id	sid	tid	token	lemma	pos
cana-4183	1	1	communications	communication	NOUN
cana-4183	1	2	on	on	ADP
cana-4183	1	3	applied	apply	VERB
cana-4183	1	4	nonlinear	nonlinear	ADJ
cana-4183	1	5	analysis	analysis	NOUN
cana-4183	1	6	issn	issn	NOUN
cana-4183	1	7	:	:	PUNCT
cana-4183	1	8	1074	1074	NUM
cana-4183	1	9	-	-	PUNCT
cana-4183	1	10	133x	133x	NUM
cana-4183	1	11	vol	vol	NOUN
cana-4183	1	12	32	32	NUM
cana-4183	1	13	no	no	NOUN
cana-4183	1	14	.	.	PUNCT
cana-4183	2	1	9s	9s	NUM
cana-4183	2	2	(	(	PUNCT
cana-4183	2	3	2025	2025	NUM
cana-4183	2	4	)	)	PUNCT
cana-4183	2	5	1504	1504	NUM
cana-4183	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4183	2	7	exploring	explore	VERB
cana-4183	2	8	stolarsky-3	stolarsky-3	PRON
cana-4183	2	9	mean	mean	ADJ
cana-4183	2	10	cordial	cordial	ADJ
cana-4183	2	11	labeling	labeling	NOUN
cana-4183	2	12	properties	property	NOUN
cana-4183	2	13	in	in	ADP
cana-4183	2	14	graph	graph	NOUN
cana-4183	2	15	classes	class	NOUN
cana-4183	2	16	with	with	ADP
cana-4183	2	17	a	a	DET
cana-4183	2	18	python	python	NOUN
cana-4183	2	19	module	module	NOUN
cana-4183	2	20	c.	c.	PROPN
cana-4183	2	21	muthulakshmi@sasikala1	muthulakshmi@sasikala1	PROPN
cana-4183	2	22	,	,	PUNCT
cana-4183	2	23	a.akil	a.akil	ADJ
cana-4183	2	24	nivetha2	nivetha2	NOUN
cana-4183	2	25	1associate	1associate	NUM
cana-4183	2	26	professor	professor	NOUN
cana-4183	2	27	,	,	PUNCT
cana-4183	2	28	department	department	NOUN
cana-4183	2	29	of	of	ADP
cana-4183	2	30	mathematics	mathematic	NOUN
cana-4183	2	31	,	,	PUNCT
cana-4183	2	32	sri	sri	PROPN
cana-4183	2	33	paramakalyani	paramakalyani	PROPN
cana-4183	2	34	,	,	PUNCT
cana-4183	2	35	college	college	NOUN
cana-4183	2	36	,	,	PUNCT
cana-4183	2	37	alwarkurichi-627412,affiliated	alwarkurichi-627412,affiliate	VERB
cana-4183	2	38	to	to	ADP
cana-4183	2	39	manonmaniam	manonmaniam	PROPN
cana-4183	2	40	sundaranar	sundaranar	PROPN
cana-4183	2	41	,	,	PUNCT
cana-4183	2	42	university	university	NOUN
cana-4183	2	43	,	,	PUNCT
cana-4183	2	44	tirunelveli	tirunelveli	ADJ
cana-4183	2	45	,	,	PUNCT
cana-4183	2	46	tamilnadu	tamilnadu	NOUN
cana-4183	2	47	,	,	PUNCT
cana-4183	2	48	kalasasispkc@gmail.com	kalasasispkc@gmail.com	X
cana-4183	3	1	2research	2research	NUM
cana-4183	3	2	scholar(reg	scholar(reg	NOUN
cana-4183	3	3	no:20211232092001),department	no:20211232092001),department	NUM
cana-4183	3	4	of	of	ADP
cana-4183	3	5	mathematics	mathematic	NOUN
cana-4183	3	6	,	,	PUNCT
cana-4183	3	7	sri	sri	PROPN
cana-4183	3	8	,	,	PUNCT
cana-4183	3	9	paramakalyani	paramakalyani	PROPN
cana-4183	3	10	college	college	PROPN
cana-4183	3	11	,	,	PUNCT
cana-4183	3	12	alwarkurichi627412,affiliated	alwarkurichi627412,affiliate	VERB
cana-4183	3	13	to	to	ADP
cana-4183	3	14	,	,	PUNCT
cana-4183	3	15	manonmaniam	manonmaniam	PROPN
cana-4183	3	16	sundaranar	sundaranar	PROPN
cana-4183	3	17	,	,	PUNCT
cana-4183	3	18	university	university	NOUN
cana-4183	3	19	,	,	PUNCT
cana-4183	3	20	tirunelveli	tirunelveli	ADJ
cana-4183	3	21	,	,	PUNCT
cana-4183	3	22	tamilnadu	tamilnadu	ADJ
cana-4183	3	23	,	,	PUNCT
cana-4183	3	24	siennanive2021@gmail.com	siennanive2021@gmail.com	X
cana-4183	4	1	article	article	PROPN
cana-4183	4	2	history	history	NOUN
cana-4183	4	3	:	:	PUNCT
cana-4183	4	4	received	receive	VERB
cana-4183	4	5	:	:	PUNCT
cana-4183	4	6	12	12	NUM
cana-4183	4	7	-	-	SYM
cana-4183	4	8	01	01	NUM
cana-4183	4	9	-	-	PUNCT
cana-4183	4	10	2025	2025	NUM
cana-4183	4	11	revised	revise	VERB
cana-4183	4	12	:	:	PUNCT
cana-4183	4	13	15	15	NUM
cana-4183	4	14	-	-	NUM
cana-4183	4	15	02	02	NUM
cana-4183	4	16	-	-	PUNCT
cana-4183	4	17	2025	2025	NUM
cana-4183	4	18	accepted	accept	VERB
cana-4183	4	19	:	:	PUNCT
cana-4183	4	20	01	01	NUM
cana-4183	4	21	-	-	SYM
cana-4183	4	22	03	03	NUM
cana-4183	4	23	-	-	PUNCT
cana-4183	4	24	2025	2025	NUM
cana-4183	4	25	abstract	abstract	NOUN
cana-4183	4	26	:	:	PUNCT
cana-4183	4	27	a	a	DET
cana-4183	4	28	graph	graph	NOUN
cana-4183	4	29	g=	g=	NOUN
cana-4183	4	30	(	(	PUNCT
cana-4183	4	31	v	v	NOUN
cana-4183	4	32	,	,	PUNCT
cana-4183	4	33	e	e	NOUN
cana-4183	4	34	)	)	PUNCT
cana-4183	4	35	,	,	PUNCT
cana-4183	4	36	where	where	SCONJ
cana-4183	4	37	v	v	NOUN
cana-4183	4	38	is	be	AUX
cana-4183	4	39	the	the	DET
cana-4183	4	40	set	set	NOUN
cana-4183	4	41	of	of	ADP
cana-4183	4	42	vertices	vertex	NOUN
cana-4183	4	43	and	and	CCONJ
cana-4183	4	44	e	e	NOUN
cana-4183	4	45	is	be	AUX
cana-4183	4	46	the	the	DET
cana-4183	4	47	set	set	NOUN
cana-4183	4	48	of	of	ADP
cana-4183	4	49	edges	edge	NOUN
cana-4183	4	50	,	,	PUNCT
cana-4183	4	51	with	with	ADP
cana-4183	4	52	p	p	NOUN
cana-4183	4	53	vertices	vertex	NOUN
cana-4183	4	54	and	and	CCONJ
cana-4183	4	55	q	q	NOUN
cana-4183	4	56	edges	edge	NOUN
cana-4183	4	57	.	.	PUNCT
cana-4183	5	1	a	a	DET
cana-4183	5	2	graph	graph	NOUN
cana-4183	5	3	g	g	NOUN
cana-4183	5	4	is	be	AUX
cana-4183	5	5	referred	refer	VERB
cana-4183	5	6	to	to	ADP
cana-4183	5	7	as	as	ADP
cana-4183	5	8	a	a	DET
cana-4183	5	9	stolarsky-3	stolarsky-3	NUM
cana-4183	5	10	mean	mean	ADJ
cana-4183	5	11	cordial	cordial	ADJ
cana-4183	5	12	graph	graph	NOUN
cana-4183	5	13	if	if	SCONJ
cana-4183	5	14	we	we	PRON
cana-4183	5	15	can	can	AUX
cana-4183	5	16	assign	assign	VERB
cana-4183	5	17	distinct	distinct	ADJ
cana-4183	5	18	labels	label	NOUN
cana-4183	5	19	to	to	ADP
cana-4183	5	20	each	each	DET
cana-4183	5	21	vertex	vertex	NOUN
cana-4183	5	22	x	x	PUNCT
cana-4183	5	23	∈	∈	NOUN
cana-4183	5	24	v	v	NOUN
cana-4183	5	25	from	from	ADP
cana-4183	5	26	the	the	DET
cana-4183	5	27	set	set	NOUN
cana-4183	5	28	{	{	PUNCT
cana-4183	5	29	0,1,2	0,1,2	NUM
cana-4183	5	30	}	}	PUNCT
cana-4183	5	31	,	,	PUNCT
cana-4183	5	32	denoted	denote	VERB
cana-4183	5	33	by	by	ADP
cana-4183	5	34	f(x	f(x	PROPN
cana-4183	5	35	)	)	PUNCT
cana-4183	5	36	,	,	PUNCT
cana-4183	5	37	and	and	CCONJ
cana-4183	5	38	distinct	distinct	ADJ
cana-4183	5	39	labels	label	NOUN
cana-4183	5	40	to	to	ADP
cana-4183	5	41	each	each	DET
cana-4183	5	42	edge	edge	NOUN
cana-4183	5	43	e	e	NOUN
cana-4183	5	44	=	=	PUNCT
cana-4183	5	45	uv	uv	NOUN
cana-4183	5	46	∈	∈	PROPN
cana-4183	5	47	e	e	NOUN
cana-4183	5	48	based	base	VERB
cana-4183	5	49	on	on	ADP
cana-4183	5	50	the	the	DET
cana-4183	5	51	values	value	NOUN
cana-4183	5	52	assigned	assign	VERB
cana-4183	5	53	to	to	ADP
cana-4183	5	54	the	the	DET
cana-4183	5	55	endpoints	endpoint	NOUN
cana-4183	5	56	u	u	NOUN
cana-4183	5	57	and	and	CCONJ
cana-4183	5	58	v.	v.	ADP
cana-4183	5	59	the	the	DET
cana-4183	5	60	label	label	NOUN
cana-4183	5	61	for	for	ADP
cana-4183	5	62	the	the	DET
cana-4183	5	63	edge	edge	NOUN
cana-4183	5	64	e	e	NOUN
cana-4183	5	65	=	=	NOUN
cana-4183	5	66	uv	uv	NOUN
cana-4183	5	67	is	be	AUX
cana-4183	5	68	calculated	calculate	VERB
cana-4183	5	69	using	use	VERB
cana-4183	5	70	one	one	NUM
cana-4183	5	71	of	of	ADP
cana-4183	5	72	the	the	DET
cana-4183	5	73	following	follow	VERB
cana-4183	5	74	stolarsky3	stolarsky3	NOUN
cana-4183	5	75	mean	mean	VERB
cana-4183	5	76	cordial	cordial	ADJ
cana-4183	5	77	formula	formula	NOUN
cana-4183	5	78	:	:	PUNCT
cana-4183	5	79	𝑓(𝑒	𝑓(𝑒	PROPN
cana-4183	5	80	=	=	SYM
cana-4183	5	81	𝑢𝑣	𝑢𝑣	NOUN
cana-4183	5	82	)	)	PUNCT
cana-4183	5	83	=	=	PUNCT
cana-4183	6	1	√	√	PROPN
cana-4183	6	2	𝑓(𝑢)2	𝑓(𝑢)2	NOUN
cana-4183	6	3	+	+	NOUN
cana-4183	6	4	f(u)f(v	f(u)f(v	NUM
cana-4183	6	5	)	)	PUNCT
cana-4183	6	6	+	+	CCONJ
cana-4183	6	7	𝑓(𝑣)2	𝑓(𝑣)2	ADP
cana-4183	6	8	3	3	NUM
cana-4183	7	1	the	the	DET
cana-4183	7	2	function	function	NOUN
cana-4183	7	3	f	f	PROPN
cana-4183	7	4	is	be	AUX
cana-4183	7	5	referred	refer	VERB
cana-4183	7	6	to	to	ADP
cana-4183	7	7	as	as	ADP
cana-4183	7	8	a	a	DET
cana-4183	7	9	stolarsky-3	stolarsky-3	NUM
cana-4183	7	10	mean	mean	ADJ
cana-4183	7	11	cordial	cordial	ADJ
cana-4183	7	12	labeling	labeling	NOUN
cana-4183	7	13	if	if	SCONJ
cana-4183	7	14	the	the	DET
cana-4183	7	15	conditions	condition	NOUN
cana-4183	7	16	|vf	|vf	PUNCT
cana-4183	7	17	(	(	PUNCT
cana-4183	7	18	i	i	NOUN
cana-4183	7	19	)	)	PUNCT
cana-4183	7	20	vf	vf	X
cana-4183	7	21	(	(	PUNCT
cana-4183	7	22	j)|	j)|	PROPN
cana-4183	7	23	1	1	NUM
cana-4183	7	24	and	and	CCONJ
cana-4183	7	25	|ef	|ef	NUM
cana-4183	7	26	(	(	PUNCT
cana-4183	7	27	i	i	NOUN
cana-4183	7	28	)	)	PUNCT
cana-4183	7	29	ef	ef	PROPN
cana-4183	7	30	(	(	PUNCT
cana-4183	7	31	j)|	j)|	PROPN
cana-4183	7	32	1	1	NUM
cana-4183	7	33	.	.	PUNCT
cana-4183	8	1	hold	hold	VERB
cana-4183	8	2	for	for	ADP
cana-4183	8	3	i	i	PRON
cana-4183	8	4	,	,	PUNCT
cana-4183	8	5	j	j	PROPN
cana-4183	8	6	ɛ{0,1,2	ɛ{0,1,2	ADJ
cana-4183	8	7	}	}	PUNCT
cana-4183	8	8	,	,	PUNCT
cana-4183	8	9	where	where	SCONJ
cana-4183	8	10	vf(x	vf(x	ADP
cana-4183	8	11	)	)	PUNCT
cana-4183	8	12	and	and	CCONJ
cana-4183	8	13	ef(x	ef(x	PUNCT
cana-4183	8	14	)	)	PUNCT
cana-4183	8	15	represent	represent	VERB
cana-4183	8	16	the	the	DET
cana-4183	8	17	number	number	NOUN
cana-4183	8	18	of	of	ADP
cana-4183	8	19	vertices	vertex	NOUN
cana-4183	8	20	and	and	CCONJ
cana-4183	8	21	edges	edge	NOUN
cana-4183	8	22	respectively	respectively	ADV
cana-4183	8	23	,	,	PUNCT
cana-4183	8	24	labeled	label	VERB
cana-4183	8	25	with	with	ADP
cana-4183	8	26	x	x	PUNCT
cana-4183	8	27	(	(	PUNCT
cana-4183	8	28	x=	x=	NOUN
cana-4183	8	29	0,1,2	0,1,2	NUM
cana-4183	8	30	)	)	PUNCT
cana-4183	8	31	.	.	PUNCT
cana-4183	9	1	a	a	DET
cana-4183	9	2	graph	graph	NOUN
cana-4183	9	3	that	that	PRON
cana-4183	9	4	admits	admit	VERB
cana-4183	9	5	such	such	DET
cana-4183	9	6	a	a	DET
cana-4183	9	7	labeling	labeling	NOUN
cana-4183	9	8	is	be	AUX
cana-4183	9	9	called	call	VERB
cana-4183	9	10	a	a	DET
cana-4183	9	11	mean	mean	ADJ
cana-4183	9	12	cordial	cordial	ADJ
cana-4183	9	13	graph	graph	NOUN
cana-4183	9	14	.	.	PUNCT
cana-4183	10	1	such	such	ADJ
cana-4183	10	2	that	that	SCONJ
cana-4183	10	3	the	the	DET
cana-4183	10	4	edge	edge	NOUN
cana-4183	10	5	labels	label	NOUN
cana-4183	10	6	are	be	AUX
cana-4183	10	7	derived	derive	VERB
cana-4183	10	8	from	from	ADP
cana-4183	10	9	the	the	DET
cana-4183	10	10	flooring	floor	VERB
cana-4183	10	11	function	function	NOUN
cana-4183	10	12	of	of	ADP
cana-4183	10	13	the	the	DET
cana-4183	10	14	stolarsky-3	stolarsky-3	PROPN
cana-4183	10	15	mean	mean	NOUN
cana-4183	10	16	of	of	ADP
cana-4183	10	17	the	the	DET
cana-4183	10	18	labels	label	NOUN
cana-4183	10	19	of	of	ADP
cana-4183	10	20	the	the	DET
cana-4183	10	21	two	two	NUM
cana-4183	10	22	end	end	NOUN
cana-4183	10	23	vertices	vertex	NOUN
cana-4183	10	24	of	of	ADP
cana-4183	10	25	each	each	DET
cana-4183	10	26	edge	edge	NOUN
cana-4183	10	27	.	.	PUNCT
cana-4183	11	1	in	in	ADP
cana-4183	11	2	this	this	DET
cana-4183	11	3	paper	paper	NOUN
cana-4183	11	4	,	,	PUNCT
cana-4183	11	5	we	we	PRON
cana-4183	11	6	have	have	AUX
cana-4183	11	7	created	create	VERB
cana-4183	11	8	python	python	NOUN
cana-4183	11	9	module	module	NOUN
cana-4183	11	10	to	to	ADP
cana-4183	11	11	analysis	analysis	NOUN
cana-4183	11	12	the	the	DET
cana-4183	11	13	stolarsky-3	stolarsky-3	PROPN
cana-4183	11	14	mean	mean	ADJ
cana-4183	11	15	cordial	cordial	ADJ
cana-4183	11	16	labeling	labeling	NOUN
cana-4183	11	17	properties	property	NOUN
cana-4183	11	18	of	of	ADP
cana-4183	11	19	various	various	ADJ
cana-4183	11	20	graph	graph	NOUN
cana-4183	11	21	classes	class	NOUN
cana-4183	11	22	,	,	PUNCT
cana-4183	11	23	including	include	VERB
cana-4183	11	24	path	path	NOUN
cana-4183	11	25	(	(	PUNCT
cana-4183	11	26	pn	pn	NOUN
cana-4183	11	27	)	)	PUNCT
cana-4183	11	28	,	,	PUNCT
cana-4183	11	29	cycle	cycle	NOUN
cana-4183	11	30	(	(	PUNCT
cana-4183	11	31	cn	cn	PROPN
cana-4183	11	32	)	)	PUNCT
cana-4183	11	33	,	,	PUNCT
cana-4183	11	34	wheel	wheel	NOUN
cana-4183	11	35	(	(	PUNCT
cana-4183	11	36	wn	wn	PROPN
cana-4183	11	37	)	)	PUNCT
cana-4183	11	38	,	,	PUNCT
cana-4183	11	39	star	star	NOUN
cana-4183	11	40	graph	graph	NOUN
cana-4183	11	41	(	(	PUNCT
cana-4183	11	42	k1,n	k1,n	PROPN
cana-4183	11	43	or	or	CCONJ
cana-4183	11	44	sn	sn	NOUN
cana-4183	11	45	)	)	PUNCT
cana-4183	11	46	&	&	CCONJ
cana-4183	11	47	wheel	wheel	NOUN
cana-4183	11	48	and	and	CCONJ
cana-4183	11	49	path	path	NOUN
cana-4183	11	50	graph	graph	NOUN
cana-4183	11	51	(	(	PUNCT
cana-4183	11	52	wnpm	wnpm	PROPN
cana-4183	11	53	)	)	PUNCT
cana-4183	11	54	.	.	PUNCT
cana-4183	12	1	keywords	keyword	NOUN
cana-4183	12	2	:	:	PUNCT
cana-4183	12	3	stolarsky-3	stolarsky-3	NOUN
cana-4183	12	4	mean	mean	VERB
cana-4183	12	5	,	,	PUNCT
cana-4183	12	6	mean	mean	NOUN
cana-4183	12	7	cordial	cordial	ADJ
cana-4183	12	8	,	,	PUNCT
cana-4183	12	9	path	path	NOUN
cana-4183	12	10	,	,	PUNCT
cana-4183	12	11	cycle	cycle	NOUN
cana-4183	12	12	,	,	PUNCT
cana-4183	12	13	wheel	wheel	NOUN
cana-4183	12	14	,	,	PUNCT
cana-4183	12	15	star	star	NOUN
cana-4183	12	16	graph	graph	NOUN
cana-4183	12	17	1	1	NUM
cana-4183	12	18	.	.	PUNCT
cana-4183	13	1	introduction	introduction	NOUN
cana-4183	13	2	one	one	NUM
cana-4183	13	3	important	important	ADJ
cana-4183	13	4	topic	topic	NOUN
cana-4183	13	5	of	of	ADP
cana-4183	13	6	research	research	NOUN
cana-4183	13	7	in	in	ADP
cana-4183	13	8	graph	graph	NOUN
cana-4183	13	9	theory	theory	NOUN
cana-4183	13	10	is	be	AUX
cana-4183	13	11	graph	graph	NOUN
cana-4183	13	12	labeling	labeling	NOUN
cana-4183	13	13	,	,	PUNCT
cana-4183	13	14	which	which	PRON
cana-4183	13	15	is	be	AUX
cana-4183	13	16	the	the	DET
cana-4183	13	17	process	process	NOUN
cana-4183	13	18	of	of	ADP
cana-4183	13	19	assigning	assign	VERB
cana-4183	13	20	labels	label	NOUN
cana-4183	13	21	typically	typically	ADV
cana-4183	13	22	numbers	number	VERB
cana-4183	13	23	to	to	ADP
cana-4183	13	24	a	a	DET
cana-4183	13	25	graph	graph	NOUN
cana-4183	13	26	's	's	PART
cana-4183	13	27	vertices	vertex	NOUN
cana-4183	13	28	,	,	PUNCT
cana-4183	13	29	edges	edge	NOUN
cana-4183	13	30	,	,	PUNCT
cana-4183	13	31	or	or	CCONJ
cana-4183	13	32	both	both	PRON
cana-4183	13	33	in	in	ADP
cana-4183	13	34	accordance	accordance	NOUN
