019	137	35	ud	ud	INTJ
ejpam-5019	137	36	(	(	PUNCT
ejpam-5019	137	37	g	g	NOUN
ejpam-5019	137	38	)	)	PUNCT
ejpam-5019	137	39	.	.	PUNCT
ejpam-5019	138	1	this	this	PRON
ejpam-5019	138	2	completes	complete	VERB
ejpam-5019	138	3	the	the	DET
ejpam-5019	138	4	proof	proof	NOUN
ejpam-5019	138	5	.	.	PUNCT
ejpam-5019	139	1	corollary	corollary	ADJ
ejpam-5019	139	2	2	2	NUM
ejpam-5019	139	3	.	.	PUNCT
ejpam-5019	140	1	the	the	DET
ejpam-5019	140	2	universal	universal	ADJ
ejpam-5019	140	3	distance	distance	NOUN
ejpam-5019	140	4	spectrum	spectrum	NOUN
ejpam-5019	140	5	of	of	ADP
ejpam-5019	140	6	complete	complete	ADJ
ejpam-5019	140	7	bipartite	bipartite	PROPN
ejpam-5019	140	8	graph	graph	NOUN
ejpam-5019	140	9	kp	kp	PROPN
ejpam-5019	140	10	,	,	PUNCT
ejpam-5019	140	11	q	q	PROPN
ejpam-5019	140	12	=	=	PUNCT
ejpam-5019	140	13	kp∇kq	kp∇kq	X
ejpam-5019	140	14	consists	consist	VERB
ejpam-5019	140	15	of	of	ADP
ejpam-5019	140	16	the	the	DET
ejpam-5019	140	17	eigenvalues	eigenvalue	NOUN
ejpam-5019	140	18	{	{	PUNCT
ejpam-5019	140	19	α	α	NOUN
ejpam-5019	140	20	(	(	PUNCT
ejpam-5019	140	21	2p+	2p+	NUM
ejpam-5019	140	22	q	q	NOUN
ejpam-5019	140	23	−	−	NOUN
ejpam-5019	140	24	2	2	NUM
ejpam-5019	140	25	)	)	PUNCT
ejpam-5019	140	26	+	+	CCONJ
ejpam-5019	140	27	δ}p−1	δ}p−1	ADJ
ejpam-5019	140	28	,	,	PUNCT
ejpam-5019	140	29	{	{	PUNCT
ejpam-5019	140	30	α	α	X
ejpam-5019	140	31	(	(	PUNCT
ejpam-5019	140	32	2q	2q	NOUN
ejpam-5019	140	33	+	+	CCONJ
ejpam-5019	141	1	p−	p−	NOUN
ejpam-5019	141	2	2	2	NUM
ejpam-5019	141	3	)	)	PUNCT
ejpam-5019	141	4	+	+	CCONJ
ejpam-5019	141	5	δ}q−1	δ}q−1	NOUN
ejpam-5019	141	6	and	and	CCONJ
ejpam-5019	141	7	1	1	NUM
ejpam-5019	141	8	2	2	NUM
ejpam-5019	141	9	[	[	PUNCT
ejpam-5019	141	10	(	(	PUNCT
ejpam-5019	141	11	t1	t1	NOUN
ejpam-5019	141	12	+	+	CCONJ
ejpam-5019	141	13	t2)±	t2)±	PROPN
ejpam-5019	141	14	√	√	PROPN
ejpam-5019	141	15	(	(	PUNCT
ejpam-5019	141	16	t1	t1	NOUN
ejpam-5019	141	17	−	−	PROPN
ejpam-5019	141	18	t2	t2	NOUN
ejpam-5019	141	19	)	)	PUNCT
ejpam-5019	141	20	2	2	NUM
ejpam-5019	141	21	+	+	NUM
ejpam-5019	141	22	4	4	NUM
ejpam-5019	141	23	(	(	PUNCT
ejpam-5019	141	24	β	β	X
ejpam-5019	141	25	+	+	CCONJ
ejpam-5019	141	26	γ)2	γ)2	PROPN
ejpam-5019	141	27	pq	pq	PROPN
ejpam-5019	141	28	,	,	PUNCT
ejpam-5019	141	29	where	where	SCONJ
ejpam-5019	141	30	t1	t1	NOUN
ejpam-5019	141	31	=	=	PUNCT
ejpam-5019	141	32	α	α	PROPN
ejpam-5019	141	33	(	(	PUNCT
ejpam-5019	141	34	2p+	2p+	NUM
ejpam-5019	141	35	q	q	NOUN
ejpam-5019	142	1	−	−	PROPN
ejpam-5019	142	2	2)+2β+pγ+δ	2)+2β+pγ+δ	NOUN
ejpam-5019	142	3	,	,	PUNCT
ejpam-5019	142	4	t2	t2	NOUN
ejpam-5019	142	5	=	=	SYM
ejpam-5019	142	6	α	α	PROPN
ejpam-5019	142	7	(	(	PUNCT
ejpam-5019	142	8	2q	2q	NOUN
ejpam-5019	142	9	+	+	CCONJ
ejpam-5019	142	10	p−	p−	NOUN
ejpam-5019	142	11	2	2	NUM
ejpam-5019	142	12	)	)	PUNCT
ejpam-5019	142	13	+	+	CCONJ
ejpam-5019	142	14	2β	2β	NOUN
ejpam-5019	142	15	+	+	CCONJ
ejpam-5019	142	16	qγ	qγ	NOUN
ejpam-5019	142	17	+	+	CCONJ
ejpam-5019	142	18	δ	δ	PROPN
ejpam-5019	142	19	.	.	PUNCT
ejpam-5019	143	1	proof	proof	NOUN
ejpam-5019	143	2	.	.	PUNCT
ejpam-5019	144	1	by	by	ADP
ejpam-5019	144	2	substituting	substitute	VERB
ejpam-5019	144	3	n1	n1	NOUN
ejpam-5019	144	4	=	=	SYM
ejpam-5019	144	5	p	p	NOUN
ejpam-5019	144	6	,	,	PUNCT
ejpam-5019	144	7	r1	r1	NOUN
ejpam-5019	144	8	=	=	SYM
ejpam-5019	144	9	0	0	NUM
ejpam-5019	144	10	,	,	PUNCT
ejpam-5019	144	11	n2	n2	NOUN
ejpam-5019	144	12	=	=	SYM
ejpam-5019	144	13	q	q	PROPN
ejpam-5019	144	14	,	,	PUNCT
ejpam-5019	144	15	r2	r2	PROPN
ejpam-5019	144	16	=	=	SYM
ejpam-5019	144	17	0	0	NUM
ejpam-5019	144	18	,	,	PUNCT
ejpam-5019	144	19	λ1	λ1	ADJ
ejpam-5019	144	20	2	2	NUM
ejpam-5019	144	21	=	=	SYM
ejpam-5019	144	22	λ1	λ1	PROPN
ejpam-5019	144	23	3	3	NUM
ejpam-5019	144	24	=	=	SYM
ejpam-5019	144	25	·	·	PUNCT
ejpam-5019	144	26	·	·	PUNCT
ejpam-5019	144	27	·	·	PUNCT
ejpam-5019	145	1	=	=	SYM
ejpam-5019	145	2	λ1	λ1	PROPN
ejpam-5019	145	3	p	p	NOUN
ejpam-5019	145	4	=	=	NOUN
ejpam-5019	145	5	0	0	NUM
ejpam-5019	145	6	,	,	PUNCT
ejpam-5019	145	7	and	and	CCONJ
ejpam-5019	145	8	λ2	λ2	NOUN
ejpam-5019	145	9	2	2	NUM
ejpam-5019	145	10	=	=	SYM
ejpam-5019	145	11	λ2	λ2	NOUN
ejpam-5019	145	12	3	3	NUM
ejpam-5019	145	13	=	=	SYM
ejpam-5019	145	14	·	·	PUNCT
ejpam-5019	145	15	·	·	PUNCT
ejpam-5019	145	16	·	·	PUNCT
ejpam-5019	146	1	=	=	PUNCT
ejpam-5019	146	2	λ2	λ2	NOUN
ejpam-5019	146	3	q	q	NOUN
ejpam-5019	146	4	=	=	NOUN
ejpam-5019	146	5	0	0	NUM
ejpam-5019	146	6	,	,	PUNCT
ejpam-5019	146	7	in	in	ADP
ejpam-5019	146	8	theorem	theorem	NOUN
ejpam-5019	146	9	2	2	NUM
ejpam-5019	146	10	,	,	PUNCT
ejpam-5019	146	11	the	the	DET
ejpam-5019	146	12	universal	universal	ADJ
ejpam-5019	146	13	spectrum	spectrum	NOUN
ejpam-5019	146	14	of	of	ADP
ejpam-5019	146	15	kp	kp	PROPN
ejpam-5019	146	16	,	,	PUNCT
ejpam-5019	146	17	q	q	NOUN
ejpam-5019	146	18	graph	graph	NOUN
ejpam-5019	146	19	is	be	AUX
ejpam-5019	146	20	obtained	obtain	VERB
ejpam-5019	146	21	.	.	PUNCT
ejpam-5019	147	1	hence	hence	ADV
ejpam-5019	147	2	the	the	DET
ejpam-5019	147	3	result	result	NOUN
ejpam-5019	147	4	.	.	PUNCT
ejpam-5019	148	1	corollary	corollary	ADJ
ejpam-5019	148	2	3	3	NUM
ejpam-5019	148	3	.	.	PUNCT
ejpam-5019	149	1	the	the	DET
ejpam-5019	149	2	universal	universal	ADJ
ejpam-5019	149	3	distance	distance	NOUN
ejpam-5019	149	4	spectrum	spectrum	NOUN
ejpam-5019	149	5	of	of	ADP
ejpam-5019	149	6	wheel	wheel	NOUN
ejpam-5019	149	7	graph	graph	NOUN
ejpam-5019	149	8	wn	wn	PROPN
ejpam-5019	149	9	=	=	PUNCT
ejpam-5019	149	10	cn∇k1	cn∇k1	PROPN
ejpam-5019	149	11	consists	consist	VERB
ejpam-5019	149	12	of	of	ADP
ejpam-5019	149	13	the	the	DET
ejpam-5019	149	14	eigenvalues	eigenvalues	PROPN
ejpam-5019	149	15	nα+	nα+	PROPN
ejpam-5019	149	16	δ	δ	PROPN
ejpam-5019	149	17	,	,	PUNCT
ejpam-5019	149	18	α	α	PROPN
ejpam-5019	149	19	(	(	PUNCT
ejpam-5019	149	20	2n−	2n−	PROPN
ejpam-5019	149	21	3)−	3)−	PROPN
ejpam-5019	149	22	βcos	βco	NOUN
ejpam-5019	149	23	(	(	PUNCT
ejpam-5019	149	24	2(i−1)π	2(i−1)π	NUM
ejpam-5019	149	25	n	n	NOUN
ejpam-5019	149	26	)	)	PUNCT
ejpam-5019	150	1	+	+	CCONJ
ejpam-5019	150	2	δ	δ	PROPN
ejpam-5019	150	3	;	;	PUNCT
ejpam-5019	150	4	i	i	NOUN
ejpam-5019	150	5	=	=	NOUN
ejpam-5019	150	6	2	2	NUM
ejpam-5019	150	7	,	,	PUNCT
ejpam-5019	150	8	3	3	NUM
ejpam-5019	150	9	,	,	PUNCT
ejpam-5019	150	10	.	.	PUNCT
ejpam-5019	150	11	.	.	PUNCT
ejpam-5019	150	12	.	.	PUNCT
ejpam-5019	151	1	,	,	PUNCT
ejpam-5019	152	1	n	n	PROPN
ejpam-5019	152	2	and	and	CCONJ
ejpam-5019	152	3	1	1	NUM
ejpam-5019	152	4	2	2	NUM
ejpam-5019	152	5	[	[	PUNCT
ejpam-5019	152	6	(	(	PUNCT
ejpam-5019	152	7	l1	l1	PROPN
ejpam-5019	152	8	+	+	CCONJ
ejpam-5019	152	9	l2	l2	NOUN
ejpam-5019	152	10	)	)	PUNCT
ejpam-5019	152	11	±	±	NOUN
ejpam-5019	152	12	√	√	PROPN
ejpam-5019	152	13	(	(	PUNCT
ejpam-5019	152	14	l1	l1	PROPN
ejpam-5019	152	15	−	−	PROPN
ejpam-5019	152	16	l2	l2	PROPN
ejpam-5019	152	17	)	)	PUNCT
ejpam-5019	152	18	2	2	NUM
ejpam-5019	153	1	+	+	NUM
ejpam-5019	153	2	4	4	NUM
ejpam-5019	153	3	(	(	PUNCT
ejpam-5019	154	1	β	β	X
ejpam-5019	154	2	+	+	X
ejpam-5019	154	3	γ)2	γ)2	NOUN
ejpam-5019	154	4	n	n	CCONJ
ejpam-5019	154	5	,	,	PUNCT
ejpam-5019	154	6	where	where	SCONJ
ejpam-5019	154	7	l1	l1	PROPN
ejpam-5019	154	8	=	=	PROPN
ejpam-5019	154	9	α	α	PROPN
ejpam-5019	154	10	(	(	PUNCT
ejpam-5019	154	11	2n−	2n−	PROPN
ejpam-5019	154	12	3	3	NUM
ejpam-5019	154	13	)	)	PUNCT
ejpam-5019	154	14	+	+	NUM
ejpam-5019	154	15	γn	γn	X
ejpam-5019	154	16	+	+	CCONJ
ejpam-5019	154	17	δ	δ	PROPN
ejpam-5019	154	18	,	,	PUNCT
ejpam-5019	154	19	l2	l2	NOUN
ejpam-5019	154	20	=	=	SYM
ejpam-5019	154	21	nα	nα	ADP
ejpam-5019	154	22	+	+	NOUN
ejpam-5019	154	23	2β	2β	NOUN
ejpam-5019	154	24	+	+	CCONJ
ejpam-5019	154	25	γ	γ	X
ejpam-5019	154	26	+	+	ADJ
ejpam-5019	154	27	δ	δ	PROPN
ejpam-5019	154	28	proof	proof	NOUN
ejpam-5019	154	29	.	.	PUNCT
ejpam-5019	155	1	by	by	ADP
ejpam-5019	155	2	substituting	substitute	VERB
ejpam-5019	155	3	n1	n1	NOUN
ejpam-5019	155	4	=	=	SYM
ejpam-5019	155	5	n	n	CCONJ
ejpam-5019	155	6	,	,	PUNCT
ejpam-5019	155	7	r1	r1	NOUN
ejpam-5019	155	8	=	=	SYM
ejpam-5019	155	9	2	2	NUM
ejpam-5019	155	10	,	,	PUNCT
ejpam-5019	155	11	n2	n2	NOUN
ejpam-5019	155	12	=	=	SYM
ejpam-5019	155	13	1	1	NUM
ejpam-5019	155	14	,	,	PUNCT
ejpam-5019	155	15	r2	r2	PROPN
ejpam-5019	155	16	=	=	SYM
ejpam-5019	155	17	0	0	NUM
ejpam-5019	155	18	,	,	PUNCT
ejpam-5019	155	19	and	and	CCONJ
ejpam-5019	155	20	λ1	λ1	ADJ
ejpam-5019	155	21	i	i	NOUN
ejpam-5019	155	22	=	=	SYM
ejpam-5019	155	23	2cos	2co	NOUN
ejpam-5019	155	24	(	(	PUNCT
ejpam-5019	155	25	2(i−1)π	2(i−1)π	NUM
ejpam-5019	155	26	n	n	NOUN
ejpam-5019	155	27	)	)	PUNCT
ejpam-5019	156	1	+	+	NOUN
ejpam-5019	156	2	δ	δ	PROPN
ejpam-5019	156	3	;	;	PUNCT
ejpam-5019	156	4	i	i	NOUN
ejpam-5019	156	5	=	=	NOUN
ejpam-5019	156	6	2	2	NUM
ejpam-5019	156	7	,	,	PUNCT
ejpam-5019	156	8	3	3	NUM
ejpam-5019	156	9	,	,	PUNCT
ejpam-5019	156	10	.	.	PUNCT
ejpam-5019	156	11	.	.	PUNCT
ejpam-5019	156	12	.	.	PUNCT
ejpam-5019	157	1	,	,	PUNCT
ejpam-5019	157	2	n	n	CCONJ
ejpam-5019	157	3	,	,	PUNCT
ejpam-5019	157	4	in	in	ADP
ejpam-5019	157	5	theorem	theorem	NOUN
ejpam-5019	157	6	2	2	NUM
ejpam-5019	157	7	,	,	PUNCT
ejpam-5019	157	8	we	we	PRON
ejpam-5019	157	9	obtain	obtain	VERB
ejpam-5019	157	10	the	the	DET
ejpam-5019	157	11	universal	universal	ADJ
ejpam-5019	157	12	distance	distance	NOUN
ejpam-5019	157	13	spectrum	spectrum	NOUN
ejpam-5019	157	14	of	of	ADP
ejpam-5019	157	15	wn	wn	PROPN
ejpam-5019	157	16	graph	graph	NOUN
ejpam-5019	157	17	.	.	PUNCT
ejpam-5019	158	1	hence	hence	ADV
ejpam-5019	158	2	the	the	DET
ejpam-5019	158	3	result	result	NOUN
ejpam-5019	158	4	.	.	PUNCT
ejpam-5019	159	1	corollary	corollary	ADJ
ejpam-5019	159	2	4	4	NUM
ejpam-5019	159	3	.	.	PUNCT
ejpam-5019	160	1	the	the	DET
ejpam-5019	160	2	universal	universal	ADJ
ejpam-5019	160	3	distance	distance	NOUN
ejpam-5019	160	4	spectrum	spectrum	NOUN
ejpam-5019	160	5	of	of	ADP
ejpam-5019	160	6	complete	complete	ADJ
ejpam-5019	160	7	split	split	NOUN
ejpam-5019	160	8	graph	graph	NOUN
ejpam-5019	160	9	csm	csm	NOUN
ejpam-5019	160	10	,	,	PUNCT
ejpam-5019	160	11	n−m	n−m	X
ejpam-5019	160	12	=	=	SYM
ejpam-5019	160	13	km∇kn−m	km∇kn−m	PROPN
ejpam-5019	160	14	consists	consist	VERB
ejpam-5019	160	15	of	of	ADP
ejpam-5019	160	16	the	the	DET
ejpam-5019	160	17	eigenvalues	eigenvalue	NOUN
ejpam-5019	160	18	{	{	PUNCT
ejpam-5019	160	19	α	α	NOUN
ejpam-5019	160	20	(	(	PUNCT
ejpam-5019	160	21	n−	n−	NOUN
ejpam-5019	160	22	1)−	1)−	PROPN
ejpam-5019	160	23	β	β	NOUN
ejpam-5019	160	24	+	+	CCONJ
ejpam-5019	160	25	δ}m−1	δ}m−1	ADV
ejpam-5019	160	26	,	,	PUNCT
ejpam-5019	160	27	{	{	PUNCT
ejpam-5019	160	28	α	α	X
ejpam-5019	160	29	(	(	PUNCT
ejpam-5019	160	30	2n−m−	2n−m−	NUM
ejpam-5019	160	31	2	2	NUM
ejpam-5019	160	32	)	)	PUNCT
ejpam-5019	160	33	+	+	CCONJ
ejpam-5019	160	34	δ}n−m−1	δ}n−m−1	NOUN
ejpam-5019	160	35	and	and	CCONJ
ejpam-5019	160	36	1	1	NUM
ejpam-5019	160	37	2	2	NUM
ejpam-5019	160	38	[	[	PUNCT
ejpam-5019	160	39	(	(	PUNCT
ejpam-5019	160	40	g1	g1	PROPN
ejpam-5019	160	41	+	+	CCONJ
ejpam-5019	160	42	g2)±	g2)±	VERB
ejpam-5019	160	43	√	√	NUM
ejpam-5019	160	44	(	(	PUNCT
ejpam-5019	160	45	g1	g1	PROPN
ejpam-5019	160	46	−	−	PROPN
ejpam-5019	160	47	g2	g2	PROPN
ejpam-5019	160	48	)	)	PUNCT
ejpam-5019	160	49	2	2	NUM
ejpam-5019	161	1	+	+	NUM
ejpam-5019	161	2	4	4	NUM
ejpam-5019	161	3	(	(	PUNCT
ejpam-5019	161	4	β	β	X
ejpam-5019	161	5	+	+	X
ejpam-5019	161	6	γ)2	γ)2	PROPN
ejpam-5019	161	7	m	m	PROPN
ejpam-5019	161	8	(	(	PUNCT
ejpam-5019	161	9	n−m	n−m	PROPN
ejpam-5019	161	10	)	)	PUNCT
ejpam-5019	161	11	,	,	PUNCT
ejpam-5019	161	12	where	where	SCONJ
ejpam-5019	161	13	g1	g1	PROPN
ejpam-5019	161	14	=	=	PROPN
ejpam-5019	161	15	α	α	PROPN
ejpam-5019	161	16	(	(	PUNCT
ejpam-5019	161	17	n−	n−	NOUN
ejpam-5019	161	18	1)+β	1)+β	NUM
ejpam-5019	161	19	(	(	PUNCT
ejpam-5019	161	20	3−m)+	3−m)+	NUM
ejpam-5019	161	21	γm+	γm+	PROPN
ejpam-5019	161	22	δ	δ	PROPN
ejpam-5019	161	23	,	,	PUNCT
ejpam-5019	161	24	g2	g2	PROPN
ejpam-5019	161	25	=	=	PUNCT
ejpam-5019	162	1	α	α	PROPN
ejpam-5019	162	2	(	(	PUNCT
ejpam-5019	162	3	3n−	3n−	PROPN
ejpam-5019	162	4	3m−	3m−	NUM
ejpam-5019	162	5	2	2	NUM
ejpam-5019	162	6	)	)	PUNCT
ejpam-5019	162	7	+	+	CCONJ
ejpam-5019	162	8	2β	2β	NOUN
ejpam-5019	163	1	+	+	CCONJ
ejpam-5019	163	2	γ	γ	X
ejpam-5019	163	3	(	(	PUNCT
ejpam-5019	163	4	n−m	n−m	PROPN
ejpam-5019	163	5	)	)	PUNCT
ejpam-5019	163	6	+	+	CCONJ
ejpam-5019	163	7	δ	δ	PROPN
ejpam-5019	163	8	.	.	PUNCT
ejpam-5019	163	9	proof	proof	NOUN
ejpam-5019	163	10	.	.	PUNCT
ejpam-5019	164	1	in	in	ADP
ejpam-5019	164	2	theorem	theorem	NOUN
ejpam-5019	164	3	2	2	NUM
ejpam-5019	164	4	,	,	PUNCT
ejpam-5019	164	5	by	by	ADP
ejpam-5019	164	6	substituting	substitute	VERB
ejpam-5019	164	7	n1	n1	PROPN
ejpam-5019	164	8	=	=	SYM
ejpam-5019	164	9	m	m	PROPN
ejpam-5019	164	10	,	,	PUNCT
ejpam-5019	164	11	r1	r1	PROPN
ejpam-5019	164	12	=	=	PUNCT
ejpam-5019	164	13	m−	m−	PROPN
ejpam-5019	164	14	1	1	NUM
ejpam-5019	164	15	,	,	PUNCT
ejpam-5019	164	16	λ1	λ1	PROPN
ejpam-5019	164	17	2	2	NUM
ejpam-5019	164	18	=	=	SYM
ejpam-5019	164	19	λ1	λ1	PROPN
ejpam-5019	164	20	3	3	NUM
ejpam-5019	164	21	=	=	SYM
ejpam-5019	164	22	·	·	PUNCT
ejpam-5019	164	23	·	·	PUNCT
ejpam-5019	164	24	·	·	PUNCT
ejpam-5019	165	1	=	=	SYM
ejpam-5019	165	2	λ1	λ1	ADJ
ejpam-5019	165	3	m	m	NOUN
ejpam-5019	165	4	=	=	NOUN
ejpam-5019	165	5	−1	−1	NOUN
ejpam-5019	165	6	and	and	CCONJ
ejpam-5019	165	7	λ2	λ2	NOUN
ejpam-5019	165	8	2	2	NUM
ejpam-5019	165	9	=	=	SYM
ejpam-5019	165	10	λ2	λ2	NOUN
ejpam-5019	165	11	3	3	NUM
ejpam-5019	165	12	=	=	SYM
ejpam-5019	165	13	·	·	PUNCT
ejpam-5019	165	14	·	·	PUNCT
ejpam-5019	165	15	·	·	PUNCT
ejpam-5019	166	1	=	=	PUNCT
ejpam-5019	166	2	λ2	λ2	NOUN
ejpam-5019	166	3	n−m	n−m	NOUN
ejpam-5019	166	4	=	=	SYM
ejpam-5019	166	5	0	0	NUM
ejpam-5019	166	6	,	,	PUNCT
ejpam-5019	166	7	n2	n2	NOUN
ejpam-5019	166	8	=	=	PUNCT
ejpam-5019	166	9	n−m	n−m	PROPN
ejpam-5019	166	10	,	,	PUNCT
ejpam-5019	166	11	r2	r2	PROPN
ejpam-5019	166	12	=	=	SYM
ejpam-5019	166	13	0	0	NUM
ejpam-5019	166	14	,	,	PUNCT
ejpam-5019	166	15	we	we	PRON
ejpam-5019	166	16	obtain	obtain	VERB
ejpam-5019	166	17	the	the	DET
ejpam-5019	166	18	result	result	NOUN
ejpam-5019	166	19	.	.	PUNCT
ejpam-5019	167	1	2.3	2.3	NUM
ejpam-5019	167	2	.	.	PUNCT
ejpam-5019	168	1	eigenvalues	eigenvalue	NOUN
ejpam-5019	168	2	of	of	ADP
ejpam-5019	168	3	universal	universal	ADJ
ejpam-5019	168	4	distance	distance	NOUN
ejpam-5019	168	5	matrix	matrix	NOUN
ejpam-5019	168	6	of	of	ADP
ejpam-5019	168	7	joined	joined	ADJ
ejpam-5019	168	8	union	union	NOUN
ejpam-5019	168	9	of	of	ADP
ejpam-5019	168	10	graphs	graph	NOUN
ejpam-5019	168	11	in	in	ADP
ejpam-5019	168	12	this	this	DET
ejpam-5019	168	13	subsection	subsection	NOUN
ejpam-5019	168	14	,	,	PUNCT
ejpam-5019	168	15	we	we	PRON
ejpam-5019	168	16	describe	describe	VERB
ejpam-5019	168	17	the	the	DET
ejpam-5019	168	18	universal	universal	ADJ
ejpam-5019	168	19	distance	distance	NOUN
ejpam-5019	168	20	spectrum	spectrum	NOUN
ejpam-5019	168	21	of	of	ADP
ejpam-5019	168	22	joined	joined	ADJ
ejpam-5019	168	23	union	union	NOUN
ejpam-5019	168	24	of	of	ADP
ejpam-5019	168	25	three	three	NUM
ejpam-5019	168	26	regular	regular	ADJ
ejpam-5019	168	27	graphs	graph	NOUN
ejpam-5019	168	28	and	and	CCONJ
ejpam-5019	168	29	obtain	obtain	VERB
ejpam-5019	168	30	the	the	DET
ejpam-5019	168	31	universal	universal	ADJ
ejpam-5019	168	32	distance	distance	NOUN
ejpam-5019	168	33	spectrum	spectrum	NOUN
ejpam-5019	168	34	of	of	ADP
ejpam-5019	168	35	this	this	DET
ejpam-5019	168	36	graph	graph	NOUN
ejpam-5019	168	37	.	.	PUNCT
ejpam-5019	169	1	in	in	ADP
ejpam-5019	169	2	particular	particular	ADJ
ejpam-5019	169	3	,	,	PUNCT
ejpam-5019	169	4	we	we	PRON
ejpam-5019	169	5	obtain	obtain	VERB
ejpam-5019	169	6	the	the	DET
ejpam-5019	169	7	universal	universal	ADJ
ejpam-5019	169	8	distance	distance	NOUN
ejpam-5019	169	9	spectrum	spectrum	NOUN
ejpam-5019	169	10	of	of	ADP
ejpam-5019	169	11	joined	joined	ADJ
ejpam-5019	169	12	union	union	NOUN
ejpam-5019	169	13	of	of	ADP
ejpam-5019	169	14	graphs	graph	NOUN
ejpam-5019	169	15	related	relate	VERB
ejpam-5019	169	16	to	to	ADP
ejpam-5019	169	17	complete	complete	ADJ
ejpam-5019	169	18	graph	graph	NOUN
ejpam-5019	169	19	.	.	PUNCT
ejpam-5019	170	1	s.	s.	PROPN
ejpam-5019	170	2	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	170	3	,	,	PUNCT
ejpam-5019	170	4	k.	k.	PROPN
ejpam-5019	170	5	desikan	desikan	PROPN
ejpam-5019	170	6	/	/	SYM
ejpam-5019	170	7	eur	eur	PROPN
ejpam-5019	170	8	.	.	PUNCT
ejpam-5019	171	1	j.	j.	PROPN
ejpam-5019	171	2	pure	pure	PROPN
ejpam-5019	171	3	appl	appl	PROPN
ejpam-5019	171	4	.	.	PROPN
ejpam-5019	171	5	math	math	PROPN
ejpam-5019	171	6	,	,	PUNCT
ejpam-5019	171	7	17	17	NUM
ejpam-5019	171	8	(	(	PUNCT
ejpam-5019	171	9	1	1	NUM
ejpam-5019	171	10	)	)	PUNCT
ejpam-5019	171	11	(	(	PUNCT
ejpam-5019	171	12	2024	2024	NUM
ejpam-5019	171	13	)	)	PUNCT
ejpam-5019	171	14	,	,	PUNCT
ejpam-5019	171	15	462	462	NUM
ejpam-5019	171	16	-	-	SYM
ejpam-5019	171	17	476	476	NUM
ejpam-5019	171	18	468	468	NUM
ejpam-5019	171	19	theorem	theorem	NOUN
ejpam-5019	171	20	3	3	X
ejpam-5019	171	21	.	.	PUNCT
ejpam-5019	172	1	let	let	VERB
ejpam-5019	172	2	gi	gi	PART
ejpam-5019	172	3	be	be	AUX
ejpam-5019	172	4	ri−	ri−	ADJ
ejpam-5019	172	5	regular	regular	ADJ
ejpam-5019	172	6	graph	graph	NOUN
ejpam-5019	172	7	of	of	ADP
ejpam-5019	172	8	order	order	NOUN
ejpam-5019	172	9	ni	ni	PROPN
ejpam-5019	172	10	,	,	PUNCT
ejpam-5019	172	11	for	for	ADP
ejpam-5019	172	12	i	i	PROPN
ejpam-5019	172	13	=	=	SYM
ejpam-5019	172	14	1	1	NUM
ejpam-5019	172	15	,	,	PUNCT
ejpam-5019	172	16	2	2	NUM
ejpam-5019	172	17	,	,	PUNCT
ejpam-5019	172	18	3	3	NUM
ejpam-5019	172	19	.	.	PUNCT
ejpam-5019	173	1	let	let	VERB
ejpam-5019	173	2	a	a	DET
ejpam-5019	173	3	(	(	PUNCT
ejpam-5019	173	4	gi	gi	INTJ
ejpam-5019	173	5	)	)	PUNCT
ejpam-5019	173	6	denote	denote	VERB
ejpam-5019	173	7	the	the	DET
ejpam-5019	173	8	adjacency	adjacency	NOUN
ejpam-5019	173	9	matrix	matrix	NOUN
ejpam-5019	173	10	of	of	ADP
ejpam-5019	173	11	gi	gi	NOUN
ejpam-5019	173	12	and	and	CCONJ
ejpam-5019	173	13	the	the	DET
ejpam-5019	173	14	eigenvalues	eigenvalue	NOUN
ejpam-5019	173	15	be	be	VERB
ejpam-5019	173	16	ri	ri	PROPN
ejpam-5019	173	17	=	=	PUNCT
ejpam-5019	173	18	λi	λi	ADP
ejpam-5019	173	19	1	1	NUM
ejpam-5019	173	20	,	,	PUNCT
ejpam-5019	173	21	λ	λ	VERB
ejpam-5019	173	22	i	i	PRON
ejpam-5019	173	23	2	2	NUM
ejpam-5019	173	24	,	,	PUNCT
ejpam-5019	173	25	.	.	PUNCT
