id	sid	tid	token	lemma	pos
ejpam-1580	1	1	9_xxx_bozkurt.dvi	9_xxx_bozkurt.dvi	NUM
ejpam-1580	1	2	european	european	ADJ
ejpam-1580	1	3	journal	journal	NOUN
ejpam-1580	1	4	of	of	ADP
ejpam-1580	1	5	pure	pure	ADJ
ejpam-1580	1	6	and	and	CCONJ
ejpam-1580	1	7	applied	apply	VERB
ejpam-1580	1	8	mathematics	mathematic	NOUN
ejpam-1580	1	9	vol	vol	NOUN
ejpam-1580	1	10	.	.	PROPN
ejpam-1580	1	11	5	5	NUM
ejpam-1580	1	12	,	,	PUNCT
ejpam-1580	1	13	no	no	INTJ
ejpam-1580	1	14	.	.	NOUN
ejpam-1580	1	15	1	1	NUM
ejpam-1580	1	16	,	,	PUNCT
ejpam-1580	1	17	2012	2012	NUM
ejpam-1580	1	18	,	,	PUNCT
ejpam-1580	1	19	88	88	NUM
ejpam-1580	1	20	-	-	SYM
ejpam-1580	1	21	96	96	NUM
ejpam-1580	1	22	issn	issn	PROPN
ejpam-1580	1	23	1307	1307	NUM
ejpam-1580	1	24	-	-	SYM
ejpam-1580	1	25	5543	5543	NUM
ejpam-1580	1	26	–	–	PUNCT
ejpam-1580	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1580	1	28	special	special	ADJ
ejpam-1580	1	29	issue	issue	NOUN
ejpam-1580	1	30	for	for	ADP
ejpam-1580	1	31	the	the	DET
ejpam-1580	1	32	international	international	ADJ
ejpam-1580	1	33	conference	conference	NOUN
ejpam-1580	1	34	on	on	ADP
ejpam-1580	1	35	applied	apply	VERB
ejpam-1580	1	36	analysis	analysis	NOUN
ejpam-1580	1	37	and	and	CCONJ
ejpam-1580	1	38	algebra	algebra	NOUN
ejpam-1580	1	39	29	29	NUM
ejpam-1580	1	40	june	june	PROPN
ejpam-1580	1	41	02	02	NUM
ejpam-1580	1	42	july	july	PROPN
ejpam-1580	1	43	2011	2011	NUM
ejpam-1580	1	44	,	,	PUNCT
ejpam-1580	1	45	istanbul	istanbul	PROPN
ejpam-1580	1	46	turkey	turkey	PROPN
ejpam-1580	1	47	randić	randić	PROPN
ejpam-1580	1	48	energy	energy	NOUN
ejpam-1580	1	49	and	and	CCONJ
ejpam-1580	1	50	randić	randić	NOUN
ejpam-1580	1	51	estrada	estrada	PROPN
ejpam-1580	1	52	index	index	NOUN
ejpam-1580	1	53	of	of	ADP
ejpam-1580	1	54	a	a	DET
ejpam-1580	1	55	graph	graph	NOUN
ejpam-1580	1	56	ş.	ş.	PROPN
ejpam-1580	1	57	burcu	burcu	PROPN
ejpam-1580	1	58	bozkurt	bozkurt	PROPN
ejpam-1580	1	59	!	!	PUNCT
ejpam-1580	1	60	,	,	PUNCT
ejpam-1580	1	61	durmuş	durmuş	VERB
ejpam-1580	1	62	bozkurt	bozkurt	PROPN
ejpam-1580	1	63	department	department	NOUN
ejpam-1580	1	64	of	of	ADP
ejpam-1580	1	65	mathematics	mathematics	PROPN
ejpam-1580	1	66	,	,	PUNCT
ejpam-1580	1	67	science	science	NOUN
ejpam-1580	1	68	faculty	faculty	NOUN
ejpam-1580	1	69	,	,	PUNCT
ejpam-1580	1	70	selçuk	selçuk	PROPN
ejpam-1580	1	71	university	university	NOUN
ejpam-1580	1	72	,	,	PUNCT
ejpam-1580	1	73	42075	42075	NUM
ejpam-1580	1	74	,	,	PUNCT
ejpam-1580	1	75	campus	campus	PROPN
ejpam-1580	1	76	,	,	PUNCT
ejpam-1580	1	77	konya	konya	PROPN
ejpam-1580	1	78	,	,	PUNCT
ejpam-1580	1	79	turkey	turkey	PROPN
ejpam-1580	1	80	abstract	abstract	NOUN
ejpam-1580	1	81	.	.	PUNCT
ejpam-1580	2	1	let	let	VERB
ejpam-1580	2	2	g	g	PRON
ejpam-1580	2	3	be	be	AUX
ejpam-1580	2	4	a	a	DET
ejpam-1580	2	5	simple	simple	ADJ
ejpam-1580	2	6	connected	connected	ADJ
ejpam-1580	2	7	graph	graph	NOUN
ejpam-1580	2	8	with	with	ADP
ejpam-1580	2	9	n	n	ADP
ejpam-1580	2	10	vertices	vertex	NOUN
ejpam-1580	2	11	and	and	CCONJ
ejpam-1580	2	12	let	let	VERB
ejpam-1580	2	13	di	di	PART
ejpam-1580	2	14	be	be	AUX
ejpam-1580	2	15	the	the	DET
ejpam-1580	2	16	degree	degree	NOUN
ejpam-1580	2	17	of	of	ADP
ejpam-1580	2	18	its	its	PRON
ejpam-1580	2	19	i	i	NOUN
ejpam-1580	2	20	-	-	PUNCT
ejpam-1580	2	21	th	th	NUM
ejpam-1580	2	22	vertex	vertex	NOUN
ejpam-1580	2	23	.	.	PUNCT
ejpam-1580	3	1	the	the	DET
ejpam-1580	3	2	randić	randić	NOUN
ejpam-1580	3	3	matrix	matrix	NOUN
ejpam-1580	3	4	of	of	ADP
ejpam-1580	3	5	g	g	PROPN
ejpam-1580	3	6	is	be	AUX
ejpam-1580	3	7	the	the	DET
ejpam-1580	3	8	square	square	ADJ
ejpam-1580	3	9	matrix	matrix	NOUN
ejpam-1580	3	10	of	of	ADP
ejpam-1580	3	11	order	order	NOUN
ejpam-1580	3	12	n	n	X
ejpam-1580	3	13	whose	whose	DET
ejpam-1580	3	14	!	!	PUNCT
ejpam-1580	4	1	i	i	PRON
ejpam-1580	4	2	,	,	PUNCT
ejpam-1580	4	3	j	j	PROPN
ejpam-1580	4	4	"	"	PUNCT
ejpam-1580	4	5	-entry	-entry	PROPN
ejpam-1580	4	6	is	be	AUX
ejpam-1580	4	7	equal	equal	ADJ
ejpam-1580	4	8	to	to	ADP
ejpam-1580	4	9	1/	1/	NUM
ejpam-1580	4	10	#	#	NOUN
ejpam-1580	4	11	didj	didj	NOUN
ejpam-1580	4	12	if	if	SCONJ
ejpam-1580	4	13	the	the	DET
ejpam-1580	4	14	i	i	PROPN
ejpam-1580	4	15	-	-	PUNCT
ejpam-1580	4	16	th	th	X
ejpam-1580	4	17	and	and	CCONJ
ejpam-1580	4	18	j	j	PROPN
ejpam-1580	4	19	-	-	PUNCT
ejpam-1580	4	20	th	th	X
ejpam-1580	4	21	vertex	vertex	NOUN
ejpam-1580	4	22	of	of	ADP
ejpam-1580	4	23	g	g	PROPN
ejpam-1580	4	24	are	be	AUX
ejpam-1580	4	25	adjacent	adjacent	ADJ
ejpam-1580	4	26	,	,	PUNCT
ejpam-1580	4	27	and	and	CCONJ
ejpam-1580	4	28	zero	zero	NUM
ejpam-1580	4	29	otherwise	otherwise	ADV
ejpam-1580	4	30	.	.	PUNCT
ejpam-1580	5	1	the	the	DET
ejpam-1580	5	2	randić	randić	NOUN
ejpam-1580	5	3	eigenvalues	eigenvalue	NOUN
ejpam-1580	5	4	are	be	AUX
ejpam-1580	5	5	the	the	DET
ejpam-1580	5	6	eigenvalues	eigenvalue	NOUN
ejpam-1580	5	7	of	of	ADP
ejpam-1580	5	8	the	the	DET
ejpam-1580	5	9	randić	randić	NOUN
ejpam-1580	5	10	matrix	matrix	NOUN
ejpam-1580	5	11	.	.	PUNCT
ejpam-1580	6	1	the	the	DET
ejpam-1580	6	2	randić	randić	NOUN
ejpam-1580	6	3	energy	energy	NOUN
ejpam-1580	6	4	is	be	AUX
ejpam-1580	6	5	the	the	DET
ejpam-1580	6	6	sum	sum	NOUN
ejpam-1580	6	7	of	of	ADP
ejpam-1580	6	8	the	the	DET
ejpam-1580	6	9	absolute	absolute	ADJ
ejpam-1580	6	10	values	value	NOUN
ejpam-1580	6	11	of	of	ADP
ejpam-1580	6	12	the	the	DET
ejpam-1580	6	13	randić	randić	NOUN
ejpam-1580	6	14	eigenvalues	eigenvalue	NOUN
ejpam-1580	6	15	.	.	PUNCT
ejpam-1580	7	1	in	in	ADP
ejpam-1580	7	2	this	this	DET
ejpam-1580	7	3	paper	paper	NOUN
ejpam-1580	7	4	,	,	PUNCT
ejpam-1580	7	5	we	we	PRON
ejpam-1580	7	6	introduce	introduce	VERB
ejpam-1580	7	7	a	a	DET
ejpam-1580	7	8	new	new	ADJ
ejpam-1580	7	9	index	index	NOUN
ejpam-1580	7	10	of	of	ADP
ejpam-1580	7	11	the	the	DET
ejpam-1580	7	12	graph	graph	NOUN
ejpam-1580	7	13	g	g	NOUN
ejpam-1580	7	14	which	which	PRON
ejpam-1580	7	15	is	be	AUX
ejpam-1580	7	16	called	call	VERB
ejpam-1580	7	17	randić	randić	NOUN
ejpam-1580	7	18	estrada	estrada	PROPN
ejpam-1580	7	19	index	index	PROPN
ejpam-1580	7	20	.	.	PUNCT
ejpam-1580	8	1	in	in	ADP
ejpam-1580	8	2	addition	addition	NOUN
ejpam-1580	8	3	,	,	PUNCT
ejpam-1580	8	4	we	we	PRON
ejpam-1580	8	5	obtain	obtain	VERB
ejpam-1580	8	6	lower	low	ADJ
ejpam-1580	8	7	and	and	CCONJ
ejpam-1580	8	8	upper	upper	ADJ
ejpam-1580	8	9	bounds	bound	NOUN
ejpam-1580	8	10	for	for	ADP
ejpam-1580	8	11	the	the	DET
ejpam-1580	8	12	randić	randić	ADJ
ejpam-1580	8	13	energy	energy	NOUN
ejpam-1580	8	14	and	and	CCONJ
ejpam-1580	8	15	the	the	DET
ejpam-1580	8	16	randić	randić	NOUN
ejpam-1580	8	17	estrada	estrada	PROPN
ejpam-1580	8	18	index	index	NOUN
ejpam-1580	8	19	of	of	ADP
ejpam-1580	8	20	g.	g.	PROPN
ejpam-1580	8	21	2000	2000	NUM
ejpam-1580	8	22	mathematics	mathematic	NOUN
ejpam-1580	8	23	subject	subject	NOUN
ejpam-1580	8	24	classifications	classification	NOUN
ejpam-1580	8	25	:	:	PUNCT
ejpam-1580	8	26	05c50,15a18	05c50,15a18	NUM
ejpam-1580	8	27	key	key	ADJ
ejpam-1580	8	28	words	word	NOUN
ejpam-1580	8	29	and	and	CCONJ
ejpam-1580	8	30	phrases	phrase	NOUN
ejpam-1580	8	31	:	:	PUNCT
ejpam-1580	8	32	randić	randić	NOUN
ejpam-1580	8	33	matrix	matrix	NOUN
ejpam-1580	8	34	,	,	PUNCT
ejpam-1580	8	35	randić	randić	NOUN
ejpam-1580	8	36	eigenvalue	eigenvalue	NOUN
ejpam-1580	8	37	,	,	PUNCT
ejpam-1580	8	38	randić	randić	NOUN
ejpam-1580	8	39	energy	energy	NOUN
ejpam-1580	8	40	,	,	PUNCT
ejpam-1580	8	41	randić	randić	NOUN
ejpam-1580	8	42	estrada	estrada	PROPN
ejpam-1580	8	43	index	index	PROPN
ejpam-1580	8	44	1	1	NUM
ejpam-1580	8	45	.	.	PUNCT
ejpam-1580	9	1	introduction	introduction	NOUN
ejpam-1580	9	2	let	let	VERB
ejpam-1580	9	3	g	g	PRON
ejpam-1580	9	4	be	be	AUX
ejpam-1580	9	5	a	a	DET
ejpam-1580	9	6	simple	simple	ADJ
ejpam-1580	9	7	connected	connected	ADJ
ejpam-1580	9	8	graph	graph	NOUN
ejpam-1580	9	9	with	with	ADP
ejpam-1580	9	10	n	n	ADP
ejpam-1580	9	11	vertices	vertex	NOUN
ejpam-1580	9	12	and	and	CCONJ
ejpam-1580	9	13	m	m	PRON
ejpam-1580	9	14	edges	edge	NOUN
ejpam-1580	9	15	.	.	PUNCT
ejpam-1580	10	1	throughout	throughout	ADP
ejpam-1580	10	2	this	this	DET
ejpam-1580	10	3	paper	paper	NOUN
ejpam-1580	10	4	,	,	PUNCT
ejpam-1580	10	5	such	such	DET
ejpam-1580	10	6	a	a	DET
ejpam-1580	10	7	graph	graph	NOUN
ejpam-1580	10	8	will	will	AUX
ejpam-1580	10	9	be	be	AUX
ejpam-1580	10	10	refered	refer	VERB
ejpam-1580	10	11	to	to	ADP
ejpam-1580	10	12	as	as	ADP
ejpam-1580	10	13	connected	connect	VERB
ejpam-1580	10	14	(	(	PUNCT
ejpam-1580	10	15	n	n	CCONJ
ejpam-1580	10	16	,	,	PUNCT
ejpam-1580	10	17	m)-graph	m)-graph	NOUN
ejpam-1580	10	18	.	.	PUNCT
ejpam-1580	11	1	let	let	VERB
ejpam-1580	11	2	v	v	X
ejpam-1580	11	3	(	(	PUNCT
ejpam-1580	11	4	g	g	NOUN
ejpam-1580	11	5	)	)	PUNCT
ejpam-1580	11	6	=	=	SYM
ejpam-1580	11	7	$	$	SYM
ejpam-1580	11	8	v1	v1	NOUN
ejpam-1580	11	9	,	,	PUNCT
ejpam-1580	11	10	v2	v2	NOUN
ejpam-1580	11	11	,	,	PUNCT
ejpam-1580	11	12	.	.	PUNCT
ejpam-1580	11	13	.	.	PUNCT
ejpam-1580	12	1	.	.	PUNCT
ejpam-1580	13	1	,	,	PUNCT
ejpam-1580	13	2	vn	vn	INTJ
ejpam-1580	13	3	%	%	INTJ
ejpam-1580	13	4	be	be	AUX
ejpam-1580	13	5	the	the	DET
ejpam-1580	13	6	vertex	vertex	NOUN
ejpam-1580	13	7	set	set	NOUN
ejpam-1580	13	8	of	of	ADP
ejpam-1580	13	9	g.	g.	PROPN
ejpam-1580	13	10	if	if	SCONJ
ejpam-1580	13	11	any	any	DET
ejpam-1580	13	12	two	two	NUM
ejpam-1580	13	13	vetices	vetice	NOUN
ejpam-1580	13	14	vi	vi	NOUN
ejpam-1580	13	15	and	and	CCONJ
ejpam-1580	13	16	vj	vj	NOUN
ejpam-1580	13	17	of	of	ADP
ejpam-1580	13	18	g	g	PROPN
ejpam-1580	13	19	are	be	AUX
ejpam-1580	13	20	adjacent	adjacent	ADJ
ejpam-1580	13	21	,	,	PUNCT
ejpam-1580	13	22	then	then	ADV
ejpam-1580	13	23	we	we	PRON
ejpam-1580	13	24	use	use	VERB
ejpam-1580	13	25	the	the	DET
ejpam-1580	13	26	notation	notation	NOUN
ejpam-1580	13	27	vi	vi	PROPN
ejpam-1580	13	28	"	"	PUNCT
ejpam-1580	13	29	vj	vj	INTJ
ejpam-1580	13	30	.	.	PUNCT
ejpam-1580	14	1	for	for	ADP
ejpam-1580	14	2	vi	vi	NOUN
ejpam-1580	14	3	#	#	NOUN
ejpam-1580	14	4	v	v	NOUN
ejpam-1580	14	5	(	(	PUNCT
ejpam-1580	14	6	g	g	NOUN
ejpam-1580	14	7	)	)	PUNCT
ejpam-1580	14	8	,	,	PUNCT
ejpam-1580	14	9	the	the	DET
ejpam-1580	14	10	degree	degree	NOUN
ejpam-1580	14	11	of	of	ADP
ejpam-1580	14	12	the	the	DET
ejpam-1580	14	13	vertex	vertex	NOUN
ejpam-1580	14	14	vi	vi	PROPN
ejpam-1580	14	15	,	,	PUNCT
ejpam-1580	14	16	denoted	denote	VERB
ejpam-1580	14	17	by	by	ADP
ejpam-1580	14	18	di	di	NOUN
ejpam-1580	14	19	,	,	PUNCT
ejpam-1580	14	20	is	be	AUX
ejpam-1580	14	21	the	the	DET
ejpam-1580	14	22	number	number	NOUN
ejpam-1580	14	23	of	of	ADP
ejpam-1580	14	24	the	the	DET
ejpam-1580	14	25	vertices	vertex	NOUN
ejpam-1580	14	26	adjacent	adjacent	ADJ
ejpam-1580	14	27	to	to	ADP
ejpam-1580	14	28	vi	vi	PROPN
ejpam-1580	14	29	.	.	PUNCT
ejpam-1580	15	1	let	let	AUX
ejpam-1580	15	2	a(g	a(g	PROPN
ejpam-1580	15	3	)	)	PUNCT
ejpam-1580	15	4	be	be	AUX
ejpam-1580	15	5	the	the	DET
ejpam-1580	15	6	(	(	PUNCT
ejpam-1580	15	7	0,1)-adjacency	0,1)-adjacency	NUM
ejpam-1580	15	8	matrix	matrix	NOUN
ejpam-1580	15	9	of	of	ADP
ejpam-1580	15	10	g	g	PROPN
ejpam-1580	15	11	and	and	CCONJ
ejpam-1580	15	12	!	!	PUNCT
ejpam-1580	16	1	1,!2	1,!2	NUM
ejpam-1580	16	2	,	,	PUNCT
ejpam-1580	16	3	.	.	PUNCT
ejpam-1580	16	4	.	.	PUNCT
ejpam-1580	16	5	.	.	PUNCT
ejpam-1580	17	1	,	,	PUNCT
ejpam-1580	17	2	!	!	PUNCT
ejpam-1580	18	1	n	n	CCONJ
ejpam-1580	18	2	be	be	AUX
ejpam-1580	18	3	its	its	PRON
ejpam-1580	18	4	eigenvalues	eigenvalue	NOUN
ejpam-1580	18	5	.	.	PUNCT
ejpam-1580	19	1	these	these	PRON
ejpam-1580	19	2	are	be	AUX
ejpam-1580	19	3	said	say	VERB
ejpam-1580	19	4	to	to	PART
ejpam-1580	19	5	be	be	AUX
ejpam-1580	19	6	eigenvalues	eigenvalue	NOUN
ejpam-1580	19	7	of	of	ADP
ejpam-1580	19	8	the	the	DET
ejpam-1580	19	9	graph	graph	NOUN
ejpam-1580	19	10	g	g	NOUN
ejpam-1580	19	11	and	and	CCONJ
ejpam-1580	19	12	to	to	PART
ejpam-1580	19	13	form	form	VERB
ejpam-1580	19	14	its	its	PRON
ejpam-1580	19	15	spectrum	spectrum	NOUN
ejpam-1580	19	16	[	[	X
ejpam-1580	19	17	3	3	NUM
ejpam-1580	19	18	]	]	PUNCT
ejpam-1580	19	19	.	.	PUNCT
ejpam-1580	20	1	the	the	DET
ejpam-1580	20	2	randić	randić	NOUN
ejpam-1580	20	3	matrix	matrix	NOUN
ejpam-1580	20	4	of	of	ADP
ejpam-1580	20	5	g	g	PROPN
ejpam-1580	20	6	is	be	AUX
ejpam-1580	20	7	the	the	DET
ejpam-1580	20	8	n$	n$	NOUN
ejpam-1580	20	9	n	n	PRON
ejpam-1580	20	10	matrix	matrix	VERB
ejpam-1580	20	11	r=	r=	ADJ
ejpam-1580	20	12	r	r	NOUN
ejpam-1580	20	13	(	(	PUNCT
ejpam-1580	20	14	g	g	NOUN
ejpam-1580	20	15	)	)	PUNCT
ejpam-1580	20	16	=	=	SYM
ejpam-1580	20	17	&	&	CCONJ
ejpam-1580	20	18	ri	ri	PROPN
ejpam-1580	20	19	j	j	PROPN
ejpam-1580	20	20	'	'	PUNCT
ejpam-1580	20	21	as	as	ADP
ejpam-1580	20	22	the	the	DET
ejpam-1580	20	23	following	follow	VERB
ejpam-1580	20	24	ri	ri	PROPN
ejpam-1580	20	25	j	j	PROPN
ejpam-1580	20	26	=	=	PRON
ejpam-1580	20	27	(	(	PUNCT
ejpam-1580	20	28	1	1	NUM
ejpam-1580	20	29	%	%	NOUN
ejpam-1580	20	30	di	di	NOUN
ejpam-1580	20	31	dj	dj	NOUN
ejpam-1580	20	32	,	,	PUNCT
ejpam-1580	20	33	vi	vi	PROPN
ejpam-1580	20	34	"	"	PUNCT
ejpam-1580	21	1	vj	vj	PROPN
ejpam-1580	21	2	0	0	NUM
ejpam-1580	21	3	,	,	PUNCT
ejpam-1580	21	4	otherwise	otherwise	ADV
ejpam-1580	21	5	!	!	PUNCT
ejpam-1580	22	1	corresponding	correspond	VERB
ejpam-1580	22	2	author	author	NOUN
ejpam-1580	22	3	.	.	PUNCT
ejpam-1580	23	1	email	email	NOUN
ejpam-1580	23	2	addresses	address	NOUN
ejpam-1580	23	3	:	:	PUNCT
ejpam-1580	23	4	(	(	PUNCT
ejpam-1580	23	5	ş.	ş.	PROPN
