id	sid	tid	token	lemma	pos
cana-5925	1	1	communications	communication	NOUN
cana-5925	1	2	on	on	ADP
cana-5925	1	3	applied	apply	VERB
cana-5925	1	4	nonlinear	nonlinear	ADJ
cana-5925	1	5	analysis	analysis	NOUN
cana-5925	1	6	issn	issn	NOUN
cana-5925	1	7	:	:	PUNCT
cana-5925	1	8	1074	1074	NUM
cana-5925	1	9	-	-	PUNCT
cana-5925	1	10	133x	133x	NUM
cana-5925	1	11	vol	vol	NOUN
cana-5925	1	12	32	32	NUM
cana-5925	1	13	no	no	NOUN
cana-5925	1	14	.	.	NOUN
cana-5925	1	15	3	3	NUM
cana-5925	1	16	(	(	PUNCT
cana-5925	1	17	2025	2025	NUM
cana-5925	1	18	)	)	PUNCT
cana-5925	1	19	1040	1040	NUM
cana-5925	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5925	1	21	topological	topological	ADJ
cana-5925	1	22	cordial	cordial	ADJ
cana-5925	1	23	labeling	labeling	NOUN
cana-5925	1	24	of	of	ADP
cana-5925	1	25	some	some	DET
cana-5925	1	26	graphs	graph	NOUN
cana-5925	1	27	dr	dr	PROPN
cana-5925	1	28	.	.	PROPN
cana-5925	1	29	s.	s.	PROPN
cana-5925	1	30	selestin	selestin	PROPN
cana-5925	1	31	lina	lina	PROPN
cana-5925	1	32	assistant	assistant	PROPN
cana-5925	1	33	professor	professor	PROPN
cana-5925	1	34	,	,	PUNCT
cana-5925	1	35	department	department	NOUN
cana-5925	1	36	of	of	ADP
cana-5925	1	37	mathematics	mathematic	NOUN
cana-5925	1	38	,	,	PUNCT
cana-5925	1	39	nanjil	nanjil	ADP
cana-5925	1	40	catholic	catholic	PROPN
cana-5925	1	41	college	college	PROPN
cana-5925	1	42	of	of	ADP
cana-5925	1	43	arts	art	NOUN
cana-5925	1	44	and	and	CCONJ
cana-5925	1	45	science	science	NOUN
cana-5925	1	46	,	,	PUNCT
cana-5925	1	47	kaliyakkavilai	kaliyakkavilai	PROPN
cana-5925	1	48	,	,	PUNCT
cana-5925	1	49	kanyakumari	kanyakumari	PROPN
cana-5925	1	50	district	district	PROPN
cana-5925	1	51	,	,	PUNCT
cana-5925	1	52	affiliated	affiliate	VERB
cana-5925	1	53	to	to	ADP
cana-5925	1	54	manonmaniam	manonmaniam	PROPN
cana-5925	1	55	sundaranar	sundaranar	PROPN
cana-5925	1	56	university	university	NOUN
cana-5925	1	57	,	,	PUNCT
cana-5925	1	58	tirunelveli-627012	tirunelveli-627012	NOUN
cana-5925	1	59	,	,	PUNCT
cana-5925	1	60	tamil	tamil	PROPN
cana-5925	1	61	nadu	nadu	PROPN
cana-5925	1	62	,	,	PUNCT
cana-5925	1	63	india	india	PROPN
cana-5925	1	64	.	.	PUNCT
cana-5925	2	1	e	e	X
cana-5925	2	2	-	-	NOUN
cana-5925	2	3	mail	mail	NOUN
cana-5925	2	4	:	:	PUNCT
cana-5925	3	1	selestinlina@gmail.com	selestinlina@gmail.com	X
cana-5925	3	2	article	article	NOUN
cana-5925	3	3	history	history	NOUN
cana-5925	3	4	:	:	PUNCT
cana-5925	3	5	received	receive	VERB
cana-5925	3	6	:	:	PUNCT
cana-5925	3	7	02	02	NUM
cana-5925	3	8	-	-	PUNCT
cana-5925	3	9	01	01	NUM
cana-5925	3	10	-	-	PUNCT
cana-5925	3	11	2025	2025	NUM
cana-5925	3	12	revised	revise	VERB
cana-5925	3	13	:	:	PUNCT
cana-5925	3	14	25	25	NUM
cana-5925	3	15	-	-	PUNCT
cana-5925	3	16	02	02	NUM
cana-5925	3	17	-	-	PUNCT
cana-5925	3	18	2025	2025	NUM
cana-5925	3	19	accepted	accept	VERB
cana-5925	3	20	:	:	PUNCT
cana-5925	3	21	20	20	NUM
cana-5925	3	22	-	-	SYM
cana-5925	3	23	03	03	NUM
cana-5925	3	24	-	-	PUNCT
cana-5925	3	25	2025	2025	NUM
cana-5925	3	26	abstract	abstract	ADJ
cana-5925	3	27	b.d	b.d	PROPN
cana-5925	3	28	.	.	PROPN
cana-5925	3	29	acharya	acharya	PROPN
cana-5925	4	1	[	[	X
cana-5925	4	2	3	3	X
cana-5925	4	3	]	]	PUNCT
cana-5925	4	4	introduced	introduce	VERB
cana-5925	4	5	the	the	DET
cana-5925	4	6	notion	notion	NOUN
cana-5925	4	7	of	of	ADP
cana-5925	4	8	set	set	NOUN
cana-5925	4	9	–	–	PUNCT
cana-5925	4	10	valuation	valuation	NOUN
cana-5925	4	11	as	as	ADP
cana-5925	4	12	set	set	VERB
cana-5925	4	13	analogue	analogue	NOUN
cana-5925	4	14	of	of	ADP
cana-5925	4	15	number	number	NOUN
cana-5925	4	16	valuation	valuation	NOUN
cana-5925	4	17	as	as	SCONJ
cana-5925	4	18	introduced	introduce	VERB
cana-5925	4	19	by	by	ADP
cana-5925	4	20	a.	a.	PROPN
cana-5925	4	21	rosa	rosa	PROPN
cana-5925	5	1	[	[	X
cana-5925	5	2	5	5	NUM
cana-5925	5	3	]	]	PUNCT
cana-5925	5	4	.	.	PUNCT
cana-5925	6	1	let	let	VERB
cana-5925	6	2	g	g	PRON
cana-5925	6	3	be	be	AUX
cana-5925	6	4	a	a	DET
cana-5925	6	5	graph	graph	NOUN
cana-5925	6	6	and	and	CCONJ
cana-5925	6	7	x	x	NOUN
cana-5925	6	8	,	,	PUNCT
cana-5925	6	9	a	a	DET
cana-5925	6	10	non	non	ADJ
cana-5925	6	11	-	-	ADJ
cana-5925	6	12	empty	empty	ADJ
cana-5925	6	13	set	set	NOUN
cana-5925	6	14	.	.	PUNCT
cana-5925	7	1	define	define	VERB
cana-5925	7	2	an	an	DET
cana-5925	7	3	injective	injective	ADJ
cana-5925	7	4	function	function	NOUN
cana-5925	8	1	f	f	NOUN
cana-5925	8	2	:	:	PUNCT
cana-5925	8	3	v(g)→2^x	v(g)→2^x	INTJ
cana-5925	8	4	such	such	ADJ
cana-5925	8	5	that	that	SCONJ
cana-5925	8	6	{	{	PUNCT
cana-5925	8	7	f(v(g	f(v(g	PROPN
cana-5925	8	8	)	)	PUNCT
cana-5925	8	9	)	)	PUNCT
cana-5925	8	10	}	}	PUNCT
cana-5925	8	11	is	be	AUX
cana-5925	8	12	a	a	DET
cana-5925	8	13	topology	topology	NOUN
cana-5925	8	14	on	on	ADP
cana-5925	8	15	x.	x.	NOUN
cana-5925	8	16	if	if	SCONJ
cana-5925	8	17	the	the	DET
cana-5925	8	18	induced	induce	VERB
cana-5925	8	19	function	function	NOUN
cana-5925	8	20	f^	f^	VERB
cana-5925	8	21	*	*	VERB
cana-5925	8	22	on	on	ADP
cana-5925	8	23	e(g	e(g	PROPN
cana-5925	8	24	)	)	PUNCT
cana-5925	8	25	is	be	AUX
cana-5925	8	26	defined	define	VERB
cana-5925	8	27	by	by	ADP
cana-5925	8	28	f^	f^	PROPN
cana-5925	8	29	*	*	SYM
cana-5925	8	30	(	(	PUNCT
cana-5925	8	31	uv)={	uv)={	PROPN
cana-5925	8	32	■	■	NOUN
cana-5925	8	33	(1	(1	NOUN
cana-5925	8	34	if	if	SCONJ
cana-5925	8	35	f(u)∩f(v	f(u)∩f(v	NOUN
cana-5925	8	36	)	)	PUNCT
cana-5925	8	37	is	be	AUX
cana-5925	8	38	not	not	PART
cana-5925	8	39	an	an	DET
cana-5925	8	40	empty	empty	ADJ
cana-5925	8	41	set	set	NOUN
cana-5925	8	42	and	and	CCONJ
cana-5925	8	43	singleton	singleton	PROPN
cana-5925	8	44	set@0	set@0	NOUN
cana-5925	8	45	otherwise	otherwise	ADV
cana-5925	8	46	)	)	PUNCT
cana-5925	8	47	┤	┤	PROPN
cana-5925	8	48	for	for	ADP
cana-5925	8	49	every	every	DET
cana-5925	8	50	uv∈e(g	uv∈e(g	NOUN
cana-5925	8	51	)	)	PUNCT
cana-5925	9	1	such	such	ADJ
cana-5925	9	2	that	that	SCONJ
cana-5925	9	3	|e_f	|e_f	PROPN
cana-5925	9	4	(	(	PUNCT
cana-5925	9	5	0)-e_f	0)-e_f	NUM
cana-5925	9	6	(	(	PUNCT
cana-5925	9	7	1)|≤1	1)|≤1	NUM
cana-5925	9	8	where	where	SCONJ
cana-5925	9	9	e_f	e_f	PROPN
cana-5925	9	10	(	(	PUNCT
cana-5925	9	11	0)=	0)=	NUM
cana-5925	9	12	number	number	NOUN
cana-5925	9	13	of	of	ADP
cana-5925	9	14	edges	edge	NOUN
cana-5925	9	15	labeled	label	VERB
cana-5925	9	16	with	with	ADP
cana-5925	9	17	0	0	NUM
cana-5925	9	18	and〖	and〖	PROPN
cana-5925	9	19	e〗	e〗	PROPN
cana-5925	10	1	_	_	PUNCT
cana-5925	10	2	f	f	X
cana-5925	10	3	(	(	PUNCT
cana-5925	10	4	1)=	1)=	NUM
cana-5925	10	5	number	number	NOUN
cana-5925	10	6	of	of	ADP
cana-5925	10	7	edges	edge	NOUN
cana-5925	10	8	labeled	label	VERB
cana-5925	10	9	with	with	ADP
cana-5925	10	10	1	1	NUM
cana-5925	10	11	then	then	ADV
cana-5925	10	12	f	f	PROPN
cana-5925	10	13	is	be	AUX
cana-5925	10	14	a	a	DET
cana-5925	10	15	topological	topological	ADJ
cana-5925	10	16	cordial	cordial	ADJ
cana-5925	10	17	labeling	labeling	NOUN
cana-5925	10	18	and	and	CCONJ
cana-5925	10	19	a	a	DET
cana-5925	10	20	graph	graph	NOUN
cana-5925	10	21	which	which	PRON
cana-5925	10	22	admits	admit	VERB
cana-5925	10	23	such	such	DET
cana-5925	10	24	a	a	DET
cana-5925	10	25	labeling	labeling	NOUN
cana-5925	10	26	is	be	AUX
cana-5925	10	27	called	call	VERB
cana-5925	10	28	topological	topological	ADJ
cana-5925	10	29	cordial	cordial	ADJ
cana-5925	10	30	graph	graph	NOUN
cana-5925	10	31	.	.	PUNCT
cana-5925	11	1	in	in	ADP
cana-5925	11	2	this	this	DET
cana-5925	11	3	paper	paper	NOUN
cana-5925	11	4	we	we	PRON
cana-5925	11	5	proved	prove	VERB
cana-5925	11	6	dodecahedral	dodecahedral	ADJ
cana-5925	11	7	graph	graph	NOUN
cana-5925	11	8	,	,	PUNCT
cana-5925	11	9	paley	paley	ADJ
cana-5925	11	10	graph	graph	NOUN
cana-5925	11	11	and	and	CCONJ
cana-5925	11	12	some	some	DET
cana-5925	11	13	constructed	construct	VERB
cana-5925	11	14	graphs	graph	NOUN
cana-5925	11	15	are	be	AUX
cana-5925	11	16	topological	topological	ADJ
cana-5925	11	17	cordial	cordial	ADJ
cana-5925	11	18	graph	graph	NOUN
cana-5925	11	19	.	.	PUNCT
cana-5925	12	1	key	key	ADJ
cana-5925	12	2	words:-dodecahedral	words:-dodecahedral	ADJ
cana-5925	12	3	graph	graph	NOUN
cana-5925	12	4	,	,	PUNCT
cana-5925	12	5	paley	paley	ADJ
cana-5925	12	6	graph	graph	NOUN
cana-5925	12	7	and	and	CCONJ
cana-5925	12	8	topological	topological	ADJ
cana-5925	12	9	cordial	cordial	ADJ
cana-5925	12	10	graph	graph	NOUN
cana-5925	12	11	.	.	PUNCT
cana-5925	13	1	introduction	introduction	NOUN
cana-5925	13	2	the	the	DET
cana-5925	13	3	graphs	graph	NOUN
cana-5925	13	4	treated	treat	VERB
cana-5925	13	5	in	in	ADP
cana-5925	13	6	this	this	DET
cana-5925	13	7	paper	paper	NOUN
cana-5925	13	8	are	be	AUX
cana-5925	13	9	simple	simple	ADJ
cana-5925	13	10	.	.	PUNCT
cana-5925	14	1	for	for	ADP
cana-5925	14	2	standard	standard	ADJ
cana-5925	14	3	terminology	terminology	NOUN
cana-5925	14	4	and	and	CCONJ
cana-5925	14	5	notations	notation	NOUN
cana-5925	14	6	we	we	PRON
cana-5925	14	7	follow	follow	VERB
cana-5925	14	8	f.	f.	PROPN
cana-5925	14	9	harary	harary	PROPN
cana-5925	15	1	[	[	X
cana-5925	15	2	4	4	NUM
cana-5925	15	3	]	]	PUNCT
cana-5925	15	4	.	.	PUNCT
cana-5925	16	1	given	give	VERB
cana-5925	16	2	a	a	DET
cana-5925	16	3	graph	graph	NOUN
cana-5925	16	4	𝐺	𝐺	NOUN
cana-5925	16	5	=	=	SYM
cana-5925	16	6	(	(	PUNCT
cana-5925	16	7	𝑉	𝑉	PROPN
cana-5925	16	8	,	,	PUNCT
cana-5925	16	9	𝐸	𝐸	PROPN
cana-5925	16	10	)	)	PUNCT
cana-5925	16	11	,	,	PUNCT
cana-5925	16	12	we	we	PRON
