id	sid	tid	token	lemma	pos
cana-4367	1	1	communications	communication	NOUN
cana-4367	1	2	on	on	ADP
cana-4367	1	3	applied	apply	VERB
cana-4367	1	4	nonlinear	nonlinear	ADJ
cana-4367	1	5	analysis	analysis	NOUN
cana-4367	1	6	issn	issn	NOUN
cana-4367	1	7	:	:	PUNCT
cana-4367	1	8	1074	1074	NUM
cana-4367	1	9	-	-	PUNCT
cana-4367	1	10	133x	133x	NUM
cana-4367	1	11	vol	vol	NOUN
cana-4367	1	12	32	32	NUM
cana-4367	1	13	no	no	NOUN
cana-4367	1	14	.	.	PUNCT
cana-4367	2	1	9s	9s	NUM
cana-4367	2	2	(	(	PUNCT
cana-4367	2	3	2025	2025	NUM
cana-4367	2	4	)	)	PUNCT
cana-4367	2	5	1919	1919	NUM
cana-4367	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4367	2	7	even	even	ADV
cana-4367	2	8	hamming	ham	VERB
cana-4367	2	9	distance	distance	NOUN
cana-4367	2	10	labeling	labeling	NOUN
cana-4367	2	11	of	of	ADP
cana-4367	2	12	some	some	DET
cana-4367	2	13	path	path	NOUN
cana-4367	2	14	related	relate	VERB
cana-4367	2	15	graphs	graph	NOUN
cana-4367	2	16	e.esakkiammal	e.esakkiammal	ADJ
cana-4367	2	17	1	1	NUM
cana-4367	2	18	,	,	PUNCT
cana-4367	2	19	k.thirusangu2	k.thirusangu2	PROPN
cana-4367	2	20	and	and	CCONJ
cana-4367	2	21	s.seethalakshmi3	s.seethalakshmi3	PROPN
cana-4367	2	22	1,2	1,2	NUM
cana-4367	2	23	department	department	NOUN
cana-4367	2	24	of	of	ADP
cana-4367	2	25	mathematics	mathematic	NOUN
cana-4367	2	26	,	,	PUNCT
cana-4367	2	27	s.i.v.e.t	s.i.v.e.t	NOUN
cana-4367	2	28	.	.	PUNCT
cana-4367	3	1	college	college	NOUN
cana-4367	3	2	,	,	PUNCT
cana-4367	3	3	gowrivakkam	gowrivakkam	NOUN
cana-4367	3	4	,	,	PUNCT
cana-4367	3	5	chennai	chennai	PROPN
cana-4367	3	6	,	,	PUNCT
cana-4367	3	7	india	india	PROPN
cana-4367	3	8	.	.	PROPN
cana-4367	3	9	3	3	NUM
cana-4367	3	10	department	department	NOUN
cana-4367	3	11	of	of	ADP
cana-4367	3	12	mathematics	mathematics	PROPN
cana-4367	3	13	,	,	PUNCT
cana-4367	3	14	r.v	r.v	PROPN
cana-4367	3	15	.	.	PROPN
cana-4367	3	16	govt	govt	PROPN
cana-4367	3	17	.	.	PUNCT
cana-4367	4	1	arts	arts	PROPN
cana-4367	4	2	college	college	PROPN
cana-4367	4	3	,	,	PUNCT
cana-4367	4	4	chengalpattu	chengalpattu	ADV
cana-4367	4	5	,	,	PUNCT
cana-4367	4	6	chennai	chennai	PROPN
cana-4367	4	7	,	,	PUNCT
cana-4367	4	8	india	india	PROPN
cana-4367	4	9	.	.	PUNCT
cana-4367	5	1	1esakkiammal2682@gmail.com.2kthirusangu@gmail.com,3seetha0687@gmail.com	1esakkiammal2682@gmail.com.2kthirusangu@gmail.com,3seetha0687@gmail.com	X
cana-4367	5	2	.	.	PUNCT
cana-4367	5	3	article	article	NOUN
cana-4367	5	4	history	history	NOUN
cana-4367	5	5	:	:	PUNCT
cana-4367	5	6	received	receive	VERB
cana-4367	5	7	:	:	PUNCT
cana-4367	5	8	12	12	NUM
cana-4367	5	9	-	-	SYM
cana-4367	5	10	01	01	NUM
cana-4367	5	11	-	-	PUNCT
cana-4367	5	12	2025	2025	NUM
cana-4367	5	13	revised	revise	VERB
cana-4367	5	14	:	:	PUNCT
cana-4367	5	15	15	15	NUM
cana-4367	5	16	-	-	NUM
cana-4367	5	17	02	02	NUM
cana-4367	5	18	-	-	PUNCT
cana-4367	5	19	2025	2025	NUM
cana-4367	5	20	accepted	accept	VERB
cana-4367	5	21	:	:	PUNCT
cana-4367	5	22	01	01	NUM
cana-4367	5	23	-	-	SYM
cana-4367	5	24	03	03	NUM
cana-4367	5	25	-	-	PUNCT
cana-4367	5	26	2025	2025	NUM
cana-4367	5	27	abstract	abstract	ADJ
cana-4367	5	28	hamming	hamming	NOUN
cana-4367	5	29	distance	distance	NOUN
cana-4367	5	30	is	be	AUX
cana-4367	5	31	used	use	VERB
cana-4367	5	32	in	in	ADP
cana-4367	5	33	error	error	NOUN
cana-4367	5	34	correction	correction	NOUN
cana-4367	5	35	while	while	SCONJ
cana-4367	5	36	transmitting	transmit	VERB
cana-4367	5	37	data	datum	NOUN
cana-4367	5	38	over	over	ADP
cana-4367	5	39	computer	computer	NOUN
cana-4367	5	40	networks	network	NOUN
cana-4367	5	41	.	.	PUNCT
cana-4367	6	1	in	in	ADP
cana-4367	6	2	this	this	DET
cana-4367	6	3	paper	paper	NOUN
cana-4367	6	4	,	,	PUNCT
cana-4367	6	5	it	it	PRON
cana-4367	6	6	is	be	AUX
cana-4367	6	7	shown	show	VERB
cana-4367	6	8	that	that	SCONJ
cana-4367	6	9	comb	comb	NOUN
cana-4367	6	10	graph	graph	NOUN
cana-4367	6	11	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	6	12	+	+	PROPN
cana-4367	6	13	,	,	PUNCT
cana-4367	6	14	twig	twig	PROPN
cana-4367	6	15	graph	graph	VERB
cana-4367	6	16	𝑇𝑊(𝑃𝑚	𝑇𝑊(𝑃𝑚	PROPN
cana-4367	6	17	)	)	PUNCT
cana-4367	6	18	,	,	PUNCT
cana-4367	6	19	centipede	centipede	NOUN
cana-4367	6	20	(	(	PUNCT
cana-4367	6	21	𝑚	𝑚	NOUN
cana-4367	6	22	,	,	PUNCT
cana-4367	6	23	2	2	NUM
cana-4367	6	24	)	)	PUNCT
cana-4367	6	25	graph	graph	NOUN
cana-4367	6	26	,	,	PUNCT
cana-4367	6	27	and	and	CCONJ
cana-4367	6	28	comb	comb	NOUN
cana-4367	6	29	product	product	NOUN
cana-4367	6	30	of	of	ADP
cana-4367	6	31	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	6	32	and	and	CCONJ
cana-4367	6	33	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	6	34	graph(𝑃𝑚	graph(𝑃𝑚	PROPN
cana-4367	6	35	⊳	⊳	PROPN
cana-4367	6	36	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	6	37	)	)	PUNCT
cana-4367	6	38	are	be	AUX
cana-4367	6	39	even	even	ADV
cana-4367	6	40	hamming	ham	VERB
cana-4367	6	41	distance	distance	NOUN
cana-4367	6	42	labeled	label	VERB
cana-4367	6	43	graphs	graph	NOUN
cana-4367	6	44	.	.	PUNCT
cana-4367	7	1	it	it	PRON
cana-4367	7	2	is	be	AUX
cana-4367	7	3	proved	prove	VERB
cana-4367	7	4	that	that	SCONJ
cana-4367	7	5	the	the	DET
cana-4367	7	6	even	even	ADV
cana-4367	7	7	hamming	hamming	NOUN
cana-4367	7	8	distance	distance	NOUN
cana-4367	7	9	number	number	NOUN
cana-4367	7	10	of	of	ADP
cana-4367	7	11	comb	comb	NOUN
cana-4367	7	12	graph	graph	NOUN
cana-4367	7	13	and	and	CCONJ
cana-4367	7	14	twig	twig	PROPN
cana-4367	7	15	graph	graph	NOUN
cana-4367	7	16	are	be	AUX
cana-4367	7	17	6	6	NUM
cana-4367	7	18	and	and	CCONJ
cana-4367	7	19	8	8	NUM
cana-4367	7	20	respectively	respectively	ADV
cana-4367	7	21	.	.	PUNCT
cana-4367	8	1	also	also	ADV
cana-4367	8	2	the	the	DET
cana-4367	8	3	even	even	ADV
cana-4367	8	4	hamming	hamming	NOUN
cana-4367	8	5	distance	distance	NOUN
cana-4367	8	6	number	number	NOUN
cana-4367	8	7	of	of	ADP
cana-4367	8	8	centipede	centipede	NOUN
cana-4367	8	9	graph	graph	NOUN
cana-4367	8	10	(	(	PUNCT
cana-4367	8	11	m,2	m,2	NUM
cana-4367	8	12	)	)	PUNCT
cana-4367	8	13	is	be	AUX
cana-4367	8	14	6	6	NUM
cana-4367	8	15	if	if	SCONJ
cana-4367	8	16	m=1	m=1	X
cana-4367	8	17	and	and	CCONJ
cana-4367	8	18	8	8	NUM
cana-4367	8	19	if	if	SCONJ
cana-4367	8	20	𝑚	𝑚	PROPN
cana-4367	8	21	>	>	X
cana-4367	8	22	1	1	NUM
cana-4367	8	23	and	and	CCONJ
cana-4367	8	24	for	for	ADP
cana-4367	8	25	the	the	DET
cana-4367	8	26	comb	comb	NOUN
cana-4367	8	27	product	product	NOUN
cana-4367	8	28	of	of	ADP
cana-4367	8	29	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	8	30	and	and	CCONJ
cana-4367	8	31	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	8	32	graph	graph	NOUN
cana-4367	8	33	is	be	AUX
cana-4367	8	34	4	4	NUM
cana-4367	8	35	if	if	SCONJ
cana-4367	8	36	𝑚	𝑚	NOUN
cana-4367	8	37	=	=	SYM
cana-4367	8	38	1	1	NUM
cana-4367	8	39	and	and	CCONJ
cana-4367	8	40	6	6	NUM
cana-4367	8	41	if	if	SCONJ
cana-4367	8	42	𝑚	𝑚	PROPN
cana-4367	8	43	>	>	X
cana-4367	8	44	1	1	NUM
cana-4367	8	45	are	be	AUX
cana-4367	8	46	obtained	obtain	VERB
cana-4367	8	47	.	.	PUNCT
cana-4367	9	1	this	this	DET
cana-4367	9	2	labeling	labeling	NOUN
cana-4367	9	3	is	be	AUX
cana-4367	9	4	applied	apply	VERB
cana-4367	9	5	in	in	ADP
cana-4367	9	6	cryptography	cryptography	NOUN
cana-4367	9	7	for	for	ADP
cana-4367	9	8	sharing	share	VERB
cana-4367	9	9	secret	secret	ADJ
cana-4367	9	10	messages	message	NOUN
cana-4367	9	11	.	.	PUNCT
cana-4367	10	1	keywords	keyword	NOUN
cana-4367	10	2	:	:	PUNCT
cana-4367	10	3	even	even	ADV
cana-4367	10	4	hamming	ham	VERB
cana-4367	10	5	distance	distance	NOUN
cana-4367	10	6	labeling	labeling	NOUN
cana-4367	10	7	,	,	PUNCT
cana-4367	10	8	comb	comb	NOUN
cana-4367	10	9	graph	graph	NOUN
cana-4367	10	10	,	,	PUNCT
cana-4367	10	11	twig	twig	PROPN
cana-4367	10	12	graph	graph	NOUN
cana-4367	10	13	,	,	PUNCT
cana-4367	10	14	centipede	centipede	NOUN
cana-4367	10	15	graph	graph	NOUN
cana-4367	10	16	and	and	CCONJ
cana-4367	10	17	comb	comb	VERB
cana-4367	10	18	product	product	NOUN
cana-4367	10	19	of	of	ADP
cana-4367	10	20	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	10	21	and	and	CCONJ
cana-4367	10	22	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	10	23	graph	graph	NOUN
cana-4367	10	24	.	.	PUNCT
cana-4367	11	1	1.introduction	1.introduction	NUM
cana-4367	11	2	let	let	VERB
cana-4367	11	3	g	g	NOUN
cana-4367	11	4	be	be	AUX
cana-4367	11	5	a	a	DET
cana-4367	11	6	graph	graph	NOUN
cana-4367	11	7	with	with	ADP
cana-4367	11	8	vertex	vertex	NOUN
cana-4367	11	9	set	set	VERB
cana-4367	11	10	v	v	NOUN
cana-4367	11	11	and	and	CCONJ
cana-4367	11	12	edge	edge	NOUN
cana-4367	11	13	set	set	VERB
cana-4367	11	14	e.	e.	PROPN
cana-4367	12	1	an	an	DET
cana-4367	12	2	alternating	alternate	VERB
cana-4367	12	3	sequence	sequence	NOUN
cana-4367	12	4	of	of	ADP
cana-4367	12	5	vertices	vertex	NOUN
cana-4367	12	6	and	and	CCONJ
cana-4367	12	7	edges	edge	NOUN
cana-4367	12	8	,	,	PUNCT
cana-4367	12	9	beginning	begin	VERB
cana-4367	12	10	and	and	CCONJ
cana-4367	12	11	ending	end	VERB
cana-4367	12	12	with	with	ADP
cana-4367	12	13	vertices	vertex	NOUN
cana-4367	12	14	is	be	AUX
cana-4367	12	15	called	call	VERB
cana-4367	12	16	a	a	DET
cana-4367	12	17	path	path	NOUN
cana-4367	12	18	graph[3	graph[3	X
cana-4367	12	19	]	]	PUNCT
cana-4367	12	20	.	.	PUNCT
cana-4367	13	1	a	a	DET
cana-4367	13	2	path	path	NOUN
cana-4367	13	3	graph	graph	NOUN
cana-4367	13	4	on	on	ADP
cana-4367	13	5	m+1	m+1	NUM
cana-4367	13	6	vertices	vertex	NOUN
cana-4367	13	7	is	be	AUX
cana-4367	13	8	denoted	denote	VERB
cana-4367	13	9	by	by	ADP
cana-4367	13	10	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	13	11	,	,	PUNCT
cana-4367	13	12	𝑚	𝑚	X
cana-4367	13	13	≥	≥	NUM
cana-4367	13	14	1	1	NUM
cana-4367	13	15	.	.	PUNCT
cana-4367	14	1	the	the	DET
cana-4367	14	2	corona	corona	NOUN
cana-4367	14	3	of	of	ADP
cana-4367	14	4	path	path	NOUN
cana-4367	14	5	graph	graph	NOUN
cana-4367	14	6	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	14	7	is	be	AUX
cana-4367	14	8	obtained	obtain	VERB
cana-4367	14	9	from	from	ADP
cana-4367	14	10	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	14	11	by	by	ADP
cana-4367	14	12	attaching	attach	VERB
cana-4367	14	13	a	a	DET
cana-4367	14	14	pendent	pendent	ADJ
cana-4367	14	15	vertex	vertex	NOUN
cana-4367	14	16	to	to	ADP
cana-4367	14	17	each	each	DET
cana-4367	14	18	vertex	vertex	NOUN
cana-4367	14	19	of	of	ADP
cana-4367	14	20	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	14	21	and	and	CCONJ
cana-4367	14	22	it	it	PRON
cana-4367	14	23	is	be	AUX
cana-4367	14	24	denoted	denote	VERB
cana-4367	14	25	by	by	ADP
cana-4367	14	26	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	14	27	+	+	PROPN
cana-4367	14	28	.	.	PUNCT
cana-4367	15	1	this	this	DET
cana-4367	15	2	graph	graph	NOUN
cana-4367	15	3	is	be	AUX
cana-4367	15	4	also	also	ADV
cana-4367	15	5	known	know	VERB
cana-4367	15	6	as	as	ADP
cana-4367	15	7	comb	comb	NOUN
cana-4367	15	8	graph[2	graph[2	NOUN
cana-4367	15	9	]	]	X
cana-4367	15	10	.	.	PUNCT
cana-4367	16	1	a	a	DET
cana-4367	16	2	twig	twig	PROPN
cana-4367	16	3	tw(𝑃𝑚	tw(𝑃𝑚	PROPN
cana-4367	16	4	)	)	PUNCT
cana-4367	16	5	,	,	PUNCT
cana-4367	16	6	𝑛	𝑛	DET
cana-4367	16	7	≥	≥	NUM
cana-4367	16	8	2	2	NUM
cana-4367	16	9	is	be	AUX
cana-4367	16	10	a	a	DET
cana-4367	16	11	graph	graph	NOUN
cana-4367	16	12	obtained	obtain	VERB
cana-4367	16	13	from	from	ADP
cana-4367	16	14	a	a	DET
cana-4367	16	15	path	path	NOUN
cana-4367	16	16	by	by	ADP
cana-4367	16	17	attaching	attach	VERB
cana-4367	16	18	exactly	exactly	ADV
cana-4367	16	19	two	two	NUM
cana-4367	16	20	pendant	pendant	ADJ
cana-4367	16	21	vertices	vertex	NOUN
cana-4367	16	22	to	to	ADP
cana-4367	16	23	each	each	DET
cana-4367	16	24	internal	internal	ADJ
cana-4367	16	25	vertices	vertex	NOUN
cana-4367	16	26	of	of	ADP
cana-4367	16	27	the	the	DET
cana-4367	16	28	path[1	path[1	NOUN
cana-4367	16	29	]	]	PUNCT
cana-4367	16	30	.	.	PUNCT
cana-4367	17	1	centipede	centipede	NOUN
cana-4367	17	2	graph	graph	NOUN
cana-4367	17	3	(	(	PUNCT
cana-4367	17	4	m,2	m,2	NUM
cana-4367	17	5	)	)	PUNCT
cana-4367	17	6	is	be	AUX
cana-4367	17	7	a	a	DET
cana-4367	17	8	graph	graph	NOUN
cana-4367	17	9	on	on	ADP
cana-4367	17	10	3n	3n	NUM
cana-4367	17	11	vertices	vertex	NOUN
cana-4367	17	12	obtained	obtain	VERB
cana-4367	17	13	by	by	ADP
cana-4367	17	14	joining	join	VERB
cana-4367	17	15	two	two	NUM
cana-4367	17	16	pendant	pendant	ADJ
cana-4367	17	17	edges	edge	NOUN
cana-4367	17	18	that	that	PRON
cana-4367	17	19	are	be	AUX
cana-4367	17	20	adjacent	adjacent	ADJ
cana-4367	17	21	in	in	ADP
cana-4367	17	22	each	each	DET
cana-4367	17	23	vertex	vertex	NOUN
cana-4367	17	24	of	of	ADP
cana-4367	17	25	a	a	DET
cana-4367	17	26	path[6].the	path[6].the	NOUN
cana-4367	17	27	comb	comb	NOUN
cana-4367	17	28	product	product	NOUN
cana-4367	17	29	between	between	ADP
cana-4367	17	30	graphs	graph	NOUN
cana-4367	17	31	pm	pm	NOUN
cana-4367	17	32	and	and	CCONJ
cana-4367	17	33	pr	pr	NOUN
cana-4367	17	34	is	be	AUX
cana-4367	17	35	a	a	DET
cana-4367	17	36	graph	graph	NOUN
cana-4367	17	37	obtained	obtain	VERB
cana-4367	17	38	by	by	ADP
cana-4367	17	39	taking	take	VERB
cana-4367	17	40	one	one	NUM
cana-4367	17	41	copy	copy	NOUN
cana-4367	17	42	of	of	ADP
cana-4367	17	43	pm	pm	NOUN
cana-4367	17	44	and	and	CCONJ
cana-4367	17	45	|v(pm)|	|v(pm)|	ADJ
cana-4367	17	46	copies	copy	NOUN
cana-4367	17	47	of	of	ADP
cana-4367	17	48	pr	pr	NOUN
cana-4367	17	49	and	and	CCONJ
cana-4367	17	50	joining	join	VERB
cana-4367	17	51	each	each	DET
cana-4367	17	52	copy	copy	NOUN
cana-4367	17	53	of	of	ADP
cana-4367	17	54	pr	pr	NOUN
cana-4367	17	55	with	with	ADP
cana-4367	17	56	each	each	DET
cana-4367	17	57	vertex	vertex	NOUN
cana-4367	17	58	of	of	ADP
cana-4367	17	59	pm	pm	NOUN
cana-4367	17	60	and	and	CCONJ
cana-4367	17	61	this	this	DET
cana-4367	17	62	graph	graph	NOUN
cana-4367	17	63	is	be	AUX
cana-4367	17	64	denoted	denote	VERB
cana-4367	17	65	by	by	ADP
cana-4367	17	66	pm	pm	NOUN
cana-4367	17	67	⊳	⊳	NOUN
cana-4367	17	68	pr	pr	NOUN
cana-4367	18	1	[	[	X
cana-4367	18	2	4	4	NUM
cana-4367	18	3	]	]	PUNCT
cana-4367	18	4	.	.	PUNCT
cana-4367	19	1	2	2	X
cana-4367	19	2	.	.	X
cana-4367	19	3	even	even	ADV
cana-4367	19	4	hamming	ham	VERB
cana-4367	19	5	distance	distance	NOUN
cana-4367	19	6	labelling	labelling	NOUN
cana-4367	19	7	of	of	ADP
cana-4367	19	8	some	some	DET
cana-4367	19	9	graphs	graph	NOUN
cana-4367	19	10	2.1	2.1	NUM
cana-4367	19	11	.	.	PUNCT
cana-4367	20	1	definition	definition	NOUN
cana-4367	20	2	:	:	PUNCT
cana-4367	20	3	let	let	VERB
cana-4367	20	4	g	g	PROPN
cana-4367	20	5	=	=	SYM
cana-4367	20	6	(	(	PUNCT
cana-4367	20	7	v	v	NOUN
cana-4367	20	8	,	,	PUNCT
cana-4367	20	9	e	e	NOUN
cana-4367	20	10	)	)	PUNCT
cana-4367	20	11	be	be	AUX
cana-4367	20	12	a	a	DET
cana-4367	20	13	graph	graph	NOUN
cana-4367	20	14	.	.	PUNCT
cana-4367	21	1	a	a	DET
cana-4367	21	2	function	function	NOUN
cana-4367	21	3	𝑓:𝑉	𝑓:𝑉	PROPN
cana-4367	21	4	→	→	PUNCT
cana-4367	21	5	𝑁	𝑁	PROPN
cana-4367	21	6	∪	∪	ADJ
cana-4367	21	7	{	{	PUNCT
cana-4367	21	8	0	0	NUM
cana-4367	21	9	}	}	PUNCT
cana-4367	21	10	is	be	AUX
cana-4367	21	11	said	say	VERB
cana-4367	21	12	to	to	PART
cana-4367	21	13	be	be	AUX
cana-4367	21	14	an	an	DET
cana-4367	21	15	even	even	ADV
cana-4367	21	16	hamming	ham	VERB
cana-4367	21	17	distance	distance	NOUN
cana-4367	21	18	labeling	labeling	NOUN
cana-4367	21	19	if	if	SCONJ
cana-4367	21	20	there	there	PRON
cana-4367	21	21	exist	exist	VERB
cana-4367	21	22	an	an	DET
cana-4367	21	23	induced	induced	ADJ
cana-4367	21	24	function	function	NOUN
cana-4367	21	25	𝑓∗	𝑓∗	NOUN
cana-4367	21	26	∶	∶	PROPN
cana-4367	21	27	𝐸	𝐸	PROPN
cana-4367	21	28	→	→	SYM
cana-4367	21	29	{	{	PUNCT
cana-4367	21	30	2,4,6	2,4,6	NUM
cana-4367	21	31	,	,	PUNCT
cana-4367	21	32	…	…	PUNCT
cana-4367	21	33	,	,	PUNCT
cana-4367	21	34	n	n	CCONJ
cana-4367	21	35	}	}	PUNCT
cana-4367	21	36	such	such	ADJ
cana-4367	21	37	that	that	PRON
cana-4367	21	38	for	for	ADP
cana-4367	21	39	every	every	DET
cana-4367	21	40	𝑢𝑣	𝑢𝑣	PROPN
cana-4367	21	41	∈	∈	PROPN
cana-4367	21	42	𝐸	𝐸	PROPN
cana-4367	21	43	,	,	PUNCT
cana-4367	21	44	𝑓∗(𝑢𝑣	𝑓∗(𝑢𝑣	PROPN
cana-4367	21	45	)	)	PUNCT
cana-4367	21	46	=	=	SYM
cana-4367	21	47	ℎ𝑑([𝑓(𝑢)]2	ℎ𝑑([𝑓(𝑢)]2	ADJ
cana-4367	21	48	,	,	PUNCT
cana-4367	21	49	[	[	X
cana-4367	21	50	𝑓(𝑣)]2	𝑓(𝑣)]2	X
cana-4367	21	51	)	)	PUNCT
cana-4367	21	52	satisfying	satisfy	VERB
cana-4367	21	53	the	the	DET
cana-4367	21	54	following	follow	VERB
cana-4367	21	55	conditions	condition	NOUN
cana-4367	21	56	:	:	PUNCT
cana-4367	21	57	(	(	PUNCT
cana-4367	21	58	i	i	NOUN
cana-4367	21	59	)	)	PUNCT
cana-4367	21	60	for	for	ADP
cana-4367	21	61	every	every	DET
cana-4367	21	62	vertex	vertex	NOUN
cana-4367	21	63	𝑣	𝑣	ADP
cana-4367	21	64	𝜖	𝜖	PROPN
cana-4367	21	65	𝑉	𝑉	PROPN
cana-4367	21	66	,	,	PUNCT
cana-4367	21	67	the	the	DET
cana-4367	21	68	set	set	NOUN
cana-4367	21	69	of	of	ADP
cana-4367	21	70	all	all	DET
cana-4367	21	71	edges	edge	NOUN
cana-4367	21	72	incident	incident	NOUN
cana-4367	21	73	with	with	ADP
cana-4367	21	74	𝑣	𝑣	PART
cana-4367	21	75	receive	receive	VERB
cana-4367	21	76	distinct	distinct	NOUN
cana-4367	21	77	even	even	ADV
cana-4367	21	78	labels	label	NOUN
cana-4367	21	79	.	.	PUNCT
cana-4367	22	1	(	(	PUNCT
cana-4367	22	2	ii	ii	NOUN
cana-4367	22	3	)	)	PUNCT
cana-4367	22	4	for	for	ADP
cana-4367	22	5	every	every	DET
cana-4367	22	6	edge	edge	NOUN
cana-4367	22	7	𝑒	𝑒	ADP
cana-4367	22	8	=	=	SYM
cana-4367	22	9	𝑢𝑣	𝑢𝑣	PROPN
cana-4367	22	10	,	,	PUNCT
cana-4367	22	11	the	the	DET
cana-4367	22	12	adjacent	adjacent	ADJ
cana-4367	22	13	vertices	vertice	VERB
cana-4367	22	14	𝑢	𝑢	PRON
cana-4367	22	15	and	and	CCONJ
cana-4367	22	16	𝑣	𝑣	PART
cana-4367	22	17	receive	receive	VERB
cana-4367	22	18	distinct	distinct	ADJ
cana-4367	22	19	labels	label	NOUN
cana-4367	22	20	.	.	PUNCT
cana-4367	23	1	a	a	DET
cana-4367	23	2	graph	graph	NOUN
cana-4367	23	3	which	which	PRON
cana-4367	23	4	admits	admit	VERB
cana-4367	23	5	even	even	ADV
cana-4367	23	6	hamming	ham	VERB
cana-4367	23	7	distance	distance	NOUN
cana-4367	23	8	labeling	labeling	NOUN
cana-4367	23	9	is	be	AUX
cana-4367	23	10	called	call	VERB