ejpam-5019	173	26	.	.	PUNCT
ejpam-5019	174	1	.	.	PUNCT
ejpam-5019	175	1	,	,	PUNCT
ejpam-5019	175	2	λ	λ	INTJ
ejpam-5019	175	3	i	i	PRON
ejpam-5019	175	4	ni	ni	PROPN
ejpam-5019	175	5	,	,	PUNCT
ejpam-5019	175	6	respectively	respectively	ADV
ejpam-5019	175	7	.	.	PUNCT
ejpam-5019	176	1	let	let	VERB
ejpam-5019	176	2	g	g	PROPN
ejpam-5019	176	3	=	=	SYM
ejpam-5019	176	4	g1∇	g1∇	PROPN
ejpam-5019	176	5	(	(	PUNCT
ejpam-5019	176	6	g2	g2	PROPN
ejpam-5019	176	7	∪g3	∪g3	NOUN
ejpam-5019	176	8	)	)	PUNCT
ejpam-5019	176	9	.	.	PUNCT
ejpam-5019	177	1	the	the	DET
ejpam-5019	177	2	graph	graph	NOUN
ejpam-5019	177	3	g	g	PROPN
ejpam-5019	177	4	is	be	AUX
ejpam-5019	177	5	the	the	DET
ejpam-5019	177	6	join	join	NOUN
ejpam-5019	177	7	of	of	ADP
ejpam-5019	177	8	g1	g1	PROPN
ejpam-5019	177	9	and	and	CCONJ
ejpam-5019	177	10	union	union	NOUN
ejpam-5019	177	11	of	of	ADP
ejpam-5019	177	12	two	two	NUM
ejpam-5019	177	13	graphs	graph	NOUN
ejpam-5019	177	14	g2	g2	PROPN
ejpam-5019	177	15	∪	∪	PROPN
ejpam-5019	177	16	g3	g3	PROPN
ejpam-5019	177	17	.	.	PUNCT
ejpam-5019	178	1	the	the	DET
ejpam-5019	178	2	universal	universal	ADJ
ejpam-5019	178	3	distance	distance	NOUN
ejpam-5019	178	4	spectrum	spectrum	NOUN
ejpam-5019	178	5	of	of	ADP
ejpam-5019	178	6	g	g	NOUN
ejpam-5019	178	7	consists	consist	VERB
ejpam-5019	178	8	of	of	ADP
ejpam-5019	178	9	the	the	DET
ejpam-5019	178	10	eigenvalues	eigenvalues	PROPN
ejpam-5019	178	11	(	(	PUNCT
ejpam-5019	178	12	i	i	NOUN
ejpam-5019	178	13	)	)	PUNCT
ejpam-5019	178	14	[	[	PUNCT
ejpam-5019	178	15	α	α	X
ejpam-5019	178	16	(	(	PUNCT
ejpam-5019	178	17	n	n	NOUN
ejpam-5019	178	18	+	+	CCONJ
ejpam-5019	178	19	n1	n1	ADJ
ejpam-5019	178	20	−	−	PROPN
ejpam-5019	178	21	r1	r1	NOUN
ejpam-5019	178	22	−	−	PROPN
ejpam-5019	178	23	2)−	2)−	NUM
ejpam-5019	178	24	2β	2β	PROPN
ejpam-5019	178	25	+	+	CCONJ
ejpam-5019	178	26	δ	δ	X
ejpam-5019	178	27	]	]	PUNCT
ejpam-5019	179	1	−	−	PROPN
ejpam-5019	179	2	βλ1	βλ1	NUM
ejpam-5019	179	3	l	l	NOUN
ejpam-5019	179	4	;	;	PUNCT
ejpam-5019	180	1	l	l	NOUN
ejpam-5019	180	2	=	=	SYM
ejpam-5019	180	3	2	2	NUM
ejpam-5019	180	4	,	,	PUNCT
ejpam-5019	180	5	3	3	NUM
ejpam-5019	180	6	,	,	PUNCT
ejpam-5019	180	7	.	.	PUNCT
ejpam-5019	180	8	.	.	PUNCT
ejpam-5019	180	9	.	.	PUNCT
ejpam-5019	181	1	,	,	PUNCT
ejpam-5019	181	2	n1	n1	PROPN
ejpam-5019	181	3	,	,	PUNCT
ejpam-5019	181	4	(	(	PUNCT
ejpam-5019	181	5	ii	ii	NOUN
ejpam-5019	181	6	)	)	PUNCT
ejpam-5019	181	7	[	[	PUNCT
ejpam-5019	181	8	α	α	X
ejpam-5019	181	9	(	(	PUNCT
ejpam-5019	181	10	2n	2n	X
ejpam-5019	181	11	+	+	CCONJ
ejpam-5019	181	12	n1	n1	ADJ
ejpam-5019	181	13	−	−	PROPN
ejpam-5019	181	14	r2	r2	NOUN
ejpam-5019	181	15	−	−	PROPN
ejpam-5019	181	16	2)−	2)−	NUM
ejpam-5019	181	17	2β	2β	PROPN
ejpam-5019	182	1	+	+	CCONJ
ejpam-5019	182	2	δ	δ	X
ejpam-5019	182	3	]	]	X
ejpam-5019	183	1	−	−	X
ejpam-5019	183	2	βλ2	βλ2	X
ejpam-5019	183	3	m	m	PROPN
ejpam-5019	183	4	;	;	PUNCT
ejpam-5019	183	5	m	m	VERB
ejpam-5019	183	6	=	=	SYM
ejpam-5019	183	7	2	2	NUM
ejpam-5019	183	8	,	,	PUNCT
ejpam-5019	183	9	3	3	NUM
ejpam-5019	183	10	,	,	PUNCT
ejpam-5019	183	11	.	.	PUNCT
ejpam-5019	183	12	.	.	PUNCT
ejpam-5019	184	1	.	.	PUNCT
ejpam-5019	185	1	,	,	PUNCT
ejpam-5019	185	2	n2	n2	NOUN
ejpam-5019	185	3	,	,	PUNCT
ejpam-5019	185	4	(	(	PUNCT
ejpam-5019	185	5	iii	iii	NOUN
ejpam-5019	185	6	)	)	PUNCT
ejpam-5019	185	7	[	[	PUNCT
ejpam-5019	185	8	α	α	X
ejpam-5019	185	9	(	(	PUNCT
ejpam-5019	185	10	2n	2n	X
ejpam-5019	185	11	+	+	CCONJ
ejpam-5019	185	12	n1	n1	ADJ
ejpam-5019	185	13	−	−	PROPN
ejpam-5019	185	14	r3	r3	PROPN
ejpam-5019	185	15	−	−	PROPN
ejpam-5019	185	16	2)−	2)−	NUM
ejpam-5019	185	17	2β	2β	NOUN
ejpam-5019	186	1	+	+	CCONJ
ejpam-5019	186	2	δ	δ	X
ejpam-5019	186	3	]	]	PUNCT
ejpam-5019	186	4	−	−	X
ejpam-5019	186	5	βλ3	βλ3	NOUN
ejpam-5019	186	6	s	s	PART
ejpam-5019	186	7	;	;	PUNCT
ejpam-5019	186	8	s	s	X
ejpam-5019	186	9	=	=	SYM
ejpam-5019	186	10	2	2	NUM
ejpam-5019	186	11	,	,	PUNCT
ejpam-5019	186	12	3	3	NUM
ejpam-5019	186	13	,	,	PUNCT
ejpam-5019	186	14	.	.	PUNCT
ejpam-5019	186	15	.	.	PUNCT
ejpam-5019	187	1	.	.	PUNCT
ejpam-5019	188	1	,	,	PUNCT
ejpam-5019	188	2	n3	n3	NOUN
ejpam-5019	188	3	,	,	PUNCT
ejpam-5019	188	4	and	and	CCONJ
ejpam-5019	188	5	the	the	DET
ejpam-5019	188	6	eigenvalues	eigenvalue	NOUN
ejpam-5019	188	7	of	of	ADP
ejpam-5019	188	8	the	the	DET
ejpam-5019	188	9	matrix	matrix	NOUN
ejpam-5019	188	10	(	(	PUNCT
ejpam-5019	188	11	iv	iv	X
ejpam-5019	188	12	)	)	PUNCT
ejpam-5019	188	13			NOUN
ejpam-5019	188	14	α	α	PROPN
ejpam-5019	188	15	(	(	PUNCT
ejpam-5019	188	16	n	n	NOUN
ejpam-5019	188	17	+	+	CCONJ
ejpam-5019	188	18	n1	n1	ADJ
ejpam-5019	188	19	−	−	PROPN
ejpam-5019	188	20	r1	r1	PROPN
ejpam-5019	188	21	−	−	PROPN
ejpam-5019	188	22	2)+	2)+	NUM
ejpam-5019	188	23	(	(	PUNCT
ejpam-5019	188	24	2n1	2n1	NUM
ejpam-5019	188	25	−	−	PROPN
ejpam-5019	188	26	r1	r1	PROPN
ejpam-5019	188	27	−	−	PROPN
ejpam-5019	188	28	2)β	2)β	NOUN
ejpam-5019	188	29	+	+	CCONJ
ejpam-5019	188	30	γn1	γn1	NOUN
ejpam-5019	189	1	+	+	CCONJ
ejpam-5019	189	2	δ	δ	PROPN
ejpam-5019	189	3	(	(	PUNCT
ejpam-5019	189	4	β	β	X
ejpam-5019	189	5	+	+	X
ejpam-5019	189	6	γ)n2	γ)n2	PROPN
ejpam-5019	189	7	(	(	PUNCT
ejpam-5019	189	8	β	β	X
ejpam-5019	189	9	+	+	X
ejpam-5019	189	10	γ)n3	γ)n3	PROPN
ejpam-5019	189	11	(	(	PUNCT
ejpam-5019	189	12	β	β	X
ejpam-5019	189	13	+	+	CCONJ
ejpam-5019	189	14	γ)n1	γ)n1	PROPN
ejpam-5019	189	15	α	α	PROPN
ejpam-5019	189	16	(	(	PUNCT
ejpam-5019	189	17	2n	2n	X
ejpam-5019	189	18	+	+	CCONJ
ejpam-5019	189	19	n1	n1	ADJ
ejpam-5019	189	20	−	−	PROPN
ejpam-5019	189	21	r2	r2	PROPN
ejpam-5019	189	22	−	−	PROPN
ejpam-5019	189	23	2)+	2)+	NUM
ejpam-5019	189	24	(	(	PUNCT
ejpam-5019	189	25	2n2	2n2	NUM
ejpam-5019	189	26	−	−	PROPN
ejpam-5019	189	27	r2	r2	PROPN
ejpam-5019	189	28	−	−	PROPN
ejpam-5019	189	29	2)β	2)β	NOUN
ejpam-5019	189	30	+	+	CCONJ
ejpam-5019	189	31	γn2	γn2	NOUN
ejpam-5019	189	32	+	+	CCONJ
ejpam-5019	189	33	δ	δ	PROPN
ejpam-5019	189	34	(	(	PUNCT
ejpam-5019	189	35	2β	2β	NOUN
ejpam-5019	189	36	+	+	CCONJ
ejpam-5019	189	37	γ)n3	γ)n3	PROPN
ejpam-5019	189	38	(	(	PUNCT
ejpam-5019	189	39	β	β	X
ejpam-5019	189	40	+	+	X
ejpam-5019	189	41	γ)n1	γ)n1	PROPN
ejpam-5019	189	42	(	(	PUNCT
ejpam-5019	189	43	2β	2β	NOUN
ejpam-5019	189	44	+	+	CCONJ
ejpam-5019	189	45	γ)n2	γ)n2	ADJ
ejpam-5019	189	46	α	α	NOUN
ejpam-5019	189	47	(	(	PUNCT
ejpam-5019	189	48	2n	2n	X
ejpam-5019	189	49	+	+	CCONJ
ejpam-5019	189	50	n1	n1	ADJ
ejpam-5019	189	51	−	−	PROPN
ejpam-5019	189	52	r2	r2	PROPN
ejpam-5019	189	53	−	−	PROPN
ejpam-5019	189	54	2)+	2)+	NUM
ejpam-5019	189	55	(	(	PUNCT
ejpam-5019	189	56	2n3	2n3	NUM
ejpam-5019	189	57	−	−	PROPN
ejpam-5019	189	58	r3	r3	PROPN
ejpam-5019	189	59	−	−	PROPN
ejpam-5019	189	60	2)β	2)β	NOUN
ejpam-5019	189	61	+	+	CCONJ
ejpam-5019	189	62	γn3	γn3	NOUN
ejpam-5019	189	63	+	+	CCONJ
ejpam-5019	189	64	δ	δ	PROPN
ejpam-5019	189	65			NOUN
ejpam-5019	189	66	where	where	SCONJ
ejpam-5019	189	67	n	n	ADV
ejpam-5019	189	68	=	=	SYM
ejpam-5019	189	69	∑3	∑3	PROPN
ejpam-5019	189	70	i=1	i=1	PROPN
ejpam-5019	189	71	ni	ni	PROPN
ejpam-5019	189	72	.	.	PROPN
ejpam-5019	189	73	proof	proof	PROPN
ejpam-5019	189	74	.	.	PUNCT
ejpam-5019	190	1	letgi	letgi	PROPN
ejpam-5019	190	2	be	be	AUX
ejpam-5019	190	3	ri−regular	ri−regular	ADJ
ejpam-5019	190	4	graph	graph	NOUN
ejpam-5019	190	5	of	of	ADP
ejpam-5019	190	6	order	order	NOUN
ejpam-5019	190	7	ni	ni	PROPN
ejpam-5019	190	8	,	,	PUNCT
ejpam-5019	190	9	for	for	ADP
ejpam-5019	190	10	i	i	PROPN
ejpam-5019	190	11	=	=	SYM
ejpam-5019	190	12	1	1	NUM
ejpam-5019	190	13	,	,	PUNCT
ejpam-5019	190	14	2	2	NUM
ejpam-5019	190	15	,	,	PUNCT
ejpam-5019	190	16	3	3	NUM
ejpam-5019	190	17	.	.	X
ejpam-5019	191	1	let	let	VERB
ejpam-5019	191	2	v	v	X
ejpam-5019	191	3	(	(	PUNCT
ejpam-5019	191	4	gi	gi	INTJ
ejpam-5019	191	5	)	)	PUNCT
ejpam-5019	191	6	=	=	PRON
ejpam-5019	191	7	{	{	PUNCT
ejpam-5019	191	8	vi1	vi1	PROPN
ejpam-5019	191	9	,	,	PUNCT
ejpam-5019	191	10	v	v	ADP
ejpam-5019	191	11	i	i	PRON
ejpam-5019	191	12	2	2	NUM
ejpam-5019	191	13	,	,	PUNCT
ejpam-5019	191	14	.	.	PUNCT
ejpam-5019	191	15	.	.	PUNCT
ejpam-5019	192	1	.	.	PUNCT
ejpam-5019	193	1	,	,	PUNCT
ejpam-5019	193	2	v	v	INTJ
ejpam-5019	193	3	i	i	PRON
ejpam-5019	193	4	ni	ni	PROPN
ejpam-5019	193	5	}	}	PUNCT
ejpam-5019	193	6	be	be	VERB
ejpam-5019	193	7	the	the	DET
ejpam-5019	193	8	vertex	vertex	NOUN
ejpam-5019	193	9	set	set	NOUN
ejpam-5019	193	10	of	of	ADP
ejpam-5019	193	11	the	the	DET
ejpam-5019	193	12	graphgi	graphgi	NOUN
ejpam-5019	193	13	.	.	PUNCT
ejpam-5019	194	1	consider	consider	VERB
ejpam-5019	194	2	the	the	DET
ejpam-5019	194	3	adjacency	adjacency	NOUN
ejpam-5019	194	4	spectrum	spectrum	PROPN
ejpam-5019	194	5	ofgi	ofgi	PROPN
ejpam-5019	194	6	,	,	PUNCT
ejpam-5019	194	7	ri	ri	PROPN
ejpam-5019	195	1	=	=	SYM
ejpam-5019	195	2	λi	λi	ADP
ejpam-5019	195	3	1	1	NUM
ejpam-5019	195	4	,	,	PUNCT
ejpam-5019	195	5	λ	λ	VERB
ejpam-5019	195	6	i	i	PRON
ejpam-5019	195	7	2	2	NUM
ejpam-5019	195	8	,	,	PUNCT
ejpam-5019	195	9	.	.	PUNCT
ejpam-5019	195	10	.	.	PUNCT
ejpam-5019	195	11	.	.	PUNCT
ejpam-5019	196	1	,	,	PUNCT
ejpam-5019	196	2	λ	λ	INTJ
ejpam-5019	196	3	i	i	PRON
ejpam-5019	196	4	ni	ni	PROPN
ejpam-5019	196	5	.	.	PUNCT
ejpam-5019	197	1	let	let	VERB
ejpam-5019	197	2	g	g	PROPN
ejpam-5019	197	3	=	=	SYM
ejpam-5019	197	4	g1∇	g1∇	PROPN
ejpam-5019	197	5	(	(	PUNCT
ejpam-5019	197	6	g2	g2	PROPN
ejpam-5019	197	7	∪g3	∪g3	NOUN
ejpam-5019	197	8	)	)	PUNCT
ejpam-5019	197	9	.	.	PUNCT
ejpam-5019	198	1	the	the	DET
ejpam-5019	198	2	vertex	vertex	NOUN
ejpam-5019	198	3	set	set	VERB
ejpam-5019	198	4	v	v	NOUN
ejpam-5019	198	5	(	(	PUNCT
ejpam-5019	198	6	g	g	NOUN
ejpam-5019	198	7	)	)	PUNCT
ejpam-5019	198	8	=	=	NOUN
ejpam-5019	198	9	v	v	X
ejpam-5019	198	10	(	(	PUNCT
ejpam-5019	198	11	g1	g1	PROPN
ejpam-5019	198	12	)	)	PUNCT
ejpam-5019	198	13	∪	∪	NOUN
ejpam-5019	198	14	v	v	PROPN
ejpam-5019	198	15	(	(	PUNCT
ejpam-5019	198	16	g2	g2	PROPN
ejpam-5019	198	17	)	)	PUNCT
ejpam-5019	198	18	∪	∪	ADP
ejpam-5019	198	19	v	v	PROPN
ejpam-5019	198	20	(	(	PUNCT
ejpam-5019	198	21	g3	g3	NOUN
ejpam-5019	198	22	)	)	PUNCT
ejpam-5019	198	23	and	and	CCONJ
ejpam-5019	198	24	n	n	CCONJ
ejpam-5019	198	25	=	=	NUM
ejpam-5019	198	26	∑3	∑3	PROPN
ejpam-5019	198	27	i=1	i=1	PROPN
ejpam-5019	198	28	ni	ni	PROPN
ejpam-5019	198	29	.	.	PROPN
ejpam-5019	199	1	obviously	obviously	ADV
ejpam-5019	199	2	,	,	PUNCT
ejpam-5019	199	3	g	g	PROPN
ejpam-5019	199	4	is	be	AUX
ejpam-5019	199	5	of	of	ADP
ejpam-5019	199	6	diameter	diameter	NOUN
ejpam-5019	199	7	two	two	NUM
ejpam-5019	199	8	.	.	PUNCT
ejpam-5019	200	1	for	for	ADP
ejpam-5019	200	2	all	all	DET
ejpam-5019	200	3	v1j	v1j	ADJ
ejpam-5019	200	4	∈	∈	NOUN
ejpam-5019	200	5	v	v	NOUN
ejpam-5019	200	6	(	(	PUNCT
ejpam-5019	200	7	g1	g1	PROPN
ejpam-5019	200	8	)	)	PUNCT
ejpam-5019	200	9	,	,	PUNCT
ejpam-5019	200	10	we	we	PRON
ejpam-5019	200	11	have	have	AUX
ejpam-5019	200	12	trg1	trg1	VERB
ejpam-5019	200	13	(	(	PUNCT
ejpam-5019	200	14	v1j	v1j	NOUN
ejpam-5019	200	15	)	)	PUNCT
ejpam-5019	200	16	=	=	SYM
ejpam-5019	200	17	n	n	PROPN
ejpam-5019	200	18	+	+	CCONJ
ejpam-5019	200	19	n1	n1	ADJ
ejpam-5019	200	20	−	−	PROPN
ejpam-5019	200	21	r1	r1	NOUN
ejpam-5019	200	22	−	−	PROPN
ejpam-5019	200	23	2	2	NUM
ejpam-5019	200	24	;	;	PUNCT
ejpam-5019	200	25	j	j	PROPN
ejpam-5019	200	26	=	=	SYM
ejpam-5019	200	27	1	1	NUM
ejpam-5019	200	28	,	,	PUNCT
ejpam-5019	200	29	2	2	NUM
ejpam-5019	200	30	,	,	PUNCT
ejpam-5019	200	31	.	.	PUNCT
ejpam-5019	200	32	.	.	PUNCT
ejpam-5019	200	33	.	.	PUNCT
ejpam-5019	201	1	,	,	PUNCT
ejpam-5019	201	2	n1	n1	PROPN
ejpam-5019	201	3	.	.	PUNCT
ejpam-5019	202	1	for	for	ADP
ejpam-5019	202	2	all	all	DET
ejpam-5019	202	3	v2k	v2k	NOUN
ejpam-5019	202	4	∈	∈	NOUN
ejpam-5019	202	5	v	v	NOUN
ejpam-5019	202	6	(	(	PUNCT
ejpam-5019	202	7	g2	g2	PROPN
ejpam-5019	202	8	)	)	PUNCT
ejpam-5019	202	9	,	,	PUNCT
ejpam-5019	202	10	we	we	PRON
ejpam-5019	202	11	have	have	AUX
ejpam-5019	202	12	trg2	trg2	VERB
ejpam-5019	202	13	(	(	PUNCT
ejpam-5019	202	14	v2k	v2k	NOUN
ejpam-5019	202	15	)	)	PUNCT
ejpam-5019	202	16	=	=	SYM
ejpam-5019	202	17	2n	2n	NUM
ejpam-5019	203	1	+	+	CCONJ
ejpam-5019	203	2	n1	n1	ADJ
ejpam-5019	203	3	−	−	PROPN
ejpam-5019	203	4	r2	r2	NOUN
ejpam-5019	203	5	−	−	PROPN
ejpam-5019	203	6	2	2	NUM
ejpam-5019	203	7	;	;	PUNCT
ejpam-5019	203	8	k	k	X
ejpam-5019	203	9	=	=	SYM
ejpam-5019	203	10	1	1	NUM
ejpam-5019	203	11	,	,	PUNCT
ejpam-5019	203	12	2	2	NUM
ejpam-5019	203	13	,	,	PUNCT
ejpam-5019	203	14	.	.	PUNCT
ejpam-5019	203	15	.	.	PUNCT
ejpam-5019	203	16	.	.	PUNCT
ejpam-5019	204	1	,	,	PUNCT
ejpam-5019	204	2	n2	n2	PROPN
ejpam-5019	204	3	.	.	PUNCT
ejpam-5019	205	1	for	for	ADP
ejpam-5019	205	2	all	all	DET
ejpam-5019	205	3	v3l	v3l	NOUN
ejpam-5019	205	4	∈	∈	PROPN
ejpam-5019	205	5	v	v	NOUN
ejpam-5019	205	6	(	(	PUNCT
ejpam-5019	205	7	g3	g3	NOUN
ejpam-5019	205	8	)	)	PUNCT
ejpam-5019	205	9	we	we	PRON
ejpam-5019	205	10	have	have	VERB
ejpam-5019	205	11	,	,	PUNCT
ejpam-5019	205	12	trg3	trg3	NOUN
ejpam-5019	205	13	(	(	PUNCT
ejpam-5019	205	14	v3l	v3l	X
ejpam-5019	205	15	)	)	PUNCT
ejpam-5019	205	16	=	=	SYM
ejpam-5019	205	17	2n	2n	NUM
ejpam-5019	206	1	+	+	CCONJ
ejpam-5019	206	2	n1	n1	ADJ
ejpam-5019	206	3	−	−	PROPN
ejpam-5019	206	4	r3	r3	PROPN
ejpam-5019	206	5	−	−	ADP
ejpam-5019	206	6	2	2	NUM
ejpam-5019	206	7	;	;	PUNCT
ejpam-5019	206	8	l	l	NOUN
ejpam-5019	206	9	=	=	SYM
ejpam-5019	206	10	1	1	NUM
ejpam-5019	206	11	,	,	PUNCT
ejpam-5019	206	12	2	2	NUM
ejpam-5019	206	13	,	,	PUNCT
ejpam-5019	206	14	.	.	PUNCT
ejpam-5019	206	15	.	.	PUNCT
ejpam-5019	206	16	.	.	PUNCT
ejpam-5019	207	1	,	,	PUNCT
ejpam-5019	207	2	n3	n3	PROPN
ejpam-5019	207	3	.	.	PROPN
ejpam-5019	207	4	label	label	VERB
ejpam-5019	207	5	the	the	DET
ejpam-5019	207	6	vertices	vertex	NOUN
ejpam-5019	207	7	of	of	ADP
ejpam-5019	207	8	graph	graph	NOUN
ejpam-5019	207	9	g	g	PROPN
ejpam-5019	207	10	such	such	ADJ
ejpam-5019	207	11	that	that	SCONJ
ejpam-5019	207	12	the	the	DET
ejpam-5019	207	13	first	first	ADJ
ejpam-5019	207	14	n1	n1	ADJ
ejpam-5019	207	15	vertices	vertex	NOUN
ejpam-5019	207	16	are	be	AUX
ejpam-5019	207	17	from	from	ADP
ejpam-5019	207	18	g1	g1	PROPN
ejpam-5019	207	19	,	,	PUNCT
ejpam-5019	207	20	the	the	DET
ejpam-5019	207	21	next	next	ADJ
ejpam-5019	207	22	n2	n2	ADJ
ejpam-5019	207	23	vertices	vertex	NOUN
ejpam-5019	207	24	are	be	AUX
ejpam-5019	207	25	from	from	ADP
ejpam-5019	207	26	g2	g2	PROPN
ejpam-5019	207	27	and	and	CCONJ
ejpam-5019	207	28	the	the	DET
ejpam-5019	207	29	next	next	ADJ
ejpam-5019	207	30	n3	n3	NOUN
ejpam-5019	207	31	vertices	vertex	NOUN
ejpam-5019	207	32	are	be	AUX
ejpam-5019	207	33	from	from	ADP
ejpam-5019	207	34	g3	g3	PROPN
ejpam-5019	207	35	.	.	PUNCT
ejpam-5019	208	1	the	the	DET
ejpam-5019	208	2	universal	universal	ADJ
ejpam-5019	208	3	distance	distance	NOUN
ejpam-5019	208	4	matrix	matrix	NOUN
ejpam-5019	208	5	of	of	ADP
ejpam-5019	208	6	g	g	NOUN
ejpam-5019	208	7	can	can	AUX
ejpam-5019	208	8	be	be	AUX
ejpam-5019	208	9	expressed	express	VERB
ejpam-5019	208	10	as	as	ADP
ejpam-5019	208	11	ud	ud	INTJ
ejpam-5019	208	12	(	(	PUNCT
ejpam-5019	208	13	g	g	NOUN
ejpam-5019	208	14	)	)	PUNCT
ejpam-5019	208	15	=	=	SYM
ejpam-5019	208	16	s.	s.	PROPN
ejpam-5019	208	17	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	208	18	,	,	PUNCT
ejpam-5019	208	19	k.	k.	PROPN
ejpam-5019	208	20	desikan	desikan	PROPN
ejpam-5019	208	21	/	/	SYM
ejpam-5019	208	22	eur	eur	PROPN
ejpam-5019	208	23	.	.	PUNCT
ejpam-5019	209	1	j.	j.	PROPN
ejpam-5019	209	2	pure	pure	PROPN
ejpam-5019	209	3	appl	appl	PROPN
ejpam-5019	209	4	.	.	PROPN
ejpam-5019	209	5	math	math	PROPN
ejpam-5019	209	6	,	,	PUNCT
ejpam-5019	209	7	17	17	NUM
ejpam-5019	209	8	(	(	PUNCT
ejpam-5019	209	9	1	1	NUM
ejpam-5019	209	10	)	)	PUNCT
ejpam-5019	209	11	(	(	PUNCT
ejpam-5019	209	12	2024	2024	NUM
ejpam-5019	209	13	)	)	PUNCT
ejpam-5019	209	14	,	,	PUNCT
ejpam-5019	209	15	462	462	NUM
ejpam-5019	209	16	-	-	SYM
ejpam-5019	209	17	476	476	NUM
ejpam-5019	209	18	469	469	NOUN
ejpam-5019	209	19	[	[	PUNCT
ejpam-5019	209	20	α	α	X
ejpam-5019	209	21	(	(	PUNCT
ejpam-5019	209	22	n	n	NOUN
ejpam-5019	209	23	+	+	CCONJ
ejpam-5019	209	24	n1	n1	ADJ
ejpam-5019	209	25	−	−	PROPN
ejpam-5019	209	26	r1	r1	NOUN
ejpam-5019	209	27	−	−	PROPN
ejpam-5019	209	28	2	2	NUM
ejpam-5019	209	29	)	)	PUNCT
ejpam-5019	209	30	−2β	−2β	PROPN
ejpam-5019	210	1	+	+	NUM
ejpam-5019	210	2	δ	δ	PROPN
ejpam-5019	210	3	]	]	X
ejpam-5019	210	4	in1	in1	PROPN
ejpam-5019	210	5	+	+	CCONJ
ejpam-5019	210	6	(	(	PUNCT
ejpam-5019	210	7	β	β	X
ejpam-5019	210	8	+	+	CCONJ
ejpam-5019	210	9	γ	γ	X
ejpam-5019	210	10	)	)	PUNCT
ejpam-5019	210	11	jn1×n2	jn1×n2	NOUN
ejpam-5019	210	12	(	(	PUNCT
ejpam-5019	210	13	β	β	X
ejpam-5019	210	14	+	+	CCONJ
ejpam-5019	210	15	γ	γ	X
ejpam-5019	210	16	)	)	PUNCT
ejpam-5019	210	17	jn1×n3	jn1×n3	PROPN
ejpam-5019	210	18	(	(	PUNCT
ejpam-5019	210	19	2β	2β	NOUN
ejpam-5019	210	20	+	+	CCONJ
ejpam-5019	210	21	γ	γ	X
ejpam-5019	210	22	)	)	PUNCT
ejpam-5019	210	23	jn1	jn1	NOUN
ejpam-5019	210	24	−	−	X
ejpam-5019	211	1	βa	βa	INTJ
ejpam-5019	211	2	(	(	PUNCT
ejpam-5019	211	3	g1	g1	PROPN
ejpam-5019	211	4	)	)	PUNCT
ejpam-5019	211	5	(	(	PUNCT
ejpam-5019	211	6	β	β	X
ejpam-5019	211	7	+	+	CCONJ
ejpam-5019	211	8	γ	γ	X
ejpam-5019	211	9	)	)	PUNCT
ejpam-5019	211	10	jn2×n1	jn2×n1	PROPN
ejpam-5019	211	11	[	[	PUNCT
ejpam-5019	211	12	α	α	PROPN
ejpam-5019	211	13	(	(	PUNCT
ejpam-5019	211	14	2n	2n	X
ejpam-5019	211	15	+	+	CCONJ
ejpam-5019	211	16	n1	n1	ADJ
ejpam-5019	211	17	−	−	PROPN
ejpam-5019	211	18	r2	r2	NOUN
ejpam-5019	211	19	−	−	PROPN
ejpam-5019	211	20	2	2	NUM
ejpam-5019	211	21	)	)	PUNCT
ejpam-5019	211	22	(	(	PUNCT
ejpam-5019	211	23	2β	2β	NOUN
ejpam-5019	211	24	+	+	CCONJ
ejpam-5019	211	25	γ	γ	X
ejpam-5019	211	26	)	)	PUNCT
ejpam-5019	211	27	jn2×n3	jn2×n3	PROPN
ejpam-5019	211	28	−2β	−2β	PROPN
ejpam-5019	211	29	+	+	NUM
ejpam-5019	211	30	δ	δ	PROPN
ejpam-5019	211	31	]	]	PUNCT
ejpam-5019	211	32	in2	in2	PROPN
ejpam-5019	212	1	+	+	CCONJ
ejpam-5019	212	2	(	(	PUNCT
ejpam-5019	212	3	2β	2β	AUX
ejpam-5019	212	4	+	+	CCONJ
ejpam-5019	212	5	γ	γ	X
ejpam-5019	212	6	)	)	PUNCT
ejpam-5019	212	7	jn2	jn2	VERB
ejpam-5019	212	8	−βa	−βa	PROPN
ejpam-5019	212	9	(	(	PUNCT
ejpam-5019	212	10	g2	g2	PROPN
ejpam-5019	212	11	)	)	PUNCT
ejpam-5019	212	12	(	(	PUNCT
ejpam-5019	212	13	β	β	X
ejpam-5019	212	14	+	+	CCONJ
ejpam-5019	212	15	γ	γ	X
ejpam-5019	212	16	)	)	PUNCT
ejpam-5019	212	17	jn3×n1	jn3×n1	PROPN
ejpam-5019	212	18	(	(	PUNCT
ejpam-5019	212	19	2β	2β	NOUN
ejpam-5019	212	20	+	+	CCONJ
ejpam-5019	212	21	γ	γ	X
