id	sid	tid	token	lemma	pos
cana-5662	1	1	communications	communication	NOUN
cana-5662	1	2	on	on	ADP
cana-5662	1	3	applied	apply	VERB
cana-5662	1	4	nonlinear	nonlinear	ADJ
cana-5662	1	5	analysis	analysis	NOUN
cana-5662	1	6	issn	issn	NOUN
cana-5662	1	7	:	:	PUNCT
cana-5662	1	8	1074	1074	NUM
cana-5662	1	9	-	-	PUNCT
cana-5662	1	10	133x	133x	NUM
cana-5662	1	11	vol	vol	NOUN
cana-5662	1	12	31	31	NUM
cana-5662	1	13	no	no	NOUN
cana-5662	1	14	.	.	PUNCT
cana-5662	2	1	7s	7	NOUN
cana-5662	2	2	(	(	PUNCT
cana-5662	2	3	2024	2024	NUM
cana-5662	2	4	)	)	PUNCT
cana-5662	2	5	753	753	NUM
cana-5662	3	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	3	2	complementary	complementary	ADJ
cana-5662	3	3	tree	tree	NOUN
cana-5662	3	4	domination	domination	NOUN
cana-5662	3	5	number	number	NOUN
cana-5662	3	6	of	of	ADP
cana-5662	3	7	corona	corona	NOUN
cana-5662	3	8	product	product	NOUN
cana-5662	3	9	of	of	ADP
cana-5662	3	10	complete	complete	ADJ
cana-5662	3	11	graph	graph	NOUN
cana-5662	3	12	with	with	ADP
cana-5662	3	13	some	some	DET
cana-5662	3	14	graphs	graph	NOUN
cana-5662	3	15	*	*	PUNCT
cana-5662	3	16	s.	s.	PROPN
cana-5662	3	17	jayalakshmi	jayalakshmi	PROPN
cana-5662	3	18	1	1	NUM
cana-5662	3	19	and	and	CCONJ
cana-5662	3	20	p.	p.	NOUN
cana-5662	3	21	vidhya2	vidhya2	NOUN
cana-5662	4	1	1research	1research	NUM
cana-5662	4	2	scholar	scholar	NOUN
cana-5662	4	3	(	(	PUNCT
cana-5662	4	4	part	part	NOUN
cana-5662	4	5	time	time	NOUN
cana-5662	4	6	)	)	PUNCT
cana-5662	4	7	,	,	PUNCT
cana-5662	4	8	school	school	NOUN
cana-5662	4	9	of	of	ADP
cana-5662	4	10	mathematics	mathematics	PROPN
cana-5662	4	11	madurai	madurai	PROPN
cana-5662	4	12	kamaraj	kamaraj	ADJ
cana-5662	4	13	university	university	NOUN
cana-5662	4	14	,	,	PUNCT
cana-5662	4	15	madurai	madurai	NOUN
cana-5662	4	16	625021	625021	NUM
cana-5662	4	17	,	,	PUNCT
cana-5662	4	18	tamilnadu	tamilnadu	NOUN
cana-5662	4	19	,	,	PUNCT
cana-5662	4	20	india	india	PROPN
cana-5662	4	21	e	e	PROPN
cana-5662	4	22	-	-	NOUN
cana-5662	4	23	mail	mail	NOUN
cana-5662	4	24	:	:	PUNCT
cana-5662	4	25	jayark83@gmail.com	jayark83@gmail.com	X
cana-5662	4	26	,	,	PUNCT
cana-5662	4	27	jayalakshmi.s1@sdnbvc.edu.in	jayalakshmi.s1@sdnbvc.edu.in	PROPN
cana-5662	4	28	2associate	2associate	NUM
cana-5662	4	29	professor	professor	NOUN
cana-5662	4	30	,	,	PUNCT
cana-5662	4	31	department	department	NOUN
cana-5662	4	32	of	of	ADP
cana-5662	4	33	mathematics	mathematics	PROPN
cana-5662	4	34	,	,	PUNCT
cana-5662	4	35	emg	emg	PROPN
cana-5662	4	36	yadava	yadava	PROPN
cana-5662	4	37	women	women	PROPN
cana-5662	4	38	’s	’s	PART
cana-5662	4	39	college	college	NOUN
cana-5662	4	40	madurai	madurai	PROPN
cana-5662	4	41	625014	625014	NUM
cana-5662	4	42	,	,	PUNCT
cana-5662	4	43	tamilnadu	tamilnadu	NOUN
cana-5662	4	44	,	,	PUNCT
cana-5662	4	45	india	india	PROPN
cana-5662	4	46	e	e	PROPN
cana-5662	4	47	-	-	NOUN
cana-5662	4	48	mail	mail	NOUN
cana-5662	4	49	:	:	PUNCT
cana-5662	4	50	vidhyaramman@gmail.com	vidhyaramman@gmail.com	X
cana-5662	4	51	,	,	PUNCT
cana-5662	4	52	p.vidhya-mat@emgywomenscollege.ac.in	p.vidhya-mat@emgywomenscollege.ac.in	NUM
cana-5662	4	53	article	article	NOUN
cana-5662	4	54	history	history	NOUN
cana-5662	4	55	:	:	PUNCT
cana-5662	4	56	received	receive	VERB
cana-5662	4	57	:	:	PUNCT
cana-5662	4	58	12	12	NUM
cana-5662	4	59	-	-	SYM
cana-5662	4	60	08	08	NUM
cana-5662	4	61	-	-	PUNCT
cana-5662	4	62	2024	2024	NUM
cana-5662	4	63	revised	revise	VERB
cana-5662	4	64	:	:	PUNCT
cana-5662	4	65	15	15	NUM
cana-5662	4	66	-	-	SYM
cana-5662	4	67	09	09	NUM
cana-5662	4	68	-	-	PUNCT
cana-5662	4	69	2024	2024	NUM
cana-5662	4	70	accepted	accept	VERB
cana-5662	4	71	:	:	PUNCT
cana-5662	4	72	25	25	NUM
cana-5662	4	73	-	-	SYM
cana-5662	4	74	10	10	NUM
cana-5662	4	75	-	-	PUNCT
cana-5662	4	76	2024	2024	NUM
cana-5662	4	77	abstract	abstract	NOUN
cana-5662	4	78	:	:	PUNCT
cana-5662	4	79	a	a	DET
cana-5662	4	80	set	set	NOUN
cana-5662	4	81	d	d	NOUN
cana-5662	4	82	of	of	ADP
cana-5662	4	83	a	a	DET
cana-5662	4	84	graph	graph	NOUN
cana-5662	4	85	g	g	NOUN
cana-5662	4	86	=	=	SYM
cana-5662	4	87	(	(	PUNCT
cana-5662	4	88	v	v	NOUN
cana-5662	4	89	,	,	PUNCT
cana-5662	4	90	e	e	NOUN
cana-5662	4	91	)	)	PUNCT
cana-5662	4	92	is	be	AUX
cana-5662	4	93	a	a	DET
cana-5662	4	94	dominating	dominating	NOUN
cana-5662	4	95	set	set	NOUN
cana-5662	4	96	,	,	PUNCT
cana-5662	4	97	if	if	SCONJ
cana-5662	4	98	every	every	DET
cana-5662	4	99	vertex	vertex	NOUN
cana-5662	4	100	in	in	ADP
cana-5662	4	101	v	v	NOUN
cana-5662	4	102	−	−	PROPN
cana-5662	5	1	d	d	NOUN
cana-5662	5	2	is	be	AUX
cana-5662	5	3	adjacent	adjacent	ADJ
cana-5662	5	4	to	to	ADP
cana-5662	5	5	some	some	DET
cana-5662	5	6	vertex	vertex	NOUN
cana-5662	5	7	in	in	ADP
cana-5662	5	8	d.	d.	PROPN
cana-5662	5	9	the	the	DET
cana-5662	5	10	domination	domination	NOUN
cana-5662	5	11	number	number	PROPN
cana-5662	5	12	γ(g	γ(g	PROPN
cana-5662	5	13	)	)	PUNCT
cana-5662	5	14	of	of	ADP
cana-5662	5	15	g	g	PROPN
cana-5662	5	16	is	be	AUX
cana-5662	5	17	the	the	DET
cana-5662	5	18	minimum	minimum	ADJ
cana-5662	5	19	cardinality	cardinality	NOUN
cana-5662	5	20	of	of	ADP
cana-5662	5	21	a	a	DET
cana-5662	5	22	dominating	dominating	NOUN
cana-5662	5	23	set	set	NOUN
cana-5662	5	24	.	.	PUNCT
cana-5662	6	1	a	a	DET
cana-5662	6	2	dominating	dominating	NOUN
cana-5662	6	3	set	set	NOUN
cana-5662	6	4	d	d	NOUN
cana-5662	6	5	is	be	AUX
cana-5662	6	6	called	call	VERB
cana-5662	6	7	a	a	DET
cana-5662	6	8	complementary	complementary	ADJ
cana-5662	6	9	tree	tree	NOUN
cana-5662	6	10	dominating	dominating	NOUN
cana-5662	6	11	set	set	VERB
cana-5662	6	12	if	if	SCONJ
cana-5662	6	13	the	the	DET
cana-5662	6	14	induced	induced	ADJ
cana-5662	6	15	subgraph	subgraph	NOUN
cana-5662	6	16	<	<	X
cana-5662	6	17	v	v	NOUN
cana-5662	6	18	−	−	PROPN
cana-5662	6	19	d	d	X
cana-5662	6	20	>	>	X
cana-5662	6	21	is	be	AUX
cana-5662	6	22	a	a	DET
cana-5662	6	23	tree	tree	NOUN
cana-5662	6	24	.	.	PUNCT
cana-5662	7	1	the	the	DET
cana-5662	7	2	minimum	minimum	ADJ
cana-5662	7	3	cardinality	cardinality	NOUN
cana-5662	7	4	of	of	ADP
cana-5662	7	5	a	a	DET
cana-5662	7	6	complementary	complementary	ADJ
cana-5662	7	7	tree	tree	NOUN
cana-5662	7	8	dominating	dominating	NOUN
cana-5662	7	9	set	set	NOUN
cana-5662	7	10	is	be	AUX
cana-5662	7	11	called	call	VERB
cana-5662	7	12	the	the	DET
cana-5662	7	13	complementary	complementary	ADJ
cana-5662	7	14	tree	tree	NOUN
cana-5662	7	15	domination	domination	NOUN
cana-5662	7	16	number	number	NOUN
cana-5662	7	17	of	of	ADP
cana-5662	7	18	g	g	NOUN
cana-5662	7	19	and	and	CCONJ
cana-5662	7	20	is	be	AUX
cana-5662	7	21	denoted	denote	VERB
cana-5662	7	22	by	by	ADP
cana-5662	7	23	γctd(g	γctd(g	PROPN
cana-5662	7	24	)	)	PUNCT
cana-5662	7	25	.	.	PUNCT
cana-5662	8	1	the	the	DET
cana-5662	8	2	corona	corona	NOUN
cana-5662	8	3	g1	g1	PROPN
cana-5662	8	4	◦	◦	PROPN
cana-5662	8	5	g2	g2	PROPN
cana-5662	8	6	of	of	ADP
cana-5662	8	7	two	two	NUM
cana-5662	8	8	graphs	graph	NOUN
cana-5662	8	9	g1	g1	NOUN
cana-5662	8	10	and	and	CCONJ
cana-5662	8	11	g2	g2	PROPN
cana-5662	8	12	are	be	AUX
cana-5662	8	13	defined	define	VERB
cana-5662	8	14	as	as	ADP
cana-5662	8	15	the	the	DET
cana-5662	8	16	graph	graph	NOUN
cana-5662	8	17	g	g	PROPN
cana-5662	8	18	obtained	obtain	VERB
cana-5662	8	19	by	by	ADP
cana-5662	8	20	taking	take	VERB
cana-5662	8	21	one	one	NUM
cana-5662	8	22	copy	copy	NOUN
cana-5662	8	23	of	of	ADP
cana-5662	8	24	g1	g1	NOUN
cana-5662	8	25	of	of	ADP
cana-5662	8	26	order	order	NOUN
cana-5662	8	27	p1	p1	NOUN
cana-5662	8	28	and	and	CCONJ
cana-5662	8	29	p1	p1	PROPN
cana-5662	8	30	copies	copy	NOUN
cana-5662	8	31	of	of	ADP
cana-5662	8	32	g2	g2	PROPN
cana-5662	8	33	and	and	CCONJ
cana-5662	8	34	then	then	ADV
cana-5662	8	35	joining	join	VERB
cana-5662	8	36	the	the	DET
cana-5662	8	37	ith	ith	PROPN
cana-5662	8	38	vertex	vertex	NOUN
cana-5662	8	39	of	of	ADP
cana-5662	8	40	g1	g1	PROPN
cana-5662	8	41	to	to	ADP
cana-5662	8	42	every	every	DET
cana-5662	8	43	vertex	vertex	NOUN
cana-5662	8	44	in	in	ADP
cana-5662	8	45	the	the	DET
cana-5662	8	46	ith	ith	PROPN
cana-5662	8	47	copy	copy	NOUN
cana-5662	8	48	of	of	ADP
cana-5662	8	49	g2	g2	PROPN
cana-5662	8	50	.	.	PUNCT
cana-5662	9	1	the	the	DET
cana-5662	9	2	corona	corona	NOUN
cana-5662	9	3	g1	g1	PROPN
cana-5662	9	4	◦	◦	PROPN
cana-5662	9	5	g2	g2	PROPN
cana-5662	9	6	has	have	VERB
cana-5662	9	7	p1(1	p1(1	PROPN
cana-5662	9	8	+	+	CCONJ
cana-5662	9	9	p2	p2	NOUN
cana-5662	9	10	)	)	PUNCT
cana-5662	9	11	vertices	vertex	NOUN
cana-5662	9	12	and	and	CCONJ
cana-5662	9	13	q1	q1	NOUN
cana-5662	9	14	+	+	CCONJ
cana-5662	9	15	p1q2	p1q2	PROPN
cana-5662	9	16	+	+	CCONJ
cana-5662	9	17	p1p2	p1p2	ADJ
cana-5662	9	18	edges	edge	NOUN
cana-5662	9	19	.	.	PUNCT
cana-5662	10	1	in	in	ADP
cana-5662	10	2	this	this	DET
cana-5662	10	3	paper	paper	NOUN
cana-5662	10	4	,	,	PUNCT
cana-5662	10	5	we	we	PRON
cana-5662	10	6	discussed	discuss	VERB
cana-5662	10	7	complementary	complementary	ADJ
cana-5662	10	8	tree	tree	NOUN
cana-5662	10	9	domination	domination	NOUN
cana-5662	10	10	number	number	NOUN
cana-5662	10	11	of	of	ADP
cana-5662	10	12	corona	corona	NOUN
cana-5662	10	13	product	product	NOUN
cana-5662	10	14	of	of	ADP
cana-5662	10	15	complete	complete	ADJ
cana-5662	10	16	graph	graph	NOUN
cana-5662	10	17	with	with	ADP
cana-5662	10	18	some	some	DET
cana-5662	10	19	graphs	graph	NOUN
cana-5662	10	20	.	.	PUNCT
cana-5662	11	1	ams	am	NOUN
cana-5662	11	2	subject	subject	ADJ
cana-5662	11	3	classification	classification	NOUN
cana-5662	11	4	:	:	PUNCT
cana-5662	11	5	05c69	05c69	X
cana-5662	11	6	.	.	PUNCT
cana-5662	12	1	keywords	keyword	NOUN
cana-5662	12	2	:	:	PUNCT
cana-5662	12	3	dominating	dominate	VERB
cana-5662	12	4	set	set	NOUN
cana-5662	12	5	,	,	PUNCT
cana-5662	12	6	complementary	complementary	ADJ
cana-5662	12	7	tree	tree	NOUN
cana-5662	12	8	domination	domination	NOUN
cana-5662	12	9	number.a	number.a	PROPN
cana-5662	12	10	subset	subset	NOUN
cana-5662	13	1	d	d	NOUN
cana-5662	13	2	of	of	ADP
cana-5662	13	3	the	the	DET
cana-5662	13	4	vertex	vertex	NOUN
cana-5662	13	5	set	set	VERB
cana-5662	13	6	v(g	v(g	PROPN
cana-5662	13	7	)	)	PUNCT
cana-5662	13	8	of	of	ADP
cana-5662	13	9	a	a	DET
cana-5662	13	10	graph	graph	NOUN
cana-5662	13	11	g	g	NOUN
cana-5662	13	12	is	be	AUX
cana-5662	13	13	said	say	VERB
cana-5662	13	14	to	to	PART
cana-5662	13	15	be	be	AUX
cana-5662	13	16	a	a	DET
cana-5662	13	17	dominating	dominating	NOUN
cana-5662	13	18	set	set	NOUN
cana-5662	13	19	if	if	SCONJ
cana-5662	13	20	every	every	DET
cana-5662	13	21	vertex	vertex	NOUN
cana-5662	13	22	not	not	PART
cana-5662	13	23	in	in	ADP
cana-5662	13	24	d	d	PROPN
cana-5662	13	25	is	be	AUX
cana-5662	13	26	adjacent	adjacent	ADJ
cana-5662	13	27	to	to	ADP
cana-5662	13	28	at	at	ADV
cana-5662	13	29	least	least	ADV
cana-5662	13	30	one	one	NUM
cana-5662	13	31	vertex	vertex	NOUN
cana-5662	13	32	in	in	ADP
cana-5662	13	33	d.	d.	PROPN
cana-5662	13	34	a	a	DET
cana-5662	13	35	dominating	dominating	NOUN
cana-5662	13	36	set	set	NOUN
cana-5662	13	37	d	d	NOUN
cana-5662	13	38	is	be	AUX
cana-5662	13	39	said	say	VERB
cana-5662	13	40	to	to	PART
cana-5662	13	41	be	be	AUX
cana-5662	13	42	an	an	DET
cana-5662	13	43	eccentric	eccentric	ADJ
cana-5662	13	44	dominating	dominating	NOUN
cana-5662	13	45	set	set	VERB
cana-5662	13	46	if	if	SCONJ
cana-5662	13	47	for	for	ADP
cana-5662	13	48	every	every	PRON
cana-5662	13	49	,	,	PUNCT
cana-5662	13	50	there	there	PRON
cana-5662	13	51	exists	exist	VERB
cana-5662	13	52	at	at	ADP
cana-5662	13	53	least	least	ADV
cana-5662	13	54	one	one	NUM
cana-5662	13	55	eccentric	eccentric	ADJ
cana-5662	13	56	point	point	NOUN
cana-5662	13	57	of	of	ADP
cana-5662	13	58	v	v	NOUN
cana-5662	13	59	in	in	ADP
cana-5662	13	60	d.	d.	PROPN
cana-5662	13	61	an	an	DET
cana-5662	13	62	eccentric	eccentric	ADJ
cana-5662	13	63	dominating	dominating	NOUN
cana-5662	13	64	set	set	NOUN
cana-5662	13	65	d	d	NOUN
cana-5662	13	66	of	of	ADP
cana-5662	13	67	g	g	PROPN
cana-5662	13	68	is	be	AUX
cana-5662	13	69	a	a	DET
cana-5662	13	70	non	non	NOUN
cana-5662	13	71	split	split	ADJ
cana-5662	13	72	eccentric	eccentric	ADJ
cana-5662	13	73	dominating	dominating	NOUN
cana-5662	13	74	set	set	NOUN
cana-5662	13	75	if	if	SCONJ
cana-5662	13	76	the	the	DET
cana-5662	13	77	induced	induced	ADJ
cana-5662	13	78	sub	sub	NOUN
cana-5662	13	79	graph	graph	NOUN
cana-5662	13	80	<	<	X
cana-5662	13	81	vd	vd	X
cana-5662	13	82	>	>	X
cana-5662	13	83	is	be	AUX
cana-5662	13	84	connected	connect	VERB
cana-5662	13	85	.	.	PUNCT
cana-5662	14	1	the	the	DET
cana-5662	14	2	minimum	minimum	NOUN
cana-5662	14	3	of	of	ADP
cana-5662	14	4	the	the	DET
cana-5662	14	5	cardinalities	cardinality	NOUN
cana-5662	14	6	of	of	ADP
cana-5662	14	7	the	the	DET
cana-5662	14	8	non	non	NOUN
cana-5662	14	9	split	split	ADJ
cana-5662	14	10	eccentric	eccentric	ADJ
cana-5662	14	11	dominating	dominating	NOUN
cana-5662	14	12	sets	set	NOUN
cana-5662	14	13	of	of	ADP
cana-5662	14	14	g	g	PROPN
cana-5662	14	15	is	be	AUX
cana-5662	14	16	called	call	VERB
cana-5662	14	17	the	the	DET
cana-5662	14	18	non	non	NOUN
cana-5662	14	19	split	split	ADJ
cana-5662	14	20	eccentric	eccentric	ADJ
cana-5662	14	21	domination	domination	NOUN
cana-5662	14	22	number	number	NOUN
cana-5662	14	23	of	of	ADP
cana-5662	14	24	g.	g.	PROPN
cana-5662	14	25	this	this	DET
cana-5662	14	26	paper	paper	NOUN
cana-5662	14	27	evaluates	evaluate	VERB
cana-5662	14	28	the	the	DET
cana-5662	14	29	non	non	NOUN
cana-5662	14	30	split	split	VERB
cana-5662	14	31	eccentric	eccentric	ADJ
cana-5662	14	32	domination	domination	NOUN
cana-5662	14	33	number	number	NOUN
cana-5662	14	34	of	of	ADP
cana-5662	14	35	corona	corona	NOUN
cana-5662	14	36	product	product	NOUN
cana-5662	14	37	and	and	CCONJ
cana-5662	14	38	join	join	NOUN
cana-5662	14	39	of	of	ADP
cana-5662	14	40	some	some	DET
cana-5662	14	41	standard	standard	ADJ
cana-5662	14	42	graphs	graph	NOUN
cana-5662	14	43	.	.	PUNCT
cana-5662	15	1	keywords	keyword	NOUN
cana-5662	15	2	:	:	PUNCT
cana-5662	15	3	domination	domination	NOUN
cana-5662	15	4	,	,	PUNCT
cana-5662	15	5	eccentric	eccentric	ADJ
cana-5662	15	6	domination	domination	NOUN
cana-5662	15	7	,	,	PUNCT
cana-5662	15	8	non	non	X
cana-5662	15	9	split	split	VERB
cana-5662	15	10	eccentric	eccentric	ADJ
cana-5662	15	11	domination	domination	NOUN
cana-5662	15	12	,	,	PUNCT
cana-5662	15	13	corona	corona	NOUN
cana-5662	15	14	product	product	NOUN
cana-5662	15	15	,	,	PUNCT
cana-5662	15	16	join	join	VERB
cana-5662	15	17	.	.	PUNCT
cana-5662	16	1	1	1	NUM
cana-5662	16	2	introduction	introduction	NOUN
cana-5662	16	3	a	a	DET
cana-5662	16	4	graph	graph	NOUN
cana-5662	16	5	g(v	g(v	NOUN
cana-5662	16	6	,	,	PUNCT
cana-5662	16	7	e	e	NOUN
cana-5662	16	8	)	)	PUNCT
cana-5662	16	9	discussed	discuss	VERB
cana-5662	16	10	in	in	ADP
cana-5662	16	11	this	this	DET
cana-5662	16	12	paper	paper	NOUN
cana-5662	16	13	be	be	AUX
cana-5662	16	14	a	a	DET
cana-5662	16	15	simple	simple	ADJ
cana-5662	16	16	,	,	PUNCT
cana-5662	16	17	finite	finite	ADJ
cana-5662	16	18	,	,	PUNCT
cana-5662	16	19	undirected	undirected	ADJ
cana-5662	16	20	,	,	PUNCT
cana-5662	16	21	connected	connected	ADJ
cana-5662	16	22	graph	graph	NOUN
cana-5662	16	23	with	with	ADP
cana-5662	16	24	p	p	NOUN
cana-5662	16	25	vertices	vertex	NOUN
cana-5662	16	26	and	and	CCONJ
cana-5662	16	27	q	q	NOUN
cana-5662	16	28	edges	edge	NOUN
cana-5662	16	29	.	.	PUNCT
cana-5662	17	1	roberto	roberto	PROPN
cana-5662	17	2	frucht	frucht	PROPN
cana-5662	17	3	and	and	CCONJ
cana-5662	17	4	frank	frank	ADJ
cana-5662	17	5	harary	harary	NOUN
cana-5662	18	1	[	[	X
cana-5662	18	2	1	1	X
cana-5662	18	3	]	]	PUNCT
cana-5662	18	4	introduced	introduce	VERB
cana-5662	18	5	the	the	DET
cana-5662	18	6	binary	binary	ADJ
cana-5662	18	7	product	product	NOUN
cana-5662	18	8	of	of	ADP
cana-5662	18	9	two	two	NUM
cana-5662	18	10	graphs	graph	NOUN
cana-5662	18	11	named	name	VERB
cana-5662	18	12	corona	corona	NOUN
cana-5662	18	13	in	in	ADP
cana-5662	18	14	1970	1970	NUM
cana-5662	18	15	.	.	PUNCT
cana-5662	19	1	the	the	DET
cana-5662	19	2	corona	corona	NOUN
cana-5662	19	3	g1	g1	PROPN
cana-5662	19	4	◦	◦	PROPN
cana-5662	19	5	g2	g2	PROPN
cana-5662	19	6	of	of	ADP
cana-5662	19	7	two	two	NUM
cana-5662	19	8	graphs	graph	NOUN
cana-5662	19	9	g1	g1	NOUN
cana-5662	19	10	and	and	CCONJ
cana-5662	19	11	g2	g2	PROPN
cana-5662	19	12	are	be	AUX
cana-5662	19	13	defined	define	VERB
cana-5662	19	14	as	as	ADP
cana-5662	19	15	the	the	DET
cana-5662	19	16	graph	graph	NOUN
cana-5662	19	17	g	g	PROPN
cana-5662	19	18	obtained	obtain	VERB
cana-5662	19	19	by	by	ADP
cana-5662	19	20	taking	take	VERB
cana-5662	19	21	one	one	NUM
cana-5662	19	22	copy	copy	NOUN
cana-5662	19	23	of	of	ADP
cana-5662	19	24	g1	g1	NOUN
cana-5662	19	25	of	of	ADP
cana-5662	19	26	order	order	NOUN
cana-5662	19	27	p1	p1	NOUN
cana-5662	19	28	and	and	CCONJ
cana-5662	19	29	p1	p1	PROPN
cana-5662	19	30	copies	copy	NOUN
cana-5662	19	31	of	of	ADP
cana-5662	19	32	g2	g2	PROPN
cana-5662	19	33	and	and	CCONJ
cana-5662	19	34	then	then	ADV
cana-5662	19	35	joining	join	VERB
cana-5662	19	36	the	the	DET
cana-5662	19	37	ith	ith	PROPN
cana-5662	19	38	vertex	vertex	NOUN
cana-5662	19	39	of	of	ADP
cana-5662	19	40	g1	g1	PROPN
cana-5662	19	41	to	to	ADP
cana-5662	19	42	every	every	DET
cana-5662	19	43	vertex	vertex	NOUN
cana-5662	19	44	in	in	ADP
cana-5662	19	45	the	the	DET
cana-5662	19	46	ith	ith	PROPN
cana-5662	19	47	copy	copy	NOUN
cana-5662	19	48	of	of	ADP
cana-5662	19	49	g2	g2	PROPN
cana-5662	19	50	.	.	PUNCT
cana-5662	20	1	the	the	DET
cana-5662	20	2	corona	corona	NOUN
cana-5662	20	3	g1	g1	PROPN
cana-5662	20	4	◦	◦	PROPN
cana-5662	20	5	g2	g2	PROPN
cana-5662	20	6	has	have	VERB
cana-5662	20	7	p1(1	p1(1	PROPN
cana-5662	20	8	+	+	CCONJ
cana-5662	20	9	p2	p2	NOUN
cana-5662	20	10	)	)	PUNCT
cana-5662	20	11	vertices	vertex	NOUN
cana-5662	20	12	and	and	CCONJ
cana-5662	20	13	q1	q1	NOUN
cana-5662	20	14	+	+	CCONJ
cana-5662	20	15	p1q2	p1q2	PROPN
cana-5662	20	16	+	+	CCONJ
cana-5662	20	17	p1p2	p1p2	ADJ
cana-5662	20	18	edges	edge	NOUN
cana-5662	20	19	.	.	PUNCT
cana-5662	21	1	the	the	DET
cana-5662	21	2	concept	concept	NOUN
cana-5662	21	3	of	of	ADP
cana-5662	21	4	domination	domination	NOUN
cana-5662	21	5	in	in	ADP
cana-5662	21	6	graphs	graph	NOUN
cana-5662	21	7	was	be	AUX
cana-5662	21	8	introduced	introduce	VERB
cana-5662	21	9	by	by	ADP
cana-5662	21	10	ore	ore	NOUN
cana-5662	21	11	[	[	X
cana-5662	21	12	4	4	NUM
cana-5662	21	13	]	]	PUNCT
cana-5662	21	14	.	.	PUNCT
cana-5662	22	1	a	a	DET
cana-5662	22	2	set	set	NOUN
cana-5662	22	3	d	d	PROPN
cana-5662	22	4			PROPN
cana-5662	22	5	v	v	PROPN
cana-5662	22	6	is	be	AUX
cana-5662	22	7	said	say	VERB
cana-5662	22	8	to	to	PART
cana-5662	22	9	be	be	AUX
cana-5662	22	10	a	a	DET
cana-5662	22	11	dominating	dominating	NOUN
cana-5662	22	12	set	set	NOUN
cana-5662	22	13	of	of	ADP
cana-5662	22	14	g	g	NOUN
cana-5662	22	15	,	,	PUNCT
cana-5662	22	16	if	if	SCONJ
cana-5662	22	17	every	every	DET
cana-5662	22	18	vertex	vertex	NOUN
cana-5662	22	19	in	in	ADP
cana-5662	22	20	v	v	NOUN
cana-5662	22	21	-	-	SYM
cana-5662	22	22	d	d	NOUN
cana-5662	22	23	is	be	AUX
cana-5662	22	24	adjacent	adjacent	ADJ
cana-5662	22	25	to	to	ADP
cana-5662	22	26	some	some	DET
cana-5662	22	27	vertex	vertex	NOUN
cana-5662	22	28	in	in	ADP
cana-5662	22	29	d.	d.	PROPN
cana-5662	22	30	the	the	DET
cana-5662	22	31	minimum	minimum	ADJ
cana-5662	22	32	cardinality	cardinality	NOUN
cana-5662	22	33	of	of	ADP
cana-5662	22	34	a	a	DET
cana-5662	22	35	dominating	dominating	NOUN
cana-5662	22	36	set	set	NOUN
cana-5662	22	37	is	be	AUX
cana-5662	22	38	called	call	VERB
cana-5662	22	39	the	the	DET
cana-5662	22	40	domination	domination	NOUN
cana-5662	22	41	number	number	NOUN
cana-5662	22	42	of	of	ADP
cana-5662	22	43	g	g	NOUN
cana-5662	22	44	and	and	CCONJ
cana-5662	22	45	is	be	AUX
cana-5662	22	46	communications	communication	NOUN
cana-5662	22	47	on	on	ADP
cana-5662	22	48	applied	apply	VERB
cana-5662	22	49	nonlinear	nonlinear	ADJ
cana-5662	22	50	analysis	analysis	NOUN
cana-5662	22	51	issn	issn	NOUN
cana-5662	22	52	:	:	PUNCT
cana-5662	22	53	1074	1074	NUM
cana-5662	22	54	-	-	PUNCT
cana-5662	22	55	133x	133x	NUM
cana-5662	22	56	vol	vol	NOUN
cana-5662	22	57	31	31	NUM
cana-5662	22	58	no	no	NOUN
cana-5662	22	59	.	.	PUNCT
cana-5662	23	1	7s	7	NOUN
cana-5662	23	2	(	(	PUNCT
cana-5662	23	3	2024	2024	NUM
cana-5662	23	4	)	)	PUNCT
cana-5662	23	5	754	754	NUM
cana-5662	23	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	23	7	2	2	NUM
cana-5662	23	8	denoted	denote	VERB
cana-5662	23	9	by	by	ADP
cana-5662	23	10	γ(g	γ(g	PROPN
cana-5662	23	11	)	)	PUNCT
cana-5662	23	12	.	.	PUNCT
cana-5662	24	1	the	the	DET
cana-5662	24	2	complementary	complementary	ADJ
cana-5662	24	3	tree	tree	NOUN
cana-5662	24	4	domination	domination	NOUN
cana-5662	24	5	number	number	NOUN
cana-5662	24	6	of	of	ADP
cana-5662	24	7	a	a	DET
cana-5662	24	8	graph	graph	NOUN
cana-5662	24	9	was	be	AUX
cana-5662	24	10	introduced	introduce	VERB
cana-5662	24	11	by	by	ADP
cana-5662	24	12	s.	s.	PROPN
cana-5662	24	13	muthammai	muthammai	PROPN
cana-5662	24	14	,	,	PUNCT
cana-5662	24	15	m.	m.	NOUN
cana-5662	24	16	bhanumathi	bhanumathi	NOUN
cana-5662	24	17	and	and	CCONJ
cana-5662	24	18	p.	p.	NOUN
cana-5662	24	19	vidhya	vidhya	PROPN
cana-5662	25	1	[	[	X
cana-5662	25	2	3	3	X
cana-5662	25	3	]	]	PUNCT
cana-5662	25	4	have	have	AUX
cana-5662	25	5	established	establish	VERB
cana-5662	25	6	some	some	DET
cana-5662	25	7	results	result	NOUN
cana-5662	25	8	on	on	ADP
cana-5662	25	9	complementary	complementary	ADJ
cana-5662	25	10	tree	tree	NOUN
cana-5662	25	11	domination	domination	NOUN
cana-5662	25	12	number	number	NOUN
cana-5662	25	13	of	of	ADP
cana-5662	25	14	graphs	graph	NOUN
cana-5662	25	15	.	.	PUNCT
cana-5662	26	1	a	a	DET
cana-5662	26	2	set	set	NOUN
cana-5662	26	3	d	d	PROPN
cana-5662	26	4	v	v	PROPN
cana-5662	26	5	(	(	PUNCT
cana-5662	26	6	g	g	NOUN
cana-5662	26	7	)	)	PUNCT
cana-5662	26	8	is	be	AUX
cana-5662	26	9	said	say	VERB
cana-5662	26	10	to	to	PART
cana-5662	26	11	be	be	AUX
cana-5662	26	12	complementary	complementary	ADJ
cana-5662	26	13	tree	tree	NOUN
cana-5662	26	14	dominating	dominating	NOUN
cana-5662	26	15	set	set	NOUN
cana-5662	26	16	(	(	PUNCT
cana-5662	26	17	ctd	ctd	NOUN
cana-5662	26	18	-	-	PUNCT
cana-5662	26	19	set	set	NOUN
cana-5662	26	20	)	)	PUNCT
cana-5662	26	21	if	if	SCONJ
cana-5662	26	22	the	the	DET
cana-5662	26	23	induced	induced	ADJ
cana-5662	26	24	subgraph	subgraph	NOUN
cana-5662	26	25	<	<	X
cana-5662	26	26	v(g)-d	v(g)-d	X
cana-5662	26	27	>	>	X
cana-5662	26	28	is	be	AUX
cana-5662	26	29	a	a	DET