cana-4367	23	11	even	even	ADV
cana-4367	23	12	hamming	ham	VERB
cana-4367	23	13	distance	distance	NOUN
cana-4367	23	14	graph	graph	NOUN
cana-4367	23	15	.	.	PUNCT
cana-4367	24	1	the	the	DET
cana-4367	24	2	even	even	ADV
cana-4367	24	3	hamming	hamming	NOUN
cana-4367	24	4	distance	distance	NOUN
cana-4367	24	5	number	number	NOUN
cana-4367	24	6	of	of	ADP
cana-4367	24	7	a	a	DET
cana-4367	24	8	graph	graph	NOUN
cana-4367	24	9	g	g	NOUN
cana-4367	24	10	is	be	AUX
cana-4367	24	11	the	the	DET
cana-4367	24	12	least	least	ADV
cana-4367	24	13	positive	positive	ADJ
cana-4367	24	14	integer	integer	NOUN
cana-4367	24	15	n	n	CCONJ
cana-4367	24	16	such	such	ADJ
cana-4367	24	17	that	that	SCONJ
cana-4367	24	18	2𝑛	2𝑛	PROPN
cana-4367	24	19	−	−	PROPN
cana-4367	24	20	1	1	NUM
cana-4367	24	21	≥	≥	NOUN
cana-4367	24	22	𝑘	𝑘	NOUN
cana-4367	24	23	,	,	PUNCT
cana-4367	24	24	where	where	SCONJ
cana-4367	24	25	𝑘	𝑘	PROPN
cana-4367	24	26	=	=	X
cana-4367	24	27	max	max	PROPN
cana-4367	24	28	{	{	PUNCT
cana-4367	24	29	𝑓(𝑣)/𝑣	𝑓(𝑣)/𝑣	PROPN
cana-4367	24	30	∈	∈	PROPN
cana-4367	24	31	𝑉	𝑉	PROPN
cana-4367	24	32	}	}	PUNCT
cana-4367	24	33	and	and	CCONJ
cana-4367	24	34	it	it	PRON
cana-4367	24	35	is	be	AUX
cana-4367	24	36	denoted	denote	VERB
cana-4367	24	37	by	by	ADP
cana-4367	24	38	ηℎ𝑑	ηℎ𝑑	NOUN
cana-4367	24	39	′′	′′	PROPN
cana-4367	24	40	(	(	PUNCT
cana-4367	24	41	g	g	NOUN
cana-4367	24	42	)	)	PUNCT
cana-4367	24	43	.	.	PUNCT
cana-4367	25	1	mailto:esakkiammal2682@gmail.com	mailto:esakkiammal2682@gmail.com	X
cana-4367	25	2	mailto:kthirusangu@gmail.com	mailto:kthirusangu@gmail.com	NOUN
cana-4367	25	3	mailto:seetha0687@gmail.com	mailto:seetha0687@gmail.com	ADJ
cana-4367	25	4	communications	communication	NOUN
cana-4367	25	5	on	on	ADP
cana-4367	25	6	applied	apply	VERB
cana-4367	25	7	nonlinear	nonlinear	ADJ
cana-4367	25	8	analysis	analysis	NOUN
cana-4367	25	9	issn	issn	NOUN
cana-4367	25	10	:	:	PUNCT
cana-4367	25	11	1074	1074	NUM
cana-4367	25	12	-	-	PUNCT
cana-4367	25	13	133x	133x	NUM
cana-4367	25	14	vol	vol	NOUN
cana-4367	25	15	32	32	NUM
cana-4367	25	16	no	no	NOUN
cana-4367	25	17	.	.	PUNCT
cana-4367	26	1	9s	9s	NUM
cana-4367	26	2	(	(	PUNCT
cana-4367	26	3	2025	2025	NUM
cana-4367	26	4	)	)	PUNCT
cana-4367	26	5	1920	1920	NUM
cana-4367	27	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4367	27	2	we	we	PRON
cana-4367	27	3	have	have	AUX
cana-4367	27	4	proved	prove	VERB
cana-4367	27	5	the	the	DET
cana-4367	27	6	existence	existence	NOUN
cana-4367	27	7	of	of	ADP
cana-4367	27	8	even	even	ADV
cana-4367	27	9	hamming	ham	VERB
cana-4367	27	10	distance	distance	NOUN
cana-4367	27	11	labeling	labeling	NOUN
cana-4367	27	12	of	of	ADP
cana-4367	27	13	cycle	cycle	NOUN
cana-4367	27	14	related	relate	VERB
cana-4367	27	15	graphs	graph	NOUN
cana-4367	27	16	in	in	ADP
cana-4367	27	17	[	[	X
cana-4367	27	18	5	5	NUM
cana-4367	27	19	]	]	PUNCT
cana-4367	27	20	.	.	PUNCT
cana-4367	28	1	here	here	ADV
cana-4367	28	2	,	,	PUNCT
cana-4367	28	3	we	we	PRON
cana-4367	28	4	have	have	AUX
cana-4367	28	5	given	give	VERB
cana-4367	28	6	the	the	DET
cana-4367	28	7	proof	proof	NOUN
cana-4367	28	8	for	for	ADP
cana-4367	28	9	existence	existence	NOUN
cana-4367	28	10	of	of	ADP
cana-4367	28	11	even	even	ADV
cana-4367	28	12	hamming	ham	VERB
cana-4367	28	13	distance	distance	NOUN
cana-4367	28	14	labeling	labeling	NOUN
cana-4367	28	15	of	of	ADP
cana-4367	28	16	path	path	NOUN
cana-4367	28	17	related	relate	VERB
cana-4367	28	18	graphs	graph	NOUN
cana-4367	28	19	.	.	PUNCT
cana-4367	29	1	we	we	PRON
cana-4367	29	2	propose	propose	VERB
cana-4367	29	3	the	the	DET
cana-4367	29	4	following	follow	VERB
cana-4367	29	5	algorithms	algorithm	NOUN
cana-4367	29	6	only	only	ADV
cana-4367	29	7	to	to	PART
cana-4367	29	8	label	label	VERB
cana-4367	29	9	the	the	DET
cana-4367	29	10	vertices	vertex	NOUN
cana-4367	29	11	of	of	ADP
cana-4367	29	12	the	the	DET
cana-4367	29	13	graph	graph	NOUN
cana-4367	29	14	.	.	PUNCT
cana-4367	30	1	algorithm	algorithm	NOUN
cana-4367	30	2	2.1.1	2.1.1	NUM
cana-4367	30	3	:	:	PUNCT
cana-4367	30	4	even	even	ADV
cana-4367	30	5	hamming	ham	VERB
cana-4367	30	6	distance	distance	NOUN
cana-4367	30	7	labeling	labeling	NOUN
cana-4367	30	8	of	of	ADP
cana-4367	30	9	comb	comb	NOUN
cana-4367	30	10	graph	graph	NOUN
cana-4367	30	11	input	input	NOUN
cana-4367	30	12	:	:	PUNCT
cana-4367	30	13	vertices	vertex	NOUN
cana-4367	30	14	of	of	ADP
cana-4367	30	15	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	30	16	+	+	CCONJ
cana-4367	30	17	graph	graph	NOUN
cana-4367	30	18	,	,	PUNCT
cana-4367	30	19	𝑚	𝑚	X
cana-4367	30	20	≥	≥	NUM
cana-4367	30	21	1	1	NUM
cana-4367	30	22	𝑉	𝑉	PROPN
cana-4367	30	23	←	←	PROPN
cana-4367	30	24	{	{	PUNCT
cana-4367	30	25	𝑣𝑖	𝑣𝑖	NOUN
cana-4367	30	26	,	,	PUNCT
cana-4367	30	27	𝑣𝑖	𝑣𝑖	ADV
cana-4367	30	28	′/0	′/0	NUM
cana-4367	30	29	≤	≤	NOUN
cana-4367	30	30	𝑖	𝑖	PUNCT
cana-4367	30	31	≤	≤	NUM
cana-4367	30	32	𝑚	𝑚	NOUN
cana-4367	30	33	}	}	PUNCT
cana-4367	30	34	𝑣0	𝑣0	PROPN
cana-4367	30	35	←	←	PROPN
cana-4367	30	36	0	0	NUM
cana-4367	30	37	;	;	PUNCT
cana-4367	30	38	𝑣0	𝑣0	PROPN
cana-4367	30	39	′	′	PROPN
cana-4367	30	40	←	←	PROPN
cana-4367	30	41	15	15	NUM
cana-4367	30	42	;	;	PUNCT
cana-4367	30	43	for	for	ADP
cana-4367	30	44	0	0	NUM
cana-4367	30	45	≤	≤	NUM
cana-4367	30	46	𝑖	𝑖	SYM
cana-4367	30	47	≤	≤	NOUN
cana-4367	30	48	𝑚	𝑚	ADP
cana-4367	30	49	𝑣𝑖	𝑣𝑖	ADP
cana-4367	30	50	←	←	PROPN
cana-4367	30	51	{	{	PUNCT
cana-4367	30	52	3	3	NUM
cana-4367	30	53	𝑖𝑓	𝑖𝑓	ADP
cana-4367	30	54	𝑖	𝑖	SYM
cana-4367	30	55	≡	≡	PROPN
cana-4367	30	56	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	30	57	)	)	PUNCT
cana-4367	30	58	12	12	NUM
cana-4367	30	59	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	30	60	𝑖	𝑖	PROPN
cana-4367	30	61	≡	≡	PROPN
cana-4367	30	62	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	30	63	)	)	PUNCT
cana-4367	30	64	0	0	NUM
cana-4367	31	1	𝑖𝑓	𝑖𝑓	CCONJ
cana-4367	31	2	𝑖	𝑖	SYM
cana-4367	31	3	≡	≡	PROPN
cana-4367	31	4	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	31	5	)	)	PUNCT
cana-4367	31	6	15	15	NUM
cana-4367	31	7	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	31	8	𝑖	𝑖	PROPN
cana-4367	31	9	≡	≡	PROPN
cana-4367	31	10	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	31	11	)	)	PUNCT
cana-4367	31	12	;	;	PUNCT
cana-4367	31	13	end	end	VERB
cana-4367	31	14	for	for	ADP
cana-4367	31	15	for	for	ADP
cana-4367	31	16	0	0	NUM
cana-4367	31	17	≤	≤	NUM
cana-4367	31	18	𝑖	𝑖	SYM
cana-4367	31	19	≤	≤	NOUN
cana-4367	31	20	𝑚-1	𝑚-1	PRON
cana-4367	31	21	𝑣𝑖	𝑣𝑖	PROPN
cana-4367	31	22	,	,	PUNCT
cana-4367	31	23	←	←	PROPN
cana-4367	31	24	{	{	PUNCT
cana-4367	31	25	60	60	NUM
cana-4367	31	26	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	31	27	𝑖	𝑖	SYM
cana-4367	31	28	≡	≡	PROPN
cana-4367	31	29	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	31	30	)	)	PUNCT
cana-4367	31	31	51	51	NUM
cana-4367	31	32	𝑖𝑓	𝑖𝑓	SYM
cana-4367	31	33	𝑖	𝑖	PROPN
cana-4367	31	34	≡	≡	PROPN
cana-4367	31	35	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	31	36	)	)	PUNCT
cana-4367	31	37	63	63	NUM
cana-4367	31	38	𝑖𝑓	𝑖𝑓	SYM
cana-4367	31	39	𝑖	𝑖	SYM
cana-4367	31	40	≡	≡	PROPN
cana-4367	31	41	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	31	42	)	)	PUNCT
cana-4367	31	43	48	48	NUM
cana-4367	31	44	𝑖𝑓	𝑖𝑓	SYM
cana-4367	31	45	𝑖	𝑖	PROPN
cana-4367	31	46	≡	≡	PROPN
cana-4367	31	47	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	31	48	)	)	PUNCT
cana-4367	31	49	;	;	PUNCT
cana-4367	31	50	end	end	VERB
cana-4367	31	51	for	for	ADP
cana-4367	31	52	𝑣𝑚	𝑣𝑚	ADJ
cana-4367	31	53	,	,	PUNCT
cana-4367	31	54	←	←	PROPN
cana-4367	31	55	{	{	PUNCT
cana-4367	31	56	12	12	NUM
cana-4367	31	57	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	31	58	𝑚	𝑚	PROPN
cana-4367	31	59	≡	≡	PROPN
cana-4367	31	60	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	31	61	)	)	PUNCT
cana-4367	31	62	0	0	NUM
cana-4367	32	1	𝑖𝑓	𝑖𝑓	ADP
cana-4367	32	2	𝑚	𝑚	PROPN
cana-4367	32	3	≡	≡	PROPN
cana-4367	32	4	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	32	5	)	)	PUNCT
cana-4367	32	6	15	15	NUM
cana-4367	32	7	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	32	8	𝑚	𝑚	X
cana-4367	32	9	≡	≡	PROPN
cana-4367	32	10	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	32	11	)	)	PUNCT
cana-4367	32	12	3	3	NUM
cana-4367	32	13	𝑖𝑓	𝑖𝑓	ADP
cana-4367	32	14	𝑚	𝑚	PROPN
cana-4367	32	15	≡	≡	PROPN
cana-4367	32	16	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	32	17	)	)	PUNCT
cana-4367	32	18	;	;	PUNCT
cana-4367	32	19	end	end	NOUN
cana-4367	32	20	procedure	procedure	NOUN
cana-4367	32	21	output	output	NOUN
cana-4367	32	22	:	:	PUNCT
cana-4367	32	23	the	the	DET
cana-4367	32	24	labeled	label	VERB
cana-4367	32	25	vertices	vertex	NOUN
cana-4367	32	26	of	of	ADP
cana-4367	32	27	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	32	28	+	+	CCONJ
cana-4367	32	29	graph	graph	NOUN
cana-4367	32	30	.	.	PUNCT
cana-4367	33	1	theorem	theorem	ADJ
cana-4367	33	2	:	:	PUNCT
cana-4367	33	3	2.1.2	2.1.2	NUM
cana-4367	33	4	.	.	PUNCT
cana-4367	34	1	the	the	DET
cana-4367	34	2	corona	corona	NOUN
cana-4367	34	3	of	of	ADP
cana-4367	34	4	path	path	NOUN
cana-4367	34	5	(	(	PUNCT
cana-4367	34	6	comb	comb	NOUN
cana-4367	34	7	)	)	PUNCT
cana-4367	34	8	graph	graph	NOUN
cana-4367	34	9	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	34	10	+	+	CCONJ
cana-4367	34	11	is	be	AUX
cana-4367	34	12	an	an	DET
cana-4367	34	13	even	even	ADV
cana-4367	34	14	hamming	ham	VERB
cana-4367	34	15	distance	distance	NOUN
cana-4367	34	16	labeled	label	VERB
cana-4367	34	17	graph	graph	NOUN
cana-4367	34	18	and	and	CCONJ
cana-4367	34	19	the	the	DET
cana-4367	34	20	even	even	ADV
cana-4367	34	21	hamming	hamming	NOUN
cana-4367	34	22	distance	distance	NOUN
cana-4367	34	23	number	number	NOUN
cana-4367	34	24	is	be	AUX
cana-4367	34	25	ηℎ𝑑	ηℎ𝑑	NOUN
cana-4367	34	26	′′	′′	PROPN
cana-4367	34	27	(	(	PUNCT
cana-4367	34	28	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	34	29	+	+	PROPN
cana-4367	34	30	)	)	PUNCT
cana-4367	34	31	=	=	SYM
cana-4367	34	32	6	6	X
cana-4367	34	33	.	.	PUNCT
cana-4367	35	1	proof	proof	NOUN
cana-4367	35	2	:	:	PUNCT
cana-4367	35	3	let	let	VERB
cana-4367	35	4	us	we	PRON
cana-4367	35	5	consider	consider	VERB
cana-4367	35	6	the	the	DET
cana-4367	35	7	comb	comb	NOUN
cana-4367	35	8	graph	graph	VERB
cana-4367	35	9	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	35	10	+	+	CCONJ
cana-4367	35	11	with	with	ADP
cana-4367	35	12	vertex	vertex	NOUN
cana-4367	35	13	set	set	VERB
cana-4367	35	14	𝑉	𝑉	PROPN
cana-4367	35	15	=	=	PUNCT
cana-4367	35	16	{	{	PUNCT
cana-4367	35	17	{	{	PUNCT
cana-4367	35	18	𝑣0,𝑣1,𝑣2	𝑣0,𝑣1,𝑣2	NOUN
cana-4367	35	19	,	,	PUNCT
cana-4367	35	20	…	…	PUNCT
cana-4367	35	21	,	,	PUNCT
cana-4367	35	22	𝑣𝑚	𝑣𝑚	VERB
cana-4367	35	23	}	}	PUNCT
cana-4367	35	24	∪	∪	ADJ
cana-4367	35	25	{	{	PUNCT
cana-4367	35	26	𝑣0	𝑣0	PROPN
cana-4367	35	27	,	,	PUNCT
cana-4367	35	28	′	′	NUM
cana-4367	35	29	𝑣1	𝑣1	NOUN
cana-4367	35	30	,	,	PUNCT
cana-4367	35	31	′	′	NUM
cana-4367	35	32	𝑣2	𝑣2	NOUN
cana-4367	35	33	,	,	PUNCT
cana-4367	35	34	′	′	NUM
cana-4367	35	35	…	…	PUNCT
cana-4367	35	36	,	,	PUNCT
cana-4367	35	37	𝑣𝑚	𝑣𝑚	VERB
cana-4367	35	38	,	,	PUNCT
cana-4367	35	39	′	′	NUM
cana-4367	35	40	}	}	PUNCT
cana-4367	35	41	}	}	PUNCT
cana-4367	35	42	and	and	CCONJ
cana-4367	35	43	edge	edge	VERB
cana-4367	35	44	set	set	VERB
cana-4367	35	45	𝐸	𝐸	NOUN
cana-4367	35	46	=	=	PRON
cana-4367	35	47	{	{	PUNCT
cana-4367	35	48	{	{	PUNCT
cana-4367	35	49	𝑣𝑖𝑣𝑖+1	𝑣𝑖𝑣𝑖+1	PROPN
cana-4367	35	50	/	/	SYM
cana-4367	35	51	0	0	NUM
cana-4367	35	52	≤	≤	NUM
cana-4367	35	53	𝑖	𝑖	SYM
cana-4367	35	54	≤	≤	NOUN
cana-4367	35	55	𝑚	𝑚	ADP
cana-4367	35	56	−	−	PROPN
cana-4367	35	57	1	1	NUM
cana-4367	35	58	}	}	PUNCT
cana-4367	35	59	∪	∪	ADJ
cana-4367	35	60	{	{	PUNCT
cana-4367	35	61	𝑣𝑖𝑣𝑖	𝑣𝑖𝑣𝑖	NOUN
cana-4367	35	62	′/0	′/0	NUM
cana-4367	35	63	≤	≤	NUM
cana-4367	35	64	𝑖	𝑖	SYM
cana-4367	35	65	≤	≤	NUM
cana-4367	35	66	𝑚	𝑚	ADP
cana-4367	35	67	}	}	PUNCT
cana-4367	35	68	}	}	PUNCT
cana-4367	35	69	.	.	PUNCT
cana-4367	36	1	define	define	VERB
cana-4367	36	2	a	a	DET
cana-4367	36	3	function	function	NOUN
cana-4367	36	4	𝑓	𝑓	PRON
cana-4367	36	5	:	:	PUNCT
cana-4367	36	6	v	v	NOUN
cana-4367	36	7	→	→	SYM
cana-4367	36	8	n	n	CCONJ
cana-4367	36	9	∪	∪	X
cana-4367	36	10	{	{	PUNCT
cana-4367	36	11	0	0	NUM
cana-4367	36	12	}	}	PUNCT
cana-4367	36	13	such	such	ADJ
cana-4367	36	14	that	that	SCONJ
cana-4367	36	15	𝑓(𝑢	𝑓(𝑢	PROPN
cana-4367	36	16	)	)	PUNCT
cana-4367	36	17	≠	≠	PROPN
cana-4367	36	18	𝑓(𝑣	𝑓(𝑣	PROPN
cana-4367	36	19	)	)	PUNCT
cana-4367	36	20	for	for	ADP
cana-4367	36	21	any	any	DET
cana-4367	36	22	two	two	NUM
cana-4367	36	23	adjacent	adjacent	ADJ
cana-4367	36	24	vertices	vertex	NOUN
cana-4367	36	25	u	u	NOUN
cana-4367	36	26	and	and	CCONJ
cana-4367	36	27	v	v	NOUN
cana-4367	36	28	as	as	SCONJ
cana-4367	36	29	given	give	VERB
cana-4367	36	30	in	in	ADP
cana-4367	36	31	the	the	DET
cana-4367	36	32	above	above	ADJ
cana-4367	36	33	algorithm	algorithm	NOUN
cana-4367	36	34	2.1.1	2.1.1	NUM
cana-4367	36	35	.	.	PUNCT
cana-4367	37	1	hence	hence	ADV
cana-4367	37	2	the	the	DET
cana-4367	37	3	adjacent	adjacent	ADJ
cana-4367	37	4	vertices	vertex	NOUN
cana-4367	37	5	receive	receive	VERB
cana-4367	37	6	distinct	distinct	ADJ
cana-4367	37	7	labels	label	NOUN
cana-4367	37	8	.	.	PUNCT
cana-4367	38	1	the	the	DET
cana-4367	38	2	edge	edge	NOUN
cana-4367	38	3	labels	label	NOUN
cana-4367	38	4	are	be	AUX
cana-4367	38	5	obtained	obtain	VERB
cana-4367	38	6	as	as	ADP
cana-4367	38	7	follows	follow	VERB
cana-4367	38	8	:	:	PUNCT
cana-4367	38	9	𝑓∗(𝑣0𝑣0	𝑓∗(𝑣0𝑣0	PROPN
cana-4367	38	10	′	′	NUM
cana-4367	38	11	)	)	PUNCT
cana-4367	38	12	=	=	PUNCT
cana-4367	39	1	ℎ𝑑([𝑓(𝑣0)]2	ℎ𝑑([𝑓(𝑣0)]2	ADV
cana-4367	39	2	,	,	PUNCT
cana-4367	39	3	[	[	X
cana-4367	39	4	𝑓(𝑣0	𝑓(𝑣0	NOUN
cana-4367	39	5	′)]2	′)]2	ADV
cana-4367	39	6	)	)	PUNCT
cana-4367	40	1	=	=	SYM
cana-4367	41	1	hd([0]2	hd([0]2	NOUN
cana-4367	41	2	,	,	PUNCT
cana-4367	41	3	[	[	X
cana-4367	41	4	15]2	15]2	X
cana-4367	41	5	)	)	PUNCT
cana-4367	41	6	=	=	SYM
cana-4367	41	7	hd(00000	hd(00000	PROPN
cana-4367	41	8	,	,	PUNCT
cana-4367	41	9	01111	01111	NUM
cana-4367	41	10	)	)	PUNCT
cana-4367	42	1	=	=	NOUN
cana-4367	42	2	4	4	X
cana-4367	42	3	.	.	PUNCT
cana-4367	42	4	𝑓∗(𝑣0𝑣1	𝑓∗(𝑣0𝑣1	NUM
cana-4367	42	5	)	)	PUNCT
cana-4367	42	6	=	=	PUNCT
cana-4367	43	1	ℎ𝑑([𝑓(𝑣0)]2	ℎ𝑑([𝑓(𝑣0)]2	ADV
cana-4367	43	2	,	,	PUNCT
cana-4367	44	1	[	[	X
cana-4367	44	2	𝑓(𝑣1)]2)=	𝑓(𝑣1)]2)=	NOUN
cana-4367	44	3	=	=	SYM
cana-4367	45	1	hd([0]2	hd([0]2	NOUN
cana-4367	45	2	,	,	PUNCT
cana-4367	45	3	[	[	X
cana-4367	45	4	3]2	3]2	NUM
cana-4367	45	5	=	=	SYM
cana-4367	45	6	hd(00000	hd(00000	PROPN
cana-4367	45	7	,	,	PUNCT
cana-4367	45	8	00011	00011	NUM
cana-4367	45	9	)	)	PUNCT
cana-4367	46	1	=	=	SYM
cana-4367	46	2	2	2	X
cana-4367	46	3	.	.	X
cana-4367	46	4	communications	communication	NOUN
cana-4367	46	5	on	on	ADP
cana-4367	46	6	applied	apply	VERB
cana-4367	46	7	nonlinear	nonlinear	ADJ
cana-4367	46	8	analysis	analysis	NOUN
cana-4367	46	9	issn	issn	NOUN
cana-4367	46	10	:	:	PUNCT
cana-4367	46	11	1074	1074	NUM
cana-4367	46	12	-	-	PUNCT
cana-4367	46	13	133x	133x	NUM
cana-4367	46	14	vol	vol	NOUN
cana-4367	46	15	32	32	NUM
cana-4367	46	16	no	no	NOUN
cana-4367	46	17	.	.	PUNCT
cana-4367	47	1	9s	9s	NUM
cana-4367	47	2	(	(	PUNCT
cana-4367	47	3	2025	2025	NUM
cana-4367	47	4	)	)	PUNCT
cana-4367	47	5	1921	1921	NUM
cana-4367	47	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4367	47	7	for	for	ADP
cana-4367	47	8	1	1	NUM
cana-4367	47	9	≤	≤	NUM
cana-4367	47	10	i	i	PRON
cana-4367	47	11	≤	≤	NOUN
cana-4367	47	12	m	m	VERB
cana-4367	47	13	−	−	NUM
cana-4367	47	14	1	1	NUM
cana-4367	47	15	case	case	NOUN
cana-4367	47	16	(	(	PUNCT
cana-4367	47	17	i	i	NOUN
cana-4367	47	18	):	):	PUNCT
cana-4367	47	19	if	if	SCONJ
cana-4367	47	20	i	i	PRON
cana-4367	47	21	≡	≡	PROPN
cana-4367	47	22	1(mod	1(mod	NUM
cana-4367	48	1	4)or	4)or	NOUN
cana-4367	48	2	𝑚	𝑚	ADP
cana-4367	48	3	≡	≡	PROPN
cana-4367	48	4	1(𝑚𝑜𝑑	1(𝑚𝑜𝑑	ADJ
cana-4367	48	5	4	4	NUM
cana-4367	48	6	)	)	PUNCT
cana-4367	48	7	𝑓∗(vivi+1	𝑓∗(vivi+1	NUM
cana-4367	48	8	)	)	PUNCT
cana-4367	48	9	=	=	SYM
cana-4367	49	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	49	2	,	,	PUNCT
cana-4367	49	3	[	[	X
cana-4367	49	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	49	5	)	)	PUNCT
cana-4367	49	6	=	=	PUNCT
cana-4367	50	1	hd([3]2	hd([3]2	X
cana-4367	50	2	,	,	PUNCT
cana-4367	50	3	[	[	X
cana-4367	50	4	12]2	12]2	NUM
cana-4367	50	5	)	)	PUNCT
cana-4367	50	6	=	=	SYM
cana-4367	50	7	4	4	X
cana-4367	50	8	.	.	X
cana-4367	50	9	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	50	10	′	′	NOUN
cana-4367	50	11	)	)	PUNCT
cana-4367	51	1	=	=	SYM
cana-4367	51	2	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	51	3	,	,	PUNCT
cana-4367	51	4	[	[	X
cana-4367	51	5	𝑓(𝑣𝑖	𝑓(𝑣𝑖	ADP
cana-4367	51	6	′)]2	′)]2	NUM
cana-4367	51	7	)	)	PUNCT
cana-4367	51	8	=	=	PUNCT
cana-4367	52	1	hd([3]2	hd([3]2	X
cana-4367	52	2	,	,	PUNCT
cana-4367	52	3	[	[	X
cana-4367	52	4	60]2	60]2	NUM
cana-4367	52	5	)	)	PUNCT
cana-4367	52	6	=	=	PUNCT
cana-4367	52	7	6	6	X
cana-4367	52	8	.	.	PUNCT
cana-4367	52	9	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	NOUN
cana-4367	52	10	′	′	VERB
cana-4367	52	11	)	)	PUNCT
cana-4367	53	1	=	=	SYM
cana-4367	53	2	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	PROPN
cana-4367	53	3	,	,	PUNCT
cana-4367	53	4	[	[	X
cana-4367	53	5	𝑓(𝑣𝑚	𝑓(𝑣𝑚	NOUN
cana-4367	53	6	′	′	NUM
cana-4367	53	7	)	)	PUNCT
cana-4367	54	1	]	]	X
cana-4367	54	2	2)=	2)=	NUM
cana-4367	54	3	hd([3]2	hd([3]2	NOUN
cana-4367	54	4	,	,	PUNCT
cana-4367	54	5	[	[	X
cana-4367	54	6	12]2	12]2	NUM
cana-4367	54	7	)	)	PUNCT
cana-4367	54	8	=	=	SYM
cana-4367	54	9	4	4	X
cana-4367	54	10	.	.	X
cana-4367	54	11	case	case	NOUN
cana-4367	54	12	(	(	PUNCT
cana-4367	54	13	ii	ii	NUM
cana-4367	54	14	):	):	PUNCT
cana-4367	54	15	if	if	SCONJ
cana-4367	54	16	i	i	PRON
cana-4367	54	17	≡	≡	PROPN
cana-4367	54	18	2(mod4	2(mod4	NUM
cana-4367	54	19	)	)	PUNCT
cana-4367	54	20	;	;	PUNCT
cana-4367	54	21	or	or	CCONJ
cana-4367	54	22	𝑚	𝑚	ADP
cana-4367	54	23	≡	≡	PROPN
cana-4367	54	24	2(𝑚𝑜𝑑	2(𝑚𝑜𝑑	NOUN
