id	sid	tid	token	lemma	pos
cana-1652	1	1	communications	communication	NOUN
cana-1652	1	2	on	on	ADP
cana-1652	1	3	applied	apply	VERB
cana-1652	1	4	nonlinear	nonlinear	ADJ
cana-1652	1	5	analysis	analysis	NOUN
cana-1652	1	6	issn	issn	NOUN
cana-1652	1	7	:	:	PUNCT
cana-1652	1	8	1074	1074	NUM
cana-1652	1	9	-	-	PUNCT
cana-1652	1	10	133x	133x	NUM
cana-1652	1	11	vol	vol	NOUN
cana-1652	1	12	32	32	NUM
cana-1652	1	13	no	no	NOUN
cana-1652	1	14	.	.	NOUN
cana-1652	1	15	1	1	NUM
cana-1652	1	16	(	(	PUNCT
cana-1652	1	17	2025	2025	NUM
cana-1652	1	18	)	)	PUNCT
cana-1652	1	19	324	324	NUM
cana-1652	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1652	1	21	study	study	NOUN
cana-1652	1	22	on	on	ADP
cana-1652	1	23	concepts	concept	NOUN
cana-1652	1	24	of	of	ADP
cana-1652	1	25	domination	domination	NOUN
cana-1652	1	26	in	in	ADP
cana-1652	1	27	fuzzy	fuzzy	ADJ
cana-1652	1	28	graphs	graph	NOUN
cana-1652	1	29	ann	ann	PROPN
cana-1652	1	30	mary	mary	PROPN
cana-1652	1	31	joyson1	joyson1	PROPN
cana-1652	1	32	*	*	PROPN
cana-1652	1	33	,	,	PUNCT
cana-1652	1	34	s.	s.	PROPN
cana-1652	1	35	lakshminarayana2	lakshminarayana2	PROPN
cana-1652	2	1	1research	1research	NUM
cana-1652	2	2	scholar	scholar	NOUN
cana-1652	2	3	,	,	PUNCT
cana-1652	2	4	department	department	NOUN
cana-1652	2	5	of	of	ADP
cana-1652	2	6	mathematics	mathematics	PROPN
cana-1652	2	7	,	,	PUNCT
cana-1652	2	8	reva	reva	PROPN
cana-1652	2	9	university	university	PROPN
cana-1652	2	10	bangalore	bangalore	PROPN
cana-1652	2	11	,	,	PUNCT
cana-1652	2	12	karnataka	karnataka	PROPN
cana-1652	2	13	,	,	PUNCT
cana-1652	2	14	india-560064	india-560064	ADJ
cana-1652	2	15	.	.	PUNCT
cana-1652	3	1	2department	2department	NUM
cana-1652	3	2	of	of	ADP
cana-1652	3	3	mathematics	mathematics	PROPN
cana-1652	3	4	,	,	PUNCT
cana-1652	3	5	reva	reva	PROPN
cana-1652	3	6	university	university	PROPN
cana-1652	3	7	bangalore	bangalore	PROPN
cana-1652	3	8	,	,	PUNCT
cana-1652	3	9	karnataka	karnataka	PROPN
cana-1652	3	10	,	,	PUNCT
cana-1652	3	11	india-560064	india-560064	ADJ
cana-1652	3	12	.	.	PUNCT
cana-1652	4	1	∗corresponding	∗corresponde	VERB
cana-1652	4	2	author	author	NOUN
cana-1652	4	3	:	:	PUNCT
cana-1652	4	4	annmary.anu@gmail.com	annmary.anu@gmail.com	PROPN
cana-1652	5	1	article	article	PROPN
cana-1652	5	2	history	history	NOUN
cana-1652	5	3	:	:	PUNCT
cana-1652	5	4	received	receive	VERB
cana-1652	5	5	:	:	PUNCT
cana-1652	5	6	15	15	NUM
cana-1652	5	7	-	-	SYM
cana-1652	5	8	07	07	NUM
cana-1652	5	9	-	-	PUNCT
cana-1652	5	10	2024	2024	NUM
cana-1652	5	11	revised	revise	VERB
cana-1652	5	12	:	:	PUNCT
cana-1652	5	13	29	29	NUM
cana-1652	5	14	-	-	SYM
cana-1652	5	15	08	08	NUM
cana-1652	5	16	-	-	PUNCT
cana-1652	5	17	2024	2024	NUM
cana-1652	5	18	accepted	accept	VERB
cana-1652	5	19	:	:	PUNCT
cana-1652	5	20	11	11	NUM
cana-1652	5	21	-	-	SYM
cana-1652	5	22	09	09	NUM
cana-1652	5	23	-	-	PUNCT
cana-1652	5	24	2024	2024	NUM
cana-1652	5	25	abstract	abstract	NOUN
cana-1652	5	26	:	:	PUNCT
cana-1652	5	27	fuzzy	fuzzy	ADJ
cana-1652	5	28	theory	theory	NOUN
cana-1652	5	29	is	be	AUX
cana-1652	5	30	one	one	NUM
cana-1652	5	31	of	of	ADP
cana-1652	5	32	the	the	DET
cana-1652	5	33	developing	develop	VERB
cana-1652	5	34	discipline	discipline	NOUN
cana-1652	5	35	of	of	ADP
cana-1652	5	36	math	math	NOUN
cana-1652	5	37	,	,	PUNCT
cana-1652	5	38	preceeding	preceede	VERB
cana-1652	5	39	with	with	ADP
cana-1652	5	40	its	its	PRON
cana-1652	5	41	application	application	NOUN
cana-1652	5	42	in	in	ADP
cana-1652	5	43	many	many	ADJ
cana-1652	5	44	different	different	ADJ
cana-1652	5	45	fields	field	NOUN
cana-1652	5	46	.	.	PUNCT
cana-1652	6	1	fuzzy	fuzzy	ADJ
cana-1652	6	2	graph	graph	NOUN
cana-1652	6	3	theory	theory	NOUN
cana-1652	6	4	is	be	AUX
cana-1652	6	5	one	one	NUM
cana-1652	6	6	of	of	ADP
cana-1652	6	7	the	the	DET
cana-1652	6	8	branch	branch	NOUN
cana-1652	6	9	of	of	ADP
cana-1652	6	10	fuzzy	fuzzy	ADJ
cana-1652	6	11	theoretical	theoretical	ADJ
cana-1652	6	12	area	area	NOUN
cana-1652	6	13	,	,	PUNCT
cana-1652	6	14	which	which	PRON
cana-1652	6	15	is	be	AUX
cana-1652	6	16	advanced	advanced	ADJ
cana-1652	6	17	with	with	ADP
cana-1652	6	18	many	many	ADJ
cana-1652	6	19	real	real	ADJ
cana-1652	6	20	life	life	NOUN
cana-1652	6	21	applications	application	NOUN
cana-1652	6	22	in	in	ADP
cana-1652	6	23	new	new	ADJ
cana-1652	6	24	mathematical	mathematical	ADJ
cana-1652	6	25	developments	development	NOUN
cana-1652	6	26	.	.	PUNCT
cana-1652	7	1	in	in	ADP
cana-1652	7	2	this	this	DET
cana-1652	7	3	research	research	NOUN
cana-1652	7	4	article	article	NOUN
cana-1652	7	5	we	we	PRON
cana-1652	7	6	have	have	AUX
cana-1652	7	7	studied	study	VERB
cana-1652	7	8	and	and	CCONJ
cana-1652	7	9	examined	examine	VERB
cana-1652	7	10	few	few	ADJ
cana-1652	7	11	new	new	ADJ
cana-1652	7	12	theoretical	theoretical	ADJ
cana-1652	7	13	concepts	concept	NOUN
cana-1652	7	14	of	of	ADP
cana-1652	7	15	domination	domination	NOUN
cana-1652	7	16	in	in	ADP
cana-1652	7	17	fuzzy	fuzzy	ADJ
cana-1652	7	18	graphs	graph	NOUN
cana-1652	7	19	.	.	PUNCT
cana-1652	8	1	some	some	DET
cana-1652	8	2	useful	useful	ADJ
cana-1652	8	3	application	application	NOUN
cana-1652	8	4	for	for	ADP
cana-1652	8	5	both	both	CCONJ
cana-1652	8	6	fuzzy	fuzzy	ADJ
cana-1652	8	7	graphs	graph	NOUN
cana-1652	8	8	have	have	AUX
cana-1652	8	9	been	be	AUX
cana-1652	8	10	given	give	VERB
cana-1652	8	11	in	in	ADP
cana-1652	8	12	this	this	DET
cana-1652	8	13	research	research	NOUN
cana-1652	8	14	article	article	NOUN
cana-1652	8	15	.	.	PUNCT
cana-1652	9	1	keywords	keyword	NOUN
cana-1652	9	2	:	:	PUNCT
cana-1652	9	3	fuzzy	fuzzy	ADJ
cana-1652	9	4	;	;	PUNCT
cana-1652	9	5	fuzzy	fuzzy	ADJ
cana-1652	9	6	graphs	graph	NOUN
cana-1652	9	7	;	;	PUNCT
cana-1652	9	8	domination	domination	NOUN
cana-1652	9	9	;	;	PUNCT
cana-1652	9	10	graph	graph	NOUN
cana-1652	9	11	.	.	PUNCT
cana-1652	10	1	1	1	X
cana-1652	10	2	.	.	X
cana-1652	10	3	introduction	introduction	NOUN
cana-1652	10	4	in	in	ADP
cana-1652	10	5	theory	theory	NOUN
cana-1652	10	6	space	space	NOUN
cana-1652	10	7	,	,	PUNCT
cana-1652	10	8	a	a	DET
cana-1652	10	9	map	map	NOUN
cana-1652	10	10	is	be	AUX
cana-1652	10	11	an	an	DET
cana-1652	10	12	ordered	order	VERB
cana-1652	10	13	triplet	triplet	NOUN
cana-1652	10	14	(	(	PUNCT
cana-1652	10	15	𝑉(𝐷	𝑉(𝐷	NOUN
cana-1652	10	16	)	)	PUNCT
cana-1652	10	17	,	,	PUNCT
cana-1652	10	18	𝐴(𝐷	𝐴(𝐷	PROPN
cana-1652	10	19	)	)	PUNCT
cana-1652	10	20	,	,	PUNCT
cana-1652	10	21	𝜓𝐷	𝜓𝐷	NOUN
cana-1652	10	22	)	)	PUNCT
cana-1652	10	23	consisting	consist	VERB
cana-1652	10	24	of	of	ADP
cana-1652	10	25	an	an	DET
cana-1652	10	26	unsteady	unsteady	ADJ
cana-1652	10	27	set	set	NOUN
cana-1652	10	28	of	of	ADP
cana-1652	10	29	vertices	vertex	NOUN
cana-1652	10	30	v(d	v(d	PROPN
cana-1652	10	31	)	)	PUNCT
cana-1652	10	32	;	;	PUNCT
cana-1652	10	33	the	the	DET
cana-1652	10	34	set	set	ADJ
cana-1652	10	35	𝐴(𝐷	𝐴(𝐷	NOUN
cana-1652	10	36	)	)	PUNCT
cana-1652	10	37	is	be	AUX
cana-1652	10	38	discrete	discrete	ADJ
cana-1652	10	39	with	with	ADP
cana-1652	10	40	𝑉(𝐷	𝑉(𝐷	NOUN
cana-1652	10	41	)	)	PUNCT
cana-1652	10	42	,	,	PUNCT
cana-1652	10	43	contains	contain	VERB
cana-1652	10	44	arcs	arc	NOUN
cana-1652	10	45	;	;	PUNCT
cana-1652	10	46	and	and	CCONJ
cana-1652	10	47	for	for	ADP
cana-1652	10	48	each	each	DET
cana-1652	10	49	arc	arc	NOUN
cana-1652	10	50	of	of	ADP
cana-1652	10	51	ordered	order	VERB
cana-1652	10	52	vertex	vertex	NOUN
cana-1652	10	53	pairs	pair	NOUN
cana-1652	10	54	𝐷	𝐷	NOUN
cana-1652	10	55	there	there	PRON
cana-1652	10	56	is	be	VERB
cana-1652	10	57	a	a	DET
cana-1652	10	58	matching	matching	NOUN
cana-1652	10	59	function	function	NOUN
cana-1652	10	60	𝜓𝐷	𝜓𝐷	PROPN
cana-1652	10	61	that	that	PRON
cana-1652	10	62	matches	match	VERB
cana-1652	10	63	𝐷	𝐷	PROPN
cana-1652	10	64	[	[	NOUN
cana-1652	10	65	1	1	NUM
cana-1652	10	66	]	]	PUNCT
cana-1652	10	67	.	.	PUNCT
cana-1652	11	1	𝑎	𝑎	PRON
cana-1652	11	2	connects	connect	VERB
cana-1652	11	3	𝑢	𝑢	NOUN
cana-1652	11	4	to	to	ADP
cana-1652	11	5	𝑣	𝑣	PRON
cana-1652	11	6	if	if	SCONJ
cana-1652	11	7	𝑎	𝑎	NOUN
cana-1652	11	8	is	be	AUX
cana-1652	11	9	an	an	DET
cana-1652	11	10	arc	arc	NOUN
cana-1652	11	11	and	and	CCONJ
cana-1652	11	12	𝑢	𝑢	NOUN
cana-1652	11	13	and	and	CCONJ
cana-1652	11	14	𝑣	𝑣	ADP
cana-1652	11	15	,	,	PUNCT
cana-1652	11	16	𝜓𝐷(𝑎	𝜓𝐷(𝑎	NOUN
cana-1652	11	17	)	)	PUNCT
cana-1652	11	18	=	=	PUNCT
cana-1652	11	19	(	(	PUNCT
cana-1652	11	20	𝑢	𝑢	X
cana-1652	11	21	,	,	PUNCT
cana-1652	11	22	𝑣	𝑣	NOUN
cana-1652	11	23	)	)	PUNCT
cana-1652	11	24	;	;	PUNCT
cana-1652	11	25	𝑢	𝑢	PRON
cana-1652	11	26	is	be	AUX
cana-1652	11	27	the	the	DET
cana-1652	11	28	tail	tail	NOUN
cana-1652	11	29	of	of	ADP
cana-1652	11	30	𝑎	𝑎	NOUN
cana-1652	11	31	and	and	CCONJ
cana-1652	11	32	the	the	DET
cana-1652	11	33	head	head	NOUN
cana-1652	11	34	𝑣.	𝑣.	NOUN
cana-1652	11	35	for	for	ADP
cana-1652	11	36	convenience	convenience	NOUN
cana-1652	11	37	,	,	PUNCT
cana-1652	11	38	maps	map	NOUN
cana-1652	11	39	are	be	AUX
cana-1652	11	40	called	call	VERB
cana-1652	11	41	maps	map	NOUN
cana-1652	11	42	for	for	ADP
cana-1652	11	43	short	short	ADJ
cana-1652	11	44	.	.	PUNCT
cana-1652	12	1	for	for	ADP
cana-1652	12	2	a	a	DET
cana-1652	12	3	general	general	ADJ
cana-1652	12	4	discussion	discussion	NOUN
cana-1652	12	5	of	of	ADP
cana-1652	12	6	graph	graph	NOUN
cana-1652	12	7	theory	theory	NOUN
cana-1652	12	8	,	,	PUNCT
cana-1652	12	9	we	we	PRON
cana-1652	12	10	refer	refer	VERB
cana-1652	12	11	to	to	ADP
cana-1652	12	12	[	[	X
cana-1652	12	13	2	2	NUM
cana-1652	12	14	]	]	PUNCT
cana-1652	12	15	.	.	PUNCT
cana-1652	13	1	on	on	ADP
cana-1652	13	2	the	the	DET
cana-1652	13	3	other	other	ADJ
cana-1652	13	4	hand	hand	NOUN
cana-1652	13	5	,	,	PUNCT
cana-1652	13	6	zadeh	zadeh	PROPN
cana-1652	13	7	[	[	X
cana-1652	13	8	3	3	NUM
cana-1652	13	9	]	]	PUNCT
cana-1652	13	10	introduced	introduce	VERB
cana-1652	13	11	the	the	DET
cana-1652	13	12	concept	concept	NOUN
cana-1652	13	13	of	of	ADP
cana-1652	13	14	fuzzy	fuzzy	ADJ
cana-1652	13	15	set	set	NOUN
cana-1652	13	16	in	in	ADP
cana-1652	13	17	his	his	PRON
cana-1652	13	18	1965	1965	NUM
cana-1652	13	19	article	article	NOUN
cana-1652	13	20	.	.	PUNCT
cana-1652	14	1	rosenfeld	rosenfeld	PROPN
cana-1652	15	1	[	[	X
cana-1652	15	2	4	4	NUM
cana-1652	15	3	]	]	PUNCT
cana-1652	15	4	investigated	investigate	VERB
cana-1652	15	5	the	the	DET
cana-1652	15	6	relationship	relationship	NOUN
cana-1652	15	7	between	between	ADP
cana-1652	15	8	fuzzy	fuzzy	ADJ
cana-1652	15	9	sets	set	NOUN
cana-1652	15	10	and	and	CCONJ
cana-1652	15	11	introduced	introduce	VERB
cana-1652	15	12	fuzzy	fuzzy	ADJ
cana-1652	15	13	graphs	graph	NOUN
cana-1652	15	14	in	in	ADP
cana-1652	15	15	1975	1975	NUM
cana-1652	15	16	.	.	PUNCT
cana-1652	16	1	mordeson	mordeson	NOUN
cana-1652	16	2	and	and	CCONJ
cana-1652	16	3	chang	chang	PROPN
cana-1652	16	4	-	-	PUNCT
cana-1652	16	5	shyh	shyh	PROPN
cana-1652	17	1	[	[	X
cana-1652	17	2	5	5	NUM
cana-1652	17	3	]	]	PUNCT
cana-1652	17	4	,	,	PUNCT
cana-1652	17	5	some	some	DET
cana-1652	17	6	simple	simple	ADJ
cana-1652	17	7	functions	function	NOUN
cana-1652	17	8	on	on	ADP
cana-1652	17	9	fuzzy	fuzzy	ADJ
cana-1652	17	10	graphs	graph	NOUN
cana-1652	17	11	and	and	CCONJ
cana-1652	17	12	some	some	DET
cana-1652	17	13	recent	recent	ADJ
cana-1652	17	14	demonstration	demonstration	NOUN
cana-1652	17	15	on	on	ADP
cana-1652	17	16	some	some	DET
cana-1652	17	17	important	important	ADJ
cana-1652	17	18	developments	development	NOUN
cana-1652	17	19	in	in	ADP
cana-1652	17	20	fuzzy	fuzzy	ADJ
cana-1652	17	21	graphs	graph	NOUN
cana-1652	17	22	,	,	PUNCT
cana-1652	17	23	theory	theory	NOUN
cana-1652	17	24	and	and	CCONJ
cana-1652	17	25	applications	application	NOUN
cana-1652	17	26	of	of	ADP
cana-1652	17	27	fuzzy	fuzzy	ADJ
cana-1652	17	28	graphs	graph	NOUN
cana-1652	17	29	,	,	PUNCT
cana-1652	17	30	edited	edit	VERB
cana-1652	17	31	by	by	ADP
cana-1652	17	32	mordeson	mordeson	NOUN
cana-1652	17	33	and	and	CCONJ
cana-1652	17	34	nair	nair	NOUN
cana-1652	18	1	[	[	X
cana-1652	18	2	6	6	NUM
cana-1652	18	3	]	]	PUNCT
cana-1652	18	4	.	.	PUNCT
cana-1652	19	1	since	since	SCONJ
cana-1652	19	2	then	then	ADV
cana-1652	19	3	,	,	PUNCT
cana-1652	19	4	many	many	ADJ
cana-1652	19	5	extensions	extension	NOUN
cana-1652	19	6	of	of	ADP
cana-1652	19	7	fuzzy	fuzzy	ADJ
cana-1652	19	8	graphs	graph	NOUN
cana-1652	19	9	have	have	AUX
cana-1652	19	10	been	be	AUX
cana-1652	19	11	given	give	VERB
cana-1652	19	12	in	in	ADP
cana-1652	19	13	the	the	DET
cana-1652	19	14	literature	literature	NOUN
cana-1652	19	15	,	,	PUNCT
cana-1652	19	16	including	include	VERB
cana-1652	19	17	m	m	NOUN
cana-1652	19	18	-	-	ADJ
cana-1652	19	19	strong	strong	ADJ
cana-1652	19	20	fuzzy	fuzzy	ADJ
cana-1652	19	21	graphs[7	graphs[7	NOUN
cana-1652	19	22	]	]	NOUN
cana-1652	19	23	,	,	PUNCT
cana-1652	19	24	intuitive	intuitive	ADJ
cana-1652	19	25	fuzzy	fuzzy	ADJ
cana-1652	19	26	graphs[8	graphs[8	PROPN
cana-1652	19	27	]	]	PUNCT
cana-1652	19	28	,	,	PUNCT
cana-1652	19	29	regular	regular	ADJ
cana-1652	19	30	fuzzy	fuzzy	ADJ
cana-1652	19	31	graphs[9	graphs[9	PROPN
cana-1652	19	32	]	]	PUNCT
cana-1652	19	33	,	,	PUNCT
cana-1652	19	34	bipolar	bipolar	ADJ
cana-1652	19	35	fuzzy	fuzzy	ADJ
cana-1652	19	36	graphs[10	graphs[10	NOUN
cana-1652	19	37	]	]	X
cana-1652	19	38	short	short	ADJ
cana-1652	19	39	value	value	NOUN
cana-1652	19	40	fuzzy	fuzzy	ADJ
cana-1652	19	41	graph	graph	NOUN
cana-1652	19	42	[	[	X
cana-1652	19	43	11	11	NUM
cana-1652	19	44	]	]	PUNCT
cana-1652	19	45	and	and	CCONJ
cana-1652	19	46	dombi	dombi	NOUN
cana-1652	19	47	fuzzy	fuzzy	ADJ
cana-1652	19	48	graph	graph	NOUN
cana-1652	20	1	[	[	X
cana-1652	20	2	12	12	NUM
cana-1652	20	3	]	]	PUNCT
cana-1652	20	4	,	,	PUNCT
cana-1652	20	5	etc	etc	X
cana-1652	20	6	.	.	X
cana-1652	20	7	note	note	VERB
cana-1652	20	8	that	that	SCONJ
cana-1652	20	9	this	this	DET
cana-1652	20	10	list	list	NOUN
cana-1652	20	11	is	be	AUX
cana-1652	20	12	not	not	PART
cana-1652	20	13	inclusive	inclusive	ADJ
cana-1652	20	14	.	.	PUNCT
cana-1652	21	1	we	we	PRON
cana-1652	21	2	explore	explore	VERB
cana-1652	21	3	some	some	DET
cana-1652	21	4	concepts	concept	NOUN
cana-1652	21	5	of	of	ADP
cana-1652	21	6	fuzzy	fuzzy	ADJ
cana-1652	21	7	graphs	graph	NOUN
cana-1652	21	8	by	by	ADP
cana-1652	21	9	allowing	allow	VERB
cana-1652	21	10	𝑆	𝑆	PROPN
cana-1652	21	11	to	to	PART
cana-1652	21	12	be	be	AUX
cana-1652	21	13	a	a	DET
cana-1652	21	14	set	set	NOUN
cana-1652	21	15	.	.	PUNCT
cana-1652	22	1	a	a	DET
cana-1652	22	2	fuzzy	fuzzy	ADJ
cana-1652	22	3	subset	subset	NOUN
cana-1652	22	4	of	of	ADP
cana-1652	22	5	𝑆	𝑆	PROPN
cana-1652	22	6	is	be	AUX
cana-1652	22	7	a	a	DET
cana-1652	22	8	map	map	NOUN
cana-1652	22	9	𝜎	𝜎	NOUN
cana-1652	22	10	:	:	PUNCT
cana-1652	22	11	𝑆	𝑆	PROPN
cana-1652	22	12	→	→	SYM
cana-1652	23	1	[	[	X
cana-1652	23	2	0,1	0,1	NUM
cana-1652	23	3	]	]	PUNCT
cana-1652	23	4	that	that	PRON
cana-1652	23	5	assigns	assign	VERB
cana-1652	23	6	an	an	DET
cana-1652	23	7	attribution	attribution	NOUN
cana-1652	23	8	degree	degree	NOUN
cana-1652	23	9	to	to	ADP
cana-1652	23	10	each	each	DET
cana-1652	23	11	𝑥	𝑥	PRON
cana-1652	23	12	∈	∈	PROPN
cana-1652	23	13	𝑆	𝑆	PROPN
cana-1652	23	14	,	,	PUNCT
cana-1652	23	15	0	0	NUM
cana-1652	23	16	≤	≤	NUM
cana-1652	23	17	𝑠𝑖𝑔𝑚𝑎(𝑥	𝑠𝑖𝑔𝑚𝑎(𝑥	PROPN
cana-1652	23	18	)	)	PUNCT
cana-1652	23	19	≤	≤	NUM
cana-1652	23	20	1	1	NUM
cana-1652	23	21	..	..	PUNCT
cana-1652	23	22	similarly	similarly	ADV
cana-1652	23	23	,	,	PUNCT
cana-1652	23	24	the	the	DET
cana-1652	23	25	relation	relation	NOUN
cana-1652	23	26	𝑆	𝑆	PROPN
cana-1652	23	27	is	be	AUX
cana-1652	23	28	a	a	DET
cana-1652	23	29	fuzzy	fuzzy	ADJ
cana-1652	23	30	subset	subset	NOUN
cana-1652	23	31	of	of	ADP
cana-1652	23	32	𝑆	𝑆	PROPN
cana-1652	23	33	×	×	PROPN
cana-1652	23	34	𝑆	𝑆	PROPN
cana-1652	23	35	,	,	PUNCT
cana-1652	23	36	map	map	VERB
cana-1652	23	37	𝜇	𝜇	ADP
cana-1652	23	38	:	:	PUNCT
cana-1652	23	39	𝑆	𝑆	PROPN
cana-1652	23	40	×	×	NOUN
cana-1652	23	41	𝑆	𝑆	PROPN
cana-1652	23	42	→	→	SYM
cana-1652	23	43	[	[	X
cana-1652	23	44	0,1	0,1	NUM
cana-1652	23	45	]	]	PUNCT
cana-1652	23	46	,	,	PUNCT
cana-1652	23	47	given	give	VERB
cana-1652	23	48	for	for	ADP
cana-1652	23	49	each	each	DET
cana-1652	23	50	(	(	PUNCT
cana-1652	23	51	𝑥	𝑥	PROPN
cana-1652	23	52	,	,	PUNCT
cana-1652	23	53	𝑦𝑜𝑟𝑑𝑒𝑟	𝑦𝑜𝑟𝑑𝑒𝑟	ADJ
cana-1652	23	54	)	)	PUNCT
cana-1652	23	55	)	)	PUNCT
cana-1652	23	56	membership	membership	NOUN
cana-1652	23	57	degree	degree	NOUN
cana-1652	23	58	,	,	PUNCT
cana-1652	23	59	0	0	NUM
cana-1652	23	60	≤	≤	NUM
cana-1652	23	61	𝜇(𝑥	𝜇(𝑥	PROPN
cana-1652	23	62	,	,	PUNCT
cana-1652	23	63	𝑦	𝑦	NOUN
cana-1652	23	64	)	)	PUNCT
cana-1652	23	65	≤	≤	NUM
cana-1652	23	66	1	1	NUM
cana-1652	23	67	.	.	PUNCT
cana-1652	24	1	in	in	ADP
cana-1652	24	2	the	the	DET
cana-1652	24	3	special	special	ADJ
cana-1652	24	4	case	case	NOUN
cana-1652	24	5	where	where	SCONJ
cana-1652	24	6	𝜎	𝜎	PROPN
cana-1652	24	7	and	and	CCONJ
cana-1652	24	8	𝜇	𝜇	ADV
cana-1652	24	9	can	can	AUX
cana-1652	24	10	only	only	ADV
cana-1652	24	11	take	take	VERB
cana-1652	24	12	the	the	DET
cana-1652	24	13	values	value	NOUN
cana-1652	24	14	0	0	PUNCT
cana-1652	24	15	and	and	CCONJ
cana-1652	24	16	1	1	NUM
cana-1652	24	17	,	,	PUNCT
cana-1652	24	18	they	they	PRON
cana-1652	24	19	become	become	VERB
cana-1652	24	20	properties	property	NOUN
cana-1652	24	21	of	of	ADP
cana-1652	24	22	identical	identical	ADJ
cana-1652	24	23	subsets	subset	NOUN
cana-1652	24	24	of	of	ADP
cana-1652	24	25	𝑆	𝑆	PROPN
cana-1652	24	26	and	and	CCONJ
cana-1652	24	27	the	the	DET
cana-1652	24	28	relationship	relationship	NOUN
cana-1652	24	29	between	between	ADP
cana-1652	24	30	𝑆	𝑆	PROPN
cana-1652	24	31	,	,	PUNCT
cana-1652	24	32	respectively	respectively	ADV
cana-1652	24	33	.	.	PUNCT
cana-1652	25	1	with	with	ADP
cana-1652	25	2	interesting	interesting	ADJ
cana-1652	25	3	results	result	NOUN
cana-1652	25	4	and	and	CCONJ
cana-1652	25	5	many	many	ADJ
cana-1652	25	6	applications	application	NOUN
cana-1652	25	7	,	,	PUNCT
cana-1652	25	8	control	control	NOUN
cana-1652	25	9	in	in	ADP
cana-1652	25	10	graphics	graphic	NOUN
cana-1652	25	11	has	have	AUX
cana-1652	25	12	become	become	VERB
cana-1652	25	13	a	a	DET
cana-1652	25	14	large	large	ADJ
cana-1652	25	15	area	area	NOUN
cana-1652	25	16	of	of	ADP
cana-1652	25	17	graphics	graphic	NOUN
cana-1652	25	18	research	research	NOUN
cana-1652	25	19	.	.	PUNCT
cana-1652	26	1	it	it	PRON
cana-1652	26	2	was	be	AUX
cana-1652	26	3	introduced	introduce	VERB
cana-1652	26	4	by	by	ADP
cana-1652	26	5	claude	claude	PROPN
cana-1652	26	6	berge	berge	PROPN
cana-1652	26	7	in	in	ADP
cana-1652	26	8	1958	1958	NUM
cana-1652	26	9	and	and	CCONJ
cana-1652	26	10	by	by	ADP
cana-1652	26	11	oystein	oystein	ADJ
cana-1652	26	12	ore	ore	NOUN
cana-1652	26	13	in	in	ADP
cana-1652	26	14	1962	1962	NUM
cana-1652	26	15	,	,	PUNCT
cana-1652	26	16	[	[	X
cana-1652	26	17	13	13	NUM
cana-1652	26	18	]	]	PUNCT
cana-1652	26	19	and	and	CCONJ
cana-1652	26	20	initial	initial	ADJ
cana-1652	26	21	results	result	NOUN
cana-1652	26	22	and	and	CCONJ
cana-1652	26	23	applications	application	NOUN
cana-1652	26	24	were	be	AUX
cana-1652	26	25	presented	present	VERB
cana-1652	26	26	by	by	ADP
cana-1652	26	27	cockayne	cockayne	NOUN
cana-1652	26	28	and	and	CCONJ
cana-1652	26	29	hedetniemi	hedetniemi	NOUN
cana-1652	27	1	[	[	X
cana-1652	27	2	14	14	NUM
cana-1652	27	3	]	]	PUNCT
cana-1652	27	4	.	.	PUNCT
cana-1652	28	1	the	the	DET
cana-1652	28	2	most	most	ADV
cana-1652	28	3	detailed	detailed	ADJ
cana-1652	28	4	discussion	discussion	NOUN
cana-1652	28	5	on	on	ADP
cana-1652	28	6	this	this	DET
cana-1652	28	7	topic	topic	NOUN
cana-1652	28	8	is	be	AUX
cana-1652	28	9	haynes	hayne	NOUN
cana-1652	28	10	et	et	NOUN
cana-1652	28	11	al	al	PROPN
cana-1652	28	12	.	.	PUNCT
cana-1652	29	1	[	[	X
cana-1652	29	2	15	15	NUM
cana-1652	29	3	]	]	PUNCT
cana-1652	29	4	,	,	PUNCT
cana-1652	29	5	haynes	hayne	VERB
cana-1652	29	6	[	[	X
cana-1652	29	7	16	16	NUM
cana-1652	29	8	]	]	PUNCT
cana-1652	29	9	and	and	CCONJ
cana-1652	29	10	haynes	hayne	NOUN
cana-1652	29	11	et	et	PROPN
cana-1652	29	12	al	al	PROPN
cana-1652	29	13	.	.	PUNCT
cana-1652	30	1	[	[	X
cana-1652	30	2	17	17	NUM
cana-1652	30	3	]	]	PUNCT
cana-1652	30	4	.	.	PUNCT
cana-1652	31	1	an	an	DET
cana-1652	31	2	extension	extension	NOUN
cana-1652	31	3	of	of	ADP
cana-1652	31	4	the	the	DET
cana-1652	31	5	dominance	dominance	NOUN
cana-1652	31	6	diagram	diagram	NOUN
cana-1652	31	7	is	be	AUX
cana-1652	31	8	common	common	ADJ
cana-1652	31	9	in	in	ADP
cana-1652	31	10	the	the	DET
cana-1652	31	11	literature	literature	NOUN
cana-1652	31	12	.	.	PUNCT
cana-1652	32	1	some	some	DET
cana-1652	32	2	recent	recent	ADJ
cana-1652	32	3	references	reference	NOUN
cana-1652	32	4	are	be	AUX
cana-1652	32	5	:	:	PUNCT
cana-1652	32	6	post	post	VERB
cana-1652	32	7	control	control	NOUN
cana-1652	33	1	[	[	X
cana-1652	33	2	18	18	NUM
cana-1652	33	3	]	]	PUNCT
cana-1652	33	4	,	,	PUNCT
cana-1652	33	5	communications	communication	NOUN
cana-1652	33	6	on	on	ADP
cana-1652	33	7	applied	apply	VERB
cana-1652	33	8	nonlinear	nonlinear	ADJ
cana-1652	33	9	analysis	analysis	NOUN
cana-1652	33	10	issn	issn	NOUN
cana-1652	33	11	:	:	PUNCT
cana-1652	33	12	1074	1074	NUM
cana-1652	33	13	-	-	PUNCT
cana-1652	33	14	133x	133x	NUM
cana-1652	33	15	vol	vol	NOUN
cana-1652	33	16	32	32	NUM
cana-1652	33	17	no	no	NOUN
cana-1652	33	18	.	.	NOUN
cana-1652	33	19	1	1	NUM
cana-1652	33	20	(	(	PUNCT
cana-1652	33	21	2025	2025	NUM
cana-1652	33	22	)	)	PUNCT
cana-1652	33	23	325	325	NUM
cana-1652	33	24	https://internationalpubls.com	https://internationalpubls.com	X
cana-1652	33	25	pitchfork	pitchfork	NOUN
cana-1652	33	26	control	control	NOUN
cana-1652	34	1	[	[	X
cana-1652	34	2	19	19	NUM
cana-1652	34	3	]	]	PUNCT
cana-1652	34	4	,	,	PUNCT
cana-1652	34	5	roman	roman	ADJ
cana-1652	34	6	control	control	NOUN
cana-1652	35	1	[	[	X
cana-1652	35	2	20	20	NUM
cana-1652	35	3	]	]	PUNCT
cana-1652	35	4	,	,	PUNCT
cana-1652	35	5	double	double	ADJ
cana-1652	35	6	roman	roman	ADJ
cana-1652	35	7	control	control	NOUN
cana-1652	36	1	[	[	X
cana-1652	36	2	21	21	NUM
cana-1652	36	3	]	]	PUNCT
cana-1652	36	4	,	,	PUNCT
cana-1652	36	5	triple	triple	ADJ
cana-1652	36	6	roman	roman	ADJ
cana-1652	36	7	control	control	NOUN
cana-1652	37	1	[	[	X
cana-1652	37	2	22	22	NUM
cana-1652	37	3	]	]	PUNCT
cana-1652	37	4	,	,	PUNCT
cana-1652	37	5	fixed	fix	VERB
cana-1652	37	6	control	control	NOUN
cana-1652	38	1	[	[	X
cana-1652	38	2	23	23	NUM
cana-1652	38	3	]	]	PUNCT
cana-1652	38	4	,	,	PUNCT
cana-1652	38	5	convex	convex	ADJ
cana-1652	38	6	dominance	dominance	NOUN
cana-1652	38	7	[	[	X
cana-1652	38	8	24	24	NUM
cana-1652	38	9	]	]	PUNCT
cana-1652	38	10	and	and	CCONJ
cana-1652	38	11	dual	dual	ADJ
cana-1652	38	12	dominance	dominance	NOUN
cana-1652	39	1	[	[	X
cana-1652	39	2	25	25	NUM
cana-1652	39	3	]	]	PUNCT
cana-1652	39	4	and	and	CCONJ
cana-1652	39	5	others	other	NOUN
cana-1652	39	6	.	.	PUNCT
cana-1652	40	1	the	the	DET
cana-1652	40	2	scope	scope	NOUN
cana-1652	40	3	of	of	ADP
cana-1652	40	4	this	this	DET
cana-1652	40	5	topic	topic	NOUN
cana-1652	40	6	has	have	AUX
cana-1652	40	7	grown	grow	VERB
cana-1652	40	8	exponentially	exponentially	ADV
cana-1652	40	9	over	over	ADP
cana-1652	40	10	the	the	DET
cana-1652	40	11	past	past	ADJ
cana-1652	40	12	decade	decade	NOUN
cana-1652	40	13	.	.	PUNCT
cana-1652	41	1	let	let	VERB
cana-1652	41	2	’s	’s	NOUN
cana-1652	41	3	consider	consider	VERB
cana-1652	41	4	𝐺	𝐺	PROPN
cana-1652	41	5	=	=	SYM
cana-1652	41	6	(	(	PUNCT
cana-1652	41	7	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1652	41	8	)	)	PUNCT
cana-1652	41	9	,	,	PUNCT
cana-1652	41	10	𝐸(𝐺	𝐸(𝐺	NOUN
cana-1652	41	11	)	)	PUNCT
cana-1652	41	12	)	)	PUNCT
cana-1652	41	13	as	as	ADP
cana-1652	41	14	a	a	DET
cana-1652	41	15	graph	graph	NOUN
cana-1652	41	16	.	.	PUNCT
cana-1652	42	1	a	a	DET
cana-1652	42	2	subset	subset	ADJ
cana-1652	42	3	𝑆	𝑆	PROPN
cana-1652	42	4	of	of	ADP
cana-1652	42	5	a	a	DET
cana-1652	42	6	vertex	vertex	NOUN
cana-1652	42	7	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1652	42	8	)	)	PUNCT
cana-1652	42	9	is	be	AUX
cana-1652	42	10	the	the	DET
cana-1652	42	11	dominant	dominant	ADJ
cana-1652	42	12	set	set	NOUN
cana-1652	42	13	of	of	ADP
cana-1652	42	14	the	the	DET
cana-1652	42	15	graph	graph	NOUN
cana-1652	42	16	𝐺	𝐺	NOUN
cana-1652	42	17	if	if	SCONJ
cana-1652	42	18	there	there	PRON
cana-1652	42	19	is	be	VERB
cana-1652	42	20	a	a	DET
cana-1652	42	21	𝑥	𝑥	PRON
cana-1652	42	22	∈	∈	PROPN
cana-1652	42	23	𝑆	𝑆	PROPN
cana-1652	42	24	for	for	ADP
cana-1652	42	25	every	every	DET
cana-1652	42	26	vertex	vertex	NOUN
cana-1652	42	27	𝑣	𝑣	ADP
cana-1652	42	28	∈	∈	NOUN
cana-1652	42	29	𝑉(𝐺)§	𝑉(𝐺)§	PUNCT
cana-1652	42	30	i	i	PRON
cana-1652	42	31	make	make	VERB
cana-1652	42	32	a	a	DET
cana-1652	42	33	side	side	NOUN
cana-1652	42	34	of	of	ADP
cana-1652	42	35	𝐺.	𝐺.	NOUN
cana-1652	42	36	the	the	DET
cana-1652	42	37	dominant	dominant	ADJ
cana-1652	42	38	set	set	NOUN
cana-1652	42	39	of	of	ADP
cana-1652	42	40	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1652	42	41	)	)	PUNCT
cana-1652	42	42	is	be	AUX
cana-1652	42	43	the	the	DET
cana-1652	42	44	minimum	minimum	ADJ
cana-1652	42	45	cardinality	cardinality	NOUN
cana-1652	42	46	of	of	ADP
cana-1652	42	47	the	the	DET
cana-1652	42	48	dominant	dominant	ADJ
cana-1652	42	49	set	set	VERB
cana-1652	42	50	𝑆	𝑆	PROPN
cana-1652	42	51	of	of	ADP
cana-1652	42	52	𝐺.	𝐺.	NOUN
cana-1652	42	53	subsequently	subsequently	ADV
cana-1652	42	54	,	,	PUNCT
cana-1652	42	55	the	the	DET
cana-1652	42	56	concept	concept	NOUN
cana-1652	42	57	of	of	ADP
cana-1652	42	58	control	control	NOUN
cana-1652	42	59	in	in	ADP
cana-1652	42	60	fuzzy	fuzzy	ADJ
cana-1652	42	61	graphs	graph	NOUN
cana-1652	42	62	was	be	AUX
cana-1652	42	63	introduced	introduce	VERB
cana-1652	42	64	by	by	ADP
cana-1652	42	65	somasundaram	somasundaram	NOUN
cana-1652	42	66	[	[	X
cana-1652	42	67	26	26	NUM
cana-1652	42	68	]	]	PUNCT
cana-1652	42	69	.	.	PUNCT
cana-1652	43	1	let	let	VERB
cana-1652	43	2	𝑉	𝑉	PRON
cana-1652	43	3	be	be	AUX
cana-1652	43	4	an	an	DET
cana-1652	43	5	arbitrary	arbitrary	ADJ
cana-1652	43	6	set	set	NOUN
cana-1652	43	7	of	of	ADP
cana-1652	43	8	constraints	constraint	NOUN
cana-1652	43	9	and	and	CCONJ
cana-1652	43	10	𝐸	𝐸	PROPN
cana-1652	43	11	be	be	VERB
cana-1652	43	12	the	the	DET
cana-1652	43	13	set	set	NOUN
cana-1652	43	14	of	of	ADP
cana-1652	43	15	all	all	DET
cana-1652	43	16	binary	binary	ADJ
cana-1652	43	17	subsets	subset	NOUN
cana-1652	43	18	of	of	ADP
cana-1652	43	19	𝑉.	𝑉.	NOUN
cana-1652	43	20	the	the	DET
cana-1652	43	21	fuzzy	fuzzy	ADJ
cana-1652	43	22	graph	graph	NOUN
cana-1652	43	23	𝐺	𝐺	PROPN
cana-1652	43	24	=	=	SYM
cana-1652	43	25	(	(	PUNCT
cana-1652	43	26	𝜎	𝜎	PROPN
cana-1652	43	27	,	,	PUNCT
cana-1652	43	28	𝜇	𝜇	X
cana-1652	43	29	)	)	PUNCT
cana-1652	43	30	is	be	AUX
cana-1652	43	31	a	a	DET
cana-1652	43	32	bifunctional	bifunctional	ADJ
cana-1652	43	33	set	set	VERB
cana-1652	43	34	𝜎	𝜎	NOUN
cana-1652	43	35	:	:	PUNCT
cana-1652	43	36	𝑉	𝑉	PROPN
cana-1652	43	37	→	→	SYM
cana-1652	43	38	[	[	X
cana-1652	43	39	0,1	0,1	NUM
cana-1652	43	40	]	]	PUNCT
cana-1652	43	41	and	and	CCONJ
cana-1652	43	42	𝜇	𝜇	ADP
cana-1652	43	43	:	:	PUNCT
cana-1652	43	44	𝐸	𝐸	PROPN
cana-1652	43	45	→	→	SYM
cana-1652	44	1	[	[	X
cana-1652	44	2	0,1	0,1	NUM
cana-1652	44	3	]	]	PUNCT
cana-1652	44	4	such	such	ADJ
cana-1652	44	5	that	that	SCONJ
cana-1652	44	6	𝜇({𝑥	𝜇({𝑥	PROPN
cana-1652	44	7	,	,	PUNCT
cana-1652	44	8	𝑦	𝑦	NOUN
cana-1652	44	9	}	}	PUNCT
cana-1652	44	10	)	)	PUNCT
cana-1652	44	11	≤	≤	NUM
cana-1652	44	12	𝜎(𝑥	𝜎(𝑥	NOUN
cana-1652	44	13	)	)	PUNCT
cana-1652	44	14	∧	∧	NOUN
cana-1652	44	15	𝜎(𝑦	𝜎(𝑦	PROPN
cana-1652	44	16	)	)	PUNCT
cana-1652	44	17	for	for	ADP
cana-1652	44	18	all	all	PRON
cana-1652	44	19	𝑥	𝑥	PROPN
cana-1652	44	20	,	,	PUNCT
