id	sid	tid	token	lemma	pos
cana-1423	1	1	communications	communication	NOUN
cana-1423	1	2	on	on	ADP
cana-1423	1	3	applied	apply	VERB
cana-1423	1	4	nonlinear	nonlinear	ADJ
cana-1423	1	5	analysis	analysis	NOUN
cana-1423	1	6	issn	issn	NOUN
cana-1423	1	7	:	:	PUNCT
cana-1423	1	8	1074	1074	NUM
cana-1423	1	9	-	-	PUNCT
cana-1423	1	10	133x	133x	NUM
cana-1423	1	11	vol	vol	NOUN
cana-1423	1	12	31	31	NUM
cana-1423	1	13	no	no	NOUN
cana-1423	1	14	.	.	PUNCT
cana-1423	2	1	7s	7	NOUN
cana-1423	2	2	(	(	PUNCT
cana-1423	2	3	2024	2024	NUM
cana-1423	2	4	)	)	PUNCT
cana-1423	2	5	670	670	NUM
cana-1423	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1423	2	7	zagreb	zagreb	PROPN
cana-1423	2	8	indices	index	NOUN
cana-1423	2	9	of	of	ADP
cana-1423	2	10	an	an	DET
cana-1423	2	11	undirected	undirected	ADJ
cana-1423	2	12	graphs	graph	NOUN
cana-1423	2	13	𝑮𝒏	𝑮𝒏	PROPN
cana-1423	2	14	and	and	CCONJ
cana-1423	2	15	𝑮𝒎,𝒏	𝑮𝒎,𝒏	PROPN
cana-1423	2	16	𝑴	𝑴	PROPN
cana-1423	2	17	l.eswaramma1	l.eswaramma1	PROPN
cana-1423	2	18	,	,	PUNCT
cana-1423	2	19	d.venkata	d.venkata	PROPN
cana-1423	2	20	lakshmi2	lakshmi2	PROPN
cana-1423	2	21	*	*	NOUN
cana-1423	2	22	,	,	PUNCT
cana-1423	2	23	m.siva	m.siva	PROPN
cana-1423	2	24	parvathi3	parvathi3	PROPN
cana-1423	3	1	1department	1department	NUM
cana-1423	3	2	of	of	ADP
cana-1423	3	3	mathematics	mathematic	NOUN
cana-1423	3	4	,	,	PUNCT
cana-1423	3	5	rgukt	rgukt	ADJ
cana-1423	3	6	ongole	ongole	NOUN
cana-1423	3	7	campus	campus	PROPN
cana-1423	3	8	,	,	PUNCT
cana-1423	3	9	andhra	andhra	PROPN
cana-1423	3	10	pradesh	pradesh	PROPN
cana-1423	3	11	,	,	PUNCT
cana-1423	4	1	india	india	PROPN
cana-1423	4	2	.	.	PUNCT
cana-1423	4	3	email	email	NOUN
cana-1423	4	4	:	:	PUNCT
cana-1423	4	5	eswaramma@rguktong.ac.in	eswaramma@rguktong.ac.in	PROPN
cana-1423	4	6	2*school	2*school	NUM
cana-1423	4	7	of	of	ADP
cana-1423	4	8	computer	computer	NOUN
cana-1423	4	9	science	science	NOUN
cana-1423	4	10	and	and	CCONJ
cana-1423	4	11	engineering	engineering	NOUN
cana-1423	4	12	,	,	PUNCT
cana-1423	4	13	vit	vit	PROPN
cana-1423	4	14	-	-	PUNCT
cana-1423	4	15	ap	ap	PROPN
cana-1423	4	16	university	university	PROPN
cana-1423	4	17	,	,	PUNCT
cana-1423	4	18	andhra	andhra	PROPN
cana-1423	4	19	pradesh	pradesh	PROPN
cana-1423	4	20	,	,	PUNCT
cana-1423	4	21	india	india	PROPN
cana-1423	4	22	.	.	PUNCT
cana-1423	5	1	*	*	PUNCT
cana-1423	5	2	corresponding	correspond	VERB
cana-1423	5	3	author	author	NOUN
cana-1423	5	4	:	:	PUNCT
cana-1423	5	5	himaja96@gmail.com	himaja96@gmail.com	X
cana-1423	5	6	3department	3department	NUM
cana-1423	5	7	of	of	ADP
cana-1423	5	8	applied	apply	VERB
cana-1423	5	9	mathematics	mathematic	NOUN
cana-1423	5	10	,	,	PUNCT
cana-1423	5	11	sri	sri	PROPN
cana-1423	5	12	padmavati	padmavati	PROPN
cana-1423	5	13	mahilavisvavidyalayam	mahilavisvavidyalayam	PROPN
cana-1423	5	14	,	,	PUNCT
cana-1423	5	15	tirupathi	tirupathi	PROPN
cana-1423	5	16	,	,	PUNCT
cana-1423	5	17	andhra	andhra	PROPN
cana-1423	5	18	pradesh	pradesh	PROPN
cana-1423	5	19	,	,	PUNCT
cana-1423	5	20	india	india	PROPN
cana-1423	5	21	.	.	PUNCT
cana-1423	5	22	email	email	NOUN
cana-1423	5	23	:	:	PUNCT
cana-1423	5	24	parvathimani2008@gmail.com	parvathimani2008@gmail.com	X
cana-1423	6	1	article	article	NOUN
cana-1423	6	2	history	history	NOUN
cana-1423	6	3	:	:	PUNCT
cana-1423	6	4	received	receive	VERB
cana-1423	6	5	:	:	PUNCT
cana-1423	6	6	06	06	NUM
cana-1423	6	7	-	-	SYM
cana-1423	6	8	06	06	NUM
cana-1423	6	9	-	-	PUNCT
cana-1423	6	10	2024	2024	NUM
cana-1423	6	11	revised	revise	VERB
cana-1423	6	12	:	:	PUNCT
cana-1423	6	13	05	05	NUM
cana-1423	6	14	-	-	PUNCT
cana-1423	6	15	07	07	NUM
cana-1423	6	16	-	-	PUNCT
cana-1423	6	17	2024	2024	NUM
cana-1423	6	18	accepted	accept	VERB
cana-1423	6	19	:	:	PUNCT
cana-1423	6	20	30	30	NUM
cana-1423	6	21	-	-	SYM
cana-1423	6	22	07	07	NUM
cana-1423	6	23	-	-	PUNCT
cana-1423	6	24	2024	2024	NUM
cana-1423	6	25	abstract	abstract	NOUN
cana-1423	6	26	a	a	DET
cana-1423	6	27	topological	topological	ADJ
cana-1423	6	28	index	index	NOUN
cana-1423	6	29	is	be	AUX
cana-1423	6	30	a	a	DET
cana-1423	6	31	molecular	molecular	ADJ
cana-1423	6	32	structure	structure	NOUN
cana-1423	6	33	descriptor	descriptor	NOUN
cana-1423	6	34	of	of	ADP
cana-1423	6	35	a	a	DET
cana-1423	6	36	molecular	molecular	ADJ
cana-1423	6	37	graph	graph	NOUN
cana-1423	6	38	and	and	CCONJ
cana-1423	6	39	it	it	PRON
cana-1423	6	40	has	have	VERB
cana-1423	6	41	many	many	ADJ
cana-1423	6	42	applications	application	NOUN
cana-1423	6	43	in	in	ADP
cana-1423	6	44	real	real	ADJ
cana-1423	6	45	world	world	NOUN
cana-1423	6	46	issues	issue	NOUN
cana-1423	6	47	.	.	PUNCT
cana-1423	7	1	the	the	DET
cana-1423	7	2	zagreb	zagreb	PROPN
cana-1423	7	3	indices	index	NOUN
cana-1423	7	4	based	base	VERB
cana-1423	7	5	on	on	ADP
cana-1423	7	6	degree	degree	NOUN
cana-1423	7	7	of	of	ADP
cana-1423	7	8	vertices	vertex	NOUN
cana-1423	7	9	of	of	ADP
cana-1423	7	10	a	a	DET
cana-1423	7	11	graph	graph	NOUN
cana-1423	7	12	are	be	AUX
cana-1423	7	13	widely	widely	ADV
cana-1423	7	14	studied	study	VERB
cana-1423	7	15	in	in	ADP
cana-1423	7	16	chemical	chemical	NOUN
cana-1423	7	17	graph	graph	NOUN
cana-1423	7	18	theory	theory	NOUN
cana-1423	7	19	in	in	ADP
cana-1423	7	20	over	over	ADP
cana-1423	7	21	the	the	DET
cana-1423	7	22	past	past	ADJ
cana-1423	7	23	few	few	ADJ
cana-1423	7	24	years	year	NOUN
cana-1423	7	25	.	.	PUNCT
cana-1423	8	1	degree	degree	NOUN
cana-1423	8	2	based	base	VERB
cana-1423	8	3	zagreb	zagreb	PROPN
cana-1423	8	4	indices	index	NOUN
cana-1423	8	5	of	of	ADP
cana-1423	8	6	undirected	undirected	ADJ
cana-1423	8	7	graphs	graph	NOUN
cana-1423	8	8	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	8	9	𝑀	𝑀	PROPN
cana-1423	8	10	and	and	CCONJ
cana-1423	8	11	𝐺𝑛	𝐺𝑛	ADJ
cana-1423	8	12	graphs	graph	NOUN
cana-1423	8	13	are	be	AUX
cana-1423	8	14	computed	compute	VERB
cana-1423	8	15	in	in	ADP
cana-1423	8	16	this	this	DET
cana-1423	8	17	paper	paper	NOUN
cana-1423	8	18	.	.	PUNCT
cana-1423	9	1	conclusions	conclusion	NOUN
cana-1423	9	2	:	:	PUNCT
cana-1423	9	3	the	the	DET
cana-1423	9	4	authors	author	NOUN
cana-1423	9	5	of	of	ADP
cana-1423	9	6	this	this	DET
cana-1423	9	7	paper	paper	NOUN
cana-1423	9	8	have	have	AUX
cana-1423	9	9	studied	study	VERB
cana-1423	9	10	the	the	DET
cana-1423	9	11	zagreb	zagreb	PROPN
cana-1423	9	12	indices	index	NOUN
cana-1423	9	13	of	of	ADP
cana-1423	9	14	undirected	undirected	ADJ
cana-1423	9	15	graphs	graph	NOUN
cana-1423	10	1	𝐺𝑛	𝐺𝑛	SCONJ
cana-1423	10	2	when	when	SCONJ
cana-1423	10	3	𝑛	𝑛	PROPN
cana-1423	10	4	=	=	SYM
cana-1423	10	5	2𝛼	2𝛼	PROPN
cana-1423	10	6	,	,	PUNCT
cana-1423	10	7	𝛼	𝛼	X
cana-1423	10	8	>	>	X
cana-1423	10	9	2	2	NUM
cana-1423	10	10	and	and	CCONJ
cana-1423	10	11	undirected	undirected	ADJ
cana-1423	10	12	graph	graph	NOUN
cana-1423	10	13	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	10	14	𝑀	𝑀	PROPN
cana-1423	10	15	for	for	ADP
cana-1423	10	16	some	some	DET
cana-1423	10	17	cases	case	NOUN
cana-1423	10	18	that	that	PRON
cana-1423	10	19	is	be	AUX
cana-1423	10	20	when	when	SCONJ
cana-1423	10	21	𝑛	𝑛	PROPN
cana-1423	10	22	=	=	SYM
cana-1423	10	23	2𝑝	2𝑝	NOUN
cana-1423	10	24	,	,	PUNCT
cana-1423	10	25	𝑝	𝑝	PROPN
cana-1423	10	26	is	be	AUX
cana-1423	10	27	prime,𝑚	prime,𝑚	PROPN
cana-1423	10	28	>	>	SYM
cana-1423	10	29	𝑛	𝑛	PROPN
cana-1423	10	30	,	,	PUNCT
cana-1423	10	31	𝑚	𝑚	PROPN
cana-1423	10	32	is	be	AUX
cana-1423	10	33	prime	prime	ADJ
cana-1423	10	34	and	and	CCONJ
cana-1423	10	35	when	when	SCONJ
cana-1423	10	36	𝑚	𝑚	PROPN
cana-1423	10	37	>	>	X
cana-1423	10	38	𝑛	𝑛	PROPN
cana-1423	10	39	,	,	PUNCT
cana-1423	10	40	𝑚	𝑚	PROPN
cana-1423	10	41	,	,	PUNCT
cana-1423	10	42	𝑛	𝑛	PROPN
cana-1423	10	43	are	be	AUX
cana-1423	10	44	odd	odd	ADJ
cana-1423	10	45	primes	prime	NOUN
cana-1423	10	46	.	.	PUNCT
cana-1423	11	1	keywords	keyword	NOUN
cana-1423	11	2	:	:	PUNCT
cana-1423	11	3	zagreb	zagreb	PROPN
cana-1423	11	4	indices	index	NOUN
cana-1423	11	5	of	of	ADP
cana-1423	11	6	a	a	DET
cana-1423	11	7	graph	graph	NOUN
cana-1423	11	8	,	,	PUNCT
cana-1423	11	9	undirected	undirected	ADJ
cana-1423	11	10	graph	graph	NOUN
cana-1423	11	11	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	11	12	𝑀	𝑀	PROPN
cana-1423	11	13	,	,	PUNCT
cana-1423	11	14	undirected	undirected	ADJ
cana-1423	11	15	graph	graph	NOUN
cana-1423	11	16	𝐺𝑛.	𝐺𝑛.	NOUN
cana-1423	11	17	1	1	X
cana-1423	11	18	.	.	PUNCT
cana-1423	12	1	introduction	introduction	NOUN
cana-1423	12	2	topological	topological	PROPN
cana-1423	12	3	index	index	NOUN
cana-1423	12	4	is	be	AUX
cana-1423	12	5	a	a	DET
cana-1423	12	6	numerical	numerical	ADJ
cana-1423	12	7	quantity	quantity	NOUN
cana-1423	12	8	which	which	PRON
cana-1423	12	9	plays	play	VERB
cana-1423	12	10	vital	vital	ADJ
cana-1423	12	11	role	role	NOUN
cana-1423	12	12	in	in	ADP
cana-1423	12	13	qsar	qsar	NOUN
cana-1423	12	14	or	or	CCONJ
cana-1423	12	15	qspr	qspr	NOUN
cana-1423	12	16	studies	study	NOUN
cana-1423	12	17	.	.	PUNCT
cana-1423	13	1	different	different	ADJ
cana-1423	13	2	types	type	NOUN
cana-1423	13	3	of	of	ADP
cana-1423	13	4	topological	topological	ADJ
cana-1423	13	5	indices	index	NOUN
cana-1423	13	6	are	be	AUX
cana-1423	13	7	introduced	introduce	VERB
cana-1423	13	8	and	and	CCONJ
cana-1423	13	9	studied	study	VERB
cana-1423	13	10	so	so	ADV
cana-1423	13	11	far	far	ADV
cana-1423	13	12	.	.	PUNCT
cana-1423	14	1	in	in	ADP
cana-1423	14	2	1972	1972	NUM
cana-1423	14	3	gutman	gutman	NOUN
cana-1423	14	4	[	[	X
cana-1423	14	5	1	1	NUM
cana-1423	14	6	]	]	PUNCT
cana-1423	14	7	,	,	PUNCT
cana-1423	14	8	[	[	X
cana-1423	14	9	2	2	X
cana-1423	14	10	]	]	PUNCT
cana-1423	14	11	introduced	introduce	VERB
cana-1423	14	12	zagreb	zagreb	PROPN
cana-1423	14	13	indices	index	NOUN
cana-1423	14	14	to	to	PART
cana-1423	14	15	describe	describe	VERB
cana-1423	14	16	the	the	DET
cana-1423	14	17	properties	property	NOUN
cana-1423	14	18	of	of	ADP
cana-1423	14	19	chemical	chemical	NOUN
cana-1423	14	20	compounds	compound	NOUN
cana-1423	14	21	,	,	PUNCT
cana-1423	14	22	the	the	DET
cana-1423	14	23	chemical	chemical	NOUN
cana-1423	14	24	structures	structure	NOUN
cana-1423	14	25	are	be	AUX
cana-1423	14	26	described	describe	VERB
cana-1423	14	27	by	by	ADP
cana-1423	14	28	molecular	molecular	ADJ
cana-1423	14	29	graphs	graph	NOUN
cana-1423	14	30	.	.	PUNCT
cana-1423	15	1	this	this	DET
cana-1423	15	2	formula	formula	NOUN
cana-1423	15	3	in	in	ADP
cana-1423	15	4	graph	graph	NOUN
cana-1423	15	5	theory	theory	NOUN
cana-1423	15	6	represents	represent	VERB
cana-1423	15	7	atoms	atom	NOUN
cana-1423	15	8	and	and	CCONJ
cana-1423	15	9	chemical	chemical	NOUN
cana-1423	15	10	bonds	bond	NOUN
cana-1423	15	11	as	as	ADP
cana-1423	15	12	vertices	vertex	NOUN
cana-1423	15	13	and	and	CCONJ
cana-1423	15	14	edges	edge	NOUN
cana-1423	15	15	,	,	PUNCT
cana-1423	15	16	respectively	respectively	ADV
cana-1423	15	17	.	.	PUNCT
cana-1423	16	1	some	some	DET
cana-1423	16	2	bounds	bound	NOUN
cana-1423	16	3	for	for	ADP
cana-1423	16	4	the	the	DET
cana-1423	16	5	zagreb	zagreb	PROPN
cana-1423	16	6	indices	index	NOUN
cana-1423	16	7	discussed	discuss	VERB
cana-1423	16	8	in	in	ADP
cana-1423	16	9	[	[	PUNCT
cana-1423	16	10	3	3	NUM
cana-1423	16	11	-	-	SYM
cana-1423	16	12	5	5	NUM
cana-1423	16	13	]	]	PUNCT
cana-1423	16	14	.	.	PUNCT
cana-1423	17	1	the	the	DET
cana-1423	17	2	topological	topological	ADJ
