id	sid	tid	token	lemma	pos
ejpam-3710	1	1	european	european	PROPN
ejpam-3710	1	2	journal	journal	PROPN
ejpam-3710	1	3	of	of	ADP
ejpam-3710	1	4	pure	pure	ADJ
ejpam-3710	1	5	and	and	CCONJ
ejpam-3710	1	6	applied	apply	VERB
ejpam-3710	1	7	mathematics	mathematic	NOUN
ejpam-3710	1	8	vol	vol	NOUN
ejpam-3710	1	9	.	.	PROPN
ejpam-3710	2	1	13	13	NUM
ejpam-3710	2	2	,	,	PUNCT
ejpam-3710	2	3	no	no	INTJ
ejpam-3710	2	4	.	.	NOUN
ejpam-3710	2	5	5	5	NUM
ejpam-3710	2	6	,	,	PUNCT
ejpam-3710	2	7	2020	2020	NUM
ejpam-3710	2	8	,	,	PUNCT
ejpam-3710	2	9	1097	1097	NUM
ejpam-3710	2	10	-	-	SYM
ejpam-3710	2	11	1109	1109	NUM
ejpam-3710	2	12	issn	issn	PROPN
ejpam-3710	2	13	1307	1307	NUM
ejpam-3710	2	14	-	-	SYM
ejpam-3710	2	15	5543	5543	NUM
ejpam-3710	2	16	–	–	PUNCT
ejpam-3710	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3710	2	18	published	publish	VERB
ejpam-3710	2	19	by	by	ADP
ejpam-3710	2	20	new	new	PROPN
ejpam-3710	2	21	york	york	PROPN
ejpam-3710	2	22	business	business	PROPN
ejpam-3710	2	23	global	global	ADJ
ejpam-3710	2	24	special	special	ADJ
ejpam-3710	2	25	issue	issue	NOUN
ejpam-3710	2	26	dedicated	dedicate	VERB
ejpam-3710	2	27	to	to	ADP
ejpam-3710	2	28	professor	professor	NOUN
ejpam-3710	2	29	hari	hari	PROPN
ejpam-3710	2	30	m.	m.	PROPN
ejpam-3710	2	31	srivastava	srivastava	PROPN
ejpam-3710	2	32	on	on	ADP
ejpam-3710	2	33	the	the	DET
ejpam-3710	2	34	occasion	occasion	NOUN
ejpam-3710	2	35	of	of	ADP
ejpam-3710	2	36	his	his	PRON
ejpam-3710	2	37	80th	80th	ADJ
ejpam-3710	2	38	birthday	birthday	NOUN
ejpam-3710	2	39	on	on	ADP
ejpam-3710	2	40	tosha	tosha	NOUN
ejpam-3710	2	41	-	-	PUNCT
ejpam-3710	2	42	degree	degree	NOUN
ejpam-3710	2	43	of	of	ADP
ejpam-3710	2	44	an	an	DET
ejpam-3710	2	45	edge	edge	NOUN
ejpam-3710	2	46	in	in	ADP
ejpam-3710	2	47	a	a	DET
ejpam-3710	2	48	graph	graph	NOUN
ejpam-3710	2	49	r.	r.	PROPN
ejpam-3710	2	50	rajendra	rajendra	PROPN
ejpam-3710	2	51	1	1	NUM
ejpam-3710	2	52	,	,	PUNCT
ejpam-3710	2	53	p.	p.	PROPN
ejpam-3710	2	54	siva	siva	PROPN
ejpam-3710	2	55	kota	kota	PROPN
ejpam-3710	2	56	reddy	reddy	PROPN
ejpam-3710	2	57	2,∗	2,∗	NUM
ejpam-3710	2	58	1	1	NUM
ejpam-3710	2	59	department	department	NOUN
ejpam-3710	2	60	of	of	ADP
ejpam-3710	2	61	mathematics	mathematics	PROPN
ejpam-3710	2	62	,	,	PUNCT
ejpam-3710	2	63	mangalore	mangalore	PROPN
ejpam-3710	2	64	university	university	PROPN
ejpam-3710	2	65	,	,	PUNCT
ejpam-3710	2	66	mangalagangothri	mangalagangothri	PROPN
ejpam-3710	2	67	,	,	PUNCT
ejpam-3710	2	68	karnataka	karnataka	PROPN
ejpam-3710	2	69	,	,	PUNCT
ejpam-3710	2	70	india	india	PROPN
ejpam-3710	2	71	2	2	NUM
ejpam-3710	2	72	department	department	NOUN
ejpam-3710	2	73	of	of	ADP
ejpam-3710	2	74	mathematics	mathematic	NOUN
ejpam-3710	2	75	,	,	PUNCT
ejpam-3710	2	76	sri	sri	PROPN
ejpam-3710	2	77	jayachamarajendra	jayachamarajendra	PROPN
ejpam-3710	2	78	college	college	PROPN
ejpam-3710	2	79	of	of	ADP
ejpam-3710	2	80	engineering	engineering	PROPN
ejpam-3710	2	81	,	,	PUNCT
ejpam-3710	2	82	jss	jss	PROPN
ejpam-3710	2	83	science	science	PROPN
ejpam-3710	2	84	and	and	CCONJ
ejpam-3710	2	85	technology	technology	PROPN
ejpam-3710	2	86	university	university	NOUN
ejpam-3710	2	87	,	,	PUNCT
ejpam-3710	2	88	mysuru	mysuru	NOUN
ejpam-3710	2	89	,	,	PUNCT
ejpam-3710	2	90	karnataka	karnataka	PROPN
ejpam-3710	2	91	,	,	PUNCT
ejpam-3710	2	92	india	india	PROPN
ejpam-3710	2	93	abstract	abstract	NOUN
ejpam-3710	2	94	.	.	PUNCT
ejpam-3710	3	1	in	in	ADP
ejpam-3710	3	2	an	an	DET
ejpam-3710	3	3	earlier	early	ADJ
ejpam-3710	3	4	paper	paper	NOUN
ejpam-3710	3	5	,	,	PUNCT
ejpam-3710	3	6	we	we	PRON
ejpam-3710	3	7	have	have	AUX
ejpam-3710	3	8	introduced	introduce	VERB
ejpam-3710	3	9	the	the	DET
ejpam-3710	3	10	tosha	tosha	NOUN
ejpam-3710	3	11	-	-	PUNCT
ejpam-3710	3	12	degree	degree	NOUN
ejpam-3710	3	13	of	of	ADP
ejpam-3710	3	14	an	an	DET
ejpam-3710	3	15	edge	edge	NOUN
ejpam-3710	3	16	in	in	ADP
ejpam-3710	3	17	a	a	DET
ejpam-3710	3	18	graph	graph	NOUN
ejpam-3710	3	19	without	without	ADP
ejpam-3710	3	20	multiple	multiple	ADJ
ejpam-3710	3	21	edges	edge	NOUN
ejpam-3710	3	22	and	and	CCONJ
ejpam-3710	3	23	studied	study	VERB
ejpam-3710	3	24	some	some	DET
ejpam-3710	3	25	properties	property	NOUN
ejpam-3710	3	26	.	.	PUNCT
ejpam-3710	4	1	in	in	ADP
ejpam-3710	4	2	this	this	DET
ejpam-3710	4	3	paper	paper	NOUN
ejpam-3710	4	4	,	,	PUNCT
ejpam-3710	4	5	we	we	PRON
ejpam-3710	4	6	extend	extend	VERB
ejpam-3710	4	7	the	the	DET
ejpam-3710	4	8	definition	definition	NOUN
ejpam-3710	4	9	of	of	ADP
ejpam-3710	4	10	tosha	tosha	NOUN
ejpam-3710	4	11	-	-	PUNCT
ejpam-3710	4	12	degree	degree	NOUN
ejpam-3710	4	13	of	of	ADP
ejpam-3710	4	14	an	an	DET
ejpam-3710	4	15	edge	edge	NOUN
ejpam-3710	4	16	in	in	ADP
ejpam-3710	4	17	a	a	DET
ejpam-3710	4	18	graph	graph	NOUN
ejpam-3710	4	19	in	in	ADP
ejpam-3710	4	20	which	which	PRON
ejpam-3710	4	21	multiple	multiple	ADJ
ejpam-3710	4	22	edges	edge	NOUN
ejpam-3710	4	23	are	be	AUX
ejpam-3710	4	24	allowed	allow	VERB
ejpam-3710	4	25	.	.	PUNCT
ejpam-3710	5	1	also	also	ADV
ejpam-3710	5	2	,	,	PUNCT
ejpam-3710	5	3	we	we	PRON
ejpam-3710	5	4	introduce	introduce	VERB
ejpam-3710	5	5	the	the	DET
ejpam-3710	5	6	concepts	concept	NOUN
ejpam-3710	5	7	zero	zero	NUM
ejpam-3710	5	8	edges	edge	NOUN
ejpam-3710	5	9	in	in	ADP
ejpam-3710	5	10	a	a	DET
ejpam-3710	5	11	graph	graph	NOUN
ejpam-3710	5	12	,	,	PUNCT
ejpam-3710	5	13	t	t	NOUN
ejpam-3710	5	14	-line	-line	NOUN
ejpam-3710	5	15	graph	graph	NOUN
ejpam-3710	5	16	of	of	ADP
ejpam-3710	5	17	a	a	DET
ejpam-3710	5	18	multigraph	multigraph	NOUN
ejpam-3710	5	19	,	,	PUNCT
ejpam-3710	5	20	tosha	tosha	NOUN
ejpam-3710	5	21	-	-	PUNCT
ejpam-3710	5	22	adjacency	adjacency	NOUN
ejpam-3710	5	23	matrix	matrix	NOUN
ejpam-3710	5	24	,	,	PUNCT
ejpam-3710	5	25	tosha	tosha	NOUN
ejpam-3710	5	26	-	-	PUNCT
ejpam-3710	5	27	energy	energy	NOUN
ejpam-3710	5	28	,	,	PUNCT
ejpam-3710	5	29	edgeadjacency	edgeadjacency	NOUN
ejpam-3710	5	30	matrix	matrix	NOUN
ejpam-3710	5	31	and	and	CCONJ
ejpam-3710	5	32	edge	edge	NOUN
ejpam-3710	5	33	energy	energy	NOUN
ejpam-3710	5	34	of	of	ADP
ejpam-3710	5	35	a	a	DET
ejpam-3710	5	36	graph	graph	NOUN
ejpam-3710	5	37	g	g	NOUN
ejpam-3710	5	38	and	and	CCONJ
ejpam-3710	5	39	obtain	obtain	VERB
ejpam-3710	5	40	some	some	DET
ejpam-3710	5	41	results	result	NOUN
ejpam-3710	5	42	.	.	PUNCT
ejpam-3710	6	1	2020	2020	NUM
ejpam-3710	6	2	mathematics	mathematic	NOUN
ejpam-3710	6	3	subject	subject	NOUN
ejpam-3710	6	4	classifications	classification	NOUN
ejpam-3710	6	5	:	:	PUNCT
ejpam-3710	6	6	05cxx	05cxx	NOUN
ejpam-3710	6	7	,	,	PUNCT
ejpam-3710	6	8	05c07	05c07	NOUN
ejpam-3710	6	9	,	,	PUNCT
ejpam-3710	6	10	05c50	05c50	NUM
ejpam-3710	6	11	.	.	PUNCT
ejpam-3710	7	1	key	key	ADJ
ejpam-3710	7	2	words	word	NOUN
ejpam-3710	7	3	and	and	CCONJ
ejpam-3710	7	4	phrases	phrase	NOUN
ejpam-3710	7	5	:	:	PUNCT
ejpam-3710	7	6	adjacency	adjacency	PROPN
ejpam-3710	7	7	matrix	matrix	NOUN
ejpam-3710	7	8	,	,	PUNCT
ejpam-3710	7	9	degree	degree	NOUN
ejpam-3710	7	10	of	of	ADP
ejpam-3710	7	11	a	a	DET
ejpam-3710	7	12	vertex	vertex	NOUN
ejpam-3710	7	13	,	,	PUNCT
ejpam-3710	7	14	energy	energy	NOUN
ejpam-3710	7	15	,	,	PUNCT
ejpam-3710	7	16	line	line	NOUN
ejpam-3710	7	17	graph	graph	NOUN
ejpam-3710	7	18	,	,	PUNCT
ejpam-3710	7	19	tosha	tosha	NOUN
ejpam-3710	7	20	-	-	PUNCT
ejpam-3710	7	21	degree	degree	NOUN
ejpam-3710	7	22	of	of	ADP
ejpam-3710	7	23	an	an	DET
ejpam-3710	7	24	edge	edge	NOUN
ejpam-3710	7	25	1	1	NUM
ejpam-3710	7	26	.	.	PUNCT
ejpam-3710	7	27	introduction	introduction	NOUN
ejpam-3710	7	28	for	for	ADP
ejpam-3710	7	29	standard	standard	ADJ
ejpam-3710	7	30	terminology	terminology	NOUN
ejpam-3710	7	31	and	and	CCONJ
ejpam-3710	7	32	notion	notion	NOUN
ejpam-3710	7	33	in	in	ADP
ejpam-3710	7	34	graphs	graph	NOUN
ejpam-3710	7	35	and	and	CCONJ
ejpam-3710	7	36	matrices	matrix	NOUN
ejpam-3710	7	37	,	,	PUNCT
ejpam-3710	7	38	we	we	PRON
ejpam-3710	7	39	refer	refer	VERB
ejpam-3710	7	40	the	the	DET
ejpam-3710	7	41	reader	reader	NOUN
ejpam-3710	7	42	to	to	ADP
ejpam-3710	7	43	the	the	DET
ejpam-3710	7	44	text	text	NOUN
ejpam-3710	7	45	-	-	PUNCT
ejpam-3710	7	46	books	book	NOUN
ejpam-3710	7	47	of	of	ADP
ejpam-3710	7	48	harary	harary	NOUN
ejpam-3710	7	49	[	[	X
ejpam-3710	7	50	2	2	NUM
ejpam-3710	7	51	]	]	PUNCT
ejpam-3710	7	52	and	and	CCONJ
ejpam-3710	7	53	bapat	bapat	VERB
ejpam-3710	8	1	[	[	X
ejpam-3710	8	2	1	1	NUM
ejpam-3710	8	3	]	]	PUNCT
ejpam-3710	8	4	.	.	PUNCT
ejpam-3710	9	1	the	the	DET
ejpam-3710	9	2	non	non	ADJ
ejpam-3710	9	3	-	-	ADJ
ejpam-3710	9	4	standard	standard	ADJ
ejpam-3710	9	5	will	will	AUX
ejpam-3710	9	6	be	be	AUX
ejpam-3710	9	7	given	give	VERB
ejpam-3710	9	8	in	in	ADP
ejpam-3710	9	9	this	this	DET
ejpam-3710	9	10	paper	paper	NOUN
ejpam-3710	9	11	as	as	ADP
ejpam-3710	9	12	and	and	CCONJ
ejpam-3710	9	13	when	when	SCONJ
ejpam-3710	9	14	required	require	VERB
ejpam-3710	9	15	.	.	PUNCT
ejpam-3710	10	1	throughout	throughout	ADP
ejpam-3710	10	2	this	this	DET
ejpam-3710	10	3	paper	paper	NOUN
ejpam-3710	10	4	,	,	PUNCT
ejpam-3710	10	5	g	g	PROPN
ejpam-3710	10	6	=	=	SYM
ejpam-3710	10	7	(	(	PUNCT
ejpam-3710	10	8	v	v	NOUN
ejpam-3710	10	9	,	,	PUNCT
ejpam-3710	10	10	e	e	NOUN
ejpam-3710	10	11	)	)	PUNCT
ejpam-3710	10	12	denotes	denote	VERB
ejpam-3710	10	13	a	a	DET
ejpam-3710	10	14	graph	graph	NOUN
ejpam-3710	10	15	(	(	PUNCT
ejpam-3710	10	16	finite	finite	ADJ
ejpam-3710	10	17	and	and	CCONJ
ejpam-3710	10	18	undirected	undirected	ADJ
ejpam-3710	10	19	)	)	PUNCT
ejpam-3710	10	20	and	and	CCONJ
ejpam-3710	10	21	v	v	X
ejpam-3710	10	22	=	=	SYM
ejpam-3710	10	23	v	v	NOUN
ejpam-3710	10	24	(	(	PUNCT
ejpam-3710	10	25	g	g	NOUN
ejpam-3710	10	26	)	)	PUNCT
ejpam-3710	10	27	and	and	CCONJ
ejpam-3710	10	28	e	e	X
ejpam-3710	10	29	=	=	PROPN
ejpam-3710	10	30	e(g	e(g	PROPN
ejpam-3710	10	31	)	)	PUNCT
ejpam-3710	10	32	denote	denote	VERB
ejpam-3710	10	33	vertex	vertex	NOUN
ejpam-3710	10	34	set	set	NOUN
ejpam-3710	10	35	and	and	CCONJ
ejpam-3710	10	36	edge	edge	NOUN
ejpam-3710	10	37	set	set	NOUN
ejpam-3710	10	38	of	of	ADP
ejpam-3710	10	39	g	g	NOUN
ejpam-3710	10	40	,	,	PUNCT
ejpam-3710	10	41	respectively	respectively	ADV
ejpam-3710	10	42	.	.	PUNCT
ejpam-3710	11	1	the	the	DET
ejpam-3710	11	2	degree	degree	NOUN
ejpam-3710	11	3	of	of	ADP
ejpam-3710	11	4	a	a	DET
ejpam-3710	11	5	vertex	vertex	NOUN
ejpam-3710	11	6	v	v	ADP
ejpam-3710	11	7	∈	∈	NOUN
ejpam-3710	11	8	v	v	NOUN
ejpam-3710	11	9	(	(	PUNCT
ejpam-3710	11	10	g	g	NOUN
ejpam-3710	11	11	)	)	PUNCT
ejpam-3710	11	12	,	,	PUNCT
ejpam-3710	11	13	denoted	denote	VERB
ejpam-3710	11	14	by	by	ADP
ejpam-3710	11	15	d(v	d(v	PROPN
ejpam-3710	11	16	)	)	PUNCT
ejpam-3710	11	17	or	or	CCONJ
ejpam-3710	11	18	dg(v	dg(v	NOUN
ejpam-3710	11	19	)	)	PUNCT
ejpam-3710	11	20	,	,	PUNCT
ejpam-3710	11	21	is	be	AUX
ejpam-3710	11	22	the	the	DET
ejpam-3710	11	23	number	number	NOUN
ejpam-3710	11	24	of	of	ADP
ejpam-3710	11	25	edges	edge	NOUN
ejpam-3710	11	26	incident	incident	NOUN
ejpam-3710	11	27	on	on	ADP
ejpam-3710	11	28	v	v	NOUN
ejpam-3710	11	29	,	,	PUNCT
ejpam-3710	11	30	with	with	SCONJ
ejpam-3710	11	31	self	self	NOUN
ejpam-3710	11	32	-	-	PUNCT
ejpam-3710	11	33	loops	loop	NOUN
ejpam-3710	11	34	counted	count	VERB
ejpam-3710	11	35	twice	twice	ADV
ejpam-3710	11	36	.	.	PUNCT
ejpam-3710	12	1	a	a	DET
ejpam-3710	12	2	vertex	vertex	NOUN
ejpam-3710	12	3	of	of	ADP
ejpam-3710	12	4	degree	degree	NOUN
ejpam-3710	12	5	one	one	NOUN
ejpam-3710	12	6	is	be	AUX
ejpam-3710	12	7	a	a	DET
ejpam-3710	12	8	pendant	pendant	ADJ
ejpam-3710	12	9	vertex	vertex	NOUN
ejpam-3710	12	10	and	and	CCONJ
ejpam-3710	12	11	an	an	DET
ejpam-3710	12	12	edge	edge	NOUN
ejpam-3710	12	13	incident	incident	NOUN
ejpam-3710	12	14	onto	onto	ADP
ejpam-3710	12	15	a	a	DET
ejpam-3710	12	16	pendant	pendant	ADJ
ejpam-3710	12	17	vertex	vertex	NOUN
ejpam-3710	12	18	is	be	AUX
ejpam-3710	12	19	a	a	DET
ejpam-3710	12	20	pendant	pendant	ADJ
ejpam-3710	12	21	edge	edge	NOUN
ejpam-3710	12	22	.	.	PUNCT
ejpam-3710	13	1	a	a	DET
ejpam-3710	13	2	graph	graph	NOUN
ejpam-3710	13	3	g	g	PROPN
ejpam-3710	13	4	is	be	AUX
ejpam-3710	13	5	r	r	NOUN
ejpam-3710	13	6	-	-	ADJ
ejpam-3710	13	7	regular	regular	ADJ
ejpam-3710	13	8	if	if	SCONJ
ejpam-3710	13	9	every	every	DET
ejpam-3710	13	10	vertex	vertex	NOUN
ejpam-3710	13	11	∗corresponding	∗corresponde	VERB
ejpam-3710	13	12	author	author	NOUN
ejpam-3710	13	13	.	.	PUNCT
ejpam-3710	14	1	doi	doi	NOUN
ejpam-3710	14	2	:	:	PUNCT
ejpam-3710	14	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3710	https://doi.org/10.29020/nybg.ejpam.v13i5.3710	ADJ
ejpam-3710	14	4	email	email	NOUN
ejpam-3710	14	5	addresses	address	NOUN
ejpam-3710	14	6	:	:	PUNCT
ejpam-3710	14	7	rrajendrar@gmail.com	rrajendrar@gmail.com	X
ejpam-3710	14	8	(	(	PUNCT
ejpam-3710	14	9	r.	r.	PROPN
ejpam-3710	14	10	rajendra	rajendra	PROPN
ejpam-3710	14	11	)	)	PUNCT
ejpam-3710	14	12	,	,	PUNCT
ejpam-3710	14	13	pskreddy@jssstuniv.in	pskreddy@jssstuniv.in	PROPN
ejpam-3710	14	14	(	(	PUNCT
ejpam-3710	15	1	p.	p.	PROPN
ejpam-3710	15	2	s.	s.	PROPN
ejpam-3710	15	3	k.	k.	PROPN
ejpam-3710	15	4	reddy	reddy	PROPN
ejpam-3710	15	5	)	)	PUNCT
ejpam-3710	15	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3710	15	7	1097	1097	NUM
ejpam-3710	16	1	c	c	NOUN
ejpam-3710	16	2	©	©	PROPN
ejpam-3710	16	3	2020	2020	NUM
ejpam-3710	16	4	ejpam	ejpam	VERB
ejpam-3710	16	5	all	all	DET
ejpam-3710	16	6	rights	right	NOUN
ejpam-3710	16	7	reserved	reserve	VERB
ejpam-3710	16	8	.	.	PUNCT
ejpam-3710	17	1	r.	r.	PROPN
ejpam-3710	17	2	rajendra	rajendra	PROPN
ejpam-3710	17	3	,	,	PUNCT
ejpam-3710	17	4	p.	p.	PROPN
ejpam-3710	17	5	s.	s.	PROPN
ejpam-3710	18	1	k.	k.	PROPN
ejpam-3710	18	2	reddy	reddy	PROPN
ejpam-3710	18	3	/	/	SYM
ejpam-3710	18	4	eur	eur	PROPN
ejpam-3710	18	5	.	.	PUNCT
ejpam-3710	19	1	j.	j.	PROPN
ejpam-3710	19	2	pure	pure	PROPN
ejpam-3710	19	3	appl	appl	PROPN
ejpam-3710	19	4	.	.	PROPN
ejpam-3710	19	5	math	math	PROPN
ejpam-3710	19	6	,	,	PUNCT
ejpam-3710	19	7	13	13	NUM
ejpam-3710	19	8	(	(	PUNCT
ejpam-3710	19	9	5	5	NUM
ejpam-3710	19	10	)	)	PUNCT
ejpam-3710	19	11	(	(	PUNCT
ejpam-3710	19	12	2020	2020	NUM
ejpam-3710	19	13	)	)	PUNCT
ejpam-3710	19	14	,	,	PUNCT
ejpam-3710	19	15	1097	1097	NUM
ejpam-3710	19	16	-	-	SYM
ejpam-3710	19	17	1109	1109	NUM
ejpam-3710	19	18	1098	1098	NUM
ejpam-3710	19	19	of	of	ADP
ejpam-3710	19	20	g	g	PROPN
ejpam-3710	19	21	has	have	VERB
ejpam-3710	19	22	degree	degree	NOUN
ejpam-3710	19	23	r.	r.	NOUN
ejpam-3710	19	24	the	the	DET
ejpam-3710	19	25	minimum	minimum	NOUN
ejpam-3710	19	26	degree	degree	NOUN
ejpam-3710	19	27	δ(g	δ(g	ADV
ejpam-3710	19	28	)	)	PUNCT
ejpam-3710	19	29	of	of	ADP
ejpam-3710	19	30	a	a	DET
ejpam-3710	19	31	graph	graph	NOUN
ejpam-3710	19	32	g	g	NOUN
ejpam-3710	19	33	is	be	AUX
ejpam-3710	19	34	the	the	DET
ejpam-3710	19	35	minimum	minimum	ADJ
ejpam-3710	19	36	degree	degree	NOUN
ejpam-3710	19	37	among	among	ADP
ejpam-3710	19	38	all	all	DET
ejpam-3710	19	39	the	the	DET
ejpam-3710	19	40	vertices	vertex	NOUN
ejpam-3710	19	41	of	of	ADP
ejpam-3710	19	42	g	g	PROPN
ejpam-3710	19	43	and	and	CCONJ
ejpam-3710	19	44	the	the	DET
ejpam-3710	19	45	maximum	maximum	ADJ
ejpam-3710	19	46	degree	degree	NOUN
ejpam-3710	19	47	∆(g	∆(g	NOUN
ejpam-3710	19	48	)	)	PUNCT
ejpam-3710	19	49	of	of	ADP
ejpam-3710	19	50	g	g	PROPN
ejpam-3710	19	51	is	be	AUX
ejpam-3710	19	52	the	the	DET
ejpam-3710	19	53	maximum	maximum	ADJ
ejpam-3710	19	54	degree	degree	NOUN
ejpam-3710	19	55	among	among	ADP
ejpam-3710	19	56	all	all	DET
ejpam-3710	19	57	the	the	DET
ejpam-3710	19	58	vertices	vertex	NOUN
ejpam-3710	19	59	of	of	ADP
ejpam-3710	19	60	g.	g.	PROPN
ejpam-3710	19	61	two	two	NUM
ejpam-3710	19	62	non	non	ADJ
ejpam-3710	19	63	-	-	ADJ
ejpam-3710	19	64	distinct	distinct	ADJ
ejpam-3710	19	65	edges	edge	NOUN
ejpam-3710	19	66	in	in	ADP
ejpam-3710	19	67	a	a	DET
ejpam-3710	19	68	graph	graph	NOUN
ejpam-3710	19	69	are	be	AUX
ejpam-3710	19	70	adjacent	adjacent	ADJ
ejpam-3710	19	71	if	if	SCONJ
ejpam-3710	19	72	they	they	PRON
ejpam-3710	19	73	are	be	AUX
ejpam-3710	19	74	incident	incident	NOUN
ejpam-3710	19	75	on	on	ADP
ejpam-3710	19	76	a	a	DET
ejpam-3710	19	77	common	common	ADJ
ejpam-3710	19	78	vertex	vertex	NOUN
ejpam-3710	19	79	.	.	PUNCT
ejpam-3710	20	1	we	we	PRON
ejpam-3710	20	2	consider	consider	VERB
ejpam-3710	20	3	that	that	SCONJ
ejpam-3710	20	4	an	an	DET
ejpam-3710	20	5	edge	edge	NOUN
ejpam-3710	20	6	in	in	ADP
ejpam-3710	20	7	a	a	DET
ejpam-3710	20	8	graph	graph	NOUN
ejpam-3710	20	9	is	be	AUX
ejpam-3710	20	10	not	not	PART
ejpam-3710	20	11	adjacent	adjacent	ADJ
ejpam-3710	20	12	to	to	ADP
ejpam-3710	20	13	itself	itself	PRON
ejpam-3710	20	14	.	.	PUNCT
ejpam-3710	21	1	the	the	DET
ejpam-3710	21	2	letters	letter	NOUN
ejpam-3710	21	3	k	k	PROPN
ejpam-3710	21	4	,	,	PUNCT
ejpam-3710	21	5	l	l	NOUN
ejpam-3710	21	6	,	,	PUNCT
ejpam-3710	21	7	m	m	PROPN
ejpam-3710	21	8	,	,	PUNCT
ejpam-3710	21	9	n	n	CCONJ
ejpam-3710	21	10	,	,	PUNCT
ejpam-3710	21	11	and	and	CCONJ
ejpam-3710	21	12	r	r	NOUN
ejpam-3710	21	13	denote	denote	VERB
ejpam-3710	21	14	positive	positive	ADJ
ejpam-3710	21	15	integers	integer	NOUN
ejpam-3710	21	16	or	or	CCONJ
ejpam-3710	21	17	zero	zero	NUM
ejpam-3710	21	18	.	.	PUNCT
ejpam-3710	22	1	the	the	DET
ejpam-3710	22	2	line	line	NOUN
ejpam-3710	22	3	graph	graph	NOUN
ejpam-3710	22	4	l(g	l(g	NOUN
ejpam-3710	22	5	)	)	PUNCT
ejpam-3710	22	6	of	of	ADP
ejpam-3710	22	7	a	a	DET
ejpam-3710	22	8	simple	simple	ADJ
ejpam-3710	22	9	graph	graph	NOUN
ejpam-3710	22	10	with	with	ADP
ejpam-3710	22	11	at	at	ADV
ejpam-3710	22	12	least	least	ADV
ejpam-3710	22	13	one	one	NUM
ejpam-3710	22	14	edge	edge	NOUN
ejpam-3710	22	15	is	be	AUX
ejpam-3710	22	16	the	the	DET
ejpam-3710	22	17	graph	graph	NOUN
ejpam-3710	22	18	(	(	PUNCT
ejpam-3710	22	19	w	w	PROPN
ejpam-3710	22	20	,	,	PUNCT
ejpam-3710	22	21	f	f	PROPN
ejpam-3710	22	22	)	)	PUNCT
ejpam-3710	22	23	,	,	PUNCT
ejpam-3710	22	24	where	where	SCONJ
ejpam-3710	22	25	there	there	PRON
ejpam-3710	22	26	is	be	VERB
ejpam-3710	22	27	a	a	DET
ejpam-3710	22	28	one	one	NUM
ejpam-3710	22	29	-	-	PUNCT
ejpam-3710	22	30	to	to	ADP
ejpam-3710	22	31	-	-	PUNCT
ejpam-3710	22	32	one	one	NUM
ejpam-3710	22	33	correspondence	correspondence	NOUN
ejpam-3710	22	34	φ	φ	NOUN
ejpam-3710	22	35	from	from	ADP
ejpam-3710	22	36	e	e	PROPN
ejpam-3710	22	37	to	to	ADP
ejpam-3710	22	38	w	w	ADP
ejpam-3710	22	39	such	such	ADJ
ejpam-3710	22	40	that	that	SCONJ
ejpam-3710	22	41	there	there	PRON
ejpam-3710	22	42	is	be	VERB
ejpam-3710	22	43	an	an	DET
ejpam-3710	22	44	edge	edge	NOUN
ejpam-3710	22	45	between	between	ADP
ejpam-3710	22	46	φ(α	φ(α	NOUN
ejpam-3710	22	47	)	)	PUNCT
ejpam-3710	22	48	and	and	CCONJ
ejpam-3710	22	49	φ(β	φ(β	NOUN
ejpam-3710	22	50	)	)	PUNCT
ejpam-3710	22	51	if	if	SCONJ
ejpam-3710	22	52	and	and	CCONJ
ejpam-3710	22	53	only	only	ADV
ejpam-3710	22	54	if	if	SCONJ
ejpam-3710	22	55	the	the	DET
ejpam-3710	22	56	edges	edge	NOUN
ejpam-3710	22	57	α	α	NOUN
ejpam-3710	22	58	and	and	CCONJ
ejpam-3710	22	59	β	β	X
ejpam-3710	22	60	are	be	AUX
ejpam-3710	22	61	adjacent	adjacent	ADJ
ejpam-3710	22	62	.	.	PUNCT
ejpam-3710	23	1	we	we	PRON
ejpam-3710	23	2	identify	identify	VERB
ejpam-3710	23	3	the	the	DET
ejpam-3710	23	4	set	set	NOUN
ejpam-3710	23	5	w	w	NOUN
ejpam-3710	23	6	by	by	ADP
ejpam-3710	23	7	e.	e.	PROPN
ejpam-3710	23	8	the	the	DET
ejpam-3710	23	9	adjacency	adjacency	PROPN
ejpam-3710	23	10	matrix	matrix	NOUN
ejpam-3710	23	11	of	of	ADP
ejpam-3710	23	12	a	a	DET
ejpam-3710	23	13	graph	graph	NOUN
ejpam-3710	23	14	g	g	NOUN
ejpam-3710	23	15	with	with	ADP
ejpam-3710	23	16	n	n	PRON
ejpam-3710	23	17	vertices	vertex	NOUN
ejpam-3710	23	18	is	be	AUX
ejpam-3710	23	19	denoted	denote	VERB
ejpam-3710	23	20	by	by	ADP
ejpam-3710	23	21	a(g	a(g	PROPN
ejpam-3710	23	22	)	)	PUNCT
ejpam-3710	23	23	.	.	PUNCT
ejpam-3710	24	1	if	if	SCONJ
ejpam-3710	24	2	a(g	a(g	PROPN
ejpam-3710	24	3	)	)	PUNCT
ejpam-3710	24	4	is	be	AUX
ejpam-3710	24	5	an	an	DET
ejpam-3710	24	6	n×	n×	PROPN
ejpam-3710	24	7	n	n	NOUN
ejpam-3710	24	8	matrix	matrix	NOUN
ejpam-3710	24	9	and	and	CCONJ
ejpam-3710	24	10	λ1	λ1	ADJ
ejpam-3710	24	11	,	,	PUNCT
ejpam-3710	24	12	λ2	λ2	NOUN
ejpam-3710	24	13	,	,	PUNCT
ejpam-3710	24	14	.	.	PUNCT
ejpam-3710	24	15	.	.	PUNCT
ejpam-3710	25	1	.	.	PUNCT
ejpam-3710	26	1	,	,	PUNCT
ejpam-3710	26	2	λn	λn	PROPN
ejpam-3710	26	3	are	be	AUX
ejpam-3710	26	4	the	the	DET
ejpam-3710	26	5	eigenvalues	eigenvalue	NOUN
ejpam-3710	26	6	of	of	ADP
ejpam-3710	26	7	a(g	a(g	PROPN
ejpam-3710	26	8	)	)	PUNCT
ejpam-3710	26	9	,	,	PUNCT
ejpam-3710	26	10	the	the	DET
ejpam-3710	26	11	energy	energy	NOUN
ejpam-3710	26	12	of	of	ADP
ejpam-3710	26	13	g	g	PROPN
ejpam-3710	26	14	is	be	AUX
ejpam-3710	26	15	defined	define	VERB
ejpam-3710	26	16	as	as	ADP
ejpam-3710	26	17	e(g	e(g	NOUN
ejpam-3710	26	18	)	)	PUNCT
ejpam-3710	27	1	=	=	PUNCT
ejpam-3710	28	1	n∑	n∑	PROPN
ejpam-3710	28	2	i=1	i=1	PROPN
ejpam-3710	28	3	|λi|	|λi|	PROPN
ejpam-3710	28	4	.	.	PUNCT
ejpam-3710	29	1	in	in	ADP
ejpam-3710	29	2	our	our	PRON
ejpam-3710	29	3	earlier	early	ADJ
ejpam-3710	29	4	paper	paper	NOUN
ejpam-3710	29	5	[	[	X
ejpam-3710	29	6	4	4	NUM
ejpam-3710	29	7	]	]	PUNCT
ejpam-3710	29	8	,	,	PUNCT
ejpam-3710	29	9	we	we	PRON
ejpam-3710	29	10	have	have	AUX
ejpam-3710	29	11	introduced	introduce	VERB
ejpam-3710	29	12	the	the	DET
ejpam-3710	29	13	tosha	tosha	NOUN
ejpam-3710	29	14	-	-	PUNCT
ejpam-3710	29	15	degree	degree	NOUN
ejpam-3710	29	16	of	of	ADP
ejpam-3710	29	17	an	an	DET
ejpam-3710	29	18	edge	edge	NOUN
ejpam-3710	29	19	in	in	ADP
ejpam-3710	29	20	a	a	DET
ejpam-3710	29	21	graph	graph	NOUN
ejpam-3710	29	22	without	without	ADP
ejpam-3710	29	23	multiple	multiple	ADJ
ejpam-3710	29	24	edges	edge	NOUN
ejpam-3710	29	25	,	,	PUNCT
ejpam-3710	29	26	rajendra	rajendra	PROPN
ejpam-3710	29	27	-	-	PUNCT
ejpam-3710	29	28	reddy	reddy	PROPN
ejpam-3710	29	29	index	index	NOUN
ejpam-3710	29	30	of	of	ADP
ejpam-3710	29	31	a	a	DET
ejpam-3710	29	32	graph	graph	NOUN
ejpam-3710	29	33	and	and	CCONJ
ejpam-3710	29	34	tosha	tosha	NOUN
ejpam-3710	29	35	-	-	PUNCT
ejpam-3710	29	36	degree	degree	NOUN
ejpam-3710	29	37	equivalence	equivalence	NOUN
ejpam-3710	29	38	graph	graph	NOUN
ejpam-3710	29	39	of	of	ADP
ejpam-3710	29	40	a	a	DET
ejpam-3710	29	41	graph	graph	NOUN
ejpam-3710	29	42	,	,	PUNCT
ejpam-3710	29	43	and	and	CCONJ
ejpam-3710	29	44	studied	study	VERB
ejpam-3710	29	45	some	some	DET
ejpam-3710	29	46	properties	property	NOUN
ejpam-3710	29	47	.	.	PUNCT
ejpam-3710	30	1	in	in	ADP
ejpam-3710	30	2	this	this	DET
ejpam-3710	30	3	paper	paper	NOUN
ejpam-3710	30	4	,	,	PUNCT
ejpam-3710	30	5	we	we	PRON
ejpam-3710	30	6	define	define	VERB
ejpam-3710	30	7	tosha	tosha	NOUN
ejpam-3710	30	8	-	-	PUNCT
ejpam-3710	30	9	degree	degree	NOUN
ejpam-3710	30	10	of	of	ADP
ejpam-3710	30	11	an	an	DET
ejpam-3710	30	12	edge	edge	NOUN
ejpam-3710	30	13	in	in	ADP
ejpam-3710	30	14	a	a	DET
ejpam-3710	30	15	graph	graph	NOUN
ejpam-3710	30	16	in	in	ADP
ejpam-3710	30	17	which	which	PRON
ejpam-3710	30	18	multiple	multiple	ADJ
ejpam-3710	30	19	edges	edge	NOUN
ejpam-3710	30	20	are	be	AUX
ejpam-3710	30	21	allowed	allow	VERB
ejpam-3710	30	22	.	.	PUNCT
ejpam-3710	31	1	the	the	DET
ejpam-3710	31	2	aim	aim	NOUN
ejpam-3710	31	3	of	of	ADP
ejpam-3710	31	4	this	this	DET
ejpam-3710	31	5	paper	paper	NOUN
ejpam-3710	31	6	is	be	AUX
ejpam-3710	31	7	to	to	PART
ejpam-3710	31	8	introduce	introduce	VERB
ejpam-3710	31	9	the	the	DET
ejpam-3710	31	10	concepts	concept	NOUN