cana-4367	54	25	4	4	NUM
cana-4367	54	26	)	)	PUNCT
cana-4367	54	27	𝑓∗(vivi+1	𝑓∗(vivi+1	NUM
cana-4367	54	28	)	)	PUNCT
cana-4367	54	29	=	=	SYM
cana-4367	55	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	55	2	,	,	PUNCT
cana-4367	55	3	[	[	X
cana-4367	55	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	55	5	)	)	PUNCT
cana-4367	55	6	=	=	SYM
cana-4367	56	1	hd([12]2	hd([12]2	PROPN
cana-4367	56	2	,	,	PUNCT
cana-4367	56	3	[	[	X
cana-4367	56	4	0]2	0]2	X
cana-4367	56	5	)	)	PUNCT
cana-4367	56	6	=	=	SYM
cana-4367	57	1	2	2	X
cana-4367	57	2	.	.	X
cana-4367	57	3	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	57	4	′	′	NOUN
cana-4367	57	5	)	)	PUNCT
cana-4367	58	1	=	=	SYM
cana-4367	58	2	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	58	3	,	,	PUNCT
cana-4367	58	4	[	[	X
cana-4367	58	5	𝑓(𝑣𝑖	𝑓(𝑣𝑖	ADP
cana-4367	58	6	′)]2	′)]2	NUM
cana-4367	58	7	)	)	PUNCT
cana-4367	58	8	=	=	SYM
cana-4367	59	1	hd(122	hd(122	NOUN
cana-4367	59	2	,	,	PUNCT
cana-4367	59	3	[	[	X
cana-4367	59	4	51]2	51]2	NUM
cana-4367	59	5	)	)	PUNCT
cana-4367	59	6	=	=	SYM
cana-4367	59	7	6	6	X
cana-4367	59	8	.	.	PUNCT
cana-4367	60	1	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	NOUN
cana-4367	60	2	′	′	VERB
cana-4367	60	3	)	)	PUNCT
cana-4367	61	1	=	=	SYM
cana-4367	61	2	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	PROPN
cana-4367	61	3	,	,	PUNCT
cana-4367	61	4	[	[	X
cana-4367	61	5	𝑓(𝑣𝑚	𝑓(𝑣𝑚	NOUN
cana-4367	61	6	′	′	NUM
cana-4367	61	7	)	)	PUNCT
cana-4367	62	1	]	]	X
cana-4367	62	2	2)=	2)=	NUM
cana-4367	62	3	hd([12]2	hd([12]2	X
cana-4367	62	4	,	,	PUNCT
cana-4367	63	1	[	[	X
cana-4367	63	2	0]2	0]2	X
cana-4367	63	3	)	)	PUNCT
cana-4367	63	4	=	=	SYM
cana-4367	63	5	2	2	X
cana-4367	63	6	.	.	X
cana-4367	63	7	case	case	NOUN
cana-4367	63	8	(	(	PUNCT
cana-4367	63	9	iii	iii	NOUN
cana-4367	63	10	):	):	PUNCT
cana-4367	63	11	if	if	SCONJ
cana-4367	63	12	i	i	PRON
cana-4367	63	13	≡	≡	VERB
cana-4367	63	14	3(mod	3(mod	NUM
cana-4367	63	15	4	4	NUM
cana-4367	63	16	)	)	PUNCT
cana-4367	63	17	or	or	CCONJ
cana-4367	63	18	𝑚	𝑚	ADP
cana-4367	63	19	≡	≡	PROPN
cana-4367	63	20	2(𝑚𝑜𝑑	2(𝑚𝑜𝑑	NOUN
cana-4367	63	21	4	4	NUM
cana-4367	63	22	)	)	PUNCT
cana-4367	63	23	𝑓∗(vivi+1	𝑓∗(vivi+1	NUM
cana-4367	63	24	)	)	PUNCT
cana-4367	63	25	=	=	SYM
cana-4367	64	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	64	2	,	,	PUNCT
cana-4367	64	3	[	[	X
cana-4367	64	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	64	5	)	)	PUNCT
cana-4367	64	6	=	=	SYM
cana-4367	65	1	hd([0]2	hd([0]2	NOUN
cana-4367	65	2	,	,	PUNCT
cana-4367	65	3	[	[	X
cana-4367	65	4	15]2	15]2	X
cana-4367	65	5	)	)	PUNCT
cana-4367	65	6	=	=	SYM
cana-4367	65	7	4	4	NUM
cana-4367	65	8	.	.	X
cana-4367	65	9	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	65	10	′	′	NOUN
cana-4367	65	11	)	)	PUNCT
cana-4367	66	1	=	=	SYM
cana-4367	66	2	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	66	3	,	,	PUNCT
cana-4367	66	4	[	[	X
cana-4367	66	5	𝑓(𝑣𝑖	𝑓(𝑣𝑖	ADP
cana-4367	66	6	′)]2	′)]2	ADV
cana-4367	66	7	)	)	PUNCT
cana-4367	66	8	=	=	SYM
cana-4367	67	1	hd([0]2	hd([0]2	PROPN
cana-4367	67	2	,	,	PUNCT
cana-4367	67	3	[	[	X
cana-4367	67	4	63]2	63]2	NOUN
cana-4367	67	5	)	)	PUNCT
cana-4367	67	6	=	=	SYM
cana-4367	67	7	6	6	X
cana-4367	67	8	.	.	PUNCT
cana-4367	67	9	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	NOUN
cana-4367	67	10	′	′	VERB
cana-4367	67	11	)	)	PUNCT
cana-4367	68	1	=	=	SYM
cana-4367	68	2	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	PROPN
cana-4367	68	3	,	,	PUNCT
cana-4367	68	4	[	[	X
cana-4367	68	5	𝑓(𝑣𝑚	𝑓(𝑣𝑚	NOUN
cana-4367	68	6	′	′	NUM
cana-4367	68	7	)	)	PUNCT
cana-4367	69	1	]	]	X
cana-4367	69	2	2)=	2)=	NUM
cana-4367	69	3	hd([0]2	hd([0]2	NUM
cana-4367	69	4	,	,	PUNCT
cana-4367	70	1	[	[	X
cana-4367	70	2	15]2	15]2	X
cana-4367	70	3	)	)	PUNCT
cana-4367	70	4	=	=	SYM
cana-4367	70	5	4	4	X
cana-4367	70	6	.	.	X
cana-4367	70	7	case	case	NOUN
cana-4367	70	8	(	(	PUNCT
cana-4367	70	9	iv	iv	NUM
cana-4367	70	10	):	):	PUNCT
cana-4367	70	11	if	if	SCONJ
cana-4367	70	12	i	i	PRON
cana-4367	70	13	≡	≡	PROPN
cana-4367	70	14	0(mod4	0(mod4	NUM
cana-4367	70	15	)	)	PUNCT
cana-4367	70	16	;	;	PUNCT
cana-4367	70	17	𝑓∗(vivi+1	𝑓∗(vivi+1	X
cana-4367	70	18	)	)	PUNCT
cana-4367	70	19	=	=	SYM
cana-4367	71	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	71	2	,	,	PUNCT
cana-4367	71	3	[	[	X
cana-4367	71	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	71	5	)	)	PUNCT
cana-4367	71	6	=	=	SYM
cana-4367	72	1	hd([15]2	hd([15]2	NOUN
cana-4367	72	2	,	,	PUNCT
cana-4367	72	3	[	[	X
cana-4367	72	4	3]2	3]2	NUM
cana-4367	72	5	)	)	PUNCT
cana-4367	72	6	=	=	SYM
cana-4367	72	7	2	2	NUM
cana-4367	72	8	.	.	PUNCT
cana-4367	73	1	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	73	2	′	′	NOUN
cana-4367	73	3	)	)	PUNCT
cana-4367	74	1	=	=	SYM
cana-4367	74	2	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	74	3	,	,	PUNCT
cana-4367	74	4	[	[	X
cana-4367	74	5	𝑓(𝑣𝑖	𝑓(𝑣𝑖	ADP
cana-4367	74	6	′)]2	′)]2	ADV
cana-4367	74	7	)	)	PUNCT
cana-4367	74	8	=	=	SYM
cana-4367	75	1	hd([15]2	hd([15]2	NOUN
cana-4367	75	2	,	,	PUNCT
cana-4367	75	3	[	[	X
cana-4367	75	4	48]2	48]2	NOUN
cana-4367	75	5	)	)	PUNCT
cana-4367	75	6	=	=	SYM
cana-4367	75	7	6	6	X
cana-4367	75	8	.	.	PUNCT
cana-4367	75	9	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	NOUN
cana-4367	75	10	′	′	VERB
cana-4367	75	11	)	)	PUNCT
cana-4367	76	1	=	=	SYM
cana-4367	76	2	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	PROPN
cana-4367	76	3	,	,	PUNCT
cana-4367	76	4	[	[	X
cana-4367	76	5	𝑓(𝑣𝑚	𝑓(𝑣𝑚	NOUN
cana-4367	76	6	′	′	NUM
cana-4367	76	7	)	)	PUNCT
cana-4367	76	8	]	]	X
cana-4367	76	9	2)=	2)=	NUM
cana-4367	76	10	hd([15]2	hd([15]2	NOUN
cana-4367	76	11	,	,	PUNCT
cana-4367	76	12	[	[	X
cana-4367	76	13	3]2	3]2	NUM
cana-4367	76	14	)	)	PUNCT
cana-4367	76	15	=	=	SYM
cana-4367	76	16	2	2	X
cana-4367	76	17	.	.	X
cana-4367	76	18	from	from	ADP
cana-4367	76	19	all	all	DET
cana-4367	76	20	the	the	DET
cana-4367	76	21	above	above	ADJ
cana-4367	76	22	cases	case	NOUN
cana-4367	76	23	,	,	PUNCT
cana-4367	76	24	all	all	DET
cana-4367	76	25	the	the	DET
cana-4367	76	26	adjacent	adjacent	ADJ
cana-4367	76	27	edges	edge	NOUN
cana-4367	76	28	receive	receive	VERB
cana-4367	76	29	distinct	distinct	ADJ
cana-4367	76	30	even	even	ADV
cana-4367	76	31	labels	label	NOUN
cana-4367	76	32	.	.	PUNCT
cana-4367	77	1	hence	hence	ADV
cana-4367	77	2	the	the	DET
cana-4367	77	3	path	path	NOUN
cana-4367	77	4	graph	graph	NOUN
cana-4367	77	5	pm	pm	NOUN
cana-4367	77	6	admits	admit	VERB
cana-4367	77	7	even	even	ADV
cana-4367	77	8	hamming	ham	VERB
cana-4367	77	9	distance	distance	NOUN
cana-4367	77	10	labeling	labeling	NOUN
cana-4367	77	11	and	and	CCONJ
cana-4367	77	12	the	the	DET
cana-4367	77	13	even	even	ADV
cana-4367	77	14	hamming	hamming	NOUN
cana-4367	77	15	distance	distance	NOUN
cana-4367	77	16	number	number	NOUN
cana-4367	77	17	is	be	AUX
cana-4367	77	18	ηℎ𝑑	ηℎ𝑑	NOUN
cana-4367	77	19	′′	′′	PROPN
cana-4367	77	20	(	(	PUNCT
cana-4367	77	21	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	77	22	+	+	PROPN
cana-4367	77	23	)	)	PUNCT
cana-4367	77	24	=	=	SYM
cana-4367	78	1	6	6	X
cana-4367	78	2	.	.	PUNCT
cana-4367	78	3	algorithm	algorithm	PROPN
cana-4367	78	4	2.1.3	2.1.3	NUM
cana-4367	78	5	.	.	PUNCT
cana-4367	79	1	even	even	ADV
cana-4367	79	2	hamming	ham	VERB
cana-4367	79	3	distance	distance	NOUN
cana-4367	79	4	labeling	labeling	NOUN
cana-4367	79	5	of	of	ADP
cana-4367	79	6	twig	twig	PROPN
cana-4367	79	7	graph	graph	NOUN
cana-4367	79	8	𝑻𝑾(𝑷𝒎	𝑻𝑾(𝑷𝒎	NOUN
cana-4367	79	9	)	)	PUNCT
cana-4367	79	10	input	input	NOUN
cana-4367	79	11	:	:	PUNCT
cana-4367	79	12	vertices	vertex	NOUN
cana-4367	79	13	of	of	ADP
cana-4367	79	14	𝑇𝑊(𝑃𝑚	𝑇𝑊(𝑃𝑚	NOUN
cana-4367	79	15	)	)	PUNCT
cana-4367	79	16	graph	graph	NOUN
cana-4367	79	17	,	,	PUNCT
cana-4367	79	18	𝑚	𝑚	X
cana-4367	79	19	≥	≥	NUM
cana-4367	79	20	2	2	NUM
cana-4367	79	21	𝑉	𝑉	PROPN
cana-4367	79	22	←	←	PROPN
cana-4367	79	23	{	{	PUNCT
cana-4367	79	24	𝑣0	𝑣0	PROPN
cana-4367	79	25	,	,	PUNCT
cana-4367	79	26	𝑣𝑚	𝑣𝑚	ADJ
cana-4367	79	27	,	,	PUNCT
cana-4367	79	28	𝑣𝑖	𝑣𝑖	ADP
cana-4367	79	29	′	′	NUM
cana-4367	79	30	,	,	PUNCT
cana-4367	79	31	𝑣𝑖	𝑣𝑖	ADV
cana-4367	79	32	′′/1	′′/1	PUNCT
cana-4367	80	1	≤	≤	NUM
cana-4367	80	2	𝑖	𝑖	SYM
cana-4367	80	3	≤	≤	NOUN
cana-4367	80	4	𝑚	𝑚	ADP
cana-4367	80	5	−	−	PROPN
cana-4367	80	6	1	1	NUM
cana-4367	80	7	}	}	PUNCT
cana-4367	80	8	𝑣0	𝑣0	PROPN
cana-4367	80	9	←	←	PROPN
cana-4367	80	10	0	0	NUM
cana-4367	80	11	;	;	PUNCT
cana-4367	80	12	for	for	SCONJ
cana-4367	80	13	𝑖	𝑖	SYM
cana-4367	80	14	=	=	SYM
cana-4367	80	15	1	1	NUM
cana-4367	80	16	𝑡𝑜	𝑡𝑜	NOUN
cana-4367	80	17	𝑚	𝑚	NOUN
cana-4367	80	18	do	do	AUX
cana-4367	80	19	𝑣𝑖	𝑣𝑖	ADP
cana-4367	80	20	←	←	PROPN
cana-4367	80	21	{	{	PUNCT
cana-4367	80	22	3	3	NUM
cana-4367	80	23	𝑖𝑓	𝑖𝑓	ADP
cana-4367	80	24	𝑖	𝑖	SYM
cana-4367	80	25	≡	≡	PROPN
cana-4367	80	26	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	80	27	)	)	PUNCT
cana-4367	80	28	252	252	NUM
cana-4367	80	29	𝑖𝑓	𝑖𝑓	VERB
cana-4367	80	30	𝑖	𝑖	SYM
cana-4367	80	31	≡	≡	PROPN
cana-4367	80	32	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	80	33	)	)	PUNCT
cana-4367	80	34	60	60	NUM
cana-4367	80	35	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	80	36	𝑖	𝑖	SYM
cana-4367	80	37	≡	≡	PROPN
cana-4367	80	38	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	80	39	)	)	PUNCT
cana-4367	80	40	195	195	NUM
cana-4367	80	41	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	80	42	𝑖	𝑖	PROPN
cana-4367	80	43	≡	≡	PROPN
cana-4367	80	44	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	80	45	)	)	PUNCT
cana-4367	80	46	end	end	VERB
cana-4367	80	47	for	for	ADP
cana-4367	80	48	for	for	ADP
cana-4367	80	49	𝑖	𝑖	SYM
cana-4367	80	50	=	=	SYM
cana-4367	80	51	1	1	NUM
cana-4367	80	52	𝑡𝑜	𝑡𝑜	NOUN
cana-4367	80	53	𝑚	𝑚	AUX
cana-4367	80	54	−	−	PROPN
cana-4367	80	55	1	1	NUM
cana-4367	80	56	do	do	VERB
cana-4367	80	57	communications	communication	NOUN
cana-4367	80	58	on	on	ADP
cana-4367	80	59	applied	apply	VERB
cana-4367	80	60	nonlinear	nonlinear	ADJ
cana-4367	80	61	analysis	analysis	NOUN
cana-4367	80	62	issn	issn	NOUN
cana-4367	80	63	:	:	PUNCT
cana-4367	80	64	1074	1074	NUM
cana-4367	80	65	-	-	PUNCT
cana-4367	80	66	133x	133x	NUM
cana-4367	80	67	vol	vol	NOUN
cana-4367	80	68	32	32	NUM
cana-4367	80	69	no	no	NOUN
cana-4367	80	70	.	.	PUNCT
cana-4367	81	1	9s	9s	NUM
cana-4367	81	2	(	(	PUNCT
cana-4367	81	3	2025	2025	NUM
cana-4367	81	4	)	)	PUNCT
cana-4367	81	5	1922	1922	NUM
cana-4367	81	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4367	81	7	𝑣𝑖	𝑣𝑖	ADP
cana-4367	81	8	′	′	NUM
cana-4367	81	9	←	←	PROPN
cana-4367	81	10	{	{	PUNCT
cana-4367	82	1	12	12	NUM
cana-4367	82	2	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	82	3	𝑖	𝑖	SYM
cana-4367	82	4	≡	≡	PROPN
cana-4367	82	5	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	82	6	)	)	PUNCT
cana-4367	82	7	12	12	NUM
cana-4367	82	8	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	82	9	𝑖	𝑖	PROPN
cana-4367	82	10	≡	≡	PROPN
cana-4367	82	11	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	82	12	)	)	PUNCT
cana-4367	82	13	0	0	NUM
cana-4367	83	1	𝑖𝑓	𝑖𝑓	CCONJ
cana-4367	83	2	𝑖	𝑖	SYM
cana-4367	83	3	≡	≡	PROPN
cana-4367	83	4	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	83	5	)	)	PUNCT
cana-4367	83	6	0	0	NUM
cana-4367	84	1	𝑖𝑓	𝑖𝑓	CCONJ
cana-4367	84	2	𝑖	𝑖	PROPN
cana-4367	84	3	≡	≡	PROPN
cana-4367	84	4	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	84	5	)	)	PUNCT
cana-4367	84	6	𝑣𝑖	𝑣𝑖	ADP
cana-4367	84	7	′′	′′	PROPN
cana-4367	84	8	←	←	PROPN
cana-4367	84	9	{	{	PUNCT
cana-4367	84	10	60	60	NUM
cana-4367	84	11	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	84	12	𝑖	𝑖	SYM
cana-4367	84	13	≡	≡	PROPN
cana-4367	84	14	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	84	15	)	)	PUNCT
cana-4367	84	16	0	0	NUM
cana-4367	85	1	𝑖𝑓	𝑖𝑓	CCONJ
cana-4367	85	2	𝑖	𝑖	SYM
cana-4367	85	3	≡	≡	PROPN
cana-4367	85	4	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	85	5	)	)	PUNCT
cana-4367	85	6	3	3	NUM
cana-4367	85	7	𝑖𝑓	𝑖𝑓	ADP
cana-4367	85	8	𝑖	𝑖	SYM
cana-4367	85	9	≡	≡	PROPN
cana-4367	85	10	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	85	11	)	)	PUNCT
cana-4367	85	12	12	12	NUM
cana-4367	85	13	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	85	14	𝑖	𝑖	PROPN
cana-4367	85	15	≡	≡	PROPN
cana-4367	85	16	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	85	17	)	)	PUNCT
cana-4367	85	18	end	end	VERB
cana-4367	85	19	for	for	ADP
cana-4367	85	20	end	end	NOUN
cana-4367	85	21	procedure	procedure	NOUN
cana-4367	85	22	output	output	NOUN
cana-4367	85	23	:	:	PUNCT
cana-4367	85	24	the	the	DET
cana-4367	85	25	labeled	label	VERB
cana-4367	85	26	vertices	vertex	NOUN
cana-4367	85	27	of	of	ADP
cana-4367	85	28	twig	twig	PROPN
cana-4367	85	29	𝑇𝑊(𝑃𝑚	𝑇𝑊(𝑃𝑚	X
cana-4367	85	30	)	)	PUNCT
cana-4367	85	31	graph	graph	NOUN
cana-4367	85	32	.	.	PUNCT
cana-4367	86	1	theorem	theorem	PROPN
cana-4367	86	2	2.1.4	2.1.4	NUM
cana-4367	86	3	.	.	PUNCT
cana-4367	87	1	the	the	DET
cana-4367	87	2	twig	twig	PROPN
cana-4367	87	3	graph	graph	NOUN
cana-4367	87	4	𝑇𝑊(𝑃𝑚	𝑇𝑊(𝑃𝑚	PROPN
cana-4367	87	5	)	)	PUNCT
cana-4367	87	6	is	be	AUX
cana-4367	87	7	an	an	DET
cana-4367	87	8	even	even	ADV
cana-4367	87	9	hamming	ham	VERB
cana-4367	87	10	distance	distance	NOUN
cana-4367	87	11	labeled	label	VERB
cana-4367	87	12	graph	graph	NOUN
cana-4367	87	13	and	and	CCONJ
cana-4367	87	14	the	the	DET
cana-4367	87	15	even	even	ADV
cana-4367	87	16	hamming	hamming	NOUN
cana-4367	87	17	distance	distance	NOUN
cana-4367	87	18	number	number	NOUN
cana-4367	87	19	is	be	AUX
cana-4367	87	20	ηℎ𝑑	ηℎ𝑑	NOUN
cana-4367	87	21	′′	′′	PROPN
cana-4367	87	22	(	(	PUNCT
cana-4367	87	23	𝑇𝑊(𝑃𝑚	𝑇𝑊(𝑃𝑚	X
cana-4367	87	24	)	)	PUNCT
cana-4367	87	25	)	)	PUNCT
cana-4367	88	1	=	=	SYM
cana-4367	88	2	8	8	NUM
cana-4367	88	3	,	,	PUNCT
cana-4367	88	4	for	for	ADP
cana-4367	88	5	any	any	DET
cana-4367	88	6	𝑚	𝑚	PROPN
cana-4367	88	7	≥	≥	NOUN
cana-4367	88	8	2	2	NUM
cana-4367	88	9	.	.	PUNCT
cana-4367	89	1	proof	proof	NOUN
cana-4367	89	2	:	:	PUNCT
cana-4367	89	3	let	let	VERB
cana-4367	89	4	us	we	PRON
cana-4367	89	5	consider	consider	VERB
cana-4367	89	6	the	the	DET
cana-4367	89	7	twig	twig	NOUN
cana-4367	89	8	graph	graph	VERB
cana-4367	89	9	𝑇𝑊(𝑃𝑚	𝑇𝑊(𝑃𝑚	PROPN
cana-4367	89	10	)	)	PUNCT
cana-4367	89	11	with	with	ADP
cana-4367	89	12	vertex	vertex	NOUN
cana-4367	89	13	set	set	VERB
cana-4367	89	14	𝑉	𝑉	PROPN
cana-4367	89	15	=	=	PUNCT
cana-4367	89	16	{	{	PUNCT
cana-4367	89	17	𝑣0	𝑣0	PROPN
cana-4367	89	18	,	,	PUNCT
cana-4367	89	19	𝑣𝑚	𝑣𝑚	ADJ
cana-4367	89	20	,	,	PUNCT
cana-4367	89	21	𝑣𝑖	𝑣𝑖	ADP
cana-4367	89	22	′	′	NUM
cana-4367	89	23	,	,	PUNCT
cana-4367	89	24	𝑣𝑖	𝑣𝑖	ADV
cana-4367	89	25	′′/1	′′/1	PUNCT
cana-4367	89	26	≤	≤	NUM
cana-4367	89	27	𝑖	𝑖	SYM
cana-4367	89	28	≤	≤	NOUN
cana-4367	89	29	𝑚	𝑚	ADP
cana-4367	89	30	−	−	PROPN
cana-4367	89	31	1	1	NUM
cana-4367	89	32	}	}	PUNCT
cana-4367	89	33	and	and	CCONJ
cana-4367	89	34	edge	edge	VERB
cana-4367	89	35	set	set	VERB
cana-4367	89	36	𝐸	𝐸	NOUN
cana-4367	89	37	=	=	PRON
cana-4367	89	38	{	{	PUNCT
cana-4367	89	39	{	{	PUNCT
cana-4367	89	40	𝑣𝑖𝑣𝑖+1	𝑣𝑖𝑣𝑖+1	PROPN
cana-4367	89	41	/	/	SYM
cana-4367	89	42	0	0	NUM
cana-4367	89	43	≤	≤	NUM
cana-4367	89	44	𝑖	𝑖	SYM
cana-4367	89	45	≤	≤	NOUN
cana-4367	89	46	𝑚	𝑚	ADP
cana-4367	89	47	−	−	PROPN
cana-4367	89	48	1	1	NUM
cana-4367	89	49	}	}	PUNCT
cana-4367	89	50	∪	∪	ADJ
cana-4367	89	51	{	{	PUNCT
cana-4367	89	52	𝑣𝑖𝑣𝑖	𝑣𝑖𝑣𝑖	NOUN
cana-4367	89	53	′	′	NUM
cana-4367	89	54	/	/	SYM
cana-4367	89	55	1	1	NUM
cana-4367	89	56	≤	≤	NUM
cana-4367	89	57	𝑖	𝑖	SYM
cana-4367	89	58	≤	≤	NOUN
cana-4367	89	59	𝑚	𝑚	ADP
cana-4367	89	60	−	−	PROPN
cana-4367	89	61	1	1	NUM
cana-4367	89	62	}	}	PUNCT
cana-4367	89	63	∪	∪	ADJ
cana-4367	89	64	{	{	PUNCT
cana-4367	89	65	𝑣𝑖𝑣𝑖	𝑣𝑖𝑣𝑖	NOUN
cana-4367	89	66	′′	′′	PROPN
cana-4367	89	67	/	/	SYM
cana-4367	89	68	1	1	NUM
cana-4367	89	69	≤	≤	NUM
cana-4367	89	70	𝑖	𝑖	SYM
cana-4367	89	71	≤	≤	NOUN
cana-4367	89	72	𝑚	𝑚	ADP
cana-4367	89	73	−	−	PROPN
cana-4367	89	74	1	1	NUM
cana-4367	89	75	}	}	PUNCT
cana-4367	89	76	}	}	PUNCT
cana-4367	89	77	.	.	PUNCT
cana-4367	90	1	define	define	VERB
cana-4367	90	2	a	a	DET
cana-4367	90	3	function	function	NOUN
cana-4367	90	4	𝑓	𝑓	PRON
cana-4367	90	5	:	:	PUNCT
cana-4367	90	6	v	v	NOUN
cana-4367	90	7	→	→	SYM
cana-4367	90	8	n	n	CCONJ
cana-4367	90	9	∪	∪	X
cana-4367	90	10	{	{	PUNCT
cana-4367	90	11	0	0	NUM
cana-4367	90	12	}	}	PUNCT
cana-4367	90	13	such	such	ADJ
cana-4367	90	14	that	that	SCONJ
cana-4367	90	15	𝑓(𝑢	𝑓(𝑢	PROPN
cana-4367	90	16	)	)	PUNCT
cana-4367	90	17	≠	≠	PROPN
cana-4367	90	18	𝑓(𝑣	𝑓(𝑣	PROPN
cana-4367	90	19	)	)	PUNCT
cana-4367	90	20	for	for	ADP
cana-4367	90	21	any	any	DET
cana-4367	90	22	two	two	NUM
cana-4367	90	23	adjacent	adjacent	ADJ
cana-4367	90	24	vertices	vertex	NOUN
cana-4367	90	25	u	u	NOUN
cana-4367	90	26	and	and	CCONJ
cana-4367	90	27	v	v	NOUN
cana-4367	90	28	as	as	SCONJ
cana-4367	90	29	given	give	VERB
cana-4367	90	30	in	in	ADP
cana-4367	90	31	the	the	DET
cana-4367	90	32	above	above	ADJ
cana-4367	90	33	algorithm	algorithm	NOUN
cana-4367	90	34	2.1.3	2.1.3	NUM
cana-4367	90	35	.	.	PUNCT
cana-4367	91	1	hence	hence	ADV
cana-4367	91	2	the	the	DET
cana-4367	91	3	adjacent	adjacent	ADJ
cana-4367	91	4	vertices	vertex	NOUN
cana-4367	91	5	receive	receive	VERB
cana-4367	91	6	distinct	distinct	ADJ
cana-4367	91	7	labels	label	NOUN
cana-4367	91	8	.	.	PUNCT
cana-4367	92	1	the	the	DET
cana-4367	92	2	edge	edge	NOUN
cana-4367	92	3	labels	label	NOUN
cana-4367	92	4	are	be	AUX
cana-4367	92	5	obtained	obtain	VERB
cana-4367	92	6	as	as	ADP
cana-4367	92	7	follows	follow	VERB
cana-4367	92	8	:	:	PUNCT
cana-4367	92	9	𝑓∗(𝑣0𝑣1	𝑓∗(𝑣0𝑣1	NUM
cana-4367	92	10	)	)	PUNCT
cana-4367	92	11	=	=	PUNCT
cana-4367	92	12	ℎ𝑑([𝑓(𝑣0)]2	ℎ𝑑([𝑓(𝑣0)]2	ADV
cana-4367	92	13	,	,	PUNCT
cana-4367	92	14	[	[	X
cana-4367	92	15	𝑓(𝑣1)]2	𝑓(𝑣1)]2	NOUN
cana-4367	92	16	)	)	PUNCT
cana-4367	92	17	=	=	SYM
cana-4367	93	1	=	=	PUNCT
cana-4367	93	2	hd([0]2	hd([0]2	NOUN
cana-4367	93	3	,	,	PUNCT
cana-4367	93	4	[	[	X
cana-4367	93	5	3]2)=2	3]2)=2	X
cana-4367	93	6	.	.	PUNCT
cana-4367	94	1	for	for	ADP
cana-4367	94	2	1	1	NUM
