id	sid	tid	token	lemma	pos
cana-860	1	1	communications	communication	NOUN
cana-860	1	2	on	on	ADP
cana-860	1	3	applied	apply	VERB
cana-860	1	4	nonlinear	nonlinear	ADJ
cana-860	1	5	analysis	analysis	NOUN
cana-860	1	6	issn	issn	NOUN
cana-860	1	7	:	:	PUNCT
cana-860	1	8	1074	1074	NUM
cana-860	1	9	-	-	PUNCT
cana-860	1	10	133x	133x	NUM
cana-860	1	11	vol	vol	NOUN
cana-860	1	12	31	31	NUM
cana-860	1	13	no	no	NOUN
cana-860	1	14	.	.	PUNCT
cana-860	2	1	4s	4s	NUM
cana-860	2	2	(	(	PUNCT
cana-860	2	3	2024	2024	NUM
cana-860	2	4	)	)	PUNCT
cana-860	2	5	371	371	NUM
cana-860	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-860	2	7	some	some	DET
cana-860	2	8	bench	bench	NOUN
cana-860	2	9	mark	mark	NOUN
cana-860	2	10	results	result	NOUN
cana-860	2	11	on	on	ADP
cana-860	2	12	total	total	ADJ
cana-860	2	13	domination	domination	NOUN
cana-860	2	14	subdivision	subdivision	NOUN
cana-860	2	15	stable	stable	ADJ
cana-860	2	16	graph	graph	NOUN
cana-860	2	17	a.	a.	NOUN
cana-860	2	18	jeeva1	jeeva1	PROPN
cana-860	2	19	*	*	PROPN
cana-860	2	20	,	,	PUNCT
cana-860	2	21	m.	m.	NOUN
cana-860	2	22	yamuna2	yamuna2	PROPN
cana-860	2	23	,	,	PUNCT
cana-860	2	24	a.	a.	PROPN
cana-860	2	25	kuppan3	kuppan3	PROPN
cana-860	2	26	,	,	PUNCT
cana-860	2	27	v.	v.	ADP
cana-860	2	28	sivan4	sivan4	PROPN
cana-860	2	29	,	,	PUNCT
cana-860	2	30	p.	p.	NOUN
cana-860	2	31	selvaraju5	selvaraju5	PROPN
cana-860	2	32	,	,	PUNCT
cana-860	2	33	k.	k.	PROPN
cana-860	2	34	kalpana6	kalpana6	PROPN
cana-860	3	1	1department	1department	NUM
cana-860	3	2	of	of	ADP
cana-860	3	3	mathematics	mathematic	NOUN
cana-860	3	4	,	,	PUNCT
cana-860	3	5	vel	vel	PROPN
cana-860	3	6	tech	tech	PROPN
cana-860	3	7	rangarajan	rangarajan	PROPN
cana-860	3	8	dr	dr	PROPN
cana-860	3	9	.	.	PROPN
cana-860	3	10	sagunthala	sagunthala	PROPN
cana-860	3	11	r	r	PROPN
cana-860	3	12	&	&	CCONJ
cana-860	3	13	d	d	PROPN
cana-860	3	14	institute	institute	PROPN
cana-860	3	15	of	of	ADP
cana-860	3	16	science	science	NOUN
cana-860	3	17	and	and	CCONJ
cana-860	3	18	technology	technology	NOUN
cana-860	3	19	,	,	PUNCT
cana-860	3	20	chennai	chennai	PROPN
cana-860	3	21	,	,	PUNCT
cana-860	3	22	tamil	tamil	PROPN
cana-860	3	23	nadu	nadu	PROPN
cana-860	3	24	,	,	PUNCT
cana-860	3	25	india	india	PROPN
cana-860	3	26	.	.	PUNCT
cana-860	4	1	drjeevaa@veltech.edu.in	drjeevaa@veltech.edu.in	PROPN
cana-860	4	2	2department	2department	NUM
cana-860	4	3	of	of	ADP
cana-860	4	4	mathematics	mathematic	NOUN
cana-860	4	5	,	,	PUNCT
cana-860	4	6	school	school	NOUN
cana-860	4	7	of	of	ADP
cana-860	4	8	advanced	advanced	ADJ
cana-860	4	9	sciences	science	NOUN
cana-860	4	10	,	,	PUNCT
cana-860	4	11	vellore	vellore	PROPN
cana-860	4	12	institute	institute	PROPN
cana-860	4	13	of	of	ADP
cana-860	4	14	science	science	NOUN
cana-860	4	15	and	and	CCONJ
cana-860	4	16	technology	technology	NOUN
cana-860	4	17	,	,	PUNCT
cana-860	4	18	tamil	tamil	PROPN
cana-860	4	19	nadu	nadu	PROPN
cana-860	4	20	,	,	PUNCT
cana-860	4	21	india	india	PROPN
cana-860	4	22	.	.	PUNCT
cana-860	5	1	myamuna@vit.ac.in	myamuna@vit.ac.in	PROPN
cana-860	6	1	3department	3department	PROPN
cana-860	6	2	of	of	ADP
cana-860	6	3	mathematics	mathematic	NOUN
cana-860	6	4	,	,	PUNCT
cana-860	6	5	saveetha	saveetha	PROPN
cana-860	6	6	engineering	engineering	PROPN
cana-860	6	7	college	college	PROPN
cana-860	6	8	,	,	PUNCT
cana-860	6	9	chennai	chennai	PROPN
cana-860	6	10	,	,	PUNCT
cana-860	6	11	tamilnadu	tamilnadu	NOUN
cana-860	6	12	,	,	PUNCT
cana-860	6	13	india	india	PROPN
cana-860	6	14	.	.	PUNCT
cana-860	7	1	kuppanmyname@gmail.com	kuppanmyname@gmail.com	PROPN
cana-860	8	1	4department	4department	NUM
cana-860	8	2	of	of	ADP
cana-860	8	3	mathematics	mathematic	NOUN
cana-860	8	4	,	,	PUNCT
cana-860	8	5	saveetha	saveetha	PROPN
cana-860	8	6	engineering	engineering	PROPN
cana-860	8	7	college	college	PROPN
cana-860	8	8	,	,	PUNCT
cana-860	8	9	chennai	chennai	PROPN
cana-860	8	10	,	,	PUNCT
cana-860	8	11	tamilnadu	tamilnadu	NOUN
cana-860	8	12	,	,	PUNCT
cana-860	8	13	india	india	PROPN
cana-860	8	14	.	.	PUNCT
cana-860	9	1	shivan.ve@gmail.com	shivan.ve@gmail.com	PROPN
cana-860	10	1	5department	5department	NUM
cana-860	10	2	of	of	ADP
cana-860	10	3	computer	computer	NOUN
cana-860	10	4	science	science	NOUN
cana-860	10	5	and	and	CCONJ
cana-860	10	6	engineering	engineering	NOUN
cana-860	10	7	,	,	PUNCT
cana-860	10	8	saveetha	saveetha	PROPN
cana-860	10	9	school	school	PROPN
cana-860	10	10	engineering	engineering	NOUN
cana-860	10	11	,	,	PUNCT
cana-860	10	12	saveetha	saveetha	PROPN
cana-860	10	13	institute	institute	PROPN
cana-860	10	14	of	of	ADP
cana-860	10	15	medical	medical	ADJ
cana-860	10	16	and	and	CCONJ
cana-860	10	17	technical	technical	ADJ
cana-860	10	18	sciences	science	NOUN
cana-860	10	19	,	,	PUNCT
cana-860	10	20	chennai	chennai	PROPN
cana-860	10	21	,	,	PUNCT
cana-860	10	22	tamilnadu	tamilnadu	NOUN
cana-860	10	23	,	,	PUNCT
cana-860	10	24	india	india	PROPN
cana-860	10	25	pselvar@yahoo.com	pselvar@yahoo.com	X
cana-860	11	1	6department	6department	NUM
cana-860	11	2	of	of	ADP
cana-860	11	3	chemistry	chemistry	NOUN
cana-860	11	4	,	,	PUNCT
cana-860	11	5	saveetha	saveetha	PROPN
cana-860	11	6	school	school	PROPN
cana-860	11	7	of	of	ADP
cana-860	11	8	engineering	engineering	PROPN
cana-860	11	9	,	,	PUNCT
cana-860	11	10	saveetha	saveetha	PROPN
cana-860	11	11	institute	institute	PROPN
cana-860	11	12	of	of	ADP
cana-860	11	13	medical	medical	ADJ
cana-860	11	14	and	and	CCONJ
cana-860	11	15	technical	technical	ADJ
cana-860	11	16	sciences	science	NOUN
cana-860	11	17	,	,	PUNCT
cana-860	11	18	chennai	chennai	PROPN
cana-860	11	19	,	,	PUNCT
cana-860	11	20	tamilnadu	tamilnadu	NOUN
cana-860	11	21	,	,	PUNCT
cana-860	11	22	india	india	PROPN
cana-860	11	23	kalpanakumar19@gmail.com	kalpanakumar19@gmail.com	PROPN
cana-860	11	24	*	*	PUNCT
cana-860	11	25	1corresponding	1corresponding	PROPN
cana-860	11	26	author	author	NOUN
cana-860	11	27	email	email	NOUN
cana-860	11	28	i	i	PROPN
cana-860	11	29	d	d	PROPN
cana-860	11	30	:	:	PUNCT
cana-860	11	31	drjeevaa@veltech.edu.in	drjeevaa@veltech.edu.in	NOUN
cana-860	11	32	article	article	NOUN
cana-860	11	33	history	history	NOUN
cana-860	11	34	:	:	PUNCT
cana-860	11	35	received	receive	VERB
cana-860	11	36	:	:	PUNCT
cana-860	11	37	20	20	NUM
cana-860	11	38	-	-	PUNCT
cana-860	11	39	04	04	NUM
cana-860	11	40	-	-	PUNCT
cana-860	11	41	2024	2024	NUM
cana-860	11	42	revised	revise	VERB
cana-860	11	43	:	:	PUNCT
cana-860	11	44	10	10	NUM
cana-860	11	45	-	-	SYM
cana-860	11	46	06	06	NUM
cana-860	11	47	-	-	PUNCT
cana-860	11	48	2024	2024	NUM
cana-860	11	49	accepted	accept	VERB
cana-860	11	50	:	:	PUNCT
cana-860	11	51	23	23	NUM
cana-860	11	52	-	-	SYM
cana-860	11	53	06	06	NUM
cana-860	11	54	-	-	PUNCT
cana-860	11	55	2024	2024	NUM
cana-860	11	56	abstract	abstract	NOUN
cana-860	11	57	:	:	PUNCT
cana-860	11	58	for	for	ADP
cana-860	11	59	a	a	DET
cana-860	11	60	graph	graph	NOUN
cana-860	11	61	g	g	NOUN
cana-860	11	62	,	,	PUNCT
cana-860	11	63	the	the	DET
cana-860	11	64	total	total	ADJ
cana-860	11	65	dominating	dominating	NOUN
cana-860	11	66	set	set	NOUN
cana-860	11	67	defined	define	VERB
cana-860	11	68	as	as	ADP
cana-860	11	69	a	a	DET
cana-860	11	70	set	set	NOUN
cana-860	11	71	of	of	ADP
cana-860	11	72	vertices	vertex	NOUN
cana-860	11	73	in	in	ADP
cana-860	11	74	s	s	PRON
cana-860	11	75	such	such	ADJ
cana-860	11	76	that	that	SCONJ
cana-860	11	77	all	all	DET
cana-860	11	78	the	the	DET
cana-860	11	79	vertices	vertex	NOUN
cana-860	11	80	in	in	ADP
cana-860	11	81	v(g	v(g	NUM
cana-860	11	82	)	)	PUNCT
cana-860	11	83	has	have	VERB
cana-860	11	84	at	at	ADV
cana-860	11	85	least	least	ADV
cana-860	11	86	one	one	NUM
cana-860	11	87	neighbor	neighbor	NOUN
cana-860	11	88	in	in	ADP
cana-860	11	89	s	s	PROPN
cana-860	11	90	,	,	PUNCT
cana-860	11	91	the	the	DET
cana-860	11	92	least	least	ADJ
cana-860	11	93	cardinality	cardinality	NOUN
cana-860	11	94	is	be	AUX
cana-860	11	95	noted	note	VERB
cana-860	11	96	as	as	ADP
cana-860	11	97	t(g	t(g	NOUN
cana-860	11	98	)	)	PUNCT
cana-860	11	99	.	.	PUNCT
cana-860	12	1	the	the	DET
cana-860	12	2	total	total	ADJ
cana-860	12	3	domination	domination	NOUN
cana-860	12	4	number	number	NOUN
cana-860	12	5	of	of	ADP
cana-860	12	6	each	each	PRON
cana-860	12	7	and	and	CCONJ
cana-860	12	8	every	every	DET
cana-860	12	9	graph	graph	NOUN
cana-860	12	10	while	while	SCONJ
cana-860	12	11	subdividing	subdivide	VERB
cana-860	12	12	any	any	DET
cana-860	12	13	edge	edge	NOUN
cana-860	12	14	xy	xy	PROPN
cana-860	12	15	of	of	ADP
cana-860	12	16	g	g	PROPN
cana-860	12	17	is	be	AUX
cana-860	12	18	equal	equal	ADJ
cana-860	12	19	to	to	ADP
cana-860	12	20	the	the	DET
cana-860	12	21	total	total	ADJ
cana-860	12	22	domination	domination	NOUN
cana-860	12	23	number	number	NOUN
cana-860	12	24	of	of	ADP
cana-860	12	25	g	g	NOUN
cana-860	12	26	,	,	PUNCT
cana-860	12	27	which	which	PRON
cana-860	12	28	results	result	VERB
cana-860	12	29	in	in	ADP
cana-860	12	30	the	the	DET
cana-860	12	31	total	total	ADJ
cana-860	12	32	domination	domination	NOUN
cana-860	12	33	subdivision	subdivision	NOUN
cana-860	12	34	stable	stable	ADJ
cana-860	12	35	graph	graph	NOUN
cana-860	12	36	abbreviated	abbreviate	VERB
cana-860	12	37	as	as	ADP
cana-860	12	38	tdss	tdss	NOUN
cana-860	12	39	and	and	CCONJ
cana-860	12	40	the	the	DET
cana-860	12	41	symbolic	symbolic	ADJ
cana-860	12	42	expression	expression	NOUN
cana-860	12	43	is	be	AUX
cana-860	12	44	gtsd(xy	gtsd(xy	NOUN
cana-860	12	45	)	)	PUNCT
cana-860	12	46	.	.	PUNCT
cana-860	13	1	the	the	DET
cana-860	13	2	research	research	NOUN
cana-860	13	3	paper	paper	NOUN
cana-860	13	4	,	,	PUNCT
cana-860	13	5	we	we	PRON
cana-860	13	6	introduce	introduce	VERB
cana-860	13	7	tdss	tdss	NOUN
cana-860	13	8	and	and	CCONJ
cana-860	13	9	proposed	propose	VERB
cana-860	13	10	conditions	condition	NOUN
cana-860	13	11	under	under	ADP
cana-860	13	12	which	which	PRON
cana-860	13	13	a	a	DET
cana-860	13	14	graph	graph	NOUN
cana-860	13	15	is	be	AUX
cana-860	13	16	tdss	tdss	NOUN
cana-860	13	17	and	and	CCONJ
cana-860	13	18	not	not	PART
cana-860	13	19	tdss	tdss	NOUN
cana-860	13	20	.	.	PUNCT
cana-860	14	1	keywords	keyword	NOUN
cana-860	14	2	:	:	PUNCT
cana-860	14	3	total	total	ADJ
cana-860	14	4	domination	domination	NOUN
cana-860	14	5	,	,	PUNCT
cana-860	14	6	total	total	ADJ
cana-860	14	7	domination	domination	NOUN
cana-860	14	8	subdivision	subdivision	NOUN
cana-860	14	9	,	,	PUNCT
cana-860	14	10	total	total	ADJ
cana-860	14	11	domination	domination	NOUN
cana-860	14	12	subdivision	subdivision	NOUN
cana-860	14	13	stable	stable	ADJ
cana-860	14	14	(	(	PUNCT
cana-860	14	15	tdss	tdss	NOUN
cana-860	14	16	)	)	PUNCT
cana-860	14	17	.	.	PUNCT
cana-860	15	1	1	1	X
cana-860	15	2	.	.	X
cana-860	15	3	introduction	introduction	NOUN
cana-860	15	4	all	all	DET
cana-860	15	5	graphs	graph	NOUN
cana-860	15	6	considered	consider	VERB
cana-860	15	7	here	here	ADV
cana-860	15	8	simple	simple	ADJ
cana-860	15	9	,	,	PUNCT
cana-860	15	10	connected	connected	ADJ
cana-860	15	11	and	and	CCONJ
cana-860	15	12	undirected	undirected	ADJ
cana-860	15	13	graph	graph	NOUN
cana-860	15	14	with	with	ADP
cana-860	15	15	v	v	NOUN
cana-860	15	16	and	and	CCONJ
cana-860	15	17	e	e	NOUN
cana-860	15	18	which	which	PRON
cana-860	15	19	follows	follow	VERB
cana-860	15	20	vertex	vertex	NOUN
cana-860	15	21	set	set	NOUN
cana-860	15	22	and	and	CCONJ
cana-860	15	23	edge	edge	NOUN
cana-860	15	24	set	set	VERB
cana-860	15	25	.	.	PUNCT
cana-860	16	1	for	for	ADP
cana-860	16	2	basic	basic	ADJ
cana-860	16	3	terminology	terminology	NOUN
cana-860	16	4	and	and	CCONJ
cana-860	16	5	notations	notation	NOUN
cana-860	16	6	for	for	ADP
cana-860	16	7	graphs	graph	NOUN
cana-860	16	8	and	and	CCONJ
cana-860	16	9	domination	domination	NOUN
cana-860	16	10	parameters	parameter	NOUN
cana-860	16	11	which	which	PRON
cana-860	16	12	is	be	AUX