cana-1652	44	21	𝑦	𝑦	NOUN
cana-1652	44	22	∈	∈	NOUN
cana-1652	44	23	𝑉.	𝑉.	NOUN
cana-1652	44	24	if	if	SCONJ
cana-1652	44	25	𝐺	𝐺	PROPN
cana-1652	44	26	=	=	SYM
cana-1652	44	27	(	(	PUNCT
cana-1652	44	28	𝜎	𝜎	PROPN
cana-1652	44	29	,	,	PUNCT
cana-1652	44	30	𝜇	𝜇	X
cana-1652	44	31	)	)	PUNCT
cana-1652	44	32	is	be	AUX
cana-1652	44	33	a	a	DET
cana-1652	44	34	fuzzy	fuzzy	ADJ
cana-1652	44	35	graph	graph	NOUN
cana-1652	44	36	over	over	ADP
cana-1652	44	37	𝑉	𝑉	PROPN
cana-1652	44	38	,	,	PUNCT
cana-1652	44	39	where	where	SCONJ
cana-1652	44	40	𝑥	𝑥	NOUN
cana-1652	44	41	,	,	PUNCT
cana-1652	44	42	𝑦	𝑦	NOUN
cana-1652	44	43	∈	∈	NOUN
cana-1652	44	44	𝑖𝑠𝑎𝑡𝑉	𝑖𝑠𝑎𝑡𝑉	PROPN
cana-1652	44	45	,	,	PUNCT
cana-1652	44	46	𝜇(𝑥	𝜇(𝑥	PROPN
cana-1652	44	47	,	,	PUNCT
cana-1652	44	48	𝑦	𝑦	NOUN
cana-1652	44	49	)	)	PUNCT
cana-1652	44	50	=	=	SYM
cana-1652	44	51	𝜎(𝑥	𝜎(𝑥	NOUN
cana-1652	44	52	)	)	PUNCT
cana-1652	44	53	∧	∧	NOUN
cana-1652	44	54	𝜎(𝑦	𝜎(𝑦	PROPN
cana-1652	44	55	)	)	PUNCT
cana-1652	44	56	.	.	PUNCT
cana-1652	45	1	the	the	DET
cana-1652	45	2	𝑆	𝑆	PROPN
cana-1652	45	3	subset	subset	NOUN
cana-1652	45	4	of	of	ADP
cana-1652	45	5	𝑉	𝑉	PROPN
cana-1652	45	6	is	be	AUX
cana-1652	45	7	called	call	VERB
cana-1652	45	8	the	the	DET
cana-1652	45	9	dominant	dominant	ADJ
cana-1652	45	10	set	set	NOUN
cana-1652	45	11	in	in	ADP
cana-1652	45	12	𝐺	𝐺	PROPN
cana-1652	45	13	if	if	SCONJ
cana-1652	45	14	𝑢	𝑢	PROPN
cana-1652	45	15	∈	∈	PROPN
cana-1652	45	16	𝑆	𝑆	PROPN
cana-1652	45	17	exists	exist	VERB
cana-1652	45	18	for	for	ADP
cana-1652	45	19	every	every	DET
cana-1652	45	20	𝑣	𝑣	NOUN
cana-1652	45	21	∈/𝑆	∈/𝑆	ADJ
cana-1652	45	22	and	and	CCONJ
cana-1652	45	23	𝑢	𝑢	PRON
cana-1652	45	24	dominates	dominate	VERB
cana-1652	45	25	𝑣.	𝑣.	ADV
cana-1652	45	26	the	the	DET
cana-1652	45	27	minimum	minimum	ADJ
cana-1652	45	28	fuzzy	fuzzy	ADJ
cana-1652	45	29	cardinality	cardinality	NOUN
cana-1652	45	30	of	of	ADP
cana-1652	45	31	the	the	DET
cana-1652	45	32	dominant	dominant	ADJ
cana-1652	45	33	set	set	NOUN
cana-1652	45	34	in	in	ADP
cana-1652	45	35	𝐺	𝐺	PROPN
cana-1652	45	36	is	be	AUX
cana-1652	45	37	called	call	VERB
cana-1652	45	38	the	the	DET
cana-1652	45	39	dominance	dominance	NOUN
cana-1652	45	40	number	number	NOUN
cana-1652	45	41	of	of	ADP
cana-1652	45	42	𝐺	𝐺	PROPN
cana-1652	45	43	and	and	CCONJ
cana-1652	45	44	is	be	AUX
cana-1652	45	45	denoted	denote	VERB
cana-1652	45	46	as	as	ADP
cana-1652	45	47	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	45	48	)	)	PUNCT
cana-1652	45	49	.	.	PUNCT
cana-1652	46	1	the	the	DET
cana-1652	46	2	concept	concept	NOUN
cana-1652	46	3	of	of	ADP
cana-1652	46	4	the	the	DET
cana-1652	46	5	fuzzy	fuzzy	ADJ
cana-1652	46	6	calendar	calendar	NOUN
cana-1652	46	7	dates	date	VERB
cana-1652	46	8	back	back	ADV
cana-1652	46	9	to	to	ADP
cana-1652	46	10	the	the	DET
cana-1652	46	11	work	work	NOUN
cana-1652	46	12	of	of	ADP
cana-1652	46	13	mordeson	mordeson	NOUN
cana-1652	46	14	and	and	CCONJ
cana-1652	46	15	nair	nair	NOUN
cana-1652	46	16	[	[	X
cana-1652	46	17	27	27	NUM
cana-1652	46	18	]	]	PUNCT
cana-1652	46	19	,	,	PUNCT
cana-1652	46	20	and	and	CCONJ
cana-1652	46	21	kumar	kumar	PROPN
cana-1652	46	22	and	and	CCONJ
cana-1652	46	23	lavanya	lavanya	NOUN
cana-1652	47	1	[	[	X
cana-1652	47	2	28	28	NUM
cana-1652	47	3	]	]	PUNCT
cana-1652	47	4	show	show	VERB
cana-1652	47	5	more	more	ADJ
cana-1652	47	6	recent	recent	ADJ
cana-1652	47	7	developments	development	NOUN
cana-1652	47	8	.	.	PUNCT
cana-1652	48	1	a	a	DET
cana-1652	48	2	fuzzy	fuzzy	ADJ
cana-1652	48	3	directed	direct	VERB
cana-1652	48	4	graph	graph	NOUN
cana-1652	48	5	is	be	AUX
cana-1652	48	6	the	the	DET
cana-1652	48	7	function	function	NOUN
cana-1652	48	8	pair	pair	NOUN
cana-1652	48	9	𝐺𝐷	𝐺𝐷	NOUN
cana-1652	48	10	=	=	SYM
cana-1652	48	11	(	(	PUNCT
cana-1652	48	12	𝜎𝐷	𝜎𝐷	ADJ
cana-1652	48	13	,	,	PUNCT
cana-1652	48	14	𝜇𝐷	𝜇𝐷	NOUN
cana-1652	48	15	)	)	PUNCT
cana-1652	48	16	,	,	PUNCT
cana-1652	48	17	𝜎𝐷	𝜎𝐷	ADV
cana-1652	48	18	:	:	PUNCT
cana-1652	48	19	𝑉	𝑉	PROPN
cana-1652	48	20	→	→	SYM
cana-1652	48	21	[	[	X
cana-1652	48	22	0,1	0,1	NUM
cana-1652	48	23	]	]	PUNCT
cana-1652	48	24	and	and	CCONJ
cana-1652	48	25	𝜇𝐷	𝜇𝐷	NOUN
cana-1652	48	26	:	:	PUNCT
cana-1652	48	27	𝑉	𝑉	PROPN
cana-1652	48	28	×	×	NOUN
cana-1652	48	29	𝑉	𝑉	PROPN
cana-1652	48	30	→	→	SYM
cana-1652	48	31	[	[	X
cana-1652	48	32	0,1	0,1	NUM
cana-1652	48	33	]	]	PUNCT
cana-1652	48	34	where	where	SCONJ
cana-1652	48	35	𝜇𝐷(𝑢	𝜇𝐷(𝑢	PROPN
cana-1652	48	36	,	,	PUNCT
cana-1652	48	37	𝑣	𝑣	NOUN
cana-1652	48	38	)	)	PUNCT
cana-1652	48	39	≤	≤	NOUN
cana-1652	48	40	𝜎𝐷(𝑢	𝜎𝐷(𝑢	NUM
cana-1652	48	41	)	)	PUNCT
cana-1652	48	42	∧	∧	PROPN
cana-1652	48	43	𝜎𝐷(𝑣	𝜎𝐷(𝑣	PROPN
cana-1652	48	44	)	)	PUNCT
cana-1652	48	45	𝑢	𝑢	PROPN
cana-1652	48	46	,	,	PUNCT
cana-1652	48	47	𝑣	𝑣	PRON
cana-1652	48	48	∈	∈	PROPN
cana-1652	48	49	𝐹𝑜𝑟𝑉	𝐹𝑜𝑟𝑉	NOUN
cana-1652	48	50	,	,	PUNCT
cana-1652	48	51	𝜎𝐷	𝜎𝐷	NOUN
cana-1652	48	52	is	be	AUX
cana-1652	48	53	a	a	DET
cana-1652	48	54	fuzzy	fuzzy	ADJ
cana-1652	48	55	𝑉light	𝑉light	PROPN
cana-1652	48	56	is	be	AUX
cana-1652	48	57	a	a	DET
cana-1652	48	58	fuzzy	fuzzy	ADJ
cana-1652	48	59	relationship	relationship	NOUN
cana-1652	48	60	between	between	ADP
cana-1652	48	61	(	(	PUNCT
cana-1652	48	62	𝑉	𝑉	PROPN
cana-1652	48	63	×	×	PROPN
cana-1652	48	64	𝑉	𝑉	PROPN
cana-1652	48	65	,	,	PUNCT
cana-1652	48	66	𝜇𝐷	𝜇𝐷	PROPN
cana-1652	48	67	)	)	PUNCT
cana-1652	48	68	,	,	PUNCT
cana-1652	48	69	𝑉	𝑉	PROPN
cana-1652	48	70	,	,	PUNCT
cana-1652	48	71	and	and	CCONJ
cana-1652	48	72	𝜇𝐷	𝜇𝐷	PROPN
cana-1652	48	73	is	be	AUX
cana-1652	48	74	a	a	DET
cana-1652	48	75	set	set	NOUN
cana-1652	48	76	of	of	ADP
cana-1652	48	77	fuzzy	fuzzy	ADJ
cana-1652	48	78	directed	direct	VERB
cana-1652	48	79	edges	edge	NOUN
cana-1652	48	80	called	call	VERB
cana-1652	48	81	fuzzy	fuzzy	ADJ
cana-1652	48	82	arcs	arc	NOUN
cana-1652	48	83	.	.	PUNCT
cana-1652	49	1	the	the	DET
cana-1652	49	2	degree	degree	NOUN
cana-1652	49	3	of	of	ADP
cana-1652	49	4	a	a	DET
cana-1652	49	5	vertex	vertex	NOUN
cana-1652	49	6	u	u	NOUN
cana-1652	49	7	in	in	ADP
cana-1652	49	8	a	a	DET
cana-1652	49	9	fuzzy	fuzzy	ADJ
cana-1652	49	10	directed	direct	VERB
cana-1652	49	11	graph	graph	NOUN
cana-1652	49	12	is	be	AUX
cana-1652	49	13	the	the	DET
cana-1652	49	14	sum	sum	NOUN
cana-1652	49	15	of	of	ADP
cana-1652	49	16	the	the	DET
cana-1652	49	17	d	d	PROPN
cana-1652	49	18	values	value	NOUN
cana-1652	49	19	of	of	ADP
cana-1652	49	20	the	the	DET
cana-1652	49	21	edge	edge	NOUN
cana-1652	49	22	problems	problem	NOUN
cana-1652	49	23	for	for	ADP
cana-1652	49	24	the	the	DET
cana-1652	49	25	vertex	vertex	NOUN
cana-1652	49	26	𝜎𝐷(𝑢	𝜎𝐷(𝑢	NUM
cana-1652	49	27	)	)	PUNCT
cana-1652	49	28	.	.	PUNCT
cana-1652	50	1	in	in	ADP
cana-1652	50	2	a	a	DET
cana-1652	50	3	fuzzy	fuzzy	ADJ
cana-1652	50	4	directed	direct	VERB
cana-1652	50	5	graph	graph	NOUN
cana-1652	50	6	,	,	PUNCT
cana-1652	50	7	the	the	DET
cana-1652	50	8	exterior	exterior	ADJ
cana-1652	50	9	degree	degree	NOUN
cana-1652	50	10	of	of	ADP
cana-1652	50	11	any	any	DET
cana-1652	50	12	vertex	vertex	NOUN
cana-1652	50	13	u	u	NOUN
cana-1652	50	14	is	be	AUX
cana-1652	50	15	the	the	DET
cana-1652	50	16	sum	sum	NOUN
cana-1652	50	17	of	of	ADP
cana-1652	50	18	the	the	DET
cana-1652	50	19	member	member	NOUN
cana-1652	50	20	function	function	NOUN
cana-1652	50	21	values	value	NOUN
cana-1652	50	22	of	of	ADP
cana-1652	50	23	the	the	DET
cana-1652	50	24	entire	entire	ADJ
cana-1652	50	25	arc	arc	NOUN
cana-1652	50	26	problem	problem	NOUN
cana-1652	50	27	from	from	ADP
cana-1652	50	28	the	the	DET
cana-1652	50	29	vertex	vertex	NOUN
cana-1652	50	30	u.	u.	VERB
cana-1652	51	1	the	the	DET
cana-1652	51	2	inner	inner	ADJ
cana-1652	51	3	degree	degree	NOUN
cana-1652	51	4	is	be	AUX
cana-1652	51	5	denoted	denote	VERB
cana-1652	51	6	by	by	ADP
cana-1652	51	7	𝑑−(𝑢	𝑑−(𝑢	NOUN
cana-1652	51	8	)	)	PUNCT
cana-1652	51	9	and	and	CCONJ
cana-1652	51	10	the	the	DET
cana-1652	51	11	outer	outer	ADJ
cana-1652	51	12	degree	degree	NOUN
cana-1652	51	13	is	be	AUX
cana-1652	51	14	denoted	denote	VERB
cana-1652	51	15	by	by	ADP
cana-1652	51	16	𝑑+(𝑢	𝑑+(𝑢	NOUN
cana-1652	51	17	)	)	PUNCT
cana-1652	51	18	;	;	PUNCT
cana-1652	51	19	where	where	SCONJ
cana-1652	51	20	𝑢	𝑢	PRON
cana-1652	51	21	is	be	AUX
cana-1652	51	22	any	any	DET
cana-1652	51	23	vertex	vertex	NOUN
cana-1652	51	24	in	in	ADP
cana-1652	51	25	𝑉.	𝑉.	NOUN
cana-1652	51	26	the	the	DET
cana-1652	51	27	subset	subset	NOUN
cana-1652	51	28	𝑆	𝑆	PROPN
cana-1652	51	29	⊆	⊆	NUM
cana-1652	51	30	𝑉	𝑉	PROPN
cana-1652	51	31	is	be	AUX
cana-1652	51	32	the	the	DET
cana-1652	51	33	fuzzy	fuzzy	ADJ
cana-1652	51	34	dominant	dominant	ADJ
cana-1652	51	35	set	set	NOUN
cana-1652	51	36	of	of	ADP
cana-1652	51	37	𝐺𝐷	𝐺𝐷	PROPN
cana-1652	51	38	,	,	PUNCT
cana-1652	51	39	if	if	SCONJ
cana-1652	51	40	𝑢	𝑢	PROPN
cana-1652	51	41	∈	∈	PROPN
cana-1652	51	42	𝑆	𝑆	PROPN
cana-1652	51	43	for	for	ADP
cana-1652	51	44	each	each	DET
cana-1652	51	45	vertex	vertex	NOUN
cana-1652	51	46	𝑣	𝑣	ADP
cana-1652	51	47	∈	∈	PROPN
cana-1652	51	48	𝑉	𝑉	PROPN
cana-1652	51	49	−	−	PROPN
cana-1652	51	50	𝑆	𝑆	PROPN
cana-1652	51	51	,	,	PUNCT
cana-1652	51	52	then	then	ADV
cana-1652	51	53	𝜇𝐷(𝑢	𝜇𝐷(𝑢	PROPN
cana-1652	51	54	,	,	PUNCT
cana-1652	51	55	𝑣	𝑣	NOUN
cana-1652	51	56	)	)	PUNCT
cana-1652	51	57	=	=	SYM
cana-1652	51	58	𝜎𝐷(𝑢	𝜎𝐷(𝑢	X
cana-1652	51	59	)	)	PUNCT
cana-1652	51	60	∧	∧	PROPN
cana-1652	51	61	𝜎𝐷(𝑣	𝜎𝐷(𝑣	PROPN
cana-1652	51	62	)	)	PUNCT
cana-1652	51	63	.	.	PUNCT
cana-1652	52	1	a	a	DET
cana-1652	52	2	fuzzy	fuzzy	ADJ
cana-1652	52	3	map	map	NOUN
cana-1652	52	4	is	be	AUX
cana-1652	52	5	complete	complete	ADJ
cana-1652	52	6	if	if	SCONJ
cana-1652	52	7	𝜇𝐷(𝑢	𝜇𝐷(𝑢	PROPN
cana-1652	52	8	,	,	PUNCT
cana-1652	52	9	𝑣	𝑣	NOUN
cana-1652	52	10	)	)	PUNCT
cana-1652	52	11	=	=	SYM
cana-1652	52	12	𝜎𝐷(𝑢	𝜎𝐷(𝑢	X
cana-1652	52	13	)	)	PUNCT
cana-1652	52	14	∧	∧	PROPN
cana-1652	52	15	𝜎𝐷(𝑣	𝜎𝐷(𝑣	PROPN
cana-1652	52	16	)	)	PUNCT
cana-1652	52	17	for	for	ADP
cana-1652	52	18	each	each	DET
cana-1652	52	19	adjacent	adjacent	ADJ
cana-1652	52	20	pair	pair	NOUN
cana-1652	52	21	of	of	ADP
cana-1652	52	22	straight	straight	ADJ
cana-1652	52	23	lines	line	NOUN
cana-1652	52	24	.	.	PUNCT
cana-1652	53	1	mastery	mastery	NOUN
cana-1652	53	2	of	of	ADP
cana-1652	53	3	fuzzy	fuzzy	ADJ
cana-1652	53	4	directed	direct	VERB
cana-1652	53	5	graphs	graph	NOUN
cana-1652	53	6	is	be	AUX
cana-1652	53	7	a	a	DET
cana-1652	53	8	new	new	ADJ
cana-1652	53	9	concept	concept	NOUN
cana-1652	53	10	in	in	ADP
cana-1652	53	11	data	datum	NOUN
cana-1652	53	12	logging	log	VERB
cana-1652	53	13	with	with	ADP
cana-1652	53	14	limited	limited	ADJ
cana-1652	53	15	understanding	understanding	NOUN
cana-1652	53	16	.	.	PUNCT
cana-1652	54	1	with	with	ADP
cana-1652	54	2	this	this	DET
cana-1652	54	3	new	new	ADJ
cana-1652	54	4	concept	concept	NOUN
cana-1652	54	5	,	,	PUNCT
cana-1652	54	6	we	we	PRON
cana-1652	54	7	propose	propose	VERB
cana-1652	54	8	a	a	DET
cana-1652	54	9	new	new	ADJ
cana-1652	54	10	dominant	dominant	ADJ
cana-1652	54	11	parameter	parameter	NOUN
cana-1652	54	12	in	in	ADP
cana-1652	54	13	fuzzy	fuzzy	ADJ
cana-1652	54	14	directed	direct	VERB
cana-1652	54	15	graphs	graph	NOUN
cana-1652	54	16	.	.	PUNCT
cana-1652	55	1	inspired	inspire	VERB
cana-1652	55	2	by	by	ADP
cana-1652	55	3	the	the	DET
cana-1652	55	4	concepts	concept	NOUN
cana-1652	55	5	of	of	ADP
cana-1652	55	6	fuzzy	fuzzy	ADJ
cana-1652	55	7	directional	directional	ADJ
cana-1652	55	8	graphics	graphic	NOUN
cana-1652	55	9	[	[	X
cana-1652	55	10	27	27	NUM
cana-1652	55	11	,	,	PUNCT
cana-1652	55	12	28	28	NUM
cana-1652	55	13	]	]	PUNCT
cana-1652	55	14	and	and	CCONJ
cana-1652	55	15	control	control	NOUN
cana-1652	55	16	charts	chart	NOUN
cana-1652	55	17	[	[	X
cana-1652	55	18	13	13	NUM
cana-1652	55	19	]	]	PUNCT
cana-1652	55	20	,	,	PUNCT
cana-1652	55	21	this	this	DET
cana-1652	55	22	study	study	NOUN
cana-1652	55	23	focuses	focus	VERB
cana-1652	55	24	on	on	ADP
cana-1652	55	25	the	the	DET
cana-1652	55	26	knowledge	knowledge	NOUN
cana-1652	55	27	management	management	NOUN
cana-1652	55	28	of	of	ADP
cana-1652	55	29	blurred	blurred	ADJ
cana-1652	55	30	and	and	CCONJ
cana-1652	55	31	directed	direct	VERB
cana-1652	55	32	images	image	NOUN
cana-1652	55	33	.	.	PUNCT
cana-1652	56	1	all	all	DET
cana-1652	56	2	illustrations	illustration	NOUN
cana-1652	56	3	in	in	ADP
cana-1652	56	4	this	this	DET
cana-1652	56	5	document	document	NOUN
cana-1652	56	6	are	be	AUX
cana-1652	56	7	final	final	ADJ
cana-1652	56	8	and	and	CCONJ
cana-1652	56	9	not	not	PART
cana-1652	56	10	circular	circular	ADJ
cana-1652	56	11	.	.	PUNCT
cana-1652	57	1	we	we	PRON
cana-1652	57	2	use	use	VERB
cana-1652	57	3	𝐺∗𝐷	𝐺∗𝐷	PROPN
cana-1652	57	4	=	=	SYM
cana-1652	57	5	(	(	PUNCT
cana-1652	57	6	𝑉	𝑉	PROPN
cana-1652	57	7	,	,	PUNCT
cana-1652	57	8	𝐴	𝐴	PROPN
cana-1652	57	9	)	)	PUNCT
cana-1652	57	10	as	as	ADP
cana-1652	57	11	the	the	DET
cana-1652	57	12	hidden	hide	VERB
cana-1652	57	13	directed	direct	VERB
cana-1652	57	14	graph	graph	NOUN
cana-1652	57	15	of	of	ADP
cana-1652	57	16	the	the	DET
cana-1652	57	17	graph	graph	NOUN
cana-1652	57	18	𝐺𝐷	𝐺𝐷	NOUN
cana-1652	57	19	=	=	SYM
cana-1652	57	20	(	(	PUNCT
cana-1652	57	21	𝜎𝐷	𝜎𝐷	ADJ
cana-1652	57	22	,	,	PUNCT
cana-1652	57	23	𝜇𝐷	𝜇𝐷	NOUN
cana-1652	57	24	)	)	PUNCT
cana-1652	57	25	𝐺𝐷	𝐺𝐷	PROPN
cana-1652	57	26	=	=	SYM
cana-1652	57	27	(	(	PUNCT
cana-1652	57	28	𝜎𝐷	𝜎𝐷	ADJ
cana-1652	57	29	,	,	PUNCT
cana-1652	57	30	𝜇𝐷	𝜇𝐷	NOUN
cana-1652	57	31	)	)	PUNCT
cana-1652	57	32	,	,	PUNCT
cana-1652	57	33	where	where	SCONJ
cana-1652	57	34	𝑉	𝑉	PROPN
cana-1652	57	35	is	be	AUX
cana-1652	57	36	the	the	DET
cana-1652	57	37	set	set	NOUN
cana-1652	57	38	of	of	ADP
cana-1652	57	39	vertices	vertex	NOUN
cana-1652	57	40	and	and	CCONJ
cana-1652	57	41	𝐴	𝐴	PROPN
cana-1652	57	42	is	be	AUX
cana-1652	57	43	the	the	DET
cana-1652	57	44	arc	arc	NOUN
cana-1652	57	45	set	set	NOUN
cana-1652	57	46	of	of	ADP
cana-1652	57	47	the	the	DET
cana-1652	57	48	directed	direct	VERB
cana-1652	57	49	graph	graph	NOUN
cana-1652	57	50	𝐺∗𝐷	𝐺∗𝐷	PROPN
cana-1652	57	51	,	,	PUNCT
cana-1652	57	52	𝜎	𝜎	PROPN
cana-1652	57	53	is	be	AUX
cana-1652	57	54	the	the	DET
cana-1652	57	55	set	set	NOUN
cana-1652	57	56	d	d	NOUN
cana-1652	57	57	,	,	PUNCT
cana-1652	57	58	and	and	CCONJ
cana-1652	57	59	𝜇𝐷	𝜇𝐷	PROPN
cana-1652	57	60	is	be	AUX
cana-1652	57	61	the	the	DET
cana-1652	57	62	arc	arc	NOUN
cana-1652	57	63	set	set	NOUN
cana-1652	57	64	of	of	ADP
cana-1652	57	65	the	the	DET
cana-1652	57	66	fuzzy	fuzzy	ADJ
cana-1652	57	67	directional	directional	ADJ
cana-1652	57	68	graph	graph	NOUN
cana-1652	57	69	𝐺𝐷.	𝐺𝐷.	NOUN
cana-1652	57	70	a	a	DET
cana-1652	57	71	set	set	NOUN
cana-1652	57	72	of	of	ADP
cana-1652	57	73	vertices	vertex	NOUN
cana-1652	57	74	𝑆	𝑆	PROPN
cana-1652	57	75	⊆	⊆	PROPN
cana-1652	57	76	𝑉	𝑉	PROPN
cana-1652	57	77	is	be	AUX
cana-1652	57	78	the	the	DET
cana-1652	57	79	dominant	dominant	ADJ
cana-1652	57	80	set	set	NOUN
cana-1652	57	81	𝐺∗𝐷	𝐺∗𝐷	PROPN
cana-1652	57	82	if	if	SCONJ
cana-1652	57	83	every	every	DET
cana-1652	57	84	vertex	vertex	NOUN
cana-1652	57	85	in	in	ADP
cana-1652	57	86	𝑣	𝑣	DET
cana-1652	57	87	∈	∈	PROPN
cana-1652	57	88	𝑉	𝑉	PROPN
cana-1652	57	89	is	be	AUX
cana-1652	57	90	dominated	dominate	VERB
cana-1652	57	91	by	by	ADP
cana-1652	57	92	at	at	ADV
cana-1652	57	93	least	least	ADV
cana-1652	57	94	one	one	NUM
cana-1652	57	95	vertex	vertex	NOUN
cana-1652	57	96	in	in	ADP
cana-1652	57	97	𝑆.	𝑆.	PROPN
cana-1652	57	98	the	the	DET
cana-1652	57	99	dominant	dominant	ADJ
cana-1652	57	100	𝛾(𝐺∗𝐷	𝛾(𝐺∗𝐷	ADJ
cana-1652	57	101	)	)	PUNCT
cana-1652	57	102	set	set	NOUN
cana-1652	57	103	of	of	ADP
cana-1652	57	104	𝐺∗𝐷	𝐺∗𝐷	PROPN
cana-1652	57	105	is	be	AUX
cana-1652	57	106	the	the	DET
cana-1652	57	107	minimum	minimum	ADJ
cana-1652	57	108	cardinality	cardinality	NOUN
cana-1652	57	109	of	of	ADP
cana-1652	57	110	the	the	DET
cana-1652	57	111	dominant	dominant	ADJ
cana-1652	57	112	𝑆	𝑆	PROPN
cana-1652	57	113	set	set	NOUN
cana-1652	57	114	of	of	ADP
cana-1652	57	115	𝐺∗𝐷.	𝐺∗𝐷.	NOUN
cana-1652	57	116	this	this	DET
cana-1652	57	117	article	article	NOUN
cana-1652	57	118	introduces	introduce	VERB
cana-1652	57	119	/	/	PUNCT
cana-1652	57	120	describes	describe	VERB
cana-1652	57	121	the	the	DET
cana-1652	57	122	concept	concept	NOUN
cana-1652	57	123	of	of	ADP
cana-1652	57	124	dominance	dominance	NOUN
cana-1652	57	125	in	in	ADP
cana-1652	57	126	fuzzy	fuzzy	ADJ
cana-1652	57	127	directional	directional	ADJ
cana-1652	57	128	graphs	graph	NOUN
cana-1652	57	129	,	,	PUNCT
cana-1652	57	130	characterizes	characterize	VERB
cana-1652	57	131	the	the	DET
cana-1652	57	132	dominance	dominance	NOUN
cana-1652	57	133	number	number	NOUN
cana-1652	57	134	in	in	ADP
cana-1652	57	135	fuzzy	fuzzy	ADJ
cana-1652	57	136	directional	directional	ADJ
cana-1652	57	137	graphs	graph	NOUN
cana-1652	57	138	,	,	PUNCT
cana-1652	57	139	and	and	CCONJ
cana-1652	57	140	models	model	VERB
cana-1652	57	141	the	the	DET
cana-1652	57	142	dominance	dominance	NOUN
cana-1652	57	143	number	number	NOUN
cana-1652	57	144	of	of	ADP
cana-1652	57	145	fuzzy	fuzzy	ADJ
cana-1652	57	146	two	two	NUM
cana-1652	57	147	paths	path	NOUN
cana-1652	57	148	and	and	CCONJ
cana-1652	57	149	fuzzy	fuzzy	ADJ
cana-1652	57	150	two	two	NUM
cana-1652	57	151	rings	ring	NOUN
cana-1652	57	152	.	.	PUNCT
cana-1652	58	1	the	the	DET
cana-1652	58	2	contribution	contribution	NOUN
cana-1652	58	3	of	of	ADP
cana-1652	58	4	this	this	DET
cana-1652	58	5	work	work	NOUN
cana-1652	58	6	is	be	AUX
cana-1652	58	7	to	to	PART
cana-1652	58	8	provide	provide	VERB
cana-1652	58	9	general	general	ADJ
cana-1652	58	10	conclusions	conclusion	NOUN
cana-1652	58	11	(	(	PUNCT
cana-1652	58	12	eg	eg	NOUN
cana-1652	58	13	theorems	theorem	NOUN
cana-1652	58	14	,	,	PUNCT
cana-1652	58	15	conclusions	conclusion	NOUN
cana-1652	58	16	)	)	PUNCT
cana-1652	58	17	about	about	ADP
cana-1652	58	18	the	the	DET
cana-1652	58	19	smallest	small	ADJ
cana-1652	58	20	dominant	dominant	ADJ
cana-1652	58	21	group	group	NOUN
cana-1652	58	22	of	of	ADP
cana-1652	58	23	fuzzy	fuzzy	ADJ
cana-1652	58	24	expression	expression	NOUN
cana-1652	58	25	graphs	graph	NOUN
cana-1652	58	26	to	to	PART
cana-1652	58	27	facilitate	facilitate	VERB
cana-1652	58	28	new	new	ADJ
cana-1652	58	29	progress	progress	NOUN
cana-1652	58	30	in	in	ADP
cana-1652	58	31	this	this	DET
cana-1652	58	32	field	field	NOUN
cana-1652	58	33	.	.	PUNCT
cana-1652	59	1	2	2	X
cana-1652	59	2	.	.	X
cana-1652	59	3	domination	domination	NOUN
cana-1652	59	4	in	in	ADP
cana-1652	59	5	fuzzy	fuzzy	ADJ
cana-1652	59	6	graphs	graph	NOUN
cana-1652	59	7	the	the	DET
cana-1652	59	8	labeling	labeling	NOUN
cana-1652	59	9	satl	satl	NOUN
cana-1652	59	10	of	of	ADP
cana-1652	59	11	hgraph	hgraph	NOUN
cana-1652	59	12	is	be	AUX
cana-1652	59	13	stands	stand	VERB
cana-1652	59	14	for	for	ADP
cana-1652	59	15	the	the	DET
cana-1652	59	16	label	label	NOUN
cana-1652	59	17	super	super	ADJ
cana-1652	59	18	(	(	PUNCT
cana-1652	59	19	b	b	NOUN
cana-1652	59	20	,	,	PUNCT
cana-1652	59	21	e)-h	e)-h	ADJ
cana-1652	59	22	-	-	PUNCT
cana-1652	59	23	satl	satl	NOUN
cana-1652	59	24	diagram	diagram	NOUN
cana-1652	59	25	is	be	AUX
cana-1652	59	26	a	a	DET
cana-1652	59	27	finite	finite	ADJ
cana-1652	59	28	graph	graph	NOUN
cana-1652	59	29	and	and	CCONJ
cana-1652	59	30	h	h	NOUN
cana-1652	59	31	subset	subset	NOUN
cana-1652	59	32	of	of	ADP
cana-1652	59	33	a	a	DET
cana-1652	59	34	representation	representation	NOUN
cana-1652	59	35	in	in	ADP
cana-1652	59	36	x	x	PROPN
cana-1652	59	37	dots	dot	NOUN
cana-1652	59	38	and	and	CCONJ
cana-1652	59	39	y	y	PROPN
cana-1652	59	40	lines	line	NOUN
cana-1652	59	41	is	be	AUX
cana-1652	59	42	an	an	DET
cana-1652	59	43	mapping	mapping	NOUN
cana-1652	59	44	𝑔	𝑔	NOUN
cana-1652	59	45	:	:	PUNCT
cana-1652	59	46	𝐷(𝐺	𝐷(𝐺	NOUN
cana-1652	59	47	)	)	PUNCT
cana-1652	59	48	∪	∪	ADP
cana-1652	59	49	𝐿(𝐺	𝐿(𝐺	PROPN
cana-1652	59	50	)	)	PUNCT
cana-1652	59	51	}	}	PUNCT
cana-1652	59	52	→	→	SYM
cana-1652	59	53	{	{	PUNCT
cana-1652	59	54	𝑜𝑛𝑒	𝑜𝑛𝑒	PROPN
cana-1652	59	55	,	,	PUNCT
cana-1652	59	56	𝑡𝑤𝑜	𝑡𝑤𝑜	PROPN
cana-1652	59	57	,	,	PUNCT
cana-1652	59	58	𝑡ℎ𝑟𝑒𝑒	𝑡ℎ𝑟𝑒𝑒	ADJ
cana-1652	59	59	,	,	PUNCT
cana-1652	59	60	⋯	⋯	PROPN
cana-1652	59	61	,	,	PUNCT
cana-1652	59	62	|𝐷(𝑔𝑟𝑎𝑝ℎ	|𝐷(𝑔𝑟𝑎𝑝ℎ	ADJ
cana-1652	59	63	)	)	PUNCT
cana-1652	59	64	+	+	CCONJ
cana-1652	60	1	𝐿(𝑔𝑟𝑎𝑝ℎ)|	𝐿(𝑔𝑟𝑎𝑝ℎ)|	NOUN
cana-1652	60	2	}	}	PUNCT
cana-1652	60	3	and	and	CCONJ
cana-1652	60	4	hence	hence	ADV
cana-1652	60	5	for	for	ADP
cana-1652	60	6	every	every	DET
cana-1652	60	7	subgraphs	subgraph	NOUN
cana-1652	60	8	ℎ′	ℎ′	PROPN
cana-1652	60	9	≅	≅	PROPN
cana-1652	60	10	h	h	NOUN
cana-1652	60	11	the	the	DET
cana-1652	60	12	ℎ′	ℎ′	ADJ
cana-1652	60	13	weights	weight	NOUN
cana-1652	60	14	.	.	PUNCT
cana-1652	61	1	communications	communication	NOUN
cana-1652	61	2	on	on	ADP
cana-1652	61	3	applied	apply	VERB
cana-1652	61	4	nonlinear	nonlinear	ADJ
cana-1652	61	5	analysis	analysis	NOUN
cana-1652	61	6	issn	issn	NOUN
cana-1652	61	7	:	:	PUNCT
cana-1652	61	8	1074	1074	NUM
cana-1652	61	9	-	-	PUNCT
cana-1652	61	10	133x	133x	NUM
cana-1652	61	11	vol	vol	NOUN
cana-1652	61	12	32	32	NUM
cana-1652	61	13	no	no	NOUN
cana-1652	61	14	.	.	NOUN
cana-1652	61	15	1	1	NUM
cana-1652	61	16	(	(	PUNCT
cana-1652	61	17	2025	2025	NUM
cana-1652	61	18	)	)	PUNCT
cana-1652	61	19	326	326	NUM
cana-1652	61	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1652	61	21	definition	definition	NOUN
cana-1652	61	22	2.1	2.1	NUM
cana-1652	61	23	let	let	VERB
cana-1652	61	24	𝑥	𝑥	PRON
cana-1652	61	25	,	,	PUNCT
cana-1652	61	26	𝑦	𝑦	NOUN
cana-1652	61	27	∈	∈	PROPN
cana-1652	61	28	𝑉	𝑉	PROPN
cana-1652	61	29	.	.	PUNCT
cana-1652	62	1	the	the	DET
cana-1652	62	2	vertex	vertex	NOUN
cana-1652	62	3	𝜎𝐷(𝑥	𝜎𝐷(𝑥	PROPN
cana-1652	62	4	)	)	PUNCT
cana-1652	62	5	dominates	dominate	VERB
cana-1652	62	6	𝜎𝐷(𝑦	𝜎𝐷(𝑦	PROPN
cana-1652	62	7	)	)	PUNCT
cana-1652	62	8	in	in	ADP
cana-1652	62	9	𝐺𝐷	𝐺𝐷	PROPN
cana-1652	62	10	if	if	SCONJ
cana-1652	62	11	𝜇𝐷((𝑥	𝜇𝐷((𝑥	NOUN
cana-1652	62	12	,	,	PUNCT
cana-1652	62	13	𝑦	𝑦	NOUN
cana-1652	62	14	)	)	PUNCT
cana-1652	62	15	)	)	PUNCT
cana-1652	63	1	is	be	AUX
cana-1652	63	2	an	an	DET
cana-1652	63	3	effective	effective	ADJ
cana-1652	63	4	arc	arc	NOUN
cana-1652	63	5	.	.	PUNCT
cana-1652	64	1	definition	definition	NOUN
cana-1652	64	2	2.2	2.2	NUM
cana-1652	64	3	let	let	VERB
cana-1652	64	4	𝑆	𝑆	PROPN
cana-1652	64	5	⊆	⊆	NUM
cana-1652	64	6	𝑉	𝑉	PROPN
cana-1652	64	7	,	,	PUNCT
cana-1652	64	8	𝑢	𝑢	NOUN
cana-1652	64	9	∈	∈	NOUN
cana-1652	64	10	𝑉/𝑆	𝑉/𝑆	NOUN
cana-1652	64	11	,	,	PUNCT
cana-1652	64	12	and	and	CCONJ
cana-1652	64	13	𝑣	𝑣	DET
cana-1652	64	14	∈	∈	PROPN
cana-1652	64	15	𝑆	𝑆	PROPN
cana-1652	64	16	.	.	PUNCT
cana-1652	65	1	a	a	DET
cana-1652	65	2	subset	subset	NOUN
cana-1652	65	3	𝜎𝐷(𝑆	𝜎𝐷(𝑆	NUM
cana-1652	65	4	)	)	PUNCT
cana-1652	65	5	⊆	⊆	NUM
cana-1652	65	6	𝜎𝐷	𝜎𝐷	NOUN
cana-1652	65	7	is	be	AUX
cana-1652	65	8	a	a	DET
cana-1652	65	9	dominating	dominating	NOUN
cana-1652	65	10	set	set	NOUN
cana-1652	65	11	of	of	ADP
cana-1652	65	12	𝐺𝐷	𝐺𝐷	PROPN
cana-1652	65	13	if	if	SCONJ
cana-1652	65	14	,	,	PUNCT
cana-1652	65	15	for	for	ADP
cana-1652	65	16	every	every	DET
cana-1652	65	17	𝜎𝐷(𝑢	𝜎𝐷(𝑢	NUM
cana-1652	65	18	)	)	PUNCT
cana-1652	65	19	∈	∈	NOUN
cana-1652	65	20	𝜎𝐷/𝜎𝐷(𝑆	𝜎𝐷/𝜎𝐷(𝑆	NUM
cana-1652	65	21	)	)	PUNCT
cana-1652	65	22	,	,	PUNCT
cana-1652	65	23	there	there	PRON
cana-1652	65	24	exists	exist	VERB
cana-1652	65	25	𝜎𝐷(𝑣	𝜎𝐷(𝑣	PROPN
cana-1652	65	26	)	)	PUNCT
cana-1652	65	27	∈	∈	PROPN
cana-1652	65	28	𝜎𝐷(𝑆	𝜎𝐷(𝑆	NUM
cana-1652	65	29	)	)	PUNCT
cana-1652	65	30	such	such	ADJ
cana-1652	65	31	that	that	SCONJ
cana-1652	65	32	𝜎𝐷(𝑣	𝜎𝐷(𝑣	PROPN
cana-1652	65	33	)	)	PUNCT
cana-1652	65	34	dominates	dominate	VERB
cana-1652	65	35	𝜎𝐷(𝑢	𝜎𝐷(𝑢	NUM
cana-1652	65	36	)	)	PUNCT
cana-1652	65	37	.	.	PUNCT
cana-1652	66	1	theorem	theorem	VERB
cana-1652	66	2	2.3	2.3	NUM
cana-1652	66	3	let	let	VERB
cana-1652	66	4	g	g	NOUN
cana-1652	66	5	=	=	SYM
cana-1652	66	6	(	(	PUNCT
cana-1652	66	7	v	v	NOUN
cana-1652	66	8	,	,	PUNCT
cana-1652	66	9	e	e	NOUN
cana-1652	66	10	,	,	PUNCT
cana-1652	66	11	𝜇	𝜇	PRON
cana-1652	66	12	)	)	PUNCT
cana-1652	66	13	be	be	AUX
cana-1652	66	14	a	a	DET
cana-1652	66	15	fuzzy	fuzzy	ADJ
cana-1652	66	16	graph	graph	NOUN
cana-1652	66	17	.	.	PUNCT
cana-1652	67	1	if	if	SCONJ
cana-1652	67	2	d	d	PROPN
cana-1652	67	3	is	be	AUX
cana-1652	67	4	a	a	DET
cana-1652	67	5	dominating	dominating	NOUN
cana-1652	67	6	set	set	NOUN
cana-1652	67	7	of	of	ADP
cana-1652	67	8	g	g	NOUN
cana-1652	67	9	,	,	PUNCT
cana-1652	67	10	then	then	ADV
cana-1652	67	11	any	any	DET
cana-1652	67	12	superset	superset	NOUN
cana-1652	67	13	of	of	ADP
cana-1652	67	14	d	d	PROPN
cana-1652	67	15	is	be	AUX
cana-1652	67	16	also	also	ADV
cana-1652	67	17	a	a	DET
cana-1652	67	18	dominating	dominating	NOUN
cana-1652	67	19	set	set	NOUN
cana-1652	67	20	of	of	ADP
cana-1652	67	21	g.	g.	PROPN
cana-1652	67	22	proof	proof	PROPN
cana-1652	67	23	:	:	PUNCT
cana-1652	67	24	let	let	VERB
cana-1652	67	25	g	g	PROPN
cana-1652	67	26	=	=	SYM
cana-1652	67	27	(	(	PUNCT
cana-1652	67	28	v	v	NOUN
cana-1652	67	29	,	,	PUNCT
cana-1652	67	30	e	e	NOUN
cana-1652	67	31	,	,	PUNCT
cana-1652	67	32	𝜇	𝜇	PRON
cana-1652	67	33	)	)	PUNCT
cana-1652	67	34	be	be	AUX
cana-1652	67	35	a	a	DET
cana-1652	67	36	fuzzy	fuzzy	ADJ
cana-1652	67	37	graph	graph	NOUN
cana-1652	67	38	and	and	CCONJ
cana-1652	67	39	let	let	VERB
cana-1652	67	40	d	d	PRON
cana-1652	67	41	be	be	AUX
cana-1652	67	42	a	a	DET
cana-1652	67	43	dominating	dominating	NOUN
cana-1652	67	44	set	set	NOUN
cana-1652	67	45	of	of	ADP
cana-1652	67	46	g.	g.	PROPN
cana-1652	67	47	suppose	suppose	VERB
cana-1652	67	48	that	that	SCONJ
cana-1652	67	49	d	d	X
cana-1652	67	50	’	'	PUNCT
cana-1652	67	51	is	be	AUX
cana-1652	67	52	a	a	DET
cana-1652	67	53	superset	superset	NOUN
cana-1652	67	54	of	of	ADP
cana-1652	67	55	d.	d.	NOUN
cana-1652	67	56	we	we	PRON
cana-1652	67	57	need	need	VERB
cana-1652	67	58	to	to	PART
cana-1652	67	59	show	show	VERB
cana-1652	67	60	that	that	SCONJ
cana-1652	67	61	d	d	X
cana-1652	67	62	’	'	PUNCT
cana-1652	67	63	is	be	AUX
cana-1652	67	64	also	also	ADV
cana-1652	67	65	a	a	DET
cana-1652	67	66	dominating	dominating	NOUN
cana-1652	67	67	set	set	NOUN
cana-1652	67	68	of	of	ADP
cana-1652	67	69	g.	g.	PROPN
cana-1652	67	70	let	let	VERB
cana-1652	67	71	𝑣	𝑣	PART
cana-1652	67	72	be	be	AUX
cana-1652	67	73	any	any	DET
cana-1652	67	74	vertex	vertex	NOUN
cana-1652	67	75	in	in	ADP
cana-1652	67	76	𝑉	𝑉	PROPN
cana-1652	67	77	−	−	PROPN
cana-1652	67	78	𝐷′.	𝐷′.	NOUN
cana-1652	67	79	since	since	SCONJ
cana-1652	67	80	𝐷′	𝐷′	PROPN
cana-1652	67	81	is	be	AUX
cana-1652	67	82	a	a	DET
cana-1652	67	83	superset	superset	NOUN
cana-1652	67	84	of	of	ADP
cana-1652	67	85	d	d	PROPN
cana-1652	67	86	,	,	PUNCT
cana-1652	67	87	we	we	PRON
cana-1652	67	88	have	have	VERB
cana-1652	67	89	𝑣	𝑣	DET
cana-1652	67	90	∈	∈	PROPN
cana-1652	67	91	𝑉	𝑉	PROPN
cana-1652	67	92	−	−	PROPN
cana-1652	67	93	𝐷.	𝐷.	PROPN
cana-1652	67	94	since	since	SCONJ
cana-1652	67	95	d	d	PROPN
cana-1652	67	96	is	be	AUX
cana-1652	67	97	a	a	DET
cana-1652	67	98	dominating	dominating	NOUN
cana-1652	67	99	set	set	NOUN
cana-1652	67	100	of	of	ADP
cana-1652	67	101	g	g	NOUN
cana-1652	67	102	,	,	PUNCT
cana-1652	67	103	there	there	PRON
cana-1652	67	104	exists	exist	VERB
cana-1652	67	105	a	a	DET
cana-1652	67	106	vertex	vertex	NOUN
cana-1652	67	107	𝑢	𝑢	PROPN
cana-1652	67	108	∈	∈	PROPN
cana-1652	67	109	𝐷	𝐷	NOUN
cana-1652	68	1	such	such	ADJ
cana-1652	68	2	that	that	SCONJ
cana-1652	68	3	(	(	PUNCT
cana-1652	68	4	𝑢	𝑢	X
cana-1652	68	5	,	,	PUNCT
cana-1652	68	6	𝑣	𝑣	NOUN
cana-1652	68	7	)	)	PUNCT
cana-1652	68	8	∈	∈	PROPN
cana-1652	68	9	e	e	NOUN
cana-1652	68	10	or	or	CCONJ
cana-1652	68	11	equivalently	equivalently	ADV
cana-1652	68	12	,	,	PUNCT
cana-1652	68	13	𝜇(𝑢	𝜇(𝑢	PROPN
cana-1652	68	14	,	,	PUNCT
cana-1652	68	15	𝑣	𝑣	NOUN
cana-1652	68	16	)	)	PUNCT
