id	sid	tid	token	lemma	pos
ejpam-2419	1	1	compile	compile	NOUN
ejpam-2419	1	2	/	/	SYM
ejpam-2419	1	3	output.dvi	output.dvi	NOUN
ejpam-2419	1	4	european	european	ADJ
ejpam-2419	1	5	journal	journal	NOUN
ejpam-2419	1	6	of	of	ADP
ejpam-2419	1	7	pure	pure	ADJ
ejpam-2419	1	8	and	and	CCONJ
ejpam-2419	1	9	applied	apply	VERB
ejpam-2419	1	10	mathematics	mathematic	NOUN
ejpam-2419	1	11	vol	vol	NOUN
ejpam-2419	1	12	.	.	PROPN
ejpam-2419	2	1	9	9	NUM
ejpam-2419	2	2	,	,	PUNCT
ejpam-2419	2	3	no	no	INTJ
ejpam-2419	2	4	.	.	NOUN
ejpam-2419	2	5	3	3	NUM
ejpam-2419	2	6	,	,	PUNCT
ejpam-2419	2	7	2016	2016	NUM
ejpam-2419	2	8	,	,	PUNCT
ejpam-2419	2	9	340	340	NUM
ejpam-2419	2	10	-	-	SYM
ejpam-2419	2	11	345	345	NUM
ejpam-2419	2	12	issn	issn	PROPN
ejpam-2419	2	13	1307	1307	NUM
ejpam-2419	2	14	-	-	SYM
ejpam-2419	2	15	5543	5543	NUM
ejpam-2419	2	16	–	–	PUNCT
ejpam-2419	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2419	2	18	on	on	ADP
ejpam-2419	2	19	degree	degree	NOUN
ejpam-2419	2	20	sum	sum	NOUN
ejpam-2419	2	21	energy	energy	NOUN
ejpam-2419	2	22	of	of	ADP
ejpam-2419	2	23	a	a	DET
ejpam-2419	2	24	graph	graph	NOUN
ejpam-2419	2	25	sunilkumar	sunilkumar	NOUN
ejpam-2419	2	26	m.	m.	NOUN
ejpam-2419	2	27	hosamani1,∗	hosamani1,∗	PROPN
ejpam-2419	2	28	,	,	PUNCT
ejpam-2419	2	29	harishchandra	harishchandra	PROPN
ejpam-2419	2	30	s.	s.	PROPN
ejpam-2419	2	31	ramane2	ramane2	PROPN
ejpam-2419	2	32	1	1	NUM
ejpam-2419	2	33	department	department	NOUN
ejpam-2419	2	34	of	of	ADP
ejpam-2419	2	35	mathematics	mathematic	NOUN
ejpam-2419	2	36	,	,	PUNCT
ejpam-2419	2	37	rani	rani	PROPN
ejpam-2419	2	38	channamma	channamma	PROPN
ejpam-2419	2	39	university	university	PROPN
ejpam-2419	2	40	,	,	PUNCT
ejpam-2419	2	41	belagavi	belagavi	VERB
ejpam-2419	2	42	,	,	PUNCT
ejpam-2419	2	43	india	india	PROPN
ejpam-2419	2	44	2	2	NUM
ejpam-2419	2	45	department	department	NOUN
ejpam-2419	2	46	of	of	ADP
ejpam-2419	2	47	mathematics	mathematics	PROPN
ejpam-2419	2	48	,	,	PUNCT
ejpam-2419	2	49	karnatak	karnatak	PROPN
ejpam-2419	2	50	university	university	PROPN
ejpam-2419	2	51	,	,	PUNCT
ejpam-2419	2	52	dharwad	dharwad	PROPN
ejpam-2419	2	53	,	,	PUNCT
ejpam-2419	2	54	india	india	PROPN
ejpam-2419	2	55	abstract	abstract	NOUN
ejpam-2419	2	56	.	.	PUNCT
ejpam-2419	3	1	the	the	DET
ejpam-2419	3	2	degree	degree	NOUN
ejpam-2419	3	3	sum	sum	NOUN
ejpam-2419	3	4	energy	energy	NOUN
ejpam-2419	3	5	of	of	ADP
ejpam-2419	3	6	a	a	DET
ejpam-2419	3	7	graph	graph	NOUN
ejpam-2419	3	8	g	g	NOUN
ejpam-2419	3	9	is	be	AUX
ejpam-2419	3	10	defined	define	VERB
ejpam-2419	3	11	as	as	ADP
ejpam-2419	3	12	the	the	DET
ejpam-2419	3	13	sum	sum	NOUN
ejpam-2419	3	14	of	of	ADP
ejpam-2419	3	15	the	the	DET
ejpam-2419	3	16	absolute	absolute	ADJ
ejpam-2419	3	17	values	value	NOUN
ejpam-2419	3	18	of	of	ADP
ejpam-2419	3	19	the	the	DET
ejpam-2419	3	20	eigenvalues	eigenvalue	NOUN
ejpam-2419	3	21	of	of	ADP
ejpam-2419	3	22	the	the	DET
ejpam-2419	3	23	degree	degree	NOUN
ejpam-2419	3	24	sum	sum	NOUN
ejpam-2419	3	25	matrix	matrix	NOUN
ejpam-2419	3	26	of	of	ADP
ejpam-2419	3	27	g.	g.	PROPN
ejpam-2419	3	28	in	in	ADP
ejpam-2419	3	29	this	this	DET
ejpam-2419	3	30	paper	paper	NOUN
ejpam-2419	3	31	,	,	PUNCT
ejpam-2419	3	32	we	we	PRON
ejpam-2419	3	33	obtain	obtain	VERB
ejpam-2419	3	34	some	some	DET
ejpam-2419	3	35	lower	low	ADJ
ejpam-2419	3	36	bounds	bound	NOUN
ejpam-2419	3	37	for	for	ADP
ejpam-2419	3	38	the	the	DET
ejpam-2419	3	39	degree	degree	NOUN
ejpam-2419	3	40	sum	sum	NOUN
ejpam-2419	3	41	energy	energy	NOUN
ejpam-2419	3	42	of	of	ADP
ejpam-2419	3	43	a	a	DET
ejpam-2419	3	44	graph	graph	NOUN
ejpam-2419	3	45	g.	g.	NOUN
ejpam-2419	3	46	2010	2010	NUM
ejpam-2419	3	47	mathematics	mathematic	NOUN
ejpam-2419	3	48	subject	subject	NOUN
ejpam-2419	3	49	classifications	classification	NOUN
ejpam-2419	3	50	:	:	PUNCT
ejpam-2419	3	51	05c50	05c50	NUM
ejpam-2419	3	52	key	key	ADJ
ejpam-2419	3	53	words	word	NOUN
ejpam-2419	3	54	and	and	CCONJ
ejpam-2419	3	55	phrases	phrase	NOUN
ejpam-2419	3	56	:	:	PUNCT
ejpam-2419	3	57	spectrum	spectrum	NOUN
ejpam-2419	3	58	,	,	PUNCT
ejpam-2419	3	59	energy	energy	NOUN
ejpam-2419	3	60	,	,	PUNCT
ejpam-2419	3	61	degree	degree	NOUN
ejpam-2419	3	62	sum	sum	NOUN
ejpam-2419	3	63	energy	energy	NOUN
ejpam-2419	3	64	1	1	NUM
ejpam-2419	3	65	.	.	PUNCT
ejpam-2419	4	1	introduction	introduction	NOUN
ejpam-2419	4	2	we	we	PRON
ejpam-2419	4	3	consider	consider	VERB
ejpam-2419	4	4	finite	finite	ADJ
ejpam-2419	4	5	,	,	PUNCT
ejpam-2419	4	6	undirected	undirected	ADJ
ejpam-2419	4	7	and	and	CCONJ
ejpam-2419	4	8	simple	simple	ADJ
ejpam-2419	4	9	graphs	graph	NOUN
ejpam-2419	4	10	g	g	NOUN
ejpam-2419	4	11	with	with	ADP
ejpam-2419	4	12	vertex	vertex	NOUN
ejpam-2419	4	13	set	set	VERB
ejpam-2419	4	14	v	v	NOUN
ejpam-2419	4	15	(	(	PUNCT
ejpam-2419	4	16	g	g	NOUN
ejpam-2419	4	17	)	)	PUNCT
ejpam-2419	4	18	and	and	CCONJ
ejpam-2419	4	19	edge	edge	VERB
ejpam-2419	4	20	set	set	VERB
ejpam-2419	4	21	e(g	e(g	PROPN
ejpam-2419	4	22	)	)	PUNCT
ejpam-2419	4	23	.	.	PUNCT
ejpam-2419	5	1	let	let	VERB
ejpam-2419	5	2	g	g	PROPN
ejpam-2419	5	3	=	=	SYM
ejpam-2419	5	4	(	(	PUNCT
ejpam-2419	5	5	v	v	NOUN
ejpam-2419	5	6	,	,	PUNCT
ejpam-2419	5	7	e	e	NOUN
ejpam-2419	5	8	)	)	PUNCT
ejpam-2419	5	9	be	be	AUX
ejpam-2419	5	10	a	a	DET
ejpam-2419	5	11	graph	graph	NOUN
ejpam-2419	5	12	.	.	PUNCT
ejpam-2419	6	1	the	the	DET
ejpam-2419	6	2	number	number	NOUN
ejpam-2419	6	3	of	of	ADP
ejpam-2419	6	4	vertices	vertex	NOUN
ejpam-2419	6	5	of	of	ADP
ejpam-2419	6	6	g	g	PROPN
ejpam-2419	6	7	we	we	PRON
ejpam-2419	6	8	denote	denote	VERB
ejpam-2419	6	9	by	by	ADP
ejpam-2419	6	10	n	n	PROPN
ejpam-2419	6	11	and	and	CCONJ
ejpam-2419	6	12	the	the	DET
ejpam-2419	6	13	number	number	NOUN
ejpam-2419	6	14	of	of	ADP
ejpam-2419	6	15	edges	edge	NOUN
ejpam-2419	6	16	we	we	PRON
ejpam-2419	6	17	denote	denote	VERB
ejpam-2419	6	18	by	by	ADP
ejpam-2419	6	19	m	m	PRON
ejpam-2419	6	20	,	,	PUNCT
ejpam-2419	6	21	thus	thus	ADV
ejpam-2419	6	22	|v	|v	X
ejpam-2419	6	23	(	(	PUNCT
ejpam-2419	6	24	g)|=	g)|=	PROPN
ejpam-2419	6	25	n	n	CCONJ
ejpam-2419	6	26	and	and	CCONJ
ejpam-2419	6	27	|e(g)|=	|e(g)|=	ADJ
ejpam-2419	6	28	m.	m.	NOUN
ejpam-2419	6	29	the	the	DET
ejpam-2419	6	30	degree	degree	NOUN
ejpam-2419	6	31	of	of	ADP
ejpam-2419	6	32	a	a	DET
ejpam-2419	6	33	vertex	vertex	NOUN
ejpam-2419	6	34	v	v	NOUN
ejpam-2419	6	35	,	,	PUNCT
ejpam-2419	6	36	denoted	denote	VERB
ejpam-2419	6	37	by	by	ADP
ejpam-2419	6	38	di	di	NOUN
ejpam-2419	6	39	.	.	PUNCT
ejpam-2419	7	1	specially	specially	ADV
ejpam-2419	7	2	,	,	PUNCT
ejpam-2419	7	3	∆	∆	PROPN
ejpam-2419	7	4	=	=	SYM
ejpam-2419	7	5	∆(g	∆(g	PROPN
ejpam-2419	7	6	)	)	PUNCT
ejpam-2419	7	7	and	and	CCONJ
ejpam-2419	7	8	δ	δ	PROPN
ejpam-2419	7	9	=	=	PUNCT
ejpam-2419	7	10	δ(g	δ(g	X
ejpam-2419	7	11	)	)	PUNCT
ejpam-2419	7	12	are	be	AUX
ejpam-2419	7	13	called	call	VERB
ejpam-2419	7	14	the	the	DET
ejpam-2419	7	15	maximum	maximum	ADJ
ejpam-2419	7	16	and	and	CCONJ
ejpam-2419	7	17	minimum	minimum	NOUN
ejpam-2419	7	18	degree	degree	NOUN
ejpam-2419	7	19	of	of	ADP
ejpam-2419	7	20	vertices	vertex	NOUN
ejpam-2419	7	21	of	of	ADP
ejpam-2419	7	22	g	g	NOUN
ejpam-2419	7	23	respectively	respectively	ADV
ejpam-2419	7	24	.	.	PUNCT
ejpam-2419	8	1	g	g	PROPN
ejpam-2419	8	2	is	be	AUX
ejpam-2419	8	3	said	say	VERB
ejpam-2419	8	4	to	to	PART
ejpam-2419	8	5	be	be	AUX
ejpam-2419	8	6	r	r	NOUN
ejpam-2419	8	7	-	-	ADJ
ejpam-2419	8	8	regular	regular	ADJ
ejpam-2419	8	9	if	if	SCONJ
ejpam-2419	8	10	δ(g	δ(g	PROPN
ejpam-2419	8	11	)	)	PUNCT
ejpam-2419	8	12	=	=	SYM
ejpam-2419	8	13	∆(g	∆(g	NOUN
ejpam-2419	8	14	)	)	PUNCT
ejpam-2419	8	15	=	=	SYM
ejpam-2419	8	16	r	r	NOUN
ejpam-2419	8	17	for	for	ADP
ejpam-2419	8	18	some	some	DET
ejpam-2419	8	19	positive	positive	ADJ
ejpam-2419	8	20	integer	integer	NOUN
ejpam-2419	8	21	r.	r.	NOUN
ejpam-2419	8	22	for	for	ADP
ejpam-2419	8	23	any	any	DET
ejpam-2419	8	24	integer	integer	NOUN
ejpam-2419	8	25	x	x	X
ejpam-2419	8	26	,	,	PUNCT
ejpam-2419	8	27	⌊x⌋	⌊x⌋	PUNCT
ejpam-2419	8	28	is	be	AUX
ejpam-2419	8	29	the	the	DET
ejpam-2419	8	30	positive	positive	ADJ
ejpam-2419	8	31	integer	integer	NOUN
ejpam-2419	8	32	less	less	ADJ
ejpam-2419	8	33	than	than	ADP
ejpam-2419	8	34	or	or	CCONJ
ejpam-2419	8	35	equal	equal	ADJ
ejpam-2419	8	36	to	to	ADP
ejpam-2419	8	37	x	x	X
ejpam-2419	8	38	.	.	PUNCT
ejpam-2419	9	1	for	for	ADP
ejpam-2419	9	2	undefined	undefined	ADJ
ejpam-2419	9	3	terminologies	terminology	NOUN
ejpam-2419	9	4	we	we	PRON
ejpam-2419	9	5	refer	refer	VERB
ejpam-2419	9	6	the	the	DET
ejpam-2419	9	7	reader	reader	NOUN
ejpam-2419	9	8	to	to	ADP
ejpam-2419	9	9	[	[	X
