id	sid	tid	token	lemma	pos
cana-1007	1	1	communications	communication	NOUN
cana-1007	1	2	on	on	ADP
cana-1007	1	3	applied	apply	VERB
cana-1007	1	4	nonlinear	nonlinear	ADJ
cana-1007	1	5	analysis	analysis	NOUN
cana-1007	1	6	issn	issn	NOUN
cana-1007	1	7	:	:	PUNCT
cana-1007	1	8	1074	1074	NUM
cana-1007	1	9	-	-	PUNCT
cana-1007	1	10	133x	133x	NUM
cana-1007	1	11	vol	vol	NOUN
cana-1007	1	12	31	31	NUM
cana-1007	1	13	no	no	NOUN
cana-1007	1	14	.	.	PUNCT
cana-1007	2	1	5s	5s	NUM
cana-1007	2	2	(	(	PUNCT
cana-1007	2	3	2024	2024	NUM
cana-1007	2	4	)	)	PUNCT
cana-1007	2	5	129	129	NUM
cana-1007	2	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1007	2	7	inconspicuous	inconspicuous	ADJ
cana-1007	2	8	discovery	discovery	NOUN
cana-1007	2	9	of	of	ADP
cana-1007	2	10	coronavirus	coronavirus	NOUN
cana-1007	2	11	infected	infect	VERB
cana-1007	2	12	people	people	NOUN
cana-1007	2	13	based	base	VERB
cana-1007	2	14	satl	satl	NOUN
cana-1007	2	15	of	of	ADP
cana-1007	2	16	star	star	NOUN
cana-1007	2	17	graphs	graph	NOUN
cana-1007	2	18	v.	v.	ADP
cana-1007	2	19	sudhakar1	sudhakar1	PROPN
cana-1007	2	20	,	,	PUNCT
cana-1007	2	21	g.	g.	PROPN
cana-1007	2	22	uma	uma	PROPN
cana-1007	2	23	maheswari2	maheswari2	PROPN
cana-1007	2	24	,	,	PUNCT
cana-1007	2	25	suzan	suzan	PROPN
cana-1007	2	26	j.	j.	PROPN
cana-1007	2	27	obaiys3	obaiys3	PROPN
cana-1007	2	28	,	,	PUNCT
cana-1007	2	29	s.	s.	PROPN
cana-1007	2	30	manikanda	manikanda	PROPN
cana-1007	2	31	prabhu4	prabhu4	PROPN
cana-1007	2	32	,	,	PUNCT
cana-1007	2	33	p.	p.	NOUN
cana-1007	2	34	chellamani4	chellamani4	PROPN
cana-1007	2	35	,	,	PUNCT
cana-1007	2	36	v.	v.	ADP
cana-1007	2	37	balaji5	balaji5	PROPN
cana-1007	2	38	,	,	PUNCT
cana-1007	2	39	*	*	PROPN
cana-1007	2	40	1department	1department	NUM
cana-1007	2	41	of	of	ADP
cana-1007	2	42	mathematics	mathematic	NOUN
cana-1007	2	43	,	,	PUNCT
cana-1007	2	44	jerusalem	jerusalem	PROPN
cana-1007	2	45	college	college	PROPN
cana-1007	2	46	of	of	ADP
cana-1007	2	47	engineering	engineering	PROPN
cana-1007	2	48	,	,	PUNCT
cana-1007	2	49	chennai	chennai	VERB
cana-1007	2	50	600	600	NUM
cana-1007	2	51	100	100	NUM
cana-1007	2	52	,	,	PUNCT
cana-1007	2	53	tamilnadu	tamilnadu	ADJ
cana-1007	2	54	,	,	PUNCT
cana-1007	2	55	india	india	PROPN
cana-1007	2	56	.	.	PUNCT
cana-1007	3	1	2gonzaga	2gonzaga	NUM
cana-1007	3	2	college	college	NOUN
cana-1007	3	3	of	of	ADP
cana-1007	3	4	arts	art	NOUN
cana-1007	3	5	and	and	CCONJ
cana-1007	3	6	science	science	NOUN
cana-1007	3	7	for	for	ADP
cana-1007	3	8	women	woman	NOUN
cana-1007	3	9	,	,	PUNCT
cana-1007	3	10	krishnagiri	krishnagiri	NOUN
cana-1007	3	11	635	635	NUM
cana-1007	3	12	108	108	NUM
cana-1007	3	13	,	,	PUNCT
cana-1007	3	14	tamil	tamil	PROPN
cana-1007	3	15	nadu	nadu	PROPN
cana-1007	3	16	,	,	PUNCT
cana-1007	3	17	india	india	PROPN
cana-1007	3	18	.	.	PUNCT
cana-1007	4	1	3department	3department	NUM
cana-1007	4	2	of	of	ADP
cana-1007	4	3	computer	computer	NOUN
cana-1007	4	4	science	science	NOUN
cana-1007	4	5	and	and	CCONJ
cana-1007	4	6	information	information	NOUN
cana-1007	4	7	technology	technology	NOUN
cana-1007	4	8	,	,	PUNCT
cana-1007	4	9	faculty	faculty	NOUN
cana-1007	4	10	of	of	ADP
cana-1007	4	11	computer	computer	NOUN
cana-1007	4	12	science	science	NOUN
cana-1007	4	13	and	and	CCONJ
cana-1007	4	14	information	information	NOUN
cana-1007	4	15	technology	technology	NOUN
cana-1007	4	16	,	,	PUNCT
cana-1007	4	17	university	university	NOUN
cana-1007	4	18	malaya	malaya	PROPN
cana-1007	4	19	,	,	PUNCT
cana-1007	4	20	50603	50603	NUM
cana-1007	4	21	kula	kula	PROPN
cana-1007	4	22	lumbur	lumbur	PROPN
cana-1007	4	23	,	,	PUNCT
cana-1007	4	24	malayia	malayia	PROPN
cana-1007	4	25	.	.	PUNCT
cana-1007	5	1	4department	4department	NUM
cana-1007	5	2	of	of	ADP
cana-1007	5	3	mathematics	mathematics	PROPN
cana-1007	5	4	,	,	PUNCT
cana-1007	5	5	st	st	PROPN
cana-1007	5	6	.	.	PROPN
cana-1007	5	7	joseph	joseph	PROPN
cana-1007	5	8	’s	’s	PART
cana-1007	5	9	college	college	PROPN
cana-1007	5	10	of	of	ADP
cana-1007	5	11	engineering	engineering	PROPN
cana-1007	5	12	,	,	PUNCT
cana-1007	5	13	omr	omr	NOUN
cana-1007	5	14	,	,	PUNCT
cana-1007	5	15	chennai-600119	chennai-600119	PROPN
cana-1007	5	16	,	,	PUNCT
cana-1007	5	17	tamil	tamil	PROPN
cana-1007	5	18	nadu	nadu	PROPN
cana-1007	5	19	,	,	PUNCT
cana-1007	5	20	india	india	PROPN
cana-1007	5	21	.	.	PUNCT
cana-1007	6	1	5department	5department	NUM
cana-1007	6	2	of	of	ADP
cana-1007	6	3	mathematics	mathematic	NOUN
cana-1007	6	4	,	,	PUNCT
cana-1007	6	5	sacred	sacred	ADJ
cana-1007	6	6	heart	heart	NOUN
cana-1007	6	7	college	college	NOUN
cana-1007	6	8	,	,	PUNCT
cana-1007	6	9	tirupattur	tirupattur	VERB
cana-1007	6	10	635	635	NUM
cana-1007	6	11	601	601	NUM
cana-1007	6	12	,	,	PUNCT
cana-1007	6	13	india	india	PROPN
cana-1007	6	14	.	.	PUNCT
cana-1007	7	1	∗corresponding	∗corresponde	VERB
cana-1007	7	2	author	author	NOUN
cana-1007	7	3	:	:	PUNCT
cana-1007	7	4	pulibala70@gmail.com	pulibala70@gmail.com	X
cana-1007	7	5	article	article	NOUN
cana-1007	7	6	history	history	NOUN
cana-1007	7	7	:	:	PUNCT
cana-1007	7	8	received	receive	VERB
cana-1007	7	9	:	:	PUNCT
cana-1007	7	10	20	20	NUM
cana-1007	7	11	-	-	SYM
cana-1007	7	12	05	05	NUM
cana-1007	7	13	-	-	PUNCT
cana-1007	7	14	2024	2024	NUM
cana-1007	7	15	revised	revise	VERB
cana-1007	7	16	:	:	PUNCT
cana-1007	7	17	14	14	NUM
cana-1007	7	18	-	-	SYM
cana-1007	7	19	06	06	NUM
cana-1007	7	20	-	-	PUNCT
cana-1007	7	21	2024	2024	NUM
cana-1007	7	22	accepted	accept	VERB
cana-1007	7	23	:	:	PUNCT
cana-1007	7	24	30	30	NUM
cana-1007	7	25	-	-	SYM
cana-1007	7	26	06	06	NUM
cana-1007	7	27	-	-	PUNCT
cana-1007	7	28	2024	2024	NUM
cana-1007	7	29	abstract	abstract	NOUN
cana-1007	7	30	:	:	PUNCT
cana-1007	7	31	though	though	SCONJ
cana-1007	7	32	the	the	DET
cana-1007	7	33	pandemic	pandemic	NOUN
cana-1007	7	34	has	have	AUX
cana-1007	7	35	created	create	VERB
cana-1007	7	36	many	many	ADJ
cana-1007	7	37	discrepancies	discrepancy	NOUN
cana-1007	7	38	and	and	CCONJ
cana-1007	7	39	cos	cos	NOUN
cana-1007	7	40	-	-	ADJ
cana-1007	7	41	ted	te	VERB
cana-1007	7	42	many	many	ADJ
cana-1007	7	43	lives	life	NOUN
cana-1007	7	44	in	in	ADP
cana-1007	7	45	malaysia	malaysia	PROPN
cana-1007	7	46	,	,	PUNCT
cana-1007	7	47	it	it	PRON
cana-1007	7	48	has	have	AUX
cana-1007	7	49	in	in	ADP
cana-1007	7	50	one	one	NUM
cana-1007	7	51	way	way	NOUN
cana-1007	7	52	cemented	cement	VERB
cana-1007	7	53	the	the	DET
cana-1007	7	54	breached	breach	VERB
cana-1007	7	55	relationships	relationship	NOUN
cana-1007	7	56	,	,	PUNCT
cana-1007	7	57	while	while	SCONJ
cana-1007	7	58	the	the	DET
cana-1007	7	59	rapid	rapid	ADJ
cana-1007	7	60	development	development	NOUN
cana-1007	7	61	of	of	ADP
cana-1007	7	62	science	science	NOUN
cana-1007	7	63	and	and	CCONJ
cana-1007	7	64	technology	technology	NOUN
cana-1007	7	65	met	meet	VERB
cana-1007	7	66	new	new	ADJ
cana-1007	7	67	horizons	horizon	NOUN
cana-1007	7	68	,	,	PUNCT
cana-1007	7	69	humans	human	NOUN
cana-1007	7	70	were	be	AUX
cana-1007	7	71	actually	actually	ADV
cana-1007	7	72	developing	develop	VERB
cana-1007	7	73	an	an	DET
cana-1007	7	74	island	island	NOUN
cana-1007	7	75	of	of	ADP
cana-1007	7	76	a	a	DET
cana-1007	7	77	void	void	NOUN
cana-1007	7	78	.	.	PUNCT
cana-1007	8	1	but	but	CCONJ
cana-1007	8	2	this	this	DET
cana-1007	8	3	pandemic	pandemic	NOUN
cana-1007	8	4	has	have	AUX
cana-1007	8	5	made	make	VERB
cana-1007	8	6	humans	human	NOUN
cana-1007	8	7	stop	stop	VERB
cana-1007	8	8	and	and	CCONJ
cana-1007	8	9	think	think	VERB
cana-1007	8	10	about	about	ADP
cana-1007	8	11	bridging	bridge	VERB
cana-1007	8	12	the	the	DET
cana-1007	8	13	gaps	gap	NOUN
cana-1007	8	14	which	which	PRON
cana-1007	8	15	are	be	AUX
cana-1007	8	16	the	the	DET
cana-1007	8	17	side	side	NOUN
cana-1007	8	18	effects	effect	NOUN
cana-1007	8	19	of	of	ADP
cana-1007	8	20	globalization.the	globalization.the	DET
cana-1007	8	21	new	new	ADJ
cana-1007	8	22	normal	normal	ADJ
cana-1007	8	23	condition	condition	NOUN
cana-1007	8	24	which	which	PRON
cana-1007	8	25	keeps	keep	VERB
cana-1007	8	26	the	the	DET
cana-1007	8	27	most	most	ADV
cana-1007	8	28	civilized	civilized	ADJ
cana-1007	8	29	race	race	NOUN
cana-1007	8	30	indoors	indoor	NOUN
cana-1007	8	31	,	,	PUNCT
cana-1007	8	32	also	also	ADV
cana-1007	8	33	deliberates	deliberate	VERB
cana-1007	8	34	the	the	DET
cana-1007	8	35	necessity	necessity	NOUN
cana-1007	8	36	of	of	ADP
cana-1007	8	37	being	be	AUX
cana-1007	8	38	human	human	ADJ
cana-1007	8	39	and	and	CCONJ
cana-1007	8	40	sharing	share	VERB
cana-1007	8	41	humanity	humanity	NOUN
cana-1007	8	42	.	.	PUNCT
cana-1007	9	1	thanks	thank	NOUN
cana-1007	9	2	to	to	ADP
cana-1007	9	3	the	the	DET
cana-1007	9	4	same	same	ADJ
cana-1007	9	5	scientific	scientific	ADJ
cana-1007	9	6	and	and	CCONJ
cana-1007	9	7	technological	technological	ADJ
cana-1007	9	8	developments	development	NOUN
cana-1007	9	9	a	a	DET
cana-1007	9	10	new	new	ADJ
cana-1007	9	11	return	return	NOUN
cana-1007	9	12	to	to	ADP
cana-1007	9	13	nature	nature	NOUN
cana-1007	9	14	has	have	AUX
cana-1007	9	15	happened	happen	VERB
cana-1007	9	16	,	,	PUNCT
cana-1007	9	17	and	and	CCONJ
cana-1007	9	18	social	social	ADJ
cana-1007	9	19	distancing	distancing	NOUN
cana-1007	9	20	takes	take	VERB
cana-1007	9	21	a	a	DET
cana-1007	9	22	new	new	ADJ
cana-1007	9	23	turn	turn	NOUN
cana-1007	9	24	of	of	ADP
cana-1007	9	25	meeting	meeting	NOUN
cana-1007	9	26	nears	near	VERB
cana-1007	9	27	and	and	CCONJ
cana-1007	9	28	dears	dear	NOUN
cana-1007	9	29	virtually	virtually	ADV
cana-1007	9	30	.	.	PUNCT
cana-1007	10	1	this	this	DET
cana-1007	10	2	work	work	NOUN
cana-1007	10	3	analyzes	analyze	VERB
cana-1007	10	4	the	the	DET
cana-1007	10	5	data	datum	NOUN
cana-1007	10	6	of	of	ADP
cana-1007	10	7	covid-19	covid-19	PROPN
cana-1007	10	8	affected	affect	VERB
cana-1007	10	9	people	people	NOUN
cana-1007	10	10	in	in	ADP
cana-1007	10	11	a	a	DET
cana-1007	10	12	particular	particular	ADJ
cana-1007	10	13	place	place	NOUN
cana-1007	10	14	through	through	ADP
cana-1007	10	15	graph	graph	NOUN
cana-1007	10	16	labeling	labeling	NOUN
cana-1007	10	17	that	that	PRON
cana-1007	10	18	labels	label	VERB
cana-1007	10	19	the	the	DET
cana-1007	10	20	vertices	vertex	NOUN
cana-1007	10	21	with	with	ADP
cana-1007	10	22	edges	edge	NOUN
cana-1007	10	23	via	via	ADP
cana-1007	10	24	satl	satl	NOUN
cana-1007	10	25	graph	graph	NOUN
cana-1007	10	26	labeling	labeling	NOUN
cana-1007	10	27	techniques	technique	NOUN
cana-1007	10	28	.	.	PUNCT
cana-1007	11	1	such	such	ADJ
cana-1007	11	2	labeling	labeling	NOUN
cana-1007	11	3	supports	support	VERB
cana-1007	11	4	the	the	DET
cana-1007	11	5	search	search	NOUN
cana-1007	11	6	of	of	ADP
cana-1007	11	7	how	how	SCONJ
cana-1007	11	8	many	many	ADJ
cana-1007	11	9	neighbours	neighbour	NOUN
cana-1007	11	10	are	be	AUX
cana-1007	11	11	affected	affect	VERB
cana-1007	11	12	covid-19	covid-19	PROPN
cana-1007	11	13	in	in	ADP
cana-1007	11	14	priority	priority	NOUN
cana-1007	11	15	order	order	NOUN
cana-1007	11	16	.	.	PUNCT
cana-1007	12	1	keywords	keyword	NOUN
cana-1007	12	2	:	:	PUNCT
cana-1007	12	3	star	star	NOUN
cana-1007	12	4	graph	graph	NOUN
cana-1007	12	5	;	;	PUNCT
cana-1007	12	6	satl	satl	NOUN
cana-1007	12	7	graph	graph	NOUN
cana-1007	12	8	;	;	PUNCT
cana-1007	12	9	covid-19	covid-19	PROPN
cana-1007	12	10	;	;	PUNCT
cana-1007	12	11	graph	graph	NOUN
cana-1007	12	12	labeling	labeling	NOUN
cana-1007	12	13	.	.	PUNCT
cana-1007	13	1	1	1	X
cana-1007	13	2	.	.	X
cana-1007	13	3	introduction	introduction	NOUN
cana-1007	13	4	the	the	DET
cana-1007	13	5	people	people	NOUN
cana-1007	13	6	who	who	PRON
cana-1007	13	7	are	be	AUX
cana-1007	13	8	affected	affect	VERB
cana-1007	13	9	covid-19	covid-19	PROPN
cana-1007	13	10	virus	virus	NOUN
cana-1007	13	11	in	in	ADP
cana-1007	13	12	malaysia	malaysia	PROPN
cana-1007	13	13	were	be	AUX
cana-1007	13	14	isolated	isolate	VERB
cana-1007	13	15	due	due	ADP
cana-1007	13	16	to	to	ADP
cana-1007	13	17	awareness	awareness	NOUN
cana-1007	13	18	of	of	ADP
cana-1007	13	19	the	the	DET
cana-1007	13	20	virus	virus	NOUN
cana-1007	13	21	which	which	PRON
cana-1007	13	22	cause	cause	VERB
cana-1007	13	23	public	public	ADJ
cana-1007	13	24	to	to	PART
cana-1007	13	25	be	be	AUX
cana-1007	13	26	more	more	ADV
cana-1007	13	27	vigilant	vigilant	ADJ
cana-1007	13	28	.	.	PUNCT
cana-1007	14	1	the	the	DET
cana-1007	14	2	motivation	motivation	NOUN
cana-1007	14	3	of	of	ADP
cana-1007	14	4	this	this	DET
cana-1007	14	5	research	research	NOUN
cana-1007	14	6	is	be	AUX
cana-1007	14	7	to	to	PART
cana-1007	14	8	improve	improve	VERB
cana-1007	14	9	the	the	DET
cana-1007	14	10	efforts	effort	NOUN
cana-1007	14	11	of	of	ADP
cana-1007	14	12	tracking	tracking	NOUN
cana-1007	14	13	method	method	NOUN
cana-1007	14	14	for	for	ADP
cana-1007	14	15	the	the	DET
cana-1007	14	16	public	public	NOUN
cana-1007	14	17	who	who	PRON
cana-1007	14	18	affected	affect	VERB
cana-1007	14	19	covid-19	covid-19	PROPN
cana-1007	14	20	by	by	ADP
cana-1007	14	21	own	own	ADJ
cana-1007	14	22	prediction	prediction	NOUN
cana-1007	14	23	,	,	PUNCT
cana-1007	14	24	own	own	ADJ
cana-1007	14	25	suspect	suspect	NOUN
cana-1007	14	26	to	to	ADP
cana-1007	14	27	contracting	contract	VERB
cana-1007	14	28	the	the	DET
cana-1007	14	29	viruses	virus	NOUN
cana-1007	14	30	.	.	PUNCT
cana-1007	15	1	this	this	DET
cana-1007	15	2	study	study	NOUN
cana-1007	15	3	was	be	AUX
cana-1007	15	4	made	make	VERB
cana-1007	15	5	assuming	assume	VERB
cana-1007	15	6	the	the	DET
cana-1007	15	7	necessity	necessity	NOUN
cana-1007	15	8	of	of	ADP
cana-1007	15	9	finding	find	VERB
cana-1007	15	10	the	the	DET
cana-1007	15	11	direct	direct	ADJ
cana-1007	15	12	contact	contact	NOUN
cana-1007	15	13	tracking	tracking	NOUN
cana-1007	15	14	using	use	VERB
cana-1007	15	15	graph	graph	NOUN
cana-1007	15	16	labeling	labeling	NOUN
cana-1007	15	17	in	in	ADP
cana-1007	15	18	positive	positive	ADJ
cana-1007	15	19	covid-19	covid-19	PROPN
cana-1007	15	20	patients	patient	NOUN
cana-1007	15	21	.	.	PUNCT
cana-1007	16	1	an	an	DET
cana-1007	16	2	undirected	undirected	ADJ
cana-1007	16	3	graph	graph	NOUN
cana-1007	16	4	g	g	PROPN
cana-1007	16	5	be	be	AUX
cana-1007	16	6	a	a	DET
cana-1007	16	7	finite	finite	NOUN
cana-1007	16	8	and	and	CCONJ
cana-1007	16	9	simple	simple	ADJ
cana-1007	16	10	with	with	ADP
cana-1007	16	11	d	d	PROPN
cana-1007	16	12	vertices	vertex	NOUN
cana-1007	16	13	,	,	PUNCT
cana-1007	16	14	l	l	NOUN
cana-1007	16	15	edges	edge	NOUN
cana-1007	16	16	but	but	CCONJ
cana-1007	16	17	no	no	DET
cana-1007	16	18	multiple	multiple	ADJ
cana-1007	16	19	graphs	graph	NOUN
cana-1007	16	20	and	and	CCONJ
cana-1007	16	21	h	h	NOUN
cana-1007	16	22	be	be	AUX
cana-1007	16	23	a	a	DET
cana-1007	16	24	subgraph	subgraph	NOUN
cana-1007	16	25	of	of	ADP
cana-1007	16	26	an	an	DET
cana-1007	16	27	undirected	undirected	ADJ
cana-1007	16	28	graph	graph	NOUN
cana-1007	16	29	g.	g.	NOUN
cana-1007	16	30	definitions	definition	NOUN
cana-1007	16	31	and	and	CCONJ
cana-1007	16	32	terminology	terminology	NOUN
cana-1007	16	33	not	not	PART
cana-1007	16	34	mentioned	mention	VERB
cana-1007	16	35	here	here	ADV
cana-1007	16	36	but	but	CCONJ
cana-1007	16	37	may	may	AUX
cana-1007	16	38	be	be	AUX
cana-1007	16	39	refered	refer	VERB
cana-1007	16	40	to	to	ADP
cana-1007	16	41	d.b	d.b	PROPN
cana-1007	16	42	.	.	PROPN
cana-1007	16	43	west	west	NOUN
cana-1007	17	1	[	[	X
cana-1007	17	2	7	7	NUM
cana-1007	17	3	]	]	PUNCT
cana-1007	17	4	.	.	PUNCT
cana-1007	18	1	the	the	DET
cana-1007	18	2	basic	basic	ADJ
cana-1007	18	3	theory	theory	NOUN
cana-1007	18	4	of	of	ADP
cana-1007	18	5	graph	graph	NOUN
cana-1007	18	6	labeling	labeling	NOUN
cana-1007	18	7	is	be	AUX
cana-1007	18	8	initiated	initiate	VERB
cana-1007	18	9	in	in	ADP
cana-1007	18	10	[	[	X
cana-1007	18	11	3	3	NUM
cana-1007	18	12	]	]	PUNCT
cana-1007	18	13	,	,	PUNCT
cana-1007	18	14	of	of	ADP
cana-1007	18	15	one	one	NUM
cana-1007	18	16	given	give	VERB
cana-1007	18	17	by	by	ADP
cana-1007	18	18	[	[	X
cana-1007	18	19	4	4	X
cana-1007	18	20	]	]	PUNCT
cana-1007	18	21	in	in	ADP
cana-1007	18	22	1967	1967	NUM
cana-1007	18	23	.	.	PUNCT
cana-1007	19	1	for	for	ADP
cana-1007	19	2	smooth	smooth	ADJ
cana-1007	19	3	gathering	gathering	NOUN
cana-1007	19	4	of	of	ADP
cana-1007	19	5	results	result	NOUN
cana-1007	19	6	on	on	ADP
cana-1007	19	7	labeling	label	VERB
cana-1007	19	8	the	the	DET
cana-1007	19	9	authors	author	NOUN
cana-1007	19	10	refereed	refereed	VERB
cana-1007	19	11	to	to	ADP
cana-1007	19	12	[	[	X
cana-1007	19	13	9	9	NUM
cana-1007	19	14	]	]	PUNCT
cana-1007	19	15	and	and	CCONJ
cana-1007	19	16	[	[	X
cana-1007	19	17	10	10	NUM
cana-1007	19	18	]	]	PUNCT
cana-1007	19	19	and	and	CCONJ
cana-1007	19	20	survey	survey	NOUN
cana-1007	19	21	on	on	ADP
cana-1007	19	22	graph	graph	NOUN
cana-1007	19	23	labeling	labeling	NOUN
cana-1007	19	24	by	by	ADP
cana-1007	19	25	j.a	j.a	PROPN
cana-1007	19	26	gallian	gallian	PROPN
cana-1007	19	27	[	[	X
cana-1007	19	28	8	8	NUM
cana-1007	19	29	]	]	PUNCT
cana-1007	19	30	.	.	PUNCT
cana-1007	20	1	communications	communication	NOUN
cana-1007	20	2	on	on	ADP
cana-1007	20	3	applied	apply	VERB
cana-1007	20	4	nonlinear	nonlinear	ADJ
cana-1007	20	5	analysis	analysis	NOUN
cana-1007	20	6	issn	issn	NOUN
cana-1007	20	7	:	:	PUNCT
cana-1007	20	8	1074	1074	NUM
cana-1007	20	9	-	-	PUNCT
cana-1007	20	10	133x	133x	NUM
cana-1007	20	11	vol	vol	NOUN
cana-1007	20	12	31	31	NUM
cana-1007	20	13	no	no	NOUN
cana-1007	20	14	.	.	PUNCT
cana-1007	21	1	5s	5s	NUM
cana-1007	21	2	(	(	PUNCT
cana-1007	21	3	2024	2024	NUM
cana-1007	21	4	)	)	PUNCT