ejpam-3710	31	11	:	:	PUNCT
ejpam-3710	31	12	zero	zero	NUM
ejpam-3710	31	13	edges	edge	NOUN
ejpam-3710	31	14	in	in	ADP
ejpam-3710	31	15	a	a	DET
ejpam-3710	31	16	graph	graph	NOUN
ejpam-3710	31	17	,	,	PUNCT
ejpam-3710	31	18	t	t	NOUN
ejpam-3710	31	19	-line	-line	NOUN
ejpam-3710	31	20	graph	graph	NOUN
ejpam-3710	31	21	of	of	ADP
ejpam-3710	31	22	a	a	DET
ejpam-3710	31	23	multigraph	multigraph	NOUN
ejpam-3710	31	24	,	,	PUNCT
ejpam-3710	31	25	tosha	tosha	NOUN
ejpam-3710	31	26	-	-	PUNCT
ejpam-3710	31	27	adjacency	adjacency	NOUN
ejpam-3710	31	28	matrix	matrix	NOUN
ejpam-3710	31	29	,	,	PUNCT
ejpam-3710	31	30	tosha	tosha	NOUN
ejpam-3710	31	31	-	-	PUNCT
ejpam-3710	31	32	energy	energy	NOUN
ejpam-3710	31	33	,	,	PUNCT
ejpam-3710	31	34	edge	edge	NOUN
ejpam-3710	31	35	-	-	PUNCT
ejpam-3710	31	36	adjacency	adjacency	NOUN
ejpam-3710	31	37	matrix	matrix	NOUN
ejpam-3710	31	38	and	and	CCONJ
ejpam-3710	31	39	edge	edge	NOUN
ejpam-3710	31	40	energy	energy	NOUN
ejpam-3710	31	41	of	of	ADP
ejpam-3710	31	42	a	a	DET
ejpam-3710	31	43	graph	graph	NOUN
ejpam-3710	31	44	g	g	NOUN
ejpam-3710	31	45	and	and	CCONJ
ejpam-3710	31	46	obtain	obtain	VERB
ejpam-3710	31	47	some	some	DET
ejpam-3710	31	48	results	result	NOUN
ejpam-3710	31	49	.	.	PUNCT
ejpam-3710	32	1	a	a	DET
ejpam-3710	32	2	signed	sign	VERB
ejpam-3710	32	3	graph	graph	NOUN
ejpam-3710	32	4	is	be	AUX
ejpam-3710	32	5	an	an	DET
ejpam-3710	32	6	ordered	order	VERB
ejpam-3710	32	7	pair	pair	NOUN
ejpam-3710	32	8	σ	σ	NOUN
ejpam-3710	32	9	=	=	SYM
ejpam-3710	32	10	(	(	PUNCT
ejpam-3710	32	11	g	g	PROPN
ejpam-3710	32	12	,	,	PUNCT
ejpam-3710	32	13	σ	σ	PROPN
ejpam-3710	32	14	)	)	PUNCT
ejpam-3710	32	15	,	,	PUNCT
ejpam-3710	32	16	where	where	SCONJ
ejpam-3710	32	17	g	g	NOUN
ejpam-3710	32	18	=	=	SYM
ejpam-3710	32	19	(	(	PUNCT
ejpam-3710	32	20	v	v	NOUN
ejpam-3710	32	21	,	,	PUNCT
ejpam-3710	32	22	e	e	NOUN
ejpam-3710	32	23	)	)	PUNCT
ejpam-3710	32	24	is	be	AUX
ejpam-3710	32	25	a	a	DET
ejpam-3710	32	26	graph	graph	NOUN
ejpam-3710	32	27	called	call	VERB
ejpam-3710	32	28	the	the	DET
ejpam-3710	32	29	underlying	underlie	VERB
ejpam-3710	32	30	graph	graph	NOUN
ejpam-3710	32	31	of	of	ADP
ejpam-3710	32	32	σ	σ	PROPN
ejpam-3710	32	33	and	and	CCONJ
ejpam-3710	32	34	σ	σ	PROPN
ejpam-3710	32	35	:	:	PUNCT
ejpam-3710	32	36	e	e	X
ejpam-3710	32	37	→	→	PUNCT
ejpam-3710	32	38	{	{	PUNCT
ejpam-3710	32	39	+	+	ADJ
ejpam-3710	32	40	,	,	PUNCT
ejpam-3710	32	41	−	−	NOUN
ejpam-3710	32	42	}	}	PUNCT
ejpam-3710	32	43	is	be	AUX
ejpam-3710	32	44	a	a	DET
ejpam-3710	32	45	function	function	NOUN
ejpam-3710	32	46	.	.	PUNCT
ejpam-3710	33	1	a	a	DET
ejpam-3710	33	2	marking	marking	NOUN
ejpam-3710	33	3	of	of	ADP
ejpam-3710	33	4	σ	σ	PROPN
ejpam-3710	33	5	is	be	AUX
ejpam-3710	33	6	a	a	DET
ejpam-3710	33	7	function	function	NOUN
ejpam-3710	33	8	µ	µ	NOUN
ejpam-3710	33	9	:	:	PUNCT
ejpam-3710	33	10	v	v	NOUN
ejpam-3710	33	11	(	(	PUNCT
ejpam-3710	33	12	g)→	g)→	NOUN
ejpam-3710	33	13	{	{	PUNCT
ejpam-3710	33	14	+	+	NOUN
ejpam-3710	33	15	,	,	PUNCT
ejpam-3710	33	16	−	−	NOUN
ejpam-3710	33	17	}	}	PUNCT
ejpam-3710	33	18	.	.	PUNCT
ejpam-3710	34	1	in	in	ADP
ejpam-3710	34	2	[	[	X
ejpam-3710	34	3	4	4	NUM
ejpam-3710	34	4	]	]	PUNCT
ejpam-3710	34	5	,	,	PUNCT
ejpam-3710	34	6	we	we	PRON
ejpam-3710	34	7	have	have	AUX
ejpam-3710	34	8	also	also	ADV
ejpam-3710	34	9	defined	define	VERB
ejpam-3710	34	10	the	the	DET
ejpam-3710	34	11	tosha	tosha	NOUN
ejpam-3710	34	12	-	-	PUNCT
ejpam-3710	34	13	degree	degree	NOUN
ejpam-3710	34	14	equivalence	equivalence	NOUN
ejpam-3710	34	15	graph	graph	NOUN
ejpam-3710	34	16	of	of	ADP
ejpam-3710	34	17	a	a	DET
ejpam-3710	34	18	graph	graph	NOUN
ejpam-3710	34	19	which	which	PRON
ejpam-3710	34	20	is	be	AUX
ejpam-3710	34	21	motivated	motivate	VERB
ejpam-3710	34	22	us	we	PRON
ejpam-3710	34	23	to	to	PART
ejpam-3710	34	24	extend	extend	VERB
ejpam-3710	34	25	this	this	DET
ejpam-3710	34	26	notion	notion	NOUN
ejpam-3710	34	27	to	to	PART
ejpam-3710	34	28	signed	sign	VERB
ejpam-3710	34	29	graphs	graph	NOUN
ejpam-3710	34	30	as	as	SCONJ
ejpam-3710	34	31	follows	follow	VERB
ejpam-3710	34	32	:	:	PUNCT
ejpam-3710	34	33	the	the	DET
ejpam-3710	34	34	tosha	tosha	NOUN
ejpam-3710	34	35	-	-	PUNCT
ejpam-3710	34	36	degree	degree	NOUN
ejpam-3710	34	37	equivalence	equivalence	NOUN
ejpam-3710	34	38	signed	sign	VERB
ejpam-3710	34	39	graph	graph	NOUN
ejpam-3710	34	40	(	(	PUNCT
ejpam-3710	34	41	see	see	VERB
ejpam-3710	34	42	[	[	X
ejpam-3710	34	43	3	3	NUM
ejpam-3710	34	44	]	]	PUNCT
ejpam-3710	34	45	)	)	PUNCT
ejpam-3710	34	46	of	of	ADP
ejpam-3710	34	47	a	a	DET
ejpam-3710	34	48	signed	sign	VERB
ejpam-3710	34	49	graph	graph	NOUN
ejpam-3710	34	50	σ	σ	NOUN
ejpam-3710	34	51	=	=	SYM
ejpam-3710	34	52	(	(	PUNCT
ejpam-3710	34	53	g	g	PROPN
ejpam-3710	34	54	,	,	PUNCT
ejpam-3710	34	55	σ	σ	PROPN
ejpam-3710	34	56	)	)	PUNCT
ejpam-3710	34	57	as	as	ADP
ejpam-3710	34	58	a	a	DET
ejpam-3710	34	59	signed	sign	VERB
ejpam-3710	34	60	graph	graph	NOUN
ejpam-3710	34	61	t	t	PROPN
ejpam-3710	34	62	(	(	PUNCT
ejpam-3710	34	63	σ	σ	PROPN
ejpam-3710	34	64	)	)	PUNCT
ejpam-3710	34	65	=	=	SYM
ejpam-3710	34	66	(	(	PUNCT
ejpam-3710	34	67	t	t	PROPN
ejpam-3710	34	68	(	(	PUNCT
ejpam-3710	34	69	g	g	NOUN
ejpam-3710	34	70	)	)	PUNCT
ejpam-3710	34	71	,	,	PUNCT
ejpam-3710	34	72	σ′	σ′	PROPN
ejpam-3710	34	73	)	)	PUNCT
ejpam-3710	34	74	,	,	PUNCT
ejpam-3710	34	75	where	where	SCONJ
ejpam-3710	34	76	t	t	PROPN
ejpam-3710	34	77	(	(	PUNCT
ejpam-3710	34	78	g	g	NOUN
ejpam-3710	34	79	)	)	PUNCT
ejpam-3710	34	80	is	be	AUX
ejpam-3710	34	81	the	the	DET
ejpam-3710	34	82	underlying	underlie	VERB
ejpam-3710	34	83	graph	graph	NOUN
ejpam-3710	34	84	of	of	ADP
ejpam-3710	34	85	t	t	PROPN
ejpam-3710	34	86	(	(	PUNCT
ejpam-3710	34	87	σ	σ	PROPN
ejpam-3710	34	88	)	)	PUNCT
ejpam-3710	34	89	is	be	AUX
ejpam-3710	34	90	the	the	DET
ejpam-3710	34	91	tosha	tosha	NOUN
ejpam-3710	34	92	-	-	PUNCT
ejpam-3710	34	93	degree	degree	NOUN
ejpam-3710	34	94	equivalence	equivalence	NOUN
ejpam-3710	34	95	graph	graph	NOUN
ejpam-3710	34	96	of	of	ADP
ejpam-3710	34	97	g	g	NOUN
ejpam-3710	34	98	,	,	PUNCT
ejpam-3710	34	99	where	where	SCONJ
ejpam-3710	34	100	for	for	ADP
ejpam-3710	34	101	any	any	DET
ejpam-3710	34	102	edge	edge	NOUN
ejpam-3710	34	103	e1e2	e1e2	X
ejpam-3710	34	104	in	in	ADP
ejpam-3710	34	105	t	t	PROPN
ejpam-3710	34	106	(	(	PUNCT
ejpam-3710	34	107	σ	σ	PROPN
ejpam-3710	34	108	)	)	PUNCT
ejpam-3710	34	109	,	,	PUNCT
ejpam-3710	34	110	σ′(e1e2	σ′(e1e2	PROPN
ejpam-3710	34	111	)	)	PUNCT
ejpam-3710	34	112	=	=	SYM
ejpam-3710	34	113	σ(e1)σ(e2	σ(e1)σ(e2	PROPN
ejpam-3710	34	114	)	)	PUNCT
ejpam-3710	34	115	.	.	PUNCT
ejpam-3710	35	1	hence	hence	ADV
ejpam-3710	35	2	,	,	PUNCT
ejpam-3710	35	3	we	we	PRON
ejpam-3710	35	4	shall	shall	AUX
ejpam-3710	35	5	call	call	VERB
ejpam-3710	35	6	a	a	DET
ejpam-3710	35	7	given	give	VERB
ejpam-3710	35	8	signed	sign	VERB
ejpam-3710	35	9	graph	graph	NOUN
ejpam-3710	35	10	σ	σ	NOUN
ejpam-3710	35	11	as	as	ADP
ejpam-3710	35	12	tosha	tosha	NOUN
ejpam-3710	35	13	-	-	PUNCT
ejpam-3710	35	14	degree	degree	NOUN
ejpam-3710	35	15	equivalence	equivalence	NOUN
ejpam-3710	35	16	signed	sign	VERB
ejpam-3710	35	17	graph	graph	NOUN
ejpam-3710	35	18	if	if	SCONJ
ejpam-3710	35	19	it	it	PRON
ejpam-3710	35	20	is	be	AUX
ejpam-3710	35	21	isomorphic	isomorphic	ADJ
ejpam-3710	35	22	to	to	ADP
ejpam-3710	35	23	the	the	DET
ejpam-3710	35	24	tosha	tosha	NOUN
ejpam-3710	35	25	-	-	PUNCT
ejpam-3710	35	26	degree	degree	NOUN
ejpam-3710	35	27	equivalence	equivalence	NOUN
ejpam-3710	35	28	signed	sign	VERB
ejpam-3710	35	29	graph	graph	NOUN
ejpam-3710	35	30	t	t	PROPN
ejpam-3710	35	31	(	(	PUNCT
ejpam-3710	35	32	σ′	σ′	PROPN
ejpam-3710	35	33	)	)	PUNCT
ejpam-3710	35	34	of	of	ADP
ejpam-3710	35	35	some	some	DET
ejpam-3710	35	36	sigraph	sigraph	NOUN
ejpam-3710	35	37	σ′	σ′	PROPN
ejpam-3710	35	38	(	(	PUNCT
ejpam-3710	35	39	see	see	VERB
ejpam-3710	35	40	[	[	X
ejpam-3710	35	41	3	3	NUM
ejpam-3710	35	42	]	]	NUM
ejpam-3710	35	43	)	)	PUNCT
ejpam-3710	35	44	.	.	PUNCT
ejpam-3710	36	1	in	in	ADP
ejpam-3710	36	2	[	[	X
ejpam-3710	36	3	3	3	NUM
ejpam-3710	36	4	]	]	PUNCT
ejpam-3710	36	5	,	,	PUNCT
ejpam-3710	36	6	we	we	PRON
ejpam-3710	36	7	offered	offer	VERB
ejpam-3710	36	8	a	a	DET
ejpam-3710	36	9	switching	switch	VERB
ejpam-3710	36	10	equivalence	equivalence	NOUN
ejpam-3710	36	11	characterization	characterization	NOUN
ejpam-3710	36	12	of	of	ADP
ejpam-3710	36	13	signed	sign	VERB
ejpam-3710	36	14	graphs	graph	NOUN
ejpam-3710	36	15	that	that	PRON
ejpam-3710	36	16	are	be	AUX
ejpam-3710	36	17	switching	switch	VERB
ejpam-3710	36	18	equivalent	equivalent	ADJ
ejpam-3710	36	19	to	to	ADP
ejpam-3710	36	20	tosha	tosha	NOUN
ejpam-3710	36	21	-	-	PUNCT
ejpam-3710	36	22	degree	degree	NOUN
ejpam-3710	36	23	equivalence	equivalence	NOUN
ejpam-3710	36	24	signed	sign	VERB
ejpam-3710	36	25	graphs	graph	NOUN
ejpam-3710	36	26	and	and	CCONJ
ejpam-3710	36	27	kth	kth	PROPN
ejpam-3710	36	28	iterated	iterate	VERB
ejpam-3710	36	29	tosha	tosha	NOUN
ejpam-3710	36	30	-	-	PUNCT
ejpam-3710	36	31	degree	degree	NOUN
ejpam-3710	36	32	equivalence	equivalence	NOUN
ejpam-3710	36	33	signed	sign	VERB
ejpam-3710	36	34	graphs	graph	NOUN
ejpam-3710	36	35	.	.	PUNCT
ejpam-3710	37	1	further	far	ADV
ejpam-3710	37	2	,	,	PUNCT
ejpam-3710	37	3	we	we	PRON
ejpam-3710	37	4	have	have	AUX
ejpam-3710	37	5	presented	present	VERB
ejpam-3710	37	6	the	the	DET
ejpam-3710	37	7	structural	structural	ADJ
ejpam-3710	37	8	characterization	characterization	NOUN
ejpam-3710	37	9	of	of	ADP
ejpam-3710	37	10	tosha	tosha	NOUN
ejpam-3710	37	11	-	-	PUNCT
ejpam-3710	37	12	degree	degree	NOUN
ejpam-3710	37	13	equivalence	equivalence	NOUN
ejpam-3710	37	14	signed	sign	VERB
ejpam-3710	37	15	graphs	graph	NOUN
ejpam-3710	37	16	.	.	PUNCT
ejpam-3710	38	1	r.	r.	PROPN
ejpam-3710	38	2	rajendra	rajendra	PROPN
ejpam-3710	38	3	,	,	PUNCT
ejpam-3710	38	4	p.	p.	PROPN
ejpam-3710	38	5	s.	s.	PROPN
ejpam-3710	39	1	k.	k.	PROPN
ejpam-3710	39	2	reddy	reddy	PROPN
ejpam-3710	39	3	/	/	SYM
ejpam-3710	39	4	eur	eur	PROPN
ejpam-3710	39	5	.	.	PUNCT
ejpam-3710	40	1	j.	j.	PROPN
ejpam-3710	40	2	pure	pure	PROPN
ejpam-3710	40	3	appl	appl	PROPN
ejpam-3710	40	4	.	.	PROPN
ejpam-3710	40	5	math	math	PROPN
ejpam-3710	40	6	,	,	PUNCT
ejpam-3710	40	7	13	13	NUM
ejpam-3710	40	8	(	(	PUNCT
ejpam-3710	40	9	5	5	NUM
ejpam-3710	40	10	)	)	PUNCT
ejpam-3710	40	11	(	(	PUNCT
ejpam-3710	40	12	2020	2020	NUM
ejpam-3710	40	13	)	)	PUNCT
ejpam-3710	40	14	,	,	PUNCT
ejpam-3710	40	15	1097	1097	NUM
ejpam-3710	40	16	-	-	SYM
ejpam-3710	40	17	1109	1109	NUM
ejpam-3710	40	18	1099	1099	NUM
ejpam-3710	40	19	2	2	NUM
ejpam-3710	40	20	.	.	PUNCT
ejpam-3710	40	21	tosha	tosha	NOUN
ejpam-3710	40	22	-	-	PUNCT
ejpam-3710	40	23	degree	degree	NOUN
ejpam-3710	40	24	of	of	ADP
ejpam-3710	40	25	an	an	DET
ejpam-3710	40	26	edge	edge	NOUN
ejpam-3710	40	27	in	in	ADP
ejpam-3710	40	28	a	a	DET
ejpam-3710	40	29	graph	graph	NOUN
ejpam-3710	40	30	in	in	ADP
ejpam-3710	40	31	[	[	X
ejpam-3710	40	32	4	4	NUM
ejpam-3710	40	33	]	]	PUNCT
ejpam-3710	40	34	,	,	PUNCT
ejpam-3710	40	35	r.	r.	PROPN
ejpam-3710	40	36	rajendra	rajendra	PROPN
ejpam-3710	40	37	and	and	CCONJ
ejpam-3710	40	38	p.s.k	p.s.k	PROPN
ejpam-3710	40	39	.	.	PUNCT
ejpam-3710	40	40	reddy	reddy	PROPN
ejpam-3710	40	41	have	have	AUX
ejpam-3710	40	42	defined	define	VERB
ejpam-3710	40	43	the	the	DET
ejpam-3710	40	44	tosha	tosha	NOUN
ejpam-3710	40	45	-	-	PUNCT
ejpam-3710	40	46	degree	degree	NOUN
ejpam-3710	40	47	of	of	ADP
ejpam-3710	40	48	an	an	DET
ejpam-3710	40	49	edge	edge	NOUN
ejpam-3710	40	50	in	in	ADP
ejpam-3710	40	51	a	a	DET
ejpam-3710	40	52	graph	graph	NOUN
ejpam-3710	40	53	without	without	ADP
ejpam-3710	40	54	multiple	multiple	ADJ
ejpam-3710	40	55	edges	edge	NOUN
ejpam-3710	40	56	as	as	SCONJ
ejpam-3710	40	57	follows	follow	VERB
ejpam-3710	40	58	:	:	PUNCT
ejpam-3710	40	59	the	the	DET
ejpam-3710	40	60	tosha	tosha	NOUN
ejpam-3710	40	61	-	-	PUNCT
ejpam-3710	40	62	degree	degree	NOUN
ejpam-3710	40	63	of	of	ADP
ejpam-3710	40	64	an	an	DET
ejpam-3710	40	65	edge	edge	NOUN
ejpam-3710	40	66	α	α	NOUN
ejpam-3710	40	67	in	in	ADP
ejpam-3710	40	68	a	a	DET
ejpam-3710	40	69	graph	graph	NOUN
ejpam-3710	40	70	g	g	NOUN
ejpam-3710	40	71	without	without	ADP
ejpam-3710	40	72	multiple	multiple	ADJ
ejpam-3710	40	73	edges	edge	NOUN
ejpam-3710	40	74	,	,	PUNCT
ejpam-3710	40	75	denoted	denote	VERB
ejpam-3710	40	76	by	by	ADP
ejpam-3710	40	77	t	t	PROPN
ejpam-3710	40	78	(	(	PUNCT
ejpam-3710	40	79	α	α	NOUN
ejpam-3710	40	80	)	)	PUNCT
ejpam-3710	40	81	,	,	PUNCT
ejpam-3710	40	82	is	be	AUX
ejpam-3710	40	83	the	the	DET
ejpam-3710	40	84	number	number	NOUN
ejpam-3710	40	85	of	of	ADP
ejpam-3710	40	86	edges	edge	NOUN
ejpam-3710	40	87	adjacent	adjacent	ADJ
ejpam-3710	40	88	to	to	ADP
ejpam-3710	40	89	α	α	NOUN
ejpam-3710	40	90	in	in	ADP
ejpam-3710	40	91	g	g	NOUN
ejpam-3710	40	92	,	,	PUNCT
ejpam-3710	40	93	with	with	SCONJ
ejpam-3710	40	94	self	self	NOUN
ejpam-3710	40	95	-	-	PUNCT
ejpam-3710	40	96	loops	loop	NOUN
ejpam-3710	40	97	counted	count	VERB
ejpam-3710	40	98	twice	twice	ADV
ejpam-3710	40	99	.	.	PUNCT
ejpam-3710	41	1	here	here	ADV
ejpam-3710	41	2	we	we	PRON
ejpam-3710	41	3	allow	allow	VERB
ejpam-3710	41	4	graphs	graph	NOUN
ejpam-3710	41	5	with	with	ADP
ejpam-3710	41	6	multiple	multiple	ADJ
ejpam-3710	41	7	edges	edge	NOUN
ejpam-3710	41	8	(	(	PUNCT
ejpam-3710	41	9	multi	multi	ADJ
ejpam-3710	41	10	-	-	NOUN
ejpam-3710	41	11	graphs	graph	NOUN
ejpam-3710	41	12	)	)	PUNCT
ejpam-3710	41	13	and	and	CCONJ
ejpam-3710	41	14	the	the	DET
ejpam-3710	41	15	new	new	ADJ
ejpam-3710	41	16	definition	definition	NOUN
ejpam-3710	41	17	of	of	ADP
ejpam-3710	41	18	the	the	DET
ejpam-3710	41	19	tosha	tosha	NOUN
ejpam-3710	41	20	-	-	PUNCT
ejpam-3710	41	21	degree	degree	NOUN
ejpam-3710	41	22	of	of	ADP
ejpam-3710	41	23	an	an	DET
ejpam-3710	41	24	edge	edge	NOUN
ejpam-3710	41	25	in	in	ADP
ejpam-3710	41	26	a	a	DET
ejpam-3710	41	27	graph	graph	NOUN
ejpam-3710	41	28	(	(	PUNCT
ejpam-3710	41	29	with	with	ADP
ejpam-3710	41	30	or	or	CCONJ
ejpam-3710	41	31	without	without	ADP
ejpam-3710	41	32	multiple	multiple	ADJ
ejpam-3710	41	33	edges	edge	NOUN
ejpam-3710	41	34	)	)	PUNCT
ejpam-3710	41	35	is	be	AUX
ejpam-3710	41	36	given	give	VERB
ejpam-3710	41	37	below	below	ADP
ejpam-3710	41	38	:	:	PUNCT
ejpam-3710	41	39	definition	definition	NOUN
ejpam-3710	41	40	1	1	NUM
ejpam-3710	41	41	.	.	PUNCT
ejpam-3710	42	1	let	let	VERB
ejpam-3710	42	2	α	α	PRON
ejpam-3710	42	3	be	be	AUX
ejpam-3710	42	4	an	an	DET
ejpam-3710	42	5	edge	edge	NOUN
ejpam-3710	42	6	in	in	ADP
ejpam-3710	42	7	a	a	DET
ejpam-3710	42	8	graph	graph	NOUN
ejpam-3710	42	9	g.	g.	NOUN
ejpam-3710	42	10	the	the	DET
ejpam-3710	42	11	tosha	tosha	NOUN
ejpam-3710	42	12	-	-	PUNCT
ejpam-3710	42	13	degree	degree	NOUN
ejpam-3710	42	14	of	of	ADP
ejpam-3710	42	15	α	α	NOUN
ejpam-3710	42	16	,	,	PUNCT
ejpam-3710	42	17	denoted	denote	VERB
ejpam-3710	42	18	by	by	ADP
ejpam-3710	42	19	t	t	PROPN
ejpam-3710	42	20	(	(	PUNCT
ejpam-3710	42	21	α	α	NOUN
ejpam-3710	42	22	)	)	PUNCT
ejpam-3710	42	23	or	or	CCONJ
ejpam-3710	42	24	tg(α	tg(α	NUM
ejpam-3710	42	25	)	)	PUNCT
ejpam-3710	42	26	,	,	PUNCT
ejpam-3710	42	27	is	be	AUX
ejpam-3710	42	28	the	the	DET
ejpam-3710	42	29	number	number	NOUN
ejpam-3710	42	30	of	of	ADP
ejpam-3710	42	31	edges	edge	NOUN
ejpam-3710	42	32	adjacent	adjacent	ADJ
ejpam-3710	42	33	to	to	ADP
ejpam-3710	42	34	α	α	NOUN
ejpam-3710	42	35	in	in	ADP
ejpam-3710	42	36	g	g	PROPN
ejpam-3710	42	37	,	,	PUNCT
ejpam-3710	42	38	where	where	SCONJ
ejpam-3710	42	39	self	self	NOUN
ejpam-3710	42	40	-	-	PUNCT
ejpam-3710	42	41	loops	loop	NOUN
ejpam-3710	42	42	and	and	CCONJ
ejpam-3710	42	43	edges	edge	NOUN
ejpam-3710	42	44	parallel	parallel	ADJ
ejpam-3710	42	45	to	to	ADP
ejpam-3710	42	46	α	α	PROPN
ejpam-3710	42	47	are	be	AUX
ejpam-3710	42	48	counted	count	VERB
ejpam-3710	42	49	twice	twice	ADV
ejpam-3710	42	50	.	.	PUNCT
ejpam-3710	43	1	by	by	ADP
ejpam-3710	43	2	the	the	DET
ejpam-3710	43	3	definition	definition	NOUN
ejpam-3710	43	4	1	1	NUM
ejpam-3710	43	5	,	,	PUNCT
ejpam-3710	43	6	for	for	ADP
ejpam-3710	43	7	any	any	DET
ejpam-3710	43	8	edge	edge	NOUN
ejpam-3710	43	9	α	α	NOUN
ejpam-3710	43	10	in	in	ADP
ejpam-3710	43	11	a	a	DET
ejpam-3710	43	12	graph	graph	NOUN
ejpam-3710	43	13	g	g	PROPN
ejpam-3710	43	14	,	,	PUNCT
ejpam-3710	43	15	t	t	PROPN
ejpam-3710	43	16	(	(	PUNCT
ejpam-3710	43	17	α	α	NOUN
ejpam-3710	43	18	)	)	PUNCT
ejpam-3710	43	19	≥	≥	NOUN
ejpam-3710	43	20	0	0	NUM
ejpam-3710	43	21	.	.	PUNCT
ejpam-3710	44	1	definition	definition	NOUN
ejpam-3710	44	2	2	2	NUM
ejpam-3710	44	3	.	.	PUNCT
ejpam-3710	45	1	a	a	DET
ejpam-3710	45	2	graph	graph	NOUN
ejpam-3710	45	3	g	g	NOUN
ejpam-3710	45	4	is	be	AUX
ejpam-3710	45	5	said	say	VERB
ejpam-3710	45	6	to	to	PART
ejpam-3710	45	7	be	be	AUX
ejpam-3710	45	8	a	a	DET
ejpam-3710	45	9	tosha	tosha	NOUN
ejpam-3710	45	10	-	-	PUNCT
ejpam-3710	45	11	regular	regular	ADJ
ejpam-3710	45	12	graph	graph	NOUN
ejpam-3710	45	13	if	if	SCONJ
ejpam-3710	45	14	all	all	DET
ejpam-3710	45	15	edges	edge	NOUN
ejpam-3710	45	16	are	be	AUX
ejpam-3710	45	17	of	of	ADP
ejpam-3710	45	18	equal	equal	ADJ
ejpam-3710	45	19	tosha	tosha	NOUN
ejpam-3710	45	20	-	-	PUNCT
ejpam-3710	45	21	degree	degree	NOUN
ejpam-3710	45	22	.	.	PUNCT
ejpam-3710	46	1	we	we	PRON
ejpam-3710	46	2	say	say	VERB
ejpam-3710	46	3	that	that	SCONJ
ejpam-3710	46	4	g	g	PROPN
ejpam-3710	46	5	is	be	AUX
ejpam-3710	46	6	l	l	NOUN
ejpam-3710	46	7	-	-	PUNCT
ejpam-3710	46	8	tosha	tosha	NOUN
ejpam-3710	46	9	-	-	PUNCT
ejpam-3710	46	10	regular	regular	ADJ
ejpam-3710	46	11	,	,	PUNCT
ejpam-3710	46	12	if	if	SCONJ
ejpam-3710	46	13	t	t	PROPN
ejpam-3710	46	14	(	(	PUNCT
ejpam-3710	46	15	α	α	NOUN
ejpam-3710	46	16	)	)	PUNCT
ejpam-3710	46	17	=	=	SYM
ejpam-3710	46	18	l	l	NOUN
ejpam-3710	46	19	,	,	PUNCT
ejpam-3710	46	20	for	for	ADP
ejpam-3710	46	21	all	all	DET
ejpam-3710	46	22	α	α	PRON
ejpam-3710	46	23	∈	∈	PROPN
ejpam-3710	46	24	e(g	e(g	PROPN
ejpam-3710	46	25	)	)	PUNCT
ejpam-3710	46	26	.	.	PUNCT
ejpam-3710	47	1	the	the	DET
ejpam-3710	47	2	following	follow	VERB
ejpam-3710	47	3	proposition	proposition	NOUN
ejpam-3710	47	4	is	be	AUX
ejpam-3710	47	5	proved	prove	VERB
ejpam-3710	47	6	for	for	ADP
ejpam-3710	47	7	graphs	graph	NOUN
ejpam-3710	47	8	without	without	ADP
ejpam-3710	47	9	parallel	parallel	ADJ
ejpam-3710	47	10	edges	edge	NOUN
ejpam-3710	47	11	in	in	ADP
ejpam-3710	47	12	[	[	X
ejpam-3710	47	13	4	4	NUM
ejpam-3710	47	14	]	]	PUNCT
ejpam-3710	47	15	.	.	PUNCT
ejpam-3710	48	1	this	this	DET
ejpam-3710	48	2	result	result	NOUN
ejpam-3710	48	3	is	be	AUX
ejpam-3710	48	4	true	true	ADJ
ejpam-3710	48	5	for	for	ADP
ejpam-3710	48	6	graphs	graph	NOUN
ejpam-3710	48	7	having	have	VERB
ejpam-3710	48	8	parallel	parallel	ADJ
ejpam-3710	48	9	edges	edge	NOUN
ejpam-3710	48	10	also	also	ADV
ejpam-3710	48	11	with	with	ADP
ejpam-3710	48	12	respect	respect	NOUN
ejpam-3710	48	13	to	to	ADP
ejpam-3710	48	14	the	the	DET
ejpam-3710	48	15	definition	definition	NOUN
ejpam-3710	48	16	1	1	NUM
ejpam-3710	48	17	.	.	PUNCT
ejpam-3710	48	18	proposition	proposition	NOUN
ejpam-3710	48	19	1	1	NUM
ejpam-3710	48	20	.	.	PUNCT
ejpam-3710	49	1	[	[	X
ejpam-3710	49	2	4	4	X
ejpam-3710	49	3	]	]	PUNCT
ejpam-3710	49	4	let	let	VERB
ejpam-3710	49	5	α	α	PRON
ejpam-3710	49	6	be	be	AUX
ejpam-3710	49	7	an	an	DET
ejpam-3710	49	8	edge	edge	NOUN
ejpam-3710	49	9	in	in	ADP
ejpam-3710	49	10	a	a	DET
ejpam-3710	49	11	graph	graph	NOUN
ejpam-3710	49	12	g	g	NOUN
ejpam-3710	49	13	with	with	ADP
ejpam-3710	49	14	end	end	NOUN
ejpam-3710	49	15	vertices	vertice	VERB
ejpam-3710	49	16	u	u	NOUN
ejpam-3710	49	17	and	and	CCONJ
ejpam-3710	49	18	v.	v.	PROPN
ejpam-3710	49	19	(	(	PUNCT
ejpam-3710	49	20	i	i	NOUN
ejpam-3710	49	21	)	)	PUNCT
ejpam-3710	49	22	if	if	SCONJ
ejpam-3710	49	23	α	α	PRON
ejpam-3710	49	24	is	be	AUX
ejpam-3710	49	25	not	not	PART
ejpam-3710	49	26	a	a	DET
ejpam-3710	49	27	self	self	NOUN
ejpam-3710	49	28	-	-	PUNCT
ejpam-3710	49	29	loop	loop	NOUN
ejpam-3710	49	30	,	,	PUNCT
ejpam-3710	49	31	then	then	ADV
ejpam-3710	49	32	t	t	PROPN
ejpam-3710	49	33	(	(	PUNCT
ejpam-3710	49	34	α	α	NOUN
ejpam-3710	49	35	)	)	PUNCT
ejpam-3710	49	36	=	=	SYM
ejpam-3710	49	37	d(u	d(u	PROPN
ejpam-3710	49	38	)	)	PUNCT
ejpam-3710	50	1	+	+	CCONJ
ejpam-3710	50	2	d(v)−	d(v)−	PROPN
ejpam-3710	50	3	2	2	NUM
ejpam-3710	50	4	(	(	PUNCT
ejpam-3710	50	5	1	1	NUM
ejpam-3710	50	6	)	)	PUNCT
ejpam-3710	50	7	(	(	PUNCT
ejpam-3710	50	8	ii	ii	NOUN
ejpam-3710	50	9	)	)	PUNCT
ejpam-3710	50	10	if	if	SCONJ
ejpam-3710	50	11	α	α	PRON
ejpam-3710	50	12	is	be	AUX
ejpam-3710	50	13	a	a	DET
ejpam-3710	50	14	self	self	NOUN
ejpam-3710	50	15	-	-	PUNCT
ejpam-3710	50	16	loop	loop	NOUN
ejpam-3710	50	17	,	,	PUNCT
ejpam-3710	50	18	then	then	ADV
ejpam-3710	50	19	u	u	NOUN
ejpam-3710	50	20	=	=	PROPN
ejpam-3710	50	21	v	v	PROPN
ejpam-3710	50	22	and	and	CCONJ
ejpam-3710	50	23	t	t	PROPN
ejpam-3710	50	24	(	(	PUNCT
ejpam-3710	50	25	α	α	NOUN
ejpam-3710	50	26	)	)	PUNCT
ejpam-3710	51	1	=	=	SYM
ejpam-3710	51	2	d(u)−	d(u)−	PROPN
ejpam-3710	51	3	2	2	NUM
ejpam-3710	51	4	(	(	PUNCT
ejpam-3710	51	5	2	2	NUM
ejpam-3710	51	6	)	)	PUNCT
ejpam-3710	51	7	proof	proof	NOUN
ejpam-3710	51	8	.	.	PUNCT
ejpam-3710	52	1	the	the	DET
ejpam-3710	52	2	proof	proof	NOUN
ejpam-3710	52	3	follows	follow	VERB
ejpam-3710	52	4	by	by	ADP
ejpam-3710	52	5	the	the	DET
ejpam-3710	52	6	definition	definition	NOUN
ejpam-3710	52	7	1	1	NUM
ejpam-3710	52	8	,	,	PUNCT
ejpam-3710	52	9	and	and	CCONJ
ejpam-3710	52	10	the	the	DET
ejpam-3710	52	11	definition	definition	NOUN
ejpam-3710	52	12	of	of	ADP
ejpam-3710	52	13	degree	degree	NOUN
ejpam-3710	52	14	of	of	ADP
ejpam-3710	52	15	a	a	DET
ejpam-3710	52	16	vertex	vertex	NOUN
ejpam-3710	52	17	.	.	PUNCT
ejpam-3710	53	1	observation	observation	NOUN
ejpam-3710	53	2	:	:	PUNCT
ejpam-3710	53	3	by	by	SCONJ
ejpam-3710	53	4	the	the	DET
ejpam-3710	53	5	proposition	proposition	NOUN
ejpam-3710	53	6	1	1	NUM
ejpam-3710	53	7	,	,	PUNCT
ejpam-3710	53	8	for	for	ADP
ejpam-3710	53	9	an	an	DET
ejpam-3710	53	10	edge	edge	NOUN
ejpam-3710	53	11	α	α	NOUN
ejpam-3710	53	12	in	in	ADP
ejpam-3710	53	13	a	a	DET
ejpam-3710	53	14	graph	graph	NOUN
ejpam-3710	53	15	g	g	NOUN
ejpam-3710	53	16	,	,	PUNCT
ejpam-3710	53	17	it	it	PRON
ejpam-3710	53	18	follows	follow	VERB
ejpam-3710	53	19	that	that	SCONJ
ejpam-3710	53	20	,	,	PUNCT
ejpam-3710	53	21	(	(	PUNCT
ejpam-3710	53	22	a	a	X
ejpam-3710	53	23	)	)	PUNCT
ejpam-3710	53	24	if	if	SCONJ
ejpam-3710	53	25	α	α	PRON
ejpam-3710	53	26	is	be	AUX
ejpam-3710	53	27	not	not	PART
ejpam-3710	53	28	a	a	DET
ejpam-3710	53	29	self	self	NOUN
ejpam-3710	53	30	-	-	PUNCT
ejpam-3710	53	31	loop	loop	NOUN
ejpam-3710	53	32	,	,	PUNCT
ejpam-3710	53	33	then	then	ADV
ejpam-3710	53	34	2(δ(g)−	2(δ(g)−	NUM
ejpam-3710	53	35	1	1	NUM
ejpam-3710	53	36	)	)	PUNCT
ejpam-3710	53	37	≤	≤	NOUN
ejpam-3710	53	38	t	t	NOUN
ejpam-3710	53	39	(	(	PUNCT
ejpam-3710	53	40	α	α	NOUN
ejpam-3710	53	41	)	)	PUNCT
ejpam-3710	53	42	≤	≤	NOUN
ejpam-3710	53	43	2(∆(g)−	2(∆(g)−	NUM
ejpam-3710	53	44	1	1	NUM
ejpam-3710	53	45	)	)	PUNCT
ejpam-3710	53	46	;	;	PUNCT
ejpam-3710	53	47	(	(	PUNCT
ejpam-3710	53	48	b	b	X
ejpam-3710	53	49	)	)	PUNCT
ejpam-3710	53	50	if	if	SCONJ
ejpam-3710	53	51	α	α	PRON
ejpam-3710	53	52	is	be	AUX
ejpam-3710	53	53	a	a	DET
ejpam-3710	53	54	self	self	NOUN
ejpam-3710	53	55	-	-	PUNCT
ejpam-3710	53	56	loop	loop	NOUN
