id	sid	tid	token	lemma	pos
ejpam-3725	1	1	european	european	PROPN
ejpam-3725	1	2	journal	journal	PROPN
ejpam-3725	1	3	of	of	ADP
ejpam-3725	1	4	pure	pure	ADJ
ejpam-3725	1	5	and	and	CCONJ
ejpam-3725	1	6	applied	apply	VERB
ejpam-3725	1	7	mathematics	mathematic	NOUN
ejpam-3725	1	8	vol	vol	NOUN
ejpam-3725	1	9	.	.	PROPN
ejpam-3725	2	1	13	13	NUM
ejpam-3725	2	2	,	,	PUNCT
ejpam-3725	2	3	no	no	INTJ
ejpam-3725	2	4	.	.	NOUN
ejpam-3725	2	5	5	5	NUM
ejpam-3725	2	6	,	,	PUNCT
ejpam-3725	2	7	2020	2020	NUM
ejpam-3725	2	8	,	,	PUNCT
ejpam-3725	2	9	1260	1260	NUM
ejpam-3725	2	10	-	-	SYM
ejpam-3725	2	11	1269	1269	NUM
ejpam-3725	2	12	issn	issn	VERB
ejpam-3725	2	13	1307	1307	NUM
ejpam-3725	2	14	-	-	SYM
ejpam-3725	2	15	5543	5543	NUM
ejpam-3725	2	16	–	–	PUNCT
ejpam-3725	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3725	2	18	published	publish	VERB
ejpam-3725	2	19	by	by	ADP
ejpam-3725	2	20	new	new	PROPN
ejpam-3725	2	21	york	york	PROPN
ejpam-3725	2	22	business	business	PROPN
ejpam-3725	2	23	global	global	ADJ
ejpam-3725	2	24	special	special	ADJ
ejpam-3725	2	25	issue	issue	NOUN
ejpam-3725	2	26	dedicated	dedicate	VERB
ejpam-3725	2	27	to	to	ADP
ejpam-3725	2	28	professor	professor	NOUN
ejpam-3725	2	29	hari	hari	PROPN
ejpam-3725	2	30	m.	m.	PROPN
ejpam-3725	2	31	srivastava	srivastava	PROPN
ejpam-3725	2	32	on	on	ADP
ejpam-3725	2	33	the	the	DET
ejpam-3725	2	34	occasion	occasion	NOUN
ejpam-3725	2	35	of	of	ADP
ejpam-3725	2	36	his	his	PRON
ejpam-3725	2	37	80th	80th	ADJ
ejpam-3725	2	38	birthday	birthday	NOUN
ejpam-3725	2	39	harmonic	harmonic	ADJ
ejpam-3725	2	40	index	index	NOUN
ejpam-3725	2	41	and	and	CCONJ
ejpam-3725	2	42	zagreb	zagreb	PROPN
ejpam-3725	2	43	indices	index	NOUN
ejpam-3725	2	44	of	of	ADP
ejpam-3725	2	45	vertex	vertex	NOUN
ejpam-3725	2	46	-	-	PUNCT
ejpam-3725	2	47	semitotal	semitotal	ADJ
ejpam-3725	2	48	graphs	graph	NOUN
ejpam-3725	2	49	aysun	aysun	NOUN
ejpam-3725	2	50	yurttas	yurtta	NOUN
ejpam-3725	2	51	gunes1	gunes1	NOUN
ejpam-3725	2	52	,	,	PUNCT
ejpam-3725	2	53	muge	muge	PROPN
ejpam-3725	2	54	togan1	togan1	PROPN
ejpam-3725	2	55	,	,	PUNCT
ejpam-3725	2	56	musa	musa	PROPN
ejpam-3725	2	57	demirci1,∗	demirci1,∗	PROPN
ejpam-3725	2	58	,	,	PUNCT
ejpam-3725	2	59	ismail	ismail	PROPN
ejpam-3725	2	60	naci	naci	PROPN
ejpam-3725	2	61	cangul1	cangul1	PROPN
ejpam-3725	2	62	1	1	NUM
ejpam-3725	2	63	department	department	NOUN
ejpam-3725	2	64	of	of	ADP
ejpam-3725	2	65	mathematics	mathematics	PROPN
ejpam-3725	2	66	,	,	PUNCT
ejpam-3725	2	67	bursa	bursa	PROPN
ejpam-3725	2	68	uludag	uludag	PROPN
ejpam-3725	2	69	university	university	PROPN
ejpam-3725	2	70	,	,	PUNCT
ejpam-3725	2	71	16059	16059	NUM
ejpam-3725	2	72	bursa	bursa	NOUN
ejpam-3725	2	73	,	,	PUNCT
ejpam-3725	2	74	turkey	turkey	PROPN
ejpam-3725	2	75	abstract	abstract	NOUN
ejpam-3725	2	76	.	.	PUNCT
ejpam-3725	3	1	graph	graph	NOUN
ejpam-3725	3	2	theory	theory	NOUN
ejpam-3725	3	3	is	be	AUX
ejpam-3725	3	4	one	one	NUM
ejpam-3725	3	5	of	of	ADP
ejpam-3725	3	6	the	the	DET
ejpam-3725	3	7	rising	rise	VERB
ejpam-3725	3	8	areas	area	NOUN
ejpam-3725	3	9	in	in	ADP
ejpam-3725	3	10	mathematics	mathematic	NOUN
ejpam-3725	3	11	due	due	ADP
ejpam-3725	3	12	to	to	ADP
ejpam-3725	3	13	its	its	PRON
ejpam-3725	3	14	applications	application	NOUN
ejpam-3725	3	15	in	in	ADP
ejpam-3725	3	16	many	many	ADJ
ejpam-3725	3	17	areas	area	NOUN
ejpam-3725	3	18	of	of	ADP
ejpam-3725	3	19	science	science	NOUN
ejpam-3725	3	20	.	.	PUNCT
ejpam-3725	4	1	amongst	amongst	ADP
ejpam-3725	4	2	several	several	ADJ
ejpam-3725	4	3	study	study	NOUN
ejpam-3725	4	4	areas	area	NOUN
ejpam-3725	4	5	in	in	ADP
ejpam-3725	4	6	graph	graph	NOUN
ejpam-3725	4	7	theory	theory	NOUN
ejpam-3725	4	8	,	,	PUNCT
ejpam-3725	4	9	spectral	spectral	ADJ
ejpam-3725	4	10	graph	graph	NOUN
ejpam-3725	4	11	theory	theory	NOUN
ejpam-3725	4	12	and	and	CCONJ
ejpam-3725	4	13	topological	topological	ADJ
ejpam-3725	4	14	descriptors	descriptor	NOUN
ejpam-3725	4	15	are	be	AUX
ejpam-3725	4	16	in	in	ADP
ejpam-3725	4	17	front	front	ADJ
ejpam-3725	4	18	rows	row	NOUN
ejpam-3725	4	19	.	.	PUNCT
ejpam-3725	5	1	these	these	DET
ejpam-3725	5	2	descriptors	descriptor	NOUN
ejpam-3725	5	3	are	be	AUX
ejpam-3725	5	4	widely	widely	ADV
ejpam-3725	5	5	used	use	VERB
ejpam-3725	5	6	in	in	ADP
ejpam-3725	5	7	qspr	qspr	NOUN
ejpam-3725	5	8	/	/	SYM
ejpam-3725	5	9	qsar	qsar	NOUN
ejpam-3725	5	10	studies	study	NOUN
ejpam-3725	5	11	in	in	ADP
ejpam-3725	5	12	mathematical	mathematical	ADJ
ejpam-3725	5	13	chemistry	chemistry	NOUN
ejpam-3725	5	14	.	.	PUNCT
ejpam-3725	6	1	vertex	vertex	NOUN
ejpam-3725	6	2	-	-	PUNCT
ejpam-3725	6	3	semitotal	semitotal	ADJ
ejpam-3725	6	4	graphs	graph	NOUN
ejpam-3725	6	5	are	be	AUX
ejpam-3725	6	6	one	one	NUM
ejpam-3725	6	7	of	of	ADP
ejpam-3725	6	8	the	the	DET
ejpam-3725	6	9	derived	derive	VERB
ejpam-3725	6	10	graph	graph	NOUN
ejpam-3725	6	11	classes	class	NOUN
ejpam-3725	6	12	which	which	PRON
ejpam-3725	6	13	are	be	AUX
ejpam-3725	6	14	useful	useful	ADJ
ejpam-3725	6	15	in	in	ADP
ejpam-3725	6	16	calculating	calculate	VERB
ejpam-3725	6	17	several	several	ADJ
ejpam-3725	6	18	physico	physico	NOUN
ejpam-3725	6	19	-	-	PUNCT
ejpam-3725	6	20	chemical	chemical	NOUN
ejpam-3725	6	21	properties	property	NOUN
ejpam-3725	6	22	of	of	ADP
ejpam-3725	6	23	molecular	molecular	ADJ
ejpam-3725	6	24	structures	structure	NOUN
ejpam-3725	6	25	by	by	ADP
ejpam-3725	6	26	means	mean	NOUN
ejpam-3725	6	27	of	of	ADP
ejpam-3725	6	28	molecular	molecular	ADJ
ejpam-3725	6	29	graphs	graph	NOUN
ejpam-3725	6	30	modelling	model	VERB
ejpam-3725	6	31	the	the	DET
ejpam-3725	6	32	molecules	molecule	NOUN
ejpam-3725	6	33	.	.	PUNCT
ejpam-3725	7	1	in	in	ADP
ejpam-3725	7	2	this	this	DET
ejpam-3725	7	3	paper	paper	NOUN
ejpam-3725	7	4	,	,	PUNCT
ejpam-3725	7	5	several	several	ADJ
ejpam-3725	7	6	topological	topological	ADJ
ejpam-3725	7	7	descriptors	descriptor	NOUN
ejpam-3725	7	8	of	of	ADP
ejpam-3725	7	9	vertexsemitotal	vertexsemitotal	ADJ
ejpam-3725	7	10	graphs	graph	NOUN
ejpam-3725	7	11	are	be	AUX
ejpam-3725	7	12	calculated	calculate	VERB
ejpam-3725	7	13	.	.	PUNCT
ejpam-3725	8	1	some	some	DET
ejpam-3725	8	2	new	new	ADJ
ejpam-3725	8	3	relations	relation	NOUN
ejpam-3725	8	4	on	on	ADP
ejpam-3725	8	5	these	these	DET
ejpam-3725	8	6	values	value	NOUN
ejpam-3725	8	7	are	be	AUX
ejpam-3725	8	8	obtained	obtain	VERB
ejpam-3725	8	9	by	by	ADP
ejpam-3725	8	10	means	mean	NOUN
ejpam-3725	8	11	of	of	ADP
ejpam-3725	8	12	a	a	DET
ejpam-3725	8	13	recently	recently	ADV
ejpam-3725	8	14	defined	define	VERB
ejpam-3725	8	15	graph	graph	NOUN
ejpam-3725	8	16	invariant	invariant	NOUN
ejpam-3725	8	17	called	call	VERB
ejpam-3725	8	18	omega	omega	NOUN
ejpam-3725	8	19	invariant	invariant	ADJ
ejpam-3725	8	20	.	.	PUNCT
ejpam-3725	9	1	1	1	X
ejpam-3725	9	2	.	.	X
ejpam-3725	9	3	introduction	introduction	NOUN
ejpam-3725	9	4	several	several	ADJ
ejpam-3725	9	5	topological	topological	ADJ
ejpam-3725	9	6	graph	graph	NOUN
ejpam-3725	9	7	indices	index	NOUN
ejpam-3725	9	8	have	have	AUX
ejpam-3725	9	9	been	be	AUX
ejpam-3725	9	10	defined	define	VERB
ejpam-3725	9	11	and	and	CCONJ
ejpam-3725	9	12	studied	study	VERB
ejpam-3725	9	13	by	by	ADP
ejpam-3725	9	14	many	many	ADJ
ejpam-3725	9	15	mathematicians	mathematician	NOUN
ejpam-3725	9	16	and	and	CCONJ
ejpam-3725	9	17	chemists	chemist	NOUN
ejpam-3725	9	18	.	.	PUNCT
ejpam-3725	10	1	they	they	PRON
ejpam-3725	10	2	are	be	AUX
ejpam-3725	10	3	defined	define	VERB
ejpam-3725	10	4	as	as	ADP
ejpam-3725	10	5	topological	topological	ADJ
ejpam-3725	10	6	graph	graph	NOUN
ejpam-3725	10	7	invariants	invariant	NOUN
ejpam-3725	10	8	measuring	measure	VERB
ejpam-3725	10	9	several	several	ADJ
ejpam-3725	10	10	physical	physical	ADJ
ejpam-3725	10	11	,	,	PUNCT
ejpam-3725	10	12	chemical	chemical	NOUN
ejpam-3725	10	13	,	,	PUNCT
ejpam-3725	10	14	pharmacological	pharmacological	NOUN
ejpam-3725	10	15	,	,	PUNCT
ejpam-3725	10	16	pharmaceutical	pharmaceutical	NOUN
ejpam-3725	10	17	,	,	PUNCT
ejpam-3725	10	18	biological	biological	NOUN
ejpam-3725	10	19	,	,	PUNCT
ejpam-3725	10	20	etc	etc	X
ejpam-3725	10	21	.	.	X
ejpam-3725	10	22	properties	property	NOUN
ejpam-3725	10	23	of	of	ADP
ejpam-3725	10	24	graphs	graph	NOUN
ejpam-3725	10	25	which	which	PRON
ejpam-3725	10	26	are	be	AUX
ejpam-3725	10	27	modelling	model	VERB
ejpam-3725	10	28	real	real	ADJ
ejpam-3725	10	29	life	life	NOUN
ejpam-3725	10	30	situations	situation	NOUN
ejpam-3725	10	31	.	.	PUNCT
ejpam-3725	11	1	they	they	PRON
ejpam-3725	11	2	can	can	AUX
ejpam-3725	11	3	be	be	AUX
ejpam-3725	11	4	grouped	group	VERB
ejpam-3725	11	5	mainly	mainly	ADV
ejpam-3725	11	6	into	into	ADP
ejpam-3725	11	7	three	three	NUM
ejpam-3725	11	8	classes	class	NOUN
ejpam-3725	11	9	according	accord	VERB
ejpam-3725	11	10	to	to	ADP
ejpam-3725	11	11	the	the	DET
ejpam-3725	11	12	way	way	NOUN
ejpam-3725	11	13	they	they	PRON
ejpam-3725	11	14	are	be	AUX
ejpam-3725	11	15	defined	define	VERB
ejpam-3725	11	16	:	:	PUNCT
ejpam-3725	11	17	by	by	ADP
ejpam-3725	11	18	vertex	vertex	NOUN
ejpam-3725	11	19	degrees	degree	NOUN
ejpam-3725	11	20	,	,	PUNCT
ejpam-3725	11	21	by	by	ADP
ejpam-3725	11	22	matrices	matrix	NOUN
ejpam-3725	11	23	or	or	CCONJ
ejpam-3725	11	24	by	by	ADP
ejpam-3725	11	25	distances	distance	NOUN
ejpam-3725	11	26	.	.	PUNCT
ejpam-3725	12	1	we	we	PRON
ejpam-3725	12	2	consider	consider	VERB
ejpam-3725	12	3	degree	degree	NOUN
ejpam-3725	12	4	based	base	VERB
ejpam-3725	12	5	-	-	PUNCT
ejpam-3725	12	6	topological	topological	ADJ
ejpam-3725	12	7	indices	index	NOUN
ejpam-3725	12	8	of	of	ADP
ejpam-3725	12	9	some	some	DET
ejpam-3725	12	10	derived	derive	VERB
ejpam-3725	12	11	graphs	graph	NOUN
ejpam-3725	12	12	through	through	ADP
ejpam-3725	12	13	this	this	DET
ejpam-3725	12	14	paper	paper	NOUN
ejpam-3725	12	15	.	.	PUNCT
ejpam-3725	13	1	let	let	VERB
ejpam-3725	13	2	g	g	PROPN
ejpam-3725	13	3	=	=	SYM
ejpam-3725	13	4	(	(	PUNCT
ejpam-3725	13	5	v	v	NOUN
ejpam-3725	13	6	,	,	PUNCT
ejpam-3725	13	7	e	e	NOUN
ejpam-3725	13	8	)	)	PUNCT
ejpam-3725	13	9	be	be	AUX
ejpam-3725	13	10	a	a	DET
ejpam-3725	13	11	simple	simple	ADJ
ejpam-3725	13	12	graph	graph	NOUN
ejpam-3725	13	13	with	with	ADP
ejpam-3725	13	14	|	|	ADV
ejpam-3725	13	15	v	v	ADJ
ejpam-3725	13	16	(	(	PUNCT
ejpam-3725	13	17	g	g	NOUN
ejpam-3725	13	18	)	)	PUNCT
ejpam-3725	13	19	|=	|=	NOUN
ejpam-3725	13	20	n	n	PRON
ejpam-3725	13	21	vertices	vertex	NOUN
ejpam-3725	13	22	and	and	CCONJ
ejpam-3725	13	23	|	|	ADV
ejpam-3725	13	24	e(g	e(g	NOUN
ejpam-3725	13	25	)	)	PUNCT
ejpam-3725	13	26	|=	|=	NOUN
ejpam-3725	13	27	m	m	NOUN
ejpam-3725	13	28	edges	edge	NOUN
ejpam-3725	13	29	,	,	PUNCT
ejpam-3725	13	30	where	where	SCONJ
ejpam-3725	13	31	v	v	X
ejpam-3725	13	32	(	(	PUNCT
ejpam-3725	13	33	g	g	NOUN
ejpam-3725	13	34	)	)	PUNCT
ejpam-3725	13	35	=	=	SYM
ejpam-3725	13	36	{	{	PUNCT
ejpam-3725	13	37	v1	v1	PROPN
ejpam-3725	13	38	,	,	PUNCT
ejpam-3725	13	39	v2	v2	PROPN
ejpam-3725	13	40	,	,	PUNCT
ejpam-3725	13	41	·	·	PUNCT
ejpam-3725	13	42	·	·	PUNCT
ejpam-3725	13	43	·	·	PUNCT
ejpam-3725	13	44	,	,	PUNCT
ejpam-3725	13	45	vn	vn	INTJ
ejpam-3725	13	46	}	}	PUNCT
ejpam-3725	13	47	and	and	CCONJ
ejpam-3725	13	48	e(g	e(g	PROPN
ejpam-3725	13	49	)	)	PUNCT
ejpam-3725	14	1	=	=	PRON
ejpam-3725	14	2	{	{	PUNCT
ejpam-3725	14	3	vivj	vivj	NOUN
ejpam-3725	14	4	:	:	PUNCT
ejpam-3725	14	5	vi	vi	PROPN
ejpam-3725	14	6	,	,	PUNCT
ejpam-3725	14	7	vj	vj	X
ejpam-3725	14	8	∈	∈	PROPN
ejpam-3725	14	9	v	v	PROPN
ejpam-3725	14	10	(	(	PUNCT
ejpam-3725	14	11	g	g	NOUN
ejpam-3725	14	12	)	)	PUNCT
ejpam-3725	14	13	}	}	PUNCT
ejpam-3725	14	14	.	.	PUNCT
ejpam-3725	15	1	that	that	PRON
ejpam-3725	15	2	is	is	ADV
ejpam-3725	15	3	,	,	PUNCT
ejpam-3725	15	4	we	we	PRON
ejpam-3725	15	5	do	do	AUX
ejpam-3725	15	6	not	not	PART
ejpam-3725	15	7	∗corresponding	∗corresponde	VERB
ejpam-3725	15	8	author	author	NOUN
ejpam-3725	15	9	.	.	PUNCT
ejpam-3725	16	1	doi	doi	NOUN
ejpam-3725	16	2	:	:	PUNCT
ejpam-3725	16	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3725	https://doi.org/10.29020/nybg.ejpam.v13i5.3725	ADV
ejpam-3725	16	4	email	email	NOUN
ejpam-3725	16	5	addresses	address	NOUN
ejpam-3725	16	6	:	:	PUNCT
ejpam-3725	16	7	ayurttas@uludag.edu.tr	ayurttas@uludag.edu.tr	ADV
ejpam-3725	16	8	(	(	PUNCT
ejpam-3725	16	9	a.	a.	NOUN
ejpam-3725	16	10	yurttas	yurtta	NOUN
ejpam-3725	16	11	gunes	gune	NOUN
ejpam-3725	16	12	)	)	PUNCT
ejpam-3725	16	13	,	,	PUNCT
ejpam-3725	16	14	capkinm@uludag.edu.tr	capkinm@uludag.edu.tr	X
ejpam-3725	16	15	(	(	PUNCT
ejpam-3725	16	16	m.	m.	NOUN
ejpam-3725	16	17	togan	togan	PROPN
ejpam-3725	16	18	)	)	PUNCT
ejpam-3725	16	19	,	,	PUNCT
ejpam-3725	16	20	mdemirci@uludag.edu.tr	mdemirci@uludag.edu.tr	NOUN
ejpam-3725	16	21	(	(	PUNCT
ejpam-3725	16	22	m.	m.	NOUN
ejpam-3725	16	23	demirci	demirci	PROPN
ejpam-3725	16	24	)	)	PUNCT
ejpam-3725	16	25	,	,	PUNCT
ejpam-3725	16	26	cangul@uludag.edu.tr	cangul@uludag.edu.tr	NOUN
ejpam-3725	16	27	(	(	PUNCT
ejpam-3725	16	28	i.	i.	PROPN
ejpam-3725	16	29	n.	n.	PROPN
ejpam-3725	16	30	cangul	cangul	PROPN
ejpam-3725	16	31	)	)	PUNCT
ejpam-3725	16	32	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-3725	16	33	1260	1260	NUM
ejpam-3725	17	1	c	c	NOUN
ejpam-3725	17	2	©	©	NOUN
ejpam-3725	17	3	2020	2020	NUM
ejpam-3725	17	4	ejpam	ejpam	VERB
ejpam-3725	17	5	all	all	DET
ejpam-3725	17	6	rights	right	NOUN
ejpam-3725	17	7	reserved	reserve	VERB
ejpam-3725	17	8	.	.	PUNCT
ejpam-3725	18	1	m.	m.	NOUN
ejpam-3725	18	2	demirci	demirci	VERB
ejpam-3725	18	3	et	et	PROPN
ejpam-3725	18	4	al	al	PROPN
ejpam-3725	18	5	.	.	PUNCT
ejpam-3725	18	6	/	/	SYM
ejpam-3725	18	7	eur	eur	PROPN
ejpam-3725	18	8	.	.	PUNCT
ejpam-3725	19	1	j.	j.	PROPN
ejpam-3725	19	2	pure	pure	PROPN
ejpam-3725	19	3	appl	appl	PROPN
ejpam-3725	19	4	.	.	PROPN
ejpam-3725	19	5	math	math	PROPN
ejpam-3725	19	6	,	,	PUNCT
ejpam-3725	19	7	13	13	NUM
ejpam-3725	19	8	(	(	PUNCT
ejpam-3725	19	9	5	5	NUM
ejpam-3725	19	10	)	)	PUNCT
ejpam-3725	19	11	(	(	PUNCT
ejpam-3725	19	12	2020	2020	NUM
ejpam-3725	19	13	)	)	PUNCT
ejpam-3725	19	14	,	,	PUNCT
ejpam-3725	19	15	1260	1260	NUM
ejpam-3725	19	16	-	-	SYM
ejpam-3725	19	17	1269	1269	NUM
ejpam-3725	19	18	1261	1261	NUM
ejpam-3725	19	19	allow	allow	VERB
ejpam-3725	19	20	loops	loop	NOUN
ejpam-3725	19	21	or	or	CCONJ
ejpam-3725	19	22	multiple	multiple	ADJ
ejpam-3725	19	23	edges	edge	NOUN
ejpam-3725	19	24	.	.	PUNCT
ejpam-3725	20	1	for	for	ADP
ejpam-3725	20	2	any	any	DET
ejpam-3725	20	3	vertex	vertex	NOUN
ejpam-3725	20	4	v	v	ADP
ejpam-3725	20	5	∈	∈	NOUN
ejpam-3725	20	6	v	v	NOUN
ejpam-3725	20	7	(	(	PUNCT
ejpam-3725	20	8	g	g	NOUN
ejpam-3725	20	9	)	)	PUNCT
ejpam-3725	20	10	,	,	PUNCT
ejpam-3725	20	11	we	we	PRON
ejpam-3725	20	12	denote	denote	VERB
ejpam-3725	20	13	the	the	DET
ejpam-3725	20	14	degree	degree	NOUN
ejpam-3725	20	15	of	of	ADP
ejpam-3725	20	16	v	v	NUM
ejpam-3725	20	17	by	by	ADP
ejpam-3725	20	18	dg(v	dg(v	NOUN
ejpam-3725	20	19	)	)	PUNCT
ejpam-3725	20	20	or	or	CCONJ
ejpam-3725	20	21	dv	dv	PROPN
ejpam-3725	20	22	.	.	PUNCT
ejpam-3725	21	1	if	if	SCONJ
ejpam-3725	21	2	vi	vi	PROPN
ejpam-3725	21	3	and	and	CCONJ
ejpam-3725	21	4	vj	vj	PROPN