cana-1007	21	5	130	130	NUM
cana-1007	21	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1007	21	7	satl	satl	NOUN
cana-1007	21	8	label	label	NOUN
cana-1007	21	9	of	of	ADP
cana-1007	21	10	a	a	DET
cana-1007	21	11	graphical	graphical	ADJ
cana-1007	21	12	representation	representation	NOUN
cana-1007	21	13	g	g	NOUN
cana-1007	21	14	,	,	PUNCT
cana-1007	21	15	d	d	NOUN
cana-1007	21	16	dots	dot	NOUN
cana-1007	21	17	and	and	CCONJ
cana-1007	21	18	l	l	NOUN
cana-1007	21	19	lines	line	NOUN
cana-1007	21	20	is	be	AUX
cana-1007	21	21	a	a	DET
cana-1007	21	22	one	one	NUM
cana-1007	21	23	to	to	ADP
cana-1007	21	24	one	one	NUM
cana-1007	21	25	correspondence	correspondence	NOUN
cana-1007	21	26	to	to	ADP
cana-1007	21	27	the	the	DET
cana-1007	21	28	domain	domain	NOUN
cana-1007	21	29	set	set	NOUN
cana-1007	21	30	of	of	ADP
cana-1007	21	31	lines	line	NOUN
cana-1007	21	32	to	to	ADP
cana-1007	21	33	the	the	DET
cana-1007	21	34	codomain	codomain	ADJ
cana-1007	21	35	set	set	NOUN
cana-1007	21	36	of	of	ADP
cana-1007	21	37	numbers	number	NOUN
cana-1007	21	38	1,2,3,	1,2,3,	NUM
cana-1007	21	39	...	...	PUNCT
cana-1007	21	40	,l	,l	PUNCT
cana-1007	21	41	with	with	ADP
cana-1007	21	42	the	the	DET
cana-1007	21	43	pair	pair	NOUN
cana-1007	21	44	(	(	PUNCT
cana-1007	21	45	a	a	DET
cana-1007	21	46	,	,	PUNCT
cana-1007	21	47	b	b	NOUN
cana-1007	21	48	)	)	PUNCT
cana-1007	21	49	.	.	PUNCT
cana-1007	22	1	suppose	suppose	VERB
cana-1007	22	2	g	g	PROPN
cana-1007	22	3	antimagic	antimagic	ADJ
cana-1007	22	4	total	total	ADJ
cana-1007	22	5	labeling	labeling	NOUN
cana-1007	22	6	.	.	PUNCT
cana-1007	23	1	delman	delman	NOUN
cana-1007	23	2	and	and	CCONJ
cana-1007	23	3	koilraj	koilraj	X
cana-1007	23	4	[	[	X
cana-1007	23	5	5	5	NUM
cana-1007	23	6	]	]	PUNCT
cana-1007	23	7	defined	define	VERB
cana-1007	23	8	an	an	DET
cana-1007	23	9	satl	satl	NOUN
cana-1007	23	10	which	which	PRON
cana-1007	23	11	is	be	AUX
cana-1007	23	12	a	a	DET
cana-1007	23	13	generalization	generalization	NOUN
cana-1007	23	14	of	of	ADP
cana-1007	23	15	javid	javid	PROPN
cana-1007	23	16	’s	’s	X
cana-1007	23	17	of	of	ADP
cana-1007	23	18	generalized	generalized	ADJ
cana-1007	23	19	extended	extended	ADJ
cana-1007	23	20	wtrees	wtree	NOUN
cana-1007	24	1	[	[	X
cana-1007	24	2	11	11	NUM
cana-1007	24	3	]	]	PUNCT
cana-1007	24	4	and	and	CCONJ
cana-1007	24	5	deriving	derive	VERB
cana-1007	24	6	the	the	DET
cana-1007	24	7	existence	existence	NOUN
cana-1007	24	8	of	of	ADP
cana-1007	24	9	a	a	DET
cana-1007	24	10	satl	satl	NOUN
cana-1007	24	11	on	on	ADP
cana-1007	24	12	them	they	PRON
cana-1007	24	13	for	for	ADP
cana-1007	24	14	𝑒𝜖[0,1,2	𝑒𝜖[0,1,2	NOUN
cana-1007	24	15	]	]	PUNCT
cana-1007	24	16	and	and	CCONJ
cana-1007	24	17	the	the	DET
cana-1007	24	18	study	study	NOUN
cana-1007	24	19	of	of	ADP
cana-1007	24	20	vertex	vertex	NOUN
cana-1007	24	21	labeling	labeling	NOUN
cana-1007	24	22	of	of	ADP
cana-1007	24	23	a	a	DET
cana-1007	24	24	graph	graph	NOUN
cana-1007	24	25	g	g	NOUN
cana-1007	24	26	for	for	ADP
cana-1007	24	27	the	the	DET
cana-1007	24	28	edge	edge	NOUN
cana-1007	24	29	weight	weight	NOUN
cana-1007	24	30	of	of	ADP
cana-1007	24	31	𝑥𝑦	𝑥𝑦	NOUN
cana-1007	24	32	∈	∈	PROPN
cana-1007	24	33	𝐷(𝐺	𝐷(𝐺	NOUN
cana-1007	24	34	)	)	PUNCT
cana-1007	24	35	is	be	AUX
cana-1007	24	36	defined	define	VERB
cana-1007	24	37	as	as	ADP
cana-1007	24	38	w(xy)=g(x)+g(y	w(xy)=g(x)+g(y	NOUN
cana-1007	24	39	)	)	PUNCT
cana-1007	24	40	and	and	CCONJ
cana-1007	24	41	the	the	DET
cana-1007	24	42	total	total	ADJ
cana-1007	24	43	labeling	labeling	NOUN
cana-1007	24	44	for	for	ADP
cana-1007	24	45	the	the	DET
cana-1007	24	46	edge	edge	NOUN
cana-1007	24	47	weight	weight	NOUN
cana-1007	24	48	of	of	ADP
cana-1007	24	49	𝑥𝑦	𝑥𝑦	NOUN
cana-1007	24	50	∈	∈	PROPN
cana-1007	24	51	𝐷(𝐺	𝐷(𝐺	NOUN
cana-1007	24	52	)	)	PUNCT
cana-1007	24	53	is	be	AUX
cana-1007	24	54	defined	define	VERB
cana-1007	24	55	as	as	ADP
cana-1007	24	56	f(ab)=f(a)+f(b)+g(ab	f(ab)=f(a)+f(b)+g(ab	NOUN
cana-1007	24	57	)	)	PUNCT
cana-1007	24	58	have	have	AUX
cana-1007	24	59	been	be	AUX
cana-1007	24	60	proved	prove	VERB
cana-1007	24	61	by	by	ADP
cana-1007	24	62	[	[	X
cana-1007	24	63	6	6	NUM
cana-1007	24	64	]	]	PUNCT
cana-1007	24	65	.	.	PUNCT
cana-1007	25	1	moreover	moreover	ADV
cana-1007	25	2	the	the	DET
cana-1007	25	3	affected	affected	ADJ
cana-1007	25	4	patients	patient	NOUN
cana-1007	25	5	are	be	AUX
cana-1007	25	6	not	not	PART
cana-1007	25	7	published	publish	VERB
cana-1007	25	8	to	to	ADP
cana-1007	25	9	the	the	DET
cana-1007	25	10	society	society	NOUN
cana-1007	25	11	and	and	CCONJ
cana-1007	25	12	hence	hence	ADV
cana-1007	25	13	it	it	PRON
cana-1007	25	14	prevents	prevent	VERB
cana-1007	25	15	the	the	DET
cana-1007	25	16	safety	safety	NOUN
cana-1007	25	17	motivation	motivation	NOUN
cana-1007	25	18	with	with	ADP
cana-1007	25	19	the	the	DET
cana-1007	25	20	medical	medical	ADJ
cana-1007	25	21	systems	system	NOUN
cana-1007	25	22	and	and	CCONJ
cana-1007	25	23	provisions	provision	NOUN
cana-1007	25	24	[	[	X
cana-1007	25	25	13	13	NUM
cana-1007	25	26	]	]	PUNCT
cana-1007	25	27	.	.	PUNCT
cana-1007	26	1	the	the	DET
cana-1007	26	2	covid-19	covid-19	PROPN
cana-1007	26	3	predicted	predict	VERB
cana-1007	26	4	people	people	NOUN
cana-1007	26	5	are	be	AUX
cana-1007	26	6	listed	list	VERB
cana-1007	26	7	sequential	sequential	ADJ
cana-1007	26	8	order	order	NOUN
cana-1007	26	9	in	in	ADP
cana-1007	26	10	a	a	DET
cana-1007	26	11	time	time	NOUN
cana-1007	26	12	series	series	NOUN
cana-1007	26	13	data	datum	NOUN
cana-1007	26	14	is	be	AUX
cana-1007	26	15	referred	refer	VERB
cana-1007	26	16	in	in	ADP
cana-1007	26	17	[	[	X
cana-1007	26	18	14	14	NUM
cana-1007	26	19	]	]	PUNCT
cana-1007	26	20	.	.	PUNCT
cana-1007	27	1	in	in	ADP
cana-1007	27	2	[	[	X
cana-1007	27	3	1	1	X
cana-1007	27	4	]	]	PUNCT
cana-1007	27	5	they	they	PRON
cana-1007	27	6	proved	prove	VERB
cana-1007	27	7	that	that	SCONJ
cana-1007	27	8	friendhip	friendhip	NOUN
cana-1007	27	9	graph	graph	NOUN
cana-1007	27	10	contained	contain	VERB
cana-1007	27	11	in	in	ADP
cana-1007	27	12	(	(	PUNCT
cana-1007	27	13	a,1	a,1	NOUN
cana-1007	27	14	)	)	PUNCT
cana-1007	27	15	satl	satl	NOUN
cana-1007	27	16	⇔	⇔	NOUN
cana-1007	27	17	for	for	ADP
cana-1007	27	18	number	number	NOUN
cana-1007	27	19	of	of	ADP
cana-1007	27	20	vertices	vertex	NOUN
cana-1007	27	21	is	be	AUX
cana-1007	27	22	1,3,5	1,3,5	NUM
cana-1007	27	23	,	,	PUNCT
cana-1007	27	24	...	...	PUNCT
cana-1007	27	25	,	,	PUNCT
cana-1007	27	26	also	also	ADV
cana-1007	27	27	they	they	PRON
cana-1007	27	28	proved	prove	VERB
cana-1007	27	29	that	that	SCONJ
cana-1007	27	30	friendship	friendship	NOUN
cana-1007	27	31	graph	graph	NOUN
cana-1007	27	32	contains	contain	VERB
cana-1007	27	33	no	no	DET
cana-1007	27	34	(	(	PUNCT
cana-1007	27	35	a,2	a,2	NOUN
cana-1007	27	36	)	)	PUNCT
cana-1007	27	37	satl	satl	NOUN
cana-1007	27	38	when	when	SCONJ
cana-1007	27	39	n	n	X
cana-1007	27	40	is	be	AUX
cana-1007	27	41	even	even	ADV
cana-1007	27	42	and	and	CCONJ
cana-1007	27	43	𝑛	𝑛	PRON
cana-1007	27	44	≅	≅	NUM
cana-1007	27	45	4	4	NUM
cana-1007	27	46	𝑚𝑜𝑑	𝑚𝑜𝑑	NOUN
cana-1007	27	47	12	12	NUM
cana-1007	27	48	.	.	PUNCT
cana-1007	27	49	satl	satl	NOUN
cana-1007	27	50	of	of	ADP
cana-1007	27	51	covering	covering	NOUN
cana-1007	27	52	of	of	ADP
cana-1007	27	53	a	a	DET
cana-1007	27	54	graph	graph	NOUN
cana-1007	27	55	g	g	NOUN
cana-1007	27	56	is	be	AUX
cana-1007	27	57	a	a	DET
cana-1007	27	58	bijection	bijection	ADJ
cana-1007	27	59	function	function	NOUN
cana-1007	27	60	𝑔	𝑔	NOUN
cana-1007	27	61	:	:	PUNCT
cana-1007	27	62	𝐷(𝐺	𝐷(𝐺	NOUN
cana-1007	27	63	)	)	PUNCT
cana-1007	27	64	∪	∪	ADP
cana-1007	27	65	𝐿(𝐺	𝐿(𝐺	PROPN
cana-1007	27	66	)	)	PUNCT
cana-1007	27	67	}	}	PUNCT
cana-1007	27	68	→	→	SYM
cana-1007	27	69	{	{	PUNCT
cana-1007	27	70	1	1	NUM
cana-1007	27	71	,	,	PUNCT
cana-1007	27	72	2	2	NUM
cana-1007	27	73	,	,	PUNCT
cana-1007	27	74	3	3	NUM
cana-1007	27	75	,	,	PUNCT
cana-1007	27	76	⋯	⋯	NOUN
cana-1007	27	77	,	,	PUNCT
cana-1007	27	78	|𝐷(𝐺	|𝐷(𝐺	PROPN
cana-1007	27	79	)	)	PUNCT
cana-1007	28	1	+	+	PUNCT
cana-1007	28	2	𝐿(𝐺)|	𝐿(𝐺)|	PROPN
cana-1007	28	3	}	}	PUNCT
cana-1007	28	4	such	such	ADJ
cana-1007	28	5	that	that	SCONJ
cana-1007	28	6	for	for	ADP
cana-1007	28	7	all	all	DET
cana-1007	28	8	subgraphs	subgraph	NOUN
cana-1007	28	9	ℎ′	ℎ′	ADJ
cana-1007	28	10	of	of	ADP
cana-1007	28	11	g	g	PROPN
cana-1007	28	12	isomorphic	isomorphic	ADJ
cana-1007	28	13	h	h	NOUN
cana-1007	28	14	then	then	ADV
cana-1007	28	15	ℎ′	ℎ′	VERB
cana-1007	28	16	weights	weight	NOUN
cana-1007	28	17	𝑤𝑡(ℎ′	𝑤𝑡(ℎ′	PRON
cana-1007	28	18	)	)	PUNCT
cana-1007	28	19	=	=	SYM
cana-1007	28	20	∑𝑑𝜖𝐷(ℎ′	∑𝑑𝜖𝐷(ℎ′	PROPN
cana-1007	28	21	)	)	PUNCT
cana-1007	28	22	𝑔(𝑑	𝑔(𝑑	PROPN
cana-1007	28	23	)	)	PUNCT
cana-1007	29	1	+	+	CCONJ
cana-1007	30	1	∑𝑒𝜖𝐿(ℎ′	∑𝑒𝜖𝐿(ℎ′	PROPN
cana-1007	30	2	)	)	PUNCT
cana-1007	30	3	𝑔(𝑙	𝑔(𝑙	PROPN
cana-1007	30	4	)	)	PUNCT
cana-1007	30	5	form	form	NOUN
cana-1007	30	6	an	an	DET
cana-1007	30	7	a.p	a.p	PROPN
cana-1007	30	8	𝑏	𝑏	PROPN
cana-1007	30	9	,	,	PUNCT
cana-1007	30	10	𝑏	𝑏	PROPN
cana-1007	30	11	+	+	SYM
cana-1007	30	12	𝑒	𝑒	PROPN
cana-1007	30	13	,	,	PUNCT
cana-1007	30	14	𝑏	𝑏	NOUN
cana-1007	30	15	+	+	NOUN
cana-1007	30	16	2𝑒	2𝑒	NUM
cana-1007	30	17	,	,	PUNCT
cana-1007	30	18	.	.	PUNCT
cana-1007	30	19	.	.	PUNCT
cana-1007	31	1	.	.	PUNCT
cana-1007	32	1	,	,	PUNCT
cana-1007	32	2	𝑏	𝑏	PROPN
cana-1007	32	3	+	+	X
cana-1007	32	4	(	(	PUNCT
cana-1007	32	5	𝑚	𝑚	PROPN
cana-1007	32	6	−	−	PROPN
cana-1007	32	7	1)𝑒	1)𝑒	NOUN
cana-1007	32	8	,	,	PUNCT
cana-1007	32	9	where	where	SCONJ
cana-1007	32	10	𝑏	𝑏	PROPN
cana-1007	32	11	≥	≥	NOUN
cana-1007	32	12	0	0	NUM
cana-1007	32	13	and	and	CCONJ
cana-1007	32	14	𝑒	𝑒	PROPN
cana-1007	32	15	≥	≥	NUM
cana-1007	32	16	0	0	NUM
cana-1007	32	17	are	be	AUX
cana-1007	32	18	two	two	NUM
cana-1007	32	19	fixed	fix	VERB
cana-1007	32	20	integers	integer	NOUN
cana-1007	32	21	.	.	PUNCT
cana-1007	33	1	the	the	DET
cana-1007	33	2	labeling	labeling	NOUN
cana-1007	33	3	is	be	AUX
cana-1007	33	4	called	call	VERB
cana-1007	33	5	a	a	DET
cana-1007	33	6	satl	satl	NOUN
cana-1007	33	7	if	if	SCONJ
cana-1007	33	8	𝑔(𝐷(𝐺	𝑔(𝐷(𝐺	NOUN
cana-1007	33	9	)	)	PUNCT
cana-1007	33	10	)	)	PUNCT
cana-1007	34	1	=	=	PUNCT
cana-1007	34	2	1,2,3	1,2,3	NUM
cana-1007	34	3	,	,	PUNCT
cana-1007	34	4	.	.	PUNCT
cana-1007	34	5	.	.	PUNCT
cana-1007	34	6	.	.	PUNCT
cana-1007	35	1	,	,	PUNCT
cana-1007	35	2	|𝐷(𝐺)|	|𝐷(𝐺)|	X
cana-1007	35	3	.	.	PUNCT
cana-1007	35	4	by	by	ADP
cana-1007	35	5	referring	refer	VERB
cana-1007	35	6	the	the	DET
cana-1007	35	7	articles	article	NOUN
cana-1007	35	8	[	[	X
cana-1007	35	9	2	2	NUM
cana-1007	35	10	]	]	PUNCT
cana-1007	35	11	,	,	PUNCT
cana-1007	35	12	they	they	PRON
cana-1007	35	13	mentioned	mention	VERB
cana-1007	35	14	a	a	DET
cana-1007	35	15	problem	problem	NOUN
cana-1007	35	16	,	,	PUNCT
cana-1007	35	17	for	for	ADP
cana-1007	35	18	each	each	DET
cana-1007	35	19	e	e	NOUN
cana-1007	35	20	,	,	PUNCT
cana-1007	35	21	4	4	NUM
cana-1007	35	22	≤	≤	NUM
cana-1007	35	23	𝑒	𝑒	PROPN
cana-1007	35	24	≤	≤	NOUN
cana-1007	35	25	𝑑	𝑑	PROPN
cana-1007	35	26	+	+	PROPN
cana-1007	35	27	𝑙	𝑙	X
cana-1007	35	28	+	+	NUM
cana-1007	35	29	2	2	NUM
cana-1007	35	30	,	,	PUNCT
cana-1007	35	31	either	either	CCONJ
cana-1007	35	32	prove	prove	VERB
cana-1007	35	33	the	the	DET
cana-1007	35	34	satl	satl	NOUN
cana-1007	35	35	of	of	ADP
cana-1007	35	36	the	the	DET
cana-1007	35	37	graph	graph	NOUN
cana-1007	35	38	𝐺𝑥(𝑆𝑚	𝐺𝑥(𝑆𝑚	PROPN
cana-1007	35	39	)	)	PUNCT
cana-1007	35	40	,	,	PUNCT
cana-1007	35	41	𝑚	𝑚	X
cana-1007	35	42	≥	≥	NUM
cana-1007	35	43	3	3	NUM
cana-1007	35	44	,	,	PUNCT
cana-1007	35	45	here	here	ADV
cana-1007	35	46	star	star	NOUN
cana-1007	35	47	graph	graph	NOUN
cana-1007	35	48	is	be	AUX
cana-1007	35	49	a	a	DET
cana-1007	35	50	complete	complete	ADJ
cana-1007	35	51	bipartite	bipartite	NOUN
cana-1007	35	52	graph	graph	NOUN
cana-1007	35	53	denoted	denote	VERB
cana-1007	35	54	by	by	ADP
cana-1007	35	55	𝑆𝑚.	𝑆𝑚.	PROPN
cana-1007	35	56	by	by	ADP
cana-1007	35	57	inspiring	inspire	VERB
cana-1007	35	58	of	of	ADP
cana-1007	35	59	the	the	DET
cana-1007	35	60	problem	problem	NOUN
cana-1007	35	61	,	,	PUNCT
cana-1007	35	62	here	here	ADV
cana-1007	35	63	we	we	PRON
cana-1007	35	64	try	try	VERB
cana-1007	35	65	to	to	PART
cana-1007	35	66	prove	prove	VERB
cana-1007	35	67	the	the	DET
cana-1007	35	68	existence	existence	NOUN
cana-1007	35	69	of	of	ADP
cana-1007	35	70	satl	satl	NOUN
cana-1007	35	71	of	of	ADP
cana-1007	35	72	𝐺𝑥(𝑆3	𝐺𝑥(𝑆3	PROPN
cana-1007	35	73	)	)	PUNCT
cana-1007	35	74	,	,	PUNCT
cana-1007	35	75	𝐺𝑥(𝑆4	𝐺𝑥(𝑆4	NOUN
cana-1007	35	76	)	)	PUNCT
cana-1007	35	77	,	,	PUNCT
cana-1007	35	78	𝐺𝑥(𝑆5	𝐺𝑥(𝑆5	PUNCT
cana-1007	35	79	)	)	PUNCT
cana-1007	35	80	and	and	CCONJ
cana-1007	35	81	𝐺𝑥(𝑆𝑚	𝐺𝑥(𝑆𝑚	NUM
cana-1007	35	82	)	)	PUNCT
cana-1007	35	83	graphs	graph	NOUN
cana-1007	35	84	given	give	VERB
cana-1007	35	85	as	as	ADP
cana-1007	35	86	a	a	DET
cana-1007	35	87	open	open	ADJ
cana-1007	35	88	problem	problem	NOUN
cana-1007	35	89	10	10	NUM
cana-1007	35	90	in	in	ADP
cana-1007	35	91	[	[	X
cana-1007	35	92	2	2	NUM
cana-1007	35	93	]	]	PUNCT
cana-1007	35	94	.	.	PUNCT
cana-1007	36	1	figure	figure	NOUN
cana-1007	36	2	1	1	NUM
cana-1007	36	3	:	:	PUNCT
cana-1007	36	4	super	super	ADJ
cana-1007	36	5	(	(	PUNCT
cana-1007	36	6	50,5	50,5	NOUN
cana-1007	36	7	)	)	PUNCT
cana-1007	36	8	−	−	PROPN
cana-1007	36	9	𝐶4	𝐶4	ADJ
cana-1007	36	10	-	-	PUNCT
cana-1007	36	11	antimagic	antimagic	ADJ
cana-1007	36	12	total	total	ADJ
cana-1007	36	13	labeling	labeling	NOUN
cana-1007	36	14	2	2	NUM
cana-1007	36	15	.	.	X
cana-1007	36	16	main	main	ADJ
cana-1007	36	17	results	result	NOUN
cana-1007	36	18	the	the	DET
cana-1007	36	19	labeling	labeling	NOUN
cana-1007	36	20	satl	satl	NOUN
cana-1007	36	21	of	of	ADP
cana-1007	36	22	hgraph	hgraph	NOUN
cana-1007	36	23	is	be	AUX
cana-1007	36	24	stands	stand	VERB
cana-1007	36	25	for	for	ADP
cana-1007	36	26	the	the	DET
cana-1007	36	27	label	label	NOUN
cana-1007	36	28	super	super	ADJ
cana-1007	36	29	(	(	PUNCT
cana-1007	36	30	b	b	NOUN
cana-1007	36	31	,	,	PUNCT
cana-1007	36	32	e)-h	e)-h	ADJ
cana-1007	36	33	-	-	PUNCT
cana-1007	36	34	satl	satl	NOUN
cana-1007	36	35	diagram	diagram	NOUN
cana-1007	36	36	is	be	AUX
cana-1007	36	37	a	a	DET
cana-1007	36	38	finite	finite	ADJ
cana-1007	36	39	graph	graph	NOUN
cana-1007	36	40	and	and	CCONJ
cana-1007	36	41	h	h	NOUN
cana-1007	36	42	subset	subset	NOUN
cana-1007	36	43	of	of	ADP
cana-1007	36	44	a	a	DET
cana-1007	36	45	representation	representation	NOUN
cana-1007	36	46	in	in	ADP
cana-1007	36	47	x	x	PROPN
cana-1007	36	48	dots	dot	NOUN
cana-1007	36	49	and	and	CCONJ
cana-1007	36	50	y	y	PROPN
cana-1007	36	51	lines	line	NOUN
cana-1007	36	52	is	be	AUX
cana-1007	36	53	an	an	DET
cana-1007	36	54	mapping	mapping	NOUN
cana-1007	36	55	𝑔	𝑔	NOUN
cana-1007	36	56	:	:	PUNCT
cana-1007	36	57	𝐷(𝐺	𝐷(𝐺	NOUN
cana-1007	36	58	)	)	PUNCT
cana-1007	36	59	∪	∪	ADP
cana-1007	36	60	𝐿(𝐺	𝐿(𝐺	PROPN
cana-1007	36	61	)	)	PUNCT
cana-1007	36	62	}	}	PUNCT
cana-1007	37	1	→	→	SYM
cana-1007	37	2	communications	communication	NOUN
cana-1007	37	3	on	on	ADP
cana-1007	37	4	applied	apply	VERB
cana-1007	37	5	nonlinear	nonlinear	ADJ
cana-1007	37	6	analysis	analysis	NOUN
cana-1007	37	7	issn	issn	NOUN
cana-1007	37	8	:	:	PUNCT
cana-1007	37	9	1074	1074	NUM
cana-1007	37	10	-	-	PUNCT
cana-1007	37	11	133x	133x	NUM
cana-1007	37	12	vol	vol	NOUN
cana-1007	37	13	31	31	NUM
cana-1007	37	14	no	no	NOUN
cana-1007	37	15	.	.	PUNCT
cana-1007	38	1	5s	5s	NUM
cana-1007	38	2	(	(	PUNCT
cana-1007	38	3	2024	2024	NUM
cana-1007	38	4	)	)	PUNCT
cana-1007	38	5	131	131	NUM
cana-1007	38	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1007	38	7	{	{	PUNCT
cana-1007	38	8	𝑜𝑛𝑒	𝑜𝑛𝑒	PROPN
cana-1007	38	9	,	,	PUNCT
cana-1007	38	10	𝑡𝑤𝑜	𝑡𝑤𝑜	PROPN
cana-1007	38	11	,	,	PUNCT
cana-1007	38	12	𝑡ℎ𝑟𝑒𝑒	𝑡ℎ𝑟𝑒𝑒	ADJ
cana-1007	38	13	,	,	PUNCT
cana-1007	38	14	⋯	⋯	PROPN
cana-1007	38	15	,	,	PUNCT
cana-1007	38	16	|𝐷(𝑔𝑟𝑎𝑝ℎ	|𝐷(𝑔𝑟𝑎𝑝ℎ	ADJ
cana-1007	38	17	)	)	PUNCT
cana-1007	38	18	+	+	CCONJ
cana-1007	38	19	𝐿(𝑔𝑟𝑎𝑝ℎ)|	𝐿(𝑔𝑟𝑎𝑝ℎ)|	NOUN
cana-1007	38	20	}	}	PUNCT
cana-1007	38	21	and	and	CCONJ
cana-1007	38	22	hence	hence	ADV
cana-1007	38	23	for	for	ADP
cana-1007	38	24	every	every	DET
cana-1007	38	25	subgraphs	subgraph	NOUN
cana-1007	38	26	ℎ′	ℎ′	PROPN
cana-1007	38	27	≅	≅	PROPN
cana-1007	38	28	h	h	NOUN
cana-1007	39	1	the	the	DET
cana-1007	39	2	ℎ′	ℎ′	ADJ
cana-1007	39	3	weights	weight	NOUN
cana-1007	39	4	.	.	PUNCT
cana-1007	40	1	𝑤𝑡(ℎ′	𝑤𝑡(ℎ′	PRON
cana-1007	40	2	)	)	PUNCT
cana-1007	40	3	=	=	SYM
cana-1007	40	4	∑𝑑𝜖𝐷(ℎ′	∑𝑑𝜖𝐷(ℎ′	PROPN
cana-1007	40	5	)	)	PUNCT
cana-1007	40	6	𝑔(𝑑	𝑔(𝑑	PROPN
cana-1007	40	7	)	)	PUNCT
cana-1007	40	8	+	+	CCONJ
cana-1007	40	9	∑𝑒𝜖𝐿(ℎ′	∑𝑒𝜖𝐿(ℎ′	PROPN
cana-1007	40	10	)	)	PUNCT
cana-1007	40	11	𝑔(𝑙	𝑔(𝑙	PROPN
cana-1007	40	12	)	)	PUNCT
cana-1007	40	13	generate	generate	VERB
cana-1007	40	14	an	an	DET
cana-1007	40	15	arithmetic	arithmetic	ADJ
cana-1007	40	16	progression	progression	NOUN
cana-1007	40	17	a.p	a.p	PROPN
cana-1007	40	18	𝑏	𝑏	PROPN
cana-1007	40	19	,	,	PUNCT
cana-1007	40	20	𝑏	𝑏	PROPN
cana-1007	40	21	+	+	SYM
cana-1007	40	22	𝑒	𝑒	PROPN
cana-1007	40	23	,	,	PUNCT
cana-1007	40	24	𝑏	𝑏	NOUN
cana-1007	40	25	+	+	NOUN
cana-1007	40	26	2𝑒	2𝑒	NUM
cana-1007	40	27	,	,	PUNCT
cana-1007	40	28	.	.	PUNCT
cana-1007	40	29	.	.	PUNCT
cana-1007	41	1	.	.	PUNCT
cana-1007	42	1	,	,	PUNCT
cana-1007	42	2	𝑏	𝑏	PROPN
cana-1007	42	3	+	+	CCONJ
cana-1007	42	4	(	(	PUNCT
cana-1007	42	5	𝑛	𝑛	PRON
cana-1007	42	6	−	−	PROPN
cana-1007	42	7	1)𝑒	1)𝑒	NOUN
cana-1007	42	8	,	,	PUNCT
cana-1007	42	9	where	where	SCONJ
cana-1007	42	10	b	b	NOUN
cana-1007	42	11	and	and	CCONJ
cana-1007	42	12	e	e	NOUN