ejpam-2419	9	10	5	5	NUM
ejpam-2419	9	11	]	]	PUNCT
ejpam-2419	9	12	.	.	PUNCT
ejpam-2419	10	1	the	the	DET
ejpam-2419	10	2	energy	energy	PROPN
ejpam-2419	10	3	e(g	e(g	PROPN
ejpam-2419	10	4	)	)	PUNCT
ejpam-2419	10	5	of	of	ADP
ejpam-2419	10	6	a	a	DET
ejpam-2419	10	7	graph	graph	NOUN
ejpam-2419	10	8	g	g	NOUN
ejpam-2419	10	9	is	be	AUX
ejpam-2419	10	10	equal	equal	ADJ
ejpam-2419	10	11	to	to	ADP
ejpam-2419	10	12	the	the	DET
ejpam-2419	10	13	sum	sum	NOUN
ejpam-2419	10	14	of	of	ADP
ejpam-2419	10	15	the	the	DET
ejpam-2419	10	16	absolute	absolute	ADJ
ejpam-2419	10	17	values	value	NOUN
ejpam-2419	10	18	of	of	ADP
ejpam-2419	10	19	the	the	DET
ejpam-2419	10	20	eigenvalues	eigenvalue	NOUN
ejpam-2419	10	21	of	of	ADP
ejpam-2419	10	22	the	the	DET
ejpam-2419	10	23	adjacency	adjacency	NOUN
ejpam-2419	10	24	matrix	matrix	NOUN
ejpam-2419	10	25	of	of	ADP
ejpam-2419	10	26	g.	g.	PROPN
ejpam-2419	10	27	this	this	DET
ejpam-2419	10	28	quantity	quantity	NOUN
ejpam-2419	10	29	,	,	PUNCT
ejpam-2419	10	30	introduced	introduce	VERB
ejpam-2419	10	31	almost	almost	ADV
ejpam-2419	10	32	30	30	NUM
ejpam-2419	10	33	years	year	NOUN
ejpam-2419	10	34	ago	ago	ADV
ejpam-2419	10	35	[	[	X
ejpam-2419	10	36	6	6	NUM
ejpam-2419	10	37	]	]	PUNCT
ejpam-2419	10	38	and	and	CCONJ
ejpam-2419	10	39	having	have	VERB
ejpam-2419	10	40	a	a	DET
ejpam-2419	10	41	clear	clear	ADJ
ejpam-2419	10	42	connection	connection	NOUN
ejpam-2419	10	43	to	to	ADP
ejpam-2419	10	44	chemical	chemical	NOUN
ejpam-2419	10	45	problems	problem	NOUN
ejpam-2419	10	46	,	,	PUNCT
ejpam-2419	10	47	has	have	AUX
ejpam-2419	10	48	in	in	ADP
ejpam-2419	10	49	newer	new	ADJ
ejpam-2419	10	50	times	time	NOUN
ejpam-2419	10	51	attracted	attract	VERB
ejpam-2419	10	52	much	much	ADJ
ejpam-2419	10	53	attention	attention	NOUN
ejpam-2419	10	54	of	of	ADP
ejpam-2419	10	55	mathematicians	mathematician	NOUN
ejpam-2419	10	56	and	and	CCONJ
ejpam-2419	10	57	mathematical	mathematical	ADJ
ejpam-2419	10	58	chemists	chemist	NOUN
ejpam-2419	10	59	[	[	X
ejpam-2419	10	60	3	3	NUM
ejpam-2419	10	61	,	,	PUNCT
ejpam-2419	10	62	7–9	7–9	NUM
ejpam-2419	10	63	,	,	PUNCT
ejpam-2419	10	64	13–15	13–15	NUM
ejpam-2419	10	65	]	]	PUNCT
ejpam-2419	10	66	.	.	PUNCT
ejpam-2419	11	1	motivated	motivate	VERB
ejpam-2419	11	2	by	by	ADP
ejpam-2419	11	3	work	work	NOUN
ejpam-2419	11	4	on	on	ADP
ejpam-2419	11	5	maximum	maximum	ADJ
ejpam-2419	11	6	degree	degree	NOUN
ejpam-2419	11	7	energy	energy	NOUN
ejpam-2419	11	8	[	[	X
ejpam-2419	11	9	1	1	NUM
ejpam-2419	11	10	]	]	PUNCT
ejpam-2419	11	11	,	,	PUNCT
ejpam-2419	11	12	ramane	ramane	PROPN
ejpam-2419	11	13	et	et	PROPN
ejpam-2419	11	14	al	al	PROPN
ejpam-2419	11	15	.	.	PUNCT
ejpam-2419	12	1	[	[	X
ejpam-2419	12	2	12	12	NUM
ejpam-2419	12	3	]	]	PUNCT
ejpam-2419	12	4	introduced	introduce	VERB
ejpam-2419	12	5	the	the	DET
ejpam-2419	12	6	concept	concept	NOUN
ejpam-2419	12	7	of	of	ADP
ejpam-2419	12	8	degree	degree	NOUN
ejpam-2419	12	9	sum	sum	NOUN
ejpam-2419	12	10	energy	energy	NOUN
ejpam-2419	12	11	,	,	PUNCT
ejpam-2419	12	12	which	which	PRON
ejpam-2419	12	13	is	be	AUX
ejpam-2419	12	14	defined	define	VERB
ejpam-2419	12	15	as	as	ADP
ejpam-2419	12	16	follow	follow	NOUN
ejpam-2419	12	17	:	:	PUNCT
ejpam-2419	12	18	definition	definition	NOUN
ejpam-2419	12	19	1	1	NUM
ejpam-2419	12	20	.	.	PUNCT
ejpam-2419	13	1	let	let	VERB
ejpam-2419	13	2	g	g	PRON
ejpam-2419	13	3	be	be	AUX
ejpam-2419	13	4	a	a	DET
ejpam-2419	13	5	simple	simple	ADJ
ejpam-2419	13	6	graph	graph	NOUN
ejpam-2419	13	7	with	with	ADP
ejpam-2419	13	8	n	n	ADP
ejpam-2419	13	9	vertices	vertex	NOUN
ejpam-2419	13	10	v1	v1	NOUN
ejpam-2419	13	11	,	,	PUNCT
ejpam-2419	13	12	v2	v2	NOUN
ejpam-2419	13	13	,	,	PUNCT
ejpam-2419	13	14	.	.	PUNCT
ejpam-2419	13	15	.	.	PUNCT
ejpam-2419	14	1	.	.	PUNCT
ejpam-2419	15	1	,	,	PUNCT
ejpam-2419	15	2	vn	vn	PROPN
ejpam-2419	15	3	and	and	CCONJ
ejpam-2419	15	4	let	let	VERB
ejpam-2419	15	5	di	di	PART
ejpam-2419	15	6	be	be	AUX
ejpam-2419	15	7	the	the	DET
ejpam-2419	15	8	degree	degree	NOUN
ejpam-2419	15	9	of	of	ADP
ejpam-2419	15	10	vi	vi	PROPN
ejpam-2419	15	11	,	,	PUNCT
ejpam-2419	15	12	i	i	NOUN
ejpam-2419	15	13	=	=	NOUN
ejpam-2419	15	14	1,2	1,2	NUM
ejpam-2419	15	15	,	,	PUNCT
ejpam-2419	15	16	.	.	PUNCT
ejpam-2419	15	17	.	.	PUNCT
ejpam-2419	16	1	.	.	PUNCT
ejpam-2419	17	1	,	,	PUNCT
ejpam-2419	17	2	n.	n.	PROPN
ejpam-2419	17	3	then	then	ADV
ejpam-2419	17	4	ds(g	ds(g	X
ejpam-2419	17	5	)	)	PUNCT
ejpam-2419	17	6	=	=	PUNCT
ejpam-2419	18	1	[	[	X
ejpam-2419	18	2	di	di	X
ejpam-2419	18	3	j	j	X
ejpam-2419	18	4	]	]	X
ejpam-2419	18	5	is	be	AUX
ejpam-2419	18	6	called	call	VERB
ejpam-2419	18	7	the	the	DET
ejpam-2419	18	8	degree	degree	NOUN
ejpam-2419	18	9	sum	sum	NOUN
ejpam-2419	18	10	matrix	matrix	NOUN
ejpam-2419	18	11	of	of	ADP
ejpam-2419	18	12	a	a	DET
ejpam-2419	18	13	graph	graph	NOUN
ejpam-2419	18	14	g	g	NOUN
ejpam-2419	18	15	,	,	PUNCT
ejpam-2419	18	16	where	where	SCONJ
ejpam-2419	18	17	di	di	X
ejpam-2419	18	18	j	j	PROPN
ejpam-2419	18	19	=	=	PUNCT
ejpam-2419	18	20	¨	¨	X
ejpam-2419	18	21	di	di	NOUN
ejpam-2419	19	1	+	+	CCONJ
ejpam-2419	19	2	d	d	PROPN
ejpam-2419	19	3	j	j	NOUN
ejpam-2419	19	4	if	if	SCONJ
ejpam-2419	19	5	i	i	PRON
ejpam-2419	19	6	6=	6=	PROPN
ejpam-2419	19	7	j	j	PROPN
ejpam-2419	19	8	;	;	PUNCT
ejpam-2419	19	9	0	0	NUM
ejpam-2419	19	10	otherwise	otherwise	ADV
ejpam-2419	19	11	.	.	PUNCT
ejpam-2419	20	1	∗corresponding	∗corresponde	VERB
ejpam-2419	20	2	author	author	NOUN
ejpam-2419	20	3	.	.	PUNCT
ejpam-2419	21	1	email	email	NOUN
ejpam-2419	21	2	addresses	address	NOUN
ejpam-2419	21	3	:	:	PUNCT
ejpam-2419	21	4	sunilkumar.rcu@gmail.com	sunilkumar.rcu@gmail.com	PROPN
ejpam-2419	21	5	(	(	PUNCT
ejpam-2419	21	6	s.	s.	PROPN
ejpam-2419	21	7	hosamani	hosamani	PROPN
ejpam-2419	21	8	)	)	PUNCT
ejpam-2419	21	9	,	,	PUNCT
ejpam-2419	22	1	hsramane@yahoo.com	hsramane@yahoo.com	X
ejpam-2419	22	2	(	(	PUNCT
ejpam-2419	22	3	h.	h.	PROPN
ejpam-2419	22	4	ramane	ramane	PROPN
ejpam-2419	22	5	)	)	PUNCT
ejpam-2419	22	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2419	23	1	340	340	NUM
ejpam-2419	23	2	c	c	NOUN
ejpam-2419	23	3	©	©	PROPN
ejpam-2419	23	4	2016	2016	NUM
ejpam-2419	23	5	ejpam	ejpam	VERB
ejpam-2419	23	6	all	all	DET
ejpam-2419	23	7	rights	right	NOUN
ejpam-2419	23	8	reserved	reserve	VERB
ejpam-2419	23	9	.	.	PUNCT
ejpam-2419	24	1	s.	s.	PROPN
ejpam-2419	24	2	hosamani	hosamani	PROPN
ejpam-2419	24	3	and	and	CCONJ
ejpam-2419	24	4	h.	h.	PROPN
ejpam-2419	24	5	ramane	ramane	PROPN
ejpam-2419	24	6	/	/	SYM
ejpam-2419	24	7	eur	eur	PROPN
ejpam-2419	24	8	.	.	PUNCT
ejpam-2419	25	1	j.	j.	PROPN
ejpam-2419	25	2	pure	pure	PROPN
ejpam-2419	25	3	appl	appl	PROPN
ejpam-2419	25	4	.	.	PROPN
ejpam-2419	25	5	math	math	PROPN
ejpam-2419	25	6	,	,	PUNCT
ejpam-2419	25	7	9	9	NUM
ejpam-2419	25	8	(	(	PUNCT
ejpam-2419	25	9	2016	2016	NUM
ejpam-2419	25	10	)	)	PUNCT
ejpam-2419	25	11	,	,	PUNCT
ejpam-2419	25	12	340	340	NUM
ejpam-2419	25	13	-	-	SYM
ejpam-2419	25	14	345	345	NUM
ejpam-2419	25	15	341	341	NUM
ejpam-2419	25	16	the	the	DET
ejpam-2419	25	17	characteristic	characteristic	ADJ
ejpam-2419	25	18	polynomial	polynomial	NOUN
ejpam-2419	25	19	of	of	ADP
ejpam-2419	25	20	ds(g	ds(g	PROPN
ejpam-2419	25	21	)	)	PUNCT
ejpam-2419	25	22	is	be	AUX
ejpam-2419	25	23	denoted	denote	VERB
ejpam-2419	25	24	by	by	ADP
ejpam-2419	25	25	fn(g	fn(g	PROPN
ejpam-2419	25	26	,	,	PUNCT
ejpam-2419	25	27	λ	λ	NOUN
ejpam-2419	25	28	)	)	PUNCT
ejpam-2419	25	29	:	:	PUNCT
ejpam-2419	26	1	=	=	NOUN
ejpam-2419	26	2	det(λi	det(λi	ADP
ejpam-2419	26	3	−	−	NOUN
ejpam-2419	26	4	ds(g	ds(g	NUM
ejpam-2419	26	5	)	)	PUNCT
ejpam-2419	26	6	)	)	PUNCT
ejpam-2419	26	7	.	.	PUNCT
ejpam-2419	27	1	since	since	SCONJ
ejpam-2419	27	2	ds(g	ds(g	NOUN
ejpam-2419	27	3	)	)	PUNCT
ejpam-2419	27	4	is	be	AUX
ejpam-2419	27	5	real	real	ADJ
ejpam-2419	27	6	and	and	CCONJ
ejpam-2419	27	7	symmetric	symmetric	ADJ
ejpam-2419	27	8	,	,	PUNCT
ejpam-2419	27	9	its	its	PRON
ejpam-2419	27	10	eigenvalues	eigenvalue	NOUN
ejpam-2419	27	11	are	be	AUX
ejpam-2419	27	12	real	real	ADJ
ejpam-2419	27	13	numbers	number	NOUN
ejpam-2419	27	14	and	and	CCONJ
ejpam-2419	27	15	we	we	PRON
ejpam-2419	27	16	label	label	VERB
ejpam-2419	27	17	them	they	PRON
ejpam-2419	27	18	in	in	ADP
ejpam-2419	27	19	nonincreasing	nonincrease	VERB
ejpam-2419	27	20	order	order	NOUN
ejpam-2419	27	21	λ1	λ1	ADJ
ejpam-2419	27	22	≥	≥	NOUN
ejpam-2419	27	23	λ2	λ2	PROPN
ejpam-2419	27	24	≥	≥	NOUN
ejpam-2419	27	25	·	·	PUNCT
ejpam-2419	27	26	·	·	PUNCT
ejpam-2419	27	27	·	·	PUNCT
ejpam-2419	27	28	≥	≥	NUM
ejpam-2419	27	29	λn	λn	NOUN
ejpam-2419	27	30	.	.	PUNCT
ejpam-2419	28	1	the	the	DET
