id	sid	tid	token	lemma	pos
cana-1920	1	1	communications	communication	NOUN
cana-1920	1	2	on	on	ADP
cana-1920	1	3	applied	apply	VERB
cana-1920	1	4	nonlinear	nonlinear	ADJ
cana-1920	1	5	analysis	analysis	NOUN
cana-1920	1	6	issn	issn	NOUN
cana-1920	1	7	:	:	PUNCT
cana-1920	1	8	1074	1074	NUM
cana-1920	1	9	-	-	PUNCT
cana-1920	1	10	133x	133x	NUM
cana-1920	1	11	vol	vol	NOUN
cana-1920	1	12	32	32	NUM
cana-1920	1	13	no	no	NOUN
cana-1920	1	14	.	.	NOUN
cana-1920	1	15	3	3	NUM
cana-1920	1	16	(	(	PUNCT
cana-1920	1	17	2025	2025	NUM
cana-1920	1	18	)	)	PUNCT
cana-1920	1	19	71	71	NUM
cana-1920	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	2	1	some	some	DET
cana-1920	2	2	reverse	reverse	ADJ
cana-1920	2	3	topological	topological	ADJ
cana-1920	2	4	indices	index	NOUN
cana-1920	2	5	of	of	ADP
cana-1920	2	6	comet	comet	NOUN
cana-1920	2	7	and	and	CCONJ
cana-1920	2	8	double	double	ADJ
cana-1920	2	9	comet	comet	NOUN
cana-1920	2	10	graphs	graph	VERB
cana-1920	2	11	john	john	PROPN
cana-1920	2	12	rafael	rafael	PROPN
cana-1920	2	13	m.	m.	PROPN
cana-1920	3	1	antalan1	antalan1	PROPN
cana-1920	3	2	*	*	PROPN
cana-1920	3	3	,	,	PUNCT
cana-1920	3	4	richard	richard	PROPN
cana-1920	3	5	p.	p.	PROPN
cana-1920	3	6	tagle2	tagle2	PUNCT
cana-1920	4	1	1department	1department	NUM
cana-1920	4	2	of	of	ADP
cana-1920	4	3	mathematics	mathematic	NOUN
cana-1920	4	4	and	and	CCONJ
cana-1920	4	5	physics	physics	PROPN
cana-1920	4	6	,	,	PUNCT
cana-1920	4	7	college	college	PROPN
cana-1920	4	8	of	of	ADP
cana-1920	4	9	science	science	PROPN
cana-1920	4	10	central	central	PROPN
cana-1920	4	11	luzon	luzon	PROPN
cana-1920	4	12	state	state	PROPN
cana-1920	4	13	university	university	PROPN
cana-1920	4	14	2science	2science	NUM
cana-1920	4	15	city	city	NOUN
cana-1920	4	16	of	of	ADP
cana-1920	4	17	muñoz	muñoz	PROPN
cana-1920	4	18	,	,	PUNCT
cana-1920	4	19	nueva	nueva	NOUN
cana-1920	4	20	ecija	ecija	PROPN
cana-1920	4	21	,	,	PUNCT
cana-1920	4	22	3120	3120	NUM
cana-1920	4	23	,	,	PUNCT
cana-1920	4	24	philippines	philippine	NOUN
cana-1920	4	25	jrantalan@clsu.edu.ph	jrantalan@clsu.edu.ph	NOUN
cana-1920	4	26	article	article	NOUN
cana-1920	4	27	history	history	NOUN
cana-1920	4	28	:	:	PUNCT
cana-1920	4	29	received	receive	VERB
cana-1920	4	30	:	:	PUNCT
cana-1920	4	31	22	22	NUM
cana-1920	4	32	-	-	SYM
cana-1920	4	33	07	07	NUM
cana-1920	4	34	-	-	PUNCT
cana-1920	4	35	2024	2024	NUM
cana-1920	4	36	revised	revise	VERB
cana-1920	4	37	:	:	PUNCT
cana-1920	4	38	10	10	NUM
cana-1920	4	39	-	-	SYM
cana-1920	4	40	09	09	NUM
cana-1920	4	41	-	-	PUNCT
cana-1920	4	42	2024	2024	NUM
cana-1920	4	43	accepted	accept	VERB
cana-1920	4	44	:	:	PUNCT
cana-1920	4	45	29	29	NUM
cana-1920	4	46	-	-	SYM
cana-1920	4	47	09	09	NUM
cana-1920	4	48	-	-	PUNCT
cana-1920	4	49	2024	2024	NUM
cana-1920	4	50	abstract	abstract	ADJ
cana-1920	4	51	introduction	introduction	NOUN
cana-1920	4	52	:	:	PUNCT
cana-1920	4	53	chemical	chemical	NOUN
cana-1920	4	54	graph	graph	NOUN
cana-1920	4	55	theory	theory	NOUN
cana-1920	4	56	or	or	CCONJ
cana-1920	4	57	cgt	cgt	PROPN
cana-1920	4	58	for	for	ADP
cana-1920	4	59	short	short	ADJ
cana-1920	4	60	,	,	PUNCT
cana-1920	4	61	is	be	AUX
cana-1920	4	62	a	a	DET
cana-1920	4	63	transdisciplinary	transdisciplinary	ADJ
cana-1920	4	64	field	field	NOUN
cana-1920	4	65	of	of	ADP
cana-1920	4	66	mathematics	mathematic	NOUN
cana-1920	4	67	wherein	wherein	ADJ
cana-1920	4	68	graphs	graph	NOUN
cana-1920	4	69	are	be	AUX
cana-1920	4	70	used	use	VERB
cana-1920	4	71	to	to	PART
cana-1920	4	72	represent	represent	VERB
cana-1920	4	73	chemical	chemical	NOUN
cana-1920	4	74	compounds	compound	NOUN
cana-1920	4	75	.	.	PUNCT
cana-1920	5	1	under	under	ADP
cana-1920	5	2	this	this	DET
cana-1920	5	3	representation	representation	NOUN
cana-1920	5	4	,	,	PUNCT
cana-1920	5	5	the	the	DET
cana-1920	5	6	atoms	atom	NOUN
cana-1920	5	7	of	of	ADP
cana-1920	5	8	a	a	DET
cana-1920	5	9	chemical	chemical	NOUN
cana-1920	5	10	compound	compound	NOUN
cana-1920	5	11	are	be	AUX
cana-1920	5	12	expressed	express	VERB
cana-1920	5	13	as	as	ADP
cana-1920	5	14	vertices	vertex	NOUN
cana-1920	5	15	,	,	PUNCT
cana-1920	5	16	while	while	SCONJ
cana-1920	5	17	the	the	DET
cana-1920	5	18	bonds	bond	NOUN
cana-1920	5	19	connecting	connect	VERB
cana-1920	5	20	these	these	DET
cana-1920	5	21	atoms	atom	NOUN
cana-1920	5	22	are	be	AUX
cana-1920	5	23	expressed	express	VERB
cana-1920	5	24	as	as	ADP
cana-1920	5	25	edges	edge	NOUN
cana-1920	5	26	.	.	PUNCT
cana-1920	6	1	once	once	SCONJ
cana-1920	6	2	the	the	DET
cana-1920	6	3	graph	graph	NOUN
cana-1920	6	4	representation	representation	NOUN
cana-1920	6	5	of	of	ADP
cana-1920	6	6	a	a	DET
cana-1920	6	7	chemical	chemical	NOUN
cana-1920	6	8	compound	compound	NOUN
cana-1920	6	9	has	have	AUX
cana-1920	6	10	been	be	AUX
cana-1920	6	11	determined	determine	VERB
cana-1920	6	12	,	,	PUNCT
cana-1920	6	13	graph	graph	NOUN
cana-1920	6	14	-	-	PUNCT
cana-1920	6	15	theoretic	theoretic	NOUN
cana-1920	6	16	techniques	technique	NOUN
cana-1920	6	17	can	can	AUX
cana-1920	6	18	now	now	ADV
cana-1920	6	19	be	be	AUX
cana-1920	6	20	used	use	VERB
cana-1920	6	21	to	to	PART
cana-1920	6	22	determine	determine	VERB
cana-1920	6	23	various	various	ADJ
cana-1920	6	24	topological	topological	ADJ
cana-1920	6	25	indices	index	NOUN
cana-1920	6	26	associated	associate	VERB
cana-1920	6	27	with	with	ADP
cana-1920	6	28	the	the	DET
cana-1920	6	29	chemical	chemical	NOUN
cana-1920	6	30	compound	compound	NOUN
cana-1920	6	31	.	.	PUNCT
cana-1920	7	1	topological	topological	ADJ
cana-1920	7	2	indices	index	NOUN
cana-1920	7	3	are	be	AUX
cana-1920	7	4	invariants	invariant	NOUN
cana-1920	7	5	of	of	ADP
cana-1920	7	6	a	a	DET
cana-1920	7	7	graph	graph	NOUN
cana-1920	7	8	that	that	PRON
cana-1920	7	9	have	have	VERB
cana-1920	7	10	predictive	predictive	ADJ
cana-1920	7	11	power	power	NOUN
cana-1920	7	12	for	for	ADP
cana-1920	7	13	the	the	DET
cana-1920	7	14	chemical	chemical	NOUN
cana-1920	7	15	properties	property	NOUN
cana-1920	7	16	of	of	ADP
cana-1920	7	17	a	a	DET
cana-1920	7	18	chemical	chemical	NOUN
cana-1920	7	19	compound	compound	NOUN
cana-1920	7	20	.	.	PUNCT
cana-1920	8	1	in	in	ADP
cana-1920	8	2	cgt	cgt	PROPN
cana-1920	8	3	,	,	PUNCT
cana-1920	8	4	trees	tree	NOUN
cana-1920	8	5	,	,	PUNCT
cana-1920	8	6	being	be	AUX
cana-1920	8	7	connected	connect	VERB
cana-1920	8	8	and	and	CCONJ
cana-1920	8	9	acyclic	acyclic	ADJ
cana-1920	8	10	,	,	PUNCT
cana-1920	8	11	have	have	AUX
cana-1920	8	12	been	be	AUX
cana-1920	8	13	an	an	DET
cana-1920	8	14	essential	essential	ADJ
cana-1920	8	15	class	class	NOUN
cana-1920	8	16	of	of	ADP
cana-1920	8	17	graphs	graph	NOUN
cana-1920	8	18	.	.	PUNCT
cana-1920	9	1	this	this	PRON
cana-1920	9	2	is	be	AUX
cana-1920	9	3	because	because	SCONJ
cana-1920	9	4	,	,	PUNCT
cana-1920	9	5	most	most	ADJ
cana-1920	9	6	compounds	compound	NOUN
cana-1920	9	7	have	have	AUX
cana-1920	9	8	acyclic	acyclic	ADJ
cana-1920	9	9	molecular	molecular	ADJ
cana-1920	9	10	structures	structure	NOUN
cana-1920	9	11	.	.	PUNCT
cana-1920	10	1	in	in	ADP
cana-1920	10	2	the	the	DET
cana-1920	10	3	2023	2023	NUM
cana-1920	10	4	study	study	NOUN
cana-1920	10	5	by	by	ADP
cana-1920	10	6	gowtham	gowtham	PROPN
cana-1920	10	7	and	and	CCONJ
cana-1920	10	8	husin	husin	PROPN
cana-1920	10	9	,	,	PUNCT
cana-1920	10	10	various	various	ADJ
cana-1920	10	11	reverse	reverse	ADJ
cana-1920	10	12	topological	topological	ADJ
cana-1920	10	13	indices	index	NOUN
cana-1920	10	14	of	of	ADP
cana-1920	10	15	a	a	DET
cana-1920	10	16	family	family	NOUN
cana-1920	10	17	of	of	ADP
cana-1920	10	18	trees	tree	NOUN
cana-1920	10	19	called	call	VERB
cana-1920	10	20	bistar	bistar	NOUN
cana-1920	10	21	graphs	graph	NOUN
cana-1920	10	22	have	have	AUX
cana-1920	10	23	been	be	AUX
cana-1920	10	24	determined	determine	VERB
cana-1920	10	25	.	.	PUNCT
cana-1920	11	1	objectives	objective	NOUN
cana-1920	11	2	:	:	PUNCT
cana-1920	11	3	motivated	motivate	VERB
cana-1920	11	4	by	by	ADP
cana-1920	11	5	the	the	DET
cana-1920	11	6	work	work	NOUN
cana-1920	11	7	of	of	ADP
cana-1920	11	8	gowtham	gowtham	PROPN
cana-1920	11	9	and	and	CCONJ
cana-1920	11	10	husin	husin	PROPN
cana-1920	11	11	,	,	PUNCT
cana-1920	11	12	we	we	PRON
cana-1920	11	13	determine	determine	VERB
cana-1920	11	14	some	some	DET
cana-1920	11	15	reverse	reverse	ADJ
cana-1920	11	16	topological	topological	ADJ
cana-1920	11	17	indices	index	NOUN
cana-1920	11	18	of	of	ADP
cana-1920	11	19	another	another	DET
cana-1920	11	20	family	family	NOUN
cana-1920	11	21	of	of	ADP
cana-1920	11	22	trees	tree	NOUN
cana-1920	11	23	called	call	VERB
cana-1920	11	24	comets	comet	NOUN
cana-1920	11	25	and	and	CCONJ
cana-1920	11	26	double	double	ADJ
cana-1920	11	27	comets	comet	NOUN
cana-1920	11	28	.	.	PUNCT
cana-1920	12	1	double	double	ADJ
cana-1920	12	2	comets	comet	NOUN
cana-1920	12	3	are	be	AUX
cana-1920	12	4	natural	natural	ADJ
cana-1920	12	5	extension	extension	NOUN
cana-1920	12	6	of	of	ADP
cana-1920	12	7	bistar	bistar	NOUN
cana-1920	12	8	graphs	graph	NOUN
cana-1920	12	9	.	.	PUNCT
cana-1920	13	1	we	we	PRON
cana-1920	13	2	also	also	ADV
cana-1920	13	3	give	give	VERB
cana-1920	13	4	a	a	DET
cana-1920	13	5	certain	certain	ADJ
cana-1920	13	6	computational	computational	ADJ
cana-1920	13	7	application	application	NOUN
cana-1920	13	8	of	of	ADP
cana-1920	13	9	our	our	PRON
cana-1920	13	10	results	result	NOUN
cana-1920	13	11	on	on	ADP
cana-1920	13	12	double	double	ADJ
cana-1920	13	13	comet	comet	NOUN
cana-1920	13	14	graphs	graph	NOUN
cana-1920	13	15	.	.	PUNCT
cana-1920	14	1	finally	finally	ADV
cana-1920	14	2	,	,	PUNCT
cana-1920	14	3	we	we	PRON
cana-1920	14	4	investigate	investigate	VERB
cana-1920	14	5	the	the	DET
cana-1920	14	6	relationship	relationship	NOUN
cana-1920	14	7	between	between	ADP
cana-1920	14	8	the	the	DET
cana-1920	14	9	reverse	reverse	ADJ
cana-1920	14	10	topological	topological	ADJ
cana-1920	14	11	indices	index	NOUN
cana-1920	14	12	of	of	ADP
cana-1920	14	13	bistar	bistar	ADJ
cana-1920	14	14	graphs	graph	NOUN
cana-1920	14	15	and	and	CCONJ
cana-1920	14	16	double	double	ADJ
cana-1920	14	17	comets	comet	NOUN
cana-1920	14	18	.	.	PUNCT
cana-1920	15	1	methods	method	NOUN
cana-1920	15	2	:	:	PUNCT
cana-1920	15	3	several	several	ADJ
cana-1920	15	4	important	important	ADJ
cana-1920	15	5	graph	graph	NOUN
cana-1920	15	6	-	-	PUNCT
cana-1920	15	7	theoretic	theoretic	ADJ
cana-1920	15	8	concepts	concept	NOUN
cana-1920	15	9	were	be	AUX
cana-1920	15	10	used	use	VERB
cana-1920	15	11	to	to	PART
cana-1920	15	12	analyze	analyze	VERB
cana-1920	15	13	some	some	DET
cana-1920	15	14	important	important	ADJ
cana-1920	15	15	properties	property	NOUN
cana-1920	15	16	of	of	ADP
cana-1920	15	17	comets	comet	NOUN
cana-1920	15	18	and	and	CCONJ
cana-1920	15	19	double	double	ADJ
cana-1920	15	20	comets	comet	NOUN
cana-1920	15	21	,	,	PUNCT
cana-1920	15	22	leading	lead	VERB
cana-1920	15	23	to	to	ADP
cana-1920	15	24	the	the	DET
cana-1920	15	25	computation	computation	NOUN
cana-1920	15	26	of	of	ADP
cana-1920	15	27	their	their	PRON
cana-1920	15	28	reverse	reverse	ADJ
cana-1920	15	29	vertex	vertex	NOUN
cana-1920	15	30	degree	degree	NOUN
cana-1920	15	31	based	base	VERB
cana-1920	15	32	topological	topological	ADJ
cana-1920	15	33	indices	index	NOUN
cana-1920	15	34	.	.	PUNCT
cana-1920	16	1	results	result	NOUN
cana-1920	16	2	:	:	PUNCT
cana-1920	16	3	the	the	DET
cana-1920	16	4	following	follow	VERB
cana-1920	16	5	reverse	reverse	ADJ
cana-1920	16	6	vertex	vertex	NOUN
cana-1920	16	7	degree	degree	NOUN
cana-1920	16	8	-	-	PUNCT
cana-1920	16	9	based	base	VERB
cana-1920	16	10	topological	topological	ADJ
cana-1920	16	11	indices	index	NOUN
cana-1920	16	12	for	for	ADP
cana-1920	16	13	comets	comet	NOUN
cana-1920	16	14	and	and	CCONJ
cana-1920	16	15	double	double	ADJ
cana-1920	16	16	comets	comet	NOUN
cana-1920	16	17	were	be	AUX
cana-1920	16	18	determined	determine	VERB
cana-1920	16	19	:	:	PUNCT
cana-1920	16	20	reverse	reverse	ADJ
cana-1920	16	21	sum	sum	NOUN
cana-1920	16	22	-	-	PUNCT
cana-1920	16	23	connectivity	connectivity	NOUN
cana-1920	16	24	,	,	PUNCT
cana-1920	16	25	first	first	ADV
cana-1920	16	26	reverse	reverse	ADJ
cana-1920	16	27	zagreb	zagreb	PROPN
cana-1920	16	28	,	,	PUNCT
cana-1920	16	29	second	second	ADJ
cana-1920	16	30	reverse	reverse	ADJ
cana-1920	16	31	zagreb	zagreb	PROPN
cana-1920	16	32	,	,	PUNCT
cana-1920	16	33	reverse	reverse	VERB
cana-1920	16	34	arithmetic	arithmetic	ADJ
cana-1920	16	35	-	-	PUNCT
cana-1920	16	36	geometric	geometric	ADJ
cana-1920	16	37	,	,	PUNCT
cana-1920	16	38	reverse	reverse	ADJ
cana-1920	16	39	geometric	geometric	ADJ
cana-1920	16	40	-	-	PUNCT
cana-1920	16	41	arithmetic	arithmetic	ADJ
cana-1920	16	42	,	,	PUNCT
cana-1920	16	43	reverse	reverse	ADJ
cana-1920	16	44	sombor	sombor	NOUN
cana-1920	16	45	,	,	PUNCT
cana-1920	16	46	and	and	CCONJ
cana-1920	16	47	reverse	reverse	VERB
cana-1920	16	48	nirmala	nirmala	PROPN
cana-1920	16	49	.	.	PUNCT
cana-1920	17	1	a	a	DET
cana-1920	17	2	computational	computational	ADJ
cana-1920	17	3	application	application	NOUN
cana-1920	17	4	of	of	ADP
cana-1920	17	5	the	the	DET
cana-1920	17	6	results	result	NOUN
cana-1920	17	7	to	to	ADP
cana-1920	17	8	a	a	DET
cana-1920	17	9	certain	certain	ADJ
cana-1920	17	10	chemical	chemical	NOUN
cana-1920	17	11	compound	compound	NOUN
cana-1920	17	12	(	(	PUNCT
cana-1920	17	13	2,2,4,4	2,2,4,4	NUM
cana-1920	17	14	-	-	PUNCT
cana-1920	17	15	tetramethylpentane	tetramethylpentane	NOUN
cana-1920	17	16	)	)	PUNCT
cana-1920	17	17	or	or	CCONJ
cana-1920	17	18	c9h20	c9h20	PROPN
cana-1920	17	19	were	be	AUX
cana-1920	17	20	also	also	ADV
cana-1920	17	21	demonstrated	demonstrate	VERB
cana-1920	17	22	.	.	PUNCT
cana-1920	18	1	conclusions	conclusion	NOUN
cana-1920	18	2	:	:	PUNCT
cana-1920	18	3	the	the	DET
cana-1920	18	4	results	result	NOUN
cana-1920	18	5	of	of	ADP
cana-1920	18	6	the	the	DET
cana-1920	18	7	paper	paper	NOUN
cana-1920	18	8	provided	provide	VERB
cana-1920	18	9	an	an	DET
cana-1920	18	10	extension	extension	NOUN
cana-1920	18	11	to	to	ADP
cana-1920	18	12	an	an	DET
cana-1920	18	13	existing	exist	VERB
cana-1920	18	14	result	result	NOUN
cana-1920	18	15	on	on	ADP
cana-1920	18	16	the	the	DET
cana-1920	18	17	reverse	reverse	ADJ
cana-1920	18	18	vertex	vertex	NOUN
cana-1920	18	19	degree	degree	NOUN
cana-1920	18	20	-	-	PUNCT
cana-1920	18	21	based	base	VERB
cana-1920	18	22	topological	topological	ADJ
cana-1920	18	23	indices	index	NOUN
cana-1920	18	24	of	of	ADP
cana-1920	18	25	bistar	bistar	ADJ
cana-1920	18	26	graphs	graph	NOUN
cana-1920	18	27	by	by	ADP
cana-1920	18	28	considering	consider	VERB
cana-1920	18	29	double	double	ADJ
cana-1920	18	30	comet	comet	NOUN
cana-1920	18	31	graphs	graph	NOUN
cana-1920	18	32	.	.	PUNCT
cana-1920	19	1	several	several	ADJ
cana-1920	19	2	topological	topological	ADJ
cana-1920	19	3	reverse	reverse	ADJ
cana-1920	19	4	vertex	vertex	NOUN
cana-1920	19	5	degree	degree	NOUN
cana-1920	19	6	-	-	PUNCT
cana-1920	19	7	based	base	VERB
cana-1920	19	8	topological	topological	ADJ
cana-1920	19	9	indices	index	NOUN
cana-1920	19	10	were	be	AUX
cana-1920	19	11	also	also	ADV
cana-1920	19	12	computed	compute	VERB
cana-1920	19	13	for	for	ADP
cana-1920	19	14	comet	comet	NOUN
cana-1920	19	15	graphs	graph	NOUN
cana-1920	19	16	.	.	PUNCT
cana-1920	20	1	the	the	DET
cana-1920	20	2	computed	compute	VERB
cana-1920	20	3	topological	topological	ADJ
cana-1920	20	4	indices	index	NOUN
cana-1920	20	5	were	be	AUX
cana-1920	20	6	also	also	ADV
cana-1920	20	7	applied	apply	VERB
cana-1920	20	8	in	in	ADP
cana-1920	20	9	determining	determine	VERB
cana-1920	20	10	some	some	DET
cana-1920	20	11	invariants	invariant	NOUN
cana-1920	20	12	of	of	ADP
cana-1920	20	13	a	a	DET
cana-1920	20	14	certain	certain	ADJ
cana-1920	20	15	chemical	chemical	NOUN
cana-1920	20	16	compound	compound	NOUN
cana-1920	20	17	.	.	PUNCT
cana-1920	21	1	for	for	ADP
cana-1920	21	2	future	future	ADJ
cana-1920	21	3	studies	study	NOUN
cana-1920	21	4	,	,	PUNCT
cana-1920	21	5	we	we	PRON
cana-1920	21	6	recommend	recommend	VERB
cana-1920	21	7	that	that	SCONJ
cana-1920	21	8	reverse	reverse	ADJ
cana-1920	21	9	vertex	vertex	NOUN
cana-1920	21	10	degree	degree	NOUN
cana-1920	21	11	based	base	VERB
cana-1920	21	12	topological	topological	ADJ
cana-1920	21	13	indices	index	NOUN
cana-1920	21	14	of	of	ADP
cana-1920	21	15	other	other	ADJ
cana-1920	21	16	family	family	NOUN
cana-1920	21	17	of	of	ADP
cana-1920	21	18	trees	tree	NOUN
cana-1920	21	19	will	will	AUX
cana-1920	21	20	be	be	AUX
cana-1920	21	21	considered	consider	VERB
cana-1920	21	22	.	.	PUNCT
cana-1920	22	1	keywords	keyword	NOUN
cana-1920	22	2	:	:	PUNCT
cana-1920	22	3	molecular	molecular	ADJ
cana-1920	22	4	graph	graph	NOUN
cana-1920	22	5	,	,	PUNCT
cana-1920	22	6	topological	topological	ADJ
cana-1920	22	7	index	index	NOUN
cana-1920	22	8	,	,	PUNCT
cana-1920	22	9	reverse	reverse	VERB
cana-1920	22	10	vertex	vertex	NOUN
cana-1920	22	11	degree	degree	NOUN
cana-1920	22	12	,	,	PUNCT
cana-1920	22	13	comet	comet	NOUN
cana-1920	22	14	,	,	PUNCT
cana-1920	22	15	double	double	ADJ
cana-1920	22	16	comet	comet	NOUN
cana-1920	22	17	ams	am	NOUN
cana-1920	22	18	classification	classification	NOUN
cana-1920	22	19	numbers	number	NOUN
cana-1920	22	20	:	:	PUNCT
cana-1920	22	21	05c05	05c05	NOUN
cana-1920	22	22	,	,	PUNCT
cana-1920	22	23	05c07	05c07	NOUN
cana-1920	22	24	,	,	PUNCT
cana-1920	22	25	05c09	05c09	NUM
cana-1920	22	26	1	1	NUM
cana-1920	22	27	.	.	PUNCT
cana-1920	22	28	introduction	introduction	NOUN
cana-1920	22	29	mailto:jrantalan@clsu.edu.ph	mailto:jrantalan@clsu.edu.ph	NOUN
cana-1920	22	30	communications	communication	NOUN
cana-1920	22	31	on	on	ADP
cana-1920	22	32	applied	apply	VERB
cana-1920	22	33	nonlinear	nonlinear	ADJ
cana-1920	22	34	analysis	analysis	NOUN
cana-1920	22	35	issn	issn	NOUN
cana-1920	22	36	:	:	PUNCT
cana-1920	22	37	1074	1074	NUM
cana-1920	22	38	-	-	PUNCT
cana-1920	22	39	133x	133x	NUM
cana-1920	22	40	vol	vol	NOUN
cana-1920	22	41	32	32	NUM
cana-1920	22	42	no	no	NOUN
cana-1920	22	43	.	.	NOUN
cana-1920	22	44	3	3	NUM
cana-1920	22	45	(	(	PUNCT
cana-1920	22	46	2025	2025	NUM
cana-1920	22	47	)	)	PUNCT
cana-1920	22	48	72	72	NUM
cana-1920	22	49	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	22	50	in	in	ADP
cana-1920	22	51	this	this	DET
cana-1920	22	52	paper	paper	NOUN
cana-1920	22	53	,	,	PUNCT
cana-1920	22	54	the	the	DET
cana-1920	22	55	graphs	graph	NOUN
cana-1920	22	56	that	that	PRON
cana-1920	22	57	we	we	PRON
cana-1920	22	58	will	will	AUX
cana-1920	22	59	consider	consider	VERB
cana-1920	22	60	are	be	AUX
cana-1920	22	61	all	all	ADV
cana-1920	22	62	simple	simple	ADJ
cana-1920	22	63	,	,	PUNCT
cana-1920	22	64	connected	connect	VERB
cana-1920	22	65	,	,	PUNCT
cana-1920	22	66	and	and	CCONJ
cana-1920	22	67	finite	finite	PROPN
cana-1920	22	68	.	.	PUNCT
cana-1920	23	1	also	also	ADV
cana-1920	23	2	,	,	PUNCT
cana-1920	23	3	throughout	throughout	ADP
cana-1920	23	4	this	this	DET
cana-1920	23	5	paper	paper	NOUN
cana-1920	23	6	,	,	PUNCT
cana-1920	23	7	we	we	PRON
cana-1920	23	8	follow	follow	VERB
cana-1920	23	9	the	the	DET
cana-1920	23	10	common	common	ADJ
cana-1920	23	11	notation	notation	NOUN
cana-1920	23	12	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1920	23	13	)	)	PUNCT
cana-1920	23	14	and	and	CCONJ
cana-1920	23	15	𝐸(𝐺	𝐸(𝐺	PROPN
cana-1920	23	16	)	)	PUNCT
cana-1920	23	17	for	for	ADP
cana-1920	23	18	the	the	DET
cana-1920	23	19	vertex	vertex	NOUN
cana-1920	23	20	set	set	NOUN
cana-1920	23	21	and	and	CCONJ
cana-1920	23	22	edge	edge	NOUN
cana-1920	23	23	set	set	NOUN
cana-1920	23	24	of	of	ADP
cana-1920	23	25	a	a	DET
cana-1920	23	26	graph	graph	NOUN
cana-1920	23	27	𝐺	𝐺	NOUN
cana-1920	23	28	,	,	PUNCT
cana-1920	23	29	respectively	respectively	ADV
cana-1920	23	30	.	.	PUNCT
cana-1920	24	1	we	we	PRON
cana-1920	24	2	also	also	ADV
cana-1920	24	3	have	have	AUX
cana-1920	24	4	adapted	adapt	VERB
cana-1920	24	5	the	the	DET
cana-1920	24	6	graph	graph	NOUN
cana-1920	24	7	theory	theory	NOUN
cana-1920	24	8	notations	notation	NOUN
cana-1920	24	9	used	use	VERB
cana-1920	24	10	by	by	ADP
cana-1920	24	11	wagner	wagner	PROPN
cana-1920	24	12	and	and	CCONJ
cana-1920	24	13	wang	wang	PROPN
cana-1920	24	14	in	in	ADP
cana-1920	24	15	[	[	X
cana-1920	24	16	27	27	NUM
cana-1920	24	17	]	]	PUNCT
cana-1920	24	18	,	,	PUNCT
cana-1920	24	19	and	and	CCONJ
cana-1920	24	20	refer	refer	VERB
cana-1920	24	21	to	to	ADP
cana-1920	24	22	the	the	DET
cana-1920	24	23	same	same	ADJ
cana-1920	24	24	text	text	NOUN
cana-1920	24	25	,	,	PUNCT
cana-1920	24	26	for	for	ADP
cana-1920	24	27	any	any	DET
cana-1920	24	28	reader	reader	NOUN
cana-1920	24	29	who	who	PRON
cana-1920	24	30	needs	need	VERB
cana-1920	24	31	to	to	PART
cana-1920	24	32	recall	recall	VERB
cana-1920	24	33	some	some	DET
cana-1920	24	34	graph	graph	NOUN
cana-1920	24	35	-	-	PUNCT
cana-1920	24	36	theoretic	theoretic	ADJ
cana-1920	24	37	concepts	concept	NOUN
cana-1920	24	38	that	that	PRON
cana-1920	24	39	were	be	AUX
cana-1920	24	40	mentioned	mention	VERB
cana-1920	24	41	,	,	PUNCT
cana-1920	24	42	but	but	CCONJ
cana-1920	24	43	not	not	PART
cana-1920	24	44	explicitly	explicitly	ADV
cana-1920	24	45	discussed	discuss	VERB
cana-1920	24	46	in	in	ADP
cana-1920	24	47	detail	detail	NOUN
cana-1920	24	48	in	in	ADP
cana-1920	24	49	this	this	DET
cana-1920	24	50	paper	paper	NOUN
cana-1920	24	51	.	.	PUNCT
cana-1920	25	1	in	in	ADP
cana-1920	25	2	cgt	cgt	PROPN
cana-1920	25	3	,	,	PUNCT
cana-1920	25	4	the	the	DET
cana-1920	25	5	atoms	atom	NOUN
cana-1920	25	6	of	of	ADP
cana-1920	25	7	a	a	DET
cana-1920	25	8	chemical	chemical	NOUN
cana-1920	25	9	compound	compound	NOUN
cana-1920	25	10	and	and	CCONJ
cana-1920	25	11	the	the	DET
cana-1920	25	12	bonds	bond	NOUN
cana-1920	25	13	connecting	connect	VERB
cana-1920	25	14	them	they	PRON
cana-1920	25	15	are	be	AUX
cana-1920	25	16	expressed	express	VERB
cana-1920	25	17	respectively	respectively	ADV
cana-1920	25	18	as	as	ADP
cana-1920	25	19	vertices	vertex	NOUN
cana-1920	25	20	and	and	CCONJ
cana-1920	25	21	edges	edge	NOUN
cana-1920	25	22	of	of	ADP
cana-1920	25	23	a	a	DET
cana-1920	25	24	graph	graph	NOUN
cana-1920	25	25	,	,	PUNCT
cana-1920	25	26	thereby	thereby	ADV
cana-1920	25	27	obtaining	obtain	VERB
cana-1920	25	28	its	its	PRON
cana-1920	25	29	molecular	molecular	ADJ
cana-1920	25	30	graph	graph	NOUN
cana-1920	25	31	.	.	PUNCT
cana-1920	26	1	under	under	ADP
cana-1920	26	2	this	this	DET
cana-1920	26	3	representation	representation	NOUN
cana-1920	26	4	,	,	PUNCT
cana-1920	26	5	the	the	DET
cana-1920	26	6	vertices	vertex	NOUN
cana-1920	26	7	corresponding	correspond	VERB
cana-1920	26	8	to	to	ADP
cana-1920	26	9	hydrogen	hydrogen	NOUN
cana-1920	26	10	atoms	atom	NOUN
cana-1920	26	11	are	be	AUX
cana-1920	26	12	usually	usually	ADV
cana-1920	26	13	removed	remove	VERB
cana-1920	26	14	since	since	SCONJ
cana-1920	26	15	the	the	DET
cana-1920	26	16	valency	valency	NOUN
cana-1920	26	17	or	or	CCONJ
cana-1920	26	18	degree	degree	NOUN
cana-1920	26	19	of	of	ADP
cana-1920	26	20	hydrogen	hydrogen	NOUN
cana-1920	26	21	is	be	AUX
cana-1920	26	22	one	one	NUM
cana-1920	26	23	.	.	PUNCT
cana-1920	27	1	for	for	ADP
cana-1920	27	2	example	example	NOUN
cana-1920	27	3	,	,	PUNCT
cana-1920	27	4	the	the	DET
cana-1920	27	5	ball	ball	NOUN
cana-1920	27	6	and	and	CCONJ
cana-1920	27	7	stick	stick	NOUN
cana-1920	27	8	chemical	chemical	NOUN
cana-1920	27	9	structure	structure	NOUN
cana-1920	27	10	of	of	ADP
cana-1920	27	11	2,2,4,4	2,2,4,4	NUM
cana-1920	27	12	-	-	PUNCT
cana-1920	27	13	tetramethylpentane	tetramethylpentane	NOUN
cana-1920	27	14	(	(	PUNCT
cana-1920	27	15	c9h20	c9h20	PROPN
cana-1920	27	16	)	)	PUNCT
cana-1920	27	17	in	in	ADP
cana-1920	27	18	figure	figure	NOUN
cana-1920	27	19	1a	1a	PROPN
cana-1920	27	20	has	have	VERB
cana-1920	27	21	a	a	DET
cana-1920	27	22	corresponding	corresponding	ADJ
cana-1920	27	23	molecular	molecular	ADJ
cana-1920	27	24	graph	graph	NOUN
cana-1920	27	25	shown	show	VERB
cana-1920	27	26	in	in	ADP
cana-1920	27	27	figure	figure	NOUN
cana-1920	27	28	1b	1b	NUM
cana-1920	27	29	.	.	PUNCT
cana-1920	28	1	figure	figure	VERB
cana-1920	28	2	1	1	NUM
cana-1920	28	3	:	:	PUNCT
cana-1920	28	4	(	(	PUNCT
cana-1920	28	5	a)the	a)the	DET
cana-1920	28	6	ball	ball	NOUN
cana-1920	28	7	and	and	CCONJ
cana-1920	28	8	stick	stick	NOUN
cana-1920	28	9	structure	structure	NOUN
cana-1920	28	10	of	of	ADP
cana-1920	28	11	2,2,4,4	2,2,4,4	NUM
cana-1920	28	12	-	-	PUNCT
cana-1920	28	13	tetramethylpentane	tetramethylpentane	NOUN
cana-1920	28	14	c9h20	c9h20	PROPN
cana-1920	28	15	taken	take	VERB
cana-1920	28	16	from	from	ADP
cana-1920	28	17	pubchem	pubchem	NOUN
cana-1920	28	18	[	[	X
cana-1920	28	19	1	1	NUM
cana-1920	28	20	]	]	PUNCT
cana-1920	28	21	.	.	PUNCT
cana-1920	29	1	(	(	PUNCT
cana-1920	29	2	b	b	X
cana-1920	29	3	)	)	PUNCT
cana-1920	29	4	the	the	DET
cana-1920	29	5	molecular	molecular	ADJ
cana-1920	29	6	graph	graph	NOUN
cana-1920	29	7	of	of	ADP
cana-1920	29	8	2,2,4,4	2,2,4,4	NUM
cana-1920	29	9	-	-	PUNCT
cana-1920	29	10	tetramethylpentane	tetramethylpentane	NOUN
cana-1920	29	11	.	.	PUNCT
cana-1920	30	1	once	once	ADV
cana-1920	30	2	the	the	DET
cana-1920	30	3	molecular	molecular	ADJ
cana-1920	30	4	graph	graph	NOUN
cana-1920	30	5	of	of	ADP
cana-1920	30	6	a	a	DET
cana-1920	30	7	chemical	chemical	NOUN
cana-1920	30	8	compound	compound	NOUN
cana-1920	30	9	has	have	AUX
cana-1920	30	10	been	be	AUX
cana-1920	30	11	obtained	obtain	VERB
cana-1920	30	12	,	,	PUNCT
cana-1920	30	13	one	one	PRON
cana-1920	30	14	can	can	AUX
cana-1920	30	15	now	now	ADV
cana-1920	30	16	use	use	VERB
cana-1920	30	17	graph	graph	NOUN
cana-1920	30	18	theoretic	theoretic	ADJ
cana-1920	30	19	concepts	concept	NOUN
cana-1920	30	20	and	and	CCONJ
cana-1920	30	21	techniques	technique	NOUN
cana-1920	30	22	to	to	PART
cana-1920	30	23	determine	determine	VERB
cana-1920	30	24	various	various	ADJ
cana-1920	30	25	topological	topological	ADJ
cana-1920	30	26	indices	index	NOUN
cana-1920	30	27	associated	associate	VERB
cana-1920	30	28	with	with	ADP
cana-1920	30	29	the	the	DET
cana-1920	30	30	compound	compound	NOUN
cana-1920	30	31	.	.	PUNCT
cana-1920	31	1	a	a	DET
cana-1920	31	2	topological	topological	ADJ
cana-1920	31	3	index	index	NOUN
cana-1920	31	4	is	be	AUX
cana-1920	31	5	a	a	DET
cana-1920	31	6	computed	computed	ADJ
cana-1920	31	7	numerical	numerical	ADJ
cana-1920	31	8	value	value	NOUN
cana-1920	31	9	associated	associate	VERB
cana-1920	31	10	with	with	ADP
cana-1920	31	11	the	the	DET
cana-1920	31	12	molecular	molecular	ADJ
cana-1920	31	13	graph	graph	NOUN
cana-1920	31	14	that	that	PRON
cana-1920	31	15	has	have	VERB
cana-1920	31	16	predictive	predictive	ADJ
cana-1920	31	17	power	power	NOUN