cana-4367	94	3	≤	≤	NUM
cana-4367	94	4	𝑖	𝑖	SYM
cana-4367	94	5	≤	≤	NOUN
cana-4367	94	6	𝑚	𝑚	ADP
cana-4367	94	7	−	−	PROPN
cana-4367	94	8	1	1	NUM
cana-4367	94	9	,	,	PUNCT
cana-4367	94	10	case	case	NOUN
cana-4367	94	11	(	(	PUNCT
cana-4367	94	12	i	i	NOUN
cana-4367	94	13	):	):	PUNCT
cana-4367	94	14	if	if	SCONJ
cana-4367	94	15	i	i	PRON
cana-4367	94	16	≡	≡	PROPN
cana-4367	94	17	1(mod	1(mod	NUM
cana-4367	95	1	4)or	4)or	NOUN
cana-4367	95	2	m	m	NOUN
cana-4367	95	3	≡	≡	PROPN
cana-4367	95	4	1(mod	1(mod	NUM
cana-4367	95	5	4	4	X
cana-4367	95	6	)	)	PUNCT
cana-4367	95	7	𝑓∗(vivi+1	𝑓∗(vivi+1	NUM
cana-4367	95	8	)	)	PUNCT
cana-4367	95	9	=	=	SYM
cana-4367	96	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	96	2	,	,	PUNCT
cana-4367	96	3	[	[	X
cana-4367	96	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	96	5	)	)	PUNCT
cana-4367	96	6	=	=	PUNCT
cana-4367	97	1	hd([3]2	hd([3]2	X
cana-4367	97	2	,	,	PUNCT
cana-4367	97	3	[	[	X
cana-4367	97	4	252]2	252]2	NUM
cana-4367	97	5	)	)	PUNCT
cana-4367	97	6	=	=	SYM
cana-4367	97	7	8	8	X
cana-4367	97	8	.	.	PUNCT
cana-4367	97	9	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	97	10	′	′	NOUN
cana-4367	97	11	)	)	PUNCT
cana-4367	98	1	=	=	SYM
cana-4367	98	2	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	98	3	,	,	PUNCT
cana-4367	98	4	[	[	X
cana-4367	98	5	𝑓(𝑣𝑖	𝑓(𝑣𝑖	ADP
cana-4367	98	6	′)]2	′)]2	NUM
cana-4367	98	7	)	)	PUNCT
cana-4367	98	8	=	=	PUNCT
cana-4367	99	1	hd([3]2	hd([3]2	X
cana-4367	99	2	,	,	PUNCT
cana-4367	99	3	[	[	X
cana-4367	99	4	12]2	12]2	NUM
cana-4367	99	5	)	)	PUNCT
cana-4367	99	6	=	=	SYM
cana-4367	99	7	4	4	X
cana-4367	99	8	.	.	X
cana-4367	99	9	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	99	10	′′	′′	PROPN
cana-4367	99	11	)	)	PUNCT
cana-4367	99	12	=	=	PROPN
cana-4367	99	13	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	99	14	,	,	PUNCT
cana-4367	99	15	[	[	X
cana-4367	99	16	𝑓(𝑣𝑖	𝑓(𝑣𝑖	PROPN
cana-4367	99	17	′′)]2	′′)]2	PROPN
cana-4367	99	18	)	)	PUNCT
cana-4367	99	19	=	=	PUNCT
cana-4367	100	1	hd([3]2	hd([3]2	X
cana-4367	100	2	,	,	PUNCT
cana-4367	100	3	[	[	X
cana-4367	100	4	60]2	60]2	NUM
cana-4367	100	5	)	)	PUNCT
cana-4367	100	6	=	=	SYM
cana-4367	100	7	6	6	X
cana-4367	100	8	.	.	PUNCT
cana-4367	100	9	𝑓∗(vm−1vm	𝑓∗(vm−1vm	ADJ
cana-4367	100	10	)	)	PUNCT
cana-4367	100	11	=	=	SYM
cana-4367	101	1	hd([f(vm−1)]2	hd([f(vm−1)]2	NOUN
cana-4367	101	2	,	,	PUNCT
cana-4367	101	3	[	[	X
cana-4367	101	4	f(vm)]2	f(vm)]2	X
cana-4367	101	5	)	)	PUNCT
cana-4367	101	6	=	=	SYM
cana-4367	101	7	hd([195]2	hd([195]2	NOUN
cana-4367	101	8	,	,	PUNCT
cana-4367	101	9	[	[	X
cana-4367	101	10	3]2	3]2	NUM
cana-4367	101	11	)	)	PUNCT
cana-4367	101	12	=	=	SYM
cana-4367	101	13	2	2	X
cana-4367	101	14	.	.	X
cana-4367	101	15	case	case	NOUN
cana-4367	101	16	(	(	PUNCT
cana-4367	101	17	ii	ii	NUM
cana-4367	101	18	):	):	PUNCT
cana-4367	101	19	if	if	SCONJ
cana-4367	101	20	i	i	PRON
cana-4367	101	21	≡	≡	PROPN
cana-4367	101	22	2(mod4	2(mod4	NUM
cana-4367	101	23	)	)	PUNCT
cana-4367	101	24	𝑓∗(vivi+1	𝑓∗(vivi+1	NUM
cana-4367	101	25	)	)	PUNCT
cana-4367	101	26	=	=	SYM
cana-4367	102	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	102	2	,	,	PUNCT
cana-4367	102	3	[	[	X
cana-4367	102	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	102	5	)	)	PUNCT
cana-4367	102	6	=	=	SYM
cana-4367	102	7	hd([252]2	hd([252]2	X
cana-4367	102	8	,	,	PUNCT
cana-4367	102	9	[	[	X
cana-4367	102	10	60]2	60]2	NUM
cana-4367	102	11	)	)	PUNCT
cana-4367	102	12	=	=	SYM
cana-4367	103	1	2	2	X
cana-4367	103	2	.	.	X
cana-4367	103	3	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	103	4	′	′	NOUN
cana-4367	103	5	)	)	PUNCT
cana-4367	104	1	=	=	SYM
cana-4367	104	2	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	104	3	,	,	PUNCT
cana-4367	104	4	[	[	X
cana-4367	104	5	𝑓(𝑣𝑖	𝑓(𝑣𝑖	ADP
cana-4367	104	6	′)]2	′)]2	ADV
cana-4367	104	7	)	)	PUNCT
cana-4367	104	8	=	=	VERB
cana-4367	105	1	hd(2522	hd(2522	NOUN
cana-4367	105	2	,	,	PUNCT
cana-4367	105	3	[	[	X
cana-4367	105	4	12]2	12]2	NUM
cana-4367	105	5	)	)	PUNCT
cana-4367	105	6	=	=	SYM
cana-4367	105	7	4	4	X
cana-4367	105	8	.	.	X
cana-4367	105	9	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	106	1	′′	′′	PROPN
cana-4367	106	2	)	)	PUNCT
cana-4367	106	3	=	=	PROPN
cana-4367	106	4	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	106	5	,	,	PUNCT
cana-4367	106	6	[	[	X
cana-4367	106	7	𝑓(𝑣𝑖	𝑓(𝑣𝑖	PROPN
cana-4367	106	8	′′)]2	′′)]2	PROPN
cana-4367	106	9	)	)	PUNCT
cana-4367	106	10	=	=	SYM
cana-4367	106	11	hd([252]2	hd([252]2	PROPN
cana-4367	106	12	,	,	PUNCT
cana-4367	106	13	[	[	X
cana-4367	106	14	0]2	0]2	X
cana-4367	106	15	)	)	PUNCT
cana-4367	106	16	=	=	SYM
cana-4367	107	1	6	6	X
cana-4367	107	2	.	.	PUNCT
cana-4367	107	3	𝑓∗(vm−1vm	𝑓∗(vm−1vm	ADJ
cana-4367	107	4	)	)	PUNCT
cana-4367	108	1	=	=	SYM
cana-4367	108	2	hd([f(vm−1)]2	hd([f(vm−1)]2	NOUN
cana-4367	108	3	,	,	PUNCT
cana-4367	108	4	[	[	X
cana-4367	108	5	f(vm)]2	f(vm)]2	X
cana-4367	108	6	)	)	PUNCT
cana-4367	108	7	=	=	SYM
cana-4367	109	1	hd([3]2	hd([3]2	X
cana-4367	109	2	,	,	PUNCT
cana-4367	109	3	[	[	X
cana-4367	109	4	252]2	252]2	NUM
cana-4367	109	5	)	)	PUNCT
cana-4367	109	6	=	=	SYM
cana-4367	109	7	8	8	X
cana-4367	109	8	.	.	PUNCT
cana-4367	109	9	case	case	NOUN
cana-4367	109	10	(	(	PUNCT
cana-4367	109	11	iii	iii	NOUN
cana-4367	109	12	):	):	PUNCT
cana-4367	109	13	if	if	SCONJ
cana-4367	109	14	i	i	PRON
cana-4367	109	15	≡	≡	VERB
cana-4367	109	16	3(mod	3(mod	NUM
cana-4367	109	17	4	4	NUM
cana-4367	109	18	)	)	PUNCT
cana-4367	109	19	𝑓∗(vivi+1	𝑓∗(vivi+1	NUM
cana-4367	109	20	)	)	PUNCT
cana-4367	109	21	=	=	SYM
cana-4367	110	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	110	2	,	,	PUNCT
cana-4367	110	3	[	[	X
cana-4367	110	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	110	5	)	)	PUNCT
cana-4367	110	6	=	=	SYM
cana-4367	110	7	hd([60]2	hd([60]2	PROPN
cana-4367	110	8	,	,	PUNCT
cana-4367	110	9	[	[	X
cana-4367	110	10	195]2	195]2	NUM
cana-4367	110	11	)	)	PUNCT
cana-4367	110	12	=	=	SYM
cana-4367	110	13	8	8	X
cana-4367	110	14	.	.	PUNCT
cana-4367	110	15	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	110	16	′	′	NOUN
cana-4367	110	17	)	)	PUNCT
cana-4367	111	1	=	=	SYM
cana-4367	111	2	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	111	3	,	,	PUNCT
cana-4367	111	4	[	[	X
cana-4367	111	5	𝑓(𝑣𝑖	𝑓(𝑣𝑖	ADP
cana-4367	111	6	′)]2	′)]2	NUM
cana-4367	111	7	)	)	PUNCT
cana-4367	111	8	=	=	SYM
cana-4367	112	1	hd([60]2	hd([60]2	PROPN
cana-4367	112	2	,	,	PUNCT
cana-4367	112	3	[	[	X
cana-4367	112	4	0]2	0]2	X
cana-4367	112	5	)	)	PUNCT
cana-4367	112	6	=	=	PUNCT
cana-4367	113	1	4	4	X
cana-4367	113	2	.	.	X
cana-4367	113	3	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	113	4	′′	′′	PROPN
cana-4367	113	5	)	)	PUNCT
cana-4367	113	6	=	=	PROPN
cana-4367	113	7	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	113	8	,	,	PUNCT
cana-4367	113	9	[	[	X
cana-4367	113	10	𝑓(𝑣𝑖	𝑓(𝑣𝑖	PROPN
cana-4367	113	11	′′)]2	′′)]2	PROPN
cana-4367	113	12	)	)	PUNCT
cana-4367	113	13	=	=	SYM
cana-4367	113	14	hd([60]2	hd([60]2	PROPN
cana-4367	113	15	,	,	PUNCT
cana-4367	113	16	[	[	X
cana-4367	113	17	3]2	3]2	NUM
cana-4367	113	18	)	)	PUNCT
cana-4367	113	19	=	=	SYM
cana-4367	113	20	6	6	X
cana-4367	113	21	.	.	PUNCT
cana-4367	113	22	𝑓∗(vm−1vm	𝑓∗(vm−1vm	ADJ
cana-4367	113	23	)	)	PUNCT
cana-4367	113	24	=	=	SYM
cana-4367	114	1	hd([f(vm−1)]2	hd([f(vm−1)]2	NOUN
cana-4367	114	2	,	,	PUNCT
cana-4367	114	3	[	[	X
cana-4367	114	4	f(vm)]2	f(vm)]2	X
cana-4367	114	5	)	)	PUNCT
cana-4367	114	6	=	=	SYM
cana-4367	114	7	hd([252]2	hd([252]2	X
cana-4367	114	8	,	,	PUNCT
cana-4367	114	9	[	[	X
cana-4367	114	10	60]2	60]2	NUM
cana-4367	114	11	)	)	PUNCT
cana-4367	114	12	=	=	SYM
cana-4367	114	13	2	2	X
cana-4367	114	14	.	.	X
cana-4367	114	15	case	case	NOUN
cana-4367	114	16	(	(	PUNCT
cana-4367	114	17	iv	iv	NUM
cana-4367	114	18	):	):	PUNCT
cana-4367	114	19	if	if	SCONJ
cana-4367	114	20	i	i	PRON
cana-4367	114	21	≡	≡	PROPN
cana-4367	114	22	0(mod4	0(mod4	NUM
cana-4367	114	23	)	)	PUNCT
cana-4367	114	24	communications	communication	NOUN
cana-4367	114	25	on	on	ADP
cana-4367	114	26	applied	apply	VERB
cana-4367	114	27	nonlinear	nonlinear	ADJ
cana-4367	114	28	analysis	analysis	NOUN
cana-4367	114	29	issn	issn	NOUN
cana-4367	114	30	:	:	PUNCT
cana-4367	114	31	1074	1074	NUM
cana-4367	114	32	-	-	PUNCT
cana-4367	114	33	133x	133x	NUM
cana-4367	114	34	vol	vol	NOUN
cana-4367	114	35	32	32	NUM
cana-4367	115	1	no	no	NOUN
cana-4367	115	2	.	.	PUNCT
cana-4367	116	1	9s	9s	NUM
cana-4367	116	2	(	(	PUNCT
cana-4367	116	3	2025	2025	NUM
cana-4367	116	4	)	)	PUNCT
cana-4367	116	5	1923	1923	NUM
cana-4367	116	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4367	116	7	𝑓∗(vivi+1	𝑓∗(vivi+1	NOUN
cana-4367	116	8	)	)	PUNCT
cana-4367	116	9	=	=	SYM
cana-4367	117	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	117	2	,	,	PUNCT
cana-4367	117	3	[	[	X
cana-4367	117	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	117	5	)	)	PUNCT
cana-4367	117	6	=	=	SYM
cana-4367	117	7	hd([195]2	hd([195]2	NOUN
cana-4367	117	8	,	,	PUNCT
cana-4367	117	9	[	[	X
cana-4367	117	10	3]2	3]2	NUM
cana-4367	117	11	)	)	PUNCT
cana-4367	117	12	=	=	SYM
cana-4367	117	13	2	2	NUM
cana-4367	117	14	.	.	PUNCT
cana-4367	118	1	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	118	2	′	′	NOUN
cana-4367	118	3	)	)	PUNCT
cana-4367	119	1	=	=	SYM
cana-4367	119	2	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	119	3	,	,	PUNCT
cana-4367	119	4	[	[	X
cana-4367	119	5	𝑓(𝑣𝑖	𝑓(𝑣𝑖	ADP
cana-4367	119	6	′)]2	′)]2	NUM
cana-4367	119	7	)	)	PUNCT
cana-4367	119	8	=	=	SYM
cana-4367	120	1	hd([195]2	hd([195]2	NOUN
cana-4367	120	2	,	,	PUNCT
cana-4367	120	3	[	[	X
cana-4367	120	4	0]2	0]2	X
cana-4367	120	5	)	)	PUNCT
cana-4367	120	6	=	=	PUNCT
cana-4367	121	1	4	4	X
cana-4367	121	2	.	.	X
cana-4367	121	3	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	121	4	′′	′′	PROPN
cana-4367	121	5	)	)	PUNCT
cana-4367	121	6	=	=	PROPN
cana-4367	121	7	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	121	8	,	,	PUNCT
cana-4367	121	9	[	[	X
cana-4367	121	10	𝑓(𝑣𝑖	𝑓(𝑣𝑖	PROPN
cana-4367	121	11	′′)]2	′′)]2	PROPN
cana-4367	121	12	)	)	PUNCT
cana-4367	121	13	=	=	SYM
cana-4367	122	1	hd([195]2	hd([195]2	NOUN
cana-4367	122	2	,	,	PUNCT
cana-4367	122	3	[	[	X
cana-4367	122	4	12]2	12]2	NUM
cana-4367	122	5	)	)	PUNCT
cana-4367	122	6	=	=	SYM
cana-4367	122	7	6	6	X
cana-4367	122	8	.	.	PUNCT
cana-4367	122	9	𝑓∗(vm−1vm	𝑓∗(vm−1vm	ADJ
cana-4367	122	10	)	)	PUNCT
cana-4367	123	1	=	=	SYM
cana-4367	123	2	hd([f(vm−1)]2	hd([f(vm−1)]2	NOUN
cana-4367	123	3	,	,	PUNCT
cana-4367	123	4	[	[	X
cana-4367	123	5	f(vm)]2	f(vm)]2	X
cana-4367	123	6	)	)	PUNCT
cana-4367	123	7	=	=	SYM
cana-4367	123	8	hd([60]2	hd([60]2	PROPN
cana-4367	123	9	,	,	PUNCT
cana-4367	123	10	[	[	X
cana-4367	123	11	195]2	195]2	NUM
cana-4367	123	12	)	)	PUNCT
cana-4367	123	13	=	=	SYM
cana-4367	123	14	8	8	X
cana-4367	123	15	.	.	PUNCT
cana-4367	123	16	from	from	ADP
cana-4367	123	17	all	all	DET
cana-4367	123	18	the	the	DET
cana-4367	123	19	above	above	ADJ
cana-4367	123	20	cases	case	NOUN
cana-4367	123	21	,	,	PUNCT
cana-4367	123	22	all	all	DET
cana-4367	123	23	the	the	DET
cana-4367	123	24	adjacent	adjacent	ADJ
cana-4367	123	25	edges	edge	NOUN
cana-4367	123	26	receive	receive	VERB
cana-4367	123	27	distinct	distinct	ADJ
cana-4367	123	28	even	even	ADV
cana-4367	123	29	labels	label	NOUN
cana-4367	123	30	.	.	PUNCT
cana-4367	124	1	hence	hence	ADV
cana-4367	124	2	the	the	DET
cana-4367	124	3	twig	twig	NOUN
cana-4367	124	4	graph	graph	VERB
cana-4367	124	5	𝑇𝑊(𝑃𝑚	𝑇𝑊(𝑃𝑚	PROPN
cana-4367	124	6	)	)	PUNCT
cana-4367	124	7	,	,	PUNCT
cana-4367	124	8	admits	admit	VERB
cana-4367	124	9	even	even	ADV
cana-4367	124	10	hamming	ham	VERB
cana-4367	124	11	distance	distance	NOUN
cana-4367	124	12	labeling	labeling	NOUN
cana-4367	124	13	and	and	CCONJ
cana-4367	124	14	the	the	DET
cana-4367	124	15	even	even	ADV
cana-4367	124	16	hamming	hamming	NOUN
cana-4367	124	17	distance	distance	NOUN
cana-4367	124	18	number	number	NOUN
cana-4367	124	19	is	be	AUX
cana-4367	124	20	ηℎ𝑑	ηℎ𝑑	NOUN
cana-4367	124	21	′′	′′	PROPN
cana-4367	124	22	(	(	PUNCT
cana-4367	124	23	𝑇𝑊(𝑃𝑚	𝑇𝑊(𝑃𝑚	X
cana-4367	124	24	)	)	PUNCT
cana-4367	124	25	)	)	PUNCT
cana-4367	125	1	=	=	SYM
cana-4367	125	2	8	8	NUM
cana-4367	125	3	,	,	PUNCT
cana-4367	125	4	for	for	ADP
cana-4367	125	5	any	any	DET
cana-4367	125	6	𝑚	𝑚	PROPN
cana-4367	125	7	≥	≥	NOUN
cana-4367	125	8	2	2	NUM
cana-4367	125	9	.	.	PUNCT
cana-4367	126	1	algorithm	algorithm	PROPN
cana-4367	126	2	2.1.5	2.1.5	NUM
cana-4367	126	3	.	.	PUNCT
cana-4367	127	1	even	even	ADV
cana-4367	127	2	hamming	ham	VERB
cana-4367	127	3	distance	distance	NOUN
cana-4367	127	4	labeling	labeling	NOUN
cana-4367	127	5	of	of	ADP
cana-4367	127	6	centipede	centipede	NOUN
cana-4367	127	7	graph(𝒎	graph(𝒎	PROPN
cana-4367	127	8	,	,	PUNCT
cana-4367	127	9	𝟐	𝟐	NUM
cana-4367	127	10	)	)	PUNCT
cana-4367	127	11	.	.	PUNCT
cana-4367	128	1	input	input	NOUN
cana-4367	128	2	:	:	PUNCT
cana-4367	128	3	vertices	vertex	NOUN
cana-4367	128	4	of	of	ADP
cana-4367	128	5	centipede	centipede	NOUN
cana-4367	128	6	graph	graph	NOUN
cana-4367	128	7	(	(	PUNCT
cana-4367	128	8	𝑚	𝑚	NOUN
cana-4367	128	9	,	,	PUNCT
cana-4367	128	10	2	2	NUM
cana-4367	128	11	)	)	PUNCT
cana-4367	128	12	graph	graph	NOUN
cana-4367	128	13	,	,	PUNCT
cana-4367	128	14	𝑚	𝑚	X
cana-4367	128	15	≥	≥	NUM
cana-4367	128	16	1	1	NUM
cana-4367	128	17	𝑉	𝑉	PROPN
cana-4367	128	18	←	←	PROPN
cana-4367	128	19	{	{	PUNCT
cana-4367	128	20	𝑣𝑖	𝑣𝑖	NOUN
cana-4367	128	21	,	,	PUNCT
cana-4367	128	22	𝑣𝑖	𝑣𝑖	ADP
cana-4367	128	23	՚	՚	PROPN
cana-4367	128	24	,	,	PUNCT
cana-4367	128	25	𝑣𝑖	𝑣𝑖	ADP
cana-4367	128	26	՚՚/0	՚՚/0	PROPN
cana-4367	128	27	≤	≤	NUM
cana-4367	128	28	𝑖	𝑖	SYM
cana-4367	128	29	≤	≤	NUM
cana-4367	128	30	𝑚	𝑚	NOUN
cana-4367	128	31	}	}	PUNCT
cana-4367	128	32	𝑣0	𝑣0	PROPN
cana-4367	128	33	←	←	PROPN
cana-4367	128	34	0	0	NUM
cana-4367	128	35	;	;	PUNCT
cana-4367	128	36	𝑣0	𝑣0	PROPN
cana-4367	128	37	′	′	PROPN
cana-4367	128	38	←	←	PROPN
cana-4367	128	39	15	15	NUM
cana-4367	128	40	;	;	PUNCT
cana-4367	128	41	𝑣0	𝑣0	PROPN
cana-4367	128	42	′′	′′	PROPN
cana-4367	128	43	←	←	PROPN
cana-4367	128	44	63	63	NUM
cana-4367	128	45	;	;	PUNCT
cana-4367	128	46	𝑣𝑚	𝑣𝑚	VERB
cana-4367	128	47	′	′	PROPN
cana-4367	128	48	←	←	PROPN
cana-4367	128	49	{	{	PUNCT
cana-4367	128	50	12	12	NUM
cana-4367	128	51	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	128	52	𝑚	𝑚	PROPN
cana-4367	128	53	≡	≡	PROPN
cana-4367	128	54	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	128	55	)	)	PUNCT
cana-4367	128	56	0	0	NUM
cana-4367	129	1	𝑖𝑓	𝑖𝑓	ADP
cana-4367	129	2	𝑚	𝑚	PROPN
cana-4367	129	3	≡	≡	PROPN
cana-4367	129	4	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	129	5	)	)	PUNCT
cana-4367	129	6	15	15	NUM
cana-4367	129	7	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	129	8	𝑚	𝑚	X
cana-4367	129	9	≡	≡	PROPN
cana-4367	129	10	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	129	11	)	)	PUNCT
cana-4367	129	12	3	3	NUM
cana-4367	129	13	𝑖𝑓	𝑖𝑓	ADP
cana-4367	129	14	𝑚	𝑚	PROPN
cana-4367	129	15	≡	≡	PROPN
cana-4367	129	16	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	129	17	)	)	PUNCT
cana-4367	129	18	;	;	PUNCT
cana-4367	129	19	𝑣𝑚	𝑣𝑚	PUNCT
cana-4367	129	20	′′	′′	PROPN
cana-4367	129	21	←	←	PROPN
cana-4367	129	22	{	{	PUNCT
cana-4367	129	23	60	60	NUM
cana-4367	129	24	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	129	25	𝑚	𝑚	PROPN
cana-4367	129	26	≡	≡	PROPN
cana-4367	129	27	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	129	28	)	)	PUNCT
cana-4367	129	29	51	51	NUM
cana-4367	129	30	𝑖𝑓	𝑖𝑓	ADP
cana-4367	129	31	𝑚	𝑚	PROPN
cana-4367	129	32	≡	≡	PROPN
cana-4367	129	33	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	129	34	)	)	PUNCT
cana-4367	129	35	63	63	NUM
cana-4367	129	36	𝑖𝑓	𝑖𝑓	NUM
cana-4367	129	37	𝑚	𝑚	PROPN
cana-4367	129	38	≡	≡	PROPN
cana-4367	129	39	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	129	40	)	)	PUNCT
cana-4367	129	41	48	48	NUM
cana-4367	129	42	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	129	43	𝑚	𝑚	PROPN
cana-4367	129	44	≡	≡	PROPN
cana-4367	129	45	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	129	46	)	)	PUNCT
cana-4367	129	47	for	for	ADP
cana-4367	129	48	𝑖	𝑖	NOUN
cana-4367	129	49	=	=	SYM
cana-4367	129	50	1	1	NUM
cana-4367	129	51	𝑡𝑜	𝑡𝑜	NOUN
cana-4367	129	52	𝑚	𝑚	ADP
cana-4367	129	53	−	−	PROPN
cana-4367	129	54	1	1	NUM
cana-4367	129	55	do	do	AUX
cana-4367	129	56	𝑣𝑖	𝑣𝑖	ADV
cana-4367	129	57	′	′	NUM
cana-4367	129	58	←	←	PROPN
cana-4367	129	59	{	{	PUNCT
cana-4367	129	60	60	60	NUM
cana-4367	129	61	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	129	62	𝑖	𝑖	SYM
cana-4367	129	63	≡	≡	PROPN
cana-4367	129	64	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	129	65	)	)	PUNCT
cana-4367	130	1	51	51	NUM
cana-4367	130	2	𝑖𝑓	𝑖𝑓	SYM
cana-4367	130	3	𝑖	𝑖	PROPN
cana-4367	130	4	≡	≡	PROPN
cana-4367	130	5	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	130	6	)	)	PUNCT
cana-4367	130	7	63	63	NUM
cana-4367	130	8	𝑖𝑓	𝑖𝑓	SYM
cana-4367	130	9	𝑖	𝑖	SYM
cana-4367	130	10	≡	≡	PROPN
cana-4367	130	11	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	130	12	)	)	PUNCT
cana-4367	130	13	48	48	NUM
cana-4367	130	14	𝑖𝑓	𝑖𝑓	SYM
cana-4367	130	15	𝑖	𝑖	PROPN
cana-4367	130	16	≡	≡	PROPN
cana-4367	130	17	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	130	18	)	)	PUNCT
cana-4367	130	19	;	;	PUNCT
cana-4367	131	1	𝑣𝑖	𝑣𝑖	ADP
cana-4367	131	2	′′	′′	PROPN
cana-4367	131	3	←	←	PROPN
cana-4367	131	4	{	{	PUNCT
cana-4367	131	5	252	252	NUM
cana-4367	131	6	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	131	7	𝑖	𝑖	NUM
cana-4367	131	8	≡	≡	PROPN
cana-4367	131	9	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	131	10	)	)	PUNCT
cana-4367	131	11	243	243	NUM
cana-4367	131	12	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	131	13	𝑖	𝑖	SYM
cana-4367	131	14	≡	≡	PROPN
cana-4367	131	15	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	131	16	)	)	PUNCT
cana-4367	131	17	255	255	NUM
cana-4367	131	18	𝑖𝑓	𝑖𝑓	ADP
cana-4367	131	19	𝑖	𝑖	SYM
cana-4367	131	20	≡	≡	PROPN