cana-5662	26	30	tree	tree	NOUN
cana-5662	26	31	.	.	PUNCT
cana-5662	27	1	the	the	DET
cana-5662	27	2	minimum	minimum	ADJ
cana-5662	27	3	cardinality	cardinality	NOUN
cana-5662	27	4	of	of	ADP
cana-5662	27	5	a	a	DET
cana-5662	27	6	ctd	ctd	NOUN
cana-5662	27	7	-	-	PUNCT
cana-5662	27	8	set	set	NOUN
cana-5662	27	9	is	be	AUX
cana-5662	27	10	called	call	VERB
cana-5662	27	11	the	the	DET
cana-5662	27	12	complementary	complementary	ADJ
cana-5662	27	13	tree	tree	NOUN
cana-5662	27	14	domination	domination	NOUN
cana-5662	27	15	number	number	NOUN
cana-5662	27	16	of	of	ADP
cana-5662	27	17	g	g	NOUN
cana-5662	27	18	and	and	CCONJ
cana-5662	27	19	is	be	AUX
cana-5662	27	20	denoted	denote	VERB
cana-5662	27	21	by	by	ADP
cana-5662	27	22	γctd(g	γctd(g	PROPN
cana-5662	27	23	)	)	PUNCT
cana-5662	27	24	.	.	PUNCT
cana-5662	28	1	sergio	sergio	PROPN
cana-5662	28	2	canoy	canoy	PROPN
cana-5662	28	3	jr	jr	PROPN
cana-5662	28	4	and	and	CCONJ
cana-5662	28	5	carmelito	carmelito	PROPN
cana-5662	28	6	e.go	e.go	PROPN
cana-5662	29	1	[	[	X
cana-5662	29	2	5	5	NUM
cana-5662	29	3	]	]	PUNCT
cana-5662	29	4	have	have	AUX
cana-5662	29	5	obtained	obtain	VERB
cana-5662	29	6	the	the	DET
cana-5662	29	7	domination	domination	NOUN
cana-5662	29	8	number	number	NOUN
cana-5662	29	9	of	of	ADP
cana-5662	29	10	corona	corona	NOUN
cana-5662	29	11	graphs	graph	NOUN
cana-5662	29	12	.	.	PUNCT
cana-5662	30	1	any	any	DET
cana-5662	30	2	undefined	undefined	ADJ
cana-5662	30	3	term	term	NOUN
cana-5662	30	4	in	in	ADP
cana-5662	30	5	this	this	DET
cana-5662	30	6	paper	paper	NOUN
cana-5662	30	7	may	may	AUX
cana-5662	30	8	be	be	AUX
cana-5662	30	9	found	find	VERB
cana-5662	30	10	in	in	ADP
cana-5662	30	11	harary[2	harary[2	PROPN
cana-5662	30	12	]	]	PUNCT
cana-5662	30	13	for	for	ADP
cana-5662	30	14	notation	notation	NOUN
cana-5662	30	15	convenience	convenience	NOUN
cana-5662	30	16	vg2	vg2	NOUN
cana-5662	30	17	be	be	AUX
cana-5662	30	18	a	a	DET
cana-5662	30	19	copy	copy	NOUN
cana-5662	30	20	of	of	ADP
cana-5662	30	21	g2	g2	PROPN
cana-5662	30	22	corresponding	correspond	VERB
cana-5662	30	23	to	to	ADP
cana-5662	30	24	the	the	DET
cana-5662	30	25	vertex	vertex	NOUN
cana-5662	30	26	(	(	PUNCT
cana-5662	30	27	)	)	PUNCT
cana-5662	30	28	.1gvv	.1gvv	PUNCT
cana-5662	31	1	also	also	ADV
cana-5662	31	2	jiu	jiu	PROPN
cana-5662	31	3	be	be	AUX
cana-5662	31	4	the	the	DET
cana-5662	31	5	vertex	vertex	NOUN
cana-5662	31	6	of	of	ADP
cana-5662	31	7	g	g	NOUN
cana-5662	31	8	which	which	PRON
cana-5662	31	9	are	be	AUX
cana-5662	31	10	adjacent	adjacent	ADJ
cana-5662	31	11	to	to	ADP
cana-5662	31	12	the	the	DET
cana-5662	31	13	vertex	vertex	NOUN
cana-5662	31	14	(	(	PUNCT
cana-5662	31	15	)	)	PUNCT
cana-5662	31	16	.1gvvi	.1gvvi	SYM
cana-5662	31	17			NOUN
cana-5662	31	18	in	in	ADP
cana-5662	31	19	this	this	DET
cana-5662	31	20	paper	paper	NOUN
cana-5662	31	21	we	we	PRON
cana-5662	31	22	discussed	discuss	VERB
cana-5662	31	23	complementary	complementary	ADJ
cana-5662	31	24	tree	tree	NOUN
cana-5662	31	25	domination	domination	NOUN
cana-5662	31	26	number	number	NOUN
cana-5662	31	27	of	of	ADP
cana-5662	31	28	corona	corona	NOUN
cana-5662	31	29	product	product	NOUN
cana-5662	31	30	of	of	ADP
cana-5662	31	31	complete	complete	ADJ
cana-5662	31	32	graph	graph	NOUN
cana-5662	31	33	and	and	CCONJ
cana-5662	31	34	their	their	PRON
cana-5662	31	35	bounds	bound	NOUN
cana-5662	31	36	are	be	AUX
cana-5662	31	37	determined	determine	VERB
cana-5662	31	38	.	.	PUNCT
cana-5662	32	1	2	2	NUM
cana-5662	32	2	prior	prior	ADJ
cana-5662	32	3	results	result	NOUN
cana-5662	32	4	observation	observation	VERB
cana-5662	32	5	2.1	2.1	NUM
cana-5662	32	6	.	.	PUNCT
cana-5662	33	1	[	[	X
cana-5662	33	2	3	3	X
cana-5662	33	3	]	]	PUNCT
cana-5662	33	4	(	(	PUNCT
cana-5662	33	5	i	i	NOUN
cana-5662	33	6	)	)	PUNCT
cana-5662	33	7	for	for	ADP
cana-5662	33	8	any	any	DET
cana-5662	33	9	path	path	NOUN
cana-5662	33	10	pn	pn	NOUN
cana-5662	33	11	with	with	ADP
cana-5662	33	12	n	n	ADP
cana-5662	33	13	vertices	vertex	NOUN
cana-5662	33	14	,	,	PUNCT
cana-5662	33	15	γctd(pn	γctd(pn	NOUN
cana-5662	33	16	)	)	PUNCT
cana-5662	33	17	=	=	PUNCT
cana-5662	33	18	n	n	CCONJ
cana-5662	33	19	−	−	NUM
cana-5662	33	20	2	2	NUM
cana-5662	33	21	,	,	PUNCT
cana-5662	33	22	n	n	PRON
cana-5662	33	23	≥	≥	NOUN
cana-5662	33	24	4	4	NUM
cana-5662	33	25	.	.	PUNCT
cana-5662	33	26	(	(	PUNCT
cana-5662	33	27	ii	ii	NOUN
cana-5662	33	28	)	)	PUNCT
cana-5662	33	29	for	for	ADP
cana-5662	33	30	any	any	DET
cana-5662	33	31	cycle	cycle	NOUN
cana-5662	33	32	cn	cn	VERB
cana-5662	33	33	with	with	ADP
cana-5662	33	34	n	n	ADP
cana-5662	33	35	vertices	vertex	NOUN
cana-5662	33	36	,	,	PUNCT
cana-5662	33	37	γctd(cn	γctd(cn	NOUN
cana-5662	33	38	)	)	PUNCT
cana-5662	33	39	=	=	SYM
cana-5662	33	40	n	n	CCONJ
cana-5662	33	41	−	−	NUM
cana-5662	33	42	2	2	NUM
cana-5662	33	43	,	,	PUNCT
cana-5662	33	44	n	n	X
cana-5662	33	45	≥	≥	NOUN
cana-5662	33	46	3	3	NUM
cana-5662	33	47	.	.	PUNCT
cana-5662	33	48	(	(	PUNCT
cana-5662	33	49	iii	iii	NOUN
cana-5662	33	50	)	)	PUNCT
cana-5662	33	51	for	for	ADP
cana-5662	33	52	any	any	DET
cana-5662	33	53	complete	complete	ADJ
cana-5662	33	54	graph	graph	NOUN
cana-5662	33	55	kn	kn	PROPN
cana-5662	33	56	with	with	ADP
cana-5662	33	57	n	n	SYM
cana-5662	33	58	vertices	vertex	NOUN
cana-5662	33	59	,	,	PUNCT
cana-5662	33	60	γctd(kn	γctd(kn	NOUN
cana-5662	33	61	)	)	PUNCT
cana-5662	33	62	=	=	SYM
cana-5662	33	63	n	n	CCONJ
cana-5662	33	64	−	−	NUM
cana-5662	33	65	2	2	NUM
cana-5662	33	66	,	,	PUNCT
cana-5662	33	67	n	n	X
cana-5662	33	68	≥	≥	NOUN
cana-5662	33	69	3	3	NUM
cana-5662	33	70	.	.	PUNCT
cana-5662	34	1	(	(	PUNCT
cana-5662	34	2	iv	iv	X
cana-5662	34	3	)	)	PUNCT
cana-5662	34	4	for	for	ADP
cana-5662	34	5	any	any	DET
cana-5662	34	6	star	star	NOUN
cana-5662	34	7	k1,n	k1,n	PROPN
cana-5662	34	8	,	,	PUNCT
cana-5662	34	9	γctd(k1,n	γctd(k1,n	NOUN
cana-5662	34	10	)	)	PUNCT
cana-5662	34	11	=	=	SYM
cana-5662	35	1	n	n	X
cana-5662	35	2	,	,	PUNCT
cana-5662	35	3	n	n	X
cana-5662	35	4	≥	≥	NOUN
cana-5662	35	5	2	2	NUM
cana-5662	35	6	.	.	PUNCT
cana-5662	36	1	(	(	PUNCT
cana-5662	36	2	v)for	v)for	ADP
cana-5662	36	3	any	any	DET
cana-5662	36	4	complete	complete	ADJ
cana-5662	36	5	bipartite	bipartite	NOUN
cana-5662	36	6	graph	graph	NOUN
cana-5662	36	7	km	km	PROPN
cana-5662	36	8	,	,	PUNCT
cana-5662	36	9	n	n	CCONJ
cana-5662	36	10	with	with	ADP
cana-5662	36	11	m	m	PRON
cana-5662	36	12	,	,	PUNCT
cana-5662	36	13	n	n	PRON
cana-5662	36	14	≥	≥	NOUN
cana-5662	36	15	2	2	NUM
cana-5662	36	16	,	,	PUNCT
cana-5662	36	17	γctd(km	γctd(km	NOUN
cana-5662	36	18	,	,	PUNCT
cana-5662	36	19	n	n	CCONJ
cana-5662	36	20	)	)	PUNCT
cana-5662	36	21	=	=	SYM
cana-5662	36	22	min{m	min{m	PROPN
cana-5662	36	23	,	,	PUNCT
cana-5662	36	24	n	n	CCONJ
cana-5662	36	25	}	}	PUNCT
cana-5662	36	26	.	.	PUNCT
cana-5662	37	1	(	(	PUNCT
cana-5662	37	2	vi	vi	X
cana-5662	37	3	)	)	PUNCT
cana-5662	37	4	γctd(cn	γctd(cn	PROPN
cana-5662	37	5	◦	◦	NOUN
cana-5662	37	6	k1	k1	NOUN
cana-5662	37	7	)	)	PUNCT
cana-5662	37	8	=	=	SYM
cana-5662	38	1	n	n	PROPN
cana-5662	38	2	+	+	NUM
cana-5662	38	3	1	1	NUM
cana-5662	38	4	,	,	PUNCT
cana-5662	38	5	n	n	PRON
cana-5662	38	6	≥	≥	NOUN
cana-5662	38	7	3	3	NUM
cana-5662	38	8	,	,	PUNCT
cana-5662	38	9	where	where	SCONJ
cana-5662	38	10	cn	cn	PROPN
cana-5662	38	11	◦	◦	PROPN
cana-5662	38	12	k1	k1	PROPN
cana-5662	38	13	is	be	AUX
cana-5662	38	14	the	the	DET
cana-5662	38	15	corona	corona	NOUN
cana-5662	38	16	of	of	ADP
cana-5662	38	17	cn	cn	PROPN
cana-5662	38	18	and	and	CCONJ
cana-5662	38	19	k1	k1	PROPN
cana-5662	38	20	.	.	PUNCT
cana-5662	39	1	(	(	PUNCT
cana-5662	39	2	vii	vii	PROPN
cana-5662	39	3	)	)	PUNCT
cana-5662	39	4	for	for	ADP
cana-5662	39	5	any	any	DET
cana-5662	39	6	wheel	wheel	NOUN
cana-5662	39	7	wn	wn	NOUN
cana-5662	39	8	with	with	ADP
cana-5662	39	9	n	n	ADP
cana-5662	39	10	vertices	vertex	NOUN
cana-5662	39	11	,	,	PUNCT
cana-5662	39	12	γctd(wn	γctd(wn	NUM
cana-5662	39	13	)	)	PUNCT
cana-5662	39	14	=	=	SYM
cana-5662	39	15	2	2	NUM
cana-5662	39	16	,	,	PUNCT
cana-5662	39	17	n	n	PRON
cana-5662	39	18	≥	≥	NOUN
cana-5662	39	19	4	4	NUM
cana-5662	39	20	.	.	PUNCT
cana-5662	40	1	preposition	preposition	NOUN
cana-5662	40	2	2.2	2.2	NUM
cana-5662	40	3	.	.	PUNCT
cana-5662	41	1	[	[	X
cana-5662	41	2	3	3	X
cana-5662	41	3	]	]	X
cana-5662	41	4	if	if	SCONJ
cana-5662	41	5	(	(	PUNCT
cana-5662	41	6	)	)	PUNCT
cana-5662	41	7	,	,	PUNCT
cana-5662	41	8	2−	2−	NUM
cana-5662	41	9	pgctd	pgctd	NOUN
cana-5662	41	10	then	then	ADV
cana-5662	41	11	pendant	pendant	ADJ
cana-5662	41	12	vertices	vertex	NOUN
cana-5662	41	13	are	be	AUX
cana-5662	41	14	the	the	DET
cana-5662	41	15	members	member	NOUN
cana-5662	41	16	of	of	ADP
cana-5662	41	17	every	every	DET
cana-5662	41	18	ctd	ctd	NOUN
cana-5662	41	19	-	-	PUNCT
cana-5662	41	20	set	set	NOUN
cana-5662	41	21	.	.	PUNCT
cana-5662	41	22	example	example	NOUN
cana-5662	42	1	2.3	2.3	NUM
cana-5662	42	2	.	.	PUNCT
cana-5662	43	1	1v	1v	NUM
cana-5662	43	2	4v	4v	NUM
cana-5662	43	3	1u	1u	PROPN
cana-5662	43	4	2u	2u	PROPN
cana-5662	43	5	2v	2v	PROPN
cana-5662	43	6	3v	3v	PROPN
cana-5662	43	7	g1	g1	PROPN
cana-5662	43	8	g2	g2	PROPN
cana-5662	43	9	communications	communication	NOUN
cana-5662	43	10	on	on	ADP
cana-5662	43	11	applied	apply	VERB
cana-5662	43	12	nonlinear	nonlinear	ADJ
cana-5662	43	13	analysis	analysis	NOUN
cana-5662	43	14	issn	issn	NOUN
cana-5662	43	15	:	:	PUNCT
cana-5662	43	16	1074	1074	NUM
cana-5662	43	17	-	-	PUNCT
cana-5662	43	18	133x	133x	NUM
cana-5662	43	19	vol	vol	NOUN
cana-5662	43	20	31	31	NUM
cana-5662	43	21	no	no	NOUN
cana-5662	43	22	.	.	PUNCT
cana-5662	44	1	7s	7	NOUN
cana-5662	44	2	(	(	PUNCT
cana-5662	44	3	2024	2024	NUM
cana-5662	44	4	)	)	PUNCT
cana-5662	44	5	755	755	NUM
cana-5662	44	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	44	7	12u	12u	NUM
cana-5662	44	8	41u	41u	PROPN
cana-5662	44	9	11u	11u	PROPN
cana-5662	44	10	42u	42u	PROPN
cana-5662	44	11	1v	1v	NUM
cana-5662	44	12	4v	4v	NUM
cana-5662	44	13	2v	2v	PROPN
cana-5662	44	14	3v	3v	NUM
cana-5662	44	15	32u	32u	NUM
cana-5662	44	16	21u	21u	NOUN
cana-5662	44	17	22u	22u	NUM
cana-5662	44	18	31u	31u	NUM
cana-5662	44	19	21	21	NUM
cana-5662	44	20	gg	gg	NOUN
cana-5662	44	21			PROPN
cana-5662	44	22	figure	figure	VERB
cana-5662	44	23	1	1	NUM
cana-5662	44	24	:	:	PUNCT
cana-5662	44	25	for	for	ADP
cana-5662	44	26	the	the	DET
cana-5662	44	27	graph	graph	NOUN
cana-5662	44	28	g1	g1	PROPN
cana-5662	44	29	◦	◦	PROPN
cana-5662	44	30	g2	g2	PROPN
cana-5662	44	31	given	give	VERB
cana-5662	44	32	in	in	ADP
cana-5662	44	33	figure	figure	NOUN
cana-5662	44	34	1	1	NUM
cana-5662	44	35	.	.	PUNCT
cana-5662	45	1	in	in	ADP
cana-5662	45	2	the	the	DET
cana-5662	45	3	following	following	NOUN
cana-5662	45	4	,	,	PUNCT
cana-5662	45	5	a	a	DET
cana-5662	45	6	necessary	necessary	ADJ
cana-5662	45	7	and	and	CCONJ
cana-5662	45	8	sufficient	sufficient	ADJ
cana-5662	45	9	condition	condition	NOUN
cana-5662	45	10	for	for	ADP
cana-5662	45	11	a	a	DET
cana-5662	45	12	ctd	ctd	NOUN
cana-5662	45	13	-	-	PUNCT
cana-5662	45	14	set	set	NOUN
cana-5662	45	15	of	of	ADP
cana-5662	45	16	a	a	DET
cana-5662	45	17	corona	corona	NOUN
cana-5662	45	18	product	product	NOUN
cana-5662	45	19	of	of	ADP
cana-5662	45	20	graphs	graph	NOUN
cana-5662	45	21	g1	g1	PROPN
cana-5662	45	22	◦	◦	PROPN
cana-5662	45	23	g2	g2	PROPN
cana-5662	45	24	is	be	AUX
cana-5662	45	25	found	find	VERB
cana-5662	45	26	.	.	PUNCT
cana-5662	46	1	theorem	theorem	VERB
cana-5662	46	2	2.4	2.4	NUM
cana-5662	46	3	let	let	VERB
cana-5662	46	4	1	1	NUM
cana-5662	46	5	g	g	NOUN
cana-5662	46	6	and	and	CCONJ
cana-5662	46	7	2	2	NUM
cana-5662	46	8	g	g	NOUN
cana-5662	46	9	be	be	AUX
cana-5662	46	10	connected	connect	VERB
cana-5662	46	11	graphs	graph	NOUN
cana-5662	46	12	then	then	ADV
cana-5662	46	13	(	(	PUNCT
cana-5662	46	14	)	)	PUNCT
cana-5662	46	15	21	21	NUM
cana-5662	46	16	ggvd	ggvd	NOUN
cana-5662	46	17			PUNCT
cana-5662	46	18	is	be	AUX
cana-5662	46	19	a	a	DET
cana-5662	46	20	ctd	ctd	NOUN
cana-5662	46	21	-	-	PUNCT
cana-5662	46	22	set	set	NOUN
cana-5662	46	23	in	in	ADP
cana-5662	46	24	21	21	NUM
cana-5662	46	25	gg	gg	NOUN
cana-5662	46	26			PROPN
cana-5662	46	27	if	if	SCONJ
cana-5662	47	1	and	and	CCONJ
cana-5662	47	2	only	only	ADV
cana-5662	47	3	if	if	SCONJ
cana-5662	47	4	one	one	NUM
cana-5662	47	5	of	of	ADP
cana-5662	47	6	the	the	DET
cana-5662	47	7	following	follow	VERB
cana-5662	47	8	conditions	condition	NOUN
cana-5662	47	9	holds	hold	VERB
cana-5662	47	10	.	.	PUNCT
cana-5662	48	1	(	(	PUNCT
cana-5662	48	2	i	i	NOUN
cana-5662	48	3	)	)	PUNCT
cana-5662	48	4	for	for	ADP
cana-5662	48	5	each	each	PRON
cana-5662	48	6	(	(	PUNCT
cana-5662	48	7	)	)	PUNCT
cana-5662	48	8	(	(	PUNCT
cana-5662	48	9	)	)	PUNCT
cana-5662	48	10	dgvgvv	dgvgvv	NOUN
cana-5662	48	11	v	v	PART
cana-5662	48	12			PROPN
cana-5662	48	13	21	21	NUM
cana-5662	48	14	,	,	PUNCT
cana-5662	48	15	is	be	AUX
cana-5662	48	16	a	a	DET
cana-5662	48	17	dominating	dominating	NOUN
cana-5662	48	18	in	in	ADP
cana-5662	48	19	vg2	vg2	PROPN
cana-5662	48	20	and	and	CCONJ
cana-5662	48	21	(	(	PUNCT
cana-5662	48	22	)	)	PUNCT
cana-5662	48	23	(	(	PUNCT
cana-5662	48	24	)	)	PUNCT
cana-5662	48	25			PROPN
cana-5662	48	26	gvu	gvu	PROPN
cana-5662	48	27	ugvd	ugvd	ADJ
cana-5662	48	28			PROPN
cana-5662	48	29			PROPN
cana-5662	48	30	2	2	NUM
cana-5662	48	31	.	.	PUNCT
cana-5662	49	1	(	(	PUNCT
cana-5662	49	2	ii	ii	NOUN
cana-5662	49	3	)	)	PUNCT
cana-5662	49	4	(	(	PUNCT
cana-5662	49	5	)	)	PUNCT
cana-5662	49	6	dgv	dgv	PROPN
cana-5662	49	7	1	1	PROPN
cana-5662	49	8	is	be	AUX
cana-5662	49	9	a	a	DET
cana-5662	49	10	complementary	complementary	ADJ
cana-5662	49	11	tree	tree	NOUN
cana-5662	49	12	dominating	dominating	NOUN
cana-5662	49	13	in	in	ADP
cana-5662	49	14	1	1	NUM
cana-5662	49	15	g	g	NOUN
cana-5662	49	16	and	and	CCONJ
cana-5662	49	17	(	(	PUNCT
cana-5662	49	18	)	)	PUNCT
cana-5662	49	19	dgv	dgv	PROPN
cana-5662	49	20	v	v	PROPN
cana-5662	49	21	2	2	NOUN
cana-5662	49	22	whenever	whenever	SCONJ
cana-5662	49	23	(	(	PUNCT
cana-5662	49	24	)	)	PUNCT
cana-5662	49	25	dgvv	dgvv	ADV
cana-5662	49	26			ADP
cana-5662	49	27	1	1	NUM
cana-5662	49	28	and	and	CCONJ
cana-5662	49	29	(	(	PUNCT
cana-5662	49	30	)	)	PUNCT
cana-5662	49	31	dgv	dgv	PROPN
cana-5662	49	32	v	v	NUM
cana-5662	49	33	2	2	NOUN
cana-5662	49	34	is	be	AUX
cana-5662	49	35	dominating	dominate	VERB
cana-5662	49	36	in	in	ADP
cana-5662	49	37	vg2	vg2	NOUN
cana-5662	49	38	whenever	whenever	SCONJ
cana-5662	49	39	(	(	PUNCT
cana-5662	49	40	)	)	PUNCT
cana-5662	49	41	.1	.1	NUM
cana-5662	50	1	dgvv	dgvv	VERB
cana-5662	50	2	−	−	PROPN
cana-5662	50	3	proof	proof	NOUN
cana-5662	50	4	.	.	PUNCT
cana-5662	51	1	suppose	suppose	VERB
cana-5662	51	2	(	(	PUNCT
cana-5662	51	3	)	)	PUNCT
cana-5662	51	4	.1	.1	NUM
cana-5662	51	5	=	=	PROPN
cana-5662	52	1	dgv	dgv	PROPN
cana-5662	52	2	let	let	VERB
cana-5662	52	3	(	(	PUNCT
cana-5662	52	4	)	)	PUNCT
cana-5662	52	5	1gvv	1gvv	NUM
cana-5662	52	6	and	and	CCONJ
cana-5662	52	7	(	(	PUNCT
cana-5662	52	8	)	)	PUNCT
cana-5662	52	9	.2	.2	NUM
cana-5662	52	10	dgvx	dgvx	PROPN
cana-5662	52	11	v	v	NOUN
cana-5662	52	12	−	−	NOUN
cana-5662	52	13	hence	hence	ADV
cana-5662	52	14	(	(	PUNCT
cana-5662	52	15	)	)	PUNCT
cana-5662	52	16	.21	.21	NUM
cana-5662	52	17	dggvx	dggvx	NOUN
cana-5662	52	18	−	−	PROPN
cana-5662	53	1			PROPN
cana-5662	53	2	since	since	SCONJ
cana-5662	53	3	d	d	PROPN
cana-5662	53	4	is	be	AUX
cana-5662	53	5	a	a	DET
cana-5662	53	6	ctd	ctd	NOUN
cana-5662	53	7	-	-	PUNCT
cana-5662	53	8	set	set	NOUN
cana-5662	53	9	of	of	ADP
cana-5662	53	10	21	21	NUM
cana-5662	53	11	gg	gg	NOUN
cana-5662	53	12			PROPN
cana-5662	53	13	.there	.there	ADV
cana-5662	53	14	exists	exist	VERB
cana-5662	53	15	dy	dy	ADJ
cana-5662	53	16	such	such	ADJ
cana-5662	53	17	that	that	PRON
cana-5662	53	18	(	(	PUNCT
cana-5662	53	19	)	)	PUNCT
cana-5662	53	20	.1	.1	PROPN
cana-5662	53	21	,	,	PUNCT
cana-5662	53	22	21	21	NUM
cana-5662	53	23	=	=	NUM
cana-5662	53	24	yxd	yxd	NOUN
cana-5662	53	25	gg	gg	NOUN
cana-5662	53	26			PROPN
cana-5662	53	27	since	since	SCONJ
cana-5662	53	28	(	(	PUNCT
cana-5662	53	29	)	)	PUNCT
cana-5662	53	30	vgvx	vgvx	NOUN
cana-5662	53	31	2	2	NUM
cana-5662	53	32	and	and	CCONJ
cana-5662	53	33	(	(	PUNCT
cana-5662	53	34	)	)	PUNCT
cana-5662	53	35	1	1	NUM
cana-5662	53	36	,	,	PUNCT
cana-5662	53	37	21	21	NUM
cana-5662	53	38	=	=	NUM
cana-5662	53	39	yxd	yxd	NOUN
cana-5662	53	40	gg	gg	NOUN
cana-5662	53	41			PROPN
cana-5662	53	42	either	either	CCONJ
cana-5662	53	43	(	(	PUNCT
cana-5662	53	44	)	)	PUNCT
cana-5662	53	45	vgvy	vgvy	NOUN
cana-5662	53	46	2	2	NUM
cana-5662	53	47	or	or	CCONJ
cana-5662	53	48	vy	vy	X
cana-5662	53	49	=	=	X
cana-5662	53	50	.	.	PUNCT
cana-5662	54	1	if	if	SCONJ
cana-5662	54	2	vy	vy	NOUN
cana-5662	54	3	=	=	PUNCT
cana-5662	54	4	then	then	ADV
cana-5662	54	5	(	(	PUNCT
cana-5662	54	6	)	)	PUNCT
cana-5662	54	7	,	,	PUNCT
cana-5662	54	8	1	1	NUM
cana-5662	54	9	dgvy	dgvy	NOUN
cana-5662	54	10			ADP
cana-5662	54	11	a	a	DET
cana-5662	54	12	contradiction	contradiction	NOUN
cana-5662	54	13	.	.	PUNCT
cana-5662	55	1	therefore	therefore	ADV
cana-5662	55	2	(	(	PUNCT
cana-5662	55	3	)	)	PUNCT
cana-5662	55	4	dgvy	dgvy	NOUN
cana-5662	55	5	v	v	ADP
cana-5662	55	6			PROPN
cana-5662	55	7	2	2	NUM
cana-5662	55	8	is	be	AUX
cana-5662	55	9	a	a	DET
cana-5662	55	10	dominating	dominating	NOUN
cana-5662	55	11	set	set	NOUN
cana-5662	55	12	of	of	ADP
cana-5662	55	13	vg2	vg2	PROPN
cana-5662	55	14	.since	.since	NOUN
cana-5662	55	15	(	(	PUNCT
cana-5662	55	16	)	)	PUNCT
cana-5662	55	17	,	,	PUNCT
cana-5662	55	18	1	1	NUM
cana-5662	55	19	=dgv	=dgv	NOUN
cana-5662	55	20	(	(	PUNCT
cana-5662	55	21	)	)	PUNCT
cana-5662	55	22	(	(	PUNCT
cana-5662	55	23	)	)	PUNCT
cana-5662	56	1			VERB
cana-5662	56	2	1	1	NUM
cana-5662	56	3	2	2	NUM
cana-5662	56	4	gvu	gvu	ADJ
cana-5662	56	5	ugvd	ugvd	ADJ
cana-5662	56	6			PROPN
cana-5662	56	7			PROPN
cana-5662	56	8	.	.	PUNCT
cana-5662	57	1	hence	hence	ADV
cana-5662	57	2	(	(	PUNCT
cana-5662	57	3	i	i	NOUN
cana-5662	57	4	)	)	PUNCT
cana-5662	57	5	holds	hold	VERB
cana-5662	57	6	.	.	PUNCT
cana-5662	58	1	suppose	suppose	VERB
cana-5662	58	2	(	(	PUNCT
cana-5662	58	3	)	)	PUNCT
cana-5662	58	4			PROPN
cana-5662	58	5	dgv	dgv	PROPN
cana-5662	58	6	1	1	NUM
cana-5662	58	7	and	and	CCONJ
cana-5662	58	8	(	(	PUNCT
cana-5662	58	9	)	)	PUNCT
cana-5662	58	10	(	(	PUNCT
cana-5662	58	11	)	)	PUNCT
cana-5662	58	12	11	11	NUM
cana-5662	58	13	gvdgv	gvdgv	NOUN
cana-5662	58	14			X
cana-5662	58	15	.	.	PUNCT
cana-5662	59	1	communications	communication	NOUN
cana-5662	59	2	on	on	ADP
cana-5662	59	3	applied	apply	VERB
cana-5662	59	4	nonlinear	nonlinear	ADJ
cana-5662	59	5	analysis	analysis	NOUN
cana-5662	59	6	issn	issn	NOUN
cana-5662	59	7	:	:	PUNCT
cana-5662	59	8	1074	1074	NUM
cana-5662	59	9	-	-	PUNCT
cana-5662	59	10	133x	133x	NUM
cana-5662	59	11	vol	vol	NOUN
cana-5662	59	12	31	31	NUM
cana-5662	59	13	no	no	NOUN
cana-5662	59	14	.	.	PUNCT
cana-5662	60	1	7s	7	NOUN
cana-5662	60	2	(	(	PUNCT
cana-5662	60	3	2024	2024	NUM
cana-5662	60	4	)	)	PUNCT
cana-5662	60	5	756	756	NUM
cana-5662	61	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	61	2	let	let	VERB
cana-5662	61	3	(	(	PUNCT
cana-5662	61	4	)	)	PUNCT
cana-5662	61	5	dgvx	dgvx	NOUN
cana-5662	61	6	−	−	PROPN
cana-5662	62	1	1	1	NUM
cana-5662	63	1	it	it	PRON
cana-5662	63	2	follows	follow	VERB
cana-5662	63	3	(	(	PUNCT
cana-5662	63	4	)	)	PUNCT
cana-5662	63	5	dggvx	dggvx	NOUN
cana-5662	63	6	−	−	PROPN
cana-5662	63	7	21	21	NUM
cana-5662	63	8			PROPN
cana-5662	63	9	.	.	PUNCT
cana-5662	64	1	let	let	VERB
cana-5662	64	2	d	d	NOUN
cana-5662	64	3	is	be	AUX
cana-5662	64	4	a	a	DET
cana-5662	64	5	dominating	dominating	NOUN
cana-5662	64	6	set	set	NOUN
cana-5662	64	7	of	of	ADP
cana-5662	64	8	21	21	NUM
cana-5662	64	9	gg	gg	NOUN
cana-5662	64	10			PROPN
cana-5662	64	11	there	there	PRON
cana-5662	64	12	exists	exist	VERB
cana-5662	64	13	dy	dy	ADJ
cana-5662	64	14	such	such	ADJ
cana-5662	64	15	that	that	PRON
cana-5662	64	16	(	(	PUNCT
cana-5662	64	17	)	)	PUNCT
cana-5662	64	18	.1	.1	PROPN
cana-5662	64	19	,	,	PUNCT
cana-5662	64	20	21	21	NUM
cana-5662	64	21	=	=	NUM
cana-5662	64	22	yxd	yxd	NOUN
cana-5662	64	23	gg	gg	NOUN
cana-5662	64	24			PROPN
cana-5662	64	25	if	if	SCONJ
cana-5662	64	26	(	(	PUNCT
cana-5662	64	27	)	)	PUNCT
cana-5662	64	28	1gvy	1gvy	NUM
cana-5662	64	29	then	then	ADV
cana-5662	64	30	(	(	PUNCT
cana-5662	64	31	)	)	PUNCT
cana-5662	64	32	dgvy	dgvy	PROPN
cana-5662	65	1			ADP
cana-5662	65	2	1	1	NUM
cana-5662	65	3	then	then	ADV
cana-5662	65	4	(	(	PUNCT
cana-5662	65	5	)	)	PUNCT
cana-5662	65	6	.1	.1	NUM
cana-5662	65	7	,	,	PUNCT
cana-5662	65	8	=	=	NOUN
cana-5662	65	9	yxdg	yxdg	NOUN
cana-5662	65	10	hence	hence	ADV
cana-5662	65	11	(	(	PUNCT
cana-5662	65	12	)	)	PUNCT
cana-5662	65	13	dgv	dgv	PROPN
cana-5662	65	14	1	1	PROPN
cana-5662	65	15	is	be	AUX
cana-5662	65	16	a	a	DET
cana-5662	65	17	dominating	dominating	NOUN
cana-5662	65	18	set	set	VERB
cana-5662	65	19	in	in	ADP
cana-5662	65	20	.1	.1	PROPN
cana-5662	65	21	g	g	PROPN
cana-5662	65	22	now	now	ADV
cana-5662	65	23	we	we	PRON
cana-5662	65	24	have	have	VERB
cana-5662	65	25	to	to	PART
cana-5662	65	26	prove	prove	VERB
cana-5662	65	27	(	(	PUNCT
cana-5662	65	28	)	)	PUNCT
cana-5662	65	29	dgv	dgv	PROPN
cana-5662	65	30	1	1	PROPN
cana-5662	65	31	is	be	AUX
cana-5662	65	32	a	a	DET
cana-5662	65	33	complementary	complementary	ADJ
cana-5662	65	34	tree	tree	NOUN
cana-5662	65	35	dominating	dominating	NOUN
cana-5662	65	36	set	set	VERB
cana-5662	65	37	in	in	ADP
cana-5662	65	38	1	1	NUM
cana-5662	65	39	g	g	NOUN
cana-5662	65	40	it	it	PRON
cana-5662	65	41	is	be	AUX
cana-5662	65	42	enough	enough	ADJ
cana-5662	65	43	to	to	PART
cana-5662	65	44	prove	prove	VERB
cana-5662	65	45	(	(	PUNCT
cana-5662	65	46	)	)	PUNCT
cana-5662	65	47	−	−	PROPN
cana-5662	66	1	dgv	dgv	PROPN
cana-5662	66	2	1	1	NUM
cana-5662	66	3	is	be	AUX
cana-5662	66	4	a	a	DET
cana-5662	66	5	tree	tree	NOUN
cana-5662	66	6	.	.	PUNCT
cana-5662	67	1	let	let	VERB
cana-5662	67	2	(	(	PUNCT
cana-5662	67	3	)	)	PUNCT
cana-5662	67	4	.	.	PUNCT
cana-5662	68	1	,	,	PUNCT
cana-5662	68	2	1	1	NUM
cana-5662	68	3	dgvyx	dgvyx	NOUN
cana-5662	68	4	−	−	X
cana-5662	68	5	since	since	SCONJ
cana-5662	68	6	−	−	ADJ
cana-5662	68	7	dggv	dggv	PROPN
cana-5662	68	8	)	)	PUNCT
cana-5662	68	9	(	(	PUNCT
cana-5662	68	10	21	21	NUM
cana-5662	68	11			PROPN
cana-5662	68	12	is	be	AUX
cana-5662	68	13	a	a	DET
cana-5662	68	14	tree	tree	NOUN
cana-5662	68	15	t.	t.	NOUN
cana-5662	68	16	therefore	therefore	ADV
cana-5662	68	17	)	)	PUNCT
cana-5662	68	18	(	(	PUNCT
cana-5662	68	19	,	,	PUNCT
cana-5662	68	20	1gvyx	1gvyx	NUM
