id	sid	tid	token	lemma	pos
cana-1627	1	1	communications	communication	NOUN
cana-1627	1	2	on	on	ADP
cana-1627	1	3	applied	apply	VERB
cana-1627	1	4	nonlinear	nonlinear	ADJ
cana-1627	1	5	analysis	analysis	NOUN
cana-1627	1	6	issn	issn	NOUN
cana-1627	1	7	:	:	PUNCT
cana-1627	1	8	1074	1074	NUM
cana-1627	1	9	-	-	PUNCT
cana-1627	1	10	133x	133x	NUM
cana-1627	1	11	vol	vol	NOUN
cana-1627	1	12	32	32	NUM
cana-1627	1	13	no	no	NOUN
cana-1627	1	14	.	.	NOUN
cana-1627	1	15	1	1	NUM
cana-1627	1	16	(	(	PUNCT
cana-1627	1	17	2025	2025	NUM
cana-1627	1	18	)	)	PUNCT
cana-1627	1	19	148	148	NUM
cana-1627	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1627	1	21	some	some	DET
cana-1627	1	22	results	result	NOUN
cana-1627	1	23	of	of	ADP
cana-1627	1	24	total	total	ADJ
cana-1627	1	25	domatic	domatic	ADJ
cana-1627	1	26	number	number	NOUN
cana-1627	1	27	on	on	ADP
cana-1627	1	28	anti	anti	X
cana-1627	1	29	fuzzy	fuzzy	ADJ
cana-1627	1	30	graph	graph	NOUN
cana-1627	1	31	r.	r.	PROPN
cana-1627	1	32	muthuraj1	muthuraj1	PROPN
cana-1627	1	33	*	*	PROPN
cana-1627	1	34	,	,	PUNCT
cana-1627	1	35	p.	p.	NOUN
cana-1627	1	36	vijayalakshmi2	vijayalakshmi2	NOUN
cana-1627	1	37	and	and	CCONJ
cana-1627	1	38	a.	a.	NOUN
cana-1627	1	39	sasireka3	sasireka3	NOUN
cana-1627	1	40	1research	1research	NUM
cana-1627	1	41	supervisor	supervisor	NOUN
cana-1627	1	42	&	&	CCONJ
cana-1627	1	43	associate	associate	PROPN
cana-1627	1	44	professor	professor	NOUN
cana-1627	1	45	,	,	PUNCT
cana-1627	1	46	pg	pg	PROPN
cana-1627	1	47	&	&	CCONJ
cana-1627	1	48	research	research	PROPN
cana-1627	1	49	department	department	PROPN
cana-1627	1	50	of	of	ADP
cana-1627	1	51	mathematics	mathematics	PROPN
cana-1627	1	52	,	,	PUNCT
cana-1627	1	53	h.h	h.h	PROPN
cana-1627	1	54	.	.	PROPN
cana-1627	1	55	the	the	DET
cana-1627	1	56	rajah	rajah	NOUN
cana-1627	1	57	’s	’s	PART
cana-1627	1	58	college	college	NOUN
cana-1627	1	59	,	,	PUNCT
cana-1627	1	60	pudukkottai	pudukkottai	NOUN
cana-1627	1	61	–	–	PUNCT
cana-1627	1	62	622	622	NUM
cana-1627	1	63	001	001	NUM
cana-1627	1	64	,	,	PUNCT
cana-1627	1	65	tamilnadu	tamilnadu	NOUN
cana-1627	1	66	,	,	PUNCT
cana-1627	1	67	india	india	PROPN
cana-1627	1	68	.	.	PROPN
cana-1627	1	69	2	2	NUM
cana-1627	1	70	research	research	NOUN
cana-1627	1	71	scholar	scholar	NOUN
cana-1627	1	72	,	,	PUNCT
cana-1627	1	73	pg	pg	PROPN
cana-1627	1	74	&	&	CCONJ
cana-1627	1	75	research	research	PROPN
cana-1627	1	76	department	department	PROPN
cana-1627	1	77	of	of	ADP
cana-1627	1	78	mathematics	mathematics	PROPN
cana-1627	1	79	,	,	PUNCT
cana-1627	1	80	h.h	h.h	PROPN
cana-1627	1	81	.	.	PROPN
cana-1627	2	1	the	the	DET
cana-1627	2	2	rajah	rajah	NOUN
cana-1627	2	3	’s	’s	PART
cana-1627	2	4	college	college	NOUN
cana-1627	2	5	,	,	PUNCT
cana-1627	2	6	pudukkottai	pudukkottai	NOUN
cana-1627	2	7	–	–	PUNCT
cana-1627	2	8	622	622	NUM
cana-1627	2	9	001	001	NUM
cana-1627	2	10	,	,	PUNCT
cana-1627	2	11	affiliated	affiliate	VERB
cana-1627	2	12	to	to	ADP
cana-1627	2	13	bharathidhasan	bharathidhasan	PROPN
cana-1627	2	14	university	university	PROPN
cana-1627	2	15	,	,	PUNCT
cana-1627	2	16	tiruchirappalli	tiruchirappalli	PROPN
cana-1627	2	17	,	,	PUNCT
cana-1627	2	18	tamilnadu	tamilnadu	PROPN
cana-1627	2	19	,	,	PUNCT
cana-1627	2	20	india	india	PROPN
cana-1627	2	21	.	.	PUNCT
cana-1627	3	1	assistant	assistant	PROPN
cana-1627	3	2	professor	professor	NOUN
cana-1627	3	3	,	,	PUNCT
cana-1627	3	4	department	department	NOUN
cana-1627	3	5	of	of	ADP
cana-1627	3	6	mathematics	mathematics	PROPN
cana-1627	3	7	,	,	PUNCT
cana-1627	3	8	psna	psna	PROPN
cana-1627	3	9	college	college	PROPN
cana-1627	3	10	of	of	ADP
cana-1627	3	11	engineering	engineering	NOUN
cana-1627	3	12	and	and	CCONJ
cana-1627	3	13	technology	technology	NOUN
cana-1627	3	14	,	,	PUNCT
cana-1627	3	15	dindigul	dindigul	ADV
cana-1627	3	16	–	–	PUNCT
cana-1627	3	17	624	624	NUM
cana-1627	3	18	622	622	NUM
cana-1627	3	19	,	,	PUNCT
cana-1627	3	20	tamilnadu	tamilnadu	ADJ
cana-1627	3	21	,	,	PUNCT
cana-1627	3	22	india	india	PROPN
cana-1627	3	23	.	.	PUNCT
cana-1627	4	1	3assistant	3assistant	NUM
cana-1627	4	2	professor	professor	NOUN
cana-1627	4	3	,	,	PUNCT
cana-1627	4	4	department	department	NOUN
cana-1627	4	5	of	of	ADP
cana-1627	4	6	mathematics	mathematics	PROPN
cana-1627	4	7	,	,	PUNCT
cana-1627	4	8	psna	psna	PROPN
cana-1627	4	9	college	college	PROPN
cana-1627	4	10	of	of	ADP
cana-1627	4	11	engineering	engineering	NOUN
cana-1627	4	12	and	and	CCONJ
cana-1627	4	13	technology	technology	NOUN
cana-1627	4	14	,	,	PUNCT
cana-1627	4	15	dindigul	dindigul	ADV
cana-1627	4	16	–	–	PUNCT
cana-1627	4	17	624	624	NUM
cana-1627	4	18	622	622	NUM
cana-1627	4	19	,	,	PUNCT
cana-1627	4	20	tamilnadu	tamilnadu	ADJ
cana-1627	4	21	,	,	PUNCT
cana-1627	4	22	india	india	PROPN
cana-1627	4	23	.	.	PUNCT
cana-1627	5	1	e	e	X
cana-1627	5	2	-	-	NOUN
cana-1627	5	3	mail	mail	NOUN
cana-1627	5	4	rmr1973@gmail.com	rmr1973@gmail.com	NOUN
cana-1627	5	5	article	article	NOUN
cana-1627	5	6	history	history	NOUN
cana-1627	5	7	:	:	PUNCT
cana-1627	5	8	received	receive	VERB
cana-1627	5	9	:	:	PUNCT
cana-1627	5	10	10	10	NUM
cana-1627	5	11	-	-	SYM
cana-1627	5	12	07	07	NUM
cana-1627	5	13	-	-	PUNCT
cana-1627	5	14	2024	2024	NUM
cana-1627	5	15	revised	revise	VERB
cana-1627	5	16	:	:	PUNCT
cana-1627	5	17	23	23	NUM
cana-1627	5	18	-	-	SYM
cana-1627	5	19	08	08	NUM
cana-1627	5	20	-	-	PUNCT
cana-1627	5	21	2024	2024	NUM
cana-1627	5	22	accepted	accept	VERB
cana-1627	5	23	:	:	PUNCT
cana-1627	5	24	06	06	NUM
cana-1627	5	25	-	-	SYM
cana-1627	5	26	09	09	NUM
cana-1627	5	27	-	-	PUNCT
cana-1627	5	28	2024	2024	NUM
cana-1627	5	29	abstract	abstract	NOUN
cana-1627	5	30	:	:	PUNCT
cana-1627	5	31	let	let	VERB
cana-1627	5	32	ag	ag	PROPN
cana-1627	5	33	=	=	SYM
cana-1627	5	34	(	(	PUNCT
cana-1627	5	35	n	n	CCONJ
cana-1627	5	36	,	,	PUNCT
cana-1627	5	37	a	a	PRON
cana-1627	5	38	,	,	PUNCT
cana-1627	5	39	σ	σ	PROPN
cana-1627	5	40	,	,	PUNCT
cana-1627	5	41	μ	μ	NOUN
cana-1627	5	42	)	)	PUNCT
cana-1627	5	43	be	be	VERB
cana-1627	5	44	an	an	DET
cana-1627	5	45	anti	anti	ADJ
cana-1627	5	46	fuzzy	fuzzy	ADJ
cana-1627	5	47	graph	graph	NOUN
cana-1627	5	48	.	.	PUNCT
cana-1627	6	1	a	a	DET
cana-1627	6	2	partition	partition	NOUN
cana-1627	6	3	dp	dp	NOUN
cana-1627	6	4	=	=	NOUN
cana-1627	6	5	{	{	PUNCT
cana-1627	6	6	d1	d1	PROPN
cana-1627	6	7	,	,	PUNCT
cana-1627	6	8	d2	d2	PROPN
cana-1627	6	9	,	,	PUNCT
cana-1627	6	10	…	…	PUNCT
cana-1627	6	11	..	..	PUNCT
cana-1627	6	12	,	,	PUNCT
cana-1627	6	13	dk	dk	PROPN
cana-1627	6	14	}	}	PUNCT
cana-1627	6	15	of	of	ADP
cana-1627	6	16	n(ag	n(ag	NOUN
cana-1627	6	17	)	)	PUNCT
cana-1627	6	18	is	be	AUX
cana-1627	6	19	referred	refer	VERB
cana-1627	6	20	to	to	ADP
cana-1627	6	21	as	as	ADP
cana-1627	6	22	total	total	ADJ
cana-1627	6	23	domatic	domatic	ADJ
cana-1627	6	24	partition	partition	NOUN
cana-1627	6	25	of	of	ADP
cana-1627	6	26	ag	ag	PROPN
cana-1627	6	27	if	if	SCONJ
cana-1627	6	28	for	for	SCONJ
cana-1627	6	29	each	each	DET
cana-1627	6	30	di	di	NOUN
cana-1627	6	31	is	be	AUX
cana-1627	6	32	a	a	DET
cana-1627	6	33	total	total	ADJ
cana-1627	6	34	dominating	dominating	NOUN
cana-1627	6	35	set	set	NOUN
cana-1627	6	36	of	of	ADP
cana-1627	6	37	anti	anti	X
cana-1627	6	38	fuzzy	fuzzy	ADJ
cana-1627	6	39	graph	graph	NOUN
cana-1627	6	40	ag	ag	PROPN
cana-1627	6	41	and	and	CCONJ
cana-1627	6	42	n(ag)=	n(ag)=	NOUN
cana-1627	6	43	⋃di	⋃di	PROPN
cana-1627	6	44	.	.	PUNCT
cana-1627	7	1	the	the	DET
cana-1627	7	2	maximum	maximum	PROPN
cana-1627	7	3	cardinality	cardinality	NOUN
cana-1627	7	4	taken	take	VERB
cana-1627	7	5	over	over	ADP
cana-1627	7	6	all	all	DET
cana-1627	7	7	maximum	maximum	ADJ
cana-1627	7	8	number	number	NOUN
cana-1627	7	9	of	of	ADP
cana-1627	7	10	classes	class	NOUN
cana-1627	7	11	with	with	ADP
cana-1627	7	12	a	a	DET
cana-1627	7	13	minimal	minimal	ADJ
cana-1627	7	14	total	total	ADJ
cana-1627	7	15	domatic	domatic	ADJ
cana-1627	7	16	partition	partition	NOUN
cana-1627	7	17	of	of	ADP
cana-1627	7	18	ag	ag	PROPN
cana-1627	7	19	is	be	AUX
cana-1627	7	20	called	call	VERB
cana-1627	7	21	the	the	DET
cana-1627	7	22	total	total	ADJ
cana-1627	7	23	domatic	domatic	ADJ
cana-1627	7	24	number	number	NOUN
cana-1627	7	25	of	of	ADP
cana-1627	7	26	ag	ag	PROPN
cana-1627	7	27	and	and	CCONJ
cana-1627	7	28	it	it	PRON
cana-1627	7	29	is	be	AUX
cana-1627	7	30	denoted	denote	VERB
cana-1627	7	31	by	by	ADP
cana-1627	7	32	𝑑𝑡(𝐴𝐺	𝑑𝑡(𝐴𝐺	ADJ
cana-1627	7	33	)	)	PUNCT
cana-1627	7	34	.	.	PUNCT
cana-1627	8	1	the	the	DET
cana-1627	8	2	maximum	maximum	ADJ
cana-1627	8	3	number	number	NOUN
cana-1627	8	4	of	of	ADP
cana-1627	8	5	classes	class	NOUN
cana-1627	8	6	with	with	ADP
cana-1627	8	7	maximum	maximum	ADJ
cana-1627	8	8	fuzzy	fuzzy	ADJ
cana-1627	8	9	cardinality	cardinality	NOUN
cana-1627	8	10	of	of	ADP
cana-1627	8	11	a	a	DET
cana-1627	8	12	partition	partition	NOUN
cana-1627	8	13	di	di	X
cana-1627	8	14	(	(	PUNCT
cana-1627	8	15	ag	ag	PROPN
cana-1627	8	16	)	)	PUNCT
cana-1627	8	17	is	be	AUX
cana-1627	8	18	called	call	VERB
cana-1627	8	19	anti	anti	ADJ
cana-1627	8	20	fuzzy	fuzzy	ADJ
cana-1627	8	21	total	total	ADJ
cana-1627	8	22	domatic	domatic	ADJ
cana-1627	8	23	number	number	NOUN
cana-1627	8	24	of	of	ADP
cana-1627	8	25	anti	anti	X
cana-1627	8	26	fuzzy	fuzzy	ADJ
cana-1627	8	27	graph	graph	NOUN
cana-1627	8	28	ag	ag	PROPN
cana-1627	8	29	and	and	CCONJ
cana-1627	8	30	it	it	PRON
cana-1627	8	31	is	be	AUX
cana-1627	8	32	denoted	denote	VERB
cana-1627	8	33	by	by	ADP
cana-1627	8	34	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADJ
cana-1627	8	35	)	)	PUNCT
cana-1627	8	36	.	.	PUNCT
cana-1627	9	1	in	in	ADP
cana-1627	9	2	this	this	DET
cana-1627	9	3	paper	paper	NOUN
cana-1627	9	4	,	,	PUNCT
cana-1627	9	5	we	we	PRON
cana-1627	9	6	gain	gain	VERB
cana-1627	9	7	some	some	DET
cana-1627	9	8	preferred	preferred	ADJ
cana-1627	9	9	results	result	NOUN
cana-1627	9	10	and	and	CCONJ
cana-1627	9	11	limits	limit	NOUN
cana-1627	9	12	that	that	SCONJ
cana-1627	9	13	referring	refer	VERB
cana-1627	9	14	to	to	ADP
cana-1627	9	15	the	the	DET
cana-1627	9	16	full	full	ADJ
cana-1627	9	17	domatic	domatic	ADJ
cana-1627	9	18	number	number	NOUN
cana-1627	9	19	on	on	ADP
cana-1627	9	20	anti	anti	ADJ
cana-1627	9	21	fuzzy	fuzzy	ADJ
cana-1627	9	22	graph	graph	NOUN
cana-1627	9	23	.	.	PUNCT
cana-1627	10	1	keywords	keyword	NOUN
cana-1627	10	2	:	:	PUNCT
cana-1627	10	3	anti	anti	X
cana-1627	10	4	fuzzy	fuzzy	ADJ
cana-1627	10	5	graph	graph	NOUN
cana-1627	10	6	,	,	PUNCT
cana-1627	10	7	dominating	dominating	NOUN
cana-1627	10	8	set	set	NOUN
cana-1627	10	9	,	,	PUNCT
cana-1627	10	10	total	total	ADJ
cana-1627	10	11	dominating	dominating	NOUN
cana-1627	10	12	set	set	NOUN
cana-1627	10	13	,	,	PUNCT
cana-1627	10	14	vertex	vertex	NOUN
cana-1627	10	15	degree	degree	NOUN
cana-1627	10	16	.	.	PUNCT
cana-1627	11	1	1	1	X
cana-1627	11	2	.	.	X
cana-1627	11	3	introduction	introduction	NOUN
cana-1627	11	4	the	the	DET
cana-1627	11	5	notion	notion	NOUN
cana-1627	11	6	of	of	ADP
cana-1627	11	7	an	an	DET
cana-1627	11	8	anti	anti	ADJ
cana-1627	11	9	-	-	ADJ
cana-1627	11	10	fuzzy	fuzzy	ADJ
cana-1627	11	11	structure	structure	NOUN
cana-1627	11	12	on	on	ADP
cana-1627	11	13	a	a	DET
cana-1627	11	14	graph	graph	NOUN
cana-1627	11	15	was	be	AUX
cana-1627	11	16	familiar	familiar	ADJ
cana-1627	11	17	to	to	ADP
cana-1627	11	18	muhaamad	muhaamad	ADJ
cana-1627	11	19	akram	akram	PROPN
cana-1627	12	1	[	[	X
cana-1627	12	2	1	1	X
cana-1627	12	3	]	]	PUNCT
cana-1627	12	4	owing	owe	VERB
cana-1627	12	5	to	to	ADP
cana-1627	12	6	the	the	DET
cana-1627	12	7	fuzzy	fuzzy	ADJ
cana-1627	12	8	relation	relation	NOUN
cana-1627	12	9	pioneered	pioneer	VERB
cana-1627	12	10	by	by	ADP
cana-1627	12	11	zadeh	zadeh	PROPN
cana-1627	13	1	[	[	X
cana-1627	13	2	11	11	NUM
cana-1627	13	3	]	]	PUNCT
cana-1627	13	4	.	.	PUNCT
cana-1627	14	1	e.	e.	PROPN
cana-1627	14	2	j.	j.	PROPN
cana-1627	14	3	cockayne	cockayne	PROPN
cana-1627	14	4	,	,	PUNCT
cana-1627	14	5	s.	s.	PROPN
cana-1627	14	6	t.	t.	PROPN
cana-1627	14	7	hedetniemi[2	hedetniemi[2	PROPN
cana-1627	14	8	]	]	PUNCT
cana-1627	14	9	delivered	deliver	VERB
cana-1627	14	10	the	the	DET
cana-1627	14	11	idea	idea	NOUN
cana-1627	14	12	of	of	ADP
cana-1627	14	13	domatic	domatic	ADJ
cana-1627	14	14	number	number	NOUN
cana-1627	14	15	of	of	ADP
cana-1627	14	16	a	a	DET
cana-1627	14	17	graph	graph	NOUN
cana-1627	14	18	.	.	PUNCT
cana-1627	15	1	the	the	DET
cana-1627	15	2	idea	idea	NOUN
cana-1627	15	3	of	of	ADP
cana-1627	15	4	a	a	DET
cana-1627	15	5	graph	graph	NOUN
cana-1627	15	6	's	's	PART
cana-1627	15	7	anti	anti	ADJ
cana-1627	15	8	domatic	domatic	ADJ
cana-1627	15	9	number	number	NOUN
cana-1627	15	10	was	be	AUX
cana-1627	15	11	first	first	ADV
cana-1627	15	12	developed	develop	VERB
cana-1627	15	13	by	by	ADP
cana-1627	15	14	bohdan	bohdan	PROPN
cana-1627	15	15	zelinka	zelinka	PROPN
cana-1627	16	1	[	[	X
cana-1627	16	2	13	13	NUM
cana-1627	16	3	]	]	PUNCT
cana-1627	16	4	.	.	PUNCT
cana-1627	17	1	domatic	domatic	ADJ
cana-1627	17	2	number	number	NOUN
cana-1627	17	3	and	and	CCONJ
cana-1627	17	4	total	total	ADJ
cana-1627	17	5	domatic	domatic	ADJ
cana-1627	17	6	number	number	NOUN
cana-1627	17	7	of	of	ADP
cana-1627	17	8	complete	complete	ADJ
cana-1627	17	9	uniform	uniform	ADJ
cana-1627	17	10	hypergraphs	hypergraph	NOUN
cana-1627	17	11	and	and	CCONJ
cana-1627	17	12	complete	complete	ADJ