cana-4367	131	21	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	131	22	)	)	PUNCT
cana-4367	131	23	240	240	NUM
cana-4367	132	1	𝑖𝑓	𝑖𝑓	ADP
cana-4367	132	2	𝑖	𝑖	PROPN
cana-4367	132	3	≡	≡	PROPN
cana-4367	132	4	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	132	5	)	)	PUNCT
cana-4367	132	6	end	end	VERB
cana-4367	132	7	for	for	ADP
cana-4367	132	8	for	for	ADP
cana-4367	132	9	𝑖	𝑖	SYM
cana-4367	132	10	=	=	SYM
cana-4367	132	11	1	1	NUM
cana-4367	132	12	𝑡𝑜	𝑡𝑜	NOUN
cana-4367	132	13	𝑚	𝑚	AUX
cana-4367	132	14	do	do	VERB
cana-4367	132	15	𝑣𝑖	𝑣𝑖	ADP
cana-4367	132	16	←	←	PROPN
cana-4367	132	17	{	{	PUNCT
cana-4367	132	18	3	3	NUM
cana-4367	132	19	𝑖𝑓	𝑖𝑓	ADP
cana-4367	132	20	𝑖	𝑖	SYM
cana-4367	132	21	≡	≡	PROPN
cana-4367	132	22	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	132	23	)	)	PUNCT
cana-4367	132	24	12	12	NUM
cana-4367	132	25	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	132	26	𝑖	𝑖	PROPN
cana-4367	132	27	≡	≡	PROPN
cana-4367	132	28	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	132	29	)	)	PUNCT
cana-4367	132	30	0	0	NUM
cana-4367	133	1	𝑖𝑓	𝑖𝑓	CCONJ
cana-4367	133	2	𝑖	𝑖	SYM
cana-4367	133	3	≡	≡	PROPN
cana-4367	133	4	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	133	5	)	)	PUNCT
cana-4367	133	6	15	15	NUM
cana-4367	133	7	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	133	8	𝑖	𝑖	PROPN
cana-4367	133	9	≡	≡	PROPN
cana-4367	133	10	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	133	11	)	)	PUNCT
cana-4367	133	12	;	;	PUNCT
cana-4367	133	13	end	end	VERB
cana-4367	133	14	for	for	ADP
cana-4367	133	15	end	end	NOUN
cana-4367	133	16	procedure	procedure	NOUN
cana-4367	133	17	output	output	NOUN
cana-4367	133	18	:	:	PUNCT
cana-4367	133	19	the	the	DET
cana-4367	133	20	labeled	label	VERB
cana-4367	133	21	vertices	vertex	NOUN
cana-4367	133	22	of	of	ADP
cana-4367	133	23	centipede	centipede	NOUN
cana-4367	133	24	(	(	PUNCT
cana-4367	133	25	m,2	m,2	NUM
cana-4367	133	26	)	)	PUNCT
cana-4367	133	27	graph	graph	NOUN
cana-4367	133	28	.	.	PUNCT
cana-4367	134	1	theorem	theorem	VERB
cana-4367	134	2	:	:	PUNCT
cana-4367	135	1	2.1.6	2.1.6	X
cana-4367	135	2	.	.	PUNCT
cana-4367	136	1	the	the	DET
cana-4367	136	2	centipede	centipede	NOUN
cana-4367	136	3	graph	graph	NOUN
cana-4367	136	4	(	(	PUNCT
cana-4367	136	5	𝑚	𝑚	NOUN
cana-4367	136	6	,	,	PUNCT
cana-4367	136	7	2	2	NUM
cana-4367	136	8	)	)	PUNCT
cana-4367	136	9	is	be	AUX
cana-4367	136	10	an	an	DET
cana-4367	136	11	even	even	ADV
cana-4367	136	12	hamming	ham	VERB
cana-4367	136	13	distance	distance	NOUN
cana-4367	136	14	labeled	label	VERB
cana-4367	136	15	graph	graph	NOUN
cana-4367	136	16	and	and	CCONJ
cana-4367	136	17	the	the	DET
cana-4367	136	18	even	even	ADV
cana-4367	136	19	hamming	hamming	NOUN
cana-4367	136	20	distance	distance	NOUN
cana-4367	136	21	number	number	NOUN
cana-4367	136	22	is	be	AUX
cana-4367	136	23	ηℎ𝑑	ηℎ𝑑	NOUN
cana-4367	136	24	′′	′′	PROPN
cana-4367	136	25	(	(	PUNCT
cana-4367	136	26	m	m	PROPN
cana-4367	136	27	,	,	PUNCT
cana-4367	136	28	2	2	X
cana-4367	136	29	)	)	PUNCT
cana-4367	136	30	=	=	NOUN
cana-4367	136	31	{	{	PUNCT
cana-4367	136	32	6	6	NUM
cana-4367	136	33	,	,	PUNCT
cana-4367	136	34	𝑖𝑓	𝑖𝑓	ADP
cana-4367	136	35	𝑚	𝑚	NOUN
cana-4367	136	36	=	=	SYM
cana-4367	136	37	1	1	NUM
cana-4367	136	38	8	8	NUM
cana-4367	136	39	,	,	PUNCT
cana-4367	136	40	𝑖𝑓	𝑖𝑓	ADP
cana-4367	136	41	𝑚	𝑚	X
cana-4367	136	42	>	>	SYM
cana-4367	136	43	1	1	NUM
cana-4367	136	44	proof	proof	NOUN
cana-4367	136	45	:	:	PUNCT
cana-4367	136	46	let	let	VERB
cana-4367	136	47	us	we	PRON
cana-4367	136	48	consider	consider	VERB
cana-4367	136	49	the	the	DET
cana-4367	136	50	centipede	centipede	NOUN
cana-4367	136	51	graph	graph	NOUN
cana-4367	136	52	(	(	PUNCT
cana-4367	136	53	𝑚	𝑚	NOUN
cana-4367	136	54	,	,	PUNCT
cana-4367	136	55	2	2	NUM
cana-4367	136	56	)	)	PUNCT
cana-4367	136	57	with	with	ADP
cana-4367	136	58	vertex	vertex	NOUN
cana-4367	136	59	set	set	VERB
cana-4367	136	60	𝑉	𝑉	PROPN
cana-4367	136	61	=	=	PUNCT
cana-4367	136	62	{	{	PUNCT
cana-4367	136	63	{	{	PUNCT
cana-4367	136	64	𝑣0,𝑣1,𝑣2	𝑣0,𝑣1,𝑣2	NOUN
cana-4367	136	65	,	,	PUNCT
cana-4367	136	66	…	…	PUNCT
cana-4367	136	67	,	,	PUNCT
cana-4367	136	68	𝑣𝑚	𝑣𝑚	VERB
cana-4367	136	69	}	}	PUNCT
cana-4367	136	70	∪	∪	ADJ
cana-4367	136	71	{	{	PUNCT
cana-4367	136	72	𝑣0	𝑣0	PROPN
cana-4367	136	73	,	,	PUNCT
cana-4367	136	74	′	′	NUM
cana-4367	136	75	𝑣1	𝑣1	NOUN
cana-4367	136	76	,	,	PUNCT
cana-4367	136	77	′	′	NUM
cana-4367	136	78	𝑣2	𝑣2	NOUN
cana-4367	136	79	,	,	PUNCT
cana-4367	136	80	′	′	NUM
cana-4367	136	81	…	…	PUNCT
cana-4367	136	82	,	,	PUNCT
cana-4367	136	83	𝑣𝑚	𝑣𝑚	VERB
cana-4367	136	84	′	′	NOUN
cana-4367	136	85	}	}	PUNCT
cana-4367	136	86	∪	∪	VERB
cana-4367	136	87	{	{	PUNCT
cana-4367	136	88	𝑣0	𝑣0	PROPN
cana-4367	136	89	,	,	PUNCT
cana-4367	136	90	′′𝑣1	′′𝑣1	PROPN
cana-4367	136	91	,	,	PUNCT
cana-4367	136	92	′′𝑣2	′′𝑣2	X
cana-4367	136	93	,	,	PUNCT
cana-4367	136	94	′′	′′	PROPN
cana-4367	136	95	…	…	PUNCT
cana-4367	136	96	,	,	PUNCT
cana-4367	136	97	𝑣𝑚	𝑣𝑚	ADJ
cana-4367	136	98	′′	′′	PROPN
cana-4367	136	99	}	}	PUNCT
cana-4367	136	100	}	}	PUNCT
cana-4367	136	101	and	and	CCONJ
cana-4367	136	102	edge	edge	NOUN
cana-4367	136	103	set	set	VERB
cana-4367	136	104	𝐸	𝐸	NOUN
cana-4367	136	105	=	=	PUNCT
cana-4367	136	106	communications	communication	NOUN
cana-4367	136	107	on	on	ADP
cana-4367	136	108	applied	apply	VERB
cana-4367	136	109	nonlinear	nonlinear	ADJ
cana-4367	136	110	analysis	analysis	NOUN
cana-4367	136	111	issn	issn	NOUN
cana-4367	136	112	:	:	PUNCT
cana-4367	136	113	1074	1074	NUM
cana-4367	136	114	-	-	PUNCT
cana-4367	136	115	133x	133x	NUM
cana-4367	136	116	vol	vol	NOUN
cana-4367	136	117	32	32	NUM
cana-4367	136	118	no	no	NOUN
cana-4367	136	119	.	.	PUNCT
cana-4367	137	1	9s	9s	NUM
cana-4367	137	2	(	(	PUNCT
cana-4367	137	3	2025	2025	NUM
cana-4367	137	4	)	)	PUNCT
cana-4367	137	5	1924	1924	NUM
cana-4367	137	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4367	137	7	{	{	PUNCT
cana-4367	137	8	{	{	PUNCT
cana-4367	137	9	𝑣𝑖𝑣𝑖+1	𝑣𝑖𝑣𝑖+1	PROPN
cana-4367	137	10	/	/	SYM
cana-4367	137	11	0	0	NUM
cana-4367	137	12	≤	≤	NUM
cana-4367	137	13	𝑖	𝑖	SYM
cana-4367	137	14	≤	≤	NOUN
cana-4367	137	15	𝑚	𝑚	ADP
cana-4367	137	16	−	−	PROPN
cana-4367	137	17	1	1	NUM
cana-4367	137	18	}	}	PUNCT
cana-4367	137	19	∪	∪	ADJ
cana-4367	137	20	{	{	PUNCT
cana-4367	137	21	𝑣𝑖𝑣𝑖	𝑣𝑖𝑣𝑖	NOUN
cana-4367	137	22	′/0	′/0	NUM
cana-4367	137	23	≤	≤	NUM
cana-4367	137	24	𝑖	𝑖	SYM
cana-4367	137	25	≤	≤	NUM
cana-4367	137	26	𝑚	𝑚	NOUN
cana-4367	137	27	}	}	PUNCT
cana-4367	137	28	∪	∪	ADJ
cana-4367	137	29	{	{	PUNCT
cana-4367	137	30	𝑣𝑖𝑣𝑖	𝑣𝑖𝑣𝑖	NOUN
cana-4367	137	31	′′/0	′′/0	PUNCT
cana-4367	137	32	≤	≤	NUM
cana-4367	137	33	𝑖	𝑖	SYM
cana-4367	137	34	≤	≤	NUM
cana-4367	137	35	𝑚	𝑚	ADP
cana-4367	137	36	}	}	PUNCT
cana-4367	137	37	}	}	PUNCT
cana-4367	137	38	.	.	PUNCT
cana-4367	138	1	define	define	VERB
cana-4367	138	2	a	a	DET
cana-4367	138	3	function	function	NOUN
cana-4367	138	4	𝑓	𝑓	PRON
cana-4367	138	5	:	:	PUNCT
cana-4367	138	6	v	v	NOUN
cana-4367	138	7	→	→	SYM
cana-4367	138	8	n	n	CCONJ
cana-4367	138	9	∪	∪	X
cana-4367	138	10	{	{	PUNCT
cana-4367	138	11	0	0	NUM
cana-4367	138	12	}	}	PUNCT
cana-4367	138	13	such	such	ADJ
cana-4367	138	14	that	that	SCONJ
cana-4367	138	15	𝑓(𝑢	𝑓(𝑢	PROPN
cana-4367	138	16	)	)	PUNCT
cana-4367	138	17	≠	≠	PROPN
cana-4367	138	18	𝑓(𝑣	𝑓(𝑣	PROPN
cana-4367	138	19	)	)	PUNCT
cana-4367	138	20	for	for	ADP
cana-4367	138	21	any	any	DET
cana-4367	138	22	two	two	NUM
cana-4367	138	23	adjacent	adjacent	ADJ
cana-4367	138	24	vertices	vertex	NOUN
cana-4367	138	25	u	u	NOUN
cana-4367	138	26	and	and	CCONJ
cana-4367	138	27	v	v	NOUN
cana-4367	138	28	as	as	SCONJ
cana-4367	138	29	given	give	VERB
cana-4367	138	30	in	in	ADP
cana-4367	138	31	the	the	DET
cana-4367	138	32	above	above	ADJ
cana-4367	138	33	algorithm	algorithm	NOUN
cana-4367	138	34	2.1.5	2.1.5	NUM
cana-4367	138	35	.	.	PUNCT
cana-4367	139	1	hence	hence	ADV
cana-4367	139	2	the	the	DET
cana-4367	139	3	adjacent	adjacent	ADJ
cana-4367	139	4	vertices	vertex	NOUN
cana-4367	139	5	receive	receive	VERB
cana-4367	139	6	distinct	distinct	ADJ
cana-4367	139	7	labels	label	NOUN
cana-4367	139	8	.	.	PUNCT
cana-4367	140	1	the	the	DET
cana-4367	140	2	edge	edge	NOUN
cana-4367	140	3	labels	label	NOUN
cana-4367	140	4	are	be	AUX
cana-4367	140	5	obtained	obtain	VERB
cana-4367	140	6	as	as	ADP
cana-4367	140	7	follows	follow	VERB
cana-4367	140	8	:	:	PUNCT
cana-4367	140	9	𝑓∗(𝑣0𝑣0	𝑓∗(𝑣0𝑣0	PROPN
cana-4367	140	10	′	′	NUM
cana-4367	140	11	)	)	PUNCT
cana-4367	140	12	=	=	PUNCT
cana-4367	141	1	ℎ𝑑([𝑓(𝑣0)]2	ℎ𝑑([𝑓(𝑣0)]2	ADV
cana-4367	141	2	,	,	PUNCT
cana-4367	141	3	[	[	X
cana-4367	141	4	𝑓(𝑣0	𝑓(𝑣0	NOUN
cana-4367	141	5	′)]2	′)]2	ADV
cana-4367	141	6	)	)	PUNCT
cana-4367	142	1	=	=	SYM
cana-4367	143	1	hd([0]2	hd([0]2	NOUN
cana-4367	143	2	,	,	PUNCT
cana-4367	143	3	[	[	X
cana-4367	143	4	15]2	15]2	X
cana-4367	143	5	)	)	PUNCT
cana-4367	143	6	=	=	SYM
cana-4367	143	7	4	4	X
cana-4367	143	8	.	.	X
cana-4367	144	1	𝑓∗(𝑣0𝑣0	𝑓∗(𝑣0𝑣0	PROPN
cana-4367	144	2	′′	′′	PROPN
cana-4367	144	3	)	)	PUNCT
cana-4367	144	4	=	=	PUNCT
cana-4367	145	1	ℎ𝑑([𝑓(𝑣0)]2	ℎ𝑑([𝑓(𝑣0)]2	ADV
cana-4367	145	2	,	,	PUNCT
cana-4367	145	3	[	[	X
cana-4367	145	4	𝑓(𝑣0	𝑓(𝑣0	X
cana-4367	145	5	′′)]2	′′)]2	NOUN
cana-4367	145	6	=	=	PUNCT
cana-4367	146	1	hd([0]2	hd([0]2	PROPN
cana-4367	146	2	,	,	PUNCT
cana-4367	146	3	[	[	X
cana-4367	146	4	63]2	63]2	NOUN
cana-4367	146	5	)	)	PUNCT
cana-4367	146	6	=	=	SYM
cana-4367	146	7	6	6	X
cana-4367	146	8	.	.	PUNCT
cana-4367	147	1	for	for	ADP
cana-4367	147	2	1	1	NUM
cana-4367	147	3	≤	≤	NUM
cana-4367	147	4	𝑖	𝑖	SYM
cana-4367	147	5	≤	≤	NOUN
cana-4367	147	6	𝑚	𝑚	ADP
cana-4367	147	7	−	−	PROPN
cana-4367	147	8	1	1	NUM
cana-4367	147	9	,	,	PUNCT
cana-4367	147	10	case	case	NOUN
cana-4367	147	11	(	(	PUNCT
cana-4367	147	12	i	i	NOUN
cana-4367	147	13	):	):	PUNCT
cana-4367	147	14	if	if	SCONJ
cana-4367	147	15	i	i	PRON
cana-4367	147	16	≡	≡	PROPN
cana-4367	147	17	1(mod	1(mod	NUM
cana-4367	147	18	4	4	NUM
cana-4367	147	19	)	)	PUNCT
cana-4367	147	20	or	or	CCONJ
cana-4367	147	21	m	m	PROPN
cana-4367	147	22	≡	≡	ADJ
cana-4367	147	23	1(mod	1(mod	NUM
cana-4367	147	24	4	4	X
cana-4367	147	25	)	)	PUNCT
cana-4367	147	26	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	147	27	′	′	NOUN
cana-4367	147	28	)	)	PUNCT
cana-4367	147	29	=	=	PUNCT
cana-4367	147	30	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	147	31	,	,	PUNCT
cana-4367	147	32	[	[	X
cana-4367	147	33	𝑓(𝑣𝑖	𝑓(𝑣𝑖	ADP
cana-4367	147	34	′)]2	′)]2	NUM
cana-4367	147	35	)	)	PUNCT
cana-4367	147	36	=	=	PUNCT
cana-4367	147	37	hd([3]2	hd([3]2	X
cana-4367	147	38	,	,	PUNCT
cana-4367	147	39	[	[	X
cana-4367	147	40	60]2	60]2	NUM
cana-4367	147	41	)	)	PUNCT
cana-4367	147	42	=	=	PUNCT
cana-4367	147	43	6	6	NUM
cana-4367	147	44	.	.	PUNCT
cana-4367	147	45	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	147	46	′′	′′	NOUN
cana-4367	147	47	)	)	PUNCT
cana-4367	147	48	=	=	PROPN
cana-4367	147	49	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	147	50	,	,	PUNCT
cana-4367	147	51	[	[	X
cana-4367	147	52	𝑓(𝑣𝑖	𝑓(𝑣𝑖	PROPN
cana-4367	147	53	′′)]2	′′)]2	PROPN
cana-4367	147	54	)	)	PUNCT
cana-4367	147	55	=	=	PUNCT
cana-4367	147	56	hd([3]2	hd([3]2	X
cana-4367	147	57	,	,	PUNCT
cana-4367	147	58	[	[	X
cana-4367	147	59	252]2	252]2	NUM
cana-4367	147	60	)	)	PUNCT
cana-4367	147	61	=	=	SYM
cana-4367	147	62	8	8	X
cana-4367	147	63	.	.	PUNCT
cana-4367	147	64	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	NOUN
cana-4367	147	65	′	′	VERB
cana-4367	147	66	)	)	PUNCT
cana-4367	148	1	=	=	PUNCT
cana-4367	149	1	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	NUM
cana-4367	149	2	,	,	PUNCT
cana-4367	149	3	[	[	X
cana-4367	149	4	𝑓(𝑣𝑚	𝑓(𝑣𝑚	NOUN
cana-4367	149	5	′	′	NUM
cana-4367	149	6	)	)	PUNCT
cana-4367	149	7	]	]	PUNCT
cana-4367	149	8	2	2	X
cana-4367	149	9	)	)	PUNCT
cana-4367	149	10	=	=	SYM
cana-4367	149	11	hd([3]2	hd([3]2	X
cana-4367	149	12	,	,	PUNCT
cana-4367	149	13	[	[	X
cana-4367	149	14	12]2	12]2	NUM
cana-4367	149	15	)	)	PUNCT
cana-4367	149	16	=	=	SYM
cana-4367	149	17	4	4	X
cana-4367	149	18	.	.	X
cana-4367	149	19	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	PROPN
cana-4367	149	20	′′	′′	PROPN
cana-4367	149	21	)	)	PUNCT
cana-4367	149	22	=	=	PUNCT
cana-4367	150	1	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	PROPN
cana-4367	150	2	,	,	PUNCT
cana-4367	150	3	[	[	X
cana-4367	150	4	𝑓(𝑣𝑚	𝑓(𝑣𝑚	PROPN
cana-4367	150	5	′′)]2	′′)]2	PROPN
cana-4367	150	6	)	)	PUNCT
cana-4367	150	7	=	=	PUNCT
cana-4367	151	1	hd([3]2	hd([3]2	X
cana-4367	151	2	,	,	PUNCT
cana-4367	151	3	[	[	X
cana-4367	151	4	60]2	60]2	NUM
cana-4367	151	5	)	)	PUNCT
cana-4367	151	6	=	=	SYM
cana-4367	151	7	6	6	X
cana-4367	151	8	.	.	X
cana-4367	151	9	case	case	NOUN
cana-4367	151	10	(	(	PUNCT
cana-4367	151	11	ii	ii	NUM
cana-4367	151	12	):	):	PUNCT
cana-4367	151	13	if	if	SCONJ
cana-4367	151	14	i	i	PRON
cana-4367	151	15	≡	≡	PROPN
cana-4367	151	16	2(mod4	2(mod4	NUM
cana-4367	151	17	)	)	PUNCT
cana-4367	151	18	or	or	CCONJ
cana-4367	151	19	m	m	PROPN
cana-4367	151	20	≡	≡	ADJ
cana-4367	151	21	2(mod	2(mod	NUM
cana-4367	151	22	4	4	X
cana-4367	151	23	)	)	PUNCT
cana-4367	151	24	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	151	25	′	′	NOUN
cana-4367	151	26	)	)	PUNCT
cana-4367	151	27	=	=	PUNCT
cana-4367	152	1	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	152	2	,	,	PUNCT
cana-4367	152	3	[	[	X
cana-4367	152	4	𝑓(𝑣𝑖	𝑓(𝑣𝑖	ADP
cana-4367	152	5	′)]2	′)]2	NUM
cana-4367	152	6	)	)	PUNCT
cana-4367	152	7	=	=	SYM
cana-4367	153	1	hd([12]2	hd([12]2	PROPN
cana-4367	153	2	,	,	PUNCT
cana-4367	153	3	[	[	X
cana-4367	153	4	51]2	51]2	NUM
cana-4367	153	5	)	)	PUNCT
cana-4367	153	6	=	=	SYM
cana-4367	153	7	6	6	NUM
cana-4367	153	8	.	.	PUNCT
cana-4367	153	9	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	153	10	′′	′′	NOUN
cana-4367	153	11	)	)	PUNCT
cana-4367	153	12	=	=	PROPN
cana-4367	153	13	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	153	14	,	,	PUNCT
cana-4367	153	15	[	[	X
cana-4367	153	16	𝑓(𝑣𝑖	𝑓(𝑣𝑖	PROPN
cana-4367	153	17	′′)]2	′′)]2	PROPN
cana-4367	153	18	)	)	PUNCT
cana-4367	153	19	=	=	SYM
cana-4367	154	1	hd([12]2	hd([12]2	PROPN
cana-4367	154	2	,	,	PUNCT
cana-4367	154	3	[	[	X
cana-4367	154	4	243]2	243]2	X
cana-4367	154	5	)	)	PUNCT
cana-4367	154	6	=	=	SYM
cana-4367	154	7	8	8	X
cana-4367	154	8	.	.	PUNCT
cana-4367	154	9	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	NOUN
cana-4367	154	10	′	′	VERB
cana-4367	154	11	)	)	PUNCT
cana-4367	155	1	=	=	PUNCT
cana-4367	156	1	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	NUM
cana-4367	156	2	,	,	PUNCT
cana-4367	156	3	[	[	X
cana-4367	156	4	𝑓(𝑣𝑚	𝑓(𝑣𝑚	NOUN
cana-4367	156	5	′	′	NUM
cana-4367	156	6	)	)	PUNCT
cana-4367	156	7	]	]	PUNCT
cana-4367	156	8	2	2	X
cana-4367	156	9	)	)	PUNCT
cana-4367	156	10	=	=	SYM
cana-4367	156	11	hd([12]2	hd([12]2	PROPN
cana-4367	156	12	,	,	PUNCT
cana-4367	156	13	[	[	X
cana-4367	156	14	0]2	0]2	X
cana-4367	156	15	)	)	PUNCT
cana-4367	156	16	=	=	SYM
cana-4367	157	1	2	2	X
cana-4367	157	2	.	.	X
cana-4367	157	3	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	PROPN
cana-4367	157	4	′′	′′	PROPN
cana-4367	157	5	)	)	PUNCT
cana-4367	157	6	=	=	PUNCT
cana-4367	158	1	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	PROPN
cana-4367	158	2	,	,	PUNCT
cana-4367	158	3	[	[	X
cana-4367	158	4	𝑓(𝑣𝑚	𝑓(𝑣𝑚	PROPN
cana-4367	158	5	′′)]2	′′)]2	PROPN
cana-4367	158	6	)	)	PUNCT
cana-4367	158	7	=	=	SYM
cana-4367	159	1	hd([12]2	hd([12]2	PROPN
cana-4367	159	2	,	,	PUNCT
cana-4367	159	3	[	[	X
cana-4367	159	4	51]2	51]2	NUM
cana-4367	159	5	)	)	PUNCT
cana-4367	159	6	=	=	SYM
cana-4367	159	7	6	6	X
cana-4367	159	8	.	.	PUNCT
cana-4367	159	9	case	case	NOUN
cana-4367	159	10	(	(	PUNCT
cana-4367	159	11	iii	iii	NOUN
cana-4367	159	12	):	):	PUNCT
cana-4367	159	13	if	if	SCONJ
cana-4367	159	14	i	i	PRON
cana-4367	159	15	≡	≡	VERB
cana-4367	159	16	3(mod	3(mod	NUM
cana-4367	159	17	4	4	NUM
cana-4367	159	18	)	)	PUNCT
cana-4367	159	19	or	or	CCONJ
cana-4367	159	20	m	m	PROPN
cana-4367	159	21	≡	≡	PROPN
cana-4367	159	22	3(mod	3(mod	NUM
cana-4367	159	23	4	4	X
cana-4367	159	24	)	)	PUNCT
cana-4367	159	25	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	159	26	′	′	NOUN
cana-4367	159	27	)	)	PUNCT
cana-4367	159	28	=	=	PUNCT
cana-4367	160	1	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	160	2	,	,	PUNCT
cana-4367	160	3	[	[	X
cana-4367	160	4	𝑓(𝑣𝑖	𝑓(𝑣𝑖	NOUN
cana-4367	160	5	′)]2	′)]2	ADV
cana-4367	160	6	)	)	PUNCT
cana-4367	160	7	=	=	SYM
cana-4367	161	1	hd([0]2	hd([0]2	PROPN
cana-4367	161	2	,	,	PUNCT
cana-4367	161	3	[	[	X
cana-4367	161	4	63]2	63]2	NOUN
cana-4367	161	5	)	)	PUNCT
cana-4367	161	6	=	=	SYM
cana-4367	161	7	6	6	NUM
cana-4367	161	8	.	.	PUNCT
cana-4367	161	9	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	162	1	′′	′′	NOUN
cana-4367	162	2	)	)	PUNCT
cana-4367	162	3	=	=	PROPN
cana-4367	162	4	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	162	5	,	,	PUNCT
cana-4367	162	6	[	[	X
cana-4367	162	7	𝑓(𝑣𝑖	𝑓(𝑣𝑖	PROPN
cana-4367	162	8	′′)]2	′′)]2	PROPN
cana-4367	162	9	)	)	PUNCT
cana-4367	162	10	=	=	SYM
cana-4367	163	1	hd([0]2	hd([0]2	NOUN
cana-4367	163	2	,	,	PUNCT
cana-4367	163	3	[	[	X
cana-4367	163	4	255]2	255]2	NUM
cana-4367	163	5	)	)	PUNCT
cana-4367	163	6	=	=	SYM
cana-4367	163	7	8	8	X
cana-4367	163	8	.	.	PUNCT
cana-4367	164	1	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	NOUN
cana-4367	164	2	′	′	VERB
cana-4367	164	3	)	)	PUNCT
cana-4367	165	1	=	=	PUNCT
cana-4367	166	1	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	NUM
cana-4367	166	2	,	,	PUNCT
cana-4367	166	3	[	[	X
cana-4367	166	4	𝑓(𝑣𝑚	𝑓(𝑣𝑚	NOUN
cana-4367	166	5	′	′	NUM
cana-4367	166	6	)	)	PUNCT
cana-4367	166	7	]	]	PUNCT
cana-4367	166	8	2	2	X
cana-4367	166	9	)	)	PUNCT
cana-4367	166	10	=	=	SYM
cana-4367	167	1	hd([0]2	hd([0]2	NOUN
cana-4367	167	2	,	,	PUNCT
cana-4367	167	3	[	[	X
cana-4367	167	4	15]2	15]2	X
cana-4367	167	5	)	)	PUNCT
cana-4367	167	6	=	=	SYM
cana-4367	167	7	4	4	X
cana-4367	167	8	.	.	X
cana-4367	167	9	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	PROPN
cana-4367	167	10	′′	′′	PROPN
cana-4367	167	11	)	)	PUNCT
cana-4367	167	12	=	=	PUNCT