cana-4183	13	35	with	with	ADP
cana-4183	13	36	predetermined	predetermine	VERB
cana-4183	13	37	guidelines	guideline	NOUN
cana-4183	13	38	[	[	X
cana-4183	13	39	1	1	NUM
cana-4183	13	40	]	]	PUNCT
cana-4183	13	41	.	.	PUNCT
cana-4183	14	1	over	over	ADP
cana-4183	14	2	the	the	DET
cana-4183	14	3	years	year	NOUN
cana-4183	14	4	,	,	PUNCT
cana-4183	14	5	various	various	ADJ
cana-4183	14	6	types	type	NOUN
cana-4183	14	7	of	of	ADP
cana-4183	14	8	labeling	labeling	NOUN
cana-4183	14	9	techniques	technique	NOUN
cana-4183	14	10	have	have	AUX
cana-4183	14	11	been	be	AUX
cana-4183	14	12	developed	develop	VERB
cana-4183	14	13	,	,	PUNCT
cana-4183	14	14	each	each	PRON
cana-4183	14	15	with	with	ADP
cana-4183	14	16	distinct	distinct	ADJ
cana-4183	14	17	characteristics	characteristic	NOUN
cana-4183	14	18	and	and	CCONJ
cana-4183	14	19	applications	application	NOUN
cana-4183	14	20	.	.	PUNCT
cana-4183	15	1	among	among	ADP
cana-4183	15	2	these	these	PRON
cana-4183	15	3	,	,	PUNCT
cana-4183	15	4	cordial	cordial	ADJ
cana-4183	15	5	labeling	labeling	NOUN
cana-4183	15	6	has	have	AUX
cana-4183	15	7	garnered	garner	VERB
cana-4183	15	8	particular	particular	ADJ
cana-4183	15	9	interest	interest	NOUN
cana-4183	15	10	due	due	ADP
cana-4183	15	11	to	to	ADP
cana-4183	15	12	its	its	PRON
cana-4183	15	13	relatively	relatively	ADV
cana-4183	15	14	relaxed	relaxed	ADJ
cana-4183	15	15	conditions	condition	NOUN
cana-4183	15	16	compared	compare	VERB
cana-4183	15	17	to	to	ADP
cana-4183	15	18	more	more	ADV
cana-4183	15	19	restrictive	restrictive	ADJ
cana-4183	15	20	forms	form	NOUN
cana-4183	15	21	such	such	ADJ
cana-4183	15	22	as	as	ADP
cana-4183	15	23	graceful	graceful	ADJ
cana-4183	15	24	or	or	CCONJ
cana-4183	15	25	harmonious	harmonious	ADJ
cana-4183	15	26	labeling	labeling	NOUN
cana-4183	15	27	[	[	X
cana-4183	15	28	2	2	NUM
cana-4183	15	29	]	]	PUNCT
cana-4183	15	30	.	.	PUNCT
cana-4183	16	1	a	a	DET
cana-4183	16	2	function	function	NOUN
cana-4183	16	3	assigns	assigns	NOUN
cana-4183	16	4	labels	label	NOUN
cana-4183	16	5	to	to	ADP
cana-4183	16	6	the	the	DET
cana-4183	16	7	vertices	vertex	NOUN
cana-4183	16	8	and	and	CCONJ
cana-4183	16	9	edges	edge	NOUN
cana-4183	16	10	of	of	ADP
cana-4183	16	11	a	a	DET
cana-4183	16	12	graph	graph	NOUN
cana-4183	16	13	such	such	ADJ
cana-4183	16	14	that	that	SCONJ
cana-4183	16	15	the	the	DET
cana-4183	16	16	number	number	NOUN
cana-4183	16	17	of	of	ADP
cana-4183	16	18	vertices	vertex	NOUN
cana-4183	16	19	(	(	PUNCT
cana-4183	16	20	or	or	CCONJ
cana-4183	16	21	edges	edge	NOUN
cana-4183	16	22	)	)	PUNCT
cana-4183	16	23	labeled	label	VERB
cana-4183	16	24	with	with	ADP
cana-4183	16	25	0	0	NUM
cana-4183	16	26	or	or	CCONJ
cana-4183	16	27	1	1	NUM
cana-4183	16	28	differs	differ	NOUN
cana-4183	16	29	by	by	ADP
cana-4183	16	30	at	at	ADP
cana-4183	16	31	most	most	ADV
cana-4183	16	32	one	one	NUM
cana-4183	16	33	[	[	X
cana-4183	16	34	3	3	NUM
cana-4183	16	35	]	]	PUNCT
cana-4183	16	36	.	.	PUNCT
cana-4183	17	1	this	this	DET
cana-4183	17	2	type	type	NOUN
cana-4183	17	3	of	of	ADP
cana-4183	17	4	labeling	labeling	NOUN
cana-4183	17	5	has	have	AUX
cana-4183	17	6	been	be	AUX
cana-4183	17	7	widely	widely	ADV
cana-4183	17	8	studied	study	VERB
cana-4183	17	9	for	for	ADP
cana-4183	17	10	its	its	PRON
cana-4183	17	11	simplicity	simplicity	NOUN
cana-4183	17	12	and	and	CCONJ
cana-4183	17	13	applicability	applicability	NOUN
cana-4183	17	14	to	to	ADP
cana-4183	17	15	different	different	ADJ
cana-4183	17	16	types	type	NOUN
cana-4183	17	17	of	of	ADP
cana-4183	17	18	graphs	graph	NOUN
cana-4183	17	19	.	.	PUNCT
cana-4183	18	1	the	the	DET
cana-4183	18	2	researcher	researcher	NOUN
cana-4183	18	3	explored	explore	VERB
cana-4183	18	4	how	how	SCONJ
cana-4183	18	5	assigning	assigning	ADJ
cana-4183	18	6	labels	label	NOUN
cana-4183	18	7	based	base	VERB
cana-4183	18	8	on	on	ADP
cana-4183	18	9	the	the	DET
cana-4183	18	10	arithmetic	arithmetic	ADJ
cana-4183	18	11	mean	mean	NOUN
cana-4183	18	12	of	of	ADP
cana-4183	18	13	vertices	vertex	NOUN
cana-4183	18	14	can	can	AUX
cana-4183	18	15	lead	lead	VERB
cana-4183	18	16	to	to	ADP
cana-4183	18	17	communications	communication	NOUN
cana-4183	18	18	on	on	ADP
cana-4183	18	19	applied	apply	VERB
cana-4183	18	20	nonlinear	nonlinear	ADJ
cana-4183	18	21	analysis	analysis	NOUN
cana-4183	18	22	issn	issn	NOUN
cana-4183	18	23	:	:	PUNCT
cana-4183	18	24	1074	1074	NUM
cana-4183	18	25	-	-	PUNCT
cana-4183	18	26	133x	133x	NUM
cana-4183	18	27	vol	vol	NOUN
cana-4183	18	28	32	32	NUM
cana-4183	18	29	no	no	NOUN
cana-4183	18	30	.	.	PUNCT
cana-4183	19	1	9s	9s	NUM
cana-4183	19	2	(	(	PUNCT
cana-4183	19	3	2025	2025	NUM
cana-4183	19	4	)	)	PUNCT
cana-4183	19	5	1505	1505	NUM
cana-4183	19	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4183	19	7	distinct	distinct	ADJ
cana-4183	19	8	edge	edge	NOUN
cana-4183	19	9	labels	label	NOUN
cana-4183	19	10	[	[	X
cana-4183	19	11	4	4	NUM
cana-4183	19	12	,	,	PUNCT
cana-4183	19	13	5	5	NUM
cana-4183	19	14	]	]	PUNCT
cana-4183	19	15	.	.	PUNCT
cana-4183	20	1	this	this	DET
cana-4183	20	2	work	work	NOUN
cana-4183	20	3	laid	lay	VERB
cana-4183	20	4	the	the	DET
cana-4183	20	5	groundwork	groundwork	NOUN
cana-4183	20	6	for	for	ADP
cana-4183	20	7	further	further	ADJ
cana-4183	20	8	investigations	investigation	NOUN
cana-4183	20	9	into	into	ADP
cana-4183	20	10	meanbased	meanbase	VERB
cana-4183	20	11	graph	graph	NOUN
cana-4183	20	12	labeling	labeling	NOUN
cana-4183	20	13	.	.	PUNCT
cana-4183	21	1	harmonic	harmonic	ADJ
cana-4183	21	2	mean	mean	NOUN
cana-4183	21	3	of	of	ADP
cana-4183	21	4	vertex	vertex	NOUN
cana-4183	21	5	labels	label	NOUN
cana-4183	21	6	to	to	PART
cana-4183	21	7	assign	assign	VERB
cana-4183	21	8	edge	edge	NOUN
cana-4183	21	9	labels	label	NOUN
cana-4183	21	10	,	,	PUNCT
cana-4183	21	11	providing	provide	VERB
cana-4183	21	12	a	a	DET
cana-4183	21	13	different	different	ADJ
cana-4183	21	14	perspective	perspective	NOUN
cana-4183	21	15	on	on	ADP
cana-4183	21	16	mean	mean	NOUN
cana-4183	21	17	-	-	PUNCT
cana-4183	21	18	based	base	VERB
cana-4183	21	19	labeling	labeling	NOUN
cana-4183	21	20	techniques	technique	NOUN
cana-4183	21	21	[	[	X
cana-4183	21	22	6	6	NUM
cana-4183	21	23	,	,	PUNCT
cana-4183	21	24	7	7	NUM
cana-4183	21	25	]	]	PUNCT
cana-4183	21	26	.	.	PUNCT
cana-4183	22	1	this	this	DET
cana-4183	22	2	research	research	NOUN
cana-4183	22	3	expanded	expand	VERB
cana-4183	22	4	the	the	DET
cana-4183	22	5	application	application	NOUN
cana-4183	22	6	of	of	ADP
cana-4183	22	7	mean	mean	NOUN
cana-4183	22	8	-	-	PUNCT
cana-4183	22	9	based	base	VERB
cana-4183	22	10	labeling	labeling	NOUN
cana-4183	22	11	in	in	ADP
cana-4183	22	12	various	various	ADJ
cana-4183	22	13	types	type	NOUN
cana-4183	22	14	of	of	ADP
cana-4183	22	15	graphs	graph	NOUN
cana-4183	22	16	,	,	PUNCT
cana-4183	22	17	contributing	contribute	VERB
cana-4183	22	18	to	to	ADP
cana-4183	22	19	the	the	DET
cana-4183	22	20	development	development	NOUN
cana-4183	22	21	of	of	ADP
cana-4183	22	22	new	new	ADJ
cana-4183	22	23	labeling	labeling	NOUN
cana-4183	22	24	methodologies	methodology	NOUN
cana-4183	22	25	.	.	PUNCT
cana-4183	23	1	stolarsky	stolarsky	PROPN
cana-4183	23	2	mean	mean	VERB
cana-4183	23	3	labeling	labeling	NOUN
cana-4183	23	4	technique	technique	NOUN
cana-4183	23	5	[	[	X
cana-4183	23	6	8	8	NUM
cana-4183	23	7	-	-	SYM
cana-4183	23	8	11	11	NUM
cana-4183	23	9	]	]	PUNCT
cana-4183	23	10	utilizes	utilize	VERB
cana-4183	23	11	a	a	DET
cana-4183	23	12	mean	mean	ADJ
cana-4183	23	13	calculation	calculation	NOUN
cana-4183	23	14	based	base	VERB
cana-4183	23	15	on	on	ADP
cana-4183	23	16	the	the	DET
cana-4183	23	17	stolarsky	stolarsky	NOUN
cana-4183	23	18	mean	mean	NOUN
cana-4183	23	19	,	,	PUNCT
cana-4183	23	20	which	which	PRON
cana-4183	23	21	generalizes	generalize	VERB
cana-4183	23	22	several	several	ADJ
cana-4183	23	23	other	other	ADJ
cana-4183	23	24	mean	mean	ADJ
cana-4183	23	25	functions	function	NOUN
cana-4183	23	26	.	.	PUNCT
cana-4183	24	1	although	although	SCONJ
cana-4183	24	2	specific	specific	ADJ
cana-4183	24	3	literature	literature	NOUN
cana-4183	24	4	on	on	ADP
cana-4183	24	5	stolarsky	stolarsky	ADJ
cana-4183	24	6	mean	mean	VERB
cana-4183	24	7	labeling	labeling	NOUN
cana-4183	24	8	is	be	AUX
cana-4183	24	9	limited	limited	ADJ
cana-4183	24	10	,	,	PUNCT
cana-4183	24	11	it	it	PRON
cana-4183	24	12	builds	build	VERB
cana-4183	24	13	upon	upon	SCONJ
cana-4183	24	14	the	the	DET
cana-4183	24	15	earlier	early	ADJ
cana-4183	24	16	works	work	NOUN
cana-4183	24	17	on	on	ADP
cana-4183	24	18	mean	mean	VERB
cana-4183	24	19	and	and	CCONJ
cana-4183	24	20	harmonic	harmonic	ADJ
cana-4183	24	21	mean	mean	ADJ
cana-4183	24	22	labeling	labeling	NOUN
cana-4183	24	23	,	,	PUNCT
cana-4183	24	24	offering	offer	VERB
cana-4183	24	25	a	a	DET
cana-4183	24	26	novel	novel	ADJ
cana-4183	24	27	approach	approach	NOUN
cana-4183	24	28	to	to	AUX
cana-4183	24	29	graph	graph	VERB
cana-4183	24	30	labeling	labeling	NOUN
cana-4183	24	31	.	.	PUNCT
cana-4183	25	1	in	in	ADP
cana-4183	25	2	-	-	PUNCT
cana-4183	25	3	depth	depth	NOUN
cana-4183	25	4	explorations	exploration	NOUN
cana-4183	25	5	of	of	ADP
cana-4183	25	6	stolarsky	stolarsky	ADJ
cana-4183	25	7	mean	mean	VERB
cana-4183	25	8	in	in	ADP
cana-4183	25	9	graph	graph	NOUN
cana-4183	25	10	labeling	labeling	NOUN
cana-4183	25	11	and	and	CCONJ
cana-4183	25	12	its	its	PRON
cana-4183	25	13	potential	potential	ADJ
cana-4183	25	14	applications	application	NOUN
cana-4183	25	15	,	,	PUNCT
cana-4183	25	16	particularly	particularly	ADV
cana-4183	25	17	in	in	ADP
cana-4183	25	18	cryptography	cryptography	NOUN
cana-4183	25	19	,	,	PUNCT
cana-4183	25	20	and	and	CCONJ
cana-4183	25	21	network	network	NOUN
cana-4183	25	22	analysis	analysis	NOUN
cana-4183	25	23	applications	application	NOUN
cana-4183	25	24	.	.	PUNCT
cana-4183	26	1	stolarsky-3	stolarsky-3	PRON
cana-4183	26	2	mean	mean	ADJ
cana-4183	26	3	labeling	labeling	NOUN
cana-4183	26	4	remains	remain	VERB
cana-4183	26	5	a	a	DET
cana-4183	26	6	crucial	crucial	ADJ
cana-4183	26	7	area	area	NOUN
cana-4183	26	8	of	of	ADP
cana-4183	26	9	study	study	NOUN
cana-4183	26	10	within	within	ADP
cana-4183	26	11	graph	graph	NOUN
cana-4183	26	12	theory	theory	NOUN
cana-4183	26	13	,	,	PUNCT
cana-4183	26	14	focusing	focus	VERB
cana-4183	26	15	on	on	ADP
cana-4183	26	16	assigning	assign	VERB
cana-4183	26	17	labels	label	NOUN
cana-4183	26	18	to	to	PART
cana-4183	26	19	vertices	vertex	NOUN
cana-4183	26	20	and	and	CCONJ
cana-4183	26	21	edges	edge	NOUN
cana-4183	26	22	in	in	ADP
cana-4183	26	23	a	a	DET
cana-4183	26	24	way	way	NOUN
cana-4183	26	25	that	that	PRON
cana-4183	26	26	satisfies	satisfy	VERB
cana-4183	26	27	specific	specific	ADJ
cana-4183	26	28	conditions	condition	NOUN
cana-4183	26	29	[	[	X
cana-4183	26	30	12	12	NUM
cana-4183	26	31	]	]	PUNCT
cana-4183	26	32	.	.	PUNCT
cana-4183	27	1	till	till	SCONJ
cana-4183	27	2	now	now	ADV
cana-4183	27	3	no	no	DET
cana-4183	27	4	one	one	NOUN
cana-4183	27	5	is	be	AUX
cana-4183	27	6	analyzing	analyze	VERB
cana-4183	27	7	stolarsky-3	stolarsky-3	PRON
cana-4183	27	8	mean	mean	VERB
cana-4183	27	9	cordial	cordial	ADJ
cana-4183	27	10	labeling	labeling	NOUN
cana-4183	27	11	techniques	technique	NOUN
cana-4183	27	12	.	.	PUNCT
cana-4183	28	1	stolarsky-3	stolarsky-3	PRON
cana-4183	28	2	mean	mean	VERB
cana-4183	28	3	cordial	cordial	ADJ
cana-4183	28	4	labeling	labeling	NOUN
cana-4183	28	5	is	be	AUX
cana-4183	28	6	a	a	DET
cana-4183	28	7	relatively	relatively	ADV
cana-4183	28	8	recent	recent	ADJ
cana-4183	28	9	addition	addition	NOUN
cana-4183	28	10	to	to	ADP
cana-4183	28	11	this	this	DET
cana-4183	28	12	field	field	NOUN
cana-4183	28	13	,	,	PUNCT
cana-4183	28	14	expanding	expand	VERB
cana-4183	28	15	on	on	ADP
cana-4183	28	16	concepts	concept	NOUN
cana-4183	28	17	introduced	introduce	VERB
cana-4183	28	18	by	by	ADP
cana-4183	28	19	earlier	early	ADJ
cana-4183	28	20	labeling	labeling	NOUN
cana-4183	28	21	techniques	technique	NOUN
cana-4183	28	22	.	.	PUNCT
cana-4183	29	1	this	this	DET
cana-4183	29	2	research	research	NOUN
cana-4183	29	3	introduces	introduce	VERB
cana-4183	29	4	a	a	DET
cana-4183	29	5	new	new	ADJ
cana-4183	29	6	approach	approach	NOUN
cana-4183	29	7	by	by	ADP
cana-4183	29	8	pinpointing	pinpoint	VERB
cana-4183	29	9	vertex	vertex	NOUN
cana-4183	29	10	combinations	combination	NOUN
cana-4183	29	11	and	and	CCONJ
cana-4183	29	12	formulating	formulate	VERB
cana-4183	29	13	mathematical	mathematical	ADJ
cana-4183	29	14	models	model	NOUN
cana-4183	29	15	that	that	PRON
cana-4183	29	16	describe	describe	VERB
cana-4183	29	17	stolarsky-3	stolarsky-3	PRON
cana-4183	29	18	mean	mean	VERB
cana-4183	29	19	cordial	cordial	ADJ
cana-4183	29	20	labeling	labeling	NOUN
cana-4183	29	21	.	.	PUNCT
cana-4183	30	1	research	research	NOUN
cana-4183	30	2	on	on	ADP
cana-4183	30	3	stolarsky-3	stolarsky-3	PROPN
cana-4183	30	4	mean	mean	ADJ
cana-4183	30	5	labeling	labeling	NOUN
cana-4183	30	6	is	be	AUX
cana-4183	30	7	likely	likely	ADJ
cana-4183	30	8	to	to	PART
cana-4183	30	9	have	have	VERB
cana-4183	30	10	implications	implication	NOUN
cana-4183	30	11	in	in	ADP
cana-4183	30	12	areas	area	NOUN
cana-4183	30	13	where	where	SCONJ
cana-4183	30	14	graph	graph	NOUN
cana-4183	30	15	labeling	labeling	NOUN
cana-4183	30	16	is	be	AUX
cana-4183	30	17	crucial	crucial	ADJ
cana-4183	30	18	,	,	PUNCT
cana-4183	30	19	such	such	ADJ
cana-4183	30	20	as	as	ADP
cana-4183	30	21	network	network	NOUN
cana-4183	30	22	design	design	NOUN
cana-4183	30	23	and	and	CCONJ
cana-4183	30	24	communication	communication	NOUN
cana-4183	30	25	theory	theory	NOUN
cana-4183	30	26	.	.	PUNCT
cana-4183	31	1	2	2	X
cana-4183	31	2	.	.	X
cana-4183	31	3	methods	method	NOUN
cana-4183	31	4	:	:	PUNCT
cana-4183	31	5	we	we	PRON
cana-4183	31	6	have	have	AUX