cana-1423	17	3	indices	index	NOUN
cana-1423	17	4	of	of	ADP
cana-1423	17	5	graph	graph	NOUN
cana-1423	17	6	operations	operation	NOUN
cana-1423	17	7	are	be	AUX
cana-1423	17	8	computed	compute	VERB
cana-1423	17	9	in	in	ADP
cana-1423	17	10	[	[	X
cana-1423	17	11	8,9	8,9	NUM
cana-1423	17	12	]	]	PUNCT
cana-1423	17	13	.	.	PUNCT
cana-1423	18	1	new	new	ADJ
cana-1423	18	2	types	type	NOUN
cana-1423	18	3	of	of	ADP
cana-1423	18	4	zagreb	zagreb	PROPN
cana-1423	18	5	indices	index	NOUN
cana-1423	18	6	are	be	AUX
cana-1423	18	7	presented	present	VERB
cana-1423	18	8	in	in	ADP
cana-1423	18	9	[	[	X
cana-1423	18	10	10].siva	10].siva	PROPN
cana-1423	18	11	parvathi	parvathi	PROPN
cana-1423	18	12	et	et	NOUN
cana-1423	18	13	al	al	PROPN
cana-1423	19	1	[	[	X
cana-1423	19	2	11	11	NUM
cana-1423	19	3	]	]	PUNCT
cana-1423	19	4	calculated	calculate	VERB
cana-1423	19	5	the	the	DET
cana-1423	19	6	zagreb	zagreb	PROPN
cana-1423	19	7	indices	index	NOUN
cana-1423	19	8	of	of	ADP
cana-1423	19	9	selected	select	VERB
cana-1423	19	10	chemical	chemical	NOUN
cana-1423	19	11	compounds	compound	NOUN
cana-1423	19	12	of	of	ADP
cana-1423	19	13	natural	natural	ADJ
cana-1423	19	14	products	product	NOUN
cana-1423	19	15	.	.	PUNCT
cana-1423	20	1	ivy	ivy	NOUN
cana-1423	20	2	chakrabarthy	chakrabarthy	NOUN
cana-1423	20	3	et	et	PROPN
cana-1423	20	4	al	al	PROPN
cana-1423	21	1	[	[	X
cana-1423	21	2	12	12	NUM
cana-1423	21	3	]	]	PUNCT
cana-1423	21	4	introduced	introduce	VERB
cana-1423	21	5	the	the	DET
cana-1423	21	6	undirected	undirected	ADJ
cana-1423	21	7	graph	graph	NOUN
cana-1423	21	8	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	21	9	and	and	CCONJ
cana-1423	21	10	proved	prove	VERB
cana-1423	21	11	some	some	DET
cana-1423	21	12	basic	basic	ADJ
cana-1423	21	13	properties	property	NOUN
cana-1423	21	14	.	.	PUNCT
cana-1423	22	1	ivy	ivy	NOUN
cana-1423	22	2	chakrabarthy	chakrabarthy	NOUN
cana-1423	22	3	et	et	PROPN
cana-1423	22	4	al	al	PROPN
cana-1423	23	1	[	[	X
cana-1423	23	2	13	13	NUM
cana-1423	23	3	]	]	PUNCT
cana-1423	23	4	introduced	introduce	VERB
cana-1423	23	5	the	the	DET
cana-1423	23	6	undirected	undirected	ADJ
cana-1423	23	7	graph	graph	NOUN
cana-1423	23	8	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	23	9	𝑀	𝑀	PROPN
cana-1423	23	10	and	and	CCONJ
cana-1423	23	11	proved	prove	VERB
cana-1423	23	12	some	some	DET
cana-1423	23	13	basic	basic	ADJ
cana-1423	23	14	properties	property	NOUN
cana-1423	23	15	of	of	ADP
cana-1423	23	16	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	23	17	𝑀	𝑀	PROPN
cana-1423	23	18	graph	graph	NOUN
cana-1423	23	19	.	.	PUNCT
cana-1423	24	1	recently	recently	ADV
cana-1423	24	2	eswaramma	eswaramma	PROPN
cana-1423	24	3	et	et	PROPN
cana-1423	24	4	al	al	PROPN
cana-1423	25	1	[	[	X
cana-1423	25	2	14	14	NUM
cana-1423	25	3	]	]	PUNCT
cana-1423	25	4	calculated	calculate	VERB
cana-1423	25	5	energy	energy	NOUN
cana-1423	25	6	of	of	ADP
cana-1423	25	7	this	this	DET
cana-1423	25	8	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	25	9	𝑀	𝑀	PROPN
cana-1423	25	10	graph	graph	NOUN
cana-1423	25	11	.	.	PUNCT
cana-1423	26	1	anusha	anusha	PROPN
cana-1423	26	2	et	et	PROPN
cana-1423	26	3	al[15]calculated	al[15]calculate	VERB
cana-1423	26	4	the	the	DET
cana-1423	26	5	zagreb	zagreb	PROPN
cana-1423	26	6	indices	index	NOUN
cana-1423	26	7	of	of	ADP
cana-1423	26	8	arithmetic	arithmetic	ADJ
cana-1423	26	9	graphs	graph	NOUN
cana-1423	26	10	.	.	PUNCT
cana-1423	27	1	motivated	motivate	VERB
cana-1423	27	2	by	by	ADP
cana-1423	27	3	these	these	PRON
cana-1423	27	4	,	,	PUNCT
cana-1423	27	5	we	we	PRON
cana-1423	27	6	calculate	calculate	VERB
cana-1423	27	7	the	the	DET
cana-1423	27	8	zagreb	zagreb	PROPN
cana-1423	27	9	indices	index	NOUN
cana-1423	27	10	of	of	ADP
cana-1423	27	11	undirected	undirected	ADJ
cana-1423	27	12	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	27	13	𝑀graph	𝑀graph	PROPN
cana-1423	27	14	,	,	PUNCT
cana-1423	27	15	undirected	undirected	ADJ
cana-1423	27	16	𝐺𝑛graph	𝐺𝑛graph	PROPN
cana-1423	27	17	.	.	PUNCT
cana-1423	28	1	definitions	definition	NOUN
cana-1423	28	2	consider	consider	VERB
cana-1423	28	3	the	the	DET
cana-1423	28	4	simple	simple	ADJ
cana-1423	28	5	graph	graph	NOUN
cana-1423	28	6	g.	g.	PROPN
cana-1423	28	7	let	let	VERB
cana-1423	28	8	𝑑𝑖	𝑑𝑖	NOUN
cana-1423	28	9	,	,	PUNCT
cana-1423	28	10	𝑑𝑗	𝑑𝑗	PROPN
cana-1423	28	11	be	be	AUX
cana-1423	28	12	the	the	DET
cana-1423	28	13	degrees	degree	NOUN
cana-1423	28	14	of	of	ADP
cana-1423	28	15	the	the	DET
cana-1423	28	16	vertices	vertex	NOUN
cana-1423	28	17	𝑣𝑖	𝑣𝑖	VERB
cana-1423	28	18	,	,	PUNCT
cana-1423	28	19	𝑣𝑗	𝑣𝑗	ADP
cana-1423	28	20	and	and	CCONJ
cana-1423	28	21	𝑒𝑖𝑗	𝑒𝑖𝑗	NOUN
cana-1423	28	22	be	be	AUX
cana-1423	28	23	the	the	DET
cana-1423	28	24	edges	edge	NOUN
cana-1423	28	25	joining	join	VERB
cana-1423	28	26	the	the	DET
cana-1423	28	27	vertices	vertex	NOUN
cana-1423	28	28	𝑣𝑖	𝑣𝑖	ADV
cana-1423	28	29	,	,	PUNCT
cana-1423	28	30	𝑣𝑗	𝑣𝑗	ADP
cana-1423	28	31	respectively.then	respectively.then	SCONJ
cana-1423	28	32	the	the	DET
cana-1423	28	33	first	first	ADJ
cana-1423	28	34	zagreb	zagreb	PROPN
cana-1423	28	35	index	index	NOUN
cana-1423	28	36	of	of	ADP
cana-1423	28	37	graph	graph	NOUN
cana-1423	28	38	g	g	PROPN
cana-1423	28	39	is	be	AUX
cana-1423	28	40	defined	define	VERB
cana-1423	28	41	as	as	ADP
cana-1423	28	42	𝑀1(𝐺	𝑀1(𝐺	NOUN
cana-1423	28	43	)	)	PUNCT
cana-1423	28	44	=	=	PUNCT
cana-1423	28	45			X
cana-1423	28	46			NOUN
cana-1423	28	47	+	+	CCONJ
cana-1423	28	48	)	)	PUNCT
cana-1423	28	49	(	(	PUNCT
cana-1423	28	50	,	,	PUNCT
cana-1423	28	51	)	)	PUNCT
cana-1423	28	52	(	(	PUNCT
cana-1423	28	53	gevv	gevv	ADJ
cana-1423	28	54	ji	ji	PROPN
cana-1423	28	55	ji	ji	PROPN
cana-1423	28	56	dd	dd	PROPN
cana-1423	28	57	communications	communication	NOUN
cana-1423	28	58	on	on	ADP
cana-1423	28	59	applied	apply	VERB
cana-1423	28	60	nonlinear	nonlinear	ADJ
cana-1423	28	61	analysis	analysis	NOUN
cana-1423	28	62	issn	issn	NOUN
cana-1423	28	63	:	:	PUNCT
cana-1423	28	64	1074	1074	NUM
cana-1423	28	65	-	-	PUNCT
cana-1423	28	66	133x	133x	NUM
cana-1423	28	67	vol	vol	NOUN
cana-1423	28	68	31	31	NUM
cana-1423	28	69	no	no	NOUN
cana-1423	28	70	.	.	PUNCT
cana-1423	29	1	7s	7	NOUN
cana-1423	29	2	(	(	PUNCT
cana-1423	29	3	2024	2024	NUM
cana-1423	29	4	)	)	PUNCT
cana-1423	29	5	671	671	NUM
cana-1423	29	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1423	30	1	the	the	DET
cana-1423	30	2	second	second	ADJ
cana-1423	30	3	zagreb	zagreb	PROPN
cana-1423	30	4	index	index	NOUN
cana-1423	30	5	of	of	ADP
cana-1423	30	6	graph	graph	NOUN
cana-1423	30	7	g	g	PROPN
cana-1423	30	8	is	be	AUX
cana-1423	30	9	defined	define	VERB
cana-1423	30	10	as	as	ADP
cana-1423	30	11	𝑀2(𝐺	𝑀2(𝐺	NOUN
cana-1423	30	12	)	)	PUNCT
cana-1423	30	13	=	=	SYM
cana-1423	30	14			PROPN
cana-1423	30	15			PROPN
cana-1423	30	16			PROPN
cana-1423	30	17	)	)	PUNCT
cana-1423	30	18	(	(	PUNCT
cana-1423	30	19	,	,	PUNCT
cana-1423	30	20	)	)	PUNCT
cana-1423	30	21	(	(	PUNCT
cana-1423	31	1	gevv	gevv	ADJ
cana-1423	31	2	ji	ji	PROPN
cana-1423	31	3	ji	ji	PROPN
cana-1423	31	4	dd	dd	VERB
cana-1423	31	5	the	the	DET
cana-1423	31	6	hyper	hyper	ADJ
cana-1423	31	7	-	-	ADJ
cana-1423	31	8	zagreb	zagreb	PROPN
cana-1423	31	9	index	index	NOUN
cana-1423	31	10	was	be	AUX
cana-1423	31	11	introduced	introduce	VERB
cana-1423	31	12	by	by	ADP
cana-1423	31	13	shirdel	shirdel	PROPN
cana-1423	31	14	et	et	PROPN
cana-1423	31	15	al	al	PROPN
cana-1423	32	1	[	[	X
cana-1423	32	2	6	6	NUM
cana-1423	32	3	]	]	PUNCT
cana-1423	32	4	in	in	ADP
cana-1423	32	5	2013.the	2013.the	PRON
cana-1423	32	6	hyper	hyper	ADJ
cana-1423	32	7	zagreb	zagreb	PROPN
cana-1423	32	8	index	index	NOUN
cana-1423	32	9	of	of	ADP
cana-1423	32	10	graph	graph	NOUN
cana-1423	32	11	g	g	PROPN
cana-1423	32	12	is	be	AUX
cana-1423	32	13	defined	define	VERB
cana-1423	32	14	as	as	ADP
cana-1423	32	15	𝑀𝐻(𝐺	𝑀𝐻(𝐺	NOUN
cana-1423	32	16	)	)	PUNCT
cana-1423	32	17	=	=	SYM
cana-1423	32	18	2	2	X
cana-1423	32	19	)	)	PUNCT
cana-1423	32	20	(	(	PUNCT
cana-1423	32	21	,	,	PUNCT
cana-1423	32	22	)	)	PUNCT
cana-1423	32	23	(	(	PUNCT
cana-1423	32	24			X
cana-1423	32	25			NOUN
cana-1423	32	26	+	+	CCONJ
cana-1423	32	27	gevv	gevv	ADJ
cana-1423	32	28	ji	ji	X
cana-1423	32	29	ji	ji	PROPN
cana-1423	32	30	dd	dd	VERB
cana-1423	32	31	in	in	ADP
cana-1423	32	32	[	[	X
cana-1423	32	33	7	7	NUM
cana-1423	32	34	]	]	PUNCT
cana-1423	32	35	,	,	PUNCT
cana-1423	32	36	m.ghorbani	m.ghorbani	PUNCT
cana-1423	32	37	and	and	CCONJ
cana-1423	32	38	n.azimi	n.azimi	ADV
cana-1423	32	39	defined	define	VERB
cana-1423	32	40	different	different	ADJ
cana-1423	32	41	versions	version	NOUN
cana-1423	32	42	of	of	ADP
cana-1423	32	43	the	the	DET
cana-1423	32	44	zagreb	zagreb	PROPN
cana-1423	32	45	indices	index	NOUN
cana-1423	32	46	based	base	VERB
cana-1423	32	47	on	on	ADP
cana-1423	32	48	the	the	DET
cana-1423	32	49	degree	degree	NOUN
cana-1423	32	50	of	of	ADP
cana-1423	32	51	vertices	vertex	NOUN
cana-1423	32	52	.	.	PUNCT
cana-1423	33	1	first	first	ADJ
cana-1423	33	2	multiple	multiple	ADJ
cana-1423	33	3	zagreb	zagreb	PROPN
cana-1423	33	4	index	index	NOUN
cana-1423	33	5	of	of	ADP
cana-1423	33	6	the	the	DET
cana-1423	33	7	graph	graph	NOUN
cana-1423	33	8	g	g	NOUN
cana-1423	33	9	is	be	AUX
cana-1423	33	10	defined	define	VERB
cana-1423	33	11	as	as	ADP
cana-1423	33	12	𝑃𝑀1(𝐺)=	𝑃𝑀1(𝐺)=	NOUN
cana-1423	33	13			NUM
cana-1423	33	14			NOUN
cana-1423	33	15	+	+	CCONJ
cana-1423	33	16	)	)	PUNCT
cana-1423	33	17	(	(	PUNCT
cana-1423	33	18	,	,	PUNCT
cana-1423	33	19	)	)	PUNCT
cana-1423	33	20	(	(	PUNCT
cana-1423	33	21	gevv	gevv	ADJ
cana-1423	33	22	ji	ji	PROPN
cana-1423	33	23	ji	ji	PROPN
cana-1423	33	24	dd	dd	VERB
cana-1423	33	25	second	second	ADJ
cana-1423	33	26	multiple	multiple	ADJ
cana-1423	33	27	zagreb	zagreb	PROPN
cana-1423	33	28	index	index	NOUN
cana-1423	33	29	of	of	ADP
cana-1423	33	30	the	the	DET
cana-1423	33	31	graph	graph	NOUN
cana-1423	33	32	g	g	NOUN
cana-1423	33	33	is	be	AUX
cana-1423	33	34	defined	define	VERB
cana-1423	33	35	as	as	ADP
cana-1423	33	36	𝑃𝑀2(𝐺)=	𝑃𝑀2(𝐺)=	NOUN
cana-1423	33	37			NUM
cana-1423	33	38			NOUN
cana-1423	33	39			NOUN
cana-1423	33	40	)	)	PUNCT
cana-1423	33	41	(	(	PUNCT
cana-1423	33	42	,	,	PUNCT
cana-1423	33	43	)	)	PUNCT
cana-1423	33	44	(	(	PUNCT
cana-1423	33	45	gevv	gevv	ADJ
cana-1423	33	46	ji	ji	PROPN
cana-1423	33	47	ji	ji	PROPN
cana-1423	33	48	dd	dd	PROPN
cana-1423	33	49	2	2	NUM
cana-1423	33	50	.	.	X
cana-1423	33	51	zagreb	zagreb	PROPN
cana-1423	33	52	indices	index	NOUN
cana-1423	33	53	of	of	ADP
cana-1423	33	54	an	an	DET
cana-1423	33	55	undirected	undirected	ADJ
cana-1423	33	56	graph	graph	NOUN
cana-1423	33	57	𝑮𝒎,𝒏	𝑮𝒎,𝒏	NOUN
cana-1423	33	58	𝑴	𝑴	NOUN
cana-1423	33	59	the	the	DET
cana-1423	33	60	undirected	undirected	ADJ
cana-1423	33	61	simple	simple	ADJ
cana-1423	33	62	graph	graph	NOUN
cana-1423	33	63	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	33	64	𝑀	𝑀	PROPN
cana-1423	33	65	is	be	AUX
cana-1423	33	66	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	33	67	𝑀	𝑀	PROPN
cana-1423	33	68	=	=	SYM
cana-1423	33	69	(	(	PUNCT
cana-1423	33	70	𝑉	𝑉	PROPN
cana-1423	33	71	,	,	PUNCT
cana-1423	33	72	𝐸	𝐸	PROPN
cana-1423	33	73	)	)	PUNCT
cana-1423	33	74	where	where	SCONJ
cana-1423	33	75	the	the	DET
cana-1423	33	76	vertex	vertex	NOUN