cana-1920	31	18	for	for	ADP
cana-1920	31	19	the	the	DET
cana-1920	31	20	chemical	chemical	NOUN
cana-1920	31	21	properties	property	NOUN
cana-1920	31	22	of	of	ADP
cana-1920	31	23	the	the	DET
cana-1920	31	24	chemical	chemical	NOUN
cana-1920	31	25	compound	compound	NOUN
cana-1920	31	26	.	.	PUNCT
cana-1920	32	1	topological	topological	ADJ
cana-1920	32	2	indices	index	NOUN
cana-1920	32	3	may	may	AUX
cana-1920	32	4	be	be	AUX
cana-1920	32	5	classified	classify	VERB
cana-1920	32	6	according	accord	VERB
cana-1920	32	7	to	to	ADP
cana-1920	32	8	the	the	DET
cana-1920	32	9	graph	graph	NOUN
cana-1920	32	10	property	property	NOUN
cana-1920	32	11	in	in	ADP
cana-1920	32	12	which	which	PRON
cana-1920	32	13	they	they	PRON
cana-1920	32	14	are	be	AUX
cana-1920	32	15	defined	define	VERB
cana-1920	32	16	.	.	PUNCT
cana-1920	33	1	it	it	PRON
cana-1920	33	2	is	be	AUX
cana-1920	33	3	said	say	VERB
cana-1920	33	4	to	to	PART
cana-1920	33	5	be	be	AUX
cana-1920	33	6	distance	distance	NOUN
cana-1920	33	7	-	-	PUNCT
cana-1920	33	8	based	base	VERB
cana-1920	33	9	,	,	PUNCT
cana-1920	33	10	if	if	SCONJ
cana-1920	33	11	it	it	PRON
cana-1920	33	12	is	be	AUX
cana-1920	33	13	derived	derive	VERB
cana-1920	33	14	based	base	VERB
cana-1920	33	15	on	on	ADP
cana-1920	33	16	the	the	DET
cana-1920	33	17	concept	concept	NOUN
cana-1920	33	18	of	of	ADP
cana-1920	33	19	distance	distance	NOUN
cana-1920	33	20	between	between	ADP
cana-1920	33	21	each	each	DET
cana-1920	33	22	pair	pair	NOUN
cana-1920	33	23	of	of	ADP
cana-1920	33	24	vertices	vertex	NOUN
cana-1920	33	25	in	in	ADP
cana-1920	33	26	the	the	DET
cana-1920	33	27	graph	graph	NOUN
cana-1920	33	28	.	.	PUNCT
cana-1920	34	1	on	on	ADP
cana-1920	34	2	the	the	DET
cana-1920	34	3	other	other	ADJ
cana-1920	34	4	hand	hand	NOUN
cana-1920	34	5	,	,	PUNCT
cana-1920	34	6	a	a	DET
cana-1920	34	7	topological	topological	ADJ
cana-1920	34	8	index	index	NOUN
cana-1920	34	9	is	be	AUX
cana-1920	34	10	vertex	vertex	NOUN
cana-1920	34	11	degree	degree	NOUN
cana-1920	34	12	-	-	PUNCT
cana-1920	34	13	based	base	VERB
cana-1920	34	14	,	,	PUNCT
cana-1920	34	15	if	if	SCONJ
cana-1920	34	16	it	it	PRON
cana-1920	34	17	is	be	AUX
cana-1920	34	18	defined	define	VERB
cana-1920	34	19	based	base	VERB
cana-1920	34	20	on	on	ADP
cana-1920	34	21	the	the	DET
cana-1920	34	22	degree	degree	NOUN
cana-1920	34	23	of	of	ADP
cana-1920	34	24	the	the	DET
cana-1920	34	25	vertices	vertex	NOUN
cana-1920	34	26	in	in	ADP
cana-1920	34	27	the	the	DET
cana-1920	34	28	graph	graph	NOUN
cana-1920	34	29	.	.	PUNCT
cana-1920	35	1	one	one	NUM
cana-1920	35	2	popular	popular	ADJ
cana-1920	35	3	topological	topological	ADJ
cana-1920	35	4	index	index	NOUN
cana-1920	35	5	based	base	VERB
cana-1920	35	6	on	on	ADP
cana-1920	35	7	distance	distance	NOUN
cana-1920	35	8	is	be	AUX
cana-1920	35	9	the	the	DET
cana-1920	35	10	wiener	wiener	NOUN
cana-1920	35	11	index	index	NOUN
cana-1920	35	12	denoted	denote	VERB
cana-1920	35	13	by	by	ADP
cana-1920	35	14	w	w	PROPN
cana-1920	35	15	(	(	PUNCT
cana-1920	35	16	·	·	PUNCT
cana-1920	35	17	)	)	PUNCT
cana-1920	35	18	.	.	PUNCT
cana-1920	36	1	for	for	ADP
cana-1920	36	2	a	a	DET
cana-1920	36	3	graph	graph	NOUN
cana-1920	36	4	𝐺	𝐺	NOUN
cana-1920	36	5	,	,	PUNCT
cana-1920	36	6	its	its	PRON
cana-1920	36	7	wiener	wiener	NOUN
cana-1920	36	8	index	index	NOUN
cana-1920	36	9	is	be	AUX
cana-1920	36	10	defined	define	VERB
cana-1920	36	11	as	as	ADP
cana-1920	36	12	“	"	PUNCT
cana-1920	36	13	w(g	w(g	PROPN
cana-1920	36	14	)	)	PUNCT
cana-1920	36	15	=	=	SYM
cana-1920	37	1	∑	∑	PUNCT
cana-1920	37	2	d(u	d(u	PROPN
cana-1920	37	3	,	,	PUNCT
cana-1920	37	4	v	v	NOUN
cana-1920	37	5	)	)	PUNCT
cana-1920	37	6	”	"	PUNCT
cana-1920	37	7	,	,	PUNCT
cana-1920	37	8	{	{	PUNCT
cana-1920	37	9	u	u	NOUN
cana-1920	37	10	,	,	PUNCT
cana-1920	37	11	v}⊆v(g	v}⊆v(g	ADJ
cana-1920	37	12	)	)	PUNCT
cana-1920	37	13	wherein	wherein	SCONJ
cana-1920	37	14	the	the	DET
cana-1920	37	15	notation	notation	PROPN
cana-1920	37	16	d(u	d(u	PROPN
cana-1920	37	17	,	,	PUNCT
cana-1920	37	18	v	v	NOUN
cana-1920	37	19	)	)	PUNCT
cana-1920	37	20	refers	refer	VERB
cana-1920	37	21	to	to	ADP
cana-1920	37	22	the	the	DET
cana-1920	37	23	distance	distance	NOUN
cana-1920	37	24	between	between	ADP
cana-1920	37	25	the	the	DET
cana-1920	37	26	vertices	vertex	NOUN
cana-1920	37	27	u	u	NOUN
cana-1920	37	28	and	and	CCONJ
cana-1920	37	29	v	v	NOUN
cana-1920	37	30	in	in	ADP
cana-1920	37	31	𝐺.	𝐺.	NOUN
cana-1920	37	32	this	this	DET
cana-1920	37	33	index	index	NOUN
cana-1920	37	34	was	be	AUX
cana-1920	37	35	named	name	VERB
cana-1920	37	36	after	after	ADP
cana-1920	37	37	harry	harry	PROPN
cana-1920	37	38	wiener	wiener	PROPN
cana-1920	37	39	,	,	PUNCT
cana-1920	37	40	a	a	DET
cana-1920	37	41	chemist	chemist	NOUN
cana-1920	37	42	who	who	PRON
cana-1920	37	43	proposed	propose	VERB
cana-1920	37	44	this	this	DET
cana-1920	37	45	concept	concept	NOUN
cana-1920	37	46	in	in	ADP
cana-1920	37	47	1947	1947	NUM
cana-1920	37	48	[	[	X
cana-1920	37	49	29	29	NUM
cana-1920	37	50	]	]	PUNCT
cana-1920	37	51	.	.	PUNCT
cana-1920	38	1	since	since	SCONJ
cana-1920	38	2	the	the	DET
cana-1920	38	3	publication	publication	NOUN
cana-1920	38	4	of	of	ADP
cana-1920	38	5	this	this	DET
cana-1920	38	6	work	work	NOUN
cana-1920	38	7	by	by	ADP
cana-1920	38	8	wiener	wiener	NOUN
cana-1920	38	9	,	,	PUNCT
cana-1920	38	10	various	various	ADJ
cana-1920	38	11	studies	study	NOUN
cana-1920	38	12	related	relate	VERB
cana-1920	38	13	to	to	ADP
cana-1920	38	14	this	this	DET
cana-1920	38	15	index	index	NOUN
cana-1920	38	16	have	have	AUX
cana-1920	38	17	been	be	AUX
cana-1920	38	18	conducted	conduct	VERB
cana-1920	38	19	with	with	ADP
cana-1920	38	20	the	the	DET
cana-1920	38	21	recent	recent	ADJ
cana-1920	38	22	works	work	NOUN
cana-1920	38	23	provided	provide	VERB
cana-1920	38	24	in	in	ADP
cana-1920	38	25	[	[	X
cana-1920	38	26	4	4	NUM
cana-1920	38	27	,	,	PUNCT
cana-1920	38	28	5	5	NUM
cana-1920	38	29	,	,	PUNCT
cana-1920	38	30	7	7	NUM
cana-1920	38	31	,	,	PUNCT
cana-1920	38	32	6	6	NUM
cana-1920	38	33	,	,	PUNCT
cana-1920	38	34	8	8	NUM
cana-1920	38	35	,	,	PUNCT
cana-1920	38	36	9	9	NUM
cana-1920	38	37	,	,	PUNCT
cana-1920	38	38	11	11	NUM
cana-1920	38	39	,	,	PUNCT
cana-1920	38	40	20	20	NUM
cana-1920	38	41	,	,	PUNCT
cana-1920	38	42	21	21	NUM
cana-1920	38	43	,	,	PUNCT
cana-1920	38	44	31	31	NUM
cana-1920	38	45	]	]	PUNCT
cana-1920	38	46	.	.	PUNCT
cana-1920	39	1	an	an	DET
cana-1920	39	2	example	example	NOUN
cana-1920	39	3	of	of	ADP
cana-1920	39	4	a	a	DET
cana-1920	39	5	topological	topological	ADJ
cana-1920	39	6	index	index	NOUN
cana-1920	39	7	based	base	VERB
cana-1920	39	8	on	on	ADP
cana-1920	39	9	vertex	vertex	NOUN
cana-1920	39	10	degree	degree	NOUN
cana-1920	39	11	is	be	AUX
cana-1920	39	12	the	the	DET
cana-1920	39	13	randic	randic	ADJ
cana-1920	39	14	index	index	NOUN
cana-1920	39	15	and	and	CCONJ
cana-1920	39	16	its	its	PRON
cana-1920	39	17	generalization	generalization	NOUN
cana-1920	39	18	denoted	denote	VERB
cana-1920	39	19	by	by	ADP
cana-1920	39	20	r	r	PROPN
cana-1920	39	21	(	(	PUNCT
cana-1920	39	22	·	·	PUNCT
cana-1920	39	23	)	)	PUNCT
cana-1920	39	24	and	and	CCONJ
cana-1920	39	25	rα	rα	ADJ
cana-1920	39	26	(	(	PUNCT
cana-1920	39	27	·	·	PUNCT
cana-1920	39	28	)	)	PUNCT
cana-1920	39	29	respectively	respectively	ADV
cana-1920	39	30	,	,	PUNCT
cana-1920	39	31	where	where	SCONJ
cana-1920	39	32	α	α	NOUN
cana-1920	39	33	≠	≠	PROPN
cana-1920	39	34	0	0	X
cana-1920	39	35	.	.	PUNCT
cana-1920	40	1	if	if	SCONJ
cana-1920	40	2	𝐺	𝐺	PROPN
cana-1920	40	3	is	be	AUX
cana-1920	40	4	a	a	DET
cana-1920	40	5	graph	graph	NOUN
cana-1920	40	6	,	,	PUNCT
cana-1920	40	7	then	then	ADV
cana-1920	40	8	its	its	PRON
cana-1920	40	9	generalized	generalized	ADJ
cana-1920	40	10	randic	randic	ADJ
cana-1920	40	11	index	index	NOUN
cana-1920	40	12	is	be	AUX
cana-1920	40	13	given	give	VERB
cana-1920	40	14	by	by	ADP
cana-1920	40	15	“	"	PUNCT
cana-1920	40	16	rα(g	rα(g	X
cana-1920	40	17	)	)	PUNCT
cana-1920	40	18	=	=	PUNCT
cana-1920	41	1	∑	∑	PUNCT
cana-1920	41	2	[	[	X
cana-1920	41	3	degg(u)degg(v)]α	degg(u)degg(v)]α	PROPN
cana-1920	41	4	”	"	PUNCT
cana-1920	41	5	,	,	PUNCT
cana-1920	41	6	uv∈e(g	uv∈e(g	NOUN
cana-1920	41	7	)	)	PUNCT
cana-1920	41	8	communications	communication	NOUN
cana-1920	41	9	on	on	ADP
cana-1920	41	10	applied	apply	VERB
cana-1920	41	11	nonlinear	nonlinear	ADJ
cana-1920	41	12	analysis	analysis	NOUN
cana-1920	41	13	issn	issn	NOUN
cana-1920	41	14	:	:	PUNCT
cana-1920	41	15	1074	1074	NUM
cana-1920	41	16	-	-	PUNCT
cana-1920	41	17	133x	133x	NUM
cana-1920	41	18	vol	vol	NOUN
cana-1920	41	19	32	32	NUM
cana-1920	41	20	no	no	NOUN
cana-1920	41	21	.	.	NOUN
cana-1920	41	22	3	3	NUM
cana-1920	41	23	(	(	PUNCT
cana-1920	41	24	2025	2025	NUM
cana-1920	41	25	)	)	PUNCT
cana-1920	41	26	73	73	NUM
cana-1920	41	27	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	41	28	wherein	wherein	ADJ
cana-1920	41	29	degg(u	degg(u	PROPN
cana-1920	41	30	)	)	PUNCT
cana-1920	41	31	and	and	CCONJ
cana-1920	41	32	degg(v	degg(v	PROPN
cana-1920	41	33	)	)	PUNCT
cana-1920	41	34	refers	refer	VERB
cana-1920	41	35	to	to	ADP
cana-1920	41	36	the	the	DET
cana-1920	41	37	degrees	degree	NOUN
cana-1920	41	38	of	of	ADP
cana-1920	41	39	vertices	vertex	NOUN
cana-1920	41	40	u	u	NOUN
cana-1920	41	41	and	and	CCONJ
cana-1920	41	42	v	v	NOUN
cana-1920	41	43	in	in	ADP
cana-1920	41	44	g	g	NOUN
cana-1920	41	45	respectively	respectively	ADV
cana-1920	41	46	.	.	PUNCT
cana-1920	42	1	for	for	ADP
cana-1920	42	2	α	α	NOUN
cana-1920	42	3	=	=	SYM
cana-1920	42	4	−	−	PROPN
cana-1920	42	5	1	1	NUM
cana-1920	42	6	2	2	NUM
cana-1920	42	7	,	,	PUNCT
cana-1920	42	8	we	we	PRON
cana-1920	42	9	have	have	VERB
cana-1920	42	10	the	the	DET
cana-1920	42	11	“	"	PUNCT
cana-1920	42	12	randic	randic	ADJ
cana-1920	42	13	index	index	NOUN
cana-1920	42	14	”	"	PUNCT
cana-1920	42	15	while	while	SCONJ
cana-1920	42	16	for	for	ADP
cana-1920	42	17	α	α	NOUN
cana-1920	42	18	=	=	SYM
cana-1920	42	19	1	1	NUM
cana-1920	42	20	,	,	PUNCT
cana-1920	42	21	we	we	PRON
cana-1920	42	22	have	have	VERB
cana-1920	42	23	the	the	DET
cana-1920	42	24	“	"	PUNCT
cana-1920	42	25	second	second	ADJ
cana-1920	42	26	zagreb	zagreb	PROPN
cana-1920	42	27	index	index	PROPN
cana-1920	42	28	”	"	PUNCT
cana-1920	42	29	.	.	PUNCT
cana-1920	43	1	the	the	DET
cana-1920	43	2	randic	randic	ADJ
cana-1920	43	3	index	index	NOUN
cana-1920	43	4	was	be	AUX
cana-1920	43	5	named	name	VERB
cana-1920	43	6	after	after	ADP
cana-1920	43	7	milan	milan	PROPN
cana-1920	43	8	randic	randic	PROPN
cana-1920	43	9	who	who	PRON
cana-1920	43	10	proposed	propose	VERB
cana-1920	43	11	the	the	DET
cana-1920	43	12	index	index	NOUN
cana-1920	43	13	in	in	ADP
cana-1920	43	14	[	[	X
cana-1920	43	15	25	25	NUM
cana-1920	43	16	]	]	PUNCT
cana-1920	43	17	in	in	ADP
cana-1920	43	18	the	the	DET
cana-1920	43	19	year	year	NOUN
cana-1920	43	20	1975	1975	NUM
cana-1920	43	21	.	.	PUNCT
cana-1920	44	1	the	the	DET
cana-1920	44	2	second	second	PROPN
cana-1920	44	3	zagreb	zagreb	PROPN
cana-1920	44	4	index	index	PROPN
cana-1920	44	5	,	,	PUNCT
cana-1920	44	6	on	on	ADP
cana-1920	44	7	the	the	DET
cana-1920	44	8	other	other	ADJ
cana-1920	44	9	hand	hand	NOUN
cana-1920	44	10	,	,	PUNCT
cana-1920	44	11	was	be	AUX
cana-1920	44	12	introduced	introduce	VERB
cana-1920	44	13	by	by	ADP
cana-1920	44	14	ivan	ivan	PROPN
cana-1920	44	15	gutman	gutman	PROPN
cana-1920	44	16	and	and	CCONJ
cana-1920	44	17	nenad	nenad	PROPN
cana-1920	44	18	trinajstic	trinajstic	PROPN
cana-1920	44	19	in	in	ADP
cana-1920	44	20	1972	1972	NUM
cana-1920	44	21	and	and	CCONJ
cana-1920	44	22	first	first	ADV
cana-1920	44	23	appeared	appear	VERB
cana-1920	44	24	in	in	ADP
cana-1920	44	25	[	[	X
cana-1920	44	26	13	13	NUM
cana-1920	44	27	]	]	PUNCT
cana-1920	44	28	.	.	PUNCT
cana-1920	45	1	these	these	DET
cana-1920	45	2	two	two	NUM
cana-1920	45	3	vertex	vertex	NOUN
cana-1920	45	4	degree	degree	NOUN
cana-1920	45	5	-	-	PUNCT
cana-1920	45	6	based	base	VERB
cana-1920	45	7	indices	index	NOUN
cana-1920	45	8	have	have	AUX
cana-1920	45	9	been	be	AUX
cana-1920	45	10	constantly	constantly	ADV
cana-1920	45	11	considered	consider	VERB
cana-1920	45	12	as	as	ADP
cana-1920	45	13	a	a	DET
cana-1920	45	14	topic	topic	NOUN
cana-1920	45	15	of	of	ADP
cana-1920	45	16	study	study	NOUN
cana-1920	45	17	,	,	PUNCT
cana-1920	45	18	and	and	CCONJ
cana-1920	45	19	are	be	AUX
cana-1920	45	20	being	be	AUX
cana-1920	45	21	used	use	VERB
cana-1920	45	22	in	in	ADP
cana-1920	45	23	the	the	DET
cana-1920	45	24	quantitative	quantitative	ADJ
cana-1920	45	25	structure	structure	NOUN
cana-1920	45	26	-	-	PUNCT
cana-1920	45	27	property	property	NOUN
cana-1920	45	28	relationships	relationship	NOUN
cana-1920	45	29	(	(	PUNCT
cana-1920	45	30	qspr	qspr	NOUN
cana-1920	45	31	)	)	PUNCT
cana-1920	45	32	modeling	modeling	NOUN
cana-1920	45	33	.	.	PUNCT
cana-1920	46	1	some	some	DET
cana-1920	46	2	recent	recent	ADJ
cana-1920	46	3	use	use	NOUN
cana-1920	46	4	of	of	ADP
cana-1920	46	5	randic	randic	ADJ
cana-1920	46	6	and	and	CCONJ
cana-1920	46	7	the	the	DET
cana-1920	46	8	second	second	ADJ
cana-1920	46	9	zagreb	zagreb	PROPN
cana-1920	46	10	index	index	NOUN
cana-1920	46	11	and	and	CCONJ
cana-1920	46	12	their	their	PRON
cana-1920	46	13	variations	variation	NOUN
cana-1920	46	14	for	for	ADP
cana-1920	46	15	qspr	qspr	NOUN
cana-1920	46	16	modeling	modeling	NOUN
cana-1920	46	17	can	can	AUX
cana-1920	46	18	be	be	AUX
cana-1920	46	19	shown	show	VERB
cana-1920	46	20	in	in	ADP
cana-1920	46	21	[	[	X
cana-1920	46	22	3	3	NUM
cana-1920	46	23	,	,	PUNCT
cana-1920	46	24	14	14	NUM
cana-1920	46	25	,	,	PUNCT
cana-1920	46	26	15	15	NUM
cana-1920	46	27	,	,	PUNCT
cana-1920	46	28	16	16	NUM
cana-1920	46	29	,	,	PUNCT
cana-1920	46	30	17	17	NUM
cana-1920	46	31	,	,	PUNCT
cana-1920	46	32	23	23	NUM
cana-1920	46	33	,	,	PUNCT
cana-1920	46	34	24	24	NUM
cana-1920	46	35	,	,	PUNCT
cana-1920	46	36	30	30	NUM
cana-1920	46	37	,	,	PUNCT
cana-1920	46	38	33	33	NUM
cana-1920	46	39	,	,	PUNCT
cana-1920	46	40	35	35	NUM
cana-1920	46	41	]	]	PUNCT
cana-1920	46	42	.	.	PUNCT
cana-1920	47	1	in	in	ADP
cana-1920	47	2	this	this	DET
cana-1920	47	3	study	study	NOUN
cana-1920	47	4	however	however	ADV
cana-1920	47	5	,	,	PUNCT
cana-1920	47	6	we	we	PRON
cana-1920	47	7	will	will	AUX
cana-1920	47	8	consider	consider	VERB
cana-1920	47	9	another	another	DET
cana-1920	47	10	type	type	NOUN
cana-1920	47	11	of	of	ADP
cana-1920	47	12	topological	topological	ADJ
cana-1920	47	13	indices	index	NOUN
cana-1920	47	14	which	which	PRON
cana-1920	47	15	are	be	AUX
cana-1920	47	16	dependent	dependent	ADJ
cana-1920	47	17	on	on	ADP
cana-1920	47	18	the	the	DET
cana-1920	47	19	“	"	PUNCT
cana-1920	47	20	reverse	reverse	ADJ
cana-1920	47	21	vertex	vertex	NOUN
cana-1920	47	22	-	-	PUNCT
cana-1920	47	23	degree	degree	NOUN
cana-1920	47	24	”	"	PUNCT
cana-1920	47	25	of	of	ADP
cana-1920	47	26	a	a	DET
cana-1920	47	27	vertex	vertex	NOUN
cana-1920	47	28	in	in	ADP
cana-1920	47	29	a	a	DET
cana-1920	47	30	graph	graph	NOUN
cana-1920	47	31	.	.	PUNCT
cana-1920	48	1	suppose	suppose	VERB
cana-1920	48	2	𝐺	𝐺	PROPN
cana-1920	48	3	is	be	AUX
cana-1920	48	4	a	a	DET
cana-1920	48	5	graph	graph	NOUN
cana-1920	48	6	with	with	ADP
cana-1920	48	7	maximum	maximum	ADJ
cana-1920	48	8	vertex	vertex	NOUN
cana-1920	48	9	degree	degree	NOUN
cana-1920	48	10	∆(g	∆(g	NOUN
cana-1920	48	11	)	)	PUNCT
cana-1920	48	12	.	.	PUNCT
cana-1920	49	1	for	for	ADP
cana-1920	49	2	any	any	DET
cana-1920	49	3	vertex	vertex	NOUN
cana-1920	49	4	u	u	NOUN
cana-1920	49	5	in	in	ADP
cana-1920	49	6	g	g	PROPN
cana-1920	49	7	,	,	PUNCT
cana-1920	49	8	its	its	PRON
cana-1920	49	9	reverse	reverse	ADJ
cana-1920	49	10	vertex	vertex	NOUN
cana-1920	49	11	degree	degree	NOUN
cana-1920	49	12	,	,	PUNCT
cana-1920	49	13	denoted	denote	VERB
cana-1920	49	14	by	by	ADP
cana-1920	49	15	ru	ru	PROPN
cana-1920	49	16	is	be	AUX
cana-1920	49	17	the	the	DET
cana-1920	49	18	quantity	quantity	NOUN
cana-1920	49	19	∆(g)−degg(u)+1	∆(g)−degg(u)+1	NOUN
cana-1920	49	20	,	,	PUNCT
cana-1920	49	21	that	that	ADV
cana-1920	49	22	is	is	ADV
cana-1920	49	23	,	,	PUNCT
cana-1920	49	24	“	"	PUNCT
cana-1920	49	25	ru	ru	NOUN
cana-1920	49	26	=	=	SYM
cana-1920	49	27	∆(g	∆(g	PROPN
cana-1920	49	28	)	)	PUNCT
cana-1920	49	29	−	−	PROPN
cana-1920	49	30	degg(u)+1	degg(u)+1	NOUN
cana-1920	49	31	”	"	PUNCT
cana-1920	49	32	.	.	PUNCT
cana-1920	50	1	this	this	DET
cana-1920	50	2	concept	concept	NOUN
cana-1920	50	3	was	be	AUX
cana-1920	50	4	introduced	introduce	VERB
cana-1920	50	5	by	by	ADP
cana-1920	50	6	kulli	kulli	PROPN
cana-1920	50	7	in	in	ADP
cana-1920	50	8	2018	2018	NUM
cana-1920	50	9	,	,	PUNCT
cana-1920	50	10	where	where	SCONJ
cana-1920	50	11	he	he	PRON
cana-1920	50	12	computed	compute	VERB
cana-1920	50	13	the	the	DET
cana-1920	50	14	reverse	reverse	ADJ
cana-1920	50	15	zagreb	zagreb	PROPN
cana-1920	50	16	and	and	CCONJ
cana-1920	50	17	reverse	reverse	VERB
cana-1920	50	18	hyper	hyper	ADJ
cana-1920	50	19	-	-	ADJ
cana-1920	50	20	zagreb	zagreb	PROPN
cana-1920	50	21	index	index	NOUN
cana-1920	50	22	of	of	ADP
cana-1920	50	23	rhombus	rhombus	ADJ
cana-1920	50	24	silicate	silicate	NOUN
cana-1920	50	25	networks	network	NOUN
cana-1920	50	26	[	[	X
cana-1920	50	27	18	18	NUM
cana-1920	50	28	]	]	PUNCT
cana-1920	50	29	.	.	PUNCT
cana-1920	51	1	since	since	SCONJ
cana-1920	51	2	then	then	ADV
cana-1920	51	3	,	,	PUNCT
cana-1920	51	4	various	various	ADJ
cana-1920	51	5	research	research	NOUN
cana-1920	51	6	works	work	VERB
cana-1920	51	7	on	on	ADP
cana-1920	51	8	the	the	DET
cana-1920	51	9	determination	determination	NOUN
cana-1920	51	10	of	of	ADP
cana-1920	51	11	these	these	DET
cana-1920	51	12	types	type	NOUN
cana-1920	51	13	of	of	ADP
cana-1920	51	14	indices	index	NOUN
cana-1920	51	15	for	for	ADP
cana-1920	51	16	graphs	graph	NOUN
cana-1920	51	17	and	and	CCONJ
cana-1920	51	18	chemical	chemical	NOUN
cana-1920	51	19	materials	material	NOUN
cana-1920	51	20	have	have	AUX
cana-1920	51	21	been	be	AUX
cana-1920	51	22	conducted	conduct	VERB
cana-1920	51	23	.	.	PUNCT
cana-1920	52	1	these	these	DET
cana-1920	52	2	works	work	NOUN
cana-1920	52	3	can	can	AUX
cana-1920	52	4	be	be	AUX
cana-1920	52	5	viewed	view	VERB
cana-1920	52	6	in	in	ADP
cana-1920	52	7	[	[	X
cana-1920	52	8	2	2	NUM
cana-1920	52	9	,	,	PUNCT
cana-1920	52	10	19	19	NUM
cana-1920	52	11	,	,	PUNCT
cana-1920	52	12	22	22	NUM
cana-1920	52	13	,	,	PUNCT
cana-1920	52	14	26	26	NUM
cana-1920	52	15	,	,	PUNCT
cana-1920	52	16	28	28	NUM
cana-1920	52	17	,	,	PUNCT
cana-1920	52	18	32	32	NUM
cana-1920	52	19	,	,	PUNCT
cana-1920	52	20	34	34	NUM
cana-1920	52	21	,	,	PUNCT
cana-1920	52	22	36	36	NUM
cana-1920	52	23	]	]	PUNCT
cana-1920	52	24	and	and	CCONJ
cana-1920	52	25	were	be	AUX
cana-1920	52	26	discussed	discuss	VERB
cana-1920	52	27	by	by	ADP
cana-1920	52	28	gowtham	gowtham	PROPN
cana-1920	52	29	and	and	CCONJ
cana-1920	52	30	husin	husin	VERB
cana-1920	52	31	in	in	ADP
cana-1920	52	32	their	their	PRON
cana-1920	52	33	recent	recent	ADJ
cana-1920	52	34	research	research	NOUN
cana-1920	52	35	article	article	NOUN
cana-1920	52	36	[	[	X
cana-1920	52	37	12	12	NUM
cana-1920	52	38	]	]	X
cana-1920	52	39	,	,	PUNCT
cana-1920	52	40	which	which	PRON
cana-1920	52	41	is	be	AUX
cana-1920	52	42	the	the	DET
cana-1920	52	43	motivational	motivational	ADJ
cana-1920	52	44	work	work	NOUN
cana-1920	52	45	for	for	ADP
cana-1920	52	46	this	this	DET
cana-1920	52	47	research	research	NOUN
cana-1920	52	48	study	study	NOUN
cana-1920	52	49	.	.	PUNCT
cana-1920	53	1	gowtham	gowtham	PROPN
cana-1920	53	2	and	and	CCONJ
cana-1920	53	3	husin	husin	PROPN
cana-1920	53	4	computed	compute	VERB
cana-1920	53	5	some	some	DET
cana-1920	53	6	reverse	reverse	ADJ
cana-1920	53	7	vertex	vertex	NOUN
cana-1920	53	8	-	-	PUNCT
cana-1920	53	9	degree	degree	NOUN
cana-1920	53	10	-	-	PUNCT
cana-1920	53	11	based	base	VERB
cana-1920	53	12	topological	topological	ADJ
cana-1920	53	13	indices	index	NOUN
cana-1920	53	14	of	of	ADP
cana-1920	53	15	bistar	bistar	ADJ
cana-1920	53	16	graphs	graph	NOUN
cana-1920	53	17	which	which	PRON
cana-1920	53	18	is	be	AUX
cana-1920	53	19	an	an	DET
cana-1920	53	20	example	example	NOUN
cana-1920	53	21	of	of	ADP
cana-1920	53	22	a	a	DET
cana-1920	53	23	tree	tree	NOUN
cana-1920	53	24	[	[	X
cana-1920	53	25	12	12	NUM
cana-1920	53	26	]	]	PUNCT
cana-1920	53	27	.	.	PUNCT
cana-1920	54	1	trees	tree	NOUN
cana-1920	54	2	,	,	PUNCT
cana-1920	54	3	being	be	AUX
cana-1920	54	4	connected	connect	VERB
cana-1920	54	5	and	and	CCONJ
cana-1920	54	6	acyclic	acyclic	ADJ
cana-1920	54	7	,	,	PUNCT
cana-1920	54	8	have	have	AUX
cana-1920	54	9	been	be	AUX
cana-1920	54	10	an	an	DET
cana-1920	54	11	essential	essential	ADJ
cana-1920	54	12	class	class	NOUN
cana-1920	54	13	of	of	ADP
cana-1920	54	14	graphs	graph	NOUN
cana-1920	54	15	in	in	ADP
cana-1920	54	16	cgt	cgt	PROPN
cana-1920	54	17	.	.	PROPN
cana-1920	55	1	for	for	ADP
cana-1920	55	2	this	this	DET
cana-1920	55	3	study	study	NOUN
cana-1920	55	4	,	,	PUNCT
cana-1920	55	5	we	we	PRON
cana-1920	55	6	will	will	AUX
cana-1920	55	7	determine	determine	VERB
cana-1920	55	8	some	some	DET
cana-1920	55	9	reverse	reverse	ADJ
cana-1920	55	10	vertex	vertex	NOUN
cana-1920	55	11	degree	degree	NOUN
cana-1920	55	12	-	-	PUNCT
cana-1920	55	13	based	base	VERB
cana-1920	55	14	topological	topological	ADJ
cana-1920	55	15	indices	index	NOUN
cana-1920	55	16	of	of	ADP
cana-1920	55	17	other	other	ADJ
cana-1920	55	18	families	family	NOUN
cana-1920	55	19	of	of	ADP
cana-1920	55	20	trees	tree	NOUN
cana-1920	55	21	called	call	VERB
cana-1920	55	22	comets	comet	NOUN
cana-1920	55	23	and	and	CCONJ
cana-1920	55	24	double	double	ADJ
cana-1920	55	25	comets	comet	NOUN
cana-1920	55	26	.	.	PUNCT
cana-1920	56	1	2	2	X
cana-1920	56	2	.	.	X
cana-1920	56	3	preliminary	preliminary	ADJ
cana-1920	56	4	concepts	concept	NOUN
cana-1920	56	5	and	and	CCONJ
cana-1920	56	6	results	result	NOUN
cana-1920	56	7	we	we	PRON
cana-1920	56	8	will	will	AUX
cana-1920	56	9	briefly	briefly	ADV
cana-1920	56	10	discuss	discuss	VERB
cana-1920	56	11	the	the	DET
cana-1920	56	12	recent	recent	ADJ
cana-1920	56	13	research	research	NOUN
cana-1920	56	14	work	work	NOUN
cana-1920	56	15	of	of	ADP
cana-1920	56	16	gowtham	gowtham	PROPN
cana-1920	56	17	and	and	CCONJ
cana-1920	56	18	husin	husin	VERB
cana-1920	56	19	regarding	regard	VERB
cana-1920	56	20	some	some	DET
cana-1920	56	21	reverse	reverse	ADJ
cana-1920	56	22	vertex	vertex	NOUN
cana-1920	56	23	degree	degree	NOUN
cana-1920	56	24	-	-	PUNCT
cana-1920	56	25	based	base	VERB
cana-1920	56	26	topological	topological	ADJ
cana-1920	56	27	indices	index	NOUN
cana-1920	56	28	of	of	ADP
cana-1920	56	29	bistar	bistar	ADJ
cana-1920	56	30	graphs	graph	NOUN
cana-1920	56	31	[	[	X
cana-1920	56	32	12	12	NUM
cana-1920	56	33	]	]	PUNCT
cana-1920	56	34	.	.	PUNCT
cana-1920	57	1	moreover	moreover	ADV
cana-1920	57	2	,	,	PUNCT
cana-1920	57	3	essential	essential	ADJ
cana-1920	57	4	preliminary	preliminary	ADJ
cana-1920	57	5	results	result	NOUN
cana-1920	57	6	on	on	ADP
cana-1920	57	7	comets	comet	NOUN
cana-1920	57	8	and	and	CCONJ
cana-1920	57	9	double	double	ADJ
cana-1920	57	10	comets	comet	NOUN
cana-1920	57	11	will	will	AUX
cana-1920	57	12	also	also	ADV
cana-1920	57	13	be	be	AUX
cana-1920	57	14	discussed	discuss	VERB
cana-1920	57	15	which	which	PRON
cana-1920	57	16	will	will	AUX
cana-1920	57	17	be	be	AUX
cana-1920	57	18	used	use	VERB
cana-1920	57	19	in	in	ADP
cana-1920	57	20	the	the	DET
cana-1920	57	21	results	result	NOUN
cana-1920	57	22	section	section	NOUN
cana-1920	57	23	.	.	PUNCT
cana-1920	58	1	2.1	2.1	NUM
cana-1920	58	2	gowtham	gowtham	PROPN
cana-1920	58	3	and	and	CCONJ
cana-1920	58	4	husin	husin	PROPN
cana-1920	58	5	’s	’s	PART
cana-1920	58	6	results	result	NOUN
cana-1920	58	7	for	for	ADP
cana-1920	58	8	bistar	bistar	ADJ
cana-1920	58	9	graphs	graph	NOUN
cana-1920	58	10	a	a	DET
cana-1920	58	11	vertex	vertex	NOUN
cana-1920	58	12	u	u	NOUN
cana-1920	58	13	∈	∈	PROPN
cana-1920	58	14	v(g	v(g	PROPN
cana-1920	58	15	)	)	PUNCT
cana-1920	58	16	is	be	AUX
cana-1920	58	17	said	say	VERB
cana-1920	58	18	to	to	PART
cana-1920	58	19	be	be	AUX
cana-1920	58	20	a	a	DET
cana-1920	58	21	leaf	leaf	NOUN
cana-1920	58	22	if	if	SCONJ
cana-1920	58	23	degg(u	degg(u	NUM
cana-1920	58	24	)	)	PUNCT
cana-1920	58	25	=	=	SYM
cana-1920	59	1	1	1	X
cana-1920	59	2	.	.	PUNCT
cana-1920	59	3	a	a	DET
cana-1920	59	4	star	star	NOUN
cana-1920	59	5	of	of	ADP
cana-1920	59	6	order	order	NOUN
cana-1920	59	7	n+1	n+1	ADV
cana-1920	59	8	,	,	PUNCT
cana-1920	59	9	denote	denote	VERB
cana-1920	59	10	by	by	ADP
cana-1920	59	11	k1,n	k1,n	PROPN
cana-1920	59	12	is	be	AUX
cana-1920	59	13	a	a	DET
cana-1920	59	14	tree	tree	NOUN
cana-1920	59	15	with	with	ADP
cana-1920	59	16	n	n	DET
cana-1920	59	17	number	number	NOUN
cana-1920	59	18	of	of	ADP
cana-1920	59	19	leaves	leave	NOUN
cana-1920	59	20	and	and	CCONJ
cana-1920	59	21	a	a	DET
cana-1920	59	22	central	central	ADJ
cana-1920	59	23	vertex	vertex	NOUN
cana-1920	59	24	of	of	ADP
cana-1920	59	25	degree	degree	NOUN
cana-1920	59	26	n.	n.	PROPN
cana-1920	59	27	presented	present	VERB
cana-1920	59	28	in	in	ADP
cana-1920	59	29	figure	figure	NOUN
cana-1920	59	30	2	2	NUM
cana-1920	59	31	are	be	AUX
cana-1920	59	32	the	the	DET
cana-1920	59	33	stars	star	NOUN
cana-1920	59	34	k1,n	k1,n	PROPN
cana-1920	59	35	and	and	CCONJ
cana-1920	59	36	k1,m	k1,m	PROPN
cana-1920	59	37	respectively	respectively	ADV
cana-1920	59	38	.	.	PUNCT
cana-1920	60	1	figure	figure	NOUN
cana-1920	60	2	2	2	NUM
cana-1920	60	3	:	:	PUNCT
cana-1920	60	4	(	(	PUNCT
cana-1920	60	5	a	a	X
cana-1920	60	6	)	)	PUNCT
cana-1920	60	7	the	the	DET
cana-1920	60	8	star	star	NOUN
cana-1920	60	9	k1,n	k1,n	PROPN
cana-1920	60	10	.	.	PUNCT
cana-1920	61	1	(	(	PUNCT
cana-1920	61	2	b	b	X
cana-1920	61	3	)	)	PUNCT
cana-1920	61	4	the	the	DET
cana-1920	61	5	star	star	NOUN
cana-1920	61	6	k1,m	k1,m	PROPN
cana-1920	61	7	.	.	PUNCT
cana-1920	62	1	the	the	DET
cana-1920	62	2	bistar	bistar	PROPN
cana-1920	62	3	graph	graph	NOUN
cana-1920	62	4	denoted	denote	VERB
cana-1920	62	5	by	by	ADP
cana-1920	62	6	b(n;m	b(n;m	PROPN
cana-1920	62	7	)	)	PUNCT
cana-1920	62	8	is	be	AUX
cana-1920	62	9	a	a	DET
cana-1920	62	10	graph	graph	NOUN
cana-1920	62	11	obtained	obtain	VERB
cana-1920	62	12	by	by	ADP
cana-1920	62	13	connecting	connect	VERB
cana-1920	62	14	the	the	DET
cana-1920	62	15	centers	center	NOUN
cana-1920	62	16	of	of	ADP
cana-1920	62	17	two	two	NUM
cana-1920	62	18	star	star	NOUN
cana-1920	62	19	graphs	graph	NOUN
cana-1920	62	20	with	with	ADP
cana-1920	62	21	n	n	NOUN
cana-1920	62	22	and	and	CCONJ
cana-1920	62	23	m	m	ADJ
cana-1920	62	24	number	number	NOUN
cana-1920	62	25	of	of	ADP
cana-1920	62	26	leaves	leave	NOUN
