id	sid	tid	token	lemma	pos
cana-3475	1	1	communications	communication	NOUN
cana-3475	1	2	on	on	ADP
cana-3475	1	3	applied	apply	VERB
cana-3475	1	4	nonlinear	nonlinear	ADJ
cana-3475	1	5	analysis	analysis	NOUN
cana-3475	1	6	issn	issn	NOUN
cana-3475	1	7	:	:	PUNCT
cana-3475	1	8	1074	1074	NUM
cana-3475	1	9	-	-	PUNCT
cana-3475	1	10	133x	133x	NUM
cana-3475	1	11	vol	vol	NOUN
cana-3475	1	12	32	32	NUM
cana-3475	1	13	no	no	NOUN
cana-3475	1	14	.	.	PUNCT
cana-3475	2	1	7s	7	NOUN
cana-3475	2	2	(	(	PUNCT
cana-3475	2	3	2025	2025	NUM
cana-3475	2	4	)	)	PUNCT
cana-3475	2	5	688	688	NUM
cana-3475	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3475	2	7	fault	fault	NOUN
cana-3475	2	8	-	-	PUNCT
cana-3475	2	9	tolerant	tolerant	ADJ
cana-3475	2	10	strong	strong	ADJ
cana-3475	2	11	metric	metric	ADJ
cana-3475	2	12	dimension	dimension	NOUN
cana-3475	2	13	of	of	ADP
cana-3475	2	14	rooted	rooted	ADJ
cana-3475	2	15	product	product	NOUN
cana-3475	2	16	graphs	graph	VERB
cana-3475	2	17	h.	h.	PROPN
cana-3475	2	18	prathab1,2	prathab1,2	PROPN
cana-3475	2	19	,	,	PUNCT
cana-3475	2	20	s.	s.	PROPN
cana-3475	2	21	chandrasekaran3	chandrasekaran3	PROPN
cana-3475	2	22	and	and	CCONJ
cana-3475	2	23	sathish	sathish	PROPN
cana-3475	2	24	krishnan4	krishnan4	PROPN
cana-3475	2	25	*	*	PROPN
cana-3475	2	26	1department	1department	NUM
cana-3475	2	27	of	of	ADP
cana-3475	2	28	mathematics	mathematic	NOUN
cana-3475	2	29	,	,	PUNCT
cana-3475	2	30	saveetha	saveetha	PROPN
cana-3475	2	31	engineering	engineering	PROPN
cana-3475	2	32	college	college	PROPN
cana-3475	2	33	,	,	PUNCT
cana-3475	2	34	chennai	chennai	PROPN
cana-3475	2	35	,	,	PUNCT
cana-3475	2	36	602105	602105	NUM
cana-3475	2	37	,	,	PUNCT
cana-3475	2	38	india	india	PROPN
cana-3475	2	39	.	.	PUNCT
cana-3475	3	1	2research	2research	NUM
cana-3475	3	2	scholar	scholar	NOUN
cana-3475	3	3	,	,	PUNCT
cana-3475	3	4	p.g	p.g	PROPN
cana-3475	3	5	&	&	CCONJ
cana-3475	3	6	research	research	PROPN
cana-3475	3	7	department	department	PROPN
cana-3475	3	8	of	of	ADP
cana-3475	3	9	mathematics	mathematics	PROPN
cana-3475	3	10	pachaiyappa	pachaiyappa	PROPN
cana-3475	3	11	’s	’s	PART
cana-3475	3	12	college	college	PROPN
cana-3475	3	13	,	,	PUNCT
cana-3475	3	14	chennai	chennai	PROPN
cana-3475	3	15	,	,	PUNCT
cana-3475	3	16	600030	600030	NUM
cana-3475	3	17	,	,	PUNCT
cana-3475	3	18	india	india	PROPN
cana-3475	3	19	.	.	PUNCT
cana-3475	4	1	3p.g	3p.g	NUM
cana-3475	4	2	&	&	CCONJ
cana-3475	4	3	research	research	PROPN
cana-3475	4	4	department	department	PROPN
cana-3475	4	5	of	of	ADP
cana-3475	4	6	mathematics	mathematics	PROPN
cana-3475	4	7	,	,	PUNCT
cana-3475	4	8	pachaiyappa	pachaiyappa	PROPN
cana-3475	4	9	’s	’s	PART
cana-3475	4	10	college	college	PROPN
cana-3475	4	11	,	,	PUNCT
cana-3475	4	12	chennai	chennai	PROPN
cana-3475	4	13	,	,	PUNCT
cana-3475	4	14	600030	600030	NUM
cana-3475	4	15	,	,	PUNCT
cana-3475	4	16	india	india	PROPN
cana-3475	4	17	.	.	PUNCT
cana-3475	5	1	4*department	4*department	NOUN
cana-3475	5	2	of	of	ADP
cana-3475	5	3	mathematics	mathematic	NOUN
cana-3475	5	4	and	and	CCONJ
cana-3475	5	5	statistics	statistic	NOUN
cana-3475	5	6	,	,	PUNCT
cana-3475	5	7	faculty	faculty	NOUN
cana-3475	5	8	of	of	ADP
cana-3475	5	9	science	science	NOUN
cana-3475	5	10	and	and	CCONJ
cana-3475	5	11	humanities	humanity	NOUN
cana-3475	5	12	srm	srm	PROPN
cana-3475	5	13	institute	institute	PROPN
cana-3475	5	14	of	of	ADP
cana-3475	5	15	science	science	NOUN
cana-3475	5	16	and	and	CCONJ
cana-3475	5	17	technology	technology	NOUN
cana-3475	5	18	,	,	PUNCT
cana-3475	5	19	chengalpattu	chengalpattu	ADV
cana-3475	5	20	,	,	PUNCT
cana-3475	5	21	603203	603203	NUM
cana-3475	5	22	,	,	PUNCT
cana-3475	5	23	india	india	PROPN
cana-3475	5	24	.	.	PUNCT
cana-3475	6	1	*	*	PUNCT
cana-3475	6	2	corresponding	correspond	VERB
cana-3475	6	3	author	author	NOUN
cana-3475	6	4	.	.	PUNCT
cana-3475	7	1	e	e	X
cana-3475	7	2	-	-	NOUN
cana-3475	7	3	mail	mail	NOUN
cana-3475	7	4	:	:	PUNCT
cana-3475	8	1	satiskris@gmail.com	satiskris@gmail.com	X
cana-3475	9	1	sathishk6@srmist.edu.in	sathishk6@srmist.edu.in	PROPN
cana-3475	9	2	article	article	NOUN
cana-3475	9	3	history	history	NOUN
cana-3475	9	4	:	:	PUNCT
cana-3475	9	5	received	receive	VERB
cana-3475	9	6	:	:	PUNCT
cana-3475	9	7	27	27	NUM
cana-3475	9	8	-	-	SYM
cana-3475	9	9	10	10	NUM
cana-3475	9	10	-	-	PUNCT
cana-3475	9	11	2024	2024	NUM
cana-3475	9	12	revised:11	revised:11	VERB
cana-3475	9	13	-	-	SYM
cana-3475	9	14	11	11	NUM
cana-3475	9	15	-	-	PUNCT
cana-3475	9	16	2024	2024	NUM
cana-3475	9	17	accepted:19	accepted:19	VERB
cana-3475	9	18	-	-	PUNCT
cana-3475	9	19	12	12	NUM
cana-3475	9	20	-	-	PUNCT
cana-3475	9	21	2024	2024	NUM
cana-3475	9	22	abstract	abstract	NOUN
cana-3475	9	23	:	:	PUNCT
cana-3475	9	24	the	the	DET
cana-3475	9	25	concept	concept	NOUN
cana-3475	9	26	of	of	ADP
cana-3475	9	27	fault	fault	NOUN
cana-3475	9	28	tolerance	tolerance	NOUN
cana-3475	9	29	in	in	ADP
cana-3475	9	30	graph	graph	NOUN
cana-3475	9	31	theory	theory	NOUN
cana-3475	9	32	is	be	AUX
cana-3475	9	33	critical	critical	ADJ
cana-3475	9	34	in	in	ADP
cana-3475	9	35	designing	design	VERB
cana-3475	9	36	robust	robust	ADJ
cana-3475	9	37	networks	network	NOUN
cana-3475	9	38	,	,	PUNCT
cana-3475	9	39	ensuring	ensure	VERB
cana-3475	9	40	that	that	SCONJ
cana-3475	9	41	essential	essential	ADJ
cana-3475	9	42	graph	graph	NOUN
cana-3475	9	43	properties	property	NOUN
cana-3475	9	44	are	be	AUX
cana-3475	9	45	preserved	preserve	VERB
cana-3475	9	46	despite	despite	SCONJ
cana-3475	9	47	failures	failure	NOUN
cana-3475	9	48	of	of	ADP
cana-3475	9	49	vertices	vertex	NOUN
cana-3475	9	50	or	or	CCONJ
cana-3475	9	51	edges	edge	NOUN
cana-3475	9	52	.	.	PUNCT
cana-3475	10	1	in	in	ADP
cana-3475	10	2	this	this	DET
cana-3475	10	3	paper	paper	NOUN
cana-3475	10	4	,	,	PUNCT
cana-3475	10	5	we	we	PRON
cana-3475	10	6	investigate	investigate	VERB
cana-3475	10	7	the	the	DET
cana-3475	10	8	fault	fault	NOUN
cana-3475	10	9	-	-	PUNCT
cana-3475	10	10	tolerant	tolerant	ADJ
cana-3475	10	11	strong	strong	ADJ
cana-3475	10	12	metric	metric	ADJ
cana-3475	10	13	dimension	dimension	NOUN
cana-3475	10	14	of	of	ADP
cana-3475	10	15	rooted	rooted	ADJ
cana-3475	10	16	product	product	NOUN
cana-3475	10	17	graphs	graph	NOUN
cana-3475	10	18	,	,	PUNCT
cana-3475	10	19	a	a	DET
cana-3475	10	20	class	class	NOUN
cana-3475	10	21	of	of	ADP
cana-3475	10	22	graphs	graph	NOUN
cana-3475	10	23	derived	derive	VERB
cana-3475	10	24	by	by	ADP
cana-3475	10	25	attaching	attach	VERB
cana-3475	10	26	multiple	multiple	ADJ
cana-3475	10	27	copies	copy	NOUN
cana-3475	10	28	of	of	ADP
cana-3475	10	29	a	a	DET
cana-3475	10	30	rooted	rooted	ADJ
cana-3475	10	31	graph	graph	NOUN
cana-3475	10	32	to	to	ADP
cana-3475	10	33	each	each	DET
cana-3475	10	34	vertex	vertex	NOUN
cana-3475	10	35	of	of	ADP
cana-3475	10	36	a	a	DET
cana-3475	10	37	base	base	NOUN
cana-3475	10	38	graph	graph	NOUN
cana-3475	10	39	.	.	PUNCT
cana-3475	11	1	we	we	PRON
cana-3475	11	2	extend	extend	VERB
cana-3475	11	3	the	the	DET
cana-3475	11	4	notion	notion	NOUN
cana-3475	11	5	of	of	ADP
cana-3475	11	6	a	a	DET
cana-3475	11	7	strong	strong	ADJ
cana-3475	11	8	metric	metric	ADJ
cana-3475	11	9	dimension	dimension	NOUN
cana-3475	11	10	by	by	ADP
cana-3475	11	11	considering	consider	VERB
cana-3475	11	12	scenarios	scenario	NOUN
cana-3475	11	13	where	where	SCONJ
cana-3475	11	14	the	the	DET
cana-3475	11	15	strong	strong	ADJ
cana-3475	11	16	resolving	resolving	NOUN
cana-3475	11	17	set	set	NOUN
cana-3475	11	18	remains	remain	VERB
cana-3475	11	19	effective	effective	ADJ
cana-3475	11	20	even	even	ADV
cana-3475	11	21	after	after	SCONJ
cana-3475	11	22	a	a	DET
cana-3475	11	23	specific	specific	ADJ
cana-3475	11	24	number	number	NOUN
cana-3475	11	25	of	of	ADP
cana-3475	11	26	vertices	vertex	NOUN
cana-3475	11	27	have	have	AUX
cana-3475	11	28	failed	fail	VERB
cana-3475	11	29	.	.	PUNCT
cana-3475	12	1	we	we	PRON
cana-3475	12	2	provide	provide	VERB
cana-3475	12	3	exact	exact	ADJ
cana-3475	12	4	values	value	NOUN
cana-3475	12	5	for	for	ADP
cana-3475	12	6	specific	specific	ADJ
cana-3475	12	7	families	family	NOUN
cana-3475	12	8	of	of	ADP
cana-3475	12	9	rooted	rooted	ADJ
cana-3475	12	10	product	product	NOUN
cana-3475	12	11	graphs	graph	NOUN
cana-3475	12	12	and	and	CCONJ
cana-3475	12	13	demonstrate	demonstrate	VERB
cana-3475	12	14	how	how	SCONJ
cana-3475	12	15	the	the	DET
cana-3475	12	16	fault	fault	NOUN
cana-3475	12	17	-	-	PUNCT
cana-3475	12	18	tolerant	tolerant	ADJ
cana-3475	12	19	property	property	NOUN
cana-3475	12	20	varies	vary	VERB
cana-3475	12	21	with	with	ADP
cana-3475	12	22	the	the	DET
cana-3475	12	23	structure	structure	NOUN
cana-3475	12	24	of	of	ADP
cana-3475	12	25	the	the	DET
cana-3475	12	26	root	root	NOUN
cana-3475	12	27	and	and	CCONJ
cana-3475	12	28	base	base	NOUN
cana-3475	12	29	graphs	graph	NOUN
cana-3475	12	30	.	.	PUNCT
cana-3475	13	1	keywords	keyword	NOUN
cana-3475	13	2	:	:	PUNCT
cana-3475	13	3	metric	metric	ADJ
cana-3475	13	4	dimension	dimension	NOUN
cana-3475	13	5	,	,	PUNCT
cana-3475	13	6	strong	strong	ADJ
cana-3475	13	7	metric	metric	ADJ
cana-3475	13	8	dimension	dimension	NOUN
cana-3475	13	9	,	,	PUNCT
cana-3475	13	10	fault	fault	NOUN
cana-3475	13	11	-	-	PUNCT
cana-3475	13	12	tolerant	tolerant	ADJ
cana-3475	13	13	strong	strong	ADJ
cana-3475	13	14	metric	metric	ADJ
cana-3475	13	15	dimension	dimension	NOUN
cana-3475	13	16	,	,	PUNCT
cana-3475	13	17	rooted	rooted	ADJ
cana-3475	13	18	product	product	NOUN
cana-3475	13	19	graphs	graph	NOUN
cana-3475	13	20	1	1	NUM
cana-3475	13	21	.	.	PUNCT
cana-3475	14	1	introduction	introduction	NOUN
cana-3475	14	2	the	the	DET
cana-3475	14	3	study	study	NOUN
cana-3475	14	4	of	of	ADP
cana-3475	14	5	graph	graph	NOUN
cana-3475	14	6	invariants	invariant	NOUN
cana-3475	14	7	has	have	AUX
cana-3475	14	8	long	long	ADV
cana-3475	14	9	been	be	AUX
cana-3475	14	10	central	central	ADJ
cana-3475	14	11	to	to	PART
cana-3475	14	12	graph	graph	VERB
cana-3475	14	13	theory	theory	NOUN
cana-3475	14	14	,	,	PUNCT
cana-3475	14	15	offering	offer	VERB
cana-3475	14	16	a	a	DET
cana-3475	14	17	framework	framework	NOUN
cana-3475	14	18	for	for	ADP
cana-3475	14	19	understanding	understand	VERB
cana-3475	14	20	the	the	DET
cana-3475	14	21	structural	structural	ADJ
cana-3475	14	22	and	and	CCONJ
cana-3475	14	23	combinatorial	combinatorial	ADJ
cana-3475	14	24	properties	property	NOUN
cana-3475	14	25	of	of	ADP
cana-3475	14	26	networks	network	NOUN
cana-3475	14	27	.	.	PUNCT
cana-3475	15	1	among	among	ADP
cana-3475	15	2	these	these	DET
cana-3475	15	3	invariants	invariant	NOUN
cana-3475	15	4	,	,	PUNCT
cana-3475	15	5	the	the	DET
cana-3475	15	6	metric	metric	ADJ
cana-3475	15	7	dimension	dimension	NOUN
cana-3475	15	8	and	and	CCONJ
cana-3475	15	9	its	its	PRON
cana-3475	15	10	variants	variant	NOUN
cana-3475	15	11	play	play	VERB
cana-3475	15	12	a	a	DET
cana-3475	15	13	pivotal	pivotal	ADJ
cana-3475	15	14	role	role	NOUN
cana-3475	15	15	in	in	ADP
cana-3475	15	16	problems	problem	NOUN
cana-3475	15	17	related	relate	VERB
cana-3475	15	18	to	to	ADP
cana-3475	15	19	network	network	NOUN
cana-3475	15	20	navigation	navigation	NOUN
cana-3475	15	21	,	,	PUNCT
cana-3475	15	22	resource	resource	NOUN
cana-3475	15	23	allocation	allocation	NOUN
cana-3475	15	24	,	,	PUNCT
cana-3475	15	25	and	and	CCONJ
cana-3475	15	26	information	information	NOUN
cana-3475	15	27	retrieval	retrieval	NOUN
cana-3475	15	28	.	.	PUNCT
cana-3475	16	1	the	the	DET
cana-3475	16	2	metric	metric	ADJ
cana-3475	16	3	dimension	dimension	NOUN
cana-3475	16	4	of	of	ADP
cana-3475	16	5	a	a	DET
cana-3475	16	6	graph	graph	NOUN
cana-3475	16	7	quantifies	quantify	VERB
cana-3475	16	8	the	the	DET
cana-3475	16	9	minimum	minimum	ADJ
cana-3475	16	10	number	number	NOUN
cana-3475	16	11	of	of	ADP
cana-3475	16	12	vertices	vertex	NOUN
cana-3475	16	13	required	require	VERB
cana-3475	16	14	to	to	PART
cana-3475	16	15	uniquely	uniquely	ADV
cana-3475	16	16	determine	determine	VERB
cana-3475	16	17	the	the	DET
cana-3475	16	18	position	position	NOUN
cana-3475	16	19	of	of	ADP
cana-3475	16	20	any	any	DET
cana-3475	16	21	other	other	ADJ
cana-3475	16	22	vertex	vertex	NOUN
cana-3475	16	23	within	within	ADP
cana-3475	16	24	the	the	DET
cana-3475	16	25	graph	graph	NOUN
cana-3475	16	26	using	use	VERB
cana-3475	16	27	distances	distance	NOUN
cana-3475	16	28	.	.	PUNCT
cana-3475	17	1	the	the	DET
cana-3475	17	2	strong	strong	ADJ
cana-3475	17	3	metric	metric	ADJ
cana-3475	17	4	dimension	dimension	NOUN
cana-3475	17	5	strengthens	strengthen	VERB
cana-3475	17	6	the	the	DET
cana-3475	17	7	classical	classical	ADJ
cana-3475	17	8	concept	concept	NOUN
cana-3475	17	9	of	of	ADP
cana-3475	17	10	metric	metric	ADJ
cana-3475	17	11	dimension	dimension	NOUN
cana-3475	17	12	by	by	ADP
cana-3475	17	13	imposing	impose	VERB
cana-3475	17	14	stricter	strict	ADJ
cana-3475	17	15	conditions	condition	NOUN
cana-3475	17	16	on	on	ADP
cana-3475	17	17	resolving	resolve	VERB
cana-3475	17	18	sets	set	NOUN
cana-3475	17	19	,	,	PUNCT
cana-3475	17	20	making	make	VERB
cana-3475	17	21	it	it	PRON
cana-3475	17	22	particularly	particularly	ADV
cana-3475	17	23	useful	useful	ADJ
cana-3475	17	24	in	in	ADP
cana-3475	17	25	applications	application	NOUN
cana-3475	17	26	where	where	SCONJ
cana-3475	17	27	precise	precise	ADJ
cana-3475	17	28	and	and	CCONJ
cana-3475	17	29	robust	robust	ADJ
cana-3475	17	30	vertex	vertex	NOUN
cana-3475	17	31	identification	identification	NOUN
cana-3475	17	32	is	be	AUX
cana-3475	17	33	essential	essential	ADJ
cana-3475	17	34	.	.	PUNCT
cana-3475	18	1	in	in	ADP
cana-3475	18	2	modern	modern	ADJ
cana-3475	18	3	applications	application	NOUN
cana-3475	18	4	,	,	PUNCT
cana-3475	18	5	networks	network	NOUN
cana-3475	18	6	are	be	AUX
cana-3475	18	7	often	often	ADV
cana-3475	18	8	subject	subject	ADJ
cana-3475	18	9	to	to	ADP
cana-3475	18	10	failures	failure	NOUN
cana-3475	18	11	or	or	CCONJ
cana-3475	18	12	disruptions	disruption	NOUN
cana-3475	18	13	,	,	PUNCT
cana-3475	18	14	making	make	VERB
cana-3475	18	15	fault	fault	VERB
cana-3475	18	16	tolerance	tolerance	NOUN
cana-3475	18	17	a	a	DET