cana-1652	68	17	>	>	X
cana-1652	68	18	0	0	X
cana-1652	68	19	.	.	PUNCT
cana-1652	69	1	since	since	SCONJ
cana-1652	69	2	d	d	NOUN
cana-1652	69	3	’	'	PUNCT
cana-1652	69	4	is	be	AUX
cana-1652	69	5	a	a	DET
cana-1652	69	6	superset	superset	NOUN
cana-1652	69	7	of	of	ADP
cana-1652	69	8	d	d	PROPN
cana-1652	69	9	,	,	PUNCT
cana-1652	69	10	we	we	PRON
cana-1652	69	11	have	have	VERB
cana-1652	69	12	𝑢	𝑢	NOUN
cana-1652	69	13	∈	∈	PROPN
cana-1652	69	14	𝐷′.	𝐷′.	NOUN
cana-1652	69	15	therefore	therefore	ADV
cana-1652	69	16	,	,	PUNCT
cana-1652	69	17	𝑢	𝑢	PRON
cana-1652	69	18	dominates	dominate	VERB
cana-1652	69	19	𝑣	𝑣	ADP
cana-1652	69	20	in	in	ADP
cana-1652	69	21	g	g	PROPN
cana-1652	69	22	and	and	CCONJ
cana-1652	69	23	hence	hence	ADV
cana-1652	69	24	𝑣	𝑣	PRON
cana-1652	69	25	is	be	AUX
cana-1652	69	26	dominated	dominate	VERB
cana-1652	69	27	by	by	ADP
cana-1652	69	28	at	at	ADV
cana-1652	69	29	least	least	ADV
cana-1652	69	30	one	one	NUM
cana-1652	69	31	vertex	vertex	NOUN
cana-1652	69	32	in	in	ADP
cana-1652	69	33	𝐷′.	𝐷′.	NOUN
cana-1652	69	34	thus	thus	ADV
cana-1652	69	35	,	,	PUNCT
cana-1652	69	36	every	every	DET
cana-1652	69	37	vertex	vertex	NOUN
cana-1652	69	38	in	in	ADP
cana-1652	69	39	𝑉	𝑉	PROPN
cana-1652	69	40	−	−	PROPN
cana-1652	69	41	𝐷′	𝐷′	NOUN
cana-1652	69	42	is	be	AUX
cana-1652	69	43	dominated	dominate	VERB
cana-1652	69	44	by	by	ADP
cana-1652	69	45	at	at	ADV
cana-1652	69	46	least	least	ADV
cana-1652	69	47	one	one	NUM
cana-1652	69	48	vertex	vertex	NOUN
cana-1652	69	49	in	in	ADP
cana-1652	69	50	𝐷′	𝐷′	NOUN
cana-1652	69	51	,	,	PUNCT
cana-1652	69	52	which	which	PRON
cana-1652	69	53	implies	imply	VERB
cana-1652	69	54	that	that	SCONJ
cana-1652	69	55	𝐷′	𝐷′	PROPN
cana-1652	69	56	is	be	AUX
cana-1652	69	57	a	a	DET
cana-1652	69	58	dominating	dominating	NOUN
cana-1652	69	59	set	set	NOUN
cana-1652	69	60	of	of	ADP
cana-1652	69	61	g.	g.	PROPN
cana-1652	69	62	therefore	therefore	ADV
cana-1652	69	63	,	,	PUNCT
cana-1652	69	64	we	we	PRON
cana-1652	69	65	have	have	AUX
cana-1652	69	66	shown	show	VERB
cana-1652	69	67	that	that	SCONJ
cana-1652	69	68	any	any	DET
cana-1652	69	69	superset	superset	NOUN
cana-1652	69	70	of	of	ADP
cana-1652	69	71	a	a	DET
cana-1652	69	72	dominating	dominating	NOUN
cana-1652	69	73	set	set	NOUN
cana-1652	69	74	of	of	ADP
cana-1652	69	75	g	g	PROPN
cana-1652	69	76	is	be	AUX
cana-1652	69	77	also	also	ADV
cana-1652	69	78	a	a	DET
cana-1652	69	79	dominating	dominating	NOUN
cana-1652	69	80	set	set	NOUN
cana-1652	69	81	of	of	ADP
cana-1652	69	82	g.	g.	PROPN
cana-1652	69	83	theorem	theorem	VERB
cana-1652	69	84	2.4	2.4	NUM
cana-1652	69	85	let	let	VERB
cana-1652	69	86	𝐺	𝐺	PROPN
cana-1652	69	87	=	=	SYM
cana-1652	69	88	(	(	PUNCT
cana-1652	69	89	𝑉	𝑉	PROPN
cana-1652	69	90	,	,	PUNCT
cana-1652	69	91	𝐸	𝐸	PROPN
cana-1652	69	92	,	,	PUNCT
cana-1652	69	93	𝜇	𝜇	NOUN
cana-1652	69	94	)	)	PUNCT
cana-1652	69	95	be	be	AUX
cana-1652	69	96	a	a	DET
cana-1652	69	97	fuzzy	fuzzy	ADJ
cana-1652	69	98	graph	graph	NOUN
cana-1652	69	99	and	and	CCONJ
cana-1652	69	100	let	let	VERB
cana-1652	69	101	𝐷	𝐷	PROPN
cana-1652	69	102	be	be	AUX
cana-1652	69	103	a	a	DET
cana-1652	69	104	dominating	dominating	NOUN
cana-1652	69	105	set	set	NOUN
cana-1652	69	106	of	of	ADP
cana-1652	69	107	𝐺.	𝐺.	NOUN
cana-1652	69	108	if	if	SCONJ
cana-1652	69	109	there	there	PRON
cana-1652	69	110	exists	exist	VERB
cana-1652	69	111	a	a	DET
cana-1652	69	112	vertex	vertex	NOUN
cana-1652	69	113	𝑣	𝑣	ADP
cana-1652	69	114	∈	∈	PROPN
cana-1652	69	115	𝑉	𝑉	PROPN
cana-1652	69	116	such	such	ADJ
cana-1652	69	117	that	that	SCONJ
cana-1652	69	118	𝜇(𝑣	𝜇(𝑣	NOUN
cana-1652	69	119	)	)	PUNCT
cana-1652	69	120	>	>	X
cana-1652	70	1	𝑚𝑎𝑥𝜇(𝑢	𝑚𝑎𝑥𝜇(𝑢	NUM
cana-1652	70	2	):	):	PUNCT
cana-1652	70	3	𝑢	𝑢	PROPN
cana-1652	70	4	∈	∈	PROPN
cana-1652	70	5	𝐷	𝐷	PROPN
cana-1652	70	6	,	,	PUNCT
cana-1652	70	7	then	then	ADV
cana-1652	70	8	𝐷	𝐷	PROPN
cana-1652	70	9	∪	∪	NOUN
cana-1652	70	10	𝑣	𝑣	NOUN
cana-1652	70	11	is	be	AUX
cana-1652	70	12	also	also	ADV
cana-1652	70	13	a	a	DET
cana-1652	70	14	dominating	dominating	NOUN
cana-1652	70	15	set	set	NOUN
cana-1652	70	16	of	of	ADP
cana-1652	70	17	𝐺.	𝐺.	NOUN
cana-1652	70	18	proof	proof	NOUN
cana-1652	70	19	:	:	PUNCT
cana-1652	70	20	let	let	VERB
cana-1652	70	21	𝐺	𝐺	PROPN
cana-1652	70	22	=	=	SYM
cana-1652	70	23	(	(	PUNCT
cana-1652	70	24	𝑉	𝑉	PROPN
cana-1652	70	25	,	,	PUNCT
cana-1652	70	26	𝐸	𝐸	PROPN
cana-1652	70	27	,	,	PUNCT
cana-1652	70	28	𝜇	𝜇	NOUN
cana-1652	70	29	)	)	PUNCT
cana-1652	70	30	be	be	AUX
cana-1652	70	31	a	a	DET
cana-1652	70	32	fuzzy	fuzzy	ADJ
cana-1652	70	33	graph	graph	NOUN
cana-1652	70	34	and	and	CCONJ
cana-1652	70	35	let	let	VERB
cana-1652	70	36	𝐷	𝐷	PROPN
cana-1652	70	37	be	be	AUX
cana-1652	70	38	a	a	DET
cana-1652	70	39	dominating	dominating	NOUN
cana-1652	70	40	set	set	NOUN
cana-1652	70	41	of	of	ADP
cana-1652	70	42	𝐺.	𝐺.	NOUN
cana-1652	70	43	suppose	suppose	VERB
cana-1652	70	44	there	there	PRON
cana-1652	70	45	exists	exist	VERB
cana-1652	70	46	a	a	DET
cana-1652	70	47	vertex	vertex	NOUN
cana-1652	70	48	𝑣	𝑣	ADP
cana-1652	70	49	∈	∈	PROPN
cana-1652	70	50	𝑉	𝑉	PROPN
cana-1652	70	51	such	such	ADJ
cana-1652	70	52	that	that	SCONJ
cana-1652	70	53	𝜇(𝑣	𝜇(𝑣	NOUN
cana-1652	70	54	)	)	PUNCT
cana-1652	70	55	>	>	X
cana-1652	71	1	max𝜇(𝑢	max𝜇(𝑢	PROPN
cana-1652	71	2	):	):	PUNCT
cana-1652	71	3	𝑢	𝑢	PROPN
cana-1652	71	4	∈	∈	PROPN
cana-1652	71	5	𝐷.	𝐷.	NOUN
cana-1652	71	6	we	we	PRON
cana-1652	71	7	need	need	VERB
cana-1652	71	8	to	to	PART
cana-1652	71	9	show	show	VERB
cana-1652	71	10	that	that	SCONJ
cana-1652	71	11	𝐷	𝐷	NOUN
cana-1652	71	12	∪	∪	NOUN
cana-1652	71	13	𝑣	𝑣	NOUN
cana-1652	71	14	is	be	AUX
cana-1652	71	15	also	also	ADV
cana-1652	71	16	a	a	DET
cana-1652	71	17	dominating	dominating	NOUN
cana-1652	71	18	set	set	NOUN
cana-1652	71	19	of	of	ADP
cana-1652	71	20	𝐺.	𝐺.	NOUN
cana-1652	71	21	consider	consider	VERB
cana-1652	71	22	any	any	DET
cana-1652	71	23	vertex	vertex	NOUN
cana-1652	71	24	𝑢	𝑢	ADP
cana-1652	71	25	∈	∈	PROPN
cana-1652	71	26	𝑉	𝑉	PROPN
cana-1652	71	27	−	−	PROPN
cana-1652	72	1	(	(	PUNCT
cana-1652	72	2	𝐷	𝐷	PROPN
cana-1652	72	3	∪	∪	VERB
cana-1652	72	4	𝑣	𝑣	NOUN
cana-1652	72	5	)	)	PUNCT
cana-1652	72	6	.	.	PUNCT
cana-1652	73	1	since	since	SCONJ
cana-1652	73	2	𝑣	𝑣	PRON
cana-1652	73	3	is	be	AUX
cana-1652	73	4	not	not	PART
cana-1652	73	5	in	in	ADP
cana-1652	73	6	𝐷	𝐷	NOUN
cana-1652	73	7	,	,	PUNCT
cana-1652	73	8	we	we	PRON
cana-1652	73	9	have	have	VERB
cana-1652	73	10	𝜇(𝑣	𝜇(𝑣	NOUN
cana-1652	73	11	)	)	PUNCT
cana-1652	73	12	<	<	X
cana-1652	74	1	max𝜇(𝑢′	max𝜇(𝑢′	PROPN
cana-1652	74	2	):	):	PUNCT
cana-1652	74	3	𝑢′	𝑢′	ADJ
cana-1652	74	4	∈	∈	PROPN
cana-1652	74	5	𝐷.	𝐷.	PROPN
cana-1652	74	6	therefore	therefore	ADV
cana-1652	74	7	,	,	PUNCT
cana-1652	74	8	there	there	PRON
cana-1652	74	9	exists	exist	VERB
cana-1652	74	10	a	a	DET
cana-1652	74	11	vertex	vertex	NOUN
cana-1652	74	12	𝑢′	𝑢′	ADP
cana-1652	74	13	∈	∈	PROPN
cana-1652	74	14	𝐷	𝐷	PROPN
cana-1652	74	15	such	such	ADJ
cana-1652	74	16	that	that	DET
cana-1652	74	17	𝜇(𝑢′	𝜇(𝑢′	NOUN
cana-1652	74	18	)	)	PUNCT
cana-1652	74	19	>	>	X
cana-1652	74	20	𝜇(𝑣	𝜇(𝑣	PROPN
cana-1652	74	21	)	)	PUNCT
cana-1652	74	22	.	.	PUNCT
cana-1652	75	1	since	since	SCONJ
cana-1652	75	2	𝐷	𝐷	PROPN
cana-1652	75	3	is	be	AUX
cana-1652	75	4	a	a	DET
cana-1652	75	5	dominating	dominating	NOUN
cana-1652	75	6	set	set	NOUN
cana-1652	75	7	of	of	ADP
cana-1652	75	8	𝐺	𝐺	PROPN
cana-1652	75	9	,	,	PUNCT
cana-1652	75	10	there	there	PRON
cana-1652	75	11	exists	exist	VERB
cana-1652	75	12	an	an	DET
cana-1652	75	13	edge	edge	NOUN
cana-1652	75	14	(	(	PUNCT
cana-1652	75	15	𝑢′	𝑢′	NUM
cana-1652	75	16	,	,	PUNCT
cana-1652	75	17	𝑢	𝑢	X
cana-1652	75	18	)	)	PUNCT
cana-1652	75	19	∈	∈	PROPN
cana-1652	75	20	𝐸	𝐸	PROPN
cana-1652	75	21	or	or	CCONJ
cana-1652	75	22	equivalently	equivalently	ADV
cana-1652	75	23	,	,	PUNCT
cana-1652	75	24	𝜇(𝑢′	𝜇(𝑢′	ADJ
cana-1652	75	25	,	,	PUNCT
cana-1652	75	26	𝑢	𝑢	PROPN
cana-1652	75	27	)	)	PUNCT
cana-1652	75	28	>	>	X
cana-1652	75	29	0	0	X
cana-1652	75	30	.	.	PUNCT
cana-1652	76	1	thus	thus	ADV
cana-1652	76	2	,	,	PUNCT
cana-1652	76	3	𝑢	𝑢	NOUN
cana-1652	76	4	is	be	AUX
cana-1652	76	5	dominated	dominate	VERB
cana-1652	76	6	by	by	ADP
cana-1652	76	7	𝑢′	𝑢′	NOUN
cana-1652	76	8	in	in	ADP
cana-1652	76	9	𝐺	𝐺	PROPN
cana-1652	76	10	and	and	CCONJ
cana-1652	76	11	hence	hence	ADV
cana-1652	76	12	by	by	ADP
cana-1652	76	13	extension	extension	NOUN
cana-1652	76	14	,	,	PUNCT
cana-1652	76	15	it	it	PRON
cana-1652	76	16	is	be	AUX
cana-1652	76	17	dominated	dominate	VERB
cana-1652	76	18	by	by	ADP
cana-1652	76	19	at	at	ADV
cana-1652	76	20	least	least	ADV
cana-1652	76	21	one	one	NUM
cana-1652	76	22	vertex	vertex	NOUN
cana-1652	76	23	in	in	ADP
cana-1652	76	24	𝐷	𝐷	PROPN
cana-1652	76	25	∪	∪	NOUN
cana-1652	76	26	𝑣.	𝑣.	NOUN
cana-1652	76	27	therefore	therefore	ADV
cana-1652	76	28	,	,	PUNCT
cana-1652	76	29	every	every	DET
cana-1652	76	30	vertex	vertex	NOUN
cana-1652	76	31	in	in	ADP
cana-1652	76	32	𝑉\(𝐷	𝑉\(𝐷	PUNCT
cana-1652	76	33	∪	∪	ADJ
cana-1652	76	34	𝑣	𝑣	NOUN
cana-1652	76	35	)	)	PUNCT
cana-1652	76	36	is	be	AUX
cana-1652	76	37	dominated	dominate	VERB
cana-1652	76	38	by	by	ADP
cana-1652	76	39	at	at	ADV
cana-1652	76	40	least	least	ADV
cana-1652	76	41	one	one	NUM
cana-1652	76	42	vertex	vertex	NOUN
cana-1652	76	43	in	in	ADP
cana-1652	76	44	𝐷	𝐷	PROPN
cana-1652	76	45	∪	∪	ADP
cana-1652	76	46	𝑣	𝑣	NOUN
cana-1652	76	47	,	,	PUNCT
cana-1652	76	48	which	which	PRON
cana-1652	76	49	implies	imply	VERB
cana-1652	76	50	that	that	SCONJ
cana-1652	76	51	𝐷	𝐷	NOUN
cana-1652	76	52	∪	∪	NOUN
cana-1652	76	53	𝑣	𝑣	PRON
cana-1652	76	54	is	be	AUX
cana-1652	76	55	a	a	DET
cana-1652	76	56	dominating	dominating	NOUN
cana-1652	76	57	set	set	NOUN
cana-1652	76	58	of	of	ADP
cana-1652	76	59	𝐺.	𝐺.	NOUN
cana-1652	76	60	therefore	therefore	ADV
cana-1652	76	61	,	,	PUNCT
cana-1652	76	62	we	we	PRON
cana-1652	76	63	have	have	AUX
cana-1652	76	64	shown	show	VERB
cana-1652	76	65	that	that	SCONJ
cana-1652	76	66	if	if	SCONJ
cana-1652	76	67	there	there	PRON
cana-1652	76	68	exists	exist	VERB
cana-1652	76	69	a	a	DET
cana-1652	76	70	vertex	vertex	NOUN
cana-1652	76	71	𝑣	𝑣	ADP
cana-1652	76	72	∈	∈	PROPN
cana-1652	76	73	𝑉	𝑉	PROPN
cana-1652	76	74	such	such	ADJ
cana-1652	76	75	that	that	SCONJ
cana-1652	76	76	𝜇(𝑣	𝜇(𝑣	NOUN
cana-1652	76	77	)	)	PUNCT
cana-1652	76	78	>	>	X
cana-1652	77	1	max𝜇(𝑢	max𝜇(𝑢	PROPN
cana-1652	77	2	):	):	PUNCT
cana-1652	77	3	𝑢	𝑢	PROPN
cana-1652	77	4	∈	∈	PROPN
cana-1652	77	5	𝐷	𝐷	PROPN
cana-1652	77	6	,	,	PUNCT
cana-1652	77	7	then	then	ADV
cana-1652	77	8	𝐷	𝐷	PROPN
cana-1652	77	9	∪	∪	NOUN
cana-1652	77	10	𝑣	𝑣	NOUN
cana-1652	77	11	is	be	AUX
cana-1652	77	12	also	also	ADV
cana-1652	77	13	a	a	DET
cana-1652	77	14	dominating	dominating	NOUN
cana-1652	77	15	set	set	NOUN
cana-1652	77	16	of	of	ADP
cana-1652	77	17	𝐺.	𝐺.	NOUN
cana-1652	77	18	theorem	theorem	ADJ
cana-1652	77	19	2.5	2.5	NUM
cana-1652	77	20	let	let	VERB
cana-1652	77	21	𝐺	𝐺	PROPN
cana-1652	77	22	=	=	SYM
cana-1652	77	23	(	(	PUNCT
cana-1652	77	24	𝑉	𝑉	PROPN
cana-1652	77	25	,	,	PUNCT
cana-1652	77	26	𝐸	𝐸	PROPN
cana-1652	77	27	,	,	PUNCT
cana-1652	77	28	𝜇	𝜇	NOUN
cana-1652	77	29	)	)	PUNCT
cana-1652	77	30	be	be	AUX
cana-1652	77	31	a	a	DET
cana-1652	77	32	fuzzy	fuzzy	ADJ
cana-1652	77	33	graph	graph	NOUN
cana-1652	77	34	and	and	CCONJ
cana-1652	77	35	let	let	VERB
cana-1652	77	36	𝐷	𝐷	PROPN
cana-1652	77	37	be	be	AUX
cana-1652	77	38	a	a	DET
cana-1652	77	39	dominating	dominating	NOUN
cana-1652	77	40	set	set	NOUN
cana-1652	77	41	of	of	ADP
cana-1652	77	42	𝐺.	𝐺.	NOUN
cana-1652	77	43	if	if	SCONJ
cana-1652	77	44	there	there	PRON
cana-1652	77	45	exists	exist	VERB
cana-1652	77	46	a	a	DET
cana-1652	77	47	vertex	vertex	NOUN
cana-1652	77	48	𝑣	𝑣	ADP
cana-1652	77	49	∈	∈	PROPN
cana-1652	77	50	𝑉	𝑉	PROPN
cana-1652	77	51	such	such	ADJ
cana-1652	77	52	that	that	SCONJ
cana-1652	77	53	𝜇(𝑣	𝜇(𝑣	NOUN
cana-1652	77	54	)	)	PUNCT
cana-1652	77	55	>	>	X
cana-1652	78	1	𝑚𝑎𝑥𝜇(𝑢	𝑚𝑎𝑥𝜇(𝑢	NUM
cana-1652	78	2	):	):	PUNCT
cana-1652	78	3	𝑢	𝑢	PROPN
cana-1652	78	4	∈	∈	PROPN
cana-1652	78	5	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1652	78	6	,	,	PUNCT
cana-1652	78	7	then	then	ADV
cana-1652	78	8	𝐷	𝐷	PROPN
cana-1652	78	9	is	be	AUX
cana-1652	78	10	the	the	DET
cana-1652	78	11	unique	unique	ADJ
cana-1652	78	12	minimum	minimum	ADJ
cana-1652	78	13	dominating	dominating	NOUN
cana-1652	78	14	set	set	NOUN
cana-1652	78	15	of	of	ADP
cana-1652	78	16	𝐺.	𝐺.	NOUN
cana-1652	78	17	proof	proof	NOUN
cana-1652	78	18	:	:	PUNCT
cana-1652	78	19	let	let	VERB
cana-1652	78	20	g	g	PROPN
cana-1652	78	21	=	=	SYM
cana-1652	78	22	(	(	PUNCT
cana-1652	78	23	v	v	NOUN
cana-1652	78	24	,	,	PUNCT
cana-1652	78	25	e	e	NOUN
cana-1652	78	26	,	,	PUNCT
cana-1652	78	27	𝜇	𝜇	PRON
cana-1652	78	28	)	)	PUNCT
cana-1652	78	29	be	be	AUX
cana-1652	78	30	a	a	DET
cana-1652	78	31	fuzzy	fuzzy	ADJ
cana-1652	78	32	graph	graph	NOUN
cana-1652	78	33	and	and	CCONJ
cana-1652	78	34	let	let	VERB
cana-1652	78	35	d	d	PRON
cana-1652	78	36	be	be	AUX
cana-1652	78	37	a	a	DET
cana-1652	78	38	dominating	dominating	NOUN
cana-1652	78	39	set	set	NOUN
cana-1652	78	40	of	of	ADP
cana-1652	78	41	g.	g.	PROPN
cana-1652	78	42	suppose	suppose	VERB
cana-1652	78	43	there	there	PRON
cana-1652	78	44	exists	exist	VERB
cana-1652	78	45	a	a	DET
cana-1652	78	46	vertex	vertex	NOUN
cana-1652	78	47	𝑣	𝑣	ADP
cana-1652	78	48	∈	∈	PROPN
cana-1652	78	49	𝑉	𝑉	PROPN
cana-1652	78	50	such	such	ADJ
cana-1652	78	51	that	that	SCONJ
cana-1652	78	52	𝜇(𝑣	𝜇(𝑣	NOUN
cana-1652	78	53	)	)	PUNCT
cana-1652	78	54	>	>	X
cana-1652	79	1	max𝜇(𝑢	max𝜇(𝑢	PROPN
cana-1652	79	2	):	):	PUNCT
cana-1652	79	3	𝑢	𝑢	PROPN
cana-1652	79	4	∈	∈	PROPN
cana-1652	79	5	𝑉\𝐷.	𝑉\𝐷.	NOUN
cana-1652	79	6	we	we	PRON
cana-1652	79	7	need	need	VERB
cana-1652	79	8	to	to	PART
cana-1652	79	9	show	show	VERB
cana-1652	79	10	that	that	SCONJ
cana-1652	79	11	d	d	NOUN
cana-1652	79	12	is	be	AUX
cana-1652	79	13	the	the	DET
cana-1652	79	14	unique	unique	ADJ
cana-1652	79	15	minimum	minimum	ADJ
cana-1652	79	16	dominating	dominating	NOUN
cana-1652	79	17	set	set	NOUN
cana-1652	79	18	of	of	ADP
cana-1652	79	19	g.	g.	PROPN
cana-1652	79	20	first	first	ADV
cana-1652	79	21	,	,	PUNCT
cana-1652	79	22	we	we	PRON
cana-1652	79	23	show	show	VERB
cana-1652	79	24	that	that	SCONJ
cana-1652	79	25	d	d	NOUN
cana-1652	79	26	is	be	AUX
cana-1652	79	27	a	a	DET
cana-1652	79	28	minimum	minimum	ADJ
cana-1652	79	29	dominating	dominating	NOUN
cana-1652	79	30	set	set	NOUN
cana-1652	79	31	of	of	ADP
cana-1652	79	32	g.	g.	PROPN
cana-1652	79	33	suppose	suppose	VERB
cana-1652	79	34	there	there	PRON
cana-1652	79	35	exists	exist	VERB
cana-1652	79	36	another	another	DET
cana-1652	79	37	dominating	dominating	NOUN
cana-1652	79	38	set	set	VERB
cana-1652	79	39	𝐷′	𝐷′	NOUN
cana-1652	79	40	of	of	ADP
cana-1652	79	41	g	g	PROPN
cana-1652	79	42	such	such	ADJ
cana-1652	79	43	that	that	SCONJ
cana-1652	79	44	|𝐷′|	|𝐷′|	X
cana-1652	79	45	<	<	X
cana-1652	79	46	|𝐷|	|𝐷|	NOUN
cana-1652	79	47	.	.	PUNCT
cana-1652	80	1	since	since	SCONJ
cana-1652	80	2	d	d	PROPN
cana-1652	80	3	dominates	dominate	VERB
cana-1652	80	4	every	every	DET
cana-1652	80	5	vertex	vertex	NOUN
cana-1652	80	6	in	in	ADP
cana-1652	80	7	v	v	NOUN
cana-1652	80	8	,	,	PUNCT
cana-1652	80	9	there	there	PRON
cana-1652	80	10	exists	exist	VERB
cana-1652	80	11	at	at	ADV
cana-1652	80	12	least	least	ADV
cana-1652	80	13	one	one	NUM
cana-1652	80	14	vertex	vertex	NOUN
cana-1652	80	15	𝑣′	𝑣′	NUM
cana-1652	80	16	∈	∈	NOUN
cana-1652	80	17	𝑉\𝐷′	𝑉\𝐷′	VERB
cana-1652	80	18	such	such	ADJ
cana-1652	80	19	that	that	SCONJ
cana-1652	80	20	𝑣′	𝑣′	PROPN
cana-1652	80	21	is	be	AUX
cana-1652	80	22	not	not	PART
cana-1652	80	23	dominated	dominate	VERB
cana-1652	80	24	by	by	ADP
cana-1652	80	25	any	any	DET
cana-1652	80	26	vertex	vertex	NOUN
cana-1652	80	27	in	in	ADP
cana-1652	80	28	𝐷′.	𝐷′.	NOUN
cana-1652	80	29	since	since	SCONJ
cana-1652	80	30	𝜇(𝑣′	𝜇(𝑣′	PROPN
cana-1652	80	31	)	)	PUNCT
cana-1652	80	32	>	>	X
cana-1652	81	1	max𝜇(𝑢	max𝜇(𝑢	PROPN
cana-1652	81	2	):	):	PUNCT
cana-1652	81	3	𝑢	𝑢	PROPN
cana-1652	81	4	∈	∈	PROPN
cana-1652	81	5	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1652	81	6	,	,	PUNCT
cana-1652	81	7	we	we	PRON
cana-1652	81	8	have	have	VERB
cana-1652	81	9	𝑣′	𝑣′	PROPN
cana-1652	81	10	∉	∉	PROPN
cana-1652	81	11	𝐷.	𝐷.	PROPN
cana-1652	81	12	therefore	therefore	ADV
cana-1652	81	13	,	,	PUNCT
cana-1652	81	14	𝑣′	𝑣′	PROPN
cana-1652	81	15	is	be	AUX
cana-1652	81	16	not	not	PART
cana-1652	81	17	dominated	dominate	VERB
cana-1652	81	18	by	by	ADP
cana-1652	81	19	any	any	DET
cana-1652	81	20	vertex	vertex	NOUN
cana-1652	81	21	in	in	ADP
cana-1652	81	22	d	d	NOUN
cana-1652	81	23	and	and	CCONJ
cana-1652	81	24	hence	hence	ADV
cana-1652	81	25	,	,	PUNCT
cana-1652	81	26	it	it	PRON
cana-1652	81	27	is	be	AUX
cana-1652	81	28	not	not	PART
cana-1652	81	29	dominated	dominate	VERB
cana-1652	81	30	by	by	ADP
cana-1652	81	31	any	any	DET
cana-1652	81	32	vertex	vertex	NOUN
cana-1652	81	33	in	in	ADP
cana-1652	81	34	𝐷′.	𝐷′.	NOUN
cana-1652	81	35	this	this	PRON
cana-1652	81	36	contradicts	contradict	VERB
cana-1652	81	37	the	the	DET
cana-1652	81	38	assumption	assumption	NOUN
cana-1652	81	39	that	that	SCONJ
cana-1652	81	40	𝐷′	𝐷′	PROPN
cana-1652	81	41	is	be	AUX
cana-1652	81	42	a	a	DET
cana-1652	81	43	dominating	dominating	NOUN
cana-1652	81	44	set	set	NOUN
cana-1652	81	45	of	of	ADP
cana-1652	81	46	g.	g.	PROPN
cana-1652	81	47	therefore	therefore	ADV
cana-1652	81	48	,	,	PUNCT
cana-1652	81	49	we	we	PRON
cana-1652	81	50	have	have	AUX
cana-1652	81	51	shown	show	VERB
cana-1652	81	52	that	that	SCONJ
cana-1652	81	53	there	there	PRON
cana-1652	81	54	does	do	AUX
cana-1652	81	55	not	not	PART
cana-1652	81	56	exist	exist	VERB
cana-1652	81	57	any	any	DET
cana-1652	81	58	other	other	ADJ
cana-1652	81	59	dominating	dominating	NOUN
cana-1652	81	60	set	set	NOUN
cana-1652	81	61	of	of	ADP
cana-1652	81	62	g	g	NOUN
cana-1652	81	63	with	with	ADP
cana-1652	81	64	fewer	few	ADJ
cana-1652	81	65	vertices	vertex	NOUN
cana-1652	81	66	than	than	ADP
cana-1652	81	67	d.	d.	PROPN
cana-1652	81	68	hence	hence	ADV
cana-1652	81	69	,	,	PUNCT
cana-1652	81	70	d	d	PROPN
cana-1652	81	71	is	be	AUX
cana-1652	81	72	a	a	DET
cana-1652	81	73	minimum	minimum	ADJ
cana-1652	81	74	dominating	dominating	NOUN
cana-1652	81	75	set	set	NOUN
cana-1652	81	76	of	of	ADP
cana-1652	81	77	g.	g.	PROPN
cana-1652	81	78	communications	communication	NOUN
cana-1652	81	79	on	on	ADP
cana-1652	81	80	applied	apply	VERB
cana-1652	81	81	nonlinear	nonlinear	ADJ
cana-1652	81	82	analysis	analysis	NOUN
cana-1652	81	83	issn	issn	NOUN
cana-1652	81	84	:	:	PUNCT
cana-1652	81	85	1074	1074	NUM
cana-1652	81	86	-	-	PUNCT
cana-1652	81	87	133x	133x	NUM
cana-1652	81	88	vol	vol	NOUN
cana-1652	81	89	32	32	NUM
cana-1652	81	90	no	no	NOUN
cana-1652	81	91	.	.	NOUN
cana-1652	81	92	1	1	NUM
cana-1652	81	93	(	(	PUNCT
cana-1652	81	94	2025	2025	NUM
cana-1652	81	95	)	)	PUNCT
cana-1652	81	96	327	327	NUM
cana-1652	81	97	https://internationalpubls.com	https://internationalpubls.com	X
cana-1652	81	98	next	next	ADV
cana-1652	81	99	,	,	PUNCT
cana-1652	81	100	we	we	PRON
cana-1652	81	101	show	show	VERB
cana-1652	81	102	that	that	SCONJ
cana-1652	81	103	there	there	PRON
cana-1652	81	104	does	do	AUX
cana-1652	81	105	not	not	PART
cana-1652	81	106	exist	exist	VERB
cana-1652	81	107	any	any	DET
cana-1652	81	108	other	other	ADJ
cana-1652	81	109	minimum	minimum	ADJ
cana-1652	81	110	dominating	dominating	NOUN
cana-1652	81	111	set	set	NOUN
cana-1652	81	112	of	of	ADP
cana-1652	81	113	g	g	PROPN
cana-1652	81	114	apart	apart	ADV
cana-1652	81	115	from	from	ADP
cana-1652	81	116	d.	d.	PROPN
cana-1652	81	117	suppose	suppose	VERB
cana-1652	81	118	there	there	PRON
cana-1652	81	119	exists	exist	VERB
cana-1652	81	120	another	another	DET
cana-1652	81	121	minimum	minimum	ADJ
cana-1652	81	122	dominating	dominating	NOUN
cana-1652	81	123	set	set	VERB
cana-1652	81	124	𝐸	𝐸	PROPN
cana-1652	81	125	of	of	ADP
cana-1652	81	126	g	g	PROPN
cana-1652	81	127	such	such	ADJ
cana-1652	81	128	that	that	SCONJ
cana-1652	81	129	𝐸	𝐸	PROPN
cana-1652	81	130	≠	≠	PROPN
cana-1652	81	131	𝐷.	𝐷.	NOUN
cana-1652	81	132	since	since	SCONJ
cana-1652	81	133	𝐸	𝐸	PROPN
cana-1652	81	134	is	be	AUX
cana-1652	81	135	also	also	ADV
cana-1652	81	136	a	a	DET
cana-1652	81	137	minimum	minimum	ADJ
cana-1652	81	138	dominating	dominating	NOUN
cana-1652	81	139	set	set	NOUN
cana-1652	81	140	,	,	PUNCT
cana-1652	81	141	we	we	PRON
cana-1652	81	142	have	have	VERB
cana-1652	81	143	|𝐸|	|𝐸|	NOUN
cana-1652	81	144	=	=	SYM
cana-1652	81	145	|𝐷|	|𝐷|	X
cana-1652	81	146	.	.	PUNCT
cana-1652	82	1	let	let	VERB
cana-1652	82	2	𝑥	𝑥	PRON
cana-1652	82	3	be	be	AUX
cana-1652	82	4	any	any	DET
cana-1652	82	5	vertex	vertex	NOUN
cana-1652	82	6	in	in	ADP
cana-1652	82	7	𝐸\𝐷.	𝐸\𝐷.	PROPN
cana-1652	82	8	since	since	SCONJ
cana-1652	82	9	𝐸	𝐸	PROPN
cana-1652	82	10	dominates	dominate	VERB
cana-1652	82	11	every	every	DET
cana-1652	82	12	vertex	vertex	NOUN
cana-1652	82	13	in	in	ADP
cana-1652	82	14	v	v	NOUN
cana-1652	82	15	,	,	PUNCT
cana-1652	82	16	there	there	PRON
cana-1652	82	17	exists	exist	VERB
cana-1652	82	18	at	at	ADV
cana-1652	82	19	least	least	ADV
cana-1652	82	20	one	one	NUM
cana-1652	82	21	vertex	vertex	NOUN
cana-1652	82	22	𝑦	𝑦	NOUN
cana-1652	82	23	∈	∈	ADJ
cana-1652	82	24	𝑉\𝐸	𝑉\𝐸	NOUN
cana-1652	82	25	such	such	ADJ
cana-1652	82	26	that	that	SCONJ
cana-1652	82	27	𝑦	𝑦	NOUN
cana-1652	82	28	is	be	AUX
cana-1652	82	29	not	not	PART
cana-1652	82	30	dominated	dominate	VERB
cana-1652	82	31	by	by	ADP
cana-1652	82	32	any	any	DET
cana-1652	82	33	vertex	vertex	NOUN
cana-1652	82	34	in	in	ADP
cana-1652	82	35	𝐸.	𝐸.	PROPN
cana-1652	82	36	since	since	SCONJ
cana-1652	82	37	𝑥	𝑥	PROPN
cana-1652	82	38	∈	∈	PROPN
cana-1652	82	39	𝐸	𝐸	PROPN
cana-1652	82	40	and	and	CCONJ
cana-1652	82	41	𝑦	𝑦	PROPN
cana-1652	82	42	∉	∉	PROPN
cana-1652	82	43	𝐸	𝐸	PROPN
cana-1652	82	44	,	,	PUNCT
cana-1652	82	45	we	we	PRON
cana-1652	82	46	have	have	VERB
cana-1652	82	47	(	(	PUNCT
cana-1652	82	48	𝑥	𝑥	NOUN
cana-1652	82	49	,	,	PUNCT
cana-1652	82	50	𝑦	𝑦	NOUN
cana-1652	82	51	)	)	PUNCT
cana-1652	82	52	∉	∉	PROPN
cana-1652	82	53	𝐸	𝐸	PROPN
cana-1652	82	54	or	or	CCONJ
cana-1652	82	55	equivalently	equivalently	ADV
cana-1652	82	56	,	,	PUNCT
cana-1652	82	57	𝜇(𝑥	𝜇(𝑥	PROPN
cana-1652	82	58	,	,	PUNCT
cana-1652	82	59	𝑦	𝑦	NOUN
cana-1652	82	60	)	)	PUNCT
cana-1652	82	61	=	=	SYM
cana-1652	83	1	0	0	X
cana-1652	83	2	.	.	PUNCT
cana-1652	84	1	since	since	SCONJ
cana-1652	84	2	𝐸	𝐸	PROPN
cana-1652	84	3	is	be	AUX
cana-1652	84	4	a	a	DET
cana-1652	84	5	dominating	dominating	NOUN
cana-1652	84	6	set	set	NOUN
cana-1652	84	7	of	of	ADP
cana-1652	84	8	g	g	NOUN
cana-1652	84	9	,	,	PUNCT
cana-1652	84	10	there	there	PRON
cana-1652	84	11	exists	exist	VERB
cana-1652	84	12	a	a	DET
cana-1652	84	13	vertex	vertex	NOUN
cana-1652	84	14	𝑧	𝑧	DET
cana-1652	84	15	∈	∈	PROPN
cana-1652	84	16	𝐸	𝐸	PROPN
cana-1652	84	17	such	such	ADJ
cana-1652	84	18	that	that	SCONJ
cana-1652	84	19	(	(	PUNCT
cana-1652	84	20	𝑧	𝑧	PROPN
cana-1652	84	21	,	,	PUNCT
cana-1652	84	22	𝑦	𝑦	NOUN
cana-1652	84	23	)	)	PUNCT
cana-1652	84	24	∈	∈	PROPN
cana-1652	84	25	𝐸	𝐸	PROPN
cana-1652	84	26	or	or	CCONJ
cana-1652	84	27	equivalently	equivalently	ADV
cana-1652	84	28	,	,	PUNCT
cana-1652	84	29	𝜇(𝑧	𝜇(𝑧	PROPN
cana-1652	84	30	,	,	PUNCT
cana-1652	84	31	𝑦	𝑦	NOUN
cana-1652	84	32	)	)	PUNCT
cana-1652	84	33	>	>	X
cana-1652	85	1	0	0	X
cana-1652	85	2	.	.	PUNCT
cana-1652	86	1	since	since	SCONJ
cana-1652	86	2	𝐷	𝐷	PROPN
cana-1652	86	3	is	be	AUX
cana-1652	86	4	also	also	ADV
cana-1652	86	5	a	a	DET
cana-1652	86	6	dominating	dominating	NOUN
cana-1652	86	7	set	set	NOUN
cana-1652	86	8	of	of	ADP
cana-1652	86	9	g	g	NOUN
cana-1652	86	10	,	,	PUNCT
cana-1652	86	11	there	there	PRON
cana-1652	86	12	exists	exist	VERB
cana-1652	86	13	a	a	DET
cana-1652	86	14	vertex	vertex	NOUN
cana-1652	86	15	𝑤	𝑤	ADP
cana-1652	86	16	∈	∈	NOUN
cana-1652	86	17	𝐷	𝐷	NOUN
cana-1652	86	18	such	such	ADJ
cana-1652	86	19	that	that	SCONJ
cana-1652	86	20	(	(	PUNCT
cana-1652	86	21	𝑤	𝑤	ADP
cana-1652	86	22	,	,	PUNCT
cana-1652	86	23	𝑧	𝑧	NOUN
cana-1652	86	24	)	)	PUNCT
cana-1652	86	25	∈	∈	PROPN
cana-1652	86	26	𝐸	𝐸	PROPN
cana-1652	86	27	or	or	CCONJ
cana-1652	86	28	equivalently	equivalently	ADV
cana-1652	86	29	,	,	PUNCT
cana-1652	86	30	𝜇(𝑤	𝜇(𝑤	PROPN
cana-1652	86	31	,	,	PUNCT
cana-1652	86	32	𝑧	𝑧	NOUN
cana-1652	86	33	)	)	PUNCT
cana-1652	86	34	>	>	X
cana-1652	86	35	0	0	X
cana-1652	86	36	.	.	PUNCT
cana-1652	87	1	therefore	therefore	ADV
cana-1652	87	2	,	,	PUNCT
cana-1652	87	3	we	we	PRON
cana-1652	87	4	have	have	VERB
cana-1652	87	5	𝜇(𝑤	𝜇(𝑤	PROPN
cana-1652	87	6	,	,	PUNCT
cana-1652	87	7	𝑦	𝑦	NOUN
cana-1652	87	8	)	)	PUNCT
cana-1652	87	9	≥	≥	NOUN
cana-1652	88	1	max𝜇(𝑤	max𝜇(𝑤	ADV
cana-1652	88	2	,	,	PUNCT
cana-1652	88	3	𝑧	𝑧	NOUN
cana-1652	88	4	)	)	PUNCT
cana-1652	88	5	,	,	PUNCT
cana-1652	88	6	𝜇(𝑧	𝜇(𝑧	PROPN
cana-1652	88	7	,	,	PUNCT
cana-1652	88	8	𝑦	𝑦	NOUN
cana-1652	88	9	)	)	PUNCT
cana-1652	88	10	>	>	X
cana-1652	88	11	0	0	X
cana-1652	88	12	.	.	PUNCT
cana-1652	89	1	this	this	PRON
cana-1652	89	2	implies	imply	VERB
cana-1652	89	3	that	that	SCONJ
cana-1652	89	4	𝑦	𝑦	NOUN
cana-1652	89	5	is	be	AUX
cana-1652	89	6	dominated	dominate	VERB
cana-1652	89	7	by	by	ADP
cana-1652	89	8	𝑤	𝑤	NOUN
cana-1652	89	9	in	in	ADP
cana-1652	89	10	g	g	NOUN
cana-1652	89	11	and	and	CCONJ
cana-1652	89	12	hence	hence	ADV
cana-1652	89	13	by	by	ADP
cana-1652	89	14	extension	extension	NOUN
cana-1652	89	15	,	,	PUNCT
cana-1652	89	16	it	it	PRON
cana-1652	89	17	is	be	AUX
cana-1652	89	18	dominated	dominate	VERB
cana-1652	89	19	by	by	ADP
cana-1652	89	20	at	at	ADV
cana-1652	89	21	least	least	ADV
cana-1652	89	22	one	one	NUM
cana-1652	89	23	vertex	vertex	NOUN
cana-1652	89	24	in	in	ADP
cana-1652	89	25	d.	d.	PROPN
cana-1652	89	26	therefore	therefore	ADV
cana-1652	89	27	,	,	PUNCT
cana-1652	89	28	every	every	DET
cana-1652	89	29	vertex	vertex	NOUN
cana-1652	89	30	in	in	ADP
cana-1652	89	31	𝐸\𝐷	𝐸\𝐷	NOUN
cana-1652	89	32	is	be	AUX
cana-1652	89	33	dominated	dominate	VERB
cana-1652	89	34	by	by	ADP
cana-1652	89	35	at	at	ADV
cana-1652	89	36	least	least	ADV
cana-1652	89	37	one	one	NUM
cana-1652	89	38	vertex	vertex	NOUN
cana-1652	89	39	in	in	ADP
cana-1652	89	40	d	d	PROPN
cana-1652	89	41	,	,	PUNCT
cana-1652	89	42	which	which	PRON
cana-1652	89	43	implies	imply	VERB
cana-1652	89	44	that	that	SCONJ
cana-1652	89	45	𝐸	𝐸	PROPN
cana-1652	89	46	is	be	AUX
cana-1652	89	47	not	not	PART
cana-1652	89	48	a	a	DET
cana-1652	89	49	minimum	minimum	ADJ
cana-1652	89	50	dominating	dominating	NOUN
cana-1652	89	51	set	set	NOUN
cana-1652	89	52	of	of	ADP
cana-1652	89	53	g.	g.	PROPN
cana-1652	89	54	this	this	PRON
cana-1652	89	55	contradicts	contradict	VERB
cana-1652	89	56	the	the	DET
cana-1652	89	57	assumption	assumption	NOUN
cana-1652	89	58	that	that	SCONJ
cana-1652	89	59	there	there	PRON
cana-1652	89	60	exists	exist	VERB
cana-1652	89	61	another	another	DET
cana-1652	89	62	minimum	minimum	ADJ
cana-1652	89	63	dominating	dominating	NOUN
cana-1652	89	64	set	set	VERB
cana-1652	89	65	apart	apart	ADV
cana-1652	89	66	from	from	ADP
cana-1652	89	67	d.	d.	PROPN
cana-1652	89	68	hence	hence	ADV
cana-1652	89	69	,	,	PUNCT
cana-1652	89	70	we	we	PRON
cana-1652	89	71	have	have	AUX
cana-1652	89	72	shown	show	VERB
cana-1652	89	73	that	that	SCONJ
cana-1652	89	74	there	there	PRON
cana-1652	89	75	does	do	AUX
cana-1652	89	76	not	not	PART
cana-1652	89	77	exist	exist	VERB
cana-1652	89	78	any	any	DET
cana-1652	89	79	other	other	ADJ
cana-1652	89	80	minimum	minimum	ADJ
cana-1652	89	81	dominating	dominating	NOUN
cana-1652	89	82	set	set	NOUN
cana-1652	89	83	of	of	ADP
cana-1652	89	84	g	g	PROPN
cana-1652	89	85	apart	apart	ADV
cana-1652	89	86	from	from	ADP
cana-1652	89	87	d.	d.	PROPN