cana-860	16	13	not	not	PART
cana-860	16	14	defined	define	VERB
cana-860	16	15	here	here	ADV
cana-860	16	16	refer	refer	VERB
cana-860	16	17	[	[	X
cana-860	16	18	1	1	NUM
cana-860	16	19	]	]	PUNCT
cana-860	16	20	and	and	CCONJ
cana-860	16	21	[	[	X
cana-860	16	22	2	2	NUM
cana-860	16	23	]	]	PUNCT
cana-860	16	24	respectively	respectively	ADV
cana-860	16	25	.	.	PUNCT
cana-860	17	1	the	the	DET
cana-860	17	2	boundary	boundary	NOUN
cana-860	17	3	of	of	ADP
cana-860	17	4	d	d	X
cana-860	17	5	defined	define	VERB
cana-860	17	6	[	[	X
cana-860	17	7	2	2	NUM
cana-860	17	8	]	]	PUNCT
cana-860	17	9	as	as	ADP
cana-860	17	10	b	b	PROPN
cana-860	17	11	(	(	PUNCT
cana-860	17	12	d	d	NOUN
cana-860	17	13	)	)	PUNCT
cana-860	17	14	=	=	SYM
cana-860	18	1	n	n	CCONJ
cana-860	18	2	(	(	PUNCT
cana-860	18	3	d	d	PROPN
cana-860	18	4	)	)	PUNCT
cana-860	18	5	–	–	PUNCT
cana-860	18	6	d.	d.	PROPN
cana-860	18	7	let	let	VERB
cana-860	18	8	x	x	PRON
cana-860	18	9			NOUN
cana-860	18	10	g	g	PROPN
cana-860	18	11	,	,	PUNCT
cana-860	18	12	the	the	DET
cana-860	18	13	vertex	vertex	NOUN
cana-860	18	14	x	x	PRON
cana-860	18	15	is	be	AUX
cana-860	18	16	called	call	VERB
cana-860	18	17	good	good	ADJ
cana-860	18	18	[	[	X
cana-860	18	19	3	3	NUM
cana-860	18	20	]	]	PUNCT
cana-860	18	21	such	such	ADJ
cana-860	18	22	that	that	SCONJ
cana-860	18	23	if	if	SCONJ
cana-860	18	24	all	all	DET
cana-860	18	25	possible	possible	ADJ
cana-860	18	26	t	t	NOUN
cana-860	18	27	–	–	PUNCT
cana-860	18	28	sets	set	NOUN
cana-860	18	29	contained	contain	VERB
cana-860	18	30	the	the	DET
cana-860	18	31	vertex	vertex	NOUN
cana-860	18	32	x	x	PRON
cana-860	18	33	otherwise	otherwise	ADV
cana-860	18	34	it	it	PRON
cana-860	18	35	is	be	AUX
cana-860	18	36	called	call	VERB
cana-860	18	37	bad	bad	ADJ
cana-860	18	38	vertex	vertex	NOUN
cana-860	18	39	.	.	PUNCT
cana-860	19	1	if	if	SCONJ
cana-860	19	2	a	a	DET
cana-860	19	3	vertex	vertex	NOUN
cana-860	19	4	x	x	PRON
cana-860	19	5	is	be	AUX
cana-860	19	6	needed	need	VERB
cana-860	19	7	only	only	ADV
cana-860	19	8	to	to	PART
cana-860	19	9	dominate	dominate	VERB
cana-860	19	10	itself	itself	PRON
cana-860	19	11	in	in	ADP
cana-860	19	12	the	the	DET
cana-860	19	13	minimum	minimum	ADJ
cana-860	19	14	dominating	dominating	NOUN
cana-860	19	15	set	set	NOUN
cana-860	19	16	then	then	ADV
cana-860	19	17	x	x	PUNCT
cana-860	19	18	is	be	AUX
cana-860	19	19	called	call	VERB
cana-860	19	20	selfish	selfish	ADJ
cana-860	19	21	.	.	PUNCT
cana-860	20	1	any	any	DET
cana-860	20	2	vertex	vertex	NOUN
cana-860	20	3	we	we	PRON
cana-860	20	4	call	call	VERB
cana-860	20	5	t	t	PROPN
cana-860	20	6	-	-	PUNCT
cana-860	20	7	dominated	dominate	VERB
cana-860	20	8	in	in	ADP
cana-860	20	9	v	v	NUM
cana-860	20	10	–	–	PUNCT
cana-860	20	11	d	d	NOUN
cana-860	20	12	at	at	ADP
cana-860	20	13	least	least	ADJ
cana-860	20	14	t	t	NOUN
cana-860	20	15	vertices	vertex	NOUN
cana-860	20	16	needed	need	VERB
cana-860	20	17	to	to	PART
cana-860	20	18	dominate	dominate	VERB
cana-860	20	19	that	that	DET
cana-860	20	20	vertex	vertex	NOUN
cana-860	20	21	.	.	PUNCT
cana-860	21	1	if	if	SCONJ
cana-860	21	2	,	,	PUNCT
cana-860	21	3	after	after	ADP
cana-860	21	4	removing	remove	VERB
cana-860	21	5	a	a	DET
cana-860	21	6	vertex	vertex	NOUN
cana-860	21	7	x	x	PUNCT
cana-860	21	8	from	from	ADP
cana-860	21	9	g	g	NOUN
cana-860	21	10	,	,	PUNCT
cana-860	21	11	we	we	PRON
cana-860	21	12	attain	attain	VERB
cana-860	21	13	the	the	DET
cana-860	21	14	graph	graph	NOUN
cana-860	21	15	g	g	NOUN
cana-860	21	16	–	–	PUNCT
cana-860	21	17	communications	communication	NOUN
cana-860	21	18	on	on	ADP
cana-860	21	19	applied	apply	VERB
cana-860	21	20	nonlinear	nonlinear	ADJ
cana-860	21	21	analysis	analysis	NOUN
cana-860	21	22	issn	issn	NOUN
cana-860	21	23	:	:	PUNCT
cana-860	21	24	1074	1074	NUM
cana-860	21	25	-	-	PUNCT
cana-860	21	26	133x	133x	NUM
cana-860	21	27	vol	vol	NOUN
cana-860	21	28	31	31	NUM
cana-860	21	29	no	no	NOUN
cana-860	21	30	.	.	PUNCT
cana-860	22	1	4s	4s	NUM
cana-860	22	2	(	(	PUNCT
cana-860	22	3	2024	2024	NUM
cana-860	22	4	)	)	PUNCT
cana-860	22	5	372	372	NUM
cana-860	22	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-860	22	7	x	x	SYM
cana-860	22	8	,	,	PUNCT
cana-860	22	9	which	which	PRON
cana-860	22	10	is	be	AUX
cana-860	22	11	less	less	ADJ
cana-860	22	12	than	than	ADP
cana-860	22	13	the	the	DET
cana-860	22	14	total	total	ADJ
cana-860	22	15	domination	domination	NOUN
cana-860	22	16	number	number	NOUN
cana-860	22	17	of	of	ADP
cana-860	22	18	g	g	NOUN
cana-860	22	19	,	,	PUNCT
cana-860	22	20	that	that	ADV
cana-860	22	21	is	is	ADV
cana-860	22	22	,	,	PUNCT
cana-860	22	23	t(g	t(g	PROPN
cana-860	22	24	–	–	PUNCT
cana-860	22	25	x	x	X
cana-860	22	26	)	)	PUNCT
cana-860	22	27			PROPN
cana-860	22	28	t(g	t(g	NUM
cana-860	22	29	)	)	PUNCT
cana-860	22	30	,	,	PUNCT
cana-860	22	31	then	then	ADV
cana-860	22	32	that	that	DET
cana-860	22	33	vertex	vertex	NOUN
cana-860	22	34	x	x	PUNCT
cana-860	22	35	is	be	AUX
cana-860	22	36	considered	consider	VERB
cana-860	22	37	down	down	ADP
cana-860	22	38	.	.	PUNCT
cana-860	23	1	the	the	DET
cana-860	23	2	total	total	ADJ
cana-860	23	3	domination	domination	NOUN
cana-860	23	4	subdivision	subdivision	NOUN
cana-860	23	5	number	number	NOUN
cana-860	23	6	was	be	AUX
cana-860	23	7	first	first	ADV
cana-860	23	8	investigated	investigate	VERB
cana-860	23	9	in	in	ADP
cana-860	23	10	[	[	X
cana-860	23	11	4	4	NUM
cana-860	23	12	]	]	PUNCT
cana-860	23	13	.	.	PUNCT
cana-860	24	1	the	the	DET
cana-860	24	2	total	total	ADJ
cana-860	24	3	domination	domination	NOUN
cana-860	24	4	subdivision	subdivision	NOUN
cana-860	24	5	number	number	NOUN
cana-860	24	6	increased	increase	VERB
cana-860	24	7	by	by	ADP
cana-860	24	8	subdividing	subdivide	VERB
cana-860	24	9	least	least	ADJ
cana-860	24	10	number	number	NOUN
cana-860	24	11	of	of	ADP
cana-860	24	12	edges	edge	NOUN
cana-860	24	13	of	of	ADP
cana-860	24	14	g	g	NOUN
cana-860	24	15	which	which	PRON
cana-860	24	16	is	be	AUX
cana-860	24	17	discussed	discuss	VERB
cana-860	24	18	in	in	ADP
cana-860	24	19	[	[	X
cana-860	24	20	5	5	NUM
cana-860	24	21	]	]	PUNCT
cana-860	24	22	.	.	PUNCT
cana-860	25	1	it	it	PRON
cana-860	25	2	has	have	AUX
cana-860	25	3	been	be	AUX
cana-860	25	4	studied	study	VERB
cana-860	25	5	by	by	ADP
cana-860	25	6	several	several	ADJ
cana-860	25	7	authors	author	NOUN
cana-860	25	8	in	in	ADP
cana-860	25	9	[	[	X
cana-860	25	10	6,7,8,9	6,7,8,9	NUM
cana-860	25	11	&	&	CCONJ
cana-860	25	12	10	10	NUM
cana-860	25	13	]	]	PUNCT
cana-860	25	14	.	.	PUNCT
cana-860	26	1	the	the	DET
cana-860	26	2	authors	author	NOUN
cana-860	26	3	[	[	X
cana-860	26	4	11	11	NUM
cana-860	26	5	]	]	PUNCT
cana-860	26	6	introduced	introduce	VERB
cana-860	26	7	the	the	DET
cana-860	26	8	graph	graph	NOUN
cana-860	26	9	named	name	VERB
cana-860	26	10	as	as	ADP
cana-860	26	11	domination	domination	NOUN
cana-860	26	12	subdivision	subdivision	NOUN
cana-860	26	13	stable	stable	ADJ
cana-860	26	14	graph	graph	NOUN
cana-860	26	15	is	be	AUX
cana-860	26	16	the	the	DET
cana-860	26	17	domination	domination	NOUN
cana-860	26	18	number	number	NOUN
cana-860	26	19	of	of	ADP
cana-860	26	20	each	each	PRON
cana-860	26	21	and	and	CCONJ
cana-860	26	22	every	every	DET
cana-860	26	23	graph	graph	NOUN
cana-860	26	24	while	while	SCONJ
cana-860	26	25	subdividing	subdivide	VERB
cana-860	26	26	any	any	DET
cana-860	26	27	edge	edge	NOUN
cana-860	26	28	of	of	ADP
cana-860	26	29	g	g	NOUN
cana-860	26	30	is	be	AUX
cana-860	26	31	equal	equal	ADJ
cana-860	26	32	to	to	ADP
cana-860	26	33	the	the	DET
cana-860	26	34	domination	domination	NOUN
cana-860	26	35	number	number	NOUN
cana-860	26	36	of	of	ADP
cana-860	26	37	g	g	NOUN
cana-860	26	38	,	,	PUNCT
cana-860	26	39	which	which	PRON
cana-860	26	40	is	be	AUX
cana-860	26	41	abbreviated	abbreviate	VERB
cana-860	26	42	as	as	ADP
cana-860	26	43	dss	dss	NOUN
cana-860	26	44	.	.	PUNCT
cana-860	27	1	let	let	VERB
cana-860	27	2	e	e	NOUN
cana-860	27	3	=	=	PRON
cana-860	27	4	xy	xy	PROPN
cana-860	27	5	be	be	AUX
cana-860	27	6	an	an	DET
cana-860	27	7	edge	edge	NOUN
cana-860	27	8	with	with	ADP
cana-860	27	9	end	end	NOUN
cana-860	27	10	points	point	NOUN
cana-860	27	11	{	{	PUNCT
cana-860	27	12	x	x	NOUN
cana-860	27	13	,	,	PUNCT
cana-860	27	14	y	y	NOUN
cana-860	27	15	}	}	PUNCT
cana-860	27	16	of	of	ADP
cana-860	27	17	g.	g.	PROPN
cana-860	27	18	while	while	SCONJ
cana-860	27	19	subdividing	subdivide	VERB
cana-860	27	20	it	it	PRON
cana-860	27	21	,	,	PUNCT
cana-860	27	22	we	we	PRON
cana-860	27	23	access	access	VERB
cana-860	27	24	a	a	DET
cana-860	27	25	new	new	ADJ
cana-860	27	26	one	one	NOUN
cana-860	27	27	say	say	VERB
cana-860	27	28	z	z	NOUN
cana-860	27	29	and	and	CCONJ
cana-860	27	30	having	have	VERB
cana-860	27	31	new	new	ADJ
cana-860	27	32	edges	edge	NOUN
cana-860	27	33	say	say	VERB
cana-860	27	34	{	{	PUNCT
cana-860	27	35	x	x	X
cana-860	27	36	,	,	PUNCT
cana-860	27	37	z	z	NOUN
cana-860	27	38	}	}	PUNCT
cana-860	27	39	and	and	CCONJ
cana-860	27	40	{	{	PUNCT
cana-860	27	41	z	z	NOUN
cana-860	27	42	,	,	PUNCT
cana-860	27	43	y	y	NOUN
cana-860	27	44	}	}	PUNCT
cana-860	27	45	of	of	ADP
cana-860	27	46	the	the	DET
cana-860	27	47	resulting	result	VERB
cana-860	27	48	graph	graph	NOUN
cana-860	27	49	,	,	PUNCT
cana-860	27	50	it	it	PRON
cana-860	27	51	is	be	AUX
cana-860	27	52	expressed	express	VERB
cana-860	27	53	as	as	ADP
cana-860	27	54	g	g	PROPN
cana-860	27	55	sd	sd	PROPN
cana-860	27	56	xy	xy	PROPN
cana-860	27	57	.	.	PUNCT
cana-860	28	1	based	base	VERB
cana-860	28	2	on	on	ADP
cana-860	28	3	this	this	DET
cana-860	28	4	concept	concept	NOUN
cana-860	28	5	,	,	PUNCT
cana-860	28	6	we	we	PRON
cana-860	28	7	extend	extend	VERB
cana-860	28	8	this	this	PRON
cana-860	28	9	to	to	ADP
cana-860	28	10	total	total	ADJ
cana-860	28	11	domination	domination	NOUN
cana-860	28	12	and	and	CCONJ
cana-860	28	13	introduce	introduce	VERB
cana-860	28	14	a	a	DET
cana-860	28	15	new	new	ADJ
cana-860	28	16	graph	graph	NOUN
cana-860	28	17	named	name	VERB
cana-860	28	18	as	as	ADP
cana-860	28	19	total	total	ADJ
cana-860	28	20	domination	domination	NOUN
cana-860	28	21	subdivision	subdivision	NOUN
cana-860	28	22	stable	stable	ADJ
cana-860	28	23	graph	graph	NOUN
cana-860	28	24	.	.	PUNCT
cana-860	29	1	2	2	X
cana-860	29	2	.	.	X
cana-860	29	3	main	main	ADJ
cana-860	29	4	results	result	NOUN
cana-860	29	5	the	the	DET
cana-860	29	6	focus	focus	NOUN
cana-860	29	7	of	of	ADP
cana-860	29	8	this	this	DET
cana-860	29	9	section	section	NOUN
cana-860	29	10	,	,	PUNCT
cana-860	29	11	we	we	PRON
cana-860	29	12	defined	define	VERB
cana-860	29	13	total	total	ADJ
cana-860	29	14	domination	domination	NOUN
cana-860	29	15	subdivision	subdivision	NOUN
cana-860	29	16	stable	stable	ADJ
cana-860	29	17	graph	graph	NOUN
cana-860	29	18	and	and	CCONJ
cana-860	29	19	discussed	discuss	VERB
cana-860	29	20	basic	basic	ADJ
cana-860	29	21	properties	property	NOUN
cana-860	29	22	for	for	ADP
cana-860	29	23	obtaining	obtain	VERB
cana-860	29	24	tdss	tdss	NOUN
cana-860	29	25	from	from	ADP
cana-860	29	26	a	a	DET
cana-860	29	27	graph	graph	NOUN
cana-860	29	28	g.	g.	NOUN
cana-860	29	29	definition	definition	NOUN
cana-860	29	30	2.1	2.1	NUM
cana-860	29	31	for	for	ADP
cana-860	29	32	a	a	DET
cana-860	29	33	given	give	VERB
cana-860	29	34	graph	graph	NOUN
cana-860	29	35	g	g	PROPN
cana-860	29	36	,	,	PUNCT
cana-860	29	37	the	the	DET
cana-860	29	38	total	total	ADJ
cana-860	29	39	domination	domination	NOUN
cana-860	29	40	number	number	NOUN
cana-860	29	41	of	of	ADP
cana-860	29	42	all	all	DET
cana-860	29	43	graphs	graph	NOUN
cana-860	29	44	derived	derive	VERB
cana-860	29	45	by	by	ADP
cana-860	29	46	subdividing	subdivide	VERB
cana-860	29	47	any	any	DET
cana-860	29	48	edge	edge	NOUN
cana-860	29	49	xy	xy	PROPN
cana-860	29	50	of	of	ADP
cana-860	29	51	g	g	PROPN
cana-860	29	52	is	be	AUX
cana-860	29	53	same	same	ADJ
cana-860	29	54	for	for	ADP