ejpam-5019	212	22	)	)	PUNCT
ejpam-5019	212	23	jn3×n2	jn3×n2	NOUN
ejpam-5019	212	24	[	[	PUNCT
ejpam-5019	212	25	α	α	X
ejpam-5019	212	26	(	(	PUNCT
ejpam-5019	212	27	2n	2n	X
ejpam-5019	212	28	+	+	CCONJ
ejpam-5019	212	29	n1	n1	ADJ
ejpam-5019	212	30	−	−	PROPN
ejpam-5019	212	31	r3	r3	PROPN
ejpam-5019	212	32	−	−	NOUN
ejpam-5019	212	33	2	2	NUM
ejpam-5019	212	34	)	)	PUNCT
ejpam-5019	212	35	−2β	−2β	PROPN
ejpam-5019	213	1	+	+	NUM
ejpam-5019	213	2	δ	δ	PROPN
ejpam-5019	213	3	]	]	PUNCT
ejpam-5019	214	1	in3	in3	PROPN
ejpam-5019	214	2	+	+	CCONJ
ejpam-5019	214	3	(	(	PUNCT
ejpam-5019	214	4	2β	2β	NOUN
ejpam-5019	214	5	+	+	CCONJ
ejpam-5019	214	6	γ	γ	X
ejpam-5019	214	7	)	)	PUNCT
ejpam-5019	214	8	jn3	jn3	NOUN
ejpam-5019	215	1	−	−	PROPN
ejpam-5019	215	2	βa	βa	INTJ
ejpam-5019	215	3	(	(	PUNCT
ejpam-5019	215	4	g3	g3	PROPN
ejpam-5019	215	5	)	)	PUNCT
ejpam-5019	215	6			PRON
ejpam-5019	215	7	let	let	VERB
ejpam-5019	215	8	1n	1n	NUM
ejpam-5019	215	9	=	=	SYM
ejpam-5019	215	10	(	(	PUNCT
ejpam-5019	215	11	1	1	NUM
ejpam-5019	215	12	1	1	NUM
ejpam-5019	215	13	1	1	NUM
ejpam-5019	215	14	.	.	PUNCT
ejpam-5019	215	15	.	.	PUNCT
ejpam-5019	215	16	.	.	PUNCT
ejpam-5019	216	1	1)t	1)t	PROPN
ejpam-5019	216	2	be	be	AUX
ejpam-5019	216	3	all	all	DET
ejpam-5019	216	4	ones	one	NOUN
ejpam-5019	216	5	vector	vector	NOUN
ejpam-5019	216	6	of	of	ADP
ejpam-5019	216	7	order	order	NOUN
ejpam-5019	216	8	n.	n.	NOUN
ejpam-5019	216	9	since	since	SCONJ
ejpam-5019	216	10	gi	gi	NOUN
ejpam-5019	216	11	;	;	PUNCT
ejpam-5019	216	12	i	i	NOUN
ejpam-5019	216	13	=	=	NOUN
ejpam-5019	216	14	1	1	NUM
ejpam-5019	216	15	,	,	PUNCT
ejpam-5019	216	16	2	2	NUM
ejpam-5019	216	17	,	,	PUNCT
ejpam-5019	216	18	3	3	NUM
ejpam-5019	216	19	,	,	PUNCT
ejpam-5019	216	20	is	be	AUX
ejpam-5019	216	21	a	a	DET
ejpam-5019	216	22	ri−	ri−	ADJ
ejpam-5019	216	23	regular	regular	ADJ
ejpam-5019	216	24	graph	graph	NOUN
ejpam-5019	216	25	,	,	PUNCT
ejpam-5019	216	26	it	it	PRON
ejpam-5019	216	27	follows	follow	VERB
ejpam-5019	216	28	that	that	SCONJ
ejpam-5019	216	29	ri	ri	PROPN
ejpam-5019	216	30	is	be	AUX
ejpam-5019	216	31	the	the	DET
ejpam-5019	216	32	largest	large	ADJ
ejpam-5019	216	33	eigenvalue	eigenvalue	NOUN
ejpam-5019	216	34	and	and	CCONJ
ejpam-5019	216	35	the	the	DET
ejpam-5019	216	36	corresponding	correspond	VERB
ejpam-5019	216	37	eigenvector	eigenvector	NOUN
ejpam-5019	216	38	is	be	AUX
ejpam-5019	216	39	1ni	1ni	ADJ
ejpam-5019	216	40	.	.	PUNCT
ejpam-5019	217	1	the	the	DET
ejpam-5019	217	2	remaining	remain	VERB
ejpam-5019	217	3	eigenvectors	eigenvector	NOUN
ejpam-5019	217	4	are	be	AUX
ejpam-5019	217	5	orthogonal	orthogonal	ADJ
ejpam-5019	217	6	to	to	ADP
ejpam-5019	217	7	1ni	1ni	NOUN
ejpam-5019	217	8	.	.	PUNCT
ejpam-5019	218	1	consider	consider	VERB
ejpam-5019	218	2	λ	λ	PROPN
ejpam-5019	218	3	,	,	PUNCT
ejpam-5019	218	4	µ	µ	NOUN
ejpam-5019	218	5	,	,	PUNCT
ejpam-5019	218	6	ζ	ζ	NOUN
ejpam-5019	218	7	as	as	ADP
ejpam-5019	218	8	the	the	DET
ejpam-5019	218	9	eigenvalues	eigenvalue	NOUN
ejpam-5019	218	10	of	of	ADP
ejpam-5019	218	11	the	the	DET
ejpam-5019	218	12	adjacency	adjacency	NOUN
ejpam-5019	218	13	matrices	matrix	NOUN
ejpam-5019	218	14	of	of	ADP
ejpam-5019	218	15	g1	g1	NOUN
ejpam-5019	218	16	,	,	PUNCT
ejpam-5019	218	17	g2	g2	PROPN
ejpam-5019	218	18	,	,	PUNCT
ejpam-5019	218	19	g3	g3	NOUN
ejpam-5019	218	20	with	with	ADP
ejpam-5019	218	21	corresponding	corresponding	ADJ
ejpam-5019	218	22	eigenvectors	eigenvector	NOUN
ejpam-5019	218	23	as	as	ADP
ejpam-5019	218	24	u	u	NOUN
ejpam-5019	218	25	,	,	PUNCT
ejpam-5019	218	26	v	v	NOUN
ejpam-5019	218	27	,	,	PUNCT
ejpam-5019	218	28	w	w	NOUN
ejpam-5019	218	29	,	,	PUNCT
ejpam-5019	218	30	respectively	respectively	ADV
ejpam-5019	218	31	.	.	PUNCT
ejpam-5019	219	1	also	also	ADV
ejpam-5019	219	2	,	,	PUNCT
ejpam-5019	219	3	they	they	PRON
ejpam-5019	219	4	satisfy	satisfy	VERB
ejpam-5019	219	5	1tn1	1tn1	NUM
ejpam-5019	219	6	u	u	NOUN
ejpam-5019	219	7	=	=	PROPN
ejpam-5019	219	8	0	0	NUM
ejpam-5019	219	9	,	,	PUNCT
ejpam-5019	219	10	1tn2	1tn2	NUM
ejpam-5019	219	11	v	v	NOUN
ejpam-5019	219	12	=	=	SYM
ejpam-5019	219	13	0	0	NUM
ejpam-5019	219	14	,	,	PUNCT
ejpam-5019	219	15	1tn3	1tn3	NUM
ejpam-5019	219	16	w	w	NOUN
ejpam-5019	219	17	=	=	SYM
ejpam-5019	219	18	0	0	NUM
ejpam-5019	219	19	,	,	PUNCT
ejpam-5019	219	20	respectively	respectively	ADV
ejpam-5019	219	21	.	.	PUNCT
ejpam-5019	220	1	then	then	ADV
ejpam-5019	220	2	,	,	PUNCT
ejpam-5019	220	3	(	(	PUNCT
ejpam-5019	220	4	ut	ut	PROPN
ejpam-5019	220	5	01×n2	01×n2	NUM
ejpam-5019	220	6	01×n3	01×n3	NUM
ejpam-5019	220	7	)	)	PUNCT
ejpam-5019	220	8	t	t	NOUN
ejpam-5019	220	9	,	,	PUNCT
ejpam-5019	220	10	(	(	PUNCT
ejpam-5019	220	11	01×n1	01×n1	NOUN
ejpam-5019	220	12	vt	vt	PROPN
ejpam-5019	220	13	01×n3	01×n3	PROPN
ejpam-5019	220	14	)	)	PUNCT
ejpam-5019	220	15	t	t	PROPN
ejpam-5019	220	16	and	and	CCONJ
ejpam-5019	220	17	(	(	PUNCT
ejpam-5019	220	18	01×n1	01×n1	NUM
ejpam-5019	220	19	01×n2	01×n2	NUM
ejpam-5019	221	1	wt	wt	NOUN
ejpam-5019	221	2	)	)	PUNCT
ejpam-5019	221	3	t	t	NOUN
ejpam-5019	221	4	are	be	AUX
ejpam-5019	221	5	the	the	DET
ejpam-5019	221	6	eigenvectors	eigenvector	NOUN
ejpam-5019	221	7	of	of	ADP
ejpam-5019	221	8	ud	ud	INTJ
ejpam-5019	221	9	(	(	PUNCT
ejpam-5019	221	10	g	g	NOUN
ejpam-5019	221	11	)	)	PUNCT
ejpam-5019	221	12	with	with	ADP
ejpam-5019	221	13	corresponding	correspond	VERB
ejpam-5019	221	14	eigenvalues	eigenvalue	NOUN
ejpam-5019	221	15	[	[	PUNCT
ejpam-5019	221	16	α	α	NOUN
ejpam-5019	221	17	(	(	PUNCT
ejpam-5019	221	18	n	n	NOUN
ejpam-5019	221	19	+	+	CCONJ
ejpam-5019	221	20	n1	n1	ADJ
ejpam-5019	221	21	−	−	PROPN
ejpam-5019	221	22	r1	r1	NOUN
ejpam-5019	221	23	−	−	PROPN
ejpam-5019	221	24	2)−	2)−	NUM
ejpam-5019	221	25	2β+	2β+	NUM
ejpam-5019	221	26	δ	δ	NOUN
ejpam-5019	221	27	]	]	X
ejpam-5019	222	1	−βλ1	−βλ1	X
ejpam-5019	222	2	l	l	NOUN
ejpam-5019	222	3	;	;	PUNCT
ejpam-5019	223	1	l	l	NOUN
ejpam-5019	223	2	=	=	SYM
ejpam-5019	223	3	2	2	NUM
ejpam-5019	223	4	,	,	PUNCT
ejpam-5019	223	5	3	3	NUM
ejpam-5019	223	6	,	,	PUNCT
ejpam-5019	223	7	.	.	PUNCT
ejpam-5019	223	8	.	.	PUNCT
ejpam-5019	223	9	.	.	PUNCT
ejpam-5019	224	1	,	,	PUNCT
ejpam-5019	224	2	n1	n1	NOUN
ejpam-5019	224	3	,	,	PUNCT
ejpam-5019	224	4	[	[	PUNCT
ejpam-5019	224	5	α	α	X
ejpam-5019	224	6	(	(	PUNCT
ejpam-5019	224	7	2n	2n	X
ejpam-5019	224	8	+	+	CCONJ
ejpam-5019	224	9	n1	n1	ADJ
ejpam-5019	224	10	−	−	PROPN
ejpam-5019	224	11	r2	r2	NOUN
ejpam-5019	225	1	−	−	PROPN
ejpam-5019	225	2	2)−	2)−	NUM
ejpam-5019	225	3	2β+	2β+	NUM
ejpam-5019	225	4	δ	δ	NOUN
ejpam-5019	225	5	]	]	PUNCT
ejpam-5019	226	1	−	−	X
ejpam-5019	226	2	βλ2	βλ2	X
ejpam-5019	226	3	m	m	PROPN
ejpam-5019	226	4	;	;	PUNCT
ejpam-5019	226	5	m	m	VERB
ejpam-5019	226	6	=	=	SYM
ejpam-5019	226	7	2	2	NUM
ejpam-5019	226	8	,	,	PUNCT
ejpam-5019	226	9	3	3	NUM
ejpam-5019	226	10	,	,	PUNCT
ejpam-5019	226	11	.	.	PUNCT
ejpam-5019	226	12	.	.	PUNCT
ejpam-5019	227	1	.	.	PUNCT
ejpam-5019	228	1	,	,	PUNCT
ejpam-5019	228	2	n2	n2	NOUN
ejpam-5019	228	3	,	,	PUNCT
ejpam-5019	228	4	and	and	CCONJ
ejpam-5019	228	5	[	[	PUNCT
ejpam-5019	228	6	α	α	X
ejpam-5019	228	7	(	(	PUNCT
ejpam-5019	228	8	2n	2n	X
ejpam-5019	228	9	+	+	CCONJ
ejpam-5019	228	10	n1	n1	ADJ
ejpam-5019	228	11	−	−	PROPN
ejpam-5019	228	12	r3	r3	PROPN
ejpam-5019	228	13	−	−	NOUN
ejpam-5019	228	14	2	2	NUM
ejpam-5019	228	15	)	)	PUNCT
ejpam-5019	228	16	−	−	NOUN
ejpam-5019	229	1	2β	2β	NOUN
ejpam-5019	229	2	+	+	CCONJ
ejpam-5019	229	3	δ	δ	X
ejpam-5019	229	4	]	]	PUNCT
ejpam-5019	229	5	−	−	X
ejpam-5019	229	6	βλ3	βλ3	NOUN
ejpam-5019	229	7	s	s	PART
ejpam-5019	229	8	;	;	PUNCT
ejpam-5019	229	9	s	s	X
ejpam-5019	229	10	=	=	SYM
ejpam-5019	229	11	2	2	NUM
ejpam-5019	229	12	,	,	PUNCT
ejpam-5019	229	13	3	3	NUM
ejpam-5019	229	14	,	,	PUNCT
ejpam-5019	229	15	.	.	PUNCT
ejpam-5019	229	16	.	.	PUNCT
ejpam-5019	230	1	.	.	PUNCT
ejpam-5019	231	1	,	,	PUNCT
ejpam-5019	231	2	n3	n3	NOUN
ejpam-5019	231	3	,	,	PUNCT
ejpam-5019	231	4	respectively	respectively	ADV
ejpam-5019	231	5	.	.	PUNCT
ejpam-5019	232	1	totally	totally	ADV
ejpam-5019	232	2	,	,	PUNCT
ejpam-5019	232	3	we	we	PRON
ejpam-5019	232	4	have	have	VERB
ejpam-5019	232	5	n	n	NUM
ejpam-5019	232	6	−	−	NUM
ejpam-5019	232	7	3	3	NUM
ejpam-5019	232	8	eigenvectors	eigenvector	NOUN
ejpam-5019	232	9	and	and	CCONJ
ejpam-5019	232	10	they	they	PRON
ejpam-5019	232	11	are	be	AUX
ejpam-5019	232	12	orthogonal	orthogonal	ADJ
ejpam-5019	232	13	to	to	ADP
ejpam-5019	232	14	(	(	PUNCT
ejpam-5019	232	15	ut	ut	PROPN
ejpam-5019	232	16	01×n2	01×n2	NUM
ejpam-5019	232	17	01×n3	01×n3	NUM
ejpam-5019	232	18	)	)	PUNCT
ejpam-5019	232	19	t	t	NOUN
ejpam-5019	232	20	,	,	PUNCT
ejpam-5019	232	21	(	(	PUNCT
ejpam-5019	232	22	01×n1	01×n1	NOUN
ejpam-5019	232	23	vt	vt	PROPN
ejpam-5019	232	24	01×n3	01×n3	PROPN
ejpam-5019	232	25	)	)	PUNCT
ejpam-5019	232	26	t	t	PROPN
ejpam-5019	232	27	and	and	CCONJ
ejpam-5019	232	28	(	(	PUNCT
ejpam-5019	232	29	01×n1	01×n1	NUM
ejpam-5019	232	30	01×n2	01×n2	NUM
ejpam-5019	232	31	wt	wt	NOUN
ejpam-5019	232	32	)	)	PUNCT
ejpam-5019	232	33	t	t	PROPN
ejpam-5019	232	34	.	.	PUNCT
ejpam-5019	233	1	for	for	ADP
ejpam-5019	233	2	a	a	DET
ejpam-5019	233	3	suitable	suitable	ADJ
ejpam-5019	233	4	choice	choice	NOUN
ejpam-5019	233	5	of	of	ADP
ejpam-5019	233	6	a	a	DET
ejpam-5019	233	7	̸=	̸=	PROPN
ejpam-5019	233	8	0	0	NUM
ejpam-5019	233	9	,	,	PUNCT
ejpam-5019	233	10	b	b	X
ejpam-5019	233	11	̸=	̸=	PROPN
ejpam-5019	233	12	0	0	NUM
ejpam-5019	233	13	,	,	PUNCT
ejpam-5019	233	14	c	c	AUX
ejpam-5019	233	15	̸=	̸=	PROPN
ejpam-5019	233	16	0	0	NUM
ejpam-5019	233	17	,	,	PUNCT
ejpam-5019	233	18	the	the	DET
ejpam-5019	233	19	other	other	ADJ
ejpam-5019	233	20	three	three	NUM
ejpam-5019	233	21	eigenvectors	eigenvector	NOUN
ejpam-5019	233	22	of	of	ADP
ejpam-5019	233	23	ud	ud	INTJ
ejpam-5019	233	24	(	(	PUNCT
ejpam-5019	233	25	g	g	NOUN
ejpam-5019	233	26	)	)	PUNCT
ejpam-5019	233	27	can	can	AUX
ejpam-5019	233	28	be	be	AUX
ejpam-5019	233	29	represented	represent	VERB
ejpam-5019	233	30	by	by	ADP
ejpam-5019	233	31	(	(	PUNCT
ejpam-5019	233	32	a1tn1	a1tn1	ADJ
ejpam-5019	233	33	b1tn2	b1tn2	ADJ
ejpam-5019	233	34	c1tn3	c1tn3	NOUN
ejpam-5019	233	35	)	)	PUNCT
ejpam-5019	233	36	t	t	PROPN
ejpam-5019	233	37	.	.	PUNCT
ejpam-5019	234	1	consider	consider	VERB
ejpam-5019	234	2	ρ	ρ	NOUN
ejpam-5019	234	3	as	as	ADP
ejpam-5019	234	4	an	an	DET
ejpam-5019	234	5	eigenvalue	eigenvalue	NOUN
ejpam-5019	234	6	of	of	ADP
ejpam-5019	234	7	the	the	DET
ejpam-5019	234	8	matrix	matrix	NOUN
ejpam-5019	234	9	ud	ud	INTJ
ejpam-5019	234	10	(	(	PUNCT
ejpam-5019	234	11	g	g	NOUN
ejpam-5019	234	12	)	)	PUNCT
ejpam-5019	234	13	with	with	ADP
ejpam-5019	234	14	the	the	DET
ejpam-5019	234	15	corresponding	correspond	VERB
ejpam-5019	234	16	eigenvector	eigenvector	NOUN
ejpam-5019	234	17	z	z	NOUN
ejpam-5019	234	18	=	=	PUNCT
ejpam-5019	234	19	(	(	PUNCT
ejpam-5019	234	20	a1tn1	a1tn1	ADJ
ejpam-5019	234	21	b1tn2	b1tn2	ADJ
ejpam-5019	234	22	c1tn3	c1tn3	NOUN
ejpam-5019	234	23	)	)	PUNCT
ejpam-5019	234	24	t	t	PROPN
ejpam-5019	234	25	.	.	PUNCT
ejpam-5019	235	1	we	we	PRON
ejpam-5019	235	2	know	know	VERB
ejpam-5019	235	3	that	that	SCONJ
ejpam-5019	235	4	ud	ud	INTJ
ejpam-5019	235	5	(	(	PUNCT
ejpam-5019	235	6	g)z	g)z	NOUN
ejpam-5019	235	7	=	=	PUNCT
ejpam-5019	235	8	ρz	ρz	NOUN
ejpam-5019	235	9	and	and	CCONJ
ejpam-5019	235	10	a	a	DET
ejpam-5019	235	11	(	(	PUNCT
ejpam-5019	235	12	gi	gi	INTJ
ejpam-5019	235	13	)	)	PUNCT
ejpam-5019	235	14	=	=	SYM
ejpam-5019	236	1	ri1ni	ri1ni	ADJ
ejpam-5019	236	2	;	;	PUNCT
ejpam-5019	237	1	i	i	PRON
ejpam-5019	237	2	=	=	NOUN
ejpam-5019	237	3	1	1	NUM
ejpam-5019	237	4	,	,	PUNCT
ejpam-5019	237	5	2	2	NUM
ejpam-5019	237	6	,	,	PUNCT
ejpam-5019	237	7	3	3	NUM
ejpam-5019	237	8	.	.	PUNCT
ejpam-5019	238	1	hence	hence	ADV
ejpam-5019	238	2	we	we	PRON
ejpam-5019	238	3	have	have	VERB
ejpam-5019	238	4	the	the	DET
ejpam-5019	238	5	system	system	NOUN
ejpam-5019	238	6	of	of	ADP
ejpam-5019	238	7	linear	linear	PROPN
ejpam-5019	238	8	equations	equation	NOUN
ejpam-5019	238	9	as	as	SCONJ
ejpam-5019	238	10	follows	follow	VERB
ejpam-5019	238	11	:	:	PUNCT
ejpam-5019	238	12	[	[	PUNCT
ejpam-5019	238	13	α	α	X
ejpam-5019	238	14	(	(	PUNCT
ejpam-5019	238	15	n	n	NOUN
ejpam-5019	238	16	+	+	CCONJ
ejpam-5019	238	17	n1	n1	ADJ
ejpam-5019	238	18	−	−	PROPN
ejpam-5019	238	19	r1	r1	NOUN
ejpam-5019	238	20	−	−	PROPN
ejpam-5019	238	21	2	2	NUM
ejpam-5019	238	22	)	)	PUNCT
ejpam-5019	238	23	+	+	CCONJ
ejpam-5019	238	24	(	(	PUNCT
ejpam-5019	238	25	2n1	2n1	NUM
ejpam-5019	238	26	−	−	PROPN
ejpam-5019	238	27	r1	r1	PROPN
ejpam-5019	238	28	−	−	PROPN
ejpam-5019	238	29	2)β	2)β	NOUN
ejpam-5019	239	1	+	+	CCONJ
ejpam-5019	239	2	γn1	γn1	NOUN
ejpam-5019	239	3	+	+	CCONJ
ejpam-5019	239	4	δ	δ	NOUN
ejpam-5019	239	5	]	]	PUNCT
ejpam-5019	239	6	a+	a+	PUNCT
ejpam-5019	239	7	[	[	PUNCT
ejpam-5019	239	8	(	(	PUNCT
ejpam-5019	239	9	β	β	X
ejpam-5019	239	10	+	+	X
ejpam-5019	239	11	γ)n2	γ)n2	PROPN
ejpam-5019	239	12	]	]	PUNCT
ejpam-5019	239	13	b+	b+	X
ejpam-5019	239	14	[	[	PUNCT
ejpam-5019	239	15	(	(	PUNCT
ejpam-5019	239	16	β	β	X
ejpam-5019	239	17	+	+	X
ejpam-5019	239	18	γ)n3	γ)n3	PROPN
ejpam-5019	239	19	]	]	PUNCT
ejpam-5019	240	1	c	c	X
ejpam-5019	240	2	=	=	SYM
ejpam-5019	240	3	ρa	ρa	PROPN
ejpam-5019	240	4	,	,	PUNCT
ejpam-5019	240	5	[	[	PUNCT
ejpam-5019	240	6	(	(	PUNCT
ejpam-5019	240	7	β	β	X
ejpam-5019	240	8	+	+	X
ejpam-5019	240	9	γ)n1	γ)n1	PROPN
ejpam-5019	240	10	]	]	PUNCT
ejpam-5019	240	11	a+	a+	PUNCT
ejpam-5019	240	12	[	[	PUNCT
ejpam-5019	240	13	α	α	X
ejpam-5019	240	14	(	(	PUNCT
ejpam-5019	240	15	2n	2n	X
ejpam-5019	240	16	+	+	CCONJ
ejpam-5019	240	17	n1	n1	ADJ
ejpam-5019	240	18	−	−	PROPN
ejpam-5019	240	19	r2	r2	NOUN
ejpam-5019	240	20	−	−	PROPN
ejpam-5019	240	21	2	2	NUM
ejpam-5019	240	22	)	)	PUNCT
ejpam-5019	240	23	+	+	CCONJ
ejpam-5019	240	24	(	(	PUNCT
ejpam-5019	240	25	2n2	2n2	NUM
ejpam-5019	240	26	−	−	PROPN
ejpam-5019	240	27	r2	r2	PROPN
ejpam-5019	240	28	−	−	PROPN
ejpam-5019	240	29	2)β	2)β	NOUN
ejpam-5019	240	30	+	+	CCONJ
ejpam-5019	240	31	γn2	γn2	NOUN
ejpam-5019	240	32	+	+	CCONJ
ejpam-5019	240	33	δ	δ	X
ejpam-5019	240	34	]	]	PUNCT
ejpam-5019	240	35	b+	b+	X
ejpam-5019	240	36	[	[	PUNCT
ejpam-5019	240	37	(	(	PUNCT
ejpam-5019	240	38	2β	2β	NOUN
ejpam-5019	240	39	+	+	X
ejpam-5019	240	40	γ)n3	γ)n3	PROPN
ejpam-5019	240	41	]	]	PUNCT
ejpam-5019	241	1	c	c	X
ejpam-5019	241	2	=	=	SYM
ejpam-5019	241	3	ρb	ρb	PROPN
ejpam-5019	241	4	,	,	PUNCT
ejpam-5019	241	5	[	[	PUNCT
ejpam-5019	241	6	(	(	PUNCT
ejpam-5019	241	7	β	β	X
ejpam-5019	241	8	+	+	X
ejpam-5019	241	9	γ)n1	γ)n1	PROPN
ejpam-5019	241	10	]	]	PUNCT
ejpam-5019	241	11	a+	a+	PUNCT
ejpam-5019	241	12	[	[	PUNCT
ejpam-5019	241	13	(	(	PUNCT
ejpam-5019	241	14	2β	2β	NOUN
ejpam-5019	241	15	+	+	X
ejpam-5019	241	16	γ)n2	γ)n2	PROPN
ejpam-5019	241	17	]	]	PUNCT
ejpam-5019	241	18	b+	b+	X
ejpam-5019	241	19	[	[	PUNCT
ejpam-5019	241	20	α	α	X
ejpam-5019	241	21	(	(	PUNCT
ejpam-5019	241	22	2n	2n	X
ejpam-5019	241	23	+	+	CCONJ
ejpam-5019	241	24	n1	n1	ADJ
ejpam-5019	241	25	−	−	PROPN
ejpam-5019	241	26	r2	r2	NOUN
ejpam-5019	241	27	−	−	PROPN
ejpam-5019	241	28	2	2	NUM
ejpam-5019	241	29	)	)	PUNCT
ejpam-5019	241	30	+	+	CCONJ
ejpam-5019	241	31	(	(	PUNCT
ejpam-5019	241	32	2n3	2n3	NUM
ejpam-5019	241	33	−	−	PROPN
ejpam-5019	241	34	r3	r3	PROPN
ejpam-5019	241	35	−	−	PROPN
ejpam-5019	241	36	2)β	2)β	NOUN
ejpam-5019	241	37	+	+	CCONJ
ejpam-5019	241	38	γn3	γn3	NOUN
ejpam-5019	241	39	+	+	CCONJ
ejpam-5019	241	40	δ	δ	X
ejpam-5019	241	41	]	]	PUNCT
ejpam-5019	242	1	c	c	X
ejpam-5019	242	2	=	=	SYM
ejpam-5019	242	3	ρc	ρc	AUX
ejpam-5019	242	4	.	.	PUNCT
ejpam-5019	242	5	eliminating	eliminate	VERB
ejpam-5019	242	6	a	a	DET
ejpam-5019	242	7	,	,	PUNCT
ejpam-5019	242	8	b	b	NOUN
ejpam-5019	242	9	,	,	PUNCT
ejpam-5019	242	10	and	and	CCONJ
ejpam-5019	242	11	c	c	X
ejpam-5019	242	12	,	,	PUNCT
ejpam-5019	242	13	we	we	PRON
ejpam-5019	242	14	obtain	obtain	VERB
ejpam-5019	242	15	the	the	DET
ejpam-5019	242	16	nontrivial	nontrivial	ADJ
ejpam-5019	242	17	solution	solution	NOUN
ejpam-5019	242	18	for	for	ADP
ejpam-5019	242	19	the	the	DET
ejpam-5019	242	20	system	system	NOUN
ejpam-5019	242	21	of	of	ADP
ejpam-5019	242	22	equations	equation	NOUN
ejpam-5019	242	23	.	.	PUNCT
ejpam-5019	243	1	this	this	DET
ejpam-5019	243	2	nontrivial	nontrivial	ADJ
ejpam-5019	243	3	solution	solution	NOUN
ejpam-5019	243	4	yields	yield	VERB
ejpam-5019	243	5	the	the	DET
ejpam-5019	243	6	eigenvalues	eigenvalue	NOUN
ejpam-5019	243	7	of	of	ADP
ejpam-5019	243	8	ud	ud	INTJ
ejpam-5019	243	9	(	(	PUNCT
ejpam-5019	243	10	g	g	NOUN
ejpam-5019	243	11	)	)	PUNCT
ejpam-5019	243	12	corresponding	correspond	VERB
ejpam-5019	243	13	to	to	ADP
ejpam-5019	243	14	ρ	ρ	PROPN
ejpam-5019	243	15	.	.	PUNCT
ejpam-5019	244	1	this	this	PRON
ejpam-5019	244	2	completes	complete	VERB
ejpam-5019	244	3	the	the	DET
ejpam-5019	244	4	proof	proof	NOUN
ejpam-5019	244	5	.	.	PUNCT
ejpam-5019	245	1	s.	s.	PROPN
ejpam-5019	245	2	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	245	3	,	,	PUNCT
ejpam-5019	245	4	k.	k.	PROPN
ejpam-5019	245	5	desikan	desikan	PROPN
ejpam-5019	245	6	/	/	SYM
ejpam-5019	245	7	eur	eur	PROPN
ejpam-5019	245	8	.	.	PUNCT
ejpam-5019	246	1	j.	j.	PROPN
ejpam-5019	246	2	pure	pure	PROPN
ejpam-5019	246	3	appl	appl	PROPN
ejpam-5019	246	4	.	.	PROPN
ejpam-5019	246	5	math	math	PROPN
ejpam-5019	246	6	,	,	PUNCT
ejpam-5019	246	7	17	17	NUM
ejpam-5019	246	8	(	(	PUNCT
ejpam-5019	246	9	1	1	NUM
ejpam-5019	246	10	)	)	PUNCT
ejpam-5019	246	11	(	(	PUNCT
ejpam-5019	246	12	2024	2024	NUM
ejpam-5019	246	13	)	)	PUNCT
ejpam-5019	246	14	,	,	PUNCT
ejpam-5019	246	15	462	462	NUM
ejpam-5019	246	16	-	-	SYM
ejpam-5019	246	17	476	476	NUM
ejpam-5019	246	18	470	470	NUM
ejpam-5019	246	19	corollary	corollary	ADJ
ejpam-5019	246	20	5	5	NUM
ejpam-5019	246	21	.	.	PUNCT
ejpam-5019	247	1	the	the	DET
ejpam-5019	247	2	universal	universal	ADJ
ejpam-5019	247	3	distance	distance	NOUN
ejpam-5019	247	4	spectrum	spectrum	NOUN
ejpam-5019	247	5	of	of	ADP
ejpam-5019	247	6	g	g	NOUN
ejpam-5019	247	7	=	=	PUNCT
ejpam-5019	247	8	kn1∇	kn1∇	NOUN
ejpam-5019	247	9	(	(	PUNCT
ejpam-5019	247	10	kn2	kn2	NOUN
ejpam-5019	247	11	∪kn3	∪kn3	X
ejpam-5019	247	12	)	)	PUNCT
ejpam-5019	247	13	consists	consist	VERB
ejpam-5019	247	14	of	of	ADP
ejpam-5019	247	15	the	the	DET
ejpam-5019	247	16	eigenvalues	eigenvalues	PROPN
ejpam-5019	247	17	(	(	PUNCT
ejpam-5019	247	18	i	i	NOUN
ejpam-5019	247	19	)	)	PUNCT
ejpam-5019	247	20	(	(	PUNCT
ejpam-5019	247	21	αn	αn	NOUN
ejpam-5019	247	22	−	−	NOUN