cana-5662	68	21			NOUN
cana-5662	68	22	there	there	ADV
cana-5662	68	23	exist	exist	VERB
cana-5662	68	24	(	(	PUNCT
cana-5662	68	25	)	)	PUNCT
cana-5662	68	26	xgvu	xgvu	PROPN
cana-5662	68	27	2	2	PROPN
cana-5662	68	28	and	and	CCONJ
cana-5662	68	29	v	v	X
cana-5662	68	30	(	(	PUNCT
cana-5662	68	31	)	)	PUNCT
cana-5662	68	32	ygv	ygv	PROPN
cana-5662	68	33	2	2	NUM
cana-5662	68	34	.	.	PUNCT
cana-5662	69	1	since	since	SCONJ
cana-5662	69	2	t	t	PROPN
cana-5662	69	3	is	be	AUX
cana-5662	69	4	connected	connect	VERB
cana-5662	69	5	and	and	CCONJ
cana-5662	69	6	acyclic	acyclic	ADJ
cana-5662	69	7	.	.	PUNCT
cana-5662	70	1	there	there	PRON
cana-5662	70	2	exists	exist	VERB
cana-5662	70	3	a	a	DET
cana-5662	70	4	unique	unique	ADJ
cana-5662	70	5	path	path	NOUN
cana-5662	70	6	between	between	ADP
cana-5662	70	7	u	u	NOUN
cana-5662	70	8	and	and	CCONJ
cana-5662	70	9	v	v	NOUN
cana-5662	70	10	.hence	.hence	NOUN
cana-5662	70	11	x	x	NOUN
cana-5662	70	12	and	and	CCONJ
cana-5662	70	13	y	y	PROPN
cana-5662	70	14	are	be	AUX
cana-5662	70	15	the	the	DET
cana-5662	70	16	vertices	vertex	NOUN
cana-5662	70	17	transverse	transverse	NOUN
cana-5662	70	18	from	from	ADP
cana-5662	70	19	u	u	NOUN
cana-5662	70	20	and	and	CCONJ
cana-5662	70	21	v	v	NOUN
cana-5662	70	22	.	.	PUNCT
cana-5662	71	1	hence	hence	ADV
cana-5662	71	2	(	(	PUNCT
cana-5662	71	3	)	)	PUNCT
cana-5662	71	4	dgv	dgv	PROPN
cana-5662	71	5	1	1	PROPN
cana-5662	71	6	is	be	AUX
cana-5662	71	7	a	a	DET
cana-5662	71	8	ctd	ctd	NOUN
cana-5662	71	9	-	-	PUNCT
cana-5662	71	10	set	set	NOUN
cana-5662	71	11	in	in	ADP
cana-5662	71	12	g1	g1	PROPN
cana-5662	71	13	.	.	PUNCT
cana-5662	72	1	suppose	suppose	VERB
cana-5662	73	1	dgvv	dgvv	ADV
cana-5662	73	2			VERB
cana-5662	73	3	)	)	PUNCT
cana-5662	73	4	(	(	PUNCT
cana-5662	73	5	1	1	NUM
cana-5662	73	6	and	and	CCONJ
cana-5662	73	7	(	(	PUNCT
cana-5662	73	8	)	)	PUNCT
cana-5662	73	9	−	−	PROPN
cana-5662	73	10	dgv	dgv	PROPN
cana-5662	73	11	v	v	NUM
cana-5662	73	12	2	2	NUM
cana-5662	73	13	.	.	PUNCT
cana-5662	74	1	let	let	VERB
cana-5662	74	2	dgvu	dgvu	NOUN
cana-5662	74	3	v	v	ADP
cana-5662	74	4	−	−	PROPN
cana-5662	74	5	)	)	PUNCT
cana-5662	75	1	(	(	PUNCT
cana-5662	75	2	2	2	X
cana-5662	75	3	.	.	PUNCT
cana-5662	76	1	since	since	SCONJ
cana-5662	76	2	)	)	PUNCT
cana-5662	76	3	(	(	PUNCT
cana-5662	76	4	)	)	PUNCT
cana-5662	76	5	(	(	PUNCT
cana-5662	76	6	11	11	NUM
cana-5662	76	7	gvdgv	gvdgv	NOUN
cana-5662	76	8			X
cana-5662	76	9	there	there	ADV
cana-5662	76	10	exists	exist	VERB
cana-5662	76	11	.	.	PUNCT
cana-5662	76	12	)	)	PUNCT
cana-5662	77	1	(	(	PUNCT
cana-5662	77	2	1	1	NUM
cana-5662	77	3	dgvw	dgvw	NOUN
cana-5662	77	4	−	−	X
cana-5662	78	1	since	since	SCONJ
cana-5662	78	2	−	−	ADJ
cana-5662	78	3	dggv	dggv	PROPN
cana-5662	78	4	)	)	PUNCT
cana-5662	78	5	(	(	PUNCT
cana-5662	78	6	21	21	NUM
cana-5662	78	7			PROPN
cana-5662	78	8	is	be	AUX
cana-5662	78	9	a	a	DET
cana-5662	78	10	tree	tree	NOUN
cana-5662	78	11	.	.	PUNCT
cana-5662	79	1	there	there	PRON
cana-5662	79	2	exists	exist	VERB
cana-5662	79	3	a	a	DET
cana-5662	79	4	unique	unique	ADJ
cana-5662	79	5	path	path	NOUN
cana-5662	79	6	between	between	ADP
cana-5662	79	7	u	u	NOUN
cana-5662	79	8	w	w	VERB
cana-5662	79	9	with	with	ADP
cana-5662	79	10	vertices	vertex	NOUN
cana-5662	79	11	from	from	ADP
cana-5662	79	12	.	.	PUNCT
cana-5662	79	13	)	)	PUNCT
cana-5662	80	1	(	(	PUNCT
cana-5662	80	2	21	21	NUM
cana-5662	80	3	dggv	dggv	NOUN
cana-5662	80	4	−	−	NOUN
cana-5662	80	5	however	however	ADV
cana-5662	80	6	any	any	DET
cana-5662	80	7	u	u	PROPN
cana-5662	80	8	-	-	PROPN
cana-5662	80	9	w	w	ADJ
cana-5662	80	10	path	path	NOUN
cana-5662	80	11	must	must	AUX
cana-5662	80	12	contain	contain	VERB
cana-5662	80	13	a	a	DET
cana-5662	80	14	vertex	vertex	NOUN
cana-5662	80	15	v	v	NOUN
cana-5662	80	16	which	which	PRON
cana-5662	80	17	is	be	AUX
cana-5662	80	18	impossible	impossible	ADJ
cana-5662	80	19	.	.	PUNCT
cana-5662	81	1	hence	hence	ADV
cana-5662	81	2	.	.	PUNCT
cana-5662	81	3	)	)	PUNCT
cana-5662	82	1	(	(	PUNCT
cana-5662	82	2	2	2	NUM
cana-5662	82	3	=−	=−	NOUN
cana-5662	82	4	dgv	dgv	PROPN
cana-5662	82	5	v	v	NOUN
cana-5662	82	6	hence	hence	ADV
cana-5662	82	7	.	.	PUNCT
cana-5662	82	8	)	)	PUNCT
cana-5662	83	1	(	(	PUNCT
cana-5662	83	2	2	2	NUM
cana-5662	83	3	dgv	dgv	PROPN
cana-5662	83	4	v	v	PROPN
cana-5662	83	5			PROPN
cana-5662	83	6	suppose	suppose	VERB
cana-5662	83	7	dgvv	dgvv	ADV
cana-5662	83	8	−	−	PROPN
cana-5662	83	9	)	)	PUNCT
cana-5662	84	1	(	(	PUNCT
cana-5662	84	2	1	1	X
cana-5662	84	3	.	.	PUNCT
cana-5662	85	1	let	let	VERB
cana-5662	85	2	dgvx	dgvx	VERB
cana-5662	85	3	v	v	NOUN
cana-5662	85	4	−	−	PROPN
cana-5662	85	5	)	)	PUNCT
cana-5662	86	1	(	(	PUNCT
cana-5662	86	2	2	2	X
cana-5662	86	3	.	.	PUNCT
cana-5662	87	1	this	this	PRON
cana-5662	87	2	implies	imply	VERB
cana-5662	87	3	that	that	PRON
cana-5662	87	4	.	.	PUNCT
cana-5662	87	5	)	)	PUNCT
cana-5662	88	1	(	(	PUNCT
cana-5662	88	2	21	21	NUM
cana-5662	88	3	−	−	NOUN
cana-5662	88	4	dggvx	dggvx	NOUN
cana-5662	88	5			PROPN
cana-5662	88	6	since	since	SCONJ
cana-5662	88	7	d	d	PROPN
cana-5662	88	8	is	be	AUX
cana-5662	88	9	a	a	DET
cana-5662	88	10	ctd	ctd	NOUN
cana-5662	88	11	-	-	PUNCT
cana-5662	88	12	set	set	NOUN
cana-5662	88	13	in	in	ADP
cana-5662	88	14	21	21	NUM
cana-5662	88	15	gg	gg	NOUN
cana-5662	88	16			PROPN
cana-5662	88	17	there	there	PRON
cana-5662	88	18	exists	exist	VERB
cana-5662	88	19	dy	dy	ADJ
cana-5662	88	20	such	such	ADJ
cana-5662	88	21	that	that	PRON
cana-5662	88	22	(	(	PUNCT
cana-5662	88	23	)	)	PUNCT
cana-5662	88	24	.1	.1	PROPN
cana-5662	88	25	,	,	PUNCT
cana-5662	88	26	21	21	NUM
cana-5662	88	27	=	=	NUM
cana-5662	88	28	yxd	yxd	NOUN
cana-5662	88	29	gg	gg	NOUN
cana-5662	88	30			PROPN
cana-5662	88	31	consequently	consequently	ADV
cana-5662	88	32	vy	vy	VERB
cana-5662	88	33	=	=	PUNCT
cana-5662	88	34	or	or	CCONJ
cana-5662	88	35	)	)	PUNCT
cana-5662	88	36	.	.	PUNCT
cana-5662	89	1	(	(	PUNCT
cana-5662	89	2	2	2	X
cana-5662	89	3	vgvy	vgvy	NOUN
cana-5662	89	4	since	since	SCONJ
cana-5662	89	5	dy	dy	PROPN
cana-5662	89	6	and	and	CCONJ
cana-5662	89	7	.	.	PUNCT
cana-5662	89	8	)	)	PUNCT
cana-5662	90	1	(	(	PUNCT
cana-5662	90	2	1	1	X
cana-5662	90	3	dgvv	dgvv	NOUN
cana-5662	90	4	−	−	PROPN
cana-5662	91	1	hence	hence	ADV
cana-5662	91	2	vy	vy	PROPN
cana-5662	91	3			PROPN
cana-5662	91	4	then	then	ADV
cana-5662	91	5	it	it	PRON
cana-5662	91	6	follows	follow	VERB
cana-5662	91	7	)	)	PUNCT
cana-5662	91	8	(	(	PUNCT
cana-5662	91	9	2	2	X
cana-5662	91	10	vgvy	vgvy	VERB
cana-5662	91	11	now	now	ADV
cana-5662	91	12	(	(	PUNCT
cana-5662	91	13	)	)	PUNCT
cana-5662	91	14	1	1	NUM
cana-5662	91	15	,	,	PUNCT
cana-5662	91	16	21	21	NUM
cana-5662	91	17	=	=	NUM
cana-5662	91	18	yxd	yxd	NOUN
cana-5662	91	19	gg	gg	NOUN
cana-5662	91	20			PROPN
cana-5662	91	21	implies	imply	VERB
cana-5662	91	22	(	(	PUNCT
cana-5662	91	23	)	)	PUNCT
cana-5662	91	24	.1	.1	NOUN
cana-5662	91	25	,	,	PUNCT
cana-5662	91	26	2	2	NUM
cana-5662	91	27	=	=	NOUN
cana-5662	91	28	yxd	yxd	NOUN
cana-5662	91	29	vg	vg	NOUN
cana-5662	91	30	hence	hence	ADV
cana-5662	91	31	dgv	dgv	PROPN
cana-5662	91	32	v	v	NOUN
cana-5662	91	33			X
cana-5662	91	34	)	)	PUNCT
cana-5662	91	35	(	(	PUNCT
cana-5662	91	36	2	2	NUM
cana-5662	91	37	is	be	AUX
cana-5662	91	38	a	a	DET
cana-5662	91	39	dominating	dominating	NOUN
cana-5662	91	40	set	set	VERB
cana-5662	91	41	in	in	ADP
cana-5662	91	42	vg2	vg2	PROPN
cana-5662	91	43	.therefore	.therefore	PRON
cana-5662	91	44	(	(	PUNCT
cana-5662	91	45	iii	iii	NOUN
cana-5662	91	46	)	)	PUNCT
cana-5662	91	47	holds	hold	VERB
cana-5662	91	48	.	.	PUNCT
cana-5662	92	1	conversely	conversely	ADV
cana-5662	92	2	,	,	PUNCT
cana-5662	92	3	suppose	suppose	VERB
cana-5662	92	4	(	(	PUNCT
cana-5662	92	5	i	i	NOUN
cana-5662	92	6	)	)	PUNCT
cana-5662	92	7	holds	hold	VERB
cana-5662	92	8	.	.	PUNCT
cana-5662	93	1	let	let	VERB
cana-5662	93	2	.	.	PUNCT
cana-5662	93	3	)	)	PUNCT
cana-5662	94	1	(	(	PUNCT
cana-5662	94	2	21	21	NUM
cana-5662	94	3	dggvx	dggvx	NOUN
cana-5662	94	4	−	−	PROPN
cana-5662	95	1			PRON
cana-5662	95	2	suppose	suppose	VERB
cana-5662	95	3	)	)	PUNCT
cana-5662	95	4	(	(	PUNCT
cana-5662	95	5	1gvx	1gvx	NUM
cana-5662	95	6	.since	.since	NOUN
cana-5662	96	1	dgv	dgv	PROPN
cana-5662	96	2	x	x	INTJ
cana-5662	96	3			X
cana-5662	96	4	)	)	PUNCT
cana-5662	96	5	(	(	PUNCT
cana-5662	96	6	2	2	NUM
cana-5662	96	7	is	be	AUX
cana-5662	96	8	dominating	dominate	VERB
cana-5662	96	9	set	set	VERB
cana-5662	96	10	in	in	ADP
cana-5662	96	11	xg2	xg2	PROPN
cana-5662	96	12	and	and	CCONJ
cana-5662	96	13	.	.	PUNCT
cana-5662	96	14	)	)	PUNCT
cana-5662	97	1	(	(	PUNCT
cana-5662	97	2	2	2	NUM
cana-5662	97	3	dgv	dgv	NOUN
cana-5662	97	4	x	x	PRON
cana-5662	97	5	let	let	VERB
cana-5662	97	6	.	.	PUNCT
cana-5662	97	7	)	)	PUNCT
cana-5662	98	1	(	(	PUNCT
cana-5662	98	2	2	2	NUM
cana-5662	98	3	dgvu	dgvu	NOUN
cana-5662	98	4	x	x	PUNCT
cana-5662	99	1			VERB
cana-5662	99	2	then	then	ADV
cana-5662	99	3	1	1	NUM
cana-5662	99	4	)	)	PUNCT
cana-5662	99	5	,	,	PUNCT
cana-5662	99	6	(	(	PUNCT
cana-5662	99	7	21	21	NUM
cana-5662	99	8	=	=	NUM
cana-5662	99	9	yxd	yxd	NOUN
cana-5662	99	10	gg	gg	NOUN
cana-5662	99	11			PROPN
cana-5662	99	12	.	.	PUNCT
cana-5662	100	1	suppose	suppose	VERB
cana-5662	100	2	)	)	PUNCT
cana-5662	100	3	(	(	PUNCT
cana-5662	100	4	1gvx	1gvx	NUM
cana-5662	100	5	then	then	ADV
cana-5662	100	6	there	there	PRON
cana-5662	100	7	exist	exist	VERB
cana-5662	100	8	)	)	PUNCT
cana-5662	100	9	(	(	PUNCT
cana-5662	100	10	1gvy	1gvy	NUM
cana-5662	100	11	such	such	ADJ
cana-5662	100	12	that	that	PRON
cana-5662	100	13	(	(	PUNCT
cana-5662	100	14	)	)	PUNCT
cana-5662	100	15	.2	.2	NUM
cana-5662	100	16	ygvx	ygvx	PROPN
cana-5662	100	17	since	since	SCONJ
cana-5662	100	18	dgv	dgv	PROPN
cana-5662	100	19	y	y	PROPN
cana-5662	100	20			PROPN
cana-5662	100	21	)	)	PUNCT
cana-5662	100	22	(	(	PUNCT
cana-5662	100	23	2	2	NUM
cana-5662	100	24	is	be	AUX
cana-5662	100	25	a	a	DET
cana-5662	100	26	dominating	dominating	NOUN
cana-5662	100	27	set	set	VERB
cana-5662	100	28	in	in	ADP
cana-5662	100	29	yg2	yg2	NOUN
cana-5662	100	30	and	and	CCONJ
cana-5662	100	31	dgvx	dgvx	VERB
cana-5662	100	32	y	y	PROPN
cana-5662	100	33	−	−	PROPN
cana-5662	100	34	)	)	PUNCT
cana-5662	100	35	(	(	PUNCT
cana-5662	100	36	2	2	NUM
cana-5662	100	37	there	there	PRON
cana-5662	100	38	exist	exist	VERB
cana-5662	100	39	dgvt	dgvt	NOUN
cana-5662	100	40	y	y	PROPN
cana-5662	100	41			PROPN
cana-5662	100	42	)	)	PUNCT
cana-5662	100	43	(	(	PUNCT
cana-5662	100	44	2	2	NUM
cana-5662	100	45	such	such	ADJ
cana-5662	100	46	that	that	DET
cana-5662	100	47	1	1	NUM
cana-5662	100	48	)	)	PUNCT
cana-5662	100	49	,	,	PUNCT
cana-5662	100	50	(	(	PUNCT
cana-5662	100	51	21	21	NUM
cana-5662	100	52	=	=	NUM
cana-5662	100	53	txd	txd	NOUN
cana-5662	100	54	gg	gg	NOUN
cana-5662	100	55			PROPN
cana-5662	100	56	then	then	ADV
cana-5662	100	57	d	d	PROPN
cana-5662	100	58	is	be	AUX
cana-5662	100	59	a	a	DET
cana-5662	100	60	dominating	dominating	NOUN
cana-5662	100	61	set	set	NOUN
cana-5662	100	62	in	in	ADP
cana-5662	100	63	21	21	NUM
cana-5662	100	64	gg	gg	NOUN
cana-5662	100	65			PROPN
cana-5662	100	66	.	.	PUNCT
cana-5662	101	1	since	since	SCONJ
cana-5662	101	2	(	(	PUNCT
cana-5662	101	3	)	)	PUNCT
cana-5662	101	4	(	(	PUNCT
cana-5662	101	5	)	)	PUNCT
cana-5662	101	6	(	(	PUNCT
cana-5662	101	7	)	)	PUNCT
cana-5662	101	8	.12	.12	NUM
cana-5662	101	9	1	1	NUM
cana-5662	101	10	=	=	NUM
cana-5662	101	11			NOUN
cana-5662	101	12	dgvandgvd	dgvandgvd	VERB
cana-5662	101	13	gvu	gvu	PROPN
cana-5662	101	14	u	u	PROPN
cana-5662	101	15	consequently	consequently	ADV
cana-5662	101	16	,	,	PUNCT
cana-5662	101	17	)	)	PUNCT
cana-5662	101	18	(	(	PUNCT
cana-5662	101	19	)	)	PUNCT
cana-5662	101	20	(	(	PUNCT
cana-5662	101	21	)	)	PUNCT
cana-5662	101	22	(	(	PUNCT
cana-5662	101	23	1	1	NUM
cana-5662	101	24	)	)	PUNCT
cana-5662	101	25	(	(	PUNCT
cana-5662	101	26	221	221	NUM
cana-5662	101	27	gvdgvdggv	gvdgvdggv	NOUN
cana-5662	101	28	gvv	gvv	NOUN
cana-5662	101	29	v	v	ADP
cana-5662	101	30	−=−	−=−	ADP
cana-5662	101	31			NOUN
cana-5662	101	32			NOUN
cana-5662	101	33	.let	.let	PUNCT
cana-5662	102	1	qpdggvqp	qpdggvqp	PROPN
cana-5662	102	2	−	−	PROPN
cana-5662	102	3	,	,	PUNCT
cana-5662	102	4	)	)	PUNCT
cana-5662	102	5	(	(	PUNCT
cana-5662	102	6	,	,	PUNCT
cana-5662	102	7	21	21	NUM
cana-5662	102	8			X
cana-5662	102	9	.	.	PUNCT
cana-5662	103	1	if	if	SCONJ
cana-5662	103	2	dgvqp	dgvqp	NOUN
cana-5662	103	3	v	v	ADP
cana-5662	103	4	−	−	PROPN
cana-5662	103	5	)	)	PUNCT
cana-5662	103	6	(	(	PUNCT
cana-5662	103	7	,	,	PUNCT
cana-5662	103	8	2	2	NUM
cana-5662	103	9	for	for	ADP
cana-5662	103	10	some	some	PRON
cana-5662	103	11	)	)	PUNCT
cana-5662	103	12	(	(	PUNCT
cana-5662	103	13	1gvv	1gvv	NUM
cana-5662	103	14	then	then	ADV
cana-5662	103	15	there	there	PRON
cana-5662	103	16	is	be	VERB
cana-5662	103	17	a	a	DET
cana-5662	103	18	path	path	NOUN
cana-5662	103	19	with	with	ADP
cana-5662	103	20	vertices	vertex	NOUN
cana-5662	103	21	qvp	qvp	NOUN
cana-5662	103	22	,	,	PUNCT
cana-5662	103	23	,	,	PUNCT
cana-5662	103	24	in	in	ADP
cana-5662	103	25	.	.	PUNCT
cana-5662	103	26	)	)	PUNCT
cana-5662	104	1	(	(	PUNCT
cana-5662	104	2	21	21	NUM
cana-5662	104	3	dggv	dggv	NOUN
cana-5662	104	4	−	−	NOUN
cana-5662	104	5	if	if	SCONJ
cana-5662	104	6	)	)	PUNCT
cana-5662	104	7	(	(	PUNCT
cana-5662	104	8	,	,	PUNCT
cana-5662	104	9	1gvqp	1gvqp	NUM
cana-5662	104	10			NOUN
cana-5662	104	11	.then	.then	PUNCT
cana-5662	104	12	there	there	PRON
cana-5662	104	13	is	be	VERB
cana-5662	104	14	a	a	DET
cana-5662	104	15	tree	tree	NOUN
cana-5662	104	16	which	which	PRON
cana-5662	104	17	contains	contain	VERB
cana-5662	104	18	a	a	DET
cana-5662	104	19	p	p	NOUN
cana-5662	104	20	-	-	PUNCT
cana-5662	104	21	q	q	NOUN
cana-5662	104	22	path	path	NOUN
cana-5662	104	23	in	in	ADP
cana-5662	104	24	dggv	dggv	PROPN
cana-5662	104	25	−	−	PROPN
cana-5662	104	26	)	)	PUNCT
cana-5662	104	27	(	(	PUNCT
cana-5662	104	28	21	21	NUM
cana-5662	104	29			PROPN
cana-5662	104	30	.since	.since	NOUN
cana-5662	104	31	g1	g1	PROPN
cana-5662	104	32	is	be	AUX
cana-5662	104	33	connected	connect	VERB
cana-5662	104	34	.	.	PUNCT
cana-5662	105	1	if	if	SCONJ
cana-5662	105	2	(	(	PUNCT
cana-5662	105	3	)	)	PUNCT
cana-5662	105	4	1gvp	1gvp	NUM
cana-5662	105	5	and	and	CCONJ
cana-5662	105	6	(	(	PUNCT
cana-5662	105	7	)	)	PUNCT
cana-5662	105	8	dgvq	dgvq	VERB
cana-5662	105	9	v	v	ADP
cana-5662	105	10	−	−	PROPN
cana-5662	105	11	2	2	NUM
cana-5662	105	12	for	for	ADP
cana-5662	105	13	some	some	PRON
cana-5662	105	14	(	(	PUNCT
cana-5662	105	15	)	)	PUNCT
cana-5662	105	16	1gvv	1gvv	NUM
cana-5662	105	17	then	then	ADV
cana-5662	105	18	dggv	dggv	VERB
cana-5662	105	19	−	−	PROPN
cana-5662	105	20	)	)	PUNCT
cana-5662	105	21	(	(	PUNCT
cana-5662	105	22	21	21	NUM
cana-5662	105	23			PROPN
cana-5662	105	24	contains	contain	VERB
cana-5662	105	25	a	a	DET
cana-5662	105	26	tree	tree	NOUN
cana-5662	105	27	with	with	ADP
cana-5662	105	28	vertices	vertex	NOUN
cana-5662	105	29	p	p	NOUN
cana-5662	105	30	and	and	CCONJ
cana-5662	105	31	v	v	NOUN
cana-5662	105	32	.	.	PUNCT
cana-5662	106	1	suppose	suppose	VERB
cana-5662	106	2	vp	vp	PROPN
cana-5662	106	3			PROPN
cana-5662	106	4	since	since	SCONJ
cana-5662	106	5	g1	g1	PROPN
cana-5662	106	6	is	be	AUX
cana-5662	106	7	connected	connect	VERB
cana-5662	106	8	then	then	ADV
cana-5662	106	9	dggv	dggv	VERB
cana-5662	106	10	−	−	PROPN
cana-5662	106	11	)	)	PUNCT
cana-5662	106	12	(	(	PUNCT
cana-5662	106	13	21	21	NUM
cana-5662	106	14			PROPN
cana-5662	106	15	contains	contain	VERB
cana-5662	106	16	a	a	DET
cana-5662	106	17	tree	tree	NOUN
cana-5662	106	18	with	with	ADP
cana-5662	106	19	vertices	vertex	NOUN
cana-5662	106	20	qvp	qvp	NOUN
cana-5662	106	21	,	,	PUNCT
cana-5662	106	22	,	,	PUNCT
cana-5662	106	23	.suppose	.suppose	X
cana-5662	106	24	(	(	PUNCT
cana-5662	106	25	)	)	PUNCT
cana-5662	106	26	dgvp	dgvp	VERB
cana-5662	106	27	v	v	ADP
cana-5662	106	28	−	−	PROPN
cana-5662	106	29	2	2	NUM
cana-5662	106	30	and	and	CCONJ
cana-5662	106	31	(	(	PUNCT
cana-5662	106	32	)	)	PUNCT
cana-5662	106	33	wgvq	wgvq	NOUN
cana-5662	106	34	2	2	NUM
cana-5662	106	35	for	for	ADP
cana-5662	106	36	some	some	DET
cana-5662	106	37	communications	communication	NOUN
cana-5662	106	38	on	on	ADP
cana-5662	106	39	applied	apply	VERB
cana-5662	106	40	nonlinear	nonlinear	ADJ
cana-5662	106	41	analysis	analysis	NOUN
cana-5662	106	42	issn	issn	NOUN
cana-5662	106	43	:	:	PUNCT
cana-5662	106	44	1074	1074	NUM
cana-5662	106	45	-	-	PUNCT
cana-5662	106	46	133x	133x	NUM
cana-5662	106	47	vol	vol	NOUN
cana-5662	106	48	31	31	NUM
cana-5662	106	49	no	no	NOUN
cana-5662	106	50	.	.	PUNCT
cana-5662	107	1	7s	7	NOUN
cana-5662	107	2	(	(	PUNCT
cana-5662	107	3	2024	2024	NUM
cana-5662	107	4	)	)	PUNCT
cana-5662	107	5	757	757	PROPN
cana-5662	107	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	107	7	)	)	PUNCT
cana-5662	107	8	.	.	PUNCT
cana-5662	108	1	(	(	PUNCT
cana-5662	108	2	,	,	PUNCT
cana-5662	108	3	1gvwv	1gvwv	NUM
cana-5662	108	4			NOUN
cana-5662	108	5	since	since	SCONJ
cana-5662	108	6	g1	g1	PROPN
cana-5662	108	7	is	be	AUX
cana-5662	108	8	connected	connect	VERB
cana-5662	108	9	then	then	ADV
cana-5662	108	10	there	there	PRON
cana-5662	108	11	exist	exist	VERB
cana-5662	108	12	a	a	DET
cana-5662	108	13	tree	tree	NOUN
cana-5662	108	14	with	with	ADP
cana-5662	108	15	vertices	vertex	NOUN
cana-5662	108	16	qwvp	qwvp	NOUN
cana-5662	108	17	,	,	PUNCT
cana-5662	108	18	,	,	PUNCT
cana-5662	108	19	,	,	PUNCT
cana-5662	108	20	in	in	ADP
cana-5662	108	21	dggv	dggv	PROPN
cana-5662	108	22	−	−	PROPN
cana-5662	108	23	)	)	PUNCT
cana-5662	108	24	(	(	PUNCT
cana-5662	108	25	21	21	NUM
cana-5662	108	26			PROPN
cana-5662	108	27	.hence	.hence	ADP
cana-5662	108	28	dggv	dggv	PROPN
cana-5662	108	29	−	−	PROPN
cana-5662	108	30	)	)	PUNCT
cana-5662	108	31	(	(	PUNCT
cana-5662	108	32	21	21	NUM
cana-5662	108	33			PROPN
cana-5662	108	34	is	be	AUX
cana-5662	108	35	connected	connect	VERB
cana-5662	108	36	and	and	CCONJ
cana-5662	108	37	acyclic	acyclic	ADJ
cana-5662	108	38	.	.	PUNCT
cana-5662	109	1	therefore	therefore	ADV
cana-5662	109	2	dggv	dggv	PROPN
cana-5662	109	3	−	−	PROPN
cana-5662	109	4	)	)	PUNCT
cana-5662	109	5	(	(	PUNCT
cana-5662	109	6	21	21	NUM
cana-5662	109	7			PROPN
cana-5662	109	8	is	be	AUX
cana-5662	109	9	a	a	DET
cana-5662	109	10	tree	tree	NOUN
cana-5662	109	11	.	.	PUNCT
cana-5662	110	1	hence	hence	ADV
cana-5662	110	2	d	d	PROPN
cana-5662	110	3	is	be	AUX
cana-5662	110	4	a	a	DET
cana-5662	110	5	complementary	complementary	ADJ
cana-5662	110	6	tree	tree	NOUN
cana-5662	110	7	dominating	dominating	NOUN
cana-5662	110	8	in	in	ADP
cana-5662	110	9	21	21	NUM
cana-5662	110	10	gg	gg	PROPN
cana-5662	110	11			PROPN
cana-5662	110	12	.	.	PUNCT
cana-5662	111	1	suppose	suppose	VERB
cana-5662	111	2	(	(	PUNCT
cana-5662	111	3	ii	ii	NOUN
cana-5662	111	4	)	)	PUNCT
cana-5662	111	5	holds	hold	VERB
cana-5662	111	6	.	.	PUNCT
cana-5662	112	1	let	let	VERB
cana-5662	112	2	.	.	PUNCT
cana-5662	112	3	)	)	PUNCT
cana-5662	113	1	(	(	PUNCT
cana-5662	113	2	21	21	NUM
cana-5662	113	3	dggvx	dggvx	NOUN
cana-5662	113	4	−	−	PROPN
cana-5662	114	1			PRON
cana-5662	114	2	suppose	suppose	VERB
cana-5662	114	3	.	.	PUNCT
cana-5662	114	4	)	)	PUNCT
cana-5662	114	5	(	(	PUNCT
cana-5662	114	6	)	)	PUNCT
cana-5662	114	7	.	.	PUNCT
cana-5662	115	1	(	(	PUNCT
cana-5662	115	2	)	)	PUNCT
cana-5662	115	3	(	(	PUNCT
cana-5662	115	4	11	11	NUM
cana-5662	115	5	dgvxeigvx	dgvxeigvx	NOUN
cana-5662	115	6	−	−	NOUN
cana-5662	115	7	since	since	SCONJ
cana-5662	115	8	dgv	dgv	PROPN
cana-5662	115	9			X
cana-5662	115	10	)	)	PUNCT
cana-5662	115	11	(	(	PUNCT
cana-5662	115	12	1	1	NUM
cana-5662	115	13	is	be	AUX
cana-5662	115	14	a	a	DET
cana-5662	115	15	dominating	dominating	NOUN
cana-5662	115	16	in	in	ADP
cana-5662	115	17	g1	g1	NOUN
cana-5662	115	18	,	,	PUNCT
cana-5662	115	19	there	there	PRON
cana-5662	115	20	exist	exist	VERB
cana-5662	115	21	dgvy	dgvy	ADJ
cana-5662	115	22			NOUN
cana-5662	115	23	)	)	PUNCT
cana-5662	116	1	(	(	PUNCT
cana-5662	116	2	1	1	NUM
cana-5662	116	3	such	such	ADJ
cana-5662	116	4	that	that	SCONJ
cana-5662	116	5	(	(	PUNCT
cana-5662	116	6	)	)	PUNCT
cana-5662	116	7	1	1	NUM
cana-5662	116	8	,	,	PUNCT
cana-5662	116	9	=	=	NOUN
cana-5662	116	10	txdg	txdg	NOUN
cana-5662	116	11	for	for	ADP
cana-5662	116	12	some	some	PRON
cana-5662	116	13	)	)	PUNCT
cana-5662	116	14	(	(	PUNCT
cana-5662	116	15	1gvt	1gvt	NUM
cana-5662	116	16	is	be	AUX
cana-5662	116	17	follows	follow	VERB
cana-5662	116	18	that	that	PRON
cana-5662	116	19	(	(	PUNCT
cana-5662	116	20	)	)	PUNCT
cana-5662	116	21	.1	.1	PROPN
cana-5662	116	22	,	,	PUNCT
cana-5662	116	23	21	21	NUM
cana-5662	116	24	=	=	NUM
cana-5662	116	25	yxd	yxd	NOUN
cana-5662	116	26	gg	gg	NOUN
cana-5662	116	27			PROPN
cana-5662	116	28	suppose	suppose	VERB
cana-5662	116	29	(	(	PUNCT
cana-5662	116	30	)	)	PUNCT
cana-5662	116	31	vgvx	vgvx	NOUN
cana-5662	116	32	2	2	NUM
cana-5662	116	33	for	for	ADP
cana-5662	116	34	some	some	PRON
cana-5662	116	35	)	)	PUNCT
cana-5662	116	36	(	(	PUNCT
cana-5662	116	37	1gvv	1gvv	NUM
cana-5662	116	38	.1	.1	NUM
cana-5662	116	39	)	)	PUNCT
cana-5662	116	40	,	,	PUNCT
cana-5662	116	41	(	(	PUNCT
cana-5662	116	42	)	)	PUNCT
cana-5662	116	43	.	.	PUNCT
cana-5662	117	1	(	(	PUNCT
cana-5662	117	2	)	)	PUNCT
cana-5662	117	3	(	(	PUNCT
cana-5662	117	4	)	)	PUNCT
cana-5662	117	5	.	.	PUNCT
cana-5662	118	1	(	(	PUNCT
cana-5662	118	2	212	212	NUM
cana-5662	118	3	=	=	NOUN
cana-5662	118	4	−	−	PROPN
cana-5662	118	5	vxdeidgvxei	vxdeidgvxei	PROPN
cana-5662	118	6	gg	gg	PROPN
cana-5662	118	7	v	v	NUM
cana-5662	118	8			PROPN
cana-5662	118	9	if	if	SCONJ
cana-5662	118	10	dv	dv	ADP
cana-5662	118	11	which	which	PRON
cana-5662	118	12	is	be	AUX
cana-5662	118	13	a	a	DET
cana-5662	118	14	contradiction	contradiction	NOUN
cana-5662	118	15	to	to	ADP
cana-5662	118	16	(	(	PUNCT
cana-5662	118	17	)	)	PUNCT
cana-5662	118	18	.2	.2	NUM
cana-5662	118	19	dgvx	dgvx	PROPN
cana-5662	118	20	v	v	NOUN
cana-5662	118	21	−	−	PROPN
cana-5662	119	1	hence	hence	ADV
cana-5662	119	2	dv	dv	NOUN
cana-5662	119	3	is	be	AUX
cana-5662	119	4	(	(	PUNCT
cana-5662	119	5	)	)	PUNCT
cana-5662	120	1	dgvv	dgvv	ADP
cana-5662	120	2	−	−	PROPN
cana-5662	121	1	1	1	X
cana-5662	121	2	.	.	PUNCT
cana-5662	122	1	in	in	ADP
cana-5662	122	2	this	this	DET
cana-5662	122	3	case	case	NOUN
cana-5662	122	4	(	(	PUNCT
cana-5662	122	5	)	)	PUNCT
cana-5662	122	6	dgv	dgv	PROPN
cana-5662	122	7	v	v	NUM
cana-5662	122	8	2	2	NOUN
cana-5662	122	9	is	be	AUX
cana-5662	122	10	dominating	dominate	VERB
cana-5662	122	11	in	in	ADP
cana-5662	122	12	vg2	vg2	PROPN