cana-4183	31	7	developed	develop	VERB
cana-4183	31	8	the	the	DET
cana-4183	31	9	python	python	NOUN
cana-4183	31	10	module	module	NOUN
cana-4183	31	11	to	to	PART
cana-4183	31	12	find	find	VERB
cana-4183	31	13	the	the	DET
cana-4183	31	14	graph	graph	NOUN
cana-4183	31	15	labeling	labeling	NOUN
cana-4183	31	16	properties	property	NOUN
cana-4183	31	17	.	.	PUNCT
cana-4183	32	1	2.1	2.1	NUM
cana-4183	32	2	.	.	PUNCT
cana-4183	33	1	python	python	NOUN
cana-4183	33	2	module	module	NOUN
cana-4183	33	3	import	import	NOUN
cana-4183	33	4	itertools	itertools	PROPN
cana-4183	33	5	import	import	PROPN
cana-4183	33	6	math	math	PROPN
cana-4183	33	7	def	def	PROPN
cana-4183	33	8	stolarsky_3_mean(u	stolarsky_3_mean(u	PROPN
cana-4183	33	9	,	,	PUNCT
cana-4183	33	10	v	v	NOUN
cana-4183	33	11	):	):	PUNCT
cana-4183	33	12	return	return	NOUN
cana-4183	33	13	math.floor(math.sqrt((u**2	math.floor(math.sqrt((u**2	PROPN
cana-4183	33	14	+	+	CCONJ
cana-4183	33	15	u*v	u*v	PROPN
cana-4183	33	16	+	+	CCONJ
cana-4183	33	17	v**2	v**2	NOUN
cana-4183	33	18	)	)	PUNCT
cana-4183	33	19	/	/	SYM
cana-4183	33	20	3	3	NUM
cana-4183	33	21	)	)	PUNCT
cana-4183	33	22	)	)	PUNCT
cana-4183	33	23	#	#	NOUN
cana-4183	33	24	function	function	NOUN
cana-4183	33	25	to	to	PART
cana-4183	33	26	check	check	VERB
cana-4183	33	27	the	the	DET
cana-4183	33	28	conditions	condition	NOUN
cana-4183	33	29	for	for	ADP
cana-4183	33	30	valid	valid	ADJ
cana-4183	33	31	stolarsky-3	stolarsky-3	NUM
cana-4183	33	32	mean	mean	ADJ
cana-4183	33	33	cordial	cordial	ADJ
cana-4183	33	34	labeling	labeling	NOUN
cana-4183	33	35	def	def	PROPN
cana-4183	33	36	is_valid_labeling(s1	is_valid_labeling(s1	PROPN
cana-4183	33	37	,	,	PUNCT
cana-4183	33	38	s2	s2	PROPN
cana-4183	33	39	,	,	PUNCT
cana-4183	33	40	s3	s3	PROPN
cana-4183	33	41	,	,	PUNCT
cana-4183	33	42	s4	s4	PROPN
cana-4183	33	43	,	,	PUNCT
cana-4183	33	44	s5	s5	PROPN
cana-4183	33	45	,	,	PUNCT
cana-4183	33	46	s6	s6	PROPN
cana-4183	33	47	,	,	PUNCT
cana-4183	33	48	m1	m1	PROPN
cana-4183	33	49	,	,	PUNCT
cana-4183	33	50	m2	m2	PROPN
cana-4183	33	51	,	,	PUNCT
cana-4183	33	52	m3	m3	PROPN
cana-4183	33	53	,	,	PUNCT
cana-4183	33	54	m4	m4	PROPN
cana-4183	33	55	):	):	PUNCT
cana-4183	33	56	return	return	NOUN
cana-4183	33	57	(	(	PUNCT
cana-4183	33	58	abs(s1	abs(s1	PROPN
cana-4183	33	59	s2	s2	PROPN
cana-4183	33	60	)	)	PUNCT
cana-4183	34	1	<	<	X
cana-4183	34	2	=	=	SYM
cana-4183	34	3	1	1	NUM
cana-4183	34	4	and	and	CCONJ
cana-4183	34	5	abs(s2	abs(s2	PROPN
cana-4183	34	6	s3	s3	PROPN
cana-4183	34	7	)	)	PUNCT
cana-4183	34	8	<	<	X
cana-4183	34	9	=	=	SYM
cana-4183	34	10	1	1	NUM
cana-4183	34	11	and	and	CCONJ
cana-4183	34	12	abs(s1	abs(s1	PROPN
cana-4183	34	13	s3	s3	PROPN
cana-4183	34	14	)	)	PUNCT
cana-4183	34	15	<	<	X
cana-4183	34	16	=	=	SYM
cana-4183	34	17	1	1	NUM
cana-4183	34	18	and	and	CCONJ
cana-4183	34	19	abs(s4	abs(s4	PROPN
cana-4183	34	20	s5	s5	PROPN
cana-4183	34	21	)	)	PUNCT
cana-4183	35	1	<	<	X
cana-4183	35	2	=	=	SYM
cana-4183	35	3	1	1	NUM
cana-4183	35	4	and	and	CCONJ
cana-4183	35	5	abs(s5	abs(s5	PROPN
cana-4183	35	6	s6	s6	PROPN
cana-4183	35	7	)	)	PUNCT
cana-4183	35	8	<	<	X
cana-4183	35	9	=	=	SYM
cana-4183	35	10	1	1	NUM
cana-4183	35	11	and	and	CCONJ
cana-4183	35	12	abs(s4	abs(s4	PROPN
cana-4183	35	13	s6	s6	PROPN
cana-4183	35	14	)	)	PUNCT
cana-4183	35	15	<	<	X
cana-4183	35	16	=	=	SYM
cana-4183	35	17	1	1	NUM
cana-4183	35	18	and	and	CCONJ
cana-4183	35	19	s1	s1	PROPN
cana-4183	35	20	+	+	CCONJ
cana-4183	35	21	s2	s2	NOUN
cana-4183	35	22	+	+	CCONJ
cana-4183	35	23	s3	s3	PROPN
cana-4183	35	24	=	=	PROPN
cana-4183	35	25	=	=	SYM
cana-4183	35	26	m1	m1	PROPN
cana-4183	35	27	and	and	CCONJ
cana-4183	35	28	s4	s4	PROPN
cana-4183	35	29	+	+	CCONJ
cana-4183	35	30	s5	s5	PROPN
cana-4183	35	31	+	+	CCONJ
cana-4183	35	32	s6	s6	PROPN
cana-4183	35	33	=	=	SYM
cana-4183	35	34	=	=	SYM
cana-4183	35	35	m4	m4	PROPN
cana-4183	35	36	)	)	PUNCT
cana-4183	35	37	#	#	NOUN
cana-4183	35	38	main	main	ADJ
cana-4183	35	39	function	function	NOUN
cana-4183	35	40	to	to	PART
cana-4183	35	41	generate	generate	VERB
cana-4183	35	42	and	and	CCONJ
cana-4183	35	43	validate	validate	VERB
cana-4183	35	44	stolarsky-3	stolarsky-3	NUM
cana-4183	35	45	mean	mean	ADJ
cana-4183	35	46	cordial	cordial	ADJ
cana-4183	35	47	labeling	labeling	NOUN
cana-4183	35	48	def	def	ADJ
cana-4183	35	49	stolarsky_3_mean_cordial_labeling(n	stolarsky_3_mean_cordial_labeling(n	NOUN
cana-4183	35	50	,	,	PUNCT
cana-4183	35	51	m1	m1	PROPN
cana-4183	35	52	,	,	PUNCT
cana-4183	35	53	m2	m2	PROPN
cana-4183	35	54	,	,	PUNCT
cana-4183	35	55	m3	m3	PROPN
cana-4183	35	56	,	,	PUNCT
cana-4183	35	57	m4	m4	PROPN
cana-4183	35	58	):	):	PUNCT
cana-4183	35	59	combinations	combination	NOUN
cana-4183	35	60	=	=	SYM
cana-4183	35	61	itertools.product([0	itertools.product([0	NOUN
cana-4183	35	62	,	,	PUNCT
cana-4183	35	63	1	1	NUM
cana-4183	35	64	,	,	PUNCT
cana-4183	35	65	2	2	NUM
cana-4183	35	66	]	]	PUNCT
cana-4183	35	67	,	,	PUNCT
cana-4183	35	68	repeat	repeat	NOUN
cana-4183	35	69	=	=	SYM
cana-4183	35	70	n	n	CCONJ
cana-4183	35	71	)	)	PUNCT
cana-4183	35	72	communications	communication	NOUN
cana-4183	35	73	on	on	ADP
cana-4183	35	74	applied	apply	VERB
cana-4183	35	75	nonlinear	nonlinear	ADJ
cana-4183	35	76	analysis	analysis	NOUN
cana-4183	35	77	issn	issn	NOUN
cana-4183	35	78	:	:	PUNCT
cana-4183	35	79	1074	1074	NUM
cana-4183	35	80	-	-	PUNCT
cana-4183	35	81	133x	133x	NUM
cana-4183	35	82	vol	vol	NOUN
cana-4183	35	83	32	32	NUM
cana-4183	35	84	no	no	NOUN
cana-4183	35	85	.	.	PUNCT
cana-4183	36	1	9s	9s	NUM
cana-4183	36	2	(	(	PUNCT
cana-4183	36	3	2025	2025	NUM
cana-4183	36	4	)	)	PUNCT
cana-4183	36	5	1506	1506	NUM
cana-4183	36	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4183	36	7	valid_combinations	valid_combination	NOUN
cana-4183	37	1	=	=	PUNCT
cana-4183	38	1	[	[	X
cana-4183	38	2	]	]	X
cana-4183	38	3	#	#	NOUN
cana-4183	38	4	to	to	PART
cana-4183	38	5	store	store	VERB
cana-4183	38	6	valid	valid	ADJ
cana-4183	38	7	labelings	labeling	NOUN
cana-4183	38	8	for	for	ADP
cana-4183	38	9	combination	combination	NOUN
cana-4183	38	10	in	in	ADP
cana-4183	38	11	combinations	combination	NOUN
cana-4183	38	12	:	:	PUNCT
cana-4183	38	13	s4	s4	PROPN
cana-4183	38	14	=	=	SYM
cana-4183	38	15	s5	s5	PROPN
cana-4183	38	16	=	=	SYM
cana-4183	38	17	s6	s6	PROPN
cana-4183	38	18	=	=	SYM
cana-4183	38	19	0	0	PROPN
cana-4183	38	20	for	for	ADP
cana-4183	38	21	i	i	PRON
cana-4183	38	22	in	in	ADP
cana-4183	38	23	range(len(combination	range(len(combination	NOUN
cana-4183	38	24	)	)	PUNCT
cana-4183	38	25	1	1	NUM
cana-4183	38	26	):	):	PUNCT
cana-4183	38	27	#	#	NOUN
cana-4183	38	28	assuming	assume	VERB
cana-4183	38	29	the	the	DET
cana-4183	38	30	graph	graph	NOUN
cana-4183	38	31	is	be	AUX
cana-4183	38	32	a	a	DET
cana-4183	38	33	path	path	NOUN
cana-4183	38	34	(	(	PUNCT
cana-4183	38	35	pn	pn	NOUN
cana-4183	38	36	)	)	PUNCT
cana-4183	38	37	u	u	NOUN
cana-4183	38	38	,	,	PUNCT
cana-4183	38	39	v	v	NOUN
cana-4183	38	40	=	=	SYM
cana-4183	38	41	combination[i	combination[i	X
cana-4183	38	42	]	]	PUNCT
cana-4183	38	43	,	,	PUNCT
cana-4183	38	44	combination[i	combination[i	X
cana-4183	38	45	+	+	CCONJ
cana-4183	38	46	1	1	X
cana-4183	38	47	]	]	X
cana-4183	38	48	edge_label	edge_label	NOUN
cana-4183	38	49	=	=	SYM
cana-4183	38	50	stolarsky_3_mean(u	stolarsky_3_mean(u	NOUN
cana-4183	38	51	,	,	PUNCT
cana-4183	38	52	v	v	NOUN
cana-4183	38	53	)	)	PUNCT
cana-4183	38	54	if	if	SCONJ
cana-4183	38	55	edge_label	edge_label	NOUN
cana-4183	38	56	=	=	NOUN
cana-4183	38	57	=	=	SYM
cana-4183	38	58	0	0	NUM
cana-4183	38	59	:	:	PUNCT
cana-4183	38	60	s4	s4	VERB
cana-4183	38	61	+	+	NOUN
cana-4183	38	62	=	=	SYM
cana-4183	38	63	1	1	NUM
cana-4183	38	64	elif	elif	X
cana-4183	38	65	edge_label	edge_label	NOUN
cana-4183	39	1	=	=	NOUN
cana-4183	39	2	=	=	SYM
cana-4183	39	3	1	1	NUM
cana-4183	39	4	:	:	PUNCT
cana-4183	39	5	s5	s5	PROPN
cana-4183	39	6	+	+	PROPN
cana-4183	39	7	=	=	SYM
cana-4183	39	8	1	1	NUM
cana-4183	39	9	elif	elif	X
cana-4183	39	10	edge_label	edge_label	NOUN
cana-4183	40	1	=	=	NOUN
cana-4183	40	2	=	=	SYM
cana-4183	40	3	2	2	NUM
cana-4183	40	4	:	:	PUNCT
cana-4183	40	5	s6	s6	PROPN
cana-4183	40	6	+	+	PROPN
cana-4183	40	7	=	=	SYM
cana-4183	40	8	1	1	NUM
cana-4183	40	9	if	if	SCONJ
cana-4183	40	10	is_valid_labeling(s1	is_valid_labeling(s1	PROPN
cana-4183	40	11	,	,	PUNCT
cana-4183	40	12	s2	s2	PROPN
cana-4183	40	13	,	,	PUNCT
cana-4183	40	14	s3	s3	PROPN
cana-4183	40	15	,	,	PUNCT
cana-4183	40	16	s4	s4	PROPN
cana-4183	40	17	,	,	PUNCT
cana-4183	40	18	s5	s5	PROPN
cana-4183	40	19	,	,	PUNCT
cana-4183	40	20	s6	s6	PROPN
cana-4183	40	21	,	,	PUNCT
cana-4183	40	22	m1	m1	PROPN
cana-4183	40	23	,	,	PUNCT
cana-4183	40	24	m2	m2	PROPN
cana-4183	40	25	,	,	PUNCT
cana-4183	40	26	m3	m3	PROPN
cana-4183	40	27	,	,	PUNCT
cana-4183	40	28	m4	m4	PROPN
cana-4183	40	29	):	):	PUNCT
cana-4183	40	30	valid_combinations.append((combination	valid_combinations.append((combination	NOUN
cana-4183	40	31	,	,	PUNCT
cana-4183	40	32	(	(	PUNCT
cana-4183	40	33	s1	s1	NOUN
cana-4183	40	34	,	,	PUNCT
cana-4183	40	35	s2	s2	PROPN
cana-4183	40	36	,	,	PUNCT
cana-4183	40	37	s3	s3	PROPN
cana-4183	40	38	,	,	PUNCT
cana-4183	40	39	s4	s4	PROPN
cana-4183	40	40	,	,	PUNCT
cana-4183	40	41	s5	s5	PROPN
cana-4183	40	42	,	,	PUNCT
cana-4183	40	43	s6	s6	PROPN
cana-4183	40	44	)	)	PUNCT
cana-4183	40	45	)	)	PUNCT
cana-4183	40	46	)	)	PUNCT
cana-4183	41	1	print("valid	print("valid	PROPN
cana-4183	41	2	stolarsky-3	stolarsky-3	X
cana-4183	41	3	mean	mean	ADJ
cana-4183	41	4	cordial	cordial	ADJ
cana-4183	41	5	labelings	labeling	NOUN
cana-4183	41	6	:	:	PUNCT
cana-4183	41	7	"	"	PUNCT
cana-4183	41	8	)	)	PUNCT
cana-4183	41	9	for	for	ADP
cana-4183	41	10	combo	combo	NOUN
cana-4183	41	11	,	,	PUNCT
cana-4183	41	12	counts	count	NOUN
cana-4183	41	13	in	in	ADP
cana-4183	41	14	valid_combinations	valid_combination	NOUN
cana-4183	41	15	:	:	PUNCT
cana-4183	41	16	print(f"vertex	print(f"vertex	NOUN
cana-4183	41	17	labels	label	NOUN
cana-4183	41	18	:	:	PUNCT
cana-4183	41	19	{	{	PUNCT
cana-4183	41	20	combo	combo	NOUN
cana-4183	41	21	}	}	PUNCT
cana-4183	41	22	,	,	PUNCT
cana-4183	41	23	counts	count	VERB
cana-4183	41	24	:	:	PUNCT
cana-4183	41	25	{	{	PUNCT
cana-4183	41	26	counts	count	NOUN
cana-4183	41	27	}	}	PUNCT
cana-4183	41	28	"	"	PUNCT
cana-4183	41	29	)	)	PUNCT
cana-4183	41	30	stolarsky_3_mean_cordial_labeling(n	stolarsky_3_mean_cordial_labeling(n	NOUN
cana-4183	41	31	,	,	PUNCT
cana-4183	41	32	m1	m1	NOUN
cana-4183	41	33	,	,	PUNCT
cana-4183	41	34	m2	m2	PROPN
cana-4183	41	35	,	,	PUNCT
cana-4183	41	36	m3	m3	PROPN
cana-4183	41	37	,	,	PUNCT
cana-4183	41	38	m4)he	m4)he	NOUN
cana-4183	41	39	process	process	NOUN
cana-4183	41	40	,	,	PUNCT
cana-4183	41	41	printing	print	VERB
cana-4183	41	42	only	only	ADV
cana-4183	41	43	those	those	DET
cana-4183	41	44	combinations	combination	NOUN
cana-4183	41	45	that	that	PRON
cana-4183	41	46	satisfy	satisfy	VERB
cana-4183	41	47	the	the	DET
cana-4183	41	48	specified	specified	ADJ
cana-4183	41	49	conditions	condition	NOUN
cana-4183	41	50	.	.	PUNCT
cana-4183	42	1	this	this	DET
cana-4183	42	2	python	python	NOUN
cana-4183	42	3	module	module	NOUN
cana-4183	42	4	will	will	AUX
cana-4183	42	5	analyze	analyze	VERB
cana-4183	42	6	and	and	CCONJ
cana-4183	42	7	determine	determine	VERB
cana-4183	42	8	the	the	DET
cana-4183	42	9	stolarsky-3	stolarsky-3	PROPN
cana-4183	42	10	mean	mean	ADJ
cana-4183	42	11	cordial	cordial	ADJ
cana-4183	42	12	labeling	labeling	NOUN
cana-4183	42	13	characteristics	characteristic	NOUN
cana-4183	42	14	in	in	ADP
cana-4183	42	15	various	various	ADJ
cana-4183	42	16	types	type	NOUN
cana-4183	42	17	of	of	ADP
cana-4183	42	18	graphs	graph	NOUN
cana-4183	42	19	.	.	PUNCT
cana-4183	43	1	let	let	VERB
cana-4183	43	2	me	i	PRON
cana-4183	43	3	know	know	VERB
cana-4183	43	4	if	if	SCONJ
cana-4183	43	5	you	you	PRON
cana-4183	43	6	'd	would	AUX
cana-4183	43	7	like	like	VERB
cana-4183	43	8	further	further	ADJ
cana-4183	43	9	assistance	assistance	NOUN
cana-4183	43	10	with	with	ADP
cana-4183	43	11	this	this	DET
cana-4183	43	12	paper	paper	NOUN
cana-4183	43	13	3.results	3.results	NUM
cana-4183	43	14	and	and	CCONJ
cana-4183	43	15	analysis	analysis	NOUN
cana-4183	43	16	table	table	NOUN
cana-4183	43	17	1	1	NUM
cana-4183	43	18	.	.	PUNCT
cana-4183	43	19	comparative	comparative	ADJ
cana-4183	43	20	analyses	analysis	NOUN
cana-4183	43	21	of	of	ADP
cana-4183	43	22	3	3	NUM
cana-4183	43	23	different	different	ADJ
cana-4183	43	24	mean	mean	NOUN
cana-4183	43	25	labeling	labeling	NOUN
cana-4183	43	26	with	with	ADP
cana-4183	43	27	respect	respect	NOUN
cana-4183	43	28	to	to	ADP
cana-4183	43	29	various	various	ADJ
cana-4183	43	30	graphs	graph	NOUN
cana-4183	43	31	.	.	PUNCT
cana-4183	44	1	the	the	DET
cana-4183	44	2	table	table	NOUN
cana-4183	44	3	provided	provide	VERB
cana-4183	44	4	compares	compare	VERB
cana-4183	44	5	different	different	ADJ
cana-4183	44	6	types	type	NOUN
cana-4183	44	7	of	of	ADP
cana-4183	44	8	graph	graph	NOUN
cana-4183	44	9	labeling	labeling	NOUN
cana-4183	44	10	with	with	ADP
cana-4183	44	11	respect	respect	NOUN
cana-4183	44	12	to	to	PART
cana-4183	44	13	mean	mean	VERB
cana-4183	44	14	cordial	cordial	ADJ
cana-4183	44	15	labeling	labeling	NOUN
cana-4183	44	16	,	,	PUNCT
cana-4183	44	17	stolarsky-3	stolarsky-3	PROPN
cana-4183	44	18	mean	mean	VERB
cana-4183	44	19	labeling	labeling	NOUN
cana-4183	44	20	,	,	PUNCT
cana-4183	44	21	and	and	CCONJ
cana-4183	44	22	stolarsky-3	stolarsky-3	NUM
cana-4183	44	23	mean	mean	VERB
cana-4183	44	24	cordial	cordial	ADJ
cana-4183	44	25	labeling	labeling	NOUN
cana-4183	44	26	.	.	PUNCT
cana-4183	45	1	let	let	VERB
cana-4183	45	2	's	us	PRON
cana-4183	45	3	break	break	VERB
cana-4183	45	4	down	down	ADP
cana-4183	45	5	and	and	CCONJ
cana-4183	45	6	analyze	analyze	VERB