cana-5925	16	13	can	can	AUX
cana-5925	16	14	relate	relate	VERB
cana-5925	16	15	it	it	PRON
cana-5925	16	16	to	to	ADP
cana-5925	16	17	different	different	ADJ
cana-5925	16	18	topological	topological	ADJ
cana-5925	16	19	structures	structure	NOUN
cana-5925	16	20	.	.	PUNCT
cana-5925	17	1	the	the	DET
cana-5925	17	2	relation	relation	NOUN
cana-5925	17	3	between	between	ADP
cana-5925	17	4	topology	topology	NOUN
cana-5925	17	5	and	and	CCONJ
cana-5925	17	6	graph	graph	NOUN
cana-5925	17	7	theory	theory	NOUN
cana-5925	17	8	is	be	AUX
cana-5925	17	9	undergone	undergo	VERB
cana-5925	17	10	many	many	ADJ
cana-5925	17	11	investigations	investigation	NOUN
cana-5925	17	12	.	.	PUNCT
cana-5925	18	1	in	in	ADP
cana-5925	18	2	1983	1983	NUM
cana-5925	18	3	acharya	acharya	NOUN
cana-5925	18	4	[	[	X
cana-5925	18	5	3	3	X
cana-5925	18	6	]	]	PUNCT
cana-5925	18	7	established	establish	VERB
cana-5925	18	8	another	another	DET
cana-5925	18	9	link	link	NOUN
cana-5925	18	10	between	between	ADP
cana-5925	18	11	graph	graph	NOUN
cana-5925	18	12	theory	theory	NOUN
cana-5925	18	13	and	and	CCONJ
cana-5925	18	14	point	point	NOUN
cana-5925	18	15	–	–	PUNCT
cana-5925	18	16	set	set	VERB
cana-5925	18	17	topology	topology	NOUN
cana-5925	18	18	.	.	PUNCT
cana-5925	19	1	he	he	PRON
cana-5925	19	2	defined	define	VERB
cana-5925	19	3	a	a	DET
cana-5925	19	4	set	set	NOUN
cana-5925	19	5	–	–	PUNCT
cana-5925	19	6	indexer	indexer	NOUN
cana-5925	19	7	as	as	SCONJ
cana-5925	19	8	follows	follow	VERB
cana-5925	19	9	:	:	PUNCT
cana-5925	19	10	let	let	VERB
cana-5925	19	11	𝐺	𝐺	PROPN
cana-5925	19	12	=	=	SYM
cana-5925	19	13	(	(	PUNCT
cana-5925	19	14	𝑉	𝑉	PROPN
cana-5925	19	15	,	,	PUNCT
cana-5925	19	16	𝐸	𝐸	PROPN
cana-5925	19	17	)	)	PUNCT
cana-5925	19	18	be	be	VERB
cana-5925	19	19	a	a	DET
cana-5925	19	20	graph	graph	NOUN
cana-5925	19	21	,	,	PUNCT
cana-5925	19	22	x	x	PUNCT
cana-5925	19	23	any	any	DET
cana-5925	19	24	non	non	ADJ
cana-5925	19	25	–	–	PUNCT
cana-5925	19	26	empty	empty	ADJ
cana-5925	19	27	set	set	NOUN
cana-5925	19	28	and	and	CCONJ
cana-5925	19	29	2𝑋	2𝑋	PROPN
cana-5925	19	30	denote	denote	VERB
cana-5925	19	31	the	the	DET
cana-5925	19	32	set	set	NOUN
cana-5925	19	33	of	of	ADP
cana-5925	19	34	all	all	DET
cana-5925	19	35	subsets	subset	NOUN
cana-5925	19	36	of	of	ADP
cana-5925	19	37	𝑋.	𝑋.	PROPN
cana-5925	19	38	a	a	DET
cana-5925	19	39	set	set	NOUN
cana-5925	19	40	–	–	PUNCT
cana-5925	19	41	indexer	indexer	NOUN
cana-5925	19	42	of	of	ADP
cana-5925	19	43	𝐺	𝐺	PROPN
cana-5925	19	44	is	be	AUX
cana-5925	19	45	an	an	DET
cana-5925	19	46	injective	injective	ADJ
cana-5925	19	47	set	set	NOUN
cana-5925	19	48	valued	value	VERB
cana-5925	19	49	function	function	NOUN
cana-5925	19	50	𝑓	𝑓	DET
cana-5925	19	51	∶	∶	NOUN
cana-5925	19	52	𝑉(𝐺	𝑉(𝐺	NOUN
cana-5925	19	53	)	)	PUNCT
cana-5925	19	54	→	→	PUNCT
cana-5925	19	55	2𝑋	2𝑋	PROPN
cana-5925	19	56	such	such	ADJ
cana-5925	19	57	that	that	SCONJ
cana-5925	19	58	the	the	DET
cana-5925	19	59	induced	induced	ADJ
cana-5925	19	60	function	function	NOUN
cana-5925	19	61	𝑓∗	𝑓∗	PROPN
cana-5925	19	62	∶	∶	PROPN
cana-5925	19	63	𝐸(𝐺	𝐸(𝐺	NOUN
cana-5925	19	64	)	)	PUNCT
cana-5925	19	65	→	→	SYM
cana-5925	19	66	2𝑋	2𝑋	NUM
cana-5925	19	67	−	−	PROPN
cana-5925	19	68	{	{	PUNCT
cana-5925	19	69	𝜙	𝜙	NOUN
cana-5925	19	70	}	}	PUNCT
cana-5925	19	71	defined	define	VERB
cana-5925	19	72	by	by	ADP
cana-5925	19	73	𝑓∗(𝑣1𝑣2	𝑓∗(𝑣1𝑣2	PROPN
cana-5925	19	74	)	)	PUNCT
cana-5925	20	1	=	=	SYM
cana-5925	21	1	𝑓	𝑓	PROPN
cana-5925	21	2	(	(	PUNCT
cana-5925	21	3	𝑣1	𝑣1	PROPN
cana-5925	21	4	)	)	PUNCT
cana-5925	21	5	∆	∆	PROPN
cana-5925	22	1	𝑓	𝑓	PRON
cana-5925	22	2	(	(	PUNCT
cana-5925	22	3	𝑣2	𝑣2	NOUN
cana-5925	22	4	)	)	PUNCT
cana-5925	22	5	for	for	ADP
cana-5925	22	6	every	every	DET
cana-5925	22	7	𝑣1𝑣2	𝑣1𝑣2	PROPN
cana-5925	22	8	∈	∈	PROPN
cana-5925	22	9	𝐸(𝐺	𝐸(𝐺	NOUN
cana-5925	22	10	)	)	PUNCT
cana-5925	22	11	is	be	AUX
cana-5925	22	12	also	also	ADV
cana-5925	22	13	injective	injective	ADJ
cana-5925	22	14	,	,	PUNCT
cana-5925	22	15	where	where	SCONJ
cana-5925	22	16	∆	∆	PROPN
cana-5925	22	17	denotes	denote	VERB
cana-5925	22	18	the	the	DET
cana-5925	22	19	symmetric	symmetric	ADJ
cana-5925	22	20	difference	difference	NOUN
cana-5925	22	21	of	of	ADP
cana-5925	22	22	sets	set	NOUN
cana-5925	22	23	.	.	PUNCT
cana-5925	23	1	a	a	DET
cana-5925	23	2	graph	graph	NOUN
cana-5925	23	3	𝐺	𝐺	NOUN
cana-5925	23	4	=	=	SYM
cana-5925	23	5	(	(	PUNCT
cana-5925	23	6	𝑉	𝑉	PROPN
cana-5925	23	7	,	,	PUNCT
cana-5925	23	8	𝐸	𝐸	PROPN
cana-5925	23	9	)	)	PUNCT
cana-5925	23	10	is	be	AUX
cana-5925	23	11	said	say	VERB
cana-5925	23	12	to	to	PART
cana-5925	23	13	be	be	AUX
cana-5925	23	14	a	a	DET
cana-5925	23	15	bitopological	bitopological	ADJ
cana-5925	23	16	graph	graph	NOUN
cana-5925	23	17	if	if	SCONJ
cana-5925	23	18	there	there	PRON
cana-5925	23	19	exist	exist	VERB
cana-5925	23	20	a	a	DET
cana-5925	23	21	set	set	ADJ
cana-5925	23	22	indexer	indexer	NOUN
cana-5925	23	23	𝑓	𝑓	NOUN
cana-5925	23	24	:	:	PUNCT
cana-5925	23	25	𝑉(𝐺	𝑉(𝐺	NOUN
cana-5925	23	26	)	)	PUNCT
cana-5925	23	27	→	→	PUNCT
cana-5925	23	28	2𝑋	2𝑋	PROPN
cana-5925	23	29	such	such	ADJ
cana-5925	23	30	that	that	DET
cana-5925	23	31	𝑓(𝑉	𝑓(𝑉	NOUN
cana-5925	23	32	)	)	PUNCT
cana-5925	23	33	and	and	CCONJ
cana-5925	23	34	𝑓∗(𝐸	𝑓∗(𝐸	PROPN
cana-5925	23	35	)	)	PUNCT
cana-5925	23	36	∪	∪	NOUN
cana-5925	23	37	{	{	PUNCT
cana-5925	23	38	𝜙	𝜙	NOUN
cana-5925	23	39	}	}	PUNCT
cana-5925	23	40	are	be	AUX
cana-5925	23	41	both	both	DET
cana-5925	23	42	topologies	topology	NOUN
cana-5925	23	43	on	on	ADP
cana-5925	23	44	the	the	DET
cana-5925	23	45	corresponding	corresponding	ADJ
cana-5925	23	46	ground	ground	NOUN
cana-5925	23	47	set	set	NOUN
cana-5925	23	48	.	.	PUNCT
cana-5925	24	1	let	let	VERB
cana-5925	24	2	𝐺	𝐺	PRON
cana-5925	24	3	be	be	AUX
cana-5925	24	4	a	a	DET
cana-5925	24	5	graph	graph	NOUN
cana-5925	24	6	and	and	CCONJ
cana-5925	24	7	𝑋	𝑋	PROPN
cana-5925	24	8	,	,	PUNCT
cana-5925	24	9	a	a	DET
cana-5925	24	10	non	non	ADJ
cana-5925	24	11	-	-	ADJ
cana-5925	24	12	empty	empty	ADJ
cana-5925	24	13	set	set	NOUN
cana-5925	24	14	.	.	PUNCT
cana-5925	25	1	define	define	VERB
cana-5925	25	2	an	an	DET
cana-5925	25	3	injective	injective	ADJ
cana-5925	25	4	mailto:1selestinlina@gmail.com	mailto:1selestinlina@gmail.com	PROPN
cana-5925	25	5	communications	communication	NOUN
cana-5925	25	6	on	on	ADP
cana-5925	25	7	applied	apply	VERB
cana-5925	25	8	nonlinear	nonlinear	ADJ
cana-5925	25	9	analysis	analysis	NOUN
cana-5925	25	10	issn	issn	NOUN
cana-5925	25	11	:	:	PUNCT
cana-5925	25	12	1074	1074	NUM
cana-5925	25	13	-	-	PUNCT
cana-5925	25	14	133x	133x	NUM
cana-5925	25	15	vol	vol	NOUN
cana-5925	25	16	32	32	NUM
cana-5925	25	17	no	no	NOUN
cana-5925	25	18	.	.	NOUN
cana-5925	25	19	3	3	NUM
cana-5925	25	20	(	(	PUNCT
cana-5925	25	21	2025	2025	NUM
cana-5925	25	22	)	)	PUNCT
cana-5925	25	23	1041	1041	NUM
cana-5925	25	24	https://internationalpubls.com	https://internationalpubls.com	X
cana-5925	25	25	function	function	VERB
cana-5925	25	26	𝑓	𝑓	NOUN
cana-5925	25	27	:	:	PUNCT
cana-5925	25	28	𝑉(𝐺	𝑉(𝐺	NOUN
cana-5925	25	29	)	)	PUNCT
cana-5925	25	30	→	→	PUNCT
cana-5925	25	31	2𝑋	2𝑋	PROPN
cana-5925	25	32	such	such	ADJ
cana-5925	25	33	that	that	SCONJ
cana-5925	25	34	{	{	PUNCT
cana-5925	25	35	𝑓(𝑉(𝐺	𝑓(𝑉(𝐺	NOUN
cana-5925	25	36	)	)	PUNCT
cana-5925	25	37	)	)	PUNCT
cana-5925	25	38	}	}	PUNCT
cana-5925	25	39	is	be	AUX
cana-5925	25	40	a	a	DET
cana-5925	25	41	topology	topology	NOUN
cana-5925	25	42	on	on	ADP
cana-5925	25	43	𝑋.	𝑋.	PROPN
cana-5925	25	44	if	if	SCONJ
cana-5925	25	45	the	the	DET
cana-5925	25	46	induced	induce	VERB
cana-5925	25	47	function	function	NOUN
cana-5925	25	48	𝑓∗	𝑓∗	NOUN
cana-5925	25	49	on	on	ADP
cana-5925	25	50	𝐸(𝐺	𝐸(𝐺	PROPN
cana-5925	25	51	)	)	PUNCT
cana-5925	25	52	is	be	AUX
cana-5925	25	53	defined	define	VERB
cana-5925	25	54	by	by	ADP
cana-5925	25	55	𝑓∗(𝑢𝑣	𝑓∗(𝑢𝑣	NOUN
cana-5925	25	56	)	)	PUNCT
cana-5925	25	57	=	=	PRON
cana-5925	25	58	{	{	PUNCT
cana-5925	25	59	1	1	NUM
cana-5925	25	60	if	if	SCONJ
cana-5925	25	61	𝑓(𝑢	𝑓(𝑢	NOUN
cana-5925	25	62	)	)	PUNCT
cana-5925	25	63	∩	∩	NOUN
cana-5925	25	64	𝑓(𝑣	𝑓(𝑣	NOUN
cana-5925	25	65	)	)	PUNCT
cana-5925	25	66	is	be	AUX
cana-5925	25	67	not	not	PART
cana-5925	25	68	an	an	DET
cana-5925	25	69	empty	empty	ADJ
cana-5925	25	70	set	set	NOUN
cana-5925	25	71	and	and	CCONJ
cana-5925	25	72	singleton	singleton	PROPN
cana-5925	25	73	set	set	NOUN
cana-5925	25	74	0	0	PUNCT
cana-5925	26	1	otherwise	otherwise	ADV
cana-5925	26	2	for	for	ADP
cana-5925	26	3	every	every	DET
cana-5925	26	4	𝑢𝑣	𝑢𝑣	PROPN
cana-5925	26	5	∈	∈	PROPN
cana-5925	26	6	𝐸(𝐺	𝐸(𝐺	NOUN
cana-5925	26	7	)	)	PUNCT
cana-5925	26	8	such	such	ADJ
cana-5925	26	9	that	that	DET
cana-5925	26	10	|𝑒𝑓(0	|𝑒𝑓(0	NUM
cana-5925	26	11	)	)	PUNCT
cana-5925	27	1	−	−	PROPN
cana-5925	28	1	𝑒𝑓(1)|	𝑒𝑓(1)|	PROPN
cana-5925	28	2	≤	≤	NOUN
cana-5925	28	3	1	1	NUM
cana-5925	28	4	where	where	SCONJ
cana-5925	28	5	𝑒𝑓(0	𝑒𝑓(0	PROPN
cana-5925	28	6	)	)	PUNCT
cana-5925	28	7	=	=	NOUN
cana-5925	28	8	number	number	NOUN
cana-5925	28	9	of	of	ADP
cana-5925	28	10	edges	edge	NOUN
cana-5925	28	11	labeled	label	VERB
cana-5925	28	12	with	with	ADP
cana-5925	28	13	0	0	NUM
cana-5925	28	14	and	and	CCONJ
cana-5925	28	15	𝑒𝑓(1	𝑒𝑓(1	PROPN
cana-5925	28	16	)	)	PUNCT
cana-5925	28	17	=	=	NOUN
cana-5925	28	18	number	number	NOUN
cana-5925	28	19	of	of	ADP
cana-5925	28	20	edges	edge	NOUN
cana-5925	28	21	labeled	label	VERB
cana-5925	28	22	with	with	ADP
cana-5925	28	23	1	1	NUM