ejpam-3725	21	5	are	be	AUX
ejpam-3725	21	6	adjacent	adjacent	ADJ
ejpam-3725	21	7	vertices	vertex	NOUN
ejpam-3725	21	8	of	of	ADP
ejpam-3725	21	9	g	g	NOUN
ejpam-3725	21	10	,	,	PUNCT
ejpam-3725	21	11	and	and	CCONJ
ejpam-3725	21	12	if	if	SCONJ
ejpam-3725	21	13	the	the	DET
ejpam-3725	21	14	edge	edge	NOUN
ejpam-3725	21	15	e	e	NOUN
ejpam-3725	21	16	connects	connect	VERB
ejpam-3725	21	17	them	they	PRON
ejpam-3725	21	18	,	,	PUNCT
ejpam-3725	21	19	this	this	DET
ejpam-3725	21	20	situation	situation	NOUN
ejpam-3725	21	21	will	will	AUX
ejpam-3725	21	22	be	be	AUX
ejpam-3725	21	23	denoted	denote	VERB
ejpam-3725	21	24	by	by	ADP
ejpam-3725	21	25	e	e	NOUN
ejpam-3725	21	26	=	=	NOUN
ejpam-3725	21	27	vivj	vivj	NOUN
ejpam-3725	21	28	.	.	PUNCT
ejpam-3725	22	1	in	in	ADP
ejpam-3725	22	2	such	such	DET
ejpam-3725	22	3	a	a	DET
ejpam-3725	22	4	case	case	NOUN
ejpam-3725	22	5	,	,	PUNCT
ejpam-3725	22	6	the	the	DET
ejpam-3725	22	7	vertices	vertex	NOUN
ejpam-3725	22	8	vi	vi	PROPN
ejpam-3725	22	9	and	and	CCONJ
ejpam-3725	22	10	vj	vj	NOUN
ejpam-3725	22	11	are	be	AUX
ejpam-3725	22	12	called	call	VERB
ejpam-3725	22	13	adjacent	adjacent	ADJ
ejpam-3725	22	14	vertices	vertex	NOUN
ejpam-3725	22	15	and	and	CCONJ
ejpam-3725	22	16	the	the	DET
ejpam-3725	22	17	edge	edge	NOUN
ejpam-3725	22	18	e	e	NOUN
ejpam-3725	22	19	is	be	AUX
ejpam-3725	22	20	said	say	VERB
ejpam-3725	22	21	to	to	PART
ejpam-3725	22	22	be	be	AUX
ejpam-3725	22	23	incident	incident	NOUN
ejpam-3725	22	24	to	to	ADP
ejpam-3725	22	25	vi	vi	PROPN
ejpam-3725	22	26	and	and	CCONJ
ejpam-3725	22	27	vj	vj	INTJ
ejpam-3725	22	28	.	.	PUNCT
ejpam-3725	23	1	adjacency	adjacency	PROPN
ejpam-3725	23	2	and	and	CCONJ
ejpam-3725	23	3	incidency	incidency	NOUN
ejpam-3725	23	4	play	play	VERB
ejpam-3725	23	5	a	a	DET
ejpam-3725	23	6	very	very	ADV
ejpam-3725	23	7	important	important	ADJ
ejpam-3725	23	8	role	role	NOUN
ejpam-3725	23	9	in	in	ADP
ejpam-3725	23	10	the	the	DET
ejpam-3725	23	11	spectral	spectral	ADJ
ejpam-3725	23	12	graph	graph	NOUN
ejpam-3725	23	13	theory	theory	NOUN
ejpam-3725	23	14	,	,	PUNCT
ejpam-3725	23	15	the	the	DET
ejpam-3725	23	16	sub	sub	NOUN
ejpam-3725	23	17	area	area	NOUN
ejpam-3725	23	18	of	of	ADP
ejpam-3725	23	19	graph	graph	NOUN
ejpam-3725	23	20	theory	theory	NOUN
ejpam-3725	23	21	dealing	deal	VERB
ejpam-3725	23	22	with	with	ADP
ejpam-3725	23	23	linear	linear	ADJ
ejpam-3725	23	24	algebraic	algebraic	ADJ
ejpam-3725	23	25	study	study	NOUN
ejpam-3725	23	26	of	of	ADP
ejpam-3725	23	27	graphs	graph	NOUN
ejpam-3725	23	28	.	.	PUNCT
ejpam-3725	24	1	the	the	DET
ejpam-3725	24	2	smallest	small	ADJ
ejpam-3725	24	3	and	and	CCONJ
ejpam-3725	24	4	biggest	big	ADJ
ejpam-3725	24	5	vertex	vertex	NOUN
ejpam-3725	24	6	degrees	degree	NOUN
ejpam-3725	24	7	in	in	ADP
ejpam-3725	24	8	a	a	DET
ejpam-3725	24	9	graph	graph	NOUN
ejpam-3725	24	10	will	will	AUX
ejpam-3725	24	11	be	be	AUX
ejpam-3725	24	12	denoted	denote	VERB
ejpam-3725	24	13	by	by	ADP
ejpam-3725	24	14	δ	δ	PROPN
ejpam-3725	24	15	and	and	CCONJ
ejpam-3725	24	16	∆	∆	PROPN
ejpam-3725	24	17	,	,	PUNCT
ejpam-3725	24	18	respectively	respectively	ADV
ejpam-3725	24	19	.	.	PUNCT
ejpam-3725	25	1	written	write	VERB
ejpam-3725	25	2	with	with	ADP
ejpam-3725	25	3	multiplicities	multiplicity	NOUN
ejpam-3725	25	4	,	,	PUNCT
ejpam-3725	25	5	a	a	DET
ejpam-3725	25	6	degree	degree	NOUN
ejpam-3725	25	7	sequence	sequence	NOUN
ejpam-3725	25	8	in	in	ADP
ejpam-3725	25	9	general	general	ADJ
ejpam-3725	25	10	is	be	AUX
ejpam-3725	25	11	written	write	VERB
ejpam-3725	25	12	as	as	ADP
ejpam-3725	25	13	d	d	PROPN
ejpam-3725	25	14	=	=	SYM
ejpam-3725	25	15	{	{	PUNCT
ejpam-3725	25	16	1(a1	1(a1	NUM
ejpam-3725	25	17	)	)	PUNCT
ejpam-3725	25	18	,	,	PUNCT
ejpam-3725	25	19	2(a2	2(a2	NUM
ejpam-3725	25	20	)	)	PUNCT
ejpam-3725	25	21	,	,	PUNCT
ejpam-3725	25	22	3(a3	3(a3	NUM
ejpam-3725	25	23	)	)	PUNCT
ejpam-3725	25	24	,	,	PUNCT
ejpam-3725	25	25	·	·	PUNCT
ejpam-3725	25	26	·	·	PUNCT
ejpam-3725	25	27	·	·	PUNCT
ejpam-3725	25	28	,	,	PUNCT
ejpam-3725	25	29	∆(a∆	∆(a∆	NOUN
ejpam-3725	25	30	)	)	PUNCT
ejpam-3725	25	31	}	}	PUNCT
ejpam-3725	25	32	.	.	PUNCT
ejpam-3725	26	1	let	let	VERB
ejpam-3725	26	2	d	d	PRON
ejpam-3725	26	3	be	be	AUX
ejpam-3725	26	4	a	a	DET
ejpam-3725	26	5	set	set	NOUN
ejpam-3725	26	6	of	of	ADP
ejpam-3725	26	7	some	some	DET
ejpam-3725	26	8	non	non	ADJ
ejpam-3725	26	9	-	-	ADJ
ejpam-3725	26	10	decreasing	decrease	VERB
ejpam-3725	26	11	non	non	ADJ
ejpam-3725	26	12	-	-	ADJ
ejpam-3725	26	13	negative	negative	ADJ
ejpam-3725	26	14	integers	integer	NOUN
ejpam-3725	26	15	.	.	PUNCT
ejpam-3725	27	1	we	we	PRON
ejpam-3725	27	2	say	say	VERB
ejpam-3725	27	3	that	that	SCONJ
ejpam-3725	27	4	a	a	DET
ejpam-3725	27	5	graph	graph	NOUN
ejpam-3725	27	6	g	g	NOUN
ejpam-3725	27	7	is	be	AUX
ejpam-3725	27	8	a	a	DET
ejpam-3725	27	9	realization	realization	NOUN
ejpam-3725	27	10	of	of	ADP
ejpam-3725	27	11	the	the	DET
ejpam-3725	27	12	set	set	NOUN
ejpam-3725	27	13	d	d	NOUN
ejpam-3725	27	14	if	if	SCONJ
ejpam-3725	27	15	the	the	DET
ejpam-3725	27	16	degree	degree	NOUN
ejpam-3725	27	17	sequence	sequence	NOUN
ejpam-3725	27	18	of	of	ADP
ejpam-3725	27	19	g	g	PROPN
ejpam-3725	27	20	is	be	AUX
ejpam-3725	27	21	equal	equal	ADJ
ejpam-3725	27	22	to	to	ADP
ejpam-3725	27	23	d.	d.	PROPN
ejpam-3725	27	24	definition	definition	NOUN
ejpam-3725	27	25	1	1	NUM
ejpam-3725	27	26	.	.	PUNCT
ejpam-3725	28	1	[	[	X
ejpam-3725	28	2	7	7	X
ejpam-3725	28	3	]	]	X
ejpam-3725	28	4	let	let	NOUN
ejpam-3725	28	5	d	d	NOUN
ejpam-3725	28	6	=	=	PUNCT
ejpam-3725	28	7	{	{	PUNCT
ejpam-3725	28	8	1(a1	1(a1	NUM
ejpam-3725	28	9	)	)	PUNCT
ejpam-3725	28	10	,	,	PUNCT
ejpam-3725	28	11	2(a2	2(a2	NUM
ejpam-3725	28	12	)	)	PUNCT
ejpam-3725	28	13	,	,	PUNCT
ejpam-3725	28	14	3(a3	3(a3	NUM
ejpam-3725	28	15	)	)	PUNCT
ejpam-3725	28	16	,	,	PUNCT
ejpam-3725	28	17	·	·	PUNCT
ejpam-3725	28	18	·	·	PUNCT
ejpam-3725	28	19	·	·	PUNCT
ejpam-3725	28	20	,	,	PUNCT
ejpam-3725	28	21	∆(a∆	∆(a∆	NOUN
ejpam-3725	28	22	)	)	PUNCT
ejpam-3725	28	23	}	}	PUNCT
ejpam-3725	28	24	be	be	AUX
ejpam-3725	28	25	a	a	DET
ejpam-3725	28	26	realizable	realizable	ADJ
ejpam-3725	28	27	degree	degree	NOUN
ejpam-3725	28	28	sequence	sequence	NOUN
ejpam-3725	28	29	and	and	CCONJ
ejpam-3725	28	30	g	g	NOUN
ejpam-3725	28	31	be	be	AUX
ejpam-3725	28	32	one	one	NUM
ejpam-3725	28	33	of	of	ADP
ejpam-3725	28	34	its	its	PRON
ejpam-3725	28	35	realizations	realization	NOUN
ejpam-3725	28	36	.	.	PUNCT
ejpam-3725	29	1	the	the	DET
ejpam-3725	29	2	ω(g	ω(g	NOUN
ejpam-3725	29	3	)	)	PUNCT
ejpam-3725	29	4	of	of	ADP
ejpam-3725	29	5	g	g	PROPN
ejpam-3725	29	6	is	be	AUX
ejpam-3725	29	7	defined	define	VERB
ejpam-3725	29	8	in	in	ADP
ejpam-3725	29	9	terms	term	NOUN
ejpam-3725	29	10	of	of	ADP
ejpam-3725	29	11	the	the	DET
ejpam-3725	29	12	degree	degree	NOUN
ejpam-3725	29	13	sequence	sequence	NOUN
ejpam-3725	29	14	as	as	ADP
ejpam-3725	29	15	ω(g	ω(g	NOUN
ejpam-3725	29	16	)	)	PUNCT
ejpam-3725	29	17	=	=	NOUN
ejpam-3725	29	18	a3	a3	NOUN
ejpam-3725	29	19	+	+	CCONJ
ejpam-3725	29	20	2a4	2a4	NUM
ejpam-3725	29	21	+	+	NUM
ejpam-3725	29	22	3a5	3a5	NUM
ejpam-3725	29	23	+	+	NUM
ejpam-3725	29	24	·	·	PUNCT
ejpam-3725	29	25	·	·	PUNCT
ejpam-3725	29	26	·	·	PUNCT
ejpam-3725	29	27	+	+	CCONJ
ejpam-3725	29	28	(	(	PUNCT
ejpam-3725	29	29	∆−	∆−	NOUN
ejpam-3725	29	30	2)a∆	2)a∆	NUM
ejpam-3725	29	31	−	−	NOUN
ejpam-3725	29	32	a1	a1	NOUN
ejpam-3725	29	33	=	=	NOUN
ejpam-3725	29	34	∆∑	∆∑	NOUN
ejpam-3725	29	35	i=1	i=1	PROPN
ejpam-3725	29	36	ai(i−	ai(i−	PROPN
ejpam-3725	29	37	2	2	NUM
ejpam-3725	29	38	)	)	PUNCT
ejpam-3725	29	39	.	.	PUNCT
ejpam-3725	30	1	a	a	DET
ejpam-3725	30	2	vertex	vertex	NOUN
ejpam-3725	30	3	-	-	PUNCT
ejpam-3725	30	4	semitotal	semitotal	ADJ
ejpam-3725	30	5	graph	graph	NOUN
ejpam-3725	30	6	t1(g	t1(g	PROPN
ejpam-3725	30	7	)	)	PUNCT
ejpam-3725	30	8	is	be	AUX
ejpam-3725	30	9	constructed	construct	VERB
ejpam-3725	30	10	fromg	fromg	NOUN
ejpam-3725	30	11	by	by	ADP
ejpam-3725	30	12	inserting	insert	VERB
ejpam-3725	30	13	a	a	DET
ejpam-3725	30	14	new	new	ADJ
ejpam-3725	30	15	vertex	vertex	NOUN
ejpam-3725	30	16	for	for	ADP
ejpam-3725	30	17	each	each	DET
ejpam-3725	30	18	edge	edge	NOUN
ejpam-3725	30	19	of	of	ADP
ejpam-3725	30	20	g	g	NOUN
ejpam-3725	30	21	and	and	CCONJ
ejpam-3725	30	22	then	then	ADV
ejpam-3725	30	23	by	by	ADP
ejpam-3725	30	24	joining	join	VERB
ejpam-3725	30	25	every	every	DET
ejpam-3725	30	26	inserted	insert	VERB
ejpam-3725	30	27	vertex	vertex	NOUN
ejpam-3725	30	28	to	to	ADP
ejpam-3725	30	29	the	the	DET
ejpam-3725	30	30	end	end	NOUN
ejpam-3725	30	31	vertices	vertex	NOUN
ejpam-3725	30	32	of	of	ADP
ejpam-3725	30	33	the	the	DET
ejpam-3725	30	34	corresponding	corresponding	ADJ
ejpam-3725	30	35	edge	edge	NOUN
ejpam-3725	30	36	,	,	PUNCT
ejpam-3725	30	37	that	that	ADV
ejpam-3725	30	38	is	is	ADV
ejpam-3725	30	39	,	,	PUNCT
ejpam-3725	30	40	by	by	ADP
ejpam-3725	30	41	replacing	replace	VERB
ejpam-3725	30	42	each	each	DET
ejpam-3725	30	43	edge	edge	NOUN
ejpam-3725	30	44	by	by	ADP
ejpam-3725	30	45	a	a	DET
ejpam-3725	30	46	triangle	triangle	NOUN
ejpam-3725	30	47	.	.	PUNCT
ejpam-3725	31	1	see	see	VERB
ejpam-3725	31	2	fig	fig	NOUN
ejpam-3725	31	3	.	.	PUNCT
ejpam-3725	32	1	1	1	X
ejpam-3725	32	2	.	.	PUNCT
ejpam-3725	32	3	thus	thus	ADV
ejpam-3725	32	4	|v	|v	X
ejpam-3725	32	5	(	(	PUNCT
ejpam-3725	32	6	t1)|	t1)|	PROPN
ejpam-3725	32	7	=	=	PUNCT
ejpam-3725	32	8	|v	|v	PROPN
ejpam-3725	32	9	(	(	PUNCT
ejpam-3725	32	10	g)|+	g)|+	NOUN
ejpam-3725	32	11	|e(g)|	|e(g)|	PROPN
ejpam-3725	32	12	=	=	PROPN
ejpam-3725	32	13	n+m	n+m	PROPN
ejpam-3725	32	14	and	and	CCONJ
ejpam-3725	32	15	|e(t1)|	|e(t1)|	NUM
ejpam-3725	32	16	=	=	NOUN
ejpam-3725	32	17	|e(s)|+	|e(s)|+	NOUN
ejpam-3725	33	1	|e(g)|	|e(g)|	PROPN
ejpam-3725	33	2	=	=	SYM
ejpam-3725	33	3	2m+m	2m+m	NUM
ejpam-3725	33	4	=	=	SYM
ejpam-3725	33	5	3	3	NUM
ejpam-3725	33	6	m.	m.	NOUN
ejpam-3725	33	7	two	two	NUM
ejpam-3725	33	8	of	of	ADP
ejpam-3725	33	9	the	the	DET
ejpam-3725	33	10	most	most	ADV
ejpam-3725	33	11	important	important	ADJ
ejpam-3725	33	12	topological	topological	ADJ
ejpam-3725	33	13	graph	graph	NOUN
ejpam-3725	33	14	indices	index	NOUN
ejpam-3725	33	15	are	be	AUX
ejpam-3725	33	16	called	call	VERB
ejpam-3725	33	17	the	the	DET
ejpam-3725	33	18	first	first	ADJ
ejpam-3725	33	19	and	and	CCONJ
ejpam-3725	33	20	second	second	ADJ
ejpam-3725	33	21	zagreb	zagreb	PROPN
ejpam-3725	33	22	indices	index	NOUN
ejpam-3725	33	23	denoted	denote	VERB
ejpam-3725	33	24	by	by	ADP
ejpam-3725	33	25	m1(g	m1(g	NOUN
ejpam-3725	33	26	)	)	PUNCT
ejpam-3725	33	27	and	and	CCONJ
ejpam-3725	33	28	m2(g	m2(g	NOUN
ejpam-3725	33	29	)	)	PUNCT
ejpam-3725	33	30	,	,	PUNCT
ejpam-3725	33	31	respectively	respectively	ADV
ejpam-3725	33	32	:	:	PUNCT
ejpam-3725	33	33	m1(g	m1(g	NOUN
ejpam-3725	33	34	)	)	PUNCT
ejpam-3725	33	35	=	=	SYM
ejpam-3725	34	1	∑	∑	PUNCT
ejpam-3725	34	2	u∈v	u∈v	NOUN
ejpam-3725	34	3	(	(	PUNCT
ejpam-3725	34	4	g	g	NOUN
ejpam-3725	34	5	)	)	PUNCT
ejpam-3725	34	6	d2	d2	NOUN
ejpam-3725	34	7	g(u	g(u	PROPN
ejpam-3725	34	8	)	)	PUNCT
ejpam-3725	34	9	and	and	CCONJ
ejpam-3725	34	10	m2(g	m2(g	NOUN
ejpam-3725	34	11	)	)	PUNCT
ejpam-3725	34	12	=	=	SYM
ejpam-3725	34	13	∑	∑	PUNCT
ejpam-3725	34	14	uv∈e(g	uv∈e(g	NUM
ejpam-3725	34	15	)	)	PUNCT
ejpam-3725	34	16	dg(u)dg(v	dg(u)dg(v	PROPN
ejpam-3725	34	17	)	)	PUNCT
ejpam-3725	34	18	.	.	PUNCT
ejpam-3725	35	1	(	(	PUNCT
ejpam-3725	35	2	1	1	X
ejpam-3725	35	3	)	)	PUNCT
ejpam-3725	35	4	they	they	PRON
ejpam-3725	35	5	were	be	AUX
ejpam-3725	35	6	first	first	ADV
ejpam-3725	35	7	defined	define	VERB
ejpam-3725	35	8	in	in	ADP
ejpam-3725	35	9	1972	1972	NUM
ejpam-3725	35	10	by	by	ADP
ejpam-3725	35	11	gutman	gutman	NOUN
ejpam-3725	35	12	and	and	CCONJ
ejpam-3725	35	13	trinajstic	trinajstic	ADJ
ejpam-3725	35	14	,	,	PUNCT
ejpam-3725	35	15	[	[	X
ejpam-3725	35	16	12	12	NUM
ejpam-3725	35	17	]	]	PUNCT
ejpam-3725	35	18	,	,	PUNCT
ejpam-3725	35	19	and	and	CCONJ
ejpam-3725	35	20	are	be	AUX
ejpam-3725	35	21	referred	refer	VERB
ejpam-3725	35	22	to	to	ADP
ejpam-3725	35	23	due	due	ADP
ejpam-3725	35	24	to	to	ADP
ejpam-3725	35	25	their	their	PRON
ejpam-3725	35	26	uses	use	NOUN
ejpam-3725	35	27	in	in	ADP
ejpam-3725	35	28	qsar	qsar	NOUN
ejpam-3725	35	29	and	and	CCONJ
ejpam-3725	35	30	qspr	qspr	NOUN
ejpam-3725	35	31	studies	study	NOUN
ejpam-3725	35	32	.	.	PUNCT
ejpam-3725	36	1	in	in	ADP
ejpam-3725	36	2	[	[	X
ejpam-3725	36	3	4	4	NUM
ejpam-3725	36	4	]	]	PUNCT
ejpam-3725	36	5	,	,	PUNCT
ejpam-3725	36	6	some	some	PRON
ejpam-3725	36	7	results	result	VERB
ejpam-3725	36	8	on	on	ADP
ejpam-3725	36	9	the	the	DET
ejpam-3725	36	10	first	first	ADJ
ejpam-3725	36	11	zagreb	zagreb	PROPN
ejpam-3725	36	12	index	index	NOUN
ejpam-3725	36	13	together	together	ADV
ejpam-3725	36	14	with	with	ADP
ejpam-3725	36	15	some	some	DET
ejpam-3725	36	16	other	other	ADJ
ejpam-3725	36	17	indices	index	NOUN
ejpam-3725	36	18	are	be	AUX
ejpam-3725	36	19	given	give	VERB
ejpam-3725	36	20	.	.	PUNCT
ejpam-3725	37	1	for	for	ADP
ejpam-3725	37	2	some	some	DET
ejpam-3725	37	3	graph	graph	NOUN
ejpam-3725	37	4	operations	operation	NOUN
ejpam-3725	37	5	,	,	PUNCT
ejpam-3725	37	6	these	these	DET
ejpam-3725	37	7	indices	index	NOUN
ejpam-3725	37	8	are	be	AUX
ejpam-3725	37	9	calculated	calculate	VERB
ejpam-3725	37	10	in	in	ADP
ejpam-3725	37	11	[	[	X
ejpam-3725	37	12	5	5	NUM
ejpam-3725	37	13	,	,	PUNCT
ejpam-3725	37	14	14	14	NUM
ejpam-3725	37	15	,	,	PUNCT
ejpam-3725	37	16	17	17	NUM
ejpam-3725	37	17	]	]	PUNCT
ejpam-3725	37	18	.	.	PUNCT
ejpam-3725	38	1	the	the	DET
ejpam-3725	38	2	f	f	PROPN
ejpam-3725	38	3	-index	-index	PROPN
ejpam-3725	38	4	or	or	CCONJ
ejpam-3725	38	5	forgotten	forget	VERB
ejpam-3725	38	6	index	index	NOUN
ejpam-3725	38	7	of	of	ADP
ejpam-3725	38	8	a	a	DET
ejpam-3725	38	9	graph	graph	NOUN
ejpam-3725	38	10	g	g	NOUN
ejpam-3725	38	11	denoted	denote	VERB
ejpam-3725	38	12	by	by	ADP
ejpam-3725	38	13	f	f	PROPN
ejpam-3725	38	14	(	(	PUNCT
ejpam-3725	38	15	g	g	NOUN
ejpam-3725	38	16	)	)	PUNCT
ejpam-3725	38	17	or	or	CCONJ
ejpam-3725	38	18	m3(g	m3(g	NOUN
ejpam-3725	38	19	)	)	PUNCT
ejpam-3725	38	20	is	be	AUX
ejpam-3725	38	21	defined	define	VERB
ejpam-3725	38	22	as	as	ADP
ejpam-3725	38	23	f	f	PROPN
ejpam-3725	38	24	(	(	PUNCT
ejpam-3725	38	25	g	g	NOUN
ejpam-3725	38	26	)	)	PUNCT
ejpam-3725	38	27	=	=	SYM
ejpam-3725	39	1	∑	∑	PUNCT
ejpam-3725	39	2	u∈v	u∈v	NOUN
ejpam-3725	39	3	(	(	PUNCT
ejpam-3725	39	4	g	g	NOUN
ejpam-3725	39	5	)	)	PUNCT
ejpam-3725	39	6	d3	d3	PROPN
ejpam-3725	39	7	g(u	g(u	PROPN
ejpam-3725	39	8	)	)	PUNCT
ejpam-3725	39	9	.	.	PUNCT
ejpam-3725	40	1	(	(	PUNCT
ejpam-3725	40	2	2	2	X
ejpam-3725	40	3	)	)	PUNCT
ejpam-3725	40	4	m.	m.	NOUN
ejpam-3725	40	5	demirci	demirci	VERB
ejpam-3725	40	6	et	et	PROPN
ejpam-3725	40	7	al	al	PROPN
ejpam-3725	40	8	.	.	PUNCT
ejpam-3725	40	9	/	/	SYM
ejpam-3725	40	10	eur	eur	PROPN
ejpam-3725	40	11	.	.	PUNCT
ejpam-3725	41	1	j.	j.	PROPN
ejpam-3725	41	2	pure	pure	PROPN
ejpam-3725	41	3	appl	appl	PROPN
ejpam-3725	41	4	.	.	PROPN
ejpam-3725	41	5	math	math	PROPN
ejpam-3725	41	6	,	,	PUNCT
ejpam-3725	41	7	13	13	NUM
ejpam-3725	41	8	(	(	PUNCT