ejpam-1580	23	6	bozkurt	bozkurt	PROPN
ejpam-1580	23	7	)	)	PUNCT
ejpam-1580	23	8	,	,	PUNCT
ejpam-1580	23	9	(	(	PUNCT
ejpam-1580	23	10	d.	d.	PROPN
ejpam-1580	23	11	bozkurt	bozkurt	PROPN
ejpam-1580	23	12	)	)	PUNCT
ejpam-1580	23	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1580	24	1	88	88	NUM
ejpam-1580	24	2	c	c	NOUN
ejpam-1580	24	3	&	&	CCONJ
ejpam-1580	24	4	2012	2012	NUM
ejpam-1580	24	5	ejpam	ejpam	VERB
ejpam-1580	24	6	all	all	DET
ejpam-1580	24	7	rights	right	NOUN
ejpam-1580	24	8	reserved	reserve	VERB
ejpam-1580	24	9	.	.	PUNCT
ejpam-1580	25	1	ş.	ş.	PROPN
ejpam-1580	25	2	bozkurt	bozkurt	PROPN
ejpam-1580	25	3	and	and	CCONJ
ejpam-1580	25	4	d.	d.	PROPN
ejpam-1580	25	5	bozkurt	bozkurt	PROPN
ejpam-1580	25	6	/	/	SYM
ejpam-1580	25	7	eur	eur	PROPN
ejpam-1580	25	8	.	.	PUNCT
ejpam-1580	26	1	j.	j.	PROPN
ejpam-1580	26	2	pure	pure	PROPN
ejpam-1580	26	3	appl	appl	PROPN
ejpam-1580	26	4	.	.	PROPN
ejpam-1580	26	5	math	math	PROPN
ejpam-1580	26	6	,	,	PUNCT
ejpam-1580	26	7	5	5	NUM
ejpam-1580	26	8	(	(	PUNCT
ejpam-1580	26	9	2012	2012	NUM
ejpam-1580	26	10	)	)	PUNCT
ejpam-1580	26	11	,	,	PUNCT
ejpam-1580	26	12	88	88	NUM
ejpam-1580	26	13	-	-	SYM
ejpam-1580	26	14	96	96	NUM
ejpam-1580	26	15	89	89	NUM
ejpam-1580	26	16	the	the	DET
ejpam-1580	26	17	randić	randić	NOUN
ejpam-1580	26	18	eigenvalues	eigenvalue	VERB
ejpam-1580	26	19	"	"	PUNCT
ejpam-1580	26	20	1,"2	1,"2	NUM
ejpam-1580	26	21	,	,	PUNCT
ejpam-1580	26	22	.	.	PUNCT
ejpam-1580	26	23	.	.	PUNCT
ejpam-1580	26	24	.	.	PUNCT
ejpam-1580	27	1	,	,	PUNCT
ejpam-1580	27	2	"	"	PUNCT
ejpam-1580	27	3	n	n	X
ejpam-1580	27	4	of	of	ADP
ejpam-1580	27	5	the	the	DET
ejpam-1580	27	6	graph	graph	NOUN
ejpam-1580	27	7	g	g	PROPN
ejpam-1580	27	8	are	be	AUX
ejpam-1580	27	9	the	the	DET
ejpam-1580	27	10	eigenvalues	eigenvalue	NOUN
ejpam-1580	27	11	of	of	ADP
ejpam-1580	27	12	its	its	PRON
ejpam-1580	27	13	randić	randić	NOUN
ejpam-1580	27	14	matrix	matrix	NOUN
ejpam-1580	27	15	.	.	PUNCT
ejpam-1580	28	1	since	since	SCONJ
ejpam-1580	28	2	a(g	a(g	PROPN
ejpam-1580	28	3	)	)	PUNCT
ejpam-1580	28	4	and	and	CCONJ
ejpam-1580	28	5	r	r	NOUN
ejpam-1580	28	6	(	(	PUNCT
ejpam-1580	28	7	g	g	NOUN
ejpam-1580	28	8	)	)	PUNCT
ejpam-1580	28	9	are	be	AUX
ejpam-1580	28	10	real	real	ADJ
ejpam-1580	28	11	symmetric	symmetric	ADJ
ejpam-1580	28	12	matrices	matrix	NOUN
ejpam-1580	28	13	,	,	PUNCT
ejpam-1580	28	14	their	their	PRON
ejpam-1580	28	15	eigenvalues	eigenvalue	NOUN
ejpam-1580	28	16	are	be	AUX
ejpam-1580	28	17	real	real	ADJ
ejpam-1580	28	18	numbers	number	NOUN
ejpam-1580	28	19	.	.	PUNCT
ejpam-1580	29	1	so	so	ADV
ejpam-1580	29	2	we	we	PRON
ejpam-1580	29	3	can	can	AUX
ejpam-1580	29	4	order	order	VERB
ejpam-1580	29	5	them	they	PRON
ejpam-1580	29	6	so	so	SCONJ
ejpam-1580	29	7	that	that	SCONJ
ejpam-1580	29	8	!	!	PUNCT
ejpam-1580	29	9	1	1	NUM
ejpam-1580	29	10	'	'	PUNCT
ejpam-1580	29	11	!	!	PUNCT
ejpam-1580	29	12	2	2	NUM
ejpam-1580	29	13	'	'	PUNCT
ejpam-1580	29	14	.	.	PUNCT
ejpam-1580	29	15	.	.	PUNCT
ejpam-1580	29	16	.	.	PUNCT
ejpam-1580	29	17	'	'	PUNCT
ejpam-1580	29	18	!	!	PUNCT
ejpam-1580	30	1	n	n	CCONJ
ejpam-1580	30	2	and	and	CCONJ
ejpam-1580	30	3	"	"	PUNCT
ejpam-1580	30	4	1	1	NUM
ejpam-1580	30	5	'	'	PUNCT
ejpam-1580	30	6	"	"	PUNCT
ejpam-1580	30	7	2	2	NUM
ejpam-1580	30	8	'	'	PUNCT
ejpam-1580	30	9	.	.	PUNCT
ejpam-1580	30	10	.	.	PUNCT
ejpam-1580	30	11	.	.	PUNCT
ejpam-1580	30	12	'	'	PUNCT
ejpam-1580	31	1	"	"	PUNCT
ejpam-1580	31	2	n.	n.	VERB
ejpam-1580	31	3	the	the	DET
ejpam-1580	31	4	energy	energy	NOUN
ejpam-1580	31	5	of	of	ADP
ejpam-1580	31	6	the	the	DET
ejpam-1580	31	7	graph	graph	NOUN
ejpam-1580	31	8	g	g	NOUN
ejpam-1580	31	9	is	be	AUX
ejpam-1580	31	10	defined	define	VERB
ejpam-1580	31	11	in	in	ADP
ejpam-1580	31	12	[	[	X
ejpam-1580	31	13	11,12,13	11,12,13	NUM
ejpam-1580	31	14	]	]	PUNCT
ejpam-1580	31	15	as	as	ADP
ejpam-1580	31	16	:	:	PUNCT
ejpam-1580	31	17	e	e	X
ejpam-1580	31	18	=	=	SYM
ejpam-1580	31	19	e	e	X
ejpam-1580	31	20	(	(	PUNCT
ejpam-1580	31	21	g	g	NOUN
ejpam-1580	31	22	)	)	PUNCT
ejpam-1580	31	23	=	=	SYM
ejpam-1580	31	24	n	n	X
ejpam-1580	31	25	)	)	PUNCT
ejpam-1580	31	26	i=1	i=1	PROPN
ejpam-1580	32	1	*	*	PUNCT
ejpam-1580	33	1	*	*	PUNCT
ejpam-1580	33	2	!	!	PUNCT
ejpam-1580	34	1	i	i	PRON
ejpam-1580	34	2	*	*	PUNCT
ejpam-1580	35	1	*	*	PUNCT
ejpam-1580	35	2	.	.	PUNCT
ejpam-1580	36	1	(	(	PUNCT
ejpam-1580	36	2	1	1	X
ejpam-1580	36	3	)	)	PUNCT
ejpam-1580	36	4	the	the	DET
ejpam-1580	36	5	randić	randić	NOUN
ejpam-1580	36	6	energy	energy	NOUN
ejpam-1580	36	7	of	of	ADP
ejpam-1580	36	8	the	the	DET
ejpam-1580	36	9	graph	graph	NOUN
ejpam-1580	36	10	g	g	NOUN
ejpam-1580	36	11	is	be	AUX
ejpam-1580	36	12	defined	define	VERB
ejpam-1580	36	13	in	in	ADP
ejpam-1580	36	14	[	[	X
ejpam-1580	36	15	1,2	1,2	NUM
ejpam-1580	36	16	]	]	PUNCT
ejpam-1580	36	17	as	as	ADP
ejpam-1580	36	18	:	:	PUNCT
ejpam-1580	36	19	re	re	X
ejpam-1580	36	20	=	=	NOUN
ejpam-1580	36	21	re	re	X
ejpam-1580	36	22	(	(	PUNCT
ejpam-1580	36	23	g	g	NOUN
ejpam-1580	36	24	)	)	PUNCT
ejpam-1580	36	25	=	=	SYM
ejpam-1580	36	26	n	n	X
ejpam-1580	36	27	)	)	PUNCT
ejpam-1580	36	28	i=1	i=1	PROPN
ejpam-1580	37	1	*	*	PUNCT
ejpam-1580	38	1	*	*	PUNCT
ejpam-1580	38	2	"	"	PUNCT
ejpam-1580	38	3	i	i	PRON
ejpam-1580	38	4	*	*	PUNCT
ejpam-1580	38	5	*	*	PUNCT
ejpam-1580	38	6	.	.	PUNCT
ejpam-1580	39	1	(	(	PUNCT
ejpam-1580	39	2	2	2	X
ejpam-1580	39	3	)	)	PUNCT
ejpam-1580	39	4	the	the	DET
ejpam-1580	39	5	estrada	estrada	PROPN
ejpam-1580	39	6	index	index	NOUN
ejpam-1580	39	7	of	of	ADP
ejpam-1580	39	8	the	the	DET
ejpam-1580	39	9	graph	graph	NOUN
ejpam-1580	39	10	g	g	NOUN
ejpam-1580	39	11	is	be	AUX
ejpam-1580	39	12	defined	define	VERB
ejpam-1580	39	13	in	in	ADP
ejpam-1580	39	14	[	[	NOUN
ejpam-1580	39	15	7,8,9,10	7,8,9,10	NUM
ejpam-1580	39	16	]	]	X
ejpam-1580	39	17	as	as	ADP
ejpam-1580	39	18	:	:	PUNCT
ejpam-1580	39	19	ee	ee	PROPN
ejpam-1580	39	20	=	=	PROPN
ejpam-1580	39	21	ee	ee	PROPN
ejpam-1580	39	22	(	(	PUNCT
ejpam-1580	39	23	g	g	NOUN
ejpam-1580	39	24	)	)	PUNCT
ejpam-1580	39	25	=	=	SYM
ejpam-1580	39	26	n	n	X
ejpam-1580	39	27	)	)	PUNCT
ejpam-1580	39	28	i=1	i=1	ADP
ejpam-1580	39	29	e!i	e!i	PROPN
ejpam-1580	39	30	(	(	PUNCT
ejpam-1580	39	31	3	3	X
ejpam-1580	39	32	)	)	PUNCT
ejpam-1580	39	33	denoting	denote	VERB
ejpam-1580	39	34	by	by	ADP
ejpam-1580	39	35	mk	mk	NOUN
ejpam-1580	39	36	=	=	SYM
ejpam-1580	39	37	mk	mk	PROPN
ejpam-1580	39	38	(	(	PUNCT
ejpam-1580	39	39	g	g	NOUN
ejpam-1580	39	40	)	)	PUNCT
ejpam-1580	39	41	the	the	DET
ejpam-1580	39	42	k	k	NOUN
ejpam-1580	39	43	-	-	PUNCT
ejpam-1580	39	44	th	th	VERB
ejpam-1580	39	45	moment	moment	NOUN
ejpam-1580	39	46	of	of	ADP
ejpam-1580	39	47	the	the	DET
ejpam-1580	39	48	graph	graph	NOUN
ejpam-1580	39	49	g	g	PROPN
ejpam-1580	39	50	mk	mk	X
ejpam-1580	39	51	=	=	SYM
ejpam-1580	39	52	mk	mk	PROPN
ejpam-1580	39	53	(	(	PUNCT
ejpam-1580	39	54	g	g	NOUN
ejpam-1580	39	55	)	)	PUNCT
ejpam-1580	39	56	=	=	SYM
ejpam-1580	39	57	n	n	X
ejpam-1580	39	58	)	)	PUNCT
ejpam-1580	39	59	i=1	i=1	PROPN
ejpam-1580	39	60	!	!	PUNCT
ejpam-1580	39	61	!	!	PUNCT
ejpam-1580	40	1	i	i	PRON
ejpam-1580	40	2	"	"	PUNCT
ejpam-1580	40	3	k	k	X
ejpam-1580	40	4	.	.	PUNCT
ejpam-1580	41	1	recalling	recall	VERB
ejpam-1580	41	2	the	the	DET
ejpam-1580	41	3	power	power	NOUN
ejpam-1580	41	4	series	series	NOUN
ejpam-1580	41	5	expansion	expansion	NOUN
ejpam-1580	41	6	of	of	ADP
ejpam-1580	41	7	ex	ex	PRON
ejpam-1580	41	8	,	,	PUNCT
ejpam-1580	41	9	we	we	PRON
ejpam-1580	41	10	have	have	VERB
ejpam-1580	41	11	ee	ee	X
ejpam-1580	41	12	=	=	SYM
ejpam-1580	41	13	(	(	PUNCT
ejpam-1580	41	14	)	)	PUNCT
ejpam-1580	41	15	k=0	k=0	PROPN
ejpam-1580	41	16	mk	mk	X
ejpam-1580	42	1	k	k	PROPN
ejpam-1580	42	2	!	!	PUNCT
ejpam-1580	42	3	.	.	PUNCT
ejpam-1580	43	1	(	(	PUNCT
ejpam-1580	43	2	4	4	X
ejpam-1580	43	3	)	)	PUNCT
ejpam-1580	43	4	it	it	PRON
ejpam-1580	43	5	is	be	AUX
ejpam-1580	43	6	well	well	ADV
ejpam-1580	43	7	known	known	ADJ
ejpam-1580	43	8	that	that	SCONJ
ejpam-1580	43	9	[	[	X
ejpam-1580	43	10	3	3	X
ejpam-1580	43	11	]	]	X
ejpam-1580	43	12	mk	mk	NOUN
ejpam-1580	43	13	is	be	AUX
ejpam-1580	43	14	equal	equal	ADJ
ejpam-1580	43	15	to	to	ADP
ejpam-1580	43	16	the	the	DET
ejpam-1580	43	17	number	number	NOUN
ejpam-1580	43	18	of	of	ADP
ejpam-1580	43	19	closed	closed	ADJ
ejpam-1580	43	20	walks	walk	NOUN
ejpam-1580	43	21	of	of	ADP
ejpam-1580	43	22	length	length	NOUN
ejpam-1580	43	23	k	k	PROPN
ejpam-1580	43	24	in	in	ADP
ejpam-1580	43	25	the	the	DET
ejpam-1580	43	26	graph	graph	NOUN
ejpam-1580	43	27	g.	g.	PROPN
ejpam-1580	43	28	estrada	estrada	PROPN
ejpam-1580	43	29	index	index	PROPN
ejpam-1580	43	30	of	of	ADP
ejpam-1580	43	31	graphs	graph	NOUN
ejpam-1580	43	32	has	have	VERB
ejpam-1580	43	33	an	an	DET
ejpam-1580	43	34	important	important	ADJ
ejpam-1580	43	35	role	role	NOUN
ejpam-1580	43	36	in	in	ADP
ejpam-1580	43	37	chemistry	chemistry	NOUN
ejpam-1580	43	38	and	and	CCONJ
ejpam-1580	43	39	physics	physics	NOUN
ejpam-1580	43	40	.	.	PUNCT
ejpam-1580	44	1	for	for	ADP
ejpam-1580	44	2	more	more	ADJ
ejpam-1580	44	3	information	information	NOUN
ejpam-1580	44	4	we	we	PRON
ejpam-1580	44	5	refer	refer	VERB
ejpam-1580	44	6	to	to	ADP
ejpam-1580	44	7	the	the	DET
ejpam-1580	44	8	reader	reader	NOUN
ejpam-1580	44	9	[	[	X
ejpam-1580	44	10	7,8,9,10	7,8,9,10	NUM
ejpam-1580	44	11	]	]	X
ejpam-1580	44	12	.	.	PUNCT
ejpam-1580	45	1	in	in	ADP
ejpam-1580	45	2	addition	addition	NOUN
ejpam-1580	45	3	,	,	PUNCT
ejpam-1580	45	4	there	there	PRON
ejpam-1580	45	5	exist	exist	VERB
ejpam-1580	45	6	a	a	DET
ejpam-1580	45	7	vast	vast	ADJ
ejpam-1580	45	8	literature	literature	NOUN
ejpam-1580	45	9	that	that	PRON
ejpam-1580	45	10	studies	study	VERB
ejpam-1580	45	11	estrada	estrada	PROPN
ejpam-1580	45	12	index	index	PROPN
ejpam-1580	45	13	and	and	CCONJ
ejpam-1580	45	14	its	its	PRON
ejpam-1580	45	15	bounds	bound	NOUN
ejpam-1580	45	16	.	.	PUNCT
ejpam-1580	46	1	for	for	ADP
ejpam-1580	46	2	detailed	detailed	ADJ
ejpam-1580	46	3	information	information	NOUN
ejpam-1580	46	4	we	we	PRON
ejpam-1580	46	5	may	may	AUX
ejpam-1580	46	6	also	also	ADV
ejpam-1580	46	7	refer	refer	VERB
ejpam-1580	46	8	to	to	ADP
ejpam-1580	46	9	the	the	DET
ejpam-1580	46	10	reader	reader	NOUN
ejpam-1580	46	11	[	[	X
ejpam-1580	46	12	4,5,6,14	4,5,6,14	X
ejpam-1580	46	13	]	]	PUNCT
ejpam-1580	46	14	.	.	PUNCT
ejpam-1580	47	1	now	now	ADV
ejpam-1580	47	2	we	we	PRON
ejpam-1580	47	3	introduce	introduce	VERB
ejpam-1580	47	4	the	the	DET
ejpam-1580	47	5	randić	randić	NOUN
ejpam-1580	47	6	estrada	estrada	PROPN
ejpam-1580	47	7	index	index	NOUN
ejpam-1580	47	8	of	of	ADP
ejpam-1580	47	9	the	the	DET
ejpam-1580	47	10	graph	graph	NOUN
ejpam-1580	47	11	g.	g.	NOUN
ejpam-1580	47	12	definition	definition	NOUN
ejpam-1580	47	13	1	1	NUM
ejpam-1580	47	14	.	.	PUNCT
ejpam-1580	48	1	if	if	SCONJ
ejpam-1580	48	2	g	g	PROPN
ejpam-1580	48	3	is	be	AUX
ejpam-1580	48	4	a	a	DET
ejpam-1580	48	5	connected	connected	ADJ
ejpam-1580	48	6	(	(	PUNCT
ejpam-1580	48	7	n	n	CCONJ
ejpam-1580	48	8	,	,	PUNCT
ejpam-1580	48	9	m)-graph	m)-graph	NOUN
ejpam-1580	48	10	,	,	PUNCT
ejpam-1580	48	11	then	then	ADV
ejpam-1580	48	12	the	the	DET
ejpam-1580	48	13	randíc	randíc	PROPN
ejpam-1580	48	14	estrada	estrada	PROPN
ejpam-1580	48	15	index	index	NOUN
ejpam-1580	48	16	of	of	ADP
ejpam-1580	48	17	g	g	PROPN
ejpam-1580	48	18	,	,	PUNCT
ejpam-1580	48	19	denoted	denote	VERB
ejpam-1580	48	20	by	by	ADP
ejpam-1580	48	21	ree	ree	NOUN
ejpam-1580	48	22	(	(	PUNCT
ejpam-1580	48	23	g	g	NOUN
ejpam-1580	48	24	)	)	PUNCT
ejpam-1580	48	25	,	,	PUNCT
ejpam-1580	48	26	is	be	AUX
ejpam-1580	48	27	equal	equal	ADJ
ejpam-1580	48	28	to	to	ADP
ejpam-1580	48	29	ree	ree	NOUN
ejpam-1580	48	30	=	=	SYM
ejpam-1580	48	31	ree	ree	NOUN
ejpam-1580	48	32	(	(	PUNCT
ejpam-1580	48	33	g	g	NOUN
ejpam-1580	48	34	)	)	PUNCT
ejpam-1580	48	35	=	=	SYM
ejpam-1580	48	36	n	n	X
ejpam-1580	48	37	)	)	PUNCT
ejpam-1580	48	38	i=1	i=1	PROPN
ejpam-1580	48	39	e"i	e"i	PROPN
ejpam-1580	48	40	.	.	PUNCT
ejpam-1580	49	1	(	(	PUNCT
ejpam-1580	49	2	5	5	NUM
ejpam-1580	49	3	)	)	PUNCT
ejpam-1580	49	4	where	where	SCONJ
ejpam-1580	49	5	"	"	PUNCT
ejpam-1580	49	6	1,"2	1,"2	NUM
ejpam-1580	49	7	,	,	PUNCT
ejpam-1580	49	8	.	.	PUNCT
ejpam-1580	49	9	.	.	PUNCT
ejpam-1580	49	10	.	.	PUNCT
ejpam-1580	50	1	,	,	PUNCT
ejpam-1580	50	2	"	"	PUNCT
ejpam-1580	50	3	n	n	X
ejpam-1580	50	4	are	be	AUX
ejpam-1580	50	5	the	the	DET
ejpam-1580	50	6	randíc	randíc	PROPN
ejpam-1580	50	7	eigenvalues	eigenvalue	NOUN
ejpam-1580	50	8	of	of	ADP
ejpam-1580	50	9	g.	g.	PROPN
ejpam-1580	50	10	let	let	VERB
ejpam-1580	50	11	nk	nk	PROPN
ejpam-1580	50	12	=	=	PROPN
ejpam-1580	50	13	nk	nk	PROPN
ejpam-1580	50	14	(	(	PUNCT
ejpam-1580	50	15	g	g	NOUN
ejpam-1580	50	16	)	)	PUNCT
ejpam-1580	50	17	=	=	SYM
ejpam-1580	51	1	n	n	X
ejpam-1580	51	2	)	)	PUNCT
ejpam-1580	51	3	i=1	i=1	X
ejpam-1580	51	4	!	!	PUNCT
ejpam-1580	52	1	"	"	PUNCT
ejpam-1580	52	2	i	i	PRON
ejpam-1580	52	3	"	"	PUNCT
ejpam-1580	52	4	k	k	PROPN
ejpam-1580	52	5	.	.	PUNCT
ejpam-1580	53	1	ş.	ş.	PROPN
ejpam-1580	53	2	bozkurt	bozkurt	PROPN
ejpam-1580	53	3	and	and	CCONJ
ejpam-1580	53	4	d.	d.	PROPN
ejpam-1580	53	5	bozkurt	bozkurt	PROPN
ejpam-1580	53	6	/	/	SYM
ejpam-1580	53	7	eur	eur	PROPN
ejpam-1580	53	8	.	.	PUNCT
ejpam-1580	54	1	j.	j.	PROPN
ejpam-1580	54	2	pure	pure	PROPN
ejpam-1580	54	3	appl	appl	PROPN
ejpam-1580	54	4	.	.	PROPN
ejpam-1580	54	5	math	math	PROPN
ejpam-1580	54	6	,	,	PUNCT
ejpam-1580	54	7	5	5	NUM
ejpam-1580	54	8	(	(	PUNCT
ejpam-1580	54	9	2012	2012	NUM