cana-5925	28	24	then	then	ADV
cana-5925	28	25	𝑓	𝑓	PRON
cana-5925	28	26	is	be	AUX
cana-5925	28	27	a	a	DET
cana-5925	28	28	topological	topological	ADJ
cana-5925	28	29	cordial	cordial	ADJ
cana-5925	28	30	labeling	labeling	NOUN
cana-5925	28	31	and	and	CCONJ
cana-5925	28	32	a	a	DET
cana-5925	28	33	graph	graph	NOUN
cana-5925	28	34	which	which	PRON
cana-5925	28	35	admits	admit	VERB
cana-5925	28	36	such	such	DET
cana-5925	28	37	a	a	DET
cana-5925	28	38	labeling	labeling	NOUN
cana-5925	28	39	is	be	AUX
cana-5925	28	40	called	call	VERB
cana-5925	28	41	topological	topological	ADJ
cana-5925	28	42	cordial	cordial	ADJ
cana-5925	28	43	graph	graph	NOUN
cana-5925	28	44	.	.	PUNCT
cana-5925	29	1	this	this	DET
cana-5925	29	2	definition	definition	NOUN
cana-5925	29	3	is	be	AUX
cana-5925	29	4	defined	define	VERB
cana-5925	29	5	and	and	CCONJ
cana-5925	29	6	introduced	introduce	VERB
cana-5925	29	7	in	in	ADP
cana-5925	29	8	[	[	X
cana-5925	29	9	8	8	NUM
cana-5925	29	10	]	]	PUNCT
cana-5925	29	11	.	.	PUNCT
cana-5925	30	1	in	in	ADP
cana-5925	30	2	this	this	DET
cana-5925	30	3	paper	paper	NOUN
cana-5925	30	4	we	we	PRON
cana-5925	30	5	proved	prove	VERB
cana-5925	30	6	dodecahedral	dodecahedral	ADJ
cana-5925	30	7	graph	graph	NOUN
cana-5925	30	8	,	,	PUNCT
cana-5925	30	9	paley	paley	ADJ
cana-5925	30	10	graph	graph	NOUN
cana-5925	30	11	and	and	CCONJ
cana-5925	30	12	some	some	DET
cana-5925	30	13	constructed	construct	VERB
cana-5925	30	14	graphs	graph	NOUN
cana-5925	30	15	are	be	AUX
cana-5925	30	16	topological	topological	ADJ
cana-5925	30	17	cordial	cordial	ADJ
cana-5925	30	18	graph	graph	NOUN
cana-5925	30	19	.	.	PUNCT
cana-5925	31	1	1.preliminaries	1.preliminaries	NUM
cana-5925	31	2	definition	definition	NOUN
cana-5925	31	3	1.1	1.1	NUM
cana-5925	31	4	the	the	DET
cana-5925	31	5	dodecahedral	dodecahedral	ADJ
cana-5925	31	6	graph	graph	NOUN
cana-5925	31	7	is	be	AUX
cana-5925	31	8	a	a	DET
cana-5925	31	9	3	3	NUM
cana-5925	31	10	-	-	PUNCT
cana-5925	31	11	connected	connect	VERB
cana-5925	31	12	graph	graph	NOUN
cana-5925	31	13	with	with	ADP
cana-5925	31	14	20	20	NUM
cana-5925	31	15	vertices	vertex	NOUN
cana-5925	31	16	and	and	CCONJ
cana-5925	31	17	30	30	NUM
cana-5925	31	18	edges	edge	NOUN
cana-5925	31	19	.	.	PUNCT
cana-5925	32	1	definition	definition	NOUN
cana-5925	32	2	1.2	1.2	NUM
cana-5925	32	3	a	a	DET
cana-5925	32	4	complete	complete	ADJ
cana-5925	32	5	bipartite	bipartite	NOUN
cana-5925	32	6	graph	graph	NOUN
cana-5925	32	7	or	or	CCONJ
cana-5925	32	8	biclique	biclique	NOUN
cana-5925	32	9	is	be	AUX
cana-5925	32	10	a	a	DET
cana-5925	32	11	special	special	ADJ
cana-5925	32	12	kind	kind	NOUN
cana-5925	32	13	of	of	ADP
cana-5925	32	14	bipartite	bipartite	NOUN
cana-5925	32	15	graph	graph	NOUN
cana-5925	32	16	where	where	SCONJ
cana-5925	32	17	every	every	DET
cana-5925	32	18	vertex	vertex	NOUN
cana-5925	32	19	of	of	ADP
cana-5925	32	20	the	the	DET
cana-5925	32	21	first	first	ADJ
cana-5925	32	22	set	set	NOUN
cana-5925	32	23	is	be	AUX
cana-5925	32	24	connected	connect	VERB
cana-5925	32	25	to	to	ADP
cana-5925	32	26	every	every	DET
cana-5925	32	27	vertex	vertex	NOUN
cana-5925	32	28	of	of	ADP
cana-5925	32	29	the	the	DET
cana-5925	32	30	second	second	ADJ
cana-5925	32	31	set	set	NOUN
cana-5925	32	32	.	.	PUNCT
cana-5925	33	1	definition	definition	NOUN
cana-5925	33	2	1.3	1.3	NUM
cana-5925	33	3	the	the	DET
cana-5925	33	4	double	double	ADJ
cana-5925	33	5	star	star	NOUN
cana-5925	33	6	𝑆(𝑛	𝑆(𝑛	NOUN
cana-5925	33	7	,	,	PUNCT
cana-5925	33	8	𝑚	𝑚	NOUN
cana-5925	33	9	)	)	PUNCT
cana-5925	33	10	,	,	PUNCT
cana-5925	33	11	where	where	SCONJ
cana-5925	33	12	𝑛	𝑛	PRON
cana-5925	33	13	≥	≥	X
cana-5925	33	14	𝑚	𝑚	ADP
cana-5925	33	15	≥	≥	NUM
cana-5925	33	16	0	0	NUM
cana-5925	33	17	,	,	PUNCT
cana-5925	33	18	is	be	AUX
cana-5925	33	19	the	the	DET
cana-5925	33	20	graph	graph	NOUN
cana-5925	33	21	consisting	consist	VERB
cana-5925	33	22	of	of	ADP
cana-5925	33	23	the	the	DET
cana-5925	33	24	union	union	NOUN
cana-5925	33	25	of	of	ADP
cana-5925	33	26	two	two	NUM
cana-5925	33	27	stars	star	NOUN
cana-5925	33	28	𝐾1,𝑛	𝐾1,𝑛	PROPN
cana-5925	33	29	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-5925	33	30	𝐾1,𝑚	𝐾1,𝑚	PROPN
cana-5925	33	31	together	together	ADV
cana-5925	33	32	with	with	ADP
cana-5925	33	33	a	a	DET
cana-5925	33	34	line	line	NOUN
cana-5925	33	35	joining	join	VERB
cana-5925	33	36	their	their	PRON
cana-5925	33	37	centers	center	NOUN
cana-5925	33	38	.	.	PUNCT
cana-5925	34	1	definition	definition	NOUN
cana-5925	34	2	1.4	1.4	NUM
cana-5925	34	3	the	the	DET
cana-5925	34	4	paley	paley	ADJ
cana-5925	34	5	graph	graph	NOUN
cana-5925	34	6	of	of	ADP
cana-5925	34	7	order	order	NOUN
cana-5925	34	8	q	q	NOUN
cana-5925	34	9	with	with	ADP
cana-5925	34	10	q	q	PUNCT
cana-5925	34	11	a	a	DET
cana-5925	34	12	prime	prime	ADJ
cana-5925	34	13	power	power	NOUN
cana-5925	34	14	is	be	AUX
cana-5925	34	15	a	a	DET
cana-5925	34	16	graph	graph	NOUN
cana-5925	34	17	on	on	ADP
cana-5925	34	18	q	q	NOUN
cana-5925	34	19	nodes	node	NOUN
cana-5925	34	20	with	with	ADP
cana-5925	34	21	two	two	NUM
cana-5925	34	22	nodes	node	NOUN
cana-5925	34	23	adjacent	adjacent	ADJ
cana-5925	34	24	if	if	SCONJ
cana-5925	34	25	their	their	PRON
cana-5925	34	26	difference	difference	NOUN
cana-5925	34	27	is	be	AUX
cana-5925	34	28	a	a	DET
cana-5925	34	29	square	square	NOUN
cana-5925	34	30	in	in	ADP
cana-5925	34	31	the	the	DET
cana-5925	34	32	finite	finite	ADJ
cana-5925	34	33	field	field	NOUN
cana-5925	34	34	gf(q	gf(q	NOUN
cana-5925	34	35	)	)	PUNCT
cana-5925	34	36	.	.	PUNCT
cana-5925	35	1	this	this	DET
cana-5925	35	2	graph	graph	NOUN
cana-5925	35	3	is	be	AUX
cana-5925	35	4	undirected	undirected	ADJ
cana-5925	35	5	when	when	SCONJ
cana-5925	35	6	q=1	q=1	PROPN
cana-5925	35	7	(	(	PUNCT
cana-5925	35	8	mod	mod	NOUN
cana-5925	35	9	4	4	NUM
cana-5925	35	10	)	)	PUNCT
cana-5925	35	11	.	.	PUNCT
cana-5925	36	1	simple	simple	ADJ
cana-5925	36	2	paley	paley	ADJ
cana-5925	36	3	graphs	graph	NOUN
cana-5925	36	4	therefore	therefore	ADV
cana-5925	36	5	exist	exist	VERB
cana-5925	36	6	for	for	ADP
cana-5925	36	7	orders	order	NOUN
cana-5925	36	8	5	5	NUM
cana-5925	36	9	,	,	PUNCT
cana-5925	36	10	9	9	NUM
cana-5925	36	11	,	,	PUNCT
cana-5925	36	12	13	13	NUM
cana-5925	36	13	,	,	PUNCT
cana-5925	36	14	17	17	NUM
cana-5925	36	15	,	,	PUNCT
cana-5925	36	16	25	25	NUM
cana-5925	36	17	,	,	PUNCT
cana-5925	36	18	…	…	PUNCT
cana-5925	36	19	..	..	PUNCT
cana-5925	37	1	2.topological	2.topological	NUM
cana-5925	37	2	cordial	cordial	ADJ
cana-5925	37	3	labeling	labeling	NOUN
cana-5925	37	4	definition	definition	NOUN
cana-5925	37	5	2.1	2.1	NUM
cana-5925	37	6	let	let	VERB
cana-5925	37	7	𝐺	𝐺	PROPN
cana-5925	37	8	be	be	AUX
cana-5925	37	9	a	a	DET
cana-5925	37	10	graph	graph	NOUN
cana-5925	37	11	and	and	CCONJ
cana-5925	37	12	𝑋	𝑋	PROPN
cana-5925	37	13	,	,	PUNCT
cana-5925	37	14	a	a	DET
cana-5925	37	15	non	non	ADJ
cana-5925	37	16	-	-	ADJ
cana-5925	37	17	empty	empty	ADJ
cana-5925	37	18	set	set	NOUN
cana-5925	37	19	.	.	PUNCT
cana-5925	38	1	define	define	VERB
cana-5925	38	2	an	an	DET
cana-5925	38	3	injective	injective	ADJ
cana-5925	38	4	function	function	NOUN
cana-5925	38	5	𝑓	𝑓	NOUN
cana-5925	38	6	:	:	PUNCT
cana-5925	38	7	𝑉(𝐺	𝑉(𝐺	NOUN
cana-5925	38	8	)	)	PUNCT
cana-5925	38	9	→	→	PUNCT
cana-5925	38	10	2𝑋	2𝑋	PROPN
cana-5925	38	11	such	such	ADJ
cana-5925	38	12	that	that	SCONJ
cana-5925	38	13	{	{	PUNCT
cana-5925	38	14	𝑓(𝑉(𝐺	𝑓(𝑉(𝐺	NOUN
cana-5925	38	15	)	)	PUNCT
cana-5925	38	16	)	)	PUNCT
cana-5925	38	17	}	}	PUNCT
cana-5925	38	18	is	be	AUX
cana-5925	38	19	a	a	DET
cana-5925	38	20	topology	topology	NOUN
cana-5925	38	21	on	on	ADP
cana-5925	38	22	𝑋.	𝑋.	PROPN
cana-5925	38	23	if	if	SCONJ
cana-5925	38	24	the	the	DET
cana-5925	38	25	induced	induce	VERB
cana-5925	38	26	function	function	NOUN
cana-5925	38	27	𝑓∗	𝑓∗	NOUN
cana-5925	38	28	on	on	ADP
cana-5925	38	29	𝐸(𝐺	𝐸(𝐺	PROPN
cana-5925	38	30	)	)	PUNCT
cana-5925	38	31	is	be	AUX
cana-5925	38	32	defined	define	VERB
cana-5925	38	33	by	by	ADP
cana-5925	38	34	𝑓∗(𝑢𝑣	𝑓∗(𝑢𝑣	NOUN
cana-5925	38	35	)	)	PUNCT
cana-5925	38	36	=	=	PRON
cana-5925	38	37	{	{	PUNCT
cana-5925	38	38	1	1	NUM
cana-5925	38	39	if	if	SCONJ
cana-5925	38	40	𝑓(𝑢	𝑓(𝑢	NOUN
cana-5925	38	41	)	)	PUNCT
cana-5925	38	42	∩	∩	NOUN
cana-5925	38	43	𝑓(𝑣	𝑓(𝑣	NOUN
cana-5925	38	44	)	)	PUNCT
cana-5925	38	45	is	be	AUX
cana-5925	38	46	not	not	PART
cana-5925	38	47	an	an	DET
cana-5925	38	48	empty	empty	ADJ
cana-5925	38	49	set	set	NOUN
cana-5925	38	50	and	and	CCONJ
cana-5925	38	51	singleton	singleton	PROPN
cana-5925	38	52	set	set	NOUN
cana-5925	38	53	0	0	NUM
cana-5925	38	54	otherwise	otherwise	ADV
cana-5925	38	55	communications	communication	NOUN
cana-5925	38	56	on	on	ADP
cana-5925	38	57	applied	apply	VERB
cana-5925	38	58	nonlinear	nonlinear	ADJ
cana-5925	38	59	analysis	analysis	NOUN
cana-5925	38	60	issn	issn	NOUN
cana-5925	38	61	:	:	PUNCT
cana-5925	38	62	1074	1074	NUM
cana-5925	38	63	-	-	PUNCT
cana-5925	38	64	133x	133x	NUM
cana-5925	38	65	vol	vol	NOUN
cana-5925	38	66	32	32	NUM
cana-5925	38	67	no	no	NOUN
cana-5925	38	68	.	.	NOUN
cana-5925	38	69	3	3	NUM
cana-5925	38	70	(	(	PUNCT
cana-5925	38	71	2025	2025	NUM
cana-5925	38	72	)	)	PUNCT
cana-5925	38	73	1042	1042	NUM
cana-5925	38	74	https://internationalpubls.com	https://internationalpubls.com	X
cana-5925	38	75	for	for	ADP
cana-5925	38	76	every	every	DET
cana-5925	38	77	𝑢𝑣	𝑢𝑣	PROPN
cana-5925	38	78	∈	∈	PROPN
cana-5925	38	79	𝐸(𝐺	𝐸(𝐺	NOUN