ejpam-3725	41	9	5	5	NUM
ejpam-3725	41	10	)	)	PUNCT
ejpam-3725	41	11	(	(	PUNCT
ejpam-3725	41	12	2020	2020	NUM
ejpam-3725	41	13	)	)	PUNCT
ejpam-3725	41	14	,	,	PUNCT
ejpam-3725	41	15	1260	1260	NUM
ejpam-3725	41	16	-	-	SYM
ejpam-3725	41	17	1269	1269	NUM
ejpam-3725	41	18	1262	1262	NUM
ejpam-3725	41	19	figure	figure	NOUN
ejpam-3725	41	20	1	1	NUM
ejpam-3725	41	21	the	the	DET
ejpam-3725	41	22	vertex	vertex	NOUN
ejpam-3725	41	23	-	-	PUNCT
ejpam-3725	41	24	semitotal	semitotal	ADJ
ejpam-3725	41	25	graph	graph	NOUN
ejpam-3725	41	26	t1(g	t1(g	PROPN
ejpam-3725	41	27	)	)	PUNCT
ejpam-3725	41	28	of	of	ADP
ejpam-3725	41	29	t3,2	t3,2	NOUN
ejpam-3725	41	30	it	it	PRON
ejpam-3725	41	31	was	be	AUX
ejpam-3725	41	32	first	first	ADV
ejpam-3725	41	33	appeared	appear	VERB
ejpam-3725	41	34	in	in	ADP
ejpam-3725	41	35	the	the	DET
ejpam-3725	41	36	study	study	NOUN
ejpam-3725	41	37	of	of	ADP
ejpam-3725	41	38	structure	structure	NOUN
ejpam-3725	41	39	-	-	PUNCT
ejpam-3725	41	40	dependency	dependency	NOUN
ejpam-3725	41	41	of	of	ADP
ejpam-3725	41	42	total	total	ADJ
ejpam-3725	41	43	π	π	PROPN
ejpam-3725	41	44	-	-	NOUN
ejpam-3725	41	45	electron	electron	NOUN
ejpam-3725	41	46	energy	energy	NOUN
ejpam-3725	41	47	in	in	ADP
ejpam-3725	41	48	1972	1972	NUM
ejpam-3725	41	49	,	,	PUNCT
ejpam-3725	42	1	[	[	X
ejpam-3725	42	2	12	12	NUM
ejpam-3725	42	3	]	]	PUNCT
ejpam-3725	42	4	.	.	PUNCT
ejpam-3725	43	1	recently	recently	ADV
ejpam-3725	43	2	,	,	PUNCT
ejpam-3725	43	3	this	this	DET
ejpam-3725	43	4	sum	sum	NOUN
ejpam-3725	43	5	was	be	AUX
ejpam-3725	43	6	named	name	VERB
ejpam-3725	43	7	as	as	ADP
ejpam-3725	43	8	the	the	DET
ejpam-3725	43	9	forgotten	forget	VERB
ejpam-3725	43	10	index	index	NOUN
ejpam-3725	43	11	or	or	CCONJ
ejpam-3725	43	12	the	the	DET
ejpam-3725	43	13	f	f	PROPN
ejpam-3725	43	14	-index	-index	PROPN
ejpam-3725	43	15	by	by	ADP
ejpam-3725	43	16	furtula	furtula	NOUN
ejpam-3725	43	17	and	and	CCONJ
ejpam-3725	43	18	gutman	gutman	NOUN
ejpam-3725	43	19	,	,	PUNCT
ejpam-3725	43	20	[	[	X
ejpam-3725	43	21	10	10	NUM
ejpam-3725	43	22	]	]	PUNCT
ejpam-3725	43	23	.	.	PUNCT
ejpam-3725	44	1	the	the	DET
ejpam-3725	44	2	hyper	hyper	PROPN
ejpam-3725	44	3	-	-	ADJ
ejpam-3725	44	4	zagreb	zagreb	PROPN
ejpam-3725	44	5	index	index	NOUN
ejpam-3725	44	6	was	be	AUX
ejpam-3725	44	7	defined	define	VERB
ejpam-3725	44	8	as	as	ADP
ejpam-3725	44	9	a	a	DET
ejpam-3725	44	10	variety	variety	NOUN
ejpam-3725	44	11	of	of	ADP
ejpam-3725	44	12	the	the	DET
ejpam-3725	44	13	classical	classical	ADJ
ejpam-3725	44	14	zagreb	zagreb	PROPN
ejpam-3725	44	15	indices	index	NOUN
ejpam-3725	44	16	as	as	ADP
ejpam-3725	44	17	hm(g	hm(g	NOUN
ejpam-3725	44	18	)	)	PUNCT
ejpam-3725	45	1	=	=	PUNCT
ejpam-3725	45	2	∑	∑	PUNCT
ejpam-3725	45	3	uv∈e	uv∈e	PROPN
ejpam-3725	45	4	(	(	PUNCT
ejpam-3725	45	5	du	du	PROPN
ejpam-3725	45	6	+	+	CCONJ
ejpam-3725	45	7	dv	dv	PROPN
ejpam-3725	45	8	)	)	PUNCT
ejpam-3725	45	9	2	2	NUM
ejpam-3725	45	10	,	,	PUNCT
ejpam-3725	45	11	(	(	PUNCT
ejpam-3725	45	12	3	3	X
ejpam-3725	45	13	)	)	PUNCT
ejpam-3725	45	14	see	see	VERB
ejpam-3725	45	15	e.g.	e.g.	ADV
ejpam-3725	45	16	[	[	X
ejpam-3725	45	17	10	10	NUM
ejpam-3725	45	18	]	]	PUNCT
ejpam-3725	45	19	.	.	PUNCT
ejpam-3725	46	1	inspired	inspire	VERB
ejpam-3725	46	2	by	by	ADP
ejpam-3725	46	3	the	the	DET
ejpam-3725	46	4	study	study	NOUN
ejpam-3725	46	5	of	of	ADP
ejpam-3725	46	6	heat	heat	NOUN
ejpam-3725	46	7	of	of	ADP
ejpam-3725	46	8	formation	formation	NOUN
ejpam-3725	46	9	for	for	ADP
ejpam-3725	46	10	heptanes	heptane	NOUN
ejpam-3725	46	11	and	and	CCONJ
ejpam-3725	46	12	octanes	octane	NOUN
ejpam-3725	46	13	,	,	PUNCT
ejpam-3725	46	14	in	in	ADP
ejpam-3725	46	15	[	[	X
ejpam-3725	46	16	9	9	NUM
ejpam-3725	46	17	]	]	PUNCT
ejpam-3725	46	18	furtula	furtula	NOUN
ejpam-3725	46	19	et	et	PROPN
ejpam-3725	46	20	al	al	PROPN
ejpam-3725	46	21	.	.	PROPN
ejpam-3725	46	22	proposed	propose	VERB
ejpam-3725	46	23	an	an	DET
ejpam-3725	46	24	index	index	NOUN
ejpam-3725	46	25	called	call	VERB
ejpam-3725	46	26	augmented	augment	VERB
ejpam-3725	46	27	zagreb	zagreb	PROPN
ejpam-3725	46	28	index	index	NOUN
ejpam-3725	46	29	which	which	PRON
ejpam-3725	46	30	gives	give	VERB
ejpam-3725	46	31	a	a	DET
ejpam-3725	46	32	better	well	ADJ
ejpam-3725	46	33	prediction	prediction	NOUN
ejpam-3725	46	34	power	power	NOUN
ejpam-3725	46	35	.	.	PUNCT
ejpam-3725	47	1	it	it	PRON
ejpam-3725	47	2	is	be	AUX
ejpam-3725	47	3	defined	define	VERB
ejpam-3725	47	4	by	by	ADP
ejpam-3725	47	5	azi(g	azi(g	PROPN
ejpam-3725	47	6	)	)	PUNCT
ejpam-3725	48	1	=	=	SYM
ejpam-3725	48	2	∑	∑	PUNCT
ejpam-3725	48	3	uv∈e(g	uv∈e(g	NUM
ejpam-3725	48	4	)	)	PUNCT
ejpam-3725	48	5	(	(	PUNCT
ejpam-3725	48	6	dudv	dudv	ADP
ejpam-3725	48	7	du	du	PROPN
ejpam-3725	48	8	+	+	CCONJ
ejpam-3725	48	9	dv	dv	PROPN
ejpam-3725	48	10	−	−	PROPN
ejpam-3725	48	11	2	2	NUM
ejpam-3725	48	12	)	)	PUNCT
ejpam-3725	48	13	3	3	NUM
ejpam-3725	48	14	.	.	PUNCT
ejpam-3725	49	1	(	(	PUNCT
ejpam-3725	49	2	4	4	X
ejpam-3725	49	3	)	)	PUNCT
ejpam-3725	49	4	the	the	DET
ejpam-3725	49	5	harmonic	harmonic	ADJ
ejpam-3725	49	6	index	index	NOUN
ejpam-3725	49	7	was	be	AUX
ejpam-3725	49	8	introduced	introduce	VERB
ejpam-3725	49	9	by	by	ADP
ejpam-3725	49	10	zhong	zhong	PROPN
ejpam-3725	50	1	[	[	X
ejpam-3725	50	2	19	19	NUM
ejpam-3725	50	3	]	]	PUNCT
ejpam-3725	50	4	who	who	PRON
ejpam-3725	50	5	found	find	VERB
ejpam-3725	50	6	that	that	SCONJ
ejpam-3725	50	7	it	it	PRON
ejpam-3725	50	8	correlates	correlate	VERB
ejpam-3725	50	9	well	well	ADV
ejpam-3725	50	10	with	with	ADP
ejpam-3725	50	11	π	π	PROPN
ejpam-3725	50	12	-	-	NOUN
ejpam-3725	50	13	electron	electron	NOUN
ejpam-3725	50	14	energy	energy	NOUN
ejpam-3725	50	15	of	of	ADP
ejpam-3725	50	16	benzenoid	benzenoid	NOUN
ejpam-3725	50	17	hydrocarbons	hydrocarbon	NOUN
ejpam-3725	50	18	and	and	CCONJ
ejpam-3725	50	19	defined	define	VERB
ejpam-3725	50	20	as	as	ADP
ejpam-3725	50	21	h(g	h(g	NOUN
ejpam-3725	50	22	)	)	PUNCT
ejpam-3725	50	23	=	=	SYM
ejpam-3725	50	24	∑	∑	PUNCT
ejpam-3725	50	25	uv∈e(g	uv∈e(g	NUM
ejpam-3725	50	26	)	)	PUNCT
ejpam-3725	50	27	2	2	NUM
ejpam-3725	50	28	du	du	X
ejpam-3725	50	29	+	+	X
ejpam-3725	50	30	dv	dv	PROPN
ejpam-3725	50	31	.	.	PUNCT
ejpam-3725	51	1	(	(	PUNCT
ejpam-3725	51	2	5	5	X
ejpam-3725	51	3	)	)	PUNCT
ejpam-3725	51	4	ranjini	ranjini	NOUN
ejpam-3725	51	5	et	et	PROPN
ejpam-3725	51	6	al	al	PROPN
ejpam-3725	51	7	.	.	PROPN
ejpam-3725	51	8	,	,	PUNCT
ejpam-3725	52	1	[	[	X
ejpam-3725	52	2	16	16	NUM
ejpam-3725	52	3	]	]	PUNCT
ejpam-3725	52	4	,	,	PUNCT
ejpam-3725	52	5	introduced	introduce	VERB
ejpam-3725	52	6	the	the	DET
ejpam-3725	52	7	re	re	NOUN
ejpam-3725	52	8	-	-	VERB
ejpam-3725	52	9	defined	define	VERB
ejpam-3725	52	10	zagreb	zagreb	PROPN
ejpam-3725	52	11	indices	index	NOUN
ejpam-3725	52	12	,	,	PUNCT
ejpam-3725	52	13	i.e.	i.e.	X
ejpam-3725	52	14	the	the	DET
ejpam-3725	52	15	redefined	redefined	ADJ
ejpam-3725	52	16	first	first	ADV
ejpam-3725	52	17	,	,	PUNCT
ejpam-3725	52	18	m.	m.	NOUN
ejpam-3725	52	19	demirci	demirci	VERB
ejpam-3725	52	20	et	et	PROPN
ejpam-3725	52	21	al	al	PROPN
ejpam-3725	52	22	.	.	PUNCT
ejpam-3725	52	23	/	/	SYM
ejpam-3725	52	24	eur	eur	PROPN
ejpam-3725	52	25	.	.	PUNCT
ejpam-3725	53	1	j.	j.	PROPN
ejpam-3725	53	2	pure	pure	PROPN
ejpam-3725	53	3	appl	appl	PROPN
ejpam-3725	53	4	.	.	PROPN
ejpam-3725	53	5	math	math	PROPN
ejpam-3725	53	6	,	,	PUNCT
ejpam-3725	53	7	13	13	NUM
ejpam-3725	53	8	(	(	PUNCT
ejpam-3725	53	9	5	5	NUM
ejpam-3725	53	10	)	)	PUNCT
ejpam-3725	53	11	(	(	PUNCT
ejpam-3725	53	12	2020	2020	NUM
ejpam-3725	53	13	)	)	PUNCT
ejpam-3725	53	14	,	,	PUNCT
ejpam-3725	53	15	1260	1260	NUM
ejpam-3725	53	16	-	-	SYM
ejpam-3725	53	17	1269	1269	NUM
ejpam-3725	53	18	1263	1263	NUM
ejpam-3725	53	19	second	second	ADJ
ejpam-3725	53	20	and	and	CCONJ
ejpam-3725	53	21	third	third	ADJ
ejpam-3725	53	22	zagreb	zagreb	PROPN
ejpam-3725	53	23	indices	index	NOUN
ejpam-3725	53	24	for	for	ADP
ejpam-3725	53	25	a	a	DET
ejpam-3725	53	26	graph	graph	NOUN
ejpam-3725	53	27	g	g	NOUN
ejpam-3725	53	28	and	and	CCONJ
ejpam-3725	53	29	these	these	PRON
ejpam-3725	53	30	are	be	AUX
ejpam-3725	53	31	defined	define	VERB
ejpam-3725	53	32	as	as	ADP
ejpam-3725	53	33	rezg1(g	rezg1(g	NOUN
ejpam-3725	53	34	)	)	PUNCT
ejpam-3725	53	35	=	=	SYM
ejpam-3725	53	36	∑	∑	PUNCT
ejpam-3725	53	37	uv∈e(g	uv∈e(g	NUM
ejpam-3725	53	38	)	)	PUNCT
ejpam-3725	53	39	du	du	PROPN
ejpam-3725	54	1	+	+	CCONJ
ejpam-3725	54	2	dv	dv	PROPN
ejpam-3725	54	3	du	du	PROPN
ejpam-3725	54	4	·	·	PUNCT
ejpam-3725	54	5	dv	dv	PROPN
ejpam-3725	54	6	,	,	PUNCT
ejpam-3725	54	7	(	(	PUNCT
ejpam-3725	54	8	6	6	NUM
ejpam-3725	54	9	)	)	PUNCT
ejpam-3725	54	10	rezg2(g	rezg2(g	PROPN
ejpam-3725	54	11	)	)	PUNCT
ejpam-3725	54	12	=	=	SYM
ejpam-3725	54	13	∑	∑	PUNCT
ejpam-3725	54	14	uv∈e(g	uv∈e(g	NUM
ejpam-3725	54	15	)	)	PUNCT
ejpam-3725	54	16	du	du	PROPN
ejpam-3725	54	17	·	·	PUNCT
ejpam-3725	54	18	dv	dv	PROPN
ejpam-3725	54	19	du	du	PROPN
ejpam-3725	54	20	+	+	CCONJ
ejpam-3725	54	21	dv	dv	PROPN
ejpam-3725	54	22	,	,	PUNCT
ejpam-3725	54	23	(	(	PUNCT
ejpam-3725	54	24	7	7	X
ejpam-3725	54	25	)	)	PUNCT
ejpam-3725	54	26	rezg3(g	rezg3(g	NOUN
ejpam-3725	54	27	)	)	PUNCT
ejpam-3725	55	1	=	=	SYM
ejpam-3725	55	2	∑	∑	PUNCT
ejpam-3725	55	3	uv∈e(g	uv∈e(g	NUM
ejpam-3725	55	4	)	)	PUNCT
ejpam-3725	55	5	(	(	PUNCT
ejpam-3725	55	6	du	du	X
ejpam-3725	55	7	·	·	PUNCT
ejpam-3725	55	8	dv)(du	dv)(du	PROPN
ejpam-3725	55	9	+	+	CCONJ
ejpam-3725	55	10	dv	dv	PROPN
ejpam-3725	55	11	)	)	PUNCT
ejpam-3725	55	12	.	.	PUNCT
ejpam-3725	56	1	(	(	PUNCT
ejpam-3725	56	2	8)	8)	NUM
ejpam-3725	56	3	milicevic	milicevic	ADJ
ejpam-3725	56	4	et	et	PROPN
ejpam-3725	56	5	al	al	PROPN
ejpam-3725	56	6	.	.	PROPN
ejpam-3725	56	7	,	,	PUNCT
ejpam-3725	57	1	[	[	X
ejpam-3725	57	2	15	15	NUM
ejpam-3725	57	3	]	]	PUNCT
ejpam-3725	57	4	,	,	PUNCT
ejpam-3725	57	5	reformulated	reformulate	VERB
ejpam-3725	57	6	the	the	DET
ejpam-3725	57	7	zagreb	zagreb	PROPN
ejpam-3725	57	8	indices	index	NOUN
ejpam-3725	57	9	in	in	ADP
ejpam-3725	57	10	terms	term	NOUN
ejpam-3725	57	11	of	of	ADP
ejpam-3725	57	12	the	the	DET
ejpam-3725	57	13	edge	edge	NOUN
ejpam-3725	57	14	degrees	degree	NOUN
ejpam-3725	57	15	instead	instead	ADV
ejpam-3725	57	16	of	of	ADP
ejpam-3725	57	17	the	the	DET
ejpam-3725	57	18	vertex	vertex	NOUN
ejpam-3725	57	19	-	-	PUNCT
ejpam-3725	57	20	degrees	degree	NOUN
ejpam-3725	57	21	as	as	ADP
ejpam-3725	57	22	em1(g	em1(g	NUM
ejpam-3725	57	23	)	)	PUNCT
ejpam-3725	57	24	=	=	PUNCT
ejpam-3725	58	1	∑	∑	PUNCT
ejpam-3725	58	2	e	e	X
ejpam-3725	58	3	=	=	NOUN
ejpam-3725	58	4	uv∈e(g	uv∈e(g	NOUN
ejpam-3725	58	5	)	)	PUNCT
ejpam-3725	58	6	d(e)2	d(e)2	NOUN
ejpam-3725	58	7	and	and	CCONJ
ejpam-3725	58	8	em2(g	em2(g	NUM
ejpam-3725	58	9	)	)	PUNCT
ejpam-3725	59	1	=	=	SYM
ejpam-3725	59	2	∑	∑	PUNCT
ejpam-3725	59	3	e	e	PROPN
ejpam-3725	59	4	f∈e(g	f∈e(g	PROPN
ejpam-3725	59	5	)	)	PUNCT
ejpam-3725	59	6	dg(e)dg(f	dg(e)dg(f	PROPN
ejpam-3725	59	7	)	)	PUNCT
ejpam-3725	59	8	.	.	PUNCT
ejpam-3725	60	1	(	(	PUNCT
ejpam-3725	60	2	9	9	X
ejpam-3725	60	3	)	)	PUNCT
ejpam-3725	60	4	aram	aram	PROPN
ejpam-3725	60	5	and	and	CCONJ
ejpam-3725	60	6	dehgardi	dehgardi	PROPN
ejpam-3725	60	7	,	,	PUNCT
ejpam-3725	60	8	[	[	X
ejpam-3725	60	9	1	1	NUM
ejpam-3725	60	10	]	]	PUNCT
ejpam-3725	60	11	,	,	PUNCT
ejpam-3725	60	12	introduced	introduce	VERB
ejpam-3725	60	13	the	the	DET
ejpam-3725	60	14	concept	concept	NOUN
ejpam-3725	60	15	of	of	ADP
ejpam-3725	60	16	reformulated	reformulate	VERB
ejpam-3725	60	17	f	f	NOUN
ejpam-3725	60	18	-	-	PUNCT
ejpam-3725	60	19	index	index	NOUN
ejpam-3725	60	20	as	as	ADP
ejpam-3725	60	21	rf	rf	ADJ
ejpam-3725	60	22	(	(	PUNCT
ejpam-3725	60	23	g	g	NOUN
ejpam-3725	60	24	)	)	PUNCT
ejpam-3725	60	25	=	=	PUNCT
ejpam-3725	60	26	∑	∑	PUNCT
ejpam-3725	60	27	e	e	X
ejpam-3725	60	28	=	=	NOUN
ejpam-3725	60	29	uv∈e(g	uv∈e(g	NOUN
ejpam-3725	60	30	)	)	PUNCT
ejpam-3725	60	31	d(e)3	d(e)3	PROPN
ejpam-3725	60	32	.	.	PUNCT
ejpam-3725	61	1	(	(	PUNCT
ejpam-3725	61	2	10	10	NUM
ejpam-3725	61	3	)	)	PUNCT
ejpam-3725	61	4	eliasi	eliasi	NOUN
ejpam-3725	61	5	et	et	NOUN
ejpam-3725	61	6	.	.	PUNCT
ejpam-3725	62	1	al	al	PROPN
ejpam-3725	62	2	.	.	PUNCT
ejpam-3725	63	1	[	[	X
ejpam-3725	63	2	8	8	NUM
ejpam-3725	63	3	]	]	PUNCT
ejpam-3725	63	4	introduced	introduce	VERB
ejpam-3725	63	5	the	the	DET
ejpam-3725	63	6	multiplicative	multiplicative	ADJ
ejpam-3725	63	7	sum	sum	NOUN
ejpam-3725	63	8	zagreb	zagreb	PROPN
ejpam-3725	63	9	index	index	NOUN
ejpam-3725	63	10	of	of	ADP
ejpam-3725	63	11	g	g	PROPN
ejpam-3725	63	12	which	which	PRON
ejpam-3725	63	13	is	be	AUX
ejpam-3725	63	14	denoted	denote	VERB
ejpam-3725	63	15	by∏∗	by∏∗	PROPN
ejpam-3725	63	16	1(g	1(g	NUM
ejpam-3725	63	17	)	)	PUNCT
ejpam-3725	63	18	and	and	CCONJ
ejpam-3725	63	19	defined	define	VERB
ejpam-3725	63	20	by	by	ADP
ejpam-3725	63	21	∏∗	∏∗	NOUN
ejpam-3725	63	22	1	1	NUM
ejpam-3725	63	23	(	(	PUNCT
ejpam-3725	63	24	g	g	NOUN
ejpam-3725	63	25	)	)	PUNCT
ejpam-3725	63	26	=	=	SYM
ejpam-3725	63	27	∏	∏	PROPN
ejpam-3725	63	28	uv∈e(g	uv∈e(g	NOUN
ejpam-3725	63	29	)	)	PUNCT
ejpam-3725	63	30	(	(	PUNCT
ejpam-3725	63	31	dg(u	dg(u	X
ejpam-3725	63	32	)	)	PUNCT
ejpam-3725	63	33	+	+	CCONJ
ejpam-3725	63	34	dg(v	dg(v	NOUN
ejpam-3725	63	35	)	)	PUNCT
ejpam-3725	63	36	)	)	PUNCT
ejpam-3725	63	37	.	.	PUNCT
ejpam-3725	64	1	(	(	PUNCT
ejpam-3725	64	2	11	11	NUM
ejpam-3725	64	3	)	)	PUNCT
ejpam-3725	64	4	xu	xu	PROPN
ejpam-3725	64	5	et	et	PROPN
ejpam-3725	64	6	.	.	PUNCT
ejpam-3725	65	1	al	al	PROPN
ejpam-3725	65	2	.	.	PUNCT
ejpam-3725	66	1	[	[	X
ejpam-3725	66	2	18	18	NUM
ejpam-3725	66	3	]	]	PUNCT
ejpam-3725	66	4	introduced	introduce	VERB
ejpam-3725	66	5	the	the	DET
ejpam-3725	66	6	total	total	ADJ
ejpam-3725	66	7	multiplicative	multiplicative	ADJ
ejpam-3725	66	8	sum	sum	PROPN
ejpam-3725	66	9	zagreb	zagreb	PROPN
ejpam-3725	66	10	index	index	NOUN
ejpam-3725	66	11	of	of	ADP
ejpam-3725	66	12	a	a	DET
ejpam-3725	66	13	graph	graph	NOUN
ejpam-3725	66	14	g	g	NOUN
ejpam-3725	66	15	denoted	denote	VERB
ejpam-3725	66	16	by	by	ADP
ejpam-3725	66	17	∏t	∏t	PROPN
ejpam-3725	66	18	(	(	PUNCT
ejpam-3725	66	19	g	g	NOUN
ejpam-3725	66	20	)	)	PUNCT
ejpam-3725	66	21	and	and	CCONJ
ejpam-3725	66	22	defined	define	VERB
ejpam-3725	66	23	by∏t	by∏t	NOUN
ejpam-3725	66	24	(	(	PUNCT
ejpam-3725	66	25	g	g	NOUN
ejpam-3725	66	26	)	)	PUNCT
ejpam-3725	66	27	=	=	SYM
ejpam-3725	66	28	∏	∏	NUM
ejpam-3725	66	29	u	u	NOUN
ejpam-3725	66	30	,	,	PUNCT
ejpam-3725	66	31	v∈v	v∈v	NOUN
ejpam-3725	66	32	(	(	PUNCT
ejpam-3725	66	33	g	g	NOUN
ejpam-3725	66	34	)	)	PUNCT
ejpam-3725	66	35	(	(	PUNCT
ejpam-3725	66	36	dg(u	dg(u	X
ejpam-3725	66	37	)	)	PUNCT
ejpam-3725	66	38	+	+	CCONJ
ejpam-3725	66	39	dg(v	dg(v	NOUN
ejpam-3725	66	40	)	)	PUNCT
ejpam-3725	66	41	)	)	PUNCT
ejpam-3725	66	42	.	.	PUNCT
ejpam-3725	67	1	(	(	PUNCT
ejpam-3725	67	2	12	12	NUM
ejpam-3725	67	3	)	)	PUNCT
ejpam-3725	67	4	topological	topological	ADJ
ejpam-3725	67	5	indices	index	NOUN
ejpam-3725	67	6	of	of	ADP
ejpam-3725	67	7	some	some	DET
ejpam-3725	67	8	derived	derive	VERB
ejpam-3725	67	9	graphs	graph	NOUN
ejpam-3725	67	10	,	,	PUNCT
ejpam-3725	67	11	as	as	ADP