cana-1423	33	77	set	set	VERB
cana-1423	33	78	𝑉	𝑉	PROPN
cana-1423	33	79	=	=	PUNCT
cana-1423	33	80	{	{	PUNCT
cana-1423	33	81	1,2	1,2	NUM
cana-1423	33	82	,	,	PUNCT
cana-1423	33	83	…	…	PUNCT
cana-1423	33	84	.	.	PUNCT
cana-1423	34	1	𝑛	𝑛	X
cana-1423	34	2	}	}	PUNCT
cana-1423	34	3	and	and	CCONJ
cana-1423	34	4	two	two	NUM
cana-1423	34	5	distinct	distinct	ADJ
cana-1423	34	6	vertices	vertex	NOUN
cana-1423	34	7	𝑢	𝑢	PART
cana-1423	34	8	,	,	PUNCT
cana-1423	34	9	𝑣	𝑣	PRON
cana-1423	34	10	∈	∈	PROPN
cana-1423	34	11	𝑉	𝑉	PROPN
cana-1423	34	12	are	be	AUX
cana-1423	34	13	adjacent	adjacent	ADJ
cana-1423	34	14	if	if	SCONJ
cana-1423	35	1	and	and	CCONJ
cana-1423	35	2	only	only	ADV
cana-1423	35	3	if	if	SCONJ
cana-1423	35	4	𝑢	𝑢	PRON
cana-1423	35	5	≠	≠	PROPN
cana-1423	35	6	𝑣and	𝑣and	NOUN
cana-1423	35	7	𝑢.	𝑢.	NOUN
cana-1423	35	8	𝑣	𝑣	X
cana-1423	35	9	is	be	AUX
cana-1423	35	10	not	not	PART
cana-1423	35	11	divisible	divisible	ADJ
cana-1423	35	12	by	by	ADP
cana-1423	35	13	𝑚	𝑚	PROPN
cana-1423	35	14	on	on	ADP
cana-1423	35	15	natural	natural	ADJ
cana-1423	35	16	numbers	number	NOUN
cana-1423	35	17	subset	subset	VERB
cana-1423	35	18	which	which	PRON
cana-1423	35	19	is	be	AUX
cana-1423	35	20	finite	finite	ADJ
cana-1423	35	21	where	where	SCONJ
cana-1423	35	22	𝑚	𝑚	NOUN
cana-1423	35	23	,	,	PUNCT
cana-1423	35	24	𝑛	𝑛	DET
cana-1423	35	25	∈	∈	NOUN
cana-1423	35	26	𝑁.	𝑁.	PROPN
cana-1423	35	27	some	some	PRON
cana-1423	35	28	of	of	ADP
cana-1423	35	29	the	the	DET
cana-1423	35	30	properties	property	NOUN
cana-1423	35	31	are	be	AUX
cana-1423	35	32	1	1	NUM
cana-1423	35	33	.	.	PUNCT
cana-1423	36	1	let	let	VERB
cana-1423	36	2	𝑚	𝑚	NOUN
cana-1423	36	3	=	=	SYM
cana-1423	36	4	1	1	NUM
cana-1423	36	5	then	then	ADV
cana-1423	36	6	the	the	DET
cana-1423	36	7	graph	graph	NOUN
cana-1423	36	8	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	36	9	𝑀	𝑀	PROPN
cana-1423	36	10	is	be	AUX
cana-1423	36	11	a	a	DET
cana-1423	36	12	null	null	ADJ
cana-1423	36	13	graph	graph	NOUN
cana-1423	36	14	with	with	ADP
cana-1423	36	15	𝑛	𝑛	DET
cana-1423	36	16	vertices	vertex	NOUN
cana-1423	36	17	.	.	PUNCT
cana-1423	37	1	2	2	X
cana-1423	37	2	.	.	X
cana-1423	37	3	for	for	ADP
cana-1423	37	4	1	1	NUM
cana-1423	37	5	<	<	X
cana-1423	37	6	𝑚	𝑚	X
cana-1423	37	7	≤	≤	PUNCT
cana-1423	37	8	𝑛,the	𝑛,the	DET
cana-1423	37	9	graph	graph	NOUN
cana-1423	37	10	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	37	11	𝑀	𝑀	PROPN
cana-1423	37	12	is	be	AUX
cana-1423	37	13	disconnected	disconnect	VERB
cana-1423	37	14	.	.	PUNCT
cana-1423	38	1	3	3	X
cana-1423	38	2	.	.	X
cana-1423	38	3	the	the	DET
cana-1423	38	4	graph	graph	NOUN
cana-1423	38	5	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	38	6	𝑀is	𝑀is	PROPN
cana-1423	38	7	connected	connect	VERB
cana-1423	38	8	for	for	ADP
cana-1423	38	9	𝑚	𝑚	X
cana-1423	38	10	>	>	X
cana-1423	38	11	𝑛	𝑛	DET
cana-1423	38	12	4	4	NUM
cana-1423	38	13	.	.	PUNCT
cana-1423	39	1	the	the	DET
cana-1423	39	2	graph	graph	NOUN
cana-1423	39	3	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	39	4	𝑀	𝑀	PROPN
cana-1423	39	5	has	have	VERB
cana-1423	39	6	the	the	DET
cana-1423	39	7	maximum	maximum	ADJ
cana-1423	39	8	degree	degree	NOUN
cana-1423	39	9	𝑛	𝑛	PRON
cana-1423	39	10	−	−	NOUN
cana-1423	39	11	1	1	NUM
cana-1423	39	12	.	.	PUNCT
cana-1423	39	13	results	result	NOUN
cana-1423	39	14	on	on	ADP
cana-1423	39	15	various	various	ADJ
cana-1423	39	16	zagreb	zagreb	PROPN
cana-1423	39	17	indices	index	NOUN
cana-1423	39	18	of	of	ADP
cana-1423	39	19	the	the	DET
cana-1423	39	20	graph	graph	NOUN
cana-1423	39	21	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	39	22	𝑀	𝑀	PROPN
cana-1423	39	23	are	be	AUX
cana-1423	39	24	presented	present	VERB
cana-1423	39	25	in	in	ADP
cana-1423	39	26	this	this	DET
cana-1423	39	27	section	section	NOUN
cana-1423	39	28	.	.	PUNCT
cana-1423	40	1	theorem	theorem	VERB
cana-1423	40	2	2.1	2.1	NUM
cana-1423	40	3	:	:	PUNCT
cana-1423	40	4	if	if	SCONJ
cana-1423	40	5	𝐺𝑚,𝑛	𝐺𝑚,𝑛	AUX
cana-1423	40	6	𝑀	𝑀	PROPN
cana-1423	40	7	be	be	AUX
cana-1423	40	8	an	an	DET
cana-1423	40	9	undirected	undirected	ADJ
cana-1423	40	10	graph	graph	NOUN
cana-1423	40	11	where	where	SCONJ
cana-1423	40	12	𝑛	𝑛	PRON
cana-1423	40	13	=	=	SYM
cana-1423	40	14	2𝑝	2𝑝	NOUN
cana-1423	40	15	,	,	PUNCT
cana-1423	40	16	𝑝	𝑝	PROPN
cana-1423	40	17	is	be	AUX
cana-1423	40	18	prime	prime	ADJ
cana-1423	40	19	,	,	PUNCT
cana-1423	40	20	𝑚	𝑚	X
cana-1423	40	21	>	>	X
cana-1423	40	22	𝑛	𝑛	PROPN
cana-1423	40	23	,	,	PUNCT
cana-1423	40	24	𝑚	𝑚	PROPN
cana-1423	40	25	is	be	AUX
cana-1423	40	26	prime	prime	ADJ
cana-1423	40	27	.	.	PUNCT
cana-1423	41	1	then	then	ADV
cana-1423	41	2	(	(	PUNCT
cana-1423	41	3	i	i	NOUN
cana-1423	41	4	)	)	PUNCT
cana-1423	41	5	first	first	PROPN
cana-1423	41	6	zagreb	zagreb	PROPN
cana-1423	41	7	index	index	PROPN
cana-1423	41	8	𝑀1	𝑀1	PROPN
cana-1423	41	9	(	(	PUNCT
cana-1423	41	10	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	41	11	𝑀	𝑀	PROPN
cana-1423	41	12	)	)	PUNCT
cana-1423	41	13	is	be	AUX
cana-1423	41	14	𝑛(𝑛	𝑛(𝑛	PROPN
cana-1423	41	15	−	−	PROPN
cana-1423	41	16	1)2	1)2	NUM
cana-1423	41	17	.	.	PUNCT
cana-1423	42	1	(	(	PUNCT
cana-1423	42	2	ii)second	ii)second	PROPN
cana-1423	42	3	zagreb	zagreb	PROPN
cana-1423	42	4	index	index	PROPN
cana-1423	42	5	𝑀2	𝑀2	PROPN
cana-1423	42	6	(	(	PUNCT
cana-1423	42	7	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	42	8	𝑀	𝑀	PROPN
cana-1423	42	9	)	)	PUNCT
cana-1423	42	10	is	be	AUX
cana-1423	42	11	𝑛(𝑛−1)3	𝑛(𝑛−1)3	ADJ
cana-1423	42	12	2	2	NUM
cana-1423	42	13	.	.	PUNCT
cana-1423	43	1	(	(	PUNCT
cana-1423	43	2	iii)hyper	iii)hyper	PROPN
cana-1423	43	3	zagreb	zagreb	PROPN
cana-1423	43	4	index	index	PROPN
cana-1423	43	5	𝑀𝐻	𝑀𝐻	PROPN
cana-1423	43	6	(	(	PUNCT
cana-1423	43	7	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	43	8	𝑀	𝑀	PROPN
cana-1423	43	9	)	)	PUNCT
cana-1423	43	10	is	be	AUX
cana-1423	43	11	2𝑛(𝑛	2𝑛(𝑛	NUM
cana-1423	43	12	−	−	PROPN
cana-1423	44	1	1)3	1)3	PROPN
cana-1423	44	2	.	.	PUNCT
cana-1423	45	1	(	(	PUNCT
cana-1423	45	2	iv)first	iv)first	PROPN
cana-1423	45	3	multiple	multiple	ADJ
cana-1423	45	4	zagreb	zagreb	PROPN
cana-1423	45	5	index	index	PROPN
cana-1423	45	6	𝑃𝑀1	𝑃𝑀1	PROPN
cana-1423	45	7	(	(	PUNCT
cana-1423	45	8	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	45	9	𝑀	𝑀	PROPN
cana-1423	45	10	)	)	PUNCT
cana-1423	45	11	is	be	AUX
cana-1423	45	12	2(𝑛	2(𝑛	NUM
cana-1423	45	13	−	−	NUM
cana-1423	45	14	1	1	NUM
cana-1423	45	15	)	)	PUNCT
cana-1423	45	16	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	45	17	)	)	PUNCT
cana-1423	45	18	2	2	NUM
cana-1423	45	19	.	.	PUNCT
cana-1423	46	1	(	(	PUNCT
cana-1423	46	2	iv	iv	X
cana-1423	46	3	)	)	PUNCT
cana-1423	46	4	second	second	ADJ
cana-1423	46	5	multiple	multiple	ADJ
cana-1423	46	6	zagreb	zagreb	PROPN
cana-1423	46	7	index	index	NOUN
cana-1423	46	8	𝑃𝑀2	𝑃𝑀2	PROPN
cana-1423	46	9	(	(	PUNCT
cana-1423	46	10	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	46	11	𝑀	𝑀	PROPN
cana-1423	46	12	)	)	PUNCT
cana-1423	46	13	is	be	AUX
cana-1423	46	14	(	(	PUNCT
cana-1423	46	15	𝑛	𝑛	PROPN
cana-1423	46	16	−	−	PROPN
cana-1423	46	17	1)𝑛(𝑛−1	1)𝑛(𝑛−1	NUM
cana-1423	46	18	)	)	PUNCT
cana-1423	46	19	.	.	PUNCT
cana-1423	47	1	proof	proof	NOUN
cana-1423	47	2	:	:	PUNCT
cana-1423	47	3	consider	consider	VERB
cana-1423	47	4	an	an	DET
cana-1423	47	5	undirected	undirected	ADJ
cana-1423	47	6	graph	graph	NOUN
cana-1423	47	7	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	47	8	𝑀	𝑀	PROPN
cana-1423	47	9	where	where	SCONJ
cana-1423	47	10	𝑛	𝑛	PROPN
cana-1423	47	11	=	=	SYM
cana-1423	47	12	2𝑝	2𝑝	NOUN
cana-1423	47	13	,	,	PUNCT
cana-1423	47	14	𝑝	𝑝	PROPN
cana-1423	47	15	is	be	AUX
cana-1423	47	16	prime	prime	ADJ
cana-1423	47	17	,	,	PUNCT
cana-1423	47	18	𝑚	𝑚	PROPN
cana-1423	47	19	>	>	X
cana-1423	47	20	𝑛,𝑚	𝑛,𝑚	NOUN
cana-1423	47	21	is	be	AUX
cana-1423	47	22	prime	prime	ADJ
cana-1423	47	23	with	with	ADP
cana-1423	47	24	𝑉	𝑉	PROPN
cana-1423	47	25	=	=	PUNCT
cana-1423	47	26	{	{	PUNCT
cana-1423	47	27	1,2,3	1,2,3	NUM
cana-1423	47	28	…	…	PUNCT
cana-1423	47	29	𝑛	𝑛	NOUN
cana-1423	47	30	}	}	PUNCT
cana-1423	47	31	as	as	ADP
cana-1423	47	32	the	the	DET
cana-1423	47	33	vertex	vertex	NOUN
cana-1423	47	34	set	set	NOUN
cana-1423	47	35	,	,	PUNCT
cana-1423	47	36	the	the	DET
cana-1423	47	37	vertex	vertex	NOUN
cana-1423	47	38	degree	degree	NOUN
cana-1423	47	39	is	be	AUX
cana-1423	47	40	(	(	PUNCT
cana-1423	47	41	𝑛	𝑛	PRON
cana-1423	47	42	−	−	PROPN
cana-1423	47	43	1	1	NUM
cana-1423	47	44	)	)	PUNCT
cana-1423	47	45	for	for	ADP
cana-1423	47	46	every	every	DET
cana-1423	47	47	𝑣	𝑣	PRON
cana-1423	47	48	∈	∈	PROPN
cana-1423	47	49	𝑉and	𝑉and	PROPN
cana-1423	47	50	𝐸	𝐸	PROPN
cana-1423	47	51	is	be	AUX
cana-1423	47	52	the	the	DET
cana-1423	47	53	edge	edge	NOUN
cana-1423	47	54	set	set	NOUN
cana-1423	47	55	.	.	PUNCT
cana-1423	48	1	let	let	VERB
cana-1423	48	2	𝑑𝑖	𝑑𝑖	PROPN
cana-1423	48	3	,	,	PUNCT
cana-1423	48	4	𝑑𝑗	𝑑𝑗	PROPN
cana-1423	48	5	be	be	AUX
cana-1423	48	6	the	the	DET
cana-1423	48	7	degrees	degree	NOUN
cana-1423	48	8	of	of	ADP
cana-1423	48	9	the	the	DET
cana-1423	48	10	vertices	vertex	NOUN
cana-1423	48	11	𝑣𝑖	𝑣𝑖	VERB
cana-1423	48	12	,	,	PUNCT
cana-1423	48	13	𝑣𝑗	𝑣𝑗	ADP
cana-1423	48	14	and	and	CCONJ
cana-1423	48	15	𝑒𝑖𝑗	𝑒𝑖𝑗	NOUN
cana-1423	48	16	be	be	AUX
cana-1423	48	17	the	the	DET
cana-1423	48	18	edges	edge	NOUN
cana-1423	48	19	joining	join	VERB
cana-1423	48	20	the	the	DET
cana-1423	48	21	vertices	vertex	NOUN
cana-1423	48	22	𝑣𝑖	𝑣𝑖	ADV
cana-1423	48	23	,	,	PUNCT
cana-1423	48	24	𝑣𝑗	𝑣𝑗	ADP
cana-1423	48	25	.	.	PUNCT
cana-1423	49	1	communications	communication	NOUN
cana-1423	49	2	on	on	ADP
cana-1423	49	3	applied	apply	VERB
cana-1423	49	4	nonlinear	nonlinear	ADJ
cana-1423	49	5	analysis	analysis	NOUN
cana-1423	49	6	issn	issn	NOUN
cana-1423	49	7	:	:	PUNCT
cana-1423	49	8	1074	1074	NUM
cana-1423	49	9	-	-	PUNCT
cana-1423	49	10	133x	133x	NUM
cana-1423	49	11	vol	vol	NOUN
cana-1423	49	12	31	31	NUM
cana-1423	49	13	no	no	NOUN
cana-1423	49	14	.	.	PUNCT
cana-1423	50	1	7s	7	NOUN
cana-1423	50	2	(	(	PUNCT
cana-1423	50	3	2024	2024	NUM
cana-1423	50	4	)	)	PUNCT
cana-1423	50	5	672	672	NUM
cana-1423	50	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1423	50	7	then	then	ADV
cana-1423	50	8	|𝑒𝑖𝑗|	|𝑒𝑖𝑗|	PROPN
cana-1423	50	9	=	=	SYM
cana-1423	50	10	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	50	11	)	)	PUNCT
cana-1423	50	12	2	2	NUM
cana-1423	50	13	(	(	PUNCT
cana-1423	50	14	i)first	i)first	ADV
cana-1423	50	15	zagreb	zagreb	NUM
cana-1423	50	16	index	index	NOUN
cana-1423	50	17	of	of	ADP
cana-1423	50	18	the	the	DET
cana-1423	50	19	graph	graph	NOUN
cana-1423	50	20	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	50	21	𝑀	𝑀	PROPN
cana-1423	50	22	is	be	AUX
cana-1423	50	23	𝑀1	𝑀1	PROPN
cana-1423	50	24	(	(	PUNCT
cana-1423	50	25	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	50	26	𝑀	𝑀	PROPN
cana-1423	50	27	)	)	PUNCT
cana-1423	51	1	=	=	PUNCT
cana-1423	51	2			X
cana-1423	51	3			NOUN
cana-1423	51	4	+	+	CCONJ
cana-1423	51	5	evv	evv	ADV
cana-1423	51	6	ji	ji	PROPN
cana-1423	51	7	ji	ji	PROPN
cana-1423	51	8	dd	dd	PROPN
cana-1423	51	9	,	,	PUNCT
cana-1423	51	10	)	)	PUNCT
cana-1423	51	11	(	(	PUNCT
cana-1423	51	12	=	=	PUNCT
cana-1423	51	13	|𝑒𝑖𝑗|(𝑑𝑖	|𝑒𝑖𝑗|(𝑑𝑖	PROPN
cana-1423	51	14	+	+	CCONJ
cana-1423	51	15	𝑑𝑗	𝑑𝑗	NOUN
cana-1423	51	16	)	)	PUNCT
cana-1423	51	17	=	=	SYM