ejpam-3710	53	57	,	,	PUNCT
ejpam-3710	53	58	then	then	ADV
ejpam-3710	53	59	δ(g)−	δ(g)−	VERB
ejpam-3710	53	60	2	2	NUM
ejpam-3710	53	61	≤	≤	NOUN
ejpam-3710	53	62	t	t	NOUN
ejpam-3710	53	63	(	(	PUNCT
ejpam-3710	53	64	α	α	NOUN
ejpam-3710	53	65	)	)	PUNCT
ejpam-3710	53	66	≤	≤	NUM
ejpam-3710	53	67	∆(g)−	∆(g)−	PRON
ejpam-3710	53	68	2	2	NUM
ejpam-3710	53	69	.	.	PUNCT
ejpam-3710	53	70	corollary	corollary	ADJ
ejpam-3710	53	71	1	1	NUM
ejpam-3710	53	72	.	.	PUNCT
ejpam-3710	54	1	[	[	X
ejpam-3710	54	2	4	4	X
ejpam-3710	54	3	]	]	X
ejpam-3710	54	4	if	if	SCONJ
ejpam-3710	54	5	g	g	PROPN
ejpam-3710	54	6	is	be	AUX
ejpam-3710	54	7	a	a	DET
ejpam-3710	54	8	simple	simple	ADJ
ejpam-3710	54	9	graph	graph	NOUN
ejpam-3710	54	10	and	and	CCONJ
ejpam-3710	54	11	α	α	PRON
ejpam-3710	54	12	is	be	AUX
ejpam-3710	54	13	an	an	DET
ejpam-3710	54	14	edge	edge	NOUN
ejpam-3710	54	15	in	in	ADP
ejpam-3710	54	16	g	g	NOUN
ejpam-3710	54	17	,	,	PUNCT
ejpam-3710	54	18	then	then	ADV
ejpam-3710	54	19	t	t	PROPN
ejpam-3710	54	20	(	(	PUNCT
ejpam-3710	54	21	α	α	NOUN
ejpam-3710	54	22	)	)	PUNCT
ejpam-3710	54	23	=	=	SYM
ejpam-3710	54	24	dl(g)(α	dl(g)(α	NOUN
ejpam-3710	54	25	)	)	PUNCT
ejpam-3710	54	26	(	(	PUNCT
ejpam-3710	54	27	3	3	X
ejpam-3710	54	28	)	)	PUNCT
ejpam-3710	54	29	where	where	SCONJ
ejpam-3710	54	30	dl(g)(α	dl(g)(α	NOUN
ejpam-3710	54	31	)	)	PUNCT
ejpam-3710	54	32	is	be	AUX
ejpam-3710	54	33	the	the	DET
ejpam-3710	54	34	degree	degree	NOUN
ejpam-3710	54	35	of	of	ADP
ejpam-3710	54	36	α	α	PRON
ejpam-3710	54	37	as	as	ADP
ejpam-3710	54	38	a	a	DET
ejpam-3710	54	39	vertex	vertex	NOUN
ejpam-3710	54	40	in	in	ADP
ejpam-3710	54	41	the	the	DET
ejpam-3710	54	42	line	line	NOUN
ejpam-3710	54	43	graph	graph	NOUN
ejpam-3710	54	44	l(g	l(g	PROPN
ejpam-3710	54	45	)	)	PUNCT
ejpam-3710	54	46	of	of	ADP
ejpam-3710	54	47	g.	g.	PROPN
ejpam-3710	54	48	proof	proof	PROPN
ejpam-3710	54	49	.	.	PUNCT
ejpam-3710	55	1	follows	follow	VERB
ejpam-3710	55	2	from	from	ADP
ejpam-3710	55	3	the	the	DET
ejpam-3710	55	4	definition	definition	NOUN
ejpam-3710	55	5	of	of	ADP
ejpam-3710	55	6	l(g	l(g	PROPN
ejpam-3710	55	7	)	)	PUNCT
ejpam-3710	55	8	and	and	CCONJ
ejpam-3710	55	9	eq.(1	eq.(1	NUM
ejpam-3710	55	10	)	)	PUNCT
ejpam-3710	55	11	.	.	PUNCT
ejpam-3710	56	1	r.	r.	PROPN
ejpam-3710	56	2	rajendra	rajendra	PROPN
ejpam-3710	56	3	,	,	PUNCT
ejpam-3710	56	4	p.	p.	PROPN
ejpam-3710	56	5	s.	s.	PROPN
ejpam-3710	57	1	k.	k.	PROPN
ejpam-3710	57	2	reddy	reddy	PROPN
ejpam-3710	57	3	/	/	SYM
ejpam-3710	57	4	eur	eur	PROPN
ejpam-3710	57	5	.	.	PUNCT
ejpam-3710	58	1	j.	j.	PROPN
ejpam-3710	58	2	pure	pure	PROPN
ejpam-3710	58	3	appl	appl	PROPN
ejpam-3710	58	4	.	.	PROPN
ejpam-3710	58	5	math	math	PROPN
ejpam-3710	58	6	,	,	PUNCT
ejpam-3710	58	7	13	13	NUM
ejpam-3710	58	8	(	(	PUNCT
ejpam-3710	58	9	5	5	NUM
ejpam-3710	58	10	)	)	PUNCT
ejpam-3710	58	11	(	(	PUNCT
ejpam-3710	58	12	2020	2020	NUM
ejpam-3710	58	13	)	)	PUNCT
ejpam-3710	58	14	,	,	PUNCT
ejpam-3710	58	15	1097	1097	NUM
ejpam-3710	58	16	-	-	SYM
ejpam-3710	58	17	1109	1109	NUM
ejpam-3710	58	18	1100	1100	NUM
ejpam-3710	58	19	corollary	corollary	NOUN
ejpam-3710	58	20	2	2	NUM
ejpam-3710	58	21	.	.	PUNCT
ejpam-3710	59	1	in	in	ADP
ejpam-3710	59	2	a	a	DET
ejpam-3710	59	3	simple	simple	ADJ
ejpam-3710	59	4	graph	graph	NOUN
ejpam-3710	59	5	g	g	NOUN
ejpam-3710	59	6	,	,	PUNCT
ejpam-3710	59	7	the	the	DET
ejpam-3710	59	8	number	number	NOUN
ejpam-3710	59	9	of	of	ADP
ejpam-3710	59	10	odd	odd	ADJ
ejpam-3710	59	11	tosha	tosha	NOUN
ejpam-3710	59	12	-	-	PUNCT
ejpam-3710	59	13	degree	degree	NOUN
ejpam-3710	59	14	edges	edge	NOUN
ejpam-3710	59	15	is	be	AUX
ejpam-3710	59	16	even	even	ADV
ejpam-3710	59	17	.	.	PUNCT
ejpam-3710	60	1	proof	proof	NOUN
ejpam-3710	60	2	.	.	PUNCT
ejpam-3710	61	1	in	in	ADP
ejpam-3710	61	2	any	any	DET
ejpam-3710	61	3	graph	graph	NOUN
ejpam-3710	61	4	the	the	DET
ejpam-3710	61	5	number	number	NOUN
ejpam-3710	61	6	of	of	ADP
ejpam-3710	61	7	odd	odd	ADJ
ejpam-3710	61	8	degree	degree	NOUN
ejpam-3710	61	9	vertices	vertex	NOUN
ejpam-3710	61	10	is	be	AUX
ejpam-3710	61	11	even	even	ADV
ejpam-3710	61	12	.	.	PUNCT
ejpam-3710	62	1	so	so	ADV
ejpam-3710	62	2	,	,	PUNCT
ejpam-3710	62	3	the	the	DET
ejpam-3710	62	4	number	number	NOUN
ejpam-3710	62	5	of	of	ADP
ejpam-3710	62	6	odd	odd	ADJ
ejpam-3710	62	7	degree	degree	NOUN
ejpam-3710	62	8	vertices	vertex	NOUN
ejpam-3710	62	9	in	in	ADP
ejpam-3710	62	10	the	the	DET
ejpam-3710	62	11	line	line	NOUN
ejpam-3710	62	12	graph	graph	NOUN
ejpam-3710	62	13	l(g	l(g	NOUN
ejpam-3710	62	14	)	)	PUNCT
ejpam-3710	62	15	of	of	ADP
ejpam-3710	62	16	g	g	PROPN
ejpam-3710	62	17	is	be	AUX
ejpam-3710	62	18	even	even	ADV
ejpam-3710	62	19	.	.	PUNCT
ejpam-3710	63	1	since	since	SCONJ
ejpam-3710	63	2	the	the	DET
ejpam-3710	63	3	vertices	vertex	NOUN
ejpam-3710	63	4	in	in	ADP
ejpam-3710	63	5	l(g	l(g	NOUN
ejpam-3710	63	6	)	)	PUNCT
ejpam-3710	63	7	are	be	AUX
ejpam-3710	63	8	corresponding	correspond	VERB
ejpam-3710	63	9	to	to	ADP
ejpam-3710	63	10	the	the	DET
ejpam-3710	63	11	edges	edge	NOUN
ejpam-3710	63	12	in	in	ADP
ejpam-3710	63	13	g	g	NOUN
ejpam-3710	63	14	,	,	PUNCT
ejpam-3710	63	15	by	by	ADP
ejpam-3710	63	16	eq.(3	eq.(3	NOUN
ejpam-3710	63	17	)	)	PUNCT
ejpam-3710	63	18	it	it	PRON
ejpam-3710	63	19	follows	follow	VERB
ejpam-3710	63	20	that	that	SCONJ
ejpam-3710	63	21	,	,	PUNCT
ejpam-3710	63	22	the	the	DET
ejpam-3710	63	23	number	number	NOUN
ejpam-3710	63	24	of	of	ADP
ejpam-3710	63	25	odd	odd	ADJ
ejpam-3710	63	26	tosha	tosha	NOUN
ejpam-3710	63	27	-	-	PUNCT
ejpam-3710	63	28	degree	degree	NOUN
ejpam-3710	63	29	edges	edge	NOUN
ejpam-3710	63	30	in	in	ADP
ejpam-3710	63	31	g	g	PROPN
ejpam-3710	63	32	is	be	AUX
ejpam-3710	63	33	even	even	ADV
ejpam-3710	63	34	.	.	PUNCT
ejpam-3710	64	1	remark	remark	PROPN
ejpam-3710	64	2	1	1	NUM
ejpam-3710	64	3	.	.	PUNCT
ejpam-3710	65	1	the	the	DET
ejpam-3710	65	2	corollary	corollary	ADJ
ejpam-3710	65	3	2	2	NUM
ejpam-3710	65	4	may	may	AUX
ejpam-3710	65	5	not	not	PART
ejpam-3710	65	6	be	be	AUX
ejpam-3710	65	7	true	true	ADJ
ejpam-3710	65	8	for	for	SCONJ
ejpam-3710	65	9	the	the	DET
ejpam-3710	65	10	graphs	graph	NOUN
ejpam-3710	65	11	having	have	VERB
ejpam-3710	65	12	self	self	NOUN
ejpam-3710	65	13	-	-	PUNCT
ejpam-3710	65	14	loops	loop	NOUN
ejpam-3710	65	15	.	.	PUNCT
ejpam-3710	66	1	there	there	PRON
ejpam-3710	66	2	are	be	VERB
ejpam-3710	66	3	graphs	graph	NOUN
ejpam-3710	66	4	with	with	ADP
ejpam-3710	66	5	odd	odd	ADJ
ejpam-3710	66	6	number	number	NOUN
ejpam-3710	66	7	of	of	ADP
ejpam-3710	66	8	edges	edge	NOUN
ejpam-3710	66	9	and	and	CCONJ
ejpam-3710	66	10	all	all	DET
ejpam-3710	66	11	edges	edge	NOUN
ejpam-3710	66	12	are	be	AUX
ejpam-3710	66	13	of	of	ADP
ejpam-3710	66	14	odd	odd	ADJ
ejpam-3710	66	15	tosha	tosha	NOUN
ejpam-3710	66	16	-	-	PUNCT
ejpam-3710	66	17	degree	degree	NOUN
ejpam-3710	66	18	.	.	PUNCT
ejpam-3710	67	1	for	for	ADP
ejpam-3710	67	2	eg	eg	NOUN
ejpam-3710	67	3	.	.	PROPN
ejpam-3710	67	4	,	,	PUNCT
ejpam-3710	67	5	consider	consider	VERB
ejpam-3710	67	6	the	the	DET
ejpam-3710	67	7	graph	graph	NOUN
ejpam-3710	67	8	g	g	NOUN
ejpam-3710	67	9	given	give	VERB
ejpam-3710	67	10	in	in	ADP
ejpam-3710	67	11	figure	figure	NOUN
ejpam-3710	67	12	1	1	NUM
ejpam-3710	67	13	.	.	PUNCT
ejpam-3710	68	1	the	the	DET
ejpam-3710	68	2	graph	graph	NOUN
ejpam-3710	68	3	g	g	PROPN
ejpam-3710	68	4	has	have	VERB
ejpam-3710	68	5	three	three	NUM
ejpam-3710	68	6	edges	edge	NOUN
ejpam-3710	68	7	namely	namely	ADV
ejpam-3710	68	8	,	,	PUNCT
ejpam-3710	68	9	α	α	X
ejpam-3710	68	10	,	,	PUNCT
ejpam-3710	68	11	β	β	X
ejpam-3710	68	12	and	and	CCONJ
ejpam-3710	68	13	γ	γ	X
ejpam-3710	68	14	.	.	PROPN
ejpam-3710	69	1	we	we	PRON
ejpam-3710	69	2	observe	observe	VERB
ejpam-3710	69	3	that	that	SCONJ
ejpam-3710	69	4	t	t	PROPN
ejpam-3710	69	5	(	(	PUNCT
ejpam-3710	69	6	α	α	NOUN
ejpam-3710	69	7	)	)	PUNCT
ejpam-3710	69	8	=	=	SYM
ejpam-3710	69	9	1	1	NUM
ejpam-3710	69	10	,	,	PUNCT
ejpam-3710	69	11	t	t	PROPN
ejpam-3710	69	12	(	(	PUNCT
ejpam-3710	69	13	β	β	NOUN
ejpam-3710	69	14	)	)	PUNCT
ejpam-3710	69	15	=	=	SYM
ejpam-3710	70	1	3	3	NUM
ejpam-3710	70	2	,	,	PUNCT
ejpam-3710	70	3	t	t	PROPN
ejpam-3710	70	4	(	(	PUNCT
ejpam-3710	70	5	γ	γ	NOUN
ejpam-3710	70	6	)	)	PUNCT
ejpam-3710	70	7	=	=	SYM
ejpam-3710	70	8	1	1	NUM
ejpam-3710	70	9	and	and	CCONJ
ejpam-3710	70	10	hence	hence	ADV
ejpam-3710	70	11	all	all	DET
ejpam-3710	70	12	the	the	DET
ejpam-3710	70	13	edges	edge	NOUN
ejpam-3710	70	14	in	in	ADP
ejpam-3710	70	15	g	g	PROPN
ejpam-3710	70	16	are	be	AUX
ejpam-3710	70	17	of	of	ADP
ejpam-3710	70	18	odd	odd	ADJ
ejpam-3710	70	19	tosha	tosha	NOUN
ejpam-3710	70	20	-	-	PUNCT
ejpam-3710	70	21	degree	degree	NOUN
ejpam-3710	70	22	.	.	PUNCT
ejpam-3710	71	1	u	u	PRON
ejpam-3710	71	2	u	u	PROPN
ejpam-3710	71	3	u	u	PROPN
ejpam-3710	71	4	�	�	PROPN
ejpam-3710	71	5	�	�	PROPN
ejpam-3710	71	6	�	�	PROPN
ejpam-3710	71	7	�	�	PROPN
ejpam-3710	71	8	α	α	PROPN
ejpam-3710	71	9	β	β	X
ejpam-3710	71	10	γ	γ	X
ejpam-3710	71	11	g	g	PROPN
ejpam-3710	71	12	figure	figure	NOUN
ejpam-3710	71	13	1	1	NUM
ejpam-3710	71	14	:	:	PUNCT
ejpam-3710	71	15	graph	graph	NOUN
ejpam-3710	71	16	containing	contain	VERB
ejpam-3710	71	17	odd	odd	ADJ
ejpam-3710	71	18	number	number	NOUN
ejpam-3710	71	19	of	of	ADP
ejpam-3710	71	20	odd	odd	ADJ
ejpam-3710	71	21	tosha	tosha	NOUN
ejpam-3710	71	22	-	-	PUNCT
ejpam-3710	71	23	degree	degree	NOUN
ejpam-3710	71	24	edges	edge	NOUN
ejpam-3710	71	25	.	.	PUNCT
ejpam-3710	72	1	observation	observation	NOUN
ejpam-3710	72	2	:	:	PUNCT
ejpam-3710	72	3	let	let	VERB
ejpam-3710	72	4	α	α	PRON
ejpam-3710	72	5	be	be	AUX
ejpam-3710	72	6	an	an	DET
ejpam-3710	72	7	edge	edge	NOUN
ejpam-3710	72	8	in	in	ADP
ejpam-3710	72	9	a	a	DET
ejpam-3710	72	10	simple	simple	ADJ
ejpam-3710	72	11	graph	graph	NOUN
ejpam-3710	72	12	g.	g.	VERB
ejpam-3710	72	13	the	the	DET
ejpam-3710	72	14	addition	addition	NOUN
ejpam-3710	72	15	of	of	ADP
ejpam-3710	72	16	a	a	DET
ejpam-3710	72	17	parallel	parallel	ADJ
ejpam-3710	72	18	edge	edge	NOUN
ejpam-3710	72	19	β	β	X
ejpam-3710	72	20	to	to	ADP
ejpam-3710	72	21	α	α	PROPN
ejpam-3710	72	22	gives	give	VERB
ejpam-3710	72	23	a	a	DET
ejpam-3710	72	24	count	count	NOUN
ejpam-3710	72	25	plus	plus	CCONJ
ejpam-3710	72	26	two	two	NUM
ejpam-3710	72	27	to	to	ADP
ejpam-3710	72	28	the	the	DET
ejpam-3710	72	29	tosha	tosha	NOUN
ejpam-3710	72	30	-	-	PUNCT
ejpam-3710	72	31	degree	degree	NOUN
ejpam-3710	72	32	of	of	ADP
ejpam-3710	72	33	α	α	NOUN
ejpam-3710	72	34	and	and	CCONJ
ejpam-3710	72	35	to	to	ADP
ejpam-3710	72	36	the	the	DET
ejpam-3710	72	37	edges	edge	NOUN
ejpam-3710	72	38	parallel	parallel	ADJ
ejpam-3710	72	39	to	to	ADP
ejpam-3710	72	40	α	α	NUM
ejpam-3710	72	41	,	,	PUNCT
ejpam-3710	72	42	and	and	CCONJ
ejpam-3710	72	43	a	a	DET
ejpam-3710	72	44	count	count	NOUN
ejpam-3710	72	45	plus	plus	CCONJ
ejpam-3710	72	46	one	one	NUM
ejpam-3710	72	47	to	to	ADP
ejpam-3710	72	48	non	non	ADJ
ejpam-3710	72	49	-	-	ADJ
ejpam-3710	72	50	parallel	parallel	ADJ
ejpam-3710	72	51	edges	edge	NOUN
ejpam-3710	72	52	adjacent	adjacent	ADJ
ejpam-3710	72	53	to	to	ADP
ejpam-3710	72	54	α	α	NOUN
ejpam-3710	72	55	in	in	ADP
ejpam-3710	72	56	the	the	DET
ejpam-3710	72	57	new	new	ADJ
ejpam-3710	72	58	graph	graph	NOUN
ejpam-3710	72	59	g	g	PROPN
ejpam-3710	72	60	+	+	CCONJ
ejpam-3710	72	61	β	β	X
ejpam-3710	72	62	and	and	CCONJ
ejpam-3710	72	63	tosha	tosha	NOUN
ejpam-3710	72	64	-	-	PUNCT
ejpam-3710	72	65	degrees	degree	NOUN
ejpam-3710	72	66	of	of	ADP
ejpam-3710	72	67	all	all	DET
ejpam-3710	72	68	other	other	ADJ
ejpam-3710	72	69	edges	edge	NOUN
ejpam-3710	72	70	are	be	AUX
ejpam-3710	72	71	unaltered	unaltered	ADJ
ejpam-3710	72	72	g+β	g+β	NUM
ejpam-3710	72	73	.	.	PUNCT
ejpam-3710	73	1	hence	hence	ADV
ejpam-3710	73	2	an	an	DET
ejpam-3710	73	3	odd	odd	ADJ
ejpam-3710	73	4	(	(	PUNCT
ejpam-3710	73	5	even	even	ADV
ejpam-3710	73	6	)	)	PUNCT
ejpam-3710	73	7	thosha	thosha	ADJ
ejpam-3710	73	8	-	-	PUNCT
ejpam-3710	73	9	degree	degree	NOUN
ejpam-3710	73	10	edge	edge	NOUN
ejpam-3710	73	11	γ	γ	X
ejpam-3710	73	12	remains	remain	VERB
ejpam-3710	73	13	odd	odd	ADJ
ejpam-3710	73	14	(	(	PUNCT
ejpam-3710	73	15	even	even	ADV
ejpam-3710	73	16	)	)	PUNCT
ejpam-3710	73	17	tosha	tosha	NOUN
ejpam-3710	73	18	-	-	PUNCT
ejpam-3710	73	19	degree	degree	NOUN
ejpam-3710	73	20	in	in	ADP
ejpam-3710	73	21	g+β	g+β	PROPN
ejpam-3710	73	22	,	,	PUNCT
ejpam-3710	73	23	if	if	SCONJ
ejpam-3710	73	24	it	it	PRON
ejpam-3710	73	25	is	be	AUX
ejpam-3710	73	26	not	not	PART
ejpam-3710	73	27	adjacent	adjacent	ADJ
ejpam-3710	73	28	to	to	ADP
ejpam-3710	73	29	α	α	NOUN
ejpam-3710	73	30	or	or	CCONJ
ejpam-3710	73	31	γ	γ	X
ejpam-3710	73	32	=	=	SYM
ejpam-3710	73	33	α	α	PROPN
ejpam-3710	73	34	in	in	ADP
ejpam-3710	73	35	g.	g.	PROPN
ejpam-3710	73	36	corollary	corollary	NOUN
ejpam-3710	74	1	3	3	X
ejpam-3710	74	2	.	.	PUNCT
ejpam-3710	75	1	if	if	SCONJ
ejpam-3710	75	2	α	α	PROPN
ejpam-3710	75	3	and	and	CCONJ
ejpam-3710	75	4	β	β	PROPN
ejpam-3710	75	5	are	be	AUX
ejpam-3710	75	6	parallel	parallel	ADJ
ejpam-3710	75	7	edges	edge	NOUN
ejpam-3710	75	8	in	in	ADP
ejpam-3710	75	9	a	a	DET
ejpam-3710	75	10	graph	graph	NOUN
ejpam-3710	75	11	g	g	NOUN
ejpam-3710	75	12	,	,	PUNCT
ejpam-3710	75	13	then	then	ADV
ejpam-3710	75	14	t	t	PROPN
ejpam-3710	75	15	(	(	PUNCT
ejpam-3710	75	16	α	α	NOUN
ejpam-3710	75	17	)	)	PUNCT
ejpam-3710	75	18	=	=	SYM
ejpam-3710	75	19	t	t	PROPN
ejpam-3710	75	20	(	(	PUNCT
ejpam-3710	75	21	β	β	NOUN
ejpam-3710	75	22	)	)	PUNCT
ejpam-3710	75	23	in	in	ADP
ejpam-3710	75	24	g.	g.	PROPN
ejpam-3710	75	25	proof	proof	NOUN
ejpam-3710	75	26	.	.	PUNCT
ejpam-3710	76	1	the	the	DET
ejpam-3710	76	2	proof	proof	NOUN
ejpam-3710	76	3	follows	follow	VERB
ejpam-3710	76	4	by	by	ADP
ejpam-3710	76	5	proposition	proposition	NOUN
ejpam-3710	76	6	1	1	NUM
ejpam-3710	76	7	.	.	ADP
ejpam-3710	76	8	2.1	2.1	NUM
ejpam-3710	76	9	.	.	PUNCT
ejpam-3710	77	1	t	t	NOUN
ejpam-3710	77	2	-line	-line	NOUN
ejpam-3710	77	3	graph	graph	NOUN
ejpam-3710	77	4	of	of	ADP
ejpam-3710	77	5	a	a	DET
ejpam-3710	77	6	multigraph	multigraph	NOUN
ejpam-3710	77	7	definition	definition	NOUN
ejpam-3710	77	8	3	3	NUM
ejpam-3710	77	9	.	.	PUNCT
ejpam-3710	78	1	a	a	DET
ejpam-3710	78	2	multigraph	multigraph	NOUN
ejpam-3710	78	3	is	be	AUX
ejpam-3710	78	4	a	a	DET
ejpam-3710	78	5	graph	graph	NOUN
ejpam-3710	78	6	in	in	ADP
ejpam-3710	78	7	which	which	PRON
ejpam-3710	78	8	multiple	multiple	ADJ
ejpam-3710	78	9	edges	edge	NOUN
ejpam-3710	78	10	(	(	PUNCT
ejpam-3710	78	11	parallel	parallel	ADJ
ejpam-3710	78	12	edges	edge	NOUN
ejpam-3710	78	13	)	)	PUNCT
ejpam-3710	78	14	are	be	AUX
ejpam-3710	78	15	permitted	permit	VERB
ejpam-3710	78	16	between	between	ADP
ejpam-3710	78	17	any	any	DET
ejpam-3710	78	18	pair	pair	NOUN
ejpam-3710	78	19	of	of	ADP
ejpam-3710	78	20	vertices	vertex	NOUN
ejpam-3710	78	21	.	.	PUNCT
ejpam-3710	79	1	all	all	DET
ejpam-3710	79	2	multigraphs	multigraph	NOUN
ejpam-3710	79	3	in	in	ADP
ejpam-3710	79	4	this	this	DET
ejpam-3710	79	5	paper	paper	NOUN
ejpam-3710	79	6	are	be	AUX
ejpam-3710	79	7	loopless	loopless	NOUN
ejpam-3710	79	8	.	.	PUNCT
ejpam-3710	80	1	we	we	PRON
ejpam-3710	80	2	say	say	VERB
ejpam-3710	80	3	that	that	SCONJ
ejpam-3710	80	4	two	two	NUM
ejpam-3710	80	5	distinct	distinct	ADJ
ejpam-3710	80	6	edges	edge	NOUN
ejpam-3710	80	7	α	α	NOUN
ejpam-3710	80	8	and	and	CCONJ
ejpam-3710	80	9	β	β	X
ejpam-3710	80	10	in	in	ADP
ejpam-3710	80	11	a	a	DET
ejpam-3710	80	12	multigraph	multigraph	NOUN
ejpam-3710	80	13	g	g	NOUN
ejpam-3710	80	14	are	be	AUX
ejpam-3710	80	15	k	k	NOUN
ejpam-3710	80	16	-	-	NOUN
ejpam-3710	80	17	adjacent	adjacent	ADJ
ejpam-3710	80	18	if	if	SCONJ
ejpam-3710	80	19	they	they	PRON
ejpam-3710	80	20	are	be	AUX
ejpam-3710	80	21	adjacent	adjacent	ADJ
ejpam-3710	80	22	and	and	CCONJ
ejpam-3710	80	23	share	share	PROPN
ejpam-3710	80	24	k	k	PROPN
ejpam-3710	80	25	end	end	NOUN
ejpam-3710	80	26	vertices	vertex	NOUN
ejpam-3710	80	27	.	.	PUNCT
ejpam-3710	81	1	we	we	PRON
ejpam-3710	81	2	say	say	VERB
ejpam-3710	81	3	that	that	SCONJ
ejpam-3710	81	4	two	two	NUM
ejpam-3710	81	5	distinct	distinct	ADJ
ejpam-3710	81	6	vertices	vertex	NOUN
ejpam-3710	81	7	u	u	NOUN
ejpam-3710	81	8	and	and	CCONJ
ejpam-3710	81	9	v	v	NOUN
ejpam-3710	81	10	in	in	ADP
ejpam-3710	81	11	a	a	DET
ejpam-3710	81	12	multigraph	multigraph	NOUN
ejpam-3710	81	13	g	g	NOUN
ejpam-3710	81	14	are	be	AUX
ejpam-3710	81	15	r	r	NOUN
ejpam-3710	81	16	-	-	NOUN
ejpam-3710	81	17	adjacent	adjacent	ADJ
ejpam-3710	81	18	if	if	SCONJ
ejpam-3710	81	19	they	they	PRON
ejpam-3710	81	20	are	be	AUX
ejpam-3710	81	21	adjacent	adjacent	ADJ
ejpam-3710	81	22	and	and	CCONJ
ejpam-3710	81	23	the	the	DET
ejpam-3710	81	24	number	number	NOUN
ejpam-3710	81	25	of	of	ADP
ejpam-3710	81	26	edges	edge	NOUN
ejpam-3710	81	27	between	between	ADP
ejpam-3710	81	28	them	they	PRON
ejpam-3710	81	29	is	be	AUX
ejpam-3710	81	30	r	r	NOUN
ejpam-3710	81	31	(	(	PUNCT
ejpam-3710	81	32	i.e.	i.e.	X
ejpam-3710	81	33	,	,	PUNCT
ejpam-3710	81	34	r	r	NOUN
ejpam-3710	81	35	edges	edge	NOUN
ejpam-3710	81	36	have	have	VERB
ejpam-3710	81	37	common	common	ADJ
ejpam-3710	81	38	end	end	NOUN
ejpam-3710	81	39	vertices	vertice	VERB
ejpam-3710	81	40	u	u	NOUN
ejpam-3710	81	41	and	and	CCONJ
ejpam-3710	81	42	v	v	NOUN
ejpam-3710	81	43	)	)	PUNCT
ejpam-3710	81	44	.	.	PUNCT
ejpam-3710	82	1	from	from	ADP
ejpam-3710	82	2	the	the	DET
ejpam-3710	82	3	definition	definition	NOUN
ejpam-3710	82	4	3	3	NUM
ejpam-3710	82	5	,	,	PUNCT
ejpam-3710	82	6	it	it	PRON
ejpam-3710	82	7	follows	follow	VERB
ejpam-3710	82	8	that	that	SCONJ
ejpam-3710	82	9	,	,	PUNCT
ejpam-3710	82	10	when	when	SCONJ
ejpam-3710	82	11	two	two	NUM
ejpam-3710	82	12	distinct	distinct	ADJ
ejpam-3710	82	13	edges	edge	NOUN
ejpam-3710	82	14	α	α	NOUN
ejpam-3710	82	15	and	and	CCONJ
ejpam-3710	82	16	β	β	X
ejpam-3710	82	17	are	be	AUX
ejpam-3710	82	18	k	k	NOUN
ejpam-3710	82	19	-	-	NOUN
ejpam-3710	82	20	adjacent	adjacent	ADJ
ejpam-3710	82	21	in	in	ADP
ejpam-3710	82	22	a	a	DET
ejpam-3710	82	23	multigraph	multigraph	NOUN
ejpam-3710	82	24	g	g	NOUN
ejpam-3710	82	25	,	,	PUNCT
ejpam-3710	82	26	we	we	PRON
ejpam-3710	82	27	have	have	AUX
ejpam-3710	82	28	,	,	PUNCT
ejpam-3710	82	29	k	k	PROPN
ejpam-3710	83	1	=	=	X
ejpam-3710	83	2	{	{	PUNCT
ejpam-3710	83	3	1	1	NUM
ejpam-3710	83	4	,	,	PUNCT
ejpam-3710	83	5	if	if	SCONJ
ejpam-3710	83	6	α	α	PROPN
ejpam-3710	83	7	and	and	CCONJ
ejpam-3710	83	8	β	β	NOUN
ejpam-3710	83	9	are	be	AUX
ejpam-3710	83	10	not	not	PART
ejpam-3710	83	11	parallel	parallel	ADJ
ejpam-3710	83	12	;	;	PUNCT
ejpam-3710	83	13	2	2	NUM
ejpam-3710	83	14	,	,	PUNCT
ejpam-3710	83	15	if	if	SCONJ
ejpam-3710	83	16	α	α	PROPN
ejpam-3710	83	17	and	and	CCONJ
ejpam-3710	83	18	β	β	PROPN
ejpam-3710	83	19	are	be	AUX
ejpam-3710	83	20	parallel	parallel	ADJ
ejpam-3710	83	21	.	.	PUNCT
ejpam-3710	83	22	.	.	PUNCT
ejpam-3710	84	1	r.	r.	PROPN
ejpam-3710	84	2	rajendra	rajendra	PROPN
ejpam-3710	84	3	,	,	PUNCT
ejpam-3710	84	4	p.	p.	PROPN
ejpam-3710	84	5	s.	s.	PROPN
ejpam-3710	85	1	k.	k.	PROPN
ejpam-3710	85	2	reddy	reddy	PROPN
ejpam-3710	85	3	/	/	SYM
ejpam-3710	85	4	eur	eur	PROPN
ejpam-3710	85	5	.	.	PUNCT
ejpam-3710	86	1	j.	j.	PROPN
ejpam-3710	86	2	pure	pure	PROPN
ejpam-3710	86	3	appl	appl	PROPN
ejpam-3710	86	4	.	.	PROPN
ejpam-3710	86	5	math	math	PROPN
ejpam-3710	86	6	,	,	PUNCT
ejpam-3710	86	7	13	13	NUM
ejpam-3710	86	8	(	(	PUNCT
ejpam-3710	86	9	5	5	NUM
ejpam-3710	86	10	)	)	PUNCT
ejpam-3710	86	11	(	(	PUNCT
ejpam-3710	86	12	2020	2020	NUM
ejpam-3710	86	13	)	)	PUNCT
ejpam-3710	86	14	,	,	PUNCT
ejpam-3710	86	15	1097	1097	NUM
ejpam-3710	86	16	-	-	SYM
ejpam-3710	86	17	1109	1109	NUM
ejpam-3710	86	18	1101	1101	NUM
ejpam-3710	86	19	definition	definition	NOUN
ejpam-3710	86	20	4	4	NUM
ejpam-3710	86	21	.	.	PUNCT
ejpam-3710	86	22	given	give	VERB
ejpam-3710	86	23	a	a	DET
ejpam-3710	86	24	multigraph	multigraph	NOUN
ejpam-3710	86	25	g	g	NOUN
ejpam-3710	86	26	=	=	PUNCT
ejpam-3710	86	27	(	(	PUNCT
ejpam-3710	86	28	v	v	NOUN
ejpam-3710	86	29	,	,	PUNCT
ejpam-3710	86	30	e	e	NOUN
ejpam-3710	86	31	)	)	PUNCT
ejpam-3710	86	32	,	,	PUNCT
ejpam-3710	86	33	the	the	DET
ejpam-3710	86	34	t	t	NOUN
ejpam-3710	86	35	-line	-line	NOUN
ejpam-3710	86	36	graph	graph	NOUN
ejpam-3710	86	37	of	of	ADP
ejpam-3710	86	38	g	g	PROPN
ejpam-3710	86	39	denoted	denote	VERB
ejpam-3710	86	40	by	by	ADP
ejpam-3710	86	41	tl(g	tl(g	NOUN
ejpam-3710	86	42	)	)	PUNCT
ejpam-3710	86	43	,	,	PUNCT
ejpam-3710	86	44	is	be	AUX
ejpam-3710	86	45	a	a	DET
ejpam-3710	86	46	graph	graph	NOUN
ejpam-3710	86	47	with	with	ADP
ejpam-3710	86	48	vertex	vertex	NOUN
ejpam-3710	86	49	set	set	NOUN
ejpam-3710	86	50	e	e	NOUN
ejpam-3710	86	51	;	;	PUNCT
ejpam-3710	86	52	two	two	NUM
ejpam-3710	86	53	distinct	distinct	ADJ
ejpam-3710	86	54	vertices	vertex	NOUN
ejpam-3710	86	55	α	α	NOUN
ejpam-3710	86	56	and	and	CCONJ
ejpam-3710	86	57	β	β	X
ejpam-3710	86	58	are	be	AUX
ejpam-3710	86	59	k	k	NOUN
ejpam-3710	86	60	-	-	ADJ
ejpam-3710	86	61	adjacent	adjacent	ADJ
ejpam-3710	86	62	in	in	ADP
ejpam-3710	86	63	tl(g	tl(g	NOUN
ejpam-3710	86	64	)	)	PUNCT
ejpam-3710	86	65	if	if	SCONJ
ejpam-3710	86	66	and	and	CCONJ
ejpam-3710	86	67	only	only	ADV
ejpam-3710	86	68	if	if	SCONJ
ejpam-3710	86	69	their	their	PRON
ejpam-3710	86	70	corresponding	corresponding	ADJ
ejpam-3710	86	71	edges	edge	NOUN
ejpam-3710	86	72	in	in	ADP
ejpam-3710	86	73	g	g	PROPN
ejpam-3710	86	74	are	be	AUX
ejpam-3710	86	75	k	k	NOUN
ejpam-3710	86	76	-	-	NOUN
ejpam-3710	86	77	adjacent	adjacent	ADJ
ejpam-3710	86	78	.	.	PUNCT
ejpam-3710	87	1	from	from	ADP
ejpam-3710	87	2	the	the	DET
ejpam-3710	87	3	definition	definition	NOUN
ejpam-3710	87	4	4	4	NUM
ejpam-3710	87	5	,	,	PUNCT
ejpam-3710	87	6	it	it	PRON
ejpam-3710	87	7	is	be	AUX
ejpam-3710	87	8	clear	clear	ADJ
ejpam-3710	87	9	that	that	SCONJ
ejpam-3710	87	10	,	,	PUNCT
ejpam-3710	87	11	(	(	PUNCT
ejpam-3710	87	12	a	a	X
ejpam-3710	87	13	)	)	PUNCT
ejpam-3710	87	14	tl(g	tl(g	NUM
ejpam-3710	87	15	)	)	PUNCT
ejpam-3710	87	16	is	be	AUX
ejpam-3710	87	17	also	also	ADV
ejpam-3710	87	18	a	a	DET
ejpam-3710	87	19	multigraph	multigraph	NOUN
ejpam-3710	87	20	,	,	PUNCT
ejpam-3710	87	21	(	(	PUNCT
ejpam-3710	87	22	b	b	X
ejpam-3710	87	23	)	)	PUNCT
ejpam-3710	87	24	if	if	SCONJ
ejpam-3710	87	25	g	g	PROPN
ejpam-3710	87	26	is	be	AUX
ejpam-3710	87	27	a	a	DET
ejpam-3710	87	28	simple	simple	ADJ
ejpam-3710	87	29	graph	graph	NOUN
ejpam-3710	87	30	,	,	PUNCT
ejpam-3710	87	31	then	then	ADV
ejpam-3710	87	32	tl(g	tl(g	NUM
ejpam-3710	87	33	)	)	PUNCT
ejpam-3710	87	34	is	be	AUX
ejpam-3710	87	35	nothing	nothing	PRON
ejpam-3710	87	36	but	but	CCONJ
ejpam-3710	87	37	l(g	l(g	PROPN
ejpam-3710	87	38	)	)	PUNCT
ejpam-3710	87	39	.	.	PUNCT
ejpam-3710	88	1	proposition	proposition	NOUN
ejpam-3710	88	2	2	2	NUM
ejpam-3710	88	3	.	.	PUNCT
ejpam-3710	89	1	let	let	VERB
ejpam-3710	89	2	g	g	PRON
ejpam-3710	89	3	be	be	AUX
ejpam-3710	89	4	a	a	DET
ejpam-3710	89	5	multigraph	multigraph	NOUN
ejpam-3710	89	6	and	and	CCONJ
ejpam-3710	89	7	α	α	NOUN
ejpam-3710	89	8	be	be	VERB
ejpam-3710	89	9	a	a	DET
ejpam-3710	89	10	vertex	vertex	NOUN
ejpam-3710	89	11	in	in	ADP
ejpam-3710	89	12	tl(g	tl(g	NUM
ejpam-3710	89	13	)	)	PUNCT
ejpam-3710	89	14	(	(	PUNCT
ejpam-3710	89	15	so	so	ADV
ejpam-3710	89	16	α	α	PRON
ejpam-3710	89	17	is	be	AUX
ejpam-3710	89	18	an	an	DET
ejpam-3710	89	19	edge	edge	NOUN
ejpam-3710	89	20	in	in	ADP
ejpam-3710	89	21	g	g	NOUN
ejpam-3710	89	22	)	)	PUNCT
ejpam-3710	89	23	.	.	PUNCT