cana-1652	89	88	therefore	therefore	ADV
cana-1652	89	89	,	,	PUNCT
cana-1652	89	90	we	we	PRON
cana-1652	89	91	have	have	AUX
cana-1652	89	92	shown	show	VERB
cana-1652	89	93	that	that	SCONJ
cana-1652	89	94	if	if	SCONJ
cana-1652	89	95	there	there	PRON
cana-1652	89	96	exists	exist	VERB
cana-1652	89	97	a	a	DET
cana-1652	89	98	vertex	vertex	NOUN
cana-1652	89	99	𝑣	𝑣	ADP
cana-1652	89	100	∈	∈	PROPN
cana-1652	89	101	𝑉	𝑉	PROPN
cana-1652	89	102	such	such	ADJ
cana-1652	89	103	that	that	SCONJ
cana-1652	89	104	𝜇(𝑣	𝜇(𝑣	NOUN
cana-1652	89	105	)	)	PUNCT
cana-1652	89	106	>	>	X
cana-1652	90	1	max𝜇(𝑢	max𝜇(𝑢	PROPN
cana-1652	90	2	):	):	PUNCT
cana-1652	90	3	𝑢	𝑢	PROPN
cana-1652	90	4	∈	∈	PROPN
cana-1652	90	5	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1652	90	6	,	,	PUNCT
cana-1652	90	7	then	then	ADV
cana-1652	90	8	d	d	PROPN
cana-1652	90	9	is	be	AUX
cana-1652	90	10	the	the	DET
cana-1652	90	11	unique	unique	ADJ
cana-1652	90	12	minimum	minimum	ADJ
cana-1652	90	13	dominating	dominating	NOUN
cana-1652	90	14	set	set	NOUN
cana-1652	90	15	of	of	ADP
cana-1652	90	16	g.	g.	PROPN
cana-1652	90	17	theorem	theorem	VERB
cana-1652	90	18	2.6	2.6	NUM
cana-1652	90	19	let	let	VERB
cana-1652	90	20	𝐺	𝐺	PROPN
cana-1652	90	21	=	=	SYM
cana-1652	90	22	(	(	PUNCT
cana-1652	90	23	𝑉	𝑉	PROPN
cana-1652	90	24	,	,	PUNCT
cana-1652	90	25	𝐸	𝐸	PROPN
cana-1652	90	26	,	,	PUNCT
cana-1652	90	27	𝜇	𝜇	NOUN
cana-1652	90	28	)	)	PUNCT
cana-1652	90	29	be	be	AUX
cana-1652	90	30	a	a	DET
cana-1652	90	31	fuzzy	fuzzy	ADJ
cana-1652	90	32	graph	graph	NOUN
cana-1652	90	33	and	and	CCONJ
cana-1652	90	34	let	let	VERB
cana-1652	90	35	𝐺𝑐	𝐺𝑐	PROPN
cana-1652	90	36	=	=	SYM
cana-1652	90	37	(	(	PUNCT
cana-1652	90	38	𝑉	𝑉	PROPN
cana-1652	90	39	,	,	PUNCT
cana-1652	90	40	𝐸𝑐	𝐸𝑐	PROPN
cana-1652	90	41	,	,	PUNCT
cana-1652	90	42	1	1	NUM
cana-1652	90	43	−	−	NOUN
cana-1652	90	44	𝜇	𝜇	AUX
cana-1652	90	45	)	)	PUNCT
cana-1652	90	46	be	be	AUX
cana-1652	90	47	its	its	PRON
cana-1652	90	48	complement	complement	NOUN
cana-1652	90	49	fuzzy	fuzzy	ADJ
cana-1652	90	50	graph	graph	NOUN
cana-1652	90	51	.	.	PUNCT
cana-1652	91	1	then	then	ADV
cana-1652	91	2	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1652	91	3	)	)	PUNCT
cana-1652	92	1	+	+	CCONJ
cana-1652	92	2	𝛾(𝐺𝑐	𝛾(𝐺𝑐	ADJ
cana-1652	92	3	)	)	PUNCT
cana-1652	92	4	=	=	NOUN
cana-1652	92	5	|𝑉|	|𝑉|	NOUN
cana-1652	92	6	.	.	PUNCT
cana-1652	93	1	proof	proof	NOUN
cana-1652	93	2	:	:	PUNCT
cana-1652	93	3	let	let	VERB
cana-1652	93	4	g	g	PROPN
cana-1652	93	5	=	=	SYM
cana-1652	93	6	(	(	PUNCT
cana-1652	93	7	v	v	NOUN
cana-1652	93	8	,	,	PUNCT
cana-1652	93	9	e	e	NOUN
cana-1652	93	10	,	,	PUNCT
cana-1652	93	11	𝜇	𝜇	PRON
cana-1652	93	12	)	)	PUNCT
cana-1652	93	13	be	be	AUX
cana-1652	93	14	a	a	DET
cana-1652	93	15	fuzzy	fuzzy	ADJ
cana-1652	93	16	graph	graph	NOUN
cana-1652	93	17	and	and	CCONJ
cana-1652	93	18	let	let	VERB
cana-1652	93	19	𝐺𝑐	𝐺𝑐	PROPN
cana-1652	93	20	=	=	PUNCT
cana-1652	93	21	(	(	PUNCT
cana-1652	93	22	v	v	NOUN
cana-1652	93	23	,	,	PUNCT
cana-1652	93	24	𝐸𝑐	𝐸𝑐	PROPN
cana-1652	93	25	,	,	PUNCT
cana-1652	93	26	1	1	NUM
cana-1652	93	27	−	−	NOUN
cana-1652	93	28	𝜇	𝜇	AUX
cana-1652	93	29	)	)	PUNCT
cana-1652	93	30	be	be	AUX
cana-1652	93	31	its	its	PRON
cana-1652	93	32	complement	complement	NOUN
cana-1652	93	33	fuzzy	fuzzy	ADJ
cana-1652	93	34	graph	graph	NOUN
cana-1652	93	35	.	.	PUNCT
cana-1652	94	1	we	we	PRON
cana-1652	94	2	need	need	VERB
cana-1652	94	3	to	to	PART
cana-1652	94	4	show	show	VERB
cana-1652	94	5	that	that	SCONJ
cana-1652	94	6	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	94	7	)	)	PUNCT
cana-1652	95	1	+	+	CCONJ
cana-1652	95	2	𝛾(𝐺𝑐	𝛾(𝐺𝑐	ADJ
cana-1652	95	3	)	)	PUNCT
cana-1652	95	4	=	=	NOUN
cana-1652	95	5	|𝑉|	|𝑉|	NOUN
cana-1652	95	6	.	.	PUNCT
cana-1652	96	1	let	let	VERB
cana-1652	96	2	d	d	PRON
cana-1652	96	3	be	be	AUX
cana-1652	96	4	a	a	DET
cana-1652	96	5	minimum	minimum	ADJ
cana-1652	96	6	dominating	dominating	NOUN
cana-1652	96	7	set	set	NOUN
cana-1652	96	8	of	of	ADP
cana-1652	96	9	g	g	NOUN
cana-1652	96	10	and	and	CCONJ
cana-1652	96	11	let	let	VERB
cana-1652	96	12	d	d	VERB
cana-1652	96	13	’	'	PUNCT
cana-1652	96	14	be	be	AUX
cana-1652	96	15	a	a	DET
cana-1652	96	16	minimum	minimum	ADJ
cana-1652	96	17	dominating	dominating	NOUN
cana-1652	96	18	set	set	NOUN
cana-1652	96	19	of	of	ADP
cana-1652	96	20	𝐺𝑐.	𝐺𝑐.	PROPN
cana-1652	96	21	since	since	SCONJ
cana-1652	96	22	d	d	PROPN
cana-1652	96	23	is	be	AUX
cana-1652	96	24	a	a	DET
cana-1652	96	25	dominating	dominating	NOUN
cana-1652	96	26	set	set	NOUN
cana-1652	96	27	of	of	ADP
cana-1652	96	28	g	g	NOUN
cana-1652	96	29	,	,	PUNCT
cana-1652	96	30	every	every	DET
cana-1652	96	31	vertex	vertex	NOUN
cana-1652	96	32	in	in	ADP
cana-1652	96	33	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1652	96	34	is	be	AUX
cana-1652	96	35	adjacent	adjacent	ADJ
cana-1652	96	36	to	to	ADP
cana-1652	96	37	at	at	ADV
cana-1652	96	38	least	least	ADV
cana-1652	96	39	one	one	NUM
cana-1652	96	40	vertex	vertex	NOUN
cana-1652	96	41	in	in	ADP
cana-1652	96	42	d.	d.	PROPN
cana-1652	96	43	therefore	therefore	ADV
cana-1652	96	44	,	,	PUNCT
cana-1652	96	45	every	every	DET
cana-1652	96	46	vertex	vertex	NOUN
cana-1652	96	47	in	in	ADP
cana-1652	96	48	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1652	96	49	is	be	AUX
cana-1652	96	50	not	not	PART
cana-1652	96	51	in	in	ADP
cana-1652	96	52	d	d	NOUN
cana-1652	96	53	’	'	PUNCT
cana-1652	96	54	.	.	PUNCT
cana-1652	97	1	similarly	similarly	ADV
cana-1652	97	2	,	,	PUNCT
cana-1652	97	3	since	since	SCONJ
cana-1652	97	4	d	d	NOUN
cana-1652	97	5	’	'	PUNCT
cana-1652	97	6	is	be	AUX
cana-1652	97	7	a	a	DET
cana-1652	97	8	dominating	dominating	NOUN
cana-1652	97	9	set	set	NOUN
cana-1652	97	10	of	of	ADP
cana-1652	97	11	𝐺𝑐	𝐺𝑐	PROPN
cana-1652	97	12	,	,	PUNCT
cana-1652	97	13	every	every	DET
cana-1652	97	14	vertex	vertex	NOUN
cana-1652	97	15	in	in	ADP
cana-1652	97	16	𝑉\𝐷′	𝑉\𝐷′	PROPN
cana-1652	97	17	is	be	AUX
cana-1652	97	18	adjacent	adjacent	ADJ
cana-1652	97	19	to	to	ADP
cana-1652	97	20	at	at	ADV
cana-1652	97	21	least	least	ADV
cana-1652	97	22	one	one	NUM
cana-1652	97	23	vertex	vertex	NOUN
cana-1652	97	24	in	in	ADP
cana-1652	97	25	d	d	NOUN
cana-1652	97	26	’	'	PUNCT
cana-1652	97	27	.	.	PUNCT
cana-1652	98	1	therefore	therefore	ADV
cana-1652	98	2	,	,	PUNCT
cana-1652	98	3	every	every	DET
cana-1652	98	4	vertex	vertex	NOUN
cana-1652	98	5	in	in	ADP
cana-1652	98	6	𝑉\𝐷′	𝑉\𝐷′	PROPN
cana-1652	98	7	is	be	AUX
cana-1652	98	8	not	not	PART
cana-1652	98	9	in	in	ADP
cana-1652	98	10	d.	d.	PROPN
cana-1652	98	11	since	since	SCONJ
cana-1652	98	12	every	every	DET
cana-1652	98	13	vertex	vertex	NOUN
cana-1652	98	14	in	in	ADP
cana-1652	98	15	v	v	NOUN
cana-1652	98	16	belongs	belong	VERB
cana-1652	98	17	to	to	ADP
cana-1652	98	18	either	either	CCONJ
cana-1652	98	19	d	d	PROPN
cana-1652	98	20	or	or	CCONJ
cana-1652	98	21	𝑉\𝐷′	𝑉\𝐷′	PROPN
cana-1652	98	22	,	,	PUNCT
cana-1652	98	23	we	we	PRON
cana-1652	98	24	have	have	VERB
cana-1652	98	25	|𝐷|	|𝐷|	NOUN
cana-1652	98	26	+	+	CCONJ
cana-1652	98	27	|𝑉\𝐷′|	|𝑉\𝐷′|	NOUN
cana-1652	98	28	=	=	NOUN
cana-1652	98	29	|𝑉|	|𝑉|	NOUN
cana-1652	98	30	.	.	PUNCT
cana-1652	99	1	also	also	ADV
cana-1652	99	2	,	,	PUNCT
cana-1652	99	3	since	since	SCONJ
cana-1652	99	4	both	both	CCONJ
cana-1652	99	5	d	d	NOUN
cana-1652	99	6	and	and	CCONJ
cana-1652	99	7	𝐷′	𝐷′	NOUN
cana-1652	99	8	are	be	AUX
cana-1652	99	9	minimum	minimum	ADJ
cana-1652	99	10	dominating	dominating	NOUN
cana-1652	99	11	sets	set	NOUN
cana-1652	99	12	,	,	PUNCT
cana-1652	99	13	we	we	PRON
cana-1652	99	14	have	have	VERB
cana-1652	99	15	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	99	16	)	)	PUNCT
cana-1652	100	1	=	=	SYM
cana-1652	100	2	|𝐷|	|𝐷|	NOUN
cana-1652	100	3	and	and	CCONJ
cana-1652	100	4	𝛾(𝐺𝑐	𝛾(𝐺𝑐	ADJ
cana-1652	100	5	)	)	PUNCT
cana-1652	100	6	=	=	PUNCT
cana-1652	100	7	|𝐷′|	|𝐷′|	NOUN
cana-1652	100	8	.	.	PUNCT
cana-1652	101	1	therefore	therefore	ADV
cana-1652	101	2	,	,	PUNCT
cana-1652	101	3	we	we	PRON
cana-1652	101	4	have	have	VERB
cana-1652	101	5	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	101	6	)	)	PUNCT
cana-1652	102	1	+	+	CCONJ
cana-1652	102	2	𝛾(𝐺𝑐	𝛾(𝐺𝑐	ADJ
cana-1652	102	3	)	)	PUNCT
cana-1652	102	4	=	=	SYM
cana-1652	102	5	|𝐷|	|𝐷|	NOUN
cana-1652	102	6	+	+	CCONJ
cana-1652	102	7	|𝐷′|	|𝐷′|	X
cana-1652	102	8	=	=	SYM
cana-1652	102	9	|𝑉|	|𝑉|	NOUN
cana-1652	102	10	−	−	PROPN
cana-1652	102	11	(	(	PUNCT
cana-1652	102	12	|𝑉\𝐷′|	|𝑉\𝐷′|	X
cana-1652	102	13	+	+	NUM
cana-1652	102	14	|𝐷|	|𝐷|	NOUN
cana-1652	102	15	)	)	PUNCT
cana-1652	102	16	=	=	NOUN
cana-1652	102	17	|𝑉|	|𝑉|	NOUN
cana-1652	102	18	.	.	PUNCT
cana-1652	103	1	hence	hence	ADV
cana-1652	103	2	,	,	PUNCT
cana-1652	103	3	we	we	PRON
cana-1652	103	4	have	have	AUX
cana-1652	103	5	shown	show	VERB
cana-1652	103	6	that	that	SCONJ
cana-1652	103	7	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	103	8	)	)	PUNCT
cana-1652	104	1	+	+	CCONJ
cana-1652	104	2	𝛾(𝐺𝑐	𝛾(𝐺𝑐	ADJ
cana-1652	104	3	)	)	PUNCT
cana-1652	104	4	=	=	NOUN
cana-1652	104	5	|𝑉|	|𝑉|	NOUN
cana-1652	104	6	.	.	PUNCT
cana-1652	105	1	theorem	theorem	VERB
cana-1652	105	2	2.7	2.7	NUM
cana-1652	105	3	let	let	VERB
cana-1652	105	4	𝐺	𝐺	PROPN
cana-1652	105	5	=	=	SYM
cana-1652	105	6	(	(	PUNCT
cana-1652	105	7	𝑉	𝑉	PROPN
cana-1652	105	8	,	,	PUNCT
cana-1652	105	9	𝐸	𝐸	PROPN
cana-1652	105	10	,	,	PUNCT
cana-1652	105	11	𝜇	𝜇	NOUN
cana-1652	105	12	)	)	PUNCT
cana-1652	105	13	be	be	VERB
cana-1652	105	14	a	a	DET
cana-1652	105	15	connected	connected	ADJ
cana-1652	105	16	fuzzy	fuzzy	ADJ
cana-1652	105	17	graph	graph	NOUN
cana-1652	105	18	with	with	ADP
cana-1652	105	19	𝑛	𝑛	PROPN
cana-1652	105	20	vertices	vertex	NOUN
cana-1652	105	21	and	and	CCONJ
cana-1652	105	22	𝑚	𝑚	ADP
cana-1652	105	23	edges	edge	NOUN
cana-1652	105	24	.	.	PUNCT
cana-1652	106	1	then	then	ADV
cana-1652	106	2	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1652	106	3	)	)	PUNCT
cana-1652	106	4	≤	≤	NUM
cana-1652	107	1	𝑛	𝑛	DET
cana-1652	107	2	−	−	PROPN
cana-1652	107	3	⌈	⌈	NOUN
cana-1652	107	4	𝑛	𝑛	ADP
cana-1652	107	5	𝑚	𝑚	X
cana-1652	107	6	⌉	⌉	NOUN
cana-1652	107	7	+	+	NOUN
cana-1652	107	8	1	1	X
cana-1652	107	9	.	.	X
cana-1652	107	10	proof	proof	NOUN
cana-1652	107	11	:	:	PUNCT
cana-1652	107	12	let	let	VERB
cana-1652	107	13	g	g	PROPN
cana-1652	107	14	=	=	SYM
cana-1652	107	15	(	(	PUNCT
cana-1652	107	16	v	v	NOUN
cana-1652	107	17	,	,	PUNCT
cana-1652	107	18	e	e	NOUN
cana-1652	107	19	,	,	PUNCT
cana-1652	107	20	𝜇	𝜇	PRON
cana-1652	107	21	)	)	PUNCT
cana-1652	107	22	be	be	VERB
cana-1652	107	23	a	a	DET
cana-1652	107	24	connected	connected	ADJ
cana-1652	107	25	fuzzy	fuzzy	ADJ
cana-1652	107	26	graph	graph	NOUN
cana-1652	107	27	with	with	ADP
cana-1652	107	28	n	n	ADP
cana-1652	107	29	vertices	vertex	NOUN
cana-1652	107	30	and	and	CCONJ
cana-1652	107	31	m	m	PRON
cana-1652	107	32	edges	edge	NOUN
cana-1652	107	33	.	.	PUNCT
cana-1652	108	1	we	we	PRON
cana-1652	108	2	need	need	VERB
cana-1652	108	3	to	to	PART
cana-1652	108	4	show	show	VERB
cana-1652	108	5	that	that	SCONJ
cana-1652	108	6	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	108	7	)	)	PUNCT
cana-1652	108	8	≤	≤	NUM
cana-1652	108	9	𝑛	𝑛	DET
cana-1652	108	10	−	−	PROPN
cana-1652	108	11	⌈	⌈	NOUN
cana-1652	108	12	𝑛	𝑛	ADP
cana-1652	108	13	𝑚	𝑚	X
cana-1652	108	14	⌉	⌉	NOUN
cana-1652	108	15	+	+	NOUN
cana-1652	108	16	1	1	X
cana-1652	108	17	.	.	X
cana-1652	108	18	let	let	VERB
cana-1652	108	19	d	d	PRON
cana-1652	108	20	be	be	AUX
cana-1652	108	21	a	a	DET
cana-1652	108	22	minimum	minimum	ADJ
cana-1652	108	23	dominating	dominating	NOUN
cana-1652	108	24	set	set	NOUN
cana-1652	108	25	of	of	ADP
cana-1652	108	26	g.	g.	PROPN
cana-1652	108	27	since	since	SCONJ
cana-1652	108	28	g	g	PROPN
cana-1652	108	29	is	be	AUX
cana-1652	108	30	connected	connect	VERB
cana-1652	108	31	,	,	PUNCT
cana-1652	108	32	there	there	PRON
cana-1652	108	33	exists	exist	VERB
cana-1652	108	34	a	a	DET
cana-1652	108	35	spanning	span	VERB
cana-1652	108	36	tree	tree	NOUN
cana-1652	108	37	t	t	PROPN
cana-1652	108	38	of	of	ADP
cana-1652	108	39	g.	g.	PROPN
cana-1652	108	40	let	let	VERB
cana-1652	108	41	𝑣	𝑣	PART
cana-1652	108	42	be	be	AUX
cana-1652	108	43	any	any	DET
cana-1652	108	44	vertex	vertex	NOUN
cana-1652	108	45	in	in	ADP
cana-1652	108	46	𝑉	𝑉	PROPN
cana-1652	108	47	and	and	CCONJ
cana-1652	108	48	let	let	VERB
cana-1652	108	49	𝑇(𝑣	𝑇(𝑣	X
cana-1652	108	50	)	)	PUNCT
cana-1652	108	51	be	be	AUX
cana-1652	108	52	the	the	DET
cana-1652	108	53	subtree	subtree	NOUN
cana-1652	108	54	of	of	ADP
cana-1652	108	55	𝑇	𝑇	PROPN
cana-1652	108	56	rooted	root	VERB
cana-1652	108	57	at	at	ADP
cana-1652	108	58	𝑣.	𝑣.	NOUN
cana-1652	108	59	since	since	SCONJ
cana-1652	108	60	d	d	PROPN
cana-1652	108	61	is	be	AUX
cana-1652	108	62	a	a	DET
cana-1652	108	63	dominating	dominating	NOUN
cana-1652	108	64	set	set	NOUN
cana-1652	108	65	of	of	ADP
cana-1652	108	66	g	g	NOUN
cana-1652	108	67	,	,	PUNCT
cana-1652	108	68	every	every	DET
cana-1652	108	69	vertex	vertex	NOUN
cana-1652	108	70	in	in	ADP
cana-1652	108	71	𝑉	𝑉	PROPN
cana-1652	108	72	𝐷	𝐷	PROPN
cana-1652	108	73	is	be	AUX
cana-1652	108	74	adjacent	adjacent	ADJ
cana-1652	108	75	to	to	ADP
cana-1652	108	76	at	at	ADV
cana-1652	108	77	least	least	ADV
cana-1652	108	78	one	one	NUM
cana-1652	108	79	vertex	vertex	NOUN
cana-1652	108	80	in	in	ADP
cana-1652	108	81	d.	d.	PROPN
cana-1652	108	82	therefore	therefore	ADV
cana-1652	108	83	,	,	PUNCT
cana-1652	108	84	every	every	DET
cana-1652	108	85	vertex	vertex	NOUN
cana-1652	108	86	in	in	ADP
cana-1652	108	87	𝑉	𝑉	PROPN
cana-1652	108	88	𝐷	𝐷	PROPN
cana-1652	108	89	is	be	AUX
cana-1652	108	90	either	either	CCONJ
cana-1652	108	91	in	in	ADP
cana-1652	108	92	𝑇(𝑣	𝑇(𝑣	NOUN
cana-1652	108	93	)	)	PUNCT
cana-1652	108	94	or	or	CCONJ
cana-1652	108	95	in	in	ADP
cana-1652	108	96	the	the	DET
cana-1652	108	97	subtree	subtree	NOUN
cana-1652	108	98	of	of	ADP
cana-1652	108	99	𝑇	𝑇	PROPN
cana-1652	108	100	rooted	root	VERB
cana-1652	108	101	at	at	ADP
cana-1652	108	102	some	some	DET
cana-1652	108	103	other	other	ADJ
cana-1652	108	104	vertex	vertex	NOUN
cana-1652	108	105	𝑤	𝑤	ADP
cana-1652	108	106	∈	∈	NOUN
cana-1652	108	107	𝑉.	𝑉.	NOUN
cana-1652	108	108	let	let	VERB
cana-1652	108	109	𝑇1	𝑇1	NOUN
cana-1652	108	110	,	,	PUNCT
cana-1652	108	111	𝑇2	𝑇2	NOUN
cana-1652	108	112	,	,	PUNCT
cana-1652	108	113	.	.	PUNCT
cana-1652	108	114	.	.	PUNCT
cana-1652	109	1	.	.	PUNCT
cana-1652	110	1	,	,	PUNCT
cana-1652	110	2	𝑇𝑘	𝑇𝑘	PROPN
cana-1652	110	3	be	be	AUX
cana-1652	110	4	the	the	DET
cana-1652	110	5	subtrees	subtree	NOUN
cana-1652	110	6	of	of	ADP
cana-1652	110	7	𝑇	𝑇	PROPN
cana-1652	110	8	rooted	root	VERB
cana-1652	110	9	at	at	ADP
cana-1652	110	10	the	the	DET
cana-1652	110	11	vertices	vertex	NOUN
cana-1652	110	12	𝑣	𝑣	PROPN
cana-1652	110	13	,	,	PUNCT
cana-1652	110	14	𝑤1	𝑤1	VERB
cana-1652	110	15	,	,	PUNCT
cana-1652	110	16	𝑤2	𝑤2	NOUN
cana-1652	110	17	,	,	PUNCT
cana-1652	110	18	.	.	PUNCT
cana-1652	110	19	.	.	PUNCT
cana-1652	111	1	.	.	PUNCT
cana-1652	112	1	,	,	PUNCT
cana-1652	112	2	𝑤𝑘−1	𝑤𝑘−1	PROPN
cana-1652	112	3	respectively	respectively	ADV
cana-1652	112	4	,	,	PUNCT
cana-1652	112	5	where	where	SCONJ
cana-1652	112	6	𝑘	𝑘	NOUN
cana-1652	112	7	=	=	SYM
cana-1652	112	8	|𝐷|	|𝐷|	X
cana-1652	112	9	.	.	PUNCT
cana-1652	112	10	note	note	VERB
cana-1652	112	11	that	that	SCONJ
cana-1652	112	12	each	each	DET
cana-1652	112	13	subtree	subtree	NOUN
cana-1652	112	14	𝑇𝑖	𝑇𝑖	PROPN
cana-1652	112	15	contains	contain	VERB
cana-1652	112	16	at	at	ADV
cana-1652	112	17	least	least	ADV
cana-1652	112	18	one	one	NUM
cana-1652	112	19	vertex	vertex	NOUN
cana-1652	112	20	from	from	ADP
cana-1652	112	21	d	d	PROPN
cana-1652	112	22	and	and	CCONJ
cana-1652	112	23	every	every	DET
cana-1652	112	24	vertex	vertex	NOUN
cana-1652	112	25	in	in	ADP
cana-1652	112	26	𝑉	𝑉	PROPN
cana-1652	112	27	belongs	belong	VERB
cana-1652	112	28	to	to	ADP
cana-1652	112	29	exactly	exactly	ADV
cana-1652	112	30	one	one	NUM
cana-1652	112	31	subtree	subtree	NOUN
cana-1652	112	32	.	.	PUNCT
cana-1652	113	1	since	since	SCONJ
cana-1652	113	2	each	each	DET
cana-1652	113	3	subtree	subtree	NOUN
cana-1652	113	4	contains	contain	VERB
cana-1652	113	5	at	at	ADV
cana-1652	113	6	least	least	ADV
cana-1652	113	7	one	one	NUM
cana-1652	113	8	vertex	vertex	NOUN
cana-1652	113	9	from	from	ADP
cana-1652	113	10	d	d	PROPN
cana-1652	113	11	,	,	PUNCT
cana-1652	113	12	we	we	PRON
cana-1652	113	13	have	have	VERB
cana-1652	113	14	|𝑉	|𝑉	X
cana-1652	113	15	𝐷|	𝐷|	VERB
cana-1652	113	16	≤	≤	NUM
cana-1652	113	17	𝑛	𝑛	DET
cana-1652	113	18	−	−	PROPN
cana-1652	113	19	𝑘.	𝑘.	NOUN
cana-1652	113	20	also	also	ADV
cana-1652	113	21	,	,	PUNCT
cana-1652	113	22	since	since	SCONJ
cana-1652	113	23	each	each	DET
cana-1652	113	24	subtree	subtree	NOUN
cana-1652	113	25	has	have	VERB
cana-1652	113	26	at	at	ADP
cana-1652	113	27	most	most	ADJ
cana-1652	113	28	𝑚	𝑚	ADP
cana-1652	113	29	edges	edge	NOUN
cana-1652	113	30	and	and	CCONJ
cana-1652	113	31	there	there	PRON
cana-1652	113	32	are	be	VERB
cana-1652	113	33	𝑘	𝑘	DET
cana-1652	113	34	subtrees	subtree	NOUN
cana-1652	113	35	,	,	PUNCT
cana-1652	113	36	we	we	PRON
cana-1652	113	37	have	have	VERB
cana-1652	113	38	𝑚	𝑚	ADP
cana-1652	113	39	⋅	⋅	PROPN
cana-1652	113	40	𝑘	𝑘	DET
cana-1652	113	41	≥	≥	NOUN
cana-1652	113	42	𝑛	𝑛	DET
cana-1652	113	43	−	−	NUM
cana-1652	113	44	1	1	NUM
cana-1652	113	45	(	(	PUNCT
cana-1652	113	46	by	by	ADP
cana-1652	113	47	the	the	DET
cana-1652	113	48	handshake	handshake	ADJ
cana-1652	113	49	lemma	lemma	PROPN
cana-1652	113	50	)	)	PUNCT
cana-1652	113	51	.	.	PUNCT
cana-1652	114	1	therefore	therefore	ADV
cana-1652	114	2	,	,	PUNCT
cana-1652	114	3	𝑚	𝑚	PROPN
cana-1652	114	4	⋅	⋅	PROPN
cana-1652	114	5	𝑘	𝑘	PRON
cana-1652	114	6	≥	≥	NOUN
cana-1652	114	7	𝑛	𝑛	PRON
cana-1652	114	8	−	−	NUM
cana-1652	114	9	1	1	NUM
cana-1652	114	10	𝑚	𝑚	PROPN
cana-1652	114	11	⋅	⋅	PROPN
cana-1652	114	12	|𝐷|	|𝐷|	X
cana-1652	114	13	≥	≥	NOUN
cana-1652	114	14	𝑛	𝑛	DET
cana-1652	114	15	−	−	NUM
cana-1652	114	16	1	1	NUM
cana-1652	114	17	|𝐷|	|𝐷|	NOUN
cana-1652	114	18	≥	≥	NOUN
cana-1652	114	19	⌈	⌈	NOUN
cana-1652	114	20	𝑛−1	𝑛−1	PROPN
cana-1652	114	21	𝑚	𝑚	PROPN
cana-1652	114	22	⌉	⌉	PUNCT
cana-1652	114	23	since	since	SCONJ
cana-1652	114	24	|𝐷|	|𝐷|	NOUN
cana-1652	114	25	is	be	AUX
cana-1652	114	26	an	an	DET
cana-1652	114	27	integer	integer	NOUN
cana-1652	114	28	,	,	PUNCT
cana-1652	114	29	we	we	PRON
cana-1652	114	30	communications	communication	VERB
cana-1652	114	31	on	on	ADP
cana-1652	114	32	applied	apply	VERB
cana-1652	114	33	nonlinear	nonlinear	ADJ
cana-1652	114	34	analysis	analysis	NOUN
cana-1652	114	35	issn	issn	NOUN
cana-1652	114	36	:	:	PUNCT
cana-1652	114	37	1074	1074	NUM
cana-1652	114	38	-	-	PUNCT
cana-1652	114	39	133x	133x	NUM
cana-1652	114	40	vol	vol	NOUN
cana-1652	114	41	32	32	NUM
cana-1652	114	42	no	no	NOUN
cana-1652	114	43	.	.	NOUN
cana-1652	114	44	1	1	NUM
cana-1652	114	45	(	(	PUNCT
cana-1652	114	46	2025	2025	NUM
cana-1652	114	47	)	)	PUNCT
cana-1652	114	48	328	328	NUM
cana-1652	114	49	https://internationalpubls.com	https://internationalpubls.com	X
cana-1652	114	50	have	have	VERB
cana-1652	114	51	|𝐷|	|𝐷|	X
cana-1652	114	52	≥	≥	NOUN
cana-1652	114	53	⌈	⌈	NOUN
cana-1652	114	54	𝑛−1	𝑛−1	PROPN
cana-1652	114	55	𝑚	𝑚	ADV
cana-1652	114	56	⌉.	⌉.	ADV
cana-1652	114	57	therefore	therefore	ADV
cana-1652	114	58	,	,	PUNCT
cana-1652	114	59	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1652	114	60	)	)	PUNCT
cana-1652	115	1	=	=	SYM
cana-1652	115	2	|𝐷|	|𝐷|	NOUN
cana-1652	115	3	≥	≥	NOUN
cana-1652	115	4	⌈	⌈	NOUN
cana-1652	115	5	𝑛−1	𝑛−1	PROPN
cana-1652	115	6	𝑚	𝑚	X
cana-1652	115	7	⌉	⌉	PROPN
cana-1652	115	8	=	=	SYM
cana-1652	115	9	𝑛	𝑛	ADP
cana-1652	115	10	𝑚	𝑚	X
cana-1652	115	11	−	−	NUM
cana-1652	115	12	1	1	NUM
cana-1652	115	13	𝑚	𝑚	NOUN
cana-1652	115	14	+	+	NUM
cana-1652	115	15	1	1	NUM
cana-1652	115	16	≥	≥	NOUN
cana-1652	115	17	𝑛	𝑛	ADP
cana-1652	115	18	𝑚	𝑚	NOUN
cana-1652	115	19	−	−	NUM
cana-1652	115	20	1	1	NUM
cana-1652	115	21	+	+	SYM
cana-1652	115	22	1	1	NUM
cana-1652	115	23	=	=	SYM
cana-1652	115	24	𝑛	𝑛	PRON
cana-1652	115	25	−	−	PROPN
cana-1652	115	26	⌈	⌈	NOUN
cana-1652	115	27	𝑛	𝑛	ADP
cana-1652	115	28	𝑚	𝑚	X
cana-1652	115	29	⌉	⌉	NOUN
cana-1652	115	30	+	+	PROPN
cana-1652	115	31	1	1	X
cana-1652	115	32	.	.	X
cana-1652	116	1	hence	hence	ADV
cana-1652	116	2	,	,	PUNCT
cana-1652	116	3	we	we	PRON
cana-1652	116	4	have	have	AUX
cana-1652	116	5	shown	show	VERB
cana-1652	116	6	that	that	SCONJ
cana-1652	116	7	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	116	8	)	)	PUNCT
cana-1652	116	9	≤	≤	NUM
cana-1652	117	1	𝑛	𝑛	DET
cana-1652	117	2	−	−	PROPN
cana-1652	117	3	⌈	⌈	NOUN
cana-1652	117	4	𝑛	𝑛	ADP
cana-1652	117	5	𝑚	𝑚	X
cana-1652	117	6	⌉	⌉	NOUN
cana-1652	117	7	+	+	NOUN
cana-1652	117	8	1	1	X
cana-1652	117	9	.	.	X
cana-1652	117	10	theorem	theorem	VERB
cana-1652	117	11	2.8	2.8	NUM
cana-1652	117	12	let	let	VERB
cana-1652	117	13	g	g	NOUN
cana-1652	117	14	=	=	SYM
cana-1652	117	15	(	(	PUNCT
cana-1652	117	16	v	v	NOUN
cana-1652	117	17	,	,	PUNCT
cana-1652	117	18	e	e	NOUN
cana-1652	117	19	,	,	PUNCT
cana-1652	117	20	𝜇	𝜇	PRON
cana-1652	117	21	)	)	PUNCT
cana-1652	117	22	be	be	AUX
cana-1652	117	23	a	a	DET
cana-1652	117	24	fuzzy	fuzzy	ADJ
cana-1652	117	25	graph	graph	NOUN
cana-1652	117	26	.	.	PUNCT
cana-1652	118	1	then	then	ADV
cana-1652	118	2	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1652	118	3	)	)	PUNCT
cana-1652	118	4	≤	≤	NUM
cana-1652	118	5	⌊𝑛/2⌋	⌊𝑛/2⌋	NOUN
cana-1652	118	6	,	,	PUNCT
cana-1652	118	7	where	where	SCONJ
cana-1652	118	8	𝑛	𝑛	PRON
cana-1652	118	9	=	=	SYM
cana-1652	118	10	|𝑉|	|𝑉|	NOUN
cana-1652	118	11	.	.	PUNCT
cana-1652	119	1	proof	proof	NOUN
cana-1652	119	2	:	:	PUNCT
cana-1652	119	3	let	let	VERB
cana-1652	119	4	s	s	PRON
cana-1652	119	5	be	be	AUX
cana-1652	119	6	a	a	DET
cana-1652	119	7	dominating	dominating	NOUN
cana-1652	119	8	set	set	NOUN
cana-1652	119	9	of	of	ADP
cana-1652	119	10	g	g	NOUN
cana-1652	119	11	with	with	ADP
cana-1652	119	12	minimum	minimum	ADJ
cana-1652	119	13	cardinality	cardinality	NOUN
cana-1652	119	14	.	.	PUNCT
cana-1652	120	1	we	we	PRON
cana-1652	120	2	will	will	AUX
cana-1652	120	3	show	show	VERB
cana-1652	120	4	that	that	SCONJ
cana-1652	120	5	|𝑆|	|𝑆|	VERB
cana-1652	120	6	≤	≤	NOUN
cana-1652	120	7	⌊𝑛/2⌋.	⌊𝑛/2⌋.	NOUN
cana-1652	120	8	suppose	suppose	VERB
cana-1652	120	9	,	,	PUNCT
cana-1652	120	10	for	for	ADP
cana-1652	120	11	the	the	DET
cana-1652	120	12	sake	sake	NOUN
cana-1652	120	13	of	of	ADP
cana-1652	120	14	contradiction	contradiction	NOUN
cana-1652	120	15	,	,	PUNCT
cana-1652	120	16	that	that	PRON
cana-1652	120	17	|𝑆|	|𝑆|	VERB
cana-1652	120	18	>	>	X
cana-1652	120	19	⌊𝑛/2⌋.	⌊𝑛/2⌋.	NOUN
cana-1652	120	20	then	then	ADV
cana-1652	120	21	,	,	PUNCT
cana-1652	120	22	since	since	SCONJ
cana-1652	120	23	s	s	NOUN
cana-1652	120	24	is	be	AUX
cana-1652	120	25	a	a	DET
cana-1652	120	26	dominating	dominating	NOUN
cana-1652	120	27	set	set	NOUN
cana-1652	120	28	,	,	PUNCT
cana-1652	120	29	every	every	DET
cana-1652	120	30	vertex	vertex	NOUN
cana-1652	120	31	in	in	ADP
cana-1652	120	32	𝑉	𝑉	PROPN
cana-1652	120	33	−	−	PROPN
cana-1652	120	34	𝑆	𝑆	PROPN
cana-1652	120	35	must	must	AUX
cana-1652	120	36	have	have	VERB
cana-1652	120	37	at	at	ADV
cana-1652	120	38	least	least	ADV
cana-1652	120	39	one	one	NUM
cana-1652	120	40	neighbor	neighbor	NOUN
cana-1652	120	41	in	in	ADP
cana-1652	120	42	s.	s.	PROPN
cana-1652	120	43	thus	thus	ADV
cana-1652	120	44	,	,	PUNCT
cana-1652	120	45	we	we	PRON
cana-1652	120	46	have	have	VERB
cana-1652	120	47	:	:	PUNCT
cana-1652	120	48	|𝑉	|𝑉	X
cana-1652	120	49	−	−	PROPN
cana-1652	120	50	𝑆|	𝑆|	PROPN
cana-1652	120	51	≤	≤	NOUN
cana-1652	120	52	𝑛	𝑛	DET
cana-1652	120	53	−	−	PROPN
cana-1652	120	54	|𝑆|	|𝑆|	VERB
cana-1652	120	55	since	since	SCONJ
cana-1652	120	56	each	each	DET
cana-1652	120	57	vertex	vertex	NOUN
cana-1652	120	58	in	in	ADP
cana-1652	120	59	s	s	PRON
cana-1652	120	60	can	can	AUX
cana-1652	120	61	dominate	dominate	VERB
cana-1652	120	62	at	at	ADP
cana-1652	120	63	most	most	ADV
cana-1652	120	64	two	two	NUM
cana-1652	120	65	vertices	vertex	NOUN
cana-1652	120	66	in	in	ADP
cana-1652	120	67	𝑉	𝑉	PROPN
cana-1652	120	68	−	−	PROPN
cana-1652	120	69	𝑆	𝑆	PROPN
cana-1652	120	70	(	(	PUNCT
cana-1652	120	71	since	since	SCONJ
cana-1652	120	72	g	g	PROPN
cana-1652	120	73	is	be	AUX
cana-1652	120	74	undirected	undirected	ADJ
cana-1652	120	75	)	)	PUNCT
cana-1652	120	76	,	,	PUNCT
cana-1652	120	77	we	we	PRON
cana-1652	120	78	have	have	VERB
cana-1652	120	79	:	:	PUNCT
cana-1652	120	80	𝑚(𝑆	𝑚(𝑆	ADV
cana-1652	120	81	,	,	PUNCT
cana-1652	120	82	𝑉	𝑉	PROPN
cana-1652	120	83	−	−	PROPN
cana-1652	120	84	𝑆	𝑆	PROPN
cana-1652	120	85	)	)	PUNCT
cana-1652	120	86	≤	≤	NOUN
cana-1652	121	1	2|𝑆|	2|𝑆|	NUM
cana-1652	121	2	,	,	PUNCT
cana-1652	121	3	where	where	SCONJ
cana-1652	121	4	𝑚(𝑆	𝑚(𝑆	NOUN
cana-1652	121	5	,	,	PUNCT
cana-1652	121	6	𝑉	𝑉	PROPN
cana-1652	121	7	−	−	PROPN
cana-1652	121	8	𝑆	𝑆	PROPN
cana-1652	121	9	)	)	PUNCT
cana-1652	121	10	denotes	denote	VERB
cana-1652	121	11	the	the	DET
cana-1652	121	12	number	number	NOUN
cana-1652	121	13	of	of	ADP
cana-1652	121	14	edges	edge	NOUN
cana-1652	121	15	between	between	ADP
cana-1652	121	16	s	s	PRON
cana-1652	121	17	and	and	CCONJ
cana-1652	121	18	𝑉	𝑉	PROPN
cana-1652	121	19	−	−	PROPN
cana-1652	121	20	𝑆.	𝑆.	PROPN
cana-1652	121	21	now	now	ADV
cana-1652	121	22	,	,	PUNCT
cana-1652	121	23	using	use	VERB
cana-1652	121	24	the	the	DET
cana-1652	121	25	fact	fact	NOUN
cana-1652	121	26	that	that	SCONJ
cana-1652	121	27	g	g	PROPN
cana-1652	121	28	is	be	AUX
cana-1652	121	29	a	a	DET
cana-1652	121	30	fuzzy	fuzzy	ADJ
cana-1652	121	31	graph	graph	NOUN
cana-1652	121	32	,	,	PUNCT
cana-1652	121	33	we	we	PRON
cana-1652	121	34	have	have	AUX
cana-1652	121	35	:	:	PUNCT
cana-1652	121	36	∑𝑣∈𝑉	∑𝑣∈𝑉	PROPN
cana-1652	121	37	𝜇(𝑣	𝜇(𝑣	PROPN
cana-1652	121	38	)	)	PUNCT
cana-1652	121	39	=	=	SYM
cana-1652	121	40	∑(𝑢,𝑣)∈𝐸	∑(𝑢,𝑣)∈𝐸	ADJ
cana-1652	121	41	𝜇(𝑢	𝜇(𝑢	NOUN
cana-1652	121	42	,	,	PUNCT
cana-1652	121	43	𝑣	𝑣	NOUN
cana-1652	121	44	)	)	PUNCT
cana-1652	121	45	since	since	SCONJ
cana-1652	121	46	each	each	DET
cana-1652	121	47	edge	edge	NOUN
cana-1652	121	48	contributes	contribute	VERB
cana-1652	121	49	to	to	ADP
cana-1652	121	50	this	this	DET
cana-1652	121	51	sum	sum	NOUN
cana-1652	121	52	at	at	ADV
cana-1652	121	53	most	most	ADV
cana-1652	121	54	once	once	ADV
cana-1652	121	55	,	,	PUNCT
cana-1652	121	56	we	we	PRON
cana-1652	121	57	have	have	VERB
cana-1652	121	58	:	:	PUNCT
cana-1652	121	59	∑𝑣∈𝑉	∑𝑣∈𝑉	PROPN
cana-1652	121	60	𝜇(𝑣	𝜇(𝑣	PROPN
cana-1652	121	61	)	)	PUNCT
cana-1652	121	62	≤	≤	NUM
cana-1652	121	63	𝑚	𝑚	ADP
cana-1652	121	64	where	where	SCONJ
cana-1652	121	65	m	m	NOUN
cana-1652	121	66	is	be	AUX
cana-1652	121	67	the	the	DET
cana-1652	121	68	number	number	NOUN
cana-1652	121	69	of	of	ADP
cana-1652	121	70	edges	edge	NOUN
cana-1652	121	71	in	in	ADP
cana-1652	121	72	g.	g.	NOUN
cana-1652	121	73	using	use	VERB
cana-1652	121	74	these	these	DET
cana-1652	121	75	inequalities	inequality	NOUN
cana-1652	121	76	and	and	CCONJ
cana-1652	121	77	the	the	DET
cana-1652	121	78	fact	fact	NOUN
cana-1652	121	79	that	that	SCONJ
cana-1652	121	80	s	s	VERB
cana-1652	121	81	is	be	AUX
cana-1652	121	82	a	a	DET
cana-1652	121	83	dominating	dominating	NOUN
cana-1652	121	84	set	set	NOUN
cana-1652	121	85	,	,	PUNCT
cana-1652	121	86	we	we	PRON
cana-1652	121	87	obtain	obtain	VERB
cana-1652	121	88	:	:	PUNCT
cana-1652	121	89	∑𝑣∈𝑉	∑𝑣∈𝑉	PROPN
cana-1652	121	90	𝜇(𝑣	𝜇(𝑣	PROPN
cana-1652	121	91	)	)	PUNCT
cana-1652	121	92	≥	≥	NOUN
cana-1652	121	93	∑𝑣∈𝑆	∑𝑣∈𝑆	NUM
cana-1652	121	94	𝜇(𝑣	𝜇(𝑣	PROPN
cana-1652	121	95	)	)	PUNCT
cana-1652	121	96	≥	≥	NOUN
cana-1652	121	97	1	1	NUM
cana-1652	121	98	combining	combine	VERB
cana-1652	121	99	these	these	DET
cana-1652	121	100	inequalities	inequality	NOUN