ejpam-3725	67	12	subdivision	subdivision	NOUN
ejpam-3725	67	13	,	,	PUNCT
ejpam-3725	67	14	total	total	ADJ
ejpam-3725	67	15	,	,	PUNCT
ejpam-3725	67	16	semitotal	semitotal	ADJ
ejpam-3725	67	17	,	,	PUNCT
ejpam-3725	67	18	line	line	NOUN
ejpam-3725	67	19	,	,	PUNCT
ejpam-3725	67	20	paraline	paraline	NOUN
ejpam-3725	67	21	graphs	graph	NOUN
ejpam-3725	67	22	are	be	AUX
ejpam-3725	67	23	studied	study	VERB
ejpam-3725	67	24	in	in	ADP
ejpam-3725	67	25	[	[	X
ejpam-3725	67	26	2	2	NUM
ejpam-3725	67	27	]	]	PUNCT
ejpam-3725	67	28	and	and	CCONJ
ejpam-3725	67	29	[	[	X
ejpam-3725	67	30	13	13	NUM
ejpam-3725	67	31	]	]	PUNCT
ejpam-3725	67	32	.	.	PUNCT
ejpam-3725	68	1	in	in	ADP
ejpam-3725	68	2	this	this	DET
ejpam-3725	68	3	paper	paper	NOUN
ejpam-3725	68	4	,	,	PUNCT
ejpam-3725	68	5	we	we	PRON
ejpam-3725	68	6	examine	examine	VERB
ejpam-3725	68	7	some	some	DET
ejpam-3725	68	8	degree	degree	NOUN
ejpam-3725	68	9	-	-	PUNCT
ejpam-3725	68	10	based	base	VERB
ejpam-3725	68	11	topological	topological	ADJ
ejpam-3725	68	12	indices	index	NOUN
ejpam-3725	68	13	of	of	ADP
ejpam-3725	68	14	vertex	vertex	NOUN
ejpam-3725	68	15	-	-	PUNCT
ejpam-3725	68	16	semitotal	semitotal	ADJ
ejpam-3725	68	17	graph	graph	NOUN
ejpam-3725	68	18	which	which	PRON
ejpam-3725	68	19	also	also	ADV
ejpam-3725	68	20	is	be	AUX
ejpam-3725	68	21	one	one	NUM
ejpam-3725	68	22	of	of	ADP
ejpam-3725	68	23	the	the	DET
ejpam-3725	68	24	derived	derive	VERB
ejpam-3725	68	25	graphs	graph	NOUN
ejpam-3725	68	26	,	,	PUNCT
ejpam-3725	68	27	and	and	CCONJ
ejpam-3725	68	28	find	find	VERB
ejpam-3725	68	29	relations	relation	NOUN
ejpam-3725	68	30	between	between	ADP
ejpam-3725	68	31	these	these	DET
ejpam-3725	68	32	topological	topological	ADJ
ejpam-3725	68	33	indices	index	NOUN
ejpam-3725	68	34	.	.	PUNCT
ejpam-3725	69	1	2	2	X
ejpam-3725	69	2	.	.	X
ejpam-3725	69	3	main	main	ADJ
ejpam-3725	69	4	results	result	NOUN
ejpam-3725	69	5	we	we	PRON
ejpam-3725	69	6	first	first	ADV
ejpam-3725	69	7	recall	recall	VERB
ejpam-3725	69	8	some	some	DET
ejpam-3725	69	9	results	result	NOUN
ejpam-3725	69	10	on	on	ADP
ejpam-3725	69	11	the	the	DET
ejpam-3725	69	12	topological	topological	ADJ
ejpam-3725	69	13	indices	index	NOUN
ejpam-3725	69	14	of	of	ADP
ejpam-3725	69	15	the	the	DET
ejpam-3725	69	16	vertex	vertex	NOUN
ejpam-3725	69	17	-	-	PUNCT
ejpam-3725	69	18	semitotal	semitotal	ADJ
ejpam-3725	69	19	graphs	graph	NOUN
ejpam-3725	69	20	:	:	PUNCT
ejpam-3725	69	21	proposition	proposition	NOUN
ejpam-3725	69	22	1	1	NUM
ejpam-3725	69	23	.	.	PUNCT
ejpam-3725	70	1	[	[	X
ejpam-3725	70	2	11	11	NUM
ejpam-3725	70	3	]	]	PUNCT
ejpam-3725	70	4	let	let	AUX
ejpam-3725	70	5	t1(g	t1(g	PROPN
ejpam-3725	70	6	)	)	PUNCT
ejpam-3725	70	7	be	be	AUX
ejpam-3725	70	8	the	the	DET
ejpam-3725	70	9	vertex	vertex	NOUN
ejpam-3725	70	10	-	-	PUNCT
ejpam-3725	70	11	semitotal	semitotal	ADJ
ejpam-3725	70	12	graph	graph	NOUN
ejpam-3725	70	13	of	of	ADP
ejpam-3725	70	14	the	the	DET
ejpam-3725	70	15	graph	graph	NOUN
ejpam-3725	70	16	g	g	NOUN
ejpam-3725	70	17	of	of	ADP
ejpam-3725	70	18	order	order	NOUN
ejpam-3725	70	19	n	n	X
ejpam-3725	70	20	=	=	SYM
ejpam-3725	70	21	n(g	n(g	NUM
ejpam-3725	70	22	)	)	PUNCT
ejpam-3725	70	23	and	and	CCONJ
ejpam-3725	70	24	size	size	NOUN
ejpam-3725	70	25	m	m	PROPN
ejpam-3725	70	26	=	=	SYM
ejpam-3725	70	27	m(g	m(g	PROPN
ejpam-3725	70	28	)	)	PUNCT
ejpam-3725	70	29	.	.	PUNCT
ejpam-3725	71	1	then	then	ADV
ejpam-3725	71	2	m1(t1(g	m1(t1(g	NUM
ejpam-3725	71	3	)	)	PUNCT
ejpam-3725	71	4	)	)	PUNCT
ejpam-3725	72	1	=	=	SYM
ejpam-3725	72	2	4m1(g	4m1(g	NUM
ejpam-3725	72	3	)	)	PUNCT
ejpam-3725	73	1	+	+	NUM
ejpam-3725	73	2	4m(g	4m(g	NUM
ejpam-3725	73	3	)	)	PUNCT
ejpam-3725	73	4	.	.	PUNCT
ejpam-3725	74	1	m.	m.	PROPN
ejpam-3725	74	2	demirci	demirci	VERB
ejpam-3725	74	3	et	et	PROPN
ejpam-3725	74	4	al	al	PROPN
ejpam-3725	74	5	.	.	PUNCT
ejpam-3725	74	6	/	/	SYM
ejpam-3725	74	7	eur	eur	PROPN
ejpam-3725	74	8	.	.	PUNCT
ejpam-3725	75	1	j.	j.	PROPN
ejpam-3725	75	2	pure	pure	PROPN
ejpam-3725	75	3	appl	appl	PROPN
ejpam-3725	75	4	.	.	PROPN
ejpam-3725	75	5	math	math	PROPN
ejpam-3725	75	6	,	,	PUNCT
ejpam-3725	75	7	13	13	NUM
ejpam-3725	75	8	(	(	PUNCT
ejpam-3725	75	9	5	5	NUM
ejpam-3725	75	10	)	)	PUNCT
ejpam-3725	75	11	(	(	PUNCT
ejpam-3725	75	12	2020	2020	NUM
ejpam-3725	75	13	)	)	PUNCT
ejpam-3725	75	14	,	,	PUNCT
ejpam-3725	75	15	1260	1260	NUM
ejpam-3725	75	16	-	-	SYM
ejpam-3725	75	17	1269	1269	NUM
ejpam-3725	75	18	1264	1264	NUM
ejpam-3725	75	19	theorem	theorem	NOUN
ejpam-3725	75	20	1	1	NUM
ejpam-3725	75	21	.	.	PUNCT
ejpam-3725	76	1	[	[	X
ejpam-3725	76	2	2	2	X
ejpam-3725	76	3	]	]	PUNCT
ejpam-3725	76	4	let	let	VERB
ejpam-3725	76	5	g	g	PRON
ejpam-3725	76	6	be	be	AUX
ejpam-3725	76	7	a	a	DET
ejpam-3725	76	8	graph	graph	NOUN
ejpam-3725	76	9	of	of	ADP
ejpam-3725	76	10	order	order	NOUN
ejpam-3725	76	11	n	n	X
ejpam-3725	76	12	=	=	SYM
ejpam-3725	76	13	n(g	n(g	NUM
ejpam-3725	76	14	)	)	PUNCT
ejpam-3725	76	15	and	and	CCONJ
ejpam-3725	76	16	size	size	NOUN
ejpam-3725	76	17	m	m	PROPN
ejpam-3725	76	18	=	=	SYM
ejpam-3725	76	19	m(g	m(g	PROPN
ejpam-3725	76	20	)	)	PUNCT
ejpam-3725	76	21	.	.	PUNCT
ejpam-3725	77	1	then	then	ADV
ejpam-3725	77	2	m2(t1(g	m2(t1(g	PROPN
ejpam-3725	77	3	)	)	PUNCT
ejpam-3725	77	4	)	)	PUNCT
ejpam-3725	78	1	=	=	SYM
ejpam-3725	78	2	2em1(g	2em1(g	NUM
ejpam-3725	78	3	)	)	PUNCT
ejpam-3725	79	1	+	+	CCONJ
ejpam-3725	79	2	em2(g	em2(g	X
ejpam-3725	79	3	)	)	PUNCT
ejpam-3725	79	4	+	+	CCONJ
ejpam-3725	79	5	2m1(g	2m1(g	NOUN
ejpam-3725	79	6	)	)	PUNCT
ejpam-3725	80	1	+	+	NOUN
ejpam-3725	81	1	m2(g	m2(g	X
ejpam-3725	81	2	)	)	PUNCT
ejpam-3725	82	1	+	+	NUM
ejpam-3725	82	2	f	f	X
ejpam-3725	82	3	(	(	PUNCT
ejpam-3725	82	4	g)−	g)−	PROPN
ejpam-3725	82	5	4m(g	4m(g	PROPN
ejpam-3725	82	6	)	)	PUNCT
ejpam-3725	82	7	.	.	PUNCT
ejpam-3725	82	8	proposition	proposition	NOUN
ejpam-3725	82	9	2	2	NUM
ejpam-3725	82	10	.	.	PUNCT
ejpam-3725	83	1	[	[	X
ejpam-3725	83	2	6	6	NUM
ejpam-3725	83	3	]	]	PUNCT
ejpam-3725	83	4	let	let	VERB
ejpam-3725	83	5	g	g	PRON
ejpam-3725	83	6	be	be	AUX
ejpam-3725	83	7	a	a	DET
ejpam-3725	83	8	graph	graph	NOUN
ejpam-3725	83	9	of	of	ADP
ejpam-3725	83	10	order	order	NOUN
ejpam-3725	83	11	n	n	X
ejpam-3725	83	12	=	=	SYM
ejpam-3725	83	13	n(g	n(g	NUM
ejpam-3725	83	14	)	)	PUNCT
ejpam-3725	83	15	and	and	CCONJ
ejpam-3725	83	16	size	size	NOUN
ejpam-3725	83	17	m	m	PROPN
ejpam-3725	83	18	=	=	SYM
ejpam-3725	83	19	m(g	m(g	PROPN
ejpam-3725	83	20	)	)	PUNCT
ejpam-3725	83	21	.	.	PUNCT
ejpam-3725	84	1	then	then	ADV
ejpam-3725	84	2	f	f	PROPN
ejpam-3725	84	3	(	(	PUNCT
ejpam-3725	84	4	t1(g	t1(g	PROPN
ejpam-3725	84	5	)	)	PUNCT
ejpam-3725	84	6	)	)	PUNCT
ejpam-3725	85	1	=	=	PUNCT
ejpam-3725	85	2	8f	8f	NOUN
ejpam-3725	85	3	(	(	PUNCT
ejpam-3725	85	4	g	g	NOUN
ejpam-3725	85	5	)	)	PUNCT
ejpam-3725	85	6	+	+	NOUN
ejpam-3725	85	7	8m(g	8m(g	NUM
ejpam-3725	85	8	)	)	PUNCT
ejpam-3725	85	9	.	.	PUNCT
ejpam-3725	86	1	theorem	theorem	NOUN
ejpam-3725	86	2	2	2	NUM
ejpam-3725	86	3	.	.	PUNCT
ejpam-3725	87	1	[	[	X
ejpam-3725	87	2	13	13	NUM
ejpam-3725	87	3	]	]	X
ejpam-3725	87	4	if	if	SCONJ
ejpam-3725	87	5	t1(g	t1(g	PROPN
ejpam-3725	87	6	)	)	PUNCT
ejpam-3725	87	7	is	be	AUX
ejpam-3725	87	8	a	a	DET
ejpam-3725	87	9	vertex	vertex	NOUN
ejpam-3725	87	10	-	-	PUNCT
ejpam-3725	87	11	semitotal	semitotal	ADJ
ejpam-3725	87	12	graph	graph	NOUN
ejpam-3725	87	13	of	of	ADP
ejpam-3725	87	14	g	g	NOUN
ejpam-3725	87	15	of	of	ADP
ejpam-3725	87	16	order	order	NOUN
ejpam-3725	87	17	n	n	X
ejpam-3725	87	18	=	=	SYM
ejpam-3725	87	19	n(g	n(g	NUM
ejpam-3725	87	20	)	)	PUNCT
ejpam-3725	87	21	and	and	CCONJ
ejpam-3725	87	22	size	size	NOUN
ejpam-3725	87	23	m	m	PROPN
ejpam-3725	87	24	=	=	SYM
ejpam-3725	87	25	m(g	m(g	PROPN
ejpam-3725	87	26	)	)	PUNCT
ejpam-3725	87	27	.	.	PUNCT
ejpam-3725	88	1	then	then	ADV
ejpam-3725	88	2	em1(t1(g	em1(t1(g	NOUN
ejpam-3725	88	3	)	)	PUNCT
ejpam-3725	88	4	)	)	PUNCT
ejpam-3725	89	1	=	=	SYM
ejpam-3725	89	2	8(f	8(f	NUM
ejpam-3725	89	3	(	(	PUNCT
ejpam-3725	89	4	g)−m1(g	g)−m1(g	NOUN
ejpam-3725	89	5	)	)	PUNCT
ejpam-3725	89	6	+	+	NOUN
ejpam-3725	89	7	m2(g	m2(g	X
ejpam-3725	89	8	)	)	PUNCT
ejpam-3725	89	9	)	)	PUNCT
ejpam-3725	90	1	+	+	CCONJ
ejpam-3725	90	2	4m(g	4m(g	NUM
ejpam-3725	90	3	)	)	PUNCT
ejpam-3725	90	4	and	and	CCONJ
ejpam-3725	90	5	em2(t1(g	em2(t1(g	NUM
ejpam-3725	90	6	)	)	PUNCT
ejpam-3725	90	7	)	)	PUNCT
ejpam-3725	91	1	=	=	SYM
ejpam-3725	91	2	1	1	NUM
ejpam-3725	91	3	3	3	NUM
ejpam-3725	91	4	(	(	PUNCT
ejpam-3725	91	5	14(4m1(g	14(4m1(g	NUM
ejpam-3725	91	6	)	)	PUNCT
ejpam-3725	91	7	)	)	PUNCT
ejpam-3725	92	1	+	+	CCONJ
ejpam-3725	92	2	4ef	4ef	ADJ
ejpam-3725	92	3	(	(	PUNCT
ejpam-3725	92	4	g	g	NOUN
ejpam-3725	92	5	)	)	PUNCT
ejpam-3725	92	6	+	+	CCONJ
ejpam-3725	92	7	68m(g	68m(g	NUM
ejpam-3725	92	8	)	)	PUNCT
ejpam-3725	92	9	)	)	PUNCT
ejpam-3725	93	1	+	+	CCONJ
ejpam-3725	94	1	4em2(g	4em2(g	NUM
ejpam-3725	94	2	)	)	PUNCT
ejpam-3725	95	1	+	+	NUM
ejpam-3725	95	2	6f	6f	NUM
ejpam-3725	95	3	(	(	PUNCT
ejpam-3725	95	4	g)−	g)−	PROPN
ejpam-3725	95	5	30m1(g	30m1(g	PROPN
ejpam-3725	95	6	)	)	PUNCT
ejpam-3725	95	7	+	+	CCONJ
ejpam-3725	95	8	28m2(g	28m2(g	NUM
ejpam-3725	95	9	)	)	PUNCT
ejpam-3725	95	10	where	where	SCONJ
ejpam-3725	95	11	αm1(g	αm1(g	NOUN
ejpam-3725	95	12	)	)	PUNCT
ejpam-3725	95	13	=	=	SYM
ejpam-3725	95	14	∑	∑	PUNCT
ejpam-3725	95	15	v∈v	v∈v	NOUN
ejpam-3725	95	16	(	(	PUNCT
ejpam-3725	95	17	g	g	NOUN
ejpam-3725	95	18	)	)	PUNCT
ejpam-3725	95	19	d(v)α	d(v)α	PROPN
ejpam-3725	95	20	and	and	CCONJ
ejpam-3725	95	21	ef	ef	PROPN
ejpam-3725	95	22	(	(	PUNCT
ejpam-3725	95	23	g	g	NOUN
ejpam-3725	95	24	)	)	PUNCT
ejpam-3725	95	25	is	be	AUX
ejpam-3725	95	26	the	the	DET
ejpam-3725	95	27	reformulated	reformulate	VERB
ejpam-3725	95	28	forgotten	forget	VERB
ejpam-3725	95	29	index	index	NOUN
ejpam-3725	95	30	.	.	PUNCT
ejpam-3725	96	1	theorem	theorem	VERB
ejpam-3725	96	2	3	3	NUM
ejpam-3725	96	3	.	.	PUNCT
ejpam-3725	97	1	[	[	X
ejpam-3725	97	2	3	3	X
ejpam-3725	97	3	]	]	PUNCT
ejpam-3725	97	4	let	let	VERB
ejpam-3725	97	5	g	g	PRON
ejpam-3725	97	6	be	be	AUX
ejpam-3725	97	7	a	a	DET
ejpam-3725	97	8	graph	graph	NOUN
ejpam-3725	97	9	of	of	ADP
ejpam-3725	97	10	order	order	NOUN
ejpam-3725	97	11	n	n	X
ejpam-3725	97	12	=	=	SYM
ejpam-3725	97	13	n(g	n(g	NUM
ejpam-3725	97	14	)	)	PUNCT
ejpam-3725	97	15	and	and	CCONJ
ejpam-3725	97	16	size	size	NOUN
ejpam-3725	97	17	m	m	PROPN
ejpam-3725	97	18	=	=	SYM
ejpam-3725	97	19	m(g	m(g	PROPN
ejpam-3725	97	20	)	)	PUNCT
ejpam-3725	97	21	.	.	PUNCT
ejpam-3725	98	1	then∏	then∏	X
ejpam-3725	98	2	1	1	NUM
ejpam-3725	98	3	(	(	PUNCT
ejpam-3725	98	4	t1(g	t1(g	PROPN
ejpam-3725	98	5	)	)	PUNCT
ejpam-3725	98	6	)	)	PUNCT
ejpam-3725	99	1	=	=	SYM
ejpam-3725	99	2	∏	∏	PROPN
ejpam-3725	99	3	1	1	NUM
ejpam-3725	99	4	(	(	PUNCT
ejpam-3725	99	5	g	g	NOUN
ejpam-3725	99	6	)	)	PUNCT
ejpam-3725	99	7	[	[	X
ejpam-3725	99	8	∏∗	∏∗	X
ejpam-3725	99	9	1	1	NUM
ejpam-3725	99	10	(	(	PUNCT
ejpam-3725	99	11	g	g	NOUN
ejpam-3725	99	12	)	)	PUNCT
ejpam-3725	99	13	]	]	PUNCT
ejpam-3725	99	14	2	2	X
ejpam-3725	99	15	.	.	PUNCT
ejpam-3725	99	16	and	and	CCONJ
ejpam-3725	99	17	∏	∏	PROPN
ejpam-3725	99	18	2	2	NUM
ejpam-3725	99	19	(	(	PUNCT
ejpam-3725	99	20	t1(g	t1(g	PROPN
ejpam-3725	99	21	)	)	PUNCT
ejpam-3725	99	22	)	)	PUNCT
ejpam-3725	99	23	=	=	SYM
ejpam-3725	99	24	∏	∏	NUM
ejpam-3725	99	25	2	2	NUM
ejpam-3725	99	26	(	(	PUNCT
ejpam-3725	99	27	g	g	NOUN
ejpam-3725	99	28	)	)	PUNCT
ejpam-3725	99	29	∏∗	∏∗	X
ejpam-3725	99	30	2	2	NUM
ejpam-3725	99	31	(	(	PUNCT
ejpam-3725	99	32	g	g	NOUN
ejpam-3725	99	33	)	)	PUNCT
ejpam-3725	99	34	.	.	PUNCT
ejpam-3725	100	1	now	now	ADV
ejpam-3725	100	2	we	we	PRON
ejpam-3725	100	3	will	will	AUX
ejpam-3725	100	4	determine	determine	VERB
ejpam-3725	100	5	some	some	DET
ejpam-3725	100	6	well	well	ADV
ejpam-3725	100	7	-	-	PUNCT
ejpam-3725	100	8	known	know	VERB
ejpam-3725	100	9	zagreb	zagreb	PROPN
ejpam-3725	100	10	indices	index	NOUN
ejpam-3725	100	11	of	of	ADP
ejpam-3725	100	12	vertex	vertex	NOUN
ejpam-3725	100	13	-	-	PUNCT
ejpam-3725	100	14	semitotal	semitotal	ADJ
ejpam-3725	100	15	graph	graph	NOUN
ejpam-3725	100	16	of	of	ADP
ejpam-3725	100	17	g.	g.	PROPN
ejpam-3725	100	18	lemma	lemma	PROPN
ejpam-3725	101	1	1	1	X
ejpam-3725	101	2	.	.	PUNCT
ejpam-3725	101	3	let	let	VERB
ejpam-3725	101	4	g	g	PRON
ejpam-3725	101	5	be	be	AUX
ejpam-3725	101	6	a	a	DET
ejpam-3725	101	7	connected	connected	ADJ
ejpam-3725	101	8	simple	simple	ADJ
ejpam-3725	101	9	graph	graph	NOUN
ejpam-3725	101	10	of	of	ADP
ejpam-3725	101	11	order	order	NOUN
ejpam-3725	101	12	n	n	X
ejpam-3725	101	13	=	=	SYM
ejpam-3725	101	14	n(g	n(g	NUM
ejpam-3725	101	15	)	)	PUNCT
ejpam-3725	101	16	and	and	CCONJ
ejpam-3725	101	17	size	size	NOUN
ejpam-3725	101	18	m	m	PROPN
ejpam-3725	101	19	=	=	SYM
ejpam-3725	101	20	m(g	m(g	PROPN
ejpam-3725	101	21	)	)	PUNCT
ejpam-3725	101	22	and	and	CCONJ
ejpam-3725	101	23	let	let	VERB
ejpam-3725	101	24	t1(g	t1(g	PROPN
ejpam-3725	101	25	)	)	PUNCT
ejpam-3725	101	26	be	be	AUX
ejpam-3725	101	27	the	the	DET
ejpam-3725	101	28	vertex	vertex	NOUN
ejpam-3725	101	29	-	-	PUNCT
ejpam-3725	101	30	semitotal	semitotal	ADJ
ejpam-3725	101	31	graph	graph	NOUN
ejpam-3725	101	32	of	of	ADP
ejpam-3725	101	33	g.	g.	PROPN
ejpam-3725	101	34	then	then	ADV
ejpam-3725	101	35	,	,	PUNCT
ejpam-3725	101	36	ω(t1(g))−	ω(t1(g))−	NOUN
ejpam-3725	101	37	ω(g	ω(g	NOUN
ejpam-3725	101	38	)	)	PUNCT
ejpam-3725	101	39	=	=	SYM
ejpam-3725	101	40	2m(g	2m(g	NUM
ejpam-3725	101	41	)	)	PUNCT
ejpam-3725	101	42	.	.	PUNCT
ejpam-3725	102	1	the	the	DET
ejpam-3725	102	2	proof	proof	NOUN
ejpam-3725	102	3	is	be	AUX
ejpam-3725	102	4	clear	clear	ADJ
ejpam-3725	102	5	from	from	ADP
ejpam-3725	102	6	the	the	DET
ejpam-3725	102	7	definition	definition	NOUN
ejpam-3725	102	8	of	of	ADP
ejpam-3725	102	9	ω	ω	PROPN
ejpam-3725	102	10	invariant	invariant	PROPN
ejpam-3725	102	11	of	of	ADP
ejpam-3725	102	12	g.	g.	PROPN
ejpam-3725	102	13	theorem	theorem	VERB
ejpam-3725	102	14	4	4	X
ejpam-3725	102	15	.	.	PUNCT
ejpam-3725	103	1	let	let	VERB
ejpam-3725	103	2	g	g	PRON
ejpam-3725	103	3	be	be	AUX
ejpam-3725	103	4	a	a	DET
ejpam-3725	103	5	graph	graph	NOUN
ejpam-3725	103	6	with	with	ADP
ejpam-3725	103	7	order	order	NOUN
ejpam-3725	103	8	n	n	X
ejpam-3725	103	9	=	=	SYM
ejpam-3725	103	10	n(g	n(g	NUM
ejpam-3725	103	11	)	)	PUNCT
ejpam-3725	103	12	and	and	CCONJ
ejpam-3725	103	13	size	size	NOUN
ejpam-3725	103	14	m	m	PROPN
ejpam-3725	103	15	=	=	SYM
ejpam-3725	103	16	m(g	m(g	PROPN
ejpam-3725	103	17	)	)	PUNCT
ejpam-3725	103	18	.	.	PUNCT
ejpam-3725	104	1	then	then	ADV
ejpam-3725	104	2	the	the	DET
ejpam-3725	104	3	hyper	hyper	PROPN
ejpam-3725	104	4	zagreb	zagreb	PROPN
ejpam-3725	104	5	index	index	NOUN
ejpam-3725	104	6	of	of	ADP
ejpam-3725	104	7	t1(g	t1(g	PROPN
ejpam-3725	104	8	)	)	PUNCT
ejpam-3725	104	9	is	be	AUX
ejpam-3725	104	10	hm(t1(g	hm(t1(g	NOUN
ejpam-3725	104	11	)	)	PUNCT
ejpam-3725	104	12	)	)	PUNCT
ejpam-3725	105	1	=	=	SYM
ejpam-3725	105	2	4	4	NUM
ejpam-3725	105	3	(	(	PUNCT
ejpam-3725	105	4	2m1(g	2m1(g	NOUN
ejpam-3725	105	5	)	)	PUNCT
ejpam-3725	106	1	+	+	NUM
ejpam-3725	106	2	f	f	X
ejpam-3725	106	3	(	(	PUNCT