ejpam-3710	90	1	then	then	ADV
ejpam-3710	90	2	dtl(g)(α	dtl(g)(α	X
ejpam-3710	90	3	)	)	PUNCT
ejpam-3710	90	4	=	=	SYM
ejpam-3710	90	5	dg(u	dg(u	X
ejpam-3710	90	6	)	)	PUNCT
ejpam-3710	90	7	+	+	CCONJ
ejpam-3710	90	8	dg(v)−	dg(v)−	ADJ
ejpam-3710	90	9	2	2	NUM
ejpam-3710	90	10	=	=	SYM
ejpam-3710	90	11	tg(α	tg(α	NOUN
ejpam-3710	90	12	)	)	PUNCT
ejpam-3710	90	13	(	(	PUNCT
ejpam-3710	90	14	4	4	X
ejpam-3710	90	15	)	)	PUNCT
ejpam-3710	90	16	where	where	SCONJ
ejpam-3710	90	17	u	u	NOUN
ejpam-3710	90	18	and	and	CCONJ
ejpam-3710	90	19	v	v	NOUN
ejpam-3710	90	20	are	be	AUX
ejpam-3710	90	21	end	end	NOUN
ejpam-3710	90	22	vertices	vertex	NOUN
ejpam-3710	90	23	of	of	ADP
ejpam-3710	90	24	α	α	NOUN
ejpam-3710	90	25	in	in	ADP
ejpam-3710	90	26	g.	g.	PROPN
ejpam-3710	90	27	proof	proof	NOUN
ejpam-3710	90	28	.	.	PUNCT
ejpam-3710	91	1	proof	proof	NOUN
ejpam-3710	91	2	follows	follow	VERB
ejpam-3710	91	3	by	by	ADP
ejpam-3710	91	4	the	the	DET
ejpam-3710	91	5	definitions	definition	NOUN
ejpam-3710	91	6	1	1	NUM
ejpam-3710	91	7	,	,	PUNCT
ejpam-3710	91	8	3	3	NUM
ejpam-3710	91	9	and	and	CCONJ
ejpam-3710	91	10	4	4	NUM
ejpam-3710	91	11	,	,	PUNCT
ejpam-3710	91	12	and	and	CCONJ
ejpam-3710	91	13	propositions	proposition	NOUN
ejpam-3710	91	14	1	1	NUM
ejpam-3710	91	15	and	and	CCONJ
ejpam-3710	91	16	2	2	NUM
ejpam-3710	91	17	.	.	X
ejpam-3710	91	18	corollary	corollary	ADJ
ejpam-3710	91	19	4	4	NUM
ejpam-3710	91	20	.	.	PUNCT
ejpam-3710	92	1	in	in	ADP
ejpam-3710	92	2	a	a	DET
ejpam-3710	92	3	multigraph	multigraph	NOUN
ejpam-3710	92	4	g	g	NOUN
ejpam-3710	92	5	,	,	PUNCT
ejpam-3710	92	6	the	the	DET
ejpam-3710	92	7	number	number	NOUN
ejpam-3710	92	8	of	of	ADP
ejpam-3710	92	9	odd	odd	ADJ
ejpam-3710	92	10	tosha	tosha	NOUN
ejpam-3710	92	11	-	-	PUNCT
ejpam-3710	92	12	degree	degree	NOUN
ejpam-3710	92	13	edges	edge	NOUN
ejpam-3710	92	14	is	be	AUX
ejpam-3710	92	15	even	even	ADV
ejpam-3710	92	16	.	.	PUNCT
ejpam-3710	93	1	proof	proof	NOUN
ejpam-3710	93	2	.	.	PUNCT
ejpam-3710	94	1	in	in	ADP
ejpam-3710	94	2	any	any	DET
ejpam-3710	94	3	graph(multigraph	graph(multigraph	NOUN
ejpam-3710	94	4	)	)	PUNCT
ejpam-3710	94	5	the	the	DET
ejpam-3710	94	6	number	number	NOUN
ejpam-3710	94	7	of	of	ADP
ejpam-3710	94	8	odd	odd	ADJ
ejpam-3710	94	9	degree	degree	NOUN
ejpam-3710	94	10	vertices	vertex	NOUN
ejpam-3710	94	11	is	be	AUX
ejpam-3710	94	12	even	even	ADV
ejpam-3710	94	13	.	.	PUNCT
ejpam-3710	95	1	so	so	ADV
ejpam-3710	95	2	,	,	PUNCT
ejpam-3710	95	3	the	the	DET
ejpam-3710	95	4	number	number	NOUN
ejpam-3710	95	5	of	of	ADP
ejpam-3710	95	6	odd	odd	ADJ
ejpam-3710	95	7	degree	degree	NOUN
ejpam-3710	95	8	vertices	vertex	NOUN
ejpam-3710	95	9	in	in	ADP
ejpam-3710	95	10	the	the	DET
ejpam-3710	95	11	line	line	NOUN
ejpam-3710	95	12	graph	graph	NOUN
ejpam-3710	95	13	tl(g	tl(g	NUM
ejpam-3710	95	14	)	)	PUNCT
ejpam-3710	95	15	of	of	ADP
ejpam-3710	95	16	g	g	PROPN
ejpam-3710	95	17	is	be	AUX
ejpam-3710	95	18	even	even	ADV
ejpam-3710	95	19	.	.	PUNCT
ejpam-3710	96	1	since	since	SCONJ
ejpam-3710	96	2	the	the	DET
ejpam-3710	96	3	vertices	vertex	NOUN
ejpam-3710	96	4	in	in	ADP
ejpam-3710	96	5	tl(g	tl(g	NOUN
ejpam-3710	96	6	)	)	PUNCT
ejpam-3710	96	7	are	be	AUX
ejpam-3710	96	8	corresponding	correspond	VERB
ejpam-3710	96	9	to	to	ADP
ejpam-3710	96	10	the	the	DET
ejpam-3710	96	11	edges	edge	NOUN
ejpam-3710	96	12	in	in	ADP
ejpam-3710	96	13	g	g	NOUN
ejpam-3710	96	14	,	,	PUNCT
ejpam-3710	96	15	by	by	ADP
ejpam-3710	96	16	eq.(4	eq.(4	ADJ
ejpam-3710	96	17	)	)	PUNCT
ejpam-3710	96	18	,	,	PUNCT
ejpam-3710	96	19	the	the	DET
ejpam-3710	96	20	number	number	NOUN
ejpam-3710	96	21	of	of	ADP
ejpam-3710	96	22	odd	odd	ADJ
ejpam-3710	96	23	tosha	tosha	NOUN
ejpam-3710	96	24	-	-	PUNCT
ejpam-3710	96	25	degree	degree	NOUN
ejpam-3710	96	26	edges	edge	NOUN
ejpam-3710	96	27	in	in	ADP
ejpam-3710	96	28	g	g	PROPN
ejpam-3710	96	29	is	be	AUX
ejpam-3710	96	30	even	even	ADV
ejpam-3710	96	31	.	.	PUNCT
ejpam-3710	97	1	3	3	X
ejpam-3710	97	2	.	.	X
ejpam-3710	97	3	zero	zero	NUM
ejpam-3710	97	4	edges	edge	NOUN
ejpam-3710	97	5	in	in	ADP
ejpam-3710	97	6	a	a	DET
ejpam-3710	97	7	graph	graph	NOUN
ejpam-3710	97	8	definition	definition	NOUN
ejpam-3710	97	9	5	5	NUM
ejpam-3710	97	10	.	.	PUNCT
ejpam-3710	98	1	in	in	ADP
ejpam-3710	98	2	a	a	DET
ejpam-3710	98	3	graph	graph	NOUN
ejpam-3710	98	4	g	g	NOUN
ejpam-3710	98	5	,	,	PUNCT
ejpam-3710	98	6	an	an	DET
ejpam-3710	98	7	edge	edge	NOUN
ejpam-3710	98	8	α	α	NOUN
ejpam-3710	98	9	is	be	AUX
ejpam-3710	98	10	said	say	VERB
ejpam-3710	98	11	to	to	PART
ejpam-3710	98	12	be	be	AUX
ejpam-3710	98	13	a	a	DET
ejpam-3710	98	14	zero	zero	NUM
ejpam-3710	98	15	edge	edge	NOUN
ejpam-3710	98	16	if	if	SCONJ
ejpam-3710	98	17	its	its	PRON
ejpam-3710	98	18	tosha	tosha	NOUN
ejpam-3710	98	19	degree	degree	NOUN
ejpam-3710	98	20	is	be	AUX
ejpam-3710	98	21	zero	zero	NUM
ejpam-3710	98	22	i.e.	i.e.	X
ejpam-3710	98	23	,	,	PUNCT
ejpam-3710	98	24	t	t	PROPN
ejpam-3710	98	25	(	(	PUNCT
ejpam-3710	98	26	α	α	NOUN
ejpam-3710	98	27	)	)	PUNCT
ejpam-3710	99	1	=	=	SYM
ejpam-3710	99	2	0	0	X
ejpam-3710	99	3	.	.	PUNCT
ejpam-3710	99	4	observations	observation	NOUN
ejpam-3710	99	5	:	:	PUNCT
ejpam-3710	99	6	the	the	DET
ejpam-3710	99	7	edge	edge	NOUN
ejpam-3710	99	8	in	in	ADP
ejpam-3710	99	9	the	the	DET
ejpam-3710	99	10	complete	complete	ADJ
ejpam-3710	99	11	graph	graph	NOUN
ejpam-3710	99	12	k2	k2	PROPN
ejpam-3710	99	13	is	be	AUX
ejpam-3710	99	14	a	a	DET
ejpam-3710	99	15	zero	zero	NUM
ejpam-3710	99	16	edge	edge	NOUN
ejpam-3710	99	17	.	.	PUNCT
ejpam-3710	100	1	the	the	DET
ejpam-3710	100	2	self	self	NOUN
ejpam-3710	100	3	-	-	PUNCT
ejpam-3710	100	4	loop	loop	NOUN
ejpam-3710	100	5	in	in	ADP
ejpam-3710	100	6	the	the	DET
ejpam-3710	100	7	graph	graph	NOUN
ejpam-3710	100	8	containing	contain	VERB
ejpam-3710	100	9	only	only	ADV
ejpam-3710	100	10	one	one	NUM
ejpam-3710	100	11	vertex	vertex	NOUN
ejpam-3710	100	12	and	and	CCONJ
ejpam-3710	100	13	a	a	DET
ejpam-3710	100	14	self	self	NOUN
ejpam-3710	100	15	-	-	PUNCT
ejpam-3710	100	16	loop	loop	NOUN
ejpam-3710	100	17	attached	attach	VERB
ejpam-3710	100	18	to	to	ADP
ejpam-3710	100	19	that	that	DET
ejpam-3710	100	20	vertex	vertex	NOUN
ejpam-3710	100	21	,	,	PUNCT
ejpam-3710	100	22	is	be	AUX
ejpam-3710	100	23	a	a	DET
ejpam-3710	100	24	zero	zero	NUM
ejpam-3710	100	25	edge	edge	NOUN
ejpam-3710	100	26	.	.	PUNCT
ejpam-3710	101	1	proposition	proposition	NOUN
ejpam-3710	101	2	3	3	NUM
ejpam-3710	101	3	.	.	PUNCT
ejpam-3710	102	1	a	a	DET
ejpam-3710	102	2	simple	simple	ADJ
ejpam-3710	102	3	connected	connected	ADJ
ejpam-3710	102	4	graph	graph	NOUN
ejpam-3710	102	5	g	g	PROPN
ejpam-3710	102	6	has	have	VERB
ejpam-3710	102	7	a	a	DET
ejpam-3710	102	8	zero	zero	NUM
ejpam-3710	102	9	edge	edge	NOUN
ejpam-3710	102	10	if	if	SCONJ
ejpam-3710	102	11	and	and	CCONJ
ejpam-3710	102	12	only	only	ADV
ejpam-3710	102	13	if	if	SCONJ
ejpam-3710	102	14	g	g	PROPN
ejpam-3710	102	15	∼=	∼=	PROPN
ejpam-3710	102	16	k2	k2	NOUN
ejpam-3710	102	17	.	.	PUNCT
ejpam-3710	103	1	proof	proof	NOUN
ejpam-3710	103	2	.	.	PUNCT
ejpam-3710	104	1	suppose	suppose	VERB
ejpam-3710	104	2	that	that	SCONJ
ejpam-3710	104	3	g	g	PROPN
ejpam-3710	104	4	is	be	AUX
ejpam-3710	104	5	a	a	DET
ejpam-3710	104	6	simple	simple	ADJ
ejpam-3710	104	7	connected	connected	ADJ
ejpam-3710	104	8	graph	graph	NOUN
ejpam-3710	104	9	having	have	VERB
ejpam-3710	104	10	a	a	DET
ejpam-3710	104	11	zero	zero	NUM
ejpam-3710	104	12	edge	edge	NOUN
ejpam-3710	104	13	,	,	PUNCT
ejpam-3710	104	14	say	say	VERB
ejpam-3710	104	15	α	α	NOUN
ejpam-3710	104	16	=	=	NOUN
ejpam-3710	104	17	uv	uv	NOUN
ejpam-3710	104	18	,	,	PUNCT
ejpam-3710	104	19	where	where	SCONJ
ejpam-3710	104	20	u	u	NOUN
ejpam-3710	104	21	and	and	CCONJ
ejpam-3710	104	22	v	v	NOUN
ejpam-3710	104	23	are	be	AUX
ejpam-3710	104	24	end	end	NOUN
ejpam-3710	104	25	vertices	vertex	NOUN
ejpam-3710	104	26	of	of	ADP
ejpam-3710	104	27	α	α	NOUN
ejpam-3710	104	28	.	.	PUNCT
ejpam-3710	105	1	then	then	ADV
ejpam-3710	105	2	d(u	d(u	PROPN
ejpam-3710	105	3	)	)	PUNCT
ejpam-3710	106	1	+	+	CCONJ
ejpam-3710	106	2	d(v)−	d(v)−	PROPN
ejpam-3710	106	3	2	2	NUM
ejpam-3710	106	4	=	=	SYM
ejpam-3710	106	5	0	0	NUM
ejpam-3710	107	1	(	(	PUNCT
ejpam-3710	107	2	5	5	NUM
ejpam-3710	107	3	)	)	PUNCT
ejpam-3710	107	4	since	since	SCONJ
ejpam-3710	107	5	g	g	PROPN
ejpam-3710	107	6	is	be	AUX
ejpam-3710	107	7	connected	connect	VERB
ejpam-3710	107	8	,	,	PUNCT
ejpam-3710	107	9	d(u	d(u	PROPN
ejpam-3710	107	10	)	)	PUNCT
ejpam-3710	107	11	≥	≥	NOUN
ejpam-3710	107	12	1	1	NUM
ejpam-3710	107	13	and	and	CCONJ
ejpam-3710	107	14	d(v	d(v	PROPN
ejpam-3710	107	15	)	)	PUNCT
ejpam-3710	107	16	≥	≥	NOUN
ejpam-3710	107	17	1	1	NUM
ejpam-3710	107	18	;	;	PUNCT
ejpam-3710	107	19	from	from	ADP
ejpam-3710	107	20	eq.(5	eq.(5	NOUN
ejpam-3710	107	21	)	)	PUNCT
ejpam-3710	107	22	,	,	PUNCT
ejpam-3710	107	23	d(u	d(u	PROPN
ejpam-3710	107	24	)	)	PUNCT
ejpam-3710	107	25	=	=	SYM
ejpam-3710	107	26	1	1	NUM
ejpam-3710	107	27	and	and	CCONJ
ejpam-3710	107	28	d(v	d(v	ADJ
ejpam-3710	107	29	)	)	PUNCT
ejpam-3710	107	30	=	=	SYM
ejpam-3710	108	1	1	1	X
ejpam-3710	108	2	.	.	PUNCT
ejpam-3710	108	3	therefore	therefore	ADV
ejpam-3710	108	4	,	,	PUNCT
ejpam-3710	108	5	there	there	PRON
ejpam-3710	108	6	is	be	VERB
ejpam-3710	108	7	no	no	DET
ejpam-3710	108	8	other	other	ADJ
ejpam-3710	108	9	edge	edge	NOUN
ejpam-3710	108	10	in	in	ADP
ejpam-3710	108	11	g	g	PROPN
ejpam-3710	108	12	incident	incident	NOUN
ejpam-3710	108	13	to	to	ADP
ejpam-3710	108	14	u	u	PRON
ejpam-3710	108	15	and	and	CCONJ
ejpam-3710	108	16	v.	v.	ADP
ejpam-3710	108	17	so	so	ADV
ejpam-3710	108	18	g	g	PROPN
ejpam-3710	108	19	has	have	VERB
ejpam-3710	108	20	only	only	ADV
ejpam-3710	108	21	one	one	NUM
ejpam-3710	108	22	edge	edge	NOUN
ejpam-3710	108	23	α	α	NOUN
ejpam-3710	108	24	.	.	PUNCT
ejpam-3710	109	1	since	since	SCONJ
ejpam-3710	109	2	g	g	PROPN
ejpam-3710	109	3	is	be	AUX
ejpam-3710	109	4	connected	connect	VERB
ejpam-3710	109	5	,	,	PUNCT
ejpam-3710	109	6	g	g	PROPN
ejpam-3710	109	7	∼=	∼=	PROPN
ejpam-3710	109	8	k2	k2	NOUN
ejpam-3710	109	9	.	.	PUNCT
ejpam-3710	110	1	conversely	conversely	ADV
ejpam-3710	110	2	,	,	PUNCT
ejpam-3710	110	3	if	if	SCONJ
ejpam-3710	110	4	g	g	PROPN
ejpam-3710	110	5	∼=	∼=	PROPN
ejpam-3710	110	6	k2	k2	NOUN
ejpam-3710	110	7	,	,	PUNCT
ejpam-3710	110	8	then	then	ADV
ejpam-3710	110	9	clearly	clearly	ADV
ejpam-3710	110	10	g	g	PROPN
ejpam-3710	110	11	is	be	AUX
ejpam-3710	110	12	a	a	DET
ejpam-3710	110	13	simple	simple	ADJ
ejpam-3710	110	14	connected	connected	ADJ
ejpam-3710	110	15	graph	graph	NOUN
ejpam-3710	110	16	having	have	VERB
ejpam-3710	110	17	only	only	ADV
ejpam-3710	110	18	one	one	NUM
ejpam-3710	110	19	edge	edge	NOUN
ejpam-3710	110	20	whose	whose	DET
ejpam-3710	110	21	tosha	tosha	NOUN
ejpam-3710	110	22	-	-	PUNCT
ejpam-3710	110	23	degree	degree	NOUN
ejpam-3710	110	24	is	be	AUX
ejpam-3710	110	25	zero	zero	NUM
ejpam-3710	110	26	.	.	PUNCT
ejpam-3710	111	1	r.	r.	PROPN
ejpam-3710	111	2	rajendra	rajendra	PROPN
ejpam-3710	111	3	,	,	PUNCT
ejpam-3710	111	4	p.	p.	PROPN
ejpam-3710	111	5	s.	s.	PROPN
ejpam-3710	112	1	k.	k.	PROPN
ejpam-3710	112	2	reddy	reddy	PROPN
ejpam-3710	112	3	/	/	SYM
ejpam-3710	112	4	eur	eur	PROPN
ejpam-3710	112	5	.	.	PUNCT
ejpam-3710	113	1	j.	j.	PROPN
ejpam-3710	113	2	pure	pure	PROPN
ejpam-3710	113	3	appl	appl	PROPN
ejpam-3710	113	4	.	.	PROPN
ejpam-3710	113	5	math	math	PROPN
ejpam-3710	113	6	,	,	PUNCT
ejpam-3710	113	7	13	13	NUM
ejpam-3710	113	8	(	(	PUNCT
ejpam-3710	113	9	5	5	NUM
ejpam-3710	113	10	)	)	PUNCT
ejpam-3710	113	11	(	(	PUNCT
ejpam-3710	113	12	2020	2020	NUM
ejpam-3710	113	13	)	)	PUNCT
ejpam-3710	113	14	,	,	PUNCT
ejpam-3710	113	15	1097	1097	NUM
ejpam-3710	113	16	-	-	SYM
ejpam-3710	113	17	1109	1109	NUM
ejpam-3710	113	18	1102	1102	NUM
ejpam-3710	113	19	corollary	corollary	ADJ
ejpam-3710	113	20	5	5	NUM
ejpam-3710	113	21	.	.	PUNCT
ejpam-3710	114	1	a	a	DET
ejpam-3710	114	2	simple	simple	ADJ
ejpam-3710	114	3	connected	connected	ADJ
ejpam-3710	114	4	graph	graph	NOUN
ejpam-3710	114	5	g	g	NOUN
ejpam-3710	114	6	with	with	ADP
ejpam-3710	114	7	two	two	NUM
ejpam-3710	114	8	or	or	CCONJ
ejpam-3710	114	9	more	more	ADJ
ejpam-3710	114	10	edges	edge	NOUN
ejpam-3710	114	11	,	,	PUNCT
ejpam-3710	114	12	has	have	VERB
ejpam-3710	114	13	no	no	DET
ejpam-3710	114	14	zero	zero	NUM
ejpam-3710	114	15	edge	edge	NOUN
ejpam-3710	114	16	.	.	PUNCT
ejpam-3710	115	1	hence	hence	ADV
ejpam-3710	115	2	t	t	PROPN
ejpam-3710	115	3	(	(	PUNCT
ejpam-3710	115	4	α	α	NOUN
ejpam-3710	115	5	)	)	PUNCT
ejpam-3710	115	6	≥	≥	NOUN
ejpam-3710	115	7	1	1	NUM
ejpam-3710	115	8	,	,	PUNCT
ejpam-3710	115	9	∀α	∀α	VERB
ejpam-3710	115	10	∈	∈	PROPN
ejpam-3710	115	11	e(g	e(g	PROPN
ejpam-3710	115	12	)	)	PUNCT
ejpam-3710	115	13	.	.	PUNCT
ejpam-3710	116	1	proof	proof	NOUN
ejpam-3710	116	2	.	.	PUNCT
ejpam-3710	117	1	follows	follow	VERB
ejpam-3710	117	2	from	from	ADP
ejpam-3710	117	3	proposition	proposition	NOUN
ejpam-3710	117	4	3	3	NUM
ejpam-3710	117	5	.	.	PUNCT
ejpam-3710	117	6	corollary	corollary	ADJ
ejpam-3710	117	7	6	6	NUM
ejpam-3710	117	8	.	.	PUNCT
ejpam-3710	118	1	a	a	DET
ejpam-3710	118	2	simple	simple	ADJ
ejpam-3710	118	3	graph	graph	NOUN
ejpam-3710	118	4	g	g	PROPN
ejpam-3710	118	5	has	have	VERB
ejpam-3710	118	6	no	no	DET
ejpam-3710	118	7	zero	zero	NUM
ejpam-3710	118	8	edge	edge	NOUN
ejpam-3710	118	9	if	if	SCONJ
ejpam-3710	118	10	and	and	CCONJ
ejpam-3710	118	11	only	only	ADV
ejpam-3710	118	12	if	if	SCONJ
ejpam-3710	118	13	either	either	PRON
ejpam-3710	118	14	g	g	PROPN
ejpam-3710	118	15	6∼=	6∼=	NUM
ejpam-3710	118	16	k2	k2	NOUN
ejpam-3710	118	17	or	or	CCONJ
ejpam-3710	118	18	no	no	DET
ejpam-3710	118	19	component	component	NOUN
ejpam-3710	118	20	of	of	ADP
ejpam-3710	118	21	g	g	PROPN
ejpam-3710	118	22	is	be	AUX
ejpam-3710	118	23	isomorphic	isomorphic	ADJ
ejpam-3710	118	24	to	to	ADP
ejpam-3710	118	25	k2	k2	NOUN
ejpam-3710	118	26	or	or	CCONJ
ejpam-3710	118	27	no	no	DET
ejpam-3710	118	28	component	component	NOUN
ejpam-3710	118	29	of	of	ADP
ejpam-3710	118	30	g	g	PROPN
ejpam-3710	118	31	is	be	AUX
ejpam-3710	118	32	of	of	ADP
ejpam-3710	118	33	only	only	ADV
ejpam-3710	118	34	one	one	NUM
ejpam-3710	118	35	vertex	vertex	NOUN
ejpam-3710	118	36	with	with	ADP
ejpam-3710	118	37	a	a	DET
ejpam-3710	118	38	self	self	NOUN
ejpam-3710	118	39	-	-	PUNCT
ejpam-3710	118	40	loop	loop	NOUN
ejpam-3710	118	41	.	.	PUNCT
ejpam-3710	119	1	proof	proof	NOUN
ejpam-3710	119	2	.	.	PUNCT
ejpam-3710	120	1	follows	follow	VERB
ejpam-3710	120	2	from	from	ADP
ejpam-3710	120	3	proposition	proposition	NOUN
ejpam-3710	120	4	3	3	NUM
ejpam-3710	120	5	.	.	NOUN
ejpam-3710	120	6	4	4	NUM
ejpam-3710	120	7	.	.	NOUN
ejpam-3710	120	8	degree	degree	NOUN
ejpam-3710	120	9	colorable	colorable	ADJ
ejpam-3710	120	10	graphs	graph	NOUN
ejpam-3710	120	11	in	in	ADP
ejpam-3710	120	12	this	this	DET
ejpam-3710	120	13	section	section	NOUN
ejpam-3710	120	14	we	we	PRON
ejpam-3710	120	15	consider	consider	VERB
ejpam-3710	120	16	self	self	NOUN
ejpam-3710	120	17	-	-	PUNCT
ejpam-3710	120	18	loop	loop	NOUN
ejpam-3710	120	19	free	free	ADJ
ejpam-3710	120	20	graphs	graph	NOUN
ejpam-3710	120	21	(	(	PUNCT
ejpam-3710	120	22	multigraphs	multigraph	NOUN
ejpam-3710	120	23	)	)	PUNCT
ejpam-3710	120	24	.	.	PUNCT
ejpam-3710	121	1	definition	definition	NOUN
ejpam-3710	121	2	6	6	NUM
ejpam-3710	121	3	.	.	PUNCT
ejpam-3710	122	1	a	a	DET
ejpam-3710	122	2	graph	graph	NOUN
ejpam-3710	122	3	g	g	NOUN
ejpam-3710	122	4	is	be	AUX
ejpam-3710	122	5	degree	degree	NOUN
ejpam-3710	122	6	colorable	colorable	ADJ
ejpam-3710	122	7	if	if	SCONJ
ejpam-3710	122	8	no	no	DET
ejpam-3710	122	9	two	two	NUM
ejpam-3710	122	10	adjacent	adjacent	ADJ
ejpam-3710	122	11	vertices	vertex	NOUN
ejpam-3710	122	12	have	have	VERB
ejpam-3710	122	13	the	the	DET
ejpam-3710	122	14	same	same	ADJ
ejpam-3710	122	15	degree	degree	NOUN
ejpam-3710	122	16	.	.	PUNCT
ejpam-3710	123	1	theorem	theorem	NOUN
ejpam-3710	123	2	1	1	NUM
ejpam-3710	123	3	.	.	PUNCT
ejpam-3710	124	1	if	if	SCONJ
ejpam-3710	124	2	all	all	DET
ejpam-3710	124	3	the	the	DET
ejpam-3710	124	4	edges	edge	NOUN
ejpam-3710	124	5	of	of	ADP
ejpam-3710	124	6	a	a	DET
ejpam-3710	124	7	graph	graph	NOUN
ejpam-3710	124	8	g	g	NOUN
ejpam-3710	124	9	are	be	AUX
ejpam-3710	124	10	of	of	ADP
ejpam-3710	124	11	odd	odd	ADJ
ejpam-3710	124	12	tosha	tosha	NOUN
ejpam-3710	124	13	-	-	PUNCT
ejpam-3710	124	14	degree	degree	NOUN
ejpam-3710	124	15	,	,	PUNCT
ejpam-3710	124	16	then	then	ADV
ejpam-3710	124	17	g	g	PROPN
ejpam-3710	124	18	is	be	AUX
ejpam-3710	124	19	a	a	DET
ejpam-3710	124	20	degree	degree	NOUN
ejpam-3710	124	21	colorable	colorable	ADJ
ejpam-3710	124	22	graph	graph	NOUN
ejpam-3710	124	23	with	with	ADP
ejpam-3710	124	24	even	even	ADV
ejpam-3710	124	25	number	number	NOUN
ejpam-3710	124	26	of	of	ADP
ejpam-3710	124	27	vertices	vertex	NOUN
ejpam-3710	124	28	.	.	PUNCT
ejpam-3710	125	1	proof	proof	NOUN
ejpam-3710	125	2	.	.	PUNCT
ejpam-3710	126	1	suppose	suppose	VERB
ejpam-3710	126	2	that	that	SCONJ
ejpam-3710	126	3	g	g	PROPN
ejpam-3710	126	4	is	be	AUX
ejpam-3710	126	5	a	a	DET
ejpam-3710	126	6	graph	graph	NOUN
ejpam-3710	126	7	in	in	ADP
ejpam-3710	126	8	which	which	PRON
ejpam-3710	126	9	all	all	DET
ejpam-3710	126	10	the	the	DET
ejpam-3710	126	11	edges	edge	NOUN
ejpam-3710	126	12	are	be	AUX
ejpam-3710	126	13	of	of	ADP
ejpam-3710	126	14	odd	odd	ADJ
ejpam-3710	126	15	tosha	tosha	NOUN
ejpam-3710	126	16	-	-	PUNCT
ejpam-3710	126	17	degree	degree	NOUN
ejpam-3710	126	18	.	.	PUNCT
ejpam-3710	127	1	by	by	ADP
ejpam-3710	127	2	the	the	DET
ejpam-3710	127	3	corollaries	corollary	NOUN
ejpam-3710	127	4	2	2	NUM
ejpam-3710	127	5	and	and	CCONJ
ejpam-3710	127	6	4	4	NUM
ejpam-3710	127	7	,	,	PUNCT
ejpam-3710	127	8	it	it	PRON
ejpam-3710	127	9	follows	follow	VERB
ejpam-3710	127	10	that	that	SCONJ
ejpam-3710	127	11	g	g	PROPN
ejpam-3710	127	12	has	have	VERB
ejpam-3710	127	13	an	an	DET
ejpam-3710	127	14	even	even	ADJ
ejpam-3710	127	15	number	number	NOUN
ejpam-3710	127	16	of	of	ADP
ejpam-3710	127	17	vertices	vertex	NOUN
ejpam-3710	127	18	.	.	PUNCT
ejpam-3710	128	1	let	let	VERB
ejpam-3710	128	2	α	α	PRON
ejpam-3710	128	3	be	be	AUX
ejpam-3710	128	4	an	an	DET
ejpam-3710	128	5	edge	edge	NOUN
ejpam-3710	128	6	in	in	ADP
ejpam-3710	128	7	g	g	NOUN
ejpam-3710	128	8	with	with	ADP
ejpam-3710	128	9	end	end	NOUN
ejpam-3710	128	10	vertices	vertice	VERB
ejpam-3710	128	11	u	u	NOUN
ejpam-3710	128	12	and	and	CCONJ
ejpam-3710	128	13	v.	v.	CCONJ
ejpam-3710	129	1	then	then	ADV
ejpam-3710	129	2	by	by	ADP
ejpam-3710	129	3	eq.(1	eq.(1	ADJ
ejpam-3710	129	4	)	)	PUNCT
ejpam-3710	129	5	and	and	CCONJ
ejpam-3710	129	6	eq.(4	eq.(4	NUM
ejpam-3710	129	7	)	)	PUNCT
ejpam-3710	129	8	,	,	PUNCT
ejpam-3710	129	9	t	t	PROPN
ejpam-3710	129	10	(	(	PUNCT
ejpam-3710	129	11	α	α	NOUN
ejpam-3710	129	12	)	)	PUNCT
ejpam-3710	129	13	=	=	SYM
ejpam-3710	129	14	d(u	d(u	PROPN
ejpam-3710	129	15	)	)	PUNCT
ejpam-3710	130	1	+	+	CCONJ
ejpam-3710	130	2	d(v)−	d(v)−	PROPN
ejpam-3710	130	3	2	2	NUM
ejpam-3710	130	4	.	.	PUNCT
ejpam-3710	131	1	since	since	SCONJ
ejpam-3710	131	2	t	t	PROPN
ejpam-3710	131	3	(	(	PUNCT
ejpam-3710	131	4	α	α	NOUN
ejpam-3710	131	5	)	)	PUNCT
ejpam-3710	131	6	is	be	AUX
ejpam-3710	131	7	odd	odd	ADJ
ejpam-3710	131	8	,	,	PUNCT
ejpam-3710	131	9	d(u	d(u	PROPN
ejpam-3710	131	10	)	)	PUNCT
ejpam-3710	131	11	6=	6=	X
ejpam-3710	131	12	d(v	d(v	PROPN
ejpam-3710	131	13	)	)	PUNCT
ejpam-3710	131	14	.	.	PUNCT
ejpam-3710	132	1	thus	thus	ADV
ejpam-3710	132	2	,	,	PUNCT
ejpam-3710	132	3	no	no	DET
ejpam-3710	132	4	two	two	NUM
ejpam-3710	132	5	adjacent	adjacent	ADJ
ejpam-3710	132	6	vertices	vertex	NOUN
ejpam-3710	132	7	in	in	ADP
ejpam-3710	132	8	g	g	PROPN
ejpam-3710	132	9	have	have	VERB
ejpam-3710	132	10	the	the	DET
ejpam-3710	132	11	same	same	ADJ
ejpam-3710	132	12	degree	degree	NOUN
ejpam-3710	132	13	.	.	PUNCT
ejpam-3710	133	1	therefore	therefore	ADV
ejpam-3710	133	2	g	g	PROPN
ejpam-3710	133	3	is	be	AUX
ejpam-3710	133	4	a	a	DET
ejpam-3710	133	5	degree	degree	NOUN
ejpam-3710	133	6	colorable	colorable	ADJ
ejpam-3710	133	7	graph	graph	NOUN
ejpam-3710	133	8	.	.	PUNCT
ejpam-3710	134	1	by	by	ADP
ejpam-3710	134	2	theorem	theorem	NOUN
ejpam-3710	134	3	1	1	NUM
ejpam-3710	134	4	,	,	PUNCT
ejpam-3710	134	5	the	the	DET
ejpam-3710	134	6	following	follow	VERB
ejpam-3710	134	7	corollary	corollary	NOUN
ejpam-3710	134	8	is	be	AUX
ejpam-3710	134	9	immediate	immediate	ADJ
ejpam-3710	134	10	.	.	PUNCT
ejpam-3710	135	1	corollary	corollary	ADJ
ejpam-3710	135	2	7	7	NUM
ejpam-3710	135	3	.	.	PUNCT
ejpam-3710	136	1	an	an	DET
ejpam-3710	136	2	l	l	NOUN
ejpam-3710	136	3	-	-	PUNCT
ejpam-3710	136	4	tosha	tosha	NOUN
ejpam-3710	136	5	-	-	PUNCT
ejpam-3710	136	6	regular	regular	ADJ
ejpam-3710	136	7	graph	graph	NOUN
ejpam-3710	136	8	,	,	PUNCT
ejpam-3710	136	9	where	where	SCONJ
ejpam-3710	136	10	l	l	NOUN
ejpam-3710	136	11	is	be	AUX
ejpam-3710	136	12	an	an	DET
ejpam-3710	136	13	odd	odd	ADJ
ejpam-3710	136	14	positive	positive	ADJ
ejpam-3710	136	15	integer	integer	NOUN
ejpam-3710	136	16	,	,	PUNCT
ejpam-3710	136	17	is	be	AUX
ejpam-3710	136	18	degree	degree	NOUN
ejpam-3710	136	19	colourable	colourable	ADJ
ejpam-3710	136	20	.	.	PUNCT
ejpam-3710	137	1	remark	remark	NOUN
ejpam-3710	137	2	2	2	NUM
ejpam-3710	137	3	.	.	PUNCT
ejpam-3710	138	1	there	there	PRON
ejpam-3710	138	2	are	be	VERB
ejpam-3710	138	3	degree	degree	NOUN
ejpam-3710	138	4	colorable	colorable	ADJ
ejpam-3710	138	5	non	non	ADJ
ejpam-3710	138	6	-	-	ADJ
ejpam-3710	138	7	tosha	tosha	ADJ
ejpam-3710	138	8	-	-	PUNCT
ejpam-3710	138	9	regular	regular	ADJ
ejpam-3710	138	10	graphs	graph	NOUN
ejpam-3710	138	11	with	with	ADP
ejpam-3710	138	12	odd	odd	ADJ
ejpam-3710	138	13	number	number	NOUN
ejpam-3710	138	14	of	of	ADP
ejpam-3710	138	15	vertices	vertex	NOUN
ejpam-3710	138	16	.	.	PUNCT
ejpam-3710	139	1	the	the	DET
ejpam-3710	139	2	following	follow	VERB
ejpam-3710	139	3	graph	graph	NOUN
ejpam-3710	139	4	is	be	AUX
ejpam-3710	139	5	an	an	DET
ejpam-3710	139	6	example	example	NOUN
ejpam-3710	139	7	for	for	ADP
ejpam-3710	139	8	such	such	ADJ
ejpam-3710	139	9	graphs	graph	NOUN
ejpam-3710	139	10	,	,	PUNCT
ejpam-3710	139	11	in	in	ADP
ejpam-3710	139	12	which	which	PRON
ejpam-3710	139	13	the	the	DET
ejpam-3710	139	14	edges	edge	NOUN
ejpam-3710	139	15	are	be	AUX
ejpam-3710	139	16	indicated	indicate	VERB
ejpam-3710	139	17	by	by	ADP
ejpam-3710	139	18	respective	respective	ADJ
ejpam-3710	139	19	tosha	tosha	NOUN
ejpam-3710	139	20	-	-	PUNCT
ejpam-3710	139	21	degrees	degree	NOUN
ejpam-3710	139	22	.	.	PUNCT
ejpam-3710	140	1	5	5	X
ejpam-3710	140	2	.	.	X
ejpam-3710	140	3	tosha	tosha	PROPN
ejpam-3710	140	4	-	-	PUNCT
ejpam-3710	140	5	even	even	ADV
ejpam-3710	140	6	graphs	graph	VERB
ejpam-3710	140	7	definition	definition	NOUN
ejpam-3710	140	8	7	7	NUM
ejpam-3710	140	9	.	.	PUNCT
ejpam-3710	141	1	a	a	DET
ejpam-3710	141	2	graph	graph	NOUN
ejpam-3710	141	3	g	g	NOUN
ejpam-3710	141	4	is	be	AUX
ejpam-3710	141	5	said	say	VERB
ejpam-3710	141	6	to	to	PART
ejpam-3710	141	7	be	be	AUX
ejpam-3710	141	8	tosha	tosha	NOUN
ejpam-3710	141	9	-	-	PUNCT
ejpam-3710	141	10	even	even	ADV
ejpam-3710	141	11	if	if	SCONJ
ejpam-3710	141	12	all	all	DET
ejpam-3710	141	13	its	its	PRON
ejpam-3710	141	14	edges	edge	NOUN
ejpam-3710	141	15	are	be	AUX
ejpam-3710	141	16	of	of	ADP
ejpam-3710	141	17	even	even	ADV
ejpam-3710	141	18	tosha	tosha	NOUN
ejpam-3710	141	19	-	-	PUNCT
