id	sid	tid	token	lemma	pos
ejpam-3928	1	1	european	european	PROPN
ejpam-3928	1	2	journal	journal	PROPN
ejpam-3928	1	3	of	of	ADP
ejpam-3928	1	4	pure	pure	ADJ
ejpam-3928	1	5	and	and	CCONJ
ejpam-3928	1	6	applied	apply	VERB
ejpam-3928	1	7	mathematics	mathematic	NOUN
ejpam-3928	1	8	vol	vol	NOUN
ejpam-3928	1	9	.	.	PUNCT
ejpam-3928	2	1	14	14	NUM
ejpam-3928	2	2	,	,	PUNCT
ejpam-3928	2	3	no	no	INTJ
ejpam-3928	2	4	.	.	NOUN
ejpam-3928	2	5	2	2	NUM
ejpam-3928	2	6	,	,	PUNCT
ejpam-3928	2	7	2021	2021	NUM
ejpam-3928	2	8	,	,	PUNCT
ejpam-3928	2	9	358	358	NUM
ejpam-3928	2	10	-	-	SYM
ejpam-3928	2	11	365	365	NUM
ejpam-3928	2	12	issn	issn	PROPN
ejpam-3928	2	13	1307	1307	NUM
ejpam-3928	2	14	-	-	SYM
ejpam-3928	2	15	5543	5543	NUM
ejpam-3928	2	16	–	–	PUNCT
ejpam-3928	3	1	ejpam.com	ejpam.com	X
ejpam-3928	3	2	published	publish	VERB
ejpam-3928	3	3	by	by	ADP
ejpam-3928	3	4	new	new	PROPN
ejpam-3928	3	5	york	york	PROPN
ejpam-3928	3	6	business	business	PROPN
ejpam-3928	3	7	global	global	PROPN
ejpam-3928	3	8	on	on	ADP
ejpam-3928	3	9	spectral	spectral	ADJ
ejpam-3928	3	10	-	-	PUNCT
ejpam-3928	3	11	equipartite	equipartite	ADJ
ejpam-3928	3	12	graphs	graph	NOUN
ejpam-3928	3	13	and	and	CCONJ
ejpam-3928	3	14	eccentricity	eccentricity	NOUN
ejpam-3928	3	15	-	-	PUNCT
ejpam-3928	3	16	equipartite	equipartite	ADJ
ejpam-3928	3	17	graphs	graph	NOUN
ejpam-3928	3	18	arnel	arnel	PROPN
ejpam-3928	3	19	m.	m.	NOUN
ejpam-3928	3	20	yurfo1,∗	yurfo1,∗	NOUN
ejpam-3928	3	21	,	,	PUNCT
ejpam-3928	3	22	joel	joel	PROPN
ejpam-3928	3	23	g.	g.	PROPN
ejpam-3928	3	24	adanza2	adanza2	PROPN
ejpam-3928	3	25	,	,	PUNCT
ejpam-3928	3	26	michael	michael	PROPN
ejpam-3928	3	27	p.	p.	PROPN
ejpam-3928	3	28	baldado	baldado	NOUN
ejpam-3928	3	29	jr.2	jr.2	PROPN
ejpam-3928	3	30	1	1	NUM
ejpam-3928	3	31	college	college	NOUN
ejpam-3928	3	32	of	of	ADP
ejpam-3928	3	33	arts	art	NOUN
ejpam-3928	3	34	and	and	CCONJ
ejpam-3928	3	35	sciences	science	NOUN
ejpam-3928	3	36	,	,	PUNCT
ejpam-3928	3	37	negros	negros	PROPN
ejpam-3928	3	38	oriental	oriental	ADJ
ejpam-3928	3	39	state	state	PROPN
ejpam-3928	3	40	university	university	PROPN
ejpam-3928	3	41	bayawan	bayawan	PROPN
ejpam-3928	3	42	sta	sta	PROPN
ejpam-3928	3	43	.	.	PUNCT
ejpam-3928	4	1	catalina	catalina	PROPN
ejpam-3928	4	2	campus	campus	NOUN
ejpam-3928	4	3	,	,	PUNCT
ejpam-3928	4	4	bayawan	bayawan	NOUN
ejpam-3928	4	5	city	city	NOUN
ejpam-3928	4	6	,	,	PUNCT
ejpam-3928	4	7	philippines	philippine	NOUN
ejpam-3928	4	8	2	2	NUM
ejpam-3928	4	9	mathematics	mathematics	NOUN
ejpam-3928	4	10	department	department	NOUN
ejpam-3928	4	11	,	,	PUNCT
ejpam-3928	4	12	negros	negros	PROPN
ejpam-3928	4	13	oriental	oriental	ADJ
ejpam-3928	4	14	state	state	PROPN
ejpam-3928	4	15	university	university	PROPN
ejpam-3928	4	16	main	main	ADJ
ejpam-3928	4	17	campus	campus	NOUN
ejpam-3928	4	18	,	,	PUNCT
ejpam-3928	4	19	dumaguete	dumaguete	PROPN
ejpam-3928	4	20	city	city	PROPN
ejpam-3928	4	21	,	,	PUNCT
ejpam-3928	4	22	philippines	philippine	NOUN
ejpam-3928	4	23	abstract	abstract	ADJ
ejpam-3928	4	24	.	.	PUNCT
ejpam-3928	5	1	let	let	VERB
ejpam-3928	5	2	g	g	PROPN
ejpam-3928	5	3	=	=	SYM
ejpam-3928	5	4	(	(	PUNCT
ejpam-3928	5	5	v	v	NOUN
ejpam-3928	5	6	,	,	PUNCT
ejpam-3928	5	7	e	e	NOUN
ejpam-3928	5	8	)	)	PUNCT
ejpam-3928	5	9	be	be	AUX
ejpam-3928	5	10	a	a	DET
ejpam-3928	5	11	graph	graph	NOUN
ejpam-3928	5	12	of	of	ADP
ejpam-3928	5	13	order	order	NOUN
ejpam-3928	5	14	2n	2n	NUM
ejpam-3928	5	15	.	.	PUNCT
ejpam-3928	6	1	if	if	SCONJ
ejpam-3928	6	2	a	a	DET
ejpam-3928	6	3	⊆	⊆	NUM
ejpam-3928	6	4	v	v	NOUN
ejpam-3928	6	5	and	and	CCONJ
ejpam-3928	6	6	〈	〈	PROPN
ejpam-3928	6	7	a	a	DET
ejpam-3928	6	8	〉	〉	NOUN
ejpam-3928	6	9	∼=	∼=	NOUN
ejpam-3928	6	10	〈	〈	PROPN
ejpam-3928	6	11	v	v	ADJ
ejpam-3928	6	12	\a	\a	ADJ
ejpam-3928	6	13	〉	〉	NOUN
ejpam-3928	7	1	,	,	PUNCT
ejpam-3928	7	2	then	then	ADV
ejpam-3928	7	3	a	a	PRON
ejpam-3928	7	4	is	be	AUX
ejpam-3928	7	5	said	say	VERB
ejpam-3928	7	6	to	to	PART
ejpam-3928	7	7	be	be	AUX
ejpam-3928	7	8	isospectral	isospectral	ADJ
ejpam-3928	7	9	.	.	PUNCT
ejpam-3928	8	1	if	if	SCONJ
ejpam-3928	8	2	for	for	ADP
ejpam-3928	8	3	every	every	DET
ejpam-3928	8	4	n	n	CCONJ
ejpam-3928	8	5	-	-	PUNCT
ejpam-3928	8	6	element	element	NOUN
ejpam-3928	8	7	subset	subset	VERB
ejpam-3928	8	8	a	a	PRON
ejpam-3928	8	9	of	of	ADP
ejpam-3928	8	10	v	v	NOUN
ejpam-3928	8	11	we	we	PRON
ejpam-3928	8	12	have	have	VERB
ejpam-3928	8	13	〈	〈	PROPN
ejpam-3928	8	14	a	a	DET
ejpam-3928	8	15	〉	〉	NOUN
ejpam-3928	8	16	∼=	∼=	PROPN
ejpam-3928	8	17	〈	〈	PROPN
ejpam-3928	8	18	v	v	ADJ
ejpam-3928	8	19	\a	\a	ADJ
ejpam-3928	8	20	〉	〉	NUM
ejpam-3928	8	21	,	,	PUNCT
ejpam-3928	8	22	then	then	ADV
ejpam-3928	8	23	we	we	PRON
ejpam-3928	8	24	say	say	VERB
ejpam-3928	8	25	that	that	SCONJ
ejpam-3928	8	26	g	g	PROPN
ejpam-3928	8	27	is	be	AUX
ejpam-3928	8	28	spectral	spectral	ADJ
ejpam-3928	8	29	-	-	PUNCT
ejpam-3928	8	30	equipartite	equipartite	ADJ
ejpam-3928	8	31	.	.	PUNCT
ejpam-3928	9	1	in	in	ADP
ejpam-3928	9	2	[	[	X
ejpam-3928	9	3	1	1	NUM
ejpam-3928	9	4	]	]	PUNCT
ejpam-3928	9	5	,	,	PUNCT
ejpam-3928	9	6	igor	igor	PROPN
ejpam-3928	9	7	shparlinski	shparlinski	PROPN
ejpam-3928	9	8	communicated	communicate	VERB
ejpam-3928	9	9	with	with	ADP
ejpam-3928	9	10	bibak	bibak	PROPN
ejpam-3928	9	11	et	et	PROPN
ejpam-3928	9	12	al	al	PROPN
ejpam-3928	9	13	.	.	PROPN
ejpam-3928	9	14	,	,	PUNCT
ejpam-3928	9	15	proposing	propose	VERB
ejpam-3928	9	16	a	a	DET
ejpam-3928	9	17	full	full	ADJ
ejpam-3928	9	18	characterization	characterization	NOUN
ejpam-3928	9	19	of	of	ADP
ejpam-3928	9	20	spectral	spectral	ADJ
ejpam-3928	9	21	-	-	PUNCT
ejpam-3928	9	22	equipartite	equipartite	ADJ
ejpam-3928	9	23	graphs	graph	NOUN
ejpam-3928	9	24	.	.	PUNCT
ejpam-3928	10	1	in	in	ADP
ejpam-3928	10	2	this	this	DET
ejpam-3928	10	3	paper	paper	NOUN
ejpam-3928	10	4	,	,	PUNCT
ejpam-3928	10	5	we	we	PRON
ejpam-3928	10	6	gave	give	VERB
ejpam-3928	10	7	a	a	DET
ejpam-3928	10	8	characterization	characterization	NOUN
ejpam-3928	10	9	of	of	ADP
ejpam-3928	10	10	disconnected	disconnected	ADJ
ejpam-3928	10	11	spectral	spectral	ADJ
ejpam-3928	10	12	-	-	PUNCT
ejpam-3928	10	13	equipartite	equipartite	ADJ
ejpam-3928	10	14	graphs	graph	NOUN
ejpam-3928	10	15	.	.	PUNCT
ejpam-3928	11	1	moreover	moreover	ADV
ejpam-3928	11	2	,	,	PUNCT
ejpam-3928	11	3	we	we	PRON
ejpam-3928	11	4	introduced	introduce	VERB
ejpam-3928	11	5	the	the	DET
ejpam-3928	11	6	concept	concept	NOUN
ejpam-3928	11	7	eccentricityequipartite	eccentricityequipartite	ADJ
ejpam-3928	11	8	graphs	graph	NOUN
ejpam-3928	11	9	.	.	PUNCT
ejpam-3928	12	1	2020	2020	NUM
ejpam-3928	12	2	mathematics	mathematic	NOUN
ejpam-3928	12	3	subject	subject	NOUN
ejpam-3928	12	4	classifications	classification	NOUN
ejpam-3928	12	5	:	:	PUNCT
ejpam-3928	12	6	05c50	05c50	NUM
ejpam-3928	12	7	,	,	PUNCT
ejpam-3928	12	8	05c75	05c75	NUM
ejpam-3928	12	9	key	key	ADJ
ejpam-3928	12	10	words	word	NOUN
ejpam-3928	12	11	and	and	CCONJ
ejpam-3928	12	12	phrases	phrase	NOUN
ejpam-3928	12	13	:	:	PUNCT
ejpam-3928	12	14	spectral	spectral	ADJ
ejpam-3928	12	15	-	-	PUNCT
ejpam-3928	12	16	equipartite	equipartite	ADJ
ejpam-3928	12	17	graphs	graph	NOUN
ejpam-3928	12	18	,	,	PUNCT
ejpam-3928	12	19	eccentricity	eccentricity	NOUN
ejpam-3928	12	20	-	-	PUNCT
ejpam-3928	12	21	equipartite	equipartite	ADJ
ejpam-3928	12	22	graphs	graph	NOUN
ejpam-3928	12	23	,	,	PUNCT
ejpam-3928	12	24	isospectral	isospectral	ADJ
ejpam-3928	12	25	graphs	graph	NOUN
ejpam-3928	12	26	,	,	PUNCT
ejpam-3928	13	1	graph	graph	NOUN
ejpam-3928	13	2	spectra	spectra	ADJ
ejpam-3928	13	3	1	1	NUM
ejpam-3928	13	4	.	.	PUNCT
ejpam-3928	13	5	introduction	introduction	NOUN
ejpam-3928	13	6	let	let	VERB
ejpam-3928	13	7	g	g	PROPN
ejpam-3928	13	8	=	=	SYM
ejpam-3928	13	9	(	(	PUNCT
ejpam-3928	13	10	v	v	NOUN
ejpam-3928	13	11	,	,	PUNCT
ejpam-3928	13	12	e	e	NOUN
ejpam-3928	13	13	)	)	PUNCT
ejpam-3928	13	14	be	be	AUX
ejpam-3928	13	15	a	a	DET
ejpam-3928	13	16	graph	graph	NOUN
ejpam-3928	13	17	.	.	PUNCT
ejpam-3928	14	1	the	the	DET
ejpam-3928	14	2	distance	distance	NOUN
ejpam-3928	14	3	between	between	ADP
ejpam-3928	14	4	vertices	vertex	NOUN
ejpam-3928	14	5	u	u	NOUN
ejpam-3928	14	6	and	and	CCONJ
ejpam-3928	14	7	v	v	NOUN
ejpam-3928	14	8	in	in	ADP
ejpam-3928	14	9	g	g	NOUN
ejpam-3928	14	10	,	,	PUNCT
ejpam-3928	14	11	denoted	denote	VERB
ejpam-3928	14	12	by	by	ADP
ejpam-3928	14	13	d	d	PROPN
ejpam-3928	14	14	(	(	PUNCT
ejpam-3928	14	15	u	u	NOUN
ejpam-3928	14	16	,	,	PUNCT
ejpam-3928	14	17	v	v	NOUN
ejpam-3928	14	18	)	)	PUNCT
ejpam-3928	14	19	,	,	PUNCT
ejpam-3928	14	20	is	be	AUX
ejpam-3928	14	21	the	the	DET
ejpam-3928	14	22	length	length	NOUN
ejpam-3928	14	23	of	of	ADP
ejpam-3928	14	24	the	the	DET
ejpam-3928	14	25	shortest	short	ADJ
ejpam-3928	14	26	path	path	NOUN
ejpam-3928	14	27	connecting	connect	VERB
ejpam-3928	14	28	u	u	NOUN
ejpam-3928	14	29	and	and	CCONJ
ejpam-3928	14	30	v.	v.	INTJ
ejpam-3928	14	31	if	if	SCONJ
ejpam-3928	14	32	u	u	PROPN
ejpam-3928	14	33	and	and	CCONJ
ejpam-3928	14	34	v	v	NOUN
ejpam-3928	14	35	is	be	AUX
ejpam-3928	14	36	not	not	PART
ejpam-3928	14	37	connected	connect	VERB
ejpam-3928	14	38	,	,	PUNCT
ejpam-3928	14	39	then	then	ADV
ejpam-3928	14	40	we	we	PRON
ejpam-3928	14	41	define	define	VERB
ejpam-3928	14	42	d	d	X
ejpam-3928	14	43	(	(	PUNCT
ejpam-3928	14	44	u	u	NOUN
ejpam-3928	14	45	,	,	PUNCT
ejpam-3928	14	46	v	v	NOUN
ejpam-3928	14	47	)	)	PUNCT
ejpam-3928	14	48	to	to	PART
ejpam-3928	14	49	be	be	AUX
ejpam-3928	14	50	0	0	NUM
ejpam-3928	14	51	.	.	PUNCT
ejpam-3928	15	1	the	the	DET
ejpam-3928	15	2	eccentricity	eccentricity	NOUN
ejpam-3928	15	3	of	of	ADP
ejpam-3928	15	4	a	a	DET
ejpam-3928	15	5	vertex	vertex	NOUN
ejpam-3928	15	6	is	be	AUX
ejpam-3928	15	7	its	its	PRON
ejpam-3928	15	8	distance	distance	NOUN
ejpam-3928	15	9	to	to	ADP
ejpam-3928	15	10	a	a	DET
ejpam-3928	15	11	farthest	farth	ADJ
ejpam-3928	15	12	vertex	vertex	NOUN
ejpam-3928	15	13	.	.	PUNCT
ejpam-3928	16	1	g	g	NOUN
ejpam-3928	16	2	is	be	AUX
ejpam-3928	16	3	said	say	VERB
ejpam-3928	16	4	to	to	PART
ejpam-3928	16	5	be	be	AUX
ejpam-3928	16	6	k	k	NOUN
ejpam-3928	16	7	-	-	ADJ
ejpam-3928	16	8	regular	regular	ADJ
ejpam-3928	16	9	if	if	SCONJ
ejpam-3928	16	10	every	every	DET
ejpam-3928	16	11	vertex	vertex	NOUN
ejpam-3928	16	12	of	of	ADP
ejpam-3928	16	13	g	g	PROPN
ejpam-3928	16	14	has	have	VERB
ejpam-3928	16	15	the	the	DET
ejpam-3928	16	16	same	same	ADJ
ejpam-3928	16	17	degree	degree	NOUN
ejpam-3928	16	18	which	which	PRON
ejpam-3928	16	19	is	be	AUX
ejpam-3928	16	20	k.	k.	PROPN
ejpam-3928	16	21	g	g	PROPN
ejpam-3928	16	22	is	be	AUX
ejpam-3928	16	23	said	say	VERB
ejpam-3928	16	24	to	to	PART
ejpam-3928	16	25	be	be	AUX
ejpam-3928	16	26	weakly	weakly	ADV
ejpam-3928	16	27	equipartite	equipartite	ADJ
ejpam-3928	16	28	if	if	SCONJ
ejpam-3928	16	29	every	every	DET
ejpam-3928	16	30	partition	partition	NOUN
ejpam-3928	16	31	of	of	ADP
ejpam-3928	16	32	v	v	NOUN
ejpam-3928	16	33	into	into	ADP
ejpam-3928	16	34	two	two	NUM
ejpam-3928	16	35	equal	equal	ADJ
ejpam-3928	16	36	sets	set	NOUN
ejpam-3928	16	37	a	a	PRON
ejpam-3928	16	38	and	and	CCONJ
ejpam-3928	16	39	b	b	NOUN
ejpam-3928	16	40	,	,	PUNCT
ejpam-3928	16	41	we	we	PRON
ejpam-3928	16	42	have	have	AUX
ejpam-3928	16	43	〈	〈	PROPN
ejpam-3928	16	44	a	a	DET
ejpam-3928	16	45	〉	〉	NOUN
ejpam-3928	16	46	∼=	∼=	PROPN
ejpam-3928	16	47	〈	〈	PROPN
ejpam-3928	16	48	b	b	PROPN
ejpam-3928	16	49	〉	〉	PROPN
ejpam-3928	16	50	.	.	PUNCT
ejpam-3928	17	1	in	in	ADP
ejpam-3928	17	2	addition	addition	NOUN
ejpam-3928	17	3	,	,	PUNCT
ejpam-3928	17	4	if	if	SCONJ
ejpam-3928	17	5	there	there	PRON
ejpam-3928	17	6	is	be	VERB
ejpam-3928	17	7	an	an	DET
ejpam-3928	17	8	automorphism	automorphism	NOUN
ejpam-3928	17	9	mapping	mapping	NOUN
ejpam-3928	17	10	a	a	PRON
ejpam-3928	17	11	onto	onto	ADP
ejpam-3928	17	12	b	b	NOUN
ejpam-3928	17	13	,	,	PUNCT
ejpam-3928	17	14	then	then	ADV
ejpam-3928	17	15	we	we	PRON
ejpam-3928	17	16	say	say	VERB
ejpam-3928	17	17	that	that	SCONJ
ejpam-3928	17	18	g	g	PROPN
ejpam-3928	17	19	is	be	AUX
ejpam-3928	17	20	equipartite	equipartite	ADJ
ejpam-3928	17	21	.	.	PUNCT
ejpam-3928	18	1	the	the	DET
ejpam-3928	18	2	degree	degree	NOUN
ejpam-3928	18	3	sequence	sequence	NOUN
ejpam-3928	18	4	of	of	ADP
ejpam-3928	18	5	g	g	PROPN
ejpam-3928	18	6	is	be	AUX
ejpam-3928	18	7	a	a	DET
ejpam-3928	18	8	non	non	ADJ
ejpam-3928	18	9	-	-	ADJ
ejpam-3928	18	10	decreasing	decrease	VERB
ejpam-3928	18	11	sequence	sequence	NOUN
ejpam-3928	18	12	of	of	ADP
ejpam-3928	18	13	degrees	degree	NOUN
ejpam-3928	18	14	of	of	ADP
ejpam-3928	18	15	the	the	DET
ejpam-3928	18	16	vertices	vertex	NOUN
ejpam-3928	18	17	of	of	ADP
ejpam-3928	18	18	g.	g.	PROPN
ejpam-3928	18	19	g	g	PROPN
ejpam-3928	18	20	is	be	AUX
ejpam-3928	18	21	degree	degree	NOUN
ejpam-3928	18	22	-	-	PUNCT
ejpam-3928	18	23	equipartite	equipartite	ADJ
ejpam-3928	18	24	if	if	SCONJ
ejpam-3928	18	25	for	for	SCONJ
ejpam-3928	18	26	every	every	DET
ejpam-3928	18	27	n	n	CCONJ
ejpam-3928	18	28	-	-	PUNCT
ejpam-3928	18	29	element	element	NOUN
ejpam-3928	18	30	subset	subset	VERB
ejpam-3928	18	31	a	a	PRON
ejpam-3928	18	32	of	of	ADP
ejpam-3928	18	33	v	v	NOUN
ejpam-3928	18	34	,	,	PUNCT
ejpam-3928	18	35	the	the	DET
ejpam-3928	18	36	degree	degree	NOUN
ejpam-3928	18	37	sequences	sequence	NOUN
ejpam-3928	18	38	of	of	ADP
ejpam-3928	18	39	〈	〈	PROPN
ejpam-3928	18	40	a	a	DET
ejpam-3928	18	41	〉	〉	NOUN
ejpam-3928	18	42	and	and	CCONJ
ejpam-3928	18	43	〈	〈	PROPN
ejpam-3928	18	44	v	v	ADJ
ejpam-3928	18	45	\a	\a	ADJ
ejpam-3928	18	46	〉	〉	PROPN
ejpam-3928	18	47	are	be	AUX
ejpam-3928	18	48	the	the	DET
ejpam-3928	18	49	same	same	ADJ
ejpam-3928	18	50	.	.	PUNCT
ejpam-3928	19	1	the	the	DET
ejpam-3928	19	2	adjacency	adjacency	PROPN
ejpam-3928	19	3	matrix	matrix	NOUN
ejpam-3928	19	4	m	m	NOUN
ejpam-3928	19	5	=	=	PUNCT
ejpam-3928	20	1	[	[	X
ejpam-3928	20	2	aij	aij	X
ejpam-3928	20	3	]	]	PUNCT
ejpam-3928	20	4	of	of	ADP
ejpam-3928	20	5	g	g	PROPN
ejpam-3928	20	6	is	be	AUX
ejpam-3928	20	7	the	the	DET
ejpam-3928	20	8	square	square	ADJ
ejpam-3928	20	9	matrix	matrix	NOUN
ejpam-3928	20	10	of	of	ADP
ejpam-3928	20	11	order	order	NOUN
ejpam-3928	20	12	4n2	4n2	PRON
ejpam-3928	20	13	given	give	VERB
ejpam-3928	20	14	by	by	ADP
ejpam-3928	20	15	aij	aij	PROPN
ejpam-3928	20	16	=	=	SYM
ejpam-3928	20	17	1	1	NUM
ejpam-3928	20	18	if	if	SCONJ
ejpam-3928	20	19	vivj	vivj	NOUN
ejpam-3928	20	20	∈	∈	PROPN
ejpam-3928	20	21	e	e	X
ejpam-3928	20	22	(	(	PUNCT
ejpam-3928	20	23	g	g	NOUN
ejpam-3928	20	24	)	)	PUNCT
ejpam-3928	20	25	,	,	PUNCT
ejpam-3928	20	26	and	and	CCONJ
ejpam-3928	20	27	aij	aij	PROPN
ejpam-3928	20	28	=	=	SYM
ejpam-3928	20	29	0	0	NUM
ejpam-3928	20	30	otherwise	otherwise	ADV
ejpam-3928	20	31	.	.	PUNCT
ejpam-3928	21	1	∗corresponding	∗corresponde	VERB
ejpam-3928	21	2	author	author	NOUN
ejpam-3928	21	3	.	.	PUNCT
ejpam-3928	22	1	doi	doi	NOUN
ejpam-3928	22	2	:	:	PUNCT
ejpam-3928	22	3	https://doi.org/10.29020/nybg.ejpam.v14i2.3928	https://doi.org/10.29020/nybg.ejpam.v14i2.3928	PROPN
ejpam-3928	22	4	email	email	NOUN
ejpam-3928	22	5	addresses	address	VERB
ejpam-3928	22	6	:	:	PUNCT
ejpam-3928	22	7	mathematicsrocks@yahoo.com	mathematicsrocks@yahoo.com	X
ejpam-3928	22	8	(	(	PUNCT
ejpam-3928	22	9	a.	a.	NOUN
ejpam-3928	22	10	yurfo	yurfo	PROPN
ejpam-3928	22	11	)	)	PUNCT
ejpam-3928	22	12	,	,	PUNCT
ejpam-3928	22	13	joeladanza@yahoo.com	joeladanza@yahoo.com	X
ejpam-3928	22	14	(	(	PUNCT
ejpam-3928	22	15	j.	j.	PROPN
ejpam-3928	22	16	adanza	adanza	PROPN
ejpam-3928	22	17	)	)	PUNCT
ejpam-3928	22	18	,	,	PUNCT
ejpam-3928	22	19	michaelpbaldadojr@yahoo.com	michaelpbaldadojr@yahoo.com	X
ejpam-3928	22	20	(	(	PUNCT
ejpam-3928	22	21	m.	m.	PROPN
ejpam-3928	22	22	baldado	baldado	PROPN
ejpam-3928	22	23	jr	jr	PROPN
ejpam-3928	22	24	.	.	PUNCT
ejpam-3928	22	25	)	)	PUNCT
ejpam-3928	22	26	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3928	23	1	358	358	NUM
ejpam-3928	23	2	c	c	AUX
ejpam-3928	23	3	©	©	PROPN
ejpam-3928	23	4	2021	2021	NUM
ejpam-3928	23	5	ejpam	ejpam	VERB
ejpam-3928	23	6	all	all	DET
ejpam-3928	23	7	rights	right	NOUN
ejpam-3928	23	8	reserved	reserve	VERB
ejpam-3928	23	9	.	.	PUNCT
ejpam-3928	24	1	a.	a.	NOUN
ejpam-3928	24	2	yurfo	yurfo	PROPN
ejpam-3928	24	3	,	,	PUNCT
ejpam-3928	24	4	j.	j.	PROPN
ejpam-3928	24	5	adanza	adanza	PROPN
ejpam-3928	24	6	,	,	PUNCT
ejpam-3928	24	7	m.	m.	PROPN
ejpam-3928	24	8	baldado	baldado	PROPN
ejpam-3928	24	9	jr	jr	PROPN
ejpam-3928	24	10	.	.	PROPN
ejpam-3928	24	11	/	/	SYM
ejpam-3928	24	12	eur	eur	PROPN
ejpam-3928	24	13	.	.	PUNCT
ejpam-3928	25	1	j.	j.	PROPN
ejpam-3928	25	2	pure	pure	PROPN
ejpam-3928	25	3	appl	appl	PROPN
ejpam-3928	25	4	.	.	PROPN
ejpam-3928	25	5	math	math	PROPN
ejpam-3928	25	6	,	,	PUNCT
ejpam-3928	25	7	14	14	NUM
ejpam-3928	25	8	(	(	PUNCT
ejpam-3928	25	9	2	2	NUM
ejpam-3928	25	10	)	)	PUNCT
ejpam-3928	25	11	(	(	PUNCT
ejpam-3928	25	12	2021	2021	NUM
ejpam-3928	25	13	)	)	PUNCT
ejpam-3928	25	14	,	,	PUNCT
ejpam-3928	25	15	358	358	NUM
ejpam-3928	25	16	-	-	SYM
ejpam-3928	25	17	365	365	NUM
ejpam-3928	25	18	359	359	NUM
ejpam-3928	25	19	the	the	DET
ejpam-3928	25	20	spectrum	spectrum	NOUN
ejpam-3928	25	21	of	of	ADP
ejpam-3928	25	22	g	g	PROPN
ejpam-3928	25	23	is	be	AUX
ejpam-3928	25	24	the	the	DET
ejpam-3928	25	25	collection	collection	NOUN
ejpam-3928	25	26	of	of	ADP
ejpam-3928	25	27	all	all	DET
ejpam-3928	25	28	eigenvalues	eigenvalue	NOUN
ejpam-3928	25	29	of	of	ADP
ejpam-3928	25	30	all	all	DET
ejpam-3928	25	31	its	its	PRON
ejpam-3928	25	32	adjacency	adjacency	NOUN
ejpam-3928	25	33	matrix	matrix	NOUN
ejpam-3928	25	34	.	.	PUNCT
ejpam-3928	26	1	two	two	NUM
ejpam-3928	26	2	graphs	graph	NOUN
ejpam-3928	26	3	that	that	PRON
ejpam-3928	26	4	have	have	VERB
ejpam-3928	26	5	the	the	DET
ejpam-3928	26	6	same	same	ADJ
ejpam-3928	26	7	spectrum	spectrum	NOUN
ejpam-3928	26	8	are	be	AUX
ejpam-3928	26	9	said	say	VERB
ejpam-3928	26	10	to	to	PART
ejpam-3928	26	11	be	be	AUX
ejpam-3928	26	12	cospectral	cospectral	ADJ
ejpam-3928	26	13	or	or	CCONJ
ejpam-3928	26	14	isospectral	isospectral	NOUN
ejpam-3928	26	15	.	.	PUNCT
ejpam-3928	27	1	g	g	NOUN
ejpam-3928	27	2	is	be	AUX
ejpam-3928	27	3	said	say	VERB
ejpam-3928	27	4	to	to	PART
ejpam-3928	27	5	be	be	AUX
ejpam-3928	27	6	spectral	spectral	ADJ
ejpam-3928	27	7	-	-	PUNCT
ejpam-3928	27	8	equipartite	equipartite	ADJ
ejpam-3928	27	9	if	if	SCONJ
ejpam-3928	27	10	for	for	SCONJ
ejpam-3928	27	11	every	every	DET
ejpam-3928	27	12	n	n	CCONJ
ejpam-3928	27	13	-	-	PUNCT
ejpam-3928	27	14	element	element	NOUN
ejpam-3928	27	15	subset	subset	VERB
ejpam-3928	27	16	a	a	PRON
ejpam-3928	27	17	of	of	ADP
ejpam-3928	27	18	v	v	NOUN
ejpam-3928	27	19	,	,	PUNCT
ejpam-3928	27	20	the	the	DET
ejpam-3928	27	21	induced	induced	ADJ
ejpam-3928	27	22	subgraph	subgraph	NOUN
ejpam-3928	27	23	of	of	ADP
ejpam-3928	27	24	a	a	PRON
ejpam-3928	27	25	and	and	CCONJ
ejpam-3928	27	26	v	v	NOUN
ejpam-3928	27	27	\a	\a	ADJ
ejpam-3928	27	28	are	be	AUX
ejpam-3928	27	29	isospectral	isospectral	ADJ
ejpam-3928	27	30	.	.	PUNCT
ejpam-3928	28	1	ferrero	ferrero	PROPN
ejpam-3928	28	2	et	et	PROPN
ejpam-3928	28	3	al	al	PROPN
ejpam-3928	28	4	.	.	PUNCT
ejpam-3928	29	1	in	in	ADP
ejpam-3928	29	2	[	[	X
ejpam-3928	29	3	5	5	NUM
ejpam-3928	29	4	]	]	PUNCT
ejpam-3928	29	5	,	,	PUNCT
ejpam-3928	29	6	mentioned	mention	VERB
ejpam-3928	29	7	the	the	DET
ejpam-3928	29	8	eccentricity	eccentricity	NOUN
ejpam-3928	29	9	sequence	sequence	NOUN
ejpam-3928	29	10	of	of	ADP
ejpam-3928	29	11	a	a	DET
ejpam-3928	29	12	graph	graph	NOUN
ejpam-3928	29	13	g	g	NOUN
ejpam-3928	29	14	as	as	ADP
ejpam-3928	29	15	the	the	DET
ejpam-3928	29	16	nondecreasing	nondecreasing	ADJ
ejpam-3928	29	17	sequence	sequence	NOUN
ejpam-3928	29	18	of	of	ADP
ejpam-3928	29	19	eccentricities	eccentricity	NOUN
ejpam-3928	29	20	of	of	ADP
ejpam-3928	29	21	the	the	DET
ejpam-3928	29	22	vertices	vertex	NOUN
ejpam-3928	29	23	of	of	ADP
ejpam-3928	29	24	g.	g.	PROPN
ejpam-3928	29	25	a	a	DET
ejpam-3928	29	26	graph	graph	NOUN
ejpam-3928	29	27	g	g	NOUN
ejpam-3928	29	28	=	=	SYM
ejpam-3928	29	29	(	(	PUNCT
ejpam-3928	29	30	v	v	NOUN
ejpam-3928	29	31	,	,	PUNCT
ejpam-3928	29	32	e	e	NOUN
ejpam-3928	29	33	)	)	PUNCT
ejpam-3928	29	34	of	of	ADP
ejpam-3928	29	35	order	order	NOUN
ejpam-3928	29	36	2n	2n	NUM
ejpam-3928	29	37	is	be	AUX
ejpam-3928	29	38	said	say	VERB
ejpam-3928	29	39	to	to	PART
ejpam-3928	29	40	be	be	AUX
ejpam-3928	29	41	eccentricity	eccentricity	NOUN
ejpam-3928	29	42	-	-	PUNCT
ejpam-3928	29	43	equipartite	equipartite	ADJ
ejpam-3928	29	44	if	if	SCONJ
ejpam-3928	29	45	for	for	SCONJ
ejpam-3928	29	46	every	every	DET
ejpam-3928	29	47	n	n	CCONJ
ejpam-3928	29	48	-	-	PUNCT
ejpam-3928	29	49	element	element	NOUN
ejpam-3928	29	50	subset	subset	VERB
ejpam-3928	29	51	a	a	PRON
ejpam-3928	29	52	of	of	ADP
ejpam-3928	29	53	v	v	NOUN
ejpam-3928	29	54	,	,	PUNCT
ejpam-3928	29	55	the	the	DET
ejpam-3928	29	56	induced	induced	ADJ
ejpam-3928	29	57	subgraph	subgraph	NOUN
ejpam-3928	29	58	of	of	ADP
ejpam-3928	29	59	a	a	PRON
ejpam-3928	29	60	and	and	CCONJ
ejpam-3928	29	61	v	v	NOUN
ejpam-3928	29	62	\a	\a	ADJ
ejpam-3928	29	63	have	have	VERB
ejpam-3928	29	64	the	the	DET
ejpam-3928	29	65	same	same	ADJ
ejpam-3928	29	66	eccentricity	eccentricity	NOUN
ejpam-3928	29	67	sequence	sequence	NOUN
ejpam-3928	29	68	.	.	PUNCT
ejpam-3928	30	1	here	here	ADV
ejpam-3928	30	2	after	after	SCONJ