ejpam-2419	28	2	maximum	maximum	PROPN
ejpam-2419	28	3	degree	degree	NOUN
ejpam-2419	28	4	energy	energy	NOUN
ejpam-2419	28	5	of	of	ADP
ejpam-2419	28	6	g	g	PROPN
ejpam-2419	28	7	is	be	AUX
ejpam-2419	28	8	then	then	ADV
ejpam-2419	28	9	defined	define	VERB
ejpam-2419	28	10	as	as	ADP
ejpam-2419	28	11	eds(g	eds(g	X
ejpam-2419	28	12	)	)	PUNCT
ejpam-2419	28	13	=	=	PUNCT
ejpam-2419	29	1	n	n	CCONJ
ejpam-2419	29	2	∑	∑	ADV
ejpam-2419	29	3	i=1	i=1	PROPN
ejpam-2419	29	4	|λi	|λi	PROPN
ejpam-2419	29	5	|	|	NOUN
ejpam-2419	29	6	.	.	PUNCT
ejpam-2419	30	1	in	in	ADP
ejpam-2419	30	2	this	this	DET
ejpam-2419	30	3	paper	paper	NOUN
ejpam-2419	30	4	,	,	PUNCT
ejpam-2419	30	5	we	we	PRON
ejpam-2419	30	6	are	be	AUX
ejpam-2419	30	7	interested	interested	ADJ
ejpam-2419	30	8	in	in	ADP
ejpam-2419	30	9	to	to	PART
ejpam-2419	30	10	obtain	obtain	VERB
ejpam-2419	30	11	some	some	DET
ejpam-2419	30	12	new	new	ADJ
ejpam-2419	30	13	lower	low	ADJ
ejpam-2419	30	14	bounds	bound	NOUN
ejpam-2419	30	15	for	for	ADP
ejpam-2419	30	16	the	the	DET
ejpam-2419	30	17	degree	degree	NOUN
ejpam-2419	30	18	sum	sum	NOUN
ejpam-2419	30	19	energy	energy	NOUN
ejpam-2419	30	20	of	of	ADP
ejpam-2419	30	21	a	a	DET
ejpam-2419	30	22	graph	graph	NOUN
ejpam-2419	31	1	g.	g.	NOUN
ejpam-2419	31	2	2	2	NUM
ejpam-2419	31	3	.	.	PUNCT
ejpam-2419	31	4	results	result	NOUN
ejpam-2419	31	5	for	for	ADP
ejpam-2419	31	6	the	the	DET
ejpam-2419	31	7	sake	sake	NOUN
ejpam-2419	31	8	of	of	ADP
ejpam-2419	31	9	completeness	completeness	NOUN
ejpam-2419	31	10	,	,	PUNCT
ejpam-2419	31	11	we	we	PRON
ejpam-2419	31	12	mention	mention	VERB
ejpam-2419	31	13	below	below	ADP
ejpam-2419	31	14	some	some	DET
ejpam-2419	31	15	results	result	NOUN
ejpam-2419	31	16	which	which	PRON
ejpam-2419	31	17	are	be	AUX
ejpam-2419	31	18	important	important	ADJ
ejpam-2419	31	19	throughout	throughout	ADP
ejpam-2419	31	20	the	the	DET
ejpam-2419	31	21	paper	paper	NOUN
ejpam-2419	31	22	.	.	PUNCT
ejpam-2419	32	1	lemma	lemma	PROPN
ejpam-2419	32	2	1	1	NUM
ejpam-2419	32	3	(	(	PUNCT
ejpam-2419	32	4	[	[	X
ejpam-2419	32	5	12	12	NUM
ejpam-2419	32	6	]	]	PUNCT
ejpam-2419	32	7	)	)	PUNCT
ejpam-2419	32	8	.	.	PUNCT
ejpam-2419	33	1	since	since	SCONJ
ejpam-2419	33	2	t	t	PROPN
ejpam-2419	33	3	race(ds(g	race(ds(g	PROPN
ejpam-2419	33	4	)	)	PUNCT
ejpam-2419	33	5	)	)	PUNCT
ejpam-2419	33	6	=	=	SYM
ejpam-2419	33	7	0	0	NUM
ejpam-2419	33	8	,	,	PUNCT
ejpam-2419	33	9	the	the	DET
ejpam-2419	33	10	eigenvalues	eigenvalue	NOUN
ejpam-2419	33	11	of	of	ADP
ejpam-2419	33	12	ds(g	ds(g	NOUN
ejpam-2419	33	13	)	)	PUNCT
ejpam-2419	33	14	satisfied	satisfy	VERB
ejpam-2419	33	15	the	the	DET
ejpam-2419	33	16	following	follow	VERB
ejpam-2419	33	17	relations	relation	NOUN
ejpam-2419	33	18	(	(	PUNCT
ejpam-2419	33	19	1	1	NUM
ejpam-2419	33	20	)	)	PUNCT
ejpam-2419	33	21	n	n	NOUN
ejpam-2419	33	22	∑	∑	ADV
ejpam-2419	33	23	i=1	i=1	PROPN
ejpam-2419	33	24	λi	λi	NOUN
ejpam-2419	34	1	=	=	NOUN
ejpam-2419	34	2	0	0	NUM
ejpam-2419	34	3	(	(	PUNCT
ejpam-2419	34	4	2	2	NUM
ejpam-2419	34	5	)	)	PUNCT
ejpam-2419	34	6	n	n	NOUN
ejpam-2419	34	7	∑	∑	ADV
ejpam-2419	34	8	i=1	i=1	PROPN
ejpam-2419	34	9	λ	λ	PROPN
ejpam-2419	34	10	2	2	NUM
ejpam-2419	34	11	i	i	NOUN
ejpam-2419	34	12	=	=	SYM
ejpam-2419	34	13	2r	2r	NUM
ejpam-2419	34	14	,	,	PUNCT
ejpam-2419	34	15	where	where	SCONJ
ejpam-2419	34	16	r	r	NOUN
ejpam-2419	34	17	=	=	PUNCT
ejpam-2419	34	18	∑	∑	PUNCT
ejpam-2419	34	19	1≤i	1≤i	X
ejpam-2419	34	20	<	<	X
ejpam-2419	34	21	j≤n	j≤n	NOUN
ejpam-2419	34	22	(	(	PUNCT
ejpam-2419	34	23	di	di	NOUN
ejpam-2419	34	24	+	+	CCONJ
ejpam-2419	34	25	d	d	PROPN
ejpam-2419	34	26	j	j	NOUN
ejpam-2419	34	27	)	)	PUNCT
ejpam-2419	34	28	2	2	NUM
ejpam-2419	34	29	lemma	lemma	PROPN
ejpam-2419	34	30	2	2	NUM
ejpam-2419	34	31	(	(	PUNCT
ejpam-2419	34	32	[	[	X
ejpam-2419	34	33	12	12	NUM
ejpam-2419	34	34	]	]	PUNCT
ejpam-2419	34	35	)	)	PUNCT
ejpam-2419	34	36	.	.	PUNCT
ejpam-2419	35	1	if	if	SCONJ
ejpam-2419	35	2	g	g	PROPN
ejpam-2419	35	3	is	be	AUX
ejpam-2419	35	4	any	any	DET
ejpam-2419	35	5	graph	graph	NOUN
ejpam-2419	35	6	with	with	ADP
ejpam-2419	35	7	n	n	ADP
ejpam-2419	35	8	vertices	vertex	NOUN
ejpam-2419	35	9	,	,	PUNCT
ejpam-2419	35	10	then	then	ADV
ejpam-2419	35	11	p	p	X
ejpam-2419	35	12	2r	2r	NUM
ejpam-2419	35	13	≤	≤	NUM
ejpam-2419	35	14	eds(g	eds(g	PROPN
ejpam-2419	35	15	)	)	PUNCT
ejpam-2419	35	16	.	.	PUNCT
ejpam-2419	36	1	theorem	theorem	ADJ
ejpam-2419	36	2	1	1	NUM
ejpam-2419	36	3	(	(	PUNCT
ejpam-2419	36	4	[	[	X
ejpam-2419	36	5	11	11	NUM
ejpam-2419	36	6	]	]	NUM
ejpam-2419	36	7	)	)	PUNCT
ejpam-2419	36	8	.	.	PUNCT
ejpam-2419	37	1	suppose	suppose	VERB
ejpam-2419	37	2	ai	ai	VERB
ejpam-2419	37	3	and	and	CCONJ
ejpam-2419	37	4	bi	bi	ADJ
ejpam-2419	37	5	,	,	PUNCT
ejpam-2419	37	6	1≤	1≤	NUM
ejpam-2419	37	7	i	i	NOUN
ejpam-2419	37	8	≤	≤	PUNCT
ejpam-2419	38	1	n	n	CCONJ
ejpam-2419	38	2	are	be	AUX
ejpam-2419	38	3	positive	positive	ADJ
ejpam-2419	38	4	real	real	ADJ
ejpam-2419	38	5	numbers	number	NOUN
ejpam-2419	38	6	,	,	PUNCT
ejpam-2419	38	7	then	then	ADV
ejpam-2419	38	8	n	n	CCONJ
ejpam-2419	38	9	∑	∑	PROPN
ejpam-2419	38	10	i=1	i=1	PROPN
ejpam-2419	38	11	a2	a2	PROPN
ejpam-2419	38	12	i	i	PRON
ejpam-2419	38	13	n	n	CCONJ
ejpam-2419	38	14	∑	∑	PROPN
ejpam-2419	38	15	i=1	i=1	PROPN
ejpam-2419	38	16	b2	b2	NOUN
ejpam-2419	39	1	i	i	PRON
ejpam-2419	39	2	≤	≤	NOUN
ejpam-2419	39	3	1	1	NUM
ejpam-2419	39	4	4	4	NUM
ejpam-2419	39	5	�	�	NOUN
ejpam-2419	39	6	√	√	PROPN
ejpam-2419	39	7	√m1m2	√m1m2	PROPN
ejpam-2419	39	8	m1m2	m1m2	X
ejpam-2419	39	9	+	+	NOUN
ejpam-2419	39	10	√	√	PROPN
ejpam-2419	39	11	√m1m2	√m1m2	PROPN
ejpam-2419	39	12	m1m2	m1m2	PROPN
ejpam-2419	39	13	�	�	PROPN
ejpam-2419	39	14	2	2	NUM
ejpam-2419	39	15	�	�	PROPN
ejpam-2419	39	16	n	n	CCONJ
ejpam-2419	39	17	∑	∑	PROPN
ejpam-2419	39	18	i=1	i=1	PROPN
ejpam-2419	39	19	ai	ai	VERB
ejpam-2419	39	20	bi	bi	PROPN
ejpam-2419	39	21	�	�	PROPN
ejpam-2419	39	22	2	2	NUM
ejpam-2419	39	23	(	(	PUNCT
ejpam-2419	39	24	1	1	NUM
ejpam-2419	39	25	)	)	PUNCT
ejpam-2419	39	26	where	where	SCONJ
ejpam-2419	39	27	m1	m1	PROPN
ejpam-2419	39	28	=	=	PROPN
ejpam-2419	39	29	max	max	PROPN
ejpam-2419	39	30	1≤i≤n	1≤i≤n	NUM
ejpam-2419	39	31	(	(	PUNCT
ejpam-2419	39	32	ai	ai	PROPN
ejpam-2419	39	33	)	)	PUNCT
ejpam-2419	39	34	;	;	PUNCT
ejpam-2419	39	35	m2	m2	PROPN
ejpam-2419	39	36	=	=	PROPN
ejpam-2419	39	37	max	max	PROPN
ejpam-2419	39	38	1≤i≤n	1≤i≤n	NUM
ejpam-2419	39	39	(	(	PUNCT
ejpam-2419	39	40	bi	bi	NOUN
ejpam-2419	39	41	)	)	PUNCT
ejpam-2419	39	42	;	;	PUNCT
ejpam-2419	39	43	m1	m1	PROPN
ejpam-2419	39	44	=	=	SYM
ejpam-2419	39	45	min	min	PROPN
ejpam-2419	39	46	1≤i≤n	1≤i≤n	NUM
ejpam-2419	39	47	(	(	PUNCT
ejpam-2419	39	48	ai	ai	PROPN
ejpam-2419	39	49	)	)	PUNCT
ejpam-2419	39	50	and	and	CCONJ
ejpam-2419	39	51	m2	m2	PROPN
ejpam-2419	39	52	=	=	SYM
ejpam-2419	39	53	min	min	PROPN
ejpam-2419	39	54	1≤i≤n	1≤i≤n	NUM
ejpam-2419	39	55	(	(	PUNCT
ejpam-2419	39	56	bi	bi	NOUN
ejpam-2419	39	57	)	)	PUNCT
ejpam-2419	39	58	theorem	theorem	ADJ
ejpam-2419	39	59	2	2	NUM
ejpam-2419	39	60	(	(	PUNCT
ejpam-2419	39	61	[	[	X
ejpam-2419	39	62	10	10	NUM
ejpam-2419	39	63	]	]	NUM
ejpam-2419	39	64	)	)	PUNCT
ejpam-2419	39	65	.	.	PUNCT
ejpam-2419	40	1	let	let	AUX
ejpam-2419	40	2	ai	ai	VERB
ejpam-2419	40	3	and	and	CCONJ
ejpam-2419	40	4	bi	bi	ADJ
ejpam-2419	40	5	,	,	PUNCT
ejpam-2419	40	6	1≤	1≤	NUM
ejpam-2419	40	7	i	i	NOUN
ejpam-2419	40	8	≤	≤	PUNCT
ejpam-2419	41	1	n	n	CCONJ
ejpam-2419	41	2	are	be	AUX
ejpam-2419	41	3	nonnegative	nonnegative	ADJ
ejpam-2419	41	4	real	real	ADJ
ejpam-2419	41	5	numbers	number	NOUN
ejpam-2419	41	6	,	,	PUNCT
ejpam-2419	41	7	then	then	ADV
ejpam-2419	41	8	n	n	CCONJ
ejpam-2419	41	9	∑	∑	PROPN
ejpam-2419	41	10	i=1	i=1	PROPN
ejpam-2419	41	11	a2	a2	PROPN
ejpam-2419	41	12	i	i	PRON
ejpam-2419	41	13	n	n	CCONJ
ejpam-2419	41	14	∑	∑	PROPN
ejpam-2419	41	15	i=1	i=1	PROPN
ejpam-2419	41	16	b2	b2	NOUN
ejpam-2419	42	1	i	i	PRON
ejpam-2419	42	2	−	−	PROPN
ejpam-2419	42	3	�	�	PROPN
ejpam-2419	42	4	n	n	CCONJ
ejpam-2419	42	5	∑	∑	PROPN
ejpam-2419	42	6	i=1	i=1	PROPN
ejpam-2419	42	7	ai	ai	VERB
ejpam-2419	42	8	bi	bi	PROPN
ejpam-2419	42	9	�	�	PROPN
ejpam-2419	42	10	2	2	NUM
ejpam-2419	42	11	≤	≤	NOUN
ejpam-2419	42	12	n2	n2	NOUN
ejpam-2419	42	13	4	4	NUM
ejpam-2419	42	14	�	�	PROPN
ejpam-2419	42	15	m1m2	m1m2	PROPN
ejpam-2419	42	16	−m1m2	−m1m2	PROPN
ejpam-2419	42	17	�	�	PROPN
ejpam-2419	42	18	2	2	NUM
ejpam-2419	42	19	(	(	PUNCT
ejpam-2419	42	20	2	2	NUM
ejpam-2419	42	21	)	)	PUNCT
ejpam-2419	42	22	where	where	SCONJ
ejpam-2419	42	23	mi	mi	PROPN
ejpam-2419	42	24	and	and	CCONJ
ejpam-2419	42	25	mi	mi	PROPN
ejpam-2419	42	26	are	be	AUX