cana-4183	45	7	these	these	DET
cana-4183	45	8	findings	finding	NOUN
cana-4183	45	9	across	across	ADP
cana-4183	45	10	different	different	ADJ
cana-4183	45	11	graph	graph	NOUN
cana-4183	45	12	types	type	NOUN
cana-4183	45	13	:	:	PUNCT
cana-4183	45	14	path	path	NOUN
cana-4183	45	15	graph	graph	NOUN
cana-4183	45	16	(	(	PUNCT
cana-4183	45	17	pn	pn	NOUN
cana-4183	45	18	)	)	PUNCT
cana-4183	45	19	theorem	theorem	VERB
cana-4183	45	20	3.1	3.1	NUM
cana-4183	45	21	:	:	PUNCT
cana-4183	45	22	every	every	DET
cana-4183	45	23	path	path	NOUN
cana-4183	45	24	pn	pn	PROPN
cana-4183	45	25	is	be	AUX
cana-4183	45	26	stolarsky-3	stolarsky-3	NUM
cana-4183	45	27	mean	mean	PROPN
cana-4183	45	28	cordial	cordial	ADJ
cana-4183	45	29	.	.	PUNCT
cana-4183	46	1	proof	proof	NOUN
cana-4183	46	2	:	:	PUNCT
cana-4183	46	3	consider	consider	VERB
cana-4183	46	4	a	a	DET
cana-4183	46	5	path	path	NOUN
cana-4183	46	6	pn	pn	NOUN
cana-4183	46	7	with	with	ADP
cana-4183	46	8	vertices	vertex	NOUN
cana-4183	46	9	u1,u2	u1,u2	PROPN
cana-4183	46	10	,	,	PUNCT
cana-4183	46	11	.....	.....	PROPN
cana-4183	46	12	,	,	PUNCT
cana-4183	46	13	un	un	PROPN
cana-4183	46	14	.	.	PROPN
cana-4183	46	15	define	define	VERB
cana-4183	46	16	f	f	NOUN
cana-4183	46	17	:	:	PUNCT
cana-4183	46	18	v(pn	v(pn	NUM
cana-4183	46	19	)	)	PUNCT
cana-4183	46	20	_	_	PUNCT
cana-4183	47	1	_	_	PUNCT
cana-4183	48	1	_	_	PUNCT
cana-4183	49	1	_	_	PUNCT
cana-4183	49	2	{	{	PUNCT
cana-4183	49	3	1	1	NUM
cana-4183	49	4	,	,	PUNCT
cana-4183	49	5	2,	2,	NUM
cana-4183	49	6	.....	.....	PUNCT
cana-4183	49	7	,q+1	,q+1	PUNCT
cana-4183	49	8	}	}	PUNCT
cana-4183	49	9	.	.	PUNCT
cana-4183	50	1	therefore	therefore	ADV
cana-4183	50	2	f(ui	f(ui	PROPN
cana-4183	50	3	)	)	PUNCT
cana-4183	51	1	=	=	NOUN
cana-4183	51	2	i	i	PROPN
cana-4183	51	3	,	,	PUNCT
cana-4183	51	4	1≤i≤n	1≤i≤n	NUM
cana-4183	51	5	.	.	PUNCT
cana-4183	52	1	communications	communication	NOUN
cana-4183	52	2	on	on	ADP
cana-4183	52	3	applied	apply	VERB
cana-4183	52	4	nonlinear	nonlinear	ADJ
cana-4183	52	5	analysis	analysis	NOUN
cana-4183	52	6	issn	issn	NOUN
cana-4183	52	7	:	:	PUNCT
cana-4183	52	8	1074	1074	NUM
cana-4183	52	9	-	-	PUNCT
cana-4183	52	10	133x	133x	NUM
cana-4183	52	11	vol	vol	NOUN
cana-4183	52	12	32	32	NUM
cana-4183	52	13	no	no	NOUN
cana-4183	52	14	.	.	PUNCT
cana-4183	53	1	9s	9s	NUM
cana-4183	53	2	(	(	PUNCT
cana-4183	53	3	2025	2025	NUM
cana-4183	53	4	)	)	PUNCT
cana-4183	53	5	1507	1507	NUM
cana-4183	53	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4183	53	7	then	then	ADV
cana-4183	53	8	the	the	DET
cana-4183	53	9	edge	edge	NOUN
cana-4183	53	10	labels	label	NOUN
cana-4183	53	11	are	be	AUX
cana-4183	53	12	distinct	distinct	ADJ
cana-4183	53	13	.	.	PUNCT
cana-4183	54	1	case	case	NOUN
cana-4183	54	2	1	1	NUM
cana-4183	54	3	:	:	PUNCT
cana-4183	54	4	n≡0(mod3	n≡0(mod3	X
cana-4183	54	5	)	)	PUNCT
cana-4183	54	6	let	let	VERB
cana-4183	54	7	n=3t.f(ui	n=3t.f(ui	NOUN
cana-4183	54	8	)	)	PUNCT
cana-4183	54	9	=	=	SYM
cana-4183	54	10	0,1≤i≤t	0,1≤i≤t	NUM
cana-4183	54	11	,	,	PUNCT
cana-4183	54	12	f(ut+i	f(ut+i	NOUN
cana-4183	54	13	)	)	PUNCT
cana-4183	54	14	=	=	SYM
cana-4183	54	15	1	1	NUM
cana-4183	54	16	,	,	PUNCT
cana-4183	54	17	1≤i≤t	1≤i≤t	NUM
cana-4183	54	18	,	,	PUNCT
cana-4183	54	19	f(u2t+i)=2	f(u2t+i)=2	PROPN
cana-4183	54	20	,	,	PUNCT
cana-4183	54	21	1≤i≤t	1≤i≤t	NUM
cana-4183	54	22	.	.	PUNCT
cana-4183	55	1	then	then	ADV
cana-4183	55	2	vf(0	vf(0	NOUN
cana-4183	55	3	)	)	PUNCT
cana-4183	55	4	=	=	SYM
cana-4183	55	5	vf(1	vf(1	NOUN
cana-4183	55	6	)	)	PUNCT
cana-4183	55	7	=	=	SYM
cana-4183	56	1	vf(2	vf(2	X
cana-4183	56	2	)	)	PUNCT
cana-4183	56	3	=	=	NOUN
cana-4183	56	4	t	t	NOUN
cana-4183	56	5	and	and	CCONJ
cana-4183	56	6	ef(0	ef(0	PROPN
cana-4183	56	7	)	)	PUNCT
cana-4183	57	1	=	=	SYM
cana-4183	57	2	t-1	t-1	PROPN
cana-4183	57	3	,	,	PUNCT
cana-4183	57	4	ef(1)=ef(2	ef(1)=ef(2	X
cana-4183	57	5	)	)	PUNCT
cana-4183	58	1	=	=	NOUN
cana-4183	58	2	t.	t.	NOUN
cana-4183	58	3	case	case	NOUN
cana-4183	58	4	2	2	NUM
cana-4183	58	5	:	:	PUNCT
cana-4183	58	6	n≡1(mod3	n≡1(mod3	NUM
cana-4183	58	7	)	)	PUNCT
cana-4183	58	8	let	let	VERB
cana-4183	58	9	n=3t+1.f(ui	n=3t+1.f(ui	PRON
cana-4183	58	10	)	)	PUNCT
cana-4183	59	1	=	=	NOUN
cana-4183	59	2	0	0	NUM
cana-4183	59	3	,	,	PUNCT
cana-4183	59	4	1≤i≤t	1≤i≤t	NUM
cana-4183	59	5	,	,	PUNCT
cana-4183	59	6	f(ut+i)=1,1≤i≤t+1,f(u2t+1+i)=2	f(ut+i)=1,1≤i≤t+1,f(u2t+1+i)=2	NOUN
cana-4183	59	7	,	,	PUNCT
cana-4183	59	8	1≤i≤t+1	1≤i≤t+1	NUM
cana-4183	59	9	.	.	PUNCT
cana-4183	60	1	then	then	ADV
cana-4183	60	2	vf(0	vf(0	X
cana-4183	60	3	)	)	PUNCT
cana-4183	61	1	=	=	NOUN
cana-4183	61	2	t+1	t+1	PROPN
cana-4183	61	3	,	,	PUNCT
cana-4183	61	4	vf(1	vf(1	PROPN
cana-4183	61	5	)	)	PUNCT
cana-4183	61	6	=	=	SYM
cana-4183	61	7	vf(2	vf(2	X
cana-4183	61	8	)	)	PUNCT
cana-4183	61	9	=	=	NOUN
cana-4183	61	10	t	t	NOUN
cana-4183	61	11	and	and	CCONJ
cana-4183	61	12	ef(0	ef(0	PROPN
cana-4183	61	13	)	)	PUNCT
cana-4183	62	1	=	=	SYM
cana-4183	62	2	ef(1	ef(1	NOUN
cana-4183	62	3	)	)	PUNCT
cana-4183	62	4	=	=	SYM
cana-4183	62	5	ef(2	ef(2	NOUN
cana-4183	62	6	)	)	PUNCT
cana-4183	62	7	=	=	NOUN
cana-4183	62	8	t.	t.	NOUN
cana-4183	62	9	case	case	NOUN
cana-4183	62	10	3	3	NUM
cana-4183	62	11	:	:	PUNCT
cana-4183	62	12	n≡2(mod3	n≡2(mod3	NUM
cana-4183	62	13	)	)	PUNCT
cana-4183	62	14	let	let	VERB
cana-4183	62	15	n=3t+2	n=3t+2	PROPN
cana-4183	62	16	,	,	PUNCT
cana-4183	62	17	f(ui)=0	f(ui)=0	PROPN
cana-4183	62	18	,	,	PUNCT
cana-4183	62	19	1≤i≤t	1≤i≤t	NUM
cana-4183	62	20	,	,	PUNCT
cana-4183	62	21	f(ut+i)=1	f(ut+i)=1	PROPN
cana-4183	62	22	,	,	PUNCT
cana-4183	62	23	1≤i≤t+1	1≤i≤t+1	NUM
cana-4183	62	24	,	,	PUNCT
cana-4183	62	25	f(u2t+1+i)=2	f(u2t+1+i)=2	NOUN
cana-4183	62	26	,	,	PUNCT
cana-4183	62	27	1≤i≤t+1	1≤i≤t+1	NUM
cana-4183	62	28	.	.	PUNCT
cana-4183	63	1	then	then	ADV
cana-4183	63	2	vf(0	vf(0	X
cana-4183	63	3	)	)	PUNCT
cana-4183	64	1	=	=	SYM
cana-4183	64	2	t+1	t+1	PROPN
cana-4183	64	3	,	,	PUNCT
cana-4183	64	4	vf(1)=vf(2)=t	vf(1)=vf(2)=t	PROPN
cana-4183	64	5	and	and	CCONJ
cana-4183	64	6	ef(0	ef(0	PROPN
cana-4183	64	7	)	)	PUNCT
cana-4183	65	1	=	=	SYM
cana-4183	65	2	t+1	t+1	PROPN
cana-4183	65	3	,	,	PUNCT
cana-4183	65	4	ef(1)=ef(2)=t	ef(1)=ef(2)=t	X
cana-4183	65	5	.	.	PUNCT
cana-4183	66	1	hence	hence	ADV
cana-4183	66	2	the	the	DET
cana-4183	66	3	above	above	ADJ
cana-4183	66	4	three	three	NUM
cana-4183	66	5	cases	case	NOUN
cana-4183	66	6	satisfies	satisfy	VERB
cana-4183	66	7	the	the	DET
cana-4183	66	8	condition	condition	NOUN
cana-4183	66	9	|vf(i)-vf(j)|≤1	|vf(i)-vf(j)|≤1	PROPN
cana-4183	66	10	and	and	CCONJ
cana-4183	66	11	|ef(i)-ef(j	|ef(i)-ef(j	PROPN
cana-4183	66	12	)	)	PUNCT
cana-4183	66	13	|≤1	|≤1	NOUN
cana-4183	66	14	for	for	ADP
cana-4183	66	15	all	all	DET
cana-4183	66	16	i	i	PRON
cana-4183	66	17	,	,	PUNCT
cana-4183	66	18	j	j	PROPN
cana-4183	66	19	∈{0	∈{0	NOUN
cana-4183	66	20	,	,	PUNCT
cana-4183	66	21	1,2	1,2	NUM
cana-4183	66	22	}	}	PUNCT
cana-4183	66	23	.	.	PUNCT
cana-4183	67	1	hence	hence	ADV
cana-4183	67	2	f	f	PROPN
cana-4183	67	3	is	be	AUX
cana-4183	67	4	a	a	DET
cana-4183	67	5	stolarsky-3	stolarsky-3	NUM
cana-4183	67	6	mean	mean	ADJ
cana-4183	67	7	cordial	cordial	ADJ
cana-4183	67	8	labeling	labeling	NOUN
cana-4183	67	9	.	.	PUNCT
cana-4183	68	1	the	the	DET
cana-4183	68	2	stolarsky-3	stolarsky-3	PROPN
cana-4183	68	3	mean	mean	ADJ
cana-4183	68	4	cordial	cordial	ADJ
cana-4183	68	5	labeling	labeling	NOUN
cana-4183	68	6	of	of	ADP
cana-4183	68	7	the	the	DET
cana-4183	68	8	path	path	NOUN
cana-4183	68	9	graph	graph	NOUN
cana-4183	68	10	(	(	PUNCT
cana-4183	68	11	pn	pn	NOUN
cana-4183	68	12	)	)	PUNCT
cana-4183	68	13	is	be	AUX
cana-4183	68	14	illustrated	illustrate	VERB
cana-4183	68	15	in	in	ADP
cana-4183	68	16	figure	figure	NOUN
cana-4183	68	17	1	1	NUM
cana-4183	68	18	.	.	PUNCT
cana-4183	69	1	the	the	DET
cana-4183	69	2	mean	mean	ADJ
cana-4183	69	3	cordial	cordial	ADJ
cana-4183	69	4	labeling	labeling	NOUN
cana-4183	69	5	method	method	NOUN
cana-4183	69	6	is	be	AUX
cana-4183	69	7	applicable	applicable	ADJ
cana-4183	69	8	to	to	PART
cana-4183	69	9	graphs	graph	NOUN
cana-4183	69	10	with	with	ADP
cana-4183	69	11	any	any	DET
cana-4183	69	12	number	number	NOUN
cana-4183	69	13	of	of	ADP
cana-4183	69	14	vertices	vertex	NOUN
cana-4183	69	15	.	.	PUNCT
cana-4183	70	1	similarly	similarly	ADV
cana-4183	70	2	,	,	PUNCT
cana-4183	70	3	stolarsky-3	stolarsky-3	PROPN
cana-4183	70	4	mean	mean	VERB
cana-4183	70	5	labeling	labeling	NOUN
cana-4183	70	6	is	be	AUX
cana-4183	70	7	also	also	ADV
cana-4183	70	8	effective	effective	ADJ
cana-4183	70	9	for	for	ADP
cana-4183	70	10	graphs	graph	NOUN
cana-4183	70	11	with	with	ADP
cana-4183	70	12	any	any	DET
cana-4183	70	13	number	number	NOUN
cana-4183	70	14	of	of	ADP
cana-4183	70	15	vertices	vertex	NOUN
cana-4183	70	16	n.	n.	PROPN
cana-4183	70	17	furthermore	furthermore	ADV
cana-4183	70	18	,	,	PUNCT
cana-4183	70	19	stolarsky-3	stolarsky-3	PROPN
cana-4183	70	20	mean	mean	VERB
cana-4183	70	21	cordial	cordial	ADJ
cana-4183	70	22	labeling	labeling	NOUN
cana-4183	70	23	remains	remain	VERB
cana-4183	70	24	valid	valid	ADJ
cana-4183	70	25	and	and	CCONJ
cana-4183	70	26	applicable	applicable	ADJ
cana-4183	70	27	for	for	ADP
cana-4183	70	28	all	all	DET
cana-4183	70	29	values	value	NOUN
cana-4183	70	30	of	of	ADP
cana-4183	70	31	n	n	CCONJ
cana-4183	70	32	,	,	PUNCT
cana-4183	70	33	ensuring	ensure	VERB
cana-4183	70	34	its	its	PRON
cana-4183	70	35	versatility	versatility	NOUN
cana-4183	70	36	across	across	ADP
cana-4183	70	37	different	different	ADJ
cana-4183	70	38	graph	graph	NOUN
cana-4183	70	39	sizes	size	NOUN
cana-4183	70	40	(	(	PUNCT
cana-4183	70	41	table	table	NOUN
cana-4183	70	42	1	1	NUM
cana-4183	70	43	)	)	PUNCT
cana-4183	70	44	.	.	PUNCT
cana-4183	71	1	all	all	DET
cana-4183	71	2	three	three	NUM
cana-4183	71	3	labeling	labeling	NOUN
cana-4183	71	4	methods	method	NOUN
cana-4183	71	5	work	work	VERB
cana-4183	71	6	well	well	ADV
cana-4183	71	7	for	for	ADP
cana-4183	71	8	path	path	NOUN
cana-4183	71	9	graphs	graph	NOUN
cana-4183	71	10	,	,	PUNCT
cana-4183	71	11	no	no	ADV
cana-4183	71	12	matter	matter	ADV
cana-4183	71	13	how	how	SCONJ
cana-4183	71	14	many	many	ADJ
cana-4183	71	15	vertices	vertex	NOUN
cana-4183	71	16	they	they	PRON
cana-4183	71	17	have	have	VERB
cana-4183	71	18	.	.	PUNCT
cana-4183	72	1	this	this	PRON
cana-4183	72	2	is	be	AUX
cana-4183	72	3	because	because	SCONJ
cana-4183	72	4	path	path	NOUN
cana-4183	72	5	graphs	graph	NOUN
cana-4183	72	6	are	be	AUX
cana-4183	72	7	simple	simple	ADJ
cana-4183	72	8	and	and	CCONJ
cana-4183	72	9	linear	linear	ADJ
cana-4183	72	10	,	,	PUNCT
cana-4183	72	11	making	make	VERB
cana-4183	72	12	them	they	PRON
cana-4183	72	13	easy	easy	ADJ
cana-4183	72	14	to	to	PART
cana-4183	72	15	label	label	VERB
cana-4183	72	16	.	.	PUNCT
cana-4183	73	1	cycle	cycle	NOUN
cana-4183	73	2	graph	graph	NOUN
cana-4183	73	3	(	(	PUNCT
cana-4183	73	4	cn	cn	NOUN
cana-4183	73	5	)	)	PUNCT
cana-4183	73	6	theorem	theorem	VERB
cana-4183	73	7	3.2	3.2	NUM
cana-4183	73	8	:	:	PUNCT
cana-4183	73	9	the	the	DET
cana-4183	73	10	cycle	cycle	NOUN
cana-4183	73	11	cn	cn	PROPN
cana-4183	73	12	is	be	AUX
cana-4183	73	13	stolarsky-3	stolarsky-3	NUM
cana-4183	73	14	mean	mean	PROPN
cana-4183	73	15	cordial	cordial	ADJ
cana-4183	73	16	iff	iff	PROPN
cana-4183	73	17	n≡1	n≡1	NOUN
cana-4183	73	18	,	,	PUNCT
cana-4183	73	19	2(mod3	2(mod3	NUM
cana-4183	73	20	)	)	PUNCT
cana-4183	73	21	.	.	PUNCT
cana-4183	74	1	proof	proof	NOUN
cana-4183	74	2	:	:	PUNCT
cana-4183	74	3	consider	consider	VERB
cana-4183	74	4	a	a	DET
cana-4183	74	5	cycle	cycle	NOUN
cana-4183	74	6	cn	cn	NOUN
cana-4183	74	7	with	with	ADP
cana-4183	74	8	vertices	vertex	NOUN
cana-4183	74	9	u1	u1	NOUN
cana-4183	74	10	,	,	PUNCT
cana-4183	74	11	u2	u2	NOUN
cana-4183	74	12	,	,	PUNCT
cana-4183	74	13	....	....	PUNCT
cana-4183	74	14	,	,	PUNCT
cana-4183	74	15	unu1	unu1	PROPN
cana-4183	74	16	.	.	PUNCT
cana-4183	75	1	define	define	VERB
cana-4183	75	2	f	f	X
cana-4183	75	3	:	:	PUNCT
cana-4183	75	4	v(cn	v(cn	NUM
cana-4183	75	5	)	)	PUNCT
cana-4183	76	1	_	_	PUNCT
cana-4183	77	1	_	_	PUNCT
cana-4183	78	1	_	_	PUNCT
cana-4183	79	1	_	_	PUNCT
cana-4183	79	2	{	{	PUNCT
cana-4183	79	3	1	1	NUM
cana-4183	79	4	,	,	PUNCT
cana-4183	79	5	2,	2,	NUM
cana-4183	79	6	...	...	PUNCT
cana-4183	79	7	,q+1	,q+1	PUNCT
cana-4183	79	8	}	}	PUNCT
cana-4183	79	9	therefore	therefore	ADV
cana-4183	79	10	f(ui	f(ui	PROPN
cana-4183	79	11	)	)	PUNCT
cana-4183	79	12	=	=	SYM
cana-4183	79	13	i,1≤i≤n	i,1≤i≤n	PROPN
cana-4183	79	14	.	.	PUNCT
cana-4183	80	1	since	since	SCONJ
cana-4183	80	2	the	the	DET
cana-4183	80	3	edge	edge	NOUN
cana-4183	80	4	labels	label	NOUN
cana-4183	80	5	are	be	AUX
cana-4183	80	6	distinct	distinct	ADJ
cana-4183	80	7	.	.	PUNCT
cana-4183	81	1	case	case	NOUN
cana-4183	81	2	1	1	NUM
cana-4183	81	3	:	:	PUNCT
cana-4183	81	4	n≡0(mod3	n≡0(mod3	X
cana-4183	81	5	)	)	PUNCT
cana-4183	81	6	let	let	VERB
cana-4183	81	7	n=3t.if	n=3t.if	PROPN
cana-4183	81	8	cn	cn	PROPN
cana-4183	81	9	admits	admit	VERB
cana-4183	81	10	stolarsky-3mean	stolarsky-3mean	ADJ
cana-4183	81	11	cordial	cordial	ADJ
cana-4183	81	12	labeling	labeling	NOUN
cana-4183	81	13	f.	f.	PROPN
cana-4183	81	14	then	then	ADV
cana-4183	81	15	vf(0	vf(0	PROPN
cana-4183	81	16	)	)	PUNCT
cana-4183	82	1	=	=	SYM
cana-4183	82	2	vf(1	vf(1	NOUN
cana-4183	82	3	)	)	PUNCT
cana-4183	83	1	=	=	PROPN
cana-4183	83	2	vf(2)=t	vf(2)=t	PROPN
cana-4183	83	3	and	and	CCONJ
cana-4183	83	4	ef(0	ef(0	PROPN
cana-4183	83	5	)	)	PUNCT
cana-4183	83	6	=	=	SYM
cana-4183	83	7	ef(1	ef(1	NOUN
cana-4183	83	8	)	)	PUNCT
cana-4183	83	9	=	=	SYM
cana-4183	83	10	ef(2	ef(2	NOUN
cana-4183	83	11	)	)	PUNCT
cana-4183	84	1	=	=	NOUN
cana-4183	84	2	t.	t.	NOUN
cana-4183	84	3	assign	assign	NOUN
cana-4183	84	4	0	0	NUM
cana-4183	84	5	's	's	PART