cana-1627	17	13	bipartite	bipartite	PROPN
cana-1627	17	14	uniform	uniform	ADJ
cana-1627	17	15	hypergraphs	hypergraph	NOUN
cana-1627	17	16	were	be	AUX
cana-1627	17	17	computed	compute	VERB
cana-1627	17	18	by	by	ADP
cana-1627	17	19	dash	dash	NOUN
cana-1627	17	20	,	,	PUNCT
cana-1627	17	21	s.p	s.p	PROPN
cana-1627	17	22	.	.	PUNCT
cana-1627	18	1	[	[	X
cana-1627	18	2	3	3	NUM
cana-1627	18	3	]	]	PUNCT
cana-1627	18	4	.	.	PUNCT
cana-1627	19	1	the	the	DET
cana-1627	19	2	generalities	generality	NOUN
cana-1627	19	3	of	of	ADP
cana-1627	19	4	certain	certain	ADJ
cana-1627	19	5	different	different	ADJ
cana-1627	19	6	forms	form	NOUN
cana-1627	19	7	of	of	ADP
cana-1627	19	8	anti	anti	ADJ
cana-1627	19	9	-	-	ADJ
cana-1627	19	10	fuzzy	fuzzy	ADJ
cana-1627	19	11	graphs	graph	NOUN
cana-1627	19	12	were	be	AUX
cana-1627	19	13	presented	present	VERB
cana-1627	19	14	by	by	ADP
cana-1627	19	15	r.	r.	PROPN
cana-1627	19	16	muthuraj	muthuraj	PROPN
cana-1627	19	17	and	and	CCONJ
cana-1627	19	18	a.	a.	NOUN
cana-1627	19	19	sasireka	sasireka	PROPN
cana-1627	20	1	[	[	X
cana-1627	20	2	6	6	NUM
cana-1627	20	3	,	,	PUNCT
cana-1627	20	4	7&8	7&8	NUM
cana-1627	20	5	]	]	PUNCT
cana-1627	20	6	who	who	PRON
cana-1627	20	7	also	also	ADV
cana-1627	20	8	determined	determine	VERB
cana-1627	20	9	the	the	DET
cana-1627	20	10	domination	domination	NOUN
cana-1627	20	11	parameters	parameter	NOUN
cana-1627	20	12	on	on	ADP
cana-1627	20	13	anti	anti	ADJ
cana-1627	20	14	-	-	ADJ
cana-1627	20	15	fuzzy	fuzzy	ADJ
cana-1627	20	16	graphs	graph	NOUN
cana-1627	20	17	.	.	PUNCT
cana-1627	21	1	additionally	additionally	ADV
cana-1627	21	2	,	,	PUNCT
cana-1627	21	3	they	they	PRON
cana-1627	21	4	invented	invent	VERB
cana-1627	21	5	the	the	DET
cana-1627	21	6	concept	concept	NOUN
cana-1627	21	7	of	of	ADP
cana-1627	21	8	the	the	DET
cana-1627	21	9	anti	anti	ADJ
cana-1627	21	10	-	-	ADJ
cana-1627	21	11	fuzzy	fuzzy	ADJ
cana-1627	21	12	graph	graph	NOUN
cana-1627	21	13	's	's	PART
cana-1627	21	14	total	total	ADJ
cana-1627	21	15	domination	domination	NOUN
cana-1627	21	16	number	number	NOUN
cana-1627	21	17	and	and	CCONJ
cana-1627	21	18	established	establish	VERB
cana-1627	21	19	boundaries	boundary	NOUN
cana-1627	21	20	for	for	ADP
cana-1627	21	21	it	it	PRON
cana-1627	21	22	.	.	PUNCT
cana-1627	22	1	in	in	ADP
cana-1627	22	2	this	this	DET
cana-1627	22	3	paper	paper	NOUN
cana-1627	22	4	,	,	PUNCT
cana-1627	22	5	we	we	PRON
cana-1627	22	6	define	define	VERB
cana-1627	22	7	the	the	DET
cana-1627	22	8	definition	definition	NOUN
cana-1627	22	9	of	of	ADP
cana-1627	22	10	total	total	ADJ
cana-1627	22	11	domatic	domatic	ADJ
cana-1627	22	12	number	number	NOUN
cana-1627	22	13	and	and	CCONJ
cana-1627	22	14	partial	partial	ADJ
cana-1627	22	15	total	total	ADJ
cana-1627	22	16	domatic	domatic	ADJ
cana-1627	22	17	number	number	NOUN
cana-1627	22	18	on	on	ADP
cana-1627	22	19	anti	anti	X
cana-1627	22	20	fuzzy	fuzzy	ADJ
cana-1627	22	21	graph	graph	NOUN
cana-1627	22	22	ag	ag	PROPN
cana-1627	22	23	also	also	ADV
cana-1627	22	24	extant	extant	VERB
cana-1627	22	25	some	some	DET
cana-1627	22	26	general	general	ADJ
cana-1627	22	27	bounds	bound	NOUN
cana-1627	22	28	and	and	CCONJ
cana-1627	22	29	results	result	NOUN
cana-1627	22	30	that	that	PRON
cana-1627	22	31	relate	relate	VERB
cana-1627	22	32	the	the	DET
cana-1627	22	33	total	total	ADJ
cana-1627	22	34	domatic	domatic	ADJ
cana-1627	22	35	number	number	NOUN
cana-1627	22	36	of	of	ADP
cana-1627	22	37	ag	ag	PROPN
cana-1627	22	38	.	.	PROPN
cana-1627	23	1	note	note	VERB
cana-1627	23	2	the	the	DET
cana-1627	23	3	total	total	ADJ
cana-1627	23	4	dominating	dominating	NOUN
cana-1627	23	5	set	set	NOUN
cana-1627	23	6	d	d	PROPN
cana-1627	23	7	of	of	ADP
cana-1627	23	8	ag	ag	PROPN
cana-1627	23	9	contained	contain	VERB
cana-1627	23	10	each	each	DET
cana-1627	23	11	support	support	NOUN
cana-1627	23	12	node	node	NOUN
cana-1627	23	13	in	in	ADP
cana-1627	23	14	ag	ag	PROPN
cana-1627	23	15	.	.	PUNCT
cana-1627	24	1	in	in	ADP
cana-1627	24	2	both	both	CCONJ
cana-1627	24	3	n\d	n\d	PROPN
cana-1627	24	4	and	and	CCONJ
cana-1627	24	5	d	d	X
cana-1627	24	6	,	,	PUNCT
cana-1627	24	7	it	it	PRON
cana-1627	24	8	able	able	ADJ
cana-1627	24	9	to	to	PART
cana-1627	24	10	dominate	dominate	VERB
cana-1627	24	11	many	many	ADJ
cana-1627	24	12	nodes	node	NOUN
cana-1627	24	13	.	.	PUNCT
cana-1627	25	1	communications	communication	NOUN
cana-1627	25	2	on	on	ADP
cana-1627	25	3	applied	apply	VERB
cana-1627	25	4	nonlinear	nonlinear	ADJ
cana-1627	25	5	analysis	analysis	NOUN
cana-1627	25	6	issn	issn	NOUN
cana-1627	25	7	:	:	PUNCT
cana-1627	25	8	1074	1074	NUM
cana-1627	25	9	-	-	PUNCT
cana-1627	25	10	133x	133x	NUM
cana-1627	25	11	vol	vol	NOUN
cana-1627	25	12	32	32	NUM
cana-1627	25	13	no	no	NOUN
cana-1627	25	14	.	.	NOUN
cana-1627	25	15	1	1	NUM
cana-1627	25	16	(	(	PUNCT
cana-1627	25	17	2025	2025	NUM
cana-1627	25	18	)	)	PUNCT
cana-1627	25	19	149	149	NUM
cana-1627	25	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1627	25	21	2	2	NUM
cana-1627	25	22	.	.	PUNCT
cana-1627	26	1	some	some	DET
cana-1627	26	2	results	result	NOUN
cana-1627	26	3	of	of	ADP
cana-1627	26	4	total	total	ADJ
cana-1627	26	5	domatic	domatic	ADJ
cana-1627	26	6	number	number	NOUN
cana-1627	26	7	on	on	ADP
cana-1627	26	8	anti	anti	X
cana-1627	26	9	fuzzy	fuzzy	ADJ
cana-1627	26	10	graph	graph	NOUN
cana-1627	26	11	2.1	2.1	NUM
cana-1627	26	12	definition	definition	NOUN
cana-1627	26	13	let	let	VERB
cana-1627	26	14	ag	ag	PROPN
cana-1627	26	15	=	=	SYM
cana-1627	26	16	(	(	PUNCT
cana-1627	26	17	n	n	CCONJ
cana-1627	26	18	,	,	PUNCT
cana-1627	26	19	a	a	PRON
cana-1627	26	20	,	,	PUNCT
cana-1627	26	21	σ	σ	PROPN
cana-1627	26	22	,	,	PUNCT
cana-1627	26	23	μ	μ	NOUN
cana-1627	26	24	)	)	PUNCT
cana-1627	26	25	be	be	VERB
cana-1627	26	26	an	an	DET
cana-1627	26	27	anti	anti	ADJ
cana-1627	26	28	fuzzy	fuzzy	ADJ
cana-1627	26	29	graph	graph	NOUN
cana-1627	26	30	.	.	PUNCT
cana-1627	27	1	a	a	DET
cana-1627	27	2	partition	partition	NOUN
cana-1627	27	3	dtp	dtp	NOUN
cana-1627	27	4	=	=	SYM
cana-1627	27	5	{	{	PUNCT
cana-1627	27	6	td1	td1	PROPN
cana-1627	27	7	,	,	PUNCT
cana-1627	27	8	td2	td2	PROPN
cana-1627	27	9	,	,	PUNCT
cana-1627	27	10	…	…	PUNCT
cana-1627	27	11	.	.	NUM
cana-1627	27	12	,	,	PUNCT
cana-1627	27	13	tdk	tdk	NOUN
cana-1627	27	14	}	}	PUNCT
cana-1627	27	15	of	of	ADP
cana-1627	27	16	n(ag	n(ag	NOUN
cana-1627	27	17	)	)	PUNCT
cana-1627	27	18	is	be	AUX
cana-1627	27	19	called	call	VERB
cana-1627	27	20	total	total	ADJ
cana-1627	27	21	domatic	domatic	ADJ
cana-1627	27	22	partition	partition	NOUN
cana-1627	27	23	of	of	ADP
cana-1627	27	24	ag	ag	PROPN
cana-1627	27	25	if	if	SCONJ
cana-1627	27	26	for	for	SCONJ
cana-1627	27	27	each	each	DET
cana-1627	27	28	tdi	tdi	PROPN
cana-1627	27	29	is	be	AUX
cana-1627	27	30	a	a	DET
cana-1627	27	31	total	total	ADJ
cana-1627	27	32	dominating	dominating	NOUN
cana-1627	27	33	set	set	NOUN
cana-1627	28	1	[	[	X
cana-1627	28	2	tds	tds	X
cana-1627	28	3	]	]	PUNCT
cana-1627	28	4	of	of	ADP
cana-1627	28	5	anti	anti	X
cana-1627	28	6	fuzzy	fuzzy	ADJ
cana-1627	28	7	graph	graph	NOUN
cana-1627	28	8	ag	ag	PROPN
cana-1627	28	9	and	and	CCONJ
cana-1627	28	10	n(ag	n(ag	NOUN
cana-1627	28	11	)	)	PUNCT
cana-1627	28	12	=	=	SYM
cana-1627	28	13	⋃tdi	⋃tdi	PROPN
cana-1627	28	14	.	.	PUNCT
cana-1627	29	1	the	the	DET
cana-1627	29	2	maximum	maximum	PROPN
cana-1627	29	3	cardinality	cardinality	NOUN
cana-1627	29	4	taken	take	VERB
cana-1627	29	5	over	over	ADP
cana-1627	29	6	all	all	DET
cana-1627	29	7	maximum	maximum	ADJ
cana-1627	29	8	number	number	NOUN
cana-1627	29	9	of	of	ADP
cana-1627	29	10	classes	class	NOUN
cana-1627	29	11	with	with	ADP
cana-1627	29	12	a	a	DET
cana-1627	29	13	minimal	minimal	ADJ
cana-1627	29	14	total	total	ADJ
cana-1627	29	15	domatic	domatic	ADJ
cana-1627	29	16	partition	partition	NOUN
cana-1627	29	17	of	of	ADP
cana-1627	29	18	ag	ag	PROPN
cana-1627	29	19	is	be	AUX
cana-1627	29	20	called	call	VERB
cana-1627	29	21	the	the	DET
cana-1627	29	22	total	total	ADJ
cana-1627	29	23	domatic	domatic	ADJ
cana-1627	29	24	number	number	NOUN
cana-1627	30	1	[	[	X
cana-1627	30	2	tdtn	tdtn	NOUN
cana-1627	30	3	]	]	PUNCT
cana-1627	30	4	of	of	ADP
cana-1627	30	5	ag	ag	PROPN
cana-1627	30	6	and	and	CCONJ
cana-1627	30	7	it	it	PRON
cana-1627	30	8	is	be	AUX
cana-1627	30	9	denoted	denote	VERB
cana-1627	30	10	by	by	ADP
cana-1627	30	11	𝑑𝑡(𝐴𝐺	𝑑𝑡(𝐴𝐺	ADJ
cana-1627	30	12	)	)	PUNCT
cana-1627	30	13	.	.	PUNCT
cana-1627	31	1	the	the	DET
cana-1627	31	2	maximum	maximum	ADJ
cana-1627	31	3	number	number	NOUN
cana-1627	31	4	of	of	ADP
cana-1627	31	5	classes	class	NOUN
cana-1627	31	6	with	with	ADP
cana-1627	31	7	maximum	maximum	ADJ
cana-1627	31	8	fuzzy	fuzzy	ADJ
cana-1627	31	9	cardinality	cardinality	NOUN
cana-1627	31	10	of	of	ADP
cana-1627	31	11	a	a	DET
cana-1627	31	12	partition	partition	NOUN
cana-1627	31	13	tdi	tdi	PROPN
cana-1627	31	14	(	(	PUNCT
cana-1627	31	15	ag	ag	PROPN
cana-1627	31	16	)	)	PUNCT
cana-1627	31	17	is	be	AUX
cana-1627	31	18	called	call	VERB
cana-1627	31	19	anti	anti	ADJ
cana-1627	31	20	fuzzy	fuzzy	ADJ
cana-1627	31	21	total	total	ADJ
cana-1627	31	22	domatic	domatic	ADJ
cana-1627	31	23	number	number	NOUN
cana-1627	31	24	of	of	ADP
cana-1627	31	25	anti	anti	X
cana-1627	31	26	fuzzy	fuzzy	ADJ
cana-1627	31	27	graph	graph	NOUN
cana-1627	31	28	and	and	CCONJ
cana-1627	31	29	it	it	PRON
cana-1627	31	30	is	be	AUX
cana-1627	31	31	denoted	denote	VERB
cana-1627	31	32	by	by	ADP
cana-1627	31	33	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADJ
cana-1627	31	34	)	)	PUNCT
cana-1627	31	35	.	.	PUNCT
cana-1627	32	1	2.2	2.2	NUM
cana-1627	32	2	example	example	NOUN
cana-1627	32	3	figure	figure	NOUN
cana-1627	32	4	.	.	PUNCT
cana-1627	33	1	1	1	X
cana-1627	33	2	.	.	X
cana-1627	33	3	anti	anti	X
cana-1627	33	4	fuzzy	fuzzy	ADJ
cana-1627	33	5	graph	graph	NOUN
cana-1627	33	6	ag	ag	PROPN
cana-1627	33	7	from	from	ADP
cana-1627	33	8	figure	figure	NOUN
cana-1627	33	9	1	1	NUM
cana-1627	33	10	,	,	PUNCT
cana-1627	33	11	the	the	DET
cana-1627	33	12	total	total	ADJ
cana-1627	33	13	dominating	dominating	NOUN
cana-1627	33	14	sets	set	NOUN
cana-1627	33	15	are	be	AUX
cana-1627	33	16	td1	td1	NOUN
cana-1627	33	17	=	=	SYM
cana-1627	33	18	{	{	PUNCT
cana-1627	33	19	u2	u2	PROPN
cana-1627	33	20	,	,	PUNCT
cana-1627	33	21	u5	u5	PROPN
cana-1627	33	22	}	}	PUNCT
cana-1627	33	23	=	=	PUNCT
cana-1627	33	24	{	{	PUNCT
cana-1627	33	25	0.4	0.4	NUM
cana-1627	33	26	,	,	PUNCT
cana-1627	33	27	0.6	0.6	NUM
cana-1627	33	28	}	}	PUNCT
cana-1627	33	29	=	=	SYM
cana-1627	33	30	1	1	NUM
cana-1627	33	31	td2	td2	NOUN
cana-1627	33	32	=	=	SYM
cana-1627	33	33	{	{	PUNCT
cana-1627	33	34	u3	u3	PROPN
cana-1627	33	35	,	,	PUNCT
cana-1627	33	36	u4	u4	PROPN
cana-1627	33	37	}	}	PUNCT
cana-1627	33	38	=	=	PUNCT
cana-1627	33	39	{	{	PUNCT
cana-1627	33	40	0.7	0.7	NUM
cana-1627	33	41	,	,	PUNCT
cana-1627	33	42	0.3	0.3	NUM
cana-1627	33	43	}	}	PUNCT
cana-1627	33	44	=	=	SYM
cana-1627	33	45	1	1	NUM
cana-1627	33	46	td3	td3	NOUN
cana-1627	33	47	=	=	SYM
cana-1627	33	48	{	{	PUNCT
cana-1627	33	49	u1	u1	NOUN
cana-1627	33	50	,	,	PUNCT
cana-1627	33	51	u6	u6	NOUN
cana-1627	33	52	}	}	PUNCT
cana-1627	33	53	=	=	PUNCT
cana-1627	33	54	{	{	PUNCT
cana-1627	33	55	0.2	0.2	NUM
cana-1627	33	56	,	,	PUNCT
cana-1627	33	57	0.5	0.5	NUM
cana-1627	33	58	}	}	PUNCT
cana-1627	33	59	=	=	NOUN
cana-1627	33	60	0.7	0.7	NUM
cana-1627	33	61	tdp	tdp	NOUN
cana-1627	33	62	=	=	SYM
cana-1627	33	63	{	{	PUNCT
cana-1627	33	64	td1	td1	PROPN
cana-1627	33	65	,	,	PUNCT
cana-1627	33	66	td2	td2	PROPN
cana-1627	33	67	,	,	PUNCT
cana-1627	33	68	td3	td3	NOUN
cana-1627	33	69	}	}	PUNCT
cana-1627	33	70	tdt	tdt	PROPN
cana-1627	33	71	number	number	NOUN
cana-1627	33	72	of	of	ADP
cana-1627	33	73	anti	anti	X
cana-1627	33	74	fuzzy	fuzzy	ADJ
cana-1627	33	75	graph	graph	NOUN
cana-1627	33	76	ag	ag	PROPN
cana-1627	33	77	,	,	PUNCT
cana-1627	33	78	𝑑𝑡(𝐺𝐴	𝑑𝑡(𝐺𝐴	ADJ
cana-1627	33	79	)	)	PUNCT
cana-1627	33	80	=	=	SYM
cana-1627	33	81	3	3	NUM
cana-1627	33	82	anti	anti	X
cana-1627	33	83	fuzzy	fuzzy	ADJ
cana-1627	33	84	total	total	ADJ
cana-1627	33	85	domatic	domatic	ADJ
cana-1627	33	86	number	number	NOUN
cana-1627	33	87	of	of	ADP
cana-1627	33	88	anti	anti	X
cana-1627	33	89	fuzzy	fuzzy	ADJ
cana-1627	33	90	graph	graph	NOUN
cana-1627	33	91	ag	ag	PROPN
cana-1627	33	92	,	,	PUNCT
cana-1627	33	93	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	33	94	)	)	PUNCT
cana-1627	33	95	=	=	SYM
cana-1627	33	96	max	max	PROPN
cana-1627	33	97	{	{	PUNCT
cana-1627	33	98	1	1	NUM
cana-1627	33	99	,	,	PUNCT
cana-1627	33	100	1	1	NUM
cana-1627	33	101	,	,	PUNCT
cana-1627	33	102	0.7	0.7	NUM
cana-1627	33	103	}	}	PUNCT
cana-1627	33	104	=	=	SYM
cana-1627	33	105	1	1	NUM
cana-1627	33	106	2.3	2.3	NUM
cana-1627	33	107	definition	definition	NOUN
cana-1627	33	108	let	let	VERB
cana-1627	33	109	ag	ag	PROPN
cana-1627	33	110	=	=	SYM
cana-1627	33	111	(	(	PUNCT
cana-1627	33	112	n	n	CCONJ
cana-1627	33	113	,	,	PUNCT
cana-1627	33	114	a	a	PRON
cana-1627	33	115	,	,	PUNCT
cana-1627	33	116	σ	σ	PROPN
cana-1627	33	117	,	,	PUNCT
cana-1627	33	118	μ	μ	NOUN
cana-1627	33	119	)	)	PUNCT
cana-1627	33	120	be	be	VERB
cana-1627	33	121	an	an	DET
cana-1627	33	122	anti	anti	ADJ
cana-1627	33	123	fuzzy	fuzzy	ADJ
cana-1627	33	124	graph	graph	NOUN
cana-1627	33	125	.	.	PUNCT
cana-1627	34	1	a	a	DET