cana-3475	18	18	crucial	crucial	ADJ
cana-3475	18	19	consideration	consideration	NOUN
cana-3475	18	20	.	.	PUNCT
cana-3475	19	1	the	the	DET
cana-3475	19	2	fault	fault	NOUN
cana-3475	19	3	-	-	PUNCT
cana-3475	19	4	tolerant	tolerant	ADJ
cana-3475	19	5	strong	strong	ADJ
cana-3475	19	6	metric	metric	ADJ
cana-3475	19	7	dimension	dimension	NOUN
cana-3475	19	8	addresses	address	NOUN
cana-3475	19	9	this	this	DET
cana-3475	19	10	challenge	challenge	NOUN
cana-3475	19	11	by	by	ADP
cana-3475	19	12	identifying	identify	VERB
cana-3475	19	13	resolving	resolve	VERB
cana-3475	19	14	sets	set	NOUN
cana-3475	19	15	that	that	PRON
cana-3475	19	16	retain	retain	VERB
cana-3475	19	17	functionality	functionality	NOUN
cana-3475	19	18	even	even	ADV
cana-3475	19	19	when	when	SCONJ
cana-3475	19	20	certain	certain	ADJ
cana-3475	19	21	vertices	vertex	NOUN
cana-3475	19	22	or	or	CCONJ
cana-3475	19	23	edges	edge	NOUN
cana-3475	19	24	fail	fail	ADJ
cana-3475	19	25	.	.	PUNCT
cana-3475	20	1	this	this	DET
cana-3475	20	2	concept	concept	NOUN
cana-3475	20	3	is	be	AUX
cana-3475	20	4	particularly	particularly	ADV
cana-3475	20	5	significant	significant	ADJ
cana-3475	20	6	in	in	ADP
cana-3475	20	7	the	the	DET
cana-3475	20	8	design	design	NOUN
cana-3475	20	9	of	of	ADP
cana-3475	20	10	resilient	resilient	ADJ
cana-3475	20	11	communication	communication	NOUN
cana-3475	20	12	and	and	CCONJ
cana-3475	20	13	transportation	transportation	NOUN
cana-3475	20	14	networks	network	NOUN
cana-3475	20	15	,	,	PUNCT
cana-3475	20	16	where	where	SCONJ
cana-3475	20	17	the	the	DET
cana-3475	20	18	ability	ability	NOUN
cana-3475	20	19	to	to	PART
cana-3475	20	20	maintain	maintain	VERB
cana-3475	20	21	operability	operability	NOUN
cana-3475	20	22	under	under	ADP
cana-3475	20	23	adverse	adverse	ADJ
cana-3475	20	24	conditions	condition	NOUN
cana-3475	20	25	is	be	AUX
cana-3475	20	26	essential	essential	ADJ
cana-3475	20	27	.	.	PUNCT
cana-3475	21	1	mailto:satiskris@gmail.com	mailto:satiskris@gmail.com	X
cana-3475	21	2	mailto:sathishk6@srmist.edu.in	mailto:sathishk6@srmist.edu.in	PART
cana-3475	21	3	communications	communication	NOUN
cana-3475	21	4	on	on	ADP
cana-3475	21	5	applied	apply	VERB
cana-3475	21	6	nonlinear	nonlinear	ADJ
cana-3475	21	7	analysis	analysis	NOUN
cana-3475	21	8	issn	issn	NOUN
cana-3475	21	9	:	:	PUNCT
cana-3475	21	10	1074	1074	NUM
cana-3475	21	11	-	-	PUNCT
cana-3475	21	12	133x	133x	NUM
cana-3475	21	13	vol	vol	NOUN
cana-3475	21	14	32	32	NUM
cana-3475	21	15	no	no	NOUN
cana-3475	21	16	.	.	PUNCT
cana-3475	22	1	7s	7	NOUN
cana-3475	22	2	(	(	PUNCT
cana-3475	22	3	2025	2025	NUM
cana-3475	22	4	)	)	PUNCT
cana-3475	23	1	689	689	NUM
cana-3475	23	2	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-3475	23	3	rooted	rooted	ADJ
cana-3475	23	4	product	product	NOUN
cana-3475	23	5	graphs	graph	NOUN
cana-3475	23	6	,	,	PUNCT
cana-3475	23	7	a	a	DET
cana-3475	23	8	construction	construction	NOUN
cana-3475	23	9	obtained	obtain	VERB
cana-3475	23	10	by	by	ADP
cana-3475	23	11	combining	combine	VERB
cana-3475	23	12	a	a	DET
cana-3475	23	13	base	base	NOUN
cana-3475	23	14	graph	graph	NOUN
cana-3475	23	15	with	with	ADP
cana-3475	23	16	multiple	multiple	ADJ
cana-3475	23	17	rooted	rooted	ADJ
cana-3475	23	18	subgraphs	subgraph	NOUN
cana-3475	23	19	,	,	PUNCT
cana-3475	23	20	offer	offer	VERB
cana-3475	23	21	a	a	DET
cana-3475	23	22	versatile	versatile	ADJ
cana-3475	23	23	model	model	NOUN
cana-3475	23	24	for	for	ADP
cana-3475	23	25	various	various	ADJ
cana-3475	23	26	real	real	ADJ
cana-3475	23	27	-	-	PUNCT
cana-3475	23	28	world	world	NOUN
cana-3475	23	29	systems	system	NOUN
cana-3475	23	30	.	.	PUNCT
cana-3475	24	1	their	their	PRON
cana-3475	24	2	hierarchical	hierarchical	ADJ
cana-3475	24	3	structure	structure	NOUN
cana-3475	24	4	and	and	CCONJ
cana-3475	24	5	inherent	inherent	ADJ
cana-3475	24	6	modularity	modularity	NOUN
cana-3475	24	7	make	make	VERB
cana-3475	24	8	them	they	PRON
cana-3475	24	9	a	a	DET
cana-3475	24	10	natural	natural	ADJ
cana-3475	24	11	candidate	candidate	NOUN
cana-3475	24	12	for	for	ADP
cana-3475	24	13	studying	study	VERB
cana-3475	24	14	fault	fault	NOUN
cana-3475	24	15	-	-	PUNCT
cana-3475	24	16	tolerant	tolerant	ADJ
cana-3475	24	17	properties	property	NOUN
cana-3475	24	18	.	.	PUNCT
cana-3475	25	1	despite	despite	SCONJ
cana-3475	25	2	their	their	PRON
cana-3475	25	3	relevance	relevance	NOUN
cana-3475	25	4	,	,	PUNCT
cana-3475	25	5	the	the	DET
cana-3475	25	6	fault	fault	NOUN
cana-3475	25	7	-	-	PUNCT
cana-3475	25	8	tolerant	tolerant	ADJ
cana-3475	25	9	strong	strong	ADJ
cana-3475	25	10	metric	metric	ADJ
cana-3475	25	11	dimension	dimension	NOUN
cana-3475	25	12	of	of	ADP
cana-3475	25	13	rooted	rooted	ADJ
cana-3475	25	14	product	product	NOUN
cana-3475	25	15	graphs	graph	NOUN
cana-3475	25	16	remains	remain	VERB
cana-3475	25	17	underexplored	underexplored	ADJ
cana-3475	25	18	in	in	ADP
cana-3475	25	19	the	the	DET
cana-3475	25	20	literature	literature	NOUN
cana-3475	25	21	.	.	PUNCT
cana-3475	26	1	in	in	ADP
cana-3475	26	2	this	this	DET
cana-3475	26	3	paper	paper	NOUN
cana-3475	26	4	,	,	PUNCT
cana-3475	26	5	we	we	PRON
cana-3475	26	6	investigate	investigate	VERB
cana-3475	26	7	the	the	DET
cana-3475	26	8	fault	fault	NOUN
cana-3475	26	9	-	-	PUNCT
cana-3475	26	10	tolerant	tolerant	ADJ
cana-3475	26	11	strong	strong	ADJ
cana-3475	26	12	metric	metric	ADJ
cana-3475	26	13	dimension	dimension	NOUN
cana-3475	26	14	of	of	ADP
cana-3475	26	15	rooted	rooted	ADJ
cana-3475	26	16	product	product	NOUN
cana-3475	26	17	graphs	graph	NOUN
cana-3475	26	18	.	.	PUNCT
cana-3475	27	1	the	the	DET
cana-3475	27	2	results	result	NOUN
cana-3475	27	3	presented	present	VERB
cana-3475	27	4	here	here	ADV
cana-3475	27	5	contribute	contribute	VERB
cana-3475	27	6	to	to	ADP
cana-3475	27	7	the	the	DET
cana-3475	27	8	theoretical	theoretical	ADJ
cana-3475	27	9	understanding	understanding	NOUN
cana-3475	27	10	of	of	ADP
cana-3475	27	11	fault	fault	NOUN
cana-3475	27	12	-	-	PUNCT
cana-3475	27	13	tolerant	tolerant	ADJ
cana-3475	27	14	graph	graph	NOUN
cana-3475	27	15	properties	property	NOUN
cana-3475	27	16	.	.	PUNCT
cana-3475	28	1	we	we	PRON
cana-3475	28	2	exclude	exclude	VERB
cana-3475	28	3	the	the	DET
cana-3475	28	4	definitions	definition	NOUN
cana-3475	28	5	of	of	ADP
cana-3475	28	6	conventional	conventional	ADJ
cana-3475	28	7	graph	graph	NOUN
cana-3475	28	8	-	-	PUNCT
cana-3475	28	9	theoretical	theoretical	ADJ
cana-3475	28	10	concepts	concept	NOUN
cana-3475	28	11	.	.	PUNCT
cana-3475	29	1	these	these	PRON
cana-3475	29	2	can	can	AUX
cana-3475	29	3	be	be	AUX
cana-3475	29	4	read	read	VERB
cana-3475	29	5	in	in	ADP
cana-3475	29	6	[	[	X
cana-3475	29	7	1	1	NUM
cana-3475	29	8	]	]	PUNCT
cana-3475	29	9	and	and	CCONJ
cana-3475	29	10	other	other	ADJ
cana-3475	29	11	textbooks	textbook	NOUN
cana-3475	29	12	.	.	PUNCT
cana-3475	30	1	the	the	DET
cana-3475	30	2	metric	metric	ADJ
cana-3475	30	3	dimension	dimension	NOUN
cana-3475	30	4	of	of	ADP
cana-3475	30	5	a	a	DET
cana-3475	30	6	graph	graph	NOUN
cana-3475	30	7	g	g	NOUN
cana-3475	30	8	=	=	SYM
cana-3475	30	9	(	(	PUNCT
cana-3475	30	10	v	v	NOUN
cana-3475	30	11	,	,	PUNCT
cana-3475	30	12	e	e	NOUN
cana-3475	30	13	)	)	PUNCT
cana-3475	30	14	is	be	AUX
cana-3475	30	15	the	the	DET
cana-3475	30	16	minimum	minimum	ADJ
cana-3475	30	17	number	number	NOUN
cana-3475	30	18	of	of	ADP
cana-3475	30	19	vertices	vertex	NOUN
cana-3475	30	20	in	in	ADP
cana-3475	30	21	a	a	DET
cana-3475	30	22	subset	subset	NOUN
cana-3475	30	23	r	r	NOUN
cana-3475	30	24			PROPN
cana-3475	30	25	v	v	ADP
cana-3475	30	26	such	such	ADJ
cana-3475	30	27	that	that	SCONJ
cana-3475	30	28	every	every	DET
cana-3475	30	29	pair	pair	NOUN
cana-3475	30	30	of	of	ADP
cana-3475	30	31	distinct	distinct	ADJ
cana-3475	30	32	vertices	vertex	NOUN
cana-3475	30	33	in	in	ADP
cana-3475	30	34	g	g	PROPN
cana-3475	30	35	is	be	AUX
cana-3475	30	36	uniquely	uniquely	ADV
cana-3475	30	37	identified	identify	VERB
cana-3475	30	38	by	by	ADP
cana-3475	30	39	their	their	PRON
cana-3475	30	40	distances	distance	NOUN
cana-3475	30	41	to	to	ADP
cana-3475	30	42	the	the	DET
cana-3475	30	43	vertices	vertex	NOUN
cana-3475	30	44	in	in	ADP
cana-3475	30	45	r.	r.	PROPN
cana-3475	30	46	a	a	DET
cana-3475	30	47	set	set	NOUN
cana-3475	30	48	r	r	NOUN
cana-3475	30	49	with	with	ADP
cana-3475	30	50	this	this	DET
cana-3475	30	51	property	property	NOUN
cana-3475	30	52	is	be	AUX
cana-3475	30	53	called	call	VERB
cana-3475	30	54	a	a	DET
cana-3475	30	55	resolving	resolving	NOUN
cana-3475	30	56	set	set	NOUN
cana-3475	30	57	,	,	PUNCT
cana-3475	30	58	as	as	SCONJ
cana-3475	30	59	it	it	PRON
cana-3475	30	60	enables	enable	VERB
cana-3475	30	61	a	a	DET
cana-3475	30	62	unique	unique	ADJ
cana-3475	30	63	identification	identification	NOUN
cana-3475	30	64	of	of	ADP
cana-3475	30	65	vertices	vertex	NOUN
cana-3475	30	66	based	base	VERB
cana-3475	30	67	on	on	ADP
cana-3475	30	68	their	their	PRON
cana-3475	30	69	distance	distance	NOUN
cana-3475	30	70	vectors	vector	NOUN
cana-3475	30	71	relative	relative	ADJ
cana-3475	30	72	to	to	ADP
cana-3475	30	73	the	the	DET
cana-3475	30	74	elements	element	NOUN
cana-3475	30	75	of	of	ADP
cana-3475	30	76	r.	r.	PROPN
cana-3475	30	77	the	the	DET
cana-3475	30	78	concept	concept	NOUN
cana-3475	30	79	of	of	ADP
cana-3475	30	80	metric	metric	ADJ
cana-3475	30	81	dimension	dimension	NOUN
cana-3475	30	82	was	be	AUX
cana-3475	30	83	first	first	ADV
cana-3475	30	84	studied	study	VERB
cana-3475	30	85	by	by	ADP
cana-3475	30	86	slater	slater	NOUN
cana-3475	31	1	[	[	X
cana-3475	31	2	13	13	NUM
cana-3475	31	3	]	]	PUNCT
cana-3475	31	4	(	(	PUNCT
cana-3475	31	5	independently	independently	ADV
cana-3475	31	6	by	by	ADP
cana-3475	31	7	harary	harary	NOUN
cana-3475	31	8	and	and	CCONJ
cana-3475	31	9	melter	melter	NOUN
cana-3475	31	10	[	[	X
cana-3475	31	11	3	3	NUM
cana-3475	31	12	]	]	NUM
cana-3475	31	13	)	)	PUNCT
cana-3475	31	14	.	.	PUNCT
cana-3475	32	1	another	another	PRON
cana-3475	32	2	invariant	invariant	ADJ
cana-3475	32	3	,	,	PUNCT
cana-3475	32	4	more	more	ADV
cana-3475	32	5	restricted	restricted	ADJ
cana-3475	32	6	than	than	SCONJ
cana-3475	32	7	the	the	DET
cana-3475	32	8	metric	metric	ADJ
cana-3475	32	9	dimension	dimension	NOUN
cana-3475	32	10	was	be	AUX
cana-3475	32	11	presented	present	VERB
cana-3475	32	12	by	by	ADP
cana-3475	32	13	sebö	sebö	NOUN
cana-3475	32	14	and	and	CCONJ
cana-3475	32	15	tannier	tannier	NOUN
cana-3475	32	16	in	in	ADP
cana-3475	32	17	[	[	X
cana-3475	32	18	11	11	NUM
cana-3475	32	19	]	]	PUNCT
cana-3475	32	20	,	,	PUNCT
cana-3475	32	21	and	and	CCONJ
cana-3475	32	22	studied	study	VERB
cana-3475	32	23	further	far	ADV
cana-3475	32	24	in	in	ADP
cana-3475	32	25	several	several	ADJ
cana-3475	32	26	articles	article	NOUN
cana-3475	32	27	[	[	X
cana-3475	32	28	4	4	NUM
cana-3475	32	29	,	,	PUNCT
cana-3475	32	30	5	5	NUM
cana-3475	32	31	,	,	PUNCT
cana-3475	32	32	7	7	NUM
cana-3475	32	33	,	,	PUNCT
cana-3475	32	34	8	8	NUM
cana-3475	32	35	,	,	PUNCT
cana-3475	32	36	9	9	NUM
cana-3475	32	37	,	,	PUNCT
cana-3475	32	38	10	10	NUM
cana-3475	32	39	,	,	PUNCT
cana-3475	32	40	14	14	NUM
cana-3475	32	41	]	]	PUNCT
cana-3475	32	42	.	.	PUNCT
cana-3475	33	1	a	a	DET
cana-3475	33	2	vertex	vertex	NOUN
cana-3475	33	3	s	s	PART
cana-3475	33	4			NOUN
cana-3475	33	5	s	s	VERB
cana-3475	33	6	is	be	AUX
cana-3475	33	7	said	say	VERB
cana-3475	33	8	to	to	PART
cana-3475	33	9	strongly	strongly	ADV
cana-3475	33	10	resolve	resolve	VERB
cana-3475	33	11	x	x	PUNCT
cana-3475	33	12	and	and	CCONJ
cana-3475	33	13	y	y	PROPN
cana-3475	33	14	if	if	SCONJ
cana-3475	33	15	d(x	d(x	PROPN
cana-3475	33	16	,	,	PUNCT
cana-3475	33	17	s	s	NOUN
cana-3475	33	18	)	)	PUNCT
cana-3475	33	19	=	=	SYM
cana-3475	33	20	d(x	d(x	PROPN
cana-3475	33	21	,	,	PUNCT
cana-3475	33	22	y	y	NOUN
cana-3475	33	23	)	)	PUNCT
cana-3475	34	1	+	+	CCONJ
cana-3475	34	2	d(y	d(y	PROPN
cana-3475	34	3	,	,	PUNCT
cana-3475	34	4	s	s	NOUN
cana-3475	34	5	)	)	PUNCT
cana-3475	34	6	or	or	CCONJ
cana-3475	34	7	d(y	d(y	PROPN
cana-3475	34	8	,	,	PUNCT
cana-3475	34	9	s	s	NOUN
cana-3475	34	10	)	)	PUNCT
cana-3475	34	11	=	=	SYM
cana-3475	34	12	d(y	d(y	NOUN
cana-3475	34	13	,	,	PUNCT
cana-3475	34	14	x	x	NOUN
cana-3475	34	15	)	)	PUNCT
cana-3475	35	1	+	+	CCONJ
cana-3475	35	2	d(x	d(x	PROPN
cana-3475	35	3	,	,	PUNCT
cana-3475	35	4	s	s	PART
cana-3475	35	5	)	)	PUNCT
cana-3475	35	6	,	,	PUNCT
cana-3475	35	7	where	where	SCONJ
cana-3475	35	8	d(x	d(x	PROPN
cana-3475	35	9	,	,	PUNCT
cana-3475	35	10	y	y	NOUN
cana-3475	35	11	)	)	PUNCT
cana-3475	35	12	denotes	denote	VERB
cana-3475	35	13	a	a	DET
cana-3475	35	14	shortest	short	ADJ
cana-3475	35	15	path	path	NOUN
cana-3475	35	16	distance	distance	NOUN
cana-3475	35	17	between	between	ADP
cana-3475	35	18	vertices	vertex	NOUN
cana-3475	35	19	x	x	PUNCT
cana-3475	35	20	and	and	CCONJ
cana-3475	35	21	y	y	PROPN
cana-3475	35	22	in	in	ADP
cana-3475	35	23	g.	g.	PROPN
cana-3475	35	24	the	the	DET
cana-3475	35	25	strong	strong	ADJ
cana-3475	35	26	metric	metric	ADJ
cana-3475	35	27	dimension	dimension	NOUN
cana-3475	35	28	of	of	ADP
cana-3475	35	29	a	a	DET
cana-3475	35	30	graph	graph	NOUN
cana-3475	35	31	g	g	NOUN
cana-3475	35	32	=	=	SYM
cana-3475	35	33	(	(	PUNCT
cana-3475	35	34	v	v	NOUN
cana-3475	35	35	,	,	PUNCT
cana-3475	35	36	e	e	NOUN
cana-3475	35	37	)	)	PUNCT
cana-3475	35	38	is	be	AUX
cana-3475	35	39	the	the	DET
cana-3475	35	40	minimum	minimum	ADJ
cana-3475	35	41	cardinality	cardinality	NOUN
cana-3475	35	42	of	of	ADP
cana-3475	35	43	a	a	DET
cana-3475	35	44	subset	subset	NOUN
cana-3475	35	45	s	s	X
cana-3475	35	46			PROPN
cana-3475	35	47	v	v	ADP
cana-3475	35	48	such	such	ADJ
cana-3475	35	49	that	that	PRON
cana-3475	35	50	for	for	SCONJ
cana-3475	35	51	every	every	DET
cana-3475	35	52	pair	pair	NOUN
cana-3475	35	53	of	of	ADP
cana-3475	35	54	distinct	distinct	ADJ
cana-3475	35	55	vertices	vertex	NOUN
cana-3475	35	56	x	x	X
cana-3475	35	57	,	,	PUNCT
cana-3475	35	58	y	y	PROPN
cana-3475	35	59			PROPN
cana-3475	35	60	v	v	ADP
cana-3475	35	61	,	,	PUNCT
cana-3475	35	62	there	there	PRON
cana-3475	35	63	exists	exist	VERB
cana-3475	35	64	a	a	DET