ejpam-1580	54	10	)	)	PUNCT
ejpam-1580	54	11	,	,	PUNCT
ejpam-1580	54	12	88	88	NUM
ejpam-1580	54	13	-	-	SYM
ejpam-1580	54	14	96	96	NUM
ejpam-1580	54	15	90	90	NUM
ejpam-1580	54	16	recalling	recall	VERB
ejpam-1580	54	17	the	the	DET
ejpam-1580	54	18	power	power	NOUN
ejpam-1580	54	19	series	series	NOUN
ejpam-1580	54	20	expansion	expansion	NOUN
ejpam-1580	54	21	of	of	ADP
ejpam-1580	54	22	ex	ex	PRON
ejpam-1580	54	23	we	we	PRON
ejpam-1580	54	24	have	have	VERB
ejpam-1580	54	25	another	another	DET
ejpam-1580	54	26	expression	expression	NOUN
ejpam-1580	54	27	of	of	ADP
ejpam-1580	54	28	randić	randić	NOUN
ejpam-1580	54	29	estrada	estrada	PROPN
ejpam-1580	54	30	index	index	NOUN
ejpam-1580	54	31	as	as	ADP
ejpam-1580	54	32	the	the	DET
ejpam-1580	54	33	following	follow	VERB
ejpam-1580	54	34	ree	ree	NOUN
ejpam-1580	54	35	(	(	PUNCT
ejpam-1580	54	36	g	g	NOUN
ejpam-1580	54	37	)	)	PUNCT
ejpam-1580	54	38	=	=	SYM
ejpam-1580	54	39	(	(	PUNCT
ejpam-1580	54	40	)	)	PUNCT
ejpam-1580	54	41	k=0	k=0	PROPN
ejpam-1580	54	42	nk	nk	PROPN
ejpam-1580	54	43	k	k	PROPN
ejpam-1580	54	44	!	!	PUNCT
ejpam-1580	54	45	.	.	PUNCT
ejpam-1580	55	1	(	(	PUNCT
ejpam-1580	55	2	6	6	NUM
ejpam-1580	55	3	)	)	PUNCT
ejpam-1580	55	4	in	in	ADP
ejpam-1580	55	5	this	this	DET
ejpam-1580	55	6	paper	paper	NOUN
ejpam-1580	55	7	,	,	PUNCT
ejpam-1580	55	8	we	we	PRON
ejpam-1580	55	9	obtain	obtain	VERB
ejpam-1580	55	10	lower	low	ADJ
ejpam-1580	55	11	and	and	CCONJ
ejpam-1580	55	12	upper	upper	ADJ
ejpam-1580	55	13	bounds	bound	NOUN
ejpam-1580	55	14	for	for	ADP
ejpam-1580	55	15	the	the	DET
ejpam-1580	55	16	randić	randić	ADJ
ejpam-1580	55	17	energy	energy	NOUN
ejpam-1580	55	18	and	and	CCONJ
ejpam-1580	55	19	the	the	DET
ejpam-1580	55	20	randić	randić	NOUN
ejpam-1580	55	21	estrada	estrada	PROPN
ejpam-1580	55	22	index	index	NOUN
ejpam-1580	55	23	of	of	ADP
ejpam-1580	55	24	g.	g.	PROPN
ejpam-1580	55	25	firstly	firstly	ADV
ejpam-1580	55	26	,	,	PUNCT
ejpam-1580	55	27	we	we	PRON
ejpam-1580	55	28	give	give	VERB
ejpam-1580	55	29	some	some	DET
ejpam-1580	55	30	definitions	definition	NOUN
ejpam-1580	55	31	and	and	CCONJ
ejpam-1580	55	32	lemmas	lemma	NOUN
ejpam-1580	55	33	which	which	PRON
ejpam-1580	55	34	will	will	AUX
ejpam-1580	55	35	be	be	AUX
ejpam-1580	55	36	needed	need	VERB
ejpam-1580	55	37	then	then	ADV
ejpam-1580	55	38	.	.	PUNCT
ejpam-1580	56	1	definition	definition	NOUN
ejpam-1580	56	2	2	2	NUM
ejpam-1580	56	3	.	.	PUNCT
ejpam-1580	57	1	[	[	X
ejpam-1580	57	2	2	2	X
ejpam-1580	57	3	]	]	PUNCT
ejpam-1580	57	4	let	let	VERB
ejpam-1580	57	5	g	g	PRON
ejpam-1580	57	6	be	be	AUX
ejpam-1580	57	7	a	a	DET
ejpam-1580	57	8	graph	graph	NOUN
ejpam-1580	57	9	with	with	ADP
ejpam-1580	57	10	vertex	vertex	NOUN
ejpam-1580	57	11	set	set	VERB
ejpam-1580	57	12	v	v	NOUN
ejpam-1580	57	13	(	(	PUNCT
ejpam-1580	57	14	g	g	NOUN
ejpam-1580	57	15	)	)	PUNCT
ejpam-1580	57	16	=	=	SYM
ejpam-1580	57	17	$	$	SYM
ejpam-1580	57	18	v1	v1	NOUN
ejpam-1580	57	19	,	,	PUNCT
ejpam-1580	57	20	v2	v2	NOUN
ejpam-1580	57	21	,	,	PUNCT
ejpam-1580	57	22	.	.	PUNCT
ejpam-1580	57	23	.	.	PUNCT
ejpam-1580	58	1	.	.	PUNCT
ejpam-1580	59	1	,	,	PUNCT
ejpam-1580	60	1	vn	vn	INTJ
ejpam-1580	60	2	%	%	INTJ
ejpam-1580	60	3	and	and	CCONJ
ejpam-1580	60	4	randíc	randíc	PROPN
ejpam-1580	60	5	matrix	matrix	NOUN
ejpam-1580	60	6	r.	r.	PROPN
ejpam-1580	60	7	then	then	ADV
ejpam-1580	60	8	the	the	DET
ejpam-1580	60	9	randíc	randíc	NOUN
ejpam-1580	60	10	degree	degree	NOUN
ejpam-1580	60	11	of	of	ADP
ejpam-1580	60	12	vi	vi	NOUN
ejpam-1580	60	13	,	,	PUNCT
ejpam-1580	60	14	denoted	denote	VERB
ejpam-1580	60	15	by	by	ADP
ejpam-1580	60	16	ri	ri	PROPN
ejpam-1580	60	17	is	be	AUX
ejpam-1580	60	18	given	give	VERB
ejpam-1580	60	19	by	by	ADP
ejpam-1580	60	20	ri	ri	PROPN
ejpam-1580	60	21	=	=	PUNCT
ejpam-1580	60	22	n	n	PROPN
ejpam-1580	60	23	)	)	PUNCT
ejpam-1580	60	24	j=1	j=1	PROPN
ejpam-1580	60	25	ri	ri	PROPN
ejpam-1580	60	26	j.	j.	PROPN
ejpam-1580	60	27	definition	definition	PROPN
ejpam-1580	60	28	3	3	NUM
ejpam-1580	60	29	.	.	PUNCT
ejpam-1580	61	1	[	[	X
ejpam-1580	61	2	2	2	X
ejpam-1580	61	3	]	]	PUNCT
ejpam-1580	61	4	let	let	VERB
ejpam-1580	61	5	g	g	PRON
ejpam-1580	61	6	be	be	AUX
ejpam-1580	61	7	a	a	DET
ejpam-1580	61	8	graph	graph	NOUN
ejpam-1580	61	9	with	with	ADP
ejpam-1580	61	10	vertex	vertex	NOUN
ejpam-1580	61	11	set	set	VERB
ejpam-1580	61	12	v	v	NOUN
ejpam-1580	61	13	(	(	PUNCT
ejpam-1580	61	14	g	g	NOUN
ejpam-1580	61	15	)	)	PUNCT
ejpam-1580	61	16	=	=	SYM
ejpam-1580	61	17	$	$	SYM
ejpam-1580	61	18	v1	v1	NOUN
ejpam-1580	61	19	,	,	PUNCT
ejpam-1580	61	20	v2	v2	NOUN
ejpam-1580	61	21	,	,	PUNCT
ejpam-1580	61	22	.	.	PUNCT
ejpam-1580	61	23	.	.	PUNCT
ejpam-1580	62	1	.	.	PUNCT
ejpam-1580	63	1	,	,	PUNCT
ejpam-1580	64	1	vn	vn	INTJ
ejpam-1580	64	2	%	%	INTJ
ejpam-1580	64	3	and	and	CCONJ
ejpam-1580	64	4	randíc	randíc	PROPN
ejpam-1580	64	5	matrix	matrix	NOUN
ejpam-1580	64	6	r.	r.	PROPN
ejpam-1580	64	7	let	let	VERB
ejpam-1580	64	8	the	the	DET
ejpam-1580	64	9	randíc	randíc	NOUN
ejpam-1580	64	10	degree	degree	NOUN
ejpam-1580	64	11	sequence	sequence	NOUN
ejpam-1580	64	12	be	be	VERB
ejpam-1580	64	13	$	$	SYM
ejpam-1580	64	14	r1,r2	r1,r2	PROPN
ejpam-1580	64	15	,	,	PUNCT
ejpam-1580	64	16	.	.	PUNCT
ejpam-1580	64	17	.	.	PUNCT
ejpam-1580	65	1	.	.	PUNCT
ejpam-1580	66	1	,	,	PUNCT
ejpam-1580	66	2	rn	rn	PROPN
ejpam-1580	66	3	%	%	INTJ
ejpam-1580	66	4	.	.	PUNCT
ejpam-1580	67	1	then	then	ADV
ejpam-1580	67	2	for	for	ADP
ejpam-1580	67	3	each	each	DET
ejpam-1580	67	4	i	i	NOUN
ejpam-1580	67	5	=	=	NOUN
ejpam-1580	67	6	1,2	1,2	NUM
ejpam-1580	67	7	,	,	PUNCT
ejpam-1580	67	8	.	.	PUNCT
ejpam-1580	67	9	.	.	PUNCT
ejpam-1580	67	10	.	.	PUNCT
ejpam-1580	68	1	,	,	PUNCT
ejpam-1580	68	2	n	n	CCONJ
ejpam-1580	68	3	the	the	DET
ejpam-1580	68	4	sequence	sequence	NOUN
ejpam-1580	68	5	l	l	NOUN
ejpam-1580	68	6	(	(	PUNCT
ejpam-1580	68	7	1	1	X
ejpam-1580	68	8	)	)	PUNCT
ejpam-1580	68	9	i	i	PRON
ejpam-1580	68	10	,	,	PUNCT
ejpam-1580	68	11	l	l	X
ejpam-1580	68	12	(	(	PUNCT
ejpam-1580	68	13	2	2	X
ejpam-1580	68	14	)	)	PUNCT
ejpam-1580	68	15	i	i	PRON
ejpam-1580	68	16	,	,	PUNCT
ejpam-1580	68	17	.	.	PUNCT
ejpam-1580	68	18	.	.	PUNCT
ejpam-1580	69	1	.	.	PUNCT
ejpam-1580	70	1	,	,	PUNCT
ejpam-1580	70	2	l	l	NOUN
ejpam-1580	70	3	(	(	PUNCT
ejpam-1580	70	4	p	p	X
ejpam-1580	70	5	)	)	PUNCT
ejpam-1580	70	6	i	i	PRON
ejpam-1580	70	7	,	,	PUNCT
ejpam-1580	70	8	.	.	PUNCT
ejpam-1580	70	9	.	.	PUNCT
ejpam-1580	70	10	.	.	PUNCT
ejpam-1580	71	1	is	be	AUX
ejpam-1580	71	2	defined	define	VERB
ejpam-1580	71	3	as	as	SCONJ
ejpam-1580	71	4	follows	follow	VERB
ejpam-1580	71	5	:	:	PUNCT
ejpam-1580	71	6	fix	fix	VERB
ejpam-1580	71	7	#	#	NOUN
ejpam-1580	71	8	#	#	NOUN
ejpam-1580	71	9	!	!	PUNCT
ejpam-1580	72	1	,	,	PUNCT
ejpam-1580	72	2	let	let	VERB
ejpam-1580	72	3	l	l	NOUN
ejpam-1580	72	4	(	(	PUNCT
ejpam-1580	72	5	1	1	X
ejpam-1580	72	6	)	)	PUNCT
ejpam-1580	72	7	i	i	NOUN
ejpam-1580	72	8	=	=	PUNCT
ejpam-1580	73	1	r#i	r#i	PROPN
ejpam-1580	73	2	and	and	CCONJ
ejpam-1580	73	3	for	for	ADP
ejpam-1580	73	4	each	each	DET
ejpam-1580	73	5	p	p	NOUN
ejpam-1580	73	6	'	'	PUNCT
ejpam-1580	73	7	2	2	NUM
ejpam-1580	73	8	,	,	PUNCT
ejpam-1580	73	9	let	let	VERB
ejpam-1580	73	10	l	l	NOUN
ejpam-1580	73	11	(	(	PUNCT
ejpam-1580	73	12	p	p	X
ejpam-1580	73	13	)	)	PUNCT
ejpam-1580	73	14	i	i	NOUN
ejpam-1580	73	15	=	=	PUNCT
ejpam-1580	73	16	)	)	PUNCT
ejpam-1580	74	1	i	i	PRON
ejpam-1580	74	2	"	"	PUNCT
ejpam-1580	74	3	j	j	PROPN
ejpam-1580	74	4	1	1	NUM
ejpam-1580	74	5	#	#	NOUN
ejpam-1580	74	6	didj	didj	NOUN
ejpam-1580	74	7	l	l	NOUN
ejpam-1580	74	8	(	(	PUNCT
ejpam-1580	74	9	p)1	p)1	PROPN
ejpam-1580	74	10	)	)	PUNCT
ejpam-1580	74	11	j	j	PROPN
ejpam-1580	74	12	.	.	PUNCT
ejpam-1580	75	1	definition	definition	NOUN
ejpam-1580	75	2	4	4	NUM
ejpam-1580	75	3	.	.	PUNCT
ejpam-1580	76	1	[	[	X
ejpam-1580	76	2	15	15	NUM
ejpam-1580	76	3	]	]	PUNCT
ejpam-1580	76	4	let	let	VERB
ejpam-1580	76	5	g	g	PRON
ejpam-1580	76	6	be	be	AUX
ejpam-1580	76	7	a	a	DET
ejpam-1580	76	8	graph	graph	NOUN
ejpam-1580	76	9	with	with	ADP
ejpam-1580	76	10	randíc	randíc	NOUN
ejpam-1580	76	11	matrix	matrix	NOUN
ejpam-1580	76	12	r	r	NOUN
ejpam-1580	76	13	.	.	PUNCT
ejpam-1580	77	1	then	then	ADV
ejpam-1580	77	2	the	the	DET
ejpam-1580	77	3	randíc	randíc	PROPN
ejpam-1580	77	4	index	index	NOUN
ejpam-1580	77	5	of	of	ADP
ejpam-1580	77	6	g	g	NOUN
ejpam-1580	77	7	,	,	PUNCT
ejpam-1580	77	8	denoted	denote	VERB
ejpam-1580	77	9	by	by	ADP
ejpam-1580	77	10	r	r	NOUN
ejpam-1580	77	11	(	(	PUNCT
ejpam-1580	77	12	g	g	NOUN
ejpam-1580	77	13	)	)	PUNCT
ejpam-1580	77	14	is	be	AUX
ejpam-1580	77	15	given	give	VERB
ejpam-1580	77	16	by	by	ADP
ejpam-1580	77	17	r	r	NOUN
ejpam-1580	77	18	(	(	PUNCT
ejpam-1580	77	19	g	g	NOUN
ejpam-1580	77	20	)	)	PUNCT
ejpam-1580	77	21	=	=	SYM
ejpam-1580	78	1	1	1	NUM
ejpam-1580	78	2	2	2	NUM
ejpam-1580	78	3	n	n	NOUN
ejpam-1580	78	4	)	)	PUNCT
ejpam-1580	78	5	i=1	i=1	PROPN
ejpam-1580	78	6	ri	ri	PROPN
ejpam-1580	78	7	.	.	PUNCT
ejpam-1580	79	1	lemma	lemma	PROPN
ejpam-1580	79	2	1	1	NUM
ejpam-1580	79	3	.	.	PUNCT
ejpam-1580	80	1	[	[	X
ejpam-1580	80	2	1	1	X
ejpam-1580	80	3	]	]	PUNCT
ejpam-1580	80	4	let	let	VERB
ejpam-1580	80	5	g	g	PRON
ejpam-1580	80	6	be	be	AUX
ejpam-1580	80	7	a	a	DET
ejpam-1580	80	8	graph	graph	NOUN
ejpam-1580	80	9	with	with	ADP
ejpam-1580	80	10	n	n	ADP
ejpam-1580	80	11	vertices	vertex	NOUN
ejpam-1580	80	12	and	and	CCONJ
ejpam-1580	80	13	randíc	randíc	PROPN
ejpam-1580	80	14	matrix	matrix	NOUN
ejpam-1580	80	15	r.	r.	PROPN
ejpam-1580	80	16	then	then	ADV
ejpam-1580	80	17	tr	tr	PUNCT
ejpam-1580	80	18	(	(	PUNCT
ejpam-1580	80	19	r	r	NOUN
ejpam-1580	80	20	)	)	PUNCT
ejpam-1580	80	21	=	=	SYM
ejpam-1580	80	22	n	n	NOUN
ejpam-1580	80	23	)	)	PUNCT
ejpam-1580	80	24	i=1	i=1	VERB
ejpam-1580	81	1	"	"	PUNCT
ejpam-1580	81	2	i	i	NOUN
ejpam-1580	81	3	=	=	PUNCT
ejpam-1580	81	4	0	0	NUM
ejpam-1580	81	5	and	and	CCONJ
ejpam-1580	81	6	tr	tr	VERB
ejpam-1580	81	7	+	+	NUM
ejpam-1580	81	8	r2	r2	NOUN
ejpam-1580	81	9	,	,	PUNCT
ejpam-1580	81	10	=	=	SYM
ejpam-1580	81	11	n	n	NOUN
ejpam-1580	81	12	)	)	PUNCT
ejpam-1580	81	13	i=1	i=1	VERB
ejpam-1580	82	1	"	"	PUNCT
ejpam-1580	82	2	2	2	NUM
ejpam-1580	82	3	i	i	NOUN
ejpam-1580	82	4	=	=	NOUN
ejpam-1580	82	5	2	2	X
ejpam-1580	82	6	)	)	PUNCT
ejpam-1580	82	7	i	i	PRON
ejpam-1580	82	8	"	"	PUNCT
ejpam-1580	82	9	j	j	PROPN
ejpam-1580	82	10	1	1	NUM
ejpam-1580	82	11	didj	didj	NOUN
ejpam-1580	82	12	.	.	PUNCT
ejpam-1580	83	1	lemma	lemma	PROPN
ejpam-1580	83	2	2	2	NUM
ejpam-1580	83	3	.	.	PUNCT
ejpam-1580	84	1	[	[	X
ejpam-1580	84	2	2	2	X
ejpam-1580	84	3	]	]	PUNCT
ejpam-1580	84	4	let	let	VERB
ejpam-1580	84	5	g	g	PRON
ejpam-1580	84	6	be	be	AUX
ejpam-1580	84	7	a	a	DET
ejpam-1580	84	8	connected	connected	ADJ
ejpam-1580	84	9	graph	graph	NOUN
ejpam-1580	84	10	#	#	NOUN
ejpam-1580	84	11	be	be	AUX
ejpam-1580	84	12	a	a	DET
ejpam-1580	84	13	real	real	ADJ
ejpam-1580	84	14	number	number	NOUN
ejpam-1580	84	15	and	and	CCONJ
ejpam-1580	84	16	p	p	NOUN
ejpam-1580	84	17	be	be	AUX
ejpam-1580	84	18	an	an	DET
ejpam-1580	84	19	integer	integer	NOUN
ejpam-1580	84	20	.	.	PUNCT
ejpam-1580	85	1	then	then	ADV
ejpam-1580	85	2	"	"	PUNCT
ejpam-1580	85	3	1	1	NUM
ejpam-1580	85	4	'	'	PUNCT
ejpam-1580	85	5	sp+1	sp+1	NUM
ejpam-1580	85	6	sp	sp	NOUN
ejpam-1580	85	7	.	.	PUNCT
ejpam-1580	85	8	where	where	SCONJ
ejpam-1580	85	9	sp	sp	ADP
ejpam-1580	85	10	=	=	NOUN
ejpam-1580	85	11	n	n	NOUN
ejpam-1580	85	12	.	.	PUNCT
ejpam-1580	86	1	i=1	i=1	X
ejpam-1580	86	2	/	/	SYM
ejpam-1580	86	3	l	l	NOUN
ejpam-1580	86	4	(	(	PUNCT
ejpam-1580	86	5	p	p	X
ejpam-1580	86	6	)	)	PUNCT
ejpam-1580	86	7	i	i	PRON
ejpam-1580	86	8	02	02	NUM
ejpam-1580	86	9	.	.	PUNCT
ejpam-1580	87	1	moreover	moreover	ADV
ejpam-1580	87	2	,	,	PUNCT
ejpam-1580	87	3	the	the	DET
ejpam-1580	87	4	equality	equality	NOUN
ejpam-1580	87	5	holds	hold	VERB
ejpam-1580	87	6	for	for	ADP
ejpam-1580	87	7	particular	particular	ADJ
ejpam-1580	87	8	values	value	NOUN
ejpam-1580	87	9	of	of	ADP
ejpam-1580	87	10	#	#	NOUN
ejpam-1580	87	11	and	and	CCONJ
ejpam-1580	87	12	p	p	NOUN
ejpam-1580	87	13	if	if	SCONJ
ejpam-1580	88	1	and	and	CCONJ
ejpam-1580	88	2	only	only	ADV
ejpam-1580	88	3	if	if	SCONJ
ejpam-1580	88	4	l	l	PROPN
ejpam-1580	88	5	(	(	PUNCT
ejpam-1580	88	6	p+1	p+1	NOUN
ejpam-1580	88	7	)	)	PUNCT
ejpam-1580	88	8	1	1	NUM
ejpam-1580	88	9	l	l	NOUN
ejpam-1580	88	10	(	(	PUNCT
ejpam-1580	88	11	p	p	NOUN
ejpam-1580	88	12	)	)	PUNCT
ejpam-1580	88	13	1	1	NUM
ejpam-1580	88	14	=	=	SYM
ejpam-1580	88	15	l	l	NOUN
ejpam-1580	88	16	(	(	PUNCT
ejpam-1580	88	17	p+1	p+1	NOUN
ejpam-1580	88	18	)	)	PUNCT
ejpam-1580	88	19	2	2	NUM
ejpam-1580	88	20	l	l	NOUN
ejpam-1580	88	21	(	(	PUNCT
ejpam-1580	88	22	p	p	NOUN
ejpam-1580	88	23	)	)	PUNCT
ejpam-1580	88	24	2	2	NUM
ejpam-1580	88	25	=	=	SYM
ejpam-1580	88	26	·	·	PUNCT
ejpam-1580	88	27	·	·	PUNCT
ejpam-1580	88	28	·	·	PUNCT
ejpam-1580	89	1	=	=	SYM
ejpam-1580	89	2	l	l	NOUN
ejpam-1580	89	3	(	(	PUNCT
ejpam-1580	89	4	p+1	p+1	NOUN
ejpam-1580	89	5	)	)	PUNCT
ejpam-1580	89	6	n	n	PRON
ejpam-1580	89	7	l	l	NOUN
ejpam-1580	89	8	(	(	PUNCT
ejpam-1580	89	9	p	p	NOUN
ejpam-1580	89	10	)	)	PUNCT
ejpam-1580	89	11	n	n	NOUN
ejpam-1580	89	12	.	.	PUNCT
ejpam-1580	90	1	ş.	ş.	PROPN
ejpam-1580	90	2	bozkurt	bozkurt	PROPN
ejpam-1580	90	3	and	and	CCONJ
ejpam-1580	90	4	d.	d.	PROPN
ejpam-1580	90	5	bozkurt	bozkurt	PROPN
ejpam-1580	90	6	/	/	SYM
ejpam-1580	90	7	eur	eur	PROPN
ejpam-1580	90	8	.	.	PUNCT
ejpam-1580	91	1	j.	j.	PROPN
ejpam-1580	91	2	pure	pure	PROPN