cana-1627	34	2	partition	partition	NOUN
cana-1627	34	3	tdp	tdp	NOUN
cana-1627	34	4	=	=	SYM
cana-1627	34	5	{	{	PUNCT
cana-1627	34	6	td1	td1	PROPN
cana-1627	34	7	,	,	PUNCT
cana-1627	34	8	td2	td2	PROPN
cana-1627	34	9	,	,	PUNCT
cana-1627	34	10	…	…	PUNCT
cana-1627	34	11	.	.	NUM
cana-1627	34	12	,	,	PUNCT
cana-1627	34	13	tdk	tdk	NOUN
cana-1627	34	14	}	}	PUNCT
cana-1627	34	15	of	of	ADP
cana-1627	34	16	n(ag	n(ag	NOUN
cana-1627	34	17	)	)	PUNCT
cana-1627	34	18	is	be	AUX
cana-1627	34	19	called	call	VERB
cana-1627	34	20	partial	partial	ADJ
cana-1627	34	21	total	total	ADJ
cana-1627	34	22	domatic	domatic	ADJ
cana-1627	34	23	partition	partition	NOUN
cana-1627	34	24	of	of	ADP
cana-1627	34	25	ag	ag	PROPN
cana-1627	34	26	if	if	SCONJ
cana-1627	34	27	for	for	SCONJ
cana-1627	34	28	every	every	DET
cana-1627	34	29	tdi	tdi	PROPN
cana-1627	34	30	is	be	AUX
cana-1627	34	31	a	a	DET
cana-1627	34	32	total	total	ADJ
cana-1627	34	33	dominating	dominating	NOUN
cana-1627	34	34	set	set	NOUN
cana-1627	34	35	of	of	ADP
cana-1627	34	36	anti	anti	X
cana-1627	34	37	fuzzy	fuzzy	ADJ
cana-1627	34	38	graph	graph	NOUN
cana-1627	34	39	ag	ag	PROPN
cana-1627	34	40	and	and	CCONJ
cana-1627	34	41	at	at	ADP
cana-1627	34	42	the	the	DET
cana-1627	34	43	minimum	minimum	NOUN
cana-1627	34	44	of	of	ADP
cana-1627	34	45	single	single	ADJ
cana-1627	34	46	node	node	NOUN
cana-1627	34	47	does	do	AUX
cana-1627	34	48	not	not	PART
cana-1627	34	49	in	in	ADP
cana-1627	34	50	any	any	DET
cana-1627	34	51	one	one	NUM
cana-1627	34	52	of	of	ADP
cana-1627	34	53	tdi	tdi	PROPN
cana-1627	34	54	and	and	CCONJ
cana-1627	34	55	all	all	DET
cana-1627	34	56	tdi	tdi	PROPN
cana-1627	34	57	’s	’s	PART
cana-1627	34	58	are	be	AUX
cana-1627	34	59	minimal	minimal	ADJ
cana-1627	34	60	total	total	ADJ
cana-1627	34	61	dominating	dominating	NOUN
cana-1627	34	62	sets	set	NOUN
cana-1627	34	63	.	.	PUNCT
cana-1627	35	1	the	the	DET
cana-1627	35	2	maximum	maximum	ADJ
cana-1627	35	3	fuzzy	fuzzy	ADJ
cana-1627	35	4	cardinality	cardinality	NOUN
cana-1627	35	5	taken	take	VERB
cana-1627	35	6	over	over	ADP
cana-1627	35	7	all	all	DET
cana-1627	35	8	maximum	maximum	ADJ
cana-1627	35	9	number	number	NOUN
cana-1627	35	10	of	of	ADP
cana-1627	35	11	classes	class	NOUN
cana-1627	35	12	with	with	ADP
cana-1627	35	13	minimal	minimal	ADJ
cana-1627	35	14	partial	partial	ADJ
cana-1627	35	15	total	total	ADJ
cana-1627	35	16	domatic	domatic	ADJ
cana-1627	35	17	partition	partition	NOUN
cana-1627	35	18	of	of	ADP
cana-1627	35	19	ag	ag	PROPN
cana-1627	35	20	is	be	AUX
cana-1627	35	21	called	call	VERB
cana-1627	35	22	the	the	DET
cana-1627	35	23	partial	partial	ADJ
cana-1627	35	24	total	total	ADJ
cana-1627	35	25	domatic	domatic	ADJ
cana-1627	35	26	number	number	NOUN
cana-1627	35	27	[	[	X
cana-1627	35	28	ptdtn	ptdtn	X
cana-1627	35	29	]	]	PUNCT
cana-1627	35	30	of	of	ADP
cana-1627	35	31	ag	ag	PROPN
cana-1627	35	32	and	and	CCONJ
cana-1627	35	33	it	it	PRON
cana-1627	35	34	is	be	AUX
cana-1627	35	35	denoted	denote	VERB
cana-1627	35	36	by	by	ADP
cana-1627	35	37	𝑑𝑝𝑡(𝐴𝐺	𝑑𝑝𝑡(𝐴𝐺	NUM
cana-1627	35	38	)	)	PUNCT
cana-1627	35	39	.	.	PUNCT
cana-1627	36	1	the	the	DET
cana-1627	36	2	maximum	maximum	ADJ
cana-1627	36	3	number	number	NOUN
cana-1627	36	4	of	of	ADP
cana-1627	36	5	classes	class	NOUN
cana-1627	36	6	with	with	ADP
cana-1627	36	7	maximum	maximum	ADJ
cana-1627	36	8	fuzzy	fuzzy	ADJ
cana-1627	36	9	cardinality	cardinality	NOUN
cana-1627	36	10	of	of	ADP
cana-1627	36	11	a	a	DET
cana-1627	36	12	partition	partition	NOUN
cana-1627	36	13	tdi	tdi	PROPN
cana-1627	36	14	(	(	PUNCT
cana-1627	36	15	𝐴𝐺	𝐴𝐺	PROPN
cana-1627	36	16	)	)	PUNCT
cana-1627	36	17	is	be	AUX
cana-1627	36	18	called	call	VERB
cana-1627	36	19	the	the	DET
cana-1627	36	20	anti	anti	ADJ
cana-1627	36	21	fuzzy	fuzzy	ADJ
cana-1627	36	22	partial	partial	ADJ
cana-1627	36	23	total	total	ADJ
cana-1627	36	24	domatic	domatic	ADJ
cana-1627	36	25	number	number	NOUN
cana-1627	36	26	of	of	ADP
cana-1627	36	27	ag	ag	PROPN
cana-1627	36	28	and	and	CCONJ
cana-1627	36	29	it	it	PRON
cana-1627	36	30	is	be	AUX
cana-1627	36	31	denoted	denote	VERB
cana-1627	36	32	by	by	ADP
cana-1627	36	33	𝑑𝑓𝑝𝑡(𝐴𝐺	𝑑𝑓𝑝𝑡(𝐴𝐺	NOUN
cana-1627	36	34	)	)	PUNCT
cana-1627	36	35	.	.	PUNCT
cana-1627	37	1	communications	communication	NOUN
cana-1627	37	2	on	on	ADP
cana-1627	37	3	applied	apply	VERB
cana-1627	37	4	nonlinear	nonlinear	ADJ
cana-1627	37	5	analysis	analysis	NOUN
cana-1627	37	6	issn	issn	NOUN
cana-1627	37	7	:	:	PUNCT
cana-1627	37	8	1074	1074	NUM
cana-1627	37	9	-	-	PUNCT
cana-1627	37	10	133x	133x	NUM
cana-1627	37	11	vol	vol	NOUN
cana-1627	37	12	32	32	NUM
cana-1627	37	13	no	no	NOUN
cana-1627	37	14	.	.	NOUN
cana-1627	37	15	1	1	NUM
cana-1627	37	16	(	(	PUNCT
cana-1627	37	17	2025	2025	NUM
cana-1627	37	18	)	)	PUNCT
cana-1627	37	19	150	150	NUM
cana-1627	37	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1627	37	21	2.4	2.4	NUM
cana-1627	37	22	example	example	NOUN
cana-1627	37	23	figure	figure	NOUN
cana-1627	37	24	.	.	PUNCT
cana-1627	38	1	2	2	X
cana-1627	38	2	.	.	X
cana-1627	38	3	anti	anti	X
cana-1627	38	4	fuzzy	fuzzy	ADJ
cana-1627	38	5	graph	graph	NOUN
cana-1627	38	6	ag	ag	PROPN
cana-1627	38	7	from	from	ADP
cana-1627	38	8	figure	figure	NOUN
cana-1627	38	9	2	2	NUM
cana-1627	38	10	,	,	PUNCT
cana-1627	38	11	the	the	DET
cana-1627	38	12	total	total	ADJ
cana-1627	38	13	dominating	dominating	NOUN
cana-1627	38	14	set	set	NOUN
cana-1627	38	15	is	be	AUX
cana-1627	38	16	td1	td1	NOUN
cana-1627	38	17	=	=	SYM
cana-1627	38	18	{	{	PUNCT
cana-1627	38	19	u1	u1	NOUN
cana-1627	38	20	,	,	PUNCT
cana-1627	38	21	u3	u3	NOUN
cana-1627	38	22	}	}	PUNCT
cana-1627	38	23	=	=	PUNCT
cana-1627	38	24	{	{	PUNCT
cana-1627	38	25	0.5	0.5	NUM
cana-1627	38	26	,	,	PUNCT
cana-1627	38	27	0.7	0.7	NUM
cana-1627	38	28	}	}	PUNCT
cana-1627	38	29	dfpt	dfpt	NOUN
cana-1627	38	30	(	(	PUNCT
cana-1627	38	31	ag	ag	PROPN
cana-1627	38	32	)	)	PUNCT
cana-1627	38	33	=	=	PRON
cana-1627	38	34	{	{	PUNCT
cana-1627	38	35	0.5	0.5	NUM
cana-1627	38	36	,	,	PUNCT
cana-1627	38	37	0.7	0.7	NUM
cana-1627	38	38	}	}	PUNCT
cana-1627	38	39	=	=	SYM
cana-1627	38	40	1.2	1.2	NUM
cana-1627	38	41	for	for	ADP
cana-1627	38	42	finding	find	VERB
cana-1627	38	43	td2	td2	PROPN
cana-1627	38	44	,	,	PUNCT
cana-1627	38	45	u5	u5	PROPN
cana-1627	38	46	is	be	AUX
cana-1627	38	47	isolated	isolate	VERB
cana-1627	38	48	node	node	NOUN
cana-1627	38	49	.	.	PUNCT
cana-1627	39	1	so	so	ADV
cana-1627	39	2	,	,	PUNCT
cana-1627	39	3	it	it	PRON
cana-1627	39	4	dominates	dominate	VERB
cana-1627	39	5	itself	itself	PRON
cana-1627	39	6	and	and	CCONJ
cana-1627	39	7	˂td2˃	˂td2˃	NOUN
cana-1627	39	8	is	be	AUX
cana-1627	39	9	not	not	PART
cana-1627	39	10	a	a	DET
cana-1627	39	11	total	total	ADJ
cana-1627	39	12	dominating	dominating	NOUN
cana-1627	39	13	set	set	NOUN
cana-1627	39	14	.	.	PUNCT
cana-1627	40	1	since	since	SCONJ
cana-1627	40	2	,	,	PUNCT
cana-1627	40	3	td2	td2	PROPN
cana-1627	40	4	does	do	AUX
cana-1627	40	5	not	not	PART
cana-1627	40	6	exist	exist	VERB
cana-1627	40	7	.	.	PUNCT
cana-1627	41	1	therefore	therefore	ADV
cana-1627	41	2	tdp	tdp	VERB
cana-1627	41	3	=	=	SYM
cana-1627	41	4	{	{	PUNCT
cana-1627	41	5	td1	td1	NOUN
cana-1627	41	6	}	}	PUNCT
cana-1627	41	7	partial	partial	ADJ
cana-1627	41	8	total	total	ADJ
cana-1627	41	9	domatic	domatic	ADJ
cana-1627	41	10	number	number	NOUN
cana-1627	41	11	of	of	ADP
cana-1627	41	12	ag	ag	PROPN
cana-1627	41	13	domatic	domatic	ADJ
cana-1627	41	14	number	number	NOUN
cana-1627	41	15	of	of	ADP
cana-1627	41	16	ag	ag	PROPN
cana-1627	41	17	,	,	PUNCT
cana-1627	41	18	𝑑𝑝𝑡(𝐴𝐺	𝑑𝑝𝑡(𝐴𝐺	NUM
cana-1627	41	19	)	)	PUNCT
cana-1627	41	20	=	=	SYM
cana-1627	41	21	1	1	NUM
cana-1627	41	22	anti	anti	X
cana-1627	41	23	fuzzy	fuzzy	ADJ
cana-1627	41	24	partial	partial	ADJ
cana-1627	41	25	total	total	ADJ
cana-1627	41	26	domatic	domatic	ADJ
cana-1627	41	27	number	number	NOUN
cana-1627	41	28	of	of	ADP
cana-1627	41	29	ag	ag	PROPN
cana-1627	41	30	domatic	domatic	ADJ
cana-1627	41	31	number	number	NOUN
cana-1627	41	32	of	of	ADP
cana-1627	41	33	𝐴𝐺	𝐴𝐺	PROPN
cana-1627	41	34	,	,	PUNCT
cana-1627	41	35	𝑑𝑓𝑝𝑡	𝑑𝑓𝑝𝑡	NOUN
cana-1627	41	36	=	=	NUM
cana-1627	41	37	1.2	1.2	NUM
cana-1627	41	38	2.5	2.5	NUM
cana-1627	41	39	theorem	theorem	NOUN
cana-1627	41	40	let	let	VERB
cana-1627	41	41	ag	ag	PROPN
cana-1627	41	42	be	be	AUX
cana-1627	41	43	a	a	DET
cana-1627	41	44	finite	finite	ADJ
cana-1627	41	45	undirected	undirected	ADJ
cana-1627	41	46	afg	afg	NOUN
cana-1627	41	47	with	with	ADP
cana-1627	41	48	n	n	ADP
cana-1627	41	49	nodes	node	NOUN
cana-1627	41	50	of	of	ADP
cana-1627	41	51	order	order	NOUN
cana-1627	41	52	ρ	ρ	NOUN
cana-1627	41	53	,	,	PUNCT
cana-1627	41	54	and	and	CCONJ
cana-1627	41	55	τ(ag	τ(ag	X
cana-1627	41	56	)	)	PUNCT
cana-1627	41	57	be	be	VERB
cana-1627	41	58	the	the	DET
cana-1627	41	59	minimum	minimum	ADJ
cana-1627	41	60	degrees	degree	NOUN
cana-1627	41	61	of	of	ADP
cana-1627	41	62	nodes	node	NOUN
cana-1627	41	63	of	of	ADP
cana-1627	41	64	ag	ag	PROPN
cana-1627	41	65	.	.	PUNCT
cana-1627	42	1	then	then	ADV
cana-1627	42	2	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	42	3	)	)	PUNCT
cana-1627	43	1	≥	≥	NOUN
cana-1627	44	1	[	[	X
cana-1627	44	2	ρ/	ρ/	X
cana-1627	44	3	(	(	PUNCT
cana-1627	44	4	ρ𝜏𝑓(𝐴𝐺	ρ𝜏𝑓(𝐴𝐺	NUM
cana-1627	44	5	)	)	PUNCT
cana-1627	44	6	+	+	CCONJ
cana-1627	44	7	1	1	NUM
cana-1627	44	8	)	)	PUNCT
cana-1627	44	9	]	]	PUNCT
cana-1627	44	10	and	and	CCONJ
cana-1627	44	11	each	each	DET
cana-1627	44	12	total	total	ADJ
cana-1627	44	13	dominating	dominating	NOUN
cana-1627	44	14	set	set	NOUN
cana-1627	44	15	consists	consist	VERB
cana-1627	44	16	n	n	PRON
cana-1627	44	17	τ(ag	τ(ag	NUM
cana-1627	44	18	)	)	PUNCT
cana-1627	45	1	+	+	CCONJ
cana-1627	45	2	1	1	NUM
cana-1627	45	3	nodes	node	NOUN
cana-1627	45	4	of	of	ADP
cana-1627	45	5	ag	ag	PROPN
cana-1627	45	6	.	.	PUNCT
cana-1627	45	7	proof	proof	NOUN
cana-1627	45	8	let	let	VERB
cana-1627	45	9	ag	ag	PROPN
cana-1627	45	10	be	be	AUX
cana-1627	45	11	an	an	DET
cana-1627	45	12	afg	afg	NOUN
cana-1627	45	13	and	and	CCONJ
cana-1627	45	14	𝐴𝐺̅̅̅̅	𝐴𝐺̅̅̅̅	PROPN
cana-1627	45	15	is	be	AUX
cana-1627	45	16	complement	complement	NOUN
cana-1627	45	17	of	of	ADP
cana-1627	45	18	ag	ag	PROPN
cana-1627	46	1	.	.	PUNCT
cana-1627	46	2	td	td	PROPN
cana-1627	46	3	is	be	AUX
cana-1627	46	4	a	a	DET
cana-1627	46	5	total	total	ADJ
cana-1627	46	6	dominating	dominating	NOUN
cana-1627	46	7	set	set	NOUN
cana-1627	46	8	of	of	ADP
cana-1627	46	9	ag	ag	PROPN
cana-1627	46	10	which	which	PRON
cana-1627	46	11	is	be	AUX
cana-1627	46	12	a	a	DET
cana-1627	46	13	subset	subset	NOUN
cana-1627	46	14	of	of	ADP
cana-1627	46	15	the	the	DET
cana-1627	46	16	node	node	NOUN
cana-1627	46	17	set	set	VERB
cana-1627	46	18	n(ag	n(ag	NOUN
cana-1627	46	19	)	)	PUNCT
cana-1627	46	20	.	.	PUNCT
cana-1627	47	1	for	for	ADP
cana-1627	47	2	every	every	DET
cana-1627	47	3	k	k	PROPN
cana-1627	47	4	ϵ	ϵ	X
cana-1627	47	5	n(ag	n(ag	NOUN
cana-1627	47	6	)	)	PUNCT
cana-1627	47	7	there	there	PRON
cana-1627	47	8	exists	exist	VERB
cana-1627	47	9	a	a	DET
cana-1627	47	10	node	node	PROPN
cana-1627	47	11	l	l	NOUN
cana-1627	47	12	which	which	PRON
cana-1627	47	13	is	be	AUX
cana-1627	47	14	not	not	PART
cana-1627	47	15	adjacent	adjacent	ADJ
cana-1627	47	16	to	to	ADP
cana-1627	47	17	k	k	PROPN
cana-1627	47	18	in	in	ADP
cana-1627	47	19	𝐴𝐺̅̅̅̅	𝐴𝐺̅̅̅̅	PROPN
cana-1627	47	20	.	.	PUNCT
cana-1627	48	1	suppose	suppose	VERB
cana-1627	48	2	the	the	DET
cana-1627	48	3	node	node	NOUN
cana-1627	48	4	has	have	VERB
cana-1627	48	5	degree	degree	NOUN
cana-1627	48	6	r	r	NOUN
cana-1627	48	7	in	in	ADP
cana-1627	48	8	ag	ag	PROPN
cana-1627	48	9	,	,	PUNCT
cana-1627	48	10	then	then	ADV
cana-1627	48	11	its	its	PRON
cana-1627	48	12	degree	degree	NOUN
cana-1627	48	13	is	be	AUX
cana-1627	48	14	n	n	X
cana-1627	48	15	-	-	PUNCT
cana-1627	48	16	r-1	r-1	NOUN
cana-1627	48	17	in	in	ADP
cana-1627	48	18	𝐴𝐺̅̅̅̅	𝐴𝐺̅̅̅̅	PROPN
cana-1627	48	19	.	.	PUNCT
cana-1627	49	1	therefore	therefore	ADV
cana-1627	49	2	,	,	PUNCT
cana-1627	49	3	the	the	DET
cana-1627	49	4	maximum	maximum	ADJ
cana-1627	49	5	degrees	degree	NOUN
cana-1627	49	6	of	of	ADP
cana-1627	49	7	𝐴𝐺̅̅̅̅	𝐴𝐺̅̅̅̅	PROPN
cana-1627	49	8	is	be	AUX
cana-1627	49	9	𝜌	𝜌	ADP
cana-1627	49	10	−	−	PROPN
cana-1627	49	11	𝜏𝑓(𝐴𝐺	𝜏𝑓(𝐴𝐺	NUM
cana-1627	49	12	)	)	PUNCT
cana-1627	49	13	−	−	PROPN
cana-1627	50	1	1	1	X
cana-1627	50	2	.	.	PUNCT
cana-1627	51	1	let	let	VERB
cana-1627	51	2	td	td	NOUN
cana-1627	51	3	be	be	AUX
cana-1627	51	4	a	a	DET
cana-1627	51	5	subset	subset	NOUN
cana-1627	51	6	of	of	ADP
cana-1627	51	7	n(ag	n(ag	NOUN
cana-1627	51	8	)	)	PUNCT
cana-1627	51	9	having	have	VERB
cana-1627	51	10	at	at	ADP
cana-1627	51	11	the	the	DET
cana-1627	51	12	minimum	minimum	NOUN
cana-1627	51	13	of	of	ADP
cana-1627	51	14	n	n	PRON
cana-1627	51	15	τ(ag	τ(ag	NUM
cana-1627	51	16	)	)	PUNCT
cana-1627	52	1	+	+	CCONJ
cana-1627	52	2	1	1	NUM
cana-1627	52	3	nodes	node	NOUN
cana-1627	52	4	.	.	PUNCT
cana-1627	53	1	then	then	ADV
cana-1627	53	2	every	every	DET
cana-1627	53	3	node	node	NOUN
cana-1627	53	4	k	k	PROPN
cana-1627	53	5	ϵ	ϵ	X
cana-1627	53	6	n(ag	n(ag	NOUN
cana-1627	53	7	)	)	PUNCT
cana-1627	53	8	can	can	AUX
cana-1627	53	9	be	be	AUX
cana-1627	53	10	contiguous	contiguous	ADJ
cana-1627	53	11	to	to	ADP
cana-1627	53	12	at	at	ADP
cana-1627	53	13	most	most	ADV
cana-1627	53	14	n	n	PRON
cana-1627	53	15	τ(ag	τ(ag	NUM