cana-5662	122	13	)	)	PUNCT
cana-5662	122	14	.	.	PUNCT
cana-5662	123	1	(	(	PUNCT
cana-5662	123	2	ei	ei	X
cana-5662	123	3	there	there	PRON
cana-5662	123	4	exist	exist	VERB
cana-5662	123	5	(	(	PUNCT
cana-5662	123	6	)	)	PUNCT
cana-5662	123	7	dgvw	dgvw	PROPN
cana-5662	123	8	w	w	PROPN
cana-5662	123	9			PROPN
cana-5662	123	10	2	2	NUM
cana-5662	123	11	such	such	ADJ
cana-5662	123	12	that	that	DET
cana-5662	123	13	.1	.1	NOUN
cana-5662	123	14	)	)	PUNCT
cana-5662	123	15	,	,	PUNCT
cana-5662	123	16	(	(	PUNCT
cana-5662	123	17	2	2	NUM
cana-5662	123	18	=	=	NUM
cana-5662	123	19	wxd	wxd	NOUN
cana-5662	123	20	vg	vg	ADV
cana-5662	123	21	it	it	PRON
cana-5662	123	22	follows	follow	VERB
cana-5662	123	23	that	that	PRON
cana-5662	123	24	(	(	PUNCT
cana-5662	123	25	)	)	PUNCT
cana-5662	123	26	.1	.1	PROPN
cana-5662	123	27	,	,	PUNCT
cana-5662	123	28	21	21	NUM
cana-5662	123	29	=	=	NUM
cana-5662	123	30	wxd	wxd	ADJ
cana-5662	123	31	gg	gg	NOUN
cana-5662	123	32			PROPN
cana-5662	123	33	hence	hence	ADV
cana-5662	123	34	d	d	PROPN
cana-5662	123	35	is	be	AUX
cana-5662	123	36	a	a	DET
cana-5662	123	37	dominating	dominating	NOUN
cana-5662	123	38	set	set	NOUN
cana-5662	123	39	in	in	ADP
cana-5662	123	40	21	21	NUM
cana-5662	123	41	gg	gg	NOUN
cana-5662	123	42			PROPN
cana-5662	123	43	.	.	PUNCT
cana-5662	124	1	let	let	VERB
cana-5662	124	2	(	(	PUNCT
cana-5662	124	3	)	)	PUNCT
cana-5662	124	4	21	21	NUM
cana-5662	124	5	,	,	PUNCT
cana-5662	124	6	ggvyx	ggvyx	NOUN
cana-5662	124	7			AUX
cana-5662	124	8	suppose	suppose	VERB
cana-5662	124	9	(	(	PUNCT
cana-5662	124	10	)	)	PUNCT
cana-5662	124	11	1	1	NUM
cana-5662	124	12	,	,	PUNCT
cana-5662	124	13	gvyx	gvyx	VERB
cana-5662	124	14			NOUN
cana-5662	124	15	)	)	PUNCT
cana-5662	124	16	.	.	PUNCT
cana-5662	125	1	(	(	PUNCT
cana-5662	125	2	ei	ei	X
cana-5662	125	3	(	(	PUNCT
cana-5662	125	4	)	)	PUNCT
cana-5662	125	5	dgvyx	dgvyx	NOUN
cana-5662	125	6	−	−	PROPN
cana-5662	125	7	,	,	PUNCT
cana-5662	125	8	.	.	PUNCT
cana-5662	126	1	since	since	SCONJ
cana-5662	126	2	dgv	dgv	PROPN
cana-5662	126	3			NUM
cana-5662	126	4	)	)	PUNCT
cana-5662	126	5	(	(	PUNCT
cana-5662	126	6	is	be	AUX
cana-5662	126	7	a	a	DET
cana-5662	126	8	complementary	complementary	ADJ
cana-5662	126	9	tree	tree	NOUN
cana-5662	126	10	dominating	dominating	NOUN
cana-5662	126	11	set	set	VERB
cana-5662	126	12	in	in	ADP
cana-5662	126	13	g1	g1	PROPN
cana-5662	126	14	and	and	CCONJ
cana-5662	126	15	−	−	VERB
cana-5662	126	16	dgv	dgv	PROPN
cana-5662	126	17	)	)	PUNCT
cana-5662	126	18	(	(	PUNCT
cana-5662	126	19	1	1	NUM
cana-5662	126	20	is	be	AUX
cana-5662	126	21	a	a	DET
cana-5662	126	22	tree	tree	NOUN
cana-5662	126	23	.	.	PUNCT
cana-5662	127	1	from	from	ADP
cana-5662	127	2	this	this	DET
cana-5662	127	3	−	−	VERB
cana-5662	127	4	dggv	dggv	PROPN
cana-5662	127	5	)	)	PUNCT
cana-5662	127	6	(	(	PUNCT
cana-5662	127	7	21	21	NUM
cana-5662	127	8			PROPN
cana-5662	127	9	is	be	AUX
cana-5662	127	10	a	a	DET
cana-5662	127	11	tree	tree	NOUN
cana-5662	127	12	which	which	PRON
cana-5662	127	13	contains	contain	VERB
cana-5662	127	14	a	a	DET
cana-5662	127	15	path	path	NOUN
cana-5662	127	16	x	x	NOUN
cana-5662	127	17	-	-	NOUN
cana-5662	127	18	y	y	NOUN
cana-5662	127	19	in	in	ADP
cana-5662	127	20	.	.	PUNCT
cana-5662	127	21	)	)	PUNCT
cana-5662	128	1	(	(	PUNCT
cana-5662	128	2	1	1	NUM
cana-5662	128	3	dgv	dgv	PROPN
cana-5662	128	4	−	−	PROPN
cana-5662	128	5	suppose	suppose	VERB
cana-5662	128	6	(	(	PUNCT
cana-5662	128	7	)	)	PUNCT
cana-5662	128	8	1gvx	1gvx	NUM
cana-5662	128	9	and	and	CCONJ
cana-5662	128	10	(	(	PUNCT
cana-5662	128	11	)	)	PUNCT
cana-5662	128	12	vgvy	vgvy	NOUN
cana-5662	128	13	2	2	NUM
cana-5662	128	14	for	for	ADP
cana-5662	128	15	some	some	PRON
cana-5662	128	16	(	(	PUNCT
cana-5662	128	17	)	)	PUNCT
cana-5662	128	18	(	(	PUNCT
cana-5662	128	19	)	)	PUNCT
cana-5662	128	20	dgvxeigvv	dgvxeigvv	VERB
cana-5662	128	21	−	−	ADP
cana-5662	128	22	11	11	NUM
cana-5662	128	23	)	)	PUNCT
cana-5662	128	24	.	.	PUNCT
cana-5662	129	1	(	(	PUNCT
cana-5662	129	2	and	and	CCONJ
cana-5662	129	3	(	(	PUNCT
cana-5662	129	4	)	)	PUNCT
cana-5662	129	5	.2	.2	NUM
cana-5662	129	6	dgvy	dgvy	NOUN
cana-5662	129	7	v	v	ADP
cana-5662	129	8	−	−	PROPN
cana-5662	130	1	if	if	SCONJ
cana-5662	130	2	vx	vx	PROPN
cana-5662	130	3	=	=	PRON
cana-5662	130	4	there	there	PRON
cana-5662	130	5	exists	exist	VERB
cana-5662	130	6	path	path	NOUN
cana-5662	130	7	between	between	ADP
cana-5662	130	8	x	x	X
cana-5662	130	9	-	-	PUNCT
cana-5662	130	10	y.	y.	PROPN
cana-5662	130	11	suppose	suppose	VERB
cana-5662	130	12	vx	vx	PROPN
cana-5662	130	13			PROPN
cana-5662	130	14	if	if	SCONJ
cana-5662	130	15	(	(	PUNCT
cana-5662	130	16	)	)	PUNCT
cana-5662	130	17	dgvv	dgvv	ADV
cana-5662	130	18			ADP
cana-5662	130	19	1	1	NUM
cana-5662	130	20	then	then	ADV
cana-5662	130	21	(	(	PUNCT
cana-5662	130	22	)	)	PUNCT
cana-5662	130	23	.2	.2	NUM
cana-5662	130	24	dgv	dgv	PROPN
cana-5662	130	25	v	v	NUM
cana-5662	130	26			PROPN
cana-5662	130	27	this	this	PRON
cana-5662	130	28	contradicts	contradict	VERB
cana-5662	130	29	the	the	DET
cana-5662	130	30	fact	fact	NOUN
cana-5662	131	1	that	that	SCONJ
cana-5662	131	2	(	(	PUNCT
cana-5662	131	3	)	)	PUNCT
cana-5662	131	4	.02	.02	NUM
cana-5662	132	1	−	−	ADP
cana-5662	132	2	dgv	dgv	PROPN
cana-5662	132	3	v	v	NOUN
cana-5662	132	4	then	then	ADV
cana-5662	132	5	(	(	PUNCT
cana-5662	132	6	)	)	PUNCT
cana-5662	132	7	,	,	PUNCT
cana-5662	132	8	1	1	NUM
cana-5662	132	9	dgvv	dgvv	NOUN
cana-5662	132	10	−	−	VERB
cana-5662	133	1	consequently	consequently	ADV
cana-5662	133	2	,	,	PUNCT
cana-5662	133	3	(	(	PUNCT
cana-5662	133	4	)	)	PUNCT
cana-5662	133	5	dgv	dgv	PROPN
cana-5662	133	6	v	v	INTJ
cana-5662	133	7	−2	−2	PROPN
cana-5662	133	8	is	be	AUX
cana-5662	133	9	a	a	DET
cana-5662	133	10	dominating	dominating	NOUN
cana-5662	133	11	set	set	VERB
cana-5662	133	12	in	in	ADP
cana-5662	133	13	vg2	vg2	PROPN
cana-5662	133	14	)	)	PUNCT
cana-5662	133	15	.	.	PUNCT
cana-5662	134	1	(	(	PUNCT
cana-5662	134	2	ei	ei	X
cana-5662	134	3	(	(	PUNCT
cana-5662	134	4	)	)	PUNCT
cana-5662	134	5	.2	.2	NUM
cana-5662	134	6	dgv	dgv	PROPN
cana-5662	134	7	v	v	AUX
cana-5662	134	8	suppose	suppose	VERB
cana-5662	134	9	(	(	PUNCT
cana-5662	134	10	)	)	PUNCT
cana-5662	134	11	.2	.2	NUM
cana-5662	134	12	dgvx	dgvx	PROPN
cana-5662	134	13	v	v	PROPN
cana-5662	134	14			PROPN
cana-5662	134	15	since	since	SCONJ
cana-5662	134	16	(	(	PUNCT
cana-5662	134	17	)	)	PUNCT
cana-5662	134	18	dgvv	dgvv	ADP
cana-5662	134	19	−	−	PROPN
cana-5662	134	20	1	1	NUM
cana-5662	134	21	and	and	CCONJ
cana-5662	134	22	(	(	PUNCT
cana-5662	134	23	)	)	PUNCT
cana-5662	134	24	−	−	VERB
cana-5662	134	25	dgv	dgv	PROPN
cana-5662	134	26	1	1	NUM
cana-5662	134	27	contains	contain	VERB
cana-5662	134	28	a	a	DET
cana-5662	134	29	path	path	NOUN
cana-5662	134	30	with	with	ADP
cana-5662	134	31	vertices	vertex	NOUN
cana-5662	134	32	.vx	.vx	PUNCT
cana-5662	135	1	−	−	PRON
cana-5662	135	2	thus	thus	ADV
cana-5662	135	3	(	(	PUNCT
cana-5662	135	4	)	)	PUNCT
cana-5662	135	5	−	−	VERB
cana-5662	135	6	dggv	dggv	NOUN
cana-5662	135	7	21	21	NUM
cana-5662	135	8			PROPN
cana-5662	135	9	contains	contain	VERB
cana-5662	135	10	a	a	DET
cana-5662	135	11	tree	tree	NOUN
cana-5662	135	12	with	with	ADP
cana-5662	135	13	vertices	vertex	NOUN
cana-5662	135	14	.vx	.vx	PUNCT
cana-5662	136	1	−	−	PROPN
cana-5662	136	2	suppose	suppose	VERB
cana-5662	136	3	(	(	PUNCT
cana-5662	136	4	)	)	PUNCT
cana-5662	136	5	yxdgvyx	yxdgvyx	NOUN
cana-5662	136	6	v	v	NUM
cana-5662	136	7	−	−	PROPN
cana-5662	136	8	,	,	PUNCT
cana-5662	136	9	,	,	PUNCT
cana-5662	136	10	2	2	NUM
cana-5662	136	11	for	for	ADP
cana-5662	136	12	some	some	PRON
cana-5662	136	13	(	(	PUNCT
cana-5662	136	14	)	)	PUNCT
cana-5662	136	15	.gvv	.gvv	NOUN
cana-5662	136	16	if	if	SCONJ
cana-5662	136	17	,	,	PUNCT
cana-5662	136	18	dv	dv	ADP
cana-5662	136	19	then	then	ADV
cana-5662	136	20	(	(	PUNCT
cana-5662	136	21	)	)	PUNCT
cana-5662	136	22	dgv	dgv	PROPN
cana-5662	136	23	v	v	PROPN
cana-5662	136	24	2	2	NOUN
cana-5662	136	25	.this	.this	PRON
cana-5662	136	26	contradicts	contradict	VERB
cana-5662	136	27	the	the	DET
cana-5662	136	28	fact	fact	NOUN
cana-5662	136	29	that	that	SCONJ
cana-5662	136	30	(	(	PUNCT
cana-5662	136	31	)	)	PUNCT
cana-5662	136	32	.2	.2	NUM
cana-5662	136	33	−	−	PROPN
cana-5662	136	34	dgv	dgv	PROPN
cana-5662	136	35	v	v	NOUN
cana-5662	136	36	thus	thus	ADV
cana-5662	136	37	dv	dv	NOUN
cana-5662	136	38	(	(	PUNCT
cana-5662	136	39	i.e	i.e	X
cana-5662	136	40	)	)	PUNCT
cana-5662	136	41	.	.	PUNCT
cana-5662	136	42	)	)	PUNCT
cana-5662	137	1	(	(	PUNCT
cana-5662	137	2	1	1	X
cana-5662	137	3	dgvv	dgvv	ADV
cana-5662	137	4	−	−	VERB
cana-5662	138	1	now	now	ADV
cana-5662	138	2	there	there	PRON
cana-5662	138	3	exists	exist	VERB
cana-5662	138	4	a	a	DET
cana-5662	138	5	path	path	NOUN
cana-5662	138	6	with	with	ADP
cana-5662	138	7	vertices	vertex	NOUN
cana-5662	138	8	yvx	yvx	PROPN
cana-5662	138	9	,	,	PUNCT
cana-5662	138	10	,	,	PUNCT
cana-5662	138	11	in	in	ADP
cana-5662	138	12	(	(	PUNCT
cana-5662	138	13	)	)	PUNCT
cana-5662	138	14	.21	.21	NUM
cana-5662	138	15	dggv	dggv	NOUN
cana-5662	138	16	−	−	NOUN
cana-5662	138	17	suppose	suppose	VERB
cana-5662	138	18	(	(	PUNCT
cana-5662	138	19	)	)	PUNCT
cana-5662	138	20	vgvx	vgvx	NOUN
cana-5662	138	21	2	2	NUM
cana-5662	138	22	and	and	CCONJ
cana-5662	138	23	(	(	PUNCT
cana-5662	138	24	)	)	PUNCT
cana-5662	138	25	wgvy	wgvy	NOUN
cana-5662	138	26	2	2	NUM
cana-5662	138	27	for	for	ADP
cana-5662	138	28	some	some	PRON
cana-5662	138	29	(	(	PUNCT
cana-5662	138	30	)	)	PUNCT
cana-5662	138	31	.	.	PUNCT
cana-5662	139	1	,	,	PUNCT
cana-5662	139	2	,	,	PUNCT
cana-5662	139	3	wvgvwv	wvgvwv	PROPN
cana-5662	139	4			PROPN
cana-5662	139	5	then	then	ADV
cana-5662	139	6	(	(	PUNCT
cana-5662	139	7	)	)	PUNCT
cana-5662	139	8	dgvx	dgvx	NOUN
cana-5662	139	9	v	v	NOUN
cana-5662	139	10	−	−	PROPN
cana-5662	139	11	2	2	NUM
cana-5662	139	12	and	and	CCONJ
cana-5662	139	13	(	(	PUNCT
cana-5662	139	14	)	)	PUNCT
cana-5662	140	1	dgvy	dgvy	INTJ
cana-5662	140	2	w	w	NOUN
cana-5662	140	3	−	−	NOUN
cana-5662	140	4	2	2	NUM
cana-5662	140	5	if	if	SCONJ
cana-5662	140	6	dv	dv	NOUN
cana-5662	140	7	or	or	CCONJ
cana-5662	140	8	dw	dw	NOUN
cana-5662	140	9	then	then	ADV
cana-5662	140	10	(	(	PUNCT
cana-5662	140	11	)	)	PUNCT
cana-5662	140	12	dgv	dgv	PROPN
cana-5662	140	13	v	v	PROPN
cana-5662	140	14	2	2	NOUN
cana-5662	140	15	and	and	CCONJ
cana-5662	140	16	(	(	PUNCT
cana-5662	140	17	)	)	PUNCT
cana-5662	141	1	.2	.2	NUM
cana-5662	141	2	dgv	dgv	PROPN
cana-5662	141	3	w	w	PROPN
cana-5662	141	4			PROPN
cana-5662	141	5	this	this	PRON
cana-5662	141	6	contradicts	contradict	VERB
cana-5662	141	7	the	the	DET
cana-5662	141	8	facts	fact	NOUN
cana-5662	141	9	that	that	SCONJ
cana-5662	141	10	(	(	PUNCT
cana-5662	141	11	)	)	PUNCT
cana-5662	141	12	−	−	PROPN
cana-5662	141	13	dgv	dgv	PROPN
cana-5662	141	14	v	v	NUM
cana-5662	141	15	2	2	NUM
cana-5662	141	16	and	and	CCONJ
cana-5662	141	17	(	(	PUNCT
cana-5662	141	18	)	)	PUNCT
cana-5662	141	19	−	−	PROPN
cana-5662	142	1	dgv	dgv	PROPN
cana-5662	142	2	w	w	PROPN
cana-5662	142	3	2	2	NUM
cana-5662	142	4	.	.	PUNCT
cana-5662	143	1	thus	thus	ADV
cana-5662	143	2	dwv	dwv	PROPN
cana-5662	143	3			PROPN
cana-5662	143	4	,	,	PUNCT
cana-5662	143	5	that	that	ADV
cana-5662	143	6	is	is	ADV
cana-5662	143	7	(	(	PUNCT
cana-5662	143	8	)	)	PUNCT
cana-5662	143	9	(	(	PUNCT
cana-5662	143	10	)	)	PUNCT
cana-5662	143	11	.	.	PUNCT
cana-5662	144	1	,	,	PUNCT
cana-5662	144	2	211	211	NUM
cana-5662	144	3	dggvdgvwv	dggvdgvwv	NOUN
cana-5662	144	4	−−	−−	PROPN
cana-5662	144	5			PROPN
cana-5662	144	6	since	since	SCONJ
cana-5662	144	7	(	(	PUNCT
cana-5662	144	8	)	)	PUNCT
cana-5662	144	9	−	−	VERB
cana-5662	144	10	dgv	dgv	PROPN
cana-5662	144	11	1	1	NUM
cana-5662	144	12	is	be	AUX
cana-5662	144	13	a	a	DET
cana-5662	144	14	tree	tree	NOUN
cana-5662	144	15	.	.	PUNCT
cana-5662	145	1	there	there	PRON
cana-5662	145	2	is	be	VERB
cana-5662	145	3	a	a	DET
cana-5662	145	4	tree	tree	NOUN
cana-5662	145	5	with	with	ADP
cana-5662	145	6	support	support	NOUN
cana-5662	145	7	vertices	vertice	VERB
cana-5662	145	8	v	v	NOUN
cana-5662	145	9	and	and	CCONJ
cana-5662	145	10	w	w	NOUN
cana-5662	145	11	in	in	ADP
cana-5662	145	12	(	(	PUNCT
cana-5662	145	13	)	)	PUNCT
cana-5662	145	14	dggv	dggv	PROPN
cana-5662	145	15	−21	−21	PROPN
cana-5662	146	1			PROPN
cana-5662	146	2	.hence	.hence	ADP
cana-5662	146	3	(	(	PUNCT
cana-5662	146	4	)	)	PUNCT
cana-5662	146	5	−	−	VERB
cana-5662	146	6	dggv	dggv	NOUN
cana-5662	146	7	21	21	NUM
cana-5662	146	8			PROPN
cana-5662	146	9	is	be	AUX
cana-5662	146	10	a	a	DET
cana-5662	146	11	tree	tree	NOUN
cana-5662	146	12	.	.	PUNCT
cana-5662	147	1	hence	hence	ADV
cana-5662	147	2	d	d	PROPN
cana-5662	147	3	is	be	AUX
cana-5662	147	4	a	a	DET
cana-5662	147	5	complementary	complementary	ADJ
cana-5662	147	6	tree	tree	NOUN
cana-5662	147	7	dominating	dominating	NOUN
cana-5662	147	8	set	set	VERB
cana-5662	147	9	in	in	ADP
cana-5662	147	10	21	21	NUM
cana-5662	147	11	gg	gg	PROPN
cana-5662	147	12			PROPN
cana-5662	147	13	.	.	PUNCT
cana-5662	148	1	corollary	corollary	ADJ
cana-5662	148	2	2.5	2.5	NUM
cana-5662	148	3	.	.	PUNCT
cana-5662	149	1	let	let	VERB
cana-5662	149	2	1	1	NUM
cana-5662	149	3	g	g	NOUN
cana-5662	149	4	and	and	CCONJ
cana-5662	149	5	2	2	NUM
cana-5662	149	6	g	g	NOUN
cana-5662	149	7	be	be	VERB
cana-5662	149	8	any	any	DET
cana-5662	149	9	connected	connected	ADJ
cana-5662	149	10	graph	graph	NOUN
cana-5662	149	11	.	.	PUNCT
cana-5662	150	1	then	then	ADV
cana-5662	150	2	(	(	PUNCT
cana-5662	150	3	)	)	PUNCT
cana-5662	150	4	(	(	PUNCT
cana-5662	150	5	)	)	PUNCT
cana-5662	150	6	(	(	PUNCT
cana-5662	150	7	)	)	PUNCT
cana-5662	150	8	.12	.12	NUM
cana-5662	150	9	2121	2121	NUM
cana-5662	150	10	ggggctd	ggggctd	VERB
cana-5662	150	11			PUNCT
cana-5662	150	12	−	−	PROPN
cana-5662	150	13	g1	g1	PROPN
cana-5662	150	14	is	be	AUX
cana-5662	150	15	not	not	PART
cana-5662	150	16	a	a	DET
cana-5662	150	17	tree	tree	NOUN
cana-5662	150	18	.	.	PUNCT
cana-5662	151	1	proof	proof	NOUN
cana-5662	151	2	.	.	PUNCT
cana-5662	152	1	let	let	VERB
cana-5662	152	2	.1	.1	NUM
cana-5662	152	3	ng	ng	PROPN
cana-5662	153	1	=	=	PRON
cana-5662	153	2	suppose	suppose	VERB
cana-5662	153	3	there	there	PRON
cana-5662	153	4	exist	exist	VERB
cana-5662	153	5	d	d	PRON
cana-5662	153	6	such	such	ADJ
cana-5662	153	7	that	that	SCONJ
cana-5662	153	8	d	d	NOUN
cana-5662	153	9	satisfies	satisfie	NOUN
cana-5662	153	10	(	(	PUNCT
cana-5662	153	11	ii	ii	NOUN
cana-5662	153	12	)	)	PUNCT
cana-5662	153	13	of	of	ADP
cana-5662	153	14	theorem	theorem	NOUN
cana-5662	153	15	[	[	PUNCT
cana-5662	153	16	4.1.2	4.1.2	NUM
cana-5662	153	17	]	]	PUNCT
cana-5662	153	18	communications	communication	NOUN
cana-5662	153	19	on	on	ADP
cana-5662	153	20	applied	apply	VERB
cana-5662	153	21	nonlinear	nonlinear	ADJ
cana-5662	153	22	analysis	analysis	NOUN
cana-5662	153	23	issn	issn	NOUN
cana-5662	153	24	:	:	PUNCT
cana-5662	153	25	1074	1074	NUM
cana-5662	153	26	-	-	PUNCT
cana-5662	153	27	133x	133x	NUM
cana-5662	153	28	vol	vol	NOUN
cana-5662	153	29	31	31	NUM
cana-5662	153	30	no	no	NOUN
cana-5662	153	31	.	.	PUNCT
cana-5662	154	1	7s	7	NOUN
cana-5662	154	2	(	(	PUNCT
cana-5662	154	3	2024	2024	NUM
cana-5662	154	4	)	)	PUNCT
cana-5662	154	5	758	758	NUM
cana-5662	154	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	154	7	(	(	PUNCT
cana-5662	154	8	)	)	PUNCT
cana-5662	154	9	(	(	PUNCT
cana-5662	154	10	)	)	PUNCT
cana-5662	155	1	22	22	NUM
cana-5662	155	2	2	2	NUM
cana-5662	155	3	2	2	NUM
cana-5662	155	4	2	2	NUM
cana-5662	155	5	)	)	PUNCT
cana-5662	155	6	.	.	PUNCT
cana-5662	156	1	(	(	PUNCT
cana-5662	156	2	2	2	NUM
cana-5662	156	3	since	since	SCONJ
cana-5662	156	4	ggei	ggei	PROPN
cana-5662	156	5	g	g	PROPN
cana-5662	156	6	g	g	PROPN
cana-5662	156	7			NUM
cana-5662	156	8			NOUN
cana-5662	156	9			NUM
cana-5662	156	10			NUM
cana-5662	156	11	(	(	PUNCT
cana-5662	156	12	)	)	PUNCT
cana-5662	156	13	(	(	PUNCT
cana-5662	156	14	)	)	PUNCT
cana-5662	156	15	(	(	PUNCT
cana-5662	156	16	)	)	PUNCT
cana-5662	156	17	.12	.12	NUM
cana-5662	156	18	2121	2121	NUM
cana-5662	156	19	ggggctd	ggggctd	VERB
cana-5662	156	20			ADV
cana-5662	156	21	−	−	PROPN
cana-5662	156	22	corollary	corollary	NOUN
cana-5662	156	23	2.6	2.6	NUM
cana-5662	156	24	.	.	PUNCT
cana-5662	157	1	let	let	VERB
cana-5662	157	2	g1	g1	PROPN
cana-5662	157	3	be	be	AUX
cana-5662	157	4	a	a	DET
cana-5662	157	5	tree	tree	NOUN
cana-5662	157	6	and	and	CCONJ
cana-5662	157	7	g2	g2	PROPN
cana-5662	157	8	be	be	VERB
cana-5662	157	9	any	any	DET
cana-5662	157	10	connected	connected	ADJ
cana-5662	157	11	graph	graph	NOUN
cana-5662	157	12	respectively	respectively	ADV
cana-5662	157	13	.	.	PUNCT
cana-5662	158	1	then	then	ADV
cana-5662	158	2	(	(	PUNCT
cana-5662	158	3	)	)	PUNCT
cana-5662	158	4	(	(	PUNCT
cana-5662	158	5	)	)	PUNCT
cana-5662	158	6	.2121	.2121	PROPN
cana-5662	158	7	ggggctd	ggggctd	VERB
cana-5662	158	8			PRON
cana-5662	159	1	=	=	NOUN
cana-5662	159	2			NOUN
cana-5662	159	3	proof	proof	NOUN
cana-5662	159	4	.	.	PUNCT
cana-5662	160	1	for	for	ADP
cana-5662	160	2	each	each	PRON
cana-5662	160	3	(	(	PUNCT
cana-5662	160	4	)	)	PUNCT
cana-5662	160	5	.1gvv	.1gvv	PUNCT
cana-5662	160	6	let	let	VERB
cana-5662	160	7	v	v	AUX
cana-5662	160	8	g2	g2	PROPN
cana-5662	160	9	be	be	AUX
cana-5662	160	10	a	a	DET
cana-5662	160	11	copy	copy	NOUN
cana-5662	160	12	of	of	ADP
cana-5662	160	13	g2	g2	PROPN
cana-5662	160	14	corresponding	correspond	VERB
cana-5662	160	15	to	to	ADP
cana-5662	160	16	vertex	vertex	NOUN
cana-5662	160	17	.v	.v	ADV
cana-5662	160	18	further	far	ADV
cana-5662	160	19	,	,	PUNCT
cana-5662	160	20	for	for	ADP
cana-5662	160	21	each	each	PRON
cana-5662	160	22	(	(	PUNCT
cana-5662	160	23	)	)	PUNCT
cana-5662	160	24	.1gvv	.1gvv	PUNCT
cana-5662	161	1	let	let	VERB
cana-5662	161	2	vd	vd	PART
cana-5662	161	3	be	be	AUX
cana-5662	161	4	a	a	DET
cana-5662	161	5	minimum	minimum	ADJ
cana-5662	161	6	dominating	dominating	NOUN
cana-5662	161	7	set	set	VERB
cana-5662	161	8	in	in	ADP
cana-5662	161	9	.2	.2	NUM
cana-5662	161	10	vg	vg	NOUN
cana-5662	161	11	by	by	ADP
cana-5662	161	12	theorem	theorem	NOUN
cana-5662	161	13	[	[	X
cana-5662	161	14	4.1.2	4.1.2	NUM
cana-5662	161	15	]	]	X
cana-5662	161	16	(	(	PUNCT
cana-5662	161	17	)	)	PUNCT
cana-5662	161	18			PROPN
cana-5662	161	19	1gvv	1gvv	NUM
cana-5662	161	20	vdd	vdd	PROPN
cana-5662	161	21			NOUN
cana-5662	161	22	=	=	PUNCT
cana-5662	161	23	is	be	AUX
cana-5662	161	24	a	a	DET
cana-5662	161	25	complementary	complementary	ADJ
cana-5662	161	26	tree	tree	NOUN
cana-5662	161	27	dominating	dominating	NOUN
cana-5662	161	28	set	set	VERB
cana-5662	161	29	in	in	ADP
cana-5662	161	30	.21	.21	NUM
cana-5662	161	31	gg	gg	NOUN
cana-5662	161	32			PRON
cana-5662	161	33	thus	thus	ADV
cana-5662	161	34	(	(	PUNCT
cana-5662	161	35	)	)	PUNCT
cana-5662	161	36	(	(	PUNCT
cana-5662	161	37	)	)	PUNCT
cana-5662	161	38	(	(	PUNCT
cana-5662	161	39	)	)	PUNCT
cana-5662	161	40	(	(	PUNCT
cana-5662	161	41	)	)	PUNCT
cana-5662	161	42	21	21	NUM
cana-5662	161	43	21	21	NUM
cana-5662	161	44	1	1	NUM
cana-5662	161	45	1	1	NUM
cana-5662	161	46	gg	gg	NOUN
cana-5662	161	47	d	d	PROPN
cana-5662	161	48	d	d	PROPN
cana-5662	161	49	dgg	dgg	PROPN
cana-5662	161	50	gvv	gvv	PROPN
cana-5662	161	51	v	v	ADP
cana-5662	161	52	gvv	gvv	PROPN
cana-5662	161	53	v	v	ADP
cana-5662	161	54	ctd	ctd	PROPN
cana-5662	161	55			NUM
cana-5662	161	56			NUM
cana-5662	161	57	=	=	PUNCT
cana-5662	162	1	=	=	SYM
cana-5662	162	2	=	=	SYM
cana-5662	162	3			PROPN
cana-5662	162	4			VERB
cana-5662	162	5			NOUN
cana-5662	162	6			NOUN
cana-5662	162	7			PROPN
cana-5662	162	8			AUX
cana-5662	162	9	therefore	therefore	ADV
cana-5662	162	10	,	,	PUNCT
cana-5662	162	11	(	(	PUNCT
cana-5662	162	12	)	)	PUNCT
cana-5662	162	13	(	(	PUNCT
cana-5662	162	14	)	)	PUNCT
cana-5662	162	15	.2121	.2121	PROPN
cana-5662	162	16	ggggctd	ggggctd	VERB
cana-5662	162	17			ADV
cana-5662	162	18			NOUN
cana-5662	162	19	here	here	ADV
cana-5662	162	20	,	,	PUNCT
cana-5662	162	21	we	we	PRON
cana-5662	162	22	consider	consider	VERB
cana-5662	162	23	g1	g1	NOUN
cana-5662	162	24	and	and	CCONJ
cana-5662	162	25	g2	g2	PROPN
cana-5662	162	26	be	be	VERB
cana-5662	162	27	any	any	DET
cana-5662	162	28	connected	connected	ADJ
cana-5662	162	29	graph	graph	NOUN
cana-5662	162	30	of	of	ADP
cana-5662	162	31	order	order	NOUN
cana-5662	162	32	n	n	NOUN
cana-5662	162	33	and	and	CCONJ
cana-5662	162	34	m	m	VERB
cana-5662	162	35	respectively	respectively	ADV
cana-5662	162	36	.	.	PUNCT
cana-5662	163	1	then	then	ADV
cana-5662	163	2	the	the	DET
cana-5662	163	3	vertex	vertex	NOUN
cana-5662	163	4	set	set	NOUN
cana-5662	163	5	{	{	PUNCT
cana-5662	163	6	𝑢𝑖𝑗/1	𝑢𝑖𝑗/1	PROPN
cana-5662	163	7	≤	≤	PROPN
cana-5662	163	8	𝑖	𝑖	SYM
cana-5662	163	9	≤	≤	NUM
cana-5662	163	10	𝑛	𝑛	NOUN
cana-5662	163	11	,	,	PUNCT
cana-5662	163	12	1	1	NUM
cana-5662	163	13	≤	≤	NUM
cana-5662	163	14	𝑗	𝑗	PRON
cana-5662	163	15	≤	≤	NUM
cana-5662	163	16	𝑚	𝑚	NOUN
cana-5662	163	17	}	}	PUNCT
cana-5662	163	18	is	be	AUX
cana-5662	163	19	the	the	DET
cana-5662	163	20	ith	ith	PROPN
cana-5662	163	21	copy	copy	NOUN
cana-5662	163	22	of	of	ADP
cana-5662	163	23	g2	g2	PROPN
cana-5662	163	24	is	be	AUX
cana-5662	163	25	adjacent	adjacent	ADJ
cana-5662	163	26	to	to	ADP
cana-5662	163	27	the	the	DET
cana-5662	163	28	ith	ith	PROPN
cana-5662	163	29	vertex	vertex	NOUN
cana-5662	163	30	of	of	ADP
cana-5662	163	31	g1	g1	PROPN
cana-5662	163	32	and	and	CCONJ
cana-5662	163	33	let	let	VERB
cana-5662	163	34	d	d	NOUN
cana-5662	163	35	is	be	AUX
cana-5662	163	36	a	a	DET
cana-5662	163	37	minimum	minimum	ADJ
cana-5662	163	38	ctd	ctd	NOUN
cana-5662	163	39	-	-	PUNCT
cana-5662	163	40	set	set	NOUN
cana-5662	163	41	of	of	ADP
cana-5662	163	42	21	21	NUM
cana-5662	163	43	gg	gg	NOUN
cana-5662	163	44			PROPN
cana-5662	163	45	.	.	PUNCT
cana-5662	164	1	hence	hence	ADV
cana-5662	164	2	(	(	PUNCT
cana-5662	164	3	)	)	PUNCT
cana-5662	164	4	−	−	VERB
cana-5662	164	5	dggv	dggv	NOUN
cana-5662	164	6	21	21	NUM
cana-5662	164	7			PROPN
cana-5662	164	8	is	be	AUX
cana-5662	164	9	a	a	DET
cana-5662	164	10	tree	tree	NOUN
cana-5662	164	11	.	.	PUNCT
cana-5662	165	1	3	3	NUM
cana-5662	165	2	complementary	complementary	ADJ
cana-5662	165	3	tree	tree	NOUN
cana-5662	165	4	domination	domination	NOUN
cana-5662	165	5	number	number	NOUN
cana-5662	165	6	of	of	ADP
cana-5662	165	7	corona	corona	NOUN
cana-5662	165	8	product	product	NOUN
cana-5662	165	9	of	of	ADP
cana-5662	165	10	complete	complete	ADJ
cana-5662	165	11	graph	graph	NOUN
cana-5662	165	12	with	with	ADP
cana-5662	165	13	some	some	DET