ejpam-2419	42	27	defined	define	VERB
ejpam-2419	42	28	similarly	similarly	ADV
ejpam-2419	42	29	to	to	PART
ejpam-2419	42	30	theorem	theorem	NOUN
ejpam-2419	42	31	1	1	NUM
ejpam-2419	42	32	.	.	PUNCT
ejpam-2419	42	33	theorem	theorem	NOUN
ejpam-2419	42	34	3	3	NUM
ejpam-2419	42	35	(	(	PUNCT
ejpam-2419	42	36	[	[	X
ejpam-2419	42	37	2	2	NUM
ejpam-2419	42	38	]	]	PUNCT
ejpam-2419	42	39	)	)	PUNCT
ejpam-2419	42	40	.	.	PUNCT
ejpam-2419	43	1	suppose	suppose	VERB
ejpam-2419	43	2	ai	ai	VERB
ejpam-2419	43	3	and	and	CCONJ
ejpam-2419	43	4	bi	bi	ADJ
ejpam-2419	43	5	,	,	PUNCT
ejpam-2419	43	6	1≤	1≤	NUM
ejpam-2419	43	7	i	i	NOUN
ejpam-2419	43	8	≤	≤	PUNCT
ejpam-2419	44	1	n	n	CCONJ
ejpam-2419	44	2	are	be	AUX
ejpam-2419	44	3	positive	positive	ADJ
ejpam-2419	44	4	real	real	ADJ
ejpam-2419	44	5	numbers	number	NOUN
ejpam-2419	44	6	,	,	PUNCT
ejpam-2419	44	7	then	then	ADV
ejpam-2419	44	8	|n	|n	PUNCT
ejpam-2419	44	9	n	n	PROPN
ejpam-2419	44	10	∑	∑	PROPN
ejpam-2419	44	11	i=1	i=1	PROPN
ejpam-2419	44	12	ai	ai	INTJ
ejpam-2419	44	13	bi	bi	PROPN
ejpam-2419	44	14	−	−	PROPN
ejpam-2419	44	15	n	n	PROPN
ejpam-2419	44	16	∑	∑	PROPN
ejpam-2419	44	17	i=1	i=1	PROPN
ejpam-2419	44	18	ai	ai	VERB
ejpam-2419	44	19	n	n	ADV
ejpam-2419	44	20	∑	∑	PROPN
ejpam-2419	44	21	i=1	i=1	PROPN
ejpam-2419	44	22	bi	bi	NOUN
ejpam-2419	44	23	|	|	ADV
ejpam-2419	44	24	≤	≤	NUM
ejpam-2419	45	1	α(n)(a−	α(n)(a−	NUM
ejpam-2419	45	2	a)(b	a)(b	VERB
ejpam-2419	46	1	−	−	PROPN
ejpam-2419	46	2	b	b	X
ejpam-2419	46	3	)	)	PUNCT
ejpam-2419	46	4	(	(	PUNCT
ejpam-2419	46	5	3	3	X
ejpam-2419	46	6	)	)	PUNCT
ejpam-2419	46	7	where	where	SCONJ
ejpam-2419	46	8	a	a	DET
ejpam-2419	46	9	,	,	PUNCT
ejpam-2419	46	10	b	b	NOUN
ejpam-2419	46	11	,	,	PUNCT
ejpam-2419	46	12	a	a	PRON
ejpam-2419	46	13	and	and	CCONJ
ejpam-2419	46	14	b	b	NOUN
ejpam-2419	46	15	are	be	AUX
ejpam-2419	46	16	real	real	ADJ
ejpam-2419	46	17	constants	constant	NOUN
ejpam-2419	46	18	,	,	PUNCT
ejpam-2419	46	19	that	that	SCONJ
ejpam-2419	46	20	for	for	ADP
ejpam-2419	46	21	each	each	DET
ejpam-2419	46	22	i	i	PRON
ejpam-2419	46	23	,	,	PUNCT
ejpam-2419	46	24	1	1	NUM
ejpam-2419	46	25	≤	≤	NUM
ejpam-2419	46	26	i	i	PRON
ejpam-2419	46	27	≤	≤	PROPN
ejpam-2419	46	28	n	n	CCONJ
ejpam-2419	46	29	,	,	PUNCT
ejpam-2419	46	30	a	a	DET
ejpam-2419	46	31	≤	≤	NOUN
ejpam-2419	46	32	ai	ai	VERB
ejpam-2419	46	33	≤	≤	ADJ
ejpam-2419	46	34	a	a	DET
ejpam-2419	46	35	and	and	CCONJ
ejpam-2419	46	36	b	b	NOUN
ejpam-2419	46	37	≤	≤	ADJ
ejpam-2419	46	38	bi	bi	NOUN
ejpam-2419	46	39	≤	≤	PROPN
ejpam-2419	46	40	b.	b.	PROPN
ejpam-2419	46	41	further	far	ADV
ejpam-2419	46	42	,	,	PUNCT
ejpam-2419	46	43	α(n	α(n	NOUN
ejpam-2419	46	44	)	)	PUNCT
ejpam-2419	47	1	=	=	SYM
ejpam-2419	47	2	n⌊	n⌊	PROPN
ejpam-2419	47	3	n2	n2	PROPN
ejpam-2419	47	4	⌋	⌋	PROPN
ejpam-2419	47	5	�	�	PROPN
ejpam-2419	47	6	1−	1−	NUM
ejpam-2419	47	7	1	1	NUM
ejpam-2419	47	8	n⌊	n⌊	PROPN
ejpam-2419	47	9	n2	n2	PROPN
ejpam-2419	47	10	⌋	⌋	PROPN
ejpam-2419	47	11	�	�	PROPN
ejpam-2419	47	12	.	.	PUNCT
ejpam-2419	48	1	s.	s.	PROPN
ejpam-2419	48	2	hosamani	hosamani	PROPN
ejpam-2419	48	3	and	and	CCONJ
ejpam-2419	48	4	h.	h.	PROPN
ejpam-2419	48	5	ramane	ramane	PROPN
ejpam-2419	48	6	/	/	SYM
ejpam-2419	48	7	eur	eur	PROPN
ejpam-2419	48	8	.	.	PUNCT
ejpam-2419	49	1	j.	j.	PROPN
ejpam-2419	49	2	pure	pure	PROPN
ejpam-2419	49	3	appl	appl	PROPN
ejpam-2419	49	4	.	.	PROPN
ejpam-2419	49	5	math	math	PROPN
ejpam-2419	49	6	,	,	PUNCT
ejpam-2419	49	7	9	9	NUM
ejpam-2419	49	8	(	(	PUNCT
ejpam-2419	49	9	2016	2016	NUM
ejpam-2419	49	10	)	)	PUNCT
ejpam-2419	49	11	,	,	PUNCT
ejpam-2419	49	12	340	340	NUM
ejpam-2419	49	13	-	-	SYM
ejpam-2419	49	14	345	345	NUM
ejpam-2419	49	15	342	342	NUM
ejpam-2419	49	16	theorem	theorem	NOUN
ejpam-2419	49	17	4	4	NUM
ejpam-2419	49	18	(	(	PUNCT
ejpam-2419	49	19	[	[	X
ejpam-2419	49	20	4	4	NUM
ejpam-2419	49	21	]	]	NUM
ejpam-2419	49	22	)	)	PUNCT
ejpam-2419	49	23	.	.	PUNCT
ejpam-2419	50	1	let	let	AUX
ejpam-2419	50	2	ai	ai	VERB
ejpam-2419	50	3	and	and	CCONJ
ejpam-2419	50	4	bi	bi	ADJ
ejpam-2419	50	5	,	,	PUNCT
ejpam-2419	50	6	1≤	1≤	NUM
ejpam-2419	50	7	i	i	NOUN
ejpam-2419	50	8	≤	≤	PUNCT
ejpam-2419	51	1	n	n	CCONJ
ejpam-2419	51	2	are	be	AUX
ejpam-2419	51	3	nonnegative	nonnegative	ADJ
ejpam-2419	51	4	real	real	ADJ
ejpam-2419	51	5	numbers	number	NOUN
ejpam-2419	51	6	,	,	PUNCT
ejpam-2419	51	7	then	then	ADV
ejpam-2419	51	8	n	n	CCONJ
ejpam-2419	51	9	∑	∑	PROPN
ejpam-2419	51	10	i=1	i=1	PROPN
ejpam-2419	51	11	b2	b2	PROPN
ejpam-2419	52	1	i	i	PROPN
ejpam-2419	52	2	+	+	PROPN
ejpam-2419	52	3	rr	rr	PROPN
ejpam-2419	52	4	n	n	CCONJ
ejpam-2419	52	5	∑	∑	PROPN
ejpam-2419	52	6	i=1	i=1	PROPN
ejpam-2419	52	7	a2	a2	PROPN
ejpam-2419	52	8	i	i	PRON
ejpam-2419	52	9	≤	≤	X
ejpam-2419	52	10	(	(	PUNCT
ejpam-2419	52	11	r	r	NOUN
ejpam-2419	52	12	+	+	CCONJ
ejpam-2419	52	13	r	r	NOUN
ejpam-2419	52	14	)	)	PUNCT
ejpam-2419	52	15	�	�	PROPN
ejpam-2419	52	16	n	n	CCONJ
ejpam-2419	52	17	∑	∑	PROPN
ejpam-2419	52	18	i=1	i=1	PROPN
ejpam-2419	52	19	ai	ai	VERB
ejpam-2419	52	20	bi	bi	PROPN
ejpam-2419	52	21	�	�	PROPN
ejpam-2419	52	22	(	(	PUNCT
ejpam-2419	52	23	4	4	NUM
ejpam-2419	52	24	)	)	PUNCT
ejpam-2419	52	25	where	where	SCONJ
ejpam-2419	52	26	r	r	NOUN
ejpam-2419	52	27	and	and	CCONJ
ejpam-2419	52	28	r	r	NOUN
ejpam-2419	52	29	are	be	AUX
ejpam-2419	52	30	real	real	ADJ
ejpam-2419	52	31	constants	constant	NOUN
ejpam-2419	52	32	,	,	PUNCT
ejpam-2419	52	33	so	so	SCONJ
ejpam-2419	52	34	that	that	SCONJ
ejpam-2419	52	35	for	for	ADP
ejpam-2419	52	36	each	each	DET
ejpam-2419	52	37	i	i	PRON
ejpam-2419	52	38	,	,	PUNCT
ejpam-2419	52	39	1≤	1≤	INTJ
ejpam-2419	52	40	i	i	PROPN
ejpam-2419	52	41	≤	≤	PROPN
ejpam-2419	52	42	n	n	CCONJ
ejpam-2419	52	43	,	,	PUNCT
ejpam-2419	52	44	holds	hold	VERB
ejpam-2419	52	45	,	,	PUNCT
ejpam-2419	52	46	rai	rai	X
ejpam-2419	52	47	≤	≤	ADJ
ejpam-2419	52	48	bi	bi	ADJ
ejpam-2419	52	49	≤	≤	PROPN
ejpam-2419	52	50	rai	rai	X
ejpam-2419	52	51	.	.	PUNCT
ejpam-2419	53	1	3	3	X
ejpam-2419	53	2	.	.	NUM
ejpam-2419	53	3	bounds	bound	NOUN
ejpam-2419	53	4	for	for	ADP
ejpam-2419	53	5	the	the	DET
ejpam-2419	53	6	degree	degree	NOUN
ejpam-2419	53	7	sum	sum	NOUN
ejpam-2419	53	8	energy	energy	NOUN
ejpam-2419	53	9	of	of	ADP
ejpam-2419	53	10	graphs	graph	NOUN
ejpam-2419	53	11	theorem	theorem	VERB
ejpam-2419	53	12	5	5	NUM
ejpam-2419	53	13	.	.	PUNCT
ejpam-2419	54	1	let	let	VERB
ejpam-2419	54	2	g	g	PRON
ejpam-2419	54	3	be	be	AUX
ejpam-2419	54	4	a	a	DET
ejpam-2419	54	5	graph	graph	NOUN
ejpam-2419	54	6	of	of	ADP
ejpam-2419	54	7	order	order	NOUN
ejpam-2419	54	8	n	n	NOUN
ejpam-2419	54	9	and	and	CCONJ
ejpam-2419	54	10	size	size	NOUN
ejpam-2419	54	11	m	m	PROPN
ejpam-2419	54	12	,	,	PUNCT
ejpam-2419	54	13	then	then	ADV
ejpam-2419	54	14	eds(g)≥	eds(g)≥	ADP
ejpam-2419	54	15	√	√	ADJ
ejpam-2419	54	16	√	√	NUM
ejpam-2419	54	17	2rn−	2rn−	NOUN
ejpam-2419	54	18	n2	n2	NOUN
ejpam-2419	54	19	4	4	NUM
ejpam-2419	54	20	(	(	PUNCT
ejpam-2419	54	21	λ1	λ1	PROPN
ejpam-2419	54	22	−λn	−λn	NOUN
ejpam-2419	54	23	)	)	PUNCT
ejpam-2419	54	24	2	2	NUM
ejpam-2419	54	25	(	(	PUNCT
ejpam-2419	54	26	5	5	NUM
ejpam-2419	54	27	)	)	PUNCT
ejpam-2419	54	28	where	where	SCONJ
ejpam-2419	54	29	λ1	λ1	VERB
ejpam-2419	54	30	and	and	CCONJ
ejpam-2419	54	31	λn	λn	PROPN
ejpam-2419	54	32	are	be	AUX
ejpam-2419	54	33	maximum	maximum	ADJ
ejpam-2419	54	34	and	and	CCONJ
ejpam-2419	54	35	minimum	minimum	NOUN
ejpam-2419	54	36	of	of	ADP
ejpam-2419	54	37	the	the	DET
ejpam-2419	54	38	absolute	absolute	ADJ
ejpam-2419	54	39	value	value	NOUN
ejpam-2419	54	40	of	of	ADP
ejpam-2419	54	41	λ′	λ′	PROPN
ejpam-2419	54	42	i	i	PRON
ejpam-2419	54	43	s.	s.	PROPN
ejpam-2419	54	44	proof	proof	PROPN
ejpam-2419	54	45	.	.	PUNCT
ejpam-2419	55	1	suppose	suppose	VERB
ejpam-2419	55	2	λ1,λ2	λ1,λ2	PROPN
ejpam-2419	55	3	,	,	PUNCT
ejpam-2419	55	4	.	.	PUNCT
ejpam-2419	55	5	.	.	PUNCT
ejpam-2419	56	1	.	.	PUNCT
ejpam-2419	57	1	,	,	PUNCT
ejpam-2419	57	2	λn	λn	PROPN
ejpam-2419	57	3	are	be	AUX
ejpam-2419	57	4	the	the	DET
ejpam-2419	57	5	eigenvalues	eigenvalue	NOUN
ejpam-2419	57	6	of	of	ADP
ejpam-2419	57	7	ds(g	ds(g	NOUN
ejpam-2419	57	8	)	)	PUNCT
ejpam-2419	57	9	.	.	PUNCT
ejpam-2419	58	1	we	we	PRON
ejpam-2419	58	2	assume	assume	VERB
ejpam-2419	58	3	that	that	SCONJ
ejpam-2419	58	4	ai	ai	VERB
ejpam-2419	58	5	=	=	SYM
ejpam-2419	58	6	1	1	NUM
ejpam-2419	58	7	and	and	CCONJ
ejpam-2419	58	8	bi	bi	NOUN
ejpam-2419	59	1	=	=	NOUN
ejpam-2419	59	2	|λi	|λi	PROPN
ejpam-2419	59	3	|	|	ADV
ejpam-2419	59	4	,	,	PUNCT
ejpam-2419	59	5	which	which	PRON
ejpam-2419	59	6	by	by	ADP
ejpam-2419	59	7	theorem	theorem	ADJ
ejpam-2419	59	8	2	2	NUM
ejpam-2419	59	9	implies	imply	VERB
ejpam-2419	59	10	n	n	X