cana-1627	53	16	)	)	PUNCT
cana-1627	53	17	+	+	CCONJ
cana-1627	53	18	1	1	NUM
cana-1627	53	19	nodes	node	NOUN
cana-1627	53	20	of	of	ADP
cana-1627	53	21	td	td	NOUN
cana-1627	53	22	in	in	ADP
cana-1627	53	23	𝐴𝐺̅̅̅̅	𝐴𝐺̅̅̅̅	PROPN
cana-1627	53	24	;	;	PUNCT
cana-1627	53	25	although	although	SCONJ
cana-1627	53	26	k	k	PROPN
cana-1627	53	27	ϵ	ϵ	X
cana-1627	53	28	td	td	PROPN
cana-1627	53	29	,	,	PUNCT
cana-1627	53	30	then	then	ADV
cana-1627	53	31	a	a	NUM
cana-1627	53	32	node	node	NOUN
cana-1627	53	33	l	l	NOUN
cana-1627	53	34	ϵ	ϵ	X
cana-1627	53	35	td	td	NOUN
cana-1627	53	36	which	which	PRON
cana-1627	53	37	is	be	AUX
cana-1627	53	38	not	not	PART
cana-1627	53	39	contiguous	contiguous	ADJ
cana-1627	53	40	to	to	ADP
cana-1627	53	41	k	k	PROPN
cana-1627	53	42	in	in	ADP
cana-1627	53	43	𝐴𝐺̅̅̅̅	𝐴𝐺̅̅̅̅	PROPN
cana-1627	53	44	and	and	CCONJ
cana-1627	53	45	thus	thus	ADV
cana-1627	53	46	is	be	AUX
cana-1627	53	47	contiguous	contiguous	ADJ
cana-1627	53	48	to	to	ADP
cana-1627	53	49	k	k	PROPN
cana-1627	53	50	in	in	ADP
cana-1627	53	51	𝐴𝐺̅̅̅̅	𝐴𝐺̅̅̅̅	PROPN
cana-1627	53	52	.	.	PUNCT
cana-1627	54	1	which	which	PRON
cana-1627	54	2	mean	mean	VERB
cana-1627	54	3	it	it	PRON
cana-1627	54	4	every	every	DET
cana-1627	54	5	subset	subset	NOUN
cana-1627	54	6	of	of	ADP
cana-1627	54	7	n(ag	n(ag	NOUN
cana-1627	54	8	)	)	PUNCT
cana-1627	54	9	with	with	ADP
cana-1627	54	10	at	at	ADP
cana-1627	54	11	the	the	DET
cana-1627	54	12	minimum	minimum	NOUN
cana-1627	54	13	of	of	ADP
cana-1627	54	14	n	n	X
cana-1627	54	15	τ	τ	PROPN
cana-1627	54	16	(	(	PUNCT
cana-1627	54	17	ag	ag	PROPN
cana-1627	54	18	)	)	PUNCT
cana-1627	54	19	+	+	CCONJ
cana-1627	54	20	1	1	NUM
cana-1627	54	21	nodes	node	NOUN
cana-1627	54	22	is	be	AUX
cana-1627	54	23	a	a	DET
cana-1627	54	24	total	total	ADJ
cana-1627	54	25	dominating	dominating	NOUN
cana-1627	54	26	set	set	NOUN
cana-1627	54	27	in	in	ADP
cana-1627	54	28	ag	ag	PROPN
cana-1627	54	29	.	.	PUNCT
cana-1627	55	1	consider	consider	VERB
cana-1627	55	2	a	a	DET
cana-1627	55	3	partition	partition	NOUN
cana-1627	55	4	of	of	ADP
cana-1627	55	5	n(ag	n(ag	NOUN
cana-1627	55	6	)	)	PUNCT
cana-1627	55	7	into	into	ADP
cana-1627	55	8	a	a	DET
cana-1627	55	9	class	class	NOUN
cana-1627	55	10	which	which	PRON
cana-1627	55	11	having	have	VERB
cana-1627	55	12	n	n	PRON
cana-1627	55	13	τ	τ	X
cana-1627	55	14	(	(	PUNCT
cana-1627	55	15	ag	ag	PROPN
cana-1627	55	16	)	)	PUNCT
cana-1627	55	17	+	+	CCONJ
cana-1627	55	18	1	1	NUM
cana-1627	55	19	nodes	node	NOUN
cana-1627	55	20	each	each	PRON
cana-1627	55	21	,	,	PUNCT
cana-1627	55	22	with	with	ADP
cana-1627	55	23	the	the	DET
cana-1627	55	24	exception	exception	NOUN
cana-1627	55	25	of	of	ADP
cana-1627	55	26	at	at	ADP
cana-1627	55	27	most	most	ADV
cana-1627	55	28	one	one	NUM
cana-1627	55	29	which	which	PRON
cana-1627	55	30	would	would	AUX
cana-1627	55	31	have	have	VERB
cana-1627	55	32	more	more	ADJ
cana-1627	55	33	nodes	node	NOUN
cana-1627	55	34	.	.	PUNCT
cana-1627	56	1	evidently	evidently	ADV
cana-1627	56	2			NUM
cana-1627	56	3	such	such	DET
cana-1627	56	4	a	a	DET
cana-1627	56	5	partition	partition	NOUN
cana-1627	56	6	having	have	VERB
cana-1627	56	7	[	[	X
cana-1627	56	8	n/	n/	ADV
cana-1627	56	9	(	(	PUNCT
cana-1627	56	10	n	n	X
cana-1627	56	11	τ(ag	τ(ag	NUM
cana-1627	56	12	)	)	PUNCT
cana-1627	57	1	+	+	CCONJ
cana-1627	57	2	1	1	NUM
cana-1627	57	3	)	)	PUNCT
cana-1627	57	4	]	]	PUNCT
cana-1627	57	5	classes	class	NOUN
cana-1627	57	6	with	with	ADP
cana-1627	57	7	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	57	8	)	)	PUNCT
cana-1627	57	9	≥	≥	NOUN
cana-1627	58	1	[	[	X
cana-1627	58	2	ρ/(ρτ𝑓(ag	ρ/(ρτ𝑓(ag	X
cana-1627	58	3	)	)	PUNCT
cana-1627	59	1	+	+	CCONJ
cana-1627	59	2	1	1	NUM
cana-1627	59	3	)	)	PUNCT
cana-1627	59	4	]	]	PUNCT
cana-1627	59	5	this	this	PRON
cana-1627	59	6	is	be	AUX
cana-1627	59	7	a	a	DET
cana-1627	59	8	total	total	ADJ
cana-1627	59	9	domatic	domatic	ADJ
cana-1627	59	10	partition	partition	NOUN
cana-1627	59	11	.	.	PUNCT
cana-1627	60	1	communications	communication	NOUN
cana-1627	60	2	on	on	ADP
cana-1627	60	3	applied	apply	VERB
cana-1627	60	4	nonlinear	nonlinear	ADJ
cana-1627	60	5	analysis	analysis	NOUN
cana-1627	60	6	issn	issn	NOUN
cana-1627	60	7	:	:	PUNCT
cana-1627	60	8	1074	1074	NUM
cana-1627	60	9	-	-	PUNCT
cana-1627	60	10	133x	133x	NUM
cana-1627	60	11	vol	vol	NOUN
cana-1627	60	12	32	32	NUM
cana-1627	60	13	no	no	NOUN
cana-1627	60	14	.	.	NOUN
cana-1627	60	15	1	1	NUM
cana-1627	60	16	(	(	PUNCT
cana-1627	60	17	2025	2025	NUM
cana-1627	60	18	)	)	PUNCT
cana-1627	60	19	151	151	NUM
cana-1627	60	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1627	60	21	hence	hence	ADV
cana-1627	60	22	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	60	23	)	)	PUNCT
cana-1627	60	24	≥	≥	NOUN
cana-1627	61	1	[	[	X
cana-1627	61	2	ρ/	ρ/	X
cana-1627	61	3	(	(	PUNCT
cana-1627	61	4	ρτ𝑓(ag	ρτ𝑓(ag	NOUN
cana-1627	61	5	)	)	PUNCT
cana-1627	61	6	+	+	NUM
cana-1627	61	7	1	1	NUM
cana-1627	61	8	)	)	PUNCT
cana-1627	61	9	]	]	PUNCT
cana-1627	61	10	.	.	PUNCT
cana-1627	62	1	2.6	2.6	NUM
cana-1627	62	2	theorem	theorem	ADJ
cana-1627	62	3	ag	ag	PROPN
cana-1627	62	4	is	be	AUX
cana-1627	62	5	an	an	DET
cana-1627	62	6	afg	afg	NOUN
cana-1627	62	7	with	with	ADP
cana-1627	62	8	n	n	ADP
cana-1627	62	9	nodes	node	NOUN
cana-1627	62	10	,	,	PUNCT
cana-1627	62	11	3≤n≤7	3≤n≤7	NUM
cana-1627	62	12	for	for	ADP
cana-1627	62	13	which	which	PRON
cana-1627	62	14	τ(ag	τ(ag	NUM
cana-1627	62	15	)	)	PUNCT
cana-1627	62	16	=	=	SYM
cana-1627	62	17	n	n	CCONJ
cana-1627	62	18	–	–	PUNCT
cana-1627	62	19	3	3	NUM
cana-1627	62	20	and	and	CCONJ
cana-1627	62	21	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	NUM
cana-1627	62	22	)	)	PUNCT
cana-1627	63	1	=	=	SYM
cana-1627	63	2	{	{	PUNCT
cana-1627	63	3	≤	≤	X
cana-1627	63	4	[	[	PUNCT
cana-1627	63	5	𝜌	𝜌	ADP
cana-1627	63	6	2	2	NUM
cana-1627	63	7	]	]	PUNCT
cana-1627	63	8	;	;	PUNCT
cana-1627	63	9	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
cana-1627	63	10	𝑛	𝑛	X
cana-1627	63	11	=	=	SYM
cana-1627	63	12	4,7	4,7	NUM
cana-1627	63	13	≥	≥	NOUN
cana-1627	63	14	[	[	PUNCT
cana-1627	63	15	𝜌	𝜌	ADP
cana-1627	63	16	2	2	NUM
cana-1627	63	17	]	]	PUNCT
cana-1627	63	18	;	;	PUNCT
cana-1627	63	19	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
cana-1627	63	20	𝑛	𝑛	X
cana-1627	63	21	=	=	SYM
cana-1627	63	22	6	6	NUM
cana-1627	63	23	𝑑𝑜𝑒𝑠	𝑑𝑜𝑒𝑠	NOUN
cana-1627	63	24	𝑛𝑜𝑡	𝑛𝑜𝑡	PROPN
cana-1627	63	25	𝑒𝑥𝑖𝑠𝑡	𝑒𝑥𝑖𝑠𝑡	NOUN
cana-1627	63	26	;	;	PUNCT
cana-1627	63	27	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
cana-1627	63	28	𝑛	𝑛	X
cana-1627	63	29	=	=	SYM
cana-1627	63	30	3	3	NUM
cana-1627	63	31	,	,	PUNCT
cana-1627	63	32	5	5	NUM
cana-1627	63	33	.	.	PUNCT
cana-1627	64	1	proof	proof	NOUN
cana-1627	64	2	for	for	ADP
cana-1627	64	3	n	n	NOUN
cana-1627	64	4	=	=	SYM
cana-1627	64	5	3	3	NUM
cana-1627	64	6	,	,	PUNCT
cana-1627	64	7	ag	ag	PROPN
cana-1627	64	8	is	be	AUX
cana-1627	64	9	an	an	DET
cana-1627	64	10	afg	afg	NOUN
cana-1627	64	11	with	with	ADP
cana-1627	64	12	three	three	NUM
cana-1627	64	13	isolated	isolated	ADJ
cana-1627	64	14	nodes	node	NOUN
cana-1627	64	15	.	.	PUNCT
cana-1627	65	1	since	since	SCONJ
cana-1627	65	2	τ(ag	τ(ag	NUM
cana-1627	65	3	)	)	PUNCT
cana-1627	65	4	=	=	SYM
cana-1627	65	5	n	n	CCONJ
cana-1627	65	6	–	–	PUNCT
cana-1627	65	7	3	3	X
cana-1627	65	8	.	.	X
cana-1627	65	9	therefore	therefore	ADV
cana-1627	65	10	,	,	PUNCT
cana-1627	65	11	total	total	ADJ
cana-1627	65	12	dominating	dominating	NOUN
cana-1627	65	13	set	set	NOUN
cana-1627	65	14	does	do	AUX
cana-1627	65	15	not	not	PART
cana-1627	65	16	exist	exist	VERB
cana-1627	65	17	.	.	PUNCT
cana-1627	66	1	hence	hence	ADV
cana-1627	66	2	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	66	3	)	)	PUNCT
cana-1627	67	1	=	=	SYM
cana-1627	67	2	0	0	X
cana-1627	67	3	.	.	PUNCT
cana-1627	68	1	for	for	ADP
cana-1627	68	2	n	n	NOUN
cana-1627	68	3	=	=	SYM
cana-1627	68	4	4	4	NUM
cana-1627	68	5	,	,	PUNCT
cana-1627	68	6	ag	ag	PROPN
cana-1627	68	7	is	be	AUX
cana-1627	68	8	a	a	DET
cana-1627	68	9	disconnected	disconnected	ADJ
cana-1627	68	10	anti	anti	ADJ
cana-1627	68	11	fuzzy	fuzzy	ADJ
cana-1627	68	12	graph	graph	NOUN
cana-1627	68	13	with	with	ADP
cana-1627	68	14	two	two	NUM
cana-1627	68	15	components	component	NOUN
cana-1627	68	16	with	with	ADP
cana-1627	68	17	two	two	NUM
cana-1627	68	18	nodes	node	NOUN
cana-1627	68	19	each	each	PRON
cana-1627	68	20	.	.	PUNCT
cana-1627	69	1	therefore	therefore	ADV
cana-1627	69	2	,	,	PUNCT
cana-1627	69	3	there	there	PRON
cana-1627	69	4	exist	exist	VERB
cana-1627	69	5	one	one	NUM
cana-1627	69	6	partition	partition	NOUN
cana-1627	69	7	of	of	ADP
cana-1627	69	8	total	total	ADJ
cana-1627	69	9	dominating	dominating	NOUN
cana-1627	69	10	set	set	NOUN
cana-1627	69	11	.	.	PUNCT
cana-1627	70	1	therefore	therefore	ADV
cana-1627	70	2	,	,	PUNCT
cana-1627	70	3	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	70	4	)	)	PUNCT
cana-1627	71	1	=	=	PUNCT
cana-1627	71	2	[	[	PUNCT
cana-1627	71	3	𝜌	𝜌	ADP
cana-1627	71	4	2	2	NUM
cana-1627	71	5	]	]	PUNCT
cana-1627	71	6	.	.	PUNCT
cana-1627	72	1	for	for	ADP
cana-1627	72	2	n	n	NOUN
cana-1627	72	3	=	=	SYM
cana-1627	72	4	5	5	NUM
cana-1627	72	5	,	,	PUNCT
cana-1627	72	6	ag	ag	PROPN
cana-1627	72	7	is	be	AUX
cana-1627	72	8	an	an	DET
cana-1627	72	9	anti	anti	ADJ
cana-1627	72	10	fuzzy	fuzzy	ADJ
cana-1627	72	11	cycle	cycle	NOUN
cana-1627	72	12	.	.	PUNCT
cana-1627	73	1	we	we	PRON
cana-1627	73	2	know	know	VERB
cana-1627	73	3	that	that	SCONJ
cana-1627	73	4	,	,	PUNCT
cana-1627	73	5	for	for	ADP
cana-1627	73	6	any	any	DET
cana-1627	73	7	anti	anti	ADJ
cana-1627	73	8	fuzzy	fuzzy	ADJ
cana-1627	73	9	cycle	cycle	NOUN
cana-1627	73	10	total	total	NOUN
cana-1627	73	11	domatic	domatic	ADJ
cana-1627	73	12	partition	partition	NOUN
cana-1627	73	13	does	do	AUX
cana-1627	73	14	not	not	PART
cana-1627	73	15	exist	exist	VERB
cana-1627	73	16	.	.	PUNCT
cana-1627	74	1	for	for	ADP
cana-1627	74	2	n	n	NOUN
cana-1627	74	3	=	=	SYM
cana-1627	74	4	6	6	NUM
cana-1627	74	5	,	,	PUNCT
cana-1627	74	6	ag	ag	PROPN
cana-1627	74	7	is	be	AUX
cana-1627	74	8	an	an	DET
cana-1627	74	9	anti	anti	ADJ
cana-1627	74	10	fuzzy	fuzzy	ADJ
cana-1627	74	11	wheel	wheel	NOUN
cana-1627	74	12	with	with	ADP
cana-1627	74	13	two	two	NUM
cana-1627	74	14	tds	tds	NOUN
cana-1627	74	15	of	of	ADP
cana-1627	74	16	at	at	ADV
cana-1627	74	17	most	most	ADV
cana-1627	74	18	𝑛	𝑛	DET
cana-1627	74	19	2	2	NUM
cana-1627	74	20	nodes	node	NOUN
cana-1627	74	21	which	which	PRON
cana-1627	74	22	has	have	VERB
cana-1627	74	23	at	at	ADP
cana-1627	74	24	the	the	DET
cana-1627	74	25	minimum	minimum	NOUN
cana-1627	74	26	of	of	ADP
cana-1627	74	27	𝜌	𝜌	X
cana-1627	74	28	2	2	NUM
cana-1627	74	29	.	.	PUNCT
cana-1627	75	1	therefore	therefore	ADV
cana-1627	75	2	,	,	PUNCT
cana-1627	75	3	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	75	4	)	)	PUNCT
cana-1627	75	5	≥	≥	NOUN
cana-1627	75	6	[	[	PUNCT
cana-1627	75	7	𝜌	𝜌	ADP
cana-1627	75	8	2	2	NUM
cana-1627	75	9	]	]	PUNCT
cana-1627	75	10	.	.	PUNCT
cana-1627	76	1	for	for	ADP
cana-1627	76	2	n	n	NOUN
cana-1627	76	3	=	=	SYM
cana-1627	76	4	7	7	NUM
cana-1627	76	5	,	,	PUNCT
cana-1627	76	6	ag	ag	PROPN
cana-1627	76	7	is	be	AUX
cana-1627	76	8	an	an	DET
cana-1627	76	9	afg	afg	NOUN
cana-1627	76	10	with	with	ADP
cana-1627	76	11	∆(𝐴𝐺	∆(𝐴𝐺	PROPN
cana-1627	76	12	)	)	PUNCT
cana-1627	76	13	=	=	SYM
cana-1627	77	1	𝑛	𝑛	DET
cana-1627	77	2	−	−	NOUN
cana-1627	77	3	2	2	NUM
cana-1627	77	4	.	.	PUNCT
cana-1627	77	5	it	it	PRON
cana-1627	77	6	forms	form	VERB
cana-1627	77	7	three	three	NUM
cana-1627	77	8	total	total	ADJ
cana-1627	77	9	dominating	dominating	NOUN
cana-1627	77	10	sets	set	NOUN
cana-1627	77	11	with	with	ADP
cana-1627	77	12	at	at	ADP
cana-1627	77	13	most	most	ADV
cana-1627	77	14	𝑛	𝑛	DET
cana-1627	77	15	2	2	NUM
cana-1627	77	16	nodes	node	NOUN
cana-1627	77	17	which	which	PRON
cana-1627	77	18	has	have	VERB
cana-1627	77	19	at	at	ADP
cana-1627	77	20	most	most	ADJ
cana-1627	77	21	[	[	PUNCT
cana-1627	77	22	𝜌	𝜌	ADP
cana-1627	77	23	2	2	NUM
cana-1627	77	24	]	]	PUNCT
cana-1627	77	25	each	each	PRON
cana-1627	77	26	.	.	PUNCT
cana-1627	78	1	therefore	therefore	ADV
cana-1627	78	2	,	,	PUNCT
cana-1627	78	3	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	78	4	)	)	PUNCT
cana-1627	78	5	≤	≤	NOUN
cana-1627	78	6	[	[	PUNCT
cana-1627	78	7	𝜌	𝜌	ADP
cana-1627	78	8	2	2	NUM
cana-1627	78	9	]	]	PUNCT
cana-1627	78	10	.	.	PUNCT
cana-1627	79	1	2.7	2.7	NUM
cana-1627	79	2	theorem	theorem	VERB
cana-1627	79	3	if	if	SCONJ
cana-1627	79	4	ag	ag	PROPN
cana-1627	79	5	is	be	AUX
cana-1627	79	6	an	an	DET
cana-1627	79	7	afg	afg	NOUN
cana-1627	79	8	(	(	PUNCT
cana-1627	79	9	n=5	n=5	PROPN
cana-1627	79	10	)	)	PUNCT
cana-1627	79	11	with	with	ADP
cana-1627	79	12	τ(ag	τ(ag	NOUN
cana-1627	79	13	)	)	PUNCT
cana-1627	79	14	=	=	SYM
cana-1627	79	15	n	n	X
cana-1627	79	16	–	–	PUNCT
cana-1627	79	17	3	3	NUM
cana-1627	79	18	then	then	ADV
cana-1627	79	19	𝑑𝑓𝑝𝑡(𝐴𝐺	𝑑𝑓𝑝𝑡(𝐴𝐺	NOUN
cana-1627	79	20	)	)	PUNCT
cana-1627	80	1	=	=	PUNCT
cana-1627	80	2	[	[	PUNCT
cana-1627	80	3	𝜌	𝜌	ADP
cana-1627	80	4	2	2	NUM
cana-1627	80	5	]	]	PUNCT
cana-1627	80	6	.	.	PUNCT
cana-1627	81	1	proof	proof	NOUN
cana-1627	81	2	if	if	SCONJ
cana-1627	81	3	ag	ag	PROPN
cana-1627	81	4	is	be	AUX
cana-1627	81	5	an	an	DET
cana-1627	81	6	afg	afg	NOUN
cana-1627	81	7	with	with	ADP
cana-1627	81	8	n	n	NOUN
cana-1627	81	9	nodes	node	NOUN