cana-1920	62	27	respectively	respectively	ADV
cana-1920	62	28	by	by	ADP
cana-1920	62	29	an	an	DET
cana-1920	62	30	edge	edge	NOUN
cana-1920	62	31	.	.	PUNCT
cana-1920	63	1	the	the	DET
cana-1920	63	2	graph	graph	NOUN
cana-1920	63	3	b(n;m	b(n;m	PROPN
cana-1920	63	4	)	)	PUNCT
cana-1920	63	5	is	be	AUX
cana-1920	63	6	depicted	depict	VERB
cana-1920	63	7	in	in	ADP
cana-1920	63	8	figure	figure	NOUN
cana-1920	63	9	3	3	NUM
cana-1920	63	10	.	.	PUNCT
cana-1920	64	1	communications	communication	NOUN
cana-1920	64	2	on	on	ADP
cana-1920	64	3	applied	apply	VERB
cana-1920	64	4	nonlinear	nonlinear	ADJ
cana-1920	64	5	analysis	analysis	NOUN
cana-1920	64	6	issn	issn	NOUN
cana-1920	64	7	:	:	PUNCT
cana-1920	64	8	1074	1074	NUM
cana-1920	64	9	-	-	PUNCT
cana-1920	64	10	133x	133x	NUM
cana-1920	64	11	vol	vol	NOUN
cana-1920	64	12	32	32	NUM
cana-1920	64	13	no	no	NOUN
cana-1920	64	14	.	.	NOUN
cana-1920	64	15	3	3	NUM
cana-1920	64	16	(	(	PUNCT
cana-1920	64	17	2025	2025	NUM
cana-1920	64	18	)	)	PUNCT
cana-1920	64	19	74	74	NUM
cana-1920	64	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	64	21	figure	figure	NOUN
cana-1920	64	22	3	3	NUM
cana-1920	64	23	:	:	PUNCT
cana-1920	64	24	the	the	DET
cana-1920	64	25	bistar	bistar	NOUN
cana-1920	64	26	graph	graph	NOUN
cana-1920	64	27	b(n;m	b(n;m	PROPN
cana-1920	64	28	)	)	PUNCT
cana-1920	64	29	.	.	PUNCT
cana-1920	65	1	gowtham	gowtham	PROPN
cana-1920	65	2	and	and	CCONJ
cana-1920	65	3	husin	husin	PROPN
cana-1920	65	4	calculated	calculate	VERB
cana-1920	65	5	the	the	DET
cana-1920	65	6	following	follow	VERB
cana-1920	65	7	reverse	reverse	ADJ
cana-1920	65	8	vertex	vertex	NOUN
cana-1920	65	9	degree	degree	NOUN
cana-1920	65	10	-	-	PUNCT
cana-1920	65	11	based	base	VERB
cana-1920	65	12	topological	topological	ADJ
cana-1920	65	13	indices	index	NOUN
cana-1920	65	14	of	of	ADP
cana-1920	65	15	b(n;m	b(n;m	PROPN
cana-1920	65	16	):	):	PUNCT
cana-1920	65	17	reverse	reverse	ADJ
cana-1920	65	18	sum	sum	NOUN
cana-1920	65	19	-	-	PUNCT
cana-1920	65	20	connectivity	connectivity	NOUN
cana-1920	65	21	(	(	PUNCT
cana-1920	65	22	rsci	rsci	X
cana-1920	65	23	(	(	PUNCT
cana-1920	65	24	·	·	PUNCT
cana-1920	65	25	)	)	PUNCT
cana-1920	65	26	)	)	PUNCT
cana-1920	65	27	,	,	PUNCT
cana-1920	65	28	first	first	ADV
cana-1920	65	29	reverse	reverse	VERB
cana-1920	65	30	zagreb	zagreb	PROPN
cana-1920	65	31	(	(	PUNCT
cana-1920	65	32	rm1	rm1	PROPN
cana-1920	65	33	(	(	PUNCT
cana-1920	65	34	·	·	PUNCT
cana-1920	65	35	)	)	PUNCT
cana-1920	65	36	)	)	PUNCT
cana-1920	65	37	,	,	PUNCT
cana-1920	65	38	second	second	ADJ
cana-1920	65	39	reverse	reverse	ADJ
cana-1920	65	40	zagreb	zagreb	PROPN
cana-1920	65	41	(	(	PUNCT
cana-1920	65	42	rm2	rm2	PROPN
cana-1920	65	43	(	(	PUNCT
cana-1920	65	44	·	·	PUNCT
cana-1920	65	45	)	)	PUNCT
cana-1920	65	46	)	)	PUNCT
cana-1920	65	47	,	,	PUNCT
cana-1920	65	48	reverse	reverse	VERB
cana-1920	65	49	arithmetic	arithmetic	ADJ
cana-1920	65	50	-	-	PUNCT
cana-1920	65	51	geometric	geometric	ADJ
cana-1920	65	52	(	(	PUNCT
cana-1920	65	53	rag	rag	NOUN
cana-1920	65	54	(	(	PUNCT
cana-1920	65	55	·	·	PUNCT
cana-1920	65	56	)	)	PUNCT
cana-1920	65	57	)	)	PUNCT
cana-1920	65	58	,	,	PUNCT
cana-1920	65	59	reverse	reverse	VERB
cana-1920	65	60	geometric	geometric	ADJ
cana-1920	65	61	-	-	PUNCT
cana-1920	65	62	arithmetic	arithmetic	ADJ
cana-1920	65	63	(	(	PUNCT
cana-1920	65	64	rga	rga	PROPN
cana-1920	65	65	(	(	PUNCT
cana-1920	65	66	·	·	PUNCT
cana-1920	65	67	)	)	PUNCT
cana-1920	65	68	)	)	PUNCT
cana-1920	65	69	,	,	PUNCT
cana-1920	65	70	reverse	reverse	ADJ
cana-1920	65	71	sombor	sombor	NOUN
cana-1920	65	72	(	(	PUNCT
cana-1920	65	73	rso	rso	PROPN
cana-1920	65	74	(	(	PUNCT
cana-1920	65	75	·	·	PUNCT
cana-1920	65	76	)	)	PUNCT
cana-1920	65	77	)	)	PUNCT
cana-1920	65	78	,	,	PUNCT
cana-1920	65	79	and	and	CCONJ
cana-1920	65	80	reverse	reverse	VERB
cana-1920	65	81	nirmala	nirmala	PROPN
cana-1920	65	82	(	(	PUNCT
cana-1920	65	83	rn	rn	PROPN
cana-1920	65	84	(	(	PUNCT
cana-1920	65	85	·	·	PUNCT
cana-1920	65	86	)	)	PUNCT
cana-1920	65	87	)	)	PUNCT
cana-1920	65	88	in	in	ADP
cana-1920	65	89	[	[	X
cana-1920	65	90	12	12	NUM
cana-1920	65	91	]	]	PUNCT
cana-1920	65	92	.	.	PUNCT
cana-1920	66	1	their	their	PRON
cana-1920	66	2	results	result	NOUN
cana-1920	66	3	are	be	AUX
cana-1920	66	4	summarized	summarize	VERB
cana-1920	66	5	in	in	ADP
cana-1920	66	6	the	the	DET
cana-1920	66	7	table	table	NOUN
cana-1920	66	8	below	below	ADV
cana-1920	66	9	.	.	PUNCT
cana-1920	67	1	to	to	PART
cana-1920	67	2	eliminate	eliminate	VERB
cana-1920	67	3	cases	case	NOUN
cana-1920	67	4	,	,	PUNCT
cana-1920	67	5	we	we	PRON
cana-1920	67	6	introduce	introduce	VERB
cana-1920	67	7	the	the	DET
cana-1920	67	8	notations	notation	NOUN
cana-1920	67	9	m	m	VERB
cana-1920	67	10	=	=	SYM
cana-1920	67	11	max{m	max{m	NOUN
cana-1920	67	12	,	,	PUNCT
cana-1920	67	13	n	n	CCONJ
cana-1920	67	14	}	}	PUNCT
cana-1920	67	15	and	and	CCONJ
cana-1920	67	16	µ	µ	X
cana-1920	67	17	=	=	SYM
cana-1920	67	18	min{m	min{m	PROPN
cana-1920	67	19	,	,	PUNCT
cana-1920	67	20	n	n	CCONJ
cana-1920	67	21	}	}	PUNCT
cana-1920	67	22	.	.	PUNCT
cana-1920	68	1	table	table	NOUN
cana-1920	68	2	1	1	NUM
cana-1920	68	3	:	:	PUNCT
cana-1920	68	4	various	various	ADJ
cana-1920	68	5	reverse	reverse	ADJ
cana-1920	68	6	degree	degree	NOUN
cana-1920	68	7	-	-	PUNCT
cana-1920	68	8	based	base	VERB
cana-1920	68	9	topological	topological	ADJ
cana-1920	68	10	indices	index	NOUN
cana-1920	68	11	of	of	ADP
cana-1920	68	12	b(n;m	b(n;m	PROPN
cana-1920	68	13	)	)	PUNCT
cana-1920	68	14	obtained	obtain	VERB
cana-1920	68	15	by	by	ADP
cana-1920	68	16	gowtham	gowtham	PROPN
cana-1920	68	17	and	and	CCONJ
cana-1920	68	18	husin	husin	PROPN
cana-1920	68	19	.	.	PUNCT
cana-1920	69	1	motivated	motivate	VERB
cana-1920	69	2	by	by	ADP
cana-1920	69	3	the	the	DET
cana-1920	69	4	above	above	ADJ
cana-1920	69	5	results	result	NOUN
cana-1920	69	6	from	from	ADP
cana-1920	69	7	gowtham	gowtham	PROPN
cana-1920	69	8	and	and	CCONJ
cana-1920	69	9	husin	husin	PROPN
cana-1920	69	10	,	,	PUNCT
cana-1920	69	11	we	we	PRON
cana-1920	69	12	determine	determine	VERB
cana-1920	69	13	the	the	DET
cana-1920	69	14	same	same	ADJ
cana-1920	69	15	set	set	NOUN
cana-1920	69	16	of	of	ADP
cana-1920	69	17	topological	topological	ADJ
cana-1920	69	18	indices	index	NOUN
cana-1920	69	19	for	for	ADP
cana-1920	69	20	comets	comet	NOUN
cana-1920	69	21	and	and	CCONJ
cana-1920	69	22	double	double	ADJ
cana-1920	69	23	comets	comet	NOUN
cana-1920	69	24	in	in	ADP
cana-1920	69	25	this	this	DET
cana-1920	69	26	paper	paper	NOUN
cana-1920	69	27	.	.	PUNCT
cana-1920	70	1	2.2	2.2	NUM
cana-1920	70	2	.	.	PUNCT
cana-1920	71	1	reverse	reverse	ADJ
cana-1920	71	2	vertex	vertex	NOUN
cana-1920	71	3	degree	degree	NOUN
cana-1920	71	4	of	of	ADP
cana-1920	71	5	vertices	vertex	NOUN
cana-1920	71	6	of	of	ADP
cana-1920	71	7	comets	comet	NOUN
cana-1920	71	8	and	and	CCONJ
cana-1920	71	9	double	double	ADJ
cana-1920	71	10	comets	comet	NOUN
cana-1920	71	11	as	as	SCONJ
cana-1920	71	12	mentioned	mention	VERB
cana-1920	71	13	in	in	ADP
cana-1920	71	14	the	the	DET
cana-1920	71	15	previous	previous	ADJ
cana-1920	71	16	subsection	subsection	NOUN
cana-1920	71	17	,	,	PUNCT
cana-1920	71	18	this	this	DET
cana-1920	71	19	paper	paper	NOUN
cana-1920	71	20	will	will	AUX
cana-1920	71	21	investigate	investigate	VERB
cana-1920	71	22	several	several	ADJ
cana-1920	71	23	reverse	reverse	ADJ
cana-1920	71	24	vertex	vertex	NOUN
cana-1920	71	25	degreebased	degreebase	VERB
cana-1920	71	26	topological	topological	ADJ
cana-1920	71	27	indices	index	NOUN
cana-1920	71	28	of	of	ADP
cana-1920	71	29	comets	comet	NOUN
cana-1920	71	30	and	and	CCONJ
cana-1920	71	31	double	double	ADJ
cana-1920	71	32	comets	comet	NOUN
cana-1920	71	33	.	.	PUNCT
cana-1920	72	1	in	in	ADP
cana-1920	72	2	this	this	DET
cana-1920	72	3	subsection	subsection	NOUN
cana-1920	72	4	,	,	PUNCT
cana-1920	72	5	we	we	PRON
cana-1920	72	6	will	will	AUX
cana-1920	72	7	discuss	discuss	VERB
cana-1920	72	8	essential	essential	ADJ
cana-1920	72	9	preliminary	preliminary	ADJ
cana-1920	72	10	results	result	NOUN
cana-1920	72	11	on	on	ADP
cana-1920	72	12	comets	comet	NOUN
cana-1920	72	13	and	and	CCONJ
cana-1920	72	14	double	double	ADJ
cana-1920	72	15	comets	comet	NOUN
cana-1920	72	16	which	which	PRON
cana-1920	72	17	are	be	AUX
cana-1920	72	18	needed	need	VERB
cana-1920	72	19	for	for	ADP
cana-1920	72	20	the	the	DET
cana-1920	72	21	discussion	discussion	NOUN
cana-1920	72	22	of	of	ADP
cana-1920	72	23	main	main	ADJ
cana-1920	72	24	results	result	NOUN
cana-1920	72	25	.	.	PUNCT
cana-1920	73	1	we	we	PRON
cana-1920	73	2	begin	begin	VERB
cana-1920	73	3	by	by	ADP
cana-1920	73	4	providing	provide	VERB
cana-1920	73	5	the	the	DET
cana-1920	73	6	definition	definition	NOUN
cana-1920	73	7	of	of	ADP
cana-1920	73	8	a	a	DET
cana-1920	73	9	path	path	NOUN
cana-1920	73	10	.	.	PUNCT
cana-1920	74	1	a	a	DET
cana-1920	74	2	path	path	NOUN
cana-1920	74	3	with	with	ADP
cana-1920	74	4	n	n	CCONJ
cana-1920	74	5	number	number	NOUN
cana-1920	74	6	of	of	ADP
cana-1920	74	7	vertices	vertex	NOUN
cana-1920	74	8	,	,	PUNCT
cana-1920	74	9	denoted	denote	VERB
cana-1920	74	10	by	by	ADP
cana-1920	74	11	pn	pn	PROPN
cana-1920	74	12	is	be	AUX
cana-1920	74	13	the	the	DET
cana-1920	74	14	unique	unique	ADJ
cana-1920	74	15	tree	tree	NOUN
cana-1920	74	16	with	with	ADP
cana-1920	74	17	only	only	ADV
cana-1920	74	18	two	two	NUM
cana-1920	74	19	leaves	leave	NOUN
cana-1920	74	20	.	.	PUNCT
cana-1920	75	1	the	the	DET
cana-1920	75	2	non	non	ADJ
cana-1920	75	3	-	-	ADJ
cana-1920	75	4	leaf	leaf	ADJ
cana-1920	75	5	vertices	vertex	NOUN
cana-1920	75	6	of	of	ADP
cana-1920	75	7	a	a	DET
cana-1920	75	8	path	path	NOUN
cana-1920	75	9	are	be	AUX
cana-1920	75	10	called	call	VERB
cana-1920	75	11	internal	internal	ADJ
cana-1920	75	12	vertices	vertex	NOUN
cana-1920	75	13	.	.	PUNCT
cana-1920	76	1	in	in	ADP
cana-1920	76	2	general	general	ADJ
cana-1920	76	3	,	,	PUNCT
cana-1920	76	4	internal	internal	ADJ
cana-1920	76	5	vertices	vertex	NOUN
cana-1920	76	6	are	be	AUX
cana-1920	76	7	vertices	vertex	NOUN
cana-1920	76	8	of	of	ADP
cana-1920	76	9	degree	degree	NOUN
cana-1920	76	10	≥	≥	NOUN
cana-1920	76	11	2	2	NUM
cana-1920	76	12	.	.	PUNCT
cana-1920	77	1	the	the	DET
cana-1920	77	2	path	path	NOUN
cana-1920	77	3	p4	p4	ADJ
cana-1920	77	4	with	with	ADP
cana-1920	77	5	leaf	leaf	NOUN
cana-1920	77	6	vertices	vertex	NOUN
cana-1920	77	7	v1	v1	NOUN
cana-1920	77	8	and	and	CCONJ
cana-1920	77	9	v4	v4	NOUN
cana-1920	77	10	and	and	CCONJ
cana-1920	77	11	internal	internal	ADJ
cana-1920	77	12	vertices	vertex	NOUN
cana-1920	77	13	v2	v2	PROPN
cana-1920	77	14	and	and	CCONJ
cana-1920	77	15	v3	v3	PROPN
cana-1920	77	16	is	be	AUX
cana-1920	77	17	presented	present	VERB
cana-1920	77	18	in	in	ADP
cana-1920	77	19	figure	figure	NOUN
cana-1920	77	20	4	4	NUM
cana-1920	77	21	.	.	PUNCT
cana-1920	77	22	figure	figure	VERB
cana-1920	77	23	4	4	NUM
cana-1920	77	24	:	:	PUNCT
cana-1920	77	25	the	the	DET
cana-1920	77	26	path	path	NOUN
cana-1920	77	27	p4	p4	ADJ
cana-1920	77	28	with	with	ADP
cana-1920	77	29	v1	v1	NOUN
cana-1920	77	30	,	,	PUNCT
cana-1920	77	31	v4	v4	NOUN
cana-1920	77	32	as	as	ADP
cana-1920	77	33	leaves	leave	NOUN
cana-1920	77	34	and	and	CCONJ
cana-1920	77	35	v2	v2	PROPN
cana-1920	77	36	,	,	PUNCT
cana-1920	77	37	v3	v3	PROPN
cana-1920	77	38	as	as	ADP
cana-1920	77	39	internal	internal	ADJ
cana-1920	77	40	vertices	vertex	NOUN
cana-1920	77	41	.	.	PUNCT
cana-1920	78	1	communications	communication	NOUN
cana-1920	78	2	on	on	ADP
cana-1920	78	3	applied	apply	VERB
cana-1920	78	4	nonlinear	nonlinear	ADJ
cana-1920	78	5	analysis	analysis	NOUN
cana-1920	78	6	issn	issn	NOUN
cana-1920	78	7	:	:	PUNCT
cana-1920	78	8	1074	1074	NUM
cana-1920	78	9	-	-	PUNCT
cana-1920	78	10	133x	133x	NUM
cana-1920	78	11	vol	vol	NOUN
cana-1920	78	12	32	32	NUM
cana-1920	78	13	no	no	NOUN
cana-1920	78	14	.	.	NOUN
cana-1920	78	15	3	3	NUM
cana-1920	78	16	(	(	PUNCT
cana-1920	78	17	2025	2025	NUM
cana-1920	78	18	)	)	PUNCT
cana-1920	78	19	75	75	NUM
cana-1920	78	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	79	1	we	we	PRON
cana-1920	79	2	are	be	AUX
cana-1920	79	3	now	now	ADV
cana-1920	79	4	at	at	ADP
cana-1920	79	5	the	the	DET
cana-1920	79	6	position	position	NOUN
cana-1920	79	7	to	to	PART
cana-1920	79	8	define	define	VERB
cana-1920	79	9	comet	comet	NOUN
cana-1920	79	10	graphs	graph	NOUN
cana-1920	79	11	.	.	PUNCT
cana-1920	80	1	the	the	DET
cana-1920	80	2	comet	comet	NOUN
cana-1920	80	3	cm	cm	PROPN
cana-1920	80	4	,	,	PUNCT
cana-1920	80	5	n	n	X
cana-1920	80	6	is	be	AUX
cana-1920	80	7	the	the	DET
cana-1920	80	8	tree	tree	NOUN
cana-1920	80	9	obtained	obtain	VERB
cana-1920	80	10	from	from	ADP
cana-1920	80	11	path	path	NOUN
cana-1920	80	12	pm	pm	NOUN
cana-1920	80	13	by	by	ADP
cana-1920	80	14	appending	append	VERB
cana-1920	80	15	n	n	PROPN
cana-1920	80	16	>	>	SYM
cana-1920	80	17	1	1	NUM
cana-1920	80	18	edges	edge	NOUN
cana-1920	80	19	to	to	ADP
cana-1920	80	20	one	one	NUM
cana-1920	80	21	end	end	NOUN
cana-1920	80	22	of	of	ADP
cana-1920	80	23	pm	pm	NOUN
cana-1920	80	24	.	.	PUNCT
cana-1920	81	1	the	the	DET
cana-1920	81	2	end	end	NOUN
cana-1920	81	3	vertex	vertex	NOUN
cana-1920	81	4	of	of	ADP
cana-1920	81	5	pm	pm	NOUN
cana-1920	81	6	appended	append	VERB
cana-1920	81	7	by	by	ADP
cana-1920	81	8	n	n	PRON
cana-1920	81	9	number	number	NOUN
cana-1920	81	10	of	of	ADP
cana-1920	81	11	edges	edge	NOUN
cana-1920	81	12	is	be	AUX
cana-1920	81	13	called	call	VERB
cana-1920	81	14	the	the	DET
cana-1920	81	15	branching	branch	VERB
cana-1920	81	16	vertex	vertex	NOUN
cana-1920	81	17	of	of	ADP
cana-1920	81	18	cm	cm	NOUN
cana-1920	81	19	,	,	PUNCT
cana-1920	81	20	n.	n.	NOUN
cana-1920	81	21	in	in	ADP
cana-1920	81	22	general	general	ADJ
cana-1920	81	23	,	,	PUNCT
cana-1920	81	24	a	a	DET
cana-1920	81	25	branching	branch	VERB
cana-1920	81	26	vertex	vertex	NOUN
cana-1920	81	27	is	be	AUX
cana-1920	81	28	a	a	DET
cana-1920	81	29	vertex	vertex	NOUN
cana-1920	81	30	of	of	ADP
cana-1920	81	31	degree	degree	NOUN
cana-1920	81	32	≥	≥	NOUN
cana-1920	81	33	3	3	X
cana-1920	81	34	.	.	PUNCT
cana-1920	82	1	we	we	PRON
cana-1920	82	2	remark	remark	VERB
cana-1920	82	3	that	that	SCONJ
cana-1920	82	4	the	the	DET
cana-1920	82	5	notation	notation	NOUN
cana-1920	82	6	we	we	PRON
cana-1920	82	7	used	use	VERB
cana-1920	82	8	in	in	ADP
cana-1920	82	9	denoting	denote	VERB
cana-1920	82	10	comet	comet	NOUN
cana-1920	82	11	graphs	graph	NOUN
cana-1920	82	12	,	,	PUNCT
cana-1920	82	13	and	and	CCONJ
cana-1920	82	14	later	later	ADV
cana-1920	82	15	for	for	ADP
cana-1920	82	16	double	double	ADJ
cana-1920	82	17	comets	comet	NOUN
cana-1920	82	18	are	be	AUX
cana-1920	82	19	the	the	DET
cana-1920	82	20	one	one	NOUN
cana-1920	82	21	used	use	VERB
cana-1920	82	22	by	by	ADP
cana-1920	82	23	dogan	dogan	PROPN
cana-1920	82	24	durgun	durgun	PROPN
cana-1920	82	25	and	and	CCONJ
cana-1920	82	26	toprakkaya	toprakkaya	NOUN
cana-1920	82	27	in	in	ADP
cana-1920	82	28	[	[	X
cana-1920	82	29	10	10	NUM
cana-1920	82	30	]	]	PUNCT
cana-1920	82	31	.	.	PUNCT
cana-1920	83	1	the	the	DET
cana-1920	83	2	comet	comet	NOUN
cana-1920	83	3	c4,5	c4,5	VERB
cana-1920	83	4	with	with	ADP
cana-1920	83	5	branching	branch	VERB
cana-1920	83	6	vertex	vertex	NOUN
cana-1920	83	7	vb	vb	NOUN
cana-1920	83	8	is	be	AUX
cana-1920	83	9	depicted	depict	VERB
cana-1920	83	10	in	in	ADP
cana-1920	83	11	figure	figure	NOUN
cana-1920	83	12	5a	5a	NUM
cana-1920	83	13	while	while	SCONJ
cana-1920	83	14	the	the	DET
cana-1920	83	15	comet	comet	NOUN
cana-1920	83	16	cm	cm	PROPN
cana-1920	83	17	,	,	PUNCT
cana-1920	83	18	n	n	PRON
cana-1920	83	19	is	be	AUX
cana-1920	83	20	depicted	depict	VERB
cana-1920	83	21	in	in	ADP
cana-1920	83	22	figure	figure	NOUN
cana-1920	83	23	5b	5b	NUM
cana-1920	83	24	.	.	PUNCT
cana-1920	84	1	figure	figure	VERB
cana-1920	84	2	5	5	NUM
cana-1920	84	3	:	:	PUNCT
cana-1920	84	4	(	(	PUNCT
cana-1920	84	5	a	a	X
cana-1920	84	6	)	)	PUNCT
cana-1920	84	7	the	the	DET
cana-1920	84	8	comet	comet	NOUN
cana-1920	84	9	c4,5	c4,5	VERB
cana-1920	84	10	with	with	ADP
cana-1920	84	11	branching	branch	VERB
cana-1920	84	12	vertex	vertex	NOUN
cana-1920	84	13	vb	vb	NOUN
cana-1920	84	14	.	.	PUNCT
cana-1920	85	1	(	(	PUNCT
cana-1920	85	2	b	b	X
cana-1920	85	3	)	)	PUNCT
cana-1920	85	4	the	the	DET
cana-1920	85	5	comet	comet	NOUN
cana-1920	85	6	cm	cm	PROPN
cana-1920	85	7	,	,	PUNCT
cana-1920	85	8	n.	n.	NOUN
cana-1920	85	9	on	on	ADP
cana-1920	85	10	the	the	DET
cana-1920	85	11	other	other	ADJ
cana-1920	85	12	hand	hand	NOUN
cana-1920	85	13	,	,	PUNCT
cana-1920	85	14	the	the	DET
cana-1920	85	15	double	double	ADJ
cana-1920	85	16	comet	comet	NOUN
cana-1920	85	17	dc(m	dc(m	NOUN
cana-1920	85	18	,	,	PUNCT
cana-1920	85	19	m1,m2	m1,m2	PROPN
cana-1920	85	20	)	)	PUNCT
cana-1920	85	21	is	be	AUX
cana-1920	85	22	the	the	DET
cana-1920	85	23	tree	tree	NOUN
cana-1920	85	24	obtained	obtain	VERB
cana-1920	85	25	from	from	ADP
cana-1920	85	26	path	path	NOUN
cana-1920	85	27	pm	pm	NOUN
cana-1920	85	28	by	by	ADP
cana-1920	85	29	appending	append	VERB
cana-1920	85	30	m1	m1	PROPN
cana-1920	85	31	>	>	X
cana-1920	85	32	1	1	NUM
cana-1920	85	33	edges	edge	NOUN
cana-1920	85	34	to	to	ADP
cana-1920	85	35	one	one	NUM
cana-1920	85	36	end	end	NOUN
cana-1920	85	37	of	of	ADP
cana-1920	85	38	pm	pm	NOUN
cana-1920	85	39	and	and	CCONJ
cana-1920	85	40	m2	m2	PROPN
cana-1920	85	41	>	>	SYM
cana-1920	85	42	1	1	NUM
cana-1920	85	43	edges	edge	NOUN
cana-1920	85	44	on	on	ADP
cana-1920	85	45	the	the	DET
cana-1920	85	46	other	other	ADJ
cana-1920	85	47	end	end	NOUN
cana-1920	85	48	of	of	ADP
cana-1920	85	49	pm	pm	NOUN
cana-1920	85	50	.	.	PUNCT
cana-1920	86	1	in	in	ADP
cana-1920	86	2	this	this	DET
cana-1920	86	3	case	case	NOUN
cana-1920	86	4	,	,	PUNCT
cana-1920	86	5	the	the	DET
cana-1920	86	6	ends	end	NOUN
cana-1920	86	7	of	of	ADP
cana-1920	86	8	pm	pm	NOUN
cana-1920	86	9	are	be	AUX
cana-1920	86	10	the	the	DET
cana-1920	86	11	branching	branch	VERB
cana-1920	86	12	vertices	vertex	NOUN
cana-1920	86	13	of	of	ADP
cana-1920	86	14	dc(m	dc(m	NOUN
cana-1920	86	15	,	,	PUNCT
cana-1920	86	16	m1,m2	m1,m2	PROPN
cana-1920	86	17	)	)	PUNCT
cana-1920	86	18	.	.	PUNCT
cana-1920	87	1	the	the	DET
cana-1920	87	2	double	double	ADJ
cana-1920	87	3	comet	comet	NOUN
cana-1920	87	4	dc(4,3,5	dc(4,3,5	NOUN
cana-1920	87	5	)	)	PUNCT
cana-1920	87	6	is	be	AUX
cana-1920	87	7	shown	show	VERB
cana-1920	87	8	in	in	ADP
cana-1920	87	9	figure	figure	NOUN
cana-1920	87	10	6a	6a	NOUN
cana-1920	87	11	,	,	PUNCT
cana-1920	87	12	while	while	SCONJ
cana-1920	87	13	the	the	DET
cana-1920	87	14	double	double	ADJ
cana-1920	87	15	comet	comet	NOUN
cana-1920	87	16	dc(m	dc(m	NOUN
cana-1920	87	17	,	,	PUNCT
cana-1920	87	18	m1,m2	m1,m2	PROPN
cana-1920	87	19	)	)	PUNCT
cana-1920	87	20	is	be	AUX
cana-1920	87	21	depicted	depict	VERB
cana-1920	87	22	in	in	ADP
cana-1920	87	23	figure	figure	NOUN
cana-1920	87	24	6b	6b	NOUN
cana-1920	87	25	.	.	PUNCT
cana-1920	88	1	figure	figure	VERB
cana-1920	88	2	6	6	NUM
cana-1920	88	3	:	:	PUNCT
cana-1920	88	4	(	(	PUNCT
cana-1920	88	5	a	a	X
cana-1920	88	6	)	)	PUNCT
cana-1920	88	7	the	the	DET
cana-1920	88	8	double	double	ADJ
cana-1920	88	9	comet	comet	NOUN
cana-1920	88	10	dc(4,3,5	dc(4,3,5	NOUN
cana-1920	88	11	)	)	PUNCT
cana-1920	88	12	.	.	PUNCT
cana-1920	89	1	(	(	PUNCT
cana-1920	89	2	b	b	X
cana-1920	89	3	)	)	PUNCT
cana-1920	89	4	the	the	DET
cana-1920	89	5	double	double	ADJ
cana-1920	89	6	comet	comet	NOUN
cana-1920	89	7	dc(m	dc(m	NOUN
cana-1920	89	8	,	,	PUNCT
cana-1920	89	9	m1,m2	m1,m2	PROPN
cana-1920	89	10	)	)	PUNCT
cana-1920	89	11	.	.	PUNCT
cana-1920	90	1	remark	remark	VERB
cana-1920	90	2	2.1	2.1	NUM
cana-1920	90	3	.	.	PUNCT
cana-1920	91	1	before	before	SCONJ
cana-1920	91	2	we	we	PRON
cana-1920	91	3	continue	continue	VERB
cana-1920	91	4	,	,	PUNCT
cana-1920	91	5	we	we	PRON
cana-1920	91	6	remark	remark	VERB
cana-1920	91	7	that	that	SCONJ
cana-1920	91	8	although	although	SCONJ
cana-1920	91	9	based	base	VERB
cana-1920	91	10	on	on	ADP
cana-1920	91	11	definition	definition	NOUN
cana-1920	91	12	,	,	PUNCT
cana-1920	91	13	a	a	DET
cana-1920	91	14	branching	branch	VERB
cana-1920	91	15	vertex	vertex	NOUN
cana-1920	91	16	is	be	AUX
cana-1920	91	17	an	an	DET
cana-1920	91	18	internal	internal	ADJ
cana-1920	91	19	vertex	vertex	NOUN
cana-1920	91	20	,	,	PUNCT
cana-1920	91	21	we	we	PRON
cana-1920	91	22	reserve	reserve	VERB
cana-1920	91	23	the	the	DET
cana-1920	91	24	term	term	NOUN
cana-1920	91	25	“	"	PUNCT
cana-1920	91	26	internal	internal	ADJ
cana-1920	91	27	vertex	vertex	NOUN
cana-1920	91	28	”	"	PUNCT
cana-1920	91	29	for	for	ADP
cana-1920	91	30	vertices	vertex	NOUN
cana-1920	91	31	that	that	PRON
cana-1920	91	32	are	be	AUX
cana-1920	91	33	internal	internal	ADJ
cana-1920	91	34	but	but	CCONJ
cana-1920	91	35	not	not	PART
cana-1920	91	36	branching	branch	VERB
cana-1920	91	37	in	in	ADP
cana-1920	91	38	this	this	DET
cana-1920	91	39	paper	paper	NOUN
cana-1920	91	40	.	.	PUNCT
cana-1920	92	1	now	now	ADV
cana-1920	92	2	that	that	SCONJ
cana-1920	92	3	we	we	PRON
cana-1920	92	4	have	have	AUX
cana-1920	92	5	already	already	ADV
cana-1920	92	6	discussed	discuss	VERB
cana-1920	92	7	the	the	DET
cana-1920	92	8	comet	comet	NOUN
cana-1920	92	9	and	and	CCONJ
cana-1920	92	10	double	double	ADJ
cana-1920	92	11	comet	comet	NOUN
cana-1920	92	12	graphs	graph	NOUN
cana-1920	92	13	,	,	PUNCT
cana-1920	92	14	we	we	PRON
cana-1920	92	15	are	be	AUX
cana-1920	92	16	now	now	ADV
cana-1920	92	17	ready	ready	ADJ
cana-1920	92	18	to	to	PART
cana-1920	92	19	present	present	VERB
cana-1920	92	20	results	result	NOUN
cana-1920	92	21	concerning	concern	VERB
cana-1920	92	22	the	the	DET
cana-1920	92	23	reverse	reverse	ADJ
cana-1920	92	24	vertex	vertex	NOUN
cana-1920	92	25	degree	degree	NOUN
cana-1920	92	26	of	of	ADP
cana-1920	92	27	their	their	PRON
cana-1920	92	28	vertices	vertex	NOUN
cana-1920	92	29	.	.	PUNCT
cana-1920	93	1	proposition	proposition	NOUN
cana-1920	93	2	2.2	2.2	NUM
cana-1920	93	3	.	.	PUNCT
cana-1920	94	1	if	if	SCONJ
cana-1920	94	2	u	u	NOUN
cana-1920	94	3	is	be	AUX
cana-1920	94	4	a	a	DET
cana-1920	94	5	vertex	vertex	NOUN
cana-1920	94	6	in	in	ADP
cana-1920	94	7	v(cm	v(cm	NUM
cana-1920	94	8	,	,	PUNCT
cana-1920	94	9	n	n	CCONJ
cana-1920	94	10	)	)	PUNCT
cana-1920	94	11	then	then	ADV
cana-1920	94	12	proof	proof	NOUN
cana-1920	94	13	.	.	PUNCT
cana-1920	95	1	we	we	PRON
cana-1920	95	2	begin	begin	VERB
cana-1920	95	3	by	by	ADP
cana-1920	95	4	noting	note	VERB
cana-1920	95	5	that	that	SCONJ
cana-1920	95	6	for	for	ADP
cana-1920	95	7	g	g	PROPN
cana-1920	95	8	=	=	NOUN
cana-1920	95	9	cm	cm	NOUN
cana-1920	95	10	,	,	PUNCT
cana-1920	95	11	n	n	CCONJ
cana-1920	95	12	,	,	PUNCT
cana-1920	95	13	we	we	PRON
cana-1920	95	14	have	have	VERB
cana-1920	95	15	∆(g	∆(g	NOUN
cana-1920	95	16	)	)	PUNCT
cana-1920	95	17	=	=	SYM
cana-1920	96	1	n+1	n+1	X
cana-1920	96	2	.	.	PUNCT
cana-1920	96	3	let	let	VERB
cana-1920	96	4	u	u	PROPN
cana-1920	96	5	∈v(g	∈v(g	PROPN
cana-1920	96	6	)	)	PUNCT
cana-1920	96	7	.	.	PUNCT
cana-1920	97	1	since	since	SCONJ
cana-1920	97	2	u	u	NOUN
cana-1920	97	3	is	be	AUX
cana-1920	97	4	a	a	DET
cana-1920	97	5	vertex	vertex	NOUN
cana-1920	97	6	in	in	ADP
cana-1920	97	7	v(g	v(g	NUM
cana-1920	97	8	)	)	PUNCT
cana-1920	97	9	,	,	PUNCT
cana-1920	97	10	then	then	ADV
cana-1920	97	11	u	u	NOUN
cana-1920	97	12	is	be	AUX
cana-1920	97	13	either	either	CCONJ
cana-1920	97	14	a	a	DET
cana-1920	97	15	leaf	leaf	NOUN
cana-1920	97	16	with	with	ADP
cana-1920	97	17	degg(u	degg(u	PROPN
cana-1920	97	18	)	)	PUNCT
cana-1920	97	19	=	=	SYM
cana-1920	97	20	1	1	NUM
cana-1920	97	21	,	,	PUNCT
cana-1920	97	22	an	an	DET
cana-1920	97	23	internal	internal	ADJ
cana-1920	97	24	vertex	vertex	NOUN
cana-1920	97	25	with	with	ADP
cana-1920	97	26	degg(u	degg(u	PROPN
cana-1920	97	27	)	)	PUNCT
cana-1920	97	28	=	=	SYM
cana-1920	97	29	2	2	NUM
cana-1920	97	30	,	,	PUNCT
cana-1920	97	31	or	or	CCONJ
cana-1920	97	32	a	a	DET
cana-1920	97	33	branching	branch	VERB
cana-1920	97	34	vertex	vertex	NOUN
cana-1920	97	35	with	with	ADP
cana-1920	97	36	degg(u	degg(u	PROPN
cana-1920	97	37	)	)	PUNCT
cana-1920	97	38	=	=	SYM
cana-1920	98	1	n+1	n+1	PROPN
cana-1920	98	2	.	.	NOUN
cana-1920	99	1	if	if	SCONJ
cana-1920	99	2	u	u	NOUN
cana-1920	99	3	is	be	AUX
cana-1920	99	4	a	a	DET
cana-1920	99	5	leaf	leaf	NOUN
cana-1920	99	6	,	,	PUNCT
cana-1920	99	7	then	then	ADV
cana-1920	99	8	ru	ru	PROPN
cana-1920	99	9	=	=	SYM
cana-1920	99	10	∆(g	∆(g	PROPN
cana-1920	99	11	)	)	PUNCT
cana-1920	99	12	−	−	PROPN
cana-1920	99	13	degg(u	degg(u	PROPN
cana-1920	99	14	)	)	PUNCT
cana-1920	99	15	+	+	CCONJ
cana-1920	99	16	1	1	NUM
cana-1920	99	17	=	=	SYM
cana-1920	99	18	(	(	PUNCT
cana-1920	99	19	n	n	X
cana-1920	99	20	+1	+1	PROPN
cana-1920	99	21	)	)	PUNCT
cana-1920	99	22	−1	−1	NOUN
cana-1920	99	23	+	+	NOUN
cana-1920	99	24	1	1	NUM
cana-1920	99	25	=	=	SYM
cana-1920	99	26	n	n	X
cana-1920	99	27	+1	+1	NOUN
cana-1920	99	28	.	.	PUNCT
cana-1920	100	1	if	if	SCONJ
cana-1920	100	2	u	u	NOUN
cana-1920	100	3	is	be	AUX
cana-1920	100	4	an	an	DET
cana-1920	100	5	internal	internal	ADJ
cana-1920	100	6	vertex	vertex	NOUN
cana-1920	100	7	,	,	PUNCT
cana-1920	100	8	then	then	ADV
cana-1920	100	9	ru	ru	PROPN
cana-1920	100	10	=	=	SYM
cana-1920	100	11	∆(g	∆(g	PROPN
cana-1920	100	12	)	)	PUNCT
cana-1920	100	13	−	−	PROPN
cana-1920	100	14	degg(u	degg(u	PROPN
cana-1920	100	15	)	)	PUNCT
cana-1920	100	16	+	+	CCONJ
cana-1920	100	17	1	1	NUM
cana-1920	100	18	=	=	SYM
cana-1920	100	19	(	(	PUNCT
cana-1920	100	20	n	n	NOUN
cana-1920	100	21	+	+	NUM
cana-1920	100	22	1	1	NUM
cana-1920	100	23	)	)	PUNCT
cana-1920	100	24	–	–	PUNCT
cana-1920	100	25	2	2	NUM
cana-1920	100	26	+	+	SYM
cana-1920	100	27	1	1	NUM
cana-1920	100	28	=	=	SYM
cana-1920	100	29	n.	n.	NOUN
cana-1920	100	30	finally	finally	ADV
cana-1920	100	31	,	,	PUNCT
cana-1920	100	32	if	if	SCONJ
cana-1920	100	33	u	u	NOUN
cana-1920	100	34	is	be	AUX
cana-1920	100	35	a	a	DET
cana-1920	100	36	branching	branch	VERB
cana-1920	100	37	vertex	vertex	NOUN
cana-1920	100	38	,	,	PUNCT
cana-1920	100	39	then	then	ADV
cana-1920	100	40	ru	ru	PROPN
cana-1920	100	41	=	=	SYM
cana-1920	100	42	∆(g	∆(g	PROPN
cana-1920	100	43	)	)	PUNCT
cana-1920	100	44	−	−	ADP
cana-1920	101	1	degg(u	degg(u	PROPN
cana-1920	101	2	)	)	PUNCT
cana-1920	101	3	+1	+1	NOUN
cana-1920	101	4	=	=	PUNCT
cana-1920	101	5	(	(	PUNCT
cana-1920	101	6	n	n	PROPN
cana-1920	101	7	+	+	NUM
cana-1920	101	8	1	1	NUM
cana-1920	101	9	)	)	PUNCT
cana-1920	101	10	−	−	PROPN
cana-1920	101	11	(	(	PUNCT
cana-1920	101	12	n	n	NOUN
cana-1920	101	13	+	+	CCONJ
cana-1920	101	14	1	1	NUM
cana-1920	101	15	)	)	PUNCT
cana-1920	101	16	+	+	CCONJ
cana-1920	101	17	1	1	NUM
cana-1920	101	18	=	=	SYM