cana-5925	38	80	)	)	PUNCT
cana-5925	38	81	such	such	ADJ
cana-5925	38	82	that	that	DET
cana-5925	38	83	|𝑒𝑓(0	|𝑒𝑓(0	NUM
cana-5925	38	84	)	)	PUNCT
cana-5925	39	1	−	−	PROPN
cana-5925	40	1	𝑒𝑓(1)|	𝑒𝑓(1)|	PROPN
cana-5925	40	2	≤	≤	NOUN
cana-5925	40	3	1	1	NUM
cana-5925	40	4	where	where	SCONJ
cana-5925	40	5	𝑒𝑓(0	𝑒𝑓(0	PROPN
cana-5925	40	6	)	)	PUNCT
cana-5925	40	7	=	=	NOUN
cana-5925	40	8	number	number	NOUN
cana-5925	40	9	of	of	ADP
cana-5925	40	10	edges	edge	NOUN
cana-5925	40	11	labeled	label	VERB
cana-5925	40	12	with	with	ADP
cana-5925	40	13	0	0	NUM
cana-5925	40	14	and	and	CCONJ
cana-5925	40	15	𝑒𝑓(1	𝑒𝑓(1	PROPN
cana-5925	40	16	)	)	PUNCT
cana-5925	40	17	=	=	NOUN
cana-5925	40	18	number	number	NOUN
cana-5925	40	19	of	of	ADP
cana-5925	40	20	edges	edge	NOUN
cana-5925	40	21	labeled	label	VERB
cana-5925	40	22	with	with	ADP
cana-5925	40	23	1	1	NUM
cana-5925	40	24	then	then	ADV
cana-5925	40	25	𝑓	𝑓	PRON
cana-5925	40	26	is	be	AUX
cana-5925	40	27	a	a	DET
cana-5925	40	28	topological	topological	ADJ
cana-5925	40	29	cordial	cordial	ADJ
cana-5925	40	30	labeling	labeling	NOUN
cana-5925	40	31	and	and	CCONJ
cana-5925	40	32	a	a	DET
cana-5925	40	33	graph	graph	NOUN
cana-5925	40	34	which	which	PRON
cana-5925	40	35	admits	admit	VERB
cana-5925	40	36	such	such	DET
cana-5925	40	37	a	a	DET
cana-5925	40	38	labeling	labeling	NOUN
cana-5925	40	39	is	be	AUX
cana-5925	40	40	called	call	VERB
cana-5925	40	41	topological	topological	ADJ
cana-5925	40	42	cordial	cordial	ADJ
cana-5925	40	43	graph	graph	NOUN
cana-5925	40	44	.	.	PUNCT
cana-5925	41	1	2.topological	2.topological	NUM
cana-5925	41	2	cordial	cordial	ADJ
cana-5925	41	3	labeling	labeling	NOUN
cana-5925	41	4	of	of	ADP
cana-5925	41	5	named	name	VERB
cana-5925	41	6	graphs	graph	NOUN
cana-5925	41	7	theorem	theorem	VERB
cana-5925	41	8	2.1	2.1	NUM
cana-5925	41	9	.	.	PUNCT
cana-5925	42	1	dodecahedral	dodecahedral	ADJ
cana-5925	42	2	graph	graph	NOUN
cana-5925	42	3	is	be	AUX
cana-5925	42	4	topological	topological	ADJ
cana-5925	42	5	cordial	cordial	ADJ
cana-5925	42	6	graph	graph	NOUN
cana-5925	42	7	.	.	PUNCT
cana-5925	43	1	proof	proof	NOUN
cana-5925	43	2	:	:	PUNCT
cana-5925	43	3	let	let	VERB
cana-5925	43	4	𝐺	𝐺	PRON
cana-5925	43	5	be	be	AUX
cana-5925	43	6	dodecahedral	dodecahedral	ADJ
cana-5925	43	7	graph	graph	NOUN
cana-5925	43	8	with	with	ADP
cana-5925	43	9	20	20	NUM
cana-5925	43	10	vertices	vertex	NOUN
cana-5925	43	11	and	and	CCONJ
cana-5925	43	12	30	30	NUM
cana-5925	43	13	edges	edge	NOUN
cana-5925	43	14	.	.	PUNCT
cana-5925	44	1	let	let	VERB
cana-5925	44	2	𝑉(𝐺	𝑉(𝐺	NOUN
cana-5925	44	3	)	)	PUNCT
cana-5925	44	4	=	=	SYM
cana-5925	45	1	{	{	PUNCT
cana-5925	45	2	𝑣𝑖/1	𝑣𝑖/1	NOUN
cana-5925	45	3	≤	≤	NUM
cana-5925	45	4	𝑖	𝑖	SYM
cana-5925	45	5	≤	≤	NUM
cana-5925	45	6	5	5	NUM
cana-5925	45	7	}	}	PUNCT
cana-5925	45	8	∪	∪	ADJ
cana-5925	45	9	{	{	PUNCT
cana-5925	45	10	𝑢𝑖/1	𝑢𝑖/1	NOUN
cana-5925	45	11	≤	≤	NOUN
cana-5925	45	12	𝑖	𝑖	SYM
cana-5925	45	13	≤	≤	NUM
cana-5925	45	14	10	10	NUM
cana-5925	45	15	}	}	PUNCT
cana-5925	45	16	∪	∪	ADJ
cana-5925	45	17	{	{	PUNCT
cana-5925	45	18	𝑤𝑖/1	𝑤𝑖/1	NOUN
cana-5925	45	19	≤	≤	NUM
cana-5925	45	20	𝑖	𝑖	SYM
cana-5925	45	21	≤	≤	NUM
cana-5925	45	22	5	5	NUM
cana-5925	45	23	}	}	PUNCT
cana-5925	45	24	and	and	CCONJ
cana-5925	45	25	𝐸(𝐺	𝐸(𝐺	NUM
cana-5925	45	26	)	)	PUNCT
cana-5925	45	27	=	=	SYM
cana-5925	45	28	{	{	PUNCT
cana-5925	45	29	𝑣𝑖𝑣𝑖+1/1	𝑣𝑖𝑣𝑖+1/1	PROPN
cana-5925	45	30	≤	≤	PROPN
cana-5925	45	31	𝑖	𝑖	SYM
cana-5925	45	32	≤	≤	NOUN
cana-5925	45	33	𝑖	𝑖	PUNCT
cana-5925	45	34	+	+	NOUN
cana-5925	45	35	1	1	NUM
cana-5925	45	36	,	,	PUNCT
cana-5925	45	37	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	ADJ
cana-5925	45	38	𝑣𝑖+1	𝑣𝑖+1	NUM
cana-5925	45	39	=	=	SYM
cana-5925	45	40	𝑣𝑖	𝑣𝑖	PROPN
cana-5925	45	41	}	}	PUNCT
cana-5925	45	42	∪	∪	NOUN
cana-5925	45	43	{	{	PUNCT
cana-5925	45	44	𝑢𝑖𝑢𝑖+1/1	𝑢𝑖𝑢𝑖+1/1	NOUN
cana-5925	45	45	≤	≤	NUM
cana-5925	45	46	𝑖	𝑖	SYM
cana-5925	45	47	≤	≤	NOUN
cana-5925	45	48	𝑖	𝑖	PUNCT
cana-5925	45	49	+	+	NOUN
cana-5925	45	50	1	1	NUM
cana-5925	45	51	,	,	PUNCT
cana-5925	45	52	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	ADJ
cana-5925	45	53	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-5925	45	54	=	=	SYM
cana-5925	45	55	𝑢𝑖	𝑢𝑖	NOUN
cana-5925	45	56	}	}	PUNCT
cana-5925	45	57	∪	∪	X
cana-5925	45	58	{	{	PUNCT
cana-5925	45	59	𝑤𝑖𝑤𝑖+1/1	𝑤𝑖𝑤𝑖+1/1	NOUN
cana-5925	45	60	≤	≤	NUM
cana-5925	45	61	𝑖	𝑖	ADP
cana-5925	45	62	≤	≤	NUM
cana-5925	45	63	𝑖	𝑖	PUNCT
cana-5925	45	64	+	+	NOUN
cana-5925	45	65	1	1	NUM
cana-5925	45	66	,	,	PUNCT
cana-5925	45	67	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	ADJ
cana-5925	45	68	𝑤𝑖+1	𝑤𝑖+1	NOUN
cana-5925	45	69	=	=	SYM
cana-5925	45	70	𝑤𝑖	𝑤𝑖	NOUN
cana-5925	45	71	}	}	PUNCT
cana-5925	45	72	∪	∪	X
cana-5925	45	73	{	{	PUNCT
cana-5925	45	74	𝑣𝑖𝑢2𝑖−2	𝑣𝑖𝑢2𝑖−2	NUM
cana-5925	45	75	/2	/2	SYM
cana-5925	45	76	≤	≤	NUM
cana-5925	45	77	𝑖	𝑖	SYM
cana-5925	45	78	≤	≤	NUM
cana-5925	45	79	4	4	NUM
cana-5925	45	80	}	}	PUNCT
cana-5925	45	81	∪	∪	ADJ
cana-5925	45	82	{	{	PUNCT
cana-5925	45	83	𝑤𝑖𝑢2𝑖−1/1	𝑤𝑖𝑢2𝑖−1/1	NOUN
cana-5925	45	84	≤	≤	NUM
cana-5925	45	85	𝑖	𝑖	SYM
cana-5925	45	86	≤	≤	NUM
cana-5925	45	87	5	5	NUM
cana-5925	45	88	}	}	PUNCT
cana-5925	45	89	∪	∪	ADJ
cana-5925	45	90	{	{	PUNCT
cana-5925	45	91	𝑣1𝑢10	𝑣1𝑢10	NOUN
cana-5925	45	92	}	}	PUNCT
cana-5925	45	93	.	.	PUNCT
cana-5925	46	1	let	let	VERB
cana-5925	46	2	𝑋	𝑋	PROPN
cana-5925	46	3	=	=	SYM
cana-5925	46	4	{	{	PUNCT
cana-5925	46	5	1,2	1,2	NUM
cana-5925	46	6	,	,	PUNCT
cana-5925	46	7	…	…	PUNCT
cana-5925	46	8	,	,	PUNCT
cana-5925	46	9	20	20	NUM
cana-5925	46	10	}	}	PUNCT
cana-5925	46	11	.	.	PUNCT
cana-5925	47	1	now	now	ADV
cana-5925	47	2	,	,	PUNCT
cana-5925	47	3	define	define	VERB
cana-5925	47	4	𝑓	𝑓	DET
cana-5925	47	5	:	:	PUNCT
cana-5925	47	6	𝑉(𝐺	𝑉(𝐺	NOUN
cana-5925	47	7	)	)	PUNCT
cana-5925	47	8	→	→	SYM
cana-5925	47	9	2𝑋	2𝑋	PROPN
cana-5925	47	10	by	by	ADP
cana-5925	47	11	𝑓(𝑣1	𝑓(𝑣1	NOUN
cana-5925	47	12	)	)	PUNCT
cana-5925	47	13	=	=	SYM
cana-5925	47	14	𝜙	𝜙	NOUN
cana-5925	47	15	,	,	PUNCT
cana-5925	47	16	𝑓(𝑣2	𝑓(𝑣2	NOUN
cana-5925	47	17	)	)	PUNCT
cana-5925	47	18	=	=	PRON
cana-5925	47	19	{	{	PUNCT
cana-5925	47	20	1	1	NUM
cana-5925	47	21	}	}	PUNCT
cana-5925	47	22	,	,	PUNCT
cana-5925	47	23	𝑓(𝑣3	𝑓(𝑣3	NOUN
cana-5925	47	24	)	)	PUNCT
cana-5925	47	25	=	=	SYM
cana-5925	47	26	{	{	PUNCT
cana-5925	47	27	2	2	NUM
cana-5925	47	28	}	}	PUNCT
cana-5925	47	29	,	,	PUNCT
cana-5925	47	30	𝑓(𝑣4	𝑓(𝑣4	NOUN
cana-5925	47	31	)	)	PUNCT
cana-5925	47	32	=	=	PUNCT
cana-5925	47	33	{	{	PUNCT
cana-5925	47	34	1,2,3	1,2,3	NUM
cana-5925	47	35	}	}	PUNCT
cana-5925	47	36	,	,	PUNCT
cana-5925	47	37	𝑓(𝑣5	𝑓(𝑣5	NOUN
cana-5925	47	38	)	)	PUNCT
cana-5925	48	1	=	=	PUNCT
cana-5925	48	2	{	{	PUNCT
cana-5925	48	3	4	4	NUM
cana-5925	48	4	}	}	PUNCT
cana-5925	48	5	,	,	PUNCT
cana-5925	48	6	𝑓(𝑣6	𝑓(𝑣6	ADJ
cana-5925	48	7	)	)	PUNCT
cana-5925	48	8	=	=	PUNCT
cana-5925	48	9	{	{	PUNCT
cana-5925	48	10	3,4	3,4	NUM
cana-5925	48	11	}	}	PUNCT
cana-5925	48	12	,	,	PUNCT
cana-5925	48	13	𝑓(𝑣7	𝑓(𝑣7	NOUN
cana-5925	48	14	)	)	PUNCT
cana-5925	48	15	=	=	SYM
cana-5925	48	16	{	{	PUNCT
cana-5925	48	17	1,2	1,2	NUM
cana-5925	48	18	}	}	PUNCT
cana-5925	48	19	,	,	PUNCT
cana-5925	48	20	𝑓(𝑣8	𝑓(𝑣8	X
cana-5925	48	21	)	)	PUNCT
cana-5925	48	22	=	=	PUNCT
cana-5925	48	23	{	{	PUNCT
cana-5925	48	24	2,3	2,3	NUM
cana-5925	48	25	}	}	PUNCT
cana-5925	48	26	,	,	PUNCT
cana-5925	48	27	𝑓(𝑣9	𝑓(𝑣9	NOUN
cana-5925	48	28	)	)	PUNCT
cana-5925	48	29	=	=	PUNCT
cana-5925	48	30	{	{	PUNCT
cana-5925	48	31	3	3	NUM
cana-5925	48	32	}	}	PUNCT
cana-5925	48	33	,	,	PUNCT
cana-5925	48	34	𝑓(𝑣10	𝑓(𝑣10	VERB
cana-5925	48	35	)	)	PUNCT
cana-5925	48	36	=	=	PUNCT
cana-5925	48	37	{	{	PUNCT
cana-5925	48	38	1,4	1,4	NUM
cana-5925	48	39	}	}	PUNCT
cana-5925	48	40	,	,	PUNCT
cana-5925	48	41	𝑓(𝑣11	𝑓(𝑣11	X
cana-5925	48	42	)	)	PUNCT
cana-5925	48	43	=	=	PUNCT
cana-5925	48	44	{	{	PUNCT
cana-5925	48	45	1,3,4	1,3,4	NUM
cana-5925	48	46	}	}	PUNCT
cana-5925	48	47	,	,	PUNCT
cana-5925	48	48	𝑓(𝑣12	𝑓(𝑣12	NOUN
cana-5925	48	49	)	)	PUNCT
cana-5925	48	50	=	=	SYM
cana-5925	48	51	{	{	PUNCT
cana-5925	48	52	2,3,4	2,3,4	NUM
cana-5925	48	53	}	}	PUNCT
cana-5925	48	54	,	,	PUNCT
cana-5925	48	55	𝑓(𝑣13	𝑓(𝑣13	NOUN
cana-5925	48	56	)	)	PUNCT
cana-5925	48	57	=	=	PUNCT
cana-5925	48	58	{	{	PUNCT
cana-5925	48	59	1,2,3,4	1,2,3,4	NUM
cana-5925	48	60	}	}	PUNCT
cana-5925	48	61	,	,	PUNCT
cana-5925	48	62	𝑓(𝑣14	𝑓(𝑣14	NUM
cana-5925	48	63	)	)	PUNCT
cana-5925	48	64	=	=	PRON
cana-5925	48	65	{	{	PUNCT
cana-5925	48	66	1,3	1,3	NUM
cana-5925	48	67	}	}	PUNCT
cana-5925	48	68	,	,	PUNCT
cana-5925	48	69	𝑓(𝑣15	𝑓(𝑣15	NOUN
cana-5925	48	70	)	)	PUNCT
cana-5925	48	71	=	=	PRON
cana-5925	48	72	{	{	PUNCT
cana-5925	48	73	2,4	2,4	NUM
cana-5925	48	74	}	}	PUNCT
cana-5925	48	75	,	,	PUNCT
cana-5925	48	76	𝑓(𝑣16	𝑓(𝑣16	NOUN
cana-5925	48	77	)	)	PUNCT
cana-5925	49	1	=	=	PRON
cana-5925	49	2	{	{	PUNCT
cana-5925	49	3	1,2,4	1,2,4	NUM
cana-5925	49	4	}	}	PUNCT
cana-5925	49	5	,	,	PUNCT
cana-5925	49	6	𝑓(𝑣17	𝑓(𝑣17	ADJ
cana-5925	49	7	)	)	PUNCT
cana-5925	49	8	=	=	SYM
cana-5925	49	9	{	{	PUNCT
cana-5925	49	10	1,2,3,4,5	1,2,3,4,5	NUM
cana-5925	49	11	}	}	PUNCT
cana-5925	49	12	,	,	PUNCT
cana-5925	49	13	𝑓(𝑣18	𝑓(𝑣18	NOUN
cana-5925	49	14	)	)	PUNCT
cana-5925	49	15	=	=	SYM
cana-5925	49	16	{	{	PUNCT
cana-5925	49	17	1,2	1,2	NUM
cana-5925	49	18	,	,	PUNCT
cana-5925	49	19	…	…	PUNCT
cana-5925	49	20	.6	.6	NUM
cana-5925	49	21	}	}	PUNCT
cana-5925	49	22	,	,	PUNCT
cana-5925	49	23	𝑓(𝑣19	𝑓(𝑣19	NOUN
cana-5925	49	24	)	)	PUNCT