cana-1652	121	101	yields	yield	VERB
cana-1652	121	102	:	:	PUNCT
cana-1652	121	103	1	1	NUM
cana-1652	121	104	≤	≤	NUM
cana-1652	121	105	∑𝑣∈𝑆	∑𝑣∈𝑆	NOUN
cana-1652	121	106	𝜇(𝑣	𝜇(𝑣	NOUN
cana-1652	121	107	)	)	PUNCT
cana-1652	121	108	≤	≤	NUM
cana-1652	121	109	|𝑆|	|𝑆|	VERB
cana-1652	121	110	thus	thus	ADV
cana-1652	121	111	,	,	PUNCT
cana-1652	121	112	we	we	PRON
cana-1652	121	113	have	have	AUX
cana-1652	121	114	shown	show	VERB
cana-1652	121	115	that	that	SCONJ
cana-1652	121	116	|𝑆|	|𝑆|	VERB
cana-1652	121	117	>	>	X
cana-1652	121	118	⌊𝑛/2⌋	⌊𝑛/2⌋	NOUN
cana-1652	121	119	implies	imply	VERB
cana-1652	121	120	|𝑉	|𝑉	X
cana-1652	121	121	−	−	PROPN
cana-1652	121	122	𝑆|	𝑆|	PROPN
cana-1652	121	123	<	<	X
cana-1652	121	124	⌊𝑛/2⌋	⌊𝑛/2⌋	NOUN
cana-1652	121	125	,	,	PUNCT
cana-1652	121	126	which	which	PRON
cana-1652	121	127	contradicts	contradict	VERB
cana-1652	121	128	the	the	DET
cana-1652	121	129	fact	fact	NOUN
cana-1652	121	130	that	that	SCONJ
cana-1652	121	131	𝑛	𝑛	PROPN
cana-1652	121	132	=	=	SYM
cana-1652	121	133	|𝑉|	|𝑉|	NOUN
cana-1652	121	134	.	.	PUNCT
cana-1652	122	1	therefore	therefore	ADV
cana-1652	122	2	,	,	PUNCT
cana-1652	122	3	it	it	PRON
cana-1652	122	4	must	must	AUX
cana-1652	122	5	be	be	AUX
cana-1652	122	6	the	the	DET
cana-1652	122	7	case	case	NOUN
cana-1652	122	8	that	that	PRON
cana-1652	122	9	|𝑆|	|𝑆|	VERB
cana-1652	122	10	≤	≤	ADJ
cana-1652	122	11	⌊𝑛/2⌋	⌊𝑛/2⌋	NOUN
cana-1652	122	12	,	,	PUNCT
cana-1652	122	13	as	as	SCONJ
cana-1652	122	14	desired	desire	VERB
cana-1652	122	15	.	.	PUNCT
cana-1652	123	1	theorem	theorem	VERB
cana-1652	123	2	2.9	2.9	NUM
cana-1652	123	3	let	let	VERB
cana-1652	123	4	g	g	NOUN
cana-1652	123	5	=	=	SYM
cana-1652	123	6	(	(	PUNCT
cana-1652	123	7	v	v	NOUN
cana-1652	123	8	,	,	PUNCT
cana-1652	123	9	e	e	NOUN
cana-1652	123	10	,	,	PUNCT
cana-1652	123	11	𝜇	𝜇	PRON
cana-1652	123	12	)	)	PUNCT
cana-1652	123	13	be	be	AUX
cana-1652	123	14	a	a	DET
cana-1652	123	15	fuzzy	fuzzy	ADJ
cana-1652	123	16	graph	graph	NOUN
cana-1652	123	17	with	with	ADP
cana-1652	123	18	n	n	ADP
cana-1652	123	19	vertices	vertex	NOUN
cana-1652	123	20	and	and	CCONJ
cana-1652	123	21	m	m	PRON
cana-1652	123	22	edges	edge	NOUN
cana-1652	123	23	.	.	PUNCT
cana-1652	124	1	if	if	SCONJ
cana-1652	124	2	g	g	PROPN
cana-1652	124	3	is	be	AUX
cana-1652	124	4	connected	connect	VERB
cana-1652	124	5	and	and	CCONJ
cana-1652	124	6	m	m	PRON
cana-1652	124	7	≥	≥	NOUN
cana-1652	124	8	2	2	NUM
cana-1652	124	9	,	,	PUNCT
cana-1652	124	10	then	then	ADV
cana-1652	124	11	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1652	124	12	)	)	PUNCT
cana-1652	124	13	≤	≤	PUNCT
cana-1652	124	14	⌊	⌊	ADP
cana-1652	124	15	𝑛−1	𝑛−1	NUM
cana-1652	124	16	𝑚	𝑚	ADP
cana-1652	124	17	⌋	⌋	NOUN
cana-1652	124	18	+	+	CCONJ
cana-1652	124	19	1	1	X
cana-1652	124	20	.	.	X
cana-1652	124	21	proof	proof	NOUN
cana-1652	124	22	:	:	PUNCT
cana-1652	124	23	let	let	VERB
cana-1652	124	24	g	g	PROPN
cana-1652	124	25	=	=	SYM
cana-1652	124	26	(	(	PUNCT
cana-1652	124	27	v	v	NOUN
cana-1652	124	28	,	,	PUNCT
cana-1652	124	29	e	e	NOUN
cana-1652	124	30	,	,	PUNCT
cana-1652	124	31	𝜇	𝜇	PRON
cana-1652	124	32	)	)	PUNCT
cana-1652	124	33	be	be	VERB
cana-1652	124	34	a	a	DET
cana-1652	124	35	connected	connected	ADJ
cana-1652	124	36	fuzzy	fuzzy	ADJ
cana-1652	124	37	graph	graph	NOUN
cana-1652	124	38	with	with	ADP
cana-1652	124	39	𝑛	𝑛	PROPN
cana-1652	124	40	vertices	vertex	NOUN
cana-1652	124	41	and	and	CCONJ
cana-1652	124	42	𝑚	𝑚	ADP
cana-1652	124	43	edges	edge	NOUN
cana-1652	124	44	.	.	PUNCT
cana-1652	125	1	we	we	PRON
cana-1652	125	2	will	will	AUX
cana-1652	125	3	show	show	VERB
cana-1652	125	4	that	that	SCONJ
cana-1652	125	5	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	125	6	)	)	PUNCT
cana-1652	125	7	≤	≤	NUM
cana-1652	125	8	⌊	⌊	ADP
cana-1652	125	9	𝑛−1	𝑛−1	NUM
cana-1652	125	10	𝑚	𝑚	ADP
cana-1652	125	11	⌋	⌋	NOUN
cana-1652	126	1	+	+	CCONJ
cana-1652	126	2	1	1	X
cana-1652	126	3	.	.	PUNCT
cana-1652	126	4	let	let	VERB
cana-1652	126	5	𝑆	𝑆	PROPN
cana-1652	126	6	be	be	AUX
cana-1652	126	7	a	a	DET
cana-1652	126	8	dominating	dominating	NOUN
cana-1652	126	9	set	set	NOUN
cana-1652	126	10	of	of	ADP
cana-1652	126	11	𝐺	𝐺	PROPN
cana-1652	126	12	with	with	ADP
cana-1652	126	13	minimum	minimum	ADJ
cana-1652	126	14	cardinality	cardinality	NOUN
cana-1652	126	15	.	.	PUNCT
cana-1652	127	1	we	we	PRON
cana-1652	127	2	will	will	AUX
cana-1652	127	3	show	show	VERB
cana-1652	127	4	that	that	SCONJ
cana-1652	127	5	|𝑆|	|𝑆|	VERB
cana-1652	127	6	≤	≤	NUM
cana-1652	127	7	⌊	⌊	ADP
cana-1652	127	8	𝑛−1	𝑛−1	NUM
cana-1652	127	9	𝑚	𝑚	ADP
cana-1652	127	10	⌋	⌋	NOUN
cana-1652	127	11	+	+	CCONJ
cana-1652	128	1	1	1	X
cana-1652	128	2	.	.	PUNCT
cana-1652	128	3	since	since	SCONJ
cana-1652	128	4	𝐺	𝐺	PROPN
cana-1652	128	5	is	be	AUX
cana-1652	128	6	connected	connect	VERB
cana-1652	128	7	,	,	PUNCT
cana-1652	128	8	there	there	PRON
cana-1652	128	9	exists	exist	VERB
cana-1652	128	10	a	a	DET
cana-1652	128	11	spanning	span	VERB
cana-1652	128	12	tree	tree	NOUN
cana-1652	128	13	𝑇	𝑇	PROPN
cana-1652	128	14	of	of	ADP
cana-1652	128	15	𝐺.	𝐺.	NOUN
cana-1652	128	16	let	let	VERB
cana-1652	128	17	𝑣	𝑣	PART
cana-1652	128	18	be	be	AUX
cana-1652	128	19	any	any	DET
cana-1652	128	20	vertex	vertex	NOUN
cana-1652	128	21	in	in	ADP
cana-1652	128	22	𝑉.	𝑉.	PROPN
cana-1652	128	23	then	then	ADV
cana-1652	128	24	,	,	PUNCT
cana-1652	128	25	the	the	DET
cana-1652	128	26	distance	distance	NOUN
cana-1652	128	27	from	from	ADP
cana-1652	128	28	𝑣	𝑣	PRON
cana-1652	128	29	to	to	ADP
cana-1652	128	30	any	any	DET
cana-1652	128	31	other	other	ADJ
cana-1652	128	32	vertex	vertex	NOUN
cana-1652	128	33	in	in	ADP
cana-1652	128	34	𝑉	𝑉	PROPN
cana-1652	128	35	is	be	AUX
cana-1652	128	36	at	at	ADP
cana-1652	128	37	most	most	ADJ
cana-1652	128	38	𝑛	𝑛	DET
cana-1652	128	39	−	−	PROPN
cana-1652	128	40	1	1	NUM
cana-1652	128	41	(	(	PUNCT
cana-1652	128	42	since	since	SCONJ
cana-1652	128	43	𝐺	𝐺	PROPN
cana-1652	128	44	is	be	AUX
cana-1652	128	45	connected	connect	VERB
cana-1652	128	46	)	)	PUNCT
cana-1652	128	47	.	.	PUNCT
cana-1652	129	1	moreover	moreover	ADV
cana-1652	129	2	,	,	PUNCT
cana-1652	129	3	since	since	SCONJ
cana-1652	129	4	𝑇	𝑇	PROPN
cana-1652	129	5	is	be	AUX
cana-1652	129	6	a	a	DET
cana-1652	129	7	tree	tree	NOUN
cana-1652	129	8	,	,	PUNCT
cana-1652	129	9	there	there	PRON
cana-1652	129	10	exists	exist	VERB
cana-1652	129	11	a	a	DET
cana-1652	129	12	unique	unique	ADJ
cana-1652	129	13	path	path	NOUN
cana-1652	129	14	between	between	ADP
cana-1652	129	15	𝑣	𝑣	PROPN
cana-1652	129	16	and	and	CCONJ
cana-1652	129	17	any	any	DET
cana-1652	129	18	other	other	ADJ
cana-1652	129	19	vertex	vertex	NOUN
cana-1652	129	20	in	in	ADP
cana-1652	129	21	𝑉.	𝑉.	PROPN
cana-1652	129	22	for	for	ADP
cana-1652	129	23	each	each	DET
cana-1652	129	24	edge	edge	NOUN
cana-1652	129	25	𝑒	𝑒	VERB
cana-1652	129	26	=	=	PUNCT
cana-1652	129	27	(	(	PUNCT
cana-1652	129	28	𝑢	𝑢	X
cana-1652	129	29	,	,	PUNCT
cana-1652	129	30	𝑣	𝑣	NOUN
cana-1652	129	31	)	)	PUNCT
cana-1652	129	32	in	in	ADP
cana-1652	129	33	𝐸	𝐸	PROPN
cana-1652	129	34	−	−	PROPN
cana-1652	129	35	𝑇	𝑇	PROPN
cana-1652	129	36	,	,	PUNCT
cana-1652	129	37	let	let	VERB
cana-1652	129	38	𝑃(𝑒	𝑃(𝑒	PRON
cana-1652	129	39	)	)	PUNCT
cana-1652	129	40	denote	denote	VERB
cana-1652	129	41	the	the	DET
cana-1652	129	42	unique	unique	ADJ
cana-1652	129	43	path	path	NOUN
cana-1652	129	44	in	in	ADP
cana-1652	129	45	𝑇	𝑇	PROPN
cana-1652	129	46	between	between	ADP
cana-1652	129	47	𝑢	𝑢	NOUN
cana-1652	129	48	and	and	CCONJ
cana-1652	129	49	𝑣.	𝑣.	PROPN
cana-1652	129	50	let	let	VERB
cana-1652	129	51	𝑆′	𝑆′	PROPN
cana-1652	129	52	be	be	AUX
cana-1652	129	53	the	the	DET
cana-1652	129	54	set	set	NOUN
cana-1652	129	55	of	of	ADP
cana-1652	129	56	vertices	vertex	NOUN
cana-1652	129	57	that	that	PRON
cana-1652	129	58	are	be	AUX
cana-1652	129	59	either	either	CCONJ
cana-1652	129	60	in	in	ADP
cana-1652	129	61	𝑇	𝑇	PROPN
cana-1652	129	62	or	or	CCONJ
cana-1652	129	63	are	be	AUX
cana-1652	129	64	endpoints	endpoint	NOUN
cana-1652	129	65	of	of	ADP
cana-1652	129	66	edges	edge	NOUN
cana-1652	129	67	in	in	ADP
cana-1652	129	68	𝐸	𝐸	PROPN
cana-1652	129	69	−	−	PROPN
cana-1652	129	70	𝑇	𝑇	PROPN
cana-1652	129	71	such	such	ADJ
cana-1652	129	72	that	that	SCONJ
cana-1652	129	73	each	each	DET
cana-1652	129	74	edge	edge	NOUN
cana-1652	129	75	𝑒	𝑒	VERB
cana-1652	129	76	=	=	PUNCT
cana-1652	129	77	(	(	PUNCT
cana-1652	129	78	𝑢	𝑢	X
cana-1652	129	79	,	,	PUNCT
cana-1652	129	80	𝑣	𝑣	NOUN
cana-1652	129	81	)	)	PUNCT
cana-1652	129	82	in	in	ADP
cana-1652	129	83	𝐸	𝐸	PROPN
cana-1652	129	84	−	−	PROPN
cana-1652	129	85	𝑇	𝑇	PROPN
cana-1652	129	86	has	have	AUX
cana-1652	129	87	at	at	ADV
cana-1652	129	88	least	least	ADV
cana-1652	129	89	one	one	NUM
cana-1652	129	90	endpoint	endpoint	NOUN
cana-1652	129	91	in	in	ADP
cana-1652	129	92	𝑆′.	𝑆′.	PROPN
cana-1652	129	93	note	note	NOUN
cana-1652	129	94	that	that	SCONJ
cana-1652	129	95	|𝑆′|	|𝑆′|	NOUN
cana-1652	129	96	≤	≤	ADJ
cana-1652	129	97	2𝑚	2𝑚	NOUN
cana-1652	129	98	since	since	SCONJ
cana-1652	129	99	each	each	DET
cana-1652	129	100	edge	edge	NOUN
cana-1652	129	101	contributes	contribute	VERB
cana-1652	129	102	at	at	ADP
cana-1652	129	103	most	most	ADV
cana-1652	129	104	two	two	NUM
cana-1652	129	105	endpoints	endpoint	NOUN
cana-1652	129	106	to	to	ADP
cana-1652	129	107	𝑆′.	𝑆′.	VERB
cana-1652	129	108	we	we	PRON
cana-1652	129	109	claim	claim	VERB
cana-1652	129	110	that	that	SCONJ
cana-1652	129	111	𝑆′	𝑆′	PROPN
cana-1652	129	112	is	be	AUX
cana-1652	129	113	a	a	DET
cana-1652	129	114	dominating	dominating	NOUN
cana-1652	129	115	set	set	NOUN
cana-1652	129	116	of	of	ADP
cana-1652	129	117	𝐺.	𝐺.	NOUN
cana-1652	129	118	to	to	PART
cana-1652	129	119	see	see	VERB
cana-1652	129	120	this	this	PRON
cana-1652	129	121	,	,	PUNCT
cana-1652	129	122	let	let	VERB
cana-1652	129	123	𝑢	𝑢	PRON
cana-1652	129	124	be	be	AUX
cana-1652	129	125	any	any	DET
cana-1652	129	126	vertex	vertex	NOUN
cana-1652	129	127	not	not	PART
cana-1652	129	128	in	in	ADP
cana-1652	129	129	𝑆′.	𝑆′.	NOUN
cana-1652	129	130	then	then	ADV
cana-1652	129	131	,	,	PUNCT
cana-1652	129	132	either	either	CCONJ
cana-1652	129	133	𝑢	𝑢	PRON
cana-1652	129	134	is	be	AUX
cana-1652	129	135	in	in	ADP
cana-1652	129	136	𝑇	𝑇	PROPN
cana-1652	129	137	or	or	CCONJ
cana-1652	129	138	there	there	ADV
cana-1652	129	139	exists	exist	VERB
cana-1652	129	140	an	an	DET
cana-1652	129	141	edge	edge	NOUN
cana-1652	129	142	𝑒	𝑒	ADP
cana-1652	129	143	=	=	PUNCT
cana-1652	129	144	(	(	PUNCT
cana-1652	129	145	𝑢	𝑢	X
cana-1652	129	146	,	,	PUNCT
cana-1652	129	147	𝑣	𝑣	NOUN
cana-1652	129	148	)	)	PUNCT
cana-1652	129	149	in	in	ADP
cana-1652	129	150	𝐸	𝐸	PROPN
cana-1652	129	151	−	−	PROPN
cana-1652	129	152	𝑇	𝑇	PROPN
cana-1652	129	153	such	such	ADJ
cana-1652	129	154	that	that	SCONJ
cana-1652	129	155	neither	neither	CCONJ
cana-1652	129	156	𝑢	𝑢	NOUN
cana-1652	129	157	nor	nor	CCONJ
cana-1652	129	158	𝑣	𝑣	NOUN
cana-1652	129	159	is	be	AUX
cana-1652	129	160	in	in	ADP
cana-1652	129	161	𝑆′.	𝑆′.	NOUN
cana-1652	129	162	in	in	ADP
cana-1652	129	163	the	the	DET
cana-1652	129	164	former	former	ADJ
cana-1652	129	165	case	case	NOUN
cana-1652	129	166	,	,	PUNCT
cana-1652	129	167	since	since	SCONJ
cana-1652	129	168	𝑇	𝑇	PROPN
cana-1652	129	169	is	be	AUX
cana-1652	129	170	a	a	DET
cana-1652	129	171	tree	tree	NOUN
cana-1652	129	172	and	and	CCONJ
cana-1652	129	173	𝑣	𝑣	DET
cana-1652	129	174	∈	∈	PROPN
cana-1652	129	175	𝑆′	𝑆′	PROPN
cana-1652	129	176	,	,	PUNCT
cana-1652	129	177	there	there	PRON
cana-1652	129	178	exists	exist	VERB
cana-1652	129	179	a	a	DET
cana-1652	129	180	path	path	NOUN
cana-1652	129	181	from	from	ADP
cana-1652	129	182	𝑣	𝑣	PRON
cana-1652	129	183	to	to	ADP
cana-1652	129	184	𝑢	𝑢	PRON
cana-1652	129	185	that	that	PRON
cana-1652	129	186	does	do	AUX
cana-1652	129	187	not	not	PART
cana-1652	129	188	pass	pass	VERB
cana-1652	129	189	through	through	ADP
cana-1652	129	190	any	any	DET
cana-1652	129	191	other	other	ADJ
cana-1652	129	192	vertex	vertex	NOUN
cana-1652	129	193	in	in	ADP
cana-1652	129	194	𝑉	𝑉	PROPN
cana-1652	129	195	−	−	PROPN
cana-1652	129	196	𝑆′.	𝑆′.	NOUN
cana-1652	129	197	in	in	ADP
cana-1652	129	198	the	the	DET
cana-1652	129	199	latter	latter	ADJ
cana-1652	129	200	case	case	NOUN
cana-1652	129	201	,	,	PUNCT
cana-1652	129	202	since	since	SCONJ
cana-1652	129	203	𝑃(𝑒	𝑃(𝑒	NUM
cana-1652	129	204	)	)	PUNCT
cana-1652	129	205	does	do	AUX
cana-1652	129	206	not	not	PART
cana-1652	129	207	contain	contain	VERB
cana-1652	129	208	any	any	DET
cana-1652	129	209	vertex	vertex	NOUN
cana-1652	129	210	in	in	ADP
cana-1652	129	211	𝑆′	𝑆′	PROPN
cana-1652	129	212	,	,	PUNCT
cana-1652	129	213	we	we	PRON
cana-1652	129	214	have	have	VERB
cana-1652	129	215	:	:	PUNCT
cana-1652	129	216	𝜇(𝑢	𝜇(𝑢	NUM
cana-1652	129	217	,	,	PUNCT
cana-1652	129	218	𝑣	𝑣	NOUN
cana-1652	129	219	)	)	PUNCT
cana-1652	129	220	≤	≤	NUM
cana-1652	129	221	∏𝑒′∈𝑃(𝑒	∏𝑒′∈𝑃(𝑒	PROPN
cana-1652	129	222	)	)	PUNCT
cana-1652	129	223	(	(	PUNCT
cana-1652	129	224	1	1	NUM
cana-1652	129	225	−	−	PROPN
cana-1652	129	226	𝜇(𝑒′	𝜇(𝑒′	PROPN
cana-1652	129	227	)	)	PUNCT
cana-1652	129	228	)	)	PUNCT
cana-1652	129	229	since	since	SCONJ
cana-1652	129	230	each	each	DET
cana-1652	129	231	edge	edge	NOUN
cana-1652	129	232	in	in	ADP
cana-1652	129	233	𝑃(𝑒	𝑃(𝑒	PROPN
cana-1652	129	234	)	)	PUNCT
cana-1652	129	235	is	be	AUX
cana-1652	129	236	in	in	ADP
cana-1652	129	237	𝑇	𝑇	PROPN
cana-1652	129	238	,	,	PUNCT
cana-1652	129	239	we	we	PRON
cana-1652	129	240	have	have	VERB
cana-1652	129	241	:	:	PUNCT
cana-1652	129	242	∏𝑒′∈𝑃(𝑒	∏𝑒′∈𝑃(𝑒	PROPN
cana-1652	129	243	)	)	PUNCT
cana-1652	129	244	(	(	PUNCT
cana-1652	129	245	1	1	NUM
cana-1652	129	246	−	−	PROPN
cana-1652	129	247	𝜇(𝑒′	𝜇(𝑒′	PROPN
cana-1652	129	248	)	)	PUNCT
cana-1652	129	249	)	)	PUNCT
cana-1652	129	250	≤	≤	NUM
cana-1652	129	251	∏𝑒′∈𝑃(𝑒	∏𝑒′∈𝑃(𝑒	PROPN
cana-1652	129	252	)	)	PUNCT
cana-1652	129	253	(	(	PUNCT
cana-1652	129	254	1	1	NUM
cana-1652	129	255	−	−	NUM
cana-1652	129	256	1	1	NUM
cana-1652	129	257	𝑚	𝑚	NOUN
cana-1652	129	258	)	)	PUNCT
cana-1652	129	259	=	=	SYM
cana-1652	130	1	(	(	PUNCT
cana-1652	130	2	1	1	NUM
cana-1652	130	3	−	−	NUM
cana-1652	130	4	1	1	NUM
cana-1652	130	5	𝑚	𝑚	NOUN
cana-1652	130	6	)	)	PUNCT
cana-1652	130	7	𝑑(𝑢,𝑣	𝑑(𝑢,𝑣	NUM
cana-1652	130	8	)	)	PUNCT
cana-1652	130	9	where	where	SCONJ
cana-1652	130	10	𝑑(𝑢	𝑑(𝑢	NOUN
cana-1652	130	11	,	,	PUNCT
cana-1652	130	12	𝑣	𝑣	NOUN
cana-1652	130	13	)	)	PUNCT
cana-1652	130	14	denotes	denote	VERB
cana-1652	130	15	the	the	DET
cana-1652	130	16	distance	distance	NOUN
cana-1652	130	17	between	between	ADP
cana-1652	130	18	𝑢	𝑢	NOUN
cana-1652	130	19	and	and	CCONJ
cana-1652	130	20	𝑣	𝑣	PROPN
cana-1652	130	21	in	in	ADP
cana-1652	130	22	𝑇.	𝑇.	PROPN
cana-1652	130	23	since	since	SCONJ
cana-1652	130	24	𝐺	𝐺	PROPN
cana-1652	130	25	is	be	AUX
cana-1652	130	26	connected	connect	VERB
cana-1652	130	27	,	,	PUNCT
cana-1652	130	28	we	we	PRON
cana-1652	130	29	have	have	VERB
cana-1652	130	30	𝑑(𝑢	𝑑(𝑢	NOUN
cana-1652	130	31	,	,	PUNCT
cana-1652	130	32	𝑣	𝑣	NOUN
cana-1652	130	33	)	)	PUNCT
cana-1652	130	34	≤	≤	NOUN
cana-1652	131	1	𝑛	𝑛	DET
cana-1652	131	2	−	−	NOUN
cana-1652	131	3	1	1	NUM
cana-1652	131	4	.	.	PUNCT
cana-1652	132	1	thus	thus	ADV
cana-1652	132	2	,	,	PUNCT
cana-1652	132	3	we	we	PRON
cana-1652	132	4	obtain	obtain	VERB
cana-1652	132	5	:	:	PUNCT
cana-1652	132	6	𝜇(𝑢	𝜇(𝑢	NUM
cana-1652	132	7	,	,	PUNCT
cana-1652	132	8	𝑣	𝑣	NOUN
cana-1652	132	9	)	)	PUNCT
cana-1652	132	10	≤	≤	NOUN
cana-1652	132	11	(	(	PUNCT
cana-1652	132	12	1	1	NUM
cana-1652	132	13	−	−	NUM
cana-1652	132	14	1	1	NUM
cana-1652	132	15	𝑚	𝑚	NOUN
cana-1652	132	16	)	)	PUNCT
cana-1652	132	17	𝑛−1	𝑛−1	PROPN
cana-1652	132	18	since	since	SCONJ
cana-1652	132	19	this	this	PRON
cana-1652	132	20	holds	hold	VERB
cana-1652	132	21	for	for	ADP
cana-1652	132	22	any	any	DET
cana-1652	132	23	edge	edge	NOUN
cana-1652	132	24	𝑒	𝑒	ADP
cana-1652	132	25	=	=	PUNCT
cana-1652	132	26	(	(	PUNCT
cana-1652	132	27	𝑢	𝑢	X
cana-1652	132	28	,	,	PUNCT
cana-1652	132	29	𝑣	𝑣	NOUN
cana-1652	132	30	)	)	PUNCT
cana-1652	132	31	in	in	ADP
cana-1652	132	32	𝐸	𝐸	PROPN
cana-1652	132	33	−	−	PROPN
cana-1652	132	34	𝑇	𝑇	PROPN
cana-1652	132	35	,	,	PUNCT
cana-1652	132	36	we	we	PRON
cana-1652	132	37	conclude	conclude	VERB
cana-1652	132	38	that	that	SCONJ
cana-1652	132	39	𝑆′	𝑆′	PROPN
cana-1652	132	40	is	be	AUX
cana-1652	132	41	a	a	DET
cana-1652	132	42	dominating	dominating	NOUN
cana-1652	132	43	set	set	NOUN
cana-1652	132	44	of	of	ADP
cana-1652	132	45	𝐺.	𝐺.	NOUN
cana-1652	132	46	therefore	therefore	ADV
cana-1652	132	47	,	,	PUNCT
cana-1652	132	48	we	we	PRON
cana-1652	132	49	have	have	AUX
cana-1652	132	50	|𝑆|	|𝑆|	VERB
cana-1652	132	51	≤	≤	NUM
cana-1652	132	52	|𝑆′|	|𝑆′|	NOUN
cana-1652	132	53	≤	≤	NOUN
cana-1652	132	54	2𝑚	2𝑚	NOUN
cana-1652	132	55	+	+	CCONJ
cana-1652	132	56	𝑛	𝑛	DET
cana-1652	132	57	−	−	PROPN
cana-1652	132	58	𝑇	𝑇	PROPN
cana-1652	132	59	,	,	PUNCT
cana-1652	132	60	where	where	SCONJ
cana-1652	132	61	𝑛	𝑛	DET
cana-1652	132	62	−	−	PROPN
cana-1652	132	63	𝑇	𝑇	PROPN
cana-1652	132	64	denotes	denote	VERB
cana-1652	132	65	the	the	DET
cana-1652	132	66	number	number	NOUN
cana-1652	132	67	of	of	ADP
cana-1652	132	68	vertices	vertex	NOUN
cana-1652	132	69	in	in	ADP
cana-1652	132	70	𝐺	𝐺	PROPN
cana-1652	132	71	that	that	PRON
cana-1652	132	72	are	be	AUX
cana-1652	132	73	not	not	PART
cana-1652	132	74	in	in	ADP
cana-1652	132	75	𝑇.	𝑇.	PROPN
cana-1652	132	76	since	since	SCONJ
cana-1652	132	77	𝑇	𝑇	PROPN
cana-1652	132	78	has	have	VERB
cana-1652	132	79	𝑛	𝑛	DET
cana-1652	132	80	−	−	NUM
cana-1652	132	81	1	1	NUM
cana-1652	132	82	edges	edge	NOUN
cana-1652	132	83	and	and	CCONJ
cana-1652	132	84	𝑚	𝑚	X
cana-1652	132	85	≥	≥	NUM
cana-1652	132	86	2	2	NUM
cana-1652	132	87	,	,	PUNCT
cana-1652	132	88	we	we	PRON
cana-1652	132	89	have	have	VERB
cana-1652	132	90	𝑛	𝑛	DET
cana-1652	132	91	−	−	PROPN
cana-1652	132	92	𝑇	𝑇	PROPN
cana-1652	132	93	≤	≤	NOUN
cana-1652	132	94	𝑚	𝑚	ADP
cana-1652	132	95	−	−	PROPN
cana-1652	132	96	1	1	NUM
cana-1652	132	97	.	.	PUNCT
cana-1652	133	1	thus	thus	ADV
cana-1652	133	2	,	,	PUNCT
cana-1652	133	3	we	we	PRON
cana-1652	133	4	obtain	obtain	VERB
cana-1652	133	5	:	:	PUNCT
cana-1652	133	6	|𝑆|	|𝑆|	VERB
cana-1652	133	7	≤	≤	ADJ
cana-1652	133	8	2𝑚	2𝑚	NOUN
cana-1652	133	9	+	+	CCONJ
cana-1652	133	10	𝑚	𝑚	ADP
cana-1652	133	11	−	−	NUM
cana-1652	133	12	1	1	NUM
cana-1652	133	13	=	=	SYM
cana-1652	133	14	3𝑚	3𝑚	NUM
cana-1652	133	15	−	−	NOUN
cana-1652	133	16	1	1	NUM
cana-1652	133	17	on	on	ADP
cana-1652	133	18	the	the	DET
cana-1652	133	19	other	other	ADJ
cana-1652	133	20	hand	hand	NOUN
cana-1652	133	21	,	,	PUNCT
cana-1652	133	22	since	since	SCONJ
cana-1652	133	23	𝑆	𝑆	PROPN
cana-1652	133	24	is	be	AUX
cana-1652	133	25	a	a	DET
cana-1652	133	26	dominating	dominating	NOUN
cana-1652	133	27	set	set	NOUN
cana-1652	133	28	of	of	ADP
cana-1652	133	29	𝐺	𝐺	PROPN
cana-1652	133	30	,	,	PUNCT
cana-1652	133	31	each	each	DET
cana-1652	133	32	vertex	vertex	NOUN
cana-1652	133	33	in	in	ADP
cana-1652	133	34	𝑉	𝑉	PROPN
cana-1652	133	35	−	−	PROPN
cana-1652	133	36	𝑆	𝑆	PROPN
cana-1652	133	37	is	be	AUX
cana-1652	133	38	adjacent	adjacent	ADJ
cana-1652	133	39	to	to	ADP
cana-1652	133	40	at	at	ADV
cana-1652	133	41	least	least	ADV
cana-1652	133	42	one	one	NUM
cana-1652	133	43	vertex	vertex	NOUN
cana-1652	133	44	in	in	ADP
cana-1652	133	45	𝑆.	𝑆.	PROPN
cana-1652	133	46	thus	thus	ADV
cana-1652	133	47	,	,	PUNCT
cana-1652	133	48	we	we	PRON
cana-1652	133	49	have	have	VERB
cana-1652	133	50	:	:	PUNCT
cana-1652	133	51	𝑛	𝑛	DET
cana-1652	133	52	−	−	PROPN
cana-1652	133	53	|𝑆|	|𝑆|	VERB
cana-1652	133	54	≤	≤	PUNCT
cana-1652	133	55	𝑚	𝑚	ADP
cana-1652	133	56	combining	combine	VERB
cana-1652	133	57	this	this	PRON
cana-1652	133	58	with	with	ADP
cana-1652	133	59	the	the	DET
cana-1652	133	60	previous	previous	ADJ
cana-1652	133	61	inequality	inequality	NOUN
cana-1652	133	62	,	,	PUNCT
cana-1652	133	63	we	we	PRON
cana-1652	133	64	obtain	obtain	VERB
cana-1652	133	65	:	:	PUNCT
cana-1652	133	66	|𝑆|	|𝑆|	VERB
cana-1652	133	67	≥	≥	NOUN
cana-1652	134	1	𝑛	𝑛	ADP
cana-1652	134	2	−	−	NOUN
cana-1652	134	3	𝑚	𝑚	X
cana-1652	134	4	therefore	therefore	ADV
cana-1652	134	5	,	,	PUNCT
cana-1652	134	6	we	we	PRON
cana-1652	134	7	have	have	VERB
cana-1652	134	8	:	:	PUNCT
cana-1652	134	9	𝑛	𝑛	DET
cana-1652	134	10	−	−	PROPN
cana-1652	134	11	𝑚	𝑚	PROPN
cana-1652	134	12	≤	≤	NUM
cana-1652	134	13	|𝑆|	|𝑆|	VERB
cana-1652	134	14	≤	≤	ADJ
cana-1652	134	15	3𝑚	3𝑚	NOUN
cana-1652	134	16	−	−	NOUN
cana-1652	134	17	1	1	NUM
cana-1652	134	18	dividing	divide	VERB
cana-1652	134	19	both	both	DET
cana-1652	134	20	sides	side	NOUN
cana-1652	134	21	by	by	ADP
cana-1652	134	22	𝑚	𝑚	X
cana-1652	134	23	and	and	CCONJ
cana-1652	134	24	taking	take	VERB
cana-1652	134	25	the	the	DET
cana-1652	134	26	floor	floor	NOUN
cana-1652	134	27	function	function	NOUN
cana-1652	134	28	yields	yield	NOUN
cana-1652	134	29	:	:	PUNCT
cana-1652	134	30	⌊	⌊	VERB
cana-1652	134	31	𝑛−1	𝑛−1	NUM
cana-1652	134	32	𝑚	𝑚	ADP
cana-1652	134	33	⌋	⌋	NOUN
cana-1652	134	34	+	+	CCONJ
cana-1652	134	35	1	1	NUM
cana-1652	134	36	≥	≥	NOUN
cana-1652	134	37	communications	communication	NOUN
cana-1652	134	38	on	on	ADP
cana-1652	134	39	applied	apply	VERB
cana-1652	134	40	nonlinear	nonlinear	ADJ
cana-1652	134	41	analysis	analysis	NOUN
cana-1652	134	42	issn	issn	NOUN
cana-1652	134	43	:	:	PUNCT
cana-1652	134	44	1074	1074	NUM
cana-1652	134	45	-	-	PUNCT
cana-1652	134	46	133x	133x	NUM
cana-1652	134	47	vol	vol	NOUN
cana-1652	134	48	32	32	NUM
cana-1652	134	49	no	no	NOUN
cana-1652	134	50	.	.	NOUN
cana-1652	134	51	1	1	NUM
cana-1652	134	52	(	(	PUNCT
cana-1652	134	53	2025	2025	NUM
cana-1652	134	54	)	)	PUNCT
cana-1652	134	55	329	329	NUM
cana-1652	134	56	https://internationalpubls.com	https://internationalpubls.com	X
cana-1652	134	57	⌊	⌊	VERB
cana-1652	134	58	𝑛	𝑛	ADP
cana-1652	134	59	𝑚	𝑚	NOUN
cana-1652	134	60	⌋	⌋	NOUN
cana-1652	134	61	since	since	SCONJ
cana-1652	134	62	𝑆	𝑆	PROPN
cana-1652	134	63	is	be	AUX
cana-1652	134	64	a	a	DET
cana-1652	134	65	dominating	dominating	NOUN
cana-1652	134	66	set	set	NOUN
cana-1652	134	67	of	of	ADP
cana-1652	134	68	minimum	minimum	ADJ
cana-1652	134	69	cardinality	cardinality	NOUN
cana-1652	134	70	and	and	CCONJ
cana-1652	134	71	𝛾(𝐺	𝛾(𝐺	NUM
cana-1652	134	72	)	)	PUNCT
cana-1652	135	1	is	be	AUX
cana-1652	135	2	the	the	DET
cana-1652	135	3	size	size	NOUN
cana-1652	135	4	of	of	ADP
cana-1652	135	5	a	a	DET
cana-1652	135	6	smallest	small	ADJ
cana-1652	135	7	dominating	dominating	NOUN
cana-1652	135	8	set	set	NOUN
cana-1652	135	9	,	,	PUNCT
cana-1652	135	10	we	we	PRON
cana-1652	135	11	have	have	VERB
cana-1652	135	12	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	135	13	)	)	PUNCT
cana-1652	136	1	=	=	PUNCT
cana-1652	136	2	|𝑆|	|𝑆|	VERB
cana-1652	136	3	.	.	PUNCT
cana-1652	137	1	therefore	therefore	ADV
cana-1652	137	2	,	,	PUNCT
cana-1652	137	3	we	we	PRON
cana-1652	137	4	obtain	obtain	VERB
cana-1652	137	5	:	:	PUNCT
cana-1652	137	6	𝛾(𝐺	𝛾(𝐺	NUM
cana-1652	137	7	)	)	PUNCT
cana-1652	137	8	≤	≤	NUM
cana-1652	138	1	⌊	⌊	ADP
cana-1652	138	2	𝑛−1	𝑛−1	NUM
cana-1652	138	3	𝑚	𝑚	ADP
cana-1652	138	4	⌋	⌋	NOUN
cana-1652	138	5	+	+	CCONJ
cana-1652	139	1	1	1	NUM
cana-1652	140	1	this	this	PRON
cana-1652	140	2	completes	complete	VERB
cana-1652	140	3	the	the	DET
cana-1652	140	4	proof	proof	NOUN
cana-1652	140	5	of	of	ADP
cana-1652	140	6	theorem	theorem	PROPN
cana-1652	140	7	.	.	PUNCT
cana-1652	140	8	theorem	theorem	VERB
cana-1652	140	9	2.10	2.10	NUM
cana-1652	140	10	let	let	VERB
cana-1652	140	11	𝐺	𝐺	PROPN
cana-1652	140	12	=	=	SYM
cana-1652	140	13	(	(	PUNCT
cana-1652	140	14	𝑉	𝑉	PROPN
cana-1652	140	15	,	,	PUNCT
cana-1652	140	16	𝐸	𝐸	PROPN
cana-1652	140	17	,	,	PUNCT
cana-1652	140	18	𝜇	𝜇	NOUN
cana-1652	140	19	)	)	PUNCT
cana-1652	140	20	be	be	AUX
cana-1652	140	21	a	a	DET
cana-1652	140	22	fuzzy	fuzzy	ADJ
cana-1652	140	23	graph	graph	NOUN
cana-1652	140	24	with	with	ADP
cana-1652	140	25	𝑛	𝑛	PROPN
cana-1652	140	26	vertices	vertex	NOUN
cana-1652	140	27	and	and	CCONJ
cana-1652	140	28	𝑚	𝑚	ADP
cana-1652	140	29	edges	edge	NOUN
cana-1652	140	30	.	.	PUNCT
cana-1652	141	1	if	if	SCONJ
cana-1652	141	2	𝐺	𝐺	PROPN
cana-1652	141	3	is	be	AUX
cana-1652	141	4	connected	connect	VERB
cana-1652	141	5	and	and	CCONJ
cana-1652	141	6	𝑚	𝑚	X
cana-1652	141	7	≥	≥	NUM
cana-1652	141	8	4	4	NUM
cana-1652	141	9	,	,	PUNCT
cana-1652	141	10	then	then	ADV
cana-1652	141	11	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1652	141	12	)	)	PUNCT
cana-1652	141	13	≤	≤	PUNCT
cana-1652	142	1	⌊	⌊	ADP
cana-1652	142	2	𝑛−3	𝑛−3	PROPN
cana-1652	142	3	𝑚−2	𝑚−2	PROPN
cana-1652	142	4	⌋	⌋	NOUN
cana-1652	142	5	+	+	CCONJ
cana-1652	142	6	1	1	X
cana-1652	142	7	.	.	X
cana-1652	142	8	proof	proof	NOUN
cana-1652	142	9	:	:	PUNCT
cana-1652	142	10	let	let	VERB
cana-1652	142	11	g	g	PROPN
cana-1652	142	12	=	=	SYM
cana-1652	142	13	(	(	PUNCT
cana-1652	142	14	v	v	NOUN
cana-1652	142	15	,	,	PUNCT
cana-1652	142	16	e	e	NOUN
cana-1652	142	17	,	,	PUNCT
cana-1652	142	18	𝜇	𝜇	PRON
cana-1652	142	19	)	)	PUNCT
cana-1652	142	20	be	be	AUX
cana-1652	142	21	a	a	DET
cana-1652	142	22	fuzzy	fuzzy	ADJ
cana-1652	142	23	graph	graph	NOUN
cana-1652	142	24	with	with	ADP
cana-1652	142	25	𝑛	𝑛	PROPN
cana-1652	142	26	vertices	vertex	NOUN
cana-1652	142	27	and	and	CCONJ
cana-1652	142	28	𝑚	𝑚	ADP
cana-1652	142	29	edges	edge	NOUN
cana-1652	142	30	.	.	PUNCT
cana-1652	143	1	suppose	suppose	VERB
cana-1652	143	2	that	that	SCONJ
cana-1652	143	3	g	g	PROPN
cana-1652	143	4	is	be	AUX
cana-1652	143	5	connected	connect	VERB
cana-1652	143	6	and	and	CCONJ
cana-1652	143	7	𝑚	𝑚	X
cana-1652	143	8	≥	≥	NUM
cana-1652	143	9	4	4	NUM
cana-1652	143	10	.	.	PUNCT
cana-1652	144	1	let	let	VERB
cana-1652	144	2	𝑇	𝑇	PROPN
cana-1652	144	3	be	be	AUX
cana-1652	144	4	a	a	DET
cana-1652	144	5	spanning	span	VERB
cana-1652	144	6	tree	tree	NOUN
cana-1652	144	7	of	of	ADP
cana-1652	144	8	g.	g.	PROPN
cana-1652	144	9	since	since	SCONJ
cana-1652	144	10	𝑇	𝑇	PROPN
cana-1652	144	11	has	have	VERB
cana-1652	144	12	𝑛	𝑛	DET
cana-1652	144	13	−	−	NUM
cana-1652	144	14	1	1	NUM
cana-1652	144	15	edges	edge	NOUN
cana-1652	144	16	,	,	PUNCT
cana-1652	144	17	there	there	PRON
cana-1652	144	18	are	be	VERB
cana-1652	144	19	at	at	ADP
cana-1652	144	20	least	least	ADJ
cana-1652	144	21	𝑚	𝑚	ADP
cana-1652	144	22	−	−	PROPN
cana-1652	144	23	(	(	PUNCT
cana-1652	144	24	𝑛	𝑛	PROPN
cana-1652	144	25	−	−	NOUN
cana-1652	144	26	1	1	NUM
cana-1652	144	27	)	)	PUNCT
cana-1652	144	28	=	=	PUNCT
cana-1652	145	1	𝑚	𝑚	ADP
cana-1652	145	2	−	−	NUM
cana-1652	145	3	𝑛	𝑛	PRON
cana-1652	145	4	+	+	CCONJ
cana-1652	145	5	1	1	NUM
cana-1652	145	6	edges	edge	NOUN
cana-1652	145	7	in	in	ADP
cana-1652	145	8	𝐺	𝐺	PROPN
cana-1652	145	9	that	that	PRON
cana-1652	145	10	are	be	AUX
cana-1652	145	11	not	not	PART
cana-1652	145	12	in	in	ADP
cana-1652	145	13	𝑇.	𝑇.	PROPN
cana-1652	145	14	let	let	VERB
cana-1652	145	15	𝑆	𝑆	PROPN
cana-1652	145	16	be	be	AUX
cana-1652	145	17	a	a	DET
cana-1652	145	18	set	set	NOUN
cana-1652	145	19	of	of	ADP
cana-1652	145	20	vertices	vertex	NOUN
cana-1652	145	21	obtained	obtain	VERB
cana-1652	145	22	as	as	ADP
cana-1652	145	23	follows	follow	VERB
cana-1652	145	24	:	:	PUNCT
cana-1652	145	25	for	for	SCONJ
cana-1652	145	26	each	each	DET
cana-1652	145	27	edge	edge	NOUN
cana-1652	145	28	𝑒	𝑒	VERB
cana-1652	145	29	in	in	ADP
cana-1652	145	30	𝐺	𝐺	PROPN
cana-1652	145	31	that	that	PRON
cana-1652	145	32	is	be	AUX
cana-1652	145	33	not	not	PART
cana-1652	145	34	in	in	ADP
cana-1652	145	35	𝑇	𝑇	PROPN
cana-1652	145	36	,	,	PUNCT
cana-1652	145	37	choose	choose	VERB
cana-1652	145	38	an	an	DET
cana-1652	145	39	endpoint	endpoint	NOUN
cana-1652	145	40	of	of	ADP
cana-1652	145	41	𝑒	𝑒	PRON
cana-1652	145	42	and	and	CCONJ
cana-1652	145	43	add	add	VERB
cana-1652	145	44	it	it	PRON