cana-860	29	55	the	the	DET
cana-860	29	56	total	total	ADJ
cana-860	29	57	domination	domination	NOUN
cana-860	29	58	number	number	NOUN
cana-860	29	59	of	of	ADP
cana-860	29	60	g	g	NOUN
cana-860	29	61	which	which	PRON
cana-860	29	62	named	name	VERB
cana-860	29	63	as	as	ADP
cana-860	29	64	total	total	ADJ
cana-860	29	65	domination	domination	NOUN
cana-860	29	66	subdivision	subdivision	NOUN
cana-860	29	67	stable	stable	ADJ
cana-860	29	68	.	.	PUNCT
cana-860	30	1	using	use	VERB
cana-860	30	2	this	this	DET
cana-860	30	3	graph	graph	NOUN
cana-860	30	4	operation	operation	NOUN
cana-860	30	5	(	(	PUNCT
cana-860	30	6	subdivision	subdivision	NOUN
cana-860	30	7	)	)	PUNCT
cana-860	30	8	of	of	ADP
cana-860	30	9	any	any	DET
cana-860	30	10	edge	edge	NOUN
cana-860	30	11	xy	xy	INTJ
cana-860	30	12	,	,	PUNCT
cana-860	30	13	we	we	PRON
cana-860	30	14	obtain	obtain	VERB
cana-860	30	15	a	a	DET
cana-860	30	16	new	new	ADJ
cana-860	30	17	vertex	vertex	NOUN
cana-860	30	18	z	z	NOUN
cana-860	30	19	,	,	PUNCT
cana-860	30	20	the	the	DET
cana-860	30	21	expression	expression	NOUN
cana-860	30	22	of	of	ADP
cana-860	30	23	this	this	DET
cana-860	30	24	denoted	denote	VERB
cana-860	30	25	gtsd	gtsd	NOUN
cana-860	30	26	xy	xy	X
cana-860	31	1	=	=	PUNCT
cana-860	31	2	z.	z.	PROPN
cana-860	31	3	fig	fig	PROPN
cana-860	31	4	.	.	PUNCT
cana-860	32	1	1	1	NUM
cana-860	32	2	graph	graph	NOUN
cana-860	32	3	g	g	NOUN
cana-860	32	4	and	and	CCONJ
cana-860	32	5	gtsd	gtsd	PROPN
cana-860	32	6	14	14	NUM
cana-860	32	7	in	in	ADP
cana-860	32	8	fig	fig	NOUN
cana-860	32	9	1	1	NUM
cana-860	32	10	,	,	PUNCT
cana-860	32	11			NUM
cana-860	32	12	t(g	t(g	NOUN
cana-860	32	13	)	)	PUNCT
cana-860	33	1	=	=	SYM
cana-860	33	2	t(g	t(g	NOUN
cana-860	33	3	tsd	tsd	PROPN
cana-860	33	4	14	14	NUM
cana-860	33	5	)	)	PUNCT
cana-860	33	6	=	=	SYM
cana-860	33	7	4	4	X
cana-860	33	8	.	.	PUNCT
cana-860	34	1	according	accord	VERB
cana-860	34	2	to	to	ADP
cana-860	34	3	the	the	DET
cana-860	34	4	fig	fig	NOUN
cana-860	34	5	1	1	NUM
cana-860	34	6	,	,	PUNCT
cana-860	34	7	the	the	DET
cana-860	34	8	total	total	ADJ
cana-860	34	9	domination	domination	NOUN
cana-860	34	10	number	number	NOUN
cana-860	34	11	is	be	AUX
cana-860	34	12	the	the	DET
cana-860	34	13	same	same	ADJ
cana-860	34	14	for	for	ADP
cana-860	34	15	every	every	DET
cana-860	34	16	pair	pair	NOUN
cana-860	34	17	.	.	PUNCT
cana-860	35	1	therefore	therefore	ADV
cana-860	35	2	t	t	PROPN
cana-860	35	3	(	(	PUNCT
cana-860	35	4	g	g	PROPN
cana-860	35	5	tsd	tsd	PROPN
cana-860	35	6	xy	xy	PROPN
cana-860	35	7	)	)	PUNCT
cana-860	36	1	=	=	PRON
cana-860	36	2			NUM
cana-860	36	3	t	t	PROPN
cana-860	36	4	(	(	PUNCT
cana-860	36	5	g	g	PROPN
cana-860	36	6	)	)	PUNCT
cana-860	36	7	.	.	PUNCT
cana-860	37	1	theorem	theorem	VERB
cana-860	37	2	2.2	2.2	NUM
cana-860	37	3	for	for	ADP
cana-860	37	4	every	every	DET
cana-860	37	5	graph	graph	NOUN
cana-860	37	6	g	g	NOUN
cana-860	37	7	,	,	PUNCT
cana-860	37	8	t	t	PROPN
cana-860	37	9	(	(	PUNCT
cana-860	37	10	g	g	PROPN
cana-860	37	11	tsd	tsd	PROPN
cana-860	37	12	xy	xy	PROPN
cana-860	37	13	)	)	PUNCT
cana-860	37	14	≥	≥	PROPN
cana-860	37	15	t	t	NOUN
cana-860	37	16	(	(	PUNCT
cana-860	37	17	g	g	NOUN
cana-860	37	18	)	)	PUNCT
cana-860	37	19			NOUN
cana-860	37	20	xy	xy	PROPN
cana-860	38	1			PROPN
cana-860	38	2	e	e	X
cana-860	38	3	(	(	PUNCT
cana-860	38	4	g	g	NOUN
cana-860	38	5	)	)	PUNCT
cana-860	38	6	.	.	PUNCT
cana-860	39	1	proof	proof	NOUN
cana-860	39	2	let	let	VERB
cana-860	39	3	us	we	PRON
cana-860	39	4	assume	assume	VERB
cana-860	39	5	the	the	DET
cana-860	39	6	graph	graph	NOUN
cana-860	39	7	to	to	PART
cana-860	39	8	be	be	AUX
cana-860	39	9	g	g	NOUN
cana-860	39	10	and	and	CCONJ
cana-860	39	11	t	t	NOUN
cana-860	39	12	–	–	PUNCT
cana-860	39	13	set	set	NOUN
cana-860	39	14	of	of	ADP
cana-860	39	15	g	g	NOUN
cana-860	39	16	to	to	PART
cana-860	39	17	be	be	AUX
cana-860	39	18	d.	d.	PROPN
cana-860	39	19	consider	consider	VERB
cana-860	39	20	g	g	PROPN
cana-860	39	21	tsd	tsd	PROPN
cana-860	39	22	xy	xy	PROPN
cana-860	39	23	where	where	SCONJ
cana-860	39	24	e	e	X
cana-860	39	25	=	=	SYM
cana-860	39	26	xy	xy	PROPN
cana-860	39	27			NOUN
cana-860	39	28	e	e	X
cana-860	39	29	(	(	PUNCT
cana-860	39	30	g	g	NOUN
cana-860	39	31	)	)	PUNCT
cana-860	39	32	and	and	CCONJ
cana-860	39	33	assume	assume	VERB
cana-860	39	34	d1	d1	PROPN
cana-860	39	35	to	to	PART
cana-860	39	36	be	be	AUX
cana-860	39	37	a	a	DET
cana-860	39	38	t	t	NOUN
cana-860	39	39	–	–	PUNCT
cana-860	39	40	set	set	VERB
cana-860	39	41	for	for	ADP
cana-860	39	42	g	g	PROPN
cana-860	39	43	tsd	tsd	PROPN
cana-860	39	44	xy	xy	PROPN
cana-860	39	45	.	.	PUNCT
cana-860	40	1	communications	communication	NOUN
cana-860	40	2	on	on	ADP
cana-860	40	3	applied	apply	VERB
cana-860	40	4	nonlinear	nonlinear	ADJ
cana-860	40	5	analysis	analysis	NOUN
cana-860	40	6	issn	issn	NOUN
cana-860	40	7	:	:	PUNCT
cana-860	40	8	1074	1074	NUM
cana-860	40	9	-	-	PUNCT
cana-860	40	10	133x	133x	NUM
cana-860	40	11	vol	vol	NOUN
cana-860	40	12	31	31	NUM
cana-860	40	13	no	no	NOUN
cana-860	40	14	.	.	PUNCT
cana-860	41	1	4s	4s	NUM
cana-860	41	2	(	(	PUNCT
cana-860	41	3	2024	2024	NUM
cana-860	41	4	)	)	PUNCT
cana-860	41	5	373	373	NUM
cana-860	41	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-860	41	7	if	if	SCONJ
cana-860	41	8	possible	possible	ADJ
cana-860	41	9	let	let	VERB
cana-860	41	10	|	|	ADV
cana-860	41	11	d1	d1	VERB
cana-860	42	1	|	|	ADV
cana-860	42	2	<	<	X
cana-860	42	3	|	|	INTJ
cana-860	42	4	d	d	NOUN
cana-860	42	5	|	|	NOUN
cana-860	42	6	.	.	PUNCT
cana-860	43	1	case	case	NOUN
cana-860	43	2	1	1	NUM
cana-860	43	3	z	z	NOUN
cana-860	43	4			NOUN
cana-860	43	5	d1	d1	PROPN
cana-860	43	6	in	in	ADP
cana-860	43	7	this	this	DET
cana-860	43	8	case	case	NOUN
cana-860	43	9	the	the	DET
cana-860	43	10	possible	possible	ADJ
cana-860	43	11	conditions	condition	NOUN
cana-860	43	12	are	be	AUX
cana-860	43	13	either	either	ADV
cana-860	43	14	,	,	PUNCT
cana-860	43	15	1	1	X
cana-860	43	16	.	.	NUM
cana-860	43	17	x	x	X
cana-860	43	18	,	,	PUNCT
cana-860	43	19	y	y	PROPN
cana-860	43	20			NOUN
cana-860	43	21	d1	d1	PROPN
cana-860	43	22	or	or	CCONJ
cana-860	43	23	2	2	NUM
cana-860	43	24	.	.	NOUN
cana-860	43	25	x	x	SYM
cana-860	43	26	or	or	CCONJ
cana-860	43	27	y	y	PROPN
cana-860	43	28			NOUN
cana-860	43	29	d1	d1	PROPN
cana-860	43	30	.	.	PUNCT
cana-860	44	1	let	let	VERB
cana-860	44	2	x	x	PRON
cana-860	44	3	,	,	PUNCT
cana-860	44	4	y	y	PROPN
cana-860	44	5			PROPN
cana-860	44	6	d1	d1	PROPN
cana-860	44	7	ie	ie	X
cana-860	44	8	.	.	PROPN
cana-860	44	9	,	,	PUNCT
cana-860	44	10	x	x	X
cana-860	44	11	,	,	PUNCT
cana-860	44	12	y	y	PROPN
cana-860	44	13	,	,	PUNCT
cana-860	44	14	z	z	NOUN
cana-860	44	15			NOUN
cana-860	44	16	d1	d1	PROPN
cana-860	44	17	,	,	PUNCT
cana-860	44	18	then	then	ADV
cana-860	44	19	we	we	PRON
cana-860	44	20	obtain	obtain	VERB
cana-860	44	21	d2	d2	PROPN
cana-860	44	22	where	where	SCONJ
cana-860	44	23	d2	d2	NOUN
cana-860	44	24	=	=	SYM
cana-860	44	25	d1	d1	PROPN
cana-860	44	26	–	–	PUNCT
cana-860	44	27	{	{	PUNCT
cana-860	44	28	z	z	NOUN
cana-860	44	29	}	}	PUNCT
cana-860	44	30	is	be	AUX
cana-860	44	31	a	a	DET
cana-860	44	32	t	t	NOUN
cana-860	44	33	–	–	PUNCT
cana-860	44	34	set	set	VERB
cana-860	44	35	for	for	ADP
cana-860	44	36	g	g	PROPN
cana-860	44	37	so	so	SCONJ
cana-860	44	38	|	|	ADV
cana-860	44	39	d2	d2	NOUN
cana-860	45	1	|	|	ADV
cana-860	45	2	<	<	X
cana-860	46	1	|	|	INTJ
cana-860	47	1	d	d	NOUN
cana-860	47	2	|	|	ADV
cana-860	47	3	,	,	PUNCT
cana-860	47	4	we	we	PRON
cana-860	47	5	get	get	VERB
cana-860	47	6	a	a	DET
cana-860	47	7	contradiction	contradiction	NOUN
cana-860	47	8	.	.	PUNCT
cana-860	48	1	if	if	SCONJ
cana-860	48	2	either	either	CCONJ
cana-860	48	3	x	x	SYM
cana-860	48	4	or	or	CCONJ
cana-860	48	5	y	y	PROPN
cana-860	48	6			NOUN
cana-860	48	7	d1	d1	PROPN
cana-860	48	8	say	say	VERB
cana-860	48	9	x	x	PUNCT
cana-860	48	10			NOUN
cana-860	48	11	d1	d1	PROPN
cana-860	48	12	,	,	PUNCT
cana-860	48	13	then	then	ADV
cana-860	48	14	we	we	PRON
cana-860	48	15	obtain	obtain	VERB
cana-860	48	16	d3	d3	PROPN
cana-860	48	17	where	where	SCONJ
cana-860	48	18	d3	d3	PROPN
cana-860	48	19	=	=	PUNCT
cana-860	48	20	d1	d1	PROPN
cana-860	48	21	–	–	PUNCT
cana-860	48	22	{	{	PUNCT
cana-860	48	23	z	z	NOUN
cana-860	48	24	}	}	PUNCT
cana-860	48	25			NOUN
cana-860	48	26	{	{	PUNCT
cana-860	48	27	y	y	NOUN
cana-860	48	28	}	}	PUNCT
cana-860	48	29	as	as	ADP
cana-860	48	30	a	a	DET
cana-860	48	31	t	t	NOUN
cana-860	48	32	–	–	PUNCT
cana-860	48	33	set	set	VERB
cana-860	48	34	for	for	ADP
cana-860	48	35	g	g	PROPN
cana-860	48	36	such	such	ADJ
cana-860	48	37	that|	that|	X
cana-860	48	38	d3|	d3|	VERB
cana-860	48	39	<	<	X
cana-860	49	1	|	|	NOUN
cana-860	49	2	d	d	NOUN
cana-860	49	3	|	|	ADV
cana-860	49	4	,	,	PUNCT
cana-860	49	5	and	and	CCONJ
cana-860	49	6	we	we	PRON
cana-860	49	7	get	get	VERB
cana-860	49	8	a	a	DET
cana-860	49	9	contradiction	contradiction	NOUN
cana-860	49	10	.	.	PUNCT
cana-860	50	1	case	case	NOUN
cana-860	50	2	2	2	NUM
cana-860	50	3	z	z	NOUN
cana-860	50	4			NOUN
cana-860	50	5	d1	d1	NOUN
cana-860	50	6	in	in	ADP
cana-860	50	7	this	this	DET
cana-860	50	8	case	case	NOUN
cana-860	50	9	the	the	DET
cana-860	50	10	possible	possible	ADJ
cana-860	50	11	conditions	condition	NOUN
cana-860	50	12	are	be	AUX
cana-860	50	13	either	either	ADV
cana-860	50	14	,	,	PUNCT
cana-860	50	15	1	1	X
cana-860	50	16	.	.	NUM
cana-860	51	1	x	x	X
cana-860	51	2	,	,	PUNCT
cana-860	51	3	y	y	PROPN
cana-860	51	4			NOUN
cana-860	51	5	d1	d1	PROPN
cana-860	51	6	or	or	CCONJ
cana-860	51	7	2	2	NUM
cana-860	51	8	.	.	NOUN
cana-860	51	9	x	x	SYM
cana-860	51	10	or	or	CCONJ
cana-860	51	11	y	y	PROPN
cana-860	51	12			NOUN
cana-860	51	13	d1	d1	PROPN
cana-860	51	14	.	.	PUNCT
cana-860	52	1	in	in	ADP
cana-860	52	2	both	both	DET
cana-860	52	3	cases	case	NOUN
cana-860	52	4	,	,	PUNCT
cana-860	52	5	we	we	PRON
cana-860	52	6	get	get	VERB
cana-860	52	7	a	a	DET
cana-860	52	8	contradiction	contradiction	NOUN
cana-860	52	9	for	for	ADP
cana-860	52	10	a	a	DET
cana-860	52	11	t	t	NOUN
cana-860	52	12	–	–	PUNCT
cana-860	52	13	set	set	VERB
cana-860	52	14	d1	d1	NOUN
cana-860	52	15	.	.	PUNCT
cana-860	53	1	since	since	SCONJ
cana-860	53	2	for	for	ADP
cana-860	53	3	g	g	NOUN
cana-860	53	4	,	,	PUNCT
cana-860	53	5	d1	d1	PROPN
cana-860	53	6	itself	itself	PRON
cana-860	53	7	is	be	AUX
cana-860	53	8	a	a	DET
cana-860	53	9	t	t	NOUN
cana-860	53	10	–	–	PUNCT
cana-860	53	11	set	set	VERB
cana-860	53	12	we	we	PRON
cana-860	53	13	get	get	VERB
cana-860	53	14	|	|	ADV
cana-860	53	15	d1	d1	NOUN
cana-860	54	1	|	|	ADV
cana-860	54	2	<	<	X
cana-860	54	3	|	|	INTJ
cana-860	54	4	d	d	NOUN
cana-860	54	5	|	|	NOUN
cana-860	54	6	.	.	PUNCT
cana-860	55	1	thus	thus	ADV
cana-860	55	2	t	t	X
cana-860	55	3	(	(	PUNCT
cana-860	55	4	gtsd	gtsd	NOUN
cana-860	55	5	xy	xy	PROPN
cana-860	55	6	)	)	PUNCT
cana-860	55	7	≥	≥	PROPN
cana-860	55	8	t	t	NOUN
cana-860	55	9	(	(	PUNCT
cana-860	55	10	g	g	NOUN
cana-860	55	11	)	)	PUNCT
cana-860	55	12			NOUN
cana-860	55	13	e	e	NOUN
cana-860	56	1	=	=	PUNCT
cana-860	57	1	xy	xy	PROPN
cana-860	57	2	in	in	ADP
cana-860	57	3	e	e	PROPN
cana-860	57	4	(	(	PUNCT
cana-860	57	5	g	g	NOUN
cana-860	57	6	)	)	PUNCT
cana-860	57	7	.	.	PUNCT
cana-860	58	1			PUNCT
cana-860	58	2	theorem	theorem	VERB
cana-860	58	3	2.3	2.3	NUM
cana-860	58	4	for	for	ADP
cana-860	58	5	a	a	DET
cana-860	58	6	given	give	VERB
cana-860	58	7	graph	graph	NOUN
cana-860	58	8	g	g	ADP
cana-860	58	9	such	such	DET
cana-860	58	10	that	that	DET
cana-860	58	11	t	t	NOUN
cana-860	58	12	(	(	PUNCT
cana-860	58	13	g	g	NOUN
cana-860	58	14	)	)	PUNCT
cana-860	58	15	=	=	PUNCT
cana-860	58	16	2	2	NOUN
cana-860	58	17	t	t	NOUN
cana-860	58	18	(	(	PUNCT
cana-860	58	19	g	g	NOUN
cana-860	58	20	)	)	PUNCT
cana-860	58	21	,	,	PUNCT
cana-860	58	22	then	then	ADV
cana-860	58	23	g	g	PROPN
cana-860	58	24	is	be	AUX
cana-860	58	25	tdss	tdss	NOUN
cana-860	58	26	graph	graph	NOUN