ejpam-3710	141	20	degree	degree	NOUN
ejpam-3710	141	21	.	.	PUNCT
ejpam-3710	142	1	we	we	PRON
ejpam-3710	142	2	recall	recall	VERB
ejpam-3710	142	3	the	the	DET
ejpam-3710	142	4	following	follow	VERB
ejpam-3710	142	5	proposition	proposition	NOUN
ejpam-3710	142	6	from	from	ADP
ejpam-3710	142	7	[	[	X
ejpam-3710	142	8	4	4	NUM
ejpam-3710	142	9	]	]	PUNCT
ejpam-3710	142	10	.	.	PUNCT
ejpam-3710	143	1	proposition	proposition	NOUN
ejpam-3710	143	2	4	4	NUM
ejpam-3710	143	3	.	.	PUNCT
ejpam-3710	144	1	[	[	X
ejpam-3710	144	2	4	4	NUM
ejpam-3710	144	3	,	,	PUNCT
ejpam-3710	144	4	proposition	proposition	NOUN
ejpam-3710	144	5	2.15	2.15	NUM
ejpam-3710	144	6	]	]	PUNCT
ejpam-3710	144	7	if	if	SCONJ
ejpam-3710	144	8	g	g	PROPN
ejpam-3710	144	9	is	be	AUX
ejpam-3710	144	10	an	an	DET
ejpam-3710	144	11	euler	euler	NOUN
ejpam-3710	144	12	graph	graph	NOUN
ejpam-3710	144	13	,	,	PUNCT
ejpam-3710	144	14	then	then	ADV
ejpam-3710	144	15	all	all	DET
ejpam-3710	144	16	edges	edge	NOUN
ejpam-3710	144	17	in	in	ADP
ejpam-3710	144	18	g	g	PROPN
ejpam-3710	144	19	are	be	AUX
ejpam-3710	144	20	of	of	ADP
ejpam-3710	144	21	even	even	ADV
ejpam-3710	144	22	tosha	tosha	NOUN
ejpam-3710	144	23	-	-	PUNCT
ejpam-3710	144	24	degree	degree	NOUN
ejpam-3710	144	25	.	.	PUNCT
ejpam-3710	145	1	r.	r.	PROPN
ejpam-3710	145	2	rajendra	rajendra	PROPN
ejpam-3710	145	3	,	,	PUNCT
ejpam-3710	145	4	p.	p.	PROPN
ejpam-3710	145	5	s.	s.	PROPN
ejpam-3710	146	1	k.	k.	PROPN
ejpam-3710	146	2	reddy	reddy	PROPN
ejpam-3710	146	3	/	/	SYM
ejpam-3710	146	4	eur	eur	PROPN
ejpam-3710	146	5	.	.	PUNCT
ejpam-3710	147	1	j.	j.	PROPN
ejpam-3710	147	2	pure	pure	PROPN
ejpam-3710	147	3	appl	appl	PROPN
ejpam-3710	147	4	.	.	PROPN
ejpam-3710	147	5	math	math	PROPN
ejpam-3710	147	6	,	,	PUNCT
ejpam-3710	147	7	13	13	NUM
ejpam-3710	147	8	(	(	PUNCT
ejpam-3710	147	9	5	5	NUM
ejpam-3710	147	10	)	)	PUNCT
ejpam-3710	147	11	(	(	PUNCT
ejpam-3710	147	12	2020	2020	NUM
ejpam-3710	147	13	)	)	PUNCT
ejpam-3710	147	14	,	,	PUNCT
ejpam-3710	147	15	1097	1097	NUM
ejpam-3710	147	16	-	-	SYM
ejpam-3710	147	17	1109	1109	NUM
ejpam-3710	147	18	1103	1103	NUM
ejpam-3710	147	19	corollary	corollary	ADJ
ejpam-3710	147	20	8	8	NUM
ejpam-3710	147	21	.	.	PUNCT
ejpam-3710	147	22	euler	euler	NOUN
ejpam-3710	147	23	graphs	graph	NOUN
ejpam-3710	147	24	are	be	AUX
ejpam-3710	147	25	tosha	tosha	NOUN
ejpam-3710	147	26	-	-	PUNCT
ejpam-3710	147	27	even	even	ADV
ejpam-3710	147	28	.	.	PUNCT
ejpam-3710	148	1	proof	proof	NOUN
ejpam-3710	148	2	.	.	PUNCT
ejpam-3710	149	1	follows	follow	VERB
ejpam-3710	149	2	from	from	ADP
ejpam-3710	149	3	the	the	DET
ejpam-3710	149	4	proposition	proposition	NOUN
ejpam-3710	149	5	4	4	NUM
ejpam-3710	149	6	.	.	PUNCT
ejpam-3710	149	7	remark	remark	NOUN
ejpam-3710	149	8	3	3	NUM
ejpam-3710	149	9	.	.	PUNCT
ejpam-3710	150	1	.the	.the	PRON
ejpam-3710	150	2	converse	converse	NOUN
ejpam-3710	150	3	of	of	ADP
ejpam-3710	150	4	the	the	DET
ejpam-3710	150	5	corollary	corollary	ADJ
ejpam-3710	150	6	8	8	NUM
ejpam-3710	150	7	is	be	AUX
ejpam-3710	150	8	not	not	PART
ejpam-3710	150	9	true	true	ADJ
ejpam-3710	150	10	in	in	ADP
ejpam-3710	150	11	general	general	ADJ
ejpam-3710	150	12	.	.	PUNCT
ejpam-3710	151	1	there	there	PRON
ejpam-3710	151	2	are	be	VERB
ejpam-3710	151	3	connected	connected	ADJ
ejpam-3710	151	4	graphs	graph	NOUN
ejpam-3710	151	5	with	with	ADP
ejpam-3710	151	6	even	even	ADV
ejpam-3710	151	7	number	number	NOUN
ejpam-3710	151	8	of	of	ADP
ejpam-3710	151	9	vertices	vertex	NOUN
ejpam-3710	151	10	and	and	CCONJ
ejpam-3710	151	11	all	all	DET
ejpam-3710	151	12	vertices	vertex	NOUN
ejpam-3710	151	13	are	be	AUX
ejpam-3710	151	14	of	of	ADP
ejpam-3710	151	15	odd	odd	ADJ
ejpam-3710	151	16	degree	degree	NOUN
ejpam-3710	151	17	,	,	PUNCT
ejpam-3710	151	18	for	for	ADP
ejpam-3710	151	19	instance	instance	NOUN
ejpam-3710	151	20	,	,	PUNCT
ejpam-3710	151	21	k4	k4	PROPN
ejpam-3710	151	22	.	.	PUNCT
ejpam-3710	152	1	such	such	ADJ
ejpam-3710	152	2	graphs	graph	NOUN
ejpam-3710	152	3	are	be	AUX
ejpam-3710	152	4	not	not	PART
ejpam-3710	152	5	euler	euler	NOUN
ejpam-3710	152	6	graphs	graph	NOUN
ejpam-3710	152	7	,	,	PUNCT
ejpam-3710	152	8	but	but	CCONJ
ejpam-3710	152	9	are	be	AUX
ejpam-3710	152	10	tosha	tosha	NOUN
ejpam-3710	152	11	-	-	PUNCT
ejpam-3710	152	12	even	even	ADV
ejpam-3710	152	13	.	.	PUNCT
ejpam-3710	153	1	proposition	proposition	NOUN
ejpam-3710	153	2	5	5	NUM
ejpam-3710	153	3	.	.	PUNCT
ejpam-3710	154	1	there	there	PRON
ejpam-3710	154	2	exist	exist	VERB
ejpam-3710	154	3	degree	degree	NOUN
ejpam-3710	154	4	colorable	colorable	ADJ
ejpam-3710	154	5	tosha	tosha	NOUN
ejpam-3710	154	6	-	-	PUNCT
ejpam-3710	154	7	even	even	ADV
ejpam-3710	154	8	graphs	graph	NOUN
ejpam-3710	154	9	that	that	PRON
ejpam-3710	154	10	are	be	AUX
ejpam-3710	154	11	not	not	PART
ejpam-3710	154	12	euler	euler	NOUN
ejpam-3710	154	13	graphs	graph	NOUN
ejpam-3710	154	14	.	.	PUNCT
ejpam-3710	155	1	proof	proof	NOUN
ejpam-3710	155	2	.	.	PUNCT
ejpam-3710	156	1	the	the	DET
ejpam-3710	156	2	following	follow	VERB
ejpam-3710	156	3	graph	graph	NOUN
ejpam-3710	156	4	g	g	PROPN
ejpam-3710	156	5	(	(	PUNCT
ejpam-3710	156	6	see	see	VERB
ejpam-3710	156	7	figure	figure	NOUN
ejpam-3710	156	8	3	3	NUM
ejpam-3710	156	9	)	)	PUNCT
ejpam-3710	156	10	is	be	AUX
ejpam-3710	156	11	an	an	DET
ejpam-3710	156	12	example	example	NOUN
ejpam-3710	156	13	of	of	ADP
ejpam-3710	156	14	a	a	DET
ejpam-3710	156	15	degree	degree	NOUN
ejpam-3710	156	16	colorable	colorable	ADJ
ejpam-3710	156	17	toshaeven	toshaeven	ADJ
ejpam-3710	156	18	graph	graph	NOUN
ejpam-3710	156	19	which	which	PRON
ejpam-3710	156	20	is	be	AUX
ejpam-3710	156	21	not	not	PART
ejpam-3710	156	22	an	an	DET
ejpam-3710	156	23	euler	euler	NOUN
ejpam-3710	156	24	graph	graph	NOUN
ejpam-3710	156	25	.	.	PUNCT
ejpam-3710	157	1	in	in	ADP
ejpam-3710	157	2	g	g	PROPN
ejpam-3710	157	3	,	,	PUNCT
ejpam-3710	157	4	the	the	DET
ejpam-3710	157	5	vertices	vertex	NOUN
ejpam-3710	157	6	and	and	CCONJ
ejpam-3710	157	7	edges	edge	NOUN
ejpam-3710	157	8	are	be	AUX
ejpam-3710	157	9	indicated	indicate	VERB
ejpam-3710	157	10	by	by	ADP
ejpam-3710	157	11	their	their	PRON
ejpam-3710	157	12	degrees	degree	NOUN
ejpam-3710	157	13	and	and	CCONJ
ejpam-3710	157	14	tosha	tosha	NOUN
ejpam-3710	157	15	-	-	PUNCT
ejpam-3710	157	16	degrees	degree	NOUN
ejpam-3710	157	17	,	,	PUNCT
ejpam-3710	157	18	respectively	respectively	ADV
ejpam-3710	157	19	.	.	PUNCT
ejpam-3710	158	1	we	we	PRON
ejpam-3710	158	2	see	see	VERB
ejpam-3710	158	3	that	that	SCONJ
ejpam-3710	158	4	all	all	DET
ejpam-3710	158	5	vertices	vertex	NOUN
ejpam-3710	158	6	of	of	ADP
ejpam-3710	158	7	g	g	NOUN
ejpam-3710	158	8	are	be	AUX
ejpam-3710	158	9	of	of	ADP
ejpam-3710	158	10	odd	odd	ADJ
ejpam-3710	158	11	degree	degree	NOUN
ejpam-3710	158	12	and	and	CCONJ
ejpam-3710	158	13	hence	hence	ADV
ejpam-3710	158	14	g	g	PROPN
ejpam-3710	158	15	is	be	AUX
ejpam-3710	158	16	not	not	PART
ejpam-3710	158	17	an	an	DET
ejpam-3710	158	18	euler	euler	NOUN
ejpam-3710	158	19	graph	graph	NOUN
ejpam-3710	158	20	.	.	PUNCT
ejpam-3710	159	1	but	but	CCONJ
ejpam-3710	159	2	all	all	DET
ejpam-3710	159	3	edges	edge	NOUN
ejpam-3710	159	4	are	be	AUX
ejpam-3710	159	5	of	of	ADP
ejpam-3710	159	6	tosha	tosha	NOUN
ejpam-3710	159	7	-	-	PUNCT
ejpam-3710	159	8	even	even	ADV
ejpam-3710	159	9	,	,	PUNCT
ejpam-3710	159	10	so	so	ADV
ejpam-3710	159	11	g	g	PROPN
ejpam-3710	159	12	is	be	AUX
ejpam-3710	159	13	a	a	DET
ejpam-3710	159	14	tosha	tosha	NOUN
ejpam-3710	159	15	-	-	PUNCT
ejpam-3710	159	16	even	even	ADV
ejpam-3710	159	17	graph	graph	NOUN
ejpam-3710	159	18	.	.	PUNCT
ejpam-3710	160	1	6	6	NUM
ejpam-3710	160	2	.	.	X
ejpam-3710	160	3	tosha	tosha	NOUN
ejpam-3710	160	4	-	-	PUNCT
ejpam-3710	160	5	adjacency	adjacency	NOUN
ejpam-3710	160	6	matrix	matrix	NOUN
ejpam-3710	160	7	of	of	ADP
ejpam-3710	160	8	a	a	DET
ejpam-3710	160	9	graph	graph	NOUN
ejpam-3710	160	10	definition	definition	NOUN
ejpam-3710	160	11	8	8	NUM
ejpam-3710	160	12	.	.	PUNCT
ejpam-3710	161	1	if	if	SCONJ
ejpam-3710	161	2	g	g	PROPN
ejpam-3710	161	3	is	be	AUX
ejpam-3710	161	4	a	a	DET
ejpam-3710	161	5	graph	graph	NOUN
ejpam-3710	161	6	with	with	ADP
ejpam-3710	161	7	n	n	ADP
ejpam-3710	161	8	vertices	vertex	NOUN
ejpam-3710	161	9	v1	v1	NOUN
ejpam-3710	161	10	,	,	PUNCT
ejpam-3710	161	11	.	.	PUNCT
ejpam-3710	161	12	.	.	PUNCT
ejpam-3710	162	1	.	.	PUNCT
ejpam-3710	163	1	,	,	PUNCT
ejpam-3710	163	2	vn	vn	INTJ
ejpam-3710	163	3	and	and	CCONJ
ejpam-3710	163	4	no	no	DET
ejpam-3710	163	5	parallel	parallel	ADJ
ejpam-3710	163	6	edges	edge	NOUN
ejpam-3710	163	7	.	.	PUNCT
ejpam-3710	164	1	the	the	DET
ejpam-3710	164	2	toshaadjacency	toshaadjacency	NOUN
ejpam-3710	164	3	matrix	matrix	NOUN
ejpam-3710	164	4	of	of	ADP
ejpam-3710	164	5	the	the	DET
ejpam-3710	164	6	graph	graph	NOUN
ejpam-3710	164	7	g	g	PROPN
ejpam-3710	164	8	is	be	AUX
ejpam-3710	164	9	an	an	DET
ejpam-3710	164	10	n	n	NUM
ejpam-3710	164	11	×	×	NOUN
ejpam-3710	164	12	n	n	NOUN
ejpam-3710	164	13	matrix	matrix	NOUN
ejpam-3710	164	14	at	at	ADP
ejpam-3710	164	15	(	(	PUNCT
ejpam-3710	164	16	g	g	NOUN
ejpam-3710	164	17	)	)	PUNCT
ejpam-3710	164	18	=	=	SYM
ejpam-3710	164	19	(	(	PUNCT
ejpam-3710	164	20	tij	tij	NOUN
ejpam-3710	164	21	)	)	PUNCT
ejpam-3710	164	22	defined	define	VERB
ejpam-3710	164	23	over	over	ADP
ejpam-3710	164	24	the	the	DET
ejpam-3710	164	25	ring	ring	NOUN
ejpam-3710	164	26	of	of	ADP
ejpam-3710	164	27	integers	integer	NOUN
ejpam-3710	164	28	such	such	ADJ
ejpam-3710	164	29	that	that	PRON
ejpam-3710	164	30	tij	tij	PROPN
ejpam-3710	164	31	=	=	PUNCT
ejpam-3710	164	32	{	{	PUNCT
ejpam-3710	164	33	t	t	PROPN
ejpam-3710	164	34	(	(	PUNCT
ejpam-3710	164	35	vivj	vivj	NOUN
ejpam-3710	164	36	)	)	PUNCT
ejpam-3710	164	37	,	,	PUNCT
ejpam-3710	164	38	if	if	SCONJ
ejpam-3710	164	39	vivj	vivj	NOUN
ejpam-3710	164	40	∈	∈	PROPN
ejpam-3710	164	41	e	e	X
ejpam-3710	164	42	0	0	NUM
ejpam-3710	164	43	,	,	PUNCT
ejpam-3710	164	44	otherwise	otherwise	ADV
ejpam-3710	164	45	.	.	PUNCT
ejpam-3710	165	1	observations	observation	NOUN
ejpam-3710	165	2	:	:	PUNCT
ejpam-3710	165	3	u	u	PROPN
ejpam-3710	165	4	u6	u6	PROPN
ejpam-3710	165	5	6	6	NUM
ejpam-3710	165	6	u	u	NOUN
ejpam-3710	165	7	@	@	ADP
ejpam-3710	165	8	@	@	ADP
ejpam-3710	165	9	@	@	ADP
ejpam-3710	165	10	@	@	ADP
ejpam-3710	165	11	@	@	ADP
ejpam-3710	165	12	@	@	ADP
ejpam-3710	165	13	@@	@@	X
ejpam-3710	165	14	5	5	NUM
ejpam-3710	165	15	7	7	NUM
ejpam-3710	165	16	7	7	NUM
ejpam-3710	165	17	7	7	NUM
ejpam-3710	165	18	g	g	PROPN
ejpam-3710	165	19	figure	figure	NOUN
ejpam-3710	165	20	2	2	NUM
ejpam-3710	165	21	:	:	PUNCT
ejpam-3710	165	22	a	a	DET
ejpam-3710	165	23	degree	degree	NOUN
ejpam-3710	165	24	colorable	colorable	ADJ
ejpam-3710	165	25	non	non	ADJ
ejpam-3710	165	26	-	-	ADJ
ejpam-3710	165	27	tosha	tosha	ADJ
ejpam-3710	165	28	-	-	PUNCT
ejpam-3710	165	29	regular	regular	ADJ
ejpam-3710	165	30	graph	graph	NOUN
ejpam-3710	165	31	with	with	ADP
ejpam-3710	165	32	3	3	NUM
ejpam-3710	165	33	vertices	vertex	NOUN
ejpam-3710	165	34	.	.	PUNCT
ejpam-3710	166	1	u	u	PRON
ejpam-3710	166	2	u	u	NOUN
ejpam-3710	166	3	u	u	NOUN
ejpam-3710	166	4	u6	u6	PROPN
ejpam-3710	166	5	6	6	NUM
ejpam-3710	166	6	3	3	NUM
ejpam-3710	166	7	5	5	NUM
ejpam-3710	166	8	3	3	NUM
ejpam-3710	166	9	16	16	NUM
ejpam-3710	166	10	6	6	NUM
ejpam-3710	166	11	6	6	NUM
ejpam-3710	166	12	2	2	NUM
ejpam-3710	166	13	g	g	NOUN
ejpam-3710	166	14	figure	figure	NOUN
ejpam-3710	166	15	3	3	NUM
ejpam-3710	166	16	:	:	PUNCT
ejpam-3710	166	17	a	a	DET
ejpam-3710	166	18	degree	degree	NOUN
ejpam-3710	166	19	colorable	colorable	ADJ
ejpam-3710	166	20	tosha	tosha	NOUN
ejpam-3710	166	21	-	-	PUNCT
ejpam-3710	166	22	even	even	ADV
ejpam-3710	166	23	graph	graph	NOUN
ejpam-3710	166	24	which	which	PRON
ejpam-3710	166	25	is	be	AUX
ejpam-3710	166	26	not	not	PART
ejpam-3710	166	27	an	an	DET
ejpam-3710	166	28	euler	euler	NOUN
ejpam-3710	166	29	graph	graph	NOUN
ejpam-3710	166	30	.	.	PUNCT
ejpam-3710	167	1	r.	r.	PROPN
ejpam-3710	167	2	rajendra	rajendra	PROPN
ejpam-3710	167	3	,	,	PUNCT
ejpam-3710	167	4	p.	p.	PROPN
ejpam-3710	167	5	s.	s.	PROPN
ejpam-3710	168	1	k.	k.	PROPN
ejpam-3710	168	2	reddy	reddy	PROPN
ejpam-3710	168	3	/	/	SYM
ejpam-3710	168	4	eur	eur	PROPN
ejpam-3710	168	5	.	.	PUNCT
ejpam-3710	169	1	j.	j.	PROPN
ejpam-3710	169	2	pure	pure	PROPN
ejpam-3710	169	3	appl	appl	PROPN
ejpam-3710	169	4	.	.	PROPN
ejpam-3710	169	5	math	math	PROPN
ejpam-3710	169	6	,	,	PUNCT
ejpam-3710	169	7	13	13	NUM
ejpam-3710	169	8	(	(	PUNCT
ejpam-3710	169	9	5	5	NUM
ejpam-3710	169	10	)	)	PUNCT
ejpam-3710	169	11	(	(	PUNCT
ejpam-3710	169	12	2020	2020	NUM
ejpam-3710	169	13	)	)	PUNCT
ejpam-3710	169	14	,	,	PUNCT
ejpam-3710	169	15	1097	1097	NUM
ejpam-3710	169	16	-	-	SYM
ejpam-3710	169	17	1109	1109	NUM
ejpam-3710	169	18	1104	1104	NUM
ejpam-3710	169	19	(	(	PUNCT
ejpam-3710	169	20	i	i	NOUN
ejpam-3710	169	21	)	)	PUNCT
ejpam-3710	169	22	by	by	ADP
ejpam-3710	169	23	the	the	DET
ejpam-3710	169	24	definition	definition	NOUN
ejpam-3710	169	25	of	of	ADP
ejpam-3710	169	26	the	the	DET
ejpam-3710	169	27	tosha	tosha	NOUN
ejpam-3710	169	28	-	-	PUNCT
ejpam-3710	169	29	degree	degree	NOUN
ejpam-3710	169	30	of	of	ADP
ejpam-3710	169	31	an	an	DET
ejpam-3710	169	32	edge	edge	NOUN
ejpam-3710	169	33	,	,	PUNCT
ejpam-3710	169	34	we	we	PRON
ejpam-3710	169	35	have	have	VERB
ejpam-3710	169	36	t	t	PROPN
ejpam-3710	169	37	(	(	PUNCT
ejpam-3710	169	38	vivj	vivj	NOUN
ejpam-3710	169	39	)	)	PUNCT
ejpam-3710	169	40	=	=	PUNCT
ejpam-3710	170	1			PROPN
ejpam-3710	170	2	d(vi	d(vi	PROPN
ejpam-3710	170	3	)	)	PUNCT
ejpam-3710	171	1	+	+	NUM
ejpam-3710	171	2	d(vj)−	d(vj)−	NOUN
ejpam-3710	171	3	2	2	NUM
ejpam-3710	171	4	,	,	PUNCT
ejpam-3710	171	5	if	if	SCONJ
ejpam-3710	171	6	vivj	vivj	NOUN
ejpam-3710	171	7	∈	∈	PROPN
ejpam-3710	171	8	e	e	PROPN
ejpam-3710	171	9	and	and	CCONJ
ejpam-3710	171	10	i	i	PROPN
ejpam-3710	171	11	6=	6=	PROPN
ejpam-3710	171	12	j	j	PROPN
ejpam-3710	171	13	;	;	PUNCT
ejpam-3710	171	14	d(vi)−	d(vi)−	NOUN
ejpam-3710	171	15	2	2	NUM
ejpam-3710	171	16	,	,	PUNCT
ejpam-3710	171	17	if	if	SCONJ
ejpam-3710	171	18	vivj	vivj	NOUN
ejpam-3710	171	19	∈	∈	PROPN
ejpam-3710	171	20	e	e	NOUN
ejpam-3710	171	21	and	and	CCONJ
ejpam-3710	171	22	i	i	PRON
ejpam-3710	171	23	=	=	PROPN
ejpam-3710	171	24	j	j	PROPN
ejpam-3710	171	25	;	;	PUNCT
ejpam-3710	171	26	0	0	NUM
ejpam-3710	171	27	,	,	PUNCT
ejpam-3710	171	28	if	if	SCONJ
ejpam-3710	171	29	vivj	vivj	PROPN
ejpam-3710	171	30	/∈	/∈	PUNCT
ejpam-3710	172	1	e.	e.	PROPN
ejpam-3710	172	2	therefore	therefore	ADV
ejpam-3710	172	3	,	,	PUNCT
ejpam-3710	172	4	tij	tij	PROPN
ejpam-3710	172	5	=	=	SYM
ejpam-3710	172	6	tji	tji	PROPN
ejpam-3710	172	7	.	.	PUNCT
ejpam-3710	173	1	therefore	therefore	ADV
ejpam-3710	173	2	at	at	ADP
ejpam-3710	173	3	(	(	PUNCT
ejpam-3710	173	4	g	g	NOUN
ejpam-3710	173	5	)	)	PUNCT
ejpam-3710	173	6	is	be	AUX
ejpam-3710	173	7	a	a	DET
ejpam-3710	173	8	real	real	ADJ
ejpam-3710	173	9	symmetric	symmetric	ADJ
ejpam-3710	173	10	matrix	matrix	NOUN
ejpam-3710	173	11	.	.	PUNCT
ejpam-3710	174	1	(	(	PUNCT
ejpam-3710	174	2	ii	ii	X
ejpam-3710	174	3	)	)	PUNCT
ejpam-3710	174	4	the	the	DET
ejpam-3710	174	5	entries	entry	NOUN
ejpam-3710	174	6	along	along	ADP
ejpam-3710	174	7	the	the	DET
ejpam-3710	174	8	principal	principal	ADJ
ejpam-3710	174	9	diagonal	diagonal	NOUN
ejpam-3710	174	10	of	of	ADP
ejpam-3710	174	11	at	at	ADP
ejpam-3710	174	12	(	(	PUNCT
ejpam-3710	174	13	g	g	NOUN
ejpam-3710	174	14	)	)	PUNCT
ejpam-3710	174	15	are	be	AUX
ejpam-3710	174	16	all	all	PRON
ejpam-3710	174	17	0s	0s	NUM
ejpam-3710	174	18	if	if	SCONJ
ejpam-3710	174	19	and	and	CCONJ
ejpam-3710	174	20	only	only	ADV
ejpam-3710	174	21	if	if	SCONJ
ejpam-3710	174	22	either	either	DET
ejpam-3710	174	23	g	g	PROPN
ejpam-3710	174	24	has	have	VERB
ejpam-3710	174	25	no	no	DET
ejpam-3710	174	26	self	self	NOUN
ejpam-3710	174	27	-	-	PUNCT
ejpam-3710	174	28	loops	loop	NOUN
ejpam-3710	174	29	or	or	CCONJ
ejpam-3710	174	30	g	g	NOUN
ejpam-3710	174	31	has	have	VERB
ejpam-3710	174	32	only	only	ADV
ejpam-3710	174	33	self	self	NOUN
ejpam-3710	174	34	loops	loop	NOUN
ejpam-3710	174	35	that	that	PRON
ejpam-3710	174	36	are	be	AUX
ejpam-3710	174	37	zero	zero	NUM
ejpam-3710	174	38	edges	edge	NOUN
ejpam-3710	174	39	.	.	PUNCT
ejpam-3710	175	1	hence	hence	ADV
ejpam-3710	175	2	if	if	SCONJ
ejpam-3710	175	3	either	either	DET
ejpam-3710	175	4	g	g	PROPN
ejpam-3710	175	5	has	have	VERB
ejpam-3710	175	6	no	no	DET
ejpam-3710	175	7	self	self	NOUN
ejpam-3710	175	8	-	-	PUNCT
ejpam-3710	175	9	loops	loop	NOUN
ejpam-3710	175	10	or	or	CCONJ
ejpam-3710	175	11	g	g	NOUN
ejpam-3710	175	12	has	have	VERB
ejpam-3710	175	13	only	only	ADV
ejpam-3710	175	14	self	self	NOUN
ejpam-3710	175	15	loops	loop	NOUN
ejpam-3710	175	16	that	that	PRON
ejpam-3710	175	17	are	be	AUX
ejpam-3710	175	18	zero	zero	NUM
ejpam-3710	175	19	edges	edge	NOUN
ejpam-3710	175	20	,	,	PUNCT
ejpam-3710	175	21	then	then	ADV
ejpam-3710	175	22	tr(at	tr(at	NOUN
ejpam-3710	175	23	(	(	PUNCT
ejpam-3710	175	24	g	g	NOUN
ejpam-3710	175	25	)	)	PUNCT
ejpam-3710	175	26	)	)	PUNCT
ejpam-3710	176	1	=	=	PUNCT
ejpam-3710	176	2	0	0	X
ejpam-3710	176	3	.	.	PUNCT
ejpam-3710	177	1	in	in	ADP
ejpam-3710	177	2	this	this	DET
ejpam-3710	177	3	case	case	NOUN
ejpam-3710	177	4	,	,	PUNCT
ejpam-3710	177	5	if	if	SCONJ
ejpam-3710	177	6	µ1	µ1	PROPN
ejpam-3710	177	7	,	,	PUNCT
ejpam-3710	177	8	µ2	µ2	PROPN
ejpam-3710	177	9	,	,	PUNCT
ejpam-3710	177	10	.	.	PUNCT
ejpam-3710	177	11	.	.	PUNCT
ejpam-3710	178	1	.	.	PUNCT
ejpam-3710	179	1	,	,	PUNCT
ejpam-3710	179	2	µn	µn	PROPN
ejpam-3710	179	3	are	be	AUX
ejpam-3710	179	4	the	the	DET
ejpam-3710	179	5	eigenvalues	eigenvalue	NOUN
ejpam-3710	179	6	of	of	ADP
ejpam-3710	179	7	at	at	ADP
ejpam-3710	179	8	(	(	PUNCT
ejpam-3710	179	9	g	g	NOUN
ejpam-3710	179	10	)	)	PUNCT
ejpam-3710	179	11	,	,	PUNCT
ejpam-3710	179	12	then	then	ADV
ejpam-3710	179	13	n∑	n∑	NOUN
ejpam-3710	179	14	i=1	i=1	X
ejpam-3710	180	1	µi	µi	PROPN
ejpam-3710	181	1	=	=	ADJ
ejpam-3710	182	1	0	0	PROPN
ejpam-3710	182	2	.	.	PUNCT
ejpam-3710	183	1	(	(	PUNCT
ejpam-3710	183	2	iii	iii	X
ejpam-3710	183	3	)	)	PUNCT
ejpam-3710	183	4	if	if	SCONJ
ejpam-3710	183	5	g	g	PROPN
ejpam-3710	183	6	has	have	VERB
ejpam-3710	183	7	no	no	DET
ejpam-3710	183	8	zero	zero	NUM
ejpam-3710	183	9	edges	edge	NOUN
ejpam-3710	183	10	,	,	PUNCT
ejpam-3710	183	11	then	then	ADV
ejpam-3710	183	12	the	the	DET
ejpam-3710	183	13	degree	degree	NOUN
ejpam-3710	183	14	of	of	ADP
ejpam-3710	183	15	a	a	DET
ejpam-3710	183	16	vertex	vertex	NOUN
ejpam-3710	183	17	equals	equal	VERB
ejpam-3710	183	18	the	the	DET
ejpam-3710	183	19	number	number	NOUN
ejpam-3710	183	20	of	of	ADP
ejpam-3710	183	21	non	non	ADJ
ejpam-3710	183	22	-	-	ADJ
ejpam-3710	183	23	zero	zero	NUM
ejpam-3710	183	24	entries	entry	NOUN
ejpam-3710	183	25	in	in	ADP
ejpam-3710	183	26	the	the	DET
ejpam-3710	183	27	corresponding	corresponding	NOUN
ejpam-3710	183	28	row	row	NOUN
ejpam-3710	183	29	or	or	CCONJ
ejpam-3710	183	30	column	column	NOUN
ejpam-3710	183	31	;	;	PUNCT
ejpam-3710	183	32	and	and	CCONJ
ejpam-3710	183	33	the	the	DET
ejpam-3710	183	34	non	non	ADJ
ejpam-3710	183	35	-	-	ADJ
ejpam-3710	183	36	zero	zero	NUM
ejpam-3710	183	37	entry	entry	NOUN
ejpam-3710	183	38	in	in	ADP
ejpam-3710	183	39	the	the	DET
ejpam-3710	183	40	ij	ij	NOUN
ejpam-3710	183	41	-	-	PUNCT
ejpam-3710	183	42	th	th	VERB
ejpam-3710	183	43	place	place	NOUN
ejpam-3710	183	44	gives	give	VERB
ejpam-3710	183	45	the	the	DET
ejpam-3710	183	46	tosha	tosha	NOUN
ejpam-3710	183	47	-	-	PUNCT
ejpam-3710	183	48	degree	degree	NOUN
ejpam-3710	183	49	of	of	ADP
ejpam-3710	183	50	the	the	DET
ejpam-3710	183	51	corresponding	corresponding	ADJ
ejpam-3710	183	52	edge	edge	NOUN
ejpam-3710	183	53	incident	incident	NOUN
ejpam-3710	183	54	to	to	ADP
ejpam-3710	183	55	i	i	PRON
ejpam-3710	183	56	-	-	PUNCT
ejpam-3710	183	57	th	th	X
ejpam-3710	183	58	and	and	CCONJ
ejpam-3710	183	59	j	j	PROPN
ejpam-3710	183	60	-	-	PUNCT
ejpam-3710	183	61	th	th	VERB
ejpam-3710	183	62	vertices	vertex	NOUN
ejpam-3710	183	63	.	.	PUNCT
ejpam-3710	184	1	(	(	PUNCT
ejpam-3710	184	2	iv	iv	X
ejpam-3710	184	3	)	)	PUNCT
ejpam-3710	184	4	for	for	ADP
ejpam-3710	184	5	a	a	DET
ejpam-3710	184	6	zero	zero	NUM
ejpam-3710	184	7	edge	edge	NOUN
ejpam-3710	184	8	free	free	ADJ
ejpam-3710	184	9	graph	graph	NOUN
ejpam-3710	184	10	g	g	NOUN
ejpam-3710	184	11	,	,	PUNCT
ejpam-3710	184	12	the	the	DET
ejpam-3710	184	13	adjacency	adjacency	NOUN
ejpam-3710	184	14	matrix	matrix	NOUN
ejpam-3710	184	15	a(g	a(g	PROPN
ejpam-3710	184	16	)	)	PUNCT
ejpam-3710	184	17	can	can	AUX
ejpam-3710	184	18	be	be	AUX
ejpam-3710	184	19	obtained	obtain	VERB
ejpam-3710	184	20	from	from	ADP
ejpam-3710	184	21	the	the	DET
ejpam-3710	184	22	tosha	tosha	NOUN
ejpam-3710	184	23	-	-	PUNCT
ejpam-3710	184	24	adjacency	adjacency	NOUN
ejpam-3710	184	25	matrix	matrix	NOUN
ejpam-3710	184	26	at	at	ADP
ejpam-3710	184	27	(	(	PUNCT
ejpam-3710	184	28	g	g	NOUN
ejpam-3710	184	29	)	)	PUNCT
ejpam-3710	184	30	by	by	ADP
ejpam-3710	184	31	replacing	replace	VERB
ejpam-3710	184	32	all	all	DET
ejpam-3710	184	33	the	the	DET
ejpam-3710	184	34	non	non	ADJ
ejpam-3710	184	35	-	-	ADJ
ejpam-3710	184	36	zero	zero	NUM
ejpam-3710	184	37	entries	entry	NOUN
ejpam-3710	184	38	by	by	ADP
ejpam-3710	184	39	1s	1s	NUM
ejpam-3710	184	40	.	.	PUNCT
ejpam-3710	185	1	this	this	PRON
ejpam-3710	185	2	is	be	AUX
ejpam-3710	185	3	possible	possible	ADJ
ejpam-3710	185	4	because	because	SCONJ
ejpam-3710	185	5	,	,	PUNCT
ejpam-3710	185	6	in	in	ADP
ejpam-3710	185	7	a	a	DET
ejpam-3710	185	8	zero	zero	NUM
ejpam-3710	185	9	edge	edge	NOUN
ejpam-3710	185	10	free	free	ADJ
ejpam-3710	185	11	graph	graph	NOUN
ejpam-3710	185	12	tosha	tosha	NOUN
ejpam-3710	185	13	-	-	PUNCT
ejpam-3710	185	14	degrees	degree	NOUN
ejpam-3710	185	15	of	of	ADP
ejpam-3710	185	16	edges	edge	NOUN
ejpam-3710	185	17	are	be	AUX
ejpam-3710	185	18	non	non	ADJ
ejpam-3710	185	19	-	-	ADJ
ejpam-3710	185	20	zero	zero	NUM
ejpam-3710	185	21	.	.	PUNCT
ejpam-3710	186	1	thus	thus	ADV
ejpam-3710	186	2	,	,	PUNCT
ejpam-3710	186	3	reconstriction	reconstriction	NOUN
ejpam-3710	186	4	of	of	ADP
ejpam-3710	186	5	the	the	DET
ejpam-3710	186	6	graph	graph	NOUN
ejpam-3710	186	7	from	from	ADP
ejpam-3710	186	8	the	the	DET
ejpam-3710	186	9	tosha	tosha	NOUN
ejpam-3710	186	10	-	-	PUNCT
ejpam-3710	186	11	adjacency	adjacency	NOUN
ejpam-3710	186	12	matrix	matrix	NOUN
ejpam-3710	186	13	is	be	AUX
ejpam-3710	186	14	possible	possible	ADJ
ejpam-3710	186	15	if	if	SCONJ
ejpam-3710	186	16	the	the	DET
ejpam-3710	186	17	given	give	VERB
ejpam-3710	186	18	graph	graph	NOUN
ejpam-3710	186	19	has	have	VERB
ejpam-3710	186	20	no	no	DET
ejpam-3710	186	21	zero	zero	NUM
ejpam-3710	186	22	edges	edge	NOUN
ejpam-3710	186	23	.	.	PUNCT
ejpam-3710	187	1	throughout	throughout	ADP
ejpam-3710	187	2	this	this	DET
ejpam-3710	187	3	section	section	NOUN
ejpam-3710	187	4	g	g	PROPN
ejpam-3710	187	5	denotes	denote	VERB
ejpam-3710	187	6	a	a	DET
ejpam-3710	187	7	graph	graph	NOUN
ejpam-3710	187	8	with	with	ADP
ejpam-3710	187	9	no	no	DET
ejpam-3710	187	10	parallel	parallel	ADJ
ejpam-3710	187	11	edges	edge	NOUN
ejpam-3710	187	12	.	.	PUNCT
ejpam-3710	188	1	theorem	theorem	NOUN
ejpam-3710	188	2	2	2	NUM
ejpam-3710	188	3	.	.	PUNCT
ejpam-3710	189	1	if	if	SCONJ
ejpam-3710	189	2	a	a	DET
ejpam-3710	189	3	graph	graph	NOUN
ejpam-3710	189	4	g	g	NOUN
ejpam-3710	189	5	with	with	ADP