cana-1007	42	13	are	be	AUX
cana-1007	42	14	positive	positive	ADJ
cana-1007	42	15	integers	integer	NOUN
cana-1007	42	16	and	and	CCONJ
cana-1007	42	17	n	n	NOUN
cana-1007	42	18	is	be	AUX
cana-1007	42	19	the	the	DET
cana-1007	42	20	number	number	NOUN
cana-1007	42	21	of	of	ADP
cana-1007	42	22	subgraphs	subgraph	NOUN
cana-1007	42	23	of	of	ADP
cana-1007	42	24	g	g	NOUN
cana-1007	42	25	isomorphic	isomorphic	ADJ
cana-1007	42	26	to	to	ADP
cana-1007	42	27	h.	h.	PROPN
cana-1007	42	28	in	in	ADP
cana-1007	42	29	this	this	DET
cana-1007	42	30	research	research	NOUN
cana-1007	42	31	we	we	PRON
cana-1007	42	32	analyze	analyze	VERB
cana-1007	42	33	satl	satl	NOUN
cana-1007	42	34	of	of	ADP
cana-1007	42	35	general	general	ADJ
cana-1007	42	36	star	star	NOUN
cana-1007	42	37	graph	graph	NOUN
cana-1007	42	38	with	with	ADP
cana-1007	42	39	the	the	DET
cana-1007	42	40	solution	solution	NOUN
cana-1007	42	41	for	for	ADP
cana-1007	42	42	an	an	DET
cana-1007	42	43	open	open	ADJ
cana-1007	42	44	problem	problem	NOUN
cana-1007	42	45	10	10	NUM
cana-1007	42	46	in	in	ADP
cana-1007	42	47	[	[	X
cana-1007	42	48	2	2	NUM
cana-1007	42	49	]	]	PUNCT
cana-1007	42	50	.	.	PUNCT
cana-1007	43	1	let	let	VERB
cana-1007	43	2	𝐺′	𝐺′	PROPN
cana-1007	43	3	≅	≅	NUM
cana-1007	43	4	𝐺𝑥(𝑆𝑚	𝐺𝑥(𝑆𝑚	PROPN
cana-1007	43	5	)	)	PUNCT
cana-1007	43	6	then	then	ADV
cana-1007	43	7	|𝐷(𝐺′)|	|𝐷(𝐺′)|	PROPN
cana-1007	43	8	=	=	SYM
cana-1007	43	9	𝑑	𝑑	PROPN
cana-1007	43	10	+	+	X
cana-1007	43	11	𝑚	𝑚	X
cana-1007	43	12	and	and	CCONJ
cana-1007	43	13	|𝐿(𝐺′)|	|𝐿(𝐺′)|	PRON
cana-1007	43	14	=	=	PUNCT
cana-1007	43	15	𝑟	𝑟	NOUN
cana-1007	43	16	+	+	SYM
cana-1007	43	17	𝑛	𝑛	PROPN
cana-1007	43	18	,	,	PUNCT
cana-1007	43	19	referred	refer	VERB
cana-1007	43	20	by	by	ADP
cana-1007	43	21	[	[	X
cana-1007	43	22	2	2	NUM
cana-1007	43	23	]	]	PUNCT
cana-1007	43	24	.	.	PUNCT
cana-1007	44	1	theorem	theorem	VERB
cana-1007	44	2	2.1	2.1	NUM
cana-1007	44	3	the	the	DET
cana-1007	44	4	graph	graph	NOUN
cana-1007	44	5	𝐺𝑢(𝑆3	𝐺𝑢(𝑆3	PUNCT
cana-1007	44	6	)	)	PUNCT
cana-1007	44	7	admits	admit	VERB
cana-1007	44	8	a	a	DET
cana-1007	44	9	satl	satl	NOUN
cana-1007	44	10	⇔	⇔	X
cana-1007	44	11	𝑒𝜖	𝑒𝜖	PROPN
cana-1007	44	12	{	{	PUNCT
cana-1007	44	13	0,1,2	0,1,2	NOUN
cana-1007	44	14	,	,	PUNCT
cana-1007	44	15	.	.	PUNCT
cana-1007	44	16	.	.	PUNCT
cana-1007	45	1	.	.	PUNCT
cana-1007	46	1	,	,	PUNCT
cana-1007	46	2	𝑞	𝑞	PROPN
cana-1007	46	3	+	+	NOUN
cana-1007	46	4	𝑟	𝑟	NOUN
cana-1007	46	5	−	−	X
cana-1007	46	6	[	[	PUNCT
cana-1007	46	7	(	(	PUNCT
cana-1007	46	8	𝑞−1)(𝑞−2	𝑞−1)(𝑞−2	SYM
cana-1007	46	9	)	)	PUNCT
cana-1007	46	10	2	2	NUM
cana-1007	46	11	]	]	PUNCT
cana-1007	46	12	}	}	PUNCT
cana-1007	46	13	proof	proof	NOUN
cana-1007	46	14	.	.	PUNCT
cana-1007	47	1	by	by	ADP
cana-1007	47	2	refereed	refereed	ADJ
cana-1007	47	3	to	to	ADP
cana-1007	47	4	the	the	DET
cana-1007	47	5	theorems	theorem	NOUN
cana-1007	47	6	from	from	ADP
cana-1007	47	7	[	[	X
cana-1007	47	8	1	1	NUM
cana-1007	47	9	]	]	PUNCT
cana-1007	47	10	,	,	PUNCT
cana-1007	47	11	the	the	DET
cana-1007	47	12	satl	satl	NOUN
cana-1007	47	13	labeling	labeling	NOUN
cana-1007	47	14	is	be	AUX
cana-1007	47	15	structured	structure	VERB
cana-1007	47	16	as	as	ADP
cana-1007	47	17	:	:	PUNCT
cana-1007	47	18	𝑔𝑖(𝑤1	𝑔𝑖(𝑤1	ADJ
cana-1007	47	19	)	)	PUNCT
cana-1007	47	20	=	=	PUNCT
cana-1007	48	1	𝑞	𝑞	X
cana-1007	48	2	−	−	PROPN
cana-1007	48	3	𝑖	𝑖	SYM
cana-1007	48	4	,	,	PUNCT
cana-1007	48	5	𝑔𝑖(𝑒𝑞+𝑜𝑛𝑒	𝑔𝑖(𝑒𝑞+𝑜𝑛𝑒	PUNCT
cana-1007	48	6	)	)	PUNCT
cana-1007	48	7	=	=	SYM
cana-1007	49	1	𝑞	𝑞	PROPN
cana-1007	49	2	+	+	NOUN
cana-1007	49	3	𝑟	𝑟	NOUN
cana-1007	49	4	+	+	CCONJ
cana-1007	49	5	3	3	NUM
cana-1007	49	6	−	−	NOUN
cana-1007	49	7	𝑖	𝑖	NOUN
cana-1007	49	8	,	,	PUNCT
cana-1007	49	9	1	1	NUM
cana-1007	49	10	≤	≤	NUM
cana-1007	49	11	𝑖	𝑖	PUNCT
cana-1007	49	12	≤	≤	NOUN
cana-1007	49	13	𝑞	𝑞	X
cana-1007	49	14	−	−	PROPN
cana-1007	49	15	2	2	NUM
cana-1007	49	16	,	,	PUNCT
cana-1007	49	17	𝑔𝑖(𝑤2	𝑔𝑖(𝑤2	NOUN
cana-1007	49	18	)	)	PUNCT
cana-1007	49	19	=	=	PUNCT
cana-1007	50	1	𝑞	𝑞	X
cana-1007	50	2	−	−	PROPN
cana-1007	50	3	1	1	NUM
cana-1007	50	4	,	,	PUNCT
cana-1007	50	5	𝑔𝑖(𝑒𝑞+2	𝑔𝑖(𝑒𝑞+2	NOUN
cana-1007	50	6	)	)	PUNCT
cana-1007	50	7	=	=	PUNCT
cana-1007	51	1	𝑞	𝑞	PART
cana-1007	51	2	+	+	NOUN
cana-1007	51	3	𝑟	𝑟	NOUN
cana-1007	51	4	+	+	SYM
cana-1007	51	5	5	5	NUM
cana-1007	51	6	𝑔𝑖(𝑤3	𝑔𝑖(𝑤3	ADJ
cana-1007	51	7	)	)	PUNCT
cana-1007	51	8	=	=	PUNCT
cana-1007	52	1	𝑞	𝑞	PROPN
cana-1007	52	2	+	+	NOUN
cana-1007	52	3	1	1	NUM
cana-1007	52	4	+	+	NUM
cana-1007	52	5	𝑖	𝑖	SYM
cana-1007	52	6	,	,	PUNCT
cana-1007	52	7	𝑔𝑖(𝑒𝑞+3	𝑔𝑖(𝑒𝑞+3	ADJ
cana-1007	52	8	)	)	PUNCT
cana-1007	52	9	=	=	PUNCT
cana-1007	53	1	𝑞	𝑞	PROPN
cana-1007	53	2	+	+	NOUN
cana-1007	53	3	𝑟	𝑟	NOUN
cana-1007	53	4	+	+	CCONJ
cana-1007	53	5	6	6	NUM
cana-1007	53	6	therefore	therefore	ADV
cana-1007	53	7	sum	sum	NOUN
cana-1007	53	8	of	of	ADP
cana-1007	53	9	the	the	DET
cana-1007	53	10	induced	induce	VERB
cana-1007	53	11	labels	label	NOUN
cana-1007	53	12	of	of	ADP
cana-1007	53	13	𝑆3	𝑆3	PROPN
cana-1007	53	14	are	be	AUX
cana-1007	53	15	2q+r+3	2q+r+3	NUM
cana-1007	53	16	-	-	SYM
cana-1007	53	17	two(i	two(i	NOUN
cana-1007	53	18	)	)	PUNCT
cana-1007	53	19	,	,	PUNCT
cana-1007	53	20	2q+r+6	2q+r+6	NUM
cana-1007	53	21	-	-	PUNCT
cana-1007	53	22	i	i	PROPN
cana-1007	53	23	and	and	CCONJ
cana-1007	53	24	2q+r+9	2q+r+9	NUM
cana-1007	53	25	.	.	PUNCT
cana-1007	54	1	hence	hence	ADV
cana-1007	54	2	,	,	PUNCT
cana-1007	54	3	𝑒	𝑒	ADV
cana-1007	54	4	=	=	PUNCT
cana-1007	54	5	𝑡ℎ𝑟𝑒𝑒	𝑡ℎ𝑟𝑒𝑒	ADJ
cana-1007	54	6	+	+	CCONJ
cana-1007	54	7	𝑖	𝑖	X
cana-1007	54	8	,	,	PUNCT
cana-1007	54	9	𝑜𝑛𝑒	𝑜𝑛𝑒	X
cana-1007	54	10	≤	≤	PROPN
cana-1007	54	11	𝑖	𝑖	SYM
cana-1007	54	12	≤	≤	X
cana-1007	54	13	𝑞	𝑞	PRON
cana-1007	54	14	−	−	PROPN
cana-1007	54	15	𝑡𝑤𝑜	𝑡𝑤𝑜	PROPN
cana-1007	54	16	,	,	PUNCT
cana-1007	54	17	hence	hence	ADV
cana-1007	54	18	e	e	NOUN
cana-1007	54	19	=	=	NOUN
cana-1007	54	20	four	four	NUM
cana-1007	54	21	,	,	PUNCT
cana-1007	54	22	five,	five,	ADJ
cana-1007	54	23	...	...	PUNCT
cana-1007	54	24	,q+one	,q+one	PUNCT
cana-1007	54	25	,	,	PUNCT
cana-1007	54	26	for	for	SCONJ
cana-1007	54	27	all	all	DET
cana-1007	54	28	i	i	PRON
cana-1007	54	29	,	,	PUNCT
cana-1007	54	30	𝑜𝑛𝑒	𝑜𝑛𝑒	X
cana-1007	54	31	≤	≤	PROPN
cana-1007	54	32	𝑖	𝑖	SYM
cana-1007	54	33	≤	≤	NUM
cana-1007	55	1	𝑟	𝑟	X
cana-1007	55	2	−	−	X
cana-1007	55	3	[	[	PUNCT
cana-1007	55	4	(	(	PUNCT
cana-1007	55	5	𝑞−2)(𝑞−1	𝑞−2)(𝑞−1	X
cana-1007	55	6	)	)	PUNCT
cana-1007	55	7	2	2	NUM
cana-1007	55	8	]	]	PUNCT
cana-1007	55	9	−	−	PROPN
cana-1007	55	10	1	1	NUM
cana-1007	55	11	,	,	PUNCT
cana-1007	55	12	denote	denote	VERB
cana-1007	55	13	the	the	DET
cana-1007	55	14	labels	label	NOUN
cana-1007	55	15	of	of	ADP
cana-1007	55	16	𝑔𝑖	𝑔𝑖	NOUN
cana-1007	55	17	:	:	PUNCT
cana-1007	55	18	𝑔𝑖(𝑣1	𝑔𝑖(𝑣1	ADJ
cana-1007	55	19	)	)	PUNCT
cana-1007	55	20	=	=	SYM
cana-1007	55	21	𝑜𝑛𝑒	𝑜𝑛𝑒	PROPN
cana-1007	55	22	,	,	PUNCT
cana-1007	55	23	𝑔𝑖(𝑒𝑒𝑑𝑔𝑒𝑠+1	𝑔𝑖(𝑒𝑒𝑑𝑔𝑒𝑠+1	PROPN
cana-1007	55	24	)	)	PUNCT
cana-1007	55	25	=	=	SYM
cana-1007	55	26	𝑛𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑒𝑑𝑔𝑒𝑠	𝑛𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑒𝑑𝑔𝑒𝑠	NOUN
cana-1007	55	27	+	+	CCONJ
cana-1007	55	28	6	6	NUM
cana-1007	55	29	−	−	NOUN
cana-1007	55	30	2𝑖	2𝑖	NOUN
cana-1007	55	31	,	,	PUNCT
cana-1007	55	32	𝑜𝑛𝑒	𝑜𝑛𝑒	PROPN
cana-1007	55	33	≤	≤	NUM
cana-1007	55	34	𝑗	𝑗	PRON
cana-1007	55	35	≤	≤	NUM
cana-1007	55	36	𝑒𝑑𝑔𝑒𝑠	𝑒𝑑𝑔𝑒𝑠	NOUN
cana-1007	55	37	−	−	PROPN
cana-1007	56	1	[	[	PUNCT
cana-1007	56	2	(	(	PUNCT
cana-1007	56	3	𝑞−2)(𝑞−1	𝑞−2)(𝑞−1	X
cana-1007	56	4	)	)	PUNCT
cana-1007	56	5	2	2	NUM
cana-1007	56	6	]	]	PUNCT
cana-1007	56	7	−	−	PROPN
cana-1007	56	8	1	1	NUM
cana-1007	56	9	𝑔𝑖(𝑤2	𝑔𝑖(𝑤2	NOUN
cana-1007	56	10	)	)	PUNCT
cana-1007	56	11	=	=	SYM
cana-1007	56	12	3	3	NUM
cana-1007	56	13	,	,	PUNCT
cana-1007	56	14	𝑔𝑖(𝑒𝑞+2	𝑔𝑖(𝑒𝑞+2	NOUN
cana-1007	56	15	)	)	PUNCT
cana-1007	56	16	=	=	SYM
cana-1007	56	17	𝑝	𝑝	PROPN
cana-1007	56	18	+	+	NUM
cana-1007	56	19	𝑞	𝑞	X
cana-1007	56	20	+	+	NOUN
cana-1007	56	21	5	5	NUM
cana-1007	56	22	−	−	NOUN
cana-1007	56	23	𝑖	𝑖	NOUN
cana-1007	56	24	𝑔𝑖(𝑤3	𝑔𝑖(𝑤3	ADJ
cana-1007	56	25	)	)	PUNCT
cana-1007	56	26	=	=	PUNCT
cana-1007	57	1	𝑞	𝑞	X
cana-1007	57	2	+	+	ADJ
cana-1007	57	3	3	3	NUM
cana-1007	57	4	,	,	PUNCT
cana-1007	57	5	𝑔𝑖(𝑒𝑞+3	𝑔𝑖(𝑒𝑞+3	ADJ
cana-1007	57	6	)	)	PUNCT
cana-1007	57	7	=	=	PUNCT
cana-1007	58	1	𝑞	𝑞	PROPN
cana-1007	58	2	+	+	NOUN
cana-1007	58	3	𝑟	𝑟	NOUN
cana-1007	58	4	+	+	CCONJ
cana-1007	58	5	6	6	NUM
cana-1007	58	6	therefore	therefore	ADV
cana-1007	58	7	sum	sum	NOUN
cana-1007	58	8	of	of	ADP
cana-1007	58	9	the	the	DET
cana-1007	58	10	induced	induce	VERB
cana-1007	58	11	labels	label	NOUN
cana-1007	58	12	of	of	ADP
cana-1007	58	13	𝑆3	𝑆3	PROPN
cana-1007	58	14	are	be	AUX
cana-1007	58	15	r+7	r+7	NUM
cana-1007	58	16	-	-	PUNCT
cana-1007	58	17	2i	2i	NUM
cana-1007	58	18	,	,	PUNCT
cana-1007	58	19	q+r+8	q+r+8	NOUN
cana-1007	58	20	-	-	PUNCT
cana-1007	58	21	i	i	PROPN
cana-1007	58	22	and	and	CCONJ
cana-1007	58	23	2q+r+9	2q+r+9	NUM
cana-1007	58	24	.	.	PUNCT
cana-1007	59	1	hence	hence	ADV
cana-1007	59	2	e	e	X
cana-1007	59	3	=	=	NOUN
cana-1007	59	4	q+1+i	q+1+i	NOUN
cana-1007	59	5	,	,	PUNCT
cana-1007	59	6	1	1	NUM
cana-1007	59	7	≤	≤	NUM
cana-1007	59	8	𝑖	𝑖	SYM
cana-1007	59	9	≤	≤	NUM
cana-1007	59	10	𝑟	𝑟	X
cana-1007	59	11	−	−	X
cana-1007	59	12	[	[	PUNCT
cana-1007	59	13	(	(	PUNCT
cana-1007	59	14	𝑞−2)(𝑞−1	𝑞−2)(𝑞−1	X
cana-1007	59	15	)	)	PUNCT
cana-1007	59	16	2	2	NUM
cana-1007	59	17	]	]	PUNCT
cana-1007	59	18	−	−	PROPN
cana-1007	59	19	1	1	NUM
cana-1007	59	20	hence	hence	ADV
cana-1007	59	21	,	,	PUNCT
cana-1007	59	22	𝑒	𝑒	PROPN
cana-1007	59	23	=	=	PUNCT
cana-1007	59	24	𝑞	𝑞	X
cana-1007	59	25	+	+	NOUN
cana-1007	59	26	2	2	NUM
cana-1007	59	27	,	,	PUNCT
cana-1007	59	28	𝑞	𝑞	X
cana-1007	59	29	+	+	NOUN
cana-1007	59	30	3	3	NUM
cana-1007	59	31	,	,	PUNCT
cana-1007	59	32	𝑞	𝑞	X
cana-1007	59	33	+	+	NOUN
cana-1007	59	34	4	4	NUM
cana-1007	59	35	,	,	PUNCT
cana-1007	59	36	.	.	PUNCT
cana-1007	59	37	.	.	PUNCT
cana-1007	60	1	.	.	PUNCT
cana-1007	61	1	,	,	PUNCT
cana-1007	61	2	𝑞	𝑞	PROPN
cana-1007	61	3	+	+	NOUN
cana-1007	61	4	𝑟	𝑟	NOUN
cana-1007	61	5	−	−	X
cana-1007	61	6	[	[	PUNCT
cana-1007	61	7	(	(	PUNCT
cana-1007	61	8	𝑞−1)(𝑞−2	𝑞−1)(𝑞−2	SYM
cana-1007	61	9	)	)	PUNCT
cana-1007	61	10	2	2	NUM
cana-1007	61	11	]	]	PUNCT
cana-1007	61	12	theorem	theorem	VERB
cana-1007	61	13	2.2	2.2	NUM
cana-1007	61	14	𝐺𝑢(𝑆4	𝐺𝑢(𝑆4	NOUN
cana-1007	61	15	)	)	PUNCT
cana-1007	61	16	admits	admit	VERB
cana-1007	61	17	a	a	DET
cana-1007	61	18	satl	satl	NOUN
cana-1007	61	19	for	for	ADP
cana-1007	61	20	each	each	DET
cana-1007	61	21	e	e	NOUN
cana-1007	61	22	=	=	PROPN
cana-1007	61	23	i	i	PROPN
cana-1007	61	24	,	,	PUNCT
cana-1007	61	25	4	4	NUM
cana-1007	61	26	≤	≤	NUM
cana-1007	61	27	𝑖	𝑖	PUNCT
cana-1007	61	28	≤	≤	NOUN
cana-1007	62	1	𝑞	𝑞	X
cana-1007	62	2	+	+	NOUN
cana-1007	62	3	1	1	NUM
cana-1007	62	4	and	and	CCONJ
cana-1007	62	5	𝑞	𝑞	X
cana-1007	62	6	≥	≥	PROPN
cana-1007	62	7	3	3	NUM
cana-1007	62	8	.	.	PUNCT
cana-1007	63	1	proof	proof	NOUN
cana-1007	63	2	.	.	PUNCT
cana-1007	64	1	let	let	VERB
cana-1007	64	2	𝐺′	𝐺′	PROPN
cana-1007	64	3	≅	≅	NUM
cana-1007	64	4	𝐺𝑢(𝑆4	𝐺𝑢(𝑆4	PROPN
cana-1007	64	5	)	)	PUNCT
cana-1007	64	6	and	and	CCONJ
cana-1007	64	7	𝑑𝑖	𝑑𝑖	PROPN
cana-1007	64	8	,	,	PUNCT
cana-1007	64	9	𝑤1	𝑤1	PROPN
cana-1007	64	10	,	,	PUNCT
cana-1007	64	11	𝑤2	𝑤2	NOUN
cana-1007	64	12	,	,	PUNCT
cana-1007	64	13	𝑤3	𝑤3	PROPN
cana-1007	64	14	,	,	PUNCT
cana-1007	64	15	𝑤4	𝑤4	NOUN
cana-1007	64	16	,	,	PUNCT
cana-1007	64	17	1	1	NUM
cana-1007	64	18	≤	≤	NUM
cana-1007	64	19	𝑖	𝑖	PUNCT
cana-1007	64	20	≤	≤	NUM
cana-1007	64	21	𝑞	𝑞	X
cana-1007	64	22	is	be	AUX
cana-1007	64	23	the	the	DET
cana-1007	64	24	dots	dot	NOUN
cana-1007	64	25	of	of	ADP
cana-1007	64	26	the	the	DET
cana-1007	64	27	graph	graph	NOUN
cana-1007	64	28	and	and	CCONJ
cana-1007	64	29	(	(	PUNCT
cana-1007	64	30	𝑆4	𝑆4	PROPN
cana-1007	64	31	)	)	PUNCT
cana-1007	64	32	.	.	PUNCT
cana-1007	65	1	𝑙𝑖	𝑙𝑖	INTJ
cana-1007	65	2	,	,	PUNCT
cana-1007	65	3	𝑙𝑟+1	𝑙𝑟+1	PROPN
cana-1007	65	4	,	,	PUNCT
cana-1007	65	5	𝑙𝑟+2	𝑙𝑟+2	NUM
cana-1007	65	6	,	,	PUNCT
cana-1007	65	7	𝑙𝑟+3	𝑙𝑟+3	NUM
cana-1007	65	8	,	,	PUNCT
cana-1007	65	9	𝑙𝑟+4	𝑙𝑟+4	NOUN
cana-1007	65	10	,	,	PUNCT
cana-1007	65	11	1	1	NUM
cana-1007	65	12	≤	≤	NUM
cana-1007	65	13	𝑖	𝑖	SYM
cana-1007	65	14	≤	≤	NOUN
cana-1007	65	15	𝑟	𝑟	X
cana-1007	65	16	is	be	AUX
cana-1007	65	17	the	the	DET
cana-1007	65	18	joints	joint	NOUN
cana-1007	65	19	of	of	ADP
cana-1007	65	20	g	g	PROPN
cana-1007	65	21	and	and	CCONJ
cana-1007	65	22	(	(	PUNCT
cana-1007	65	23	𝑆4	𝑆4	PROPN
cana-1007	65	24	)	)	PUNCT
cana-1007	65	25	respectively	respectively	ADV
cana-1007	65	26	.	.	PUNCT
cana-1007	66	1	communications	communication	NOUN
cana-1007	66	2	on	on	ADP
cana-1007	66	3	applied	apply	VERB
cana-1007	66	4	nonlinear	nonlinear	ADJ
cana-1007	66	5	analysis	analysis	NOUN
cana-1007	66	6	issn	issn	NOUN
cana-1007	66	7	:	:	PUNCT
cana-1007	66	8	1074	1074	NUM
cana-1007	66	9	-	-	PUNCT
cana-1007	66	10	133x	133x	NUM
cana-1007	66	11	vol	vol	NOUN
cana-1007	66	12	31	31	NUM
cana-1007	66	13	no	no	NOUN
cana-1007	66	14	.	.	PUNCT
cana-1007	67	1	5s	5s	NUM
cana-1007	67	2	(	(	PUNCT
cana-1007	67	3	2024	2024	NUM
cana-1007	67	4	)	)	PUNCT
cana-1007	67	5	132	132	NUM
cana-1007	67	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1007	67	7	then	then	ADV
cana-1007	67	8	|𝐷(𝐺𝑥(𝑆4))|	|𝐷(𝐺𝑥(𝑆4))|	PROPN
cana-1007	67	9	=	=	PUNCT
cana-1007	67	10	𝑞	𝑞	PROPN
cana-1007	67	11	+	+	CCONJ
cana-1007	67	12	4	4	NUM
cana-1007	67	13	and	and	CCONJ
cana-1007	67	14	|𝐷(𝐺𝑥(𝑆4))|	|𝐷(𝐺𝑥(𝑆4))|	NOUN
cana-1007	67	15	=	=	PUNCT
cana-1007	67	16	𝑟	𝑟	NOUN
cana-1007	67	17	+	+	NOUN
cana-1007	67	18	4	4	X
cana-1007	67	19	.	.	PUNCT
cana-1007	67	20	suppose	suppose	VERB
cana-1007	67	21	there	there	PRON
cana-1007	67	22	exists	exist	VERB
cana-1007	67	23	a	a	DET
cana-1007	67	24	bijective	bijective	ADJ
cana-1007	67	25	mapping	mapping	NOUN
cana-1007	67	26	,	,	PUNCT
cana-1007	67	27	𝑔	𝑔	NOUN
cana-1007	67	28	:	:	PUNCT
cana-1007	67	29	𝑠𝑢𝑚	𝑠𝑢𝑚	NOUN
cana-1007	67	30	𝑜𝑓	𝑜𝑓	INTJ
cana-1007	67	31	𝑣𝑒𝑟𝑡𝑖𝑐𝑒𝑠	𝑣𝑒𝑟𝑡𝑖𝑐𝑒𝑠	PROPN
cana-1007	67	32	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-1007	67	33	𝑒𝑑𝑔𝑒𝑠	𝑒𝑑𝑔𝑒𝑠	NOUN
cana-1007	67	34	→	→	PUNCT
cana-1007	67	35	{	{	PUNCT
cana-1007	67	36	𝑜𝑛𝑒	𝑜𝑛𝑒	PROPN
cana-1007	67	37	,	,	PUNCT
cana-1007	67	38	𝑡𝑤𝑜	𝑡𝑤𝑜	PROPN
cana-1007	67	39	,	,	PUNCT
cana-1007	67	40	𝑡ℎ𝑟𝑒𝑒	𝑡ℎ𝑟𝑒𝑒	ADJ
cana-1007	67	41	,	,	PUNCT
cana-1007	67	42	⋯	⋯	PROPN
cana-1007	67	43	,	,	PUNCT
cana-1007	67	44	𝑒𝑑𝑔𝑒𝑠	𝑒𝑑𝑔𝑒𝑠	VERB
cana-1007	67	45	+	+	NUM
cana-1007	67	46	𝑟	𝑟	NOUN
cana-1007	67	47	+	+	CCONJ
cana-1007	67	48	8	8	NUM
cana-1007	67	49	}	}	PUNCT
cana-1007	67	50	which	which	PRON
cana-1007	67	51	is	be	AUX
cana-1007	67	52	a	a	DET
cana-1007	67	53	satl	satl	NOUN
cana-1007	67	54	of	of	ADP
cana-1007	67	55	𝐺′.	𝐺′.	NOUN
cana-1007	67	56	numbering	number	VERB
cana-1007	67	57	the	the	DET
cana-1007	67	58	vertices	vertex	NOUN
cana-1007	67	59	𝑑𝑖	𝑑𝑖	PART
cana-1007	67	60	,	,	PUNCT
cana-1007	67	61	𝑜𝑛𝑒	𝑜𝑛𝑒	ADJ
cana-1007	67	62	≤	≤	PROPN
cana-1007	67	63	𝑖	𝑖	SYM
cana-1007	67	64	≤	≤	X
cana-1007	68	1	𝑞	𝑞	SYM
cana-1007	68	2	corresponding	correspond	VERB
cana-1007	68	3	numbers	number	NOUN
cana-1007	68	4	of	of	ADP
cana-1007	68	5	a	a	DET
cana-1007	68	6	then	then	ADV
cana-1007	68	7	the	the	DET
cana-1007	68	8	edge	edge	NOUN
cana-1007	68	9	labels	label	NOUN
cana-1007	68	10	𝑜𝑛𝑒𝑖	𝑜𝑛𝑒𝑖	NOUN
cana-1007	68	11	,	,	PUNCT
cana-1007	68	12	1	1	NUM
cana-1007	68	13	≤	≤	NUM
cana-1007	68	14	𝑖	𝑖	SYM
cana-1007	68	15	≤	≤	NUM
cana-1007	68	16	𝑟	𝑟	NOUN
cana-1007	68	17	from	from	ADP
cana-1007	68	18	numbers	number	NOUN
cana-1007	68	19	in	in	ADP
cana-1007	68	20	b	b	NOUN
cana-1007	68	21	mixing	mix	VERB
cana-1007	68	22	arrangement	arrangement	NOUN
cana-1007	68	23	,	,	PUNCT
cana-1007	68	24	𝐴	𝐴	PROPN
cana-1007	68	25	=	=	PUNCT
cana-1007	69	1	[	[	X
cana-1007	69	2	𝑞	𝑞	X
cana-1007	69	3	+	+	NOUN
cana-1007	69	4	2	2	NUM
cana-1007	69	5	]	]	PUNCT
cana-1007	69	6	−	−	ADP
cana-1007	69	7	𝑞	𝑞	X
cana-1007	69	8	+	+	NOUN
cana-1007	69	9	2	2	NUM
cana-1007	69	10	−	−	NOUN
cana-1007	69	11	𝑖	𝑖	NOUN
cana-1007	69	12	,	,	PUNCT
cana-1007	69	13	𝑞	𝑞	X
cana-1007	69	14	+	+	X
cana-1007	69	15	1,by	1,by	NUM
cana-1007	69	16	the	the	DET
cana-1007	69	17	condition	condition	NOUN
cana-1007	69	18	4	4	NUM
cana-1007	69	19	≤	≤	NUM
cana-1007	69	20	𝑖	𝑖	PUNCT
cana-1007	69	21	≤	≤	NOUN
cana-1007	69	22	𝑞	𝑞	X
cana-1007	69	23	+	+	ADP
cana-1007	69	24	1	1	NUM
cana-1007	69	25	and	and	CCONJ
cana-1007	69	26	𝐵	𝐵	NOUN
cana-1007	69	27	=	=	PUNCT
cana-1007	69	28	𝑞	𝑞	PROPN
cana-1007	69	29	+	+	NOUN
cana-1007	69	30	5	5	NUM
cana-1007	69	31	,	,	PUNCT
cana-1007	69	32	𝑞	𝑞	X
cana-1007	69	33	+	+	NOUN
cana-1007	69	34	6	6	NUM
cana-1007	69	35	,	,	PUNCT
cana-1007	69	36	.	.	PUNCT
cana-1007	69	37	.	.	PUNCT
cana-1007	69	38	.	.	PUNCT
cana-1007	70	1	,	,	PUNCT
cana-1007	70	2	𝑞	𝑞	PROPN
cana-1007	70	3	+	+	NOUN
cana-1007	70	4	𝑟	𝑟	NOUN
cana-1007	71	1	+	+	CCONJ
cana-1007	71	2	7	7	NUM
cana-1007	71	3	−	−	NOUN
cana-1007	71	4	𝑞	𝑞	NOUN
cana-1007	71	5	+	+	NOUN
cana-1007	71	6	𝑟	𝑟	NOUN
cana-1007	71	7	+	+	CCONJ
cana-1007	71	8	10	10	NUM
cana-1007	71	9	−	−	NOUN
cana-1007	71	10	2𝑖	2𝑖	NOUN
cana-1007	71	11	,	,	PUNCT
cana-1007	71	12	𝑞	𝑞	X
cana-1007	71	13	+	+	NOUN
cana-1007	71	14	𝑟	𝑟	NOUN
cana-1007	71	15	+	+	CCONJ
cana-1007	71	16	11	11	NUM
cana-1007	71	17	−	−	NOUN
cana-1007	71	18	2𝑖	2𝑖	NOUN
cana-1007	71	19	,	,	PUNCT
cana-1007	71	20	𝑞	𝑞	X
cana-1007	71	21	+	+	NOUN
cana-1007	71	22	𝑟	𝑟	NOUN
cana-1007	71	23	+	+	CCONJ
cana-1007	71	24	9	9	NUM
cana-1007	71	25	−	−	NOUN
cana-1007	71	26	𝑖	𝑖	NOUN
cana-1007	71	27	,	,	PUNCT
cana-1007	71	28	4	4	NUM
cana-1007	71	29	≤	≤	NUM
cana-1007	71	30	𝑖	𝑖	PUNCT