cana-1652	145	45	to	to	ADP
cana-1652	145	46	𝑆.	𝑆.	PROPN
cana-1652	145	47	since	since	SCONJ
cana-1652	145	48	each	each	DET
cana-1652	145	49	edge	edge	NOUN
cana-1652	145	50	in	in	ADP
cana-1652	145	51	𝐺	𝐺	PROPN
cana-1652	145	52	has	have	VERB
cana-1652	145	53	at	at	ADV
cana-1652	145	54	least	least	ADV
cana-1652	145	55	one	one	NUM
cana-1652	145	56	endpoint	endpoint	NOUN
cana-1652	145	57	in	in	ADP
cana-1652	145	58	𝑇	𝑇	PROPN
cana-1652	145	59	,	,	PUNCT
cana-1652	145	60	we	we	PRON
cana-1652	145	61	have	have	AUX
cana-1652	145	62	|𝑆|	|𝑆|	VERB
cana-1652	145	63	≥	≥	NOUN
cana-1652	145	64	𝑚	𝑚	ADP
cana-1652	145	65	−	−	NOUN
cana-1652	145	66	𝑛	𝑛	PROPN
cana-1652	146	1	+	+	NOUN
cana-1652	146	2	1	1	X
cana-1652	146	3	.	.	X
cana-1652	146	4	we	we	PRON
cana-1652	146	5	claim	claim	VERB
cana-1652	146	6	that	that	SCONJ
cana-1652	146	7	𝑆	𝑆	PROPN
cana-1652	146	8	is	be	AUX
cana-1652	146	9	a	a	DET
cana-1652	146	10	dominating	dominating	NOUN
cana-1652	146	11	set	set	NOUN
cana-1652	146	12	of	of	ADP
cana-1652	146	13	𝐺.	𝐺.	NOUN
cana-1652	146	14	to	to	PART
cana-1652	146	15	see	see	VERB
cana-1652	146	16	this	this	PRON
cana-1652	146	17	,	,	PUNCT
cana-1652	146	18	let	let	VERB
cana-1652	146	19	𝑣	𝑣	PART
cana-1652	146	20	be	be	AUX
cana-1652	146	21	any	any	DET
cana-1652	146	22	vertex	vertex	NOUN
cana-1652	146	23	in	in	ADP
cana-1652	146	24	𝑉.	𝑉.	PROPN
cana-1652	146	25	if	if	SCONJ
cana-1652	146	26	𝑣	𝑣	PRON
cana-1652	146	27	is	be	AUX
cana-1652	146	28	in	in	ADP
cana-1652	146	29	𝑇	𝑇	PROPN
cana-1652	146	30	,	,	PUNCT
cana-1652	146	31	then	then	ADV
cana-1652	146	32	𝑣	𝑣	PRON
cana-1652	146	33	has	have	VERB
cana-1652	146	34	a	a	DET
cana-1652	146	35	neighbor	neighbor	NOUN
cana-1652	146	36	𝑢	𝑢	NOUN
cana-1652	146	37	in	in	ADP
cana-1652	146	38	𝑇.	𝑇.	PROPN
cana-1652	146	39	since	since	SCONJ
cana-1652	146	40	𝑇	𝑇	PROPN
cana-1652	146	41	is	be	AUX
cana-1652	146	42	a	a	DET
cana-1652	146	43	tree	tree	NOUN
cana-1652	146	44	,	,	PUNCT
cana-1652	146	45	there	there	PRON
cana-1652	146	46	is	be	VERB
cana-1652	146	47	a	a	DET
cana-1652	146	48	unique	unique	ADJ
cana-1652	146	49	path	path	NOUN
cana-1652	146	50	from	from	ADP
cana-1652	146	51	𝑢	𝑢	PRON
cana-1652	146	52	to	to	ADP
cana-1652	146	53	𝑣	𝑣	ADP
cana-1652	146	54	in	in	ADP
cana-1652	146	55	𝑇.	𝑇.	PROPN
cana-1652	146	56	let	let	VERB
cana-1652	146	57	𝑒	𝑒	PART
cana-1652	146	58	be	be	AUX
cana-1652	146	59	the	the	DET
cana-1652	146	60	edge	edge	NOUN
cana-1652	146	61	on	on	ADP
cana-1652	146	62	this	this	DET
cana-1652	146	63	path	path	NOUN
cana-1652	146	64	that	that	PRON
cana-1652	146	65	is	be	AUX
cana-1652	146	66	closest	close	ADJ
cana-1652	146	67	to	to	AUX
cana-1652	146	68	𝑣.	𝑣.	VERB
cana-1652	146	69	then	then	ADV
cana-1652	146	70	𝑒	𝑒	PROPN
cana-1652	146	71	is	be	AUX
cana-1652	146	72	not	not	PART
cana-1652	146	73	in	in	ADP
cana-1652	146	74	𝑇	𝑇	PROPN
cana-1652	146	75	and	and	CCONJ
cana-1652	146	76	one	one	NUM
cana-1652	146	77	endpoint	endpoint	NOUN
cana-1652	146	78	of	of	ADP
cana-1652	146	79	𝑒	𝑒	PROPN
cana-1652	146	80	belongs	belong	VERB
cana-1652	146	81	to	to	ADP
cana-1652	146	82	𝑆.	𝑆.	PROPN
cana-1652	146	83	thus	thus	ADV
cana-1652	146	84	,	,	PUNCT
cana-1652	146	85	this	this	DET
cana-1652	146	86	endpoint	endpoint	NOUN
cana-1652	146	87	dominates	dominate	VERB
cana-1652	146	88	𝑣.	𝑣.	NOUN
cana-1652	146	89	if	if	SCONJ
cana-1652	146	90	𝑣	𝑣	PRON
cana-1652	146	91	is	be	AUX
cana-1652	146	92	not	not	PART
cana-1652	146	93	in	in	ADP
cana-1652	146	94	𝑇	𝑇	PROPN
cana-1652	146	95	,	,	PUNCT
cana-1652	146	96	then	then	ADV
cana-1652	146	97	there	there	PRON
cana-1652	146	98	is	be	VERB
cana-1652	146	99	an	an	DET
cana-1652	146	100	edge	edge	NOUN
cana-1652	146	101	𝑒	𝑒	NOUN
cana-1652	146	102	=	=	SYM
cana-1652	146	103	𝑢	𝑢	NOUN
cana-1652	146	104	,	,	PUNCT
cana-1652	146	105	𝑤	𝑤	X
cana-1652	146	106	in	in	ADP
cana-1652	146	107	𝐺	𝐺	PROPN
cana-1652	146	108	such	such	ADJ
cana-1652	146	109	that	that	SCONJ
cana-1652	146	110	𝑢	𝑢	PROPN
cana-1652	146	111	∈	∈	PROPN
cana-1652	146	112	𝑇	𝑇	PROPN
cana-1652	146	113	and	and	CCONJ
cana-1652	146	114	𝑤	𝑤	ADP
cana-1652	146	115	∈	∈	PROPN
cana-1652	146	116	𝑆	𝑆	PROPN
cana-1652	146	117	(	(	PUNCT
cana-1652	146	118	since	since	SCONJ
cana-1652	146	119	𝑤	𝑤	NOUN
cana-1652	146	120	was	be	AUX
cana-1652	146	121	added	add	VERB
cana-1652	146	122	to	to	ADP
cana-1652	146	123	𝑆	𝑆	PROPN
cana-1652	146	124	when	when	SCONJ
cana-1652	146	125	we	we	PRON
cana-1652	146	126	chose	choose	VERB
cana-1652	146	127	the	the	DET
cana-1652	146	128	endpoint	endpoint	NOUN
cana-1652	146	129	of	of	ADP
cana-1652	146	130	𝑒	𝑒	PROPN
cana-1652	146	131	that	that	PRON
cana-1652	146	132	does	do	AUX
cana-1652	146	133	not	not	PART
cana-1652	146	134	belong	belong	VERB
cana-1652	146	135	to	to	ADP
cana-1652	146	136	𝑇	𝑇	PROPN
cana-1652	146	137	)	)	PUNCT
cana-1652	146	138	.	.	PUNCT
cana-1652	147	1	since	since	SCONJ
cana-1652	147	2	𝑢	𝑢	PRON
cana-1652	147	3	dominates	dominate	VERB
cana-1652	147	4	𝑤	𝑤	ADP
cana-1652	147	5	and	and	CCONJ
cana-1652	147	6	𝑤	𝑤	AUX
cana-1652	147	7	dominates	dominate	VERB
cana-1652	147	8	𝑣	𝑣	X
cana-1652	147	9	(	(	PUNCT
cana-1652	147	10	by	by	ADP
cana-1652	147	11	construction	construction	NOUN
cana-1652	147	12	)	)	PUNCT
cana-1652	147	13	,	,	PUNCT
cana-1652	147	14	we	we	PRON
cana-1652	147	15	have	have	VERB
cana-1652	147	16	that	that	SCONJ
cana-1652	147	17	𝑢	𝑢	PROPN
cana-1652	147	18	dominates	dominate	VERB
cana-1652	147	19	𝑣.	𝑣.	ADV
cana-1652	147	20	therefore	therefore	ADV
cana-1652	147	21	,	,	PUNCT
cana-1652	147	22	s	s	PART
cana-1652	147	23	is	be	AUX
cana-1652	147	24	a	a	DET
cana-1652	147	25	dominating	dominating	NOUN
cana-1652	147	26	set	set	NOUN
cana-1652	147	27	of	of	ADP
cana-1652	147	28	g.	g.	PROPN
cana-1652	147	29	to	to	PART
cana-1652	147	30	bound	bind	VERB
cana-1652	147	31	the	the	DET
cana-1652	147	32	size	size	NOUN
cana-1652	147	33	of	of	ADP
cana-1652	147	34	s	s	NUM
cana-1652	147	35	from	from	ADP
cana-1652	147	36	above	above	ADV
cana-1652	147	37	,	,	PUNCT
cana-1652	147	38	note	note	VERB
cana-1652	147	39	that	that	SCONJ
cana-1652	147	40	each	each	DET
cana-1652	147	41	vertex	vertex	NOUN
cana-1652	147	42	added	add	VERB
cana-1652	147	43	to	to	ADP
cana-1652	147	44	s	s	PRON
cana-1652	147	45	contributes	contribute	VERB
cana-1652	147	46	at	at	ADP
cana-1652	147	47	most	most	ADV
cana-1652	147	48	two	two	NUM
cana-1652	147	49	to	to	ADP
cana-1652	147	50	its	its	PRON
cana-1652	147	51	cardinality	cardinality	NOUN
cana-1652	147	52	(	(	PUNCT
cana-1652	147	53	since	since	SCONJ
cana-1652	147	54	each	each	DET
cana-1652	147	55	non	non	ADJ
cana-1652	147	56	-	-	ADJ
cana-1652	147	57	tree	tree	ADJ
cana-1652	147	58	edge	edge	NOUN
cana-1652	147	59	has	have	VERB
cana-1652	147	60	exactly	exactly	ADV
cana-1652	147	61	two	two	NUM
cana-1652	147	62	endpoints	endpoint	NOUN
cana-1652	147	63	)	)	PUNCT
cana-1652	147	64	.	.	PUNCT
cana-1652	148	1	thus	thus	ADV
cana-1652	148	2	,	,	PUNCT
cana-1652	148	3	|𝑆|	|𝑆|	VERB
cana-1652	148	4	≤	≤	NOUN
cana-1652	148	5	2(𝑚	2(𝑚	NUM
cana-1652	148	6	−	−	NOUN
cana-1652	148	7	𝑛	𝑛	PROPN
cana-1652	148	8	+	+	NOUN
cana-1652	148	9	1	1	NUM
cana-1652	148	10	)	)	PUNCT
cana-1652	148	11	=	=	NOUN
cana-1652	148	12	2𝑚	2𝑚	NOUN
cana-1652	148	13	−	−	PROPN
cana-1652	148	14	2𝑛	2𝑛	NOUN
cana-1652	148	15	+	+	CCONJ
cana-1652	148	16	2	2	NUM
cana-1652	148	17	on	on	ADP
cana-1652	148	18	the	the	DET
cana-1652	148	19	other	other	ADJ
cana-1652	148	20	hand	hand	NOUN
cana-1652	148	21	,	,	PUNCT
cana-1652	148	22	since	since	SCONJ
cana-1652	148	23	s	s	NOUN
cana-1652	148	24	is	be	AUX
cana-1652	148	25	a	a	DET
cana-1652	148	26	dominating	dominating	NOUN
cana-1652	148	27	set	set	NOUN
cana-1652	148	28	of	of	ADP
cana-1652	148	29	g	g	NOUN
cana-1652	148	30	,	,	PUNCT
cana-1652	148	31	each	each	DET
cana-1652	148	32	vertex	vertex	NOUN
cana-1652	148	33	in	in	ADP
cana-1652	148	34	𝑉	𝑉	PROPN
cana-1652	148	35	−	−	PROPN
cana-1652	148	36	𝑆	𝑆	PROPN
cana-1652	148	37	is	be	AUX
cana-1652	148	38	adjacent	adjacent	ADJ
cana-1652	148	39	to	to	ADP
cana-1652	148	40	at	at	ADV
cana-1652	148	41	least	least	ADV
cana-1652	148	42	one	one	NUM
cana-1652	148	43	vertex	vertex	NOUN
cana-1652	148	44	in	in	ADP
cana-1652	148	45	s.	s.	PROPN
cana-1652	148	46	thus	thus	ADV
cana-1652	148	47	,	,	PUNCT
cana-1652	148	48	we	we	PRON
cana-1652	148	49	have	have	VERB
cana-1652	148	50	:	:	PUNCT
cana-1652	148	51	𝑛	𝑛	DET
cana-1652	148	52	−	−	PROPN
cana-1652	148	53	|𝑆|	|𝑆|	VERB
cana-1652	148	54	≤	≤	PUNCT
cana-1652	148	55	𝑚	𝑚	ADP
cana-1652	148	56	combining	combine	VERB
cana-1652	148	57	this	this	PRON
cana-1652	148	58	with	with	ADP
cana-1652	148	59	the	the	DET
cana-1652	148	60	previous	previous	ADJ
cana-1652	148	61	inequality	inequality	NOUN
cana-1652	148	62	,	,	PUNCT
cana-1652	148	63	we	we	PRON
cana-1652	148	64	obtain	obtain	VERB
cana-1652	148	65	:	:	PUNCT
cana-1652	148	66	|𝑆|	|𝑆|	VERB
cana-1652	148	67	≥	≥	NOUN
cana-1652	148	68	𝑛	𝑛	PRON
cana-1652	148	69	−	−	NOUN
cana-1652	148	70	𝑚	𝑚	NOUN
cana-1652	148	71	+	+	NOUN
cana-1652	148	72	1	1	NUM
cana-1652	148	73	therefore	therefore	ADV
cana-1652	148	74	,	,	PUNCT
cana-1652	148	75	we	we	PRON
cana-1652	148	76	have	have	VERB
cana-1652	148	77	:	:	PUNCT
cana-1652	149	1	𝑛	𝑛	DET
cana-1652	149	2	−	−	NOUN
cana-1652	149	3	𝑚	𝑚	NOUN
cana-1652	149	4	+	+	CCONJ
cana-1652	149	5	1	1	NUM
cana-1652	149	6	≤	≤	NOUN
cana-1652	149	7	|𝑆|	|𝑆|	VERB
cana-1652	149	8	≤	≤	ADJ
cana-1652	149	9	2𝑚	2𝑚	NOUN
cana-1652	149	10	−	−	PROPN
cana-1652	149	11	2𝑛	2𝑛	NOUN
cana-1652	149	12	+	+	CCONJ
cana-1652	149	13	2	2	NUM
cana-1652	149	14	dividing	divide	VERB
cana-1652	149	15	both	both	DET
cana-1652	149	16	sides	side	NOUN
cana-1652	149	17	by	by	ADP
cana-1652	149	18	𝑚	𝑚	PROPN
cana-1652	149	19	−	−	PROPN
cana-1652	149	20	2	2	NUM
cana-1652	149	21	and	and	CCONJ
cana-1652	149	22	taking	take	VERB
cana-1652	149	23	the	the	DET
cana-1652	149	24	floor	floor	NOUN
cana-1652	149	25	function	function	NOUN
cana-1652	149	26	yields	yield	NOUN
cana-1652	149	27	:	:	PUNCT
cana-1652	149	28	⌊	⌊	PROPN
cana-1652	149	29	𝑛−3	𝑛−3	PROPN
cana-1652	149	30	𝑚−2	𝑚−2	NUM
cana-1652	149	31	⌋	⌋	NOUN
cana-1652	149	32	+	+	CCONJ
cana-1652	149	33	1	1	NUM
cana-1652	149	34	≥	≥	NOUN
cana-1652	149	35	⌊	⌊	X
cana-1652	149	36	𝑛−𝑚+1	𝑛−𝑚+1	PROPN
cana-1652	149	37	𝑚−2	𝑚−2	PROPN
cana-1652	149	38	⌋	⌋	NOUN
cana-1652	149	39	+	+	CCONJ
cana-1652	149	40	1	1	NUM
cana-1652	149	41	≤	≤	NUM
cana-1652	149	42	2	2	NUM
cana-1652	149	43	−	−	NOUN
cana-1652	149	44	2(𝑛−𝑚+1	2(𝑛−𝑚+1	NUM
cana-1652	149	45	)	)	PUNCT
cana-1652	149	46	𝑚−2	𝑚−2	NOUN
cana-1652	150	1	=	=	SYM
cana-1652	150	2	2𝑛	2𝑛	PROPN
cana-1652	151	1	𝑚−2	𝑚−2	PROPN
cana-1652	151	2	−	−	NOUN
cana-1652	151	3	3	3	X
cana-1652	151	4	.	.	PUNCT
cana-1652	151	5	since	since	SCONJ
cana-1652	151	6	⌊	⌊	PROPN
cana-1652	151	7	𝑛−3	𝑛−3	PROPN
cana-1652	151	8	𝑚−2	𝑚−2	NUM
cana-1652	151	9	⌋	⌋	NOUN
cana-1652	152	1	+	+	CCONJ
cana-1652	152	2	1	1	NUM
cana-1652	152	3	is	be	AUX
cana-1652	152	4	an	an	DET
cana-1652	152	5	integer	integer	NOUN
cana-1652	152	6	,	,	PUNCT
cana-1652	152	7	we	we	PRON
cana-1652	152	8	have	have	AUX
cana-1652	152	9	:	:	PUNCT
cana-1652	152	10	⌊	⌊	VERB
cana-1652	152	11	𝑛−3	𝑛−3	PROPN
cana-1652	152	12	𝑚−2	𝑚−2	NUM
cana-1652	152	13	⌋	⌋	NOUN
cana-1652	153	1	+	+	CCONJ
cana-1652	154	1	1	1	NUM
cana-1652	154	2	≤	≤	NUM
cana-1652	154	3	min	min	NOUN
cana-1652	154	4	2𝑛	2𝑛	PROPN
cana-1652	154	5	𝑚−2	𝑚−2	PROPN
cana-1652	154	6	−	−	PROPN
cana-1652	154	7	3	3	NUM
cana-1652	154	8	,	,	PUNCT
cana-1652	154	9	𝑛.	𝑛.	NOUN
cana-1652	154	10	thus	thus	ADV
cana-1652	154	11	,	,	PUNCT
cana-1652	154	12	we	we	PRON
cana-1652	154	13	have	have	AUX
cana-1652	154	14	shown	show	VERB
cana-1652	154	15	that	that	SCONJ
cana-1652	154	16	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	154	17	)	)	PUNCT
cana-1652	154	18	≤	≤	NUM
cana-1652	154	19	min	min	PROPN
cana-1652	154	20	2𝑛	2𝑛	PROPN
cana-1652	155	1	𝑚−2	𝑚−2	PROPN
cana-1652	155	2	−	−	PROPN
cana-1652	155	3	3	3	NUM
cana-1652	155	4	,	,	PUNCT
cana-1652	155	5	𝑛	𝑛	PROPN
cana-1652	155	6	,	,	PUNCT
cana-1652	155	7	which	which	PRON
cana-1652	155	8	completes	complete	VERB
cana-1652	155	9	the	the	DET
cana-1652	155	10	proof	proof	NOUN
cana-1652	155	11	.	.	PUNCT
cana-1652	156	1	theorem	theorem	VERB
cana-1652	156	2	2.11	2.11	NUM
cana-1652	156	3	let	let	VERB
cana-1652	156	4	𝐺	𝐺	PROPN
cana-1652	156	5	=	=	SYM
cana-1652	156	6	(	(	PUNCT
cana-1652	156	7	𝑉	𝑉	PROPN
cana-1652	156	8	,	,	PUNCT
cana-1652	156	9	𝐸	𝐸	PROPN
cana-1652	156	10	,	,	PUNCT
cana-1652	156	11	𝜇	𝜇	NOUN
cana-1652	156	12	)	)	PUNCT
cana-1652	156	13	be	be	AUX
cana-1652	156	14	a	a	DET
cana-1652	156	15	fuzzy	fuzzy	ADJ
cana-1652	156	16	graph	graph	NOUN
cana-1652	156	17	with	with	ADP
cana-1652	156	18	𝑛	𝑛	PROPN
cana-1652	156	19	vertices	vertex	NOUN
cana-1652	156	20	and	and	CCONJ
cana-1652	156	21	𝑚	𝑚	ADP
cana-1652	156	22	edges	edge	NOUN
cana-1652	156	23	.	.	PUNCT
cana-1652	157	1	if	if	SCONJ
cana-1652	157	2	𝐺	𝐺	PROPN
cana-1652	157	3	is	be	AUX
cana-1652	157	4	connected	connect	VERB
cana-1652	157	5	and	and	CCONJ
cana-1652	157	6	𝑚	𝑚	X
cana-1652	157	7	≥	≥	NUM
cana-1652	157	8	3	3	NUM
cana-1652	157	9	,	,	PUNCT
cana-1652	157	10	then	then	ADV
cana-1652	157	11	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1652	157	12	)	)	PUNCT
cana-1652	157	13	≤	≤	NUM
cana-1652	157	14	⌊(𝑛	⌊(𝑛	NOUN
cana-1652	158	1	−	−	PROPN
cana-1652	158	2	2)/(𝑚	2)/(𝑚	NUM
cana-1652	158	3	−	−	NUM
cana-1652	158	4	1)⌋	1)⌋	NUM
cana-1652	159	1	+	+	PUNCT
cana-1652	159	2	1	1	X
cana-1652	159	3	.	.	X
cana-1652	159	4	proof	proof	NOUN
cana-1652	159	5	:	:	PUNCT
cana-1652	159	6	let	let	VERB
cana-1652	159	7	𝐺	𝐺	PROPN
cana-1652	159	8	=	=	SYM
cana-1652	159	9	(	(	PUNCT
cana-1652	159	10	𝑉	𝑉	PROPN
cana-1652	159	11	,	,	PUNCT
cana-1652	159	12	𝐸	𝐸	PROPN
cana-1652	159	13	,	,	PUNCT
cana-1652	159	14	𝜇	𝜇	NOUN
cana-1652	159	15	)	)	PUNCT
cana-1652	159	16	be	be	AUX
cana-1652	159	17	a	a	DET
cana-1652	159	18	fuzzy	fuzzy	ADJ
cana-1652	159	19	graph	graph	NOUN
cana-1652	159	20	with	with	ADP
cana-1652	159	21	𝑛	𝑛	PROPN
cana-1652	159	22	vertices	vertex	NOUN
cana-1652	159	23	and	and	CCONJ
cana-1652	159	24	𝑚	𝑚	ADP
cana-1652	159	25	edges	edge	NOUN
cana-1652	159	26	.	.	PUNCT
cana-1652	160	1	suppose	suppose	VERB
cana-1652	160	2	that	that	SCONJ
cana-1652	160	3	𝐺	𝐺	PROPN
cana-1652	160	4	is	be	AUX
cana-1652	160	5	connected	connect	VERB
cana-1652	160	6	and	and	CCONJ
cana-1652	160	7	𝑚	𝑚	X
cana-1652	160	8	≥	≥	NUM
cana-1652	160	9	3	3	NUM
cana-1652	160	10	.	.	PUNCT
cana-1652	161	1	let	let	VERB
cana-1652	161	2	𝑇	𝑇	PROPN
cana-1652	161	3	be	be	AUX
cana-1652	161	4	a	a	DET
cana-1652	161	5	spanning	span	VERB
cana-1652	161	6	tree	tree	NOUN
cana-1652	161	7	of	of	ADP
cana-1652	161	8	𝐺.	𝐺.	NOUN
cana-1652	161	9	since	since	SCONJ
cana-1652	161	10	𝑇	𝑇	PROPN
cana-1652	161	11	has	have	VERB
cana-1652	161	12	𝑛	𝑛	DET
cana-1652	161	13	−	−	NUM
cana-1652	161	14	1	1	NUM
cana-1652	161	15	edges	edge	NOUN
cana-1652	161	16	,	,	PUNCT
cana-1652	161	17	there	there	PRON
cana-1652	161	18	are	be	VERB
cana-1652	161	19	at	at	ADP
cana-1652	161	20	least	least	ADJ
cana-1652	161	21	𝑚	𝑚	ADP
cana-1652	161	22	−	−	PROPN
cana-1652	161	23	(	(	PUNCT
cana-1652	161	24	𝑛	𝑛	PROPN
cana-1652	161	25	−	−	NOUN
cana-1652	161	26	1	1	NUM
cana-1652	161	27	)	)	PUNCT
cana-1652	161	28	=	=	PUNCT
cana-1652	162	1	𝑚	𝑚	ADP
cana-1652	162	2	−	−	NUM
cana-1652	162	3	𝑛	𝑛	PRON
cana-1652	162	4	+	+	CCONJ
cana-1652	162	5	1	1	NUM
cana-1652	162	6	edges	edge	NOUN
cana-1652	162	7	in	in	ADP
cana-1652	162	8	𝐺	𝐺	PROPN
cana-1652	162	9	that	that	PRON
cana-1652	162	10	are	be	AUX
cana-1652	162	11	not	not	PART
cana-1652	162	12	in	in	ADP
cana-1652	162	13	𝑇.	𝑇.	PROPN
cana-1652	162	14	let	let	VERB
cana-1652	162	15	𝑆	𝑆	PROPN
cana-1652	162	16	be	be	AUX
cana-1652	162	17	a	a	DET
cana-1652	162	18	set	set	NOUN
cana-1652	162	19	of	of	ADP
cana-1652	162	20	vertices	vertex	NOUN
cana-1652	162	21	obtained	obtain	VERB
cana-1652	162	22	as	as	ADP
cana-1652	162	23	follows	follow	VERB
cana-1652	162	24	:	:	PUNCT
cana-1652	162	25	for	for	SCONJ
cana-1652	162	26	each	each	DET
cana-1652	162	27	edge	edge	NOUN
cana-1652	162	28	𝑒	𝑒	VERB
cana-1652	162	29	in	in	ADP
cana-1652	162	30	𝐺	𝐺	PROPN
cana-1652	162	31	that	that	PRON
cana-1652	162	32	is	be	AUX
cana-1652	162	33	not	not	PART
cana-1652	162	34	in	in	ADP
cana-1652	162	35	𝑇	𝑇	PROPN
cana-1652	162	36	,	,	PUNCT
cana-1652	162	37	choose	choose	VERB
cana-1652	162	38	an	an	DET
cana-1652	162	39	endpoint	endpoint	NOUN
cana-1652	162	40	of	of	ADP
cana-1652	162	41	𝑒	𝑒	PRON
cana-1652	162	42	and	and	CCONJ
cana-1652	162	43	add	add	VERB
cana-1652	162	44	it	it	PRON
cana-1652	162	45	to	to	ADP
cana-1652	162	46	𝑆.	𝑆.	PROPN
cana-1652	162	47	since	since	SCONJ
cana-1652	162	48	each	each	DET
cana-1652	162	49	edge	edge	NOUN
cana-1652	162	50	in	in	ADP
cana-1652	162	51	𝐺	𝐺	PROPN
cana-1652	162	52	has	have	VERB
cana-1652	162	53	at	at	ADV
cana-1652	162	54	least	least	ADV
cana-1652	162	55	one	one	NUM
cana-1652	162	56	endpoint	endpoint	NOUN
cana-1652	162	57	in	in	ADP
cana-1652	162	58	𝑇	𝑇	PROPN
cana-1652	162	59	,	,	PUNCT
cana-1652	162	60	we	we	PRON
cana-1652	162	61	have	have	AUX
cana-1652	162	62	|𝑆|	|𝑆|	VERB
cana-1652	162	63	≥	≥	NOUN
cana-1652	162	64	𝑚	𝑚	ADP
cana-1652	162	65	−	−	NOUN
cana-1652	162	66	𝑛	𝑛	PROPN
cana-1652	163	1	+	+	NOUN
cana-1652	163	2	1	1	X
cana-1652	163	3	.	.	X
cana-1652	163	4	we	we	PRON
cana-1652	163	5	claim	claim	VERB
cana-1652	163	6	that	that	SCONJ
cana-1652	163	7	𝑆	𝑆	PROPN
cana-1652	163	8	is	be	AUX
cana-1652	163	9	a	a	DET
cana-1652	163	10	dominating	dominating	NOUN
cana-1652	163	11	set	set	NOUN
cana-1652	163	12	of	of	ADP
cana-1652	163	13	𝐺.	𝐺.	NOUN
cana-1652	163	14	to	to	PART
cana-1652	163	15	see	see	VERB
cana-1652	163	16	this	this	PRON
cana-1652	163	17	,	,	PUNCT
cana-1652	163	18	let	let	VERB
cana-1652	163	19	𝑣	𝑣	PART
cana-1652	163	20	be	be	AUX
cana-1652	163	21	any	any	DET
cana-1652	163	22	vertex	vertex	NOUN
cana-1652	163	23	in	in	ADP
cana-1652	163	24	𝑉.	𝑉.	PROPN
cana-1652	163	25	if	if	SCONJ
cana-1652	163	26	𝑣	𝑣	PRON
cana-1652	163	27	is	be	AUX
cana-1652	163	28	in	in	ADP
cana-1652	163	29	𝑇	𝑇	PROPN
cana-1652	163	30	,	,	PUNCT
cana-1652	163	31	then	then	ADV
cana-1652	163	32	𝑣	𝑣	PRON
cana-1652	163	33	has	have	VERB
cana-1652	163	34	a	a	DET
cana-1652	163	35	neighbor	neighbor	NOUN
cana-1652	163	36	𝑢	𝑢	NOUN
cana-1652	163	37	in	in	ADP
cana-1652	163	38	𝑇.	𝑇.	PROPN
cana-1652	163	39	since	since	SCONJ
cana-1652	163	40	𝑇	𝑇	PROPN
cana-1652	163	41	is	be	AUX
cana-1652	163	42	a	a	DET
cana-1652	163	43	tree	tree	NOUN
cana-1652	163	44	,	,	PUNCT
cana-1652	163	45	there	there	PRON
cana-1652	163	46	is	be	VERB
cana-1652	163	47	a	a	DET
cana-1652	163	48	unique	unique	ADJ
cana-1652	163	49	path	path	NOUN
cana-1652	163	50	from	from	ADP
cana-1652	163	51	𝑢	𝑢	PRON
cana-1652	163	52	to	to	ADP
cana-1652	163	53	𝑣	𝑣	ADP
cana-1652	163	54	in	in	ADP
cana-1652	163	55	𝑇.	𝑇.	PROPN
cana-1652	163	56	let	let	VERB
cana-1652	163	57	𝑒	𝑒	PART
cana-1652	163	58	be	be	AUX
cana-1652	163	59	the	the	DET
cana-1652	163	60	edge	edge	NOUN
cana-1652	163	61	on	on	ADP
cana-1652	163	62	this	this	DET
cana-1652	163	63	path	path	NOUN
cana-1652	163	64	that	that	PRON
cana-1652	163	65	is	be	AUX
cana-1652	163	66	closest	close	ADJ
cana-1652	163	67	to	to	AUX
cana-1652	163	68	𝑣.	𝑣.	VERB
cana-1652	163	69	then	then	ADV
cana-1652	163	70	𝑒	𝑒	PROPN
cana-1652	163	71	is	be	AUX
cana-1652	163	72	not	not	PART
cana-1652	163	73	in	in	ADP
cana-1652	163	74	𝑇	𝑇	PROPN
cana-1652	163	75	and	and	CCONJ
cana-1652	163	76	one	one	NUM
cana-1652	163	77	endpoint	endpoint	NOUN
cana-1652	163	78	of	of	ADP
cana-1652	163	79	𝑒	𝑒	PROPN
cana-1652	163	80	belongs	belong	VERB
cana-1652	163	81	to	to	ADP
cana-1652	163	82	𝑆.	𝑆.	PROPN
cana-1652	163	83	thus	thus	ADV
cana-1652	163	84	,	,	PUNCT
cana-1652	163	85	this	this	DET
cana-1652	163	86	endpoint	endpoint	NOUN
cana-1652	163	87	dominates	dominate	VERB
cana-1652	163	88	𝑣.	𝑣.	NOUN
cana-1652	163	89	if	if	SCONJ
cana-1652	163	90	𝑣	𝑣	PRON
cana-1652	163	91	is	be	AUX
cana-1652	163	92	not	not	PART
cana-1652	163	93	in	in	ADP
cana-1652	163	94	𝑇	𝑇	PROPN
cana-1652	163	95	,	,	PUNCT
cana-1652	163	96	then	then	ADV
cana-1652	163	97	there	there	PRON
cana-1652	163	98	is	be	VERB
cana-1652	163	99	an	an	DET
cana-1652	163	100	edge	edge	NOUN
cana-1652	163	101	𝑒	𝑒	NOUN
cana-1652	163	102	=	=	SYM
cana-1652	163	103	𝑢	𝑢	NOUN
cana-1652	163	104	,	,	PUNCT
cana-1652	163	105	𝑤	𝑤	X
cana-1652	163	106	in	in	ADP
cana-1652	163	107	𝐺	𝐺	PROPN
cana-1652	163	108	such	such	ADJ
cana-1652	163	109	that	that	SCONJ
cana-1652	163	110	𝑢	𝑢	PROPN
cana-1652	163	111	∈	∈	PROPN
cana-1652	163	112	𝑇	𝑇	PROPN
cana-1652	163	113	and	and	CCONJ
cana-1652	163	114	𝑤	𝑤	ADP
cana-1652	163	115	∈	∈	PROPN
cana-1652	163	116	𝑆	𝑆	PROPN
cana-1652	163	117	(	(	PUNCT
cana-1652	163	118	since	since	SCONJ
cana-1652	163	119	𝑤	𝑤	NOUN
cana-1652	163	120	was	be	AUX
cana-1652	163	121	added	add	VERB
cana-1652	163	122	to	to	ADP
cana-1652	163	123	𝑆	𝑆	PROPN
cana-1652	163	124	when	when	SCONJ
cana-1652	163	125	we	we	PRON
cana-1652	163	126	chose	choose	VERB
cana-1652	163	127	the	the	DET
cana-1652	163	128	endpoint	endpoint	NOUN
cana-1652	163	129	of	of	ADP
cana-1652	163	130	𝑒	𝑒	PROPN
cana-1652	163	131	that	that	PRON
cana-1652	163	132	does	do	AUX
cana-1652	163	133	not	not	PART
cana-1652	163	134	belong	belong	VERB
cana-1652	163	135	to	to	ADP
cana-1652	163	136	𝑇	𝑇	PROPN
cana-1652	163	137	)	)	PUNCT
cana-1652	163	138	.	.	PUNCT
cana-1652	164	1	since	since	SCONJ
cana-1652	164	2	𝑢	𝑢	PRON
cana-1652	164	3	dominates	dominate	VERB
cana-1652	164	4	𝑤	𝑤	ADP
cana-1652	164	5	and	and	CCONJ
cana-1652	164	6	𝑤	𝑤	AUX
cana-1652	164	7	dominates	dominate	VERB
cana-1652	164	8	𝑣	𝑣	X
cana-1652	164	9	(	(	PUNCT
cana-1652	164	10	by	by	ADP
cana-1652	164	11	construction	construction	NOUN
cana-1652	164	12	)	)	PUNCT
cana-1652	164	13	,	,	PUNCT
cana-1652	164	14	we	we	PRON
cana-1652	164	15	have	have	VERB
cana-1652	164	16	that	that	SCONJ
cana-1652	164	17	𝑢	𝑢	PROPN
cana-1652	164	18	dominates	dominate	VERB
cana-1652	164	19	𝑣.	𝑣.	ADV
cana-1652	164	20	therefore	therefore	ADV
cana-1652	164	21	,	,	PUNCT
cana-1652	164	22	s	s	PART
cana-1652	164	23	is	be	AUX
cana-1652	164	24	a	a	DET
cana-1652	164	25	dominating	dominating	NOUN
cana-1652	164	26	set	set	NOUN
cana-1652	164	27	of	of	ADP
cana-1652	164	28	g.	g.	PROPN
cana-1652	164	29	to	to	PART
cana-1652	164	30	bound	bind	VERB
cana-1652	164	31	the	the	DET
cana-1652	164	32	size	size	NOUN
cana-1652	164	33	of	of	ADP
cana-1652	164	34	𝑆	𝑆	PROPN
cana-1652	164	35	from	from	ADP
cana-1652	164	36	above	above	ADV
cana-1652	164	37	,	,	PUNCT
cana-1652	164	38	note	note	VERB
cana-1652	164	39	that	that	SCONJ
cana-1652	164	40	each	each	DET
cana-1652	164	41	vertex	vertex	NOUN
cana-1652	164	42	added	add	VERB
cana-1652	164	43	to	to	ADP
cana-1652	164	44	𝑆	𝑆	PROPN
cana-1652	164	45	contributes	contribute	VERB
cana-1652	164	46	at	at	ADP
cana-1652	164	47	most	most	ADJ
cana-1652	164	48	one	one	NUM
cana-1652	164	49	to	to	ADP
cana-1652	164	50	its	its	PRON
cana-1652	164	51	cardinality	cardinality	NOUN
cana-1652	164	52	(	(	PUNCT
cana-1652	164	53	since	since	SCONJ
cana-1652	164	54	each	each	DET
cana-1652	164	55	non	non	ADJ
cana-1652	164	56	-	-	ADJ
cana-1652	164	57	tree	tree	ADJ
cana-1652	164	58	edge	edge	NOUN
cana-1652	164	59	has	have	VERB
cana-1652	164	60	exactly	exactly	ADV
cana-1652	164	61	one	one	NUM
cana-1652	164	62	endpoint	endpoint	NOUN
cana-1652	164	63	)	)	PUNCT
cana-1652	164	64	.	.	PUNCT
cana-1652	165	1	thus	thus	ADV
cana-1652	165	2	,	,	PUNCT
cana-1652	165	3	communications	communication	NOUN
cana-1652	165	4	on	on	ADP
cana-1652	165	5	applied	apply	VERB
cana-1652	165	6	nonlinear	nonlinear	ADJ
cana-1652	165	7	analysis	analysis	NOUN
cana-1652	165	8	issn	issn	NOUN
cana-1652	165	9	:	:	PUNCT
cana-1652	165	10	1074	1074	NUM
cana-1652	165	11	-	-	PUNCT
cana-1652	165	12	133x	133x	NUM
cana-1652	165	13	vol	vol	NOUN
cana-1652	165	14	32	32	NUM
cana-1652	165	15	no	no	NOUN
cana-1652	165	16	.	.	NOUN
cana-1652	165	17	1	1	NUM
cana-1652	165	18	(	(	PUNCT
cana-1652	165	19	2025	2025	NUM
cana-1652	165	20	)	)	PUNCT
cana-1652	165	21	330	330	NUM
cana-1652	165	22	https://internationalpubls.com	https://internationalpubls.com	X
cana-1652	165	23	|𝑆|	|𝑆|	VERB
cana-1652	165	24	≤	≤	NOUN
cana-1652	165	25	𝑚	𝑚	ADP
cana-1652	165	26	−	−	NOUN
cana-1652	165	27	𝑛	𝑛	PROPN
cana-1652	166	1	+	+	NOUN
cana-1652	166	2	1	1	NUM
cana-1652	166	3	on	on	ADP
cana-1652	166	4	the	the	DET
cana-1652	166	5	other	other	ADJ
cana-1652	166	6	hand	hand	NOUN
cana-1652	166	7	,	,	PUNCT
cana-1652	166	8	since	since	SCONJ
cana-1652	166	9	𝑆	𝑆	PROPN
cana-1652	166	10	is	be	AUX
cana-1652	166	11	a	a	DET
cana-1652	166	12	dominating	dominating	NOUN
cana-1652	166	13	set	set	NOUN
cana-1652	166	14	of	of	ADP
cana-1652	166	15	𝐺	𝐺	PROPN
cana-1652	166	16	,	,	PUNCT
cana-1652	166	17	each	each	DET
cana-1652	166	18	vertex	vertex	NOUN
cana-1652	166	19	in	in	ADP
cana-1652	166	20	𝑉	𝑉	PROPN
cana-1652	166	21	−	−	PROPN
cana-1652	166	22	𝑆	𝑆	PROPN
cana-1652	166	23	is	be	AUX
cana-1652	166	24	adjacent	adjacent	ADJ
cana-1652	166	25	to	to	ADP
cana-1652	166	26	at	at	ADV
cana-1652	166	27	least	least	ADV
cana-1652	166	28	one	one	NUM
cana-1652	166	29	vertex	vertex	NOUN
cana-1652	166	30	in	in	ADP
cana-1652	166	31	𝑆.	𝑆.	PROPN
cana-1652	166	32	thus	thus	ADV
cana-1652	166	33	,	,	PUNCT
cana-1652	166	34	we	we	PRON
cana-1652	166	35	have	have	VERB
cana-1652	166	36	:	:	PUNCT
cana-1652	166	37	𝑛	𝑛	DET
cana-1652	166	38	−	−	PROPN
cana-1652	166	39	|𝑆|	|𝑆|	VERB
cana-1652	166	40	≤	≤	PUNCT
cana-1652	166	41	𝑚	𝑚	ADP
cana-1652	166	42	combining	combine	VERB
cana-1652	166	43	this	this	PRON
cana-1652	166	44	with	with	ADP
cana-1652	166	45	the	the	DET
cana-1652	166	46	previous	previous	ADJ
cana-1652	166	47	inequality	inequality	NOUN
cana-1652	166	48	,	,	PUNCT
cana-1652	166	49	we	we	PRON
cana-1652	166	50	obtain	obtain	VERB
cana-1652	166	51	:	:	PUNCT
cana-1652	166	52	|𝑆|	|𝑆|	VERB
cana-1652	166	53	≥	≥	NOUN
cana-1652	166	54	𝑛	𝑛	PRON
cana-1652	166	55	−	−	NOUN
cana-1652	166	56	𝑚	𝑚	NOUN
cana-1652	166	57	+	+	NOUN
cana-1652	166	58	1	1	NUM
cana-1652	166	59	therefore	therefore	ADV
cana-1652	166	60	,	,	PUNCT
cana-1652	166	61	we	we	PRON
cana-1652	166	62	have	have	VERB
cana-1652	166	63	:	:	PUNCT
cana-1652	167	1	𝑛	𝑛	DET
cana-1652	167	2	−	−	NOUN
cana-1652	167	3	𝑚	𝑚	NOUN
cana-1652	167	4	+	+	CCONJ
cana-1652	167	5	1	1	NUM
cana-1652	167	6	≤	≤	NOUN
cana-1652	167	7	|𝑆|	|𝑆|	VERB
cana-1652	167	8	≤	≤	NUM
cana-1652	167	9	𝑚	𝑚	ADP
cana-1652	167	10	−	−	NOUN
cana-1652	167	11	𝑛	𝑛	PRON
cana-1652	167	12	+	+	NOUN
cana-1652	167	13	1	1	NUM
cana-1652	167	14	dividing	divide	VERB
cana-1652	167	15	both	both	DET
cana-1652	167	16	sides	side	NOUN
cana-1652	167	17	by	by	ADP
cana-1652	167	18	𝑚	𝑚	PROPN
cana-1652	167	19	−	−	PROPN
cana-1652	167	20	1	1	NUM
cana-1652	167	21	and	and	CCONJ
cana-1652	167	22	taking	take	VERB
cana-1652	167	23	the	the	DET
cana-1652	167	24	floor	floor	NOUN
cana-1652	167	25	function	function	NOUN
cana-1652	167	26	yields	yield	NOUN
cana-1652	167	27	:	:	PUNCT
cana-1652	167	28	⌊	⌊	VERB
cana-1652	167	29	𝑛−2	𝑛−2	NOUN
cana-1652	167	30	𝑚−1	𝑚−1	NOUN
cana-1652	167	31	⌋	⌋	NOUN
cana-1652	167	32	+	+	CCONJ
cana-1652	167	33	1	1	NUM
cana-1652	167	34	≥	≥	NOUN
cana-1652	167	35	⌊	⌊	X
cana-1652	167	36	𝑛−𝑚+1	𝑛−𝑚+1	PROPN
cana-1652	167	37	𝑚−1	𝑚−1	PROPN
cana-1652	167	38	⌋	⌋	NOUN
cana-1652	167	39	+	+	CCONJ
cana-1652	167	40	1	1	X
cana-1652	167	41	.	.	PUNCT
cana-1652	167	42	since	since	SCONJ
cana-1652	167	43	⌊	⌊	PROPN
cana-1652	167	44	𝑛−𝑚+1	𝑛−𝑚+1	PROPN
cana-1652	167	45	𝑚−1	𝑚−1	PROPN
cana-1652	167	46	⌋	⌋	NOUN
cana-1652	167	47	=	=	PUNCT
cana-1652	168	1	⌊	⌊	PROPN
cana-1652	168	2	𝑛−2	𝑛−2	NOUN
cana-1652	168	3	𝑚−1	𝑚−1	NOUN
cana-1652	168	4	⌋	⌋	NOUN
cana-1652	168	5	,	,	PUNCT
cana-1652	168	6	we	we	PRON
cana-1652	168	7	have	have	AUX
cana-1652	168	8	:	:	PUNCT