ejpam-3725	106	4	g	g	NOUN
ejpam-3725	106	5	)	)	PUNCT
ejpam-3725	106	6	+	+	NOUN
ejpam-3725	106	7	hm(g	hm(g	NUM
ejpam-3725	106	8	)	)	PUNCT
ejpam-3725	106	9	+	+	NUM
ejpam-3725	106	10	2m(g	2m(g	NUM
ejpam-3725	106	11	)	)	PUNCT
ejpam-3725	106	12	)	)	PUNCT
ejpam-3725	106	13	.	.	PUNCT
ejpam-3725	107	1	proof	proof	NOUN
ejpam-3725	107	2	.	.	PUNCT
ejpam-3725	108	1	by	by	ADP
ejpam-3725	108	2	eqn	eqn	PROPN
ejpam-3725	108	3	.	.	PUNCT
ejpam-3725	109	1	(	(	PUNCT
ejpam-3725	109	2	3	3	NUM
ejpam-3725	109	3	)	)	PUNCT
ejpam-3725	109	4	,	,	PUNCT
ejpam-3725	109	5	we	we	PRON
ejpam-3725	109	6	have	have	VERB
ejpam-3725	109	7	hm(t1(g	hm(t1(g	NOUN
ejpam-3725	109	8	)	)	PUNCT
ejpam-3725	109	9	)	)	PUNCT
ejpam-3725	110	1	=	=	PUNCT
ejpam-3725	110	2	∑	∑	PUNCT
ejpam-3725	110	3	vivj∈e(t1(g	vivj∈e(t1(g	NOUN
ejpam-3725	110	4	)	)	PUNCT
ejpam-3725	110	5	)	)	PUNCT
ejpam-3725	111	1	[	[	PUNCT
ejpam-3725	111	2	dt1(g)(vi	dt1(g)(vi	X
ejpam-3725	111	3	)	)	PUNCT
ejpam-3725	111	4	+	+	NUM
ejpam-3725	111	5	dt1(g)(vj	dt1(g)(vj	NOUN
ejpam-3725	111	6	)	)	PUNCT
ejpam-3725	111	7	]	]	PUNCT
ejpam-3725	111	8	2	2	NUM
ejpam-3725	111	9	m.	m.	NOUN
ejpam-3725	111	10	demirci	demirci	VERB
ejpam-3725	111	11	et	et	PROPN
ejpam-3725	111	12	al	al	PROPN
ejpam-3725	111	13	.	.	PUNCT
ejpam-3725	111	14	/	/	SYM
ejpam-3725	111	15	eur	eur	PROPN
ejpam-3725	111	16	.	.	PUNCT
ejpam-3725	112	1	j.	j.	PROPN
ejpam-3725	112	2	pure	pure	PROPN
ejpam-3725	112	3	appl	appl	PROPN
ejpam-3725	112	4	.	.	PROPN
ejpam-3725	112	5	math	math	PROPN
ejpam-3725	112	6	,	,	PUNCT
ejpam-3725	112	7	13	13	NUM
ejpam-3725	112	8	(	(	PUNCT
ejpam-3725	112	9	5	5	NUM
ejpam-3725	112	10	)	)	PUNCT
ejpam-3725	112	11	(	(	PUNCT
ejpam-3725	112	12	2020	2020	NUM
ejpam-3725	112	13	)	)	PUNCT
ejpam-3725	112	14	,	,	PUNCT
ejpam-3725	112	15	1260	1260	NUM
ejpam-3725	112	16	-	-	SYM
ejpam-3725	112	17	1269	1269	NUM
ejpam-3725	112	18	1265	1265	NUM
ejpam-3725	112	19	=	=	SYM
ejpam-3725	112	20	∑	∑	PUNCT
ejpam-3725	112	21	vivj∈e(g	vivj∈e(g	PROPN
ejpam-3725	112	22	)	)	PUNCT
ejpam-3725	112	23	[	[	PUNCT
ejpam-3725	112	24	dt1(g)(vi	dt1(g)(vi	X
ejpam-3725	112	25	)	)	PUNCT
ejpam-3725	112	26	+	+	NUM
ejpam-3725	112	27	dt1(g)(vj	dt1(g)(vj	NOUN
ejpam-3725	112	28	)	)	PUNCT
ejpam-3725	112	29	]	]	PUNCT
ejpam-3725	112	30	2	2	X
ejpam-3725	112	31	+	+	CCONJ
ejpam-3725	112	32	∑	∑	ADV
ejpam-3725	112	33	vicij∈e(t1(g	vicij∈e(t1(g	PROPN
ejpam-3725	112	34	)	)	PUNCT
ejpam-3725	112	35	)	)	PUNCT
ejpam-3725	113	1	[	[	PUNCT
ejpam-3725	113	2	dt1(g)(vi	dt1(g)(vi	X
ejpam-3725	113	3	)	)	PUNCT
ejpam-3725	113	4	+	+	CCONJ
ejpam-3725	113	5	2	2	NUM
ejpam-3725	113	6	]	]	SYM
ejpam-3725	113	7	2	2	NUM
ejpam-3725	113	8	=	=	SYM
ejpam-3725	113	9	4	4	NUM
ejpam-3725	113	10	∑	∑	NOUN
ejpam-3725	113	11	vivj∈e(g	vivj∈e(g	NOUN
ejpam-3725	113	12	)	)	PUNCT
ejpam-3725	113	13	(	(	PUNCT
ejpam-3725	113	14	dg(vi	dg(vi	PROPN
ejpam-3725	113	15	)	)	PUNCT
ejpam-3725	113	16	+	+	NUM
ejpam-3725	113	17	dg(vj	dg(vj	NOUN
ejpam-3725	113	18	)	)	PUNCT
ejpam-3725	113	19	)	)	PUNCT
ejpam-3725	113	20	2	2	NUM
ejpam-3725	114	1	+	+	CCONJ
ejpam-3725	114	2	4	4	NUM
ejpam-3725	114	3	∑	∑	PART
ejpam-3725	114	4	vi∈v	vi∈v	X
ejpam-3725	114	5	(	(	PUNCT
ejpam-3725	114	6	g	g	NOUN
ejpam-3725	114	7	)	)	PUNCT
ejpam-3725	114	8	(	(	PUNCT
ejpam-3725	114	9	1	1	NUM
ejpam-3725	114	10	+	+	CCONJ
ejpam-3725	114	11	dg(vi	dg(vi	NOUN
ejpam-3725	114	12	)	)	PUNCT
ejpam-3725	114	13	)	)	PUNCT
ejpam-3725	115	1	2dg(vi	2dg(vi	NUM
ejpam-3725	115	2	)	)	PUNCT
ejpam-3725	115	3	,	,	PUNCT
ejpam-3725	115	4	and	and	CCONJ
ejpam-3725	115	5	the	the	DET
ejpam-3725	115	6	result	result	NOUN
ejpam-3725	115	7	follows	follow	VERB
ejpam-3725	115	8	.	.	PUNCT
ejpam-3725	116	1	theorem	theorem	ADJ
ejpam-3725	116	2	5	5	NUM
ejpam-3725	116	3	.	.	PUNCT
ejpam-3725	117	1	let	let	VERB
ejpam-3725	117	2	g	g	PRON
ejpam-3725	117	3	be	be	AUX
ejpam-3725	117	4	a	a	DET
ejpam-3725	117	5	graph	graph	NOUN
ejpam-3725	117	6	with	with	ADP
ejpam-3725	117	7	order	order	NOUN
ejpam-3725	117	8	n	n	X
ejpam-3725	117	9	=	=	SYM
ejpam-3725	117	10	n(g	n(g	NUM
ejpam-3725	117	11	)	)	PUNCT
ejpam-3725	117	12	and	and	CCONJ
ejpam-3725	117	13	size	size	NOUN
ejpam-3725	117	14	m	m	PROPN
ejpam-3725	117	15	=	=	SYM
ejpam-3725	117	16	m(g	m(g	PROPN
ejpam-3725	117	17	)	)	PUNCT
ejpam-3725	117	18	.	.	PUNCT
ejpam-3725	118	1	then	then	ADV
ejpam-3725	118	2	augmented	augment	VERB
ejpam-3725	118	3	zagreb	zagreb	PROPN
ejpam-3725	118	4	index	index	NOUN
ejpam-3725	118	5	of	of	ADP
ejpam-3725	118	6	t1(g	t1(g	PROPN
ejpam-3725	118	7	)	)	PUNCT
ejpam-3725	118	8	is	be	AUX
ejpam-3725	118	9	azi(t1(g	azi(t1(g	PROPN
ejpam-3725	118	10	)	)	PUNCT
ejpam-3725	118	11	)	)	PUNCT
ejpam-3725	119	1	=	=	SYM
ejpam-3725	119	2	8	8	NUM
ejpam-3725	119	3	∑	∑	PUNCT
ejpam-3725	119	4	vivj∈e(g	vivj∈e(g	PROPN
ejpam-3725	119	5	)	)	PUNCT
ejpam-3725	119	6	(	(	PUNCT
ejpam-3725	119	7	dg(vi)dg(vj	dg(vi)dg(vj	NOUN
ejpam-3725	119	8	)	)	PUNCT
ejpam-3725	119	9	dg(vi	dg(vi	PROPN
ejpam-3725	119	10	)	)	PUNCT
ejpam-3725	120	1	+	+	NUM
ejpam-3725	120	2	dg(vj)−	dg(vj)−	PROPN
ejpam-3725	120	3	1	1	NUM
ejpam-3725	120	4	)	)	SYM
ejpam-3725	120	5	3	3	NUM
ejpam-3725	120	6	+	+	NUM
ejpam-3725	120	7	16m(g	16m(g	NUM
ejpam-3725	120	8	)	)	PUNCT
ejpam-3725	120	9	.	.	PUNCT
ejpam-3725	121	1	proof	proof	NOUN
ejpam-3725	121	2	.	.	PUNCT
ejpam-3725	122	1	using	use	VERB
ejpam-3725	122	2	eqn.(4	eqn.(4	PROPN
ejpam-3725	122	3	)	)	PUNCT
ejpam-3725	122	4	,	,	PUNCT
ejpam-3725	122	5	we	we	PRON
ejpam-3725	122	6	get	get	VERB
ejpam-3725	122	7	azi(t1(g	azi(t1(g	NOUN
ejpam-3725	122	8	)	)	PUNCT
ejpam-3725	122	9	)	)	PUNCT
ejpam-3725	123	1	=	=	PUNCT
ejpam-3725	123	2	∑	∑	PUNCT
ejpam-3725	123	3	vivj∈e(g	vivj∈e(g	PROPN
ejpam-3725	123	4	)	)	PUNCT
ejpam-3725	123	5	(	(	PUNCT
ejpam-3725	123	6	dt1(g)(vi	dt1(g)(vi	X
ejpam-3725	123	7	)	)	PUNCT
ejpam-3725	123	8	·	·	PUNCT
ejpam-3725	123	9	dt1(g)(vj	dt1(g)(vj	X
ejpam-3725	123	10	)	)	PUNCT
ejpam-3725	123	11	dt1(g)(vi	dt1(g)(vi	NOUN
ejpam-3725	123	12	)	)	PUNCT
ejpam-3725	124	1	+	+	NUM
ejpam-3725	124	2	dt1(g)(vj)−	dt1(g)(vj)−	NOUN
ejpam-3725	124	3	2	2	NUM
ejpam-3725	124	4	)	)	PUNCT
ejpam-3725	124	5	3	3	NUM
ejpam-3725	124	6	+	+	CCONJ
ejpam-3725	124	7	∑	∑	ADV
ejpam-3725	124	8	vicij∈e(t1(g	vicij∈e(t1(g	PROPN
ejpam-3725	124	9	)	)	PUNCT
ejpam-3725	124	10	)	)	PUNCT
ejpam-3725	124	11	(	(	PUNCT
ejpam-3725	124	12	2.2dg(vi	2.2dg(vi	NUM
ejpam-3725	124	13	)	)	PUNCT
ejpam-3725	124	14	2	2	NUM
ejpam-3725	125	1	+	+	CCONJ
ejpam-3725	125	2	2dg(vi)−	2dg(vi)−	NUM
ejpam-3725	125	3	2	2	NUM
ejpam-3725	125	4	)	)	PUNCT
ejpam-3725	125	5	3	3	NUM
ejpam-3725	125	6	dg(vi	dg(vi	PROPN
ejpam-3725	125	7	)	)	PUNCT
ejpam-3725	125	8	=	=	PUNCT
ejpam-3725	125	9	∑	∑	PUNCT
ejpam-3725	125	10	vivj∈e(g	vivj∈e(g	PROPN
ejpam-3725	125	11	)	)	PUNCT
ejpam-3725	125	12	(	(	PUNCT
ejpam-3725	125	13	2dg(vi	2dg(vi	NUM
ejpam-3725	125	14	)	)	PUNCT
ejpam-3725	125	15	·	·	PUNCT
ejpam-3725	125	16	2dg(vj	2dg(vj	X
ejpam-3725	125	17	)	)	PUNCT
ejpam-3725	125	18	2dg(vi	2dg(vi	NUM
ejpam-3725	125	19	)	)	PUNCT
ejpam-3725	125	20	+	+	CCONJ
ejpam-3725	125	21	2dg(vj)−	2dg(vj)−	NUM
ejpam-3725	125	22	2	2	NUM
ejpam-3725	125	23	)	)	PUNCT
ejpam-3725	125	24	3	3	NUM
ejpam-3725	125	25	+	+	CCONJ
ejpam-3725	125	26	8	8	NUM
ejpam-3725	125	27	∑	∑	PUNCT
ejpam-3725	125	28	vi∈v	vi∈v	X
ejpam-3725	125	29	(	(	PUNCT
ejpam-3725	125	30	g	g	NOUN
ejpam-3725	125	31	)	)	PUNCT
ejpam-3725	125	32	dg(vi	dg(vi	NOUN
ejpam-3725	125	33	)	)	PUNCT
ejpam-3725	125	34	,	,	PUNCT
ejpam-3725	125	35	and	and	CCONJ
ejpam-3725	125	36	the	the	DET
ejpam-3725	125	37	result	result	NOUN
ejpam-3725	125	38	follows	follow	VERB
ejpam-3725	125	39	.	.	PUNCT
ejpam-3725	126	1	theorem	theorem	ADJ
ejpam-3725	126	2	6	6	NUM
ejpam-3725	126	3	.	.	PUNCT
ejpam-3725	127	1	let	let	VERB
ejpam-3725	127	2	g	g	PRON
ejpam-3725	127	3	be	be	AUX
ejpam-3725	127	4	a	a	DET
ejpam-3725	127	5	graph	graph	NOUN
ejpam-3725	127	6	with	with	ADP
ejpam-3725	127	7	order	order	NOUN
ejpam-3725	127	8	n	n	X
ejpam-3725	127	9	=	=	SYM
ejpam-3725	127	10	n(g	n(g	NUM
ejpam-3725	127	11	)	)	PUNCT
ejpam-3725	127	12	and	and	CCONJ
ejpam-3725	127	13	size	size	NOUN
ejpam-3725	127	14	m	m	PROPN
ejpam-3725	127	15	=	=	SYM
ejpam-3725	127	16	m(g	m(g	PROPN
ejpam-3725	127	17	)	)	PUNCT
ejpam-3725	127	18	.	.	PUNCT
ejpam-3725	128	1	re	re	VERB
ejpam-3725	128	2	-	-	VERB
ejpam-3725	128	3	defined	define	VERB
ejpam-3725	128	4	versions	version	NOUN
ejpam-3725	128	5	of	of	ADP
ejpam-3725	128	6	zagreb	zagreb	PROPN
ejpam-3725	128	7	indices	index	NOUN
ejpam-3725	128	8	of	of	ADP
ejpam-3725	128	9	t1(g	t1(g	PROPN
ejpam-3725	128	10	)	)	PUNCT
ejpam-3725	128	11	are	be	AUX
ejpam-3725	128	12	i	i	PROPN
ejpam-3725	128	13	)	)	PUNCT
ejpam-3725	128	14	rezg1(t1(g	rezg1(t1(g	PROPN
ejpam-3725	128	15	)	)	PUNCT
ejpam-3725	128	16	)	)	PUNCT
ejpam-3725	129	1	=	=	SYM
ejpam-3725	129	2	1	1	NUM
ejpam-3725	129	3	2	2	NUM
ejpam-3725	129	4	(	(	PUNCT
ejpam-3725	129	5	rezg1(g	rezg1(g	NOUN
ejpam-3725	129	6	)	)	PUNCT
ejpam-3725	129	7	+	+	NUM
ejpam-3725	129	8	n(g	n(g	NUM
ejpam-3725	129	9	)	)	PUNCT
ejpam-3725	129	10	)	)	PUNCT
ejpam-3725	130	1	+	+	PUNCT
ejpam-3725	130	2	m(g	m(g	PROPN
ejpam-3725	130	3	)	)	PUNCT
ejpam-3725	130	4	.	.	PUNCT
ejpam-3725	131	1	ii	ii	PROPN
ejpam-3725	131	2	)	)	PUNCT
ejpam-3725	131	3	rezg2(t1(g	rezg2(t1(g	NOUN
ejpam-3725	131	4	)	)	PUNCT
ejpam-3725	131	5	)	)	PUNCT
ejpam-3725	132	1	=	=	SYM
ejpam-3725	132	2	2	2	NUM
ejpam-3725	132	3	[	[	PUNCT
ejpam-3725	132	4	rezg2(g	rezg2(g	X
ejpam-3725	132	5	)	)	PUNCT
ejpam-3725	132	6	+	+	CCONJ
ejpam-3725	132	7	∑	∑	ADV
ejpam-3725	132	8	u∈v	u∈v	NOUN
ejpam-3725	132	9	(	(	PUNCT
ejpam-3725	132	10	g	g	NOUN
ejpam-3725	132	11	)	)	PUNCT
ejpam-3725	132	12	d2	d2	NOUN
ejpam-3725	132	13	g(vi	g(vi	NOUN
ejpam-3725	132	14	)	)	PUNCT
ejpam-3725	132	15	1+dg(vi	1+dg(vi	NUM
ejpam-3725	132	16	)	)	PUNCT
ejpam-3725	132	17	]	]	PUNCT
ejpam-3725	132	18	.	.	PUNCT
ejpam-3725	133	1	iii	iii	X
ejpam-3725	133	2	)	)	PUNCT
ejpam-3725	133	3	rezg3(t1(g	rezg3(t1(g	NOUN
ejpam-3725	133	4	)	)	PUNCT
ejpam-3725	133	5	)	)	PUNCT
ejpam-3725	134	1	=	=	PUNCT
ejpam-3725	134	2	rezg3(g	rezg3(g	NOUN
ejpam-3725	134	3	)	)	PUNCT
ejpam-3725	135	1	+	+	CCONJ
ejpam-3725	135	2	8	8	NUM
ejpam-3725	135	3	(	(	PUNCT
ejpam-3725	135	4	m1(g	m1(g	NOUN
ejpam-3725	135	5	)	)	PUNCT
ejpam-3725	135	6	+	+	NUM
ejpam-3725	135	7	f	f	X
ejpam-3725	135	8	(	(	PUNCT
ejpam-3725	135	9	g	g	NOUN
ejpam-3725	135	10	)	)	PUNCT
ejpam-3725	135	11	)	)	PUNCT
ejpam-3725	136	1	+	+	PUNCT
ejpam-3725	136	2	m(g	m(g	NOUN
ejpam-3725	136	3	)	)	PUNCT
ejpam-3725	136	4	.	.	PUNCT
ejpam-3725	137	1	proof	proof	NOUN
ejpam-3725	137	2	.	.	PUNCT
ejpam-3725	138	1	from	from	ADP
ejpam-3725	138	2	eqn	eqn	PROPN
ejpam-3725	138	3	.	.	PUNCT
ejpam-3725	139	1	(	(	PUNCT
ejpam-3725	139	2	6	6	NUM
ejpam-3725	139	3	)	)	PUNCT
ejpam-3725	139	4	,	,	PUNCT
ejpam-3725	139	5	we	we	PRON
ejpam-3725	139	6	have	have	VERB
ejpam-3725	139	7	rezg1(t1(g	rezg1(t1(g	NOUN
ejpam-3725	139	8	)	)	PUNCT
ejpam-3725	139	9	)	)	PUNCT
ejpam-3725	140	1	=	=	PUNCT
ejpam-3725	140	2	∑	∑	PUNCT
ejpam-3725	140	3	vivj∈e(t1(g	vivj∈e(t1(g	NOUN
ejpam-3725	140	4	)	)	PUNCT
ejpam-3725	140	5	)	)	PUNCT
ejpam-3725	141	1	dt1(g)(vi	dt1(g)(vi	NOUN
ejpam-3725	141	2	)	)	PUNCT
ejpam-3725	141	3	+	+	CCONJ
ejpam-3725	141	4	dt1(g)(vj	dt1(g)(vj	NOUN
ejpam-3725	141	5	)	)	PUNCT
ejpam-3725	141	6	dt1(g)(vi	dt1(g)(vi	NOUN
ejpam-3725	141	7	)	)	PUNCT
ejpam-3725	141	8	·	·	PUNCT
ejpam-3725	141	9	dt1(g)(vj	dt1(g)(vj	X
ejpam-3725	141	10	)	)	PUNCT
ejpam-3725	141	11	=	=	SYM
ejpam-3725	141	12	∑	∑	PUNCT
ejpam-3725	141	13	vivj∈e(g	vivj∈e(g	PROPN
ejpam-3725	141	14	)	)	PUNCT
ejpam-3725	141	15	2dg(vi	2dg(vi	NUM
ejpam-3725	141	16	)	)	PUNCT
ejpam-3725	141	17	+	+	NUM
ejpam-3725	141	18	2dg(vj	2dg(vj	NUM
ejpam-3725	141	19	)	)	PUNCT
ejpam-3725	141	20	2dg(vi	2dg(vi	NUM
ejpam-3725	141	21	)	)	PUNCT
ejpam-3725	141	22	·	·	PUNCT
ejpam-3725	141	23	2dg(vj	2dg(vj	NUM
ejpam-3725	141	24	)	)	PUNCT
ejpam-3725	142	1	+	+	CCONJ
ejpam-3725	142	2	∑	∑	ADV
ejpam-3725	142	3	vicij∈e(t1(g	vicij∈e(t1(g	PROPN
ejpam-3725	142	4	)	)	PUNCT
ejpam-3725	142	5	)	)	PUNCT
ejpam-3725	143	1	2	2	NUM
ejpam-3725	144	1	+	+	CCONJ
ejpam-3725	144	2	2dg(vi	2dg(vi	NUM
ejpam-3725	144	3	)	)	PUNCT
ejpam-3725	144	4	2	2	NUM
ejpam-3725	144	5	·	·	SYM
ejpam-3725	144	6	2dg(vi	2dg(vi	NUM
ejpam-3725	144	7	)	)	PUNCT
ejpam-3725	144	8	·	·	PUNCT
ejpam-3725	144	9	dg(vi	dg(vi	PROPN
ejpam-3725	144	10	)	)	PUNCT
ejpam-3725	144	11	m.	m.	NOUN
ejpam-3725	144	12	demirci	demirci	VERB
ejpam-3725	144	13	et	et	PROPN
ejpam-3725	144	14	al	al	PROPN
ejpam-3725	144	15	.	.	PUNCT
ejpam-3725	144	16	/	/	SYM
ejpam-3725	144	17	eur	eur	PROPN
ejpam-3725	144	18	.	.	PUNCT
ejpam-3725	145	1	j.	j.	PROPN
ejpam-3725	145	2	pure	pure	PROPN
ejpam-3725	145	3	appl	appl	PROPN
ejpam-3725	145	4	.	.	PROPN
ejpam-3725	145	5	math	math	PROPN
ejpam-3725	145	6	,	,	PUNCT
ejpam-3725	145	7	13	13	NUM
ejpam-3725	145	8	(	(	PUNCT
ejpam-3725	145	9	5	5	NUM
ejpam-3725	145	10	)	)	PUNCT
ejpam-3725	145	11	(	(	PUNCT
ejpam-3725	145	12	2020	2020	NUM
ejpam-3725	145	13	)	)	PUNCT
ejpam-3725	145	14	,	,	PUNCT
ejpam-3725	145	15	1260	1260	NUM
ejpam-3725	145	16	-	-	SYM
ejpam-3725	145	17	1269	1269	NUM
ejpam-3725	145	18	1266	1266	NUM
ejpam-3725	145	19	=	=	SYM
ejpam-3725	145	20	1	1	NUM
ejpam-3725	145	21	2	2	NUM
ejpam-3725	145	22	∑	∑	NOUN
ejpam-3725	145	23	vivj∈e(g	vivj∈e(g	NOUN
ejpam-3725	145	24	)	)	PUNCT
ejpam-3725	145	25	dg(vi	dg(vi	PROPN
ejpam-3725	145	26	)	)	PUNCT
ejpam-3725	146	1	+	+	CCONJ
ejpam-3725	146	2	dg(vj	dg(vj	NOUN
ejpam-3725	146	3	)	)	PUNCT
ejpam-3725	146	4	dg(vi	dg(vi	PROPN
ejpam-3725	146	5	)	)	PUNCT
ejpam-3725	146	6	·	·	PUNCT
ejpam-3725	147	1	dg(vj	dg(vj	NOUN
ejpam-3725	147	2	)	)	PUNCT
ejpam-3725	148	1	+	+	CCONJ
ejpam-3725	148	2	1	1	NUM
ejpam-3725	148	3	2	2	NUM
ejpam-3725	148	4	∑	∑	PUNCT
ejpam-3725	148	5	vi∈v	vi∈v	X
ejpam-3725	148	6	(	(	PUNCT
ejpam-3725	148	7	g	g	NOUN
ejpam-3725	148	8	)	)	PUNCT
ejpam-3725	148	9	(	(	PUNCT
ejpam-3725	148	10	1	1	NUM
ejpam-3725	148	11	+	+	CCONJ
ejpam-3725	148	12	dg(vi	dg(vi	NOUN
ejpam-3725	148	13	)	)	PUNCT
ejpam-3725	148	14	)	)	PUNCT
ejpam-3725	148	15	,	,	PUNCT
ejpam-3725	148	16	and	and	CCONJ
ejpam-3725	148	17	the	the	DET
ejpam-3725	148	18	result	result	NOUN
ejpam-3725	148	19	follows	follow	VERB
ejpam-3725	148	20	.	.	PUNCT
ejpam-3725	149	1	using	use	VERB
ejpam-3725	149	2	eqns.(7	eqns.(7	NOUN
ejpam-3725	149	3	)	)	PUNCT
ejpam-3725	149	4	and	and	CCONJ
ejpam-3725	149	5	(	(	PUNCT
ejpam-3725	149	6	8)	8)	NUM
ejpam-3725	149	7	,	,	PUNCT
ejpam-3725	149	8	we	we	PRON
ejpam-3725	149	9	get	get	VERB
ejpam-3725	149	10	the	the	DET
ejpam-3725	149	11	results	result	NOUN
ejpam-3725	149	12	for	for	ADP
ejpam-3725	149	13	(	(	PUNCT
ejpam-3725	149	14	ii	ii	NOUN
ejpam-3725	149	15	)	)	PUNCT
ejpam-3725	149	16	and	and	CCONJ
ejpam-3725	149	17	(	(	PUNCT
ejpam-3725	149	18	iii	iii	NOUN
ejpam-3725	149	19	)	)	PUNCT
ejpam-3725	149	20	by	by	ADP
ejpam-3725	149	21	similar	similar	ADJ
ejpam-3725	149	22	methods	method	NOUN
ejpam-3725	149	23	.	.	PUNCT
ejpam-3725	150	1	theorem	theorem	NOUN
ejpam-3725	150	2	7	7	NUM
ejpam-3725	150	3	.	.	PUNCT
ejpam-3725	151	1	let	let	VERB
ejpam-3725	151	2	g	g	PRON