ejpam-3928	30	3	please	please	INTJ
ejpam-3928	30	4	refer	refer	VERB
ejpam-3928	30	5	to	to	ADP
ejpam-3928	30	6	[	[	X
ejpam-3928	30	7	6	6	NUM
ejpam-3928	30	8	]	]	PUNCT
ejpam-3928	30	9	for	for	ADP
ejpam-3928	30	10	the	the	DET
ejpam-3928	30	11	other	other	ADJ
ejpam-3928	30	12	concepts	concept	NOUN
ejpam-3928	30	13	.	.	PUNCT
ejpam-3928	31	1	over	over	ADP
ejpam-3928	31	2	the	the	DET
ejpam-3928	31	3	past	past	ADJ
ejpam-3928	31	4	years	year	NOUN
ejpam-3928	31	5	,	,	PUNCT
ejpam-3928	31	6	various	various	ADJ
ejpam-3928	31	7	applications	application	NOUN
ejpam-3928	31	8	spectral	spectral	ADJ
ejpam-3928	31	9	graph	graph	NOUN
ejpam-3928	31	10	theory	theory	NOUN
ejpam-3928	31	11	in	in	ADP
ejpam-3928	31	12	many	many	ADJ
ejpam-3928	31	13	fields	field	NOUN
ejpam-3928	31	14	were	be	AUX
ejpam-3928	31	15	discovered	discover	VERB
ejpam-3928	31	16	.	.	PUNCT
ejpam-3928	32	1	in	in	ADP
ejpam-3928	32	2	particular	particular	ADJ
ejpam-3928	32	3	,	,	PUNCT
ejpam-3928	32	4	spectral	spectral	ADJ
ejpam-3928	32	5	graph	graph	NOUN
ejpam-3928	32	6	theory	theory	NOUN
ejpam-3928	32	7	have	have	VERB
ejpam-3928	32	8	important	important	ADJ
ejpam-3928	32	9	applications	application	NOUN
ejpam-3928	32	10	in	in	ADP
ejpam-3928	32	11	chemistry	chemistry	NOUN
ejpam-3928	32	12	,	,	PUNCT
ejpam-3928	32	13	physics	physics	NOUN
ejpam-3928	32	14	,	,	PUNCT
ejpam-3928	32	15	computer	computer	NOUN
ejpam-3928	32	16	science	science	NOUN
ejpam-3928	32	17	,	,	PUNCT
ejpam-3928	32	18	and	and	CCONJ
ejpam-3928	32	19	common	common	ADJ
ejpam-3928	32	20	real	real	ADJ
ejpam-3928	32	21	world	world	NOUN
ejpam-3928	32	22	problems	problem	NOUN
ejpam-3928	32	23	.	.	PUNCT
ejpam-3928	33	1	for	for	ADP
ejpam-3928	33	2	instance	instance	NOUN
ejpam-3928	33	3	,	,	PUNCT
ejpam-3928	33	4	in	in	ADP
ejpam-3928	33	5	computer	computer	NOUN
ejpam-3928	33	6	science	science	NOUN
ejpam-3928	33	7	,	,	PUNCT
ejpam-3928	33	8	the	the	DET
ejpam-3928	33	9	largest	large	ADJ
ejpam-3928	33	10	eigenvalue	eigenvalue	ADJ
ejpam-3928	33	11	λ1	λ1	PROPN
ejpam-3928	33	12	plays	play	VERB
ejpam-3928	33	13	a	a	DET
ejpam-3928	33	14	significant	significant	ADJ
ejpam-3928	33	15	role	role	NOUN
ejpam-3928	33	16	in	in	ADP
ejpam-3928	33	17	simulating	simulate	VERB
ejpam-3928	33	18	virus	virus	NOUN
ejpam-3928	33	19	proliferation	proliferation	NOUN
ejpam-3928	33	20	in	in	ADP
ejpam-3928	33	21	computer	computer	NOUN
ejpam-3928	33	22	networks	network	NOUN
ejpam-3928	33	23	.	.	PUNCT
ejpam-3928	34	1	also	also	ADV
ejpam-3928	34	2	mentioned	mention	VERB
ejpam-3928	34	3	in	in	ADP
ejpam-3928	34	4	[	[	X
ejpam-3928	34	5	3	3	NUM
ejpam-3928	34	6	]	]	PUNCT
ejpam-3928	34	7	,	,	PUNCT
ejpam-3928	34	8	wang	wang	PROPN
ejpam-3928	34	9	et	et	PROPN
ejpam-3928	34	10	al	al	PROPN
ejpam-3928	34	11	.	.	PUNCT
ejpam-3928	35	1	in	in	ADP
ejpam-3928	35	2	[	[	X
ejpam-3928	35	3	10	10	NUM
ejpam-3928	35	4	]	]	PUNCT
ejpam-3928	35	5	,	,	PUNCT
ejpam-3928	35	6	claimed	claim	VERB
ejpam-3928	35	7	that	that	SCONJ
ejpam-3928	35	8	the	the	DET
ejpam-3928	35	9	epidemic	epidemic	NOUN
ejpam-3928	35	10	threshold	threshold	NOUN
ejpam-3928	35	11	in	in	ADP
ejpam-3928	35	12	spreading	spread	VERB
ejpam-3928	35	13	viruses	virus	NOUN
ejpam-3928	35	14	is	be	AUX
ejpam-3928	35	15	proportional	proportional	ADJ
ejpam-3928	35	16	to	to	ADP
ejpam-3928	35	17	1	1	NUM
ejpam-3928	35	18	/	/	SYM
ejpam-3928	35	19	λ1	λ1	PROPN
ejpam-3928	35	20	.	.	PUNCT
ejpam-3928	36	1	furthermore	furthermore	ADV
ejpam-3928	36	2	,	,	PUNCT
ejpam-3928	36	3	spectral	spectral	ADJ
ejpam-3928	36	4	graph	graph	NOUN
ejpam-3928	36	5	theory	theory	NOUN
ejpam-3928	36	6	was	be	AUX
ejpam-3928	36	7	also	also	ADV
ejpam-3928	36	8	applied	apply	VERB
ejpam-3928	36	9	in	in	ADP
ejpam-3928	36	10	connection	connection	NOUN
ejpam-3928	36	11	with	with	ADP
ejpam-3928	36	12	the	the	DET
ejpam-3928	36	13	famous	famous	ADJ
ejpam-3928	36	14	’	'	PUNCT
ejpam-3928	36	15	traveling	travel	VERB
ejpam-3928	36	16	salesman	salesman	ADJ
ejpam-3928	36	17	problem	problem	NOUN
ejpam-3928	36	18	’	'	PUNCT
ejpam-3928	36	19	.	.	PUNCT
ejpam-3928	37	1	this	this	PRON
ejpam-3928	37	2	is	be	AUX
ejpam-3928	37	3	mentioned	mention	VERB
ejpam-3928	37	4	by	by	ADP
ejpam-3928	37	5	cvetković	cvetković	PROPN
ejpam-3928	37	6	et	et	PROPN
ejpam-3928	37	7	al	al	PROPN
ejpam-3928	37	8	.	.	PUNCT
ejpam-3928	38	1	in	in	ADP
ejpam-3928	38	2	[	[	X
ejpam-3928	38	3	4	4	NUM
ejpam-3928	38	4	]	]	PUNCT
ejpam-3928	38	5	.	.	PUNCT
ejpam-3928	39	1	grünbaum	grünbaum	PROPN
ejpam-3928	39	2	et	et	PROPN
ejpam-3928	39	3	al	al	PROPN
ejpam-3928	39	4	.	.	PUNCT
ejpam-3928	40	1	in	in	ADP
ejpam-3928	40	2	[	[	X
ejpam-3928	40	3	7	7	X
ejpam-3928	40	4	]	]	X
ejpam-3928	40	5	characterized	characterize	VERB
ejpam-3928	40	6	equipartite	equipartite	ADJ
ejpam-3928	40	7	graphs	graph	NOUN
ejpam-3928	40	8	.	.	PUNCT
ejpam-3928	41	1	they	they	PRON
ejpam-3928	41	2	also	also	ADV
ejpam-3928	41	3	presented	present	VERB
ejpam-3928	41	4	a	a	DET
ejpam-3928	41	5	problem	problem	NOUN
ejpam-3928	41	6	regarding	regard	VERB
ejpam-3928	41	7	the	the	DET
ejpam-3928	41	8	characterization	characterization	NOUN
ejpam-3928	41	9	of	of	ADP
ejpam-3928	41	10	degree	degree	NOUN
ejpam-3928	41	11	-	-	PUNCT
ejpam-3928	41	12	equipartite	equipartite	ADJ
ejpam-3928	41	13	graphs	graph	NOUN
ejpam-3928	41	14	.	.	PUNCT
ejpam-3928	42	1	motivated	motivate	VERB
ejpam-3928	42	2	by	by	ADP
ejpam-3928	42	3	this	this	DET
ejpam-3928	42	4	problem	problem	NOUN
ejpam-3928	42	5	,	,	PUNCT
ejpam-3928	42	6	bibak	bibak	NOUN
ejpam-3928	42	7	and	and	CCONJ
ejpam-3928	42	8	haghighi	haghighi	PROPN
ejpam-3928	43	1	[	[	X
ejpam-3928	43	2	1	1	X
ejpam-3928	43	3	]	]	PUNCT
ejpam-3928	43	4	published	publish	VERB
ejpam-3928	43	5	a	a	DET
ejpam-3928	43	6	paper	paper	NOUN
ejpam-3928	43	7	that	that	PRON
ejpam-3928	43	8	contains	contain	VERB
ejpam-3928	43	9	the	the	DET
ejpam-3928	43	10	characterization	characterization	NOUN
ejpam-3928	43	11	of	of	ADP
ejpam-3928	43	12	degreeequipartite	degreeequipartite	ADJ
ejpam-3928	43	13	graphs	graph	NOUN
ejpam-3928	43	14	.	.	PUNCT
ejpam-3928	44	1	moreover	moreover	ADV
ejpam-3928	44	2	,	,	PUNCT
ejpam-3928	44	3	they	they	PRON
ejpam-3928	44	4	introduced	introduce	VERB
ejpam-3928	44	5	a	a	DET
ejpam-3928	44	6	new	new	ADJ
ejpam-3928	44	7	type	type	NOUN
ejpam-3928	44	8	of	of	ADP
ejpam-3928	44	9	graph	graph	NOUN
ejpam-3928	44	10	called	call	VERB
ejpam-3928	44	11	the	the	DET
ejpam-3928	44	12	spectralequipartite	spectralequipartite	NOUN
ejpam-3928	44	13	graph	graph	NOUN
ejpam-3928	44	14	.	.	PUNCT
ejpam-3928	45	1	this	this	DET
ejpam-3928	45	2	new	new	ADJ
ejpam-3928	45	3	type	type	NOUN
ejpam-3928	45	4	was	be	AUX
ejpam-3928	45	5	suggested	suggest	VERB
ejpam-3928	45	6	by	by	ADP
ejpam-3928	45	7	igor	igor	PROPN
ejpam-3928	45	8	shparlinski	shparlinski	PROPN
ejpam-3928	45	9	,	,	PUNCT
ejpam-3928	45	10	who	who	PRON
ejpam-3928	45	11	also	also	ADV
ejpam-3928	45	12	asked	ask	VERB
ejpam-3928	45	13	for	for	ADP
ejpam-3928	45	14	its	its	PRON
ejpam-3928	45	15	full	full	ADJ
ejpam-3928	45	16	characterization	characterization	NOUN
ejpam-3928	45	17	.	.	PUNCT
ejpam-3928	46	1	the	the	DET
ejpam-3928	46	2	latest	late	ADJ
ejpam-3928	46	3	study	study	NOUN
ejpam-3928	46	4	on	on	ADP
ejpam-3928	46	5	equipartite	equipartite	ADJ
ejpam-3928	46	6	graphs	graph	NOUN
ejpam-3928	46	7	is	be	AUX
ejpam-3928	46	8	by	by	ADP
ejpam-3928	46	9	shirdareh	shirdareh	NOUN
ejpam-3928	46	10	haghighi	haghighi	PROPN
ejpam-3928	46	11	et	et	PROPN
ejpam-3928	46	12	al	al	PROPN
ejpam-3928	46	13	.	.	PUNCT
ejpam-3928	47	1	[	[	X
ejpam-3928	47	2	9	9	NUM
ejpam-3928	47	3	]	]	PUNCT
ejpam-3928	47	4	,	,	PUNCT
ejpam-3928	47	5	which	which	PRON
ejpam-3928	47	6	characterizes	characterize	VERB
ejpam-3928	47	7	equipartite	equipartite	ADJ
ejpam-3928	47	8	graphs	graph	NOUN
ejpam-3928	47	9	in	in	ADP
ejpam-3928	47	10	terms	term	NOUN
ejpam-3928	47	11	of	of	ADP
ejpam-3928	47	12	their	their	PRON
ejpam-3928	47	13	laplacian	laplacian	ADJ
ejpam-3928	47	14	spectra	spectra	NOUN
ejpam-3928	47	15	.	.	PROPN
ejpam-3928	47	16	2	2	X
ejpam-3928	47	17	.	.	PUNCT
ejpam-3928	47	18	known	know	VERB
ejpam-3928	47	19	results	result	NOUN
ejpam-3928	47	20	2.1	2.1	NUM
ejpam-3928	47	21	.	.	PUNCT
ejpam-3928	48	1	weakly	weakly	ADJ
ejpam-3928	48	2	-	-	PUNCT
ejpam-3928	48	3	equipartite	equipartite	ADJ
ejpam-3928	48	4	graphs	graph	NOUN
ejpam-3928	48	5	theorem	theorem	VERB
ejpam-3928	48	6	1	1	NUM
ejpam-3928	48	7	is	be	AUX
ejpam-3928	48	8	due	due	ADJ
ejpam-3928	48	9	to	to	ADP
ejpam-3928	48	10	grünbaum	grünbaum	PROPN
ejpam-3928	48	11	et	et	PROPN
ejpam-3928	48	12	al	al	PROPN
ejpam-3928	48	13	.	.	PUNCT
ejpam-3928	49	1	[	[	X
ejpam-3928	49	2	7	7	X
ejpam-3928	49	3	]	]	PUNCT
ejpam-3928	49	4	in	in	ADP
ejpam-3928	49	5	their	their	PRON
ejpam-3928	49	6	study	study	NOUN
ejpam-3928	49	7	on	on	ADP
ejpam-3928	49	8	equipartite	equipartite	ADJ
ejpam-3928	49	9	graphs	graph	NOUN
ejpam-3928	49	10	.	.	PUNCT
ejpam-3928	50	1	theorem	theorem	NOUN
ejpam-3928	50	2	1	1	NUM
ejpam-3928	50	3	.	.	PUNCT
ejpam-3928	51	1	(	(	PUNCT
ejpam-3928	51	2	[	[	X
ejpam-3928	51	3	7],theorem	7],theorem	NUM
ejpam-3928	51	4	13	13	NUM
ejpam-3928	51	5	)	)	PUNCT
ejpam-3928	51	6	a	a	DET
ejpam-3928	51	7	graph	graph	NOUN
ejpam-3928	51	8	g	g	NOUN
ejpam-3928	51	9	is	be	AUX
ejpam-3928	51	10	weakly	weakly	ADV
ejpam-3928	51	11	equipartite	equipartite	ADJ
ejpam-3928	51	12	if	if	SCONJ
ejpam-3928	52	1	and	and	CCONJ
ejpam-3928	52	2	only	only	ADV
ejpam-3928	52	3	if	if	SCONJ
ejpam-3928	52	4	it	it	PRON
ejpam-3928	52	5	is	be	AUX
ejpam-3928	52	6	one	one	NUM
ejpam-3928	52	7	of	of	ADP
ejpam-3928	52	8	the	the	DET
ejpam-3928	52	9	following	follow	VERB
ejpam-3928	52	10	graphs	graph	NOUN
ejpam-3928	52	11	:	:	PUNCT
ejpam-3928	52	12	2nk1	2nk1	NUM
ejpam-3928	52	13	,	,	PUNCT
ejpam-3928	52	14	nk2	nk2	PROPN
ejpam-3928	52	15	,	,	PUNCT
ejpam-3928	52	16	2c4	2c4	NUM
ejpam-3928	52	17	,	,	PUNCT
ejpam-3928	52	18	kn	kn	PROPN
ejpam-3928	52	19	,	,	PUNCT
ejpam-3928	52	20	n\nk2	n\nk2	NOUN
ejpam-3928	52	21	,	,	PUNCT
ejpam-3928	52	22	and	and	CCONJ
ejpam-3928	52	23	2kn	2kn	ADV
ejpam-3928	52	24	,	,	PUNCT
ejpam-3928	52	25	or	or	CCONJ
ejpam-3928	52	26	one	one	NUM
ejpam-3928	52	27	of	of	ADP
ejpam-3928	52	28	their	their	PRON
ejpam-3928	52	29	complements	complement	NOUN
ejpam-3928	52	30	:	:	PUNCT
ejpam-3928	52	31	k2n	k2n	NOUN
ejpam-3928	52	32	,	,	PUNCT
ejpam-3928	52	33	k2n\nk2	k2n\nk2	NOUN
ejpam-3928	52	34	,	,	PUNCT
ejpam-3928	52	35	k8\2c4	k8\2c4	NOUN
ejpam-3928	52	36	,	,	PUNCT
ejpam-3928	52	37	2kn	2kn	ADJ
ejpam-3928	52	38	+	+	CCONJ
ejpam-3928	52	39	nk2	nk2	PROPN
ejpam-3928	52	40	,	,	PUNCT
ejpam-3928	52	41	and	and	CCONJ
ejpam-3928	52	42	kn	kn	PROPN
ejpam-3928	52	43	,	,	PUNCT
ejpam-3928	52	44	n.	n.	PROPN
ejpam-3928	52	45	2.2	2.2	NUM
ejpam-3928	52	46	.	.	PUNCT
ejpam-3928	52	47	degree	degree	NOUN
ejpam-3928	52	48	-	-	PUNCT
ejpam-3928	52	49	equipartite	equipartite	ADJ
ejpam-3928	52	50	graphs	graph	NOUN
ejpam-3928	52	51	the	the	DET
ejpam-3928	52	52	following	follow	VERB
ejpam-3928	52	53	theorem	theorem	NOUN
ejpam-3928	52	54	is	be	AUX
ejpam-3928	52	55	due	due	ADJ
ejpam-3928	52	56	to	to	PART
ejpam-3928	52	57	bibak	bibak	VERB
ejpam-3928	52	58	et	et	PROPN
ejpam-3928	52	59	al	al	PROPN
ejpam-3928	52	60	.	.	PUNCT
ejpam-3928	53	1	[	[	X
ejpam-3928	53	2	1	1	X
ejpam-3928	53	3	]	]	PUNCT
ejpam-3928	53	4	in	in	ADP
ejpam-3928	53	5	their	their	PRON
ejpam-3928	53	6	study	study	NOUN
ejpam-3928	53	7	on	on	ADP
ejpam-3928	53	8	degree	degree	NOUN
ejpam-3928	53	9	-	-	PUNCT
ejpam-3928	53	10	equipartite	equipartite	ADJ
ejpam-3928	53	11	graphs	graph	NOUN
ejpam-3928	53	12	.	.	PUNCT
ejpam-3928	54	1	theorem	theorem	NOUN
ejpam-3928	54	2	2	2	NUM
ejpam-3928	54	3	.	.	PUNCT
ejpam-3928	55	1	(	(	PUNCT
ejpam-3928	55	2	[	[	X
ejpam-3928	55	3	1],theorem	1],theorem	NUM
ejpam-3928	55	4	10	10	NUM
ejpam-3928	55	5	)	)	PUNCT
ejpam-3928	55	6	a	a	DET
ejpam-3928	55	7	graph	graph	NOUN
ejpam-3928	55	8	g	g	NOUN
ejpam-3928	55	9	of	of	ADP
ejpam-3928	55	10	order	order	NOUN
ejpam-3928	55	11	2n	2n	NUM
ejpam-3928	55	12	is	be	AUX
ejpam-3928	55	13	degree	degree	NOUN
ejpam-3928	55	14	-	-	PUNCT
ejpam-3928	55	15	equipartite	equipartite	ADJ
ejpam-3928	55	16	if	if	SCONJ
ejpam-3928	56	1	and	and	CCONJ
ejpam-3928	56	2	only	only	ADV
ejpam-3928	56	3	if	if	SCONJ
ejpam-3928	56	4	it	it	PRON
ejpam-3928	56	5	is	be	AUX
ejpam-3928	56	6	one	one	NUM
ejpam-3928	56	7	of	of	ADP
ejpam-3928	56	8	the	the	DET
ejpam-3928	56	9	following	follow	VERB
ejpam-3928	56	10	graphs	graph	NOUN
ejpam-3928	56	11	:	:	PUNCT
ejpam-3928	56	12	2nk1	2nk1	NUM
ejpam-3928	56	13	,	,	PUNCT
ejpam-3928	56	14	nk2	nk2	PROPN
ejpam-3928	56	15	,	,	PUNCT
ejpam-3928	56	16	2c4	2c4	NUM
ejpam-3928	56	17	,	,	PUNCT
ejpam-3928	56	18	kn	kn	PROPN
ejpam-3928	56	19	,	,	PUNCT
ejpam-3928	56	20	n\nk2	n\nk2	NOUN
ejpam-3928	56	21	,	,	PUNCT
ejpam-3928	56	22	and	and	CCONJ
ejpam-3928	56	23	2kn	2kn	ADV
ejpam-3928	56	24	,	,	PUNCT
ejpam-3928	56	25	or	or	CCONJ
ejpam-3928	56	26	one	one	NUM
ejpam-3928	56	27	of	of	ADP
ejpam-3928	56	28	their	their	PRON
ejpam-3928	56	29	complements	complement	NOUN
ejpam-3928	56	30	:	:	PUNCT
ejpam-3928	56	31	k2n	k2n	NOUN
ejpam-3928	56	32	,	,	PUNCT
ejpam-3928	56	33	k2n\nk2	k2n\nk2	NOUN
ejpam-3928	56	34	,	,	PUNCT
ejpam-3928	56	35	k8\2c4	k8\2c4	NOUN
ejpam-3928	56	36	,	,	PUNCT
ejpam-3928	56	37	2kn	2kn	ADJ
ejpam-3928	56	38	+	+	CCONJ
ejpam-3928	56	39	nk2	nk2	PROPN
ejpam-3928	56	40	,	,	PUNCT
ejpam-3928	56	41	and	and	CCONJ
ejpam-3928	56	42	kn	kn	PROPN
ejpam-3928	56	43	,	,	PUNCT
ejpam-3928	56	44	n.	n.	PROPN
ejpam-3928	56	45	a.	a.	NOUN
ejpam-3928	56	46	yurfo	yurfo	PROPN
ejpam-3928	56	47	,	,	PUNCT
ejpam-3928	56	48	j.	j.	PROPN
ejpam-3928	56	49	adanza	adanza	PROPN
ejpam-3928	56	50	,	,	PUNCT
ejpam-3928	56	51	m.	m.	PROPN
ejpam-3928	56	52	baldado	baldado	PROPN
ejpam-3928	56	53	jr	jr	PROPN
ejpam-3928	56	54	.	.	PROPN
ejpam-3928	56	55	/	/	SYM
ejpam-3928	56	56	eur	eur	PROPN
ejpam-3928	56	57	.	.	PUNCT
ejpam-3928	57	1	j.	j.	PROPN
ejpam-3928	57	2	pure	pure	PROPN
ejpam-3928	57	3	appl	appl	PROPN
ejpam-3928	57	4	.	.	PROPN
ejpam-3928	57	5	math	math	PROPN
ejpam-3928	57	6	,	,	PUNCT
ejpam-3928	57	7	14	14	NUM
ejpam-3928	57	8	(	(	PUNCT
ejpam-3928	57	9	2	2	NUM
ejpam-3928	57	10	)	)	PUNCT
ejpam-3928	57	11	(	(	PUNCT
ejpam-3928	57	12	2021	2021	NUM
ejpam-3928	57	13	)	)	PUNCT
ejpam-3928	57	14	,	,	PUNCT
ejpam-3928	57	15	358	358	NUM
ejpam-3928	57	16	-	-	SYM
ejpam-3928	57	17	365	365	NUM
ejpam-3928	57	18	360	360	NUM
ejpam-3928	57	19	2.3	2.3	NUM
ejpam-3928	57	20	.	.	PUNCT
ejpam-3928	58	1	spectra	spectra	NOUN
ejpam-3928	58	2	of	of	ADP
ejpam-3928	58	3	graphs	graph	NOUN
ejpam-3928	58	4	the	the	DET
ejpam-3928	58	5	following	follow	VERB
ejpam-3928	58	6	theorems	theorem	NOUN
ejpam-3928	58	7	and	and	CCONJ
ejpam-3928	58	8	lemmas	lemma	NOUN
ejpam-3928	58	9	are	be	AUX
ejpam-3928	58	10	due	due	ADJ
ejpam-3928	58	11	to	to	ADP
ejpam-3928	58	12	the	the	DET
ejpam-3928	58	13	different	different	ADJ
ejpam-3928	58	14	studies	study	NOUN
ejpam-3928	58	15	involving	involve	VERB
ejpam-3928	58	16	the	the	DET
ejpam-3928	58	17	spectra	spectra	NOUN
ejpam-3928	58	18	of	of	ADP
ejpam-3928	58	19	graphs	graph	NOUN
ejpam-3928	58	20	.	.	PUNCT
ejpam-3928	59	1	theorem	theorem	NOUN
ejpam-3928	59	2	3	3	NUM
ejpam-3928	59	3	.	.	PUNCT
ejpam-3928	60	1	(	(	PUNCT
ejpam-3928	60	2	[	[	X
ejpam-3928	60	3	8	8	NUM
ejpam-3928	60	4	]	]	PUNCT
ejpam-3928	60	5	,	,	PUNCT
ejpam-3928	60	6	theorem	theorem	VERB
ejpam-3928	60	7	2.1	2.1	NUM
ejpam-3928	60	8	)	)	PUNCT
ejpam-3928	60	9	.	.	PUNCT
ejpam-3928	61	1	let	let	VERB
ejpam-3928	61	2	g	g	PRON
ejpam-3928	61	3	be	be	AUX
ejpam-3928	61	4	a	a	DET
ejpam-3928	61	5	simple	simple	ADJ
ejpam-3928	61	6	undirected	undirected	ADJ
ejpam-3928	61	7	graph	graph	NOUN
ejpam-3928	61	8	and	and	CCONJ
ejpam-3928	61	9	let	let	VERB
ejpam-3928	61	10	a	a	PRON
ejpam-3928	61	11	be	be	AUX
ejpam-3928	61	12	its	its	PRON
ejpam-3928	61	13	adjacency	adjacency	NOUN
ejpam-3928	61	14	matrix	matrix	NOUN
ejpam-3928	61	15	.	.	PUNCT
ejpam-3928	62	1	let	let	VERB
ejpam-3928	62	2	h	h	PRON
ejpam-3928	62	3	be	be	AUX
ejpam-3928	62	4	a	a	DET
ejpam-3928	62	5	graph	graph	NOUN
ejpam-3928	62	6	isomorphic	isomorphic	ADJ
ejpam-3928	62	7	to	to	ADP
ejpam-3928	62	8	g	g	NOUN
ejpam-3928	62	9	and	and	CCONJ
ejpam-3928	62	10	let	let	VERB
ejpam-3928	62	11	b	b	X
ejpam-3928	62	12	be	be	AUX
ejpam-3928	62	13	the	the	DET
ejpam-3928	62	14	adjacency	adjacency	NOUN
ejpam-3928	62	15	matrix	matrix	NOUN
ejpam-3928	62	16	of	of	ADP
ejpam-3928	62	17	h.	h.	PROPN
ejpam-3928	62	18	then	then	ADV
ejpam-3928	62	19	,	,	PUNCT
ejpam-3928	62	20	g	g	PROPN
ejpam-3928	62	21	and	and	CCONJ
ejpam-3928	62	22	h	h	NOUN
ejpam-3928	62	23	have	have	VERB
ejpam-3928	62	24	the	the	DET
ejpam-3928	62	25	same	same	ADJ
ejpam-3928	62	26	spectrum	spectrum	NOUN
ejpam-3928	62	27	.	.	PUNCT
ejpam-3928	63	1	the	the	DET
ejpam-3928	63	2	next	next	ADJ
ejpam-3928	63	3	theorem	theorem	NOUN
ejpam-3928	63	4	is	be	AUX
ejpam-3928	63	5	a	a	DET
ejpam-3928	63	6	consequence	consequence	NOUN
ejpam-3928	63	7	of	of	ADP
ejpam-3928	63	8	theorem	theorem	NOUN
ejpam-3928	63	9	3	3	NUM
ejpam-3928	63	10	and	and	CCONJ
ejpam-3928	63	11	the	the	DET
ejpam-3928	63	12	definition	definition	NOUN
ejpam-3928	63	13	of	of	ADP
ejpam-3928	63	14	isospectral	isospectral	ADJ
ejpam-3928	63	15	graphs	graph	NOUN
ejpam-3928	63	16	.	.	PUNCT
ejpam-3928	64	1	theorem	theorem	ADJ
ejpam-3928	64	2	4	4	NUM
ejpam-3928	64	3	.	.	PUNCT
ejpam-3928	65	1	if	if	SCONJ
ejpam-3928	65	2	two	two	NUM
ejpam-3928	65	3	graphs	graph	NOUN
ejpam-3928	65	4	are	be	AUX
ejpam-3928	65	5	isomorphic	isomorphic	ADJ
ejpam-3928	65	6	,	,	PUNCT
ejpam-3928	65	7	then	then	ADV
ejpam-3928	65	8	they	they	PRON
ejpam-3928	65	9	are	be	AUX
ejpam-3928	65	10	isospectral	isospectral	ADJ
ejpam-3928	65	11	.	.	PUNCT
ejpam-3928	66	1	lemma	lemma	PROPN
ejpam-3928	66	2	1	1	NUM
ejpam-3928	66	3	.	.	PUNCT
ejpam-3928	67	1	(	(	PUNCT
ejpam-3928	67	2	[	[	X
ejpam-3928	67	3	9	9	NUM
ejpam-3928	67	4	]	]	PUNCT
ejpam-3928	67	5	,	,	PUNCT
ejpam-3928	67	6	lemma	lemma	PROPN
ejpam-3928	67	7	2.5	2.5	NUM
ejpam-3928	67	8	)	)	PUNCT
ejpam-3928	67	9	.	.	PUNCT
ejpam-3928	68	1	if	if	SCONJ
ejpam-3928	68	2	g	g	PROPN
ejpam-3928	68	3	is	be	AUX
ejpam-3928	68	4	a	a	DET
ejpam-3928	68	5	non	non	ADJ
ejpam-3928	68	6	-	-	ADJ
ejpam-3928	68	7	complete	complete	ADJ
ejpam-3928	68	8	regular	regular	ADJ
ejpam-3928	68	9	graph	graph	NOUN
ejpam-3928	68	10	such	such	ADJ
ejpam-3928	68	11	that	that	SCONJ
ejpam-3928	68	12	every	every	DET
ejpam-3928	68	13	two	two	NUM
ejpam-3928	68	14	non	non	ADJ
ejpam-3928	68	15	-	-	ADJ
ejpam-3928	68	16	adjacent	adjacent	ADJ
ejpam-3928	68	17	vertices	vertex	NOUN
ejpam-3928	68	18	of	of	ADP
ejpam-3928	68	19	g	g	PROPN
ejpam-3928	68	20	form	form	VERB
ejpam-3928	68	21	a	a	DET
ejpam-3928	68	22	vertex	vertex	NOUN
ejpam-3928	68	23	cut	cut	NOUN
ejpam-3928	68	24	,	,	PUNCT
ejpam-3928	68	25	then	then	ADV
ejpam-3928	68	26	g	g	PROPN
ejpam-3928	68	27	is	be	AUX
ejpam-3928	68	28	a	a	DET
ejpam-3928	68	29	cycle	cycle	NOUN
ejpam-3928	68	30	.	.	PUNCT
ejpam-3928	69	1	lemma	lemma	PROPN
ejpam-3928	69	2	2	2	PROPN
ejpam-3928	69	3	can	can	AUX
ejpam-3928	69	4	be	be	AUX
ejpam-3928	69	5	verified	verify	VERB
ejpam-3928	69	6	easily	easily	ADV
ejpam-3928	69	7	as	as	ADP
ejpam-3928	69	8	a	a	DET
ejpam-3928	69	9	direct	direct	ADJ
ejpam-3928	69	10	consequence	consequence	NOUN
ejpam-3928	69	11	of	of	ADP
ejpam-3928	69	12	[	[	X
ejpam-3928	69	13	6	6	NUM
ejpam-3928	69	14	]	]	X
ejpam-3928	69	15	(	(	PUNCT
ejpam-3928	69	16	f33	f33	PROPN
ejpam-3928	69	17	,	,	PUNCT
ejpam-3928	69	18	page	page	NOUN
ejpam-3928	69	19	679	679	NUM
ejpam-3928	69	20	)	)	PUNCT
ejpam-3928	69	21	.	.	PUNCT
ejpam-3928	70	1	lemma	lemma	PROPN
ejpam-3928	70	2	2	2	X
ejpam-3928	70	3	.	.	PUNCT
ejpam-3928	71	1	if	if	SCONJ
ejpam-3928	71	2	h	h	NOUN
ejpam-3928	71	3	is	be	AUX
ejpam-3928	71	4	a	a	DET
ejpam-3928	71	5	proper	proper	ADJ
ejpam-3928	71	6	subgraph	subgraph	NOUN
ejpam-3928	71	7	of	of	ADP
ejpam-3928	71	8	g	g	PROPN
ejpam-3928	71	9	,	,	PUNCT
ejpam-3928	71	10	then	then	ADV
ejpam-3928	71	11	λ1	λ1	PROPN
ejpam-3928	71	12	(	(	PUNCT
ejpam-3928	71	13	h	h	NOUN
ejpam-3928	71	14	)	)	PUNCT
ejpam-3928	71	15	<	<	X
ejpam-3928	71	16	λ1	λ1	PROPN
ejpam-3928	71	17	(	(	PUNCT
ejpam-3928	71	18	g	g	NOUN
ejpam-3928	71	19	)	)	PUNCT
ejpam-3928	71	20	.	.	PUNCT
ejpam-3928	72	1	lemma	lemma	PROPN
ejpam-3928	72	2	3	3	X
ejpam-3928	72	3	.	.	PUNCT
ejpam-3928	73	1	(	(	PUNCT
ejpam-3928	73	2	[	[	X
ejpam-3928	73	3	6	6	NUM
ejpam-3928	73	4	]	]	PUNCT
ejpam-3928	73	5	,	,	PUNCT
ejpam-3928	73	6	f6	f6	PROPN
ejpam-3928	73	7	,	,	PUNCT
ejpam-3928	73	8	page	page	NOUN
ejpam-3928	73	9	674	674	NUM
ejpam-3928	73	10	)	)	PUNCT
ejpam-3928	73	11	.	.	PUNCT
ejpam-3928	74	1	the	the	DET
ejpam-3928	74	2	spectrum	spectrum	NOUN
ejpam-3928	74	3	of	of	ADP
ejpam-3928	74	4	a	a	DET
ejpam-3928	74	5	graph	graph	NOUN
ejpam-3928	74	6	is	be	AUX
ejpam-3928	74	7	the	the	DET
ejpam-3928	74	8	union	union	NOUN
ejpam-3928	74	9	of	of	ADP
ejpam-3928	74	10	the	the	DET
ejpam-3928	74	11	spectra	spectra	NOUN
ejpam-3928	74	12	of	of	ADP
ejpam-3928	74	13	its	its	PRON
ejpam-3928	74	14	connected	connected	ADJ
ejpam-3928	74	15	components	component	NOUN
ejpam-3928	74	16	.	.	PUNCT
ejpam-3928	75	1	lemma	lemma	PROPN
ejpam-3928	75	2	4	4	NUM
ejpam-3928	75	3	.	.	PUNCT
ejpam-3928	76	1	(	(	PUNCT
ejpam-3928	76	2	[	[	X
ejpam-3928	76	3	2	2	NUM
ejpam-3928	76	4	]	]	PUNCT