cana-4183	84	6	to	to	ADP
cana-4183	84	7	t	t	NOUN
cana-4183	84	8	number	number	NOUN
cana-4183	84	9	of	of	ADP
cana-4183	84	10	vertices	vertex	NOUN
cana-4183	84	11	cn	cn	PROPN
cana-4183	84	12	.	.	PUNCT
cana-4183	85	1	then	then	ADV
cana-4183	85	2	we	we	PRON
cana-4183	85	3	get	get	VERB
cana-4183	85	4	ef(0	ef(0	PROPN
cana-4183	85	5	)	)	PUNCT
cana-4183	85	6	>	>	PUNCT
cana-4183	86	1	t.	t.	NOUN
cana-4183	86	2	communications	communication	NOUN
cana-4183	86	3	on	on	ADP
cana-4183	86	4	applied	apply	VERB
cana-4183	86	5	nonlinear	nonlinear	ADJ
cana-4183	86	6	analysis	analysis	NOUN
cana-4183	86	7	issn	issn	NOUN
cana-4183	86	8	:	:	PUNCT
cana-4183	86	9	1074	1074	NUM
cana-4183	86	10	-	-	PUNCT
cana-4183	86	11	133x	133x	NUM
cana-4183	86	12	vol	vol	NOUN
cana-4183	86	13	32	32	NUM
cana-4183	86	14	no	no	NOUN
cana-4183	86	15	.	.	PUNCT
cana-4183	87	1	9s	9s	NUM
cana-4183	87	2	(	(	PUNCT
cana-4183	87	3	2025	2025	NUM
cana-4183	87	4	)	)	PUNCT
cana-4183	87	5	1508	1508	NUM
cana-4183	87	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4183	88	1	hence	hence	ADV
cana-4183	88	2	f	f	PROPN
cana-4183	88	3	is	be	AUX
cana-4183	88	4	not	not	PART
cana-4183	88	5	a	a	DET
cana-4183	88	6	stolarsky-3mean	stolarsky-3mean	ADJ
cana-4183	88	7	cordial	cordial	ADJ
cana-4183	88	8	labeling	labeling	NOUN
cana-4183	88	9	.	.	PUNCT
cana-4183	89	1	case	case	NOUN
cana-4183	89	2	2	2	NUM
cana-4183	89	3	:	:	PUNCT
cana-4183	89	4	n≡1(mod3	n≡1(mod3	NUM
cana-4183	89	5	)	)	PUNCT
cana-4183	89	6	let	let	VERB
cana-4183	89	7	n=3t+1	n=3t+1	PROPN
cana-4183	89	8	,	,	PUNCT
cana-4183	89	9	assign	assign	VERB
cana-4183	89	10	the	the	DET
cana-4183	89	11	label	label	NOUN
cana-4183	89	12	1	1	NUM
cana-4183	89	13	to	to	ADP
cana-4183	89	14	t+1	t+1	PRON
cana-4183	89	15	vertices	vertex	NOUN
cana-4183	89	16	and	and	CCONJ
cana-4183	89	17	the	the	DET
cana-4183	89	18	labels	label	NOUN
cana-4183	89	19	0	0	PUNCT
cana-4183	89	20	and	and	CCONJ
cana-4183	89	21	2	2	NUM
cana-4183	89	22	to	to	ADP
cana-4183	89	23	the	the	DET
cana-4183	89	24	remaining	remain	VERB
cana-4183	89	25	each	each	PRON
cana-4183	89	26	of	of	ADP
cana-4183	89	27	t	t	PROPN
cana-4183	89	28	vertices	vertex	NOUN
cana-4183	89	29	.	.	PUNCT
cana-4183	90	1	then	then	ADV
cana-4183	90	2	vf(0)=vf(1)=t	vf(0)=vf(1)=t	NOUN
cana-4183	90	3	,	,	PUNCT
cana-4183	90	4	vf(2	vf(2	ADJ
cana-4183	90	5	)	)	PUNCT
cana-4183	90	6	=	=	NOUN
cana-4183	90	7	t+1	t+1	PROPN
cana-4183	90	8	and	and	CCONJ
cana-4183	90	9	ef(0)=ef(2	ef(0)=ef(2	NUM
cana-4183	90	10	)	)	PUNCT
cana-4183	91	1	=	=	SYM
cana-4183	91	2	t	t	PROPN
cana-4183	91	3	,	,	PUNCT
cana-4183	91	4	ef(1	ef(1	PROPN
cana-4183	91	5	)	)	PUNCT
cana-4183	91	6	=	=	NOUN
cana-4183	91	7	t+1	t+1	PROPN
cana-4183	91	8	.	.	PUNCT
cana-4183	92	1	hence	hence	ADV
cana-4183	92	2	f	f	PROPN
cana-4183	92	3	is	be	AUX
cana-4183	92	4	stolarsky-3	stolarsky-3	NUM
cana-4183	92	5	mean	mean	ADJ
cana-4183	92	6	cordial	cordial	ADJ
cana-4183	92	7	labeling	labeling	NOUN
cana-4183	92	8	.	.	PUNCT
cana-4183	93	1	case	case	NOUN
cana-4183	93	2	3	3	NUM
cana-4183	93	3	:	:	PUNCT
cana-4183	93	4	n≡2(mod3	n≡2(mod3	NUM
cana-4183	93	5	)	)	PUNCT
cana-4183	93	6	let	let	VERB
cana-4183	93	7	n=3t+2	n=3t+2	PROPN
cana-4183	93	8	,	,	PUNCT
cana-4183	93	9	assign	assign	VERB
cana-4183	93	10	the	the	DET
cana-4183	93	11	label	label	NOUN
cana-4183	93	12	1	1	NUM
cana-4183	93	13	to	to	ADP
cana-4183	93	14	t	t	PROPN
cana-4183	93	15	vertices	vertex	NOUN
cana-4183	93	16	and	and	CCONJ
cana-4183	93	17	the	the	DET
cana-4183	93	18	labels	label	NOUN
cana-4183	93	19	1	1	NUM
cana-4183	93	20	and	and	CCONJ
cana-4183	93	21	2	2	NUM
cana-4183	93	22	to	to	ADP
cana-4183	93	23	the	the	DET
cana-4183	93	24	remaining	remain	VERB
cana-4183	93	25	each	each	PRON
cana-4183	93	26	of	of	ADP
cana-4183	93	27	t	t	PROPN
cana-4183	93	28	vertices	vertex	NOUN
cana-4183	93	29	.	.	PUNCT
cana-4183	94	1	then	then	ADV
cana-4183	94	2	vf(0	vf(0	NOUN
cana-4183	94	3	)	)	PUNCT
cana-4183	94	4	=	=	SYM
cana-4183	94	5	vf(1	vf(1	NOUN
cana-4183	94	6	)	)	PUNCT
cana-4183	95	1	=	=	NOUN
cana-4183	95	2	t+1	t+1	PROPN
cana-4183	95	3	,	,	PUNCT
cana-4183	95	4	vf(2	vf(2	PROPN
cana-4183	95	5	)	)	PUNCT
cana-4183	95	6	=	=	NOUN
cana-4183	95	7	t	t	NOUN
cana-4183	95	8	and	and	CCONJ
cana-4183	95	9	ef(0	ef(0	PROPN
cana-4183	95	10	)	)	PUNCT
cana-4183	96	1	=	=	SYM
cana-4183	96	2	ef(2	ef(2	X
cana-4183	96	3	)	)	PUNCT
cana-4183	96	4	=	=	NOUN
cana-4183	96	5	t+1	t+1	PROPN
cana-4183	96	6	,	,	PUNCT
cana-4183	96	7	ef(1	ef(1	PROPN
cana-4183	96	8	)	)	PUNCT
cana-4183	96	9	=	=	NOUN
cana-4183	96	10	t.	t.	NOUN
cana-4183	96	11	hence	hence	ADV
cana-4183	96	12	f	f	PROPN
cana-4183	96	13	is	be	AUX
cana-4183	96	14	stolarsky-3mean	stolarsky-3mean	ADJ
cana-4183	96	15	cordial	cordial	ADJ
cana-4183	96	16	labeling	labeling	NOUN
cana-4183	96	17	.	.	PUNCT
cana-4183	97	1	the	the	DET
cana-4183	97	2	stolarsky-3	stolarsky-3	PROPN
cana-4183	97	3	mean	mean	ADJ
cana-4183	97	4	cordial	cordial	ADJ
cana-4183	97	5	labeling	labeling	NOUN
cana-4183	97	6	of	of	ADP
cana-4183	97	7	the	the	DET
cana-4183	97	8	cycle	cycle	NOUN
cana-4183	97	9	graph	graph	NOUN
cana-4183	97	10	(	(	PUNCT
cana-4183	97	11	cn	cn	PROPN
cana-4183	97	12	)	)	PUNCT
cana-4183	97	13	is	be	AUX
cana-4183	97	14	illustrated	illustrate	VERB
cana-4183	97	15	in	in	ADP
cana-4183	97	16	figure	figure	NOUN
cana-4183	97	17	2	2	NUM
cana-4183	97	18	.	.	PUNCT
cana-4183	98	1	mean	mean	VERB
cana-4183	98	2	cordial	cordial	ADJ
cana-4183	98	3	labeling	labeling	NOUN
cana-4183	98	4	is	be	AUX
cana-4183	98	5	works	work	NOUN
cana-4183	98	6	for	for	ADP
cana-4183	98	7	most	most	ADJ
cana-4183	98	8	,	,	PUNCT
cana-4183	98	9	but	but	CCONJ
cana-4183	98	10	not	not	PART
cana-4183	98	11	when	when	SCONJ
cana-4183	98	12	(	(	PUNCT
cana-4183	98	13	n	n	NOUN
cana-4183	98	14	=	=	SYM
cana-4183	98	15	3	3	NUM
cana-4183	98	16	,	,	PUNCT
cana-4183	98	17	6	6	NUM
cana-4183	98	18	,	,	PUNCT
cana-4183	98	19	9	9	NUM
cana-4183	98	20	,	,	PUNCT
cana-4183	98	21	…	…	PUNCT
cana-4183	98	22	)	)	PUNCT
cana-4183	98	23	etc	etc	X
cana-4183	98	24	.	.	X
cana-4183	99	1	(	(	PUNCT
cana-4183	99	2	multiples	multiple	NOUN
cana-4183	99	3	of	of	ADP
cana-4183	99	4	3	3	NUM
cana-4183	99	5	)	)	PUNCT
cana-4183	99	6	.	.	PUNCT
cana-4183	100	1	this	this	PRON
cana-4183	100	2	happens	happen	VERB
cana-4183	100	3	because	because	SCONJ
cana-4183	100	4	of	of	ADP
cana-4183	100	5	an	an	DET
cana-4183	100	6	imbalance	imbalance	NOUN
cana-4183	100	7	in	in	ADP
cana-4183	100	8	how	how	SCONJ
cana-4183	100	9	vertices	vertex	NOUN
cana-4183	100	10	and	and	CCONJ
cana-4183	100	11	edges	edge	NOUN
cana-4183	100	12	are	be	AUX
cana-4183	100	13	connected	connect	VERB
cana-4183	100	14	in	in	ADP
cana-4183	100	15	these	these	DET
cana-4183	100	16	cases	case	NOUN
cana-4183	100	17	.	.	PUNCT
cana-4183	101	1	stolarsky-3	stolarsky-3	PRON
cana-4183	101	2	mean	mean	VERB
cana-4183	101	3	labeling	labeling	NOUN
cana-4183	101	4	is	be	AUX
cana-4183	101	5	works	work	NOUN
cana-4183	101	6	for	for	ADP
cana-4183	101	7	any	any	DET
cana-4183	101	8	n	n	CCONJ
cana-4183	101	9	,	,	PUNCT
cana-4183	101	10	even	even	ADV
cana-4183	101	11	multiples	multiple	NOUN
cana-4183	101	12	of	of	ADP
cana-4183	101	13	3	3	NUM
cana-4183	101	14	.	.	PUNCT
cana-4183	102	1	stolarsky-3	stolarsky-3	PRON
cana-4183	102	2	mean	mean	VERB
cana-4183	102	3	cordial	cordial	ADJ
cana-4183	102	4	labeling	labeling	NOUN
cana-4183	102	5	is	be	AUX
cana-4183	102	6	same	same	ADJ
cana-4183	102	7	as	as	ADP
cana-4183	102	8	mean	mean	ADJ
cana-4183	102	9	cordial	cordial	ADJ
cana-4183	102	10	labeling	labeling	NOUN
cana-4183	102	11	,	,	PUNCT
cana-4183	102	12	it	it	PRON
cana-4183	102	13	does	do	AUX
cana-4183	102	14	not	not	PART
cana-4183	102	15	work	work	VERB
cana-4183	102	16	when	when	SCONJ
cana-4183	102	17	(	(	PUNCT
cana-4183	102	18	n	n	NOUN
cana-4183	102	19	=	=	SYM
cana-4183	102	20	3	3	NUM
cana-4183	102	21	,	,	PUNCT
cana-4183	102	22	6	6	NUM
cana-4183	102	23	,	,	PUNCT
cana-4183	102	24	9	9	NUM
cana-4183	102	25	,	,	PUNCT
cana-4183	102	26	…	…	PUNCT
cana-4183	102	27	)	)	PUNCT
cana-4183	102	28	etc	etc	X
cana-4183	102	29	(	(	PUNCT
cana-4183	102	30	table	table	NOUN
cana-4183	102	31	1	1	NUM
cana-4183	102	32	)	)	PUNCT
cana-4183	102	33	.	.	PUNCT
cana-4183	103	1	stolarsky-3	stolarsky-3	PRON
cana-4183	103	2	mean	mean	ADJ
cana-4183	103	3	labeling	labeling	NOUN
cana-4183	103	4	is	be	AUX
cana-4183	103	5	more	more	ADV
cana-4183	103	6	flexible	flexible	ADJ
cana-4183	103	7	for	for	ADP
cana-4183	103	8	cycle	cycle	NOUN
cana-4183	103	9	graphs	graph	NOUN
cana-4183	103	10	,	,	PUNCT
cana-4183	103	11	while	while	SCONJ
cana-4183	103	12	the	the	DET
cana-4183	103	13	other	other	ADJ
cana-4183	103	14	two	two	NUM
cana-4183	103	15	methods	method	NOUN
cana-4183	103	16	have	have	VERB
cana-4183	103	17	trouble	trouble	NOUN
cana-4183	103	18	with	with	ADP
cana-4183	103	19	graphs	graph	NOUN
cana-4183	103	20	where	where	SCONJ
cana-4183	103	21	is	be	AUX
cana-4183	103	22	a	a	DET
cana-4183	103	23	multiple	multiple	NOUN
cana-4183	103	24	of	of	ADP
cana-4183	103	25	3	3	NUM
cana-4183	103	26	.	.	NOUN
cana-4183	103	27	wheel	wheel	NOUN
cana-4183	103	28	graph	graph	NOUN
cana-4183	103	29	(	(	PUNCT
cana-4183	103	30	wn	wn	NOUN
cana-4183	103	31	)	)	PUNCT
cana-4183	103	32	theorem	theorem	VERB
cana-4183	103	33	3.3	3.3	NUM
cana-4183	103	34	:	:	PUNCT
cana-4183	103	35	the	the	DET
cana-4183	103	36	wheel	wheel	NOUN
cana-4183	103	37	graph	graph	NOUN
cana-4183	103	38	wn	wn	PROPN
cana-4183	103	39	is	be	AUX
cana-4183	103	40	not	not	PART
cana-4183	103	41	a	a	DET
cana-4183	103	42	stolarsky-3	stolarsky-3	NUM
cana-4183	103	43	mean	mean	NOUN
cana-4183	103	44	cordial	cordial	ADJ
cana-4183	103	45	for	for	ADP
cana-4183	103	46	any	any	DET
cana-4183	103	47	n.	n.	NOUN
cana-4183	103	48	proof	proof	NOUN
cana-4183	103	49	:	:	PUNCT
cana-4183	103	50	consider	consider	VERB
cana-4183	103	51	the	the	DET
cana-4183	103	52	wheel	wheel	NOUN
cana-4183	103	53	graph	graph	NOUN
cana-4183	103	54	wn	wn	PROPN
cana-4183	103	55	,	,	PUNCT
cana-4183	103	56	where	where	SCONJ
cana-4183	103	57	cn	cn	PROPN
cana-4183	103	58	is	be	AUX
cana-4183	103	59	a	a	DET
cana-4183	103	60	cycle	cycle	NOUN
cana-4183	103	61	with	with	ADP
cana-4183	103	62	vertices	vertex	NOUN
cana-4183	103	63	u1	u1	NOUN
cana-4183	103	64	,	,	PUNCT
cana-4183	103	65	u2	u2	NOUN
cana-4183	103	66	,	,	PUNCT
cana-4183	103	67	.....	.....	PUNCT
cana-4183	103	68	,	,	PUNCT
cana-4183	103	69	unu1	unu1	PROPN
cana-4183	103	70	and	and	CCONJ
cana-4183	103	71	there	there	PRON
cana-4183	103	72	is	be	VERB
cana-4183	103	73	a	a	DET
cana-4183	103	74	central	central	ADJ
cana-4183	103	75	vertex	vertex	NOUN
cana-4183	103	76	u.	u.	NOUN
cana-4183	103	77	case	case	NOUN
cana-4183	103	78	1	1	NUM
cana-4183	103	79	:	:	PUNCT
cana-4183	103	80	n≡0(mod3	n≡0(mod3	X
cana-4183	103	81	)	)	PUNCT
cana-4183	103	82	let	let	VERB
cana-4183	103	83	n=3	n=3	SYM
cana-4183	103	84	t	t	NOUN
cana-4183	103	85	,	,	PUNCT
cana-4183	103	86	a	a	DET
cana-4183	103	87	contradiction	contradiction	NOUN
cana-4183	103	88	.	.	PUNCT
cana-4183	104	1	case	case	NOUN
cana-4183	104	2	2	2	NUM
cana-4183	104	3	:	:	PUNCT
cana-4183	104	4	n≡1(mod3	n≡1(mod3	NUM
cana-4183	104	5	)	)	PUNCT
cana-4183	104	6	let	let	VERB
cana-4183	104	7	n=3t+1	n=3t+1	PROPN
cana-4183	104	8	,	,	PUNCT
cana-4183	104	9	again	again	ADV
cana-4183	104	10	a	a	DET
cana-4183	104	11	contradiction	contradiction	NOUN
cana-4183	104	12	.	.	PUNCT
cana-4183	105	1	case	case	NOUN
cana-4183	105	2	3	3	NUM
cana-4183	105	3	:	:	PUNCT
cana-4183	105	4	n≡2(mod3	n≡2(mod3	NUM
cana-4183	105	5	)	)	PUNCT
cana-4183	105	6	let	let	VERB
cana-4183	105	7	n=3t+2,we	n=3t+2,we	PROPN
cana-4183	105	8	get	get	VERB
cana-4183	105	9	a	a	DET
cana-4183	105	10	contradiction	contradiction	NOUN
cana-4183	105	11	.	.	PUNCT
cana-4183	106	1	therefore	therefore	ADV
cana-4183	106	2	contradiction	contradiction	NOUN
cana-4183	106	3	arise	arise	VERB
cana-4183	106	4	from	from	ADP
cana-4183	106	5	attempting	attempt	VERB
cana-4183	106	6	to	to	PART
cana-4183	106	7	label	label	VERB
cana-4183	106	8	the	the	DET
cana-4183	106	9	edges	edge	NOUN
cana-4183	106	10	while	while	SCONJ
cana-4183	106	11	maintaining	maintain	VERB
cana-4183	106	12	distinct	distinct	ADJ
cana-4183	106	13	labels	label	NOUN
cana-4183	106	14	.	.	PUNCT
cana-4183	107	1	hence	hence	ADV
cana-4183	107	2	the	the	DET
cana-4183	107	3	wheel	wheel	NOUN
cana-4183	107	4	graph	graph	NOUN
cana-4183	107	5	wn	wn	PROPN
cana-4183	107	6	is	be	AUX
cana-4183	107	7	not	not	PART
cana-4183	107	8	a	a	DET
cana-4183	107	9	stolarsky-3mean	stolarsky-3mean	ADJ
cana-4183	107	10	cordial	cordial	ADJ
cana-4183	107	11	for	for	ADP
cana-4183	107	12	any	any	DET
cana-4183	107	13	n.	n.	NOUN
cana-4183	107	14	mean	mean	PROPN
cana-4183	107	15	cordial	cordial	ADJ
cana-4183	107	16	labeling	labeling	NOUN
cana-4183	107	17	is	be	AUX
cana-4183	107	18	not	not	PART
cana-4183	107	19	applicable	applicable	ADJ
cana-4183	107	20	to	to	PART
cana-4183	107	21	wheel	wheel	NOUN
cana-4183	107	22	graphs	graph	NOUN
cana-4183	107	23	.	.	PUNCT
cana-4183	108	1	similarly	similarly	ADV
cana-4183	108	2	,	,	PUNCT
cana-4183	108	3	stolarsky-3	stolarsky-3	PROPN
cana-4183	108	4	mean	mean	VERB
cana-4183	108	5	labeling	labeling	NOUN
cana-4183	108	6	is	be	AUX
cana-4183	108	7	also	also	ADV
cana-4183	108	8	ineffective	ineffective	ADJ
cana-4183	108	9	for	for	ADP
cana-4183	108	10	these	these	DET
cana-4183	108	11	graphs(table	graphs(table	ADJ
cana-4183	108	12	1	1	NUM
cana-4183	108	13	)	)	PUNCT
cana-4183	108	14	.	.	PUNCT
cana-4183	109	1	additionally	additionally	ADV
cana-4183	109	2	,	,	PUNCT
cana-4183	109	3	stolarsky-3	stolarsky-3	PROPN
cana-4183	109	4	mean	mean	VERB
cana-4183	109	5	cordial	cordial	ADJ
cana-4183	109	6	labeling	labeling	NOUN
cana-4183	109	7	does	do	AUX
cana-4183	109	8	not	not	PART
cana-4183	109	9	apply	apply	VERB