ejpam-5019	248	1	β	β	X
ejpam-5019	249	1	+	+	CCONJ
ejpam-5019	249	2	δ	δ	PROPN
ejpam-5019	249	3	−	−	NOUN
ejpam-5019	249	4	α	α	NOUN
ejpam-5019	249	5	)	)	PUNCT
ejpam-5019	249	6	with	with	ADP
ejpam-5019	249	7	algebraic	algebraic	ADJ
ejpam-5019	249	8	multiplicity	multiplicity	NOUN
ejpam-5019	249	9	n1	n1	NOUN
ejpam-5019	249	10	−	−	PROPN
ejpam-5019	249	11	1	1	NUM
ejpam-5019	249	12	,	,	PUNCT
ejpam-5019	249	13	(	(	PUNCT
ejpam-5019	249	14	ii	ii	NOUN
ejpam-5019	249	15	)	)	PUNCT
ejpam-5019	249	16	α	α	PROPN
ejpam-5019	249	17	(	(	PUNCT
ejpam-5019	249	18	2n	2n	NUM
ejpam-5019	249	19	−	−	PROPN
ejpam-5019	249	20	n1	n1	PROPN
ejpam-5019	249	21	−	−	PROPN
ejpam-5019	249	22	n2	n2	NOUN
ejpam-5019	249	23	−	−	PROPN
ejpam-5019	249	24	1)−	1)−	PROPN
ejpam-5019	249	25	β	β	PROPN
ejpam-5019	249	26	+	+	CCONJ
ejpam-5019	249	27	δ	δ	PROPN
ejpam-5019	249	28	with	with	ADP
ejpam-5019	249	29	algebraic	algebraic	ADJ
ejpam-5019	249	30	multiplicity	multiplicity	NOUN
ejpam-5019	249	31	n2	n2	NOUN
ejpam-5019	249	32	−	−	PROPN
ejpam-5019	249	33	1	1	NUM
ejpam-5019	249	34	,	,	PUNCT
ejpam-5019	249	35	(	(	PUNCT
ejpam-5019	249	36	iii	iii	X
ejpam-5019	249	37	)	)	PUNCT
ejpam-5019	249	38	α	α	PROPN
ejpam-5019	249	39	(	(	PUNCT
ejpam-5019	249	40	2n	2n	NUM
ejpam-5019	249	41	−	−	NOUN
ejpam-5019	249	42	n1	n1	PROPN
ejpam-5019	249	43	−	−	PROPN
ejpam-5019	249	44	n3	n3	NOUN
ejpam-5019	249	45	−	−	PROPN
ejpam-5019	249	46	1)−	1)−	PROPN
ejpam-5019	249	47	β	β	PROPN
ejpam-5019	249	48	+	+	CCONJ
ejpam-5019	249	49	δ	δ	PROPN
ejpam-5019	249	50	with	with	ADP
ejpam-5019	249	51	algebraic	algebraic	ADJ
ejpam-5019	249	52	multiplicity	multiplicity	NOUN
ejpam-5019	249	53	n3	n3	NOUN
ejpam-5019	249	54	−	−	PROPN
ejpam-5019	249	55	1	1	NUM
ejpam-5019	249	56	,	,	PUNCT
ejpam-5019	249	57	and	and	CCONJ
ejpam-5019	249	58	the	the	DET
ejpam-5019	249	59	eigenvalues	eigenvalue	NOUN
ejpam-5019	249	60	of	of	ADP
ejpam-5019	249	61	the	the	DET
ejpam-5019	249	62	matrix	matrix	NOUN
ejpam-5019	249	63	(	(	PUNCT
ejpam-5019	249	64	iv	iv	X
ejpam-5019	249	65	)	)	PUNCT
ejpam-5019	249	66			ADJ
ejpam-5019	249	67	α	α	NOUN
ejpam-5019	249	68	(	(	PUNCT
ejpam-5019	249	69	n	n	CCONJ
ejpam-5019	249	70	−	−	PROPN
ejpam-5019	249	71	1	1	NUM
ejpam-5019	249	72	)	)	PUNCT
ejpam-5019	249	73	+	+	CCONJ
ejpam-5019	249	74	(	(	PUNCT
ejpam-5019	249	75	n1	n1	NOUN
ejpam-5019	249	76	−	−	PROPN
ejpam-5019	249	77	1)β+	1)β+	NUM
ejpam-5019	249	78	γn1	γn1	NOUN
ejpam-5019	250	1	+	+	CCONJ
ejpam-5019	250	2	δ	δ	PROPN
ejpam-5019	250	3	(	(	PUNCT
ejpam-5019	250	4	β	β	X
ejpam-5019	250	5	+	+	X
ejpam-5019	250	6	γ)n2	γ)n2	PROPN
ejpam-5019	250	7	(	(	PUNCT
ejpam-5019	250	8	β	β	X
ejpam-5019	250	9	+	+	X
ejpam-5019	250	10	γ)n3	γ)n3	PROPN
ejpam-5019	250	11	(	(	PUNCT
ejpam-5019	250	12	β	β	X
ejpam-5019	250	13	+	+	CCONJ
ejpam-5019	250	14	γ)n1	γ)n1	PROPN
ejpam-5019	250	15	α	α	PROPN
ejpam-5019	250	16	(	(	PUNCT
ejpam-5019	250	17	2n	2n	NUM
ejpam-5019	250	18	−	−	PROPN
ejpam-5019	250	19	n1	n1	PROPN
ejpam-5019	250	20	−	−	PROPN
ejpam-5019	250	21	n2	n2	NOUN
ejpam-5019	250	22	−	−	PROPN
ejpam-5019	250	23	1)+	1)+	NUM
ejpam-5019	250	24	(	(	PUNCT
ejpam-5019	250	25	2β	2β	NOUN
ejpam-5019	250	26	+	+	CCONJ
ejpam-5019	250	27	γ)n3	γ)n3	PROPN
ejpam-5019	250	28	(	(	PUNCT
ejpam-5019	250	29	n2	n2	ADJ
ejpam-5019	250	30	−	−	PROPN
ejpam-5019	250	31	1)β	1)β	NUM
ejpam-5019	250	32	+	+	CCONJ
ejpam-5019	250	33	γn2	γn2	NOUN
ejpam-5019	251	1	+	+	CCONJ
ejpam-5019	251	2	δ	δ	PROPN
ejpam-5019	251	3	(	(	PUNCT
ejpam-5019	251	4	β	β	X
ejpam-5019	251	5	+	+	X
ejpam-5019	251	6	γ)n1	γ)n1	PROPN
ejpam-5019	251	7	(	(	PUNCT
ejpam-5019	251	8	2β	2β	NOUN
ejpam-5019	251	9	+	+	CCONJ
ejpam-5019	251	10	γ)n2	γ)n2	ADJ
ejpam-5019	251	11	α	α	NOUN
ejpam-5019	251	12	(	(	PUNCT
ejpam-5019	251	13	2n	2n	NUM
ejpam-5019	251	14	−	−	NOUN
ejpam-5019	251	15	n1	n1	PROPN
ejpam-5019	251	16	−	−	PROPN
ejpam-5019	251	17	n3	n3	NOUN
ejpam-5019	251	18	−	−	PROPN
ejpam-5019	251	19	1)+	1)+	NUM
ejpam-5019	251	20	(	(	PUNCT
ejpam-5019	251	21	n3	n3	NOUN
ejpam-5019	251	22	−	−	PROPN
ejpam-5019	251	23	1)β	1)β	PROPN
ejpam-5019	251	24	+	+	CCONJ
ejpam-5019	251	25	γn3	γn3	NOUN
ejpam-5019	251	26	+	+	CCONJ
ejpam-5019	251	27	δ	δ	NOUN
ejpam-5019	251	28			NOUN
ejpam-5019	251	29	proof	proof	NOUN
ejpam-5019	251	30	.	.	PUNCT
ejpam-5019	252	1	in	in	ADP
ejpam-5019	252	2	theorem	theorem	NOUN
ejpam-5019	252	3	3	3	NUM
ejpam-5019	252	4	,	,	PUNCT
ejpam-5019	252	5	by	by	ADP
ejpam-5019	252	6	substituting	substitute	VERB
ejpam-5019	252	7	ri	ri	PROPN
ejpam-5019	252	8	=	=	PROPN
ejpam-5019	252	9	ni−1	ni−1	PROPN
ejpam-5019	252	10	,	,	PUNCT
ejpam-5019	252	11	λi	λi	NOUN
ejpam-5019	252	12	2	2	NUM
ejpam-5019	252	13	,	,	PUNCT
ejpam-5019	252	14	λ	λ	PROPN
ejpam-5019	252	15	i	i	PRON
ejpam-5019	252	16	3	3	NUM
ejpam-5019	252	17	,	,	PUNCT
ejpam-5019	252	18	.	.	PUNCT
ejpam-5019	252	19	.	.	PUNCT
ejpam-5019	252	20	.	.	PUNCT
ejpam-5019	253	1	λ	λ	INTJ
ejpam-5019	253	2	i	i	PRON
ejpam-5019	253	3	ni	ni	PROPN
ejpam-5019	253	4	=	=	PROPN
ejpam-5019	253	5	−1	−1	PROPN
ejpam-5019	253	6	,	,	PUNCT
ejpam-5019	253	7	for	for	ADP
ejpam-5019	253	8	all	all	DET
ejpam-5019	253	9	i	i	PRON
ejpam-5019	253	10	=	=	NOUN
ejpam-5019	253	11	1	1	NUM
ejpam-5019	253	12	,	,	PUNCT
ejpam-5019	253	13	2	2	NUM
ejpam-5019	253	14	,	,	PUNCT
ejpam-5019	253	15	3	3	NUM
ejpam-5019	253	16	,	,	PUNCT
ejpam-5019	253	17	we	we	PRON
ejpam-5019	253	18	obtain	obtain	VERB
ejpam-5019	253	19	the	the	DET
ejpam-5019	253	20	universal	universal	ADJ
ejpam-5019	253	21	distance	distance	NOUN
ejpam-5019	253	22	spectrum	spectrum	NOUN
ejpam-5019	253	23	of	of	ADP
ejpam-5019	253	24	g.	g.	PROPN
ejpam-5019	253	25	this	this	PRON
ejpam-5019	253	26	completes	complete	VERB
ejpam-5019	253	27	the	the	DET
ejpam-5019	253	28	proof	proof	NOUN
ejpam-5019	253	29	.	.	PUNCT
ejpam-5019	254	1	3	3	X
ejpam-5019	254	2	.	.	X
ejpam-5019	254	3	eigenvalues	eigenvalue	NOUN
ejpam-5019	254	4	of	of	ADP
ejpam-5019	254	5	universal	universal	ADJ
ejpam-5019	254	6	distance	distance	NOUN
ejpam-5019	254	7	matrix	matrix	NOUN
ejpam-5019	254	8	of	of	ADP
ejpam-5019	254	9	generalized	generalized	ADJ
ejpam-5019	254	10	joined	join	VERB
ejpam-5019	254	11	union	union	NOUN
ejpam-5019	254	12	of	of	ADP
ejpam-5019	254	13	graphs	graph	NOUN
ejpam-5019	254	14	the	the	DET
ejpam-5019	254	15	generalized	generalize	VERB
ejpam-5019	254	16	joined	joined	ADJ
ejpam-5019	254	17	union	union	NOUN
ejpam-5019	254	18	is	be	AUX
ejpam-5019	254	19	a	a	DET
ejpam-5019	254	20	nice	nice	ADJ
ejpam-5019	254	21	graph	graph	NOUN
ejpam-5019	254	22	operation	operation	NOUN
ejpam-5019	254	23	.	.	PUNCT
ejpam-5019	255	1	it	it	PRON
ejpam-5019	255	2	is	be	AUX
ejpam-5019	255	3	also	also	ADV
ejpam-5019	255	4	called	call	VERB
ejpam-5019	255	5	h	h	NOUN
ejpam-5019	255	6	-	-	PUNCT
ejpam-5019	255	7	join	join	NOUN
ejpam-5019	255	8	[	[	X
ejpam-5019	255	9	6	6	NUM
ejpam-5019	255	10	]	]	PUNCT
ejpam-5019	255	11	or	or	CCONJ
ejpam-5019	255	12	generalized	generalized	ADJ
ejpam-5019	255	13	composition	composition	NOUN
ejpam-5019	255	14	[	[	X
ejpam-5019	255	15	19	19	NUM
ejpam-5019	255	16	]	]	PUNCT
ejpam-5019	255	17	.	.	PUNCT
ejpam-5019	256	1	let	let	VERB
ejpam-5019	256	2	h	h	NOUN
ejpam-5019	256	3	=	=	PUNCT
ejpam-5019	256	4	(	(	PUNCT
ejpam-5019	256	5	v	v	NOUN
ejpam-5019	256	6	,	,	PUNCT
ejpam-5019	256	7	e	e	NOUN
ejpam-5019	256	8	)	)	PUNCT
ejpam-5019	256	9	be	be	VERB
ejpam-5019	256	10	any	any	DET
ejpam-5019	256	11	arbitrary	arbitrary	ADJ
ejpam-5019	256	12	graph	graph	NOUN
ejpam-5019	256	13	of	of	ADP
ejpam-5019	256	14	order	order	NOUN
ejpam-5019	256	15	n	n	NOUN
ejpam-5019	256	16	and	and	CCONJ
ejpam-5019	256	17	gi	gi	INTJ
ejpam-5019	256	18	=	=	SYM
ejpam-5019	256	19	(	(	PUNCT
ejpam-5019	256	20	vi	vi	PROPN
ejpam-5019	256	21	,	,	PUNCT
ejpam-5019	256	22	ei	ei	NOUN
ejpam-5019	256	23	)	)	PUNCT
ejpam-5019	256	24	be	be	AUX
ejpam-5019	256	25	regular	regular	ADJ
ejpam-5019	256	26	graphs	graph	NOUN
ejpam-5019	256	27	of	of	ADP
ejpam-5019	256	28	order	order	NOUN
ejpam-5019	256	29	ni	ni	NOUN
ejpam-5019	256	30	;	;	PUNCT
ejpam-5019	256	31	i	i	NOUN
ejpam-5019	256	32	=	=	NOUN
ejpam-5019	256	33	1	1	NUM
ejpam-5019	256	34	,	,	PUNCT
ejpam-5019	256	35	2	2	NUM
ejpam-5019	256	36	,	,	PUNCT
ejpam-5019	256	37	.	.	PUNCT
ejpam-5019	256	38	.	.	PUNCT
ejpam-5019	256	39	.	.	PUNCT
ejpam-5019	257	1	n.	n.	VERB
ejpam-5019	257	2	the	the	DET
ejpam-5019	257	3	generalized	generalize	VERB
ejpam-5019	257	4	joined	joined	ADJ
ejpam-5019	257	5	union	union	NOUN
ejpam-5019	257	6	graph	graph	NOUN
ejpam-5019	257	7	is	be	AUX
ejpam-5019	257	8	denoted	denote	VERB
ejpam-5019	257	9	by	by	ADP
ejpam-5019	257	10	g	g	PROPN
ejpam-5019	257	11	(	(	PUNCT
ejpam-5019	257	12	p	p	X
ejpam-5019	257	13	,	,	PUNCT
ejpam-5019	257	14	q	q	NOUN
ejpam-5019	257	15	)	)	PUNCT
ejpam-5019	257	16	=	=	SYM
ejpam-5019	257	17	h	h	NOUN
ejpam-5019	257	18	(	(	PUNCT
ejpam-5019	257	19	g1	g1	PROPN
ejpam-5019	257	20	,	,	PUNCT
ejpam-5019	257	21	g2	g2	PROPN
ejpam-5019	257	22	,	,	PUNCT
ejpam-5019	257	23	.	.	PUNCT
ejpam-5019	257	24	.	.	PUNCT
ejpam-5019	258	1	.	.	PUNCT
ejpam-5019	259	1	,	,	PUNCT
ejpam-5019	259	2	gn	gn	PROPN
ejpam-5019	259	3	)	)	PUNCT
ejpam-5019	259	4	with	with	ADP
ejpam-5019	259	5	vertex	vertex	NOUN
ejpam-5019	259	6	set	set	NOUN
ejpam-5019	259	7	p	p	NOUN
ejpam-5019	259	8	(	(	PUNCT
ejpam-5019	259	9	g	g	NOUN
ejpam-5019	259	10	)	)	PUNCT
ejpam-5019	259	11	=	=	SYM
ejpam-5019	259	12	⋃n	⋃n	PROPN
ejpam-5019	259	13	i=1	i=1	PROPN
ejpam-5019	259	14	v	v	PROPN
ejpam-5019	259	15	(	(	PUNCT
ejpam-5019	259	16	gi	gi	NOUN
ejpam-5019	259	17	)	)	PUNCT
ejpam-5019	259	18	and	and	CCONJ
ejpam-5019	259	19	edge	edge	NOUN
ejpam-5019	259	20	set	set	VERB
ejpam-5019	259	21	q	q	PROPN
ejpam-5019	260	1	(	(	PUNCT
ejpam-5019	260	2	g	g	NOUN
ejpam-5019	260	3	)	)	PUNCT
ejpam-5019	260	4	=	=	SYM
ejpam-5019	260	5	(	(	PUNCT
ejpam-5019	260	6	⋃n	⋃n	PROPN
ejpam-5019	260	7	i=1e	i=1e	PROPN
ejpam-5019	260	8	(	(	PUNCT
ejpam-5019	260	9	gi	gi	NOUN
ejpam-5019	260	10	)	)	PUNCT
ejpam-5019	260	11	)	)	PUNCT
ejpam-5019	261	1	∪	∪	ADP
ejpam-5019	261	2	(	(	PUNCT
ejpam-5019	261	3	⋃	⋃	NOUN
ejpam-5019	261	4	vi	vi	NOUN
ejpam-5019	261	5	,	,	PUNCT
ejpam-5019	261	6	vj∈e(h	vj∈e(h	NOUN
ejpam-5019	261	7	)	)	PUNCT
ejpam-5019	261	8	{	{	PUNCT
ejpam-5019	261	9	e	e	X
ejpam-5019	261	10	(	(	PUNCT
ejpam-5019	261	11	gi∇gj	gi∇gj	NOUN
ejpam-5019	261	12	)	)	PUNCT
ejpam-5019	261	13	}	}	PUNCT
ejpam-5019	261	14	)	)	PUNCT
ejpam-5019	261	15	.	.	PUNCT
ejpam-5019	262	1	where	where	SCONJ
ejpam-5019	262	2	e	e	X
ejpam-5019	262	3	(	(	PUNCT
ejpam-5019	262	4	gi∇gj	gi∇gj	X
ejpam-5019	262	5	)	)	PUNCT
ejpam-5019	262	6	=	=	PRON
ejpam-5019	262	7	{	{	PUNCT
ejpam-5019	262	8	xy	xy	NOUN
ejpam-5019	262	9	:	:	PUNCT
ejpam-5019	262	10	x	x	X
ejpam-5019	262	11	∈	∈	NOUN
ejpam-5019	262	12	v	v	X
ejpam-5019	262	13	(	(	PUNCT
ejpam-5019	262	14	gi	gi	INTJ
ejpam-5019	262	15	)	)	PUNCT
ejpam-5019	262	16	,	,	PUNCT
ejpam-5019	262	17	y	y	PROPN
ejpam-5019	262	18	∈	∈	PROPN
ejpam-5019	262	19	v	v	PROPN
ejpam-5019	262	20	(	(	PUNCT
ejpam-5019	262	21	gj	gj	NOUN
ejpam-5019	262	22	)	)	PUNCT
ejpam-5019	262	23	}	}	PUNCT
ejpam-5019	262	24	.	.	PUNCT
ejpam-5019	263	1	this	this	DET
ejpam-5019	263	2	graph	graph	NOUN
ejpam-5019	263	3	g	g	PROPN
ejpam-5019	263	4	can	can	AUX
ejpam-5019	263	5	be	be	AUX
ejpam-5019	263	6	constructed	construct	VERB
ejpam-5019	263	7	by	by	ADP
ejpam-5019	263	8	taking	take	VERB
ejpam-5019	263	9	the	the	DET
ejpam-5019	263	10	union	union	NOUN
ejpam-5019	263	11	of	of	ADP
ejpam-5019	263	12	g1	g1	PROPN
ejpam-5019	263	13	,	,	PUNCT
ejpam-5019	263	14	g2	g2	PROPN
ejpam-5019	263	15	,	,	PUNCT
ejpam-5019	263	16	.	.	PUNCT
ejpam-5019	263	17	.	.	PUNCT
ejpam-5019	264	1	.	.	PUNCT
ejpam-5019	265	1	,	,	PUNCT
ejpam-5019	265	2	gn	gn	PROPN
ejpam-5019	265	3	and	and	CCONJ
ejpam-5019	265	4	joining	join	VERB
ejpam-5019	265	5	every	every	DET
ejpam-5019	265	6	pair	pair	NOUN
ejpam-5019	265	7	of	of	ADP
ejpam-5019	265	8	vertices	vertex	NOUN
ejpam-5019	265	9	between	between	ADP
ejpam-5019	265	10	gi	gi	NOUN
ejpam-5019	265	11	and	and	CCONJ
ejpam-5019	265	12	gj	gj	VERB
ejpam-5019	265	13	whenever	whenever	SCONJ
ejpam-5019	265	14	vi	vi	PROPN
ejpam-5019	265	15	and	and	CCONJ
ejpam-5019	265	16	vj	vj	NOUN
ejpam-5019	265	17	are	be	AUX
ejpam-5019	265	18	adjacent	adjacent	ADJ
ejpam-5019	265	19	in	in	ADP
ejpam-5019	265	20	h.	h.	PROPN
ejpam-5019	265	21	s.	s.	PROPN
ejpam-5019	265	22	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	265	23	,	,	PUNCT
ejpam-5019	265	24	k.	k.	PROPN
ejpam-5019	265	25	desikan	desikan	PROPN
ejpam-5019	265	26	/	/	SYM
ejpam-5019	265	27	eur	eur	PROPN
ejpam-5019	265	28	.	.	PUNCT
ejpam-5019	266	1	j.	j.	PROPN
ejpam-5019	266	2	pure	pure	PROPN
ejpam-5019	266	3	appl	appl	PROPN
ejpam-5019	266	4	.	.	PROPN
ejpam-5019	266	5	math	math	PROPN
ejpam-5019	266	6	,	,	PUNCT
ejpam-5019	266	7	17	17	NUM
ejpam-5019	266	8	(	(	PUNCT
ejpam-5019	266	9	1	1	NUM
ejpam-5019	266	10	)	)	PUNCT
ejpam-5019	266	11	(	(	PUNCT
ejpam-5019	266	12	2024	2024	NUM
ejpam-5019	266	13	)	)	PUNCT
ejpam-5019	266	14	,	,	PUNCT
ejpam-5019	266	15	462	462	NUM
ejpam-5019	266	16	-	-	SYM
ejpam-5019	266	17	476	476	NUM
ejpam-5019	266	18	471	471	NUM
ejpam-5019	266	19	theorem	theorem	NOUN
ejpam-5019	266	20	4	4	NUM
ejpam-5019	266	21	.	.	PUNCT
ejpam-5019	266	22	suppose	suppose	VERB
ejpam-5019	266	23	h	h	NOUN
ejpam-5019	266	24	is	be	AUX
ejpam-5019	266	25	a	a	DET
ejpam-5019	266	26	graph	graph	NOUN
ejpam-5019	266	27	and	and	CCONJ
ejpam-5019	266	28	its	its	PRON
ejpam-5019	266	29	vertex	vertex	NOUN
ejpam-5019	266	30	set	set	VERB
ejpam-5019	266	31	v	v	NOUN
ejpam-5019	266	32	(	(	PUNCT
ejpam-5019	266	33	h	h	NOUN
ejpam-5019	266	34	)	)	PUNCT
ejpam-5019	266	35	=	=	SYM
ejpam-5019	266	36	{	{	PUNCT
ejpam-5019	266	37	v1	v1	PROPN
ejpam-5019	266	38	,	,	PUNCT
ejpam-5019	266	39	v2	v2	PROPN
ejpam-5019	266	40	,	,	PUNCT
ejpam-5019	266	41	.	.	PUNCT
ejpam-5019	266	42	.	.	PUNCT
ejpam-5019	267	1	.	.	PUNCT
ejpam-5019	268	1	,	,	PUNCT
ejpam-5019	268	2	vn	vn	VERB
ejpam-5019	268	3	}	}	PUNCT
ejpam-5019	268	4	with	with	ADP
ejpam-5019	268	5	diameter	diameter	NOUN
ejpam-5019	268	6	at	at	ADP
ejpam-5019	268	7	most	most	ADV
ejpam-5019	268	8	2	2	NUM
ejpam-5019	268	9	.	.	PUNCT
ejpam-5019	269	1	let	let	VERB
ejpam-5019	269	2	gi	gi	PART
ejpam-5019	269	3	be	be	AUX
ejpam-5019	269	4	a	a	DET
ejpam-5019	269	5	ri−regular	ri−regular	ADJ
ejpam-5019	269	6	graph	graph	NOUN
ejpam-5019	269	7	of	of	ADP
ejpam-5019	269	8	order	order	NOUN
ejpam-5019	269	9	ni	ni	PROPN
ejpam-5019	269	10	.	.	PROPN
ejpam-5019	269	11	denote	denote	VERB
ejpam-5019	269	12	the	the	DET
ejpam-5019	269	13	adjacency	adjacency	NOUN
ejpam-5019	269	14	eigenvalues	eigenvalue	VERB
ejpam-5019	269	15	of	of	ADP
ejpam-5019	269	16	gi	gi	NOUN
ejpam-5019	269	17	as	as	ADP
ejpam-5019	269	18	ri	ri	PROPN
ejpam-5019	269	19	=	=	SYM
ejpam-5019	269	20	λi	λi	ADP
ejpam-5019	269	21	1	1	NUM
ejpam-5019	269	22	,	,	PUNCT
ejpam-5019	269	23	λ	λ	VERB
ejpam-5019	269	24	i	i	PRON
ejpam-5019	269	25	2	2	NUM
ejpam-5019	269	26	,	,	PUNCT
ejpam-5019	269	27	.	.	PUNCT
ejpam-5019	269	28	.	.	PUNCT
ejpam-5019	270	1	.	.	PUNCT
ejpam-5019	271	1	,	,	PUNCT
ejpam-5019	271	2	λ	λ	INTJ
ejpam-5019	271	3	i	i	PRON
ejpam-5019	271	4	ni	ni	PROPN
ejpam-5019	271	5	;	;	PUNCT
ejpam-5019	271	6	i	i	NOUN
ejpam-5019	271	7	=	=	NOUN
ejpam-5019	271	8	1	1	NUM
ejpam-5019	271	9	,	,	PUNCT
ejpam-5019	271	10	2	2	NUM
ejpam-5019	271	11	,	,	PUNCT
ejpam-5019	271	12	.	.	PUNCT
ejpam-5019	271	13	.	.	PUNCT
ejpam-5019	272	1	.	.	PUNCT
ejpam-5019	273	1	,	,	PUNCT
ejpam-5019	273	2	n	n	CCONJ
ejpam-5019	273	3	,	,	PUNCT
ejpam-5019	273	4	respectively	respectively	ADV
ejpam-5019	273	5	.	.	PUNCT
ejpam-5019	274	1	the	the	DET
ejpam-5019	274	2	universal	universal	ADJ
ejpam-5019	274	3	distance	distance	NOUN
ejpam-5019	274	4	spectrum	spectrum	NOUN
ejpam-5019	274	5	of	of	ADP
ejpam-5019	274	6	the	the	DET
ejpam-5019	274	7	generalized	generalize	VERB
ejpam-5019	274	8	joined	join	VERB
ejpam-5019	274	9	union	union	PROPN
ejpam-5019	274	10	g	g	PROPN
ejpam-5019	274	11	=	=	PROPN
ejpam-5019	274	12	h	h	PROPN
ejpam-5019	274	13	(	(	PUNCT
ejpam-5019	274	14	g1	g1	PROPN
ejpam-5019	274	15	,	,	PUNCT
ejpam-5019	274	16	g2	g2	PROPN
ejpam-5019	274	17	,	,	PUNCT
ejpam-5019	274	18	.	.	PUNCT
ejpam-5019	274	19	.	.	PUNCT
ejpam-5019	275	1	.	.	PUNCT
ejpam-5019	276	1	,	,	PUNCT
ejpam-5019	276	2	gn	gn	PROPN
ejpam-5019	276	3	)	)	PUNCT
ejpam-5019	276	4	consists	consist	VERB
ejpam-5019	276	5	of	of	ADP
ejpam-5019	276	6	the	the	DET
ejpam-5019	276	7	eigenvalues	eigenvalues	PROPN
ejpam-5019	276	8	α	α	PROPN
ejpam-5019	276	9	(	(	PUNCT
ejpam-5019	276	10	2n	2n	NUM
ejpam-5019	276	11	−	−	PROPN
ejpam-5019	276	12	ri	ri	NOUN
ejpam-5019	277	1	−mi	−mi	ADV
ejpam-5019	278	1	−	−	PROPN
ejpam-5019	279	1	2)−	2)−	NUM
ejpam-5019	280	1	(	(	PUNCT
ejpam-5019	280	2	λi	λi	ADP
ejpam-5019	280	3	k	k	X
ejpam-5019	280	4	+	+	PROPN
ejpam-5019	280	5	2	2	NUM
ejpam-5019	280	6	)	)	PUNCT
ejpam-5019	280	7	β+δ	β+δ	NUM
ejpam-5019	280	8	;	;	PUNCT
ejpam-5019	280	9	i	i	NOUN
ejpam-5019	280	10	=	=	NOUN
ejpam-5019	280	11	1	1	NUM
ejpam-5019	280	12	,	,	PUNCT
ejpam-5019	280	13	2	2	NUM
ejpam-5019	280	14	,	,	PUNCT
ejpam-5019	280	15	.	.	PUNCT
ejpam-5019	280	16	.	.	PUNCT
ejpam-5019	281	1	.	.	PUNCT
ejpam-5019	282	1	,	,	PUNCT
ejpam-5019	282	2	n	n	CCONJ
ejpam-5019	282	3	,	,	PUNCT
ejpam-5019	282	4	k	k	PROPN
ejpam-5019	282	5	=	=	SYM
ejpam-5019	282	6	2	2	NUM
ejpam-5019	282	7	,	,	PUNCT
ejpam-5019	282	8	3	3	NUM
ejpam-5019	282	9	,	,	PUNCT
ejpam-5019	282	10	.	.	PUNCT
ejpam-5019	282	11	.	.	PUNCT
ejpam-5019	283	1	.	.	PUNCT
ejpam-5019	284	1	,	,	PUNCT
ejpam-5019	284	2	ni	ni	PROPN
ejpam-5019	284	3	,	,	PUNCT
ejpam-5019	284	4	where	where	SCONJ
ejpam-5019	284	5	n	n	NOUN
ejpam-5019	284	6	=	=	SYM
ejpam-5019	284	7	∑n	∑n	PROPN
ejpam-5019	284	8	i=1	i=1	PROPN
ejpam-5019	284	9	ni	ni	PROPN
ejpam-5019	284	10	and	and	CCONJ
ejpam-5019	284	11	mi	mi	PROPN
ejpam-5019	284	12	=	=	PROPN
ejpam-5019	284	13	∑	∑	PROPN
ejpam-5019	284	14	e(gi∇gj	e(gi∇gj	PROPN
ejpam-5019	284	15	)	)	PUNCT
ejpam-5019	284	16	nj	nj	PROPN
ejpam-5019	284	17	and	and	CCONJ
ejpam-5019	284	18	the	the	DET
ejpam-5019	284	19	other	other	ADJ
ejpam-5019	284	20	n	n	PROPN
ejpam-5019	284	21	eigenvalues	eigenvalue	NOUN
ejpam-5019	284	22	of	of	ADP
ejpam-5019	284	23	the	the	DET
ejpam-5019	284	24	quotient	quotient	NOUN
ejpam-5019	284	25	matrix	matrix	NOUN
ejpam-5019	284	26			NOUN
ejpam-5019	284	27	r11	r11	NOUN
ejpam-5019	284	28	[	[	PUNCT
ejpam-5019	284	29	β	β	X
ejpam-5019	284	30	dh	dh	NOUN
ejpam-5019	284	31	(	(	PUNCT