ejpam-3928	76	5	,	,	PUNCT
ejpam-3928	76	6	1.4.1	1.4.1	NUM
ejpam-3928	76	7	and	and	CCONJ
ejpam-3928	76	8	1.4.2	1.4.2	NUM
ejpam-3928	76	9	)	)	PUNCT
ejpam-3928	76	10	.	.	PUNCT
ejpam-3928	77	1	let	let	VERB
ejpam-3928	77	2	m	m	PRON
ejpam-3928	77	3	,	,	PUNCT
ejpam-3928	77	4	n	n	PROPN
ejpam-3928	77	5	∈	∈	PROPN
ejpam-3928	77	6	n.	n.	NOUN
ejpam-3928	77	7	the	the	DET
ejpam-3928	77	8	spectrum	spectrum	NOUN
ejpam-3928	77	9	of	of	ADP
ejpam-3928	77	10	a	a	DET
ejpam-3928	77	11	complete	complete	ADJ
ejpam-3928	77	12	graph	graph	NOUN
ejpam-3928	77	13	kn	kn	PROPN
ejpam-3928	77	14	is	be	AUX
ejpam-3928	77	15	{	{	PUNCT
ejpam-3928	77	16	−1n−1	−1n−1	PROPN
ejpam-3928	77	17	,	,	PUNCT
ejpam-3928	77	18	n−1	n−1	PROPN
ejpam-3928	77	19	}	}	PUNCT
ejpam-3928	77	20	and	and	CCONJ
ejpam-3928	77	21	the	the	DET
ejpam-3928	77	22	spectrum	spectrum	NOUN
ejpam-3928	77	23	of	of	ADP
ejpam-3928	77	24	a	a	DET
ejpam-3928	77	25	complete	complete	ADJ
ejpam-3928	77	26	bipartite	bipartite	NOUN
ejpam-3928	77	27	graph	graph	NOUN
ejpam-3928	77	28	km	km	PROPN
ejpam-3928	77	29	,	,	PUNCT
ejpam-3928	77	30	n	n	X
ejpam-3928	77	31	is	be	AUX
ejpam-3928	77	32	{	{	PUNCT
ejpam-3928	77	33	±	±	NUM
ejpam-3928	77	34	√	√	PROPN
ejpam-3928	77	35	mn	mn	PROPN
ejpam-3928	77	36	,	,	PUNCT
ejpam-3928	77	37	0m+n−2	0m+n−2	NUM
ejpam-3928	77	38	}	}	PUNCT
ejpam-3928	77	39	.	.	PUNCT
ejpam-3928	78	1	lemma	lemma	PROPN
ejpam-3928	78	2	5	5	NUM
ejpam-3928	78	3	is	be	AUX
ejpam-3928	78	4	a	a	DET
ejpam-3928	78	5	direct	direct	ADJ
ejpam-3928	78	6	consequence	consequence	NOUN
ejpam-3928	78	7	of	of	ADP
ejpam-3928	78	8	lemma	lemma	PROPN
ejpam-3928	78	9	3	3	NUM
ejpam-3928	78	10	and	and	CCONJ
ejpam-3928	78	11	lemma	lemma	PROPN
ejpam-3928	78	12	4	4	X
ejpam-3928	78	13	.	.	PUNCT
ejpam-3928	78	14	lemma	lemma	PROPN
ejpam-3928	78	15	5	5	X
ejpam-3928	78	16	.	.	PUNCT
ejpam-3928	79	1	let	let	VERB
ejpam-3928	79	2	n	n	PRON
ejpam-3928	79	3	∈	∈	PROPN
ejpam-3928	79	4	n.	n.	NOUN
ejpam-3928	79	5	the	the	DET
ejpam-3928	79	6	spectrum	spectrum	NOUN
ejpam-3928	79	7	of	of	ADP
ejpam-3928	79	8	an	an	DET
ejpam-3928	79	9	empty	empty	ADJ
ejpam-3928	79	10	graph	graph	NOUN
ejpam-3928	79	11	nk1	nk1	NOUN
ejpam-3928	79	12	is	be	AUX
ejpam-3928	79	13	{	{	PUNCT
ejpam-3928	79	14	0n	0n	NUM
ejpam-3928	79	15	}	}	PUNCT
ejpam-3928	79	16	.	.	PUNCT
ejpam-3928	80	1	theorem	theorem	NOUN
ejpam-3928	80	2	5	5	NUM
ejpam-3928	80	3	.	.	PUNCT
ejpam-3928	81	1	(	(	PUNCT
ejpam-3928	81	2	[	[	X
ejpam-3928	81	3	1	1	NUM
ejpam-3928	81	4	]	]	PUNCT
ejpam-3928	81	5	,	,	PUNCT
ejpam-3928	81	6	problem	problem	NOUN
ejpam-3928	81	7	1	1	NUM
ejpam-3928	81	8	,	,	PUNCT
ejpam-3928	81	9	page	page	NOUN
ejpam-3928	81	10	891	891	NUM
ejpam-3928	81	11	)	)	PUNCT
ejpam-3928	81	12	.	.	PUNCT
ejpam-3928	82	1	every	every	DET
ejpam-3928	82	2	spectral	spectral	ADJ
ejpam-3928	82	3	-	-	PUNCT
ejpam-3928	82	4	equipartite	equipartite	ADJ
ejpam-3928	82	5	graph	graph	NOUN
ejpam-3928	82	6	is	be	AUX
ejpam-3928	82	7	regular	regular	ADJ
ejpam-3928	82	8	.	.	PUNCT
ejpam-3928	83	1	3	3	X
ejpam-3928	83	2	.	.	X
ejpam-3928	83	3	main	main	ADJ
ejpam-3928	83	4	results	result	NOUN
ejpam-3928	83	5	this	this	DET
ejpam-3928	83	6	section	section	NOUN
ejpam-3928	83	7	presents	present	VERB
ejpam-3928	83	8	the	the	DET
ejpam-3928	83	9	main	main	ADJ
ejpam-3928	83	10	results	result	NOUN
ejpam-3928	83	11	of	of	ADP
ejpam-3928	83	12	the	the	DET
ejpam-3928	83	13	study	study	NOUN
ejpam-3928	83	14	.	.	PUNCT
ejpam-3928	84	1	3.1	3.1	NUM
ejpam-3928	84	2	.	.	PUNCT
ejpam-3928	84	3	characterization	characterization	NOUN
ejpam-3928	84	4	of	of	ADP
ejpam-3928	84	5	disconnected	disconnected	ADJ
ejpam-3928	84	6	spectral	spectral	ADJ
ejpam-3928	84	7	-	-	PUNCT
ejpam-3928	84	8	equipartite	equipartite	ADJ
ejpam-3928	84	9	graphs	graph	NOUN
ejpam-3928	84	10	the	the	DET
ejpam-3928	84	11	following	follow	VERB
ejpam-3928	84	12	results	result	NOUN
ejpam-3928	84	13	lead	lead	VERB
ejpam-3928	84	14	to	to	ADP
ejpam-3928	84	15	the	the	DET
ejpam-3928	84	16	characterization	characterization	NOUN
ejpam-3928	84	17	of	of	ADP
ejpam-3928	84	18	disconnected	disconnected	ADJ
ejpam-3928	84	19	spectral	spectral	ADJ
ejpam-3928	84	20	-	-	PUNCT
ejpam-3928	84	21	equipartite	equipartite	ADJ
ejpam-3928	84	22	graphs	graph	NOUN
ejpam-3928	84	23	.	.	PUNCT
ejpam-3928	85	1	this	this	DET
ejpam-3928	85	2	section	section	NOUN
ejpam-3928	85	3	also	also	ADV
ejpam-3928	85	4	shows	show	VERB
ejpam-3928	85	5	that	that	SCONJ
ejpam-3928	85	6	the	the	DET
ejpam-3928	85	7	complement	complement	NOUN
ejpam-3928	85	8	of	of	ADP
ejpam-3928	85	9	a	a	DET
ejpam-3928	85	10	disconnected	disconnected	ADJ
ejpam-3928	85	11	spectral	spectral	ADJ
ejpam-3928	85	12	-	-	PUNCT
ejpam-3928	85	13	equipartite	equipartite	ADJ
ejpam-3928	85	14	graph	graph	NOUN
ejpam-3928	85	15	is	be	AUX
ejpam-3928	85	16	also	also	ADV
ejpam-3928	85	17	spectral	spectral	ADJ
ejpam-3928	85	18	-	-	PUNCT
ejpam-3928	85	19	equipartite	equipartite	ADJ
ejpam-3928	85	20	.	.	PUNCT
ejpam-3928	86	1	theorem	theorem	VERB
ejpam-3928	86	2	6	6	NUM
ejpam-3928	86	3	.	.	PUNCT
ejpam-3928	87	1	every	every	DET
ejpam-3928	87	2	weakly	weakly	ADJ
ejpam-3928	87	3	-	-	PUNCT
ejpam-3928	87	4	equipartite	equipartite	ADJ
ejpam-3928	87	5	graph	graph	NOUN
ejpam-3928	87	6	is	be	AUX
ejpam-3928	87	7	spectral	spectral	ADJ
ejpam-3928	87	8	-	-	PUNCT
ejpam-3928	87	9	equipartite	equipartite	ADJ
ejpam-3928	87	10	.	.	PUNCT
ejpam-3928	88	1	proof	proof	NOUN
ejpam-3928	88	2	.	.	PUNCT
ejpam-3928	89	1	let	let	VERB
ejpam-3928	89	2	g	g	PROPN
ejpam-3928	89	3	=	=	SYM
ejpam-3928	89	4	(	(	PUNCT
ejpam-3928	89	5	v	v	NOUN
ejpam-3928	89	6	,	,	PUNCT
ejpam-3928	89	7	e	e	NOUN
ejpam-3928	89	8	)	)	PUNCT
ejpam-3928	89	9	be	be	AUX
ejpam-3928	89	10	a	a	DET
ejpam-3928	89	11	weakly	weakly	ADV
ejpam-3928	89	12	-	-	PUNCT
ejpam-3928	89	13	equipartite	equipartite	ADJ
ejpam-3928	89	14	graph	graph	NOUN
ejpam-3928	89	15	of	of	ADP
ejpam-3928	89	16	order	order	NOUN
ejpam-3928	89	17	2n	2n	NUM
ejpam-3928	89	18	and	and	CCONJ
ejpam-3928	89	19	let	let	VERB
ejpam-3928	89	20	a	a	PRON
ejpam-3928	89	21	be	be	AUX
ejpam-3928	89	22	an	an	DET
ejpam-3928	89	23	n	n	PRON
ejpam-3928	89	24	element	element	NOUN
ejpam-3928	89	25	subset	subset	NOUN
ejpam-3928	89	26	of	of	ADP
ejpam-3928	89	27	v	v	NOUN
ejpam-3928	89	28	.	.	PUNCT
ejpam-3928	90	1	then	then	ADV
ejpam-3928	90	2	,	,	PUNCT
ejpam-3928	90	3	〈	〈	PROPN
ejpam-3928	90	4	a	a	DET
ejpam-3928	90	5	〉	〉	NOUN
ejpam-3928	90	6	and	and	CCONJ
ejpam-3928	90	7	〈	〈	PROPN
ejpam-3928	90	8	v	v	ADJ
ejpam-3928	90	9	\a	\a	ADJ
ejpam-3928	90	10	〉	〉	NOUN
ejpam-3928	90	11	are	be	AUX
ejpam-3928	90	12	isomorphic	isomorphic	ADJ
ejpam-3928	90	13	.	.	PUNCT
ejpam-3928	91	1	thus	thus	ADV
ejpam-3928	91	2	,	,	PUNCT
ejpam-3928	91	3	by	by	ADP
ejpam-3928	91	4	theorem	theorem	NOUN
ejpam-3928	91	5	4	4	NUM
ejpam-3928	91	6	,	,	PUNCT
ejpam-3928	91	7	〈	〈	PROPN
ejpam-3928	91	8	a	a	DET
ejpam-3928	91	9	〉	〉	NOUN
ejpam-3928	91	10	and	and	CCONJ
ejpam-3928	91	11	〈	〈	PROPN
ejpam-3928	91	12	v	v	ADJ
ejpam-3928	91	13	\a	\a	ADJ
ejpam-3928	91	14	〉	〉	PROPN
ejpam-3928	91	15	are	be	AUX
ejpam-3928	91	16	isospectral	isospectral	ADJ
ejpam-3928	91	17	.	.	PUNCT
ejpam-3928	92	1	this	this	PRON
ejpam-3928	92	2	shows	show	VERB
ejpam-3928	92	3	that	that	SCONJ
ejpam-3928	92	4	g	g	PROPN
ejpam-3928	92	5	is	be	AUX
ejpam-3928	92	6	spectral	spectral	ADJ
ejpam-3928	92	7	-	-	PUNCT
ejpam-3928	92	8	equipartite	equipartite	ADJ
ejpam-3928	92	9	.	.	PUNCT
ejpam-3928	93	1	a.	a.	NOUN
ejpam-3928	93	2	yurfo	yurfo	PROPN
ejpam-3928	93	3	,	,	PUNCT
ejpam-3928	93	4	j.	j.	PROPN
ejpam-3928	93	5	adanza	adanza	PROPN
ejpam-3928	93	6	,	,	PUNCT
ejpam-3928	93	7	m.	m.	PROPN
ejpam-3928	93	8	baldado	baldado	PROPN
ejpam-3928	93	9	jr	jr	PROPN
ejpam-3928	93	10	.	.	PROPN
ejpam-3928	93	11	/	/	SYM
ejpam-3928	93	12	eur	eur	PROPN
ejpam-3928	93	13	.	.	PUNCT
ejpam-3928	94	1	j.	j.	PROPN
ejpam-3928	94	2	pure	pure	PROPN
ejpam-3928	94	3	appl	appl	PROPN
ejpam-3928	94	4	.	.	PROPN
ejpam-3928	94	5	math	math	PROPN
ejpam-3928	94	6	,	,	PUNCT
ejpam-3928	94	7	14	14	NUM
ejpam-3928	94	8	(	(	PUNCT
ejpam-3928	94	9	2	2	NUM
ejpam-3928	94	10	)	)	PUNCT
ejpam-3928	94	11	(	(	PUNCT
ejpam-3928	94	12	2021	2021	NUM
ejpam-3928	94	13	)	)	PUNCT
ejpam-3928	94	14	,	,	PUNCT
ejpam-3928	94	15	358	358	NUM
ejpam-3928	94	16	-	-	SYM
ejpam-3928	94	17	365	365	NUM
ejpam-3928	94	18	361	361	NUM
ejpam-3928	94	19	theorem	theorem	NOUN
ejpam-3928	94	20	7	7	NUM
ejpam-3928	94	21	.	.	PUNCT
ejpam-3928	95	1	every	every	DET
ejpam-3928	95	2	degree	degree	NOUN
ejpam-3928	95	3	-	-	PUNCT
ejpam-3928	95	4	equipartite	equipartite	ADJ
ejpam-3928	95	5	graph	graph	NOUN
ejpam-3928	95	6	is	be	AUX
ejpam-3928	95	7	spectral	spectral	ADJ
ejpam-3928	95	8	-	-	PUNCT
ejpam-3928	95	9	equipartite	equipartite	ADJ
ejpam-3928	95	10	.	.	PUNCT
ejpam-3928	96	1	proof	proof	NOUN
ejpam-3928	96	2	.	.	PUNCT
ejpam-3928	97	1	let	let	VERB
ejpam-3928	97	2	g	g	PRON
ejpam-3928	97	3	be	be	AUX
ejpam-3928	97	4	a	a	DET
ejpam-3928	97	5	degree	degree	NOUN
ejpam-3928	97	6	-	-	PUNCT
ejpam-3928	97	7	equipartite	equipartite	ADJ
ejpam-3928	97	8	graph	graph	NOUN
ejpam-3928	97	9	.	.	PUNCT
ejpam-3928	98	1	by	by	ADP
ejpam-3928	98	2	theorem	theorem	NOUN
ejpam-3928	98	3	1	1	NUM
ejpam-3928	98	4	and	and	CCONJ
ejpam-3928	98	5	theorem	theorem	VERB
ejpam-3928	98	6	2	2	NUM
ejpam-3928	98	7	,	,	PUNCT
ejpam-3928	98	8	every	every	DET
ejpam-3928	98	9	weakly	weakly	ADJ
ejpam-3928	98	10	-	-	PUNCT
ejpam-3928	98	11	equipartite	equipartite	ADJ
ejpam-3928	98	12	graph	graph	NOUN
ejpam-3928	98	13	is	be	AUX
ejpam-3928	98	14	degree	degree	NOUN
ejpam-3928	98	15	-	-	PUNCT
ejpam-3928	98	16	equipartite	equipartite	ADJ
ejpam-3928	98	17	,	,	PUNCT
ejpam-3928	98	18	and	and	CCONJ
ejpam-3928	98	19	every	every	DET
ejpam-3928	98	20	degree	degree	NOUN
ejpam-3928	98	21	-	-	PUNCT
ejpam-3928	98	22	equipartite	equipartite	ADJ
ejpam-3928	98	23	graph	graph	NOUN
ejpam-3928	98	24	is	be	AUX
ejpam-3928	98	25	weakly	weakly	ADV
ejpam-3928	98	26	-	-	PUNCT
ejpam-3928	98	27	equipartite	equipartite	ADJ
ejpam-3928	98	28	.	.	PUNCT
ejpam-3928	99	1	hence	hence	ADV
ejpam-3928	99	2	,	,	PUNCT
ejpam-3928	99	3	by	by	ADP
ejpam-3928	99	4	theorem	theorem	NOUN
ejpam-3928	99	5	6	6	NUM
ejpam-3928	99	6	,	,	PUNCT
ejpam-3928	99	7	g	g	PROPN
ejpam-3928	99	8	is	be	AUX
ejpam-3928	99	9	spectral	spectral	ADJ
ejpam-3928	99	10	-	-	PUNCT
ejpam-3928	99	11	equipartite	equipartite	ADJ
ejpam-3928	99	12	.	.	PUNCT
ejpam-3928	100	1	remark	remark	PROPN
ejpam-3928	100	2	1	1	NUM
ejpam-3928	100	3	.	.	PUNCT
ejpam-3928	101	1	there	there	PRON
ejpam-3928	101	2	exists	exist	VERB
ejpam-3928	101	3	a	a	DET
ejpam-3928	101	4	disconnected	disconnected	ADJ
ejpam-3928	101	5	k	k	NOUN
ejpam-3928	101	6	-	-	NOUN
ejpam-3928	101	7	regular	regular	ADJ
ejpam-3928	101	8	(	(	PUNCT
ejpam-3928	101	9	with	with	ADP
ejpam-3928	101	10	k	k	PROPN
ejpam-3928	101	11	>	>	X
ejpam-3928	101	12	1	1	X
ejpam-3928	101	13	)	)	PUNCT
ejpam-3928	101	14	spectral	spectral	ADJ
ejpam-3928	101	15	-	-	PUNCT
ejpam-3928	101	16	equipartite	equipartite	ADJ
ejpam-3928	101	17	graph	graph	NOUN
ejpam-3928	101	18	.	.	PUNCT
ejpam-3928	102	1	to	to	PART
ejpam-3928	102	2	see	see	VERB
ejpam-3928	102	3	this	this	PRON
ejpam-3928	102	4	,	,	PUNCT
ejpam-3928	102	5	the	the	DET
ejpam-3928	102	6	following	follow	VERB
ejpam-3928	102	7	are	be	AUX
ejpam-3928	102	8	disconnected	disconnect	VERB
ejpam-3928	102	9	k	k	ADJ
ejpam-3928	102	10	-	-	ADJ
ejpam-3928	102	11	regular	regular	ADJ
ejpam-3928	102	12	(	(	PUNCT
ejpam-3928	102	13	with	with	ADP
ejpam-3928	102	14	k	k	PROPN
ejpam-3928	102	15	>	>	X
ejpam-3928	102	16	1	1	X
ejpam-3928	102	17	)	)	PUNCT
ejpam-3928	102	18	spectral	spectral	ADJ
ejpam-3928	102	19	-	-	PUNCT
ejpam-3928	102	20	equipartite	equipartite	ADJ
ejpam-3928	102	21	graph	graph	NOUN
ejpam-3928	102	22	:	:	PUNCT
ejpam-3928	102	23	2nk1	2nk1	NUM
ejpam-3928	102	24	;	;	PUNCT
ejpam-3928	102	25	nk2	nk2	NOUN
ejpam-3928	102	26	;	;	PUNCT
ejpam-3928	102	27	2c4	2c4	NUM
ejpam-3928	102	28	;	;	PUNCT
ejpam-3928	102	29	and	and	CCONJ
ejpam-3928	102	30	2kn	2kn	ADV
ejpam-3928	102	31	.	.	PUNCT
ejpam-3928	103	1	lemma	lemma	PROPN
ejpam-3928	103	2	6	6	NUM
ejpam-3928	103	3	.	.	PUNCT
ejpam-3928	104	1	if	if	SCONJ
ejpam-3928	104	2	a1	a1	PROPN
ejpam-3928	104	3	,	,	PUNCT
ejpam-3928	104	4	a2	a2	PROPN
ejpam-3928	104	5	,	,	PUNCT
ejpam-3928	104	6	.	.	PUNCT
ejpam-3928	104	7	.	.	PUNCT
ejpam-3928	105	1	.	.	PUNCT
ejpam-3928	106	1	,	,	PUNCT
ejpam-3928	106	2	an	an	DET
ejpam-3928	106	3	∈	∈	PROPN
ejpam-3928	106	4	n	n	NOUN
ejpam-3928	106	5	with	with	ADP
ejpam-3928	106	6	a1	a1	PROPN
ejpam-3928	106	7	≥	≥	PROPN
ejpam-3928	106	8	a2	a2	PROPN
ejpam-3928	106	9	≥	≥	PROPN
ejpam-3928	106	10	.	.	PUNCT
ejpam-3928	106	11	.	.	PUNCT
ejpam-3928	107	1	.	.	PUNCT
ejpam-3928	108	1	≥	≥	AUX
ejpam-3928	108	2	an	an	DET
ejpam-3928	108	3	≥	≥	NOUN
ejpam-3928	108	4	4	4	NUM
ejpam-3928	108	5	,	,	PUNCT
ejpam-3928	108	6	then	then	ADV
ejpam-3928	108	7	(	(	PUNCT
ejpam-3928	108	8	a1	a1	NOUN
ejpam-3928	108	9	+	+	CCONJ
ejpam-3928	108	10	a2	a2	PROPN
ejpam-3928	108	11	+	+	CCONJ
ejpam-3928	108	12	·	·	PUNCT
ejpam-3928	108	13	·	·	PUNCT
ejpam-3928	108	14	·	·	PUNCT
ejpam-3928	109	1	+	+	CCONJ
ejpam-3928	109	2	an−1)−	an−1)−	PROPN
ejpam-3928	109	3	2	2	NUM
ejpam-3928	109	4	(	(	PUNCT
ejpam-3928	109	5	n−	n−	NOUN
ejpam-3928	109	6	1	1	NUM
ejpam-3928	109	7	)	)	PUNCT
ejpam-3928	109	8	≥	≥	NOUN
ejpam-3928	109	9	an	an	PRON
ejpam-3928	109	10	for	for	ADP
ejpam-3928	109	11	all	all	DET
ejpam-3928	109	12	positive	positive	ADJ
ejpam-3928	109	13	integer	integer	NOUN
ejpam-3928	109	14	n	n	PRON
ejpam-3928	109	15	≥	≥	NOUN
ejpam-3928	109	16	3	3	NUM
ejpam-3928	109	17	.	.	PUNCT
ejpam-3928	110	1	proof	proof	NOUN
ejpam-3928	110	2	.	.	PUNCT
ejpam-3928	111	1	we	we	PRON
ejpam-3928	111	2	use	use	VERB
ejpam-3928	111	3	induction	induction	NOUN
ejpam-3928	111	4	.	.	PUNCT
ejpam-3928	112	1	for	for	ADP
ejpam-3928	112	2	n	n	NOUN
ejpam-3928	112	3	=	=	SYM
ejpam-3928	112	4	3	3	NUM
ejpam-3928	112	5	,	,	PUNCT
ejpam-3928	112	6	we	we	PRON
ejpam-3928	112	7	have	have	VERB
ejpam-3928	112	8	a1	a1	PROPN
ejpam-3928	112	9	≥	≥	PROPN
ejpam-3928	112	10	a2	a2	PROPN
ejpam-3928	112	11	≥	≥	PROPN
ejpam-3928	112	12	a3	a3	PROPN
ejpam-3928	112	13	≥	≥	NOUN
ejpam-3928	112	14	4	4	NUM
ejpam-3928	112	15	,	,	PUNCT
ejpam-3928	112	16	that	that	PRON
ejpam-3928	112	17	is	is	ADV
ejpam-3928	112	18	a1	a1	PROPN
ejpam-3928	112	19	≥	≥	NOUN
ejpam-3928	112	20	a3	a3	NOUN
ejpam-3928	112	21	and	and	CCONJ
ejpam-3928	112	22	a2	a2	PROPN
ejpam-3928	112	23	≥	≥	PROPN
ejpam-3928	112	24	a3	a3	PROPN
ejpam-3928	112	25	.	.	PUNCT
ejpam-3928	113	1	since	since	SCONJ
ejpam-3928	113	2	a3	a3	PROPN
ejpam-3928	113	3	≥	≥	PROPN
ejpam-3928	113	4	4	4	NUM
ejpam-3928	113	5	,	,	PUNCT
ejpam-3928	113	6	a2	a2	PROPN
ejpam-3928	113	7	−	−	PROPN
ejpam-3928	113	8	4	4	NUM
ejpam-3928	113	9	≥	≥	NOUN
ejpam-3928	113	10	0	0	NUM
ejpam-3928	113	11	.	.	PUNCT
ejpam-3928	114	1	thus	thus	ADV
ejpam-3928	114	2	,	,	PUNCT
ejpam-3928	114	3	a1	a1	PROPN
ejpam-3928	114	4	+	+	CCONJ
ejpam-3928	114	5	a2	a2	PROPN
ejpam-3928	114	6	−	−	PROPN
ejpam-3928	114	7	4	4	NUM
ejpam-3928	114	8	≥	≥	NOUN
ejpam-3928	114	9	a3	a3	NOUN
ejpam-3928	114	10	,	,	PUNCT
ejpam-3928	114	11	that	that	PRON
ejpam-3928	114	12	is	be	AUX
ejpam-3928	114	13	a1	a1	NOUN
ejpam-3928	114	14	+	+	CCONJ
ejpam-3928	114	15	a2	a2	PROPN
ejpam-3928	114	16	−	−	PROPN
ejpam-3928	114	17	2(3−	2(3−	NUM
ejpam-3928	114	18	1	1	NUM
ejpam-3928	114	19	)	)	PUNCT
ejpam-3928	114	20	≥	≥	NOUN
ejpam-3928	114	21	a3	a3	NOUN
ejpam-3928	114	22	.	.	PUNCT
ejpam-3928	115	1	hence	hence	ADV
ejpam-3928	115	2	the	the	DET
ejpam-3928	115	3	assertion	assertion	NOUN
ejpam-3928	115	4	holds	hold	VERB
ejpam-3928	115	5	for	for	ADP
ejpam-3928	115	6	n	n	NOUN
ejpam-3928	115	7	=	=	SYM
ejpam-3928	115	8	3	3	X
ejpam-3928	115	9	.	.	PUNCT
ejpam-3928	116	1	now	now	ADV
ejpam-3928	116	2	,	,	PUNCT
ejpam-3928	116	3	let	let	VERB
ejpam-3928	116	4	k	k	PROPN
ejpam-3928	116	5	≥	≥	NUM
ejpam-3928	116	6	3	3	NUM
ejpam-3928	116	7	and	and	CCONJ
ejpam-3928	116	8	assume	assume	VERB
ejpam-3928	116	9	that	that	SCONJ
ejpam-3928	116	10	the	the	DET
ejpam-3928	116	11	assertion	assertion	NOUN
ejpam-3928	116	12	holds	hold	VERB
ejpam-3928	116	13	for	for	ADP
ejpam-3928	116	14	k.	k.	PROPN
ejpam-3928	116	15	then	then	ADV
ejpam-3928	116	16	,	,	PUNCT
ejpam-3928	116	17	(	(	PUNCT
ejpam-3928	116	18	a1+a2	a1+a2	PROPN
ejpam-3928	116	19	+	+	PROPN
ejpam-3928	116	20	·	·	PUNCT
ejpam-3928	116	21	·	·	PUNCT
ejpam-3928	116	22	·	·	PUNCT
ejpam-3928	117	1	+	+	ADJ
ejpam-3928	117	2	ak−1)−2	ak−1)−2	NOUN
ejpam-3928	117	3	(	(	PUNCT
ejpam-3928	117	4	k	k	NOUN
ejpam-3928	117	5	−	−	PROPN
ejpam-3928	117	6	1	1	NUM
ejpam-3928	117	7	)	)	PUNCT
ejpam-3928	117	8	≥	≥	NOUN
ejpam-3928	117	9	ak	ak	PROPN
ejpam-3928	117	10	≥	≥	NOUN
ejpam-3928	117	11	ak+1	ak+1	VERB
ejpam-3928	117	12	.	.	PUNCT
ejpam-3928	118	1	since	since	SCONJ
ejpam-3928	118	2	ak	ak	PROPN
ejpam-3928	118	3	≥	≥	PROPN
ejpam-3928	118	4	ak+1	ak+1	VERB
ejpam-3928	118	5	≥	≥	NUM
ejpam-3928	118	6	4	4	NUM
ejpam-3928	118	7	,	,	PUNCT
ejpam-3928	118	8	ak−2	ak−2	PROPN
ejpam-3928	118	9	≥	≥	NOUN
ejpam-3928	118	10	0	0	NUM
ejpam-3928	118	11	.	.	PUNCT
ejpam-3928	119	1	thus	thus	ADV
ejpam-3928	119	2	,	,	PUNCT
ejpam-3928	119	3	(	(	PUNCT
ejpam-3928	119	4	a1	a1	NOUN
ejpam-3928	119	5	+	+	CCONJ
ejpam-3928	119	6	a2	a2	PROPN
ejpam-3928	119	7	+	+	CCONJ
ejpam-3928	119	8	·	·	PUNCT
ejpam-3928	119	9	·	·	PUNCT
ejpam-3928	119	10	·	·	PUNCT
ejpam-3928	119	11	+	+	NUM
ejpam-3928	119	12	ak	ak	PROPN
ejpam-3928	119	13	)	)	PUNCT
ejpam-3928	119	14	−	−	PROPN
ejpam-3928	119	15	2k	2k	PROPN
ejpam-3928	119	16	≥	≥	NOUN
ejpam-3928	119	17	ak+1	ak+1	NOUN
ejpam-3928	119	18	.	.	PUNCT
ejpam-3928	120	1	thus	thus	ADV
ejpam-3928	120	2	,	,	PUNCT
ejpam-3928	120	3	the	the	DET
ejpam-3928	120	4	assertion	assertion	NOUN
ejpam-3928	120	5	also	also	ADV
ejpam-3928	120	6	holds	hold	VERB
ejpam-3928	120	7	for	for	ADP
ejpam-3928	120	8	k	k	PROPN
ejpam-3928	120	9	+	+	PROPN
ejpam-3928	120	10	1	1	X
ejpam-3928	120	11	.	.	PUNCT
ejpam-3928	121	1	this	this	PRON
ejpam-3928	121	2	shows	show	VERB
ejpam-3928	121	3	the	the	DET
ejpam-3928	121	4	lemma	lemma	PROPN
ejpam-3928	121	5	.	.	PUNCT
ejpam-3928	122	1	lemma	lemma	PROPN
ejpam-3928	122	2	7	7	X
ejpam-3928	122	3	.	.	PUNCT
ejpam-3928	123	1	if	if	SCONJ
ejpam-3928	123	2	a1	a1	PROPN
ejpam-3928	123	3	,	,	PUNCT
ejpam-3928	123	4	a2	a2	PROPN
ejpam-3928	123	5	,	,	PUNCT
ejpam-3928	123	6	.	.	PUNCT
ejpam-3928	123	7	.	.	PUNCT
ejpam-3928	124	1	.	.	PUNCT
ejpam-3928	125	1	,	,	PUNCT
ejpam-3928	125	2	an	an	DET
ejpam-3928	125	3	∈	∈	PROPN
ejpam-3928	125	4	n	n	NOUN
ejpam-3928	125	5	with	with	ADP
ejpam-3928	125	6	a1	a1	PROPN
ejpam-3928	125	7	≥	≥	PROPN
ejpam-3928	125	8	a2	a2	PROPN
ejpam-3928	125	9	≥	≥	PROPN
ejpam-3928	125	10	.	.	PUNCT
ejpam-3928	125	11	.	.	PUNCT
ejpam-3928	126	1	.	.	PUNCT
ejpam-3928	127	1	≥	≥	AUX
ejpam-3928	127	2	an	an	DET
ejpam-3928	127	3	≥	≥	NOUN
ejpam-3928	127	4	4	4	NUM
ejpam-3928	127	5	,	,	PUNCT
ejpam-3928	127	6	then	then	ADV
ejpam-3928	127	7	there	there	PRON
ejpam-3928	127	8	exists	exist	VERB
ejpam-3928	127	9	r	r	NOUN
ejpam-3928	127	10	∈	∈	PROPN
ejpam-3928	127	11	n	n	PRON
ejpam-3928	127	12	such	such	ADJ
ejpam-3928	127	13	that	that	SCONJ
ejpam-3928	127	14	(	(	PUNCT
ejpam-3928	127	15	a1+a2	a1+a2	PROPN
ejpam-3928	127	16	+	+	PROPN
ejpam-3928	127	17	·	·	PUNCT
ejpam-3928	127	18	·	·	PUNCT
ejpam-3928	127	19	·	·	PUNCT
ejpam-3928	128	1	+	+	X
ejpam-3928	128	2	ar)−2	ar)−2	PROPN
ejpam-3928	128	3	(	(	PUNCT
ejpam-3928	128	4	r	r	NOUN
ejpam-3928	128	5	)	)	PUNCT
ejpam-3928	128	6	≥	≥	NOUN
ejpam-3928	128	7	ar+1+ar+2	ar+1+ar+2	NOUN
ejpam-3928	128	8	+	+	PROPN
ejpam-3928	128	9	·	·	PUNCT
ejpam-3928	128	10	·	·	PUNCT
ejpam-3928	128	11	·	·	PUNCT
ejpam-3928	128	12	+	+	NOUN
ejpam-3928	128	13	an	an	DET
ejpam-3928	128	14	and	and	CCONJ
ejpam-3928	128	15	(	(	PUNCT
ejpam-3928	128	16	a1+a2	a1+a2	PROPN
ejpam-3928	128	17	+	+	PROPN
ejpam-3928	128	18	·	·	PUNCT
ejpam-3928	128	19	·	·	PUNCT
ejpam-3928	128	20	·	·	PUNCT
ejpam-3928	128	21	+	+	NOUN
ejpam-3928	128	22	ar−1)−2	ar−1)−2	ADJ
ejpam-3928	128	23	(	(	PUNCT
ejpam-3928	128	24	r	r	NOUN
ejpam-3928	128	25	−	−	NOUN
ejpam-3928	128	26	1	1	NUM
ejpam-3928	128	27	)	)	PUNCT
ejpam-3928	128	28	<	<	X
ejpam-3928	128	29	ar	ar	PROPN
ejpam-3928	128	30	+	+	NOUN
ejpam-3928	128	31	ar+1	ar+1	NOUN
ejpam-3928	128	32	+	+	CCONJ
ejpam-3928	128	33	ar+2	ar+2	X
ejpam-3928	128	34	·	·	PUNCT
ejpam-3928	128	35	·	·	PUNCT
ejpam-3928	128	36	·	·	PUNCT
ejpam-3928	128	37	+	+	CCONJ
ejpam-3928	128	38	an	an	X
ejpam-3928	128	39	.	.	PUNCT
ejpam-3928	128	40	proof	proof	NOUN
ejpam-3928	128	41	.	.	PUNCT
ejpam-3928	129	1	let	let	VERB
ejpam-3928	129	2	s	s	PRON
ejpam-3928	129	3	=	=	PUNCT
ejpam-3928	129	4	{	{	PUNCT
ejpam-3928	129	5	k	k	PROPN
ejpam-3928	129	6	∈	∈	PROPN
ejpam-3928	129	7	n	n	NOUN
ejpam-3928	129	8	:	:	PUNCT
ejpam-3928	129	9	(	(	PUNCT
ejpam-3928	129	10	a1	a1	NOUN
ejpam-3928	129	11	+	+	CCONJ
ejpam-3928	129	12	a2	a2	PROPN
ejpam-3928	129	13	+	+	CCONJ
ejpam-3928	129	14	·	·	PUNCT
ejpam-3928	129	15	·	·	PUNCT
ejpam-3928	129	16	·	·	PUNCT
ejpam-3928	129	17	+	+	CCONJ
ejpam-3928	129	18	ak)−	ak)−	ADJ
ejpam-3928	129	19	2	2	NUM
ejpam-3928	129	20	(	(	PUNCT
ejpam-3928	129	21	k	k	NOUN
ejpam-3928	129	22	)	)	PUNCT
ejpam-3928	129	23	≥	≥	NOUN
ejpam-3928	129	24	ak+1	ak+1	VERB
ejpam-3928	129	25	+	+	X
ejpam-3928	129	26	ak+2	ak+2	NUM