cana-4183	109	10	to	to	ADP
cana-4183	109	11	wheel	wheel	NOUN
cana-4183	109	12	graphs	graph	NOUN
cana-4183	109	13	either	either	ADV
cana-4183	109	14	.	.	PUNCT
cana-4183	110	1	wheel	wheel	NOUN
cana-4183	110	2	graphs	graph	NOUN
cana-4183	110	3	are	be	AUX
cana-4183	110	4	tricky	tricky	ADJ
cana-4183	110	5	because	because	SCONJ
cana-4183	110	6	the	the	DET
cana-4183	110	7	central	central	ADJ
cana-4183	110	8	hub	hub	NOUN
cana-4183	110	9	vertex	vertex	NOUN
cana-4183	110	10	makes	make	VERB
cana-4183	110	11	it	it	PRON
cana-4183	110	12	hard	hard	ADJ
cana-4183	110	13	to	to	PART
cana-4183	110	14	balance	balance	VERB
cana-4183	110	15	the	the	DET
cana-4183	110	16	labels	label	NOUN
cana-4183	110	17	.	.	PUNCT
cana-4183	111	1	none	none	NOUN
cana-4183	111	2	of	of	ADP
cana-4183	111	3	the	the	DET
cana-4183	111	4	three	three	NUM
cana-4183	111	5	methods	method	NOUN
cana-4183	111	6	work	work	VERB
cana-4183	111	7	for	for	ADP
cana-4183	111	8	this	this	DET
cana-4183	111	9	type	type	NOUN
cana-4183	111	10	of	of	ADP
cana-4183	111	11	graph	graph	NOUN
cana-4183	111	12	.	.	PUNCT
cana-4183	112	1	communications	communication	NOUN
cana-4183	112	2	on	on	ADP
cana-4183	112	3	applied	apply	VERB
cana-4183	112	4	nonlinear	nonlinear	ADJ
cana-4183	112	5	analysis	analysis	NOUN
cana-4183	112	6	issn	issn	NOUN
cana-4183	112	7	:	:	PUNCT
cana-4183	112	8	1074	1074	NUM
cana-4183	112	9	-	-	PUNCT
cana-4183	112	10	133x	133x	NUM
cana-4183	112	11	vol	vol	NOUN
cana-4183	112	12	32	32	NUM
cana-4183	112	13	no	no	NOUN
cana-4183	112	14	.	.	PUNCT
cana-4183	113	1	9s	9s	NUM
cana-4183	113	2	(	(	PUNCT
cana-4183	113	3	2025	2025	NUM
cana-4183	113	4	)	)	PUNCT
cana-4183	113	5	1509	1509	NUM
cana-4183	113	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4183	113	7	star	star	NOUN
cana-4183	113	8	graph	graph	NOUN
cana-4183	113	9	k	k	PROPN
cana-4183	113	10	1,n	1,n	X
cana-4183	113	11	or	or	CCONJ
cana-4183	113	12	sn	sn	PROPN
cana-4183	113	13	theorem	theorem	VERB
cana-4183	113	14	3.4	3.4	NUM
cana-4183	113	15	:	:	PUNCT
cana-4183	113	16	the	the	DET
cana-4183	113	17	star	star	PROPN
cana-4183	113	18	graph(k1	graph(k1	PROPN
cana-4183	113	19	,	,	PUNCT
cana-4183	113	20	n	n	CCONJ
cana-4183	113	21	)	)	PUNCT
cana-4183	113	22	(	(	PUNCT
cana-4183	113	23	sn	sn	INTJ
cana-4183	113	24	)	)	PUNCT
cana-4183	113	25	is	be	AUX
cana-4183	113	26	a	a	DET
cana-4183	113	27	stolarsky-3	stolarsky-3	NUM
cana-4183	113	28	mean	mean	NOUN
cana-4183	113	29	cordial	cordial	ADJ
cana-4183	113	30	if	if	SCONJ
cana-4183	113	31	n	n	ADV
cana-4183	113	32	15	15	NUM
cana-4183	113	33	.	.	PUNCT
cana-4183	114	1	proof	proof	NOUN
cana-4183	114	2	:	:	PUNCT
cana-4183	114	3	consider	consider	VERB
cana-4183	114	4	the	the	DET
cana-4183	114	5	star	star	NOUN
cana-4183	114	6	graph	graph	NOUN
cana-4183	114	7	(	(	PUNCT
cana-4183	114	8	k1,n	k1,n	PROPN
cana-4183	114	9	)	)	PUNCT
cana-4183	114	10	with	with	ADP
cana-4183	114	11	vertices	vertex	NOUN
cana-4183	114	12	v1	v1	NOUN
cana-4183	114	13	,	,	PUNCT
cana-4183	114	14	v2	v2	PROPN
cana-4183	114	15	,	,	PUNCT
cana-4183	114	16	...	...	PUNCT
cana-4183	114	17	,	,	PUNCT
cana-4183	114	18	vn	vn	X
cana-4183	114	19	respectively	respectively	ADV
cana-4183	114	20	.	.	PUNCT
cana-4183	115	1	case	case	NOUN
cana-4183	115	2	1	1	NUM
cana-4183	115	3	:	:	PUNCT
cana-4183	115	4	for	for	ADP
cana-4183	115	5	2≤n≤8	2≤n≤8	NUM
cana-4183	115	6	assign	assign	NOUN
cana-4183	115	7	u=1	u=1	PROPN
cana-4183	115	8	,	,	PUNCT
cana-4183	115	9	v1=2,vi	v1=2,vi	X
cana-4183	116	1	=	=	SYM
cana-4183	116	2	2i-1	2i-1	PROPN
cana-4183	116	3	for	for	ADP
cana-4183	116	4	2≤i≤8	2≤i≤8	NUM
cana-4183	116	5	.	.	PUNCT
cana-4183	117	1	case	case	NOUN
cana-4183	117	2	2	2	NUM
cana-4183	117	3	:	:	PUNCT
cana-4183	117	4	for	for	ADP
cana-4183	117	5	9≤n≤15	9≤n≤15	NUM
cana-4183	117	6	assign	assign	VERB
cana-4183	117	7	u=1	u=1	NOUN
cana-4183	117	8	,	,	PUNCT
cana-4183	117	9	v1=2	v1=2	PROPN
cana-4183	117	10	and	and	CCONJ
cana-4183	117	11	for	for	ADP
cana-4183	117	12	vi	vi	NOUN
cana-4183	117	13	increase	increase	NOUN
cana-4183	117	14	systematically	systematically	ADV
cana-4183	117	15	to	to	PART
cana-4183	117	16	ensure	ensure	VERB
cana-4183	117	17	unique	unique	ADJ
cana-4183	117	18	values	value	NOUN
cana-4183	117	19	.	.	PUNCT
cana-4183	118	1	case	case	NOUN
cana-4183	118	2	3	3	NUM
cana-4183	118	3	:	:	SYM
cana-4183	118	4	n>15	n>15	NUM
cana-4183	118	5	if	if	SCONJ
cana-4183	118	6	n>15	n>15	NUM
cana-4183	118	7	,	,	PUNCT
cana-4183	118	8	label	label	NOUN
cana-4183	118	9	u=1	u=1	X
cana-4183	118	10	and	and	CCONJ
cana-4183	118	11	vi=2i-3	vi=2i-3	PROPN
cana-4183	118	12	for	for	ADP
cana-4183	118	13	4≤i≤n	4≤i≤n	NUM
cana-4183	118	14	.	.	PUNCT
cana-4183	119	1	therefore	therefore	ADV
cana-4183	119	2	k1	k1	PROPN
cana-4183	119	3	,	,	PUNCT
cana-4183	119	4	n	n	PRON
cana-4183	119	5	is	be	AUX
cana-4183	119	6	not	not	PART
cana-4183	119	7	a	a	DET
cana-4183	119	8	stolarsky-3	stolarsky-3	NUM
cana-4183	119	9	mean	mean	NOUN
cana-4183	119	10	cordial	cordial	ADJ
cana-4183	119	11	for	for	ADP
cana-4183	119	12	all	all	DET
cana-4183	119	13	n>15	n>15	NOUN
cana-4183	119	14	.	.	PUNCT
cana-4183	120	1	from	from	ADP
cana-4183	120	2	case	case	NOUN
cana-4183	120	3	1,2,3,we	1,2,3,we	NUM
cana-4183	120	4	conclude	conclude	VERB
cana-4183	120	5	that	that	SCONJ
cana-4183	120	6	k1	k1	NOUN
cana-4183	120	7	,	,	PUNCT
cana-4183	120	8	n	n	X
cana-4183	120	9	is	be	AUX
cana-4183	120	10	stolarsky-3	stolarsky-3	NUM
cana-4183	120	11	mean	mean	VERB
cana-4183	120	12	cordial	cordial	ADJ
cana-4183	120	13	if	if	SCONJ
cana-4183	120	14	n≤15	n≤15	PROPN
cana-4183	120	15	the	the	DET
cana-4183	120	16	stolarsky-3	stolarsky-3	PROPN
cana-4183	120	17	mean	mean	ADJ
cana-4183	120	18	cordial	cordial	ADJ
cana-4183	120	19	labeling	labeling	NOUN
cana-4183	120	20	of	of	ADP
cana-4183	120	21	the	the	DET
cana-4183	120	22	star	star	NOUN
cana-4183	120	23	graph	graph	NOUN
cana-4183	120	24	(	(	PUNCT
cana-4183	120	25	sn	sn	PROPN
cana-4183	120	26	)	)	PUNCT
cana-4183	120	27	is	be	AUX
cana-4183	120	28	illustrated	illustrate	VERB
cana-4183	120	29	in	in	ADP
cana-4183	120	30	figure	figure	NOUN
cana-4183	120	31	3	3	NUM
cana-4183	120	32	.	.	PUNCT
cana-4183	121	1	mean	mean	VERB
cana-4183	121	2	cordial	cordial	ADJ
cana-4183	121	3	labeling	labeling	NOUN
cana-4183	121	4	:	:	PUNCT
cana-4183	121	5	only	only	ADV
cana-4183	121	6	works	work	VERB
cana-4183	121	7	when	when	SCONJ
cana-4183	121	8	n	n	X
cana-4183	121	9	<	<	X
cana-4183	121	10	3	3	NUM
cana-4183	121	11	.	.	PUNCT
cana-4183	122	1	stolarsky-3	stolarsky-3	PRON
cana-4183	122	2	mean	mean	VERB
cana-4183	122	3	labeling	labeling	NOUN
cana-4183	122	4	:	:	PUNCT
cana-4183	122	5	works	work	VERB
cana-4183	122	6	when	when	SCONJ
cana-4183	122	7	n	n	X
cana-4183	122	8	<	<	X
cana-4183	122	9	16	16	NUM
cana-4183	122	10	,	,	PUNCT
cana-4183	122	11	but	but	CCONJ
cana-4183	122	12	not	not	PART
cana-4183	122	13	for	for	ADP
cana-4183	122	14	larger	large	ADJ
cana-4183	122	15	.	.	PUNCT
cana-4183	123	1	stolarsky-3	stolarsky-3	NUM
cana-4183	123	2	mean	mean	VERB
cana-4183	123	3	cordial	cordial	ADJ
cana-4183	123	4	labeling	labeling	NOUN
cana-4183	123	5	:	:	PUNCT
cana-4183	123	6	works	work	VERB
cana-4183	123	7	for	for	ADP
cana-4183	123	8	any	any	DET
cana-4183	123	9	n.	n.	NOUN
cana-4183	123	10	the	the	DET
cana-4183	123	11	stolarsky-3	stolarsky-3	PROPN
cana-4183	123	12	mean	mean	ADJ
cana-4183	123	13	cordial	cordial	ADJ
cana-4183	123	14	labeling	labeling	NOUN
cana-4183	123	15	is	be	AUX
cana-4183	123	16	the	the	DET
cana-4183	123	17	best	good	ADJ
cana-4183	123	18	option	option	NOUN
cana-4183	123	19	for	for	ADP
cana-4183	123	20	star	star	NOUN
cana-4183	123	21	graphs	graph	NOUN
cana-4183	123	22	,	,	PUNCT
cana-4183	123	23	as	as	SCONJ
cana-4183	123	24	it	it	PRON
cana-4183	123	25	works	work	VERB
cana-4183	123	26	no	no	ADV
cana-4183	123	27	matter	matter	ADV
cana-4183	123	28	how	how	SCONJ
cana-4183	123	29	many	many	ADJ
cana-4183	123	30	vertices	vertice	VERB
cana-4183	123	31	the	the	DET
cana-4183	123	32	graph	graph	NOUN
cana-4183	123	33	has	have	VERB
cana-4183	123	34	.	.	PUNCT
cana-4183	124	1	the	the	DET
cana-4183	124	2	other	other	ADJ
cana-4183	124	3	two	two	NUM
cana-4183	124	4	methods	method	NOUN
cana-4183	124	5	only	only	ADV
cana-4183	124	6	work	work	VERB
cana-4183	124	7	for	for	ADP
cana-4183	124	8	smaller	small	ADJ
cana-4183	124	9	graphs	graph	NOUN
cana-4183	124	10	.	.	PUNCT
cana-4183	125	1	wheel	wheel	NOUN
cana-4183	125	2	and	and	CCONJ
cana-4183	125	3	path	path	NOUN
cana-4183	125	4	graph	graph	NOUN
cana-4183	125	5	wnpm	wnpm	PROPN
cana-4183	125	6	theorem	theorem	VERB
cana-4183	125	7	3.5	3.5	NUM
cana-4183	125	8	:	:	PUNCT
cana-4183	125	9	the	the	DET
cana-4183	125	10	wheel	wheel	NOUN
cana-4183	125	11	graph	graph	NOUN
cana-4183	125	12	wn	wn	VERB
cana-4183	125	13	connected	connect	VERB
cana-4183	125	14	with	with	ADP
cana-4183	125	15	a	a	DET
cana-4183	125	16	path	path	NOUN
cana-4183	125	17	graph	graph	NOUN
cana-4183	125	18	pm(denoted	pm(denote	VERB
cana-4183	125	19	as	as	ADP
cana-4183	125	20	wnpm	wnpm	PROPN
cana-4183	125	21	)	)	PUNCT
cana-4183	125	22	is	be	AUX
cana-4183	125	23	stolarsky	stolarsky	ADJ
cana-4183	125	24	3	3	NUM
cana-4183	125	25	mean	mean	VERB
cana-4183	125	26	cordial	cordial	ADJ
cana-4183	125	27	labeling	labeling	NOUN
cana-4183	125	28	for	for	ADP
cana-4183	125	29	any	any	DET
cana-4183	125	30	n.	n.	NOUN
cana-4183	125	31	proof	proof	NOUN
cana-4183	125	32	:	:	PUNCT
cana-4183	125	33	consider	consider	VERB
cana-4183	125	34	the	the	DET
cana-4183	125	35	graph	graph	NOUN
cana-4183	125	36	wnpm	wnpm	PROPN
cana-4183	125	37	,	,	PUNCT
cana-4183	125	38	which	which	PRON
cana-4183	125	39	consists	consist	VERB
cana-4183	125	40	of	of	ADP
cana-4183	125	41	the	the	DET
cana-4183	125	42	wheel	wheel	NOUN
cana-4183	125	43	graph	graph	NOUN
cana-4183	125	44	wn	wn	PROPN
cana-4183	125	45	connected	connect	VERB
cana-4183	125	46	to	to	ADP
cana-4183	125	47	a	a	DET
cana-4183	125	48	path	path	NOUN
cana-4183	125	49	graph	graph	NOUN
cana-4183	125	50	pm	pm	NOUN
cana-4183	125	51	.	.	PUNCT
cana-4183	126	1	the	the	DET
cana-4183	126	2	wheel	wheel	NOUN
cana-4183	126	3	graph	graph	NOUN
cana-4183	126	4	wn	wn	PROPN
cana-4183	126	5	has	have	VERB
cana-4183	126	6	a	a	DET
cana-4183	126	7	cycle	cycle	NOUN
cana-4183	126	8	cn	cn	NOUN
cana-4183	126	9	with	with	ADP
cana-4183	126	10	the	the	DET
cana-4183	126	11	vertices	vertex	NOUN
cana-4183	126	12	u1,u2,	u1,u2,	NUM
cana-4183	126	13	…	…	SYM
cana-4183	126	14	,un	,un	PUNCT
cana-4183	126	15	and	and	CCONJ
cana-4183	126	16	a	a	DET
cana-4183	126	17	central	central	ADJ
cana-4183	126	18	vertex	vertex	NOUN
cana-4183	126	19	u	u	NOUN
cana-4183	126	20	connected	connect	VERB
cana-4183	126	21	to	to	ADP
cana-4183	126	22	all	all	DET
cana-4183	126	23	other	other	ADJ
cana-4183	126	24	vertices	vertex	NOUN
cana-4183	126	25	in	in	ADP
cana-4183	126	26	the	the	DET
cana-4183	126	27	cycle.the	cycle.the	DET
cana-4183	126	28	path	path	NOUN
cana-4183	126	29	graph	graph	NOUN
cana-4183	126	30	pm	pm	NOUN
cana-4183	126	31	consists	consist	VERB
cana-4183	126	32	of	of	ADP
cana-4183	126	33	vertices	vertex	NOUN
cana-4183	126	34	v1,v2,	v1,v2,	NOUN
cana-4183	126	35	…	…	SYM
cana-4183	126	36	,vn	,vn	PUNCT
cana-4183	126	37	.	.	PUNCT
cana-4183	127	1	case	case	NOUN
cana-4183	127	2	1	1	NUM
cana-4183	127	3	:	:	PUNCT
cana-4183	127	4	n+m≡0(mod3	n+m≡0(mod3	NOUN
cana-4183	127	5	)	)	PUNCT
cana-4183	127	6	let	let	VERB
cana-4183	127	7	n+m=3t	n+m=3t	PROPN
cana-4183	127	8	,	,	PUNCT
cana-4183	127	9	where	where	SCONJ
cana-4183	127	10	t	t	PROPN
cana-4183	127	11	is	be	AUX
cana-4183	127	12	an	an	DET
cana-4183	127	13	integer	integer	NOUN
cana-4183	127	14	.	.	PUNCT
cana-4183	128	1	vf(0)=vf(1)=vf(2)=t	vf(0)=vf(1)=vf(2)=t	PROPN
cana-4183	128	2	,	,	PUNCT
cana-4183	128	3	ef(0)=ef(1)=ef(2)=t	ef(0)=ef(1)=ef(2)=t	PROPN
cana-4183	128	4	.	.	PUNCT
cana-4183	129	1	hence	hence	ADV
cana-4183	129	2	it	it	PRON
cana-4183	129	3	is	be	AUX
cana-4183	129	4	stolarsky-3	stolarsky-3	NUM
cana-4183	129	5	mean	mean	PROPN
cana-4183	129	6	cordial	cordial	ADJ
cana-4183	129	7	.	.	PUNCT
cana-4183	130	1	case	case	NOUN
cana-4183	130	2	2	2	NUM
cana-4183	130	3	:	:	PUNCT
cana-4183	130	4	n+m≡1(mod3	n+m≡1(mod3	NOUN
cana-4183	130	5	)	)	PUNCT
cana-4183	130	6	let	let	VERB
cana-4183	130	7	n+m=3t+1,where	n+m=3t+1,where	ADV
cana-4183	130	8	t	t	PROPN
cana-4183	130	9	is	be	AUX
cana-4183	130	10	an	an	DET
cana-4183	130	11	integer	integer	NOUN
cana-4183	130	12	.	.	PUNCT
cana-4183	131	1	vf(0)+vf(2)=t	vf(0)+vf(2)=t	NOUN
cana-4183	131	2	,	,	PUNCT
cana-4183	131	3	vf(1)=t+1,ef(0)=ef(1)=ef(2)=t	vf(1)=t+1,ef(0)=ef(1)=ef(2)=t	PROPN
cana-4183	131	4	.	.	PUNCT
cana-4183	132	1	hence	hence	ADV
cana-4183	132	2	it	it	PRON
cana-4183	132	3	is	be	AUX
cana-4183	132	4	stolarsky-3mean	stolarsky-3mean	ADJ
cana-4183	132	5	cordial	cordial	ADJ
cana-4183	132	6	.	.	PUNCT
cana-4183	133	1	communications	communication	NOUN
cana-4183	133	2	on	on	ADP
cana-4183	133	3	applied	apply	VERB
cana-4183	133	4	nonlinear	nonlinear	ADJ
cana-4183	133	5	analysis	analysis	NOUN
cana-4183	133	6	issn	issn	NOUN
cana-4183	133	7	:	:	PUNCT
cana-4183	133	8	1074	1074	NUM
cana-4183	133	9	-	-	PUNCT
cana-4183	133	10	133x	133x	NUM
cana-4183	133	11	vol	vol	NOUN
cana-4183	133	12	32	32	NUM
cana-4183	133	13	no	no	NOUN
cana-4183	133	14	.	.	PUNCT
cana-4183	134	1	9s	9s	NUM
cana-4183	134	2	(	(	PUNCT
cana-4183	134	3	2025	2025	NUM
cana-4183	134	4	)	)	PUNCT
cana-4183	134	5	1510	1510	NUM
cana-4183	134	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4183	135	1	case3	case3	PROPN
cana-4183	135	2	:	:	PUNCT
cana-4183	135	3	n+m≡2(mod3	n+m≡2(mod3	NOUN
cana-4183	135	4	)	)	PUNCT
cana-4183	135	5	let	let	VERB
cana-4183	135	6	n+m=3t+2,where	n+m=3t+2,where	ADV
cana-4183	135	7	t	t	PROPN
cana-4183	135	8	is	be	AUX
cana-4183	135	9	an	an	DET