ejpam-2419	59	11	∑	∑	PROPN
ejpam-2419	59	12	i=1	i=1	PROPN
ejpam-2419	59	13	12	12	NUM
ejpam-2419	59	14	n	n	NOUN
ejpam-2419	59	15	∑	∑	ADV
ejpam-2419	59	16	i=1	i=1	PROPN
ejpam-2419	59	17	|λi	|λi	PROPN
ejpam-2419	59	18	|2	|2	NUM
ejpam-2419	59	19	−	−	PROPN
ejpam-2419	59	20	�	�	PROPN
ejpam-2419	59	21	n	n	CCONJ
ejpam-2419	59	22	∑	∑	PROPN
ejpam-2419	59	23	i=1	i=1	PROPN
ejpam-2419	59	24	|λi	|λi	PROPN
ejpam-2419	59	25	|	|	ADV
ejpam-2419	59	26	�	�	NOUN
ejpam-2419	59	27	2	2	NUM
ejpam-2419	59	28	≤n2	≤n2	X
ejpam-2419	59	29	4	4	NUM
ejpam-2419	59	30	�	�	PROPN
ejpam-2419	59	31	λ1	λ1	PROPN
ejpam-2419	59	32	−λn	−λn	NOUN
ejpam-2419	59	33	�	�	PROPN
ejpam-2419	59	34	2	2	NUM
ejpam-2419	59	35	2rn−	2rn−	NOUN
ejpam-2419	59	36	(	(	PUNCT
ejpam-2419	59	37	eds(g	eds(g	PROPN
ejpam-2419	59	38	)	)	PUNCT
ejpam-2419	59	39	)	)	PUNCT
ejpam-2419	59	40	2	2	NUM
ejpam-2419	59	41	≤n2	≤n2	X
ejpam-2419	59	42	4	4	NUM
ejpam-2419	59	43	�	�	PROPN
ejpam-2419	59	44	λ1	λ1	PROPN
ejpam-2419	59	45	−λn	−λn	NOUN
ejpam-2419	59	46	�	�	PROPN
ejpam-2419	59	47	2	2	NUM
ejpam-2419	59	48	eds(g)≥	eds(g)≥	NUM
ejpam-2419	59	49	√	√	NUM
ejpam-2419	59	50	√	√	NUM
ejpam-2419	59	51	2rn−	2rn−	NOUN
ejpam-2419	59	52	n2	n2	NOUN
ejpam-2419	59	53	4	4	NUM
ejpam-2419	59	54	(	(	PUNCT
ejpam-2419	59	55	λ1	λ1	PROPN
ejpam-2419	59	56	−λn	−λn	NOUN
ejpam-2419	59	57	)	)	PUNCT
ejpam-2419	59	58	2	2	NUM
ejpam-2419	59	59	,	,	PUNCT
ejpam-2419	59	60	as	as	SCONJ
ejpam-2419	59	61	asserted	assert	VERB
ejpam-2419	59	62	.	.	PUNCT
ejpam-2419	60	1	theorem	theorem	ADJ
ejpam-2419	60	2	6	6	NUM
ejpam-2419	60	3	.	.	PUNCT
ejpam-2419	61	1	suppose	suppose	VERB
ejpam-2419	61	2	zero	zero	NUM
ejpam-2419	61	3	is	be	AUX
ejpam-2419	61	4	not	not	PART
ejpam-2419	61	5	an	an	DET
ejpam-2419	61	6	eigenvalue	eigenvalue	NOUN
ejpam-2419	61	7	of	of	ADP
ejpam-2419	61	8	ds(g	ds(g	NOUN
ejpam-2419	61	9	)	)	PUNCT
ejpam-2419	61	10	.	.	PUNCT
ejpam-2419	62	1	then	then	ADV
ejpam-2419	62	2	eds(g)≥	eds(g)≥	VERB
ejpam-2419	62	3	2	2	NUM
ejpam-2419	62	4	p	p	NOUN
ejpam-2419	62	5	λ1λn	λ1λn	PUNCT
ejpam-2419	62	6	p	p	PROPN
ejpam-2419	62	7	2rn	2rn	PROPN
ejpam-2419	62	8	λ1	λ1	PROPN
ejpam-2419	63	1	+	+	PROPN
ejpam-2419	63	2	λn	λn	NOUN
ejpam-2419	63	3	.	.	PUNCT
ejpam-2419	64	1	(	(	PUNCT
ejpam-2419	64	2	6	6	NUM
ejpam-2419	64	3	)	)	PUNCT
ejpam-2419	64	4	where	where	SCONJ
ejpam-2419	64	5	λ1	λ1	VERB
ejpam-2419	64	6	and	and	CCONJ
ejpam-2419	64	7	λn	λn	NOUN
ejpam-2419	64	8	are	be	AUX
ejpam-2419	64	9	minimum	minimum	ADJ
ejpam-2419	64	10	and	and	CCONJ
ejpam-2419	64	11	maximum	maximum	NOUN
ejpam-2419	64	12	of	of	ADP
ejpam-2419	64	13	the	the	DET
ejpam-2419	64	14	absolute	absolute	ADJ
ejpam-2419	64	15	value	value	NOUN
ejpam-2419	64	16	of	of	ADP
ejpam-2419	64	17	λ′	λ′	PROPN
ejpam-2419	64	18	i	i	PRON
ejpam-2419	64	19	s.	s.	PROPN
ejpam-2419	64	20	proof	proof	PROPN
ejpam-2419	64	21	.	.	PUNCT
ejpam-2419	65	1	suppose	suppose	VERB
ejpam-2419	65	2	λ1,λ2	λ1,λ2	PROPN
ejpam-2419	65	3	,	,	PUNCT
ejpam-2419	65	4	.	.	PUNCT
ejpam-2419	65	5	.	.	PUNCT
ejpam-2419	66	1	.	.	PUNCT
ejpam-2419	67	1	,	,	PUNCT
ejpam-2419	67	2	λn	λn	PROPN
ejpam-2419	67	3	are	be	AUX
ejpam-2419	67	4	the	the	DET
ejpam-2419	67	5	eigenvalues	eigenvalue	NOUN
ejpam-2419	67	6	of	of	ADP
ejpam-2419	67	7	ds(g	ds(g	NOUN
ejpam-2419	67	8	)	)	PUNCT
ejpam-2419	67	9	.	.	PUNCT
ejpam-2419	68	1	we	we	PRON
ejpam-2419	68	2	assume	assume	VERB
ejpam-2419	68	3	that	that	SCONJ
ejpam-2419	68	4	ai	ai	VERB
ejpam-2419	68	5	=	=	PUNCT
ejpam-2419	68	6	|λi	|λi	VERB
ejpam-2419	68	7	|	|	ADV
ejpam-2419	68	8	and	and	CCONJ
ejpam-2419	68	9	bi	bi	NOUN
ejpam-2419	68	10	=	=	NOUN
ejpam-2419	68	11	1	1	NUM
ejpam-2419	68	12	,	,	PUNCT
ejpam-2419	68	13	which	which	PRON
ejpam-2419	68	14	by	by	ADP
ejpam-2419	68	15	theorem	theorem	NOUN
ejpam-2419	68	16	1	1	NUM
ejpam-2419	68	17	implies	imply	VERB
ejpam-2419	68	18	n	n	X
ejpam-2419	68	19	∑	∑	ADV
ejpam-2419	68	20	i=1	i=1	PROPN
ejpam-2419	68	21	|λi	|λi	PROPN
ejpam-2419	68	22	|2	|2	NUM
ejpam-2419	69	1	n	n	NOUN
ejpam-2419	69	2	∑	∑	PROPN
ejpam-2419	69	3	i=1	i=1	PROPN
ejpam-2419	69	4	12	12	NUM
ejpam-2419	69	5	≤1	≤1	PROPN
ejpam-2419	69	6	4	4	NUM
ejpam-2419	69	7	�	�	PROPN
ejpam-2419	69	8	√	√	ADP
ejpam-2419	69	9	√λn	√λn	PROPN
ejpam-2419	69	10	λ1	λ1	PROPN
ejpam-2419	69	11	+	+	CCONJ
ejpam-2419	69	12	√	√	PROPN
ejpam-2419	69	13	√λ1	√λ1	NUM
ejpam-2419	69	14	λn	λn	PROPN
ejpam-2419	69	15	�	�	PROPN
ejpam-2419	69	16	2	2	NUM
ejpam-2419	69	17	�	�	PROPN
ejpam-2419	69	18	n	n	ADP
ejpam-2419	69	19	∑	∑	PROPN
ejpam-2419	69	20	i=1	i=1	PROPN
ejpam-2419	69	21	|λi	|λi	PROPN
ejpam-2419	69	22	|	|	ADV
ejpam-2419	69	23	�	�	PROPN
ejpam-2419	69	24	2	2	NUM
ejpam-2419	69	25	2rn≤1	2rn≤1	NUM
ejpam-2419	69	26	4	4	NUM
ejpam-2419	69	27	�	�	PROPN
ejpam-2419	69	28	(	(	PUNCT
ejpam-2419	69	29	λ1	λ1	PROPN
ejpam-2419	69	30	+	+	PROPN
ejpam-2419	69	31	λn	λn	NOUN
ejpam-2419	69	32	)	)	PUNCT
ejpam-2419	69	33	2	2	NUM
ejpam-2419	69	34	λ1λn	λ1λn	X
ejpam-2419	69	35	�	�	PROPN
ejpam-2419	69	36	(	(	PUNCT
ejpam-2419	69	37	eds(g	eds(g	PROPN
ejpam-2419	69	38	)	)	PUNCT
ejpam-2419	69	39	)	)	PUNCT
ejpam-2419	70	1	2	2	NUM
ejpam-2419	70	2	eds(g)≥	eds(g)≥	NUM
ejpam-2419	70	3	2	2	NUM
ejpam-2419	70	4	p	p	NOUN
ejpam-2419	70	5	λ1λn	λ1λn	PUNCT
ejpam-2419	70	6	p	p	PROPN
ejpam-2419	70	7	2rn	2rn	PROPN
ejpam-2419	70	8	λ1	λ1	PROPN
ejpam-2419	71	1	+	+	PROPN
ejpam-2419	71	2	λn	λn	NOUN
ejpam-2419	71	3	,	,	PUNCT
ejpam-2419	71	4	as	as	SCONJ
ejpam-2419	71	5	desired	desire	VERB
ejpam-2419	71	6	.	.	PUNCT
ejpam-2419	72	1	s.	s.	PROPN
ejpam-2419	72	2	hosamani	hosamani	PROPN
ejpam-2419	72	3	and	and	CCONJ
ejpam-2419	72	4	h.	h.	PROPN
ejpam-2419	72	5	ramane	ramane	PROPN
ejpam-2419	72	6	/	/	SYM
ejpam-2419	72	7	eur	eur	PROPN
ejpam-2419	72	8	.	.	PUNCT
ejpam-2419	73	1	j.	j.	PROPN
ejpam-2419	73	2	pure	pure	PROPN
ejpam-2419	73	3	appl	appl	PROPN
ejpam-2419	73	4	.	.	PROPN
ejpam-2419	73	5	math	math	PROPN
ejpam-2419	73	6	,	,	PUNCT
ejpam-2419	73	7	9	9	NUM
ejpam-2419	73	8	(	(	PUNCT
ejpam-2419	73	9	2016	2016	NUM
ejpam-2419	73	10	)	)	PUNCT
ejpam-2419	73	11	,	,	PUNCT
ejpam-2419	73	12	340	340	NUM
ejpam-2419	73	13	-	-	SYM
ejpam-2419	73	14	345	345	NUM
ejpam-2419	73	15	343	343	NUM
ejpam-2419	73	16	theorem	theorem	VERB
ejpam-2419	73	17	7	7	NUM
ejpam-2419	73	18	.	.	PUNCT
ejpam-2419	74	1	let	let	VERB
ejpam-2419	74	2	g	g	PRON
ejpam-2419	74	3	be	be	AUX
ejpam-2419	74	4	a	a	DET
ejpam-2419	74	5	graph	graph	NOUN
ejpam-2419	74	6	of	of	ADP
ejpam-2419	74	7	order	order	NOUN
ejpam-2419	74	8	n	n	NOUN
ejpam-2419	74	9	and	and	CCONJ
ejpam-2419	74	10	size	size	NOUN
ejpam-2419	74	11	m.	m.	NOUN
ejpam-2419	74	12	let	let	VERB
ejpam-2419	74	13	λ1	λ1	PROPN
ejpam-2419	74	14	≥	≥	NOUN
ejpam-2419	74	15	λ2	λ2	NOUN
ejpam-2419	74	16	≥	≥	NOUN
ejpam-2419	74	17	·	·	PUNCT
ejpam-2419	74	18	·	·	PUNCT
ejpam-2419	74	19	·	·	PUNCT
ejpam-2419	74	20	≥	≥	PRON
ejpam-2419	74	21	λn	λn	AUX
ejpam-2419	74	22	be	be	AUX
ejpam-2419	74	23	a	a	DET
ejpam-2419	74	24	non	non	ADJ
ejpam-2419	74	25	-	-	ADJ
ejpam-2419	74	26	increasing	increasing	ADJ
ejpam-2419	74	27	arrangement	arrangement	NOUN
ejpam-2419	74	28	of	of	ADP
ejpam-2419	74	29	eigenvalues	eigenvalue	NOUN
ejpam-2419	74	30	of	of	ADP
ejpam-2419	74	31	ds(g	ds(g	NOUN
ejpam-2419	74	32	)	)	PUNCT
ejpam-2419	74	33	.	.	PUNCT
ejpam-2419	75	1	then	then	ADV
ejpam-2419	75	2	eds(g)≥	eds(g)≥	VERB
ejpam-2419	75	3	æ	æ	PROPN
ejpam-2419	75	4	2rn−α(n)(|λ1|	2rn−α(n)(|λ1|	NUM
ejpam-2419	75	5	−	−	NOUN
ejpam-2419	75	6	|λn|)2	|λn|)2	X
ejpam-2419	75	7	(	(	PUNCT
ejpam-2419	75	8	7	7	NUM
ejpam-2419	75	9	)	)	PUNCT
ejpam-2419	75	10	where	where	SCONJ
ejpam-2419	75	11	α(n	α(n	NOUN
ejpam-2419	75	12	)	)	PUNCT
ejpam-2419	75	13	=	=	SYM
ejpam-2419	75	14	n⌊	n⌊	PROPN
ejpam-2419	75	15	n2	n2	PROPN
ejpam-2419	75	16	⌋	⌋	PROPN
ejpam-2419	75	17	�	�	PROPN
ejpam-2419	75	18	1−	1−	NUM
ejpam-2419	75	19	1	1	NUM
ejpam-2419	75	20	n⌊	n⌊	PROPN
ejpam-2419	75	21	n2	n2	PROPN
ejpam-2419	75	22	⌋	⌋	PROPN
ejpam-2419	75	23	�	�	PROPN
ejpam-2419	75	24	.	.	PUNCT
ejpam-2419	76	1	proof	proof	NOUN
ejpam-2419	76	2	.	.	PUNCT
ejpam-2419	77	1	suppose	suppose	VERB
ejpam-2419	77	2	λ1,λ2	λ1,λ2	PROPN
ejpam-2419	77	3	,	,	PUNCT
ejpam-2419	77	4	.	.	PUNCT
ejpam-2419	77	5	.	.	PUNCT
ejpam-2419	78	1	.	.	PUNCT
ejpam-2419	79	1	,	,	PUNCT
ejpam-2419	79	2	λn	λn	PROPN
ejpam-2419	79	3	are	be	AUX
ejpam-2419	79	4	the	the	DET
ejpam-2419	79	5	eigenvalues	eigenvalue	NOUN
ejpam-2419	79	6	of	of	ADP
ejpam-2419	79	7	ds(g	ds(g	NOUN
ejpam-2419	79	8	)	)	PUNCT
ejpam-2419	79	9	.	.	PUNCT
ejpam-2419	80	1	we	we	PRON
ejpam-2419	80	2	assume	assume	VERB
ejpam-2419	80	3	that	that	SCONJ
ejpam-2419	80	4	ai	ai	VERB
ejpam-2419	80	5	=	=	PUNCT
ejpam-2419	80	6	|λi	|λi	PROPN