cana-860	58	27	proof	proof	NOUN
cana-860	58	28	assume	assume	VERB
cana-860	58	29	that	that	SCONJ
cana-860	58	30	a	a	DET
cana-860	58	31	total	total	ADJ
cana-860	58	32	2	2	NUM
cana-860	58	33	–	–	PUNCT
cana-860	58	34	dominated	dominate	VERB
cana-860	58	35	graph	graph	NOUN
cana-860	58	36	is	be	AUX
cana-860	58	37	g	g	NOUN
cana-860	58	38	and	and	CCONJ
cana-860	58	39	the	the	DET
cana-860	58	40	t	t	NOUN
cana-860	58	41	–	–	PUNCT
cana-860	58	42	set	set	VERB
cana-860	58	43	for	for	ADP
cana-860	58	44	g	g	PROPN
cana-860	58	45	is	be	AUX
cana-860	58	46	d.	d.	PROPN
cana-860	58	47	let	let	VERB
cana-860	58	48	e	e	X
cana-860	58	49	=	=	PUNCT
cana-860	58	50	xy	xy	PROPN
cana-860	59	1			NOUN
cana-860	59	2	e	e	X
cana-860	59	3	(	(	PUNCT
cana-860	59	4	g	g	NOUN
cana-860	59	5	)	)	PUNCT
cana-860	59	6	.	.	PUNCT
cana-860	60	1	case	case	NOUN
cana-860	60	2	1	1	NUM
cana-860	60	3	x	x	NOUN
cana-860	60	4	,	,	PUNCT
cana-860	60	5	y	y	PROPN
cana-860	60	6	in	in	ADP
cana-860	61	1	d	d	PROPN
cana-860	61	2	let	let	VERB
cana-860	61	3	gtsd	gtsd	NOUN
cana-860	61	4	xy	xy	PROPN
cana-860	62	1	=	=	PUNCT
cana-860	62	2	z.	z.	PROPN
cana-860	62	3	then	then	ADV
cana-860	62	4	we	we	PRON
cana-860	62	5	get	get	VERB
cana-860	62	6	a	a	DET
cana-860	62	7	t	t	NOUN
cana-860	62	8	–	–	PUNCT
cana-860	62	9	set	set	VERB
cana-860	62	10	for	for	ADP
cana-860	62	11	gtsd	gtsd	NOUN
cana-860	62	12	xy	xy	PROPN
cana-860	62	13	is	be	AUX
cana-860	62	14	d	d	PROPN
cana-860	62	15	–	–	PUNCT
cana-860	62	16	{	{	PUNCT
cana-860	62	17	x	x	NOUN
cana-860	62	18	}	}	PUNCT
cana-860	62	19			NOUN
cana-860	62	20	{	{	PUNCT
cana-860	62	21	z	z	NOUN
cana-860	62	22	}	}	PUNCT
cana-860	62	23	ie	ie	PROPN
cana-860	62	24	.	.	PROPN
cana-860	62	25	,	,	PUNCT
cana-860	63	1	t	t	PROPN
cana-860	63	2	(	(	PUNCT
cana-860	63	3	gtsd	gtsd	NOUN
cana-860	63	4	xy	xy	PRON
cana-860	63	5	)	)	PUNCT
cana-860	64	1	=	=	VERB
cana-860	64	2	t	t	NOUN
cana-860	64	3	(	(	PUNCT
cana-860	64	4	g	g	NOUN
cana-860	64	5	)	)	PUNCT
cana-860	64	6	.	.	PUNCT
cana-860	65	1	case	case	NOUN
cana-860	65	2	2	2	NUM
cana-860	65	3	x	x	SYM
cana-860	65	4	not	not	PART
cana-860	65	5	in	in	ADP
cana-860	65	6	d	d	PROPN
cana-860	65	7	,	,	PUNCT
cana-860	65	8	y	y	PROPN
cana-860	65	9	in	in	ADP
cana-860	65	10	d	d	PROPN
cana-860	65	11	claim	claim	NOUN
cana-860	65	12	if	if	SCONJ
cana-860	65	13	y	y	PROPN
cana-860	65	14	is	be	AUX
cana-860	65	15	a	a	DET
cana-860	65	16	2	2	NUM
cana-860	65	17	–	–	PUNCT
cana-860	65	18	dominated	dominate	VERB
cana-860	65	19	vertex	vertex	NOUN
cana-860	65	20	such	such	ADJ
cana-860	65	21	that	that	SCONJ
cana-860	65	22	y	y	PROPN
cana-860	65	23	is	be	AUX
cana-860	65	24	adjacent	adjacent	ADJ
cana-860	65	25	to	to	ADP
cana-860	65	26	x	x	SYM
cana-860	65	27	,	,	PUNCT
cana-860	65	28	z	z	PROPN
cana-860	65	29	where	where	SCONJ
cana-860	65	30	x	x	X
cana-860	65	31	,	,	PUNCT
cana-860	65	32	z	z	PROPN
cana-860	65	33			PROPN
cana-860	65	34	t	t	NOUN
cana-860	65	35	(	(	PUNCT
cana-860	65	36	g	g	NOUN
cana-860	65	37	)	)	PUNCT
cana-860	65	38	,	,	PUNCT
cana-860	65	39	then	then	ADV
cana-860	65	40	we	we	PRON
cana-860	65	41	get	get	VERB
cana-860	66	1	t	t	NOUN
cana-860	66	2	(	(	PUNCT
cana-860	66	3	gtsd	gtsd	NOUN
cana-860	66	4	xy	xy	PRON
cana-860	66	5	)	)	PUNCT
cana-860	67	1	=	=	VERB
cana-860	67	2	t	t	NOUN
cana-860	67	3	(	(	PUNCT
cana-860	67	4	g	g	NOUN
cana-860	67	5	)	)	PUNCT
cana-860	67	6	and	and	CCONJ
cana-860	67	7	also	also	ADV
cana-860	67	8	t	t	PROPN
cana-860	67	9	(	(	PUNCT
cana-860	67	10	gtsd	gtsd	NOUN
cana-860	67	11	zy	zy	PROPN
cana-860	67	12	)	)	PUNCT
cana-860	67	13	=	=	VERB
cana-860	68	1	t	t	NOUN
cana-860	68	2	(	(	PUNCT
cana-860	68	3	g	g	NOUN
cana-860	68	4	)	)	PUNCT
cana-860	68	5	.	.	PUNCT
cana-860	69	1	proof	proof	NOUN
cana-860	69	2	let	let	VERB
cana-860	69	3	g	g	NOUN
cana-860	69	4	be	be	AUX
cana-860	69	5	any	any	DET
cana-860	69	6	graph	graph	NOUN
cana-860	69	7	and	and	CCONJ
cana-860	69	8	the	the	DET
cana-860	69	9	2dominated	2dominated	NUM
cana-860	69	10	vertex	vertex	NOUN
cana-860	69	11	is	be	AUX
cana-860	69	12	x.	x.	NOUN
cana-860	69	13	let	let	VERB
cana-860	69	14	gtsd	gtsd	VERB
cana-860	69	15	xy	xy	PROPN
cana-860	70	1	=	=	PUNCT
cana-860	70	2	s.	s.	PROPN
cana-860	70	3	in	in	ADP
cana-860	70	4	gtsd	gtsd	PROPN
cana-860	70	5	xy	xy	PROPN
cana-860	70	6	,	,	PUNCT
cana-860	70	7	vertex	vertex	X
cana-860	70	8	x	x	PUNCT
cana-860	70	9	dominates	dominate	VERB
cana-860	70	10	s	s	PRON
cana-860	70	11	and	and	CCONJ
cana-860	70	12	z	z	NOUN
cana-860	70	13	dominates	dominate	VERB
cana-860	70	14	y.	y.	PROPN
cana-860	70	15	hence	hence	ADV
cana-860	70	16	t	t	PROPN
cana-860	70	17	(	(	PUNCT
cana-860	70	18	gtsd	gtsd	NOUN
cana-860	70	19	xy	xy	PRON
cana-860	70	20	)	)	PUNCT
cana-860	71	1	=	=	VERB
cana-860	71	2	t	t	NOUN
cana-860	71	3	(	(	PUNCT
cana-860	71	4	g	g	NOUN
cana-860	71	5	)	)	PUNCT
cana-860	71	6	.	.	PUNCT
cana-860	72	1	similarly	similarly	ADV
cana-860	72	2	t	t	PROPN
cana-860	72	3	(	(	PUNCT
cana-860	72	4	gtsd	gtsd	PROPN
cana-860	72	5	zy	zy	PROPN
cana-860	72	6	)	)	PUNCT
cana-860	72	7	=	=	VERB
cana-860	73	1	t	t	NOUN
cana-860	73	2	(	(	PUNCT
cana-860	73	3	g	g	NOUN
cana-860	73	4	)	)	PUNCT
cana-860	73	5	.	.	PUNCT
cana-860	74	1	by	by	ADP
cana-860	74	2	the	the	DET
cana-860	74	3	above	above	ADJ
cana-860	74	4	claim	claim	NOUN
cana-860	74	5	,	,	PUNCT
cana-860	74	6	t	t	PROPN
cana-860	74	7	(	(	PUNCT
cana-860	74	8	gtsd	gtsd	NOUN
cana-860	74	9	xy	xy	PRON
cana-860	74	10	)	)	PUNCT
cana-860	74	11	=	=	VERB
cana-860	74	12	t	t	NOUN
cana-860	74	13	(	(	PUNCT
cana-860	74	14	g	g	NOUN
cana-860	74	15	)	)	PUNCT
cana-860	74	16	.	.	PUNCT
cana-860	75	1	communications	communication	NOUN
cana-860	75	2	on	on	ADP
cana-860	75	3	applied	apply	VERB
cana-860	75	4	nonlinear	nonlinear	ADJ
cana-860	75	5	analysis	analysis	NOUN
cana-860	75	6	issn	issn	NOUN
cana-860	75	7	:	:	PUNCT
cana-860	75	8	1074	1074	NUM
cana-860	75	9	-	-	PUNCT
cana-860	75	10	133x	133x	NUM
cana-860	75	11	vol	vol	NOUN
cana-860	75	12	31	31	NUM
cana-860	75	13	no	no	NOUN
cana-860	75	14	.	.	PUNCT
cana-860	76	1	4s	4s	NUM
cana-860	76	2	(	(	PUNCT
cana-860	76	3	2024	2024	NUM
cana-860	76	4	)	)	PUNCT
cana-860	76	5	374	374	NUM
cana-860	76	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-860	76	7	case	case	NOUN
cana-860	76	8	3	3	NUM
cana-860	76	9	x	x	PUNCT
cana-860	76	10	in	in	ADP
cana-860	76	11	d	d	PROPN
cana-860	76	12	,	,	PUNCT
cana-860	76	13	y	y	PROPN
cana-860	76	14	not	not	PART
cana-860	76	15	in	in	ADP
cana-860	76	16	d	d	NOUN
cana-860	76	17	similarly	similarly	ADV
cana-860	76	18	if	if	SCONJ
cana-860	76	19	x	x	PRON
cana-860	76	20	in	in	ADP
cana-860	76	21	d	d	PROPN
cana-860	76	22	and	and	CCONJ
cana-860	76	23	y	y	PROPN
cana-860	76	24	not	not	PART
cana-860	76	25	in	in	ADP
cana-860	76	26	d	d	PROPN
cana-860	76	27	,	,	PUNCT
cana-860	76	28	we	we	PRON
cana-860	76	29	get	get	VERB
cana-860	76	30	t	t	NOUN
cana-860	76	31	(	(	PUNCT
cana-860	76	32	gtsd	gtsd	NOUN
cana-860	76	33	xy	xy	PRON
cana-860	76	34	)	)	PUNCT
cana-860	76	35	=	=	VERB
cana-860	77	1	t	t	NOUN
cana-860	77	2	(	(	PUNCT
cana-860	77	3	g	g	NOUN
cana-860	77	4	)	)	PUNCT
cana-860	77	5	.	.	PUNCT
cana-860	78	1	this	this	PRON
cana-860	78	2	is	be	AUX
cana-860	78	3	true	true	ADJ
cana-860	78	4			NOUN
cana-860	78	5	e	e	NOUN
cana-860	78	6	=	=	PUNCT
cana-860	78	7	xy	xy	PROPN
cana-860	79	1			NOUN
cana-860	79	2	e	e	X
cana-860	79	3	(	(	PUNCT
cana-860	79	4	g	g	NOUN
cana-860	79	5	)	)	PUNCT
cana-860	79	6	.	.	PUNCT
cana-860	80	1	therefore	therefore	ADV
cana-860	80	2	,	,	PUNCT
cana-860	80	3	g	g	PROPN
cana-860	80	4	is	be	AUX
cana-860	80	5	tdss	tdss	NOUN
cana-860	80	6	.	.	PUNCT
cana-860	81	1			PUNCT
cana-860	81	2	converse	converse	NOUN
cana-860	81	3	need	need	AUX
cana-860	81	4	not	not	PART
cana-860	81	5	be	be	AUX
cana-860	81	6	true	true	ADJ
cana-860	81	7	.	.	PUNCT
cana-860	82	1	example	example	NOUN
cana-860	82	2	fig	fig	NOUN
cana-860	82	3	.	.	PUNCT
cana-860	83	1	2	2	NUM
cana-860	83	2	tdss	tdss	NOUN
cana-860	83	3	graph	graph	NOUN
cana-860	83	4	in	in	ADP
cana-860	83	5	fig.2	fig.2	PROPN
cana-860	83	6	,	,	PUNCT
cana-860	83	7	g	g	PROPN
cana-860	83	8	is	be	AUX
cana-860	83	9	tdss	tdss	NOUN
cana-860	83	10	but	but	CCONJ
cana-860	83	11	x	x	X
cana-860	83	12	is	be	AUX
cana-860	83	13	not	not	PART
cana-860	83	14	a	a	DET
cana-860	83	15	2	2	NUM
cana-860	83	16	–	–	PUNCT
cana-860	83	17	dominated	dominate	VERB
cana-860	83	18	vertex	vertex	NOUN
cana-860	83	19	.	.	PUNCT
cana-860	84	1	corollary	corollary	ADJ
cana-860	84	2	if	if	SCONJ
cana-860	84	3	g	g	PROPN
cana-860	84	4	is	be	AUX
cana-860	84	5	a	a	DET
cana-860	84	6	graph	graph	NOUN
cana-860	84	7	with	with	ADP
cana-860	84	8	x	x	PROPN
cana-860	84	9	,	,	PUNCT
cana-860	84	10	y	y	PROPN
cana-860	84	11			PROPN
cana-860	84	12	v	v	PROPN
cana-860	84	13	(	(	PUNCT
cana-860	84	14	g	g	NOUN
cana-860	84	15	)	)	PUNCT
cana-860	84	16	,	,	PUNCT
cana-860	84	17			PRON
cana-860	84	18	a	a	DET
cana-860	84	19	t	t	NOUN
cana-860	84	20	–	–	PUNCT
cana-860	84	21	set	set	NOUN
cana-860	84	22	d	d	NOUN
cana-860	84	23	where	where	SCONJ
cana-860	84	24	x	x	PRON
cana-860	84	25	is	be	AUX
cana-860	84	26	adjacent	adjacent	ADJ
cana-860	84	27	to	to	ADP
cana-860	84	28	y	y	PROPN
cana-860	84	29	,	,	PUNCT
cana-860	84	30	x	x	SYM
cana-860	84	31			NOUN
cana-860	84	32	d	d	NOUN
cana-860	84	33	and	and	CCONJ
cana-860	84	34	y	y	PROPN
cana-860	84	35	is	be	AUX
cana-860	84	36	2	2	NUM
cana-860	84	37	–	–	PUNCT
cana-860	84	38	dominated	dominate	VERB
cana-860	84	39	then	then	ADV
cana-860	84	40	g	g	PROPN
cana-860	84	41	is	be	AUX
cana-860	84	42	tdss	tdss	NOUN
cana-860	84	43	.	.	PUNCT
cana-860	85	1	proof	proof	NOUN
cana-860	85	2	let	let	VERB
cana-860	85	3	x	x	PRON
cana-860	85	4	,	,	PUNCT
cana-860	85	5	y	y	PROPN
cana-860	85	6			PROPN
cana-860	85	7	v	v	PROPN
cana-860	85	8	(	(	PUNCT
cana-860	85	9	g	g	NOUN
cana-860	85	10	)	)	PUNCT
cana-860	85	11	and	and	CCONJ
cana-860	85	12	t	t	NOUN
cana-860	85	13	–	–	PUNCT
cana-860	85	14	set	set	VERB
cana-860	85	15	for	for	ADP
cana-860	85	16	g	g	PROPN
cana-860	85	17	be	be	AUX
cana-860	85	18	d	d	PRON
cana-860	85	19	such	such	ADJ
cana-860	85	20	that	that	SCONJ
cana-860	85	21	x	x	PRON
cana-860	85	22			NOUN
cana-860	85	23	d	d	NOUN
cana-860	85	24	and	and	CCONJ
cana-860	85	25	y	y	PROPN
cana-860	85	26	is	be	AUX
cana-860	85	27	2	2	NUM
cana-860	85	28	–	–	PUNCT
cana-860	85	29	dominated	dominate	VERB
cana-860	85	30	.	.	PUNCT
cana-860	86	1	let	let	AUX
cana-860	86	2	gtsd	gtsd	VERB
cana-860	86	3	xy	xy	PROPN
cana-860	87	1	=	=	PUNCT
cana-860	87	2	z.	z.	PROPN
cana-860	87	3	by	by	ADP
cana-860	87	4	theorem	theorem	NOUN
cana-860	87	5	2.3	2.3	NUM
cana-860	87	6	,	,	PUNCT
cana-860	87	7	we	we	PRON
cana-860	87	8	have	have	VERB
cana-860	87	9	d	d	NOUN
cana-860	87	10	is	be	AUX
cana-860	87	11	a	a	DET
cana-860	87	12	t	t	NOUN
cana-860	87	13	–	–	PUNCT
cana-860	87	14	set	set	VERB
cana-860	87	15	for	for	ADP
cana-860	87	16	gtsd	gtsd	NOUN
cana-860	87	17	xy	xy	PROPN
cana-860	87	18	.	.	PUNCT
cana-860	88	1	it	it	PRON
cana-860	88	2	is	be	AUX
cana-860	88	3	true	true	ADJ
cana-860	88	4	for	for	ADP
cana-860	88	5	remaining	remain	VERB
cana-860	88	6	x	x	NOUN
cana-860	88	7	,	,	PUNCT
cana-860	88	8	y	y	PROPN
cana-860	88	9			PROPN
cana-860	88	10	v	v	PROPN
cana-860	88	11	(	(	PUNCT
cana-860	88	12	g	g	NOUN
cana-860	88	13	)	)	PUNCT
cana-860	88	14	.	.	PUNCT
cana-860	89	1	therefore	therefore	ADV
cana-860	89	2	,	,	PUNCT
cana-860	89	3	g	g	PROPN
cana-860	89	4	is	be	AUX
cana-860	89	5	tdss	tdss	NOUN
cana-860	89	6	.	.	PUNCT
cana-860	90	1			PUNCT
cana-860	90	2	example	example	NOUN
cana-860	90	3	fig	fig	NOUN
cana-860	90	4	.	.	PUNCT
cana-860	91	1	3	3	NUM
cana-860	91	2	graph	graph	NOUN
cana-860	91	3	g	g	NOUN
cana-860	91	4	in	in	ADP
cana-860	91	5	fig	fig	NOUN
cana-860	91	6	.	.	PUNCT
cana-860	92	1	3	3	NUM
cana-860	92	2	,	,	PUNCT
cana-860	92	3	the	the	DET
cana-860	92	4	vertices	vertex	NOUN
cana-860	92	5	x	x	PUNCT
cana-860	92	6	and	and	CCONJ
cana-860	92	7	y	y	PROPN