cana-1423	51	18	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	51	19	)	)	PUNCT
cana-1423	51	20	2	2	NUM
cana-1423	52	1	[	[	X
cana-1423	52	2	(	(	PUNCT
cana-1423	52	3	𝑛	𝑛	PRON
cana-1423	52	4	−	−	PROPN
cana-1423	52	5	1	1	NUM
cana-1423	52	6	)	)	PUNCT
cana-1423	52	7	+	+	CCONJ
cana-1423	52	8	(	(	PUNCT
cana-1423	52	9	𝑛	𝑛	PRON
cana-1423	52	10	−	−	PROPN
cana-1423	52	11	1	1	NUM
cana-1423	52	12	)	)	PUNCT
cana-1423	52	13	]	]	PUNCT
cana-1423	52	14	=	=	PUNCT
cana-1423	53	1	𝑛(𝑛	𝑛(𝑛	PROPN
cana-1423	53	2	−	−	PROPN
cana-1423	53	3	1)2	1)2	NUM
cana-1423	53	4	.	.	PUNCT
cana-1423	54	1	(	(	PUNCT
cana-1423	54	2	ii)second	ii)second	PROPN
cana-1423	54	3	zagreb	zagreb	PROPN
cana-1423	54	4	index	index	NOUN
cana-1423	54	5	of	of	ADP
cana-1423	54	6	the	the	DET
cana-1423	54	7	graph	graph	NOUN
cana-1423	54	8	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	54	9	𝑀	𝑀	PROPN
cana-1423	54	10	is	be	AUX
cana-1423	54	11	𝑀2	𝑀2	PROPN
cana-1423	54	12	(	(	PUNCT
cana-1423	54	13	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	54	14	𝑀	𝑀	PROPN
cana-1423	54	15	)	)	PUNCT
cana-1423	55	1	=	=	PUNCT
cana-1423	55	2			PROPN
cana-1423	55	3			NOUN
cana-1423	55	4			VERB
cana-1423	55	5	evv	evv	PROPN
cana-1423	55	6	ji	ji	PROPN
cana-1423	55	7	ji	ji	PROPN
cana-1423	55	8	dd	dd	PROPN
cana-1423	55	9	,	,	PUNCT
cana-1423	55	10	)	)	PUNCT
cana-1423	55	11	(	(	PUNCT
cana-1423	55	12	=	=	PUNCT
cana-1423	55	13	|𝑒𝑖𝑗|(𝑑𝑖	|𝑒𝑖𝑗|(𝑑𝑖	PROPN
cana-1423	55	14	×	×	NOUN
cana-1423	55	15	𝑑𝑗	𝑑𝑗	NOUN
cana-1423	55	16	)	)	PUNCT
cana-1423	55	17	=	=	SYM
cana-1423	55	18	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	55	19	)	)	PUNCT
cana-1423	55	20	2	2	NUM
cana-1423	56	1	[	[	X
cana-1423	56	2	(	(	PUNCT
cana-1423	56	3	𝑛	𝑛	PRON
cana-1423	56	4	−	−	PROPN
cana-1423	56	5	1	1	NUM
cana-1423	56	6	)	)	PUNCT
cana-1423	56	7	×	×	NOUN
cana-1423	56	8	(	(	PUNCT
cana-1423	56	9	𝑛	𝑛	PROPN
cana-1423	56	10	−	−	PROPN
cana-1423	56	11	1	1	NUM
cana-1423	56	12	)	)	PUNCT
cana-1423	56	13	]	]	PUNCT
cana-1423	57	1	=	=	PUNCT
cana-1423	57	2	𝑛(𝑛−1)3	𝑛(𝑛−1)3	ADJ
cana-1423	57	3	2	2	NUM
cana-1423	57	4	(	(	PUNCT
cana-1423	57	5	iii	iii	NOUN
cana-1423	57	6	)	)	PUNCT
cana-1423	57	7	hyper	hyper	PROPN
cana-1423	57	8	zagreb	zagreb	PROPN
cana-1423	57	9	index	index	NOUN
cana-1423	57	10	of	of	ADP
cana-1423	57	11	the	the	DET
cana-1423	57	12	graph	graph	NOUN
cana-1423	57	13	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	57	14	𝑀	𝑀	PROPN
cana-1423	57	15	is	be	AUX
cana-1423	57	16	𝑀𝐻	𝑀𝐻	PROPN
cana-1423	57	17	(	(	PUNCT
cana-1423	57	18	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	57	19	𝑀	𝑀	PROPN
cana-1423	57	20	)	)	PUNCT
cana-1423	57	21	=	=	SYM
cana-1423	57	22	2	2	X
cana-1423	57	23	)	)	PUNCT
cana-1423	57	24	(	(	PUNCT
cana-1423	57	25	,	,	PUNCT
cana-1423	57	26	)	)	PUNCT
cana-1423	57	27	(	(	PUNCT
cana-1423	57	28			X
cana-1423	57	29			NOUN
cana-1423	57	30	+	+	CCONJ
cana-1423	57	31	gevv	gevv	ADJ
cana-1423	58	1	ji	ji	X
cana-1423	58	2	ji	ji	PROPN
cana-1423	58	3	dd	dd	PROPN
cana-1423	58	4	=	=	PUNCT
cana-1423	58	5	|𝑒𝑖𝑗|(𝑑𝑖	|𝑒𝑖𝑗|(𝑑𝑖	PROPN
cana-1423	58	6	+	+	CCONJ
cana-1423	58	7	𝑑𝑗)2	𝑑𝑗)2	PROPN
cana-1423	58	8	=	=	SYM
cana-1423	58	9	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	58	10	)	)	PUNCT
cana-1423	58	11	2	2	NUM
cana-1423	59	1	[	[	X
cana-1423	59	2	(	(	PUNCT
cana-1423	59	3	𝑛	𝑛	PRON
cana-1423	59	4	−	−	PROPN
cana-1423	59	5	1	1	NUM
cana-1423	59	6	)	)	PUNCT
cana-1423	59	7	+	+	CCONJ
cana-1423	59	8	(	(	PUNCT
cana-1423	59	9	𝑛	𝑛	PRON
cana-1423	59	10	−	−	PROPN
cana-1423	59	11	1)]2	1)]2	NUM
cana-1423	59	12	=	=	SYM
cana-1423	59	13	2𝑛(𝑛	2𝑛(𝑛	PROPN
cana-1423	60	1	−	−	PROPN
cana-1423	60	2	1)3	1)3	PROPN
cana-1423	60	3	.	.	PUNCT
cana-1423	61	1	(	(	PUNCT
cana-1423	61	2	iv)first	iv)first	PROPN
cana-1423	61	3	multiple	multiple	ADJ
cana-1423	61	4	zagreb	zagreb	PROPN
cana-1423	61	5	index	index	NOUN
cana-1423	61	6	of	of	ADP
cana-1423	61	7	the	the	DET
cana-1423	61	8	graph	graph	NOUN
cana-1423	61	9	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	61	10	𝑀	𝑀	PROPN
cana-1423	61	11	is	be	AUX
cana-1423	61	12	𝑃𝑀1	𝑃𝑀1	PROPN
cana-1423	61	13	(	(	PUNCT
cana-1423	61	14	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	61	15	𝑀)=	𝑀)=	VERB
cana-1423	61	16			PROPN
cana-1423	61	17			NOUN
cana-1423	61	18	+	+	CCONJ
cana-1423	61	19	)	)	PUNCT
cana-1423	61	20	(	(	PUNCT
cana-1423	61	21	,	,	PUNCT
cana-1423	61	22	)	)	PUNCT
cana-1423	61	23	(	(	PUNCT
cana-1423	61	24	gevv	gevv	ADJ
cana-1423	61	25	ji	ji	X
cana-1423	61	26	ji	ji	PROPN
cana-1423	61	27	dd	dd	PROPN
cana-1423	62	1	=	=	PUNCT
cana-1423	62	2	(	(	PUNCT
cana-1423	62	3	𝑑𝑖	𝑑𝑖	PROPN
cana-1423	62	4	+	+	NUM
cana-1423	62	5	𝑑𝑗)|𝑒𝑖𝑗|	𝑑𝑗)|𝑒𝑖𝑗|	PUNCT
cana-1423	63	1	=	=	PUNCT
cana-1423	64	1	[	[	X
cana-1423	64	2	(	(	PUNCT
cana-1423	64	3	𝑛	𝑛	PROPN
cana-1423	64	4	−	−	NUM
cana-1423	64	5	1)+(𝑛	1)+(𝑛	NUM
cana-1423	64	6	−	−	NOUN
cana-1423	64	7	1	1	NUM
cana-1423	64	8	)	)	PUNCT
cana-1423	64	9	]	]	PUNCT
cana-1423	64	10	𝑛(𝑛−1	𝑛(𝑛−1	X
cana-1423	64	11	)	)	PUNCT
cana-1423	64	12	2	2	NUM
cana-1423	64	13	=	=	SYM
cana-1423	64	14	(	(	PUNCT
cana-1423	64	15	2(𝑛	2(𝑛	NUM
cana-1423	64	16	−	−	NUM
cana-1423	64	17	1	1	NUM
cana-1423	64	18	)	)	PUNCT
cana-1423	64	19	)	)	PUNCT
cana-1423	64	20	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	64	21	)	)	PUNCT
cana-1423	64	22	2	2	NUM
cana-1423	64	23	.	.	PUNCT
cana-1423	65	1	(	(	PUNCT
cana-1423	65	2	v	v	NOUN
cana-1423	65	3	)	)	PUNCT
cana-1423	65	4	second	second	ADJ
cana-1423	65	5	multiple	multiple	ADJ
cana-1423	65	6	zagreb	zagreb	PROPN
cana-1423	65	7	index	index	NOUN
cana-1423	65	8	of	of	ADP
cana-1423	65	9	the	the	DET
cana-1423	65	10	graph	graph	NOUN
cana-1423	65	11	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	65	12	𝑀	𝑀	PROPN
cana-1423	65	13	is	be	AUX
cana-1423	65	14	𝑃𝑀2	𝑃𝑀2	PROPN
cana-1423	65	15	(	(	PUNCT
cana-1423	65	16	𝐺𝑚,𝑛	𝐺𝑚,𝑛	AUX
cana-1423	65	17	𝑀)=	𝑀)=	ADP
cana-1423	65	18			PROPN
cana-1423	65	19			NOUN
cana-1423	65	20			VERB
cana-1423	65	21	evv	evv	NOUN
cana-1423	65	22	ji	ji	PROPN
cana-1423	65	23	ji	ji	PROPN
cana-1423	65	24	dd	dd	PROPN
cana-1423	65	25	,	,	PUNCT
cana-1423	65	26	)	)	PUNCT
cana-1423	65	27	(	(	PUNCT
cana-1423	65	28	=	=	SYM
cana-1423	65	29	(	(	PUNCT
cana-1423	65	30	𝑑𝑖	𝑑𝑖	PROPN
cana-1423	65	31	×	×	NOUN
cana-1423	65	32	𝑑𝑗)|𝑒𝑖𝑗|	𝑑𝑗)|𝑒𝑖𝑗|	PUNCT
cana-1423	66	1	=	=	PUNCT
cana-1423	67	1	[	[	X
cana-1423	67	2	(	(	PUNCT
cana-1423	67	3	𝑛	𝑛	PROPN
cana-1423	67	4	−	−	NOUN
cana-1423	67	5	1)(𝑛	1)(𝑛	NUM
cana-1423	67	6	−	−	NOUN
cana-1423	67	7	1	1	NUM
cana-1423	67	8	)	)	PUNCT
cana-1423	67	9	]	]	PUNCT
cana-1423	67	10	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	67	11	)	)	PUNCT
cana-1423	67	12	2	2	NUM
cana-1423	67	13	communications	communication	NOUN
cana-1423	67	14	on	on	ADP
cana-1423	67	15	applied	apply	VERB
cana-1423	67	16	nonlinear	nonlinear	ADJ
cana-1423	67	17	analysis	analysis	NOUN
cana-1423	67	18	issn	issn	NOUN
cana-1423	67	19	:	:	PUNCT
cana-1423	67	20	1074	1074	NUM
cana-1423	67	21	-	-	PUNCT
cana-1423	67	22	133x	133x	NUM
cana-1423	67	23	vol	vol	NOUN
cana-1423	67	24	31	31	NUM
cana-1423	67	25	no	no	NOUN
cana-1423	67	26	.	.	PUNCT
cana-1423	68	1	7s	7	NOUN
cana-1423	68	2	(	(	PUNCT
cana-1423	68	3	2024	2024	NUM
cana-1423	68	4	)	)	PUNCT
cana-1423	68	5	673	673	NUM
cana-1423	68	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1423	68	7	=	=	SYM
cana-1423	68	8	(	(	PUNCT
cana-1423	68	9	𝑛	𝑛	PROPN
cana-1423	68	10	−	−	PROPN
cana-1423	68	11	1)𝑛(𝑛−1	1)𝑛(𝑛−1	NUM
cana-1423	68	12	)	)	PUNCT
cana-1423	68	13	.	.	PUNCT
cana-1423	69	1	theorem	theorem	VERB
cana-1423	69	2	2.2	2.2	NUM
cana-1423	69	3	:	:	PUNCT
cana-1423	69	4	if	if	SCONJ
cana-1423	69	5	𝐺𝑚,𝑛	𝐺𝑚,𝑛	AUX
cana-1423	69	6	𝑀	𝑀	PROPN
cana-1423	69	7	be	be	AUX
cana-1423	69	8	an	an	DET
cana-1423	69	9	undirected	undirected	ADJ
cana-1423	69	10	graph	graph	NOUN
cana-1423	69	11	where	where	SCONJ
cana-1423	69	12	𝑚	𝑚	X
cana-1423	69	13	>	>	X
cana-1423	69	14	𝑛	𝑛	PROPN
cana-1423	69	15	,	,	PUNCT
cana-1423	69	16	𝑚	𝑚	PROPN
cana-1423	69	17	,	,	PUNCT
cana-1423	69	18	𝑛	𝑛	PROPN
cana-1423	69	19	are	be	AUX
cana-1423	69	20	odd	odd	ADJ
cana-1423	69	21	primes	prime	NOUN
cana-1423	69	22	.	.	PUNCT
cana-1423	70	1	then	then	ADV
cana-1423	70	2	(	(	PUNCT
cana-1423	70	3	i	i	NOUN
cana-1423	70	4	)	)	PUNCT
cana-1423	70	5	first	first	PROPN
cana-1423	70	6	zagreb	zagreb	PROPN
cana-1423	70	7	index	index	PROPN
cana-1423	70	8	𝑀1	𝑀1	PROPN
cana-1423	70	9	(	(	PUNCT
cana-1423	70	10	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	70	11	𝑀	𝑀	PROPN
cana-1423	70	12	)	)	PUNCT
cana-1423	70	13	is	be	AUX
cana-1423	70	14	𝑛(𝑛	𝑛(𝑛	PROPN
cana-1423	70	15	−	−	PROPN
cana-1423	70	16	1)2	1)2	NUM
cana-1423	70	17	.	.	PUNCT
cana-1423	71	1	(	(	PUNCT
cana-1423	71	2	ii)second	ii)second	PROPN
cana-1423	71	3	zagreb	zagreb	PROPN
cana-1423	71	4	index	index	PROPN
cana-1423	71	5	𝑀2	𝑀2	PROPN
cana-1423	71	6	(	(	PUNCT
cana-1423	71	7	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	71	8	𝑀	𝑀	PROPN
cana-1423	71	9	)	)	PUNCT
cana-1423	71	10	is	be	AUX
cana-1423	71	11	𝑛(𝑛−1)3	𝑛(𝑛−1)3	ADJ
cana-1423	71	12	2	2	NUM
cana-1423	71	13	.	.	PUNCT
cana-1423	72	1	(	(	PUNCT
cana-1423	72	2	iii)hyper	iii)hyper	PROPN
cana-1423	72	3	zagreb	zagreb	PROPN
cana-1423	72	4	index	index	PROPN
cana-1423	72	5	𝑀𝐻	𝑀𝐻	PROPN
cana-1423	72	6	(	(	PUNCT
cana-1423	72	7	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	72	8	𝑀	𝑀	PROPN
cana-1423	72	9	)	)	PUNCT
cana-1423	72	10	is2𝑛(𝑛	is2𝑛(𝑛	PROPN
cana-1423	72	11	−	−	PROPN
cana-1423	72	12	1)3	1)3	PROPN
cana-1423	72	13	.	.	PUNCT
cana-1423	73	1	(	(	PUNCT
cana-1423	73	2	iv)first	iv)first	PROPN
cana-1423	73	3	multiple	multiple	ADJ
cana-1423	73	4	zagreb	zagreb	PROPN
cana-1423	73	5	index	index	PROPN
cana-1423	73	6	𝑃𝑀1	𝑃𝑀1	PROPN
cana-1423	73	7	(	(	PUNCT
cana-1423	73	8	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	73	9	𝑀	𝑀	PROPN
cana-1423	73	10	)	)	PUNCT
cana-1423	73	11	is	be	AUX
cana-1423	73	12	2(𝑛	2(𝑛	NUM
cana-1423	73	13	−	−	NUM
cana-1423	73	14	1	1	NUM
cana-1423	73	15	)	)	PUNCT
cana-1423	73	16	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	73	17	)	)	PUNCT
cana-1423	73	18	2	2	NUM
cana-1423	73	19	.	.	PUNCT
cana-1423	74	1	(	(	PUNCT
cana-1423	74	2	iv	iv	X
cana-1423	74	3	)	)	PUNCT
cana-1423	74	4	second	second	ADJ
cana-1423	74	5	multiple	multiple	ADJ
cana-1423	74	6	zagreb	zagreb	PROPN
cana-1423	74	7	index	index	NOUN
cana-1423	74	8	𝑃𝑀2	𝑃𝑀2	PROPN
cana-1423	74	9	(	(	PUNCT
cana-1423	74	10	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	74	11	𝑀	𝑀	PROPN
cana-1423	74	12	)	)	PUNCT
cana-1423	74	13	is	be	AUX
cana-1423	74	14	(	(	PUNCT
cana-1423	74	15	𝑛	𝑛	PROPN
cana-1423	74	16	−	−	PROPN
cana-1423	74	17	1)𝑛(𝑛−1	1)𝑛(𝑛−1	NUM
cana-1423	74	18	)	)	PUNCT
cana-1423	74	19	.	.	PUNCT
cana-1423	75	1	proof	proof	NOUN
cana-1423	75	2	:	:	PUNCT
cana-1423	75	3	consider	consider	VERB
cana-1423	75	4	an	an	DET
cana-1423	75	5	undirected	undirected	ADJ
cana-1423	75	6	graph	graph	NOUN
cana-1423	75	7	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	75	8	𝑀	𝑀	PROPN
cana-1423	75	9	with	with	ADP
cana-1423	75	10	𝑚	𝑚	PROPN
cana-1423	75	11	>	>	SYM
cana-1423	75	12	𝑛	𝑛	PROPN
cana-1423	75	13	,	,	PUNCT
cana-1423	75	14	𝑚	𝑚	PROPN
cana-1423	75	15	,	,	PUNCT
cana-1423	75	16	𝑛	𝑛	PROPN
cana-1423	75	17	are	be	AUX
cana-1423	75	18	odd	odd	ADJ
cana-1423	75	19	primes	prime	NOUN
cana-1423	75	20	and	and	CCONJ
cana-1423	75	21	𝑉	𝑉	PROPN