ejpam-3928	129	27	+	+	CCONJ
ejpam-3928	129	28	·	·	PUNCT
ejpam-3928	129	29	·	·	PUNCT
ejpam-3928	129	30	·	·	PUNCT
ejpam-3928	130	1	+	+	CCONJ
ejpam-3928	130	2	an	an	X
ejpam-3928	130	3	}	}	PUNCT
ejpam-3928	130	4	.	.	PUNCT
ejpam-3928	131	1	by	by	ADP
ejpam-3928	131	2	lemma	lemma	PROPN
ejpam-3928	131	3	6	6	NUM
ejpam-3928	131	4	,	,	PUNCT
ejpam-3928	131	5	n	n	CCONJ
ejpam-3928	131	6	−	−	PROPN
ejpam-3928	131	7	1	1	NUM
ejpam-3928	131	8	∈	∈	PROPN
ejpam-3928	131	9	s	s	NOUN
ejpam-3928	131	10	,	,	PUNCT
ejpam-3928	131	11	that	that	ADV
ejpam-3928	131	12	is	is	ADV
ejpam-3928	131	13	,	,	PUNCT
ejpam-3928	131	14	s	s	PART
ejpam-3928	131	15	6=	6=	X
ejpam-3928	131	16	∅.	∅.	NOUN
ejpam-3928	131	17	by	by	ADP
ejpam-3928	131	18	the	the	DET
ejpam-3928	131	19	well	well	ADV
ejpam-3928	131	20	-	-	PUNCT
ejpam-3928	131	21	ordering	order	VERB
ejpam-3928	131	22	principle	principle	NOUN
ejpam-3928	131	23	,	,	PUNCT
ejpam-3928	131	24	s	s	NOUN
ejpam-3928	131	25	contains	contain	VERB
ejpam-3928	131	26	a	a	DET
ejpam-3928	131	27	least	least	ADJ
ejpam-3928	131	28	element	element	NOUN
ejpam-3928	131	29	,	,	PUNCT
ejpam-3928	131	30	say	say	VERB
ejpam-3928	131	31	r.	r.	NOUN
ejpam-3928	131	32	if	if	SCONJ
ejpam-3928	131	33	r	r	NOUN
ejpam-3928	131	34	∈	∈	PROPN
ejpam-3928	131	35	s	s	PART
ejpam-3928	131	36	,	,	PUNCT
ejpam-3928	131	37	then	then	ADV
ejpam-3928	131	38	(	(	PUNCT
ejpam-3928	131	39	a1	a1	NOUN
ejpam-3928	131	40	+	+	CCONJ
ejpam-3928	131	41	a2	a2	PROPN
ejpam-3928	131	42	+	+	CCONJ
ejpam-3928	131	43	·	·	PUNCT
ejpam-3928	131	44	·	·	PUNCT
ejpam-3928	131	45	·	·	PUNCT
ejpam-3928	132	1	+	+	NUM
ejpam-3928	132	2	ar	ar	NOUN
ejpam-3928	132	3	)	)	PUNCT
ejpam-3928	132	4	−	−	PROPN
ejpam-3928	132	5	2	2	NUM
ejpam-3928	132	6	(	(	PUNCT
ejpam-3928	132	7	r	r	NOUN
ejpam-3928	132	8	)	)	PUNCT
ejpam-3928	132	9	≥	≥	NOUN
ejpam-3928	132	10	ar+1	ar+1	NOUN
ejpam-3928	132	11	+	+	CCONJ
ejpam-3928	132	12	ar+2	ar+2	X
ejpam-3928	132	13	+	+	CCONJ
ejpam-3928	132	14	·	·	PUNCT
ejpam-3928	132	15	·	·	PUNCT
ejpam-3928	132	16	·	·	PUNCT
ejpam-3928	133	1	+	+	CCONJ
ejpam-3928	133	2	an	an	X
ejpam-3928	133	3	.	.	PUNCT
ejpam-3928	134	1	since	since	SCONJ
ejpam-3928	134	2	r	r	NOUN
ejpam-3928	134	3	is	be	AUX
ejpam-3928	134	4	the	the	DET
ejpam-3928	134	5	least	least	ADJ
ejpam-3928	134	6	element	element	NOUN
ejpam-3928	134	7	of	of	ADP
ejpam-3928	134	8	s	s	PROPN
ejpam-3928	134	9	,	,	PUNCT
ejpam-3928	134	10	r	r	NOUN
ejpam-3928	134	11	−	−	PROPN
ejpam-3928	134	12	1	1	NUM
ejpam-3928	134	13	/∈	/∈	PUNCT
ejpam-3928	134	14	s.	s.	PROPN
ejpam-3928	134	15	hence	hence	ADV
ejpam-3928	134	16	,	,	PUNCT
ejpam-3928	134	17	(	(	PUNCT
ejpam-3928	134	18	a1	a1	NOUN
ejpam-3928	134	19	+	+	CCONJ
ejpam-3928	134	20	a2	a2	PROPN
ejpam-3928	134	21	+	+	CCONJ
ejpam-3928	134	22	·	·	PUNCT
ejpam-3928	134	23	·	·	PUNCT
ejpam-3928	134	24	·	·	PUNCT
ejpam-3928	135	1	+	+	CCONJ
ejpam-3928	135	2	ar−1	ar−1	PROPN
ejpam-3928	135	3	)	)	PUNCT
ejpam-3928	135	4	−	−	PROPN
ejpam-3928	135	5	2	2	NUM
ejpam-3928	135	6	(	(	PUNCT
ejpam-3928	135	7	r	r	NOUN
ejpam-3928	135	8	−	−	PROPN
ejpam-3928	135	9	1	1	NUM
ejpam-3928	135	10	)	)	PUNCT
ejpam-3928	135	11	<	<	X
ejpam-3928	135	12	ar	ar	PROPN
ejpam-3928	136	1	+	+	NOUN
ejpam-3928	136	2	ar+1	ar+1	NOUN
ejpam-3928	136	3	+	+	CCONJ
ejpam-3928	136	4	ar+2	ar+2	X
ejpam-3928	136	5	·	·	PUNCT
ejpam-3928	136	6	·	·	PUNCT
ejpam-3928	136	7	·	·	PUNCT
ejpam-3928	136	8	+	+	CCONJ
ejpam-3928	137	1	an	an	X
ejpam-3928	137	2	.	.	PUNCT
ejpam-3928	138	1	the	the	DET
ejpam-3928	138	2	following	follow	VERB
ejpam-3928	138	3	remark	remark	NOUN
ejpam-3928	138	4	follows	follow	VERB
ejpam-3928	138	5	from	from	ADP
ejpam-3928	138	6	lemma	lemma	PROPN
ejpam-3928	138	7	7	7	NUM
ejpam-3928	138	8	.	.	NOUN
ejpam-3928	138	9	remark	remark	NOUN
ejpam-3928	138	10	2	2	NUM
ejpam-3928	138	11	.	.	PUNCT
ejpam-3928	139	1	let	let	VERB
ejpam-3928	139	2	n	n	PRON
ejpam-3928	139	3	≥	≥	X
ejpam-3928	139	4	3	3	NUM
ejpam-3928	139	5	and	and	CCONJ
ejpam-3928	139	6	a	a	DET
ejpam-3928	139	7	=	=	X
ejpam-3928	139	8	{	{	PUNCT
ejpam-3928	139	9	g1	g1	PROPN
ejpam-3928	139	10	,	,	PUNCT
ejpam-3928	139	11	g2	g2	PROPN
ejpam-3928	139	12	,	,	PUNCT
ejpam-3928	139	13	.	.	PUNCT
ejpam-3928	139	14	.	.	PUNCT
ejpam-3928	140	1	.	.	PUNCT
ejpam-3928	141	1	,	,	PUNCT
ejpam-3928	141	2	gn	gn	AUX
ejpam-3928	141	3	}	}	PUNCT
ejpam-3928	141	4	be	be	AUX
ejpam-3928	141	5	the	the	DET
ejpam-3928	141	6	set	set	NOUN
ejpam-3928	141	7	of	of	ADP
ejpam-3928	141	8	all	all	DET
ejpam-3928	141	9	components	component	NOUN
ejpam-3928	141	10	of	of	ADP
ejpam-3928	141	11	a	a	DET
ejpam-3928	141	12	disconnected	disconnected	ADJ
ejpam-3928	141	13	k	k	NOUN
ejpam-3928	141	14	-	-	ADJ
ejpam-3928	141	15	regular	regular	ADJ
ejpam-3928	141	16	(	(	PUNCT
ejpam-3928	141	17	k	k	X
ejpam-3928	141	18	>	>	X
ejpam-3928	141	19	1	1	NUM
ejpam-3928	141	20	)	)	PUNCT
ejpam-3928	141	21	graph	graph	NOUN
ejpam-3928	141	22	.	.	PUNCT
ejpam-3928	142	1	then	then	ADV
ejpam-3928	142	2	there	there	PRON
ejpam-3928	142	3	exists	exist	VERB
ejpam-3928	142	4	a	a	DET
ejpam-3928	142	5	set	set	NOUN
ejpam-3928	142	6	b	b	NOUN
ejpam-3928	142	7	=	=	SYM
ejpam-3928	142	8	{	{	PUNCT
ejpam-3928	142	9	gi1	gi1	PROPN
ejpam-3928	142	10	,	,	PUNCT
ejpam-3928	142	11	gi2	gi2	NOUN
ejpam-3928	142	12	,	,	PUNCT
ejpam-3928	142	13	.	.	PUNCT
ejpam-3928	142	14	.	.	PUNCT
ejpam-3928	142	15	.	.	PUNCT
ejpam-3928	143	1	,	,	PUNCT
ejpam-3928	143	2	gir	gir	PROPN
ejpam-3928	143	3	}	}	PUNCT
ejpam-3928	143	4	(	(	PUNCT
ejpam-3928	143	5	r	r	NOUN
ejpam-3928	143	6	<	<	X
ejpam-3928	143	7	n	n	CCONJ
ejpam-3928	143	8	)	)	PUNCT
ejpam-3928	143	9	subset	subset	NOUN
ejpam-3928	143	10	of	of	ADP
ejpam-3928	143	11	a	a	DET
ejpam-3928	143	12	such	such	ADJ
ejpam-3928	143	13	that	that	SCONJ
ejpam-3928	143	14	|v	|v	PROPN
ejpam-3928	143	15	(	(	PUNCT
ejpam-3928	143	16	gi1)\{u1	gi1)\{u1	PROPN
ejpam-3928	143	17	}	}	PUNCT
ejpam-3928	143	18	∪	∪	NOUN
ejpam-3928	143	19	v	v	NOUN
ejpam-3928	143	20	(	(	PUNCT
ejpam-3928	143	21	gi2)\{u2	gi2)\{u2	PROPN
ejpam-3928	143	22	}	}	PUNCT
ejpam-3928	143	23	∪	∪	X
ejpam-3928	143	24	·	·	PUNCT
ejpam-3928	143	25	·	·	PUNCT
ejpam-3928	143	26	·	·	PUNCT
ejpam-3928	143	27	∪	∪	ADP
ejpam-3928	143	28	v	v	NOUN
ejpam-3928	143	29	(	(	PUNCT
ejpam-3928	143	30	gir)\{ur}|	gir)\{ur}|	PROPN
ejpam-3928	143	31	≥	≥	NOUN
ejpam-3928	143	32	|v	|v	NOUN
ejpam-3928	143	33	(	(	PUNCT
ejpam-3928	143	34	gir+1)∪v	gir+1)∪v	X
ejpam-3928	143	35	(	(	PUNCT
ejpam-3928	143	36	gir+2)∪	gir+2)∪	NOUN
ejpam-3928	143	37	·	·	PUNCT
ejpam-3928	143	38	·	·	PUNCT
ejpam-3928	143	39	·	·	PUNCT
ejpam-3928	143	40	∪v	∪v	ADP
ejpam-3928	143	41	(	(	PUNCT
ejpam-3928	143	42	gin)∪{u1	gin)∪{u1	PROPN
ejpam-3928	143	43	,	,	PUNCT
ejpam-3928	143	44	u2	u2	NOUN
ejpam-3928	143	45	,	,	PUNCT
ejpam-3928	143	46	.	.	PUNCT
ejpam-3928	143	47	.	.	PUNCT
ejpam-3928	144	1	.	.	PUNCT
ejpam-3928	145	1	,	,	PUNCT
ejpam-3928	145	2	ur	ur	INTJ
ejpam-3928	145	3	}	}	PUNCT
ejpam-3928	145	4	|	|	ADV
ejpam-3928	145	5	,	,	PUNCT
ejpam-3928	145	6	and	and	CCONJ
ejpam-3928	145	7	|v	|v	PROPN
ejpam-3928	145	8	(	(	PUNCT
ejpam-3928	145	9	gi1)\{u1}∪v	gi1)\{u1}∪v	X
ejpam-3928	145	10	(	(	PUNCT
ejpam-3928	145	11	gi2)\{u2}∪	gi2)\{u2}∪	PROPN
ejpam-3928	145	12	·	·	PUNCT
ejpam-3928	145	13	·	·	PUNCT
ejpam-3928	145	14	·	·	PUNCT
ejpam-3928	145	15	∪v	∪v	SYM
ejpam-3928	145	16	(	(	PUNCT
ejpam-3928	145	17	gir−1)\{ur−1}|	gir−1)\{ur−1}|	NOUN
ejpam-3928	145	18	<	<	X
ejpam-3928	145	19	|v	|v	PROPN
ejpam-3928	145	20	(	(	PUNCT
ejpam-3928	145	21	gir)∪v	gir)∪v	X
ejpam-3928	145	22	(	(	PUNCT
ejpam-3928	145	23	gir+1)∪v	gir+1)∪v	X
ejpam-3928	145	24	(	(	PUNCT
ejpam-3928	145	25	gir+2)∪	gir+2)∪	NOUN
ejpam-3928	145	26	·	·	PUNCT
ejpam-3928	145	27	·	·	PUNCT
ejpam-3928	145	28	·	·	PUNCT
ejpam-3928	145	29	∪v	∪v	ADP
ejpam-3928	145	30	(	(	PUNCT
ejpam-3928	145	31	gin)∪{u1	gin)∪{u1	PROPN
ejpam-3928	145	32	,	,	PUNCT
ejpam-3928	145	33	u2	u2	NOUN
ejpam-3928	145	34	,	,	PUNCT
ejpam-3928	145	35	.	.	PUNCT
ejpam-3928	145	36	.	.	PUNCT
ejpam-3928	146	1	.	.	PUNCT
ejpam-3928	147	1	,	,	PUNCT
ejpam-3928	147	2	ur−1	ur−1	PROPN
ejpam-3928	147	3	}	}	PUNCT
ejpam-3928	147	4	|	|	NOUN
ejpam-3928	147	5	.	.	PUNCT
ejpam-3928	148	1	lemma	lemma	PROPN
ejpam-3928	148	2	8	8	NUM
ejpam-3928	148	3	.	.	PUNCT
ejpam-3928	149	1	a	a	DET
ejpam-3928	149	2	disconnected	disconnected	ADJ
ejpam-3928	149	3	k	k	NOUN
ejpam-3928	149	4	-	-	ADJ
ejpam-3928	149	5	regular	regular	ADJ
ejpam-3928	149	6	(	(	PUNCT
ejpam-3928	149	7	k	k	X
ejpam-3928	149	8	>	>	X
ejpam-3928	149	9	1	1	X
ejpam-3928	149	10	)	)	PUNCT
ejpam-3928	149	11	spectral	spectral	ADJ
ejpam-3928	149	12	-	-	PUNCT
ejpam-3928	149	13	equipartite	equipartite	ADJ
ejpam-3928	149	14	graph	graph	NOUN
ejpam-3928	149	15	can	can	AUX
ejpam-3928	149	16	not	not	PART
ejpam-3928	149	17	have	have	VERB
ejpam-3928	149	18	more	more	ADJ
ejpam-3928	149	19	than	than	ADP
ejpam-3928	149	20	two	two	NUM
ejpam-3928	149	21	components	component	NOUN
ejpam-3928	149	22	.	.	PUNCT
ejpam-3928	150	1	proof	proof	NOUN
ejpam-3928	150	2	.	.	PUNCT
ejpam-3928	151	1	supposed	suppose	VERB
ejpam-3928	151	2	g	g	PROPN
ejpam-3928	151	3	=	=	SYM
ejpam-3928	151	4	(	(	PUNCT
ejpam-3928	151	5	v	v	NOUN
ejpam-3928	151	6	,	,	PUNCT
ejpam-3928	151	7	e	e	NOUN
ejpam-3928	151	8	)	)	PUNCT
ejpam-3928	151	9	has	have	VERB
ejpam-3928	151	10	more	more	ADJ
ejpam-3928	151	11	than	than	ADP
ejpam-3928	151	12	two	two	NUM
ejpam-3928	151	13	components	component	NOUN
ejpam-3928	151	14	,	,	PUNCT
ejpam-3928	151	15	say	say	VERB
ejpam-3928	151	16	a	a	DET
ejpam-3928	151	17	=	=	PUNCT
ejpam-3928	151	18	g1	g1	PROPN
ejpam-3928	151	19	∪	∪	ADP
ejpam-3928	151	20	g2	g2	PROPN
ejpam-3928	151	21	∪	∪	NOUN
ejpam-3928	151	22	.	.	PUNCT
ejpam-3928	151	23	.	.	PUNCT
ejpam-3928	151	24	.	.	PUNCT
ejpam-3928	152	1	∪	∪	PROPN
ejpam-3928	152	2	gn	gn	PROPN
ejpam-3928	152	3	(	(	PUNCT
ejpam-3928	152	4	n	n	CCONJ
ejpam-3928	152	5	>	>	X
ejpam-3928	152	6	2	2	NUM
ejpam-3928	152	7	)	)	PUNCT
ejpam-3928	152	8	,	,	PUNCT
ejpam-3928	152	9	where	where	SCONJ
ejpam-3928	152	10	gi	gi	PRON
ejpam-3928	152	11	is	be	AUX
ejpam-3928	152	12	a	a	DET
ejpam-3928	152	13	component	component	NOUN
ejpam-3928	152	14	for	for	ADP
ejpam-3928	152	15	i	i	PRON
ejpam-3928	152	16	=	=	NOUN
ejpam-3928	152	17	1	1	NUM
ejpam-3928	152	18	,	,	PUNCT
ejpam-3928	152	19	2	2	NUM
ejpam-3928	152	20	,	,	PUNCT
ejpam-3928	152	21	.	.	PUNCT
ejpam-3928	152	22	.	.	PUNCT
ejpam-3928	152	23	.	.	PUNCT
ejpam-3928	153	1	,	,	PUNCT
ejpam-3928	153	2	n.	n.	NOUN
ejpam-3928	153	3	by	by	ADP
ejpam-3928	153	4	remark	remark	NOUN
ejpam-3928	153	5	2	2	NUM
ejpam-3928	153	6	,	,	PUNCT
ejpam-3928	153	7	then	then	ADV
ejpam-3928	153	8	there	there	PRON
ejpam-3928	153	9	exists	exist	VERB
ejpam-3928	153	10	a	a	DET
ejpam-3928	153	11	set	set	NOUN
ejpam-3928	153	12	b	b	NOUN
ejpam-3928	153	13	=	=	SYM
ejpam-3928	153	14	{	{	PUNCT
ejpam-3928	153	15	gi1	gi1	PROPN
ejpam-3928	153	16	,	,	PUNCT
ejpam-3928	153	17	gi2	gi2	NOUN
ejpam-3928	153	18	,	,	PUNCT
ejpam-3928	153	19	.	.	PUNCT
ejpam-3928	153	20	.	.	PUNCT
ejpam-3928	154	1	.	.	PUNCT
ejpam-3928	155	1	,	,	PUNCT
ejpam-3928	155	2	gir	gir	PROPN
ejpam-3928	155	3	}	}	PUNCT
ejpam-3928	155	4	(	(	PUNCT
ejpam-3928	155	5	r	r	NOUN
ejpam-3928	155	6	<	<	X
ejpam-3928	155	7	n	n	CCONJ
ejpam-3928	155	8	)	)	PUNCT
ejpam-3928	155	9	subset	subset	NOUN
ejpam-3928	155	10	of	of	ADP
ejpam-3928	155	11	a	a	DET
ejpam-3928	155	12	such	such	ADJ
ejpam-3928	155	13	that	that	SCONJ
ejpam-3928	155	14	|v	|v	PROPN
ejpam-3928	155	15	(	(	PUNCT
ejpam-3928	155	16	gi1)\{u1	gi1)\{u1	PROPN
ejpam-3928	155	17	}	}	PUNCT
ejpam-3928	155	18	∪	∪	ADJ
ejpam-3928	155	19	a.	a.	NOUN
ejpam-3928	155	20	yurfo	yurfo	NOUN
ejpam-3928	155	21	,	,	PUNCT
ejpam-3928	155	22	j.	j.	PROPN
ejpam-3928	155	23	adanza	adanza	PROPN
ejpam-3928	155	24	,	,	PUNCT
ejpam-3928	155	25	m.	m.	PROPN
ejpam-3928	155	26	baldado	baldado	PROPN
ejpam-3928	155	27	jr	jr	PROPN
ejpam-3928	155	28	.	.	PROPN
ejpam-3928	155	29	/	/	SYM
ejpam-3928	155	30	eur	eur	PROPN
ejpam-3928	155	31	.	.	PUNCT
ejpam-3928	156	1	j.	j.	PROPN
ejpam-3928	156	2	pure	pure	PROPN
ejpam-3928	156	3	appl	appl	PROPN
ejpam-3928	156	4	.	.	PROPN
ejpam-3928	156	5	math	math	PROPN
ejpam-3928	156	6	,	,	PUNCT
ejpam-3928	156	7	14	14	NUM
ejpam-3928	156	8	(	(	PUNCT
ejpam-3928	156	9	2	2	NUM
ejpam-3928	156	10	)	)	PUNCT
ejpam-3928	156	11	(	(	PUNCT
ejpam-3928	156	12	2021	2021	NUM
ejpam-3928	156	13	)	)	PUNCT
ejpam-3928	156	14	,	,	PUNCT
ejpam-3928	156	15	358	358	NUM
ejpam-3928	156	16	-	-	SYM
ejpam-3928	156	17	365	365	NUM
ejpam-3928	156	18	362	362	NUM
ejpam-3928	156	19	v	v	NOUN
ejpam-3928	156	20	(	(	PUNCT
ejpam-3928	156	21	gi2)\{u2}∪	gi2)\{u2}∪	PROPN
ejpam-3928	156	22	·	·	PUNCT
ejpam-3928	156	23	·	·	PUNCT
ejpam-3928	156	24	·	·	PUNCT
ejpam-3928	156	25	∪v	∪v	X
ejpam-3928	156	26	(	(	PUNCT
ejpam-3928	156	27	gir)\{ur}|	gir)\{ur}|	PROPN
ejpam-3928	156	28	≥	≥	NOUN
ejpam-3928	156	29	|v	|v	NOUN
ejpam-3928	156	30	(	(	PUNCT
ejpam-3928	156	31	gir+1)∪v	gir+1)∪v	X
ejpam-3928	156	32	(	(	PUNCT
ejpam-3928	156	33	gir+2)∪	gir+2)∪	NOUN
ejpam-3928	156	34	·	·	PUNCT
ejpam-3928	156	35	·	·	PUNCT
ejpam-3928	156	36	·	·	PUNCT
ejpam-3928	156	37	∪v	∪v	ADP
ejpam-3928	156	38	(	(	PUNCT
ejpam-3928	156	39	gin)∪{u1	gin)∪{u1	PROPN
ejpam-3928	156	40	,	,	PUNCT
ejpam-3928	156	41	u2	u2	NOUN
ejpam-3928	156	42	,	,	PUNCT
ejpam-3928	156	43	.	.	PUNCT
ejpam-3928	156	44	.	.	PUNCT
ejpam-3928	157	1	.	.	PUNCT
ejpam-3928	158	1	,	,	PUNCT
ejpam-3928	158	2	ur	ur	INTJ
ejpam-3928	158	3	}	}	PUNCT
ejpam-3928	158	4	|	|	ADV
ejpam-3928	158	5	,	,	PUNCT
ejpam-3928	158	6	and	and	CCONJ
ejpam-3928	158	7	|v	|v	PROPN
ejpam-3928	158	8	(	(	PUNCT
ejpam-3928	158	9	gi1)\{u1}∪v	gi1)\{u1}∪v	X
ejpam-3928	158	10	(	(	PUNCT
ejpam-3928	158	11	gi2)\{u2}∪	gi2)\{u2}∪	PROPN
ejpam-3928	158	12	·	·	PUNCT
ejpam-3928	158	13	·	·	PUNCT
ejpam-3928	158	14	·	·	PUNCT
ejpam-3928	158	15	∪v	∪v	SYM
ejpam-3928	158	16	(	(	PUNCT
ejpam-3928	158	17	gir−1)\{ur−1}|	gir−1)\{ur−1}|	NOUN
ejpam-3928	158	18	<	<	X
ejpam-3928	158	19	|v	|v	PROPN
ejpam-3928	158	20	(	(	PUNCT
ejpam-3928	158	21	gir)∪v	gir)∪v	X
ejpam-3928	158	22	(	(	PUNCT
ejpam-3928	158	23	gir+1)∪v	gir+1)∪v	X
ejpam-3928	158	24	(	(	PUNCT
ejpam-3928	158	25	gir+2)∪	gir+2)∪	NOUN
ejpam-3928	158	26	·	·	PUNCT
ejpam-3928	158	27	·	·	PUNCT
ejpam-3928	158	28	·	·	PUNCT
ejpam-3928	158	29	∪v	∪v	PRON
ejpam-3928	158	30	(	(	PUNCT
ejpam-3928	158	31	gin)∪{u1	gin)∪{u1	PROPN
ejpam-3928	158	32	,	,	PUNCT
ejpam-3928	158	33	u2	u2	NOUN
ejpam-3928	158	34	,	,	PUNCT
ejpam-3928	158	35	.	.	PUNCT
ejpam-3928	158	36	.	.	PUNCT
ejpam-3928	159	1	.	.	PUNCT
ejpam-3928	160	1	,	,	PUNCT
ejpam-3928	160	2	ur−1	ur−1	PROPN
ejpam-3928	160	3	}	}	PUNCT
ejpam-3928	160	4	|	|	NOUN
ejpam-3928	160	5	.	.	PUNCT
ejpam-3928	161	1	partition	partition	NOUN
ejpam-3928	161	2	v	v	PROPN
ejpam-3928	161	3	as	as	SCONJ
ejpam-3928	161	4	follows	follow	VERB
ejpam-3928	161	5	:	:	PUNCT
ejpam-3928	161	6	(	(	PUNCT
ejpam-3928	161	7	1	1	X
ejpam-3928	161	8	)	)	PUNCT
ejpam-3928	161	9	remove	remove	VERB
ejpam-3928	161	10	from	from	ADP
ejpam-3928	161	11	v	v	NOUN
ejpam-3928	161	12	(	(	PUNCT
ejpam-3928	161	13	gij	gij	PROPN
ejpam-3928	161	14	)	)	PUNCT
ejpam-3928	161	15	a	a	DET
ejpam-3928	161	16	nonempty	nonempty	ADV
ejpam-3928	161	17	set	set	NOUN
ejpam-3928	161	18	of	of	ADP
ejpam-3928	161	19	vertices	vertex	NOUN
ejpam-3928	161	20	aj	aj	PROPN
ejpam-3928	161	21	from	from	ADP
ejpam-3928	161	22	v	v	NUM
ejpam-3928	161	23	(	(	PUNCT
ejpam-3928	161	24	gij	gij	NOUN
ejpam-3928	161	25	)	)	PUNCT
ejpam-3928	161	26	to	to	PART
ejpam-3928	161	27	form	form	VERB
ejpam-3928	161	28	v	v	ADP
ejpam-3928	161	29	′j	′j	NOUN
ejpam-3928	161	30	=	=	SYM
ejpam-3928	161	31	v	v	X
ejpam-3928	161	32	(	(	PUNCT
ejpam-3928	161	33	gij	gij	NOUN
ejpam-3928	161	34	)	)	PUNCT
ejpam-3928	161	35	\aj	\aj	NOUN
ejpam-3928	161	36	for	for	ADP
ejpam-3928	161	37	j	j	PROPN
ejpam-3928	161	38	=	=	SYM
ejpam-3928	161	39	1	1	NUM
ejpam-3928	161	40	,	,	PUNCT
ejpam-3928	161	41	2	2	NUM
ejpam-3928	161	42	,	,	PUNCT
ejpam-3928	161	43	.	.	PUNCT
ejpam-3928	161	44	.	.	PUNCT
ejpam-3928	162	1	.	.	PUNCT
ejpam-3928	163	1	,	,	PUNCT
ejpam-3928	163	2	r	r	NOUN
ejpam-3928	163	3	such	such	ADJ
ejpam-3928	163	4	that	that	SCONJ
ejpam-3928	163	5	|v	|v	PROPN
ejpam-3928	163	6	′1∪v	′1∪v	PROPN
ejpam-3928	163	7	′2∪	′2∪	NOUN
ejpam-3928	163	8	·	·	PUNCT
ejpam-3928	163	9	·	·	PUNCT
ejpam-3928	163	10	·	·	PUNCT
ejpam-3928	163	11	∪v	∪v	NOUN
ejpam-3928	164	1	′r	′r	PROPN
ejpam-3928	164	2	|	|	NOUN
ejpam-3928	164	3	=	=	SYM
ejpam-3928	164	4	|v	|v	X
ejpam-3928	164	5	(	(	PUNCT
ejpam-3928	164	6	gir+1)∪v	gir+1)∪v	X
ejpam-3928	164	7	(	(	PUNCT
ejpam-3928	164	8	gir+2)∪	gir+2)∪	NOUN
ejpam-3928	164	9	·	·	PUNCT
ejpam-3928	164	10	·	·	PUNCT
ejpam-3928	164	11	·	·	PUNCT
ejpam-3928	164	12	(	(	PUNCT
ejpam-3928	164	13	gin)∪a1∪a2∪	gin)∪a1∪a2∪	X
ejpam-3928	164	14	·	·	PUNCT
ejpam-3928	164	15	·	·	PUNCT
ejpam-3928	164	16	·	·	PUNCT
ejpam-3928	164	17	∪ar|	∪ar|	X
ejpam-3928	164	18	.	.	PUNCT
ejpam-3928	165	1	(	(	PUNCT
ejpam-3928	165	2	2	2	X
ejpam-3928	165	3	)	)	PUNCT
ejpam-3928	165	4	leth1	leth1	NOUN
ejpam-3928	165	5	=	=	SYM
ejpam-3928	165	6	⋃r	⋃r	PROPN
ejpam-3928	166	1	j=1	j=1	NOUN
ejpam-3928	166	2	v	v	ADP
ejpam-3928	166	3	′	′	NUM
ejpam-3928	166	4	j	j	PROPN
ejpam-3928	166	5	and	and	CCONJ
ejpam-3928	166	6	h2	h2	PROPN
ejpam-3928	166	7	=	=	SYM
ejpam-3928	166	8	(	(	PUNCT
ejpam-3928	166	9	⋃n	⋃n	PROPN
ejpam-3928	166	10	j	j	PROPN
ejpam-3928	166	11	=	=	PROPN
ejpam-3928	166	12	r+1	r+1	PROPN
ejpam-3928	166	13	v	v	X
ejpam-3928	166	14	(	(	PUNCT
ejpam-3928	166	15	gij	gij	PROPN
ejpam-3928	166	16	)	)	PUNCT
ejpam-3928	166	17	)	)	PUNCT
ejpam-3928	166	18	∪	∪	PROPN
ejpam-3928	166	19	(	(	PUNCT
ejpam-3928	166	20	⋃r	⋃r	PROPN
ejpam-3928	166	21	j=1ai	j=1ai	NUM
ejpam-3928	166	22	)	)	PUNCT
ejpam-3928	166	23	.	.	PUNCT
ejpam-3928	167	1	then	then	ADV
ejpam-3928	167	2	〈	〈	PROPN
ejpam-3928	167	3	h2	h2	PROPN
ejpam-3928	167	4	〉	〉	PROPN
ejpam-3928	167	5	has	have	VERB
ejpam-3928	167	6	k	k	ADJ
ejpam-3928	167	7	-	-	ADJ
ejpam-3928	167	8	regular	regular	ADJ
ejpam-3928	167	9	components	component	NOUN
ejpam-3928	167	10	while	while	SCONJ
ejpam-3928	167	11	〈	〈	PROPN
ejpam-3928	167	12	h1	h1	PROPN
ejpam-3928	167	13	〉	〉	PROPN
ejpam-3928	167	14	does	do	AUX
ejpam-3928	167	15	not	not	PART
ejpam-3928	167	16	have	have	VERB
ejpam-3928	167	17	.	.	PUNCT
ejpam-3928	168	1	thus	thus	ADV
ejpam-3928	168	2	,	,	PUNCT
ejpam-3928	168	3	by	by	ADP
ejpam-3928	168	4	lemma	lemma	PROPN
ejpam-3928	168	5	2	2	PROPN
ejpam-3928	168	6	and	and	CCONJ
ejpam-3928	168	7	lemma	lemma	PROPN
ejpam-3928	168	8	3	3	NUM
ejpam-3928	168	9	spec(〈h1	spec(〈h1	PROPN
ejpam-3928	168	10	〉	〉	PROPN
ejpam-3928	168	11	)	)	PUNCT
ejpam-3928	168	12	6=	6=	ADP
ejpam-3928	168	13	spec(〈h2	spec(〈h2	PROPN
ejpam-3928	168	14	〉	〉	PROPN
ejpam-3928	168	15	)	)	PUNCT
ejpam-3928	168	16	.	.	PUNCT
ejpam-3928	169	1	this	this	PRON
ejpam-3928	169	2	shows	show	VERB
ejpam-3928	169	3	the	the	DET
ejpam-3928	169	4	lemma	lemma	PROPN
ejpam-3928	169	5	.	.	PUNCT
ejpam-3928	170	1	lemma	lemma	PROPN
ejpam-3928	170	2	9	9	NUM
ejpam-3928	170	3	.	.	PUNCT
ejpam-3928	171	1	let	let	VERB
ejpam-3928	171	2	g	g	PRON
ejpam-3928	171	3	be	be	AUX
ejpam-3928	171	4	a	a	DET
ejpam-3928	171	5	disconnected	disconnected	ADJ
ejpam-3928	171	6	k	k	NOUN
ejpam-3928	171	7	-	-	NOUN
ejpam-3928	171	8	regular	regular	ADJ
ejpam-3928	171	9	(	(	PUNCT
ejpam-3928	171	10	with	with	ADP
ejpam-3928	171	11	k	k	PROPN
ejpam-3928	171	12	>	>	X
ejpam-3928	171	13	1	1	X
ejpam-3928	171	14	)	)	PUNCT
ejpam-3928	171	15	graph	graph	NOUN
ejpam-3928	171	16	of	of	ADP
ejpam-3928	171	17	order	order	NOUN
ejpam-3928	171	18	2n	2n	NUM
ejpam-3928	171	19	.	.	PUNCT
ejpam-3928	172	1	if	if	SCONJ
ejpam-3928	172	2	g	g	PROPN
ejpam-3928	172	3	is	be	AUX
ejpam-3928	172	4	a	a	DET
ejpam-3928	172	5	spectral	spectral	ADJ
ejpam-3928	172	6	-	-	PUNCT
ejpam-3928	172	7	equipartite	equipartite	ADJ
ejpam-3928	172	8	graph	graph	NOUN
ejpam-3928	172	9	,	,	PUNCT
ejpam-3928	172	10	then	then	ADV
ejpam-3928	172	11	it	it	PRON
ejpam-3928	172	12	has	have	VERB
ejpam-3928	172	13	only	only	ADV
ejpam-3928	172	14	two	two	NUM
ejpam-3928	172	15	components	component	NOUN
ejpam-3928	172	16	which	which	PRON
ejpam-3928	172	17	are	be	AUX
ejpam-3928	172	18	both	both	PRON
ejpam-3928	172	19	of	of	ADP
ejpam-3928	172	20	order	order	NOUN
ejpam-3928	172	21	n.	n.	NOUN
ejpam-3928	172	22	proof	proof	NOUN
ejpam-3928	172	23	.	.	PUNCT
ejpam-3928	173	1	let	let	VERB
ejpam-3928	173	2	g	g	PRON
ejpam-3928	173	3	be	be	AUX
ejpam-3928	173	4	a	a	DET
ejpam-3928	173	5	disconnected	disconnected	ADJ
ejpam-3928	173	6	k	k	NOUN
ejpam-3928	173	7	-	-	ADJ
ejpam-3928	173	8	regular	regular	ADJ
ejpam-3928	173	9	(	(	PUNCT
ejpam-3928	173	10	k	k	X
ejpam-3928	173	11	>	>	X
ejpam-3928	173	12	1	1	X
ejpam-3928	173	13	)	)	PUNCT
ejpam-3928	173	14	graph	graph	NOUN
ejpam-3928	173	15	of	of	ADP
ejpam-3928	173	16	order	order	NOUN
ejpam-3928	173	17	2n	2n	NUM
ejpam-3928	173	18	and	and	CCONJ
ejpam-3928	173	19	v	v	NOUN
ejpam-3928	173	20	be	be	AUX
ejpam-3928	173	21	the	the	DET
ejpam-3928	173	22	vertex	vertex	NOUN
ejpam-3928	173	23	set	set	NOUN
ejpam-3928	173	24	of	of	ADP
ejpam-3928	173	25	g.	g.	PROPN
ejpam-3928	173	26	suppose	suppose	VERB
ejpam-3928	173	27	g	g	PROPN
ejpam-3928	173	28	is	be	AUX
ejpam-3928	173	29	a	a	DET
ejpam-3928	173	30	spectral	spectral	ADJ
ejpam-3928	173	31	-	-	PUNCT
ejpam-3928	173	32	equipartite	equipartite	ADJ
ejpam-3928	173	33	graph	graph	NOUN
ejpam-3928	173	34	.	.	PUNCT