cana-5925	49	25	=	=	SYM
cana-5925	49	26	{	{	PUNCT
cana-5925	49	27	1,2	1,2	NUM
cana-5925	49	28	,	,	PUNCT
cana-5925	49	29	…	…	PUNCT
cana-5925	49	30	.	.	PUNCT
cana-5925	50	1	.7	.7	NUM
cana-5925	50	2	}	}	PUNCT
cana-5925	50	3	,	,	PUNCT
cana-5925	50	4	𝑓(𝑣20	𝑓(𝑣20	VERB
cana-5925	50	5	)	)	PUNCT
cana-5925	50	6	=	=	SYM
cana-5925	51	1	𝑋	𝑋	NOUN
cana-5925	51	2	then	then	ADV
cana-5925	51	3	the	the	DET
cana-5925	51	4	vertex	vertex	NOUN
cana-5925	51	5	labels	label	NOUN
cana-5925	51	6	are	be	AUX
cana-5925	51	7	distinct	distinct	ADJ
cana-5925	51	8	and	and	CCONJ
cana-5925	51	9	{	{	PUNCT
cana-5925	51	10	𝑓(𝑉(𝐺	𝑓(𝑉(𝐺	NOUN
cana-5925	51	11	)	)	PUNCT
cana-5925	51	12	)	)	PUNCT
cana-5925	51	13	}	}	PUNCT
cana-5925	51	14	is	be	AUX
cana-5925	51	15	a	a	DET
cana-5925	51	16	topology	topology	NOUN
cana-5925	51	17	on	on	ADP
cana-5925	51	18	𝑋.	𝑋.	PROPN
cana-5925	51	19	the	the	DET
cana-5925	51	20	induced	induce	VERB
cana-5925	51	21	function	function	NOUN
cana-5925	51	22	𝑓∗	𝑓∗	NOUN
cana-5925	51	23	on	on	ADP
cana-5925	51	24	𝐸(𝐺	𝐸(𝐺	PROPN
cana-5925	51	25	)	)	PUNCT
cana-5925	51	26	is	be	AUX
cana-5925	51	27	defined	define	VERB
cana-5925	51	28	as	as	ADP
cana-5925	51	29	follows	follow	VERB
cana-5925	51	30	:	:	PUNCT
cana-5925	51	31	𝑓∗(𝑢𝑣	𝑓∗(𝑢𝑣	VERB
cana-5925	51	32	)	)	PUNCT
cana-5925	51	33	=	=	PRON
cana-5925	51	34	{	{	PUNCT
cana-5925	51	35	1	1	NUM
cana-5925	51	36	if	if	SCONJ
cana-5925	51	37	𝑓(𝑢	𝑓(𝑢	NOUN
cana-5925	51	38	)	)	PUNCT
cana-5925	51	39	∩	∩	NOUN
cana-5925	51	40	𝑓(𝑣	𝑓(𝑣	NOUN
cana-5925	51	41	)	)	PUNCT
cana-5925	51	42	is	be	AUX
cana-5925	51	43	not	not	PART
cana-5925	51	44	an	an	DET
cana-5925	51	45	empty	empty	ADJ
cana-5925	51	46	set	set	NOUN
cana-5925	51	47	and	and	CCONJ
cana-5925	51	48	singleton	singleton	PROPN
cana-5925	51	49	set	set	NOUN
cana-5925	51	50	0	0	PUNCT
cana-5925	52	1	otherwise	otherwise	ADV
cana-5925	52	2	for	for	ADP
cana-5925	52	3	every	every	DET
cana-5925	52	4	𝑢𝑣	𝑢𝑣	PROPN
cana-5925	52	5	∈	∈	PROPN
cana-5925	52	6	𝐸(𝐺	𝐸(𝐺	NOUN
cana-5925	52	7	)	)	PUNCT
cana-5925	52	8	.	.	PUNCT
cana-5925	53	1	then	then	ADV
cana-5925	53	2	,	,	PUNCT
cana-5925	53	3	|𝑒𝑓(0	|𝑒𝑓(0	NUM
cana-5925	53	4	)	)	PUNCT
cana-5925	53	5	−	−	PROPN
cana-5925	53	6	𝑒𝑓(1)|	𝑒𝑓(1)|	NOUN
cana-5925	53	7	=	=	NOUN
cana-5925	53	8	15	15	NUM
cana-5925	53	9	−	−	NUM
cana-5925	53	10	15	15	NUM
cana-5925	53	11	=	=	SYM
cana-5925	53	12	0	0	NUM
cana-5925	53	13	≤	≤	NUM
cana-5925	53	14	1	1	NUM
cana-5925	53	15	where	where	SCONJ
cana-5925	53	16	𝑒𝑓(0	𝑒𝑓(0	PROPN
cana-5925	53	17	)	)	PUNCT
cana-5925	53	18	=	=	NOUN
cana-5925	53	19	number	number	NOUN
cana-5925	53	20	of	of	ADP
cana-5925	53	21	edges	edge	NOUN
cana-5925	53	22	labeled	label	VERB
cana-5925	53	23	with	with	ADP
cana-5925	53	24	0	0	NUM
cana-5925	53	25	and	and	CCONJ
cana-5925	53	26	𝑒𝑓(1	𝑒𝑓(1	PROPN
cana-5925	53	27	)	)	PUNCT
cana-5925	53	28	=	=	NOUN
cana-5925	53	29	number	number	NOUN
cana-5925	53	30	of	of	ADP
cana-5925	53	31	edges	edge	NOUN
cana-5925	53	32	labeled	label	VERB
cana-5925	53	33	with	with	ADP
cana-5925	53	34	1	1	NUM
cana-5925	53	35	.	.	PUNCT
cana-5925	54	1	hence	hence	ADV
cana-5925	54	2	𝑓	𝑓	PRON
cana-5925	54	3	is	be	AUX
cana-5925	54	4	a	a	DET
cana-5925	54	5	topological	topological	ADJ
cana-5925	54	6	cordial	cordial	ADJ
cana-5925	54	7	labeling	labeling	NOUN
cana-5925	54	8	.	.	PUNCT
cana-5925	55	1	thus	thus	ADV
cana-5925	55	2	𝐺	𝐺	PROPN
cana-5925	55	3	is	be	AUX
cana-5925	55	4	topological	topological	ADJ
cana-5925	55	5	cordial	cordial	ADJ
cana-5925	55	6	graph	graph	NOUN
cana-5925	55	7	.	.	PUNCT
cana-5925	56	1	illustration	illustration	NOUN
cana-5925	56	2	2.1	2.1	NUM
cana-5925	56	3	.	.	PUNCT
cana-5925	57	1	dodecahedral	dodecahedral	ADJ
cana-5925	57	2	graph	graph	NOUN
cana-5925	57	3	is	be	AUX
cana-5925	57	4	topological	topological	ADJ
cana-5925	57	5	cordial	cordial	ADJ
cana-5925	57	6	graph	graph	NOUN
cana-5925	57	7	.	.	PUNCT
cana-5925	58	1	communications	communication	NOUN
cana-5925	58	2	on	on	ADP
cana-5925	58	3	applied	apply	VERB
cana-5925	58	4	nonlinear	nonlinear	ADJ
cana-5925	58	5	analysis	analysis	NOUN
cana-5925	58	6	issn	issn	NOUN
cana-5925	58	7	:	:	PUNCT
cana-5925	58	8	1074	1074	NUM
cana-5925	58	9	-	-	PUNCT
cana-5925	58	10	133x	133x	NUM
cana-5925	58	11	vol	vol	NOUN
cana-5925	58	12	32	32	NUM
cana-5925	58	13	no	no	NOUN
cana-5925	58	14	.	.	NOUN
cana-5925	58	15	3	3	NUM
cana-5925	58	16	(	(	PUNCT
cana-5925	58	17	2025	2025	NUM
cana-5925	58	18	)	)	PUNCT
cana-5925	58	19	1043	1043	NUM
cana-5925	58	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5925	58	21	fig	fig	NOUN
cana-5925	58	22	.	.	PUNCT
cana-5925	59	1	2.1	2.1	NUM
cana-5925	59	2	theorem	theorem	VERB
cana-5925	59	3	2.2	2.2	NUM
cana-5925	59	4	a	a	DET
cana-5925	59	5	paley	paley	ADJ
cana-5925	59	6	graph	graph	NOUN
cana-5925	59	7	of	of	ADP
cana-5925	59	8	order	order	NOUN
cana-5925	59	9	13	13	NUM
cana-5925	59	10	is	be	AUX
cana-5925	59	11	a	a	DET
cana-5925	59	12	topological	topological	ADJ
cana-5925	59	13	cordial	cordial	ADJ
cana-5925	59	14	graph	graph	NOUN
cana-5925	59	15	.	.	PUNCT
cana-5925	60	1	proof	proof	NOUN
cana-5925	60	2	:	:	PUNCT
cana-5925	60	3	let	let	VERB
cana-5925	60	4	𝐺	𝐺	PRON
cana-5925	60	5	be	be	AUX
cana-5925	60	6	a	a	DET
cana-5925	60	7	paley	paley	ADJ
cana-5925	60	8	graph	graph	NOUN
cana-5925	60	9	of	of	ADP
cana-5925	60	10	order	order	NOUN
cana-5925	60	11	13	13	NUM
cana-5925	60	12	.	.	PUNCT
cana-5925	61	1	thus	thus	ADV
cana-5925	61	2	it	it	PRON
cana-5925	61	3	has	have	VERB
cana-5925	61	4	13	13	NUM
cana-5925	61	5	vertices	vertex	NOUN
cana-5925	61	6	and	and	CCONJ
cana-5925	61	7	39	39	NUM
cana-5925	61	8	edges	edge	NOUN
cana-5925	61	9	.	.	PUNCT
cana-5925	62	1	let	let	VERB
cana-5925	62	2	𝑉(𝐺	𝑉(𝐺	NOUN
cana-5925	62	3	)	)	PUNCT
cana-5925	62	4	=	=	SYM
cana-5925	63	1	{	{	PUNCT
cana-5925	63	2	𝑣𝑖/1	𝑣𝑖/1	NOUN
cana-5925	63	3	≤	≤	NUM
cana-5925	63	4	𝑖	𝑖	SYM
cana-5925	63	5	≤	≤	NUM
cana-5925	63	6	13	13	NUM
cana-5925	63	7	}	}	PUNCT
cana-5925	63	8	an	an	DET
cana-5925	63	9	𝐸(𝐺	𝐸(𝐺	NOUN
cana-5925	63	10	)	)	PUNCT
cana-5925	63	11	=	=	SYM
cana-5925	63	12	{	{	PUNCT
cana-5925	63	13	𝑣𝑖𝑣𝑖+1/1	𝑣𝑖𝑣𝑖+1/1	PROPN
cana-5925	63	14	≤	≤	PROPN
cana-5925	63	15	𝑖	𝑖	SYM
cana-5925	63	16	≤	≤	NOUN
cana-5925	63	17	13	13	NUM
cana-5925	64	1	where	where	SCONJ
cana-5925	64	2	𝑣13	𝑣13	NOUN
cana-5925	64	3	=	=	SYM
cana-5925	64	4	𝑣1	𝑣1	PROPN
cana-5925	64	5	}	}	PUNCT
cana-5925	64	6	∪	∪	NOUN
cana-5925	64	7	{	{	PUNCT
cana-5925	64	8	𝑣𝑖𝑣𝑖+3/1	𝑣𝑖𝑣𝑖+3/1	NOUN
cana-5925	64	9	≤	≤	NUM
cana-5925	64	10	𝑖	𝑖	SYM
cana-5925	64	11	≤	≤	NUM
cana-5925	64	12	10	10	NUM
cana-5925	64	13	}	}	PUNCT
cana-5925	64	14	∪	∪	X
cana-5925	64	15	{	{	PUNCT
cana-5925	64	16	𝑣1𝑣𝑖+4/1	𝑣1𝑣𝑖+4/1	ADJ
cana-5925	64	17	≤	≤	PROPN
cana-5925	64	18	𝑖	𝑖	SYM
cana-5925	64	19	≤	≤	NUM
cana-5925	64	20	9	9	NUM
cana-5925	64	21	}	}	PUNCT
cana-5925	64	22	∪	∪	ADJ
cana-5925	64	23	{	{	PUNCT
cana-5925	64	24	𝑣𝑖𝑣𝑖+10/1	𝑣𝑖𝑣𝑖+10/1	NUM
cana-5925	64	25	≤	≤	NUM
cana-5925	64	26	𝑖	𝑖	SYM
cana-5925	64	27	≤	≤	NUM
cana-5925	64	28	3	3	NUM
cana-5925	64	29	}	}	PUNCT
cana-5925	64	30	∪	∪	ADJ
cana-5925	64	31	{	{	PUNCT
cana-5925	64	32	𝑣𝑖𝑣𝑖+9/1	𝑣𝑖𝑣𝑖+9/1	ADP
cana-5925	64	33	≤	≤	NUM
cana-5925	64	34	𝑖	𝑖	SYM
cana-5925	64	35	≤	≤	NOUN
cana-5925	64	36	4	4	NUM
cana-5925	64	37	}	}	PUNCT
cana-5925	64	38	.	.	PUNCT
cana-5925	65	1	let	let	VERB
cana-5925	65	2	𝑋	𝑋	PROPN
cana-5925	65	3	=	=	SYM
cana-5925	65	4	{	{	PUNCT
cana-5925	65	5	1,2	1,2	NUM
cana-5925	65	6	,	,	PUNCT
cana-5925	65	7	…	…	PUNCT
cana-5925	65	8	,	,	PUNCT
cana-5925	65	9	13	13	NUM
cana-5925	65	10	}	}	PUNCT
cana-5925	65	11	.	.	PUNCT
cana-5925	66	1	define	define	VERB
cana-5925	66	2	𝑓	𝑓	DET
cana-5925	66	3	:	:	PUNCT
cana-5925	66	4	𝑉(𝐺	𝑉(𝐺	NOUN
cana-5925	66	5	)	)	PUNCT
cana-5925	66	6	→	→	SYM
cana-5925	66	7	2𝑋	2𝑋	PROPN
cana-5925	66	8	by	by	ADP
cana-5925	66	9	𝑓(𝑣1	𝑓(𝑣1	NOUN
cana-5925	66	10	)	)	PUNCT
cana-5925	66	11	=	=	SYM
cana-5925	66	12	𝜙	𝜙	NOUN
cana-5925	66	13	,	,	PUNCT
cana-5925	66	14	𝑓(𝑣𝑖+1	𝑓(𝑣𝑖+1	NOUN
cana-5925	66	15	)	)	PUNCT
cana-5925	66	16	=	=	SYM
cana-5925	66	17	{	{	PUNCT
cana-5925	66	18	1,2	1,2	NUM
cana-5925	66	19	,	,	PUNCT
cana-5925	66	20	.	.	PUNCT
cana-5925	66	21	.	.	PUNCT
cana-5925	66	22	.	.	PUNCT
cana-5925	67	1	,	,	PUNCT
cana-5925	67	2	𝑖	𝑖	X
cana-5925	67	3	}	}	PUNCT
cana-5925	67	4	,	,	PUNCT
cana-5925	67	5	1	1	NUM
cana-5925	67	6	≤	≤	NUM
cana-5925	67	7	𝑖	𝑖	SYM
cana-5925	67	8	≤	≤	NOUN
cana-5925	67	9	3	3	NUM
cana-5925	67	10	,	,	PUNCT
cana-5925	67	11	𝑓(𝑣𝑖	𝑓(𝑣𝑖	NOUN
cana-5925	67	12	)	)	PUNCT
cana-5925	67	13	=	=	SYM
cana-5925	67	14	{	{	PUNCT
cana-5925	67	15	1,2	1,2	NUM
cana-5925	67	16	,	,	PUNCT
cana-5925	67	17	…	…	PUNCT
cana-5925	67	18	,	,	PUNCT
cana-5925	67	19	𝑖	𝑖	SYM
cana-5925	67	20	+	+	NOUN
cana-5925	67	21	1	1	NUM
cana-5925	67	22	}	}	PUNCT
cana-5925	67	23	,	,	PUNCT
cana-5925	67	24	8	8	NUM
cana-5925	67	25	≤	≤	NUM
cana-5925	67	26	𝑖	𝑖	SYM
cana-5925	67	27	≤	≤	NUM
cana-5925	67	28	12	12	NUM
cana-5925	67	29	,	,	PUNCT
cana-5925	67	30	𝑓(13	𝑓(13	ADJ
cana-5925	67	31	)	)	PUNCT
cana-5925	67	32	=	=	SYM
cana-5925	67	33	𝑋.	𝑋.	PROPN
cana-5925	67	34	then	then	ADV
cana-5925	67	35	the	the	DET
cana-5925	67	36	vertex	vertex	NOUN
cana-5925	67	37	labels	label	NOUN
cana-5925	67	38	are	be	AUX
cana-5925	67	39	distinct	distinct	ADJ
cana-5925	67	40	and	and	CCONJ
cana-5925	67	41	{	{	PUNCT
cana-5925	67	42	𝑓(𝑉(𝐺	𝑓(𝑉(𝐺	NOUN
cana-5925	67	43	)	)	PUNCT
cana-5925	67	44	)	)	PUNCT
cana-5925	67	45	}	}	PUNCT
cana-5925	67	46	is	be	AUX
cana-5925	67	47	a	a	DET
cana-5925	67	48	topology	topology	NOUN
cana-5925	67	49	on	on	ADP