cana-1423	75	22	=	=	PUNCT
cana-1423	75	23	{	{	PUNCT
cana-1423	75	24	1,2,3	1,2,3	NUM
cana-1423	75	25	…	…	PUNCT
cana-1423	75	26	𝑛}is	𝑛}is	ADP
cana-1423	75	27	the	the	DET
cana-1423	75	28	vertex	vertex	NOUN
cana-1423	75	29	set	set	NOUN
cana-1423	75	30	.here	.here	ADP
cana-1423	75	31	the	the	DET
cana-1423	75	32	degree	degree	NOUN
cana-1423	75	33	of	of	ADP
cana-1423	75	34	the	the	DET
cana-1423	75	35	vertex	vertex	NOUN
cana-1423	75	36	is	be	AUX
cana-1423	75	37	(	(	PUNCT
cana-1423	75	38	𝑛	𝑛	PRON
cana-1423	75	39	−	−	PROPN
cana-1423	75	40	1	1	NUM
cana-1423	75	41	)	)	PUNCT
cana-1423	75	42	for	for	SCONJ
cana-1423	75	43	every	every	DET
cana-1423	75	44	𝑣	𝑣	PROPN
cana-1423	75	45	∈	∈	PROPN
cana-1423	75	46	𝑉.	𝑉.	NOUN
cana-1423	75	47	let	let	VERB
cana-1423	75	48	𝑑𝑖	𝑑𝑖	PROPN
cana-1423	75	49	,	,	PUNCT
cana-1423	75	50	𝑑𝑗	𝑑𝑗	PROPN
cana-1423	75	51	be	be	AUX
cana-1423	75	52	the	the	DET
cana-1423	75	53	degrees	degree	NOUN
cana-1423	75	54	of	of	ADP
cana-1423	75	55	the	the	DET
cana-1423	75	56	vertices	vertex	NOUN
cana-1423	75	57	𝑣𝑖	𝑣𝑖	VERB
cana-1423	75	58	,	,	PUNCT
cana-1423	75	59	𝑣𝑗	𝑣𝑗	ADP
cana-1423	75	60	and	and	CCONJ
cana-1423	75	61	𝑒𝑖𝑗	𝑒𝑖𝑗	NOUN
cana-1423	75	62	be	be	AUX
cana-1423	75	63	the	the	DET
cana-1423	75	64	edges	edge	NOUN
cana-1423	75	65	joining	join	VERB
cana-1423	75	66	the	the	DET
cana-1423	75	67	vertices	vertex	NOUN
cana-1423	75	68	𝑣𝑖	𝑣𝑖	ADV
cana-1423	75	69	,	,	PUNCT
cana-1423	75	70	𝑣𝑗	𝑣𝑗	ADP
cana-1423	75	71	.	.	PUNCT
cana-1423	76	1	then	then	ADV
cana-1423	76	2	|𝑒𝑖𝑗|	|𝑒𝑖𝑗|	PROPN
cana-1423	76	3	=	=	SYM
cana-1423	76	4	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	76	5	)	)	PUNCT
cana-1423	76	6	2	2	NUM
cana-1423	76	7	.	.	PUNCT
cana-1423	77	1	(	(	PUNCT
cana-1423	77	2	i)first	i)first	ADV
cana-1423	77	3	zagreb	zagreb	NUM
cana-1423	77	4	index	index	NOUN
cana-1423	77	5	of	of	ADP
cana-1423	77	6	the	the	DET
cana-1423	77	7	graph	graph	NOUN
cana-1423	77	8	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	77	9	𝑀	𝑀	PROPN
cana-1423	77	10	is	be	AUX
cana-1423	77	11	𝑀1	𝑀1	PROPN
cana-1423	77	12	(	(	PUNCT
cana-1423	77	13	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	77	14	𝑀	𝑀	PROPN
cana-1423	77	15	)	)	PUNCT
cana-1423	78	1	=	=	PUNCT
cana-1423	78	2			X
cana-1423	78	3			NOUN
cana-1423	78	4	+	+	CCONJ
cana-1423	78	5	evv	evv	ADV
cana-1423	78	6	ji	ji	PROPN
cana-1423	78	7	ji	ji	PROPN
cana-1423	78	8	dd	dd	PROPN
cana-1423	78	9	,	,	PUNCT
cana-1423	78	10	)	)	PUNCT
cana-1423	78	11	(	(	PUNCT
cana-1423	78	12	=	=	PUNCT
cana-1423	78	13	|𝑒𝑖𝑗|(𝑑𝑖	|𝑒𝑖𝑗|(𝑑𝑖	PROPN
cana-1423	78	14	+	+	CCONJ
cana-1423	78	15	𝑑𝑗	𝑑𝑗	NOUN
cana-1423	78	16	)	)	PUNCT
cana-1423	78	17	=	=	SYM
cana-1423	78	18	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	78	19	)	)	PUNCT
cana-1423	78	20	2	2	NUM
cana-1423	79	1	[	[	X
cana-1423	79	2	(	(	PUNCT
cana-1423	79	3	𝑛	𝑛	PRON
cana-1423	79	4	−	−	PROPN
cana-1423	79	5	1	1	NUM
cana-1423	79	6	)	)	PUNCT
cana-1423	79	7	+	+	CCONJ
cana-1423	79	8	(	(	PUNCT
cana-1423	79	9	𝑛	𝑛	PRON
cana-1423	79	10	−	−	PROPN
cana-1423	79	11	1	1	NUM
cana-1423	79	12	)	)	PUNCT
cana-1423	79	13	]	]	PUNCT
cana-1423	79	14	=	=	PUNCT
cana-1423	80	1	𝑛(𝑛	𝑛(𝑛	PROPN
cana-1423	80	2	−	−	PROPN
cana-1423	80	3	1)2	1)2	NUM
cana-1423	80	4	.	.	PUNCT
cana-1423	81	1	(	(	PUNCT
cana-1423	81	2	ii)second	ii)second	PROPN
cana-1423	81	3	zagreb	zagreb	PROPN
cana-1423	81	4	index	index	NOUN
cana-1423	81	5	of	of	ADP
cana-1423	81	6	the	the	DET
cana-1423	81	7	graph	graph	NOUN
cana-1423	81	8	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	81	9	𝑀	𝑀	PROPN
cana-1423	81	10	is	be	AUX
cana-1423	81	11	𝑀2	𝑀2	PROPN
cana-1423	81	12	(	(	PUNCT
cana-1423	81	13	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	81	14	𝑀	𝑀	PROPN
cana-1423	81	15	)	)	PUNCT
cana-1423	82	1	=	=	PUNCT
cana-1423	82	2			PROPN
cana-1423	82	3			NOUN
cana-1423	82	4			VERB
cana-1423	82	5	evv	evv	PROPN
cana-1423	82	6	ji	ji	PROPN
cana-1423	82	7	ji	ji	PROPN
cana-1423	82	8	dd	dd	PROPN
cana-1423	82	9	,	,	PUNCT
cana-1423	82	10	)	)	PUNCT
cana-1423	82	11	(	(	PUNCT
cana-1423	82	12	=	=	PUNCT
cana-1423	82	13	|𝑒𝑖𝑗|(𝑑𝑖	|𝑒𝑖𝑗|(𝑑𝑖	PROPN
cana-1423	82	14	×	×	NOUN
cana-1423	82	15	𝑑𝑗	𝑑𝑗	NOUN
cana-1423	82	16	)	)	PUNCT
cana-1423	82	17	=	=	SYM
cana-1423	82	18	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	82	19	)	)	PUNCT
cana-1423	82	20	2	2	NUM
cana-1423	83	1	[	[	X
cana-1423	83	2	(	(	PUNCT
cana-1423	83	3	𝑛	𝑛	PRON
cana-1423	83	4	−	−	PROPN
cana-1423	83	5	1	1	NUM
cana-1423	83	6	)	)	PUNCT
cana-1423	83	7	×	×	NOUN
cana-1423	83	8	(	(	PUNCT
cana-1423	83	9	𝑛	𝑛	PROPN
cana-1423	83	10	−	−	PROPN
cana-1423	83	11	1	1	NUM
cana-1423	83	12	)	)	PUNCT
cana-1423	83	13	]	]	PUNCT
cana-1423	84	1	=	=	PUNCT
cana-1423	84	2	𝑛(𝑛−1)3	𝑛(𝑛−1)3	ADJ
cana-1423	84	3	2	2	NUM
cana-1423	84	4	(	(	PUNCT
cana-1423	84	5	iii	iii	NOUN
cana-1423	84	6	)	)	PUNCT
cana-1423	84	7	hyper	hyper	PROPN
cana-1423	84	8	zagreb	zagreb	PROPN
cana-1423	84	9	index	index	NOUN
cana-1423	84	10	of	of	ADP
cana-1423	84	11	the	the	DET
cana-1423	84	12	graph	graph	NOUN
cana-1423	84	13	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	84	14	𝑀	𝑀	PROPN
cana-1423	84	15	is	be	AUX
cana-1423	84	16	𝑀𝐻	𝑀𝐻	PROPN
cana-1423	84	17	(	(	PUNCT
cana-1423	84	18	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	84	19	𝑀	𝑀	PROPN
cana-1423	84	20	)	)	PUNCT
cana-1423	84	21	=	=	SYM
cana-1423	84	22	2	2	NUM
cana-1423	84	23	,	,	PUNCT
cana-1423	84	24	)	)	PUNCT
cana-1423	84	25	(	(	PUNCT
cana-1423	84	26			PROPN
cana-1423	84	27			NOUN
cana-1423	84	28	+	+	CCONJ
cana-1423	84	29	evv	evv	ADV
cana-1423	84	30	ji	ji	PROPN
cana-1423	84	31	ji	ji	PROPN
cana-1423	84	32	dd	dd	PROPN
cana-1423	84	33	=	=	PUNCT
cana-1423	84	34	|𝑒𝑖𝑗|(𝑑𝑖	|𝑒𝑖𝑗|(𝑑𝑖	PROPN
cana-1423	84	35	+	+	CCONJ
cana-1423	84	36	𝑑𝑗)2	𝑑𝑗)2	PROPN
cana-1423	84	37	=	=	SYM
cana-1423	84	38	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	84	39	)	)	PUNCT
cana-1423	84	40	2	2	NUM
cana-1423	85	1	[	[	X
cana-1423	85	2	(	(	PUNCT
cana-1423	85	3	𝑛	𝑛	PRON
cana-1423	85	4	−	−	PROPN
cana-1423	85	5	1	1	NUM
cana-1423	85	6	)	)	PUNCT
cana-1423	85	7	+	+	CCONJ
cana-1423	85	8	(	(	PUNCT
cana-1423	85	9	𝑛	𝑛	PRON
cana-1423	85	10	−	−	PROPN
cana-1423	85	11	1)]2	1)]2	NUM
cana-1423	85	12	=	=	SYM
cana-1423	85	13	2𝑛(𝑛	2𝑛(𝑛	PROPN
cana-1423	86	1	−	−	PROPN
cana-1423	86	2	1)3	1)3	PROPN
cana-1423	86	3	.	.	PUNCT
cana-1423	87	1	(	(	PUNCT
cana-1423	87	2	iv)first	iv)first	PROPN
cana-1423	87	3	multiple	multiple	ADJ
cana-1423	87	4	zagreb	zagreb	PROPN
cana-1423	87	5	index	index	NOUN
cana-1423	87	6	of	of	ADP
cana-1423	87	7	the	the	DET
cana-1423	87	8	graph	graph	NOUN
cana-1423	87	9	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	87	10	𝑀	𝑀	PROPN
cana-1423	87	11	is	be	AUX
cana-1423	87	12	communications	communication	NOUN
cana-1423	87	13	on	on	ADP
cana-1423	87	14	applied	apply	VERB
cana-1423	87	15	nonlinear	nonlinear	ADJ
cana-1423	87	16	analysis	analysis	NOUN
cana-1423	87	17	issn	issn	NOUN
cana-1423	87	18	:	:	PUNCT
cana-1423	87	19	1074	1074	NUM
cana-1423	87	20	-	-	PUNCT
cana-1423	87	21	133x	133x	NUM
cana-1423	87	22	vol	vol	NOUN
cana-1423	87	23	31	31	NUM
cana-1423	87	24	no	no	NOUN
cana-1423	87	25	.	.	PUNCT
cana-1423	88	1	7s	7	NOUN
cana-1423	88	2	(	(	PUNCT
cana-1423	88	3	2024	2024	NUM
cana-1423	88	4	)	)	PUNCT
cana-1423	88	5	674	674	NUM
cana-1423	88	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1423	88	7	𝑃𝑀1	𝑃𝑀1	PROPN
cana-1423	88	8	(	(	PUNCT
cana-1423	88	9	𝐺𝑚,𝑛	𝐺𝑚,𝑛	AUX
cana-1423	88	10	𝑀)=	𝑀)=	ADP
cana-1423	88	11			PROPN
cana-1423	88	12			NOUN
cana-1423	88	13	+	+	CCONJ
cana-1423	88	14	evv	evv	ADV
cana-1423	88	15	ji	ji	PROPN
cana-1423	88	16	ji	ji	PROPN
cana-1423	88	17	dd	dd	PROPN
cana-1423	88	18	,	,	PUNCT
cana-1423	88	19	)	)	PUNCT
cana-1423	88	20	(	(	PUNCT
cana-1423	88	21	=	=	SYM
cana-1423	88	22	(	(	PUNCT
cana-1423	88	23	𝑑𝑖	𝑑𝑖	PROPN
cana-1423	88	24	+	+	NUM
cana-1423	88	25	𝑑𝑗)|𝑒𝑖𝑗|	𝑑𝑗)|𝑒𝑖𝑗|	PUNCT
cana-1423	89	1	=	=	PUNCT
cana-1423	90	1	[	[	X
cana-1423	90	2	(	(	PUNCT
cana-1423	90	3	𝑛	𝑛	PROPN
cana-1423	90	4	−	−	NUM
cana-1423	90	5	1)+(𝑛	1)+(𝑛	NUM
cana-1423	90	6	−	−	NOUN
cana-1423	90	7	1	1	NUM
cana-1423	90	8	)	)	PUNCT
cana-1423	90	9	]	]	PUNCT
cana-1423	90	10	𝑛(𝑛−1	𝑛(𝑛−1	X
cana-1423	90	11	)	)	PUNCT
cana-1423	90	12	2	2	NUM
cana-1423	90	13	=	=	SYM
cana-1423	90	14	(	(	PUNCT
cana-1423	90	15	2(𝑛	2(𝑛	NUM
cana-1423	90	16	−	−	NUM
cana-1423	90	17	1	1	NUM
cana-1423	90	18	)	)	PUNCT
cana-1423	90	19	)	)	PUNCT
cana-1423	90	20	𝑛(𝑛−1	𝑛(𝑛−1	NOUN
cana-1423	90	21	)	)	PUNCT
cana-1423	90	22	2	2	NUM
cana-1423	90	23	.	.	PUNCT
cana-1423	91	1	(	(	PUNCT
cana-1423	91	2	v	v	NOUN
cana-1423	91	3	)	)	PUNCT
cana-1423	91	4	second	second	ADJ
cana-1423	91	5	multiple	multiple	ADJ
cana-1423	91	6	zagreb	zagreb	PROPN
cana-1423	91	7	index	index	NOUN
cana-1423	91	8	of	of	ADP
cana-1423	91	9	the	the	DET
cana-1423	91	10	graph	graph	NOUN
cana-1423	91	11	𝐺𝑚,𝑛	𝐺𝑚,𝑛	PROPN
cana-1423	91	12	𝑀	𝑀	PROPN
cana-1423	91	13	is	be	AUX
cana-1423	91	14	𝑃𝑀2	𝑃𝑀2	PROPN
cana-1423	91	15	(	(	PUNCT
cana-1423	91	16	𝐺𝑚,𝑛	𝐺𝑚,𝑛	AUX
cana-1423	91	17	𝑀)=	𝑀)=	ADP
cana-1423	91	18			PROPN
cana-1423	91	19			NOUN
cana-1423	91	20			VERB
cana-1423	91	21	evv	evv	NOUN
cana-1423	91	22	ji	ji	PROPN
cana-1423	91	23	ji	ji	PROPN
cana-1423	91	24	dd	dd	PROPN
cana-1423	91	25	,	,	PUNCT
cana-1423	91	26	)	)	PUNCT
cana-1423	91	27	(	(	PUNCT
cana-1423	91	28	=	=	SYM
cana-1423	91	29	(	(	PUNCT
cana-1423	91	30	𝑑𝑖	𝑑𝑖	PROPN
cana-1423	91	31	×	×	NOUN
cana-1423	91	32	𝑑𝑗)|𝑒𝑖𝑗|	𝑑𝑗)|𝑒𝑖𝑗|	PUNCT
cana-1423	92	1	=	=	PUNCT
cana-1423	93	1	[	[	X
cana-1423	93	2	(	(	PUNCT
cana-1423	93	3	𝑛	𝑛	PROPN
cana-1423	93	4	−	−	NOUN
cana-1423	93	5	1)(𝑛	1)(𝑛	NUM
cana-1423	93	6	−	−	NOUN
cana-1423	93	7	1	1	NUM
cana-1423	93	8	)	)	PUNCT
cana-1423	93	9	]	]	PUNCT
cana-1423	93	10	𝑛(𝑛−1	𝑛(𝑛−1	X
cana-1423	93	11	)	)	PUNCT
cana-1423	93	12	2	2	NUM
cana-1423	93	13	=	=	SYM
cana-1423	93	14	(	(	PUNCT
cana-1423	93	15	𝑛	𝑛	PROPN
cana-1423	93	16	−	−	PROPN
cana-1423	93	17	1)𝑛(𝑛−1	1)𝑛(𝑛−1	NUM
cana-1423	93	18	)	)	PUNCT
cana-1423	93	19	.	.	PUNCT
cana-1423	94	1	3	3	X
cana-1423	94	2	.	.	X
cana-1423	94	3	zagreb	zagreb	PROPN
cana-1423	94	4	indices	index	NOUN
cana-1423	94	5	of	of	ADP
cana-1423	94	6	the	the	DET
cana-1423	94	7	undirected	undirected	ADJ
cana-1423	94	8	graph	graph	NOUN
cana-1423	94	9	𝑮𝒏	𝑮𝒏	PROPN
cana-1423	94	10	let	let	VERB
cana-1423	94	11	an	an	DET
cana-1423	94	12	undirected	undirected	ADJ
cana-1423	94	13	simple	simple	ADJ
cana-1423	94	14	graph	graph	NOUN
cana-1423	94	15	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	94	16	=	=	SYM
cana-1423	94	17	(	(	PUNCT
cana-1423	94	18	𝑉	𝑉	PROPN
cana-1423	94	19	,	,	PUNCT
cana-1423	94	20	𝐸	𝐸	PROPN
cana-1423	94	21	)	)	PUNCT
cana-1423	94	22	whose	whose	DET
cana-1423	94	23	vertex	vertex	NOUN
cana-1423	94	24	set	set	NOUN
cana-1423	94	25	𝑉	𝑉	PROPN
cana-1423	94	26	is	be	AUX
cana-1423	94	27	a	a	DET
cana-1423	94	28	subset	subset	NOUN
cana-1423	94	29	of	of	ADP
cana-1423	94	30	natural	natural	ADJ
cana-1423	94	31	numbers	number	NOUN
cana-1423	94	32	defined	define	VERB
cana-1423	94	33	as	as	ADP
cana-1423	94	34	𝑉	𝑉	PROPN
cana-1423	94	35	=	=	PUNCT
cana-1423	94	36	{	{	PUNCT
cana-1423	94	37	𝑥	𝑥	NOUN
cana-1423	94	38	∈	∈	PROPN
cana-1423	94	39	𝑁/(𝑥	𝑁/(𝑥	NOUN
cana-1423	94	40	,	,	PUNCT
cana-1423	94	41	𝑛	𝑛	ADJ
cana-1423	94	42	)	)	PUNCT
cana-1423	94	43	≠	≠	PROPN
cana-1423	94	44	1	1	NUM
cana-1423	94	45	,	,	PUNCT
cana-1423	94	46	𝑥	𝑥	PRON
cana-1423	94	47	<	<	X