cana-1920	101	19	1	1	NUM
cana-1920	101	20	.	.	PUNCT
cana-1920	102	1	this	this	PRON
cana-1920	102	2	proves	prove	VERB
cana-1920	102	3	proposition	proposition	NOUN
cana-1920	102	4	2.2	2.2	NUM
cana-1920	102	5	.	.	PUNCT
cana-1920	103	1	we	we	PRON
cana-1920	103	2	now	now	ADV
cana-1920	103	3	end	end	VERB
cana-1920	103	4	the	the	DET
cana-1920	103	5	section	section	NOUN
cana-1920	103	6	by	by	ADP
cana-1920	103	7	stating	state	VERB
cana-1920	103	8	and	and	CCONJ
cana-1920	103	9	proving	prove	VERB
cana-1920	103	10	the	the	DET
cana-1920	103	11	next	next	ADJ
cana-1920	103	12	proposition	proposition	NOUN
cana-1920	103	13	.	.	PUNCT
cana-1920	104	1	communications	communication	NOUN
cana-1920	104	2	on	on	ADP
cana-1920	104	3	applied	apply	VERB
cana-1920	104	4	nonlinear	nonlinear	ADJ
cana-1920	104	5	analysis	analysis	NOUN
cana-1920	104	6	issn	issn	NOUN
cana-1920	104	7	:	:	PUNCT
cana-1920	104	8	1074	1074	NUM
cana-1920	104	9	-	-	PUNCT
cana-1920	104	10	133x	133x	NUM
cana-1920	104	11	vol	vol	NOUN
cana-1920	104	12	32	32	NUM
cana-1920	104	13	no	no	NOUN
cana-1920	104	14	.	.	NOUN
cana-1920	104	15	3	3	NUM
cana-1920	104	16	(	(	PUNCT
cana-1920	104	17	2025	2025	NUM
cana-1920	104	18	)	)	PUNCT
cana-1920	105	1	76	76	NUM
cana-1920	105	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	105	3	proposition	proposition	NOUN
cana-1920	105	4	2.3	2.3	NUM
cana-1920	105	5	.	.	PUNCT
cana-1920	106	1	let	let	VERB
cana-1920	106	2	m	m	NOUN
cana-1920	106	3	=	=	PUNCT
cana-1920	106	4	max{m1,m2	max{m1,m2	PROPN
cana-1920	106	5	}	}	PUNCT
cana-1920	106	6	and	and	CCONJ
cana-1920	106	7	µ	µ	X
cana-1920	106	8	=	=	SYM
cana-1920	106	9	min{m1,m2	min{m1,m2	NOUN
cana-1920	106	10	}	}	PUNCT
cana-1920	106	11	.	.	PUNCT
cana-1920	107	1	if	if	SCONJ
cana-1920	107	2	u	u	NOUN
cana-1920	107	3	is	be	AUX
cana-1920	107	4	a	a	DET
cana-1920	107	5	vertex	vertex	NOUN
cana-1920	107	6	in	in	ADP
cana-1920	107	7	v(dc(m	v(dc(m	PROPN
cana-1920	107	8	,	,	PUNCT
cana-1920	107	9	m1,m2	m1,m2	PROPN
cana-1920	107	10	)	)	PUNCT
cana-1920	107	11	)	)	PUNCT
cana-1920	107	12	then	then	ADV
cana-1920	107	13	proof	proof	NOUN
cana-1920	107	14	.	.	PUNCT
cana-1920	108	1	we	we	PRON
cana-1920	108	2	begin	begin	VERB
cana-1920	108	3	by	by	ADP
cana-1920	108	4	noting	note	VERB
cana-1920	108	5	that	that	SCONJ
cana-1920	108	6	for	for	ADP
cana-1920	108	7	g	g	NOUN
cana-1920	108	8	=	=	SYM
cana-1920	108	9	dc(m	dc(m	NOUN
cana-1920	108	10	,	,	PUNCT
cana-1920	108	11	m1,m2	m1,m2	PROPN
cana-1920	108	12	)	)	PUNCT
cana-1920	108	13	,	,	PUNCT
cana-1920	108	14	we	we	PRON
cana-1920	108	15	have	have	VERB
cana-1920	108	16	∆(g	∆(g	NOUN
cana-1920	108	17	)	)	PUNCT
cana-1920	108	18	=	=	PUNCT
cana-1920	109	1	m	m	VERB
cana-1920	109	2	+1	+1	ADJ
cana-1920	109	3	.	.	PUNCT
cana-1920	110	1	let	let	VERB
cana-1920	110	2	u	u	PRON
cana-1920	110	3	∈	∈	NOUN
cana-1920	110	4	v(g	v(g	PROPN
cana-1920	110	5	)	)	PUNCT
cana-1920	110	6	.	.	PUNCT
cana-1920	111	1	since	since	SCONJ
cana-1920	111	2	u	u	NOUN
cana-1920	111	3	is	be	AUX
cana-1920	111	4	a	a	DET
cana-1920	111	5	vertex	vertex	NOUN
cana-1920	111	6	in	in	ADP
cana-1920	111	7	v(g	v(g	NUM
cana-1920	111	8	)	)	PUNCT
cana-1920	111	9	,	,	PUNCT
cana-1920	111	10	then	then	ADV
cana-1920	111	11	u	u	NOUN
cana-1920	111	12	is	be	AUX
cana-1920	111	13	either	either	CCONJ
cana-1920	111	14	a	a	DET
cana-1920	111	15	leaf	leaf	NOUN
cana-1920	111	16	with	with	ADP
cana-1920	111	17	degg(u	degg(u	PROPN
cana-1920	111	18	)	)	PUNCT
cana-1920	111	19	=	=	SYM
cana-1920	111	20	1	1	NUM
cana-1920	111	21	,	,	PUNCT
cana-1920	111	22	an	an	DET
cana-1920	111	23	internal	internal	ADJ
cana-1920	111	24	vertex	vertex	NOUN
cana-1920	111	25	with	with	ADP
cana-1920	111	26	degg(u	degg(u	PROPN
cana-1920	111	27	)	)	PUNCT
cana-1920	111	28	=	=	SYM
cana-1920	111	29	2	2	NUM
cana-1920	111	30	,	,	PUNCT
cana-1920	111	31	a	a	DET
cana-1920	111	32	branching	branch	VERB
cana-1920	111	33	vertex	vertex	NOUN
cana-1920	111	34	with	with	ADP
cana-1920	111	35	degg(u	degg(u	PROPN
cana-1920	111	36	)	)	PUNCT
cana-1920	111	37	=	=	SYM
cana-1920	111	38	µ	µ	X
cana-1920	111	39	+1	+1	PROPN
cana-1920	111	40	,	,	PUNCT
cana-1920	111	41	and	and	CCONJ
cana-1920	111	42	a	a	DET
cana-1920	111	43	branching	branch	VERB
cana-1920	111	44	vertex	vertex	NOUN
cana-1920	111	45	with	with	ADP
cana-1920	111	46	degg(u	degg(u	PROPN
cana-1920	111	47	)	)	PUNCT
cana-1920	111	48	=	=	NOUN
cana-1920	112	1	m	m	VERB
cana-1920	112	2	+1	+1	ADJ
cana-1920	112	3	.	.	PUNCT
cana-1920	113	1	if	if	SCONJ
cana-1920	113	2	u	u	NOUN
cana-1920	113	3	is	be	AUX
cana-1920	113	4	a	a	DET
cana-1920	113	5	leaf	leaf	NOUN
cana-1920	113	6	,	,	PUNCT
cana-1920	113	7	then	then	ADV
cana-1920	113	8	ru	ru	PROPN
cana-1920	113	9	=	=	SYM
cana-1920	113	10	∆(g	∆(g	PROPN
cana-1920	113	11	)	)	PUNCT
cana-1920	113	12	−	−	PROPN
cana-1920	113	13	degg(u	degg(u	PROPN
cana-1920	113	14	)	)	PUNCT
cana-1920	113	15	+	+	CCONJ
cana-1920	113	16	1	1	NUM
cana-1920	113	17	=	=	SYM
cana-1920	113	18	(	(	PUNCT
cana-1920	113	19	m	m	PROPN
cana-1920	113	20	+1)−1	+1)−1	ADP
cana-1920	113	21	+	+	NOUN
cana-1920	113	22	1	1	NUM
cana-1920	113	23	=	=	SYM
cana-1920	113	24	m	m	VERB
cana-1920	113	25	+1	+1	ADJ
cana-1920	113	26	.	.	PUNCT
cana-1920	114	1	if	if	SCONJ
cana-1920	114	2	u	u	NOUN
cana-1920	114	3	is	be	AUX
cana-1920	114	4	an	an	DET
cana-1920	114	5	internal	internal	ADJ
cana-1920	114	6	vertex	vertex	NOUN
cana-1920	114	7	,	,	PUNCT
cana-1920	114	8	then	then	ADV
cana-1920	114	9	ru	ru	PROPN
cana-1920	114	10	=	=	PROPN
cana-1920	114	11	∆(g	∆(g	NOUN
cana-1920	114	12	)	)	PUNCT
cana-1920	114	13	−	−	PROPN
cana-1920	114	14	degg(u)+1	degg(u)+1	NOUN
cana-1920	114	15	=(	=(	NOUN
cana-1920	114	16	m	m	PROPN
cana-1920	114	17	+	+	NOUN
cana-1920	114	18	1	1	NUM
cana-1920	114	19	)	)	PUNCT
cana-1920	114	20	–	–	PUNCT
cana-1920	114	21	2	2	NUM
cana-1920	114	22	+1	+1	NOUN
cana-1920	114	23	=	=	PUNCT
cana-1920	114	24	m.	m.	NOUN
cana-1920	114	25	if	if	SCONJ
cana-1920	114	26	u	u	NOUN
cana-1920	114	27	is	be	AUX
cana-1920	114	28	a	a	DET
cana-1920	114	29	branching	branch	VERB
cana-1920	114	30	vertex	vertex	NOUN
cana-1920	114	31	with	with	ADP
cana-1920	114	32	degg(u)=	degg(u)=	PROPN
cana-1920	114	33	µ	µ	X
cana-1920	114	34	+1	+1	PROPN
cana-1920	114	35	,	,	PUNCT
cana-1920	114	36	then	then	ADV
cana-1920	114	37	ru	ru	PROPN
cana-1920	114	38	=	=	SYM
cana-1920	114	39	∆(g	∆(g	PROPN
cana-1920	114	40	)	)	PUNCT
cana-1920	114	41	−	−	NOUN
cana-1920	114	42	degg(u)+1	degg(u)+1	NOUN
cana-1920	114	43	=	=	SYM
cana-1920	114	44	(	(	PUNCT
cana-1920	114	45	m	m	VERB
cana-1920	114	46	+	+	ADJ
cana-1920	114	47	1	1	NUM
cana-1920	114	48	)	)	PUNCT
cana-1920	114	49	−	−	PROPN
cana-1920	114	50	(	(	PUNCT
cana-1920	114	51	µ	µ	X
cana-1920	114	52	+1	+1	NOUN
cana-1920	114	53	)	)	PUNCT
cana-1920	114	54	+	+	CCONJ
cana-1920	114	55	1	1	NUM
cana-1920	114	56	=	=	SYM
cana-1920	114	57	m	m	VERB
cana-1920	114	58	−	−	PROPN
cana-1920	114	59	µ	µ	X
cana-1920	114	60	+1	+1	PROPN
cana-1920	114	61	.	.	PUNCT
cana-1920	115	1	finally	finally	ADV
cana-1920	115	2	,	,	PUNCT
cana-1920	115	3	if	if	SCONJ
cana-1920	115	4	u	u	NOUN
cana-1920	115	5	is	be	AUX
cana-1920	115	6	a	a	DET
cana-1920	115	7	branching	branch	VERB
cana-1920	115	8	vertex	vertex	NOUN
cana-1920	115	9	with	with	ADP
cana-1920	115	10	degg(u	degg(u	PROPN
cana-1920	115	11	)	)	PUNCT
cana-1920	115	12	=	=	PUNCT
cana-1920	115	13	m	m	AUX
cana-1920	115	14	+	+	ADJ
cana-1920	115	15	1	1	NUM
cana-1920	115	16	,	,	PUNCT
cana-1920	115	17	then	then	ADV
cana-1920	115	18	ru	ru	PROPN
cana-1920	115	19	=	=	SYM
cana-1920	115	20	∆(g	∆(g	PROPN
cana-1920	115	21	)	)	PUNCT
cana-1920	115	22	−	−	NOUN
cana-1920	115	23	degg(u)+	degg(u)+	VERB
cana-1920	115	24	1	1	NUM
cana-1920	115	25	=	=	SYM
cana-1920	115	26	(	(	PUNCT
cana-1920	115	27	m	m	VERB
cana-1920	115	28	+	+	ADJ
cana-1920	115	29	1	1	NUM
cana-1920	115	30	)	)	PUNCT
cana-1920	115	31	−	−	PROPN
cana-1920	116	1	(	(	PUNCT
cana-1920	116	2	m	m	VERB
cana-1920	116	3	+	+	ADJ
cana-1920	116	4	1	1	NUM
cana-1920	116	5	)	)	PUNCT
cana-1920	116	6	+	+	CCONJ
cana-1920	116	7	1	1	NUM
cana-1920	116	8	=	=	SYM
cana-1920	116	9	1	1	NUM
cana-1920	116	10	.	.	PUNCT
cana-1920	117	1	this	this	PRON
cana-1920	117	2	proves	prove	VERB
cana-1920	117	3	proposition	proposition	NOUN
cana-1920	117	4	2.3	2.3	NUM
cana-1920	117	5	.	.	PUNCT
cana-1920	118	1	3	3	X
cana-1920	118	2	.	.	X
cana-1920	118	3	several	several	ADJ
cana-1920	118	4	reverse	reverse	ADJ
cana-1920	118	5	vertex	vertex	NOUN
cana-1920	118	6	degree	degree	NOUN
cana-1920	118	7	indices	index	NOUN
cana-1920	118	8	of	of	ADP
cana-1920	118	9	comets	comet	NOUN
cana-1920	118	10	and	and	CCONJ
cana-1920	118	11	double	double	ADJ
cana-1920	118	12	comets	comet	NOUN
cana-1920	118	13	3.1	3.1	NUM
cana-1920	118	14	.	.	PUNCT
cana-1920	119	1	results	result	NOUN
cana-1920	119	2	for	for	ADP
cana-1920	119	3	comet	comet	NOUN
cana-1920	119	4	graphs	graph	NOUN
cana-1920	119	5	we	we	PRON
cana-1920	119	6	now	now	ADV
cana-1920	119	7	present	present	VERB
cana-1920	119	8	our	our	PRON
cana-1920	119	9	results	result	NOUN
cana-1920	119	10	for	for	ADP
cana-1920	119	11	comet	comet	NOUN
cana-1920	119	12	graphs	graph	NOUN
cana-1920	119	13	.	.	PUNCT
cana-1920	120	1	throughout	throughout	ADP
cana-1920	120	2	this	this	DET
cana-1920	120	3	subsection	subsection	NOUN
cana-1920	120	4	,	,	PUNCT
cana-1920	120	5	we	we	PRON
cana-1920	120	6	denote	denote	VERB
cana-1920	120	7	the	the	DET
cana-1920	120	8	comet	comet	NOUN
cana-1920	120	9	graph	graph	NOUN
cana-1920	120	10	cm	cm	PROPN
cana-1920	120	11	,	,	PUNCT
cana-1920	120	12	n	n	CCONJ
cana-1920	120	13	by	by	ADP
cana-1920	120	14	g.	g.	PROPN
cana-1920	120	15	theorem	theorem	VERB
cana-1920	120	16	3.1	3.1	NUM
cana-1920	120	17	.	.	PUNCT
cana-1920	121	1	let	let	VERB
cana-1920	121	2	g	g	NOUN
cana-1920	121	3	=	=	NOUN
cana-1920	121	4	cm	cm	PROPN
cana-1920	121	5	,	,	PUNCT
cana-1920	121	6	n.	n.	NOUN
cana-1920	121	7	the	the	DET
cana-1920	121	8	“	"	PUNCT
cana-1920	121	9	reverse	reverse	ADJ
cana-1920	121	10	sum	sum	NOUN
cana-1920	121	11	-	-	PUNCT
cana-1920	121	12	connectivity	connectivity	NOUN
cana-1920	121	13	index	index	NOUN
cana-1920	121	14	”	"	PUNCT
cana-1920	121	15	of	of	ADP
cana-1920	121	16	g	g	PROPN
cana-1920	121	17	denoted	denote	VERB
cana-1920	121	18	by	by	ADP
cana-1920	121	19	rsci(g	rsci(g	NOUN
cana-1920	121	20	)	)	PUNCT
cana-1920	121	21	is	be	AUX
cana-1920	121	22	given	give	VERB
cana-1920	121	23	by	by	ADP
cana-1920	121	24	proof	proof	NOUN
cana-1920	121	25	.	.	PUNCT
cana-1920	122	1	we	we	PRON
cana-1920	122	2	start	start	VERB
cana-1920	122	3	by	by	ADP
cana-1920	122	4	noting	note	VERB
cana-1920	122	5	that	that	SCONJ
cana-1920	122	6	the	the	DET
cana-1920	122	7	graph	graph	NOUN
cana-1920	122	8	g	g	PROPN
cana-1920	122	9	=	=	NOUN
cana-1920	122	10	cm	cm	PROPN
cana-1920	122	11	,	,	PUNCT
cana-1920	122	12	n	n	PRON
cana-1920	122	13	has	have	VERB
cana-1920	122	14	m	m	PROPN
cana-1920	122	15	–	–	PUNCT
cana-1920	122	16	1	1	NUM
cana-1920	122	17	+	+	CCONJ
cana-1920	122	18	n	n	NOUN
cana-1920	122	19	edges	edge	VERB
cana-1920	122	20	with	with	ADP
cana-1920	122	21	the	the	DET
cana-1920	122	22	following	follow	VERB
cana-1920	122	23	classification	classification	NOUN
cana-1920	122	24	based	base	VERB
cana-1920	122	25	on	on	ADP
cana-1920	122	26	their	their	PRON
cana-1920	122	27	end	end	NOUN
cana-1920	122	28	vertices	vertex	NOUN
cana-1920	122	29	:	:	PUNCT
cana-1920	122	30	1	1	NUM
cana-1920	122	31	leaf	leaf	NOUN
cana-1920	122	32	-	-	PUNCT
cana-1920	122	33	internal	internal	ADJ
cana-1920	122	34	edge	edge	NOUN
cana-1920	122	35	,	,	PUNCT
cana-1920	122	36	m	m	VERB
cana-1920	122	37	−	−	NOUN
cana-1920	122	38	3	3	NUM
cana-1920	122	39	internal	internal	ADJ
cana-1920	122	40	-	-	PUNCT
cana-1920	122	41	internal	internal	ADJ
cana-1920	122	42	edges	edge	NOUN
cana-1920	122	43	,	,	PUNCT
cana-1920	122	44	1	1	NUM
cana-1920	122	45	internal	internal	ADJ
cana-1920	122	46	-	-	PUNCT
cana-1920	122	47	branching	branch	VERB
cana-1920	122	48	edge	edge	NOUN
cana-1920	122	49	,	,	PUNCT
cana-1920	122	50	and	and	CCONJ
cana-1920	122	51	n	n	ADV
cana-1920	122	52	branching	branch	VERB
cana-1920	122	53	-	-	PUNCT
cana-1920	122	54	internal	internal	ADJ
cana-1920	122	55	edges	edge	NOUN
cana-1920	122	56	.	.	PUNCT
cana-1920	123	1	combining	combine	VERB
cana-1920	123	2	these	these	DET
cana-1920	123	3	information	information	NOUN
cana-1920	123	4	with	with	ADP
cana-1920	123	5	equation	equation	NOUN
cana-1920	123	6	(	(	PUNCT
cana-1920	123	7	1	1	NUM
cana-1920	123	8	)	)	PUNCT
cana-1920	123	9	in	in	ADP
cana-1920	123	10	proposition	proposition	NOUN
cana-1920	123	11	2.2	2.2	NUM
cana-1920	123	12	and	and	CCONJ
cana-1920	123	13	the	the	DET
cana-1920	123	14	definition	definition	NOUN
cana-1920	123	15	of	of	ADP
cana-1920	123	16	the	the	DET
cana-1920	123	17	reverse	reverse	ADJ
cana-1920	123	18	sum	sum	NOUN
cana-1920	123	19	-	-	PUNCT
cana-1920	123	20	connectivity	connectivity	NOUN
cana-1920	123	21	index	index	NOUN
cana-1920	123	22	,	,	PUNCT
cana-1920	123	23	we	we	PRON
cana-1920	123	24	arrive	arrive	VERB
cana-1920	123	25	at	at	ADP
cana-1920	123	26	theorem	theorem	NOUN
cana-1920	123	27	3.2	3.2	NUM
cana-1920	123	28	.	.	PUNCT
cana-1920	124	1	let	let	VERB
cana-1920	124	2	g	g	NOUN
cana-1920	124	3	=	=	NOUN
cana-1920	124	4	cm	cm	PROPN
cana-1920	124	5	,	,	PUNCT
cana-1920	124	6	n.	n.	NOUN
cana-1920	124	7	the	the	DET
cana-1920	124	8	“	"	PUNCT
cana-1920	124	9	first	first	ADJ
cana-1920	124	10	reverse	reverse	ADJ
cana-1920	124	11	zagreb	zagreb	PROPN
cana-1920	124	12	index	index	PROPN
cana-1920	124	13	”	"	PUNCT
cana-1920	124	14	of	of	ADP
cana-1920	124	15	g	g	PROPN
cana-1920	124	16	denoted	denote	VERB
cana-1920	124	17	by	by	ADP
cana-1920	124	18	rm1(g	rm1(g	PROPN
cana-1920	124	19	)	)	PUNCT
cana-1920	124	20	is	be	AUX
cana-1920	124	21	given	give	VERB
cana-1920	124	22	by	by	ADP
cana-1920	124	23	rm1(g	rm1(g	PROPN
cana-1920	124	24	)	)	PUNCT
cana-1920	125	1	=	=	PUNCT
cana-1920	125	2	(	(	PUNCT
cana-1920	125	3	n	n	PROPN
cana-1920	125	4	+	+	CCONJ
cana-1920	126	1	1)3	1)3	PROPN
cana-1920	126	2	+	+	PROPN
cana-1920	126	3	mn	mn	PROPN
cana-1920	126	4	2−	2−	NUM
cana-1920	126	5	2n2	2n2	NUM
cana-1920	126	6	+	+	CCONJ
cana-1920	126	7	1	1	NUM
cana-1920	126	8	.	.	X
cana-1920	127	1	proof	proof	NOUN
cana-1920	127	2	.	.	PUNCT
cana-1920	128	1	we	we	PRON
cana-1920	128	2	start	start	VERB
cana-1920	128	3	by	by	ADP
cana-1920	128	4	noting	note	VERB
cana-1920	128	5	that	that	SCONJ
cana-1920	128	6	the	the	DET
cana-1920	128	7	graph	graph	NOUN
cana-1920	128	8	g	g	PROPN
cana-1920	128	9	=	=	NOUN
cana-1920	128	10	cm	cm	PROPN
cana-1920	128	11	,	,	PUNCT
cana-1920	128	12	n	n	PRON
cana-1920	128	13	has	have	VERB
cana-1920	128	14	m	m	PROPN
cana-1920	128	15	+	+	NOUN
cana-1920	128	16	n	n	DET
cana-1920	128	17	vertices	vertex	NOUN
cana-1920	128	18	with	with	ADP
cana-1920	128	19	the	the	DET
cana-1920	128	20	following	follow	VERB
cana-1920	128	21	classification	classification	NOUN
cana-1920	128	22	:	:	PUNCT
cana-1920	128	23	n+1	n+1	NUM
cana-1920	128	24	leaf	leaf	NOUN
cana-1920	128	25	vertices	vertex	NOUN
cana-1920	128	26	,	,	PUNCT
cana-1920	128	27	m	m	VERB
cana-1920	128	28	−2	−2	NOUN
cana-1920	128	29	internal	internal	ADJ
cana-1920	128	30	vertices	vertex	NOUN
cana-1920	128	31	,	,	PUNCT
cana-1920	128	32	and	and	CCONJ
cana-1920	128	33	1	1	NUM
cana-1920	128	34	branching	branch	VERB
cana-1920	128	35	vertex	vertex	NOUN
cana-1920	128	36	.	.	PUNCT
cana-1920	129	1	combining	combine	VERB
cana-1920	129	2	these	these	DET
cana-1920	129	3	information	information	NOUN
cana-1920	129	4	with	with	ADP
cana-1920	129	5	equation	equation	NOUN
cana-1920	129	6	(	(	PUNCT
cana-1920	129	7	1	1	NUM
cana-1920	129	8	)	)	PUNCT
cana-1920	129	9	in	in	ADP
cana-1920	129	10	proposition	proposition	NOUN
cana-1920	129	11	2.2	2.2	NUM
cana-1920	129	12	and	and	CCONJ
cana-1920	129	13	the	the	DET
cana-1920	129	14	definition	definition	NOUN
cana-1920	129	15	of	of	ADP
cana-1920	129	16	the	the	DET
cana-1920	129	17	first	first	ADJ
cana-1920	129	18	reverse	reverse	ADJ
cana-1920	129	19	zagreb	zagreb	PROPN
cana-1920	129	20	index	index	PROPN
cana-1920	129	21	,	,	PUNCT
cana-1920	129	22	we	we	PRON
cana-1920	129	23	arrive	arrive	VERB
cana-1920	129	24	at	at	ADP
cana-1920	129	25	communications	communication	NOUN
cana-1920	129	26	on	on	ADP
cana-1920	129	27	applied	apply	VERB
cana-1920	129	28	nonlinear	nonlinear	ADJ
cana-1920	129	29	analysis	analysis	NOUN
cana-1920	129	30	issn	issn	NOUN
cana-1920	129	31	:	:	PUNCT
cana-1920	129	32	1074	1074	NUM
cana-1920	129	33	-	-	PUNCT
cana-1920	129	34	133x	133x	NUM
cana-1920	129	35	vol	vol	NOUN
cana-1920	129	36	32	32	NUM
cana-1920	129	37	no	no	NOUN
cana-1920	129	38	.	.	NOUN
cana-1920	129	39	3	3	NUM
cana-1920	129	40	(	(	PUNCT
cana-1920	129	41	2025	2025	NUM
cana-1920	129	42	)	)	PUNCT
cana-1920	129	43	77	77	NUM
cana-1920	129	44	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	129	45	theorem	theorem	VERB
cana-1920	129	46	3.3	3.3	NUM
cana-1920	129	47	.	.	PUNCT
cana-1920	130	1	let	let	VERB
cana-1920	130	2	g	g	NOUN
cana-1920	130	3	=	=	NOUN
cana-1920	130	4	cm	cm	PROPN
cana-1920	130	5	,	,	PUNCT
cana-1920	130	6	n.	n.	NOUN
cana-1920	130	7	the	the	DET
cana-1920	130	8	“	"	PUNCT
cana-1920	130	9	second	second	ADJ
cana-1920	130	10	reverse	reverse	ADJ
cana-1920	130	11	zagreb	zagreb	PROPN
cana-1920	130	12	index	index	PROPN
cana-1920	130	13	”	"	PUNCT
cana-1920	130	14	of	of	ADP
cana-1920	130	15	g	g	PROPN
cana-1920	130	16	denoted	denote	VERB
cana-1920	130	17	by	by	ADP
cana-1920	130	18	rm2(g	rm2(g	NOUN
cana-1920	130	19	)	)	PUNCT
cana-1920	130	20	is	be	AUX
cana-1920	130	21	given	give	VERB
cana-1920	130	22	by	by	ADP
cana-1920	130	23	rm2(g	rm2(g	NOUN
cana-1920	130	24	)	)	PUNCT
cana-1920	130	25	=	=	PUNCT
cana-1920	130	26	n(mn	n(mn	ADV
cana-1920	130	27	–	–	PUNCT
cana-1920	130	28	n	n	NOUN
cana-1920	130	29	+	+	CCONJ
cana-1920	130	30	3	3	NUM
cana-1920	130	31	)	)	PUNCT
cana-1920	130	32	.	.	PUNCT
cana-1920	131	1	proof	proof	NOUN
cana-1920	131	2	.	.	PUNCT
cana-1920	132	1	the	the	DET
cana-1920	132	2	proof	proof	NOUN
cana-1920	132	3	is	be	AUX
cana-1920	132	4	similar	similar	ADJ
cana-1920	132	5	to	to	ADP
cana-1920	132	6	the	the	DET
cana-1920	132	7	proof	proof	NOUN
cana-1920	132	8	of	of	ADP
cana-1920	132	9	theorem	theorem	ADJ
cana-1920	132	10	3.1	3.1	NUM
cana-1920	132	11	.	.	PUNCT
cana-1920	133	1	theorem	theorem	VERB
cana-1920	133	2	3.4	3.4	NUM
cana-1920	133	3	.	.	PUNCT
cana-1920	134	1	let	let	VERB
cana-1920	134	2	g	g	NOUN
cana-1920	134	3	=	=	SYM
cana-1920	134	4	cm	cm	PROPN
cana-1920	134	5	,	,	PUNCT
cana-1920	134	6	n.	n.	NOUN
cana-1920	134	7	the	the	DET
cana-1920	134	8	“	"	PUNCT
cana-1920	134	9	reverse	reverse	ADJ
cana-1920	134	10	arithmetic	arithmetic	ADJ
cana-1920	134	11	-	-	PUNCT
cana-1920	134	12	geometric	geometric	ADJ
cana-1920	134	13	index	index	NOUN
cana-1920	134	14	”	"	PUNCT
cana-1920	134	15	of	of	ADP
cana-1920	134	16	g	g	PROPN
cana-1920	134	17	denoted	denote	VERB
cana-1920	134	18	by	by	ADP
cana-1920	134	19	rag(g	rag(g	PROPN
cana-1920	134	20	)	)	PUNCT
cana-1920	134	21	is	be	AUX
cana-1920	134	22	given	give	VERB
cana-1920	134	23	by	by	ADP
cana-1920	134	24	proof	proof	NOUN
cana-1920	134	25	.	.	PUNCT
cana-1920	135	1	we	we	PRON
cana-1920	135	2	start	start	VERB
cana-1920	135	3	by	by	ADP
cana-1920	135	4	noting	note	VERB
cana-1920	135	5	that	that	SCONJ
cana-1920	135	6	the	the	DET
cana-1920	135	7	graph	graph	NOUN
cana-1920	135	8	g	g	PROPN
cana-1920	135	9	=	=	NOUN
cana-1920	135	10	cm	cm	PROPN
cana-1920	135	11	,	,	PUNCT
cana-1920	135	12	n	n	PRON
cana-1920	135	13	has	have	VERB
cana-1920	135	14	m−1+n	m−1+n	PROPN
cana-1920	135	15	edges	edge	NOUN
cana-1920	135	16	with	with	ADP
cana-1920	135	17	the	the	DET
cana-1920	135	18	following	follow	VERB
cana-1920	135	19	classification	classification	NOUN
cana-1920	135	20	based	base	VERB
cana-1920	135	21	on	on	ADP
cana-1920	135	22	their	their	PRON
cana-1920	135	23	end	end	NOUN
cana-1920	135	24	vertices	vertex	NOUN
cana-1920	135	25	:	:	PUNCT
cana-1920	135	26	1	1	NUM
cana-1920	135	27	leaf	leaf	NOUN
cana-1920	135	28	-	-	PUNCT
cana-1920	135	29	internal	internal	ADJ
cana-1920	135	30	edge	edge	NOUN
cana-1920	135	31	,	,	PUNCT
cana-1920	135	32	m−3	m−3	PROPN
cana-1920	135	33	internal	internal	ADJ
cana-1920	135	34	-	-	PUNCT
cana-1920	135	35	internal	internal	ADJ
cana-1920	135	36	edges	edge	NOUN
cana-1920	135	37	,	,	PUNCT
cana-1920	135	38	1	1	NUM
cana-1920	135	39	internal	internal	ADJ
cana-1920	135	40	-	-	PUNCT
cana-1920	135	41	branching	branch	VERB
cana-1920	135	42	edge	edge	NOUN
cana-1920	135	43	,	,	PUNCT
cana-1920	135	44	and	and	CCONJ
cana-1920	135	45	n	n	ADV
cana-1920	135	46	branching	branch	VERB
cana-1920	135	47	-	-	PUNCT
cana-1920	135	48	internal	internal	ADJ
cana-1920	135	49	edges	edge	NOUN
cana-1920	135	50	.	.	PUNCT
cana-1920	136	1	combining	combine	VERB
cana-1920	136	2	these	these	DET
cana-1920	136	3	information	information	NOUN
cana-1920	136	4	with	with	ADP
cana-1920	136	5	equation	equation	NOUN
cana-1920	136	6	(	(	PUNCT
cana-1920	136	7	1	1	NUM
cana-1920	136	8	)	)	PUNCT
cana-1920	136	9	in	in	ADP
cana-1920	136	10	proposition	proposition	NOUN
cana-1920	136	11	2.2	2.2	NUM
cana-1920	136	12	and	and	CCONJ
cana-1920	136	13	the	the	DET
cana-1920	136	14	definition	definition	NOUN
cana-1920	136	15	of	of	ADP
cana-1920	136	16	the	the	DET
cana-1920	136	17	reverse	reverse	ADJ
cana-1920	136	18	arithmetic	arithmetic	ADJ
cana-1920	136	19	-	-	PUNCT
cana-1920	136	20	geometric	geometric	ADJ
cana-1920	136	21	index	index	NOUN
cana-1920	136	22	,	,	PUNCT
cana-1920	136	23	we	we	PRON
cana-1920	136	24	arrive	arrive	VERB
cana-1920	136	25	at	at	ADP
cana-1920	136	26	theorem	theorem	NOUN
cana-1920	136	27	3.5	3.5	NUM
cana-1920	136	28	.	.	PUNCT
cana-1920	137	1	let	let	VERB
cana-1920	137	2	g	g	NOUN
cana-1920	137	3	=	=	SYM
cana-1920	137	4	cm	cm	PROPN
cana-1920	137	5	,	,	PUNCT
cana-1920	137	6	n.	n.	NOUN
cana-1920	137	7	the	the	DET
cana-1920	137	8	“	"	PUNCT
cana-1920	137	9	reverse	reverse	ADJ
cana-1920	137	10	geometric	geometric	ADJ
cana-1920	137	11	-	-	PUNCT
cana-1920	137	12	arithmetic	arithmetic	ADJ
cana-1920	137	13	index	index	NOUN
cana-1920	137	14	”	"	PUNCT
cana-1920	137	15	of	of	ADP
cana-1920	137	16	g	g	PROPN
cana-1920	137	17	denoted	denote	VERB
cana-1920	137	18	by	by	ADP
cana-1920	137	19	rga(g	rga(g	PROPN
cana-1920	137	20	)	)	PUNCT
cana-1920	137	21	is	be	AUX
cana-1920	137	22	given	give	VERB
cana-1920	137	23	by	by	ADP
cana-1920	137	24	proof	proof	NOUN
cana-1920	137	25	.	.	PUNCT
cana-1920	138	1	the	the	DET
cana-1920	138	2	proof	proof	NOUN
cana-1920	138	3	is	be	AUX
cana-1920	138	4	similar	similar	ADJ
cana-1920	138	5	to	to	ADP
cana-1920	138	6	the	the	DET
cana-1920	138	7	proof	proof	NOUN
cana-1920	138	8	of	of	ADP
cana-1920	138	9	theorem	theorem	ADJ
cana-1920	138	10	3.4	3.4	NUM
cana-1920	138	11	.	.	PUNCT
cana-1920	139	1	theorem	theorem	VERB
cana-1920	139	2	3.6	3.6	NUM
cana-1920	139	3	.	.	PUNCT
cana-1920	140	1	let	let	VERB
cana-1920	140	2	g	g	NOUN
cana-1920	140	3	=	=	NOUN
cana-1920	140	4	cm	cm	PROPN
cana-1920	140	5	,	,	PUNCT
cana-1920	140	6	n.	n.	NOUN
cana-1920	140	7	the	the	DET
cana-1920	140	8	“	"	PUNCT
cana-1920	140	9	reverse	reverse	ADJ
cana-1920	140	10	sombor	sombor	NOUN
cana-1920	140	11	index	index	NOUN
cana-1920	140	12	”	"	PUNCT
cana-1920	140	13	of	of	ADP
cana-1920	140	14	g	g	PROPN
cana-1920	140	15	denoted	denote	VERB
cana-1920	140	16	by	by	ADP
cana-1920	140	17	rso(g	rso(g	PROPN
cana-1920	140	18	)	)	PUNCT
cana-1920	140	19	is	be	AUX
cana-1920	140	20	given	give	VERB
cana-1920	140	21	by	by	ADP
cana-1920	140	22	proof	proof	NOUN
cana-1920	140	23	.	.	PUNCT
cana-1920	141	1	as	as	ADP
cana-1920	141	2	with	with	ADP
cana-1920	141	3	the	the	DET
cana-1920	141	4	previous	previous	ADJ
cana-1920	141	5	proofs	proof	NOUN
cana-1920	141	6	,	,	PUNCT
cana-1920	141	7	we	we	PRON
cana-1920	141	8	start	start	VERB
cana-1920	141	9	with	with	ADP
cana-1920	141	10	the	the	DET
cana-1920	141	11	fact	fact	NOUN
cana-1920	141	12	that	that	SCONJ
cana-1920	141	13	the	the	DET
cana-1920	141	14	graph	graph	NOUN
cana-1920	141	15	g	g	PROPN
cana-1920	141	16	=	=	NOUN
cana-1920	141	17	cm	cm	PROPN
cana-1920	141	18	,	,	PUNCT
cana-1920	141	19	n	n	PRON
cana-1920	141	20	has	have	AUX
cana-1920	141	21	m	m	PROPN
cana-1920	141	22	–	–	PUNCT
cana-1920	141	23	1	1	NUM
cana-1920	141	24	+	+	CCONJ
cana-1920	141	25	n	n	NOUN
cana-1920	141	26	edges	edge	VERB
cana-1920	141	27	with	with	ADP
cana-1920	141	28	the	the	DET
cana-1920	141	29	following	follow	VERB
cana-1920	141	30	classification	classification	NOUN
cana-1920	141	31	based	base	VERB
cana-1920	141	32	on	on	ADP
cana-1920	141	33	their	their	PRON
cana-1920	141	34	end	end	NOUN
cana-1920	141	35	vertices	vertex	NOUN
cana-1920	141	36	:	:	PUNCT
cana-1920	141	37	1	1	NUM
cana-1920	141	38	leaf	leaf	NOUN
cana-1920	141	39	-	-	PUNCT
cana-1920	141	40	internal	internal	ADJ
cana-1920	141	41	edge	edge	NOUN
cana-1920	141	42	,	,	PUNCT
cana-1920	141	43	m−3	m−3	PROPN
cana-1920	141	44	internal	internal	ADJ
cana-1920	141	45	-	-	PUNCT
cana-1920	141	46	internal	internal	ADJ
cana-1920	141	47	edges	edge	NOUN
cana-1920	141	48	,	,	PUNCT
cana-1920	141	49	1	1	NUM
cana-1920	141	50	internal	internal	ADJ
cana-1920	141	51	-	-	PUNCT
cana-1920	141	52	branching	branch	VERB
cana-1920	141	53	edge	edge	NOUN
cana-1920	141	54	,	,	PUNCT
cana-1920	141	55	and	and	CCONJ
cana-1920	141	56	n	n	ADV
cana-1920	141	57	branching	branch	VERB
cana-1920	141	58	-	-	PUNCT
cana-1920	141	59	internal	internal	ADJ
cana-1920	141	60	edges	edge	NOUN
cana-1920	141	61	.	.	PUNCT
cana-1920	142	1	combining	combine	VERB
cana-1920	142	2	these	these	DET
cana-1920	142	3	information	information	NOUN
cana-1920	142	4	with	with	ADP
cana-1920	142	5	equation	equation	NOUN
cana-1920	142	6	(	(	PUNCT
cana-1920	142	7	1	1	NUM
cana-1920	142	8	)	)	PUNCT
cana-1920	142	9	in	in	ADP
cana-1920	142	10	proposition	proposition	NOUN
cana-1920	142	11	2.2	2.2	NUM
cana-1920	142	12	and	and	CCONJ
cana-1920	142	13	the	the	DET
cana-1920	142	14	definition	definition	NOUN
cana-1920	142	15	of	of	ADP
cana-1920	142	16	the	the	DET
cana-1920	142	17	reverse	reverse	ADJ
cana-1920	142	18	sombor	sombor	NOUN
cana-1920	142	19	index	index	NOUN
cana-1920	142	20	,	,	PUNCT
cana-1920	142	21	we	we	PRON
cana-1920	142	22	arrive	arrive	VERB
cana-1920	142	23	at	at	ADP
cana-1920	142	24	communications	communication	NOUN
cana-1920	142	25	on	on	ADP
cana-1920	142	26	applied	apply	VERB
cana-1920	142	27	nonlinear	nonlinear	ADJ
cana-1920	142	28	analysis	analysis	NOUN
cana-1920	142	29	issn	issn	NOUN
cana-1920	142	30	:	:	PUNCT
cana-1920	142	31	1074	1074	NUM
cana-1920	142	32	-	-	PUNCT
cana-1920	142	33	133x	133x	NUM
cana-1920	142	34	vol	vol	NOUN
cana-1920	142	35	32	32	NUM