cana-5925	67	50	𝑋.	𝑋.	PROPN
cana-5925	67	51	the	the	DET
cana-5925	67	52	induced	induce	VERB
cana-5925	67	53	function	function	NOUN
cana-5925	67	54	𝑓∗	𝑓∗	NOUN
cana-5925	67	55	on	on	ADP
cana-5925	67	56	𝐸(𝐺	𝐸(𝐺	PROPN
cana-5925	67	57	)	)	PUNCT
cana-5925	67	58	is	be	AUX
cana-5925	67	59	defined	define	VERB
cana-5925	67	60	as	as	ADP
cana-5925	67	61	follows	follow	VERB
cana-5925	67	62	:	:	PUNCT
cana-5925	67	63	𝑓∗(𝑢𝑣	𝑓∗(𝑢𝑣	VERB
cana-5925	67	64	)	)	PUNCT
cana-5925	67	65	=	=	PRON
cana-5925	67	66	{	{	PUNCT
cana-5925	67	67	1	1	NUM
cana-5925	67	68	if	if	SCONJ
cana-5925	67	69	𝑓(𝑢	𝑓(𝑢	NOUN
cana-5925	67	70	)	)	PUNCT
cana-5925	67	71	∩	∩	NOUN
cana-5925	67	72	𝑓(𝑣	𝑓(𝑣	NOUN
cana-5925	67	73	)	)	PUNCT
cana-5925	67	74	is	be	AUX
cana-5925	67	75	not	not	PART
cana-5925	67	76	an	an	DET
cana-5925	67	77	empty	empty	ADJ
cana-5925	67	78	set	set	NOUN
cana-5925	67	79	and	and	CCONJ
cana-5925	67	80	singleton	singleton	PROPN
cana-5925	67	81	set	set	NOUN
cana-5925	67	82	0	0	PUNCT
cana-5925	68	1	otherwise	otherwise	ADV
cana-5925	68	2	for	for	ADP
cana-5925	68	3	every	every	DET
cana-5925	68	4	𝑢𝑣	𝑢𝑣	PROPN
cana-5925	68	5	∈	∈	PROPN
cana-5925	68	6	𝐸(𝐺	𝐸(𝐺	NOUN
cana-5925	68	7	)	)	PUNCT
cana-5925	68	8	.	.	PUNCT
cana-5925	69	1	then	then	ADV
cana-5925	69	2	,	,	PUNCT
cana-5925	69	3	|𝑒𝑓(0	|𝑒𝑓(0	NUM
cana-5925	69	4	)	)	PUNCT
cana-5925	69	5	−	−	PROPN
cana-5925	70	1	𝑒𝑓(1)|	𝑒𝑓(1)|	PROPN
cana-5925	70	2	≤	≤	NOUN
cana-5925	70	3	1	1	NUM
cana-5925	70	4	where	where	SCONJ
cana-5925	70	5	𝑒𝑓(0	𝑒𝑓(0	PROPN
cana-5925	70	6	)	)	PUNCT
cana-5925	70	7	=	=	NOUN
cana-5925	70	8	number	number	NOUN
cana-5925	70	9	of	of	ADP
cana-5925	70	10	edges	edge	NOUN
cana-5925	70	11	labeled	label	VERB
cana-5925	70	12	with	with	ADP
cana-5925	70	13	0	0	NUM
cana-5925	70	14	and	and	CCONJ
cana-5925	70	15	𝑒𝑓(1	𝑒𝑓(1	PROPN
cana-5925	70	16	)	)	PUNCT
cana-5925	70	17	=	=	NOUN
cana-5925	70	18	number	number	NOUN
cana-5925	70	19	of	of	ADP
cana-5925	70	20	edges	edge	NOUN
cana-5925	70	21	labeled	label	VERB
cana-5925	70	22	with	with	ADP
cana-5925	70	23	1	1	NUM
cana-5925	70	24	.	.	PUNCT
cana-5925	71	1	hence	hence	ADV
cana-5925	71	2	𝑓	𝑓	PRON
cana-5925	71	3	is	be	AUX
cana-5925	71	4	a	a	DET
cana-5925	71	5	topological	topological	ADJ
cana-5925	71	6	cordial	cordial	ADJ
cana-5925	71	7	labeling	labeling	NOUN
cana-5925	71	8	.	.	PUNCT
cana-5925	72	1	thus	thus	ADV
cana-5925	72	2	𝐺	𝐺	PROPN
cana-5925	72	3	is	be	AUX
cana-5925	72	4	topological	topological	ADJ
cana-5925	72	5	cordial	cordial	ADJ
cana-5925	72	6	graph	graph	NOUN
cana-5925	72	7	.	.	PUNCT
cana-5925	73	1	illustration	illustration	NOUN
cana-5925	73	2	2.2	2.2	NUM
cana-5925	73	3	a	a	DET
cana-5925	73	4	paley	paley	ADJ
cana-5925	73	5	graph	graph	NOUN
cana-5925	73	6	of	of	ADP
cana-5925	73	7	order	order	NOUN
cana-5925	73	8	13	13	NUM
cana-5925	73	9	is	be	AUX
cana-5925	73	10	a	a	DET
cana-5925	73	11	topological	topological	ADJ
cana-5925	73	12	cordial	cordial	ADJ
cana-5925	73	13	graph	graph	NOUN
cana-5925	73	14	.	.	PUNCT
cana-5925	74	1	communications	communication	NOUN
cana-5925	74	2	on	on	ADP
cana-5925	74	3	applied	apply	VERB
cana-5925	74	4	nonlinear	nonlinear	ADJ
cana-5925	74	5	analysis	analysis	NOUN
cana-5925	74	6	issn	issn	NOUN
cana-5925	74	7	:	:	PUNCT
cana-5925	74	8	1074	1074	NUM
cana-5925	74	9	-	-	PUNCT
cana-5925	74	10	133x	133x	NUM
cana-5925	74	11	vol	vol	NOUN
cana-5925	74	12	32	32	NUM
cana-5925	74	13	no	no	NOUN
cana-5925	74	14	.	.	NOUN
cana-5925	74	15	3	3	NUM
cana-5925	74	16	(	(	PUNCT
cana-5925	74	17	2025	2025	NUM
cana-5925	74	18	)	)	PUNCT
cana-5925	74	19	1044	1044	NUM
cana-5925	74	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5925	75	1	ig	ig	PROPN
cana-5925	75	2	2.2	2.2	NUM
cana-5925	75	3	3.topological	3.topological	NUM
cana-5925	75	4	cordial	cordial	ADJ
cana-5925	75	5	labeling	labeling	NOUN
cana-5925	75	6	of	of	ADP
cana-5925	75	7	generalized	generalized	ADJ
cana-5925	75	8	graphs	graph	NOUN
cana-5925	75	9	theorem	theorem	VERB
cana-5925	75	10	3.1	3.1	NUM
cana-5925	75	11	.	.	PUNCT
cana-5925	76	1	the	the	DET
cana-5925	76	2	graph	graph	NOUN
cana-5925	76	3	𝐾(𝑚	𝐾(𝑚	PROPN
cana-5925	76	4	,	,	PUNCT
cana-5925	76	5	𝑛	𝑛	NOUN
cana-5925	76	6	)	)	PUNCT
cana-5925	76	7	is	be	AUX
cana-5925	76	8	topological	topological	ADJ
cana-5925	76	9	cordial	cordial	ADJ
cana-5925	76	10	graph	graph	NOUN
cana-5925	76	11	,	,	PUNCT
cana-5925	76	12	if	if	SCONJ
cana-5925	76	13	3	3	NUM
cana-5925	76	14	≤	≤	NUM
cana-5925	76	15	𝑛	𝑛	DET
cana-5925	76	16	≤	≤	NUM
cana-5925	76	17	6	6	NUM
cana-5925	76	18	.	.	PUNCT
cana-5925	77	1	proof	proof	NOUN
cana-5925	77	2	:	:	PUNCT
cana-5925	77	3	let	let	VERB
cana-5925	77	4	𝐾(𝑚	𝐾(𝑚	NOUN
cana-5925	77	5	,	,	PUNCT
cana-5925	77	6	𝑛	𝑛	NOUN
cana-5925	77	7	)	)	PUNCT
cana-5925	77	8	be	be	VERB
cana-5925	77	9	a	a	DET
cana-5925	77	10	complete	complete	ADJ
cana-5925	77	11	bipartite	bipartite	NOUN
cana-5925	77	12	graph	graph	NOUN
cana-5925	77	13	.	.	PUNCT
cana-5925	78	1	let	let	VERB
cana-5925	78	2	𝑉(𝐾	𝑉(𝐾	NOUN
cana-5925	78	3	)	)	PUNCT
cana-5925	78	4	=	=	SYM
cana-5925	79	1	{	{	PUNCT
cana-5925	79	2	𝑣𝑖/1	𝑣𝑖/1	NOUN
cana-5925	79	3	≤	≤	NUM
cana-5925	79	4	𝑖	𝑖	SYM
cana-5925	79	5	≤	≤	NUM
cana-5925	79	6	𝑛	𝑛	PRON
cana-5925	79	7	}	}	PUNCT
cana-5925	79	8	∪	∪	ADJ
cana-5925	79	9	{	{	PUNCT
cana-5925	79	10	𝑤𝑗/1	𝑤𝑗/1	NOUN
cana-5925	79	11	≤	≤	NUM
cana-5925	79	12	𝑗	𝑗	PRON
cana-5925	79	13	≤	≤	NUM
cana-5925	79	14	𝑛	𝑛	NOUN
cana-5925	79	15	}	}	PUNCT
cana-5925	79	16	and	and	CCONJ
cana-5925	79	17	𝐸(𝐾	𝐸(𝐾	VERB
cana-5925	79	18	)	)	PUNCT
cana-5925	80	1	=	=	SYM
cana-5925	80	2	{	{	PUNCT
cana-5925	80	3	𝑣𝑖𝑤𝑗/1	𝑣𝑖𝑤𝑗/1	X
cana-5925	80	4	≤	≤	NUM
cana-5925	80	5	𝑖	𝑖	SYM
cana-5925	80	6	≤	≤	NUM
cana-5925	80	7	𝑛	𝑛	NOUN
cana-5925	80	8	,	,	PUNCT
cana-5925	80	9	1	1	NUM
cana-5925	80	10	≤	≤	NUM
cana-5925	80	11	𝑗	𝑗	PRON
cana-5925	80	12	≤	≤	NUM
cana-5925	80	13	𝑛	𝑛	NOUN
cana-5925	80	14	,	,	PUNCT
cana-5925	80	15	where	where	SCONJ
cana-5925	80	16	3	3	NUM
cana-5925	80	17	≤	≤	NUM
cana-5925	80	18	𝑛	𝑛	DET
cana-5925	80	19	≤	≤	NUM
cana-5925	80	20	6	6	NUM
cana-5925	80	21	}	}	PUNCT
cana-5925	80	22	let	let	VERB
cana-5925	80	23	𝑋	𝑋	PROPN
cana-5925	80	24	=	=	SYM
cana-5925	80	25	{	{	PUNCT
cana-5925	80	26	1,2,3	1,2,3	NUM
cana-5925	80	27	,	,	PUNCT
cana-5925	80	28	…	…	PUNCT
cana-5925	80	29	,	,	PUNCT
cana-5925	80	30	𝑛	𝑛	DET
cana-5925	80	31	−	−	NOUN
cana-5925	80	32	1	1	NUM
cana-5925	80	33	}	}	PUNCT
cana-5925	80	34	,	,	PUNCT
cana-5925	80	35	define	define	VERB
cana-5925	80	36	𝑓	𝑓	DET
cana-5925	80	37	:	:	PUNCT
cana-5925	80	38	𝑉(𝐾	𝑉(𝐾	NUM
cana-5925	80	39	)	)	PUNCT
cana-5925	80	40	→	→	SYM
cana-5925	80	41	2𝑋	2𝑋	PROPN
cana-5925	80	42	.	.	PUNCT
cana-5925	81	1	we	we	PRON
cana-5925	81	2	label	label	VERB
cana-5925	81	3	the	the	DET
cana-5925	81	4	vertices	vertex	NOUN
cana-5925	81	5	and	and	CCONJ
cana-5925	81	6	edges	edge	NOUN
cana-5925	81	7	satisfying	satisfy	VERB
cana-5925	81	8	the	the	DET
cana-5925	81	9	condition	condition	NOUN
cana-5925	81	10	of	of	ADP
cana-5925	81	11	topology	topology	NOUN
cana-5925	81	12	.	.	PUNCT
cana-5925	82	1	therefore	therefore	ADV
cana-5925	82	2	the	the	DET
cana-5925	82	3	vertex	vertex	NOUN
cana-5925	82	4	labels	label	NOUN
cana-5925	82	5	are	be	AUX
cana-5925	82	6	distinct	distinct	ADJ
cana-5925	82	7	and	and	CCONJ
cana-5925	82	8	{	{	PUNCT
cana-5925	82	9	𝑓(𝑉(𝐾	𝑓(𝑉(𝐾	NOUN
cana-5925	82	10	)	)	PUNCT
cana-5925	82	11	)	)	PUNCT
cana-5925	82	12	}	}	PUNCT
cana-5925	82	13	is	be	AUX
cana-5925	82	14	a	a	DET
cana-5925	82	15	topology	topology	NOUN
cana-5925	82	16	on	on	ADP
cana-5925	82	17	𝑋.the	𝑋.the	DET
cana-5925	82	18	induced	induce	VERB
cana-5925	82	19	function	function	NOUN
cana-5925	82	20	𝑓∗	𝑓∗	NOUN
cana-5925	82	21	on	on	ADP
cana-5925	82	22	𝐸(𝐾	𝐸(𝐾	NOUN
cana-5925	82	23	)	)	PUNCT
cana-5925	82	24	is	be	AUX
cana-5925	82	25	defined	define	VERB
cana-5925	82	26	as	as	SCONJ
cana-5925	82	27	follows	follow	VERB
cana-5925	82	28	:	:	PUNCT
cana-5925	82	29	𝑓∗(𝑢𝑣	𝑓∗(𝑢𝑣	VERB
cana-5925	82	30	)	)	PUNCT
cana-5925	82	31	=	=	PRON
cana-5925	82	32	{	{	PUNCT
cana-5925	82	33	1	1	NUM
cana-5925	82	34	if	if	SCONJ
cana-5925	82	35	𝑓(𝑢	𝑓(𝑢	NOUN
cana-5925	82	36	)	)	PUNCT
cana-5925	82	37	∩	∩	NOUN
cana-5925	82	38	𝑓(𝑣	𝑓(𝑣	NOUN
cana-5925	82	39	)	)	PUNCT
cana-5925	82	40	is	be	AUX
cana-5925	82	41	not	not	PART
cana-5925	82	42	an	an	DET
cana-5925	82	43	empty	empty	ADJ
cana-5925	82	44	set	set	NOUN
cana-5925	82	45	and	and	CCONJ
cana-5925	82	46	singleton	singleton	PROPN
cana-5925	82	47	set	set	NOUN
cana-5925	82	48	0	0	PUNCT
cana-5925	83	1	otherwise	otherwise	ADV
cana-5925	83	2	for	for	SCONJ
cana-5925	83	3	every	every	DET
cana-5925	83	4	𝑢𝑣	𝑢𝑣	NOUN
cana-5925	83	5	∈	∈	PROPN
cana-5925	83	6	𝐸(𝐾	𝐸(𝐾	NOUN
cana-5925	83	7	)	)	PUNCT
cana-5925	83	8	.	.	PUNCT
cana-5925	84	1	then	then	ADV
cana-5925	84	2	,	,	PUNCT
cana-5925	84	3	|𝑒𝑓(0	|𝑒𝑓(0	NUM
cana-5925	84	4	)	)	PUNCT
cana-5925	84	5	−	−	PROPN
cana-5925	85	1	𝑒𝑓(1)|	𝑒𝑓(1)|	PROPN
cana-5925	85	2	≤	≤	NOUN
cana-5925	85	3	1	1	NUM
cana-5925	85	4	where	where	SCONJ
cana-5925	85	5	𝑒𝑓(0	𝑒𝑓(0	PROPN
cana-5925	85	6	)	)	PUNCT
cana-5925	85	7	=	=	NOUN
cana-5925	85	8	number	number	NOUN
cana-5925	85	9	of	of	ADP
cana-5925	85	10	edges	edge	NOUN
cana-5925	85	11	labeled	label	VERB
cana-5925	85	12	with	with	ADP
cana-5925	85	13	0	0	NUM
cana-5925	85	14	and	and	CCONJ
cana-5925	85	15	𝑒𝑓(1	𝑒𝑓(1	PROPN
cana-5925	85	16	)	)	PUNCT
cana-5925	85	17	=	=	NOUN
cana-5925	85	18	number	number	NOUN
cana-5925	85	19	of	of	ADP
cana-5925	85	20	edges	edge	NOUN
cana-5925	85	21	labeled	label	VERB
cana-5925	85	22	with	with	ADP