cana-3475	35	65	vertex	vertex	NOUN
cana-3475	35	66	s	s	PART
cana-3475	35	67			NOUN
cana-3475	35	68	s	s	VERB
cana-3475	35	69	that	that	SCONJ
cana-3475	35	70	strongly	strongly	ADV
cana-3475	35	71	resolves	resolve	VERB
cana-3475	35	72	x	x	PUNCT
cana-3475	35	73	and	and	CCONJ
cana-3475	35	74	y.	y.	NOUN
cana-3475	35	75	a	a	DET
cana-3475	35	76	fault	fault	NOUN
cana-3475	35	77	-	-	PUNCT
cana-3475	35	78	tolerant	tolerant	ADJ
cana-3475	35	79	strong	strong	ADJ
cana-3475	35	80	resolving	resolving	NOUN
cana-3475	35	81	set	set	NOUN
cana-3475	35	82	s	s	PRON
cana-3475	35	83	for	for	ADP
cana-3475	35	84	a	a	DET
cana-3475	35	85	graph	graph	NOUN
cana-3475	35	86	g	g	NOUN
cana-3475	35	87	is	be	AUX
cana-3475	35	88	a	a	DET
cana-3475	35	89	set	set	NOUN
cana-3475	35	90	such	such	ADJ
cana-3475	35	91	that	that	PRON
cana-3475	35	92	for	for	ADP
cana-3475	35	93	every	every	DET
cana-3475	35	94	vertex	vertex	NOUN
cana-3475	35	95	s	s	PART
cana-3475	35	96			NOUN
cana-3475	35	97	s	s	PART
cana-3475	35	98	,	,	PUNCT
cana-3475	35	99	the	the	DET
cana-3475	35	100	set	set	NOUN
cana-3475	35	101	s	s	PART
cana-3475	35	102	\	\	X
cana-3475	35	103	{	{	PUNCT
cana-3475	35	104	s	s	NOUN
cana-3475	35	105	}	}	PUNCT
cana-3475	35	106	remains	remain	VERB
cana-3475	35	107	a	a	DET
cana-3475	35	108	strong	strong	ADJ
cana-3475	35	109	resolving	resolving	NOUN
cana-3475	35	110	set	set	VERB
cana-3475	35	111	for	for	ADP
cana-3475	35	112	g.	g.	NOUN
cana-3475	35	113	the	the	DET
cana-3475	35	114	fault	fault	NOUN
cana-3475	35	115	-	-	PUNCT
cana-3475	35	116	tolerant	tolerant	ADJ
cana-3475	35	117	strong	strong	ADJ
cana-3475	35	118	metric	metric	ADJ
cana-3475	35	119	dimension	dimension	NOUN
cana-3475	35	120	of	of	ADP
cana-3475	35	121	g	g	NOUN
cana-3475	35	122	,	,	PUNCT
cana-3475	35	123	denoted	denote	VERB
cana-3475	35	124	dimfs(g	dimfs(g	PROPN
cana-3475	35	125	)	)	PUNCT
cana-3475	35	126	,	,	PUNCT
cana-3475	35	127	is	be	AUX
cana-3475	35	128	the	the	DET
cana-3475	35	129	smallest	small	ADJ
cana-3475	35	130	cardinality	cardinality	NOUN
cana-3475	35	131	of	of	ADP
cana-3475	35	132	a	a	DET
cana-3475	35	133	fault	fault	NOUN
cana-3475	35	134	-	-	PUNCT
cana-3475	35	135	tolerant	tolerant	ADJ
cana-3475	35	136	strong	strong	ADJ
cana-3475	35	137	resolving	resolving	NOUN
cana-3475	35	138	set	set	VERB
cana-3475	35	139	for	for	ADP
cana-3475	35	140	g	g	NOUN
cana-3475	35	141	[	[	X
cana-3475	35	142	6	6	NUM
cana-3475	35	143	]	]	PUNCT
cana-3475	35	144	.	.	PUNCT
cana-3475	36	1	a	a	DET
cana-3475	36	2	vertex	vertex	NOUN
cana-3475	36	3	u	u	NOUN
cana-3475	36	4	of	of	ADP
cana-3475	36	5	g	g	PROPN
cana-3475	36	6	is	be	AUX
cana-3475	36	7	said	say	VERB
cana-3475	36	8	to	to	PART
cana-3475	36	9	be	be	AUX
cana-3475	36	10	maximally	maximally	ADV
cana-3475	36	11	distant	distant	ADJ
cana-3475	36	12	from	from	ADP
cana-3475	36	13	v	v	PRON
cana-3475	36	14	if	if	SCONJ
cana-3475	36	15	for	for	ADP
cana-3475	36	16	every	every	DET
cana-3475	36	17	w	w	PROPN
cana-3475	36	18			PROPN
cana-3475	36	19	n(u	n(u	PROPN
cana-3475	36	20	)	)	PUNCT
cana-3475	36	21	,	,	PUNCT
cana-3475	36	22	d(v	d(v	PROPN
cana-3475	36	23	,	,	PUNCT
cana-3475	36	24	w	w	NOUN
cana-3475	36	25	)	)	PUNCT
cana-3475	36	26			NOUN
cana-3475	36	27	d(v	d(v	PROPN
cana-3475	36	28	,	,	PUNCT
cana-3475	36	29	u	u	NOUN
cana-3475	36	30	)	)	PUNCT
cana-3475	36	31	.	.	PUNCT
cana-3475	37	1	if	if	SCONJ
cana-3475	37	2	u	u	NOUN
cana-3475	37	3	is	be	AUX
cana-3475	37	4	maximally	maximally	ADV
cana-3475	37	5	distant	distant	ADJ
cana-3475	37	6	from	from	ADP
cana-3475	37	7	v	v	NOUN
cana-3475	37	8	and	and	CCONJ
cana-3475	37	9	v	v	NOUN
cana-3475	37	10	is	be	AUX
cana-3475	37	11	maximally	maximally	ADV
cana-3475	37	12	distant	distant	ADJ
cana-3475	37	13	from	from	ADP
cana-3475	37	14	u	u	NOUN
cana-3475	37	15	,	,	PUNCT
cana-3475	37	16	then	then	ADV
cana-3475	37	17	u	u	NOUN
cana-3475	37	18	and	and	CCONJ
cana-3475	37	19	v	v	NOUN
cana-3475	37	20	are	be	AUX
cana-3475	37	21	said	say	VERB
cana-3475	37	22	to	to	PART
cana-3475	37	23	be	be	AUX
cana-3475	37	24	mutually	mutually	ADV
cana-3475	37	25	maximally	maximally	ADV
cana-3475	37	26	distant	distant	ADJ
cana-3475	37	27	.	.	PUNCT
cana-3475	38	1	the	the	DET
cana-3475	38	2	following	follow	VERB
cana-3475	38	3	lemma	lemma	PROPN
cana-3475	38	4	and	and	CCONJ
cana-3475	38	5	theorem	theorem	NOUN
cana-3475	38	6	mentioned	mention	VERB
cana-3475	38	7	in	in	ADP
cana-3475	38	8	[	[	X
cana-3475	38	9	6	6	NUM
cana-3475	38	10	]	]	PUNCT
cana-3475	38	11	is	be	AUX
cana-3475	38	12	useful	useful	ADJ
cana-3475	38	13	in	in	ADP
cana-3475	38	14	the	the	DET
cana-3475	38	15	sequel	sequel	NOUN
cana-3475	38	16	.	.	PUNCT
cana-3475	39	1	lemma	lemma	PROPN
cana-3475	39	2	1	1	NUM
cana-3475	39	3	:	:	PUNCT
cana-3475	39	4	[	[	X
cana-3475	39	5	6	6	NUM
cana-3475	39	6	]	]	PUNCT
cana-3475	39	7	let	let	VERB
cana-3475	39	8	g	g	PRON
cana-3475	39	9	be	be	AUX
cana-3475	39	10	a	a	DET
cana-3475	39	11	simple	simple	ADJ
cana-3475	39	12	connected	connected	ADJ
cana-3475	39	13	graph	graph	NOUN
cana-3475	39	14	and	and	CCONJ
cana-3475	39	15	let	let	VERB
cana-3475	39	16	s	s	PRON
cana-3475	39	17	be	be	AUX
cana-3475	39	18	a	a	DET
cana-3475	39	19	fault	fault	NOUN
cana-3475	39	20	-	-	PUNCT
cana-3475	39	21	tolerant	tolerant	ADJ
cana-3475	39	22	strong	strong	ADJ
cana-3475	39	23	resolving	resolving	NOUN
cana-3475	39	24	set	set	NOUN
cana-3475	39	25	of	of	ADP
cana-3475	39	26	g.	g.	PROPN
cana-3475	39	27	let	let	VERB
cana-3475	39	28	u	u	NOUN
cana-3475	39	29	,	,	PUNCT
cana-3475	39	30	v	v	ADP
cana-3475	39	31			PROPN
cana-3475	39	32	v	v	AUX
cana-3475	39	33	be	be	VERB
cana-3475	39	34	mutually	mutually	ADV
cana-3475	39	35	maximally	maximally	ADV
cana-3475	39	36	distant	distant	ADJ
cana-3475	39	37	in	in	ADP
cana-3475	39	38	g.	g.	PROPN
cana-3475	39	39	then	then	ADV
cana-3475	39	40	both	both	CCONJ
cana-3475	39	41	u	u	NOUN
cana-3475	39	42	and	and	CCONJ
cana-3475	39	43	v	v	ADP
cana-3475	39	44			PROPN
cana-3475	39	45	s.	s.	PROPN
cana-3475	39	46	theorem	theorem	VERB
cana-3475	39	47	1	1	NUM
cana-3475	39	48	:	:	PUNCT
cana-3475	39	49	[	[	X
cana-3475	39	50	6	6	NUM
cana-3475	39	51	]	]	PUNCT
cana-3475	39	52	a	a	DET
cana-3475	39	53	strong	strong	ADJ
cana-3475	39	54	resolving	resolving	NOUN
cana-3475	39	55	set	set	NOUN
cana-3475	39	56	s	s	PRON
cana-3475	39	57	of	of	ADP
cana-3475	39	58	a	a	DET
cana-3475	39	59	graph	graph	NOUN
cana-3475	39	60	g	g	NOUN
cana-3475	39	61	is	be	AUX
cana-3475	39	62	a	a	DET
cana-3475	39	63	fault	fault	NOUN
cana-3475	39	64	-	-	PUNCT
cana-3475	39	65	tolerant	tolerant	ADJ
cana-3475	39	66	strong	strong	ADJ
cana-3475	39	67	resolving	resolving	NOUN
cana-3475	39	68	set	set	VERB
cana-3475	39	69	if	if	SCONJ
cana-3475	39	70	and	and	CCONJ
cana-3475	39	71	only	only	ADV
cana-3475	39	72	if	if	SCONJ
cana-3475	39	73	every	every	DET
cana-3475	39	74	pair	pair	NOUN
cana-3475	39	75	of	of	ADP
cana-3475	39	76	vertices	vertex	NOUN
cana-3475	39	77	in	in	ADP
cana-3475	39	78	g	g	PROPN
cana-3475	39	79	is	be	AUX
cana-3475	39	80	strongly	strongly	ADV
cana-3475	39	81	resolved	resolve	VERB
cana-3475	39	82	by	by	ADP
cana-3475	39	83	at	at	ADV
cana-3475	39	84	least	least	ADV
cana-3475	39	85	two	two	NUM
cana-3475	39	86	vertices	vertex	NOUN
cana-3475	39	87	of	of	ADP
cana-3475	39	88	s.	s.	PROPN
cana-3475	39	89	2	2	NUM
cana-3475	39	90	.	.	PUNCT
cana-3475	39	91	main	main	ADJ
cana-3475	39	92	results	result	NOUN
cana-3475	39	93	a	a	DET
cana-3475	39	94	graph	graph	NOUN
cana-3475	39	95	in	in	ADP
cana-3475	39	96	which	which	PRON
cana-3475	39	97	one	one	NUM
cana-3475	39	98	vertex	vertex	NOUN
cana-3475	39	99	is	be	AUX
cana-3475	39	100	fixed	fix	VERB
cana-3475	39	101	as	as	ADP
cana-3475	39	102	a	a	DET
cana-3475	39	103	root	root	NOUN
cana-3475	39	104	vertex	vertex	NOUN
cana-3475	39	105	to	to	PART
cana-3475	39	106	distinguish	distinguish	VERB
cana-3475	39	107	it	it	PRON
cana-3475	39	108	from	from	ADP
cana-3475	39	109	other	other	ADJ
cana-3475	39	110	vertices	vertex	NOUN
cana-3475	39	111	is	be	AUX
cana-3475	39	112	called	call	VERB
cana-3475	39	113	a	a	DET
cana-3475	39	114	rooted	rooted	ADJ
cana-3475	39	115	graph	graph	NOUN
cana-3475	39	116	.	.	PUNCT
cana-3475	40	1	let	let	VERB
cana-3475	40	2	g	g	PRON
cana-3475	40	3	be	be	AUX
cana-3475	40	4	a	a	DET
cana-3475	40	5	graph	graph	NOUN
cana-3475	40	6	with	with	ADP
cana-3475	40	7	n	n	ADP
cana-3475	40	8	vertices	vertex	NOUN
cana-3475	40	9	and	and	CCONJ
cana-3475	40	10	h	h	NOUN
cana-3475	40	11	be	be	VERB
cana-3475	40	12	a	a	DET
cana-3475	40	13	sequence	sequence	NOUN
cana-3475	40	14	of	of	ADP
cana-3475	40	15	n	n	CCONJ
cana-3475	40	16	rooted	rooted	ADJ
cana-3475	40	17	graphs	graph	NOUN
cana-3475	40	18	h1	h1	PROPN
cana-3475	40	19	,	,	PUNCT
cana-3475	40	20	h2	h2	PROPN
cana-3475	40	21	…	…	PUNCT
cana-3475	40	22	hn	hn	PROPN
cana-3475	40	23	.	.	PUNCT
cana-3475	41	1	the	the	DET
cana-3475	41	2	rooted	rooted	ADJ
cana-3475	41	3	product	product	NOUN
cana-3475	41	4	graph	graph	NOUN
cana-3475	41	5	g(h	g(h	PROPN
cana-3475	41	6	)	)	PUNCT
cana-3475	41	7	is	be	AUX
cana-3475	41	8	obtained	obtain	VERB
cana-3475	41	9	from	from	ADP
cana-3475	41	10	the	the	DET
cana-3475	41	11	graphs	graph	NOUN
cana-3475	41	12	g	g	ADP
cana-3475	41	13	,	,	PUNCT
cana-3475	41	14	h1	h1	PROPN
cana-3475	41	15	,	,	PUNCT
cana-3475	41	16	h2	h2	PROPN
cana-3475	41	17	…	…	PUNCT
cana-3475	41	18	hn	hn	PROPN
cana-3475	41	19	by	by	ADP
cana-3475	41	20	identifying	identify	VERB
cana-3475	41	21	the	the	DET
cana-3475	41	22	root	root	NOUN
cana-3475	41	23	vertex	vertex	NOUN
cana-3475	41	24	of	of	ADP
cana-3475	41	25	hi	hi	INTJ
cana-3475	41	26	with	with	ADP
cana-3475	41	27	the	the	DET
cana-3475	41	28	ith	ith	PROPN
cana-3475	41	29	vertex	vertex	NOUN
cana-3475	41	30	of	of	ADP
cana-3475	41	31	g	g	PROPN
cana-3475	42	1	[	[	X
cana-3475	42	2	2	2	NUM
cana-3475	42	3	]	]	PUNCT
cana-3475	42	4	.	.	PUNCT
cana-3475	43	1	communications	communication	NOUN
cana-3475	43	2	on	on	ADP
cana-3475	43	3	applied	apply	VERB
cana-3475	43	4	nonlinear	nonlinear	ADJ
cana-3475	43	5	analysis	analysis	NOUN
cana-3475	43	6	issn	issn	NOUN
cana-3475	43	7	:	:	PUNCT
cana-3475	43	8	1074	1074	NUM
cana-3475	43	9	-	-	PUNCT
cana-3475	43	10	133x	133x	NUM
cana-3475	43	11	vol	vol	NOUN
cana-3475	43	12	32	32	NUM
cana-3475	43	13	no	no	NOUN
cana-3475	43	14	.	.	PUNCT
cana-3475	44	1	7s	7	NOUN
cana-3475	44	2	(	(	PUNCT
cana-3475	44	3	2025	2025	NUM
cana-3475	44	4	)	)	PUNCT
cana-3475	44	5	690	690	NUM
cana-3475	44	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3475	44	7	if	if	SCONJ
cana-3475	44	8	h	h	NOUN
cana-3475	44	9	consists	consist	VERB
cana-3475	44	10	of	of	ADP
cana-3475	44	11	n	n	CCONJ
cana-3475	44	12	isomorphic	isomorphic	ADJ
cana-3475	44	13	rooted	rooted	ADJ
cana-3475	44	14	graphs	graph	NOUN
cana-3475	44	15	h1	h1	VERB
cana-3475	44	16			PROPN
cana-3475	44	17	h2	h2	PROPN
cana-3475	44	18			PROPN
cana-3475	45	1	…	…	PUNCT
cana-3475	45	2			PROPN
cana-3475	45	3	hn	hn	PROPN
cana-3475	45	4	,	,	PUNCT
cana-3475	45	5	then	then	ADV
cana-3475	45	6	a	a	DET
cana-3475	45	7	particular	particular	ADJ
cana-3475	45	8	kind	kind	NOUN
cana-3475	45	9	of	of	ADP
cana-3475	45	10	rooted	rooted	ADJ
cana-3475	45	11	product	product	NOUN
cana-3475	45	12	graph	graph	NOUN
cana-3475	45	13	is	be	AUX
cana-3475	45	14	generated	generate	VERB
cana-3475	45	15	from	from	ADP
cana-3475	45	16	g	g	PROPN
cana-3475	45	17	and	and	CCONJ
cana-3475	45	18	h	h	NOUN
cana-3475	45	19	,	,	PUNCT
cana-3475	45	20	where	where	SCONJ
cana-3475	46	1	h	h	NOUN
cana-3475	46	2			PROPN
cana-3475	46	3	hi	hi	INTJ
cana-3475	46	4	for	for	ADP
cana-3475	46	5	all	all	PRON
cana-3475	46	6	i	i	PRON
cana-3475	46	7			NOUN
cana-3475	46	8	n.	n.	VERB
cana-3475	46	9	such	such	DET
cana-3475	46	10	a	a	DET
cana-3475	46	11	graph	graph	NOUN
cana-3475	46	12	is	be	AUX
cana-3475	46	13	denoted	denote	VERB
cana-3475	46	14	by	by	ADP
cana-3475	46	15	𝐺𝜊𝑣𝐻	𝐺𝜊𝑣𝐻	PROPN
cana-3475	46	16	,	,	PUNCT
cana-3475	46	17	where	where	SCONJ
cana-3475	46	18	v	v	NOUN
cana-3475	46	19	is	be	AUX
cana-3475	46	20	the	the	DET
cana-3475	46	21	root	root	NOUN
cana-3475	46	22	vertex	vertex	NOUN
cana-3475	46	23	of	of	ADP
cana-3475	46	24	h	h	NOUN
cana-3475	47	1	[	[	X
cana-3475	47	2	12	12	NUM
cana-3475	47	3	]	]	PUNCT
cana-3475	47	4	.	.	PUNCT
cana-3475	48	1	for	for	ADP
cana-3475	48	2	v(g	v(g	NUM
cana-3475	48	3	)	)	PUNCT
cana-3475	48	4	=	=	SYM
cana-3475	48	5	{	{	PUNCT
cana-3475	48	6	u1	u1	NOUN
cana-3475	48	7	,	,	PUNCT
cana-3475	48	8	u2	u2	PROPN
cana-3475	48	9	…	…	PUNCT
cana-3475	48	10	un	un	ADJ
cana-3475	48	11	}	}	PUNCT
cana-3475	48	12	,	,	PUNCT
cana-3475	48	13	the	the	DET
cana-3475	48	14	vertex	vertex	NOUN
cana-3475	48	15	set	set	VERB
cana-3475	48	16	v	v	NOUN
cana-3475	48	17	and	and	CCONJ
cana-3475	48	18	edge	edge	VERB
cana-3475	48	19	set	set	ADJ
cana-3475	48	20	e	e	NOUN
cana-3475	48	21	of	of	ADP
cana-3475	48	22	the	the	DET
cana-3475	48	23	rooted	rooted	ADJ
cana-3475	48	24	product	product	NOUN
cana-3475	48	25	graph	graph	NOUN
cana-3475	48	26	𝐺𝜊𝑣𝐻	𝐺𝜊𝑣𝐻	NOUN
cana-3475	48	27	is	be	AUX
cana-3475	48	28	defined	define	VERB
cana-3475	48	29	as	as	ADP
cana-3475	48	30	v	v	NOUN
cana-3475	48	31	=	=	SYM
cana-3475	48	32	v(g	v(g	ADJ
cana-3475	48	33	)	)	PUNCT
cana-3475	48	34			NOUN
cana-3475	48	35	v(h	v(h	NOUN
cana-3475	48	36	)	)	PUNCT
cana-3475	48	37	and	and	CCONJ
cana-3475	48	38	𝐸	𝐸	PROPN
cana-3475	48	39	=	=	SYM
cana-3475	48	40	⋃	⋃	NOUN
cana-3475	48	41	{	{	PUNCT
cana-3475	48	42	(	(	PUNCT
cana-3475	48	43	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	48	44	,	,	PUNCT
cana-3475	48	45	𝑏)(𝑢𝑖	𝑏)(𝑢𝑖	X
cana-3475	48	46	,	,	PUNCT
cana-3475	48	47	𝑦	𝑦	X
cana-3475	48	48	)	)	PUNCT
cana-3475	48	49	∶	∶	NOUN
cana-3475	48	50	𝑏𝑦	𝑏𝑦	NOUN
cana-3475	48	51	∈	∈	PROPN
cana-3475	48	52	𝐸(𝐻	𝐸(𝐻	PROPN
cana-3475	48	53	)	)	PUNCT
cana-3475	48	54	}	}	PUNCT
cana-3475	48	55	∪	∪	VERB
cana-3475	48	56	{	{	PUNCT
cana-3475	48	57	(	(	PUNCT
cana-3475	48	58	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	48	59	,	,	PUNCT
cana-3475	48	60	𝑣)(𝑢𝑗	𝑣)(𝑢𝑗	NOUN
cana-3475	48	61	,	,	PUNCT
cana-3475	48	62	𝑣	𝑣	NOUN
cana-3475	48	63	)	)	PUNCT
cana-3475	48	64	∶	∶	NOUN
cana-3475	48	65	𝑢𝑖𝑢𝑗	𝑢𝑖𝑢𝑗	NOUN
cana-3475	48	66	∈	∈	PROPN