ejpam-1580	91	3	appl	appl	PROPN
ejpam-1580	91	4	.	.	PROPN
ejpam-1580	91	5	math	math	PROPN
ejpam-1580	91	6	,	,	PUNCT
ejpam-1580	91	7	5	5	NUM
ejpam-1580	91	8	(	(	PUNCT
ejpam-1580	91	9	2012	2012	NUM
ejpam-1580	91	10	)	)	PUNCT
ejpam-1580	91	11	,	,	PUNCT
ejpam-1580	91	12	88	88	NUM
ejpam-1580	91	13	-	-	SYM
ejpam-1580	91	14	96	96	NUM
ejpam-1580	91	15	91	91	NUM
ejpam-1580	91	16	lemma	lemma	PROPN
ejpam-1580	91	17	3	3	X
ejpam-1580	91	18	.	.	PUNCT
ejpam-1580	92	1	[	[	X
ejpam-1580	92	2	2	2	X
ejpam-1580	92	3	]	]	PUNCT
ejpam-1580	92	4	a	a	DET
ejpam-1580	92	5	simple	simple	ADJ
ejpam-1580	92	6	connected	connected	ADJ
ejpam-1580	92	7	graph	graph	NOUN
ejpam-1580	92	8	g	g	PROPN
ejpam-1580	92	9	has	have	VERB
ejpam-1580	92	10	two	two	NUM
ejpam-1580	92	11	distinct	distinct	ADJ
ejpam-1580	92	12	randíc	randíc	NOUN
ejpam-1580	92	13	eigenvalues	eigenvalue	VERB
ejpam-1580	92	14	if	if	SCONJ
ejpam-1580	92	15	and	and	CCONJ
ejpam-1580	92	16	only	only	ADV
ejpam-1580	92	17	if	if	SCONJ
ejpam-1580	92	18	g	g	PROPN
ejpam-1580	92	19	is	be	AUX
ejpam-1580	92	20	complete	complete	ADJ
ejpam-1580	92	21	.	.	PUNCT
ejpam-1580	93	1	2	2	X
ejpam-1580	93	2	.	.	NUM
ejpam-1580	93	3	bounds	bound	NOUN
ejpam-1580	93	4	for	for	ADP
ejpam-1580	93	5	the	the	DET
ejpam-1580	93	6	randić	randić	ADJ
ejpam-1580	93	7	energy	energy	NOUN
ejpam-1580	93	8	of	of	ADP
ejpam-1580	93	9	a	a	DET
ejpam-1580	93	10	graph	graph	NOUN
ejpam-1580	93	11	in	in	ADP
ejpam-1580	93	12	this	this	DET
ejpam-1580	93	13	section	section	NOUN
ejpam-1580	93	14	,	,	PUNCT
ejpam-1580	93	15	we	we	PRON
ejpam-1580	93	16	obtain	obtain	VERB
ejpam-1580	93	17	lower	low	ADJ
ejpam-1580	93	18	and	and	CCONJ
ejpam-1580	93	19	upper	upper	ADJ
ejpam-1580	93	20	bounds	bound	NOUN
ejpam-1580	93	21	for	for	ADP
ejpam-1580	93	22	the	the	DET
ejpam-1580	93	23	randić	randić	ADJ
ejpam-1580	93	24	energy	energy	NOUN
ejpam-1580	93	25	of	of	ADP
ejpam-1580	93	26	connected	connected	ADJ
ejpam-1580	93	27	(	(	PUNCT
ejpam-1580	93	28	n	n	CCONJ
ejpam-1580	93	29	,	,	PUNCT
ejpam-1580	93	30	m)-graph	m)-graph	NOUN
ejpam-1580	93	31	g.	g.	PROPN
ejpam-1580	93	32	let	let	VERB
ejpam-1580	93	33	n	n	NOUN
ejpam-1580	93	34	and	and	CCONJ
ejpam-1580	93	35	m	m	AUX
ejpam-1580	93	36	be	be	AUX
ejpam-1580	93	37	two	two	NUM
ejpam-1580	93	38	positive	positive	ADJ
ejpam-1580	93	39	integers	integer	NOUN
ejpam-1580	93	40	.	.	PUNCT
ejpam-1580	94	1	we	we	PRON
ejpam-1580	94	2	first	first	ADV
ejpam-1580	94	3	consider	consider	VERB
ejpam-1580	94	4	the	the	DET
ejpam-1580	94	5	following	follow	VERB
ejpam-1580	94	6	auxiliary	auxiliary	ADJ
ejpam-1580	94	7	quantity	quantity	NOUN
ejpam-1580	94	8	q	q	NOUN
ejpam-1580	94	9	as	as	ADP
ejpam-1580	94	10	q	q	NOUN
ejpam-1580	94	11	=	=	X
ejpam-1580	94	12	q	q	X
ejpam-1580	94	13	(	(	PUNCT
ejpam-1580	94	14	g	g	NOUN
ejpam-1580	94	15	)	)	PUNCT
ejpam-1580	94	16	=	=	SYM
ejpam-1580	95	1	n	n	X
ejpam-1580	95	2	)	)	PUNCT
ejpam-1580	95	3	i=1	i=1	PROPN
ejpam-1580	96	1	qi	qi	PROPN
ejpam-1580	96	2	(	(	PUNCT
ejpam-1580	96	3	7	7	NUM
ejpam-1580	96	4	)	)	PUNCT
ejpam-1580	96	5	where	where	SCONJ
ejpam-1580	96	6	qi	qi	PROPN
ejpam-1580	96	7	,	,	PUNCT
ejpam-1580	96	8	i	i	NOUN
ejpam-1580	96	9	=	=	NOUN
ejpam-1580	96	10	1,2	1,2	NUM
ejpam-1580	96	11	,	,	PUNCT
ejpam-1580	96	12	.	.	PUNCT
ejpam-1580	96	13	.	.	PUNCT
ejpam-1580	96	14	.	.	PUNCT
ejpam-1580	97	1	,	,	PUNCT
ejpam-1580	97	2	n	n	PRON
ejpam-1580	97	3	are	be	AUX
ejpam-1580	97	4	some	some	DET
ejpam-1580	97	5	numbers	number	NOUN
ejpam-1580	97	6	which	which	PRON
ejpam-1580	97	7	some	some	PRON
ejpam-1580	97	8	how	how	SCONJ
ejpam-1580	97	9	can	can	AUX
ejpam-1580	97	10	be	be	AUX
ejpam-1580	97	11	computed	compute	VERB
ejpam-1580	97	12	from	from	ADP
ejpam-1580	97	13	the	the	DET
ejpam-1580	97	14	graph	graph	NOUN
ejpam-1580	97	15	g.	g.	NOUN
ejpam-1580	97	16	for	for	ADP
ejpam-1580	97	17	which	which	PRON
ejpam-1580	97	18	we	we	PRON
ejpam-1580	97	19	only	only	ADV
ejpam-1580	97	20	need	need	VERB
ejpam-1580	97	21	to	to	PART
ejpam-1580	97	22	know	know	VERB
ejpam-1580	97	23	that	that	SCONJ
ejpam-1580	97	24	they	they	PRON
ejpam-1580	97	25	satisfy	satisfy	VERB
ejpam-1580	97	26	the	the	DET
ejpam-1580	97	27	conditions	condition	NOUN
ejpam-1580	97	28	qi	qi	NOUN
ejpam-1580	97	29	'	'	PART
ejpam-1580	97	30	0	0	NUM
ejpam-1580	97	31	,	,	PUNCT
ejpam-1580	97	32	for	for	ADP
ejpam-1580	97	33	all	all	DET
ejpam-1580	97	34	i	i	NOUN
ejpam-1580	97	35	=	=	SYM
ejpam-1580	97	36	1,2	1,2	NUM
ejpam-1580	97	37	,	,	PUNCT
ejpam-1580	97	38	.	.	PUNCT
ejpam-1580	97	39	.	.	PUNCT
ejpam-1580	98	1	.	.	PUNCT
ejpam-1580	99	1	,	,	PUNCT
ejpam-1580	99	2	n	n	PROPN
ejpam-1580	99	3	and	and	CCONJ
ejpam-1580	99	4	n	n	CCONJ
ejpam-1580	99	5	)	)	PUNCT
ejpam-1580	99	6	i=1	i=1	PROPN
ejpam-1580	99	7	!	!	PUNCT
ejpam-1580	100	1	qi	qi	NOUN
ejpam-1580	100	2	"	"	PUNCT
ejpam-1580	100	3	2	2	NUM
ejpam-1580	100	4	=	=	SYM
ejpam-1580	100	5	2	2	NUM
ejpam-1580	100	6	m	m	NOUN
ejpam-1580	100	7	(	(	PUNCT
ejpam-1580	100	8	8)	8)	NUM
ejpam-1580	100	9	or	or	CCONJ
ejpam-1580	100	10	,	,	PUNCT
ejpam-1580	100	11	the	the	DET
ejpam-1580	100	12	conditions	condition	NOUN
ejpam-1580	100	13	(	(	PUNCT
ejpam-1580	100	14	7	7	NUM
ejpam-1580	100	15	)	)	PUNCT
ejpam-1580	100	16	,	,	PUNCT
ejpam-1580	100	17	(	(	PUNCT
ejpam-1580	100	18	8)	8)	NUM
ejpam-1580	100	19	and	and	CCONJ
ejpam-1580	100	20	p	p	NOUN
ejpam-1580	100	21	=	=	NOUN
ejpam-1580	100	22	p	p	X
ejpam-1580	100	23	(	(	PUNCT
ejpam-1580	100	24	g	g	NOUN
ejpam-1580	100	25	)	)	PUNCT
ejpam-1580	100	26	=	=	SYM
ejpam-1580	100	27	n	n	PRON
ejpam-1580	100	28	1	1	NUM
ejpam-1580	100	29	i=1	i=1	PROPN
ejpam-1580	100	30	qi	qi	PROPN
ejpam-1580	100	31	(	(	PUNCT
ejpam-1580	100	32	9	9	NUM
ejpam-1580	100	33	)	)	PUNCT
ejpam-1580	100	34	if	if	SCONJ
ejpam-1580	100	35	all	all	DET
ejpam-1580	100	36	the	the	DET
ejpam-1580	100	37	conditions	condition	NOUN
ejpam-1580	100	38	(	(	PUNCT
ejpam-1580	100	39	7)-(9	7)-(9	NOUN
ejpam-1580	100	40	)	)	PUNCT
ejpam-1580	100	41	are	be	AUX
ejpam-1580	100	42	taken	take	VERB
ejpam-1580	100	43	into	into	ADP
ejpam-1580	100	44	account	account	NOUN
ejpam-1580	100	45	then	then	ADV
ejpam-1580	100	46	[	[	X
ejpam-1580	100	47	11	11	NUM
ejpam-1580	100	48	]	]	PUNCT
ejpam-1580	100	49	#	#	NOUN
ejpam-1580	100	50	2mn	2mn	NOUN
ejpam-1580	100	51	)	)	PUNCT
ejpam-1580	100	52	(	(	PUNCT
ejpam-1580	100	53	n	n	X
ejpam-1580	100	54	)	)	PUNCT
ejpam-1580	100	55	1)d	1)d	NUM
ejpam-1580	101	1	*	*	PUNCT
ejpam-1580	101	2	q	q	PUNCT
ejpam-1580	101	3	*	*	PUNCT
ejpam-1580	101	4	#	#	NOUN
ejpam-1580	101	5	2mn	2mn	NOUN
ejpam-1580	101	6	)	)	PUNCT
ejpam-1580	102	1	d	d	X
ejpam-1580	102	2	(	(	PUNCT
ejpam-1580	102	3	10	10	NUM
ejpam-1580	102	4	)	)	PUNCT
ejpam-1580	102	5	where	where	SCONJ
ejpam-1580	102	6	d	d	NOUN
ejpam-1580	102	7	=	=	SYM
ejpam-1580	102	8	2	2	NUM
ejpam-1580	102	9	m	m	NOUN
ejpam-1580	102	10	)	)	PUNCT
ejpam-1580	103	1	n	n	CCONJ
ejpam-1580	103	2	p2	p2	NOUN
ejpam-1580	103	3	/	/	SYM
ejpam-1580	103	4	n	n	NOUN
ejpam-1580	103	5	.	.	PUNCT
ejpam-1580	104	1	(	(	PUNCT
ejpam-1580	104	2	11	11	NUM
ejpam-1580	104	3	)	)	PUNCT
ejpam-1580	104	4	for	for	ADP
ejpam-1580	104	5	the	the	DET
ejpam-1580	104	6	graph	graph	NOUN
ejpam-1580	104	7	energy	energy	NOUN
ejpam-1580	104	8	(	(	PUNCT
ejpam-1580	104	9	namely	namely	ADV
ejpam-1580	104	10	by	by	SCONJ
ejpam-1580	104	11	setting	set	VERB
ejpam-1580	104	12	into	into	ADP
ejpam-1580	104	13	(	(	PUNCT
ejpam-1580	104	14	10	10	NUM
ejpam-1580	104	15	)	)	PUNCT
ejpam-1580	104	16	and	and	CCONJ
ejpam-1580	104	17	(	(	PUNCT
ejpam-1580	104	18	11	11	NUM
ejpam-1580	104	19	)	)	PUNCT
ejpam-1580	104	20	n	n	NOUN
ejpam-1580	104	21	=	=	SYM
ejpam-1580	104	22	n	n	CCONJ
ejpam-1580	104	23	,	,	PUNCT
ejpam-1580	104	24	m	m	VERB
ejpam-1580	104	25	=	=	NOUN
ejpam-1580	104	26	m	m	PROPN
ejpam-1580	104	27	and	and	CCONJ
ejpam-1580	104	28	p	p	NOUN
ejpam-1580	104	29	=	=	PROPN
ejpam-1580	104	30	|det	|det	NOUN
ejpam-1580	104	31	a|	a|	PROPN
ejpam-1580	104	32	)	)	PUNCT
ejpam-1580	104	33	,	,	PUNCT
ejpam-1580	104	34	this	this	DET
ejpam-1580	104	35	yields	yield	NOUN
ejpam-1580	104	36	[	[	X
ejpam-1580	104	37	11	11	NUM
ejpam-1580	104	38	]	]	SYM
ejpam-1580	104	39	2	2	NUM
ejpam-1580	104	40	2m+	2m+	NUM
ejpam-1580	104	41	n	n	NOUN
ejpam-1580	104	42	(	(	PUNCT
ejpam-1580	104	43	n	n	CCONJ
ejpam-1580	104	44	)	)	PUNCT
ejpam-1580	104	45	1	1	NUM
ejpam-1580	104	46	)	)	PUNCT
ejpam-1580	104	47	|det	|det	NOUN
ejpam-1580	104	48	a|2	a|2	PROPN
ejpam-1580	104	49	/	/	SYM
ejpam-1580	104	50	n	n	PROPN
ejpam-1580	104	51	*	*	PUNCT
ejpam-1580	104	52	e	e	X
ejpam-1580	104	53	(	(	PUNCT
ejpam-1580	104	54	g	g	NOUN
ejpam-1580	104	55	)	)	PUNCT
ejpam-1580	104	56	*	*	NOUN
ejpam-1580	104	57	2	2	NUM
ejpam-1580	104	58	2	2	NUM
ejpam-1580	104	59	m	m	NOUN
ejpam-1580	104	60	(	(	PUNCT
ejpam-1580	104	61	n	n	CCONJ
ejpam-1580	104	62	)	)	PUNCT
ejpam-1580	104	63	1	1	NUM
ejpam-1580	104	64	)	)	PUNCT
ejpam-1580	104	65	+	+	NUM
ejpam-1580	104	66	n	n	CCONJ
ejpam-1580	104	67	|det	|det	NOUN
ejpam-1580	104	68	a|2	a|2	PROPN
ejpam-1580	104	69	/	/	SYM
ejpam-1580	104	70	n.	n.	NOUN
ejpam-1580	104	71	the	the	DET
ejpam-1580	104	72	randić	randić	NOUN
ejpam-1580	104	73	energy	energy	NOUN
ejpam-1580	104	74	-	-	PUNCT
ejpam-1580	104	75	counterpart	counterpart	NOUN
ejpam-1580	104	76	of	of	ADP
ejpam-1580	104	77	the	the	DET
ejpam-1580	104	78	estimates	estimate	NOUN
ejpam-1580	104	79	(	(	PUNCT
ejpam-1580	104	80	10	10	NUM
ejpam-1580	104	81	)	)	PUNCT
ejpam-1580	104	82	and	and	CCONJ
ejpam-1580	104	83	(	(	PUNCT
ejpam-1580	104	84	11	11	NUM
ejpam-1580	104	85	)	)	PUNCT
ejpam-1580	104	86	is	be	AUX
ejpam-1580	104	87	obtained	obtain	VERB
ejpam-1580	104	88	as	as	ADP
ejpam-1580	104	89	the	the	DET
ejpam-1580	104	90	following	follow	VERB
ejpam-1580	104	91	result	result	NOUN
ejpam-1580	104	92	.	.	PUNCT
ejpam-1580	105	1	theorem	theorem	NOUN
ejpam-1580	105	2	1	1	X
ejpam-1580	105	3	.	.	PUNCT
ejpam-1580	106	1	let	let	VERB
ejpam-1580	106	2	g	g	PRON
ejpam-1580	106	3	be	be	AUX
ejpam-1580	106	4	a	a	DET
ejpam-1580	106	5	connected	connect	VERB
ejpam-1580	106	6	(	(	PUNCT
ejpam-1580	106	7	n	n	CCONJ
ejpam-1580	106	8	,	,	PUNCT
ejpam-1580	106	9	m)-graph	m)-graph	NOUN
ejpam-1580	106	10	and	and	CCONJ
ejpam-1580	106	11	!	!	PUNCT
ejpam-1580	107	1	be	be	AUX
ejpam-1580	107	2	the	the	DET
ejpam-1580	107	3	absolute	absolute	ADJ
ejpam-1580	107	4	value	value	NOUN
ejpam-1580	107	5	of	of	ADP
ejpam-1580	107	6	the	the	DET
ejpam-1580	107	7	determinant	determinant	NOUN
ejpam-1580	107	8	of	of	ADP
ejpam-1580	107	9	the	the	DET
ejpam-1580	107	10	randíc	randíc	PROPN
ejpam-1580	107	11	matrix	matrix	NOUN
ejpam-1580	107	12	r.	r.	PROPN
ejpam-1580	107	13	then	then	ADV
ejpam-1580	107	14	re	re	PROPN
ejpam-1580	107	15	(	(	PUNCT
ejpam-1580	107	16	g	g	NOUN
ejpam-1580	107	17	)	)	PUNCT
ejpam-1580	107	18	'	'	PART
ejpam-1580	107	19	3	3	NUM
ejpam-1580	107	20	2	2	NUM
ejpam-1580	107	21	)	)	PUNCT
ejpam-1580	108	1	i	i	PRON
ejpam-1580	108	2	"	"	PUNCT
ejpam-1580	108	3	j	j	PROPN
ejpam-1580	108	4	1	1	NUM
ejpam-1580	108	5	didj	didj	NOUN
ejpam-1580	108	6	+	+	CCONJ
ejpam-1580	108	7	n	n	CCONJ
ejpam-1580	108	8	(	(	PUNCT
ejpam-1580	108	9	n	n	CCONJ
ejpam-1580	108	10	)	)	PUNCT
ejpam-1580	108	11	1)!2	1)!2	NUM
ejpam-1580	108	12	/	/	SYM
ejpam-1580	108	13	n	n	PROPN
ejpam-1580	108	14	(	(	PUNCT
ejpam-1580	108	15	12	12	NUM
ejpam-1580	108	16	)	)	PUNCT
ejpam-1580	108	17	ş.	ş.	PROPN
ejpam-1580	108	18	bozkurt	bozkurt	PROPN
ejpam-1580	108	19	and	and	CCONJ
ejpam-1580	108	20	d.	d.	PROPN
ejpam-1580	108	21	bozkurt	bozkurt	PROPN
ejpam-1580	108	22	/	/	SYM
ejpam-1580	108	23	eur	eur	PROPN
ejpam-1580	108	24	.	.	PUNCT
ejpam-1580	109	1	j.	j.	PROPN
ejpam-1580	109	2	pure	pure	PROPN
ejpam-1580	109	3	appl	appl	PROPN
ejpam-1580	109	4	.	.	PROPN
ejpam-1580	109	5	math	math	PROPN
ejpam-1580	109	6	,	,	PUNCT
ejpam-1580	109	7	5	5	NUM
ejpam-1580	109	8	(	(	PUNCT
ejpam-1580	109	9	2012	2012	NUM
ejpam-1580	109	10	)	)	PUNCT
ejpam-1580	109	11	,	,	PUNCT
ejpam-1580	109	12	88	88	NUM
ejpam-1580	109	13	-	-	SYM
ejpam-1580	109	14	96	96	NUM
ejpam-1580	109	15	92	92	NUM
ejpam-1580	109	16	and	and	CCONJ
ejpam-1580	109	17	re	re	ADJ
ejpam-1580	109	18	(	(	PUNCT
ejpam-1580	109	19	g	g	NOUN
ejpam-1580	109	20	)	)	PUNCT
ejpam-1580	109	21	*	*	SYM
ejpam-1580	109	22	3	3	NUM
ejpam-1580	109	23	2	2	NUM
ejpam-1580	109	24	(	(	PUNCT
ejpam-1580	109	25	n	n	CCONJ
ejpam-1580	109	26	)	)	PUNCT
ejpam-1580	109	27	1	1	NUM
ejpam-1580	109	28	)	)	PUNCT
ejpam-1580	109	29	)	)	PUNCT
ejpam-1580	110	1	i	i	PRON
ejpam-1580	110	2	"	"	PUNCT
ejpam-1580	110	3	j	j	PROPN
ejpam-1580	110	4	1	1	NUM
ejpam-1580	110	5	didj	didj	NOUN
ejpam-1580	110	6	+	+	CCONJ
ejpam-1580	110	7	n!2	n!2	NUM
ejpam-1580	110	8	/	/	SYM
ejpam-1580	110	9	n.	n.	NOUN
ejpam-1580	110	10	(	(	PUNCT
ejpam-1580	110	11	13	13	NUM
ejpam-1580	110	12	)	)	PUNCT
ejpam-1580	110	13	proof	proof	NOUN
ejpam-1580	110	14	.	.	PUNCT
ejpam-1580	111	1	the	the	DET
ejpam-1580	111	2	result	result	NOUN
ejpam-1580	111	3	is	be	AUX
ejpam-1580	111	4	easily	easily	ADV
ejpam-1580	111	5	obtained	obtain	VERB
ejpam-1580	111	6	using	use	VERB
ejpam-1580	111	7	the	the	DET
ejpam-1580	111	8	estimates	estimate	NOUN
ejpam-1580	111	9	(	(	PUNCT
ejpam-1580	111	10	10	10	NUM
ejpam-1580	111	11	)	)	PUNCT
ejpam-1580	111	12	,	,	PUNCT
ejpam-1580	111	13	(	(	PUNCT
ejpam-1580	111	14	11	11	NUM
ejpam-1580	111	15	)	)	PUNCT
ejpam-1580	111	16	and	and	CCONJ
ejpam-1580	111	17	lemma	lemma	PROPN
ejpam-1580	111	18	1	1	X
ejpam-1580	111	19	.	.	PUNCT
ejpam-1580	112	1	in	in	ADP
ejpam-1580	112	2	[	[	X