cana-860	92	8	are	be	AUX
cana-860	92	9	such	such	ADJ
cana-860	92	10	that	that	SCONJ
cana-860	92	11	x	x	SYM
cana-860	92	12			PROPN
cana-860	92	13	t	t	NOUN
cana-860	92	14	(	(	PUNCT
cana-860	92	15	g	g	NOUN
cana-860	92	16	)	)	PUNCT
cana-860	92	17	and	and	CCONJ
cana-860	92	18	y	y	PROPN
cana-860	92	19	is	be	AUX
cana-860	92	20	2	2	NUM
cana-860	92	21	–	–	PUNCT
cana-860	92	22	dominated	dominate	VERB
cana-860	92	23	for	for	ADP
cana-860	92	24	the	the	DET
cana-860	92	25	t	t	NOUN
cana-860	92	26	–	–	PUNCT
cana-860	92	27	set	set	NOUN
cana-860	92	28	of	of	ADP
cana-860	92	29	g.	g.	PROPN
cana-860	92	30	therefore	therefore	ADV
cana-860	92	31	g	g	PROPN
cana-860	92	32	is	be	AUX
cana-860	92	33	tdss	tdss	NOUN
cana-860	92	34	.	.	PUNCT
cana-860	93	1	remark	remark	VERB
cana-860	93	2	if	if	SCONJ
cana-860	93	3	every	every	DET
cana-860	93	4	vertex	vertex	NOUN
cana-860	93	5	is	be	AUX
cana-860	93	6	2	2	NUM
cana-860	93	7	–	–	PUNCT
cana-860	93	8	dominated	dominate	VERB
cana-860	93	9	in	in	ADP
cana-860	93	10	v	v	NUM
cana-860	93	11	–	–	PUNCT
cana-860	93	12	d	d	NOUN
cana-860	93	13	,	,	PUNCT
cana-860	93	14	then	then	ADV
cana-860	93	15	it	it	PRON
cana-860	93	16	follows	follow	VERB
cana-860	93	17	the	the	DET
cana-860	93	18	above	above	ADJ
cana-860	93	19	corollary	corollary	NOUN
cana-860	93	20	.	.	PUNCT
cana-860	94	1	theorem	theorem	VERB
cana-860	94	2	2.4	2.4	NUM
cana-860	94	3	for	for	ADP
cana-860	94	4	every	every	DET
cana-860	94	5	vertex	vertex	NOUN
cana-860	94	6	is	be	AUX
cana-860	94	7	2	2	NUM
cana-860	94	8	–	–	PUNCT
cana-860	94	9	dominated	dominate	VERB
cana-860	94	10	in	in	ADP
cana-860	94	11	v	v	NUM
cana-860	94	12	–	–	PUNCT
cana-860	94	13	d	d	NOUN
cana-860	94	14			NOUN
cana-860	94	15	t	t	NOUN
cana-860	94	16	–	–	PUNCT
cana-860	94	17	set	set	NOUN
cana-860	94	18	of	of	ADP
cana-860	94	19	g	g	PROPN
cana-860	94	20	then	then	ADV
cana-860	94	21	,	,	PUNCT
cana-860	94	22	communications	communication	NOUN
cana-860	94	23	on	on	ADP
cana-860	94	24	applied	apply	VERB
cana-860	94	25	nonlinear	nonlinear	ADJ
cana-860	94	26	analysis	analysis	NOUN
cana-860	94	27	issn	issn	NOUN
cana-860	94	28	:	:	PUNCT
cana-860	94	29	1074	1074	NUM
cana-860	94	30	-	-	PUNCT
cana-860	94	31	133x	133x	NUM
cana-860	94	32	vol	vol	NOUN
cana-860	94	33	31	31	NUM
cana-860	94	34	no	no	NOUN
cana-860	94	35	.	.	PUNCT
cana-860	95	1	4s	4s	NUM
cana-860	95	2	(	(	PUNCT
cana-860	95	3	2024	2024	NUM
cana-860	95	4	)	)	PUNCT
cana-860	95	5	375	375	NUM
cana-860	95	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-860	95	7	(	(	PUNCT
cana-860	95	8	1	1	X
cana-860	95	9	)	)	PUNCT
cana-860	95	10	g	g	NOUN
cana-860	95	11	does	do	AUX
cana-860	95	12	not	not	PART
cana-860	95	13	have	have	VERB
cana-860	95	14	any	any	DET
cana-860	95	15	pendant	pendant	ADJ
cana-860	95	16	vertex	vertex	NOUN
cana-860	95	17	.	.	PUNCT
cana-860	96	1	(	(	PUNCT
cana-860	96	2	2	2	X
cana-860	96	3	)	)	PUNCT
cana-860	96	4	if	if	SCONJ
cana-860	96	5	for	for	ADP
cana-860	96	6	x	x	X
cana-860	96	7	,	,	PUNCT
cana-860	96	8	z	z	PROPN
cana-860	96	9			PROPN
cana-860	96	10	t	t	NOUN
cana-860	96	11	(	(	PUNCT
cana-860	96	12	g	g	NOUN
cana-860	96	13	)	)	PUNCT
cana-860	96	14	,	,	PUNCT
cana-860	96	15	x	x	X
cana-860	96	16	is	be	AUX
cana-860	96	17	a	a	DET
cana-860	96	18	down	down	ADJ
cana-860	96	19	vertex	vertex	NOUN
cana-860	96	20	and	and	CCONJ
cana-860	96	21	x	x	NOUN
cana-860	96	22	adjacent	adjacent	ADJ
cana-860	96	23	to	to	ADP
cana-860	96	24	z.	z.	PROPN
cana-860	96	25	then	then	ADV
cana-860	96	26			VERB
cana-860	96	27	one	one	NUM
cana-860	96	28	s	s	NOUN
cana-860	96	29	which	which	PRON
cana-860	96	30	is	be	AUX
cana-860	96	31	not	not	PART
cana-860	96	32	adjacent	adjacent	ADJ
cana-860	96	33	to	to	ADP
cana-860	96	34	x	x	PROPN
cana-860	97	1	but	but	CCONJ
cana-860	97	2	s	s	NOUN
cana-860	97	3	is	be	AUX
cana-860	97	4	adjacent	adjacent	ADJ
cana-860	97	5	to	to	ADP
cana-860	97	6	z.	z.	PROPN
cana-860	97	7	proof	proof	NOUN
cana-860	97	8	let	let	VERB
cana-860	97	9	g	g	NOUN
cana-860	97	10	be	be	AUX
cana-860	97	11	a	a	DET
cana-860	97	12	given	give	VERB
cana-860	97	13	graph	graph	NOUN
cana-860	97	14	in	in	ADP
cana-860	97	15	which	which	PRON
cana-860	97	16	all	all	DET
cana-860	97	17	vertices	vertice	VERB
cana-860	97	18	in	in	ADP
cana-860	97	19	v	v	NOUN
cana-860	97	20	–	–	PUNCT
cana-860	97	21	d	d	NOUN
cana-860	97	22	is	be	AUX
cana-860	97	23	2	2	NUM
cana-860	97	24	–	–	PUNCT
cana-860	97	25	dominated	dominate	VERB
cana-860	97	26	for	for	ADP
cana-860	97	27	all	all	DET
cana-860	97	28	the	the	DET
cana-860	97	29	t	t	NOUN
cana-860	97	30	–	–	PUNCT
cana-860	97	31	set	set	NOUN
cana-860	97	32	of	of	ADP
cana-860	97	33	g.	g.	PROPN
cana-860	97	34	(	(	PUNCT
cana-860	97	35	1	1	X
cana-860	97	36	)	)	PUNCT
cana-860	97	37	assume	assume	VERB
cana-860	97	38	that	that	SCONJ
cana-860	97	39	y	y	PROPN
cana-860	97	40	is	be	AUX
cana-860	97	41	a	a	DET
cana-860	97	42	pendant	pendant	ADJ
cana-860	97	43	vertex	vertex	NOUN
cana-860	97	44	of	of	ADP
cana-860	97	45	g.	g.	PROPN
cana-860	97	46	since	since	SCONJ
cana-860	97	47	all	all	DET
cana-860	97	48	the	the	DET
cana-860	97	49	vertices	vertex	NOUN
cana-860	97	50	in	in	ADP
cana-860	97	51	v	v	NOUN
cana-860	97	52	–	–	PUNCT
cana-860	97	53	d	d	NOUN
cana-860	97	54	is	be	AUX
cana-860	97	55	2	2	NUM
cana-860	97	56	–	–	PUNCT
cana-860	97	57	dominated	dominate	VERB
cana-860	97	58	,	,	PUNCT
cana-860	97	59	this	this	PRON
cana-860	97	60	implies	imply	VERB
cana-860	97	61	that	that	SCONJ
cana-860	97	62	every	every	DET
cana-860	97	63	pendant	pendant	ADJ
cana-860	97	64	vertex	vertex	NOUN
cana-860	97	65	must	must	AUX
cana-860	97	66	be	be	AUX
cana-860	97	67	included	include	VERB
cana-860	97	68	in	in	ADP
cana-860	97	69	every	every	DET
cana-860	97	70	t	t	NOUN
cana-860	97	71	–	–	PUNCT
cana-860	97	72	set	set	NOUN
cana-860	97	73	of	of	ADP
cana-860	97	74	g.	g.	PROPN
cana-860	97	75	consider	consider	VERB
cana-860	97	76	x	x	PRON
cana-860	97	77	be	be	AUX
cana-860	97	78	a	a	DET
cana-860	97	79	support	support	NOUN
cana-860	97	80	vertex	vertex	NOUN
cana-860	97	81	of	of	ADP
cana-860	97	82	y	y	PRON
cana-860	97	83	where	where	SCONJ
cana-860	97	84	x	x	PRON
cana-860	97	85	is	be	AUX
cana-860	97	86	neighbor	neighbor	NOUN
cana-860	97	87	of	of	ADP
cana-860	97	88	y.	y.	PROPN
cana-860	97	89	therefore	therefore	ADV
cana-860	97	90	,	,	PUNCT
cana-860	97	91			PROPN
cana-860	97	92	atleast	atleast	ADJ
cana-860	97	93	one	one	NUM
cana-860	97	94	z	z	NOUN
cana-860	97	95	such	such	ADJ
cana-860	97	96	that	that	SCONJ
cana-860	97	97	z	z	PROPN
cana-860	97	98	≠	≠	PROPN
cana-860	97	99	y	y	PROPN
cana-860	97	100	,	,	PUNCT
cana-860	97	101	z	z	NOUN
cana-860	97	102			NOUN
cana-860	97	103	d	d	NOUN
cana-860	97	104	,	,	PUNCT
cana-860	97	105	z	z	NOUN
cana-860	97	106			PROPN
cana-860	97	107	n	n	PROPN
cana-860	97	108	(	(	PUNCT
cana-860	97	109	x	x	NOUN
cana-860	97	110	)	)	PUNCT
cana-860	97	111	.	.	PUNCT
cana-860	98	1	then	then	ADV
cana-860	98	2	,	,	PUNCT
cana-860	98	3	we	we	PRON
cana-860	98	4	have	have	VERB
cana-860	98	5	a	a	DET
cana-860	98	6	t	t	NOUN
cana-860	98	7	–	–	PUNCT
cana-860	98	8	set	set	VERB
cana-860	98	9	d1	d1	NOUN
cana-860	98	10	=	=	PUNCT
cana-860	99	1	d	d	PROPN
cana-860	99	2	–	–	PUNCT
cana-860	99	3	{	{	PUNCT
cana-860	99	4	y	y	NOUN
cana-860	99	5	}	}	PUNCT
cana-860	99	6			NOUN
cana-860	99	7	{	{	PUNCT
cana-860	99	8	z	z	NOUN
cana-860	99	9	}	}	PUNCT
cana-860	99	10	such	such	ADJ
cana-860	99	11	that	that	SCONJ
cana-860	99	12	y	y	PROPN
cana-860	99	13	is	be	AUX
cana-860	99	14	single	single	ADJ
cana-860	99	15	dominated	dominate	VERB
cana-860	99	16	,	,	PUNCT
cana-860	99	17	we	we	PRON
cana-860	99	18	get	get	VERB
cana-860	99	19	a	a	DET
cana-860	99	20	contradiction	contradiction	NOUN
cana-860	99	21	.	.	PUNCT
cana-860	100	1	hence	hence	ADV
cana-860	100	2	,	,	PUNCT
cana-860	100	3	d	d	PROPN
cana-860	100	4	does	do	AUX
cana-860	100	5	not	not	PART
cana-860	100	6	have	have	VERB
cana-860	100	7	any	any	DET
cana-860	100	8	pendant	pendant	ADJ
cana-860	100	9	vertex	vertex	NOUN
cana-860	100	10	,	,	PUNCT
cana-860	100	11	ie	ie	X
cana-860	100	12	.	.	PROPN
cana-860	100	13	,	,	PUNCT
cana-860	100	14			NOUN
cana-860	100	15	x	x	SYM
cana-860	100	16			NOUN
cana-860	100	17	v	v	X
cana-860	100	18	(	(	PUNCT
cana-860	100	19	g	g	NOUN
cana-860	100	20	)	)	PUNCT
cana-860	100	21	,	,	PUNCT
cana-860	100	22	n	n	PROPN
cana-860	100	23	(	(	PUNCT
cana-860	100	24	x	x	X
cana-860	100	25	)	)	PUNCT
cana-860	100	26	≥	≥	NOUN
cana-860	100	27	2	2	NUM
cana-860	100	28	.	.	PUNCT
cana-860	101	1	(	(	PUNCT
cana-860	101	2	2	2	NUM
cana-860	101	3	)	)	PUNCT
cana-860	101	4	for	for	ADP
cana-860	101	5	each	each	PRON
cana-860	101	6	and	and	CCONJ
cana-860	101	7	every	every	PRON
cana-860	101	8	x	x	ADJ
cana-860	101	9			PROPN
cana-860	101	10	t	t	NOUN
cana-860	101	11	(	(	PUNCT
cana-860	101	12	g	g	NOUN
cana-860	101	13	)	)	PUNCT
cana-860	101	14	,	,	PUNCT
cana-860	101	15	pn	pn	X
cana-860	102	1	[	[	X
cana-860	102	2	x	x	X
cana-860	102	3	,	,	PUNCT
cana-860	102	4	d	d	X
cana-860	102	5	]	]	X
cana-860	102	6	=	=	X
cana-860	102	7	.	.	NOUN
cana-860	102	8	let	let	VERB
cana-860	102	9	us	we	PRON
cana-860	102	10	consider	consider	VERB
cana-860	102	11	x	x	PRON
cana-860	102	12	,	,	PUNCT
cana-860	102	13	z	z	NOUN
cana-860	102	14	such	such	ADJ
cana-860	102	15	that	that	PRON
cana-860	102	16	x	x	PRON
cana-860	102	17	is	be	AUX
cana-860	102	18	adjacent	adjacent	ADJ
cana-860	102	19	to	to	ADP
cana-860	102	20	z	z	PROPN
cana-860	102	21	that	that	PRON
cana-860	102	22	belongs	belong	VERB
cana-860	102	23	to	to	ADP
cana-860	102	24	t	t	NOUN
cana-860	102	25	(	(	PUNCT
cana-860	102	26	g	g	NOUN
cana-860	102	27	)	)	PUNCT
cana-860	102	28	.	.	PUNCT
cana-860	103	1	consider	consider	VERB
cana-860	103	2	the	the	DET
cana-860	103	3	graph	graph	NOUN
cana-860	103	4	g	g	PROPN
cana-860	103	5	–	–	PUNCT
cana-860	103	6	x	x	X
cana-860	103	7	,	,	PUNCT
cana-860	103	8	we	we	PRON
cana-860	103	9	have	have	VERB
cana-860	103	10	the	the	DET
cana-860	103	11	t	t	NOUN
cana-860	103	12	–	–	PUNCT
cana-860	103	13	set	set	VERB
cana-860	103	14	for	for	ADP
cana-860	103	15	g	g	NOUN
cana-860	103	16	–	–	PUNCT
cana-860	103	17	x	x	PUNCT
cana-860	103	18	is	be	AUX
cana-860	103	19	t	t	VERB
cana-860	103	20	(	(	PUNCT
cana-860	103	21	g	g	NOUN
cana-860	103	22	)	)	PUNCT
cana-860	103	23	–	–	PUNCT
cana-860	103	24	{	{	PUNCT
cana-860	103	25	z	z	NOUN
cana-860	103	26	}	}	PUNCT
cana-860	103	27	–	–	PUNCT
cana-860	103	28	{	{	PUNCT
cana-860	103	29	x	x	NOUN
cana-860	103	30	}	}	PUNCT
cana-860	103	31			NOUN
cana-860	103	32	{	{	PUNCT
cana-860	103	33	s	s	NOUN
cana-860	103	34	}	}	PUNCT
cana-860	103	35	where	where	SCONJ
cana-860	103	36	s	s	VERB
cana-860	103	37			PROPN
cana-860	103	38	n	n	CCONJ
cana-860	103	39	(	(	PUNCT
cana-860	103	40	z	z	NOUN
cana-860	103	41	)	)	PUNCT
cana-860	103	42	.	.	PUNCT
cana-860	104	1	therefore	therefore	ADV
cana-860	104	2	,	,	PUNCT
cana-860	104	3	we	we	PRON
cana-860	104	4	get	get	AUX
cana-860	104	5	t	t	NOUN
cana-860	104	6	(	(	PUNCT
cana-860	104	7	g	g	NOUN
cana-860	104	8	–	–	PUNCT
cana-860	104	9	x	x	NOUN
cana-860	104	10	)	)	PUNCT
cana-860	104	11	=	=	SYM
cana-860	105	1	t	t	NOUN
cana-860	105	2	(	(	PUNCT
cana-860	105	3	g	g	NOUN
cana-860	105	4	)	)	PUNCT
cana-860	105	5	–	–	PUNCT
cana-860	105	6	1	1	X
cana-860	105	7	.	.	X
cana-860	106	1	thus	thus	ADV
cana-860	106	2	x	x	PRON
cana-860	106	3	is	be	AUX
cana-860	106	4	a	a	DET
cana-860	106	5	down	down	ADJ
cana-860	106	6	vertex	vertex	NOUN
cana-860	106	7	if	if	SCONJ
cana-860	106	8	x	x	SYM
cana-860	106	9			PROPN
cana-860	106	10	t	t	NOUN
cana-860	106	11	(	(	PUNCT
cana-860	106	12	g	g	NOUN
cana-860	106	13	)	)	PUNCT
cana-860	106	14	.	.	PUNCT
cana-860	107	1			PUNCT
cana-860	107	2	remark	remark	NOUN
cana-860	107	3	1	1	NUM
cana-860	107	4	.	.	PUNCT
cana-860	107	5	by	by	ADP
cana-860	107	6	theorem	theorem	ADJ
cana-860	107	7	2.3	2.3	NUM
cana-860	107	8	and	and	CCONJ
cana-860	107	9	2.4	2.4	NUM
cana-860	107	10	we	we	PRON