cana-1007	71	31	≤	≤	NOUN
cana-1007	71	32	𝑞	𝑞	X
cana-1007	71	33	+	+	NOUN
cana-1007	71	34	1	1	X
cana-1007	71	35	.	.	PUNCT
cana-1007	72	1	the	the	DET
cana-1007	72	2	graph	graph	NOUN
cana-1007	72	3	g	g	PROPN
cana-1007	72	4	and	and	CCONJ
cana-1007	72	5	the	the	DET
cana-1007	72	6	subgraph	subgraph	NOUN
cana-1007	72	7	having	have	VERB
cana-1007	72	8	the	the	DET
cana-1007	72	9	equal	equal	ADJ
cana-1007	72	10	sweights	sweight	NOUN
cana-1007	72	11	(	(	PUNCT
cana-1007	72	12	𝐺	𝐺	NOUN
cana-1007	72	13	+	+	CCONJ
cana-1007	72	14	𝑙𝑖	𝑙𝑖	NOUN
cana-1007	72	15	)	)	PUNCT
cana-1007	72	16	,	,	PUNCT
cana-1007	72	17	i=1,2,3,4	i=1,2,3,4	PROPN
cana-1007	72	18	.	.	PUNCT
cana-1007	73	1	it	it	PRON
cana-1007	73	2	is	be	AUX
cana-1007	73	3	sufficient	sufficient	ADJ
cana-1007	73	4	to	to	PART
cana-1007	73	5	prove	prove	VERB
cana-1007	73	6	the	the	DET
cana-1007	73	7	numbers	number	NOUN
cana-1007	73	8	of	of	ADP
cana-1007	73	9	the	the	DET
cana-1007	73	10	star	star	NOUN
cana-1007	73	11	graph	graph	NOUN
cana-1007	73	12	𝑆4	𝑆4	PROPN
cana-1007	73	13	,	,	PUNCT
cana-1007	73	14	for	for	SCONJ
cana-1007	73	15	every	every	DET
cana-1007	73	16	’	'	PUNCT
cana-1007	73	17	i	i	NOUN
cana-1007	73	18	’	'	PUNCT
cana-1007	73	19	4	4	NUM
cana-1007	73	20	≤	≤	NUM
cana-1007	73	21	𝑖	𝑖	PRON
cana-1007	73	22	≤	≤	PROPN
cana-1007	73	23	𝑝	𝑝	PROPN
cana-1007	73	24	+	+	NUM
cana-1007	73	25	𝑞	𝑞	X
cana-1007	73	26	−	−	PROPN
cana-1007	73	27	[	[	PUNCT
cana-1007	73	28	𝑘(𝑘+3	𝑘(𝑘+3	NOUN
cana-1007	73	29	)	)	PUNCT
cana-1007	73	30	𝑡𝑤𝑜	𝑡𝑤𝑜	VERB
cana-1007	73	31	]	]	PUNCT
cana-1007	73	32	,	,	PUNCT
cana-1007	73	33	then	then	ADV
cana-1007	73	34	𝑓𝑖	𝑓𝑖	PROPN
cana-1007	73	35	is	be	AUX
cana-1007	73	36	defined	define	VERB
cana-1007	73	37	as	as	ADP
cana-1007	73	38	:	:	PUNCT
cana-1007	73	39	𝑔𝑖(𝑤1	𝑔𝑖(𝑤1	NUM
cana-1007	73	40	)	)	PUNCT
cana-1007	73	41	=	=	SYM
cana-1007	74	1	𝑞	𝑞	PROPN
cana-1007	74	2	+	+	NOUN
cana-1007	74	3	2	2	NUM
cana-1007	74	4	−	−	NOUN
cana-1007	74	5	𝑖	𝑖	NOUN
cana-1007	74	6	,	,	PUNCT
cana-1007	74	7	𝑔𝑖(𝑒𝑞+𝑜𝑛𝑒	𝑔𝑖(𝑒𝑞+𝑜𝑛𝑒	PUNCT
cana-1007	74	8	)	)	PUNCT
cana-1007	74	9	=	=	SYM
cana-1007	75	1	𝑞	𝑞	PROPN
cana-1007	75	2	+	+	NOUN
cana-1007	75	3	𝑟	𝑟	NOUN
cana-1007	75	4	+	+	CCONJ
cana-1007	75	5	10	10	NUM
cana-1007	75	6	−	−	NOUN
cana-1007	75	7	2𝑖	2𝑖	NOUN
cana-1007	75	8	,	,	PUNCT
cana-1007	75	9	4	4	NUM
cana-1007	75	10	≤	≤	NUM
cana-1007	75	11	𝑖	𝑖	PUNCT
cana-1007	75	12	≤	≤	NOUN
cana-1007	75	13	𝑞	𝑞	X
cana-1007	75	14	+	+	NOUN
cana-1007	75	15	1	1	NUM
cana-1007	75	16	,	,	PUNCT
cana-1007	75	17	𝑔𝑖(𝑤2	𝑔𝑖(𝑤2	NOUN
cana-1007	75	18	)	)	PUNCT
cana-1007	75	19	=	=	PUNCT
cana-1007	76	1	𝑞	𝑞	X
cana-1007	76	2	+	+	ADJ
cana-1007	76	3	1	1	NUM
cana-1007	76	4	,	,	PUNCT
cana-1007	76	5	𝑔𝑖(𝑒𝑞+2	𝑔𝑖(𝑒𝑞+2	NOUN
cana-1007	76	6	)	)	PUNCT
cana-1007	76	7	=	=	PUNCT
cana-1007	76	8	𝑞	𝑞	PART
cana-1007	76	9	+	+	NOUN
cana-1007	76	10	𝑟	𝑟	NOUN
cana-1007	76	11	+	+	CCONJ
cana-1007	76	12	11	11	NUM
cana-1007	76	13	−	−	NOUN
cana-1007	76	14	2𝑖	2𝑖	NOUN
cana-1007	76	15	𝑔𝑖(𝑤3	𝑔𝑖(𝑤3	VERB
cana-1007	76	16	)	)	PUNCT
cana-1007	76	17	=	=	PUNCT
cana-1007	77	1	𝑞	𝑞	X
cana-1007	77	2	+	+	ADJ
cana-1007	77	3	3	3	NUM
cana-1007	77	4	,	,	PUNCT
cana-1007	77	5	𝑔𝑖(𝑒𝑞+3	𝑔𝑖(𝑒𝑞+3	ADJ
cana-1007	77	6	)	)	PUNCT
cana-1007	77	7	=	=	PUNCT
cana-1007	78	1	𝑞	𝑞	PROPN
cana-1007	78	2	+	+	NOUN
cana-1007	78	3	𝑟	𝑟	NOUN
cana-1007	78	4	+	+	CCONJ
cana-1007	78	5	9	9	NUM
cana-1007	78	6	−	−	NOUN
cana-1007	78	7	𝑖	𝑖	SYM
cana-1007	78	8	𝑔𝑖(𝑤4	𝑔𝑖(𝑤4	NOUN
cana-1007	78	9	)	)	PUNCT
cana-1007	78	10	=	=	PUNCT
cana-1007	78	11	𝑞	𝑞	X
cana-1007	78	12	+	+	ADJ
cana-1007	78	13	4	4	NUM
cana-1007	78	14	,	,	PUNCT
cana-1007	78	15	𝑔𝑖(𝑒𝑞+4	𝑔𝑖(𝑒𝑞+4	NOUN
cana-1007	78	16	)	)	PUNCT
cana-1007	78	17	=	=	SYM
cana-1007	79	1	𝑞	𝑞	PROPN
cana-1007	79	2	+	+	NOUN
cana-1007	79	3	𝑟	𝑟	NOUN
cana-1007	79	4	+	+	SYM
cana-1007	79	5	8	8	NUM
cana-1007	79	6	therefore	therefore	ADV
cana-1007	79	7	the	the	DET
cana-1007	79	8	labels	label	NOUN
cana-1007	79	9	of	of	ADP
cana-1007	79	10	𝑆4	𝑆4	PROPN
cana-1007	79	11	are	be	AUX
cana-1007	79	12	2q+r+12	2q+r+12	NOUN
cana-1007	79	13	-	-	PUNCT
cana-1007	79	14	3i	3i	NOUN
cana-1007	79	15	,	,	PUNCT
cana-1007	79	16	2q+r+12	2q+r+12	PROPN
cana-1007	79	17	-	-	PUNCT
cana-1007	79	18	2i,2r+q+12	2i,2r+q+12	NUM
cana-1007	79	19	-	-	PUNCT
cana-1007	79	20	i	i	PRON
cana-1007	79	21	and	and	CCONJ
cana-1007	79	22	2q+r+12	2q+r+12	NUM
cana-1007	79	23	.	.	PUNCT
cana-1007	80	1	hence	hence	ADV
cana-1007	80	2	,	,	PUNCT
cana-1007	80	3	𝑒	𝑒	PROPN
cana-1007	80	4	=	=	SYM
cana-1007	80	5	𝑖	𝑖	PROPN
cana-1007	80	6	,	,	PUNCT
cana-1007	80	7	4	4	NUM
cana-1007	80	8	≤	≤	NUM
cana-1007	80	9	𝑖	𝑖	PUNCT
cana-1007	80	10	≤	≤	NOUN
cana-1007	80	11	𝑞	𝑞	X
cana-1007	80	12	+	+	NOUN
cana-1007	80	13	1	1	X
cana-1007	80	14	.	.	X
cana-1007	80	15	theorem	theorem	VERB
cana-1007	80	16	2.3	2.3	NUM
cana-1007	80	17	𝐺𝑢(𝑆4	𝐺𝑢(𝑆4	NOUN
cana-1007	80	18	)	)	PUNCT
cana-1007	80	19	admits	admit	VERB
cana-1007	80	20	a	a	DET
cana-1007	80	21	satl	satl	NOUN
cana-1007	80	22	for	for	ADP
cana-1007	80	23	each	each	DET
cana-1007	80	24	e	e	NOUN
cana-1007	80	25	=	=	PROPN
cana-1007	80	26	i	i	PROPN
cana-1007	80	27	,	,	PUNCT
cana-1007	80	28	4	4	NUM
cana-1007	80	29	≤	≤	NUM
cana-1007	80	30	𝑖	𝑖	PUNCT
cana-1007	80	31	≤	≤	NOUN
cana-1007	80	32	𝑞	𝑞	X
cana-1007	80	33	,	,	PUNCT
cana-1007	80	34	𝑤ℎ𝑒𝑟𝑒𝑞	𝑤ℎ𝑒𝑟𝑒𝑞	ADJ
cana-1007	80	35	≥	≥	NOUN
cana-1007	80	36	4	4	NUM
cana-1007	80	37	.	.	PUNCT
cana-1007	81	1	proof	proof	NOUN
cana-1007	81	2	.	.	PUNCT
cana-1007	82	1	let	let	VERB
cana-1007	82	2	𝐺′	𝐺′	PROPN
cana-1007	82	3	≅	≅	NUM
cana-1007	82	4	𝐺𝑢(𝑆5	𝐺𝑢(𝑆5	PROPN
cana-1007	82	5	)	)	PUNCT
cana-1007	82	6	and	and	CCONJ
cana-1007	82	7	𝑑𝑖	𝑑𝑖	PROPN
cana-1007	82	8	,	,	PUNCT
cana-1007	82	9	𝑤1	𝑤1	PROPN
cana-1007	82	10	,	,	PUNCT
cana-1007	82	11	𝑤2	𝑤2	NOUN
cana-1007	82	12	,	,	PUNCT
cana-1007	82	13	𝑤3	𝑤3	PROPN
cana-1007	82	14	,	,	PUNCT
cana-1007	82	15	𝑤4	𝑤4	NOUN
cana-1007	82	16	,	,	PUNCT
cana-1007	82	17	𝑤5	𝑤5	NOUN
cana-1007	82	18	,	,	PUNCT
cana-1007	82	19	1	1	NUM
cana-1007	82	20	≤	≤	NUM
cana-1007	82	21	𝑖	𝑖	PUNCT
cana-1007	82	22	≤	≤	NOUN
cana-1007	82	23	𝑞	𝑞	PART
cana-1007	82	24	be	be	AUX
cana-1007	82	25	the	the	DET
cana-1007	82	26	vertices	vertex	NOUN
cana-1007	82	27	of	of	ADP
cana-1007	82	28	g	g	PROPN
cana-1007	82	29	and	and	CCONJ
cana-1007	82	30	(	(	PUNCT
cana-1007	82	31	𝑆5	𝑆5	PROPN
cana-1007	82	32	)	)	PUNCT
cana-1007	82	33	.	.	PUNCT
cana-1007	83	1	let	let	VERB
cana-1007	83	2	𝑙𝑖	𝑙𝑖	VERB
cana-1007	83	3	,	,	PUNCT
cana-1007	83	4	𝑙𝑟+1	𝑙𝑟+1	PROPN
cana-1007	83	5	,	,	PUNCT
cana-1007	83	6	𝑙𝑟+2	𝑙𝑟+2	NUM
cana-1007	83	7	,	,	PUNCT
cana-1007	83	8	𝑙𝑟+3	𝑙𝑟+3	NUM
cana-1007	83	9	,	,	PUNCT
cana-1007	83	10	𝑙𝑟+4	𝑙𝑟+4	NOUN
cana-1007	83	11	,	,	PUNCT
cana-1007	83	12	𝑙𝑟+5	𝑙𝑟+5	X
cana-1007	83	13	,	,	PUNCT
cana-1007	83	14	1	1	NUM
cana-1007	83	15	≤	≤	NUM
cana-1007	83	16	𝑖	𝑖	SYM
cana-1007	83	17	≤	≤	NOUN
cana-1007	83	18	𝑟	𝑟	NOUN
cana-1007	83	19	be	be	AUX
cana-1007	83	20	the	the	DET
cana-1007	83	21	edges	edge	NOUN
cana-1007	83	22	of	of	ADP
cana-1007	83	23	g	g	PROPN
cana-1007	83	24	and	and	CCONJ
cana-1007	83	25	(	(	PUNCT
cana-1007	83	26	𝑆5	𝑆5	PROPN
cana-1007	83	27	)	)	PUNCT
cana-1007	83	28	.	.	PUNCT
cana-1007	84	1	then	then	ADV
cana-1007	84	2	|𝐷(𝐺𝑥(𝑆5))|	|𝐷(𝐺𝑥(𝑆5))|	VERB
cana-1007	84	3	=	=	PUNCT
cana-1007	84	4	𝑞	𝑞	X
cana-1007	84	5	+	+	CCONJ
cana-1007	84	6	5	5	NUM
cana-1007	84	7	and	and	CCONJ
cana-1007	84	8	|𝐿(𝐺𝑢(𝑆5))|	|𝐿(𝐺𝑢(𝑆5))|	NOUN
cana-1007	84	9	=	=	PUNCT
cana-1007	84	10	𝑟	𝑟	NOUN
cana-1007	84	11	+	+	SYM
cana-1007	84	12	5	5	NUM
cana-1007	84	13	,	,	PUNCT
cana-1007	84	14	and	and	CCONJ
cana-1007	84	15	defined	define	VERB
cana-1007	84	16	a	a	DET
cana-1007	84	17	bijective	bijective	ADJ
cana-1007	84	18	mapping	mapping	NOUN
cana-1007	84	19	,	,	PUNCT
cana-1007	84	20	𝑔	𝑔	NOUN
cana-1007	84	21	:	:	PUNCT
cana-1007	84	22	𝑣𝑒𝑟𝑡𝑒𝑥(𝐺′	𝑣𝑒𝑟𝑡𝑒𝑥(𝐺′	ADJ
cana-1007	84	23	)	)	PUNCT
cana-1007	84	24	∪	∪	NOUN
cana-1007	84	25	𝐿(𝐺′	𝐿(𝐺′	NOUN
cana-1007	84	26	)	)	PUNCT
cana-1007	84	27	}	}	PUNCT
cana-1007	84	28	→	→	SYM
cana-1007	84	29	{	{	PUNCT
cana-1007	84	30	𝑜𝑛𝑒	𝑜𝑛𝑒	PROPN
cana-1007	84	31	,	,	PUNCT
cana-1007	84	32	𝑡𝑤𝑜	𝑡𝑤𝑜	PROPN
cana-1007	84	33	,	,	PUNCT
cana-1007	84	34	𝑡ℎ𝑟𝑒𝑒	𝑡ℎ𝑟𝑒𝑒	ADJ
cana-1007	84	35	,	,	PUNCT
cana-1007	84	36	⋯	⋯	NOUN
cana-1007	84	37	,	,	PUNCT
cana-1007	84	38	𝑛𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑒𝑑𝑔𝑒𝑠	𝑛𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑒𝑑𝑔𝑒𝑠	NOUN
cana-1007	84	39	+	+	CCONJ
cana-1007	84	40	𝑟	𝑟	NOUN
cana-1007	84	41	+	+	CCONJ
cana-1007	84	42	𝑡𝑒𝑛	𝑡𝑒𝑛	ADJ
cana-1007	84	43	}	}	PUNCT
cana-1007	84	44	it	it	PRON
cana-1007	84	45	describes	describe	VERB
cana-1007	84	46	satl	satl	NOUN
cana-1007	84	47	of	of	ADP
cana-1007	84	48	𝐺′.	𝐺′.	NOUN
cana-1007	84	49	numbering	number	VERB
cana-1007	84	50	the	the	DET
cana-1007	84	51	graph	graph	NOUN
cana-1007	84	52	g	g	NOUN
cana-1007	84	53	with	with	ADP
cana-1007	84	54	𝑑𝑖	𝑑𝑖	PROPN
cana-1007	84	55	,	,	PUNCT
cana-1007	84	56	𝑜𝑛𝑒	𝑜𝑛𝑒	ADJ
cana-1007	84	57	≤	≤	PROPN
cana-1007	84	58	𝑖	𝑖	SYM
cana-1007	84	59	≤	≤	NOUN
cana-1007	84	60	𝑞	𝑞	X
cana-1007	84	61	with	with	ADP
cana-1007	84	62	the	the	DET
cana-1007	84	63	labels	label	NOUN
cana-1007	84	64	of	of	ADP
cana-1007	84	65	a	a	PRON
cana-1007	84	66	with	with	ADP
cana-1007	84	67	the	the	DET
cana-1007	84	68	numbers	number	NOUN
cana-1007	84	69	𝑜𝑛𝑒𝑖	𝑜𝑛𝑒𝑖	VERB
cana-1007	84	70	,	,	PUNCT
cana-1007	84	71	1	1	NUM
cana-1007	84	72	≤	≤	NUM
cana-1007	84	73	𝑖	𝑖	SYM
cana-1007	84	74	≤	≤	NOUN
cana-1007	84	75	𝑟	𝑟	NOUN
cana-1007	84	76	and	and	CCONJ
cana-1007	84	77	labels	label	NOUN
cana-1007	84	78	of	of	ADP
cana-1007	84	79	b	b	NOUN
cana-1007	84	80	,	,	PUNCT
cana-1007	84	81	𝐴	𝐴	PROPN
cana-1007	84	82	=	=	PUNCT
cana-1007	85	1	[	[	X
cana-1007	85	2	𝑞	𝑞	X
cana-1007	85	3	+	+	NOUN
cana-1007	85	4	1	1	NUM
cana-1007	85	5	]	]	PUNCT
cana-1007	85	6	−	−	ADP
cana-1007	85	7	𝑞	𝑞	X
cana-1007	85	8	−	−	PROPN
cana-1007	85	9	1	1	NUM
cana-1007	85	10	,	,	PUNCT
cana-1007	85	11	4	4	NUM
cana-1007	85	12	≤	≤	NUM
cana-1007	85	13	𝑖	𝑖	SYM
cana-1007	85	14	≤	≤	NOUN
cana-1007	85	15	𝑞	𝑞	X
cana-1007	85	16	and	and	CCONJ
cana-1007	85	17	𝐵	𝐵	NOUN
cana-1007	85	18	=	=	PUNCT
cana-1007	85	19	𝑞	𝑞	PROPN
cana-1007	85	20	+	+	NOUN
cana-1007	85	21	6	6	NUM
cana-1007	85	22	,	,	PUNCT
cana-1007	85	23	𝑞	𝑞	X
cana-1007	85	24	+	+	NOUN
cana-1007	85	25	7	7	NUM
cana-1007	85	26	,	,	PUNCT
cana-1007	85	27	.	.	PUNCT
cana-1007	85	28	.	.	PUNCT
cana-1007	86	1	.	.	PUNCT
cana-1007	87	1	,	,	PUNCT
cana-1007	87	2	𝑞	𝑞	PROPN
cana-1007	87	3	+	+	NOUN
cana-1007	87	4	𝑟	𝑟	NOUN
cana-1007	88	1	+	+	CCONJ
cana-1007	88	2	9	9	NUM
cana-1007	88	3	−	−	NOUN
cana-1007	88	4	𝑞	𝑞	NOUN
cana-1007	88	5	+	+	NOUN
cana-1007	88	6	𝑟	𝑟	NOUN
cana-1007	88	7	+	+	CCONJ
cana-1007	88	8	16	16	NUM
cana-1007	88	9	−	−	NOUN
cana-1007	88	10	4𝑖	4𝑖	NOUN
cana-1007	88	11	,	,	PUNCT
cana-1007	88	12	𝑞	𝑞	X
cana-1007	88	13	+	+	NOUN
cana-1007	88	14	𝑟	𝑟	NOUN
cana-1007	88	15	+	+	CCONJ
cana-1007	88	16	13	13	NUM
cana-1007	88	17	−	−	PROPN
cana-1007	88	18	3𝑖	3𝑖	NOUN
cana-1007	88	19	,	,	PUNCT
cana-1007	88	20	𝑞	𝑞	X
cana-1007	88	21	+	+	NOUN
cana-1007	88	22	𝑟	𝑟	NOUN
cana-1007	88	23	+	+	CCONJ
cana-1007	88	24	12	12	NUM
cana-1007	88	25	−	−	NOUN
cana-1007	88	26	2𝑖	2𝑖	NOUN
cana-1007	88	27	,	,	PUNCT
cana-1007	88	28	𝑞	𝑞	X
cana-1007	88	29	+	+	NOUN
cana-1007	88	30	𝑟	𝑟	NOUN
cana-1007	88	31	+	+	CCONJ
cana-1007	88	32	11	11	NUM
cana-1007	88	33	−	−	NOUN
cana-1007	88	34	𝑖	𝑖	NOUN
cana-1007	88	35	,	,	PUNCT
cana-1007	88	36	4	4	NUM
cana-1007	88	37	≤	≤	NUM
cana-1007	88	38	𝑖	𝑖	SYM
cana-1007	88	39	≤	≤	ADJ
cana-1007	88	40	𝑞.	𝑞.	ADJ
cana-1007	88	41	communications	communication	NOUN
cana-1007	88	42	on	on	ADP
cana-1007	88	43	applied	apply	VERB
cana-1007	88	44	nonlinear	nonlinear	ADJ
cana-1007	88	45	analysis	analysis	NOUN
cana-1007	88	46	issn	issn	NOUN
cana-1007	88	47	:	:	PUNCT
cana-1007	88	48	1074	1074	NUM
cana-1007	88	49	-	-	PUNCT
cana-1007	88	50	133x	133x	NUM
cana-1007	88	51	vol	vol	NOUN
cana-1007	88	52	31	31	NUM
cana-1007	88	53	no	no	NOUN
cana-1007	88	54	.	.	PUNCT
cana-1007	89	1	5s	5s	NUM
cana-1007	89	2	(	(	PUNCT
cana-1007	89	3	2024	2024	NUM
cana-1007	89	4	)	)	PUNCT
cana-1007	89	5	133	133	NUM
cana-1007	89	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1007	89	7	the	the	DET
cana-1007	89	8	graph	graph	NOUN
cana-1007	89	9	and	and	CCONJ
cana-1007	89	10	subgraphs	subgraph	NOUN
cana-1007	89	11	having	have	VERB
cana-1007	89	12	the	the	DET
cana-1007	89	13	equal	equal	ADJ
cana-1007	89	14	weight	weight	NOUN
cana-1007	89	15	(	(	PUNCT
cana-1007	89	16	𝐺	𝐺	NOUN
cana-1007	89	17	+	+	CCONJ
cana-1007	89	18	𝑙𝑖	𝑙𝑖	NOUN
cana-1007	89	19	)	)	PUNCT
cana-1007	89	20	,	,	PUNCT
cana-1007	89	21	i=1,2,3,4,5	i=1,2,3,4,5	NOUN
cana-1007	89	22	.	.	PUNCT
cana-1007	90	1	it	it	PRON
cana-1007	90	2	is	be	AUX
cana-1007	90	3	possible	possible	ADJ
cana-1007	90	4	to	to	PART
cana-1007	90	5	find	find	VERB
cana-1007	90	6	the	the	DET
cana-1007	90	7	labels	label	NOUN
cana-1007	90	8	of	of	ADP
cana-1007	90	9	the	the	DET
cana-1007	90	10	graph	graph	NOUN
cana-1007	90	11	𝑆5	𝑆5	PROPN
cana-1007	90	12	,	,	PUNCT
cana-1007	90	13	every	every	DET
cana-1007	90	14	i	i	NOUN
cana-1007	90	15	4	4	NUM
cana-1007	90	16	≤	≤	NUM
cana-1007	90	17	𝑖	𝑖	PUNCT
cana-1007	90	18	≤	≤	NOUN
cana-1007	90	19	𝑞	𝑞	X
cana-1007	90	20	,	,	PUNCT
cana-1007	90	21	we	we	PRON
cana-1007	90	22	express	express	VERB
cana-1007	90	23	the	the	DET
cana-1007	90	24	label	label	NOUN
cana-1007	90	25	𝑔𝑖	𝑔𝑖	NOUN
cana-1007	90	26	:	:	PUNCT
cana-1007	90	27	𝑔𝑖(𝑤1	𝑔𝑖(𝑤1	ADJ
cana-1007	90	28	)	)	PUNCT
cana-1007	90	29	=	=	SYM
cana-1007	91	1	𝑞	𝑞	PROPN
cana-1007	91	2	−	−	PROPN
cana-1007	91	3	𝑜𝑛𝑒	𝑜𝑛𝑒	PROPN
cana-1007	91	4	,	,	PUNCT
cana-1007	91	5	𝑔𝑖(𝑒𝑞+1	𝑔𝑖(𝑒𝑞+1	PROPN
cana-1007	91	6	)	)	PUNCT
cana-1007	91	7	=	=	SYM
cana-1007	92	1	𝑞	𝑞	PROPN
cana-1007	92	2	+	+	NOUN
cana-1007	92	3	𝑟	𝑟	NOUN
cana-1007	93	1	+	+	CCONJ
cana-1007	93	2	16	16	NUM
cana-1007	93	3	−	−	NOUN
cana-1007	93	4	4𝑖	4𝑖	NOUN
cana-1007	93	5	,	,	PUNCT
cana-1007	93	6	4	4	NUM
cana-1007	93	7	≤	≤	NUM
cana-1007	93	8	𝑖	𝑖	SYM
cana-1007	93	9	≤	≤	PROPN
cana-1007	93	10	𝑝	𝑝	PROPN
cana-1007	93	11	+	+	NUM
cana-1007	93	12	𝑞	𝑞	X
cana-1007	93	13	−	−	PROPN
cana-1007	93	14	[	[	PUNCT
cana-1007	93	15	𝑘(𝑘+1	𝑘(𝑘+1	NOUN
cana-1007	93	16	)	)	PUNCT
cana-1007	93	17	2	2	NUM
cana-1007	93	18	]	]	PUNCT
cana-1007	93	19	,	,	PUNCT
cana-1007	93	20	𝑔𝑖(𝑤2	𝑔𝑖(𝑤2	NOUN
cana-1007	93	21	)	)	PUNCT
cana-1007	93	22	=	=	PUNCT
cana-1007	94	1	𝑞	𝑞	X
cana-1007	94	2	+	+	ADJ
cana-1007	94	3	2	2	NUM
cana-1007	94	4	,	,	PUNCT
cana-1007	94	5	𝑔𝑖(𝑒𝑞+2	𝑔𝑖(𝑒𝑞+2	ADJ
cana-1007	94	6	)	)	PUNCT
cana-1007	94	7	=	=	PUNCT
cana-1007	94	8	𝑞	𝑞	PART
cana-1007	94	9	+	+	NOUN
cana-1007	94	10	𝑟	𝑟	NOUN
cana-1007	94	11	+	+	CCONJ
cana-1007	94	12	13	13	NUM
cana-1007	94	13	−	−	PROPN
cana-1007	94	14	3𝑖	3𝑖	NUM
cana-1007	94	15	𝑔𝑖(𝑤3	𝑔𝑖(𝑤3	ADJ
cana-1007	94	16	)	)	PUNCT
cana-1007	94	17	=	=	PUNCT
cana-1007	95	1	𝑞	𝑞	X
cana-1007	95	2	+	+	ADJ
cana-1007	95	3	3	3	NUM
cana-1007	95	4	,	,	PUNCT
cana-1007	95	5	𝑔𝑖(𝑒𝑞+3	𝑔𝑖(𝑒𝑞+3	ADJ
cana-1007	95	6	)	)	PUNCT
cana-1007	95	7	=	=	PUNCT
cana-1007	96	1	𝑞	𝑞	PROPN
cana-1007	96	2	+	+	NOUN
cana-1007	96	3	𝑟	𝑟	NOUN
cana-1007	96	4	+	+	CCONJ
cana-1007	96	5	12	12	NUM
cana-1007	96	6	−	−	PROPN
cana-1007	96	7	2𝑖	2𝑖	NOUN
cana-1007	96	8	𝑔𝑖(𝑤4	𝑔𝑖(𝑤4	NOUN
cana-1007	96	9	)	)	PUNCT
cana-1007	96	10	=	=	PUNCT
cana-1007	96	11	𝑞	𝑞	X
cana-1007	96	12	+	+	ADJ
cana-1007	96	13	4	4	NUM
cana-1007	96	14	,	,	PUNCT
cana-1007	96	15	𝑔𝑖(𝑒𝑞+4	𝑔𝑖(𝑒𝑞+4	NOUN
cana-1007	96	16	)	)	PUNCT
cana-1007	96	17	=	=	SYM
cana-1007	97	1	𝑞	𝑞	PROPN
cana-1007	97	2	+	+	NOUN
cana-1007	97	3	𝑟	𝑟	NOUN
cana-1007	97	4	+	+	CCONJ
cana-1007	97	5	11	11	NUM
cana-1007	97	6	−	−	NOUN
cana-1007	97	7	𝑖	𝑖	SYM
cana-1007	97	8	𝑔𝑖(𝑤5	𝑔𝑖(𝑤5	NUM
cana-1007	97	9	)	)	PUNCT
cana-1007	97	10	=	=	PUNCT
cana-1007	98	1	𝑞	𝑞	X
cana-1007	98	2	+	+	ADJ
cana-1007	98	3	5	5	NUM
cana-1007	98	4	,	,	PUNCT
cana-1007	98	5	𝑔𝑖(𝑒𝑞+5	𝑔𝑖(𝑒𝑞+5	ADJ
cana-1007	98	6	)	)	PUNCT
cana-1007	98	7	=	=	PUNCT
cana-1007	98	8	𝑞	𝑞	PROPN
cana-1007	98	9	+	+	NOUN
cana-1007	98	10	𝑟	𝑟	NOUN
cana-1007	98	11	+	+	CCONJ
cana-1007	98	12	10	10	NUM
cana-1007	98	13	therefore	therefore	ADV
cana-1007	98	14	the	the	DET
cana-1007	98	15	labels	label	NOUN
cana-1007	98	16	of	of	ADP
cana-1007	98	17	𝑆5	𝑆5	PROPN
cana-1007	98	18	are	be	AUX
cana-1007	98	19	2q+r+15	2q+r+15	NUM
cana-1007	98	20	-	-	PUNCT
cana-1007	98	21	4i	4i	NUM
cana-1007	98	22	,	,	PUNCT
cana-1007	98	23	2q+r+15	2q+r+15	NUM
cana-1007	98	24	-	-	SYM
cana-1007	98	25	3i,2q+r+15	3i,2q+r+15	NUM
cana-1007	98	26	-	-	PUNCT
cana-1007	98	27	2i,2q+r+15	2i,2q+r+15	NUM
cana-1007	98	28	-	-	PUNCT
cana-1007	98	29	i	i	PROPN
cana-1007	98	30	and	and	CCONJ
cana-1007	98	31	2q+r+15	2q+r+15	NOUN
cana-1007	98	32	.	.	PUNCT
cana-1007	99	1	hence	hence	ADV
cana-1007	99	2	,	,	PUNCT
cana-1007	99	3	𝑑	𝑑	PROPN
cana-1007	99	4	=	=	SYM
cana-1007	99	5	𝑖	𝑖	PROPN
cana-1007	99	6	,	,	PUNCT
cana-1007	99	7	4	4	NUM
cana-1007	99	8	≤	≤	NUM
cana-1007	99	9	𝑖	𝑖	PRON
cana-1007	99	10	≤	≤	NUM
cana-1007	99	11	𝑞.	𝑞.	NOUN
cana-1007	99	12	theorem	theorem	VERB
cana-1007	99	13	2.4	2.4	NUM
cana-1007	99	14	𝐺𝑢(𝑆𝑚	𝐺𝑢(𝑆𝑚	NOUN
cana-1007	99	15	)	)	PUNCT
cana-1007	99	16	where	where	SCONJ
cana-1007	99	17	𝑛	𝑛	DET
cana-1007	99	18	≥	≥	NUM
cana-1007	99	19	6	6	NUM
cana-1007	99	20	generates	generate	VERB
cana-1007	99	21	a	a	DET
cana-1007	99	22	satl	satl	NOUN
cana-1007	99	23	for	for	ADP
cana-1007	99	24	all	all	DET
cana-1007	99	25	e	e	NOUN
cana-1007	99	26	=	=	NOUN
cana-1007	99	27	i	i	PROPN
cana-1007	99	28	,	,	PUNCT
cana-1007	99	29	4	4	NUM
cana-1007	99	30	≤	≤	NUM
cana-1007	99	31	𝑖	𝑖	PUNCT
cana-1007	99	32	≤	≤	NOUN
cana-1007	99	33	𝑞	𝑞	X
cana-1007	99	34	−	−	PROPN
cana-1007	99	35	𝑚	𝑚	PROPN
cana-1007	99	36	+	+	PROPN
cana-1007	99	37	5	5	NUM
cana-1007	99	38	,	,	PUNCT
cana-1007	99	39	where	where	SCONJ