ejpam-1580	112	3	1	1	X
ejpam-1580	112	4	]	]	X
ejpam-1580	112	5	the	the	DET
ejpam-1580	112	6	following	following	ADJ
ejpam-1580	112	7	result	result	NOUN
ejpam-1580	112	8	for	for	ADP
ejpam-1580	112	9	re	re	ADJ
ejpam-1580	112	10	(	(	PUNCT
ejpam-1580	112	11	g	g	NOUN
ejpam-1580	112	12	)	)	PUNCT
ejpam-1580	112	13	was	be	AUX
ejpam-1580	112	14	obtained	obtain	VERB
ejpam-1580	112	15	re	re	ADP
ejpam-1580	112	16	(	(	PUNCT
ejpam-1580	112	17	g	g	NOUN
ejpam-1580	112	18	)	)	PUNCT
ejpam-1580	112	19	*	*	PUNCT
ejpam-1580	112	20	3	3	NUM
ejpam-1580	112	21	2n	2n	NUM
ejpam-1580	112	22	)	)	PUNCT
ejpam-1580	113	1	i	i	PRON
ejpam-1580	113	2	"	"	PUNCT
ejpam-1580	113	3	j	j	PROPN
ejpam-1580	113	4	1	1	NUM
ejpam-1580	113	5	didj	didj	NOUN
ejpam-1580	113	6	(	(	PUNCT
ejpam-1580	113	7	14	14	NUM
ejpam-1580	113	8	)	)	PUNCT
ejpam-1580	113	9	remark	remark	NOUN
ejpam-1580	113	10	1	1	NUM
ejpam-1580	113	11	.	.	PUNCT
ejpam-1580	114	1	the	the	DET
ejpam-1580	114	2	upper	upper	ADJ
ejpam-1580	114	3	bound	bound	ADJ
ejpam-1580	114	4	(	(	PUNCT
ejpam-1580	114	5	13	13	NUM
ejpam-1580	114	6	)	)	PUNCT
ejpam-1580	114	7	is	be	AUX
ejpam-1580	114	8	sharper	sharp	ADJ
ejpam-1580	114	9	than	than	ADP
ejpam-1580	114	10	the	the	DET
ejpam-1580	114	11	upper	upper	ADJ
ejpam-1580	114	12	bound	bound	ADJ
ejpam-1580	114	13	(	(	PUNCT
ejpam-1580	114	14	14	14	NUM
ejpam-1580	114	15	)	)	PUNCT
ejpam-1580	114	16	.	.	PUNCT
ejpam-1580	115	1	using	use	VERB
ejpam-1580	115	2	arithmeticgeometric	arithmeticgeometric	ADJ
ejpam-1580	115	3	mean	mean	ADJ
ejpam-1580	115	4	inequality	inequality	NOUN
ejpam-1580	115	5	,	,	PUNCT
ejpam-1580	115	6	we	we	PRON
ejpam-1580	115	7	obtain	obtain	VERB
ejpam-1580	115	8	2	2	NUM
ejpam-1580	115	9	)	)	PUNCT
ejpam-1580	116	1	i	i	PRON
ejpam-1580	116	2	"	"	PUNCT
ejpam-1580	116	3	j	j	PROPN
ejpam-1580	116	4	1	1	NUM
ejpam-1580	116	5	didj	didj	NOUN
ejpam-1580	116	6	'	'	PUNCT
ejpam-1580	116	7	n!2	n!2	NOUN
ejpam-1580	116	8	/	/	SYM
ejpam-1580	116	9	n	n	CCONJ
ejpam-1580	116	10	and	and	CCONJ
ejpam-1580	116	11	considering	consider	VERB
ejpam-1580	116	12	the	the	DET
ejpam-1580	116	13	upper	upper	ADJ
ejpam-1580	116	14	bound	bind	VERB
ejpam-1580	116	15	(	(	PUNCT
ejpam-1580	116	16	13	13	NUM
ejpam-1580	116	17	)	)	PUNCT
ejpam-1580	116	18	we	we	PRON
ejpam-1580	116	19	arrive	arrive	VERB
ejpam-1580	116	20	at	at	ADP
ejpam-1580	116	21	re	re	PROPN
ejpam-1580	116	22	(	(	PUNCT
ejpam-1580	116	23	g	g	NOUN
ejpam-1580	116	24	)	)	PUNCT
ejpam-1580	116	25	*	*	PUNCT
ejpam-1580	116	26	3	3	NUM
ejpam-1580	116	27	2n	2n	NUM
ejpam-1580	116	28	)	)	PUNCT
ejpam-1580	117	1	i	i	PRON
ejpam-1580	117	2	"	"	PUNCT
ejpam-1580	117	3	j	j	PROPN
ejpam-1580	117	4	1	1	NUM
ejpam-1580	117	5	didj	didj	NOUN
ejpam-1580	117	6	which	which	PRON
ejpam-1580	117	7	is	be	AUX
ejpam-1580	117	8	the	the	DET
ejpam-1580	117	9	upper	upper	ADJ
ejpam-1580	117	10	bound	bound	ADJ
ejpam-1580	117	11	(	(	PUNCT
ejpam-1580	117	12	14	14	NUM
ejpam-1580	117	13	)	)	PUNCT
ejpam-1580	117	14	.	.	PUNCT
ejpam-1580	118	1	3	3	X
ejpam-1580	118	2	.	.	NUM
ejpam-1580	118	3	bounds	bound	NOUN
ejpam-1580	118	4	for	for	ADP
ejpam-1580	118	5	the	the	DET
ejpam-1580	118	6	randić	randić	ADJ
ejpam-1580	118	7	estrada	estrada	PROPN
ejpam-1580	118	8	index	index	NOUN
ejpam-1580	118	9	of	of	ADP
ejpam-1580	118	10	a	a	DET
ejpam-1580	118	11	graph	graph	NOUN
ejpam-1580	118	12	in	in	ADP
ejpam-1580	118	13	this	this	DET
ejpam-1580	118	14	section	section	NOUN
ejpam-1580	118	15	,	,	PUNCT
ejpam-1580	118	16	we	we	PRON
ejpam-1580	118	17	consider	consider	VERB
ejpam-1580	118	18	the	the	DET
ejpam-1580	118	19	randić	randić	NOUN
ejpam-1580	118	20	estrada	estrada	PROPN
ejpam-1580	118	21	index	index	NOUN
ejpam-1580	118	22	of	of	ADP
ejpam-1580	118	23	connected	connected	ADJ
ejpam-1580	118	24	(	(	PUNCT
ejpam-1580	118	25	n	n	CCONJ
ejpam-1580	118	26	,	,	PUNCT
ejpam-1580	118	27	m)-graph	m)-graph	NOUN
ejpam-1580	118	28	g.	g.	NOUN
ejpam-1580	118	29	we	we	PRON
ejpam-1580	118	30	also	also	ADV
ejpam-1580	118	31	adapt	adapt	VERB
ejpam-1580	118	32	the	the	DET
ejpam-1580	118	33	some	some	DET
ejpam-1580	118	34	results	result	NOUN
ejpam-1580	118	35	in	in	ADP
ejpam-1580	118	36	[	[	X
ejpam-1580	118	37	4	4	NUM
ejpam-1580	118	38	]	]	PUNCT
ejpam-1580	118	39	and	and	CCONJ
ejpam-1580	119	1	[	[	X
ejpam-1580	119	2	14	14	NUM
ejpam-1580	119	3	]	]	PUNCT
ejpam-1580	119	4	on	on	ADP
ejpam-1580	119	5	the	the	DET
ejpam-1580	119	6	randić	randić	NOUN
ejpam-1580	119	7	estrada	estrada	PROPN
ejpam-1580	119	8	index	index	PROPN
ejpam-1580	119	9	to	to	PART
ejpam-1580	119	10	give	give	VERB
ejpam-1580	119	11	lower	low	ADJ
ejpam-1580	119	12	and	and	CCONJ
ejpam-1580	119	13	upper	upper	ADJ
ejpam-1580	119	14	bounds	bound	NOUN
ejpam-1580	119	15	for	for	ADP
ejpam-1580	119	16	it	it	PRON
ejpam-1580	119	17	.	.	PUNCT
ejpam-1580	120	1	theorem	theorem	NOUN
ejpam-1580	120	2	2	2	NUM
ejpam-1580	120	3	.	.	PUNCT
ejpam-1580	121	1	let	let	VERB
ejpam-1580	121	2	g	g	PRON
ejpam-1580	121	3	be	be	AUX
ejpam-1580	121	4	a	a	DET
ejpam-1580	121	5	connected	connect	VERB
ejpam-1580	121	6	(	(	PUNCT
ejpam-1580	121	7	n	n	CCONJ
ejpam-1580	121	8	,	,	PUNCT
ejpam-1580	121	9	m)-graph	m)-graph	NOUN
ejpam-1580	121	10	.	.	PUNCT
ejpam-1580	122	1	then	then	ADV
ejpam-1580	122	2	ree(g	ree(g	PROPN
ejpam-1580	122	3	)	)	PUNCT
ejpam-1580	122	4	'	'	PUNCT
ejpam-1580	122	5	e	e	NOUN
ejpam-1580	122	6	4	4	NUM
ejpam-1580	122	7	sp+1	sp+1	NOUN
ejpam-1580	122	8	sp	sp	ADP
ejpam-1580	122	9	+	+	NOUN
ejpam-1580	122	10	n	n	CCONJ
ejpam-1580	122	11	)	)	PUNCT
ejpam-1580	122	12	1	1	NUM
ejpam-1580	122	13	e	e	SYM
ejpam-1580	122	14	1	1	NUM
ejpam-1580	122	15	n)1	n)1	NOUN
ejpam-1580	122	16	4	4	NUM
ejpam-1580	122	17	sp+1	sp+1	NOUN
ejpam-1580	122	18	sp	sp	NOUN
ejpam-1580	122	19	.	.	PUNCT
ejpam-1580	123	1	(	(	PUNCT
ejpam-1580	123	2	15	15	NUM
ejpam-1580	123	3	)	)	PUNCT
ejpam-1580	123	4	where	where	SCONJ
ejpam-1580	123	5	#	#	NOUN
ejpam-1580	123	6	is	be	AUX
ejpam-1580	123	7	a	a	DET
ejpam-1580	123	8	real	real	ADJ
ejpam-1580	123	9	number	number	NOUN
ejpam-1580	123	10	,	,	PUNCT
ejpam-1580	123	11	p	p	NOUN
ejpam-1580	123	12	is	be	AUX
ejpam-1580	123	13	an	an	DET
ejpam-1580	123	14	integer	integer	NOUN
ejpam-1580	123	15	and	and	CCONJ
ejpam-1580	123	16	sp	sp	ADP
ejpam-1580	123	17	=	=	NOUN
ejpam-1580	123	18	n	n	PROPN
ejpam-1580	123	19	.	.	PUNCT
ejpam-1580	124	1	i=1	i=1	X
ejpam-1580	124	2	/	/	SYM
ejpam-1580	124	3	l	l	NOUN
ejpam-1580	124	4	(	(	PUNCT
ejpam-1580	124	5	p	p	X
ejpam-1580	124	6	)	)	PUNCT
ejpam-1580	124	7	i	i	PRON
ejpam-1580	124	8	02	02	NUM
ejpam-1580	124	9	.	.	PUNCT
ejpam-1580	125	1	moreover	moreover	ADV
ejpam-1580	125	2	,	,	PUNCT
ejpam-1580	125	3	the	the	DET
ejpam-1580	125	4	equality	equality	NOUN
ejpam-1580	125	5	holds	hold	VERB
ejpam-1580	125	6	in	in	ADP
ejpam-1580	125	7	(	(	PUNCT
ejpam-1580	125	8	15	15	NUM
ejpam-1580	125	9	)	)	PUNCT
ejpam-1580	125	10	if	if	SCONJ
ejpam-1580	126	1	and	and	CCONJ
ejpam-1580	126	2	only	only	ADV
ejpam-1580	126	3	if	if	SCONJ
ejpam-1580	126	4	g	g	PROPN
ejpam-1580	126	5	is	be	AUX
ejpam-1580	126	6	the	the	DET
ejpam-1580	126	7	complete	complete	ADJ
ejpam-1580	126	8	graph	graph	NOUN
ejpam-1580	126	9	kn	kn	PROPN
ejpam-1580	126	10	.	.	PUNCT
ejpam-1580	127	1	proof	proof	NOUN
ejpam-1580	127	2	.	.	PUNCT
ejpam-1580	128	1	starting	start	VERB
ejpam-1580	128	2	with	with	ADP
ejpam-1580	128	3	the	the	DET
ejpam-1580	128	4	equation	equation	NOUN
ejpam-1580	128	5	(	(	PUNCT
ejpam-1580	128	6	5	5	NUM
ejpam-1580	128	7	)	)	PUNCT
ejpam-1580	128	8	and	and	CCONJ
ejpam-1580	128	9	using	use	VERB
ejpam-1580	128	10	arithmetic	arithmetic	ADJ
ejpam-1580	128	11	-	-	PUNCT
ejpam-1580	128	12	geometric	geometric	ADJ
ejpam-1580	128	13	mean	mean	NOUN
ejpam-1580	128	14	inequality	inequality	NOUN
ejpam-1580	128	15	,	,	PUNCT
ejpam-1580	128	16	we	we	PRON
ejpam-1580	128	17	obtain	obtain	VERB
ejpam-1580	128	18	ree(g	ree(g	NOUN
ejpam-1580	128	19	)	)	PUNCT
ejpam-1580	128	20	=	=	PUNCT
ejpam-1580	129	1	e"1	e"1	PROPN
ejpam-1580	129	2	+	+	NUM
ejpam-1580	129	3	e"2	e"2	NOUN
ejpam-1580	129	4	+	+	X
ejpam-1580	129	5	·	·	PUNCT
ejpam-1580	129	6	·	·	PUNCT
ejpam-1580	129	7	·	·	PUNCT
ejpam-1580	129	8	+	+	NUM
ejpam-1580	129	9	e"n	e"n	PROPN
ejpam-1580	129	10	ş.	ş.	PROPN
ejpam-1580	129	11	bozkurt	bozkurt	PROPN
ejpam-1580	129	12	and	and	CCONJ
ejpam-1580	129	13	d.	d.	PROPN
ejpam-1580	129	14	bozkurt	bozkurt	PROPN
ejpam-1580	129	15	/	/	SYM
ejpam-1580	129	16	eur	eur	PROPN
ejpam-1580	129	17	.	.	PUNCT
ejpam-1580	130	1	j.	j.	PROPN
ejpam-1580	130	2	pure	pure	PROPN
ejpam-1580	130	3	appl	appl	PROPN
ejpam-1580	130	4	.	.	PROPN
ejpam-1580	130	5	math	math	PROPN
ejpam-1580	130	6	,	,	PUNCT
ejpam-1580	130	7	5	5	NUM
ejpam-1580	130	8	(	(	PUNCT
ejpam-1580	130	9	2012	2012	NUM
ejpam-1580	130	10	)	)	PUNCT
ejpam-1580	130	11	,	,	PUNCT
ejpam-1580	130	12	88	88	NUM
ejpam-1580	130	13	-	-	SYM
ejpam-1580	130	14	96	96	NUM
ejpam-1580	130	15	93	93	NUM
ejpam-1580	130	16	'	'	PUNCT
ejpam-1580	130	17	e"1	e"1	ADV
ejpam-1580	130	18	+	+	CCONJ
ejpam-1580	130	19	(	(	PUNCT
ejpam-1580	130	20	n	n	CCONJ
ejpam-1580	130	21	)	)	PUNCT
ejpam-1580	130	22	1	1	NUM
ejpam-1580	130	23	)	)	PUNCT
ejpam-1580	130	24	5	5	NUM
ejpam-1580	130	25	n	n	SYM
ejpam-1580	130	26	1	1	NUM
ejpam-1580	130	27	i=2	i=2	PROPN
ejpam-1580	130	28	e"i	e"i	PROPN
ejpam-1580	130	29	6	6	NUM
ejpam-1580	130	30	1	1	NUM
ejpam-1580	130	31	n)1	n)1	NOUN
ejpam-1580	130	32	(	(	PUNCT
ejpam-1580	130	33	16	16	NUM
ejpam-1580	130	34	)	)	PUNCT
ejpam-1580	130	35	=	=	PUNCT
ejpam-1580	131	1	e"1	e"1	PROPN
ejpam-1580	131	2	+	+	CCONJ
ejpam-1580	131	3	(	(	PUNCT
ejpam-1580	131	4	n	n	CCONJ
ejpam-1580	131	5	)	)	PUNCT
ejpam-1580	131	6	1	1	NUM
ejpam-1580	131	7	)	)	PUNCT
ejpam-1580	131	8	+	+	NUM
ejpam-1580	131	9	e)"1	e)"1	NUM
ejpam-1580	131	10	,	,	PUNCT
ejpam-1580	131	11	1	1	NUM
ejpam-1580	131	12	n)1	n)1	NOUN
ejpam-1580	131	13	,	,	PUNCT
ejpam-1580	131	14	since	since	SCONJ
ejpam-1580	131	15	n	n	NUM
ejpam-1580	131	16	)	)	PUNCT
ejpam-1580	131	17	i=1	i=1	VERB
ejpam-1580	132	1	"	"	PUNCT
ejpam-1580	132	2	i	i	NOUN
ejpam-1580	132	3	=	=	NOUN
ejpam-1580	132	4	0	0	X
ejpam-1580	132	5	.	.	PUNCT
ejpam-1580	133	1	(	(	PUNCT
ejpam-1580	133	2	17	17	NUM
ejpam-1580	133	3	)	)	PUNCT
ejpam-1580	133	4	now	now	ADV
ejpam-1580	133	5	we	we	PRON
ejpam-1580	133	6	consider	consider	VERB
ejpam-1580	133	7	the	the	DET
ejpam-1580	133	8	following	follow	VERB
ejpam-1580	133	9	function	function	NOUN
ejpam-1580	133	10	f	f	PROPN
ejpam-1580	133	11	(	(	PUNCT
ejpam-1580	133	12	x	x	X
ejpam-1580	133	13	)	)	PUNCT
ejpam-1580	133	14	=	=	SYM
ejpam-1580	133	15	ex	ex	X
ejpam-1580	133	16	+	+	NOUN
ejpam-1580	133	17	n	n	CCONJ
ejpam-1580	133	18	)	)	PUNCT
ejpam-1580	133	19	1	1	NUM
ejpam-1580	133	20	e	e	NOUN
ejpam-1580	133	21	x	x	NOUN
ejpam-1580	133	22	n)1	n)1	VERB
ejpam-1580	133	23	for	for	ADP
ejpam-1580	133	24	x	x	PUNCT
ejpam-1580	133	25	>	>	X
ejpam-1580	134	1	0	0	X
ejpam-1580	134	2	.	.	PUNCT
ejpam-1580	135	1	we	we	PRON
ejpam-1580	135	2	have	have	VERB
ejpam-1580	135	3	f	f	PROPN
ejpam-1580	135	4	(	(	PUNCT
ejpam-1580	135	5	x	x	NOUN
ejpam-1580	135	6	)	)	PUNCT
ejpam-1580	135	7	=	=	SYM
ejpam-1580	135	8	ex	ex	X
ejpam-1580	135	9	)	)	PUNCT
ejpam-1580	135	10	e	e	X
ejpam-1580	135	11	)	)	PUNCT
ejpam-1580	135	12	x	x	SYM
ejpam-1580	135	13	n)1	n)1	VERB
ejpam-1580	135	14	>	>	X
ejpam-1580	135	15	0	0	PUNCT
ejpam-1580	136	1	for	for	ADP
ejpam-1580	136	2	x	x	PUNCT
ejpam-1580	136	3	>	>	X
ejpam-1580	136	4	0	0	X
ejpam-1580	136	5	.	.	PUNCT
ejpam-1580	137	1	it	it	PRON
ejpam-1580	137	2	is	be	AUX
ejpam-1580	137	3	easy	easy	ADJ
ejpam-1580	137	4	to	to	PART
ejpam-1580	137	5	see	see	VERB
ejpam-1580	137	6	that	that	SCONJ
ejpam-1580	137	7	f	f	PROPN
ejpam-1580	137	8	is	be	AUX
ejpam-1580	137	9	an	an	DET
ejpam-1580	137	10	increasing	increase	VERB
ejpam-1580	137	11	function	function	NOUN
ejpam-1580	137	12	for	for	ADP
ejpam-1580	137	13	x	x	PUNCT
ejpam-1580	137	14	>	>	X
ejpam-1580	137	15	0	0	NUM
ejpam-1580	137	16	.	.	PUNCT
ejpam-1580	137	17	from	from	ADP
ejpam-1580	137	18	the	the	DET
ejpam-1580	137	19	equation	equation	NOUN
ejpam-1580	137	20	(	(	PUNCT
ejpam-1580	137	21	17	17	NUM
ejpam-1580	137	22	)	)	PUNCT
ejpam-1580	137	23	and	and	CCONJ
ejpam-1580	137	24	lemma	lemma	PROPN
ejpam-1580	137	25	2	2	NUM
ejpam-1580	137	26	,	,	PUNCT
ejpam-1580	137	27	we	we	PRON
ejpam-1580	137	28	obtain	obtain	VERB
ejpam-1580	137	29	ree(g	ree(g	NOUN
ejpam-1580	137	30	)	)	PUNCT
ejpam-1580	137	31	'	'	PUNCT
ejpam-1580	137	32	e	e	NOUN
ejpam-1580	137	33	4	4	NUM
ejpam-1580	137	34	sp+1	sp+1	NOUN
ejpam-1580	137	35	sp	sp	ADP
ejpam-1580	137	36	+	+	NOUN
ejpam-1580	137	37	n	n	CCONJ
ejpam-1580	137	38	)	)	PUNCT
ejpam-1580	137	39	1	1	NUM
ejpam-1580	137	40	e	e	SYM
ejpam-1580	137	41	1	1	NUM
ejpam-1580	137	42	n)1	n)1	NOUN
ejpam-1580	137	43	7	7	NUM
ejpam-1580	137	44	sp+1	sp+1	PROPN
ejpam-1580	137	45	sp	sp	NOUN
ejpam-1580	137	46	.	.	PUNCT
ejpam-1580	138	1	(	(	PUNCT
ejpam-1580	138	2	18	18	NUM
ejpam-1580	138	3	)	)	PUNCT
ejpam-1580	138	4	now	now	ADV
ejpam-1580	138	5	we	we	PRON
ejpam-1580	138	6	assume	assume	VERB
ejpam-1580	138	7	that	that	SCONJ
ejpam-1580	138	8	the	the	DET
ejpam-1580	138	9	equality	equality	NOUN
ejpam-1580	138	10	holds	hold	VERB
ejpam-1580	138	11	in	in	ADP
ejpam-1580	138	12	(	(	PUNCT
ejpam-1580	138	13	15	15	NUM
ejpam-1580	138	14	)	)	PUNCT
ejpam-1580	138	15	.	.	PUNCT
ejpam-1580	139	1	then	then	ADV
ejpam-1580	139	2	all	all	DET
ejpam-1580	139	3	inequalities	inequality	NOUN
ejpam-1580	139	4	in	in	ADP
ejpam-1580	139	5	the	the	DET