cana-5925	85	23	1	1	NUM
cana-5925	85	24	.	.	PUNCT
cana-5925	86	1	hence	hence	ADV
cana-5925	86	2	𝑓	𝑓	PRON
cana-5925	86	3	is	be	AUX
cana-5925	86	4	a	a	DET
cana-5925	86	5	topological	topological	ADJ
cana-5925	86	6	cordial	cordial	ADJ
cana-5925	86	7	labeling	labeling	NOUN
cana-5925	86	8	.	.	PUNCT
cana-5925	87	1	thus	thus	ADV
cana-5925	87	2	𝐾	𝐾	PROPN
cana-5925	87	3	is	be	AUX
cana-5925	87	4	topological	topological	ADJ
cana-5925	87	5	cordial	cordial	ADJ
cana-5925	87	6	graph	graph	NOUN
cana-5925	87	7	.	.	PUNCT
cana-5925	88	1	illustration	illustration	NOUN
cana-5925	88	2	3.1	3.1	NUM
cana-5925	88	3	𝐾(5,5	𝐾(5,5	NOUN
cana-5925	88	4	)	)	PUNCT
cana-5925	88	5	is	be	AUX
cana-5925	88	6	topological	topological	ADJ
cana-5925	88	7	cordial	cordial	ADJ
cana-5925	88	8	graph	graph	NOUN
cana-5925	88	9	.	.	PUNCT
cana-5925	89	1	communications	communication	NOUN
cana-5925	89	2	on	on	ADP
cana-5925	89	3	applied	apply	VERB
cana-5925	89	4	nonlinear	nonlinear	ADJ
cana-5925	89	5	analysis	analysis	NOUN
cana-5925	89	6	issn	issn	NOUN
cana-5925	89	7	:	:	PUNCT
cana-5925	89	8	1074	1074	NUM
cana-5925	89	9	-	-	PUNCT
cana-5925	89	10	133x	133x	NUM
cana-5925	89	11	vol	vol	NOUN
cana-5925	89	12	32	32	NUM
cana-5925	89	13	no	no	NOUN
cana-5925	89	14	.	.	NOUN
cana-5925	89	15	3	3	NUM
cana-5925	89	16	(	(	PUNCT
cana-5925	89	17	2025	2025	NUM
cana-5925	89	18	)	)	PUNCT
cana-5925	89	19	1045	1045	NUM
cana-5925	89	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5925	89	21	fig	fig	NOUN
cana-5925	89	22	3.1	3.1	NUM
cana-5925	89	23	theorem	theorem	VERB
cana-5925	89	24	3.2	3.2	NUM
cana-5925	89	25	a	a	DET
cana-5925	89	26	double	double	ADJ
cana-5925	89	27	star	star	NOUN
cana-5925	89	28	𝑆(𝑛	𝑆(𝑛	NOUN
cana-5925	89	29	,	,	PUNCT
cana-5925	89	30	𝑚	𝑚	NOUN
cana-5925	89	31	)	)	PUNCT
cana-5925	89	32	is	be	AUX
cana-5925	89	33	a	a	DET
cana-5925	89	34	topological	topological	ADJ
cana-5925	89	35	cordial	cordial	ADJ
cana-5925	89	36	graph	graph	NOUN
cana-5925	89	37	.	.	PUNCT
cana-5925	90	1	proof	proof	NOUN
cana-5925	90	2	:	:	PUNCT
cana-5925	90	3	let	let	VERB
cana-5925	90	4	𝐺	𝐺	PRON
cana-5925	90	5	be	be	AUX
cana-5925	90	6	a	a	DET
cana-5925	90	7	double	double	ADJ
cana-5925	90	8	star	star	NOUN
cana-5925	90	9	𝑆(𝑛	𝑆(𝑛	NOUN
cana-5925	90	10	,	,	PUNCT
cana-5925	90	11	𝑚	𝑚	NOUN
cana-5925	90	12	)	)	PUNCT
cana-5925	90	13	.	.	PUNCT
cana-5925	91	1	let	let	VERB
cana-5925	91	2	𝑉(𝐺	𝑉(𝐺	NOUN
cana-5925	91	3	)	)	PUNCT
cana-5925	91	4	=	=	PRON
cana-5925	91	5	{	{	PUNCT
cana-5925	91	6	𝑢0	𝑢0	PROPN
cana-5925	91	7	,	,	PUNCT
cana-5925	91	8	𝑢1	𝑢1	NOUN
cana-5925	91	9	,	,	PUNCT
cana-5925	91	10	𝑢2	𝑢2	PROPN
cana-5925	91	11	,	,	PUNCT
cana-5925	91	12	…	…	PUNCT
cana-5925	91	13	…	…	PUNCT
cana-5925	91	14	.	.	PUNCT
cana-5925	92	1	𝑢𝑛	𝑢𝑛	X
cana-5925	92	2	}	}	PUNCT
cana-5925	92	3	∪	∪	ADJ
cana-5925	92	4	{	{	PUNCT
cana-5925	92	5	𝑣0	𝑣0	PROPN
cana-5925	92	6	,	,	PUNCT
cana-5925	92	7	𝑣1	𝑣1	PROPN
cana-5925	92	8	,	,	PUNCT
cana-5925	92	9	𝑣2	𝑣2	PROPN
cana-5925	92	10	,	,	PUNCT
cana-5925	92	11	…	…	PUNCT
cana-5925	92	12	.	.	PUNCT
cana-5925	92	13	.	.	PUNCT
cana-5925	93	1	𝑣𝑚	𝑣𝑚	VERB
cana-5925	93	2	}	}	PUNCT
cana-5925	93	3	and	and	CCONJ
cana-5925	93	4	𝐸(𝐺	𝐸(𝐺	NUM
cana-5925	93	5	)	)	PUNCT
cana-5925	93	6	=	=	PRON
cana-5925	93	7	{	{	PUNCT
cana-5925	93	8	𝑢0𝑣0	𝑢0𝑣0	NOUN
cana-5925	93	9	}	}	PUNCT
cana-5925	93	10	∪	∪	ADJ
cana-5925	93	11	{	{	PUNCT
cana-5925	93	12	𝑢0𝑢𝑖/1	𝑢0𝑢𝑖/1	ADJ
cana-5925	93	13	≤	≤	NUM
cana-5925	93	14	𝑖	𝑖	SYM
cana-5925	93	15	≤	≤	NUM
cana-5925	93	16	𝑛	𝑛	PRON
cana-5925	93	17	}	}	PUNCT
cana-5925	93	18	∪	∪	ADJ
cana-5925	93	19	{	{	PUNCT
cana-5925	93	20	𝑣0𝑣𝑖/1	𝑣0𝑣𝑖/1	NOUN
cana-5925	93	21	≤	≤	NUM
cana-5925	93	22	𝑖	𝑖	SYM
cana-5925	93	23	≤	≤	NUM
cana-5925	93	24	𝑚	𝑚	ADP
cana-5925	93	25	}	}	PUNCT
cana-5925	93	26	.	.	PUNCT
cana-5925	94	1	then	then	ADV
cana-5925	94	2	g	g	PROPN
cana-5925	94	3	has	have	VERB
cana-5925	94	4	𝑚	𝑚	PROPN
cana-5925	94	5	+	+	NOUN
cana-5925	94	6	𝑛	𝑛	PRON
cana-5925	94	7	+	+	SYM
cana-5925	94	8	2	2	NUM
cana-5925	94	9	𝑣𝑒𝑟𝑡𝑖𝑐𝑒𝑠	𝑣𝑒𝑟𝑡𝑖𝑐𝑒𝑠	NOUN
cana-5925	94	10	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5925	94	11	𝑛	𝑛	PROPN
cana-5925	95	1	+	+	X
cana-5925	95	2	𝑚	𝑚	X
cana-5925	95	3	+	+	SYM
cana-5925	95	4	1	1	NUM
cana-5925	95	5	𝑒𝑑𝑔𝑒𝑠	𝑒𝑑𝑔𝑒𝑠	NOUN
cana-5925	95	6	let	let	VERB
cana-5925	95	7	𝑋	𝑋	PROPN
cana-5925	95	8	=	=	SYM
cana-5925	95	9	{	{	PUNCT
cana-5925	95	10	1,2	1,2	NUM
cana-5925	95	11	,	,	PUNCT
cana-5925	95	12	…	…	PUNCT
cana-5925	95	13	…	…	PUNCT
cana-5925	95	14	𝑛	𝑛	PRON
cana-5925	95	15	+	+	NUM
cana-5925	95	16	𝑚	𝑚	X
cana-5925	95	17	+	+	ADJ
cana-5925	95	18	2	2	NUM
cana-5925	95	19	}	}	PUNCT
cana-5925	95	20	define	define	VERB
cana-5925	95	21	𝑓	𝑓	DET
cana-5925	95	22	:	:	PUNCT
cana-5925	95	23	𝑉(𝐺	𝑉(𝐺	NOUN
cana-5925	95	24	)	)	PUNCT
cana-5925	95	25	→	→	SYM
cana-5925	95	26	2𝑋	2𝑋	PROPN
cana-5925	95	27	.	.	PUNCT
cana-5925	96	1	we	we	PRON
cana-5925	96	2	label	label	VERB
cana-5925	96	3	the	the	DET
cana-5925	96	4	vertices	vertex	NOUN
cana-5925	96	5	and	and	CCONJ
cana-5925	96	6	edges	edge	NOUN
cana-5925	96	7	satisfying	satisfy	VERB
cana-5925	96	8	the	the	DET
cana-5925	96	9	condition	condition	NOUN
cana-5925	96	10	of	of	ADP
cana-5925	96	11	topology	topology	NOUN
cana-5925	96	12	.	.	PUNCT
cana-5925	97	1	then	then	ADV
cana-5925	97	2	the	the	DET
cana-5925	97	3	vertex	vertex	NOUN
cana-5925	97	4	labels	label	NOUN
cana-5925	97	5	are	be	AUX
cana-5925	97	6	distinct	distinct	ADJ
cana-5925	97	7	and	and	CCONJ
cana-5925	97	8	{	{	PUNCT
cana-5925	97	9	𝑓(𝑉(𝐺	𝑓(𝑉(𝐺	NOUN
cana-5925	97	10	)	)	PUNCT
cana-5925	97	11	)	)	PUNCT
cana-5925	97	12	}	}	PUNCT
cana-5925	97	13	is	be	AUX
cana-5925	97	14	a	a	DET
cana-5925	97	15	topology	topology	NOUN
cana-5925	97	16	on	on	ADP
cana-5925	97	17	𝑋.	𝑋.	PROPN
cana-5925	97	18	the	the	DET
cana-5925	97	19	induced	induce	VERB
cana-5925	97	20	function	function	NOUN
cana-5925	97	21	𝑓∗	𝑓∗	NOUN
cana-5925	97	22	on	on	ADP
cana-5925	97	23	𝐸(𝐺	𝐸(𝐺	PROPN
cana-5925	97	24	)	)	PUNCT
cana-5925	97	25	is	be	AUX
cana-5925	97	26	defined	define	VERB
cana-5925	97	27	as	as	ADP
cana-5925	97	28	follows	follow	VERB
cana-5925	97	29	:	:	PUNCT
cana-5925	97	30	𝑓∗(𝑢𝑣	𝑓∗(𝑢𝑣	VERB
cana-5925	97	31	)	)	PUNCT
cana-5925	97	32	=	=	PRON
cana-5925	97	33	{	{	PUNCT
cana-5925	97	34	1	1	NUM
cana-5925	97	35	if	if	SCONJ
cana-5925	97	36	𝑓(𝑢	𝑓(𝑢	NOUN
cana-5925	97	37	)	)	PUNCT
cana-5925	97	38	∩	∩	NOUN
cana-5925	97	39	𝑓(𝑣	𝑓(𝑣	NOUN
cana-5925	97	40	)	)	PUNCT
cana-5925	97	41	is	be	AUX
cana-5925	97	42	not	not	PART
cana-5925	97	43	an	an	DET
cana-5925	97	44	empty	empty	ADJ
cana-5925	97	45	set	set	NOUN
cana-5925	97	46	and	and	CCONJ
cana-5925	97	47	singleton	singleton	PROPN
cana-5925	97	48	set	set	NOUN
cana-5925	97	49	0	0	PUNCT
cana-5925	98	1	otherwise	otherwise	ADV
cana-5925	98	2	for	for	ADP
cana-5925	98	3	every	every	DET
cana-5925	98	4	𝑢𝑣	𝑢𝑣	PROPN
cana-5925	98	5	∈	∈	PROPN
cana-5925	98	6	𝐸(𝐺	𝐸(𝐺	NOUN
cana-5925	98	7	)	)	PUNCT
cana-5925	98	8	.	.	PUNCT
cana-5925	99	1	therefore	therefore	ADV
cana-5925	99	2	,	,	PUNCT
cana-5925	99	3	|𝑒𝑓(0	|𝑒𝑓(0	NUM
cana-5925	99	4	)	)	PUNCT
cana-5925	99	5	−	−	PROPN
cana-5925	100	1	𝑒𝑓(1)|	𝑒𝑓(1)|	PROPN
cana-5925	100	2	≤	≤	NOUN
cana-5925	100	3	1	1	NUM
cana-5925	100	4	where	where	SCONJ
cana-5925	100	5	𝑒𝑓(0	𝑒𝑓(0	PROPN
cana-5925	100	6	)	)	PUNCT
cana-5925	100	7	=	=	NOUN
cana-5925	100	8	number	number	NOUN
cana-5925	100	9	of	of	ADP
cana-5925	100	10	edges	edge	NOUN
cana-5925	100	11	labeled	label	VERB
cana-5925	100	12	with	with	ADP
cana-5925	100	13	0	0	NUM
cana-5925	100	14	and	and	CCONJ
cana-5925	100	15	𝑒𝑓(1	𝑒𝑓(1	PROPN
cana-5925	100	16	)	)	PUNCT
cana-5925	100	17	=	=	NOUN
cana-5925	100	18	number	number	NOUN
cana-5925	100	19	of	of	ADP
cana-5925	100	20	edges	edge	NOUN
cana-5925	100	21	labeled	label	VERB
cana-5925	100	22	with	with	ADP
cana-5925	100	23	1	1	NUM
cana-5925	100	24	.	.	PUNCT
cana-5925	101	1	hence	hence	ADV
cana-5925	101	2	𝑓	𝑓	PRON
cana-5925	101	3	is	be	AUX
cana-5925	101	4	a	a	DET
cana-5925	101	5	topological	topological	ADJ
cana-5925	101	6	cordial	cordial	ADJ
cana-5925	101	7	labeling	labeling	NOUN
cana-5925	101	8	.	.	PUNCT
cana-5925	102	1	thus	thus	ADV
cana-5925	102	2	𝐺	𝐺	PROPN
cana-5925	102	3	is	be	AUX
cana-5925	102	4	topological	topological	ADJ
cana-5925	102	5	cordial	cordial	ADJ
cana-5925	102	6	graph	graph	NOUN
cana-5925	102	7	.	.	PUNCT
cana-5925	103	1	illustration	illustration	NOUN
cana-5925	103	2	3.2	3.2	NUM
cana-5925	103	3	a	a	DET
cana-5925	103	4	double	double	ADJ
cana-5925	103	5	star	star	NOUN
cana-5925	103	6	𝑆(2,4	𝑆(2,4	NOUN
cana-5925	103	7	)	)	PUNCT
cana-5925	103	8	is	be	AUX
cana-5925	103	9	a	a	DET
cana-5925	103	10	topological	topological	ADJ
cana-5925	103	11	cordial	cordial	ADJ
cana-5925	103	12	graph	graph	NOUN
cana-5925	103	13	.	.	PUNCT
cana-5925	104	1	communications	communication	NOUN
cana-5925	104	2	on	on	ADP
cana-5925	104	3	applied	apply	VERB
cana-5925	104	4	nonlinear	nonlinear	ADJ
cana-5925	104	5	analysis	analysis	NOUN
cana-5925	104	6	issn	issn	NOUN
cana-5925	104	7	:	:	PUNCT
cana-5925	104	8	1074	1074	NUM
cana-5925	104	9	-	-	PUNCT
cana-5925	104	10	133x	133x	NUM
cana-5925	104	11	vol	vol	NOUN
cana-5925	104	12	32	32	NUM
cana-5925	104	13	no	no	NOUN
cana-5925	104	14	.	.	NOUN
cana-5925	104	15	3	3	NUM
cana-5925	104	16	(	(	PUNCT
cana-5925	104	17	2025	2025	NUM
cana-5925	104	18	)	)	PUNCT
cana-5925	104	19	1046	1046	NUM
cana-5925	104	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5925	104	21	fig	fig	NOUN
cana-5925	104	22	.	.	PUNCT
cana-5925	105	1	3.2	3.2	NUM