ejpam-3928	174	1	by	by	ADP
ejpam-3928	174	2	lemma	lemma	PROPN
ejpam-3928	174	3	8	8	NUM
ejpam-3928	174	4	and	and	CCONJ
ejpam-3928	174	5	by	by	ADP
ejpam-3928	174	6	the	the	DET
ejpam-3928	174	7	definition	definition	NOUN
ejpam-3928	174	8	of	of	ADP
ejpam-3928	174	9	disconnected	disconnected	ADJ
ejpam-3928	174	10	graphs	graph	NOUN
ejpam-3928	174	11	,	,	PUNCT
ejpam-3928	174	12	g	g	PROPN
ejpam-3928	174	13	has	have	VERB
ejpam-3928	174	14	exactly	exactly	ADV
ejpam-3928	174	15	two	two	NUM
ejpam-3928	174	16	components	component	NOUN
ejpam-3928	174	17	.	.	PUNCT
ejpam-3928	175	1	next	next	ADV
ejpam-3928	175	2	,	,	PUNCT
ejpam-3928	175	3	we	we	PRON
ejpam-3928	175	4	will	will	AUX
ejpam-3928	175	5	prove	prove	VERB
ejpam-3928	175	6	that	that	SCONJ
ejpam-3928	175	7	the	the	DET
ejpam-3928	175	8	two	two	NUM
ejpam-3928	175	9	components	component	NOUN
ejpam-3928	175	10	of	of	ADP
ejpam-3928	175	11	g	g	PROPN
ejpam-3928	175	12	are	be	AUX
ejpam-3928	175	13	both	both	PRON
ejpam-3928	175	14	of	of	ADP
ejpam-3928	175	15	order	order	NOUN
ejpam-3928	175	16	n.	n.	NOUN
ejpam-3928	175	17	let	let	VERB
ejpam-3928	175	18	g1	g1	PROPN
ejpam-3928	175	19	and	and	CCONJ
ejpam-3928	175	20	g2	g2	PROPN
ejpam-3928	175	21	be	be	VERB
ejpam-3928	175	22	the	the	DET
ejpam-3928	175	23	components	component	NOUN
ejpam-3928	175	24	of	of	ADP
ejpam-3928	175	25	g.	g.	PROPN
ejpam-3928	175	26	suppose	suppose	VERB
ejpam-3928	175	27	to	to	ADP
ejpam-3928	175	28	the	the	DET
ejpam-3928	175	29	contrary	contrary	ADJ
ejpam-3928	175	30	|v	|v	PROPN
ejpam-3928	175	31	(	(	PUNCT
ejpam-3928	175	32	g1)|	g1)|	PROPN
ejpam-3928	175	33	6=	6=	PROPN
ejpam-3928	175	34	|v	|v	PROPN
ejpam-3928	175	35	(	(	PUNCT
ejpam-3928	175	36	g2)|	g2)|	NOUN
ejpam-3928	175	37	.	.	PUNCT
ejpam-3928	176	1	without	without	ADP
ejpam-3928	176	2	loss	loss	NOUN
ejpam-3928	176	3	of	of	ADP
ejpam-3928	176	4	generality	generality	NOUN
ejpam-3928	176	5	,	,	PUNCT
ejpam-3928	176	6	assume	assume	VERB
ejpam-3928	176	7	that	that	SCONJ
ejpam-3928	176	8	|v	|v	PROPN
ejpam-3928	176	9	(	(	PUNCT
ejpam-3928	176	10	g1)|	g1)|	PROPN
ejpam-3928	176	11	<	<	X
ejpam-3928	176	12	|v	|v	PROPN
ejpam-3928	176	13	(	(	PUNCT
ejpam-3928	176	14	g2)|	g2)|	NOUN
ejpam-3928	176	15	.	.	PUNCT
ejpam-3928	177	1	let	let	VERB
ejpam-3928	177	2	|v	|v	PROPN
ejpam-3928	177	3	(	(	PUNCT
ejpam-3928	177	4	g2)|	g2)|	NOUN
ejpam-3928	177	5	−	−	PROPN
ejpam-3928	177	6	|v	|v	NOUN
ejpam-3928	177	7	(	(	PUNCT
ejpam-3928	177	8	g1)|	g1)|	PROPN
ejpam-3928	177	9	=	=	SYM
ejpam-3928	177	10	m.	m.	NOUN
ejpam-3928	177	11	partition	partition	NOUN
ejpam-3928	177	12	v	v	NOUN
ejpam-3928	177	13	into	into	ADP
ejpam-3928	177	14	two	two	NUM
ejpam-3928	177	15	sets	set	NOUN
ejpam-3928	177	16	a	a	PRON
ejpam-3928	177	17	and	and	CCONJ
ejpam-3928	177	18	b	b	NOUN
ejpam-3928	177	19	with	with	ADP
ejpam-3928	177	20	〈	〈	PROPN
ejpam-3928	177	21	a	a	DET
ejpam-3928	177	22	〉	〉	NOUN
ejpam-3928	177	23	=	=	SYM
ejpam-3928	178	1	〈	〈	PROPN
ejpam-3928	178	2	v	v	X
ejpam-3928	178	3	(	(	PUNCT
ejpam-3928	178	4	g2	g2	PROPN
ejpam-3928	178	5	)	)	PUNCT
ejpam-3928	178	6	\v	\v	PUNCT
ejpam-3928	178	7	(	(	PUNCT
ejpam-3928	178	8	mk1	mk1	NOUN
ejpam-3928	178	9	)	)	PUNCT
ejpam-3928	178	10	〉	〉	PROPN
ejpam-3928	178	11	and	and	CCONJ
ejpam-3928	178	12	〈	〈	PROPN
ejpam-3928	178	13	b	b	PROPN
ejpam-3928	178	14	〉	〉	PROPN
ejpam-3928	178	15	=	=	SYM
ejpam-3928	178	16	g1∪mk1	g1∪mk1	PROPN
ejpam-3928	178	17	.	.	PUNCT
ejpam-3928	178	18	by	by	ADP
ejpam-3928	178	19	lemma	lemma	PROPN
ejpam-3928	178	20	2	2	PROPN
ejpam-3928	178	21	and	and	CCONJ
ejpam-3928	178	22	lemma	lemma	PROPN
ejpam-3928	178	23	3	3	NUM
ejpam-3928	178	24	,	,	PUNCT
ejpam-3928	178	25	the	the	DET
ejpam-3928	178	26	spectrum	spectrum	NOUN
ejpam-3928	178	27	of	of	ADP
ejpam-3928	178	28	〈	〈	PROPN
ejpam-3928	178	29	a	a	DET
ejpam-3928	178	30	〉	〉	NOUN
ejpam-3928	178	31	does	do	AUX
ejpam-3928	178	32	not	not	PART
ejpam-3928	178	33	contain	contain	VERB
ejpam-3928	178	34	k	k	NOUN
ejpam-3928	178	35	while	while	SCONJ
ejpam-3928	178	36	the	the	DET
ejpam-3928	178	37	spectrum	spectrum	NOUN
ejpam-3928	178	38	of	of	ADP
ejpam-3928	178	39	〈	〈	PROPN
ejpam-3928	178	40	b	b	PROPN
ejpam-3928	178	41	〉	〉	PROPN
ejpam-3928	178	42	does	do	VERB
ejpam-3928	178	43	.	.	PUNCT
ejpam-3928	179	1	hence	hence	ADV
ejpam-3928	179	2	,	,	PUNCT
ejpam-3928	179	3	spec	spec	PROPN
ejpam-3928	179	4	(	(	PUNCT
ejpam-3928	179	5	〈	〈	PROPN
ejpam-3928	179	6	a	a	PRON
ejpam-3928	179	7	〉	〉	NOUN
ejpam-3928	179	8	)	)	PUNCT
ejpam-3928	179	9	6=	6=	NUM
ejpam-3928	179	10	spec	spec	PROPN
ejpam-3928	179	11	(	(	PUNCT
ejpam-3928	179	12	〈	〈	PROPN
ejpam-3928	179	13	b	b	PROPN
ejpam-3928	179	14	〉	〉	PROPN
ejpam-3928	179	15	)	)	PUNCT
ejpam-3928	179	16	.	.	PUNCT
ejpam-3928	180	1	thus	thus	ADV
ejpam-3928	180	2	,	,	PUNCT
ejpam-3928	180	3	〈	〈	PROPN
ejpam-3928	180	4	a	a	DET
ejpam-3928	180	5	〉	〉	NOUN
ejpam-3928	180	6	and	and	CCONJ
ejpam-3928	180	7	〈	〈	PROPN
ejpam-3928	180	8	b	b	PROPN
ejpam-3928	180	9	〉	〉	PROPN
ejpam-3928	180	10	are	be	AUX
ejpam-3928	180	11	not	not	PART
ejpam-3928	180	12	isospectral	isospectral	ADJ
ejpam-3928	180	13	,	,	PUNCT
ejpam-3928	180	14	and	and	CCONJ
ejpam-3928	180	15	g	g	NOUN
ejpam-3928	180	16	is	be	AUX
ejpam-3928	180	17	not	not	PART
ejpam-3928	180	18	spectral	spectral	ADJ
ejpam-3928	180	19	-	-	PUNCT
ejpam-3928	180	20	equipartite	equipartite	ADJ
ejpam-3928	180	21	.	.	PUNCT
ejpam-3928	181	1	this	this	PRON
ejpam-3928	181	2	proves	prove	VERB
ejpam-3928	181	3	that	that	SCONJ
ejpam-3928	181	4	the	the	DET
ejpam-3928	181	5	two	two	NUM
ejpam-3928	181	6	components	component	NOUN
ejpam-3928	181	7	of	of	ADP
ejpam-3928	181	8	g	g	PROPN
ejpam-3928	181	9	have	have	VERB
ejpam-3928	181	10	an	an	DET
ejpam-3928	181	11	equal	equal	ADJ
ejpam-3928	181	12	number	number	NOUN
ejpam-3928	181	13	of	of	ADP
ejpam-3928	181	14	vertices	vertex	NOUN
ejpam-3928	181	15	which	which	PRON
ejpam-3928	181	16	is	be	AUX
ejpam-3928	181	17	n.	n.	NOUN
ejpam-3928	181	18	this	this	PRON
ejpam-3928	181	19	shows	show	VERB
ejpam-3928	181	20	the	the	DET
ejpam-3928	181	21	lemma	lemma	PROPN
ejpam-3928	181	22	.	.	PUNCT
ejpam-3928	181	23	theorem	theorem	VERB
ejpam-3928	181	24	8	8	NUM
ejpam-3928	181	25	.	.	PUNCT
ejpam-3928	182	1	let	let	VERB
ejpam-3928	182	2	g	g	PRON
ejpam-3928	182	3	be	be	AUX
ejpam-3928	182	4	a	a	DET
ejpam-3928	182	5	disconnected	disconnected	ADJ
ejpam-3928	182	6	k	k	NOUN
ejpam-3928	182	7	-	-	NOUN
ejpam-3928	182	8	regular	regular	ADJ
ejpam-3928	182	9	(	(	PUNCT
ejpam-3928	182	10	with	with	ADP
ejpam-3928	182	11	k	k	PROPN
ejpam-3928	182	12	>	>	X
ejpam-3928	182	13	1	1	X
ejpam-3928	182	14	)	)	PUNCT
ejpam-3928	182	15	graph	graph	NOUN
ejpam-3928	182	16	of	of	ADP
ejpam-3928	182	17	order	order	NOUN
ejpam-3928	182	18	2n	2n	NUM
ejpam-3928	182	19	.	.	PUNCT
ejpam-3928	183	1	if	if	SCONJ
ejpam-3928	183	2	g	g	PROPN
ejpam-3928	183	3	is	be	AUX
ejpam-3928	183	4	a	a	DET
ejpam-3928	183	5	spectral	spectral	ADJ
ejpam-3928	183	6	-	-	PUNCT
ejpam-3928	183	7	equipartite	equipartite	ADJ
ejpam-3928	183	8	graph	graph	NOUN
ejpam-3928	183	9	,	,	PUNCT
ejpam-3928	183	10	then	then	ADV
ejpam-3928	183	11	g	g	PROPN
ejpam-3928	183	12	=	=	PUNCT
ejpam-3928	183	13	2kn	2kn	ADJ
ejpam-3928	183	14	or	or	CCONJ
ejpam-3928	183	15	g	g	NOUN
ejpam-3928	183	16	=	=	NOUN
ejpam-3928	183	17	2c4	2c4	NUM
ejpam-3928	183	18	.	.	PUNCT
ejpam-3928	184	1	proof	proof	NOUN
ejpam-3928	184	2	.	.	PUNCT
ejpam-3928	185	1	by	by	ADP
ejpam-3928	185	2	lemma	lemma	PROPN
ejpam-3928	185	3	9	9	NUM
ejpam-3928	185	4	,	,	PUNCT
ejpam-3928	185	5	the	the	DET
ejpam-3928	185	6	two	two	NUM
ejpam-3928	185	7	components	component	NOUN
ejpam-3928	185	8	of	of	ADP
ejpam-3928	185	9	g	g	NOUN
ejpam-3928	185	10	,	,	PUNCT
ejpam-3928	185	11	say	say	VERB
ejpam-3928	185	12	g1	g1	PROPN
ejpam-3928	185	13	and	and	CCONJ
ejpam-3928	185	14	g2	g2	PROPN
ejpam-3928	185	15	,	,	PUNCT
ejpam-3928	185	16	has	have	VERB
ejpam-3928	185	17	n	n	NUM
ejpam-3928	185	18	vertices	vertex	NOUN
ejpam-3928	185	19	each	each	PRON
ejpam-3928	185	20	.	.	PUNCT
ejpam-3928	186	1	suppose	suppose	VERB
ejpam-3928	186	2	to	to	ADP
ejpam-3928	186	3	the	the	DET
ejpam-3928	186	4	contrary	contrary	NOUN
ejpam-3928	186	5	that	that	SCONJ
ejpam-3928	186	6	g1	g1	PROPN
ejpam-3928	186	7	is	be	AUX
ejpam-3928	186	8	not	not	PART
ejpam-3928	186	9	a	a	DET
ejpam-3928	186	10	complete	complete	ADJ
ejpam-3928	186	11	graph	graph	NOUN
ejpam-3928	186	12	nor	nor	CCONJ
ejpam-3928	186	13	a	a	DET
ejpam-3928	186	14	cycle	cycle	NOUN
ejpam-3928	186	15	.	.	PUNCT
ejpam-3928	187	1	by	by	ADP
ejpam-3928	187	2	lemma	lemma	PROPN
ejpam-3928	187	3	1	1	NUM
ejpam-3928	187	4	,	,	PUNCT
ejpam-3928	187	5	we	we	PRON
ejpam-3928	187	6	can	can	AUX
ejpam-3928	187	7	find	find	VERB
ejpam-3928	187	8	two	two	NUM
ejpam-3928	187	9	non	non	ADJ
ejpam-3928	187	10	-	-	ADJ
ejpam-3928	187	11	adjacent	adjacent	ADJ
ejpam-3928	187	12	vertices	vertex	NOUN
ejpam-3928	187	13	,	,	PUNCT
ejpam-3928	187	14	say	say	VERB
ejpam-3928	187	15	x	x	PUNCT
ejpam-3928	187	16	and	and	CCONJ
ejpam-3928	187	17	y	y	PROPN
ejpam-3928	187	18	,	,	PUNCT
ejpam-3928	187	19	in	in	ADP
ejpam-3928	187	20	g1	g1	PROPN
ejpam-3928	187	21	where	where	SCONJ
ejpam-3928	187	22	g1\	g1\	PROPN
ejpam-3928	187	23	{	{	PUNCT
ejpam-3928	187	24	x	x	PROPN
ejpam-3928	187	25	,	,	PUNCT
ejpam-3928	187	26	y	y	PRON
ejpam-3928	187	27	}	}	PUNCT
ejpam-3928	187	28	is	be	AUX
ejpam-3928	187	29	connected	connect	VERB
ejpam-3928	187	30	.	.	PUNCT
ejpam-3928	188	1	let	let	VERB
ejpam-3928	188	2	pq	pq	INTJ
ejpam-3928	188	3	be	be	AUX
ejpam-3928	188	4	an	an	PRON
ejpam-3928	188	5	in	in	ADP
ejpam-3928	188	6	g2	g2	PROPN
ejpam-3928	188	7	.	.	PUNCT
ejpam-3928	189	1	we	we	PRON
ejpam-3928	189	2	can	can	AUX
ejpam-3928	189	3	partition	partition	VERB
ejpam-3928	189	4	v	v	ADP
ejpam-3928	189	5	(	(	PUNCT
ejpam-3928	189	6	g	g	NOUN
ejpam-3928	189	7	)	)	PUNCT
ejpam-3928	189	8	into	into	ADP
ejpam-3928	189	9	two	two	NUM
ejpam-3928	189	10	sets	set	NOUN
ejpam-3928	189	11	,	,	PUNCT
ejpam-3928	189	12	a	a	PRON
ejpam-3928	189	13	and	and	CCONJ
ejpam-3928	189	14	b	b	NOUN
ejpam-3928	189	15	,	,	PUNCT
ejpam-3928	189	16	with	with	ADP
ejpam-3928	189	17	n	n	PRON
ejpam-3928	189	18	vertices	vertice	VERB
ejpam-3928	189	19	each	each	DET
ejpam-3928	189	20	such	such	ADJ
ejpam-3928	189	21	that	that	SCONJ
ejpam-3928	189	22	〈	〈	PROPN
ejpam-3928	189	23	a	a	DET
ejpam-3928	189	24	〉	〉	NOUN
ejpam-3928	190	1	=	=	SYM
ejpam-3928	190	2	〈	〈	PROPN
ejpam-3928	190	3	v	v	X
ejpam-3928	190	4	(	(	PUNCT
ejpam-3928	190	5	g1	g1	PROPN
ejpam-3928	190	6	)	)	PUNCT
ejpam-3928	190	7	\	\	NOUN
ejpam-3928	191	1	{	{	PUNCT
ejpam-3928	191	2	x	x	NOUN
ejpam-3928	191	3	,	,	PUNCT
ejpam-3928	191	4	y}〉∪(p	y}〉∪(p	ADJ
ejpam-3928	191	5	,	,	PUNCT
ejpam-3928	191	6	q	q	NOUN
ejpam-3928	191	7	)	)	PUNCT
ejpam-3928	191	8	and	and	CCONJ
ejpam-3928	191	9	〈	〈	PROPN
ejpam-3928	191	10	b	b	PROPN
ejpam-3928	191	11	〉	〉	PROPN
ejpam-3928	192	1	=	=	SYM
ejpam-3928	192	2	〈	〈	PROPN
ejpam-3928	192	3	v	v	X
ejpam-3928	192	4	(	(	PUNCT
ejpam-3928	192	5	g2	g2	PROPN
ejpam-3928	192	6	)	)	PUNCT
ejpam-3928	192	7	\	\	NOUN
ejpam-3928	192	8	{	{	PUNCT
ejpam-3928	192	9	p	p	X
ejpam-3928	192	10	,	,	PUNCT
ejpam-3928	192	11	q}〉∪〈{x}〉∪〈{y	q}〉∪〈{x}〉∪〈{y	PROPN
ejpam-3928	192	12	}	}	PUNCT
ejpam-3928	192	13	〉	〉	PROPN
ejpam-3928	192	14	.	.	PUNCT
ejpam-3928	193	1	by	by	ADP
ejpam-3928	193	2	lemma	lemma	PROPN
ejpam-3928	193	3	3	3	NUM
ejpam-3928	193	4	,	,	PUNCT
ejpam-3928	193	5	lemma	lemma	PROPN
ejpam-3928	193	6	4	4	NUM
ejpam-3928	193	7	,	,	PUNCT
ejpam-3928	193	8	and	and	CCONJ
ejpam-3928	193	9	lemma	lemma	PROPN
ejpam-3928	193	10	5	5	NUM
ejpam-3928	193	11	,	,	PUNCT
ejpam-3928	193	12	we	we	PRON
ejpam-3928	193	13	have	have	VERB
ejpam-3928	193	14	spec	spec	NOUN
ejpam-3928	193	15	(	(	PUNCT
ejpam-3928	193	16	〈	〈	PROPN
ejpam-3928	193	17	a	a	PRON
ejpam-3928	193	18	〉	〉	NOUN
ejpam-3928	193	19	)	)	PUNCT
ejpam-3928	194	1	=	=	SYM
ejpam-3928	194	2	spec	spec	NOUN
ejpam-3928	194	3	(	(	PUNCT
ejpam-3928	194	4	〈	〈	PROPN
ejpam-3928	194	5	v	v	PRON
ejpam-3928	194	6	(	(	PUNCT
ejpam-3928	194	7	g1	g1	PROPN
ejpam-3928	194	8	)	)	PUNCT
ejpam-3928	194	9	\	\	NOUN
ejpam-3928	194	10	{	{	PUNCT
ejpam-3928	194	11	x	x	NOUN
ejpam-3928	194	12	,	,	PUNCT
ejpam-3928	194	13	y	y	PROPN
ejpam-3928	194	14	}	}	PUNCT
ejpam-3928	194	15	〉	〉	PROPN
ejpam-3928	194	16	)	)	PUNCT
ejpam-3928	194	17	∪	∪	NOUN
ejpam-3928	194	18	{	{	PUNCT
ejpam-3928	194	19	1,−1	1,−1	NUM
ejpam-3928	194	20	}	}	PUNCT
ejpam-3928	194	21	and	and	CCONJ
ejpam-3928	194	22	spec	spec	PROPN
ejpam-3928	194	23	(	(	PUNCT
ejpam-3928	194	24	〈	〈	PROPN
ejpam-3928	194	25	b	b	PROPN
ejpam-3928	194	26	〉	〉	NUM
ejpam-3928	194	27	)	)	PUNCT
ejpam-3928	194	28	=	=	SYM
ejpam-3928	194	29	spec	spec	NOUN
ejpam-3928	194	30	(	(	PUNCT
ejpam-3928	194	31	〈	〈	PROPN
ejpam-3928	194	32	v	v	X
ejpam-3928	194	33	(	(	PUNCT
ejpam-3928	194	34	g2	g2	PROPN
ejpam-3928	194	35	)	)	PUNCT
ejpam-3928	194	36	\	\	NOUN
ejpam-3928	194	37	{	{	PUNCT
ejpam-3928	194	38	p	p	X
ejpam-3928	194	39	,	,	PUNCT
ejpam-3928	194	40	q	q	ADJ
ejpam-3928	194	41	}	}	PUNCT
ejpam-3928	194	42	〉	〉	NOUN
ejpam-3928	194	43	)	)	PUNCT
ejpam-3928	194	44	∪	∪	X
ejpam-3928	194	45	{	{	PUNCT
ejpam-3928	194	46	0	0	NUM
ejpam-3928	194	47	}	}	PUNCT
ejpam-3928	194	48	∪	∪	X
ejpam-3928	194	49	{	{	PUNCT
ejpam-3928	194	50	0	0	NUM
ejpam-3928	194	51	}	}	PUNCT
ejpam-3928	194	52	.	.	PUNCT
ejpam-3928	195	1	consider	consider	VERB
ejpam-3928	195	2	the	the	DET
ejpam-3928	195	3	following	follow	VERB
ejpam-3928	195	4	cases	case	NOUN
ejpam-3928	195	5	:	:	PUNCT
ejpam-3928	195	6	case	case	NOUN
ejpam-3928	195	7	1	1	NUM
ejpam-3928	195	8	.	.	PUNCT
ejpam-3928	196	1	both	both	CCONJ
ejpam-3928	196	2	g1	g1	PROPN
ejpam-3928	196	3	and	and	CCONJ
ejpam-3928	196	4	g2	g2	PROPN
ejpam-3928	196	5	are	be	AUX
ejpam-3928	196	6	not	not	PART
ejpam-3928	196	7	bipartite	bipartite	ADJ
ejpam-3928	196	8	if	if	SCONJ
ejpam-3928	196	9	both	both	DET
ejpam-3928	196	10	g1	g1	NOUN
ejpam-3928	196	11	and	and	CCONJ
ejpam-3928	196	12	g2	g2	PROPN
ejpam-3928	196	13	are	be	AUX
ejpam-3928	196	14	not	not	PART
ejpam-3928	196	15	bipartite	bipartite	ADJ
ejpam-3928	196	16	,	,	PUNCT
ejpam-3928	196	17	then	then	ADV
ejpam-3928	196	18	spec	spec	PROPN
ejpam-3928	196	19	(	(	PUNCT
ejpam-3928	196	20	〈	〈	PROPN
ejpam-3928	196	21	v	v	X
ejpam-3928	196	22	(	(	PUNCT
ejpam-3928	196	23	g2	g2	PROPN
ejpam-3928	196	24	)	)	PUNCT
ejpam-3928	196	25	\	\	NOUN
ejpam-3928	197	1	{	{	PUNCT
ejpam-3928	197	2	p	p	X
ejpam-3928	197	3	,	,	PUNCT
ejpam-3928	197	4	q	q	ADJ
ejpam-3928	197	5	}	}	PUNCT
ejpam-3928	197	6	〉	〉	NOUN
ejpam-3928	197	7	)	)	PUNCT
ejpam-3928	197	8	can	can	AUX
ejpam-3928	197	9	not	not	PART
ejpam-3928	197	10	have	have	VERB
ejpam-3928	197	11	1	1	NUM
ejpam-3928	197	12	and	and	CCONJ
ejpam-3928	197	13	−1	−1	NOUN
ejpam-3928	197	14	at	at	ADP
ejpam-3928	197	15	the	the	DET
ejpam-3928	197	16	same	same	ADJ
ejpam-3928	197	17	time	time	NOUN
ejpam-3928	197	18	as	as	ADP
ejpam-3928	197	19	elements	element	NOUN
ejpam-3928	197	20	.	.	PUNCT
ejpam-3928	198	1	hence	hence	ADV
ejpam-3928	198	2	,	,	PUNCT
ejpam-3928	198	3	spec	spec	PROPN
ejpam-3928	198	4	(	(	PUNCT
ejpam-3928	198	5	〈	〈	PROPN
ejpam-3928	198	6	a	a	PRON
ejpam-3928	198	7	〉	〉	NOUN
ejpam-3928	198	8	)	)	PUNCT
ejpam-3928	198	9	6=	6=	NUM
ejpam-3928	198	10	spec	spec	PROPN
ejpam-3928	198	11	(	(	PUNCT
ejpam-3928	198	12	〈	〈	PROPN
ejpam-3928	198	13	b	b	PROPN
ejpam-3928	198	14	〉	〉	PROPN
ejpam-3928	198	15	)	)	PUNCT
ejpam-3928	198	16	.	.	PUNCT
ejpam-3928	199	1	thus	thus	ADV
ejpam-3928	199	2	,	,	PUNCT
ejpam-3928	199	3	〈	〈	PROPN
ejpam-3928	199	4	a	a	DET
ejpam-3928	199	5	〉	〉	NOUN
ejpam-3928	199	6	and	and	CCONJ
ejpam-3928	199	7	〈	〈	PROPN
ejpam-3928	199	8	b	b	PROPN
ejpam-3928	199	9	〉	〉	PROPN
ejpam-3928	199	10	are	be	AUX
ejpam-3928	199	11	not	not	PART
ejpam-3928	199	12	isospectral	isospectral	ADJ
ejpam-3928	199	13	,	,	PUNCT
ejpam-3928	199	14	and	and	CCONJ
ejpam-3928	199	15	g	g	NOUN
ejpam-3928	199	16	is	be	AUX
ejpam-3928	199	17	not	not	PART
ejpam-3928	199	18	spectral	spectral	ADJ
ejpam-3928	199	19	-	-	PUNCT
ejpam-3928	199	20	equipartite	equipartite	ADJ
ejpam-3928	199	21	.	.	PUNCT
ejpam-3928	200	1	case	case	NOUN
ejpam-3928	200	2	2	2	NUM
ejpam-3928	200	3	.	.	PUNCT
ejpam-3928	200	4	only	only	ADV
ejpam-3928	200	5	one	one	NUM
ejpam-3928	200	6	between	between	ADP
ejpam-3928	200	7	g1	g1	PROPN
ejpam-3928	200	8	and	and	CCONJ
ejpam-3928	200	9	g2	g2	PROPN
ejpam-3928	200	10	is	be	AUX
ejpam-3928	200	11	bipartite	bipartite	PROPN
ejpam-3928	200	12	suppose	suppose	VERB
ejpam-3928	200	13	that	that	SCONJ
ejpam-3928	200	14	g1	g1	PROPN
ejpam-3928	200	15	is	be	AUX
ejpam-3928	200	16	bipartite	bipartite	ADJ
ejpam-3928	200	17	and	and	CCONJ
ejpam-3928	200	18	g2	g2	PROPN
ejpam-3928	200	19	is	be	AUX
ejpam-3928	200	20	not	not	PART
ejpam-3928	200	21	.	.	PUNCT
ejpam-3928	201	1	hence	hence	ADV
ejpam-3928	201	2	,	,	PUNCT
ejpam-3928	201	3	using	use	VERB
ejpam-3928	201	4	the	the	DET
ejpam-3928	201	5	same	same	ADJ
ejpam-3928	201	6	argument	argument	NOUN
ejpam-3928	201	7	in	in	ADP
ejpam-3928	201	8	case	case	NOUN
ejpam-3928	201	9	1	1	NUM
ejpam-3928	201	10	above	above	ADV
ejpam-3928	201	11	,	,	PUNCT
ejpam-3928	201	12	if	if	SCONJ
ejpam-3928	201	13	g2	g2	PROPN
ejpam-3928	201	14	is	be	AUX
ejpam-3928	201	15	not	not	PART
ejpam-3928	201	16	bipartite	bipartite	ADJ
ejpam-3928	201	17	,	,	PUNCT
ejpam-3928	201	18	then	then	ADV
ejpam-3928	201	19	spec	spec	PROPN
ejpam-3928	201	20	(	(	PUNCT
ejpam-3928	201	21	〈	〈	PROPN
ejpam-3928	201	22	v	v	X
ejpam-3928	201	23	(	(	PUNCT
ejpam-3928	201	24	g2	g2	PROPN
ejpam-3928	201	25	)	)	PUNCT
ejpam-3928	201	26	\	\	NOUN
ejpam-3928	202	1	{	{	PUNCT
ejpam-3928	202	2	p	p	X
ejpam-3928	202	3	,	,	PUNCT
ejpam-3928	202	4	q	q	ADJ
ejpam-3928	202	5	}	}	PUNCT
ejpam-3928	202	6	〉	〉	NOUN
ejpam-3928	202	7	)	)	PUNCT
ejpam-3928	202	8	can	can	AUX
ejpam-3928	202	9	not	not	PART
ejpam-3928	202	10	have	have	VERB
ejpam-3928	202	11	1	1	NUM
ejpam-3928	202	12	and	and	CCONJ
ejpam-3928	202	13	−1	−1	NOUN
ejpam-3928	202	14	at	at	ADP
ejpam-3928	202	15	the	the	DET
ejpam-3928	202	16	same	same	ADJ
ejpam-3928	202	17	time	time	NOUN
ejpam-3928	202	18	as	as	ADP
ejpam-3928	202	19	elements	element	NOUN
ejpam-3928	202	20	.	.	PUNCT
ejpam-3928	203	1	hence	hence	ADV
ejpam-3928	203	2	,	,	PUNCT
ejpam-3928	203	3	spec	spec	PROPN
ejpam-3928	203	4	(	(	PUNCT
ejpam-3928	203	5	〈	〈	PROPN
ejpam-3928	203	6	a	a	PRON
ejpam-3928	203	7	〉	〉	NOUN
ejpam-3928	203	8	)	)	PUNCT
ejpam-3928	203	9	6=	6=	NUM
ejpam-3928	203	10	spec	spec	PROPN
ejpam-3928	203	11	(	(	PUNCT
ejpam-3928	203	12	〈	〈	PROPN
ejpam-3928	203	13	b	b	PROPN
ejpam-3928	203	14	〉	〉	PROPN
ejpam-3928	203	15	)	)	PUNCT
ejpam-3928	203	16	.	.	PUNCT
ejpam-3928	204	1	thus	thus	ADV
ejpam-3928	204	2	,	,	PUNCT
ejpam-3928	204	3	〈	〈	PROPN
ejpam-3928	204	4	a	a	DET
ejpam-3928	204	5	〉	〉	NOUN
ejpam-3928	204	6	and	and	CCONJ
ejpam-3928	204	7	〈	〈	PROPN
ejpam-3928	204	8	b	b	PROPN
ejpam-3928	204	9	〉	〉	PROPN
ejpam-3928	204	10	are	be	AUX
ejpam-3928	204	11	not	not	PART
ejpam-3928	204	12	isospectral	isospectral	ADJ
ejpam-3928	204	13	,	,	PUNCT
ejpam-3928	204	14	and	and	CCONJ
ejpam-3928	204	15	g	g	NOUN
ejpam-3928	204	16	is	be	AUX
ejpam-3928	204	17	not	not	PART
ejpam-3928	204	18	spectral	spectral	ADJ
ejpam-3928	204	19	-	-	PUNCT
ejpam-3928	204	20	equipartite	equipartite	ADJ
ejpam-3928	204	21	.	.	PUNCT
ejpam-3928	205	1	a.	a.	NOUN
ejpam-3928	205	2	yurfo	yurfo	PROPN
ejpam-3928	205	3	,	,	PUNCT
ejpam-3928	205	4	j.	j.	PROPN
ejpam-3928	205	5	adanza	adanza	PROPN
ejpam-3928	205	6	,	,	PUNCT
ejpam-3928	205	7	m.	m.	PROPN
ejpam-3928	205	8	baldado	baldado	PROPN
ejpam-3928	205	9	jr	jr	PROPN
ejpam-3928	205	10	.	.	PROPN
ejpam-3928	205	11	/	/	SYM
ejpam-3928	205	12	eur	eur	PROPN
ejpam-3928	205	13	.	.	PUNCT
ejpam-3928	206	1	j.	j.	PROPN
ejpam-3928	206	2	pure	pure	PROPN
ejpam-3928	206	3	appl	appl	PROPN
ejpam-3928	206	4	.	.	PROPN
ejpam-3928	206	5	math	math	PROPN
ejpam-3928	206	6	,	,	PUNCT
ejpam-3928	206	7	14	14	NUM
ejpam-3928	206	8	(	(	PUNCT
ejpam-3928	206	9	2	2	NUM
ejpam-3928	206	10	)	)	PUNCT
ejpam-3928	206	11	(	(	PUNCT
ejpam-3928	206	12	2021	2021	NUM
ejpam-3928	206	13	)	)	PUNCT
ejpam-3928	206	14	,	,	PUNCT
ejpam-3928	206	15	358	358	NUM
ejpam-3928	206	16	-	-	SYM
ejpam-3928	206	17	365	365	NUM
ejpam-3928	206	18	363	363	NUM
ejpam-3928	206	19	suppose	suppose	VERB
ejpam-3928	206	20	that	that	SCONJ
ejpam-3928	206	21	g2	g2	PROPN
ejpam-3928	206	22	is	be	AUX
ejpam-3928	206	23	bipartite	bipartite	ADJ
ejpam-3928	206	24	and	and	CCONJ
ejpam-3928	206	25	g1	g1	NOUN
ejpam-3928	206	26	is	be	AUX
ejpam-3928	206	27	not	not	PART
ejpam-3928	206	28	.	.	PUNCT
ejpam-3928	207	1	by	by	ADP
ejpam-3928	207	2	lemma	lemma	PROPN
ejpam-3928	207	3	2	2	NUM
ejpam-3928	207	4	,	,	PUNCT
ejpam-3928	207	5	λ1	λ1	PROPN
ejpam-3928	207	6	(	(	PUNCT
ejpam-3928	207	7	〈	〈	PROPN
ejpam-3928	207	8	v	v	PROPN
ejpam-3928	207	9	(	(	PUNCT
ejpam-3928	207	10	g2	g2	PROPN
ejpam-3928	207	11	)	)	PUNCT
ejpam-3928	207	12	\	\	NOUN
ejpam-3928	208	1	{	{	PUNCT
ejpam-3928	208	2	p	p	X
ejpam-3928	208	3	,	,	PUNCT
ejpam-3928	208	4	q	q	ADJ
ejpam-3928	208	5	}	}	PUNCT
ejpam-3928	208	6	〉	〉	NUM
ejpam-3928	208	7	)	)	PUNCT
ejpam-3928	208	8	>	>	X
ejpam-3928	208	9	1	1	NUM
ejpam-3928	208	10	since	since	SCONJ
ejpam-3928	208	11	k2	k2	PROPN
ejpam-3928	208	12	⊂	⊂	PROPN
ejpam-3928	208	13	〈	〈	PROPN
ejpam-3928	208	14	v	v	X
ejpam-3928	208	15	(	(	PUNCT
ejpam-3928	208	16	g2	g2	PROPN