cana-1423	94	48	𝑛	𝑛	PROPN
cana-1423	94	49	}	}	PUNCT
cana-1423	94	50	,	,	PUNCT
cana-1423	94	51	where	where	SCONJ
cana-1423	94	52	𝑛	𝑛	DET
cana-1423	94	53	∈	∈	PROPN
cana-1423	94	54	𝑁and	𝑁and	PROPN
cana-1423	94	55	𝑛	𝑛	PROPN
cana-1423	94	56	is	be	AUX
cana-1423	94	57	not	not	PART
cana-1423	94	58	a	a	DET
cana-1423	94	59	prime	prime	ADJ
cana-1423	94	60	number	number	NOUN
cana-1423	94	61	and	and	CCONJ
cana-1423	94	62	a	a	DET
cana-1423	94	63	pair	pair	NOUN
cana-1423	94	64	of	of	ADP
cana-1423	94	65	vertices	vertex	NOUN
cana-1423	94	66	𝑥	𝑥	PRON
cana-1423	94	67	,	,	PUNCT
cana-1423	94	68	𝑦	𝑦	NOUN
cana-1423	94	69	∈	∈	PROPN
cana-1423	94	70	𝑉	𝑉	PROPN
cana-1423	94	71	is	be	AUX
cana-1423	94	72	adjacent	adjacent	ADJ
cana-1423	94	73	if	if	SCONJ
cana-1423	94	74	and	and	CCONJ
cana-1423	94	75	only	only	ADV
cana-1423	94	76	if	if	SCONJ
cana-1423	94	77	gcd	gcd	X
cana-1423	94	78	(	(	PUNCT
cana-1423	94	79	𝑥	𝑥	NOUN
cana-1423	94	80	,	,	PUNCT
cana-1423	94	81	𝑦	𝑦	NOUN
cana-1423	94	82	)	)	PUNCT
cana-1423	94	83	>	>	X
cana-1423	95	1	1.some	1.some	NUM
cana-1423	95	2	of	of	ADP
cana-1423	95	3	the	the	DET
cana-1423	95	4	properties	property	NOUN
cana-1423	95	5	of	of	ADP
cana-1423	95	6	graph	graph	NOUN
cana-1423	95	7	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	95	8	as	as	SCONJ
cana-1423	95	9	follows	follow	VERB
cana-1423	95	10	1	1	NUM
cana-1423	95	11	.	.	PUNCT
cana-1423	96	1	the	the	DET
cana-1423	96	2	graph	graph	NOUN
cana-1423	96	3	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	96	4	is	be	AUX
cana-1423	96	5	complete	complete	ADJ
cana-1423	96	6	if	if	SCONJ
cana-1423	96	7	and	and	CCONJ
cana-1423	96	8	only	only	ADV
cana-1423	96	9	if	if	SCONJ
cana-1423	96	10	𝑛	𝑛	PRON
cana-1423	96	11	=	=	PUNCT
cana-1423	96	12	𝑝𝑚	𝑝𝑚	ADP
cana-1423	96	13	where	where	SCONJ
cana-1423	96	14	𝑝	𝑝	NOUN
cana-1423	96	15	is	be	AUX
cana-1423	96	16	prime	prime	ADJ
cana-1423	96	17	.	.	PUNCT
cana-1423	97	1	2	2	X
cana-1423	97	2	.	.	X
cana-1423	97	3	the	the	DET
cana-1423	97	4	graph	graph	NOUN
cana-1423	97	5	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	97	6	is	be	AUX
cana-1423	97	7	disconnected	disconnect	VERB
cana-1423	97	8	if	if	SCONJ
cana-1423	97	9	and	and	CCONJ
cana-1423	97	10	only	only	ADV
cana-1423	97	11	if	if	SCONJ
cana-1423	97	12	𝑛	𝑛	PROPN
cana-1423	97	13	=	=	SYM
cana-1423	97	14	2𝑝	2𝑝	NOUN
cana-1423	97	15	where	where	SCONJ
cana-1423	97	16	𝑝	𝑝	NOUN
cana-1423	97	17	is	be	AUX
cana-1423	97	18	an	an	DET
cana-1423	97	19	odd	odd	ADJ
cana-1423	97	20	prime	prime	NOUN
cana-1423	97	21	.	.	PUNCT
cana-1423	98	1	results	result	NOUN
cana-1423	98	2	on	on	ADP
cana-1423	98	3	various	various	ADJ
cana-1423	98	4	zagreb	zagreb	PROPN
cana-1423	98	5	indices	index	NOUN
cana-1423	98	6	of	of	ADP
cana-1423	98	7	the	the	DET
cana-1423	98	8	graph	graph	NOUN
cana-1423	98	9	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	98	10	are	be	AUX
cana-1423	98	11	presented	present	VERB
cana-1423	98	12	in	in	ADP
cana-1423	98	13	this	this	DET
cana-1423	98	14	section	section	NOUN
cana-1423	98	15	.	.	PUNCT
cana-1423	99	1	theorem	theorem	VERB
cana-1423	99	2	3.1	3.1	NUM
cana-1423	99	3	:	:	PUNCT
cana-1423	99	4	if	if	SCONJ
cana-1423	99	5	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	99	6	be	be	VERB
cana-1423	99	7	an	an	DET
cana-1423	99	8	undirected	undirected	ADJ
cana-1423	99	9	graph	graph	NOUN
cana-1423	99	10	where	where	SCONJ
cana-1423	99	11	𝑛	𝑛	PRON
cana-1423	99	12	=	=	SYM
cana-1423	99	13	2𝛼	2𝛼	PROPN
cana-1423	99	14	,	,	PUNCT
cana-1423	99	15	>	>	X
cana-1423	99	16	2	2	NUM
cana-1423	99	17	.	.	PUNCT
cana-1423	100	1	then	then	ADV
cana-1423	100	2	(	(	PUNCT
cana-1423	100	3	i	i	NOUN
cana-1423	100	4	)	)	PUNCT
cana-1423	100	5	first	first	PROPN
cana-1423	100	6	zagreb	zagreb	PROPN
cana-1423	100	7	index	index	PROPN
cana-1423	100	8	𝑀1(𝐺𝑛	𝑀1(𝐺𝑛	PROPN
cana-1423	100	9	)	)	PUNCT
cana-1423	100	10	is	be	AUX
cana-1423	100	11	(	(	PUNCT
cana-1423	100	12	2α−1	2α−1	NUM
cana-1423	100	13	−	−	PROPN
cana-1423	100	14	1)(2α−1	1)(2α−1	NOUN
cana-1423	100	15	−	−	PROPN
cana-1423	100	16	2)2	2)2	NUM
cana-1423	100	17	.	.	PUNCT
cana-1423	101	1	(	(	PUNCT
cana-1423	101	2	ii)second	ii)second	PROPN
cana-1423	101	3	zagreb	zagreb	PROPN
cana-1423	101	4	index	index	PROPN
cana-1423	101	5	𝑀2(𝐺𝑛	𝑀2(𝐺𝑛	PROPN
cana-1423	101	6	)	)	PUNCT
cana-1423	101	7	is	be	AUX
cana-1423	101	8	(	(	PUNCT
cana-1423	101	9	2𝛼−1−1)(2𝛼−1−2)3	2𝛼−1−1)(2𝛼−1−2)3	NUM
cana-1423	101	10	2	2	NUM
cana-1423	101	11	.	.	PUNCT
cana-1423	102	1	(	(	PUNCT
cana-1423	102	2	iii)hyper	iii)hyper	PROPN
cana-1423	102	3	zagreb	zagreb	PROPN
cana-1423	102	4	index	index	PROPN
cana-1423	102	5	𝑀𝐻(𝐺𝑛	𝑀𝐻(𝐺𝑛	NOUN
cana-1423	102	6	)	)	PUNCT
cana-1423	102	7	is	be	AUX
cana-1423	102	8	2(2𝛼−1	2(2𝛼−1	NUM
cana-1423	102	9	−	−	NUM
cana-1423	102	10	1)(2𝛼−1	1)(2𝛼−1	NUM
cana-1423	102	11	−	−	PROPN
cana-1423	102	12	2)3	2)3	NUM
cana-1423	102	13	.	.	PUNCT
cana-1423	103	1	(	(	PUNCT
cana-1423	103	2	iv)first	iv)first	PROPN
cana-1423	103	3	multiple	multiple	ADJ
cana-1423	103	4	zagreb	zagreb	PROPN
cana-1423	103	5	index	index	PROPN
cana-1423	103	6	𝑃𝑀1(𝐺𝑛	𝑃𝑀1(𝐺𝑛	PROPN
cana-1423	103	7	)	)	PUNCT
cana-1423	103	8	is	be	AUX
cana-1423	103	9	(	(	PUNCT
cana-1423	103	10	2(2𝛼−1	2(2𝛼−1	NUM
cana-1423	103	11	−	−	NUM
cana-1423	103	12	2	2	NUM
cana-1423	103	13	)	)	PUNCT
cana-1423	103	14	)	)	PUNCT
cana-1423	103	15	(	(	PUNCT
cana-1423	103	16	2𝛼−1−1)(2𝛼−1−2	2𝛼−1−1)(2𝛼−1−2	NUM
cana-1423	103	17	)	)	PUNCT
cana-1423	103	18	2	2	NUM
cana-1423	103	19	.	.	PUNCT
cana-1423	104	1	(	(	PUNCT
cana-1423	104	2	iv	iv	X
cana-1423	104	3	)	)	PUNCT
cana-1423	104	4	second	second	ADJ
cana-1423	104	5	multiple	multiple	ADJ
cana-1423	104	6	zagreb	zagreb	PROPN
cana-1423	104	7	index	index	NOUN
cana-1423	104	8	𝑃𝑀2(𝐺𝑛	𝑃𝑀2(𝐺𝑛	PROPN
cana-1423	104	9	)	)	PUNCT
cana-1423	104	10	is	be	AUX
cana-1423	104	11	(	(	PUNCT
cana-1423	104	12	2𝛼−1	2𝛼−1	NUM
cana-1423	104	13	−	−	PROPN
cana-1423	104	14	2)(2𝛼−1−1)(2𝛼−1−2	2)(2𝛼−1−1)(2𝛼−1−2	NUM
cana-1423	104	15	)	)	PUNCT
cana-1423	104	16	.	.	PUNCT
cana-1423	105	1	proof	proof	NOUN
cana-1423	105	2	:	:	PUNCT
cana-1423	105	3	consider	consider	VERB
cana-1423	105	4	an	an	DET
cana-1423	105	5	undirected	undirected	ADJ
cana-1423	105	6	graph	graph	NOUN
cana-1423	105	7	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	105	8	where	where	SCONJ
cana-1423	105	9	𝑛	𝑛	PRON
cana-1423	105	10	=	=	SYM
cana-1423	105	11	2𝛼	2𝛼	PROPN
cana-1423	105	12	,	,	PUNCT
cana-1423	105	13	𝛼	𝛼	X
cana-1423	105	14	>	>	X
cana-1423	105	15	2	2	NUM
cana-1423	105	16	with	with	ADP
cana-1423	105	17	the	the	DET
cana-1423	105	18	vertex	vertex	NOUN
cana-1423	105	19	set𝑉	set𝑉	ADP
cana-1423	105	20	=	=	SYM
cana-1423	105	21	{	{	PUNCT
cana-1423	105	22	2,2.2,3.2	2,2.2,3.2	NUM
cana-1423	105	23	,	,	PUNCT
cana-1423	105	24	…	…	PUNCT
cana-1423	105	25	.	.	PUNCT
cana-1423	106	1	(	(	PUNCT
cana-1423	106	2	2𝛼−1	2𝛼−1	NUM
cana-1423	106	3	−	−	NOUN
cana-1423	106	4	1	1	NUM
cana-1423	106	5	)	)	PUNCT
cana-1423	106	6	.	.	PUNCT
cana-1423	107	1	2}and	2}and	NUM
cana-1423	107	2	𝐸	𝐸	PROPN
cana-1423	107	3	is	be	AUX
cana-1423	107	4	the	the	DET
cana-1423	107	5	edge	edge	NOUN
cana-1423	107	6	set.here	set.here	ADP
cana-1423	107	7	the	the	DET
cana-1423	107	8	degree	degree	NOUN
cana-1423	107	9	of	of	ADP
cana-1423	107	10	the	the	DET
cana-1423	107	11	vertex	vertex	NOUN
cana-1423	107	12	is	be	AUX
cana-1423	107	13	(	(	PUNCT
cana-1423	107	14	2𝛼−1	2𝛼−1	NUM
cana-1423	107	15	−	−	NOUN
cana-1423	107	16	2	2	NUM
cana-1423	107	17	)	)	PUNCT
cana-1423	107	18	for	for	SCONJ
cana-1423	107	19	every	every	DET
cana-1423	107	20	𝑣	𝑣	PROPN
cana-1423	107	21	∈	∈	PROPN
cana-1423	107	22	𝑉.	𝑉.	NOUN
cana-1423	107	23	let	let	VERB
cana-1423	107	24	𝑑𝑖	𝑑𝑖	PROPN
cana-1423	107	25	,	,	PUNCT
cana-1423	107	26	𝑑𝑗	𝑑𝑗	PROPN
cana-1423	107	27	be	be	AUX
cana-1423	107	28	the	the	DET
cana-1423	107	29	degrees	degree	NOUN
cana-1423	107	30	of	of	ADP
cana-1423	107	31	the	the	DET
cana-1423	107	32	vertices	vertex	NOUN
cana-1423	107	33	𝑣𝑖	𝑣𝑖	VERB
cana-1423	107	34	,	,	PUNCT
cana-1423	107	35	𝑣𝑗	𝑣𝑗	ADP
cana-1423	107	36	and	and	CCONJ
cana-1423	107	37	𝑒𝑖𝑗	𝑒𝑖𝑗	NOUN
cana-1423	107	38	be	be	AUX
cana-1423	107	39	the	the	DET
cana-1423	107	40	edges	edge	NOUN
cana-1423	107	41	joining	join	VERB
cana-1423	107	42	the	the	DET
cana-1423	107	43	vertices	vertex	NOUN
cana-1423	107	44	𝑣𝑖	𝑣𝑖	ADV
cana-1423	107	45	,	,	PUNCT
cana-1423	107	46	𝑣𝑗	𝑣𝑗	ADP
cana-1423	107	47	.	.	PUNCT
cana-1423	108	1	then	then	ADV
cana-1423	108	2	|𝑒𝑖𝑗|	|𝑒𝑖𝑗|	PROPN
cana-1423	108	3	=	=	SYM
cana-1423	108	4	(	(	PUNCT
cana-1423	108	5	2𝛼−1−1)(2𝛼−1−2	2𝛼−1−1)(2𝛼−1−2	NUM
cana-1423	108	6	)	)	PUNCT
cana-1423	108	7	2	2	NUM
cana-1423	108	8	(	(	PUNCT
cana-1423	108	9	i)first	i)first	ADV
cana-1423	108	10	zagreb	zagreb	NUM
cana-1423	108	11	index	index	NOUN
cana-1423	108	12	of	of	ADP
cana-1423	108	13	the	the	DET
cana-1423	108	14	graph	graph	NOUN
cana-1423	108	15	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	108	16	where	where	SCONJ
cana-1423	108	17	𝑛	𝑛	PRON
cana-1423	108	18	=	=	SYM
cana-1423	108	19	2𝛼	2𝛼	PROPN
cana-1423	108	20	,	,	PUNCT
cana-1423	108	21	𝛼	𝛼	X
cana-1423	108	22	>	>	X
cana-1423	108	23	2	2	NUM
cana-1423	108	24	is	be	AUX
cana-1423	108	25	communications	communication	NOUN
cana-1423	108	26	on	on	ADP
cana-1423	108	27	applied	apply	VERB
cana-1423	108	28	nonlinear	nonlinear	ADJ
cana-1423	108	29	analysis	analysis	NOUN
cana-1423	108	30	issn	issn	NOUN
cana-1423	108	31	:	:	PUNCT
cana-1423	108	32	1074	1074	NUM
cana-1423	108	33	-	-	PUNCT
cana-1423	108	34	133x	133x	NUM
cana-1423	108	35	vol	vol	NOUN
cana-1423	108	36	31	31	NUM
cana-1423	108	37	no	no	NOUN
cana-1423	108	38	.	.	PUNCT
cana-1423	109	1	7s	7	NOUN
cana-1423	109	2	(	(	PUNCT
cana-1423	109	3	2024	2024	NUM
cana-1423	109	4	)	)	PUNCT
cana-1423	109	5	675	675	NUM
cana-1423	109	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1423	109	7	𝑀1(𝐺𝑛	𝑀1(𝐺𝑛	NOUN
cana-1423	109	8	)	)	PUNCT
cana-1423	109	9	=	=	PUNCT
cana-1423	109	10			X
cana-1423	109	11			NOUN
cana-1423	109	12	+	+	CCONJ
cana-1423	109	13	evv	evv	ADV
cana-1423	109	14	ji	ji	PROPN
cana-1423	109	15	ji	ji	PROPN
cana-1423	109	16	dd	dd	PROPN
cana-1423	109	17	,	,	PUNCT
cana-1423	109	18	)	)	PUNCT
cana-1423	109	19	(	(	PUNCT
cana-1423	109	20	=	=	PUNCT
cana-1423	109	21	|𝑒𝑖𝑗|(𝑑𝑖	|𝑒𝑖𝑗|(𝑑𝑖	PROPN
cana-1423	109	22	+	+	CCONJ
cana-1423	109	23	𝑑𝑗	𝑑𝑗	NOUN
cana-1423	109	24	)	)	PUNCT
cana-1423	109	25	=	=	PUNCT
cana-1423	109	26	(	(	PUNCT
cana-1423	109	27	2𝛼−1−1)(2𝛼−1−2	2𝛼−1−1)(2𝛼−1−2	NUM
cana-1423	109	28	)	)	PUNCT
cana-1423	109	29	2	2	NUM
cana-1423	110	1	[	[	X
cana-1423	110	2	(	(	PUNCT
cana-1423	110	3	2𝛼−1	2𝛼−1	NUM
cana-1423	110	4	−	−	NOUN
cana-1423	110	5	2	2	NUM
cana-1423	110	6	)	)	PUNCT
cana-1423	110	7	+	+	CCONJ
cana-1423	110	8	(	(	PUNCT
cana-1423	110	9	2𝛼−1	2𝛼−1	NUM
cana-1423	110	10	−	−	NOUN
cana-1423	110	11	2	2	NUM
cana-1423	110	12	)	)	PUNCT
cana-1423	110	13	]	]	PUNCT
cana-1423	111	1	=	=	PUNCT
cana-1423	111	2	(	(	PUNCT
cana-1423	111	3	2α−1	2α−1	NUM
cana-1423	111	4	−	−	PROPN
cana-1423	111	5	1)(2α−1	1)(2α−1	NOUN
cana-1423	111	6	−	−	PROPN
cana-1423	111	7	2)2	2)2	NUM
cana-1423	111	8	.	.	PUNCT
cana-1423	112	1	(	(	PUNCT
cana-1423	112	2	ii)second	ii)second	PROPN
cana-1423	112	3	zagreb	zagreb	PROPN
cana-1423	112	4	index	index	NOUN
cana-1423	112	5	of	of	ADP
cana-1423	112	6	the	the	DET
cana-1423	112	7	graph	graph	NOUN