ejpam-3710	189	6	n	n	NOUN
ejpam-3710	189	7	vertices	vertex	NOUN
ejpam-3710	189	8	is	be	AUX
ejpam-3710	189	9	l	l	NOUN
ejpam-3710	189	10	-	-	PUNCT
ejpam-3710	189	11	tosha	tosha	NOUN
ejpam-3710	189	12	-	-	PUNCT
ejpam-3710	189	13	regular	regular	NOUN
ejpam-3710	189	14	,	,	PUNCT
ejpam-3710	189	15	then	then	ADV
ejpam-3710	189	16	at	at	ADP
ejpam-3710	189	17	(	(	PUNCT
ejpam-3710	189	18	g	g	NOUN
ejpam-3710	189	19	)	)	PUNCT
ejpam-3710	189	20	=	=	SYM
ejpam-3710	189	21	l	l	NOUN
ejpam-3710	189	22	·	·	PUNCT
ejpam-3710	189	23	a(g	a(g	PROPN
ejpam-3710	189	24	)	)	PUNCT
ejpam-3710	189	25	.	.	PUNCT
ejpam-3710	190	1	proof	proof	NOUN
ejpam-3710	190	2	.	.	PUNCT
ejpam-3710	191	1	suppose	suppose	VERB
ejpam-3710	191	2	that	that	SCONJ
ejpam-3710	191	3	g	g	PROPN
ejpam-3710	191	4	is	be	AUX
ejpam-3710	191	5	l	l	NOUN
ejpam-3710	191	6	-	-	PUNCT
ejpam-3710	191	7	tosha	tosha	NOUN
ejpam-3710	191	8	-	-	PUNCT
ejpam-3710	191	9	regular	regular	NOUN
ejpam-3710	191	10	.	.	PUNCT
ejpam-3710	192	1	then	then	ADV
ejpam-3710	192	2	t	t	PROPN
ejpam-3710	192	3	(	(	PUNCT
ejpam-3710	192	4	α	α	NOUN
ejpam-3710	192	5	)	)	PUNCT
ejpam-3710	192	6	=	=	SYM
ejpam-3710	192	7	l	l	NOUN
ejpam-3710	192	8	,	,	PUNCT
ejpam-3710	192	9	for	for	ADP
ejpam-3710	192	10	all	all	DET
ejpam-3710	192	11	α	α	PRON
ejpam-3710	192	12	∈	∈	PROPN
ejpam-3710	192	13	e(g	e(g	PROPN
ejpam-3710	192	14	)	)	PUNCT
ejpam-3710	192	15	.	.	PUNCT
ejpam-3710	193	1	let	let	VERB
ejpam-3710	193	2	a(g	a(g	PROPN
ejpam-3710	193	3	)	)	PUNCT
ejpam-3710	193	4	=	=	PUNCT
ejpam-3710	193	5	(	(	PUNCT
ejpam-3710	193	6	aij	aij	PROPN
ejpam-3710	193	7	)	)	PUNCT
ejpam-3710	193	8	and	and	CCONJ
ejpam-3710	193	9	at	at	ADP
ejpam-3710	193	10	(	(	PUNCT
ejpam-3710	193	11	g	g	NOUN
ejpam-3710	193	12	)	)	PUNCT
ejpam-3710	193	13	=	=	SYM
ejpam-3710	193	14	(	(	PUNCT
ejpam-3710	193	15	tij	tij	PROPN
ejpam-3710	193	16	)	)	PUNCT
ejpam-3710	193	17	be	be	VERB
ejpam-3710	193	18	the	the	DET
ejpam-3710	193	19	adjacency	adjacency	NOUN
ejpam-3710	193	20	matrix	matrix	NOUN
ejpam-3710	193	21	and	and	CCONJ
ejpam-3710	193	22	the	the	DET
ejpam-3710	193	23	tosha	tosha	NOUN
ejpam-3710	193	24	-	-	PUNCT
ejpam-3710	193	25	adjacency	adjacency	NOUN
ejpam-3710	193	26	matrix	matrix	NOUN
ejpam-3710	193	27	of	of	ADP
ejpam-3710	193	28	g	g	NOUN
ejpam-3710	193	29	,	,	PUNCT
ejpam-3710	193	30	respectively	respectively	ADV
ejpam-3710	193	31	.	.	PUNCT
ejpam-3710	194	1	then	then	ADV
ejpam-3710	194	2	by	by	ADP
ejpam-3710	194	3	the	the	DET
ejpam-3710	194	4	definition	definition	NOUN
ejpam-3710	194	5	of	of	ADP
ejpam-3710	194	6	the	the	DET
ejpam-3710	194	7	tosha	tosha	NOUN
ejpam-3710	194	8	-	-	PUNCT
ejpam-3710	194	9	adjacency	adjacency	NOUN
ejpam-3710	194	10	matrix	matrix	NOUN
ejpam-3710	194	11	at	at	ADP
ejpam-3710	194	12	(	(	PUNCT
ejpam-3710	194	13	g	g	NOUN
ejpam-3710	194	14	)	)	PUNCT
ejpam-3710	194	15	,	,	PUNCT
ejpam-3710	194	16	we	we	PRON
ejpam-3710	194	17	have	have	VERB
ejpam-3710	194	18	tij	tij	NOUN
ejpam-3710	194	19	=	=	PUNCT
ejpam-3710	194	20	{	{	PUNCT
ejpam-3710	194	21	l	l	NOUN
ejpam-3710	194	22	,	,	PUNCT
ejpam-3710	194	23	if	if	SCONJ
ejpam-3710	194	24	vivj	vivj	NOUN
ejpam-3710	194	25	∈	∈	PROPN
ejpam-3710	194	26	e	e	NOUN
ejpam-3710	194	27	0	0	NUM
ejpam-3710	194	28	,	,	PUNCT
ejpam-3710	194	29	otherwise	otherwise	ADV
ejpam-3710	194	30	=	=	SYM
ejpam-3710	194	31	l	l	NOUN
ejpam-3710	194	32	·	·	PUNCT
ejpam-3710	194	33	aij	aij	PROPN
ejpam-3710	194	34	.	.	PUNCT
ejpam-3710	195	1	therefore	therefore	ADV
ejpam-3710	195	2	,	,	PUNCT
ejpam-3710	195	3	at	at	ADP
ejpam-3710	195	4	(	(	PUNCT
ejpam-3710	195	5	g	g	NOUN
ejpam-3710	195	6	)	)	PUNCT
ejpam-3710	195	7	=	=	SYM
ejpam-3710	195	8	l	l	NOUN
ejpam-3710	195	9	·	·	PUNCT
ejpam-3710	195	10	a(g	a(g	PROPN
ejpam-3710	195	11	)	)	PUNCT
ejpam-3710	195	12	.	.	PUNCT
ejpam-3710	196	1	r.	r.	PROPN
ejpam-3710	196	2	rajendra	rajendra	PROPN
ejpam-3710	196	3	,	,	PUNCT
ejpam-3710	196	4	p.	p.	PROPN
ejpam-3710	196	5	s.	s.	PROPN
ejpam-3710	197	1	k.	k.	PROPN
ejpam-3710	197	2	reddy	reddy	PROPN
ejpam-3710	197	3	/	/	SYM
ejpam-3710	197	4	eur	eur	PROPN
ejpam-3710	197	5	.	.	PUNCT
ejpam-3710	198	1	j.	j.	PROPN
ejpam-3710	198	2	pure	pure	PROPN
ejpam-3710	198	3	appl	appl	PROPN
ejpam-3710	198	4	.	.	PROPN
ejpam-3710	198	5	math	math	PROPN
ejpam-3710	198	6	,	,	PUNCT
ejpam-3710	198	7	13	13	NUM
ejpam-3710	198	8	(	(	PUNCT
ejpam-3710	198	9	5	5	NUM
ejpam-3710	198	10	)	)	PUNCT
ejpam-3710	198	11	(	(	PUNCT
ejpam-3710	198	12	2020	2020	NUM
ejpam-3710	198	13	)	)	PUNCT
ejpam-3710	198	14	,	,	PUNCT
ejpam-3710	198	15	1097	1097	NUM
ejpam-3710	198	16	-	-	SYM
ejpam-3710	198	17	1109	1109	NUM
ejpam-3710	198	18	1105	1105	NUM
ejpam-3710	198	19	corollary	corollary	NOUN
ejpam-3710	198	20	9	9	NUM
ejpam-3710	198	21	.	.	PUNCT
ejpam-3710	199	1	if	if	SCONJ
ejpam-3710	199	2	a	a	DET
ejpam-3710	199	3	graph	graph	NOUN
ejpam-3710	199	4	g	g	NOUN
ejpam-3710	199	5	with	with	ADP
ejpam-3710	199	6	n	n	NOUN
ejpam-3710	199	7	vertices	vertex	NOUN
ejpam-3710	199	8	is	be	AUX
ejpam-3710	199	9	r	r	NOUN
ejpam-3710	199	10	-	-	ADJ
ejpam-3710	199	11	regular	regular	ADJ
ejpam-3710	199	12	,	,	PUNCT
ejpam-3710	199	13	then	then	ADV
ejpam-3710	199	14	at	at	ADP
ejpam-3710	199	15	(	(	PUNCT
ejpam-3710	199	16	g	g	NOUN
ejpam-3710	199	17	)	)	PUNCT
ejpam-3710	199	18	=	=	SYM
ejpam-3710	200	1	2(r	2(r	NUM
ejpam-3710	200	2	−	−	NUM
ejpam-3710	200	3	1)a(g	1)a(g	NUM
ejpam-3710	200	4	)	)	PUNCT
ejpam-3710	200	5	.	.	PUNCT
ejpam-3710	201	1	proof	proof	NOUN
ejpam-3710	201	2	.	.	PUNCT
ejpam-3710	202	1	if	if	SCONJ
ejpam-3710	202	2	a	a	DET
ejpam-3710	202	3	graph	graph	NOUN
ejpam-3710	202	4	g	g	NOUN
ejpam-3710	202	5	with	with	ADP
ejpam-3710	202	6	n	n	NOUN
ejpam-3710	202	7	vertices	vertex	NOUN
ejpam-3710	202	8	is	be	AUX
ejpam-3710	202	9	r	r	NOUN
ejpam-3710	202	10	-	-	ADJ
ejpam-3710	202	11	regular	regular	ADJ
ejpam-3710	202	12	,	,	PUNCT
ejpam-3710	202	13	then	then	ADV
ejpam-3710	202	14	g	g	PROPN
ejpam-3710	202	15	is	be	AUX
ejpam-3710	202	16	2(r	2(r	NUM
ejpam-3710	202	17	−	−	NOUN
ejpam-3710	202	18	1)-tosha	1)-tosha	NUM
ejpam-3710	202	19	-	-	PUNCT
ejpam-3710	202	20	regular(by	regular(by	NOUN
ejpam-3710	202	21	[	[	X
ejpam-3710	202	22	4	4	NUM
ejpam-3710	202	23	,	,	PUNCT
ejpam-3710	202	24	corollary	corollary	ADJ
ejpam-3710	202	25	2.6	2.6	NUM
ejpam-3710	202	26	]	]	PUNCT
ejpam-3710	202	27	)	)	PUNCT
ejpam-3710	202	28	and	and	CCONJ
ejpam-3710	202	29	hence	hence	ADV
ejpam-3710	202	30	by	by	ADP
ejpam-3710	202	31	theorem	theorem	NOUN
ejpam-3710	202	32	2	2	NUM
ejpam-3710	202	33	,	,	PUNCT
ejpam-3710	202	34	at	at	ADP
ejpam-3710	202	35	(	(	PUNCT
ejpam-3710	202	36	g	g	NOUN
ejpam-3710	202	37	)	)	PUNCT
ejpam-3710	202	38	=	=	SYM
ejpam-3710	203	1	2(r	2(r	NUM
ejpam-3710	203	2	−	−	NUM
ejpam-3710	203	3	1)a(g	1)a(g	NUM
ejpam-3710	203	4	)	)	PUNCT
ejpam-3710	203	5	.	.	PUNCT
ejpam-3710	204	1	corollary	corollary	ADJ
ejpam-3710	204	2	10	10	NUM
ejpam-3710	204	3	.	.	PUNCT
ejpam-3710	205	1	a	a	DET
ejpam-3710	205	2	graph	graph	NOUN
ejpam-3710	205	3	g	g	NOUN
ejpam-3710	205	4	is	be	AUX
ejpam-3710	205	5	1	1	NUM
ejpam-3710	205	6	-	-	PUNCT
ejpam-3710	205	7	tosha	tosha	NOUN
ejpam-3710	205	8	-	-	PUNCT
ejpam-3710	205	9	regular	regular	NOUN
ejpam-3710	205	10	if	if	SCONJ
ejpam-3710	206	1	and	and	CCONJ
ejpam-3710	206	2	only	only	ADV
ejpam-3710	206	3	if	if	SCONJ
ejpam-3710	206	4	at	at	ADP
ejpam-3710	206	5	(	(	PUNCT
ejpam-3710	206	6	g	g	NOUN
ejpam-3710	206	7	)	)	PUNCT
ejpam-3710	206	8	=	=	PUNCT
ejpam-3710	206	9	a(g	a(g	PROPN
ejpam-3710	206	10	)	)	PUNCT
ejpam-3710	206	11	.	.	PUNCT
ejpam-3710	207	1	proof	proof	NOUN
ejpam-3710	207	2	.	.	PUNCT
ejpam-3710	208	1	(	(	PUNCT
ejpam-3710	208	2	⇐	⇐	NOUN
ejpam-3710	208	3	:)	:)	PROPN
ejpam-3710	208	4	suppose	suppose	VERB
ejpam-3710	208	5	that	that	SCONJ
ejpam-3710	208	6	for	for	ADP
ejpam-3710	208	7	a	a	DET
ejpam-3710	208	8	graph	graph	NOUN
ejpam-3710	208	9	g	g	NOUN
ejpam-3710	208	10	,	,	PUNCT
ejpam-3710	208	11	at	at	ADP
ejpam-3710	208	12	(	(	PUNCT
ejpam-3710	208	13	g	g	NOUN
ejpam-3710	208	14	)	)	PUNCT
ejpam-3710	208	15	=	=	PUNCT
ejpam-3710	208	16	a(g	a(g	PROPN
ejpam-3710	208	17	)	)	PUNCT
ejpam-3710	208	18	.	.	PUNCT
ejpam-3710	209	1	then	then	ADV
ejpam-3710	209	2	by	by	ADP
ejpam-3710	209	3	the	the	DET
ejpam-3710	209	4	definitions	definition	NOUN
ejpam-3710	209	5	of	of	ADP
ejpam-3710	209	6	at	at	ADP
ejpam-3710	209	7	(	(	PUNCT
ejpam-3710	209	8	g	g	NOUN
ejpam-3710	209	9	)	)	PUNCT
ejpam-3710	209	10	and	and	CCONJ
ejpam-3710	209	11	a(g	a(g	PROPN
ejpam-3710	209	12	)	)	PUNCT
ejpam-3710	209	13	,	,	PUNCT
ejpam-3710	209	14	it	it	PRON
ejpam-3710	209	15	follows	follow	VERB
ejpam-3710	209	16	that	that	SCONJ
ejpam-3710	209	17	,	,	PUNCT
ejpam-3710	209	18	t	t	PROPN
ejpam-3710	209	19	(	(	PUNCT
ejpam-3710	209	20	α	α	NOUN
ejpam-3710	209	21	)	)	PUNCT
ejpam-3710	209	22	=	=	SYM
ejpam-3710	209	23	1	1	NUM
ejpam-3710	209	24	,	,	PUNCT
ejpam-3710	209	25	∀α	∀α	VERB
ejpam-3710	209	26	∈	∈	PROPN
ejpam-3710	209	27	e(g	e(g	NOUN
ejpam-3710	209	28	)	)	PUNCT
ejpam-3710	209	29	.	.	PUNCT
ejpam-3710	210	1	hence	hence	ADV
ejpam-3710	210	2	,	,	PUNCT
ejpam-3710	210	3	g	g	PROPN
ejpam-3710	210	4	is	be	AUX
ejpam-3710	210	5	1	1	NUM
ejpam-3710	210	6	-	-	PUNCT
ejpam-3710	210	7	tosha	tosha	NOUN
ejpam-3710	210	8	-	-	PUNCT
ejpam-3710	210	9	regular	regular	NOUN
ejpam-3710	210	10	.	.	PUNCT
ejpam-3710	211	1	(	(	PUNCT
ejpam-3710	211	2	⇒	⇒	NOUN
ejpam-3710	211	3	:)	:)	NOUN
ejpam-3710	211	4	follows	follow	VERB
ejpam-3710	211	5	by	by	ADP
ejpam-3710	211	6	theorem	theorem	NOUN
ejpam-3710	211	7	2	2	NUM
ejpam-3710	211	8	.	.	NOUN
ejpam-3710	211	9	7	7	NUM
ejpam-3710	211	10	.	.	X
ejpam-3710	211	11	tosha	tosha	NOUN
ejpam-3710	211	12	-	-	PUNCT
ejpam-3710	211	13	energy	energy	NOUN
ejpam-3710	211	14	of	of	ADP
ejpam-3710	211	15	a	a	DET
ejpam-3710	211	16	graph	graph	NOUN
ejpam-3710	211	17	definition	definition	NOUN
ejpam-3710	211	18	9	9	NUM
ejpam-3710	211	19	.	.	PUNCT
ejpam-3710	212	1	let	let	VERB
ejpam-3710	212	2	g	g	NOUN
ejpam-3710	212	3	be	be	AUX
ejpam-3710	212	4	graph	graph	NOUN
ejpam-3710	212	5	with	with	ADP
ejpam-3710	212	6	n	n	ADP
ejpam-3710	212	7	vertices	vertex	NOUN
ejpam-3710	212	8	v1	v1	NOUN
ejpam-3710	212	9	,	,	PUNCT
ejpam-3710	212	10	.	.	PUNCT
ejpam-3710	212	11	.	.	PUNCT
ejpam-3710	213	1	.	.	PUNCT
ejpam-3710	214	1	,	,	PUNCT
ejpam-3710	214	2	vn	vn	INTJ
ejpam-3710	214	3	and	and	CCONJ
ejpam-3710	214	4	no	no	DET
ejpam-3710	214	5	parallel	parallel	ADJ
ejpam-3710	214	6	edges	edge	NOUN
ejpam-3710	214	7	.	.	PUNCT
ejpam-3710	215	1	let	let	VERB
ejpam-3710	215	2	µ1	µ1	PROPN
ejpam-3710	215	3	,	,	PUNCT
ejpam-3710	215	4	µ2	µ2	PROPN
ejpam-3710	215	5	,	,	PUNCT
ejpam-3710	215	6	.	.	PUNCT
ejpam-3710	215	7	.	.	PUNCT
ejpam-3710	216	1	.	.	PUNCT
ejpam-3710	217	1	,	,	PUNCT
ejpam-3710	217	2	µn	µn	PROPN
ejpam-3710	217	3	be	be	AUX
ejpam-3710	217	4	the	the	DET
ejpam-3710	217	5	eigenvalues	eigenvalue	NOUN
ejpam-3710	217	6	of	of	ADP
ejpam-3710	217	7	the	the	DET
ejpam-3710	217	8	tosha	tosha	NOUN
ejpam-3710	217	9	-	-	PUNCT
ejpam-3710	217	10	adjacency	adjacency	NOUN
ejpam-3710	217	11	matrix	matrix	NOUN
ejpam-3710	217	12	at	at	ADP
ejpam-3710	217	13	(	(	PUNCT
ejpam-3710	217	14	g	g	NOUN
ejpam-3710	217	15	)	)	PUNCT
ejpam-3710	217	16	of	of	ADP
ejpam-3710	217	17	g.	g.	PROPN
ejpam-3710	217	18	the	the	DET
ejpam-3710	217	19	toshaenergy	toshaenergy	NOUN
ejpam-3710	217	20	of	of	ADP
ejpam-3710	217	21	g	g	NOUN
ejpam-3710	217	22	,	,	PUNCT
ejpam-3710	217	23	denoted	denote	VERB
ejpam-3710	217	24	by	by	ADP
ejpam-3710	217	25	et	et	PROPN
ejpam-3710	217	26	(	(	PUNCT
ejpam-3710	217	27	g	g	NOUN
ejpam-3710	217	28	)	)	PUNCT
ejpam-3710	217	29	,	,	PUNCT
ejpam-3710	217	30	is	be	AUX
ejpam-3710	217	31	defined	define	VERB
ejpam-3710	217	32	as	as	ADP
ejpam-3710	217	33	et	et	PROPN
ejpam-3710	217	34	(	(	PUNCT
ejpam-3710	217	35	g	g	NOUN
ejpam-3710	217	36	)	)	PUNCT
ejpam-3710	218	1	=	=	SYM
ejpam-3710	218	2	n∑	n∑	PROPN
ejpam-3710	218	3	i=1	i=1	PROPN
ejpam-3710	218	4	|µi|	|µi|	PROPN
ejpam-3710	218	5	.	.	PUNCT
ejpam-3710	219	1	(	(	PUNCT
ejpam-3710	219	2	6	6	NUM
ejpam-3710	219	3	)	)	PUNCT
ejpam-3710	219	4	throughout	throughout	ADP
ejpam-3710	219	5	this	this	DET
ejpam-3710	219	6	section	section	NOUN
ejpam-3710	219	7	g	g	PROPN
ejpam-3710	219	8	denotes	denote	VERB
ejpam-3710	219	9	a	a	DET
ejpam-3710	219	10	graph	graph	NOUN
ejpam-3710	219	11	with	with	ADP
ejpam-3710	219	12	no	no	DET
ejpam-3710	219	13	parallel	parallel	ADJ
ejpam-3710	219	14	edges	edge	NOUN
ejpam-3710	219	15	.	.	PUNCT
ejpam-3710	220	1	proposition	proposition	NOUN
ejpam-3710	220	2	6	6	NUM
ejpam-3710	220	3	.	.	PUNCT
ejpam-3710	221	1	the	the	DET
ejpam-3710	221	2	tosha	tosha	NOUN
ejpam-3710	221	3	-	-	PUNCT
ejpam-3710	221	4	energy	energy	NOUN
ejpam-3710	221	5	of	of	ADP
ejpam-3710	221	6	an	an	DET
ejpam-3710	221	7	l	l	NOUN
ejpam-3710	221	8	-	-	PUNCT
ejpam-3710	221	9	tosha	tosha	NOUN
ejpam-3710	221	10	-	-	PUNCT
ejpam-3710	221	11	regular	regular	ADJ
ejpam-3710	221	12	graph	graph	NOUN
ejpam-3710	221	13	g	g	NOUN
ejpam-3710	221	14	with	with	ADP
ejpam-3710	221	15	n	n	DET
ejpam-3710	221	16	vertices	vertex	NOUN
ejpam-3710	221	17	is	be	AUX
ejpam-3710	221	18	given	give	VERB
ejpam-3710	221	19	by	by	ADP
ejpam-3710	221	20	et	et	PROPN
ejpam-3710	221	21	(	(	PUNCT
ejpam-3710	221	22	g	g	NOUN
ejpam-3710	221	23	)	)	PUNCT
ejpam-3710	221	24	=	=	SYM
ejpam-3710	221	25	l	l	NOUN
ejpam-3710	221	26	·	·	PUNCT
ejpam-3710	221	27	e(g	e(g	NOUN
ejpam-3710	221	28	)	)	PUNCT
ejpam-3710	221	29	(	(	PUNCT
ejpam-3710	221	30	7	7	X
ejpam-3710	221	31	)	)	PUNCT
ejpam-3710	221	32	where	where	SCONJ
ejpam-3710	221	33	e(g	e(g	NOUN
ejpam-3710	221	34	)	)	PUNCT
ejpam-3710	221	35	is	be	AUX
ejpam-3710	221	36	the	the	DET
ejpam-3710	221	37	energy	energy	NOUN
ejpam-3710	221	38	of	of	ADP
ejpam-3710	221	39	g.	g.	PROPN
ejpam-3710	221	40	proof	proof	NOUN
ejpam-3710	221	41	.	.	PUNCT
ejpam-3710	222	1	le	le	PROPN
ejpam-3710	223	1	g	g	PROPN
ejpam-3710	223	2	be	be	AUX
ejpam-3710	223	3	an	an	DET
ejpam-3710	223	4	l	l	NOUN
ejpam-3710	223	5	-	-	PUNCT
ejpam-3710	223	6	tosha	tosha	NOUN
ejpam-3710	223	7	-	-	PUNCT
ejpam-3710	223	8	regular	regular	ADJ
ejpam-3710	223	9	graph	graph	NOUN
ejpam-3710	223	10	with	with	ADP
ejpam-3710	223	11	n	n	ADP
ejpam-3710	223	12	vertices	vertex	NOUN
ejpam-3710	223	13	.	.	PUNCT
ejpam-3710	224	1	then	then	ADV
ejpam-3710	224	2	by	by	ADP
ejpam-3710	224	3	the	the	DET
ejpam-3710	224	4	theorem	theorem	NOUN
ejpam-3710	224	5	2	2	NUM
ejpam-3710	224	6	,	,	PUNCT
ejpam-3710	224	7	the	the	DET
ejpam-3710	224	8	tosha	tosha	NOUN
ejpam-3710	224	9	-	-	PUNCT
ejpam-3710	224	10	adjacency	adjacency	NOUN
ejpam-3710	224	11	matrix	matrix	NOUN
ejpam-3710	224	12	of	of	ADP
ejpam-3710	224	13	g	g	PROPN
ejpam-3710	224	14	is	be	AUX
ejpam-3710	224	15	at	at	ADP
ejpam-3710	224	16	(	(	PUNCT
ejpam-3710	224	17	g	g	NOUN
ejpam-3710	224	18	)	)	PUNCT
ejpam-3710	224	19	=	=	SYM
ejpam-3710	224	20	l	l	NOUN
ejpam-3710	224	21	·	·	PUNCT
ejpam-3710	224	22	a(g	a(g	PROPN
ejpam-3710	224	23	)	)	PUNCT
ejpam-3710	224	24	(	(	PUNCT
ejpam-3710	224	25	8)	8)	NUM
ejpam-3710	224	26	where	where	SCONJ
ejpam-3710	224	27	a(g	a(g	PROPN
ejpam-3710	224	28	)	)	PUNCT
ejpam-3710	224	29	is	be	AUX
ejpam-3710	224	30	the	the	DET
ejpam-3710	224	31	adjacency	adjacency	NOUN
ejpam-3710	224	32	matrix	matrix	NOUN
ejpam-3710	224	33	of	of	ADP
ejpam-3710	224	34	g.	g.	PROPN
ejpam-3710	224	35	for	for	ADP
ejpam-3710	224	36	brevity	brevity	NOUN
ejpam-3710	224	37	we	we	PRON
ejpam-3710	224	38	write	write	VERB
ejpam-3710	224	39	a	a	PRON
ejpam-3710	224	40	for	for	ADP
ejpam-3710	224	41	a(g	a(g	PROPN
ejpam-3710	224	42	)	)	PUNCT
ejpam-3710	224	43	and	and	CCONJ
ejpam-3710	224	44	at	at	ADP
ejpam-3710	224	45	for	for	ADP
ejpam-3710	224	46	at	at	ADP
ejpam-3710	224	47	(	(	PUNCT
ejpam-3710	224	48	g	g	NOUN
ejpam-3710	224	49	)	)	PUNCT
ejpam-3710	224	50	.	.	PUNCT
ejpam-3710	225	1	we	we	PRON
ejpam-3710	225	2	consider	consider	VERB
ejpam-3710	225	3	two	two	NUM
ejpam-3710	225	4	cases	case	NOUN
ejpam-3710	225	5	:	:	PUNCT
ejpam-3710	225	6	(	(	PUNCT
ejpam-3710	225	7	i	i	NOUN
ejpam-3710	225	8	)	)	PUNCT
ejpam-3710	226	1	when	when	SCONJ
ejpam-3710	226	2	l	l	X
ejpam-3710	226	3	>	>	X
ejpam-3710	226	4	0	0	PUNCT
ejpam-3710	227	1	and	and	CCONJ
ejpam-3710	227	2	(	(	PUNCT
ejpam-3710	227	3	i	i	NOUN
ejpam-3710	227	4	)	)	PUNCT
ejpam-3710	228	1	when	when	SCONJ
ejpam-3710	228	2	l	l	NOUN
ejpam-3710	228	3	=	=	SYM
ejpam-3710	228	4	0	0	X
ejpam-3710	228	5	.	.	PUNCT
ejpam-3710	228	6	case	case	NOUN
ejpam-3710	228	7	(	(	PUNCT
ejpam-3710	228	8	i	i	NOUN
ejpam-3710	228	9	):	):	PUNCT
ejpam-3710	228	10	when	when	SCONJ
ejpam-3710	228	11	l	l	X
ejpam-3710	228	12	>	>	X
ejpam-3710	228	13	0	0	X
ejpam-3710	228	14	.	.	PUNCT
ejpam-3710	229	1	let	let	VERB
ejpam-3710	229	2	µ	µ	X
ejpam-3710	229	3	be	be	AUX
ejpam-3710	229	4	an	an	DET
ejpam-3710	229	5	eigenvalue	eigenvalue	NOUN
ejpam-3710	229	6	of	of	ADP
ejpam-3710	229	7	at	at	ADP
ejpam-3710	229	8	.	.	PUNCT
ejpam-3710	230	1	from	from	ADP
ejpam-3710	230	2	eq.(8	eq.(8	ADV
ejpam-3710	230	3	)	)	PUNCT
ejpam-3710	231	1	we	we	PRON
ejpam-3710	231	2	have	have	AUX
ejpam-3710	231	3	,	,	PUNCT
ejpam-3710	231	4	det(at	det(at	VERB
ejpam-3710	231	5	−	−	PROPN
ejpam-3710	231	6	µi	µi	PROPN
ejpam-3710	231	7	)	)	PUNCT
ejpam-3710	231	8	=	=	SYM
ejpam-3710	231	9	0	0	NUM
ejpam-3710	231	10	⇐	⇐	PROPN
ejpam-3710	231	11	⇒	⇒	PROPN
ejpam-3710	231	12	det	det	PROPN
ejpam-3710	231	13	(	(	PUNCT
ejpam-3710	231	14	la−	la−	PROPN
ejpam-3710	231	15	µi	µi	PROPN
ejpam-3710	231	16	)	)	PUNCT
ejpam-3710	232	1	=	=	SYM
ejpam-3710	232	2	0	0	NUM
ejpam-3710	232	3	⇐	⇐	ADJ
ejpam-3710	232	4	⇒	⇒	PROPN
ejpam-3710	232	5	ln	ln	PROPN
ejpam-3710	232	6	det	det	PROPN
ejpam-3710	232	7	(	(	PUNCT
ejpam-3710	232	8	a−	a−	PROPN
ejpam-3710	232	9	µ	µ	X
ejpam-3710	232	10	l	l	NOUN
ejpam-3710	232	11	i	i	NOUN
ejpam-3710	232	12	)	)	PUNCT
ejpam-3710	233	1	=	=	SYM
ejpam-3710	233	2	0	0	NUM
ejpam-3710	234	1	⇐	⇐	PROPN
ejpam-3710	234	2	⇒	⇒	PROPN
ejpam-3710	234	3	det	det	PROPN
ejpam-3710	234	4	(	(	PUNCT
ejpam-3710	234	5	a−	a−	PROPN
ejpam-3710	234	6	µ	µ	X
ejpam-3710	234	7	l	l	NOUN
ejpam-3710	234	8	i	i	NOUN
ejpam-3710	234	9	)	)	PUNCT
ejpam-3710	235	1	=	=	PUNCT
ejpam-3710	235	2	0	0	X
ejpam-3710	235	3	.	.	PUNCT
ejpam-3710	235	4	r.	r.	PROPN
ejpam-3710	235	5	rajendra	rajendra	PROPN
ejpam-3710	235	6	,	,	PUNCT
ejpam-3710	235	7	p.	p.	PROPN
ejpam-3710	235	8	s.	s.	PROPN
ejpam-3710	236	1	k.	k.	PROPN
ejpam-3710	236	2	reddy	reddy	PROPN
ejpam-3710	236	3	/	/	SYM
ejpam-3710	236	4	eur	eur	PROPN
ejpam-3710	236	5	.	.	PUNCT
ejpam-3710	237	1	j.	j.	PROPN
ejpam-3710	237	2	pure	pure	PROPN
ejpam-3710	237	3	appl	appl	PROPN
ejpam-3710	237	4	.	.	PROPN
ejpam-3710	237	5	math	math	PROPN
ejpam-3710	237	6	,	,	PUNCT
ejpam-3710	237	7	13	13	NUM
ejpam-3710	237	8	(	(	PUNCT
ejpam-3710	237	9	5	5	NUM
ejpam-3710	237	10	)	)	PUNCT
ejpam-3710	237	11	(	(	PUNCT
ejpam-3710	237	12	2020	2020	NUM
ejpam-3710	237	13	)	)	PUNCT
ejpam-3710	237	14	,	,	PUNCT
ejpam-3710	237	15	1097	1097	NUM
ejpam-3710	237	16	-	-	SYM
ejpam-3710	237	17	1109	1109	NUM
ejpam-3710	237	18	1106	1106	NUM
ejpam-3710	237	19	therefore	therefore	ADV
ejpam-3710	237	20	,	,	PUNCT
ejpam-3710	237	21	µ	µ	X
ejpam-3710	237	22	is	be	AUX
ejpam-3710	237	23	an	an	DET
ejpam-3710	237	24	eigenvalue	eigenvalue	NOUN
ejpam-3710	237	25	of	of	ADP
ejpam-3710	237	26	at	at	ADP
ejpam-3710	237	27	if	if	SCONJ
ejpam-3710	237	28	and	and	CCONJ
ejpam-3710	237	29	only	only	ADV
ejpam-3710	237	30	if	if	SCONJ
ejpam-3710	237	31	µ	µ	PRON
ejpam-3710	237	32	l	l	NOUN
ejpam-3710	237	33	is	be	AUX
ejpam-3710	237	34	an	an	DET
ejpam-3710	237	35	eigenvalue	eigenvalue	NOUN
ejpam-3710	237	36	of	of	ADP
ejpam-3710	237	37	a.	a.	NOUN
ejpam-3710	237	38	let	let	VERB
ejpam-3710	237	39	µ1	µ1	PROPN
ejpam-3710	237	40	,	,	PUNCT
ejpam-3710	237	41	µ2	µ2	PROPN
ejpam-3710	237	42	,	,	PUNCT
ejpam-3710	237	43	.	.	PUNCT
ejpam-3710	237	44	.	.	PUNCT
ejpam-3710	238	1	.	.	PUNCT
ejpam-3710	238	2	,	,	PUNCT
ejpam-3710	238	3	µn	µn	PROPN
ejpam-3710	238	4	be	be	AUX
ejpam-3710	238	5	the	the	DET
ejpam-3710	238	6	eigenvalues	eigenvalue	NOUN
ejpam-3710	238	7	of	of	ADP
ejpam-3710	238	8	the	the	DET
ejpam-3710	238	9	at	at	NOUN
ejpam-3710	238	10	.	.	PUNCT
ejpam-3710	239	1	then	then	ADV
ejpam-3710	239	2	µ1	µ1	PROPN
ejpam-3710	239	3	l	l	NOUN
ejpam-3710	239	4	,	,	PUNCT
ejpam-3710	239	5	µ2	µ2	PROPN
ejpam-3710	239	6	l	l	NOUN
ejpam-3710	239	7	,	,	PUNCT
ejpam-3710	239	8	.	.	PUNCT
ejpam-3710	239	9	.	.	PUNCT
ejpam-3710	240	1	.	.	PUNCT
ejpam-3710	240	2	,	,	PUNCT
ejpam-3710	240	3	µn	µn	PROPN
ejpam-3710	240	4	l	l	NOUN
ejpam-3710	240	5	are	be	AUX
ejpam-3710	240	6	the	the	DET
ejpam-3710	240	7	eigenvalues	eigenvalue	NOUN
ejpam-3710	240	8	of	of	ADP
ejpam-3710	240	9	a	a	PRON
ejpam-3710	240	10	and	and	CCONJ
ejpam-3710	240	11	the	the	DET
ejpam-3710	240	12	tosha	tosha	NOUN
ejpam-3710	240	13	-	-	PUNCT
ejpam-3710	240	14	energy	energy	NOUN
ejpam-3710	240	15	of	of	ADP
ejpam-3710	240	16	g	g	PROPN
ejpam-3710	240	17	is	be	AUX
ejpam-3710	240	18	et	et	NOUN
ejpam-3710	240	19	(	(	PUNCT
ejpam-3710	240	20	g	g	NOUN
ejpam-3710	240	21	)	)	PUNCT
ejpam-3710	241	1	=	=	SYM
ejpam-3710	242	1	n∑	n∑	NOUN
ejpam-3710	242	2	i=1	i=1	PROPN
ejpam-3710	242	3	|µi|	|µi|	PROPN
ejpam-3710	243	1	=	=	SYM
ejpam-3710	243	2	l	l	NOUN
ejpam-3710	243	3	·	·	PUNCT
ejpam-3710	244	1	n∑	n∑	NOUN
ejpam-3710	244	2	i=1	i=1	PROPN
ejpam-3710	245	1	∣∣∣µi	∣∣∣µi	VERB
ejpam-3710	245	2	l	l	NOUN
ejpam-3710	245	3	∣∣∣	∣∣∣	NOUN
ejpam-3710	245	4	=	=	SYM
ejpam-3710	245	5	l	l	NOUN
ejpam-3710	245	6	·	·	PUNCT
ejpam-3710	245	7	e(g	e(g	PROPN
ejpam-3710	245	8	)	)	PUNCT
ejpam-3710	245	9	.	.	PUNCT
ejpam-3710	246	1	case	case	NOUN
ejpam-3710	246	2	(	(	PUNCT
ejpam-3710	246	3	ii	ii	NOUN
ejpam-3710	246	4	):	):	PUNCT
ejpam-3710	246	5	when	when	SCONJ
ejpam-3710	246	6	l	l	NOUN
ejpam-3710	246	7	=	=	SYM
ejpam-3710	246	8	0	0	X
ejpam-3710	246	9	.	.	PUNCT
ejpam-3710	246	10	from	from	ADP
ejpam-3710	246	11	eq.(7	eq.(7	NOUN
ejpam-3710	246	12	)	)	PUNCT
ejpam-3710	246	13	,	,	PUNCT
ejpam-3710	246	14	at	at	ADP
ejpam-3710	246	15	=	=	NOUN
ejpam-3710	246	16	0	0	PUNCT
ejpam-3710	247	1	and	and	CCONJ
ejpam-3710	247	2	so	so	ADV
ejpam-3710	247	3	zero	zero	NUM
ejpam-3710	247	4	is	be	AUX
ejpam-3710	247	5	the	the	DET
ejpam-3710	247	6	only	only	ADJ
ejpam-3710	247	7	eigenvalue	eigenvalue	NOUN
ejpam-3710	247	8	of	of	ADP
ejpam-3710	247	9	at	at	ADP
ejpam-3710	247	10	of	of	ADP
ejpam-3710	247	11	multiplicity	multiplicity	NOUN
ejpam-3710	247	12	n.	n.	NOUN
ejpam-3710	247	13	in	in	ADP
ejpam-3710	247	14	this	this	DET
ejpam-3710	247	15	case	case	NOUN
ejpam-3710	247	16	,	,	PUNCT
ejpam-3710	247	17	et	et	PROPN
ejpam-3710	247	18	(	(	PUNCT
ejpam-3710	247	19	g	g	NOUN
ejpam-3710	247	20	)	)	PUNCT
ejpam-3710	247	21	=	=	SYM
ejpam-3710	247	22	0	0	PUNCT
ejpam-3710	248	1	=	=	SYM
ejpam-3710	248	2	0	0	PUNCT
ejpam-3710	248	3	·	·	PUNCT
ejpam-3710	248	4	e(g	e(g	PROPN
ejpam-3710	248	5	)	)	PUNCT
ejpam-3710	248	6	.	.	PUNCT
ejpam-3710	249	1	corollary	corollary	ADJ
ejpam-3710	249	2	11	11	NUM
ejpam-3710	249	3	.	.	PUNCT
ejpam-3710	250	1	the	the	DET
ejpam-3710	250	2	tosha	tosha	NOUN
ejpam-3710	250	3	-	-	PUNCT
ejpam-3710	250	4	energy	energy	NOUN
ejpam-3710	250	5	of	of	ADP
ejpam-3710	250	6	an	an	DET
ejpam-3710	250	7	r	r	NOUN
ejpam-3710	250	8	-	-	PUNCT
ejpam-3710	250	9	regular	regular	ADJ
ejpam-3710	250	10	graph	graph	NOUN
ejpam-3710	250	11	g	g	NOUN
ejpam-3710	250	12	with	with	ADP
ejpam-3710	250	13	n	n	DET
ejpam-3710	250	14	vertices	vertex	NOUN