ejpam-3928	208	17	)	)	PUNCT
ejpam-3928	208	18	\	\	NOUN
ejpam-3928	209	1	{	{	PUNCT
ejpam-3928	209	2	p	p	X
ejpam-3928	209	3	,	,	PUNCT
ejpam-3928	209	4	q	q	ADJ
ejpam-3928	209	5	}	}	PUNCT
ejpam-3928	209	6	〉	〉	PROPN
ejpam-3928	209	7	.	.	PUNCT
ejpam-3928	210	1	since	since	SCONJ
ejpam-3928	210	2	g1	g1	PROPN
ejpam-3928	210	3	is	be	AUX
ejpam-3928	210	4	not	not	PART
ejpam-3928	210	5	bipartite	bipartite	ADJ
ejpam-3928	210	6	,	,	PUNCT
ejpam-3928	210	7	only	only	ADV
ejpam-3928	210	8	one	one	NUM
ejpam-3928	210	9	between	between	ADP
ejpam-3928	210	10	λ1	λ1	PROPN
ejpam-3928	210	11	and	and	CCONJ
ejpam-3928	210	12	−λ1	−λ1	PROPN
ejpam-3928	210	13	may	may	AUX
ejpam-3928	210	14	exist	exist	VERB
ejpam-3928	210	15	as	as	ADP
ejpam-3928	210	16	an	an	DET
ejpam-3928	210	17	eigenvalue	eigenvalue	NOUN
ejpam-3928	210	18	of	of	ADP
ejpam-3928	210	19	〈	〈	PROPN
ejpam-3928	210	20	v	v	PROPN
ejpam-3928	210	21	(	(	PUNCT
ejpam-3928	210	22	g1	g1	PROPN
ejpam-3928	210	23	)	)	PUNCT
ejpam-3928	210	24	\	\	NOUN
ejpam-3928	211	1	{	{	PUNCT
ejpam-3928	211	2	x	x	NOUN
ejpam-3928	211	3	,	,	PUNCT
ejpam-3928	211	4	y	y	PROPN
ejpam-3928	211	5	}	}	PUNCT
ejpam-3928	211	6	〉	〉	PROPN
ejpam-3928	211	7	.	.	PUNCT
ejpam-3928	212	1	thus	thus	ADV
ejpam-3928	212	2	,	,	PUNCT
ejpam-3928	212	3	spec	spec	PROPN
ejpam-3928	212	4	(	(	PUNCT
ejpam-3928	212	5	〈	〈	PROPN
ejpam-3928	212	6	a	a	PRON
ejpam-3928	212	7	〉	〉	NOUN
ejpam-3928	212	8	)	)	PUNCT
ejpam-3928	212	9	6=	6=	NUM
ejpam-3928	212	10	spec	spec	PROPN
ejpam-3928	212	11	(	(	PUNCT
ejpam-3928	212	12	〈	〈	PROPN
ejpam-3928	212	13	b	b	PROPN
ejpam-3928	212	14	〉	〉	PROPN
ejpam-3928	212	15	)	)	PUNCT
ejpam-3928	212	16	.	.	PUNCT
ejpam-3928	213	1	thus	thus	ADV
ejpam-3928	213	2	,	,	PUNCT
ejpam-3928	213	3	〈	〈	PROPN
ejpam-3928	213	4	a	a	DET
ejpam-3928	213	5	〉	〉	NOUN
ejpam-3928	213	6	and	and	CCONJ
ejpam-3928	213	7	〈	〈	PROPN
ejpam-3928	213	8	b	b	PROPN
ejpam-3928	213	9	〉	〉	PROPN
ejpam-3928	213	10	are	be	AUX
ejpam-3928	213	11	not	not	PART
ejpam-3928	213	12	isospectral	isospectral	ADJ
ejpam-3928	213	13	,	,	PUNCT
ejpam-3928	213	14	and	and	CCONJ
ejpam-3928	213	15	g	g	NOUN
ejpam-3928	213	16	is	be	AUX
ejpam-3928	213	17	not	not	PART
ejpam-3928	213	18	spectral	spectral	ADJ
ejpam-3928	213	19	-	-	PUNCT
ejpam-3928	213	20	equipartite	equipartite	ADJ
ejpam-3928	213	21	.	.	PUNCT
ejpam-3928	214	1	case	case	NOUN
ejpam-3928	214	2	3	3	NUM
ejpam-3928	214	3	.	.	PUNCT
ejpam-3928	215	1	both	both	CCONJ
ejpam-3928	215	2	g1	g1	PROPN
ejpam-3928	215	3	and	and	CCONJ
ejpam-3928	215	4	g2	g2	PROPN
ejpam-3928	215	5	are	be	AUX
ejpam-3928	215	6	bipartite	bipartite	ADJ
ejpam-3928	215	7	if	if	SCONJ
ejpam-3928	215	8	both	both	PRON
ejpam-3928	215	9	g1	g1	NOUN
ejpam-3928	215	10	and	and	CCONJ
ejpam-3928	215	11	g2	g2	PROPN
ejpam-3928	215	12	are	be	AUX
ejpam-3928	215	13	bipartite	bipartite	ADJ
ejpam-3928	215	14	,	,	PUNCT
ejpam-3928	215	15	then	then	ADV
ejpam-3928	215	16	we	we	PRON
ejpam-3928	215	17	have	have	VERB
ejpam-3928	215	18	the	the	DET
ejpam-3928	215	19	following	follow	VERB
ejpam-3928	215	20	subcases	subcase	NOUN
ejpam-3928	215	21	:	:	PUNCT
ejpam-3928	215	22	subcase	subcase	NOUN
ejpam-3928	215	23	1	1	NUM
ejpam-3928	215	24	.	.	PUNCT
ejpam-3928	216	1	both	both	PRON
ejpam-3928	216	2	g1	g1	PROPN
ejpam-3928	216	3	and	and	CCONJ
ejpam-3928	216	4	g2	g2	PROPN
ejpam-3928	216	5	are	be	AUX
ejpam-3928	216	6	not	not	PART
ejpam-3928	216	7	complete	complete	ADJ
ejpam-3928	216	8	bipartite	bipartite	NOUN
ejpam-3928	216	9	graphs	graph	NOUN
ejpam-3928	216	10	.	.	PUNCT
ejpam-3928	217	1	if	if	SCONJ
ejpam-3928	217	2	both	both	DET
ejpam-3928	217	3	g1	g1	PROPN
ejpam-3928	217	4	and	and	CCONJ
ejpam-3928	217	5	g2	g2	PROPN
ejpam-3928	217	6	are	be	AUX
ejpam-3928	217	7	not	not	PART
ejpam-3928	217	8	complete	complete	ADJ
ejpam-3928	217	9	bipartite	bipartite	NOUN
ejpam-3928	217	10	graphs	graph	NOUN
ejpam-3928	217	11	,	,	PUNCT
ejpam-3928	217	12	then	then	ADV
ejpam-3928	217	13	we	we	PRON
ejpam-3928	217	14	will	will	AUX
ejpam-3928	217	15	partition	partition	VERB
ejpam-3928	217	16	g	g	NOUN
ejpam-3928	217	17	into	into	ADP
ejpam-3928	217	18	two	two	NUM
ejpam-3928	217	19	sets	set	NOUN
ejpam-3928	217	20	a	a	PRON
ejpam-3928	217	21	and	and	CCONJ
ejpam-3928	217	22	b	b	NOUN
ejpam-3928	217	23	with	with	ADP
ejpam-3928	217	24	n	n	NOUN
ejpam-3928	217	25	vertices	vertice	VERB
ejpam-3928	217	26	each	each	DET
ejpam-3928	217	27	such	such	ADJ
ejpam-3928	217	28	that	that	SCONJ
ejpam-3928	217	29	〈	〈	PROPN
ejpam-3928	217	30	a	a	DET
ejpam-3928	217	31	〉	〉	NOUN
ejpam-3928	218	1	=	=	SYM
ejpam-3928	218	2	〈	〈	PROPN
ejpam-3928	218	3	v	v	X
ejpam-3928	218	4	(	(	PUNCT
ejpam-3928	218	5	g1	g1	PROPN
ejpam-3928	218	6	)	)	PUNCT
ejpam-3928	218	7	\	\	NOUN
ejpam-3928	219	1	{	{	PUNCT
ejpam-3928	219	2	x	x	NOUN
ejpam-3928	219	3	,	,	PUNCT
ejpam-3928	219	4	y	y	PROPN
ejpam-3928	219	5	}	}	PUNCT
ejpam-3928	219	6	〉	〉	PROPN
ejpam-3928	219	7	∪	∪	X
ejpam-3928	219	8	(	(	PUNCT
ejpam-3928	219	9	p	p	X
ejpam-3928	219	10	,	,	PUNCT
ejpam-3928	219	11	q	q	NOUN
ejpam-3928	219	12	)	)	PUNCT
ejpam-3928	219	13	and	and	CCONJ
ejpam-3928	219	14	〈	〈	PROPN
ejpam-3928	219	15	b	b	PROPN
ejpam-3928	219	16	〉	〉	PROPN
ejpam-3928	219	17	=	=	SYM
ejpam-3928	220	1	〈	〈	PROPN
ejpam-3928	220	2	v	v	X
ejpam-3928	220	3	(	(	PUNCT
ejpam-3928	220	4	g2	g2	PROPN
ejpam-3928	220	5	)	)	PUNCT
ejpam-3928	220	6	\	\	NOUN
ejpam-3928	220	7	{	{	PUNCT
ejpam-3928	220	8	p	p	X
ejpam-3928	220	9	,	,	PUNCT
ejpam-3928	220	10	q	q	ADJ
ejpam-3928	220	11	}	}	PUNCT
ejpam-3928	220	12	〉	〉	PROPN
ejpam-3928	220	13	∪	∪	ADJ
ejpam-3928	220	14	〈	〈	PROPN
ejpam-3928	220	15	{	{	PUNCT
ejpam-3928	220	16	x	x	NOUN
ejpam-3928	220	17	}	}	PUNCT
ejpam-3928	220	18	〉	〉	PROPN
ejpam-3928	220	19	∪	∪	ADP
ejpam-3928	220	20	〈	〈	PROPN
ejpam-3928	220	21	{	{	PUNCT
ejpam-3928	220	22	y	y	PROPN
ejpam-3928	220	23	}	}	PUNCT
ejpam-3928	220	24	〉	〉	PROPN
ejpam-3928	220	25	.	.	PUNCT
ejpam-3928	221	1	since	since	SCONJ
ejpam-3928	221	2	g1	g1	PROPN
ejpam-3928	221	3	is	be	AUX
ejpam-3928	221	4	not	not	PART
ejpam-3928	221	5	a	a	DET
ejpam-3928	221	6	complete	complete	ADJ
ejpam-3928	221	7	bipartite	bipartite	NOUN
ejpam-3928	221	8	graph	graph	NOUN
ejpam-3928	221	9	,	,	PUNCT
ejpam-3928	221	10	we	we	PRON
ejpam-3928	221	11	can	can	AUX
ejpam-3928	221	12	have	have	VERB
ejpam-3928	221	13	two	two	NUM
ejpam-3928	221	14	non	non	ADJ
ejpam-3928	221	15	-	-	ADJ
ejpam-3928	221	16	adjacent	adjacent	ADJ
ejpam-3928	221	17	vertices	vertex	NOUN
ejpam-3928	221	18	,	,	PUNCT
ejpam-3928	221	19	x	x	PRON
ejpam-3928	221	20	,	,	PUNCT
ejpam-3928	221	21	and	and	CCONJ
ejpam-3928	221	22	y	y	PROPN
ejpam-3928	221	23	,	,	PUNCT
ejpam-3928	221	24	to	to	PART
ejpam-3928	221	25	belong	belong	VERB
ejpam-3928	221	26	to	to	ADP
ejpam-3928	221	27	different	different	ADJ
ejpam-3928	221	28	partite	partite	ADJ
ejpam-3928	221	29	sets	set	NOUN
ejpam-3928	221	30	.	.	PUNCT
ejpam-3928	222	1	hence	hence	ADV
ejpam-3928	222	2	,	,	PUNCT
ejpam-3928	222	3	they	they	PRON
ejpam-3928	222	4	do	do	AUX
ejpam-3928	222	5	not	not	PART
ejpam-3928	222	6	have	have	VERB
ejpam-3928	222	7	a	a	DET
ejpam-3928	222	8	common	common	ADJ
ejpam-3928	222	9	neighbor	neighbor	NOUN
ejpam-3928	222	10	.	.	PUNCT
ejpam-3928	223	1	thus	thus	ADV
ejpam-3928	223	2	,	,	PUNCT
ejpam-3928	223	3	for	for	ADP
ejpam-3928	223	4	〈	〈	PROPN
ejpam-3928	223	5	v	v	PRON
ejpam-3928	223	6	(	(	PUNCT
ejpam-3928	223	7	g1	g1	PROPN
ejpam-3928	223	8	)	)	PUNCT
ejpam-3928	223	9	\	\	NOUN
ejpam-3928	223	10	{	{	PUNCT
ejpam-3928	223	11	x	x	NOUN
ejpam-3928	223	12	,	,	PUNCT
ejpam-3928	223	13	y	y	PROPN
ejpam-3928	223	14	}	}	PUNCT
ejpam-3928	223	15	〉	〉	PROPN
ejpam-3928	223	16	,	,	PUNCT
ejpam-3928	223	17	there	there	PRON
ejpam-3928	223	18	are	be	VERB
ejpam-3928	223	19	2k	2k	NUM
ejpam-3928	223	20	vertices	vertex	NOUN
ejpam-3928	223	21	with	with	ADP
ejpam-3928	223	22	degree	degree	NOUN
ejpam-3928	224	1	k	k	NOUN
ejpam-3928	224	2	−	−	PROPN
ejpam-3928	224	3	1	1	NUM
ejpam-3928	225	1	and	and	CCONJ
ejpam-3928	225	2	(	(	PUNCT
ejpam-3928	225	3	n−	n−	NOUN
ejpam-3928	225	4	2	2	NUM
ejpam-3928	225	5	)	)	PUNCT
ejpam-3928	225	6	−	−	PROPN
ejpam-3928	225	7	2k	2k	NOUN
ejpam-3928	225	8	vertices	vertex	NOUN
ejpam-3928	225	9	of	of	ADP
ejpam-3928	225	10	degree	degree	NOUN
ejpam-3928	225	11	k.	k.	PROPN
ejpam-3928	225	12	on	on	ADP
ejpam-3928	225	13	the	the	DET
ejpam-3928	225	14	other	other	ADJ
ejpam-3928	225	15	hand	hand	NOUN
ejpam-3928	225	16	,	,	PUNCT
ejpam-3928	225	17	since	since	SCONJ
ejpam-3928	225	18	pq	pq	PROPN
ejpam-3928	225	19	is	be	AUX
ejpam-3928	225	20	an	an	DET
ejpam-3928	225	21	edge	edge	NOUN
ejpam-3928	225	22	,	,	PUNCT
ejpam-3928	225	23	p	p	NOUN
ejpam-3928	225	24	and	and	CCONJ
ejpam-3928	225	25	q	q	PROPN
ejpam-3928	225	26	must	must	AUX
ejpam-3928	225	27	belong	belong	VERB
ejpam-3928	225	28	to	to	ADP
ejpam-3928	225	29	different	different	ADJ
ejpam-3928	225	30	partite	partite	ADJ
ejpam-3928	225	31	sets	set	NOUN
ejpam-3928	225	32	,	,	PUNCT
ejpam-3928	225	33	so	so	SCONJ
ejpam-3928	225	34	they	they	PRON
ejpam-3928	225	35	do	do	AUX
ejpam-3928	225	36	not	not	PART
ejpam-3928	225	37	have	have	VERB
ejpam-3928	225	38	a	a	DET
ejpam-3928	225	39	common	common	ADJ
ejpam-3928	225	40	neighbor	neighbor	NOUN
ejpam-3928	225	41	.	.	PUNCT
ejpam-3928	226	1	hence	hence	ADV
ejpam-3928	226	2	,	,	PUNCT
ejpam-3928	226	3	for	for	ADP
ejpam-3928	226	4	〈	〈	PROPN
ejpam-3928	226	5	v	v	PROPN
ejpam-3928	226	6	(	(	PUNCT
ejpam-3928	226	7	g2	g2	PROPN
ejpam-3928	226	8	)	)	PUNCT
ejpam-3928	226	9	\	\	NOUN
ejpam-3928	227	1	{	{	PUNCT
ejpam-3928	227	2	p	p	X
ejpam-3928	227	3	,	,	PUNCT
ejpam-3928	227	4	q	q	ADJ
ejpam-3928	227	5	}	}	PUNCT
ejpam-3928	227	6	〉	〉	NUM
ejpam-3928	227	7	,	,	PUNCT
ejpam-3928	227	8	there	there	PRON
ejpam-3928	227	9	are	be	VERB
ejpam-3928	227	10	2k	2k	NUM
ejpam-3928	227	11	−	−	NUM
ejpam-3928	227	12	2	2	NUM
ejpam-3928	227	13	vertices	vertex	NOUN
ejpam-3928	227	14	of	of	ADP
ejpam-3928	227	15	degree	degree	NOUN
ejpam-3928	227	16	k	k	NOUN
ejpam-3928	227	17	−	−	PROPN
ejpam-3928	227	18	1	1	NUM
ejpam-3928	228	1	and	and	CCONJ
ejpam-3928	228	2	(	(	PUNCT
ejpam-3928	228	3	n−	n−	NOUN
ejpam-3928	228	4	2	2	NUM
ejpam-3928	228	5	)	)	PUNCT
ejpam-3928	228	6	−	−	PROPN
ejpam-3928	228	7	(	(	PUNCT
ejpam-3928	228	8	2k	2k	NOUN
ejpam-3928	228	9	−	−	NOUN
ejpam-3928	228	10	2	2	NUM
ejpam-3928	228	11	)	)	PUNCT
ejpam-3928	228	12	=	=	SYM
ejpam-3928	229	1	n	n	NUM
ejpam-3928	229	2	−	−	PROPN
ejpam-3928	229	3	2k	2k	NOUN
ejpam-3928	229	4	vertices	vertice	VERB
ejpam-3928	229	5	with	with	ADP
ejpam-3928	229	6	degree	degree	NOUN
ejpam-3928	229	7	k.	k.	PROPN
ejpam-3928	230	1	clearly	clearly	ADV
ejpam-3928	230	2	,	,	PUNCT
ejpam-3928	230	3	〈	〈	PROPN
ejpam-3928	230	4	v	v	X
ejpam-3928	230	5	(	(	PUNCT
ejpam-3928	230	6	g2	g2	PROPN
ejpam-3928	230	7	)	)	PUNCT
ejpam-3928	230	8	\	\	NOUN
ejpam-3928	231	1	{	{	PUNCT
ejpam-3928	231	2	p	p	X
ejpam-3928	231	3	,	,	PUNCT
ejpam-3928	231	4	q	q	ADJ
ejpam-3928	231	5	}	}	PUNCT
ejpam-3928	231	6	〉	〉	PROPN
ejpam-3928	231	7	contains	contain	VERB
ejpam-3928	231	8	one	one	NUM
ejpam-3928	231	9	more	more	ADJ
ejpam-3928	231	10	edge	edge	NOUN
ejpam-3928	231	11	when	when	SCONJ
ejpam-3928	231	12	compared	compare	VERB
ejpam-3928	231	13	to	to	ADP
ejpam-3928	231	14	〈	〈	PROPN
ejpam-3928	231	15	v	v	PROPN
ejpam-3928	231	16	(	(	PUNCT
ejpam-3928	231	17	g1	g1	PROPN
ejpam-3928	231	18	)	)	PUNCT
ejpam-3928	231	19	\	\	NOUN
ejpam-3928	231	20	{	{	PUNCT
ejpam-3928	231	21	x	x	NOUN
ejpam-3928	231	22	,	,	PUNCT
ejpam-3928	231	23	y	y	PROPN
ejpam-3928	231	24	}	}	PUNCT
ejpam-3928	231	25	〉	〉	PROPN
ejpam-3928	231	26	.	.	PUNCT
ejpam-3928	232	1	with	with	ADP
ejpam-3928	232	2	2k	2k	NOUN
ejpam-3928	232	3	−	−	ADP
ejpam-3928	232	4	2	2	NUM
ejpam-3928	232	5	<	<	X
ejpam-3928	232	6	2k	2k	NOUN
ejpam-3928	232	7	for	for	ADP
ejpam-3928	232	8	vertices	vertex	NOUN
ejpam-3928	232	9	with	with	ADP
ejpam-3928	232	10	degree	degree	NOUN
ejpam-3928	233	1	k	k	NOUN
ejpam-3928	233	2	−	−	PROPN
ejpam-3928	233	3	1	1	NUM
ejpam-3928	233	4	and	and	CCONJ
ejpam-3928	233	5	n	n	CCONJ
ejpam-3928	233	6	−	−	PROPN
ejpam-3928	233	7	2k	2k	NOUN
ejpam-3928	233	8	>	>	X
ejpam-3928	233	9	(	(	PUNCT
ejpam-3928	233	10	n−	n−	NOUN
ejpam-3928	233	11	2	2	NUM
ejpam-3928	233	12	)	)	PUNCT
ejpam-3928	233	13	−	−	PROPN
ejpam-3928	233	14	2k	2k	NOUN
ejpam-3928	233	15	for	for	ADP
ejpam-3928	233	16	vertices	vertex	NOUN
ejpam-3928	233	17	with	with	ADP
ejpam-3928	233	18	degree	degree	NOUN
ejpam-3928	233	19	k	k	NOUN
ejpam-3928	233	20	,	,	PUNCT
ejpam-3928	233	21	we	we	PRON
ejpam-3928	233	22	could	could	AUX
ejpam-3928	233	23	say	say	VERB
ejpam-3928	233	24	that	that	SCONJ
ejpam-3928	233	25	〈	〈	PROPN
ejpam-3928	233	26	v	v	PRON
ejpam-3928	233	27	(	(	PUNCT
ejpam-3928	233	28	g1	g1	PROPN
ejpam-3928	233	29	)	)	PUNCT
ejpam-3928	233	30	\	\	NOUN
ejpam-3928	234	1	{	{	PUNCT
ejpam-3928	234	2	x	x	NOUN
ejpam-3928	234	3	,	,	PUNCT
ejpam-3928	234	4	y	y	PROPN
ejpam-3928	234	5	}	}	PUNCT
ejpam-3928	234	6	〉	〉	PROPN
ejpam-3928	234	7	is	be	AUX
ejpam-3928	234	8	isomorphic	isomorphic	ADJ
ejpam-3928	234	9	to	to	ADP
ejpam-3928	234	10	some	some	DET
ejpam-3928	234	11	proper	proper	ADJ
ejpam-3928	234	12	subgraph	subgraph	NOUN
ejpam-3928	234	13	of	of	ADP
ejpam-3928	234	14	〈	〈	PROPN
ejpam-3928	234	15	v	v	PROPN
ejpam-3928	234	16	(	(	PUNCT
ejpam-3928	234	17	g2	g2	PROPN
ejpam-3928	234	18	)	)	PUNCT
ejpam-3928	234	19	\	\	NOUN
ejpam-3928	235	1	{	{	PUNCT
ejpam-3928	235	2	p	p	X
ejpam-3928	235	3	,	,	PUNCT
ejpam-3928	235	4	q	q	ADJ
ejpam-3928	235	5	}	}	PUNCT
ejpam-3928	235	6	〉	〉	NUM
ejpam-3928	235	7	.	.	PUNCT
ejpam-3928	236	1	thus	thus	ADV
ejpam-3928	236	2	,	,	PUNCT
ejpam-3928	236	3	by	by	ADP
ejpam-3928	236	4	lemma	lemma	PROPN
ejpam-3928	236	5	2	2	NUM
ejpam-3928	236	6	λ1	λ1	NOUN
ejpam-3928	236	7	(	(	PUNCT
ejpam-3928	236	8	〈	〈	PROPN
ejpam-3928	236	9	v	v	PROPN
ejpam-3928	236	10	(	(	PUNCT
ejpam-3928	236	11	g2	g2	PROPN
ejpam-3928	236	12	)	)	PUNCT
ejpam-3928	236	13	\	\	NOUN
ejpam-3928	237	1	{	{	PUNCT
ejpam-3928	237	2	p	p	X
ejpam-3928	237	3	,	,	PUNCT
ejpam-3928	237	4	q	q	ADJ
ejpam-3928	237	5	}	}	PUNCT
ejpam-3928	237	6	〉	〉	PROPN
ejpam-3928	237	7	)	)	PUNCT
ejpam-3928	237	8	>	>	X
ejpam-3928	238	1	λ1	λ1	PROPN
ejpam-3928	238	2	(	(	PUNCT
ejpam-3928	238	3	〈	〈	PROPN
ejpam-3928	238	4	v	v	ADJ
ejpam-3928	238	5	(	(	PUNCT
ejpam-3928	238	6	g1	g1	PROPN
ejpam-3928	238	7	)	)	PUNCT
ejpam-3928	238	8	\	\	NOUN
ejpam-3928	238	9	{	{	PUNCT
ejpam-3928	238	10	x	x	NOUN
ejpam-3928	238	11	,	,	PUNCT
ejpam-3928	238	12	y	y	PROPN
ejpam-3928	238	13	}	}	PUNCT
ejpam-3928	238	14	〉	〉	PROPN
ejpam-3928	238	15	)	)	PUNCT
ejpam-3928	238	16	.	.	PUNCT
ejpam-3928	239	1	since	since	SCONJ
ejpam-3928	239	2	k2	k2	PROPN
ejpam-3928	239	3	is	be	AUX
ejpam-3928	239	4	a	a	DET
ejpam-3928	239	5	proper	proper	ADJ
ejpam-3928	239	6	subset	subset	NOUN
ejpam-3928	239	7	of	of	ADP
ejpam-3928	239	8	〈	〈	PROPN
ejpam-3928	239	9	v	v	PROPN
ejpam-3928	239	10	(	(	PUNCT
ejpam-3928	239	11	g2	g2	PROPN
ejpam-3928	239	12	)	)	PUNCT
ejpam-3928	239	13	\	\	NOUN
ejpam-3928	240	1	{	{	PUNCT
ejpam-3928	240	2	p	p	X
ejpam-3928	240	3	,	,	PUNCT
ejpam-3928	240	4	q	q	ADJ
ejpam-3928	240	5	}	}	PUNCT
ejpam-3928	240	6	〉	〉	PROPN
ejpam-3928	240	7	,	,	PUNCT
ejpam-3928	240	8	then	then	ADV
ejpam-3928	240	9	λ1	λ1	PROPN
ejpam-3928	240	10	(	(	PUNCT
ejpam-3928	240	11	〈	〈	PROPN
ejpam-3928	240	12	v	v	PROPN
ejpam-3928	240	13	(	(	PUNCT
ejpam-3928	240	14	g2	g2	PROPN
ejpam-3928	240	15	)	)	PUNCT
ejpam-3928	240	16	\	\	NOUN
ejpam-3928	241	1	{	{	PUNCT
ejpam-3928	241	2	p	p	X
ejpam-3928	241	3	,	,	PUNCT
ejpam-3928	241	4	q	q	ADJ
ejpam-3928	241	5	}	}	PUNCT
ejpam-3928	241	6	〉	〉	NUM
ejpam-3928	241	7	)	)	PUNCT
ejpam-3928	241	8	>	>	X
ejpam-3928	242	1	1	1	X
ejpam-3928	242	2	.	.	PUNCT
ejpam-3928	243	1	hence	hence	ADV
ejpam-3928	243	2	,	,	PUNCT
ejpam-3928	243	3	spec	spec	PROPN
ejpam-3928	243	4	(	(	PUNCT
ejpam-3928	243	5	〈	〈	PROPN
ejpam-3928	243	6	a	a	PRON
ejpam-3928	243	7	〉	〉	NOUN
ejpam-3928	243	8	)	)	PUNCT
ejpam-3928	243	9	6=	6=	NUM
ejpam-3928	243	10	spec	spec	PROPN
ejpam-3928	243	11	(	(	PUNCT
ejpam-3928	243	12	〈	〈	PROPN
ejpam-3928	243	13	b	b	PROPN
ejpam-3928	243	14	〉	〉	PROPN
ejpam-3928	243	15	)	)	PUNCT
ejpam-3928	243	16	.	.	PUNCT
ejpam-3928	244	1	thus	thus	ADV
ejpam-3928	244	2	,	,	PUNCT
ejpam-3928	244	3	〈	〈	PROPN
ejpam-3928	244	4	a	a	DET
ejpam-3928	244	5	〉	〉	NOUN
ejpam-3928	244	6	and	and	CCONJ
ejpam-3928	244	7	〈	〈	PROPN
ejpam-3928	244	8	b	b	PROPN
ejpam-3928	244	9	〉	〉	PROPN
ejpam-3928	244	10	are	be	AUX
ejpam-3928	244	11	not	not	PART
ejpam-3928	244	12	isospectral	isospectral	ADJ
ejpam-3928	244	13	,	,	PUNCT
ejpam-3928	244	14	so	so	SCONJ
ejpam-3928	244	15	g	g	PROPN
ejpam-3928	244	16	is	be	AUX
ejpam-3928	244	17	not	not	PART
ejpam-3928	244	18	spectral	spectral	ADJ
ejpam-3928	244	19	-	-	PUNCT
ejpam-3928	244	20	equipartite	equipartite	ADJ
ejpam-3928	244	21	.	.	PUNCT
ejpam-3928	245	1	subcase	subcase	PROPN
ejpam-3928	245	2	2	2	NUM
ejpam-3928	245	3	.	.	PUNCT
ejpam-3928	246	1	both	both	PRON
ejpam-3928	246	2	g1	g1	PROPN
ejpam-3928	246	3	and	and	CCONJ
ejpam-3928	246	4	g2	g2	PROPN
ejpam-3928	246	5	are	be	AUX
ejpam-3928	246	6	complete	complete	ADJ
ejpam-3928	246	7	bipartite	bipartite	NOUN
ejpam-3928	246	8	graphs	graph	NOUN
ejpam-3928	246	9	.	.	PUNCT
ejpam-3928	247	1	if	if	SCONJ
ejpam-3928	247	2	both	both	DET
ejpam-3928	247	3	g1	g1	PROPN
ejpam-3928	247	4	and	and	CCONJ
ejpam-3928	247	5	g2	g2	PROPN
ejpam-3928	247	6	are	be	AUX
ejpam-3928	247	7	complete	complete	ADJ
ejpam-3928	247	8	bipartite	bipartite	NOUN
ejpam-3928	247	9	graphs	graph	NOUN
ejpam-3928	247	10	,	,	PUNCT
ejpam-3928	247	11	then	then	ADV
ejpam-3928	247	12	we	we	PRON
ejpam-3928	247	13	will	will	AUX
ejpam-3928	247	14	use	use	VERB
ejpam-3928	247	15	a	a	DET
ejpam-3928	247	16	different	different	ADJ
ejpam-3928	247	17	partitioning	partitioning	NOUN
ejpam-3928	247	18	of	of	ADP
ejpam-3928	247	19	the	the	DET
ejpam-3928	247	20	graph	graph	NOUN
ejpam-3928	247	21	g	g	NOUN
ejpam-3928	247	22	into	into	ADP
ejpam-3928	247	23	two	two	NUM
ejpam-3928	247	24	sets	set	NOUN
ejpam-3928	247	25	,	,	PUNCT
ejpam-3928	247	26	a	a	PRON
ejpam-3928	247	27	and	and	CCONJ
ejpam-3928	247	28	b	b	NOUN
ejpam-3928	247	29	,	,	PUNCT
ejpam-3928	247	30	with	with	ADP
ejpam-3928	247	31	n	n	PRON
ejpam-3928	247	32	vertices	vertex	NOUN
ejpam-3928	247	33	each	each	PRON
ejpam-3928	247	34	and	and	CCONJ
ejpam-3928	247	35	consider	consider	VERB
ejpam-3928	247	36	the	the	DET
ejpam-3928	247	37	following	follow	VERB
ejpam-3928	247	38	subsubcases	subsubcase	NOUN
ejpam-3928	247	39	:	:	PUNCT
ejpam-3928	247	40	subsubcase	subsubcase	VERB
ejpam-3928	247	41	1	1	NUM
ejpam-3928	247	42	.	.	PUNCT
ejpam-3928	248	1	n/2	n/2	PRON
ejpam-3928	248	2	is	be	AUX
ejpam-3928	248	3	even	even	ADV
ejpam-3928	248	4	.	.	PUNCT
ejpam-3928	249	1	if	if	SCONJ
ejpam-3928	249	2	n/2	n/2	PRON
ejpam-3928	249	3	is	be	AUX
ejpam-3928	249	4	even	even	ADV
ejpam-3928	249	5	,	,	PUNCT
ejpam-3928	249	6	then	then	ADV
ejpam-3928	249	7	we	we	PRON
ejpam-3928	249	8	will	will	AUX
ejpam-3928	249	9	partition	partition	VERB
ejpam-3928	249	10	v	v	ADP
ejpam-3928	249	11	(	(	PUNCT
ejpam-3928	249	12	g	g	NOUN
ejpam-3928	249	13	)	)	PUNCT
ejpam-3928	249	14	into	into	ADP
ejpam-3928	249	15	two	two	NUM
ejpam-3928	249	16	sets	set	NOUN
ejpam-3928	249	17	,	,	PUNCT
ejpam-3928	249	18	a	a	PRON
ejpam-3928	249	19	and	and	CCONJ
ejpam-3928	249	20	b	b	NOUN
ejpam-3928	249	21	,	,	PUNCT
ejpam-3928	249	22	with	with	ADP
ejpam-3928	249	23	n	n	PRON
ejpam-3928	249	24	vertices	vertice	VERB
ejpam-3928	249	25	each	each	DET
ejpam-3928	249	26	such	such	ADJ
ejpam-3928	249	27	that	that	SCONJ
ejpam-3928	249	28	〈	〈	PROPN
ejpam-3928	249	29	a	a	DET
ejpam-3928	249	30	〉	〉	NOUN
ejpam-3928	249	31	=	=	SYM
ejpam-3928	249	32	(	(	PUNCT
ejpam-3928	249	33	n	n	ADV
ejpam-3928	249	34	2	2	NUM
ejpam-3928	249	35	−	−	NUM
ejpam-3928	249	36	1	1	X
ejpam-3928	249	37	)	)	PUNCT
ejpam-3928	249	38	k1	k1	PROPN
ejpam-3928	249	39	∪	∪	ADP
ejpam-3928	249	40	kn	kn	PROPN
ejpam-3928	249	41	4	4	NUM
ejpam-3928	249	42	,	,	PUNCT
ejpam-3928	249	43	n+4	n+4	NUM
ejpam-3928	249	44	4	4	NUM
ejpam-3928	249	45	,	,	PUNCT
ejpam-3928	249	46	and	and	CCONJ
ejpam-3928	249	47	〈	〈	PROPN
ejpam-3928	249	48	b	b	PROPN
ejpam-3928	249	49	〉	〉	NOUN
ejpam-3928	249	50	=	=	SYM
ejpam-3928	249	51	k1,n	k1,n	PROPN
ejpam-3928	249	52	2	2	NUM
ejpam-3928	249	53	∪	∪	ADP
ejpam-3928	249	54	kn	kn	PROPN
ejpam-3928	249	55	4	4	NUM
ejpam-3928	249	56	,	,	PUNCT
ejpam-3928	249	57	n+4	n+4	NUM
ejpam-3928	249	58	4	4	NUM
ejpam-3928	249	59	.	.	PUNCT
ejpam-3928	250	1	thus	thus	ADV
ejpam-3928	250	2	,	,	PUNCT
ejpam-3928	250	3	by	by	ADP
ejpam-3928	250	4	lemma	lemma	PROPN
ejpam-3928	250	5	3	3	NUM
ejpam-3928	250	6	and	and	CCONJ
ejpam-3928	250	7	lemma	lemma	PROPN
ejpam-3928	250	8	4	4	NUM
ejpam-3928	250	9	,	,	PUNCT
ejpam-3928	250	10	we	we	PRON
ejpam-3928	250	11	have	have	VERB
ejpam-3928	250	12	spec	spec	PROPN
ejpam-3928	250	13	〈	〈	PROPN
ejpam-3928	250	14	(	(	PUNCT
ejpam-3928	250	15	a	a	NOUN
ejpam-3928	250	16	)	)	PUNCT
ejpam-3928	250	17	〉	〉	NOUN
ejpam-3928	250	18	=	=	SYM
ejpam-3928	250	19	{	{	PUNCT
ejpam-3928	250	20	0	0	NUM
ejpam-3928	250	21	n	n	NUM
ejpam-3928	250	22	2	2	NUM
ejpam-3928	250	23	−1	−1	NOUN
ejpam-3928	250	24	}	}	PUNCT
ejpam-3928	250	25	∪	∪	X
ejpam-3928	250	26	{	{	PUNCT
ejpam-3928	250	27	±	±	NOUN
ejpam-3928	250	28	√	√	PROPN
ejpam-3928	250	29	n	n	PRON
ejpam-3928	250	30	4	4	NUM
ejpam-3928	250	31	(	(	PUNCT