cana-4367	168	1	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	PROPN
cana-4367	168	2	,	,	PUNCT
cana-4367	168	3	[	[	X
cana-4367	168	4	𝑓(𝑣𝑚	𝑓(𝑣𝑚	PROPN
cana-4367	168	5	′′)]2	′′)]2	PROPN
cana-4367	168	6	)	)	PUNCT
cana-4367	168	7	=	=	SYM
cana-4367	169	1	hd([0]2	hd([0]2	PROPN
cana-4367	169	2	,	,	PUNCT
cana-4367	169	3	[	[	X
cana-4367	169	4	63]2	63]2	NOUN
cana-4367	169	5	)	)	PUNCT
cana-4367	169	6	=	=	SYM
cana-4367	169	7	6	6	X
cana-4367	169	8	.	.	PUNCT
cana-4367	170	1	case	case	NOUN
cana-4367	170	2	(	(	PUNCT
cana-4367	170	3	iv	iv	NUM
cana-4367	170	4	):	):	PUNCT
cana-4367	170	5	if	if	SCONJ
cana-4367	170	6	i	i	PRON
cana-4367	170	7	≡	≡	PROPN
cana-4367	170	8	0(mod4	0(mod4	NUM
cana-4367	170	9	)	)	PUNCT
cana-4367	170	10	or	or	CCONJ
cana-4367	170	11	m	m	PROPN
cana-4367	170	12	≡	≡	ADJ
cana-4367	170	13	0(mod	0(mod	NOUN
cana-4367	170	14	4	4	X
cana-4367	170	15	)	)	PUNCT
cana-4367	170	16	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	170	17	′	′	NOUN
cana-4367	170	18	)	)	PUNCT
cana-4367	170	19	=	=	PUNCT
cana-4367	171	1	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	171	2	,	,	PUNCT
cana-4367	171	3	[	[	X
cana-4367	171	4	𝑓(𝑣𝑖	𝑓(𝑣𝑖	ADP
cana-4367	171	5	′)]2	′)]2	ADV
cana-4367	171	6	)	)	PUNCT
cana-4367	171	7	=	=	SYM
cana-4367	172	1	hd([15]2	hd([15]2	NOUN
cana-4367	172	2	,	,	PUNCT
cana-4367	172	3	[	[	X
cana-4367	172	4	48]2	48]2	NOUN
cana-4367	172	5	)	)	PUNCT
cana-4367	172	6	=	=	SYM
cana-4367	172	7	6	6	NUM
cana-4367	172	8	.	.	PUNCT
cana-4367	172	9	𝑓∗(𝑣𝑖𝑣𝑖	𝑓∗(𝑣𝑖𝑣𝑖	PROPN
cana-4367	172	10	′′	′′	NOUN
cana-4367	172	11	)	)	PUNCT
cana-4367	172	12	=	=	PROPN
cana-4367	172	13	ℎ𝑑([𝑓(𝑣𝑖)]2	ℎ𝑑([𝑓(𝑣𝑖)]2	PROPN
cana-4367	172	14	,	,	PUNCT
cana-4367	172	15	[	[	X
cana-4367	172	16	𝑓(𝑣𝑖	𝑓(𝑣𝑖	PROPN
cana-4367	172	17	′′)]2	′′)]2	PROPN
cana-4367	172	18	)	)	PUNCT
cana-4367	172	19	=	=	SYM
cana-4367	173	1	hd([15]2	hd([15]2	NOUN
cana-4367	173	2	,	,	PUNCT
cana-4367	173	3	[	[	X
cana-4367	173	4	240]2	240]2	ADV
cana-4367	173	5	)	)	PUNCT
cana-4367	173	6	=	=	SYM
cana-4367	173	7	8	8	X
cana-4367	173	8	.	.	PUNCT
cana-4367	173	9	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	NOUN
cana-4367	173	10	′	′	VERB
cana-4367	173	11	)	)	PUNCT
cana-4367	174	1	=	=	PUNCT
cana-4367	175	1	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	NUM
cana-4367	175	2	,	,	PUNCT
cana-4367	175	3	[	[	X
cana-4367	175	4	𝑓(𝑣𝑚	𝑓(𝑣𝑚	NOUN
cana-4367	175	5	′	′	NUM
cana-4367	175	6	)	)	PUNCT
cana-4367	175	7	]	]	PUNCT
cana-4367	175	8	2	2	X
cana-4367	175	9	)	)	PUNCT
cana-4367	175	10	=	=	SYM
cana-4367	175	11	hd([15]2	hd([15]2	NOUN
cana-4367	175	12	,	,	PUNCT
cana-4367	175	13	[	[	X
cana-4367	175	14	3]2	3]2	NUM
cana-4367	175	15	)	)	PUNCT
cana-4367	175	16	=	=	SYM
cana-4367	175	17	2	2	X
cana-4367	175	18	.	.	X
cana-4367	175	19	𝑓∗(𝑣𝑚𝑣𝑚	𝑓∗(𝑣𝑚𝑣𝑚	PROPN
cana-4367	175	20	′′	′′	PROPN
cana-4367	175	21	)	)	PUNCT
cana-4367	175	22	=	=	PUNCT
cana-4367	176	1	ℎ𝑑([𝑓(𝑣𝑚)]2	ℎ𝑑([𝑓(𝑣𝑚)]2	PROPN
cana-4367	176	2	,	,	PUNCT
cana-4367	176	3	[	[	X
cana-4367	176	4	𝑓(𝑣𝑚	𝑓(𝑣𝑚	PROPN
cana-4367	176	5	′′)]2	′′)]2	PROPN
cana-4367	176	6	)	)	PUNCT
cana-4367	176	7	=	=	SYM
cana-4367	177	1	hd([15]2	hd([15]2	NOUN
cana-4367	177	2	,	,	PUNCT
cana-4367	177	3	[	[	X
cana-4367	177	4	48]2	48]2	NOUN
cana-4367	177	5	)	)	PUNCT
cana-4367	177	6	=	=	SYM
cana-4367	177	7	6	6	NUM
cana-4367	177	8	.	.	PUNCT
cana-4367	177	9	from	from	ADP
cana-4367	177	10	all	all	DET
cana-4367	177	11	the	the	DET
cana-4367	177	12	above	above	ADJ
cana-4367	177	13	cases	case	NOUN
cana-4367	177	14	,	,	PUNCT
cana-4367	177	15	all	all	DET
cana-4367	177	16	adjacent	adjacent	ADJ
cana-4367	177	17	edges	edge	NOUN
cana-4367	177	18	receive	receive	VERB
cana-4367	177	19	distinc	distinc	NOUN
cana-4367	177	20	event	event	NOUN
cana-4367	177	21	labels	label	NOUN
cana-4367	177	22	.	.	PUNCT
cana-4367	178	1	hence	hence	ADV
cana-4367	178	2	it	it	PRON
cana-4367	178	3	is	be	AUX
cana-4367	178	4	proved	prove	VERB
cana-4367	178	5	that	that	SCONJ
cana-4367	178	6	the	the	DET
cana-4367	178	7	centipede	centipede	NOUN
cana-4367	178	8	graph	graph	NOUN
cana-4367	178	9	(	(	PUNCT
cana-4367	178	10	m,2	m,2	PROPN
cana-4367	178	11	)	)	PUNCT
cana-4367	178	12	admits	admit	VERB
cana-4367	178	13	even	even	ADV
cana-4367	178	14	hamming	ham	VERB
cana-4367	178	15	distance	distance	NOUN
cana-4367	178	16	labeling	labeling	NOUN
cana-4367	178	17	and	and	CCONJ
cana-4367	178	18	the	the	DET
cana-4367	178	19	even	even	ADV
cana-4367	178	20	hamming	hamming	NOUN
cana-4367	178	21	distance	distance	NOUN
cana-4367	178	22	number	number	NOUN
cana-4367	178	23	is	be	AUX
cana-4367	178	24	ηℎ𝑑	ηℎ𝑑	NOUN
cana-4367	178	25	′′	′′	PROPN
cana-4367	178	26	(	(	PUNCT
cana-4367	178	27	m	m	PROPN
cana-4367	178	28	,	,	PUNCT
cana-4367	178	29	2	2	X
cana-4367	178	30	)	)	PUNCT
cana-4367	178	31	=	=	NOUN
cana-4367	178	32	{	{	PUNCT
cana-4367	178	33	6	6	NUM
cana-4367	178	34	,	,	PUNCT
cana-4367	178	35	𝑖𝑓	𝑖𝑓	ADP
cana-4367	178	36	𝑚	𝑚	NOUN
cana-4367	178	37	=	=	SYM
cana-4367	178	38	1	1	NUM
cana-4367	178	39	8	8	NUM
cana-4367	178	40	,	,	PUNCT
cana-4367	178	41	𝑖𝑓	𝑖𝑓	ADP
cana-4367	178	42	𝑚	𝑚	X
cana-4367	178	43	>	>	X
cana-4367	178	44	1	1	NUM
cana-4367	178	45	.	.	PUNCT
cana-4367	179	1	algorithm	algorithm	PROPN
cana-4367	179	2	2.1.7	2.1.7	NUM
cana-4367	179	3	.	.	PUNCT
cana-4367	180	1	even	even	ADV
cana-4367	180	2	hamming	ham	VERB
cana-4367	180	3	distance	distance	NOUN
cana-4367	180	4	labeling	labeling	NOUN
cana-4367	180	5	of	of	ADP
cana-4367	180	6	comb	comb	NOUN
cana-4367	180	7	product	product	NOUN
cana-4367	180	8	of	of	ADP
cana-4367	180	9	𝑷𝒎	𝑷𝒎	PROPN
cana-4367	180	10	and	and	CCONJ
cana-4367	180	11	𝑷𝒓	𝑷𝒓	PROPN
cana-4367	180	12	:	:	PUNCT
cana-4367	180	13	input	input	NOUN
cana-4367	180	14	:	:	PUNCT
cana-4367	180	15	vertices	vertex	NOUN
cana-4367	180	16	of	of	ADP
cana-4367	180	17	(	(	PUNCT
cana-4367	180	18	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	180	19	⊳	⊳	PROPN
cana-4367	180	20	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	180	21	)	)	PUNCT
cana-4367	180	22	graph	graph	NOUN
cana-4367	180	23	,	,	PUNCT
cana-4367	180	24	𝑚	𝑚	PROPN
cana-4367	180	25	,	,	PUNCT
cana-4367	180	26	𝑟	𝑟	PRON
cana-4367	180	27	≥	≥	NUM
cana-4367	180	28	1	1	NUM
cana-4367	180	29	communications	communication	NOUN
cana-4367	180	30	on	on	ADP
cana-4367	180	31	applied	apply	VERB
cana-4367	180	32	nonlinear	nonlinear	ADJ
cana-4367	180	33	analysis	analysis	NOUN
cana-4367	180	34	issn	issn	NOUN
cana-4367	180	35	:	:	PUNCT
cana-4367	180	36	1074	1074	NUM
cana-4367	180	37	-	-	PUNCT
cana-4367	180	38	133x	133x	NUM
cana-4367	180	39	vol	vol	NOUN
cana-4367	180	40	32	32	NUM
cana-4367	180	41	no	no	NOUN
cana-4367	180	42	.	.	PUNCT
cana-4367	181	1	9s	9s	NUM
cana-4367	181	2	(	(	PUNCT
cana-4367	181	3	2025	2025	NUM
cana-4367	181	4	)	)	PUNCT
cana-4367	181	5	1925	1925	NUM
cana-4367	182	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4367	182	2	𝑉	𝑉	PROPN
cana-4367	182	3	←	←	PROPN
cana-4367	182	4	{	{	PUNCT
cana-4367	182	5	𝑣𝑖	𝑣𝑖	NOUN
cana-4367	182	6	,	,	PUNCT
cana-4367	182	7	𝑢𝑖	𝑢𝑖	INTJ
cana-4367	182	8	(	(	PUNCT
cana-4367	182	9	𝑗)/0	𝑗)/0	PROPN
cana-4367	182	10	≤	≤	PROPN
cana-4367	182	11	𝑖	𝑖	SYM
cana-4367	182	12	≤	≤	PROPN
cana-4367	182	13	𝑚	𝑚	ADP
cana-4367	182	14	,	,	PUNCT
cana-4367	182	15	2	2	NUM
cana-4367	182	16	≤	≤	NUM
cana-4367	182	17	𝑗	𝑗	PRON
cana-4367	182	18	≤	≤	ADJ
cana-4367	182	19	𝑟	𝑟	NOUN
cana-4367	182	20	+	+	SYM
cana-4367	182	21	1	1	NUM
cana-4367	182	22	,	,	PUNCT
cana-4367	182	23	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	ADJ
cana-4367	182	24	𝑣𝑖	𝑣𝑖	NOUN
cana-4367	182	25	=	=	NOUN
cana-4367	182	26	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	182	27	(	(	PUNCT
cana-4367	182	28	1	1	NUM
cana-4367	182	29	)	)	PUNCT
cana-4367	182	30	}	}	PUNCT
cana-4367	182	31	𝑣0	𝑣0	PROPN
cana-4367	182	32	=	=	SYM
cana-4367	182	33	𝑢0	𝑢0	PROPN
cana-4367	182	34	(	(	PUNCT
cana-4367	182	35	1	1	NUM
cana-4367	182	36	)	)	PUNCT
cana-4367	182	37	←	←	PROPN
cana-4367	182	38	0	0	NUM
cana-4367	182	39	;	;	PUNCT
cana-4367	182	40	𝑢0	𝑢0	PROPN
cana-4367	182	41	(	(	PUNCT
cana-4367	182	42	2	2	NUM
cana-4367	182	43	)	)	PUNCT
cana-4367	182	44	←	←	PROPN
cana-4367	182	45	15	15	NUM
cana-4367	182	46	;	;	PUNCT
cana-4367	182	47	for	for	ADP
cana-4367	182	48	𝑖	𝑖	SYM
cana-4367	182	49	=	=	SYM
cana-4367	182	50	1	1	NUM
cana-4367	182	51	𝑡𝑜	𝑡𝑜	NOUN
cana-4367	182	52	𝑚	𝑚	AUX
cana-4367	182	53	do	do	VERB
cana-4367	182	54	𝑣𝑖	𝑣𝑖	ADV
cana-4367	182	55	=	=	NOUN
cana-4367	182	56	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	182	57	(	(	PUNCT
cana-4367	182	58	1	1	NUM
cana-4367	182	59	)	)	PUNCT
cana-4367	182	60	←	←	PROPN
cana-4367	182	61	{	{	PUNCT
cana-4367	182	62	3	3	NUM
cana-4367	182	63	𝑖𝑓	𝑖𝑓	ADP
cana-4367	182	64	𝑖	𝑖	SYM
cana-4367	182	65	≡	≡	PROPN
cana-4367	182	66	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	182	67	)	)	PUNCT
cana-4367	182	68	60	60	NUM
cana-4367	182	69	𝑖𝑓	𝑖𝑓	SYM
cana-4367	182	70	𝑖	𝑖	SYM
cana-4367	182	71	≡	≡	PROPN
cana-4367	182	72	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	182	73	)	)	PUNCT
cana-4367	182	74	12	12	NUM
cana-4367	182	75	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	182	76	𝑖	𝑖	NUM
cana-4367	182	77	≡	≡	PROPN
cana-4367	182	78	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	182	79	)	)	PUNCT
cana-4367	182	80	51	51	NUM
cana-4367	182	81	𝑖𝑓	𝑖𝑓	SYM
cana-4367	182	82	𝑖	𝑖	PROPN
cana-4367	182	83	≡	≡	PROPN
cana-4367	182	84	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	182	85	)	)	PUNCT
cana-4367	182	86	;	;	PUNCT
cana-4367	182	87	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	182	88	(	(	PUNCT
cana-4367	182	89	2	2	NUM
cana-4367	182	90	)	)	PUNCT
cana-4367	182	91	←	←	PROPN
cana-4367	182	92	{	{	PUNCT
cana-4367	182	93	12	12	NUM
cana-4367	182	94	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	182	95	𝑖	𝑖	SYM
cana-4367	182	96	≡	≡	PROPN
cana-4367	182	97	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	182	98	)	)	PUNCT
cana-4367	182	99	0	0	NUM
cana-4367	183	1	𝑖𝑓	𝑖𝑓	CCONJ
cana-4367	183	2	𝑖	𝑖	SYM
cana-4367	183	3	≡	≡	PROPN
cana-4367	183	4	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	183	5	)	)	PUNCT
cana-4367	183	6	3	3	NUM
cana-4367	183	7	𝑖𝑓	𝑖𝑓	ADP
cana-4367	183	8	𝑖	𝑖	PROPN
cana-4367	183	9	≡	≡	PROPN
cana-4367	183	10	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	183	11	)	)	PUNCT
cana-4367	183	12	0	0	NUM
cana-4367	184	1	𝑖𝑓	𝑖𝑓	CCONJ
cana-4367	184	2	𝑖	𝑖	PROPN
cana-4367	184	3	≡	≡	PROPN
cana-4367	184	4	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	184	5	)	)	PUNCT
cana-4367	184	6	end	end	VERB
cana-4367	184	7	for	for	ADP
cana-4367	184	8	for	for	ADP
cana-4367	184	9	i	i	PROPN
cana-4367	184	10	=	=	NOUN
cana-4367	184	11	0	0	NUM
cana-4367	184	12	to	to	PART
cana-4367	184	13	m	m	AUX
cana-4367	184	14	do	do	VERB
cana-4367	184	15	for	for	ADP
cana-4367	184	16	j	j	PROPN
cana-4367	184	17	=	=	SYM
cana-4367	184	18	3	3	NUM
cana-4367	184	19	to	to	PART
cana-4367	184	20	r+1	r+1	PROPN
cana-4367	184	21	do	do	VERB
cana-4367	184	22	if	if	SCONJ
cana-4367	184	23	i	i	PRON
cana-4367	184	24	≡	≡	PROPN
cana-4367	184	25	1(𝑚𝑜𝑑2	1(𝑚𝑜𝑑2	NUM
cana-4367	184	26	)	)	PUNCT
cana-4367	184	27	do	do	VERB
cana-4367	184	28	𝑢𝑖	𝑢𝑖	PRON
cana-4367	184	29	(	(	PUNCT
cana-4367	184	30	𝑗	𝑗	PROPN
cana-4367	184	31	)	)	PUNCT
cana-4367	184	32	←	←	PROPN
cana-4367	184	33	{	{	PUNCT
cana-4367	184	34	3	3	NUM
cana-4367	184	35	𝑖𝑓	𝑖𝑓	ADP
cana-4367	184	36	𝑗	𝑗	PROPN
cana-4367	184	37	≡	≡	PROPN
cana-4367	184	38	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	184	39	)	)	PUNCT
cana-4367	184	40	12	12	NUM
cana-4367	185	1	𝑖𝑓	𝑖𝑓	NUM
cana-4367	185	2	𝑗	𝑗	PROPN
cana-4367	185	3	≡	≡	PROPN
cana-4367	185	4	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	185	5	)	)	PUNCT
cana-4367	185	6	0	0	PUNCT
cana-4367	186	1	𝑖𝑓	𝑖𝑓	NUM
cana-4367	186	2	𝑗	𝑗	PROPN
cana-4367	186	3	≡	≡	PROPN
cana-4367	186	4	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	186	5	)	)	PUNCT
cana-4367	186	6	15	15	NUM
cana-4367	186	7	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	186	8	𝑗	𝑗	PROPN
cana-4367	186	9	≡	≡	PROPN
cana-4367	186	10	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	186	11	)	)	PUNCT
cana-4367	186	12	else	else	ADV
cana-4367	186	13	𝑢𝑖	𝑢𝑖	X
cana-4367	186	14	(	(	PUNCT
cana-4367	186	15	𝑗	𝑗	NOUN
cana-4367	186	16	)	)	PUNCT
cana-4367	186	17	←	←	PROPN
cana-4367	186	18	{	{	PUNCT
cana-4367	186	19	0	0	NUM
cana-4367	186	20	𝑖𝑓	𝑖𝑓	NUM
cana-4367	186	21	𝑗	𝑗	PROPN
cana-4367	186	22	≡	≡	PROPN
cana-4367	186	23	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	186	24	)	)	PUNCT
cana-4367	186	25	15	15	NUM
cana-4367	186	26	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	186	27	𝑗	𝑗	PROPN
cana-4367	186	28	≡	≡	PROPN
cana-4367	186	29	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	186	30	)	)	PUNCT
cana-4367	186	31	3	3	NUM
cana-4367	186	32	𝑖𝑓	𝑖𝑓	ADP
cana-4367	186	33	𝑗	𝑗	PROPN
cana-4367	186	34	≡	≡	PROPN
cana-4367	186	35	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	186	36	)	)	PUNCT
cana-4367	186	37	12	12	NUM
cana-4367	186	38	𝑖𝑓	𝑖𝑓	NOUN
cana-4367	186	39	𝑗	𝑗	PROPN
cana-4367	186	40	≡	≡	PROPN
cana-4367	186	41	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	186	42	)	)	PUNCT
cana-4367	186	43	end	end	VERB
cana-4367	186	44	if	if	SCONJ
cana-4367	186	45	end	end	NOUN
cana-4367	186	46	for	for	ADP
cana-4367	186	47	end	end	NOUN
cana-4367	186	48	for	for	ADP
cana-4367	186	49	end	end	NOUN
cana-4367	186	50	procedure	procedure	NOUN
cana-4367	186	51	output	output	NOUN
cana-4367	186	52	:	:	PUNCT
cana-4367	186	53	the	the	DET
cana-4367	186	54	labeled	label	VERB
cana-4367	186	55	vertices	vertex	NOUN
cana-4367	186	56	of	of	ADP
cana-4367	186	57	comb	comb	NOUN
cana-4367	186	58	product	product	NOUN
cana-4367	186	59	(	(	PUNCT
cana-4367	186	60	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	186	61	⊳	⊳	NOUN
cana-4367	186	62	𝑃𝑟)graph	𝑃𝑟)graph	NOUN
cana-4367	186	63	.	.	PUNCT
cana-4367	187	1	theorem	theorem	PROPN
cana-4367	187	2	2.1.8	2.1.8	PROPN
cana-4367	187	3	.	.	PUNCT
cana-4367	188	1	the	the	DET
cana-4367	188	2	comb	comb	NOUN
cana-4367	188	3	product	product	NOUN
cana-4367	188	4	of	of	ADP
cana-4367	188	5	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	188	6	and	and	CCONJ
cana-4367	188	7	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	188	8	graph	graph	NOUN
cana-4367	188	9	(	(	PUNCT
cana-4367	188	10	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	188	11	⊳	⊳	PROPN
cana-4367	188	12	𝑃𝑟)is	𝑃𝑟)i	VERB
cana-4367	188	13	an	an	DET
cana-4367	188	14	even	even	ADV
cana-4367	188	15	hamming	ham	VERB
cana-4367	188	16	distance	distance	NOUN
cana-4367	188	17	labeled	label	VERB
cana-4367	188	18	graph	graph	NOUN
cana-4367	188	19	and	and	CCONJ
cana-4367	188	20	the	the	DET
cana-4367	188	21	even	even	ADV
cana-4367	188	22	hamming	hamming	NOUN
cana-4367	188	23	distance	distance	NOUN
cana-4367	188	24	number	number	NOUN
cana-4367	188	25	is	be	AUX
cana-4367	188	26	ηℎ𝑑	ηℎ𝑑	NOUN
cana-4367	188	27	′′	′′	PROPN
cana-4367	188	28	(	(	PUNCT
cana-4367	188	29	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	188	30	⊳	⊳	PROPN
cana-4367	188	31	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	188	32	)	)	PUNCT
cana-4367	188	33	=	=	NOUN
cana-4367	188	34	{	{	PUNCT
cana-4367	188	35	4	4	NUM
cana-4367	188	36	,	,	PUNCT
cana-4367	188	37	𝑖𝑓	𝑖𝑓	ADP
cana-4367	188	38	𝑚	𝑚	NOUN
cana-4367	188	39	=	=	SYM
cana-4367	188	40	1	1	NUM
cana-4367	188	41	6	6	NUM
cana-4367	188	42	,	,	PUNCT
cana-4367	188	43	𝑖𝑓	𝑖𝑓	ADP
cana-4367	188	44	𝑚	𝑚	X
cana-4367	188	45	>	>	X
cana-4367	188	46	1	1	NUM
cana-4367	188	47	.	.	PUNCT
cana-4367	189	1	proof	proof	NOUN
cana-4367	189	2	:	:	PUNCT
cana-4367	189	3	let	let	VERB
cana-4367	189	4	us	we	PRON
cana-4367	189	5	consider	consider	VERB
cana-4367	189	6	the	the	DET
cana-4367	189	7	comb	comb	NOUN
cana-4367	189	8	product	product	NOUN
cana-4367	189	9	of	of	ADP
cana-4367	189	10	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	189	11	and	and	CCONJ
cana-4367	189	12	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	189	13	graph	graph	NOUN
cana-4367	189	14	(	(	PUNCT
cana-4367	189	15	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	189	16	⊳	⊳	PROPN
cana-4367	189	17	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	189	18	)	)	PUNCT
cana-4367	189	19	with	with	ADP
cana-4367	189	20	vertex	vertex	NOUN
cana-4367	189	21	set	set	VERB
cana-4367	189	22	𝑉	𝑉	PROPN
cana-4367	189	23	=	=	PUNCT
cana-4367	189	24	{	{	PUNCT
cana-4367	189	25	𝑣𝑖	𝑣𝑖	NOUN
cana-4367	189	26	,	,	PUNCT
cana-4367	189	27	𝑢𝑖	𝑢𝑖	INTJ
cana-4367	189	28	(	(	PUNCT
cana-4367	189	29	𝑗	𝑗	NOUN
cana-4367	189	30	)	)	PUNCT
cana-4367	189	31	/0	/0	NOUN
cana-4367	190	1	≤	≤	NUM
cana-4367	190	2	𝑖	𝑖	SYM
cana-4367	190	3	≤	≤	NUM
cana-4367	190	4	𝑚	𝑚	ADP
cana-4367	190	5	,	,	PUNCT
cana-4367	190	6	2	2	NUM
cana-4367	190	7	≤	≤	NUM
cana-4367	190	8	𝑗	𝑗	PRON
cana-4367	190	9	≤	≤	NUM
cana-4367	190	10	𝑟,𝑤ℎ𝑒𝑟𝑒	𝑟,𝑤ℎ𝑒𝑟𝑒	NUM
cana-4367	190	11	𝑣𝑖	𝑣𝑖	ADP
cana-4367	190	12	=	=	NOUN
cana-4367	190	13	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	190	14	(	(	PUNCT
cana-4367	190	15	1	1	NUM
cana-4367	190	16	)	)	PUNCT
cana-4367	190	17	}	}	PUNCT
cana-4367	190	18	and	and	CCONJ
cana-4367	190	19	edge	edge	VERB
cana-4367	190	20	se𝑡	se𝑡	PRON
cana-4367	190	21	𝐸	𝐸	NOUN
cana-4367	190	22	=	=	PUNCT
cana-4367	190	23	{	{	PUNCT
cana-4367	190	24	{	{	PUNCT
cana-4367	190	25	𝑣𝑖𝑣𝑖+1	𝑣𝑖𝑣𝑖+1	PROPN
cana-4367	190	26	/	/	SYM
cana-4367	190	27	0	0	NUM
cana-4367	190	28	≤	≤	NUM
cana-4367	190	29	𝑖	𝑖	SYM
cana-4367	190	30	≤	≤	NOUN
cana-4367	190	31	𝑚	𝑚	ADP
cana-4367	190	32	−	−	PROPN
cana-4367	190	33	1	1	NUM
cana-4367	190	34	}	}	PUNCT
cana-4367	190	35	∪	∪	ADJ
cana-4367	190	36	{	{	PUNCT
cana-4367	190	37	𝑢𝑖	𝑢𝑖	INTJ
cana-4367	190	38	(	(	PUNCT
cana-4367	190	39	𝑗	𝑗	NOUN
cana-4367	190	40	)	)	PUNCT
cana-4367	190	41	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-4367	190	42	(	(	PUNCT
cana-4367	190	43	𝑗+1	𝑗+1	NOUN
cana-4367	190	44	)	)	PUNCT
cana-4367	190	45	/0	/0	NOUN
cana-4367	191	1	≤	≤	NUM
cana-4367	191	2	𝑖	𝑖	SYM
cana-4367	191	3	≤	≤	NUM
cana-4367	191	4	𝑚	𝑚	ADP
cana-4367	191	5	,	,	PUNCT
cana-4367	191	6	1	1	NUM
cana-4367	191	7	≤	≤	NUM
cana-4367	191	8	𝑗	𝑗	PRON