cana-1423	112	8	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	112	9	where	where	SCONJ
cana-1423	112	10	𝑛	𝑛	PRON
cana-1423	112	11	=	=	SYM
cana-1423	112	12	2𝛼	2𝛼	PROPN
cana-1423	112	13	,	,	PUNCT
cana-1423	112	14	𝛼	𝛼	X
cana-1423	112	15	>	>	X
cana-1423	112	16	2	2	NUM
cana-1423	112	17	is	be	AUX
cana-1423	112	18	𝑀2(𝐺𝑛	𝑀2(𝐺𝑛	X
cana-1423	112	19	)	)	PUNCT
cana-1423	112	20	=	=	PUNCT
cana-1423	112	21			PROPN
cana-1423	112	22			NOUN
cana-1423	112	23			VERB
cana-1423	112	24	evv	evv	PROPN
cana-1423	112	25	ji	ji	PROPN
cana-1423	112	26	ji	ji	PROPN
cana-1423	112	27	dd	dd	PROPN
cana-1423	112	28	,	,	PUNCT
cana-1423	112	29	)	)	PUNCT
cana-1423	112	30	(	(	PUNCT
cana-1423	112	31	=	=	PUNCT
cana-1423	112	32	|𝑒𝑖𝑗|(𝑑𝑖	|𝑒𝑖𝑗|(𝑑𝑖	PROPN
cana-1423	112	33	×	×	NOUN
cana-1423	112	34	𝑑𝑗	𝑑𝑗	NOUN
cana-1423	112	35	)	)	PUNCT
cana-1423	112	36	=	=	PRON
cana-1423	112	37	(	(	PUNCT
cana-1423	112	38	2𝛼−1−1)(2𝛼−1−2	2𝛼−1−1)(2𝛼−1−2	NUM
cana-1423	112	39	)	)	PUNCT
cana-1423	112	40	2	2	NUM
cana-1423	113	1	[	[	X
cana-1423	113	2	(	(	PUNCT
cana-1423	113	3	2𝛼−1	2𝛼−1	NUM
cana-1423	113	4	−	−	NOUN
cana-1423	113	5	2	2	NUM
cana-1423	113	6	)	)	PUNCT
cana-1423	113	7	×	×	NOUN
cana-1423	113	8	(	(	PUNCT
cana-1423	113	9	2𝛼−1	2𝛼−1	NUM
cana-1423	113	10	−	−	NOUN
cana-1423	113	11	2	2	NUM
cana-1423	113	12	)	)	PUNCT
cana-1423	113	13	]	]	PUNCT
cana-1423	114	1	=	=	PUNCT
cana-1423	114	2	(	(	PUNCT
cana-1423	114	3	2𝛼−1−1)(2𝛼−1−2)3	2𝛼−1−1)(2𝛼−1−2)3	NUM
cana-1423	114	4	2	2	NUM
cana-1423	114	5	(	(	PUNCT
cana-1423	114	6	iii	iii	NOUN
cana-1423	114	7	)	)	PUNCT
cana-1423	114	8	hyper	hyper	PROPN
cana-1423	114	9	zagreb	zagreb	PROPN
cana-1423	114	10	index	index	NOUN
cana-1423	114	11	of	of	ADP
cana-1423	114	12	the	the	DET
cana-1423	114	13	graph	graph	NOUN
cana-1423	114	14	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	114	15	where	where	SCONJ
cana-1423	114	16	𝑛	𝑛	PRON
cana-1423	114	17	=	=	SYM
cana-1423	114	18	2𝛼	2𝛼	PROPN
cana-1423	114	19	,	,	PUNCT
cana-1423	114	20	𝛼	𝛼	X
cana-1423	114	21	>	>	X
cana-1423	114	22	2	2	NUM
cana-1423	114	23	is	be	AUX
cana-1423	114	24	𝑀𝐻(𝐺𝑛	𝑀𝐻(𝐺𝑛	NOUN
cana-1423	114	25	)	)	PUNCT
cana-1423	114	26	=	=	SYM
cana-1423	114	27	2	2	NUM
cana-1423	114	28	,	,	PUNCT
cana-1423	114	29	)	)	PUNCT
cana-1423	114	30	(	(	PUNCT
cana-1423	114	31			PROPN
cana-1423	114	32			NOUN
cana-1423	114	33	+	+	CCONJ
cana-1423	114	34	evv	evv	ADV
cana-1423	114	35	ji	ji	PROPN
cana-1423	114	36	ji	ji	PROPN
cana-1423	114	37	dd	dd	PROPN
cana-1423	114	38	=	=	PUNCT
cana-1423	114	39	|𝑒𝑖𝑗|(𝑑𝑖	|𝑒𝑖𝑗|(𝑑𝑖	PROPN
cana-1423	114	40	+	+	CCONJ
cana-1423	114	41	𝑑𝑗)2	𝑑𝑗)2	PROPN
cana-1423	114	42	=	=	SYM
cana-1423	114	43	(	(	PUNCT
cana-1423	114	44	2𝛼−1−1)(2𝛼−1−2	2𝛼−1−1)(2𝛼−1−2	NUM
cana-1423	114	45	)	)	PUNCT
cana-1423	114	46	2	2	NUM
cana-1423	114	47	[	[	X
cana-1423	114	48	(	(	PUNCT
cana-1423	114	49	2𝛼−1	2𝛼−1	NUM
cana-1423	114	50	−	−	NOUN
cana-1423	114	51	2	2	NUM
cana-1423	114	52	)	)	PUNCT
cana-1423	114	53	+	+	CCONJ
cana-1423	114	54	(	(	PUNCT
cana-1423	114	55	2𝛼−1	2𝛼−1	NUM
cana-1423	114	56	−	−	NOUN
cana-1423	114	57	2)]2	2)]2	NUM
cana-1423	114	58	=	=	SYM
cana-1423	115	1	2(2𝛼−1	2(2𝛼−1	NUM
cana-1423	115	2	−	−	NUM
cana-1423	115	3	1)(2𝛼−1	1)(2𝛼−1	NUM
cana-1423	115	4	−	−	PROPN
cana-1423	115	5	2)3	2)3	NUM
cana-1423	115	6	.	.	PUNCT
cana-1423	115	7	(	(	PUNCT
cana-1423	115	8	iv	iv	X
cana-1423	115	9	)	)	PUNCT
cana-1423	115	10	first	first	ADJ
cana-1423	115	11	multiple	multiple	ADJ
cana-1423	115	12	zagreb	zagreb	PROPN
cana-1423	115	13	index	index	NOUN
cana-1423	115	14	of	of	ADP
cana-1423	115	15	the	the	DET
cana-1423	115	16	graph	graph	NOUN
cana-1423	115	17	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	115	18	where	where	SCONJ
cana-1423	115	19	𝑛	𝑛	PRON
cana-1423	115	20	=	=	SYM
cana-1423	115	21	2𝛼	2𝛼	PROPN
cana-1423	115	22	,	,	PUNCT
cana-1423	115	23	𝛼	𝛼	X
cana-1423	115	24	>	>	X
cana-1423	115	25	2	2	NUM
cana-1423	115	26	is	be	AUX
cana-1423	115	27	𝑃𝑀1(𝐺𝑛)=	𝑃𝑀1(𝐺𝑛)=	NOUN
cana-1423	115	28			NUM
cana-1423	115	29			NOUN
cana-1423	115	30	+	+	CCONJ
cana-1423	115	31	evv	evv	ADV
cana-1423	115	32	ji	ji	PROPN
cana-1423	115	33	ji	ji	PROPN
cana-1423	115	34	dd	dd	PROPN
cana-1423	115	35	,	,	PUNCT
cana-1423	115	36	)	)	PUNCT
cana-1423	115	37	(	(	PUNCT
cana-1423	115	38	=	=	SYM
cana-1423	115	39	(	(	PUNCT
cana-1423	115	40	𝑑𝑖	𝑑𝑖	PROPN
cana-1423	115	41	+	+	NUM
cana-1423	115	42	𝑑𝑗)|𝑒𝑖𝑗|	𝑑𝑗)|𝑒𝑖𝑗|	X
cana-1423	115	43	=[	=[	NOUN
cana-1423	115	44	(	(	PUNCT
cana-1423	115	45	2𝛼−1	2𝛼−1	NUM
cana-1423	115	46	−	−	NOUN
cana-1423	115	47	2	2	NUM
cana-1423	115	48	)	)	PUNCT
cana-1423	115	49	+	+	CCONJ
cana-1423	115	50	(	(	PUNCT
cana-1423	115	51	2𝛼−1	2𝛼−1	NUM
cana-1423	115	52	−	−	NOUN
cana-1423	115	53	2	2	NUM
cana-1423	115	54	)	)	PUNCT
cana-1423	115	55	]	]	PUNCT
cana-1423	115	56	(	(	PUNCT
cana-1423	115	57	2𝛼−1−1)(2𝛼−1−2	2𝛼−1−1)(2𝛼−1−2	NUM
cana-1423	115	58	)	)	PUNCT
cana-1423	115	59	2	2	NUM
cana-1423	115	60	=	=	SYM
cana-1423	115	61	(	(	PUNCT
cana-1423	115	62	2(2𝛼−1	2(2𝛼−1	NUM
cana-1423	115	63	−	−	NUM
cana-1423	115	64	2	2	NUM
cana-1423	115	65	)	)	PUNCT
cana-1423	115	66	)	)	PUNCT
cana-1423	115	67	(	(	PUNCT
cana-1423	115	68	2𝛼−1−1)(2𝛼−1−2	2𝛼−1−1)(2𝛼−1−2	NUM
cana-1423	115	69	)	)	PUNCT
cana-1423	115	70	2	2	NUM
cana-1423	115	71	.	.	PUNCT
cana-1423	116	1	(	(	PUNCT
cana-1423	116	2	v	v	NOUN
cana-1423	116	3	)	)	PUNCT
cana-1423	116	4	second	second	ADJ
cana-1423	116	5	multiple	multiple	ADJ
cana-1423	116	6	zagreb	zagreb	PROPN
cana-1423	116	7	index	index	NOUN
cana-1423	116	8	of	of	ADP
cana-1423	116	9	the	the	DET
cana-1423	116	10	graph	graph	NOUN
cana-1423	117	1	𝐺𝑛	𝐺𝑛	PROPN
cana-1423	117	2	where	where	SCONJ
cana-1423	117	3	𝑛	𝑛	PRON
cana-1423	117	4	=	=	SYM
cana-1423	117	5	2𝛼	2𝛼	PROPN
cana-1423	117	6	,	,	PUNCT
cana-1423	117	7	𝛼	𝛼	X
cana-1423	117	8	>	>	X
cana-1423	117	9	2	2	NUM
cana-1423	117	10	is	be	AUX
cana-1423	117	11	𝑃𝑀2(𝐺𝑛	𝑃𝑀2(𝐺𝑛	NOUN
cana-1423	117	12	)	)	PUNCT
cana-1423	117	13	=	=	SYM
cana-1423	118	1			PROPN
cana-1423	118	2			NOUN
cana-1423	118	3			VERB
cana-1423	118	4	evv	evv	PROPN
cana-1423	118	5	ji	ji	PROPN
cana-1423	118	6	ji	ji	PROPN
cana-1423	118	7	dd	dd	PROPN
cana-1423	118	8	,	,	PUNCT
cana-1423	118	9	)	)	PUNCT
cana-1423	118	10	(	(	PUNCT
cana-1423	118	11	=	=	SYM
cana-1423	118	12	(	(	PUNCT
cana-1423	118	13	𝑑𝑖	𝑑𝑖	PROPN
cana-1423	118	14	×	×	NOUN
cana-1423	118	15	𝑑𝑗)|𝑒𝑖𝑗|	𝑑𝑗)|𝑒𝑖𝑗|	PUNCT
cana-1423	118	16	=	=	PUNCT
cana-1423	119	1	[	[	X
cana-1423	119	2	(	(	PUNCT
cana-1423	119	3	2𝛼−1	2𝛼−1	NUM
cana-1423	119	4	−	−	NOUN
cana-1423	119	5	2)(2𝛼−1	2)(2𝛼−1	NUM
cana-1423	119	6	−	−	PROPN
cana-1423	119	7	2	2	NUM
cana-1423	119	8	)	)	PUNCT
cana-1423	119	9	]	]	PUNCT
cana-1423	119	10	(	(	PUNCT
cana-1423	119	11	2𝛼−1−1)(2𝛼−1−2	2𝛼−1−1)(2𝛼−1−2	NUM
cana-1423	119	12	)	)	PUNCT
cana-1423	119	13	2	2	NUM
cana-1423	119	14	=	=	SYM
cana-1423	119	15	(	(	PUNCT
cana-1423	119	16	2𝛼−1	2𝛼−1	NUM
cana-1423	119	17	−	−	PROPN
cana-1423	119	18	2)(2𝛼−1−1)(2𝛼−1−2	2)(2𝛼−1−1)(2𝛼−1−2	NUM
cana-1423	119	19	)	)	PUNCT
cana-1423	119	20	.	.	PUNCT
cana-1423	120	1	communications	communication	NOUN
cana-1423	120	2	on	on	ADP
cana-1423	120	3	applied	apply	VERB
cana-1423	120	4	nonlinear	nonlinear	ADJ
cana-1423	120	5	analysis	analysis	NOUN
cana-1423	120	6	issn	issn	NOUN
cana-1423	120	7	:	:	PUNCT
cana-1423	120	8	1074	1074	NUM
cana-1423	120	9	-	-	PUNCT
cana-1423	120	10	133x	133x	NUM
cana-1423	120	11	vol	vol	NOUN
cana-1423	120	12	31	31	NUM
cana-1423	120	13	no	no	NOUN
cana-1423	120	14	.	.	PUNCT
cana-1423	121	1	7s	7	NOUN
cana-1423	121	2	(	(	PUNCT
cana-1423	121	3	2024	2024	NUM
cana-1423	121	4	)	)	PUNCT
cana-1423	121	5	676	676	NUM
cana-1423	121	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1423	121	7	4	4	NUM
cana-1423	121	8	.	.	X
cana-1423	121	9	conclusion	conclusion	VERB
cana-1423	121	10	the	the	DET
cana-1423	121	11	authors	author	NOUN
cana-1423	121	12	of	of	ADP
cana-1423	121	13	this	this	DET
cana-1423	121	14	paper	paper	NOUN
cana-1423	121	15	have	have	AUX
cana-1423	121	16	studied	study	VERB
cana-1423	121	17	the	the	DET
cana-1423	121	18	zagreb	zagreb	PROPN
cana-1423	121	19	indices	index	NOUN
cana-1423	121	20	of	of	ADP
cana-1423	121	21	undirected	undirected	ADJ
cana-1423	121	22	graphs	graph	NOUN
cana-1423	122	1	𝐺𝑛	𝐺𝑛	SCONJ
cana-1423	122	2	when	when	SCONJ
cana-1423	122	3	𝑛	𝑛	PROPN
cana-1423	122	4	=	=	SYM
cana-1423	122	5	2𝛼	2𝛼	PROPN
cana-1423	122	6	,	,	PUNCT
cana-1423	122	7	𝛼	𝛼	X
cana-1423	122	8	>	>	X
cana-1423	122	9	2	2	NUM
cana-1423	122	10	and	and	CCONJ
cana-1423	122	11	undirected	undirected	ADJ
cana-1423	122	12	graph	graph	NOUN
cana-1423	122	13	𝐺𝑚,𝑛	𝐺𝑚,𝑛	ADP
cana-1423	122	14	𝑀	𝑀	PROPN
cana-1423	122	15	for	for	ADP
cana-1423	122	16	some	some	DET
cana-1423	122	17	cases	case	NOUN
cana-1423	122	18	that	that	PRON
cana-1423	122	19	is	be	AUX
cana-1423	122	20	when	when	SCONJ
cana-1423	122	21	𝑛	𝑛	PROPN
cana-1423	122	22	=	=	SYM
cana-1423	122	23	2𝑝	2𝑝	NOUN
cana-1423	122	24	,	,	PUNCT
cana-1423	122	25	𝑝	𝑝	PROPN
cana-1423	122	26	is	be	AUX
cana-1423	122	27	prime,𝑚	prime,𝑚	PROPN
cana-1423	122	28	>	>	SYM
cana-1423	122	29	𝑛	𝑛	PROPN
cana-1423	122	30	,	,	PUNCT
cana-1423	122	31	𝑚	𝑚	PROPN
cana-1423	122	32	is	be	AUX
cana-1423	122	33	prime	prime	ADJ
cana-1423	122	34	and	and	CCONJ
cana-1423	122	35	when	when	SCONJ
cana-1423	122	36	𝑚	𝑚	PROPN
cana-1423	122	37	>	>	X
cana-1423	122	38	𝑛	𝑛	PROPN
cana-1423	122	39	,	,	PUNCT
cana-1423	122	40	𝑚	𝑚	PROPN
cana-1423	122	41	,	,	PUNCT
cana-1423	122	42	𝑛	𝑛	PROPN
cana-1423	122	43	are	be	AUX
cana-1423	122	44	odd	odd	ADJ
cana-1423	122	45	primes	prime	NOUN
cana-1423	122	46	.	.	PUNCT
cana-1423	123	1	5	5	X
cana-1423	123	2	.	.	X
cana-1423	123	3	refrences	refrence	VERB
cana-1423	123	4	[	[	X
cana-1423	123	5	1	1	X
cana-1423	123	6	]	]	PUNCT
cana-1423	123	7	i.gutman	i.gutman	ADJ
cana-1423	123	8	and	and	CCONJ
cana-1423	123	9	n.trinajstic	n.trinajstic	ADJ
cana-1423	123	10	,	,	PUNCT
cana-1423	123	11	graph	graph	NOUN
cana-1423	123	12	theory	theory	NOUN
cana-1423	123	13	and	and	CCONJ
cana-1423	123	14	molecular	molecular	ADJ
cana-1423	123	15	orbitals	orbital	NOUN
cana-1423	123	16	,	,	PUNCT
cana-1423	123	17	total	total	ADJ
cana-1423	123	18	𝜋-electron	𝜋-electron	NOUN
cana-1423	123	19	energy	energy	NOUN
cana-1423	123	20	of	of	ADP
cana-1423	123	21	alternant	alternant	ADJ
cana-1423	123	22	hydrocarbons	hydrocarbon	NOUN
cana-1423	123	23	,	,	PUNCT
cana-1423	123	24	chem.phys.lett.17(1972),533	chem.phys.lett.17(1972),533	PROPN
cana-1423	123	25	-	-	PUNCT
cana-1423	123	26	538	538	NUM
cana-1423	123	27	.	.	PUNCT
cana-1423	124	1	[	[	X
cana-1423	124	2	2	2	X
cana-1423	124	3	]	]	PUNCT
cana-1423	124	4	gutman.i	gutman.i	PROPN
cana-1423	124	5	.	.	PUNCT
cana-1423	124	6	,rusic.r	,rusic.r	PROPN
cana-1423	124	7	.	.	PUNCT
cana-1423	124	8	,	,	PUNCT
cana-1423	124	9	trinajstic.n	trinajstic.n	PROPN
cana-1423	124	10	.	.	PUNCT
cana-1423	125	1	,-graph	,-graph	PUNCT
cana-1423	125	2	theory	theory	NOUN
cana-1423	125	3	and	and	CCONJ
cana-1423	125	4	molecular	molecular	ADJ
cana-1423	125	5	orbitals	orbital	NOUN
cana-1423	125	6	,	,	PUNCT
cana-1423	125	7	xii	xii	X
cana-1423	125	8	acyclic	acyclic	ADJ
cana-1423	125	9	polynes.j.chem.phys.62,1975,pp.3399	polynes.j.chem.phys.62,1975,pp.3399	PROPN
cana-1423	125	10	-	-	PUNCT
cana-1423	125	11	3405	3405	NUM
cana-1423	125	12	.	.	PUNCT
cana-1423	126	1	[	[	X
cana-1423	126	2	3	3	X
cana-1423	126	3	]	]	X
cana-1423	126	4	k.c.das	k.c.das	PROPN
cana-1423	126	5	,	,	PUNCT
cana-1423	126	6	i.gutman	i.gutman	NOUN