ejpam-3928	250	32	n	n	ADV
ejpam-3928	250	33	4	4	NUM
ejpam-3928	250	34	+	+	SYM
ejpam-3928	250	35	1	1	NUM
ejpam-3928	250	36	)	)	PUNCT
ejpam-3928	250	37	,	,	PUNCT
ejpam-3928	250	38	0	0	NUM
ejpam-3928	250	39	n	n	SYM
ejpam-3928	250	40	2	2	NUM
ejpam-3928	250	41	−1	−1	NOUN
ejpam-3928	250	42	}	}	PUNCT
ejpam-3928	250	43	and	and	CCONJ
ejpam-3928	250	44	spec	spec	PROPN
ejpam-3928	250	45	(	(	PUNCT
ejpam-3928	250	46	〈	〈	PROPN
ejpam-3928	250	47	b	b	PROPN
ejpam-3928	250	48	〉	〉	NUM
ejpam-3928	250	49	)	)	PUNCT
ejpam-3928	251	1	=	=	NOUN
ejpam-3928	251	2	{	{	PUNCT
ejpam-3928	251	3	±	±	NUM
ejpam-3928	251	4	√	√	PROPN
ejpam-3928	251	5	n	n	PRON
ejpam-3928	251	6	2	2	NUM
ejpam-3928	251	7	,	,	PUNCT
ejpam-3928	251	8	0	0	NUM
ejpam-3928	251	9	n	n	CCONJ
ejpam-3928	251	10	2	2	NUM
ejpam-3928	251	11	−1	−1	NOUN
ejpam-3928	251	12	}	}	PUNCT
ejpam-3928	251	13	∪	∪	X
ejpam-3928	251	14	{	{	PUNCT
ejpam-3928	251	15	±	±	NOUN
ejpam-3928	251	16	√	√	PROPN
ejpam-3928	251	17	n	n	PRON
ejpam-3928	251	18	4	4	NUM
ejpam-3928	251	19	(	(	PUNCT
ejpam-3928	251	20	n	n	ADV
ejpam-3928	251	21	4	4	NUM
ejpam-3928	251	22	−	−	NOUN
ejpam-3928	251	23	1	1	NUM
ejpam-3928	251	24	)	)	PUNCT
ejpam-3928	251	25	,	,	PUNCT
ejpam-3928	251	26	0	0	NUM
ejpam-3928	251	27	n	n	CCONJ
ejpam-3928	251	28	2	2	NUM
ejpam-3928	251	29	−3	−3	NOUN
ejpam-3928	251	30	}	}	PUNCT
ejpam-3928	251	31	.	.	PUNCT
ejpam-3928	252	1	hence	hence	ADV
ejpam-3928	252	2	,	,	PUNCT
ejpam-3928	252	3	spec	spec	PROPN
ejpam-3928	252	4	(	(	PUNCT
ejpam-3928	252	5	〈	〈	PROPN
ejpam-3928	252	6	a	a	PRON
ejpam-3928	252	7	〉	〉	NOUN
ejpam-3928	252	8	)	)	PUNCT
ejpam-3928	252	9	6=	6=	NUM
ejpam-3928	252	10	spec	spec	PROPN
ejpam-3928	252	11	(	(	PUNCT
ejpam-3928	252	12	〈	〈	PROPN
ejpam-3928	252	13	b	b	PROPN
ejpam-3928	252	14	〉	〉	PROPN
ejpam-3928	252	15	)	)	PUNCT
ejpam-3928	252	16	.	.	PUNCT
ejpam-3928	253	1	thus	thus	ADV
ejpam-3928	253	2	,	,	PUNCT
ejpam-3928	253	3	〈	〈	PROPN
ejpam-3928	253	4	a	a	DET
ejpam-3928	253	5	〉	〉	NOUN
ejpam-3928	253	6	and	and	CCONJ
ejpam-3928	253	7	〈	〈	PROPN
ejpam-3928	253	8	b	b	PROPN
ejpam-3928	253	9	〉	〉	PROPN
ejpam-3928	253	10	are	be	AUX
ejpam-3928	253	11	not	not	PART
ejpam-3928	253	12	isospectral	isospectral	ADJ
ejpam-3928	253	13	,	,	PUNCT
ejpam-3928	253	14	and	and	CCONJ
ejpam-3928	253	15	so	so	ADV
ejpam-3928	253	16	g	g	PROPN
ejpam-3928	253	17	is	be	AUX
ejpam-3928	253	18	not	not	PART
ejpam-3928	253	19	spectral	spectral	ADJ
ejpam-3928	253	20	-	-	PUNCT
ejpam-3928	253	21	equipartite	equipartite	ADJ
ejpam-3928	253	22	.	.	PUNCT
ejpam-3928	254	1	subsubcase	subsubcase	PROPN
ejpam-3928	254	2	2	2	NUM
ejpam-3928	254	3	.	.	X
ejpam-3928	255	1	n/2	n/2	PRON
ejpam-3928	255	2	is	be	AUX
ejpam-3928	255	3	odd	odd	ADJ
ejpam-3928	255	4	.	.	PUNCT
ejpam-3928	256	1	if	if	SCONJ
ejpam-3928	256	2	n/2	n/2	PRON
ejpam-3928	256	3	is	be	AUX
ejpam-3928	256	4	odd	odd	ADJ
ejpam-3928	256	5	,	,	PUNCT
ejpam-3928	256	6	then	then	ADV
ejpam-3928	256	7	we	we	PRON
ejpam-3928	256	8	will	will	AUX
ejpam-3928	256	9	partition	partition	VERB
ejpam-3928	256	10	v	v	ADP
ejpam-3928	256	11	(	(	PUNCT
ejpam-3928	256	12	g	g	NOUN
ejpam-3928	256	13	)	)	PUNCT
ejpam-3928	256	14	into	into	ADP
ejpam-3928	256	15	two	two	NUM
ejpam-3928	256	16	sets	set	NOUN
ejpam-3928	256	17	,	,	PUNCT
ejpam-3928	256	18	a	a	PRON
ejpam-3928	256	19	and	and	CCONJ
ejpam-3928	256	20	b	b	NOUN
ejpam-3928	256	21	,	,	PUNCT
ejpam-3928	256	22	with	with	ADP
ejpam-3928	256	23	n	n	PRON
ejpam-3928	256	24	vertices	vertice	VERB
ejpam-3928	256	25	each	each	DET
ejpam-3928	256	26	such	such	ADJ
ejpam-3928	256	27	that	that	SCONJ
ejpam-3928	256	28	〈	〈	PROPN
ejpam-3928	256	29	a	a	DET
ejpam-3928	256	30	〉	〉	NOUN
ejpam-3928	256	31	=	=	SYM
ejpam-3928	256	32	(	(	PUNCT
ejpam-3928	256	33	n	n	ADV
ejpam-3928	256	34	2	2	NUM
ejpam-3928	256	35	−	−	NUM
ejpam-3928	256	36	1	1	NUM
ejpam-3928	256	37	)	)	PUNCT
ejpam-3928	256	38	k1	k1	NOUN
ejpam-3928	256	39	∪kn+2	∪kn+2	SYM
ejpam-3928	256	40	4	4	NUM
ejpam-3928	256	41	,	,	PUNCT
ejpam-3928	256	42	n+2	n+2	PRON
ejpam-3928	256	43	4	4	NUM
ejpam-3928	256	44	,	,	PUNCT
ejpam-3928	256	45	and	and	CCONJ
ejpam-3928	256	46	〈	〈	PROPN
ejpam-3928	256	47	b	b	PROPN
ejpam-3928	256	48	〉	〉	NOUN
ejpam-3928	256	49	=	=	SYM
ejpam-3928	256	50	k1,n	k1,n	PROPN
ejpam-3928	256	51	2	2	NUM
ejpam-3928	256	52	∪kn−2	∪kn−2	ADP
ejpam-3928	256	53	4	4	NUM
ejpam-3928	256	54	,	,	PUNCT
ejpam-3928	256	55	n−2	n−2	PROPN
ejpam-3928	256	56	4	4	NUM
ejpam-3928	256	57	.	.	PUNCT
ejpam-3928	257	1	thus	thus	ADV
ejpam-3928	257	2	,	,	PUNCT
ejpam-3928	257	3	by	by	ADP
ejpam-3928	257	4	lemma	lemma	PROPN
ejpam-3928	257	5	3	3	NUM
ejpam-3928	257	6	,	,	PUNCT
ejpam-3928	257	7	lemma	lemma	PROPN
ejpam-3928	257	8	4	4	NUM
ejpam-3928	257	9	,	,	PUNCT
ejpam-3928	257	10	and	and	CCONJ
ejpam-3928	257	11	lemma	lemma	PROPN
ejpam-3928	257	12	5	5	NUM
ejpam-3928	257	13	,	,	PUNCT
ejpam-3928	257	14	spec	spec	PROPN
ejpam-3928	257	15	〈	〈	PROPN
ejpam-3928	257	16	(	(	PUNCT
ejpam-3928	257	17	a	a	NOUN
ejpam-3928	257	18	)	)	PUNCT
ejpam-3928	257	19	〉	〉	NOUN
ejpam-3928	257	20	=	=	SYM
ejpam-3928	257	21	{	{	PUNCT
ejpam-3928	257	22	0	0	NUM
ejpam-3928	257	23	n	n	NUM
ejpam-3928	257	24	2	2	NUM
ejpam-3928	257	25	−1	−1	NOUN
ejpam-3928	257	26	}	}	PUNCT
ejpam-3928	257	27	∪	∪	ADJ
ejpam-3928	257	28	{	{	PUNCT
ejpam-3928	257	29	±n+2	±n+2	NOUN
ejpam-3928	257	30	4	4	NUM
ejpam-3928	257	31	,	,	PUNCT
ejpam-3928	257	32	0	0	NUM
ejpam-3928	257	33	n	n	CCONJ
ejpam-3928	257	34	2	2	NUM
ejpam-3928	257	35	−1	−1	NOUN
ejpam-3928	257	36	}	}	PUNCT
ejpam-3928	257	37	and	and	CCONJ
ejpam-3928	257	38	spec	spec	PROPN
ejpam-3928	257	39	〈	〈	PROPN
ejpam-3928	257	40	(	(	PUNCT
ejpam-3928	257	41	b	b	NOUN
ejpam-3928	257	42	)	)	PUNCT
ejpam-3928	257	43	〉	〉	NOUN
ejpam-3928	257	44	=	=	NOUN
ejpam-3928	257	45	{	{	PUNCT
ejpam-3928	257	46	±	±	NUM
ejpam-3928	257	47	√	√	PROPN
ejpam-3928	257	48	n	n	PRON
ejpam-3928	257	49	2	2	NUM
ejpam-3928	257	50	,	,	PUNCT
ejpam-3928	257	51	0	0	NUM
ejpam-3928	257	52	n	n	CCONJ
ejpam-3928	257	53	2	2	NUM
ejpam-3928	257	54	−1	−1	NOUN
ejpam-3928	257	55	}	}	PUNCT
ejpam-3928	257	56	∪	∪	ADJ
ejpam-3928	257	57	{	{	PUNCT
ejpam-3928	257	58	±n−2	±n−2	ADP
ejpam-3928	257	59	4	4	NUM
ejpam-3928	257	60	,	,	PUNCT
ejpam-3928	257	61	0	0	NUM
ejpam-3928	257	62	n	n	CCONJ
ejpam-3928	257	63	2	2	NUM
ejpam-3928	257	64	−3	−3	NOUN
ejpam-3928	257	65	}	}	PUNCT
ejpam-3928	257	66	.	.	PUNCT
ejpam-3928	258	1	hence	hence	ADV
ejpam-3928	258	2	,	,	PUNCT
ejpam-3928	258	3	spec	spec	PROPN
ejpam-3928	258	4	(	(	PUNCT
ejpam-3928	258	5	〈	〈	PROPN
ejpam-3928	258	6	a	a	PRON
ejpam-3928	258	7	〉	〉	NOUN
ejpam-3928	258	8	)	)	PUNCT
ejpam-3928	258	9	6=	6=	NUM
ejpam-3928	258	10	spec	spec	PROPN
ejpam-3928	258	11	(	(	PUNCT
ejpam-3928	258	12	〈	〈	PROPN
ejpam-3928	258	13	b	b	PROPN
ejpam-3928	258	14	〉	〉	PROPN
ejpam-3928	258	15	)	)	PUNCT
ejpam-3928	258	16	.	.	PUNCT
ejpam-3928	259	1	thus	thus	ADV
ejpam-3928	259	2	,	,	PUNCT
ejpam-3928	259	3	〈	〈	PROPN
ejpam-3928	259	4	a	a	DET
ejpam-3928	259	5	〉	〉	NOUN
ejpam-3928	259	6	and	and	CCONJ
ejpam-3928	259	7	〈	〈	PROPN
ejpam-3928	259	8	b	b	PROPN
ejpam-3928	259	9	〉	〉	PROPN
ejpam-3928	259	10	are	be	AUX
ejpam-3928	259	11	not	not	PART
ejpam-3928	259	12	isospectral	isospectral	ADJ
ejpam-3928	259	13	,	,	PUNCT
ejpam-3928	259	14	and	and	CCONJ
ejpam-3928	259	15	so	so	ADV
ejpam-3928	259	16	g	g	PROPN
ejpam-3928	259	17	is	be	AUX
ejpam-3928	259	18	not	not	PART
ejpam-3928	259	19	spectral	spectral	ADJ
ejpam-3928	259	20	-	-	PUNCT
ejpam-3928	259	21	equipartite	equipartite	ADJ
ejpam-3928	259	22	.	.	PUNCT
ejpam-3928	260	1	by	by	ADP
ejpam-3928	260	2	cases	case	NOUN
ejpam-3928	260	3	1,2	1,2	NUM
ejpam-3928	260	4	,	,	PUNCT
ejpam-3928	260	5	and	and	CCONJ
ejpam-3928	260	6	3	3	NUM
ejpam-3928	260	7	,	,	PUNCT
ejpam-3928	260	8	we	we	PRON
ejpam-3928	260	9	have	have	AUX
ejpam-3928	260	10	shown	show	VERB
ejpam-3928	260	11	that	that	SCONJ
ejpam-3928	260	12	if	if	SCONJ
ejpam-3928	260	13	g1	g1	PROPN
ejpam-3928	260	14	is	be	AUX
ejpam-3928	260	15	neither	neither	CCONJ
ejpam-3928	260	16	a	a	DET
ejpam-3928	260	17	complete	complete	ADJ
ejpam-3928	260	18	graph	graph	NOUN
ejpam-3928	260	19	nor	nor	CCONJ
ejpam-3928	260	20	a	a	DET
ejpam-3928	260	21	cycle	cycle	NOUN
ejpam-3928	260	22	,	,	PUNCT
ejpam-3928	260	23	then	then	ADV
ejpam-3928	260	24	g	g	PROPN
ejpam-3928	260	25	will	will	AUX
ejpam-3928	260	26	not	not	PART
ejpam-3928	260	27	be	be	AUX
ejpam-3928	260	28	a	a	DET
ejpam-3928	260	29	spectral	spectral	ADJ
ejpam-3928	260	30	-	-	PUNCT
ejpam-3928	260	31	equipartite	equipartite	ADJ
ejpam-3928	260	32	graph	graph	NOUN
ejpam-3928	260	33	.	.	PUNCT
ejpam-3928	261	1	thus	thus	ADV
ejpam-3928	261	2	,	,	PUNCT
ejpam-3928	261	3	g1	g1	PROPN
ejpam-3928	261	4	must	must	AUX
ejpam-3928	261	5	either	either	CCONJ
ejpam-3928	261	6	be	be	AUX
ejpam-3928	261	7	a	a	DET
ejpam-3928	261	8	complete	complete	ADJ
ejpam-3928	261	9	a.	a.	NOUN
ejpam-3928	261	10	yurfo	yurfo	NOUN
ejpam-3928	261	11	,	,	PUNCT
ejpam-3928	261	12	j.	j.	PROPN
ejpam-3928	261	13	adanza	adanza	PROPN
ejpam-3928	261	14	,	,	PUNCT
ejpam-3928	261	15	m.	m.	PROPN
ejpam-3928	261	16	baldado	baldado	PROPN
ejpam-3928	261	17	jr	jr	PROPN
ejpam-3928	261	18	.	.	PROPN
ejpam-3928	261	19	/	/	SYM
ejpam-3928	261	20	eur	eur	PROPN
ejpam-3928	261	21	.	.	PUNCT
ejpam-3928	262	1	j.	j.	PROPN
ejpam-3928	262	2	pure	pure	PROPN
ejpam-3928	262	3	appl	appl	PROPN
ejpam-3928	262	4	.	.	PROPN
ejpam-3928	262	5	math	math	PROPN
ejpam-3928	262	6	,	,	PUNCT
ejpam-3928	262	7	14	14	NUM
ejpam-3928	262	8	(	(	PUNCT
ejpam-3928	262	9	2	2	NUM
ejpam-3928	262	10	)	)	PUNCT
ejpam-3928	262	11	(	(	PUNCT
ejpam-3928	262	12	2021	2021	NUM
ejpam-3928	262	13	)	)	PUNCT
ejpam-3928	262	14	,	,	PUNCT
ejpam-3928	262	15	358	358	NUM
ejpam-3928	262	16	-	-	SYM
ejpam-3928	262	17	365	365	NUM
ejpam-3928	262	18	364	364	NUM
ejpam-3928	262	19	graph	graph	NOUN
ejpam-3928	262	20	or	or	CCONJ
ejpam-3928	262	21	a	a	DET
ejpam-3928	262	22	cycle	cycle	NOUN
ejpam-3928	262	23	.	.	PUNCT
ejpam-3928	263	1	if	if	SCONJ
ejpam-3928	263	2	g1	g1	PROPN
ejpam-3928	263	3	is	be	AUX
ejpam-3928	263	4	complete	complete	ADJ
ejpam-3928	263	5	,	,	PUNCT
ejpam-3928	263	6	then	then	ADV
ejpam-3928	263	7	g2	g2	PROPN
ejpam-3928	263	8	having	have	VERB
ejpam-3928	263	9	the	the	DET
ejpam-3928	263	10	same	same	ADJ
ejpam-3928	263	11	order	order	NOUN
ejpam-3928	263	12	and	and	CCONJ
ejpam-3928	263	13	size	size	NOUN
ejpam-3928	263	14	as	as	SCONJ
ejpam-3928	263	15	g1	g1	PROPN
ejpam-3928	263	16	is	be	AUX
ejpam-3928	263	17	also	also	ADV
ejpam-3928	263	18	complete	complete	ADJ
ejpam-3928	263	19	.	.	PUNCT
ejpam-3928	264	1	whence	whence	NOUN
ejpam-3928	264	2	,	,	PUNCT
ejpam-3928	264	3	g	g	NOUN
ejpam-3928	264	4	=	=	PUNCT
ejpam-3928	264	5	2kn	2kn	ADV
ejpam-3928	264	6	.	.	PUNCT
ejpam-3928	265	1	if	if	SCONJ
ejpam-3928	265	2	g1	g1	PROPN
ejpam-3928	265	3	is	be	AUX
ejpam-3928	265	4	a	a	DET
ejpam-3928	265	5	cycle	cycle	NOUN
ejpam-3928	265	6	cn	cn	PROPN
ejpam-3928	265	7	,	,	PUNCT
ejpam-3928	265	8	then	then	ADV
ejpam-3928	265	9	k	k	PROPN
ejpam-3928	265	10	=	=	SYM
ejpam-3928	265	11	2	2	NUM
ejpam-3928	265	12	and	and	CCONJ
ejpam-3928	265	13	g2	g2	PROPN
ejpam-3928	265	14	is	be	AUX
ejpam-3928	265	15	also	also	ADV
ejpam-3928	265	16	cn	cn	PROPN
ejpam-3928	265	17	.	.	PROPN
ejpam-3928	265	18	suppose	suppose	VERB
ejpam-3928	265	19	n	n	PROPN
ejpam-3928	265	20	>	>	X
ejpam-3928	265	21	4	4	X
ejpam-3928	265	22	.	.	PUNCT
ejpam-3928	266	1	then	then	ADV
ejpam-3928	266	2	,	,	PUNCT
ejpam-3928	266	3	we	we	PRON
ejpam-3928	266	4	choose	choose	VERB
ejpam-3928	266	5	two	two	NUM
ejpam-3928	266	6	non	non	ADJ
ejpam-3928	266	7	-	-	ADJ
ejpam-3928	266	8	adjacent	adjacent	ADJ
ejpam-3928	266	9	vertices	vertex	NOUN
ejpam-3928	266	10	,	,	PUNCT
ejpam-3928	266	11	a	a	PRON
ejpam-3928	266	12	and	and	CCONJ
ejpam-3928	266	13	b	b	NOUN
ejpam-3928	266	14	,	,	PUNCT
ejpam-3928	266	15	from	from	ADP
ejpam-3928	266	16	g1	g1	PROPN
ejpam-3928	266	17	that	that	PRON
ejpam-3928	266	18	have	have	VERB
ejpam-3928	266	19	a	a	DET
ejpam-3928	266	20	common	common	ADJ
ejpam-3928	266	21	neighbor	neighbor	NOUN
ejpam-3928	266	22	and	and	CCONJ
ejpam-3928	266	23	two	two	NUM
ejpam-3928	266	24	adjacent	adjacent	ADJ
ejpam-3928	266	25	vertices	vertex	NOUN
ejpam-3928	266	26	,	,	PUNCT
ejpam-3928	266	27	c	c	NOUN
ejpam-3928	266	28	and	and	CCONJ
ejpam-3928	266	29	d	d	NOUN
ejpam-3928	266	30	,	,	PUNCT
ejpam-3928	266	31	from	from	ADP
ejpam-3928	266	32	g2	g2	PROPN
ejpam-3928	266	33	.	.	PUNCT
ejpam-3928	267	1	now	now	ADV
ejpam-3928	267	2	,	,	PUNCT
ejpam-3928	267	3	we	we	PRON
ejpam-3928	267	4	partition	partition	VERB
ejpam-3928	267	5	g	g	NOUN
ejpam-3928	267	6	into	into	ADP
ejpam-3928	267	7	two	two	NUM
ejpam-3928	267	8	sets	set	NOUN
ejpam-3928	267	9	,	,	PUNCT
ejpam-3928	267	10	a	a	PRON
ejpam-3928	267	11	and	and	CCONJ
ejpam-3928	267	12	b	b	NOUN
ejpam-3928	267	13	,	,	PUNCT
ejpam-3928	267	14	with	with	ADP
ejpam-3928	267	15	n	n	PRON
ejpam-3928	267	16	vertices	vertice	VERB
ejpam-3928	267	17	each	each	DET
ejpam-3928	267	18	such	such	ADJ
ejpam-3928	267	19	that	that	SCONJ
ejpam-3928	267	20	〈	〈	PROPN
ejpam-3928	267	21	a	a	DET
ejpam-3928	267	22	〉	〉	NOUN
ejpam-3928	268	1	=	=	SYM
ejpam-3928	268	2	〈	〈	PROPN
ejpam-3928	268	3	v	v	X
ejpam-3928	268	4	(	(	PUNCT
ejpam-3928	268	5	g2	g2	PROPN
ejpam-3928	268	6	)	)	PUNCT
ejpam-3928	268	7	\	\	NOUN
ejpam-3928	268	8	{	{	PUNCT
ejpam-3928	268	9	c	c	X
ejpam-3928	268	10	,	,	PUNCT
ejpam-3928	268	11	d	d	NOUN
ejpam-3928	268	12	}	}	PUNCT
ejpam-3928	268	13	〉	〉	PROPN
ejpam-3928	268	14	∪	∪	NOUN
ejpam-3928	268	15	〈	〈	PROPN
ejpam-3928	268	16	{	{	PUNCT
ejpam-3928	268	17	a	a	PRON
ejpam-3928	268	18	,	,	PUNCT
ejpam-3928	268	19	b	b	NOUN
ejpam-3928	268	20	}	}	PUNCT
ejpam-3928	268	21	〉	〉	PROPN
ejpam-3928	268	22	and	and	CCONJ
ejpam-3928	268	23	〈	〈	PROPN
ejpam-3928	268	24	b	b	PROPN
ejpam-3928	268	25	〉	〉	PROPN
ejpam-3928	268	26	=	=	SYM
ejpam-3928	269	1	〈	〈	PROPN
ejpam-3928	269	2	v	v	X
ejpam-3928	269	3	(	(	PUNCT
ejpam-3928	269	4	g1	g1	PROPN
ejpam-3928	269	5	)	)	PUNCT
ejpam-3928	269	6	\	\	NOUN
ejpam-3928	269	7	{	{	PUNCT
ejpam-3928	269	8	a	a	PROPN
ejpam-3928	269	9	,	,	PUNCT
ejpam-3928	269	10	b	b	NOUN
ejpam-3928	269	11	}	}	PUNCT
ejpam-3928	269	12	〉	〉	PROPN
ejpam-3928	269	13	∪	∪	NOUN
ejpam-3928	269	14	〈	〈	PROPN
ejpam-3928	269	15	{	{	PUNCT
ejpam-3928	269	16	c	c	NOUN
ejpam-3928	269	17	,	,	PUNCT
ejpam-3928	269	18	d	d	NOUN
ejpam-3928	269	19	}	}	PUNCT
ejpam-3928	269	20	〉	〉	PROPN
ejpam-3928	269	21	.	.	PUNCT
ejpam-3928	270	1	then	then	ADV
ejpam-3928	270	2	〈	〈	PROPN
ejpam-3928	270	3	a	a	PRON
ejpam-3928	270	4	〉	〉	NOUN
ejpam-3928	270	5	=	=	SYM
ejpam-3928	270	6	pn−2	pn−2	PROPN
ejpam-3928	270	7	∪k1	∪k1	ADV
ejpam-3928	270	8	∪k1	∪k1	ADV
ejpam-3928	271	1	and	and	CCONJ
ejpam-3928	271	2	〈	〈	PROPN
ejpam-3928	271	3	b	b	PROPN
ejpam-3928	271	4	〉	〉	PROPN
ejpam-3928	271	5	=	=	PUNCT
ejpam-3928	271	6	pn−3	pn−3	VERB
ejpam-3928	271	7	∪k1	∪k1	ADV
ejpam-3928	271	8	∪	∪	ADJ
ejpam-3928	271	9	p2	p2	NOUN
ejpam-3928	271	10	.	.	PUNCT
ejpam-3928	272	1	clearly	clearly	ADV
ejpam-3928	272	2	,	,	PUNCT
ejpam-3928	272	3	pn−3	pn−3	ADJ
ejpam-3928	272	4	,	,	PUNCT
ejpam-3928	272	5	p2	p2	NOUN
ejpam-3928	272	6	,	,	PUNCT
ejpam-3928	272	7	and	and	CCONJ
ejpam-3928	272	8	k1	k1	NOUN
ejpam-3928	272	9	are	be	AUX
ejpam-3928	272	10	proper	proper	ADJ
ejpam-3928	272	11	subgraphs	subgraph	NOUN
ejpam-3928	272	12	of	of	ADP
ejpam-3928	272	13	pn−2	pn−2	PROPN
ejpam-3928	272	14	.	.	PUNCT
ejpam-3928	273	1	by	by	ADP
ejpam-3928	273	2	lemma	lemma	PROPN
ejpam-3928	273	3	2	2	NUM
ejpam-3928	273	4	,	,	PUNCT
ejpam-3928	273	5	λ1	λ1	PROPN
ejpam-3928	273	6	(	(	PUNCT
ejpam-3928	273	7	pn−2	pn−2	PROPN
ejpam-3928	273	8	)	)	PUNCT
ejpam-3928	273	9	>	>	X
ejpam-3928	274	1	λ1	λ1	PROPN
ejpam-3928	274	2	(	(	PUNCT
ejpam-3928	274	3	pn−3	pn−3	PROPN
ejpam-3928	274	4	)	)	PUNCT
ejpam-3928	274	5	>	>	X
ejpam-3928	275	1	λ1	λ1	PROPN
ejpam-3928	275	2	(	(	PUNCT
ejpam-3928	275	3	p2	p2	PROPN
ejpam-3928	275	4	)	)	PUNCT
ejpam-3928	275	5	>	>	X
ejpam-3928	275	6	0	0	X
ejpam-3928	275	7	.	.	PUNCT
ejpam-3928	276	1	hence	hence	ADV
ejpam-3928	276	2	,	,	PUNCT
ejpam-3928	276	3	by	by	ADP
ejpam-3928	276	4	lemma	lemma	PROPN
ejpam-3928	276	5	3	3	NUM
ejpam-3928	276	6	,	,	PUNCT
ejpam-3928	276	7	spec	spec	PROPN
ejpam-3928	276	8	(	(	PUNCT
ejpam-3928	276	9	〈	〈	PROPN
ejpam-3928	276	10	a	a	PRON
ejpam-3928	276	11	〉	〉	NOUN
ejpam-3928	276	12	)	)	PUNCT
ejpam-3928	276	13	6=	6=	NUM
ejpam-3928	276	14	spec	spec	PROPN
ejpam-3928	276	15	(	(	PUNCT
ejpam-3928	276	16	〈	〈	PROPN
ejpam-3928	276	17	b	b	PROPN
ejpam-3928	276	18	〉	〉	PROPN
ejpam-3928	276	19	)	)	PUNCT
ejpam-3928	276	20	.	.	PUNCT
ejpam-3928	277	1	therefore	therefore	ADV
ejpam-3928	277	2	,	,	PUNCT
ejpam-3928	277	3	n	n	ADV
ejpam-3928	277	4	≤	≤	ADV
ejpam-3928	277	5	4	4	NUM
ejpam-3928	277	6	.	.	PUNCT
ejpam-3928	277	7	for	for	ADP
ejpam-3928	277	8	n	n	NOUN
ejpam-3928	277	9	=	=	SYM
ejpam-3928	277	10	1	1	NUM
ejpam-3928	277	11	,	,	PUNCT
ejpam-3928	277	12	2	2	NUM
ejpam-3928	277	13	or	or	CCONJ
ejpam-3928	277	14	3	3	NUM
ejpam-3928	277	15	,	,	PUNCT
ejpam-3928	277	16	we	we	PRON
ejpam-3928	277	17	will	will	AUX
ejpam-3928	277	18	have	have	VERB
ejpam-3928	277	19	k1	k1	NOUN
ejpam-3928	277	20	,	,	PUNCT
ejpam-3928	277	21	k2	k2	NOUN
ejpam-3928	277	22	,	,	PUNCT
ejpam-3928	277	23	and	and	CCONJ
ejpam-3928	277	24	k3	k3	PROPN
ejpam-3928	277	25	,	,	PUNCT
ejpam-3928	277	26	respectively	respectively	ADV
ejpam-3928	277	27	,	,	PUNCT
ejpam-3928	277	28	and	and	CCONJ
ejpam-3928	277	29	for	for	ADP
ejpam-3928	277	30	n	n	NOUN
ejpam-3928	277	31	=	=	SYM
ejpam-3928	277	32	4	4	NUM
ejpam-3928	277	33	,	,	PUNCT
ejpam-3928	277	34	we	we	PRON
ejpam-3928	277	35	have	have	VERB
ejpam-3928	277	36	c4	c4	NOUN
ejpam-3928	277	37	.	.	PUNCT
ejpam-3928	278	1	thus	thus	ADV
ejpam-3928	278	2	,	,	PUNCT
ejpam-3928	278	3	we	we	PRON
ejpam-3928	278	4	have	have	VERB
ejpam-3928	278	5	g	g	NOUN
ejpam-3928	278	6	=	=	SYM
ejpam-3928	278	7	2k1	2k1	NUM
ejpam-3928	278	8	,	,	PUNCT
ejpam-3928	278	9	2k2	2k2	NUM
ejpam-3928	278	10	,	,	PUNCT
ejpam-3928	278	11	2k3	2k3	NUM
ejpam-3928	278	12	,	,	PUNCT
ejpam-3928	278	13	and	and	CCONJ
ejpam-3928	278	14	2c4	2c4	NUM
ejpam-3928	278	15	.	.	PUNCT
ejpam-3928	279	1	therefore	therefore	ADV
ejpam-3928	279	2	,	,	PUNCT
ejpam-3928	279	3	if	if	SCONJ
ejpam-3928	279	4	g	g	PROPN
ejpam-3928	279	5	is	be	AUX
ejpam-3928	279	6	a	a	DET
ejpam-3928	279	7	disconnected	disconnected	ADJ
ejpam-3928	279	8	k	k	ADJ
ejpam-3928	279	9	-	-	ADJ
ejpam-3928	279	10	regular	regular	ADJ
ejpam-3928	279	11	spectral	spectral	ADJ
ejpam-3928	279	12	-	-	PUNCT
ejpam-3928	279	13	equipartite	equipartite	ADJ
ejpam-3928	279	14	graph	graph	NOUN
ejpam-3928	279	15	of	of	ADP
ejpam-3928	279	16	order	order	NOUN
ejpam-3928	279	17	2n	2n	NUM
ejpam-3928	279	18	with	with	ADP
ejpam-3928	279	19	k	k	PROPN
ejpam-3928	279	20	>	>	X
ejpam-3928	279	21	1	1	NUM
ejpam-3928	279	22	,	,	PUNCT
ejpam-3928	279	23	then	then	ADV
ejpam-3928	279	24	g	g	PROPN
ejpam-3928	279	25	=	=	PUNCT
ejpam-3928	279	26	2kn	2kn	ADJ
ejpam-3928	279	27	or	or	CCONJ
ejpam-3928	279	28	g	g	NOUN
ejpam-3928	279	29	=	=	SYM
ejpam-3928	279	30	2c4	2c4	NUM
ejpam-3928	279	31	.	.	PUNCT
ejpam-3928	279	32	theorem	theorem	VERB
ejpam-3928	279	33	9	9	NUM
ejpam-3928	279	34	.	.	PUNCT
ejpam-3928	280	1	let	let	VERB
ejpam-3928	280	2	g	g	PRON
ejpam-3928	280	3	be	be	AUX
ejpam-3928	280	4	a	a	DET
ejpam-3928	280	5	disconnected	disconnected	ADJ
ejpam-3928	280	6	graph	graph	NOUN
ejpam-3928	280	7	of	of	ADP
ejpam-3928	280	8	order	order	NOUN
ejpam-3928	280	9	2n	2n	NUM
ejpam-3928	280	10	.	.	PUNCT
ejpam-3928	281	1	g	g	PROPN
ejpam-3928	281	2	is	be	AUX
ejpam-3928	281	3	spectral	spectral	ADJ
ejpam-3928	281	4	-	-	PUNCT
ejpam-3928	281	5	equipartite	equipartite	ADJ
ejpam-3928	281	6	if	if	SCONJ
ejpam-3928	282	1	and	and	CCONJ
ejpam-3928	282	2	only	only	ADV
ejpam-3928	282	3	if	if	SCONJ
ejpam-3928	282	4	it	it	PRON
ejpam-3928	282	5	is	be	AUX
ejpam-3928	282	6	one	one	NUM
ejpam-3928	282	7	of	of	ADP
ejpam-3928	282	8	the	the	DET
ejpam-3928	282	9	following	follow	VERB
ejpam-3928	282	10	graphs	graph	NOUN
ejpam-3928	282	11	:	:	PUNCT
ejpam-3928	282	12	2nk1	2nk1	NUM
ejpam-3928	282	13	,	,	PUNCT
ejpam-3928	282	14	nk2	nk2	NOUN
ejpam-3928	282	15	,	,	PUNCT
ejpam-3928	282	16	2kn	2kn	ADV
ejpam-3928	282	17	,	,	PUNCT
ejpam-3928	282	18	and	and	CCONJ
ejpam-3928	282	19	2c4	2c4	NUM
ejpam-3928	282	20	.	.	PUNCT
ejpam-3928	283	1	proof	proof	NOUN
ejpam-3928	283	2	.	.	PUNCT
ejpam-3928	284	1	suppose	suppose	VERB
ejpam-3928	284	2	g	g	PROPN
ejpam-3928	284	3	is	be	AUX
ejpam-3928	284	4	one	one	NUM
ejpam-3928	284	5	of	of	ADP
ejpam-3928	284	6	the	the	DET
ejpam-3928	284	7	graphs	graph	NOUN
ejpam-3928	284	8	2nk1	2nk1	NUM
ejpam-3928	284	9	,	,	PUNCT
ejpam-3928	284	10	nk2	nk2	NOUN
ejpam-3928	284	11	,	,	PUNCT
ejpam-3928	284	12	2kn	2kn	ADV
ejpam-3928	284	13	,	,	PUNCT
ejpam-3928	284	14	and	and	CCONJ
ejpam-3928	284	15	2c4	2c4	NUM
ejpam-3928	284	16	.	.	PUNCT
ejpam-3928	285	1	by	by	ADP
ejpam-3928	285	2	theorem	theorem	NOUN
ejpam-3928	285	3	2	2	NUM
ejpam-3928	285	4	,	,	PUNCT
ejpam-3928	285	5	g	g	PROPN
ejpam-3928	285	6	is	be	AUX
ejpam-3928	285	7	weakly	weakly	ADV
ejpam-3928	285	8	-	-	PUNCT
ejpam-3928	285	9	equipartite	equipartite	ADJ
ejpam-3928	285	10	,	,	PUNCT
ejpam-3928	285	11	and	and	CCONJ
ejpam-3928	285	12	by	by	ADP
ejpam-3928	285	13	theorem	theorem	NOUN
ejpam-3928	285	14	6	6	NUM
ejpam-3928	285	15	,	,	PUNCT
ejpam-3928	285	16	it	it	PRON