cana-4367	191	9	≤	≤	ADJ
cana-4367	191	10	𝑟	𝑟	NOUN
cana-4367	191	11	−	−	PROPN
cana-4367	191	12	1	1	NUM
cana-4367	191	13	}	}	PUNCT
cana-4367	191	14	}	}	PUNCT
cana-4367	191	15	.	.	PUNCT
cana-4367	192	1	define	define	VERB
cana-4367	192	2	a	a	DET
cana-4367	192	3	function	function	NOUN
cana-4367	192	4	𝑓	𝑓	PRON
cana-4367	192	5	:	:	PUNCT
cana-4367	192	6	v	v	NOUN
cana-4367	192	7	→	→	SYM
cana-4367	192	8	n	n	CCONJ
cana-4367	192	9	∪	∪	X
cana-4367	192	10	{	{	PUNCT
cana-4367	192	11	0	0	NUM
cana-4367	192	12	}	}	PUNCT
cana-4367	192	13	such	such	ADJ
cana-4367	192	14	that	that	SCONJ
cana-4367	192	15	𝑓(𝑢	𝑓(𝑢	PROPN
cana-4367	192	16	)	)	PUNCT
cana-4367	192	17	≠	≠	PROPN
cana-4367	192	18	𝑓(𝑣	𝑓(𝑣	PROPN
cana-4367	192	19	)	)	PUNCT
cana-4367	192	20	for	for	ADP
cana-4367	192	21	any	any	DET
cana-4367	192	22	two	two	NUM
cana-4367	192	23	adjacent	adjacent	ADJ
cana-4367	192	24	vertices	vertex	NOUN
cana-4367	192	25	u	u	NOUN
cana-4367	192	26	and	and	CCONJ
cana-4367	192	27	v	v	NOUN
cana-4367	192	28	as	as	SCONJ
cana-4367	192	29	given	give	VERB
cana-4367	192	30	in	in	ADP
cana-4367	192	31	the	the	DET
cana-4367	192	32	above	above	ADJ
cana-4367	192	33	algorithm	algorithm	NOUN
cana-4367	192	34	2.1.7	2.1.7	NUM
cana-4367	192	35	.	.	PUNCT
cana-4367	193	1	hence	hence	ADV
cana-4367	193	2	the	the	DET
cana-4367	193	3	adjacent	adjacent	ADJ
cana-4367	193	4	vertices	vertex	NOUN
cana-4367	193	5	communications	communication	NOUN
cana-4367	193	6	on	on	ADP
cana-4367	193	7	applied	apply	VERB
cana-4367	193	8	nonlinear	nonlinear	ADJ
cana-4367	193	9	analysis	analysis	NOUN
cana-4367	193	10	issn	issn	NOUN
cana-4367	193	11	:	:	PUNCT
cana-4367	193	12	1074	1074	NUM
cana-4367	193	13	-	-	PUNCT
cana-4367	193	14	133x	133x	NUM
cana-4367	193	15	vol	vol	NOUN
cana-4367	193	16	32	32	NUM
cana-4367	193	17	no	no	NOUN
cana-4367	193	18	.	.	PUNCT
cana-4367	194	1	9s	9s	NUM
cana-4367	194	2	(	(	PUNCT
cana-4367	194	3	2025	2025	NUM
cana-4367	194	4	)	)	PUNCT
cana-4367	194	5	1926	1926	NUM
cana-4367	195	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4367	195	2	receive	receive	VERB
cana-4367	195	3	distinct	distinct	ADJ
cana-4367	195	4	labels	label	NOUN
cana-4367	195	5	.	.	PUNCT
cana-4367	196	1	the	the	DET
cana-4367	196	2	edge	edge	NOUN
cana-4367	196	3	labels	label	NOUN
cana-4367	196	4	are	be	AUX
cana-4367	196	5	obtained	obtain	VERB
cana-4367	196	6	as	as	ADP
cana-4367	196	7	follows:𝑓∗(𝑢0	follows:𝑓∗(𝑢0	ADJ
cana-4367	196	8	(	(	PUNCT
cana-4367	196	9	1	1	NUM
cana-4367	196	10	)	)	PUNCT
cana-4367	196	11	𝑢0	𝑢0	NOUN
cana-4367	196	12	(	(	PUNCT
cana-4367	196	13	2	2	NUM
cana-4367	196	14	)	)	PUNCT
cana-4367	196	15	)	)	PUNCT
cana-4367	197	1	=	=	PUNCT
cana-4367	197	2	ℎ𝑑([𝑓(𝑢0	ℎ𝑑([𝑓(𝑢0	X
cana-4367	198	1	(	(	PUNCT
cana-4367	198	2	1	1	NUM
cana-4367	198	3	)	)	PUNCT
cana-4367	198	4	)	)	PUNCT
cana-4367	198	5	]	]	PUNCT
cana-4367	199	1	2	2	X
cana-4367	199	2	,	,	PUNCT
cana-4367	199	3	[	[	X
cana-4367	199	4	𝑓(𝑢0	𝑓(𝑢0	ADJ
cana-4367	199	5	(	(	PUNCT
cana-4367	199	6	2	2	NUM
cana-4367	199	7	)	)	PUNCT
cana-4367	199	8	)	)	PUNCT
cana-4367	199	9	]	]	PUNCT
cana-4367	199	10	2	2	X
cana-4367	199	11	)	)	PUNCT
cana-4367	199	12	=	=	SYM
cana-4367	200	1	hd([0]2	hd([0]2	NOUN
cana-4367	200	2	,	,	PUNCT
cana-4367	200	3	[	[	X
cana-4367	200	4	15]2	15]2	X
cana-4367	200	5	)	)	PUNCT
cana-4367	200	6	=	=	NOUN
cana-4367	200	7	4	4	X
cana-4367	200	8	.	.	X
cana-4367	201	1	𝑓∗(𝑢0	𝑓∗(𝑢0	ADJ
cana-4367	201	2	(	(	PUNCT
cana-4367	201	3	2	2	NUM
cana-4367	201	4	)	)	PUNCT
cana-4367	201	5	𝑢0	𝑢0	NOUN
cana-4367	201	6	(	(	PUNCT
cana-4367	201	7	3	3	NUM
cana-4367	201	8	)	)	PUNCT
cana-4367	201	9	)	)	PUNCT
cana-4367	202	1	=	=	PUNCT
cana-4367	202	2	ℎ𝑑([𝑓(𝑢0	ℎ𝑑([𝑓(𝑢0	X
cana-4367	202	3	(	(	PUNCT
cana-4367	202	4	2	2	NUM
cana-4367	202	5	)	)	PUNCT
cana-4367	202	6	)	)	PUNCT
cana-4367	202	7	]	]	PUNCT
cana-4367	202	8	2	2	X
cana-4367	202	9	,	,	PUNCT
cana-4367	202	10	[	[	X
cana-4367	202	11	𝑓(𝑢0	𝑓(𝑢0	ADJ
cana-4367	202	12	(	(	PUNCT
cana-4367	202	13	3	3	NUM
cana-4367	202	14	)	)	PUNCT
cana-4367	202	15	)	)	PUNCT
cana-4367	202	16	]	]	PUNCT
cana-4367	203	1	2	2	X
cana-4367	203	2	)	)	PUNCT
cana-4367	203	3	=	=	SYM
cana-4367	203	4	hd([15]2	hd([15]2	NOUN
cana-4367	203	5	,	,	PUNCT
cana-4367	203	6	[	[	X
cana-4367	203	7	3]2	3]2	NUM
cana-4367	203	8	)	)	PUNCT
cana-4367	203	9	=	=	SYM
cana-4367	203	10	2	2	X
cana-4367	203	11	.	.	X
cana-4367	203	12	𝑓∗(v0v1	𝑓∗(v0v1	NUM
cana-4367	203	13	)	)	PUNCT
cana-4367	204	1	=	=	SYM
cana-4367	204	2	hd([f(v0)]2	hd([f(v0)]2	NOUN
cana-4367	204	3	,	,	PUNCT
cana-4367	204	4	[	[	X
cana-4367	204	5	f(v1)]2	f(v1)]2	NOUN
cana-4367	204	6	)	)	PUNCT
cana-4367	204	7	=	=	SYM
cana-4367	205	1	hd([0]2	hd([0]2	NOUN
cana-4367	205	2	,	,	PUNCT
cana-4367	205	3	[	[	X
cana-4367	205	4	3]2	3]2	NOUN
cana-4367	205	5	)	)	PUNCT
cana-4367	205	6	=	=	SYM
cana-4367	205	7	2	2	X
cana-4367	205	8	.	.	X
cana-4367	205	9	for	for	ADP
cana-4367	205	10	1	1	NUM
cana-4367	205	11	≤	≤	NUM
cana-4367	205	12	𝑖	𝑖	SYM
cana-4367	205	13	≤	≤	NOUN
cana-4367	205	14	𝑚	𝑚	ADP
cana-4367	205	15	−	−	NUM
cana-4367	205	16	1	1	NUM
cana-4367	205	17	case	case	NOUN
cana-4367	205	18	(	(	PUNCT
cana-4367	205	19	i	i	NOUN
cana-4367	205	20	):	):	PUNCT
cana-4367	205	21	if	if	SCONJ
cana-4367	205	22	𝑖	𝑖	ADP
cana-4367	205	23	≡	≡	PROPN
cana-4367	205	24	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	205	25	)	)	PUNCT
cana-4367	205	26	or	or	CCONJ
cana-4367	205	27	𝑚	𝑚	ADP
cana-4367	205	28	≡	≡	PROPN
cana-4367	205	29	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	205	30	)	)	PUNCT
cana-4367	205	31	𝑓∗(vivi+1	𝑓∗(vivi+1	NUM
cana-4367	205	32	)	)	PUNCT
cana-4367	205	33	=	=	SYM
cana-4367	206	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	206	2	,	,	PUNCT
cana-4367	206	3	[	[	X
cana-4367	206	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	206	5	)	)	PUNCT
cana-4367	206	6	=	=	PUNCT
cana-4367	207	1	hd([3]2	hd([3]2	X
cana-4367	207	2	,	,	PUNCT
cana-4367	207	3	[	[	X
cana-4367	207	4	60]2	60]2	NUM
cana-4367	207	5	)	)	PUNCT
cana-4367	207	6	=	=	SYM
cana-4367	207	7	6	6	X
cana-4367	207	8	.	.	PUNCT
cana-4367	208	1	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	NOUN
cana-4367	208	2	(	(	PUNCT
cana-4367	208	3	1	1	X
cana-4367	208	4	)	)	PUNCT
cana-4367	208	5	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	208	6	(	(	PUNCT
cana-4367	208	7	2	2	NUM
cana-4367	208	8	)	)	PUNCT
cana-4367	208	9	)	)	PUNCT
cana-4367	209	1	=	=	SYM
cana-4367	209	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	209	3	(	(	PUNCT
cana-4367	209	4	1	1	NUM
cana-4367	209	5	)	)	PUNCT
cana-4367	209	6	)	)	PUNCT
cana-4367	209	7	]	]	PUNCT
cana-4367	209	8	2	2	X
cana-4367	209	9	,	,	PUNCT
cana-4367	209	10	[	[	X
cana-4367	209	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	209	12	(	(	PUNCT
cana-4367	209	13	2	2	NUM
cana-4367	209	14	)	)	PUNCT
cana-4367	209	15	)	)	PUNCT
cana-4367	209	16	]	]	PUNCT
cana-4367	209	17	2	2	X
cana-4367	209	18	)	)	PUNCT
cana-4367	209	19	=	=	SYM
cana-4367	209	20	hd([3]2	hd([3]2	X
cana-4367	209	21	,	,	PUNCT
cana-4367	209	22	[	[	X
cana-4367	209	23	12]2	12]2	NUM
cana-4367	209	24	)	)	PUNCT
cana-4367	209	25	=	=	SYM
cana-4367	209	26	4	4	X
cana-4367	209	27	.	.	X
cana-4367	210	1	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	NOUN
cana-4367	210	2	(	(	PUNCT
cana-4367	210	3	2	2	X
cana-4367	210	4	)	)	PUNCT
cana-4367	210	5	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	210	6	(	(	PUNCT
cana-4367	210	7	3	3	NUM
cana-4367	210	8	)	)	PUNCT
cana-4367	210	9	)	)	PUNCT
cana-4367	211	1	=	=	SYM
cana-4367	211	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	211	3	(	(	PUNCT
cana-4367	211	4	2	2	NUM
cana-4367	211	5	)	)	PUNCT
cana-4367	211	6	)	)	PUNCT
cana-4367	211	7	]	]	PUNCT
cana-4367	211	8	2	2	X
cana-4367	211	9	,	,	PUNCT
cana-4367	211	10	[	[	X
cana-4367	211	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	211	12	(	(	PUNCT
cana-4367	211	13	3	3	NUM
cana-4367	211	14	)	)	PUNCT
cana-4367	211	15	)	)	PUNCT
cana-4367	211	16	]	]	PUNCT
cana-4367	211	17	2	2	X
cana-4367	211	18	)	)	PUNCT
cana-4367	211	19	=	=	SYM
cana-4367	211	20	hd([12]2	hd([12]2	PROPN
cana-4367	211	21	,	,	PUNCT
cana-4367	211	22	[	[	X
cana-4367	211	23	0]2	0]2	X
cana-4367	211	24	)	)	PUNCT
cana-4367	211	25	=	=	SYM
cana-4367	211	26	2	2	X
cana-4367	211	27	.	.	PUNCT
cana-4367	211	28	𝑓∗(vm−1vm	𝑓∗(vm−1vm	ADJ
cana-4367	211	29	)	)	PUNCT
cana-4367	211	30	=	=	SYM
cana-4367	212	1	hd([f(vm−1)]2	hd([f(vm−1)]2	NOUN
cana-4367	212	2	,	,	PUNCT
cana-4367	212	3	[	[	X
cana-4367	212	4	f(vm)]2	f(vm)]2	X
cana-4367	212	5	)	)	PUNCT
cana-4367	212	6	=	=	SYM
cana-4367	212	7	hd([51]2	hd([51]2	PROPN
cana-4367	212	8	,	,	PUNCT
cana-4367	212	9	[	[	X
cana-4367	212	10	3]2	3]2	NUM
cana-4367	212	11	)	)	PUNCT
cana-4367	212	12	=	=	SYM
cana-4367	212	13	2	2	X
cana-4367	212	14	.	.	X
cana-4367	212	15	case	case	NOUN
cana-4367	212	16	(	(	PUNCT
cana-4367	212	17	ii	ii	NOUN
cana-4367	212	18	):	):	PUNCT
cana-4367	212	19	if	if	SCONJ
cana-4367	212	20	𝑖	𝑖	ADP
cana-4367	212	21	≡	≡	PROPN
cana-4367	212	22	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	212	23	)	)	PUNCT
cana-4367	212	24	or	or	CCONJ
cana-4367	212	25	𝑚	𝑚	PROPN
cana-4367	212	26	≡	≡	PROPN
cana-4367	212	27	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	212	28	)	)	PUNCT
cana-4367	212	29	𝑓∗(vivi+1	𝑓∗(vivi+1	PROPN
cana-4367	212	30	)	)	PUNCT
cana-4367	212	31	=	=	SYM
cana-4367	213	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	213	2	,	,	PUNCT
cana-4367	213	3	[	[	X
cana-4367	213	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	213	5	)	)	PUNCT
cana-4367	213	6	=	=	SYM
cana-4367	213	7	hd([60]2	hd([60]2	PROPN
cana-4367	213	8	,	,	PUNCT
cana-4367	213	9	[	[	X
cana-4367	213	10	12]2	12]2	NUM
cana-4367	213	11	)	)	PUNCT
cana-4367	213	12	=	=	SYM
cana-4367	213	13	2	2	X
cana-4367	213	14	.	.	X
cana-4367	214	1	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	NOUN
cana-4367	214	2	(	(	PUNCT
cana-4367	214	3	1	1	X
cana-4367	214	4	)	)	PUNCT
cana-4367	214	5	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	214	6	(	(	PUNCT
cana-4367	214	7	2	2	NUM
cana-4367	214	8	)	)	PUNCT
cana-4367	214	9	)	)	PUNCT
cana-4367	215	1	=	=	SYM
cana-4367	215	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	215	3	(	(	PUNCT
cana-4367	215	4	1	1	NUM
cana-4367	215	5	)	)	PUNCT
cana-4367	215	6	)	)	PUNCT
cana-4367	215	7	]	]	PUNCT
cana-4367	215	8	2	2	X
cana-4367	215	9	,	,	PUNCT
cana-4367	215	10	[	[	X
cana-4367	215	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	215	12	(	(	PUNCT
cana-4367	215	13	2	2	NUM
cana-4367	215	14	)	)	PUNCT
cana-4367	215	15	)	)	PUNCT
cana-4367	215	16	]	]	PUNCT
cana-4367	215	17	2	2	X
cana-4367	215	18	)	)	PUNCT
cana-4367	215	19	=	=	SYM
cana-4367	215	20	hd([60]2	hd([60]2	PROPN
cana-4367	215	21	,	,	PUNCT
cana-4367	215	22	[	[	X
cana-4367	215	23	0]2	0]2	X
cana-4367	215	24	)	)	PUNCT
cana-4367	215	25	=	=	SYM
cana-4367	216	1	4	4	X
cana-4367	216	2	.	.	X
cana-4367	217	1	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	NOUN
cana-4367	217	2	(	(	PUNCT
cana-4367	217	3	2	2	X
cana-4367	217	4	)	)	PUNCT
cana-4367	217	5	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	217	6	(	(	PUNCT
cana-4367	217	7	3	3	NUM
cana-4367	217	8	)	)	PUNCT
cana-4367	217	9	)	)	PUNCT
cana-4367	218	1	=	=	SYM
cana-4367	218	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	218	3	(	(	PUNCT
cana-4367	218	4	2	2	NUM
cana-4367	218	5	)	)	PUNCT
cana-4367	218	6	)	)	PUNCT
cana-4367	218	7	]	]	PUNCT
cana-4367	218	8	2	2	X
cana-4367	218	9	,	,	PUNCT
cana-4367	218	10	[	[	X
cana-4367	218	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	218	12	(	(	PUNCT
cana-4367	218	13	3	3	NUM
cana-4367	218	14	)	)	PUNCT
cana-4367	218	15	)	)	PUNCT
cana-4367	218	16	]	]	PUNCT
cana-4367	218	17	2	2	X
cana-4367	218	18	)	)	PUNCT
cana-4367	218	19	=	=	SYM
cana-4367	218	20	hd([0]2	hd([0]2	NOUN
cana-4367	218	21	,	,	PUNCT
cana-4367	218	22	[	[	X
cana-4367	218	23	3]2	3]2	NOUN
cana-4367	218	24	)	)	PUNCT
cana-4367	218	25	=	=	SYM
cana-4367	218	26	2	2	X
cana-4367	218	27	.	.	PUNCT
cana-4367	218	28	𝑓∗(vm−1vm	𝑓∗(vm−1vm	ADJ
cana-4367	218	29	)	)	PUNCT
cana-4367	219	1	=	=	SYM
cana-4367	219	2	hd([f(vm−1)]2	hd([f(vm−1)]2	NOUN
cana-4367	219	3	,	,	PUNCT
cana-4367	219	4	[	[	X
cana-4367	219	5	f(vm)]2	f(vm)]2	NOUN
cana-4367	219	6	)	)	PUNCT
cana-4367	219	7	=	=	SYM
cana-4367	219	8	hd(32	hd(32	PROPN
cana-4367	219	9	,	,	PUNCT
cana-4367	219	10	[	[	X
cana-4367	219	11	60]2	60]2	NUM
cana-4367	219	12	)	)	PUNCT
cana-4367	219	13	=	=	SYM
cana-4367	220	1	6	6	X
cana-4367	220	2	.	.	PUNCT
cana-4367	220	3	case	case	NOUN
cana-4367	220	4	(	(	PUNCT
cana-4367	220	5	iii	iii	NOUN
cana-4367	220	6	):	):	PUNCT
cana-4367	220	7	if	if	SCONJ
cana-4367	220	8	𝑖	𝑖	ADP
cana-4367	220	9	≡	≡	PROPN
cana-4367	220	10	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	220	11	)	)	PUNCT
cana-4367	220	12	or	or	CCONJ
cana-4367	220	13	𝑚	𝑚	X
cana-4367	220	14	≡	≡	PROPN
cana-4367	220	15	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	220	16	)	)	PUNCT
cana-4367	220	17	𝑓∗(vivi+1	𝑓∗(vivi+1	PROPN
cana-4367	220	18	)	)	PUNCT
cana-4367	220	19	=	=	SYM
cana-4367	221	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	221	2	,	,	PUNCT
cana-4367	221	3	[	[	X
cana-4367	221	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	221	5	)	)	PUNCT
cana-4367	221	6	=	=	SYM
cana-4367	222	1	hd([12]2	hd([12]2	PROPN
cana-4367	222	2	,	,	PUNCT
cana-4367	222	3	[	[	X
cana-4367	222	4	51]2	51]2	NUM
cana-4367	222	5	)	)	PUNCT
cana-4367	222	6	=	=	SYM
cana-4367	222	7	6	6	X
cana-4367	222	8	.	.	PUNCT
cana-4367	223	1	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	NOUN
cana-4367	223	2	(	(	PUNCT
cana-4367	223	3	1	1	X
cana-4367	223	4	)	)	PUNCT
cana-4367	223	5	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	223	6	(	(	PUNCT
cana-4367	223	7	2	2	NUM
cana-4367	223	8	)	)	PUNCT
cana-4367	223	9	)	)	PUNCT
cana-4367	224	1	=	=	SYM
cana-4367	224	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	224	3	(	(	PUNCT
cana-4367	224	4	1	1	NUM
cana-4367	224	5	)	)	PUNCT
cana-4367	224	6	)	)	PUNCT
cana-4367	224	7	]	]	PUNCT
cana-4367	224	8	2	2	X
cana-4367	224	9	,	,	PUNCT
cana-4367	224	10	[	[	X
cana-4367	224	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	224	12	(	(	PUNCT
cana-4367	224	13	2	2	NUM
cana-4367	224	14	)	)	PUNCT
cana-4367	224	15	)	)	PUNCT
cana-4367	224	16	]	]	PUNCT
cana-4367	224	17	2	2	X
cana-4367	224	18	)	)	PUNCT
cana-4367	224	19	=	=	SYM
cana-4367	224	20	hd([12]2	hd([12]2	PROPN
cana-4367	224	21	,	,	PUNCT
cana-4367	224	22	[	[	X
cana-4367	224	23	3]2	3]2	NUM
cana-4367	224	24	)	)	PUNCT
cana-4367	224	25	=	=	SYM
cana-4367	224	26	4	4	X
cana-4367	224	27	.	.	X
cana-4367	225	1	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	NOUN
cana-4367	225	2	(	(	PUNCT
cana-4367	225	3	2	2	X
cana-4367	225	4	)	)	PUNCT
cana-4367	225	5	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	225	6	(	(	PUNCT
cana-4367	225	7	3	3	NUM
cana-4367	225	8	)	)	PUNCT
cana-4367	225	9	)	)	PUNCT
cana-4367	226	1	=	=	SYM
cana-4367	226	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	226	3	(	(	PUNCT
cana-4367	226	4	2	2	NUM
cana-4367	226	5	)	)	PUNCT
cana-4367	226	6	)	)	PUNCT
cana-4367	226	7	]	]	PUNCT
cana-4367	226	8	2	2	X
cana-4367	226	9	,	,	PUNCT
cana-4367	226	10	[	[	X
cana-4367	226	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	226	12	(	(	PUNCT
cana-4367	226	13	3	3	NUM
cana-4367	226	14	)	)	PUNCT
cana-4367	226	15	)	)	PUNCT
cana-4367	226	16	]	]	PUNCT
cana-4367	226	17	2	2	X
cana-4367	226	18	)	)	PUNCT
cana-4367	226	19	=	=	SYM
cana-4367	226	20	hd([3]2	hd([3]2	X
cana-4367	226	21	,	,	PUNCT
cana-4367	226	22	[	[	X
cana-4367	226	23	0]2	0]2	X
cana-4367	226	24	)	)	PUNCT
cana-4367	226	25	=	=	SYM
cana-4367	226	26	2	2	X
cana-4367	226	27	.	.	PUNCT
cana-4367	226	28	𝑓∗(vm−1vm	𝑓∗(vm−1vm	ADJ
cana-4367	226	29	)	)	PUNCT
cana-4367	226	30	=	=	SYM
cana-4367	227	1	hd([f(vm−1)]2	hd([f(vm−1)]2	NOUN
cana-4367	227	2	,	,	PUNCT
cana-4367	227	3	[	[	X
cana-4367	227	4	f(vm)]2	f(vm)]2	X
cana-4367	227	5	)	)	PUNCT
cana-4367	227	6	=	=	SYM
cana-4367	227	7	hd([60]2	hd([60]2	PROPN
cana-4367	227	8	,	,	PUNCT
cana-4367	227	9	[	[	X
cana-4367	227	10	12]2	12]2	NUM
cana-4367	227	11	)	)	PUNCT
cana-4367	227	12	=	=	SYM
cana-4367	227	13	2	2	X
cana-4367	227	14	.	.	X
cana-4367	227	15	case	case	NOUN
cana-4367	227	16	(	(	PUNCT
cana-4367	227	17	iv	iv	NUM
cana-4367	227	18	):	):	PUNCT
cana-4367	227	19	if	if	SCONJ
cana-4367	227	20	𝑖	𝑖	ADP
cana-4367	227	21	≡	≡	PROPN
cana-4367	227	22	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	227	23	)	)	PUNCT
cana-4367	227	24	or	or	CCONJ
cana-4367	227	25	𝑚	𝑚	PROPN
cana-4367	227	26	≡	≡	PROPN
cana-4367	227	27	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	227	28	)	)	PUNCT
cana-4367	227	29	𝑓∗(vivi+1	𝑓∗(vivi+1	ADP
cana-4367	227	30	)	)	PUNCT
cana-4367	227	31	=	=	SYM
cana-4367	228	1	hd([f(vi)]2	hd([f(vi)]2	NUM
cana-4367	228	2	,	,	PUNCT
cana-4367	228	3	[	[	X
cana-4367	228	4	f(vi+1)]2	f(vi+1)]2	X
cana-4367	228	5	)	)	PUNCT
cana-4367	228	6	=	=	SYM
cana-4367	229	1	hd([51]2	hd([51]2	PROPN
cana-4367	229	2	,	,	PUNCT
cana-4367	229	3	[	[	X
cana-4367	229	4	3]2	3]2	NUM
cana-4367	229	5	)	)	PUNCT
cana-4367	229	6	=	=	SYM
cana-4367	229	7	2	2	X
cana-4367	229	8	.	.	X
cana-4367	230	1	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	NOUN
cana-4367	230	2	(	(	PUNCT
cana-4367	230	3	1	1	X
cana-4367	230	4	)	)	PUNCT
cana-4367	230	5	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	230	6	(	(	PUNCT
cana-4367	230	7	2	2	NUM
cana-4367	230	8	)	)	PUNCT
cana-4367	230	9	)	)	PUNCT
cana-4367	231	1	=	=	SYM
cana-4367	231	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	231	3	(	(	PUNCT
cana-4367	231	4	1	1	NUM
cana-4367	231	5	)	)	PUNCT
cana-4367	231	6	)	)	PUNCT
cana-4367	231	7	]	]	PUNCT
cana-4367	231	8	2	2	X
cana-4367	231	9	,	,	PUNCT
cana-4367	231	10	[	[	X
cana-4367	231	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	231	12	(	(	PUNCT
cana-4367	231	13	2	2	NUM
cana-4367	231	14	)	)	PUNCT
cana-4367	231	15	)	)	PUNCT
cana-4367	231	16	]	]	PUNCT
cana-4367	231	17	2	2	X
cana-4367	231	18	)	)	PUNCT
cana-4367	231	19	=	=	SYM
cana-4367	231	20	hd(512	hd(512	NOUN
cana-4367	231	21	,	,	PUNCT