cana-1627	81	10	and	and	CCONJ
cana-1627	81	11	τ(ag	τ(ag	NUM
cana-1627	81	12	)	)	PUNCT
cana-1627	81	13	=	=	SYM
cana-1627	81	14	n	n	X
cana-1627	81	15	–	–	PUNCT
cana-1627	81	16	3	3	NUM
cana-1627	81	17	then	then	ADV
cana-1627	81	18	ag	ag	PROPN
cana-1627	81	19	has	have	VERB
cana-1627	81	20	an	an	DET
cana-1627	81	21	anti	anti	ADJ
cana-1627	81	22	fuzzy	fuzzy	ADJ
cana-1627	81	23	cycle	cycle	NOUN
cana-1627	81	24	.	.	PUNCT
cana-1627	82	1	therefore	therefore	ADV
cana-1627	82	2	,	,	PUNCT
cana-1627	82	3	there	there	PRON
cana-1627	82	4	exist	exist	VERB
cana-1627	82	5	one	one	NUM
cana-1627	82	6	partial	partial	ADJ
cana-1627	82	7	total	total	ADJ
cana-1627	82	8	dominating	dominating	NOUN
cana-1627	82	9	set	set	NOUN
cana-1627	82	10	exist	exist	VERB
cana-1627	82	11	with	with	ADP
cana-1627	82	12	at	at	ADP
cana-1627	82	13	most	most	ADJ
cana-1627	82	14	[	[	PUNCT
cana-1627	82	15	𝜌	𝜌	ADP
cana-1627	82	16	2	2	NUM
cana-1627	82	17	]	]	PUNCT
cana-1627	82	18	.	.	PUNCT
cana-1627	83	1	hence	hence	ADV
cana-1627	83	2	,	,	PUNCT
cana-1627	83	3	𝑑𝑓𝑝𝑡(𝐴𝐺	𝑑𝑓𝑝𝑡(𝐴𝐺	NOUN
cana-1627	83	4	)	)	PUNCT
cana-1627	83	5	=	=	PUNCT
cana-1627	84	1	[	[	PUNCT
cana-1627	84	2	𝜌	𝜌	ADP
cana-1627	84	3	2	2	NUM
cana-1627	84	4	]	]	PUNCT
cana-1627	84	5	.	.	PUNCT
cana-1627	85	1	2.8	2.8	NUM
cana-1627	85	2	theorem	theorem	NOUN
cana-1627	85	3	let	let	VERB
cana-1627	85	4	ag	ag	PROPN
cana-1627	85	5	be	be	AUX
cana-1627	85	6	a	a	DET
cana-1627	85	7	complete	complete	ADJ
cana-1627	85	8	bipartite	bipartite	NOUN
cana-1627	85	9	afg	afg	NOUN
cana-1627	85	10	with	with	ADP
cana-1627	85	11	‘	'	PUNCT
cana-1627	85	12	n	n	CCONJ
cana-1627	85	13	’	'	PUNCT
cana-1627	85	14	nodes	node	NOUN
cana-1627	85	15	.	.	PUNCT
cana-1627	86	1	n1	n1	PROPN
cana-1627	86	2	and	and	CCONJ
cana-1627	86	3	n2	n2	NOUN
cana-1627	86	4	are	be	AUX
cana-1627	86	5	node	node	ADJ
cana-1627	86	6	partition	partition	NOUN
cana-1627	86	7	of	of	ADP
cana-1627	86	8	n(ag	n(ag	NOUN
cana-1627	86	9	)	)	PUNCT
cana-1627	86	10	.	.	PUNCT
cana-1627	87	1	then	then	ADV
cana-1627	87	2	𝑑𝑡(𝐴𝐺	𝑑𝑡(𝐴𝐺	ADV
cana-1627	87	3	)	)	PUNCT
cana-1627	88	1	=	=	SYM
cana-1627	88	2	⌊	⌊	VERB
cana-1627	88	3	𝑛	𝑛	DET
cana-1627	88	4	2	2	NUM
cana-1627	88	5	⌋.	⌋.	NOUN
cana-1627	88	6	proof	proof	NOUN
cana-1627	88	7	let	let	VERB
cana-1627	88	8	ag	ag	PROPN
cana-1627	88	9	be	be	AUX
cana-1627	88	10	any	any	DET
cana-1627	88	11	complete	complete	ADJ
cana-1627	88	12	bipartite	bipartite	NOUN
cana-1627	88	13	afg	afg	NOUN
cana-1627	88	14	with	with	ADP
cana-1627	88	15	disjoint	disjoint	PROPN
cana-1627	88	16	node	node	NOUN
cana-1627	88	17	partitioned	partition	VERB
cana-1627	88	18	set	set	NOUN
cana-1627	88	19	n1	n1	NOUN
cana-1627	88	20	,	,	PUNCT
cana-1627	88	21	n2	n2	ADJ
cana-1627	88	22	and	and	CCONJ
cana-1627	88	23	|𝑁1(𝐴𝐺	|𝑁1(𝐴𝐺	ADJ
cana-1627	88	24	)	)	PUNCT
cana-1627	89	1	|	|	NOUN
cana-1627	89	2	=	=	SYM
cana-1627	89	3	𝑛	𝑛	NOUN
cana-1627	89	4	,	,	PUNCT
cana-1627	89	5	|𝑁2(𝐴𝐺	|𝑁2(𝐴𝐺	ADJ
cana-1627	89	6	)	)	PUNCT
cana-1627	89	7	|	|	ADV
cana-1627	89	8	=	=	SYM
cana-1627	89	9	𝑚	𝑚	NOUN
cana-1627	89	10	consider	consider	VERB
cana-1627	89	11	n	n	PRON
cana-1627	89	12	˂	˂	PROPN
cana-1627	89	13	m	m	PRON
cana-1627	89	14	(=	(=	NOUN
cana-1627	89	15	n+1	n+1	X
cana-1627	89	16	)	)	PUNCT
cana-1627	89	17	there	there	PRON
cana-1627	89	18	is	be	VERB
cana-1627	89	19	no	no	DET
cana-1627	89	20	edge	edge	NOUN
cana-1627	89	21	between	between	ADP
cana-1627	89	22	the	the	DET
cana-1627	89	23	nodes	node	NOUN
cana-1627	89	24	in	in	ADP
cana-1627	89	25	n1	n1	NOUN
cana-1627	89	26	and	and	CCONJ
cana-1627	89	27	communications	communication	NOUN
cana-1627	89	28	on	on	ADP
cana-1627	89	29	applied	apply	VERB
cana-1627	89	30	nonlinear	nonlinear	ADJ
cana-1627	89	31	analysis	analysis	NOUN
cana-1627	89	32	issn	issn	NOUN
cana-1627	89	33	:	:	PUNCT
cana-1627	89	34	1074	1074	NUM
cana-1627	89	35	-	-	PUNCT
cana-1627	89	36	133x	133x	NUM
cana-1627	89	37	vol	vol	NOUN
cana-1627	89	38	32	32	NUM
cana-1627	89	39	no	no	NOUN
cana-1627	89	40	.	.	NOUN
cana-1627	89	41	1	1	NUM
cana-1627	89	42	(	(	PUNCT
cana-1627	89	43	2025	2025	NUM
cana-1627	89	44	)	)	PUNCT
cana-1627	89	45	152	152	NUM
cana-1627	89	46	https://internationalpubls.com	https://internationalpubls.com	X
cana-1627	89	47	also	also	ADV
cana-1627	89	48	in	in	ADP
cana-1627	89	49	n2	n2	PROPN
cana-1627	89	50	.	.	PUNCT
cana-1627	90	1	let	let	VERB
cana-1627	90	2	k1	k1	PROPN
cana-1627	90	3	ϵ	ϵ	X
cana-1627	90	4	n1(ag	n1(ag	PROPN
cana-1627	90	5	)	)	PUNCT
cana-1627	90	6	which	which	PRON
cana-1627	90	7	dominates	dominate	VERB
cana-1627	90	8	all	all	DET
cana-1627	90	9	the	the	DET
cana-1627	90	10	nodes	node	NOUN
cana-1627	90	11	in	in	ADP
cana-1627	90	12	n2	n2	ADJ
cana-1627	90	13	.	.	PUNCT
cana-1627	91	1	let	let	VERB
cana-1627	91	2	k1ϵ	k1ϵ	PROPN
cana-1627	91	3	n2(ag	n2(ag	X
cana-1627	91	4	)	)	PUNCT
cana-1627	91	5	which	which	PRON
cana-1627	91	6	dominates	dominate	VERB
cana-1627	91	7	all	all	DET
cana-1627	91	8	the	the	DET
cana-1627	91	9	nodes	node	NOUN
cana-1627	91	10	in	in	ADP
cana-1627	91	11	n1	n1	NOUN
cana-1627	91	12	.	.	PUNCT
cana-1627	92	1	since	since	SCONJ
cana-1627	92	2	there	there	PRON
cana-1627	92	3	exist	exist	VERB
cana-1627	92	4	an	an	DET
cana-1627	92	5	edge	edge	NOUN
cana-1627	92	6	between	between	ADP
cana-1627	92	7	k1	k1	NOUN
cana-1627	92	8	and	and	CCONJ
cana-1627	92	9	l1	l1	PROPN
cana-1627	92	10	.	.	PUNCT
cana-1627	93	1	therefore	therefore	ADV
cana-1627	93	2	{	{	PUNCT
cana-1627	93	3	k1	k1	PROPN
cana-1627	93	4	,	,	PUNCT
cana-1627	93	5	l1	l1	PROPN
cana-1627	93	6	}	}	PUNCT
cana-1627	93	7	forms	form	VERB
cana-1627	93	8	a	a	DET
cana-1627	93	9	minimal	minimal	ADJ
cana-1627	93	10	tds	tds	NOUN
cana-1627	93	11	of	of	ADP
cana-1627	93	12	ag	ag	PROPN
cana-1627	93	13	.	.	PUNCT
cana-1627	93	14	similarly	similarly	ADV
cana-1627	93	15	,	,	PUNCT
cana-1627	93	16	{	{	PUNCT
cana-1627	93	17	k2	k2	ADJ
cana-1627	93	18	,	,	PUNCT
cana-1627	93	19	l2	l2	NOUN
cana-1627	93	20	}	}	PUNCT
cana-1627	93	21	,	,	PUNCT
cana-1627	93	22	{	{	PUNCT
cana-1627	93	23	k3	k3	PROPN
cana-1627	93	24	,	,	PUNCT
cana-1627	93	25	l3	l3	PROPN
cana-1627	93	26	}	}	PUNCT
cana-1627	93	27	,	,	PUNCT
cana-1627	93	28	...	...	PUNCT
cana-1627	93	29	,	,	PUNCT
cana-1627	93	30	{	{	PUNCT
cana-1627	93	31	kn-1	kn-1	X
cana-1627	93	32	,	,	PUNCT
cana-1627	93	33	ln-1	ln-1	NOUN
cana-1627	93	34	}	}	PUNCT
cana-1627	93	35	forms	form	VERB
cana-1627	93	36	a	a	DET
cana-1627	93	37	minimal	minimal	ADJ
cana-1627	93	38	tds	tds	NOUN
cana-1627	93	39	of	of	ADP
cana-1627	93	40	ag	ag	PROPN
cana-1627	93	41	.	.	PUNCT
cana-1627	93	42	forms	form	VERB
cana-1627	93	43	a	a	DET
cana-1627	93	44	minimal	minimal	ADJ
cana-1627	93	45	tds	tds	NOUN
cana-1627	93	46	of	of	ADP
cana-1627	93	47	ag	ag	PROPN
cana-1627	93	48	and	and	CCONJ
cana-1627	93	49	{	{	PUNCT
cana-1627	93	50	kn	kn	PROPN
cana-1627	93	51	,	,	PUNCT
cana-1627	93	52	ln	ln	ADJ
cana-1627	93	53	,	,	PUNCT
cana-1627	93	54	ln+1	ln+1	ADJ
cana-1627	93	55	}	}	PUNCT
cana-1627	93	56	forms	form	VERB
cana-1627	93	57	a	a	DET
cana-1627	93	58	tds	tds	NOUN
cana-1627	93	59	of	of	ADP
cana-1627	93	60	ag	ag	PROPN
cana-1627	93	61	.	.	PUNCT
cana-1627	93	62	therefore	therefore	ADV
cana-1627	93	63	,	,	PUNCT
cana-1627	93	64	𝑑𝑡(𝐴𝐺	𝑑𝑡(𝐴𝐺	ADJ
cana-1627	93	65	)	)	PUNCT
cana-1627	93	66	=	=	PUNCT
cana-1627	94	1	⌊	⌊	AUX
cana-1627	94	2	𝑛	𝑛	DET
cana-1627	94	3	2	2	NUM
cana-1627	94	4	⌋.	⌋.	NOUN
cana-1627	94	5	consider	consider	VERB
cana-1627	94	6	if	if	SCONJ
cana-1627	94	7	n	n	NOUN
cana-1627	94	8	=	=	PRON
cana-1627	94	9	m	m	VERB
cana-1627	94	10	then	then	ADV
cana-1627	94	11	{	{	PUNCT
cana-1627	94	12	k1	k1	PROPN
cana-1627	94	13	,	,	PUNCT
cana-1627	94	14	l1	l1	PROPN
cana-1627	94	15	}	}	PUNCT
cana-1627	94	16	,	,	PUNCT
cana-1627	94	17	{	{	PUNCT
cana-1627	94	18	k2	k2	ADJ
cana-1627	94	19	,	,	PUNCT
cana-1627	94	20	l2	l2	NOUN
cana-1627	94	21	}	}	PUNCT
cana-1627	94	22	,	,	PUNCT
cana-1627	94	23	{	{	PUNCT
cana-1627	94	24	k3	k3	PROPN
cana-1627	94	25	,	,	PUNCT
cana-1627	94	26	l3	l3	PROPN
cana-1627	94	27	}	}	PUNCT
cana-1627	94	28	,	,	PUNCT
cana-1627	94	29	…	…	PUNCT
cana-1627	94	30	.	.	PUNCT
cana-1627	94	31	,	,	PUNCT
cana-1627	94	32	{	{	PUNCT
cana-1627	94	33	kn	kn	PROPN
cana-1627	94	34	,	,	PUNCT
cana-1627	94	35	l	l	PROPN
cana-1627	94	36	n	n	CCONJ
cana-1627	94	37	}	}	PUNCT
cana-1627	94	38	are	be	AUX
cana-1627	94	39	classes	class	NOUN
cana-1627	94	40	of	of	ADP
cana-1627	94	41	total	total	ADJ
cana-1627	94	42	domatic	domatic	ADJ
cana-1627	94	43	partition	partition	NOUN
cana-1627	94	44	of	of	ADP
cana-1627	94	45	ag	ag	PROPN
cana-1627	94	46	.	.	PUNCT
cana-1627	94	47	therefore	therefore	ADV
cana-1627	94	48	,	,	PUNCT
cana-1627	94	49	𝑑𝑡(𝐴𝐺	𝑑𝑡(𝐴𝐺	ADJ
cana-1627	94	50	)	)	PUNCT
cana-1627	94	51	=	=	PUNCT
cana-1627	95	1	⌊	⌊	VERB
cana-1627	95	2	𝑛	𝑛	DET
cana-1627	95	3	2	2	NUM
cana-1627	95	4	⌋.	⌋.	NOUN
cana-1627	95	5	2.9	2.9	NUM
cana-1627	95	6	proposition	proposition	NOUN
cana-1627	95	7	for	for	ADP
cana-1627	95	8	afg	afg	PROPN
cana-1627	95	9	ag	ag	PROPN
cana-1627	95	10	,	,	PUNCT
cana-1627	95	11	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	95	12	)	)	PUNCT
cana-1627	95	13	≤	≤	NUM
cana-1627	95	14	2𝜌	2𝜌	NOUN
cana-1627	95	15	3	3	NUM
cana-1627	95	16	where	where	SCONJ
cana-1627	95	17	ag	ag	PROPN
cana-1627	95	18	is	be	AUX
cana-1627	95	19	a	a	DET
cana-1627	95	20	not	not	PART
cana-1627	95	21	an	an	DET
cana-1627	95	22	anti	anti	ADJ
cana-1627	95	23	fuzzy	fuzzy	ADJ
cana-1627	95	24	cycle	cycle	NOUN
cana-1627	95	25	.	.	PUNCT
cana-1627	96	1	proof	proof	NOUN
cana-1627	96	2	let	let	VERB
cana-1627	96	3	ag	ag	PROPN
cana-1627	96	4	is	be	AUX
cana-1627	96	5	an	an	DET
cana-1627	96	6	afg	afg	NOUN
cana-1627	96	7	and	and	CCONJ
cana-1627	96	8	consider	consider	VERB
cana-1627	96	9	that	that	SCONJ
cana-1627	96	10	ag	ag	PROPN
cana-1627	96	11	is	be	AUX
cana-1627	96	12	not	not	PART
cana-1627	96	13	an	an	DET
cana-1627	96	14	anti	anti	ADJ
cana-1627	96	15	fuzzy	fuzzy	ADJ
cana-1627	96	16	cycle	cycle	NOUN
cana-1627	96	17	with	with	ADP
cana-1627	96	18	n	n	ADP
cana-1627	96	19	nodes	node	NOUN
cana-1627	96	20	and	and	CCONJ
cana-1627	96	21	its	its	PRON
cana-1627	96	22	order	order	NOUN
cana-1627	96	23	ρ	ρ	NOUN
cana-1627	96	24	.	.	PUNCT
cana-1627	97	1	since	since	SCONJ
cana-1627	97	2	every	every	DET
cana-1627	97	3	node	node	NOUN
cana-1627	97	4	in	in	ADP
cana-1627	97	5	ag	ag	PROPN
cana-1627	97	6	has	have	AUX
cana-1627	97	7	adjacent	adjacent	ADJ
cana-1627	97	8	to	to	PART
cana-1627	97	9	at	at	ADP
cana-1627	97	10	the	the	DET
cana-1627	97	11	minimum	minimum	NOUN
cana-1627	97	12	of	of	ADP
cana-1627	97	13	two	two	NUM
cana-1627	97	14	nodes	node	NOUN
cana-1627	97	15	and	and	CCONJ
cana-1627	97	16	does	do	AUX
cana-1627	97	17	not	not	PART
cana-1627	97	18	have	have	VERB
cana-1627	97	19	any	any	DET
cana-1627	97	20	pendent	pendent	ADJ
cana-1627	97	21	node	node	NOUN
cana-1627	97	22	.	.	PUNCT
cana-1627	98	1	so	so	ADV
cana-1627	98	2	,	,	PUNCT
cana-1627	98	3	each	each	DET
cana-1627	98	4	node	node	NOUN
cana-1627	98	5	of	of	ADP
cana-1627	98	6	ag	ag	PROPN
cana-1627	98	7	dominates	dominate	VERB
cana-1627	98	8	at	at	ADP
cana-1627	98	9	the	the	DET
cana-1627	98	10	minimum	minimum	NOUN
cana-1627	98	11	of	of	ADP
cana-1627	98	12	two	two	NUM
cana-1627	98	13	.	.	PUNCT
cana-1627	99	1	therefore	therefore	ADV
cana-1627	99	2	,	,	PUNCT
cana-1627	99	3	it	it	PRON
cana-1627	99	4	frames	frame	VERB
cana-1627	99	5	at	at	ADP
cana-1627	99	6	most	most	ADV
cana-1627	99	7	three	three	NUM
cana-1627	99	8	minimal	minimal	ADJ
cana-1627	99	9	total	total	ADJ
cana-1627	99	10	dominating	dominating	NOUN
cana-1627	99	11	sets	set	NOUN
cana-1627	99	12	of	of	ADP
cana-1627	99	13	tdtp	tdtp	NOUN
cana-1627	99	14	of	of	ADP
cana-1627	99	15	ag	ag	PROPN
cana-1627	99	16	.	.	PUNCT
cana-1627	99	17	hence	hence	ADV
cana-1627	99	18	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	99	19	)	)	PUNCT
cana-1627	99	20	≤	≤	NOUN
cana-1627	99	21	2𝜌	2𝜌	NOUN
cana-1627	99	22	3	3	NUM
cana-1627	99	23	.	.	PUNCT
cana-1627	100	1	2.10	2.10	NUM
cana-1627	100	2	theorem	theorem	NOUN
cana-1627	100	3	let	let	VERB
cana-1627	100	4	ag	ag	PROPN
cana-1627	100	5	be	be	AUX
cana-1627	100	6	a	a	DET
cana-1627	100	7	simple	simple	ADJ
cana-1627	100	8	connected	connect	VERB
cana-1627	100	9	afg	afg	NOUN
cana-1627	100	10	and	and	CCONJ
cana-1627	100	11	𝐴𝐺̅̅̅̅	𝐴𝐺̅̅̅̅	ADJ
cana-1627	100	12	be	be	AUX
cana-1627	100	13	an	an	DET
cana-1627	100	14	anti	anti	ADJ
cana-1627	100	15	-	-	NOUN
cana-1627	100	16	complement	complement	NOUN
cana-1627	100	17	of	of	ADP
cana-1627	100	18	ag	ag	PROPN
cana-1627	100	19	then	then	ADV
cana-1627	100	20	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	100	21	)	)	PUNCT
cana-1627	101	1	+	+	CCONJ
cana-1627	101	2	𝑑𝑓𝑡(𝐴𝐺̅̅̅̅	𝑑𝑓𝑡(𝐴𝐺̅̅̅̅	ADJ
cana-1627	101	3	)	)	PUNCT
cana-1627	101	4	≤	≤	NOUN
cana-1627	101	5	5𝜌	5𝜌	NUM
cana-1627	101	6	3	3	NUM
cana-1627	101	7	.	.	PUNCT
cana-1627	102	1	proof	proof	NOUN
cana-1627	102	2	ag	ag	PROPN
cana-1627	102	3	is	be	AUX
cana-1627	102	4	a	a	DET
cana-1627	102	5	simple	simple	ADJ
cana-1627	102	6	connected	connect	VERB
cana-1627	102	7	afg	afg	NOUN
cana-1627	102	8	without	without	ADP
cana-1627	102	9	isolated	isolated	ADJ
cana-1627	102	10	nodes	node	NOUN
cana-1627	102	11	then	then	ADV
cana-1627	102	12	𝐴𝐺̅̅̅̅	𝐴𝐺̅̅̅̅	PROPN
cana-1627	102	13	does	do	AUX
cana-1627	102	14	not	not	PART
cana-1627	102	15	have	have	VERB
cana-1627	102	16	any	any	DET