ejpam-2419	80	7	|=	|=	NOUN
ejpam-2419	80	8	bi	bi	NOUN
ejpam-2419	80	9	,	,	PUNCT
ejpam-2419	80	10	a	a	DET
ejpam-2419	80	11	=	=	X
ejpam-2419	80	12	|λn|=	|λn|=	PROPN
ejpam-2419	80	13	b	b	PROPN
ejpam-2419	80	14	and	and	CCONJ
ejpam-2419	80	15	a=	a=	ADJ
ejpam-2419	80	16	|λ1|=	|λ1|=	PROPN
ejpam-2419	80	17	b	b	PROPN
ejpam-2419	80	18	,	,	PUNCT
ejpam-2419	80	19	which	which	PRON
ejpam-2419	80	20	by	by	ADP
ejpam-2419	80	21	theorem	theorem	ADJ
ejpam-2419	80	22	3	3	NUM
ejpam-2419	80	23	implies	imply	VERB
ejpam-2419	80	24	|n	|n	ADJ
ejpam-2419	80	25	n	n	PROPN
ejpam-2419	80	26	∑	∑	PROPN
ejpam-2419	80	27	i=1	i=1	PROPN
ejpam-2419	80	28	|λi	|λi	PROPN
ejpam-2419	80	29	|2	|2	NUM
ejpam-2419	80	30	−	−	PROPN
ejpam-2419	80	31	�	�	PROPN
ejpam-2419	81	1	n	n	CCONJ
ejpam-2419	81	2	∑	∑	PROPN
ejpam-2419	81	3	i=1	i=1	PROPN
ejpam-2419	81	4	|λi	|λi	PROPN
ejpam-2419	81	5	|	|	ADV
ejpam-2419	81	6	�	�	NOUN
ejpam-2419	81	7	2	2	NUM
ejpam-2419	81	8	|	|	ADV
ejpam-2419	81	9	≤	≤	NUM
ejpam-2419	81	10	α(n)(|λ1|	α(n)(|λ1|	NOUN
ejpam-2419	81	11	−	−	PROPN
ejpam-2419	82	1	|λn|)2	|λn|)2	PROPN
ejpam-2419	82	2	(	(	PUNCT
ejpam-2419	82	3	8)	8)	NUM
ejpam-2419	82	4	since	since	ADV
ejpam-2419	82	5	,	,	PUNCT
ejpam-2419	82	6	eds(g	eds(g	X
ejpam-2419	82	7	)	)	PUNCT
ejpam-2419	82	8	=	=	SYM
ejpam-2419	83	1	n	n	CCONJ
ejpam-2419	83	2	∑	∑	ADV
ejpam-2419	83	3	i=1	i=1	PROPN
ejpam-2419	83	4	|λi	|λi	PROPN
ejpam-2419	83	5	|	|	NOUN
ejpam-2419	83	6	,	,	PUNCT
ejpam-2419	83	7	n	n	CCONJ
ejpam-2419	83	8	∑	∑	ADV
ejpam-2419	83	9	i=1	i=1	PROPN
ejpam-2419	83	10	|λi	|λi	PROPN
ejpam-2419	83	11	|2	|2	NOUN
ejpam-2419	83	12	=	=	SYM
ejpam-2419	83	13	2r	2r	NUM
ejpam-2419	83	14	,	,	PUNCT
ejpam-2419	83	15	the	the	DET
ejpam-2419	83	16	above	above	ADJ
ejpam-2419	83	17	inequality	inequality	NOUN
ejpam-2419	83	18	becomes	become	VERB
ejpam-2419	83	19	2rn−	2rn−	NOUN
ejpam-2419	83	20	eds(g	eds(g	SYM
ejpam-2419	83	21	)	)	PUNCT
ejpam-2419	83	22	2	2	NUM
ejpam-2419	83	23	≤	≤	NOUN
ejpam-2419	83	24	α(n)(|λ1|	α(n)(|λ1|	NOUN
ejpam-2419	83	25	−	−	PROPN
ejpam-2419	84	1	|λn|)2	|λn|)2	PROPN
ejpam-2419	84	2	and	and	CCONJ
ejpam-2419	84	3	a	a	DET
ejpam-2419	84	4	simple	simple	ADJ
ejpam-2419	84	5	calculation	calculation	NOUN
ejpam-2419	84	6	gives	give	VERB
ejpam-2419	84	7	us	we	PRON
ejpam-2419	84	8	the	the	DET
ejpam-2419	84	9	required	require	VERB
ejpam-2419	84	10	result	result	NOUN
ejpam-2419	84	11	.	.	PUNCT
ejpam-2419	85	1	corollary	corollary	ADJ
ejpam-2419	85	2	1	1	NUM
ejpam-2419	85	3	.	.	PUNCT
ejpam-2419	86	1	since	since	SCONJ
ejpam-2419	86	2	α(n)≤	α(n)≤	ADJ
ejpam-2419	86	3	n2	n2	NOUN
ejpam-2419	86	4	4	4	NUM
ejpam-2419	86	5	,	,	PUNCT
ejpam-2419	86	6	then	then	ADV
ejpam-2419	86	7	according	accord	VERB
ejpam-2419	86	8	to	to	ADP
ejpam-2419	86	9	(	(	PUNCT
ejpam-2419	86	10	7	7	NUM
ejpam-2419	86	11	)	)	PUNCT
ejpam-2419	86	12	,	,	PUNCT
ejpam-2419	86	13	we	we	PRON
ejpam-2419	86	14	have	have	VERB
ejpam-2419	86	15	eds(g)≥	eds(g)≥	VERB
ejpam-2419	87	1	æ	æ	PROPN
ejpam-2419	87	2	2rn−α(n)(|λ1|	2rn−α(n)(|λ1|	NUM
ejpam-2419	87	3	−	−	PROPN
ejpam-2419	87	4	|λn|)2	|λn|)2	NUM
ejpam-2419	87	5	≥	≥	NOUN
ejpam-2419	87	6	√	√	NUM
ejpam-2419	87	7	√	√	NUM
ejpam-2419	87	8	2rn−	2rn−	NOUN
ejpam-2419	87	9	n2	n2	NOUN
ejpam-2419	87	10	4	4	NUM
ejpam-2419	87	11	(	(	PUNCT
ejpam-2419	87	12	|λ1|	|λ1|	ADP
ejpam-2419	87	13	−	−	PROPN
ejpam-2419	87	14	|λn|)2	|λn|)2	NOUN
ejpam-2419	87	15	.	.	PUNCT
ejpam-2419	88	1	this	this	PRON
ejpam-2419	88	2	means	mean	VERB
ejpam-2419	88	3	that	that	SCONJ
ejpam-2419	88	4	inequality	inequality	NOUN
ejpam-2419	88	5	(	(	PUNCT
ejpam-2419	88	6	7	7	NUM
ejpam-2419	88	7	)	)	PUNCT
ejpam-2419	88	8	is	be	AUX
ejpam-2419	88	9	stronger	strong	ADJ
ejpam-2419	88	10	of	of	ADP
ejpam-2419	88	11	inequality	inequality	NOUN
ejpam-2419	88	12	(	(	PUNCT
ejpam-2419	88	13	5	5	NUM
ejpam-2419	88	14	)	)	PUNCT
ejpam-2419	88	15	.	.	PUNCT
ejpam-2419	89	1	theorem	theorem	ADJ
ejpam-2419	89	2	8	8	NUM
ejpam-2419	89	3	.	.	PUNCT
ejpam-2419	90	1	let	let	VERB
ejpam-2419	90	2	g	g	PRON
ejpam-2419	90	3	be	be	AUX
ejpam-2419	90	4	a	a	DET
ejpam-2419	90	5	graph	graph	NOUN
ejpam-2419	90	6	of	of	ADP
ejpam-2419	90	7	order	order	NOUN
ejpam-2419	90	8	n	n	NOUN
ejpam-2419	90	9	and	and	CCONJ
ejpam-2419	90	10	size	size	NOUN
ejpam-2419	90	11	m.	m.	NOUN
ejpam-2419	90	12	let	let	VERB
ejpam-2419	90	13	λ1	λ1	PROPN
ejpam-2419	90	14	≥	≥	NOUN
ejpam-2419	90	15	λ2	λ2	NOUN
ejpam-2419	90	16	≥	≥	NOUN
ejpam-2419	90	17	·	·	PUNCT
ejpam-2419	90	18	·	·	PUNCT
ejpam-2419	90	19	·	·	PUNCT
ejpam-2419	91	1	≥	≥	PRON
ejpam-2419	91	2	λn	λn	AUX
ejpam-2419	91	3	be	be	AUX
ejpam-2419	91	4	a	a	DET
ejpam-2419	91	5	non	non	ADJ
ejpam-2419	91	6	-	-	ADJ
ejpam-2419	91	7	increasing	increasing	ADJ
ejpam-2419	91	8	arrangement	arrangement	NOUN
ejpam-2419	91	9	of	of	ADP
ejpam-2419	91	10	eigenvalues	eigenvalue	NOUN
ejpam-2419	91	11	of	of	ADP
ejpam-2419	91	12	ds(g	ds(g	NOUN
ejpam-2419	91	13	)	)	PUNCT
ejpam-2419	91	14	.	.	PUNCT
ejpam-2419	92	1	then	then	ADV
ejpam-2419	92	2	eds(g)≥	eds(g)≥	NOUN
ejpam-2419	92	3	|λ1||λn|n+	|λ1||λn|n+	VERB
ejpam-2419	92	4	2r	2r	NUM
ejpam-2419	92	5	|λ1|+	|λ1|+	SYM
ejpam-2419	92	6	|λn|	|λn|	NOUN
ejpam-2419	92	7	(	(	PUNCT
ejpam-2419	92	8	9	9	NUM
ejpam-2419	92	9	)	)	PUNCT
ejpam-2419	92	10	where	where	SCONJ
ejpam-2419	92	11	λ1	λ1	VERB
ejpam-2419	92	12	and	and	CCONJ
ejpam-2419	92	13	λn	λn	NOUN
ejpam-2419	92	14	are	be	AUX
ejpam-2419	92	15	minimum	minimum	ADJ
ejpam-2419	92	16	and	and	CCONJ
ejpam-2419	92	17	maximum	maximum	NOUN
ejpam-2419	92	18	of	of	ADP
ejpam-2419	92	19	the	the	DET
ejpam-2419	92	20	absolute	absolute	ADJ
ejpam-2419	92	21	value	value	NOUN
ejpam-2419	92	22	of	of	ADP
ejpam-2419	92	23	λ′	λ′	PROPN
ejpam-2419	92	24	i	i	PRON
ejpam-2419	92	25	s.	s.	PROPN
ejpam-2419	92	26	proof	proof	PROPN
ejpam-2419	92	27	.	.	PUNCT
ejpam-2419	93	1	suppose	suppose	VERB
ejpam-2419	93	2	λ1,λ2	λ1,λ2	PROPN
ejpam-2419	93	3	,	,	PUNCT
ejpam-2419	93	4	.	.	PUNCT
ejpam-2419	93	5	.	.	PUNCT
ejpam-2419	94	1	.	.	PUNCT
ejpam-2419	95	1	,	,	PUNCT
ejpam-2419	95	2	λn	λn	PROPN
ejpam-2419	95	3	are	be	AUX
ejpam-2419	95	4	the	the	DET
ejpam-2419	95	5	eigenvalues	eigenvalue	NOUN
ejpam-2419	95	6	of	of	ADP
ejpam-2419	95	7	ds(g	ds(g	NOUN
ejpam-2419	95	8	)	)	PUNCT
ejpam-2419	95	9	.	.	PUNCT
ejpam-2419	96	1	we	we	PRON
ejpam-2419	96	2	assume	assume	VERB
ejpam-2419	96	3	that	that	SCONJ
ejpam-2419	96	4	bi	bi	NOUN
ejpam-2419	96	5	=	=	NOUN
ejpam-2419	96	6	|λi	|λi	PROPN
ejpam-2419	96	7	|	|	ADV
ejpam-2419	96	8	,	,	PUNCT
ejpam-2419	96	9	ai	ai	VERB
ejpam-2419	96	10	=	=	ADJ
ejpam-2419	96	11	1	1	NUM
ejpam-2419	96	12	,	,	PUNCT
ejpam-2419	96	13	r	r	NOUN
ejpam-2419	96	14	=	=	SYM
ejpam-2419	96	15	|λn|	|λn|	NOUN
ejpam-2419	96	16	and	and	CCONJ
ejpam-2419	96	17	r=	r=	ADJ
ejpam-2419	96	18	|λ1|	|λ1|	NOUN
ejpam-2419	96	19	,	,	PUNCT
ejpam-2419	96	20	which	which	PRON
ejpam-2419	96	21	by	by	ADP
ejpam-2419	96	22	theorem	theorem	NOUN
ejpam-2419	96	23	4	4	NUM
ejpam-2419	96	24	implies	imply	VERB
ejpam-2419	96	25	n	n	X
ejpam-2419	96	26	∑	∑	PROPN
ejpam-2419	96	27	i	i	PROPN
ejpam-2419	96	28	=	=	PROPN
ejpam-2419	96	29	n	n	PROPN
ejpam-2419	96	30	|λi	|λi	PROPN
ejpam-2419	96	31	|2	|2	NUM
ejpam-2419	96	32	+	+	NUM
ejpam-2419	96	33	|λ1||λn|	|λ1||λn|	NOUN
ejpam-2419	96	34	n	n	CCONJ
ejpam-2419	96	35	∑	∑	PROPN
ejpam-2419	96	36	i=1	i=1	PROPN
ejpam-2419	96	37	1≤	1≤	PROPN
ejpam-2419	96	38	(	(	PUNCT
ejpam-2419	96	39	|λ1|+	|λ1|+	SYM
ejpam-2419	96	40	|λn|	|λn|	NOUN
ejpam-2419	96	41	)	)	PUNCT
ejpam-2419	97	1	n	n	NOUN
ejpam-2419	97	2	∑	∑	ADV
ejpam-2419	97	3	i=1	i=1	PROPN
ejpam-2419	97	4	|λi	|λi	PROPN
ejpam-2419	97	5	|	|	NOUN
ejpam-2419	97	6	.	.	PUNCT
ejpam-2419	98	1	(	(	PUNCT
ejpam-2419	98	2	10	10	NUM
ejpam-2419	98	3	)	)	PUNCT
ejpam-2419	98	4	since	since	SCONJ
ejpam-2419	98	5	,	,	PUNCT
ejpam-2419	98	6	eds(g	eds(g	X
ejpam-2419	98	7	)	)	PUNCT
ejpam-2419	98	8	=	=	SYM
ejpam-2419	99	1	n	n	CCONJ
ejpam-2419	99	2	∑	∑	ADV
ejpam-2419	99	3	i=1	i=1	PROPN
ejpam-2419	99	4	|λi	|λi	PROPN
ejpam-2419	99	5	|	|	NOUN
ejpam-2419	99	6	,	,	PUNCT
ejpam-2419	99	7	n	n	CCONJ
ejpam-2419	99	8	∑	∑	ADV
ejpam-2419	99	9	i=1	i=1	PROPN
ejpam-2419	99	10	|λi	|λi	PROPN
ejpam-2419	99	11	|2	|2	NOUN
ejpam-2419	99	12	=	=	SYM
ejpam-2419	99	13	2r	2r	NUM
ejpam-2419	99	14	,	,	PUNCT
ejpam-2419	99	15	from	from	ADP
ejpam-2419	99	16	(	(	PUNCT
ejpam-2419	99	17	10	10	NUM
ejpam-2419	99	18	)	)	PUNCT
ejpam-2419	99	19	,	,	PUNCT
ejpam-2419	99	20	inequality	inequality	NOUN
ejpam-2419	99	21	(	(	PUNCT
ejpam-2419	99	22	9	9	NUM
ejpam-2419	99	23	)	)	PUNCT
ejpam-2419	99	24	directly	directly	ADV
ejpam-2419	99	25	follows	follow	VERB
ejpam-2419	99	26	from	from	ADP