cana-5662	165	14	graphs	graph	NOUN
cana-5662	165	15	in	in	ADP
cana-5662	165	16	this	this	DET
cana-5662	165	17	section	section	NOUN
cana-5662	165	18	,	,	PUNCT
cana-5662	165	19	for	for	ADP
cana-5662	165	20	4n	4n	NUM
cana-5662	165	21	complementary	complementary	ADJ
cana-5662	165	22	tree	tree	NOUN
cana-5662	165	23	domination	domination	NOUN
cana-5662	165	24	number	number	NOUN
cana-5662	165	25	of	of	ADP
cana-5662	165	26	,	,	PUNCT
cana-5662	165	27	1gkn	1gkn	PROPN
cana-5662	165	28			PROPN
cana-5662	165	29	where	where	SCONJ
cana-5662	165	30	g1	g1	PROPN
cana-5662	165	31	is	be	AUX
cana-5662	165	32	any	any	DET
cana-5662	165	33	connected	connected	ADJ
cana-5662	165	34	graph	graph	NOUN
cana-5662	165	35	with	with	ADP
cana-5662	165	36	3m	3m	NUM
cana-5662	165	37	vertices	vertex	NOUN
cana-5662	165	38	are	be	AUX
cana-5662	165	39	obtained	obtain	VERB
cana-5662	165	40	.	.	PUNCT
cana-5662	166	1	here	here	ADV
cana-5662	166	2	,	,	PUNCT
cana-5662	166	3	we	we	PRON
cana-5662	166	4	consider	consider	VERB
cana-5662	166	5	d1	d1	PROPN
cana-5662	166	6	is	be	AUX
cana-5662	166	7	a	a	DET
cana-5662	166	8	ctd	ctd	NOUN
cana-5662	166	9	-	-	PUNCT
cana-5662	166	10	set	set	NOUN
cana-5662	166	11	of	of	ADP
cana-5662	166	12	kn	kn	PROPN
cana-5662	166	13	,	,	PUNCT
cana-5662	166	14	hence	hence	ADV
cana-5662	166	15	21	21	NUM
cana-5662	166	16	−=	−=	NOUN
cana-5662	166	17	nd	nd	NOUN
cana-5662	166	18	and	and	CCONJ
cana-5662	166	19	d2	d2	PROPN
cana-5662	166	20	be	be	AUX
cana-5662	166	21	the	the	DET
cana-5662	166	22	set	set	NOUN
cana-5662	166	23	whose	whose	DET
cana-5662	166	24	elements	element	NOUN
cana-5662	166	25	are	be	AUX
cana-5662	166	26	the	the	DET
cana-5662	166	27	vertices	vertex	NOUN
cana-5662	166	28	of	of	ADP
cana-5662	166	29	g1	g1	NOUN
cana-5662	166	30	which	which	PRON
cana-5662	166	31	are	be	AUX
cana-5662	166	32	adjacent	adjacent	ADJ
cana-5662	166	33	to	to	ADP
cana-5662	166	34	each	each	DET
cana-5662	166	35	vertex	vertex	NOUN
cana-5662	166	36	of	of	ADP
cana-5662	166	37	(	(	PUNCT
cana-5662	166	38	)	)	PUNCT
cana-5662	166	39	(	(	PUNCT
cana-5662	166	40	)	)	PUNCT
cana-5662	166	41	(	(	PUNCT
cana-5662	166	42	)	)	PUNCT
cana-5662	166	43	(	(	PUNCT
cana-5662	166	44	)	)	PUNCT
cana-5662	166	45	(	(	PUNCT
cana-5662	166	46	)	)	PUNCT
cana-5662	166	47	(	(	PUNCT
cana-5662	166	48	)	)	PUNCT
cana-5662	166	49	(	(	PUNCT
cana-5662	166	50	)	)	PUNCT
cana-5662	166	51	(	(	PUNCT
cana-5662	166	52	)	)	PUNCT
cana-5662	166	53	21	21	NUM
cana-5662	166	54	2	2	NUM
cana-5662	166	55	22	22	NUM
cana-5662	166	56	2	2	NUM
cana-5662	166	57	12	12	NUM
cana-5662	166	58	12	12	NUM
cana-5662	166	59	222	222	NUM
cana-5662	166	60	.2)2	.2)2	SYM
cana-5662	166	61	(	(	PUNCT
cana-5662	166	62	gg	gg	PROPN
cana-5662	166	63	gn	gn	PROPN
cana-5662	166	64	ggnd	ggnd	PROPN
cana-5662	166	65	ggnd	ggnd	NOUN
cana-5662	166	66			NUM
cana-5662	166	67			NUM
cana-5662	166	68			PRON
cana-5662	166	69			NUM
cana-5662	166	70	−	−	PROPN
cana-5662	166	71	−=	−=	ADJ
cana-5662	166	72	+	+	PROPN
cana-5662	166	73	−	−	ADJ
cana-5662	166	74	+	+	ADJ
cana-5662	166	75	−	−	ADJ
cana-5662	166	76	communications	communication	NOUN
cana-5662	166	77	on	on	ADP
cana-5662	166	78	applied	apply	VERB
cana-5662	166	79	nonlinear	nonlinear	ADJ
cana-5662	166	80	analysis	analysis	NOUN
cana-5662	166	81	issn	issn	NOUN
cana-5662	166	82	:	:	PUNCT
cana-5662	166	83	1074	1074	NUM
cana-5662	166	84	-	-	PUNCT
cana-5662	166	85	133x	133x	NUM
cana-5662	166	86	vol	vol	NOUN
cana-5662	166	87	31	31	NUM
cana-5662	166	88	no	no	NOUN
cana-5662	166	89	.	.	PUNCT
cana-5662	167	1	7s	7	NOUN
cana-5662	167	2	(	(	PUNCT
cana-5662	167	3	2024	2024	NUM
cana-5662	167	4	)	)	PUNCT
cana-5662	167	5	759	759	NUM
cana-5662	167	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	167	7	d1.hence	d1.hence	NOUN
cana-5662	167	8	mnd	mnd	PROPN
cana-5662	167	9	)	)	PUNCT
cana-5662	167	10	2(2	2(2	NUM
cana-5662	167	11	−=	−=	VERB
cana-5662	167	12	.clearly	.clearly	ADV
cana-5662	167	13	,	,	PUNCT
cana-5662	167	14	ddd	ddd	PROPN
cana-5662	167	15			PROPN
cana-5662	167	16	21	21	NUM
cana-5662	167	17	,	,	PUNCT
cana-5662	167	18	where	where	SCONJ
cana-5662	167	19	d	d	NOUN
cana-5662	167	20	is	be	AUX
cana-5662	167	21	a	a	DET
cana-5662	167	22	minimum	minimum	ADJ
cana-5662	167	23	ctd	ctd	NOUN
cana-5662	167	24	-	-	PUNCT
cana-5662	167	25	set	set	NOUN
cana-5662	167	26	of	of	ADP
cana-5662	167	27	1gkn	1gkn	NUM
cana-5662	167	28			PROPN
cana-5662	167	29	and	and	CCONJ
cana-5662	167	30	(	(	PUNCT
cana-5662	167	31	)	)	PUNCT
cana-5662	167	32	(	(	PUNCT
cana-5662	167	33	)	)	PUNCT
cana-5662	167	34	.2121	.2121	PROPN
cana-5662	168	1	−+=	−+=	PROPN
cana-5662	168	2	nmdd	nmdd	PROPN
cana-5662	168	3	proposition	proposition	NOUN
cana-5662	168	4	3.1	3.1	NUM
cana-5662	168	5	.	.	PUNCT
cana-5662	169	1	(	(	PUNCT
cana-5662	169	2	)	)	PUNCT
cana-5662	169	3	.221	.221	NUM
cana-5662	169	4	−=	−=	ADJ
cana-5662	169	5	nkknctd	nkknctd	VERB
cana-5662	169	6			NOUN
cana-5662	169	7	proof	proof	NOUN
cana-5662	169	8	.	.	PUNCT
cana-5662	170	1	let	let	VERB
cana-5662	170	2	𝐺	𝐺	PROPN
cana-5662	170	3	=	=	NOUN
cana-5662	170	4	nk	nk	PROPN
cana-5662	170	5	∘	∘	PROPN
cana-5662	170	6	𝐾1	𝐾1	PROPN
cana-5662	170	7	.	.	PUNCT
cana-5662	171	1	let	let	VERB
cana-5662	171	2	𝑉(𝐾𝑛	𝑉(𝐾𝑛	NOUN
cana-5662	171	3	)	)	PUNCT
cana-5662	172	1	=	=	PRON
cana-5662	172	2	{	{	PUNCT
cana-5662	172	3	𝑣1	𝑣1	PROPN
cana-5662	172	4	,	,	PUNCT
cana-5662	172	5	𝑣2	𝑣2	PROPN
cana-5662	172	6	,	,	PUNCT
cana-5662	172	7	.	.	PUNCT
cana-5662	172	8	.	.	PUNCT
cana-5662	172	9	.	.	PUNCT
cana-5662	172	10	.	.	PUNCT
cana-5662	172	11	.	.	PUNCT
cana-5662	172	12	.	.	PUNCT
cana-5662	172	13	.	.	PUNCT
cana-5662	173	1	𝑣𝑛	𝑣𝑛	X
cana-5662	173	2	}	}	PUNCT
cana-5662	173	3	and	and	CCONJ
cana-5662	173	4	vertex	vertex	NOUN
cana-5662	173	5	𝑢𝑖	𝑢𝑖	NOUN
cana-5662	173	6	be	be	AUX
cana-5662	173	7	the	the	DET
cana-5662	173	8	ith	ith	PROPN
cana-5662	173	9	copy	copy	NOUN
cana-5662	173	10	of	of	ADP
cana-5662	173	11	𝐾1	𝐾1	PROPN
cana-5662	173	12	attached	attach	VERB
cana-5662	173	13	to	to	ADP
cana-5662	173	14	the	the	DET
cana-5662	173	15	vertex	vertex	NOUN
cana-5662	173	16	𝑣𝑖	𝑣𝑖	ADP
cana-5662	173	17	.then	.then	AUX
cana-5662	173	18	𝑉(𝐺	𝑉(𝐺	VERB
cana-5662	173	19	)	)	PUNCT
cana-5662	173	20	=	=	PRON
cana-5662	173	21	{	{	PUNCT
cana-5662	173	22	𝑣𝑖	𝑣𝑖	NOUN
cana-5662	173	23	,	,	PUNCT
cana-5662	173	24	𝑢𝑖/1	𝑢𝑖/1	ADJ
cana-5662	173	25	≤	≤	NOUN
cana-5662	173	26	𝑖	𝑖	SYM
cana-5662	173	27	≤	≤	NOUN
cana-5662	173	28	𝑛}.here	𝑛}.here	NUM
cana-5662	173	29	𝑢1	𝑢1	PROPN
cana-5662	173	30	,	,	PUNCT
cana-5662	173	31	𝑢2	𝑢2	PROPN
cana-5662	173	32	.	.	PUNCT
cana-5662	173	33	.	.	PUNCT
cana-5662	173	34	.	.	PUNCT
cana-5662	173	35	.	.	PUNCT
cana-5662	173	36	.	.	PUNCT
cana-5662	173	37	.	.	PUNCT
cana-5662	173	38	.	.	PUNCT
cana-5662	174	1	𝑢𝑛	𝑢𝑛	PROPN
cana-5662	174	2	are	be	AUX
cana-5662	174	3	the	the	DET
cana-5662	174	4	pendant	pendant	ADJ
cana-5662	174	5	vertices	vertex	NOUN
cana-5662	174	6	of	of	ADP
cana-5662	174	7	𝐺.	𝐺.	NOUN
cana-5662	174	8	we	we	PRON
cana-5662	174	9	have	have	VERB
cana-5662	174	10	pendant	pendant	ADJ
cana-5662	174	11	vertices	vertex	NOUN
cana-5662	174	12	are	be	AUX
cana-5662	174	13	members	member	NOUN
cana-5662	174	14	of	of	ADP
cana-5662	174	15	ctd	ctd	NOUN
cana-5662	174	16	-	-	PUNCT
cana-5662	174	17	set	set	NOUN
cana-5662	174	18	of	of	ADP
cana-5662	174	19	g	g	NOUN
cana-5662	175	1	[	[	X
cana-5662	175	2	3	3	NUM
cana-5662	175	3	]	]	PUNCT
cana-5662	175	4	.	.	PUNCT
cana-5662	176	1	hence	hence	ADV
cana-5662	176	2	,	,	PUNCT
cana-5662	176	3	d	d	PROPN
cana-5662	176	4	=	=	PRON
cana-5662	176	5	{	{	PUNCT
cana-5662	176	6	vi	vi	NOUN
cana-5662	176	7	:	:	PUNCT
cana-5662	176	8	1	1	NUM
cana-5662	176	9	≤	≤	NUM
cana-5662	176	10	i	i	PRON
cana-5662	176	11	≤	≤	NOUN
cana-5662	176	12	n	n	CCONJ
cana-5662	176	13	−	−	PROPN
cana-5662	176	14	2}∪{ui	2}∪{ui	NOUN
cana-5662	176	15	:	:	PUNCT
cana-5662	176	16	1	1	NUM
cana-5662	176	17	≤	≤	NUM
cana-5662	176	18	i	i	PRON
cana-5662	176	19	≤	≤	NOUN
cana-5662	176	20	n	n	CCONJ
cana-5662	176	21	}	}	PUNCT
cana-5662	176	22	=	=	SYM
cana-5662	176	23	n	n	CCONJ
cana-5662	176	24	−	−	NUM
cana-5662	176	25	2	2	NUM
cana-5662	176	26	+	+	CCONJ
cana-5662	176	27	n	n	CCONJ
cana-5662	176	28	=	=	SYM
cana-5662	176	29	2	2	NUM
cana-5662	176	30	n	n	NOUN
cana-5662	176	31	−	−	NUM
cana-5662	176	32	2	2	NUM
cana-5662	176	33	.	.	PUNCT
cana-5662	176	34	is	be	AUX
cana-5662	176	35	a	a	DET
cana-5662	176	36	minimum	minimum	ADJ
cana-5662	176	37	ctd	ctd	NOUN
cana-5662	176	38	-	-	PUNCT
cana-5662	176	39	set	set	NOUN
cana-5662	176	40	of	of	ADP
cana-5662	176	41	𝐺.	𝐺.	NOUN
cana-5662	176	42	hence	hence	ADV
cana-5662	176	43	,	,	PUNCT
cana-5662	176	44	|𝐷|	|𝐷|	X
cana-5662	176	45	  	  	SPACE
cana-5662	176	46	=	=	SYM
cana-5662	176	47	 	 	SPACE
cana-5662	176	48	𝛾𝑐𝑡𝑑(𝐺	𝛾𝑐𝑡𝑑(𝐺	NUM
cana-5662	176	49	)	)	PUNCT
cana-5662	177	1	=	=	SYM
cana-5662	177	2	2𝑛	2𝑛	PROPN
cana-5662	177	3	−	−	NOUN
cana-5662	177	4	2	2	X
cana-5662	177	5	.	.	PUNCT
cana-5662	177	6	proposition	proposition	NOUN
cana-5662	177	7	3.2	3.2	NUM
cana-5662	177	8	.	.	PUNCT
cana-5662	178	1	(	(	PUNCT
cana-5662	178	2	)	)	PUNCT
cana-5662	178	3	.432	.432	NUM
cana-5662	179	1	−=	−=	ADP
cana-5662	179	2	nkknctd	nkknctd	VERB
cana-5662	179	3			NOUN
cana-5662	179	4	proof	proof	NOUN
cana-5662	179	5	.	.	PUNCT
cana-5662	180	1	let	let	VERB
cana-5662	180	2	v	v	X
cana-5662	180	3	(	(	PUNCT
cana-5662	180	4	kn	kn	PROPN
cana-5662	180	5	)	)	PUNCT
cana-5662	180	6	=	=	SYM
cana-5662	180	7	{	{	PUNCT
cana-5662	180	8	v1	v1	PROPN
cana-5662	180	9	,	,	PUNCT
cana-5662	180	10	v2	v2	PROPN
cana-5662	180	11	,	,	PUNCT
cana-5662	180	12	.	.	PUNCT
cana-5662	180	13	.	.	PUNCT
cana-5662	181	1	.	.	PUNCT
cana-5662	182	1	,	,	PUNCT
cana-5662	182	2	vn	vn	NOUN
cana-5662	182	3	}	}	PUNCT
cana-5662	182	4	and	and	CCONJ
cana-5662	182	5	v	v	NOUN
cana-5662	182	6	(	(	PUNCT
cana-5662	182	7	k2	k2	NOUN
cana-5662	182	8	)	)	PUNCT
cana-5662	182	9	=	=	SYM
cana-5662	182	10	{	{	PUNCT
cana-5662	182	11	u1	u1	NOUN
cana-5662	182	12	,	,	PUNCT
cana-5662	182	13	u2	u2	PROPN
cana-5662	182	14	}	}	PUNCT
cana-5662	182	15	.	.	PUNCT
cana-5662	183	1	then	then	ADV
cana-5662	183	2	v	v	X
cana-5662	183	3	(	(	PUNCT
cana-5662	183	4	kn	kn	PROPN
cana-5662	183	5	◦	◦	PROPN
cana-5662	183	6	k2	k2	NOUN
cana-5662	183	7	)	)	PUNCT
cana-5662	183	8	=	=	PRON
cana-5662	184	1	{	{	PUNCT
cana-5662	184	2	vi/1	vi/1	NOUN
cana-5662	184	3	≤	≤	NUM
cana-5662	184	4	i	i	PRON
cana-5662	184	5	≤	≤	PROPN
cana-5662	184	6	n	n	CCONJ
cana-5662	184	7	}	}	PUNCT
cana-5662	184	8	∪{uij/1	∪{uij/1	VERB
cana-5662	184	9	≤	≤	ADJ
cana-5662	184	10	i	i	NOUN
cana-5662	184	11	≤	≤	PROPN
cana-5662	184	12	n	n	CCONJ
cana-5662	184	13	,	,	PUNCT
cana-5662	184	14	1	1	NUM
cana-5662	184	15	≤	≤	NUM
cana-5662	184	16	j	j	PROPN
cana-5662	184	17	≤	≤	ADV
cana-5662	184	18	2	2	NUM
cana-5662	184	19	}	}	PUNCT
cana-5662	184	20	.we	.we	PUNCT
cana-5662	185	1	have	have	AUX
cana-5662	185	2	,	,	PUNCT
cana-5662	185	3	γctd	γctd	VERB
cana-5662	185	4	(	(	PUNCT
cana-5662	185	5	kn	kn	PROPN
cana-5662	185	6	)	)	PUNCT
cana-5662	185	7	=	=	SYM
cana-5662	186	1	n	n	CCONJ
cana-5662	186	2	−	−	NUM
cana-5662	186	3	2	2	NUM
cana-5662	187	1	[	[	X
cana-5662	187	2	3	3	NUM
cana-5662	187	3	]	]	PUNCT
cana-5662	187	4	.	.	PUNCT
cana-5662	188	1	by	by	ADP
cana-5662	188	2	choosing	choose	VERB
cana-5662	188	3	(	(	PUNCT
cana-5662	188	4	n	n	CCONJ
cana-5662	188	5	−	−	PROPN
cana-5662	188	6	2	2	NUM
cana-5662	188	7	)	)	PUNCT
cana-5662	188	8	vertices	vertex	NOUN
cana-5662	188	9	of	of	ADP
cana-5662	188	10	kn	kn	PROPN
cana-5662	188	11	say	say	VERB
cana-5662	188	12	v1	v1	PROPN
cana-5662	188	13	,	,	PUNCT
cana-5662	188	14	v2	v2	PROPN
cana-5662	188	15	,	,	PUNCT
cana-5662	188	16	.	.	PUNCT
cana-5662	188	17	.	.	PUNCT
cana-5662	189	1	.	.	PUNCT
cana-5662	190	1	,	,	PUNCT
cana-5662	190	2	vn−2	vn−2	PROPN
cana-5662	190	3	which	which	PRON
cana-5662	190	4	form	form	VERB
cana-5662	190	5	a	a	DET
cana-5662	190	6	minimum	minimum	ADJ
cana-5662	190	7	ctd	ctd	NOUN
cana-5662	190	8	-	-	PUNCT
cana-5662	190	9	set	set	NOUN
cana-5662	190	10	in	in	ADP
cana-5662	190	11	kn	kn	PROPN
cana-5662	190	12	and	and	CCONJ
cana-5662	190	13	vertices	vertex	NOUN
cana-5662	190	14	which	which	PRON
cana-5662	190	15	are	be	AUX
cana-5662	190	16	adjacent	adjacent	ADJ
cana-5662	190	17	to	to	PART
cana-5662	190	18	{	{	PUNCT
cana-5662	190	19	v1	v1	NOUN
cana-5662	190	20	,	,	PUNCT
cana-5662	190	21	v2	v2	NOUN
cana-5662	190	22	,	,	PUNCT
cana-5662	190	23	.	.	PUNCT
cana-5662	190	24	.	.	PUNCT
cana-5662	191	1	.	.	PUNCT
cana-5662	192	1	,	,	PUNCT
cana-5662	192	2	vn−2	vn−2	PROPN
cana-5662	192	3	}	}	PUNCT
cana-5662	192	4	are	be	AUX
cana-5662	192	5	{	{	PUNCT
cana-5662	192	6	uij/1	uij/1	PROPN
cana-5662	192	7	≤	≤	PROPN
cana-5662	192	8	i	i	NOUN
cana-5662	192	9	≤	≤	NOUN
cana-5662	192	10	n	n	CCONJ
cana-5662	192	11	−	−	PROPN
cana-5662	192	12	2	2	NUM
cana-5662	192	13	,	,	PUNCT
cana-5662	192	14	1	1	NUM
cana-5662	192	15	≤	≤	NUM
cana-5662	192	16	j	j	PROPN
cana-5662	192	17	≤	≤	ADV
cana-5662	192	18	2	2	NUM
cana-5662	192	19	}	}	PUNCT
cana-5662	192	20	.	.	PUNCT
cana-5662	193	1	therefore	therefore	ADV
cana-5662	193	2	,	,	PUNCT
cana-5662	193	3	d	d	PROPN
cana-5662	193	4	=	=	PRON
cana-5662	193	5	{	{	PUNCT
cana-5662	193	6	vi	vi	NOUN
cana-5662	193	7	:	:	PUNCT
cana-5662	193	8	1	1	NUM
cana-5662	193	9	≤	≤	NUM
cana-5662	193	10	i	i	PRON
cana-5662	193	11	≤	≤	ADJ
cana-5662	193	12	n	n	CCONJ
cana-5662	193	13	−	−	PROPN
cana-5662	193	14	2	2	NUM
cana-5662	193	15	}	}	PUNCT
cana-5662	193	16	∪	∪	ADJ
cana-5662	193	17	{	{	PUNCT
cana-5662	193	18	uij	uij	PRON
cana-5662	193	19	:	:	PUNCT
cana-5662	193	20	1	1	NUM
cana-5662	193	21	≤	≤	NUM
cana-5662	193	22	i	i	PRON
cana-5662	193	23	≤	≤	PUNCT
cana-5662	193	24	n-2	n-2	NOUN
cana-5662	193	25	,	,	PUNCT
cana-5662	193	26	1	1	NUM
cana-5662	193	27	≤	≤	NUM
cana-5662	193	28	j	j	PROPN
cana-5662	193	29	≤	≤	NUM
cana-5662	193	30	2}∪	2}∪	NUM
cana-5662	193	31	1,1,1	1,1,1	NOUN
cana-5662	193	32	,	,	PUNCT
cana-5662	193	33	nn	nn	X
cana-5662	193	34	uu	uu	INTJ
cana-5662	193	35	−	−	PROPN
cana-5662	194	1	=	=	SYM
cana-5662	194	2	n	n	CCONJ
cana-5662	194	3	−	−	NUM
cana-5662	194	4	2	2	NUM
cana-5662	194	5	+	+	NUM
cana-5662	194	6	2n	2n	NUM
cana-5662	194	7	–	–	PUNCT
cana-5662	194	8	4	4	NUM
cana-5662	194	9	+	+	SYM
cana-5662	194	10	2	2	NUM
cana-5662	194	11	=	=	SYM
cana-5662	194	12	3n	3n	NUM
cana-5662	194	13	−	−	NOUN
cana-5662	194	14	4	4	NUM
cana-5662	194	15	proposition	proposition	NOUN
cana-5662	194	16	3.3	3.3	NUM
cana-5662	194	17	.	.	PUNCT
cana-5662	195	1	for	for	ADP
cana-5662	195	2	m	m	PROPN
cana-5662	195	3	≥	≥	NOUN
cana-5662	195	4	2	2	NUM
cana-5662	195	5	,	,	PUNCT
cana-5662	195	6	γctd(kn	γctd(kn	NOUN
cana-5662	195	7	◦	◦	NOUN
cana-5662	195	8	mk	mk	NOUN
cana-5662	195	9	)	)	PUNCT
cana-5662	196	1	=	=	SYM
cana-5662	196	2	mn	mn	PROPN
cana-5662	196	3	+	+	CCONJ
cana-5662	196	4	n	n	CCONJ
cana-5662	196	5	−	−	PROPN
cana-5662	196	6	2	2	NUM
cana-5662	196	7	.	.	PUNCT
cana-5662	196	8	proof	proof	NOUN
cana-5662	196	9	.	.	PUNCT
cana-5662	197	1	take	take	VERB
cana-5662	197	2	g	g	NOUN
cana-5662	197	3	=	=	SYM
cana-5662	197	4	kn	kn	PROPN
cana-5662	197	5	◦	◦	PROPN
cana-5662	197	6	mk	mk	PROPN
cana-5662	197	7	.	.	PUNCT
cana-5662	198	1	let	let	VERB
cana-5662	198	2	v	v	X
cana-5662	198	3	(	(	PUNCT
cana-5662	198	4	kn	kn	PROPN
cana-5662	198	5	)	)	PUNCT
cana-5662	198	6	=	=	SYM
cana-5662	198	7	{	{	PUNCT
cana-5662	198	8	v1	v1	PROPN
cana-5662	198	9	,	,	PUNCT
cana-5662	198	10	v2	v2	PROPN
cana-5662	198	11	,	,	PUNCT
cana-5662	198	12	.	.	PUNCT
cana-5662	198	13	.	.	PUNCT
cana-5662	199	1	.	.	PUNCT
cana-5662	200	1	,	,	PUNCT
cana-5662	200	2	vn	vn	PROPN
cana-5662	200	3	}	}	PUNCT
cana-5662	200	4	and	and	CCONJ
cana-5662	200	5	{	{	PUNCT
cana-5662	200	6	u1	u1	NOUN
cana-5662	200	7	,	,	PUNCT
cana-5662	200	8	u2	u2	NOUN
cana-5662	200	9	,	,	PUNCT
cana-5662	200	10	.	.	PUNCT
cana-5662	200	11	.	.	PUNCT
cana-5662	200	12	.	.	PUNCT
cana-5662	201	1	,	,	PUNCT
cana-5662	201	2	um	um	INTJ
cana-5662	201	3	}	}	PUNCT
cana-5662	201	4	be	be	AUX
cana-5662	201	5	the	the	DET
cana-5662	201	6	vertex	vertex	NOUN
cana-5662	201	7	set	set	NOUN
cana-5662	201	8	of	of	ADP
cana-5662	201	9	the	the	DET
cana-5662	201	10	ith	ith	PROPN
cana-5662	201	11	copy	copy	NOUN
cana-5662	201	12	of	of	ADP
cana-5662	201	13	mk	mk	PROPN
cana-5662	201	14	is	be	AUX
cana-5662	201	15	adjacent	adjacent	ADJ
cana-5662	201	16	to	to	ADP
cana-5662	201	17	the	the	DET
cana-5662	201	18	vertex	vertex	NOUN
cana-5662	201	19	vi	vi	PROPN
cana-5662	201	20	.	.	PUNCT
cana-5662	202	1	then	then	ADV
cana-5662	202	2	v	v	X
cana-5662	202	3	(	(	PUNCT
cana-5662	202	4	g	g	NOUN
cana-5662	202	5	)	)	PUNCT
cana-5662	202	6	=	=	PRON
cana-5662	203	1	{	{	PUNCT
cana-5662	203	2	vi/1	vi/1	NOUN
cana-5662	203	3	≤	≤	NUM
cana-5662	203	4	i	i	PRON
cana-5662	203	5	≤	≤	NOUN
cana-5662	203	6	n	n	CCONJ
cana-5662	203	7	}	}	PUNCT
cana-5662	203	8	∪	∪	X
cana-5662	203	9	{	{	PUNCT
cana-5662	203	10	uij/1	uij/1	PROPN
cana-5662	203	11	≤	≤	PROPN
cana-5662	203	12	i	i	PROPN
cana-5662	203	13	≤	≤	PROPN
cana-5662	203	14	n	n	CCONJ
cana-5662	203	15	,	,	PUNCT
cana-5662	203	16	1	1	NUM
cana-5662	203	17	≤	≤	NUM
cana-5662	203	18	j	j	PROPN
cana-5662	203	19	≤	≤	PROPN
cana-5662	203	20	m	m	VERB
cana-5662	203	21	}	}	PUNCT
cana-5662	203	22	where	where	SCONJ
cana-5662	203	23	uij	uij	PRON
cana-5662	203	24	’s	’	VERB
cana-5662	203	25	is	be	AUX
cana-5662	203	26	the	the	DET
cana-5662	203	27	ith	ith	PROPN
cana-5662	203	28	copy	copy	NOUN
cana-5662	203	29	of	of	ADP
cana-5662	203	30	mk	mk	PROPN
cana-5662	203	31	is	be	AUX
cana-5662	203	32	adjacent	adjacent	ADJ
cana-5662	203	33	to	to	ADP
cana-5662	203	34	the	the	DET
cana-5662	203	35	vertex	vertex	NOUN
cana-5662	203	36	vi	vi	PROPN
cana-5662	203	37	in	in	ADP
cana-5662	203	38	kn	kn	PROPN
cana-5662	203	39	.	.	PUNCT
cana-5662	204	1	let	let	VERB
cana-5662	204	2	d	d	PRON
cana-5662	204	3	be	be	AUX
cana-5662	204	4	a	a	DET
cana-5662	204	5	minimum	minimum	ADJ
cana-5662	204	6	ctd	ctd	NOUN
cana-5662	204	7	-	-	PUNCT
cana-5662	204	8	set	set	NOUN
cana-5662	204	9	of	of	ADP
cana-5662	204	10	g.	g.	PROPN
cana-5662	204	11	since	since	SCONJ
cana-5662	204	12	pendant	pendant	ADJ
cana-5662	204	13	vertices	vertex	NOUN
cana-5662	204	14	are	be	AUX
cana-5662	204	15	members	member	NOUN
cana-5662	204	16	of	of	ADP
cana-5662	204	17	every	every	DET
cana-5662	204	18	ctd	ctd	NOUN
cana-5662	204	19	-	-	PUNCT
cana-5662	204	20	set	set	VERB
cana-5662	204	21	g.	g.	NOUN
cana-5662	204	22	by	by	ADP
cana-5662	204	23	choosing	choose	VERB
cana-5662	204	24	pendant	pendant	ADJ
cana-5662	204	25	vertices	vertex	NOUN
cana-5662	204	26	,	,	PUNCT
cana-5662	204	27	it	it	PRON
cana-5662	204	28	dominates	dominate	VERB
cana-5662	204	29	all	all	DET
cana-5662	204	30	the	the	DET
cana-5662	204	31	vertices	vertex	NOUN
cana-5662	204	32	of	of	ADP
cana-5662	204	33	kn	kn	PROPN
cana-5662	204	34	but	but	CCONJ
cana-5662	204	35	⟨v(g	⟨v(g	CCONJ
cana-5662	204	36	)	)	PUNCT
cana-5662	204	37	−	−	NOUN
cana-5662	204	38	d⟩	d⟩	NOUN
cana-5662	204	39	forms	form	VERB
cana-5662	204	40	a	a	DET
cana-5662	204	41	cycle	cycle	NOUN
cana-5662	204	42	.	.	PUNCT
cana-5662	205	1	so	so	ADV
cana-5662	205	2	we	we	PRON
cana-5662	205	3	are	be	AUX
cana-5662	205	4	choosing	choose	VERB
cana-5662	205	5			PROPN
cana-5662	205	6			PROPN
cana-5662	205	7	2	2	NUM
cana-5662	205	8	1	1	NUM
cana-5662	205	9	−	−	NOUN
cana-5662	205	10	=	=	SYM
cana-5662	205	11	n	n	CCONJ
cana-5662	205	12	iiv	iiv	NOUN
cana-5662	205	13	and	and	CCONJ
cana-5662	205	14	all	all	DET
cana-5662	205	15	the	the	DET
cana-5662	205	16	pendant	pendant	ADJ
cana-5662	205	17	vertices	vertex	NOUN
cana-5662	205	18	in	in	ADP
cana-5662	205	19	a	a	DET
cana-5662	205	20	graph	graph	NOUN
cana-5662	205	21	g.	g.	NOUN
cana-5662	205	22	therefore	therefore	ADV
cana-5662	205	23	,	,	PUNCT
cana-5662	205	24	d	d	PROPN
cana-5662	205	25	=	=	PRON
cana-5662	205	26	{	{	PUNCT
cana-5662	205	27	vi	vi	NOUN
cana-5662	205	28	:	:	PUNCT
cana-5662	205	29	1	1	NUM
cana-5662	205	30	≤	≤	NUM
cana-5662	205	31	i	i	PRON
cana-5662	205	32	≤	≤	ADJ
cana-5662	205	33	n	n	CCONJ
cana-5662	205	34	−	−	PROPN
cana-5662	205	35	2	2	NUM
cana-5662	205	36	}	}	PUNCT
cana-5662	205	37	∪	∪	ADJ
cana-5662	205	38	{	{	PUNCT
cana-5662	205	39	uij	uij	PRON
cana-5662	205	40	:	:	PUNCT
cana-5662	205	41	1	1	NUM
cana-5662	205	42	≤	≤	NUM
cana-5662	205	43	i	i	PRON
cana-5662	205	44	≤	≤	PROPN
cana-5662	205	45	n	n	CCONJ
cana-5662	205	46	,	,	PUNCT
cana-5662	205	47	1	1	NUM
cana-5662	205	48	≤	≤	NUM
cana-5662	205	49	j	j	PROPN
cana-5662	205	50	≤	≤	PROPN
cana-5662	205	51	m	m	PROPN
cana-5662	205	52	}	}	PUNCT
cana-5662	205	53	communications	communication	NOUN
cana-5662	205	54	on	on	ADP
cana-5662	205	55	applied	apply	VERB
cana-5662	205	56	nonlinear	nonlinear	ADJ
cana-5662	205	57	analysis	analysis	NOUN
cana-5662	205	58	issn	issn	NOUN
cana-5662	205	59	:	:	PUNCT
cana-5662	205	60	1074	1074	NUM
cana-5662	205	61	-	-	PUNCT
cana-5662	205	62	133x	133x	NUM
cana-5662	205	63	vol	vol	NOUN
cana-5662	205	64	31	31	NUM
cana-5662	205	65	no	no	NOUN
cana-5662	205	66	.	.	PUNCT
cana-5662	206	1	7s	7	NOUN
cana-5662	206	2	(	(	PUNCT
cana-5662	206	3	2024	2024	NUM
cana-5662	206	4	)	)	PUNCT
cana-5662	206	5	760	760	NUM
cana-5662	206	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	206	7	=	=	SYM
cana-5662	206	8	n	n	CCONJ
cana-5662	206	9	−	−	NUM
cana-5662	206	10	2	2	NUM
cana-5662	206	11	+	+	NUM
cana-5662	206	12	nm	nm	ADJ
cana-5662	206	13	=	=	SYM
cana-5662	206	14	mn	mn	PROPN
cana-5662	206	15	+	+	CCONJ
cana-5662	206	16	n	n	CCONJ
cana-5662	206	17	−	−	PROPN
cana-5662	206	18	2	2	NUM
cana-5662	206	19	.	.	PUNCT
cana-5662	206	20	proposition	proposition	NOUN
cana-5662	206	21	3.4	3.4	NUM
cana-5662	206	22	.	.	PUNCT
cana-5662	207	1	for	for	ADP
cana-5662	207	2	m	m	PROPN
cana-5662	207	3	≥	≥	NOUN
cana-5662	207	4	3	3	NUM
cana-5662	207	5	,	,	PUNCT
cana-5662	207	6	γctd(kn	γctd(kn	VERB
cana-5662	207	7	◦	◦	NOUN
cana-5662	207	8	k	k	PROPN
cana-5662	207	9	1,m−1	1,m−1	NUM
cana-5662	207	10	)	)	PUNCT
cana-5662	208	1	=	=	SYM
cana-5662	209	1	n	n	PROPN
cana-5662	210	1	+	+	CCONJ
cana-5662	211	1	(	(	PUNCT
cana-5662	211	2	m+1)(n	m+1)(n	PROPN
cana-5662	211	3	−	−	PROPN
cana-5662	211	4	2	2	NUM
cana-5662	211	5	)	)	PUNCT
cana-5662	211	6	.	.	PUNCT
cana-5662	212	1	proof	proof	NOUN
cana-5662	212	2	.	.	PUNCT
cana-5662	213	1	take	take	VERB
cana-5662	213	2	g	g	NOUN
cana-5662	213	3	=	=	PUNCT
cana-5662	213	4	kn	kn	PROPN
cana-5662	213	5	◦	◦	PROPN
cana-5662	213	6	k1,m−1	k1,m−1	PROPN
cana-5662	213	7	.	.	PUNCT
cana-5662	214	1	let	let	VERB
cana-5662	214	2	v	v	X
cana-5662	214	3	(	(	PUNCT
cana-5662	214	4	kn	kn	PROPN
cana-5662	214	5	)	)	PUNCT
cana-5662	214	6	=	=	PRON