ejpam-1580	139	6	above	above	ADJ
ejpam-1580	139	7	argument	argument	NOUN
ejpam-1580	139	8	must	must	AUX
ejpam-1580	139	9	be	be	AUX
ejpam-1580	139	10	equalities	equality	NOUN
ejpam-1580	139	11	.	.	PUNCT
ejpam-1580	140	1	from	from	ADP
ejpam-1580	140	2	(	(	PUNCT
ejpam-1580	140	3	18	18	NUM
ejpam-1580	140	4	)	)	PUNCT
ejpam-1580	140	5	we	we	PRON
ejpam-1580	140	6	have	have	VERB
ejpam-1580	140	7	"	"	PUNCT
ejpam-1580	140	8	1	1	NUM
ejpam-1580	140	9	=	=	SYM
ejpam-1580	140	10	sp+1	sp+1	PROPN
ejpam-1580	140	11	sp	sp	ADP
ejpam-1580	140	12	which	which	PRON
ejpam-1580	140	13	implies	imply	VERB
ejpam-1580	140	14	l	l	NOUN
ejpam-1580	140	15	(	(	PUNCT
ejpam-1580	140	16	p+1	p+1	NOUN
ejpam-1580	140	17	)	)	PUNCT
ejpam-1580	140	18	1	1	NUM
ejpam-1580	140	19	l	l	NOUN
ejpam-1580	140	20	(	(	PUNCT
ejpam-1580	140	21	p	p	NOUN
ejpam-1580	140	22	)	)	PUNCT
ejpam-1580	140	23	1	1	NUM
ejpam-1580	140	24	=	=	SYM
ejpam-1580	140	25	l	l	NOUN
ejpam-1580	140	26	(	(	PUNCT
ejpam-1580	140	27	p+1	p+1	NOUN
ejpam-1580	140	28	)	)	PUNCT
ejpam-1580	140	29	2	2	NUM
ejpam-1580	140	30	l	l	NOUN
ejpam-1580	140	31	(	(	PUNCT
ejpam-1580	140	32	p	p	NOUN
ejpam-1580	140	33	)	)	PUNCT
ejpam-1580	140	34	2	2	NUM
ejpam-1580	140	35	=	=	SYM
ejpam-1580	140	36	·	·	PUNCT
ejpam-1580	140	37	·	·	PUNCT
ejpam-1580	140	38	·	·	PUNCT
ejpam-1580	141	1	=	=	SYM
ejpam-1580	141	2	l	l	NOUN
ejpam-1580	141	3	(	(	PUNCT
ejpam-1580	141	4	p+1	p+1	NOUN
ejpam-1580	141	5	)	)	PUNCT
ejpam-1580	141	6	n	n	PRON
ejpam-1580	141	7	l	l	NOUN
ejpam-1580	141	8	(	(	PUNCT
ejpam-1580	141	9	p	p	NOUN
ejpam-1580	141	10	)	)	PUNCT
ejpam-1580	141	11	n	n	NOUN
ejpam-1580	141	12	.	.	PUNCT
ejpam-1580	142	1	from	from	ADP
ejpam-1580	142	2	(	(	PUNCT
ejpam-1580	142	3	16	16	NUM
ejpam-1580	142	4	)	)	PUNCT
ejpam-1580	142	5	and	and	CCONJ
ejpam-1580	142	6	arithmetic	arithmetic	ADJ
ejpam-1580	142	7	-	-	PUNCT
ejpam-1580	142	8	geometric	geometric	ADJ
ejpam-1580	142	9	mean	mean	NOUN
ejpam-1580	142	10	inequality	inequality	NOUN
ejpam-1580	142	11	we	we	PRON
ejpam-1580	142	12	get	get	VERB
ejpam-1580	142	13	"	"	PUNCT
ejpam-1580	142	14	2	2	NUM
ejpam-1580	142	15	=	=	SYM
ejpam-1580	142	16	"	"	PUNCT
ejpam-1580	142	17	3	3	NUM
ejpam-1580	142	18	=	=	SYM
ejpam-1580	142	19	·	·	PUNCT
ejpam-1580	142	20	·	·	PUNCT
ejpam-1580	142	21	·	·	PUNCT
ejpam-1580	142	22	=	=	PUNCT
ejpam-1580	142	23	"	"	PUNCT
ejpam-1580	142	24	n.	n.	NOUN
ejpam-1580	142	25	therefore	therefore	ADV
ejpam-1580	142	26	g	g	PROPN
ejpam-1580	142	27	has	have	VERB
ejpam-1580	142	28	exactly	exactly	ADV
ejpam-1580	142	29	two	two	NUM
ejpam-1580	142	30	distinct	distinct	ADJ
ejpam-1580	142	31	randić	randić	NOUN
ejpam-1580	142	32	eigenvalues	eigenvalue	NOUN
ejpam-1580	142	33	,	,	PUNCT
ejpam-1580	142	34	by	by	ADP
ejpam-1580	142	35	lemma	lemma	PROPN
ejpam-1580	142	36	3	3	NUM
ejpam-1580	142	37	,	,	PUNCT
ejpam-1580	142	38	g	g	PROPN
ejpam-1580	142	39	is	be	AUX
ejpam-1580	142	40	the	the	DET
ejpam-1580	142	41	complete	complete	ADJ
ejpam-1580	142	42	graph	graph	NOUN
ejpam-1580	142	43	kn	kn	PROPN
ejpam-1580	142	44	.	.	PUNCT
ejpam-1580	143	1	conversely	conversely	ADV
ejpam-1580	143	2	,	,	PUNCT
ejpam-1580	143	3	one	one	PRON
ejpam-1580	143	4	can	can	AUX
ejpam-1580	143	5	easily	easily	ADV
ejpam-1580	143	6	see	see	VERB
ejpam-1580	143	7	that	that	SCONJ
ejpam-1580	143	8	the	the	DET
ejpam-1580	143	9	equality	equality	NOUN
ejpam-1580	143	10	holds	hold	VERB
ejpam-1580	143	11	in	in	ADP
ejpam-1580	143	12	(	(	PUNCT
ejpam-1580	143	13	15	15	NUM
ejpam-1580	143	14	)	)	PUNCT
ejpam-1580	143	15	for	for	ADP
ejpam-1580	143	16	the	the	DET
ejpam-1580	143	17	complete	complete	ADJ
ejpam-1580	143	18	graph	graph	NOUN
ejpam-1580	143	19	kn	kn	PROPN
ejpam-1580	143	20	.	.	PUNCT
ejpam-1580	144	1	this	this	PRON
ejpam-1580	144	2	completes	complete	VERB
ejpam-1580	144	3	the	the	DET
ejpam-1580	144	4	proof	proof	NOUN
ejpam-1580	144	5	of	of	ADP
ejpam-1580	144	6	theorem	theorem	PROPN
ejpam-1580	144	7	.	.	PUNCT
ejpam-1580	145	1	now	now	ADV
ejpam-1580	145	2	we	we	PRON
ejpam-1580	145	3	give	give	VERB
ejpam-1580	145	4	a	a	DET
ejpam-1580	145	5	result	result	NOUN
ejpam-1580	145	6	which	which	PRON
ejpam-1580	145	7	states	state	VERB
ejpam-1580	145	8	a	a	DET
ejpam-1580	145	9	lower	lower	ADV
ejpam-1580	145	10	bound	bind	VERB
ejpam-1580	145	11	for	for	ADP
ejpam-1580	145	12	the	the	DET
ejpam-1580	145	13	randić	randić	NOUN
ejpam-1580	145	14	estrada	estrada	PROPN
ejpam-1580	145	15	index	index	PROPN
ejpam-1580	145	16	involving	involve	VERB
ejpam-1580	145	17	randić	randić	NOUN
ejpam-1580	145	18	index	index	NOUN
ejpam-1580	145	19	.	.	PUNCT
ejpam-1580	146	1	corollary	corollary	ADJ
ejpam-1580	146	2	1	1	NUM
ejpam-1580	146	3	.	.	PUNCT
ejpam-1580	147	1	let	let	VERB
ejpam-1580	147	2	g	g	PRON
ejpam-1580	147	3	be	be	AUX
ejpam-1580	147	4	a	a	DET
ejpam-1580	147	5	connected	connect	VERB
ejpam-1580	147	6	(	(	PUNCT
ejpam-1580	147	7	n	n	CCONJ
ejpam-1580	147	8	,	,	PUNCT
ejpam-1580	147	9	m)-graph	m)-graph	NOUN
ejpam-1580	147	10	.	.	PUNCT
ejpam-1580	148	1	then	then	ADV
ejpam-1580	148	2	ree(g	ree(g	PROPN
ejpam-1580	148	3	)	)	PUNCT
ejpam-1580	148	4	'	'	PART
ejpam-1580	148	5	e	e	X
ejpam-1580	148	6	2r(g	2r(g	NUM
ejpam-1580	148	7	)	)	PUNCT
ejpam-1580	148	8	n	n	PROPN
ejpam-1580	148	9	+	+	CCONJ
ejpam-1580	148	10	n	n	CCONJ
ejpam-1580	148	11	)	)	PUNCT
ejpam-1580	148	12	1	1	NUM
ejpam-1580	148	13	e	e	NOUN
ejpam-1580	148	14	2r(g	2r(g	NUM
ejpam-1580	148	15	)	)	PUNCT
ejpam-1580	148	16	n(n)1	n(n)1	PROPN
ejpam-1580	148	17	)	)	PUNCT
ejpam-1580	148	18	(	(	PUNCT
ejpam-1580	148	19	19	19	NUM
ejpam-1580	148	20	)	)	PUNCT
ejpam-1580	148	21	where	where	SCONJ
ejpam-1580	148	22	r	r	NOUN
ejpam-1580	148	23	(	(	PUNCT
ejpam-1580	148	24	g	g	NOUN
ejpam-1580	148	25	)	)	PUNCT
ejpam-1580	148	26	denotes	denote	VERB
ejpam-1580	148	27	the	the	DET
ejpam-1580	148	28	randíc	randíc	PROPN
ejpam-1580	148	29	index	index	NOUN
ejpam-1580	148	30	of	of	ADP
ejpam-1580	148	31	the	the	DET
ejpam-1580	148	32	graph	graph	NOUN
ejpam-1580	148	33	g.	g.	NOUN
ejpam-1580	148	34	moreover	moreover	ADV
ejpam-1580	148	35	the	the	DET
ejpam-1580	148	36	equality	equality	NOUN
ejpam-1580	148	37	holds	hold	VERB
ejpam-1580	148	38	in	in	ADP
ejpam-1580	148	39	(	(	PUNCT
ejpam-1580	148	40	19	19	NUM
ejpam-1580	148	41	)	)	PUNCT
ejpam-1580	148	42	if	if	SCONJ
ejpam-1580	149	1	and	and	CCONJ
ejpam-1580	149	2	only	only	ADV
ejpam-1580	149	3	if	if	SCONJ
ejpam-1580	149	4	g	g	PROPN
ejpam-1580	149	5	is	be	AUX
ejpam-1580	149	6	the	the	DET
ejpam-1580	149	7	complete	complete	ADJ
ejpam-1580	149	8	graph	graph	NOUN
ejpam-1580	149	9	kn	kn	PROPN
ejpam-1580	149	10	.	.	PUNCT
ejpam-1580	150	1	proof	proof	NOUN
ejpam-1580	150	2	.	.	PUNCT
ejpam-1580	151	1	in	in	ADP
ejpam-1580	151	2	[	[	X
ejpam-1580	151	3	2	2	NUM
ejpam-1580	151	4	]	]	PUNCT
ejpam-1580	151	5	,	,	PUNCT
ejpam-1580	151	6	the	the	DET
ejpam-1580	151	7	authors	author	NOUN
ejpam-1580	151	8	showed	show	VERB
ejpam-1580	151	9	that	that	SCONJ
ejpam-1580	151	10	the	the	DET
ejpam-1580	151	11	folllowing	folllowe	VERB
ejpam-1580	151	12	inequality	inequality	NOUN
ejpam-1580	151	13	(	(	PUNCT
ejpam-1580	151	14	see	see	VERB
ejpam-1580	151	15	theorem	theorem	NOUN
ejpam-1580	151	16	4	4	NUM
ejpam-1580	151	17	)	)	PUNCT
ejpam-1580	151	18	"	"	PUNCT
ejpam-1580	151	19	1	1	NUM
ejpam-1580	151	20	'	'	PUNCT
ejpam-1580	151	21	sp+1	sp+1	NOUN
ejpam-1580	151	22	sp	sp	ADP
ejpam-1580	151	23	'	'	PUNCT
ejpam-1580	151	24	8	8	NUM
ejpam-1580	151	25	9	9	NUM
ejpam-1580	151	26	9	9	NUM
ejpam-1580	151	27	:	:	PUNCT
ejpam-1580	151	28	n	n	X
ejpam-1580	151	29	.	.	PUNCT
ejpam-1580	152	1	i=1	i=1	PROPN
ejpam-1580	153	1	r2	r2	PROPN
ejpam-1580	154	1	i	i	PRON
ejpam-1580	154	2	n	n	VERB
ejpam-1580	154	3	'	'	PUNCT
ejpam-1580	154	4	2r	2r	NUM
ejpam-1580	154	5	(	(	PUNCT
ejpam-1580	154	6	g	g	NOUN
ejpam-1580	154	7	)	)	PUNCT
ejpam-1580	154	8	n	n	CCONJ
ejpam-1580	154	9	(	(	PUNCT
ejpam-1580	154	10	20	20	NUM
ejpam-1580	154	11	)	)	PUNCT
ejpam-1580	154	12	ş.	ş.	PROPN
ejpam-1580	154	13	bozkurt	bozkurt	PROPN
ejpam-1580	154	14	and	and	CCONJ
ejpam-1580	154	15	d.	d.	PROPN
ejpam-1580	154	16	bozkurt	bozkurt	PROPN
ejpam-1580	154	17	/	/	SYM
ejpam-1580	154	18	eur	eur	PROPN
ejpam-1580	154	19	.	.	PUNCT
ejpam-1580	155	1	j.	j.	PROPN
ejpam-1580	155	2	pure	pure	PROPN
ejpam-1580	155	3	appl	appl	PROPN
ejpam-1580	155	4	.	.	PROPN
ejpam-1580	155	5	math	math	PROPN
ejpam-1580	155	6	,	,	PUNCT
ejpam-1580	155	7	5	5	NUM
ejpam-1580	155	8	(	(	PUNCT
ejpam-1580	155	9	2012	2012	NUM
ejpam-1580	155	10	)	)	PUNCT
ejpam-1580	155	11	,	,	PUNCT
ejpam-1580	155	12	88	88	NUM
ejpam-1580	155	13	-	-	SYM
ejpam-1580	155	14	96	96	NUM
ejpam-1580	155	15	94	94	NUM
ejpam-1580	155	16	where	where	SCONJ
ejpam-1580	155	17	sp=	sp=	NOUN
ejpam-1580	155	18	n	n	ADV
ejpam-1580	155	19	.	.	PUNCT
ejpam-1580	156	1	i=1	i=1	X
ejpam-1580	156	2	/	/	SYM
ejpam-1580	156	3	l	l	NOUN
ejpam-1580	156	4	(	(	PUNCT
ejpam-1580	156	5	p	p	X
ejpam-1580	156	6	)	)	PUNCT
ejpam-1580	156	7	i	i	PRON
ejpam-1580	156	8	02	02	NUM
ejpam-1580	156	9	.	.	PUNCT
ejpam-1580	157	1	combining	combine	VERB
ejpam-1580	157	2	theorem	theorem	ADJ
ejpam-1580	157	3	2	2	NUM
ejpam-1580	157	4	and	and	CCONJ
ejpam-1580	157	5	(	(	PUNCT
ejpam-1580	157	6	20	20	NUM
ejpam-1580	157	7	)	)	PUNCT
ejpam-1580	157	8	we	we	PRON
ejpam-1580	157	9	get	get	VERB
ejpam-1580	157	10	the	the	DET
ejpam-1580	157	11	inequality	inequality	NOUN
ejpam-1580	157	12	(	(	PUNCT
ejpam-1580	157	13	19	19	NUM
ejpam-1580	157	14	)	)	PUNCT
ejpam-1580	157	15	.	.	PUNCT
ejpam-1580	158	1	also	also	ADV
ejpam-1580	158	2	,	,	PUNCT
ejpam-1580	158	3	the	the	DET
ejpam-1580	158	4	equality	equality	NOUN
ejpam-1580	158	5	holds	hold	VERB
ejpam-1580	158	6	in	in	ADP
ejpam-1580	158	7	(	(	PUNCT
ejpam-1580	158	8	19	19	NUM
ejpam-1580	158	9	)	)	PUNCT
ejpam-1580	158	10	if	if	SCONJ
ejpam-1580	159	1	and	and	CCONJ
ejpam-1580	159	2	only	only	ADV
ejpam-1580	159	3	if	if	SCONJ
ejpam-1580	159	4	g	g	PROPN
ejpam-1580	159	5	is	be	AUX
ejpam-1580	159	6	the	the	DET
ejpam-1580	159	7	complete	complete	ADJ
ejpam-1580	159	8	graph	graph	NOUN
ejpam-1580	159	9	kn	kn	PROPN
ejpam-1580	159	10	.	.	PUNCT
ejpam-1580	159	11	theorem	theorem	PROPN
ejpam-1580	159	12	3	3	X
ejpam-1580	159	13	.	.	PUNCT
ejpam-1580	160	1	let	let	VERB
ejpam-1580	160	2	g	g	PRON
ejpam-1580	160	3	be	be	AUX
ejpam-1580	160	4	a	a	DET
ejpam-1580	160	5	connected	connect	VERB
ejpam-1580	160	6	(	(	PUNCT
ejpam-1580	160	7	n	n	CCONJ
ejpam-1580	160	8	,	,	PUNCT
ejpam-1580	160	9	m)-graph.then	m)-graph.then	AUX
ejpam-1580	160	10	the	the	DET
ejpam-1580	160	11	randíc	randíc	PROPN
ejpam-1580	160	12	estrada	estrada	PROPN
ejpam-1580	160	13	index	index	PROPN
ejpam-1580	160	14	ree	ree	NOUN
ejpam-1580	160	15	(	(	PUNCT
ejpam-1580	160	16	g	g	NOUN
ejpam-1580	160	17	)	)	PUNCT
ejpam-1580	160	18	and	and	CCONJ
ejpam-1580	160	19	the	the	DET
ejpam-1580	160	20	randíc	randíc	PROPN
ejpam-1580	160	21	energy	energy	NOUN
ejpam-1580	160	22	re	re	X
ejpam-1580	160	23	(	(	PUNCT
ejpam-1580	160	24	g	g	NOUN
ejpam-1580	160	25	)	)	PUNCT
ejpam-1580	160	26	satisfy	satisfy	VERB
ejpam-1580	160	27	the	the	DET
ejpam-1580	160	28	following	follow	VERB
ejpam-1580	160	29	inequality	inequality	NOUN
ejpam-1580	160	30	1	1	NUM
ejpam-1580	160	31	2	2	NUM
ejpam-1580	160	32	re	re	X
ejpam-1580	160	33	(	(	PUNCT
ejpam-1580	160	34	g	g	NOUN
ejpam-1580	160	35	)	)	PUNCT
ejpam-1580	160	36	(	(	PUNCT
ejpam-1580	160	37	e	e	NOUN
ejpam-1580	160	38	)	)	PUNCT
ejpam-1580	160	39	1)+	1)+	NUM
ejpam-1580	160	40	n	n	CCONJ
ejpam-1580	160	41	)	)	PUNCT
ejpam-1580	160	42	n+	n+	NUM
ejpam-1580	161	1	*	*	PUNCT
ejpam-1580	161	2	ree	ree	NOUN
ejpam-1580	161	3	(	(	PUNCT
ejpam-1580	161	4	g	g	NOUN
ejpam-1580	161	5	)	)	PUNCT
ejpam-1580	161	6	*	*	PUNCT
ejpam-1580	161	7	n	n	CCONJ
ejpam-1580	161	8	)	)	PUNCT
ejpam-1580	161	9	1	1	NUM
ejpam-1580	161	10	+	+	NUM
ejpam-1580	161	11	e	e	NOUN
ejpam-1580	161	12	re(g	re(g	X
ejpam-1580	161	13	)	)	PUNCT
ejpam-1580	161	14	2	2	NUM
ejpam-1580	161	15	.	.	PUNCT
ejpam-1580	162	1	(	(	PUNCT
ejpam-1580	162	2	21	21	NUM
ejpam-1580	162	3	)	)	PUNCT
ejpam-1580	163	1	where	where	SCONJ
ejpam-1580	163	2	n+	n+	PRON
ejpam-1580	163	3	denotes	denote	VERB
ejpam-1580	163	4	the	the	DET
ejpam-1580	163	5	number	number	NOUN
ejpam-1580	163	6	of	of	ADP
ejpam-1580	163	7	positive	positive	ADJ
ejpam-1580	163	8	randíc	randíc	NOUN
ejpam-1580	163	9	eigenvalues	eigenvalue	NOUN
ejpam-1580	163	10	of	of	ADP
ejpam-1580	163	11	g.	g.	PROPN
ejpam-1580	163	12	moreover	moreover	ADV
ejpam-1580	163	13	,	,	PUNCT
ejpam-1580	163	14	the	the	DET
ejpam-1580	163	15	equality	equality	NOUN
ejpam-1580	163	16	holds	hold	VERB
ejpam-1580	163	17	on	on	ADP
ejpam-1580	163	18	both	both	DET
ejpam-1580	163	19	sides	side	NOUN
ejpam-1580	163	20	of	of	ADP
ejpam-1580	163	21	(	(	PUNCT
ejpam-1580	163	22	21	21	NUM
ejpam-1580	163	23	)	)	PUNCT
ejpam-1580	163	24	if	if	SCONJ
ejpam-1580	164	1	and	and	CCONJ
ejpam-1580	164	2	only	only	ADV
ejpam-1580	164	3	if	if	SCONJ
ejpam-1580	164	4	g	g	PROPN
ejpam-1580	164	5	=	=	SYM
ejpam-1580	164	6	k1	k1	PROPN
ejpam-1580	164	7	.	.	PUNCT
ejpam-1580	165	1	proof	proof	NOUN
ejpam-1580	165	2	.	.	PUNCT
ejpam-1580	166	1	lower	lower	ADV
ejpam-1580	166	2	bound	bound	ADJ
ejpam-1580	166	3	:	:	PUNCT
ejpam-1580	166	4	since	since	SCONJ
ejpam-1580	166	5	ex	ex	NOUN
ejpam-1580	166	6	'	'	PUNCT
ejpam-1580	166	7	ex	ex	X
ejpam-1580	166	8	,	,	PUNCT
ejpam-1580	166	9	equality	equality	NOUN
ejpam-1580	166	10	holds	hold	VERB
ejpam-1580	166	11	if	if	SCONJ
ejpam-1580	166	12	and	and	CCONJ