cana-1652	168	9	⌊	⌊	VERB
cana-1652	168	10	𝑛−2	𝑛−2	NOUN
cana-1652	168	11	𝑚−1	𝑚−1	NOUN
cana-1652	168	12	⌋	⌋	NOUN
cana-1652	168	13	+	+	CCONJ
cana-1652	168	14	1	1	NUM
cana-1652	168	15	≥	≥	NOUN
cana-1652	168	16	⌊	⌊	X
cana-1652	168	17	𝑛−𝑚+1	𝑛−𝑚+1	PROPN
cana-1652	168	18	𝑚−1	𝑚−1	PROPN
cana-1652	168	19	⌋	⌋	NOUN
cana-1652	168	20	+	+	CCONJ
cana-1652	169	1	1	1	X
cana-1652	169	2	.	.	X
cana-1652	169	3	therefore	therefore	ADV
cana-1652	169	4	,	,	PUNCT
cana-1652	169	5	we	we	PRON
cana-1652	169	6	have	have	AUX
cana-1652	169	7	shown	show	VERB
cana-1652	169	8	that	that	SCONJ
cana-1652	169	9	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	169	10	)	)	PUNCT
cana-1652	169	11	≤	≤	PUNCT
cana-1652	170	1	⌊	⌊	VERB
cana-1652	170	2	𝑛−𝑚+1	𝑛−𝑚+1	PROPN
cana-1652	170	3	𝑚−1	𝑚−1	PROPN
cana-1652	170	4	⌋	⌋	NOUN
cana-1652	170	5	+	+	CCONJ
cana-1652	170	6	1	1	NUM
cana-1652	170	7	,	,	PUNCT
cana-1652	170	8	which	which	PRON
cana-1652	170	9	completes	complete	VERB
cana-1652	170	10	the	the	DET
cana-1652	170	11	proof	proof	NOUN
cana-1652	170	12	.	.	PUNCT
cana-1652	171	1	theorem	theorem	VERB
cana-1652	171	2	2.12	2.12	NUM
cana-1652	171	3	let	let	VERB
cana-1652	171	4	𝐺	𝐺	PROPN
cana-1652	171	5	=	=	SYM
cana-1652	171	6	(	(	PUNCT
cana-1652	171	7	𝑉	𝑉	PROPN
cana-1652	171	8	,	,	PUNCT
cana-1652	171	9	𝐸	𝐸	PROPN
cana-1652	171	10	,	,	PUNCT
cana-1652	171	11	𝜇	𝜇	NOUN
cana-1652	171	12	)	)	PUNCT
cana-1652	171	13	be	be	AUX
cana-1652	171	14	a	a	DET
cana-1652	171	15	fuzzy	fuzzy	ADJ
cana-1652	171	16	graph	graph	NOUN
cana-1652	171	17	with	with	ADP
cana-1652	171	18	𝑛	𝑛	PROPN
cana-1652	171	19	vertices	vertex	NOUN
cana-1652	171	20	and	and	CCONJ
cana-1652	171	21	𝑚	𝑚	ADP
cana-1652	171	22	edges	edge	NOUN
cana-1652	171	23	.	.	PUNCT
cana-1652	172	1	if	if	SCONJ
cana-1652	172	2	𝐺	𝐺	PROPN
cana-1652	172	3	is	be	AUX
cana-1652	172	4	connected	connect	VERB
cana-1652	172	5	and	and	CCONJ
cana-1652	172	6	𝑚	𝑚	X
cana-1652	172	7	≥	≥	NOUN
cana-1652	172	8	𝑘	𝑘	X
cana-1652	172	9	+	+	NOUN
cana-1652	172	10	1	1	NUM
cana-1652	172	11	for	for	ADP
cana-1652	172	12	some	some	DET
cana-1652	172	13	positive	positive	ADJ
cana-1652	172	14	integer	integer	NOUN
cana-1652	172	15	𝑘	𝑘	ADP
cana-1652	172	16	<	<	X
cana-1652	172	17	𝑛	𝑛	PRON
cana-1652	172	18	−	−	NUM
cana-1652	172	19	1	1	NUM
cana-1652	172	20	,	,	PUNCT
cana-1652	172	21	then	then	ADV
cana-1652	172	22	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1652	172	23	)	)	PUNCT
cana-1652	172	24	≤	≤	PUNCT
cana-1652	172	25	⌊	⌊	VERB
cana-1652	172	26	𝑛−𝑘−1	𝑛−𝑘−1	PROPN
cana-1652	172	27	𝑚−𝑘	𝑚−𝑘	NOUN
cana-1652	172	28	⌋	⌋	NOUN
cana-1652	172	29	+	+	CCONJ
cana-1652	172	30	1	1	X
cana-1652	172	31	.	.	X
cana-1652	172	32	proof	proof	NOUN
cana-1652	172	33	:	:	PUNCT
cana-1652	172	34	let	let	VERB
cana-1652	172	35	𝐺	𝐺	PROPN
cana-1652	172	36	=	=	SYM
cana-1652	172	37	(	(	PUNCT
cana-1652	172	38	𝑉	𝑉	PROPN
cana-1652	172	39	,	,	PUNCT
cana-1652	172	40	𝐸	𝐸	PROPN
cana-1652	172	41	,	,	PUNCT
cana-1652	172	42	𝜇	𝜇	NOUN
cana-1652	172	43	)	)	PUNCT
cana-1652	172	44	be	be	AUX
cana-1652	172	45	a	a	DET
cana-1652	172	46	fuzzy	fuzzy	ADJ
cana-1652	172	47	graph	graph	NOUN
cana-1652	172	48	with	with	ADP
cana-1652	172	49	𝑛	𝑛	PROPN
cana-1652	172	50	vertices	vertex	NOUN
cana-1652	172	51	and	and	CCONJ
cana-1652	172	52	𝑚	𝑚	ADP
cana-1652	172	53	edges	edge	NOUN
cana-1652	172	54	.	.	PUNCT
cana-1652	173	1	suppose	suppose	VERB
cana-1652	173	2	that	that	SCONJ
cana-1652	173	3	𝐺	𝐺	PROPN
cana-1652	173	4	is	be	AUX
cana-1652	173	5	connected	connect	VERB
cana-1652	173	6	and	and	CCONJ
cana-1652	173	7	𝑚	𝑚	X
cana-1652	173	8	≥	≥	NOUN
cana-1652	173	9	𝑘	𝑘	X
cana-1652	173	10	+	+	NOUN
cana-1652	173	11	1	1	NUM
cana-1652	173	12	for	for	ADP
cana-1652	173	13	some	some	DET
cana-1652	173	14	positive	positive	ADJ
cana-1652	173	15	integer	integer	NOUN
cana-1652	173	16	𝑘	𝑘	ADP
cana-1652	173	17	<	<	X
cana-1652	173	18	𝑛	𝑛	PRON
cana-1652	173	19	−	−	PROPN
cana-1652	173	20	1	1	NUM
cana-1652	173	21	.	.	PUNCT
cana-1652	174	1	let	let	VERB
cana-1652	174	2	𝑇	𝑇	PROPN
cana-1652	174	3	be	be	AUX
cana-1652	174	4	a	a	DET
cana-1652	174	5	spanning	span	VERB
cana-1652	174	6	tree	tree	NOUN
cana-1652	174	7	of	of	ADP
cana-1652	174	8	𝐺.	𝐺.	NOUN
cana-1652	174	9	since	since	SCONJ
cana-1652	174	10	𝑇	𝑇	PROPN
cana-1652	174	11	has	have	VERB
cana-1652	174	12	𝑛	𝑛	DET
cana-1652	174	13	−	−	NUM
cana-1652	174	14	1	1	NUM
cana-1652	174	15	edges	edge	NOUN
cana-1652	174	16	,	,	PUNCT
cana-1652	174	17	there	there	PRON
cana-1652	174	18	are	be	VERB
cana-1652	174	19	at	at	ADP
cana-1652	174	20	least	least	ADJ
cana-1652	174	21	𝑚	𝑚	ADP
cana-1652	174	22	−	−	NOUN
cana-1652	174	23	𝑘	𝑘	PRON
cana-1652	174	24	−	−	PROPN
cana-1652	174	25	1	1	NUM
cana-1652	174	26	edges	edge	NOUN
cana-1652	174	27	in	in	ADP
cana-1652	174	28	𝐺	𝐺	PROPN
cana-1652	174	29	that	that	PRON
cana-1652	174	30	are	be	AUX
cana-1652	174	31	not	not	PART
cana-1652	174	32	in	in	ADP
cana-1652	174	33	𝑇.	𝑇.	PROPN
cana-1652	174	34	let	let	VERB
cana-1652	174	35	𝑆	𝑆	PROPN
cana-1652	174	36	be	be	AUX
cana-1652	174	37	a	a	DET
cana-1652	174	38	set	set	NOUN
cana-1652	174	39	of	of	ADP
cana-1652	174	40	vertices	vertex	NOUN
cana-1652	174	41	obtained	obtain	VERB
cana-1652	174	42	as	as	ADP
cana-1652	174	43	follows	follow	VERB
cana-1652	174	44	:	:	PUNCT
cana-1652	174	45	for	for	SCONJ
cana-1652	174	46	each	each	DET
cana-1652	174	47	edge	edge	NOUN
cana-1652	174	48	𝑒	𝑒	VERB
cana-1652	174	49	in	in	ADP
cana-1652	174	50	𝐺	𝐺	PROPN
cana-1652	174	51	that	that	PRON
cana-1652	174	52	is	be	AUX
cana-1652	174	53	not	not	PART
cana-1652	174	54	in	in	ADP
cana-1652	174	55	𝑇	𝑇	PROPN
cana-1652	174	56	,	,	PUNCT
cana-1652	174	57	choose	choose	VERB
cana-1652	174	58	an	an	DET
cana-1652	174	59	endpoint	endpoint	NOUN
cana-1652	174	60	of	of	ADP
cana-1652	174	61	𝑒	𝑒	PRON
cana-1652	174	62	and	and	CCONJ
cana-1652	174	63	add	add	VERB
cana-1652	174	64	it	it	PRON
cana-1652	174	65	to	to	ADP
cana-1652	174	66	𝑆.	𝑆.	PROPN
cana-1652	174	67	since	since	SCONJ
cana-1652	174	68	each	each	DET
cana-1652	174	69	edge	edge	NOUN
cana-1652	174	70	in	in	ADP
cana-1652	174	71	𝐺	𝐺	PROPN
cana-1652	174	72	has	have	VERB
cana-1652	174	73	at	at	ADV
cana-1652	174	74	least	least	ADV
cana-1652	174	75	one	one	NUM
cana-1652	174	76	endpoint	endpoint	NOUN
cana-1652	174	77	in	in	ADP
cana-1652	174	78	𝑇	𝑇	PROPN
cana-1652	174	79	,	,	PUNCT
cana-1652	174	80	we	we	PRON
cana-1652	174	81	have	have	AUX
cana-1652	174	82	|𝑆|	|𝑆|	VERB
cana-1652	174	83	≥	≥	NOUN
cana-1652	174	84	𝑚	𝑚	ADP
cana-1652	174	85	−	−	PROPN
cana-1652	174	86	𝑘	𝑘	PRON
cana-1652	174	87	−	−	PROPN
cana-1652	174	88	1	1	X
cana-1652	174	89	.	.	PUNCT
cana-1652	175	1	we	we	PRON
cana-1652	175	2	claim	claim	VERB
cana-1652	175	3	that	that	SCONJ
cana-1652	175	4	𝑆	𝑆	PROPN
cana-1652	175	5	is	be	AUX
cana-1652	175	6	a	a	DET
cana-1652	175	7	dominating	dominating	NOUN
cana-1652	175	8	set	set	NOUN
cana-1652	175	9	of	of	ADP
cana-1652	175	10	𝐺.	𝐺.	NOUN
cana-1652	175	11	to	to	PART
cana-1652	175	12	see	see	VERB
cana-1652	175	13	this	this	PRON
cana-1652	175	14	,	,	PUNCT
cana-1652	175	15	let	let	VERB
cana-1652	175	16	𝑣	𝑣	PART
cana-1652	175	17	be	be	AUX
cana-1652	175	18	any	any	DET
cana-1652	175	19	vertex	vertex	NOUN
cana-1652	175	20	in	in	ADP
cana-1652	175	21	𝑉.	𝑉.	PROPN
cana-1652	175	22	if	if	SCONJ
cana-1652	175	23	𝑣	𝑣	PRON
cana-1652	175	24	is	be	AUX
cana-1652	175	25	in	in	ADP
cana-1652	175	26	𝑇	𝑇	PROPN
cana-1652	175	27	,	,	PUNCT
cana-1652	175	28	then	then	ADV
cana-1652	175	29	𝑣	𝑣	PRON
cana-1652	175	30	has	have	VERB
cana-1652	175	31	a	a	DET
cana-1652	175	32	neighbor	neighbor	NOUN
cana-1652	175	33	𝑢	𝑢	NOUN
cana-1652	175	34	in	in	ADP
cana-1652	175	35	𝑇.	𝑇.	PROPN
cana-1652	175	36	since	since	SCONJ
cana-1652	175	37	𝑇	𝑇	PROPN
cana-1652	175	38	is	be	AUX
cana-1652	175	39	a	a	DET
cana-1652	175	40	tree	tree	NOUN
cana-1652	175	41	,	,	PUNCT
cana-1652	175	42	there	there	PRON
cana-1652	175	43	is	be	VERB
cana-1652	175	44	a	a	DET
cana-1652	175	45	unique	unique	ADJ
cana-1652	175	46	path	path	NOUN
cana-1652	175	47	from	from	ADP
cana-1652	175	48	𝑢	𝑢	PRON
cana-1652	175	49	to	to	ADP
cana-1652	175	50	𝑣	𝑣	ADP
cana-1652	175	51	in	in	ADP
cana-1652	175	52	𝑇.	𝑇.	PROPN
cana-1652	175	53	let	let	VERB
cana-1652	175	54	𝑒	𝑒	PART
cana-1652	175	55	be	be	AUX
cana-1652	175	56	the	the	DET
cana-1652	175	57	edge	edge	NOUN
cana-1652	175	58	on	on	ADP
cana-1652	175	59	this	this	DET
cana-1652	175	60	path	path	NOUN
cana-1652	175	61	that	that	PRON
cana-1652	175	62	is	be	AUX
cana-1652	175	63	closest	close	ADJ
cana-1652	175	64	to	to	AUX
cana-1652	175	65	𝑣.	𝑣.	VERB
cana-1652	175	66	then	then	ADV
cana-1652	175	67	𝑒	𝑒	PROPN
cana-1652	175	68	is	be	AUX
cana-1652	175	69	not	not	PART
cana-1652	175	70	in	in	ADP
cana-1652	175	71	𝑇	𝑇	PROPN
cana-1652	175	72	and	and	CCONJ
cana-1652	175	73	one	one	NUM
cana-1652	175	74	endpoint	endpoint	NOUN
cana-1652	175	75	of	of	ADP
cana-1652	175	76	𝑒	𝑒	PROPN
cana-1652	175	77	belongs	belong	VERB
cana-1652	175	78	to	to	ADP
cana-1652	175	79	𝑆.	𝑆.	PROPN
cana-1652	175	80	thus	thus	ADV
cana-1652	175	81	,	,	PUNCT
cana-1652	175	82	this	this	DET
cana-1652	175	83	endpoint	endpoint	NOUN
cana-1652	175	84	dominates	dominate	VERB
cana-1652	175	85	𝑣.	𝑣.	NOUN
cana-1652	175	86	if	if	SCONJ
cana-1652	175	87	𝑣	𝑣	PRON
cana-1652	175	88	is	be	AUX
cana-1652	175	89	not	not	PART
cana-1652	175	90	in	in	ADP
cana-1652	175	91	𝑇	𝑇	PROPN
cana-1652	175	92	,	,	PUNCT
cana-1652	175	93	then	then	ADV
cana-1652	175	94	there	there	PRON
cana-1652	175	95	is	be	VERB
cana-1652	175	96	an	an	DET
cana-1652	175	97	edge	edge	NOUN
cana-1652	175	98	𝑒	𝑒	NOUN
cana-1652	175	99	=	=	SYM
cana-1652	175	100	𝑢	𝑢	NOUN
cana-1652	175	101	,	,	PUNCT
cana-1652	175	102	𝑤	𝑤	X
cana-1652	175	103	in	in	ADP
cana-1652	175	104	𝐺	𝐺	PROPN
cana-1652	175	105	such	such	ADJ
cana-1652	175	106	that	that	SCONJ
cana-1652	175	107	𝑢	𝑢	PROPN
cana-1652	175	108	∈	∈	PROPN
cana-1652	175	109	𝑇	𝑇	PROPN
cana-1652	175	110	and	and	CCONJ
cana-1652	175	111	𝑤	𝑤	ADP
cana-1652	175	112	∈	∈	PROPN
cana-1652	175	113	𝑆	𝑆	PROPN
cana-1652	175	114	(	(	PUNCT
cana-1652	175	115	since	since	SCONJ
cana-1652	175	116	𝑤	𝑤	NOUN
cana-1652	175	117	was	be	AUX
cana-1652	175	118	added	add	VERB
cana-1652	175	119	to	to	ADP
cana-1652	175	120	𝑆	𝑆	PROPN
cana-1652	175	121	when	when	SCONJ
cana-1652	175	122	we	we	PRON
cana-1652	175	123	chose	choose	VERB
cana-1652	175	124	the	the	DET
cana-1652	175	125	endpoint	endpoint	NOUN
cana-1652	175	126	of	of	ADP
cana-1652	175	127	𝑒	𝑒	PROPN
cana-1652	175	128	that	that	PRON
cana-1652	175	129	does	do	AUX
cana-1652	175	130	not	not	PART
cana-1652	175	131	belong	belong	VERB
cana-1652	175	132	to	to	ADP
cana-1652	175	133	𝑇	𝑇	PROPN
cana-1652	175	134	)	)	PUNCT
cana-1652	175	135	.	.	PUNCT
cana-1652	176	1	since	since	SCONJ
cana-1652	176	2	𝑢	𝑢	PRON
cana-1652	176	3	dominates	dominate	VERB
cana-1652	176	4	𝑤	𝑤	ADP
cana-1652	176	5	and	and	CCONJ
cana-1652	176	6	𝑤	𝑤	AUX
cana-1652	176	7	dominates	dominate	VERB
cana-1652	176	8	𝑣	𝑣	X
cana-1652	176	9	(	(	PUNCT
cana-1652	176	10	by	by	ADP
cana-1652	176	11	construction	construction	NOUN
cana-1652	176	12	)	)	PUNCT
cana-1652	176	13	,	,	PUNCT
cana-1652	176	14	we	we	PRON
cana-1652	176	15	have	have	VERB
cana-1652	176	16	that	that	SCONJ
cana-1652	176	17	𝑢	𝑢	PROPN
cana-1652	176	18	dominates	dominate	VERB
cana-1652	176	19	𝑣.	𝑣.	ADV
cana-1652	176	20	therefore	therefore	ADV
cana-1652	176	21	,	,	PUNCT
cana-1652	176	22	𝑆	𝑆	PROPN
cana-1652	176	23	is	be	AUX
cana-1652	176	24	a	a	DET
cana-1652	176	25	dominating	dominating	NOUN
cana-1652	176	26	set	set	NOUN
cana-1652	176	27	of	of	ADP
cana-1652	176	28	𝐺.	𝐺.	NOUN
cana-1652	176	29	to	to	PART
cana-1652	176	30	bound	bind	VERB
cana-1652	176	31	the	the	DET
cana-1652	176	32	size	size	NOUN
cana-1652	176	33	of	of	ADP
cana-1652	176	34	𝑆	𝑆	PROPN
cana-1652	176	35	from	from	ADP
cana-1652	176	36	above	above	ADV
cana-1652	176	37	,	,	PUNCT
cana-1652	176	38	note	note	VERB
cana-1652	176	39	that	that	SCONJ
cana-1652	176	40	each	each	DET
cana-1652	176	41	vertex	vertex	NOUN
cana-1652	176	42	added	add	VERB
cana-1652	176	43	to	to	ADP
cana-1652	176	44	𝑆	𝑆	PROPN
cana-1652	176	45	contributes	contribute	VERB
cana-1652	176	46	at	at	ADP
cana-1652	176	47	most	most	ADJ
cana-1652	176	48	one	one	NUM
cana-1652	176	49	to	to	ADP
cana-1652	176	50	its	its	PRON
cana-1652	176	51	cardinality	cardinality	NOUN
cana-1652	176	52	(	(	PUNCT
cana-1652	176	53	since	since	SCONJ
cana-1652	176	54	each	each	DET
cana-1652	176	55	non	non	ADJ
cana-1652	176	56	-	-	ADJ
cana-1652	176	57	tree	tree	ADJ
cana-1652	176	58	edge	edge	NOUN
cana-1652	176	59	has	have	VERB
cana-1652	176	60	exactly	exactly	ADV
cana-1652	176	61	one	one	NUM
cana-1652	176	62	endpoint	endpoint	NOUN
cana-1652	176	63	)	)	PUNCT
cana-1652	176	64	.	.	PUNCT
cana-1652	177	1	thus	thus	ADV
cana-1652	177	2	,	,	PUNCT
cana-1652	177	3	|𝑆|	|𝑆|	VERB
cana-1652	177	4	≤	≤	NOUN
cana-1652	177	5	𝑚	𝑚	ADP
cana-1652	177	6	−	−	PROPN
cana-1652	177	7	𝑘	𝑘	PRON
cana-1652	177	8	−	−	PROPN
cana-1652	177	9	1	1	NUM
cana-1652	177	10	on	on	ADP
cana-1652	177	11	the	the	DET
cana-1652	177	12	other	other	ADJ
cana-1652	177	13	hand	hand	NOUN
cana-1652	177	14	,	,	PUNCT
cana-1652	177	15	since	since	SCONJ
cana-1652	177	16	𝑆	𝑆	PROPN
cana-1652	177	17	is	be	AUX
cana-1652	177	18	a	a	DET
cana-1652	177	19	dominating	dominating	NOUN
cana-1652	177	20	set	set	NOUN
cana-1652	177	21	of	of	ADP
cana-1652	177	22	𝐺	𝐺	PROPN
cana-1652	177	23	,	,	PUNCT
cana-1652	177	24	each	each	DET
cana-1652	177	25	vertex	vertex	NOUN
cana-1652	177	26	in	in	ADP
cana-1652	177	27	𝑉	𝑉	PROPN
cana-1652	177	28	−	−	PROPN
cana-1652	177	29	𝑆	𝑆	PROPN
cana-1652	177	30	is	be	AUX
cana-1652	177	31	adjacent	adjacent	ADJ
cana-1652	177	32	to	to	ADP
cana-1652	177	33	at	at	ADV
cana-1652	177	34	least	least	ADV
cana-1652	177	35	one	one	NUM
cana-1652	177	36	vertex	vertex	NOUN
cana-1652	177	37	in	in	ADP
cana-1652	177	38	𝑆.	𝑆.	PROPN
cana-1652	177	39	thus	thus	ADV
cana-1652	177	40	,	,	PUNCT
cana-1652	177	41	we	we	PRON
cana-1652	177	42	have	have	VERB
cana-1652	177	43	:	:	PUNCT
cana-1652	177	44	𝑛	𝑛	DET
cana-1652	177	45	−	−	PROPN
cana-1652	177	46	|𝑆|	|𝑆|	ADJ
cana-1652	177	47	≤	≤	ADJ
cana-1652	177	48	𝑘𝑚	𝑘𝑚	NOUN
cana-1652	177	49	combining	combine	VERB
cana-1652	177	50	this	this	PRON
cana-1652	177	51	with	with	ADP
cana-1652	177	52	the	the	DET
cana-1652	177	53	previous	previous	ADJ
cana-1652	177	54	inequality	inequality	NOUN
cana-1652	177	55	,	,	PUNCT
cana-1652	177	56	we	we	PRON
cana-1652	177	57	obtain	obtain	VERB
cana-1652	177	58	:	:	PUNCT
cana-1652	177	59	|𝑆|	|𝑆|	VERB
cana-1652	177	60	≥	≥	NOUN
cana-1652	178	1	𝑛	𝑛	PRON
cana-1652	178	2	−	−	NOUN
cana-1652	179	1	𝑘𝑚	𝑘𝑚	NOUN
cana-1652	179	2	therefore	therefore	ADV
cana-1652	179	3	,	,	PUNCT
cana-1652	179	4	we	we	PRON
cana-1652	179	5	have	have	VERB
cana-1652	179	6	:	:	PUNCT
cana-1652	179	7	𝑛	𝑛	DET
cana-1652	179	8	−	−	NOUN
cana-1652	179	9	𝑘𝑚	𝑘𝑚	NOUN
cana-1652	179	10	≤	≤	NOUN
cana-1652	179	11	|𝑆|	|𝑆|	VERB
cana-1652	179	12	≤	≤	NOUN
cana-1652	179	13	𝑚	𝑚	ADP
cana-1652	179	14	−	−	PROPN
cana-1652	179	15	𝑘	𝑘	DET
cana-1652	179	16	−	−	PROPN
cana-1652	179	17	1	1	NUM
cana-1652	179	18	dividing	divide	VERB
cana-1652	179	19	both	both	DET
cana-1652	179	20	sides	side	NOUN
cana-1652	179	21	by	by	ADP
cana-1652	179	22	𝑚	𝑚	PROPN
cana-1652	179	23	−	−	PROPN
cana-1652	179	24	𝑘	𝑘	PROPN
cana-1652	179	25	and	and	CCONJ
cana-1652	179	26	taking	take	VERB
cana-1652	179	27	the	the	DET
cana-1652	179	28	floor	floor	NOUN
cana-1652	179	29	function	function	NOUN
cana-1652	179	30	yields	yield	NOUN
cana-1652	179	31	:	:	PUNCT
cana-1652	179	32	⌊	⌊	PROPN
cana-1652	179	33	𝑛−𝑘−1	𝑛−𝑘−1	PROPN
cana-1652	179	34	𝑚−𝑘	𝑚−𝑘	NOUN
cana-1652	179	35	⌋	⌋	NOUN
cana-1652	179	36	+	+	CCONJ
cana-1652	179	37	1	1	NUM
cana-1652	179	38	≥	≥	NOUN
cana-1652	179	39	⌊	⌊	NOUN
cana-1652	179	40	𝑛−𝑘𝑚	𝑛−𝑘𝑚	VERB
cana-1652	179	41	𝑚−𝑘	𝑚−𝑘	NOUN
cana-1652	179	42	⌋	⌋	NOUN
cana-1652	179	43	+	+	CCONJ
cana-1652	180	1	1	1	X
cana-1652	180	2	.	.	PUNCT
cana-1652	180	3	since	since	SCONJ
cana-1652	180	4	⌊	⌊	PROPN
cana-1652	180	5	𝑛−𝑘𝑚	𝑛−𝑘𝑚	VERB
cana-1652	180	6	𝑚−𝑘	𝑚−𝑘	NOUN
cana-1652	180	7	⌋	⌋	NOUN
cana-1652	180	8	=	=	PUNCT
cana-1652	180	9	⌊	⌊	PROPN
cana-1652	180	10	𝑛−𝑘−1	𝑛−𝑘−1	PROPN
cana-1652	180	11	𝑚−𝑘	𝑚−𝑘	NOUN
cana-1652	180	12	⌋	⌋	NOUN
cana-1652	180	13	,	,	PUNCT
cana-1652	180	14	we	we	PRON
cana-1652	180	15	have	have	AUX
cana-1652	180	16	:	:	PUNCT
cana-1652	180	17	⌊	⌊	PROPN
cana-1652	180	18	𝑛−𝑘−1	𝑛−𝑘−1	PROPN
cana-1652	180	19	𝑚−𝑘	𝑚−𝑘	NOUN
cana-1652	180	20	⌋	⌋	NOUN
cana-1652	180	21	+	+	CCONJ
cana-1652	180	22	1	1	NUM
cana-1652	180	23	≥	≥	NOUN
cana-1652	180	24	⌊	⌊	X
cana-1652	180	25	𝑛−𝑚+1	𝑛−𝑚+1	PROPN
cana-1652	180	26	𝑚−𝑘	𝑚−𝑘	NOUN
cana-1652	180	27	⌋	⌋	NOUN
cana-1652	180	28	+	+	CCONJ
cana-1652	180	29	1	1	X
cana-1652	180	30	.	.	X
cana-1652	180	31	therefore	therefore	ADV
cana-1652	180	32	,	,	PUNCT
cana-1652	180	33	we	we	PRON
cana-1652	180	34	have	have	AUX
cana-1652	180	35	shown	show	VERB
cana-1652	180	36	that	that	SCONJ
cana-1652	180	37	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	180	38	)	)	PUNCT
cana-1652	180	39	≤	≤	PUNCT
cana-1652	180	40	⌊	⌊	PUNCT
cana-1652	180	41	𝑛−𝑚+1	𝑛−𝑚+1	PROPN
cana-1652	180	42	𝑚−𝑘	𝑚−𝑘	NOUN
cana-1652	180	43	⌋	⌋	NOUN
cana-1652	180	44	+	+	CCONJ
cana-1652	180	45	1	1	X
cana-1652	180	46	.	.	X
cana-1652	180	47	communications	communication	NOUN
cana-1652	180	48	on	on	ADP
cana-1652	180	49	applied	apply	VERB
cana-1652	180	50	nonlinear	nonlinear	ADJ
cana-1652	180	51	analysis	analysis	NOUN
cana-1652	180	52	issn	issn	NOUN
cana-1652	180	53	:	:	PUNCT
cana-1652	180	54	1074	1074	NUM
cana-1652	180	55	-	-	PUNCT
cana-1652	180	56	133x	133x	NUM
cana-1652	180	57	vol	vol	NOUN
cana-1652	180	58	32	32	NUM
cana-1652	180	59	no	no	NOUN
cana-1652	180	60	.	.	NOUN
cana-1652	180	61	1	1	NUM
cana-1652	180	62	(	(	PUNCT
cana-1652	180	63	2025	2025	NUM
cana-1652	180	64	)	)	PUNCT
cana-1652	180	65	331	331	NUM
cana-1652	180	66	https://internationalpubls.com	https://internationalpubls.com	X
cana-1652	180	67	theorem	theorem	VERB
cana-1652	180	68	2.13	2.13	NUM
cana-1652	180	69	let	let	VERB
cana-1652	180	70	𝐺	𝐺	PROPN
cana-1652	180	71	=	=	SYM
cana-1652	180	72	(	(	PUNCT
cana-1652	180	73	𝑉	𝑉	PROPN
cana-1652	180	74	,	,	PUNCT
cana-1652	180	75	𝐸	𝐸	PROPN
cana-1652	180	76	,	,	PUNCT
cana-1652	180	77	𝜇	𝜇	NOUN
cana-1652	180	78	)	)	PUNCT
cana-1652	180	79	be	be	AUX
cana-1652	180	80	a	a	DET
cana-1652	180	81	fuzzy	fuzzy	ADJ
cana-1652	180	82	graph	graph	NOUN
cana-1652	180	83	with	with	ADP
cana-1652	180	84	𝑛	𝑛	PROPN
cana-1652	180	85	vertices	vertex	NOUN
cana-1652	180	86	and	and	CCONJ
cana-1652	180	87	𝑚	𝑚	ADP
cana-1652	180	88	edges	edge	NOUN
cana-1652	180	89	.	.	PUNCT
cana-1652	181	1	if	if	SCONJ
cana-1652	181	2	𝐺	𝐺	PROPN
cana-1652	181	3	is	be	AUX
cana-1652	181	4	connected	connect	VERB
cana-1652	181	5	and	and	CCONJ
cana-1652	181	6	𝑚	𝑚	ADP
cana-1652	181	7	≥	≥	NOUN
cana-1652	181	8	𝑛	𝑛	PRON
cana-1652	181	9	−	−	NUM
cana-1652	181	10	1	1	NUM
cana-1652	181	11	,	,	PUNCT
cana-1652	181	12	then	then	ADV
cana-1652	181	13	𝛾(𝐺	𝛾(𝐺	NUM
cana-1652	181	14	)	)	PUNCT
cana-1652	182	1	=	=	SYM
cana-1652	182	2	1	1	X
cana-1652	182	3	.	.	X
cana-1652	183	1	proof	proof	NOUN
cana-1652	183	2	:	:	PUNCT
cana-1652	183	3	let	let	VERB
cana-1652	183	4	𝐺	𝐺	PROPN
cana-1652	183	5	=	=	SYM
cana-1652	183	6	(	(	PUNCT
cana-1652	183	7	𝑉	𝑉	PROPN
cana-1652	183	8	,	,	PUNCT
cana-1652	183	9	𝐸	𝐸	PROPN
cana-1652	183	10	,	,	PUNCT
cana-1652	183	11	𝜇	𝜇	NOUN
cana-1652	183	12	)	)	PUNCT
cana-1652	183	13	be	be	AUX
cana-1652	183	14	a	a	DET
cana-1652	183	15	fuzzy	fuzzy	ADJ
cana-1652	183	16	graph	graph	NOUN
cana-1652	183	17	with	with	ADP
cana-1652	183	18	𝑛	𝑛	PROPN
cana-1652	183	19	vertices	vertex	NOUN
cana-1652	183	20	and	and	CCONJ
cana-1652	183	21	𝑚	𝑚	ADP
cana-1652	183	22	edges	edge	NOUN
cana-1652	183	23	.	.	PUNCT
cana-1652	184	1	suppose	suppose	VERB
cana-1652	184	2	that	that	SCONJ
cana-1652	184	3	𝐺	𝐺	PROPN
cana-1652	184	4	is	be	AUX
cana-1652	184	5	connected	connect	VERB
cana-1652	184	6	and	and	CCONJ
cana-1652	184	7	𝑚	𝑚	ADP
cana-1652	184	8	≥	≥	NOUN
cana-1652	184	9	𝑛	𝑛	PRON
cana-1652	184	10	−	−	NOUN
cana-1652	184	11	1	1	NUM
cana-1652	184	12	.	.	PUNCT
cana-1652	185	1	we	we	PRON
cana-1652	185	2	need	need	VERB
cana-1652	185	3	to	to	PART
cana-1652	185	4	show	show	VERB
cana-1652	185	5	that	that	SCONJ
cana-1652	185	6	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	185	7	)	)	PUNCT
cana-1652	185	8	=	=	SYM
cana-1652	186	1	1	1	X
cana-1652	186	2	.	.	PUNCT
cana-1652	186	3	let	let	VERB
cana-1652	186	4	𝑇	𝑇	PROPN
cana-1652	186	5	be	be	AUX
cana-1652	186	6	a	a	DET
cana-1652	186	7	spanning	span	VERB
cana-1652	186	8	tree	tree	NOUN
cana-1652	186	9	of	of	ADP
cana-1652	186	10	𝐺.	𝐺.	NOUN
cana-1652	186	11	since	since	SCONJ
cana-1652	186	12	𝑇	𝑇	PROPN
cana-1652	186	13	has	have	VERB
cana-1652	186	14	𝑛	𝑛	DET
cana-1652	186	15	−	−	NUM
cana-1652	186	16	1	1	NUM
cana-1652	186	17	edges	edge	NOUN
cana-1652	186	18	,	,	PUNCT
cana-1652	186	19	there	there	PRON
cana-1652	186	20	is	be	VERB
cana-1652	186	21	at	at	ADP
cana-1652	186	22	most	most	ADV
cana-1652	186	23	one	one	NUM
cana-1652	186	24	edge	edge	NOUN
cana-1652	186	25	in	in	ADP
cana-1652	186	26	𝐺	𝐺	PROPN
cana-1652	186	27	that	that	PRON
cana-1652	186	28	is	be	AUX
cana-1652	186	29	not	not	PART
cana-1652	186	30	in	in	ADP
cana-1652	186	31	𝑇.	𝑇.	PROPN
cana-1652	186	32	let	let	VERB
cana-1652	186	33	𝑒	𝑒	PART
cana-1652	186	34	be	be	AUX
cana-1652	186	35	this	this	DET
cana-1652	186	36	edge	edge	NOUN
cana-1652	186	37	(	(	PUNCT
cana-1652	186	38	if	if	SCONJ
cana-1652	186	39	it	it	PRON
cana-1652	186	40	exists	exist	VERB
cana-1652	186	41	)	)	PUNCT
cana-1652	186	42	.	.	PUNCT
cana-1652	187	1	then	then	ADV
cana-1652	187	2	𝑒	𝑒	PROPN
cana-1652	187	3	connects	connect	VERB
cana-1652	187	4	two	two	NUM
cana-1652	187	5	vertices	vertex	NOUN
cana-1652	187	6	𝑢	𝑢	NOUN
cana-1652	187	7	and	and	CCONJ
cana-1652	187	8	𝑣	𝑣	X
cana-1652	187	9	in	in	ADP
cana-1652	187	10	𝑇	𝑇	PROPN
cana-1652	187	11	,	,	PUNCT
cana-1652	187	12	and	and	CCONJ
cana-1652	187	13	we	we	PRON
cana-1652	187	14	can	can	AUX
cana-1652	187	15	add	add	VERB
cana-1652	187	16	𝑒	𝑒	PUNCT
cana-1652	187	17	to	to	ADP
cana-1652	187	18	𝑇	𝑇	PROPN
cana-1652	187	19	to	to	PART
cana-1652	187	20	obtain	obtain	VERB
cana-1652	187	21	a	a	DET
cana-1652	187	22	spanning	span	VERB
cana-1652	187	23	tree	tree	NOUN
cana-1652	187	24	of	of	ADP
cana-1652	187	25	𝐺.	𝐺.	NOUN
cana-1652	187	26	since	since	SCONJ
cana-1652	187	27	every	every	DET
cana-1652	187	28	vertex	vertex	NOUN
cana-1652	187	29	in	in	ADP
cana-1652	187	30	𝐺	𝐺	PROPN
cana-1652	187	31	is	be	AUX
cana-1652	187	32	connected	connect	VERB
cana-1652	187	33	to	to	ADP
cana-1652	187	34	some	some	DET
cana-1652	187	35	vertex	vertex	NOUN
cana-1652	187	36	in	in	ADP
cana-1652	187	37	𝑇	𝑇	PROPN
cana-1652	187	38	by	by	ADP
cana-1652	187	39	a	a	DET
cana-1652	187	40	unique	unique	ADJ
cana-1652	187	41	path	path	NOUN
cana-1652	187	42	,	,	PUNCT
cana-1652	187	43	it	it	PRON
cana-1652	187	44	follows	follow	VERB
cana-1652	187	45	that	that	SCONJ
cana-1652	187	46	every	every	DET
cana-1652	187	47	vertex	vertex	NOUN
cana-1652	187	48	in	in	ADP
cana-1652	187	49	𝑉	𝑉	PROPN
cana-1652	187	50	−	−	PROPN
cana-1652	187	51	𝑇	𝑇	PROPN
cana-1652	187	52	is	be	AUX
cana-1652	187	53	adjacent	adjacent	ADJ
cana-1652	187	54	to	to	ADP
cana-1652	187	55	either	either	CCONJ
cana-1652	187	56	𝑢	𝑢	NOUN
cana-1652	187	57	or	or	CCONJ
cana-1652	187	58	𝑣.	𝑣.	PROPN
cana-1652	187	59	therefore	therefore	ADV
cana-1652	187	60	,	,	PUNCT
cana-1652	187	61	𝑢	𝑢	X
cana-1652	187	62	,	,	PUNCT
cana-1652	187	63	𝑣	𝑣	PRON
cana-1652	187	64	is	be	AUX
cana-1652	187	65	a	a	DET
cana-1652	187	66	dominating	dominating	NOUN
cana-1652	187	67	set	set	NOUN
cana-1652	187	68	of	of	ADP
cana-1652	187	69	𝐺.	𝐺.	NOUN
cana-1652	187	70	thus	thus	ADV
cana-1652	187	71	,	,	PUNCT
cana-1652	187	72	we	we	PRON
cana-1652	187	73	have	have	AUX
cana-1652	187	74	shown	show	VERB
cana-1652	187	75	that	that	SCONJ
cana-1652	187	76	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	187	77	)	)	PUNCT
cana-1652	187	78	≤	≤	NUM
cana-1652	187	79	1	1	NUM
cana-1652	187	80	.	.	PUNCT
cana-1652	188	1	on	on	ADP
cana-1652	188	2	the	the	DET
cana-1652	188	3	other	other	ADJ
cana-1652	188	4	hand	hand	NOUN
cana-1652	188	5	,	,	PUNCT
cana-1652	188	6	since	since	SCONJ
cana-1652	188	7	𝐺	𝐺	PROPN
cana-1652	188	8	is	be	AUX
cana-1652	188	9	connected	connect	VERB
cana-1652	188	10	,	,	PUNCT
cana-1652	188	11	there	there	PRON
cana-1652	188	12	exists	exist	VERB
cana-1652	188	13	at	at	ADV
cana-1652	188	14	least	least	ADV
cana-1652	188	15	one	one	NUM
cana-1652	188	16	dominating	dominating	NOUN
cana-1652	188	17	set	set	NOUN
cana-1652	188	18	of	of	ADP
cana-1652	188	19	size	size	NOUN
cana-1652	188	20	1	1	NUM
cana-1652	188	21	(	(	PUNCT
cana-1652	188	22	namely	namely	ADV
cana-1652	188	23	any	any	DET
cana-1652	188	24	singleton	singleton	NOUN
cana-1652	188	25	set	set	NOUN
cana-1652	188	26	containing	contain	VERB
cana-1652	188	27	a	a	DET
cana-1652	188	28	vertex	vertex	NOUN
cana-1652	188	29	of	of	ADP
cana-1652	188	30	𝐺	𝐺	PROPN
cana-1652	188	31	)	)	PUNCT
cana-1652	188	32	.	.	PUNCT
cana-1652	189	1	therefore	therefore	ADV
cana-1652	189	2	,	,	PUNCT
cana-1652	189	3	we	we	PRON
cana-1652	189	4	have	have	VERB
cana-1652	189	5	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	189	6	)	)	PUNCT
cana-1652	189	7	≥	≥	NOUN
cana-1652	190	1	1	1	NUM
cana-1652	190	2	.	.	PUNCT
cana-1652	190	3	combining	combine	VERB
cana-1652	190	4	these	these	DET
cana-1652	190	5	inequalities	inequality	NOUN
cana-1652	190	6	yields	yield	NOUN
cana-1652	190	7	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1652	190	8	)	)	PUNCT
cana-1652	191	1	=	=	SYM
cana-1652	191	2	1	1	NUM
cana-1652	191	3	,	,	PUNCT
cana-1652	191	4	as	as	SCONJ
cana-1652	191	5	desired	desire	VERB
cana-1652	191	6	.	.	PUNCT
cana-1652	192	1	theorem	theorem	VERB
cana-1652	192	2	2.14	2.14	NUM
cana-1652	192	3	let	let	VERB
cana-1652	192	4	𝐺	𝐺	PROPN
cana-1652	192	5	=	=	SYM
cana-1652	192	6	(	(	PUNCT
cana-1652	192	7	𝑉	𝑉	PROPN
cana-1652	192	8	,	,	PUNCT
cana-1652	192	9	𝐸	𝐸	PROPN
cana-1652	192	10	,	,	PUNCT
cana-1652	192	11	𝜇	𝜇	NOUN
cana-1652	192	12	)	)	PUNCT
cana-1652	192	13	be	be	AUX
cana-1652	192	14	a	a	DET
cana-1652	192	15	fuzzy	fuzzy	ADJ
cana-1652	192	16	graph	graph	NOUN
cana-1652	192	17	with	with	ADP
cana-1652	192	18	𝑛	𝑛	PROPN
cana-1652	192	19	vertices	vertex	NOUN
cana-1652	192	20	and	and	CCONJ
cana-1652	192	21	𝑚	𝑚	ADP
cana-1652	192	22	edges	edge	NOUN
cana-1652	192	23	.	.	PUNCT
cana-1652	193	1	suppose	suppose	VERB
cana-1652	193	2	that	that	SCONJ
cana-1652	193	3	𝐺	𝐺	PROPN
cana-1652	193	4	is	be	AUX
cana-1652	193	5	connected	connect	VERB
cana-1652	193	6	and	and	CCONJ
cana-1652	193	7	𝑚	𝑚	X
cana-1652	193	8	<	<	X
cana-1652	193	9	𝑛	𝑛	PRON
cana-1652	193	10	−	−	NOUN
cana-1652	193	11	1	1	NUM
cana-1652	193	12	.	.	PUNCT
cana-1652	194	1	we	we	PRON
cana-1652	194	2	need	need	VERB
cana-1652	194	3	to	to	PART
cana-1652	194	4	show	show	VERB
cana-1652	194	5	that	that	SCONJ
cana-1652	194	6	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	194	7	)	)	PUNCT
cana-1652	194	8	≤	≤	NOUN
cana-1652	194	9	⌊𝑛/2⌋.	⌊𝑛/2⌋.	X
cana-1652	194	10	proof	proof	NOUN
cana-1652	194	11	:	:	PUNCT
cana-1652	194	12	let	let	VERB
cana-1652	194	13	𝐺	𝐺	PROPN
cana-1652	194	14	=	=	SYM
cana-1652	194	15	(	(	PUNCT
cana-1652	194	16	𝑉	𝑉	PROPN
cana-1652	194	17	,	,	PUNCT
cana-1652	194	18	𝐸	𝐸	PROPN
cana-1652	194	19	,	,	PUNCT
cana-1652	194	20	𝜇	𝜇	NOUN
cana-1652	194	21	)	)	PUNCT
cana-1652	194	22	be	be	AUX
cana-1652	194	23	a	a	DET
cana-1652	194	24	fuzzy	fuzzy	ADJ
cana-1652	194	25	graph	graph	NOUN
cana-1652	194	26	with	with	ADP
cana-1652	194	27	𝑛	𝑛	PROPN
cana-1652	194	28	vertices	vertex	NOUN
cana-1652	194	29	and	and	CCONJ
cana-1652	194	30	𝑚	𝑚	ADP
cana-1652	194	31	edges	edge	NOUN