ejpam-5019	284	32	v1	v1	PROPN
ejpam-5019	284	33	,	,	PUNCT
ejpam-5019	284	34	v2	v2	PROPN
ejpam-5019	284	35	)	)	PUNCT
ejpam-5019	285	1	+	+	CCONJ
ejpam-5019	285	2	γ	γ	X
ejpam-5019	285	3	]	]	PUNCT
ejpam-5019	285	4	n2	n2	PROPN
ejpam-5019	285	5	.	.	PUNCT
ejpam-5019	285	6	.	.	PUNCT
ejpam-5019	285	7	.	.	PUNCT
ejpam-5019	286	1	[	[	PUNCT
ejpam-5019	286	2	β	β	X
ejpam-5019	286	3	dh	dh	NOUN
ejpam-5019	286	4	(	(	PUNCT
ejpam-5019	286	5	v1	v1	PROPN
ejpam-5019	286	6	,	,	PUNCT
ejpam-5019	286	7	vn	vn	NOUN
ejpam-5019	286	8	)	)	PUNCT
ejpam-5019	287	1	+	+	CCONJ
ejpam-5019	287	2	γ	γ	X
ejpam-5019	287	3	]	]	PUNCT
ejpam-5019	287	4	nn	nn	PROPN
ejpam-5019	287	5	[	[	X
ejpam-5019	287	6	β	β	X
ejpam-5019	287	7	dh	dh	NOUN
ejpam-5019	287	8	(	(	PUNCT
ejpam-5019	287	9	v2	v2	PROPN
ejpam-5019	287	10	,	,	PUNCT
ejpam-5019	287	11	v1	v1	NOUN
ejpam-5019	287	12	)	)	PUNCT
ejpam-5019	288	1	+	+	CCONJ
ejpam-5019	288	2	γ	γ	X
ejpam-5019	288	3	]	]	PUNCT
ejpam-5019	288	4	n1	n1	PROPN
ejpam-5019	288	5	r22	r22	NOUN
ejpam-5019	288	6	.	.	PUNCT
ejpam-5019	288	7	.	.	PUNCT
ejpam-5019	288	8	.	.	PUNCT
ejpam-5019	289	1	[	[	PUNCT
ejpam-5019	289	2	β	β	X
ejpam-5019	289	3	dh	dh	NOUN
ejpam-5019	289	4	(	(	PUNCT
ejpam-5019	289	5	v2	v2	PROPN
ejpam-5019	289	6	,	,	PUNCT
ejpam-5019	289	7	vn	vn	NOUN
ejpam-5019	289	8	)	)	PUNCT
ejpam-5019	290	1	+	+	CCONJ
ejpam-5019	290	2	γ	γ	X
ejpam-5019	290	3	]	]	PUNCT
ejpam-5019	290	4	nn	nn	PROPN
ejpam-5019	290	5	...	...	PUNCT
ejpam-5019	290	6	...	...	PUNCT
ejpam-5019	290	7	...	...	PUNCT
ejpam-5019	290	8	...	...	PUNCT
ejpam-5019	291	1	[	[	PUNCT
ejpam-5019	291	2	β	β	X
ejpam-5019	291	3	dh	dh	NOUN
ejpam-5019	291	4	(	(	PUNCT
ejpam-5019	291	5	vn	vn	PROPN
ejpam-5019	291	6	,	,	PUNCT
ejpam-5019	291	7	v1	v1	NOUN
ejpam-5019	291	8	)	)	PUNCT
ejpam-5019	292	1	+	+	CCONJ
ejpam-5019	292	2	γ	γ	X
ejpam-5019	292	3	]	]	X
ejpam-5019	292	4	n1	n1	PROPN
ejpam-5019	292	5	[	[	PUNCT
ejpam-5019	292	6	β	β	X
ejpam-5019	292	7	dh	dh	NOUN
ejpam-5019	292	8	(	(	PUNCT
ejpam-5019	292	9	vn	vn	PROPN
ejpam-5019	292	10	,	,	PUNCT
ejpam-5019	292	11	v2	v2	PROPN
ejpam-5019	292	12	)	)	PUNCT
ejpam-5019	293	1	+	+	CCONJ
ejpam-5019	293	2	γ	γ	X
ejpam-5019	293	3	]	]	PUNCT
ejpam-5019	293	4	n2	n2	PROPN
ejpam-5019	293	5	.	.	PUNCT
ejpam-5019	293	6	.	.	PUNCT
ejpam-5019	293	7	.	.	PUNCT
ejpam-5019	294	1	rnn	rnn	PROPN
ejpam-5019	294	2			PROPN
ejpam-5019	294	3	,	,	PUNCT
ejpam-5019	294	4	where	where	SCONJ
ejpam-5019	294	5	rii	rii	NOUN
ejpam-5019	294	6	=	=	PUNCT
ejpam-5019	294	7	α	α	PROPN
ejpam-5019	294	8	(	(	PUNCT
ejpam-5019	294	9	2n	2n	NUM
ejpam-5019	294	10	−	−	PROPN
ejpam-5019	294	11	ri	ri	NOUN
ejpam-5019	295	1	−mi	−mi	ADV
ejpam-5019	295	2	−	−	ADP
ejpam-5019	295	3	2	2	NUM
ejpam-5019	295	4	)	)	PUNCT
ejpam-5019	295	5	−	−	PROPN
ejpam-5019	295	6	(	(	PUNCT
ejpam-5019	295	7	ri	ri	NOUN
ejpam-5019	295	8	−	−	NUM
ejpam-5019	295	9	2ni	2ni	NOUN
ejpam-5019	296	1	+	+	CCONJ
ejpam-5019	296	2	2)β	2)β	NOUN
ejpam-5019	296	3	+	+	CCONJ
ejpam-5019	296	4	γni	γni	PROPN
ejpam-5019	296	5	+	+	CCONJ
ejpam-5019	296	6	δ	δ	PROPN
ejpam-5019	296	7	,	,	PUNCT
ejpam-5019	296	8	;	;	PUNCT
ejpam-5019	296	9	i	i	NOUN
ejpam-5019	296	10	=	=	NOUN
ejpam-5019	296	11	1	1	NUM
ejpam-5019	296	12	,	,	PUNCT
ejpam-5019	296	13	2	2	NUM
ejpam-5019	296	14	,	,	PUNCT
ejpam-5019	296	15	.	.	PUNCT
ejpam-5019	296	16	.	.	PUNCT
ejpam-5019	297	1	.	.	PUNCT
ejpam-5019	298	1	,	,	PUNCT
ejpam-5019	298	2	n	n	CCONJ
ejpam-5019	298	3	,	,	PUNCT
ejpam-5019	298	4	and	and	CCONJ
ejpam-5019	298	5	dh	dh	PROPN
ejpam-5019	298	6	(	(	PUNCT
ejpam-5019	298	7	vi	vi	PROPN
ejpam-5019	298	8	,	,	PUNCT
ejpam-5019	298	9	vj	vj	NOUN
ejpam-5019	298	10	)	)	PUNCT
ejpam-5019	298	11	is	be	AUX
ejpam-5019	298	12	the	the	DET
ejpam-5019	298	13	length	length	NOUN
ejpam-5019	298	14	of	of	ADP
ejpam-5019	298	15	the	the	DET
ejpam-5019	298	16	shortest	short	ADJ
ejpam-5019	298	17	path	path	NOUN
ejpam-5019	298	18	between	between	ADP
ejpam-5019	298	19	vi	vi	PROPN
ejpam-5019	298	20	and	and	CCONJ
ejpam-5019	298	21	vj	vj	PROPN
ejpam-5019	298	22	in	in	ADP
ejpam-5019	298	23	h.	h.	PROPN
ejpam-5019	298	24	proof	proof	NOUN
ejpam-5019	298	25	.	.	PUNCT
ejpam-5019	299	1	using	use	VERB
ejpam-5019	299	2	the	the	DET
ejpam-5019	299	3	appropriate	appropriate	ADJ
ejpam-5019	299	4	labelling	labelling	NOUN
ejpam-5019	299	5	of	of	ADP
ejpam-5019	299	6	the	the	DET
ejpam-5019	299	7	vertices	vertex	NOUN
ejpam-5019	299	8	of	of	ADP
ejpam-5019	299	9	the	the	DET
ejpam-5019	299	10	graph	graph	NOUN
ejpam-5019	299	11	g	g	NOUN
ejpam-5019	299	12	,	,	PUNCT
ejpam-5019	299	13	the	the	DET
ejpam-5019	299	14	universal	universal	ADJ
ejpam-5019	299	15	distance	distance	NOUN
ejpam-5019	299	16	spectrum	spectrum	NOUN
ejpam-5019	299	17	of	of	ADP
ejpam-5019	299	18	the	the	DET
ejpam-5019	299	19	generalized	generalize	VERB
ejpam-5019	299	20	distance	distance	NOUN
ejpam-5019	299	21	matrix	matrix	NOUN
ejpam-5019	299	22	can	can	AUX
ejpam-5019	299	23	be	be	AUX
ejpam-5019	299	24	expressed	express	VERB
ejpam-5019	299	25	in	in	ADP
ejpam-5019	299	26	the	the	DET
ejpam-5019	299	27	following	follow	VERB
ejpam-5019	299	28	form	form	NOUN
ejpam-5019	299	29	ud	ud	INTJ
ejpam-5019	299	30	(	(	PUNCT
ejpam-5019	299	31	g	g	NOUN
ejpam-5019	299	32	)	)	PUNCT
ejpam-5019	299	33	=	=	SYM
ejpam-5019	299	34	αtr	αtr	NOUN
ejpam-5019	299	35	(	(	PUNCT
ejpam-5019	299	36	g	g	NOUN
ejpam-5019	299	37	)	)	PUNCT
ejpam-5019	299	38	+	+	NUM
ejpam-5019	299	39	βd	βd	INTJ
ejpam-5019	299	40	(	(	PUNCT
ejpam-5019	299	41	g	g	NOUN
ejpam-5019	299	42	)	)	PUNCT
ejpam-5019	299	43	+	+	CCONJ
ejpam-5019	299	44	γj	γj	ADP
ejpam-5019	299	45	+	+	CCONJ
ejpam-5019	299	46	δ	δ	NOUN
ejpam-5019	299	47	=	=	SYM
ejpam-5019	299	48			NOUN
ejpam-5019	300	1	s11	s11	X
ejpam-5019	300	2	[	[	PUNCT
ejpam-5019	300	3	β	β	X
ejpam-5019	300	4	dh	dh	NOUN
ejpam-5019	300	5	(	(	PUNCT
ejpam-5019	300	6	v1	v1	PROPN
ejpam-5019	300	7	,	,	PUNCT
ejpam-5019	300	8	v2	v2	PROPN
ejpam-5019	300	9	)	)	PUNCT
ejpam-5019	301	1	+	+	CCONJ
ejpam-5019	301	2	γ	γ	X
ejpam-5019	301	3	]	]	X
ejpam-5019	301	4	jn1×n2	jn1×n2	PROPN
ejpam-5019	301	5	.	.	PUNCT
ejpam-5019	301	6	.	.	PUNCT
ejpam-5019	301	7	.	.	PUNCT
ejpam-5019	302	1	[	[	PUNCT
ejpam-5019	302	2	β	β	X
ejpam-5019	302	3	dh	dh	NOUN
ejpam-5019	302	4	(	(	PUNCT
ejpam-5019	302	5	v1	v1	PROPN
ejpam-5019	302	6	,	,	PUNCT
ejpam-5019	302	7	vn	vn	NOUN
ejpam-5019	302	8	)	)	PUNCT
ejpam-5019	303	1	+	+	CCONJ
ejpam-5019	303	2	γ	γ	X
ejpam-5019	303	3	]	]	PUNCT
ejpam-5019	303	4	jn1×nn	jn1×nn	PROPN
ejpam-5019	303	5	[	[	PUNCT
ejpam-5019	303	6	β	β	X
ejpam-5019	303	7	dh	dh	NOUN
ejpam-5019	303	8	(	(	PUNCT
ejpam-5019	303	9	v2	v2	PROPN
ejpam-5019	303	10	,	,	PUNCT
ejpam-5019	303	11	v1	v1	NOUN
ejpam-5019	303	12	)	)	PUNCT
ejpam-5019	303	13	+	+	CCONJ
ejpam-5019	303	14	γ	γ	X
ejpam-5019	303	15	]	]	PUNCT
ejpam-5019	303	16	jn2×n1	jn2×n1	PROPN
ejpam-5019	303	17	s22	s22	NOUN
ejpam-5019	303	18	.	.	PUNCT
ejpam-5019	303	19	.	.	PUNCT
ejpam-5019	303	20	.	.	PUNCT
ejpam-5019	304	1	[	[	PUNCT
ejpam-5019	304	2	β	β	X
ejpam-5019	304	3	dh	dh	NOUN
ejpam-5019	304	4	(	(	PUNCT
ejpam-5019	304	5	v2	v2	PROPN
ejpam-5019	304	6	,	,	PUNCT
ejpam-5019	304	7	vn	vn	NOUN
ejpam-5019	304	8	)	)	PUNCT
ejpam-5019	305	1	+	+	CCONJ
ejpam-5019	305	2	γ	γ	X
ejpam-5019	305	3	]	]	X
ejpam-5019	305	4	jn2×nn	jn2×nn	PROPN
ejpam-5019	305	5	...	...	PUNCT
ejpam-5019	305	6	...	...	PUNCT
ejpam-5019	305	7	...	...	PUNCT
ejpam-5019	305	8	...	...	PUNCT
ejpam-5019	306	1	[	[	PUNCT
ejpam-5019	306	2	β	β	X
ejpam-5019	306	3	dh	dh	NOUN
ejpam-5019	306	4	(	(	PUNCT
ejpam-5019	306	5	vn	vn	PROPN
ejpam-5019	306	6	,	,	PUNCT
ejpam-5019	306	7	v1	v1	NOUN
ejpam-5019	306	8	)	)	PUNCT
ejpam-5019	307	1	+	+	CCONJ
ejpam-5019	307	2	γ	γ	X
ejpam-5019	307	3	]	]	PUNCT
ejpam-5019	307	4	jnn×n1	jnn×n1	PROPN
ejpam-5019	307	5	[	[	PUNCT
ejpam-5019	307	6	β	β	X
ejpam-5019	307	7	dh	dh	NOUN
ejpam-5019	307	8	(	(	PUNCT
ejpam-5019	307	9	vn	vn	PROPN
ejpam-5019	307	10	,	,	PUNCT
ejpam-5019	307	11	v2	v2	PROPN
ejpam-5019	307	12	)	)	PUNCT
ejpam-5019	308	1	+	+	CCONJ
ejpam-5019	308	2	γ	γ	X
ejpam-5019	308	3	]	]	X
ejpam-5019	308	4	jn2×nn	jn2×nn	PROPN
ejpam-5019	308	5	.	.	PUNCT
ejpam-5019	308	6	.	.	PUNCT
ejpam-5019	308	7	.	.	PUNCT
ejpam-5019	309	1	snn	snn	PROPN
ejpam-5019	309	2	,	,	PUNCT
ejpam-5019	309	3			VERB
ejpam-5019	309	4	where	where	SCONJ
ejpam-5019	309	5	sii	sii	ADV
ejpam-5019	309	6	=	=	PUNCT
ejpam-5019	309	7	[	[	PUNCT
ejpam-5019	309	8	α	α	X
ejpam-5019	309	9	(	(	PUNCT
ejpam-5019	309	10	2n	2n	NUM
ejpam-5019	309	11	−	−	PROPN
ejpam-5019	309	12	ri	ri	NOUN
ejpam-5019	309	13	−mi	−mi	ADV
ejpam-5019	309	14	−	−	PROPN
ejpam-5019	310	1	2)−	2)−	NUM
ejpam-5019	310	2	2β	2β	NOUN
ejpam-5019	310	3	+	+	CCONJ
ejpam-5019	310	4	δ	δ	X
ejpam-5019	310	5	]	]	PUNCT
ejpam-5019	310	6	ini	ini	PROPN
ejpam-5019	310	7	+	+	CCONJ
ejpam-5019	310	8	(	(	PUNCT
ejpam-5019	310	9	2β	2β	NOUN
ejpam-5019	310	10	+	+	CCONJ
ejpam-5019	310	11	γ	γ	X
ejpam-5019	310	12	)	)	PUNCT
ejpam-5019	310	13	jni	jni	NOUN
ejpam-5019	310	14	−a	−a	NOUN
ejpam-5019	310	15	(	(	PUNCT
ejpam-5019	310	16	gi)β	gi)β	NOUN
ejpam-5019	310	17	;	;	PUNCT
ejpam-5019	310	18	i	i	NOUN
ejpam-5019	310	19	=	=	NOUN
ejpam-5019	310	20	1	1	NUM
ejpam-5019	310	21	,	,	PUNCT
ejpam-5019	310	22	2	2	NUM
ejpam-5019	310	23	,	,	PUNCT
ejpam-5019	310	24	.	.	PUNCT
ejpam-5019	310	25	.	.	PUNCT
ejpam-5019	311	1	.	.	PUNCT
ejpam-5019	312	1	,	,	PUNCT
ejpam-5019	312	2	n	n	CCONJ
ejpam-5019	312	3	,	,	PUNCT
ejpam-5019	312	4	ini	ini	PROPN
ejpam-5019	312	5	is	be	AUX
ejpam-5019	312	6	the	the	DET
ejpam-5019	312	7	identity	identity	NOUN
ejpam-5019	312	8	matrix	matrix	NOUN
ejpam-5019	312	9	of	of	ADP
ejpam-5019	312	10	order	order	NOUN
ejpam-5019	312	11	ni	ni	PROPN
ejpam-5019	312	12	,	,	PUNCT
ejpam-5019	312	13	and	and	CCONJ
ejpam-5019	312	14	jni	jni	NOUN
ejpam-5019	312	15	is	be	AUX
ejpam-5019	312	16	the	the	DET
ejpam-5019	312	17	all	all	DET
ejpam-5019	312	18	-	-	PUNCT
ejpam-5019	312	19	ones	one	NOUN
ejpam-5019	312	20	matrix	matrix	NOUN
ejpam-5019	312	21	of	of	ADP
ejpam-5019	312	22	order	order	NOUN
ejpam-5019	312	23	ni	ni	PROPN
ejpam-5019	312	24	.	.	PROPN
ejpam-5019	313	1	since	since	SCONJ
ejpam-5019	313	2	gi	gi	PROPN
ejpam-5019	313	3	is	be	AUX
ejpam-5019	313	4	ri−regular	ri−regular	NOUN
ejpam-5019	313	5	,	,	PUNCT
ejpam-5019	313	6	1ni×1	1ni×1	NUM
ejpam-5019	313	7	the	the	DET
ejpam-5019	313	8	all	all	DET
ejpam-5019	313	9	-	-	PUNCT
ejpam-5019	313	10	ones	one	NOUN
ejpam-5019	313	11	vector	vector	NOUN
ejpam-5019	313	12	is	be	AUX
ejpam-5019	313	13	an	an	DET
ejpam-5019	313	14	eigenvector	eigenvector	NOUN
ejpam-5019	313	15	of	of	ADP
ejpam-5019	313	16	a	a	DET
ejpam-5019	313	17	(	(	PUNCT
ejpam-5019	313	18	gi	gi	INTJ
ejpam-5019	313	19	)	)	PUNCT
ejpam-5019	313	20	corresponding	correspond	VERB
ejpam-5019	313	21	to	to	ADP
ejpam-5019	313	22	eigenvalue	eigenvalue	PROPN
ejpam-5019	313	23	ri	ri	PROPN
ejpam-5019	313	24	.	.	PUNCT
ejpam-5019	314	1	the	the	DET
ejpam-5019	314	2	remaining	remain	VERB
ejpam-5019	314	3	eigenvectors	eigenvector	NOUN
ejpam-5019	314	4	are	be	AUX
ejpam-5019	314	5	orthogonal	orthogonal	ADJ
ejpam-5019	314	6	to	to	ADP
ejpam-5019	314	7	1ni×1	1ni×1	NUM
ejpam-5019	314	8	.	.	PUNCT
ejpam-5019	315	1	consider	consider	VERB
ejpam-5019	315	2	λ	λ	PROPN
ejpam-5019	315	3	the	the	DET
ejpam-5019	315	4	eigenvalue	eigenvalue	NOUN
ejpam-5019	315	5	of	of	ADP
ejpam-5019	315	6	a	a	DET
ejpam-5019	315	7	(	(	PUNCT
ejpam-5019	315	8	gi	gi	INTJ
ejpam-5019	315	9	)	)	PUNCT
ejpam-5019	315	10	corresponding	correspond	VERB
ejpam-5019	315	11	to	to	ADP
ejpam-5019	315	12	the	the	DET
ejpam-5019	315	13	eigenvector	eigenvector	NOUN
ejpam-5019	315	14	xi	xi	ADP
ejpam-5019	315	15	=	=	PUNCT
ejpam-5019	315	16	(	(	PUNCT
ejpam-5019	315	17	xi1	xi1	PROPN
ejpam-5019	315	18	xi2	xi2	PROPN
ejpam-5019	315	19	.	.	PUNCT
ejpam-5019	315	20	.	.	PUNCT
ejpam-5019	315	21	.	.	PUNCT
ejpam-5019	316	1	xini	xini	PROPN
ejpam-5019	316	2	)	)	PUNCT
ejpam-5019	317	1	t	t	PROPN
ejpam-5019	317	2	,	,	PUNCT
ejpam-5019	317	3	satisfying	satisfy	VERB
ejpam-5019	317	4	1tni×1xi	1tni×1xi	NUM
ejpam-5019	317	5	=	=	SYM
ejpam-5019	317	6	0	0	NUM
ejpam-5019	317	7	;	;	PUNCT
ejpam-5019	317	8	i	i	PROPN
ejpam-5019	317	9	=	=	NOUN
ejpam-5019	317	10	2	2	NUM
ejpam-5019	317	11	,	,	PUNCT
ejpam-5019	317	12	3	3	NUM
ejpam-5019	317	13	,	,	PUNCT
ejpam-5019	317	14	.	.	PUNCT
ejpam-5019	317	15	.	.	PUNCT
ejpam-5019	317	16	.	.	PUNCT
ejpam-5019	318	1	,	,	PUNCT
ejpam-5019	318	2	n.	n.	NOUN
ejpam-5019	318	3	consider	consider	VERB
ejpam-5019	318	4	the	the	DET
ejpam-5019	318	5	vector	vector	NOUN
ejpam-5019	318	6	yti	yti	NOUN
ejpam-5019	318	7	,	,	PUNCT
ejpam-5019	318	8	where	where	SCONJ
ejpam-5019	318	9	y1	y1	NOUN
ejpam-5019	318	10	=	=	PUNCT
ejpam-5019	318	11	{	{	PUNCT
ejpam-5019	318	12	x1j	x1j	PROPN
ejpam-5019	318	13	,	,	PUNCT
ejpam-5019	318	14	v1j	v1j	PUNCT
ejpam-5019	318	15	∈	∈	NOUN
ejpam-5019	318	16	v	v	X
ejpam-5019	318	17	(	(	PUNCT
ejpam-5019	318	18	g1	g1	PROPN
ejpam-5019	318	19	)	)	PUNCT
ejpam-5019	318	20	;	;	PUNCT
ejpam-5019	318	21	j	j	PROPN
ejpam-5019	318	22	=	=	SYM
ejpam-5019	318	23	2	2	NUM
ejpam-5019	318	24	,	,	PUNCT
ejpam-5019	318	25	3	3	NUM
ejpam-5019	318	26	,	,	PUNCT
ejpam-5019	318	27	.	.	PUNCT
ejpam-5019	318	28	.	.	PUNCT
ejpam-5019	319	1	.	.	PUNCT
ejpam-5019	320	1	,	,	PUNCT
ejpam-5019	320	2	n1	n1	PROPN
ejpam-5019	320	3	.	.	PROPN
ejpam-5019	320	4	0	0	NUM
ejpam-5019	320	5	,	,	PUNCT
ejpam-5019	320	6	otherwise	otherwise	ADV
ejpam-5019	320	7	s.	s.	PROPN
ejpam-5019	320	8	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	320	9	,	,	PUNCT
ejpam-5019	320	10	k.	k.	PROPN
ejpam-5019	320	11	desikan	desikan	PROPN
ejpam-5019	320	12	/	/	SYM
ejpam-5019	320	13	eur	eur	PROPN
ejpam-5019	320	14	.	.	PUNCT
ejpam-5019	321	1	j.	j.	PROPN
ejpam-5019	321	2	pure	pure	PROPN
ejpam-5019	321	3	appl	appl	PROPN
ejpam-5019	321	4	.	.	PROPN
ejpam-5019	321	5	math	math	PROPN
ejpam-5019	321	6	,	,	PUNCT
ejpam-5019	321	7	17	17	NUM
ejpam-5019	321	8	(	(	PUNCT
ejpam-5019	321	9	1	1	NUM
ejpam-5019	321	10	)	)	PUNCT
ejpam-5019	321	11	(	(	PUNCT
ejpam-5019	321	12	2024	2024	NUM
ejpam-5019	321	13	)	)	PUNCT
ejpam-5019	321	14	,	,	PUNCT
ejpam-5019	321	15	462	462	NUM
ejpam-5019	321	16	-	-	SYM
ejpam-5019	321	17	476	476	NUM
ejpam-5019	321	18	472	472	NUM
ejpam-5019	321	19	y2	y2	NOUN
ejpam-5019	321	20	=	=	SYM
ejpam-5019	321	21	{	{	PUNCT
ejpam-5019	321	22	x2j	x2j	PROPN
ejpam-5019	321	23	,	,	PUNCT
ejpam-5019	321	24	v2j	v2j	PROPN
ejpam-5019	321	25	∈	∈	PROPN
ejpam-5019	321	26	v	v	PROPN
ejpam-5019	321	27	(	(	PUNCT
ejpam-5019	321	28	g2	g2	PROPN
ejpam-5019	321	29	)	)	PUNCT
ejpam-5019	321	30	;	;	PUNCT
ejpam-5019	322	1	j	j	PROPN
ejpam-5019	322	2	=	=	SYM
ejpam-5019	322	3	2	2	NUM
ejpam-5019	322	4	,	,	PUNCT
ejpam-5019	322	5	3	3	NUM
ejpam-5019	322	6	,	,	PUNCT
ejpam-5019	322	7	.	.	PUNCT
ejpam-5019	322	8	.	.	PUNCT
ejpam-5019	323	1	.	.	PUNCT
ejpam-5019	324	1	,	,	PUNCT
ejpam-5019	324	2	n2	n2	PROPN
ejpam-5019	324	3	.	.	PROPN
ejpam-5019	324	4	0	0	NUM
ejpam-5019	324	5	,	,	PUNCT
ejpam-5019	324	6	otherwise	otherwise	ADV
ejpam-5019	324	7	.	.	PUNCT
ejpam-5019	324	8	.	.	PUNCT
ejpam-5019	324	9	.	.	PUNCT
ejpam-5019	325	1	yn	yn	PRON
ejpam-5019	325	2	=	=	PRON
ejpam-5019	325	3	{	{	PUNCT
ejpam-5019	325	4	xnj	xnj	PROPN
ejpam-5019	325	5	,	,	PUNCT
ejpam-5019	325	6	vnj	vnj	NOUN
ejpam-5019	325	7	∈	∈	PROPN
ejpam-5019	325	8	v	v	NOUN
ejpam-5019	325	9	(	(	PUNCT
ejpam-5019	325	10	gn	gn	PROPN
ejpam-5019	325	11	)	)	PUNCT
ejpam-5019	325	12	;	;	PUNCT
ejpam-5019	325	13	j	j	PROPN
ejpam-5019	325	14	=	=	SYM
ejpam-5019	325	15	2	2	NUM
ejpam-5019	325	16	,	,	PUNCT
ejpam-5019	325	17	3	3	NUM
ejpam-5019	325	18	,	,	PUNCT
ejpam-5019	325	19	.	.	PUNCT
ejpam-5019	325	20	.	.	PUNCT
ejpam-5019	325	21	.	.	PUNCT
ejpam-5019	326	1	,	,	PUNCT
ejpam-5019	326	2	nn	nn	PROPN
ejpam-5019	326	3	.	.	PROPN
ejpam-5019	326	4	0	0	NUM
ejpam-5019	326	5	,	,	PUNCT
ejpam-5019	326	6	otherwise	otherwise	ADV
ejpam-5019	326	7	clearly	clearly	ADV
ejpam-5019	326	8	,	,	PUNCT
ejpam-5019	326	9	the	the	DET
ejpam-5019	326	10	vector	vector	NOUN
ejpam-5019	326	11	yti	yti	NOUN
ejpam-5019	326	12	is	be	AUX
ejpam-5019	326	13	an	an	DET
ejpam-5019	326	14	eigenvector	eigenvector	NOUN
ejpam-5019	326	15	of	of	ADP
ejpam-5019	326	16	ud	ud	INTJ
ejpam-5019	326	17	(	(	PUNCT
ejpam-5019	326	18	g	g	NOUN
ejpam-5019	326	19	)	)	PUNCT
ejpam-5019	326	20	corresponding	correspond	VERB
ejpam-5019	326	21	to	to	ADP
ejpam-5019	326	22	the	the	DET
ejpam-5019	326	23	eigenvalue	eigenvalue	PROPN
ejpam-5019	326	24	α	α	PROPN
ejpam-5019	326	25	(	(	PUNCT
ejpam-5019	326	26	2n	2n	NUM
ejpam-5019	326	27	−	−	PROPN
ejpam-5019	326	28	ri	ri	NOUN
ejpam-5019	327	1	−mi	−mi	ADV
ejpam-5019	327	2	−	−	ADP
ejpam-5019	327	3	2	2	NUM
ejpam-5019	327	4	)	)	PUNCT
ejpam-5019	327	5	−	−	PROPN
ejpam-5019	328	1	(	(	PUNCT
ejpam-5019	328	2	λi	λi	ADP
ejpam-5019	328	3	k	k	X
ejpam-5019	328	4	+	+	PROPN
ejpam-5019	328	5	2	2	X
ejpam-5019	328	6	)	)	PUNCT
ejpam-5019	328	7	β	β	NOUN
ejpam-5019	329	1	+	+	CCONJ
ejpam-5019	329	2	δ	δ	PROPN
ejpam-5019	329	3	;	;	PUNCT
ejpam-5019	329	4	i	i	NOUN
ejpam-5019	329	5	=	=	NOUN
ejpam-5019	329	6	1	1	NUM
ejpam-5019	329	7	,	,	PUNCT
ejpam-5019	329	8	2	2	NUM
ejpam-5019	329	9	,	,	PUNCT
ejpam-5019	329	10	.	.	PUNCT
ejpam-5019	329	11	.	.	PUNCT
ejpam-5019	329	12	.	.	PUNCT
ejpam-5019	330	1	,	,	PUNCT
ejpam-5019	330	2	n	n	CCONJ
ejpam-5019	330	3	,	,	PUNCT
ejpam-5019	330	4	k	k	PROPN
ejpam-5019	330	5	=	=	SYM
ejpam-5019	330	6	2	2	NUM
ejpam-5019	330	7	,	,	PUNCT
ejpam-5019	330	8	3	3	NUM
ejpam-5019	330	9	,	,	PUNCT
ejpam-5019	330	10	.	.	PUNCT
ejpam-5019	330	11	.	.	PUNCT
ejpam-5019	331	1	.	.	PUNCT
ejpam-5019	332	1	,	,	PUNCT
ejpam-5019	332	2	ni	ni	PROPN
ejpam-5019	332	3	.	.	PROPN
ejpam-5019	332	4	totally	totally	ADV
ejpam-5019	332	5	,	,	PUNCT
ejpam-5019	332	6	we	we	PRON
ejpam-5019	332	7	have	have	VERB
ejpam-5019	332	8	n	n	NUM
ejpam-5019	332	9	−	−	NOUN
ejpam-5019	332	10	n	n	CCONJ
ejpam-5019	332	11	mutually	mutually	ADV
ejpam-5019	332	12	orthogonal	orthogonal	ADJ
ejpam-5019	332	13	eigenvectors	eigenvector	NOUN
ejpam-5019	332	14	of	of	ADP
ejpam-5019	332	15	ud	ud	INTJ
ejpam-5019	332	16	(	(	PUNCT
ejpam-5019	332	17	g	g	NOUN
ejpam-5019	332	18	)	)	PUNCT
ejpam-5019	332	19	.	.	PUNCT
ejpam-5019	333	1	these	these	DET
ejpam-5019	333	2	vectors	vector	NOUN
ejpam-5019	333	3	are	be	AUX
ejpam-5019	333	4	orthogonal	orthogonal	ADJ
ejpam-5019	333	5	to	to	ADP
ejpam-5019	333	6	the	the	DET
ejpam-5019	333	7	vector	vector	NOUN
ejpam-5019	333	8	1i	1i	NOUN
ejpam-5019	333	9	=	=	SYM
ejpam-5019	333	10	{	{	PUNCT
ejpam-5019	333	11	1ni×1	1ni×1	NUM
ejpam-5019	333	12	,	,	PUNCT