cana-860	107	11	see	see	VERB
cana-860	107	12	that	that	SCONJ
cana-860	107	13	if	if	SCONJ
cana-860	107	14	g	g	PROPN
cana-860	107	15	is	be	AUX
cana-860	107	16	a	a	DET
cana-860	107	17	tdss	tdss	NOUN
cana-860	107	18	graph	graph	NOUN
cana-860	107	19	such	such	ADJ
cana-860	107	20	that	that	SCONJ
cana-860	107	21	every	every	DET
cana-860	107	22	t	t	NOUN
cana-860	107	23	–	–	PUNCT
cana-860	107	24	set	set	NOUN
cana-860	107	25	of	of	ADP
cana-860	107	26	g	g	PROPN
cana-860	107	27	is	be	AUX
cana-860	107	28	2	2	NUM
cana-860	107	29	–	–	PUNCT
cana-860	107	30	dominating	dominating	NOUN
cana-860	107	31	,	,	PUNCT
cana-860	107	32	then	then	ADV
cana-860	107	33	every	every	DET
cana-860	107	34	t	t	NOUN
cana-860	107	35	–	–	PUNCT
cana-860	107	36	set	set	NOUN
cana-860	107	37	of	of	ADP
cana-860	107	38	g	g	PROPN
cana-860	107	39	includes	include	VERB
cana-860	107	40	all	all	PRON
cana-860	107	41	pendant	pendant	ADJ
cana-860	107	42	and	and	CCONJ
cana-860	107	43	support	support	NOUN
cana-860	107	44	vertices	vertex	NOUN
cana-860	107	45	.	.	PUNCT
cana-860	108	1	2	2	X
cana-860	108	2	.	.	X
cana-860	108	3	if	if	SCONJ
cana-860	108	4	x	x	PRON
cana-860	108	5	is	be	AUX
cana-860	108	6	a	a	DET
cana-860	108	7	t	t	NOUN
cana-860	108	8	–	–	PUNCT
cana-860	108	9	dominated	dominate	VERB
cana-860	108	10	vertex	vertex	NOUN
cana-860	108	11	say	say	VERB
cana-860	108	12	y	y	PROPN
cana-860	108	13	adjacent	adjacent	ADJ
cana-860	108	14	to	to	ADP
cana-860	108	15	y1	y1	PROPN
cana-860	108	16	,	,	PUNCT
cana-860	108	17	y2	y2	PROPN
cana-860	108	18	,	,	PUNCT
cana-860	108	19	…	…	PUNCT
cana-860	108	20	,	,	PUNCT
cana-860	108	21	yt	yt	VERB
cana-860	108	22	where	where	SCONJ
cana-860	108	23	y1	y1	NOUN
cana-860	108	24	,	,	PUNCT
cana-860	108	25	y2	y2	PROPN
cana-860	108	26	,	,	PUNCT
cana-860	108	27	…	…	PUNCT
cana-860	108	28	,	,	PUNCT
cana-860	108	29	yt	yt	PROPN
cana-860	108	30			PROPN
cana-860	108	31	t	t	PROPN
cana-860	108	32	(	(	PUNCT
cana-860	108	33	g),t	g),t	X
cana-860	108	34	(	(	PUNCT
cana-860	108	35	gtsd	gtsd	PROPN
cana-860	108	36	xy1	xy1	PROPN
cana-860	108	37	)	)	PUNCT
cana-860	109	1	=	=	SYM
cana-860	109	2	t	t	NOUN
cana-860	109	3	(	(	PUNCT
cana-860	109	4	gtsd	gtsd	PROPN
cana-860	109	5	xy2	xy2	PROPN
cana-860	109	6	)	)	PUNCT
cana-860	109	7	=	=	PUNCT
cana-860	109	8	.	.	PUNCT
cana-860	109	9	.	.	PUNCT
cana-860	109	10	.	.	PUNCT
cana-860	109	11	.	.	PUNCT
cana-860	110	1	=	=	PRON
cana-860	110	2	t	t	PROPN
cana-860	110	3	(	(	PUNCT
cana-860	110	4	gtsd	gtsd	PROPN
cana-860	110	5	xyk	xyk	PROPN
cana-860	110	6	)	)	PUNCT
cana-860	111	1	=	=	PRON
cana-860	111	2	t	t	NOUN
cana-860	111	3	(	(	PUNCT
cana-860	111	4	g	g	NOUN
cana-860	111	5	)	)	PUNCT
cana-860	111	6	ie	ie	PROPN
cana-860	111	7	.	.	PROPN
cana-860	111	8	,	,	PUNCT
cana-860	111	9	a	a	DET
cana-860	111	10	t	t	NOUN
cana-860	111	11	–	–	PUNCT
cana-860	111	12	dominated	dominate	VERB
cana-860	111	13	graph	graph	NOUN
cana-860	111	14	is	be	AUX
cana-860	111	15	tdss	tdss	NOUN
cana-860	111	16	.	.	PUNCT
cana-860	112	1	theorem	theorem	VERB
cana-860	112	2	2.5	2.5	NUM
cana-860	112	3	if	if	SCONJ
cana-860	112	4	either	either	CCONJ
cana-860	112	5	x	x	SYM
cana-860	112	6	or	or	CCONJ
cana-860	112	7	y	y	PROPN
cana-860	112	8	is	be	AUX
cana-860	112	9	selfish	selfish	ADJ
cana-860	112	10	and	and	CCONJ
cana-860	112	11	t	t	NOUN
cana-860	112	12	(	(	PUNCT
cana-860	112	13	g	g	NOUN
cana-860	112	14	)	)	PUNCT
cana-860	112	15	=	=	SYM
cana-860	113	1	2	2	NUM
cana-860	113	2	such	such	ADJ
cana-860	113	3	that	that	SCONJ
cana-860	113	4	x	x	NOUN
cana-860	113	5	,	,	PUNCT
cana-860	113	6	y	y	PROPN
cana-860	113	7			PROPN
cana-860	113	8	t	t	NOUN
cana-860	113	9	(	(	PUNCT
cana-860	113	10	g	g	NOUN
cana-860	113	11	)	)	PUNCT
cana-860	113	12	then	then	ADV
cana-860	113	13	g	g	PROPN
cana-860	113	14	is	be	AUX
cana-860	113	15	tdss	tdss	NOUN
cana-860	113	16	.	.	PUNCT
cana-860	114	1	proof	proof	NOUN
cana-860	114	2	let	let	VERB
cana-860	114	3	x	x	PRON
cana-860	114	4	,	,	PUNCT
cana-860	114	5	y	y	PROPN
cana-860	114	6			PROPN
cana-860	114	7	t	t	NOUN
cana-860	114	8	(	(	PUNCT
cana-860	114	9	g	g	NOUN
cana-860	114	10	)	)	PUNCT
cana-860	114	11	,	,	PUNCT
cana-860	114	12	the	the	DET
cana-860	114	13	vertex	vertex	NOUN
cana-860	114	14	y	y	PROPN
cana-860	114	15	is	be	AUX
cana-860	114	16	selfish	selfish	ADJ
cana-860	114	17	.	.	PUNCT
cana-860	115	1	let	let	AUX
cana-860	115	2	gtsd	gtsd	PROPN
cana-860	115	3	xs	xs	PROPN
cana-860	115	4	=	=	SYM
cana-860	115	5	t	t	PROPN
cana-860	115	6	for	for	ADP
cana-860	115	7	some	some	PRON
cana-860	115	8	s	s	PART
cana-860	115	9			NOUN
cana-860	115	10	v	v	NOUN
cana-860	115	11	(	(	PUNCT
cana-860	115	12	g	g	NOUN
cana-860	115	13	)	)	PUNCT
cana-860	115	14	.	.	PUNCT
cana-860	116	1	then	then	ADV
cana-860	116	2	we	we	PRON
cana-860	116	3	have	have	VERB
cana-860	116	4	a	a	DET
cana-860	116	5	t	t	NOUN
cana-860	116	6	–	–	PUNCT
cana-860	116	7	set	set	VERB
cana-860	116	8	for	for	ADP
cana-860	116	9	gtsd	gtsd	PROPN
cana-860	116	10	xs	xs	PROPN
cana-860	116	11	as	as	ADP
cana-860	116	12	t	t	NOUN
cana-860	116	13	(	(	PUNCT
cana-860	116	14	g	g	NOUN
cana-860	116	15	)	)	PUNCT
cana-860	116	16	–	–	PUNCT
cana-860	116	17	{	{	PUNCT
cana-860	116	18	y	y	NOUN
cana-860	116	19	}	}	PUNCT
cana-860	116	20			NOUN
cana-860	116	21	{	{	PUNCT
cana-860	116	22	t}.therefore	t}.therefore	PROPN
cana-860	116	23	,	,	PUNCT
cana-860	116	24	g	g	PROPN
cana-860	116	25	is	be	AUX
cana-860	116	26	tdss	tdss	NOUN
cana-860	116	27	.	.	PUNCT
cana-860	117	1			PUNCT
cana-860	117	2	converse	converse	NOUN
cana-860	117	3	need	need	AUX
cana-860	117	4	not	not	PART
cana-860	117	5	be	be	AUX
cana-860	117	6	true	true	ADJ
cana-860	117	7	.	.	PUNCT
cana-860	118	1	example	example	NOUN
cana-860	118	2	fig	fig	NOUN
cana-860	118	3	.	.	PUNCT
cana-860	119	1	4	4	NUM
cana-860	119	2	tdss	tdss	NOUN
cana-860	119	3	graph	graph	NOUN
cana-860	119	4	with	with	ADP
cana-860	119	5	neither	neither	CCONJ
cana-860	119	6	x	x	SYM
cana-860	119	7	nor	nor	CCONJ
cana-860	119	8	y	y	PROPN
cana-860	119	9	is	be	AUX
cana-860	119	10	selfish	selfish	ADJ
cana-860	119	11	communications	communication	NOUN
cana-860	119	12	on	on	ADP
cana-860	119	13	applied	apply	VERB
cana-860	119	14	nonlinear	nonlinear	ADJ
cana-860	119	15	analysis	analysis	NOUN
cana-860	119	16	issn	issn	NOUN
cana-860	119	17	:	:	PUNCT
cana-860	119	18	1074	1074	NUM
cana-860	119	19	-	-	PUNCT
cana-860	119	20	133x	133x	NUM
cana-860	119	21	vol	vol	NOUN
cana-860	119	22	31	31	NUM
cana-860	119	23	no	no	NOUN
cana-860	119	24	.	.	PUNCT
cana-860	120	1	4s	4s	NUM
cana-860	120	2	(	(	PUNCT
cana-860	120	3	2024	2024	NUM
cana-860	120	4	)	)	PUNCT
cana-860	120	5	376	376	NUM
cana-860	120	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-860	120	7	in	in	ADP
cana-860	120	8	fig.4	fig.4	PROPN
cana-860	120	9	,	,	PUNCT
cana-860	120	10	neither	neither	CCONJ
cana-860	120	11	x	x	PUNCT
cana-860	120	12	nor	nor	CCONJ
cana-860	120	13	y	y	PROPN
cana-860	120	14	is	be	AUX
cana-860	120	15	selfish	selfish	ADJ
cana-860	120	16	but	but	CCONJ
cana-860	120	17	g	g	NOUN
cana-860	120	18	is	be	AUX
cana-860	120	19	a	a	DET
cana-860	120	20	tdss	tdss	NOUN
cana-860	120	21	graph	graph	NOUN
cana-860	120	22	.	.	PUNCT
cana-860	121	1	theorem	theorem	VERB
cana-860	121	2	2.6	2.6	NUM
cana-860	121	3	let	let	VERB
cana-860	121	4	g	g	NOUN
cana-860	121	5	be	be	AUX
cana-860	121	6	a	a	DET
cana-860	121	7	graph	graph	NOUN
cana-860	121	8	with	with	ADP
cana-860	121	9	x	x	SYM
cana-860	121	10			NOUN
cana-860	121	11	v	v	X
cana-860	121	12	(	(	PUNCT
cana-860	121	13	g	g	NOUN
cana-860	121	14	)	)	PUNCT
cana-860	121	15	.	.	PUNCT
cana-860	122	1	let	let	VERB
cana-860	122	2	t	t	NOUN
cana-860	122	3	–	–	PUNCT
cana-860	122	4	set	set	VERB
cana-860	122	5	for	for	ADP
cana-860	122	6	g	g	PROPN
cana-860	122	7	is	be	AUX
cana-860	122	8	d	d	PRON
cana-860	122	9	such	such	ADJ
cana-860	122	10	that	that	SCONJ
cana-860	122	11	x	x	NOUN
cana-860	122	12	,	,	PUNCT
cana-860	122	13	y	y	PROPN
cana-860	122	14			PROPN
cana-860	123	1	d	d	PROPN
cana-860	123	2	,	,	PUNCT
cana-860	123	3	x	x	X
cana-860	123	4	adjacent	adjacent	ADJ
cana-860	123	5	to	to	ADP
cana-860	123	6	y	y	PROPN
cana-860	123	7	where	where	SCONJ
cana-860	123	8	y	y	PROPN
cana-860	123	9	is	be	AUX
cana-860	123	10	selfish	selfish	ADJ
cana-860	123	11	,	,	PUNCT
cana-860	123	12	b	b	X
cana-860	123	13	(	(	PUNCT
cana-860	123	14	{	{	PUNCT
cana-860	123	15	x	x	NOUN
cana-860	123	16	,	,	PUNCT
cana-860	123	17	y	y	NOUN
cana-860	123	18	}	}	PUNCT
cana-860	123	19	)	)	PUNCT
cana-860	123	20			PUNCT
cana-860	123	21	d	d	X
cana-860	123	22	=	=	PUNCT
cana-860	123	23	.	.	PUNCT
cana-860	123	24	if	if	SCONJ
cana-860	123	25	this	this	PRON
cana-860	123	26	is	be	AUX
cana-860	123	27	possible	possible	ADJ
cana-860	123	28	for	for	ADP
cana-860	123	29	each	each	DET
cana-860	123	30	and	and	CCONJ
cana-860	123	31	every	every	PRON
cana-860	123	32	vertices	vertex	NOUN
cana-860	123	33	of	of	ADP
cana-860	123	34	g	g	NOUN
cana-860	123	35	,	,	PUNCT
cana-860	123	36	then	then	ADV
cana-860	123	37	g	g	PROPN
cana-860	123	38	is	be	AUX
cana-860	123	39	a	a	DET
cana-860	123	40	tdss	tdss	NOUN
cana-860	123	41	.	.	PUNCT
cana-860	124	1	proof	proof	NOUN
cana-860	124	2	let	let	VERB
cana-860	124	3	g	g	NOUN
cana-860	124	4	be	be	AUX
cana-860	124	5	a	a	DET
cana-860	124	6	graph	graph	NOUN
cana-860	124	7	with	with	ADP
cana-860	124	8	x	x	X
cana-860	124	9	v	v	X
cana-860	124	10	(	(	PUNCT
cana-860	124	11	g	g	NOUN
cana-860	124	12	)	)	PUNCT
cana-860	124	13	and	and	CCONJ
cana-860	124	14	t	t	NOUN
cana-860	124	15	–	–	PUNCT
cana-860	124	16	set	set	VERB
cana-860	124	17	for	for	ADP
cana-860	124	18	g	g	PROPN
cana-860	124	19	is	be	AUX
cana-860	124	20	d.	d.	PROPN
cana-860	124	21	by	by	ADP
cana-860	124	22	given	give	VERB
cana-860	124	23	condition	condition	NOUN
cana-860	124	24			NUM
cana-860	124	25	one	one	NUM
cana-860	124	26	y	y	NOUN
cana-860	124	27	such	such	ADJ
cana-860	125	1	that	that	SCONJ
cana-860	125	2	x	x	NOUN
cana-860	125	3	,	,	PUNCT
cana-860	125	4	y	y	PROPN
cana-860	125	5			PROPN
cana-860	125	6	d	d	PROPN
cana-860	125	7	,	,	PUNCT
cana-860	125	8	where	where	SCONJ
cana-860	125	9	y	y	PROPN
cana-860	125	10	is	be	AUX
cana-860	125	11	selfish	selfish	ADJ
cana-860	125	12	,	,	PUNCT
cana-860	125	13	x	x	PUNCT
cana-860	125	14	adjacent	adjacent	ADJ
cana-860	125	15	to	to	ADP
cana-860	125	16	y	y	PROPN
cana-860	125	17	and	and	CCONJ
cana-860	125	18	b	b	PROPN
cana-860	125	19	(	(	PUNCT
cana-860	125	20	{	{	PUNCT
cana-860	125	21	x	x	NOUN
cana-860	125	22	,	,	PUNCT
cana-860	125	23	y	y	NOUN
cana-860	125	24	}	}	PUNCT
cana-860	125	25	)	)	PUNCT
cana-860	125	26			PUNCT
cana-860	125	27	d	d	NOUN
cana-860	125	28	=	=	SYM
cana-860	125	29			NOUN
cana-860	125	30	.	.	PUNCT
cana-860	126	1	let	let	VERB
cana-860	126	2	gtsd	gtsd	VERB
cana-860	126	3	xs	xs	PROPN
cana-860	127	1	=	=	PUNCT
cana-860	127	2	z	z	PROPN
cana-860	127	3	where	where	SCONJ
cana-860	127	4	s	s	VERB
cana-860	127	5			PROPN
cana-860	127	6	n	n	CCONJ
cana-860	127	7	(	(	PUNCT
cana-860	127	8	x	x	NOUN
cana-860	127	9	)	)	PUNCT
cana-860	127	10	.	.	PUNCT
cana-860	128	1	then	then	ADV
cana-860	128	2	we	we	PRON
cana-860	128	3	have	have	AUX
cana-860	128	4	t	t	VERB
cana-860	128	5	–	–	PUNCT
cana-860	128	6	set	set	VERB
cana-860	128	7	for	for	ADP
cana-860	128	8	gtsd	gtsd	PROPN
cana-860	128	9	xs	xs	PROPN
cana-860	128	10	is	be	AUX
cana-860	128	11	d1	d1	PROPN
cana-860	129	1	=	=	PUNCT
cana-860	129	2	d	d	PROPN
cana-860	129	3	–	–	PUNCT
cana-860	129	4	{	{	PUNCT
cana-860	129	5	y	y	NOUN
cana-860	129	6	}	}	PUNCT
cana-860	129	7			NOUN
cana-860	129	8	{	{	PUNCT
cana-860	129	9	z	z	NOUN
cana-860	129	10	}	}	PUNCT
cana-860	129	11	.	.	PUNCT
cana-860	130	1	that	that	PRON
cana-860	130	2	is	be	AUX
cana-860	130	3	true	true	ADJ
cana-860	130	4	for	for	ADP
cana-860	130	5	each	each	PRON
cana-860	130	6	and	and	CCONJ
cana-860	130	7	every	every	PRON
cana-860	130	8	x	x	ADJ
cana-860	130	9			NOUN
cana-860	130	10	v	v	X