cana-3475	48	67	𝐸(𝐺)}𝑛	𝐸(𝐺)}𝑛	NOUN
cana-3475	48	68	𝑖=1	𝑖=1	PROPN
cana-3475	48	69	.	.	PUNCT
cana-3475	49	1	we	we	PRON
cana-3475	49	2	start	start	VERB
cana-3475	49	3	by	by	ADP
cana-3475	49	4	stating	state	VERB
cana-3475	49	5	the	the	DET
cana-3475	49	6	following	follow	VERB
cana-3475	49	7	easily	easily	ADV
cana-3475	49	8	verified	verify	VERB
cana-3475	49	9	theorem	theorem	VERB
cana-3475	49	10	.	.	PUNCT
cana-3475	49	11	theorem	theorem	NOUN
cana-3475	49	12	2	2	NUM
cana-3475	49	13	:	:	PUNCT
cana-3475	49	14	let	let	VERB
cana-3475	49	15	g	g	NOUN
cana-3475	49	16	and	and	CCONJ
cana-3475	49	17	h	h	NOUN
cana-3475	49	18	be	be	VERB
cana-3475	49	19	two	two	NUM
cana-3475	49	20	graphs	graph	NOUN
cana-3475	49	21	of	of	ADP
cana-3475	49	22	order	order	NOUN
cana-3475	49	23	n1	n1	NOUN
cana-3475	49	24	and	and	CCONJ
cana-3475	49	25	n2	n2	ADJ
cana-3475	49	26	respectively	respectively	ADV
cana-3475	49	27	.	.	PUNCT
cana-3475	50	1	then	then	ADV
cana-3475	50	2	no	no	DET
cana-3475	50	3	two	two	NUM
cana-3475	50	4	vertices	vertex	NOUN
cana-3475	50	5	of	of	ADP
cana-3475	50	6	g	g	NOUN
cana-3475	50	7	are	be	AUX
cana-3475	50	8	mutually	mutually	ADV
cana-3475	50	9	maximally	maximally	ADV
cana-3475	50	10	distant	distant	ADJ
cana-3475	50	11	in	in	ADP
cana-3475	50	12	𝐺𝜊𝑣𝐻.	𝐺𝜊𝑣𝐻.	ADJ
cana-3475	50	13	proof	proof	NOUN
cana-3475	50	14	.	.	PUNCT
cana-3475	51	1	assume	assume	VERB
cana-3475	51	2	the	the	DET
cana-3475	51	3	contrary	contrary	NOUN
cana-3475	51	4	.	.	PUNCT
cana-3475	52	1	suppose	suppose	VERB
cana-3475	52	2	that	that	SCONJ
cana-3475	52	3	there	there	PRON
cana-3475	52	4	exist	exist	VERB
cana-3475	52	5	two	two	NUM
cana-3475	52	6	vertices	vertex	NOUN
cana-3475	52	7	(	(	PUNCT
cana-3475	52	8	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	52	9	,	,	PUNCT
cana-3475	52	10	𝑣	𝑣	NOUN
cana-3475	52	11	)	)	PUNCT
cana-3475	52	12	,	,	PUNCT
cana-3475	52	13	(	(	PUNCT
cana-3475	52	14	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	52	15	,	,	PUNCT
cana-3475	52	16	𝑣	𝑣	NOUN
cana-3475	52	17	)	)	PUNCT
cana-3475	52	18	,	,	PUNCT
cana-3475	52	19	𝑖	𝑖	PROPN
cana-3475	52	20	≠	≠	PROPN
cana-3475	52	21	𝑗	𝑗	PROPN
cana-3475	52	22	,	,	PUNCT
cana-3475	52	23	1	1	NUM
cana-3475	52	24	≤	≤	NUM
cana-3475	52	25	𝑖	𝑖	PUNCT
cana-3475	52	26	,	,	PUNCT
cana-3475	52	27	𝑗	𝑗	PROPN
cana-3475	52	28	≤	≤	PUNCT
cana-3475	52	29	𝑛1	𝑛1	NOUN
cana-3475	52	30	which	which	PRON
cana-3475	52	31	are	be	AUX
cana-3475	52	32	mutually	mutually	ADV
cana-3475	52	33	maximally	maximally	ADV
cana-3475	52	34	distant	distant	ADJ
cana-3475	52	35	in	in	ADP
cana-3475	52	36	𝐺𝜊𝑣𝐻.	𝐺𝜊𝑣𝐻.	ADJ
cana-3475	52	37	then	then	ADV
cana-3475	52	38	for	for	ADP
cana-3475	52	39	every	every	DET
cana-3475	52	40	(	(	PUNCT
cana-3475	52	41	𝑢𝑘	𝑢𝑘	PROPN
cana-3475	52	42	,	,	PUNCT
cana-3475	52	43	𝑣	𝑣	NOUN
cana-3475	52	44	)	)	PUNCT
cana-3475	52	45	∈	∈	NOUN
cana-3475	52	46	𝑁	𝑁	PROPN
cana-3475	52	47	(	(	PUNCT
cana-3475	52	48	(	(	PUNCT
cana-3475	52	49	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	52	50	,	,	PUNCT
cana-3475	52	51	𝑣	𝑣	NOUN
cana-3475	52	52	)	)	PUNCT
cana-3475	52	53	)	)	PUNCT
cana-3475	52	54	,	,	PUNCT
cana-3475	52	55	𝑑((𝑢𝑖	𝑑((𝑢𝑖	NOUN
cana-3475	52	56	,	,	PUNCT
cana-3475	52	57	𝑣	𝑣	NOUN
cana-3475	52	58	)	)	PUNCT
cana-3475	52	59	,	,	PUNCT
cana-3475	52	60	(	(	PUNCT
cana-3475	52	61	𝑢𝑘	𝑢𝑘	X
cana-3475	52	62	,	,	PUNCT
cana-3475	52	63	𝑣	𝑣	NOUN
cana-3475	52	64	)	)	PUNCT
cana-3475	52	65	)	)	PUNCT
cana-3475	52	66	≤	≤	NUM
cana-3475	52	67	𝑑	𝑑	X
cana-3475	52	68	(	(	PUNCT
cana-3475	52	69	(	(	PUNCT
cana-3475	52	70	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	52	71	,	,	PUNCT
cana-3475	52	72	𝑣	𝑣	NOUN
cana-3475	52	73	)	)	PUNCT
cana-3475	52	74	,	,	PUNCT
cana-3475	52	75	(	(	PUNCT
cana-3475	52	76	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	52	77	,	,	PUNCT
cana-3475	52	78	𝑣	𝑣	NOUN
cana-3475	52	79	)	)	PUNCT
cana-3475	52	80	)	)	PUNCT
cana-3475	52	81	.	.	PUNCT
cana-3475	53	1	let	let	VERB
cana-3475	53	2	𝑑	𝑑	PRON
cana-3475	53	3	(	(	PUNCT
cana-3475	53	4	(	(	PUNCT
cana-3475	53	5	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	53	6	,	,	PUNCT
cana-3475	53	7	𝑣	𝑣	NOUN
cana-3475	53	8	)	)	PUNCT
cana-3475	53	9	,	,	PUNCT
cana-3475	53	10	(	(	PUNCT
cana-3475	53	11	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	53	12	,	,	PUNCT
cana-3475	53	13	𝑣	𝑣	NOUN
cana-3475	53	14	)	)	PUNCT
cana-3475	53	15	)	)	PUNCT
cana-3475	54	1	=	=	VERB
cana-3475	55	1	𝑙.	𝑙.	ADV
cana-3475	55	2	since	since	SCONJ
cana-3475	55	3	(	(	PUNCT
cana-3475	55	4	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	55	5	,	,	PUNCT
cana-3475	55	6	𝑣	𝑣	NOUN
cana-3475	55	7	)	)	PUNCT
cana-3475	55	8	,	,	PUNCT
cana-3475	55	9	(	(	PUNCT
cana-3475	55	10	𝑢𝑗	𝑢𝑗	X
cana-3475	55	11	,	,	PUNCT
cana-3475	55	12	𝑤	𝑤	NOUN
cana-3475	55	13	)	)	PUNCT
cana-3475	55	14	∈	∈	PROPN
cana-3475	55	15	𝐸(𝐺𝜊𝑣𝐻	𝐸(𝐺𝜊𝑣𝐻	PROPN
cana-3475	55	16	)	)	PUNCT
cana-3475	56	1	for	for	ADP
cana-3475	56	2	some	some	DET
cana-3475	56	3	𝑣𝑤	𝑣𝑤	ADP
cana-3475	56	4	∈	∈	NOUN
cana-3475	56	5	𝐸(𝐻𝑗	𝐸(𝐻𝑗	NOUN
cana-3475	56	6	)	)	PUNCT
cana-3475	56	7	in	in	ADP
cana-3475	56	8	𝐺𝜊𝑣𝐻	𝐺𝜊𝑣𝐻	PROPN
cana-3475	56	9	,	,	PUNCT
cana-3475	56	10	𝑑	𝑑	PRON
cana-3475	56	11	(	(	PUNCT
cana-3475	56	12	(	(	PUNCT
cana-3475	56	13	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	56	14	,	,	PUNCT
cana-3475	56	15	𝑣	𝑣	NOUN
cana-3475	56	16	)	)	PUNCT
cana-3475	56	17	,	,	PUNCT
cana-3475	56	18	(	(	PUNCT
cana-3475	56	19	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	56	20	,	,	PUNCT
cana-3475	56	21	𝑤	𝑤	NOUN
cana-3475	56	22	)	)	PUNCT
cana-3475	56	23	)	)	PUNCT
cana-3475	57	1	=	=	SYM
cana-3475	57	2	𝑑	𝑑	PROPN
cana-3475	57	3	(	(	PUNCT
cana-3475	57	4	(	(	PUNCT
cana-3475	57	5	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	57	6	,	,	PUNCT
cana-3475	57	7	𝑣	𝑣	NOUN
cana-3475	57	8	)	)	PUNCT
cana-3475	57	9	,	,	PUNCT
cana-3475	57	10	(	(	PUNCT
cana-3475	57	11	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	57	12	,	,	PUNCT
cana-3475	57	13	𝑣	𝑣	NOUN
cana-3475	57	14	)	)	PUNCT
cana-3475	57	15	)	)	PUNCT
cana-3475	58	1	+	+	CCONJ
cana-3475	58	2	1	1	NUM
cana-3475	58	3	=	=	SYM
cana-3475	58	4	𝑙	𝑙	NOUN
cana-3475	58	5	+	+	NUM
cana-3475	58	6	1	1	NUM
cana-3475	58	7	,	,	PUNCT
cana-3475	58	8	which	which	PRON
cana-3475	58	9	contradicts	contradict	VERB
cana-3475	58	10	the	the	DET
cana-3475	58	11	fact	fact	NOUN
cana-3475	58	12	that	that	SCONJ
cana-3475	58	13	𝑑((𝑢𝑖	𝑑((𝑢𝑖	NOUN
cana-3475	58	14	,	,	PUNCT
cana-3475	58	15	𝑣	𝑣	NOUN
cana-3475	58	16	)	)	PUNCT
cana-3475	58	17	,	,	PUNCT
cana-3475	58	18	(	(	PUNCT
cana-3475	58	19	𝑢𝑘	𝑢𝑘	X
cana-3475	58	20	,	,	PUNCT
cana-3475	58	21	𝑣	𝑣	NOUN
cana-3475	58	22	)	)	PUNCT
cana-3475	58	23	)	)	PUNCT
cana-3475	58	24	≤	≤	NUM
cana-3475	58	25	𝑑	𝑑	X
cana-3475	58	26	(	(	PUNCT
cana-3475	58	27	(	(	PUNCT
cana-3475	58	28	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	58	29	,	,	PUNCT
cana-3475	58	30	𝑣	𝑣	NOUN
cana-3475	58	31	)	)	PUNCT
cana-3475	58	32	,	,	PUNCT
cana-3475	58	33	(	(	PUNCT
cana-3475	58	34	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	58	35	,	,	PUNCT
cana-3475	58	36	𝑣	𝑣	NOUN
cana-3475	58	37	)	)	PUNCT
cana-3475	58	38	)	)	PUNCT
cana-3475	58	39	.	.	PUNCT
cana-3475	59	1	hence	hence	ADV
cana-3475	59	2	vertices	vertice	VERB
cana-3475	59	3	(	(	PUNCT
cana-3475	59	4	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	59	5	,	,	PUNCT
cana-3475	59	6	𝑣	𝑣	NOUN
cana-3475	59	7	)	)	PUNCT
cana-3475	59	8	and	and	CCONJ
cana-3475	59	9	(	(	PUNCT
cana-3475	59	10	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	59	11	,	,	PUNCT
cana-3475	59	12	𝑣	𝑣	NOUN
cana-3475	59	13	)	)	PUNCT
cana-3475	59	14	are	be	AUX
cana-3475	59	15	not	not	PART
cana-3475	59	16	mutually	mutually	ADV
cana-3475	59	17	maximally	maximally	ADV
cana-3475	59	18	distant	distant	ADJ
cana-3475	59	19	.	.	PUNCT
cana-3475	60	1	by	by	ADP
cana-3475	60	2	theorem	theorem	NOUN
cana-3475	60	3	2	2	NUM
cana-3475	60	4	,	,	PUNCT
cana-3475	60	5	the	the	DET
cana-3475	60	6	following	follow	VERB
cana-3475	60	7	results	result	NOUN
cana-3475	60	8	are	be	AUX
cana-3475	60	9	obvious	obvious	ADJ
cana-3475	60	10	.	.	PUNCT
cana-3475	61	1	lemma	lemma	PROPN
cana-3475	61	2	2	2	NUM
cana-3475	61	3	:	:	PUNCT
cana-3475	61	4	let	let	VERB
cana-3475	61	5	g	g	PRON
cana-3475	61	6	be	be	AUX
cana-3475	61	7	a	a	DET
cana-3475	61	8	connected	connected	ADJ
cana-3475	61	9	graph	graph	NOUN
cana-3475	61	10	of	of	ADP
cana-3475	61	11	order	order	NOUN
cana-3475	61	12	n	n	CCONJ
cana-3475	61	13			NUM
cana-3475	61	14	2	2	NUM
cana-3475	61	15	and	and	CCONJ
cana-3475	61	16	h	h	NOUN
cana-3475	61	17	be	be	VERB
cana-3475	61	18	a	a	DET
cana-3475	61	19	connected	connected	ADJ
cana-3475	61	20	graph	graph	NOUN
cana-3475	61	21	.	.	PUNCT
cana-3475	62	1	let	let	VERB
cana-3475	62	2	m	m	PRON
cana-3475	62	3	be	be	AUX
cana-3475	62	4	the	the	DET
cana-3475	62	5	set	set	NOUN
cana-3475	62	6	of	of	ADP
cana-3475	62	7	all	all	DET
cana-3475	62	8	mutually	mutually	ADV
cana-3475	62	9	maximally	maximally	ADV
cana-3475	62	10	distant	distant	ADJ
cana-3475	62	11	vertices	vertex	NOUN
cana-3475	62	12	in	in	ADP
cana-3475	62	13	h.	h.	PROPN
cana-3475	62	14	then	then	ADV
cana-3475	63	1	1	1	X
cana-3475	63	2	.	.	PUNCT
cana-3475	64	1	if	if	SCONJ
cana-3475	64	2	v	v	ADP
cana-3475	64	3			PROPN
cana-3475	64	4	m	m	NOUN
cana-3475	64	5	,	,	PUNCT
cana-3475	64	6	then	then	ADV
cana-3475	64	7	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣h	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣h	PROPN
cana-3475	64	8	)	)	PUNCT
cana-3475	65	1	=	=	PUNCT
cana-3475	65	2	𝑛|𝑀\{𝑣}|	𝑛|𝑀\{𝑣}|	NOUN
cana-3475	65	3	.	.	PUNCT
cana-3475	66	1	2	2	X
cana-3475	66	2	.	.	X
cana-3475	66	3	if	if	SCONJ
cana-3475	66	4	v	v	ADP
cana-3475	66	5			NOUN
cana-3475	66	6	m	m	NOUN
cana-3475	66	7	,	,	PUNCT
cana-3475	66	8	then	then	ADV
cana-3475	66	9	𝑑𝑖𝑚𝑓𝑠(𝐺𝜊𝑣h	𝑑𝑖𝑚𝑓𝑠(𝐺𝜊𝑣h	PROPN
cana-3475	66	10	)	)	PUNCT
cana-3475	67	1	=	=	SYM
cana-3475	67	2	𝑛|𝑀|	𝑛|𝑀|	PROPN
cana-3475	67	3	.	.	PUNCT
cana-3475	67	4	figure	figure	NOUN
cana-3475	67	5	1	1	NUM
cana-3475	67	6	(	(	PUNCT
cana-3475	67	7	a	a	NOUN
cana-3475	67	8	)	)	PUNCT
cana-3475	67	9	graph	graph	NOUN
cana-3475	67	10	g	g	PROPN
cana-3475	67	11	(	(	PUNCT
cana-3475	67	12	b	b	NOUN
cana-3475	67	13	)	)	PUNCT
cana-3475	67	14	p3	p3	NOUN
cana-3475	67	15	(	(	PUNCT
cana-3475	67	16	c	c	NOUN
cana-3475	67	17	)	)	PUNCT
cana-3475	67	18	g𝜊𝑣𝑃3	g𝜊𝑣𝑃3	VERB
cana-3475	67	19	where	where	SCONJ
cana-3475	67	20	𝑣	𝑣	PRON
cana-3475	67	21	has	have	VERB
cana-3475	67	22	degree	degree	NOUN
cana-3475	67	23	1	1	NUM
cana-3475	67	24	.	.	PUNCT
cana-3475	67	25	consider	consider	VERB
cana-3475	67	26	the	the	DET
cana-3475	67	27	rooted	rooted	ADJ
cana-3475	67	28	product	product	NOUN
cana-3475	67	29	graph	graph	NOUN
cana-3475	67	30	𝐺𝜊𝑣𝑃𝑚	𝐺𝜊𝑣𝑃𝑚	PROPN
cana-3475	67	31	,	,	PUNCT
cana-3475	67	32	where	where	SCONJ
cana-3475	67	33	m	m	PROPN
cana-3475	67	34			NUM
cana-3475	67	35	2	2	NUM
cana-3475	67	36	.	.	PUNCT
cana-3475	68	1	the	the	DET
cana-3475	68	2	degree	degree	NOUN
cana-3475	68	3	of	of	ADP
cana-3475	68	4	root	root	NOUN
cana-3475	68	5	vertex	vertex	NOUN
cana-3475	68	6	v	v	NOUN
cana-3475	68	7	of	of	ADP
cana-3475	68	8	pm	pm	NOUN
cana-3475	68	9	,	,	PUNCT
cana-3475	68	10	can	can	AUX
cana-3475	68	11	be	be	AUX
cana-3475	68	12	either	either	PRON
cana-3475	68	13	1	1	NUM
cana-3475	68	14	or	or	CCONJ
cana-3475	68	15	2	2	NUM
cana-3475	68	16	.	.	PUNCT
cana-3475	69	1	depending	depend	VERB
cana-3475	69	2	on	on	ADP
cana-3475	69	3	the	the	DET
cana-3475	69	4	degree	degree	NOUN
cana-3475	69	5	of	of	ADP
cana-3475	69	6	root	root	NOUN
cana-3475	69	7	vertex	vertex	NOUN
cana-3475	69	8	in	in	ADP
cana-3475	69	9	pm	pm	NOUN
cana-3475	69	10	,	,	PUNCT
cana-3475	69	11	the	the	DET
cana-3475	69	12	different	different	ADJ
cana-3475	69	13	classes	class	NOUN
cana-3475	69	14	of	of	ADP
cana-3475	69	15	graphs	graph	NOUN
cana-3475	69	16	can	can	AUX
cana-3475	69	17	be	be	AUX
cana-3475	69	18	generated	generate	VERB
cana-3475	69	19	.	.	PUNCT
cana-3475	70	1	if	if	SCONJ
cana-3475	70	2	the	the	DET
cana-3475	70	3	degree	degree	NOUN
cana-3475	70	4	of	of	ADP
cana-3475	70	5	the	the	DET
cana-3475	70	6	root	root	NOUN
cana-3475	70	7	vertex	vertex	NOUN
cana-3475	70	8	v	v	NOUN
cana-3475	70	9	is	be	AUX
cana-3475	70	10	1	1	NUM
cana-3475	70	11	,	,	PUNCT
cana-3475	70	12	then	then	ADV
cana-3475	70	13	the	the	DET
cana-3475	70	14	vertices	vertex	NOUN
cana-3475	70	15	of	of	ADP
cana-3475	70	16	ith	ith	PROPN
cana-3475	70	17	copy	copy	NOUN
cana-3475	70	18	of	of	ADP
cana-3475	70	19	pm	pm	NOUN
cana-3475	70	20	are	be	AUX
cana-3475	70	21	labelled	label	VERB
cana-3475	70	22	as	as	ADP
cana-3475	70	23	(	(	PUNCT
cana-3475	70	24	ui	ui	PROPN
cana-3475	70	25	,	,	PUNCT
cana-3475	70	26	j	j	PROPN
cana-3475	70	27	)	)	PUNCT
cana-3475	70	28	,	,	PUNCT
cana-3475	70	29	1	1	NUM
cana-3475	70	30			NUM
cana-3475	70	31	j	j	PROPN
cana-3475	70	32			NUM
cana-3475	70	33	m	m	VERB
cana-3475	70	34	–	–	PUNCT
cana-3475	70	35	1	1	NUM
cana-3475	70	36	in	in	ADP
cana-3475	70	37	𝐺𝜊𝑣𝑃𝑚	𝐺𝜊𝑣𝑃𝑚	PROPN
cana-3475	70	38	,	,	PUNCT
cana-3475	70	39	except	except	SCONJ
cana-3475	70	40	(	(	PUNCT
cana-3475	70	41	ui	ui	PROPN
cana-3475	70	42	,	,	PUNCT
cana-3475	70	43	v	v	NOUN
cana-3475	70	44	)	)	PUNCT
cana-3475	70	45	.	.	PUNCT
cana-3475	71	1	see	see	VERB
cana-3475	71	2	figure	figure	NOUN
cana-3475	71	3	1	1	NUM
cana-3475	71	4	.	.	PUNCT
cana-3475	72	1	if	if	SCONJ
cana-3475	72	2	the	the	DET
cana-3475	72	3	degree	degree	NOUN
cana-3475	72	4	of	of	ADP
cana-3475	72	5	the	the	DET
cana-3475	72	6	root	root	NOUN
cana-3475	72	7	vertex	vertex	NOUN
cana-3475	72	8	v	v	NOUN
cana-3475	72	9	is	be	AUX
cana-3475	72	10	2	2	NUM
cana-3475	72	11	,	,	PUNCT
cana-3475	72	12	then	then	ADV
cana-3475	72	13	the	the	DET
cana-3475	72	14	ith	ith	PROPN
cana-3475	72	15	copy	copy	NOUN
cana-3475	72	16	of	of	ADP
cana-3475	72	17	pm	pm	NOUN
cana-3475	72	18	will	will	AUX
cana-3475	72	19	have	have	VERB
cana-3475	72	20	two	two	NUM
cana-3475	72	21	distinct	distinct	ADJ
cana-3475	72	22	paths	path	NOUN
cana-3475	72	23	(	(	PUNCT
cana-3475	72	24	ui	ui	NOUN
cana-3475	72	25	,	,	PUNCT
cana-3475	72	26	1	1	NUM
cana-3475	72	27	)	)	PUNCT
cana-3475	72	28	,	,	PUNCT
cana-3475	72	29	(	(	PUNCT
cana-3475	72	30	ui	ui	NOUN