ejpam-5019	333	13	vij	vij	PROPN
ejpam-5019	333	14	∈	∈	PROPN
ejpam-5019	333	15	v	v	PROPN
ejpam-5019	333	16	(	(	PUNCT
ejpam-5019	333	17	gi	gi	INTJ
ejpam-5019	333	18	)	)	PUNCT
ejpam-5019	333	19	;	;	PUNCT
ejpam-5019	334	1	i	i	PRON
ejpam-5019	334	2	=	=	NOUN
ejpam-5019	334	3	1	1	NUM
ejpam-5019	334	4	,	,	PUNCT
ejpam-5019	334	5	2	2	NUM
ejpam-5019	334	6	,	,	PUNCT
ejpam-5019	334	7	.	.	PUNCT
ejpam-5019	334	8	.	.	PUNCT
ejpam-5019	334	9	.	.	PUNCT
ejpam-5019	334	10	,	,	PUNCT
ejpam-5019	334	11	n	n	CCONJ
ejpam-5019	334	12	,	,	PUNCT
ejpam-5019	334	13	j	j	PROPN
ejpam-5019	334	14	=	=	SYM
ejpam-5019	334	15	1	1	NUM
ejpam-5019	334	16	,	,	PUNCT
ejpam-5019	334	17	2	2	NUM
ejpam-5019	334	18	,	,	PUNCT
ejpam-5019	334	19	.	.	PUNCT
ejpam-5019	334	20	.	.	PUNCT
ejpam-5019	334	21	.	.	PUNCT
ejpam-5019	335	1	,	,	PUNCT
ejpam-5019	335	2	ni	ni	PROPN
ejpam-5019	335	3	.	.	PROPN
ejpam-5019	335	4	0	0	NUM
ejpam-5019	335	5	,	,	PUNCT
ejpam-5019	335	6	otherwise	otherwise	ADV
ejpam-5019	335	7	for	for	ADP
ejpam-5019	335	8	suitable	suitable	ADJ
ejpam-5019	335	9	choice	choice	NOUN
ejpam-5019	335	10	of	of	ADP
ejpam-5019	335	11	arbitrary	arbitrary	ADJ
ejpam-5019	335	12	values	value	NOUN
ejpam-5019	335	13	α1	α1	PROPN
ejpam-5019	335	14	,	,	PUNCT
ejpam-5019	335	15	α2	α2	ADJ
ejpam-5019	335	16	,	,	PUNCT
ejpam-5019	335	17	.	.	PUNCT
ejpam-5019	335	18	.	.	PUNCT
ejpam-5019	336	1	.	.	PUNCT
ejpam-5019	337	1	,	,	PUNCT
ejpam-5019	337	2	αn	αn	INTJ
ejpam-5019	337	3	we	we	PRON
ejpam-5019	337	4	have	have	VERB
ejpam-5019	337	5	1	1	NUM
ejpam-5019	337	6	=	=	SYM
ejpam-5019	337	7	(	(	PUNCT
ejpam-5019	337	8	α11	α11	NUM
ejpam-5019	337	9	1	1	NUM
ejpam-5019	337	10	α21	α21	NOUN
ejpam-5019	337	11	2	2	NUM
ejpam-5019	337	12	.	.	PUNCT
ejpam-5019	337	13	.	.	PUNCT
ejpam-5019	337	14	.	.	PUNCT
ejpam-5019	338	1	αn1	αn1	NOUN
ejpam-5019	338	2	n	n	CCONJ
ejpam-5019	338	3	)	)	PUNCT
ejpam-5019	338	4	as	as	SCONJ
ejpam-5019	338	5	the	the	DET
ejpam-5019	338	6	eigenvector	eigenvector	NOUN
ejpam-5019	338	7	corresponding	correspond	VERB
ejpam-5019	338	8	to	to	ADP
ejpam-5019	338	9	the	the	DET
ejpam-5019	338	10	eigenvalues	eigenvalue	NOUN
ejpam-5019	338	11	of	of	ADP
ejpam-5019	338	12	the	the	DET
ejpam-5019	338	13	n×n	n×n	PROPN
ejpam-5019	338	14	quotient	quotient	NOUN
ejpam-5019	338	15	matrix	matrix	NOUN
ejpam-5019	338	16	of	of	ADP
ejpam-5019	338	17	ud	ud	INTJ
ejpam-5019	338	18	(	(	PUNCT
ejpam-5019	338	19	g	g	NOUN
ejpam-5019	338	20	)	)	PUNCT
ejpam-5019	338	21	of	of	ADP
ejpam-5019	338	22	the	the	DET
ejpam-5019	338	23	form	form	NOUN
ejpam-5019	338	24	r11	r11	NOUN
ejpam-5019	338	25	[	[	PUNCT
ejpam-5019	338	26	β	β	X
ejpam-5019	338	27	dh	dh	NOUN
ejpam-5019	338	28	(	(	PUNCT
ejpam-5019	338	29	v1	v1	PROPN
ejpam-5019	338	30	,	,	PUNCT
ejpam-5019	338	31	v2	v2	PROPN
ejpam-5019	338	32	)	)	PUNCT
ejpam-5019	338	33	+	+	CCONJ
ejpam-5019	338	34	γ	γ	X
ejpam-5019	338	35	]	]	PUNCT
ejpam-5019	338	36	n2	n2	PROPN
ejpam-5019	338	37	.	.	PUNCT
ejpam-5019	338	38	.	.	PUNCT
ejpam-5019	338	39	.	.	PUNCT
ejpam-5019	339	1	[	[	PUNCT
ejpam-5019	339	2	β	β	X
ejpam-5019	339	3	dh	dh	NOUN
ejpam-5019	339	4	(	(	PUNCT
ejpam-5019	339	5	v1	v1	PROPN
ejpam-5019	339	6	,	,	PUNCT
ejpam-5019	339	7	vn	vn	NOUN
ejpam-5019	339	8	)	)	PUNCT
ejpam-5019	340	1	+	+	CCONJ
ejpam-5019	340	2	γ	γ	X
ejpam-5019	340	3	]	]	PUNCT
ejpam-5019	340	4	nn	nn	PROPN
ejpam-5019	340	5	[	[	X
ejpam-5019	340	6	β	β	X
ejpam-5019	340	7	dh	dh	NOUN
ejpam-5019	340	8	(	(	PUNCT
ejpam-5019	340	9	v2	v2	PROPN
ejpam-5019	340	10	,	,	PUNCT
ejpam-5019	340	11	v1	v1	NOUN
ejpam-5019	340	12	)	)	PUNCT
ejpam-5019	341	1	+	+	CCONJ
ejpam-5019	341	2	γ	γ	X
ejpam-5019	341	3	]	]	PUNCT
ejpam-5019	341	4	n1	n1	PROPN
ejpam-5019	341	5	r22	r22	NOUN
ejpam-5019	341	6	.	.	PUNCT
ejpam-5019	341	7	.	.	PUNCT
ejpam-5019	341	8	.	.	PUNCT
ejpam-5019	342	1	[	[	PUNCT
ejpam-5019	342	2	β	β	X
ejpam-5019	342	3	dh	dh	NOUN
ejpam-5019	342	4	(	(	PUNCT
ejpam-5019	342	5	v2	v2	PROPN
ejpam-5019	342	6	,	,	PUNCT
ejpam-5019	342	7	vn	vn	NOUN
ejpam-5019	342	8	)	)	PUNCT
ejpam-5019	343	1	+	+	CCONJ
ejpam-5019	343	2	γ	γ	X
ejpam-5019	343	3	]	]	PUNCT
ejpam-5019	343	4	nn	nn	PROPN
ejpam-5019	343	5	...	...	PUNCT
ejpam-5019	343	6	...	...	PUNCT
ejpam-5019	343	7	...	...	PUNCT
ejpam-5019	343	8	...	...	PUNCT
ejpam-5019	344	1	[	[	PUNCT
ejpam-5019	344	2	β	β	X
ejpam-5019	344	3	dh	dh	NOUN
ejpam-5019	344	4	(	(	PUNCT
ejpam-5019	344	5	vn	vn	PROPN
ejpam-5019	344	6	,	,	PUNCT
ejpam-5019	344	7	v1	v1	NOUN
ejpam-5019	344	8	)	)	PUNCT
ejpam-5019	345	1	+	+	CCONJ
ejpam-5019	345	2	γ	γ	X
ejpam-5019	345	3	]	]	X
ejpam-5019	345	4	n1	n1	PROPN
ejpam-5019	345	5	[	[	PUNCT
ejpam-5019	345	6	β	β	X
ejpam-5019	345	7	dh	dh	NOUN
ejpam-5019	345	8	(	(	PUNCT
ejpam-5019	345	9	vn	vn	PROPN
ejpam-5019	345	10	,	,	PUNCT
ejpam-5019	345	11	v2	v2	PROPN
ejpam-5019	345	12	)	)	PUNCT
ejpam-5019	346	1	+	+	CCONJ
ejpam-5019	346	2	γ	γ	X
ejpam-5019	346	3	]	]	PUNCT
ejpam-5019	346	4	n2	n2	PROPN
ejpam-5019	346	5	.	.	PUNCT
ejpam-5019	346	6	.	.	PUNCT
ejpam-5019	346	7	.	.	PUNCT
ejpam-5019	347	1	rnn	rnn	PROPN
ejpam-5019	347	2			PROPN
ejpam-5019	347	3	,	,	PUNCT
ejpam-5019	347	4	where	where	SCONJ
ejpam-5019	347	5	rii	rii	NOUN
ejpam-5019	347	6	=	=	PUNCT
ejpam-5019	347	7	α	α	PROPN
ejpam-5019	347	8	(	(	PUNCT
ejpam-5019	347	9	2n	2n	NUM
ejpam-5019	347	10	−	−	PROPN
ejpam-5019	347	11	ri	ri	NOUN
ejpam-5019	347	12	−mi	−mi	ADV
ejpam-5019	348	1	−	−	PROPN
ejpam-5019	348	2	2)−	2)−	NUM
ejpam-5019	348	3	(	(	PUNCT
ejpam-5019	348	4	ri	ri	PROPN
ejpam-5019	348	5	−	−	NUM
ejpam-5019	348	6	2ni	2ni	NOUN
ejpam-5019	349	1	+	+	CCONJ
ejpam-5019	349	2	2)β	2)β	NOUN
ejpam-5019	349	3	+	+	CCONJ
ejpam-5019	349	4	γni	γni	PROPN
ejpam-5019	349	5	+	+	CCONJ
ejpam-5019	349	6	δ	δ	PROPN
ejpam-5019	349	7	,	,	PUNCT
ejpam-5019	349	8	;	;	PUNCT
ejpam-5019	349	9	i	i	NOUN
ejpam-5019	349	10	=	=	NOUN
ejpam-5019	349	11	1	1	NUM
ejpam-5019	349	12	,	,	PUNCT
ejpam-5019	349	13	2	2	NUM
ejpam-5019	349	14	,	,	PUNCT
ejpam-5019	349	15	.	.	PUNCT
ejpam-5019	349	16	.	.	PUNCT
ejpam-5019	349	17	.	.	PUNCT
ejpam-5019	350	1	,	,	PUNCT
ejpam-5019	350	2	n.	n.	PROPN
ejpam-5019	350	3	this	this	PRON
ejpam-5019	350	4	completes	complete	VERB
ejpam-5019	350	5	the	the	DET
ejpam-5019	350	6	proof	proof	NOUN
ejpam-5019	350	7	.	.	PUNCT
ejpam-5019	351	1	corollary	corollary	ADJ
ejpam-5019	351	2	6	6	NUM
ejpam-5019	351	3	.	.	PUNCT
ejpam-5019	352	1	the	the	DET
ejpam-5019	352	2	universal	universal	ADJ
ejpam-5019	352	3	distance	distance	NOUN
ejpam-5019	352	4	spectrum	spectrum	NOUN
ejpam-5019	352	5	of	of	ADP
ejpam-5019	352	6	complete	complete	ADJ
ejpam-5019	352	7	t−partite	t−partite	X
ejpam-5019	352	8	graph	graph	NOUN
ejpam-5019	352	9	g	g	NOUN
ejpam-5019	352	10	=	=	SYM
ejpam-5019	352	11	kn1,n2,	kn1,n2,	NOUN
ejpam-5019	352	12	...	...	PUNCT
ejpam-5019	352	13	,nt	,nt	PUNCT
ejpam-5019	352	14	with	with	ADP
ejpam-5019	352	15	n	n	NOUN
ejpam-5019	352	16	=	=	SYM
ejpam-5019	352	17	∑t	∑t	PROPN
ejpam-5019	352	18	i=1	i=1	PROPN
ejpam-5019	352	19	ni	ni	PROPN
ejpam-5019	352	20	consists	consist	VERB
ejpam-5019	352	21	of	of	ADP
ejpam-5019	352	22	the	the	DET
ejpam-5019	352	23	eigenvalues	eigenvalues	PROPN
ejpam-5019	352	24	α	α	X
ejpam-5019	352	25	(	(	PUNCT
ejpam-5019	352	26	n	n	PROPN
ejpam-5019	352	27	+	+	CCONJ
ejpam-5019	352	28	ni	ni	PROPN
ejpam-5019	352	29	−	−	PROPN
ejpam-5019	352	30	2)−	2)−	NUM
ejpam-5019	352	31	2β	2β	PROPN
ejpam-5019	352	32	+	+	CCONJ
ejpam-5019	352	33	δ	δ	PROPN
ejpam-5019	352	34	;	;	PUNCT
ejpam-5019	352	35	i	i	NOUN
ejpam-5019	352	36	=	=	NOUN
ejpam-5019	352	37	1	1	NUM
ejpam-5019	352	38	,	,	PUNCT
ejpam-5019	352	39	2	2	NUM
ejpam-5019	352	40	,	,	PUNCT
ejpam-5019	352	41	.	.	PUNCT
ejpam-5019	352	42	.	.	PUNCT
ejpam-5019	353	1	.	.	PUNCT
ejpam-5019	354	1	,	,	PUNCT
ejpam-5019	354	2	t	t	NOUN
ejpam-5019	354	3	with	with	ADP
ejpam-5019	354	4	algebraic	algebraic	PROPN
ejpam-5019	354	5	multiplicity	multiplicity	NOUN
ejpam-5019	354	6	ni	ni	PROPN
ejpam-5019	354	7	and	and	CCONJ
ejpam-5019	354	8	t	t	PROPN
ejpam-5019	354	9	eigenvalues	eigenvalue	NOUN
ejpam-5019	354	10	of	of	ADP
ejpam-5019	354	11	the	the	DET
ejpam-5019	354	12	matrix	matrix	PROPN
ejpam-5019	354	13	m11	m11	NOUN
ejpam-5019	354	14	(	(	PUNCT
ejpam-5019	354	15	β	β	X
ejpam-5019	354	16	+	+	X
ejpam-5019	354	17	γ)n2	γ)n2	ADJ
ejpam-5019	354	18	.	.	PUNCT
ejpam-5019	354	19	.	.	PUNCT
ejpam-5019	354	20	.	.	PUNCT
ejpam-5019	355	1	(	(	PUNCT
ejpam-5019	355	2	β	β	X
ejpam-5019	355	3	+	+	X
ejpam-5019	356	1	γ)nt	γ)nt	PROPN
ejpam-5019	356	2	(	(	PUNCT
ejpam-5019	356	3	β	β	X
ejpam-5019	356	4	+	+	NUM
ejpam-5019	356	5	γ)n1	γ)n1	PROPN
ejpam-5019	356	6	m22	m22	PROPN
ejpam-5019	356	7	.	.	PUNCT
ejpam-5019	356	8	.	.	PUNCT
ejpam-5019	356	9	.	.	PUNCT
ejpam-5019	357	1	(	(	PUNCT
ejpam-5019	357	2	β	β	X
ejpam-5019	357	3	+	+	PUNCT
ejpam-5019	357	4	γ)nt	γ)nt	PROPN
ejpam-5019	357	5	...	...	PUNCT
ejpam-5019	357	6	...	...	PUNCT
ejpam-5019	357	7	.	.	PUNCT
ejpam-5019	357	8	.	.	PUNCT
ejpam-5019	357	9	.	.	PUNCT
ejpam-5019	358	1	...	...	PUNCT
ejpam-5019	359	1	(	(	PUNCT
ejpam-5019	359	2	β	β	X
ejpam-5019	359	3	+	+	X
ejpam-5019	359	4	γ)n1	γ)n1	PROPN
ejpam-5019	359	5	(	(	PUNCT
ejpam-5019	359	6	β	β	X
ejpam-5019	359	7	+	+	X
ejpam-5019	359	8	γ)n2	γ)n2	ADJ
ejpam-5019	359	9	.	.	PUNCT
ejpam-5019	359	10	.	.	PUNCT
ejpam-5019	359	11	.	.	PUNCT
ejpam-5019	360	1	mtt	mtt	PROPN
ejpam-5019	360	2	,	,	PUNCT
ejpam-5019	360	3			PRON
ejpam-5019	361	1	where	where	SCONJ
ejpam-5019	361	2	mii	mii	NOUN
ejpam-5019	361	3	=	=	PROPN
ejpam-5019	361	4	α	α	PROPN
ejpam-5019	361	5	(	(	PUNCT
ejpam-5019	361	6	n	n	PROPN
ejpam-5019	361	7	+	+	CCONJ
ejpam-5019	361	8	ni	ni	PROPN
ejpam-5019	361	9	−	−	PROPN
ejpam-5019	361	10	2	2	NUM
ejpam-5019	361	11	)	)	PUNCT
ejpam-5019	361	12	+	+	CCONJ
ejpam-5019	361	13	(	(	PUNCT
ejpam-5019	361	14	2ni	2ni	ADJ
ejpam-5019	361	15	−	−	PROPN
ejpam-5019	361	16	2)β	2)β	NOUN
ejpam-5019	361	17	+	+	CCONJ
ejpam-5019	361	18	γni	γni	PROPN
ejpam-5019	361	19	+	+	CCONJ
ejpam-5019	361	20	δ	δ	PROPN
ejpam-5019	361	21	;	;	PUNCT
ejpam-5019	361	22	i	i	NOUN
ejpam-5019	361	23	=	=	NOUN
ejpam-5019	361	24	1	1	NUM
ejpam-5019	361	25	,	,	PUNCT
ejpam-5019	361	26	2	2	NUM
ejpam-5019	361	27	,	,	PUNCT
ejpam-5019	361	28	.	.	PUNCT
ejpam-5019	361	29	.	.	PUNCT
ejpam-5019	361	30	.	.	PUNCT
ejpam-5019	362	1	,	,	PUNCT
ejpam-5019	362	2	t.	t.	NOUN
ejpam-5019	362	3	proof	proof	NOUN
ejpam-5019	362	4	.	.	PUNCT
ejpam-5019	363	1	in	in	ADP
ejpam-5019	363	2	theorem	theorem	NOUN
ejpam-5019	363	3	4	4	NUM
ejpam-5019	363	4	,	,	PUNCT
ejpam-5019	363	5	by	by	ADP
ejpam-5019	363	6	substituting	substitute	VERB
ejpam-5019	363	7	ri	ri	PROPN
ejpam-5019	363	8	=	=	PUNCT
ejpam-5019	363	9	0,mi	0,mi	NOUN
ejpam-5019	363	10	=	=	SYM
ejpam-5019	363	11	n	n	CCONJ
ejpam-5019	363	12	−	−	PROPN
ejpam-5019	363	13	ni	ni	PROPN
ejpam-5019	363	14	;	;	PUNCT
ejpam-5019	363	15	i	i	NOUN
ejpam-5019	363	16	=	=	NOUN
ejpam-5019	363	17	1	1	NUM
ejpam-5019	363	18	,	,	PUNCT
ejpam-5019	363	19	2	2	NUM
ejpam-5019	363	20	,	,	PUNCT
ejpam-5019	363	21	.	.	PUNCT
ejpam-5019	363	22	.	.	PUNCT
ejpam-5019	363	23	.	.	PUNCT
ejpam-5019	364	1	,	,	PUNCT
ejpam-5019	364	2	t	t	PROPN
ejpam-5019	364	3	,	,	PUNCT
ejpam-5019	364	4	we	we	PRON
ejpam-5019	364	5	obtain	obtain	VERB
ejpam-5019	364	6	the	the	DET
ejpam-5019	364	7	universal	universal	ADJ
ejpam-5019	364	8	distance	distance	NOUN
ejpam-5019	364	9	spectrum	spectrum	NOUN
ejpam-5019	364	10	of	of	ADP
ejpam-5019	364	11	g.	g.	PROPN
ejpam-5019	364	12	s.	s.	PROPN
ejpam-5019	364	13	kaliyaperumal	kaliyaperumal	PROPN
ejpam-5019	364	14	,	,	PUNCT
ejpam-5019	364	15	k.	k.	PROPN
ejpam-5019	364	16	desikan	desikan	PROPN
ejpam-5019	364	17	/	/	SYM
ejpam-5019	364	18	eur	eur	PROPN
ejpam-5019	364	19	.	.	PUNCT
ejpam-5019	365	1	j.	j.	PROPN
ejpam-5019	365	2	pure	pure	PROPN
ejpam-5019	365	3	appl	appl	PROPN
ejpam-5019	365	4	.	.	PROPN
ejpam-5019	365	5	math	math	PROPN
ejpam-5019	365	6	,	,	PUNCT
ejpam-5019	365	7	17	17	NUM
ejpam-5019	365	8	(	(	PUNCT
ejpam-5019	365	9	1	1	NUM
ejpam-5019	365	10	)	)	PUNCT
ejpam-5019	365	11	(	(	PUNCT
ejpam-5019	365	12	2024	2024	NUM
ejpam-5019	365	13	)	)	PUNCT
ejpam-5019	365	14	,	,	PUNCT
ejpam-5019	365	15	462	462	NUM
ejpam-5019	365	16	-	-	SYM
ejpam-5019	365	17	476	476	NUM
ejpam-5019	365	18	473	473	NUM
ejpam-5019	365	19	example	example	NOUN
ejpam-5019	365	20	1	1	NUM
ejpam-5019	365	21	.	.	X
ejpam-5019	365	22	consider	consider	VERB
ejpam-5019	365	23	the	the	DET
ejpam-5019	365	24	graph	graph	NOUN
ejpam-5019	365	25	g	g	PROPN
ejpam-5019	365	26	=	=	ADJ
ejpam-5019	365	27	h	h	PROPN
ejpam-5019	365	28	(	(	PUNCT
ejpam-5019	365	29	g1	g1	PROPN
ejpam-5019	365	30	,	,	PUNCT
ejpam-5019	365	31	g2	g2	PROPN
ejpam-5019	365	32	,	,	PUNCT
ejpam-5019	365	33	g3	g3	PROPN
ejpam-5019	365	34	)	)	PUNCT
ejpam-5019	365	35	as	as	SCONJ
ejpam-5019	365	36	depicted	depict	VERB
ejpam-5019	365	37	in	in	ADP
ejpam-5019	365	38	figure	figure	NOUN
ejpam-5019	365	39	1	1	NUM
ejpam-5019	365	40	,	,	PUNCT
ejpam-5019	365	41	where	where	SCONJ
ejpam-5019	365	42	h	h	NOUN
ejpam-5019	365	43	=	=	PROPN
ejpam-5019	365	44	p3	p3	PROPN
ejpam-5019	365	45	the	the	DET
ejpam-5019	365	46	path	path	NOUN
ejpam-5019	365	47	graph	graph	NOUN
ejpam-5019	365	48	of	of	ADP
ejpam-5019	365	49	order	order	NOUN
ejpam-5019	365	50	3	3	NUM
ejpam-5019	365	51	,	,	PUNCT
ejpam-5019	365	52	g1	g1	NOUN
ejpam-5019	365	53	=	=	PRON
ejpam-5019	365	54	c4	c4	VERB
ejpam-5019	365	55	the	the	DET
ejpam-5019	365	56	cycle	cycle	NOUN
ejpam-5019	365	57	graph	graph	NOUN
ejpam-5019	365	58	of	of	ADP
ejpam-5019	365	59	order	order	NOUN
ejpam-5019	365	60	4	4	NUM
ejpam-5019	365	61	,	,	PUNCT
ejpam-5019	365	62	g2	g2	PROPN
ejpam-5019	365	63	=	=	SYM
ejpam-5019	365	64	k2	k2	PROPN
ejpam-5019	365	65	and	and	CCONJ
ejpam-5019	365	66	g3	g3	NOUN
ejpam-5019	365	67	=	=	PUNCT
ejpam-5019	365	68	k3	k3	VERB
ejpam-5019	365	69	the	the	DET
ejpam-5019	365	70	complete	complete	ADJ
ejpam-5019	365	71	graphs	graph	NOUN
ejpam-5019	365	72	of	of	ADP
ejpam-5019	365	73	order	order	NOUN
ejpam-5019	365	74	2	2	NUM
ejpam-5019	365	75	and	and	CCONJ
ejpam-5019	365	76	3	3	NUM
ejpam-5019	365	77	,	,	PUNCT
ejpam-5019	365	78	respectively	respectively	ADV
ejpam-5019	365	79	.	.	PUNCT
ejpam-5019	366	1	the	the	DET
ejpam-5019	366	2	universal	universal	ADJ
ejpam-5019	366	3	distance	distance	NOUN
ejpam-5019	366	4	matrix	matrix	NOUN
ejpam-5019	366	5	ud	ud	INTJ
ejpam-5019	366	6	(	(	PUNCT
ejpam-5019	366	7	g	g	NOUN
ejpam-5019	366	8	)	)	PUNCT
ejpam-5019	366	9	of	of	ADP
ejpam-5019	366	10	the	the	DET
ejpam-5019	366	11	generalized	generalize	VERB
ejpam-5019	366	12	joined	join	VERB
ejpam-5019	366	13	union	union	PROPN
ejpam-5019	366	14	g	g	PROPN
ejpam-5019	366	15	=	=	PROPN
ejpam-5019	366	16	h	h	PROPN
ejpam-5019	366	17	(	(	PUNCT
ejpam-5019	366	18	g1	g1	PROPN
ejpam-5019	366	19	,	,	PUNCT
ejpam-5019	366	20	g2	g2	PROPN
ejpam-5019	366	21	,	,	PUNCT
ejpam-5019	366	22	g3	g3	PROPN
ejpam-5019	366	23	)	)	PUNCT
ejpam-5019	366	24	is	be	AUX
ejpam-5019	366	25	a	a	DET
ejpam-5019	366	26	block	block	NOUN
ejpam-5019	366	27	matrix	matrix	NOUN
ejpam-5019	366	28	of	of	ADP
ejpam-5019	366	29	the	the	DET
ejpam-5019	366	30	form	form	PROPN
ejpam-5019	366	31	w11	w11	NOUN
ejpam-5019	366	32	(	(	PUNCT
ejpam-5019	366	33	β	β	X
ejpam-5019	366	34	+	+	CCONJ
ejpam-5019	366	35	γ	γ	X
ejpam-5019	366	36	)	)	PUNCT
ejpam-5019	366	37	jn1×n2	jn1×n2	NOUN
ejpam-5019	366	38	(	(	PUNCT
ejpam-5019	366	39	2β	2β	NOUN
ejpam-5019	366	40	+	+	CCONJ
ejpam-5019	366	41	γ	γ	X
ejpam-5019	366	42	)	)	PUNCT
ejpam-5019	366	43	jn1×n3	jn1×n3	PROPN
ejpam-5019	366	44	(	(	PUNCT
ejpam-5019	366	45	β	β	X
ejpam-5019	366	46	+	+	CCONJ
ejpam-5019	366	47	γ	γ	X
ejpam-5019	366	48	)	)	PUNCT
ejpam-5019	366	49	jn2×n1	jn2×n1	PROPN
ejpam-5019	366	50	w22	w22	VERB
ejpam-5019	366	51	(	(	PUNCT
ejpam-5019	366	52	β	β	X
ejpam-5019	366	53	+	+	CCONJ
ejpam-5019	366	54	γ	γ	X
ejpam-5019	366	55	)	)	PUNCT
ejpam-5019	366	56	jn2×n3	jn2×n3	PROPN
ejpam-5019	366	57	(	(	PUNCT
ejpam-5019	366	58	2β	2β	NOUN
ejpam-5019	366	59	+	+	CCONJ
ejpam-5019	366	60	γ	γ	X
ejpam-5019	366	61	)	)	PUNCT
ejpam-5019	366	62	jn3×n1	jn3×n1	PROPN
ejpam-5019	366	63	(	(	PUNCT
ejpam-5019	366	64	β	β	X
ejpam-5019	366	65	+	+	CCONJ
ejpam-5019	366	66	γ	γ	X
ejpam-5019	366	67	)	)	PUNCT
ejpam-5019	366	68	jn3×n2	jn3×n2	PROPN
ejpam-5019	366	69	w33	w33	PROPN
ejpam-5019	366	70			PROPN
ejpam-5019	366	71	,	,	PUNCT
ejpam-5019	366	72	where	where	SCONJ
ejpam-5019	366	73	wii	wii	NOUN
ejpam-5019	366	74	=	=	SYM
ejpam-5019	366	75	α	α	PROPN
ejpam-5019	366	76	(	(	PUNCT
ejpam-5019	366	77	2n	2n	NUM
ejpam-5019	366	78	−	−	PROPN
ejpam-5019	366	79	ri	ri	NOUN
ejpam-5019	367	1	−mi	−mi	ADV
ejpam-5019	368	1	−	−	PROPN
ejpam-5019	369	1	2)−	2)−	NUM
ejpam-5019	369	2	(	(	PUNCT
ejpam-5019	369	3	ri	ri	PROPN
ejpam-5019	369	4	−	−	NUM
ejpam-5019	369	5	2ni	2ni	NOUN
ejpam-5019	370	1	+	+	CCONJ
ejpam-5019	370	2	2)β	2)β	NOUN
ejpam-5019	370	3	+	+	CCONJ
ejpam-5019	370	4	γni	γni	PROPN
ejpam-5019	370	5	+	+	CCONJ
ejpam-5019	370	6	δ	δ	PROPN
ejpam-5019	370	7	,	,	PUNCT
ejpam-5019	370	8	;	;	PUNCT
ejpam-5019	370	9	i	i	NOUN
ejpam-5019	370	10	=	=	NOUN
ejpam-5019	370	11	1	1	NUM
ejpam-5019	370	12	,	,	PUNCT
ejpam-5019	370	13	2	2	NUM
ejpam-5019	370	14	,	,	PUNCT
ejpam-5019	370	15	3	3	NUM
ejpam-5019	370	16	.	.	X
ejpam-5019	370	17	figure	figure	NOUN
ejpam-5019	370	18	1	1	NUM
ejpam-5019	370	19	:	:	PUNCT
ejpam-5019	370	20	p3	p3	NOUN
ejpam-5019	370	21	(	(	PUNCT
ejpam-5019	370	22	c4,k2,k3	c4,k2,k3	PROPN
ejpam-5019	370	23	)	)	PUNCT
ejpam-5019	370	24	the	the	DET
ejpam-5019	370	25	adjacency	adjacency	PROPN
ejpam-5019	370	26	spectra	spectra	NOUN
ejpam-5019	370	27	of	of	ADP
ejpam-5019	370	28	g1	g1	PROPN
ejpam-5019	370	29	,	,	PUNCT
ejpam-5019	370	30	g2	g2	PROPN
ejpam-5019	370	31	and	and	CCONJ
ejpam-5019	370	32	g3	g3	PROPN
ejpam-5019	370	33	are	be	AUX
ejpam-5019	370	34	speca	speca	NOUN
ejpam-5019	370	35	(	(	PUNCT
ejpam-5019	370	36	g1	g1	PROPN
ejpam-5019	370	37	)	)	PUNCT
ejpam-5019	370	38	=	=	PUNCT
ejpam-5019	370	39	{	{	PUNCT
ejpam-5019	370	40	2	2	NUM
ejpam-5019	370	41	,	,	PUNCT
ejpam-5019	370	42	0	0	NUM
ejpam-5019	370	43	,	,	PUNCT
ejpam-5019	370	44	0,−2	0,−2	NUM
ejpam-5019	370	45	}	}	PUNCT
ejpam-5019	370	46	,	,	PUNCT
ejpam-5019	370	47	speca	speca	NOUN
ejpam-5019	370	48	(	(	PUNCT
ejpam-5019	370	49	g2	g2	PROPN
ejpam-5019	370	50	)	)	PUNCT
ejpam-5019	370	51	=	=	PRON
ejpam-5019	370	52	{	{	PUNCT
ejpam-5019	370	53	1,−1	1,−1	NUM
ejpam-5019	370	54	}	}	PUNCT
ejpam-5019	370	55	,	,	PUNCT
ejpam-5019	370	56	and	and	CCONJ
ejpam-5019	370	57	speca	speca	NOUN
ejpam-5019	370	58	(	(	PUNCT
ejpam-5019	370	59	g3	g3	PROPN