ejpam-1580	166	13	only	only	ADV
ejpam-1580	166	14	if	if	SCONJ
ejpam-1580	166	15	x	x	SYM
ejpam-1580	166	16	=	=	SYM
ejpam-1580	166	17	1	1	NUM
ejpam-1580	166	18	and	and	CCONJ
ejpam-1580	166	19	ex	ex	PRON
ejpam-1580	166	20	'	'	PART
ejpam-1580	167	1	1	1	NUM
ejpam-1580	167	2	+	+	NUM
ejpam-1580	167	3	x	x	NOUN
ejpam-1580	167	4	,	,	PUNCT
ejpam-1580	167	5	equality	equality	NOUN
ejpam-1580	167	6	holds	hold	VERB
ejpam-1580	167	7	if	if	SCONJ
ejpam-1580	167	8	and	and	CCONJ
ejpam-1580	167	9	only	only	ADV
ejpam-1580	167	10	if	if	SCONJ
ejpam-1580	167	11	x	x	SYM
ejpam-1580	167	12	=	=	SYM
ejpam-1580	167	13	0	0	NUM
ejpam-1580	167	14	,	,	PUNCT
ejpam-1580	167	15	we	we	PRON
ejpam-1580	167	16	get	get	VERB
ejpam-1580	167	17	ree	ree	ADJ
ejpam-1580	167	18	(	(	PUNCT
ejpam-1580	167	19	g	g	NOUN
ejpam-1580	167	20	)	)	PUNCT
ejpam-1580	167	21	=	=	SYM
ejpam-1580	168	1	n	n	X
ejpam-1580	168	2	)	)	PUNCT
ejpam-1580	168	3	i=1	i=1	PROPN
ejpam-1580	168	4	e"i	e"i	PROPN
ejpam-1580	168	5	=	=	X
ejpam-1580	168	6	)	)	PUNCT
ejpam-1580	169	1	"	"	PUNCT
ejpam-1580	169	2	i>0	i>0	PROPN
ejpam-1580	169	3	e"i	e"i	PROPN
ejpam-1580	169	4	+	+	CCONJ
ejpam-1580	169	5	)	)	PUNCT
ejpam-1580	169	6	"	"	PUNCT
ejpam-1580	169	7	i*0	i*0	ADJ
ejpam-1580	169	8	e"i	e"i	NOUN
ejpam-1580	169	9	'	'	PUNCT
ejpam-1580	169	10	)	)	PUNCT
ejpam-1580	170	1	"	"	PUNCT
ejpam-1580	170	2	i>0	i>0	PROPN
ejpam-1580	170	3	e"i	e"i	PROPN
ejpam-1580	170	4	+	+	CCONJ
ejpam-1580	170	5	)	)	PUNCT
ejpam-1580	170	6	"	"	PUNCT
ejpam-1580	170	7	i*0	i*0	NOUN
ejpam-1580	170	8	!	!	PUNCT
ejpam-1580	170	9	1+"i	1+"i	NUM
ejpam-1580	171	1	"	"	PUNCT
ejpam-1580	171	2	=	=	SYM
ejpam-1580	171	3	e	e	X
ejpam-1580	171	4	+	+	CCONJ
ejpam-1580	171	5	"	"	PUNCT
ejpam-1580	171	6	1+"2	1+"2	NUM
ejpam-1580	171	7	+	+	X
ejpam-1580	171	8	·	·	PUNCT
ejpam-1580	171	9	·	·	PUNCT
ejpam-1580	171	10	·	·	PUNCT
ejpam-1580	171	11	+	+	ADJ
ejpam-1580	171	12	"	"	PUNCT
ejpam-1580	171	13	n+	n+	INTJ
ejpam-1580	171	14	,	,	PUNCT
ejpam-1580	171	15	+	+	CCONJ
ejpam-1580	171	16	!	!	PUNCT
ejpam-1580	171	17	n	n	CCONJ
ejpam-1580	171	18	)	)	PUNCT
ejpam-1580	171	19	n+	n+	PUNCT
ejpam-1580	171	20	"	"	PUNCT
ejpam-1580	172	1	+	+	CCONJ
ejpam-1580	172	2	+	+	CCONJ
ejpam-1580	172	3	"	"	PUNCT
ejpam-1580	172	4	n++1	n++1	NOUN
ejpam-1580	172	5	+	+	X
ejpam-1580	172	6	·	·	PUNCT
ejpam-1580	172	7	·	·	PUNCT
ejpam-1580	172	8	·	·	PUNCT
ejpam-1580	172	9	+	+	ADJ
ejpam-1580	172	10	"	"	PUNCT
ejpam-1580	172	11	n	n	NOUN
ejpam-1580	172	12	,	,	PUNCT
ejpam-1580	172	13	=	=	SYM
ejpam-1580	172	14	(	(	PUNCT
ejpam-1580	172	15	e	e	NOUN
ejpam-1580	172	16	)	)	PUNCT
ejpam-1580	172	17	1	1	NUM
ejpam-1580	172	18	)	)	PUNCT
ejpam-1580	172	19	+	+	CCONJ
ejpam-1580	172	20	"	"	PUNCT
ejpam-1580	172	21	1	1	NUM
ejpam-1580	172	22	+	+	ADJ
ejpam-1580	172	23	"	"	PUNCT
ejpam-1580	172	24	2	2	NUM
ejpam-1580	172	25	+	+	NUM
ejpam-1580	172	26	·	·	PUNCT
ejpam-1580	172	27	·	·	PUNCT
ejpam-1580	172	28	·	·	PUNCT
ejpam-1580	172	29	+	+	ADJ
ejpam-1580	172	30	"	"	PUNCT
ejpam-1580	172	31	n+	n+	INTJ
ejpam-1580	172	32	,	,	PUNCT
ejpam-1580	172	33	+	+	CCONJ
ejpam-1580	172	34	!	!	PUNCT
ejpam-1580	172	35	n	n	CCONJ
ejpam-1580	172	36	)	)	PUNCT
ejpam-1580	172	37	n+	n+	PUNCT
ejpam-1580	172	38	"	"	PUNCT
ejpam-1580	172	39	+	+	CCONJ
ejpam-1580	172	40	n	n	CCONJ
ejpam-1580	172	41	)	)	PUNCT
ejpam-1580	172	42	i=1	i=1	VERB
ejpam-1580	173	1	"	"	PUNCT
ejpam-1580	173	2	i	i	PRON
ejpam-1580	173	3	=	=	NOUN
ejpam-1580	173	4	1	1	NUM
ejpam-1580	173	5	2	2	NUM
ejpam-1580	173	6	re	re	X
ejpam-1580	173	7	(	(	PUNCT
ejpam-1580	173	8	g	g	NOUN
ejpam-1580	173	9	)	)	PUNCT
ejpam-1580	173	10	(	(	PUNCT
ejpam-1580	173	11	e	e	NOUN
ejpam-1580	173	12	)	)	PUNCT
ejpam-1580	173	13	1	1	NUM
ejpam-1580	173	14	)	)	PUNCT
ejpam-1580	173	15	+	+	NUM
ejpam-1580	173	16	n	n	CCONJ
ejpam-1580	173	17	)	)	PUNCT
ejpam-1580	173	18	n+	n+	PROPN
ejpam-1580	173	19	.	.	PUNCT
ejpam-1580	174	1	upper	upper	ADJ
ejpam-1580	174	2	bound	bound	NOUN
ejpam-1580	174	3	:	:	PUNCT
ejpam-1580	174	4	since	since	SCONJ
ejpam-1580	174	5	f	f	PROPN
ejpam-1580	174	6	(	(	PUNCT
ejpam-1580	174	7	x	x	X
ejpam-1580	174	8	)	)	PUNCT
ejpam-1580	174	9	=	=	SYM
ejpam-1580	174	10	ex	ex	X
ejpam-1580	174	11	monotonically	monotonically	ADV
ejpam-1580	174	12	increases	increase	VERB
ejpam-1580	174	13	in	in	ADP
ejpam-1580	174	14	the	the	DET
ejpam-1580	174	15	interval	interval	NOUN
ejpam-1580	174	16	(	(	PUNCT
ejpam-1580	174	17	)	)	PUNCT
ejpam-1580	174	18	(	(	PUNCT
ejpam-1580	174	19	,	,	PUNCT
ejpam-1580	174	20	+	+	PROPN
ejpam-1580	174	21	(	(	PUNCT
ejpam-1580	174	22	)	)	PUNCT
ejpam-1580	174	23	,	,	PUNCT
ejpam-1580	174	24	we	we	PRON
ejpam-1580	174	25	get	get	VERB
ejpam-1580	174	26	ree	ree	ADJ
ejpam-1580	174	27	(	(	PUNCT
ejpam-1580	174	28	g	g	NOUN
ejpam-1580	174	29	)	)	PUNCT
ejpam-1580	174	30	=	=	SYM
ejpam-1580	175	1	n	n	X
ejpam-1580	175	2	)	)	PUNCT
ejpam-1580	175	3	i=1	i=1	PROPN
ejpam-1580	175	4	e"i	e"i	PROPN
ejpam-1580	175	5	*	*	PUNCT
ejpam-1580	175	6	n	n	CCONJ
ejpam-1580	175	7	)	)	PUNCT
ejpam-1580	175	8	n+	n+	PUNCT
ejpam-1580	176	1	+	+	SYM
ejpam-1580	176	2	n+	n+	X
ejpam-1580	176	3	)	)	PUNCT
ejpam-1580	176	4	i=1	i=1	PROPN
ejpam-1580	176	5	e"i	e"i	PROPN
ejpam-1580	176	6	therefore	therefore	ADV
ejpam-1580	176	7	ree	ree	NOUN
ejpam-1580	176	8	(	(	PUNCT
ejpam-1580	176	9	g	g	NOUN
ejpam-1580	176	10	)	)	PUNCT
ejpam-1580	176	11	=	=	SYM
ejpam-1580	176	12	n	n	CCONJ
ejpam-1580	176	13	)	)	PUNCT
ejpam-1580	176	14	n+	n+	PUNCT
ejpam-1580	177	1	+	+	SYM
ejpam-1580	177	2	n+	n+	X
ejpam-1580	177	3	)	)	PUNCT
ejpam-1580	177	4	i=1	i=1	X
ejpam-1580	177	5	)	)	PUNCT
ejpam-1580	177	6	k'0	k'0	NOUN
ejpam-1580	177	7	!	!	PUNCT
ejpam-1580	178	1	"	"	PUNCT
ejpam-1580	178	2	i	i	PRON
ejpam-1580	178	3	"	"	PUNCT
ejpam-1580	178	4	k	k	PROPN
ejpam-1580	178	5	k	k	X
ejpam-1580	178	6	!	!	PUNCT
ejpam-1580	178	7	=	=	PRON
ejpam-1580	179	1	n+	n+	X
ejpam-1580	179	2	)	)	PUNCT
ejpam-1580	180	1	k'1	k'1	ADP
ejpam-1580	180	2	1	1	NUM
ejpam-1580	180	3	k	k	X
ejpam-1580	180	4	!	!	PUNCT
ejpam-1580	180	5	n+	n+	NUM
ejpam-1580	180	6	)	)	PUNCT
ejpam-1580	181	1	i=1	i=1	X
ejpam-1580	181	2	!	!	PUNCT
ejpam-1580	182	1	"	"	PUNCT
ejpam-1580	182	2	i	i	PRON
ejpam-1580	182	3	"	"	PUNCT
ejpam-1580	182	4	k	k	PROPN
ejpam-1580	182	5	*	*	PUNCT
ejpam-1580	182	6	n+	n+	NUM
ejpam-1580	182	7	)	)	PUNCT
ejpam-1580	182	8	k'1	k'1	ADP
ejpam-1580	182	9	1	1	NUM
ejpam-1580	182	10	k	k	X
ejpam-1580	182	11	!	!	PUNCT
ejpam-1580	182	12	;	;	PUNCT
ejpam-1580	182	13	<	<	X
ejpam-1580	182	14	n+	n+	X
ejpam-1580	182	15	)	)	PUNCT
ejpam-1580	182	16	i=1	i=1	VERB
ejpam-1580	183	1	"	"	PUNCT
ejpam-1580	183	2	i	i	PRON
ejpam-1580	183	3	=	=	PUNCT
ejpam-1580	183	4	>	>	X
ejpam-1580	183	5	k	k	PROPN
ejpam-1580	183	6	=	=	PUNCT
ejpam-1580	183	7	n	n	CCONJ
ejpam-1580	183	8	)	)	PUNCT
ejpam-1580	183	9	1	1	NUM
ejpam-1580	183	10	+	+	NUM
ejpam-1580	183	11	e	e	NOUN
ejpam-1580	183	12	re(g	re(g	X
ejpam-1580	183	13	)	)	PUNCT
ejpam-1580	183	14	2	2	NUM
ejpam-1580	183	15	.	.	PUNCT
ejpam-1580	184	1	it	it	PRON
ejpam-1580	184	2	is	be	AUX
ejpam-1580	184	3	easy	easy	ADJ
ejpam-1580	184	4	to	to	PART
ejpam-1580	184	5	see	see	VERB
ejpam-1580	184	6	that	that	SCONJ
ejpam-1580	184	7	the	the	DET
ejpam-1580	184	8	equality	equality	NOUN
ejpam-1580	184	9	holds	hold	VERB
ejpam-1580	184	10	on	on	ADP
ejpam-1580	184	11	both	both	DET
ejpam-1580	184	12	sides	side	NOUN
ejpam-1580	184	13	of	of	ADP
ejpam-1580	184	14	(	(	PUNCT
ejpam-1580	184	15	21	21	NUM
ejpam-1580	184	16	)	)	PUNCT
ejpam-1580	185	1	if	if	SCONJ
ejpam-1580	186	1	and	and	CCONJ
ejpam-1580	186	2	only	only	ADV
ejpam-1580	186	3	if	if	SCONJ
ejpam-1580	186	4	re	re	X
ejpam-1580	186	5	(	(	PUNCT
ejpam-1580	186	6	g	g	NOUN
ejpam-1580	186	7	)	)	PUNCT
ejpam-1580	186	8	=	=	SYM
ejpam-1580	187	1	0	0	X
ejpam-1580	187	2	.	.	PUNCT
ejpam-1580	188	1	since	since	SCONJ
ejpam-1580	188	2	g	g	PROPN
ejpam-1580	188	3	is	be	AUX
ejpam-1580	188	4	a	a	DET
ejpam-1580	188	5	connected	connected	ADJ
ejpam-1580	188	6	graph	graph	NOUN
ejpam-1580	188	7	this	this	PRON
ejpam-1580	188	8	only	only	ADV
ejpam-1580	188	9	happens	happen	VERB
ejpam-1580	188	10	in	in	ADP
ejpam-1580	188	11	the	the	DET
ejpam-1580	188	12	case	case	NOUN
ejpam-1580	188	13	of	of	ADP
ejpam-1580	188	14	g	g	PROPN
ejpam-1580	188	15	=	=	SYM
ejpam-1580	188	16	k1	k1	PROPN
ejpam-1580	188	17	.	.	PUNCT
ejpam-1580	189	1	references	reference	NOUN
ejpam-1580	189	2	95	95	NUM
ejpam-1580	189	3	4	4	NUM
ejpam-1580	189	4	.	.	PUNCT
ejpam-1580	189	5	concluding	conclude	VERB
ejpam-1580	189	6	remarks	remark	NOUN
ejpam-1580	189	7	in	in	ADP
ejpam-1580	189	8	this	this	DET
ejpam-1580	189	9	paper	paper	NOUN
ejpam-1580	189	10	,	,	PUNCT
ejpam-1580	189	11	the	the	DET
ejpam-1580	189	12	randić	randić	NOUN
ejpam-1580	189	13	estrada	estrada	PROPN
ejpam-1580	189	14	index	index	NOUN
ejpam-1580	189	15	of	of	ADP
ejpam-1580	189	16	a	a	DET
ejpam-1580	189	17	graph	graph	NOUN
ejpam-1580	189	18	is	be	AUX
ejpam-1580	189	19	introduced	introduce	VERB
ejpam-1580	189	20	.	.	PUNCT
ejpam-1580	190	1	also	also	ADV
ejpam-1580	190	2	the	the	DET
ejpam-1580	190	3	randić	randić	NOUN
ejpam-1580	190	4	energy	energy	NOUN
ejpam-1580	190	5	and	and	CCONJ
ejpam-1580	190	6	the	the	DET
ejpam-1580	190	7	randić	randić	NOUN
ejpam-1580	190	8	estrada	estrada	PROPN
ejpam-1580	190	9	index	index	NOUN
ejpam-1580	190	10	are	be	AUX
ejpam-1580	190	11	studied	study	VERB
ejpam-1580	190	12	.	.	PUNCT
ejpam-1580	191	1	in	in	ADP
ejpam-1580	191	2	section	section	NOUN
ejpam-1580	191	3	2	2	NUM
ejpam-1580	191	4	,	,	PUNCT
ejpam-1580	191	5	a	a	DET
ejpam-1580	191	6	sharper	sharper	ADV
ejpam-1580	191	7	upper	upper	ADJ
ejpam-1580	191	8	bound	bind	VERB
ejpam-1580	191	9	and	and	CCONJ
ejpam-1580	191	10	a	a	DET
ejpam-1580	191	11	new	new	ADJ
ejpam-1580	191	12	lower	lower	ADV
ejpam-1580	191	13	bound	bind	VERB
ejpam-1580	191	14	for	for	ADP
ejpam-1580	191	15	the	the	DET
ejpam-1580	191	16	randić	randić	NOUN
ejpam-1580	191	17	energy	energy	NOUN
ejpam-1580	191	18	are	be	AUX
ejpam-1580	191	19	obtained	obtain	VERB
ejpam-1580	191	20	.	.	PUNCT
ejpam-1580	192	1	in	in	ADP
ejpam-1580	192	2	section	section	NOUN
ejpam-1580	192	3	3	3	NUM
ejpam-1580	192	4	,	,	PUNCT
ejpam-1580	192	5	some	some	PRON
ejpam-1580	192	6	bounds	bound	VERB
ejpam-1580	192	7	for	for	ADP
ejpam-1580	192	8	the	the	DET
ejpam-1580	192	9	randić	randić	ADJ
ejpam-1580	192	10	estrada	estrada	PROPN
ejpam-1580	192	11	index	index	PROPN
ejpam-1580	192	12	involving	involve	VERB
ejpam-1580	192	13	randić	randić	NOUN
ejpam-1580	192	14	index	index	NOUN
ejpam-1580	192	15	,	,	PUNCT
ejpam-1580	192	16	randić	randić	NOUN
ejpam-1580	192	17	energy	energy	NOUN
ejpam-1580	192	18	and	and	CCONJ
ejpam-1580	192	19	some	some	DET
ejpam-1580	192	20	other	other	ADJ
ejpam-1580	192	21	graph	graph	NOUN
ejpam-1580	192	22	invariants	invariant	NOUN
ejpam-1580	192	23	are	be	AUX
ejpam-1580	192	24	also	also	ADV
ejpam-1580	192	25	put	put	VERB
ejpam-1580	192	26	forward	forward	ADV
ejpam-1580	192	27	.	.	PUNCT
ejpam-1580	193	1	acknowledgements	acknowledgement	NOUN
ejpam-1580	193	2	:	:	PUNCT
ejpam-1580	193	3	the	the	DET
ejpam-1580	193	4	authors	author	NOUN
ejpam-1580	193	5	thank	thank	VERB
ejpam-1580	193	6	the	the	DET
ejpam-1580	193	7	referees	referee	NOUN
ejpam-1580	193	8	for	for	ADP
ejpam-1580	193	9	their	their	PRON
ejpam-1580	193	10	helpful	helpful	ADJ
ejpam-1580	193	11	suggestions	suggestion	NOUN
ejpam-1580	193	12	concerning	concern	VERB
ejpam-1580	193	13	the	the	DET
ejpam-1580	193	14	presentation	presentation	NOUN
ejpam-1580	193	15	of	of	ADP
ejpam-1580	193	16	this	this	DET
ejpam-1580	193	17	paper	paper	NOUN
ejpam-1580	193	18	.	.	PUNCT
ejpam-1580	194	1	references	reference	NOUN
ejpam-1580	194	2	[	[	X
ejpam-1580	194	3	1	1	NUM
ejpam-1580	194	4	]	]	PUNCT
ejpam-1580	194	5	ş	ş	PROPN
ejpam-1580	194	6	bozkurt	bozkurt	PROPN
ejpam-1580	194	7	,	,	PUNCT
ejpam-1580	194	8	a	a	DET
ejpam-1580	194	9	güngör	güngör	NOUN
ejpam-1580	194	10	,	,	PUNCT
ejpam-1580	194	11	i	i	PRON
ejpam-1580	194	12	gutman	gutman	NOUN
ejpam-1580	194	13	and	and	CCONJ
ejpam-1580	194	14	a	a	DET
ejpam-1580	194	15	çevik	çevik	NOUN
ejpam-1580	194	16	.	.	PUNCT
ejpam-1580	194	17	randić	randić	NOUN
ejpam-1580	194	18	matrix	matrix	NOUN
ejpam-1580	194	19	and	and	CCONJ
ejpam-1580	194	20	randić	randić	NOUN
ejpam-1580	194	21	energy	energy	NOUN
ejpam-1580	194	22	.	.	PUNCT
ejpam-1580	195	1	match	match	PROPN
ejpam-1580	195	2	commun	commun	PROPN
ejpam-1580	195	3	.	.	PUNCT
ejpam-1580	195	4	math	math	PROPN
ejpam-1580	195	5	.	.	PUNCT
ejpam-1580	196	1	comput	comput	NOUN
ejpam-1580	196	2	.	.	PUNCT
ejpam-1580	197	1	chem	chem	NOUN
ejpam-1580	197	2	.	.	PUNCT
ejpam-1580	198	1	64	64	NUM
ejpam-1580	198	2	.	.	X
ejpam-1580	199	1	239	239	NUM
ejpam-1580	199	2	-	-	SYM
ejpam-1580	199	3	250	250	NUM
ejpam-1580	199	4	.	.	PUNCT
ejpam-1580	200	1	2010	2010	NUM
ejpam-1580	200	2	.	.	PUNCT
ejpam-1580	201	1	[	[	X
ejpam-1580	201	2	2	2	X
ejpam-1580	201	3	]	]	PUNCT
ejpam-1580	201	4	ş	ş	PROPN
ejpam-1580	201	5	bozkurt	bozkurt	PROPN
ejpam-1580	201	6	,	,	PUNCT
ejpam-1580	201	7	a	a	DET
ejpam-1580	201	8	güngör	güngör	NOUN
ejpam-1580	201	9	,	,	PUNCT
ejpam-1580	201	10	and	and	CCONJ
ejpam-1580	201	11	i	i	PROPN
ejpam-1580	201	12	gutman	gutman	PROPN
ejpam-1580	201	13	.	.	PUNCT
ejpam-1580	202	1	randić	randić	PROPN
ejpam-1580	202	2	spectral	spectral	ADJ
ejpam-1580	202	3	radius	radius	NOUN
ejpam-1580	202	4	and	and	CCONJ
ejpam-1580	202	5	randić	randić	NOUN
ejpam-1580	202	6	energy	energy	NOUN
ejpam-1580	202	7	.	.	PUNCT
ejpam-1580	203	1	match	match	PROPN