cana-1007	99	40	𝑞	𝑞	X
cana-1007	99	41	≥	≥	X
cana-1007	99	42	𝑚	𝑚	ADP
cana-1007	99	43	−	−	PROPN
cana-1007	99	44	1	1	NUM
cana-1007	99	45	.	.	PUNCT
cana-1007	100	1	proof	proof	NOUN
cana-1007	100	2	.	.	PUNCT
cana-1007	101	1	let	let	VERB
cana-1007	101	2	𝐺′	𝐺′	PUNCT
cana-1007	101	3	isomorphic	isomorphic	VERB
cana-1007	101	4	to	to	ADP
cana-1007	101	5	𝐺𝑢(𝑆𝑚	𝐺𝑢(𝑆𝑚	PRON
cana-1007	101	6	)	)	PUNCT
cana-1007	101	7	.	.	PUNCT
cana-1007	102	1	let	let	VERB
cana-1007	102	2	𝑑1	𝑑1	NOUN
cana-1007	102	3	,	,	PUNCT
cana-1007	102	4	𝑑2	𝑑2	NOUN
cana-1007	102	5	,	,	PUNCT
cana-1007	102	6	𝑑3	𝑑3	NOUN
cana-1007	102	7	,	,	PUNCT
cana-1007	102	8	.	.	PUNCT
cana-1007	102	9	.	.	PUNCT
cana-1007	103	1	.	.	PUNCT
cana-1007	104	1	,	,	PUNCT
cana-1007	104	2	𝑑𝑞	𝑑𝑞	PROPN
cana-1007	104	3	correspondingly	correspondingly	ADV
cana-1007	104	4	𝑤1	𝑤1	VERB
cana-1007	104	5	,	,	PUNCT
cana-1007	104	6	𝑤2	𝑤2	NOUN
cana-1007	104	7	,	,	PUNCT
cana-1007	104	8	𝑤3	𝑤3	PROPN
cana-1007	104	9	,	,	PUNCT
cana-1007	104	10	.	.	PUNCT
cana-1007	104	11	.	.	PUNCT
cana-1007	105	1	.	.	PUNCT
cana-1007	106	1	,	,	PUNCT
cana-1007	106	2	𝑤𝑚	𝑤𝑚	PRON
cana-1007	106	3	be	be	VERB
cana-1007	106	4	the	the	DET
cana-1007	106	5	vertices	vertex	NOUN
cana-1007	106	6	of	of	ADP
cana-1007	106	7	g	g	PROPN
cana-1007	106	8	and	and	CCONJ
cana-1007	106	9	(	(	PUNCT
cana-1007	106	10	𝑆𝑚	𝑆𝑚	PROPN
cana-1007	106	11	)	)	PUNCT
cana-1007	106	12	.	.	PUNCT
cana-1007	107	1	let	let	VERB
cana-1007	107	2	𝑙1	𝑙1	PROPN
cana-1007	107	3	,	,	PUNCT
cana-1007	107	4	𝑙2	𝑙2	PROPN
cana-1007	107	5	,	,	PUNCT
cana-1007	107	6	𝑙3	𝑙3	VERB
cana-1007	107	7	,	,	PUNCT
cana-1007	107	8	.	.	PUNCT
cana-1007	107	9	.	.	PUNCT
cana-1007	108	1	.	.	PUNCT
cana-1007	109	1	,	,	PUNCT
cana-1007	109	2	𝑙𝑟	𝑙𝑟	ADV
cana-1007	109	3	and	and	CCONJ
cana-1007	109	4	𝑙𝑟+1	𝑙𝑟+1	NUM
cana-1007	109	5	,	,	PUNCT
cana-1007	109	6	𝑙𝑟+2	𝑙𝑟+2	NUM
cana-1007	109	7	,	,	PUNCT
cana-1007	109	8	𝑙𝑟+3	𝑙𝑟+3	NUM
cana-1007	109	9	,	,	PUNCT
cana-1007	109	10	.	.	PUNCT
cana-1007	109	11	.	.	PUNCT
cana-1007	110	1	.	.	PUNCT
cana-1007	111	1	,	,	PUNCT
cana-1007	111	2	𝑙𝑟+𝑛	𝑙𝑟+𝑛	PROPN
cana-1007	111	3	be	be	AUX
cana-1007	111	4	the	the	DET
cana-1007	111	5	adjacents	adjacent	NOUN
cana-1007	111	6	of	of	ADP
cana-1007	111	7	g	g	PROPN
cana-1007	111	8	and	and	CCONJ
cana-1007	111	9	(	(	PUNCT
cana-1007	111	10	𝑆𝑚	𝑆𝑚	PROPN
cana-1007	111	11	)	)	PUNCT
cana-1007	111	12	.	.	PUNCT
cana-1007	112	1	then	then	ADV
cana-1007	112	2	|𝐷(𝐺𝑥(𝑆𝑚))|	|𝐷(𝐺𝑥(𝑆𝑚))|	ADV
cana-1007	112	3	=	=	PUNCT
cana-1007	112	4	𝑞	𝑞	X
cana-1007	112	5	+	+	X
cana-1007	112	6	𝑚	𝑚	PROPN
cana-1007	112	7	and	and	CCONJ
cana-1007	112	8	|𝐿(𝐺𝑥(𝑆𝑚))|	|𝐿(𝐺𝑥(𝑆𝑚))|	NOUN
cana-1007	112	9	=	=	SYM
cana-1007	112	10	𝑟	𝑟	NOUN
cana-1007	112	11	+	+	CCONJ
cana-1007	112	12	𝑚.	𝑚.	NOUN
cana-1007	112	13	suppose	suppose	VERB
cana-1007	112	14	the	the	DET
cana-1007	112	15	mapping	mapping	NOUN
cana-1007	112	16	is	be	AUX
cana-1007	112	17	arises	arise	NOUN
cana-1007	112	18	which	which	PRON
cana-1007	112	19	is	be	AUX
cana-1007	112	20	a	a	DET
cana-1007	112	21	bijective	bijective	ADJ
cana-1007	112	22	,	,	PUNCT
cana-1007	112	23	𝑔	𝑔	NOUN
cana-1007	112	24	:	:	PUNCT
cana-1007	112	25	(	(	PUNCT
cana-1007	112	26	𝑠𝑢𝑚	𝑠𝑢𝑚	NOUN
cana-1007	112	27	𝑜𝑓	𝑜𝑓	INTJ
cana-1007	112	28	𝑣𝑒𝑟𝑡𝑖𝑐𝑒𝑠	𝑣𝑒𝑟𝑡𝑖𝑐𝑒𝑠	PROPN
cana-1007	112	29	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-1007	112	30	𝑒𝑑𝑔𝑒𝑠	𝑒𝑑𝑔𝑒𝑠	NOUN
cana-1007	112	31	)	)	PUNCT
cana-1007	112	32	→	→	SYM
cana-1007	112	33	{	{	PUNCT
cana-1007	112	34	𝑜𝑛𝑒	𝑜𝑛𝑒	PROPN
cana-1007	112	35	,	,	PUNCT
cana-1007	112	36	𝑡𝑤𝑜	𝑡𝑤𝑜	PROPN
cana-1007	112	37	,	,	PUNCT
cana-1007	112	38	𝑡ℎ𝑟𝑒𝑒	𝑡ℎ𝑟𝑒𝑒	ADJ
cana-1007	112	39	,	,	PUNCT
cana-1007	112	40	⋯	⋯	PROPN
cana-1007	112	41	,	,	PUNCT
cana-1007	112	42	𝑞	𝑞	X
cana-1007	112	43	+	+	NOUN
cana-1007	112	44	𝑟	𝑟	NOUN
cana-1007	112	45	+	+	SYM
cana-1007	112	46	2(𝑚	2(𝑚	NUM
cana-1007	112	47	)	)	PUNCT
cana-1007	112	48	}	}	PUNCT
cana-1007	112	49	which	which	PRON
cana-1007	112	50	is	be	AUX
cana-1007	112	51	a	a	DET
cana-1007	112	52	satl	satl	NOUN
cana-1007	112	53	of	of	ADP
cana-1007	112	54	𝐺′.	𝐺′.	NOUN
cana-1007	112	55	numbering	number	VERB
cana-1007	112	56	the	the	DET
cana-1007	112	57	vertices	vertex	NOUN
cana-1007	112	58	𝑑𝑖	𝑑𝑖	PART
cana-1007	112	59	,	,	PUNCT
cana-1007	112	60	𝑜𝑛𝑒	𝑜𝑛𝑒	ADJ
cana-1007	112	61	≤	≤	PROPN
cana-1007	112	62	𝑖	𝑖	SYM
cana-1007	112	63	≤	≤	NOUN
cana-1007	112	64	𝑞	𝑞	X
cana-1007	112	65	with	with	ADP
cana-1007	112	66	the	the	DET
cana-1007	112	67	numbers	number	NOUN
cana-1007	112	68	of	of	ADP
cana-1007	112	69	a	a	PRON
cana-1007	112	70	and	and	CCONJ
cana-1007	112	71	number	number	NOUN
cana-1007	112	72	the	the	DET
cana-1007	112	73	edges	edge	NOUN
cana-1007	112	74	𝑙𝑖	𝑙𝑖	NOUN
cana-1007	112	75	,	,	PUNCT
cana-1007	112	76	1	1	NUM
cana-1007	112	77	≤	≤	NUM
cana-1007	112	78	𝑖	𝑖	SYM
cana-1007	112	79	≤	≤	NUM
cana-1007	112	80	𝑟	𝑟	NOUN
cana-1007	112	81	from	from	ADP
cana-1007	112	82	numbers	number	NOUN
cana-1007	112	83	in	in	ADP
cana-1007	112	84	b	b	NOUN
cana-1007	112	85	,	,	PUNCT
cana-1007	112	86	where	where	SCONJ
cana-1007	112	87	𝐴	𝐴	PROPN
cana-1007	112	88	=	=	PUNCT
cana-1007	113	1	[	[	X
cana-1007	113	2	𝑞	𝑞	X
cana-1007	113	3	+	+	X
cana-1007	113	4	𝑚	𝑚	X
cana-1007	113	5	]	]	X
cana-1007	113	6	−	−	NOUN
cana-1007	113	7	𝑞	𝑞	X
cana-1007	113	8	+	+	CCONJ
cana-1007	113	9	𝑚	𝑚	PROPN
cana-1007	113	10	,	,	PUNCT
cana-1007	113	11	𝑞	𝑞	X
cana-1007	113	12	+	+	NOUN
cana-1007	113	13	𝑚	𝑚	ADP
cana-1007	113	14	−	−	PROPN
cana-1007	113	15	1	1	NUM
cana-1007	113	16	,	,	PUNCT
cana-1007	113	17	𝑞	𝑞	X
cana-1007	113	18	+	+	X
cana-1007	113	19	𝑚	𝑚	PROPN
cana-1007	113	20	−	−	PROPN
cana-1007	113	21	2	2	NUM
cana-1007	113	22	,	,	PUNCT
cana-1007	113	23	𝑞	𝑞	X
cana-1007	113	24	+	+	X
cana-1007	113	25	𝑚	𝑚	PROPN
cana-1007	113	26	−	−	PROPN
cana-1007	113	27	3	3	NUM
cana-1007	113	28	,	,	PUNCT
cana-1007	113	29	.	.	PUNCT
cana-1007	113	30	.	.	PUNCT
cana-1007	113	31	.	.	PUNCT
cana-1007	114	1	,	,	PUNCT
cana-1007	114	2	𝑞	𝑞	PROPN
cana-1007	114	3	+	+	CCONJ
cana-1007	114	4	1	1	NUM
cana-1007	114	5	and	and	CCONJ
cana-1007	114	6	𝐵	𝐵	NOUN
cana-1007	114	7	=	=	PUNCT
cana-1007	115	1	[	[	X
cana-1007	115	2	𝑞	𝑞	X
cana-1007	115	3	+	+	NOUN
cana-1007	115	4	𝑟	𝑟	NOUN
cana-1007	115	5	+	+	CCONJ
cana-1007	115	6	2𝑚	2𝑚	NOUN
cana-1007	115	7	]	]	PUNCT
cana-1007	115	8	−	−	PUNCT
cana-1007	115	9	𝑞	𝑞	X
cana-1007	115	10	+	+	NOUN
cana-1007	115	11	𝑟	𝑟	NOUN
cana-1007	115	12	+	+	CCONJ
cana-1007	115	13	2𝑚	2𝑚	NOUN
cana-1007	115	14	,	,	PUNCT
cana-1007	115	15	𝑞	𝑞	X
cana-1007	115	16	+	+	NOUN
cana-1007	115	17	𝑟	𝑟	NOUN
cana-1007	116	1	+	+	CCONJ
cana-1007	116	2	2𝑚	2𝑚	NUM
cana-1007	116	3	+	+	CCONJ
cana-1007	116	4	4	4	NUM
cana-1007	116	5	−	−	NOUN
cana-1007	116	6	4𝑖	4𝑖	NOUN
cana-1007	116	7	,	,	PUNCT
cana-1007	116	8	.	.	PUNCT
cana-1007	116	9	.	.	PUNCT
cana-1007	117	1	.	.	PUNCT
cana-1007	118	1	,	,	PUNCT
cana-1007	118	2	𝑞	𝑞	PROPN
cana-1007	118	3	+	+	NOUN
cana-1007	118	4	𝑟	𝑟	NOUN
cana-1007	119	1	+	+	CCONJ
cana-1007	119	2	𝑚	𝑚	ADP
cana-1007	119	3	−	−	PROPN
cana-1007	119	4	𝑚𝑖.	𝑚𝑖.	PRON
cana-1007	119	5	by	by	ADP
cana-1007	119	6	the	the	DET
cana-1007	119	7	above	above	ADJ
cana-1007	119	8	theorems	theorem	NOUN
cana-1007	119	9	we	we	PRON
cana-1007	119	10	have	have	VERB
cana-1007	119	11	n=3,4,5	n=3,4,5	NOUN
cana-1007	119	12	.	.	PUNCT
cana-1007	120	1	the	the	DET
cana-1007	120	2	graph	graph	NOUN
cana-1007	120	3	g	g	NOUN
cana-1007	120	4	and	and	CCONJ
cana-1007	120	5	the	the	DET
cana-1007	120	6	subgraphs	subgraph	NOUN
cana-1007	120	7	(	(	PUNCT
cana-1007	120	8	𝐺	𝐺	NOUN
cana-1007	120	9	+	+	CCONJ
cana-1007	120	10	𝑒𝑖	𝑒𝑖	NOUN
cana-1007	120	11	)	)	PUNCT
cana-1007	120	12	,	,	PUNCT
cana-1007	120	13	i=1,2,3,	i=1,2,3,	NOUN
cana-1007	120	14	...	...	PUNCT
cana-1007	120	15	,m	,m	PUNCT
cana-1007	120	16	,	,	PUNCT
cana-1007	120	17	having	have	VERB
cana-1007	120	18	the	the	DET
cana-1007	120	19	same	same	ADJ
cana-1007	120	20	weight	weight	NOUN
cana-1007	120	21	and	and	CCONJ
cana-1007	120	22	hence	hence	ADV
cana-1007	120	23	it	it	PRON
cana-1007	120	24	is	be	AUX
cana-1007	120	25	possible	possible	ADJ
cana-1007	120	26	to	to	PART
cana-1007	120	27	prove	prove	VERB
cana-1007	120	28	the	the	DET
cana-1007	120	29	numbers	number	NOUN
cana-1007	120	30	of	of	ADP
cana-1007	120	31	the	the	DET
cana-1007	120	32	star	star	NOUN
cana-1007	120	33	𝑆𝑚	𝑆𝑚	PROPN
cana-1007	120	34	,	,	PUNCT
cana-1007	120	35	for	for	ADP
cana-1007	120	36	all	all	PRON
cana-1007	120	37	i	i	PRON
cana-1007	120	38	there	there	PRON
cana-1007	120	39	is	be	VERB
cana-1007	120	40	a	a	DET
cana-1007	120	41	fnction	fnction	NOUN
cana-1007	120	42	𝑔𝑖	𝑔𝑖	NOUN
cana-1007	120	43	:	:	PUNCT
cana-1007	120	44	𝑔𝑖(𝑤1	𝑔𝑖(𝑤1	ADJ
cana-1007	120	45	)	)	PUNCT
cana-1007	120	46	=	=	SYM
cana-1007	120	47	𝑞	𝑞	X
cana-1007	120	48	+	+	ADJ
cana-1007	120	49	1	1	NUM
cana-1007	120	50	,	,	PUNCT
cana-1007	120	51	communications	communication	NOUN
cana-1007	120	52	on	on	ADP
cana-1007	120	53	applied	apply	VERB
cana-1007	120	54	nonlinear	nonlinear	ADJ
cana-1007	120	55	analysis	analysis	NOUN
cana-1007	120	56	issn	issn	NOUN
cana-1007	120	57	:	:	PUNCT
cana-1007	120	58	1074	1074	NUM
cana-1007	120	59	-	-	PUNCT
cana-1007	120	60	133x	133x	NUM
cana-1007	120	61	vol	vol	NOUN
cana-1007	120	62	31	31	NUM
cana-1007	120	63	no	no	NOUN
cana-1007	120	64	.	.	PUNCT
cana-1007	121	1	5s	5s	NUM
cana-1007	121	2	(	(	PUNCT
cana-1007	121	3	2024	2024	NUM
cana-1007	121	4	)	)	PUNCT
cana-1007	121	5	134	134	NUM
cana-1007	121	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1007	121	7	𝑔𝑖(𝑙𝑟+1	𝑔𝑖(𝑙𝑟+1	NOUN
cana-1007	121	8	)	)	PUNCT
cana-1007	121	9	=	=	SYM
cana-1007	122	1	𝑞	𝑞	PROPN
cana-1007	122	2	+	+	NOUN
cana-1007	122	3	𝑟	𝑟	NOUN
cana-1007	123	1	+	+	CCONJ
cana-1007	123	2	𝑚	𝑚	ADP
cana-1007	123	3	−	−	NUM
cana-1007	123	4	𝑚𝑖	𝑚𝑖	NOUN
cana-1007	123	5	𝑔𝑖(𝑤2	𝑔𝑖(𝑤2	NOUN
cana-1007	123	6	)	)	PUNCT
cana-1007	123	7	=	=	PUNCT
cana-1007	124	1	𝑞	𝑞	X
cana-1007	124	2	+	+	ADJ
cana-1007	124	3	2	2	NUM
cana-1007	124	4	,	,	PUNCT
cana-1007	124	5	𝑔𝑖(𝑙𝑟+2	𝑔𝑖(𝑙𝑟+2	NOUN
cana-1007	124	6	)	)	PUNCT
cana-1007	124	7	=	=	PUNCT
cana-1007	125	1	𝑞	𝑞	PROPN
cana-1007	125	2	+	+	NOUN
cana-1007	125	3	𝑟	𝑟	NOUN
cana-1007	125	4	+	+	CCONJ
cana-1007	125	5	(	(	PUNCT
cana-1007	125	6	𝑚	𝑚	PROPN
cana-1007	125	7	−	−	PROPN
cana-1007	125	8	1	1	NUM
cana-1007	125	9	)	)	PUNCT
cana-1007	125	10	−	−	PROPN
cana-1007	126	1	(	(	PUNCT
cana-1007	126	2	𝑚	𝑚	PROPN
cana-1007	126	3	−	−	PROPN
cana-1007	126	4	1)𝑖	1)𝑖	PROPN
cana-1007	126	5	𝑔𝑖(𝑤3	𝑔𝑖(𝑤3	PROPN
cana-1007	126	6	)	)	PUNCT
cana-1007	126	7	=	=	PUNCT
cana-1007	127	1	𝑞	𝑞	PROPN
cana-1007	127	2	+	+	ADJ
cana-1007	127	3	3	3	NUM
cana-1007	127	4	,	,	PUNCT
cana-1007	127	5	𝑔𝑖(𝑙𝑟+3	𝑔𝑖(𝑙𝑟+3	NOUN
cana-1007	127	6	)	)	PUNCT
cana-1007	127	7	=	=	PUNCT
cana-1007	128	1	𝑞	𝑞	PROPN
cana-1007	128	2	+	+	NOUN
cana-1007	128	3	𝑟	𝑟	NOUN
cana-1007	128	4	+	+	CCONJ
cana-1007	128	5	(	(	PUNCT
cana-1007	128	6	𝑚	𝑚	PROPN
cana-1007	128	7	−	−	PROPN
cana-1007	128	8	2	2	NUM
cana-1007	128	9	)	)	PUNCT
cana-1007	128	10	−	−	PROPN
cana-1007	129	1	(	(	PUNCT
cana-1007	129	2	𝑚	𝑚	PROPN
cana-1007	129	3	−	−	PROPN
cana-1007	129	4	2)𝑖	2)𝑖	ADV
cana-1007	129	5	𝑔𝑖(𝑤4	𝑔𝑖(𝑤4	NOUN
cana-1007	129	6	)	)	PUNCT
cana-1007	129	7	=	=	PUNCT
cana-1007	130	1	𝑞	𝑞	X
cana-1007	130	2	+	+	NOUN
cana-1007	130	3	4	4	NUM
cana-1007	130	4	,	,	PUNCT
cana-1007	130	5	𝑔𝑖(𝑙𝑟+4	𝑔𝑖(𝑙𝑟+4	PROPN
cana-1007	130	6	)	)	PUNCT
cana-1007	130	7	=	=	PUNCT
cana-1007	131	1	𝑞	𝑞	PROPN
cana-1007	131	2	+	+	NOUN
cana-1007	131	3	𝑟	𝑟	NOUN
cana-1007	131	4	+	+	CCONJ
cana-1007	131	5	(	(	PUNCT
cana-1007	131	6	𝑚	𝑚	PROPN
cana-1007	131	7	−	−	PROPN
cana-1007	131	8	3	3	NUM
cana-1007	131	9	)	)	PUNCT
cana-1007	131	10	−	−	PROPN
cana-1007	132	1	(	(	PUNCT
cana-1007	132	2	𝑚	𝑚	PROPN
cana-1007	132	3	−	−	PROPN
cana-1007	132	4	3)𝑖	3)𝑖	NUM
cana-1007	132	5	..	..	PUNCT
cana-1007	132	6	..	..	PUNCT
cana-1007	132	7	..	..	PUNCT
cana-1007	132	8	..	..	PUNCT
cana-1007	133	1	..	..	PUNCT
cana-1007	133	2	𝑔𝑖(𝑤𝑚−4	𝑔𝑖(𝑤𝑚−4	NOUN
cana-1007	133	3	)	)	PUNCT
cana-1007	133	4	=	=	SYM
cana-1007	133	5	𝑞	𝑞	PROPN
cana-1007	133	6	+	+	ADP
cana-1007	133	7	𝑚	𝑚	X
cana-1007	133	8	−	−	PROPN
cana-1007	133	9	4	4	NUM
cana-1007	133	10	,	,	PUNCT
cana-1007	133	11	𝑔𝑖(𝑙𝑟+𝑚−4	𝑔𝑖(𝑙𝑟+𝑚−4	NOUN
cana-1007	133	12	)	)	PUNCT
cana-1007	133	13	=	=	SYM
cana-1007	134	1	𝑞	𝑞	PROPN
cana-1007	134	2	+	+	ADJ
cana-1007	134	3	𝑟	𝑟	NOUN
cana-1007	134	4	+	+	CCONJ
cana-1007	134	5	2𝑚	2𝑚	NUM
cana-1007	134	6	+	+	CCONJ
cana-1007	134	7	4	4	NUM
cana-1007	134	8	−	−	NOUN
cana-1007	134	9	4𝑖	4𝑖	NOUN
cana-1007	134	10	𝑔𝑖(𝑤𝑚−3	𝑔𝑖(𝑤𝑚−3	PROPN
cana-1007	134	11	)	)	PUNCT
cana-1007	135	1	=	=	PUNCT
cana-1007	135	2	𝑞	𝑞	PROPN
cana-1007	136	1	+	+	ADP
cana-1007	136	2	𝑚	𝑚	PRON
cana-1007	136	3	−	−	PROPN
cana-1007	136	4	3	3	NUM
cana-1007	136	5	,	,	PUNCT
cana-1007	136	6	𝑔𝑖(𝑙𝑟+𝑚−3	𝑔𝑖(𝑙𝑟+𝑚−3	PROPN
cana-1007	136	7	)	)	PUNCT
cana-1007	136	8	=	=	PUNCT
cana-1007	137	1	𝑞	𝑞	PROPN
cana-1007	137	2	+	+	ADJ
cana-1007	137	3	𝑟	𝑟	NOUN
cana-1007	137	4	+	+	CCONJ
cana-1007	137	5	2𝑚	2𝑚	NOUN
cana-1007	137	6	+	+	CCONJ
cana-1007	137	7	3	3	NUM
cana-1007	137	8	−	−	PROPN
cana-1007	137	9	3𝑖	3𝑖	NUM
cana-1007	137	10	,	,	PUNCT
cana-1007	137	11	𝑔𝑖(𝑤𝑚−2	𝑔𝑖(𝑤𝑚−2	NOUN
cana-1007	137	12	)	)	PUNCT
cana-1007	137	13	=	=	SYM
cana-1007	138	1	𝑞	𝑞	PROPN
cana-1007	138	2	+	+	ADP
cana-1007	138	3	𝑚	𝑚	X
cana-1007	138	4	−	−	NUM
cana-1007	138	5	2	2	NUM
cana-1007	138	6	,	,	PUNCT
cana-1007	138	7	𝑔𝑖(𝑙𝑟+𝑚−2	𝑔𝑖(𝑙𝑟+𝑚−2	NOUN
cana-1007	138	8	)	)	PUNCT
cana-1007	138	9	=	=	SYM
cana-1007	139	1	𝑞	𝑞	X
cana-1007	139	2	+	+	ADJ
cana-1007	139	3	𝑟	𝑟	NOUN
cana-1007	139	4	+	+	CCONJ
cana-1007	139	5	2𝑚	2𝑚	NUM
cana-1007	139	6	+	+	CCONJ
cana-1007	139	7	2	2	NUM
cana-1007	139	8	−	−	NOUN
cana-1007	139	9	2𝑖	2𝑖	NOUN
cana-1007	139	10	𝑔𝑖(𝑤𝑚−1	𝑔𝑖(𝑤𝑚−1	NUM
cana-1007	139	11	)	)	PUNCT
cana-1007	140	1	=	=	SYM
cana-1007	140	2	𝑞	𝑞	PROPN
cana-1007	141	1	+	+	ADP
cana-1007	141	2	𝑚	𝑚	X
cana-1007	141	3	−	−	PROPN
cana-1007	141	4	1	1	NUM
cana-1007	141	5	,	,	PUNCT
cana-1007	141	6	𝑔𝑖(𝑙𝑟+𝑚−1	𝑔𝑖(𝑙𝑟+𝑚−1	PROPN
cana-1007	141	7	)	)	PUNCT
cana-1007	141	8	=	=	PUNCT
cana-1007	142	1	𝑞	𝑞	PROPN
cana-1007	142	2	+	+	ADJ
cana-1007	142	3	𝑟	𝑟	NOUN
cana-1007	142	4	+	+	CCONJ
cana-1007	142	5	2𝑚	2𝑚	NUM
cana-1007	142	6	+	+	CCONJ
cana-1007	142	7	1	1	NUM
cana-1007	142	8	−	−	PROPN
cana-1007	142	9	𝑖	𝑖	SYM
cana-1007	142	10	𝑔𝑖(𝑤𝑛	𝑔𝑖(𝑤𝑛	PROPN
cana-1007	142	11	)	)	PUNCT
cana-1007	142	12	=	=	PUNCT
cana-1007	143	1	𝑞	𝑞	PROPN
cana-1007	143	2	+	+	CCONJ
cana-1007	143	3	𝑚	𝑚	NOUN
cana-1007	143	4	,	,	PUNCT
cana-1007	143	5	𝑔𝑖(𝑙𝑟+𝑚	𝑔𝑖(𝑙𝑟+𝑚	NOUN
cana-1007	143	6	)	)	PUNCT
cana-1007	143	7	=	=	SYM
cana-1007	144	1	𝑞	𝑞	PROPN
cana-1007	144	2	+	+	ADJ
cana-1007	144	3	𝑟	𝑟	NOUN
cana-1007	144	4	+	+	CCONJ
cana-1007	144	5	2𝑚	2𝑚	NOUN
cana-1007	144	6	therefore	therefore	ADV
cana-1007	144	7	labels	label	NOUN
cana-1007	144	8	of	of	ADP
cana-1007	144	9	𝑆𝑚	𝑆𝑚	PROPN
cana-1007	144	10	are	be	AUX
cana-1007	144	11	2𝑞	2𝑞	NUM
cana-1007	144	12	+	+	CCONJ
cana-1007	144	13	𝑟	𝑟	NOUN
cana-1007	144	14	+	+	SYM
cana-1007	144	15	1	1	NUM
cana-1007	145	1	+	+	CCONJ
cana-1007	145	2	𝑚	𝑚	ADP
cana-1007	145	3	−	−	PROPN
cana-1007	145	4	𝑚𝑖	𝑚𝑖	NOUN
cana-1007	145	5	,	,	PUNCT
cana-1007	145	6	2𝑞	2𝑞	NUM
cana-1007	145	7	+	+	SYM
cana-1007	145	8	𝑟	𝑟	NOUN
cana-1007	145	9	+	+	SYM
cana-1007	145	10	2	2	NUM
cana-1007	145	11	+	+	CCONJ
cana-1007	145	12	(	(	PUNCT
cana-1007	145	13	𝑚	𝑚	PROPN
cana-1007	145	14	−	−	PROPN
cana-1007	145	15	𝑜𝑛𝑒	𝑜𝑛𝑒	PROPN
cana-1007	145	16	)	)	PUNCT
cana-1007	145	17	−	−	PROPN
cana-1007	146	1	(	(	PUNCT
cana-1007	146	2	𝑚	𝑚	PROPN
cana-1007	146	3	−	−	PROPN
cana-1007	146	4	𝑜𝑛𝑒)𝑖	𝑜𝑛𝑒)𝑖	PROPN
cana-1007	146	5	,	,	PUNCT
cana-1007	146	6	2𝑞	2𝑞	NUM
cana-1007	146	7	+	+	CCONJ
cana-1007	146	8	𝑟	𝑟	NOUN
cana-1007	147	1	+	+	SYM
cana-1007	147	2	2	2	NUM
cana-1007	147	3	+	+	CCONJ
cana-1007	147	4	(	(	PUNCT
cana-1007	147	5	𝑚	𝑚	PROPN
cana-1007	147	6	−	−	PROPN
cana-1007	147	7	1	1	NUM
cana-1007	147	8	+	+	NUM
cana-1007	147	9	1	1	NUM
cana-1007	147	10	)	)	PUNCT
cana-1007	147	11	−	−	PROPN
cana-1007	147	12	(	(	PUNCT
cana-1007	147	13	𝑚	𝑚	PROPN
cana-1007	147	14	−	−	PROPN
cana-1007	147	15	1	1	NUM
cana-1007	147	16	+	+	SYM
cana-1007	147	17	1)𝑖	1)𝑖	NUM
cana-1007	147	18	,	,	PUNCT
cana-1007	147	19	2𝑞	2𝑞	NOUN
cana-1007	147	20	+	+	CCONJ
cana-1007	147	21	𝑟	𝑟	NOUN
cana-1007	147	22	+	+	CCONJ
cana-1007	147	23	1	1	NUM
cana-1007	148	1	+	+	NUM
cana-1007	148	2	1	1	NUM
cana-1007	148	3	+	+	CCONJ
cana-1007	148	4	(	(	PUNCT
cana-1007	148	5	𝑚	𝑚	PROPN
cana-1007	148	6	−	−	PROPN
cana-1007	148	7	3	3	NUM
cana-1007	148	8	)	)	PUNCT
cana-1007	148	9	−	−	PROPN
cana-1007	149	1	(	(	PUNCT
cana-1007	149	2	𝑚	𝑚	PROPN
cana-1007	149	3	−	−	PROPN
cana-1007	149	4	3)𝑖	3)𝑖	NUM
cana-1007	149	5	,	,	PUNCT
cana-1007	149	6	.	.	PUNCT
cana-1007	149	7	.	.	PUNCT
cana-1007	150	1	.	.	PUNCT
cana-1007	151	1	,	,	PUNCT
cana-1007	151	2	2𝑞	2𝑞	NOUN
cana-1007	151	3	+	+	CCONJ
cana-1007	151	4	𝑟	𝑟	NOUN
cana-1007	151	5	+	+	CCONJ
cana-1007	151	6	3𝑚	3𝑚	NUM
cana-1007	151	7	−	−	PROPN
cana-1007	151	8	3𝑖	3𝑖	NUM
cana-1007	151	9	,	,	PUNCT
cana-1007	151	10	2𝑞	2𝑞	NOUN
cana-1007	151	11	+	+	CCONJ
cana-1007	151	12	𝑟	𝑟	NOUN
cana-1007	152	1	+	+	CCONJ
cana-1007	152	2	3𝑚	3𝑚	NUM
cana-1007	152	3	−	−	PROPN
cana-1007	152	4	2𝑖	2𝑖	NOUN
cana-1007	152	5	,	,	PUNCT
cana-1007	152	6	2𝑞	2𝑞	NOUN
cana-1007	152	7	+	+	CCONJ
cana-1007	152	8	𝑟	𝑟	NOUN
cana-1007	153	1	+	+	CCONJ
cana-1007	153	2	3𝑚	3𝑚	NUM
cana-1007	153	3	−	−	PROPN
cana-1007	153	4	𝑖	𝑖	NOUN
cana-1007	153	5	,	,	PUNCT
cana-1007	153	6	2𝑞	2𝑞	NOUN
cana-1007	153	7	+	+	CCONJ
cana-1007	153	8	𝑟	𝑟	NOUN
cana-1007	153	9	+	+	CCONJ
cana-1007	153	10	3𝑚	3𝑚	NUM
cana-1007	153	11	,	,	PUNCT
cana-1007	153	12	where	where	SCONJ
cana-1007	153	13	𝑚	𝑚	PROPN
cana-1007	153	14	≥	≥	NUM
cana-1007	153	15	6	6	NUM
cana-1007	153	16	.	.	PUNCT
cana-1007	154	1	hence	hence	ADV
cana-1007	154	2	,	,	PUNCT