cana-1920	142	36	no	no	NOUN
cana-1920	142	37	.	.	NOUN
cana-1920	142	38	3	3	NUM
cana-1920	142	39	(	(	PUNCT
cana-1920	142	40	2025	2025	NUM
cana-1920	142	41	)	)	PUNCT
cana-1920	142	42	78	78	NUM
cana-1920	142	43	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	142	44	theorem	theorem	VERB
cana-1920	142	45	3.7	3.7	NUM
cana-1920	142	46	.	.	PUNCT
cana-1920	143	1	let	let	VERB
cana-1920	143	2	g	g	NOUN
cana-1920	143	3	=	=	NOUN
cana-1920	143	4	cm	cm	PROPN
cana-1920	143	5	,	,	PUNCT
cana-1920	143	6	n.	n.	NOUN
cana-1920	143	7	the	the	DET
cana-1920	143	8	“	"	PUNCT
cana-1920	143	9	reverse	reverse	ADJ
cana-1920	143	10	nirmala	nirmala	PROPN
cana-1920	143	11	index	index	PROPN
cana-1920	143	12	”	"	PUNCT
cana-1920	143	13	of	of	ADP
cana-1920	143	14	g	g	PROPN
cana-1920	143	15	denoted	denote	VERB
cana-1920	143	16	by	by	ADP
cana-1920	143	17	rn(g	rn(g	NUM
cana-1920	143	18	)	)	PUNCT
cana-1920	143	19	is	be	AUX
cana-1920	143	20	given	give	VERB
cana-1920	143	21	by	by	ADP
cana-1920	143	22	proof	proof	NOUN
cana-1920	143	23	.	.	PUNCT
cana-1920	144	1	the	the	DET
cana-1920	144	2	proof	proof	NOUN
cana-1920	144	3	is	be	AUX
cana-1920	144	4	similar	similar	ADJ
cana-1920	144	5	to	to	ADP
cana-1920	144	6	the	the	DET
cana-1920	144	7	proof	proof	NOUN
cana-1920	144	8	of	of	ADP
cana-1920	144	9	theorem	theorem	ADJ
cana-1920	144	10	3.6	3.6	NUM
cana-1920	144	11	.	.	NOUN
cana-1920	144	12	3.2	3.2	NUM
cana-1920	144	13	.	.	PUNCT
cana-1920	145	1	results	result	NOUN
cana-1920	145	2	for	for	ADP
cana-1920	145	3	double	double	ADJ
cana-1920	145	4	comet	comet	NOUN
cana-1920	145	5	graphs	graph	NOUN
cana-1920	145	6	next	next	ADV
cana-1920	145	7	,	,	PUNCT
cana-1920	145	8	we	we	PRON
cana-1920	145	9	present	present	VERB
cana-1920	145	10	our	our	PRON
cana-1920	145	11	results	result	NOUN
cana-1920	145	12	for	for	ADP
cana-1920	145	13	double	double	ADJ
cana-1920	145	14	comet	comet	NOUN
cana-1920	145	15	graphs	graph	NOUN
cana-1920	145	16	.	.	PUNCT
cana-1920	146	1	throughout	throughout	ADP
cana-1920	146	2	this	this	DET
cana-1920	146	3	subsection	subsection	NOUN
cana-1920	146	4	,	,	PUNCT
cana-1920	146	5	we	we	PRON
cana-1920	146	6	denote	denote	VERB
cana-1920	146	7	the	the	DET
cana-1920	146	8	double	double	ADJ
cana-1920	146	9	comet	comet	NOUN
cana-1920	146	10	graph	graph	NOUN
cana-1920	146	11	dc(m	dc(m	NOUN
cana-1920	146	12	,	,	PUNCT
cana-1920	146	13	m1,m2	m1,m2	PROPN
cana-1920	146	14	)	)	PUNCT
cana-1920	146	15	by	by	ADP
cana-1920	146	16	g	g	PROPN
cana-1920	146	17	,	,	PUNCT
cana-1920	146	18	the	the	DET
cana-1920	146	19	maximum	maximum	NOUN
cana-1920	146	20	of	of	ADP
cana-1920	146	21	{	{	PUNCT
cana-1920	146	22	m1,m2	m1,m2	PROPN
cana-1920	146	23	}	}	PUNCT
cana-1920	146	24	by	by	ADP
cana-1920	146	25	m	m	PROPN
cana-1920	146	26	,	,	PUNCT
cana-1920	146	27	and	and	CCONJ
cana-1920	146	28	the	the	DET
cana-1920	146	29	minimum	minimum	NOUN
cana-1920	146	30	of	of	ADP
cana-1920	146	31	{	{	PUNCT
cana-1920	146	32	m1,m2	m1,m2	PROPN
cana-1920	146	33	}	}	PUNCT
cana-1920	146	34	by	by	ADP
cana-1920	146	35	µ.	µ.	PROPN
cana-1920	146	36	theorem	theorem	VERB
cana-1920	146	37	3.8	3.8	NUM
cana-1920	146	38	.	.	PUNCT
cana-1920	147	1	let	let	VERB
cana-1920	147	2	g	g	NOUN
cana-1920	147	3	=	=	SYM
cana-1920	147	4	dc(m	dc(m	NOUN
cana-1920	147	5	,	,	PUNCT
cana-1920	147	6	m1,m2	m1,m2	PROPN
cana-1920	147	7	)	)	PUNCT
cana-1920	147	8	.	.	PUNCT
cana-1920	148	1	denote	denote	VERB
cana-1920	148	2	by	by	ADP
cana-1920	148	3	m	m	PROPN
cana-1920	148	4	=	=	PUNCT
cana-1920	148	5	max{m1,m2	max{m1,m2	PROPN
cana-1920	148	6	}	}	PUNCT
cana-1920	148	7	and	and	CCONJ
cana-1920	148	8	µ	µ	X
cana-1920	148	9	=	=	SYM
cana-1920	148	10	min{m1,m2	min{m1,m2	NOUN
cana-1920	148	11	}	}	PUNCT
cana-1920	148	12	.	.	PUNCT
cana-1920	149	1	the	the	DET
cana-1920	149	2	“	"	PUNCT
cana-1920	149	3	reverse	reverse	ADJ
cana-1920	149	4	sum	sum	NOUN
cana-1920	149	5	-	-	PUNCT
cana-1920	149	6	connectivity	connectivity	NOUN
cana-1920	149	7	index	index	NOUN
cana-1920	149	8	”	"	PUNCT
cana-1920	149	9	of	of	ADP
cana-1920	149	10	g	g	PROPN
cana-1920	149	11	denoted	denote	VERB
cana-1920	149	12	by	by	ADP
cana-1920	149	13	rsci(g	rsci(g	NOUN
cana-1920	149	14	)	)	PUNCT
cana-1920	149	15	is	be	AUX
cana-1920	149	16	given	give	VERB
cana-1920	149	17	by	by	ADP
cana-1920	149	18	proof	proof	NOUN
cana-1920	149	19	.	.	PUNCT
cana-1920	150	1	for	for	ADP
cana-1920	150	2	the	the	DET
cana-1920	150	3	proof	proof	NOUN
cana-1920	150	4	of	of	ADP
cana-1920	150	5	this	this	DET
cana-1920	150	6	result	result	NOUN
cana-1920	150	7	,	,	PUNCT
cana-1920	150	8	we	we	PRON
cana-1920	150	9	refer	refer	VERB
cana-1920	150	10	the	the	DET
cana-1920	150	11	readers	reader	NOUN
cana-1920	150	12	to	to	ADP
cana-1920	150	13	the	the	DET
cana-1920	150	14	proof	proof	NOUN
cana-1920	150	15	provided	provide	VERB
cana-1920	150	16	in	in	ADP
cana-1920	150	17	theorem	theorem	NOUN
cana-1920	150	18	3.10	3.10	NUM
cana-1920	150	19	,	,	PUNCT
cana-1920	150	20	since	since	SCONJ
cana-1920	150	21	they	they	PRON
cana-1920	150	22	are	be	AUX
cana-1920	150	23	similar	similar	ADJ
cana-1920	150	24	in	in	ADP
cana-1920	150	25	nature	nature	NOUN
cana-1920	150	26	.	.	PUNCT
cana-1920	151	1	theorem	theorem	VERB
cana-1920	151	2	3.9	3.9	NUM
cana-1920	151	3	.	.	PUNCT
cana-1920	152	1	let	let	VERB
cana-1920	152	2	g	g	NOUN
cana-1920	152	3	=	=	SYM
cana-1920	152	4	dc(m	dc(m	NOUN
cana-1920	152	5	,	,	PUNCT
cana-1920	152	6	m1,m2	m1,m2	PROPN
cana-1920	152	7	)	)	PUNCT
cana-1920	152	8	.	.	PUNCT
cana-1920	153	1	denote	denote	VERB
cana-1920	153	2	by	by	ADP
cana-1920	153	3	m	m	PROPN
cana-1920	153	4	=	=	PUNCT
cana-1920	153	5	max{m1,m2	max{m1,m2	PROPN
cana-1920	153	6	}	}	PUNCT
cana-1920	153	7	and	and	CCONJ
cana-1920	153	8	µ	µ	X
cana-1920	153	9	=	=	SYM
cana-1920	153	10	min{m1,m2	min{m1,m2	NOUN
cana-1920	153	11	}	}	PUNCT
cana-1920	153	12	.	.	PUNCT
cana-1920	154	1	the	the	DET
cana-1920	154	2	“	"	PUNCT
cana-1920	154	3	first	first	ADJ
cana-1920	154	4	reverse	reverse	ADJ
cana-1920	154	5	zagreb	zagreb	PROPN
cana-1920	154	6	index	index	PROPN
cana-1920	154	7	”	"	PUNCT
cana-1920	154	8	of	of	ADP
cana-1920	154	9	g	g	PROPN
cana-1920	154	10	denoted	denote	VERB
cana-1920	154	11	by	by	ADP
cana-1920	154	12	rm1(g	rm1(g	PROPN
cana-1920	154	13	)	)	PUNCT
cana-1920	154	14	is	be	AUX
cana-1920	154	15	given	give	VERB
cana-1920	154	16	by	by	ADP
cana-1920	154	17	proof	proof	NOUN
cana-1920	154	18	.	.	PUNCT
cana-1920	155	1	we	we	PRON
cana-1920	155	2	start	start	VERB
cana-1920	155	3	by	by	ADP
cana-1920	155	4	noting	note	VERB
cana-1920	155	5	that	that	SCONJ
cana-1920	155	6	the	the	DET
cana-1920	155	7	graph	graph	NOUN
cana-1920	155	8	g	g	NOUN
cana-1920	155	9	=	=	SYM
cana-1920	155	10	dc(m	dc(m	NOUN
cana-1920	155	11	,	,	PUNCT
cana-1920	155	12	m1,m2	m1,m2	PROPN
cana-1920	155	13	)	)	PUNCT
cana-1920	155	14	has	have	VERB
cana-1920	155	15	m	m	PROPN
cana-1920	155	16	+	+	NOUN
cana-1920	155	17	m1	m1	PROPN
cana-1920	155	18	+	+	PROPN
cana-1920	155	19	m2	m2	PROPN
cana-1920	155	20	=	=	SYM
cana-1920	155	21	m	m	PROPN
cana-1920	155	22	+	+	NOUN
cana-1920	155	23	µ	µ	VERB
cana-1920	155	24	+	+	NUM
cana-1920	155	25	m	m	NOUN
cana-1920	155	26	vertices	vertex	NOUN
cana-1920	155	27	with	with	ADP
cana-1920	155	28	the	the	DET
cana-1920	155	29	following	follow	VERB
cana-1920	155	30	classification	classification	NOUN
cana-1920	155	31	:	:	PUNCT
cana-1920	155	32	m1	m1	PROPN
cana-1920	155	33	+	+	CCONJ
cana-1920	155	34	m2	m2	PROPN
cana-1920	155	35	=	=	SYM
cana-1920	155	36	µ	µ	PROPN
cana-1920	155	37	+	+	NUM
cana-1920	155	38	m	m	NOUN
cana-1920	155	39	leaf	leaf	NOUN
cana-1920	155	40	vertices	vertex	NOUN
cana-1920	155	41	,	,	PUNCT
cana-1920	155	42	m	m	VERB
cana-1920	155	43	−	−	NUM
cana-1920	155	44	2	2	NUM
cana-1920	155	45	internal	internal	ADJ
cana-1920	155	46	vertices	vertex	NOUN
cana-1920	155	47	,	,	PUNCT
cana-1920	155	48	1	1	NUM
cana-1920	155	49	branching	branch	VERB
cana-1920	155	50	vertex	vertex	NOUN
cana-1920	155	51	of	of	ADP
cana-1920	155	52	degree	degree	NOUN
cana-1920	155	53	µ	µ	X
cana-1920	155	54	+1	+1	NOUN
cana-1920	155	55	,	,	PUNCT
cana-1920	155	56	and	and	CCONJ
cana-1920	155	57	1	1	NUM
cana-1920	155	58	branching	branch	VERB
cana-1920	155	59	vertex	vertex	NOUN
cana-1920	155	60	of	of	ADP
cana-1920	155	61	degree	degree	NOUN
cana-1920	155	62	m	m	NOUN
cana-1920	155	63	+1	+1	PROPN
cana-1920	155	64	.	.	PUNCT
cana-1920	156	1	combining	combine	VERB
cana-1920	156	2	these	these	DET
cana-1920	156	3	information	information	NOUN
cana-1920	156	4	with	with	ADP
cana-1920	156	5	equation	equation	NOUN
cana-1920	156	6	(	(	PUNCT
cana-1920	156	7	2	2	NUM
cana-1920	156	8	)	)	PUNCT
cana-1920	156	9	in	in	ADP
cana-1920	156	10	proposition	proposition	NOUN
cana-1920	156	11	2.3	2.3	NUM
cana-1920	156	12	and	and	CCONJ
cana-1920	156	13	the	the	DET
cana-1920	156	14	definition	definition	NOUN
cana-1920	156	15	of	of	ADP
cana-1920	156	16	the	the	DET
cana-1920	156	17	first	first	ADJ
cana-1920	156	18	reverse	reverse	ADJ
cana-1920	156	19	zagreb	zagreb	PROPN
cana-1920	156	20	index	index	PROPN
cana-1920	156	21	,	,	PUNCT
cana-1920	156	22	we	we	PRON
cana-1920	156	23	arrive	arrive	VERB
cana-1920	156	24	at	at	ADP
cana-1920	156	25	theorem	theorem	NOUN
cana-1920	156	26	3.10	3.10	NUM
cana-1920	156	27	.	.	PUNCT
cana-1920	157	1	let	let	VERB
cana-1920	157	2	g	g	NOUN
cana-1920	157	3	=	=	SYM
cana-1920	157	4	dc(m	dc(m	NOUN
cana-1920	157	5	,	,	PUNCT
cana-1920	157	6	m1,m2	m1,m2	PROPN
cana-1920	157	7	)	)	PUNCT
cana-1920	157	8	.	.	PUNCT
cana-1920	158	1	denote	denote	VERB
cana-1920	158	2	by	by	ADP
cana-1920	158	3	m	m	PROPN
cana-1920	158	4	=	=	PUNCT
cana-1920	158	5	max{m1,m2	max{m1,m2	PROPN
cana-1920	158	6	}	}	PUNCT
cana-1920	158	7	and	and	CCONJ
cana-1920	158	8	µ	µ	X
cana-1920	158	9	=	=	SYM
cana-1920	158	10	min{m1,m2	min{m1,m2	NOUN
cana-1920	158	11	}	}	PUNCT
cana-1920	158	12	.	.	PUNCT
cana-1920	159	1	the“second	the“second	PROPN
cana-1920	159	2	reverse	reverse	PROPN
cana-1920	159	3	zagreb	zagreb	PROPN
cana-1920	159	4	index	index	PROPN
cana-1920	159	5	”	"	PUNCT
cana-1920	159	6	of	of	ADP
cana-1920	159	7	g	g	PROPN
cana-1920	159	8	denoted	denote	VERB
cana-1920	159	9	by	by	ADP
cana-1920	159	10	rm2(g	rm2(g	NOUN
cana-1920	159	11	)	)	PUNCT
cana-1920	159	12	is	be	AUX
cana-1920	159	13	given	give	VERB
cana-1920	159	14	by	by	ADP
cana-1920	159	15	proof	proof	NOUN
cana-1920	159	16	.	.	PUNCT
cana-1920	160	1	we	we	PRON
cana-1920	160	2	start	start	VERB
cana-1920	160	3	by	by	ADP
cana-1920	160	4	noting	note	VERB
cana-1920	160	5	that	that	SCONJ
cana-1920	160	6	the	the	DET
cana-1920	160	7	graph	graph	NOUN
cana-1920	160	8	g	g	NOUN
cana-1920	160	9	=	=	SYM
cana-1920	160	10	dc(m	dc(m	NOUN
cana-1920	160	11	,	,	PUNCT
cana-1920	160	12	m1,m2	m1,m2	PROPN
cana-1920	160	13	)	)	PUNCT
cana-1920	160	14	has	have	VERB
cana-1920	160	15	(	(	PUNCT
cana-1920	160	16	m	m	NOUN
cana-1920	160	17	−1	−1	NOUN
cana-1920	160	18	)	)	PUNCT
cana-1920	161	1	+	+	CCONJ
cana-1920	161	2	m1	m1	PROPN
cana-1920	161	3	+	+	CCONJ
cana-1920	161	4	m2	m2	PROPN
cana-1920	161	5	=	=	SYM
cana-1920	161	6	(	(	PUNCT
cana-1920	161	7	m	m	VERB
cana-1920	162	1	−1)+µ	−1)+µ	VERB
cana-1920	162	2	+	+	NOUN
cana-1920	162	3	m	m	VERB
cana-1920	162	4	edges	edge	VERB
cana-1920	162	5	with	with	ADP
cana-1920	162	6	the	the	DET
cana-1920	162	7	following	follow	VERB
cana-1920	162	8	classification	classification	NOUN
cana-1920	162	9	based	base	VERB
cana-1920	162	10	on	on	ADP
cana-1920	162	11	their	their	PRON
cana-1920	162	12	end	end	NOUN
cana-1920	162	13	vertices	vertex	NOUN
cana-1920	162	14	:	:	PUNCT
cana-1920	162	15	µ	µ	DET
cana-1920	162	16	+	+	NOUN
cana-1920	162	17	m	m	NOUN
cana-1920	162	18	leaf	leaf	NOUN
cana-1920	162	19	-	-	PUNCT
cana-1920	162	20	branching	branch	VERB
cana-1920	162	21	(	(	PUNCT
cana-1920	162	22	branching	branch	VERB
cana-1920	162	23	-	-	PUNCT
cana-1920	162	24	leaf	leaf	NOUN
cana-1920	162	25	)	)	PUNCT
cana-1920	162	26	edge	edge	NOUN
cana-1920	162	27	,	,	PUNCT
cana-1920	162	28	2	2	NUM
cana-1920	162	29	internal	internal	ADV
cana-1920	162	30	-	-	PUNCT
cana-1920	162	31	branching	branch	VERB
cana-1920	162	32	(	(	PUNCT
cana-1920	162	33	branching	branch	VERB
cana-1920	162	34	-	-	PUNCT
cana-1920	162	35	internal	internal	ADJ
cana-1920	162	36	)	)	PUNCT
cana-1920	162	37	edge	edge	NOUN
cana-1920	162	38	,	,	PUNCT
cana-1920	162	39	and	and	CCONJ
cana-1920	162	40	m−3	m−3	PROPN
cana-1920	162	41	internal	internal	ADJ
cana-1920	162	42	-	-	PUNCT
cana-1920	162	43	internal	internal	ADJ
cana-1920	162	44	edges	edge	NOUN
cana-1920	162	45	.	.	PUNCT
cana-1920	163	1	before	before	SCONJ
cana-1920	163	2	we	we	PRON
cana-1920	163	3	proceed	proceed	VERB
cana-1920	163	4	,	,	PUNCT
cana-1920	163	5	we	we	PRON
cana-1920	163	6	emphasize	emphasize	VERB
cana-1920	163	7	that	that	SCONJ
cana-1920	163	8	in	in	ADP
cana-1920	163	9	the	the	DET
cana-1920	163	10	µ	µ	ADJ
cana-1920	163	11	+	+	NOUN
cana-1920	163	12	m	m	NOUN
cana-1920	163	13	leaf	leaf	NOUN
cana-1920	163	14	-	-	PUNCT
cana-1920	163	15	branching	branch	VERB
cana-1920	163	16	(	(	PUNCT
cana-1920	163	17	branching	branch	VERB
cana-1920	163	18	-	-	PUNCT
cana-1920	163	19	leaf	leaf	NOUN
cana-1920	163	20	)	)	PUNCT
cana-1920	163	21	edge	edge	NOUN
cana-1920	163	22	type	type	NOUN
cana-1920	163	23	,	,	PUNCT
cana-1920	163	24	there	there	PRON
cana-1920	163	25	are	be	VERB
cana-1920	163	26	µ	µ	DET
cana-1920	163	27	number	number	NOUN
cana-1920	163	28	of	of	ADP
cana-1920	163	29	edges	edge	NOUN
cana-1920	163	30	whose	whose	DET
cana-1920	163	31	one	one	NUM
cana-1920	163	32	end	end	NOUN
cana-1920	163	33	is	be	AUX
cana-1920	163	34	the	the	DET
cana-1920	163	35	vertex	vertex	NOUN
cana-1920	163	36	with	with	ADP
cana-1920	163	37	degree	degree	NOUN
cana-1920	163	38	µ	µ	X
cana-1920	163	39	+1	+1	ADJ
cana-1920	163	40	and	and	CCONJ
cana-1920	163	41	m	m	ADJ
cana-1920	163	42	number	number	NOUN
cana-1920	163	43	of	of	ADP
cana-1920	163	44	edges	edge	NOUN
cana-1920	163	45	whose	whose	DET
cana-1920	163	46	one	one	NUM
cana-1920	163	47	end	end	NOUN
cana-1920	163	48	is	be	AUX
cana-1920	163	49	the	the	DET
cana-1920	163	50	vertex	vertex	NOUN
cana-1920	163	51	with	with	ADP
cana-1920	163	52	degree	degree	NOUN
cana-1920	163	53	m	m	NOUN
cana-1920	163	54	+1	+1	PROPN
cana-1920	163	55	.	.	PUNCT
cana-1920	164	1	also	also	ADV
cana-1920	164	2	in	in	ADP
cana-1920	164	3	the	the	DET
cana-1920	164	4	2	2	NUM
cana-1920	164	5	internal	internal	ADV
cana-1920	164	6	-	-	PUNCT
cana-1920	164	7	branching	branch	VERB
cana-1920	164	8	(	(	PUNCT
cana-1920	164	9	branching	branch	VERB
cana-1920	164	10	-	-	PUNCT
cana-1920	164	11	internal	internal	ADJ
cana-1920	164	12	)	)	PUNCT
cana-1920	164	13	edge	edge	NOUN
cana-1920	164	14	type	type	NOUN
cana-1920	164	15	,	,	PUNCT
cana-1920	164	16	1	1	NUM
cana-1920	164	17	edge	edge	NOUN
cana-1920	164	18	has	have	VERB
cana-1920	164	19	communications	communication	NOUN
cana-1920	164	20	on	on	ADP
cana-1920	164	21	applied	apply	VERB
cana-1920	164	22	nonlinear	nonlinear	ADJ
cana-1920	164	23	analysis	analysis	NOUN
cana-1920	164	24	issn	issn	NOUN
cana-1920	164	25	:	:	PUNCT
cana-1920	164	26	1074	1074	NUM
cana-1920	164	27	-	-	PUNCT
cana-1920	164	28	133x	133x	NUM
cana-1920	164	29	vol	vol	NOUN
cana-1920	164	30	32	32	NUM
cana-1920	164	31	no	no	NOUN
cana-1920	164	32	.	.	NOUN
cana-1920	164	33	3	3	NUM
cana-1920	164	34	(	(	PUNCT
cana-1920	164	35	2025	2025	NUM
cana-1920	164	36	)	)	PUNCT
cana-1920	164	37	79	79	NUM
cana-1920	164	38	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	165	1	the	the	DET
cana-1920	165	2	vertex	vertex	NOUN
cana-1920	165	3	of	of	ADP
cana-1920	165	4	degree	degree	NOUN
cana-1920	165	5	µ	µ	X
cana-1920	165	6	+1	+1	NOUN
cana-1920	165	7	as	as	ADP
cana-1920	165	8	one	one	NUM
cana-1920	165	9	end	end	NOUN
cana-1920	165	10	vertex	vertex	NOUN
cana-1920	165	11	,	,	PUNCT
cana-1920	165	12	while	while	SCONJ
cana-1920	165	13	the	the	DET
cana-1920	165	14	other	other	ADJ
cana-1920	165	15	edge	edge	NOUN
cana-1920	165	16	has	have	VERB
cana-1920	165	17	the	the	DET
cana-1920	165	18	vertex	vertex	NOUN
cana-1920	165	19	of	of	ADP
cana-1920	165	20	degree	degree	NOUN
cana-1920	166	1	m	m	VERB
cana-1920	166	2	+1	+1	ADJ
cana-1920	166	3	as	as	ADP
cana-1920	166	4	one	one	NUM
cana-1920	166	5	end	end	NOUN
cana-1920	166	6	vertex	vertex	NOUN
cana-1920	166	7	.	.	PUNCT
cana-1920	167	1	combining	combine	VERB
cana-1920	167	2	these	these	DET
cana-1920	167	3	information	information	NOUN
cana-1920	167	4	with	with	ADP
cana-1920	167	5	equation	equation	NOUN
cana-1920	167	6	(	(	PUNCT
cana-1920	167	7	2	2	NUM
cana-1920	167	8	)	)	PUNCT
cana-1920	167	9	in	in	ADP
cana-1920	167	10	proposition	proposition	NOUN
cana-1920	167	11	2.3	2.3	NUM
cana-1920	167	12	and	and	CCONJ
cana-1920	167	13	the	the	DET
cana-1920	167	14	definition	definition	NOUN
cana-1920	167	15	of	of	ADP
cana-1920	167	16	the	the	DET
cana-1920	167	17	second	second	ADJ
cana-1920	167	18	reverse	reverse	NOUN
cana-1920	167	19	zagreb	zagreb	PROPN
cana-1920	167	20	index	index	PROPN
cana-1920	167	21	,	,	PUNCT
cana-1920	167	22	we	we	PRON
cana-1920	167	23	arrive	arrive	VERB
cana-1920	167	24	at	at	ADP
cana-1920	167	25	theorem	theorem	NOUN
cana-1920	167	26	3.11	3.11	NUM
cana-1920	167	27	.	.	PUNCT
cana-1920	168	1	let	let	VERB
cana-1920	168	2	g	g	NOUN
cana-1920	168	3	=	=	SYM
cana-1920	168	4	dc(m	dc(m	NOUN
cana-1920	168	5	,	,	PUNCT
cana-1920	168	6	m1,m2	m1,m2	PROPN
cana-1920	168	7	)	)	PUNCT
cana-1920	168	8	.	.	PUNCT
cana-1920	169	1	denote	denote	VERB
cana-1920	169	2	by	by	ADP
cana-1920	169	3	m	m	PROPN
cana-1920	169	4	=	=	PUNCT
cana-1920	169	5	max{m1,m2	max{m1,m2	PROPN
cana-1920	169	6	}	}	PUNCT
cana-1920	169	7	and	and	CCONJ
cana-1920	169	8	µ	µ	X
cana-1920	169	9	=	=	SYM
cana-1920	169	10	min{m1,m2	min{m1,m2	NOUN
cana-1920	169	11	}	}	PUNCT
cana-1920	169	12	.	.	PUNCT
cana-1920	170	1	the	the	DET
cana-1920	170	2	“	"	PUNCT
cana-1920	170	3	reverse	reverse	ADJ
cana-1920	170	4	arithmetic	arithmetic	ADJ
cana-1920	170	5	-	-	PUNCT
cana-1920	170	6	geometric	geometric	ADJ
cana-1920	170	7	index	index	NOUN
cana-1920	170	8	”	"	PUNCT
cana-1920	170	9	of	of	ADP
cana-1920	170	10	g	g	PROPN
cana-1920	170	11	denoted	denote	VERB
cana-1920	170	12	by	by	ADP
cana-1920	170	13	rag(g	rag(g	PROPN
cana-1920	170	14	)	)	PUNCT
cana-1920	170	15	is	be	AUX
cana-1920	170	16	given	give	VERB
cana-1920	170	17	by	by	ADP
cana-1920	170	18	proof	proof	NOUN
cana-1920	170	19	.	.	PUNCT
cana-1920	171	1	the	the	DET
cana-1920	171	2	proof	proof	NOUN
cana-1920	171	3	is	be	AUX
cana-1920	171	4	similar	similar	ADJ
cana-1920	171	5	to	to	ADP
cana-1920	171	6	the	the	DET
cana-1920	171	7	proof	proof	NOUN
cana-1920	171	8	provided	provide	VERB
cana-1920	171	9	in	in	ADP
cana-1920	171	10	theorem	theorem	ADJ
cana-1920	171	11	3.12	3.12	NUM
cana-1920	171	12	.	.	PUNCT
cana-1920	172	1	theorem	theorem	VERB
cana-1920	172	2	3.12	3.12	NUM
cana-1920	172	3	.	.	PUNCT
cana-1920	173	1	let	let	VERB
cana-1920	173	2	g	g	NOUN
cana-1920	173	3	=	=	SYM
cana-1920	173	4	dc(m	dc(m	NOUN
cana-1920	173	5	,	,	PUNCT
cana-1920	173	6	m1,m2	m1,m2	PROPN
cana-1920	173	7	)	)	PUNCT
cana-1920	173	8	.	.	PUNCT
cana-1920	174	1	denote	denote	VERB
cana-1920	174	2	by	by	ADP
cana-1920	174	3	m	m	PROPN
cana-1920	174	4	=	=	PUNCT
cana-1920	174	5	max{m1,m2	max{m1,m2	PROPN
cana-1920	174	6	}	}	PUNCT
cana-1920	174	7	and	and	CCONJ
cana-1920	174	8	µ	µ	X
cana-1920	174	9	=	=	SYM
cana-1920	174	10	min{m1,m2	min{m1,m2	NOUN
cana-1920	174	11	}	}	PUNCT
cana-1920	174	12	.	.	PUNCT
cana-1920	175	1	the	the	DET
cana-1920	175	2	“	"	PUNCT
cana-1920	175	3	reverse	reverse	ADJ
cana-1920	175	4	geometric	geometric	ADJ
cana-1920	175	5	-	-	PUNCT
cana-1920	175	6	arithmetic	arithmetic	ADJ
cana-1920	175	7	index	index	NOUN
cana-1920	175	8	”	"	PUNCT
cana-1920	175	9	of	of	ADP
cana-1920	175	10	g	g	PROPN
cana-1920	175	11	denoted	denote	VERB
cana-1920	175	12	by	by	ADP
cana-1920	175	13	rga(g	rga(g	PROPN
cana-1920	175	14	)	)	PUNCT
cana-1920	175	15	is	be	AUX
cana-1920	175	16	given	give	VERB
cana-1920	175	17	by	by	ADP
cana-1920	175	18	proof	proof	NOUN
cana-1920	175	19	.	.	PUNCT
cana-1920	176	1	similar	similar	ADJ
cana-1920	176	2	to	to	ADP
cana-1920	176	3	what	what	PRON
cana-1920	176	4	we	we	PRON
cana-1920	176	5	did	do	AUX
cana-1920	176	6	earlier	early	ADV
cana-1920	176	7	,	,	PUNCT
cana-1920	176	8	we	we	PRON
cana-1920	176	9	start	start	VERB
cana-1920	176	10	by	by	ADP
cana-1920	176	11	noting	note	VERB
cana-1920	176	12	that	that	SCONJ
cana-1920	176	13	the	the	DET
cana-1920	176	14	graph	graph	NOUN
cana-1920	176	15	g	g	NOUN
cana-1920	176	16	=	=	SYM
cana-1920	176	17	dc(m	dc(m	NOUN
cana-1920	176	18	,	,	PUNCT
cana-1920	176	19	m1	m1	PROPN
cana-1920	176	20	,	,	PUNCT
cana-1920	176	21	m2	m2	PROPN
cana-1920	176	22	)	)	PUNCT
cana-1920	176	23	has	have	VERB
cana-1920	176	24	(	(	PUNCT
cana-1920	176	25	m−	m−	PROPN
cana-1920	176	26	1	1	NUM
cana-1920	176	27	)	)	PUNCT
cana-1920	177	1	+	+	CCONJ
cana-1920	177	2	m1	m1	PROPN
cana-1920	177	3	+	+	CCONJ
cana-1920	177	4	m2	m2	PROPN
cana-1920	177	5	=	=	SYM
cana-1920	177	6	(	(	PUNCT
cana-1920	177	7	m	m	NOUN
cana-1920	177	8	−1	−1	NOUN
cana-1920	177	9	)	)	PUNCT
cana-1920	178	1	+	+	CCONJ
cana-1920	178	2	µ	µ	PRON
cana-1920	178	3	+	+	NOUN
cana-1920	178	4	m	m	NOUN
cana-1920	178	5	edges	edge	NOUN
cana-1920	178	6	with	with	ADP
cana-1920	178	7	the	the	DET
cana-1920	178	8	following	follow	VERB
cana-1920	178	9	classification	classification	NOUN
cana-1920	178	10	based	base	VERB
cana-1920	178	11	on	on	ADP
cana-1920	178	12	their	their	PRON
cana-1920	178	13	end	end	NOUN
cana-1920	178	14	vertices	vertex	NOUN
cana-1920	178	15	:	:	PUNCT
cana-1920	178	16	µ+m	µ+m	PUNCT
cana-1920	178	17	leaf	leaf	NOUN
cana-1920	178	18	-	-	PUNCT
cana-1920	178	19	branching	branch	VERB
cana-1920	178	20	(	(	PUNCT
cana-1920	178	21	branching	branch	VERB
cana-1920	178	22	-	-	PUNCT
cana-1920	178	23	leaf	leaf	NOUN
cana-1920	178	24	)	)	PUNCT
cana-1920	178	25	edge	edge	NOUN
cana-1920	178	26	,	,	PUNCT
cana-1920	178	27	2	2	NUM
cana-1920	178	28	internal	internal	ADV
cana-1920	178	29	-	-	PUNCT
cana-1920	178	30	branching	branch	VERB
cana-1920	178	31	(	(	PUNCT
cana-1920	178	32	branching	branch	VERB
cana-1920	178	33	-	-	PUNCT
cana-1920	178	34	internal	internal	ADJ
cana-1920	178	35	)	)	PUNCT
cana-1920	178	36	edge	edge	NOUN
cana-1920	178	37	,	,	PUNCT
cana-1920	178	38	and	and	CCONJ
cana-1920	178	39	m−3	m−3	PROPN
cana-1920	178	40	internal	internal	ADJ
cana-1920	178	41	-	-	PUNCT
cana-1920	178	42	internal	internal	ADJ
cana-1920	178	43	edges	edge	NOUN
cana-1920	178	44	.	.	PUNCT
cana-1920	179	1	again	again	ADV
cana-1920	179	2	,	,	PUNCT
cana-1920	179	3	we	we	PRON
cana-1920	179	4	emphasize	emphasize	VERB
cana-1920	179	5	that	that	SCONJ
cana-1920	179	6	in	in	ADP
cana-1920	179	7	the	the	DET
cana-1920	179	8	µ	µ	ADJ
cana-1920	179	9	+	+	NOUN
cana-1920	179	10	m	m	NOUN
cana-1920	179	11	leaf	leaf	NOUN
cana-1920	179	12	-	-	PUNCT
cana-1920	179	13	branching	branch	VERB
cana-1920	179	14	(	(	PUNCT
cana-1920	179	15	branching	branch	VERB
cana-1920	179	16	-	-	PUNCT
cana-1920	179	17	leaf	leaf	NOUN
cana-1920	179	18	)	)	PUNCT
cana-1920	179	19	edge	edge	NOUN
cana-1920	179	20	type	type	NOUN
cana-1920	179	21	,	,	PUNCT
cana-1920	179	22	there	there	PRON
cana-1920	179	23	are	be	VERB
cana-1920	179	24	µ	µ	DET
cana-1920	179	25	number	number	NOUN
cana-1920	179	26	of	of	ADP
cana-1920	179	27	edges	edge	NOUN
cana-1920	179	28	whose	whose	DET
cana-1920	179	29	one	one	NUM
cana-1920	179	30	end	end	NOUN
cana-1920	179	31	is	be	AUX
cana-1920	179	32	the	the	DET
cana-1920	179	33	vertex	vertex	NOUN
cana-1920	179	34	with	with	ADP
cana-1920	179	35	degree	degree	NOUN
cana-1920	179	36	µ	µ	X
cana-1920	179	37	+1	+1	ADJ
cana-1920	179	38	and	and	CCONJ
cana-1920	179	39	m	m	ADJ
cana-1920	179	40	number	number	NOUN
cana-1920	179	41	of	of	ADP
cana-1920	179	42	edges	edge	NOUN
cana-1920	179	43	whose	whose	DET
cana-1920	179	44	one	one	NUM
cana-1920	179	45	end	end	NOUN
cana-1920	179	46	is	be	AUX
cana-1920	179	47	the	the	DET
cana-1920	179	48	vertex	vertex	NOUN
cana-1920	179	49	with	with	ADP
cana-1920	179	50	degree	degree	NOUN
cana-1920	180	1	m	m	NOUN
cana-1920	181	1	+1	+1	PROPN
cana-1920	181	2	.	.	PUNCT
cana-1920	182	1	also	also	ADV
cana-1920	182	2	in	in	ADP
cana-1920	182	3	the	the	DET
cana-1920	182	4	2	2	NUM
cana-1920	182	5	internal	internal	ADV
cana-1920	182	6	-	-	PUNCT
cana-1920	182	7	branching	branch	VERB
cana-1920	182	8	(	(	PUNCT
cana-1920	182	9	branchinginternal	branchinginternal	ADJ
cana-1920	182	10	)	)	PUNCT
cana-1920	182	11	edge	edge	NOUN
cana-1920	182	12	type	type	NOUN
cana-1920	182	13	,	,	PUNCT
cana-1920	182	14	1	1	NUM
cana-1920	182	15	edge	edge	NOUN
cana-1920	182	16	has	have	VERB
cana-1920	182	17	the	the	DET
cana-1920	182	18	vertex	vertex	NOUN
cana-1920	182	19	of	of	ADP
cana-1920	182	20	degree	degree	NOUN
cana-1920	182	21	µ	µ	X
cana-1920	182	22	+	+	CCONJ
cana-1920	182	23	1	1	NUM
cana-1920	182	24	as	as	ADP
cana-1920	182	25	one	one	NUM
cana-1920	182	26	end	end	NOUN
cana-1920	182	27	vertex	vertex	NOUN
cana-1920	182	28	,	,	PUNCT
cana-1920	182	29	while	while	SCONJ
cana-1920	182	30	the	the	DET
cana-1920	182	31	other	other	ADJ
cana-1920	182	32	edge	edge	NOUN
cana-1920	182	33	has	have	VERB
cana-1920	182	34	the	the	DET
cana-1920	182	35	vertex	vertex	NOUN
cana-1920	182	36	of	of	ADP
cana-1920	182	37	degree	degree	NOUN
cana-1920	182	38	m	m	VERB
cana-1920	182	39	+1	+1	ADJ
cana-1920	182	40	as	as	ADP
cana-1920	182	41	one	one	NUM
cana-1920	182	42	end	end	NOUN
cana-1920	182	43	vertex	vertex	NOUN
cana-1920	182	44	.	.	PUNCT
cana-1920	183	1	combining	combine	VERB
cana-1920	183	2	these	these	DET
cana-1920	183	3	information	information	NOUN
cana-1920	183	4	with	with	ADP
cana-1920	183	5	equation	equation	NOUN
cana-1920	183	6	(	(	PUNCT
cana-1920	183	7	2	2	NUM
cana-1920	183	8	)	)	PUNCT
cana-1920	183	9	in	in	ADP
cana-1920	183	10	proposition	proposition	NOUN
cana-1920	183	11	2.3	2.3	NUM
cana-1920	183	12	and	and	CCONJ
cana-1920	183	13	the	the	DET
cana-1920	183	14	definition	definition	NOUN
cana-1920	183	15	of	of	ADP
cana-1920	183	16	the	the	DET
cana-1920	183	17	reverse	reverse	ADJ
cana-1920	183	18	geometric	geometric	ADJ
cana-1920	183	19	-	-	PUNCT
cana-1920	183	20	arithmetic	arithmetic	ADJ
cana-1920	183	21	index	index	NOUN
cana-1920	183	22	,	,	PUNCT
cana-1920	183	23	we	we	PRON
cana-1920	183	24	arrive	arrive	VERB
cana-1920	183	25	at	at	ADP
cana-1920	183	26	simplifying	simplify	VERB
cana-1920	183	27	the	the	DET
cana-1920	183	28	above	above	ADJ
cana-1920	183	29	displayed	display	VERB
cana-1920	183	30	equation	equation	NOUN
cana-1920	183	31	will	will	AUX
cana-1920	183	32	give	give	VERB
cana-1920	183	33	us	we	PRON
cana-1920	183	34	this	this	PRON
cana-1920	183	35	proves	prove	VERB