ejpam-2419	99	27	theorem	theorem	ADJ
ejpam-2419	99	28	4	4	NUM
ejpam-2419	99	29	.	.	PUNCT
ejpam-2419	99	30	references	reference	NOUN
ejpam-2419	99	31	344	344	NUM
ejpam-2419	99	32	acknowledgements	acknowledgement	NOUN
ejpam-2419	99	33	this	this	DET
ejpam-2419	99	34	work	work	NOUN
ejpam-2419	99	35	is	be	AUX
ejpam-2419	99	36	supported	support	VERB
ejpam-2419	99	37	by	by	ADP
ejpam-2419	99	38	the	the	DET
ejpam-2419	99	39	science	science	NOUN
ejpam-2419	99	40	and	and	CCONJ
ejpam-2419	99	41	engineering	engineering	NOUN
ejpam-2419	99	42	research	research	NOUN
ejpam-2419	99	43	board	board	NOUN
ejpam-2419	99	44	,	,	PUNCT
ejpam-2419	99	45	new	new	PROPN
ejpam-2419	99	46	delhi	delhi	PROPN
ejpam-2419	99	47	india	india	PROPN
ejpam-2419	99	48	under	under	ADP
ejpam-2419	99	49	the	the	DET
ejpam-2419	99	50	major	major	ADJ
ejpam-2419	99	51	research	research	NOUN
ejpam-2419	99	52	project	project	NOUN
ejpam-2419	99	53	no	no	INTJ
ejpam-2419	99	54	.	.	PUNCT
ejpam-2419	100	1	serb	serb	PROPN
ejpam-2419	100	2	/	/	SYM
ejpam-2419	100	3	f/4168/2012	f/4168/2012	PROPN
ejpam-2419	100	4	-	-	PUNCT
ejpam-2419	100	5	13	13	NUM
ejpam-2419	100	6	dated	date	VERB
ejpam-2419	100	7	03.10.2013	03.10.2013	NOUN
ejpam-2419	100	8	.	.	PUNCT
ejpam-2419	101	1	references	reference	NOUN
ejpam-2419	101	2	[	[	X
ejpam-2419	101	3	1	1	NUM
ejpam-2419	101	4	]	]	PUNCT
ejpam-2419	101	5	c.	c.	PROPN
ejpam-2419	101	6	adiga	adiga	PROPN
ejpam-2419	101	7	and	and	CCONJ
ejpam-2419	101	8	m.	m.	PROPN
ejpam-2419	101	9	smitha	smitha	PROPN
ejpam-2419	101	10	.	.	PUNCT
ejpam-2419	102	1	on	on	ADP
ejpam-2419	102	2	maximum	maximum	ADJ
ejpam-2419	102	3	degree	degree	NOUN
ejpam-2419	102	4	energy	energy	NOUN
ejpam-2419	102	5	of	of	ADP
ejpam-2419	102	6	a	a	DET
ejpam-2419	102	7	graph	graph	NOUN
ejpam-2419	102	8	.	.	PUNCT
ejpam-2419	103	1	international	international	ADJ
ejpam-2419	103	2	journal	journal	PROPN
ejpam-2419	103	3	of	of	ADP
ejpam-2419	103	4	contemporary	contemporary	PROPN
ejpam-2419	103	5	mathematical	mathematical	PROPN
ejpam-2419	103	6	sciences	sciences	PROPN
ejpam-2419	103	7	,	,	PUNCT
ejpam-2419	103	8	4(8	4(8	NUM
ejpam-2419	103	9	)	)	PUNCT
ejpam-2419	103	10	.	.	PUNCT
ejpam-2419	104	1	385–396	385–396	NUM
ejpam-2419	104	2	.	.	PUNCT
ejpam-2419	104	3	2009	2009	NUM
ejpam-2419	104	4	.	.	PUNCT
ejpam-2419	105	1	[	[	X
ejpam-2419	105	2	2	2	NUM
ejpam-2419	105	3	]	]	PUNCT
ejpam-2419	105	4	m.	m.	NOUN
ejpam-2419	105	5	biernacki	biernacki	PROPN
ejpam-2419	105	6	,	,	PUNCT
ejpam-2419	105	7	h.	h.	PROPN
ejpam-2419	105	8	pidek	pidek	PROPN
ejpam-2419	105	9	,	,	PUNCT
ejpam-2419	105	10	and	and	CCONJ
ejpam-2419	105	11	c.	c.	PROPN
ejpam-2419	105	12	ryll	ryll	PROPN
ejpam-2419	105	13	-	-	PUNCT
ejpam-2419	105	14	nardzewsk	nardzewsk	NOUN
ejpam-2419	105	15	.	.	PUNCT
ejpam-2419	106	1	sur	sur	PROPN
ejpam-2419	106	2	une	une	PROPN
ejpam-2419	106	3	iné	iné	PROPN
ejpam-2419	106	4	galité	galité	PROPN
ejpam-2419	106	5	entre	entre	PROPN
ejpam-2419	106	6	des	des	PROPN
ejpam-2419	106	7	intégrales	intégrales	PROPN
ejpam-2419	106	8	définies	définie	NOUN
ejpam-2419	106	9	.	.	PUNCT
ejpam-2419	107	1	maria	maria	PROPN
ejpam-2419	107	2	curie	curie	PROPN
ejpam-2419	107	3	skåćodowska	skåćodowska	PROPN
ejpam-2419	107	4	university	university	PROPN
ejpam-2419	107	5	,	,	PUNCT
ejpam-2419	107	6	a4	a4	PROPN
ejpam-2419	107	7	,	,	PUNCT
ejpam-2419	107	8	1	1	NUM
ejpam-2419	107	9	-	-	SYM
ejpam-2419	107	10	4	4	NUM
ejpam-2419	107	11	.	.	NOUN
ejpam-2419	107	12	1950	1950	NUM
ejpam-2419	107	13	.	.	PUNCT
ejpam-2419	108	1	[	[	X
ejpam-2419	108	2	3	3	X
ejpam-2419	108	3	]	]	PUNCT
ejpam-2419	108	4	v.	v.	ADP
ejpam-2419	108	5	consonni	consonni	PROPN
ejpam-2419	108	6	and	and	CCONJ
ejpam-2419	108	7	r.	r.	PROPN
ejpam-2419	108	8	todeschini	todeschini	PROPN
ejpam-2419	108	9	.	.	PUNCT
ejpam-2419	109	1	new	new	ADJ
ejpam-2419	109	2	spectral	spectral	ADJ
ejpam-2419	109	3	index	index	NOUN
ejpam-2419	109	4	for	for	ADP
ejpam-2419	109	5	molecule	molecule	NOUN
ejpam-2419	109	6	description	description	NOUN
ejpam-2419	109	7	.	.	PUNCT
ejpam-2419	110	1	match	match	VERB
ejpam-2419	110	2	communications	communication	NOUN
ejpam-2419	110	3	in	in	ADP
ejpam-2419	110	4	mathematical	mathematical	ADJ
ejpam-2419	110	5	and	and	CCONJ
ejpam-2419	110	6	in	in	ADP
ejpam-2419	110	7	computer	computer	NOUN
ejpam-2419	110	8	chemistry	chemistry	NOUN
ejpam-2419	110	9	,	,	PUNCT
ejpam-2419	110	10	60	60	NUM
ejpam-2419	110	11	,	,	PUNCT
ejpam-2419	110	12	3	3	NUM
ejpam-2419	110	13	-	-	SYM
ejpam-2419	110	14	14	14	NUM
ejpam-2419	110	15	.	.	PUNCT
ejpam-2419	110	16	2008	2008	NUM
ejpam-2419	110	17	.	.	PUNCT
ejpam-2419	111	1	[	[	X
ejpam-2419	111	2	4	4	X
ejpam-2419	111	3	]	]	PUNCT
ejpam-2419	111	4	j.	j.	PROPN
ejpam-2419	111	5	b.	b.	PROPN
ejpam-2419	111	6	diaz	diaz	PROPN
ejpam-2419	111	7	and	and	CCONJ
ejpam-2419	111	8	f.	f.	PROPN
ejpam-2419	111	9	t.	t.	PROPN
ejpam-2419	111	10	metcalf	metcalf	PROPN
ejpam-2419	111	11	.	.	PUNCT
ejpam-2419	112	1	stronger	strong	ADJ
ejpam-2419	112	2	forms	form	NOUN
ejpam-2419	112	3	of	of	ADP
ejpam-2419	112	4	a	a	DET
ejpam-2419	112	5	class	class	NOUN
ejpam-2419	112	6	of	of	ADP
ejpam-2419	112	7	inequalities	inequality	NOUN
ejpam-2419	112	8	of	of	ADP
ejpam-2419	112	9	g.	g.	PROPN
ejpam-2419	112	10	pólya	pólya	PROPN
ejpam-2419	112	11	-	-	PUNCT
ejpam-2419	112	12	g.szegő	g.szegő	PROPN
ejpam-2419	112	13	and	and	CCONJ
ejpam-2419	112	14	l.	l.	PROPN
ejpam-2419	112	15	v.	v.	PROPN
ejpam-2419	112	16	kantorovich	kantorovich	PROPN
ejpam-2419	112	17	.	.	PUNCT
ejpam-2419	113	1	bulletin	bulletin	NOUN
ejpam-2419	113	2	of	of	ADP
ejpam-2419	113	3	the	the	DET
ejpam-2419	113	4	ams	am	NOUN
ejpam-2419	113	5	american	american	PROPN
ejpam-2419	113	6	mathematical	mathematical	PROPN
ejpam-2419	113	7	society	society	NOUN
ejpam-2419	113	8	,	,	PUNCT
ejpam-2419	113	9	69	69	NUM
ejpam-2419	113	10	,	,	PUNCT
ejpam-2419	113	11	415	415	NUM
ejpam-2419	113	12	-	-	SYM
ejpam-2419	113	13	418	418	NUM
ejpam-2419	113	14	.	.	PUNCT
ejpam-2419	113	15	1963	1963	NUM
ejpam-2419	113	16	.	.	PUNCT
ejpam-2419	114	1	[	[	X
ejpam-2419	114	2	5	5	X
ejpam-2419	114	3	]	]	PUNCT
ejpam-2419	114	4	f.	f.	PROPN
ejpam-2419	114	5	harary	harary	PROPN
ejpam-2419	114	6	.	.	PUNCT
ejpam-2419	115	1	graph	graph	NOUN
ejpam-2419	115	2	theory	theory	NOUN
ejpam-2419	115	3	,	,	PUNCT
ejpam-2419	115	4	addison	addison	PROPN
ejpam-2419	115	5	-	-	PUNCT
ejpam-2419	115	6	wesley	wesley	PROPN
ejpam-2419	115	7	,	,	PUNCT
ejpam-2419	115	8	reading	reading	NOUN
ejpam-2419	115	9	,	,	PUNCT
ejpam-2419	115	10	1969	1969	NUM
ejpam-2419	115	11	.	.	PUNCT
ejpam-2419	116	1	[	[	X
ejpam-2419	116	2	6	6	NUM
ejpam-2419	116	3	]	]	PUNCT
ejpam-2419	116	4	i.	i.	NOUN
ejpam-2419	116	5	gutman	gutman	PROPN
ejpam-2419	116	6	.	.	PUNCT
ejpam-2419	117	1	the	the	DET
ejpam-2419	117	2	energy	energy	NOUN
ejpam-2419	117	3	of	of	ADP
ejpam-2419	117	4	a	a	DET
ejpam-2419	117	5	graph	graph	NOUN
ejpam-2419	117	6	.	.	PUNCT
ejpam-2419	118	1	berlin	berlin	PROPN
ejpam-2419	118	2	mathmatics	mathmatics	PROPN
ejpam-2419	118	3	-	-	PUNCT
ejpam-2419	118	4	statistics	statistic	NOUN
ejpam-2419	118	5	forschungszentrum	forschungszentrum	NOUN
ejpam-2419	118	6	,	,	PUNCT
ejpam-2419	118	7	103	103	NUM
ejpam-2419	118	8	,	,	PUNCT
ejpam-2419	118	9	1	1	NUM
ejpam-2419	118	10	-	-	SYM
ejpam-2419	118	11	22	22	NUM
ejpam-2419	118	12	.	.	PUNCT
ejpam-2419	118	13	1978	1978	NUM
ejpam-2419	118	14	.	.	PUNCT
ejpam-2419	119	1	[	[	X
ejpam-2419	119	2	7	7	NUM
ejpam-2419	119	3	]	]	X
ejpam-2419	119	4	i.	i.	NOUN
ejpam-2419	119	5	gutman	gutman	PROPN
ejpam-2419	119	6	and	and	CCONJ
ejpam-2419	119	7	o.	o.	PROPN
ejpam-2419	119	8	e.	e.	PROPN
ejpam-2419	119	9	polansky	polansky	PROPN
ejpam-2419	119	10	.	.	PUNCT
ejpam-2419	120	1	mathematical	mathematical	ADJ
ejpam-2419	120	2	concepts	concept	NOUN
ejpam-2419	120	3	in	in	ADP
ejpam-2419	120	4	organic	organic	ADJ
ejpam-2419	120	5	chemistry	chemistry	NOUN
ejpam-2419	120	6	,	,	PUNCT
ejpam-2419	120	7	springerverlag	springerverlag	NOUN
ejpam-2419	120	8	,	,	PUNCT
ejpam-2419	120	9	berlin	berlin	PROPN
ejpam-2419	120	10	,	,	PUNCT
ejpam-2419	120	11	1986	1986	NUM
ejpam-2419	120	12	.	.	PUNCT
ejpam-2419	121	1	[	[	X
ejpam-2419	121	2	8	8	NUM
ejpam-2419	121	3	]	]	X
ejpam-2419	121	4	g.	g.	PROPN
ejpam-2419	121	5	hossein	hossein	PROPN
ejpam-2419	121	6	,	,	PUNCT
ejpam-2419	121	7	f.	f.	PROPN
ejpam-2419	121	8	tabar	tabar	PROPN
ejpam-2419	121	9	,	,	PUNCT
ejpam-2419	121	10	and	and	CCONJ
ejpam-2419	121	11	a.	a.	PROPN
ejpam-2419	121	12	r.	r.	PROPN
ejpam-2419	121	13	ashrafi	ashrafi	PROPN
ejpam-2419	121	14	.	.	PUNCT
ejpam-2419	122	1	some	some	DET
ejpam-2419	122	2	remarks	remark	NOUN