cana-1007	154	3	𝑒	𝑒	PROPN
cana-1007	154	4	=	=	SYM
cana-1007	154	5	𝑖	𝑖	PROPN
cana-1007	154	6	,	,	PUNCT
cana-1007	154	7	4	4	NUM
cana-1007	154	8	≤	≤	NUM
cana-1007	154	9	𝑖	𝑖	PUNCT
cana-1007	154	10	≤	≤	NOUN
cana-1007	154	11	𝑞	𝑞	X
cana-1007	154	12	−	−	PROPN
cana-1007	154	13	1	1	NUM
cana-1007	154	14	where	where	SCONJ
cana-1007	154	15	𝑞	𝑞	PRON
cana-1007	154	16	≥	≥	X
cana-1007	154	17	𝑚	𝑚	ADV
cana-1007	154	18	−	−	PROPN
cana-1007	154	19	1	1	NUM
cana-1007	154	20	.	.	PUNCT
cana-1007	155	1	hence	hence	ADV
cana-1007	155	2	the	the	DET
cana-1007	155	3	proof	proof	NOUN
cana-1007	155	4	.	.	PUNCT
cana-1007	156	1	3	3	X
cana-1007	156	2	.	.	X
cana-1007	156	3	observation	observation	NOUN
cana-1007	156	4	here	here	ADV
cana-1007	156	5	is	be	AUX
cana-1007	156	6	the	the	DET
cana-1007	156	7	graph	graph	NOUN
cana-1007	156	8	that	that	PRON
cana-1007	156	9	shows	show	VERB
cana-1007	156	10	satl	satl	NOUN
cana-1007	156	11	of	of	ADP
cana-1007	156	12	the	the	DET
cana-1007	156	13	graph	graph	NOUN
cana-1007	156	14	𝐺𝑢(𝑆7	𝐺𝑢(𝑆7	PROPN
cana-1007	156	15	)	)	PUNCT
cana-1007	156	16	.	.	PUNCT
cana-1007	157	1	let	let	VERB
cana-1007	157	2	𝐺′	𝐺′	PROPN
cana-1007	157	3	≅	≅	PROPN
cana-1007	157	4	𝐺𝑢(𝑆7	𝐺𝑢(𝑆7	PROPN
cana-1007	157	5	)	)	PUNCT
cana-1007	157	6	,	,	PUNCT
cana-1007	157	7	{	{	PUNCT
cana-1007	157	8	1,3	1,3	NUM
cana-1007	157	9	,	,	PUNCT
cana-1007	157	10	.	.	PUNCT
cana-1007	157	11	.	.	PUNCT
cana-1007	158	1	.	.	PUNCT
cana-1007	159	1	,	,	PUNCT
cana-1007	159	2	7	7	X
cana-1007	159	3	}	}	PUNCT
cana-1007	159	4	and	and	CCONJ
cana-1007	159	5	{	{	PUNCT
cana-1007	159	6	8,9,10	8,9,10	NUM
cana-1007	159	7	,	,	PUNCT
cana-1007	159	8	.	.	PUNCT
cana-1007	159	9	.	.	PUNCT
cana-1007	159	10	.	.	PUNCT
cana-1007	160	1	,	,	PUNCT
cana-1007	160	2	14	14	NUM
cana-1007	160	3	}	}	PUNCT
cana-1007	160	4	be	be	AUX
cana-1007	160	5	the	the	DET
cana-1007	160	6	dots	dot	NOUN
cana-1007	160	7	of	of	ADP
cana-1007	160	8	g	g	PROPN
cana-1007	160	9	and	and	CCONJ
cana-1007	160	10	(	(	PUNCT
cana-1007	160	11	𝑆7	𝑆7	PROPN
cana-1007	160	12	)	)	PUNCT
cana-1007	160	13	r.	r.	NOUN
cana-1007	160	14	communications	communication	NOUN
cana-1007	160	15	on	on	ADP
cana-1007	160	16	applied	apply	VERB
cana-1007	160	17	nonlinear	nonlinear	ADJ
cana-1007	160	18	analysis	analysis	NOUN
cana-1007	160	19	issn	issn	NOUN
cana-1007	160	20	:	:	PUNCT
cana-1007	160	21	1074	1074	NUM
cana-1007	160	22	-	-	PUNCT
cana-1007	160	23	133x	133x	NUM
cana-1007	160	24	vol	vol	NOUN
cana-1007	160	25	31	31	NUM
cana-1007	160	26	no	no	NOUN
cana-1007	160	27	.	.	PUNCT
cana-1007	161	1	5s	5s	NUM
cana-1007	161	2	(	(	PUNCT
cana-1007	161	3	2024	2024	NUM
cana-1007	161	4	)	)	PUNCT
cana-1007	161	5	135	135	NUM
cana-1007	161	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1007	161	7	let	let	VERB
cana-1007	161	8	{	{	PUNCT
cana-1007	161	9	15,16	15,16	NUM
cana-1007	161	10	,	,	PUNCT
cana-1007	161	11	,	,	PUNCT
cana-1007	161	12	17	17	NUM
cana-1007	161	13	.	.	PUNCT
cana-1007	161	14	.	.	PUNCT
cana-1007	161	15	.	.	PUNCT
cana-1007	162	1	,	,	PUNCT
cana-1007	162	2	21	21	NUM
cana-1007	162	3	}	}	PUNCT
cana-1007	162	4	and	and	CCONJ
cana-1007	162	5	{	{	PUNCT
cana-1007	162	6	22,23,24	22,23,24	NUM
cana-1007	162	7	,	,	PUNCT
cana-1007	162	8	.	.	PUNCT
cana-1007	162	9	.	.	PUNCT
cana-1007	162	10	.	.	PUNCT
cana-1007	163	1	,	,	PUNCT
cana-1007	163	2	42	42	NUM
cana-1007	163	3	}	}	PUNCT
cana-1007	163	4	be	be	AUX
cana-1007	163	5	the	the	DET
cana-1007	163	6	lines	line	NOUN
cana-1007	163	7	of	of	ADP
cana-1007	163	8	g	g	PROPN
cana-1007	163	9	and	and	CCONJ
cana-1007	163	10	(	(	PUNCT
cana-1007	163	11	𝑆7	𝑆7	NOUN
cana-1007	163	12	)	)	PUNCT
cana-1007	163	13	.	.	PUNCT
cana-1007	164	1	then	then	ADV
cana-1007	164	2	|𝐷(𝐺′)|=14	|𝐷(𝐺′)|=14	NOUN
cana-1007	164	3	and	and	CCONJ
cana-1007	164	4	|𝐿(𝐺′)|=28	|𝐿(𝐺′)|=28	PROPN
cana-1007	164	5	.	.	PUNCT
cana-1007	165	1	therefore	therefore	ADV
cana-1007	165	2	there	there	PRON
cana-1007	165	3	is	be	VERB
cana-1007	165	4	an	an	DET
cana-1007	165	5	arises	arise	NOUN
cana-1007	165	6	of	of	ADP
cana-1007	165	7	map	map	NOUN
cana-1007	165	8	,	,	PUNCT
cana-1007	165	9	when	when	SCONJ
cana-1007	165	10	i=5	i=5	ADP
cana-1007	165	11	in	in	ADP
cana-1007	165	12	the	the	DET
cana-1007	165	13	labeling	labeling	NOUN
cana-1007	165	14	of	of	ADP
cana-1007	165	15	the	the	DET
cana-1007	165	16	theorem(2.4	theorem(2.4	NOUN
cana-1007	165	17	)	)	PUNCT
cana-1007	165	18	constitutes	constitute	VERB
cana-1007	165	19	an	an	DET
cana-1007	165	20	arithmetic	arithmetic	ADJ
cana-1007	165	21	progression	progression	NOUN
cana-1007	165	22	we	we	PRON
cana-1007	165	23	get	get	VERB
cana-1007	165	24	e=5	e=5	PRON
cana-1007	165	25	and	and	CCONJ
cana-1007	165	26	all	all	DET
cana-1007	165	27	the	the	DET
cana-1007	165	28	subgraphs	subgraph	NOUN
cana-1007	165	29	which	which	PRON
cana-1007	165	30	is	be	AUX
cana-1007	165	31	≅	≅	PROPN
cana-1007	165	32	to	to	ADP
cana-1007	165	33	h.	h.	PROPN
cana-1007	165	34	also	also	ADV
cana-1007	165	35	here	here	ADV
cana-1007	165	36	𝑔(𝐷(𝐺	𝑔(𝐷(𝐺	PROPN
cana-1007	165	37	)	)	PUNCT
cana-1007	165	38	)	)	PUNCT
cana-1007	166	1	=	=	PRON
cana-1007	166	2	{	{	PUNCT
cana-1007	166	3	1,3	1,3	NUM
cana-1007	166	4	,	,	PUNCT
cana-1007	166	5	.	.	PUNCT
cana-1007	166	6	.	.	PUNCT
cana-1007	166	7	.	.	PUNCT
cana-1007	167	1	,	,	PUNCT
cana-1007	167	2	7	7	X
cana-1007	167	3	}	}	PUNCT
cana-1007	167	4	then	then	ADV
cana-1007	167	5	𝑔	𝑔	PROPN
cana-1007	167	6	is	be	AUX
cana-1007	167	7	a	a	DET
cana-1007	167	8	satl	satl	NOUN
cana-1007	167	9	.	.	PUNCT
cana-1007	168	1	figure	figure	NOUN
cana-1007	168	2	2	2	NUM
cana-1007	168	3	:	:	PUNCT
cana-1007	168	4	satl	satl	NOUN
cana-1007	168	5	of	of	ADP
cana-1007	168	6	(	(	PUNCT
cana-1007	168	7	26,5	26,5	NUM
cana-1007	168	8	)	)	PUNCT
cana-1007	168	9	3.1	3.1	NUM
cana-1007	168	10	observation	observation	NOUN
cana-1007	168	11	in	in	ADP
cana-1007	168	12	[	[	X
cana-1007	168	13	2	2	NUM
cana-1007	168	14	]	]	PUNCT
cana-1007	168	15	,	,	PUNCT
cana-1007	168	16	there	there	PRON
cana-1007	168	17	is	be	VERB
cana-1007	168	18	a	a	DET
cana-1007	168	19	problem	problem	NOUN
cana-1007	168	20	,	,	PUNCT
cana-1007	168	21	for	for	ADP
cana-1007	168	22	all	all	DET
cana-1007	168	23	e	e	NOUN
cana-1007	168	24	,	,	PUNCT
cana-1007	168	25	4	4	NUM
cana-1007	168	26	≤	≤	NUM
cana-1007	168	27	𝑒	𝑒	PROPN
cana-1007	168	28	≤	≤	NOUN
cana-1007	168	29	𝑞	𝑞	X
cana-1007	168	30	+	+	NOUN
cana-1007	168	31	𝑟	𝑟	NOUN
cana-1007	168	32	+	+	SYM
cana-1007	168	33	2	2	NUM
cana-1007	168	34	,	,	PUNCT
cana-1007	168	35	either	either	CCONJ
cana-1007	168	36	prove	prove	VERB
cana-1007	168	37	𝐺𝑥(𝑆𝑚	𝐺𝑥(𝑆𝑚	NOUN
cana-1007	168	38	)	)	PUNCT
cana-1007	168	39	,	,	PUNCT
cana-1007	168	40	𝑚	𝑚	X
cana-1007	168	41	≥	≥	NUM
cana-1007	168	42	3	3	NUM
cana-1007	168	43	,	,	PUNCT
cana-1007	168	44	or	or	CCONJ
cana-1007	168	45	find	find	VERB
cana-1007	168	46	the	the	DET
cana-1007	168	47	graph	graph	NOUN
cana-1007	168	48	is	be	AUX
cana-1007	168	49	not	not	PART
cana-1007	168	50	exists	exist	NOUN
cana-1007	168	51	.	.	PUNCT
cana-1007	169	1	here	here	ADV
cana-1007	169	2	we	we	PRON
cana-1007	169	3	proved	prove	VERB
cana-1007	169	4	the	the	DET
cana-1007	169	5	upper	upper	ADJ
cana-1007	169	6	limit	limit	NOUN
cana-1007	169	7	for	for	ADP
cana-1007	169	8	𝑒	𝑒	PROPN
cana-1007	169	9	=	=	SYM
cana-1007	169	10	𝑞	𝑞	X
cana-1007	169	11	+	+	NOUN
cana-1007	169	12	𝑟	𝑟	NOUN
cana-1007	169	13	+	+	SYM
cana-1007	169	14	2	2	NUM
cana-1007	169	15	does	do	AUX
cana-1007	169	16	not	not	PART
cana-1007	169	17	exists	exist	VERB
cana-1007	169	18	but	but	CCONJ
cana-1007	169	19	the	the	DET
cana-1007	169	20	lower	low	ADJ
cana-1007	169	21	limit	limit	NOUN
cana-1007	169	22	for	for	ADP
cana-1007	169	23	𝑒	𝑒	PROPN
cana-1007	169	24	=	=	SYM
cana-1007	169	25	4,5,6,7	4,5,6,7	NUM
cana-1007	169	26	,	,	PUNCT
cana-1007	169	27	.	.	PUNCT
cana-1007	170	1	..	..	PUNCT
cana-1007	170	2	exists	exist	VERB
cana-1007	170	3	for	for	ADP
cana-1007	170	4	𝐺𝑥(𝑆𝑚	𝐺𝑥(𝑆𝑚	PROPN
cana-1007	170	5	)	)	PUNCT
cana-1007	170	6	for	for	ADP
cana-1007	170	7	𝑚	𝑚	NOUN
cana-1007	170	8	=	=	SYM
cana-1007	170	9	3,4,5	3,4,5	NUM
cana-1007	170	10	.	.	PUNCT
cana-1007	171	1	by	by	ADP
cana-1007	171	2	refereed	refereed	ADJ
cana-1007	171	3	to	to	ADP
cana-1007	171	4	the	the	DET
cana-1007	171	5	lemma	lemma	PROPN
cana-1007	171	6	4	4	NUM
cana-1007	171	7	in	in	ADP
cana-1007	171	8	[	[	X
cana-1007	171	9	2	2	NUM
cana-1007	171	10	]	]	PUNCT
cana-1007	171	11	,	,	PUNCT
cana-1007	171	12	we	we	PRON
cana-1007	171	13	have	have	VERB
cana-1007	171	14	,	,	PUNCT
cana-1007	171	15	that	that	SCONJ
cana-1007	171	16	the	the	DET
cana-1007	171	17	value	value	NOUN
cana-1007	171	18	of	of	ADP
cana-1007	171	19	a	a	PRON
cana-1007	171	20	is	be	AUX
cana-1007	171	21	(	(	PUNCT
cana-1007	171	22	𝑞	𝑞	X
cana-1007	171	23	+	+	PUNCT
cana-1007	171	24	𝑛)(𝑟	𝑛)(𝑟	PUNCT
cana-1007	171	25	+	+	CCONJ
cana-1007	171	26	1	1	NUM
cana-1007	171	27	)	)	PUNCT
cana-1007	171	28	+	+	CCONJ
cana-1007	171	29	(	(	PUNCT
cana-1007	171	30	𝑞+1)(𝑞+2)+(𝑞+1)(𝑞+2	𝑞+1)(𝑞+2)+(𝑞+1)(𝑞+2	PROPN
cana-1007	171	31	)	)	PUNCT
cana-1007	171	32	2	2	NUM
cana-1007	172	1	and	and	CCONJ
cana-1007	172	2	it	it	PRON
cana-1007	172	3	is	be	AUX
cana-1007	172	4	the	the	DET
cana-1007	172	5	weight	weight	NOUN
cana-1007	172	6	of	of	ADP
cana-1007	172	7	the	the	DET
cana-1007	172	8	first	first	ADJ
cana-1007	172	9	subgraph	subgraph	NOUN
cana-1007	172	10	𝑠1	𝑠1	PROPN
cana-1007	172	11	for	for	ADP
cana-1007	172	12	a	a	DET
cana-1007	172	13	real	real	ADJ
cana-1007	172	14	numbers	number	NOUN
cana-1007	172	15	of	of	ADP
cana-1007	172	16	q	q	NOUN
cana-1007	172	17	and	and	CCONJ
cana-1007	172	18	r	r	NOUN
cana-1007	172	19	,	,	PUNCT
cana-1007	172	20	it	it	PRON
cana-1007	172	21	is	be	AUX
cana-1007	172	22	less	less	ADJ
cana-1007	172	23	than	than	ADP
cana-1007	172	24	0	0	NUM
cana-1007	172	25	,	,	PUNCT
cana-1007	172	26	therefore	therefore	ADV
cana-1007	172	27	it	it	PRON
cana-1007	172	28	is	be	AUX
cana-1007	172	29	not	not	PART
cana-1007	172	30	possible	possible	ADJ
cana-1007	172	31	for	for	ADP
cana-1007	172	32	𝑒	𝑒	PROPN
cana-1007	172	33	=	=	SYM
cana-1007	172	34	𝑞	𝑞	X
cana-1007	172	35	+	+	NOUN
cana-1007	172	36	𝑟	𝑟	NOUN
cana-1007	172	37	+	+	CCONJ
cana-1007	172	38	2	2	NUM
cana-1007	173	1	but	but	CCONJ
cana-1007	173	2	it	it	PRON
cana-1007	173	3	is	be	AUX
cana-1007	173	4	possible	possible	ADJ
cana-1007	173	5	for	for	SCONJ
cana-1007	173	6	the	the	DET
cana-1007	173	7	graph	graph	NOUN
cana-1007	173	8	𝐺𝑥(𝑆𝑚	𝐺𝑥(𝑆𝑚	PROPN
cana-1007	173	9	)	)	PUNCT
cana-1007	173	10	is	be	AUX
cana-1007	173	11	4	4	NUM
cana-1007	173	12	≤	≤	NUM
cana-1007	173	13	𝑑	𝑑	PROPN
cana-1007	173	14	≤	≤	NOUN
cana-1007	173	15	𝑞	𝑞	PART
cana-1007	173	16	−	−	PROPN
cana-1007	173	17	1	1	NUM
cana-1007	173	18	and	and	CCONJ
cana-1007	173	19	the	the	DET
cana-1007	173	20	proof	proof	NOUN
cana-1007	173	21	is	be	AUX
cana-1007	173	22	given	give	VERB
cana-1007	173	23	in	in	ADP
cana-1007	173	24	the	the	DET
cana-1007	173	25	theorem	theorem	NOUN
cana-1007	173	26	(	(	PUNCT
cana-1007	173	27	2.4	2.4	NUM
cana-1007	173	28	)	)	PUNCT
cana-1007	173	29	.	.	PUNCT
cana-1007	174	1	4	4	X
cana-1007	174	2	.	.	X
cana-1007	174	3	goals	goal	NOUN
cana-1007	174	4	and	and	CCONJ
cana-1007	174	5	objectives	objective	NOUN
cana-1007	174	6	from	from	ADP
cana-1007	174	7	the	the	DET
cana-1007	174	8	theory	theory	NOUN
cana-1007	174	9	of	of	ADP
cana-1007	174	10	graph	graph	NOUN
cana-1007	174	11	network	network	NOUN
cana-1007	174	12	,	,	PUNCT
cana-1007	174	13	the	the	DET
cana-1007	174	14	undirected	undirected	ADJ
cana-1007	174	15	graph	graph	NOUN
cana-1007	174	16	is	be	AUX
cana-1007	174	17	the	the	DET
cana-1007	174	18	set	set	NOUN
cana-1007	174	19	of	of	ADP
cana-1007	174	20	all	all	DET
cana-1007	174	21	nodes	node	NOUN
cana-1007	174	22	and	and	CCONJ
cana-1007	174	23	lines	line	NOUN
cana-1007	174	24	.	.	PUNCT
cana-1007	175	1	graph	graph	NOUN
cana-1007	175	2	network	network	NOUN
cana-1007	175	3	may	may	AUX
cana-1007	175	4	be	be	AUX
cana-1007	175	5	known	know	VERB
cana-1007	175	6	as	as	ADP
cana-1007	175	7	a	a	DET
cana-1007	175	8	link	link	NOUN
cana-1007	175	9	,	,	PUNCT
cana-1007	175	10	a	a	DET
cana-1007	175	11	node	node	NOUN
cana-1007	175	12	-	-	PUNCT
cana-1007	175	13	link	link	NOUN
cana-1007	175	14	,	,	PUNCT
cana-1007	175	15	a	a	DET
cana-1007	175	16	map	map	NOUN
cana-1007	175	17	network	network	NOUN
cana-1007	175	18	,	,	PUNCT
cana-1007	175	19	or	or	CCONJ
cana-1007	175	20	simply	simply	ADV
cana-1007	175	21	a	a	DET
cana-1007	175	22	graph	graph	NOUN
cana-1007	175	23	.	.	PUNCT
cana-1007	176	1	nowadays	nowadays	ADV
cana-1007	176	2	we	we	PRON
cana-1007	176	3	are	be	AUX
cana-1007	176	4	surrounding	surround	VERB
cana-1007	176	5	by	by	ADP
cana-1007	176	6	countless	countless	ADJ
cana-1007	176	7	connections	connection	NOUN
cana-1007	176	8	and	and	CCONJ
cana-1007	176	9	networks	network	NOUN
cana-1007	176	10	;	;	PUNCT
cana-1007	176	11	railway	railway	NOUN
cana-1007	176	12	tracks	track	NOUN
cana-1007	176	13	,	,	PUNCT
cana-1007	176	14	telephone	telephone	NOUN
cana-1007	176	15	lines	line	NOUN
cana-1007	176	16	,	,	PUNCT
cana-1007	176	17	roads	road	NOUN
cana-1007	176	18	,	,	PUNCT
cana-1007	176	19	the	the	DET
cana-1007	176	20	internet	internet	NOUN
cana-1007	176	21	,	,	PUNCT
cana-1007	176	22	electronic	electronic	ADJ
cana-1007	176	23	circuits	circuit	NOUN
cana-1007	176	24	,	,	PUNCT
cana-1007	176	25	and	and	CCONJ
cana-1007	176	26	even	even	ADV
cana-1007	176	27	social	social	ADJ
cana-1007	176	28	networks	network	NOUN
cana-1007	176	29	between	between	ADP
cana-1007	176	30	friends	friend	NOUN
cana-1007	176	31	and	and	CCONJ
cana-1007	176	32	families	family	NOUN
cana-1007	176	33	.	.	PUNCT
cana-1007	177	1	communications	communication	NOUN
cana-1007	177	2	on	on	ADP
cana-1007	177	3	applied	apply	VERB
cana-1007	177	4	nonlinear	nonlinear	ADJ
cana-1007	177	5	analysis	analysis	NOUN
cana-1007	177	6	issn	issn	NOUN
cana-1007	177	7	:	:	PUNCT
cana-1007	177	8	1074	1074	NUM
cana-1007	177	9	-	-	PUNCT
cana-1007	177	10	133x	133x	NUM
cana-1007	177	11	vol	vol	NOUN
cana-1007	177	12	31	31	NUM
cana-1007	177	13	no	no	NOUN
cana-1007	177	14	.	.	PUNCT
cana-1007	178	1	5s	5s	NUM
cana-1007	178	2	(	(	PUNCT
cana-1007	178	3	2024	2024	NUM
cana-1007	178	4	)	)	PUNCT
cana-1007	178	5	136	136	NUM
cana-1007	178	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1007	178	7	cryptography	cryptography	NOUN
cana-1007	178	8	is	be	AUX
cana-1007	178	9	the	the	DET
cana-1007	178	10	science	science	NOUN
cana-1007	178	11	containing	contain	VERB
cana-1007	178	12	methods	method	NOUN
cana-1007	178	13	to	to	PART
cana-1007	178	14	transform	transform	VERB
cana-1007	178	15	an	an	DET
cana-1007	178	16	intelligible	intelligible	ADJ
cana-1007	178	17	message	message	NOUN
cana-1007	178	18	into	into	ADP
cana-1007	178	19	one	one	NUM
cana-1007	178	20	that	that	PRON
cana-1007	178	21	is	be	AUX
cana-1007	178	22	unintelligible	unintelligible	ADJ
cana-1007	178	23	and	and	CCONJ
cana-1007	178	24	transform	transform	VERB
cana-1007	178	25	the	the	DET
cana-1007	178	26	message	message	NOUN
cana-1007	178	27	back	back	ADV
cana-1007	178	28	to	to	ADP
cana-1007	178	29	its	its	PRON
cana-1007	178	30	original	original	ADJ
cana-1007	178	31	form	form	NOUN
cana-1007	178	32	.	.	PUNCT
cana-1007	179	1	the	the	DET
cana-1007	179	2	original	original	ADJ
cana-1007	179	3	intelligible	intelligible	ADJ
cana-1007	179	4	message	message	NOUN
cana-1007	179	5	is	be	AUX
cana-1007	179	6	known	know	VERB
cana-1007	179	7	as	as	ADP
cana-1007	179	8	plain	plain	ADJ
cana-1007	179	9	text	text	NOUN
cana-1007	179	10	and	and	CCONJ
cana-1007	179	11	the	the	DET
cana-1007	179	12	transformed	transform	VERB
cana-1007	179	13	message	message	NOUN
cana-1007	179	14	is	be	AUX
cana-1007	179	15	known	know	VERB
cana-1007	179	16	as	as	ADP
cana-1007	179	17	cipher	cipher	ADJ
cana-1007	179	18	text	text	NOUN
cana-1007	179	19	.	.	PUNCT
cana-1007	180	1	the	the	DET
cana-1007	180	2	procedure	procedure	NOUN
cana-1007	180	3	for	for	ADP
cana-1007	180	4	converting	convert	VERB
cana-1007	180	5	a	a	DET
cana-1007	180	6	text	text	NOUN
cana-1007	180	7	by	by	ADP
cana-1007	180	8	convertion	convertion	NOUN
cana-1007	180	9	and	and	CCONJ
cana-1007	180	10	replacing	replace	VERB
cana-1007	180	11	techniques	technique	NOUN
cana-1007	180	12	is	be	AUX
cana-1007	180	13	called	call	VERB
cana-1007	180	14	as	as	ADV
cana-1007	180	15	cipher	cipher	ADJ
cana-1007	180	16	.	.	PUNCT
cana-1007	181	1	each	each	DET
cana-1007	181	2	letter	letter	NOUN
cana-1007	181	3	is	be	AUX
cana-1007	181	4	replaced	replace	VERB
cana-1007	181	5	by	by	ADP
cana-1007	181	6	the	the	DET
cana-1007	181	7	three	three	NUM
cana-1007	181	8	positions	position	NOUN
cana-1007	181	9	further	far	ADV
cana-1007	181	10	down	down	ADP
cana-1007	181	11	the	the	DET
cana-1007	181	12	alphabet	alphabet	NOUN
cana-1007	181	13	.	.	PUNCT
cana-1007	182	1	caesar	caesar	PROPN
cana-1007	182	2	used	use	VERB
cana-1007	182	3	a	a	DET
cana-1007	182	4	key	key	NOUN
cana-1007	182	5	for	for	ADP
cana-1007	182	6	his	his	PRON
cana-1007	182	7	communication	communication	NOUN
cana-1007	182	8	and	and	CCONJ
cana-1007	182	9	it	it	PRON
cana-1007	182	10	’s	’s	AUX
cana-1007	182	11	known	know	VERB
cana-1007	182	12	as	as	ADP
cana-1007	182	13	caesar	caesar	PROPN
cana-1007	182	14	cipher	cipher	ADJ
cana-1007	182	15	or	or	CCONJ
cana-1007	182	16	shift	shift	VERB
cana-1007	182	17	cipher	cipher	ADJ
cana-1007	182	18	.	.	PUNCT
cana-1007	183	1	graph	graph	NOUN
cana-1007	183	2	representations	representation	NOUN
cana-1007	183	3	may	may	AUX
cana-1007	183	4	be	be	AUX
cana-1007	183	5	used	use	VERB
cana-1007	183	6	for	for	ADP