cana-1920	183	36	the	the	DET
cana-1920	183	37	theorem	theorem	NOUN
cana-1920	183	38	.	.	PUNCT
cana-1920	184	1	communications	communication	NOUN
cana-1920	184	2	on	on	ADP
cana-1920	184	3	applied	apply	VERB
cana-1920	184	4	nonlinear	nonlinear	ADJ
cana-1920	184	5	analysis	analysis	NOUN
cana-1920	184	6	issn	issn	NOUN
cana-1920	184	7	:	:	PUNCT
cana-1920	184	8	1074	1074	NUM
cana-1920	184	9	-	-	PUNCT
cana-1920	184	10	133x	133x	NUM
cana-1920	184	11	vol	vol	NOUN
cana-1920	184	12	32	32	NUM
cana-1920	184	13	no	no	NOUN
cana-1920	184	14	.	.	NOUN
cana-1920	184	15	3	3	NUM
cana-1920	184	16	(	(	PUNCT
cana-1920	184	17	2025	2025	NUM
cana-1920	184	18	)	)	PUNCT
cana-1920	184	19	80	80	NUM
cana-1920	184	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	184	21	theorem	theorem	VERB
cana-1920	184	22	3.13	3.13	NUM
cana-1920	184	23	.	.	PUNCT
cana-1920	185	1	let	let	VERB
cana-1920	185	2	g	g	NOUN
cana-1920	185	3	=	=	SYM
cana-1920	185	4	dc(m	dc(m	NOUN
cana-1920	185	5	,	,	PUNCT
cana-1920	185	6	m1,m2	m1,m2	PROPN
cana-1920	185	7	)	)	PUNCT
cana-1920	185	8	.	.	PUNCT
cana-1920	186	1	denote	denote	VERB
cana-1920	186	2	by	by	ADP
cana-1920	186	3	m	m	PROPN
cana-1920	186	4	=	=	PUNCT
cana-1920	186	5	max{m1,m2	max{m1,m2	PROPN
cana-1920	186	6	}	}	PUNCT
cana-1920	186	7	and	and	CCONJ
cana-1920	186	8	µ	µ	X
cana-1920	186	9	=	=	SYM
cana-1920	186	10	min{m1,m2	min{m1,m2	NOUN
cana-1920	186	11	}	}	PUNCT
cana-1920	186	12	.	.	PUNCT
cana-1920	187	1	the	the	DET
cana-1920	187	2	“	"	PUNCT
cana-1920	187	3	reverse	reverse	ADJ
cana-1920	187	4	sombor	sombor	NOUN
cana-1920	187	5	index	index	NOUN
cana-1920	187	6	”	"	PUNCT
cana-1920	187	7	of	of	ADP
cana-1920	187	8	g	g	PROPN
cana-1920	187	9	denoted	denote	VERB
cana-1920	187	10	by	by	ADP
cana-1920	187	11	rso(g	rso(g	PROPN
cana-1920	187	12	)	)	PUNCT
cana-1920	187	13	is	be	AUX
cana-1920	187	14	given	give	VERB
cana-1920	187	15	by	by	ADP
cana-1920	187	16	proof	proof	NOUN
cana-1920	187	17	.	.	PUNCT
cana-1920	188	1	the	the	DET
cana-1920	188	2	proof	proof	NOUN
cana-1920	188	3	of	of	ADP
cana-1920	188	4	this	this	DET
cana-1920	188	5	theorem	theorem	NOUN
cana-1920	188	6	is	be	AUX
cana-1920	188	7	similar	similar	ADJ
cana-1920	188	8	to	to	ADP
cana-1920	188	9	the	the	DET
cana-1920	188	10	proof	proof	NOUN
cana-1920	188	11	of	of	ADP
cana-1920	188	12	theorem	theorem	ADJ
cana-1920	188	13	3.14	3.14	NUM
cana-1920	188	14	.	.	PUNCT
cana-1920	189	1	theorem	theorem	VERB
cana-1920	189	2	3.14	3.14	NUM
cana-1920	189	3	.	.	PUNCT
cana-1920	190	1	let	let	VERB
cana-1920	190	2	g	g	NOUN
cana-1920	190	3	=	=	SYM
cana-1920	190	4	dc(m	dc(m	NOUN
cana-1920	190	5	,	,	PUNCT
cana-1920	190	6	m1,m2	m1,m2	PROPN
cana-1920	190	7	)	)	PUNCT
cana-1920	190	8	.	.	PUNCT
cana-1920	191	1	denote	denote	VERB
cana-1920	191	2	by	by	ADP
cana-1920	191	3	m	m	PROPN
cana-1920	191	4	=	=	PUNCT
cana-1920	191	5	max{m1,m2	max{m1,m2	PROPN
cana-1920	191	6	}	}	PUNCT
cana-1920	191	7	and	and	CCONJ
cana-1920	191	8	µ	µ	X
cana-1920	191	9	=	=	SYM
cana-1920	191	10	min{m1,m2	min{m1,m2	NOUN
cana-1920	191	11	}	}	PUNCT
cana-1920	191	12	.	.	PUNCT
cana-1920	192	1	the	the	DET
cana-1920	192	2	“	"	PUNCT
cana-1920	192	3	reverse	reverse	ADJ
cana-1920	192	4	nirmala	nirmala	PROPN
cana-1920	192	5	index	index	PROPN
cana-1920	192	6	”	"	PUNCT
cana-1920	192	7	of	of	ADP
cana-1920	192	8	g	g	PROPN
cana-1920	192	9	denoted	denote	VERB
cana-1920	192	10	by	by	ADP
cana-1920	192	11	rn(g	rn(g	NUM
cana-1920	192	12	)	)	PUNCT
cana-1920	192	13	is	be	AUX
cana-1920	192	14	given	give	VERB
cana-1920	192	15	by	by	ADP
cana-1920	192	16	proof	proof	NOUN
cana-1920	192	17	.	.	PUNCT
cana-1920	193	1	again	again	ADV
cana-1920	193	2	,	,	PUNCT
cana-1920	193	3	we	we	PRON
cana-1920	193	4	start	start	VERB
cana-1920	193	5	by	by	ADP
cana-1920	193	6	noting	note	VERB
cana-1920	193	7	that	that	SCONJ
cana-1920	193	8	the	the	DET
cana-1920	193	9	graph	graph	NOUN
cana-1920	193	10	g	g	NOUN
cana-1920	193	11	=	=	SYM
cana-1920	193	12	dc(m	dc(m	NOUN
cana-1920	193	13	,	,	PUNCT
cana-1920	193	14	m1,m2	m1,m2	PROPN
cana-1920	193	15	)	)	PUNCT
cana-1920	193	16	has	have	VERB
cana-1920	193	17	(	(	PUNCT
cana-1920	193	18	m	m	NOUN
cana-1920	193	19	−1	−1	NOUN
cana-1920	193	20	)	)	PUNCT
cana-1920	194	1	+	+	CCONJ
cana-1920	194	2	m1	m1	PROPN
cana-1920	194	3	+	+	CCONJ
cana-1920	194	4	m2	m2	PROPN
cana-1920	194	5	=	=	SYM
cana-1920	194	6	(	(	PUNCT
cana-1920	194	7	m	m	NOUN
cana-1920	194	8	−	−	NOUN
cana-1920	194	9	1	1	NUM
cana-1920	194	10	)	)	PUNCT
cana-1920	195	1	+	+	NOUN
cana-1920	195	2	µ	µ	ADJ
cana-1920	195	3	+	+	NUM
cana-1920	195	4	m	m	VERB
cana-1920	195	5	edges	edge	NOUN
cana-1920	195	6	with	with	ADP
cana-1920	195	7	the	the	DET
cana-1920	195	8	following	follow	VERB
cana-1920	195	9	classification	classification	NOUN
cana-1920	195	10	based	base	VERB
cana-1920	195	11	on	on	ADP
cana-1920	195	12	their	their	PRON
cana-1920	195	13	end	end	NOUN
cana-1920	195	14	vertices	vertex	NOUN
cana-1920	195	15	:	:	PUNCT
cana-1920	195	16	µ	µ	DET
cana-1920	195	17	+	+	NOUN
cana-1920	195	18	m	m	NOUN
cana-1920	195	19	leaf	leaf	NOUN
cana-1920	195	20	-	-	PUNCT
cana-1920	195	21	branching	branch	VERB
cana-1920	195	22	(	(	PUNCT
cana-1920	195	23	branching	branch	VERB
cana-1920	195	24	-	-	PUNCT
cana-1920	195	25	leaf	leaf	NOUN
cana-1920	195	26	)	)	PUNCT
cana-1920	195	27	edge	edge	NOUN
cana-1920	195	28	,	,	PUNCT
cana-1920	195	29	2	2	NUM
cana-1920	195	30	internal	internal	ADV
cana-1920	195	31	-	-	PUNCT
cana-1920	195	32	branching	branch	VERB
cana-1920	195	33	(	(	PUNCT
cana-1920	195	34	branching	branch	VERB
cana-1920	195	35	-	-	PUNCT
cana-1920	195	36	internal	internal	ADJ
cana-1920	195	37	)	)	PUNCT
cana-1920	195	38	edge	edge	NOUN
cana-1920	195	39	,	,	PUNCT
cana-1920	195	40	and	and	CCONJ
cana-1920	195	41	m	m	PRON
cana-1920	195	42	−	−	PROPN
cana-1920	195	43	3	3	NUM
cana-1920	195	44	internal	internal	ADJ
cana-1920	195	45	-	-	PUNCT
cana-1920	195	46	internal	internal	ADJ
cana-1920	195	47	edges	edge	NOUN
cana-1920	195	48	.	.	PUNCT
cana-1920	196	1	moreover	moreover	ADV
cana-1920	196	2	,	,	PUNCT
cana-1920	196	3	we	we	PRON
cana-1920	196	4	emphasize	emphasize	VERB
cana-1920	196	5	that	that	SCONJ
cana-1920	196	6	in	in	ADP
cana-1920	196	7	the	the	DET
cana-1920	196	8	µ+m	µ+m	ADP
cana-1920	196	9	leaf	leaf	NOUN
cana-1920	196	10	-	-	PUNCT
cana-1920	196	11	branching	branch	VERB
cana-1920	196	12	(	(	PUNCT
cana-1920	196	13	branching	branch	VERB
cana-1920	196	14	-	-	PUNCT
cana-1920	196	15	leaf	leaf	NOUN
cana-1920	196	16	)	)	PUNCT
cana-1920	196	17	edge	edge	NOUN
cana-1920	196	18	type	type	NOUN
cana-1920	196	19	,	,	PUNCT
cana-1920	196	20	there	there	PRON
cana-1920	196	21	are	be	VERB
cana-1920	196	22	µ	µ	DET
cana-1920	196	23	number	number	NOUN
cana-1920	196	24	of	of	ADP
cana-1920	196	25	edges	edge	NOUN
cana-1920	196	26	whose	whose	DET
cana-1920	196	27	one	one	NUM
cana-1920	196	28	end	end	NOUN
cana-1920	196	29	is	be	AUX
cana-1920	196	30	the	the	DET
cana-1920	196	31	vertex	vertex	NOUN
cana-1920	196	32	with	with	ADP
cana-1920	196	33	degree	degree	NOUN
cana-1920	196	34	µ	µ	X
cana-1920	196	35	+1	+1	ADJ
cana-1920	196	36	and	and	CCONJ
cana-1920	196	37	m	m	ADJ
cana-1920	196	38	number	number	NOUN
cana-1920	196	39	of	of	ADP
cana-1920	196	40	edges	edge	NOUN
cana-1920	196	41	whose	whose	DET
cana-1920	196	42	one	one	NUM
cana-1920	196	43	end	end	NOUN
cana-1920	196	44	is	be	AUX
cana-1920	196	45	the	the	DET
cana-1920	196	46	vertex	vertex	NOUN
cana-1920	196	47	with	with	ADP
cana-1920	196	48	degree	degree	NOUN
cana-1920	196	49	m	m	NOUN
cana-1920	196	50	+1	+1	PROPN
cana-1920	196	51	.	.	PUNCT
cana-1920	197	1	also	also	ADV
cana-1920	197	2	in	in	ADP
cana-1920	197	3	the	the	DET
cana-1920	197	4	2	2	NUM
cana-1920	197	5	internal	internal	ADV
cana-1920	197	6	-	-	PUNCT
cana-1920	197	7	branching	branch	VERB
cana-1920	197	8	(	(	PUNCT
cana-1920	197	9	branching	branch	VERB
cana-1920	197	10	-	-	PUNCT
cana-1920	197	11	internal	internal	ADJ
cana-1920	197	12	)	)	PUNCT
cana-1920	197	13	edge	edge	NOUN
cana-1920	197	14	type	type	NOUN
cana-1920	197	15	,	,	PUNCT
cana-1920	197	16	1	1	NUM
cana-1920	197	17	edge	edge	NOUN
cana-1920	197	18	has	have	VERB
cana-1920	197	19	the	the	DET
cana-1920	197	20	vertex	vertex	NOUN
cana-1920	197	21	of	of	ADP
cana-1920	197	22	degree	degree	NOUN
cana-1920	197	23	µ	µ	X
cana-1920	197	24	+1	+1	NOUN
cana-1920	197	25	as	as	ADP
cana-1920	197	26	one	one	NUM
cana-1920	197	27	end	end	NOUN
cana-1920	197	28	vertex	vertex	NOUN
cana-1920	197	29	,	,	PUNCT
cana-1920	197	30	while	while	SCONJ
cana-1920	197	31	the	the	DET
cana-1920	197	32	other	other	ADJ
cana-1920	197	33	edge	edge	NOUN
cana-1920	197	34	has	have	VERB
cana-1920	197	35	the	the	DET
cana-1920	197	36	vertex	vertex	NOUN
cana-1920	197	37	of	of	ADP
cana-1920	197	38	degree	degree	NOUN
cana-1920	197	39	m	m	VERB
cana-1920	197	40	+1	+1	ADJ
cana-1920	197	41	as	as	ADP
cana-1920	197	42	one	one	NUM
cana-1920	197	43	end	end	NOUN
cana-1920	197	44	vertex	vertex	NOUN
cana-1920	197	45	.	.	PUNCT
cana-1920	198	1	combining	combine	VERB
cana-1920	198	2	these	these	DET
cana-1920	198	3	information	information	NOUN
cana-1920	198	4	with	with	ADP
cana-1920	198	5	equation	equation	NOUN
cana-1920	198	6	(	(	PUNCT
cana-1920	198	7	2	2	NUM
cana-1920	198	8	)	)	PUNCT
cana-1920	198	9	in	in	ADP
cana-1920	198	10	proposition	proposition	NOUN
cana-1920	198	11	2.3	2.3	NUM
cana-1920	198	12	and	and	CCONJ
cana-1920	198	13	the	the	DET
cana-1920	198	14	definition	definition	NOUN
cana-1920	198	15	of	of	ADP
cana-1920	198	16	the	the	DET
cana-1920	198	17	reverse	reverse	ADJ
cana-1920	198	18	nirmala	nirmala	PROPN
cana-1920	198	19	index	index	PROPN
cana-1920	198	20	,	,	PUNCT
cana-1920	198	21	we	we	PRON
cana-1920	198	22	arrive	arrive	VERB
cana-1920	198	23	at	at	ADP
cana-1920	198	24	3.3	3.3	NUM
cana-1920	198	25	reverse	reverse	NOUN
cana-1920	198	26	vertex	vertex	NOUN
cana-1920	198	27	degree	degree	NOUN
cana-1920	198	28	indices	index	NOUN
cana-1920	198	29	of	of	ADP
cana-1920	198	30	2,2,4,4	2,2,4,4	NUM
cana-1920	198	31	-	-	PUNCT
cana-1920	198	32	tetramethylpentane	tetramethylpentane	NOUN
cana-1920	198	33	for	for	ADP
cana-1920	198	34	this	this	DET
cana-1920	198	35	subsection	subsection	NOUN
cana-1920	198	36	,	,	PUNCT
cana-1920	198	37	we	we	PRON
cana-1920	198	38	illustrate	illustrate	VERB
cana-1920	198	39	a	a	DET
cana-1920	198	40	particular	particular	ADJ
cana-1920	198	41	computational	computational	ADJ
cana-1920	198	42	application	application	NOUN
cana-1920	198	43	of	of	ADP
cana-1920	198	44	theorems	theorem	NOUN
cana-1920	198	45	3.8	3.8	NUM
cana-1920	198	46	3.14	3.14	NUM
cana-1920	198	47	obtained	obtain	VERB
cana-1920	198	48	in	in	ADP
cana-1920	198	49	the	the	DET
cana-1920	198	50	previous	previous	ADJ
cana-1920	198	51	section	section	NOUN
cana-1920	198	52	.	.	PUNCT
cana-1920	199	1	observe	observe	VERB
cana-1920	199	2	that	that	SCONJ
cana-1920	199	3	the	the	DET
cana-1920	199	4	molecule	molecule	NOUN
cana-1920	199	5	2,2,4,4	2,2,4,4	NUM
cana-1920	199	6	-	-	PUNCT
cana-1920	199	7	tetramethylpentane	tetramethylpentane	NOUN
cana-1920	199	8	in	in	ADP
cana-1920	199	9	the	the	DET
cana-1920	199	10	introductory	introductory	ADJ
cana-1920	199	11	section	section	NOUN
cana-1920	199	12	has	have	VERB
cana-1920	199	13	dc(3,3,3	dc(3,3,3	PROPN
cana-1920	199	14	)	)	PUNCT
cana-1920	199	15	as	as	ADP
cana-1920	199	16	a	a	DET
cana-1920	199	17	molecular	molecular	ADJ
cana-1920	199	18	graph	graph	NOUN
cana-1920	199	19	.	.	PUNCT
cana-1920	200	1	hence	hence	ADV
cana-1920	200	2	,	,	PUNCT
cana-1920	200	3	we	we	PRON
cana-1920	200	4	have	have	VERB
cana-1920	200	5	the	the	DET
cana-1920	200	6	following	follow	VERB
cana-1920	200	7	immediate	immediate	ADJ
cana-1920	200	8	results	result	NOUN
cana-1920	200	9	.	.	PUNCT
cana-1920	201	1	corollary	corollary	ADJ
cana-1920	201	2	3.15	3.15	NUM
cana-1920	201	3	.	.	PUNCT
cana-1920	202	1	let	let	VERB
cana-1920	202	2	g	g	NOUN
cana-1920	202	3	denote	denote	VERB
cana-1920	202	4	the	the	DET
cana-1920	202	5	molecular	molecular	ADJ
cana-1920	202	6	graph	graph	NOUN
cana-1920	202	7	of	of	ADP
cana-1920	202	8	2,2,4,4	2,2,4,4	NUM
cana-1920	202	9	-	-	PUNCT
cana-1920	202	10	tetramethylpentane	tetramethylpentane	NOUN
cana-1920	202	11	,	,	PUNCT
cana-1920	202	12	then	then	ADV
cana-1920	202	13	communications	communication	NOUN
cana-1920	202	14	on	on	ADP
cana-1920	202	15	applied	apply	VERB
cana-1920	202	16	nonlinear	nonlinear	ADJ
cana-1920	202	17	analysis	analysis	NOUN
cana-1920	202	18	issn	issn	NOUN
cana-1920	202	19	:	:	PUNCT
cana-1920	202	20	1074	1074	NUM
cana-1920	202	21	-	-	PUNCT
cana-1920	202	22	133x	133x	NUM
cana-1920	202	23	vol	vol	NOUN
cana-1920	202	24	32	32	NUM
cana-1920	202	25	no	no	NOUN
cana-1920	202	26	.	.	NOUN
cana-1920	202	27	3	3	NUM
cana-1920	202	28	(	(	PUNCT
cana-1920	202	29	2025	2025	NUM
cana-1920	202	30	)	)	PUNCT
cana-1920	202	31	81	81	NUM
cana-1920	202	32	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	202	33	3.4	3.4	NUM
cana-1920	202	34	relationship	relationship	NOUN
cana-1920	202	35	between	between	ADP
cana-1920	202	36	the	the	DET
cana-1920	202	37	results	result	NOUN
cana-1920	202	38	for	for	ADP
cana-1920	202	39	bistar	bistar	NOUN
cana-1920	202	40	and	and	CCONJ
cana-1920	202	41	for	for	ADP
cana-1920	202	42	double	double	ADJ
cana-1920	202	43	comet	comet	NOUN
cana-1920	202	44	this	this	DET
cana-1920	202	45	subsection	subsection	NOUN
cana-1920	202	46	investigates	investigate	VERB
cana-1920	202	47	the	the	DET
cana-1920	202	48	relationship	relationship	NOUN
cana-1920	202	49	between	between	ADP
cana-1920	202	50	the	the	DET
cana-1920	202	51	reverse	reverse	ADJ
cana-1920	202	52	vertex	vertex	NOUN
cana-1920	202	53	degree	degree	NOUN
cana-1920	202	54	-	-	PUNCT
cana-1920	202	55	based	base	VERB
cana-1920	202	56	topological	topological	ADJ
cana-1920	202	57	indices	index	NOUN
cana-1920	202	58	of	of	ADP
cana-1920	202	59	bistars	bistar	NOUN
cana-1920	202	60	and	and	CCONJ
cana-1920	202	61	double	double	ADJ
cana-1920	202	62	comets	comet	NOUN
cana-1920	202	63	.	.	PUNCT
cana-1920	203	1	the	the	DET
cana-1920	203	2	motivation	motivation	NOUN
cana-1920	203	3	for	for	ADP
cana-1920	203	4	this	this	DET
cana-1920	203	5	subsection	subsection	NOUN
cana-1920	203	6	is	be	AUX
cana-1920	203	7	the	the	DET
cana-1920	203	8	fact	fact	NOUN
cana-1920	203	9	that	that	SCONJ
cana-1920	203	10	the	the	DET
cana-1920	203	11	bistar	bistar	PROPN
cana-1920	203	12	b(m1	b(m1	PROPN
cana-1920	203	13	,	,	PUNCT
cana-1920	203	14	m2	m2	PROPN
cana-1920	203	15	)	)	PUNCT
cana-1920	203	16	is	be	AUX
cana-1920	203	17	the	the	DET
cana-1920	203	18	double	double	ADJ
cana-1920	203	19	comet	comet	NOUN
cana-1920	203	20	dc(2	dc(2	PROPN
cana-1920	203	21	m1	m1	PROPN
cana-1920	203	22	,	,	PUNCT
cana-1920	203	23	m2	m2	PROPN
cana-1920	203	24	)	)	PUNCT
cana-1920	203	25	.	.	PUNCT
cana-1920	204	1	hence	hence	ADV
cana-1920	204	2	,	,	PUNCT
cana-1920	204	3	we	we	PRON
cana-1920	204	4	can	can	AUX
cana-1920	204	5	obtain	obtain	VERB
cana-1920	204	6	dc(m	dc(m	NOUN
cana-1920	204	7	,	,	PUNCT
cana-1920	204	8	m1	m1	PROPN
cana-1920	204	9	,	,	PUNCT
cana-1920	204	10	m2	m2	PROPN
cana-1920	204	11	)	)	PUNCT
cana-1920	204	12	from	from	ADP
cana-1920	204	13	dc(2	dc(2	PROPN
cana-1920	204	14	,	,	PUNCT
cana-1920	204	15	m1	m1	PROPN
cana-1920	204	16	,	,	PUNCT
cana-1920	204	17	m2	m2	PROPN
cana-1920	204	18	)	)	PUNCT
cana-1920	204	19	by	by	ADP
cana-1920	204	20	expanding	expand	VERB
cana-1920	204	21	p2	p2	PROPN
cana-1920	204	22	to	to	PART
cana-1920	204	23	pm	pm	VERB
cana-1920	204	24	.	.	PUNCT
cana-1920	205	1	specifically	specifically	ADV
cana-1920	205	2	,	,	PUNCT
cana-1920	205	3	by	by	ADP
cana-1920	205	4	adding	add	VERB
cana-1920	205	5	vertices	vertex	NOUN
cana-1920	205	6	and	and	CCONJ
cana-1920	205	7	edges	edge	NOUN
cana-1920	205	8	to	to	ADP
cana-1920	205	9	p2	p2	NOUN
cana-1920	205	10	to	to	PART
cana-1920	205	11	become	become	VERB
cana-1920	205	12	pm	pm	NOUN
cana-1920	205	13	.	.	PUNCT
cana-1920	206	1	the	the	DET
cana-1920	206	2	results	result	NOUN
cana-1920	206	3	in	in	ADP
cana-1920	206	4	this	this	DET
cana-1920	206	5	subsection	subsection	NOUN
cana-1920	206	6	are	be	AUX
cana-1920	206	7	obtained	obtain	VERB
cana-1920	206	8	by	by	ADP
cana-1920	206	9	calculating	calculate	VERB
cana-1920	206	10	the	the	DET
cana-1920	206	11	difference	difference	NOUN
cana-1920	206	12	between	between	ADP
cana-1920	206	13	a	a	DET
cana-1920	206	14	particular	particular	ADJ
cana-1920	206	15	reverse	reverse	ADJ
cana-1920	206	16	topological	topological	ADJ
cana-1920	206	17	index	index	NOUN
cana-1920	206	18	of	of	ADP
cana-1920	206	19	the	the	DET
cana-1920	206	20	double	double	ADJ
cana-1920	206	21	comet	comet	NOUN
cana-1920	206	22	and	and	CCONJ
cana-1920	206	23	bistar	bistar	NOUN
cana-1920	206	24	.	.	PUNCT
cana-1920	207	1	for	for	ADP
cana-1920	207	2	instance	instance	NOUN
cana-1920	207	3	,	,	PUNCT
cana-1920	207	4	if	if	SCONJ
cana-1920	207	5	the	the	DET
cana-1920	207	6	concerned	concerned	ADJ
cana-1920	207	7	topological	topological	ADJ
cana-1920	207	8	index	index	NOUN
cana-1920	207	9	is	be	AUX
cana-1920	207	10	rm1	rm1	PROPN
cana-1920	207	11	,	,	PUNCT
cana-1920	207	12	then	then	ADV
cana-1920	207	13	we	we	PRON
cana-1920	207	14	calculate	calculate	VERB
cana-1920	207	15	rm1(dc(m	rm1(dc(m	NOUN
cana-1920	207	16	,	,	PUNCT
cana-1920	207	17	m1,m2))−rm1(b(m1,m2	m1,m2))−rm1(b(m1,m2	NOUN
cana-1920	207	18	)	)	PUNCT
cana-1920	207	19	)	)	PUNCT
cana-1920	207	20	.	.	PUNCT
cana-1920	208	1	the	the	DET
cana-1920	208	2	computation	computation	NOUN
cana-1920	208	3	is	be	AUX
cana-1920	208	4	of	of	ADP
cana-1920	208	5	course	course	NOUN
cana-1920	208	6	based	base	VERB
cana-1920	208	7	on	on	ADP
cana-1920	208	8	the	the	DET
cana-1920	208	9	results	result	NOUN
cana-1920	208	10	of	of	ADP
cana-1920	208	11	gowtham	gowtham	PROPN
cana-1920	208	12	and	and	CCONJ
cana-1920	208	13	husin	husin	NOUN
cana-1920	208	14	summarized	summarize	VERB
cana-1920	208	15	in	in	ADP
cana-1920	208	16	subsection	subsection	NOUN
cana-1920	208	17	2.1	2.1	NUM
cana-1920	208	18	,	,	PUNCT
cana-1920	208	19	and	and	CCONJ
cana-1920	208	20	the	the	DET
cana-1920	208	21	results	result	NOUN
cana-1920	208	22	of	of	ADP
cana-1920	208	23	this	this	DET
cana-1920	208	24	paper	paper	NOUN
cana-1920	208	25	provided	provide	VERB
cana-1920	208	26	in	in	ADP
cana-1920	208	27	subsection	subsection	NOUN
cana-1920	208	28	3.2	3.2	NUM
cana-1920	208	29	.	.	PUNCT
cana-1920	209	1	theorem	theorem	VERB
cana-1920	209	2	3.16	3.16	NUM
cana-1920	209	3	.	.	PUNCT
cana-1920	210	1	let	let	VERB
cana-1920	210	2	g1	g1	PROPN
cana-1920	210	3	=	=	PRON
cana-1920	210	4	dc(m	dc(m	NOUN
cana-1920	210	5	,	,	PUNCT
cana-1920	210	6	m1,m2	m1,m2	PROPN
cana-1920	210	7	)	)	PUNCT
cana-1920	210	8	and	and	CCONJ
cana-1920	210	9	g2	g2	PROPN
cana-1920	210	10	=	=	PRON
cana-1920	210	11	b(m1,m2	b(m1,m2	NUM
cana-1920	210	12	)	)	PUNCT
cana-1920	210	13	.	.	PUNCT
cana-1920	211	1	if	if	SCONJ
cana-1920	211	2	m	m	NOUN
cana-1920	211	3	=	=	VERB
cana-1920	211	4	max{m1,m2	max{m1,m2	NOUN
cana-1920	211	5	}	}	PUNCT
cana-1920	211	6	and	and	CCONJ
cana-1920	211	7	µ	µ	X
cana-1920	211	8	=	=	SYM
cana-1920	211	9	min{m1,m2	min{m1,m2	NOUN
cana-1920	211	10	}	}	PUNCT
cana-1920	211	11	,	,	PUNCT
cana-1920	211	12	then	then	ADV
cana-1920	211	13	theorem	theorem	VERB
cana-1920	211	14	3.17	3.17	NUM
cana-1920	211	15	.	.	PUNCT
cana-1920	212	1	let	let	VERB
cana-1920	212	2	g1	g1	PROPN
cana-1920	212	3	=	=	PRON
cana-1920	212	4	dc(m	dc(m	NOUN
cana-1920	212	5	,	,	PUNCT
cana-1920	212	6	m1,m2	m1,m2	PROPN
cana-1920	212	7	)	)	PUNCT
cana-1920	212	8	and	and	CCONJ
cana-1920	212	9	g2	g2	PROPN
cana-1920	212	10	=	=	PRON
cana-1920	212	11	b(m1,m2	b(m1,m2	NUM
cana-1920	212	12	)	)	PUNCT
cana-1920	212	13	.	.	PUNCT
cana-1920	213	1	if	if	SCONJ
cana-1920	213	2	m	m	NOUN
cana-1920	213	3	=	=	VERB
cana-1920	213	4	max{m1,m2	max{m1,m2	NOUN
cana-1920	213	5	}	}	PUNCT
cana-1920	213	6	and	and	CCONJ
cana-1920	213	7	µ	µ	X
cana-1920	213	8	=	=	SYM
cana-1920	213	9	min{m1,m2	min{m1,m2	NOUN
cana-1920	213	10	}	}	PUNCT
cana-1920	213	11	,	,	PUNCT
cana-1920	213	12	then	then	ADV
cana-1920	213	13	theorem	theorem	VERB
cana-1920	213	14	3.18	3.18	NUM
cana-1920	213	15	.	.	PUNCT
cana-1920	214	1	let	let	VERB
cana-1920	214	2	g1	g1	PROPN
cana-1920	214	3	=	=	PRON
cana-1920	214	4	dc(m	dc(m	NOUN
cana-1920	214	5	,	,	PUNCT
cana-1920	214	6	m1,m2	m1,m2	PROPN
cana-1920	214	7	)	)	PUNCT
cana-1920	214	8	and	and	CCONJ
cana-1920	214	9	g2	g2	PROPN
cana-1920	214	10	=	=	PRON
cana-1920	214	11	b(m1,m2	b(m1,m2	NUM
cana-1920	214	12	)	)	PUNCT
cana-1920	214	13	.	.	PUNCT
cana-1920	215	1	if	if	SCONJ
cana-1920	215	2	m	m	NOUN
cana-1920	215	3	=	=	VERB
cana-1920	215	4	max{m1,m2	max{m1,m2	NOUN
cana-1920	215	5	}	}	PUNCT
cana-1920	215	6	and	and	CCONJ
cana-1920	215	7	µ	µ	X
cana-1920	215	8	=	=	SYM
cana-1920	215	9	min{m1,m2	min{m1,m2	NOUN
cana-1920	215	10	}	}	PUNCT
cana-1920	215	11	,	,	PUNCT
cana-1920	215	12	then	then	ADV
cana-1920	215	13	theorem	theorem	VERB
cana-1920	215	14	3.19	3.19	NUM
cana-1920	215	15	.	.	PUNCT
cana-1920	216	1	let	let	VERB
cana-1920	216	2	g1	g1	PROPN
cana-1920	216	3	=	=	PRON
cana-1920	216	4	dc(m	dc(m	NOUN
cana-1920	216	5	,	,	PUNCT
cana-1920	216	6	m1,m2	m1,m2	PROPN
cana-1920	216	7	)	)	PUNCT
cana-1920	216	8	and	and	CCONJ
cana-1920	216	9	g2	g2	PROPN
cana-1920	216	10	=	=	PRON
cana-1920	216	11	b(m1,m2	b(m1,m2	NUM
cana-1920	216	12	)	)	PUNCT
cana-1920	216	13	.	.	PUNCT
cana-1920	217	1	if	if	SCONJ
cana-1920	217	2	m	m	NOUN
cana-1920	217	3	=	=	VERB
cana-1920	217	4	max{m1,m2	max{m1,m2	NOUN
cana-1920	217	5	}	}	PUNCT
cana-1920	217	6	and	and	CCONJ
cana-1920	217	7	µ	µ	X
cana-1920	217	8	=	=	SYM
cana-1920	217	9	min{m1,m2	min{m1,m2	NOUN
cana-1920	217	10	}	}	PUNCT
cana-1920	217	11	,	,	PUNCT
cana-1920	217	12	then	then	ADV
cana-1920	217	13	theorem	theorem	VERB
cana-1920	217	14	3.20	3.20	NUM
cana-1920	217	15	.	.	PUNCT
cana-1920	218	1	let	let	VERB
cana-1920	218	2	g1	g1	PROPN
cana-1920	218	3	=	=	PRON
cana-1920	218	4	dc(m	dc(m	NOUN
cana-1920	218	5	,	,	PUNCT
cana-1920	218	6	m1,m2	m1,m2	PROPN
cana-1920	218	7	)	)	PUNCT
cana-1920	218	8	and	and	CCONJ
cana-1920	218	9	g2	g2	PROPN
cana-1920	218	10	=	=	PRON
cana-1920	218	11	b(m1,m2	b(m1,m2	NUM
cana-1920	218	12	)	)	PUNCT
cana-1920	218	13	.	.	PUNCT
cana-1920	219	1	if	if	SCONJ
cana-1920	219	2	m	m	NOUN
cana-1920	219	3	=	=	VERB
cana-1920	219	4	max{m1,m2	max{m1,m2	NOUN
cana-1920	219	5	}	}	PUNCT
cana-1920	219	6	and	and	CCONJ
cana-1920	219	7	µ	µ	X
cana-1920	219	8	=	=	SYM
cana-1920	219	9	min{m1,m2	min{m1,m2	NOUN
cana-1920	219	10	}	}	PUNCT
cana-1920	219	11	,	,	PUNCT
cana-1920	219	12	then	then	ADV
cana-1920	219	13	theorem	theorem	VERB
cana-1920	219	14	3.21	3.21	NUM
cana-1920	219	15	.	.	PUNCT
cana-1920	220	1	let	let	VERB
cana-1920	220	2	g1	g1	PROPN
cana-1920	220	3	=	=	PRON
cana-1920	220	4	dc(m	dc(m	NOUN
cana-1920	220	5	,	,	PUNCT
cana-1920	220	6	m1,m2	m1,m2	PROPN
cana-1920	220	7	)	)	PUNCT
cana-1920	220	8	and	and	CCONJ
cana-1920	220	9	g2	g2	PROPN
cana-1920	220	10	=	=	PRON
cana-1920	220	11	b(m1,m2	b(m1,m2	NUM
cana-1920	220	12	)	)	PUNCT
cana-1920	220	13	.	.	PUNCT
cana-1920	221	1	if	if	SCONJ
cana-1920	221	2	m	m	NOUN
cana-1920	221	3	=	=	VERB
cana-1920	221	4	max{m1,m2	max{m1,m2	NOUN
cana-1920	221	5	}	}	PUNCT
cana-1920	221	6	and	and	CCONJ
cana-1920	221	7	µ	µ	X
cana-1920	221	8	=	=	SYM
cana-1920	221	9	min{m1,m2	min{m1,m2	NOUN
cana-1920	221	10	}	}	PUNCT
cana-1920	221	11	,	,	PUNCT
cana-1920	221	12	then	then	ADV
cana-1920	221	13	theorem	theorem	VERB
cana-1920	221	14	3.22	3.22	NUM
cana-1920	221	15	.	.	PUNCT
cana-1920	222	1	let	let	VERB
cana-1920	222	2	g1	g1	PROPN
cana-1920	222	3	=	=	PRON
cana-1920	222	4	dc(m	dc(m	NOUN
cana-1920	222	5	,	,	PUNCT
cana-1920	222	6	m1,m2	m1,m2	PROPN
cana-1920	222	7	)	)	PUNCT
cana-1920	222	8	and	and	CCONJ
cana-1920	222	9	g2	g2	PROPN
cana-1920	222	10	=	=	PRON
cana-1920	222	11	b(m1,m2	b(m1,m2	NUM
cana-1920	222	12	)	)	PUNCT
cana-1920	222	13	.	.	PUNCT
cana-1920	223	1	if	if	SCONJ
cana-1920	223	2	m	m	NOUN
cana-1920	223	3	=	=	VERB
cana-1920	223	4	max{m1,m2	max{m1,m2	NOUN
cana-1920	223	5	}	}	PUNCT
cana-1920	223	6	and	and	CCONJ
cana-1920	223	7	µ	µ	X
cana-1920	223	8	=	=	SYM
cana-1920	223	9	min{m1,m2	min{m1,m2	NOUN
cana-1920	223	10	}	}	PUNCT
cana-1920	223	11	,	,	PUNCT
cana-1920	223	12	then	then	ADV
cana-1920	223	13	4	4	X
cana-1920	223	14	.	.	NOUN
cana-1920	223	15	conclusion	conclusion	NOUN
cana-1920	223	16	and	and	CCONJ
cana-1920	223	17	future	future	ADJ
cana-1920	223	18	work	work	NOUN
cana-1920	223	19	in	in	ADP
cana-1920	223	20	this	this	DET
cana-1920	223	21	paper	paper	NOUN
cana-1920	223	22	,	,	PUNCT
cana-1920	223	23	the	the	DET
cana-1920	223	24	results	result	NOUN
cana-1920	223	25	obtained	obtain	VERB
cana-1920	223	26	in	in	ADP
cana-1920	223	27	theorem	theorem	ADJ
cana-1920	223	28	3.1	3.1	NUM
cana-1920	223	29	theorem	theorem	NOUN
cana-1920	223	30	3.7	3.7	NUM
cana-1920	223	31	show	show	NOUN
cana-1920	223	32	that	that	SCONJ
cana-1920	223	33	we	we	PRON
cana-1920	223	34	were	be	AUX
cana-1920	223	35	able	able	ADJ
cana-1920	223	36	to	to	PART
cana-1920	223	37	compute	compute	VERB
cana-1920	223	38	for	for	ADP
cana-1920	223	39	the	the	DET
cana-1920	223	40	reverse	reverse	ADJ
cana-1920	223	41	sum	sum	NOUN
cana-1920	223	42	-	-	PUNCT
cana-1920	223	43	connectivity	connectivity	NOUN
cana-1920	223	44	(	(	PUNCT
cana-1920	223	45	rsci	rsci	X
cana-1920	223	46	(	(	PUNCT
cana-1920	223	47	·	·	PUNCT
cana-1920	223	48	)	)	PUNCT
cana-1920	223	49	)	)	PUNCT
cana-1920	223	50	,	,	PUNCT
cana-1920	223	51	first	first	ADV
cana-1920	223	52	reverse	reverse	VERB
cana-1920	223	53	zagreb	zagreb	PROPN
cana-1920	223	54	(	(	PUNCT
cana-1920	223	55	rm1	rm1	PROPN
cana-1920	223	56	(	(	PUNCT
cana-1920	223	57	·	·	PUNCT
cana-1920	223	58	)	)	PUNCT
cana-1920	223	59	)	)	PUNCT
cana-1920	223	60	,	,	PUNCT
cana-1920	223	61	second	second	ADJ
cana-1920	223	62	reverse	reverse	ADJ
cana-1920	223	63	zagreb	zagreb	PROPN
cana-1920	223	64	communications	communication	NOUN
cana-1920	223	65	on	on	ADP
cana-1920	223	66	applied	apply	VERB
cana-1920	223	67	nonlinear	nonlinear	ADJ
cana-1920	223	68	analysis	analysis	NOUN
cana-1920	223	69	issn	issn	NOUN
cana-1920	223	70	:	:	PUNCT
cana-1920	223	71	1074	1074	NUM
cana-1920	223	72	-	-	PUNCT
cana-1920	223	73	133x	133x	NUM
cana-1920	223	74	vol	vol	NOUN
cana-1920	223	75	32	32	NUM
cana-1920	223	76	no	no	NOUN
cana-1920	223	77	.	.	NOUN
cana-1920	223	78	3	3	NUM
cana-1920	223	79	(	(	PUNCT
cana-1920	223	80	2025	2025	NUM
cana-1920	223	81	)	)	PUNCT
cana-1920	223	82	82	82	NUM
cana-1920	223	83	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	223	84	(	(	PUNCT
cana-1920	223	85	rm2	rm2	PROPN
cana-1920	223	86	(	(	PUNCT
cana-1920	223	87	·	·	PUNCT
cana-1920	223	88	)	)	PUNCT