cana-4183	135	10	integer	integer	NOUN
cana-4183	135	11	.	.	PUNCT
cana-4183	136	1	vf(0)=vf(2)=t+1,vf(1)=t	vf(0)=vf(2)=t+1,vf(1)=t	NOUN
cana-4183	136	2	,	,	PUNCT
cana-4183	136	3	ef(0)=ef(2)=t+1,ef(1)=t	ef(0)=ef(2)=t+1,ef(1)=t	NOUN
cana-4183	136	4	.	.	PUNCT
cana-4183	137	1	hence	hence	ADV
cana-4183	137	2	it	it	PRON
cana-4183	137	3	is	be	AUX
cana-4183	137	4	stolarsky-3	stolarsky-3	NUM
cana-4183	137	5	mean	mean	PROPN
cana-4183	137	6	cordial	cordial	ADJ
cana-4183	137	7	.	.	PUNCT
cana-4183	138	1	in	in	ADP
cana-4183	138	2	all	all	DET
cana-4183	138	3	cases	case	NOUN
cana-4183	138	4	,	,	PUNCT
cana-4183	138	5	the	the	DET
cana-4183	138	6	graph	graph	NOUN
cana-4183	138	7	satisfies	satisfy	VERB
cana-4183	138	8	the	the	DET
cana-4183	138	9	stolarsky-3	stolarsky-3	PROPN
cana-4183	138	10	mean	mean	ADJ
cana-4183	138	11	cordail	cordail	NOUN
cana-4183	138	12	labeling	labeling	NOUN
cana-4183	138	13	.	.	PUNCT
cana-4183	139	1	hence	hence	ADV
cana-4183	139	2	the	the	DET
cana-4183	139	3	graph	graph	NOUN
cana-4183	139	4	wnpm	wnpm	PROPN
cana-4183	139	5	is	be	AUX
cana-4183	139	6	stolarsky-3	stolarsky-3	NUM
cana-4183	139	7	mean	mean	PROPN
cana-4183	139	8	cordial	cordial	ADJ
cana-4183	139	9	for	for	ADP
cana-4183	139	10	any	any	DET
cana-4183	139	11	n.	n.	NOUN
cana-4183	139	12	the	the	DET
cana-4183	139	13	stolarsky-3	stolarsky-3	PROPN
cana-4183	139	14	mean	mean	ADJ
cana-4183	139	15	cordial	cordial	ADJ
cana-4183	139	16	labeling	labeling	NOUN
cana-4183	139	17	of	of	ADP
cana-4183	139	18	the	the	DET
cana-4183	139	19	wheel	wheel	NOUN
cana-4183	139	20	and	and	CCONJ
cana-4183	139	21	path	path	NOUN
cana-4183	139	22	graph	graph	NOUN
cana-4183	139	23	(	(	PUNCT
cana-4183	139	24	wnpm	wnpm	PROPN
cana-4183	139	25	)	)	PUNCT
cana-4183	139	26	is	be	AUX
cana-4183	139	27	illustrated	illustrate	VERB
cana-4183	139	28	in	in	ADP
cana-4183	139	29	figure	figure	NOUN
cana-4183	139	30	4	4	NUM
cana-4183	139	31	.	.	PUNCT
cana-4183	140	1	mean	mean	VERB
cana-4183	140	2	cordial	cordial	ADJ
cana-4183	140	3	labeling	labeling	NOUN
cana-4183	140	4	works	work	VERB
cana-4183	140	5	for	for	ADP
cana-4183	140	6	any	any	DET
cana-4183	140	7	n.stolarsky-3	n.stolarsky-3	PROPN
cana-4183	140	8	mean	mean	ADJ
cana-4183	140	9	labeling	labeling	NOUN
cana-4183	140	10	does	do	AUX
cana-4183	140	11	not	not	PART
cana-4183	140	12	work	work	VERB
cana-4183	140	13	.	.	PUNCT
cana-4183	141	1	stolarsky-3	stolarsky-3	PRON
cana-4183	141	2	mean	mean	VERB
cana-4183	141	3	cordial	cordial	ADJ
cana-4183	141	4	labeling	labeling	NOUN
cana-4183	141	5	works	work	VERB
cana-4183	141	6	for	for	ADP
cana-4183	141	7	any	any	DET
cana-4183	141	8	n.	n.	NOUN
cana-4183	141	9	combining	combine	VERB
cana-4183	141	10	a	a	DET
cana-4183	141	11	wheel	wheel	NOUN
cana-4183	141	12	and	and	CCONJ
cana-4183	141	13	a	a	DET
cana-4183	141	14	path	path	NOUN
cana-4183	141	15	makes	make	VERB
cana-4183	141	16	stolarsky-3	stolarsky-3	PRON
cana-4183	141	17	mean	mean	VERB
cana-4183	141	18	labeling	labeling	NOUN
cana-4183	141	19	fail	fail	ADJ
cana-4183	141	20	,	,	PUNCT
cana-4183	141	21	but	but	CCONJ
cana-4183	141	22	the	the	DET
cana-4183	141	23	other	other	ADJ
cana-4183	141	24	two	two	NUM
cana-4183	141	25	methods	method	NOUN
cana-4183	141	26	can	can	AUX
cana-4183	141	27	handle	handle	VERB
cana-4183	141	28	this	this	DET
cana-4183	141	29	graph	graph	NOUN
cana-4183	141	30	type(table	type(table	PROPN
cana-4183	141	31	1	1	NUM
cana-4183	141	32	)	)	PUNCT
cana-4183	141	33	.	.	PUNCT
cana-4183	142	1	this	this	DET
cana-4183	142	2	comparative	comparative	ADJ
cana-4183	142	3	analysis	analysis	NOUN
cana-4183	142	4	highlights	highlight	NOUN
cana-4183	142	5	how	how	SCONJ
cana-4183	142	6	different	different	ADJ
cana-4183	142	7	graph	graph	NOUN
cana-4183	142	8	structures	structure	NOUN
cana-4183	142	9	interact	interact	VERB
cana-4183	142	10	with	with	ADP
cana-4183	142	11	various	various	ADJ
cana-4183	142	12	labeling	labeling	NOUN
cana-4183	142	13	schemes	scheme	NOUN
cana-4183	142	14	,	,	PUNCT
cana-4183	142	15	providing	provide	VERB
cana-4183	142	16	insights	insight	NOUN
cana-4183	142	17	into	into	ADP
cana-4183	142	18	their	their	PRON
cana-4183	142	19	mathematical	mathematical	ADJ
cana-4183	142	20	properties	property	NOUN
cana-4183	142	21	and	and	CCONJ
cana-4183	142	22	practical	practical	ADJ
cana-4183	142	23	applications	application	NOUN
cana-4183	142	24	in	in	ADP
cana-4183	142	25	graph	graph	NOUN
cana-4183	142	26	theory	theory	NOUN
cana-4183	142	27	.	.	PUNCT
cana-4183	143	1	4	4	X
cana-4183	143	2	.	.	X
cana-4183	143	3	conclusion	conclusion	VERB
cana-4183	143	4	different	different	ADJ
cana-4183	143	5	patterns	pattern	NOUN
cana-4183	143	6	emerge	emerge	VERB
cana-4183	143	7	when	when	SCONJ
cana-4183	143	8	different	different	ADJ
cana-4183	143	9	graph	graph	NOUN
cana-4183	143	10	architectures	architecture	NOUN
cana-4183	143	11	are	be	AUX
cana-4183	143	12	analyzed	analyze	VERB
cana-4183	143	13	for	for	ADP
cana-4183	143	14	compatibility	compatibility	NOUN
cana-4183	143	15	with	with	ADP
cana-4183	143	16	mean	mean	ADJ
cana-4183	143	17	cordial	cordial	ADJ
cana-4183	143	18	labeling	labeling	NOUN
cana-4183	143	19	,	,	PUNCT
cana-4183	143	20	stolarsky-3	stolarsky-3	PROPN
cana-4183	143	21	mean	mean	VERB
cana-4183	143	22	labeling	labeling	NOUN
cana-4183	143	23	,	,	PUNCT
cana-4183	143	24	and	and	CCONJ
cana-4183	143	25	stolarsky-3	stolarsky-3	NUM
cana-4183	143	26	mean	mean	VERB
cana-4183	143	27	cordial	cordial	ADJ
cana-4183	143	28	labeling	labeling	NOUN
cana-4183	143	29	.	.	PUNCT
cana-4183	144	1	the	the	DET
cana-4183	144	2	versatility	versatility	NOUN
cana-4183	144	3	of	of	ADP
cana-4183	144	4	path	path	NOUN
cana-4183	144	5	graphs	graph	NOUN
cana-4183	144	6	(	(	PUNCT
cana-4183	144	7	pn	pn	NOUN
cana-4183	144	8	)	)	PUNCT
cana-4183	144	9	is	be	AUX
cana-4183	144	10	demonstrated	demonstrate	VERB
cana-4183	144	11	by	by	ADP
cana-4183	144	12	their	their	PRON
cana-4183	144	13	support	support	NOUN
cana-4183	144	14	for	for	ADP
cana-4183	144	15	all	all	DET
cana-4183	144	16	three	three	NUM
cana-4183	144	17	labeling	labeling	NOUN
cana-4183	144	18	techniques	technique	NOUN
cana-4183	144	19	.	.	PUNCT
cana-4183	145	1	cycle	cycle	NOUN
cana-4183	145	2	graphs	graph	NOUN
cana-4183	145	3	only	only	ADV
cana-4183	145	4	face	face	VERB
cana-4183	145	5	issues	issue	NOUN
cana-4183	145	6	for	for	ADP
cana-4183	145	7	multiples	multiple	NOUN
cana-4183	145	8	of	of	ADP
cana-4183	145	9	3	3	NUM
cana-4183	145	10	with	with	ADP
cana-4183	145	11	mean	mean	PROPN
cana-4183	145	12	cordial	cordial	ADJ
cana-4183	145	13	and	and	CCONJ
cana-4183	145	14	stolarsky-3	stolarsky-3	NUM
cana-4183	145	15	mean	mean	ADJ
cana-4183	145	16	cordial	cordial	ADJ
cana-4183	145	17	labeling	labeling	NOUN
cana-4183	145	18	.	.	PUNCT
cana-4183	146	1	wheel	wheel	NOUN
cana-4183	146	2	graphs	graph	NOUN
cana-4183	146	3	can	can	AUX
cana-4183	146	4	not	not	PART
cana-4183	146	5	be	be	AUX
cana-4183	146	6	labeled	label	VERB
cana-4183	146	7	by	by	ADP
cana-4183	146	8	any	any	DET
cana-4183	146	9	method	method	NOUN
cana-4183	146	10	due	due	ADP
cana-4183	146	11	to	to	ADP
cana-4183	146	12	their	their	PRON
cana-4183	146	13	complex	complex	ADJ
cana-4183	146	14	structure	structure	NOUN
cana-4183	146	15	.	.	PUNCT
cana-4183	147	1	star	star	NOUN
cana-4183	147	2	graphs	graph	NOUN
cana-4183	147	3	are	be	AUX
cana-4183	147	4	best	well	ADV
cana-4183	147	5	labeled	label	VERB
cana-4183	147	6	with	with	ADP
cana-4183	147	7	stolarsky-3	stolarsky-3	PROPN
cana-4183	147	8	mean	mean	ADJ
cana-4183	147	9	cordial	cordial	ADJ
cana-4183	147	10	labeling	labeling	NOUN
cana-4183	147	11	,	,	PUNCT
cana-4183	147	12	which	which	PRON
cana-4183	147	13	works	work	VERB
cana-4183	147	14	for	for	ADP
cana-4183	147	15	all	all	PRON
cana-4183	147	16	.	.	PUNCT
cana-4183	148	1	combined	combine	VERB
cana-4183	148	2	wheel	wheel	NOUN
cana-4183	148	3	and	and	CCONJ
cana-4183	148	4	path	path	NOUN
cana-4183	148	5	graphs	graph	NOUN
cana-4183	148	6	are	be	AUX
cana-4183	148	7	compatible	compatible	ADJ
cana-4183	148	8	with	with	ADP
cana-4183	148	9	mean	mean	PROPN
cana-4183	148	10	cordial	cordial	ADJ
cana-4183	148	11	and	and	CCONJ
cana-4183	148	12	stolarsky-3	stolarsky-3	NUM
cana-4183	148	13	mean	mean	ADJ
cana-4183	148	14	cordial	cordial	ADJ
cana-4183	148	15	labeling	labeling	NOUN
cana-4183	148	16	.	.	PUNCT
cana-4183	149	1	in	in	ADP
cana-4183	149	2	summary	summary	NOUN
cana-4183	149	3	,	,	PUNCT
cana-4183	149	4	stolarsky-3	stolarsky-3	PROPN
cana-4183	149	5	mean	mean	VERB
cana-4183	149	6	cordial	cordial	ADJ
cana-4183	149	7	labeling	labeling	NOUN
cana-4183	149	8	is	be	AUX
cana-4183	149	9	the	the	DET
cana-4183	149	10	most	most	ADV
cana-4183	149	11	versatile	versatile	ADJ
cana-4183	149	12	method	method	NOUN
cana-4183	149	13	,	,	PUNCT
cana-4183	149	14	but	but	CCONJ
cana-4183	149	15	wheel	wheel	NOUN
cana-4183	149	16	graphs	graph	NOUN
cana-4183	149	17	remain	remain	VERB
cana-4183	149	18	a	a	DET
cana-4183	149	19	challenge	challenge	NOUN
cana-4183	149	20	for	for	ADP
cana-4183	149	21	all	all	PRON
cana-4183	149	22	.	.	PUNCT
cana-4183	150	1	these	these	DET
cana-4183	150	2	findings	finding	NOUN
cana-4183	150	3	support	support	VERB
cana-4183	150	4	specific	specific	ADJ
cana-4183	150	5	applications	application	NOUN
cana-4183	150	6	by	by	ADP
cana-4183	150	7	highlighting	highlight	VERB
cana-4183	150	8	the	the	DET
cana-4183	150	9	significance	significance	NOUN
cana-4183	150	10	of	of	ADP
cana-4183	150	11	network	network	NOUN
cana-4183	150	12	topology	topology	NOUN
cana-4183	150	13	in	in	ADP
cana-4183	150	14	assessing	assess	VERB
cana-4183	150	15	labeling	labeling	NOUN
cana-4183	150	16	feasibility	feasibility	NOUN
cana-4183	150	17	.	.	PUNCT
cana-4183	151	1	references	reference	NOUN
cana-4183	151	2	1	1	NUM
cana-4183	151	3	.	.	PUNCT
cana-4183	151	4	harary	harary	PROPN
cana-4183	151	5	f.	f.	PROPN
cana-4183	151	6	graph	graph	PROPN
cana-4183	151	7	theory	theory	PROPN
cana-4183	151	8	.	.	PUNCT
cana-4183	152	1	addison	addison	PROPN
cana-4183	152	2	wesley	wesley	PROPN
cana-4183	152	3	;	;	PUNCT
cana-4183	152	4	1969	1969	NUM
cana-4183	152	5	.	.	X
cana-4183	153	1	2	2	X
cana-4183	153	2	.	.	X
cana-4183	153	3	gallian	gallian	PROPN
cana-4183	153	4	ja	ja	PROPN
cana-4183	153	5	.	.	PUNCT
cana-4183	154	1	a	a	DET
cana-4183	154	2	dynamic	dynamic	ADJ
cana-4183	154	3	survey	survey	NOUN
cana-4183	154	4	of	of	ADP
cana-4183	154	5	graph	graph	NOUN
cana-4183	154	6	labeling	labeling	NOUN
cana-4183	154	7	.	.	PUNCT
cana-4183	155	1	electronic	electronic	ADJ
cana-4183	155	2	journal	journal	NOUN
cana-4183	155	3	of	of	ADP
cana-4183	155	4	combinatorics	combinatoric	NOUN
cana-4183	155	5	2022	2022	NUM
cana-4183	155	6	.	.	PUNCT
cana-4183	156	1	3	3	X
cana-4183	156	2	.	.	X
cana-4183	156	3	cahit	cahit	ADJ
cana-4183	156	4	i.	i.	PROPN
cana-4183	156	5	cordial	cordial	ADJ
cana-4183	156	6	graphs	graph	NOUN
cana-4183	156	7	:	:	PUNCT
cana-4183	156	8	a	a	DET
cana-4183	156	9	weaker	weak	ADJ
cana-4183	156	10	version	version	NOUN
cana-4183	156	11	of	of	ADP
cana-4183	156	12	graceful	graceful	ADJ
cana-4183	156	13	and	and	CCONJ
cana-4183	156	14	harmonious	harmonious	ADJ
cana-4183	156	15	graphs	graph	NOUN
cana-4183	156	16	.	.	PUNCT
cana-4183	157	1	ars	ar	NOUN
cana-4183	157	2	combinatoria	combinatoria	PROPN
cana-4183	157	3	1987	1987	NUM
cana-4183	157	4	;	;	PUNCT
cana-4183	157	5	23	23	NUM
cana-4183	157	6	suppl	suppl	ADJ
cana-4183	157	7	3	3	NUM
cana-4183	157	8	:	:	PUNCT
cana-4183	157	9	201	201	NUM
cana-4183	157	10	-	-	SYM
cana-4183	157	11	208	208	NUM
cana-4183	157	12	.	.	PUNCT
cana-4183	157	13	4	4	NUM
cana-4183	157	14	.	.	NUM
cana-4183	157	15	dhanalakshmi	dhanalakshmi	PROPN
cana-4183	157	16	s	s	PROPN
cana-4183	157	17	,	,	PUNCT
cana-4183	157	18	parvathi	parvathi	PROPN
cana-4183	157	19	n.	n.	PROPN
cana-4183	157	20	mean	mean	PROPN
cana-4183	157	21	square	square	ADJ
cana-4183	157	22	cordial	cordial	ADJ
cana-4183	157	23	labeling	labeling	NOUN
cana-4183	157	24	on	on	ADP
cana-4183	157	25	star	star	NOUN
cana-4183	157	26	related	relate	VERB
cana-4183	157	27	graphs	graph	NOUN
cana-4183	157	28	.	.	PUNCT
cana-4183	158	1	j.phys	j.phy	NOUN
cana-4183	158	2	.	.	PUNCT
cana-4183	158	3	:	:	PUNCT
cana-4183	158	4	conf	conf	PROPN
cana-4183	158	5	.	.	PUNCT
cana-4183	158	6	ser	ser	PROPN
cana-4183	158	7	.	.	PROPN
cana-4183	158	8	2019	2019	NUM
cana-4183	158	9	:	:	PUNCT
cana-4183	158	10	1377	1377	NUM
cana-4183	158	11	.	.	X
cana-4183	159	1	5	5	X
cana-4183	159	2	.	.	X
cana-4183	159	3	ponraj	ponraj	ADJ
cana-4183	159	4	r	r	PROPN
cana-4183	159	5	,	,	PUNCT
cana-4183	159	6	sivakumar	sivakumar	PROPN
cana-4183	159	7	m	m	PROPN
cana-4183	159	8	,	,	PUNCT
cana-4183	159	9	sundaram	sundaram	PROPN
cana-4183	159	10	m.	m.	NOUN
cana-4183	159	11	mean	mean	VERB
cana-4183	159	12	cordial	cordial	ADJ
cana-4183	159	13	labeling	labeling	NOUN
cana-4183	159	14	of	of	ADP
cana-4183	159	15	graphs	graph	NOUN
cana-4183	159	16	.	.	PUNCT
cana-4183	160	1	open	open	ADJ
cana-4183	160	2	journal	journal	NOUN
cana-4183	160	3	of	of	ADP
cana-4183	160	4	discrete	discrete	ADJ
cana-4183	160	5	mathematics	mathematic	NOUN
cana-4183	160	6	2012	2012	NUM
cana-4183	160	7	;	;	PUNCT
cana-4183	160	8	2	2	NUM
cana-4183	160	9	:	:	SYM
cana-4183	160	10	145	145	NUM
cana-4183	160	11	-	-	SYM
cana-4183	160	12	148	148	NUM
cana-4183	160	13	.	.	PUNCT
cana-4183	161	1	6	6	NUM
cana-4183	161	2	.	.	X
cana-4183	161	3	sandhya	sandhya	PROPN
cana-4183	161	4	ss	ss	PROPN
cana-4183	161	5	,	,	PUNCT
cana-4183	161	6	somasundaram	somasundaram	PROPN
cana-4183	161	7	s	s	PROPN
cana-4183	161	8	,	,	PUNCT
cana-4183	161	9	ponraj	ponraj	ADJ
cana-4183	161	10	r.	r.	PROPN
cana-4183	161	11	harmonic	harmonic	PROPN
cana-4183	161	12	mean	mean	VERB
cana-4183	161	13	labeling	labeling	NOUN
cana-4183	161	14	of	of	ADP