cana-1627	102	17	isolated	isolate	VERB
cana-1627	102	18	nodes	node	NOUN
cana-1627	102	19	then	then	ADV
cana-1627	102	20	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	102	21	)	)	PUNCT
cana-1627	102	22	≤	≤	NUM
cana-1627	102	23	2𝜌	2𝜌	NOUN
cana-1627	102	24	3	3	NUM
cana-1627	102	25	&	&	CCONJ
cana-1627	102	26	𝑑𝑓𝑡(𝐴𝐺̅̅̅̅	𝑑𝑓𝑡(𝐴𝐺̅̅̅̅	ADJ
cana-1627	102	27	)	)	PUNCT
cana-1627	102	28	≤	≤	NUM
cana-1627	102	29	ρ	ρ	PROPN
cana-1627	102	30	.	.	PUNCT
cana-1627	102	31	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADJ
cana-1627	102	32	)	)	PUNCT
cana-1627	103	1	+	+	CCONJ
cana-1627	103	2	𝑑𝑓𝑡(𝐴𝐺̅̅̅̅	𝑑𝑓𝑡(𝐴𝐺̅̅̅̅	ADJ
cana-1627	103	3	)	)	PUNCT
cana-1627	103	4	≤	≤	NOUN
cana-1627	103	5	2𝜌	2𝜌	NOUN
cana-1627	103	6	3	3	NUM
cana-1627	103	7	+	+	CCONJ
cana-1627	103	8	𝜌	𝜌	ADP
cana-1627	103	9	≤	≤	ADJ
cana-1627	103	10	5ρ	5ρ	NUM
cana-1627	103	11	3	3	NUM
cana-1627	103	12	.	.	PUNCT
cana-1627	104	1	2.11	2.11	NUM
cana-1627	104	2	theorem	theorem	NOUN
cana-1627	104	3	for	for	ADP
cana-1627	104	4	any	any	DET
cana-1627	104	5	complete	complete	ADJ
cana-1627	104	6	uninodal	uninodal	ADJ
cana-1627	104	7	afg	afg	PROPN
cana-1627	104	8	ag	ag	PROPN
cana-1627	104	9	with	with	ADP
cana-1627	104	10	n	n	PRON
cana-1627	104	11	nodes	node	NOUN
cana-1627	104	12	,	,	PUNCT
cana-1627	104	13	𝑑𝑓𝑡(𝐴𝐺)=	𝑑𝑓𝑡(𝐴𝐺)=	NOUN
cana-1627	104	14	{	{	PUNCT
cana-1627	104	15	2σ(𝑢1	2σ(𝑢1	NUM
cana-1627	104	16	)	)	PUNCT
cana-1627	104	17	;	;	PUNCT
cana-1627	104	18	𝑖𝑓	𝑖𝑓	ADP
cana-1627	104	19	𝑛	𝑛	PRON
cana-1627	104	20	𝑖𝑠	𝑖𝑠	NOUN
cana-1627	104	21	𝑒𝑣𝑒𝑛	𝑒𝑣𝑒𝑛	ADJ
cana-1627	104	22	3σ(𝑢1	3σ(𝑢1	NUM
cana-1627	104	23	)	)	PUNCT
cana-1627	104	24	;	;	PUNCT
cana-1627	104	25	𝑖𝑓𝑛	𝑖𝑓𝑛	PROPN
cana-1627	104	26	𝑖𝑠	𝑖𝑠	PROPN
cana-1627	104	27	𝑜𝑑𝑑	𝑜𝑑𝑑	PROPN
cana-1627	104	28	for	for	ADP
cana-1627	104	29	all	all	DET
cana-1627	104	30	k1∈	k1∈	PROPN
cana-1627	104	31	n(ag	n(ag	NOUN
cana-1627	104	32	)	)	PUNCT
cana-1627	104	33	.	.	PUNCT
cana-1627	105	1	proof	proof	NOUN
cana-1627	105	2	consider	consider	VERB
cana-1627	105	3	ag	ag	PROPN
cana-1627	105	4	is	be	AUX
cana-1627	105	5	a	a	DET
cana-1627	105	6	complete	complete	ADJ
cana-1627	105	7	uninodal	uninodal	ADJ
cana-1627	105	8	afg	afg	NOUN
cana-1627	105	9	and	and	CCONJ
cana-1627	105	10	td	td	NOUN
cana-1627	105	11	is	be	AUX
cana-1627	105	12	a	a	DET
cana-1627	105	13	total	total	ADJ
cana-1627	105	14	domatic	domatic	ADJ
cana-1627	105	15	partition	partition	NOUN
cana-1627	105	16	of	of	ADP
cana-1627	105	17	ag	ag	PROPN
cana-1627	105	18	which	which	PRON
cana-1627	105	19	has	have	VERB
cana-1627	105	20	td1	td1	PROPN
cana-1627	105	21	,	,	PUNCT
cana-1627	105	22	td2	td2	PROPN
cana-1627	105	23	,	,	PUNCT
cana-1627	105	24	…	…	PUNCT
cana-1627	105	25	,	,	PUNCT
cana-1627	105	26	are	be	AUX
cana-1627	105	27	its	its	PRON
cana-1627	105	28	classes	class	NOUN
cana-1627	105	29	.	.	PUNCT
cana-1627	106	1	which	which	PRON
cana-1627	106	2	yields	yield	VERB
cana-1627	106	3	the	the	DET
cana-1627	106	4	classes	class	NOUN
cana-1627	106	5	td1	td1	PROPN
cana-1627	106	6	,	,	PUNCT
cana-1627	106	7	td2	td2	PROPN
cana-1627	106	8	,	,	PUNCT
cana-1627	106	9	…	…	PUNCT
cana-1627	106	10	,	,	PUNCT
cana-1627	106	11	tdn/2	tdn/2	PROPN
cana-1627	106	12	are	be	AUX
cana-1627	106	13	total	total	ADJ
cana-1627	106	14	dominating	dominating	NOUN
cana-1627	106	15	sets	set	NOUN
cana-1627	106	16	with	with	ADP
cana-1627	106	17	same	same	ADJ
cana-1627	106	18	cardinality	cardinality	NOUN
cana-1627	106	19	.	.	PUNCT
cana-1627	107	1	let	let	VERB
cana-1627	107	2	k1ϵ	k1ϵ	NOUN
cana-1627	107	3	td1	td1	VERB
cana-1627	107	4	and	and	CCONJ
cana-1627	107	5	has	have	VERB
cana-1627	107	6	adjacent	adjacent	ADJ
cana-1627	107	7	to	to	PART
cana-1627	107	8	n-1	n-1	VERB
cana-1627	107	9	nodes	node	NOUN
cana-1627	107	10	with	with	ADP
cana-1627	107	11	degree	degree	NOUN
cana-1627	107	12	(	(	PUNCT
cana-1627	107	13	n-1	n-1	NUM
cana-1627	107	14	)	)	PUNCT
cana-1627	107	15	k1	k1	PROPN
cana-1627	107	16	.	.	PUNCT
cana-1627	108	1	l1ϵn(ag	l1ϵn(ag	X
cana-1627	108	2	)	)	PUNCT
cana-1627	108	3	and	and	CCONJ
cana-1627	108	4	k1	k1	NOUN
cana-1627	108	5	,	,	PUNCT
cana-1627	108	6	l1ϵ	l1ϵ	PROPN
cana-1627	108	7	td1	td1	NOUN
cana-1627	108	8	.	.	PUNCT
cana-1627	109	1	since	since	SCONJ
cana-1627	109	2	,	,	PUNCT
cana-1627	109	3	k1	k1	PROPN
cana-1627	109	4	,	,	PUNCT
cana-1627	109	5	l1	l1	PROPN
cana-1627	109	6	are	be	AUX
cana-1627	109	7	also	also	ADV
cana-1627	109	8	adjacent	adjacent	ADJ
cana-1627	109	9	and	and	CCONJ
cana-1627	109	10	dominates	dominate	VERB
cana-1627	109	11	all	all	DET
cana-1627	109	12	other	other	ADJ
cana-1627	109	13	nodes	node	NOUN
cana-1627	109	14	in	in	ADP
cana-1627	109	15	ag	ag	PROPN
cana-1627	109	16	.	.	PUNCT
cana-1627	110	1	if	if	SCONJ
cana-1627	110	2	n	n	PRON
cana-1627	110	3	is	be	AUX
cana-1627	110	4	an	an	DET
cana-1627	110	5	even	even	ADJ
cana-1627	110	6	number	number	NOUN
cana-1627	110	7	,	,	PUNCT
cana-1627	110	8	we	we	PRON
cana-1627	110	9	get	get	VERB
cana-1627	110	10	td1	td1	PROPN
cana-1627	110	11	,	,	PUNCT
cana-1627	110	12	td2	td2	PROPN
cana-1627	110	13	,	,	PUNCT
cana-1627	110	14	…	…	PUNCT
cana-1627	110	15	,	,	PUNCT
cana-1627	110	16	tdn/2	tdn/2	NOUN
cana-1627	110	17	classes	class	NOUN
cana-1627	110	18	in	in	ADP
cana-1627	110	19	total	total	ADJ
cana-1627	110	20	domatic	domatic	ADJ
cana-1627	110	21	partition	partition	NOUN
cana-1627	110	22	of	of	ADP
cana-1627	110	23	ag	ag	PROPN
cana-1627	110	24	.	.	PUNCT
cana-1627	111	1	hence	hence	ADV
cana-1627	111	2	,	,	PUNCT
cana-1627	111	3	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	111	4	)	)	PUNCT
cana-1627	111	5	=	=	SYM
cana-1627	111	6	2σ(𝑘1	2σ(𝑘1	NUM
cana-1627	111	7	)	)	PUNCT
cana-1627	111	8	.	.	PUNCT
cana-1627	112	1	if	if	SCONJ
cana-1627	112	2	n	n	NOUN
cana-1627	112	3	is	be	AUX
cana-1627	112	4	odd	odd	ADJ
cana-1627	112	5	then	then	ADV
cana-1627	112	6	ag	ag	PROPN
cana-1627	112	7	has	have	AUX
cana-1627	112	8	td1	td1	PROPN
cana-1627	112	9	,	,	PUNCT
cana-1627	112	10	td2	td2	PROPN
cana-1627	112	11	,	,	PUNCT
cana-1627	112	12	…	…	PUNCT
cana-1627	112	13	,	,	PUNCT
cana-1627	112	14	td𝑛	td𝑛	NOUN
cana-1627	112	15	2	2	NUM
cana-1627	112	16	−1	−1	NOUN
cana-1627	112	17	classes	class	NOUN
cana-1627	112	18	have	have	VERB
cana-1627	112	19	equal	equal	ADJ
cana-1627	112	20	number	number	NOUN
cana-1627	112	21	of	of	ADP
cana-1627	112	22	nodes	node	NOUN
cana-1627	112	23	which	which	PRON
cana-1627	112	24	forms	form	VERB
cana-1627	112	25	a	a	DET
cana-1627	112	26	tds	tds	ADJ
cana-1627	112	27	classes	class	NOUN
cana-1627	112	28	in	in	ADP
cana-1627	112	29	total	total	ADJ
cana-1627	112	30	domatic	domatic	ADJ
cana-1627	112	31	partition	partition	NOUN
cana-1627	112	32	of	of	ADP
cana-1627	112	33	ga	ga	PROPN
cana-1627	112	34	.	.	PUNCT
cana-1627	113	1	but	but	CCONJ
cana-1627	113	2	kn	kn	PROPN
cana-1627	113	3	does	do	AUX
cana-1627	113	4	not	not	PART
cana-1627	113	5	belongs	belong	VERB
cana-1627	113	6	to	to	ADP
cana-1627	113	7	any	any	DET
cana-1627	113	8	other	other	ADJ
cana-1627	113	9	classes	class	NOUN
cana-1627	113	10	of	of	ADP
cana-1627	113	11	total	total	ADJ
cana-1627	113	12	communications	communication	NOUN
cana-1627	113	13	on	on	ADP
cana-1627	113	14	applied	apply	VERB
cana-1627	113	15	nonlinear	nonlinear	ADJ
cana-1627	113	16	analysis	analysis	NOUN
cana-1627	113	17	issn	issn	NOUN
cana-1627	113	18	:	:	PUNCT
cana-1627	113	19	1074	1074	NUM
cana-1627	113	20	-	-	PUNCT
cana-1627	113	21	133x	133x	NUM
cana-1627	113	22	vol	vol	NOUN
cana-1627	113	23	32	32	NUM
cana-1627	113	24	no	no	NOUN
cana-1627	113	25	.	.	NOUN
cana-1627	113	26	1	1	NUM
cana-1627	113	27	(	(	PUNCT
cana-1627	113	28	2025	2025	NUM
cana-1627	113	29	)	)	PUNCT
cana-1627	113	30	153	153	NUM
cana-1627	113	31	https://internationalpubls.com	https://internationalpubls.com	PROPN
cana-1627	113	32	domatic	domatic	ADJ
cana-1627	113	33	partitions	partition	NOUN
cana-1627	113	34	of	of	ADP
cana-1627	113	35	ag	ag	PROPN
cana-1627	113	36	.	.	PUNCT
cana-1627	114	1	therefore	therefore	ADV
cana-1627	114	2	,	,	PUNCT
cana-1627	114	3	the	the	DET
cana-1627	114	4	node	node	PROPN
cana-1627	114	5	kn	kn	PROPN
cana-1627	114	6	adding	add	VERB
cana-1627	114	7	into	into	ADP
cana-1627	114	8	the	the	DET
cana-1627	114	9	total	total	ADJ
cana-1627	114	10	dominating	dominating	NOUN
cana-1627	114	11	set	set	NOUN
cana-1627	114	12	|td𝑛	|td𝑛	ADV
cana-1627	114	13	2	2	NUM
cana-1627	114	14	|	|	NOUN
cana-1627	114	15	=	=	NOUN
cana-1627	114	16	2σ(𝑘1	2σ(𝑘1	NUM
cana-1627	114	17	)	)	PUNCT
cana-1627	115	1	+	+	CCONJ
cana-1627	115	2	σ(𝑘𝑛	σ(𝑘𝑛	NOUN
cana-1627	115	3	)	)	PUNCT
cana-1627	115	4	=	=	SYM
cana-1627	115	5	2σ(𝑘1	2σ(𝑘1	NUM
cana-1627	115	6	)	)	PUNCT
cana-1627	116	1	+	+	NUM
cana-1627	116	2	σ(𝑘1	σ(𝑘1	NOUN
cana-1627	116	3	)	)	PUNCT
cana-1627	116	4	{	{	PUNCT
cana-1627	116	5	since	since	SCONJ
cana-1627	116	6	ag	ag	PROPN
cana-1627	116	7	is	be	AUX
cana-1627	116	8	uninodal	uninodal	ADJ
cana-1627	116	9	anti	anti	ADJ
cana-1627	116	10	fuzzy	fuzzy	ADJ
cana-1627	116	11	graph	graph	NOUN
cana-1627	116	12	}	}	PUNCT
cana-1627	116	13	=	=	SYM
cana-1627	116	14	3σ(𝑘1	3σ(𝑘1	NUM
cana-1627	116	15	)	)	PUNCT
cana-1627	116	16	hence	hence	ADV
cana-1627	116	17	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	116	18	)	)	PUNCT
cana-1627	116	19	=	=	SYM
cana-1627	116	20	3σ(𝑘1	3σ(𝑘1	NUM
cana-1627	116	21	)	)	PUNCT
cana-1627	116	22	.	.	PUNCT
cana-1627	117	1	2.12	2.12	NUM
cana-1627	117	2	theorem	theorem	VERB
cana-1627	117	3	if	if	SCONJ
cana-1627	117	4	ag	ag	PROPN
cana-1627	117	5	is	be	AUX
cana-1627	117	6	an	an	DET
cana-1627	117	7	af	af	NOUN
cana-1627	117	8	path	path	NOUN
cana-1627	117	9	,	,	PUNCT
cana-1627	117	10	then	then	ADV
cana-1627	117	11	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	117	12	)	)	PUNCT
cana-1627	117	13	≤	≤	NOUN
cana-1627	117	14	𝜌	𝜌	ADP
cana-1627	117	15	−	−	PROPN
cana-1627	117	16	𝜏	𝜏	NOUN
cana-1627	117	17	,	,	PUNCT
cana-1627	117	18	where	where	SCONJ
cana-1627	117	19	τ	τ	PROPN
cana-1627	117	20	is	be	AUX
cana-1627	117	21	minimum	minimum	NOUN
cana-1627	117	22	degree	degree	NOUN
cana-1627	117	23	of	of	ADP
cana-1627	117	24	ag	ag	PROPN
cana-1627	117	25	.	.	PUNCT
cana-1627	118	1	proof	proof	NOUN
cana-1627	118	2	consider	consider	VERB
cana-1627	118	3	ag	ag	PROPN
cana-1627	118	4	is	be	AUX
cana-1627	118	5	an	an	DET
cana-1627	118	6	af	af	NOUN
cana-1627	118	7	path	path	NOUN
cana-1627	118	8	with	with	ADP
cana-1627	118	9	order	order	NOUN
cana-1627	118	10	‘	'	PUNCT
cana-1627	118	11	ρ	ρ	NOUN
cana-1627	118	12	’	'	PUNCT
cana-1627	118	13	and	and	CCONJ
cana-1627	118	14	has	have	VERB
cana-1627	118	15	minimum	minimum	NOUN
cana-1627	118	16	degree	degree	NOUN
cana-1627	118	17	τ	τ	X
cana-1627	118	18	.	.	PUNCT
cana-1627	119	1	let	let	VERB
cana-1627	119	2	td	td	NOUN
cana-1627	119	3	be	be	AUX
cana-1627	119	4	minimal	minimal	ADJ
cana-1627	119	5	tds	tds	ADV
cana-1627	119	6	of	of	ADP
cana-1627	119	7	ag	ag	PROPN
cana-1627	119	8	.	.	PUNCT
cana-1627	120	1	let	let	VERB
cana-1627	120	2	k	k	NOUN
cana-1627	120	3	and	and	CCONJ
cana-1627	120	4	l	l	NOUN
cana-1627	120	5	are	be	AUX
cana-1627	120	6	the	the	DET
cana-1627	120	7	initial	initial	ADJ
cana-1627	120	8	and	and	CCONJ
cana-1627	120	9	end	end	VERB
cana-1627	120	10	node	node	NOUN
cana-1627	120	11	of	of	ADP
cana-1627	120	12	an	an	DET
cana-1627	120	13	anti	anti	ADJ
cana-1627	120	14	fuzzy	fuzzy	ADJ
cana-1627	120	15	path	path	PROPN
cana-1627	120	16	ag	ag	PROPN
cana-1627	120	17	.	.	PUNCT
cana-1627	121	1	since	since	ADV
cana-1627	121	2	,	,	PUNCT
cana-1627	121	3	it	it	PRON
cana-1627	121	4	has	have	VERB
cana-1627	121	5	the	the	DET
cana-1627	121	6	degree	degree	NOUN
cana-1627	121	7	as	as	ADP
cana-1627	121	8	one	one	NUM
cana-1627	121	9	and	and	CCONJ
cana-1627	121	10	the	the	DET
cana-1627	121	11	remaining	remain	VERB
cana-1627	121	12	nodes	node	NOUN
cana-1627	121	13	of	of	ADP
cana-1627	121	14	ag	ag	PROPN
cana-1627	121	15	has	have	AUX
cana-1627	121	16	degree	degree	NOUN
cana-1627	121	17	two	two	NUM
cana-1627	121	18	.	.	PUNCT
cana-1627	122	1	therefore	therefore	ADV
cana-1627	122	2	,	,	PUNCT
cana-1627	122	3	alternative	alternative	ADJ
cana-1627	122	4	pair	pair	NOUN
cana-1627	122	5	of	of	ADP
cana-1627	122	6	nodes	node	NOUN
cana-1627	122	7	consist	consist	VERB
cana-1627	122	8	in	in	ADP
cana-1627	122	9	tds	tds	PROPN
cana-1627	122	10	.	.	PUNCT
cana-1627	123	1	hence	hence	ADV
cana-1627	123	2	,	,	PUNCT
cana-1627	123	3	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	123	4	)	)	PUNCT
cana-1627	123	5	≤	≤	NOUN
cana-1627	124	1	𝜌	𝜌	ADP
cana-1627	124	2	−	−	PROPN
cana-1627	124	3	𝜏	𝜏	SYM
cana-1627	124	4	2.13	2.13	NUM
cana-1627	124	5	theorem	theorem	NOUN
cana-1627	124	6	for	for	ADP
cana-1627	124	7	any	any	DET
cana-1627	124	8	two	two	NUM
cana-1627	124	9	anti	anti	ADJ
cana-1627	124	10	fuzzy	fuzzy	ADJ
cana-1627	124	11	graphs	graph	NOUN
cana-1627	124	12	ag	ag	PROPN
cana-1627	124	13	and	and	CCONJ
cana-1627	124	14	ah	ah	INTJ
cana-1627	124	15	without	without	ADP
cana-1627	124	16	an	an	DET
cana-1627	124	17	isolated	isolated	ADJ
cana-1627	124	18	node	node	NOUN
cana-1627	124	19	,	,	PUNCT
cana-1627	124	20	then	then	ADV
cana-1627	124	21	the	the	DET
cana-1627	124	22	following	follow	VERB
cana-1627	124	23	conditions	condition	NOUN
cana-1627	124	24	holds	hold	VERB
cana-1627	124	25	.	.	PUNCT
cana-1627	125	1	(	(	PUNCT
cana-1627	125	2	i	i	NOUN
cana-1627	125	3	)	)	PUNCT