cana-1007	183	7	public	public	ADJ
cana-1007	183	8	key	key	ADJ
cana-1007	183	9	ciphers	cipher	NOUN
cana-1007	183	10	[	[	X
cana-1007	183	11	2	2	NUM
cana-1007	183	12	]	]	PUNCT
cana-1007	183	13	.	.	PUNCT
cana-1007	184	1	sharing	share	VERB
cana-1007	184	2	secrecy	secrecy	NOUN
cana-1007	184	3	on	on	ADP
cana-1007	184	4	graphs	graph	NOUN
cana-1007	184	5	has	have	VERB
cana-1007	184	6	applications	application	NOUN
cana-1007	184	7	on	on	ADP
cana-1007	184	8	two	two	NUM
cana-1007	184	9	levels	level	NOUN
cana-1007	184	10	.	.	PUNCT
cana-1007	185	1	1	1	X
cana-1007	185	2	.	.	X
cana-1007	185	3	sharing	share	VERB
cana-1007	185	4	secrecy	secrecy	NOUN
cana-1007	185	5	on	on	ADP
cana-1007	185	6	theoretical	theoretical	ADJ
cana-1007	185	7	research	research	NOUN
cana-1007	185	8	.	.	PUNCT
cana-1007	186	1	2	2	X
cana-1007	186	2	.	.	X
cana-1007	186	3	secret	secret	ADJ
cana-1007	186	4	sharing	sharing	NOUN
cana-1007	186	5	schemes	scheme	NOUN
cana-1007	186	6	using	use	VERB
cana-1007	186	7	structures	structure	NOUN
cana-1007	186	8	.	.	PUNCT
cana-1007	187	1	sharing	share	VERB
cana-1007	187	2	secret	secret	ADJ
cana-1007	187	3	messages	message	NOUN
cana-1007	187	4	are	be	AUX
cana-1007	187	5	expected	expect	VERB
cana-1007	187	6	to	to	PART
cana-1007	187	7	be	be	AUX
cana-1007	187	8	useful	useful	ADJ
cana-1007	187	9	,	,	PUNCT
cana-1007	187	10	providing	provide	VERB
cana-1007	187	11	coding	code	VERB
cana-1007	187	12	techniques	technique	NOUN
cana-1007	187	13	,	,	PUNCT
cana-1007	187	14	meant	mean	VERB
cana-1007	187	15	for	for	ADP
cana-1007	187	16	communicating	communicate	VERB
cana-1007	187	17	any	any	DET
cana-1007	187	18	message	message	NOUN
cana-1007	187	19	personally	personally	ADV
cana-1007	187	20	,	,	PUNCT
cana-1007	187	21	official	official	ADJ
cana-1007	187	22	,	,	PUNCT
cana-1007	187	23	governmental	governmental	ADJ
cana-1007	187	24	,	,	PUNCT
cana-1007	187	25	or	or	CCONJ
cana-1007	187	26	military	military	ADJ
cana-1007	187	27	services	service	NOUN
cana-1007	187	28	with	with	ADP
cana-1007	187	29	high	high	ADJ
cana-1007	187	30	-	-	PUNCT
cana-1007	187	31	level	level	NOUN
cana-1007	187	32	secrecy	secrecy	NOUN
cana-1007	187	33	,	,	PUNCT
cana-1007	187	34	intricacy	intricacy	ADJ
cana-1007	187	35	,	,	PUNCT
cana-1007	187	36	and	and	CCONJ
cana-1007	187	37	a	a	DET
cana-1007	187	38	sense	sense	NOUN
cana-1007	187	39	of	of	ADP
cana-1007	187	40	sufficiency	sufficiency	NOUN
cana-1007	187	41	which	which	PRON
cana-1007	187	42	are	be	AUX
cana-1007	187	43	the	the	DET
cana-1007	187	44	most	most	ADV
cana-1007	187	45	important	important	ADJ
cana-1007	187	46	factors	factor	NOUN
cana-1007	187	47	for	for	ADP
cana-1007	187	48	coding	code	VERB
cana-1007	187	49	.	.	PUNCT
cana-1007	188	1	the	the	DET
cana-1007	188	2	main	main	ADJ
cana-1007	188	3	action	action	NOUN
cana-1007	188	4	of	of	ADP
cana-1007	188	5	the	the	DET
cana-1007	188	6	research	research	NOUN
cana-1007	188	7	is	be	AUX
cana-1007	188	8	to	to	PART
cana-1007	188	9	achieve	achieve	VERB
cana-1007	188	10	the	the	DET
cana-1007	188	11	following	follow	VERB
cana-1007	188	12	goals	goal	NOUN
cana-1007	188	13	and	and	CCONJ
cana-1007	188	14	objectives	objective	NOUN
cana-1007	188	15	,	,	PUNCT
cana-1007	188	16	which	which	PRON
cana-1007	188	17	will	will	AUX
cana-1007	188	18	be	be	AUX
cana-1007	188	19	finalized	finalize	VERB
cana-1007	188	20	in	in	ADP
cana-1007	188	21	several	several	ADJ
cana-1007	188	22	publications	publication	NOUN
cana-1007	188	23	in	in	ADP
cana-1007	188	24	high	high	ADJ
cana-1007	188	25	impact	impact	NOUN
cana-1007	188	26	factor	factor	NOUN
cana-1007	188	27	journals	journal	NOUN
cana-1007	188	28	.	.	PUNCT
cana-1007	189	1	1	1	X
cana-1007	189	2	.	.	X
cana-1007	189	3	to	to	PART
cana-1007	189	4	apply	apply	VERB
cana-1007	189	5	the	the	DET
cana-1007	189	6	algorithm	algorithm	NOUN
cana-1007	189	7	of	of	ADP
cana-1007	189	8	the	the	DET
cana-1007	189	9	graph	graph	NOUN
cana-1007	189	10	cipher	cipher	ADJ
cana-1007	189	11	key	key	NOUN
cana-1007	189	12	and	and	CCONJ
cana-1007	189	13	the	the	DET
cana-1007	189	14	subset	subset	NOUN
cana-1007	189	15	x	x	NOUN
cana-1007	189	16	=	=	NOUN
cana-1007	189	17	pi	pi	NOUN
cana-1007	189	18	of	of	ADP
cana-1007	189	19	the	the	DET
cana-1007	189	20	polynomials	polynomial	NOUN
cana-1007	189	21	over	over	ADP
cana-1007	189	22	finite	finite	ADJ
cana-1007	189	23	field	field	NOUN
cana-1007	189	24	f	f	X
cana-1007	189	25	,	,	PUNCT
cana-1007	189	26	such	such	ADJ
cana-1007	189	27	that	that	PRON
cana-1007	189	28	for	for	ADP
cana-1007	189	29	every	every	DET
cana-1007	189	30	i	i	PROPN
cana-1007	189	31	,	,	PUNCT
cana-1007	189	32	pi(z)=0	pi(z)=0	PROPN
cana-1007	189	33	,	,	PUNCT
cana-1007	189	34	and	and	CCONJ
cana-1007	189	35	mathematical	mathematical	ADJ
cana-1007	189	36	or	or	CCONJ
cana-1007	189	37	non	non	ADJ
cana-1007	189	38	-	-	ADJ
cana-1007	189	39	mathematical	mathematical	ADJ
cana-1007	189	40	clues	clue	NOUN
cana-1007	189	41	as	as	ADP
cana-1007	189	42	a	a	DET
cana-1007	189	43	public	public	ADJ
cana-1007	189	44	key	key	NOUN
cana-1007	189	45	.	.	PUNCT
cana-1007	190	1	2	2	X
cana-1007	190	2	.	.	PUNCT
cana-1007	190	3	to	to	PART
cana-1007	190	4	encrypt	encrypt	VERB
cana-1007	190	5	a	a	DET
cana-1007	190	6	given	give	VERB
cana-1007	190	7	message	message	NOUN
cana-1007	190	8	obtaining	obtain	VERB
cana-1007	190	9	coded	code	VERB
cana-1007	190	10	message	message	NOUN
cana-1007	190	11	using	use	VERB
cana-1007	190	12	cipher	cipher	ADJ
cana-1007	190	13	polynomial	polynomial	ADJ
cana-1007	190	14	y	y	PROPN
cana-1007	190	15	as	as	ADP
cana-1007	190	16	a	a	DET
cana-1007	190	17	public	public	ADJ
cana-1007	190	18	key	key	NOUN
cana-1007	190	19	(	(	PUNCT
cana-1007	190	20	a	a	DET
cana-1007	190	21	randomly	randomly	ADV
cana-1007	190	22	chosen	choose	VERB
cana-1007	190	23	letter	letter	NOUN
cana-1007	190	24	generated	generate	VERB
cana-1007	190	25	by	by	ADP
cana-1007	190	26	x	x	NOUN
cana-1007	190	27	)	)	PUNCT
cana-1007	190	28	3	3	NUM
cana-1007	190	29	.	.	PUNCT
cana-1007	190	30	to	to	PART
cana-1007	190	31	decrypt	decrypt	VERB
cana-1007	190	32	a	a	DET
cana-1007	190	33	given	give	VERB
cana-1007	190	34	message	message	NOUN
cana-1007	190	35	by	by	ADP
cana-1007	190	36	finding	find	VERB
cana-1007	190	37	the	the	DET
cana-1007	190	38	value	value	NOUN
cana-1007	190	39	of	of	ADP
cana-1007	190	40	polynomial	polynomial	ADJ
cana-1007	190	41	y	y	PROPN
cana-1007	190	42	at	at	ADP
cana-1007	190	43	z.	z.	PROPN
cana-1007	190	44	4	4	NUM
cana-1007	190	45	.	.	PUNCT
cana-1007	191	1	the	the	DET
cana-1007	191	2	goal	goal	NOUN
cana-1007	191	3	of	of	ADP
cana-1007	191	4	this	this	DET
cana-1007	191	5	research	research	NOUN
cana-1007	191	6	is	be	AUX
cana-1007	191	7	to	to	PART
cana-1007	191	8	implement	implement	VERB
cana-1007	191	9	mathematical	mathematical	ADJ
cana-1007	191	10	modeling	modeling	NOUN
cana-1007	191	11	in	in	ADP
cana-1007	191	12	coding	code	VERB
cana-1007	191	13	,	,	PUNCT
cana-1007	191	14	network	network	NOUN
cana-1007	191	15	communication	communication	NOUN
cana-1007	191	16	and	and	CCONJ
cana-1007	191	17	introduce	introduce	VERB
cana-1007	191	18	the	the	DET
cana-1007	191	19	matlab	matlab	PROPN
cana-1007	191	20	platform	platform	NOUN
cana-1007	191	21	.	.	PUNCT
cana-1007	192	1	5	5	X
cana-1007	192	2	.	.	X
cana-1007	192	3	scope	scope	NOUN
cana-1007	192	4	of	of	ADP
cana-1007	192	5	work	work	NOUN
cana-1007	192	6	network	network	NOUN
cana-1007	192	7	communication	communication	NOUN
cana-1007	192	8	has	have	VERB
cana-1007	192	9	an	an	DET
cana-1007	192	10	important	important	ADJ
cana-1007	192	11	infrastructure	infrastructure	NOUN
cana-1007	192	12	in	in	ADP
cana-1007	192	13	contemporary	contemporary	ADJ
cana-1007	192	14	society	society	NOUN
cana-1007	192	15	.	.	PUNCT
cana-1007	193	1	theory	theory	NOUN
cana-1007	193	2	of	of	ADP
cana-1007	193	3	graph	graph	NOUN
cana-1007	193	4	uses	use	NOUN
cana-1007	193	5	in	in	ADP
cana-1007	193	6	network	network	NOUN
cana-1007	193	7	theory	theory	NOUN
cana-1007	193	8	specifically	specifically	ADV
cana-1007	193	9	in	in	ADP
cana-1007	193	10	network	network	NOUN
cana-1007	193	11	communications	communication	NOUN
cana-1007	193	12	and	and	CCONJ
cana-1007	193	13	coding	code	VERB
cana-1007	193	14	theory	theory	NOUN
cana-1007	193	15	.	.	PUNCT
cana-1007	194	1	network	network	NOUN
cana-1007	194	2	communication	communication	NOUN
cana-1007	194	3	is	be	AUX
cana-1007	194	4	mathematical	mathematical	ADJ
cana-1007	194	5	modeling	modeling	NOUN
cana-1007	194	6	that	that	DET
cana-1007	194	7	process	process	NOUN
cana-1007	194	8	and	and	CCONJ
cana-1007	194	9	learns	learn	VERB
cana-1007	194	10	from	from	ADP
cana-1007	194	11	graph	graph	NOUN
cana-1007	194	12	-	-	PUNCT
cana-1007	194	13	structured	structure	VERB
cana-1007	194	14	data	datum	NOUN
cana-1007	194	15	.	.	PUNCT
cana-1007	195	1	this	this	DET
cana-1007	195	2	work	work	NOUN
cana-1007	195	3	is	be	AUX
cana-1007	195	4	the	the	DET
cana-1007	195	5	rapidly	rapidly	ADV
cana-1007	195	6	growing	grow	VERB
cana-1007	195	7	body	body	NOUN
cana-1007	195	8	of	of	ADP
cana-1007	195	9	research	research	NOUN
cana-1007	195	10	using	use	VERB
cana-1007	195	11	different	different	ADJ
cana-1007	195	12	graph	graph	NOUN
cana-1007	195	13	based	base	VERB
cana-1007	195	14	deep	deep	ADJ
cana-1007	195	15	learning	learning	NOUN
cana-1007	195	16	models	model	NOUN
cana-1007	195	17	eg	eg	VERB
cana-1007	195	18	;	;	PUNCT
cana-1007	195	19	assigning	assign	VERB
cana-1007	195	20	numbers	number	NOUN
cana-1007	195	21	to	to	ADP
cana-1007	195	22	the	the	DET
cana-1007	195	23	vertices	vertex	NOUN
cana-1007	195	24	and	and	CCONJ
cana-1007	195	25	edges	edge	NOUN
cana-1007	195	26	of	of	ADP
cana-1007	195	27	a	a	DET
cana-1007	195	28	graph	graph	NOUN
cana-1007	195	29	and	and	CCONJ
cana-1007	195	30	graphical	graphical	ADJ
cana-1007	195	31	representation	representation	NOUN
cana-1007	195	32	,	,	PUNCT
cana-1007	195	33	in	in	ADP
cana-1007	195	34	different	different	ADJ
cana-1007	195	35	situations	situation	NOUN
cana-1007	195	36	from	from	ADP
cana-1007	195	37	various	various	ADJ
cana-1007	195	38	kinds	kind	NOUN
cana-1007	195	39	of	of	ADP
cana-1007	195	40	network	network	NOUN
cana-1007	195	41	communication	communication	NOUN
cana-1007	195	42	eg	eg	NOUN
cana-1007	195	43	:	:	PUNCT
cana-1007	195	44	information	information	NOUN
cana-1007	195	45	technology	technology	NOUN
cana-1007	195	46	networks	network	NOUN
cana-1007	195	47	.	.	PUNCT
cana-1007	196	1	the	the	DET
cana-1007	196	2	communication	communication	NOUN
cana-1007	196	3	becomes	become	VERB
cana-1007	196	4	very	very	ADV
cana-1007	196	5	much	much	ADV
cana-1007	196	6	limited	limit	VERB
cana-1007	196	7	between	between	ADP
cana-1007	196	8	the	the	DET
cana-1007	196	9	sender	sender	NOUN
cana-1007	196	10	and	and	CCONJ
cana-1007	196	11	the	the	DET
cana-1007	196	12	receiver	receiver	NOUN
cana-1007	196	13	and	and	CCONJ
cana-1007	196	14	not	not	PART
cana-1007	196	15	to	to	PART
cana-1007	196	16	be	be	AUX
cana-1007	196	17	understand	understand	VERB
cana-1007	196	18	by	by	ADP
cana-1007	196	19	others	other	NOUN
cana-1007	196	20	.	.	PUNCT
cana-1007	197	1	in	in	ADP
cana-1007	197	2	this	this	DET
cana-1007	197	3	project	project	NOUN
cana-1007	197	4	,	,	PUNCT
cana-1007	197	5	the	the	DET
cana-1007	197	6	use	use	NOUN
cana-1007	197	7	of	of	ADP
cana-1007	197	8	mathematical	mathematical	ADJ
cana-1007	197	9	algorithms	algorithm	NOUN
cana-1007	197	10	based	base	VERB
cana-1007	197	11	on	on	ADP
cana-1007	197	12	network	network	NOUN
cana-1007	197	13	communication	communication	NOUN
cana-1007	197	14	and	and	CCONJ
cana-1007	197	15	sharing	share	VERB
cana-1007	197	16	secrecy	secrecy	NOUN
cana-1007	197	17	with	with	ADP
cana-1007	197	18	the	the	DET
cana-1007	197	19	applications	application	NOUN
cana-1007	197	20	of	of	ADP
cana-1007	197	21	graph	graph	NOUN
cana-1007	197	22	theory	theory	NOUN
cana-1007	197	23	and	and	CCONJ
cana-1007	197	24	matlab	matlab	PROPN
cana-1007	197	25	environment	environment	NOUN
cana-1007	197	26	.	.	PUNCT
cana-1007	198	1	the	the	DET
cana-1007	198	2	research	research	NOUN
cana-1007	198	3	propose	propose	VERB
cana-1007	198	4	to	to	PART
cana-1007	198	5	work	work	VERB
cana-1007	198	6	on	on	ADP
cana-1007	198	7	graph	graph	NOUN
cana-1007	198	8	theory	theory	NOUN
cana-1007	198	9	,	,	PUNCT
cana-1007	198	10	coding	code	VERB
cana-1007	198	11	theory	theory	NOUN
cana-1007	198	12	,	,	PUNCT
cana-1007	198	13	and	and	CCONJ
cana-1007	198	14	networks	network	NOUN
cana-1007	198	15	approach	approach	NOUN
cana-1007	198	16	which	which	PRON
cana-1007	198	17	are	be	AUX
cana-1007	198	18	derived	derive	VERB
cana-1007	198	19	from	from	ADP
cana-1007	198	20	graph	graph	NOUN
cana-1007	198	21	representations	representation	NOUN
cana-1007	198	22	.	.	PUNCT
cana-1007	199	1	the	the	DET
cana-1007	199	2	experimental	experimental	ADJ
cana-1007	199	3	testing	testing	NOUN
cana-1007	199	4	will	will	AUX
cana-1007	199	5	be	be	AUX
cana-1007	199	6	developed	develop	VERB
cana-1007	199	7	for	for	ADP
cana-1007	199	8	new	new	ADJ
cana-1007	199	9	algorithms	algorithm	NOUN
cana-1007	199	10	to	to	PART
cana-1007	199	11	optimize	optimize	VERB
cana-1007	199	12	the	the	DET
cana-1007	199	13	mathematical	mathematical	ADJ
cana-1007	199	14	properties	property	NOUN
cana-1007	199	15	in	in	ADP
cana-1007	199	16	their	their	PRON
cana-1007	199	17	graph	graph	NOUN
cana-1007	199	18	structures	structure	NOUN
cana-1007	199	19	.	.	PUNCT
cana-1007	200	1	network	network	NOUN
cana-1007	200	2	communication	communication	NOUN
cana-1007	200	3	is	be	AUX
cana-1007	200	4	completely	completely	ADV
cana-1007	200	5	a	a	DET
cana-1007	200	6	mathematical	mathematical	ADJ
cana-1007	200	7	model	model	NOUN
cana-1007	200	8	,	,	PUNCT
cana-1007	200	9	graphical	graphical	ADJ
cana-1007	200	10	representation	representation	NOUN
cana-1007	200	11	of	of	ADP
cana-1007	200	12	communication	communication	NOUN
cana-1007	200	13	provides	provide	VERB
cana-1007	200	14	simpler	simple	ADJ
cana-1007	200	15	views	view	NOUN
cana-1007	200	16	,	,	PUNCT
cana-1007	200	17	and	and	CCONJ
cana-1007	200	18	graph	graph	VERB
cana-1007	200	19	theoretical	theoretical	ADJ
cana-1007	200	20	techniques	technique	NOUN
cana-1007	200	21	provide	provide	VERB
cana-1007	200	22	litral	litral	ADJ
cana-1007	200	23	reviews	review	NOUN
cana-1007	200	24	and	and	CCONJ
cana-1007	200	25	theory	theory	NOUN
cana-1007	200	26	of	of	ADP
cana-1007	200	27	graph	graph	NOUN
cana-1007	200	28	applications	application	NOUN
cana-1007	200	29	gives	give	VERB
cana-1007	200	30	readable	readable	ADJ
cana-1007	200	31	proofs	proof	NOUN
cana-1007	200	32	for	for	ADP
cana-1007	200	33	many	many	ADJ
cana-1007	200	34	problems	problem	NOUN
cana-1007	200	35	generating	generate	VERB
cana-1007	200	36	in	in	ADP
cana-1007	200	37	communicative	communicative	ADJ
cana-1007	200	38	networks	network	NOUN
cana-1007	200	39	.	.	PUNCT
cana-1007	201	1	this	this	DET
cana-1007	201	2	research	research	NOUN
cana-1007	201	3	work	work	NOUN
cana-1007	201	4	starts	start	VERB
cana-1007	201	5	with	with	ADP
cana-1007	201	6	an	an	DET
cana-1007	201	7	exploration	exploration	NOUN
cana-1007	201	8	of	of	ADP
cana-1007	201	9	theory	theory	NOUN
cana-1007	201	10	of	of	ADP
cana-1007	201	11	graphs	graph	NOUN
cana-1007	201	12	in	in	ADP
cana-1007	201	13	network	network	NOUN
cana-1007	201	14	communications	communication	NOUN
cana-1007	201	15	on	on	ADP
cana-1007	201	16	applied	apply	VERB
cana-1007	201	17	nonlinear	nonlinear	ADJ
cana-1007	201	18	analysis	analysis	NOUN
cana-1007	201	19	issn	issn	NOUN
cana-1007	201	20	:	:	PUNCT
cana-1007	201	21	1074	1074	NUM
cana-1007	201	22	-	-	PUNCT
cana-1007	201	23	133x	133x	NUM
cana-1007	201	24	vol	vol	NOUN
cana-1007	201	25	31	31	NUM
cana-1007	201	26	no	no	NOUN
cana-1007	201	27	.	.	PUNCT
cana-1007	202	1	5s	5s	NUM
cana-1007	202	2	(	(	PUNCT
cana-1007	202	3	2024	2024	NUM
cana-1007	202	4	)	)	PUNCT
cana-1007	202	5	137	137	NUM
cana-1007	202	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1007	202	7	communication	communication	NOUN
cana-1007	202	8	by	by	ADP
cana-1007	202	9	using	use	VERB
cana-1007	202	10	matlab	matlab	PROPN
cana-1007	202	11	and	and	CCONJ
cana-1007	202	12	obtaining	obtain	VERB
cana-1007	202	13	a	a	DET
cana-1007	202	14	secret	secret	ADJ
cana-1007	202	15	code	code	NOUN
cana-1007	202	16	by	by	ADP
cana-1007	202	17	encrypt	encrypt	NOUN
cana-1007	202	18	and	and	CCONJ
cana-1007	202	19	decrypt	decrypt	VERB
cana-1007	202	20	algorithms	algorithm	NOUN
cana-1007	202	21	in	in	ADP
cana-1007	202	22	coding	code	VERB
cana-1007	202	23	theory	theory	NOUN
cana-1007	202	24	.	.	PUNCT
cana-1007	203	1	the	the	DET
cana-1007	203	2	outcome	outcome	NOUN
cana-1007	203	3	of	of	ADP
cana-1007	203	4	this	this	DET
cana-1007	203	5	research	research	NOUN
cana-1007	203	6	is	be	AUX
cana-1007	203	7	not	not	PART
cana-1007	203	8	necessarily	necessarily	ADV
cana-1007	203	9	limited	limit	VERB
cana-1007	203	10	to	to	PART
cana-1007	203	11	graphs	graph	NOUN
cana-1007	203	12	in	in	ADP
cana-1007	203	13	coding	code	VERB
cana-1007	203	14	theory	theory	NOUN
cana-1007	203	15	but	but	CCONJ
cana-1007	203	16	also	also	ADV
cana-1007	203	17	be	be	AUX
cana-1007	203	18	applied	apply	VERB
cana-1007	203	19	in	in	ADP
cana-1007	203	20	other	other	ADJ
cana-1007	203	21	domains	domain	NOUN
cana-1007	203	22	such	such	ADJ
cana-1007	203	23	as	as	ADP
cana-1007	203	24	cryptographic	cryptographic	ADJ
cana-1007	203	25	methods	method	NOUN
cana-1007	203	26	,	,	PUNCT
cana-1007	203	27	public	public	ADJ