cana-4367	231	22	[	[	X
cana-4367	231	23	0]2	0]2	X
cana-4367	231	24	)	)	PUNCT
cana-4367	231	25	=	=	SYM
cana-4367	232	1	4	4	X
cana-4367	232	2	.	.	X
cana-4367	233	1	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	NOUN
cana-4367	233	2	(	(	PUNCT
cana-4367	233	3	2	2	X
cana-4367	233	4	)	)	PUNCT
cana-4367	233	5	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	233	6	(	(	PUNCT
cana-4367	233	7	3	3	NUM
cana-4367	233	8	)	)	PUNCT
cana-4367	233	9	)	)	PUNCT
cana-4367	234	1	=	=	SYM
cana-4367	234	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	234	3	(	(	PUNCT
cana-4367	234	4	2	2	NUM
cana-4367	234	5	)	)	PUNCT
cana-4367	234	6	)	)	PUNCT
cana-4367	234	7	]	]	PUNCT
cana-4367	234	8	2	2	X
cana-4367	234	9	,	,	PUNCT
cana-4367	234	10	[	[	X
cana-4367	234	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	234	12	(	(	PUNCT
cana-4367	234	13	3	3	NUM
cana-4367	234	14	)	)	PUNCT
cana-4367	234	15	)	)	PUNCT
cana-4367	234	16	]	]	PUNCT
cana-4367	234	17	2	2	X
cana-4367	234	18	)	)	PUNCT
cana-4367	234	19	=	=	SYM
cana-4367	234	20	hd([0]2	hd([0]2	NOUN
cana-4367	234	21	,	,	PUNCT
cana-4367	234	22	[	[	X
cana-4367	234	23	3]2	3]2	NOUN
cana-4367	234	24	)	)	PUNCT
cana-4367	234	25	=	=	SYM
cana-4367	234	26	2	2	X
cana-4367	234	27	.	.	PUNCT
cana-4367	234	28	𝑓∗(vm−1vm	𝑓∗(vm−1vm	ADJ
cana-4367	234	29	)	)	PUNCT
cana-4367	235	1	=	=	SYM
cana-4367	235	2	hd([f(vm−1)]2	hd([f(vm−1)]2	NOUN
cana-4367	235	3	,	,	PUNCT
cana-4367	235	4	[	[	X
cana-4367	235	5	f(vm)]2	f(vm)]2	X
cana-4367	235	6	)	)	PUNCT
cana-4367	235	7	=	=	SYM
cana-4367	236	1	hd([12]2	hd([12]2	PROPN
cana-4367	236	2	,	,	PUNCT
cana-4367	236	3	[	[	X
cana-4367	236	4	51]2	51]2	NUM
cana-4367	236	5	)	)	PUNCT
cana-4367	236	6	=	=	PUNCT
cana-4367	236	7	6	6	X
cana-4367	236	8	.	.	PUNCT
cana-4367	237	1	for	for	ADP
cana-4367	237	2	0	0	NUM
cana-4367	237	3	≤	≤	NUM
cana-4367	237	4	𝑖	𝑖	SYM
cana-4367	237	5	≤	≤	NOUN
cana-4367	237	6	𝑚	𝑚	ADP
cana-4367	237	7	;	;	PUNCT
cana-4367	237	8	3	3	NUM
cana-4367	237	9	≤	≤	NUM
cana-4367	237	10	𝑗	𝑗	PRON
cana-4367	237	11	≤	≤	ADJ
cana-4367	237	12	𝑟	𝑟	NOUN
cana-4367	237	13	if	if	SCONJ
cana-4367	237	14	𝑗	𝑗	PROPN
cana-4367	237	15	≡	≡	PROPN
cana-4367	237	16	1(𝑚𝑜𝑑4	1(𝑚𝑜𝑑4	NUM
cana-4367	237	17	)	)	PUNCT
cana-4367	237	18	;	;	PUNCT
cana-4367	237	19	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	PROPN
cana-4367	237	20	(	(	PUNCT
cana-4367	237	21	𝑗	𝑗	NOUN
cana-4367	237	22	)	)	PUNCT
cana-4367	237	23	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	237	24	(	(	PUNCT
cana-4367	237	25	𝑗+1	𝑗+1	NOUN
cana-4367	237	26	)	)	PUNCT
cana-4367	237	27	)	)	PUNCT
cana-4367	238	1	=	=	SYM
cana-4367	238	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	238	3	(	(	PUNCT
cana-4367	238	4	𝑗	𝑗	NOUN
cana-4367	238	5	)	)	PUNCT
cana-4367	238	6	)	)	PUNCT
cana-4367	238	7	]	]	PUNCT
cana-4367	238	8	2	2	X
cana-4367	238	9	,	,	PUNCT
cana-4367	238	10	[	[	X
cana-4367	238	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	238	12	(	(	PUNCT
cana-4367	238	13	𝑗+1	𝑗+1	NOUN
cana-4367	238	14	)	)	PUNCT
cana-4367	238	15	)	)	PUNCT
cana-4367	238	16	]	]	PUNCT
cana-4367	238	17	2	2	X
cana-4367	238	18	)	)	PUNCT
cana-4367	238	19	=	=	SYM
cana-4367	239	1	hd([0]2	hd([0]2	NOUN
cana-4367	239	2	,	,	PUNCT
cana-4367	239	3	[	[	X
cana-4367	239	4	15]2	15]2	X
cana-4367	239	5	)	)	PUNCT
cana-4367	239	6	=	=	SYM
cana-4367	239	7	4	4	X
cana-4367	239	8	.	.	X
cana-4367	240	1	if	if	SCONJ
cana-4367	240	2	𝑗	𝑗	PROPN
cana-4367	240	3	≡	≡	PROPN
cana-4367	240	4	2(𝑚𝑜𝑑4	2(𝑚𝑜𝑑4	NUM
cana-4367	240	5	)	)	PUNCT
cana-4367	240	6	;	;	PUNCT
cana-4367	240	7	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	PROPN
cana-4367	240	8	(	(	PUNCT
cana-4367	240	9	𝑗	𝑗	NOUN
cana-4367	240	10	)	)	PUNCT
cana-4367	240	11	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	240	12	(	(	PUNCT
cana-4367	240	13	𝑗+1	𝑗+1	NOUN
cana-4367	240	14	)	)	PUNCT
cana-4367	240	15	)	)	PUNCT
cana-4367	241	1	=	=	SYM
cana-4367	241	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	241	3	(	(	PUNCT
cana-4367	241	4	𝑗	𝑗	NOUN
cana-4367	241	5	)	)	PUNCT
cana-4367	241	6	)	)	PUNCT
cana-4367	241	7	]	]	PUNCT
cana-4367	241	8	2	2	X
cana-4367	241	9	,	,	PUNCT
cana-4367	241	10	[	[	X
cana-4367	241	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	241	12	(	(	PUNCT
cana-4367	241	13	𝑗+1	𝑗+1	NOUN
cana-4367	241	14	)	)	PUNCT
cana-4367	241	15	)	)	PUNCT
cana-4367	241	16	]	]	PUNCT
cana-4367	241	17	2	2	X
cana-4367	241	18	)	)	PUNCT
cana-4367	241	19	=	=	SYM
cana-4367	241	20	hd([15]2	hd([15]2	NOUN
cana-4367	241	21	,	,	PUNCT
cana-4367	241	22	[	[	X
cana-4367	241	23	3]2	3]2	NUM
cana-4367	241	24	)	)	PUNCT
cana-4367	241	25	=	=	SYM
cana-4367	241	26	2	2	X
cana-4367	241	27	.	.	X
cana-4367	242	1	if	if	SCONJ
cana-4367	242	2	𝑗	𝑗	PROPN
cana-4367	242	3	≡	≡	PROPN
cana-4367	242	4	3(𝑚𝑜𝑑4	3(𝑚𝑜𝑑4	NUM
cana-4367	242	5	)	)	PUNCT
cana-4367	242	6	;	;	PUNCT
cana-4367	242	7	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	PROPN
cana-4367	242	8	(	(	PUNCT
cana-4367	242	9	𝑗	𝑗	NOUN
cana-4367	242	10	)	)	PUNCT
cana-4367	242	11	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	242	12	(	(	PUNCT
cana-4367	242	13	𝑗+1	𝑗+1	NOUN
cana-4367	242	14	)	)	PUNCT
cana-4367	242	15	)	)	PUNCT
cana-4367	243	1	=	=	SYM
cana-4367	243	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	243	3	(	(	PUNCT
cana-4367	243	4	𝑗	𝑗	NOUN
cana-4367	243	5	)	)	PUNCT
cana-4367	243	6	)	)	PUNCT
cana-4367	243	7	]	]	PUNCT
cana-4367	243	8	2	2	X
cana-4367	243	9	,	,	PUNCT
cana-4367	243	10	[	[	X
cana-4367	243	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	243	12	(	(	PUNCT
cana-4367	243	13	𝑗+1	𝑗+1	NOUN
cana-4367	243	14	)	)	PUNCT
cana-4367	243	15	)	)	PUNCT
cana-4367	243	16	]	]	PUNCT
cana-4367	243	17	2	2	X
cana-4367	243	18	)	)	PUNCT
cana-4367	243	19	=	=	SYM
cana-4367	243	20	hd([3]2	hd([3]2	X
cana-4367	243	21	,	,	PUNCT
cana-4367	243	22	[	[	X
cana-4367	243	23	12]2	12]2	NUM
cana-4367	243	24	)	)	PUNCT
cana-4367	243	25	=	=	SYM
cana-4367	243	26	4	4	X
cana-4367	243	27	.	.	X
cana-4367	244	1	if	if	SCONJ
cana-4367	244	2	𝑗	𝑗	PROPN
cana-4367	244	3	≡	≡	PROPN
cana-4367	244	4	0(𝑚𝑜𝑑4	0(𝑚𝑜𝑑4	PROPN
cana-4367	244	5	)	)	PUNCT
cana-4367	245	1	;	;	PUNCT
cana-4367	245	2	𝑓∗(𝑢𝑖	𝑓∗(𝑢𝑖	PROPN
cana-4367	245	3	(	(	PUNCT
cana-4367	245	4	𝑗	𝑗	NOUN
cana-4367	245	5	)	)	PUNCT
cana-4367	245	6	𝑢𝑖	𝑢𝑖	NOUN
cana-4367	245	7	(	(	PUNCT
cana-4367	245	8	𝑗+1	𝑗+1	NOUN
cana-4367	245	9	)	)	PUNCT
cana-4367	245	10	)	)	PUNCT
cana-4367	246	1	=	=	SYM
cana-4367	246	2	ℎ𝑑([𝑓(𝑢𝑖	ℎ𝑑([𝑓(𝑢𝑖	PROPN
cana-4367	246	3	(	(	PUNCT
cana-4367	246	4	𝑗	𝑗	NOUN
cana-4367	246	5	)	)	PUNCT
cana-4367	246	6	)	)	PUNCT
cana-4367	246	7	]	]	PUNCT
cana-4367	246	8	2	2	X
cana-4367	246	9	,	,	PUNCT
cana-4367	246	10	[	[	X
cana-4367	246	11	𝑓(𝑢𝑖	𝑓(𝑢𝑖	NOUN
cana-4367	246	12	(	(	PUNCT
cana-4367	246	13	𝑗+1	𝑗+1	NOUN
cana-4367	246	14	)	)	PUNCT
cana-4367	246	15	)	)	PUNCT
cana-4367	246	16	]	]	PUNCT
cana-4367	246	17	2	2	X
cana-4367	246	18	)	)	PUNCT
cana-4367	246	19	=	=	SYM
cana-4367	246	20	hd([12]2	hd([12]2	PROPN
cana-4367	246	21	,	,	PUNCT
cana-4367	246	22	[	[	X
cana-4367	246	23	0]2	0]2	X
cana-4367	246	24	)	)	PUNCT
cana-4367	246	25	=	=	SYM
cana-4367	246	26	2	2	NUM
cana-4367	246	27	communications	communication	NOUN
cana-4367	246	28	on	on	ADP
cana-4367	246	29	applied	apply	VERB
cana-4367	246	30	nonlinear	nonlinear	ADJ
cana-4367	246	31	analysis	analysis	NOUN
cana-4367	246	32	issn	issn	NOUN
cana-4367	246	33	:	:	PUNCT
cana-4367	246	34	1074	1074	NUM
cana-4367	246	35	-	-	PUNCT
cana-4367	246	36	133x	133x	NUM
cana-4367	246	37	vol	vol	NOUN
cana-4367	246	38	32	32	NUM
cana-4367	246	39	no	no	NOUN
cana-4367	246	40	.	.	PUNCT
cana-4367	247	1	9s	9s	NUM
cana-4367	247	2	(	(	PUNCT
cana-4367	247	3	2025	2025	NUM
cana-4367	247	4	)	)	PUNCT
cana-4367	247	5	1927	1927	NUM
cana-4367	247	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4367	247	7	from	from	ADP
cana-4367	247	8	all	all	DET
cana-4367	247	9	the	the	DET
cana-4367	247	10	above	above	ADJ
cana-4367	247	11	cases	case	NOUN
cana-4367	247	12	,	,	PUNCT
cana-4367	247	13	all	all	DET
cana-4367	247	14	adjacent	adjacent	ADJ
cana-4367	247	15	edges	edge	NOUN
cana-4367	247	16	receive	receive	VERB
cana-4367	247	17	distinct	distinct	ADJ
cana-4367	247	18	even	even	ADV
cana-4367	247	19	labels	label	NOUN
cana-4367	247	20	.	.	PUNCT
cana-4367	248	1	hence	hence	ADV
cana-4367	248	2	it	it	PRON
cana-4367	248	3	is	be	AUX
cana-4367	248	4	proved	prove	VERB
cana-4367	248	5	that	that	SCONJ
cana-4367	248	6	the	the	DET
cana-4367	248	7	comb	comb	NOUN
cana-4367	248	8	product	product	NOUN
cana-4367	248	9	of	of	ADP
cana-4367	248	10	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	248	11	and	and	CCONJ
cana-4367	248	12	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	248	13	graph	graph	NOUN
cana-4367	248	14	(	(	PUNCT
cana-4367	248	15	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	248	16	⊳	⊳	PROPN
cana-4367	248	17	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	248	18	)	)	PUNCT
cana-4367	248	19	admits	admit	VERB
cana-4367	248	20	even	even	ADV
cana-4367	248	21	hamming	ham	VERB
cana-4367	248	22	distance	distance	NOUN
cana-4367	248	23	labeling	labeling	NOUN
cana-4367	248	24	and	and	CCONJ
cana-4367	248	25	the	the	DET
cana-4367	248	26	even	even	ADV
cana-4367	248	27	hamming	hamming	NOUN
cana-4367	248	28	distance	distance	NOUN
cana-4367	248	29	number	number	NOUN
cana-4367	248	30	is	be	AUX
cana-4367	248	31	ηℎ𝑑	ηℎ𝑑	NOUN
cana-4367	248	32	′′	′′	PROPN
cana-4367	248	33	(	(	PUNCT
cana-4367	248	34	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	248	35	⊳	⊳	PROPN
cana-4367	248	36	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	248	37	)	)	PUNCT
cana-4367	248	38	=	=	NOUN
cana-4367	248	39	{	{	PUNCT
cana-4367	248	40	4	4	NUM
cana-4367	248	41	,	,	PUNCT
cana-4367	248	42	𝑖𝑓	𝑖𝑓	ADP
cana-4367	248	43	𝑚	𝑚	NOUN
cana-4367	248	44	=	=	SYM
cana-4367	248	45	1	1	NUM
cana-4367	248	46	6	6	NUM
cana-4367	248	47	,	,	PUNCT
cana-4367	248	48	𝑖𝑓	𝑖𝑓	ADP
cana-4367	248	49	𝑚	𝑚	X
cana-4367	248	50	>	>	X
cana-4367	248	51	1	1	NUM
cana-4367	248	52	.	.	PUNCT
cana-4367	249	1	3	3	X
cana-4367	249	2	.	.	X
cana-4367	249	3	conclusion	conclusion	NOUN
cana-4367	249	4	in	in	ADP
cana-4367	249	5	this	this	DET
cana-4367	249	6	paper	paper	NOUN
cana-4367	249	7	,	,	PUNCT
cana-4367	249	8	the	the	DET
cana-4367	249	9	even	even	ADV
cana-4367	249	10	hamming	hamming	NOUN
cana-4367	249	11	distance	distance	NOUN
cana-4367	249	12	number	number	NOUN
cana-4367	249	13	of	of	ADP
cana-4367	249	14	comb	comb	NOUN
cana-4367	249	15	graph	graph	NOUN
cana-4367	249	16	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	249	17	+	+	PROPN
cana-4367	249	18	,	,	PUNCT
cana-4367	249	19	twig	twig	PROPN
cana-4367	249	20	graph	graph	VERB
cana-4367	249	21	𝑇𝑊(𝑃𝑚	𝑇𝑊(𝑃𝑚	PROPN
cana-4367	249	22	)	)	PUNCT
cana-4367	249	23	,	,	PUNCT
cana-4367	249	24	centipede	centipede	NOUN
cana-4367	249	25	graph(𝑚	graph(𝑚	PROPN
cana-4367	249	26	,	,	PUNCT
cana-4367	249	27	2	2	NUM
cana-4367	249	28	)	)	PUNCT
cana-4367	249	29	,	,	PUNCT
cana-4367	249	30	and	and	CCONJ
cana-4367	249	31	comb	comb	VERB
cana-4367	249	32	product	product	NOUN
cana-4367	249	33	of	of	ADP
cana-4367	249	34	𝑃𝑚	𝑃𝑚	PROPN
cana-4367	249	35	and	and	CCONJ
cana-4367	249	36	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	249	37	graph(𝑃𝑚	graph(𝑃𝑚	PROPN
cana-4367	249	38	⊳	⊳	PROPN
cana-4367	249	39	𝑃𝑟	𝑃𝑟	PROPN
cana-4367	249	40	)	)	PUNCT
cana-4367	249	41	were	be	AUX
cana-4367	249	42	obtained	obtain	VERB
cana-4367	249	43	.	.	PUNCT
cana-4367	250	1	references	reference	NOUN
cana-4367	250	2	[	[	X
cana-4367	250	3	1].durai	1].durai	NUM
cana-4367	250	4	baskar.a	baskar.a	NOUN
cana-4367	250	5	and	and	CCONJ
cana-4367	250	6	manivannan.p	manivannan.p	PROPN
cana-4367	250	7	,	,	PUNCT
cana-4367	250	8	f	f	X
cana-4367	250	9	-	-	PUNCT
cana-4367	250	10	heronian	heronian	ADJ
cana-4367	250	11	mean	mean	ADJ
cana-4367	250	12	labeling	labeling	NOUN
cana-4367	250	13	of	of	ADP
cana-4367	250	14	graphs	graph	NOUN
cana-4367	250	15	,	,	PUNCT
cana-4367	250	16	international	international	ADJ
cana-4367	250	17	journal	journal	NOUN
cana-4367	250	18	of	of	ADP
cana-4367	250	19	pure	pure	ADJ
cana-4367	250	20	and	and	CCONJ
cana-4367	250	21	applied	applied	ADJ
cana-4367	250	22	mathematics	mathematic	NOUN
cana-4367	250	23	,	,	PUNCT
cana-4367	250	24	volume	volume	NOUN
cana-4367	250	25	117(5	117(5	NUM
cana-4367	250	26	)	)	PUNCT
cana-4367	250	27	,	,	PUNCT
cana-4367	250	28	2017	2017	NUM
cana-4367	250	29	,	,	PUNCT
cana-4367	250	30	55	55	NUM
cana-4367	250	31	-	-	SYM
cana-4367	250	32	62	62	NUM
cana-4367	250	33	.	.	PUNCT
cana-4367	251	1	[	[	X
cana-4367	251	2	2].esakkiammal.e	2].esakkiammal.e	X
cana-4367	251	3	.	.	PUNCT
cana-4367	251	4	thirusangu.k	thirusangu.k	PROPN
cana-4367	251	5	and	and	CCONJ
cana-4367	251	6	seethalakshmi.s	seethalakshmi.s	PROPN
cana-4367	251	7	,	,	PUNCT
cana-4367	251	8	d	d	ADJ
cana-4367	251	9	-	-	PUNCT
cana-4367	251	10	lucky	lucky	ADJ
cana-4367	251	11	labeling	labeling	NOUN
cana-4367	251	12	of	of	ADP
cana-4367	251	13	arbitrary	arbitrary	ADJ
cana-4367	251	14	super	super	ADJ
cana-4367	251	15	subdivision	subdivision	NOUN
cana-4367	251	16	of	of	ADP
cana-4367	251	17	some	some	DET
cana-4367	251	18	graphs	graph	NOUN
cana-4367	251	19	,	,	PUNCT
cana-4367	251	20	international	international	ADJ
cana-4367	251	21	journal	journal	NOUN
cana-4367	251	22	of	of	ADP
cana-4367	251	23	pure	pure	ADJ
cana-4367	251	24	and	and	CCONJ
cana-4367	251	25	applied	applied	ADJ
cana-4367	251	26	mathematics	mathematic	NOUN
cana-4367	251	27	,	,	PUNCT
cana-4367	251	28	volume	volume	NOUN
cana-4367	251	29	113(7	113(7	NUM
cana-4367	251	30	)	)	PUNCT
cana-4367	251	31	,	,	PUNCT
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cana-4367	251	33	,	,	PUNCT
cana-4367	251	34	93	93	NUM
cana-4367	251	35	-	-	SYM
cana-4367	251	36	101	101	NUM
cana-4367	251	37	.	.	PUNCT
cana-4367	252	1	[	[	X
cana-4367	252	2	3	3	NUM
cana-4367	252	3	]	]	PUNCT
cana-4367	252	4	gallian	gallian	PROPN
cana-4367	252	5	j.a	j.a	PROPN
cana-4367	252	6	.	.	PROPN
cana-4367	253	1	a	a	DET
cana-4367	253	2	dynamic	dynamic	ADJ
cana-4367	253	3	survey	survey	NOUN
cana-4367	253	4	of	of	ADP
cana-4367	253	5	graph	graph	NOUN
cana-4367	253	6	labeling	labeling	NOUN
cana-4367	253	7	,	,	PUNCT
cana-4367	253	8	the	the	DET
cana-4367	253	9	electronic	electronic	ADJ
cana-4367	253	10	journal	journal	NOUN
cana-4367	253	11	of	of	ADP
cana-4367	253	12	combinatorics	combinatoric	NOUN
cana-4367	253	13	.	.	PUNCT
cana-4367	254	1	2019	2019	NUM
cana-4367	254	2	.	.	PUNCT
cana-4367	255	1	ds6	ds6	NOUN
cana-4367	255	2	.	.	PUNCT
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cana-4367	256	2	4	4	NUM
cana-4367	256	3	]	]	X
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cana-4367	256	5	prakash	prakash	PROPN
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cana-4367	256	8	rajedran	rajedran	NOUN
cana-4367	256	9	,	,	PUNCT
cana-4367	256	10	neighbourhood	neighbourhood	ADJ
cana-4367	256	11	prime	prime	ADJ
cana-4367	256	12	labelling	labelling	NOUN
cana-4367	256	13	on	on	ADP
cana-4367	256	14	some	some	DET
cana-4367	256	15	path	path	NOUN
cana-4367	256	16	related	relate	VERB
cana-4367	256	17	graphs	graph	NOUN
cana-4367	256	18	,	,	PUNCT
cana-4367	256	19	international	international	ADJ
cana-4367	256	20	journal	journal	NOUN
cana-4367	256	21	of	of	ADP
cana-4367	256	22	pure	pure	ADJ
cana-4367	256	23	and	and	CCONJ
cana-4367	256	24	applied	applied	ADJ
cana-4367	256	25	mathematics	mathematic	NOUN
cana-4367	256	26	,	,	PUNCT
cana-4367	256	27	volume	volume	NOUN
cana-4367	256	28	118(20	118(20	NUM
cana-4367	256	29	)	)	PUNCT
cana-4367	256	30	,	,	PUNCT
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cana-4367	256	32	,	,	PUNCT
cana-4367	256	33	18931901	18931901	NUM
cana-4367	256	34	.	.	PUNCT
cana-4367	257	1	[	[	X
cana-4367	257	2	5	5	NUM
cana-4367	257	3	]	]	PUNCT
cana-4367	257	4	seethalakshmi.s	seethalakshmi.s	PROPN
cana-4367	257	5	,	,	PUNCT
cana-4367	257	6	thirusangu.k	thirusangu.k	PROPN
cana-4367	257	7	,	,	PUNCT
cana-4367	257	8	esakkiammal.e	esakkiammal.e	VERB
cana-4367	257	9	,	,	PUNCT
cana-4367	257	10	hamming	ham	VERB
cana-4367	257	11	distance	distance	NOUN
cana-4367	257	12	labeling	labeling	NOUN
cana-4367	257	13	of	of	ADP
cana-4367	257	14	certain	certain	ADJ
cana-4367	257	15	graphs	graph	NOUN
cana-4367	257	16	,	,	PUNCT
cana-4367	257	17	journal	journal	NOUN
cana-4367	257	18	of	of	ADP
cana-4367	257	19	tianjin	tianjin	PROPN
cana-4367	257	20	university	university	PROPN
cana-4367	257	21	science	science	NOUN
cana-4367	257	22	and	and	CCONJ
cana-4367	257	23	technology	technology	NOUN
cana-4367	257	24	,	,	PUNCT
cana-4367	257	25	2021	2021	NUM
cana-4367	257	26	54(10	54(10	NUM
cana-4367	257	27	)	)	PUNCT
cana-4367	257	28	,	,	PUNCT
cana-4367	257	29	106	106	NUM
cana-4367	257	30	-	-	SYM
cana-4367	257	31	113	113	NUM
cana-4367	257	32	,	,	PUNCT
cana-4367	257	33	doi:10.17605	doi:10.17605	NOUN
cana-4367	257	34	/	/	SYM
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cana-4367	257	36	/	/	SYM
cana-4367	257	37	fma2q	fma2q	PROPN
cana-4367	257	38	.	.	PUNCT
cana-4367	258	1	[	[	X
cana-4367	258	2	6	6	NUM
cana-4367	258	3	]	]	PUNCT
cana-4367	258	4	sunoj	sunoj	NOUN
cana-4367	258	5	b.s	b.s	PROPN
cana-4367	258	6	,	,	PUNCT
cana-4367	258	7	mathew	mathew	PROPN
cana-4367	258	8	varkey	varkey	PROPN
cana-4367	258	9	t	t	PROPN
cana-4367	258	10	k	k	PROPN
cana-4367	258	11	,	,	PUNCT
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cana-4367	258	13	difference	difference	NOUN
cana-4367	258	14	prime	prime	ADJ
cana-4367	258	15	labeling	labeling	NOUN
cana-4367	258	16	for	for	ADP
cana-4367	258	17	some	some	DET
cana-4367	258	18	tree	tree	NOUN
cana-4367	258	19	graphs	graph	NOUN
cana-4367	258	20	,	,	PUNCT
cana-4367	258	21	ijedr	ijedr	NOUN
cana-4367	258	22	,	,	PUNCT
cana-4367	258	23	2017	2017	NUM
cana-4367	258	24	,	,	PUNCT
cana-4367	258	25	vol.5(4	vol.5(4	NOUN
cana-4367	258	26	)	)	PUNCT
cana-4367	258	27	,	,	PUNCT
cana-4367	258	28	issn	issn	PROPN
cana-4367	258	29	:	:	PUNCT
cana-4367	258	30	2321	2321	NUM
cana-4367	258	31	-	-	SYM
cana-4367	258	32	9939	9939	NUM
cana-4367	258	33	.	.	PUNCT