ejpam-2419	122	3	on	on	ADP
ejpam-2419	122	4	laplacian	laplacian	ADJ
ejpam-2419	122	5	eigenvalues	eigenvalue	NOUN
ejpam-2419	122	6	and	and	CCONJ
ejpam-2419	122	7	laplacian	laplacian	ADJ
ejpam-2419	122	8	energy	energy	NOUN
ejpam-2419	122	9	of	of	ADP
ejpam-2419	122	10	graphs	graph	NOUN
ejpam-2419	122	11	.	.	PUNCT
ejpam-2419	123	1	mathematical	mathematical	ADJ
ejpam-2419	123	2	communications	communication	NOUN
ejpam-2419	123	3	,	,	PUNCT
ejpam-2419	123	4	15(2	15(2	NUM
ejpam-2419	123	5	)	)	PUNCT
ejpam-2419	123	6	,	,	PUNCT
ejpam-2419	123	7	443	443	NUM
ejpam-2419	123	8	-	-	SYM
ejpam-2419	123	9	451	451	NUM
ejpam-2419	123	10	.	.	PUNCT
ejpam-2419	123	11	2010	2010	NUM
ejpam-2419	123	12	.	.	PUNCT
ejpam-2419	124	1	[	[	X
ejpam-2419	124	2	9	9	NUM
ejpam-2419	124	3	]	]	PUNCT
ejpam-2419	124	4	i.	i.	NOUN
ejpam-2419	124	5	ž	ž	PROPN
ejpam-2419	124	6	.	.	PUNCT
ejpam-2419	124	7	milovanovć	milovanovć	PROPN
ejpam-2419	124	8	,	,	PUNCT
ejpam-2419	124	9	e.	e.	PROPN
ejpam-2419	124	10	i.	i.	PROPN
ejpam-2419	124	11	milovanovć	milovanovć	PROPN
ejpam-2419	124	12	,	,	PUNCT
ejpam-2419	124	13	and	and	CCONJ
ejpam-2419	124	14	a.	a.	NOUN
ejpam-2419	124	15	zakić.	zakić.	PROPN
ejpam-2419	124	16	a	a	DET
ejpam-2419	124	17	short	short	ADJ
ejpam-2419	124	18	note	note	NOUN
ejpam-2419	124	19	on	on	ADP
ejpam-2419	124	20	graph	graph	NOUN
ejpam-2419	124	21	energy	energy	NOUN
ejpam-2419	124	22	.	.	PUNCT
ejpam-2419	125	1	match	match	VERB
ejpam-2419	125	2	communications	communication	NOUN
ejpam-2419	125	3	in	in	ADP
ejpam-2419	125	4	mathematical	mathematical	ADJ
ejpam-2419	125	5	and	and	CCONJ
ejpam-2419	125	6	in	in	ADP
ejpam-2419	125	7	computer	computer	NOUN
ejpam-2419	125	8	chemistry	chemistry	NOUN
ejpam-2419	125	9	,	,	PUNCT
ejpam-2419	125	10	72	72	NUM
ejpam-2419	125	11	,	,	PUNCT
ejpam-2419	125	12	179	179	NUM
ejpam-2419	125	13	-	-	SYM
ejpam-2419	125	14	182	182	NUM
ejpam-2419	125	15	.	.	PUNCT
ejpam-2419	125	16	2014	2014	NUM
ejpam-2419	125	17	.	.	PUNCT
ejpam-2419	126	1	[	[	X
ejpam-2419	126	2	10	10	NUM
ejpam-2419	126	3	]	]	X
ejpam-2419	126	4	n.	n.	PROPN
ejpam-2419	126	5	ozeki	ozeki	PROPN
ejpam-2419	126	6	.	.	PUNCT
ejpam-2419	127	1	on	on	ADP
ejpam-2419	127	2	the	the	DET
ejpam-2419	127	3	estimation	estimation	NOUN
ejpam-2419	127	4	of	of	ADP
ejpam-2419	127	5	inequalities	inequality	NOUN
ejpam-2419	127	6	by	by	ADP
ejpam-2419	127	7	maximum	maximum	ADJ
ejpam-2419	127	8	and	and	CCONJ
ejpam-2419	127	9	minimum	minimum	ADJ
ejpam-2419	127	10	values	value	NOUN
ejpam-2419	127	11	.	.	PUNCT
ejpam-2419	128	1	journal	journal	NOUN
ejpam-2419	128	2	of	of	ADP
ejpam-2419	128	3	college	college	NOUN
ejpam-2419	128	4	arts	art	NOUN
ejpam-2419	128	5	and	and	CCONJ
ejpam-2419	128	6	science	science	NOUN
ejpam-2419	128	7	,	,	PUNCT
ejpam-2419	128	8	chiba	chiba	PROPN
ejpam-2419	128	9	university	university	PROPN
ejpam-2419	128	10	,	,	PUNCT
ejpam-2419	128	11	5	5	NUM
ejpam-2419	128	12	,	,	PUNCT
ejpam-2419	128	13	199	199	NUM
ejpam-2419	128	14	-	-	SYM
ejpam-2419	128	15	203	203	NUM
ejpam-2419	128	16	.	.	PUNCT
ejpam-2419	128	17	1968	1968	NUM
ejpam-2419	128	18	.	.	PUNCT
ejpam-2419	129	1	(	(	PUNCT
ejpam-2419	129	2	in	in	ADP
ejpam-2419	129	3	japanese	japanese	PROPN
ejpam-2419	129	4	)	)	PUNCT
ejpam-2419	130	1	[	[	X
ejpam-2419	130	2	11	11	NUM
ejpam-2419	130	3	]	]	X
ejpam-2419	130	4	g.	g.	NOUN
ejpam-2419	130	5	pólya	pólya	PROPN
ejpam-2419	130	6	and	and	CCONJ
ejpam-2419	130	7	g.	g.	PROPN
ejpam-2419	130	8	szegő.	szegő.	PROPN
ejpam-2419	130	9	problems	problem	NOUN
ejpam-2419	130	10	and	and	CCONJ
ejpam-2419	130	11	theorems	theorem	NOUN
ejpam-2419	130	12	in	in	ADP
ejpam-2419	130	13	analysis	analysis	NOUN
ejpam-2419	130	14	.	.	PUNCT
ejpam-2419	131	1	series	series	NOUN
ejpam-2419	131	2	,	,	PUNCT
ejpam-2419	131	3	integral	integral	ADJ
ejpam-2419	131	4	calculus	calculus	NOUN
ejpam-2419	131	5	,	,	PUNCT
ejpam-2419	131	6	theory	theory	NOUN
ejpam-2419	131	7	of	of	ADP
ejpam-2419	131	8	functions	function	NOUN
ejpam-2419	131	9	,	,	PUNCT
ejpam-2419	131	10	springer	springer	NOUN
ejpam-2419	131	11	,	,	PUNCT
ejpam-2419	131	12	berlin	berlin	PROPN
ejpam-2419	131	13	,	,	PUNCT
ejpam-2419	131	14	1972	1972	NUM
ejpam-2419	131	15	.	.	PUNCT
ejpam-2419	132	1	[	[	X
ejpam-2419	132	2	12	12	NUM
ejpam-2419	132	3	]	]	PUNCT
ejpam-2419	132	4	h.	h.	PROPN
ejpam-2419	132	5	s.	s.	PROPN
ejpam-2419	132	6	ramane	ramane	PROPN
ejpam-2419	132	7	,	,	PUNCT
ejpam-2419	132	8	d.	d.	PROPN
ejpam-2419	132	9	s.	s.	PROPN
ejpam-2419	132	10	revankar	revankar	PROPN
ejpam-2419	132	11	,	,	PUNCT
ejpam-2419	132	12	and	and	CCONJ
ejpam-2419	132	13	j.	j.	PROPN
ejpam-2419	132	14	b.	b.	PROPN
ejpam-2419	132	15	patil	patil	PROPN
ejpam-2419	132	16	.	.	PUNCT
ejpam-2419	133	1	bounds	bound	VERB
ejpam-2419	133	2	for	for	ADP
ejpam-2419	133	3	the	the	DET
ejpam-2419	133	4	degree	degree	NOUN
ejpam-2419	133	5	sum	sum	NOUN
ejpam-2419	133	6	eigenvalues	eigenvalue	NOUN
ejpam-2419	133	7	and	and	CCONJ
ejpam-2419	133	8	degree	degree	NOUN
ejpam-2419	133	9	sum	sum	NOUN
ejpam-2419	133	10	energy	energy	NOUN
ejpam-2419	133	11	of	of	ADP
ejpam-2419	133	12	a	a	DET
ejpam-2419	133	13	graph	graph	NOUN
ejpam-2419	133	14	.	.	PUNCT
ejpam-2419	134	1	international	international	ADJ
ejpam-2419	134	2	journal	journal	NOUN
ejpam-2419	134	3	of	of	ADP
ejpam-2419	134	4	pure	pure	ADJ
ejpam-2419	134	5	and	and	CCONJ
ejpam-2419	134	6	applied	applied	ADJ
ejpam-2419	134	7	mathematical	mathematical	ADJ
ejpam-2419	134	8	sciences	science	NOUN
ejpam-2419	134	9	,	,	PUNCT
ejpam-2419	134	10	6(2	6(2	NUM
ejpam-2419	134	11	)	)	PUNCT
ejpam-2419	134	12	,	,	PUNCT
ejpam-2419	134	13	161	161	NUM
ejpam-2419	134	14	-	-	SYM
ejpam-2419	134	15	167	167	NUM
ejpam-2419	134	16	.	.	PUNCT
ejpam-2419	135	1	2013	2013	NUM
ejpam-2419	135	2	.	.	PUNCT
ejpam-2419	136	1	[	[	X
ejpam-2419	136	2	13	13	NUM
ejpam-2419	136	3	]	]	PUNCT
ejpam-2419	136	4	i.	i.	NOUN
ejpam-2419	136	5	shparlinski	shparlinski	PROPN
ejpam-2419	136	6	.	.	PUNCT
ejpam-2419	137	1	on	on	ADP
ejpam-2419	137	2	the	the	DET
ejpam-2419	137	3	energy	energy	NOUN
ejpam-2419	137	4	of	of	ADP
ejpam-2419	137	5	some	some	DET
ejpam-2419	137	6	circulant	circulant	ADJ
ejpam-2419	137	7	graphs	graph	NOUN
ejpam-2419	137	8	.	.	PUNCT
ejpam-2419	138	1	linear	linear	ADJ
ejpam-2419	138	2	algebra	algebra	NOUN
ejpam-2419	138	3	and	and	CCONJ
ejpam-2419	138	4	its	its	PRON
ejpam-2419	138	5	applications	application	NOUN
ejpam-2419	138	6	,	,	PUNCT
ejpam-2419	138	7	414	414	NUM
ejpam-2419	138	8	,	,	PUNCT
ejpam-2419	138	9	378	378	NUM
ejpam-2419	138	10	-	-	SYM
ejpam-2419	138	11	382	382	NUM
ejpam-2419	138	12	.	.	PUNCT
ejpam-2419	138	13	2006	2006	NUM
ejpam-2419	138	14	.	.	PUNCT
ejpam-2419	139	1	[	[	X
ejpam-2419	139	2	14	14	NUM
ejpam-2419	139	3	]	]	X
ejpam-2419	139	4	n.	n.	NOUN
ejpam-2419	139	5	trinajstić.	trinajstić.	PROPN
ejpam-2419	139	6	chemical	chemical	NOUN
ejpam-2419	139	7	graph	graph	NOUN
ejpam-2419	139	8	theory	theory	NOUN
ejpam-2419	139	9	.	.	PUNCT
ejpam-2419	140	1	n.	n.	PROPN
ejpam-2419	140	2	trinajstic	trinajstic	PROPN
ejpam-2419	140	3	,	,	PUNCT
ejpam-2419	140	4	chemical	chemical	NOUN
ejpam-2419	140	5	graph	graph	NOUN
ejpam-2419	140	6	theory	theory	NOUN
ejpam-2419	140	7	,	,	PUNCT
ejpam-2419	140	8	vol	vol	NOUN
ejpam-2419	140	9	.	.	PROPN
ejpam-2419	140	10	2	2	NUM
ejpam-2419	140	11	,	,	PUNCT
ejpam-2419	140	12	crc	crc	NOUN
ejpam-2419	140	13	press	press	NOUN
ejpam-2419	140	14	,	,	PUNCT
ejpam-2419	140	15	boca	boca	PROPN
ejpam-2419	140	16	raton	raton	PROPN
ejpam-2419	140	17	,	,	PUNCT
ejpam-2419	140	18	florida	florida	PROPN
ejpam-2419	140	19	,	,	PUNCT
ejpam-2419	140	20	1983	1983	NUM
ejpam-2419	140	21	.	.	PUNCT
ejpam-2419	141	1	references	reference	NOUN
ejpam-2419	141	2	345	345	NUM
ejpam-2419	141	3	[	[	X
ejpam-2419	141	4	15	15	NUM
ejpam-2419	141	5	]	]	X
ejpam-2419	141	6	b.	b.	PROPN
ejpam-2419	141	7	zhou	zhou	PROPN
ejpam-2419	141	8	.	.	PUNCT
ejpam-2419	142	1	energy	energy	NOUN
ejpam-2419	142	2	of	of	ADP
ejpam-2419	142	3	a	a	DET
ejpam-2419	142	4	graph	graph	NOUN
ejpam-2419	142	5	.	.	PUNCT
ejpam-2419	143	1	match	match	NOUN
ejpam-2419	143	2	communications	communication	NOUN
ejpam-2419	143	3	in	in	ADP
ejpam-2419	143	4	mathematical	mathematical	ADJ
ejpam-2419	143	5	and	and	CCONJ
ejpam-2419	143	6	in	in	ADP
ejpam-2419	143	7	computer	computer	NOUN
ejpam-2419	143	8	chemistry	chemistry	NOUN
ejpam-2419	143	9	,	,	PUNCT
ejpam-2419	143	10	51	51	NUM
ejpam-2419	143	11	,	,	PUNCT
ejpam-2419	143	12	111	111	NUM
ejpam-2419	143	13	-	-	SYM
ejpam-2419	143	14	118	118	NUM
ejpam-2419	143	15	.	.	PUNCT
ejpam-2419	143	16	2004	2004	NUM
ejpam-2419	143	17	.	.	PUNCT