cana-5662	214	7	{	{	PUNCT
cana-5662	214	8	vi	vi	NOUN
cana-5662	214	9	/1	/1	NOUN
cana-5662	214	10	≤	≤	NUM
cana-5662	215	1	i	i	PRON
cana-5662	215	2	≤	≤	NOUN
cana-5662	215	3	n	n	CCONJ
cana-5662	215	4	}	}	PUNCT
cana-5662	215	5	and	and	CCONJ
cana-5662	215	6	v	v	X
cana-5662	215	7	(	(	PUNCT
cana-5662	215	8	k1,m−1	k1,m−1	PROPN
cana-5662	215	9	)	)	PUNCT
cana-5662	215	10	=	=	PRON
cana-5662	215	11	{	{	PUNCT
cana-5662	215	12	w	w	PROPN
cana-5662	215	13	,	,	PUNCT
cana-5662	215	14	u1	u1	NOUN
cana-5662	215	15	,	,	PUNCT
cana-5662	215	16	u2	u2	NOUN
cana-5662	215	17	,	,	PUNCT
cana-5662	215	18	.	.	PUNCT
cana-5662	215	19	.	.	PUNCT
cana-5662	215	20	.	.	PUNCT
cana-5662	216	1	,	,	PUNCT
cana-5662	216	2	um−1	um−1	PROPN
cana-5662	216	3	}	}	PUNCT
cana-5662	216	4	.	.	PUNCT
cana-5662	217	1	then	then	ADV
cana-5662	217	2	v	v	X
cana-5662	217	3	(	(	PUNCT
cana-5662	217	4	g	g	NOUN
cana-5662	217	5	)	)	PUNCT
cana-5662	217	6	=	=	PRON
cana-5662	218	1	{	{	PUNCT
cana-5662	218	2	vi/1	vi/1	NOUN
cana-5662	218	3	≤	≤	NUM
cana-5662	219	1	i	i	PRON
cana-5662	220	1	≤	≤	ADJ
cana-5662	221	1	n}∪{wi	n}∪{wi	PROPN
cana-5662	221	2	uij	uij	PRON
cana-5662	221	3	,	,	PUNCT
cana-5662	221	4	1	1	NUM
cana-5662	221	5	≤	≤	NUM
cana-5662	221	6	i	i	PRON
cana-5662	221	7	≤	≤	PROPN
cana-5662	221	8	n	n	CCONJ
cana-5662	221	9	,	,	PUNCT
cana-5662	221	10	1	1	NUM
cana-5662	221	11	≤	≤	NUM
cana-5662	221	12	j	j	PROPN
cana-5662	221	13	≤	≤	NUM
cana-5662	221	14	m	m	VERB
cana-5662	221	15	−	−	NOUN
cana-5662	221	16	1	1	NUM
cana-5662	221	17	}	}	PUNCT
cana-5662	221	18	.	.	PUNCT
cana-5662	222	1	by	by	ADP
cana-5662	222	2	choosing	choose	VERB
cana-5662	222	3	a	a	DET
cana-5662	222	4	vertex	vertex	NOUN
cana-5662	222	5	{	{	PUNCT
cana-5662	222	6	c	c	NOUN
cana-5662	222	7	i	i	PRON
cana-5662	222	8	/1	/1	VERB
cana-5662	222	9	≤	≤	NUM
cana-5662	223	1	i	i	PRON
cana-5662	223	2	≤	≤	PROPN
cana-5662	223	3	n	n	CCONJ
cana-5662	223	4	}	}	PUNCT
cana-5662	223	5	which	which	PRON
cana-5662	223	6	dominates	dominate	VERB
cana-5662	223	7	all	all	DET
cana-5662	223	8	the	the	DET
cana-5662	223	9	vertices	vertex	NOUN
cana-5662	223	10	of	of	ADP
cana-5662	223	11	kn	kn	PROPN
cana-5662	223	12	◦	◦	PROPN
cana-5662	223	13	k1,m−1	k1,m−1	PROPN
cana-5662	223	14	.	.	PUNCT
cana-5662	224	1	but	but	CCONJ
cana-5662	224	2	⟨v	⟨v	NUM
cana-5662	224	3	(	(	PUNCT
cana-5662	224	4	g	g	NOUN
cana-5662	224	5	)	)	PUNCT
cana-5662	224	6	−d⟩	−d⟩	PRON
cana-5662	224	7	mn	mn	PROPN
cana-5662	224	8	pk	pk	X
cana-5662	224	9			NUM
cana-5662	224	10	which	which	PRON
cana-5662	224	11	contains	contain	VERB
cana-5662	224	12	a	a	DET
cana-5662	224	13	cycle	cycle	NOUN
cana-5662	224	14	.	.	PUNCT
cana-5662	225	1	let	let	VERB
cana-5662	225	2	d	d	NOUN
cana-5662	225	3	=	=	SYM
cana-5662	225	4	d1	d1	PROPN
cana-5662	225	5	∪	∪	ADP
cana-5662	225	6	d2	d2	PROPN
cana-5662	225	7	∪{c1	∪{c1	PROPN
cana-5662	225	8	,	,	PUNCT
cana-5662	225	9	c2	c2	PROPN
cana-5662	225	10	,	,	PUNCT
cana-5662	225	11	.	.	PUNCT
cana-5662	225	12	.	.	PUNCT
cana-5662	226	1	.	.	PUNCT
cana-5662	227	1	,	,	PUNCT
cana-5662	227	2	cn	cn	X
cana-5662	227	3	}	}	PUNCT
cana-5662	227	4	is	be	AUX
cana-5662	227	5	a	a	DET
cana-5662	227	6	minimum	minimum	ADJ
cana-5662	227	7	ctd	ctd	NOUN
cana-5662	227	8	-	-	PUNCT
cana-5662	227	9	set	set	NOUN
cana-5662	227	10	of	of	ADP
cana-5662	227	11	g.	g.	PROPN
cana-5662	227	12	|d|	|d|	PROPN
cana-5662	227	13	=	=	SYM
cana-5662	228	1	n	n	PROPN
cana-5662	229	1	+	+	CCONJ
cana-5662	229	2	(	(	PUNCT
cana-5662	229	3	m+1)(n	m+1)(n	PROPN
cana-5662	229	4	−	−	PROPN
cana-5662	229	5	2	2	NUM
cana-5662	229	6	)	)	PUNCT
cana-5662	229	7	.	.	PUNCT
cana-5662	230	1	proposition	proposition	NOUN
cana-5662	230	2	3.5	3.5	NUM
cana-5662	230	3	.	.	PUNCT
cana-5662	231	1	for	for	ADP
cana-5662	231	2	,	,	PUNCT
cana-5662	231	3	m	m	VERB
cana-5662	231	4	≥	≥	NOUN
cana-5662	231	5	3	3	NUM
cana-5662	231	6	,	,	PUNCT
cana-5662	231	7	(	(	PUNCT
cana-5662	231	8	)	)	PUNCT
cana-5662	231	9	(	(	PUNCT
cana-5662	231	10	)	)	PUNCT
cana-5662	231	11	(	(	PUNCT
cana-5662	231	12	)	)	PUNCT
cana-5662	231	13	.	.	PUNCT
cana-5662	232	1	2	2	NUM
cana-5662	232	2	221	221	NUM
cana-5662	232	3			PROPN
cana-5662	232	4			PROPN
cana-5662	232	5			PROPN
cana-5662	232	6			NOUN
cana-5662	232	7			NOUN
cana-5662	232	8			X
cana-5662	232	9	+	+	NOUN
cana-5662	232	10	−+=	−+=	X
cana-5662	232	11	m	m	VERB
cana-5662	232	12	nmpk	nmpk	PROPN
cana-5662	232	13	mnctd	mnctd	VERB
cana-5662	232	14			NOUN
cana-5662	232	15	proof	proof	NOUN
cana-5662	232	16	.	.	PUNCT
cana-5662	233	1	let	let	VERB
cana-5662	233	2	v	v	X
cana-5662	233	3	(	(	PUNCT
cana-5662	233	4	kn	kn	PROPN
cana-5662	233	5	)	)	PUNCT
cana-5662	233	6	=	=	SYM
cana-5662	233	7	{	{	PUNCT
cana-5662	233	8	v1	v1	PROPN
cana-5662	233	9	,	,	PUNCT
cana-5662	233	10	v2	v2	PROPN
cana-5662	233	11	,	,	PUNCT
cana-5662	233	12	.	.	PUNCT
cana-5662	233	13	.	.	PUNCT
cana-5662	234	1	.	.	PUNCT
cana-5662	235	1	,	,	PUNCT
cana-5662	235	2	vn	vn	NOUN
cana-5662	235	3	}	}	PUNCT
cana-5662	235	4	and	and	CCONJ
cana-5662	235	5	v	v	NOUN
cana-5662	235	6	(	(	PUNCT
cana-5662	235	7	pn	pn	NOUN
cana-5662	235	8	)	)	PUNCT
cana-5662	235	9	=	=	SYM
cana-5662	235	10	{	{	PUNCT
cana-5662	235	11	u1	u1	NOUN
cana-5662	235	12	,	,	PUNCT
cana-5662	235	13	u2	u2	NOUN
cana-5662	235	14	,	,	PUNCT
cana-5662	235	15	.	.	PUNCT
cana-5662	235	16	.	.	PUNCT
cana-5662	236	1	.	.	PUNCT
cana-5662	237	1	,	,	PUNCT
cana-5662	237	2	um	um	INTJ
cana-5662	237	3	}	}	PUNCT
cana-5662	237	4	.	.	PUNCT
cana-5662	238	1	then	then	ADV
cana-5662	238	2	v	v	X
cana-5662	238	3	(	(	PUNCT
cana-5662	238	4	kn	kn	NOUN
cana-5662	238	5	◦	◦	PROPN
cana-5662	238	6	pm	pm	NOUN
cana-5662	238	7	)	)	PUNCT
cana-5662	238	8	=	=	PRON
cana-5662	239	1	{	{	PUNCT
cana-5662	239	2	vi/1	vi/1	NOUN
cana-5662	239	3	≤	≤	NUM
cana-5662	239	4	i	i	PRON
cana-5662	239	5	≤	≤	PROPN
cana-5662	239	6	n	n	CCONJ
cana-5662	239	7	}	}	PUNCT
cana-5662	239	8	∪{uij/1	∪{uij/1	VERB
cana-5662	239	9	≤	≤	ADJ
cana-5662	239	10	i	i	NOUN
cana-5662	239	11	≤	≤	PROPN
cana-5662	239	12	n	n	CCONJ
cana-5662	239	13	,	,	PUNCT
cana-5662	239	14	1	1	NUM
cana-5662	239	15	≤	≤	NUM
cana-5662	239	16	j	j	PROPN
cana-5662	239	17	≤	≤	PROPN
cana-5662	239	18	m	m	PROPN
cana-5662	239	19	}	}	PUNCT
cana-5662	239	20	.we	.we	PUNCT
cana-5662	240	1	have	have	AUX
cana-5662	240	2	,	,	PUNCT
cana-5662	240	3	γctd(pm	γctd(pm	NOUN
cana-5662	240	4	)	)	PUNCT
cana-5662	240	5	=	=	PUNCT
cana-5662	241	1	m	m	VERB
cana-5662	241	2	−	−	NOUN
cana-5662	241	3	2	2	NUM
cana-5662	241	4	,	,	PUNCT
cana-5662	241	5	γctd(kn	γctd(kn	NOUN
cana-5662	241	6	)	)	PUNCT
cana-5662	241	7	=	=	SYM
cana-5662	242	1	n	n	CCONJ
cana-5662	242	2	−	−	NUM
cana-5662	242	3	2	2	NUM
cana-5662	243	1	[	[	X
cana-5662	243	2	3	3	NUM
cana-5662	243	3	]	]	PUNCT
cana-5662	243	4	.	.	PUNCT
cana-5662	244	1	by	by	ADP
cana-5662	244	2	choosing	choose	VERB
cana-5662	244	3	(	(	PUNCT
cana-5662	244	4	n	n	CCONJ
cana-5662	244	5	−	−	PROPN
cana-5662	244	6	2	2	NUM
cana-5662	244	7	)	)	PUNCT
cana-5662	244	8	vertices	vertex	NOUN
cana-5662	244	9	of	of	ADP
cana-5662	244	10	kn	kn	PROPN
cana-5662	244	11	say	say	VERB
cana-5662	244	12	v1	v1	PROPN
cana-5662	244	13	,	,	PUNCT
cana-5662	244	14	v2	v2	PROPN
cana-5662	244	15	,	,	PUNCT
cana-5662	244	16	.	.	PUNCT
cana-5662	244	17	.	.	PUNCT
cana-5662	245	1	.	.	PUNCT
cana-5662	246	1	,	,	PUNCT
cana-5662	246	2	vn−2	vn−2	PROPN
cana-5662	246	3	which	which	PRON
cana-5662	246	4	form	form	VERB
cana-5662	246	5	a	a	DET
cana-5662	246	6	minimum	minimum	ADJ
cana-5662	246	7	ctd	ctd	NOUN
cana-5662	246	8	-	-	PUNCT
cana-5662	246	9	set	set	NOUN
cana-5662	246	10	in	in	ADP
cana-5662	246	11	kn	kn	PROPN
cana-5662	246	12	and	and	CCONJ
cana-5662	246	13	vertices	vertex	NOUN
cana-5662	246	14	which	which	PRON
cana-5662	246	15	are	be	AUX
cana-5662	246	16	adjacent	adjacent	ADJ
cana-5662	246	17	to	to	PART
cana-5662	246	18	{	{	PUNCT
cana-5662	246	19	v1	v1	NOUN
cana-5662	246	20	,	,	PUNCT
cana-5662	246	21	v2	v2	NOUN
cana-5662	246	22	,	,	PUNCT
cana-5662	246	23	.	.	PUNCT
cana-5662	246	24	.	.	PUNCT
cana-5662	247	1	.	.	PUNCT
cana-5662	248	1	,	,	PUNCT
cana-5662	248	2	vn−2	vn−2	PROPN
cana-5662	248	3	}	}	PUNCT
cana-5662	248	4	are	be	AUX
cana-5662	248	5	{	{	PUNCT
cana-5662	248	6	uij/1	uij/1	PROPN
cana-5662	248	7	≤	≤	PROPN
cana-5662	248	8	i	i	NOUN
cana-5662	248	9	≤	≤	NOUN
cana-5662	248	10	n	n	CCONJ
cana-5662	248	11	−	−	PROPN
cana-5662	248	12	2	2	NUM
cana-5662	248	13	,	,	PUNCT
cana-5662	248	14	1	1	NUM
cana-5662	248	15	≤	≤	NUM
cana-5662	248	16	j	j	PROPN
cana-5662	248	17	≤	≤	PROPN
cana-5662	248	18	m	m	PROPN
cana-5662	248	19	}	}	PUNCT
cana-5662	248	20	.	.	PUNCT
cana-5662	249	1	by	by	ADP
cana-5662	249	2	proposition	proposition	NOUN
cana-5662	249	3	2.3	2.3	NUM
cana-5662	249	4	case	case	NOUN
cana-5662	249	5	i	i	PRON
cana-5662	249	6	:	:	PUNCT
cana-5662	249	7	m	m	VERB
cana-5662	249	8	is	be	AUX
cana-5662	249	9	even	even	ADV
cana-5662	249	10			PROPN
cana-5662	249	11			PROPN
cana-5662	249	12			PROPN
cana-5662	249	13	mnnnmnnnn	mnnnmnnnn	NOUN
cana-5662	249	14	uuuuuuuddd	uuuuuuuddd	NOUN
cana-5662	249	15	,	,	PUNCT
cana-5662	249	16	3,1,,15,13,11,121	3,1,,15,13,11,121	NUM
cana-5662	249	17	,	,	PUNCT
cana-5662	249	18	.....	.....	PUNCT
cana-5662	249	19	,	,	PUNCT
cana-5662	249	20	,	,	PUNCT
cana-5662	249	21	.....	.....	PUNCT
cana-5662	249	22	,	,	PUNCT
cana-5662	249	23	,	,	PUNCT
cana-5662	249	24	=	=	PROPN
cana-5662	249	25	−−−−	−−−−	X
cana-5662	249	26	is	be	AUX
cana-5662	249	27	a	a	DET
cana-5662	249	28	minimum	minimum	ADJ
cana-5662	249	29	ctd	ctd	NOUN
cana-5662	249	30	-	-	PUNCT
cana-5662	249	31	set	set	NOUN
cana-5662	249	32	of	of	ADP
cana-5662	249	33	mn	mn	PROPN
cana-5662	249	34	pk	pk	PROPN
cana-5662	249	35			PROPN
cana-5662	249	36	and	and	CCONJ
cana-5662	249	37	(	(	PUNCT
cana-5662	249	38	)	)	PUNCT
cana-5662	249	39	2	2	NUM
cana-5662	249	40	,	,	PUNCT
cana-5662	249	41	2	2	NUM
cana-5662	249	42	mmmn	mmmn	ADJ
cana-5662	249	43	sdpkv	sdpkv	NOUN
cana-5662	249	44	−	−	PROPN
cana-5662	249	45			PROPN
cana-5662	249	46	case	case	NOUN
cana-5662	249	47	ii	ii	PROPN
cana-5662	249	48	:	:	PUNCT
cana-5662	249	49	m	m	VERB
cana-5662	249	50	is	be	AUX
cana-5662	249	51	odd	odd	ADJ
cana-5662	249	52			PROPN
cana-5662	249	53			PROPN
cana-5662	249	54			PROPN
cana-5662	249	55	1,3,1,1,15,13,11,121	1,3,1,1,15,13,11,121	PROPN
cana-5662	249	56	,	,	PUNCT
cana-5662	249	57	.....	.....	PUNCT
cana-5662	249	58	,	,	PUNCT
cana-5662	249	59	,	,	PUNCT
cana-5662	249	60	.....	.....	PUNCT
cana-5662	249	61	,	,	PUNCT
cana-5662	249	62	,	,	PUNCT
cana-5662	249	63	−−−−−−	−−−−−−	PUNCT
cana-5662	249	64	=	=	PROPN
cana-5662	249	65	mnnnmnnnn	mnnnmnnnn	PROPN
cana-5662	249	66	uuuuuuuddd	uuuuuuuddd	PROPN
cana-5662	249	67	is	be	AUX
cana-5662	249	68	a	a	DET
cana-5662	249	69	minimum	minimum	ADJ
cana-5662	249	70	ctd	ctd	NOUN
cana-5662	249	71	-	-	PUNCT
cana-5662	249	72	set	set	NOUN
cana-5662	249	73	of	of	ADP
cana-5662	249	74	mn	mn	PROPN
cana-5662	249	75	pk	pk	PROPN
cana-5662	249	76			PROPN
cana-5662	249	77	and	and	CCONJ
cana-5662	249	78	(	(	PUNCT
cana-5662	249	79	)	)	PUNCT
cana-5662	249	80			PROPN
cana-5662	250	1			PROPN
cana-5662	250	2			PROPN
cana-5662	250	3			NOUN
cana-5662	250	4			NOUN
cana-5662	250	5			NOUN
cana-5662	250	6			PROPN
cana-5662	250	7			PROPN
cana-5662	250	8			PROPN
cana-5662	250	9			NOUN
cana-5662	250	10			NOUN
cana-5662	250	11			X
cana-5662	250	12	−	−	PROPN
cana-5662	250	13	22	22	NUM
cana-5662	250	14	mmmn	mmmn	ADJ
cana-5662	250	15	sdpkv	sdpkv	NOUN
cana-5662	250	16			PROPN
cana-5662	250	17	(	(	PUNCT
cana-5662	250	18	)	)	PUNCT
cana-5662	250	19	(	(	PUNCT
cana-5662	250	20	)	)	PUNCT
cana-5662	250	21	)	)	PUNCT
cana-5662	250	22	1	1	NUM
cana-5662	250	23	(	(	PUNCT
cana-5662	250	24	.	.	NUM
cana-5662	250	25	2	2	NUM
cana-5662	250	26	221	221	NUM
cana-5662	250	27	22	22	NUM
cana-5662	250	28	21	21	NUM
cana-5662	250	29			PROPN
cana-5662	250	30			NOUN
cana-5662	250	31			PRON
cana-5662	250	32			PROPN
cana-5662	250	33			PROPN
cana-5662	250	34			NOUN
cana-5662	250	35	+	+	NOUN
cana-5662	250	36	−+=	−+=	X
cana-5662	250	37			DET
cana-5662	250	38			NOUN
cana-5662	250	39			PRON
cana-5662	250	40			PROPN
cana-5662	250	41			PROPN
cana-5662	250	42			NOUN
cana-5662	251	1	+	+	NOUN
cana-5662	251	2			PROPN
cana-5662	251	3			NOUN
cana-5662	251	4			PRON
cana-5662	251	5			PROPN
cana-5662	251	6			PROPN
cana-5662	251	7			NOUN
cana-5662	252	1	+	+	PROPN
cana-5662	252	2	+	+	PROPN
cana-5662	252	3	=	=	NOUN
cana-5662	252	4	m	m	VERB
cana-5662	252	5	nm	nm	VERB
cana-5662	252	6	mm	mm	PROPN
cana-5662	252	7	ddd	ddd	NOUN
cana-5662	252	8	communications	communication	NOUN
cana-5662	252	9	on	on	ADP
cana-5662	252	10	applied	apply	VERB
cana-5662	252	11	nonlinear	nonlinear	ADJ
cana-5662	252	12	analysis	analysis	NOUN
cana-5662	252	13	issn	issn	NOUN
cana-5662	252	14	:	:	PUNCT
cana-5662	252	15	1074	1074	NUM
cana-5662	252	16	-	-	PUNCT
cana-5662	252	17	133x	133x	NUM
cana-5662	252	18	vol	vol	NOUN
cana-5662	252	19	31	31	NUM
cana-5662	252	20	no	no	NOUN
cana-5662	252	21	.	.	PUNCT
cana-5662	253	1	7s	7	NOUN
cana-5662	253	2	(	(	PUNCT
cana-5662	253	3	2024	2024	NUM
cana-5662	253	4	)	)	PUNCT
cana-5662	253	5	761	761	NUM
cana-5662	254	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	254	2			PROPN
cana-5662	255	1			PROPN
cana-5662	255	2			PROPN
cana-5662	255	3			NOUN
cana-5662	255	4			X
cana-5662	255	5			X
cana-5662	255	6	+	+	ADJ
cana-5662	255	7			PROPN
cana-5662	255	8			PROPN
cana-5662	255	9			PROPN
cana-5662	255	10			NOUN
cana-5662	255	11			NOUN
cana-5662	255	12			X
cana-5662	255	13	+	+	NOUN
cana-5662	255	14	+	+	NOUN
cana-5662	255	15	=	=	SYM
cana-5662	255	16	22	22	NUM
cana-5662	255	17	21	21	NUM
cana-5662	255	18	mm	mm	NOUN
cana-5662	255	19	ddd	ddd	NOUN
cana-5662	255	20	(	(	PUNCT
cana-5662	255	21	2	2	NUM
cana-5662	255	22	)	)	PUNCT
cana-5662	255	23	from	from	ADP
cana-5662	255	24	1	1	NUM
cana-5662	255	25	&	&	CCONJ
cana-5662	255	26	2	2	NUM
cana-5662	255	27	=	=	SYM
cana-5662	255	28	d	d	PROPN
cana-5662	255	29	(	(	PUNCT
cana-5662	255	30	)	)	PUNCT
cana-5662	255	31	(	(	PUNCT
cana-5662	255	32	)	)	PUNCT
cana-5662	255	33	(	(	PUNCT
cana-5662	255	34	)	)	PUNCT
cana-5662	255	35	.	.	PUNCT
cana-5662	256	1	2	2	NUM
cana-5662	256	2	221	221	NUM
cana-5662	256	3			PROPN
cana-5662	256	4			PROPN
cana-5662	256	5			PROPN
cana-5662	256	6			NOUN
cana-5662	256	7			NOUN
cana-5662	256	8			X
cana-5662	256	9	+	+	NOUN
cana-5662	256	10	−+=	−+=	X
cana-5662	256	11	m	m	VERB
cana-5662	256	12	nmpk	nmpk	PROPN
cana-5662	256	13	mnctd	mnctd	VERB
cana-5662	256	14			NOUN
cana-5662	256	15	proposition	proposition	NOUN
cana-5662	256	16	3.6	3.6	NUM
cana-5662	256	17	.	.	PUNCT
cana-5662	257	1	for	for	ADP
cana-5662	257	2	m	m	PROPN
cana-5662	257	3	≥	≥	NOUN
cana-5662	257	4	3	3	NUM
cana-5662	257	5	,	,	PUNCT
cana-5662	257	6	(	(	PUNCT
cana-5662	257	7	)	)	PUNCT
cana-5662	257	8	(	(	PUNCT
cana-5662	257	9	)	)	PUNCT
cana-5662	257	10	(	(	PUNCT
cana-5662	257	11	)	)	PUNCT
cana-5662	257	12	.	.	PUNCT
cana-5662	258	1	2	2	NUM
cana-5662	258	2	221	221	NUM
cana-5662	258	3			PROPN
cana-5662	258	4			PROPN
cana-5662	258	5			PROPN
cana-5662	258	6			NOUN
cana-5662	258	7			NOUN
cana-5662	258	8			X
cana-5662	258	9	+	+	NOUN
cana-5662	258	10	−+=	−+=	X
cana-5662	258	11	m	m	PROPN
cana-5662	258	12	nmck	nmck	NOUN
cana-5662	258	13	mnctd	mnctd	NOUN
cana-5662	258	14			NOUN
cana-5662	258	15	proof	proof	NOUN
cana-5662	258	16	.	.	PUNCT
cana-5662	259	1	let	let	VERB
cana-5662	259	2	v	v	X
cana-5662	259	3	(	(	PUNCT
cana-5662	259	4	kn	kn	PROPN
cana-5662	259	5	)	)	PUNCT
cana-5662	259	6	=	=	SYM
cana-5662	259	7	{	{	PUNCT
cana-5662	259	8	v1	v1	PROPN
cana-5662	259	9	,	,	PUNCT
cana-5662	259	10	v2	v2	PROPN
cana-5662	259	11	,	,	PUNCT
cana-5662	259	12	.	.	PUNCT
cana-5662	259	13	.	.	PUNCT
cana-5662	260	1	.	.	PUNCT
cana-5662	261	1	,	,	PUNCT
cana-5662	261	2	vn	vn	PROPN
cana-5662	261	3	}	}	PUNCT
cana-5662	261	4	and	and	CCONJ
cana-5662	261	5	the	the	DET
cana-5662	261	6	set	set	NOUN
cana-5662	261	7	{	{	PUNCT
cana-5662	261	8	u1	u1	NOUN
cana-5662	261	9	,	,	PUNCT
cana-5662	261	10	u2	u2	NOUN
cana-5662	261	11	,	,	PUNCT
cana-5662	261	12	.	.	PUNCT
cana-5662	261	13	.	.	PUNCT
cana-5662	261	14	.	.	PUNCT
cana-5662	262	1	,	,	PUNCT
cana-5662	262	2	um	um	INTJ
cana-5662	262	3	}	}	PUNCT
cana-5662	262	4	be	be	AUX
cana-5662	262	5	the	the	DET
cana-5662	262	6	vertices	vertex	NOUN
cana-5662	262	7	of	of	ADP
cana-5662	262	8	cm	cm	NOUN
cana-5662	262	9	.	.	PUNCT
cana-5662	263	1	then	then	ADV
cana-5662	263	2	v	v	X
cana-5662	263	3	(	(	PUNCT
cana-5662	263	4	kn	kn	NOUN
cana-5662	263	5	◦	◦	NOUN
cana-5662	263	6	cm	cm	NOUN
cana-5662	263	7	)	)	PUNCT
cana-5662	264	1	=	=	NOUN
cana-5662	264	2	{	{	PUNCT
cana-5662	264	3	vi/1	vi/1	NOUN
cana-5662	264	4	≤	≤	NUM
cana-5662	264	5	i	i	PRON
cana-5662	264	6	≤	≤	PROPN
cana-5662	264	7	n	n	CCONJ
cana-5662	264	8	}	}	PUNCT
cana-5662	264	9	∪{uij/1	∪{uij/1	VERB
cana-5662	264	10	≤	≤	ADJ
cana-5662	264	11	i	i	NOUN
cana-5662	264	12	≤	≤	PROPN
cana-5662	264	13	n	n	CCONJ
cana-5662	264	14	,	,	PUNCT
cana-5662	264	15	1	1	NUM
cana-5662	264	16	≤	≤	NUM
cana-5662	264	17	j	j	PROPN
cana-5662	264	18	≤	≤	PROPN
cana-5662	264	19	m	m	VERB
cana-5662	264	20	}	}	PUNCT
cana-5662	264	21	by	by	ADP
cana-5662	264	22	preposition	preposition	NOUN
cana-5662	264	23	2.4	2.4	NUM
cana-5662	264	24	case	case	NOUN
cana-5662	264	25	i	i	PRON
cana-5662	264	26	:	:	PUNCT
cana-5662	264	27	m	m	VERB
cana-5662	264	28	is	be	AUX
cana-5662	264	29	even	even	ADV
cana-5662	264	30			PROPN
cana-5662	264	31			PROPN
cana-5662	264	32			PROPN
cana-5662	264	33	1,3,1,1,15,13,11,121	1,3,1,1,15,13,11,121	PROPN
cana-5662	264	34	,	,	PUNCT
cana-5662	264	35	.....	.....	PUNCT
cana-5662	264	36	,	,	PUNCT
cana-5662	264	37	,	,	PUNCT
cana-5662	264	38	.....	.....	PUNCT
cana-5662	264	39	,	,	PUNCT
cana-5662	264	40	,	,	PUNCT
cana-5662	264	41	−−−−−−	−−−−−−	PUNCT
cana-5662	264	42	=	=	PROPN
cana-5662	264	43	mnnnmnnnn	mnnnmnnnn	PROPN
cana-5662	264	44	uuuuuuuddd	uuuuuuuddd	PROPN
cana-5662	264	45	is	be	AUX
cana-5662	264	46	a	a	DET
cana-5662	264	47	minimum	minimum	ADJ
cana-5662	264	48	ctd	ctd	NOUN
cana-5662	264	49	-	-	PUNCT
cana-5662	264	50	set	set	NOUN
cana-5662	264	51	of	of	ADP
cana-5662	264	52	mn	mn	PROPN
cana-5662	264	53	ck	ck	PROPN
cana-5662	264	54			PROPN
cana-5662	264	55	and	and	CCONJ
cana-5662	264	56	(	(	PUNCT
cana-5662	264	57	)	)	PUNCT
cana-5662	264	58	2	2	NUM
cana-5662	264	59	,	,	PUNCT
cana-5662	264	60	2	2	NUM
cana-5662	264	61	mmmn	mmmn	NOUN
cana-5662	264	62	sdckv	sdckv	NOUN
cana-5662	264	63	−	−	PROPN
cana-5662	264	64			PROPN
cana-5662	264	65	case	case	NOUN
cana-5662	264	66	ii	ii	PROPN
cana-5662	264	67	:	:	PUNCT
cana-5662	264	68	m	m	VERB
cana-5662	264	69	is	be	AUX
cana-5662	264	70	odd	odd	ADJ
cana-5662	264	71			PROPN
cana-5662	264	72			PROPN
cana-5662	264	73			PROPN
cana-5662	264	74	mnnnmnnnn	mnnnmnnnn	NOUN
cana-5662	264	75	uuuuuuuddd	uuuuuuuddd	NOUN
cana-5662	264	76	,	,	PUNCT
cana-5662	264	77	3,1,,15,13,11,121	3,1,,15,13,11,121	NUM
cana-5662	264	78	,	,	PUNCT
cana-5662	264	79	.....	.....	PUNCT
cana-5662	264	80	,	,	PUNCT
cana-5662	264	81	,	,	PUNCT
cana-5662	264	82	.....	.....	PUNCT
cana-5662	264	83	,	,	PUNCT
cana-5662	264	84	,	,	PUNCT
cana-5662	264	85	=	=	PROPN
cana-5662	264	86	−−−−	−−−−	X
cana-5662	264	87	is	be	AUX
cana-5662	264	88	a	a	DET
cana-5662	264	89	minimum	minimum	ADJ
cana-5662	264	90	ctd	ctd	NOUN
cana-5662	264	91	-	-	PUNCT
cana-5662	264	92	set	set	NOUN
cana-5662	264	93	of	of	ADP
cana-5662	264	94	mn	mn	PROPN
cana-5662	265	1	ck	ck	PROPN
cana-5662	265	2			PROPN
cana-5662	265	3	and	and	CCONJ
cana-5662	265	4	(	(	PUNCT
cana-5662	265	5	)	)	PUNCT
cana-5662	265	6	2	2	NUM
cana-5662	265	7	1	1	NUM
cana-5662	265	8	2	2	NUM
cana-5662	265	9	1	1	NUM
cana-5662	265	10	+	+	NOUN
cana-5662	265	11	+	+	ADJ
cana-5662	265	12	−	−	X
cana-5662	265	13	mmmn	mmmn	NOUN
cana-5662	265	14	sdckv	sdckv	NOUN
cana-5662	265	15			AUX
cana-5662	265	16			PROPN
cana-5662	265	17			NOUN
cana-5662	265	18			PRON
cana-5662	265	19			PROPN
cana-5662	266	1			PROPN
cana-5662	266	2			NOUN
cana-5662	267	1	+	+	PROPN
cana-5662	267	2	+	+	PROPN
cana-5662	267	3	=	=	SYM
cana-5662	267	4	2	2	NUM
cana-5662	267	5	221	221	NUM
cana-5662	267	6	m	m	NOUN
cana-5662	267	7	ddd	ddd	NOUN
cana-5662	267	8	(	(	PUNCT
cana-5662	267	9	4	4	NUM
cana-5662	267	10	)	)	PUNCT
cana-5662	267	11	from	from	ADP
cana-5662	267	12	3	3	NUM
cana-5662	267	13	&	&	CCONJ
cana-5662	267	14	4	4	NUM
cana-5662	267	15	=	=	SYM
cana-5662	267	16	d	d	PROPN
cana-5662	267	17	(	(	PUNCT
cana-5662	267	18	)	)	PUNCT
cana-5662	267	19	(	(	PUNCT
cana-5662	267	20	)	)	PUNCT
cana-5662	267	21	(	(	PUNCT
cana-5662	267	22	)	)	PUNCT
cana-5662	267	23	.	.	PUNCT
cana-5662	268	1	2	2	NUM
cana-5662	268	2	221	221	NUM
cana-5662	268	3			NOUN
cana-5662	268	4			NOUN
cana-5662	268	5			X
cana-5662	268	6			NOUN
cana-5662	268	7			X
cana-5662	268	8			PROPN
cana-5662	268	9	+	+	PROPN
cana-5662	268	10	−+=	−+=	ADJ
cana-5662	268	11	m	m	PROPN
cana-5662	268	12	nmck	nmck	NOUN
cana-5662	268	13	mnctd	mnctd	VERB
cana-5662	268	14			NOUN
cana-5662	268	15	(	(	PUNCT
cana-5662	268	16	)	)	PUNCT
cana-5662	268	17	(	(	PUNCT
cana-5662	268	18	)	)	PUNCT
cana-5662	268	19	)	)	PUNCT
cana-5662	268	20	3	3	X
cana-5662	268	21	(	(	PUNCT
cana-5662	268	22	.	.	PUNCT
cana-5662	268	23	2	2	NUM
cana-5662	268	24	221	221	NUM
cana-5662	268	25	22	22	NUM
cana-5662	268	26	21	21	NUM
cana-5662	268	27			PROPN
cana-5662	268	28			NOUN
cana-5662	268	29			PRON
cana-5662	268	30			PROPN
cana-5662	268	31			PROPN
cana-5662	268	32			NOUN
cana-5662	268	33	+	+	NOUN
cana-5662	268	34	−+=	−+=	X
cana-5662	268	35			PRON
cana-5662	268	36			NOUN
cana-5662	268	37			PRON
cana-5662	268	38			PROPN
cana-5662	268	39			PROPN
cana-5662	268	40			NOUN
cana-5662	269	1	+	+	NOUN
cana-5662	269	2			PROPN
cana-5662	269	3			NOUN
cana-5662	269	4			PRON
cana-5662	269	5			PROPN
cana-5662	269	6			PROPN
cana-5662	269	7			NOUN
cana-5662	270	1	+	+	PROPN
cana-5662	270	2	+	+	PROPN
cana-5662	270	3	=	=	NOUN
cana-5662	270	4	m	m	VERB
cana-5662	270	5	nm	nm	VERB
cana-5662	270	6	mm	mm	PROPN
cana-5662	270	7	ddd	ddd	NOUN
cana-5662	270	8	communications	communication	NOUN
cana-5662	270	9	on	on	ADP
cana-5662	270	10	applied	apply	VERB
cana-5662	270	11	nonlinear	nonlinear	ADJ
cana-5662	270	12	analysis	analysis	NOUN
cana-5662	270	13	issn	issn	NOUN
cana-5662	270	14	:	:	PUNCT
cana-5662	270	15	1074	1074	NUM
cana-5662	270	16	-	-	PUNCT
cana-5662	270	17	133x	133x	NUM
cana-5662	270	18	vol	vol	NOUN
cana-5662	270	19	31	31	NUM
cana-5662	270	20	no	no	NOUN
cana-5662	270	21	.	.	PUNCT
cana-5662	271	1	7s	7	NOUN
cana-5662	271	2	(	(	PUNCT
cana-5662	271	3	2024	2024	NUM
cana-5662	271	4	)	)	PUNCT
cana-5662	271	5	762	762	NUM