cana-860	130	11	(	(	PUNCT
cana-860	130	12	g	g	NOUN
cana-860	130	13	)	)	PUNCT
cana-860	130	14	of	of	ADP
cana-860	130	15	g.	g.	PROPN
cana-860	130	16	therefore	therefore	ADV
cana-860	130	17	g	g	PROPN
cana-860	130	18	is	be	AUX
cana-860	130	19	tdss	tdss	NOUN
cana-860	130	20	.	.	PUNCT
cana-860	131	1			PUNCT
cana-860	131	2	corollary	corollary	ADJ
cana-860	131	3	for	for	ADP
cana-860	131	4	a	a	DET
cana-860	131	5	graph	graph	NOUN
cana-860	131	6	g	g	ADP
cana-860	131	7	such	such	DET
cana-860	131	8	that	that	SCONJ
cana-860	131	9			NOUN
cana-860	131	10	x	x	NOUN
cana-860	131	11	,	,	PUNCT
cana-860	131	12	y	y	PROPN
cana-860	131	13			PROPN
cana-860	131	14	v	v	PROPN
cana-860	131	15	(	(	PUNCT
cana-860	131	16	g	g	NOUN
cana-860	131	17	)	)	PUNCT
cana-860	131	18	,	,	PUNCT
cana-860	131	19	there	there	PRON
cana-860	131	20	exists	exist	VERB
cana-860	131	21	a	a	DET
cana-860	131	22	t	t	NOUN
cana-860	131	23	–	–	PUNCT
cana-860	131	24	set	set	VERB
cana-860	132	1	d	d	ADP
cana-860	132	2	such	such	ADJ
cana-860	132	3	that	that	DET
cana-860	132	4	b	b	NOUN
cana-860	132	5	(	(	PUNCT
cana-860	132	6	{	{	PUNCT
cana-860	132	7	x	x	NOUN
cana-860	132	8	,	,	PUNCT
cana-860	132	9	y	y	NOUN
cana-860	132	10	}	}	PUNCT
cana-860	132	11	)	)	PUNCT
cana-860	133	1			PUNCT
cana-860	133	2	d	d	NOUN
cana-860	133	3	=	=	SYM
cana-860	133	4			NOUN
cana-860	133	5	and	and	CCONJ
cana-860	133	6	either	either	CCONJ
cana-860	133	7	x	x	SYM
cana-860	133	8	or	or	CCONJ
cana-860	133	9	y	y	PROPN
cana-860	133	10	is	be	AUX
cana-860	133	11	selfish	selfish	ADJ
cana-860	133	12	.	.	PUNCT
cana-860	134	1	then	then	ADV
cana-860	134	2	,	,	PUNCT
cana-860	134	3	g	g	PROPN
cana-860	134	4	is	be	AUX
cana-860	134	5	tdss	tdss	NOUN
cana-860	134	6	.	.	PUNCT
cana-860	135	1	proof	proof	NOUN
cana-860	135	2	let	let	VERB
cana-860	135	3	g	g	NOUN
cana-860	135	4	be	be	AUX
cana-860	135	5	a	a	DET
cana-860	135	6	graph	graph	NOUN
cana-860	135	7	with	with	ADP
cana-860	135	8	x	x	PROPN
cana-860	135	9	,	,	PUNCT
cana-860	135	10	y	y	PROPN
cana-860	135	11			PROPN
cana-860	135	12	v	v	PROPN
cana-860	135	13	(	(	PUNCT
cana-860	135	14	g	g	NOUN
cana-860	135	15	)	)	PUNCT
cana-860	135	16	such	such	ADJ
cana-860	135	17	that	that	SCONJ
cana-860	135	18	x	x	SYM
cana-860	135	19	adjacent	adjacent	ADJ
cana-860	135	20	to	to	ADP
cana-860	135	21	y.	y.	PROPN
cana-860	135	22	given	give	VERB
cana-860	135	23	that	that	SCONJ
cana-860	135	24			PROPN
cana-860	135	25	one	one	NUM
cana-860	135	26	t	t	NOUN
cana-860	135	27	–	–	PUNCT
cana-860	135	28	set	set	NOUN
cana-860	135	29	d	d	PROPN
cana-860	135	30	where	where	SCONJ
cana-860	135	31	x	x	X
cana-860	135	32	,	,	PUNCT
cana-860	135	33	y	y	PROPN
cana-860	135	34			PROPN
cana-860	135	35	d	d	PROPN
cana-860	135	36	,	,	PUNCT
cana-860	135	37	such	such	ADJ
cana-860	135	38	that	that	PRON
cana-860	135	39	b	b	X
cana-860	135	40	(	(	PUNCT
cana-860	135	41	{	{	PUNCT
cana-860	135	42	x	x	NOUN
cana-860	135	43	,	,	PUNCT
cana-860	135	44	y	y	NOUN
cana-860	135	45	}	}	PUNCT
cana-860	135	46	)	)	PUNCT
cana-860	135	47			PUNCT
cana-860	135	48	d	d	NOUN
cana-860	135	49	=	=	SYM
cana-860	135	50			NOUN
cana-860	135	51	and	and	CCONJ
cana-860	135	52	either	either	CCONJ
cana-860	135	53	x	x	SYM
cana-860	135	54	or	or	CCONJ
cana-860	135	55	y	y	PROPN
cana-860	135	56	is	be	AUX
cana-860	135	57	selfish	selfish	ADJ
cana-860	135	58	.	.	PUNCT
cana-860	136	1	let	let	VERB
cana-860	136	2	us	we	PRON
cana-860	136	3	assume	assume	VERB
cana-860	136	4	that	that	SCONJ
cana-860	136	5	x	x	PRON
cana-860	136	6	is	be	AUX
cana-860	136	7	selfish	selfish	ADJ
cana-860	136	8	and	and	CCONJ
cana-860	136	9	gtsd	gtsd	VERB
cana-860	136	10	xy	xy	PROPN
cana-860	137	1	=	=	PUNCT
cana-860	137	2	z.	z.	PROPN
cana-860	137	3	then	then	ADV
cana-860	137	4	we	we	PRON
cana-860	137	5	have	have	AUX
cana-860	137	6	t	t	VERB
cana-860	137	7	–	–	PUNCT
cana-860	137	8	set	set	VERB
cana-860	137	9	for	for	ADP
cana-860	137	10	gtsd	gtsd	NOUN
cana-860	137	11	xy	xy	PROPN
cana-860	137	12	is	be	AUX
cana-860	137	13	d	d	PROPN
cana-860	137	14	–	–	PUNCT
cana-860	137	15	{	{	PUNCT
cana-860	137	16	x	x	NOUN
cana-860	137	17	}	}	PUNCT
cana-860	137	18			NOUN
cana-860	137	19	{	{	PUNCT
cana-860	137	20	z	z	NOUN
cana-860	137	21	}	}	PUNCT
cana-860	137	22	.	.	PUNCT
cana-860	138	1	by	by	ADP
cana-860	138	2	theorem	theorem	NOUN
cana-860	138	3	2.5	2.5	NUM
cana-860	138	4	,	,	PUNCT
cana-860	138	5	this	this	PRON
cana-860	138	6	is	be	AUX
cana-860	138	7	true	true	ADJ
cana-860	138	8	for	for	ADP
cana-860	138	9	all	all	DET
cana-860	138	10	x	x	NOUN
cana-860	138	11	,	,	PUNCT
cana-860	138	12	y	y	PROPN
cana-860	138	13			PROPN
cana-860	138	14	v	v	PROPN
cana-860	138	15	(	(	PUNCT
cana-860	138	16	g	g	NOUN
cana-860	138	17	)	)	PUNCT
cana-860	138	18	.	.	PUNCT
cana-860	139	1	therefore	therefore	ADV
cana-860	139	2	g	g	PROPN
cana-860	139	3	is	be	AUX
cana-860	139	4	tdss	tdss	NOUN
cana-860	139	5	.	.	PUNCT
cana-860	140	1			PUNCT
cana-860	140	2	converse	converse	NOUN
cana-860	140	3	need	need	AUX
cana-860	140	4	not	not	PART
cana-860	140	5	be	be	AUX
cana-860	140	6	true	true	ADJ
cana-860	140	7	.	.	PUNCT
cana-860	141	1	example	example	NOUN
cana-860	141	2	fig	fig	NOUN
cana-860	141	3	.	.	PUNCT
cana-860	142	1	5	5	NUM
cana-860	142	2	tdss	tdss	NOUN
cana-860	142	3	graph	graph	NOUN
cana-860	142	4	with	with	ADP
cana-860	142	5	b	b	PROPN
cana-860	142	6	(	(	PUNCT
cana-860	142	7	{	{	PUNCT
cana-860	142	8	x	x	NOUN
cana-860	142	9	,	,	PUNCT
cana-860	142	10	y	y	NOUN
cana-860	142	11	}	}	PUNCT
cana-860	142	12	)	)	PUNCT
cana-860	142	13			PUNCT
cana-860	142	14	d	d	PROPN
cana-860	142	15			NOUN
cana-860	142	16			NOUN
cana-860	142	17	in	in	ADP
cana-860	142	18	fig.5	fig.5	PROPN
cana-860	142	19	,	,	PUNCT
cana-860	142	20	we	we	PRON
cana-860	142	21	have	have	AUX
cana-860	142	22	b	b	NUM
cana-860	142	23	(	(	PUNCT
cana-860	142	24	{	{	PUNCT
cana-860	142	25	x	x	NOUN
cana-860	142	26	,	,	PUNCT
cana-860	142	27	y	y	NOUN
cana-860	142	28	}	}	PUNCT
cana-860	142	29	)	)	PUNCT
cana-860	142	30			PUNCT
cana-860	142	31	d	d	PROPN
cana-860	142	32			NOUN
cana-860	142	33	.	.	PUNCT
cana-860	142	34	then	then	ADV
cana-860	142	35	g	g	PROPN
cana-860	142	36	is	be	AUX
cana-860	142	37	tdss	tdss	NOUN
cana-860	142	38	with	with	ADP
cana-860	142	39	x	x	PROPN
cana-860	142	40	,	,	PUNCT
cana-860	142	41	y	y	PROPN
cana-860	143	1			PROPN
cana-860	143	2	d	d	PROPN
cana-860	143	3	,	,	PUNCT
cana-860	143	4	x	x	X
cana-860	143	5	adjacent	adjacent	ADJ
cana-860	143	6	to	to	ADP
cana-860	143	7	y	y	PRON
cana-860	143	8	such	such	ADJ
cana-860	143	9	that	that	SCONJ
cana-860	143	10	y	y	PROPN
cana-860	143	11	is	be	AUX
cana-860	143	12	selfish	selfish	ADJ
cana-860	143	13	.	.	PUNCT
cana-860	144	1	theorem	theorem	VERB
cana-860	144	2	2.7	2.7	NUM
cana-860	144	3	if	if	SCONJ
cana-860	144	4	g	g	PROPN
cana-860	144	5	is	be	AUX
cana-860	144	6	tdss	tdss	NOUN
cana-860	144	7	,	,	PUNCT
cana-860	144	8	then	then	ADV
cana-860	144	9	every	every	DET
cana-860	144	10	pendant	pendant	ADJ
cana-860	144	11	vertex	vertex	NOUN
cana-860	144	12	of	of	ADP
cana-860	144	13	g	g	PROPN
cana-860	144	14	is	be	AUX
cana-860	144	15	included	include	VERB
cana-860	144	16	in	in	ADP
cana-860	144	17	some	some	DET
cana-860	144	18	t	t	NOUN
cana-860	144	19	–	–	PUNCT
cana-860	144	20	set	set	NOUN
cana-860	144	21	.	.	PUNCT
cana-860	145	1	communications	communication	NOUN
cana-860	145	2	on	on	ADP
cana-860	145	3	applied	apply	VERB
cana-860	145	4	nonlinear	nonlinear	ADJ
cana-860	145	5	analysis	analysis	NOUN
cana-860	145	6	issn	issn	NOUN
cana-860	145	7	:	:	PUNCT
cana-860	145	8	1074	1074	NUM
cana-860	145	9	-	-	PUNCT
cana-860	145	10	133x	133x	NUM
cana-860	145	11	vol	vol	NOUN
cana-860	145	12	31	31	NUM
cana-860	145	13	no	no	NOUN
cana-860	145	14	.	.	PUNCT
cana-860	146	1	4s	4s	NUM
cana-860	146	2	(	(	PUNCT
cana-860	146	3	2024	2024	NUM
cana-860	146	4	)	)	PUNCT
cana-860	146	5	377	377	NUM
cana-860	146	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-860	146	7	proof	proof	NOUN
cana-860	146	8	let	let	VERB
cana-860	146	9	g	g	NOUN
cana-860	146	10	be	be	AUX
cana-860	146	11	tdss	tdss	NOUN
cana-860	146	12	with	with	ADP
cana-860	146	13	x	x	PROPN
cana-860	146	14	,	,	PUNCT
cana-860	146	15	y	y	PROPN
cana-860	146	16			PROPN
cana-860	146	17	v	v	PROPN
cana-860	146	18	(	(	PUNCT
cana-860	146	19	g	g	NOUN
cana-860	146	20	)	)	PUNCT
cana-860	146	21	,	,	PUNCT
cana-860	146	22	here	here	ADV
cana-860	146	23	the	the	DET
cana-860	146	24	pendant	pendant	ADJ
cana-860	146	25	vertex	vertex	NOUN
cana-860	146	26	is	be	AUX
cana-860	146	27	y	y	PROPN
cana-860	146	28	and	and	CCONJ
cana-860	146	29	support	support	VERB
cana-860	146	30	vertex	vertex	NOUN
cana-860	146	31	is	be	AUX
cana-860	146	32	x.	x.	NOUN
cana-860	146	33	let	let	VERB
cana-860	146	34	gtsd	gtsd	VERB
cana-860	146	35	xy	xy	PROPN
cana-860	147	1	=	=	PUNCT
cana-860	147	2	z.	z.	PROPN
cana-860	147	3	in	in	ADP
cana-860	147	4	gtsd	gtsd	PROPN
cana-860	147	5	xy	xy	PROPN
cana-860	147	6	,	,	PUNCT
cana-860	147	7	either	either	CCONJ
cana-860	147	8	y	y	PROPN
cana-860	147	9			PROPN
cana-860	147	10	t	t	PROPN
cana-860	147	11	(	(	PUNCT
cana-860	147	12	gtsd	gtsd	NOUN
cana-860	147	13	xy	xy	PROPN
cana-860	147	14	)	)	PUNCT
cana-860	147	15	or	or	CCONJ
cana-860	147	16	y	y	PROPN
cana-860	147	17			PROPN
cana-860	147	18	t	t	NOUN
cana-860	147	19	(	(	PUNCT
cana-860	147	20	gtsd	gtsd	NOUN
cana-860	147	21	xy	xy	PROPN
cana-860	147	22	)	)	PUNCT
cana-860	147	23	.	.	PUNCT
cana-860	148	1	if	if	SCONJ
cana-860	148	2	y	y	PROPN
cana-860	148	3			PROPN
cana-860	148	4	t	t	PROPN
cana-860	148	5	(	(	PUNCT
cana-860	148	6	gtsd	gtsd	PROPN
cana-860	148	7	xy	xy	PROPN
cana-860	148	8	)	)	PUNCT
cana-860	148	9	,	,	PUNCT
cana-860	148	10	then	then	ADV
cana-860	148	11	z	z	PROPN
cana-860	148	12			PROPN
cana-860	148	13	t	t	PROPN
cana-860	148	14	(	(	PUNCT
cana-860	148	15	gtsd	gtsd	PROPN
cana-860	148	16	xy	xy	PROPN
cana-860	148	17	)	)	PUNCT
cana-860	148	18	,	,	PUNCT
cana-860	148	19	x	x	PUNCT
cana-860	148	20			NUM
cana-860	148	21			NUM
cana-860	148	22	t	t	PROPN
cana-860	148	23	(	(	PUNCT
cana-860	148	24	gtsd	gtsd	PROPN
cana-860	148	25	xy	xy	PROPN
cana-860	148	26	)	)	PUNCT
cana-860	148	27	.	.	PUNCT
cana-860	149	1	here	here	ADV
cana-860	149	2	,	,	PUNCT
cana-860	149	3	the	the	DET
cana-860	149	4	t	t	NOUN
cana-860	149	5	–	–	PUNCT
cana-860	149	6	set	set	VERB
cana-860	149	7	for	for	ADP
cana-860	149	8	g	g	NOUN
cana-860	149	9	containing	contain	VERB
cana-860	149	10	y	y	PROPN
cana-860	149	11	is	be	AUX
cana-860	149	12	t	t	VERB
cana-860	149	13	(	(	PUNCT
cana-860	149	14	gtsd	gtsd	NOUN
cana-860	149	15	xy	xy	PROPN
cana-860	149	16	)	)	PUNCT
cana-860	149	17	–	–	PUNCT
cana-860	149	18	{	{	PUNCT
cana-860	149	19	z	z	NOUN
cana-860	149	20	}	}	PUNCT
cana-860	149	21			NOUN
cana-860	149	22	{	{	PUNCT
cana-860	149	23	x	x	NOUN
cana-860	149	24	}	}	PUNCT
cana-860	149	25	.	.	PUNCT
cana-860	150	1	if	if	SCONJ
cana-860	150	2	y	y	PROPN
cana-860	150	3			PROPN
cana-860	150	4			NUM
cana-860	150	5	t	t	PROPN
cana-860	150	6	(	(	PUNCT
cana-860	150	7	gtsd	gtsd	PROPN
cana-860	150	8	xy	xy	PROPN
cana-860	150	9	)	)	PUNCT
cana-860	150	10	,	,	PUNCT
cana-860	150	11	then	then	ADV
cana-860	150	12	x	x	X
cana-860	150	13	,	,	PUNCT
cana-860	150	14	z	z	PROPN
cana-860	150	15			PROPN
cana-860	150	16	t	t	NOUN
cana-860	150	17	(	(	PUNCT
cana-860	150	18	gtsd	gtsd	NOUN
cana-860	150	19	xy	xy	PROPN
cana-860	150	20	)	)	PUNCT
cana-860	150	21	.	.	PUNCT
cana-860	151	1	here	here	ADV
cana-860	151	2	also	also	ADV
cana-860	151	3	the	the	DET
cana-860	151	4	t	t	NOUN
cana-860	151	5	–	–	PUNCT
cana-860	151	6	set	set	VERB
cana-860	151	7	for	for	ADP
cana-860	151	8	g	g	NOUN
cana-860	151	9	containing	contain	VERB
cana-860	151	10	y	y	PROPN
cana-860	151	11	is	be	AUX
cana-860	151	12	t	t	VERB
cana-860	151	13	(	(	PUNCT
cana-860	151	14	gtsd	gtsd	NOUN
cana-860	151	15	xy	xy	PROPN
cana-860	151	16	)	)	PUNCT
cana-860	151	17	–	–	PUNCT
cana-860	151	18	{	{	PUNCT
cana-860	151	19	z	z	NOUN