cana-1920	223	89	)	)	PUNCT
cana-1920	223	90	,	,	PUNCT
cana-1920	223	91	reverse	reverse	VERB
cana-1920	223	92	arithmetic	arithmetic	ADJ
cana-1920	223	93	-	-	PUNCT
cana-1920	223	94	geometric	geometric	ADJ
cana-1920	223	95	(	(	PUNCT
cana-1920	223	96	rag	rag	NOUN
cana-1920	223	97	(	(	PUNCT
cana-1920	223	98	·	·	PUNCT
cana-1920	223	99	)	)	PUNCT
cana-1920	223	100	)	)	PUNCT
cana-1920	223	101	,	,	PUNCT
cana-1920	223	102	reverse	reverse	VERB
cana-1920	223	103	geometric	geometric	ADJ
cana-1920	223	104	-	-	PUNCT
cana-1920	223	105	arithmetic	arithmetic	ADJ
cana-1920	223	106	(	(	PUNCT
cana-1920	223	107	rga	rga	PROPN
cana-1920	223	108	(	(	PUNCT
cana-1920	223	109	·	·	PUNCT
cana-1920	223	110	)	)	PUNCT
cana-1920	223	111	)	)	PUNCT
cana-1920	223	112	,	,	PUNCT
cana-1920	223	113	reverse	reverse	ADJ
cana-1920	223	114	sombor	sombor	NOUN
cana-1920	223	115	(	(	PUNCT
cana-1920	223	116	rso	rso	PROPN
cana-1920	223	117	(	(	PUNCT
cana-1920	223	118	·	·	PUNCT
cana-1920	223	119	)	)	PUNCT
cana-1920	223	120	)	)	PUNCT
cana-1920	223	121	,	,	PUNCT
cana-1920	223	122	and	and	CCONJ
cana-1920	223	123	reverse	reverse	VERB
cana-1920	223	124	nirmala	nirmala	PROPN
cana-1920	223	125	(	(	PUNCT
cana-1920	223	126	rn	rn	PROPN
cana-1920	223	127	(	(	PUNCT
cana-1920	223	128	·	·	PUNCT
cana-1920	223	129	)	)	PUNCT
cana-1920	223	130	)	)	PUNCT
cana-1920	223	131	of	of	ADP
cana-1920	223	132	comet	comet	NOUN
cana-1920	223	133	graphs	graph	NOUN
cana-1920	223	134	.	.	PUNCT
cana-1920	224	1	the	the	DET
cana-1920	224	2	same	same	ADJ
cana-1920	224	3	reverse	reverse	ADJ
cana-1920	224	4	vertex	vertex	NOUN
cana-1920	224	5	degreebased	degreebase	VERB
cana-1920	224	6	topological	topological	ADJ
cana-1920	224	7	indices	index	NOUN
cana-1920	224	8	were	be	AUX
cana-1920	224	9	calculated	calculate	VERB
cana-1920	224	10	for	for	ADP
cana-1920	224	11	double	double	ADJ
cana-1920	224	12	comet	comet	NOUN
cana-1920	224	13	graphs	graph	NOUN
cana-1920	224	14	and	and	CCONJ
cana-1920	224	15	were	be	AUX
cana-1920	224	16	presented	present	VERB
cana-1920	224	17	in	in	ADP
cana-1920	224	18	theorem	theorem	ADJ
cana-1920	224	19	3.8	3.8	NUM
cana-1920	224	20	theorem	theorem	VERB
cana-1920	224	21	3.14	3.14	NUM
cana-1920	224	22	.	.	PUNCT
cana-1920	225	1	we	we	PRON
cana-1920	225	2	also	also	ADV
cana-1920	225	3	have	have	AUX
cana-1920	225	4	presented	present	VERB
cana-1920	225	5	a	a	DET
cana-1920	225	6	computational	computational	ADJ
cana-1920	225	7	application	application	NOUN
cana-1920	225	8	of	of	ADP
cana-1920	225	9	our	our	PRON
cana-1920	225	10	results	result	NOUN
cana-1920	225	11	to	to	ADP
cana-1920	225	12	a	a	DET
cana-1920	225	13	specific	specific	ADJ
cana-1920	225	14	molecule	molecule	NOUN
cana-1920	225	15	.	.	PUNCT
cana-1920	226	1	lastly	lastly	ADV
cana-1920	226	2	,	,	PUNCT
cana-1920	226	3	we	we	PRON
cana-1920	226	4	have	have	AUX
cana-1920	226	5	determined	determine	VERB
cana-1920	226	6	the	the	DET
cana-1920	226	7	relationship	relationship	NOUN
cana-1920	226	8	between	between	ADP
cana-1920	226	9	various	various	ADJ
cana-1920	226	10	reverse	reverse	ADJ
cana-1920	226	11	vertex	vertex	NOUN
cana-1920	226	12	degree	degree	NOUN
cana-1920	226	13	-	-	PUNCT
cana-1920	226	14	based	base	VERB
cana-1920	226	15	topological	topological	ADJ
cana-1920	226	16	indices	index	NOUN
cana-1920	226	17	of	of	ADP
cana-1920	226	18	bistar	bistar	NOUN
cana-1920	226	19	and	and	CCONJ
cana-1920	226	20	double	double	ADJ
cana-1920	226	21	comet	comet	NOUN
cana-1920	226	22	graphs	graph	NOUN
cana-1920	226	23	as	as	SCONJ
cana-1920	226	24	presented	present	VERB
cana-1920	226	25	in	in	ADP
cana-1920	226	26	theorem	theorem	ADJ
cana-1920	226	27	3.16	3.16	NUM
cana-1920	226	28	theorem	theorem	VERB
cana-1920	226	29	3.22	3.22	NUM
cana-1920	226	30	.	.	PUNCT
cana-1920	227	1	for	for	ADP
cana-1920	227	2	future	future	ADJ
cana-1920	227	3	studies	study	NOUN
cana-1920	227	4	,	,	PUNCT
cana-1920	227	5	we	we	PRON
cana-1920	227	6	recommend	recommend	VERB
cana-1920	227	7	the	the	DET
cana-1920	227	8	study	study	NOUN
cana-1920	227	9	of	of	ADP
cana-1920	227	10	the	the	DET
cana-1920	227	11	determination	determination	NOUN
cana-1920	227	12	of	of	ADP
cana-1920	227	13	reverse	reverse	ADJ
cana-1920	227	14	vertex	vertex	NOUN
cana-1920	227	15	degree	degree	NOUN
cana-1920	227	16	-	-	PUNCT
cana-1920	227	17	based	base	VERB
cana-1920	227	18	topological	topological	ADJ
cana-1920	227	19	indices	index	NOUN
cana-1920	227	20	for	for	ADP
cana-1920	227	21	other	other	ADJ
cana-1920	227	22	families	family	NOUN
cana-1920	227	23	of	of	ADP
cana-1920	227	24	trees	tree	NOUN
cana-1920	227	25	.	.	PUNCT
cana-1920	228	1	5	5	X
cana-1920	228	2	.	.	X
cana-1920	228	3	acknowledgements	acknowledgement	NOUN
cana-1920	228	4	the	the	DET
cana-1920	228	5	authors	author	NOUN
cana-1920	228	6	would	would	AUX
cana-1920	228	7	like	like	VERB
cana-1920	228	8	to	to	PART
cana-1920	228	9	thank	thank	VERB
cana-1920	228	10	the	the	DET
cana-1920	228	11	anonymous	anonymous	ADJ
cana-1920	228	12	reviewers	reviewer	NOUN
cana-1920	228	13	for	for	SCONJ
cana-1920	228	14	their	their	PRON
cana-1920	228	15	comments	comment	NOUN
cana-1920	228	16	and	and	CCONJ
cana-1920	228	17	suggestions	suggestion	NOUN
cana-1920	228	18	that	that	PRON
cana-1920	228	19	helped	helped	AUX
cana-1920	228	20	improve	improve	VERB
cana-1920	228	21	the	the	DET
cana-1920	228	22	overall	overall	ADJ
cana-1920	228	23	content	content	NOUN
cana-1920	228	24	of	of	ADP
cana-1920	228	25	the	the	DET
cana-1920	228	26	paper	paper	NOUN
cana-1920	228	27	.	.	PUNCT
cana-1920	229	1	special	special	ADJ
cana-1920	229	2	thanks	thank	NOUN
cana-1920	229	3	to	to	ADP
cana-1920	229	4	the	the	DET
cana-1920	229	5	central	central	PROPN
cana-1920	229	6	luzon	luzon	PROPN
cana-1920	229	7	state	state	PROPN
cana-1920	229	8	university	university	PROPN
cana-1920	229	9	and	and	CCONJ
cana-1920	229	10	its	its	PRON
cana-1920	229	11	administration	administration	NOUN
cana-1920	229	12	for	for	ADP
cana-1920	229	13	their	their	PRON
cana-1920	229	14	motivation	motivation	NOUN
cana-1920	229	15	and	and	CCONJ
cana-1920	229	16	support	support	NOUN
cana-1920	229	17	throughout	throughout	ADP
cana-1920	229	18	the	the	DET
cana-1920	229	19	conduct	conduct	NOUN
cana-1920	229	20	and	and	CCONJ
cana-1920	229	21	publication	publication	NOUN
cana-1920	229	22	of	of	ADP
cana-1920	229	23	this	this	DET
cana-1920	229	24	study	study	NOUN
cana-1920	229	25	.	.	PUNCT
cana-1920	230	1	references	reference	NOUN
cana-1920	230	2	[	[	X
cana-1920	230	3	1	1	NUM
cana-1920	230	4	]	]	PUNCT
cana-1920	230	5	compound	compound	NOUN
cana-1920	230	6	summary	summary	NOUN
cana-1920	230	7	2,2,4,4	2,2,4,4	NUM
cana-1920	230	8	-	-	PUNCT
cana-1920	230	9	tetramethylpentane	tetramethylpentane	NOUN
cana-1920	230	10	.	.	PUNCT
cana-1920	231	1	https://pubchem.ncbi.nlm.nih.gov/	https://pubchem.ncbi.nlm.nih.gov/	PROPN
cana-1920	231	2	compound/2_2_4_4tetramethylpentane	compound/2_2_4_4tetramethylpentane	PROPN
cana-1920	231	3	.	.	PUNCT
cana-1920	232	1	accessed	access	VERB
cana-1920	232	2	:	:	PUNCT
cana-1920	232	3	2024	2024	NUM
cana-1920	232	4	-	-	SYM
cana-1920	232	5	03	03	NUM
cana-1920	232	6	-	-	SYM
cana-1920	232	7	25	25	NUM
cana-1920	232	8	.	.	PUNCT
cana-1920	233	1	[	[	X
cana-1920	233	2	2	2	NUM
cana-1920	233	3	]	]	PUNCT
cana-1920	233	4	a.	a.	NOUN
cana-1920	233	5	ahmad	ahmad	PROPN
cana-1920	233	6	,	,	PUNCT
cana-1920	233	7	a.	a.	PROPN
cana-1920	233	8	n.	n.	PROPN
cana-1920	233	9	koam	koam	PROPN
cana-1920	233	10	,	,	PUNCT
cana-1920	233	11	and	and	CCONJ
cana-1920	233	12	m.	m.	PROPN
cana-1920	233	13	azeem	azeem	PROPN
cana-1920	233	14	.	.	PUNCT
cana-1920	234	1	reverse	reverse	NOUN
cana-1920	234	2	-	-	PUNCT
cana-1920	234	3	degree	degree	NOUN
cana-1920	234	4	-	-	PUNCT
cana-1920	234	5	based	base	VERB
cana-1920	234	6	topological	topological	ADJ
cana-1920	234	7	indices	index	NOUN
cana-1920	234	8	of	of	ADP
cana-1920	234	9	fullerene	fullerene	NOUN
cana-1920	234	10	cage	cage	NOUN
cana-1920	234	11	networks	network	NOUN
cana-1920	234	12	.	.	PUNCT
cana-1920	235	1	molecular	molecular	ADJ
cana-1920	235	2	physics	physic	NOUN
cana-1920	235	3	,	,	PUNCT
cana-1920	235	4	121(14	121(14	NUM
cana-1920	235	5	):	):	PUNCT
cana-1920	235	6	e2212533	e2212533	PROPN
cana-1920	235	7	,	,	PUNCT
cana-1920	235	8	2023	2023	NUM
cana-1920	235	9	.	.	PUNCT
cana-1920	236	1	[	[	X
cana-1920	236	2	3	3	X
cana-1920	236	3	]	]	X
cana-1920	236	4	w.	w.	PROPN
cana-1920	236	5	ahmed	ahmed	PROPN
cana-1920	236	6	,	,	PUNCT
cana-1920	236	7	k.	k.	PROPN
cana-1920	236	8	ali	ali	PROPN
cana-1920	236	9	,	,	PUNCT
cana-1920	236	10	s.	s.	PROPN
cana-1920	236	11	zaman	zaman	PROPN
cana-1920	236	12	,	,	PUNCT
cana-1920	236	13	and	and	CCONJ
cana-1920	236	14	a.	a.	NOUN
cana-1920	236	15	raza	raza	PROPN
cana-1920	236	16	.	.	PUNCT
cana-1920	237	1	molecular	molecular	ADJ
cana-1920	237	2	insights	insight	NOUN
cana-1920	237	3	into	into	ADP
cana-1920	237	4	anti	anti	ADJ
cana-1920	237	5	-	-	ADJ
cana-1920	237	6	alzheimers	alzheimers	ADJ
cana-1920	237	7	drugs	drug	NOUN
cana-1920	237	8	through	through	ADP
cana-1920	237	9	predictive	predictive	ADJ
cana-1920	237	10	modeling	modeling	NOUN
cana-1920	237	11	using	use	VERB
cana-1920	237	12	linear	linear	ADJ
cana-1920	237	13	regression	regression	NOUN
cana-1920	237	14	and	and	CCONJ
cana-1920	237	15	qspr	qspr	ADJ
cana-1920	237	16	analysis	analysis	NOUN
cana-1920	237	17	.	.	PUNCT
cana-1920	238	1	modern	modern	ADJ
cana-1920	238	2	physics	physics	NOUN
cana-1920	238	3	letters	letters	PROPN
cana-1920	238	4	b	b	NOUN
cana-1920	238	5	,	,	PUNCT
cana-1920	238	6	page	page	NOUN
cana-1920	238	7	2450260	2450260	NUM
cana-1920	238	8	,	,	PUNCT
cana-1920	238	9	2024	2024	NUM
cana-1920	238	10	.	.	PUNCT
cana-1920	239	1	[	[	X
cana-1920	239	2	4	4	X
cana-1920	239	3	]	]	PUNCT
cana-1920	239	4	m.	m.	NOUN
cana-1920	239	5	al	al	PROPN
cana-1920	239	6	-	-	PUNCT
cana-1920	239	7	sharafi	sharafi	PROPN
cana-1920	239	8	and	and	CCONJ
cana-1920	239	9	a.	a.	NOUN
cana-1920	239	10	alameri	alameri	PROPN
cana-1920	239	11	.	.	PUNCT
cana-1920	240	1	computation	computation	NOUN
cana-1920	240	2	of	of	ADP
cana-1920	240	3	wiener	wiener	NOUN
cana-1920	240	4	polynomial	polynomial	ADJ
cana-1920	240	5	and	and	CCONJ
cana-1920	240	6	index	index	NOUN
cana-1920	240	7	of	of	ADP
cana-1920	240	8	line	line	NOUN
cana-1920	240	9	subdivision	subdivision	NOUN
cana-1920	240	10	friendship	friendship	NOUN
cana-1920	240	11	and	and	CCONJ
cana-1920	240	12	line	line	NOUN
cana-1920	240	13	subdivision	subdivision	NOUN
cana-1920	240	14	bifriendship	bifriendship	NOUN
cana-1920	240	15	graphs	graph	NOUN
cana-1920	240	16	using	use	VERB
cana-1920	240	17	matlab	matlab	PROPN
cana-1920	240	18	program	program	NOUN
cana-1920	240	19	.	.	PUNCT
cana-1920	241	1	proyecciones	proyeccione	NOUN
cana-1920	241	2	(	(	PUNCT
cana-1920	241	3	antofagasta	antofagasta	PROPN
cana-1920	241	4	,	,	PUNCT
cana-1920	241	5	on	on	ADP
cana-1920	241	6	line	line	NOUN
cana-1920	241	7	)	)	PUNCT
cana-1920	241	8	,	,	PUNCT
cana-1920	241	9	43(1	43(1	NOUN
cana-1920	241	10	)	)	PUNCT
cana-1920	241	11	,	,	PUNCT
cana-1920	241	12	2024	2024	NUM
cana-1920	241	13	.	.	PUNCT
cana-1920	242	1	[	[	X
cana-1920	242	2	5	5	X
cana-1920	242	3	]	]	X
cana-1920	242	4	u.	u.	PROPN
cana-1920	242	5	ali	ali	PROPN
cana-1920	242	6	,	,	PUNCT
cana-1920	242	7	j.	j.	PROPN
cana-1920	242	8	li	li	PROPN
cana-1920	242	9	,	,	PUNCT
cana-1920	242	10	y.	y.	PROPN
cana-1920	242	11	ahmad	ahmad	PROPN
cana-1920	242	12	,	,	PUNCT
cana-1920	242	13	and	and	CCONJ
cana-1920	242	14	z.	z.	PROPN
cana-1920	242	15	raza	raza	PROPN
cana-1920	242	16	.	.	PUNCT
cana-1920	243	1	computing	compute	VERB
cana-1920	243	2	the	the	DET
cana-1920	243	3	laplacian	laplacian	ADJ
cana-1920	243	4	spectrum	spectrum	NOUN
cana-1920	243	5	and	and	CCONJ
cana-1920	243	6	wiener	wiener	NOUN
cana-1920	243	7	index	index	NOUN
cana-1920	243	8	of	of	ADP
cana-1920	243	9	pentagonal	pentagonal	ADJ
cana-1920	243	10	-	-	PUNCT
cana-1920	243	11	derivation	derivation	NOUN
cana-1920	243	12	cylinder	cylinder	NOUN
cana-1920	243	13	/	/	SYM
cana-1920	243	14	mobius	mobius	PROPN
cana-1920	243	15	network.¨	network.¨	PROPN
cana-1920	243	16	heliyon	heliyon	NOUN
cana-1920	243	17	,	,	PUNCT
cana-1920	243	18	10(2	10(2	NUM
cana-1920	243	19	)	)	PUNCT
cana-1920	243	20	,	,	PUNCT
cana-1920	243	21	2024	2024	NUM
cana-1920	243	22	.	.	PUNCT
cana-1920	244	1	[	[	X
cana-1920	244	2	6	6	NUM
cana-1920	244	3	]	]	PUNCT
cana-1920	244	4	j.	j.	PROPN
cana-1920	244	5	antalan	antalan	PROPN
cana-1920	244	6	and	and	CCONJ
cana-1920	244	7	f.	f.	PROPN
cana-1920	244	8	campena	campena	PROPN
cana-1920	244	9	.	.	PUNCT
cana-1920	245	1	distance	distance	NOUN
cana-1920	245	2	eigenvalues	eigenvalue	NOUN
cana-1920	245	3	,	,	PUNCT
cana-1920	245	4	forwarding	forwarding	NOUN
cana-1920	245	5	indices	index	NOUN
cana-1920	245	6	,	,	PUNCT
cana-1920	245	7	and	and	CCONJ
cana-1920	245	8	distance	distance	NOUN
cana-1920	245	9	-	-	PUNCT
cana-1920	245	10	based˜	based˜	NOUN
cana-1920	245	11	topological	topological	ADJ
cana-1920	245	12	indices	index	NOUN
cana-1920	245	13	of	of	ADP
cana-1920	245	14	complement	complement	NOUN
cana-1920	245	15	of	of	ADP
cana-1920	245	16	two	two	NUM
cana-1920	245	17	circulant	circulant	ADJ
cana-1920	245	18	networks	network	NOUN
cana-1920	245	19	.	.	PUNCT
cana-1920	246	1	twms	twms	PROPN
cana-1920	246	2	journal	journal	PROPN
cana-1920	246	3	of	of	ADP
cana-1920	246	4	applied	applied	PROPN
cana-1920	246	5	&	&	CCONJ
cana-1920	246	6	engineering	engineering	NOUN
cana-1920	246	7	mathematics	mathematic	NOUN
cana-1920	246	8	,	,	PUNCT
cana-1920	246	9	13(3	13(3	NUM
cana-1920	246	10	)	)	PUNCT
cana-1920	246	11	,	,	PUNCT
cana-1920	246	12	2023	2023	NUM
cana-1920	246	13	.	.	PUNCT
cana-1920	247	1	[	[	X
cana-1920	247	2	7	7	X
cana-1920	247	3	]	]	X
cana-1920	247	4	j.	j.	PROPN
cana-1920	247	5	r.	r.	PROPN
cana-1920	247	6	m.	m.	PROPN
cana-1920	247	7	antalan	antalan	PROPN
cana-1920	247	8	,	,	PUNCT
cana-1920	247	9	f.	f.	PROPN
cana-1920	247	10	j.	j.	PROPN
cana-1920	247	11	h.	h.	PROPN
cana-1920	247	12	campena	campena	PROPN
cana-1920	247	13	,	,	PUNCT
cana-1920	247	14	and	and	CCONJ
cana-1920	247	15	e.	e.	PROPN
cana-1920	247	16	d.	d.	PROPN
cana-1920	247	17	iba˜	iba˜	PROPN
cana-1920	247	18	nez	nez	PROPN
cana-1920	247	19	.	.	PUNCT
cana-1920	248	1	a	a	DET
cana-1920	248	2	note	note	NOUN
cana-1920	248	3	on	on	ADP
cana-1920	248	4	some	some	DET
cana-1920	248	5	distance	distance	NOUN
cana-1920	248	6	-	-	PUNCT
cana-1920	248	7	based	base	VERB
cana-1920	248	8	topo-˜	topo-˜	PROPN
cana-1920	248	9	logical	logical	ADJ
cana-1920	248	10	indices	index	NOUN
cana-1920	248	11	of	of	ADP
cana-1920	248	12	circulant	circulant	ADJ
cana-1920	248	13	network	network	NOUN
cana-1920	248	14	cn	cn	PROPN
cana-1920	248	15	(	(	PUNCT
cana-1920	248	16	1	1	NUM
cana-1920	248	17	,	,	PUNCT
cana-1920	248	18	a	a	PRON
cana-1920	248	19	)	)	PUNCT
cana-1920	248	20	.	.	PUNCT
cana-1920	249	1	journal	journal	PROPN
cana-1920	249	2	of	of	ADP
cana-1920	249	3	discrete	discrete	ADJ
cana-1920	249	4	mathematical	mathematical	ADJ
cana-1920	249	5	sciences	science	NOUN
cana-1920	249	6	and	and	CCONJ
cana-1920	249	7	cryptography	cryptography	NOUN
cana-1920	249	8	,	,	PUNCT
cana-1920	249	9	25(1):107–125	25(1):107–125	PROPN
cana-1920	249	10	,	,	PUNCT
cana-1920	249	11	2022	2022	NUM
cana-1920	249	12	.	.	PUNCT
cana-1920	250	1	[	[	X
cana-1920	250	2	8	8	X
cana-1920	250	3	]	]	PUNCT
cana-1920	250	4	s.	s.	PROPN
cana-1920	250	5	a.	a.	PROPN
cana-1920	250	6	u.	u.	PROPN
cana-1920	250	7	h.	h.	PROPN
cana-1920	250	8	bokhary	bokhary	PROPN
cana-1920	250	9	,	,	PUNCT
cana-1920	250	10	p.	p.	PROPN
cana-1920	250	11	bashir	bashir	PROPN
cana-1920	250	12	,	,	PUNCT
cana-1920	250	13	a.	a.	NOUN
cana-1920	250	14	nawaz	nawaz	NOUN
cana-1920	250	15	,	,	PUNCT
cana-1920	250	16	s.	s.	PROPN
cana-1920	250	17	o.	o.	PROPN
cana-1920	250	18	hilali	hilali	PROPN
cana-1920	250	19	,	,	PUNCT
cana-1920	250	20	m.	m.	NOUN
cana-1920	250	21	alhagyan	alhagyan	NOUN
cana-1920	250	22	,	,	PUNCT
cana-1920	250	23	a.	a.	PROPN
cana-1920	250	24	gargouri	gargouri	PROPN
cana-1920	250	25	,	,	PUNCT
cana-1920	250	26	m.	m.	NOUN
cana-1920	250	27	almazah	almazah	PROPN
cana-1920	250	28	,	,	PUNCT
cana-1920	250	29	et	et	PROPN
cana-1920	250	30	al	al	PROPN
cana-1920	250	31	.	.	PROPN
cana-1920	250	32	computation	computation	NOUN
cana-1920	250	33	of	of	ADP
cana-1920	250	34	wiener	wiener	NOUN
cana-1920	250	35	and	and	CCONJ
cana-1920	250	36	wiener	wiener	NOUN
cana-1920	250	37	polarity	polarity	NOUN
cana-1920	250	38	indices	index	NOUN
cana-1920	250	39	of	of	ADP
cana-1920	250	40	a	a	DET
cana-1920	250	41	class	class	NOUN
cana-1920	250	42	of	of	ADP
cana-1920	250	43	nanostar	nanostar	ADJ
cana-1920	250	44	dendrimer	dendrimer	PROPN
cana-1920	250	45	using	use	VERB
cana-1920	250	46	vertex	vertex	NOUN
cana-1920	250	47	weighted	weight	VERB
cana-1920	250	48	graphs	graph	NOUN
cana-1920	250	49	.	.	PUNCT
cana-1920	251	1	journal	journal	NOUN
cana-1920	251	2	of	of	ADP
cana-1920	251	3	mathematics	mathematic	NOUN
cana-1920	251	4	,	,	PUNCT
cana-1920	251	5	2024	2024	NUM
cana-1920	251	6	,	,	PUNCT
cana-1920	251	7	2024	2024	NUM
cana-1920	251	8	.	.	PUNCT
cana-1920	252	1	[	[	X
cana-1920	252	2	9	9	NUM
cana-1920	252	3	]	]	PUNCT
cana-1920	252	4	a.	a.	NOUN
cana-1920	252	5	a.	a.	PROPN
cana-1920	252	6	dobrynin	dobrynin	PROPN
cana-1920	252	7	and	and	CCONJ
cana-1920	252	8	k.	k.	PROPN
cana-1920	253	1	v.	v.	CCONJ
cana-1920	253	2	vorobev	vorobev	PROPN
cana-1920	253	3	.	.	PUNCT
cana-1920	254	1	some	some	DET
cana-1920	254	2	results	result	NOUN
cana-1920	254	3	on	on	ADP
cana-1920	254	4	the	the	DET
cana-1920	254	5	wiener	wiener	NOUN
cana-1920	254	6	index	index	NOUN
cana-1920	254	7	related	relate	VERB
cana-1920	254	8	to	to	ADP
cana-1920	254	9	the	the	DET
cana-1920	254	10	soltˇ	soltˇ	ADJ
cana-1920	254	11	es	es	PROPN
cana-1920	254	12	problem	problem	NOUN
cana-1920	254	13	´	´	NOUN
cana-1920	254	14	of	of	ADP
cana-1920	254	15	graphs	graph	NOUN
cana-1920	254	16	.	.	PUNCT
cana-1920	255	1	discrete	discrete	ADJ
cana-1920	255	2	applied	applied	ADJ
cana-1920	255	3	mathematics	mathematic	NOUN
cana-1920	255	4	,	,	PUNCT
cana-1920	255	5	344:154–160	344:154–160	NUM
cana-1920	255	6	,	,	PUNCT
cana-1920	255	7	2024	2024	NUM
cana-1920	255	8	.	.	PUNCT
cana-1920	256	1	[	[	X
cana-1920	256	2	10	10	NUM
cana-1920	256	3	]	]	X
cana-1920	256	4	d.	d.	PROPN
cana-1920	256	5	d.	d.	PROPN
cana-1920	256	6	durgun	durgun	PROPN
cana-1920	256	7	and	and	CCONJ
cana-1920	256	8	e.	e.	PROPN
cana-1920	256	9	n.	n.	PROPN
cana-1920	256	10	toprakkaya	toprakkaya	PROPN
cana-1920	256	11	.	.	PUNCT
cana-1920	257	1	roman	roman	ADJ
cana-1920	257	2	domination	domination	NOUN
cana-1920	257	3	of	of	ADP
cana-1920	257	4	the	the	DET
cana-1920	257	5	comet	comet	NOUN
cana-1920	257	6	,	,	PUNCT
cana-1920	257	7	double	double	ADJ
cana-1920	257	8	comet	comet	NOUN
cana-1920	257	9	,	,	PUNCT
cana-1920	257	10	and	and	CCONJ
cana-1920	257	11	comb	comb	VERB
cana-1920	257	12	graphs	graph	NOUN
cana-1920	257	13	.	.	PUNCT
cana-1920	258	1	arxiv	arxiv	PROPN
cana-1920	258	2	preprint	preprint	PROPN
cana-1920	258	3	arxiv:2102.07902	arxiv:2102.07902	VERB
cana-1920	258	4	,	,	PUNCT
cana-1920	258	5	2021	2021	NUM
cana-1920	258	6	.	.	PUNCT
cana-1920	259	1	[	[	X
cana-1920	259	2	11	11	NUM
cana-1920	259	3	]	]	PUNCT
cana-1920	259	4	m.	m.	NOUN
cana-1920	259	5	c.	c.	PROPN
cana-1920	259	6	g.	g.	PROPN
cana-1920	259	7	egan	egan	PROPN
cana-1920	259	8	,	,	PUNCT
cana-1920	259	9	j.	j.	PROPN
cana-1920	259	10	r.	r.	PROPN
cana-1920	259	11	m.	m.	PROPN
cana-1920	259	12	antalan	antalan	PROPN
cana-1920	259	13	,	,	PUNCT
cana-1920	259	14	et	et	PROPN
cana-1920	259	15	al	al	PROPN
cana-1920	259	16	.	.	PROPN
cana-1920	260	1	on	on	ADP
cana-1920	260	2	the	the	DET
cana-1920	260	3	wiener	wiener	NOUN
cana-1920	260	4	and	and	CCONJ
cana-1920	260	5	harary	harary	ADJ
cana-1920	260	6	index	index	NOUN
cana-1920	260	7	of	of	ADP
cana-1920	260	8	splitting	splitting	NOUN
cana-1920	260	9	graphs	graph	NOUN
cana-1920	260	10	.	.	PUNCT
cana-1920	261	1	european	european	ADJ
cana-1920	261	2	journal	journal	PROPN
cana-1920	261	3	of	of	ADP
cana-1920	261	4	pure	pure	ADJ
cana-1920	261	5	and	and	CCONJ
cana-1920	261	6	applied	applied	ADJ
cana-1920	261	7	mathematics	mathematic	NOUN
cana-1920	261	8	,	,	PUNCT
cana-1920	261	9	15(2):602–619	15(2):602–619	NUM
cana-1920	261	10	,	,	PUNCT
cana-1920	261	11	2022	2022	NUM
cana-1920	261	12	.	.	PUNCT
cana-1920	262	1	[	[	X
cana-1920	262	2	12	12	NUM
cana-1920	262	3	]	]	PUNCT
cana-1920	262	4	k.	k.	PROPN
cana-1920	262	5	gowtham	gowtham	PROPN
cana-1920	262	6	and	and	CCONJ
cana-1920	262	7	m.	m.	NOUN
cana-1920	262	8	husin	husin	PROPN
cana-1920	262	9	.	.	PUNCT
cana-1920	263	1	a	a	DET
cana-1920	263	2	study	study	NOUN
cana-1920	263	3	of	of	ADP
cana-1920	263	4	families	family	NOUN
cana-1920	263	5	of	of	ADP
cana-1920	263	6	bistar	bistar	NOUN
cana-1920	263	7	and	and	CCONJ
cana-1920	263	8	corona	corona	NOUN
cana-1920	263	9	product	product	NOUN
cana-1920	263	10	of	of	ADP
cana-1920	263	11	graph	graph	NOUN
cana-1920	263	12	:	:	PUNCT
cana-1920	263	13	reverse	reverse	VERB
cana-1920	263	14	topological	topological	ADJ
cana-1920	263	15	indices	index	NOUN
cana-1920	263	16	.	.	PUNCT
cana-1920	264	1	malaysian	malaysian	ADJ
cana-1920	264	2	journal	journal	PROPN
cana-1920	264	3	of	of	ADP
cana-1920	264	4	mathematical	mathematical	ADJ
cana-1920	264	5	sciences	science	NOUN
cana-1920	264	6	,	,	PUNCT
cana-1920	264	7	17(4	17(4	NUM
cana-1920	264	8	)	)	PUNCT
cana-1920	264	9	,	,	PUNCT
cana-1920	264	10	2023	2023	NUM
cana-1920	264	11	.	.	PUNCT
cana-1920	265	1	[	[	X
cana-1920	265	2	13	13	NUM
cana-1920	265	3	]	]	SYM
cana-1920	265	4	i.	i.	PROPN
cana-1920	265	5	gutman	gutman	PROPN
cana-1920	265	6	and	and	CCONJ
cana-1920	265	7	n.	n.	PROPN
cana-1920	265	8	trinajstic	trinajstic	PROPN
cana-1920	265	9	.	.	PUNCT
cana-1920	266	1	graph	graph	NOUN
cana-1920	266	2	theory	theory	NOUN
cana-1920	266	3	and	and	CCONJ
cana-1920	266	4	molecular	molecular	ADJ
cana-1920	266	5	orbitals	orbital	NOUN
cana-1920	266	6	.	.	PUNCT
cana-1920	267	1	total	total	ADJ
cana-1920	267	2	´	´	NOUN
cana-1920	267	3	ϕ-electron	ϕ-electron	PROPN
cana-1920	268	1	energy	energy	NOUN
cana-1920	268	2	of	of	ADP
cana-1920	268	3	alternant	alternant	ADJ
cana-1920	268	4	hydrocarbons	hydrocarbon	NOUN
cana-1920	268	5	.	.	PUNCT
cana-1920	269	1	chemical	chemical	PROPN
cana-1920	269	2	physics	physics	PROPN
cana-1920	269	3	letters	letter	NOUN
cana-1920	269	4	,	,	PUNCT
cana-1920	269	5	17(4):535–538	17(4):535–538	NUM
cana-1920	269	6	,	,	PUNCT
cana-1920	269	7	1972	1972	NUM
cana-1920	269	8	.	.	PUNCT
cana-1920	270	1	[	[	X
cana-1920	270	2	14	14	NUM
cana-1920	270	3	]	]	PUNCT
cana-1920	270	4	m.	m.	NOUN
cana-1920	270	5	hasani	hasani	PROPN
cana-1920	270	6	and	and	CCONJ
cana-1920	270	7	m.	m.	NOUN
cana-1920	270	8	ghods	ghod	NOUN
cana-1920	270	9	.	.	PUNCT
cana-1920	271	1	calculation	calculation	NOUN
cana-1920	271	2	of	of	ADP
cana-1920	271	3	topological	topological	ADJ
cana-1920	271	4	indices	index	NOUN
cana-1920	271	5	along	along	ADP
cana-1920	271	6	with	with	ADP
cana-1920	271	7	matlab	matlab	PROPN
cana-1920	271	8	coding	code	VERB
cana-1920	271	9	in	in	ADP
cana-1920	271	10	qspr	qspr	ADJ
cana-1920	271	11	analysis	analysis	NOUN
cana-1920	271	12	of	of	ADP
cana-1920	271	13	calcium	calcium	NOUN
cana-1920	271	14	channel	channel	NOUN
cana-1920	271	15	-	-	PUNCT
cana-1920	271	16	blocking	block	VERB
cana-1920	271	17	cardiac	cardiac	ADJ
cana-1920	271	18	drugs	drug	NOUN
cana-1920	271	19	.	.	PUNCT
cana-1920	272	1	journal	journal	PROPN
cana-1920	272	2	of	of	ADP
cana-1920	272	3	mathematical	mathematical	ADJ
cana-1920	272	4	chemistry	chemistry	NOUN
cana-1920	272	5	,	,	PUNCT
cana-1920	272	6	pages	page	NOUN
cana-1920	272	7	1–22	1–22	PROPN
cana-1920	272	8	,	,	PUNCT
cana-1920	272	9	2024	2024	NUM
cana-1920	272	10	.	.	PUNCT
cana-1920	273	1	[	[	X
cana-1920	273	2	15	15	NUM
cana-1920	273	3	]	]	PUNCT
cana-1920	273	4	m.	m.	NOUN
cana-1920	273	5	hasani	hasani	PROPN
cana-1920	273	6	and	and	CCONJ
cana-1920	273	7	m.	m.	NOUN
cana-1920	273	8	ghods	ghod	NOUN
cana-1920	273	9	.	.	PUNCT
cana-1920	274	1	topological	topological	ADJ
cana-1920	274	2	indices	index	NOUN
cana-1920	274	3	and	and	CCONJ
cana-1920	274	4	qspr	qspr	ADJ
cana-1920	274	5	analysis	analysis	NOUN
cana-1920	274	6	of	of	ADP
cana-1920	274	7	some	some	DET
cana-1920	274	8	chemical	chemical	NOUN
cana-1920	274	9	structures	structure	NOUN
cana-1920	274	10	applied	apply	VERB
cana-1920	274	11	for	for	ADP
cana-1920	274	12	the	the	DET
cana-1920	274	13	treatment	treatment	NOUN
cana-1920	274	14	of	of	ADP
cana-1920	274	15	heart	heart	NOUN
cana-1920	274	16	patients	patient	NOUN
cana-1920	274	17	.	.	PUNCT
cana-1920	275	1	international	international	ADJ
cana-1920	275	2	journal	journal	NOUN
cana-1920	275	3	of	of	ADP
cana-1920	275	4	quantum	quantum	ADJ
cana-1920	275	5	chemistry	chemistry	NOUN
cana-1920	275	6	,	,	PUNCT
cana-1920	275	7	124(1):e27234	124(1):e27234	NUM
cana-1920	275	8	,	,	PUNCT
cana-1920	275	9	2024	2024	NUM
cana-1920	275	10	.	.	PUNCT
cana-1920	276	1	[	[	X
cana-1920	276	2	16	16	NUM
cana-1920	276	3	]	]	X
cana-1920	276	4	r.	r.	PROPN
cana-1920	276	5	huang	huang	PROPN
cana-1920	276	6	,	,	PUNCT
cana-1920	276	7	a.	a.	PROPN
cana-1920	276	8	mahboob	mahboob	PROPN
cana-1920	276	9	,	,	PUNCT
cana-1920	276	10	m.	m.	PROPN
cana-1920	276	11	w.	w.	PROPN
cana-1920	276	12	rasheed	rasheed	PROPN
cana-1920	276	13	,	,	PUNCT
cana-1920	276	14	s.	s.	PROPN
cana-1920	276	15	m.	m.	PROPN
cana-1920	276	16	alam	alam	PROPN
cana-1920	276	17	,	,	PUNCT
cana-1920	276	18	and	and	CCONJ
cana-1920	276	19	m.	m.	PROPN
cana-1920	276	20	k.	k.	PROPN
cana-1920	276	21	siddiqui	siddiqui	PROPN
cana-1920	276	22	.	.	PUNCT
cana-1920	277	1	on	on	ADP
cana-1920	277	2	molecular	molecular	ADJ
cana-1920	277	3	modeling	modeling	NOUN
cana-1920	277	4	and	and	CCONJ
cana-1920	277	5	qspr	qspr	ADJ
cana-1920	277	6	analysis	analysis	NOUN
cana-1920	277	7	of	of	ADP
cana-1920	277	8	lyme	lyme	NOUN
cana-1920	277	9	disease	disease	NOUN
cana-1920	277	10	medicines	medicine	NOUN
cana-1920	277	11	via	via	ADP
cana-1920	277	12	topological	topological	ADJ
cana-1920	277	13	indices	index	NOUN
cana-1920	277	14	.	.	PUNCT
cana-1920	278	1	the	the	DET
cana-1920	278	2	european	european	PROPN
cana-1920	278	3	physical	physical	PROPN
cana-1920	278	4	journal	journal	PROPN
cana-1920	278	5	plus	plus	CCONJ
cana-1920	278	6	,	,	PUNCT
cana-1920	278	7	138(3):243	138(3):243	NUM
cana-1920	278	8	,	,	PUNCT
cana-1920	278	9	2023	2023	NUM
cana-1920	278	10	.	.	PUNCT
cana-1920	279	1	[	[	X
cana-1920	279	2	17	17	NUM
cana-1920	279	3	]	]	PUNCT
cana-1920	279	4	s.	s.	PROPN
cana-1920	279	5	a.	a.	PROPN