cana-5662	271	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	271	7	proposition	proposition	NOUN
cana-5662	271	8	3.7	3.7	NUM
cana-5662	271	9	.	.	PUNCT
cana-5662	272	1	for	for	ADP
cana-5662	272	2	m	m	PROPN
cana-5662	272	3	≥	≥	NOUN
cana-5662	272	4	4	4	NUM
cana-5662	272	5	,	,	PUNCT
cana-5662	272	6	γctd(kn	γctd(kn	NOUN
cana-5662	272	7	◦	◦	NOUN
cana-5662	272	8	wm	wm	PROPN
cana-5662	272	9	)	)	PUNCT
cana-5662	272	10	=	=	PUNCT
cana-5662	273	1	(	(	PUNCT
cana-5662	273	2	m+1)(n	m+1)(n	PROPN
cana-5662	273	3	−	−	PROPN
cana-5662	273	4	2	2	NUM
cana-5662	273	5	)	)	PUNCT
cana-5662	273	6	+2	+2	PRON
cana-5662	273	7			NOUN
cana-5662	274	1			NOUN
cana-5662	274	2			X
cana-5662	274	3			NOUN
cana-5662	274	4			VERB
cana-5662	274	5			NOUN
cana-5662	274	6	−	−	NUM
cana-5662	274	7	2	2	NUM
cana-5662	274	8	1	1	NUM
cana-5662	274	9	m	m	NOUN
cana-5662	274	10	proof	proof	NOUN
cana-5662	274	11	.	.	PUNCT
cana-5662	275	1	let	let	VERB
cana-5662	275	2	v	v	X
cana-5662	275	3	(	(	PUNCT
cana-5662	275	4	kn	kn	PROPN
cana-5662	275	5	)	)	PUNCT
cana-5662	275	6	=	=	PRON
cana-5662	275	7	{	{	PUNCT
cana-5662	275	8	vi	vi	NOUN
cana-5662	275	9	/1	/1	NOUN
cana-5662	275	10	≤	≤	NUM
cana-5662	276	1	i	i	PRON
cana-5662	276	2	≤	≤	NOUN
cana-5662	276	3	n	n	CCONJ
cana-5662	276	4	}	}	PUNCT
cana-5662	276	5	and	and	CCONJ
cana-5662	276	6	v	v	ADP
cana-5662	276	7	(	(	PUNCT
cana-5662	276	8	wm	wm	PROPN
cana-5662	276	9	)	)	PUNCT
cana-5662	276	10	=	=	PUNCT
cana-5662	276	11	{	{	PUNCT
cana-5662	276	12	c	c	X
cana-5662	276	13	,	,	PUNCT
cana-5662	276	14	uj	uj	PROPN
cana-5662	276	15	/1	/1	PROPN
cana-5662	276	16	≤	≤	PROPN
cana-5662	277	1	j	j	PROPN
cana-5662	277	2	≤	≤	NUM
cana-5662	277	3	m	m	VERB
cana-5662	277	4	−	−	PROPN
cana-5662	277	5	1	1	NUM
cana-5662	277	6	}	}	PUNCT
cana-5662	277	7	and	and	CCONJ
cana-5662	277	8	v	v	X
cana-5662	277	9	(	(	PUNCT
cana-5662	277	10	kn	kn	PROPN
cana-5662	277	11	◦	◦	PROPN
cana-5662	277	12	wm	wm	PROPN
cana-5662	277	13	)	)	PUNCT
cana-5662	277	14	=	=	SYM
cana-5662	277	15	{	{	PUNCT
cana-5662	277	16	v1	v1	PROPN
cana-5662	277	17	,	,	PUNCT
cana-5662	277	18	v2	v2	PROPN
cana-5662	277	19	,	,	PUNCT
cana-5662	277	20	.	.	PUNCT
cana-5662	277	21	.	.	PUNCT
cana-5662	278	1	.	.	PUNCT
cana-5662	279	1	,	,	PUNCT
cana-5662	279	2	vn}∪{ci	vn}∪{ci	NOUN
cana-5662	279	3	uij	uij	PRON
cana-5662	279	4	/1	/1	NOUN
cana-5662	280	1	≤	≤	NUM
cana-5662	280	2	i	i	PRON
cana-5662	280	3	≤	≤	PROPN
cana-5662	280	4	n	n	CCONJ
cana-5662	280	5	,	,	PUNCT
cana-5662	280	6	1	1	NUM
cana-5662	280	7	≤	≤	NUM
cana-5662	280	8	j	j	PROPN
cana-5662	280	9	≤	≤	PROPN
cana-5662	280	10	m−1	m−1	PROPN
cana-5662	280	11	}	}	PUNCT
cana-5662	280	12	.let	.let	PUNCT
cana-5662	281	1	d	d	NOUN
cana-5662	281	2	=	=	PUNCT
cana-5662	281	3	d1∪	d1∪	PROPN
cana-5662	281	4	d2∪	d2∪	PROPN
cana-5662	281	5	{	{	PUNCT
cana-5662	281	6	nn	nn	PROPN
cana-5662	281	7	cc	cc	PROPN
cana-5662	281	8	,	,	PUNCT
cana-5662	281	9	1−	1−	NUM
cana-5662	281	10	}	}	PUNCT
cana-5662	281	11	∪	∪	X
cana-5662	281	12	{	{	PUNCT
cana-5662	281	13	ctd	ctd	NOUN
cana-5662	281	14	-	-	PUNCT
cana-5662	281	15	set	set	NOUN
cana-5662	281	16	of	of	ADP
cana-5662	281	17	1−mn	1−mn	NUM
cana-5662	281	18	ck	ck	PROPN
cana-5662	281	19			PROPN
cana-5662	281	20	}	}	PUNCT
cana-5662	281	21	and	and	CCONJ
cana-5662	281	22	(	(	PUNCT
cana-5662	281	23	)	)	PUNCT
cana-5662	281	24			PROPN
cana-5662	282	1			PROPN
cana-5662	282	2			PROPN
cana-5662	282	3			NOUN
cana-5662	282	4			NOUN
cana-5662	282	5			X
cana-5662	282	6	−	−	PROPN
cana-5662	282	7	2	2	NUM
cana-5662	282	8	mmn	mmn	NOUN
cana-5662	282	9	sdwkv	sdwkv	ADJ
cana-5662	282	10			PROPN
cana-5662	282	11	|d|	|d|	PROPN
cana-5662	282	12	=	=	SYM
cana-5662	282	13	(	(	PUNCT
cana-5662	282	14	n	n	CCONJ
cana-5662	282	15	−	−	PROPN
cana-5662	282	16	2	2	NUM
cana-5662	282	17	)	)	PUNCT
cana-5662	283	1	+	+	ADP
cana-5662	283	2	m(n	m(n	PROPN
cana-5662	283	3	−	−	PROPN
cana-5662	283	4	2	2	NUM
cana-5662	283	5	)	)	PUNCT
cana-5662	283	6	+2	+2	ADV
cana-5662	283	7			NOUN
cana-5662	284	1			NOUN
cana-5662	284	2			X
cana-5662	284	3			NOUN
cana-5662	284	4			VERB
cana-5662	284	5			NOUN
cana-5662	284	6	−	−	NUM
cana-5662	284	7	2	2	NUM
cana-5662	284	8	1	1	NUM
cana-5662	284	9	m	m	VERB
cana-5662	284	10	therefore	therefore	ADV
cana-5662	284	11	,	,	PUNCT
cana-5662	284	12	|d|	|d|	PROPN
cana-5662	284	13	=(	=(	NOUN
cana-5662	284	14	m+1)(n	m+1)(n	PROPN
cana-5662	284	15	−	−	PROPN
cana-5662	284	16	2	2	NUM
cana-5662	284	17	)	)	PUNCT
cana-5662	284	18	+2	+2	PRON
cana-5662	284	19			NOUN
cana-5662	285	1			NOUN
cana-5662	285	2			X
cana-5662	285	3			NOUN
cana-5662	285	4			VERB
cana-5662	285	5			NOUN
cana-5662	285	6	−	−	NUM
cana-5662	285	7	2	2	NUM
cana-5662	285	8	1	1	NUM
cana-5662	285	9	m	m	NOUN
cana-5662	285	10	.	.	PUNCT
cana-5662	286	1	proposition	proposition	NOUN
cana-5662	286	2	3.8	3.8	NUM
cana-5662	286	3	.	.	PUNCT
cana-5662	287	1	for	for	ADP
cana-5662	287	2	m	m	PROPN
cana-5662	287	3	≥	≥	NOUN
cana-5662	287	4	4	4	NUM
cana-5662	287	5	,	,	PUNCT
cana-5662	287	6	γctd(kn	γctd(kn	VERB
cana-5662	287	7	◦	◦	NOUN
cana-5662	287	8	km	km	NOUN
cana-5662	287	9	)	)	PUNCT
cana-5662	287	10	=	=	PUNCT
cana-5662	287	11	n(m	n(m	PROPN
cana-5662	287	12	+	+	CCONJ
cana-5662	287	13	1	1	X
cana-5662	287	14	)	)	PUNCT
cana-5662	287	15	−	−	ADP
cana-5662	287	16	4	4	X
cana-5662	287	17	.	.	PUNCT
cana-5662	287	18	proof	proof	NOUN
cana-5662	287	19	.	.	PUNCT
cana-5662	288	1	take	take	VERB
cana-5662	288	2	g	g	NOUN
cana-5662	288	3	=	=	PUNCT
cana-5662	288	4	kn	kn	PROPN
cana-5662	288	5	◦	◦	PROPN
cana-5662	288	6	km	km	PROPN
cana-5662	288	7	.	.	PUNCT
cana-5662	289	1	let	let	VERB
cana-5662	289	2	v	v	X
cana-5662	289	3	(	(	PUNCT
cana-5662	289	4	kn	kn	PROPN
cana-5662	289	5	)	)	PUNCT
cana-5662	289	6	=	=	SYM
cana-5662	289	7	{	{	PUNCT
cana-5662	289	8	v1	v1	PROPN
cana-5662	289	9	,	,	PUNCT
cana-5662	289	10	v2	v2	PROPN
cana-5662	289	11	,	,	PUNCT
cana-5662	289	12	.	.	PUNCT
cana-5662	289	13	.	.	PUNCT
cana-5662	290	1	.	.	PUNCT
cana-5662	291	1	,	,	PUNCT
cana-5662	291	2	vn	vn	NOUN
cana-5662	291	3	}	}	PUNCT
cana-5662	291	4	and	and	CCONJ
cana-5662	291	5	v	v	NOUN
cana-5662	291	6	(	(	PUNCT
cana-5662	291	7	km	km	NOUN
cana-5662	291	8	)	)	PUNCT
cana-5662	291	9	=	=	PRON
cana-5662	291	10	{	{	PUNCT
cana-5662	291	11	u1	u1	NOUN
cana-5662	291	12	,	,	PUNCT
cana-5662	291	13	u2	u2	NOUN
cana-5662	291	14	,	,	PUNCT
cana-5662	291	15	.	.	PUNCT
cana-5662	291	16	.	.	PUNCT
cana-5662	292	1	.	.	PUNCT
cana-5662	293	1	,	,	PUNCT
cana-5662	293	2	um	um	INTJ
cana-5662	293	3	}	}	PUNCT
cana-5662	293	4	.	.	PUNCT
cana-5662	294	1	then	then	ADV
cana-5662	294	2	v	v	X
cana-5662	294	3	(	(	PUNCT
cana-5662	294	4	g	g	NOUN
cana-5662	294	5	)	)	PUNCT
cana-5662	294	6	=	=	PRON
cana-5662	295	1	{	{	PUNCT
cana-5662	295	2	vi/1	vi/1	NOUN
cana-5662	295	3	≤	≤	NUM
cana-5662	295	4	i	i	PRON
cana-5662	295	5	≤	≤	NOUN
cana-5662	295	6	n	n	CCONJ
cana-5662	295	7	}	}	PUNCT
cana-5662	295	8	∪	∪	X
cana-5662	295	9	{	{	PUNCT
cana-5662	295	10	uij/1	uij/1	PROPN
cana-5662	295	11	≤	≤	PROPN
cana-5662	295	12	i	i	PROPN
cana-5662	295	13	≤	≤	PROPN
cana-5662	295	14	n	n	CCONJ
cana-5662	295	15	,	,	PUNCT
cana-5662	295	16	1	1	NUM
cana-5662	295	17	≤	≤	NUM
cana-5662	295	18	j	j	PROPN
cana-5662	295	19	≤	≤	PROPN
cana-5662	295	20	m	m	PROPN
cana-5662	295	21	}	}	PUNCT
cana-5662	295	22	.we	.we	PUNCT
cana-5662	295	23	have	have	AUX
cana-5662	295	24	,	,	PUNCT
cana-5662	295	25	γctd(kn	γctd(kn	NOUN
cana-5662	295	26	)	)	PUNCT
cana-5662	295	27	=	=	SYM
cana-5662	296	1	n	n	CCONJ
cana-5662	296	2	−	−	NUM
cana-5662	296	3	2	2	NUM
cana-5662	297	1	[	[	X
cana-5662	297	2	3	3	NUM
cana-5662	297	3	]	]	PUNCT
cana-5662	297	4	.	.	PUNCT
cana-5662	298	1	suppose	suppose	VERB
cana-5662	298	2	by	by	ADP
cana-5662	298	3	choosing	choose	VERB
cana-5662	298	4	(	(	PUNCT
cana-5662	298	5	n−2	n−2	PROPN
cana-5662	298	6	)	)	PUNCT
cana-5662	298	7	vertices	vertex	NOUN
cana-5662	298	8	of	of	ADP
cana-5662	298	9	kn	kn	PROPN
cana-5662	298	10	which	which	PRON
cana-5662	298	11	dominates	dominate	VERB
cana-5662	298	12	all	all	DET
cana-5662	298	13	the	the	DET
cana-5662	298	14	vertices	vertex	NOUN
cana-5662	298	15	of	of	ADP
cana-5662	298	16	i	i	PRON
cana-5662	298	17	mk	mk	PROPN
cana-5662	298	18	1	1	NUM
cana-5662	298	19	≤	≤	PUNCT
cana-5662	299	1	i	i	PRON
cana-5662	299	2	≤	≤	NOUN
cana-5662	299	3	n	n	CCONJ
cana-5662	299	4	−	−	PROPN
cana-5662	299	5	2	2	NUM
cana-5662	300	1	but	but	CCONJ
cana-5662	300	2	it	it	PRON
cana-5662	300	3	does	do	AUX
cana-5662	300	4	not	not	PART
cana-5662	300	5	dominates	dominate	VERB
cana-5662	300	6	n	n	PRON
cana-5662	300	7	and	and	CCONJ
cana-5662	300	8	n	n	CCONJ
cana-5662	300	9	−	−	PROPN
cana-5662	300	10	1	1	NUM
cana-5662	300	11	copy	copy	NOUN
cana-5662	300	12	of	of	ADP
cana-5662	300	13	km	km	NOUN
cana-5662	300	14	which	which	PRON
cana-5662	300	15	contradict	contradict	VERB
cana-5662	300	16	the	the	DET
cana-5662	300	17	ctd	ctd	NOUN
cana-5662	300	18	-	-	PUNCT
cana-5662	300	19	set	set	NOUN
cana-5662	300	20	.	.	PUNCT
cana-5662	301	1	suppose	suppose	VERB
cana-5662	301	2	by	by	ADP
cana-5662	301	3	choosing	choose	VERB
cana-5662	301	4	(	(	PUNCT
cana-5662	301	5	m	m	NOUN
cana-5662	301	6	−	−	NOUN
cana-5662	301	7	2	2	NUM
cana-5662	301	8	)	)	PUNCT
cana-5662	301	9	vertices	vertex	NOUN
cana-5662	301	10	of	of	ADP
cana-5662	301	11	km	km	NOUN
cana-5662	301	12	which	which	PRON
cana-5662	301	13	dominates	dominate	VERB
cana-5662	301	14	all	all	DET
cana-5662	301	15	the	the	DET
cana-5662	301	16	vertices	vertex	NOUN
cana-5662	301	17	of	of	ADP
cana-5662	301	18	kn	kn	PROPN
cana-5662	302	1	but	but	CCONJ
cana-5662	302	2	⟨v(g)−d⟩	⟨v(g)−d⟩	NUM
cana-5662	302	3	contains	contain	VERB
cana-5662	302	4	a	a	DET
cana-5662	302	5	cycle	cycle	NOUN
cana-5662	302	6	which	which	PRON
cana-5662	302	7	is	be	AUX
cana-5662	302	8	contradict	contradict	ADJ
cana-5662	302	9	to	to	ADP
cana-5662	302	10	ctd	ctd	NOUN
cana-5662	302	11	-	-	PUNCT
cana-5662	302	12	set	set	NOUN
cana-5662	302	13	.	.	PUNCT
cana-5662	303	1	let	let	VERB
cana-5662	303	2	d	d	NOUN
cana-5662	303	3	=	=	SYM
cana-5662	303	4	d1∪d2∪	d1∪d2∪	NUM
cana-5662	303	5			PROPN
cana-5662	303	6	11,,1/	11,,1/	PROPN
cana-5662	303	7	−−=	−−=	PROPN
cana-5662	303	8	mjnniuij	mjnniuij	NOUN
cana-5662	303	9	is	be	AUX
cana-5662	303	10	a	a	DET
cana-5662	303	11	minimum	minimum	ADJ
cana-5662	303	12	ctd	ctd	NOUN
cana-5662	303	13	-	-	PUNCT
cana-5662	303	14	set	set	NOUN
cana-5662	303	15	of	of	ADP
cana-5662	303	16	g.	g.	PROPN
cana-5662	303	17	=	=	PUNCT
cana-5662	304	1	n	n	CCONJ
cana-5662	304	2	−	−	NUM
cana-5662	304	3	2	2	NUM
cana-5662	304	4	+	+	CCONJ
cana-5662	304	5	m(n	m(n	PROPN
cana-5662	304	6	−	−	PROPN
cana-5662	304	7	2	2	NUM
cana-5662	304	8	)	)	PUNCT
cana-5662	304	9	+	+	NUM
cana-5662	304	10	m	m	VERB
cana-5662	304	11	−	−	NUM
cana-5662	304	12	1	1	NUM
cana-5662	305	1	+	+	NUM
cana-5662	305	2	m	m	VERB
cana-5662	305	3	−	−	NOUN
cana-5662	305	4	1	1	NUM
cana-5662	305	5	hence	hence	ADV
cana-5662	305	6	,	,	PUNCT
cana-5662	306	1	|d|	|d|	PROPN
cana-5662	306	2	=	=	SYM
cana-5662	306	3	n(m	n(m	PROPN
cana-5662	306	4	+	+	CCONJ
cana-5662	306	5	1	1	X
cana-5662	306	6	)	)	PUNCT
cana-5662	306	7	−	−	ADP
cana-5662	306	8	4	4	X
cana-5662	306	9	.	.	PUNCT
cana-5662	306	10	proposition	proposition	NOUN
cana-5662	306	11	3.9	3.9	NUM
cana-5662	306	12	.	.	PUNCT
cana-5662	307	1	for	for	ADP
cana-5662	307	2	m1,m2	m1,m2	PROPN
cana-5662	307	3	≥	≥	NUM
cana-5662	307	4	2,γctd(kn	2,γctd(kn	NUM
cana-5662	307	5	◦	◦	NOUN
cana-5662	307	6	k	k	X
cana-5662	307	7	m1,m2	m1,m2	PROPN
cana-5662	307	8	)	)	PUNCT
cana-5662	307	9	=	=	PUNCT
cana-5662	307	10	(	(	PUNCT
cana-5662	307	11	n	n	CCONJ
cana-5662	307	12	−	−	PROPN
cana-5662	307	13	2)(m1+m2	2)(m1+m2	NOUN
cana-5662	307	14	+	+	NOUN
cana-5662	307	15	1	1	NUM
cana-5662	307	16	)	)	PUNCT
cana-5662	307	17	+	+	CCONJ
cana-5662	307	18	2	2	NUM
cana-5662	307	19	min(m1,m2	min(m1,m2	NUM
cana-5662	307	20	)	)	PUNCT
cana-5662	307	21	.	.	PUNCT
cana-5662	308	1	proof	proof	NOUN
cana-5662	308	2	.	.	PUNCT
cana-5662	309	1	take	take	VERB
cana-5662	309	2	g	g	NOUN
cana-5662	309	3	=	=	PUNCT
cana-5662	309	4	kn	kn	PROPN
cana-5662	309	5	◦	◦	NOUN
cana-5662	310	1	k	k	PROPN
cana-5662	310	2	m1,m2	m1,m2	PROPN
cana-5662	310	3	.	.	PUNCT
cana-5662	311	1	let	let	VERB
cana-5662	311	2	v	v	X
cana-5662	311	3	(	(	PUNCT
cana-5662	311	4	kn	kn	PROPN
cana-5662	311	5	)	)	PUNCT
cana-5662	311	6	=	=	PRON
cana-5662	312	1	{	{	PUNCT
cana-5662	312	2	vi/1	vi/1	NOUN
cana-5662	312	3	≤	≤	NUM
cana-5662	312	4	i	i	PRON
cana-5662	312	5	≤	≤	ADV
cana-5662	312	6	n},v	n},v	ADJ
cana-5662	312	7	(	(	PUNCT
cana-5662	312	8	k	k	PROPN
cana-5662	312	9	m1,m2	m1,m2	PROPN
cana-5662	312	10	)	)	PUNCT
cana-5662	312	11	=	=	PRON
cana-5662	312	12	{	{	PUNCT
cana-5662	312	13	uj/1	uj/1	PROPN
cana-5662	312	14	≤	≤	PROPN
cana-5662	312	15	j	j	PROPN
cana-5662	312	16	≤	≤	PROPN
cana-5662	312	17	m1	m1	NOUN
cana-5662	312	18	}	}	PUNCT
cana-5662	312	19	∪	∪	X
cana-5662	312	20	{	{	PUNCT
cana-5662	312	21	wj/1	wj/1	PROPN
cana-5662	312	22	≤	≤	PROPN
cana-5662	312	23	j	j	PROPN
cana-5662	312	24	≤	≤	PROPN
cana-5662	312	25	m2	m2	PROPN
cana-5662	312	26	}	}	PUNCT
cana-5662	312	27	.	.	PUNCT
cana-5662	313	1	then	then	ADV
cana-5662	313	2	v	v	X
cana-5662	313	3	(	(	PUNCT
cana-5662	313	4	g	g	NOUN
cana-5662	313	5	)	)	PUNCT
cana-5662	313	6	=	=	SYM
cana-5662	313	7	{	{	PUNCT
cana-5662	313	8	vi/	vi/	NOUN
cana-5662	313	9	1	1	NUM
cana-5662	313	10	≤	≤	NUM
cana-5662	313	11	i	i	PRON
cana-5662	313	12	≤	≤	ADV
cana-5662	313	13	n}∪{uij/1	n}∪{uij/1	ADJ
cana-5662	313	14	≤	≤	NUM
cana-5662	313	15	i	i	NOUN
cana-5662	313	16	≤	≤	NOUN
cana-5662	313	17	n	n	CCONJ
cana-5662	313	18	;	;	PUNCT
cana-5662	313	19	1	1	NUM
cana-5662	313	20	≤	≤	NUM
cana-5662	313	21	j	j	PROPN
cana-5662	313	22	≤	≤	PROPN
cana-5662	313	23	m1}∪{wij/1	m1}∪{wij/1	PROPN
cana-5662	313	24	≤	≤	PROPN
cana-5662	313	25	i	i	PRON
cana-5662	313	26	≤	≤	PROPN
cana-5662	313	27	n	n	CCONJ
cana-5662	313	28	;	;	PUNCT
cana-5662	313	29	1	1	NUM
cana-5662	313	30	≤	≤	NUM
cana-5662	313	31	j	j	PROPN
cana-5662	313	32	≤	≤	PROPN
cana-5662	313	33	m2	m2	PROPN
cana-5662	313	34	}	}	PUNCT
cana-5662	313	35	.	.	PUNCT
cana-5662	314	1	let	let	VERB
cana-5662	314	2	d	d	PRON
cana-5662	314	3	be	be	AUX
cana-5662	314	4	the	the	DET
cana-5662	314	5	minimum	minimum	ADJ
cana-5662	314	6	ctd	ctd	NOUN
cana-5662	314	7	-	-	PUNCT
cana-5662	314	8	set	set	NOUN
cana-5662	314	9	of	of	ADP
cana-5662	314	10	kn	kn	PROPN
cana-5662	314	11	◦	◦	PROPN
cana-5662	314	12	k	k	PROPN
cana-5662	314	13	m1,m2	m1,m2	PROPN
cana-5662	314	14	.	.	PUNCT
cana-5662	315	1	case	case	NOUN
cana-5662	315	2	i.	i.	PROPN
cana-5662	315	3	m1	m1	PROPN
cana-5662	315	4	<	<	X
cana-5662	315	5	m2	m2	PROPN
cana-5662	315	6	communications	communication	NOUN
cana-5662	315	7	on	on	ADP
cana-5662	315	8	applied	apply	VERB
cana-5662	315	9	nonlinear	nonlinear	ADJ
cana-5662	315	10	analysis	analysis	NOUN
cana-5662	315	11	issn	issn	NOUN
cana-5662	315	12	:	:	PUNCT
cana-5662	315	13	1074	1074	NUM
cana-5662	315	14	-	-	PUNCT
cana-5662	315	15	133x	133x	NUM
cana-5662	315	16	vol	vol	NOUN
cana-5662	315	17	31	31	NUM
cana-5662	315	18	no	no	NOUN
cana-5662	315	19	.	.	PUNCT
cana-5662	316	1	7s	7	NOUN
cana-5662	316	2	(	(	PUNCT
cana-5662	316	3	2024	2024	NUM
cana-5662	316	4	)	)	PUNCT
cana-5662	316	5	763	763	NUM
cana-5662	316	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	316	7	by	by	ADP
cana-5662	316	8	choosing	choose	VERB
cana-5662	316	9	{	{	PUNCT
cana-5662	316	10	uij/1	uij/1	PROPN
cana-5662	316	11	≤	≤	PROPN
cana-5662	316	12	i	i	PROPN
cana-5662	316	13	≤	≤	PROPN
cana-5662	316	14	n	n	CCONJ
cana-5662	316	15	,	,	PUNCT
cana-5662	316	16	1	1	NUM
cana-5662	316	17	≤	≤	NUM
cana-5662	316	18	j	j	PROPN
cana-5662	316	19	≤	≤	PROPN
cana-5662	316	20	m1	m1	PROPN
cana-5662	316	21	}	}	PUNCT
cana-5662	316	22	which	which	PRON
cana-5662	316	23	dominates	dominate	VERB
cana-5662	316	24	all	all	DET
cana-5662	316	25	the	the	DET
cana-5662	316	26	vertices	vertex	NOUN
cana-5662	316	27	of	of	ADP
cana-5662	316	28	g	g	NOUN
cana-5662	316	29	and	and	CCONJ
cana-5662	316	30	⟨v	⟨v	NUM
cana-5662	316	31	(	(	PUNCT
cana-5662	316	32	g	g	NOUN
cana-5662	316	33	)	)	PUNCT
cana-5662	316	34	−	−	PROPN
cana-5662	316	35	d⟩	d⟩	NOUN
cana-5662	316	36			PROPN
cana-5662	316	37	2mn	2mn	PROPN
cana-5662	316	38	kk	kk	PROPN
cana-5662	316	39			PROPN
cana-5662	316	40	forms	form	VERB
cana-5662	316	41	a	a	DET
cana-5662	316	42	cycle	cycle	NOUN
cana-5662	316	43	.	.	PUNCT
cana-5662	317	1	let	let	VERB
cana-5662	317	2	d	d	NOUN
cana-5662	317	3	=	=	PUNCT
cana-5662	317	4	d1	d1	PROPN
cana-5662	317	5	∪	∪	ADP
cana-5662	317	6	d2	d2	PROPN
cana-5662	317	7	∪	∪	X
cana-5662	317	8	{	{	PUNCT
cana-5662	317	9	un−1,1	un−1,1	NOUN
cana-5662	317	10	,	,	PUNCT
cana-5662	317	11	un−1,2	un−1,2	NUM
cana-5662	317	12	,	,	PUNCT
cana-5662	317	13	.	.	PUNCT
cana-5662	317	14	.	.	PUNCT
cana-5662	318	1	.	.	PUNCT
cana-5662	319	1	,	,	PUNCT
cana-5662	319	2	un−1,m1	un−1,m1	PROPN
cana-5662	319	3	}	}	PUNCT
cana-5662	319	4	∪	∪	NOUN
cana-5662	319	5	{	{	PUNCT
cana-5662	319	6	un,1	un,1	PROPN
cana-5662	319	7	,	,	PUNCT
cana-5662	319	8	un,2	un,2	ADJ
cana-5662	319	9	,	,	PUNCT
cana-5662	319	10	.	.	PUNCT
cana-5662	319	11	.	.	PUNCT
cana-5662	319	12	.	.	PUNCT
cana-5662	320	1	,	,	PUNCT
cana-5662	320	2	un	un	PROPN
cana-5662	320	3	,	,	PUNCT
cana-5662	320	4	m1	m1	NOUN
cana-5662	320	5	}	}	PUNCT
cana-5662	320	6	is	be	AUX
cana-5662	320	7	a	a	DET
cana-5662	320	8	minimum	minimum	ADJ
cana-5662	320	9	ctd	ctd	NOUN
cana-5662	320	10	-	-	PUNCT
cana-5662	320	11	set	set	NOUN
cana-5662	320	12	of	of	ADP
cana-5662	320	13	g.	g.	PROPN
cana-5662	320	14	hence	hence	ADV
cana-5662	320	15	,	,	PUNCT
cana-5662	320	16	|d|	|d|	PROPN
cana-5662	320	17	=	=	PROPN
cana-5662	320	18	n	n	CCONJ
cana-5662	320	19	−	−	NUM
cana-5662	320	20	2	2	NUM
cana-5662	321	1	+	+	CCONJ
cana-5662	321	2	m1(n	m1(n	PRON
cana-5662	321	3	−	−	PROPN
cana-5662	321	4	2	2	NUM
cana-5662	321	5	)	)	PUNCT
cana-5662	321	6	+	+	CCONJ
cana-5662	321	7	m2(n	m2(n	ADJ
cana-5662	321	8	−	−	ADP
cana-5662	321	9	2	2	NUM
cana-5662	321	10	)	)	PUNCT
cana-5662	321	11	+	+	NUM
cana-5662	321	12	2m1	2m1	NUM
cana-5662	321	13	=	=	SYM
cana-5662	321	14	(	(	PUNCT
cana-5662	321	15	n	n	CCONJ
cana-5662	321	16	−	−	PROPN
cana-5662	321	17	2)(m1	2)(m1	NOUN
cana-5662	321	18	+	+	CCONJ
cana-5662	321	19	m2	m2	PROPN
cana-5662	321	20	+	+	PROPN
cana-5662	321	21	1	1	NUM
cana-5662	321	22	)	)	PUNCT
cana-5662	321	23	+	+	NUM
cana-5662	321	24	2m1	2m1	NUM
cana-5662	321	25	(	(	PUNCT
cana-5662	321	26	5	5	NUM
cana-5662	321	27	)	)	PUNCT
cana-5662	321	28	case	case	NOUN
cana-5662	321	29	ii	ii	NOUN
cana-5662	321	30	.	.	PUNCT
cana-5662	322	1	m2	m2	PROPN
cana-5662	322	2	<	<	X
cana-5662	322	3	m1	m1	PROPN
cana-5662	322	4	by	by	ADP
cana-5662	322	5	choosing	choose	VERB
cana-5662	322	6	a	a	DET
cana-5662	322	7	vertex	vertex	NOUN
cana-5662	323	1	d	d	NOUN
cana-5662	323	2	=	=	PUNCT
cana-5662	323	3	d1	d1	PROPN
cana-5662	323	4	∪	∪	ADP
cana-5662	323	5	d2	d2	PROPN
cana-5662	323	6	∪	∪	X
cana-5662	323	7	{	{	PUNCT
cana-5662	323	8	wn−1,1	wn−1,1	NUM
cana-5662	323	9	,	,	PUNCT
cana-5662	323	10	wn−1,2	wn−1,2	ADJ
cana-5662	323	11	,	,	PUNCT
cana-5662	323	12	.	.	PUNCT
cana-5662	323	13	.	.	PUNCT
cana-5662	324	1	.	.	PUNCT
cana-5662	325	1	,	,	PUNCT
cana-5662	325	2	wn−1,m2	wn−1,m2	NOUN
cana-5662	325	3	}	}	PUNCT
cana-5662	325	4	∪	∪	NOUN
cana-5662	325	5	{	{	PUNCT
cana-5662	325	6	wn,1	wn,1	PROPN
cana-5662	325	7	,	,	PUNCT
cana-5662	325	8	wn,2	wn,2	VERB
cana-5662	325	9	,	,	PUNCT
cana-5662	325	10	.	.	PUNCT
cana-5662	325	11	.	.	PUNCT
cana-5662	325	12	.	.	PUNCT
cana-5662	326	1	,	,	PUNCT
cana-5662	326	2	wn	wn	PROPN
cana-5662	326	3	,	,	PUNCT
cana-5662	326	4	m2	m2	PROPN
cana-5662	326	5	}	}	PUNCT
cana-5662	326	6	which	which	PRON
cana-5662	326	7	dominates	dominate	VERB
cana-5662	326	8	all	all	DET
cana-5662	326	9	the	the	DET
cana-5662	326	10	vertices	vertex	NOUN
cana-5662	326	11	of	of	ADP
cana-5662	326	12	v	v	NOUN
cana-5662	326	13	(	(	PUNCT
cana-5662	326	14	g	g	NOUN
cana-5662	326	15	)	)	PUNCT
cana-5662	326	16	and	and	CCONJ
cana-5662	326	17	⟨v(g)−d⟩	⟨v(g)−d⟩	NUM
cana-5662	326	18	is	be	AUX
cana-5662	326	19	a	a	DET
cana-5662	326	20	tree	tree	NOUN
cana-5662	326	21	.	.	PUNCT
cana-5662	327	1	here	here	ADV
cana-5662	327	2	d	d	X
cana-5662	327	3	is	be	AUX
cana-5662	327	4	a	a	DET
cana-5662	327	5	ctd	ctd	NOUN
cana-5662	327	6	-	-	PUNCT
cana-5662	327	7	set	set	NOUN
cana-5662	327	8	of	of	ADP
cana-5662	327	9	g.	g.	PROPN
cana-5662	327	10	hence	hence	ADV
cana-5662	327	11	,	,	PUNCT
cana-5662	327	12	|d|	|d|	PROPN
cana-5662	327	13	=	=	PROPN
cana-5662	327	14	n	n	CCONJ
cana-5662	327	15	−	−	NUM
cana-5662	327	16	2	2	NUM
cana-5662	328	1	+	+	CCONJ
cana-5662	328	2	m1(n	m1(n	PRON
cana-5662	328	3	−	−	PROPN
cana-5662	328	4	2	2	NUM
cana-5662	328	5	)	)	PUNCT
cana-5662	328	6	+	+	CCONJ
cana-5662	328	7	m2(n	m2(n	ADJ
cana-5662	328	8	−	−	ADP
cana-5662	328	9	2	2	NUM
cana-5662	328	10	)	)	PUNCT
cana-5662	328	11	+	+	CCONJ
cana-5662	328	12	2m2	2m2	NUM
cana-5662	328	13	=	=	SYM
cana-5662	328	14	(	(	PUNCT
cana-5662	328	15	n	n	CCONJ
cana-5662	328	16	−	−	PROPN
cana-5662	328	17	2)(n1	2)(n1	NOUN
cana-5662	328	18	+	+	CCONJ
cana-5662	328	19	n2	n2	ADJ
cana-5662	328	20	+	+	CCONJ
cana-5662	328	21	1	1	NUM
cana-5662	328	22	)	)	PUNCT
cana-5662	328	23	+	+	CCONJ
cana-5662	328	24	2m2	2m2	NUM
cana-5662	328	25	(	(	PUNCT
cana-5662	328	26	6	6	NUM
cana-5662	328	27	)	)	PUNCT
cana-5662	328	28	from	from	ADP
cana-5662	328	29	(	(	PUNCT
cana-5662	328	30	5	5	NUM
cana-5662	328	31	)	)	PUNCT
cana-5662	328	32	and	and	CCONJ
cana-5662	328	33	(	(	PUNCT
cana-5662	328	34	6	6	X
cana-5662	328	35	)	)	PUNCT
cana-5662	328	36	|d|	|d|	NOUN
cana-5662	328	37	=	=	SYM
cana-5662	328	38	(	(	PUNCT
cana-5662	328	39	n	n	CCONJ
cana-5662	328	40	−	−	PROPN
cana-5662	328	41	2)(m1	2)(m1	NOUN
cana-5662	328	42	+	+	CCONJ
cana-5662	328	43	m2	m2	PROPN
cana-5662	328	44	+	+	CCONJ
cana-5662	328	45	1	1	NUM
cana-5662	328	46	)	)	PUNCT
cana-5662	328	47	+	+	CCONJ
cana-5662	328	48	2	2	NUM
cana-5662	328	49	min(m1,m2	min(m1,m2	NUM
cana-5662	328	50	)	)	PUNCT
cana-5662	328	51	.	.	PUNCT
cana-5662	329	1	proposition	proposition	NOUN
cana-5662	329	2	3.10	3.10	NUM
cana-5662	329	3	.	.	PUNCT
cana-5662	330	1	for	for	ADP
cana-5662	330	2	,	,	PUNCT
cana-5662	330	3	m	m	VERB
cana-5662	330	4	≥	≥	NOUN
cana-5662	330	5	2	2	NUM
cana-5662	330	6	,	,	PUNCT
cana-5662	330	7	γctd(kn	γctd(kn	VERB
cana-5662	330	8	◦	◦	NOUN
cana-5662	330	9	km	km	PROPN
cana-5662	330	10	)	)	PUNCT
cana-5662	330	11	≥	≥	AUX
cana-5662	330	12	n(m	n(m	PROPN
cana-5662	330	13	+	+	CCONJ
cana-5662	330	14	1	1	X
cana-5662	330	15	)	)	PUNCT
cana-5662	330	16	−	−	ADP
cana-5662	330	17	4	4	X
cana-5662	330	18	.	.	PUNCT
cana-5662	330	19	proof	proof	NOUN