ejpam-3725	151	3	be	be	AUX
ejpam-3725	151	4	a	a	DET
ejpam-3725	151	5	graph	graph	NOUN
ejpam-3725	151	6	with	with	ADP
ejpam-3725	151	7	order	order	NOUN
ejpam-3725	151	8	n	n	X
ejpam-3725	151	9	=	=	SYM
ejpam-3725	151	10	n(g	n(g	NUM
ejpam-3725	151	11	)	)	PUNCT
ejpam-3725	151	12	and	and	CCONJ
ejpam-3725	151	13	size	size	NOUN
ejpam-3725	151	14	m	m	PROPN
ejpam-3725	151	15	=	=	SYM
ejpam-3725	151	16	m(g	m(g	PROPN
ejpam-3725	151	17	)	)	PUNCT
ejpam-3725	151	18	.	.	PUNCT
ejpam-3725	152	1	reformulated	reformulate	VERB
ejpam-3725	152	2	forgotten	forget	VERB
ejpam-3725	152	3	index	index	NOUN
ejpam-3725	152	4	of	of	ADP
ejpam-3725	152	5	t1(g	t1(g	PROPN
ejpam-3725	152	6	)	)	PUNCT
ejpam-3725	152	7	is	be	AUX
ejpam-3725	152	8	rf	rf	ADJ
ejpam-3725	152	9	(	(	PUNCT
ejpam-3725	152	10	t1(g	t1(g	PROPN
ejpam-3725	152	11	)	)	PUNCT
ejpam-3725	152	12	)	)	PUNCT
ejpam-3725	153	1	=	=	SYM
ejpam-3725	153	2	8	8	NUM
ejpam-3725	153	3	(	(	PUNCT
ejpam-3725	153	4	2m4(g	2m4(g	NOUN
ejpam-3725	153	5	)	)	PUNCT
ejpam-3725	153	6	+	+	NUM
ejpam-3725	153	7	3rezg3(g)−m(g	3rezg3(g)−m(g	NUM
ejpam-3725	153	8	)	)	PUNCT
ejpam-3725	153	9	)	)	PUNCT
ejpam-3725	154	1	−	−	PROPN
ejpam-3725	154	2	24	24	NUM
ejpam-3725	154	3	(	(	PUNCT
ejpam-3725	154	4	f	f	X
ejpam-3725	154	5	(	(	PUNCT
ejpam-3725	154	6	g	g	NOUN
ejpam-3725	154	7	)	)	PUNCT
ejpam-3725	154	8	+	+	NOUN
ejpam-3725	154	9	2m2(g)−m1(g	2m2(g)−m1(g	NUM
ejpam-3725	154	10	)	)	PUNCT
ejpam-3725	154	11	)	)	PUNCT
ejpam-3725	154	12	.	.	PUNCT
ejpam-3725	155	1	proof	proof	NOUN
ejpam-3725	155	2	.	.	PUNCT
ejpam-3725	156	1	for	for	ADP
ejpam-3725	156	2	vertex	vertex	NOUN
ejpam-3725	156	3	-	-	PUNCT
ejpam-3725	156	4	semitotal	semitotal	ADJ
ejpam-3725	156	5	graph	graph	NOUN
ejpam-3725	156	6	t1(g	t1(g	PROPN
ejpam-3725	156	7	)	)	PUNCT
ejpam-3725	156	8	of	of	ADP
ejpam-3725	156	9	a	a	DET
ejpam-3725	156	10	graph	graph	NOUN
ejpam-3725	156	11	g	g	NOUN
ejpam-3725	156	12	,	,	PUNCT
ejpam-3725	156	13	there	there	PRON
ejpam-3725	156	14	are	be	VERB
ejpam-3725	156	15	two	two	NUM
ejpam-3725	156	16	types	type	NOUN
ejpam-3725	156	17	of	of	ADP
ejpam-3725	156	18	vertices	vertex	NOUN
ejpam-3725	156	19	:	:	PUNCT
ejpam-3725	156	20	firstly	firstly	ADV
ejpam-3725	156	21	,	,	PUNCT
ejpam-3725	156	22	the	the	DET
ejpam-3725	156	23	vertices	vertex	NOUN
ejpam-3725	156	24	corresponding	correspond	VERB
ejpam-3725	156	25	to	to	ADP
ejpam-3725	156	26	the	the	DET
ejpam-3725	156	27	vertices	vertex	NOUN
ejpam-3725	156	28	of	of	ADP
ejpam-3725	156	29	g	g	NOUN
ejpam-3725	156	30	,	,	PUNCT
ejpam-3725	156	31	secondly	secondly	ADV
ejpam-3725	156	32	,	,	PUNCT
ejpam-3725	156	33	the	the	DET
ejpam-3725	156	34	vertices	vertex	NOUN
ejpam-3725	156	35	corresponding	correspond	VERB
ejpam-3725	156	36	to	to	ADP
ejpam-3725	156	37	the	the	DET
ejpam-3725	156	38	edges	edge	NOUN
ejpam-3725	156	39	of	of	ADP
ejpam-3725	156	40	g.	g.	NOUN
ejpam-3725	156	41	we	we	PRON
ejpam-3725	156	42	will	will	AUX
ejpam-3725	156	43	denote	denote	VERB
ejpam-3725	156	44	them	they	PRON
ejpam-3725	156	45	vi	vi	PROPN
ejpam-3725	156	46	and	and	CCONJ
ejpam-3725	156	47	cij	cij	PROPN
ejpam-3725	156	48	,	,	PUNCT
ejpam-3725	156	49	respectively	respectively	ADV
ejpam-3725	156	50	.	.	PUNCT
ejpam-3725	157	1	depending	depend	VERB
ejpam-3725	157	2	on	on	ADP
ejpam-3725	157	3	the	the	DET
ejpam-3725	157	4	nature	nature	NOUN
ejpam-3725	157	5	of	of	ADP
ejpam-3725	157	6	end	end	NOUN
ejpam-3725	157	7	vertices	vertex	NOUN
ejpam-3725	157	8	,	,	PUNCT
ejpam-3725	157	9	we	we	PRON
ejpam-3725	157	10	can	can	AUX
ejpam-3725	157	11	divide	divide	VERB
ejpam-3725	157	12	the	the	DET
ejpam-3725	157	13	edges	edge	NOUN
ejpam-3725	157	14	of	of	ADP
ejpam-3725	157	15	t1	t1	NOUN
ejpam-3725	157	16	into	into	ADP
ejpam-3725	157	17	two	two	NUM
ejpam-3725	157	18	types	type	NOUN
ejpam-3725	157	19	:	:	PUNCT
ejpam-3725	157	20	i	i	NOUN
ejpam-3725	157	21	)	)	PUNCT
ejpam-3725	157	22	vivj	vivj	NOUN
ejpam-3725	157	23	-	-	PUNCT
ejpam-3725	157	24	edge	edge	NOUN
ejpam-3725	157	25	:	:	PUNCT
ejpam-3725	157	26	an	an	DET
ejpam-3725	157	27	edge	edge	NOUN
ejpam-3725	157	28	between	between	ADP
ejpam-3725	157	29	two	two	NUM
ejpam-3725	157	30	vertices	vertex	NOUN
ejpam-3725	157	31	in	in	ADP
ejpam-3725	157	32	g.	g.	PROPN
ejpam-3725	157	33	ii	ii	PROPN
ejpam-3725	157	34	)	)	PUNCT
ejpam-3725	157	35	vicij	vicij	NOUN
ejpam-3725	157	36	-	-	PUNCT
ejpam-3725	157	37	edge	edge	NOUN
ejpam-3725	157	38	:	:	PUNCT
ejpam-3725	157	39	an	an	DET
ejpam-3725	157	40	edge	edge	NOUN
ejpam-3725	157	41	between	between	ADP
ejpam-3725	157	42	the	the	DET
ejpam-3725	157	43	vertices	vertex	NOUN
ejpam-3725	157	44	of	of	ADP
ejpam-3725	157	45	g	g	NOUN
ejpam-3725	157	46	and	and	CCONJ
ejpam-3725	157	47	the	the	DET
ejpam-3725	157	48	vertices	vertex	NOUN
ejpam-3725	157	49	corresponding	correspond	VERB
ejpam-3725	157	50	to	to	ADP
ejpam-3725	157	51	the	the	DET
ejpam-3725	157	52	edges	edge	NOUN
ejpam-3725	157	53	of	of	ADP
ejpam-3725	157	54	g.	g.	NOUN
ejpam-3725	157	55	using	use	VERB
ejpam-3725	157	56	eqn	eqn	NOUN
ejpam-3725	157	57	.	.	PUNCT
ejpam-3725	158	1	(	(	PUNCT
ejpam-3725	158	2	9	9	NUM
ejpam-3725	158	3	)	)	PUNCT
ejpam-3725	158	4	,	,	PUNCT
ejpam-3725	158	5	we	we	PRON
ejpam-3725	158	6	have	have	VERB
ejpam-3725	158	7	rf	rf	NUM
ejpam-3725	158	8	(	(	PUNCT
ejpam-3725	158	9	t1(g	t1(g	PROPN
ejpam-3725	158	10	)	)	PUNCT
ejpam-3725	158	11	)	)	PUNCT
ejpam-3725	159	1	=	=	PUNCT
ejpam-3725	159	2	∑	∑	PUNCT
ejpam-3725	159	3	e∈e(t1(g	e∈e(t1(g	PROPN
ejpam-3725	159	4	)	)	PUNCT
ejpam-3725	159	5	)	)	PUNCT
ejpam-3725	160	1	(	(	PUNCT
ejpam-3725	160	2	de	de	X
ejpam-3725	160	3	)	)	PUNCT
ejpam-3725	160	4	3	3	NUM
ejpam-3725	160	5	=	=	SYM
ejpam-3725	160	6	∑	∑	PUNCT
ejpam-3725	160	7	evivj∈e(t1	evivj∈e(t1	PROPN
ejpam-3725	160	8	)	)	PUNCT
ejpam-3725	160	9	dt1(evivj	dt1(evivj	PROPN
ejpam-3725	160	10	)	)	PUNCT
ejpam-3725	160	11	3	3	NUM
ejpam-3725	161	1	+	+	CCONJ
ejpam-3725	161	2	∑	∑	PROPN
ejpam-3725	161	3	evicij∈e(t1	evicij∈e(t1	PROPN
ejpam-3725	161	4	)	)	PUNCT
ejpam-3725	162	1	dt1(evicij	dt1(evicij	CCONJ
ejpam-3725	162	2	)	)	PUNCT
ejpam-3725	162	3	3	3	NUM
ejpam-3725	162	4	=	=	SYM
ejpam-3725	162	5	∑	∑	PUNCT
ejpam-3725	162	6	vivj∈e(t1	vivj∈e(t1	PROPN
ejpam-3725	162	7	)	)	PUNCT
ejpam-3725	163	1	[	[	X
ejpam-3725	163	2	dt1(vi	dt1(vi	X
ejpam-3725	163	3	)	)	PUNCT
ejpam-3725	163	4	+	+	CCONJ
ejpam-3725	163	5	dt1(vj)−	dt1(vj)−	PROPN
ejpam-3725	163	6	2]3	2]3	NUM
ejpam-3725	163	7	+	+	CCONJ
ejpam-3725	163	8	∑	∑	PUNCT
ejpam-3725	163	9	vicij∈e(t1	vicij∈e(t1	PROPN
ejpam-3725	163	10	)	)	PUNCT
ejpam-3725	164	1	[	[	X
ejpam-3725	164	2	dt1(vi	dt1(vi	X
ejpam-3725	164	3	)	)	PUNCT
ejpam-3725	165	1	+	+	NUM
ejpam-3725	165	2	dt1(cij)−	dt1(cij)−	NOUN
ejpam-3725	165	3	2]3	2]3	ADJ
ejpam-3725	165	4	.	.	PUNCT
ejpam-3725	166	1	for	for	ADP
ejpam-3725	166	2	vicij	vicij	NOUN
ejpam-3725	166	3	-	-	PUNCT
ejpam-3725	166	4	edges	edge	NOUN
ejpam-3725	166	5	in	in	ADP
ejpam-3725	166	6	the	the	DET
ejpam-3725	166	7	second	second	ADJ
ejpam-3725	166	8	term	term	NOUN
ejpam-3725	166	9	,	,	PUNCT
ejpam-3725	166	10	it	it	PRON
ejpam-3725	166	11	is	be	AUX
ejpam-3725	166	12	clear	clear	ADJ
ejpam-3725	166	13	that	that	SCONJ
ejpam-3725	166	14	every	every	DET
ejpam-3725	166	15	vi	vi	NOUN
ejpam-3725	166	16	vertex	vertex	NOUN
ejpam-3725	166	17	of	of	ADP
ejpam-3725	166	18	t1(g	t1(g	PROPN
ejpam-3725	166	19	)	)	PUNCT
ejpam-3725	166	20	is	be	AUX
ejpam-3725	166	21	connected	connect	VERB
ejpam-3725	166	22	with	with	ADP
ejpam-3725	166	23	dg(vi	dg(vi	PROPN
ejpam-3725	166	24	)	)	PUNCT
ejpam-3725	166	25	cij	cij	PROPN
ejpam-3725	166	26	vertices	vertex	NOUN
ejpam-3725	166	27	,	,	PUNCT
ejpam-3725	166	28	each	each	PRON
ejpam-3725	166	29	of	of	ADP
ejpam-3725	166	30	degree	degree	NOUN
ejpam-3725	166	31	2	2	NUM
ejpam-3725	166	32	.	.	PUNCT
ejpam-3725	167	1	therefore	therefore	ADV
ejpam-3725	167	2	,	,	PUNCT
ejpam-3725	167	3	corresponding	correspond	VERB
ejpam-3725	167	4	to	to	ADP
ejpam-3725	167	5	every	every	DET
ejpam-3725	167	6	vertex	vertex	NOUN
ejpam-3725	167	7	vi	vi	NOUN
ejpam-3725	167	8	in	in	ADP
ejpam-3725	167	9	g	g	NOUN
ejpam-3725	167	10	,	,	PUNCT
ejpam-3725	167	11	there	there	PRON
ejpam-3725	167	12	are	be	VERB
ejpam-3725	167	13	dg(vi	dg(vi	NOUN
ejpam-3725	167	14	)	)	PUNCT
ejpam-3725	167	15	edges	edge	NOUN
ejpam-3725	167	16	in	in	ADP
ejpam-3725	167	17	t1	t1	NOUN
ejpam-3725	167	18	each	each	PRON
ejpam-3725	167	19	of	of	ADP
ejpam-3725	167	20	edge	edge	NOUN
ejpam-3725	167	21	degree	degree	NOUN
ejpam-3725	168	1	[	[	X
ejpam-3725	168	2	2dg(vi	2dg(vi	NUM
ejpam-3725	168	3	)	)	PUNCT
ejpam-3725	168	4	+	+	CCONJ
ejpam-3725	168	5	2−	2−	NUM
ejpam-3725	168	6	2	2	NUM
ejpam-3725	168	7	]	]	PUNCT
ejpam-3725	168	8	.	.	PUNCT
ejpam-3725	169	1	so	so	ADV
ejpam-3725	169	2	,	,	PUNCT
ejpam-3725	169	3	rf	rf	PROPN
ejpam-3725	169	4	(	(	PUNCT
ejpam-3725	169	5	t1(g	t1(g	PROPN
ejpam-3725	169	6	)	)	PUNCT
ejpam-3725	169	7	)	)	PUNCT
ejpam-3725	170	1	=	=	PUNCT
ejpam-3725	170	2	∑	∑	PUNCT
ejpam-3725	170	3	vivj∈e(g	vivj∈e(g	PROPN
ejpam-3725	170	4	)	)	PUNCT
ejpam-3725	171	1	[	[	X
ejpam-3725	171	2	2dg(vi	2dg(vi	NUM
ejpam-3725	171	3	)	)	PUNCT
ejpam-3725	171	4	+	+	NUM
ejpam-3725	171	5	2dg(vj)−	2dg(vj)−	NUM
ejpam-3725	171	6	2]3	2]3	NUM
ejpam-3725	172	1	+	+	CCONJ
ejpam-3725	172	2	∑	∑	PUNCT
ejpam-3725	172	3	vi∈v	vi∈v	X
ejpam-3725	172	4	(	(	PUNCT
ejpam-3725	172	5	g	g	NOUN
ejpam-3725	172	6	)	)	PUNCT
ejpam-3725	172	7	dg(vi)[2dg(vi	dg(vi)[2dg(vi	PUNCT
ejpam-3725	172	8	)	)	PUNCT
ejpam-3725	173	1	+	+	CCONJ
ejpam-3725	173	2	2−	2−	NUM
ejpam-3725	173	3	2]3	2]3	NUM
ejpam-3725	173	4	=	=	SYM
ejpam-3725	173	5	8	8	NUM
ejpam-3725	173	6			NOUN
ejpam-3725	173	7	∑	∑	PROPN
ejpam-3725	173	8	vivj∈e(g	vivj∈e(g	PROPN
ejpam-3725	173	9	)	)	PUNCT
ejpam-3725	173	10	(	(	PUNCT
ejpam-3725	173	11	d3	d3	PROPN
ejpam-3725	173	12	g(vi	g(vi	NUM
ejpam-3725	173	13	)	)	PUNCT
ejpam-3725	174	1	+	+	NUM
ejpam-3725	174	2	d3	d3	PROPN
ejpam-3725	174	3	g(vj	g(vj	PROPN
ejpam-3725	174	4	)	)	PUNCT
ejpam-3725	174	5	)	)	PUNCT
ejpam-3725	175	1	+	+	CCONJ
ejpam-3725	175	2	3	3	NUM
ejpam-3725	175	3	∑	∑	NOUN
ejpam-3725	175	4	vivj∈e(g	vivj∈e(g	NOUN
ejpam-3725	175	5	)	)	PUNCT
ejpam-3725	175	6	dg(vi)dg(vj)(dg(vi	dg(vi)dg(vj)(dg(vi	PROPN
ejpam-3725	175	7	)	)	PUNCT
ejpam-3725	175	8	+	+	NUM
ejpam-3725	175	9	dg(vj	dg(vj	NOUN
ejpam-3725	175	10	)	)	PUNCT
ejpam-3725	175	11	)	)	PUNCT
ejpam-3725	175	12			NOUN
ejpam-3725	175	13	−	−	PROPN
ejpam-3725	175	14	6	6	NUM
ejpam-3725	175	15	∑	∑	NOUN
ejpam-3725	175	16	vivj∈e(g	vivj∈e(g	NOUN
ejpam-3725	175	17	)	)	PUNCT
ejpam-3725	175	18	(	(	PUNCT
ejpam-3725	175	19	2dg(vi	2dg(vi	NUM
ejpam-3725	175	20	)	)	PUNCT
ejpam-3725	175	21	+	+	NUM
ejpam-3725	175	22	dg(vj	dg(vj	NOUN
ejpam-3725	175	23	)	)	PUNCT
ejpam-3725	175	24	)	)	PUNCT
ejpam-3725	175	25	2	2	NUM
ejpam-3725	176	1	+	+	CCONJ
ejpam-3725	176	2	12	12	NUM
ejpam-3725	176	3	∑	∑	NOUN
ejpam-3725	176	4	vivj∈e(g	vivj∈e(g	NOUN
ejpam-3725	176	5	)	)	PUNCT
ejpam-3725	176	6	(	(	PUNCT
ejpam-3725	176	7	2dg(vi	2dg(vi	NUM
ejpam-3725	176	8	)	)	PUNCT
ejpam-3725	176	9	+	+	NUM
ejpam-3725	176	10	dg(vj	dg(vj	NOUN
ejpam-3725	176	11	)	)	PUNCT
ejpam-3725	176	12	)	)	PUNCT
ejpam-3725	177	1	−	−	NUM
ejpam-3725	177	2	∑	∑	PUNCT
ejpam-3725	177	3	vivj∈e(g	vivj∈e(g	NOUN
ejpam-3725	177	4	)	)	PUNCT
ejpam-3725	177	5	8	8	NUM
ejpam-3725	178	1	+	+	CCONJ
ejpam-3725	178	2	8	8	NUM
ejpam-3725	178	3	∑	∑	PUNCT
ejpam-3725	178	4	vi∈v	vi∈v	X
ejpam-3725	178	5	(	(	PUNCT
ejpam-3725	178	6	g	g	NOUN
ejpam-3725	178	7	)	)	PUNCT
ejpam-3725	178	8	d4	d4	PROPN
ejpam-3725	178	9	g(vi	g(vi	X
ejpam-3725	178	10	)	)	PUNCT
ejpam-3725	179	1	=	=	SYM
ejpam-3725	179	2	8	8	NUM
ejpam-3725	179	3	[	[	PUNCT
ejpam-3725	179	4	m4(g	m4(g	NOUN
ejpam-3725	179	5	)	)	PUNCT
ejpam-3725	179	6	+	+	NUM
ejpam-3725	179	7	3rezg3(g)−m(g	3rezg3(g)−m(g	NUM
ejpam-3725	179	8	)	)	PUNCT
ejpam-3725	179	9	]	]	PUNCT
ejpam-3725	180	1	−	−	PROPN
ejpam-3725	181	1	24	24	NUM
ejpam-3725	182	1	[	[	X
ejpam-3725	182	2	f	f	X
ejpam-3725	182	3	(	(	PUNCT
ejpam-3725	182	4	g	g	NOUN
ejpam-3725	182	5	)	)	PUNCT
ejpam-3725	182	6	+	+	NOUN
ejpam-3725	182	7	2m2(g)−m1(g	2m2(g)−m1(g	NUM
ejpam-3725	182	8	)	)	PUNCT
ejpam-3725	182	9	]	]	PUNCT
ejpam-3725	182	10	.	.	PUNCT
ejpam-3725	183	1	m.	m.	PROPN
ejpam-3725	183	2	demirci	demirci	VERB
ejpam-3725	183	3	et	et	PROPN
ejpam-3725	183	4	al	al	PROPN
ejpam-3725	183	5	.	.	PUNCT
ejpam-3725	183	6	/	/	SYM
ejpam-3725	183	7	eur	eur	PROPN
ejpam-3725	183	8	.	.	PUNCT
ejpam-3725	184	1	j.	j.	PROPN
ejpam-3725	184	2	pure	pure	PROPN
ejpam-3725	184	3	appl	appl	PROPN
ejpam-3725	184	4	.	.	PROPN
ejpam-3725	184	5	math	math	PROPN
ejpam-3725	184	6	,	,	PUNCT
ejpam-3725	184	7	13	13	NUM
ejpam-3725	184	8	(	(	PUNCT
ejpam-3725	184	9	5	5	NUM
ejpam-3725	184	10	)	)	PUNCT
ejpam-3725	184	11	(	(	PUNCT
ejpam-3725	184	12	2020	2020	NUM
ejpam-3725	184	13	)	)	PUNCT
ejpam-3725	184	14	,	,	PUNCT
ejpam-3725	184	15	1260	1260	NUM
ejpam-3725	184	16	-	-	SYM
ejpam-3725	184	17	1269	1269	NUM
ejpam-3725	184	18	1267	1267	NUM
ejpam-3725	184	19	theorem	theorem	NOUN
ejpam-3725	184	20	8	8	NUM
ejpam-3725	184	21	.	.	PUNCT
ejpam-3725	185	1	let	let	VERB
ejpam-3725	185	2	g	g	PRON
ejpam-3725	185	3	be	be	AUX
ejpam-3725	185	4	a	a	DET
ejpam-3725	185	5	graph	graph	NOUN
ejpam-3725	185	6	of	of	ADP
ejpam-3725	185	7	order	order	NOUN
ejpam-3725	185	8	n	n	X
ejpam-3725	185	9	=	=	SYM
ejpam-3725	185	10	n(g	n(g	NUM
ejpam-3725	185	11	)	)	PUNCT
ejpam-3725	185	12	and	and	CCONJ
ejpam-3725	185	13	size	size	NOUN
ejpam-3725	185	14	m	m	PROPN
ejpam-3725	185	15	=	=	SYM
ejpam-3725	185	16	m(g	m(g	PROPN
ejpam-3725	185	17	)	)	PUNCT
ejpam-3725	185	18	.	.	PUNCT
ejpam-3725	186	1	multiplicative	multiplicative	PROPN
ejpam-3725	186	2	sum	sum	PROPN
ejpam-3725	186	3	zagreb	zagreb	PROPN
ejpam-3725	186	4	index	index	NOUN
ejpam-3725	186	5	of	of	ADP
ejpam-3725	186	6	t1(g	t1(g	PROPN
ejpam-3725	186	7	)	)	PUNCT
ejpam-3725	187	1	is∏∗	is∏∗	ADV
ejpam-3725	187	2	1	1	NUM
ejpam-3725	187	3	(	(	PUNCT
ejpam-3725	187	4	t1(g	t1(g	PROPN
ejpam-3725	187	5	)	)	PUNCT
ejpam-3725	187	6	)	)	PUNCT
ejpam-3725	187	7	=	=	SYM
ejpam-3725	187	8	4	4	NUM
ejpam-3725	187	9	∏∗	∏∗	X
ejpam-3725	187	10	1	1	NUM
ejpam-3725	187	11	(	(	PUNCT
ejpam-3725	187	12	g	g	NOUN
ejpam-3725	187	13	)	)	PUNCT
ejpam-3725	187	14	∏	∏	PROPN
ejpam-3725	188	1	vi∈v	vi∈v	X
ejpam-3725	189	1	(	(	PUNCT
ejpam-3725	189	2	g	g	NOUN
ejpam-3725	189	3	)	)	PUNCT
ejpam-3725	189	4	(	(	PUNCT
ejpam-3725	189	5	1	1	NUM
ejpam-3725	189	6	+	+	CCONJ
ejpam-3725	189	7	dg(vi	dg(vi	NOUN
ejpam-3725	189	8	)	)	PUNCT
ejpam-3725	189	9	)	)	PUNCT
ejpam-3725	189	10	.	.	PUNCT
ejpam-3725	190	1	proof.∏∗	proof.∏∗	PROPN
ejpam-3725	190	2	1	1	NUM
ejpam-3725	190	3	(	(	PUNCT
ejpam-3725	190	4	t1(g	t1(g	PROPN
ejpam-3725	190	5	)	)	PUNCT
ejpam-3725	190	6	)	)	PUNCT
ejpam-3725	191	1	=	=	SYM
ejpam-3725	191	2	∏	∏	NUM
ejpam-3725	191	3	vivj∈e(t	vivj∈e(t	PROPN
ejpam-3725	191	4	(	(	PUNCT
ejpam-3725	191	5	g	g	NOUN
ejpam-3725	191	6	)	)	PUNCT
ejpam-3725	191	7	)	)	PUNCT
ejpam-3725	191	8	(	(	PUNCT
ejpam-3725	191	9	dt	dt	X
ejpam-3725	191	10	(	(	PUNCT
ejpam-3725	191	11	g)(vi	g)(vi	X
ejpam-3725	191	12	)	)	PUNCT
ejpam-3725	191	13	+	+	NUM
ejpam-3725	191	14	dt	dt	X