cana-1920	279	6	k.	k.	PROPN
cana-1920	279	7	kirmani	kirmani	PROPN
cana-1920	279	8	,	,	PUNCT
cana-1920	279	9	p.	p.	PROPN
cana-1920	279	10	ali	ali	PROPN
cana-1920	279	11	,	,	PUNCT
cana-1920	279	12	and	and	CCONJ
cana-1920	279	13	f.	f.	PROPN
cana-1920	279	14	azam	azam	PROPN
cana-1920	279	15	.	.	PUNCT
cana-1920	280	1	topological	topological	ADJ
cana-1920	280	2	indices	index	NOUN
cana-1920	280	3	and	and	CCONJ
cana-1920	280	4	qspr	qspr	NOUN
cana-1920	280	5	/	/	SYM
cana-1920	280	6	qsar	qsar	NOUN
cana-1920	280	7	analysis	analysis	NOUN
cana-1920	280	8	of	of	ADP
cana-1920	280	9	some	some	DET
cana-1920	280	10	antiviral	antiviral	ADJ
cana-1920	280	11	drugs	drug	NOUN
cana-1920	280	12	being	be	AUX
cana-1920	280	13	investigated	investigate	VERB
cana-1920	280	14	for	for	ADP
cana-1920	280	15	the	the	DET
cana-1920	280	16	treatment	treatment	NOUN
cana-1920	280	17	of	of	ADP
cana-1920	280	18	covid-19	covid-19	PROPN
cana-1920	280	19	patients	patient	NOUN
cana-1920	280	20	.	.	PUNCT
cana-1920	281	1	international	international	ADJ
cana-1920	281	2	journal	journal	NOUN
cana-1920	281	3	of	of	ADP
cana-1920	281	4	quantum	quantum	ADJ
cana-1920	281	5	chemistry	chemistry	NOUN
cana-1920	281	6	,	,	PUNCT
cana-1920	281	7	121(9):e26594	121(9):e26594	PROPN
cana-1920	281	8	,	,	PUNCT
cana-1920	281	9	2021	2021	NUM
cana-1920	281	10	.	.	PUNCT
cana-1920	282	1	[	[	X
cana-1920	282	2	18	18	NUM
cana-1920	282	3	]	]	X
cana-1920	282	4	v.	v.	CCONJ
cana-1920	282	5	kulli	kulli	PROPN
cana-1920	282	6	.	.	PUNCT
cana-1920	283	1	reverse	reverse	VERB
cana-1920	283	2	zagreb	zagreb	PROPN
cana-1920	283	3	and	and	CCONJ
cana-1920	283	4	reverse	reverse	VERB
cana-1920	283	5	hyper	hyper	ADJ
cana-1920	283	6	-	-	ADJ
cana-1920	283	7	zagreb	zagreb	PROPN
cana-1920	283	8	indices	index	NOUN
cana-1920	283	9	and	and	CCONJ
cana-1920	283	10	their	their	PRON
cana-1920	283	11	polynomials	polynomial	NOUN
cana-1920	283	12	of	of	ADP
cana-1920	283	13	rhombus	rhombus	ADJ
cana-1920	283	14	silicate	silicate	NOUN
cana-1920	283	15	networks	network	NOUN
cana-1920	283	16	.	.	PUNCT
cana-1920	284	1	annals	annal	NOUN
cana-1920	284	2	of	of	ADP
cana-1920	284	3	pure	pure	ADJ
cana-1920	284	4	and	and	CCONJ
cana-1920	284	5	applied	applied	ADJ
cana-1920	284	6	mathematics	mathematic	NOUN
cana-1920	284	7	,	,	PUNCT
cana-1920	284	8	16(1):47–51	16(1):47–51	NUM
cana-1920	284	9	,	,	PUNCT
cana-1920	284	10	2018	2018	NUM
cana-1920	284	11	.	.	PUNCT
cana-1920	285	1	https://pubchem.ncbi.nlm.nih.gov/compound/2_2_4_4-tetramethylpentane	https://pubchem.ncbi.nlm.nih.gov/compound/2_2_4_4-tetramethylpentane	PROPN
cana-1920	285	2	https://pubchem.ncbi.nlm.nih.gov/compound/2_2_4_4-tetramethylpentane	https://pubchem.ncbi.nlm.nih.gov/compound/2_2_4_4-tetramethylpentane	PROPN
cana-1920	285	3	https://pubchem.ncbi.nlm.nih.gov/compound/2_2_4_4-tetramethylpentane	https://pubchem.ncbi.nlm.nih.gov/compound/2_2_4_4-tetramethylpentane	PROPN
cana-1920	285	4	https://pubchem.ncbi.nlm.nih.gov/compound/2_2_4_4-tetramethylpentane	https://pubchem.ncbi.nlm.nih.gov/compound/2_2_4_4-tetramethylpentane	PROPN
cana-1920	285	5	communications	communication	NOUN
cana-1920	285	6	on	on	ADP
cana-1920	285	7	applied	apply	VERB
cana-1920	285	8	nonlinear	nonlinear	ADJ
cana-1920	285	9	analysis	analysis	NOUN
cana-1920	285	10	issn	issn	NOUN
cana-1920	285	11	:	:	PUNCT
cana-1920	285	12	1074	1074	NUM
cana-1920	285	13	-	-	PUNCT
cana-1920	285	14	133x	133x	NUM
cana-1920	285	15	vol	vol	NOUN
cana-1920	285	16	32	32	NUM
cana-1920	285	17	no	no	NOUN
cana-1920	285	18	.	.	NOUN
cana-1920	285	19	3	3	NUM
cana-1920	285	20	(	(	PUNCT
cana-1920	285	21	2025	2025	NUM
cana-1920	285	22	)	)	PUNCT
cana-1920	285	23	83	83	NUM
cana-1920	285	24	https://internationalpubls.com	https://internationalpubls.com	X
cana-1920	286	1	[	[	X
cana-1920	286	2	19	19	NUM
cana-1920	286	3	]	]	X
cana-1920	286	4	y.	y.	PROPN
cana-1920	286	5	c.	c.	PROPN
cana-1920	286	6	kwun	kwun	PROPN
cana-1920	286	7	,	,	PUNCT
cana-1920	286	8	a.	a.	PROPN
cana-1920	286	9	u.	u.	PROPN
cana-1920	286	10	r.	r.	PROPN
cana-1920	286	11	virk	virk	PROPN
cana-1920	286	12	,	,	PUNCT
cana-1920	286	13	m.	m.	NOUN
cana-1920	286	14	rafaqat	rafaqat	PROPN
cana-1920	286	15	,	,	PUNCT
cana-1920	286	16	m.	m.	NOUN
cana-1920	286	17	u.	u.	PROPN
cana-1920	286	18	rehman	rehman	PROPN
cana-1920	286	19	,	,	PUNCT
cana-1920	286	20	and	and	CCONJ
cana-1920	286	21	w.	w.	PROPN
cana-1920	286	22	nazeer	nazeer	PROPN
cana-1920	286	23	.	.	PUNCT
cana-1920	287	1	some	some	PRON
cana-1920	287	2	reversed	reverse	VERB
cana-1920	287	3	degreebased	degreebase	VERB
cana-1920	287	4	topological	topological	ADJ
cana-1920	287	5	indices	index	NOUN
cana-1920	287	6	for	for	ADP
cana-1920	287	7	graphene	graphene	NOUN
cana-1920	287	8	.	.	PUNCT
cana-1920	288	1	journal	journal	NOUN
cana-1920	288	2	of	of	ADP
cana-1920	288	3	discrete	discrete	ADJ
cana-1920	288	4	mathematical	mathematical	ADJ
cana-1920	288	5	sciences	science	NOUN
cana-1920	288	6	and	and	CCONJ
cana-1920	288	7	cryptography	cryptography	NOUN
cana-1920	288	8	,	,	PUNCT
cana-1920	288	9	22(7):1305–1314	22(7):1305–1314	PROPN
cana-1920	288	10	,	,	PUNCT
cana-1920	288	11	2019	2019	NUM
cana-1920	288	12	.	.	PUNCT
cana-1920	289	1	[	[	X
cana-1920	289	2	20	20	NUM
cana-1920	289	3	]	]	PUNCT
cana-1920	289	4	l.	l.	PROPN
cana-1920	289	5	li	li	PROPN
cana-1920	289	6	,	,	PUNCT
cana-1920	289	7	x.	x.	PROPN
cana-1920	289	8	li	li	PROPN
cana-1920	289	9	,	,	PUNCT
cana-1920	289	10	and	and	CCONJ
cana-1920	289	11	w.	w.	PROPN
cana-1920	289	12	liu	liu	PROPN
cana-1920	289	13	.	.	PUNCT
cana-1920	290	1	note	note	VERB
cana-1920	290	2	on	on	ADP
cana-1920	290	3	the	the	DET
cana-1920	290	4	product	product	NOUN
cana-1920	290	5	of	of	ADP
cana-1920	290	6	wiener	wiener	NOUN
cana-1920	290	7	and	and	CCONJ
cana-1920	290	8	harary	harary	NOUN
cana-1920	290	9	indices	index	NOUN
cana-1920	290	10	.	.	PUNCT
cana-1920	291	1	match	match	PROPN
cana-1920	291	2	commun	commun	PROPN
cana-1920	291	3	.	.	PUNCT
cana-1920	291	4	math	math	PROPN
cana-1920	291	5	.	.	PUNCT
cana-1920	292	1	comput	comput	NOUN
cana-1920	292	2	.	.	PUNCT
cana-1920	293	1	chem	chem	PROPN
cana-1920	293	2	,	,	PUNCT
cana-1920	293	3	91:299–305	91:299–305	NUM
cana-1920	293	4	,	,	PUNCT
cana-1920	293	5	2024	2024	NUM
cana-1920	293	6	.	.	PUNCT
cana-1920	294	1	[	[	X
cana-1920	294	2	21	21	NUM
cana-1920	294	3	]	]	PUNCT
cana-1920	294	4	z.	z.	PROPN
cana-1920	294	5	li	li	PROPN
cana-1920	294	6	and	and	CCONJ
cana-1920	294	7	b.	b.	PROPN
cana-1920	294	8	wu	wu	PROPN
cana-1920	294	9	.	.	PUNCT
cana-1920	295	1	orientations	orientation	NOUN
cana-1920	295	2	of	of	ADP
cana-1920	295	3	graphs	graph	NOUN
cana-1920	295	4	with	with	ADP
cana-1920	295	5	maximum	maximum	ADJ
cana-1920	295	6	wiener	wiener	NOUN
cana-1920	295	7	index	index	NOUN
cana-1920	295	8	.	.	PUNCT
cana-1920	296	1	journal	journal	PROPN
cana-1920	296	2	of	of	ADP
cana-1920	296	3	graph	graph	NOUN
cana-1920	296	4	theory	theory	NOUN
cana-1920	296	5	.	.	PUNCT
cana-1920	297	1	[	[	X
cana-1920	297	2	22	22	NUM
cana-1920	297	3	]	]	X
cana-1920	297	4	y.	y.	PROPN
cana-1920	297	5	liu	liu	PROPN
cana-1920	297	6	,	,	PUNCT
cana-1920	297	7	m.	m.	NOUN
cana-1920	297	8	rezaei	rezaei	PROPN
cana-1920	297	9	,	,	PUNCT
cana-1920	297	10	m.	m.	PROPN
cana-1920	297	11	r.	r.	PROPN
cana-1920	297	12	farahani	farahani	PROPN
cana-1920	297	13	,	,	PUNCT
cana-1920	297	14	m.	m.	NOUN
cana-1920	297	15	n.	n.	PROPN
cana-1920	297	16	husin	husin	PROPN
cana-1920	297	17	,	,	PUNCT
cana-1920	297	18	and	and	CCONJ
cana-1920	297	19	m.	m.	NOUN
cana-1920	297	20	imran	imran	PROPN
cana-1920	297	21	.	.	PUNCT
cana-1920	298	1	the	the	DET
cana-1920	298	2	omega	omega	NOUN
cana-1920	298	3	polynomial	polynomial	NOUN
cana-1920	298	4	and	and	CCONJ
cana-1920	298	5	the	the	DET
cana-1920	298	6	cluj	cluj	NOUN
cana-1920	298	7	-	-	PUNCT
cana-1920	298	8	ilmenau	ilmenau	ADJ
cana-1920	298	9	index	index	NOUN
cana-1920	298	10	of	of	ADP
cana-1920	298	11	an	an	DET
cana-1920	298	12	infinite	infinite	ADJ
cana-1920	298	13	class	class	NOUN
cana-1920	298	14	of	of	ADP
cana-1920	298	15	the	the	DET
cana-1920	298	16	titania	titania	NOUN
cana-1920	298	17	nanotubes	nanotube	NOUN
cana-1920	298	18	tio2	tio2	NOUN
cana-1920	298	19	(	(	PUNCT
cana-1920	298	20	m	m	PROPN
cana-1920	298	21	,	,	PUNCT
cana-1920	298	22	n	n	CCONJ
cana-1920	298	23	)	)	PUNCT
cana-1920	298	24	.	.	PUNCT
cana-1920	299	1	journal	journal	PROPN
cana-1920	299	2	of	of	ADP
cana-1920	299	3	computational	computational	ADJ
cana-1920	299	4	and	and	CCONJ
cana-1920	299	5	theoretical	theoretical	ADJ
cana-1920	299	6	nanoscience	nanoscience	NOUN
cana-1920	299	7	,	,	PUNCT
cana-1920	299	8	14(7):3429–3432	14(7):3429–3432	NUM
cana-1920	299	9	,	,	PUNCT
cana-1920	299	10	2017	2017	NUM
cana-1920	299	11	.	.	PUNCT
cana-1920	300	1	[	[	X
cana-1920	300	2	23	23	NUM
cana-1920	300	3	]	]	PUNCT
cana-1920	300	4	a.	a.	NOUN
cana-1920	300	5	mahboob	mahboob	PROPN
cana-1920	300	6	,	,	PUNCT
cana-1920	300	7	m.	m.	PROPN
cana-1920	300	8	w.	w.	PROPN
cana-1920	300	9	rasheed	rasheed	PROPN
cana-1920	300	10	,	,	PUNCT
cana-1920	300	11	a.	a.	NOUN
cana-1920	300	12	m.	m.	PROPN
cana-1920	300	13	dhiaa	dhiaa	PROPN
cana-1920	300	14	,	,	PUNCT
cana-1920	300	15	i.	i.	PROPN
cana-1920	300	16	hanif	hanif	PROPN
cana-1920	300	17	,	,	PUNCT
cana-1920	300	18	and	and	CCONJ
cana-1920	300	19	l.	l.	PROPN
cana-1920	300	20	amin	amin	PROPN
cana-1920	300	21	.	.	PROPN
cana-1920	301	1	on	on	ADP
cana-1920	301	2	quantitative	quantitative	ADJ
cana-1920	301	3	structureproperty	structureproperty	NOUN
cana-1920	301	4	relationship	relationship	NOUN
cana-1920	301	5	(	(	PUNCT
cana-1920	301	6	qspr	qspr	NOUN
cana-1920	301	7	)	)	PUNCT
cana-1920	301	8	analysis	analysis	NOUN
cana-1920	301	9	of	of	ADP
cana-1920	301	10	physicochemical	physicochemical	ADJ
cana-1920	301	11	properties	property	NOUN
cana-1920	301	12	and	and	CCONJ
cana-1920	301	13	anti	anti	ADJ
cana-1920	301	14	-	-	ADJ
cana-1920	301	15	hepatitis	hepatitis	ADJ
cana-1920	301	16	prescription	prescription	NOUN
cana-1920	301	17	drugs	drug	NOUN
cana-1920	301	18	using	use	VERB
cana-1920	301	19	a	a	DET
cana-1920	301	20	linear	linear	ADJ
cana-1920	301	21	regression	regression	NOUN
cana-1920	301	22	model	model	NOUN
cana-1920	301	23	.	.	PUNCT
cana-1920	302	1	heliyon	heliyon	NOUN
cana-1920	302	2	,	,	PUNCT
cana-1920	302	3	2024	2024	NUM
cana-1920	302	4	.	.	PUNCT
cana-1920	303	1	[	[	X
cana-1920	303	2	24	24	NUM
cana-1920	303	3	]	]	PUNCT
cana-1920	303	4	a.	a.	NOUN
cana-1920	303	5	mahboob	mahboob	PROPN
cana-1920	303	6	,	,	PUNCT
cana-1920	303	7	m.	m.	PROPN
cana-1920	303	8	w.	w.	PROPN
cana-1920	303	9	rasheed	rasheed	PROPN
cana-1920	303	10	,	,	PUNCT
cana-1920	303	11	i.	i.	PROPN
cana-1920	303	12	hanif	hanif	PROPN
cana-1920	303	13	,	,	PUNCT
cana-1920	303	14	l.	l.	PROPN
cana-1920	303	15	amin	amin	PROPN
cana-1920	303	16	,	,	PUNCT
cana-1920	303	17	and	and	CCONJ
cana-1920	303	18	a.	a.	NOUN
cana-1920	303	19	alameri	alameri	PROPN
cana-1920	303	20	.	.	PUNCT
cana-1920	304	1	role	role	NOUN
cana-1920	304	2	of	of	ADP
cana-1920	304	3	molecular	molecular	ADJ
cana-1920	304	4	descriptors	descriptor	NOUN
cana-1920	304	5	in	in	ADP
cana-1920	304	6	quantitative	quantitative	ADJ
cana-1920	304	7	structure	structure	NOUN
cana-1920	304	8	-	-	PUNCT
cana-1920	304	9	property	property	NOUN
cana-1920	304	10	relationship	relationship	NOUN
cana-1920	304	11	analysis	analysis	NOUN
cana-1920	304	12	of	of	ADP
cana-1920	304	13	kidney	kidney	NOUN
cana-1920	304	14	cancer	cancer	NOUN
cana-1920	304	15	therapeutics	therapeutic	NOUN
cana-1920	304	16	.	.	PUNCT
cana-1920	305	1	international	international	ADJ
cana-1920	305	2	journal	journal	NOUN
cana-1920	305	3	of	of	ADP
cana-1920	305	4	quantum	quantum	ADJ
cana-1920	305	5	chemistry	chemistry	NOUN
cana-1920	305	6	,	,	PUNCT
cana-1920	305	7	124(1):e27241	124(1):e27241	NUM
cana-1920	305	8	,	,	PUNCT
cana-1920	305	9	2024	2024	NUM
cana-1920	305	10	.	.	PUNCT
cana-1920	306	1	[	[	X
cana-1920	306	2	25	25	NUM
cana-1920	306	3	]	]	PUNCT
cana-1920	306	4	m.	m.	NOUN
cana-1920	306	5	randic	randic	PROPN
cana-1920	306	6	.	.	PUNCT
cana-1920	306	7	characterization	characterization	NOUN
cana-1920	306	8	of	of	ADP
cana-1920	306	9	molecular	molecular	ADJ
cana-1920	306	10	branching	branching	NOUN
cana-1920	306	11	.	.	PUNCT
cana-1920	307	1	journal	journal	NOUN
cana-1920	307	2	of	of	ADP
cana-1920	307	3	the	the	DET
cana-1920	307	4	american	american	PROPN
cana-1920	307	5	chemical	chemical	PROPN
cana-1920	307	6	society	society	PROPN
cana-1920	307	7	,	,	PUNCT
cana-1920	307	8	97(23):6609–6615	97(23):6609–6615	NUM
cana-1920	307	9	,	,	PUNCT
cana-1920	307	10	1975	1975	NUM
cana-1920	307	11	.	.	PUNCT
cana-1920	308	1	[	[	X
cana-1920	308	2	26	26	NUM
cana-1920	308	3	]	]	PUNCT
cana-1920	308	4	m.	m.	NOUN
cana-1920	308	5	s.	s.	PROPN
cana-1920	308	6	rosary	rosary	PROPN
cana-1920	308	7	.	.	PUNCT
cana-1920	309	1	on	on	ADP
cana-1920	309	2	reverse	reverse	ADJ
cana-1920	309	3	valency	valency	NOUN
cana-1920	309	4	based	base	VERB
cana-1920	309	5	topological	topological	ADJ
cana-1920	309	6	indices	index	NOUN
cana-1920	309	7	of	of	ADP
cana-1920	309	8	metal	metal	NOUN
cana-1920	309	9	–	–	PUNCT
cana-1920	309	10	organic	organic	ADJ
cana-1920	309	11	framework	framework	NOUN
cana-1920	309	12	.	.	PUNCT
cana-1920	310	1	polycyclic	polycyclic	ADJ
cana-1920	310	2	aromatic	aromatic	ADJ
cana-1920	310	3	compounds	compound	NOUN
cana-1920	310	4	,	,	PUNCT
cana-1920	310	5	43(1):860–873	43(1):860–873	PROPN
cana-1920	310	6	,	,	PUNCT
cana-1920	310	7	2023	2023	NUM
cana-1920	310	8	.	.	PUNCT
cana-1920	311	1	[	[	X
cana-1920	311	2	27	27	NUM
cana-1920	311	3	]	]	X
cana-1920	311	4	s.	s.	PROPN
cana-1920	311	5	wagner	wagner	PROPN
cana-1920	311	6	and	and	CCONJ
cana-1920	311	7	h.	h.	PROPN
cana-1920	311	8	wang	wang	PROPN
cana-1920	311	9	.	.	PUNCT
cana-1920	312	1	introduction	introduction	NOUN
cana-1920	312	2	to	to	ADP
cana-1920	312	3	chemical	chemical	NOUN
cana-1920	312	4	graph	graph	NOUN
cana-1920	312	5	theory	theory	NOUN
cana-1920	312	6	.	.	PUNCT
cana-1920	313	1	crc	crc	PROPN
cana-1920	313	2	press	press	PROPN
cana-1920	313	3	,	,	PUNCT
cana-1920	313	4	taylor	taylor	PROPN
cana-1920	313	5	&	&	CCONJ
cana-1920	313	6	francis	francis	PROPN
cana-1920	313	7	group	group	PROPN
cana-1920	313	8	,	,	PUNCT
cana-1920	313	9	boca	boca	PROPN
cana-1920	313	10	raton	raton	PROPN
cana-1920	313	11	,	,	PUNCT
cana-1920	313	12	fl	fl	PROPN
cana-1920	313	13	,	,	PUNCT
cana-1920	313	14	2018	2018	NUM
cana-1920	313	15	.	.	PUNCT
cana-1920	314	1	[	[	X
cana-1920	314	2	28	28	NUM
cana-1920	314	3	]	]	X
cana-1920	314	4	j.	j.	PROPN
cana-1920	314	5	wei	wei	PROPN
cana-1920	314	6	,	,	PUNCT
cana-1920	314	7	a.	a.	PROPN
cana-1920	314	8	khalid	khalid	PROPN
cana-1920	314	9	,	,	PUNCT
cana-1920	314	10	p.	p.	PROPN
cana-1920	314	11	ali	ali	PROPN
cana-1920	314	12	,	,	PUNCT
cana-1920	314	13	m.	m.	PROPN
cana-1920	314	14	k.	k.	PROPN
cana-1920	314	15	siddiqui	siddiqui	PROPN
cana-1920	314	16	,	,	PUNCT
cana-1920	314	17	a.	a.	NOUN
cana-1920	314	18	nawaz	nawaz	NOUN
cana-1920	314	19	,	,	PUNCT
cana-1920	314	20	and	and	CCONJ
cana-1920	314	21	m.	m.	NOUN
cana-1920	314	22	hussain	hussain	PROPN
cana-1920	314	23	.	.	PUNCT
cana-1920	315	1	computing	compute	VERB
cana-1920	315	2	reverse	reverse	NOUN
cana-1920	315	3	degree	degree	NOUN
cana-1920	315	4	based	base	VERB
cana-1920	315	5	topological	topological	ADJ
cana-1920	315	6	indices	index	NOUN
cana-1920	315	7	of	of	ADP
cana-1920	315	8	vanadium	vanadium	NOUN
cana-1920	315	9	carbide	carbide	NOUN
cana-1920	315	10	.	.	PUNCT
cana-1920	316	1	polycyclic	polycyclic	ADJ
cana-1920	316	2	aromatic	aromatic	ADJ
cana-1920	316	3	compounds	compound	NOUN
cana-1920	316	4	,	,	PUNCT
cana-1920	316	5	43(2):1172	43(2):1172	NUM
cana-1920	316	6	–	–	PUNCT
cana-1920	316	7	1191	1191	NUM
cana-1920	316	8	,	,	PUNCT
cana-1920	316	9	2023	2023	NUM
cana-1920	316	10	.	.	PUNCT
cana-1920	317	1	[	[	X
cana-1920	317	2	29	29	NUM
cana-1920	317	3	]	]	X
cana-1920	317	4	h.	h.	PROPN
cana-1920	317	5	wiener	wiener	NOUN
cana-1920	317	6	.	.	PUNCT
cana-1920	318	1	correlation	correlation	NOUN
cana-1920	318	2	of	of	ADP
cana-1920	318	3	heats	heat	NOUN
cana-1920	318	4	of	of	ADP
cana-1920	318	5	isomerization	isomerization	NOUN
cana-1920	318	6	,	,	PUNCT
cana-1920	318	7	and	and	CCONJ
cana-1920	318	8	differences	difference	NOUN
cana-1920	318	9	in	in	ADP
cana-1920	318	10	heats	heat	NOUN
cana-1920	318	11	of	of	ADP
cana-1920	318	12	vaporization	vaporization	NOUN
cana-1920	318	13	of	of	ADP
cana-1920	318	14	isomers	isomer	NOUN
cana-1920	318	15	.	.	PUNCT
cana-1920	319	1	journal	journal	PROPN
cana-1920	319	2	of	of	ADP
cana-1920	319	3	american	american	PROPN
cana-1920	319	4	chemical	chemical	PROPN
cana-1920	319	5	society	society	NOUN
cana-1920	319	6	,	,	PUNCT
cana-1920	319	7	69:2636–2638	69:2636–2638	NOUN
cana-1920	319	8	,	,	PUNCT
cana-1920	319	9	1947	1947	NUM
cana-1920	319	10	.	.	PUNCT
cana-1920	320	1	[	[	X
cana-1920	320	2	30	30	NUM
cana-1920	320	3	]	]	X
cana-1920	320	4	s.	s.	PROPN
cana-1920	320	5	zaman	zaman	PROPN
cana-1920	320	6	,	,	PUNCT
cana-1920	320	7	h.	h.	PROPN
cana-1920	320	8	s.	s.	PROPN
cana-1920	320	9	a.	a.	PROPN
cana-1920	320	10	yaqoob	yaqoob	PROPN
cana-1920	320	11	,	,	PUNCT
cana-1920	320	12	a.	a.	PROPN
cana-1920	320	13	ullah	ullah	PROPN
cana-1920	320	14	,	,	PUNCT
cana-1920	320	15	and	and	CCONJ
cana-1920	320	16	m.	m.	NOUN
cana-1920	320	17	sheikh	sheikh	PROPN
cana-1920	320	18	.	.	PUNCT
cana-1920	321	1	qspr	qspr	NOUN
cana-1920	321	2	analysis	analysis	NOUN
cana-1920	321	3	of	of	ADP
cana-1920	321	4	some	some	DET
cana-1920	321	5	novel	novel	ADJ
cana-1920	321	6	drugs	drug	NOUN
cana-1920	321	7	used	use	VERB
cana-1920	321	8	in	in	ADP
cana-1920	321	9	blood	blood	NOUN
cana-1920	321	10	cancer	cancer	NOUN
cana-1920	321	11	treatment	treatment	NOUN
cana-1920	321	12	via	via	ADP
cana-1920	321	13	degree	degree	NOUN
cana-1920	321	14	based	base	VERB
cana-1920	321	15	topological	topological	ADJ
cana-1920	321	16	indices	index	NOUN
cana-1920	321	17	and	and	CCONJ
cana-1920	321	18	regression	regression	NOUN
cana-1920	321	19	models	model	NOUN
cana-1920	321	20	.	.	PUNCT
cana-1920	322	1	polycyclic	polycyclic	ADJ
cana-1920	322	2	aromatic	aromatic	ADJ
cana-1920	322	3	compounds	compound	NOUN
cana-1920	322	4	,	,	PUNCT
cana-1920	322	5	pages	page	NOUN
cana-1920	322	6	1–17	1–17	PROPN
cana-1920	322	7	,	,	PUNCT
cana-1920	322	8	2023	2023	NUM
cana-1920	322	9	.	.	PUNCT
cana-1920	323	1	[	[	X
cana-1920	323	2	31	31	NUM
cana-1920	323	3	]	]	PUNCT
cana-1920	323	4	s.	s.	PROPN
cana-1920	323	5	zhang	zhang	PROPN
cana-1920	323	6	,	,	PUNCT
cana-1920	323	7	x.	x.	PROPN
cana-1920	323	8	chen	chen	PROPN
cana-1920	323	9	,	,	PUNCT
cana-1920	323	10	z.-w	z.-w	PROPN
cana-1920	323	11	.	.	PUNCT
cana-1920	324	1	ma	ma	PROPN
cana-1920	324	2	,	,	PUNCT
cana-1920	324	3	x.-d	x.-d	PROPN
cana-1920	324	4	.	.	PUNCT
cana-1920	325	1	zhang	zhang	PROPN
cana-1920	325	2	,	,	PUNCT
cana-1920	325	3	and	and	CCONJ
cana-1920	325	4	y.-h	y.-h	NOUN
cana-1920	325	5	.	.	PUNCT
cana-1920	326	1	chen	chen	PROPN
cana-1920	326	2	.	.	PUNCT
cana-1920	327	1	the	the	DET
cana-1920	327	2	minimum	minimum	PROPN
cana-1920	327	3	wiener	wiener	NOUN
cana-1920	327	4	index	index	NOUN
cana-1920	327	5	of	of	ADP
cana-1920	327	6	unicyclic	unicyclic	ADJ
cana-1920	327	7	graphs	graph	NOUN
cana-1920	327	8	with	with	ADP
cana-1920	327	9	maximum	maximum	ADJ
cana-1920	327	10	degree	degree	NOUN
cana-1920	327	11	.	.	PUNCT
cana-1920	328	1	applied	apply	VERB
cana-1920	328	2	mathematics	mathematic	NOUN
cana-1920	328	3	and	and	CCONJ
cana-1920	328	4	computation	computation	NOUN
cana-1920	328	5	,	,	PUNCT
cana-1920	328	6	470:128581	470:128581	NUM
cana-1920	328	7	,	,	PUNCT
cana-1920	328	8	2024	2024	NUM
cana-1920	328	9	.	.	PUNCT
cana-1920	329	1	[	[	X
cana-1920	329	2	32	32	NUM
cana-1920	329	3	]	]	PUNCT
cana-1920	329	4	x.	x.	PROPN
cana-1920	329	5	zhang	zhang	PROPN
cana-1920	329	6	,	,	PUNCT
cana-1920	329	7	a.	a.	PROPN
cana-1920	329	8	rauf	rauf	PROPN
cana-1920	329	9	,	,	PUNCT
cana-1920	329	10	m.	m.	NOUN
cana-1920	329	11	ishtiaq	ishtiaq	PROPN
cana-1920	329	12	,	,	PUNCT
cana-1920	329	13	m.	m.	PROPN
cana-1920	329	14	k.	k.	PROPN
cana-1920	329	15	siddiqui	siddiqui	PROPN
cana-1920	329	16	,	,	PUNCT
cana-1920	329	17	and	and	CCONJ
cana-1920	329	18	m.	m.	PROPN
cana-1920	329	19	h.	h.	PROPN
cana-1920	329	20	muhammad	muhammad	PROPN
cana-1920	329	21	.	.	PROPN
cana-1920	330	1	on	on	ADP
cana-1920	330	2	degree	degree	NOUN
cana-1920	330	3	based	base	VERB
cana-1920	330	4	topological	topological	ADJ
cana-1920	330	5	properties	property	NOUN
cana-1920	330	6	of	of	ADP
cana-1920	330	7	two	two	NUM
cana-1920	330	8	carbon	carbon	NOUN
cana-1920	330	9	nanotubes	nanotube	NOUN
cana-1920	330	10	.	.	PUNCT
cana-1920	331	1	polycyclic	polycyclic	ADJ
cana-1920	331	2	aromatic	aromatic	ADJ
cana-1920	331	3	compounds	compound	NOUN
cana-1920	331	4	,	,	PUNCT
cana-1920	331	5	42(3):866–884	42(3):866–884	PROPN
cana-1920	331	6	,	,	PUNCT
cana-1920	331	7	2022	2022	NUM
cana-1920	331	8	.	.	PUNCT
cana-1920	332	1	[	[	X
cana-1920	332	2	33	33	NUM
cana-1920	332	3	]	]	PUNCT
cana-1920	332	4	x.	x.	PROPN
cana-1920	332	5	zhang	zhang	PROPN
cana-1920	332	6	,	,	PUNCT
cana-1920	332	7	h.	h.	PROPN
cana-1920	332	8	reddy	reddy	PROPN
cana-1920	332	9	,	,	PUNCT
cana-1920	332	10	a.	a.	PROPN
cana-1920	332	11	usha	usha	PROPN
cana-1920	332	12	,	,	PUNCT
cana-1920	332	13	m.	m.	NOUN
cana-1920	332	14	shanmukha	shanmukha	PROPN
cana-1920	332	15	,	,	PUNCT
cana-1920	332	16	m.	m.	NOUN
cana-1920	332	17	reza	reza	PROPN
cana-1920	332	18	farahani	farahani	PROPN
cana-1920	332	19	,	,	PUNCT
cana-1920	332	20	and	and	CCONJ
cana-1920	332	21	m.	m.	NOUN
cana-1920	332	22	alaeiyan	alaeiyan	PROPN
cana-1920	332	23	.	.	PUNCT
cana-1920	333	1	a	a	DET
cana-1920	333	2	study	study	NOUN
cana-1920	333	3	on	on	ADP
cana-1920	333	4	anti	anti	ADJ
cana-1920	333	5	-	-	ADJ
cana-1920	333	6	malaria	malaria	ADJ
cana-1920	333	7	drugs	drug	NOUN
cana-1920	333	8	using	use	VERB
cana-1920	333	9	degree	degree	NOUN
cana-1920	333	10	-	-	PUNCT
cana-1920	333	11	based	base	VERB
cana-1920	333	12	topological	topological	ADJ
cana-1920	333	13	indices	index	NOUN
cana-1920	333	14	through	through	ADP
cana-1920	333	15	qspr	qspr	ADJ
cana-1920	333	16	analysis	analysis	NOUN
cana-1920	333	17	.	.	PUNCT
cana-1920	333	18	2022	2022	NUM
cana-1920	333	19	.	.	PUNCT
cana-1920	334	1	[	[	X
cana-1920	334	2	34	34	NUM
cana-1920	334	3	]	]	PUNCT
cana-1920	334	4	x.	x.	PROPN
cana-1920	334	5	zhang	zhang	PROPN
cana-1920	334	6	,	,	PUNCT
cana-1920	334	7	m.	m.	PROPN
cana-1920	334	8	k.	k.	PROPN
cana-1920	334	9	siddiqui	siddiqui	PROPN
cana-1920	334	10	,	,	PUNCT
cana-1920	334	11	s.	s.	PROPN
cana-1920	334	12	javed	javed	PROPN
cana-1920	334	13	,	,	PUNCT
cana-1920	334	14	l.	l.	PROPN
cana-1920	334	15	sherin	sherin	PROPN
cana-1920	334	16	,	,	PUNCT
cana-1920	334	17	f.	f.	PROPN
cana-1920	334	18	kausar	kausar	PROPN
cana-1920	334	19	,	,	PUNCT
cana-1920	334	20	and	and	CCONJ
cana-1920	334	21	m.	m.	PROPN
cana-1920	334	22	h.	h.	PROPN
cana-1920	334	23	muhammad	muhammad	PROPN
cana-1920	334	24	.	.	PROPN
cana-1920	334	25	physical	physical	ADJ
cana-1920	334	26	analysis	analysis	NOUN
cana-1920	334	27	of	of	ADP
cana-1920	334	28	heat	heat	NOUN
cana-1920	334	29	for	for	ADP
cana-1920	334	30	formation	formation	NOUN
cana-1920	334	31	and	and	CCONJ
cana-1920	334	32	entropy	entropy	NOUN
cana-1920	334	33	of	of	ADP
cana-1920	334	34	ceria	ceria	PROPN
cana-1920	334	35	oxide	oxide	NOUN
cana-1920	334	36	using	use	VERB
cana-1920	334	37	topological	topological	ADJ
cana-1920	334	38	indices	index	NOUN
cana-1920	334	39	.	.	PUNCT
cana-1920	335	1	combinatorial	combinatorial	ADJ
cana-1920	335	2	chemistry	chemistry	NOUN
cana-1920	335	3	&	&	CCONJ
cana-1920	335	4	high	high	ADJ
cana-1920	335	5	throughput	throughput	NOUN
cana-1920	335	6	screening	screening	NOUN
cana-1920	335	7	,	,	PUNCT
cana-1920	335	8	25(3):441–450	25(3):441–450	NUM
cana-1920	335	9	,	,	PUNCT
cana-1920	335	10	2022	2022	NUM
cana-1920	335	11	.	.	PUNCT
cana-1920	336	1	[	[	X
cana-1920	336	2	35	35	NUM
cana-1920	336	3	]	]	X
cana-1920	336	4	h.	h.	PROPN
cana-1920	336	5	zhou	zhou	PROPN
cana-1920	336	6	,	,	PUNCT
cana-1920	336	7	a.	a.	NOUN
cana-1920	336	8	mahboob	mahboob	PROPN
cana-1920	336	9	,	,	PUNCT
cana-1920	336	10	m.	m.	PROPN
cana-1920	336	11	w.	w.	PROPN
cana-1920	336	12	rasheed	rasheed	PROPN
cana-1920	336	13	,	,	PUNCT
cana-1920	336	14	a.	a.	PROPN
cana-1920	336	15	ovais	ovais	PROPN
cana-1920	336	16	,	,	PUNCT
cana-1920	336	17	m.	m.	PROPN
cana-1920	336	18	k.	k.	PROPN
cana-1920	336	19	siddiqui	siddiqui	PROPN
cana-1920	336	20	,	,	PUNCT
cana-1920	336	21	and	and	CCONJ
cana-1920	336	22	i.	i.	PROPN
cana-1920	336	23	z.	z.	PROPN
cana-1920	336	24	cheema	cheema	PROPN
cana-1920	336	25	.	.	PUNCT
cana-1920	337	1	on	on	ADP
cana-1920	337	2	qspr	qspr	ADJ
cana-1920	337	3	analysis	analysis	NOUN
cana-1920	337	4	of	of	ADP
cana-1920	337	5	molecular	molecular	ADJ
cana-1920	337	6	descriptor	descriptor	NOUN
cana-1920	337	7	and	and	CCONJ
cana-1920	337	8	thermodynamic	thermodynamic	ADJ
cana-1920	337	9	features	feature	NOUN
cana-1920	337	10	of	of	ADP
cana-1920	337	11	narcotic	narcotic	ADJ
cana-1920	337	12	drugs	drug	NOUN
cana-1920	337	13	.	.	PUNCT
cana-1920	338	1	polycyclic	polycyclic	ADJ
cana-1920	338	2	aromatic	aromatic	ADJ
cana-1920	338	3	compounds	compound	NOUN
cana-1920	338	4	,	,	PUNCT
cana-1920	338	5	pages	page	NOUN
cana-1920	338	6	1–21	1–21	PROPN
cana-1920	338	7	,	,	PUNCT
cana-1920	338	8	2023	2023	NUM
cana-1920	338	9	.	.	PUNCT
cana-1920	339	1	[	[	X
cana-1920	339	2	36	36	NUM
cana-1920	339	3	]	]	PUNCT
cana-1920	339	4	x.	x.	NOUN
cana-1920	339	5	zuo	zuo	PROPN
cana-1920	339	6	,	,	PUNCT
cana-1920	339	7	j.-b	j.-b	PROPN
cana-1920	339	8	.	.	PUNCT
cana-1920	340	1	liu	liu	PROPN
cana-1920	340	2	,	,	PUNCT
cana-1920	340	3	h.	h.	PROPN
cana-1920	340	4	iqbal	iqbal	PROPN
cana-1920	340	5	,	,	PUNCT
cana-1920	340	6	k.	k.	PROPN
cana-1920	340	7	ali	ali	PROPN
cana-1920	340	8	,	,	PUNCT
cana-1920	340	9	and	and	CCONJ
cana-1920	340	10	s.	s.	PROPN
cana-1920	340	11	t.	t.	PROPN
cana-1920	340	12	r.	r.	PROPN
cana-1920	340	13	rizvi	rizvi	PROPN
cana-1920	340	14	.	.	PUNCT
cana-1920	341	1	topological	topological	ADJ
cana-1920	341	2	indices	index	NOUN
cana-1920	341	3	of	of	ADP
cana-1920	341	4	certain	certain	ADJ
cana-1920	341	5	transformed	transform	VERB
cana-1920	341	6	chemical	chemical	NOUN
cana-1920	341	7	structures	structure	NOUN
cana-1920	341	8	.	.	PUNCT
cana-1920	342	1	journal	journal	NOUN
cana-1920	342	2	of	of	ADP
cana-1920	342	3	chemistry	chemistry	NOUN
cana-1920	342	4	,	,	PUNCT
cana-1920	342	5	2020:1–7	2020:1–7	PRON
cana-1920	342	6	,	,	PUNCT
cana-1920	342	7	2020	2020	NUM
cana-1920	342	8	.	.	PUNCT