cana-3475	72	31	,	,	PUNCT
cana-3475	72	32	2	2	NUM
cana-3475	72	33	)	)	PUNCT
cana-3475	72	34	…	…	PUNCT
cana-3475	72	35	(	(	PUNCT
cana-3475	72	36	ui	ui	NOUN
cana-3475	72	37	,	,	PUNCT
cana-3475	72	38	a	a	PRON
cana-3475	72	39	)	)	PUNCT
cana-3475	72	40			NOUN
cana-3475	72	41	pa	pa	PROPN
cana-3475	72	42	and	and	CCONJ
cana-3475	72	43	(	(	PUNCT
cana-3475	72	44	wi	wi	PROPN
cana-3475	72	45	,	,	PUNCT
cana-3475	72	46	1	1	NUM
cana-3475	72	47	)	)	PUNCT
cana-3475	72	48	,	,	PUNCT
cana-3475	72	49	(	(	PUNCT
cana-3475	72	50	wi	wi	PROPN
cana-3475	72	51	,	,	PUNCT
cana-3475	72	52	2	2	NUM
cana-3475	72	53	)	)	PUNCT
cana-3475	72	54	…	…	PUNCT
cana-3475	72	55	(	(	PUNCT
cana-3475	72	56	wi	wi	PROPN
cana-3475	72	57	,	,	PUNCT
cana-3475	72	58	b	b	NOUN
cana-3475	72	59	)	)	PUNCT
cana-3475	72	60			NOUN
cana-3475	72	61	pb	pb	ADP
cana-3475	72	62	in	in	ADP
cana-3475	72	63	𝐺𝜊𝑣𝑃𝑚	𝐺𝜊𝑣𝑃𝑚	PROPN
cana-3475	72	64	such	such	ADJ
cana-3475	72	65	that	that	SCONJ
cana-3475	72	66	a	a	DET
cana-3475	72	67	+	+	NOUN
cana-3475	72	68	b	b	NOUN
cana-3475	72	69	+	+	CCONJ
cana-3475	72	70	1	1	NUM
cana-3475	72	71	=	=	NOUN
cana-3475	72	72	m.	m.	NOUN
cana-3475	72	73	see	see	VERB
cana-3475	72	74	figure	figure	NOUN
cana-3475	72	75	2	2	NUM
cana-3475	72	76	.	.	PUNCT
cana-3475	72	77	u1	u1	PROPN
cana-3475	72	78	u2	u2	PROPN
cana-3475	72	79	u3u4	u3u4	NOUN
cana-3475	72	80	v	v	PROPN
cana-3475	72	81	1	1	NUM
cana-3475	72	82	2	2	NUM
cana-3475	72	83	(	(	PUNCT
cana-3475	72	84	u1	u1	NOUN
cana-3475	72	85	,	,	PUNCT
cana-3475	72	86	v	v	NOUN
cana-3475	72	87	)	)	PUNCT
cana-3475	72	88	(	(	PUNCT
cana-3475	72	89	u2	u2	PROPN
cana-3475	72	90	,	,	PUNCT
cana-3475	72	91	v	v	NOUN
cana-3475	72	92	)	)	PUNCT
cana-3475	72	93	(	(	PUNCT
cana-3475	72	94	u2	u2	NOUN
cana-3475	72	95	,	,	PUNCT
cana-3475	72	96	1	1	NUM
cana-3475	72	97	)	)	PUNCT
cana-3475	72	98	(	(	PUNCT
cana-3475	72	99	u2	u2	NOUN
cana-3475	72	100	,	,	PUNCT
cana-3475	72	101	2	2	NUM
cana-3475	72	102	)	)	PUNCT
cana-3475	72	103	(	(	PUNCT
cana-3475	72	104	u1	u1	NOUN
cana-3475	72	105	,	,	PUNCT
cana-3475	72	106	1	1	NUM
cana-3475	72	107	)	)	PUNCT
cana-3475	72	108	(	(	PUNCT
cana-3475	72	109	u1	u1	NOUN
cana-3475	72	110	,	,	PUNCT
cana-3475	72	111	2	2	NUM
cana-3475	72	112	)	)	PUNCT
cana-3475	72	113	(	(	PUNCT
cana-3475	72	114	u3	u3	NOUN
cana-3475	72	115	,	,	PUNCT
cana-3475	72	116	v	v	NOUN
cana-3475	72	117	)	)	PUNCT
cana-3475	72	118	(	(	PUNCT
cana-3475	72	119	u3	u3	NOUN
cana-3475	72	120	,	,	PUNCT
cana-3475	72	121	1	1	NUM
cana-3475	72	122	)	)	PUNCT
cana-3475	72	123	(	(	PUNCT
cana-3475	72	124	u3	u3	NOUN
cana-3475	72	125	,	,	PUNCT
cana-3475	72	126	2	2	NUM
cana-3475	72	127	)	)	PUNCT
cana-3475	72	128	(	(	PUNCT
cana-3475	72	129	u4	u4	PROPN
cana-3475	72	130	,	,	PUNCT
cana-3475	72	131	v	v	NOUN
cana-3475	72	132	)	)	PUNCT
cana-3475	72	133	(	(	PUNCT
cana-3475	72	134	u4	u4	PROPN
cana-3475	72	135	,	,	PUNCT
cana-3475	72	136	1	1	NUM
cana-3475	72	137	)	)	PUNCT
cana-3475	72	138	(	(	PUNCT
cana-3475	72	139	u4	u4	PROPN
cana-3475	72	140	,	,	PUNCT
cana-3475	72	141	2	2	NUM
cana-3475	72	142	)	)	PUNCT
cana-3475	72	143	(	(	PUNCT
cana-3475	72	144	a	a	X
cana-3475	72	145	)	)	PUNCT
cana-3475	72	146	(	(	PUNCT
cana-3475	72	147	b	b	X
cana-3475	72	148	)	)	PUNCT
cana-3475	72	149	(	(	PUNCT
cana-3475	72	150	c	c	X
cana-3475	72	151	)	)	PUNCT
cana-3475	72	152	communications	communication	NOUN
cana-3475	72	153	on	on	ADP
cana-3475	72	154	applied	apply	VERB
cana-3475	72	155	nonlinear	nonlinear	ADJ
cana-3475	72	156	analysis	analysis	NOUN
cana-3475	72	157	issn	issn	NOUN
cana-3475	72	158	:	:	PUNCT
cana-3475	72	159	1074	1074	NUM
cana-3475	72	160	-	-	PUNCT
cana-3475	72	161	133x	133x	NUM
cana-3475	72	162	vol	vol	NOUN
cana-3475	72	163	32	32	NUM
cana-3475	72	164	no	no	NOUN
cana-3475	72	165	.	.	PUNCT
cana-3475	73	1	7s	7	NOUN
cana-3475	73	2	(	(	PUNCT
cana-3475	73	3	2025	2025	NUM
cana-3475	73	4	)	)	PUNCT
cana-3475	73	5	691	691	NUM
cana-3475	73	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3475	73	7	theorem	theorem	VERB
cana-3475	73	8	3	3	NUM
cana-3475	73	9	:	:	PUNCT
cana-3475	73	10	let	let	VERB
cana-3475	73	11	g	g	PRON
cana-3475	73	12	be	be	AUX
cana-3475	73	13	a	a	DET
cana-3475	73	14	connected	connected	ADJ
cana-3475	73	15	graph	graph	NOUN
cana-3475	73	16	of	of	ADP
cana-3475	73	17	order	order	NOUN
cana-3475	73	18	n	n	CCONJ
cana-3475	73	19			NUM
cana-3475	73	20	2	2	NUM
cana-3475	73	21	.	.	PUNCT
cana-3475	74	1	for	for	ADP
cana-3475	74	2	m	m	PROPN
cana-3475	74	3			NUM
cana-3475	74	4	2	2	NUM
cana-3475	74	5	,	,	PUNCT
cana-3475	74	6	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣𝑃𝑚	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣𝑃𝑚	PROPN
cana-3475	74	7	)	)	PUNCT
cana-3475	74	8	=	=	PRON
cana-3475	74	9	{	{	PUNCT
cana-3475	74	10	𝑛	𝑛	PROPN
cana-3475	74	11	,	,	PUNCT
cana-3475	74	12	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	PROPN
cana-3475	74	13	)	)	PUNCT
cana-3475	74	14	=	=	SYM
cana-3475	74	15	1	1	NUM
cana-3475	74	16	;	;	PUNCT
cana-3475	74	17	2𝑛	2𝑛	NUM
cana-3475	74	18	,	,	PUNCT
cana-3475	74	19	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NOUN
cana-3475	74	20	)	)	PUNCT
cana-3475	74	21	=	=	SYM
cana-3475	74	22	2	2	X
cana-3475	74	23	.	.	PUNCT
cana-3475	74	24	proof	proof	NOUN
cana-3475	74	25	.	.	PUNCT
cana-3475	75	1	we	we	PRON
cana-3475	75	2	have	have	VERB
cana-3475	75	3	two	two	NUM
cana-3475	75	4	cases	case	NOUN
cana-3475	75	5	.	.	PUNCT
cana-3475	76	1	case	case	NOUN
cana-3475	76	2	1	1	NUM
cana-3475	76	3	:	:	PUNCT
cana-3475	76	4	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
cana-3475	76	5	)	)	PUNCT
cana-3475	76	6	=	=	SYM
cana-3475	77	1	1	1	X
cana-3475	77	2	.	.	X
cana-3475	78	1	let	let	AUX
cana-3475	78	2	(	(	PUNCT
cana-3475	78	3	ui	ui	PROPN
cana-3475	78	4	,	,	PUNCT
cana-3475	78	5	m	m	PROPN
cana-3475	78	6	–	–	PUNCT
cana-3475	78	7	1	1	NUM
cana-3475	78	8	)	)	PUNCT
cana-3475	78	9	,	,	PUNCT
cana-3475	78	10	1	1	NUM
cana-3475	78	11			NOUN
cana-3475	78	12	i	i	PRON
cana-3475	78	13			NOUN
cana-3475	78	14	n	n	CCONJ
cana-3475	78	15	be	be	VERB
cana-3475	78	16	the	the	DET
cana-3475	78	17	pendant	pendant	ADJ
cana-3475	78	18	vertices	vertex	NOUN
cana-3475	78	19	of	of	ADP
cana-3475	78	20	g𝜊𝑣𝑃𝑚.	g𝜊𝑣𝑃𝑚.	NOUN
cana-3475	78	21	clearly	clearly	ADV
cana-3475	78	22	the	the	DET
cana-3475	78	23	pendant	pendant	ADJ
cana-3475	78	24	vertices	vertex	NOUN
cana-3475	78	25	(	(	PUNCT
cana-3475	78	26	ui	ui	PROPN
cana-3475	78	27	,	,	PUNCT
cana-3475	78	28	m	m	PROPN
cana-3475	78	29	–	–	PUNCT
cana-3475	78	30	1	1	NUM
cana-3475	78	31	)	)	PUNCT
cana-3475	78	32	are	be	AUX
cana-3475	78	33	pairwise	pairwise	NOUN
cana-3475	78	34	mutually	mutually	ADV
cana-3475	78	35	maximally	maximally	ADV
cana-3475	78	36	distant	distant	ADJ
cana-3475	78	37	.	.	PUNCT
cana-3475	79	1	hence	hence	ADV
cana-3475	79	2	by	by	ADP
cana-3475	79	3	lemma	lemma	PROPN
cana-3475	79	4	1	1	NUM
cana-3475	79	5	,	,	PUNCT
cana-3475	79	6	any	any	DET
cana-3475	79	7	faulttolerant	faulttolerant	ADJ
cana-3475	79	8	strong	strong	ADJ
cana-3475	79	9	resolving	resolving	NOUN
cana-3475	79	10	set	set	NOUN
cana-3475	79	11	of	of	ADP
cana-3475	79	12	g𝜊𝑣𝑃𝑚	g𝜊𝑣𝑃𝑚	PROPN
cana-3475	79	13	contains	contain	VERB
cana-3475	79	14	the	the	DET
cana-3475	79	15	pendant	pendant	ADJ
cana-3475	79	16	vertices	vertex	NOUN
cana-3475	79	17	.	.	PUNCT
cana-3475	80	1	define	define	VERB
cana-3475	80	2	w	w	NOUN
cana-3475	80	3	=	=	SYM
cana-3475	80	4	{	{	PUNCT
cana-3475	80	5	(	(	PUNCT
cana-3475	80	6	ui	ui	PROPN
cana-3475	80	7	,	,	PUNCT
cana-3475	80	8	m	m	PROPN
cana-3475	80	9	–	–	PUNCT
cana-3475	80	10	1	1	NUM
cana-3475	80	11	)	)	PUNCT
cana-3475	80	12	:	:	PUNCT
cana-3475	80	13	1	1	NUM
cana-3475	80	14			NOUN
cana-3475	80	15	i	i	PRON
cana-3475	80	16			NOUN
cana-3475	80	17	n	n	CCONJ
cana-3475	80	18	}	}	PUNCT
cana-3475	80	19	.	.	PUNCT
cana-3475	81	1	figure	figure	NOUN
cana-3475	81	2	2	2	NUM
cana-3475	81	3	(	(	PUNCT
cana-3475	81	4	a	a	NOUN
cana-3475	81	5	)	)	PUNCT
cana-3475	81	6	graph	graph	NOUN
cana-3475	81	7	g	g	PROPN
cana-3475	81	8	(	(	PUNCT
cana-3475	81	9	b	b	NOUN
cana-3475	81	10	)	)	PUNCT
cana-3475	81	11	p3	p3	NOUN
cana-3475	81	12	(	(	PUNCT
cana-3475	81	13	c	c	NOUN
cana-3475	81	14	)	)	PUNCT
cana-3475	81	15	g𝜊𝑣𝑃3	g𝜊𝑣𝑃3	VERB
cana-3475	81	16	where	where	SCONJ
cana-3475	81	17	𝑣	𝑣	PRON
cana-3475	81	18	has	have	VERB
cana-3475	81	19	degree	degree	NOUN
cana-3475	81	20	2	2	NUM
cana-3475	81	21	.	.	PUNCT
cana-3475	82	1	on	on	ADP
cana-3475	82	2	the	the	DET
cana-3475	82	3	other	other	ADJ
cana-3475	82	4	hand	hand	NOUN
cana-3475	82	5	,	,	PUNCT
cana-3475	82	6	let	let	VERB
cana-3475	82	7	𝑊	𝑊	VERB
cana-3475	82	8	=	=	SYM
cana-3475	82	9	{	{	PUNCT
cana-3475	82	10	(	(	PUNCT
cana-3475	82	11	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	82	12	,	,	PUNCT
cana-3475	82	13	𝑚	𝑚	ADP
cana-3475	82	14	−	−	PROPN
cana-3475	82	15	1	1	NUM
cana-3475	82	16	):	):	PUNCT
cana-3475	82	17	1	1	NUM
cana-3475	82	18	≤	≤	NUM
cana-3475	82	19	𝑖	𝑖	SYM
cana-3475	82	20	≤	≤	NUM
cana-3475	82	21	𝑛	𝑛	NOUN
cana-3475	82	22	}	}	PUNCT
cana-3475	82	23	and	and	CCONJ
cana-3475	82	24	let	let	VERB
cana-3475	82	25	(	(	PUNCT
cana-3475	82	26	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	82	27	,	,	PUNCT
cana-3475	82	28	𝑘1	𝑘1	PROPN
cana-3475	82	29	)	)	PUNCT
cana-3475	82	30	,	,	PUNCT
cana-3475	83	1	(	(	PUNCT
cana-3475	83	2	𝑢𝑗	𝑢𝑗	X
cana-3475	83	3	,	,	PUNCT
cana-3475	83	4	𝑘2	𝑘2	PROPN
cana-3475	83	5	)	)	PUNCT
cana-3475	83	6	∈	∈	PROPN
cana-3475	83	7	𝑉\𝑊.	𝑉\𝑊.	NOUN
cana-3475	83	8	clearly	clearly	ADV
cana-3475	83	9	the	the	DET
cana-3475	83	10	vertices	vertex	NOUN
cana-3475	83	11	(	(	PUNCT
cana-3475	83	12	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	83	13	,	,	PUNCT
cana-3475	83	14	𝑘1	𝑘1	ADJ
cana-3475	83	15	)	)	PUNCT
cana-3475	83	16	and	and	CCONJ
cana-3475	83	17	(	(	PUNCT
cana-3475	83	18	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	83	19	,	,	PUNCT
cana-3475	83	20	𝑘2	𝑘2	PROPN
cana-3475	83	21	)	)	PUNCT
cana-3475	83	22	are	be	AUX
cana-3475	83	23	strongly	strongly	ADV
cana-3475	83	24	resolved	resolve	VERB
cana-3475	83	25	by	by	ADP
cana-3475	83	26	both	both	DET
cana-3475	83	27	(	(	PUNCT
cana-3475	83	28	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	83	29	,	,	PUNCT
cana-3475	83	30	𝑚	𝑚	ADP
cana-3475	83	31	−	−	PROPN
cana-3475	83	32	1	1	NUM
cana-3475	83	33	)	)	PUNCT
cana-3475	83	34	and	and	CCONJ
cana-3475	83	35	(	(	PUNCT
cana-3475	83	36	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	83	37	,	,	PUNCT
cana-3475	83	38	𝑚	𝑚	PROPN
cana-3475	83	39	−	−	PROPN
cana-3475	83	40	1	1	NUM
cana-3475	83	41	)	)	PUNCT
cana-3475	83	42	;	;	PUNCT
cana-3475	83	43	the	the	DET
cana-3475	83	44	shortest	short	ADJ
cana-3475	83	45	path	path	NOUN
cana-3475	83	46	from	from	ADP
cana-3475	83	47	(	(	PUNCT
cana-3475	83	48	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	83	49	,	,	PUNCT
cana-3475	83	50	𝑘1	𝑘1	NOUN
cana-3475	83	51	)	)	PUNCT
cana-3475	83	52	to	to	ADP
cana-3475	83	53	(	(	PUNCT
cana-3475	83	54	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	83	55	,	,	PUNCT
cana-3475	83	56	𝑚	𝑚	PROPN
cana-3475	83	57	−	−	PROPN
cana-3475	83	58	1	1	NUM
cana-3475	83	59	)	)	PUNCT
cana-3475	83	60	contains	contain	VERB
cana-3475	83	61	(	(	PUNCT
cana-3475	83	62	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	83	63	,	,	PUNCT
cana-3475	83	64	𝑘2	𝑘2	PROPN
cana-3475	83	65	)	)	PUNCT
cana-3475	83	66	and	and	CCONJ
cana-3475	83	67	similarly	similarly	ADV
cana-3475	83	68	the	the	DET
cana-3475	83	69	shortest	short	ADJ
cana-3475	83	70	path	path	NOUN
cana-3475	83	71	from	from	ADP
cana-3475	83	72	(	(	PUNCT
cana-3475	83	73	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	83	74	,	,	PUNCT
cana-3475	83	75	𝑘2	𝑘2	PROPN
cana-3475	83	76	)	)	PUNCT
cana-3475	83	77	to	to	PART
cana-3475	83	78	(	(	PUNCT
cana-3475	83	79	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	83	80	,	,	PUNCT
cana-3475	83	81	𝑚	𝑚	ADP
cana-3475	83	82	−	−	PROPN
cana-3475	83	83	1	1	NUM
cana-3475	83	84	)	)	PUNCT
cana-3475	83	85	contains	contain	VERB
cana-3475	83	86	(	(	PUNCT
cana-3475	83	87	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	83	88	,	,	PUNCT
cana-3475	83	89	𝑘1	𝑘1	PROPN
cana-3475	83	90	)	)	PUNCT
cana-3475	83	91	.	.	PUNCT
cana-3475	84	1	hence	hence	ADV
cana-3475	84	2	by	by	ADP
cana-3475	84	3	theorem	theorem	NOUN
cana-3475	84	4	2	2	NUM
cana-3475	84	5	,	,	PUNCT
cana-3475	84	6	𝑊	𝑊	PROPN
cana-3475	84	7	is	be	AUX
cana-3475	84	8	a	a	DET
cana-3475	84	9	fault	fault	NOUN
cana-3475	84	10	-	-	PUNCT
cana-3475	84	11	tolerant	tolerant	ADJ
cana-3475	84	12	strong	strong	ADJ
cana-3475	84	13	resolving	resolving	NOUN
cana-3475	84	14	set	set	NOUN
cana-3475	84	15	.	.	PUNCT
cana-3475	85	1	case	case	NOUN
cana-3475	85	2	2	2	NUM
cana-3475	85	3	:	:	PUNCT
cana-3475	85	4	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
cana-3475	85	5	)	)	PUNCT
cana-3475	85	6	=	=	SYM
cana-3475	85	7	2	2	X
cana-3475	85	8	.	.	X
cana-3475	86	1	let	let	VERB
cana-3475	86	2	(	(	PUNCT
cana-3475	86	3	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	86	4	,	,	PUNCT
cana-3475	86	5	𝑎	𝑎	NOUN
cana-3475	86	6	)	)	PUNCT
cana-3475	86	7	and	and	CCONJ
cana-3475	86	8	(	(	PUNCT
cana-3475	86	9	𝑤𝑖	𝑤𝑖	NOUN
cana-3475	86	10	,	,	PUNCT
cana-3475	86	11	𝑏	𝑏	NOUN
cana-3475	86	12	)	)	PUNCT
cana-3475	86	13	,	,	PUNCT
cana-3475	86	14	1	1	NUM
cana-3475	86	15	≤	≤	NUM
cana-3475	86	16	𝑖	𝑖	SYM
cana-3475	86	17	≤	≤	NOUN
cana-3475	86	18	𝑛	𝑛	NOUN
cana-3475	86	19	,	,	PUNCT
cana-3475	86	20	be	be	VERB
cana-3475	86	21	the	the	DET
cana-3475	86	22	pendant	pendant	ADJ
cana-3475	86	23	vertices	vertex	NOUN
cana-3475	86	24	of	of	ADP
cana-3475	86	25	g𝜊𝑣𝑃𝑚.	g𝜊𝑣𝑃𝑚.	NOUN
cana-3475	86	26	clearly	clearly	ADV
cana-3475	86	27	the	the	DET
cana-3475	86	28	pendant	pendant	ADJ
cana-3475	86	29	vertices	vertex	NOUN
cana-3475	86	30	(	(	PUNCT
cana-3475	86	31	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	86	32	,	,	PUNCT
cana-3475	86	33	𝑎	𝑎	NOUN
cana-3475	86	34	)	)	PUNCT
cana-3475	86	35	and	and	CCONJ
cana-3475	86	36	(	(	PUNCT
cana-3475	86	37	𝑤𝑖	𝑤𝑖	NOUN
cana-3475	86	38	,	,	PUNCT
cana-3475	86	39	𝑏	𝑏	NOUN
cana-3475	86	40	)	)	PUNCT
cana-3475	86	41	are	be	AUX
cana-3475	86	42	pairwise	pairwise	NOUN
cana-3475	86	43	mutually	mutually	ADV