cana-1627	125	4	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	ADV
cana-1627	125	5	×	×	PROPN
cana-1627	125	6	𝐴𝐻	𝐴𝐻	PROPN
cana-1627	125	7	)	)	PUNCT
cana-1627	125	8	≥	≥	NOUN
cana-1627	125	9	𝑑(𝐴𝐺	𝑑(𝐴𝐺	VERB
cana-1627	125	10	)	)	PUNCT
cana-1627	125	11	∨	∨	NUM
cana-1627	125	12	𝑑(𝐴𝐻	𝑑(𝐴𝐻	PROPN
cana-1627	125	13	)	)	PUNCT
cana-1627	125	14	(	(	PUNCT
cana-1627	125	15	ii	ii	NOUN
cana-1627	125	16	)	)	PUNCT
cana-1627	125	17	𝑑(𝐴𝐺	𝑑(𝐴𝐺	NUM
cana-1627	125	18	×	×	PROPN
cana-1627	125	19	𝐴𝐻	𝐴𝐻	PROPN
cana-1627	125	20	)	)	PUNCT
cana-1627	125	21	≥	≥	NOUN
cana-1627	125	22	𝑑𝑡(𝐴𝐺	𝑑𝑡(𝐴𝐺	ADV
cana-1627	125	23	×	×	PROPN
cana-1627	125	24	𝐴𝐻	𝐴𝐻	PROPN
cana-1627	125	25	)	)	PUNCT
cana-1627	125	26	.	.	PUNCT
cana-1627	126	1	proof	proof	NOUN
cana-1627	126	2	(	(	PUNCT
cana-1627	126	3	i	i	NOUN
cana-1627	126	4	)	)	PUNCT
cana-1627	126	5	consider	consider	VERB
cana-1627	126	6	ag	ag	PROPN
cana-1627	126	7	and	and	CCONJ
cana-1627	126	8	ah	ah	INTJ
cana-1627	126	9	are	be	AUX
cana-1627	126	10	anti	anti	X
cana-1627	126	11	fuzzy	fuzzy	ADJ
cana-1627	126	12	graphs	graph	NOUN
cana-1627	126	13	with	with	ADP
cana-1627	126	14	order	order	NOUN
cana-1627	126	15	ρ1	ρ1	NOUN
cana-1627	126	16	and	and	CCONJ
cana-1627	126	17	ρ2	ρ2	NOUN
cana-1627	126	18	respectively	respectively	ADV
cana-1627	126	19	.	.	PUNCT
cana-1627	127	1	let	let	VERB
cana-1627	127	2	ρ1≥	ρ1≥	PROPN
cana-1627	127	3	ρ2	ρ2	VERB
cana-1627	127	4	with	with	ADP
cana-1627	127	5	n1	n1	PROPN
cana-1627	127	6	≥	≥	NOUN
cana-1627	127	7	n2	n2	NOUN
cana-1627	127	8	where	where	SCONJ
cana-1627	127	9	n1	n1	PROPN
cana-1627	127	10	and	and	CCONJ
cana-1627	127	11	n2	n2	NOUN
cana-1627	127	12	are	be	AUX
cana-1627	127	13	number	number	NOUN
cana-1627	127	14	of	of	ADP
cana-1627	127	15	nodes	node	NOUN
cana-1627	127	16	of	of	ADP
cana-1627	127	17	ag	ag	PROPN
cana-1627	127	18	and	and	CCONJ
cana-1627	127	19	ah	ah	INTJ
cana-1627	127	20	.	.	PUNCT
cana-1627	128	1	let	let	VERB
cana-1627	128	2	td	td	NOUN
cana-1627	128	3	be	be	AUX
cana-1627	128	4	a	a	DET
cana-1627	128	5	total	total	ADJ
cana-1627	128	6	domatic	domatic	ADJ
cana-1627	128	7	partition	partition	NOUN
cana-1627	128	8	of	of	ADP
cana-1627	128	9	𝐴𝐺	𝐴𝐺	PROPN
cana-1627	128	10	×	×	NOUN
cana-1627	128	11	𝐴𝐻	𝐴𝐻	PROPN
cana-1627	128	12	which	which	PRON
cana-1627	128	13	having	have	VERB
cana-1627	128	14	at	at	ADP
cana-1627	128	15	most	most	ADJ
cana-1627	128	16	n2	n2	ADJ
cana-1627	128	17	classes	class	NOUN
cana-1627	128	18	.	.	PUNCT
cana-1627	129	1	let	let	VERB
cana-1627	129	2	ρ1	ρ1	NOUN
cana-1627	129	3	,	,	PUNCT
cana-1627	129	4	ρ2	ρ2	NOUN
cana-1627	129	5	be	be	AUX
cana-1627	129	6	the	the	DET
cana-1627	129	7	domatic	domatic	ADJ
cana-1627	129	8	numbers	number	NOUN
cana-1627	129	9	of	of	ADP
cana-1627	129	10	ag	ag	PROPN
cana-1627	129	11	and	and	CCONJ
cana-1627	129	12	ah	ah	INTJ
cana-1627	129	13	respectively	respectively	ADV
cana-1627	129	14	.	.	PUNCT
cana-1627	130	1	if	if	SCONJ
cana-1627	130	2	ρ1	ρ1	NOUN
cana-1627	130	3	≥	≥	NOUN
cana-1627	130	4	ρ2	ρ2	NOUN
cana-1627	130	5	then	then	ADV
cana-1627	130	6	td1	td1	PROPN
cana-1627	130	7	,	,	PUNCT
cana-1627	130	8	td2	td2	PROPN
cana-1627	130	9	,	,	PUNCT
cana-1627	130	10	…	…	PUNCT
cana-1627	130	11	.	.	PUNCT
cana-1627	130	12	,	,	PUNCT
cana-1627	130	13	tdn1	tdn1	PROPN
cana-1627	130	14	be	be	AUX
cana-1627	130	15	the	the	DET
cana-1627	130	16	domatic	domatic	ADJ
cana-1627	130	17	partition	partition	NOUN
cana-1627	130	18	of	of	ADP
cana-1627	130	19	n(ga	n(ga	NOUN
cana-1627	130	20	)	)	PUNCT
cana-1627	130	21	for	for	ADP
cana-1627	130	22	1	1	NUM
cana-1627	130	23	≤	≤	NUM
cana-1627	130	24	i	i	NOUN
cana-1627	130	25	≤	≤	ADJ
cana-1627	130	26	n1	n1	NOUN
cana-1627	130	27	,	,	PUNCT
cana-1627	130	28	any	any	DET
cana-1627	130	29	node	node	ADJ
cana-1627	130	30	u1	u1	NOUN
cana-1627	130	31	ϵ	ϵ	PROPN
cana-1627	130	32	tdi	tdi	PROPN
cana-1627	130	33	and	and	CCONJ
cana-1627	130	34	v1	v1	PROPN
cana-1627	130	35	ϵn(ha	ϵn(ha	PROPN
cana-1627	130	36	)	)	PUNCT
cana-1627	130	37	then	then	ADV
cana-1627	130	38	the	the	DET
cana-1627	130	39	node	node	NOUN
cana-1627	130	40	(	(	PUNCT
cana-1627	130	41	u1	u1	NOUN
cana-1627	130	42	,	,	PUNCT
cana-1627	130	43	v1	v1	NOUN
cana-1627	130	44	)	)	PUNCT
cana-1627	131	1	ϵ	ϵ	PRON
cana-1627	131	2	𝐴𝐺	𝐴𝐺	PROPN
cana-1627	131	3	×	×	NOUN
cana-1627	131	4	𝐴𝐻	𝐴𝐻	PROPN
cana-1627	131	5	dominates	dominate	VERB
cana-1627	131	6	at	at	ADP
cana-1627	131	7	most	most	ADJ
cana-1627	131	8	four	four	NUM
cana-1627	131	9	nodes	node	NOUN
cana-1627	131	10	in	in	ADP
cana-1627	131	11	n	n	PROPN
cana-1627	131	12	(	(	PUNCT
cana-1627	131	13	𝐴𝐺	𝐴𝐺	PROPN
cana-1627	131	14	×	×	NOUN
cana-1627	131	15	𝐴𝐻	𝐴𝐻	PROPN
cana-1627	131	16	)	)	PUNCT
cana-1627	131	17	.	.	PUNCT
cana-1627	132	1	since	since	SCONJ
cana-1627	132	2	ha	ha	INTJ
cana-1627	132	3	does	do	AUX
cana-1627	132	4	not	not	PART
cana-1627	132	5	have	have	VERB
cana-1627	132	6	any	any	DET
cana-1627	132	7	isolated	isolated	ADJ
cana-1627	132	8	node	node	NOUN
cana-1627	132	9	then	then	ADV
cana-1627	132	10	td	td	NOUN
cana-1627	132	11	is	be	AUX
cana-1627	132	12	a	a	DET
cana-1627	132	13	total	total	ADJ
cana-1627	132	14	domatic	domatic	ADJ
cana-1627	132	15	partition	partition	NOUN
cana-1627	132	16	of	of	ADP
cana-1627	132	17	𝐴𝐺	𝐴𝐺	PROPN
cana-1627	132	18	×	×	NOUN
cana-1627	132	19	𝐴𝐻	𝐴𝐻	PROPN
cana-1627	132	20	with	with	ADP
cana-1627	132	21	ρ1	ρ1	NOUN
cana-1627	132	22	,	,	PUNCT
cana-1627	132	23	hence	hence	ADV
cana-1627	132	24	,	,	PUNCT
cana-1627	132	25	𝑑𝑓𝑡(𝐴𝐺	𝑑𝑓𝑡(𝐴𝐺	SCONJ
cana-1627	132	26	×	×	NOUN
cana-1627	132	27	𝐴𝐻	𝐴𝐻	PROPN
cana-1627	132	28	)	)	PUNCT
cana-1627	132	29	≥	≥	NOUN
cana-1627	132	30	𝑑(𝐴𝐺	𝑑(𝐴𝐺	VERB
cana-1627	132	31	)	)	PUNCT
cana-1627	132	32	∨	∨	NUM
cana-1627	132	33	𝑑(𝐴𝐻	𝑑(𝐴𝐻	PROPN
cana-1627	132	34	)	)	PUNCT
cana-1627	132	35	.	.	PUNCT
cana-1627	133	1	(	(	PUNCT
cana-1627	133	2	ii	ii	NOUN
cana-1627	133	3	)	)	PUNCT
cana-1627	133	4	since	since	SCONJ
cana-1627	133	5	dp	dp	NOUN
cana-1627	133	6	is	be	AUX
cana-1627	133	7	a	a	DET
cana-1627	133	8	domatic	domatic	ADJ
cana-1627	133	9	partition	partition	NOUN
cana-1627	133	10	of	of	ADP
cana-1627	133	11	ag	ag	PROPN
cana-1627	133	12	which	which	PRON
cana-1627	133	13	have	have	VERB
cana-1627	133	14	at	at	ADP
cana-1627	133	15	most	most	ADJ
cana-1627	133	16	n1	n1	ADJ
cana-1627	133	17	classes	class	NOUN
cana-1627	133	18	.	.	PUNCT
cana-1627	134	1	since	since	SCONJ
cana-1627	134	2	,	,	PUNCT
cana-1627	134	3	a	a	DET
cana-1627	134	4	single	single	ADJ
cana-1627	134	5	node	node	NOUN
cana-1627	134	6	can	can	AUX
cana-1627	134	7	dominate	dominate	VERB
cana-1627	134	8	all	all	DET
cana-1627	134	9	other	other	ADJ
cana-1627	134	10	nodes	node	NOUN
cana-1627	134	11	in	in	ADP
cana-1627	134	12	𝐴𝐺	𝐴𝐺	PROPN
cana-1627	134	13	×	×	NOUN
cana-1627	134	14	𝐴𝐻.	𝐴𝐻.	NOUN
cana-1627	134	15	but	but	CCONJ
cana-1627	134	16	to	to	PART
cana-1627	134	17	form	form	VERB
cana-1627	134	18	a	a	DET
cana-1627	134	19	total	total	ADJ
cana-1627	134	20	dominating	dominating	NOUN
cana-1627	134	21	set	set	NOUN
cana-1627	134	22	we	we	PRON
cana-1627	134	23	need	need	VERB
cana-1627	134	24	at	at	ADP
cana-1627	134	25	the	the	DET
cana-1627	134	26	minimum	minimum	NOUN
cana-1627	134	27	of	of	ADP
cana-1627	134	28	two	two	NUM
cana-1627	134	29	nodes	node	NOUN
cana-1627	134	30	in	in	ADP
cana-1627	134	31	each	each	DET
cana-1627	134	32	domatic	domatic	ADJ
cana-1627	134	33	partition	partition	NOUN
cana-1627	134	34	of	of	ADP
cana-1627	134	35	𝐴𝐺	𝐴𝐺	PROPN
cana-1627	134	36	×	×	NOUN
cana-1627	134	37	𝐴𝐻	𝐴𝐻	PROPN
cana-1627	134	38	.	.	PUNCT
cana-1627	135	1	therefore	therefore	ADV
cana-1627	135	2	,	,	PUNCT
cana-1627	135	3	𝑑(𝐴𝐺	𝑑(𝐴𝐺	NUM
cana-1627	135	4	×	×	PROPN
cana-1627	135	5	𝐴𝐻	𝐴𝐻	PROPN
cana-1627	135	6	)	)	PUNCT
cana-1627	135	7	≥	≥	NOUN
cana-1627	135	8	𝑑𝑡(𝐴𝐺	𝑑𝑡(𝐴𝐺	ADV
cana-1627	135	9	×	×	PROPN
cana-1627	135	10	𝐴𝐻	𝐴𝐻	PROPN
cana-1627	135	11	)	)	PUNCT
cana-1627	135	12	.	.	PUNCT
cana-1627	136	1	3	3	X
cana-1627	136	2	.	.	X
cana-1627	136	3	conclusion	conclusion	NOUN
cana-1627	136	4	total	total	NOUN
cana-1627	136	5	and	and	CCONJ
cana-1627	136	6	partial	partial	ADJ
cana-1627	136	7	total	total	ADJ
cana-1627	136	8	domatic	domatic	ADJ
cana-1627	136	9	number	number	NOUN
cana-1627	136	10	on	on	ADP
cana-1627	136	11	an	an	DET
cana-1627	136	12	anti	anti	ADJ
cana-1627	136	13	fuzzy	fuzzy	ADJ
cana-1627	136	14	graph	graph	NOUN
cana-1627	136	15	ag	ag	PROPN
cana-1627	136	16	,	,	PUNCT
cana-1627	136	17	and	and	CCONJ
cana-1627	136	18	they	they	PRON
cana-1627	136	19	are	be	AUX
cana-1627	136	20	applied	apply	VERB
cana-1627	136	21	to	to	ADP
cana-1627	136	22	different	different	ADJ
cana-1627	136	23	types	type	NOUN
cana-1627	136	24	of	of	ADP
cana-1627	136	25	anti	anti	ADJ
cana-1627	136	26	-	-	ADJ
cana-1627	136	27	fuzzy	fuzzy	ADJ
cana-1627	136	28	graphs	graph	NOUN
cana-1627	136	29	to	to	PART
cana-1627	136	30	produce	produce	VERB
cana-1627	136	31	bounds	bound	NOUN
cana-1627	136	32	.	.	PUNCT
cana-1627	137	1	the	the	DET
cana-1627	137	2	bounds	bound	NOUN
cana-1627	137	3	on	on	ADP
cana-1627	137	4	them	they	PRON
cana-1627	137	5	were	be	AUX
cana-1627	137	6	established	establish	VERB
cana-1627	137	7	by	by	ADP
cana-1627	137	8	applying	apply	VERB
cana-1627	137	9	the	the	DET
cana-1627	137	10	total	total	ADJ
cana-1627	137	11	domatic	domatic	ADJ
cana-1627	137	12	number	number	NOUN
cana-1627	137	13	concept	concept	NOUN
cana-1627	137	14	to	to	ADP
cana-1627	137	15	the	the	DET
cana-1627	137	16	anti	anti	ADJ
cana-1627	137	17	-	-	ADJ
cana-1627	137	18	cartesian	cartesian	ADJ
cana-1627	137	19	product	product	NOUN
cana-1627	137	20	of	of	ADP
cana-1627	137	21	anti	anti	ADJ
cana-1627	137	22	-	-	ADJ
cana-1627	137	23	fuzzy	fuzzy	ADJ
cana-1627	137	24	graphs	graph	NOUN
cana-1627	137	25	such	such	ADJ
cana-1627	137	26	as	as	ADP
cana-1627	137	27	path	path	NOUN
cana-1627	137	28	,	,	PUNCT
cana-1627	137	29	anti	anti	ADJ
cana-1627	137	30	-	-	ADJ
cana-1627	137	31	fuzzy	fuzzy	ADJ
cana-1627	137	32	cycle	cycle	NOUN
cana-1627	137	33	,	,	PUNCT
cana-1627	137	34	and	and	CCONJ
cana-1627	137	35	full	full	ADJ
cana-1627	137	36	anti	anti	ADJ
cana-1627	137	37	-	-	ADJ
cana-1627	137	38	fuzzy	fuzzy	ADJ
cana-1627	137	39	graph	graph	NOUN
cana-1627	137	40	.	.	PUNCT
cana-1627	138	1	a	a	DET
cana-1627	138	2	few	few	ADJ
cana-1627	138	3	theorems	theorem	NOUN
cana-1627	138	4	and	and	CCONJ
cana-1627	138	5	propositions	proposition	NOUN
cana-1627	138	6	are	be	AUX
cana-1627	138	7	produced	produce	VERB
cana-1627	138	8	for	for	ADP
cana-1627	138	9	the	the	DET
cana-1627	138	10	results	result	NOUN
cana-1627	138	11	once	once	SCONJ
cana-1627	138	12	they	they	PRON
cana-1627	138	13	have	have	AUX
cana-1627	138	14	been	be	AUX
cana-1627	138	15	analysed	analyse	VERB
cana-1627	138	16	.	.	PUNCT
cana-1627	139	1	communications	communication	NOUN
cana-1627	139	2	on	on	ADP
cana-1627	139	3	applied	apply	VERB
cana-1627	139	4	nonlinear	nonlinear	ADJ
cana-1627	139	5	analysis	analysis	NOUN
cana-1627	139	6	issn	issn	NOUN
cana-1627	139	7	:	:	PUNCT
cana-1627	139	8	1074	1074	NUM
cana-1627	139	9	-	-	PUNCT
cana-1627	139	10	133x	133x	NUM
cana-1627	139	11	vol	vol	NOUN
cana-1627	139	12	32	32	NUM
cana-1627	139	13	no	no	NOUN
cana-1627	139	14	.	.	NOUN
cana-1627	139	15	1	1	NUM
cana-1627	139	16	(	(	PUNCT
cana-1627	139	17	2025	2025	NUM
cana-1627	139	18	)	)	PUNCT
cana-1627	139	19	154	154	NUM
cana-1627	139	20	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1627	139	21	references	reference	NOUN
cana-1627	139	22	[	[	X
cana-1627	139	23	1	1	NUM
cana-1627	139	24	]	]	X
cana-1627	139	25	akram	akram	NOUN
cana-1627	139	26	,	,	PUNCT
cana-1627	139	27	m.	m.	NOUN
cana-1627	139	28	,	,	PUNCT
cana-1627	139	29	2012	2012	NUM
cana-1627	139	30	.	.	PUNCT
cana-1627	140	1	anti	anti	ADJ
cana-1627	140	2	fuzzy	fuzzy	ADJ
cana-1627	140	3	structures	structure	NOUN
cana-1627	140	4	on	on	ADP
cana-1627	140	5	graphs	graph	NOUN
cana-1627	140	6	.	.	PUNCT
cana-1627	141	1	middle	middle	ADJ
cana-1627	141	2	-	-	PUNCT
cana-1627	141	3	east	east	NOUN
cana-1627	141	4	journal	journal	NOUN
cana-1627	141	5	of	of	ADP
cana-1627	141	6	scientific	scientific	ADJ
cana-1627	141	7	research	research	NOUN
cana-1627	141	8	,	,	PUNCT
cana-1627	141	9	11(12	11(12	NUM
cana-1627	141	10	)	)	PUNCT
cana-1627	141	11	,	,	PUNCT
cana-1627	141	12	pp.1641	pp.1641	PROPN
cana-1627	141	13	-	-	PUNCT
cana-1627	141	14	1648	1648	NUM
cana-1627	141	15	.	.	PUNCT
cana-1627	142	1	available	available	ADJ
cana-1627	142	2	from	from	ADP
cana-1627	142	3	:	:	PUNCT
cana-1627	142	4	doi	doi	NOUN
cana-1627	142	5	:	:	PUNCT
cana-1627	142	6	10.5829	10.5829	NUM
cana-1627	142	7	/	/	SYM
cana-1627	142	8	idosi.mejsr.2012.11.12.131012	idosi.mejsr.2012.11.12.131012	NOUN
cana-1627	143	1	[	[	X
cana-1627	143	2	2	2	NUM
cana-1627	143	3	]	]	PUNCT
cana-1627	143	4	cockayne	cockayne	NOUN
cana-1627	143	5	,	,	PUNCT
cana-1627	143	6	e.j	e.j	PROPN
cana-1627	143	7	.	.	PROPN
cana-1627	143	8	and	and	CCONJ
cana-1627	143	9	hedetniemi	hedetniemi	ADV
cana-1627	143	10	,	,	PUNCT
cana-1627	143	11	s.t	s.t	PROPN
cana-1627	143	12	.	.	PROPN
cana-1627	143	13	,	,	PUNCT
cana-1627	143	14	1977	1977	NUM
cana-1627	143	15	.	.	PUNCT
cana-1627	144	1	towards	towards	ADP
cana-1627	144	2	a	a	DET
cana-1627	144	3	theory	theory	NOUN
cana-1627	144	4	of	of	ADP
cana-1627	144	5	domination	domination	NOUN
cana-1627	144	6	in	in	ADP
cana-1627	144	7	graphs	graph	NOUN
cana-1627	144	8	.	.	PUNCT
cana-1627	145	1	networks	network	NOUN