ejpam-3710	250	15	is	be	AUX
ejpam-3710	250	16	given	give	VERB
ejpam-3710	250	17	by	by	ADP
ejpam-3710	250	18	et	et	PROPN
ejpam-3710	250	19	(	(	PUNCT
ejpam-3710	250	20	g	g	NOUN
ejpam-3710	250	21	)	)	PUNCT
ejpam-3710	250	22	=	=	SYM
ejpam-3710	251	1	2(r	2(r	NUM
ejpam-3710	251	2	−	−	NUM
ejpam-3710	251	3	1)e(g	1)e(g	NUM
ejpam-3710	251	4	)	)	PUNCT
ejpam-3710	251	5	(	(	PUNCT
ejpam-3710	251	6	9	9	NUM
ejpam-3710	251	7	)	)	PUNCT
ejpam-3710	251	8	where	where	SCONJ
ejpam-3710	251	9	e(g	e(g	NOUN
ejpam-3710	251	10	)	)	PUNCT
ejpam-3710	251	11	is	be	AUX
ejpam-3710	251	12	the	the	DET
ejpam-3710	251	13	energy	energy	NOUN
ejpam-3710	251	14	of	of	ADP
ejpam-3710	251	15	g.	g.	PROPN
ejpam-3710	251	16	proof	proof	PROPN
ejpam-3710	251	17	.	.	PUNCT
ejpam-3710	252	1	let	let	VERB
ejpam-3710	252	2	g	g	PRON
ejpam-3710	252	3	be	be	AUX
ejpam-3710	252	4	an	an	DET
ejpam-3710	252	5	r	r	NOUN
ejpam-3710	252	6	-	-	PUNCT
ejpam-3710	252	7	regular	regular	ADJ
ejpam-3710	252	8	graph	graph	NOUN
ejpam-3710	252	9	with	with	ADP
ejpam-3710	252	10	n	n	ADP
ejpam-3710	252	11	vertices	vertex	NOUN
ejpam-3710	252	12	.	.	PUNCT
ejpam-3710	253	1	by	by	ADP
ejpam-3710	253	2	[	[	X
ejpam-3710	253	3	4	4	NUM
ejpam-3710	253	4	,	,	PUNCT
ejpam-3710	253	5	corollary	corollary	ADJ
ejpam-3710	253	6	2.6	2.6	NUM
ejpam-3710	253	7	]	]	X
ejpam-3710	253	8	g	g	NOUN
ejpam-3710	253	9	is	be	AUX
ejpam-3710	253	10	a	a	DET
ejpam-3710	253	11	2(r	2(r	NUM
ejpam-3710	253	12	−	−	NOUN
ejpam-3710	253	13	1)-tosha	1)-tosha	NUM
ejpam-3710	253	14	-	-	PUNCT
ejpam-3710	253	15	regular	regular	ADJ
ejpam-3710	253	16	graph	graph	NOUN
ejpam-3710	253	17	.	.	PUNCT
ejpam-3710	254	1	then	then	ADV
ejpam-3710	254	2	by	by	ADP
ejpam-3710	254	3	proposition	proposition	NOUN
ejpam-3710	254	4	6	6	NUM
ejpam-3710	254	5	,	,	PUNCT
ejpam-3710	254	6	the	the	DET
ejpam-3710	254	7	proof	proof	NOUN
ejpam-3710	254	8	follows	follow	VERB
ejpam-3710	254	9	.	.	PUNCT
ejpam-3710	255	1	corollary	corollary	ADJ
ejpam-3710	255	2	12	12	NUM
ejpam-3710	255	3	.	.	PUNCT
ejpam-3710	256	1	(	(	PUNCT
ejpam-3710	256	2	i	i	NOUN
ejpam-3710	256	3	)	)	PUNCT
ejpam-3710	256	4	for	for	ADP
ejpam-3710	256	5	the	the	DET
ejpam-3710	256	6	complete	complete	ADJ
ejpam-3710	256	7	graph	graph	NOUN
ejpam-3710	256	8	kn	kn	PROPN
ejpam-3710	256	9	on	on	ADP
ejpam-3710	256	10	n	n	PROPN
ejpam-3710	256	11	>	>	SYM
ejpam-3710	256	12	1	1	NUM
ejpam-3710	256	13	vertices	vertex	NOUN
ejpam-3710	256	14	,	,	PUNCT
ejpam-3710	256	15	et	et	PROPN
ejpam-3710	256	16	(	(	PUNCT
ejpam-3710	256	17	kn	kn	PROPN
ejpam-3710	256	18	)	)	PUNCT
ejpam-3710	256	19	=	=	PROPN
ejpam-3710	257	1	2(n−	2(n−	NUM
ejpam-3710	257	2	2)e(kn	2)e(kn	NUM
ejpam-3710	257	3	)	)	PUNCT
ejpam-3710	258	1	=	=	SYM
ejpam-3710	258	2	4(n−	4(n−	NUM
ejpam-3710	259	1	1)(n−	1)(n−	NUM
ejpam-3710	259	2	2	2	NUM
ejpam-3710	259	3	)	)	PUNCT
ejpam-3710	259	4	.	.	PUNCT
ejpam-3710	260	1	(	(	PUNCT
ejpam-3710	260	2	ii	ii	NOUN
ejpam-3710	260	3	)	)	PUNCT
ejpam-3710	260	4	for	for	ADP
ejpam-3710	260	5	the	the	DET
ejpam-3710	260	6	cycle	cycle	NOUN
ejpam-3710	260	7	graph	graph	NOUN
ejpam-3710	260	8	cn	cn	PROPN
ejpam-3710	260	9	on	on	ADP
ejpam-3710	260	10	n	n	PROPN
ejpam-3710	260	11	>	>	SYM
ejpam-3710	260	12	1	1	NUM
ejpam-3710	260	13	vertices	vertex	NOUN
ejpam-3710	260	14	,	,	PUNCT
ejpam-3710	260	15	et	et	PROPN
ejpam-3710	260	16	(	(	PUNCT
ejpam-3710	260	17	cn	cn	PROPN
ejpam-3710	260	18	)	)	PUNCT
ejpam-3710	260	19	=	=	SYM
ejpam-3710	260	20	2e(cn	2e(cn	NUM
ejpam-3710	260	21	)	)	PUNCT
ejpam-3710	261	1	=	=	SYM
ejpam-3710	261	2	4	4	NUM
ejpam-3710	261	3	n−1∑	n−1∑	PROPN
ejpam-3710	261	4	i=0	i=0	PROPN
ejpam-3710	261	5	∣∣∣∣cos	∣∣∣∣cos	X
ejpam-3710	261	6	(	(	PUNCT
ejpam-3710	261	7	2πi	2πi	ADJ
ejpam-3710	261	8	n	n	CCONJ
ejpam-3710	261	9	)	)	PUNCT
ejpam-3710	261	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3710	261	11	.	.	PUNCT
ejpam-3710	262	1	(	(	PUNCT
ejpam-3710	262	2	iii	iii	NOUN
ejpam-3710	262	3	)	)	PUNCT
ejpam-3710	262	4	for	for	ADP
ejpam-3710	262	5	the	the	DET
ejpam-3710	262	6	complete	complete	ADJ
ejpam-3710	262	7	bipartite	bipartite	PROPN
ejpam-3710	262	8	graph	graph	NOUN
ejpam-3710	262	9	km	km	PROPN
ejpam-3710	262	10	,	,	PUNCT
ejpam-3710	262	11	n	n	CCONJ
ejpam-3710	262	12	,	,	PUNCT
ejpam-3710	262	13	et	et	PROPN
ejpam-3710	262	14	(	(	PUNCT
ejpam-3710	262	15	km	km	PROPN
ejpam-3710	262	16	,	,	PUNCT
ejpam-3710	262	17	n	n	CCONJ
ejpam-3710	262	18	)	)	PUNCT
ejpam-3710	262	19	=	=	SYM
ejpam-3710	263	1	(	(	PUNCT
ejpam-3710	263	2	m+	m+	NUM
ejpam-3710	263	3	n−	n−	PROPN
ejpam-3710	263	4	2)e(km	2)e(km	NUM
ejpam-3710	263	5	,	,	PUNCT
ejpam-3710	263	6	n	n	CCONJ
ejpam-3710	263	7	)	)	PUNCT
ejpam-3710	263	8	=	=	SYM
ejpam-3710	263	9	2(m+	2(m+	NUM
ejpam-3710	263	10	n−	n−	NOUN
ejpam-3710	263	11	2	2	NUM
ejpam-3710	263	12	)	)	PUNCT
ejpam-3710	263	13	√	√	PROPN
ejpam-3710	263	14	mn	mn	PROPN
ejpam-3710	263	15	.	.	PUNCT
ejpam-3710	264	1	proof	proof	NOUN
ejpam-3710	264	2	.	.	PUNCT
ejpam-3710	265	1	(	(	PUNCT
ejpam-3710	265	2	i	i	NOUN
ejpam-3710	265	3	)	)	PUNCT
ejpam-3710	265	4	the	the	DET
ejpam-3710	265	5	eigen	eigen	PROPN
ejpam-3710	265	6	values	value	NOUN
ejpam-3710	265	7	of	of	ADP
ejpam-3710	265	8	a(kn	a(kn	NOUN
ejpam-3710	265	9	)	)	PUNCT
ejpam-3710	265	10	are	be	AUX
ejpam-3710	265	11	given	give	VERB
ejpam-3710	265	12	below	below	ADV
ejpam-3710	265	13	:	:	PUNCT
ejpam-3710	265	14	eigen	eigen	PROPN
ejpam-3710	265	15	value	value	NOUN
ejpam-3710	265	16	→	→	PUNCT
ejpam-3710	265	17	multiplicity	multiplicity	NOUN
ejpam-3710	265	18	→	→	SYM
ejpam-3710	265	19	(	(	PUNCT
ejpam-3710	265	20	n−	n−	NOUN
ejpam-3710	265	21	1	1	NUM
ejpam-3710	265	22	−1	−1	NOUN
ejpam-3710	265	23	1	1	NUM
ejpam-3710	265	24	n−	n−	NOUN
ejpam-3710	265	25	1	1	NUM
ejpam-3710	265	26	)	)	PUNCT
ejpam-3710	265	27	therefore	therefore	ADV
ejpam-3710	265	28	e(kn	e(kn	NUM
ejpam-3710	265	29	)	)	PUNCT
ejpam-3710	265	30	=	=	SYM
ejpam-3710	265	31	|n−	|n−	NOUN
ejpam-3710	265	32	1|+	1|+	NUM
ejpam-3710	265	33	(	(	PUNCT
ejpam-3710	265	34	n−	n−	NOUN
ejpam-3710	265	35	1)|	1)|	NUM
ejpam-3710	265	36	−	−	NOUN
ejpam-3710	265	37	1|	1|	NUM
ejpam-3710	265	38	=	=	SYM
ejpam-3710	265	39	2(n−	2(n−	NUM
ejpam-3710	265	40	1	1	NUM
ejpam-3710	265	41	)	)	PUNCT
ejpam-3710	265	42	.	.	PUNCT
ejpam-3710	266	1	r.	r.	PROPN
ejpam-3710	266	2	rajendra	rajendra	PROPN
ejpam-3710	266	3	,	,	PUNCT
ejpam-3710	266	4	p.	p.	PROPN
ejpam-3710	266	5	s.	s.	PROPN
ejpam-3710	267	1	k.	k.	PROPN
ejpam-3710	267	2	reddy	reddy	PROPN
ejpam-3710	267	3	/	/	SYM
ejpam-3710	267	4	eur	eur	PROPN
ejpam-3710	267	5	.	.	PUNCT
ejpam-3710	268	1	j.	j.	PROPN
ejpam-3710	268	2	pure	pure	PROPN
ejpam-3710	268	3	appl	appl	PROPN
ejpam-3710	268	4	.	.	PROPN
ejpam-3710	268	5	math	math	PROPN
ejpam-3710	268	6	,	,	PUNCT
ejpam-3710	268	7	13	13	NUM
ejpam-3710	268	8	(	(	PUNCT
ejpam-3710	268	9	5	5	NUM
ejpam-3710	268	10	)	)	PUNCT
ejpam-3710	268	11	(	(	PUNCT
ejpam-3710	268	12	2020	2020	NUM
ejpam-3710	268	13	)	)	PUNCT
ejpam-3710	268	14	,	,	PUNCT
ejpam-3710	268	15	1097	1097	NUM
ejpam-3710	268	16	-	-	SYM
ejpam-3710	268	17	1109	1109	NUM
ejpam-3710	268	18	1107	1107	NUM
ejpam-3710	268	19	since	since	SCONJ
ejpam-3710	268	20	kn	kn	PROPN
ejpam-3710	268	21	is	be	AUX
ejpam-3710	268	22	an	an	DET
ejpam-3710	268	23	(	(	PUNCT
ejpam-3710	268	24	n−	n−	NOUN
ejpam-3710	268	25	1)-regular	1)-regular	NUM
ejpam-3710	268	26	graph	graph	NOUN
ejpam-3710	268	27	,	,	PUNCT
ejpam-3710	268	28	from	from	ADP
ejpam-3710	268	29	eq.(9	eq.(9	ADJ
ejpam-3710	268	30	)	)	PUNCT
ejpam-3710	268	31	we	we	PRON
ejpam-3710	268	32	have	have	VERB
ejpam-3710	268	33	,	,	PUNCT
ejpam-3710	268	34	et	et	PROPN
ejpam-3710	268	35	(	(	PUNCT
ejpam-3710	268	36	kn	kn	PROPN
ejpam-3710	268	37	)	)	PUNCT
ejpam-3710	268	38	=	=	PROPN
ejpam-3710	269	1	2(n−	2(n−	NUM
ejpam-3710	269	2	2)e(kn	2)e(kn	NUM
ejpam-3710	269	3	)	)	PUNCT
ejpam-3710	270	1	=	=	PUNCT
ejpam-3710	271	1	2(n−	2(n−	NUM
ejpam-3710	271	2	2	2	NUM
ejpam-3710	271	3	)	)	PUNCT
ejpam-3710	271	4	·	·	PUNCT
ejpam-3710	272	1	2(n−	2(n−	NUM
ejpam-3710	272	2	1	1	NUM
ejpam-3710	272	3	)	)	PUNCT
ejpam-3710	272	4	=	=	SYM
ejpam-3710	272	5	4(n−	4(n−	NUM
ejpam-3710	272	6	1)(n−	1)(n−	NUM
ejpam-3710	272	7	2	2	NUM
ejpam-3710	272	8	)	)	PUNCT
ejpam-3710	272	9	.	.	PUNCT
ejpam-3710	273	1	(	(	PUNCT
ejpam-3710	273	2	ii	ii	X
ejpam-3710	273	3	)	)	PUNCT
ejpam-3710	273	4	the	the	DET
ejpam-3710	273	5	eigen	eigen	PROPN
ejpam-3710	273	6	values	value	NOUN
ejpam-3710	273	7	of	of	ADP
ejpam-3710	273	8	a(cn	a(cn	PROPN
ejpam-3710	273	9	)	)	PUNCT
ejpam-3710	273	10	are	be	AUX
ejpam-3710	273	11	2	2	NUM
ejpam-3710	273	12	cos	cos	X
ejpam-3710	273	13	(	(	PUNCT
ejpam-3710	273	14	2πi	2πi	NOUN
ejpam-3710	273	15	n	n	CCONJ
ejpam-3710	273	16	)	)	PUNCT
ejpam-3710	273	17	,	,	PUNCT
ejpam-3710	273	18	i	i	PRON
ejpam-3710	273	19	=	=	NOUN
ejpam-3710	273	20	0	0	NUM
ejpam-3710	273	21	,	,	PUNCT
ejpam-3710	273	22	1	1	NUM
ejpam-3710	273	23	,	,	PUNCT
ejpam-3710	273	24	.	.	PUNCT
ejpam-3710	273	25	.	.	PUNCT
ejpam-3710	274	1	.	.	PUNCT
ejpam-3710	275	1	,	,	PUNCT
ejpam-3710	275	2	n−	n−	NOUN
ejpam-3710	275	3	1	1	NUM
ejpam-3710	275	4	.	.	PUNCT
ejpam-3710	275	5	therefore	therefore	ADV
ejpam-3710	275	6	e(cn	e(cn	ADJ
ejpam-3710	275	7	)	)	PUNCT
ejpam-3710	275	8	=	=	SYM
ejpam-3710	275	9	2	2	NUM
ejpam-3710	275	10	n−1∑	n−1∑	PROPN
ejpam-3710	275	11	i=0	i=0	PROPN
ejpam-3710	275	12	∣∣∣∣cos	∣∣∣∣cos	X
ejpam-3710	275	13	(	(	PUNCT
ejpam-3710	275	14	2πi	2πi	ADJ
ejpam-3710	275	15	n	n	CCONJ
ejpam-3710	275	16	)	)	PUNCT
ejpam-3710	275	17	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3710	275	18	.	.	PUNCT
ejpam-3710	276	1	since	since	SCONJ
ejpam-3710	276	2	cn	cn	PROPN
ejpam-3710	276	3	is	be	AUX
ejpam-3710	276	4	an	an	DET
ejpam-3710	276	5	2	2	NUM
ejpam-3710	276	6	-	-	PUNCT
ejpam-3710	276	7	regular	regular	ADJ
ejpam-3710	276	8	graph	graph	NOUN
ejpam-3710	276	9	,	,	PUNCT
ejpam-3710	276	10	from	from	ADP
ejpam-3710	276	11	eq.(9	eq.(9	ADJ
ejpam-3710	276	12	)	)	PUNCT
ejpam-3710	276	13	we	we	PRON
ejpam-3710	276	14	have	have	VERB
ejpam-3710	276	15	,	,	PUNCT
ejpam-3710	276	16	et	et	PROPN
ejpam-3710	276	17	(	(	PUNCT
ejpam-3710	276	18	cn	cn	PROPN
ejpam-3710	276	19	)	)	PUNCT
ejpam-3710	276	20	=	=	SYM
ejpam-3710	276	21	2	2	NUM
ejpam-3710	276	22	·	·	PUNCT
ejpam-3710	276	23	e(cn	e(cn	NOUN
ejpam-3710	276	24	)	)	PUNCT
ejpam-3710	276	25	=	=	SYM
ejpam-3710	276	26	4	4	NUM
ejpam-3710	276	27	n−1∑	n−1∑	PROPN
ejpam-3710	276	28	i=0	i=0	PROPN
ejpam-3710	276	29	∣∣∣∣cos	∣∣∣∣cos	X
ejpam-3710	276	30	(	(	PUNCT
ejpam-3710	276	31	2πi	2πi	ADJ
ejpam-3710	276	32	n	n	CCONJ
ejpam-3710	276	33	)	)	PUNCT
ejpam-3710	276	34	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3710	276	35	.	.	PUNCT
ejpam-3710	277	1	(	(	PUNCT
ejpam-3710	277	2	iii	iii	X
ejpam-3710	277	3	)	)	PUNCT
ejpam-3710	277	4	the	the	DET
ejpam-3710	277	5	eigen	eigen	PROPN
ejpam-3710	277	6	values	value	NOUN
ejpam-3710	277	7	of	of	ADP
ejpam-3710	277	8	a(kn	a(kn	NOUN
ejpam-3710	277	9	)	)	PUNCT
ejpam-3710	277	10	are	be	AUX
ejpam-3710	277	11	given	give	VERB
ejpam-3710	277	12	below	below	ADV
ejpam-3710	277	13	:	:	PUNCT
ejpam-3710	277	14	eigen	eigen	PROPN
ejpam-3710	277	15	value	value	NOUN
ejpam-3710	277	16	→	→	PUNCT
ejpam-3710	277	17	multiplicity	multiplicity	NOUN
ejpam-3710	277	18	→	→	SYM
ejpam-3710	277	19	(	(	PUNCT
ejpam-3710	277	20	−	−	PROPN
ejpam-3710	277	21	√	√	PROPN
ejpam-3710	277	22	mn	mn	PROPN
ejpam-3710	277	23	0	0	PROPN
ejpam-3710	277	24	√	√	PROPN
ejpam-3710	277	25	mn	mn	PROPN
ejpam-3710	277	26	1	1	NUM
ejpam-3710	277	27	n+m−	n+m−	NOUN
ejpam-3710	277	28	2	2	NUM
ejpam-3710	277	29	1	1	NUM
ejpam-3710	277	30	)	)	PUNCT
ejpam-3710	277	31	therefore	therefore	ADV
ejpam-3710	277	32	e(km	e(km	PROPN
ejpam-3710	277	33	,	,	PUNCT
ejpam-3710	277	34	n	n	CCONJ
ejpam-3710	277	35	)	)	PUNCT
ejpam-3710	277	36	=	=	SYM
ejpam-3710	277	37	2	2	NUM
ejpam-3710	277	38	√	√	NUM
ejpam-3710	277	39	mn	mn	PROPN
ejpam-3710	277	40	.	.	PROPN
ejpam-3710	278	1	since	since	SCONJ
ejpam-3710	278	2	km	km	PROPN
ejpam-3710	278	3	,	,	PUNCT
ejpam-3710	278	4	n	n	PRON
ejpam-3710	278	5	is	be	AUX
ejpam-3710	278	6	an	an	DET
ejpam-3710	278	7	(	(	PUNCT
ejpam-3710	278	8	m+	m+	NUM
ejpam-3710	278	9	n−	n−	NOUN
ejpam-3710	278	10	2)-tosha	2)-tosha	NUM
ejpam-3710	278	11	-	-	PUNCT
ejpam-3710	278	12	regular	regular	ADJ
ejpam-3710	278	13	graph	graph	NOUN
ejpam-3710	278	14	,	,	PUNCT
ejpam-3710	278	15	from	from	ADP
ejpam-3710	278	16	eq.(8	eq.(8	ADV
ejpam-3710	278	17	)	)	PUNCT
ejpam-3710	278	18	we	we	PRON
ejpam-3710	278	19	have	have	VERB
ejpam-3710	278	20	,	,	PUNCT
ejpam-3710	278	21	et	et	PROPN
ejpam-3710	278	22	(	(	PUNCT
ejpam-3710	278	23	km	km	PROPN
ejpam-3710	278	24	,	,	PUNCT
ejpam-3710	278	25	n	n	CCONJ
ejpam-3710	278	26	)	)	PUNCT
ejpam-3710	278	27	=	=	SYM
ejpam-3710	279	1	(	(	PUNCT
ejpam-3710	279	2	m+	m+	NUM
ejpam-3710	279	3	n−	n−	PROPN
ejpam-3710	279	4	2)e(km	2)e(km	NUM
ejpam-3710	279	5	,	,	PUNCT
ejpam-3710	279	6	n	n	CCONJ
ejpam-3710	279	7	)	)	PUNCT
ejpam-3710	279	8	=	=	SYM
ejpam-3710	280	1	2(m+	2(m+	NUM
ejpam-3710	280	2	n−	n−	NOUN
ejpam-3710	280	3	2	2	NUM
ejpam-3710	280	4	)	)	PUNCT
ejpam-3710	280	5	√	√	PROPN
ejpam-3710	280	6	mn	mn	PROPN
ejpam-3710	280	7	.	.	PUNCT
ejpam-3710	280	8	corollary	corollary	ADJ
ejpam-3710	280	9	13	13	NUM
ejpam-3710	280	10	.	.	PUNCT
ejpam-3710	281	1	(	(	PUNCT
ejpam-3710	281	2	i	i	NOUN
ejpam-3710	281	3	)	)	PUNCT
ejpam-3710	281	4	for	for	ADP
ejpam-3710	281	5	the	the	DET
ejpam-3710	281	6	path	path	NOUN
ejpam-3710	281	7	p2	p2	NOUN
ejpam-3710	281	8	of	of	ADP
ejpam-3710	281	9	2	2	NUM
ejpam-3710	281	10	vertices	vertex	NOUN
ejpam-3710	281	11	,	,	PUNCT
ejpam-3710	281	12	et	et	NOUN
ejpam-3710	281	13	(	(	PUNCT
ejpam-3710	281	14	p2	p2	PROPN
ejpam-3710	281	15	)	)	PUNCT
ejpam-3710	281	16	=	=	SYM
ejpam-3710	281	17	0	0	X
ejpam-3710	281	18	.	.	PUNCT
ejpam-3710	281	19	(	(	PUNCT
ejpam-3710	281	20	ii	ii	NOUN
ejpam-3710	281	21	)	)	PUNCT
ejpam-3710	281	22	for	for	ADP
ejpam-3710	281	23	the	the	DET
ejpam-3710	281	24	path	path	NOUN
ejpam-3710	281	25	p3	p3	PROPN
ejpam-3710	281	26	of	of	ADP
ejpam-3710	281	27	3	3	NUM
ejpam-3710	281	28	vertices	vertex	NOUN
ejpam-3710	281	29	,	,	PUNCT
ejpam-3710	281	30	et	et	PROPN
ejpam-3710	281	31	(	(	PUNCT
ejpam-3710	281	32	p3	p3	PROPN
ejpam-3710	281	33	)	)	PUNCT
ejpam-3710	281	34	=	=	SYM
ejpam-3710	281	35	e(p3	e(p3	NOUN
ejpam-3710	281	36	)	)	PUNCT
ejpam-3710	282	1	=	=	SYM
ejpam-3710	282	2	2	2	NUM
ejpam-3710	282	3	√	√	NUM
ejpam-3710	282	4	2	2	NUM
ejpam-3710	282	5	.	.	PUNCT
ejpam-3710	283	1	proof	proof	NOUN
ejpam-3710	283	2	.	.	PUNCT
ejpam-3710	284	1	since	since	SCONJ
ejpam-3710	284	2	p2	p2	PROPN
ejpam-3710	284	3	=	=	SYM
ejpam-3710	284	4	k1,1	k1,1	PROPN
ejpam-3710	284	5	and	and	CCONJ
ejpam-3710	284	6	p3	p3	PROPN
ejpam-3710	284	7	=	=	SYM
ejpam-3710	284	8	k2,1	k2,1	PROPN
ejpam-3710	284	9	,	,	PUNCT
ejpam-3710	284	10	(	(	PUNCT
ejpam-3710	284	11	i	i	NOUN
ejpam-3710	284	12	)	)	PUNCT
ejpam-3710	284	13	and	and	CCONJ
ejpam-3710	284	14	(	(	PUNCT
ejpam-3710	284	15	ii	ii	NOUN
ejpam-3710	284	16	)	)	PUNCT
ejpam-3710	284	17	follow	follow	VERB
ejpam-3710	284	18	immediately	immediately	ADV
ejpam-3710	284	19	from	from	ADP
ejpam-3710	284	20	corollary	corollary	ADJ
ejpam-3710	284	21	12	12	NUM
ejpam-3710	284	22	(	(	PUNCT
ejpam-3710	284	23	iii	iii	NOUN
ejpam-3710	284	24	)	)	PUNCT
ejpam-3710	284	25	.	.	PUNCT
ejpam-3710	285	1	theorem	theorem	NOUN
ejpam-3710	285	2	3	3	X
ejpam-3710	285	3	.	.	PUNCT
ejpam-3710	286	1	let	let	VERB
ejpam-3710	286	2	g	g	PRON
ejpam-3710	286	3	be	be	AUX
ejpam-3710	286	4	a	a	DET
ejpam-3710	286	5	simple	simple	ADJ
ejpam-3710	286	6	connected	connected	ADJ
ejpam-3710	286	7	graph	graph	NOUN
ejpam-3710	286	8	with	with	ADP
ejpam-3710	286	9	at	at	ADV
ejpam-3710	286	10	least	least	ADV
ejpam-3710	286	11	one	one	NUM
ejpam-3710	286	12	edge	edge	NOUN
ejpam-3710	286	13	.	.	PUNCT
ejpam-3710	287	1	then	then	ADV
ejpam-3710	287	2	at	at	ADP
ejpam-3710	287	3	(	(	PUNCT
ejpam-3710	287	4	g	g	NOUN
ejpam-3710	287	5	)	)	PUNCT
ejpam-3710	287	6	=	=	PUNCT
ejpam-3710	288	1	a(g)	a(g)	VERB
ejpam-3710	288	2	⇐	⇐	ADJ
ejpam-3710	288	3	⇒	⇒	NOUN
ejpam-3710	288	4	g	g	PROPN
ejpam-3710	288	5	=	=	SYM
ejpam-3710	288	6	p3	p3	PROPN
ejpam-3710	288	7	.	.	PUNCT
ejpam-3710	289	1	proof	proof	NOUN
ejpam-3710	289	2	.	.	PUNCT
ejpam-3710	290	1	(	(	PUNCT
ejpam-3710	290	2	⇐	⇐	ADP
ejpam-3710	290	3	:)	:)	INTJ
ejpam-3710	290	4	if	if	SCONJ
ejpam-3710	290	5	g	g	PROPN
ejpam-3710	290	6	=	=	SYM
ejpam-3710	290	7	p3	p3	PROPN
ejpam-3710	290	8	,	,	PUNCT
ejpam-3710	290	9	then	then	ADV
ejpam-3710	290	10	it	it	PRON
ejpam-3710	290	11	has	have	VERB
ejpam-3710	290	12	two	two	NUM
ejpam-3710	290	13	edges	edge	NOUN
ejpam-3710	290	14	and	and	CCONJ
ejpam-3710	290	15	each	each	PRON
ejpam-3710	290	16	of	of	ADP
ejpam-3710	290	17	these	these	PRON
ejpam-3710	290	18	are	be	AUX
ejpam-3710	290	19	of	of	ADP
ejpam-3710	290	20	tosha	tosha	NOUN
ejpam-3710	290	21	-	-	PUNCT
ejpam-3710	290	22	degree	degree	NOUN
ejpam-3710	290	23	1	1	NUM
ejpam-3710	290	24	.	.	PUNCT
ejpam-3710	291	1	therefore	therefore	ADV
ejpam-3710	291	2	,	,	PUNCT
ejpam-3710	291	3	it	it	PRON
ejpam-3710	291	4	is	be	AUX
ejpam-3710	291	5	1	1	NUM
ejpam-3710	291	6	-	-	PUNCT
ejpam-3710	291	7	tosha	tosha	NOUN
ejpam-3710	291	8	-	-	PUNCT
ejpam-3710	291	9	regular	regular	ADJ
ejpam-3710	291	10	and	and	CCONJ
ejpam-3710	291	11	hence	hence	ADV
ejpam-3710	291	12	by	by	ADP
ejpam-3710	291	13	theorem	theorem	NOUN
ejpam-3710	291	14	2	2	NUM
ejpam-3710	291	15	,	,	PUNCT
ejpam-3710	291	16	at	at	ADP
ejpam-3710	291	17	(	(	PUNCT
ejpam-3710	291	18	g	g	NOUN
ejpam-3710	291	19	)	)	PUNCT
ejpam-3710	291	20	=	=	PUNCT
ejpam-3710	291	21	a(g	a(g	PROPN
ejpam-3710	291	22	)	)	PUNCT
ejpam-3710	291	23	.	.	PUNCT
ejpam-3710	292	1	(	(	PUNCT
ejpam-3710	292	2	⇒	⇒	NOUN
ejpam-3710	292	3	:)	:)	INTJ
ejpam-3710	292	4	suppose	suppose	VERB
ejpam-3710	292	5	that	that	SCONJ
ejpam-3710	292	6	at	at	ADP
ejpam-3710	292	7	(	(	PUNCT
ejpam-3710	292	8	g	g	NOUN
ejpam-3710	292	9	)	)	PUNCT
ejpam-3710	292	10	=	=	PUNCT
ejpam-3710	292	11	a(g	a(g	PROPN
ejpam-3710	292	12	)	)	PUNCT
ejpam-3710	292	13	.	.	PUNCT
ejpam-3710	293	1	then	then	ADV
ejpam-3710	293	2	g	g	PROPN
ejpam-3710	293	3	is	be	AUX
ejpam-3710	293	4	1	1	NUM
ejpam-3710	293	5	-	-	PUNCT
ejpam-3710	293	6	tosha	tosha	NOUN
ejpam-3710	293	7	-	-	PUNCT
ejpam-3710	293	8	regular	regular	ADJ
ejpam-3710	293	9	and	and	CCONJ
ejpam-3710	293	10	hence	hence	ADV
ejpam-3710	293	11	t	t	PROPN
ejpam-3710	293	12	(	(	PUNCT
ejpam-3710	293	13	vivj	vivj	NOUN
ejpam-3710	293	14	)	)	PUNCT
ejpam-3710	293	15	=	=	SYM
ejpam-3710	293	16	1	1	NUM
ejpam-3710	293	17	,	,	PUNCT
ejpam-3710	293	18	∀	∀	X
ejpam-3710	293	19	vivj	vivj	NOUN
ejpam-3710	293	20	∈	∈	PROPN
ejpam-3710	293	21	e(g	e(g	PROPN
ejpam-3710	293	22	)	)	PUNCT
ejpam-3710	294	1	r.	r.	PROPN
ejpam-3710	294	2	rajendra	rajendra	PROPN
ejpam-3710	294	3	,	,	PUNCT
ejpam-3710	294	4	p.	p.	PROPN
ejpam-3710	294	5	s.	s.	PROPN
ejpam-3710	295	1	k.	k.	PROPN
ejpam-3710	295	2	reddy	reddy	PROPN
ejpam-3710	295	3	/	/	SYM
ejpam-3710	295	4	eur	eur	PROPN
ejpam-3710	295	5	.	.	PUNCT
ejpam-3710	296	1	j.	j.	PROPN
ejpam-3710	296	2	pure	pure	PROPN
ejpam-3710	296	3	appl	appl	PROPN
ejpam-3710	296	4	.	.	PROPN
ejpam-3710	296	5	math	math	PROPN
ejpam-3710	296	6	,	,	PUNCT
ejpam-3710	296	7	13	13	NUM
ejpam-3710	296	8	(	(	PUNCT
ejpam-3710	296	9	5	5	NUM
ejpam-3710	296	10	)	)	PUNCT
ejpam-3710	296	11	(	(	PUNCT
ejpam-3710	296	12	2020	2020	NUM
ejpam-3710	296	13	)	)	PUNCT
ejpam-3710	296	14	,	,	PUNCT
ejpam-3710	296	15	1097	1097	NUM
ejpam-3710	296	16	-	-	SYM
ejpam-3710	296	17	1109	1109	NUM
ejpam-3710	296	18	1108	1108	NUM
ejpam-3710	296	19	=	=	NOUN
ejpam-3710	296	20	⇒	⇒	NOUN
ejpam-3710	296	21	d(vi	d(vi	PROPN
ejpam-3710	296	22	)	)	PUNCT
ejpam-3710	297	1	+	+	NUM
ejpam-3710	297	2	d(vj)−	d(vj)−	NOUN
ejpam-3710	297	3	2	2	NUM
ejpam-3710	297	4	=	=	SYM
ejpam-3710	297	5	1	1	NUM
ejpam-3710	297	6	,	,	PUNCT
ejpam-3710	297	7	∀	∀	X
ejpam-3710	297	8	vivj	vivj	NOUN
ejpam-3710	297	9	∈	∈	PROPN
ejpam-3710	297	10	e(g	e(g	PROPN
ejpam-3710	297	11	)	)	PUNCT
ejpam-3710	298	1	=	=	SYM
ejpam-3710	298	2	⇒	⇒	VERB
ejpam-3710	298	3	d(vi	d(vi	PROPN
ejpam-3710	298	4	)	)	PUNCT
ejpam-3710	298	5	=	=	PUNCT
ejpam-3710	298	6	3−	3−	NUM
ejpam-3710	298	7	d(vj	d(vj	NUM
ejpam-3710	298	8	)	)	PUNCT
ejpam-3710	298	9	,	,	PUNCT
ejpam-3710	298	10	∀	∀	X
ejpam-3710	298	11	vivj	vivj	NOUN
ejpam-3710	298	12	∈	∈	PROPN
ejpam-3710	298	13	e(g	e(g	PROPN
ejpam-3710	298	14	)	)	PUNCT
ejpam-3710	298	15	therefore	therefore	ADV
ejpam-3710	298	16	,	,	PUNCT
ejpam-3710	298	17	for	for	ADP
ejpam-3710	298	18	any	any	DET
ejpam-3710	298	19	edge	edge	NOUN
ejpam-3710	298	20	α	α	NOUN
ejpam-3710	298	21	in	in	ADP
ejpam-3710	298	22	g	g	NOUN
ejpam-3710	298	23	with	with	ADP
ejpam-3710	298	24	end	end	NOUN
ejpam-3710	298	25	vertices	vertice	VERB
ejpam-3710	298	26	u	u	NOUN
ejpam-3710	298	27	and	and	CCONJ
ejpam-3710	298	28	v	v	NOUN
ejpam-3710	298	29	,	,	PUNCT
ejpam-3710	298	30	d(u	d(u	PROPN
ejpam-3710	298	31	)	)	PUNCT
ejpam-3710	298	32	=	=	PUNCT
ejpam-3710	299	1	3−	3−	NUM
ejpam-3710	299	2	d(v	d(v	PROPN
ejpam-3710	299	3	)	)	PUNCT
ejpam-3710	299	4	(	(	PUNCT
ejpam-3710	299	5	10	10	NUM
ejpam-3710	299	6	)	)	PUNCT
ejpam-3710	299	7	since	since	SCONJ
ejpam-3710	299	8	g	g	PROPN
ejpam-3710	299	9	is	be	AUX
ejpam-3710	299	10	connected	connect	VERB
ejpam-3710	299	11	,	,	PUNCT
ejpam-3710	299	12	d(v	d(v	PROPN
ejpam-3710	299	13	)	)	PUNCT
ejpam-3710	299	14	>	>	X
ejpam-3710	299	15	0	0	PUNCT
ejpam-3710	299	16	and	and	CCONJ
ejpam-3710	299	17	d(u	d(u	PROPN
ejpam-3710	299	18	)	)	PUNCT
ejpam-3710	299	19	>	>	X
ejpam-3710	299	20	0	0	NUM
ejpam-3710	299	21	,	,	PUNCT
ejpam-3710	299	22	and	and	CCONJ
ejpam-3710	299	23	from	from	ADP
ejpam-3710	299	24	eq.(10	eq.(10	ADJ
ejpam-3710	299	25	)	)	PUNCT
ejpam-3710	299	26	we	we	PRON
ejpam-3710	299	27	have	have	VERB
ejpam-3710	299	28	,	,	PUNCT
ejpam-3710	299	29	d(u	d(u	PROPN
ejpam-3710	299	30	)	)	PUNCT
ejpam-3710	299	31	<	<	X
ejpam-3710	299	32	3	3	NUM
ejpam-3710	299	33	;	;	PUNCT
ejpam-3710	299	34	which	which	PRON
ejpam-3710	299	35	implies	imply	VERB
ejpam-3710	299	36	d(u	d(u	PROPN
ejpam-3710	299	37	)	)	PUNCT
ejpam-3710	299	38	=	=	SYM
ejpam-3710	299	39	1	1	NUM
ejpam-3710	299	40	or	or	CCONJ
ejpam-3710	299	41	2	2	NUM
ejpam-3710	299	42	.	.	PUNCT
ejpam-3710	300	1	(	(	PUNCT
ejpam-3710	300	2	11	11	NUM
ejpam-3710	300	3	)	)	PUNCT
ejpam-3710	300	4	let	let	VERB
ejpam-3710	300	5	u	u	PRON
ejpam-3710	300	6	be	be	AUX
ejpam-3710	300	7	an	an	DET
ejpam-3710	300	8	arbitrary	arbitrary	ADJ
ejpam-3710	300	9	vertex	vertex	NOUN
ejpam-3710	300	10	in	in	ADP
ejpam-3710	300	11	g.	g.	PROPN
ejpam-3710	300	12	since	since	SCONJ
ejpam-3710	300	13	g	g	PROPN
ejpam-3710	300	14	is	be	AUX
ejpam-3710	300	15	a	a	DET
ejpam-3710	300	16	simple	simple	ADJ
ejpam-3710	300	17	connected	connected	ADJ
ejpam-3710	300	18	graph	graph	NOUN
ejpam-3710	300	19	with	with	ADP
ejpam-3710	300	20	at	at	ADV
ejpam-3710	300	21	least	least	ADV
ejpam-3710	300	22	one	one	NUM
ejpam-3710	300	23	edge	edge	NOUN
ejpam-3710	300	24	,	,	PUNCT
ejpam-3710	300	25	u	u	NOUN
ejpam-3710	300	26	is	be	AUX
ejpam-3710	300	27	an	an	DET
ejpam-3710	300	28	end	end	NOUN
ejpam-3710	300	29	vertex	vertex	NOUN
ejpam-3710	300	30	of	of	ADP
ejpam-3710	300	31	at	at	ADV
ejpam-3710	300	32	least	least	ADV
ejpam-3710	300	33	one	one	NUM
ejpam-3710	300	34	edge	edge	NOUN
ejpam-3710	300	35	say	say	VERB
ejpam-3710	300	36	α	α	X
ejpam-3710	300	37	.	.	PUNCT
ejpam-3710	301	1	let	let	VERB