cana-3475	86	44	maximally	maximally	ADV
cana-3475	86	45	distant	distant	ADJ
cana-3475	86	46	.	.	PUNCT
cana-3475	87	1	hence	hence	ADV
cana-3475	87	2	by	by	ADP
cana-3475	87	3	lemma	lemma	PROPN
cana-3475	87	4	1	1	NUM
cana-3475	87	5	,	,	PUNCT
cana-3475	87	6	any	any	DET
cana-3475	87	7	fault	fault	NOUN
cana-3475	87	8	-	-	PUNCT
cana-3475	87	9	tolerant	tolerant	ADJ
cana-3475	87	10	strong	strong	ADJ
cana-3475	87	11	resolving	resolving	NOUN
cana-3475	87	12	set	set	NOUN
cana-3475	87	13	of	of	ADP
cana-3475	87	14	g𝜊𝑣𝑃𝑚	g𝜊𝑣𝑃𝑚	PROPN
cana-3475	87	15	contains	contain	VERB
cana-3475	87	16	the	the	DET
cana-3475	87	17	pendant	pendant	ADJ
cana-3475	87	18	vertices	vertex	NOUN
cana-3475	87	19	.	.	PUNCT
cana-3475	88	1	define	define	VERB
cana-3475	88	2	𝑊	𝑊	PROPN
cana-3475	88	3	=	=	SYM
cana-3475	88	4	{	{	PUNCT
cana-3475	88	5	(	(	PUNCT
cana-3475	88	6	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	88	7	,	,	PUNCT
cana-3475	88	8	𝑎	𝑎	NOUN
cana-3475	88	9	)	)	PUNCT
cana-3475	88	10	,	,	PUNCT
cana-3475	88	11	(	(	PUNCT
cana-3475	88	12	𝑤𝑖	𝑤𝑖	NOUN
cana-3475	88	13	,	,	PUNCT
cana-3475	88	14	𝑏	𝑏	NOUN
cana-3475	88	15	)	)	PUNCT
cana-3475	88	16	∶	∶	NOUN
cana-3475	88	17	1	1	NUM
cana-3475	88	18	≤	≤	NOUN
cana-3475	88	19	𝑖	𝑖	SYM
cana-3475	88	20	≤	≤	NUM
cana-3475	88	21	𝑛	𝑛	NOUN
cana-3475	88	22	}	}	PUNCT
cana-3475	88	23	.	.	PUNCT
cana-3475	89	1	on	on	ADP
cana-3475	89	2	the	the	DET
cana-3475	89	3	other	other	ADJ
cana-3475	89	4	hand	hand	NOUN
cana-3475	89	5	,	,	PUNCT
cana-3475	89	6	let	let	VERB
cana-3475	89	7	𝑊	𝑊	VERB
cana-3475	89	8	=	=	SYM
cana-3475	89	9	{	{	PUNCT
cana-3475	89	10	(	(	PUNCT
cana-3475	89	11	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	89	12	,	,	PUNCT
cana-3475	89	13	𝑎	𝑎	NOUN
cana-3475	89	14	)	)	PUNCT
cana-3475	89	15	,	,	PUNCT
cana-3475	89	16	(	(	PUNCT
cana-3475	89	17	𝑤𝑖	𝑤𝑖	NOUN
cana-3475	89	18	,	,	PUNCT
cana-3475	89	19	𝑏	𝑏	NOUN
cana-3475	89	20	)	)	PUNCT
cana-3475	89	21	∶	∶	NOUN
cana-3475	89	22	1	1	NUM
cana-3475	89	23	≤	≤	NOUN
cana-3475	89	24	𝑖	𝑖	SYM
cana-3475	89	25	≤	≤	NUM
cana-3475	89	26	𝑛	𝑛	NOUN
cana-3475	89	27	}	}	PUNCT
cana-3475	89	28	and	and	CCONJ
cana-3475	89	29	let	let	VERB
cana-3475	89	30	(	(	PUNCT
cana-3475	89	31	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	89	32	,	,	PUNCT
cana-3475	89	33	𝑘1),(𝑢𝑗	𝑘1),(𝑢𝑗	NOUN
cana-3475	89	34	,	,	PUNCT
cana-3475	89	35	𝑘2	𝑘2	PROPN
cana-3475	89	36	)	)	PUNCT
cana-3475	89	37	∈	∈	PROPN
cana-3475	89	38	𝑉\𝑊.	𝑉\𝑊.	NOUN
cana-3475	89	39	clearly	clearly	ADV
cana-3475	89	40	the	the	DET
cana-3475	89	41	vertices	vertex	NOUN
cana-3475	89	42	(	(	PUNCT
cana-3475	89	43	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	89	44	,	,	PUNCT
cana-3475	89	45	𝑘1	𝑘1	ADJ
cana-3475	89	46	)	)	PUNCT
cana-3475	89	47	and	and	CCONJ
cana-3475	89	48	(	(	PUNCT
cana-3475	89	49	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	89	50	,	,	PUNCT
cana-3475	89	51	𝑘2	𝑘2	PROPN
cana-3475	89	52	)	)	PUNCT
cana-3475	89	53	are	be	AUX
cana-3475	89	54	strongly	strongly	ADV
cana-3475	89	55	resolved	resolve	VERB
cana-3475	89	56	by	by	ADP
cana-3475	89	57	both	both	DET
cana-3475	89	58	(	(	PUNCT
cana-3475	89	59	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	89	60	,	,	PUNCT
cana-3475	89	61	𝑎	𝑎	NOUN
cana-3475	89	62	)	)	PUNCT
cana-3475	89	63	,	,	PUNCT
cana-3475	89	64	(	(	PUNCT
cana-3475	89	65	𝑤𝑖	𝑤𝑖	NOUN
cana-3475	89	66	,	,	PUNCT
cana-3475	89	67	𝑏	𝑏	NOUN
cana-3475	89	68	)	)	PUNCT
cana-3475	89	69	and	and	CCONJ
cana-3475	89	70	(	(	PUNCT
cana-3475	89	71	𝑢𝑗	𝑢𝑗	NOUN
cana-3475	89	72	,	,	PUNCT
cana-3475	89	73	𝑎	𝑎	NOUN
cana-3475	89	74	)	)	PUNCT
cana-3475	89	75	,	,	PUNCT
cana-3475	89	76	(	(	PUNCT
cana-3475	89	77	𝑤𝑗	𝑤𝑗	X
cana-3475	89	78	,	,	PUNCT
cana-3475	89	79	𝑏	𝑏	NOUN
cana-3475	89	80	)	)	PUNCT
cana-3475	89	81	.	.	PUNCT
cana-3475	90	1	hence	hence	ADV
cana-3475	90	2	by	by	ADP
cana-3475	90	3	theorem	theorem	NOUN
cana-3475	90	4	2	2	NUM
cana-3475	90	5	,	,	PUNCT
cana-3475	90	6	𝑊	𝑊	PROPN
cana-3475	90	7	is	be	AUX
cana-3475	90	8	a	a	DET
cana-3475	90	9	faulttolerant	faulttolerant	ADJ
cana-3475	90	10	strong	strong	ADJ
cana-3475	90	11	resolving	resolving	NOUN
cana-3475	90	12	set	set	NOUN
cana-3475	90	13	.	.	PUNCT
cana-3475	91	1	figure	figure	NOUN
cana-3475	91	2	3	3	NUM
cana-3475	91	3	(	(	PUNCT
cana-3475	91	4	a	a	NOUN
cana-3475	91	5	)	)	PUNCT
cana-3475	91	6	graph	graph	NOUN
cana-3475	91	7	g	g	PROPN
cana-3475	91	8	(	(	PUNCT
cana-3475	91	9	b	b	NOUN
cana-3475	91	10	)	)	PUNCT
cana-3475	91	11	c3	c3	NOUN
cana-3475	91	12	(	(	PUNCT
cana-3475	91	13	c	c	NOUN
cana-3475	91	14	)	)	PUNCT
cana-3475	91	15	𝐺𝜊𝑣𝐶3	𝐺𝜊𝑣𝐶3	PROPN
cana-3475	91	16	where	where	SCONJ
cana-3475	91	17	v	v	NOUN
cana-3475	91	18	has	have	VERB
cana-3475	91	19	degree	degree	NOUN
cana-3475	91	20	2	2	NUM
cana-3475	91	21	.	.	PUNCT
cana-3475	91	22	u1	u1	PROPN
cana-3475	91	23	u2	u2	PROPN
cana-3475	92	1	u3u4	u3u4	NOUN
cana-3475	92	2	v	v	PROPN
cana-3475	92	3	1	1	NUM
cana-3475	92	4	1	1	NUM
cana-3475	92	5	(	(	PUNCT
cana-3475	92	6	u1	u1	NOUN
cana-3475	92	7	,	,	PUNCT
cana-3475	92	8	1	1	NUM
cana-3475	92	9	)	)	PUNCT
cana-3475	92	10	(	(	PUNCT
cana-3475	92	11	u2	u2	NOUN
cana-3475	92	12	,	,	PUNCT
cana-3475	92	13	1	1	NUM
cana-3475	92	14	)	)	PUNCT
cana-3475	92	15	(	(	PUNCT
cana-3475	92	16	u2	u2	PROPN
cana-3475	92	17	,	,	PUNCT
cana-3475	92	18	v	v	NOUN
cana-3475	92	19	)	)	PUNCT
cana-3475	92	20	(	(	PUNCT
cana-3475	92	21	w2	w2	NOUN
cana-3475	92	22	,	,	PUNCT
cana-3475	92	23	1	1	NUM
cana-3475	92	24	)	)	PUNCT
cana-3475	92	25	(	(	PUNCT
cana-3475	92	26	u1	u1	NOUN
cana-3475	92	27	,	,	PUNCT
cana-3475	92	28	v	v	NOUN
cana-3475	92	29	)	)	PUNCT
cana-3475	92	30	(	(	PUNCT
cana-3475	92	31	w1	w1	NOUN
cana-3475	92	32	,	,	PUNCT
cana-3475	92	33	1	1	NUM
cana-3475	92	34	)	)	PUNCT
cana-3475	92	35	(	(	PUNCT
cana-3475	92	36	u3	u3	NOUN
cana-3475	92	37	,	,	PUNCT
cana-3475	92	38	1	1	NUM
cana-3475	92	39	)	)	PUNCT
cana-3475	92	40	(	(	PUNCT
cana-3475	92	41	u3	u3	NOUN
cana-3475	92	42	,	,	PUNCT
cana-3475	92	43	v	v	NOUN
cana-3475	92	44	)	)	PUNCT
cana-3475	92	45	(	(	PUNCT
cana-3475	92	46	w3	w3	PROPN
cana-3475	92	47	,	,	PUNCT
cana-3475	92	48	1	1	NUM
cana-3475	92	49	)	)	PUNCT
cana-3475	92	50	(	(	PUNCT
cana-3475	92	51	a	a	X
cana-3475	92	52	)	)	PUNCT
cana-3475	92	53	(	(	PUNCT
cana-3475	92	54	b	b	X
cana-3475	92	55	)	)	PUNCT
cana-3475	92	56	(	(	PUNCT
cana-3475	92	57	c	c	X
cana-3475	92	58	)	)	PUNCT
cana-3475	92	59	(	(	PUNCT
cana-3475	92	60	u4	u4	PROPN
cana-3475	92	61	,	,	PUNCT
cana-3475	92	62	1	1	NUM
cana-3475	92	63	)	)	PUNCT
cana-3475	92	64	(	(	PUNCT
cana-3475	92	65	u4	u4	PROPN
cana-3475	92	66	,	,	PUNCT
cana-3475	92	67	v	v	NOUN
cana-3475	92	68	)	)	PUNCT
cana-3475	92	69	(	(	PUNCT
cana-3475	92	70	w4	w4	NOUN
cana-3475	92	71	,	,	PUNCT
cana-3475	92	72	1	1	NUM
cana-3475	92	73	)	)	PUNCT
cana-3475	92	74	u1	u1	NOUN
cana-3475	92	75	u2	u2	PROPN
cana-3475	92	76	u3u4	u3u4	PROPN
cana-3475	92	77	(	(	PUNCT
cana-3475	92	78	a	a	NOUN
cana-3475	92	79	)	)	PUNCT
cana-3475	92	80	(	(	PUNCT
cana-3475	92	81	b	b	X
cana-3475	92	82	)	)	PUNCT
cana-3475	92	83	(	(	PUNCT
cana-3475	92	84	c	c	X
cana-3475	92	85	)	)	PUNCT
cana-3475	92	86	v	v	NOUN
cana-3475	92	87	2	2	NUM
cana-3475	92	88	1	1	NUM
cana-3475	92	89	(	(	PUNCT
cana-3475	92	90	u1	u1	NOUN
cana-3475	92	91	,	,	PUNCT
cana-3475	92	92	v	v	NOUN
cana-3475	92	93	)	)	PUNCT
cana-3475	92	94	(	(	PUNCT
cana-3475	92	95	u2	u2	PROPN
cana-3475	92	96	,	,	PUNCT
cana-3475	92	97	v	v	NOUN
cana-3475	92	98	)	)	PUNCT
cana-3475	92	99	(	(	PUNCT
cana-3475	92	100	u2	u2	NOUN
cana-3475	92	101	,	,	PUNCT
cana-3475	92	102	1)(u2	1)(u2	NUM
cana-3475	92	103	,	,	PUNCT
cana-3475	92	104	2)(u1	2)(u1	NUM
cana-3475	92	105	,	,	PUNCT
cana-3475	92	106	1)(u1	1)(u1	NUM
cana-3475	92	107	,	,	PUNCT
cana-3475	92	108	2	2	NUM
cana-3475	92	109	)	)	PUNCT
cana-3475	92	110	(	(	PUNCT
cana-3475	92	111	u3	u3	NOUN
cana-3475	92	112	,	,	PUNCT
cana-3475	92	113	v	v	NOUN
cana-3475	92	114	)	)	PUNCT
cana-3475	92	115	(	(	PUNCT
cana-3475	92	116	u3	u3	PROPN
cana-3475	92	117	,	,	PUNCT
cana-3475	92	118	1)(u3	1)(u3	NUM
cana-3475	92	119	,	,	PUNCT
cana-3475	92	120	2	2	NUM
cana-3475	92	121	)	)	PUNCT
cana-3475	92	122	(	(	PUNCT
cana-3475	92	123	u4	u4	PROPN
cana-3475	92	124	,	,	PUNCT
cana-3475	92	125	v	v	NOUN
cana-3475	92	126	)	)	PUNCT
cana-3475	92	127	(	(	PUNCT
cana-3475	92	128	u4	u4	PROPN
cana-3475	92	129	,	,	PUNCT
cana-3475	92	130	1)(u4	1)(u4	NUM
cana-3475	92	131	,	,	PUNCT
cana-3475	92	132	2	2	X
cana-3475	92	133	)	)	PUNCT
cana-3475	92	134	communications	communication	NOUN
cana-3475	92	135	on	on	ADP
cana-3475	92	136	applied	apply	VERB
cana-3475	92	137	nonlinear	nonlinear	ADJ
cana-3475	92	138	analysis	analysis	NOUN
cana-3475	92	139	issn	issn	NOUN
cana-3475	92	140	:	:	PUNCT
cana-3475	92	141	1074	1074	NUM
cana-3475	92	142	-	-	PUNCT
cana-3475	92	143	133x	133x	NUM
cana-3475	92	144	vol	vol	NOUN
cana-3475	92	145	32	32	NUM
cana-3475	92	146	no	no	NOUN
cana-3475	92	147	.	.	PUNCT
cana-3475	93	1	7s	7	NOUN
cana-3475	93	2	(	(	PUNCT
cana-3475	93	3	2025	2025	NUM
cana-3475	93	4	)	)	PUNCT
cana-3475	93	5	692	692	NUM
cana-3475	93	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3475	93	7	consider	consider	VERB
cana-3475	93	8	the	the	DET
cana-3475	93	9	rooted	rooted	ADJ
cana-3475	93	10	graph	graph	NOUN
cana-3475	93	11	g𝜊𝑣𝐶𝑚	g𝜊𝑣𝐶𝑚	NOUN
cana-3475	93	12	,	,	PUNCT
cana-3475	93	13	where	where	SCONJ
cana-3475	93	14	𝑚	𝑚	PROPN
cana-3475	93	15	≥	≥	NUM
cana-3475	93	16	3	3	NUM
cana-3475	93	17	.	.	PUNCT
cana-3475	94	1	clearly	clearly	ADV
cana-3475	94	2	the	the	DET
cana-3475	94	3	degree	degree	NOUN
cana-3475	94	4	of	of	ADP
cana-3475	94	5	root	root	NOUN
cana-3475	94	6	vertex	vertex	NOUN
cana-3475	94	7	𝑣	𝑣	NOUN
cana-3475	94	8	is	be	AUX
cana-3475	94	9	2	2	NUM
cana-3475	94	10	and	and	CCONJ
cana-3475	94	11	the	the	DET
cana-3475	94	12	vertices	vertex	NOUN
cana-3475	94	13	of	of	ADP
cana-3475	94	14	ith	ith	PROPN
cana-3475	94	15	copy	copy	NOUN
cana-3475	94	16	of	of	ADP
cana-3475	94	17	cm	cm	NOUN
cana-3475	94	18	are	be	AUX
cana-3475	94	19	labelled	label	VERB
cana-3475	94	20	as	as	ADP
cana-3475	94	21	(	(	PUNCT
cana-3475	94	22	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	94	23	,	,	PUNCT
cana-3475	94	24	𝑗	𝑗	NOUN
cana-3475	94	25	)	)	PUNCT
cana-3475	94	26	,	,	PUNCT
cana-3475	94	27	1	1	NUM
cana-3475	94	28	≤	≤	NUM
cana-3475	94	29	𝑖	𝑖	SYM
cana-3475	94	30	≤	≤	NOUN
cana-3475	94	31	𝑚	𝑚	ADP
cana-3475	94	32	−	−	PROPN
cana-3475	94	33	1	1	NUM
cana-3475	94	34	in	in	ADP
cana-3475	94	35	g𝜊𝑣𝐶𝑚	g𝜊𝑣𝐶𝑚	PROPN
cana-3475	94	36	except	except	SCONJ
cana-3475	94	37	(	(	PUNCT
cana-3475	94	38	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	94	39	,	,	PUNCT
cana-3475	94	40	𝑣	𝑣	NOUN
cana-3475	94	41	)	)	PUNCT
cana-3475	94	42	.	.	PUNCT
cana-3475	95	1	see	see	VERB
cana-3475	95	2	figure	figure	NOUN
cana-3475	95	3	3	3	NUM
cana-3475	95	4	.	.	PUNCT
cana-3475	95	5	theorem	theorem	NOUN
cana-3475	95	6	4	4	NUM
cana-3475	95	7	:	:	PUNCT
cana-3475	95	8	let	let	VERB
cana-3475	95	9	g	g	PRON
cana-3475	95	10	be	be	AUX
cana-3475	95	11	a	a	DET
cana-3475	95	12	connected	connected	ADJ
cana-3475	95	13	graph	graph	NOUN
cana-3475	95	14	of	of	ADP
cana-3475	95	15	order	order	NOUN
cana-3475	95	16	n	n	CCONJ
cana-3475	95	17			NUM
cana-3475	95	18	2	2	NUM
cana-3475	95	19	.	.	PUNCT
cana-3475	96	1	for	for	ADP
cana-3475	96	2	m	m	PROPN
cana-3475	96	3			NUM
cana-3475	96	4	2	2	NUM
cana-3475	96	5	,	,	PUNCT
cana-3475	96	6	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣𝐶𝑚	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣𝐶𝑚	NUM
cana-3475	96	7	)	)	PUNCT
cana-3475	96	8	=	=	PUNCT
cana-3475	96	9	𝑛(𝑚	𝑛(𝑚	NOUN
cana-3475	96	10	−	−	NOUN
cana-3475	96	11	1	1	NUM
cana-3475	96	12	)	)	PUNCT
cana-3475	96	13	.	.	PUNCT
cana-3475	97	1	proof	proof	NOUN
cana-3475	97	2	.	.	PUNCT
cana-3475	98	1	let	let	VERB
cana-3475	98	2	(	(	PUNCT
cana-3475	98	3	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	98	4	,	,	PUNCT
cana-3475	98	5	𝑣	𝑣	NOUN
cana-3475	98	6	)	)	PUNCT
cana-3475	98	7	,	,	PUNCT
cana-3475	98	8	(	(	PUNCT
cana-3475	98	9	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	98	10	,	,	PUNCT
cana-3475	98	11	1	1	NUM
cana-3475	98	12	)	)	PUNCT
cana-3475	98	13	,	,	PUNCT
cana-3475	98	14	(	(	PUNCT
cana-3475	98	15	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	98	16	,	,	PUNCT
cana-3475	98	17	2	2	NUM
cana-3475	98	18	)	)	PUNCT
cana-3475	98	19	…	…	PUNCT
cana-3475	98	20	(	(	PUNCT
cana-3475	98	21	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	98	22	,	,	PUNCT
cana-3475	98	23	𝑚	𝑚	ADP
cana-3475	98	24	−	−	PROPN
cana-3475	98	25	1	1	NUM
cana-3475	98	26	)	)	PUNCT
cana-3475	98	27	be	be	AUX
cana-3475	98	28	the	the	DET
cana-3475	98	29	vertices	vertex	NOUN
cana-3475	98	30	of	of	ADP
cana-3475	98	31	ith	ith	PROPN
cana-3475	98	32	copy	copy	NOUN
cana-3475	98	33	of	of	ADP
cana-3475	98	34	cm	cm	PROPN
cana-3475	98	35	in	in	ADP
cana-3475	98	36	g𝜊𝑣𝐶𝑚.	g𝜊𝑣𝐶𝑚.	NOUN
cana-3475	98	37	if	if	SCONJ
cana-3475	98	38	m	m	NOUN
cana-3475	98	39	is	be	AUX
cana-3475	98	40	even	even	ADV
cana-3475	98	41	,	,	PUNCT
cana-3475	98	42	then	then	ADV
cana-3475	98	43	there	there	PRON
cana-3475	98	44	is	be	VERB
cana-3475	98	45	exactly	exactly	ADV
cana-3475	98	46	one	one	NUM
cana-3475	98	47	antipodal	antipodal	NOUN
cana-3475	98	48	vertex	vertex	NOUN
cana-3475	98	49	(	(	PUNCT
cana-3475	98	50	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	98	51	,	,	PUNCT
cana-3475	98	52	𝑘∗	𝑘∗	PROPN
cana-3475	98	53	)	)	PUNCT
cana-3475	98	54	from	from	ADP
cana-3475	98	55	(	(	PUNCT
cana-3475	98	56	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	98	57	,	,	PUNCT
cana-3475	98	58	𝑘	𝑘	NOUN
cana-3475	98	59	)	)	PUNCT
cana-3475	98	60	,	,	PUNCT
cana-3475	98	61	1	1	NUM
cana-3475	98	62	≤	≤	NUM
cana-3475	98	63	𝑖	𝑖	SYM
cana-3475	98	64	≤	≤	NUM
cana-3475	98	65	𝑛	𝑛	NOUN
cana-3475	98	66	,	,	PUNCT
cana-3475	98	67	1	1	NUM
cana-3475	98	68	≤	≤	NOUN
cana-3475	98	69	𝑘	𝑘	DET
cana-3475	98	70	≤	≤	NOUN
cana-3475	98	71	𝑚	𝑚	ADP
cana-3475	98	72	−	−	PROPN
cana-3475	98	73	1	1	NUM
cana-3475	98	74	.	.	PUNCT
cana-3475	99	1	hence	hence	ADV
cana-3475	99	2	the	the	DET
cana-3475	99	3	vertices	vertex	NOUN
cana-3475	99	4	(	(	PUNCT
cana-3475	99	5	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	99	6	,	,	PUNCT