cana-860	151	20	}	}	PUNCT
cana-860	151	21			NOUN
cana-860	151	22	{	{	PUNCT
cana-860	151	23	y	y	NOUN
cana-860	151	24	}	}	PUNCT
cana-860	151	25	.	.	PUNCT
cana-860	152	1	in	in	ADP
cana-860	152	2	all	all	DET
cana-860	152	3	cases	case	NOUN
cana-860	152	4	,	,	PUNCT
cana-860	152	5	there	there	PRON
cana-860	152	6	is	be	VERB
cana-860	152	7	a	a	DET
cana-860	152	8	t	t	NOUN
cana-860	152	9	–	–	PUNCT
cana-860	152	10	set	set	VERB
cana-860	152	11	containing	contain	VERB
cana-860	152	12	y.	y.	NOUN
cana-860	152	13			PUNCT
cana-860	152	14	corollary	corollary	NOUN
cana-860	152	15	if	if	SCONJ
cana-860	152	16	g	g	PROPN
cana-860	152	17	has	have	VERB
cana-860	152	18	at	at	ADV
cana-860	152	19	least	least	ADV
cana-860	152	20	one	one	NUM
cana-860	152	21	pendant	pendant	ADJ
cana-860	152	22	vertex	vertex	NOUN
cana-860	152	23	that	that	PRON
cana-860	152	24	is	be	AUX
cana-860	152	25	tdss	tdss	NOUN
cana-860	152	26	.	.	PUNCT
cana-860	153	1	then	then	ADV
cana-860	153	2	g	g	PROPN
cana-860	153	3	has	have	VERB
cana-860	153	4	at	at	ADV
cana-860	153	5	least	least	ADV
cana-860	153	6	one	one	NUM
cana-860	153	7	selfish	selfish	ADJ
cana-860	153	8	vertex	vertex	NOUN
cana-860	153	9	.	.	PUNCT
cana-860	154	1	proof	proof	NOUN
cana-860	154	2	by	by	ADP
cana-860	154	3	the	the	DET
cana-860	154	4	above	above	ADJ
cana-860	154	5	theorem	theorem	NOUN
cana-860	154	6	2.7	2.7	NUM
cana-860	154	7	mentioned	mention	VERB
cana-860	154	8	if	if	SCONJ
cana-860	154	9			NUM
cana-860	154	10	a	a	DET
cana-860	154	11	t	t	NOUN
cana-860	154	12	–	–	PUNCT
cana-860	154	13	set	set	VERB
cana-860	154	14	d	d	NOUN
cana-860	154	15	containing	contain	VERB
cana-860	154	16	y	y	PROPN
cana-860	154	17	which	which	PRON
cana-860	154	18	is	be	AUX
cana-860	154	19	pendant	pendant	ADJ
cana-860	154	20	and	and	CCONJ
cana-860	154	21	x	x	NOUN
cana-860	154	22	,	,	PUNCT
cana-860	154	23	y	y	PROPN
cana-860	154	24			PROPN
cana-860	154	25	d	d	X
cana-860	154	26	where	where	SCONJ
cana-860	154	27	x	x	PRON
cana-860	154	28	is	be	AUX
cana-860	154	29	support	support	NOUN
cana-860	154	30	vertex	vertex	NOUN
cana-860	154	31	.	.	PUNCT
cana-860	155	1	for	for	ADP
cana-860	155	2	this	this	DET
cana-860	155	3	t	t	NOUN
cana-860	155	4	–	–	PUNCT
cana-860	155	5	set	set	NOUN
cana-860	155	6	d	d	PROPN
cana-860	155	7	,	,	PUNCT
cana-860	155	8	y	y	PROPN
cana-860	155	9	is	be	AUX
cana-860	155	10	selfish	selfish	ADJ
cana-860	155	11	.	.	PUNCT
cana-860	156	1			PUNCT
cana-860	156	2	3	3	X
cana-860	156	3	.	.	X
cana-860	156	4	conclusion	conclusion	NOUN
cana-860	156	5	in	in	ADP
cana-860	156	6	the	the	DET
cana-860	156	7	research	research	NOUN
cana-860	156	8	paper	paper	NOUN
cana-860	156	9	,	,	PUNCT
cana-860	156	10	we	we	PRON
cana-860	156	11	introduce	introduce	VERB
cana-860	156	12	new	new	ADJ
cana-860	156	13	graph	graph	NOUN
cana-860	156	14	class	class	NOUN
cana-860	156	15	by	by	ADP
cana-860	156	16	using	use	VERB
cana-860	156	17	subdivision	subdivision	NOUN
cana-860	156	18	of	of	ADP
cana-860	156	19	an	an	DET
cana-860	156	20	edge	edge	NOUN
cana-860	156	21	which	which	PRON
cana-860	156	22	is	be	AUX
cana-860	156	23	total	total	ADJ
cana-860	156	24	domination	domination	NOUN
cana-860	156	25	subdivision	subdivision	NOUN
cana-860	156	26	stable	stable	ADJ
cana-860	156	27	graph	graph	NOUN
cana-860	156	28	and	and	CCONJ
cana-860	156	29	studied	study	VERB
cana-860	156	30	the	the	DET
cana-860	156	31	basic	basic	ADJ
cana-860	156	32	results	result	NOUN
cana-860	156	33	for	for	ADP
cana-860	156	34	a	a	DET
cana-860	156	35	graph	graph	NOUN
cana-860	156	36	to	to	PART
cana-860	156	37	be	be	AUX
cana-860	156	38	tdss	tdss	NOUN
cana-860	156	39	.	.	PUNCT
cana-860	157	1	further	far	ADV
cana-860	157	2	,	,	PUNCT
cana-860	157	3	we	we	PRON
cana-860	157	4	proposed	propose	VERB
cana-860	157	5	the	the	DET
cana-860	157	6	condition	condition	NOUN
cana-860	157	7	by	by	ADP
cana-860	157	8	obtaining	obtain	VERB
cana-860	157	9	tdss	tdss	NOUN
cana-860	157	10	graph	graph	NOUN
cana-860	157	11	from	from	ADP
cana-860	157	12	a	a	DET
cana-860	157	13	given	give	VERB
cana-860	157	14	graph	graph	NOUN
cana-860	157	15	g	g	PROPN
cana-860	157	16	and	and	CCONJ
cana-860	157	17	proved	prove	VERB
cana-860	157	18	few	few	ADJ
cana-860	157	19	results	result	NOUN
cana-860	157	20	of	of	ADP
cana-860	157	21	tdss	tdss	NOUN
cana-860	157	22	graph	graph	NOUN
cana-860	157	23	.	.	PUNCT
cana-860	158	1	references	reference	NOUN
cana-860	158	2	[	[	X
cana-860	158	3	1	1	NUM
cana-860	158	4	]	]	PUNCT
cana-860	158	5	d.b.west	d.b.w	ADJ
cana-860	158	6	,	,	PUNCT
cana-860	158	7	introduction	introduction	NOUN
cana-860	158	8	to	to	AUX
cana-860	158	9	graph	graph	NOUN
cana-860	158	10	theory	theory	NOUN
cana-860	158	11	,	,	PUNCT
cana-860	158	12	second	second	ADJ
cana-860	158	13	ed	ed	NOUN
cana-860	158	14	.	.	PROPN
cana-860	158	15	,	,	PUNCT
cana-860	158	16	prentice	prentice	NOUN
cana-860	158	17	-	-	PUNCT
cana-860	158	18	hall	hall	NOUN
cana-860	158	19	,	,	PUNCT
cana-860	158	20	englewood	englewood	PROPN
cana-860	158	21	cliffs	cliffs	PROPN
cana-860	158	22	,	,	PUNCT
cana-860	158	23	nj	nj	PROPN
cana-860	158	24	,	,	PUNCT
cana-860	158	25	(	(	PUNCT
cana-860	158	26	2001	2001	NUM
cana-860	158	27	)	)	PUNCT
cana-860	158	28	.	.	PUNCT
cana-860	159	1	[	[	X
cana-860	159	2	2	2	NUM
cana-860	159	3	]	]	PUNCT
cana-860	159	4	t.w.haynes	t.w.hayne	NOUN
cana-860	159	5	,	,	PUNCT
cana-860	159	6	s.t.hedetniemi	s.t.hedetniemi	ADV
cana-860	159	7	,	,	PUNCT
cana-860	159	8	and	and	CCONJ
cana-860	159	9	p.j.slater	p.j.slater	NOUN
cana-860	159	10	,	,	PUNCT
cana-860	159	11	fundamentals	fundamental	NOUN
cana-860	159	12	of	of	ADP
cana-860	159	13	domination	domination	NOUN
cana-860	159	14	in	in	ADP
cana-860	159	15	graphs	graph	NOUN
cana-860	159	16	,	,	PUNCT
cana-860	159	17	marcel	marcel	PROPN
cana-860	159	18	dekker	dekker	PROPN
cana-860	159	19	,	,	PUNCT
cana-860	159	20	inc	inc	PROPN
cana-860	159	21	.	.	PROPN
cana-860	159	22	,	,	PUNCT
cana-860	159	23	new	new	PROPN
cana-860	159	24	york	york	PROPN
cana-860	159	25	,	,	PUNCT
cana-860	159	26	(	(	PUNCT
cana-860	159	27	1998	1998	NUM
cana-860	159	28	)	)	PUNCT
cana-860	159	29	.	.	PUNCT
cana-860	160	1	[	[	X
cana-860	160	2	3	3	NUM
cana-860	160	3	]	]	X
cana-860	160	4	t.w.haynes	t.w.hayne	NOUN
cana-860	160	5	and	and	CCONJ
cana-860	160	6	m.a.henning	m.a.henning	NOUN
cana-860	160	7	,	,	PUNCT
cana-860	160	8	total	total	ADJ
cana-860	160	9	domination	domination	NOUN
cana-860	160	10	good	good	ADJ
cana-860	160	11	vertices	vertex	NOUN
cana-860	160	12	in	in	ADP
cana-860	160	13	graphs	graph	NOUN
cana-860	160	14	,	,	PUNCT
cana-860	160	15	australasian	australasian	ADJ
cana-860	160	16	journal	journal	NOUN
cana-860	160	17	of	of	ADP
cana-860	160	18	combinatorics	combinatoric	NOUN
cana-860	160	19	,	,	PUNCT
cana-860	160	20	(	(	PUNCT
cana-860	160	21	2002	2002	NUM
cana-860	160	22	)	)	PUNCT
cana-860	160	23	,	,	PUNCT
cana-860	160	24	26	26	NUM
cana-860	160	25	,	,	PUNCT
cana-860	160	26	305	305	NUM
cana-860	160	27	-	-	SYM
cana-860	160	28	315	315	NUM
cana-860	160	29	.	.	PUNCT
cana-860	161	1	[	[	X
cana-860	161	2	4	4	X
cana-860	161	3	]	]	X
cana-860	161	4	s.	s.	PROPN
cana-860	161	5	velammal	velammal	PROPN
cana-860	161	6	,	,	PUNCT
cana-860	161	7	studies	study	NOUN
cana-860	161	8	in	in	ADP
cana-860	161	9	graph	graph	NOUN
cana-860	161	10	theory	theory	NOUN
cana-860	161	11	:	:	PUNCT
cana-860	161	12	covering	covering	NOUN
cana-860	161	13	,	,	PUNCT
cana-860	161	14	independence	independence	NOUN
cana-860	161	15	,	,	PUNCT
cana-860	161	16	domination	domination	NOUN
cana-860	161	17	and	and	CCONJ
cana-860	161	18	related	related	ADJ
cana-860	161	19	topics	topic	NOUN
cana-860	161	20	,	,	PUNCT
cana-860	161	21	ph.d	ph.d	PROPN
cana-860	161	22	thesis	thesis	NOUN
cana-860	161	23	,	,	PUNCT
cana-860	161	24	1997	1997	NUM
cana-860	161	25	.	.	PUNCT
cana-860	162	1	[	[	X
cana-860	162	2	5	5	NUM
cana-860	162	3	]	]	PUNCT
cana-860	162	4	t.w.haynes	t.w.hayne	NOUN
cana-860	162	5	,	,	PUNCT
cana-860	162	6	s.t.hedetniemi	s.t.hedetniemi	ADV
cana-860	162	7	and	and	CCONJ
cana-860	162	8	l.c.vander	l.c.vander	PROPN
cana-860	162	9	merwe	merwe	PROPN
cana-860	162	10	,	,	PUNCT
cana-860	162	11	total	total	ADJ
cana-860	162	12	domination	domination	NOUN
cana-860	162	13	subdivision	subdivision	NOUN
cana-860	162	14	numbers	number	NOUN
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cana-860	162	20	)	)	PUNCT
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cana-860	163	3	]	]	PUNCT
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cana-860	163	18	domination	domination	NOUN
cana-860	163	19	subdivision	subdivision	NOUN
cana-860	163	20	numbers	number	NOUN
cana-860	163	21	,	,	PUNCT
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cana-860	163	29	)	)	PUNCT
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cana-860	164	3	]	]	PUNCT
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cana-860	164	21	,	,	PUNCT
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cana-860	164	25	(	(	PUNCT
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cana-860	164	27	)	)	PUNCT
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cana-860	165	3	]	]	PUNCT
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cana-860	165	7	,	,	PUNCT
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cana-860	165	14	total	total	ADJ
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cana-860	165	16	subdivision	subdivision	NOUN
cana-860	165	17	number	number	NOUN
cana-860	165	18	in	in	ADP
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cana-860	165	20	classes	class	NOUN
cana-860	165	21	of	of	ADP
cana-860	165	22	graps	grap	NOUN
cana-860	165	23	,	,	PUNCT
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cana-860	165	26	(	(	PUNCT
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cana-860	165	28	)	)	PUNCT
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cana-860	165	31	,	,	PUNCT
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cana-860	165	33	-	-	SYM
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cana-860	166	2	9	9	NUM
cana-860	166	3	]	]	PUNCT
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cana-860	166	5	,	,	PUNCT
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cana-860	166	14	of	of	ADP
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cana-860	166	16	,	,	PUNCT
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cana-860	166	20	)	)	PUNCT
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cana-860	166	23	-	-	SYM
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cana-860	166	25	.	.	PUNCT
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cana-860	167	2	10	10	NUM
cana-860	167	3	]	]	X
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cana-860	167	5	,	,	PUNCT
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cana-860	167	9	,	,	PUNCT
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cana-860	167	13	number	number	NOUN
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cana-860	167	16	,	,	PUNCT
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cana-860	167	19	(	(	PUNCT
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cana-860	167	21	)	)	PUNCT
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cana-860	167	24	,	,	PUNCT
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cana-860	167	26	-	-	SYM
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cana-860	168	3	]	]	SYM
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cana-860	168	7	,	,	PUNCT
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cana-860	168	9	subdivision	subdivision	NOUN
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cana-860	168	12	,	,	PUNCT
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cana-860	168	19	(	(	PUNCT
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cana-860	168	21	)	)	PUNCT
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