cana-1007	203	28	key	key	NOUN
cana-1007	203	29	cipher	cipher	ADJ
cana-1007	203	30	,	,	PUNCT
cana-1007	203	31	graph	graph	VERB
cana-1007	203	32	cipher	cipher	ADJ
cana-1007	203	33	,	,	PUNCT
cana-1007	203	34	and	and	CCONJ
cana-1007	203	35	wireless	wireless	ADJ
cana-1007	203	36	and	and	CCONJ
cana-1007	203	37	non	non	ADJ
cana-1007	203	38	-	-	ADJ
cana-1007	203	39	wireless	wireless	ADJ
cana-1007	203	40	networks	network	NOUN
cana-1007	203	41	.	.	PUNCT
cana-1007	204	1	6	6	X
cana-1007	204	2	.	.	X
cana-1007	204	3	conclusion	conclusion	NOUN
cana-1007	204	4	there	there	PRON
cana-1007	204	5	is	be	VERB
cana-1007	204	6	a	a	DET
cana-1007	204	7	proof	proof	NOUN
cana-1007	204	8	for	for	ADP
cana-1007	204	9	the	the	DET
cana-1007	204	10	long	long	ADV
cana-1007	204	11	-	-	PUNCT
cana-1007	204	12	standing	stand	VERB
cana-1007	204	13	open	open	ADJ
cana-1007	204	14	problem	problem	NOUN
cana-1007	204	15	,	,	PUNCT
cana-1007	204	16	that	that	SCONJ
cana-1007	204	17	there	there	PRON
cana-1007	204	18	is	be	VERB
cana-1007	204	19	satl	satl	NOUN
cana-1007	204	20	where	where	SCONJ
cana-1007	204	21	𝑒	𝑒	VERB
cana-1007	204	22	=	=	PUNCT
cana-1007	204	23	𝑞	𝑞	X
cana-1007	204	24	+	+	NOUN
cana-1007	204	25	𝑟	𝑟	NOUN
cana-1007	204	26	+	+	SYM
cana-1007	204	27	2	2	NUM
cana-1007	204	28	of	of	ADP
cana-1007	204	29	the	the	DET
cana-1007	204	30	graph	graph	NOUN
cana-1007	204	31	𝐺𝑥(𝑆𝑚	𝐺𝑥(𝑆𝑚	PROPN
cana-1007	204	32	)	)	PUNCT
cana-1007	204	33	,	,	PUNCT
cana-1007	204	34	𝑚	𝑚	X
cana-1007	204	35	≥	≥	NUM
cana-1007	204	36	3	3	NUM
cana-1007	204	37	.	.	PUNCT
cana-1007	205	1	the	the	DET
cana-1007	205	2	above	above	ADJ
cana-1007	205	3	theorems	theorem	NOUN
cana-1007	205	4	have	have	AUX
cana-1007	205	5	shown	show	VERB
cana-1007	205	6	that	that	DET
cana-1007	205	7	satl	satl	NOUN
cana-1007	205	8	is	be	AUX
cana-1007	205	9	exist	exist	VERB
cana-1007	205	10	for	for	ADP
cana-1007	205	11	𝐺𝑥(𝑆𝑚	𝐺𝑥(𝑆𝑚	NUM
cana-1007	205	12	)	)	PUNCT
cana-1007	205	13	for	for	ADP
cana-1007	205	14	𝑚	𝑚	NOUN
cana-1007	205	15	=	=	SYM
cana-1007	205	16	3,4,5	3,4,5	NUM
cana-1007	205	17	,	,	PUNCT
cana-1007	205	18	and	and	CCONJ
cana-1007	205	19	generalized	generalize	VERB
cana-1007	205	20	for	for	ADP
cana-1007	205	21	𝑆𝑚	𝑆𝑚	PROPN
cana-1007	205	22	for	for	ADP
cana-1007	205	23	different	different	ADJ
cana-1007	205	24	values	value	NOUN
cana-1007	205	25	of	of	ADP
cana-1007	205	26	𝑒.	𝑒.	NOUN
cana-1007	205	27	the	the	DET
cana-1007	205	28	author	author	NOUN
cana-1007	205	29	’s	’s	PART
cana-1007	205	30	future	future	ADJ
cana-1007	205	31	work	work	NOUN
cana-1007	205	32	will	will	AUX
cana-1007	205	33	include	include	VERB
cana-1007	205	34	investigating	investigate	VERB
cana-1007	205	35	the	the	DET
cana-1007	205	36	remaining	remain	VERB
cana-1007	205	37	open	open	ADJ
cana-1007	205	38	problems	problem	NOUN
cana-1007	205	39	have	have	AUX
cana-1007	205	40	yet	yet	ADV
cana-1007	205	41	been	be	AUX
cana-1007	205	42	solved	solve	VERB
cana-1007	205	43	.	.	PUNCT
cana-1007	206	1	references	reference	NOUN
cana-1007	206	2	[	[	X
cana-1007	206	3	1	1	NUM
cana-1007	206	4	]	]	PUNCT
cana-1007	206	5	s.arumugam	s.arumugam	NOUN
cana-1007	206	6	,	,	PUNCT
cana-1007	206	7	m.nalliah	m.nalliah	NOUN
cana-1007	206	8	,	,	PUNCT
cana-1007	206	9	super	sup	ADJ
cana-1007	206	10	(	(	PUNCT
cana-1007	206	11	a	a	PRON
cana-1007	206	12	,	,	PUNCT
cana-1007	206	13	d)-edge	d)-edge	ADJ
cana-1007	206	14	antimagic	antimagic	ADJ
cana-1007	206	15	total	total	ADJ
cana-1007	206	16	labelings	labeling	NOUN
cana-1007	206	17	of	of	ADP
cana-1007	206	18	friendship	friendship	NOUN
cana-1007	206	19	graphs	graph	NOUN
cana-1007	206	20	,	,	PUNCT
cana-1007	206	21	australian	australian	ADJ
cana-1007	206	22	journal	journal	NOUN
cana-1007	206	23	of	of	ADP
cana-1007	206	24	combinatorics	combinatorics	PROPN
cana-1007	206	25	,	,	PUNCT
cana-1007	206	26	volume	volume	NOUN
cana-1007	206	27	53(2012	53(2012	NUM
cana-1007	206	28	)	)	PUNCT
cana-1007	206	29	,	,	PUNCT
cana-1007	206	30	pages	page	NOUN
cana-1007	206	31	237	237	NUM
cana-1007	206	32	-	-	SYM
cana-1007	206	33	243	243	NUM
cana-1007	206	34	.	.	PUNCT
cana-1007	207	1	[	[	X
cana-1007	207	2	2	2	X
cana-1007	207	3	]	]	X
cana-1007	207	4	k.m	k.m	PROPN
cana-1007	207	5	kathiresan	kathiresan	PROPN
cana-1007	207	6	,	,	PUNCT
cana-1007	207	7	on	on	ADP
cana-1007	207	8	super	super	ADJ
cana-1007	207	9	(	(	PUNCT
cana-1007	207	10	a	a	PRON
cana-1007	207	11	,	,	PUNCT
cana-1007	207	12	d)-hantimagic	d)-hantimagic	ADJ
cana-1007	207	13	total	total	ADJ
cana-1007	207	14	covering	covering	NOUN
cana-1007	207	15	of	of	ADP
cana-1007	207	16	star	star	NOUN
cana-1007	207	17	related	relate	VERB
cana-1007	207	18	graphs	graph	NOUN
cana-1007	207	19	,	,	PUNCT
cana-1007	207	20	discussiones	discussione	NOUN
cana-1007	207	21	mathematicae	mathematicae	VERB
cana-1007	207	22	,	,	PUNCT
cana-1007	207	23	graph	graph	NOUN
cana-1007	207	24	theory	theory	NOUN
cana-1007	207	25	35	35	NUM
cana-1007	207	26	(	(	PUNCT
cana-1007	207	27	2015	2015	NUM
cana-1007	207	28	)	)	PUNCT
cana-1007	207	29	,	,	PUNCT
cana-1007	207	30	pages	page	VERB
cana-1007	207	31	755	755	NUM
cana-1007	207	32	-	-	SYM
cana-1007	207	33	764	764	NUM
cana-1007	207	34	.	.	PUNCT
cana-1007	208	1	[	[	X
cana-1007	208	2	3	3	NUM
cana-1007	208	3	]	]	PUNCT
cana-1007	208	4	a.kotzig	a.kotzig	NOUN
cana-1007	208	5	and	and	CCONJ
cana-1007	208	6	a.rosa	a.rosa	CCONJ
cana-1007	208	7	,	,	PUNCT
cana-1007	208	8	magic	magic	ADJ
cana-1007	208	9	valuation	valuation	NOUN
cana-1007	208	10	of	of	ADP
cana-1007	208	11	complete	complete	ADJ
cana-1007	208	12	graphs	graph	NOUN
cana-1007	208	13	,	,	PUNCT
cana-1007	208	14	center	center	NOUN
cana-1007	208	15	de	de	X
cana-1007	208	16	researchers	researcher	NOUN
cana-1007	208	17	,	,	PUNCT
cana-1007	208	18	mathematiques	mathematique	NOUN
cana-1007	208	19	,	,	PUNCT
cana-1007	208	20	universities	university	NOUN
cana-1007	208	21	de	de	ADP
cana-1007	208	22	montreal	montreal	PROPN
cana-1007	208	23	(	(	PUNCT
cana-1007	208	24	1972	1972	NUM
cana-1007	208	25	)	)	PUNCT
cana-1007	208	26	,	,	PUNCT
cana-1007	208	27	crm-175	crm-175	X
cana-1007	208	28	.	.	PUNCT
cana-1007	209	1	[	[	X
cana-1007	209	2	4	4	NUM
cana-1007	209	3	]	]	PUNCT
cana-1007	209	4	a.kotzig	a.kotzig	NOUN
cana-1007	209	5	and	and	CCONJ
cana-1007	209	6	a.rosa	a.rosa	CCONJ
cana-1007	209	7	,	,	PUNCT
cana-1007	209	8	magic	magic	ADJ
cana-1007	209	9	valuation	valuation	NOUN
cana-1007	209	10	of	of	ADP
cana-1007	209	11	finite	finite	PROPN
cana-1007	209	12	graphs	graph	NOUN
cana-1007	209	13	,	,	PUNCT
cana-1007	209	14	canad.math.bull	canad.math.bull	PROPN
cana-1007	209	15	13(1970	13(1970	NUM
cana-1007	209	16	)	)	PUNCT
cana-1007	209	17	,	,	PUNCT
cana-1007	209	18	pages	page	VERB
cana-1007	209	19	451	451	NUM
cana-1007	209	20	461	461	NUM
cana-1007	209	21	.	.	PUNCT
cana-1007	210	1	[	[	X
cana-1007	210	2	5	5	NUM
cana-1007	210	3	]	]	PUNCT
cana-1007	210	4	a.	a.	NOUN
cana-1007	210	5	delman	delman	NOUN
cana-1007	210	6	and	and	CCONJ
cana-1007	210	7	s.koilraj	s.koilraj	ADJ
cana-1007	210	8	,	,	PUNCT
cana-1007	210	9	super	super	ADJ
cana-1007	210	10	edge	edge	VERB
cana-1007	210	11	antimagic	antimagic	ADJ
cana-1007	210	12	total	total	ADJ
cana-1007	210	13	labeling	labeling	NOUN
cana-1007	210	14	of	of	ADP
cana-1007	210	15	fully	fully	ADV
cana-1007	210	16	generalized	generalize	VERB
cana-1007	210	17	extended	extended	ADJ
cana-1007	210	18	tree	tree	NOUN
cana-1007	210	19	,	,	PUNCT
cana-1007	210	20	international	international	ADJ
cana-1007	210	21	journal	journal	NOUN
cana-1007	210	22	of	of	ADP
cana-1007	210	23	scientific	scientific	ADJ
cana-1007	210	24	and	and	CCONJ
cana-1007	210	25	innovative	innovative	ADJ
cana-1007	210	26	mathematical	mathematical	ADJ
cana-1007	210	27	research	research	NOUN
cana-1007	210	28	,	,	PUNCT
cana-1007	210	29	volume	volume	NOUN
cana-1007	210	30	3	3	NUM
cana-1007	210	31	,	,	PUNCT
cana-1007	210	32	issue	issue	NOUN
cana-1007	210	33	11	11	NUM
cana-1007	210	34	,	,	PUNCT
cana-1007	210	35	november	november	PROPN
cana-1007	210	36	2015	2015	NUM
cana-1007	210	37	,	,	PUNCT
cana-1007	210	38	pages	page	NOUN
cana-1007	210	39	28	28	NUM
cana-1007	210	40	-	-	SYM
cana-1007	210	41	35	35	NUM
cana-1007	210	42	.	.	PUNCT
cana-1007	211	1	[	[	X
cana-1007	211	2	6	6	NUM
cana-1007	211	3	]	]	SYM
cana-1007	211	4	c.palanivelu	c.palanivelu	NOUN
cana-1007	211	5	and	and	CCONJ
cana-1007	211	6	n.neela	n.neela	NOUN
cana-1007	211	7	,	,	PUNCT
cana-1007	211	8	super	sup	ADJ
cana-1007	211	9	(	(	PUNCT
cana-1007	211	10	a	a	PRON
cana-1007	211	11	,	,	PUNCT
cana-1007	211	12	d)edge	d)edge	PROPN
cana-1007	211	13	antimagic	antimagic	ADJ
cana-1007	211	14	total	total	ADJ
cana-1007	211	15	labeling	labeling	NOUN
cana-1007	211	16	of	of	ADP
cana-1007	211	17	union	union	NOUN
cana-1007	211	18	of	of	ADP
cana-1007	211	19	stars	star	NOUN
cana-1007	211	20	,	,	PUNCT
cana-1007	211	21	international	international	ADJ
cana-1007	211	22	journal	journal	NOUN
cana-1007	211	23	of	of	ADP
cana-1007	211	24	applied	apply	VERB
cana-1007	211	25	engineering	engineering	NOUN
cana-1007	211	26	research	research	NOUN
cana-1007	211	27	,	,	PUNCT
cana-1007	211	28	issn	issn	PROPN
cana-1007	211	29	0973	0973	NUM
cana-1007	211	30	-	-	SYM
cana-1007	211	31	4562	4562	NUM
cana-1007	211	32	,	,	PUNCT
cana-1007	211	33	volume	volume	NOUN
cana-1007	211	34	14	14	NUM
cana-1007	211	35	,	,	PUNCT
cana-1007	211	36	november	november	PROPN
cana-1007	211	37	9(2019	9(2019	NUM
cana-1007	211	38	)	)	PUNCT
cana-1007	211	39	,	,	PUNCT
cana-1007	211	40	pages	page	NOUN
cana-1007	211	41	2089	2089	NUM
cana-1007	211	42	2092	2092	NUM
cana-1007	211	43	.	.	PUNCT
cana-1007	212	1	[	[	X
cana-1007	212	2	7	7	X
cana-1007	212	3	]	]	X
cana-1007	212	4	d.b	d.b	X
cana-1007	212	5	west	west	PROPN
cana-1007	212	6	,	,	PUNCT
cana-1007	212	7	an	an	DET
cana-1007	212	8	introduction	introduction	NOUN
cana-1007	212	9	to	to	AUX
cana-1007	212	10	graph	graph	NOUN
cana-1007	212	11	theory	theory	NOUN
cana-1007	212	12	,	,	PUNCT
cana-1007	212	13	prentice	prentice	NOUN
cana-1007	212	14	hall	hall	NOUN
cana-1007	212	15	,	,	PUNCT
cana-1007	212	16	1996	1996	NUM
cana-1007	212	17	.	.	PUNCT
cana-1007	213	1	[	[	X
cana-1007	213	2	8	8	X
cana-1007	213	3	]	]	X
cana-1007	213	4	j.a	j.a	PROPN
cana-1007	213	5	gallian	gallian	NOUN
cana-1007	213	6	,	,	PUNCT
cana-1007	213	7	a	a	DET
cana-1007	213	8	dynamic	dynamic	ADJ
cana-1007	213	9	survey	survey	NOUN
cana-1007	213	10	of	of	ADP
cana-1007	213	11	graph	graph	NOUN
cana-1007	213	12	labeling	labeling	NOUN
cana-1007	213	13	,	,	PUNCT
cana-1007	213	14	the	the	DET
cana-1007	213	15	electronic	electronic	ADJ
cana-1007	213	16	journal	journal	NOUN
cana-1007	213	17	of	of	ADP
cana-1007	213	18	combinatorics	combinatoric	NOUN
cana-1007	213	19	(	(	PUNCT
cana-1007	213	20	2018	2018	NUM
cana-1007	213	21	)	)	PUNCT
cana-1007	213	22	.	.	PUNCT
cana-1007	214	1	[	[	X
cana-1007	214	2	9	9	NUM
cana-1007	214	3	]	]	X
cana-1007	214	4	g.	g.	PROPN
cana-1007	214	5	uma	uma	PROPN
cana-1007	214	6	maheswari	maheswari	PROPN
cana-1007	214	7	,	,	PUNCT
cana-1007	214	8	g.	g.	PROPN
cana-1007	214	9	margaret	margaret	PROPN
cana-1007	214	10	joan	joan	PROPN
cana-1007	214	11	jebarani	jebarani	PROPN
cana-1007	214	12	and	and	CCONJ
cana-1007	214	13	v.	v.	ADP
cana-1007	214	14	balaji	balaji	PROPN
cana-1007	214	15	,	,	PUNCT
cana-1007	214	16	on	on	ADP
cana-1007	214	17	similar	similar	ADJ
cana-1007	214	18	super	super	ADV
cana-1007	214	19	mean	mean	ADJ
cana-1007	214	20	labeling	labeling	NOUN
cana-1007	214	21	for	for	ADP
cana-1007	214	22	two	two	NUM
cana-1007	214	23	star	star	NOUN
cana-1007	214	24	graph	graph	NOUN
cana-1007	214	25	,	,	PUNCT
cana-1007	214	26	asian	asian	ADJ
cana-1007	214	27	journal	journal	NOUN
cana-1007	214	28	of	of	ADP
cana-1007	214	29	mathematics	mathematics	PROPN
cana-1007	214	30	and	and	CCONJ
cana-1007	214	31	computer	computer	NOUN
cana-1007	214	32	research	research	NOUN
cana-1007	214	33	,	,	PUNCT
cana-1007	214	34	volume	volume	NOUN
cana-1007	214	35	21(2	21(2	NUM
cana-1007	214	36	)	)	PUNCT
cana-1007	214	37	2017	2017	NUM
cana-1007	214	38	,	,	PUNCT
cana-1007	214	39	53	53	NUM
cana-1007	214	40	−	−	NOUN
cana-1007	214	41	62	62	NUM
cana-1007	214	42	.	.	PUNCT
cana-1007	215	1	[	[	X
cana-1007	215	2	10	10	NUM
cana-1007	215	3	]	]	X
cana-1007	215	4	g.	g.	PROPN
cana-1007	215	5	uma	uma	PROPN
cana-1007	215	6	maheswari	maheswari	PROPN
cana-1007	215	7	,	,	PUNCT
cana-1007	215	8	g.	g.	PROPN
cana-1007	215	9	margaret	margaret	PROPN
cana-1007	215	10	joan	joan	PROPN
cana-1007	215	11	jebarani	jebarani	PROPN
cana-1007	215	12	and	and	CCONJ
cana-1007	215	13	v.	v.	ADP
cana-1007	215	14	balaji	balaji	PROPN
cana-1007	215	15	,	,	PUNCT
cana-1007	215	16	sub	sub	VERB
cana-1007	215	17	super	super	ADV
cana-1007	215	18	mean	mean	ADJ
cana-1007	215	19	labeling	labeling	NOUN
cana-1007	215	20	on	on	ADP
cana-1007	215	21	a	a	DET
cana-1007	215	22	general	general	ADJ
cana-1007	215	23	three	three	NUM
cana-1007	215	24	star	star	NOUN
cana-1007	215	25	graph	graph	NOUN
cana-1007	215	26	,	,	PUNCT
cana-1007	215	27	international	international	ADJ
cana-1007	215	28	journal	journal	NOUN
cana-1007	215	29	of	of	ADP
cana-1007	215	30	mathematics	mathematic	NOUN
cana-1007	215	31	and	and	CCONJ
cana-1007	215	32	its	its	PRON
cana-1007	215	33	applications	application	NOUN
cana-1007	215	34	,	,	PUNCT
cana-1007	215	35	volume	volume	NOUN
cana-1007	215	36	6(1	6(1	NUM
cana-1007	215	37	)	)	PUNCT
cana-1007	215	38	,	,	PUNCT
cana-1007	215	39	2018	2018	NUM
cana-1007	215	40	,	,	PUNCT
cana-1007	215	41	147	147	NUM
cana-1007	215	42	−	−	NUM
cana-1007	215	43	153	153	NUM
cana-1007	215	44	.	.	PUNCT
cana-1007	216	1	[	[	X
cana-1007	216	2	11	11	NUM
cana-1007	216	3	]	]	SYM
cana-1007	216	4	m.javid	m.javid	NOUN
cana-1007	216	5	,	,	PUNCT
cana-1007	216	6	on	on	ADP
cana-1007	216	7	super	super	ADJ
cana-1007	216	8	edge	edge	NOUN
cana-1007	216	9	-	-	PUNCT
cana-1007	216	10	antimagic	antimagic	NOUN
cana-1007	216	11	total	total	ADJ
cana-1007	216	12	labeling	labeling	NOUN
cana-1007	216	13	on	on	ADP
cana-1007	216	14	generalized	generalize	VERB
cana-1007	216	15	extended	extended	ADJ
cana-1007	216	16	w	w	NOUN
cana-1007	216	17	-	-	PUNCT
cana-1007	216	18	trees	tree	NOUN
cana-1007	216	19	,	,	PUNCT
cana-1007	216	20	international	international	ADJ
cana-1007	216	21	journal	journal	NOUN
cana-1007	216	22	of	of	ADP
cana-1007	216	23	mathematics	mathematic	NOUN
cana-1007	216	24	and	and	CCONJ
cana-1007	216	25	soft	soft	ADJ
cana-1007	216	26	computing	computing	NOUN
cana-1007	216	27	,	,	PUNCT
cana-1007	216	28	volume	volume	NOUN
cana-1007	216	29	4(1	4(1	NOUN
cana-1007	216	30	)	)	PUNCT
cana-1007	216	31	(	(	PUNCT
cana-1007	216	32	2014),17	2014),17	NUM
cana-1007	216	33	-	-	SYM
cana-1007	216	34	25	25	NUM
cana-1007	216	35	.	.	PUNCT
cana-1007	217	1	[	[	X
cana-1007	217	2	12	12	NUM
cana-1007	217	3	]	]	PUNCT
cana-1007	217	4	n.inayah	n.inayah	NOUN
cana-1007	217	5	,	,	PUNCT
cana-1007	217	6	r.simanjuntak	r.simanjuntak	NOUN
cana-1007	217	7	and	and	CCONJ
cana-1007	217	8	a.n.m	a.n.m	PROPN
cana-1007	217	9	.	.	PUNCT
cana-1007	218	1	salman	salman	PROPN
cana-1007	218	2	,	,	PUNCT
cana-1007	218	3	super	sup	ADJ
cana-1007	218	4	(	(	PUNCT
cana-1007	218	5	a	a	DET
cana-1007	218	6	,	,	PUNCT
cana-1007	218	7	d)-h	d)-h	NOUN
cana-1007	218	8	-	-	ADJ
cana-1007	218	9	antimagic	antimagic	ADJ
cana-1007	218	10	total	total	ADJ
cana-1007	218	11	labelings	labeling	NOUN
cana-1007	218	12	for	for	ADP
cana-1007	218	13	shackles	shackle	NOUN
cana-1007	218	14	of	of	ADP
cana-1007	218	15	a	a	DET
cana-1007	218	16	connected	connected	ADJ
cana-1007	218	17	graph	graph	NOUN
cana-1007	218	18	h	h	NOUN
cana-1007	218	19	,	,	PUNCT
cana-1007	218	20	australas	australa	NOUN
cana-1007	218	21	.	.	PUNCT
cana-1007	219	1	j.	j.	PROPN
cana-1007	219	2	combin	combin	PROPN
cana-1007	219	3	.	.	PUNCT
cana-1007	220	1	57	57	NUM
cana-1007	220	2	(	(	PUNCT
cana-1007	220	3	2013	2013	NUM
cana-1007	220	4	)	)	PUNCT
cana-1007	220	5	127	127	NUM
cana-1007	220	6	-	-	SYM
cana-1007	220	7	138	138	NUM
cana-1007	220	8	.	.	PUNCT
cana-1007	221	1	[	[	X
cana-1007	221	2	13	13	NUM
cana-1007	221	3	]	]	PUNCT
cana-1007	221	4	k.kominfo	k.kominfo	NOUN
cana-1007	221	5	2020	2020	NUM
cana-1007	221	6	care	care	NOUN
cana-1007	221	7	and	and	CCONJ
cana-1007	221	8	protect	protect	VERB
cana-1007	221	9	kominfo	kominfo	PROPN
cana-1007	221	10	ministry	ministry	PROPN
cana-1007	221	11	indonesia	indonesia	PROPN
cana-1007	221	12	.	.	PUNCT
cana-1007	222	1	[	[	X
cana-1007	222	2	14	14	NUM
cana-1007	222	3	]	]	X
cana-1007	222	4	a	a	DET
cana-1007	222	5	g	g	NOUN
cana-1007	222	6	c	c	PROPN
cana-1007	222	7	p	p	NOUN
cana-1007	222	8	a	a	DET
cana-1007	222	9	r	r	NOUN
cana-1007	222	10	a	a	DET
cana-1007	222	11	k	k	NOUN
cana-1007	222	12	r	r	NOUN
cana-1007	222	13	hrasko	hrasko	ADV
cana-1007	222	14	2019	2019	NUM
cana-1007	222	15	time	time	NOUN
cana-1007	222	16	series	series	NOUN
cana-1007	222	17	prediction	prediction	NOUN
cana-1007	222	18	using	use	VERB
cana-1007	222	19	restricted	restrict	VERB
cana-1007	222	20	boltzmann	boltzmann	PROPN
cana-1007	222	21	machines	machine	NOUN
cana-1007	222	22	and	and	CCONJ
cana-1007	222	23	backpropagation	backpropagation	NOUN
cana-1007	222	24	procedia	procedia	PROPN
cana-1007	222	25	comput	comput	NOUN
cana-1007	222	26	.	.	PUNCT
cana-1007	223	1	sci	sci	PROPN
cana-1007	223	2	.	.	PUNCT
cana-1007	223	3	vol	vol	NOUN
cana-1007	223	4	.	.	PUNCT
cana-1007	224	1	55	55	NUM
cana-1007	224	2	pp	pp	NOUN
cana-1007	224	3	.	.	PUNCT
cana-1007	225	1	990	990	NUM
cana-1007	225	2	-	-	SYM
cana-1007	225	3	999	999	NUM
cana-1007	225	4	.	.	PUNCT