cana-3475	99	7	𝑘	𝑘	NOUN
cana-3475	99	8	)	)	PUNCT
cana-3475	99	9	,	,	PUNCT
cana-3475	99	10	1	1	NUM
cana-3475	99	11	≤	≤	NOUN
cana-3475	99	12	𝑘	𝑘	DET
cana-3475	99	13	≤	≤	NOUN
cana-3475	99	14	𝑚	𝑚	ADP
cana-3475	99	15	−	−	PROPN
cana-3475	99	16	1	1	NUM
cana-3475	99	17	,	,	PUNCT
cana-3475	99	18	must	must	AUX
cana-3475	99	19	belong	belong	VERB
cana-3475	99	20	to	to	ADP
cana-3475	99	21	any	any	DET
cana-3475	99	22	fault	fault	NOUN
cana-3475	99	23	-	-	PUNCT
cana-3475	99	24	tolerant	tolerant	ADJ
cana-3475	99	25	strong	strong	ADJ
cana-3475	99	26	resolving	resolving	NOUN
cana-3475	99	27	set	set	VERB
cana-3475	99	28	w.	w.	NOUN
cana-3475	99	29	if	if	SCONJ
cana-3475	99	30	m	m	PROPN
cana-3475	99	31	is	be	AUX
cana-3475	99	32	odd	odd	ADJ
cana-3475	99	33	,	,	PUNCT
cana-3475	99	34	then	then	ADV
cana-3475	99	35	there	there	PRON
cana-3475	99	36	are	be	VERB
cana-3475	99	37	exactly	exactly	ADV
cana-3475	99	38	two	two	NUM
cana-3475	99	39	antipodal	antipodal	PROPN
cana-3475	99	40	vertices	vertex	NOUN
cana-3475	99	41	,	,	PUNCT
cana-3475	99	42	say	say	VERB
cana-3475	99	43	(	(	PUNCT
cana-3475	99	44	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	99	45	,	,	PUNCT
cana-3475	99	46	𝑘1	𝑘1	ADJ
cana-3475	99	47	∗	∗	NOUN
cana-3475	99	48	)	)	PUNCT
cana-3475	99	49	and	and	CCONJ
cana-3475	99	50	(	(	PUNCT
cana-3475	99	51	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	99	52	,	,	PUNCT
cana-3475	99	53	𝑘2	𝑘2	PROPN
cana-3475	99	54	∗	∗	NOUN
cana-3475	99	55	)	)	PUNCT
cana-3475	99	56	from	from	ADP
cana-3475	99	57	(	(	PUNCT
cana-3475	99	58	𝑢𝑖	𝑢𝑖	INTJ
cana-3475	99	59	,	,	PUNCT
cana-3475	99	60	𝑘	𝑘	NOUN
cana-3475	99	61	)	)	PUNCT
cana-3475	99	62	,	,	PUNCT
cana-3475	99	63	1	1	NUM
cana-3475	99	64	≤	≤	NUM
cana-3475	99	65	𝑖	𝑖	SYM
cana-3475	99	66	≤	≤	NUM
cana-3475	99	67	𝑛	𝑛	NOUN
cana-3475	99	68	,	,	PUNCT
cana-3475	99	69	1	1	NUM
cana-3475	99	70	≤	≤	NOUN
cana-3475	99	71	𝑘	𝑘	DET
cana-3475	99	72	≤	≤	NOUN
cana-3475	99	73	𝑚	𝑚	ADP
cana-3475	99	74	−	−	PROPN
cana-3475	99	75	1	1	NUM
cana-3475	99	76	.	.	PUNCT
cana-3475	100	1	hence	hence	ADV
cana-3475	100	2	the	the	DET
cana-3475	100	3	vertices	vertex	NOUN
cana-3475	100	4	(	(	PUNCT
cana-3475	100	5	𝑢𝑖	𝑢𝑖	NOUN
cana-3475	100	6	,	,	PUNCT
cana-3475	100	7	𝑘	𝑘	NOUN
cana-3475	100	8	)	)	PUNCT
cana-3475	100	9	,	,	PUNCT
cana-3475	100	10	1	1	NUM
cana-3475	100	11	≤	≤	NOUN
cana-3475	100	12	𝑘	𝑘	DET
cana-3475	100	13	≤	≤	NOUN
cana-3475	100	14	𝑚	𝑚	ADP
cana-3475	100	15	−	−	PROPN
cana-3475	100	16	1	1	NUM
cana-3475	100	17	,	,	PUNCT
cana-3475	100	18	must	must	AUX
cana-3475	100	19	belong	belong	VERB
cana-3475	100	20	to	to	ADP
cana-3475	100	21	any	any	DET
cana-3475	100	22	fault	fault	NOUN
cana-3475	100	23	-	-	PUNCT
cana-3475	100	24	tolerant	tolerant	ADJ
cana-3475	100	25	strong	strong	ADJ
cana-3475	100	26	resolving	resolving	NOUN
cana-3475	100	27	set	set	VERB
cana-3475	100	28	w.	w.	NOUN
cana-3475	100	29	since	since	SCONJ
cana-3475	100	30	this	this	PRON
cana-3475	100	31	is	be	AUX
cana-3475	100	32	true	true	ADJ
cana-3475	100	33	for	for	ADP
cana-3475	100	34	every	every	DET
cana-3475	100	35	𝑖	𝑖	NOUN
cana-3475	100	36	,	,	PUNCT
cana-3475	100	37	1	1	NUM
cana-3475	100	38	≤	≤	NUM
cana-3475	100	39	𝑖	𝑖	SYM
cana-3475	100	40	≤	≤	NUM
cana-3475	100	41	𝑛	𝑛	NOUN
cana-3475	100	42	,	,	PUNCT
cana-3475	100	43	|𝑊|	|𝑊|	NOUN
cana-3475	100	44	=	=	PUNCT
cana-3475	100	45	𝑛(𝑚	𝑛(𝑚	NOUN
cana-3475	100	46	−	−	NOUN
cana-3475	100	47	1	1	NUM
cana-3475	100	48	)	)	PUNCT
cana-3475	100	49	.	.	PUNCT
cana-3475	101	1	similarly	similarly	ADV
cana-3475	101	2	,	,	PUNCT
cana-3475	101	3	we	we	PRON
cana-3475	101	4	have	have	VERB
cana-3475	101	5	the	the	DET
cana-3475	101	6	following	follow	VERB
cana-3475	101	7	results	result	NOUN
cana-3475	101	8	.	.	PUNCT
cana-3475	102	1	theorem	theorem	ADJ
cana-3475	102	2	5	5	NUM
cana-3475	102	3	:	:	PUNCT
cana-3475	102	4	let	let	VERB
cana-3475	102	5	g	g	PRON
cana-3475	102	6	be	be	AUX
cana-3475	102	7	a	a	DET
cana-3475	102	8	connected	connected	ADJ
cana-3475	102	9	graph	graph	NOUN
cana-3475	102	10	of	of	ADP
cana-3475	102	11	order	order	NOUN
cana-3475	102	12	n	n	CCONJ
cana-3475	102	13			NUM
cana-3475	102	14	2	2	NUM
cana-3475	102	15	.	.	PUNCT
cana-3475	103	1	for	for	ADP
cana-3475	103	2	m	m	PROPN
cana-3475	103	3			NUM
cana-3475	103	4	3	3	NUM
cana-3475	103	5	,	,	PUNCT
cana-3475	103	6	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣𝐾𝑚	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣𝐾𝑚	PROPN
cana-3475	103	7	)	)	PUNCT
cana-3475	103	8	=	=	PUNCT
cana-3475	103	9	𝑛(𝑚	𝑛(𝑚	NOUN
cana-3475	103	10	−	−	NOUN
cana-3475	103	11	1	1	NUM
cana-3475	103	12	)	)	PUNCT
cana-3475	103	13	.	.	PUNCT
cana-3475	104	1	theorem	theorem	ADJ
cana-3475	104	2	6	6	NUM
cana-3475	104	3	:	:	PUNCT
cana-3475	104	4	let	let	VERB
cana-3475	104	5	g	g	PRON
cana-3475	104	6	be	be	AUX
cana-3475	104	7	a	a	DET
cana-3475	104	8	connected	connected	ADJ
cana-3475	104	9	graph	graph	NOUN
cana-3475	104	10	of	of	ADP
cana-3475	104	11	order	order	NOUN
cana-3475	104	12	n	n	CCONJ
cana-3475	104	13			NUM
cana-3475	104	14	2	2	NUM
cana-3475	104	15	and	and	CCONJ
cana-3475	104	16	t	t	PROPN
cana-3475	104	17	be	be	AUX
cana-3475	104	18	a	a	DET
cana-3475	104	19	tree	tree	NOUN
cana-3475	104	20	.	.	PUNCT
cana-3475	105	1	then	then	ADV
cana-3475	105	2	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣𝑇	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣𝑇	PROPN
cana-3475	105	3	)	)	PUNCT
cana-3475	105	4	equals	equal	VERB
cana-3475	105	5	the	the	DET
cana-3475	105	6	number	number	NOUN
cana-3475	105	7	of	of	ADP
cana-3475	105	8	leaves	leave	NOUN
cana-3475	105	9	in	in	ADP
cana-3475	105	10	g𝜊𝑣𝑇.	g𝜊𝑣𝑇.	NOUN
cana-3475	105	11	a	a	DET
cana-3475	105	12	wheel	wheel	NOUN
cana-3475	105	13	graph	graph	NOUN
cana-3475	105	14	w1,m	w1,m	PROPN
cana-3475	105	15	,	,	PUNCT
cana-3475	105	16	m	m	PROPN
cana-3475	105	17			NUM
cana-3475	105	18	3	3	NUM
cana-3475	105	19	,	,	PUNCT
cana-3475	105	20	can	can	AUX
cana-3475	105	21	also	also	ADV
cana-3475	105	22	be	be	AUX
cana-3475	105	23	seen	see	VERB
cana-3475	105	24	as	as	ADP
cana-3475	105	25	the	the	DET
cana-3475	105	26	graph	graph	NOUN
cana-3475	105	27	obtained	obtain	VERB
cana-3475	105	28	by	by	ADP
cana-3475	105	29	adding	add	VERB
cana-3475	105	30	a	a	DET
cana-3475	105	31	single	single	ADJ
cana-3475	105	32	vertex	vertex	NOUN
cana-3475	105	33	(	(	PUNCT
cana-3475	105	34	the	the	DET
cana-3475	105	35	hub	hub	NOUN
cana-3475	105	36	)	)	PUNCT
cana-3475	105	37	to	to	ADP
cana-3475	105	38	a	a	DET
cana-3475	105	39	cycle	cycle	NOUN
cana-3475	105	40	cm	cm	NOUN
cana-3475	105	41	where	where	SCONJ
cana-3475	105	42	the	the	DET
cana-3475	105	43	hub	hub	NOUN
cana-3475	105	44	is	be	AUX
cana-3475	105	45	connected	connect	VERB
cana-3475	105	46	to	to	ADP
cana-3475	105	47	all	all	DET
cana-3475	105	48	vertices	vertex	NOUN
cana-3475	105	49	in	in	ADP
cana-3475	105	50	cn	cn	PROPN
cana-3475	105	51	.	.	PUNCT
cana-3475	105	52	theorem	theorem	ADJ
cana-3475	105	53	7	7	NUM
cana-3475	105	54	:	:	PUNCT
cana-3475	105	55	let	let	VERB
cana-3475	105	56	g	g	PRON
cana-3475	105	57	be	be	AUX
cana-3475	105	58	a	a	DET
cana-3475	105	59	connected	connected	ADJ
cana-3475	105	60	graph	graph	NOUN
cana-3475	105	61	of	of	ADP
cana-3475	105	62	order	order	NOUN
cana-3475	105	63	n	n	CCONJ
cana-3475	105	64			NUM
cana-3475	105	65	2	2	NUM
cana-3475	105	66	.	.	PUNCT
cana-3475	106	1	for	for	ADP
cana-3475	106	2	m	m	PROPN
cana-3475	106	3			NUM
cana-3475	106	4	3	3	NUM
cana-3475	106	5	,	,	PUNCT
cana-3475	106	6	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣𝑊𝑚	𝑑𝑖𝑚𝑓𝑠(g𝜊𝑣𝑊𝑚	PROPN
cana-3475	106	7	)	)	PUNCT
cana-3475	106	8	=	=	PRON
cana-3475	106	9	{	{	PUNCT
cana-3475	106	10	𝑚𝑛	𝑚𝑛	NOUN
cana-3475	106	11	−	−	PROPN
cana-3475	106	12	1	1	NUM
cana-3475	106	13	,	,	PUNCT
cana-3475	106	14	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NOUN
cana-3475	106	15	)	)	PUNCT
cana-3475	106	16	=	=	SYM
cana-3475	106	17	𝑚	𝑚	PROPN
cana-3475	106	18	;	;	PUNCT
cana-3475	106	19	𝑛	𝑛	ADJ
cana-3475	106	20	,	,	PUNCT
cana-3475	106	21	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NOUN
cana-3475	106	22	)	)	PUNCT
cana-3475	106	23	=	=	PUNCT
cana-3475	106	24	𝑚	𝑚	ADP
cana-3475	106	25	−	−	NUM
cana-3475	106	26	1	1	NUM
cana-3475	106	27	.	.	NOUN
cana-3475	106	28	3	3	X
cana-3475	106	29	.	.	X
cana-3475	106	30	conclusion	conclusion	NOUN
cana-3475	106	31	in	in	ADP
cana-3475	106	32	this	this	DET
cana-3475	106	33	paper	paper	NOUN
cana-3475	106	34	,	,	PUNCT
cana-3475	106	35	we	we	PRON
cana-3475	106	36	have	have	AUX
cana-3475	106	37	explored	explore	VERB
cana-3475	106	38	the	the	DET
cana-3475	106	39	fault	fault	NOUN
cana-3475	106	40	-	-	PUNCT
cana-3475	106	41	tolerant	tolerant	ADJ
cana-3475	106	42	strong	strong	ADJ
cana-3475	106	43	metric	metric	ADJ
cana-3475	106	44	dimension	dimension	NOUN
cana-3475	106	45	of	of	ADP
cana-3475	106	46	rooted	rooted	ADJ
cana-3475	106	47	product	product	NOUN
cana-3475	106	48	graphs	graph	NOUN
cana-3475	106	49	,	,	PUNCT
cana-3475	106	50	extending	extend	VERB
cana-3475	106	51	the	the	DET
cana-3475	106	52	concept	concept	NOUN
cana-3475	106	53	of	of	ADP
cana-3475	106	54	strong	strong	ADJ
cana-3475	106	55	metric	metric	ADJ
cana-3475	106	56	dimension	dimension	NOUN
cana-3475	106	57	to	to	PART
cana-3475	106	58	account	account	VERB
cana-3475	106	59	for	for	ADP
cana-3475	106	60	vertex	vertex	NOUN
cana-3475	106	61	.	.	PUNCT
cana-3475	107	1	we	we	PRON
cana-3475	107	2	have	have	AUX
cana-3475	107	3	computed	compute	VERB
cana-3475	107	4	exact	exact	ADJ
cana-3475	107	5	values	value	NOUN
cana-3475	107	6	for	for	ADP
cana-3475	107	7	several	several	ADJ
cana-3475	107	8	families	family	NOUN
cana-3475	107	9	of	of	ADP
cana-3475	107	10	rooted	rooted	ADJ
cana-3475	107	11	product	product	NOUN
cana-3475	107	12	graphs	graph	NOUN
cana-3475	107	13	,	,	PUNCT
cana-3475	107	14	highlighting	highlight	VERB
cana-3475	107	15	how	how	SCONJ
cana-3475	107	16	the	the	DET
cana-3475	107	17	fault	fault	NOUN
cana-3475	107	18	-	-	PUNCT
cana-3475	107	19	tolerant	tolerant	ADJ
cana-3475	107	20	property	property	NOUN
cana-3475	107	21	depends	depend	VERB
cana-3475	107	22	on	on	ADP
cana-3475	107	23	the	the	DET
cana-3475	107	24	structural	structural	ADJ
cana-3475	107	25	characteristics	characteristic	NOUN
cana-3475	107	26	of	of	ADP
cana-3475	107	27	both	both	CCONJ
cana-3475	107	28	the	the	DET
cana-3475	107	29	root	root	NOUN
cana-3475	107	30	and	and	CCONJ
cana-3475	107	31	base	base	NOUN
cana-3475	107	32	graphs	graph	NOUN
cana-3475	107	33	.	.	PUNCT
cana-3475	108	1	future	future	ADJ
cana-3475	108	2	work	work	NOUN
cana-3475	108	3	may	may	AUX
cana-3475	108	4	involve	involve	VERB
cana-3475	108	5	exploring	explore	VERB
cana-3475	108	6	fault	fault	NOUN
cana-3475	108	7	-	-	PUNCT
cana-3475	108	8	tolerance	tolerance	NOUN
cana-3475	108	9	in	in	ADP
cana-3475	108	10	other	other	ADJ
cana-3475	108	11	graph	graph	NOUN
cana-3475	108	12	products	product	NOUN
cana-3475	108	13	or	or	CCONJ
cana-3475	108	14	generalizing	generalize	VERB
cana-3475	108	15	these	these	DET
cana-3475	108	16	results	result	NOUN
cana-3475	108	17	to	to	ADP
cana-3475	108	18	other	other	ADJ
cana-3475	108	19	graph	graph	NOUN
cana-3475	108	20	families	family	NOUN
cana-3475	108	21	,	,	PUNCT
cana-3475	108	22	with	with	ADP
cana-3475	108	23	potential	potential	ADJ
cana-3475	108	24	applications	application	NOUN
cana-3475	108	25	in	in	ADP
cana-3475	108	26	areas	area	NOUN
cana-3475	108	27	such	such	ADJ
cana-3475	108	28	as	as	ADP
cana-3475	108	29	distributed	distribute	VERB
cana-3475	108	30	computing	computing	NOUN
cana-3475	108	31	,	,	PUNCT
cana-3475	108	32	network	network	NOUN
cana-3475	108	33	topology	topology	NOUN
cana-3475	108	34	,	,	PUNCT
cana-3475	108	35	and	and	CCONJ
cana-3475	108	36	communication	communication	NOUN
cana-3475	108	37	systems	system	NOUN
cana-3475	108	38	.	.	PUNCT
cana-3475	109	1	references	reference	NOUN
cana-3475	109	2	[	[	X
cana-3475	109	3	1	1	X
cana-3475	109	4	]	]	PUNCT
cana-3475	109	5	j.	j.	PROPN
cana-3475	109	6	a.	a.	PROPN
cana-3475	109	7	bondy	bondy	PROPN
cana-3475	109	8	and	and	CCONJ
cana-3475	109	9	u.	u.	PROPN
cana-3475	109	10	s.	s.	PROPN
cana-3475	109	11	r.	r.	PROPN
cana-3475	109	12	murty	murty	PROPN
cana-3475	109	13	,	,	PUNCT
cana-3475	109	14	graph	graph	NOUN
cana-3475	109	15	theory	theory	NOUN
cana-3475	109	16	with	with	ADP
cana-3475	109	17	applications	application	NOUN
cana-3475	109	18	,	,	PUNCT
cana-3475	109	19	macmillan	macmillan	PROPN
cana-3475	109	20	,	,	PUNCT
cana-3475	109	21	new	new	PROPN
cana-3475	109	22	york	york	PROPN
cana-3475	109	23	,	,	PUNCT
cana-3475	109	24	1976	1976	NUM
cana-3475	109	25	.	.	PUNCT
cana-3475	110	1	[	[	X
cana-3475	110	2	2	2	NUM
cana-3475	110	3	]	]	PUNCT
cana-3475	110	4	c.	c.	PROPN
cana-3475	110	5	d.	d.	PROPN
cana-3475	110	6	godsil	godsil	PROPN
cana-3475	110	7	and	and	CCONJ
cana-3475	110	8	b.	b.	PROPN
cana-3475	110	9	d.	d.	PROPN
cana-3475	110	10	mckay	mckay	PROPN
cana-3475	110	11	,	,	PUNCT
cana-3475	110	12	a	a	DET
cana-3475	110	13	new	new	ADJ
cana-3475	110	14	graph	graph	NOUN
cana-3475	110	15	product	product	NOUN
cana-3475	110	16	and	and	CCONJ
cana-3475	110	17	its	its	PRON
cana-3475	110	18	spectrum	spectrum	NOUN
cana-3475	110	19	,	,	PUNCT
cana-3475	110	20	bull	bull	NOUN
cana-3475	110	21	.	.	PUNCT
cana-3475	111	1	aust	aust	PROPN
cana-3475	111	2	.	.	PUNCT
cana-3475	111	3	math	math	PROPN
cana-3475	111	4	.	.	PUNCT
cana-3475	112	1	soc	soc	PROPN
cana-3475	112	2	.	.	PUNCT
cana-3475	113	1	18	18	NUM
cana-3475	113	2	(	(	PUNCT
cana-3475	113	3	1978	1978	NUM
cana-3475	113	4	)	)	PUNCT
cana-3475	113	5	21	21	NUM
cana-3475	113	6	-	-	SYM
cana-3475	113	7	28	28	NUM
cana-3475	113	8	.	.	PUNCT
cana-3475	114	1	[	[	X
cana-3475	114	2	3	3	X
cana-3475	114	3	]	]	X
cana-3475	114	4	f.	f.	PROPN
cana-3475	114	5	harary	harary	PROPN
cana-3475	114	6	and	and	CCONJ
cana-3475	114	7	r.	r.	PROPN
cana-3475	114	8	a.	a.	NOUN
cana-3475	114	9	melter	melter	NOUN
cana-3475	114	10	,	,	PUNCT
cana-3475	114	11	on	on	ADP
cana-3475	114	12	the	the	DET
cana-3475	114	13	metric	metric	ADJ
cana-3475	114	14	dimension	dimension	NOUN
cana-3475	114	15	of	of	ADP
cana-3475	114	16	a	a	DET