ejpam-3928	285	17	must	must	AUX
ejpam-3928	285	18	be	be	AUX
ejpam-3928	285	19	spectral	spectral	ADJ
ejpam-3928	285	20	-	-	PUNCT
ejpam-3928	285	21	equipartite	equipartite	ADJ
ejpam-3928	285	22	.	.	PUNCT
ejpam-3928	286	1	now	now	ADV
ejpam-3928	286	2	suppose	suppose	VERB
ejpam-3928	286	3	that	that	SCONJ
ejpam-3928	286	4	g	g	PROPN
ejpam-3928	286	5	is	be	AUX
ejpam-3928	286	6	a	a	DET
ejpam-3928	286	7	disconnected	disconnected	ADJ
ejpam-3928	286	8	spectral	spectral	ADJ
ejpam-3928	286	9	-	-	PUNCT
ejpam-3928	286	10	equipartite	equipartite	ADJ
ejpam-3928	286	11	graph	graph	NOUN
ejpam-3928	286	12	.	.	PUNCT
ejpam-3928	287	1	by	by	ADP
ejpam-3928	287	2	theorem	theorem	NOUN
ejpam-3928	287	3	5	5	NUM
ejpam-3928	287	4	,	,	PUNCT
ejpam-3928	287	5	g	g	PROPN
ejpam-3928	287	6	must	must	AUX
ejpam-3928	287	7	be	be	AUX
ejpam-3928	287	8	a	a	DET
ejpam-3928	287	9	k	k	ADJ
ejpam-3928	287	10	-	-	ADJ
ejpam-3928	287	11	regular	regular	ADJ
ejpam-3928	287	12	graph	graph	NOUN
ejpam-3928	287	13	of	of	ADP
ejpam-3928	287	14	order	order	NOUN
ejpam-3928	287	15	2n	2n	NUM
ejpam-3928	287	16	.	.	PUNCT
ejpam-3928	288	1	if	if	SCONJ
ejpam-3928	288	2	k	k	PROPN
ejpam-3928	288	3	=	=	SYM
ejpam-3928	288	4	0	0	PROPN
ejpam-3928	288	5	,	,	PUNCT
ejpam-3928	288	6	then	then	ADV
ejpam-3928	288	7	the	the	DET
ejpam-3928	288	8	2n	2n	NUM
ejpam-3928	288	9	vertices	vertex	NOUN
ejpam-3928	288	10	of	of	ADP
ejpam-3928	288	11	g	g	NOUN
ejpam-3928	288	12	are	be	AUX
ejpam-3928	288	13	isolated	isolate	VERB
ejpam-3928	288	14	.	.	PUNCT
ejpam-3928	289	1	hence	hence	ADV
ejpam-3928	289	2	,	,	PUNCT
ejpam-3928	289	3	we	we	PRON
ejpam-3928	289	4	have	have	VERB
ejpam-3928	289	5	g	g	NOUN
ejpam-3928	289	6	=	=	SYM
ejpam-3928	289	7	2nk1	2nk1	NUM
ejpam-3928	289	8	.	.	PUNCT
ejpam-3928	290	1	if	if	SCONJ
ejpam-3928	290	2	k	k	PROPN
ejpam-3928	290	3	=	=	SYM
ejpam-3928	290	4	1	1	NUM
ejpam-3928	290	5	,	,	PUNCT
ejpam-3928	290	6	then	then	ADV
ejpam-3928	290	7	g	g	PROPN
ejpam-3928	290	8	is	be	AUX
ejpam-3928	290	9	just	just	ADV
ejpam-3928	290	10	the	the	DET
ejpam-3928	290	11	union	union	NOUN
ejpam-3928	290	12	of	of	ADP
ejpam-3928	290	13	the	the	DET
ejpam-3928	290	14	n	n	PROPN
ejpam-3928	290	15	copies	copy	NOUN
ejpam-3928	290	16	of	of	ADP
ejpam-3928	290	17	k2	k2	NOUN
ejpam-3928	290	18	.	.	PUNCT
ejpam-3928	291	1	hence	hence	ADV
ejpam-3928	291	2	,	,	PUNCT
ejpam-3928	291	3	we	we	PRON
ejpam-3928	291	4	have	have	VERB
ejpam-3928	291	5	g	g	NOUN
ejpam-3928	291	6	=	=	SYM
ejpam-3928	291	7	nk2	nk2	PROPN
ejpam-3928	291	8	.	.	PUNCT
ejpam-3928	292	1	if	if	SCONJ
ejpam-3928	292	2	k	k	PROPN
ejpam-3928	292	3	>	>	X
ejpam-3928	292	4	1	1	NUM
ejpam-3928	292	5	,	,	PUNCT
ejpam-3928	292	6	then	then	ADV
ejpam-3928	292	7	by	by	ADP
ejpam-3928	292	8	theorem	theorem	NOUN
ejpam-3928	292	9	8	8	NUM
ejpam-3928	292	10	,	,	PUNCT
ejpam-3928	292	11	g	g	NOUN
ejpam-3928	292	12	=	=	SYM
ejpam-3928	292	13	2kn	2kn	ADJ
ejpam-3928	292	14	or	or	CCONJ
ejpam-3928	292	15	g	g	NOUN
ejpam-3928	292	16	=	=	SYM
ejpam-3928	292	17	2c4	2c4	NUM
ejpam-3928	292	18	.	.	PUNCT
ejpam-3928	292	19	theorem	theorem	VERB
ejpam-3928	292	20	10	10	NUM
ejpam-3928	292	21	.	.	PUNCT
ejpam-3928	293	1	if	if	SCONJ
ejpam-3928	293	2	g	g	PROPN
ejpam-3928	293	3	is	be	AUX
ejpam-3928	293	4	a	a	DET
ejpam-3928	293	5	disconnected	disconnected	ADJ
ejpam-3928	293	6	spectral	spectral	ADJ
ejpam-3928	293	7	-	-	PUNCT
ejpam-3928	293	8	equipartite	equipartite	ADJ
ejpam-3928	293	9	graph	graph	NOUN
ejpam-3928	293	10	,	,	PUNCT
ejpam-3928	293	11	then	then	ADV
ejpam-3928	293	12	its	its	PRON
ejpam-3928	293	13	complement	complement	NOUN
ejpam-3928	293	14	is	be	AUX
ejpam-3928	293	15	also	also	ADV
ejpam-3928	293	16	spectral	spectral	ADJ
ejpam-3928	293	17	-	-	PUNCT
ejpam-3928	293	18	equipartite	equipartite	ADJ
ejpam-3928	293	19	.	.	PUNCT
ejpam-3928	294	1	proof	proof	NOUN
ejpam-3928	294	2	.	.	PUNCT
ejpam-3928	295	1	let	let	VERB
ejpam-3928	295	2	g	g	PRON
ejpam-3928	295	3	be	be	AUX
ejpam-3928	295	4	a	a	DET
ejpam-3928	295	5	disconnected	disconnected	ADJ
ejpam-3928	295	6	spectral	spectral	ADJ
ejpam-3928	295	7	-	-	PUNCT
ejpam-3928	295	8	equipartite	equipartite	ADJ
ejpam-3928	295	9	graph	graph	NOUN
ejpam-3928	295	10	.	.	PUNCT
ejpam-3928	296	1	by	by	ADP
ejpam-3928	296	2	theorem	theorem	NOUN
ejpam-3928	296	3	9	9	NUM
ejpam-3928	296	4	,	,	PUNCT
ejpam-3928	296	5	g	g	PROPN
ejpam-3928	296	6	is	be	AUX
ejpam-3928	296	7	one	one	NUM
ejpam-3928	296	8	of	of	ADP
ejpam-3928	296	9	the	the	DET
ejpam-3928	296	10	graphs	graph	NOUN
ejpam-3928	296	11	2nk1	2nk1	NUM
ejpam-3928	296	12	,	,	PUNCT
ejpam-3928	296	13	nk2	nk2	PROPN
ejpam-3928	296	14	,	,	PUNCT
ejpam-3928	296	15	2c4	2c4	NUM
ejpam-3928	296	16	,	,	PUNCT
ejpam-3928	296	17	and	and	CCONJ
ejpam-3928	296	18	2kn	2kn	ADV
ejpam-3928	296	19	.	.	PUNCT
ejpam-3928	297	1	observe	observe	VERB
ejpam-3928	297	2	that	that	SCONJ
ejpam-3928	297	3	the	the	DET
ejpam-3928	297	4	complements	complement	NOUN
ejpam-3928	297	5	of	of	ADP
ejpam-3928	297	6	these	these	DET
ejpam-3928	297	7	graphs	graph	NOUN
ejpam-3928	297	8	are	be	AUX
ejpam-3928	297	9	k2n	k2n	NOUN
ejpam-3928	297	10	,	,	PUNCT
ejpam-3928	297	11	k2n\nk2	k2n\nk2	NOUN
ejpam-3928	297	12	,	,	PUNCT
ejpam-3928	297	13	k8\2c4	k8\2c4	NOUN
ejpam-3928	297	14	,	,	PUNCT
ejpam-3928	297	15	and	and	CCONJ
ejpam-3928	297	16	kn	kn	PROPN
ejpam-3928	297	17	,	,	PUNCT
ejpam-3928	297	18	n.	n.	NOUN
ejpam-3928	297	19	by	by	ADP
ejpam-3928	297	20	theorem	theorem	NOUN
ejpam-3928	297	21	2	2	NUM
ejpam-3928	297	22	,	,	PUNCT
ejpam-3928	297	23	these	these	DET
ejpam-3928	297	24	graphs	graph	NOUN
ejpam-3928	297	25	are	be	AUX
ejpam-3928	297	26	weakly	weakly	ADV
ejpam-3928	297	27	equipartite	equipartite	ADJ
ejpam-3928	297	28	,	,	PUNCT
ejpam-3928	297	29	and	and	CCONJ
ejpam-3928	297	30	by	by	ADP
ejpam-3928	297	31	theorem	theorem	NOUN
ejpam-3928	297	32	6	6	NUM
ejpam-3928	297	33	,	,	PUNCT
ejpam-3928	297	34	they	they	PRON
ejpam-3928	297	35	must	must	AUX
ejpam-3928	297	36	be	be	AUX
ejpam-3928	297	37	spectral	spectral	ADJ
ejpam-3928	297	38	-	-	PUNCT
ejpam-3928	297	39	equipartite	equipartite	ADJ
ejpam-3928	297	40	.	.	PUNCT
ejpam-3928	298	1	3.2	3.2	NUM
ejpam-3928	298	2	.	.	PUNCT
ejpam-3928	299	1	eccentricity	eccentricity	NOUN
ejpam-3928	299	2	-	-	PUNCT
ejpam-3928	299	3	equipartite	equipartite	ADJ
ejpam-3928	299	4	graphs	graph	NOUN
ejpam-3928	299	5	this	this	DET
ejpam-3928	299	6	section	section	NOUN
ejpam-3928	299	7	gives	give	VERB
ejpam-3928	299	8	some	some	DET
ejpam-3928	299	9	eccentricity	eccentricity	NOUN
ejpam-3928	299	10	-	-	PUNCT
ejpam-3928	299	11	equipartite	equipartite	ADJ
ejpam-3928	299	12	graphs	graph	NOUN
ejpam-3928	299	13	.	.	PUNCT
ejpam-3928	300	1	theorem	theorem	VERB
ejpam-3928	300	2	11	11	NUM
ejpam-3928	300	3	.	.	PUNCT
ejpam-3928	301	1	every	every	DET
ejpam-3928	301	2	weakly	weakly	ADJ
ejpam-3928	301	3	-	-	PUNCT
ejpam-3928	301	4	equipartite	equipartite	ADJ
ejpam-3928	301	5	graph	graph	NOUN
ejpam-3928	301	6	is	be	AUX
ejpam-3928	301	7	eccentricity	eccentricity	NOUN
ejpam-3928	301	8	-	-	PUNCT
ejpam-3928	301	9	equipartite	equipartite	ADJ
ejpam-3928	301	10	.	.	PUNCT
ejpam-3928	302	1	proof	proof	NOUN
ejpam-3928	302	2	.	.	PUNCT
ejpam-3928	303	1	let	let	VERB
ejpam-3928	303	2	g	g	PRON
ejpam-3928	303	3	be	be	AUX
ejpam-3928	303	4	a	a	DET
ejpam-3928	303	5	weakly	weakly	ADJ
ejpam-3928	303	6	-	-	PUNCT
ejpam-3928	303	7	equipartite	equipartite	ADJ
ejpam-3928	303	8	graph	graph	NOUN
ejpam-3928	303	9	.	.	PUNCT
ejpam-3928	304	1	thus	thus	ADV
ejpam-3928	304	2	,	,	PUNCT
ejpam-3928	304	3	every	every	DET
ejpam-3928	304	4	partition	partition	NOUN
ejpam-3928	304	5	of	of	ADP
ejpam-3928	304	6	v	v	NOUN
ejpam-3928	304	7	(	(	PUNCT
ejpam-3928	304	8	g	g	NOUN
ejpam-3928	304	9	)	)	PUNCT
ejpam-3928	304	10	into	into	ADP
ejpam-3928	304	11	two	two	NUM
ejpam-3928	304	12	sets	set	NOUN
ejpam-3928	304	13	,	,	PUNCT
ejpam-3928	304	14	a	a	PRON
ejpam-3928	304	15	and	and	CCONJ
ejpam-3928	304	16	b	b	NOUN
ejpam-3928	304	17	,	,	PUNCT
ejpam-3928	304	18	with	with	ADP
ejpam-3928	304	19	n	n	NOUN
ejpam-3928	304	20	vertices	vertex	NOUN
ejpam-3928	304	21	each	each	PRON
ejpam-3928	304	22	,	,	PUNCT
ejpam-3928	304	23	〈	〈	PROPN
ejpam-3928	304	24	a	a	DET
ejpam-3928	304	25	〉	〉	NOUN
ejpam-3928	304	26	and	and	CCONJ
ejpam-3928	304	27	〈	〈	PROPN
ejpam-3928	304	28	b	b	PROPN
ejpam-3928	304	29	〉	〉	PROPN
ejpam-3928	304	30	are	be	AUX
ejpam-3928	304	31	isomorphic	isomorphic	ADJ
ejpam-3928	304	32	.	.	PUNCT
ejpam-3928	305	1	hence	hence	ADV
ejpam-3928	305	2	,	,	PUNCT
ejpam-3928	305	3	〈	〈	PROPN
ejpam-3928	305	4	a	a	DET
ejpam-3928	305	5	〉	〉	NOUN
ejpam-3928	305	6	and	and	CCONJ
ejpam-3928	305	7	〈	〈	PROPN
ejpam-3928	305	8	b	b	PROPN
ejpam-3928	305	9	〉	〉	PROPN
ejpam-3928	305	10	have	have	VERB
ejpam-3928	305	11	the	the	DET
ejpam-3928	305	12	same	same	ADJ
ejpam-3928	305	13	eccentricity	eccentricity	NOUN
ejpam-3928	305	14	sequence	sequence	NOUN
ejpam-3928	305	15	.	.	PUNCT
ejpam-3928	306	1	thus	thus	ADV
ejpam-3928	306	2	,	,	PUNCT
ejpam-3928	306	3	g	g	PROPN
ejpam-3928	306	4	is	be	AUX
ejpam-3928	306	5	eccentricity	eccentricity	NOUN
ejpam-3928	306	6	-	-	PUNCT
ejpam-3928	306	7	equipartite	equipartite	ADJ
ejpam-3928	306	8	.	.	PUNCT
ejpam-3928	307	1	corollary	corollary	ADJ
ejpam-3928	307	2	1	1	NUM
ejpam-3928	307	3	.	.	PUNCT
ejpam-3928	308	1	let	let	VERB
ejpam-3928	308	2	n	n	PRON
ejpam-3928	308	3	∈	∈	PROPN
ejpam-3928	308	4	n.	n.	NOUN
ejpam-3928	308	5	the	the	DET
ejpam-3928	308	6	following	follow	VERB
ejpam-3928	308	7	graphs	graph	NOUN
ejpam-3928	308	8	are	be	AUX
ejpam-3928	308	9	eccentricity	eccentricity	NOUN
ejpam-3928	308	10	-	-	PUNCT
ejpam-3928	308	11	equipartite	equipartite	ADJ
ejpam-3928	308	12	:	:	PUNCT
ejpam-3928	308	13	2nk1	2nk1	NUM
ejpam-3928	308	14	;	;	PUNCT
ejpam-3928	308	15	nk2	nk2	NOUN
ejpam-3928	308	16	;	;	PUNCT
ejpam-3928	308	17	2c4	2c4	NUM
ejpam-3928	308	18	;	;	PUNCT
ejpam-3928	308	19	kn	kn	PROPN
ejpam-3928	308	20	,	,	PUNCT
ejpam-3928	308	21	n\nk2	n\nk2	NUM
ejpam-3928	308	22	;	;	PUNCT
ejpam-3928	308	23	2kn	2kn	ADV
ejpam-3928	308	24	;	;	PUNCT
ejpam-3928	308	25	k2n	k2n	NOUN
ejpam-3928	308	26	;	;	PUNCT
ejpam-3928	308	27	k2n\nk2	k2n\nk2	NUM
ejpam-3928	308	28	;	;	PUNCT
ejpam-3928	308	29	k8\2c4	k8\2c4	NOUN
ejpam-3928	308	30	;	;	PUNCT
ejpam-3928	308	31	2kn	2kn	ADJ
ejpam-3928	308	32	+	+	CCONJ
ejpam-3928	308	33	nk2	nk2	NOUN
ejpam-3928	308	34	and	and	CCONJ
ejpam-3928	308	35	kn	kn	PROPN
ejpam-3928	308	36	,	,	PUNCT
ejpam-3928	308	37	n.	n.	NOUN
ejpam-3928	308	38	proof	proof	NOUN
ejpam-3928	308	39	.	.	PUNCT
ejpam-3928	309	1	the	the	DET
ejpam-3928	309	2	statement	statement	NOUN
ejpam-3928	309	3	immediately	immediately	ADV
ejpam-3928	309	4	follows	follow	VERB
ejpam-3928	309	5	from	from	ADP
ejpam-3928	309	6	theorem	theorem	ADJ
ejpam-3928	309	7	1	1	NUM
ejpam-3928	309	8	and	and	CCONJ
ejpam-3928	309	9	theorem	theorem	VERB
ejpam-3928	309	10	11	11	NUM
ejpam-3928	309	11	.	.	PUNCT
ejpam-3928	310	1	references	reference	NOUN
ejpam-3928	310	2	365	365	NUM
ejpam-3928	310	3	theorem	theorem	NOUN
ejpam-3928	310	4	12	12	NUM
ejpam-3928	310	5	.	.	PUNCT
ejpam-3928	311	1	every	every	DET
ejpam-3928	311	2	degree	degree	NOUN
ejpam-3928	311	3	-	-	PUNCT
ejpam-3928	311	4	equipartite	equipartite	ADJ
ejpam-3928	311	5	graph	graph	NOUN
ejpam-3928	311	6	is	be	AUX
ejpam-3928	311	7	eccentricity	eccentricity	NOUN
ejpam-3928	311	8	-	-	PUNCT
ejpam-3928	311	9	equipartite	equipartite	ADJ
ejpam-3928	311	10	.	.	PUNCT
ejpam-3928	312	1	proof	proof	NOUN
ejpam-3928	312	2	.	.	PUNCT
ejpam-3928	313	1	the	the	DET
ejpam-3928	313	2	proof	proof	NOUN
ejpam-3928	313	3	for	for	ADP
ejpam-3928	313	4	this	this	DET
ejpam-3928	313	5	theorem	theorem	NOUN
ejpam-3928	313	6	will	will	AUX
ejpam-3928	313	7	immediately	immediately	ADV
ejpam-3928	313	8	follow	follow	VERB
ejpam-3928	313	9	from	from	ADP
ejpam-3928	313	10	theorem	theorem	ADJ
ejpam-3928	313	11	2	2	NUM
ejpam-3928	313	12	and	and	CCONJ
ejpam-3928	313	13	corollary	corollary	ADJ
ejpam-3928	313	14	1	1	NUM
ejpam-3928	313	15	.	.	PUNCT
ejpam-3928	314	1	acknowledgements	acknowledgement	NOUN
ejpam-3928	314	2	the	the	DET
ejpam-3928	314	3	authors	author	NOUN
ejpam-3928	314	4	would	would	AUX
ejpam-3928	314	5	like	like	VERB
ejpam-3928	314	6	to	to	PART
ejpam-3928	314	7	thank	thank	VERB
ejpam-3928	314	8	the	the	DET
ejpam-3928	314	9	rural	rural	ADJ
ejpam-3928	314	10	engineering	engineering	NOUN
ejpam-3928	314	11	and	and	CCONJ
ejpam-3928	314	12	technology	technology	NOUN
ejpam-3928	314	13	center	center	NOUN
ejpam-3928	314	14	of	of	ADP
ejpam-3928	314	15	negros	negros	PROPN
ejpam-3928	314	16	oriental	oriental	ADJ
ejpam-3928	314	17	state	state	PROPN
ejpam-3928	314	18	university	university	PROPN
ejpam-3928	314	19	for	for	ADP
ejpam-3928	314	20	partially	partially	ADV
ejpam-3928	314	21	supporting	support	VERB
ejpam-3928	314	22	this	this	DET
ejpam-3928	314	23	research	research	NOUN
ejpam-3928	314	24	.	.	PUNCT
ejpam-3928	315	1	references	reference	NOUN
ejpam-3928	315	2	[	[	X
ejpam-3928	315	3	1	1	NUM
ejpam-3928	315	4	]	]	X
ejpam-3928	315	5	kh	kh	PROPN
ejpam-3928	315	6	.	.	PROPN
ejpam-3928	315	7	bibak	bibak	PROPN
ejpam-3928	315	8	and	and	CCONJ
ejpam-3928	315	9	m.h	m.h	PROPN
ejpam-3928	315	10	.	.	PROPN
ejpam-3928	315	11	shirdareh	shirdareh	PROPN
ejpam-3928	315	12	haghighi	haghighi	PROPN
ejpam-3928	315	13	.	.	PUNCT
ejpam-3928	315	14	degree	degree	NOUN
ejpam-3928	315	15	-	-	PUNCT
ejpam-3928	315	16	equipartite	equipartite	ADJ
ejpam-3928	315	17	graphs	graph	NOUN
ejpam-3928	315	18	.	.	PUNCT
ejpam-3928	316	1	discrete	discrete	ADJ
ejpam-3928	316	2	mathematics	mathematic	NOUN
ejpam-3928	316	3	,	,	PUNCT
ejpam-3928	316	4	311(10):888–891	311(10):888–891	NUM
ejpam-3928	316	5	,	,	PUNCT
ejpam-3928	316	6	2011	2011	NUM
ejpam-3928	316	7	.	.	PUNCT
ejpam-3928	317	1	[	[	X
ejpam-3928	317	2	2	2	NUM
ejpam-3928	317	3	]	]	X
ejpam-3928	317	4	a.e	a.e	PROPN
ejpam-3928	317	5	.	.	PROPN
ejpam-3928	317	6	brouwer	brouwer	PROPN
ejpam-3928	317	7	and	and	CCONJ
ejpam-3928	317	8	w.h	w.h	PROPN
ejpam-3928	317	9	.	.	PROPN
ejpam-3928	317	10	haemers	haemer	NOUN
ejpam-3928	317	11	.	.	PUNCT
ejpam-3928	318	1	graph	graph	NOUN
ejpam-3928	318	2	spectrum	spectrum	NOUN
ejpam-3928	318	3	.	.	PUNCT
ejpam-3928	319	1	springer	springer	NOUN
ejpam-3928	319	2	,	,	PUNCT
ejpam-3928	319	3	new	new	PROPN
ejpam-3928	319	4	york	york	PROPN
ejpam-3928	319	5	,	,	PUNCT
ejpam-3928	319	6	ny	ny	PROPN
ejpam-3928	319	7	,	,	PUNCT
ejpam-3928	319	8	2011	2011	NUM
ejpam-3928	319	9	.	.	PUNCT
ejpam-3928	320	1	[	[	X
ejpam-3928	320	2	3	3	X
ejpam-3928	320	3	]	]	X
ejpam-3928	320	4	d.	d.	NOUN
ejpam-3928	320	5	cvetković.	cvetković.	PROPN
ejpam-3928	320	6	applications	application	NOUN
ejpam-3928	320	7	of	of	ADP
ejpam-3928	320	8	graph	graph	NOUN
ejpam-3928	320	9	spectra	spectra	PROPN
ejpam-3928	320	10	:	:	PUNCT
ejpam-3928	320	11	an	an	DET
ejpam-3928	320	12	introduction	introduction	NOUN
ejpam-3928	320	13	to	to	ADP
ejpam-3928	320	14	the	the	DET
ejpam-3928	320	15	literature	literature	NOUN
ejpam-3928	320	16	.	.	PUNCT
ejpam-3928	321	1	2009	2009	NUM
ejpam-3928	321	2	.	.	PUNCT
ejpam-3928	322	1	[	[	X
ejpam-3928	322	2	4	4	X
ejpam-3928	322	3	]	]	X
ejpam-3928	322	4	d.	d.	PROPN
ejpam-3928	322	5	cvetković	cvetković	PROPN
ejpam-3928	322	6	,	,	PUNCT
ejpam-3928	322	7	v.	v.	ADP
ejpam-3928	322	8	dimitrijević	dimitrijević	NOUN
ejpam-3928	322	9	,	,	PUNCT
ejpam-3928	322	10	and	and	CCONJ
ejpam-3928	322	11	m.	m.	NOUN
ejpam-3928	322	12	milosavljević.	milosavljević.	PROPN
ejpam-3928	322	13	variations	variation	NOUN
ejpam-3928	322	14	on	on	ADP
ejpam-3928	322	15	the	the	DET
ejpam-3928	322	16	travelling	travel	VERB
ejpam-3928	322	17	salesman	salesman	ADJ
ejpam-3928	322	18	theme	theme	NOUN
ejpam-3928	322	19	.	.	PUNCT
ejpam-3928	323	1	libra	libra	PROPN
ejpam-3928	323	2	produkt	produkt	PROPN
ejpam-3928	323	3	,	,	PUNCT
ejpam-3928	323	4	belgrade	belgrade	PROPN
ejpam-3928	323	5	,	,	PUNCT
ejpam-3928	323	6	1996	1996	NUM
ejpam-3928	323	7	.	.	PUNCT
ejpam-3928	324	1	[	[	X
ejpam-3928	324	2	5	5	NUM
ejpam-3928	324	3	]	]	PUNCT
ejpam-3928	324	4	d.	d.	PROPN
ejpam-3928	324	5	ferrero	ferrero	PROPN
ejpam-3928	324	6	and	and	CCONJ
ejpam-3928	324	7	f.	f.	PROPN
ejpam-3928	324	8	harary	harary	PROPN
ejpam-3928	324	9	.	.	PUNCT
ejpam-3928	325	1	on	on	ADP
ejpam-3928	325	2	eccentricity	eccentricity	NOUN
ejpam-3928	325	3	sequences	sequence	NOUN
ejpam-3928	325	4	of	of	ADP
ejpam-3928	325	5	connected	connected	ADJ
ejpam-3928	325	6	graphs	graph	NOUN
ejpam-3928	325	7	.	.	PUNCT
ejpam-3928	326	1	akce	akce	PROPN
ejpam-3928	326	2	j.	j.	PROPN
ejpam-3928	326	3	graphs	graphs	PROPN
ejpam-3928	326	4	combin	combin	PROPN
ejpam-3928	326	5	.	.	PROPN
ejpam-3928	326	6	,	,	PUNCT
ejpam-3928	326	7	6:401–408	6:401–408	NUM
ejpam-3928	326	8	,	,	PUNCT
ejpam-3928	326	9	2009	2009	NUM
ejpam-3928	326	10	.	.	PUNCT
ejpam-3928	327	1	[	[	X
ejpam-3928	327	2	6	6	NUM
ejpam-3928	327	3	]	]	X
ejpam-3928	327	4	jonathan	jonathan	PROPN
ejpam-3928	327	5	l	l	PROPN
ejpam-3928	327	6	gross	gross	PROPN
ejpam-3928	327	7	,	,	PUNCT
ejpam-3928	327	8	jay	jay	PROPN
ejpam-3928	327	9	yellen	yellen	VERB
ejpam-3928	327	10	,	,	PUNCT
ejpam-3928	327	11	and	and	CCONJ
ejpam-3928	327	12	ping	ping	PROPN
ejpam-3928	327	13	zhang	zhang	PROPN
ejpam-3928	327	14	.	.	PROPN
ejpam-3928	328	1	handbook	handbook	NOUN
ejpam-3928	328	2	of	of	ADP
ejpam-3928	328	3	graph	graph	NOUN
ejpam-3928	328	4	theory	theory	NOUN
ejpam-3928	328	5	(	(	PUNCT
ejpam-3928	328	6	2nd	2nd	ADJ
ejpam-3928	328	7	ed	ed	NOUN
ejpam-3928	328	8	.	.	PUNCT
ejpam-3928	328	9	)	)	PUNCT
ejpam-3928	328	10	.	.	PUNCT
ejpam-3928	329	1	chapman	chapman	NOUN
ejpam-3928	329	2	and	and	CCONJ
ejpam-3928	329	3	hall	hall	PROPN
ejpam-3928	329	4	/	/	SYM
ejpam-3928	329	5	crc	crc	PROPN
ejpam-3928	329	6	,	,	PUNCT
ejpam-3928	329	7	2013	2013	NUM
ejpam-3928	329	8	.	.	PUNCT
ejpam-3928	330	1	[	[	X
ejpam-3928	330	2	7	7	X
ejpam-3928	330	3	]	]	X
ejpam-3928	330	4	b.	b.	PROPN
ejpam-3928	330	5	grünbaum	grünbaum	PROPN
ejpam-3928	330	6	,	,	PUNCT
ejpam-3928	330	7	t.	t.	PROPN
ejpam-3928	330	8	kaiser	kaiser	PROPN
ejpam-3928	330	9	,	,	PUNCT
ejpam-3928	330	10	d.	d.	PROPN
ejpam-3928	330	11	krá́l	krá́l	PROPN
ejpam-3928	330	12	,	,	PUNCT
ejpam-3928	330	13	and	and	CCONJ
ejpam-3928	330	14	m.	m.	NOUN
ejpam-3928	330	15	rosenfeld	rosenfeld	PROPN
ejpam-3928	330	16	.	.	PUNCT
ejpam-3928	331	1	equipartite	equipartite	ADJ
ejpam-3928	331	2	graphs	graph	NOUN
ejpam-3928	331	3	.	.	PUNCT
ejpam-3928	332	1	israel	israel	PROPN
ejpam-3928	332	2	journal	journal	PROPN
ejpam-3928	332	3	of	of	ADP
ejpam-3928	332	4	mathematics	mathematic	NOUN
ejpam-3928	332	5	,	,	PUNCT
ejpam-3928	332	6	168:431–444	168:431–444	NUM
ejpam-3928	332	7	,	,	PUNCT
ejpam-3928	332	8	2008	2008	NUM
ejpam-3928	332	9	.	.	PUNCT
ejpam-3928	333	1	[	[	X
ejpam-3928	333	2	8	8	NUM
ejpam-3928	333	3	]	]	SYM
ejpam-3928	333	4	sanguthevar	sanguthevar	NOUN
ejpam-3928	333	5	rajasekaran	rajasekaran	NOUN
ejpam-3928	333	6	and	and	CCONJ
ejpam-3928	333	7	vamsi	vamsi	PROPN
ejpam-3928	333	8	kundeti	kundeti	PROPN
ejpam-3928	333	9	.	.	PUNCT
ejpam-3928	334	1	spectrum	spectrum	PROPN
ejpam-3928	334	2	based	base	VERB
ejpam-3928	334	3	algorithms	algorithm	NOUN
ejpam-3928	334	4	for	for	ADP
ejpam-3928	334	5	graph	graph	NOUN
ejpam-3928	334	6	isomorphism	isomorphism	NOUN
ejpam-3928	334	7	.	.	PUNCT
ejpam-3928	335	1	03	03	NUM
ejpam-3928	335	2	2021	2021	NUM
ejpam-3928	335	3	.	.	PUNCT
ejpam-3928	336	1	[	[	X
ejpam-3928	336	2	9	9	NUM
ejpam-3928	336	3	]	]	X
ejpam-3928	336	4	m.h	m.h	PROPN
ejpam-3928	336	5	.	.	PROPN
ejpam-3928	336	6	shirdareh	shirdareh	PROPN
ejpam-3928	336	7	haghighi	haghighi	PROPN
ejpam-3928	336	8	,	,	PUNCT
ejpam-3928	336	9	f.	f.	PROPN
ejpam-3928	336	10	motialah	motialah	PROPN
ejpam-3928	336	11	,	,	PUNCT
ejpam-3928	336	12	and	and	CCONJ
ejpam-3928	336	13	b.	b.	PROPN
ejpam-3928	336	14	amini	amini	PROPN
ejpam-3928	336	15	.	.	PUNCT
ejpam-3928	337	1	a	a	DET
ejpam-3928	337	2	new	new	ADJ
ejpam-3928	337	3	characterization	characterization	NOUN
ejpam-3928	337	4	of	of	ADP
ejpam-3928	337	5	equipartite	equipartite	ADJ
ejpam-3928	337	6	graphs	graph	NOUN
ejpam-3928	337	7	.	.	PUNCT
ejpam-3928	338	1	discrete	discrete	ADJ
ejpam-3928	338	2	mathematics	mathematic	NOUN
ejpam-3928	338	3	,	,	PUNCT
ejpam-3928	338	4	340(9):2086–2090	340(9):2086–2090	PROPN
ejpam-3928	338	5	,	,	PUNCT
ejpam-3928	338	6	2017	2017	NUM
ejpam-3928	338	7	.	.	PUNCT
ejpam-3928	339	1	[	[	X
ejpam-3928	339	2	10	10	NUM
ejpam-3928	339	3	]	]	X
ejpam-3928	339	4	y.	y.	PROPN
ejpam-3928	339	5	wang	wang	PROPN
ejpam-3928	339	6	,	,	PUNCT
ejpam-3928	339	7	deepayan	deepayan	PROPN
ejpam-3928	339	8	chakrabarti	chakrabarti	PROPN
ejpam-3928	339	9	,	,	PUNCT
ejpam-3928	339	10	c.	c.	PROPN
ejpam-3928	339	11	wang	wang	PROPN
ejpam-3928	339	12	,	,	PUNCT
ejpam-3928	339	13	and	and	CCONJ
ejpam-3928	339	14	c.	c.	PROPN
ejpam-3928	339	15	faloutsos	faloutsos	PROPN
ejpam-3928	339	16	.	.	PUNCT
ejpam-3928	340	1	epidemic	epidemic	NOUN
ejpam-3928	340	2	spreading	spread	VERB
ejpam-3928	340	3	in	in	ADP
ejpam-3928	340	4	real	real	ADJ
ejpam-3928	340	5	networks	network	NOUN
ejpam-3928	340	6	:	:	PUNCT
ejpam-3928	340	7	an	an	DET
ejpam-3928	340	8	eigenvalue	eigenvalue	NOUN
ejpam-3928	340	9	viewpoint	viewpoint	NOUN
ejpam-3928	340	10	.	.	PUNCT
ejpam-3928	341	1	pages	page	NOUN
ejpam-3928	341	2	25–34	25–34	NUM
ejpam-3928	341	3	,	,	PUNCT
ejpam-3928	341	4	2003	2003	NUM
ejpam-3928	341	5	.	.	PUNCT