ejpam-3710	301	2	v	v	PART
ejpam-3710	301	3	be	be	AUX
ejpam-3710	301	4	the	the	DET
ejpam-3710	301	5	other	other	ADJ
ejpam-3710	301	6	end	end	NOUN
ejpam-3710	301	7	vertex	vertex	NOUN
ejpam-3710	301	8	of	of	ADP
ejpam-3710	301	9	α	α	PROPN
ejpam-3710	301	10	in	in	ADP
ejpam-3710	301	11	g.	g.	PROPN
ejpam-3710	301	12	then	then	ADV
ejpam-3710	301	13	by	by	ADP
ejpam-3710	301	14	eq.(10	eq.(10	ADJ
ejpam-3710	301	15	)	)	PUNCT
ejpam-3710	301	16	and	and	CCONJ
ejpam-3710	301	17	eq.(11	eq.(11	PROPN
ejpam-3710	301	18	)	)	PUNCT
ejpam-3710	301	19	,	,	PUNCT
ejpam-3710	301	20	either	either	CCONJ
ejpam-3710	301	21	d(u	d(u	PROPN
ejpam-3710	301	22	)	)	PUNCT
ejpam-3710	301	23	=	=	SYM
ejpam-3710	301	24	1	1	NUM
ejpam-3710	301	25	and	and	CCONJ
ejpam-3710	301	26	d(v	d(v	ADJ
ejpam-3710	301	27	)	)	PUNCT
ejpam-3710	301	28	=	=	SYM
ejpam-3710	301	29	2	2	NUM
ejpam-3710	301	30	or	or	CCONJ
ejpam-3710	301	31	d(u	d(u	NOUN
ejpam-3710	301	32	)	)	PUNCT
ejpam-3710	301	33	=	=	SYM
ejpam-3710	301	34	1	1	NUM
ejpam-3710	301	35	and	and	CCONJ
ejpam-3710	301	36	d(v	d(v	ADJ
ejpam-3710	301	37	)	)	PUNCT
ejpam-3710	301	38	=	=	SYM
ejpam-3710	302	1	2	2	X
ejpam-3710	302	2	.	.	X
ejpam-3710	302	3	if	if	SCONJ
ejpam-3710	302	4	d(u	d(u	PROPN
ejpam-3710	302	5	)	)	PUNCT
ejpam-3710	302	6	=	=	SYM
ejpam-3710	302	7	1	1	NUM
ejpam-3710	302	8	and	and	CCONJ
ejpam-3710	302	9	d(v	d(v	ADJ
ejpam-3710	302	10	)	)	PUNCT
ejpam-3710	302	11	=	=	SYM
ejpam-3710	302	12	2	2	NUM
ejpam-3710	302	13	,	,	PUNCT
ejpam-3710	302	14	there	there	PRON
ejpam-3710	302	15	is	be	VERB
ejpam-3710	302	16	another	another	DET
ejpam-3710	302	17	vertex	vertex	NOUN
ejpam-3710	302	18	w	w	NOUN
ejpam-3710	302	19	adjacent	adjacent	ADJ
ejpam-3710	302	20	to	to	ADP
ejpam-3710	302	21	v	v	NOUN
ejpam-3710	302	22	and	and	CCONJ
ejpam-3710	302	23	d(w	d(w	PROPN
ejpam-3710	302	24	)	)	PUNCT
ejpam-3710	302	25	=	=	SYM
ejpam-3710	302	26	1	1	NUM
ejpam-3710	302	27	(	(	PUNCT
ejpam-3710	302	28	by	by	ADP
ejpam-3710	302	29	above	above	ADP
ejpam-3710	302	30	argument	argument	NOUN
ejpam-3710	302	31	)	)	PUNCT
ejpam-3710	302	32	.	.	PUNCT
ejpam-3710	303	1	there	there	PRON
ejpam-3710	303	2	are	be	VERB
ejpam-3710	303	3	no	no	DET
ejpam-3710	303	4	other	other	ADJ
ejpam-3710	303	5	vertices	vertex	NOUN
ejpam-3710	303	6	adjacent	adjacent	ADJ
ejpam-3710	303	7	to	to	ADP
ejpam-3710	303	8	the	the	DET
ejpam-3710	303	9	vertices	vertex	NOUN
ejpam-3710	303	10	u	u	NOUN
ejpam-3710	303	11	,	,	PUNCT
ejpam-3710	303	12	v	v	NOUN
ejpam-3710	303	13	and	and	CCONJ
ejpam-3710	303	14	w.	w.	PROPN
ejpam-3710	304	1	so	so	ADV
ejpam-3710	304	2	,	,	PUNCT
ejpam-3710	304	3	g	g	PROPN
ejpam-3710	304	4	is	be	AUX
ejpam-3710	304	5	a	a	DET
ejpam-3710	304	6	path	path	NOUN
ejpam-3710	304	7	with	with	ADP
ejpam-3710	304	8	3	3	NUM
ejpam-3710	304	9	vertices	vertex	NOUN
ejpam-3710	304	10	.	.	PUNCT
ejpam-3710	305	1	a	a	DET
ejpam-3710	305	2	similar	similar	ADJ
ejpam-3710	305	3	argument	argument	NOUN
ejpam-3710	305	4	can	can	AUX
ejpam-3710	305	5	be	be	AUX
ejpam-3710	305	6	used	use	VERB
ejpam-3710	305	7	for	for	ADP
ejpam-3710	305	8	the	the	DET
ejpam-3710	305	9	case	case	NOUN
ejpam-3710	305	10	d(u	d(u	PROPN
ejpam-3710	305	11	)	)	PUNCT
ejpam-3710	305	12	=	=	SYM
ejpam-3710	305	13	1	1	NUM
ejpam-3710	305	14	and	and	CCONJ
ejpam-3710	305	15	d(v	d(v	ADJ
ejpam-3710	305	16	)	)	PUNCT
ejpam-3710	305	17	=	=	SYM
ejpam-3710	306	1	2	2	NUM
ejpam-3710	306	2	,	,	PUNCT
ejpam-3710	306	3	to	to	PART
ejpam-3710	306	4	show	show	VERB
ejpam-3710	306	5	that	that	SCONJ
ejpam-3710	306	6	g	g	PROPN
ejpam-3710	306	7	is	be	AUX
ejpam-3710	306	8	p3	p3	PROPN
ejpam-3710	306	9	.	.	PUNCT
ejpam-3710	307	1	8	8	NUM
ejpam-3710	307	2	.	.	PUNCT
ejpam-3710	307	3	edge	edge	NOUN
ejpam-3710	307	4	-	-	PUNCT
ejpam-3710	307	5	adjacency	adjacency	NOUN
ejpam-3710	307	6	matrix	matrix	NOUN
ejpam-3710	307	7	and	and	CCONJ
ejpam-3710	307	8	edge	edge	NOUN
ejpam-3710	307	9	-	-	PUNCT
ejpam-3710	307	10	energy	energy	NOUN
ejpam-3710	307	11	of	of	ADP
ejpam-3710	307	12	a	a	DET
ejpam-3710	307	13	graph	graph	NOUN
ejpam-3710	307	14	definition	definition	NOUN
ejpam-3710	307	15	10	10	NUM
ejpam-3710	307	16	.	.	PUNCT
ejpam-3710	308	1	we	we	PRON
ejpam-3710	308	2	say	say	VERB
ejpam-3710	308	3	that	that	SCONJ
ejpam-3710	308	4	two	two	NUM
ejpam-3710	308	5	distinct	distinct	ADJ
ejpam-3710	308	6	edges	edge	NOUN
ejpam-3710	308	7	α	α	NOUN
ejpam-3710	308	8	and	and	CCONJ
ejpam-3710	308	9	β	β	X
ejpam-3710	308	10	in	in	ADP
ejpam-3710	308	11	a	a	DET
ejpam-3710	308	12	graph	graph	NOUN
ejpam-3710	308	13	g	g	NOUN
ejpam-3710	308	14	(	(	PUNCT
ejpam-3710	308	15	where	where	SCONJ
ejpam-3710	308	16	self	self	NOUN
ejpam-3710	308	17	-	-	PUNCT
ejpam-3710	308	18	loops	loop	NOUN
ejpam-3710	308	19	and	and	CCONJ
ejpam-3710	308	20	parallel	parallel	ADJ
ejpam-3710	308	21	edges	edge	NOUN
ejpam-3710	308	22	are	be	AUX
ejpam-3710	308	23	allowed	allow	VERB
ejpam-3710	308	24	)	)	PUNCT
ejpam-3710	308	25	are	be	AUX
ejpam-3710	308	26	k	k	X
ejpam-3710	308	27	-	-	NOUN
ejpam-3710	308	28	adjacent	adjacent	ADJ
ejpam-3710	308	29	if	if	SCONJ
ejpam-3710	308	30	they	they	PRON
ejpam-3710	308	31	are	be	AUX
ejpam-3710	308	32	adjacent	adjacent	ADJ
ejpam-3710	308	33	and	and	CCONJ
ejpam-3710	308	34	share	share	PROPN
ejpam-3710	308	35	k	k	PROPN
ejpam-3710	308	36	end	end	NOUN
ejpam-3710	308	37	vertices	vertex	NOUN
ejpam-3710	308	38	.	.	PUNCT
ejpam-3710	309	1	we	we	PRON
ejpam-3710	309	2	consider	consider	VERB
ejpam-3710	309	3	that	that	SCONJ
ejpam-3710	309	4	an	an	DET
ejpam-3710	309	5	edge	edge	NOUN
ejpam-3710	309	6	in	in	ADP
ejpam-3710	309	7	a	a	DET
ejpam-3710	309	8	graph	graph	NOUN
ejpam-3710	309	9	is	be	AUX
ejpam-3710	309	10	not	not	PART
ejpam-3710	309	11	adjacent	adjacent	ADJ
ejpam-3710	309	12	to	to	ADP
ejpam-3710	309	13	itself	itself	PRON
ejpam-3710	309	14	.	.	PUNCT
ejpam-3710	310	1	definition	definition	NOUN
ejpam-3710	310	2	11	11	NUM
ejpam-3710	310	3	.	.	PUNCT
ejpam-3710	311	1	if	if	SCONJ
ejpam-3710	311	2	g	g	PROPN
ejpam-3710	311	3	is	be	AUX
ejpam-3710	311	4	a	a	DET
ejpam-3710	311	5	graph	graph	NOUN
ejpam-3710	311	6	with	with	ADP
ejpam-3710	311	7	m	m	PROPN
ejpam-3710	311	8	edges	edge	NOUN
ejpam-3710	311	9	e1	e1	NOUN
ejpam-3710	311	10	,	,	PUNCT
ejpam-3710	311	11	.	.	PUNCT
ejpam-3710	311	12	.	.	PUNCT
ejpam-3710	312	1	.	.	PUNCT
ejpam-3710	313	1	,	,	PUNCT
ejpam-3710	313	2	em	em	PRON
ejpam-3710	313	3	.	.	PUNCT
ejpam-3710	314	1	the	the	DET
ejpam-3710	314	2	edge	edge	NOUN
ejpam-3710	314	3	-	-	PUNCT
ejpam-3710	314	4	adjacency	adjacency	NOUN
ejpam-3710	314	5	matrix	matrix	NOUN
ejpam-3710	314	6	of	of	ADP
ejpam-3710	314	7	the	the	DET
ejpam-3710	314	8	graph	graph	NOUN
ejpam-3710	314	9	g	g	PROPN
ejpam-3710	314	10	is	be	AUX
ejpam-3710	314	11	an	an	DET
ejpam-3710	314	12	m×m	m×m	ADJ
ejpam-3710	314	13	matrix	matrix	NOUN
ejpam-3710	314	14	ae(g	ae(g	NOUN
ejpam-3710	314	15	)	)	PUNCT
ejpam-3710	315	1	=	=	SYM
ejpam-3710	315	2	(	(	PUNCT
ejpam-3710	315	3	xij	xij	X
ejpam-3710	315	4	)	)	PUNCT
ejpam-3710	315	5	defined	define	VERB
ejpam-3710	315	6	over	over	ADP
ejpam-3710	315	7	the	the	DET
ejpam-3710	315	8	ring	ring	NOUN
ejpam-3710	315	9	of	of	ADP
ejpam-3710	315	10	integers	integer	NOUN
ejpam-3710	315	11	such	such	ADJ
ejpam-3710	315	12	that	that	SCONJ
ejpam-3710	315	13	xij	xij	PRON
ejpam-3710	315	14	=	=	PRON
ejpam-3710	315	15	{	{	PUNCT
ejpam-3710	315	16	k	k	NOUN
ejpam-3710	315	17	,	,	PUNCT
ejpam-3710	315	18	if	if	SCONJ
ejpam-3710	315	19	ei	ei	PROPN
ejpam-3710	315	20	and	and	CCONJ
ejpam-3710	315	21	ej	ej	PROPN
ejpam-3710	315	22	are	be	AUX
ejpam-3710	315	23	k−adjacent	k−adjacent	NOUN
ejpam-3710	315	24	;	;	PUNCT
ejpam-3710	315	25	0	0	NUM
ejpam-3710	315	26	,	,	PUNCT
ejpam-3710	315	27	otherwise	otherwise	ADV
ejpam-3710	315	28	.	.	PUNCT
ejpam-3710	316	1	observations	observation	NOUN
ejpam-3710	316	2	:	:	PUNCT
ejpam-3710	316	3	(	(	PUNCT
ejpam-3710	316	4	i	i	NOUN
ejpam-3710	316	5	)	)	PUNCT
ejpam-3710	316	6	ae(g	ae(g	ADV
ejpam-3710	316	7	)	)	PUNCT
ejpam-3710	316	8	is	be	AUX
ejpam-3710	316	9	a	a	DET
ejpam-3710	316	10	{	{	PUNCT
ejpam-3710	316	11	0	0	NUM
ejpam-3710	316	12	,	,	PUNCT
ejpam-3710	316	13	1	1	NUM
ejpam-3710	316	14	,	,	PUNCT
ejpam-3710	316	15	2}-matrix	2}-matrix	NUM
ejpam-3710	316	16	and	and	CCONJ
ejpam-3710	316	17	it	it	PRON
ejpam-3710	316	18	is	be	AUX
ejpam-3710	316	19	real	real	ADV
ejpam-3710	316	20	symmetric	symmetric	ADJ
ejpam-3710	316	21	.	.	PUNCT
ejpam-3710	317	1	if	if	SCONJ
ejpam-3710	317	2	g	g	PROPN
ejpam-3710	317	3	is	be	AUX
ejpam-3710	317	4	a	a	DET
ejpam-3710	317	5	simple	simple	ADJ
ejpam-3710	317	6	graph	graph	NOUN
ejpam-3710	317	7	,	,	PUNCT
ejpam-3710	317	8	then	then	ADV
ejpam-3710	317	9	ae(g	ae(g	PUNCT
ejpam-3710	317	10	)	)	PUNCT
ejpam-3710	317	11	is	be	AUX
ejpam-3710	317	12	a	a	DET
ejpam-3710	317	13	{	{	PUNCT
ejpam-3710	317	14	0	0	NUM
ejpam-3710	317	15	,	,	PUNCT
ejpam-3710	317	16	1}-matrix	1}-matrix	NUM
ejpam-3710	317	17	.	.	PUNCT
ejpam-3710	318	1	(	(	PUNCT
ejpam-3710	318	2	ii	ii	X
ejpam-3710	318	3	)	)	PUNCT
ejpam-3710	318	4	the	the	DET
ejpam-3710	318	5	entries	entry	NOUN
ejpam-3710	318	6	along	along	ADP
ejpam-3710	318	7	the	the	DET
ejpam-3710	318	8	principal	principal	ADJ
ejpam-3710	318	9	diagonal	diagonal	NOUN
ejpam-3710	318	10	of	of	ADP
ejpam-3710	318	11	ae(g	ae(g	ADV
ejpam-3710	318	12	)	)	PUNCT
ejpam-3710	318	13	are	be	AUX
ejpam-3710	318	14	all	all	PRON
ejpam-3710	318	15	0s	0s	NOUN
ejpam-3710	318	16	.	.	PUNCT
ejpam-3710	319	1	therefore	therefore	ADV
ejpam-3710	319	2	,	,	PUNCT
ejpam-3710	319	3	tr(ae(g	tr(ae(g	NOUN
ejpam-3710	319	4	)	)	PUNCT
ejpam-3710	319	5	)	)	PUNCT
ejpam-3710	320	1	=	=	PUNCT
ejpam-3710	320	2	0	0	X
ejpam-3710	320	3	.	.	PUNCT
ejpam-3710	321	1	hence	hence	ADV
ejpam-3710	321	2	if	if	SCONJ
ejpam-3710	321	3	ν1	ν1	NOUN
ejpam-3710	321	4	,	,	PUNCT
ejpam-3710	321	5	ν2	ν2	NOUN
ejpam-3710	321	6	,	,	PUNCT
ejpam-3710	321	7	.	.	PUNCT
ejpam-3710	321	8	.	.	PUNCT
ejpam-3710	321	9	.	.	PUNCT
ejpam-3710	322	1	,	,	PUNCT
ejpam-3710	322	2	νm	νm	INTJ
ejpam-3710	322	3	are	be	AUX
ejpam-3710	322	4	the	the	DET
ejpam-3710	322	5	eigenvalues	eigenvalue	NOUN
ejpam-3710	322	6	of	of	ADP
ejpam-3710	322	7	ae(g	ae(g	NOUN
ejpam-3710	322	8	)	)	PUNCT
ejpam-3710	322	9	,	,	PUNCT
ejpam-3710	322	10	then	then	ADV
ejpam-3710	322	11	m∑	m∑	INTJ
ejpam-3710	322	12	i=1	i=1	VERB
ejpam-3710	322	13	νi	νi	PRON
ejpam-3710	323	1	=	=	ADJ
ejpam-3710	324	1	0	0	PROPN
ejpam-3710	324	2	.	.	PUNCT
ejpam-3710	325	1	(	(	PUNCT
ejpam-3710	325	2	iii	iii	X
ejpam-3710	325	3	)	)	PUNCT
ejpam-3710	325	4	if	if	SCONJ
ejpam-3710	325	5	g	g	PROPN
ejpam-3710	325	6	has	have	VERB
ejpam-3710	325	7	no	no	DET
ejpam-3710	325	8	self	self	NOUN
ejpam-3710	325	9	-	-	PUNCT
ejpam-3710	325	10	loops	loop	NOUN
ejpam-3710	325	11	,	,	PUNCT
ejpam-3710	325	12	then	then	ADV
ejpam-3710	325	13	the	the	DET
ejpam-3710	325	14	tosha	tosha	NOUN
ejpam-3710	325	15	-	-	PUNCT
ejpam-3710	325	16	degree	degree	NOUN
ejpam-3710	325	17	of	of	ADP
ejpam-3710	325	18	an	an	DET
ejpam-3710	325	19	edge	edge	NOUN
ejpam-3710	325	20	equals	equal	VERB
ejpam-3710	325	21	the	the	DET
ejpam-3710	325	22	sum	sum	NOUN
ejpam-3710	325	23	of	of	ADP
ejpam-3710	325	24	entries	entry	NOUN
ejpam-3710	325	25	in	in	ADP
ejpam-3710	325	26	the	the	DET
ejpam-3710	325	27	corresponding	corresponding	NOUN
ejpam-3710	325	28	row	row	NOUN
ejpam-3710	325	29	or	or	CCONJ
ejpam-3710	325	30	column	column	NOUN
ejpam-3710	325	31	of	of	ADP
ejpam-3710	325	32	ae(g	ae(g	NOUN
ejpam-3710	325	33	)	)	PUNCT
ejpam-3710	325	34	.	.	PUNCT
ejpam-3710	326	1	references	reference	NOUN
ejpam-3710	326	2	1109	1109	NUM
ejpam-3710	326	3	proposition	proposition	NOUN
ejpam-3710	326	4	7	7	NUM
ejpam-3710	326	5	.	.	X
ejpam-3710	326	6	for	for	ADP
ejpam-3710	326	7	a	a	DET
ejpam-3710	326	8	multigraph	multigraph	NOUN
ejpam-3710	326	9	g	g	NOUN
ejpam-3710	326	10	,	,	PUNCT
ejpam-3710	326	11	the	the	DET
ejpam-3710	326	12	edge	edge	NOUN
ejpam-3710	326	13	-	-	PUNCT
ejpam-3710	326	14	adjacency	adjacency	NOUN
ejpam-3710	326	15	matrix	matrix	NOUN
ejpam-3710	326	16	of	of	ADP
ejpam-3710	326	17	g	g	PROPN
ejpam-3710	326	18	is	be	AUX
ejpam-3710	326	19	the	the	DET
ejpam-3710	326	20	adjacency	adjacency	NOUN
ejpam-3710	326	21	matrix	matrix	NOUN
ejpam-3710	326	22	of	of	ADP
ejpam-3710	326	23	the	the	DET
ejpam-3710	326	24	t	t	NOUN
ejpam-3710	326	25	-line	-line	PROPN
ejpam-3710	326	26	graph	graph	NOUN
ejpam-3710	326	27	of	of	ADP
ejpam-3710	326	28	g.	g.	PROPN
ejpam-3710	326	29	that	that	PRON
ejpam-3710	326	30	is	be	AUX
ejpam-3710	326	31	,	,	PUNCT
ejpam-3710	326	32	ae(g	ae(g	ADV
ejpam-3710	326	33	)	)	PUNCT
ejpam-3710	326	34	=	=	SYM
ejpam-3710	327	1	a(tl(g	a(tl(g	PROPN
ejpam-3710	327	2	)	)	PUNCT
ejpam-3710	327	3	)	)	PUNCT
ejpam-3710	327	4	.	.	PUNCT
ejpam-3710	328	1	proof	proof	NOUN
ejpam-3710	328	2	.	.	PUNCT
ejpam-3710	329	1	follows	follow	VERB
ejpam-3710	329	2	by	by	ADP
ejpam-3710	329	3	the	the	DET
ejpam-3710	329	4	definitions	definition	NOUN
ejpam-3710	329	5	4	4	NUM
ejpam-3710	329	6	and	and	CCONJ
ejpam-3710	329	7	11	11	NUM
ejpam-3710	329	8	.	.	PUNCT
ejpam-3710	330	1	corollary	corollary	ADJ
ejpam-3710	330	2	14	14	NUM
ejpam-3710	330	3	.	.	PUNCT
ejpam-3710	331	1	for	for	ADP
ejpam-3710	331	2	a	a	DET
ejpam-3710	331	3	simple	simple	ADJ
ejpam-3710	331	4	graph	graph	NOUN
ejpam-3710	331	5	g	g	PROPN
ejpam-3710	331	6	,	,	PUNCT
ejpam-3710	331	7	the	the	DET
ejpam-3710	331	8	edge	edge	NOUN
ejpam-3710	331	9	-	-	PUNCT
ejpam-3710	331	10	adjacency	adjacency	NOUN
ejpam-3710	331	11	matrix	matrix	NOUN
ejpam-3710	331	12	of	of	ADP
ejpam-3710	331	13	g	g	PROPN
ejpam-3710	331	14	is	be	AUX
ejpam-3710	331	15	the	the	DET
ejpam-3710	331	16	adjacency	adjacency	NOUN
ejpam-3710	331	17	matrix	matrix	NOUN
ejpam-3710	331	18	of	of	ADP
ejpam-3710	331	19	the	the	DET
ejpam-3710	331	20	line	line	NOUN
ejpam-3710	331	21	graph	graph	NOUN
ejpam-3710	331	22	of	of	ADP
ejpam-3710	331	23	g.	g.	PROPN
ejpam-3710	331	24	that	that	PRON
ejpam-3710	331	25	is	be	AUX
ejpam-3710	331	26	,	,	PUNCT
ejpam-3710	331	27	ae(g	ae(g	ADV
ejpam-3710	331	28	)	)	PUNCT
ejpam-3710	331	29	=	=	SYM
ejpam-3710	331	30	a(l(g	a(l(g	PROPN
ejpam-3710	331	31	)	)	PUNCT
ejpam-3710	331	32	)	)	PUNCT
ejpam-3710	331	33	.	.	PUNCT
ejpam-3710	332	1	proof	proof	NOUN
ejpam-3710	332	2	.	.	PUNCT
ejpam-3710	333	1	for	for	ADP
ejpam-3710	333	2	simple	simple	ADJ
ejpam-3710	333	3	graph	graph	NOUN
ejpam-3710	333	4	g	g	NOUN
ejpam-3710	333	5	,	,	PUNCT
ejpam-3710	333	6	tl(g	tl(g	NUM
ejpam-3710	333	7	)	)	PUNCT
ejpam-3710	333	8	=	=	SYM
ejpam-3710	333	9	l(g	l(g	X
ejpam-3710	333	10	)	)	PUNCT
ejpam-3710	333	11	and	and	CCONJ
ejpam-3710	333	12	so	so	ADV
ejpam-3710	333	13	by	by	ADP
ejpam-3710	333	14	proposition	proposition	NOUN
ejpam-3710	333	15	7	7	NUM
ejpam-3710	333	16	the	the	DET
ejpam-3710	333	17	result	result	NOUN
ejpam-3710	333	18	follows	follow	VERB
ejpam-3710	333	19	.	.	PUNCT
ejpam-3710	334	1	definition	definition	NOUN
ejpam-3710	334	2	12	12	NUM
ejpam-3710	334	3	.	.	PUNCT
ejpam-3710	335	1	let	let	VERB
ejpam-3710	335	2	g	g	NOUN
ejpam-3710	335	3	be	be	AUX
ejpam-3710	335	4	graph	graph	NOUN
ejpam-3710	335	5	with	with	ADP
ejpam-3710	335	6	m	m	PROPN
ejpam-3710	335	7	edges	edge	NOUN
ejpam-3710	335	8	e1	e1	NOUN
ejpam-3710	335	9	,	,	PUNCT
ejpam-3710	335	10	.	.	PUNCT
ejpam-3710	335	11	.	.	PUNCT
ejpam-3710	336	1	.	.	PUNCT
ejpam-3710	337	1	,	,	PUNCT
ejpam-3710	337	2	em	em	PRON
ejpam-3710	337	3	.	.	PUNCT
ejpam-3710	338	1	let	let	VERB
ejpam-3710	338	2	ν1	ν1	NOUN
ejpam-3710	338	3	,	,	PUNCT
ejpam-3710	338	4	ν2	ν2	NOUN
ejpam-3710	338	5	,	,	PUNCT
ejpam-3710	338	6	.	.	PUNCT
ejpam-3710	338	7	.	.	PUNCT
ejpam-3710	339	1	.	.	PUNCT
ejpam-3710	340	1	,	,	PUNCT
ejpam-3710	340	2	νm	νm	INTJ
ejpam-3710	340	3	be	be	AUX
ejpam-3710	340	4	the	the	DET
ejpam-3710	340	5	eigenvalues	eigenvalue	NOUN
ejpam-3710	340	6	of	of	ADP
ejpam-3710	340	7	the	the	DET
ejpam-3710	340	8	edge	edge	NOUN
ejpam-3710	340	9	-	-	PUNCT
ejpam-3710	340	10	adjacency	adjacency	NOUN
ejpam-3710	340	11	matrix	matrix	NOUN
ejpam-3710	340	12	ae(g	ae(g	NOUN
ejpam-3710	340	13	)	)	PUNCT
ejpam-3710	340	14	of	of	ADP
ejpam-3710	340	15	g.	g.	PROPN
ejpam-3710	340	16	the	the	DET
ejpam-3710	340	17	edge	edge	NOUN
ejpam-3710	340	18	-	-	PUNCT
ejpam-3710	340	19	energy	energy	NOUN
ejpam-3710	340	20	of	of	ADP
ejpam-3710	340	21	g	g	NOUN
ejpam-3710	340	22	,	,	PUNCT
ejpam-3710	340	23	denoted	denote	VERB
ejpam-3710	340	24	by	by	ADP
ejpam-3710	340	25	ee(g	ee(g	NOUN
ejpam-3710	340	26	)	)	PUNCT
ejpam-3710	340	27	,	,	PUNCT
ejpam-3710	340	28	is	be	AUX
ejpam-3710	340	29	defined	define	VERB
ejpam-3710	340	30	as	as	ADP
ejpam-3710	340	31	ee(g	ee(g	NOUN
ejpam-3710	340	32	)	)	PUNCT
ejpam-3710	341	1	=	=	PUNCT
ejpam-3710	341	2	m∑	m∑	INTJ
ejpam-3710	341	3	i=1	i=1	PROPN
ejpam-3710	341	4	|νi|	|νi|	PROPN
ejpam-3710	341	5	.	.	PUNCT
ejpam-3710	342	1	(	(	PUNCT
ejpam-3710	342	2	12	12	NUM
ejpam-3710	342	3	)	)	PUNCT
ejpam-3710	342	4	corollary	corollary	ADJ
ejpam-3710	342	5	15	15	NUM
ejpam-3710	342	6	.	.	PUNCT
ejpam-3710	343	1	for	for	ADP
ejpam-3710	343	2	a	a	DET
ejpam-3710	343	3	multigraph	multigraph	NOUN
ejpam-3710	343	4	g	g	NOUN
ejpam-3710	343	5	,	,	PUNCT
ejpam-3710	343	6	the	the	DET
ejpam-3710	343	7	edge	edge	NOUN
ejpam-3710	343	8	-	-	PUNCT
ejpam-3710	343	9	energy	energy	NOUN
ejpam-3710	343	10	of	of	ADP
ejpam-3710	343	11	g	g	PROPN
ejpam-3710	343	12	is	be	AUX
ejpam-3710	343	13	the	the	DET
ejpam-3710	343	14	energy	energy	NOUN
ejpam-3710	343	15	of	of	ADP
ejpam-3710	343	16	the	the	DET
ejpam-3710	343	17	t	t	NOUN
ejpam-3710	343	18	-line	-line	PROPN
ejpam-3710	343	19	graph	graph	NOUN
ejpam-3710	343	20	of	of	ADP
ejpam-3710	343	21	g.	g.	PROPN
ejpam-3710	343	22	that	that	PRON
ejpam-3710	343	23	is	be	AUX
ejpam-3710	343	24	,	,	PUNCT
ejpam-3710	343	25	ee(g	ee(g	NOUN
ejpam-3710	343	26	)	)	PUNCT
ejpam-3710	343	27	=	=	SYM
ejpam-3710	343	28	e(tl(g	e(tl(g	NOUN
ejpam-3710	343	29	)	)	PUNCT
ejpam-3710	343	30	)	)	PUNCT
ejpam-3710	343	31	.	.	PUNCT
ejpam-3710	344	1	proof	proof	NOUN
ejpam-3710	344	2	.	.	PUNCT
ejpam-3710	345	1	follows	follow	VERB
ejpam-3710	345	2	by	by	ADP
ejpam-3710	345	3	proposition	proposition	NOUN
ejpam-3710	345	4	7	7	NUM
ejpam-3710	345	5	.	.	PUNCT
ejpam-3710	346	1	corollary	corollary	ADJ
ejpam-3710	346	2	16	16	NUM
ejpam-3710	346	3	.	.	PUNCT
ejpam-3710	347	1	for	for	ADP
ejpam-3710	347	2	a	a	DET
ejpam-3710	347	3	simple	simple	ADJ
ejpam-3710	347	4	graph	graph	NOUN
ejpam-3710	347	5	g	g	PROPN
ejpam-3710	347	6	,	,	PUNCT
ejpam-3710	347	7	the	the	DET
ejpam-3710	347	8	edge	edge	NOUN
ejpam-3710	347	9	-	-	PUNCT
ejpam-3710	347	10	energy	energy	NOUN
ejpam-3710	347	11	of	of	ADP
ejpam-3710	347	12	g	g	PROPN
ejpam-3710	347	13	is	be	AUX
ejpam-3710	347	14	the	the	DET
ejpam-3710	347	15	energy	energy	NOUN
ejpam-3710	347	16	of	of	ADP
ejpam-3710	347	17	the	the	DET
ejpam-3710	347	18	line	line	NOUN
ejpam-3710	347	19	graph	graph	NOUN
ejpam-3710	347	20	of	of	ADP
ejpam-3710	347	21	g.	g.	PROPN
ejpam-3710	347	22	that	that	PRON
ejpam-3710	347	23	is	be	AUX
ejpam-3710	347	24	,	,	PUNCT
ejpam-3710	347	25	ee(g	ee(g	NOUN
ejpam-3710	347	26	)	)	PUNCT
ejpam-3710	348	1	=	=	PUNCT
ejpam-3710	348	2	e(l(g	e(l(g	NOUN
ejpam-3710	348	3	)	)	PUNCT
ejpam-3710	348	4	)	)	PUNCT
ejpam-3710	348	5	.	.	PUNCT
ejpam-3710	349	1	proof	proof	NOUN
ejpam-3710	349	2	.	.	PUNCT
ejpam-3710	350	1	follows	follow	VERB
ejpam-3710	350	2	by	by	ADP
ejpam-3710	350	3	corollary	corollary	ADJ
ejpam-3710	350	4	14	14	NUM
ejpam-3710	350	5	.	.	PUNCT
ejpam-3710	351	1	acknowledgements	acknowledgement	NOUN
ejpam-3710	351	2	the	the	DET
ejpam-3710	351	3	authors	author	NOUN
ejpam-3710	351	4	would	would	AUX
ejpam-3710	351	5	like	like	VERB
ejpam-3710	351	6	to	to	PART
ejpam-3710	351	7	thank	thank	VERB
ejpam-3710	351	8	the	the	DET
ejpam-3710	351	9	referees	referee	NOUN
ejpam-3710	351	10	for	for	ADP
ejpam-3710	351	11	their	their	PRON
ejpam-3710	351	12	invaluable	invaluable	ADJ
ejpam-3710	351	13	comments	comment	NOUN
ejpam-3710	351	14	and	and	CCONJ
ejpam-3710	351	15	suggestions	suggestion	NOUN
ejpam-3710	351	16	which	which	PRON
ejpam-3710	351	17	led	lead	VERB
ejpam-3710	351	18	to	to	ADP
ejpam-3710	351	19	the	the	DET
ejpam-3710	351	20	improvement	improvement	NOUN
ejpam-3710	351	21	of	of	ADP
ejpam-3710	351	22	the	the	DET
ejpam-3710	351	23	manuscript	manuscript	NOUN
ejpam-3710	351	24	.	.	PUNCT
ejpam-3710	352	1	references	reference	NOUN
ejpam-3710	352	2	[	[	X
ejpam-3710	352	3	1	1	NUM
ejpam-3710	352	4	]	]	X
ejpam-3710	352	5	r	r	NOUN
ejpam-3710	352	6	b	b	NOUN
ejpam-3710	352	7	bapat	bapat	PROPN
ejpam-3710	352	8	.	.	PUNCT
ejpam-3710	353	1	graphs	graph	NOUN
ejpam-3710	353	2	and	and	CCONJ
ejpam-3710	353	3	matrices	matrix	NOUN
ejpam-3710	353	4	.	.	PUNCT
ejpam-3710	354	1	springer	springer	PROPN
ejpam-3710	354	2	,	,	PUNCT
ejpam-3710	354	3	london	london	PROPN
ejpam-3710	354	4	,	,	PUNCT
ejpam-3710	354	5	2010	2010	NUM
ejpam-3710	354	6	.	.	PUNCT
ejpam-3710	355	1	[	[	X
ejpam-3710	355	2	2	2	NUM
ejpam-3710	355	3	]	]	PUNCT
ejpam-3710	355	4	f	f	PROPN
ejpam-3710	355	5	harary	harary	NOUN
ejpam-3710	355	6	.	.	PUNCT
ejpam-3710	356	1	graph	graph	NOUN
ejpam-3710	356	2	theory	theory	NOUN
ejpam-3710	356	3	.	.	PUNCT
ejpam-3710	357	1	addison	addison	PROPN
ejpam-3710	357	2	-	-	PUNCT
ejpam-3710	357	3	wesley	wesley	PROPN
ejpam-3710	357	4	pub	pub	PROPN
ejpam-3710	357	5	.	.	PUNCT
ejpam-3710	358	1	co.	co.	PROPN
ejpam-3710	358	2	,	,	PUNCT
ejpam-3710	358	3	massachusetts	massachusetts	PROPN
ejpam-3710	358	4	,	,	PUNCT
ejpam-3710	358	5	1969	1969	NUM
ejpam-3710	358	6	.	.	PUNCT
ejpam-3710	359	1	[	[	X
ejpam-3710	359	2	3	3	NUM
ejpam-3710	359	3	]	]	X
ejpam-3710	359	4	r	r	NOUN
ejpam-3710	359	5	rajendra	rajendra	PROPN
ejpam-3710	359	6	and	and	CCONJ
ejpam-3710	359	7	p	p	PROPN
ejpam-3710	359	8	siva	siva	PROPN
ejpam-3710	359	9	kota	kota	PROPN
ejpam-3710	359	10	reddy	reddy	PROPN
ejpam-3710	359	11	.	.	PUNCT
ejpam-3710	360	1	tosha	tosha	NOUN
ejpam-3710	360	2	-	-	PUNCT
ejpam-3710	360	3	degree	degree	NOUN
ejpam-3710	360	4	equivalence	equivalence	NOUN
ejpam-3710	360	5	signed	sign	VERB
ejpam-3710	360	6	graphs	graph	NOUN
ejpam-3710	360	7	.	.	PUNCT
ejpam-3710	361	1	vladikavkaz	vladikavkaz	PROPN
ejpam-3710	361	2	.	.	PUNCT
ejpam-3710	362	1	mat	mat	PROPN
ejpam-3710	362	2	.	.	PUNCT
ejpam-3710	363	1	zh	zh	PROPN
ejpam-3710	363	2	.	.	PROPN
ejpam-3710	363	3	,	,	PUNCT
ejpam-3710	363	4	22(2):48–52	22(2):48–52	NUM
ejpam-3710	363	5	,	,	PUNCT
ejpam-3710	363	6	2020	2020	NUM
ejpam-3710	363	7	.	.	PUNCT
ejpam-3710	364	1	[	[	X
ejpam-3710	364	2	4	4	NUM
ejpam-3710	364	3	]	]	X
ejpam-3710	364	4	r	r	NOUN
ejpam-3710	364	5	rajendra	rajendra	PROPN
ejpam-3710	364	6	and	and	CCONJ
ejpam-3710	364	7	p	p	PROPN
ejpam-3710	364	8	siva	siva	PROPN
ejpam-3710	364	9	kota	kota	PROPN
ejpam-3710	364	10	reddy	reddy	PROPN
ejpam-3710	364	11	.	.	PUNCT
ejpam-3710	365	1	tosha	tosha	NOUN
ejpam-3710	365	2	-	-	PUNCT
ejpam-3710	365	3	degree	degree	NOUN
ejpam-3710	365	4	of	of	ADP
ejpam-3710	365	5	an	an	DET
ejpam-3710	365	6	edge	edge	NOUN
ejpam-3710	365	7	in	in	ADP
ejpam-3710	365	8	a	a	DET
ejpam-3710	365	9	graph	graph	NOUN
ejpam-3710	365	10	.	.	PUNCT
ejpam-3710	366	1	southeast	southeast	ADJ
ejpam-3710	366	2	asian	asian	ADJ
ejpam-3710	366	3	bull	bull	PROPN
ejpam-3710	366	4	.	.	PUNCT
ejpam-3710	367	1	math	math	NOUN
ejpam-3710	367	2	.	.	PUNCT
ejpam-3710	368	1	,	,	PUNCT
ejpam-3710	368	2	accepted	accept	VERB
ejpam-3710	368	3	for	for	ADP
ejpam-3710	368	4	publication	publication	NOUN
ejpam-3710	368	5	.	.	PUNCT