cana-5925	105	2	4.conclusion	4.conclusion	NUM
cana-5925	105	3	in	in	ADP
cana-5925	105	4	this	this	DET
cana-5925	105	5	paper	paper	NOUN
cana-5925	105	6	deals	deal	NOUN
cana-5925	105	7	with	with	ADP
cana-5925	105	8	topological	topological	ADJ
cana-5925	105	9	cordial	cordial	ADJ
cana-5925	105	10	graphs	graph	NOUN
cana-5925	105	11	.	.	PUNCT
cana-5925	106	1	the	the	DET
cana-5925	106	2	aim	aim	NOUN
cana-5925	106	3	of	of	ADP
cana-5925	106	4	this	this	DET
cana-5925	106	5	paper	paper	NOUN
cana-5925	106	6	is	be	AUX
cana-5925	106	7	to	to	PART
cana-5925	106	8	make	make	VERB
cana-5925	106	9	some	some	DET
cana-5925	106	10	progress	progress	NOUN
cana-5925	106	11	to	to	ADP
cana-5925	106	12	a	a	DET
cana-5925	106	13	better	well	ADJ
cana-5925	106	14	understanding	understanding	NOUN
cana-5925	106	15	of	of	ADP
cana-5925	106	16	topological	topological	ADJ
cana-5925	106	17	cordial	cordial	ADJ
cana-5925	106	18	labeling	labeling	NOUN
cana-5925	106	19	.	.	PUNCT
cana-5925	107	1	references	reference	NOUN
cana-5925	107	2	:	:	PUNCT
cana-5925	108	1	[	[	X
cana-5925	108	2	1	1	X
cana-5925	108	3	]	]	PUNCT
cana-5925	108	4	acharya	acharya	PROPN
cana-5925	108	5	b.d	b.d	PROPN
cana-5925	108	6	.	.	PROPN
cana-5925	108	7	,	,	PUNCT
cana-5925	108	8	set	set	VERB
cana-5925	108	9	indexers	indexer	NOUN
cana-5925	108	10	of	of	ADP
cana-5925	108	11	a	a	DET
cana-5925	108	12	graph	graph	NOUN
cana-5925	108	13	and	and	CCONJ
cana-5925	108	14	set	set	VERB
cana-5925	108	15	–	–	PUNCT
cana-5925	108	16	graceful	graceful	ADJ
cana-5925	108	17	graphs	graph	NOUN
cana-5925	108	18	,	,	PUNCT
cana-5925	108	19	bull	bull	NOUN
cana-5925	108	20	.	.	PUNCT
cana-5925	109	1	allahabad	allahabad	PROPN
cana-5925	109	2	math	math	PROPN
cana-5925	109	3	.	.	PUNCT
cana-5925	110	1	soc	soc	PROPN
cana-5925	110	2	.	.	PUNCT
cana-5925	110	3	,	,	PUNCT
cana-5925	110	4	16	16	NUM
cana-5925	110	5	(	(	PUNCT
cana-5925	110	6	2001	2001	NUM
cana-5925	110	7	)	)	PUNCT
cana-5925	110	8	,	,	PUNCT
cana-5925	110	9	1	1	NUM
cana-5925	110	10	-	-	SYM
cana-5925	110	11	23	23	NUM
cana-5925	110	12	[	[	X
cana-5925	110	13	2	2	NUM
cana-5925	110	14	]	]	PUNCT
cana-5925	110	15	acharya	acharya	PROPN
cana-5925	110	16	b.d	b.d	PROPN
cana-5925	110	17	,	,	PUNCT
cana-5925	110	18	germina	germina	PROPN
cana-5925	110	19	k.a	k.a	PROPN
cana-5925	110	20	,	,	PUNCT
cana-5925	110	21	princy	princy	PROPN
cana-5925	110	22	k.l	k.l	PROPN
cana-5925	110	23	and	and	CCONJ
cana-5925	110	24	rao	rao	PROPN
cana-5925	110	25	s.b	s.b	PROPN
cana-5925	110	26	.	.	PROPN
cana-5925	110	27	,	,	PUNCT
cana-5925	110	28	topologically	topologically	ADV
cana-5925	110	29	set	set	VERB
cana-5925	110	30	graceful	graceful	ADJ
cana-5925	110	31	graphs	graph	NOUN
cana-5925	110	32	,	,	PUNCT
cana-5925	110	33	paper	paper	NOUN
cana-5925	110	34	under	under	ADP
cana-5925	110	35	revision	revision	NOUN
cana-5925	110	36	.	.	PUNCT
cana-5925	111	1	[	[	X
cana-5925	111	2	3	3	X
cana-5925	111	3	]	]	PUNCT
cana-5925	111	4	acharya	acharya	PROPN
cana-5925	111	5	b.d	b.d	PROPN
cana-5925	111	6	.	.	PROPN
cana-5925	111	7	,	,	PUNCT
cana-5925	111	8	set	set	VERB
cana-5925	111	9	valuations	valuation	NOUN
cana-5925	111	10	and	and	CCONJ
cana-5925	111	11	their	their	PRON
cana-5925	111	12	applications	application	NOUN
cana-5925	111	13	,	,	PUNCT
cana-5925	111	14	mri	mri	NOUN
cana-5925	111	15	lecture	lecture	NOUN
cana-5925	111	16	note	note	NOUN
cana-5925	111	17	in	in	ADP
cana-5925	111	18	applied	applied	ADJ
cana-5925	111	19	mathematics	mathematic	NOUN
cana-5925	111	20	,	,	PUNCT
cana-5925	111	21	no.2	no.2	PROPN
cana-5925	111	22	,	,	PUNCT
cana-5925	111	23	mehta	mehta	PROPN
cana-5925	111	24	research	research	PROPN
cana-5925	111	25	institute	institute	PROPN
cana-5925	111	26	of	of	ADP
cana-5925	111	27	mathematics	mathematics	PROPN
cana-5925	111	28	and	and	CCONJ
cana-5925	111	29	mathematical	mathematical	ADJ
cana-5925	111	30	physics	physics	NOUN
cana-5925	111	31	,	,	PUNCT
cana-5925	111	32	1983	1983	NUM
cana-5925	111	33	.	.	PUNCT
cana-5925	112	1	[	[	X
cana-5925	112	2	4	4	NUM
cana-5925	112	3	]	]	X
cana-5925	112	4	germina	germina	PROPN
cana-5925	112	5	k.a	k.a	PROPN
cana-5925	112	6	,	,	PUNCT
cana-5925	112	7	bindhu	bindhu	NOUN
cana-5925	112	8	k.thomas	k.thomas	PROPN
cana-5925	112	9	.	.	PUNCT
cana-5925	112	10	,	,	PUNCT
cana-5925	112	11	on	on	ADP
cana-5925	112	12	bitopological	bitopological	ADJ
cana-5925	112	13	graphs	graph	NOUN
cana-5925	112	14	,	,	PUNCT
cana-5925	112	15	international	international	ADJ
cana-5925	112	16	journel	journel	NOUN
cana-5925	112	17	of	of	ADP
cana-5925	112	18	algorithm	algorithm	NOUN
cana-5925	112	19	,	,	PUNCT
cana-5925	112	20	computing	computing	NOUN
cana-5925	112	21	and	and	CCONJ
cana-5925	112	22	mathematics	mathematic	NOUN
cana-5925	112	23	,	,	PUNCT
cana-5925	112	24	vol.4	vol.4	PROPN
cana-5925	112	25	no.1	no.1	NUM
cana-5925	112	26	,	,	PUNCT
cana-5925	112	27	feb.2011	feb.2011	NUM
cana-5925	112	28	.	.	PUNCT
cana-5925	113	1	[	[	X
cana-5925	113	2	5	5	X
cana-5925	113	3	]	]	X
cana-5925	113	4	haraey	haraey	PROPN
cana-5925	113	5	f.	f.	PROPN
cana-5925	113	6	,	,	PUNCT
cana-5925	113	7	graph	graph	NOUN
cana-5925	113	8	theory	theory	NOUN
cana-5925	113	9	,	,	PUNCT
cana-5925	113	10	addison	addison	PROPN
cana-5925	113	11	wesley	wesley	PROPN
cana-5925	113	12	,	,	PUNCT
cana-5925	113	13	reading	read	VERB
cana-5925	113	14	massachusetts	massachusetts	PROPN
cana-5925	113	15	,	,	PUNCT
cana-5925	113	16	1969	1969	NUM
cana-5925	113	17	.	.	PUNCT
cana-5925	114	1	[	[	X
cana-5925	114	2	6	6	NUM
cana-5925	114	3	]	]	X
cana-5925	114	4	joseph	joseph	PROPN
cana-5925	114	5	a	a	DET
cana-5925	114	6	gallian	gallian	ADJ
cana-5925	114	7	2015	2015	NUM
cana-5925	114	8	,	,	PUNCT
cana-5925	114	9	‘	'	PUNCT
cana-5925	114	10	a	a	DET
cana-5925	114	11	dynamic	dynamic	ADJ
cana-5925	114	12	survey	survey	NOUN
cana-5925	114	13	of	of	ADP
cana-5925	114	14	graph	graph	NOUN
cana-5925	114	15	labeling	labeling	NOUN
cana-5925	114	16	’	'	PUNCT
cana-5925	114	17	,	,	PUNCT
cana-5925	114	18	the	the	DET
cana-5925	114	19	electronic	electronic	ADJ
cana-5925	114	20	journal	journal	NOUN
cana-5925	114	21	of	of	ADP
cana-5925	114	22	combinatorics	combinatoric	NOUN
cana-5925	114	23	.	.	PUNCT
cana-5925	115	1	[	[	X
cana-5925	115	2	7	7	X
cana-5925	115	3	]	]	X
cana-5925	115	4	rosa	rosa	PROPN
cana-5925	115	5	a.	a.	PROPN
cana-5925	115	6	,	,	PUNCT
cana-5925	115	7	on	on	ADP
cana-5925	115	8	certain	certain	ADJ
cana-5925	115	9	valuations	valuation	NOUN
cana-5925	115	10	of	of	ADP
cana-5925	115	11	the	the	DET
cana-5925	115	12	vertices	vertex	NOUN
cana-5925	115	13	of	of	ADP
cana-5925	115	14	a	a	DET
cana-5925	115	15	graph	graph	NOUN
cana-5925	115	16	,	,	PUNCT
cana-5925	115	17	gorden	gorden	PROPN
cana-5925	115	18	and	and	CCONJ
cana-5925	115	19	breach	breach	PROPN
cana-5925	115	20	,	,	PUNCT
cana-5925	115	21	new	new	PROPN
cana-5925	115	22	york	york	PROPN
cana-5925	115	23	and	and	CCONJ
cana-5925	115	24	dunod	dunod	PROPN
cana-5925	115	25	,	,	PUNCT
cana-5925	115	26	paris	paris	PROPN
cana-5925	115	27	,	,	PUNCT
cana-5925	115	28	1967	1967	NUM
cana-5925	115	29	,	,	PUNCT
cana-5925	115	30	proceedings	proceeding	NOUN
cana-5925	115	31	of	of	ADP
cana-5925	115	32	the	the	DET
cana-5925	115	33	international	international	ADJ
cana-5925	115	34	symposium	symposium	NOUN
cana-5925	115	35	in	in	ADP
cana-5925	115	36	rome	rome	PROPN
cana-5925	115	37	.	.	PUNCT
cana-5925	116	1	[	[	X
cana-5925	116	2	8	8	NUM
cana-5925	116	3	]	]	X
cana-5925	116	4	selestin	selestin	NOUN
cana-5925	116	5	lina	lina	PROPN
cana-5925	116	6	s	s	PROPN
cana-5925	116	7	,	,	PUNCT
cana-5925	116	8	asha	asha	PROPN
cana-5925	116	9	s	s	PROPN
cana-5925	116	10	,	,	PUNCT
cana-5925	116	11	‘	'	PUNCT
cana-5925	116	12	on	on	ADP
cana-5925	116	13	topological	topological	ADJ
cana-5925	116	14	cordial	cordial	ADJ
cana-5925	116	15	graphs	graph	NOUN
cana-5925	116	16	’	'	PUNCT
cana-5925	116	17	,	,	PUNCT
cana-5925	116	18	journal	journal	NOUN
cana-5925	116	19	of	of	ADP
cana-5925	116	20	science	science	NOUN
cana-5925	116	21	and	and	CCONJ
cana-5925	116	22	technology	technology	NOUN
cana-5925	116	23	,	,	PUNCT
cana-5925	116	24	vol.5	vol.5	PROPN
cana-5925	116	25	,	,	PUNCT
cana-5925	116	26	jan	jan	PROPN
cana-5925	116	27	-	-	PROPN
cana-5925	116	28	feb	feb	PROPN
cana-5925	116	29	2020	2020	NUM
cana-5925	116	30	,	,	PUNCT
cana-5925	116	31	25	25	NUM
cana-5925	116	32	-	-	SYM
cana-5925	116	33	28	28	NUM
cana-5925	116	34	.	.	PUNCT
cana-5925	117	1	[	[	X
cana-5925	117	2	9	9	NUM
cana-5925	117	3	]	]	PUNCT
cana-5925	117	4	selestin	selestin	NOUN
cana-5925	117	5	lina	lina	PROPN
cana-5925	117	6	s	s	PROPN
cana-5925	117	7	,	,	PUNCT
cana-5925	117	8	asha	asha	PROPN
cana-5925	117	9	s	s	PROPN
cana-5925	117	10	,	,	PUNCT
cana-5925	117	11	‘	'	PUNCT
cana-5925	117	12	topological	topological	ADJ
cana-5925	117	13	cordial	cordial	ADJ
cana-5925	117	14	labeling	labeling	NOUN
cana-5925	117	15	of	of	ADP
cana-5925	117	16	some	some	DET
cana-5925	117	17	graphs	graph	NOUN
cana-5925	117	18	’	'	PUNCT
cana-5925	117	19	,	,	PUNCT
cana-5925	117	20	malaya	malaya	PROPN
cana-5925	117	21	journal	journal	PROPN
cana-5925	117	22	of	of	ADP
cana-5925	117	23	matematik	matematik	PROPN
cana-5925	117	24	,	,	PUNCT
cana-5925	117	25	vol.9	vol.9	PROPN
cana-5925	117	26	,	,	PUNCT
cana-5925	117	27	no.1	no.1	NUM
cana-5925	117	28	,	,	PUNCT
cana-5925	117	29	861	861	NUM
cana-5925	117	30	-	-	PUNCT
cana-5925	117	31	863,2021	863,2021	NUM
cana-5925	117	32	.	.	PUNCT