ejpam-5019	370	60	)	)	PUNCT
ejpam-5019	371	1	=	=	PRON
ejpam-5019	371	2	{	{	PUNCT
ejpam-5019	371	3	2,−1,−1	2,−1,−1	NOUN
ejpam-5019	371	4	}	}	PUNCT
ejpam-5019	371	5	,	,	PUNCT
ejpam-5019	371	6	respectively	respectively	ADV
ejpam-5019	371	7	.	.	PUNCT
ejpam-5019	372	1	then	then	ADV
ejpam-5019	372	2	from	from	ADP
ejpam-5019	372	3	theorem	theorem	ADJ
ejpam-5019	372	4	4	4	NUM
ejpam-5019	372	5	,	,	PUNCT
ejpam-5019	372	6	the	the	DET
ejpam-5019	372	7	universal	universal	ADJ
ejpam-5019	372	8	distance	distance	NOUN
ejpam-5019	372	9	spectrum	spectrum	NOUN
ejpam-5019	372	10	of	of	ADP
ejpam-5019	372	11	g	g	PROPN
ejpam-5019	372	12	=	=	PROPN
ejpam-5019	372	13	h	h	PROPN
ejpam-5019	372	14	(	(	PUNCT
ejpam-5019	372	15	g1	g1	PROPN
ejpam-5019	372	16	,	,	PUNCT
ejpam-5019	372	17	g2	g2	PROPN
ejpam-5019	372	18	,	,	PUNCT
ejpam-5019	372	19	g3	g3	PROPN
ejpam-5019	372	20	)	)	PUNCT
ejpam-5019	372	21	consists	consist	VERB
ejpam-5019	372	22	of	of	ADP
ejpam-5019	372	23	the	the	DET
ejpam-5019	372	24	eigenvalues	eigenvalues	PROPN
ejpam-5019	372	25	(	(	PUNCT
ejpam-5019	372	26	i	i	NOUN
ejpam-5019	372	27	)	)	PUNCT
ejpam-5019	372	28	12α−	12α−	NUM
ejpam-5019	372	29	2β	2β	NOUN
ejpam-5019	373	1	+	+	CCONJ
ejpam-5019	373	2	δ	δ	NOUN
ejpam-5019	373	3	with	with	ADP
ejpam-5019	373	4	algebraic	algebraic	ADJ
ejpam-5019	373	5	multiplicity	multiplicity	NOUN
ejpam-5019	373	6	2	2	NUM
ejpam-5019	373	7	,	,	PUNCT
ejpam-5019	373	8	(	(	PUNCT
ejpam-5019	373	9	ii	ii	NOUN
ejpam-5019	373	10	)	)	PUNCT
ejpam-5019	373	11	12α+	12α+	PROPN
ejpam-5019	373	12	δ	δ	PROPN
ejpam-5019	373	13	,	,	PUNCT
ejpam-5019	373	14	(	(	PUNCT
ejpam-5019	373	15	iii	iii	NOUN
ejpam-5019	373	16	)	)	PUNCT
ejpam-5019	373	17	8α−	8α−	PROPN
ejpam-5019	373	18	β	β	X
ejpam-5019	373	19	+	+	CCONJ
ejpam-5019	373	20	δ	δ	PROPN
ejpam-5019	373	21	,	,	PUNCT
ejpam-5019	373	22	(	(	PUNCT
ejpam-5019	373	23	iv	iv	X
ejpam-5019	373	24	)	)	PUNCT
ejpam-5019	373	25	12α−	12α−	NUM
ejpam-5019	373	26	β	β	X
ejpam-5019	373	27	+	+	X
ejpam-5019	373	28	δ	δ	PROPN
ejpam-5019	373	29	with	with	ADP
ejpam-5019	373	30	algebraic	algebraic	ADJ
ejpam-5019	373	31	multiplicity	multiplicity	NOUN
ejpam-5019	373	32	2	2	NUM
ejpam-5019	373	33	,	,	PUNCT
ejpam-5019	373	34	and	and	CCONJ
ejpam-5019	373	35	the	the	DET
ejpam-5019	373	36	eigenvalues	eigenvalue	NOUN
ejpam-5019	373	37	of	of	ADP
ejpam-5019	373	38	the	the	DET
ejpam-5019	373	39	matrix	matrix	NOUN
ejpam-5019	373	40	(	(	PUNCT
ejpam-5019	373	41	v	v	NOUN
ejpam-5019	373	42	)	)	PUNCT
ejpam-5019	373	43	12α+	12α+	NUM
ejpam-5019	373	44	4β	4β	NOUN
ejpam-5019	374	1	+	+	CCONJ
ejpam-5019	374	2	4γ	4γ	NOUN
ejpam-5019	374	3	+	+	CCONJ
ejpam-5019	374	4	δ	δ	PROPN
ejpam-5019	374	5	2	2	NUM
ejpam-5019	374	6	(	(	PUNCT
ejpam-5019	374	7	β	β	X
ejpam-5019	374	8	+	+	CCONJ
ejpam-5019	374	9	γ	γ	X
ejpam-5019	374	10	)	)	PUNCT
ejpam-5019	374	11	3	3	NUM
ejpam-5019	374	12	(	(	PUNCT
ejpam-5019	374	13	2β	2β	NOUN
ejpam-5019	374	14	+	+	CCONJ
ejpam-5019	374	15	γ	γ	X
ejpam-5019	374	16	)	)	PUNCT
ejpam-5019	374	17	4	4	NUM
ejpam-5019	374	18	(	(	PUNCT
ejpam-5019	374	19	β	β	X
ejpam-5019	374	20	+	+	CCONJ
ejpam-5019	374	21	γ	γ	X
ejpam-5019	374	22	)	)	PUNCT
ejpam-5019	374	23	8α+	8α+	NUM
ejpam-5019	375	1	β	β	X
ejpam-5019	375	2	+	+	CCONJ
ejpam-5019	375	3	2γ	2γ	NOUN
ejpam-5019	375	4	+	+	CCONJ
ejpam-5019	375	5	δ	δ	NOUN
ejpam-5019	375	6	3	3	NUM
ejpam-5019	375	7	(	(	PUNCT
ejpam-5019	375	8	2β	2β	NOUN
ejpam-5019	375	9	+	+	CCONJ
ejpam-5019	375	10	γ	γ	X
ejpam-5019	375	11	)	)	PUNCT
ejpam-5019	375	12	4	4	NUM
ejpam-5019	375	13	(	(	PUNCT
ejpam-5019	375	14	2β	2β	NOUN
ejpam-5019	375	15	+	+	CCONJ
ejpam-5019	375	16	γ	γ	X
ejpam-5019	375	17	)	)	PUNCT
ejpam-5019	375	18	2	2	NUM
ejpam-5019	375	19	(	(	PUNCT
ejpam-5019	375	20	β	β	X
ejpam-5019	375	21	+	+	CCONJ
ejpam-5019	375	22	γ	γ	X
ejpam-5019	375	23	)	)	PUNCT
ejpam-5019	375	24	12α+	12α+	NUM
ejpam-5019	375	25	2β	2β	NOUN
ejpam-5019	375	26	+	+	CCONJ
ejpam-5019	375	27	3γ	3γ	NUM
ejpam-5019	375	28	+	+	CCONJ
ejpam-5019	375	29	δ	δ	PROPN
ejpam-5019	375	30			PROPN
ejpam-5019	375	31	note	note	VERB
ejpam-5019	375	32	that	that	SCONJ
ejpam-5019	375	33	,	,	PUNCT
ejpam-5019	375	34	when	when	SCONJ
ejpam-5019	375	35	α	α	PROPN
ejpam-5019	375	36	=	=	SYM
ejpam-5019	375	37	0	0	PROPN
ejpam-5019	375	38	,	,	PUNCT
ejpam-5019	375	39	β	β	X
ejpam-5019	375	40	=	=	SYM
ejpam-5019	375	41	1	1	NUM
ejpam-5019	375	42	,	,	PUNCT
ejpam-5019	375	43	γ	γ	NOUN
ejpam-5019	375	44	=	=	SYM
ejpam-5019	375	45	0	0	PROPN
ejpam-5019	375	46	,	,	PUNCT
ejpam-5019	375	47	δ	δ	X
ejpam-5019	375	48	=	=	SYM
ejpam-5019	375	49	0	0	NUM
ejpam-5019	375	50	,	,	PUNCT
ejpam-5019	375	51	ud	ud	INTJ
ejpam-5019	375	52	(	(	PUNCT
ejpam-5019	375	53	g	g	NOUN
ejpam-5019	375	54	)	)	PUNCT
ejpam-5019	375	55	=	=	SYM
ejpam-5019	376	1	d	d	X
ejpam-5019	376	2	(	(	PUNCT
ejpam-5019	376	3	g	g	NOUN
ejpam-5019	376	4	)	)	PUNCT
ejpam-5019	376	5	and	and	CCONJ
ejpam-5019	376	6	we	we	PRON
ejpam-5019	376	7	obtain	obtain	VERB
ejpam-5019	376	8	the	the	DET
ejpam-5019	376	9	distance	distance	NOUN
ejpam-5019	376	10	spectrum	spectrum	NOUN
ejpam-5019	376	11	of	of	ADP
ejpam-5019	376	12	g	g	NOUN
ejpam-5019	376	13	as	as	ADP
ejpam-5019	376	14	specd	specd	NOUN
ejpam-5019	376	15	(	(	PUNCT
ejpam-5019	376	16	g	g	NOUN
ejpam-5019	376	17	)	)	PUNCT
ejpam-5019	376	18	=	=	SYM
ejpam-5019	376	19	{	{	PUNCT
ejpam-5019	376	20	11.3523	11.3523	NUM
ejpam-5019	376	21	,	,	PUNCT
ejpam-5019	376	22	0,−0.3523,−1,−1,−1,−2,−2,−4	0,−0.3523,−1,−1,−1,−2,−2,−4	NUM
ejpam-5019	376	23	}	}	PUNCT
ejpam-5019	376	24	.	.	PUNCT
ejpam-5019	377	1	also	also	ADV
ejpam-5019	377	2	,	,	PUNCT
ejpam-5019	377	3	when	when	SCONJ
ejpam-5019	377	4	α	α	PROPN
ejpam-5019	377	5	=	=	SYM
ejpam-5019	377	6	0	0	PROPN
ejpam-5019	377	7	,	,	PUNCT
ejpam-5019	377	8	β	β	X
ejpam-5019	377	9	=	=	SYM
ejpam-5019	377	10	−2	−2	NOUN
ejpam-5019	377	11	,	,	PUNCT
ejpam-5019	377	12	γ	γ	NOUN
ejpam-5019	377	13	=	=	SYM
ejpam-5019	377	14	1	1	NUM
ejpam-5019	377	15	,	,	PUNCT
ejpam-5019	377	16	δ	δ	PROPN
ejpam-5019	377	17	=	=	SYM
ejpam-5019	377	18	−1	−1	NOUN
ejpam-5019	377	19	,	,	PUNCT
ejpam-5019	377	20	ud	ud	INTJ
ejpam-5019	377	21	(	(	PUNCT
ejpam-5019	377	22	g	g	NOUN
ejpam-5019	377	23	)	)	PUNCT
ejpam-5019	377	24	=	=	SYM
ejpam-5019	378	1	ds	ds	ADJ
ejpam-5019	378	2	(	(	PUNCT
ejpam-5019	378	3	g	g	NOUN
ejpam-5019	378	4	)	)	PUNCT
ejpam-5019	378	5	=	=	SYM
ejpam-5019	379	1	j	j	PROPN
ejpam-5019	379	2	−	−	NOUN
ejpam-5019	380	1	i	i	PRON
ejpam-5019	380	2	−	−	PROPN
ejpam-5019	380	3	2d	2d	NOUN
ejpam-5019	380	4	(	(	PUNCT
ejpam-5019	380	5	g	g	NOUN
ejpam-5019	380	6	)	)	PUNCT
ejpam-5019	380	7	and	and	CCONJ
ejpam-5019	380	8	we	we	PRON
ejpam-5019	380	9	obtain	obtain	VERB
ejpam-5019	380	10	the	the	DET
ejpam-5019	380	11	eigenvalues	eigenvalue	NOUN
ejpam-5019	380	12	of	of	ADP
ejpam-5019	380	13	the	the	DET
ejpam-5019	380	14	distance	distance	NOUN
ejpam-5019	380	15	seidal	seidal	NOUN
ejpam-5019	380	16	matrix	matrix	NOUN
ejpam-5019	380	17	of	of	ADP
ejpam-5019	380	18	g.	g.	PROPN
ejpam-5019	380	19	references	reference	NOUN
ejpam-5019	380	20	474	474	NUM
ejpam-5019	380	21	4	4	NUM
ejpam-5019	380	22	.	.	PUNCT
ejpam-5019	381	1	conclusion	conclusion	NOUN
ejpam-5019	381	2	in	in	ADP
ejpam-5019	381	3	this	this	DET
ejpam-5019	381	4	paper	paper	NOUN
ejpam-5019	381	5	,	,	PUNCT
ejpam-5019	381	6	we	we	PRON
ejpam-5019	381	7	have	have	AUX
ejpam-5019	381	8	introduced	introduce	VERB
ejpam-5019	381	9	a	a	DET
ejpam-5019	381	10	new	new	ADJ
ejpam-5019	381	11	unified	unified	ADJ
ejpam-5019	381	12	matrix	matrix	NOUN
ejpam-5019	381	13	called	call	VERB
ejpam-5019	381	14	the	the	DET
ejpam-5019	381	15	universal	universal	ADJ
ejpam-5019	381	16	distance	distance	NOUN
ejpam-5019	381	17	matrix	matrix	NOUN
ejpam-5019	381	18	.	.	PUNCT
ejpam-5019	382	1	as	as	ADP
ejpam-5019	382	2	a	a	DET
ejpam-5019	382	3	consequence	consequence	NOUN
ejpam-5019	382	4	,	,	PUNCT
ejpam-5019	382	5	we	we	PRON
ejpam-5019	382	6	can	can	AUX
ejpam-5019	382	7	obtain	obtain	VERB
ejpam-5019	382	8	the	the	DET
ejpam-5019	382	9	eigenvalues	eigenvalue	NOUN
ejpam-5019	382	10	of	of	ADP
ejpam-5019	382	11	distance	distance	NOUN
ejpam-5019	382	12	matrix	matrix	NOUN
ejpam-5019	382	13	,	,	PUNCT
ejpam-5019	382	14	distance	distance	NOUN
ejpam-5019	382	15	laplacian	laplacian	ADJ
ejpam-5019	382	16	matrix	matrix	NOUN
ejpam-5019	382	17	,	,	PUNCT
ejpam-5019	382	18	distance	distance	NOUN
ejpam-5019	382	19	signless	signless	NOUN
ejpam-5019	382	20	laplacian	laplacian	ADJ
ejpam-5019	382	21	matrix	matrix	NOUN
ejpam-5019	382	22	,	,	PUNCT
ejpam-5019	382	23	generalized	generalized	ADJ
ejpam-5019	382	24	distance	distance	NOUN
ejpam-5019	382	25	matrix	matrix	NOUN
ejpam-5019	382	26	,	,	PUNCT
ejpam-5019	382	27	distance	distance	NOUN
ejpam-5019	382	28	seidal	seidal	NOUN
ejpam-5019	382	29	matrix	matrix	NOUN
ejpam-5019	382	30	and	and	CCONJ
ejpam-5019	382	31	distance	distance	NOUN
ejpam-5019	382	32	matrices	matrix	NOUN
ejpam-5019	382	33	of	of	ADP
ejpam-5019	382	34	graph	graph	NOUN
ejpam-5019	382	35	complements	complement	NOUN
ejpam-5019	382	36	.	.	PUNCT
ejpam-5019	383	1	we	we	PRON
ejpam-5019	383	2	have	have	AUX
ejpam-5019	383	3	derived	derive	VERB
ejpam-5019	383	4	the	the	DET
ejpam-5019	383	5	universal	universal	ADJ
ejpam-5019	383	6	distance	distance	NOUN
ejpam-5019	383	7	spectra	spectra	NOUN
ejpam-5019	383	8	of	of	ADP
ejpam-5019	383	9	r−	r−	PROPN
ejpam-5019	383	10	regular	regular	ADJ
ejpam-5019	383	11	graphs	graph	NOUN
ejpam-5019	383	12	,	,	PUNCT
ejpam-5019	383	13	join	join	NOUN
ejpam-5019	383	14	of	of	ADP
ejpam-5019	383	15	two	two	NUM
ejpam-5019	383	16	regulars	regular	NOUN
ejpam-5019	383	17	,	,	PUNCT
ejpam-5019	383	18	joined	join	VERB
ejpam-5019	383	19	union	union	NOUN
ejpam-5019	383	20	of	of	ADP
ejpam-5019	383	21	three	three	NUM
ejpam-5019	383	22	regular	regular	ADJ
ejpam-5019	383	23	graphs	graph	NOUN
ejpam-5019	383	24	and	and	CCONJ
ejpam-5019	383	25	generalized	generalize	VERB
ejpam-5019	383	26	joined	join	VERB
ejpam-5019	383	27	union	union	NOUN
ejpam-5019	383	28	of	of	ADP
ejpam-5019	383	29	g1	g1	PROPN
ejpam-5019	383	30	,	,	PUNCT
ejpam-5019	383	31	g2	g2	PROPN
ejpam-5019	383	32	,	,	PUNCT
ejpam-5019	383	33	.	.	PUNCT
ejpam-5019	383	34	.	.	PUNCT
ejpam-5019	384	1	.	.	PUNCT
ejpam-5019	385	1	,	,	PUNCT
ejpam-5019	385	2	gn	gn	PROPN
ejpam-5019	385	3	regular	regular	ADJ
ejpam-5019	385	4	graphs	graph	NOUN
ejpam-5019	385	5	with	with	ADP
ejpam-5019	385	6	an	an	DET
ejpam-5019	385	7	arbitrary	arbitrary	ADJ
ejpam-5019	385	8	graph	graph	NOUN
ejpam-5019	385	9	of	of	ADP
ejpam-5019	385	10	order	order	NOUN
ejpam-5019	385	11	n.	n.	NOUN
ejpam-5019	385	12	also	also	ADV
ejpam-5019	385	13	,	,	PUNCT
ejpam-5019	385	14	we	we	PRON
ejpam-5019	385	15	obtained	obtain	VERB
ejpam-5019	385	16	the	the	DET
ejpam-5019	385	17	universal	universal	ADJ
ejpam-5019	385	18	distance	distance	NOUN
ejpam-5019	385	19	spectra	spectra	NOUN
ejpam-5019	385	20	of	of	ADP
ejpam-5019	385	21	petersen	petersen	PROPN
ejpam-5019	385	22	graph	graph	NOUN
ejpam-5019	385	23	,	,	PUNCT
ejpam-5019	385	24	complete	complete	ADJ
ejpam-5019	385	25	bipartite	bipartite	NOUN
ejpam-5019	385	26	graph	graph	NOUN
ejpam-5019	385	27	,	,	PUNCT
ejpam-5019	385	28	wheel	wheel	NOUN
ejpam-5019	385	29	graph	graph	NOUN
ejpam-5019	385	30	,	,	PUNCT
ejpam-5019	385	31	complete	complete	ADJ
ejpam-5019	385	32	split	split	NOUN
ejpam-5019	385	33	graph	graph	NOUN
ejpam-5019	385	34	.	.	PUNCT
ejpam-5019	386	1	we	we	PRON
ejpam-5019	386	2	have	have	AUX
ejpam-5019	386	3	also	also	ADV
ejpam-5019	386	4	illustrated	illustrate	VERB
ejpam-5019	386	5	our	our	PRON
ejpam-5019	386	6	results	result	NOUN
ejpam-5019	386	7	through	through	ADP
ejpam-5019	386	8	an	an	DET
ejpam-5019	386	9	example	example	NOUN
ejpam-5019	386	10	for	for	ADP
ejpam-5019	386	11	h	h	NOUN
ejpam-5019	386	12	-	-	PUNCT
ejpam-5019	386	13	join	join	NOUN
ejpam-5019	386	14	of	of	ADP
ejpam-5019	386	15	graphs	graph	NOUN
ejpam-5019	386	16	.	.	PUNCT
ejpam-5019	387	1	our	our	PRON
ejpam-5019	387	2	current	current	ADJ
ejpam-5019	387	3	study	study	NOUN
ejpam-5019	387	4	pertains	pertain	VERB
ejpam-5019	387	5	only	only	ADV
ejpam-5019	387	6	to	to	ADP
ejpam-5019	387	7	regular	regular	ADJ
ejpam-5019	387	8	graphs	graph	NOUN
ejpam-5019	387	9	.	.	PUNCT
ejpam-5019	388	1	this	this	DET
ejpam-5019	388	2	study	study	NOUN
ejpam-5019	388	3	can	can	AUX
ejpam-5019	388	4	be	be	AUX
ejpam-5019	388	5	extended	extend	VERB
ejpam-5019	388	6	to	to	ADP
ejpam-5019	388	7	general	general	ADJ
ejpam-5019	388	8	graphs	graph	NOUN
ejpam-5019	388	9	.	.	PUNCT
ejpam-5019	389	1	we	we	PRON
ejpam-5019	389	2	conclude	conclude	VERB
ejpam-5019	389	3	with	with	ADP
ejpam-5019	389	4	the	the	DET
ejpam-5019	389	5	following	following	ADJ
ejpam-5019	389	6	open	open	ADJ
ejpam-5019	389	7	problems	problem	NOUN
ejpam-5019	389	8	:	:	PUNCT
ejpam-5019	389	9	problem	problem	NOUN
ejpam-5019	389	10	1	1	X
ejpam-5019	389	11	.	.	PUNCT
ejpam-5019	390	1	characterize	characterize	VERB
ejpam-5019	390	2	graphs	graph	NOUN
ejpam-5019	390	3	with	with	ADP
ejpam-5019	390	4	minimal	minimal	ADJ
ejpam-5019	390	5	universal	universal	ADJ
ejpam-5019	390	6	distance	distance	NOUN
ejpam-5019	390	7	spectral	spectral	ADJ
ejpam-5019	390	8	radius	radius	NOUN
ejpam-5019	390	9	.	.	PUNCT
ejpam-5019	391	1	problem	problem	NOUN
ejpam-5019	391	2	2	2	NUM
ejpam-5019	391	3	.	.	PUNCT
ejpam-5019	391	4	find	find	VERB
ejpam-5019	391	5	k−	k−	NOUN
ejpam-5019	391	6	transmission	transmission	NOUN
ejpam-5019	391	7	regular	regular	ADJ
ejpam-5019	391	8	graphs	graph	NOUN
ejpam-5019	391	9	for	for	ADP
ejpam-5019	391	10	particular	particular	ADJ
ejpam-5019	391	11	values	value	NOUN
ejpam-5019	391	12	of	of	ADP
ejpam-5019	391	13	α	α	PROPN
ejpam-5019	391	14	,	,	PUNCT
ejpam-5019	391	15	β	β	X
ejpam-5019	391	16	,	,	PUNCT
ejpam-5019	391	17	γ	γ	PROPN
ejpam-5019	391	18	,	,	PUNCT
ejpam-5019	391	19	δ	δ	PROPN
ejpam-5019	391	20	∈	∈	PROPN
ejpam-5019	391	21	r.	r.	PROPN
ejpam-5019	391	22	problem	problem	NOUN
ejpam-5019	391	23	3	3	X
ejpam-5019	391	24	.	.	PUNCT
ejpam-5019	391	25	find	find	VERB
ejpam-5019	391	26	the	the	DET
ejpam-5019	391	27	upper	upper	ADJ
ejpam-5019	391	28	bound	bind	VERB
ejpam-5019	391	29	for	for	ADP
ejpam-5019	391	30	the	the	DET
ejpam-5019	391	31	largest	large	ADJ
ejpam-5019	391	32	universal	universal	ADJ
ejpam-5019	391	33	distance	distance	NOUN
ejpam-5019	391	34	eigenvalue	eigenvalue	NOUN
ejpam-5019	391	35	and	and	CCONJ
ejpam-5019	391	36	universal	universal	ADJ
ejpam-5019	391	37	distance	distance	NOUN
ejpam-5019	391	38	energy	energy	NOUN
ejpam-5019	391	39	.	.	PUNCT
ejpam-5019	392	1	acknowledgements	acknowledgement	NOUN
ejpam-5019	392	2	we	we	PRON
ejpam-5019	392	3	are	be	AUX
ejpam-5019	392	4	highly	highly	ADV
ejpam-5019	392	5	thankful	thankful	ADJ
ejpam-5019	392	6	to	to	ADP
ejpam-5019	392	7	the	the	DET
ejpam-5019	392	8	anonymous	anonymous	ADJ
ejpam-5019	392	9	referees	referee	NOUN
ejpam-5019	392	10	for	for	SCONJ
ejpam-5019	392	11	their	their	PRON
ejpam-5019	392	12	comments	comment	NOUN
ejpam-5019	392	13	and	and	CCONJ
ejpam-5019	392	14	suggestions	suggestion	NOUN
ejpam-5019	392	15	to	to	PART
ejpam-5019	392	16	enhance	enhance	VERB
ejpam-5019	392	17	our	our	PRON
ejpam-5019	392	18	paper	paper	NOUN
ejpam-5019	392	19	.	.	PUNCT
ejpam-5019	393	1	references	reference	NOUN
ejpam-5019	393	2	[	[	X
ejpam-5019	393	3	1	1	X
ejpam-5019	393	4	]	]	PUNCT
ejpam-5019	393	5	abdollah	abdollah	PROPN
ejpam-5019	393	6	alhevaz	alhevaz	PROPN
ejpam-5019	393	7	,	,	PUNCT
ejpam-5019	393	8	maryam	maryam	PROPN
ejpam-5019	393	9	baghipur	baghipur	PROPN
ejpam-5019	393	10	,	,	PUNCT
ejpam-5019	393	11	hilal	hilal	PROPN
ejpam-5019	393	12	a.	a.	PROPN
ejpam-5019	393	13	ganie	ganie	PROPN
ejpam-5019	393	14	,	,	PUNCT
ejpam-5019	393	15	and	and	CCONJ
ejpam-5019	393	16	yilun	yilun	PROPN
ejpam-5019	393	17	shang	shang	PROPN
ejpam-5019	393	18	.	.	PUNCT
ejpam-5019	394	1	the	the	DET
ejpam-5019	394	2	generalized	generalized	ADJ
ejpam-5019	394	3	distance	distance	NOUN
ejpam-5019	394	4	spectrum	spectrum	NOUN
ejpam-5019	394	5	of	of	ADP
ejpam-5019	394	6	the	the	DET
ejpam-5019	394	7	join	join	NOUN
ejpam-5019	394	8	of	of	ADP
ejpam-5019	394	9	graphs	graph	NOUN
ejpam-5019	394	10	.	.	PUNCT
ejpam-5019	395	1	symmetry	symmetry	NOUN
ejpam-5019	395	2	,	,	PUNCT
ejpam-5019	395	3	12(1):169	12(1):169	PROPN
ejpam-5019	395	4	,	,	PUNCT
ejpam-5019	395	5	2020	2020	NUM
ejpam-5019	395	6	.	.	PUNCT
ejpam-5019	396	1	[	[	X
ejpam-5019	396	2	2	2	X
ejpam-5019	396	3	]	]	PUNCT
ejpam-5019	396	4	mustapha	mustapha	PROPN
ejpam-5019	396	5	aouchiche	aouchiche	NOUN
ejpam-5019	396	6	and	and	CCONJ
ejpam-5019	396	7	pierre	pierre	PROPN
ejpam-5019	396	8	hansen	hansen	PROPN
ejpam-5019	396	9	.	.	PROPN
ejpam-5019	397	1	two	two	NUM
ejpam-5019	397	2	laplacians	laplacian	NOUN
ejpam-5019	397	3	for	for	ADP
ejpam-5019	397	4	the	the	DET
ejpam-5019	397	5	distance	distance	NOUN
ejpam-5019	397	6	matrix	matrix	NOUN
ejpam-5019	397	7	of	of	ADP
ejpam-5019	397	8	a	a	DET
ejpam-5019	397	9	graph	graph	NOUN
ejpam-5019	397	10	.	.	PUNCT
ejpam-5019	398	1	linear	linear	ADJ
ejpam-5019	398	2	algebra	algebra	NOUN
ejpam-5019	398	3	and	and	CCONJ
ejpam-5019	398	4	its	its	PRON
ejpam-5019	398	5	applications	application	NOUN
ejpam-5019	398	6	,	,	PUNCT
ejpam-5019	398	7	439(1):21–33	439(1):21–33	NOUN
ejpam-5019	398	8	,	,	PUNCT
ejpam-5019	398	9	2013	2013	NUM
ejpam-5019	398	10	.	.	PUNCT
ejpam-5019	399	1	[	[	X
ejpam-5019	399	2	3	3	X
ejpam-5019	399	3	]	]	X
ejpam-5019	399	4	maryam	maryam	PROPN
ejpam-5019	399	5	baghipur	baghipur	PROPN
ejpam-5019	399	6	,	,	PUNCT
ejpam-5019	399	7	modjtaba	modjtaba	NOUN
ejpam-5019	399	8	ghorbani	ghorbani	NOUN
ejpam-5019	399	9	,	,	PUNCT
ejpam-5019	399	10	hilal	hilal	PROPN
ejpam-5019	399	11	a	a	DET
ejpam-5019	399	12	ganie	ganie	NOUN
ejpam-5019	399	13	,	,	PUNCT
ejpam-5019	399	14	and	and	CCONJ
ejpam-5019	399	15	yilun	yilun	PROPN
ejpam-5019	399	16	shang	shang	PROPN
ejpam-5019	399	17	.	.	PUNCT
ejpam-5019	400	1	on	on	ADP
ejpam-5019	400	2	the	the	DET
ejpam-5019	400	3	second	second	ADV
ejpam-5019	400	4	-	-	PUNCT
ejpam-5019	400	5	largest	large	ADJ
ejpam-5019	400	6	reciprocal	reciprocal	ADJ
ejpam-5019	400	7	distance	distance	NOUN
ejpam-5019	400	8	signless	signless	NOUN
ejpam-5019	400	9	laplacian	laplacian	ADJ
ejpam-5019	400	10	eigenvalue	eigenvalue	PROPN
ejpam-5019	400	11	.	.	PUNCT
ejpam-5019	400	12	mathematics	mathematic	NOUN
ejpam-5019	400	13	,	,	PUNCT
ejpam-5019	400	14	9(5):512	9(5):512	NUM
ejpam-5019	400	15	,	,	PUNCT
ejpam-5019	400	16	2021	2021	NUM