cana-1423	126	7	and	and	CCONJ
cana-1423	126	8	b.zhou	b.zhou	NOUN
cana-1423	126	9	.	.	PUNCT
cana-1423	126	10	,”new	,”new	PROPN
cana-1423	126	11	upper	upper	ADJ
cana-1423	126	12	bounds	bound	NOUN
cana-1423	126	13	on	on	ADP
cana-1423	126	14	zagreb	zagreb	PROPN
cana-1423	126	15	indices”,journal	indices”,journal	ADJ
cana-1423	126	16	of	of	ADP
cana-1423	126	17	mathematical	mathematical	ADJ
cana-1423	126	18	chemistry	chemistry	NOUN
cana-1423	126	19	,	,	PUNCT
cana-1423	126	20	vol.46,no.2,pp.514	vol.46,no.2,pp.514	NOUN
cana-1423	126	21	-	-	SYM
cana-1423	126	22	521,2009	521,2009	NUM
cana-1423	126	23	.	.	PUNCT
cana-1423	127	1	[	[	X
cana-1423	127	2	4	4	X
cana-1423	127	3	]	]	X
cana-1423	127	4	k.c.das	k.c.da	NOUN
cana-1423	127	5	a.yurttas	a.yurtta	NOUN
cana-1423	127	6	,	,	PUNCT
cana-1423	127	7	m	m	NOUN
cana-1423	127	8	,	,	PUNCT
cana-1423	127	9	togan	togan	ADJ
cana-1423	127	10	,	,	PUNCT
cana-1423	127	11	a.s.cevik	a.s.cevik	ADV
cana-1423	127	12	,	,	PUNCT
cana-1423	127	13	i.n.cangul,”the	i.n.cangul,”the	DET
cana-1423	127	14	multiplicative	multiplicative	PROPN
cana-1423	127	15	zagreb	zagreb	PROPN
cana-1423	127	16	indices	index	NOUN
cana-1423	127	17	of	of	ADP
cana-1423	127	18	graph	graph	NOUN
cana-1423	127	19	operations”,journal	operations”,journal	ADJ
cana-1423	127	20	of	of	ADP
cana-1423	127	21	inequalities	inequality	NOUN
cana-1423	127	22	and	and	CCONJ
cana-1423	127	23	applications	application	NOUN
cana-1423	127	24	,	,	PUNCT
cana-1423	127	25	vol.2013,article	vol.2013,article	X
cana-1423	127	26	i	i	PROPN
cana-1423	127	27	d	d	PROPN
cana-1423	127	28	90,2013	90,2013	NUM
cana-1423	127	29	.	.	PUNCT
cana-1423	128	1	[	[	X
cana-1423	128	2	5	5	NUM
cana-1423	128	3	]	]	X
cana-1423	128	4	g.h.fath	g.h.fath	NOUN
cana-1423	128	5	–	–	PUNCT
cana-1423	128	6	tabar	tabar	ADJ
cana-1423	128	7	.	.	PUNCT
cana-1423	129	1	,”old	,”old	PUNCT
cana-1423	130	1	and	and	CCONJ
cana-1423	130	2	new	new	ADJ
cana-1423	130	3	zagreb	zagreb	PROPN
cana-1423	130	4	indices	index	NOUN
cana-1423	130	5	of	of	ADP
cana-1423	130	6	graphs”,match	graphs”,match	PROPN
cana-1423	130	7	communications	communication	NOUN
cana-1423	130	8	in	in	ADP
cana-1423	130	9	mathematical	mathematical	ADJ
cana-1423	130	10	and	and	CCONJ
cana-1423	130	11	in	in	ADP
cana-1423	130	12	computer	computer	NOUN
cana-1423	130	13	chemistry	chemistry	NOUN
cana-1423	130	14	,	,	PUNCT
cana-1423	130	15	vol.65,pp.79	vol.65,pp.79	NOUN
cana-1423	130	16	-	-	PUNCT
cana-1423	130	17	84,2011	84,2011	NUM
cana-1423	130	18	.	.	PUNCT
cana-1423	131	1	[	[	X
cana-1423	131	2	6	6	NUM
cana-1423	131	3	]	]	PUNCT
cana-1423	131	4	shirdel	shirdel	PROPN
cana-1423	131	5	gh	gh	PROPN
cana-1423	131	6	,	,	PUNCT
cana-1423	131	7	rezapour	rezapour	PROPN
cana-1423	131	8	h	h	NOUN
cana-1423	131	9	,	,	PUNCT
cana-1423	131	10	am	be	AUX
cana-1423	131	11	sayadi-“the	sayadi-“the	DET
cana-1423	131	12	hyper	hyper	PROPN
cana-1423	131	13	-	-	PROPN
cana-1423	131	14	zagreb	zagreb	PROPN
cana-1423	131	15	index	index	NOUN
cana-1423	131	16	of	of	ADP
cana-1423	131	17	graph	graph	NOUN
cana-1423	131	18	operations	operation	NOUN
cana-1423	131	19	”	"	PUNCT
cana-1423	131	20	,	,	PUNCT
cana-1423	131	21	iranian	iranian	ADJ
cana-1423	131	22	journal	journal	PROPN
cana-1423	131	23	of	of	ADP
cana-1423	131	24	mathematical	mathematical	ADJ
cana-1423	131	25	chemistry,4(2),pp.213	chemistry,4(2),pp.213	NOUN
cana-1423	131	26	-	-	PUNCT
cana-1423	131	27	220,2013	220,2013	NUM
cana-1423	131	28	.	.	PUNCT
cana-1423	132	1	[	[	X
cana-1423	132	2	7	7	NUM
cana-1423	132	3	]	]	SYM
cana-1423	132	4	ghorbani.m	ghorbani.m	NOUN
cana-1423	132	5	,	,	PUNCT
cana-1423	132	6	azimi	azimi	NOUN
cana-1423	132	7	a-“a	a-“a	ADJ
cana-1423	132	8	note	note	NOUN
cana-1423	132	9	on	on	ADP
cana-1423	132	10	multiplicative	multiplicative	ADJ
cana-1423	132	11	zagreb	zagreb	PROPN
cana-1423	132	12	indices	index	NOUN
cana-1423	132	13	”	"	PUNCT
cana-1423	132	14	,	,	PUNCT
cana-1423	132	15	iranian	iranian	ADJ
cana-1423	132	16	journal	journal	PROPN
cana-1423	132	17	of	of	ADP
cana-1423	132	18	mathematical	mathematical	ADJ
cana-1423	132	19	chemistry,3(2),pp.137	chemistry,3(2),pp.137	PROPN
cana-1423	132	20	-	-	NOUN
cana-1423	132	21	143,2012	143,2012	NUM
cana-1423	132	22	.	.	PUNCT
cana-1423	133	1	[	[	X
cana-1423	133	2	8	8	NUM
cana-1423	133	3	]	]	SYM
cana-1423	133	4	das.k.c	das.k.c	NOUN
cana-1423	133	5	.	.	PUNCT
cana-1423	133	6	,gutman.i	,gutman.i	PROPN
cana-1423	133	7	,	,	PUNCT
cana-1423	133	8	“	"	PUNCT
cana-1423	133	9	some	some	DET
cana-1423	133	10	properties	property	NOUN
cana-1423	133	11	of	of	ADP
cana-1423	133	12	the	the	DET
cana-1423	133	13	second	second	ADJ
cana-1423	133	14	zagreb	zagreb	PROPN
cana-1423	133	15	index	index	PROPN
cana-1423	133	16	”	"	PUNCT
cana-1423	133	17	,	,	PUNCT
cana-1423	133	18	match	match	VERB
cana-1423	133	19	commun.math.comput.chem.52	commun.math.comput.chem.52	NOUN
cana-1423	133	20	,	,	PUNCT
cana-1423	133	21	pp.103	pp.103	NOUN
cana-1423	133	22	-	-	NOUN
cana-1423	133	23	112,2004	112,2004	NUM
cana-1423	133	24	.	.	PUNCT
cana-1423	134	1	[	[	X
cana-1423	134	2	9	9	NUM
cana-1423	134	3	]	]	PUNCT
cana-1423	134	4	a.r.ashrafi	a.r.ashrafi	NOUN
cana-1423	134	5	,	,	PUNCT
cana-1423	134	6	t.doslic	t.doslic	ADJ
cana-1423	134	7	,	,	PUNCT
cana-1423	134	8	a.hamzeh,-“the	a.hamzeh,-“the	DET
cana-1423	134	9	zagreb	zagreb	PROPN
cana-1423	134	10	coindices	coindice	NOUN
cana-1423	134	11	of	of	ADP
cana-1423	134	12	graph	graph	NOUN
cana-1423	134	13	operations”,discrete	operations”,discrete	ADJ
cana-1423	134	14	appl	appl	NOUN
cana-1423	134	15	,	,	PUNCT
cana-1423	134	16	math.158,15711578,2010	math.158,15711578,2010	NOUN
cana-1423	134	17	.	.	PUNCT
cana-1423	135	1	[	[	X
cana-1423	135	2	10	10	NUM
cana-1423	135	3	]	]	PUNCT
cana-1423	135	4	zhou.b.-zagreb	zhou.b.-zagreb	PROPN
cana-1423	135	5	indices	index	NOUN
cana-1423	135	6	,	,	PUNCT
cana-1423	135	7	match	match	VERB
cana-1423	135	8	commun.math.comput.chem.52,pp.113	commun.math.comput.chem.52,pp.113	NOUN
cana-1423	135	9	-	-	PUNCT
cana-1423	135	10	118,2004	118,2004	NUM
cana-1423	135	11	.	.	PUNCT
cana-1423	136	1	[	[	X
cana-1423	136	2	11	11	NUM
cana-1423	136	3	]	]	X
cana-1423	136	4	m.siva	m.siva	PROPN
cana-1423	136	5	parvathi	parvathi	PROPN
cana-1423	136	6	,	,	PUNCT
cana-1423	136	7	d.sujatha	d.sujatha	VERB
cana-1423	136	8	and	and	CCONJ
cana-1423	136	9	t.sukeerthi,“a	t.sukeerthi,“a	VERB
cana-1423	136	10	stastical	stastical	ADJ
cana-1423	136	11	comparision	comparision	NOUN
cana-1423	136	12	between	between	ADP
cana-1423	136	13	zagreb	zagreb	PROPN
cana-1423	136	14	indices	index	NOUN
cana-1423	136	15	for	for	ADP
cana-1423	136	16	correlation	correlation	NOUN
cana-1423	136	17	with	with	ADP
cana-1423	136	18	toxicity	toxicity	NOUN
cana-1423	136	19	predictions	prediction	NOUN
cana-1423	136	20	of	of	ADP
cana-1423	136	21	natural	natural	ADJ
cana-1423	136	22	products	product	NOUN
cana-1423	136	23	“	"	PUNCT
cana-1423	136	24	,	,	PUNCT
cana-1423	136	25	international	international	ADJ
cana-1423	136	26	journal	journal	NOUN
cana-1423	136	27	of	of	ADP
cana-1423	136	28	research	research	NOUN
cana-1423	136	29	in	in	ADP
cana-1423	136	30	pharmaceutical	pharmaceutical	ADJ
cana-1423	136	31	sciences	science	NOUN
cana-1423	136	32	,	,	PUNCT
cana-1423	136	33	vol.13.no.1,2022	vol.13.no.1,2022	PROPN
cana-1423	136	34	.	.	PUNCT
cana-1423	137	1	[	[	X
cana-1423	137	2	12	12	NUM
cana-1423	137	3	]	]	X
cana-1423	137	4	ivy	ivy	PROPN
cana-1423	137	5	chakrabarthy	chakrabarthy	PROPN
cana-1423	137	6	,	,	PUNCT
cana-1423	137	7	joseph	joseph	PROPN
cana-1423	137	8	varghese	varghese	PROPN
cana-1423	137	9	kureethara	kureethara	PROPN
cana-1423	137	10	and	and	CCONJ
cana-1423	137	11	muktiacharya	muktiacharya	NOUN
cana-1423	137	12	,	,	PUNCT
cana-1423	137	13	a	a	DET
cana-1423	137	14	study	study	NOUN
cana-1423	137	15	of	of	ADP
cana-1423	137	16	an	an	DET
cana-1423	137	17	undirected	undirected	ADJ
cana-1423	137	18	graph	graph	NOUN
cana-1423	137	19	on	on	ADP
cana-1423	137	20	a	a	DET
cana-1423	137	21	finite	finite	NOUN
cana-1423	137	22	subset	subset	NOUN
cana-1423	137	23	of	of	ADP
cana-1423	137	24	natural	natural	ADJ
cana-1423	137	25	numbers	number	NOUN
cana-1423	137	26	,	,	PUNCT
cana-1423	137	27	south	south	PROPN
cana-1423	137	28	east	east	PROPN
cana-1423	137	29	asian	asian	PROPN
cana-1423	137	30	j.of	j.of	PROPN
cana-1423	137	31	mathematics	mathematic	NOUN
cana-1423	137	32	and	and	CCONJ
cana-1423	137	33	mathematical	mathematical	ADJ
cana-1423	137	34	sciences	science	NOUN
cana-1423	137	35	,	,	PUNCT
cana-1423	137	36	vol	vol	NOUN
cana-1423	137	37	18,no.3(2022),433	18,no.3(2022),433	NUM
cana-1423	137	38	-	-	SYM
cana-1423	137	39	448	448	NUM
cana-1423	137	40	.	.	PUNCT
cana-1423	138	1	[	[	X
cana-1423	138	2	13	13	NUM
cana-1423	138	3	]	]	SYM
cana-1423	138	4	i.chakrabarty	i.chakrabarty	NOUN
cana-1423	138	5	,	,	PUNCT
cana-1423	138	6	j.	j.	PROPN
cana-1423	138	7	v.	v.	PROPN
cana-1423	138	8	kureethara	kureethara	PROPN
cana-1423	138	9	,	,	PUNCT
cana-1423	138	10	m.	m.	NOUN
cana-1423	138	11	acharya	acharya	PROPN
cana-1423	138	12	,	,	PUNCT
cana-1423	138	13	the	the	DET
cana-1423	138	14	𝐺	𝐺	PROPN
cana-1423	138	15	𝑚,𝑛	𝑚,𝑛	PROPN
cana-1423	138	16	𝑀	𝑀	PROPN
cana-1423	138	17	graph	graph	NOUN
cana-1423	138	18	on	on	ADP
cana-1423	138	19	a	a	DET
cana-1423	138	20	finite	finite	NOUN
cana-1423	138	21	subset	subset	NOUN
cana-1423	138	22	of	of	ADP
cana-1423	138	23	natural	natural	ADJ
cana-1423	138	24	numbers	number	NOUN
cana-1423	138	25	,	,	PUNCT
cana-1423	138	26	proceedings	proceeding	NOUN
cana-1423	138	27	of	of	ADP
cana-1423	138	28	iam	iam	PROPN
cana-1423	138	29	,	,	PUNCT
cana-1423	138	30	v.10	v.10	ADP
cana-1423	138	31	,	,	PUNCT
cana-1423	138	32	n.1	n.1	NUM
cana-1423	138	33	,	,	PUNCT
cana-1423	138	34	2021	2021	NUM
cana-1423	138	35	,	,	PUNCT
cana-1423	138	36	pp.45	pp.45	NOUN
cana-1423	138	37	-	-	PUNCT
cana-1423	138	38	59	59	NUM
cana-1423	138	39	.	.	PUNCT
cana-1423	139	1	[	[	X
cana-1423	139	2	14	14	NUM
cana-1423	139	3	]	]	X
cana-1423	139	4	l.eswaramma	l.eswaramma	X
cana-1423	139	5	and	and	CCONJ
cana-1423	139	6	d.venkata	d.venkata	ADJ
cana-1423	139	7	lakshmi,”energy	lakshmi,”energy	NOUN
cana-1423	139	8	and	and	CCONJ
cana-1423	139	9	spectrum	spectrum	NOUN
cana-1423	139	10	of	of	ADP
cana-1423	139	11	𝐺	𝐺	PROPN
cana-1423	139	12	𝑚,𝑛	𝑚,𝑛	PROPN
cana-1423	139	13	𝑀graph”,eur.chem.bull.12,issue	𝑀graph”,eur.chem.bull.12,issue	NOUN
cana-1423	139	14	2,pp.321329,2023	2,pp.321329,2023	NUM
cana-1423	139	15	.	.	PUNCT
cana-1423	140	1	[	[	X
cana-1423	140	2	15	15	NUM
cana-1423	140	3	]	]	X
cana-1423	140	4	m.venkata	m.venkata	NOUN
cana-1423	140	5	anusha	anusha	NOUN
cana-1423	140	6	,	,	PUNCT
cana-1423	140	7	m.siva	m.siva	PROPN
cana-1423	140	8	parvathi	parvathi	PROPN
cana-1423	140	9	and	and	CCONJ
cana-1423	140	10	g.s.shanmuga	g.s.shanmuga	PROPN
cana-1423	140	11	priya,”zagreb	priya,”zagreb	PROPN
cana-1423	140	12	indices	indice	VERB
cana-1423	140	13	on	on	ADP
cana-1423	140	14	arithmetic	arithmetic	ADJ
cana-1423	140	15	graphs”,zeichen	graphs”,zeichen	PROPN
cana-1423	140	16	journal	journal	NOUN
cana-1423	140	17	,	,	PUNCT
cana-1423	140	18	vol	vol	NOUN
cana-1423	140	19	7,issue	7,issue	NUM
cana-1423	140	20	1,pp.144	1,pp.144	NUM
cana-1423	140	21	-	-	SYM
cana-1423	140	22	151,2021	151,2021	NUM