ejpam-3725	191	15	(	(	PUNCT
ejpam-3725	191	16	g)(vj	g)(vj	NOUN
ejpam-3725	191	17	)	)	PUNCT
ejpam-3725	191	18	)	)	PUNCT
ejpam-3725	191	19	=	=	SYM
ejpam-3725	192	1	∏	∏	PROPN
ejpam-3725	192	2	vivj∈e(g	vivj∈e(g	NOUN
ejpam-3725	192	3	)	)	PUNCT
ejpam-3725	192	4	(	(	PUNCT
ejpam-3725	192	5	dt	dt	X
ejpam-3725	192	6	(	(	PUNCT
ejpam-3725	192	7	g)(vi	g)(vi	X
ejpam-3725	192	8	)	)	PUNCT
ejpam-3725	192	9	+	+	NUM
ejpam-3725	192	10	dt	dt	X
ejpam-3725	192	11	(	(	PUNCT
ejpam-3725	192	12	g)(vj	g)(vj	NOUN
ejpam-3725	192	13	)	)	PUNCT
ejpam-3725	192	14	)	)	PUNCT
ejpam-3725	192	15	·	·	PUNCT
ejpam-3725	193	1	∏	∏	X
ejpam-3725	193	2	vicij∈e(t	vicij∈e(t	X
ejpam-3725	193	3	(	(	PUNCT
ejpam-3725	193	4	g	g	NOUN
ejpam-3725	193	5	)	)	PUNCT
ejpam-3725	193	6	)	)	PUNCT
ejpam-3725	193	7	(	(	PUNCT
ejpam-3725	193	8	2	2	NUM
ejpam-3725	193	9	+	+	NUM
ejpam-3725	193	10	dt	dt	X
ejpam-3725	193	11	(	(	PUNCT
ejpam-3725	193	12	g)(vi	g)(vi	X
ejpam-3725	193	13	)	)	PUNCT
ejpam-3725	193	14	)	)	PUNCT
ejpam-3725	193	15	=	=	SYM
ejpam-3725	193	16	∏	∏	PROPN
ejpam-3725	193	17	vivj∈e(g	vivj∈e(g	NOUN
ejpam-3725	193	18	)	)	PUNCT
ejpam-3725	193	19	(	(	PUNCT
ejpam-3725	193	20	2dg(vi	2dg(vi	NUM
ejpam-3725	193	21	)	)	PUNCT
ejpam-3725	193	22	+	+	NUM
ejpam-3725	193	23	2dg(vj	2dg(vj	NOUN
ejpam-3725	193	24	)	)	PUNCT
ejpam-3725	193	25	)	)	PUNCT
ejpam-3725	193	26	·	·	PUNCT
ejpam-3725	193	27	2	2	NUM
ejpam-3725	193	28	∏	∏	NUM
ejpam-3725	193	29	vicij∈e(t	vicij∈e(t	X
ejpam-3725	193	30	(	(	PUNCT
ejpam-3725	193	31	g	g	NOUN
ejpam-3725	193	32	)	)	PUNCT
ejpam-3725	193	33	)	)	PUNCT
ejpam-3725	193	34	(	(	PUNCT
ejpam-3725	193	35	1	1	NUM
ejpam-3725	193	36	+	+	CCONJ
ejpam-3725	193	37	dg(vi	dg(vi	NOUN
ejpam-3725	193	38	)	)	PUNCT
ejpam-3725	193	39	)	)	PUNCT
ejpam-3725	194	1	and	and	CCONJ
ejpam-3725	194	2	the	the	DET
ejpam-3725	194	3	result	result	NOUN
ejpam-3725	194	4	follows	follow	VERB
ejpam-3725	194	5	.	.	PUNCT
ejpam-3725	195	1	theorem	theorem	NOUN
ejpam-3725	195	2	9	9	NUM
ejpam-3725	195	3	.	.	PUNCT
ejpam-3725	196	1	let	let	VERB
ejpam-3725	196	2	g	g	PRON
ejpam-3725	196	3	be	be	AUX
ejpam-3725	196	4	a	a	DET
ejpam-3725	196	5	graph	graph	NOUN
ejpam-3725	196	6	of	of	ADP
ejpam-3725	196	7	order	order	NOUN
ejpam-3725	196	8	n	n	X
ejpam-3725	196	9	=	=	SYM
ejpam-3725	196	10	n(g	n(g	NUM
ejpam-3725	196	11	)	)	PUNCT
ejpam-3725	196	12	and	and	CCONJ
ejpam-3725	196	13	size	size	NOUN
ejpam-3725	196	14	m	m	PROPN
ejpam-3725	196	15	=	=	SYM
ejpam-3725	196	16	m(g	m(g	PROPN
ejpam-3725	196	17	)	)	PUNCT
ejpam-3725	196	18	.	.	PUNCT
ejpam-3725	197	1	total	total	ADJ
ejpam-3725	197	2	multiplicative	multiplicative	PROPN
ejpam-3725	197	3	sum	sum	PROPN
ejpam-3725	197	4	zagreb	zagreb	PROPN
ejpam-3725	197	5	index	index	NOUN
ejpam-3725	197	6	of	of	ADP
ejpam-3725	197	7	t1(g	t1(g	PROPN
ejpam-3725	197	8	)	)	PUNCT
ejpam-3725	197	9	is∏t	is∏t	PROPN
ejpam-3725	197	10	(	(	PUNCT
ejpam-3725	197	11	t1(g	t1(g	PROPN
ejpam-3725	197	12	)	)	PUNCT
ejpam-3725	197	13	)	)	PUNCT
ejpam-3725	198	1	=	=	PUNCT
ejpam-3725	199	1	2m(g)2	2m(g)2	NUM
ejpam-3725	199	2	+	+	SYM
ejpam-3725	199	3	1	1	NUM
ejpam-3725	199	4	∏t	∏t	PRON
ejpam-3725	199	5	(	(	PUNCT
ejpam-3725	199	6	g	g	NOUN
ejpam-3725	199	7	)	)	PUNCT
ejpam-3725	199	8	∏	∏	PROPN
ejpam-3725	199	9	vi∈v	vi∈v	X
ejpam-3725	199	10	(	(	PUNCT
ejpam-3725	199	11	g	g	NOUN
ejpam-3725	199	12	)	)	PUNCT
ejpam-3725	199	13	(	(	PUNCT
ejpam-3725	199	14	1	1	NUM
ejpam-3725	199	15	+	+	CCONJ
ejpam-3725	199	16	dg(vi	dg(vi	NOUN
ejpam-3725	199	17	)	)	PUNCT
ejpam-3725	199	18	)	)	PUNCT
ejpam-3725	199	19	m(g	m(g	PROPN
ejpam-3725	199	20	)	)	PUNCT
ejpam-3725	199	21	.	.	PUNCT
ejpam-3725	200	1	proof	proof	NOUN
ejpam-3725	200	2	.	.	PUNCT
ejpam-3725	201	1	from	from	ADP
ejpam-3725	201	2	the	the	DET
ejpam-3725	201	3	definition	definition	NOUN
ejpam-3725	201	4	of	of	ADP
ejpam-3725	201	5	∏t	∏t	PROPN
ejpam-3725	201	6	(	(	PUNCT
ejpam-3725	201	7	g	g	NOUN
ejpam-3725	201	8	)	)	PUNCT
ejpam-3725	201	9	,	,	PUNCT
ejpam-3725	201	10	we	we	PRON
ejpam-3725	201	11	have∏t	have∏t	VERB
ejpam-3725	201	12	(	(	PUNCT
ejpam-3725	201	13	t1(g	t1(g	PROPN
ejpam-3725	201	14	)	)	PUNCT
ejpam-3725	201	15	)	)	PUNCT
ejpam-3725	202	1	=	=	SYM
ejpam-3725	202	2	∏	∏	PROPN
ejpam-3725	202	3	vi	vi	NOUN
ejpam-3725	202	4	,	,	PUNCT
ejpam-3725	202	5	vj∈v	vj∈v	X
ejpam-3725	202	6	(	(	PUNCT
ejpam-3725	202	7	t	t	PROPN
ejpam-3725	202	8	(	(	PUNCT
ejpam-3725	202	9	g	g	NOUN
ejpam-3725	202	10	)	)	PUNCT
ejpam-3725	202	11	)	)	PUNCT
ejpam-3725	203	1	(	(	PUNCT
ejpam-3725	203	2	dt	dt	X
ejpam-3725	203	3	(	(	PUNCT
ejpam-3725	203	4	g)(vi	g)(vi	X
ejpam-3725	203	5	)	)	PUNCT
ejpam-3725	203	6	+	+	NUM
ejpam-3725	203	7	dt	dt	X
ejpam-3725	203	8	(	(	PUNCT
ejpam-3725	203	9	g)(vj	g)(vj	NOUN
ejpam-3725	203	10	)	)	PUNCT
ejpam-3725	203	11	)	)	PUNCT
ejpam-3725	203	12	=	=	SYM
ejpam-3725	203	13	∏	∏	PROPN
ejpam-3725	203	14	vi	vi	NOUN
ejpam-3725	203	15	,	,	PUNCT
ejpam-3725	203	16	vj∈v	vj∈v	VERB
ejpam-3725	203	17	(	(	PUNCT
ejpam-3725	203	18	g	g	NOUN
ejpam-3725	203	19	)	)	PUNCT
ejpam-3725	203	20	(	(	PUNCT
ejpam-3725	203	21	2d(g)(vi	2d(g)(vi	NUM
ejpam-3725	203	22	)	)	PUNCT
ejpam-3725	203	23	+	+	NUM
ejpam-3725	203	24	2d(g)(vj	2d(g)(vj	NUM
ejpam-3725	203	25	)	)	PUNCT
ejpam-3725	203	26	)	)	PUNCT
ejpam-3725	204	1	·	·	PUNCT
ejpam-3725	204	2	∏	∏	PROPN
ejpam-3725	204	3	vi	vi	NOUN
ejpam-3725	204	4	,	,	PUNCT
ejpam-3725	204	5	cij∈v	cij∈v	NOUN
ejpam-3725	204	6	(	(	PUNCT
ejpam-3725	204	7	t	t	PROPN
ejpam-3725	204	8	(	(	PUNCT
ejpam-3725	204	9	g	g	NOUN
ejpam-3725	204	10	)	)	PUNCT
ejpam-3725	204	11	)	)	PUNCT
ejpam-3725	205	1	(	(	PUNCT
ejpam-3725	205	2	2	2	NUM
ejpam-3725	205	3	+	+	SYM
ejpam-3725	205	4	2d(g)(vi	2d(g)(vi	NUM
ejpam-3725	205	5	)	)	PUNCT
ejpam-3725	205	6	)	)	PUNCT
ejpam-3725	205	7	m(g	m(g	PROPN
ejpam-3725	205	8	)	)	PUNCT
ejpam-3725	205	9	·	·	PUNCT
ejpam-3725	205	10	∏	∏	PROPN
ejpam-3725	205	11	cij	cij	PROPN
ejpam-3725	205	12	,	,	PUNCT
ejpam-3725	205	13	ckt∈v	ckt∈v	X
ejpam-3725	205	14	(	(	PUNCT
ejpam-3725	205	15	s(g	s(g	PROPN
ejpam-3725	205	16	)	)	PUNCT
ejpam-3725	205	17	)	)	PUNCT
ejpam-3725	205	18	(	(	PUNCT
ejpam-3725	205	19	2	2	NUM
ejpam-3725	205	20	+	+	NUM
ejpam-3725	205	21	d(g)(vi	d(g)(vi	NOUN
ejpam-3725	205	22	)	)	PUNCT
ejpam-3725	205	23	)	)	PUNCT
ejpam-3725	206	1	=	=	SYM
ejpam-3725	206	2	2	2	NUM
ejpam-3725	206	3	∏t	∏t	PRON
ejpam-3725	206	4	(	(	PUNCT
ejpam-3725	206	5	g	g	NOUN
ejpam-3725	206	6	)	)	PUNCT
ejpam-3725	206	7	·	·	PUNCT
ejpam-3725	206	8	2	2	NUM
ejpam-3725	206	9	m	m	NOUN
ejpam-3725	206	10	∏	∏	NUM
ejpam-3725	206	11	vi∈v	vi∈v	X
ejpam-3725	206	12	(	(	PUNCT
ejpam-3725	206	13	g	g	NOUN
ejpam-3725	206	14	)	)	PUNCT
ejpam-3725	206	15	(	(	PUNCT
ejpam-3725	206	16	1	1	NUM
ejpam-3725	206	17	+	+	CCONJ
ejpam-3725	206	18	dg(vi	dg(vi	NOUN
ejpam-3725	206	19	)	)	PUNCT
ejpam-3725	206	20	)	)	PUNCT
ejpam-3725	206	21	m(g	m(g	PROPN
ejpam-3725	206	22	)	)	PUNCT
ejpam-3725	206	23	·	·	PUNCT
ejpam-3725	207	1	4(m(g	4(m(g	NUM
ejpam-3725	207	2	)	)	PUNCT
ejpam-3725	207	3	2	2	NUM
ejpam-3725	207	4	)	)	PUNCT
ejpam-3725	207	5	and	and	CCONJ
ejpam-3725	207	6	the	the	DET
ejpam-3725	207	7	result	result	NOUN
ejpam-3725	207	8	follows	follow	VERB
ejpam-3725	207	9	.	.	PUNCT
ejpam-3725	208	1	3	3	X
ejpam-3725	208	2	.	.	X
ejpam-3725	208	3	conclusions	conclusion	NOUN
ejpam-3725	208	4	in	in	ADP
ejpam-3725	208	5	this	this	DET
ejpam-3725	208	6	paper	paper	NOUN
ejpam-3725	208	7	,	,	PUNCT
ejpam-3725	208	8	we	we	PRON
ejpam-3725	208	9	obtained	obtain	VERB
ejpam-3725	208	10	the	the	DET
ejpam-3725	208	11	formulae	formulae	NOUN
ejpam-3725	208	12	for	for	ADP
ejpam-3725	208	13	the	the	DET
ejpam-3725	208	14	topological	topological	ADJ
ejpam-3725	208	15	indices	index	NOUN
ejpam-3725	208	16	,	,	PUNCT
ejpam-3725	208	17	especially	especially	ADV
ejpam-3725	208	18	the	the	DET
ejpam-3725	208	19	zagreb	zagreb	PROPN
ejpam-3725	208	20	indices	index	NOUN
ejpam-3725	208	21	and	and	CCONJ
ejpam-3725	208	22	harmonic	harmonic	ADJ
ejpam-3725	208	23	index	index	NOUN
ejpam-3725	208	24	,	,	PUNCT
ejpam-3725	208	25	of	of	ADP
ejpam-3725	208	26	some	some	DET
ejpam-3725	208	27	class	class	NOUN
ejpam-3725	208	28	of	of	ADP
ejpam-3725	208	29	derived	derive	VERB
ejpam-3725	208	30	graphs	graph	NOUN
ejpam-3725	208	31	called	call	VERB
ejpam-3725	208	32	vertex	vertex	NOUN
ejpam-3725	208	33	-	-	PUNCT
ejpam-3725	208	34	semitotal	semitotal	ADJ
ejpam-3725	208	35	graphs	graph	NOUN
ejpam-3725	208	36	.	.	PUNCT
ejpam-3725	209	1	we	we	PRON
ejpam-3725	209	2	used	use	VERB
ejpam-3725	209	3	for	for	ADP
ejpam-3725	209	4	the	the	DET
ejpam-3725	209	5	first	first	ADJ
ejpam-3725	209	6	time	time	NOUN
ejpam-3725	209	7	a	a	DET
ejpam-3725	209	8	newly	newly	ADV
ejpam-3725	209	9	introduced	introduce	VERB
ejpam-3725	209	10	graph	graph	NOUN
ejpam-3725	209	11	invariant	invariant	NOUN
ejpam-3725	209	12	called	call	VERB
ejpam-3725	209	13	omega	omega	NOUN
ejpam-3725	209	14	invariant	invariant	ADJ
ejpam-3725	209	15	to	to	PART
ejpam-3725	209	16	obtain	obtain	VERB
ejpam-3725	209	17	some	some	PRON
ejpam-3725	209	18	of	of	ADP
ejpam-3725	209	19	the	the	DET
ejpam-3725	209	20	relations	relation	NOUN
ejpam-3725	209	21	.	.	PUNCT
ejpam-3725	210	1	the	the	DET
ejpam-3725	210	2	methods	method	NOUN
ejpam-3725	210	3	used	use	VERB
ejpam-3725	210	4	here	here	ADV
ejpam-3725	210	5	can	can	AUX
ejpam-3725	210	6	be	be	AUX
ejpam-3725	210	7	applied	apply	VERB
ejpam-3725	210	8	to	to	ADP
ejpam-3725	210	9	all	all	DET
ejpam-3725	210	10	topological	topological	ADJ
ejpam-3725	210	11	graph	graph	NOUN
ejpam-3725	210	12	indices	index	NOUN
ejpam-3725	210	13	and	and	CCONJ
ejpam-3725	210	14	to	to	ADP
ejpam-3725	210	15	other	other	ADJ
ejpam-3725	210	16	derived	derive	VERB
ejpam-3725	210	17	graphs	graph	NOUN
ejpam-3725	210	18	and	and	CCONJ
ejpam-3725	210	19	graph	graph	NOUN
ejpam-3725	210	20	operations	operation	NOUN
ejpam-3725	210	21	.	.	PUNCT
ejpam-3725	211	1	references	reference	NOUN
ejpam-3725	211	2	1268	1268	NUM
ejpam-3725	211	3	references	reference	NOUN
ejpam-3725	211	4	[	[	X
ejpam-3725	211	5	1	1	NUM
ejpam-3725	211	6	]	]	X
ejpam-3725	211	7	h	h	PROPN
ejpam-3725	211	8	aram	aram	PROPN
ejpam-3725	211	9	and	and	CCONJ
ejpam-3725	211	10	n	n	PRON
ejpam-3725	211	11	dehgardi	dehgardi	NOUN
ejpam-3725	211	12	.	.	PUNCT
ejpam-3725	212	1	reformulated	reformulate	VERB
ejpam-3725	212	2	f	f	NOUN
ejpam-3725	212	3	-	-	PUNCT
ejpam-3725	212	4	index	index	NOUN
ejpam-3725	212	5	of	of	ADP
ejpam-3725	212	6	graph	graph	NOUN
ejpam-3725	212	7	operations	operation	NOUN
ejpam-3725	212	8	.	.	PUNCT
ejpam-3725	213	1	commun	commun	PROPN
ejpam-3725	213	2	.	.	PUNCT
ejpam-3725	213	3	comb	comb	PROPN
ejpam-3725	213	4	.	.	PUNCT
ejpam-3725	214	1	optim	optim	PROPN
ejpam-3725	214	2	.	.	PROPN
ejpam-3725	214	3	,	,	PUNCT
ejpam-3725	214	4	2:87–98	2:87–98	NUM
ejpam-3725	214	5	,	,	PUNCT
ejpam-3725	214	6	2017	2017	NUM
ejpam-3725	214	7	.	.	PUNCT
ejpam-3725	215	1	[	[	X
ejpam-3725	215	2	2	2	NUM
ejpam-3725	215	3	]	]	SYM
ejpam-3725	215	4	b	b	NOUN
ejpam-3725	215	5	basavanagoud	basavanagoud	NOUN
ejpam-3725	215	6	,	,	PUNCT
ejpam-3725	215	7	i	i	PROPN
ejpam-3725	215	8	gutman	gutman	NOUN
ejpam-3725	215	9	,	,	PUNCT
ejpam-3725	215	10	and	and	CCONJ
ejpam-3725	215	11	c	c	NOUN
ejpam-3725	215	12	s	s	VERB
ejpam-3725	215	13	gali	gali	PROPN
ejpam-3725	215	14	.	.	PUNCT
ejpam-3725	216	1	on	on	ADP
ejpam-3725	216	2	second	second	ADJ
ejpam-3725	216	3	zagreb	zagreb	PROPN
ejpam-3725	216	4	index	index	NOUN
ejpam-3725	216	5	and	and	CCONJ
ejpam-3725	216	6	coindex	coindex	NOUN
ejpam-3725	216	7	of	of	ADP
ejpam-3725	216	8	some	some	DET
ejpam-3725	216	9	derived	derive	VERB
ejpam-3725	216	10	graphs	graph	NOUN
ejpam-3725	216	11	.	.	PUNCT
ejpam-3725	217	1	kragujevac	kragujevac	PROPN
ejpam-3725	217	2	j.	j.	PROPN
ejpam-3725	217	3	sci	sci	PROPN
ejpam-3725	217	4	.	.	PROPN
ejpam-3725	217	5	,	,	PUNCT
ejpam-3725	217	6	37:113–121	37:113–121	PROPN
ejpam-3725	217	7	,	,	PUNCT
ejpam-3725	217	8	2015	2015	NUM
ejpam-3725	217	9	.	.	PUNCT
ejpam-3725	218	1	[	[	X
ejpam-3725	218	2	3	3	NUM
ejpam-3725	218	3	]	]	SYM
ejpam-3725	218	4	b	b	NOUN
ejpam-3725	218	5	basavanagoud	basavanagoud	NOUN
ejpam-3725	218	6	and	and	CCONJ
ejpam-3725	218	7	s	s	PROPN
ejpam-3725	218	8	patil	patil	PROPN
ejpam-3725	218	9	.	.	PUNCT
ejpam-3725	219	1	multiplicative	multiplicative	PROPN
ejpam-3725	219	2	zagreb	zagreb	PROPN
ejpam-3725	219	3	indices	index	NOUN
ejpam-3725	219	4	and	and	CCONJ
ejpam-3725	219	5	coindices	coindice	NOUN
ejpam-3725	219	6	of	of	ADP
ejpam-3725	219	7	some	some	DET
ejpam-3725	219	8	derived	derive	VERB
ejpam-3725	219	9	graphs	graph	NOUN
ejpam-3725	219	10	.	.	PUNCT
ejpam-3725	220	1	opuscula	opuscula	PROPN
ejpam-3725	220	2	math	math	PROPN
ejpam-3725	220	3	.	.	PUNCT
ejpam-3725	220	4	,	,	PUNCT
ejpam-3725	221	1	36(3):287–299	36(3):287–299	NOUN
ejpam-3725	221	2	,	,	PUNCT
ejpam-3725	221	3	2016	2016	NUM
ejpam-3725	221	4	.	.	PUNCT
ejpam-3725	222	1	[	[	X
ejpam-3725	222	2	4	4	X
ejpam-3725	222	3	]	]	X
ejpam-3725	222	4	k	k	PROPN
ejpam-3725	222	5	c	c	PROPN
ejpam-3725	222	6	das	das	PROPN
ejpam-3725	222	7	,	,	PUNCT
ejpam-3725	222	8	n	n	PRON
ejpam-3725	222	9	akgunes	akgune	NOUN
ejpam-3725	222	10	,	,	PUNCT
ejpam-3725	222	11	m	m	PROPN
ejpam-3725	222	12	togan	togan	ADJ
ejpam-3725	222	13	,	,	PUNCT
ejpam-3725	222	14	a	a	DET
ejpam-3725	222	15	yurttas	yurtta	NOUN
ejpam-3725	222	16	,	,	PUNCT
ejpam-3725	222	17	i	i	PRON
ejpam-3725	222	18	n	n	PRON
ejpam-3725	222	19	cangul	cangul	VERB
ejpam-3725	222	20	,	,	PUNCT
ejpam-3725	222	21	and	and	CCONJ
ejpam-3725	222	22	a	a	DET
ejpam-3725	222	23	s	s	NOUN
ejpam-3725	222	24	cevik	cevik	NOUN
ejpam-3725	222	25	.	.	PUNCT
ejpam-3725	223	1	on	on	ADP
ejpam-3725	223	2	the	the	DET
ejpam-3725	223	3	first	first	ADJ
ejpam-3725	223	4	zagreb	zagreb	PROPN
ejpam-3725	223	5	index	index	NOUN
ejpam-3725	223	6	and	and	CCONJ
ejpam-3725	223	7	multiplicative	multiplicative	PROPN
ejpam-3725	223	8	zagreb	zagreb	PROPN
ejpam-3725	223	9	coindices	coindice	NOUN
ejpam-3725	223	10	of	of	ADP
ejpam-3725	223	11	graphs	graph	NOUN
ejpam-3725	223	12	.	.	PUNCT
ejpam-3725	224	1	analele	analele	ADP
ejpam-3725	224	2	stiintifice	stiintifice	PROPN
ejpam-3725	224	3	ale	ale	PROPN
ejpam-3725	224	4	universitatii	universitatii	PROPN
ejpam-3725	224	5	ovidius	ovidius	PROPN
ejpam-3725	224	6	constanta	constanta	PROPN
ejpam-3725	224	7	,	,	PUNCT
ejpam-3725	224	8	24(1):153–176	24(1):153–176	PROPN
ejpam-3725	224	9	,	,	PUNCT
ejpam-3725	224	10	2016	2016	NUM
ejpam-3725	224	11	.	.	PUNCT
ejpam-3725	225	1	[	[	X
ejpam-3725	225	2	5	5	X
ejpam-3725	225	3	]	]	PUNCT
ejpam-3725	225	4	k	k	PROPN
ejpam-3725	225	5	c	c	PROPN
ejpam-3725	225	6	das	das	PROPN
ejpam-3725	225	7	,	,	PUNCT
ejpam-3725	225	8	a	a	DET
ejpam-3725	225	9	yurttas	yurtta	NOUN
ejpam-3725	225	10	,	,	PUNCT
ejpam-3725	225	11	m	m	NOUN
ejpam-3725	225	12	togan	togan	VERB
ejpam-3725	225	13	,	,	PUNCT
ejpam-3725	225	14	i	i	PRON
ejpam-3725	225	15	n	n	PRON
ejpam-3725	225	16	cangul	cangul	VERB
ejpam-3725	225	17	,	,	PUNCT
ejpam-3725	225	18	and	and	CCONJ
ejpam-3725	225	19	a	a	DET
ejpam-3725	225	20	s	s	NOUN
ejpam-3725	225	21	cevik	cevik	NOUN
ejpam-3725	225	22	.	.	PUNCT
ejpam-3725	226	1	the	the	DET