ejpam-1580	203	2	commun	commun	PROPN
ejpam-1580	203	3	.	.	PUNCT
ejpam-1580	203	4	math	math	PROPN
ejpam-1580	203	5	.	.	PUNCT
ejpam-1580	204	1	comput	comput	NOUN
ejpam-1580	204	2	.	.	PUNCT
ejpam-1580	205	1	chem	chem	NOUN
ejpam-1580	205	2	.	.	PUNCT
ejpam-1580	206	1	64	64	NUM
ejpam-1580	206	2	.	.	NOUN
ejpam-1580	206	3	321	321	NUM
ejpam-1580	206	4	-	-	SYM
ejpam-1580	206	5	334	334	NUM
ejpam-1580	206	6	.	.	PUNCT
ejpam-1580	207	1	2010	2010	NUM
ejpam-1580	207	2	.	.	PUNCT
ejpam-1580	208	1	[	[	X
ejpam-1580	208	2	3	3	NUM
ejpam-1580	208	3	]	]	X
ejpam-1580	208	4	d	d	X
ejpam-1580	208	5	cvetković	cvetković	PROPN
ejpam-1580	208	6	,	,	PUNCT
ejpam-1580	208	7	m	m	VERB
ejpam-1580	208	8	doob	doob	NOUN
ejpam-1580	208	9	and	and	CCONJ
ejpam-1580	208	10	h	h	NOUN
ejpam-1580	208	11	sachs	sachs	NOUN
ejpam-1580	208	12	.	.	PUNCT
ejpam-1580	209	1	spectra	spectra	NOUN
ejpam-1580	209	2	of	of	ADP
ejpam-1580	209	3	graphs	graph	NOUN
ejpam-1580	209	4	-	-	PUNCT
ejpam-1580	209	5	theory	theory	NOUN
ejpam-1580	209	6	and	and	CCONJ
ejpam-1580	209	7	application	application	NOUN
ejpam-1580	209	8	(	(	PUNCT
ejpam-1580	209	9	third	third	ADJ
ejpam-1580	209	10	ed	ed	NOUN
ejpam-1580	209	11	.	.	PUNCT
ejpam-1580	210	1	johann	johann	PROPN
ejpam-1580	210	2	ambrosius	ambrosius	PROPN
ejpam-1580	210	3	bart	bart	PROPN
ejpam-1580	210	4	verlag	verlag	PROPN
ejpam-1580	210	5	,	,	PUNCT
ejpam-1580	210	6	heidelberg	heidelberg	PROPN
ejpam-1580	210	7	,	,	PUNCT
ejpam-1580	210	8	leipzig	leipzig	NOUN
ejpam-1580	210	9	)	)	PUNCT
ejpam-1580	210	10	.	.	PUNCT
ejpam-1580	211	1	1995	1995	NUM
ejpam-1580	211	2	.	.	PUNCT
ejpam-1580	212	1	[	[	X
ejpam-1580	212	2	4	4	NUM
ejpam-1580	212	3	]	]	X
ejpam-1580	212	4	k	k	PROPN
ejpam-1580	212	5	das	das	PROPN
ejpam-1580	212	6	and	and	CCONJ
ejpam-1580	212	7	s	s	PROPN
ejpam-1580	212	8	lee	lee	PROPN
ejpam-1580	212	9	.	.	PROPN
ejpam-1580	213	1	on	on	ADP
ejpam-1580	213	2	the	the	DET
ejpam-1580	213	3	estrada	estrada	PROPN
ejpam-1580	213	4	index	index	NOUN
ejpam-1580	213	5	conjecture	conjecture	NOUN
ejpam-1580	213	6	.	.	PUNCT
ejpam-1580	214	1	linear	linear	ADJ
ejpam-1580	214	2	algebra	algebra	PROPN
ejpam-1580	214	3	appl	appl	NOUN
ejpam-1580	214	4	.	.	PUNCT
ejpam-1580	215	1	431	431	NUM
ejpam-1580	215	2	.	.	PUNCT
ejpam-1580	216	1	1351	1351	NUM
ejpam-1580	216	2	-	-	SYM
ejpam-1580	216	3	1359	1359	NUM
ejpam-1580	216	4	.	.	PUNCT
ejpam-1580	217	1	2009	2009	NUM
ejpam-1580	217	2	.	.	PUNCT
ejpam-1580	218	1	[	[	X
ejpam-1580	218	2	5	5	NUM
ejpam-1580	218	3	]	]	X
ejpam-1580	218	4	j	j	PROPN
ejpam-1580	218	5	de	de	X
ejpam-1580	218	6	la	la	X
ejpam-1580	218	7	peña	peña	PROPN
ejpam-1580	218	8	,	,	PUNCT
ejpam-1580	218	9	i	i	PRON
ejpam-1580	218	10	gutman	gutman	NOUN
ejpam-1580	218	11	and	and	CCONJ
ejpam-1580	218	12	j	j	PROPN
ejpam-1580	218	13	rada	rada	PROPN
ejpam-1580	218	14	.	.	PUNCT
ejpam-1580	219	1	estimating	estimate	VERB
ejpam-1580	219	2	the	the	DET
ejpam-1580	219	3	estrada	estrada	PROPN
ejpam-1580	219	4	index	index	PROPN
ejpam-1580	219	5	.	.	PUNCT
ejpam-1580	220	1	linear	linear	PROPN
ejpam-1580	220	2	algebra	algebra	PROPN
ejpam-1580	220	3	appl	appl	NOUN
ejpam-1580	220	4	.	.	PUNCT
ejpam-1580	221	1	427	427	NUM
ejpam-1580	221	2	.	.	X
ejpam-1580	222	1	70	70	NUM
ejpam-1580	222	2	-	-	SYM
ejpam-1580	222	3	76	76	NUM
ejpam-1580	222	4	.	.	PUNCT
ejpam-1580	223	1	2007	2007	NUM
ejpam-1580	223	2	.	.	PUNCT
ejpam-1580	224	1	[	[	X
ejpam-1580	224	2	6	6	NUM
ejpam-1580	224	3	]	]	X
ejpam-1580	224	4	h	h	PROPN
ejpam-1580	224	5	deng	deng	PROPN
ejpam-1580	224	6	,	,	PUNCT
ejpam-1580	224	7	s	s	PART
ejpam-1580	224	8	radenković	radenković	NOUN
ejpam-1580	224	9	and	and	CCONJ
ejpam-1580	224	10	i	i	PROPN
ejpam-1580	224	11	gutman	gutman	NOUN
ejpam-1580	224	12	.	.	PUNCT
ejpam-1580	225	1	the	the	DET
ejpam-1580	225	2	estrada	estrada	PROPN
ejpam-1580	225	3	index	index	NOUN
ejpam-1580	225	4	in	in	ADP
ejpam-1580	225	5	:	:	PUNCT
ejpam-1580	225	6	d.	d.	PROPN
ejpam-1580	225	7	cvetkovic	cvetkovic	PROPN
ejpam-1580	225	8	,	,	PUNCT
ejpam-1580	225	9	i.	i.	PROPN
ejpam-1580	225	10	gutman	gutman	PROPN
ejpam-1580	225	11	(	(	PUNCT
ejpam-1580	225	12	eds	eds	PROPN
ejpam-1580	225	13	.	.	PUNCT
ejpam-1580	225	14	)	)	PUNCT
ejpam-1580	225	15	applications	application	NOUN
ejpam-1580	225	16	of	of	ADP
ejpam-1580	225	17	graph	graph	NOUN
ejpam-1580	225	18	spectra	spectra	PROPN
ejpam-1580	225	19	(	(	PUNCT
ejpam-1580	225	20	math	math	NOUN
ejpam-1580	225	21	.	.	PUNCT
ejpam-1580	225	22	inst	inst	PROPN
ejpam-1580	225	23	.	.	PROPN
ejpam-1580	225	24	,	,	PUNCT
ejpam-1580	225	25	belgrade	belgrade	PROPN
ejpam-1580	225	26	)	)	PUNCT
ejpam-1580	225	27	.	.	PUNCT
ejpam-1580	226	1	123	123	NUM
ejpam-1580	226	2	-	-	SYM
ejpam-1580	226	3	140	140	NUM
ejpam-1580	226	4	.	.	PUNCT
ejpam-1580	226	5	2009	2009	NUM
ejpam-1580	226	6	.	.	PUNCT
ejpam-1580	227	1	[	[	X
ejpam-1580	227	2	7	7	NUM
ejpam-1580	227	3	]	]	X
ejpam-1580	227	4	e	e	X
ejpam-1580	227	5	estrada	estrada	PROPN
ejpam-1580	227	6	.	.	PUNCT
ejpam-1580	228	1	characterization	characterization	NOUN
ejpam-1580	228	2	of	of	ADP
ejpam-1580	228	3	3d	3d	NUM
ejpam-1580	228	4	molecular	molecular	ADJ
ejpam-1580	228	5	structure	structure	NOUN
ejpam-1580	228	6	.	.	PUNCT
ejpam-1580	229	1	chem	chem	NOUN
ejpam-1580	229	2	.	.	PUNCT
ejpam-1580	230	1	phys	phy	NOUN
ejpam-1580	230	2	.	.	PUNCT
ejpam-1580	231	1	lett	lett	PROPN
ejpam-1580	231	2	.	.	PUNCT
ejpam-1580	232	1	319	319	NUM
ejpam-1580	232	2	.	.	PUNCT
ejpam-1580	233	1	713	713	NUM
ejpam-1580	233	2	-	-	SYM
ejpam-1580	233	3	718	718	NUM
ejpam-1580	233	4	.	.	PUNCT
ejpam-1580	233	5	2000	2000	NUM
ejpam-1580	233	6	.	.	PUNCT
ejpam-1580	234	1	[	[	X
ejpam-1580	234	2	8	8	NUM
ejpam-1580	234	3	]	]	X
ejpam-1580	234	4	e	e	X
ejpam-1580	234	5	estrada	estrada	PROPN
ejpam-1580	234	6	.	.	PUNCT
ejpam-1580	235	1	characterization	characterization	NOUN
ejpam-1580	235	2	of	of	ADP
ejpam-1580	235	3	the	the	DET
ejpam-1580	235	4	folding	fold	VERB
ejpam-1580	235	5	degree	degree	NOUN
ejpam-1580	235	6	of	of	ADP
ejpam-1580	235	7	proteins	protein	NOUN
ejpam-1580	235	8	.	.	PUNCT
ejpam-1580	236	1	bioinformatics	bioinformatics	NOUN
ejpam-1580	236	2	18	18	NUM
ejpam-1580	236	3	.	.	PUNCT
ejpam-1580	236	4	697704	697704	NUM
ejpam-1580	236	5	.	.	PUNCT
ejpam-1580	237	1	2002	2002	NUM
ejpam-1580	237	2	.	.	PUNCT
ejpam-1580	238	1	[	[	X
ejpam-1580	238	2	9	9	NUM
ejpam-1580	238	3	]	]	X
ejpam-1580	238	4	e	e	X
ejpam-1580	238	5	estrada	estrada	PROPN
ejpam-1580	238	6	and	and	CCONJ
ejpam-1580	238	7	j	j	PROPN
ejpam-1580	238	8	rodríguez	rodríguez	PROPN
ejpam-1580	238	9	-	-	PUNCT
ejpam-1580	238	10	velázguez	velázguez	NOUN
ejpam-1580	238	11	.	.	PUNCT
ejpam-1580	239	1	subgraph	subgraph	NOUN
ejpam-1580	239	2	centrality	centrality	NOUN
ejpam-1580	239	3	in	in	ADP
ejpam-1580	239	4	complex	complex	ADJ
ejpam-1580	239	5	networks	network	NOUN
ejpam-1580	239	6	.	.	PUNCT
ejpam-1580	240	1	phys	phy	NOUN
ejpam-1580	240	2	.	.	PUNCT
ejpam-1580	241	1	rev	rev	PROPN
ejpam-1580	241	2	.	.	PUNCT
ejpam-1580	242	1	e	e	PROPN
ejpam-1580	242	2	71	71	NUM
ejpam-1580	242	3	.	.	NOUN
ejpam-1580	242	4	056103	056103	NUM
ejpam-1580	242	5	-	-	SYM
ejpam-1580	242	6	056103	056103	NUM
ejpam-1580	242	7	-	-	SYM
ejpam-1580	242	8	9	9	NUM
ejpam-1580	242	9	.	.	NUM
ejpam-1580	242	10	2005	2005	NUM
ejpam-1580	242	11	.	.	PUNCT
ejpam-1580	243	1	[	[	X
ejpam-1580	243	2	10	10	NUM
ejpam-1580	243	3	]	]	X
ejpam-1580	243	4	e	e	X
ejpam-1580	243	5	estrada	estrada	PROPN
ejpam-1580	243	6	,	,	PUNCT
ejpam-1580	243	7	j	j	PROPN
ejpam-1580	243	8	rodríguez	rodríguez	PROPN
ejpam-1580	243	9	-	-	PUNCT
ejpam-1580	243	10	velázguez	velázguez	NOUN
ejpam-1580	243	11	adn	adn	NOUN
ejpam-1580	243	12	m	m	NOUN
ejpam-1580	243	13	randić.	randić.	ADJ
ejpam-1580	243	14	atomic	atomic	ADJ
ejpam-1580	243	15	branching	branch	VERB
ejpam-1580	243	16	in	in	ADP
ejpam-1580	243	17	molecules	molecule	NOUN
ejpam-1580	243	18	.	.	PUNCT
ejpam-1580	244	1	int	int	NOUN
ejpam-1580	244	2	.	.	PUNCT
ejpam-1580	245	1	j.quantum	j.quantum	PROPN
ejpam-1580	245	2	chem	chem	PROPN
ejpam-1580	245	3	.	.	PUNCT
ejpam-1580	246	1	106	106	NUM
ejpam-1580	246	2	.	.	PUNCT
ejpam-1580	247	1	823	823	NUM
ejpam-1580	247	2	-	-	SYM
ejpam-1580	247	3	832	832	NUM
ejpam-1580	247	4	.	.	PUNCT
ejpam-1580	247	5	2006	2006	NUM
ejpam-1580	247	6	.	.	PUNCT
ejpam-1580	248	1	[	[	X
ejpam-1580	248	2	11	11	NUM
ejpam-1580	248	3	]	]	X
ejpam-1580	248	4	i	i	PROPN
ejpam-1580	248	5	gutman	gutman	PROPN
ejpam-1580	248	6	.	.	PUNCT
ejpam-1580	249	1	bounds	bound	VERB
ejpam-1580	249	2	for	for	ADP
ejpam-1580	249	3	total	total	ADJ
ejpam-1580	249	4	$	$	SYM
ejpam-1580	249	5	-electron	-electron	NOUN
ejpam-1580	249	6	energy	energy	NOUN
ejpam-1580	249	7	.	.	PUNCT
ejpam-1580	250	1	chem	chem	NOUN
ejpam-1580	250	2	.	.	PUNCT
ejpam-1580	251	1	phys	phy	NOUN
ejpam-1580	251	2	.	.	PUNCT
ejpam-1580	252	1	lett	lett	PROPN
ejpam-1580	252	2	.	.	PUNCT
ejpam-1580	253	1	24	24	NUM
ejpam-1580	253	2	.	.	X
ejpam-1580	253	3	283	283	NUM
ejpam-1580	253	4	-	-	SYM
ejpam-1580	253	5	285	285	NUM
ejpam-1580	253	6	.	.	PUNCT
ejpam-1580	253	7	1974	1974	NUM
ejpam-1580	253	8	.	.	PUNCT
ejpam-1580	254	1	[	[	X
ejpam-1580	254	2	12	12	NUM
ejpam-1580	254	3	]	]	X
ejpam-1580	254	4	i	i	PROPN
ejpam-1580	254	5	gutman	gutman	PROPN
ejpam-1580	254	6	.	.	PUNCT
ejpam-1580	255	1	total	total	VERB
ejpam-1580	255	2	$	$	SYM
ejpam-1580	255	3	-electron	-electron	NOUN
ejpam-1580	255	4	energy	energy	NOUN
ejpam-1580	255	5	of	of	ADP
ejpam-1580	255	6	benezoid	benezoid	ADJ
ejpam-1580	255	7	hydrocarbons	hydrocarbon	NOUN
ejpam-1580	255	8	.	.	PUNCT
ejpam-1580	256	1	topics	topic	NOUN
ejpam-1580	256	2	curr	curr	PROPN
ejpam-1580	256	3	.	.	PUNCT
ejpam-1580	256	4	chem	chem	PROPN
ejpam-1580	256	5	.	.	PUNCT
ejpam-1580	257	1	162	162	NUM
ejpam-1580	257	2	.	.	X
ejpam-1580	258	1	26	26	NUM
ejpam-1580	258	2	-	-	SYM
ejpam-1580	258	3	63	63	NUM
ejpam-1580	258	4	.	.	PUNCT
ejpam-1580	259	1	1992	1992	NUM
ejpam-1580	259	2	.	.	PUNCT
ejpam-1580	260	1	references	reference	NOUN
ejpam-1580	260	2	96	96	NUM
ejpam-1580	261	1	[	[	X
ejpam-1580	261	2	13	13	NUM
ejpam-1580	261	3	]	]	X
ejpam-1580	261	4	i	i	PROPN
ejpam-1580	261	5	gutman	gutman	PROPN
ejpam-1580	261	6	.	.	PUNCT
ejpam-1580	262	1	the	the	DET
ejpam-1580	262	2	energy	energy	NOUN
ejpam-1580	262	3	of	of	ADP
ejpam-1580	262	4	a	a	DET
ejpam-1580	262	5	graph	graph	NOUN
ejpam-1580	262	6	,	,	PUNCT
ejpam-1580	262	7	old	old	ADJ
ejpam-1580	262	8	and	and	CCONJ
ejpam-1580	262	9	new	new	ADJ
ejpam-1580	262	10	results	result	NOUN
ejpam-1580	262	11	,	,	PUNCT
ejpam-1580	262	12	in	in	ADP
ejpam-1580	262	13	:	:	PUNCT
ejpam-1580	262	14	a.	a.	NOUN
ejpam-1580	262	15	betten	betten	NOUN
ejpam-1580	262	16	,	,	PUNCT
ejpam-1580	262	17	a.	a.	PROPN
ejpam-1580	262	18	kohnert	kohnert	PROPN
ejpam-1580	262	19	,	,	PUNCT
ejpam-1580	262	20	r.	r.	PROPN
ejpam-1580	262	21	laue	laue	PROPN
ejpam-1580	262	22	,	,	PUNCT
ejpam-1580	262	23	a.	a.	NOUN
ejpam-1580	262	24	wassermann	wassermann	PROPN
ejpam-1580	262	25	(	(	PUNCT
ejpam-1580	262	26	eds	ed	NOUN
ejpam-1580	262	27	.	.	PUNCT
ejpam-1580	262	28	)	)	PUNCT
ejpam-1580	262	29	,	,	PUNCT
ejpam-1580	262	30	algebraic	algebraic	ADJ
ejpam-1580	262	31	combinatorics	combinatoric	NOUN
ejpam-1580	262	32	and	and	CCONJ
ejpam-1580	262	33	applications	application	NOUN
ejpam-1580	262	34	(	(	PUNCT
ejpam-1580	262	35	springerverlag	springerverlag	NOUN
ejpam-1580	262	36	,	,	PUNCT
ejpam-1580	262	37	berlin	berlin	PROPN
ejpam-1580	262	38	)	)	PUNCT
ejpam-1580	262	39	196	196	NUM
ejpam-1580	262	40	-	-	SYM
ejpam-1580	262	41	211	211	NUM
ejpam-1580	262	42	.	.	PUNCT
ejpam-1580	262	43	2001	2001	NUM
ejpam-1580	262	44	.	.	PUNCT
ejpam-1580	263	1	[	[	X
ejpam-1580	263	2	14	14	NUM
ejpam-1580	263	3	]	]	X
ejpam-1580	263	4	j	j	PROPN
ejpam-1580	263	5	liu	liu	PROPN
ejpam-1580	263	6	and	and	CCONJ
ejpam-1580	263	7	b	b	PROPN
ejpam-1580	263	8	liu	liu	PROPN
ejpam-1580	263	9	.	.	PUNCT
ejpam-1580	264	1	bounds	bound	NOUN
ejpam-1580	264	2	of	of	ADP
ejpam-1580	264	3	the	the	DET
ejpam-1580	264	4	estrada	estrada	PROPN
ejpam-1580	264	5	index	index	NOUN
ejpam-1580	264	6	of	of	ADP
ejpam-1580	264	7	graphs	graph	NOUN
ejpam-1580	264	8	.	.	PUNCT
ejpam-1580	265	1	appl	appl	PROPN
ejpam-1580	265	2	.	.	PROPN
ejpam-1580	265	3	math	math	PROPN
ejpam-1580	265	4	.	.	PUNCT
ejpam-1580	266	1	j.	j.	PROPN
ejpam-1580	266	2	chinese	chinese	PROPN
ejpam-1580	266	3	univ	univ	PROPN
ejpam-1580	266	4	.	.	PUNCT
ejpam-1580	267	1	25	25	NUM
ejpam-1580	267	2	(	(	PUNCT
ejpam-1580	267	3	3	3	NUM
ejpam-1580	267	4	)	)	PUNCT
ejpam-1580	267	5	.	.	PUNCT
ejpam-1580	268	1	325	325	NUM
ejpam-1580	268	2	-	-	SYM
ejpam-1580	268	3	330	330	NUM
ejpam-1580	268	4	.	.	PUNCT
ejpam-1580	269	1	2010	2010	NUM
ejpam-1580	269	2	.	.	PUNCT
ejpam-1580	270	1	[	[	X
ejpam-1580	270	2	15	15	NUM
ejpam-1580	270	3	]	]	X
ejpam-1580	270	4	m	m	VERB
ejpam-1580	270	5	randić.	randić.	NOUN
ejpam-1580	270	6	on	on	ADP
ejpam-1580	270	7	characterization	characterization	NOUN
ejpam-1580	270	8	of	of	ADP
ejpam-1580	270	9	moleculer	moleculer	NOUN
ejpam-1580	270	10	branching	branching	NOUN
ejpam-1580	270	11	,	,	PUNCT
ejpam-1580	270	12	j.	j.	PROPN
ejpam-1580	270	13	a.	a.	PROPN
ejpam-1580	270	14	chem	chem	PROPN
ejpam-1580	270	15	.	.	PUNCT
ejpam-1580	271	1	soc	soc	PROPN
ejpam-1580	271	2	.	.	PUNCT
ejpam-1580	272	1	97	97	NUM
ejpam-1580	272	2	.	.	PUNCT
ejpam-1580	272	3	6609	6609	NUM
ejpam-1580	272	4	-	-	SYM
ejpam-1580	272	5	6615	6615	NUM
ejpam-1580	272	6	.	.	PUNCT
ejpam-1580	273	1	1975	1975	NUM
ejpam-1580	273	2	.	.	PUNCT