cana-3475	114	17	graph	graph	NOUN
cana-3475	114	18	,	,	PUNCT
cana-3475	114	19	ars	ar	VERB
cana-3475	114	20	combin	combin	NOUN
cana-3475	114	21	.	.	PROPN
cana-3475	114	22	2	2	NUM
cana-3475	114	23	(	(	PUNCT
cana-3475	114	24	1976	1976	NUM
cana-3475	114	25	)	)	PUNCT
cana-3475	114	26	191	191	NUM
cana-3475	114	27	-	-	SYM
cana-3475	114	28	195	195	NUM
cana-3475	114	29	.	.	PUNCT
cana-3475	115	1	[	[	X
cana-3475	115	2	4	4	X
cana-3475	115	3	]	]	PUNCT
cana-3475	115	4	j.	j.	PROPN
cana-3475	115	5	kratica	kratica	PROPN
cana-3475	115	6	,	,	PUNCT
cana-3475	115	7	v.	v.	PROPN
cana-3475	115	8	kovačević	kovačević	NOUN
cana-3475	115	9	-	-	PUNCT
cana-3475	115	10	vujčić	vujčić	NOUN
cana-3475	115	11	,	,	PUNCT
cana-3475	115	12	m.	m.	NOUN
cana-3475	115	13	čangalović	čangalović	NOUN
cana-3475	115	14	,	,	PUNCT
cana-3475	115	15	and	and	CCONJ
cana-3475	115	16	m.	m.	NOUN
cana-3475	115	17	stojanović	stojanović	PROPN
cana-3475	115	18	,	,	PUNCT
cana-3475	115	19	minimal	minimal	ADJ
cana-3475	115	20	doubly	doubly	ADV
cana-3475	115	21	resolving	resolve	VERB
cana-3475	115	22	sets	set	NOUN
cana-3475	115	23	and	and	CCONJ
cana-3475	115	24	the	the	DET
cana-3475	115	25	strong	strong	ADJ
cana-3475	115	26	metric	metric	ADJ
cana-3475	115	27	dimension	dimension	NOUN
cana-3475	115	28	of	of	ADP
cana-3475	115	29	some	some	DET
cana-3475	115	30	convex	convex	ADJ
cana-3475	115	31	polytopes	polytope	NOUN
cana-3475	115	32	,	,	PUNCT
cana-3475	115	33	appl	appl	PROPN
cana-3475	115	34	.	.	PROPN
cana-3475	115	35	math	math	NOUN
cana-3475	115	36	.	.	PUNCT
cana-3475	116	1	comput	comput	NOUN
cana-3475	116	2	.	.	PUNCT
cana-3475	117	1	218(19	218(19	NUM
cana-3475	117	2	)	)	PUNCT
cana-3475	117	3	(	(	PUNCT
cana-3475	117	4	2012	2012	NUM
cana-3475	117	5	)	)	PUNCT
cana-3475	117	6	9790	9790	NUM
cana-3475	117	7	-	-	SYM
cana-3475	117	8	9801	9801	NUM
cana-3475	117	9	.	.	PUNCT
cana-3475	118	1	[	[	X
cana-3475	118	2	5	5	NUM
cana-3475	118	3	]	]	PUNCT
cana-3475	118	4	s.	s.	PROPN
cana-3475	118	5	krishnan	krishnan	PROPN
cana-3475	118	6	,	,	PUNCT
cana-3475	118	7	b.	b.	PROPN
cana-3475	118	8	rajan	rajan	PROPN
cana-3475	118	9	and	and	CCONJ
cana-3475	118	10	m.	m.	NOUN
cana-3475	118	11	imran	imran	PROPN
cana-3475	118	12	,	,	PUNCT
cana-3475	118	13	on	on	ADP
cana-3475	118	14	the	the	DET
cana-3475	118	15	strong	strong	ADJ
cana-3475	118	16	metric	metric	ADJ
cana-3475	118	17	dimension	dimension	NOUN
cana-3475	118	18	of	of	ADP
cana-3475	118	19	certain	certain	ADJ
cana-3475	118	20	nanostructures	nanostructure	NOUN
cana-3475	118	21	,	,	PUNCT
cana-3475	118	22	j.	j.	PROPN
cana-3475	118	23	comput	comput	PROPN
cana-3475	118	24	.	.	PUNCT
cana-3475	119	1	theor	theor	PROPN
cana-3475	119	2	.	.	PUNCT
cana-3475	120	1	nanosci	nanosci	PROPN
cana-3475	120	2	.	.	PUNCT
cana-3475	121	1	14(1	14(1	NUM
cana-3475	121	2	)	)	PUNCT
cana-3475	121	3	(	(	PUNCT
cana-3475	121	4	2017	2017	NUM
cana-3475	121	5	)	)	PUNCT
cana-3475	121	6	354	354	NUM
cana-3475	121	7	-	-	SYM
cana-3475	121	8	358	358	NUM
cana-3475	121	9	.	.	PUNCT
cana-3475	122	1	[	[	X
cana-3475	122	2	6	6	NUM
cana-3475	122	3	]	]	PUNCT
cana-3475	122	4	s.	s.	PROPN
cana-3475	122	5	krishnan	krishnan	PROPN
cana-3475	122	6	and	and	CCONJ
cana-3475	122	7	b.	b.	PROPN
cana-3475	122	8	rajan	rajan	PROPN
cana-3475	122	9	,	,	PUNCT
cana-3475	122	10	fault	fault	NOUN
cana-3475	122	11	-	-	PUNCT
cana-3475	122	12	tolerant	tolerant	ADJ
cana-3475	122	13	strong	strong	ADJ
cana-3475	122	14	metric	metric	ADJ
cana-3475	122	15	dimension	dimension	NOUN
cana-3475	122	16	of	of	ADP
cana-3475	122	17	graphs	graph	NOUN
cana-3475	122	18	,	,	PUNCT
cana-3475	122	19	discrete	discrete	ADJ
cana-3475	122	20	mathematics	mathematic	NOUN
cana-3475	122	21	,	,	PUNCT
cana-3475	122	22	algorithms	algorithm	NOUN
cana-3475	122	23	and	and	CCONJ
cana-3475	122	24	applications	application	NOUN
cana-3475	122	25	,	,	PUNCT
cana-3475	122	26	15(7	15(7	NUM
cana-3475	122	27	)	)	PUNCT
cana-3475	122	28	(	(	PUNCT
cana-3475	122	29	2023	2023	NUM
cana-3475	122	30	)	)	PUNCT
cana-3475	122	31	,	,	PUNCT
cana-3475	122	32	2250162	2250162	NUM
cana-3475	122	33	.	.	PUNCT
cana-3475	123	1	communications	communication	NOUN
cana-3475	123	2	on	on	ADP
cana-3475	123	3	applied	apply	VERB
cana-3475	123	4	nonlinear	nonlinear	ADJ
cana-3475	123	5	analysis	analysis	NOUN
cana-3475	123	6	issn	issn	NOUN
cana-3475	123	7	:	:	PUNCT
cana-3475	123	8	1074	1074	NUM
cana-3475	123	9	-	-	PUNCT
cana-3475	123	10	133x	133x	NUM
cana-3475	123	11	vol	vol	NOUN
cana-3475	123	12	32	32	NUM
cana-3475	123	13	no	no	NOUN
cana-3475	123	14	.	.	PUNCT
cana-3475	124	1	7s	7	NOUN
cana-3475	124	2	(	(	PUNCT
cana-3475	124	3	2025	2025	NUM
cana-3475	124	4	)	)	PUNCT
cana-3475	124	5	693	693	NUM
cana-3475	124	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3475	125	1	[	[	X
cana-3475	125	2	7	7	X
cana-3475	125	3	]	]	X
cana-3475	125	4	d.	d.	PROPN
cana-3475	125	5	kuziak	kuziak	PROPN
cana-3475	125	6	,	,	PUNCT
cana-3475	125	7	i.	i.	PROPN
cana-3475	125	8	g.	g.	PROPN
cana-3475	125	9	yero	yero	PROPN
cana-3475	125	10	and	and	CCONJ
cana-3475	125	11	j.	j.	PROPN
cana-3475	125	12	a.	a.	PROPN
cana-3475	125	13	rodríguez	rodríguez	PROPN
cana-3475	125	14	-	-	PUNCT
cana-3475	125	15	velázquez	velázquez	NOUN
cana-3475	125	16	,	,	PUNCT
cana-3475	125	17	on	on	ADP
cana-3475	125	18	the	the	DET
cana-3475	125	19	strong	strong	ADJ
cana-3475	125	20	metric	metric	ADJ
cana-3475	125	21	dimension	dimension	NOUN
cana-3475	125	22	of	of	ADP
cana-3475	125	23	corona	corona	NOUN
cana-3475	125	24	product	product	NOUN
cana-3475	125	25	graphs	graph	NOUN
cana-3475	125	26	and	and	CCONJ
cana-3475	125	27	join	join	VERB
cana-3475	125	28	graphs	graph	NOUN
cana-3475	125	29	,	,	PUNCT
cana-3475	125	30	discret	discret	PROPN
cana-3475	125	31	.	.	PUNCT
cana-3475	125	32	appl	appl	PROPN
cana-3475	125	33	.	.	PROPN
cana-3475	125	34	math	math	NOUN
cana-3475	125	35	.	.	PUNCT
cana-3475	126	1	161(7	161(7	NUM
cana-3475	126	2	-	-	SYM
cana-3475	126	3	8)	8)	NUM
cana-3475	126	4	(	(	PUNCT
cana-3475	126	5	2013	2013	NUM
cana-3475	126	6	)	)	PUNCT
cana-3475	126	7	1022	1022	NUM
cana-3475	126	8	-	-	SYM
cana-3475	126	9	1027	1027	NUM
cana-3475	126	10	.	.	PUNCT
cana-3475	127	1	[	[	X
cana-3475	127	2	8	8	NUM
cana-3475	127	3	]	]	X
cana-3475	127	4	o.	o.	PROPN
cana-3475	127	5	r.	r.	PROPN
cana-3475	127	6	oellermann	oellermann	PROPN
cana-3475	127	7	and	and	CCONJ
cana-3475	127	8	j.	j.	PROPN
cana-3475	127	9	peters	peters	PROPN
cana-3475	127	10	-	-	PUNCT
cana-3475	127	11	fransen	fransen	PROPN
cana-3475	127	12	,	,	PUNCT
cana-3475	127	13	the	the	DET
cana-3475	127	14	strong	strong	ADJ
cana-3475	127	15	metric	metric	ADJ
cana-3475	127	16	dimension	dimension	NOUN
cana-3475	127	17	of	of	ADP
cana-3475	127	18	graphs	graph	NOUN
cana-3475	127	19	and	and	CCONJ
cana-3475	127	20	digraphs	digraph	NOUN
cana-3475	127	21	,	,	PUNCT
cana-3475	127	22	discret	discret	ADJ
cana-3475	127	23	.	.	PUNCT
cana-3475	128	1	appl	appl	PROPN
cana-3475	128	2	.	.	PROPN
cana-3475	128	3	math	math	NOUN
cana-3475	128	4	.	.	PUNCT
cana-3475	129	1	155(3	155(3	NUM
cana-3475	129	2	)	)	PUNCT
cana-3475	129	3	(	(	PUNCT
cana-3475	129	4	2007	2007	NUM
cana-3475	129	5	)	)	PUNCT
cana-3475	129	6	356	356	NUM
cana-3475	129	7	-	-	SYM
cana-3475	129	8	364	364	NUM
cana-3475	129	9	.	.	PUNCT
cana-3475	130	1	[	[	X
cana-3475	130	2	9	9	NUM
cana-3475	130	3	]	]	PUNCT
cana-3475	130	4	k.	k.	PROPN
cana-3475	130	5	sathish	sathish	PROPN
cana-3475	130	6	and	and	CCONJ
cana-3475	130	7	b.	b.	PROPN
cana-3475	130	8	rajan	rajan	PROPN
cana-3475	130	9	,	,	PUNCT
cana-3475	130	10	on	on	ADP
cana-3475	130	11	strong	strong	ADJ
cana-3475	130	12	metric	metric	ADJ
cana-3475	130	13	dimension	dimension	NOUN
cana-3475	130	14	of	of	ADP
cana-3475	130	15	certain	certain	ADJ
cana-3475	130	16	triangular	triangular	NOUN
cana-3475	130	17	tessellations	tessellation	NOUN
cana-3475	130	18	,	,	PUNCT
cana-3475	130	19	int	int	NOUN
cana-3475	130	20	.	.	PUNCT
cana-3475	131	1	j.	j.	PROPN
cana-3475	131	2	pure	pure	PROPN
cana-3475	131	3	appl	appl	PROPN
cana-3475	131	4	.	.	PUNCT
cana-3475	131	5	math	math	NOUN
cana-3475	131	6	.	.	PUNCT
cana-3475	132	1	101(5	101(5	NUM
cana-3475	132	2	)	)	PUNCT
cana-3475	132	3	(	(	PUNCT
cana-3475	132	4	2015	2015	NUM
cana-3475	132	5	)	)	PUNCT
cana-3475	132	6	637	637	NUM
cana-3475	132	7	-	-	SYM
cana-3475	132	8	645	645	NUM
cana-3475	132	9	.	.	PUNCT
cana-3475	133	1	[	[	X
cana-3475	133	2	10	10	NUM
cana-3475	133	3	]	]	PUNCT
cana-3475	133	4	k.	k.	PROPN
cana-3475	133	5	sathish	sathish	PROPN
cana-3475	133	6	and	and	CCONJ
cana-3475	133	7	h.	h.	PROPN
cana-3475	133	8	prathab	prathab	PROPN
cana-3475	133	9	,	,	PUNCT
cana-3475	133	10	on	on	ADP
cana-3475	133	11	strong	strong	ADJ
cana-3475	133	12	metric	metric	ADJ
cana-3475	133	13	dimension	dimension	NOUN
cana-3475	133	14	of	of	ADP
cana-3475	133	15	certain	certain	ADJ
cana-3475	133	16	interconnection	interconnection	NOUN
cana-3475	133	17	networks	network	NOUN
cana-3475	133	18	,	,	PUNCT
cana-3475	133	19	aip	aip	PROPN
cana-3475	133	20	conference	conference	NOUN
cana-3475	133	21	proceeding	proceeding	NOUN
cana-3475	133	22	,	,	PUNCT
cana-3475	133	23	2852(1	2852(1	NOUN
cana-3475	133	24	)	)	PUNCT
cana-3475	133	25	(	(	PUNCT
cana-3475	133	26	2023	2023	NUM
cana-3475	133	27	)	)	PUNCT
cana-3475	133	28	020009	020009	NUM
cana-3475	133	29	.	.	PUNCT
cana-3475	134	1	[	[	X
cana-3475	134	2	11	11	NUM
cana-3475	134	3	]	]	PUNCT
cana-3475	134	4	a.	a.	NOUN
cana-3475	134	5	sebö	sebö	PROPN
cana-3475	134	6	and	and	CCONJ
cana-3475	134	7	e.	e.	PROPN
cana-3475	134	8	tannier	tannier	PROPN
cana-3475	134	9	,	,	PUNCT
cana-3475	134	10	on	on	ADP
cana-3475	134	11	metric	metric	ADJ
cana-3475	134	12	generators	generator	NOUN
cana-3475	134	13	of	of	ADP
cana-3475	134	14	graphs	graph	NOUN
cana-3475	134	15	,	,	PUNCT
cana-3475	134	16	math	math	NOUN
cana-3475	134	17	.	.	PUNCT
cana-3475	135	1	oper	oper	PROPN
cana-3475	135	2	.	.	PUNCT
cana-3475	136	1	res	re	NOUN
cana-3475	136	2	.	.	PUNCT
cana-3475	137	1	29(2	29(2	X
cana-3475	137	2	)	)	PUNCT
cana-3475	137	3	(	(	PUNCT
cana-3475	137	4	2004	2004	NUM
cana-3475	137	5	)	)	PUNCT
cana-3475	137	6	383	383	NUM
cana-3475	137	7	-	-	SYM
cana-3475	137	8	393	393	NUM
cana-3475	137	9	.	.	PUNCT
cana-3475	138	1	[	[	X
cana-3475	138	2	12	12	NUM
cana-3475	138	3	]	]	PUNCT
cana-3475	138	4	a.	a.	NOUN
cana-3475	138	5	j.	j.	PROPN
cana-3475	138	6	schwenk	schwenk	PROPN
cana-3475	138	7	,	,	PUNCT
cana-3475	138	8	computing	compute	VERB
cana-3475	138	9	the	the	DET
cana-3475	138	10	characteristic	characteristic	ADJ
cana-3475	138	11	polynomial	polynomial	NOUN
cana-3475	138	12	of	of	ADP
cana-3475	138	13	a	a	DET
cana-3475	138	14	graph	graph	NOUN
cana-3475	138	15	,	,	PUNCT
cana-3475	138	16	graphs	graph	NOUN
cana-3475	138	17	and	and	CCONJ
cana-3475	138	18	combinatorics	combinatoric	NOUN
cana-3475	138	19	:	:	PUNCT
cana-3475	138	20	proceedings	proceeding	NOUN
cana-3475	138	21	of	of	ADP
cana-3475	138	22	the	the	DET
cana-3475	138	23	capital	capital	NOUN
cana-3475	138	24	conference	conference	NOUN
cana-3475	138	25	on	on	ADP
cana-3475	138	26	graph	graph	NOUN
cana-3475	138	27	theory	theory	NOUN
cana-3475	138	28	and	and	CCONJ
cana-3475	138	29	combinatorics	combinatoric	NOUN
cana-3475	138	30	at	at	ADP
cana-3475	138	31	the	the	DET
cana-3475	138	32	george	george	PROPN
cana-3475	138	33	washington	washington	PROPN
cana-3475	138	34	university	university	PROPN
cana-3475	138	35	june	june	PROPN
cana-3475	138	36	18	18	NUM
cana-3475	138	37	-	-	SYM
cana-3475	138	38	22	22	NUM
cana-3475	138	39	,	,	PUNCT
cana-3475	138	40	1973	1973	NUM
cana-3475	138	41	.	.	PUNCT
cana-3475	139	1	berlin	berlin	PROPN
cana-3475	139	2	,	,	PUNCT
cana-3475	139	3	heidelberg	heidelberg	PROPN
cana-3475	139	4	:	:	PUNCT
cana-3475	139	5	springer	springer	PROPN
cana-3475	139	6	berlin	berlin	PROPN
cana-3475	139	7	heidelberg	heidelberg	PROPN
cana-3475	139	8	,	,	PUNCT
cana-3475	139	9	2006	2006	NUM
cana-3475	139	10	.	.	PUNCT
cana-3475	140	1	[	[	X
cana-3475	140	2	13	13	NUM
cana-3475	140	3	]	]	PUNCT
cana-3475	140	4	p.	p.	PROPN
cana-3475	140	5	j.	j.	PROPN
cana-3475	140	6	slater	slater	PROPN
cana-3475	140	7	,	,	PUNCT
cana-3475	140	8	leaves	leave	NOUN
cana-3475	140	9	of	of	ADP
cana-3475	140	10	trees	tree	NOUN
cana-3475	140	11	,	,	PUNCT
cana-3475	140	12	proceeding	proceeding	NOUN
cana-3475	140	13	of	of	ADP
cana-3475	140	14	the	the	DET
cana-3475	140	15	6th	6th	ADJ
cana-3475	140	16	southeastern	southeastern	ADJ
cana-3475	140	17	conference	conference	NOUN
cana-3475	140	18	on	on	ADP
cana-3475	140	19	combinatorics	combinatoric	NOUN
cana-3475	140	20	,	,	PUNCT
cana-3475	140	21	graph	graph	NOUN
cana-3475	140	22	theory	theory	NOUN
cana-3475	140	23	,	,	PUNCT
cana-3475	140	24	and	and	CCONJ
cana-3475	140	25	computing	computing	NOUN
cana-3475	140	26	,	,	PUNCT
cana-3475	140	27	congressus	congressus	PROPN
cana-3475	140	28	numerantium	numerantium	PROPN
cana-3475	140	29	14	14	NUM
cana-3475	140	30	(	(	PUNCT
cana-3475	140	31	1975	1975	NUM
cana-3475	140	32	)	)	PUNCT
cana-3475	140	33	549	549	NUM
cana-3475	140	34	-	-	SYM
cana-3475	140	35	559	559	NUM
cana-3475	140	36	.	.	PUNCT
cana-3475	141	1	[	[	X
cana-3475	141	2	14	14	NUM
cana-3475	141	3	]	]	X
cana-3475	141	4	e.	e.	PROPN
cana-3475	141	5	yi	yi	PROPN
cana-3475	141	6	,	,	PUNCT
cana-3475	141	7	on	on	ADP
cana-3475	141	8	strong	strong	ADJ
cana-3475	141	9	metric	metric	ADJ
cana-3475	141	10	dimension	dimension	NOUN
cana-3475	141	11	of	of	ADP
cana-3475	141	12	graphs	graph	NOUN
cana-3475	141	13	and	and	CCONJ
cana-3475	141	14	their	their	PRON
cana-3475	141	15	complements	complement	NOUN
cana-3475	141	16	,	,	PUNCT
cana-3475	141	17	acta	acta	PROPN
cana-3475	141	18	.	.	PUNCT
cana-3475	142	1	math	math	NOUN
cana-3475	142	2	.	.	PUNCT
cana-3475	143	1	sin	sin	NOUN
cana-3475	143	2	.	.	PUNCT
cana-3475	144	1	english	english	PROPN
cana-3475	144	2	ser	ser	PROPN
cana-3475	144	3	.	.	PUNCT
cana-3475	145	1	29(8	29(8	NUM
cana-3475	145	2	)	)	PUNCT
cana-3475	145	3	(	(	PUNCT
cana-3475	145	4	2013	2013	NUM
cana-3475	145	5	)	)	PUNCT
cana-3475	145	6	1479	1479	NUM
cana-3475	145	7	-	-	SYM
cana-3475	145	8	1492	1492	NUM
cana-3475	145	9	.	.	PUNCT