ejpam-3725	226	2	multiplicative	multiplicative	PROPN
ejpam-3725	226	3	zagreb	zagreb	PROPN
ejpam-3725	226	4	indices	index	NOUN
ejpam-3725	226	5	of	of	ADP
ejpam-3725	226	6	graph	graph	NOUN
ejpam-3725	226	7	operations	operation	NOUN
ejpam-3725	226	8	.	.	PUNCT
ejpam-3725	227	1	journal	journal	PROPN
ejpam-3725	227	2	of	of	ADP
ejpam-3725	227	3	inequalities	inequality	NOUN
ejpam-3725	227	4	and	and	CCONJ
ejpam-3725	227	5	applications	application	NOUN
ejpam-3725	227	6	,	,	PUNCT
ejpam-3725	227	7	90	90	NUM
ejpam-3725	227	8	,	,	PUNCT
ejpam-3725	227	9	2013	2013	NUM
ejpam-3725	227	10	.	.	PUNCT
ejpam-3725	228	1	[	[	X
ejpam-3725	228	2	6	6	NUM
ejpam-3725	228	3	]	]	PUNCT
ejpam-3725	228	4	n	n	X
ejpam-3725	228	5	de	de	X
ejpam-3725	228	6	.	.	PROPN
ejpam-3725	228	7	f	f	X
ejpam-3725	228	8	-	-	PUNCT
ejpam-3725	228	9	index	index	NOUN
ejpam-3725	228	10	and	and	CCONJ
ejpam-3725	228	11	coindex	coindex	NOUN
ejpam-3725	228	12	of	of	ADP
ejpam-3725	228	13	some	some	DET
ejpam-3725	228	14	derived	derive	VERB
ejpam-3725	228	15	graphs	graph	NOUN
ejpam-3725	228	16	.	.	PUNCT
ejpam-3725	229	1	bulletin	bulletin	NOUN
ejpam-3725	229	2	of	of	ADP
ejpam-3725	229	3	the	the	DET
ejpam-3725	229	4	international	international	ADJ
ejpam-3725	229	5	mathematical	mathematical	ADJ
ejpam-3725	229	6	virtual	virtual	PROPN
ejpam-3725	229	7	institute	institute	PROPN
ejpam-3725	229	8	,	,	PUNCT
ejpam-3725	229	9	8:81–88	8:81–88	NUM
ejpam-3725	229	10	,	,	PUNCT
ejpam-3725	229	11	2018	2018	NUM
ejpam-3725	229	12	.	.	PUNCT
ejpam-3725	230	1	[	[	X
ejpam-3725	230	2	7	7	NUM
ejpam-3725	230	3	]	]	X
ejpam-3725	230	4	s	s	VERB
ejpam-3725	230	5	delen	delen	NOUN
ejpam-3725	231	1	and	and	CCONJ
ejpam-3725	231	2	i	i	PRON
ejpam-3725	231	3	n	n	PRON
ejpam-3725	231	4	cangul	cangul	VERB
ejpam-3725	231	5	.	.	PUNCT
ejpam-3725	232	1	a	a	DET
ejpam-3725	232	2	new	new	ADJ
ejpam-3725	232	3	graph	graph	NOUN
ejpam-3725	232	4	invariant	invariant	ADJ
ejpam-3725	232	5	.	.	PUNCT
ejpam-3725	233	1	turkish	turkish	ADJ
ejpam-3725	233	2	journal	journal	NOUN
ejpam-3725	233	3	of	of	ADP
ejpam-3725	233	4	analysis	analysis	NOUN
ejpam-3725	233	5	and	and	CCONJ
ejpam-3725	233	6	number	number	NOUN
ejpam-3725	233	7	theory	theory	NOUN
ejpam-3725	233	8	,	,	PUNCT
ejpam-3725	233	9	6(1):30–33	6(1):30–33	NUM
ejpam-3725	233	10	,	,	PUNCT
ejpam-3725	233	11	2018	2018	NUM
ejpam-3725	233	12	.	.	PUNCT
ejpam-3725	234	1	[	[	X
ejpam-3725	234	2	8	8	NUM
ejpam-3725	234	3	]	]	X
ejpam-3725	234	4	m	m	VERB
ejpam-3725	234	5	eliasi	eliasi	NOUN
ejpam-3725	234	6	,	,	PUNCT
ejpam-3725	234	7	a	a	DET
ejpam-3725	234	8	iranmanesh	iranmanesh	NOUN
ejpam-3725	234	9	,	,	PUNCT
ejpam-3725	234	10	and	and	CCONJ
ejpam-3725	234	11	i	i	PROPN
ejpam-3725	234	12	gutman	gutman	PROPN
ejpam-3725	234	13	.	.	PUNCT
ejpam-3725	235	1	multiplicative	multiplicative	ADJ
ejpam-3725	235	2	versions	version	NOUN
ejpam-3725	235	3	of	of	ADP
ejpam-3725	235	4	first	first	PROPN
ejpam-3725	235	5	zagreb	zagreb	PROPN
ejpam-3725	235	6	index	index	PROPN
ejpam-3725	235	7	.	.	PUNCT
ejpam-3725	236	1	match	match	PROPN
ejpam-3725	236	2	commun	commun	PROPN
ejpam-3725	236	3	.	.	PUNCT
ejpam-3725	236	4	math	math	PROPN
ejpam-3725	236	5	.	.	PUNCT
ejpam-3725	237	1	comput	comput	NOUN
ejpam-3725	237	2	.	.	PUNCT
ejpam-3725	238	1	chem	chem	NOUN
ejpam-3725	238	2	.	.	PUNCT
ejpam-3725	238	3	,	,	PUNCT
ejpam-3725	238	4	68:217–230	68:217–230	NUM
ejpam-3725	238	5	,	,	PUNCT
ejpam-3725	238	6	2012	2012	NUM
ejpam-3725	238	7	.	.	PUNCT
ejpam-3725	239	1	[	[	X
ejpam-3725	239	2	9	9	NUM
ejpam-3725	239	3	]	]	SYM
ejpam-3725	239	4	b	b	X
ejpam-3725	239	5	furtula	furtula	NOUN
ejpam-3725	239	6	,	,	PUNCT
ejpam-3725	239	7	a	a	DET
ejpam-3725	239	8	graovac	graovac	NOUN
ejpam-3725	239	9	,	,	PUNCT
ejpam-3725	239	10	and	and	CCONJ
ejpam-3725	239	11	d	d	ADP
ejpam-3725	239	12	vukicevic	vukicevic	NOUN
ejpam-3725	239	13	.	.	PUNCT
ejpam-3725	240	1	augmented	augment	VERB
ejpam-3725	240	2	zagreb	zagreb	PROPN
ejpam-3725	240	3	index	index	PROPN
ejpam-3725	240	4	.	.	PUNCT
ejpam-3725	241	1	journal	journal	PROPN
ejpam-3725	241	2	of	of	ADP
ejpam-3725	241	3	mathematical	mathematical	ADJ
ejpam-3725	241	4	chemistry	chemistry	NOUN
ejpam-3725	241	5	,	,	PUNCT
ejpam-3725	241	6	48:370–380	48:370–380	PROPN
ejpam-3725	241	7	,	,	PUNCT
ejpam-3725	241	8	2010	2010	NUM
ejpam-3725	241	9	.	.	PUNCT
ejpam-3725	242	1	[	[	X
ejpam-3725	242	2	10	10	NUM
ejpam-3725	242	3	]	]	X
ejpam-3725	242	4	b	b	NOUN
ejpam-3725	242	5	furtula	furtula	NOUN
ejpam-3725	242	6	and	and	CCONJ
ejpam-3725	242	7	i	i	PROPN
ejpam-3725	242	8	gutman	gutman	PROPN
ejpam-3725	242	9	.	.	PUNCT
ejpam-3725	243	1	a	a	DET
ejpam-3725	243	2	forgotten	forget	VERB
ejpam-3725	243	3	topological	topological	ADJ
ejpam-3725	243	4	index	index	NOUN
ejpam-3725	243	5	.	.	PUNCT
ejpam-3725	244	1	j.	j.	PROPN
ejpam-3725	244	2	math	math	PROPN
ejpam-3725	244	3	.	.	PUNCT
ejpam-3725	245	1	chem	chem	PROPN
ejpam-3725	245	2	.	.	PUNCT
ejpam-3725	245	3	,	,	PUNCT
ejpam-3725	246	1	53(4):1184	53(4):1184	NUM
ejpam-3725	246	2	–	–	PUNCT
ejpam-3725	246	3	1190	1190	NUM
ejpam-3725	246	4	,	,	PUNCT
ejpam-3725	246	5	2015	2015	NUM
ejpam-3725	246	6	.	.	PUNCT
ejpam-3725	247	1	[	[	X
ejpam-3725	247	2	11	11	NUM
ejpam-3725	247	3	]	]	X
ejpam-3725	247	4	i	i	PROPN
ejpam-3725	247	5	gutman	gutman	PROPN
ejpam-3725	247	6	,	,	PUNCT
ejpam-3725	247	7	b	b	NOUN
ejpam-3725	247	8	furtula	furtula	NOUN
ejpam-3725	247	9	,	,	PUNCT
ejpam-3725	247	10	z	z	NOUN
ejpam-3725	247	11	k	k	PROPN
ejpam-3725	247	12	vukicevic	vukicevic	NOUN
ejpam-3725	247	13	,	,	PUNCT
ejpam-3725	247	14	and	and	CCONJ
ejpam-3725	247	15	g	g	PROPN
ejpam-3725	247	16	popidova	popidova	PROPN
ejpam-3725	247	17	.	.	PUNCT
ejpam-3725	248	1	on	on	ADP
ejpam-3725	248	2	zagreb	zagreb	PROPN
ejpam-3725	248	3	indices	index	NOUN
ejpam-3725	248	4	and	and	CCONJ
ejpam-3725	248	5	coindices	coindice	NOUN
ejpam-3725	248	6	.	.	PUNCT
ejpam-3725	249	1	match	match	PROPN
ejpam-3725	249	2	commun	commun	PROPN
ejpam-3725	249	3	.	.	PUNCT
ejpam-3725	249	4	math	math	PROPN
ejpam-3725	249	5	.	.	PUNCT
ejpam-3725	250	1	comput	comput	NOUN
ejpam-3725	250	2	.	.	PUNCT
ejpam-3725	251	1	chem	chem	NOUN
ejpam-3725	251	2	.	.	PUNCT
ejpam-3725	251	3	,	,	PUNCT
ejpam-3725	251	4	74:5–16	74:5–16	NOUN
ejpam-3725	251	5	,	,	PUNCT
ejpam-3725	251	6	2015	2015	NUM
ejpam-3725	251	7	.	.	PUNCT
ejpam-3725	252	1	[	[	X
ejpam-3725	252	2	12	12	NUM
ejpam-3725	252	3	]	]	X
ejpam-3725	252	4	i	i	PRON
ejpam-3725	252	5	gutman	gutman	NOUN
ejpam-3725	252	6	and	and	CCONJ
ejpam-3725	252	7	n	n	PRON
ejpam-3725	252	8	trinajstic	trinajstic	ADJ
ejpam-3725	252	9	.	.	PUNCT
ejpam-3725	253	1	graph	graph	NOUN
ejpam-3725	253	2	theory	theory	NOUN
ejpam-3725	253	3	and	and	CCONJ
ejpam-3725	253	4	molecular	molecular	ADJ
ejpam-3725	253	5	orbitals	orbital	NOUN
ejpam-3725	253	6	iii	iii	PROPN
ejpam-3725	253	7	.	.	PUNCT
ejpam-3725	254	1	total	total	ADJ
ejpam-3725	254	2	π	π	PROPN
ejpam-3725	254	3	-	-	PUNCT
ejpam-3725	254	4	electron	electron	NOUN
ejpam-3725	254	5	energy	energy	NOUN
ejpam-3725	254	6	of	of	ADP
ejpam-3725	254	7	alternant	alternant	ADJ
ejpam-3725	254	8	hydrocarbons	hydrocarbon	NOUN
ejpam-3725	254	9	.	.	PUNCT
ejpam-3725	255	1	chem	chem	NOUN
ejpam-3725	255	2	.	.	PUNCT
ejpam-3725	256	1	phys	phy	NOUN
ejpam-3725	256	2	.	.	PUNCT
ejpam-3725	257	1	lett	lett	PROPN
ejpam-3725	257	2	.	.	PROPN
ejpam-3725	257	3	,	,	PUNCT
ejpam-3725	257	4	17(1):535–538	17(1):535–538	NUM
ejpam-3725	257	5	,	,	PUNCT
ejpam-3725	257	6	1972	1972	NUM
ejpam-3725	257	7	.	.	PUNCT
ejpam-3725	258	1	[	[	X
ejpam-3725	258	2	13	13	NUM
ejpam-3725	258	3	]	]	SYM
ejpam-3725	258	4	j	j	PROPN
ejpam-3725	258	5	b	b	PROPN
ejpam-3725	258	6	liu	liu	PROPN
ejpam-3725	258	7	,	,	PUNCT
ejpam-3725	258	8	a	a	DET
ejpam-3725	258	9	bahadur	bahadur	NOUN
ejpam-3725	258	10	,	,	PUNCT
ejpam-3725	258	11	m	m	VERB
ejpam-3725	258	12	a	a	DET
ejpam-3725	258	13	malik	malik	PROPN
ejpam-3725	258	14	,	,	PUNCT
ejpam-3725	258	15	h	h	PROPN
ejpam-3725	258	16	m	m	VERB
ejpam-3725	258	17	a	a	DET
ejpam-3725	258	18	siddiqui	siddiqui	NOUN
ejpam-3725	258	19	,	,	PUNCT
ejpam-3725	258	20	and	and	CCONJ
ejpam-3725	258	21	m	m	PROPN
ejpam-3725	258	22	imran	imran	ADJ
ejpam-3725	258	23	.	.	PUNCT
ejpam-3725	259	1	reformulated	reformulate	VERB
ejpam-3725	259	2	zagreb	zagreb	PROPN
ejpam-3725	259	3	indices	index	NOUN
ejpam-3725	259	4	of	of	ADP
ejpam-3725	259	5	some	some	DET
ejpam-3725	259	6	derived	derive	VERB
ejpam-3725	259	7	graphs	graph	NOUN
ejpam-3725	259	8	.	.	PUNCT
ejpam-3725	260	1	mathematics	mathematic	NOUN
ejpam-3725	260	2	,	,	PUNCT
ejpam-3725	260	3	7(4):366	7(4):366	NUM
ejpam-3725	260	4	,	,	PUNCT
ejpam-3725	260	5	2019	2019	NUM
ejpam-3725	260	6	.	.	PUNCT
ejpam-3725	261	1	[	[	X
ejpam-3725	261	2	14	14	NUM
ejpam-3725	261	3	]	]	SYM
ejpam-3725	261	4	v	v	ADP
ejpam-3725	261	5	lokesha	lokesha	NOUN
ejpam-3725	261	6	,	,	PUNCT
ejpam-3725	261	7	r	r	NOUN
ejpam-3725	261	8	shruti	shruti	PROPN
ejpam-3725	261	9	,	,	PUNCT
ejpam-3725	261	10	p	p	PROPN
ejpam-3725	261	11	s	s	NOUN
ejpam-3725	261	12	ranjini	ranjini	NOUN
ejpam-3725	261	13	and	and	CCONJ
ejpam-3725	261	14	a.	a.	PROPN
ejpam-3725	261	15	s.	s.	PROPN
ejpam-3725	261	16	cevik	cevik	PROPN
ejpam-3725	261	17	.	.	PUNCT
ejpam-3725	262	1	on	on	ADP
ejpam-3725	262	2	certain	certain	ADJ
ejpam-3725	262	3	topological	topological	ADJ
ejpam-3725	262	4	indices	index	NOUN
ejpam-3725	262	5	of	of	ADP
ejpam-3725	262	6	nanostructures	nanostructure	NOUN
ejpam-3725	262	7	using	use	VERB
ejpam-3725	262	8	q(g	q(g	PROPN
ejpam-3725	262	9	)	)	PUNCT
ejpam-3725	262	10	and	and	CCONJ
ejpam-3725	262	11	r(g	r(g	NUM
ejpam-3725	262	12	)	)	PUNCT
ejpam-3725	262	13	operators	operator	NOUN
ejpam-3725	262	14	.	.	PUNCT
ejpam-3725	263	1	communications	communications	PROPN
ejpam-3725	263	2	fac	fac	PROPN
ejpam-3725	263	3	.	.	PUNCT
ejpam-3725	264	1	sci	sci	PROPN
ejpam-3725	264	2	.	.	PROPN
ejpam-3725	264	3	univ	univ	PROPN
ejpam-3725	264	4	.	.	PUNCT
ejpam-3725	265	1	ank	ank	PROPN
ejpam-3725	265	2	.	.	PROPN
ejpam-3725	265	3	ser	ser	PROPN
ejpam-3725	265	4	.	.	PUNCT
ejpam-3725	266	1	a1	a1	PROPN
ejpam-3725	266	2	:	:	PUNCT
ejpam-3725	266	3	math	math	NOUN
ejpam-3725	266	4	.	.	PUNCT
ejpam-3725	267	1	and	and	CCONJ
ejpam-3725	267	2	stat	stat	PROPN
ejpam-3725	267	3	.	.	PUNCT
ejpam-3725	267	4	,	,	PUNCT
ejpam-3725	267	5	66(2):1	66(2):1	NUM
ejpam-3725	267	6	-	-	SYM
ejpam-3725	267	7	10	10	NUM
ejpam-3725	267	8	,	,	PUNCT
ejpam-3725	267	9	2018	2018	NUM
ejpam-3725	267	10	.	.	PUNCT
ejpam-3725	268	1	[	[	X
ejpam-3725	268	2	15	15	NUM
ejpam-3725	268	3	]	]	X
ejpam-3725	268	4	a	a	DET
ejpam-3725	268	5	milicevic	milicevic	ADJ
ejpam-3725	268	6	,	,	PUNCT
ejpam-3725	268	7	s	s	NOUN
ejpam-3725	268	8	nikolic	nikolic	NOUN
ejpam-3725	268	9	,	,	PUNCT
ejpam-3725	268	10	and	and	CCONJ
ejpam-3725	268	11	n	n	PRON
ejpam-3725	268	12	trinajstic	trinajstic	NOUN
ejpam-3725	268	13	.	.	PUNCT
ejpam-3725	269	1	on	on	ADP
ejpam-3725	269	2	reformulated	reformulate	VERB
ejpam-3725	269	3	zagreb	zagreb	PROPN
ejpam-3725	269	4	indices	index	NOUN
ejpam-3725	269	5	.	.	PUNCT
ejpam-3725	269	6	mol	mol	X
ejpam-3725	269	7	.	.	PUNCT
ejpam-3725	270	1	divers	divers	PROPN
ejpam-3725	270	2	.	.	PUNCT
ejpam-3725	270	3	,	,	PUNCT
ejpam-3725	270	4	8:393–399	8:393–399	NUM
ejpam-3725	270	5	,	,	PUNCT
ejpam-3725	270	6	2004	2004	NUM
ejpam-3725	270	7	.	.	PUNCT
ejpam-3725	271	1	references	reference	NOUN
ejpam-3725	271	2	1269	1269	NUM
ejpam-3725	272	1	[	[	X
ejpam-3725	272	2	16	16	NUM
ejpam-3725	272	3	]	]	X
ejpam-3725	272	4	p	p	X
ejpam-3725	272	5	s	s	PROPN
ejpam-3725	272	6	ranjini	ranjini	NOUN
ejpam-3725	272	7	,	,	PUNCT
ejpam-3725	272	8	v	v	ADP
ejpam-3725	272	9	lokesha	lokesha	NOUN
ejpam-3725	272	10	,	,	PUNCT
ejpam-3725	272	11	and	and	CCONJ
ejpam-3725	272	12	a	a	DET
ejpam-3725	272	13	usha	usha	PROPN
ejpam-3725	272	14	.	.	PUNCT
ejpam-3725	272	15	relation	relation	NOUN
ejpam-3725	272	16	between	between	ADP
ejpam-3725	272	17	phenylene	phenylene	ADJ
ejpam-3725	272	18	and	and	CCONJ
ejpam-3725	272	19	hexagonal	hexagonal	ADJ
ejpam-3725	272	20	squeeze	squeeze	NOUN
ejpam-3725	272	21	using	use	VERB
ejpam-3725	272	22	harmonic	harmonic	ADJ
ejpam-3725	272	23	index	index	NOUN
ejpam-3725	272	24	.	.	PUNCT
ejpam-3725	273	1	int	int	NOUN
ejpam-3725	273	2	j	j	PROPN
ejpam-3725	273	3	graph	graph	NOUN
ejpam-3725	273	4	theory	theory	NOUN
ejpam-3725	273	5	,	,	PUNCT
ejpam-3725	273	6	1:116–121	1:116–121	NUM
ejpam-3725	273	7	,	,	PUNCT
ejpam-3725	273	8	2013	2013	NUM
ejpam-3725	273	9	.	.	PUNCT
ejpam-3725	274	1	[	[	X
ejpam-3725	274	2	17	17	NUM
ejpam-3725	274	3	]	]	SYM
ejpam-3725	274	4	b	b	PROPN
ejpam-3725	274	5	s	s	X
ejpam-3725	274	6	shetty	shetty	PROPN
ejpam-3725	274	7	,	,	PUNCT
ejpam-3725	274	8	v	v	ADP
ejpam-3725	274	9	lokesha	lokesha	NOUN
ejpam-3725	274	10	,	,	PUNCT
ejpam-3725	274	11	and	and	CCONJ
ejpam-3725	274	12	p	p	NOUN
ejpam-3725	274	13	s	s	NOUN
ejpam-3725	274	14	ranjini	ranjini	NOUN
ejpam-3725	274	15	.	.	PUNCT
ejpam-3725	275	1	on	on	ADP
ejpam-3725	275	2	the	the	DET
ejpam-3725	275	3	harmonic	harmonic	ADJ
ejpam-3725	275	4	index	index	NOUN
ejpam-3725	275	5	of	of	ADP
ejpam-3725	275	6	graph	graph	NOUN
ejpam-3725	275	7	operations	operation	NOUN
ejpam-3725	275	8	.	.	PUNCT
ejpam-3725	276	1	transactions	transaction	NOUN
ejpam-3725	276	2	on	on	ADP
ejpam-3725	276	3	combinatorics	combinatoric	NOUN
ejpam-3725	276	4	,	,	PUNCT
ejpam-3725	276	5	4(4):5	4(4):5	PROPN
ejpam-3725	276	6	-	-	PUNCT
ejpam-3725	276	7	14	14	NUM
ejpam-3725	276	8	,	,	PUNCT
ejpam-3725	276	9	2015	2015	NUM
ejpam-3725	276	10	.	.	PUNCT
ejpam-3725	277	1	[	[	X
ejpam-3725	277	2	18	18	NUM
ejpam-3725	277	3	]	]	X
ejpam-3725	277	4	k	k	PROPN
ejpam-3725	277	5	xu	xu	PROPN
ejpam-3725	277	6	,	,	PUNCT
ejpam-3725	277	7	k	k	PROPN
ejpam-3725	277	8	c	c	PROPN
ejpam-3725	277	9	das	das	PROPN
ejpam-3725	277	10	,	,	PUNCT
ejpam-3725	277	11	and	and	CCONJ
ejpam-3725	277	12	k	k	PROPN
ejpam-3725	277	13	tang	tang	PROPN
ejpam-3725	277	14	.	.	PUNCT
ejpam-3725	278	1	on	on	ADP
ejpam-3725	278	2	the	the	DET
ejpam-3725	278	3	multiplicative	multiplicative	PROPN
ejpam-3725	278	4	zagreb	zagreb	PROPN
ejpam-3725	278	5	coindex	coindex	PROPN
ejpam-3725	278	6	of	of	ADP
ejpam-3725	278	7	graphs	graph	NOUN
ejpam-3725	278	8	.	.	PUNCT
ejpam-3725	279	1	opuscula	opuscula	PROPN
ejpam-3725	279	2	math	math	PROPN
ejpam-3725	279	3	.	.	PUNCT
ejpam-3725	279	4	,	,	PUNCT
ejpam-3725	279	5	33:191–204	33:191–204	NUM
ejpam-3725	279	6	,	,	PUNCT
ejpam-3725	279	7	2013	2013	NUM
ejpam-3725	279	8	.	.	PUNCT
ejpam-3725	280	1	[	[	X
ejpam-3725	280	2	19	19	NUM
ejpam-3725	280	3	]	]	PUNCT
ejpam-3725	280	4	l	l	X
ejpam-3725	280	5	zhong	zhong	PROPN
ejpam-3725	280	6	.	.	PUNCT
ejpam-3725	281	1	the	the	DET
ejpam-3725	281	2	harmonic	harmonic	ADJ
ejpam-3725	281	3	index	index	NOUN
ejpam-3725	281	4	on	on	ADP
ejpam-3725	281	5	graphs	graph	NOUN
ejpam-3725	281	6	.	.	PUNCT
ejpam-3725	282	1	applied	apply	VERB
ejpam-3725	282	2	mathematics	mathematics	NOUN
ejpam-3725	282	3	letters	letter	NOUN
ejpam-3725	282	4	,	,	PUNCT
ejpam-3725	282	5	25:561–566	25:561–566	PROPN
ejpam-3725	282	6	,	,	PUNCT
ejpam-3725	282	7	2012	2012	NUM
ejpam-3725	282	8	.	.	PUNCT