ejpam-5019	400	17	.	.	PUNCT
ejpam-5019	401	1	[	[	X
ejpam-5019	401	2	4	4	NUM
ejpam-5019	401	3	]	]	X
ejpam-5019	401	4	sasmita	sasmita	PROPN
ejpam-5019	401	5	barik	barik	PROPN
ejpam-5019	401	6	,	,	PUNCT
ejpam-5019	401	7	deabajit	deabajit	PROPN
ejpam-5019	401	8	kalita	kalita	PROPN
ejpam-5019	401	9	,	,	PUNCT
ejpam-5019	401	10	sukanta	sukanta	PROPN
ejpam-5019	401	11	pati	pati	PROPN
ejpam-5019	401	12	,	,	PUNCT
ejpam-5019	401	13	and	and	CCONJ
ejpam-5019	401	14	gopinath	gopinath	PROPN
ejpam-5019	401	15	sahoo	sahoo	PROPN
ejpam-5019	401	16	.	.	PUNCT
ejpam-5019	401	17	spectra	spectra	PROPN
ejpam-5019	401	18	of	of	ADP
ejpam-5019	401	19	graphs	graph	NOUN
ejpam-5019	401	20	resulting	result	VERB
ejpam-5019	401	21	from	from	ADP
ejpam-5019	401	22	various	various	ADJ
ejpam-5019	401	23	graph	graph	NOUN
ejpam-5019	401	24	operations	operation	NOUN
ejpam-5019	401	25	and	and	CCONJ
ejpam-5019	401	26	products	product	NOUN
ejpam-5019	401	27	:	:	PUNCT
ejpam-5019	401	28	a	a	DET
ejpam-5019	401	29	survey	survey	NOUN
ejpam-5019	401	30	.	.	PUNCT
ejpam-5019	402	1	special	special	ADJ
ejpam-5019	402	2	matrices	matrix	NOUN
ejpam-5019	402	3	,	,	PUNCT
ejpam-5019	402	4	6(1):323–342	6(1):323–342	NOUN
ejpam-5019	402	5	,	,	PUNCT
ejpam-5019	402	6	2018	2018	NUM
ejpam-5019	402	7	.	.	PUNCT
ejpam-5019	403	1	[	[	X
ejpam-5019	403	2	5	5	X
ejpam-5019	403	3	]	]	X
ejpam-5019	403	4	andries	andries	PROPN
ejpam-5019	403	5	e	e	PROPN
ejpam-5019	403	6	brouwer	brouwer	PROPN
ejpam-5019	403	7	and	and	CCONJ
ejpam-5019	403	8	willem	willem	PROPN
ejpam-5019	403	9	h	h	PROPN
ejpam-5019	403	10	haemers	haemer	NOUN
ejpam-5019	403	11	.	.	PUNCT
ejpam-5019	404	1	spectra	spectra	NOUN
ejpam-5019	404	2	of	of	ADP
ejpam-5019	404	3	graphs	graph	NOUN
ejpam-5019	404	4	.	.	PUNCT
ejpam-5019	405	1	springer	springer	NOUN
ejpam-5019	405	2	science	science	PROPN
ejpam-5019	405	3	&	&	CCONJ
ejpam-5019	405	4	business	business	NOUN
ejpam-5019	405	5	media	medium	NOUN
ejpam-5019	405	6	,	,	PUNCT
ejpam-5019	405	7	2011	2011	NUM
ejpam-5019	405	8	.	.	PUNCT
ejpam-5019	406	1	references	reference	NOUN
ejpam-5019	406	2	475	475	NUM
ejpam-5019	406	3	[	[	X
ejpam-5019	406	4	6	6	NUM
ejpam-5019	406	5	]	]	PUNCT
ejpam-5019	406	6	domingos	domingos	PROPN
ejpam-5019	406	7	m	m	PROPN
ejpam-5019	406	8	cardoso	cardoso	PROPN
ejpam-5019	406	9	,	,	PUNCT
ejpam-5019	406	10	maria	maria	PROPN
ejpam-5019	406	11	aguieiras	aguieiras	PROPN
ejpam-5019	406	12	a	a	DET
ejpam-5019	406	13	de	de	X
ejpam-5019	406	14	freitas	freita	NOUN
ejpam-5019	406	15	,	,	PUNCT
ejpam-5019	406	16	enide	enide	NOUN
ejpam-5019	406	17	andrade	andrade	PROPN
ejpam-5019	406	18	martins	martins	PROPN
ejpam-5019	406	19	,	,	PUNCT
ejpam-5019	406	20	and	and	CCONJ
ejpam-5019	406	21	maŕıa	maŕıa	ADV
ejpam-5019	406	22	robbiano	robbiano	ADJ
ejpam-5019	406	23	.	.	PUNCT
ejpam-5019	407	1	spectra	spectra	NOUN
ejpam-5019	407	2	of	of	ADP
ejpam-5019	407	3	graphs	graph	NOUN
ejpam-5019	407	4	obtained	obtain	VERB
ejpam-5019	407	5	by	by	ADP
ejpam-5019	407	6	a	a	DET
ejpam-5019	407	7	generalization	generalization	NOUN
ejpam-5019	407	8	of	of	ADP
ejpam-5019	407	9	the	the	DET
ejpam-5019	407	10	join	join	NOUN
ejpam-5019	407	11	graph	graph	NOUN
ejpam-5019	407	12	operation	operation	NOUN
ejpam-5019	407	13	.	.	PUNCT
ejpam-5019	408	1	discrete	discrete	ADJ
ejpam-5019	408	2	mathematics	mathematic	NOUN
ejpam-5019	408	3	,	,	PUNCT
ejpam-5019	408	4	313(5):733–741	313(5):733–741	NUM
ejpam-5019	408	5	,	,	PUNCT
ejpam-5019	408	6	2013	2013	NUM
ejpam-5019	408	7	.	.	PUNCT
ejpam-5019	409	1	[	[	X
ejpam-5019	409	2	7	7	X
ejpam-5019	409	3	]	]	X
ejpam-5019	409	4	domingos	domingos	PROPN
ejpam-5019	409	5	m	m	PROPN
ejpam-5019	409	6	cardoso	cardoso	PROPN
ejpam-5019	409	7	,	,	PUNCT
ejpam-5019	409	8	helena	helena	PROPN
ejpam-5019	409	9	gomes	gome	NOUN
ejpam-5019	409	10	,	,	PUNCT
ejpam-5019	409	11	and	and	CCONJ
ejpam-5019	409	12	sofia	sofia	PROPN
ejpam-5019	409	13	j	j	PROPN
ejpam-5019	409	14	pinheiro	pinheiro	PROPN
ejpam-5019	409	15	.	.	PUNCT
ejpam-5019	410	1	the	the	DET
ejpam-5019	410	2	h	h	NOUN
ejpam-5019	410	3	-	-	PUNCT
ejpam-5019	410	4	join	join	NOUN
ejpam-5019	410	5	of	of	ADP
ejpam-5019	410	6	arbitrary	arbitrary	ADJ
ejpam-5019	410	7	families	family	NOUN
ejpam-5019	410	8	of	of	ADP
ejpam-5019	410	9	graphs	graph	NOUN
ejpam-5019	410	10	-	-	PUNCT
ejpam-5019	410	11	the	the	DET
ejpam-5019	410	12	universal	universal	ADJ
ejpam-5019	410	13	adjacency	adjacency	NOUN
ejpam-5019	410	14	spectrum	spectrum	NOUN
ejpam-5019	410	15	.	.	PUNCT
ejpam-5019	411	1	linear	linear	PROPN
ejpam-5019	411	2	algebra	algebra	NOUN
ejpam-5019	411	3	and	and	CCONJ
ejpam-5019	411	4	its	its	PRON
ejpam-5019	411	5	applications	application	NOUN
ejpam-5019	411	6	,	,	PUNCT
ejpam-5019	411	7	648:160–180	648:160–180	NUM
ejpam-5019	411	8	,	,	PUNCT
ejpam-5019	411	9	2022	2022	NUM
ejpam-5019	411	10	.	.	PUNCT
ejpam-5019	412	1	[	[	X
ejpam-5019	412	2	8	8	NUM
ejpam-5019	412	3	]	]	X
ejpam-5019	412	4	shu	shu	PROPN
ejpam-5019	412	5	-	-	PUNCT
ejpam-5019	412	6	yu	yu	PROPN
ejpam-5019	412	7	cui	cui	PROPN
ejpam-5019	412	8	,	,	PUNCT
ejpam-5019	412	9	jing	je	VERB
ejpam-5019	412	10	-	-	PUNCT
ejpam-5019	412	11	xiang	xiang	PROPN
ejpam-5019	412	12	he	he	PRON
ejpam-5019	412	13	,	,	PUNCT
ejpam-5019	412	14	and	and	CCONJ
ejpam-5019	412	15	gui	gui	PROPN
ejpam-5019	412	16	-	-	PUNCT
ejpam-5019	412	17	xian	xian	NOUN
ejpam-5019	412	18	tian	tian	PROPN
ejpam-5019	412	19	.	.	PUNCT
ejpam-5019	413	1	the	the	DET
ejpam-5019	413	2	generalized	generalized	ADJ
ejpam-5019	413	3	distance	distance	NOUN
ejpam-5019	413	4	matrix	matrix	NOUN
ejpam-5019	413	5	.	.	PUNCT
ejpam-5019	414	1	linear	linear	ADJ
ejpam-5019	414	2	algebra	algebra	NOUN
ejpam-5019	414	3	and	and	CCONJ
ejpam-5019	414	4	its	its	PRON
ejpam-5019	414	5	applications	application	NOUN
ejpam-5019	414	6	,	,	PUNCT
ejpam-5019	414	7	563:1–23	563:1–23	NUM
ejpam-5019	414	8	,	,	PUNCT
ejpam-5019	414	9	2019	2019	NUM
ejpam-5019	414	10	.	.	PUNCT
ejpam-5019	415	1	[	[	X
ejpam-5019	415	2	9	9	NUM
ejpam-5019	415	3	]	]	X
ejpam-5019	415	4	dragos	dragos	PROPN
ejpam-5019	415	5	m	m	PROPN
ejpam-5019	415	6	cvetkovic	cvetkovic	ADJ
ejpam-5019	415	7	,	,	PUNCT
ejpam-5019	415	8	michael	michael	PROPN
ejpam-5019	415	9	doob	doob	PROPN
ejpam-5019	415	10	,	,	PUNCT
ejpam-5019	415	11	and	and	CCONJ
ejpam-5019	415	12	horst	horst	PROPN
ejpam-5019	415	13	sachs	sachs	PROPN
ejpam-5019	415	14	.	.	PUNCT
ejpam-5019	416	1	spectra	spectra	PROPN
ejpam-5019	416	2	of	of	ADP
ejpam-5019	416	3	graphs	graph	NOUN
ejpam-5019	416	4	.	.	PUNCT
ejpam-5019	417	1	theory	theory	NOUN
ejpam-5019	417	2	and	and	CCONJ
ejpam-5019	417	3	application	application	NOUN
ejpam-5019	417	4	.	.	PUNCT
ejpam-5019	418	1	1980	1980	NUM
ejpam-5019	418	2	.	.	PUNCT
ejpam-5019	419	1	[	[	X
ejpam-5019	419	2	10	10	NUM
ejpam-5019	419	3	]	]	X
ejpam-5019	419	4	roberto	roberto	PROPN
ejpam-5019	419	5	c	c	PROPN
ejpam-5019	419	6	dı́az	dı́az	PROPN
ejpam-5019	419	7	,	,	PUNCT
ejpam-5019	419	8	germain	germain	PROPN
ejpam-5019	419	9	pastén	pastén	PROPN
ejpam-5019	419	10	,	,	PUNCT
ejpam-5019	419	11	and	and	CCONJ
ejpam-5019	419	12	oscar	oscar	PROPN
ejpam-5019	419	13	rojo	rojo	PROPN
ejpam-5019	419	14	.	.	PUNCT
ejpam-5019	420	1	new	new	ADJ
ejpam-5019	420	2	results	result	NOUN
ejpam-5019	420	3	on	on	ADP
ejpam-5019	420	4	the	the	DET
ejpam-5019	420	5	dα	dα	NOUN
ejpam-5019	420	6	-	-	PUNCT
ejpam-5019	420	7	matrix	matrix	NOUN
ejpam-5019	420	8	of	of	ADP
ejpam-5019	420	9	connected	connected	ADJ
ejpam-5019	420	10	graphs	graph	NOUN
ejpam-5019	420	11	.	.	PUNCT
ejpam-5019	421	1	linear	linear	ADJ
ejpam-5019	421	2	algebra	algebra	NOUN
ejpam-5019	421	3	and	and	CCONJ
ejpam-5019	421	4	its	its	PRON
ejpam-5019	421	5	applications	application	NOUN
ejpam-5019	421	6	,	,	PUNCT
ejpam-5019	421	7	577:168–185	577:168–185	NUM
ejpam-5019	421	8	,	,	PUNCT
ejpam-5019	421	9	2019	2019	NUM
ejpam-5019	421	10	.	.	PUNCT
ejpam-5019	422	1	[	[	X
ejpam-5019	422	2	11	11	NUM
ejpam-5019	422	3	]	]	X
ejpam-5019	422	4	willem	willem	NOUN
ejpam-5019	422	5	h	h	PROPN
ejpam-5019	422	6	haemers	haemer	NOUN
ejpam-5019	422	7	.	.	PUNCT
ejpam-5019	423	1	regularity	regularity	NOUN
ejpam-5019	423	2	and	and	CCONJ
ejpam-5019	423	3	the	the	DET
ejpam-5019	423	4	spectra	spectra	NOUN
ejpam-5019	423	5	of	of	ADP
ejpam-5019	423	6	graphs	graph	NOUN
ejpam-5019	423	7	.	.	PUNCT
ejpam-5019	424	1	surveys	survey	NOUN
ejpam-5019	424	2	in	in	ADP
ejpam-5019	424	3	combinatorics	combinatoric	NOUN
ejpam-5019	424	4	,	,	PUNCT
ejpam-5019	424	5	365:75–90	365:75–90	NUM
ejpam-5019	424	6	,	,	PUNCT
ejpam-5019	424	7	2009	2009	NUM
ejpam-5019	424	8	.	.	PUNCT
ejpam-5019	425	1	[	[	X
ejpam-5019	425	2	12	12	NUM
ejpam-5019	425	3	]	]	PUNCT
ejpam-5019	425	4	willem	willem	NOUN
ejpam-5019	425	5	h	h	PROPN
ejpam-5019	425	6	haemers	haemer	NOUN
ejpam-5019	425	7	and	and	CCONJ
ejpam-5019	425	8	mohammad	mohammad	PROPN
ejpam-5019	425	9	reza	reza	PROPN
ejpam-5019	425	10	oboudi	oboudi	PROPN
ejpam-5019	425	11	.	.	PUNCT
ejpam-5019	426	1	universal	universal	ADJ
ejpam-5019	426	2	spectra	spectra	NOUN
ejpam-5019	426	3	of	of	ADP
ejpam-5019	426	4	the	the	DET
ejpam-5019	426	5	disjoint	disjoint	PROPN
ejpam-5019	426	6	union	union	NOUN
ejpam-5019	426	7	of	of	ADP
ejpam-5019	426	8	regular	regular	ADJ
ejpam-5019	426	9	graphs	graph	NOUN
ejpam-5019	426	10	.	.	PUNCT
ejpam-5019	427	1	linear	linear	ADJ
ejpam-5019	427	2	algebra	algebra	NOUN
ejpam-5019	427	3	and	and	CCONJ
ejpam-5019	427	4	its	its	PRON
ejpam-5019	427	5	applications	application	NOUN
ejpam-5019	427	6	,	,	PUNCT
ejpam-5019	427	7	606:244–248	606:244–248	NUM
ejpam-5019	427	8	,	,	PUNCT
ejpam-5019	427	9	2020	2020	NUM
ejpam-5019	427	10	.	.	PUNCT
ejpam-5019	428	1	[	[	X
ejpam-5019	428	2	13	13	NUM
ejpam-5019	428	3	]	]	X
ejpam-5019	428	4	chithra	chithra	PROPN
ejpam-5019	428	5	haritha	haritha	PROPN
ejpam-5019	428	6	et	et	PROPN
ejpam-5019	428	7	al	al	PROPN
ejpam-5019	428	8	.	.	PROPN
ejpam-5019	428	9	distance	distance	PROPN
ejpam-5019	428	10	seidel	seidel	PROPN
ejpam-5019	428	11	matrix	matrix	NOUN
ejpam-5019	428	12	of	of	ADP
ejpam-5019	428	13	a	a	DET
ejpam-5019	428	14	connected	connected	ADJ
ejpam-5019	428	15	graph	graph	NOUN
ejpam-5019	428	16	.	.	PUNCT
ejpam-5019	429	1	arxiv	arxiv	PROPN
ejpam-5019	429	2	preprint	preprint	PROPN
ejpam-5019	429	3	arxiv:2210.05940	arxiv:2210.05940	NOUN
ejpam-5019	429	4	,	,	PUNCT
ejpam-5019	429	5	2022	2022	NUM
ejpam-5019	429	6	.	.	PUNCT
ejpam-5019	430	1	[	[	X
ejpam-5019	430	2	14	14	NUM
ejpam-5019	430	3	]	]	X
ejpam-5019	430	4	pavel	pavel	PROPN
ejpam-5019	430	5	hic	hic	PROPN
ejpam-5019	430	6	,	,	PUNCT
ejpam-5019	430	7	milan	milan	PROPN
ejpam-5019	430	8	pokorny	pokorny	PROPN
ejpam-5019	430	9	,	,	PUNCT
ejpam-5019	430	10	and	and	CCONJ
ejpam-5019	430	11	dragan	dragan	VERB
ejpam-5019	430	12	stevanovic	stevanovic	VERB
ejpam-5019	430	13	.	.	PUNCT
ejpam-5019	431	1	seidel	seidel	PROPN
ejpam-5019	431	2	integral	integral	ADJ
ejpam-5019	431	3	complete	complete	ADJ
ejpam-5019	431	4	split	split	NOUN
ejpam-5019	431	5	graphs	graph	NOUN
ejpam-5019	431	6	.	.	PUNCT
ejpam-5019	432	1	mathematics	mathematic	NOUN
ejpam-5019	432	2	interdisciplinary	interdisciplinary	ADJ
ejpam-5019	432	3	research	research	NOUN
ejpam-5019	432	4	,	,	PUNCT
ejpam-5019	432	5	4(2):137–150	4(2):137–150	NUM
ejpam-5019	432	6	,	,	PUNCT
ejpam-5019	432	7	2019	2019	NUM
ejpam-5019	432	8	.	.	PUNCT
ejpam-5019	433	1	[	[	X
ejpam-5019	433	2	15	15	NUM
ejpam-5019	433	3	]	]	X
ejpam-5019	433	4	gopalapillai	gopalapillai	ADJ
ejpam-5019	433	5	indulal	indulal	NOUN
ejpam-5019	433	6	.	.	PUNCT
ejpam-5019	434	1	distance	distance	NOUN
ejpam-5019	434	2	spectrum	spectrum	NOUN
ejpam-5019	434	3	of	of	ADP
ejpam-5019	434	4	graph	graph	NOUN
ejpam-5019	434	5	compositions	composition	NOUN
ejpam-5019	434	6	.	.	PUNCT
ejpam-5019	435	1	ars	ars	PROPN
ejpam-5019	435	2	math	math	PROPN
ejpam-5019	435	3	.	.	PUNCT
ejpam-5019	436	1	contemp	contemp	NOUN
ejpam-5019	436	2	.	.	PUNCT
ejpam-5019	436	3	,	,	PUNCT
ejpam-5019	436	4	2(1):93–100	2(1):93–100	NUM
ejpam-5019	436	5	,	,	PUNCT
ejpam-5019	436	6	2009	2009	NUM
ejpam-5019	436	7	.	.	PUNCT
ejpam-5019	437	1	[	[	X
ejpam-5019	437	2	16	16	NUM
ejpam-5019	437	3	]	]	X
ejpam-5019	437	4	saleem	saleem	PROPN
ejpam-5019	437	5	khan	khan	PROPN
ejpam-5019	437	6	,	,	PUNCT
ejpam-5019	437	7	shariefuddin	shariefuddin	VERB
ejpam-5019	437	8	pirzada	pirzada	PROPN
ejpam-5019	437	9	,	,	PUNCT
ejpam-5019	437	10	and	and	CCONJ
ejpam-5019	437	11	yilun	yilun	PROPN
ejpam-5019	437	12	shang	shang	PROPN
ejpam-5019	437	13	.	.	PUNCT
ejpam-5019	438	1	on	on	ADP
ejpam-5019	438	2	the	the	DET
ejpam-5019	438	3	sum	sum	NOUN
ejpam-5019	438	4	and	and	CCONJ
ejpam-5019	438	5	spread	spread	VERB
ejpam-5019	438	6	of	of	ADP
ejpam-5019	438	7	reciprocal	reciprocal	ADJ
ejpam-5019	438	8	distance	distance	NOUN
ejpam-5019	438	9	laplacian	laplacian	ADJ
ejpam-5019	438	10	eigenvalues	eigenvalue	NOUN
ejpam-5019	438	11	of	of	ADP
ejpam-5019	438	12	graphs	graph	NOUN
ejpam-5019	438	13	in	in	ADP
ejpam-5019	438	14	terms	term	NOUN
ejpam-5019	438	15	of	of	ADP
ejpam-5019	438	16	harary	harary	PROPN
ejpam-5019	438	17	index	index	PROPN
ejpam-5019	438	18	.	.	PUNCT
ejpam-5019	439	1	symmetry	symmetry	PROPN
ejpam-5019	439	2	,	,	PUNCT
ejpam-5019	439	3	14(9):1937	14(9):1937	NUM
ejpam-5019	439	4	,	,	PUNCT
ejpam-5019	439	5	2022	2022	NUM
ejpam-5019	439	6	.	.	PUNCT
ejpam-5019	440	1	[	[	X
ejpam-5019	440	2	17	17	NUM
ejpam-5019	440	3	]	]	PUNCT
ejpam-5019	440	4	bilal	bilal	NOUN
ejpam-5019	440	5	a	a	DET
ejpam-5019	440	6	rather	rather	PROPN
ejpam-5019	440	7	,	,	PUNCT
ejpam-5019	440	8	hilal	hilal	PROPN
ejpam-5019	440	9	a	a	DET
ejpam-5019	440	10	ganie	ganie	NOUN
ejpam-5019	440	11	,	,	PUNCT
ejpam-5019	440	12	and	and	CCONJ
ejpam-5019	440	13	yilun	yilun	PROPN
ejpam-5019	440	14	shang	shang	PROPN
ejpam-5019	440	15	.	.	PUNCT
ejpam-5019	441	1	distance	distance	PROPN
ejpam-5019	441	2	laplacian	laplacian	PROPN
ejpam-5019	441	3	spectral	spectral	ADJ
ejpam-5019	441	4	ordering	ordering	NOUN
ejpam-5019	441	5	of	of	ADP
ejpam-5019	441	6	sun	sun	NOUN
ejpam-5019	441	7	type	type	NOUN
ejpam-5019	441	8	graphs	graph	NOUN
ejpam-5019	441	9	.	.	PUNCT
ejpam-5019	442	1	applied	apply	VERB
ejpam-5019	442	2	mathematics	mathematic	NOUN
ejpam-5019	442	3	and	and	CCONJ
ejpam-5019	442	4	computation	computation	NOUN
ejpam-5019	442	5	,	,	PUNCT
ejpam-5019	442	6	445:127847	445:127847	NUM
ejpam-5019	442	7	,	,	PUNCT
ejpam-5019	442	8	2023	2023	NUM
ejpam-5019	442	9	.	.	PUNCT
ejpam-5019	443	1	[	[	X
ejpam-5019	443	2	18	18	NUM
ejpam-5019	443	3	]	]	X
ejpam-5019	443	4	m	m	PROPN
ejpam-5019	443	5	saravanan	saravanan	PROPN
ejpam-5019	443	6	,	,	PUNCT
ejpam-5019	443	7	sp	sp	ADP
ejpam-5019	443	8	murugan	murugan	PROPN
ejpam-5019	443	9	,	,	PUNCT
ejpam-5019	443	10	and	and	CCONJ
ejpam-5019	443	11	g	g	PROPN
ejpam-5019	443	12	arunkumar	arunkumar	PROPN
ejpam-5019	443	13	.	.	PUNCT
ejpam-5019	444	1	a	a	DET
ejpam-5019	444	2	generalization	generalization	NOUN
ejpam-5019	444	3	of	of	ADP
ejpam-5019	444	4	fiedler	fiedler	PROPN
ejpam-5019	444	5	’s	’s	PART
ejpam-5019	444	6	lemma	lemma	PROPN
ejpam-5019	444	7	and	and	CCONJ
ejpam-5019	444	8	the	the	DET
ejpam-5019	444	9	spectra	spectra	NOUN
ejpam-5019	444	10	of	of	ADP
ejpam-5019	444	11	h	h	NOUN
ejpam-5019	444	12	-	-	PUNCT
ejpam-5019	444	13	join	join	NOUN
ejpam-5019	444	14	of	of	ADP
ejpam-5019	444	15	graphs	graph	NOUN
ejpam-5019	444	16	.	.	PUNCT
ejpam-5019	445	1	linear	linear	ADJ
ejpam-5019	445	2	algebra	algebra	NOUN
ejpam-5019	445	3	and	and	CCONJ
ejpam-5019	445	4	its	its	PRON
ejpam-5019	445	5	applications	application	NOUN
ejpam-5019	445	6	,	,	PUNCT
ejpam-5019	445	7	625:20–43	625:20–43	NOUN
ejpam-5019	445	8	,	,	PUNCT
ejpam-5019	445	9	2021	2021	NUM
ejpam-5019	445	10	.	.	PUNCT
ejpam-5019	446	1	[	[	X
ejpam-5019	446	2	19	19	NUM
ejpam-5019	446	3	]	]	X
ejpam-5019	446	4	allen	allen	PROPN
ejpam-5019	446	5	j	j	PROPN
ejpam-5019	446	6	schwenk	schwenk	ADV
ejpam-5019	446	7	.	.	PUNCT
ejpam-5019	447	1	computing	compute	VERB
ejpam-5019	447	2	the	the	DET
ejpam-5019	447	3	characteristic	characteristic	ADJ
ejpam-5019	447	4	polynomial	polynomial	NOUN
ejpam-5019	447	5	of	of	ADP
ejpam-5019	447	6	a	a	DET
ejpam-5019	447	7	graph	graph	NOUN
ejpam-5019	447	8	.	.	PUNCT
ejpam-5019	448	1	in	in	ADP
ejpam-5019	448	2	graphs	graph	NOUN
ejpam-5019	448	3	and	and	CCONJ
ejpam-5019	448	4	combinatorics	combinatoric	NOUN
ejpam-5019	448	5	:	:	PUNCT
ejpam-5019	448	6	proceedings	proceeding	NOUN
ejpam-5019	448	7	of	of	ADP
ejpam-5019	448	8	the	the	DET
ejpam-5019	448	9	capital	capital	NOUN
ejpam-5019	448	10	conference	conference	NOUN
ejpam-5019	448	11	on	on	ADP
ejpam-5019	448	12	graph	graph	NOUN
ejpam-5019	448	13	theory	theory	NOUN
ejpam-5019	448	14	and	and	CCONJ
ejpam-5019	448	15	combinatorics	combinatoric	NOUN
ejpam-5019	448	16	at	at	ADP
ejpam-5019	448	17	the	the	DET
ejpam-5019	448	18	george	george	PROPN
ejpam-5019	448	19	washington	washington	PROPN
ejpam-5019	448	20	university	university	PROPN
ejpam-5019	448	21	june	june	PROPN
ejpam-5019	448	22	18–22	18–22	NUM
ejpam-5019	448	23	,	,	PUNCT
ejpam-5019	448	24	1973	1973	NUM
ejpam-5019	448	25	,	,	PUNCT
ejpam-5019	448	26	pages	page	NOUN
ejpam-5019	448	27	153	153	NUM
ejpam-5019	448	28	–	–	PUNCT
ejpam-5019	448	29	172	172	NUM
ejpam-5019	448	30	.	.	PUNCT
ejpam-5019	448	31	springer	springer	NOUN
ejpam-5019	448	32	,	,	PUNCT
ejpam-5019	448	33	2006	2006	NUM
ejpam-5019	448	34	.	.	PUNCT
ejpam-5019	449	1	references	reference	NOUN
ejpam-5019	449	2	476	476	NUM
ejpam-5019	450	1	[	[	X
ejpam-5019	450	2	20	20	NUM
ejpam-5019	450	3	]	]	PUNCT
ejpam-5019	450	4	dragan	dragan	VERB
ejpam-5019	450	5	stevanović	stevanović	NOUN
ejpam-5019	450	6	and	and	CCONJ
ejpam-5019	450	7	gopalapillai	gopalapillai	NOUN
ejpam-5019	450	8	indulal	indulal	NOUN
ejpam-5019	450	9	.	.	PUNCT
ejpam-5019	451	1	the	the	DET
ejpam-5019	451	2	distance	distance	NOUN
ejpam-5019	451	3	spectrum	spectrum	NOUN
ejpam-5019	451	4	and	and	CCONJ
ejpam-5019	451	5	energy	energy	NOUN
ejpam-5019	451	6	of	of	ADP
ejpam-5019	451	7	the	the	DET
ejpam-5019	451	8	compositions	composition	NOUN
ejpam-5019	451	9	of	of	ADP
ejpam-5019	451	10	regular	regular	ADJ
ejpam-5019	451	11	graphs	graph	NOUN
ejpam-5019	451	12	.	.	PUNCT
ejpam-5019	452	1	applied	apply	VERB
ejpam-5019	452	2	mathematics	mathematics	NOUN
ejpam-5019	452	3	letters	letter	NOUN
ejpam-5019	452	4	,	,	PUNCT
ejpam-5019	452	5	22(7):1136–1140	22(7):1136–1140	NUM
ejpam-5019	452	6	,	,	PUNCT
ejpam-5019	452	7	2009	2009	NUM
ejpam-5019	452	8	.	.	PUNCT