cana-4183	161	15	some	some	DET
cana-4183	161	16	cycle	cycle	NOUN
cana-4183	161	17	related	relate	VERB
cana-4183	161	18	graphs	graph	NOUN
cana-4183	161	19	.	.	PUNCT
cana-4183	162	1	int	int	NOUN
cana-4183	162	2	.	.	PUNCT
cana-4183	163	1	journal	journal	PROPN
cana-4183	163	2	of	of	ADP
cana-4183	163	3	math	math	NOUN
cana-4183	163	4	.	.	PUNCT
cana-4183	164	1	analysis	analysis	NOUN
cana-4183	164	2	2012	2012	NUM
cana-4183	164	3	;	;	PUNCT
cana-4183	164	4	6	6	NUM
cana-4183	164	5	suppl	suppl	ADJ
cana-4183	164	6	40	40	NUM
cana-4183	164	7	:	:	SYM
cana-4183	164	8	19972005	19972005	NUM
cana-4183	164	9	.	.	PUNCT
cana-4183	165	1	7	7	X
cana-4183	165	2	.	.	X
cana-4183	165	3	sharma	sharma	PROPN
cana-4183	165	4	k	k	PROPN
cana-4183	165	5	,	,	PUNCT
cana-4183	165	6	tripathi	tripathi	PROPN
cana-4183	165	7	a.	a.	NOUN
cana-4183	165	8	advancements	advancement	NOUN
cana-4183	165	9	in	in	ADP
cana-4183	165	10	mean	mean	NOUN
cana-4183	165	11	and	and	CCONJ
cana-4183	165	12	harmonic	harmonic	ADJ
cana-4183	165	13	mean	mean	ADJ
cana-4183	165	14	labeling	labeling	NOUN
cana-4183	165	15	of	of	ADP
cana-4183	165	16	graphs	graph	NOUN
cana-4183	165	17	.	.	PUNCT
cana-4183	166	1	international	international	ADJ
cana-4183	166	2	journal	journal	NOUN
cana-4183	166	3	of	of	ADP
cana-4183	166	4	graph	graph	NOUN
cana-4183	166	5	theory	theory	NOUN
cana-4183	166	6	and	and	CCONJ
cana-4183	166	7	applications	application	NOUN
cana-4183	166	8	2023	2023	NUM
cana-4183	166	9	;	;	PUNCT
cana-4183	166	10	8	8	NUM
cana-4183	166	11	suppl	suppl	NOUN
cana-4183	166	12	2	2	NUM
cana-4183	166	13	:	:	SYM
cana-4183	166	14	145158	145158	NUM
cana-4183	166	15	.	.	PUNCT
cana-4183	167	1	communications	communication	NOUN
cana-4183	167	2	on	on	ADP
cana-4183	167	3	applied	apply	VERB
cana-4183	167	4	nonlinear	nonlinear	ADJ
cana-4183	167	5	analysis	analysis	NOUN
cana-4183	167	6	issn	issn	NOUN
cana-4183	167	7	:	:	PUNCT
cana-4183	167	8	1074	1074	NUM
cana-4183	167	9	-	-	PUNCT
cana-4183	167	10	133x	133x	NUM
cana-4183	167	11	vol	vol	NOUN
cana-4183	167	12	32	32	NUM
cana-4183	167	13	no	no	NOUN
cana-4183	167	14	.	.	PUNCT
cana-4183	168	1	9s	9s	NUM
cana-4183	168	2	(	(	PUNCT
cana-4183	168	3	2025	2025	NUM
cana-4183	168	4	)	)	PUNCT
cana-4183	168	5	1511	1511	NUM
cana-4183	168	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4183	168	7	8	8	NUM
cana-4183	168	8	.	.	PUNCT
cana-4183	168	9	muthukumar	muthukumar	PROPN
cana-4183	168	10	s	s	PROPN
cana-4183	168	11	,	,	PUNCT
cana-4183	168	12	ramaswamy	ramaswamy	ADJ
cana-4183	168	13	g.	g.	PROPN
cana-4183	168	14	stolarsky	stolarsky	PROPN
cana-4183	168	15	mean	mean	NOUN
cana-4183	168	16	-	-	PUNCT
cana-4183	168	17	based	base	VERB
cana-4183	168	18	graph	graph	NOUN
cana-4183	168	19	labeling	labeling	NOUN
cana-4183	168	20	:	:	PUNCT
cana-4183	168	21	new	new	ADJ
cana-4183	168	22	perspectives	perspective	NOUN
cana-4183	168	23	and	and	CCONJ
cana-4183	168	24	applications	application	NOUN
cana-4183	168	25	.	.	PUNCT
cana-4183	169	1	journal	journal	NOUN
cana-4183	169	2	of	of	ADP
cana-4183	169	3	discrete	discrete	ADJ
cana-4183	169	4	mathematical	mathematical	ADJ
cana-4183	169	5	sciences	sciences	PROPN
cana-4183	169	6	&	&	CCONJ
cana-4183	169	7	cryptography	cryptography	NOUN
cana-4183	169	8	2023	2023	NUM
cana-4183	169	9	,	,	PUNCT
cana-4183	169	10	26	26	NUM
cana-4183	169	11	suppl	suppl	ADJ
cana-4183	169	12	3	3	NUM
cana-4183	169	13	:	:	SYM
cana-4183	169	14	565578	565578	NUM
cana-4183	169	15	.	.	PUNCT
cana-4183	170	1	9	9	X
cana-4183	170	2	.	.	X
cana-4183	170	3	ravi	ravi	PROPN
cana-4183	170	4	v	v	PROPN
cana-4183	170	5	,	,	PUNCT
cana-4183	170	6	kumar	kumar	PROPN
cana-4183	170	7	ps	ps	PROPN
cana-4183	170	8	.	.	PROPN
cana-4183	171	1	graph	graph	NOUN
cana-4183	171	2	labeling	labeling	NOUN
cana-4183	171	3	using	use	VERB
cana-4183	171	4	stolarsky	stolarsky	PROPN
cana-4183	171	5	means	mean	NOUN
cana-4183	171	6	:	:	PUNCT
cana-4183	171	7	a	a	DET
cana-4183	171	8	novel	novel	ADJ
cana-4183	171	9	approach	approach	NOUN
cana-4183	171	10	for	for	ADP
cana-4183	171	11	complex	complex	ADJ
cana-4183	171	12	networks	network	NOUN
cana-4183	171	13	.	.	PUNCT
cana-4183	172	1	complexity	complexity	NOUN
cana-4183	172	2	2023	2023	NUM
cana-4183	172	3	;	;	PUNCT
cana-4183	172	4	1	1	NUM
cana-4183	172	5	-	-	SYM
cana-4183	172	6	12	12	NUM
cana-4183	172	7	.	.	PUNCT
cana-4183	172	8	10	10	NUM
cana-4183	172	9	.	.	X
cana-4183	173	1	patil	patil	PROPN
cana-4183	173	2	as	as	ADP
cana-4183	173	3	,	,	PUNCT
cana-4183	173	4	singh	singh	ADJ
cana-4183	173	5	rk	rk	NOUN
cana-4183	173	6	.	.	PROPN
cana-4183	173	7	harmonic	harmonic	PROPN
cana-4183	173	8	and	and	CCONJ
cana-4183	173	9	stolarsky	stolarsky	NOUN
cana-4183	173	10	mean	mean	VERB
cana-4183	173	11	labeling	labeling	NOUN
cana-4183	173	12	in	in	ADP
cana-4183	173	13	graph	graph	NOUN
cana-4183	173	14	theory	theory	NOUN
cana-4183	173	15	:	:	PUNCT
cana-4183	173	16	a	a	DET
cana-4183	173	17	comparative	comparative	ADJ
cana-4183	173	18	study	study	NOUN
cana-4183	173	19	.	.	PUNCT
cana-4183	174	1	mathematics	mathematic	NOUN
cana-4183	174	2	and	and	CCONJ
cana-4183	174	3	computers	computer	NOUN
cana-4183	174	4	in	in	ADP
cana-4183	174	5	simulation	simulation	NOUN
cana-4183	174	6	2022	2022	NUM
cana-4183	174	7	;	;	PUNCT
cana-4183	174	8	195	195	NUM
cana-4183	174	9	:	:	SYM
cana-4183	174	10	215	215	NUM
cana-4183	174	11	-	-	SYM
cana-4183	174	12	229	229	NUM
cana-4183	174	13	.	.	PUNCT
cana-4183	174	14	11	11	NUM
cana-4183	174	15	.	.	PUNCT
cana-4183	175	1	gupta	gupta	PROPN
cana-4183	175	2	n	n	CCONJ
cana-4183	175	3	,	,	PUNCT
cana-4183	175	4	meena	meena	PROPN
cana-4183	175	5	p.	p.	PROPN
cana-4183	175	6	(	(	PUNCT
cana-4183	175	7	)	)	PUNCT
cana-4183	175	8	.	.	PUNCT
cana-4183	176	1	applications	application	NOUN
cana-4183	176	2	of	of	ADP
cana-4183	176	3	stolarsky	stolarsky	NOUN
cana-4183	176	4	mean	mean	VERB
cana-4183	176	5	in	in	ADP
cana-4183	176	6	graph	graph	NOUN
cana-4183	176	7	labeling	labeling	NOUN
cana-4183	176	8	:	:	PUNCT
cana-4183	176	9	emerging	emerge	VERB
cana-4183	176	10	trends	trend	NOUN
cana-4183	176	11	.	.	PUNCT
cana-4183	177	1	journal	journal	NOUN
cana-4183	177	2	of	of	ADP
cana-4183	177	3	applied	apply	VERB
cana-4183	177	4	mathematics	mathematic	NOUN
cana-4183	177	5	and	and	CCONJ
cana-4183	177	6	computing	computing	NOUN
cana-4183	177	7	2023	2023	NUM
cana-4183	177	8	;	;	PUNCT
cana-4183	177	9	71	71	NUM
cana-4183	177	10	suppl	suppl	ADJ
cana-4183	177	11	2	2	NUM
cana-4183	177	12	:	:	PUNCT
cana-4183	177	13	509	509	NUM
cana-4183	177	14	-	-	SYM
cana-4183	177	15	523	523	NUM
cana-4183	177	16	.	.	PUNCT
cana-4183	177	17	12	12	NUM
cana-4183	177	18	.	.	PUNCT
cana-4183	178	1	kavitha	kavitha	PROPN
cana-4183	178	2	s	s	PROPN
cana-4183	178	3	,	,	PUNCT
cana-4183	178	4	sandhya	sandhya	PROPN
cana-4183	178	5	ss	ss	PROPN
cana-4183	178	6	.	.	PROPN
cana-4183	178	7	(	(	PUNCT
cana-4183	178	8	)	)	PUNCT
cana-4183	178	9	.	.	PUNCT
cana-4183	179	1	exploring	explore	VERB
cana-4183	179	2	new	new	ADJ
cana-4183	179	3	horizons	horizon	NOUN
cana-4183	179	4	in	in	ADP
cana-4183	179	5	graph	graph	NOUN
cana-4183	179	6	labeling	labeling	NOUN
cana-4183	179	7	:	:	PUNCT
cana-4183	179	8	stolarsky-3	stolarsky-3	NUM
cana-4183	179	9	mean	mean	VERB
cana-4183	179	10	and	and	CCONJ
cana-4183	179	11	beyond	beyond	ADP
cana-4183	179	12	.	.	PUNCT
cana-4183	180	1	advances	advance	NOUN
cana-4183	180	2	in	in	ADP
cana-4183	180	3	graph	graph	NOUN
cana-4183	180	4	theory	theory	NOUN
cana-4183	180	5	2024	2024	NUM
cana-4183	180	6	;	;	PUNCT
cana-4183	180	7	45	45	NUM
cana-4183	180	8	suppl	suppl	ADJ
cana-4183	180	9	1	1	NUM
cana-4183	180	10	:	:	SYM
cana-4183	180	11	67	67	NUM
cana-4183	180	12	-	-	SYM
cana-4183	180	13	81	81	NUM
cana-4183	180	14	.	.	PUNCT
cana-4183	180	15	table	table	NOUN
cana-4183	180	16	1	1	NUM
cana-4183	180	17	.	.	PUNCT
cana-4183	180	18	comparative	comparative	ADJ
cana-4183	180	19	analyses	analysis	NOUN
cana-4183	180	20	of	of	ADP
cana-4183	180	21	3	3	NUM
cana-4183	180	22	different	different	ADJ
cana-4183	180	23	mean	mean	NOUN
cana-4183	180	24	labeling	labeling	NOUN
cana-4183	180	25	with	with	ADP
cana-4183	180	26	respect	respect	NOUN
cana-4183	180	27	to	to	ADP
cana-4183	180	28	various	various	ADJ
cana-4183	180	29	graphs	graph	NOUN
cana-4183	180	30	.	.	PUNCT
cana-4183	181	1	graph	graph	NOUN
cana-4183	181	2	type	type	NOUN
cana-4183	181	3	mean	mean	VERB
cana-4183	181	4	cordial	cordial	ADJ
cana-4183	181	5	labeling	labeling	NOUN
cana-4183	181	6	(	(	PUNCT
cana-4183	181	7	n	n	X
cana-4183	181	8	is	be	AUX
cana-4183	181	9	number	number	NOUN
cana-4183	181	10	of	of	ADP
cana-4183	181	11	vertices	vertex	NOUN
cana-4183	181	12	)	)	PUNCT
cana-4183	182	1	stolarsky-3	stolarsky-3	NUM
cana-4183	182	2	mean	mean	ADJ
cana-4183	182	3	labeling	labeling	NOUN
cana-4183	182	4	(	(	PUNCT
cana-4183	182	5	n	n	X
cana-4183	182	6	is	be	AUX
cana-4183	182	7	number	number	NOUN
cana-4183	182	8	of	of	ADP
cana-4183	182	9	vertices	vertex	NOUN
cana-4183	182	10	)	)	PUNCT
cana-4183	183	1	stolarsky-3	stolarsky-3	NUM
cana-4183	183	2	mean	mean	VERB
cana-4183	183	3	cordial	cordial	ADJ
cana-4183	183	4	labeling(n	labeling(n	NOUN
cana-4183	183	5	is	be	AUX
cana-4183	183	6	number	number	NOUN
cana-4183	183	7	of	of	ADP
cana-4183	183	8	vertices	vertex	NOUN
cana-4183	183	9	)	)	PUNCT
cana-4183	183	10	path	path	NOUN
cana-4183	183	11	pn	pn	NOUN
cana-4183	183	12	for	for	ADP
cana-4183	183	13	any	any	DET
cana-4183	183	14	n	n	NOUN
cana-4183	183	15	for	for	ADP
cana-4183	183	16	any	any	DET
cana-4183	183	17	n	n	NOUN
cana-4183	183	18	for	for	ADP
cana-4183	183	19	any	any	DET
cana-4183	183	20	n	n	DET
cana-4183	183	21	cycle	cycle	NOUN
cana-4183	183	22	cn	cn	PROPN
cana-4183	183	23	for	for	ADP
cana-4183	183	24	any	any	DET
cana-4183	183	25	n	n	CCONJ
cana-4183	183	26	,	,	PUNCT
cana-4183	183	27	except	except	SCONJ
cana-4183	183	28	n=3,6,9	n=3,6,9	NUM
cana-4183	183	29	..	..	PUNCT
cana-4183	183	30	for	for	ADP
cana-4183	183	31	any	any	DET
cana-4183	183	32	n	n	NOUN
cana-4183	183	33	for	for	ADP
cana-4183	183	34	any	any	DET
cana-4183	183	35	n	n	CCONJ
cana-4183	183	36	,	,	PUNCT
cana-4183	183	37	except	except	SCONJ
cana-4183	183	38	n=3,6,9	n=3,6,9	X
cana-4183	183	39	..	..	PUNCT
cana-4183	183	40	wheel	wheel	NOUN
cana-4183	184	1	wn	wn	INTJ
cana-4183	184	2	no	no	INTJ
cana-4183	184	3	no	no	INTJ
cana-4183	184	4	no	no	DET
cana-4183	184	5	star	star	NOUN
cana-4183	184	6	graph	graph	NOUN
cana-4183	184	7	k1,n	k1,n	PROPN
cana-4183	184	8	or	or	CCONJ
cana-4183	184	9	sn	sn	PROPN
cana-4183	184	10	n<3	n<3	NOUN
cana-4183	184	11	n<16	n<16	NOUN
cana-4183	184	12	for	for	ADP
cana-4183	184	13	any	any	DET
cana-4183	184	14	n	n	NOUN
cana-4183	184	15	wheel	wheel	NOUN
cana-4183	184	16	and	and	CCONJ
cana-4183	184	17	path	path	NOUN
cana-4183	184	18	graph	graph	NOUN
cana-4183	184	19	wnpm	wnpm	PROPN
cana-4183	184	20	for	for	ADP
cana-4183	184	21	any	any	DET
cana-4183	184	22	n	n	DET
cana-4183	184	23	no	no	NOUN
cana-4183	184	24	for	for	ADP
cana-4183	184	25	any	any	DET
cana-4183	184	26	n	n	DET
cana-4183	184	27	fig	fig	NOUN
cana-4183	184	28	.	.	PUNCT
cana-4183	185	1	1	1	X
cana-4183	185	2	.	.	PUNCT
cana-4183	186	1	stolarsky-3	stolarsky-3	PRON
cana-4183	186	2	mean	mean	VERB
cana-4183	186	3	cordial	cordial	ADJ
cana-4183	186	4	labeling	labeling	NOUN
cana-4183	186	5	of	of	ADP
cana-4183	186	6	path	path	NOUN
cana-4183	186	7	(	(	PUNCT
cana-4183	186	8	p10	p10	NOUN
cana-4183	186	9	➔	➔	PROPN
cana-4183	186	10	0000111222	0000111222	NUM
cana-4183	186	11	)	)	PUNCT
cana-4183	186	12	graph	graph	NOUN
cana-4183	186	13	fig	fig	NOUN
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cana-4183	187	2	.	.	X
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cana-4183	188	6	cycle	cycle	NOUN
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cana-4183	188	8	c11	c11	NOUN
cana-4183	188	9	➔	➔	PROPN
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cana-4183	188	11	)	)	PUNCT
cana-4183	188	12	graph	graph	NOUN
cana-4183	188	13	.	.	PUNCT
cana-4183	189	1	communications	communication	NOUN
cana-4183	189	2	on	on	ADP
cana-4183	189	3	applied	apply	VERB
cana-4183	189	4	nonlinear	nonlinear	ADJ
cana-4183	189	5	analysis	analysis	NOUN
cana-4183	189	6	issn	issn	NOUN
cana-4183	189	7	:	:	PUNCT
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cana-4183	189	9	-	-	PUNCT
cana-4183	189	10	133x	133x	NUM
cana-4183	189	11	vol	vol	NOUN
cana-4183	189	12	32	32	NUM
cana-4183	189	13	no	no	NOUN
cana-4183	189	14	.	.	PUNCT
cana-4183	190	1	9s	9s	NUM
cana-4183	190	2	(	(	PUNCT
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cana-4183	190	4	)	)	PUNCT
cana-4183	190	5	1512	1512	NUM
cana-4183	190	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4183	190	7	fig	fig	NOUN
cana-4183	190	8	.	.	PUNCT
cana-4183	191	1	3	3	X
cana-4183	191	2	.	.	X
cana-4183	192	1	stolarsky-3	stolarsky-3	PRON
cana-4183	192	2	mean	mean	VERB
cana-4183	192	3	cordial	cordial	ADJ
cana-4183	192	4	labeling	labeling	NOUN
cana-4183	192	5	of	of	ADP
cana-4183	192	6	star	star	NOUN
cana-4183	192	7	(	(	PUNCT
cana-4183	192	8	s16	s16	PROPN
cana-4183	192	9	➔	➔	PROPN
cana-4183	192	10	00000011111122222	00000011111122222	NUM
cana-4183	192	11	)	)	PUNCT
cana-4183	192	12	graph	graph	NOUN
cana-4183	192	13	fig.4	fig.4	PROPN
cana-4183	192	14	.	.	PUNCT
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cana-4183	193	2	mean	mean	VERB
cana-4183	193	3	cordial	cordial	ADJ
cana-4183	193	4	labeling	labeling	NOUN
cana-4183	193	5	of	of	ADP
cana-4183	193	6	wheel	wheel	NOUN
cana-4183	193	7	and	and	CCONJ
cana-4183	193	8	path	path	NOUN
cana-4183	193	9	graph	graph	NOUN
cana-4183	193	10	(	(	PUNCT
cana-4183	193	11	w9p6	w9p6	PROPN
cana-4183	193	12	➔	➔	PROPN
cana-4183	193	13	00000111211222	00000111211222	NUM
cana-4183	193	14	)	)	PUNCT
cana-4183	193	15	graph	graph	NOUN
cana-4183	193	16	.	.	PUNCT