cana-5662	330	20	.	.	PUNCT
cana-5662	331	1	take	take	VERB
cana-5662	331	2	g	g	NOUN
cana-5662	331	3	=	=	PROPN
cana-5662	331	4	kn	kn	PROPN
cana-5662	331	5	◦	◦	PROPN
cana-5662	331	6	km	km	PROPN
cana-5662	331	7	.	.	PUNCT
cana-5662	332	1	let	let	VERB
cana-5662	332	2	v	v	X
cana-5662	332	3	(	(	PUNCT
cana-5662	332	4	kn	kn	PROPN
cana-5662	332	5	)	)	PUNCT
cana-5662	332	6	=	=	SYM
cana-5662	332	7	{	{	PUNCT
cana-5662	332	8	v1	v1	PROPN
cana-5662	332	9	,	,	PUNCT
cana-5662	332	10	v2	v2	PROPN
cana-5662	332	11	,	,	PUNCT
cana-5662	332	12	.	.	PUNCT
cana-5662	332	13	.	.	PUNCT
cana-5662	333	1	.	.	PUNCT
cana-5662	334	1	,	,	PUNCT
cana-5662	334	2	vn	vn	PROPN
cana-5662	334	3	}	}	PUNCT
cana-5662	334	4	and	and	CCONJ
cana-5662	334	5	{	{	PUNCT
cana-5662	334	6	u1	u1	NOUN
cana-5662	334	7	,	,	PUNCT
cana-5662	334	8	u2	u2	NOUN
cana-5662	334	9	,	,	PUNCT
cana-5662	334	10	.	.	PUNCT
cana-5662	334	11	.	.	PUNCT
cana-5662	335	1	.	.	PUNCT
cana-5662	336	1	,	,	PUNCT
cana-5662	336	2	um}be	um}be	NOUN
cana-5662	336	3	the	the	DET
cana-5662	336	4	vertex	vertex	NOUN
cana-5662	336	5	set	set	NOUN
cana-5662	336	6	of	of	ADP
cana-5662	336	7	the	the	DET
cana-5662	336	8	ith	ith	PROPN
cana-5662	336	9	copy	copy	NOUN
cana-5662	336	10	of	of	ADP
cana-5662	336	11	km	km	PROPN
cana-5662	336	12	is	be	AUX
cana-5662	336	13	adjacent	adjacent	ADJ
cana-5662	336	14	to	to	ADP
cana-5662	336	15	the	the	DET
cana-5662	336	16	vertex	vertex	NOUN
cana-5662	336	17	vi	vi	NOUN
cana-5662	336	18	in	in	ADP
cana-5662	336	19	kn.then	kn.then	PROPN
cana-5662	336	20	v	v	ADP
cana-5662	336	21	(	(	PUNCT
cana-5662	336	22	g	g	NOUN
cana-5662	336	23	)	)	PUNCT
cana-5662	336	24	=	=	PRON
cana-5662	337	1	{	{	PUNCT
cana-5662	337	2	vi/1	vi/1	NOUN
cana-5662	337	3	≤	≤	NUM
cana-5662	337	4	i	i	PRON
cana-5662	337	5	≤	≤	NOUN
cana-5662	337	6	n	n	CCONJ
cana-5662	337	7	}	}	PUNCT
cana-5662	337	8	∪	∪	X
cana-5662	337	9	{	{	PUNCT
cana-5662	337	10	uij/1	uij/1	PROPN
cana-5662	337	11	≤	≤	PROPN
cana-5662	337	12	i	i	PROPN
cana-5662	337	13	≤	≤	PROPN
cana-5662	337	14	n	n	CCONJ
cana-5662	337	15	,	,	PUNCT
cana-5662	337	16	1	1	NUM
cana-5662	337	17	≤	≤	NUM
cana-5662	337	18	j	j	PROPN
cana-5662	337	19	≤	≤	PROPN
cana-5662	337	20	m	m	PROPN
cana-5662	337	21	}	}	PUNCT
cana-5662	337	22	.	.	PUNCT
cana-5662	338	1	let	let	VERB
cana-5662	338	2	d	d	PRON
cana-5662	338	3	be	be	AUX
cana-5662	338	4	a	a	DET
cana-5662	338	5	minimum	minimum	ADJ
cana-5662	338	6	ctd	ctd	NOUN
cana-5662	338	7	-	-	PUNCT
cana-5662	338	8	set	set	NOUN
cana-5662	338	9	of	of	ADP
cana-5662	338	10	g.	g.	NOUN
cana-5662	338	11	by	by	ADP
cana-5662	338	12	choosing	choose	VERB
cana-5662	338	13	{	{	PUNCT
cana-5662	338	14	uij/1	uij/1	PROPN
cana-5662	338	15	≤	≤	PROPN
cana-5662	338	16	i	i	PROPN
cana-5662	338	17	≤	≤	PROPN
cana-5662	338	18	n	n	CCONJ
cana-5662	338	19	,	,	PUNCT
cana-5662	338	20	1	1	NUM
cana-5662	338	21	≤	≤	NUM
cana-5662	338	22	j	j	PROPN
cana-5662	338	23	≤	≤	PROPN
cana-5662	338	24			PROPN
cana-5662	339	1			PROPN
cana-5662	339	2			PROPN
cana-5662	339	3			NOUN
cana-5662	339	4			NOUN
cana-5662	339	5			NOUN
cana-5662	339	6	+	+	CCONJ
cana-5662	339	7	2	2	NUM
cana-5662	339	8	1	1	NUM
cana-5662	339	9	m	m	VERB
cana-5662	339	10	}	}	PUNCT
cana-5662	339	11	dominates	dominate	VERB
cana-5662	339	12	all	all	DET
cana-5662	339	13	the	the	DET
cana-5662	339	14	vertices	vertex	NOUN
cana-5662	339	15	in	in	ADP
cana-5662	339	16	a	a	DET
cana-5662	339	17	graph	graph	NOUN
cana-5662	339	18	g	g	NOUN
cana-5662	339	19	but	but	CCONJ
cana-5662	339	20	⟨v	⟨v	NUM
cana-5662	339	21	(	(	PUNCT
cana-5662	339	22	g	g	NOUN
cana-5662	339	23	)	)	PUNCT
cana-5662	340	1	−	−	PROPN
cana-5662	340	2	d⟩	d⟩	NOUN
cana-5662	340	3	forms	form	VERB
cana-5662	340	4	a	a	DET
cana-5662	340	5	cycle	cycle	NOUN
cana-5662	340	6	so	so	SCONJ
cana-5662	340	7	we	we	PRON
cana-5662	340	8	are	be	AUX
cana-5662	340	9	choosing	choose	VERB
cana-5662	340	10	(	(	PUNCT
cana-5662	340	11	n	n	CCONJ
cana-5662	340	12	−	−	PROPN
cana-5662	340	13	2	2	NUM
cana-5662	340	14	)	)	PUNCT
cana-5662	340	15	vertices	vertex	NOUN
cana-5662	340	16	from	from	ADP
cana-5662	340	17	{	{	PUNCT
cana-5662	340	18	vi	vi	NOUN
cana-5662	340	19	}	}	PUNCT
cana-5662	340	20	then	then	ADV
cana-5662	340	21	their	their	PRON
cana-5662	340	22	corresponding	correspond	VERB
cana-5662	340	23	{	{	PUNCT
cana-5662	340	24	uij	uij	PRON
cana-5662	340	25	}	}	PUNCT
cana-5662	340	26	vertices	vertex	NOUN
cana-5662	340	27	and	and	CCONJ
cana-5662	340	28	for	for	ADP
cana-5662	340	29	the	the	DET
cana-5662	340	30	remaining	remain	VERB
cana-5662	340	31	n	n	CCONJ
cana-5662	340	32	−	−	NUM
cana-5662	340	33	1	1	NUM
cana-5662	340	34	and	and	CCONJ
cana-5662	340	35	n	n	PRON
cana-5662	340	36	vertices	vertex	NOUN
cana-5662	340	37	we	we	PRON
cana-5662	340	38	choose	choose	VERB
cana-5662	340	39			PROPN
cana-5662	340	40			PROPN
cana-5662	340	41			PROPN
cana-5662	340	42			NOUN
cana-5662	340	43			NOUN
cana-5662	340	44			NOUN
cana-5662	340	45	+	+	CCONJ
cana-5662	340	46	2	2	NUM
cana-5662	340	47	1	1	NUM
cana-5662	340	48	m	m	NOUN
cana-5662	340	49	vertices	vertex	NOUN
cana-5662	340	50	from	from	ADP
cana-5662	340	51	{	{	PUNCT
cana-5662	340	52	uij}.therefore	uij}.therefore	NOUN
cana-5662	340	53	,	,	PUNCT
cana-5662	340	54	|d|	|d|	PROPN
cana-5662	340	55	≥	≥	NOUN
cana-5662	340	56	n(m	n(m	PROPN
cana-5662	341	1	+	+	CCONJ
cana-5662	341	2	1	1	X
cana-5662	341	3	)	)	PUNCT
cana-5662	341	4	−	−	ADP
cana-5662	341	5	4	4	NUM
cana-5662	341	6	.	.	SYM
cana-5662	341	7	4	4	NUM
cana-5662	341	8	bounds	bound	NOUN
cana-5662	341	9	for	for	ADP
cana-5662	341	10	complementary	complementary	ADJ
cana-5662	341	11	tree	tree	NOUN
cana-5662	341	12	domination	domination	NOUN
cana-5662	341	13	number	number	NOUN
cana-5662	341	14	of	of	ADP
cana-5662	341	15	corona	corona	NOUN
cana-5662	341	16	product	product	NOUN
cana-5662	341	17	of	of	ADP
cana-5662	341	18	complete	complete	ADJ
cana-5662	341	19	graph	graph	NOUN
cana-5662	341	20	with	with	SCONJ
cana-5662	341	21	some	some	DET
cana-5662	341	22	graphs	graph	NOUN
cana-5662	341	23	theorem	theorem	VERB
cana-5662	341	24	4.1	4.1	NUM
cana-5662	341	25	.	.	PUNCT
cana-5662	342	1	for	for	ADP
cana-5662	342	2	any	any	DET
cana-5662	342	3	connected	connected	ADJ
cana-5662	342	4	graph	graph	NOUN
cana-5662	342	5	g	g	NOUN
cana-5662	342	6	,	,	PUNCT
cana-5662	342	7	with	with	ADP
cana-5662	342	8	m	m	PROPN
cana-5662	342	9	≥	≥	NUM
cana-5662	342	10	2	2	NUM
cana-5662	342	11	vertices	vertex	NOUN
cana-5662	342	12	then	then	ADV
cana-5662	342	13	3n	3n	NUM
cana-5662	342	14	−	−	PROPN
cana-5662	342	15	4	4	NUM
cana-5662	342	16	≤	≤	NOUN
cana-5662	342	17	γctd(kn	γctd(kn	NOUN
cana-5662	342	18	◦	◦	NOUN
cana-5662	342	19	g	g	NOUN
cana-5662	342	20	)	)	PUNCT
cana-5662	342	21	≤	≤	NOUN
cana-5662	342	22	(	(	PUNCT
cana-5662	342	23	m	m	VERB
cana-5662	342	24	+	+	NOUN
cana-5662	342	25	1)(n	1)(n	NUM
cana-5662	342	26	−	−	NOUN
cana-5662	342	27	2	2	NUM
cana-5662	342	28	)	)	PUNCT
cana-5662	342	29	+	+	NUM
cana-5662	342	30	2(m	2(m	NUM
cana-5662	342	31	−	−	PROPN
cana-5662	342	32	β0	β0	NOUN
cana-5662	342	33	)	)	PUNCT
cana-5662	342	34	.	.	PUNCT
cana-5662	343	1	proof	proof	NOUN
cana-5662	343	2	.	.	PUNCT
cana-5662	344	1	let	let	VERB
cana-5662	344	2	v	v	X
cana-5662	344	3	(	(	PUNCT
cana-5662	344	4	kn	kn	PROPN
cana-5662	344	5	)	)	PUNCT
cana-5662	344	6	=	=	SYM
cana-5662	344	7	{	{	PUNCT
cana-5662	344	8	v1	v1	PROPN
cana-5662	344	9	,	,	PUNCT
cana-5662	344	10	v2	v2	PROPN
cana-5662	344	11	,	,	PUNCT
cana-5662	344	12	.	.	PUNCT
cana-5662	344	13	.	.	PUNCT
cana-5662	345	1	.	.	PUNCT
cana-5662	346	1	,	,	PUNCT
cana-5662	346	2	vn	vn	PROPN
cana-5662	346	3	}	}	PUNCT
cana-5662	346	4	.	.	PUNCT
cana-5662	347	1	let	let	VERB
cana-5662	347	2	t	t	NOUN
cana-5662	347	3	be	be	AUX
cana-5662	347	4	any	any	DET
cana-5662	347	5	induced	induced	ADJ
cana-5662	347	6	subgraph	subgraph	NOUN
cana-5662	347	7	of	of	ADP
cana-5662	347	8	kn	kn	PROPN
cana-5662	347	9	having	have	VERB
cana-5662	347	10	maximum	maximum	ADJ
cana-5662	347	11	number	number	NOUN
cana-5662	347	12	of	of	ADP
cana-5662	347	13	edges	edge	NOUN
cana-5662	347	14	such	such	ADJ
cana-5662	347	15	that	that	SCONJ
cana-5662	347	16	t	t	PROPN
cana-5662	347	17			PROPN
cana-5662	347	18	k2	k2	PROPN
cana-5662	347	19	is	be	AUX
cana-5662	347	20	a	a	DET
cana-5662	347	21	tree	tree	NOUN
cana-5662	347	22	.	.	PUNCT
cana-5662	348	1	then	then	ADV
cana-5662	348	2	|t|	|t|	VERB
cana-5662	348	3	=	=	NOUN
cana-5662	348	4	2	2	X
cana-5662	348	5	.	.	PUNCT
cana-5662	348	6	let	let	VERB
cana-5662	348	7	s	s	PRON
cana-5662	348	8	be	be	AUX
cana-5662	348	9	a	a	DET
cana-5662	348	10	maximum	maximum	ADJ
cana-5662	348	11	independent	independent	ADJ
cana-5662	348	12	communications	communication	NOUN
cana-5662	348	13	on	on	ADP
cana-5662	348	14	applied	apply	VERB
cana-5662	348	15	nonlinear	nonlinear	ADJ
cana-5662	348	16	analysis	analysis	NOUN
cana-5662	348	17	issn	issn	NOUN
cana-5662	348	18	:	:	PUNCT
cana-5662	348	19	1074	1074	NUM
cana-5662	348	20	-	-	PUNCT
cana-5662	348	21	133x	133x	NUM
cana-5662	348	22	vol	vol	NOUN
cana-5662	348	23	31	31	NUM
cana-5662	348	24	no	no	NOUN
cana-5662	348	25	.	.	PUNCT
cana-5662	349	1	7s	7	NOUN
cana-5662	349	2	(	(	PUNCT
cana-5662	349	3	2024	2024	NUM
cana-5662	349	4	)	)	PUNCT
cana-5662	349	5	764	764	NUM
cana-5662	350	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5662	350	2	set	set	NOUN
cana-5662	350	3	of	of	ADP
cana-5662	350	4	g	g	NOUN
cana-5662	350	5	such	such	ADJ
cana-5662	350	6	that	that	PRON
cana-5662	350	7	|s|	|s|	PROPN
cana-5662	350	8	=	=	SYM
cana-5662	350	9	β0.let	β0.let	PUNCT
cana-5662	350	10	d1	d1	PROPN
cana-5662	350	11	be	be	AUX
cana-5662	350	12	the	the	DET
cana-5662	350	13	set	set	NOUN
cana-5662	350	14	of	of	ADP
cana-5662	350	15	vertices	vertex	NOUN
cana-5662	350	16	of	of	ADP
cana-5662	350	17	s	s	PRON
cana-5662	350	18	in	in	ADP
cana-5662	350	19	copies	copy	NOUN
cana-5662	350	20	of	of	ADP
cana-5662	350	21	g	g	NOUN
cana-5662	350	22	which	which	PRON
cana-5662	350	23	are	be	AUX
cana-5662	350	24	adjacent	adjacent	ADJ
cana-5662	350	25	to	to	ADP
cana-5662	350	26	the	the	DET
cana-5662	350	27	vertices	vertex	NOUN
cana-5662	350	28	of	of	ADP
cana-5662	350	29	t.	t.	NOUN
cana-5662	350	30	then	then	ADV
cana-5662	350	31	|d1|	|d1|	PROPN
cana-5662	350	32	=	=	SYM
cana-5662	350	33	2β0	2β0	X
cana-5662	350	34	.	.	PUNCT
cana-5662	351	1	let	let	VERB
cana-5662	351	2	d	d	NOUN
cana-5662	351	3	=	=	SYM
cana-5662	351	4	v	v	PROPN
cana-5662	351	5	(	(	PUNCT
cana-5662	351	6	kn	kn	NOUN
cana-5662	351	7	◦	◦	NOUN
cana-5662	351	8	g	g	NOUN
cana-5662	351	9	)	)	PUNCT
cana-5662	352	1	−	−	PROPN
cana-5662	353	1	(	(	PUNCT
cana-5662	353	2	v	v	NOUN
cana-5662	353	3	(	(	PUNCT
cana-5662	353	4	k2	k2	NOUN
cana-5662	353	5	)	)	PUNCT
cana-5662	353	6	∪	∪	ADP
cana-5662	353	7	d1	d1	NOUN
cana-5662	353	8	)	)	PUNCT
cana-5662	353	9	.	.	PUNCT
cana-5662	354	1	then	then	ADV
cana-5662	354	2	v	v	INTJ
cana-5662	354	3	(	(	PUNCT
cana-5662	354	4	kn	kn	NOUN
cana-5662	354	5	◦	◦	NOUN
cana-5662	354	6	g	g	NOUN
cana-5662	354	7	)	)	PUNCT
cana-5662	354	8	−	−	PROPN
cana-5662	355	1	d	d	NOUN
cana-5662	355	2	=	=	SYM
cana-5662	355	3	v	v	PROPN
cana-5662	355	4	(	(	PUNCT
cana-5662	355	5	k2	k2	NOUN
cana-5662	355	6	)	)	PUNCT
cana-5662	355	7	∪	∪	NOUN
cana-5662	355	8	d1	d1	PROPN
cana-5662	355	9	and	and	CCONJ
cana-5662	355	10	each	each	DET
cana-5662	355	11	vertex	vertex	NOUN
cana-5662	355	12	in	in	ADP
cana-5662	355	13	v	v	NOUN
cana-5662	355	14	(	(	PUNCT
cana-5662	355	15	k2	k2	NOUN
cana-5662	355	16	)	)	PUNCT
cana-5662	355	17	is	be	AUX
cana-5662	355	18	adjacent	adjacent	ADJ
cana-5662	355	19	to	to	PART
cana-5662	355	20	m−β0	m−β0	VERB
cana-5662	355	21	vertices	vertex	NOUN
cana-5662	355	22	in	in	ADP
cana-5662	355	23	a	a	DET
cana-5662	355	24	copy	copy	NOUN
cana-5662	355	25	of	of	ADP
cana-5662	355	26	g.	g.	PROPN
cana-5662	355	27	also	also	ADV
cana-5662	355	28	,	,	PUNCT
cana-5662	355	29	each	each	DET
cana-5662	355	30	vertex	vertex	NOUN
cana-5662	355	31	in	in	ADP
cana-5662	355	32	d1	d1	PROPN
cana-5662	355	33	is	be	AUX
cana-5662	355	34	adjacent	adjacent	ADJ
cana-5662	355	35	to	to	PART
cana-5662	355	36	atleast	atleast	VERB
cana-5662	355	37	m−β0	m−β0	X
cana-5662	355	38	vertex	vertex	NOUN
cana-5662	355	39	in	in	ADP
cana-5662	355	40	a	a	DET
cana-5662	355	41	copy	copy	NOUN
cana-5662	355	42	of	of	ADP
cana-5662	355	43	g.	g.	PROPN
cana-5662	356	1	therefore	therefore	ADV
cana-5662	356	2	d	d	PROPN
cana-5662	356	3	is	be	AUX
cana-5662	356	4	a	a	DET
cana-5662	356	5	dominating	dominating	NOUN
cana-5662	356	6	set	set	NOUN
cana-5662	356	7	of	of	ADP
cana-5662	356	8	kn	kn	PROPN
cana-5662	356	9	◦	◦	PROPN
cana-5662	356	10	g	g	PROPN
cana-5662	356	11	and	and	CCONJ
cana-5662	356	12	⟨v	⟨v	NUM
cana-5662	356	13	(	(	PUNCT
cana-5662	356	14	kn	kn	NOUN
cana-5662	356	15	◦	◦	VERB
cana-5662	356	16	g	g	NOUN
cana-5662	356	17	)	)	PUNCT
cana-5662	357	1	−	−	PROPN
cana-5662	357	2	d⟩	d⟩	NOUN
cana-5662	357	3	is	be	AUX
cana-5662	357	4	the	the	DET
cana-5662	357	5	tree	tree	NOUN
cana-5662	357	6	obtained	obtain	VERB
cana-5662	357	7	from	from	ADP
cana-5662	357	8	t	t	NOUN
cana-5662	357	9	by	by	ADP
cana-5662	357	10	attaching	attach	VERB
cana-5662	357	11	m	m	PROPN
cana-5662	357	12	−	−	PROPN
cana-5662	357	13	β0	β0	ADJ
cana-5662	357	14	pendant	pendant	ADJ
cana-5662	357	15	edges	edge	NOUN
cana-5662	357	16	at	at	ADP
cana-5662	357	17	each	each	DET
cana-5662	357	18	vertex	vertex	NOUN
cana-5662	357	19	of	of	ADP
cana-5662	357	20	k2	k2	PROPN
cana-5662	357	21	.	.	PUNCT
cana-5662	358	1	therefore	therefore	ADV
cana-5662	358	2	d	d	X
cana-5662	358	3	is	be	AUX
cana-5662	358	4	a	a	DET
cana-5662	358	5	ctd	ctd	NOUN
cana-5662	358	6	-	-	PUNCT
cana-5662	358	7	set	set	NOUN
cana-5662	358	8	of	of	ADP
cana-5662	358	9	kn	kn	PROPN
cana-5662	358	10	◦	◦	PROPN
cana-5662	358	11	g	g	NOUN
cana-5662	358	12	,	,	PUNCT
cana-5662	358	13	γctd(kn	γctd(kn	VERB
cana-5662	358	14	◦	◦	NOUN
cana-5662	358	15	g	g	NOUN
cana-5662	358	16	)	)	PUNCT
cana-5662	358	17	≤	≤	NUM
cana-5662	358	18	|d|	|d|	PROPN
cana-5662	358	19	=	=	SYM
cana-5662	358	20	|v	|v	PROPN
cana-5662	358	21	(	(	PUNCT
cana-5662	358	22	kn	kn	NOUN
cana-5662	358	23	◦	◦	NOUN
cana-5662	358	24	g	g	NOUN
cana-5662	358	25	)	)	PUNCT
cana-5662	359	1	−	−	PROPN
cana-5662	359	2	(	(	PUNCT
cana-5662	359	3	v	v	NOUN
cana-5662	359	4	(	(	PUNCT
cana-5662	359	5	k2	k2	NOUN
cana-5662	359	6	)	)	PUNCT
cana-5662	359	7	∪	∪	NOUN
cana-5662	359	8	d1)|	d1)|	PROPN
cana-5662	359	9	=	=	SYM
cana-5662	359	10	mn	mn	PROPN
cana-5662	359	11	+	+	CCONJ
cana-5662	359	12	n	n	CCONJ
cana-5662	359	13	−	−	PROPN
cana-5662	359	14	(	(	PUNCT
cana-5662	359	15	2	2	NUM
cana-5662	359	16	+	+	NUM
cana-5662	359	17	2β0	2β0	NUM
cana-5662	359	18	)	)	PUNCT
cana-5662	360	1	=	=	NOUN
cana-5662	361	1	m(n	m(n	NOUN
cana-5662	361	2	−	−	PROPN
cana-5662	361	3	2	2	X
cana-5662	361	4	)	)	PUNCT
cana-5662	361	5	+	+	CCONJ
cana-5662	361	6	(	(	PUNCT
cana-5662	361	7	n	n	CCONJ
cana-5662	361	8	−	−	PROPN
cana-5662	361	9	2	2	NUM
cana-5662	361	10	)	)	PUNCT
cana-5662	361	11	+	+	NUM
cana-5662	361	12	2(m	2(m	NUM
cana-5662	361	13	−	−	ADP
cana-5662	361	14	β0	β0	NOUN
cana-5662	361	15	)	)	PUNCT
cana-5662	361	16	=	=	PUNCT
cana-5662	361	17	(	(	PUNCT
cana-5662	361	18	n	n	CCONJ
cana-5662	361	19	−	−	PROPN
cana-5662	361	20	2)(m	2)(m	NUM
cana-5662	361	21	+	+	CCONJ
cana-5662	361	22	1	1	NUM
cana-5662	361	23	)	)	PUNCT
cana-5662	361	24	+	+	NUM
cana-5662	361	25	2(m	2(m	NUM
cana-5662	361	26	−	−	PROPN
cana-5662	361	27	β0	β0	NOUN
cana-5662	361	28	)	)	PUNCT
cana-5662	361	29	the	the	DET
cana-5662	361	30	lower	lower	ADV
cana-5662	361	31	bound	bind	VERB
cana-5662	361	32	equality	equality	NOUN
cana-5662	361	33	holds	hold	VERB
cana-5662	361	34	if	if	SCONJ
cana-5662	361	35	g	g	PROPN
cana-5662	361	36			PROPN
cana-5662	361	37	k2	k2	PROPN
cana-5662	361	38	.	.	PUNCT
cana-5662	362	1	references	reference	NOUN
cana-5662	362	2	[	[	X
cana-5662	362	3	1	1	NUM
cana-5662	362	4	]	]	PUNCT
cana-5662	362	5	r.frucht	r.frucht	NOUN
cana-5662	362	6	and	and	CCONJ
cana-5662	362	7	f.harary	f.harary	ADJ
cana-5662	362	8	,	,	PUNCT
cana-5662	362	9	“	"	PUNCT
cana-5662	362	10	on	on	ADP
cana-5662	362	11	the	the	DET
cana-5662	362	12	corona	corona	NOUN
cana-5662	362	13	of	of	ADP
cana-5662	362	14	two	two	NUM
cana-5662	362	15	graphs	graph	NOUN
cana-5662	362	16	”	"	PUNCT
cana-5662	362	17	,	,	PUNCT
cana-5662	362	18	aequationes	aequatione	VERB
cana-5662	362	19	math	math	PROPN
cana-5662	362	20	.	.	PUNCT
cana-5662	363	1	,	,	PUNCT
cana-5662	363	2	vol	vol	NOUN
cana-5662	363	3	.	.	PUNCT
cana-5662	364	1	4,pp	4,pp	NUM
cana-5662	364	2	.	.	PUNCT
cana-5662	365	1	322–325	322–325	NUM
cana-5662	365	2	,	,	PUNCT
cana-5662	365	3	1970	1970	NUM
cana-5662	365	4	.	.	PUNCT
cana-5662	366	1	[	[	X
cana-5662	366	2	2	2	NUM
cana-5662	366	3	]	]	PUNCT
cana-5662	366	4	f.harary,“graph	f.harary,“graph	ADJ
cana-5662	366	5	theory	theory	NOUN
cana-5662	366	6	”	"	PUNCT
cana-5662	366	7	,	,	PUNCT
cana-5662	366	8	addison	addison	PROPN
cana-5662	366	9	wesley	wesley	PROPN
cana-5662	366	10	,	,	PUNCT
cana-5662	366	11	reading	read	VERB
cana-5662	366	12	mass,1972	mass,1972	NOUN
cana-5662	366	13	.	.	PUNCT
cana-5662	367	1	[	[	X
cana-5662	367	2	3	3	NUM
cana-5662	367	3	]	]	SYM
cana-5662	367	4	s.muthammai	s.muthammai	NOUN
cana-5662	367	5	,	,	PUNCT
cana-5662	367	6	m.bhanumathi	m.bhanumathi	NOUN
cana-5662	367	7	and	and	CCONJ
cana-5662	367	8	p.vidhya	p.vidhya	ADV
cana-5662	367	9	,	,	PUNCT
cana-5662	367	10	“	"	PUNCT
cana-5662	367	11	complementary	complementary	ADJ
cana-5662	367	12	tree	tree	NOUN
cana-5662	367	13	domination	domination	NOUN
cana-5662	367	14	number	number	NOUN
cana-5662	367	15	of	of	ADP
cana-5662	367	16	a	a	DET
cana-5662	367	17	graph	graph	NOUN
cana-5662	367	18	”	"	PUNCT
cana-5662	367	19	,	,	PUNCT
cana-5662	367	20	international	international	PROPN
cana-5662	367	21	mathematical	mathematical	ADJ
cana-5662	367	22	forum	forum	PROPN
cana-5662	367	23	,	,	PUNCT
cana-5662	367	24	vol	vol	NOUN
cana-5662	367	25	.	.	PROPN
cana-5662	368	1	6	6	NUM
cana-5662	368	2	,	,	PUNCT
cana-5662	368	3	no	no	INTJ
cana-5662	368	4	.	.	PUNCT
cana-5662	369	1	26,pp	26,pp	NUM
cana-5662	369	2	.	.	PUNCT
cana-5662	370	1	1273	1273	NUM
cana-5662	370	2	–	–	PUNCT
cana-5662	370	3	1282	1282	NUM
cana-5662	370	4	,	,	PUNCT
cana-5662	370	5	2011	2011	NUM
cana-5662	370	6	.	.	PUNCT
cana-5662	371	1	[	[	X
cana-5662	371	2	4	4	NUM
cana-5662	371	3	]	]	PUNCT
cana-5662	371	4	o.ore	o.ore	ADV
cana-5662	371	5	,	,	PUNCT
cana-5662	371	6	“	"	PUNCT
cana-5662	371	7	theory	theory	NOUN
cana-5662	371	8	of	of	ADP
cana-5662	371	9	graphs	graph	NOUN
cana-5662	371	10	”	"	PUNCT
cana-5662	371	11	,	,	PUNCT
cana-5662	371	12	amer	amer	PROPN
cana-5662	371	13	.	.	PROPN
cana-5662	371	14	math	math	PROPN
cana-5662	371	15	.	.	PUNCT
cana-5662	372	1	soc	soc	PROPN
cana-5662	372	2	.	.	PUNCT
cana-5662	373	1	colloq	colloq	PROPN
cana-5662	373	2	.	.	PUNCT
cana-5662	374	1	publ	publ	PROPN
cana-5662	374	2	.	.	PUNCT
cana-5662	374	3	,	,	PUNCT
cana-5662	374	4	vol	vol	NOUN
cana-5662	374	5	.	.	PUNCT
cana-5662	375	1	38,1962	38,1962	NUM
cana-5662	375	2	.	.	PUNCT
cana-5662	376	1	[	[	X
cana-5662	376	2	5	5	X
cana-5662	376	3	]	]	X
cana-5662	376	4	sergio	sergio	PROPN
cana-5662	376	5	canoyjr	canoyjr	PROPN
cana-5662	376	6	and	and	CCONJ
cana-5662	376	7	carmelito	carmelito	PROPN
cana-5662	376	8	e.go	e.go	PROPN
cana-5662	376	9	,	,	PUNCT
cana-5662	376	10	“	"	PUNCT
cana-5662	376	11	domination	domination	NOUN
cana-5662	376	12	in	in	ADP
cana-5662	376	13	the	the	DET
cana-5662	376	14	corona	corona	NOUN
cana-5662	376	15	and	and	CCONJ
cana-5662	376	16	join	join	VERB
cana-5662	376	17	of	of	ADP
cana-5662	376	18	graphs	graph	NOUN
cana-5662	376	19	”	"	PUNCT
cana-5662	376	20	,	,	PUNCT
cana-5662	376	21	international	international	PROPN
cana-5662	376	22	mathematical	mathematical	ADJ
cana-5662	376	23	forum	forum	PROPN
cana-5662	376	24	,	,	PUNCT
cana-5662	376	25	vol	vol	NOUN
cana-5662	376	26	.	.	PROPN
cana-5662	376	27	6	6	NUM
cana-5662	376	28	,	,	PUNCT
cana-5662	376	29	no	no	INTJ
cana-5662	376	30	.	.	PUNCT
cana-5662	376	31	13,2011	13,2011	NUM
cana-5662	376	32	.	.	PUNCT
cana-5662	377	1	[	[	X
cana-5662	377	2	6	6	NUM
cana-5662	377	3	]	]	PUNCT
cana-5662	377	4	p.	p.	NOUN
cana-5662	377	5	vidhya	vidhya	PROPN
cana-5662	377	6	and	and	CCONJ
cana-5662	377	7	s.	s.	PROPN
cana-5662	377	8	jayalakshmi	jayalakshmi	PROPN
cana-5662	377	9	,	,	PUNCT
cana-5662	377	10	“	"	PUNCT
cana-5662	377	11	complementary	complementary	ADJ
cana-5662	377	12	tree	tree	NOUN
cana-5662	377	13	domination	domination	NOUN
cana-5662	377	14	of	of	ADP
cana-5662	377	15	corona	corona	NOUN
cana-5662	377	16	product	product	NOUN
cana-5662	377	17	of	of	ADP
cana-5662	377	18	cycle	cycle	NOUN
cana-5662	377	19	cn	cn	PROPN
cana-5662	377	20	with	with	ADP
cana-5662	377	21	some	some	DET
cana-5662	377	22	standard	standard	ADJ
cana-5662	377	23	graphs	graph	NOUN
cana-5662	377	24	”	"	PUNCT
cana-5662	377	25	,	,	PUNCT
cana-5662	377	26	design	design	NOUN
cana-5662	377	27	engineering	engineering	NOUN
cana-5662	377	28	,	,	PUNCT
cana-5662	377	29	vol	vol	NOUN
cana-5662	377	30	.	.	PUNCT
cana-5662	378	1	9,2021	9,2021	NUM
cana-5662	378	2	.	.	PUNCT
cana-5662	379	1	[	[	X
cana-5662	379	2	7	7	X
cana-5662	379	3	]	]	X
cana-5662	379	4	s.	s.	PROPN
cana-5662	379	5	muthammai	muthammai	PROPN
cana-5662	379	6	and	and	CCONJ
cana-5662	379	7	p.	p.	PROPN
cana-5662	379	8	vidhya	vidhya	PROPN
cana-5662	379	9	,	,	PUNCT
cana-5662	379	10	“	"	PUNCT
cana-5662	379	11	more	more	ADJ
cana-5662	379	12	results	result	NOUN
cana-5662	379	13	on	on	ADP
cana-5662	379	14	complementary	complementary	ADJ
cana-5662	379	15	tree	tree	NOUN
cana-5662	379	16	domination	domination	NOUN
cana-5662	379	17	number	number	NOUN
cana-5662	379	18	of	of	ADP
cana-5662	379	19	graphs	graph	NOUN
cana-5662	379	20	”	"	PUNCT
cana-5662	379	21	,	,	PUNCT
cana-5662	379	22	international	international	ADJ
cana-5662	379	23	journal	journal	NOUN
cana-5662	379	24	of	of	ADP
cana-5662	379	25	mathematics	mathematic	NOUN
cana-5662	379	26	and	and	CCONJ
cana-5662	379	27	its	its	PRON
cana-5662	379	28	applications	application	NOUN
cana-5662	379	29	,	,	PUNCT
cana-5662	379	30	vol	vol	NOUN
cana-5662	379	31	.	.	PROPN
cana-5662	379	32	4	4	NUM
cana-5662	379	33	,	,	PUNCT
cana-5662	379	34	no	no	INTJ
cana-5662	379	35	.	.	NOUN
cana-5662	379	36	1	1	NUM
cana-5662	379	37	-	-	SYM
cana-5662	379	38	d	d	PROPN
cana-5662	379	39	,	,	PUNCT
cana-5662	379	40	pp	pp	ADJ
cana-5662	379	41	.	.	PUNCT
cana-5662	380	1	17	17	NUM
cana-5662	380	2	-	-	SYM
cana-5662	380	3	20	20	NUM
cana-5662	380	4	,	,	PUNCT
cana-5662	380	5	2016	2016	NUM
cana-5662	380	6	.	.	PUNCT