cana-1627	145	2	,	,	PUNCT
cana-1627	145	3	7(3	7(3	NUM
cana-1627	145	4	)	)	PUNCT
cana-1627	145	5	,	,	PUNCT
cana-1627	145	6	pp.247	pp.247	PROPN
cana-1627	145	7	-	-	PUNCT
cana-1627	145	8	261	261	NUM
cana-1627	145	9	.	.	PUNCT
cana-1627	145	10	available	available	ADJ
cana-1627	145	11	from	from	ADP
cana-1627	145	12	:	:	PUNCT
cana-1627	145	13	http://dx.doi.org/10.1002/net.3230070305	http://dx.doi.org/10.1002/net.3230070305	NOUN
cana-1627	145	14	[	[	X
cana-1627	145	15	3	3	NUM
cana-1627	145	16	]	]	PUNCT
cana-1627	145	17	dash	dash	NOUN
cana-1627	145	18	,	,	PUNCT
cana-1627	145	19	s.p	s.p	PROPN
cana-1627	145	20	.	.	PROPN
cana-1627	145	21	,	,	PUNCT
cana-1627	145	22	2020	2020	NUM
cana-1627	145	23	.	.	PUNCT
cana-1627	146	1	vertex	vertex	NOUN
cana-1627	146	2	-	-	PUNCT
cana-1627	146	3	domatic	domatic	ADJ
cana-1627	146	4	,	,	PUNCT
cana-1627	146	5	edge	edge	NOUN
cana-1627	146	6	-	-	PUNCT
cana-1627	146	7	domatic	domatic	ADJ
cana-1627	146	8	and	and	CCONJ
cana-1627	146	9	total	total	ADJ
cana-1627	146	10	domatic	domatic	ADJ
cana-1627	146	11	number	number	NOUN
cana-1627	146	12	of	of	ADP
cana-1627	146	13	uniform	uniform	ADJ
cana-1627	146	14	hypergraphs	hypergraph	NOUN
cana-1627	146	15	.	.	PUNCT
cana-1627	147	1	arxiv	arxiv	PROPN
cana-1627	147	2	preprint	preprint	NOUN
cana-1627	147	3	arxiv:2009.02783	arxiv:2009.02783	NOUN
cana-1627	147	4	.	.	PUNCT
cana-1627	148	1	available	available	ADJ
cana-1627	148	2	from	from	ADP
cana-1627	148	3	:	:	PUNCT
cana-1627	148	4	https://doi.org/10.48550/arxiv.2009.02783	https://doi.org/10.48550/arxiv.2009.02783	PROPN
cana-1627	148	5	[	[	X
cana-1627	148	6	4	4	NUM
cana-1627	148	7	]	]	SYM
cana-1627	148	8	francis	francis	PROPN
cana-1627	148	9	,	,	PUNCT
cana-1627	148	10	p.	p.	NOUN
cana-1627	148	11	and	and	CCONJ
cana-1627	148	12	rajendraprasad	rajendraprasad	PROPN
cana-1627	148	13	,	,	PUNCT
cana-1627	148	14	d.	d.	PROPN
cana-1627	148	15	,	,	PUNCT
cana-1627	148	16	2021	2021	NUM
cana-1627	148	17	.	.	PUNCT
cana-1627	149	1	on	on	ADP
cana-1627	149	2	domatic	domatic	ADJ
cana-1627	149	3	and	and	CCONJ
cana-1627	149	4	total	total	ADJ
cana-1627	149	5	domatic	domatic	ADJ
cana-1627	149	6	numbers	number	NOUN
cana-1627	149	7	of	of	ADP
cana-1627	149	8	a	a	DET
cana-1627	149	9	product	product	NOUN
cana-1627	149	10	graphs	graph	NOUN
cana-1627	149	11	.	.	PUNCT
cana-1627	150	1	arxiv	arxiv	PROPN
cana-1627	150	2	preprint	preprint	VERB
cana-1627	150	3	arxiv:2103.10713	arxiv:2103.10713	PROPN
cana-1627	150	4	.	.	PUNCT
cana-1627	151	1	available	available	ADJ
cana-1627	151	2	from	from	ADP
cana-1627	151	3	:	:	PUNCT
cana-1627	151	4	https://doi.org/10.48550	https://doi.org/10.48550	PROPN
cana-1627	151	5	/	/	SYM
cana-1627	151	6	arxiv.2103.10713	arxiv.2103.10713	NOUN
cana-1627	152	1	[	[	X
cana-1627	152	2	5	5	NUM
cana-1627	152	3	]	]	PUNCT
cana-1627	152	4	haynes	hayne	NOUN
cana-1627	152	5	,	,	PUNCT
cana-1627	152	6	t.w	t.w	PROPN
cana-1627	152	7	.	.	PROPN
cana-1627	152	8	,	,	PUNCT
cana-1627	152	9	hedetniemi	hedetniemi	PROPN
cana-1627	152	10	,	,	PUNCT
cana-1627	152	11	s.t	s.t	PROPN
cana-1627	152	12	.	.	PROPN
cana-1627	152	13	and	and	CCONJ
cana-1627	152	14	slater	slater	PROPN
cana-1627	152	15	,	,	PUNCT
cana-1627	152	16	p.j	p.j	PROPN
cana-1627	152	17	.	.	PROPN
cana-1627	152	18	,	,	PUNCT
cana-1627	152	19	1998	1998	NUM
cana-1627	152	20	.	.	PUNCT
cana-1627	153	1	fundamentals	fundamental	NOUN
cana-1627	153	2	of	of	ADP
cana-1627	153	3	domination	domination	NOUN
cana-1627	153	4	in	in	ADP
cana-1627	153	5	graphs	graph	NOUN
cana-1627	153	6	marcel	marcel	PROPN
cana-1627	153	7	dekker	dekker	PROPN
cana-1627	153	8	.	.	PUNCT
cana-1627	153	9	inc	inc	PROPN
cana-1627	153	10	.	.	PROPN
cana-1627	153	11	,	,	PUNCT
cana-1627	153	12	new	new	PROPN
cana-1627	153	13	york	york	PROPN
cana-1627	153	14	.	.	PUNCT
cana-1627	154	1	available	available	ADJ
cana-1627	154	2	from	from	ADP
cana-1627	154	3	:	:	PUNCT
cana-1627	154	4	https://doi.org/10.1201/9781482246582	https://doi.org/10.1201/9781482246582	NOUN
cana-1627	155	1	[	[	X
cana-1627	155	2	6	6	NUM
cana-1627	155	3	]	]	SYM
cana-1627	155	4	muthuraj	muthuraj	NOUN
cana-1627	155	5	,	,	PUNCT
cana-1627	155	6	r.	r.	PROPN
cana-1627	155	7	and	and	CCONJ
cana-1627	155	8	sasireka	sasireka	PROPN
cana-1627	155	9	,	,	PUNCT
cana-1627	155	10	a.	a.	NOUN
cana-1627	155	11	,	,	PUNCT
cana-1627	155	12	2018	2018	NUM
cana-1627	155	13	.	.	PUNCT
cana-1627	156	1	domination	domination	NOUN
cana-1627	156	2	on	on	ADP
cana-1627	156	3	anti	anti	X
cana-1627	156	4	fuzzy	fuzzy	ADJ
cana-1627	156	5	graph	graph	NOUN
cana-1627	156	6	.	.	PUNCT
cana-1627	157	1	international	international	ADJ
cana-1627	157	2	journal	journal	PROPN
cana-1627	157	3	of	of	ADP
cana-1627	157	4	mathematical	mathematical	ADJ
cana-1627	157	5	archive	archive	NOUN
cana-1627	157	6	,	,	PUNCT
cana-1627	157	7	9(5	9(5	NUM
cana-1627	157	8	)	)	PUNCT
cana-1627	157	9	,	,	PUNCT
cana-1627	157	10	pp.82	pp.82	NOUN
cana-1627	157	11	-	-	PUNCT
cana-1627	157	12	92	92	NUM
cana-1627	157	13	.	.	PUNCT
cana-1627	158	1	available	available	ADJ
cana-1627	158	2	from	from	ADP
cana-1627	158	3	:	:	PUNCT
cana-1627	158	4	http://dx.doi.org/10.20852/ntmsci.2018.312	http://dx.doi.org/10.20852/ntmsci.2018.312	PROPN
cana-1627	159	1	[	[	X
cana-1627	159	2	7	7	NUM
cana-1627	159	3	]	]	X
cana-1627	159	4	muthuraj	muthuraj	NOUN
cana-1627	159	5	,	,	PUNCT
cana-1627	159	6	r.	r.	PROPN
cana-1627	159	7	and	and	CCONJ
cana-1627	159	8	sasireka	sasireka	PROPN
cana-1627	159	9	,	,	PUNCT
cana-1627	159	10	a.	a.	NOUN
cana-1627	159	11	,	,	PUNCT
cana-1627	159	12	2018	2018	NUM
cana-1627	159	13	.	.	PUNCT
cana-1627	160	1	total	total	ADJ
cana-1627	160	2	domination	domination	NOUN
cana-1627	160	3	on	on	ADP
cana-1627	160	4	anti	anti	X
cana-1627	160	5	fuzzy	fuzzy	ADJ
cana-1627	160	6	graph	graph	NOUN
cana-1627	160	7	.	.	PUNCT
cana-1627	161	1	new	new	ADJ
cana-1627	161	2	trends	trend	NOUN
cana-1627	161	3	in	in	ADP
cana-1627	161	4	mathematical	mathematical	ADJ
cana-1627	161	5	sciences	science	NOUN
cana-1627	161	6	,	,	PUNCT
cana-1627	161	7	6(4	6(4	NUM
cana-1627	161	8	)	)	PUNCT
cana-1627	161	9	,	,	PUNCT
cana-1627	161	10	pp.28	pp.28	NOUN
cana-1627	161	11	-	-	PUNCT
cana-1627	161	12	39	39	NUM
cana-1627	161	13	.	.	PUNCT
cana-1627	162	1	available	available	ADJ
cana-1627	162	2	from	from	ADP
cana-1627	162	3	:	:	PUNCT
cana-1627	162	4	http://dx.doi.org/10.20852/ntmsci.2018.312	http://dx.doi.org/10.20852/ntmsci.2018.312	PROPN
cana-1627	163	1	[	[	X
cana-1627	163	2	8	8	NUM
cana-1627	163	3	]	]	SYM
cana-1627	163	4	muthuraj	muthuraj	X
cana-1627	163	5	.	.	PUNCT
cana-1627	164	1	r.	r.	PROPN
cana-1627	164	2	,	,	PUNCT
cana-1627	164	3	and	and	CCONJ
cana-1627	164	4	sasireka	sasireka	PROPN
cana-1627	164	5	.	.	PUNCT
cana-1627	165	1	a.	a.	NOUN
cana-1627	165	2	,	,	PUNCT
cana-1627	165	3	2017	2017	NUM
cana-1627	165	4	,	,	PUNCT
cana-1627	165	5	on	on	ADP
cana-1627	165	6	anti	anti	X
cana-1627	165	7	fuzzy	fuzzy	ADJ
cana-1627	165	8	graph	graph	NOUN
cana-1627	165	9	,	,	PUNCT
cana-1627	165	10	advances	advance	NOUN
cana-1627	165	11	in	in	ADP
cana-1627	165	12	fuzzy	fuzzy	ADJ
cana-1627	165	13	mathematics	mathematic	NOUN
cana-1627	165	14	,	,	PUNCT
cana-1627	165	15	12(5	12(5	NUM
cana-1627	165	16	)	)	PUNCT
cana-1627	165	17	,	,	PUNCT
cana-1627	165	18	pp	pp	ADP
cana-1627	165	19	:	:	PUNCT
cana-1627	165	20	1123	1123	NUM
cana-1627	165	21	-	-	SYM
cana-1627	165	22	1135	1135	NUM
cana-1627	165	23	.	.	PUNCT
cana-1627	166	1	available	available	ADJ
cana-1627	166	2	from	from	ADP
cana-1627	166	3	:	:	PUNCT
cana-1627	166	4	https://www.ripublication.com/afm17/afmv12n5_06.pdf	https://www.ripublication.com/afm17/afmv12n5_06.pdf	NOUN
cana-1627	167	1	[	[	X
cana-1627	167	2	9	9	NUM
cana-1627	167	3	]	]	SYM
cana-1627	167	4	muthuraj	muthuraj	NOUN
cana-1627	167	5	,	,	PUNCT
cana-1627	167	6	r.	r.	PROPN
cana-1627	167	7	,vijayalakshmi	,vijayalakshmi	PUNCT
cana-1627	167	8	,	,	PUNCT
cana-1627	167	9	p.	p.	NOUN
cana-1627	167	10	,	,	PUNCT
cana-1627	167	11	and	and	CCONJ
cana-1627	167	12	sasireka	sasireka	PROPN
cana-1627	167	13	,	,	PUNCT
cana-1627	167	14	a.	a.	NOUN
cana-1627	167	15	,	,	PUNCT
cana-1627	167	16	domatic	domatic	ADJ
cana-1627	167	17	number	number	NOUN
cana-1627	167	18	on	on	ADP
cana-1627	167	19	anti	anti	X
cana-1627	167	20	fuzzy	fuzzy	ADJ
cana-1627	167	21	graph	graph	NOUN
cana-1627	167	22	,	,	PUNCT
cana-1627	167	23	aip	aip	PROPN
cana-1627	167	24	conference	conference	NOUN
cana-1627	167	25	proceeding	proceeding	NOUN
cana-1627	167	26	.	.	PUNCT
cana-1627	168	1	[	[	PUNCT
cana-1627	168	2	accepted	accept	VERB
cana-1627	168	3	]	]	X
cana-1627	168	4	[	[	X
cana-1627	168	5	10	10	NUM
cana-1627	168	6	]	]	X
cana-1627	168	7	somasundaram	somasundaram	PROPN
cana-1627	168	8	,	,	PUNCT
cana-1627	168	9	a.	a.	NOUN
cana-1627	168	10	and	and	CCONJ
cana-1627	168	11	somasundaram	somasundaram	PROPN
cana-1627	168	12	,	,	PUNCT
cana-1627	168	13	s.	s.	PROPN
cana-1627	168	14	,	,	PUNCT
cana-1627	168	15	1998	1998	NUM
cana-1627	168	16	.	.	PUNCT
cana-1627	169	1	domination	domination	NOUN
cana-1627	169	2	in	in	ADP
cana-1627	169	3	fuzzy	fuzzy	ADJ
cana-1627	169	4	graphs	graph	NOUN
cana-1627	169	5	–	–	PUNCT
cana-1627	169	6	i.	i.	NOUN
cana-1627	169	7	pattern	pattern	NOUN
cana-1627	169	8	recognition	recognition	NOUN
cana-1627	169	9	letters	letter	NOUN
cana-1627	169	10	,	,	PUNCT
cana-1627	169	11	19(9	19(9	NUM
cana-1627	169	12	)	)	PUNCT
cana-1627	169	13	,	,	PUNCT
cana-1627	169	14	pp.787	pp.787	NOUN
cana-1627	169	15	-	-	PUNCT
cana-1627	169	16	791	791	NUM
cana-1627	169	17	.	.	PUNCT
cana-1627	169	18	available	available	ADJ
cana-1627	169	19	from	from	ADP
cana-1627	169	20	:	:	PUNCT
cana-1627	169	21	https://doi.org/10.1016/s0167-8655(98)00064-6	https://doi.org/10.1016/s0167-8655(98)00064-6	PROPN
cana-1627	170	1	[	[	X
cana-1627	170	2	11	11	NUM
cana-1627	170	3	]	]	X
cana-1627	170	4	zadeh	zadeh	PROPN
cana-1627	170	5	,	,	PUNCT
cana-1627	170	6	l.a	l.a	PROPN
cana-1627	170	7	.	.	PROPN
cana-1627	170	8	,	,	PUNCT
cana-1627	170	9	1996	1996	NUM
cana-1627	170	10	.	.	PUNCT
cana-1627	171	1	fuzzy	fuzzy	ADJ
cana-1627	171	2	sets	set	NOUN
cana-1627	171	3	.	.	PUNCT
cana-1627	172	1	in	in	ADP
cana-1627	172	2	fuzzy	fuzzy	ADJ
cana-1627	172	3	sets	set	NOUN
cana-1627	172	4	,	,	PUNCT
cana-1627	172	5	fuzzy	fuzzy	ADJ
cana-1627	172	6	logic	logic	NOUN
cana-1627	172	7	,	,	PUNCT
cana-1627	172	8	and	and	CCONJ
cana-1627	172	9	fuzzy	fuzzy	ADJ
cana-1627	172	10	systems	system	NOUN
cana-1627	172	11	:	:	PUNCT
cana-1627	172	12	selected	select	VERB
cana-1627	172	13	papers	paper	NOUN
cana-1627	172	14	by	by	ADP
cana-1627	172	15	lotfi	lotfi	PROPN
cana-1627	172	16	a	a	DET
cana-1627	172	17	zadeh	zadeh	PROPN
cana-1627	172	18	(	(	PUNCT
cana-1627	172	19	pp	pp	PROPN
cana-1627	172	20	.	.	PUNCT
cana-1627	172	21	394	394	NUM
cana-1627	172	22	-	-	NUM
cana-1627	172	23	432	432	NUM
cana-1627	172	24	)	)	PUNCT
cana-1627	172	25	.	.	PUNCT
cana-1627	173	1	available	available	ADJ
cana-1627	173	2	from	from	ADP
cana-1627	173	3	:	:	PUNCT
cana-1627	173	4	https://doi.org/10.1142/9789814261302_0021	https://doi.org/10.1142/9789814261302_0021	PROPN
cana-1627	173	5	[	[	X
cana-1627	173	6	12	12	NUM
cana-1627	173	7	]	]	PUNCT
cana-1627	173	8	zelinka	zelinka	PROPN
cana-1627	173	9	,	,	PUNCT
cana-1627	173	10	b.	b.	PROPN
cana-1627	173	11	,	,	PUNCT
cana-1627	173	12	1989	1989	NUM
cana-1627	173	13	.	.	PUNCT
cana-1627	174	1	total	total	ADJ
cana-1627	174	2	domatic	domatic	ADJ
cana-1627	174	3	number	number	NOUN
cana-1627	174	4	and	and	CCONJ
cana-1627	174	5	degrees	degree	NOUN
cana-1627	174	6	of	of	ADP
cana-1627	174	7	vertices	vertex	NOUN
cana-1627	174	8	of	of	ADP
cana-1627	174	9	a	a	DET
cana-1627	174	10	graph	graph	NOUN
cana-1627	174	11	.	.	PUNCT
cana-1627	175	1	mathematica	mathematica	PROPN
cana-1627	175	2	slovaca	slovaca	PROPN
cana-1627	175	3	,	,	PUNCT
cana-1627	175	4	39(1	39(1	NUM
cana-1627	175	5	)	)	PUNCT
cana-1627	175	6	,	,	PUNCT
cana-1627	175	7	pp.7	pp.7	PROPN
cana-1627	175	8	-	-	SYM
cana-1627	175	9	11	11	NUM
cana-1627	175	10	.	.	PUNCT
cana-1627	175	11	available	available	ADJ
cana-1627	175	12	from	from	ADP
cana-1627	175	13	:	:	PUNCT
cana-1627	175	14	https://dml.cz/bitstream/handle/10338.dmlcz/133187/mathslov_39-1989-1_2.pdf	https://dml.cz/bitstream/handle/10338.dmlcz/133187/mathslov_39-1989-1_2.pdf	NOUN
cana-1627	176	1	[	[	X
cana-1627	176	2	13	13	NUM
cana-1627	176	3	]	]	PUNCT
cana-1627	176	4	zelinka	zelinka	PROPN
cana-1627	176	5	,	,	PUNCT
cana-1627	176	6	b.	b.	PROPN
cana-1627	176	7	,	,	PUNCT
cana-1627	176	8	1997	1997	NUM
cana-1627	176	9	.	.	PUNCT
cana-1627	177	1	antidomatic	antidomatic	ADJ
cana-1627	177	2	number	number	NOUN
cana-1627	177	3	of	of	ADP
cana-1627	177	4	a	a	DET
cana-1627	177	5	graph	graph	NOUN
cana-1627	177	6	.	.	PUNCT
cana-1627	178	1	archivum	archivum	PROPN
cana-1627	178	2	mathematicum	mathematicum	PROPN
cana-1627	178	3	,	,	PUNCT
cana-1627	178	4	33(2	33(2	NUM
cana-1627	178	5	)	)	PUNCT
cana-1627	178	6	,	,	PUNCT
cana-1627	178	7	pp.191	pp.191	NOUN
cana-1627	178	8	-	-	SYM
cana-1627	178	9	195	195	NUM
cana-1627	178	10	.	.	PUNCT
cana-1627	178	11	available	available	ADJ
cana-1627	178	12	from	from	ADP
cana-1627	178	13	:	:	PUNCT
cana-1627	178	14	https://dml.cz/bitstream/handle/10338.dmlcz/107610/archmathretro_033-1997-2_2.pdf	https://dml.cz/bitstream/handle/10338.dmlcz/107610/archmathretro_033-1997-2_2.pdf	X