cana-1652	194	32	.	.	PUNCT
cana-1652	195	1	suppose	suppose	VERB
cana-1652	195	2	that	that	SCONJ
cana-1652	195	3	𝐺	𝐺	PROPN
cana-1652	195	4	is	be	AUX
cana-1652	195	5	connected	connect	VERB
cana-1652	195	6	and	and	CCONJ
cana-1652	195	7	𝑚	𝑚	X
cana-1652	195	8	<	<	X
cana-1652	195	9	𝑛	𝑛	PRON
cana-1652	195	10	−	−	NOUN
cana-1652	195	11	1	1	NUM
cana-1652	195	12	.	.	PUNCT
cana-1652	196	1	we	we	PRON
cana-1652	196	2	need	need	VERB
cana-1652	196	3	to	to	PART
cana-1652	196	4	show	show	VERB
cana-1652	196	5	that	that	SCONJ
cana-1652	196	6	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	196	7	)	)	PUNCT
cana-1652	196	8	≤	≤	NOUN
cana-1652	196	9	⌊𝑛/2⌋.	⌊𝑛/2⌋.	NOUN
cana-1652	196	10	let	let	VERB
cana-1652	196	11	𝑆	𝑆	PROPN
cana-1652	196	12	be	be	AUX
cana-1652	196	13	a	a	DET
cana-1652	196	14	dominating	dominating	NOUN
cana-1652	196	15	set	set	NOUN
cana-1652	196	16	of	of	ADP
cana-1652	196	17	𝐺.	𝐺.	NOUN
cana-1652	196	18	since	since	SCONJ
cana-1652	196	19	𝑆	𝑆	PROPN
cana-1652	196	20	is	be	AUX
cana-1652	196	21	a	a	DET
cana-1652	196	22	dominating	dominating	NOUN
cana-1652	196	23	set	set	NOUN
cana-1652	196	24	,	,	PUNCT
cana-1652	196	25	every	every	DET
cana-1652	196	26	vertex	vertex	NOUN
cana-1652	196	27	in	in	ADP
cana-1652	196	28	𝑉	𝑉	PROPN
cana-1652	196	29	−	−	PROPN
cana-1652	196	30	𝑆	𝑆	PROPN
cana-1652	196	31	is	be	AUX
cana-1652	196	32	adjacent	adjacent	ADJ
cana-1652	196	33	to	to	ADP
cana-1652	196	34	at	at	ADV
cana-1652	196	35	least	least	ADV
cana-1652	196	36	one	one	NUM
cana-1652	196	37	vertex	vertex	NOUN
cana-1652	196	38	in	in	ADP
cana-1652	196	39	𝑆.	𝑆.	PROPN
cana-1652	196	40	therefore	therefore	ADV
cana-1652	196	41	,	,	PUNCT
cana-1652	196	42	we	we	PRON
cana-1652	196	43	have	have	AUX
cana-1652	196	44	|𝑆|	|𝑆|	VERB
cana-1652	196	45	≥	≥	NOUN
cana-1652	196	46	𝑛	𝑛	PRON
cana-1652	196	47	−	−	PROPN
cana-1652	196	48	|𝑉	|𝑉	NUM
cana-1652	196	49	−	−	NOUN
cana-1652	196	50	𝑆|	𝑆|	PROPN
cana-1652	196	51	.	.	PUNCT
cana-1652	197	1	now	now	ADV
cana-1652	197	2	,	,	PUNCT
cana-1652	197	3	let	let	VERB
cana-1652	197	4	𝑇	𝑇	PROPN
cana-1652	197	5	be	be	AUX
cana-1652	197	6	the	the	DET
cana-1652	197	7	set	set	NOUN
cana-1652	197	8	of	of	ADP
cana-1652	197	9	vertices	vertex	NOUN
cana-1652	197	10	in	in	ADP
cana-1652	197	11	𝑉	𝑉	PROPN
cana-1652	197	12	−	−	PROPN
cana-1652	197	13	𝑆	𝑆	PROPN
cana-1652	197	14	that	that	PRON
cana-1652	197	15	are	be	AUX
cana-1652	197	16	adjacent	adjacent	ADJ
cana-1652	197	17	to	to	ADP
cana-1652	197	18	an	an	DET
cana-1652	197	19	odd	odd	ADJ
cana-1652	197	20	number	number	NOUN
cana-1652	197	21	of	of	ADP
cana-1652	197	22	vertices	vertex	NOUN
cana-1652	197	23	in	in	ADP
cana-1652	197	24	𝑆.	𝑆.	PROPN
cana-1652	197	25	since	since	SCONJ
cana-1652	197	26	every	every	DET
cana-1652	197	27	vertex	vertex	NOUN
cana-1652	197	28	in	in	ADP
cana-1652	197	29	𝑉	𝑉	PROPN
cana-1652	197	30	−	−	PROPN
cana-1652	197	31	𝑆	𝑆	PROPN
cana-1652	197	32	is	be	AUX
cana-1652	197	33	adjacent	adjacent	ADJ
cana-1652	197	34	to	to	ADP
cana-1652	197	35	at	at	ADV
cana-1652	197	36	least	least	ADV
cana-1652	197	37	one	one	NUM
cana-1652	197	38	vertex	vertex	NOUN
cana-1652	197	39	in	in	ADP
cana-1652	197	40	𝑆	𝑆	PROPN
cana-1652	197	41	,	,	PUNCT
cana-1652	197	42	it	it	PRON
cana-1652	197	43	follows	follow	VERB
cana-1652	197	44	that	that	SCONJ
cana-1652	197	45	𝑇	𝑇	PROPN
cana-1652	197	46	is	be	AUX
cana-1652	197	47	nonempty	nonempty	ADJ
cana-1652	197	48	.	.	PUNCT
cana-1652	198	1	we	we	PRON
cana-1652	198	2	claim	claim	VERB
cana-1652	198	3	that	that	SCONJ
cana-1652	198	4	|𝑇|	|𝑇|	PROPN
cana-1652	198	5	≤	≤	NOUN
cana-1652	198	6	⌊𝑛/2⌋.	⌊𝑛/2⌋.	NOUN
cana-1652	198	7	to	to	PART
cana-1652	198	8	see	see	VERB
cana-1652	198	9	why	why	SCONJ
cana-1652	198	10	this	this	PRON
cana-1652	198	11	is	be	AUX
cana-1652	198	12	true	true	ADJ
cana-1652	198	13	,	,	PUNCT
cana-1652	198	14	note	note	VERB
cana-1652	198	15	that	that	SCONJ
cana-1652	198	16	each	each	DET
cana-1652	198	17	vertex	vertex	NOUN
cana-1652	198	18	in	in	ADP
cana-1652	198	19	𝑇	𝑇	PROPN
cana-1652	198	20	contributes	contribute	VERB
cana-1652	198	21	an	an	DET
cana-1652	198	22	odd	odd	ADJ
cana-1652	198	23	number	number	NOUN
cana-1652	198	24	of	of	ADP
cana-1652	198	25	edges	edge	NOUN
cana-1652	198	26	to	to	ADP
cana-1652	198	27	the	the	DET
cana-1652	198	28	subgraph	subgraph	NOUN
cana-1652	198	29	induced	induce	VERB
cana-1652	198	30	by	by	ADP
cana-1652	198	31	𝑆	𝑆	PROPN
cana-1652	198	32	∪	∪	PROPN
cana-1652	198	33	𝑇.	𝑇.	PROPN
cana-1652	198	34	therefore	therefore	ADV
cana-1652	198	35	,	,	PUNCT
cana-1652	198	36	the	the	DET
cana-1652	198	37	total	total	ADJ
cana-1652	198	38	number	number	NOUN
cana-1652	198	39	of	of	ADP
cana-1652	198	40	edges	edge	NOUN
cana-1652	198	41	in	in	ADP
cana-1652	198	42	this	this	DET
cana-1652	198	43	subgraph	subgraph	NOUN
cana-1652	198	44	is	be	AUX
cana-1652	198	45	odd	odd	ADJ
cana-1652	198	46	.	.	PUNCT
cana-1652	199	1	on	on	ADP
cana-1652	199	2	the	the	DET
cana-1652	199	3	other	other	ADJ
cana-1652	199	4	hand	hand	NOUN
cana-1652	199	5	,	,	PUNCT
cana-1652	199	6	since	since	SCONJ
cana-1652	199	7	every	every	DET
cana-1652	199	8	vertex	vertex	NOUN
cana-1652	199	9	in	in	ADP
cana-1652	199	10	𝑉	𝑉	PROPN
cana-1652	199	11	−	−	PROPN
cana-1652	199	12	𝑆	𝑆	PROPN
cana-1652	199	13	is	be	AUX
cana-1652	199	14	adjacent	adjacent	ADJ
cana-1652	199	15	to	to	ADP
cana-1652	199	16	at	at	ADV
cana-1652	199	17	least	least	ADV
cana-1652	199	18	one	one	NUM
cana-1652	199	19	vertex	vertex	NOUN
cana-1652	199	20	in	in	ADP
cana-1652	199	21	𝑆	𝑆	PROPN
cana-1652	199	22	and	and	CCONJ
cana-1652	199	23	every	every	DET
cana-1652	199	24	vertex	vertex	NOUN
cana-1652	199	25	in	in	ADP
cana-1652	199	26	𝑇	𝑇	PROPN
cana-1652	199	27	is	be	AUX
cana-1652	199	28	adjacent	adjacent	ADJ
cana-1652	199	29	to	to	ADP
cana-1652	199	30	an	an	DET
cana-1652	199	31	odd	odd	ADJ
cana-1652	199	32	number	number	NOUN
cana-1652	199	33	of	of	ADP
cana-1652	199	34	vertices	vertex	NOUN
cana-1652	199	35	in	in	ADP
cana-1652	199	36	𝑆	𝑆	PROPN
cana-1652	199	37	,	,	PUNCT
cana-1652	199	38	it	it	PRON
cana-1652	199	39	follows	follow	VERB
cana-1652	199	40	that	that	SCONJ
cana-1652	199	41	every	every	DET
cana-1652	199	42	vertex	vertex	NOUN
cana-1652	199	43	not	not	PART
cana-1652	199	44	in	in	ADP
cana-1652	199	45	𝑇	𝑇	PROPN
cana-1652	199	46	is	be	AUX
cana-1652	199	47	adjacent	adjacent	ADJ
cana-1652	199	48	to	to	ADP
cana-1652	199	49	an	an	DET
cana-1652	199	50	even	even	ADJ
cana-1652	199	51	number	number	NOUN
cana-1652	199	52	of	of	ADP
cana-1652	199	53	vertices	vertex	NOUN
cana-1652	199	54	in	in	ADP
cana-1652	199	55	𝑆.	𝑆.	PROPN
cana-1652	199	56	therefore	therefore	ADV
cana-1652	199	57	,	,	PUNCT
cana-1652	199	58	the	the	DET
cana-1652	199	59	total	total	ADJ
cana-1652	199	60	number	number	NOUN
cana-1652	199	61	of	of	ADP
cana-1652	199	62	edges	edge	NOUN
cana-1652	199	63	between	between	ADP
cana-1652	199	64	𝑉	𝑉	PROPN
cana-1652	199	65	−	−	PROPN
cana-1652	199	66	𝑆	𝑆	PROPN
cana-1652	199	67	and	and	CCONJ
cana-1652	199	68	𝑆	𝑆	PROPN
cana-1652	199	69	∪	∪	NOUN
cana-1652	199	70	𝑇	𝑇	PROPN
cana-1652	199	71	is	be	AUX
cana-1652	199	72	even	even	ADV
cana-1652	199	73	.	.	PUNCT
cana-1652	200	1	since	since	SCONJ
cana-1652	200	2	the	the	DET
cana-1652	200	3	total	total	ADJ
cana-1652	200	4	number	number	NOUN
cana-1652	200	5	of	of	ADP
cana-1652	200	6	edges	edge	NOUN
cana-1652	200	7	between	between	ADP
cana-1652	200	8	𝑉	𝑉	PROPN
cana-1652	200	9	−	−	PROPN
cana-1652	200	10	𝑆	𝑆	PROPN
cana-1652	200	11	and	and	CCONJ
cana-1652	200	12	𝑆	𝑆	PROPN
cana-1652	200	13	∪	∪	NOUN
cana-1652	200	14	𝑇	𝑇	PROPN
cana-1652	200	15	must	must	AUX
cana-1652	200	16	be	be	AUX
cana-1652	200	17	equal	equal	ADJ
cana-1652	200	18	to	to	ADP
cana-1652	200	19	𝑚	𝑚	PROPN
cana-1652	200	20	−	−	PROPN
cana-1652	200	21	|𝑆|	|𝑆|	VERB
cana-1652	200	22	+	+	X
cana-1652	200	23	|𝑇|	|𝑇|	NOUN
cana-1652	200	24	(	(	PUNCT
cana-1652	200	25	counting	count	VERB
cana-1652	200	26	each	each	DET
cana-1652	200	27	edge	edge	NOUN
cana-1652	200	28	once	once	ADV
cana-1652	200	29	)	)	PUNCT
cana-1652	200	30	,	,	PUNCT
cana-1652	200	31	we	we	PRON
cana-1652	200	32	have	have	VERB
cana-1652	200	33	:	:	PUNCT
cana-1652	200	34	𝑚	𝑚	X
cana-1652	200	35	−	−	PROPN
cana-1652	200	36	|𝑆|	|𝑆|	VERB
cana-1652	200	37	+	+	X
cana-1652	200	38	|𝑇|	|𝑇|	PROPN
cana-1652	200	39	≡	≡	PROPN
cana-1652	200	40	1(mod2	1(mod2	NUM
cana-1652	200	41	)	)	PUNCT
cana-1652	200	42	or	or	CCONJ
cana-1652	200	43	equivalently	equivalently	ADV
cana-1652	200	44	,	,	PUNCT
cana-1652	200	45	|𝑚	|𝑚	ADP
cana-1652	200	46	−	−	NOUN
cana-1652	200	47	𝑛	𝑛	PROPN
cana-1652	200	48	+	+	CCONJ
cana-1652	200	49	|𝑆|	|𝑆|	VERB
cana-1652	200	50	−	−	NOUN
cana-1652	200	51	|𝑇||	|𝑇||	PROPN
cana-1652	200	52	≡	≡	PROPN
cana-1652	200	53	1(mod2	1(mod2	NUM
cana-1652	200	54	)	)	PUNCT
cana-1652	200	55	since	since	SCONJ
cana-1652	200	56	𝑚	𝑚	X
cana-1652	200	57	<	<	X
cana-1652	200	58	𝑛	𝑛	PRON
cana-1652	200	59	−	−	NUM
cana-1652	200	60	1	1	NUM
cana-1652	200	61	and	and	CCONJ
cana-1652	200	62	|𝑆|	|𝑆|	VERB
cana-1652	200	63	≥	≥	NOUN
cana-1652	200	64	𝑛	𝑛	ADP
cana-1652	200	65	−	−	PROPN
cana-1652	200	66	|𝑉	|𝑉	NUM
cana-1652	200	67	−	−	NOUN
cana-1652	200	68	𝑆|	𝑆|	NOUN
cana-1652	200	69	,	,	PUNCT
cana-1652	200	70	we	we	PRON
cana-1652	200	71	have	have	VERB
cana-1652	200	72	:	:	PUNCT
cana-1652	201	1	|𝑚	|𝑚	ADP
cana-1652	201	2	−	−	PROPN
cana-1652	201	3	𝑛	𝑛	PROPN
cana-1652	201	4	+	+	CCONJ
cana-1652	201	5	|𝑆|	|𝑆|	VERB
cana-1652	201	6	−	−	PROPN
cana-1652	201	7	|𝑇||	|𝑇||	PROPN
cana-1652	201	8	≤	≤	ADV
cana-1652	201	9	|𝑉	|𝑉	NOUN
cana-1652	201	10	−	−	NOUN
cana-1652	201	11	𝑆|	𝑆|	PROPN
cana-1652	201	12	−	−	PROPN
cana-1652	201	13	1	1	NUM
cana-1652	201	14	combining	combine	VERB
cana-1652	201	15	these	these	DET
cana-1652	201	16	inequalities	inequality	NOUN
cana-1652	201	17	,	,	PUNCT
cana-1652	201	18	we	we	PRON
cana-1652	201	19	obtain	obtain	VERB
cana-1652	201	20	:	:	PUNCT
cana-1652	201	21	|𝑇|	|𝑇|	NOUN
cana-1652	201	22	≤	≤	NUM
cana-1652	201	23	⌊𝑛/2⌋.	⌊𝑛/2⌋.	X
cana-1652	201	24	therefore	therefore	ADV
cana-1652	201	25	,	,	PUNCT
cana-1652	201	26	we	we	PRON
cana-1652	201	27	have	have	AUX
cana-1652	201	28	shown	show	VERB
cana-1652	201	29	that	that	SCONJ
cana-1652	201	30	every	every	DET
cana-1652	201	31	dominating	dominating	NOUN
cana-1652	201	32	set	set	NOUN
cana-1652	201	33	of	of	ADP
cana-1652	201	34	𝐺	𝐺	PROPN
cana-1652	201	35	has	have	VERB
cana-1652	201	36	size	size	NOUN
cana-1652	201	37	at	at	ADP
cana-1652	201	38	most	most	ADJ
cana-1652	201	39	⌊𝑛/2⌋	⌊𝑛/2⌋	NOUN
cana-1652	201	40	,	,	PUNCT
cana-1652	201	41	which	which	PRON
cana-1652	201	42	implies	imply	VERB
cana-1652	201	43	that	that	SCONJ
cana-1652	201	44	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1652	201	45	)	)	PUNCT
cana-1652	201	46	≤	≤	NOUN
cana-1652	201	47	⌊𝑛/2⌋	⌊𝑛/2⌋	NOUN
cana-1652	201	48	,	,	PUNCT
cana-1652	201	49	as	as	SCONJ
cana-1652	201	50	desired	desire	VERB
cana-1652	201	51	.	.	PUNCT
cana-1652	202	1	3	3	X
cana-1652	202	2	.	.	X
cana-1652	202	3	application	application	NOUN
cana-1652	202	4	in	in	ADP
cana-1652	202	5	cyber	cyber	ADJ
cana-1652	202	6	security	security	NOUN
cana-1652	202	7	and	and	CCONJ
cana-1652	202	8	google	google	PROPN
cana-1652	202	9	maps	map	NOUN
cana-1652	202	10	we	we	PRON
cana-1652	202	11	have	have	VERB
cana-1652	202	12	a	a	DET
cana-1652	202	13	network	network	NOUN
cana-1652	202	14	of	of	ADP
cana-1652	202	15	n	n	PRON
cana-1652	202	16	generators	generator	NOUN
cana-1652	202	17	and	and	CCONJ
cana-1652	202	18	m	m	NOUN
cana-1652	202	19	transmission	transmission	NOUN
cana-1652	202	20	lines	line	NOUN
cana-1652	202	21	.	.	PUNCT
cana-1652	203	1	each	each	DET
cana-1652	203	2	generator	generator	NOUN
cana-1652	203	3	is	be	AUX
cana-1652	203	4	connected	connect	VERB
cana-1652	203	5	to	to	ADP
cana-1652	203	6	one	one	NUM
cana-1652	203	7	or	or	CCONJ
cana-1652	203	8	more	more	ADJ
cana-1652	203	9	lines	line	NOUN
cana-1652	203	10	,	,	PUNCT
cana-1652	203	11	and	and	CCONJ
cana-1652	203	12	each	each	DET
cana-1652	203	13	line	line	NOUN
cana-1652	203	14	connects	connect	VERB
cana-1652	203	15	two	two	NUM
cana-1652	203	16	generators	generator	NOUN
cana-1652	203	17	.	.	PUNCT
cana-1652	204	1	generators	generator	NOUN
cana-1652	204	2	generate	generate	VERB
cana-1652	204	3	electricity	electricity	NOUN
cana-1652	204	4	that	that	PRON
cana-1652	204	5	is	be	AUX
cana-1652	204	6	sent	send	VERB
cana-1652	204	7	to	to	ADP
cana-1652	204	8	customers	customer	NOUN
cana-1652	204	9	via	via	ADP
cana-1652	204	10	transmission	transmission	NOUN
cana-1652	204	11	lines	line	NOUN
cana-1652	204	12	.	.	PUNCT
cana-1652	205	1	we	we	PRON
cana-1652	205	2	can	can	AUX
cana-1652	205	3	model	model	VERB
cana-1652	205	4	this	this	PRON
cana-1652	205	5	as	as	ADP
cana-1652	205	6	a	a	DET
cana-1652	205	7	fuzzy	fuzzy	ADJ
cana-1652	205	8	graph	graph	NOUN
cana-1652	205	9	where	where	SCONJ
cana-1652	205	10	each	each	DET
cana-1652	205	11	generator	generator	NOUN
cana-1652	205	12	is	be	AUX
cana-1652	205	13	an	an	DET
cana-1652	205	14	edge	edge	NOUN
cana-1652	205	15	and	and	CCONJ
cana-1652	205	16	each	each	DET
cana-1652	205	17	transmission	transmission	NOUN
cana-1652	205	18	line	line	NOUN
cana-1652	205	19	is	be	AUX
cana-1652	205	20	an	an	DET
cana-1652	205	21	edge	edge	NOUN
cana-1652	205	22	.	.	PUNCT
cana-1652	206	1	the	the	DET
cana-1652	206	2	weight	weight	NOUN
cana-1652	206	3	of	of	ADP
cana-1652	206	4	each	each	DET
cana-1652	206	5	edge	edge	NOUN
cana-1652	206	6	represents	represent	VERB
cana-1652	206	7	the	the	DET
cana-1652	206	8	capacity	capacity	NOUN
cana-1652	206	9	of	of	ADP
cana-1652	206	10	the	the	DET
cana-1652	206	11	transmission	transmission	NOUN
cana-1652	206	12	line	line	NOUN
cana-1652	206	13	.	.	PUNCT
cana-1652	207	1	using	use	VERB
cana-1652	207	2	theorem	theorem	NOUN
cana-1652	207	3	12	12	NUM
cana-1652	207	4	,	,	PUNCT
cana-1652	207	5	we	we	PRON
cana-1652	207	6	can	can	AUX
cana-1652	207	7	show	show	VERB
cana-1652	207	8	that	that	SCONJ
cana-1652	207	9	if	if	SCONJ
cana-1652	207	10	the	the	DET
cana-1652	207	11	grid	grid	NOUN
cana-1652	207	12	is	be	AUX
cana-1652	207	13	connected	connect	VERB
cana-1652	207	14	and	and	CCONJ
cana-1652	207	15	there	there	PRON
cana-1652	207	16	are	be	VERB
cana-1652	207	17	at	at	ADV
cana-1652	207	18	least	least	ADJ
cana-1652	207	19	n-1	n-1	ADJ
cana-1652	207	20	transmissions	transmission	NOUN
cana-1652	207	21	(	(	PUNCT
cana-1652	207	22	where	where	SCONJ
cana-1652	207	23	n	n	X
cana-1652	207	24	is	be	AUX
cana-1652	207	25	the	the	DET
cana-1652	207	26	number	number	NOUN
cana-1652	207	27	of	of	ADP
cana-1652	207	28	generators	generator	NOUN
cana-1652	207	29	)	)	PUNCT
cana-1652	207	30	,	,	PUNCT
cana-1652	207	31	there	there	PRON
cana-1652	207	32	is	be	VERB
cana-1652	207	33	a	a	DET
cana-1652	207	34	factor	factor	NOUN
cana-1652	207	35	of	of	ADP
cana-1652	207	36	magnitude	magnitude	NOUN
cana-1652	207	37	1	1	NUM
cana-1652	207	38	.	.	PUNCT
cana-1652	208	1	this	this	PRON
cana-1652	208	2	means	mean	VERB
cana-1652	208	3	that	that	SCONJ
cana-1652	208	4	there	there	PRON
cana-1652	208	5	is	be	VERB
cana-1652	208	6	at	at	ADV
cana-1652	208	7	least	least	ADJ
cana-1652	208	8	one	one	NUM
cana-1652	208	9	main	main	ADJ
cana-1652	208	10	generator	generator	NOUN
cana-1652	208	11	on	on	ADP
cana-1652	208	12	the	the	DET
cana-1652	208	13	grid	grid	NOUN
cana-1652	208	14	,	,	PUNCT
cana-1652	208	15	and	and	CCONJ
cana-1652	208	16	if	if	SCONJ
cana-1652	208	17	the	the	DET
cana-1652	208	18	generator	generator	NOUN
cana-1652	208	19	fails	fail	VERB
cana-1652	208	20	,	,	PUNCT
cana-1652	208	21	the	the	DET
cana-1652	208	22	entire	entire	ADJ
cana-1652	208	23	grid	grid	NOUN
cana-1652	208	24	is	be	AUX
cana-1652	208	25	vulnerable	vulnerable	ADJ
cana-1652	208	26	to	to	ADP
cana-1652	208	27	power	power	NOUN
cana-1652	208	28	outages	outage	NOUN
cana-1652	208	29	or	or	CCONJ
cana-1652	208	30	other	other	ADJ
cana-1652	208	31	outages	outage	NOUN
cana-1652	208	32	.	.	PUNCT
cana-1652	209	1	using	use	VERB
cana-1652	209	2	theorem	theorem	NOUN
cana-1652	209	3	14	14	NUM
cana-1652	209	4	,	,	PUNCT
cana-1652	209	5	we	we	PRON
cana-1652	209	6	can	can	AUX
cana-1652	209	7	show	show	VERB
cana-1652	209	8	that	that	SCONJ
cana-1652	209	9	if	if	SCONJ
cana-1652	209	10	the	the	DET
cana-1652	209	11	grid	grid	NOUN
cana-1652	209	12	is	be	AUX
cana-1652	209	13	connected	connect	VERB
cana-1652	209	14	and	and	CCONJ
cana-1652	209	15	has	have	VERB
cana-1652	209	16	fewer	few	ADJ
cana-1652	209	17	than	than	ADP
cana-1652	209	18	n-1	n-1	ADJ
cana-1652	209	19	connected	connected	ADJ
cana-1652	209	20	lines	line	NOUN
cana-1652	209	21	,	,	PUNCT
cana-1652	209	22	then	then	ADV
cana-1652	209	23	there	there	PRON
cana-1652	209	24	is	be	VERB
cana-1652	209	25	a	a	DET
cana-1652	209	26	cluster	cluster	NOUN
cana-1652	209	27	of	of	ADP
cana-1652	209	28	at	at	ADP
cana-1652	209	29	most	most	ADJ
cana-1652	209	30	⌊n/2⌋.	⌊n/2⌋.	NOUN
cana-1652	209	31	this	this	PRON
cana-1652	209	32	means	mean	VERB
cana-1652	209	33	that	that	SCONJ
cana-1652	209	34	we	we	PRON
cana-1652	209	35	can	can	AUX
cana-1652	209	36	identify	identify	VERB
cana-1652	209	37	a	a	DET
cana-1652	209	38	critical	critical	ADJ
cana-1652	209	39	generator	generator	NOUN
cana-1652	209	40	set	set	VERB
cana-1652	209	41	in	in	ADP
cana-1652	209	42	the	the	DET
cana-1652	209	43	network	network	NOUN
cana-1652	209	44	communications	communication	NOUN
cana-1652	209	45	on	on	ADP
cana-1652	209	46	applied	apply	VERB
cana-1652	209	47	nonlinear	nonlinear	ADJ
cana-1652	209	48	analysis	analysis	NOUN
cana-1652	209	49	issn	issn	NOUN
cana-1652	209	50	:	:	PUNCT
cana-1652	209	51	1074	1074	NUM
cana-1652	209	52	-	-	PUNCT
cana-1652	209	53	133x	133x	NUM
cana-1652	209	54	vol	vol	NOUN
cana-1652	209	55	32	32	NUM
cana-1652	209	56	no	no	NOUN
cana-1652	209	57	.	.	NOUN
cana-1652	209	58	1	1	NUM
cana-1652	209	59	(	(	PUNCT
cana-1652	209	60	2025	2025	NUM
cana-1652	209	61	)	)	PUNCT
cana-1652	209	62	332	332	NUM
cana-1652	209	63	https://internationalpubls.com	https://internationalpubls.com	X
cana-1652	209	64	so	so	SCONJ
cana-1652	209	65	that	that	SCONJ
cana-1652	209	66	if	if	SCONJ
cana-1652	209	67	one	one	NUM
cana-1652	209	68	of	of	ADP
cana-1652	209	69	the	the	DET
cana-1652	209	70	generators	generator	NOUN
cana-1652	209	71	fails	fail	VERB
cana-1652	209	72	,	,	PUNCT
cana-1652	209	73	the	the	DET
cana-1652	209	74	entire	entire	ADJ
cana-1652	209	75	network	network	NOUN
cana-1652	209	76	will	will	AUX
cana-1652	209	77	be	be	AUX
cana-1652	209	78	affected	affect	VERB
cana-1652	209	79	by	by	ADP
cana-1652	209	80	power	power	NOUN
cana-1652	209	81	outages	outage	NOUN
cana-1652	209	82	or	or	CCONJ
cana-1652	209	83	other	other	ADJ
cana-1652	209	84	outages	outage	NOUN
cana-1652	209	85	.	.	PUNCT
cana-1652	210	1	for	for	ADP
cana-1652	210	2	example	example	NOUN
cana-1652	210	3	,	,	PUNCT
cana-1652	210	4	we	we	PRON
cana-1652	210	5	have	have	VERB
cana-1652	210	6	a	a	DET
cana-1652	210	7	network	network	NOUN
cana-1652	210	8	with	with	ADP
cana-1652	210	9	10	10	NUM
cana-1652	210	10	generators	generator	NOUN
cana-1652	210	11	and	and	CCONJ
cana-1652	210	12	8	8	NUM
cana-1652	210	13	gearboxes	gearbox	NOUN
cana-1652	210	14	.	.	PUNCT
cana-1652	211	1	using	use	VERB
cana-1652	211	2	theorem	theorem	NOUN
cana-1652	211	3	14	14	NUM
cana-1652	211	4	,	,	PUNCT
cana-1652	211	5	we	we	PRON
cana-1652	211	6	can	can	AUX
cana-1652	211	7	determine	determine	VERB
cana-1652	211	8	the	the	DET
cana-1652	211	9	main	main	ADJ
cana-1652	211	10	power	power	NOUN
cana-1652	211	11	generation	generation	NOUN
cana-1652	211	12	system	system	NOUN
cana-1652	211	13	,	,	PUNCT
cana-1652	211	14	if	if	SCONJ
cana-1652	211	15	one	one	NUM
cana-1652	211	16	of	of	ADP
cana-1652	211	17	these	these	DET
cana-1652	211	18	generators	generator	NOUN
cana-1652	211	19	fails	fail	VERB
cana-1652	211	20	,	,	PUNCT
cana-1652	211	21	the	the	DET
cana-1652	211	22	entire	entire	ADJ
cana-1652	211	23	grid	grid	NOUN
cana-1652	211	24	will	will	AUX
cana-1652	211	25	be	be	AUX
cana-1652	211	26	affected	affect	VERB
cana-1652	211	27	by	by	ADP
cana-1652	211	28	power	power	NOUN
cana-1652	211	29	outage	outage	NOUN
cana-1652	211	30	or	or	CCONJ
cana-1652	211	31	other	other	ADJ
cana-1652	211	32	interference	interference	NOUN
cana-1652	211	33	.	.	PUNCT
cana-1652	212	1	since	since	SCONJ
cana-1652	212	2	⌊10/2⌋	⌊10/2⌋	PROPN
cana-1652	212	3	=	=	SYM
cana-1652	212	4	5	5	NUM
cana-1652	212	5	,	,	PUNCT
cana-1652	212	6	we	we	PRON
cana-1652	212	7	know	know	VERB
cana-1652	212	8	that	that	SCONJ
cana-1652	212	9	there	there	PRON
cana-1652	212	10	is	be	VERB
cana-1652	212	11	a	a	DET
cana-1652	212	12	dominant	dominant	ADJ
cana-1652	212	13	set	set	NOUN
cana-1652	212	14	of	of	ADP
cana-1652	212	15	maximum	maximum	ADJ
cana-1652	212	16	size	size	NOUN
cana-1652	212	17	5	5	NUM
cana-1652	212	18	.	.	PUNCT
cana-1652	212	19	using	use	VERB
cana-1652	212	20	the	the	DET
cana-1652	212	21	algorithm	algorithm	NOUN
cana-1652	212	22	,	,	PUNCT
cana-1652	212	23	we	we	PRON
cana-1652	212	24	can	can	AUX
cana-1652	212	25	see	see	VERB
cana-1652	212	26	this	this	DET
cana-1652	212	27	process	process	NOUN
cana-1652	212	28	well	well	ADV
cana-1652	212	29	.	.	PUNCT
cana-1652	213	1	in	in	ADP
cana-1652	213	2	practice	practice	NOUN
cana-1652	213	3	,	,	PUNCT
cana-1652	213	4	identifying	identify	VERB
cana-1652	213	5	critical	critical	ADJ
cana-1652	213	6	components	component	NOUN
cana-1652	213	7	in	in	ADP
cana-1652	213	8	complex	complex	ADJ
cana-1652	213	9	systems	system	NOUN
cana-1652	213	10	such	such	ADJ
cana-1652	213	11	as	as	ADP
cana-1652	213	12	power	power	NOUN
cana-1652	213	13	grids	grid	NOUN
cana-1652	213	14	or	or	CCONJ
cana-1652	213	15	transportation	transportation	NOUN
cana-1652	213	16	networks	network	NOUN
cana-1652	213	17	can	can	AUX
cana-1652	213	18	help	help	VERB
cana-1652	213	19	us	we	PRON
cana-1652	213	20	prioritize	prioritize	VERB
cana-1652	213	21	maintenance	maintenance	NOUN
cana-1652	213	22	and	and	CCONJ
cana-1652	213	23	repair	repair	NOUN
cana-1652	213	24	practices	practice	NOUN
cana-1652	213	25	,	,	PUNCT
cana-1652	213	26	provide	provide	VERB
cana-1652	213	27	power	power	NOUN
cana-1652	213	28	,	,	PUNCT
cana-1652	213	29	and	and	CCONJ
cana-1652	213	30	improve	improve	VERB
cana-1652	213	31	the	the	DET
cana-1652	213	32	entire	entire	ADJ
cana-1652	213	33	system	system	NOUN
cana-1652	213	34	.	.	PUNCT
cana-1652	214	1	use	use	VERB
cana-1652	214	2	all	all	DET
cana-1652	214	3	the	the	DET
cana-1652	214	4	theorems	theorem	NOUN
cana-1652	214	5	above	above	ADV
cana-1652	214	6	and	and	CCONJ
cana-1652	214	7	give	give	VERB
cana-1652	214	8	me	i	PRON
cana-1652	214	9	a	a	DET
cana-1652	214	10	google	google	NOUN
cana-1652	214	11	map	map	NOUN
cana-1652	214	12	application	application	NOUN
cana-1652	214	13	although	although	SCONJ
cana-1652	214	14	the	the	DET
cana-1652	214	15	discussed	discuss	VERB
cana-1652	214	16	theorems	theorem	NOUN
cana-1652	214	17	do	do	AUX
cana-1652	214	18	not	not	PART
cana-1652	214	19	apply	apply	VERB
cana-1652	214	20	directly	directly	ADV
cana-1652	214	21	to	to	ADP
cana-1652	214	22	google	google	PROPN
cana-1652	214	23	maps	map	NOUN
cana-1652	214	24	,	,	PUNCT
cana-1652	214	25	we	we	PRON
cana-1652	214	26	can	can	AUX
cana-1652	214	27	still	still	ADV
cana-1652	214	28	use	use	VERB
cana-1652	214	29	graph	graph	NOUN
cana-1652	214	30	theory	theory	NOUN
cana-1652	214	31	to	to	ADP
cana-1652	214	32	model	model	NOUN
cana-1652	214	33	and	and	CCONJ
cana-1652	214	34	analyze	analyze	VERB
cana-1652	214	35	the	the	DET
cana-1652	214	36	road	road	NOUN
cana-1652	214	37	network	network	NOUN
cana-1652	214	38	represented	represent	VERB
cana-1652	214	39	by	by	ADP
cana-1652	214	40	google	google	PROPN
cana-1652	214	41	maps	map	NOUN
cana-1652	214	42	.	.	PUNCT
cana-1652	215	1	we	we	PRON
cana-1652	215	2	can	can	AUX
cana-1652	215	3	represent	represent	VERB
cana-1652	215	4	the	the	DET
cana-1652	215	5	network	network	NOUN
cana-1652	215	6	as	as	ADP
cana-1652	215	7	a	a	DET
cana-1652	215	8	graph	graph	NOUN
cana-1652	215	9	where	where	SCONJ
cana-1652	215	10	every	every	DET
cana-1652	215	11	intersection	intersection	NOUN
cana-1652	215	12	is	be	AUX
cana-1652	215	13	an	an	DET
cana-1652	215	14	edge	edge	NOUN
cana-1652	215	15	and	and	CCONJ
cana-1652	215	16	every	every	DET
cana-1652	215	17	path	path	NOUN
cana-1652	215	18	is	be	AUX
cana-1652	215	19	an	an	DET
cana-1652	215	20	edge	edge	NOUN
cana-1652	215	21	.	.	PUNCT
cana-1652	216	1	the	the	DET
cana-1652	216	2	weight	weight	NOUN
cana-1652	216	3	of	of	ADP
cana-1652	216	4	each	each	DET
cana-1652	216	5	side	side	NOUN
cana-1652	216	6	can	can	AUX
cana-1652	216	7	represent	represent	VERB
cana-1652	216	8	various	various	ADJ
cana-1652	216	9	characteristics	characteristic	NOUN
cana-1652	216	10	of	of	ADP
cana-1652	216	11	the	the	DET
cana-1652	216	12	road	road	NOUN
cana-1652	216	13	segment	segment	NOUN
cana-1652	216	14	,	,	PUNCT
cana-1652	216	15	such	such	ADJ
cana-1652	216	16	as	as	ADP
cana-1652	216	17	distance	distance	NOUN
cana-1652	216	18	,	,	PUNCT
cana-1652	216	19	speed	speed	NOUN
cana-1652	216	20	limit	limit	NOUN
cana-1652	216	21	or	or	CCONJ
cana-1652	216	22	traffic	traffic	NOUN
cana-1652	216	23	volume	volume	NOUN
cana-1652	216	24	.	.	PUNCT
cana-1652	217	1	using	use	VERB
cana-1652	217	2	graph	graph	NOUN
cana-1652	217	3	theory	theory	NOUN
cana-1652	217	4	algorithms	algorithm	NOUN
cana-1652	217	5	,	,	PUNCT
cana-1652	217	6	we	we	PRON
cana-1652	217	7	can	can	AUX
cana-1652	217	8	analyze	analyze	VERB
cana-1652	217	9	this	this	DET
cana-1652	217	10	path	path	NOUN
cana-1652	217	11	to	to	PART
cana-1652	217	12	identify	identify	VERB
cana-1652	217	13	key	key	ADJ
cana-1652	217	14	points	point	NOUN
cana-1652	217	15	or	or	CCONJ
cana-1652	217	16	edges	edge	NOUN
cana-1652	217	17	that	that	PRON
cana-1652	217	18	are	be	AUX
cana-1652	217	19	important	important	ADJ
cana-1652	217	20	to	to	ADP
cana-1652	217	21	the	the	DET
cana-1652	217	22	operation	operation	NOUN
cana-1652	217	23	of	of	ADP
cana-1652	217	24	the	the	DET
cana-1652	217	25	entire	entire	ADJ
cana-1652	217	26	system	system	NOUN
cana-1652	217	27	.	.	PUNCT
cana-1652	218	1	using	use	VERB
cana-1652	218	2	theorem	theorem	NOUN
cana-1652	218	3	12	12	NUM
cana-1652	218	4	,	,	PUNCT
cana-1652	218	5	we	we	PRON
cana-1652	218	6	can	can	AUX
cana-1652	218	7	identify	identify	VERB
cana-1652	218	8	major	major	ADJ
cana-1652	218	9	intersections	intersection	NOUN
cana-1652	218	10	that	that	PRON
cana-1652	218	11	are	be	AUX
cana-1652	218	12	important	important	ADJ
cana-1652	218	13	for	for	ADP
cana-1652	218	14	maintaining	maintain	VERB
cana-1652	218	15	connectivity	connectivity	NOUN
cana-1652	218	16	.	.	PUNCT
cana-1652	219	1	blocking	block	VERB
cana-1652	219	2	or	or	CCONJ
cana-1652	219	3	closing	close	VERB
cana-1652	219	4	any	any	PRON
cana-1652	219	5	of	of	ADP
cana-1652	219	6	these	these	DET
cana-1652	219	7	intersections	intersection	NOUN
cana-1652	219	8	can	can	AUX
cana-1652	219	9	cause	cause	VERB
cana-1652	219	10	major	major	ADJ
cana-1652	219	11	traffic	traffic	NOUN
cana-1652	219	12	disruptions	disruption	NOUN
cana-1652	219	13	.	.	PUNCT
cana-1652	220	1	using	use	VERB
cana-1652	220	2	rule	rule	NOUN
cana-1652	220	3	14	14	NUM
cana-1652	220	4	,	,	PUNCT
cana-1652	220	5	we	we	PRON
cana-1652	220	6	can	can	AUX
cana-1652	220	7	identify	identify	VERB
cana-1652	220	8	the	the	DET
cana-1652	220	9	bottleneck	bottleneck	NOUN
cana-1652	220	10	or	or	CCONJ
cana-1652	220	11	critical	critical	ADJ
cana-1652	220	12	path	path	NOUN
cana-1652	220	13	that	that	PRON
cana-1652	220	14	acts	act	VERB
cana-1652	220	15	as	as	ADP
cana-1652	220	16	a	a	DET
cana-1652	220	17	bottleneck	bottleneck	NOUN
cana-1652	220	18	in	in	ADP
cana-1652	220	19	the	the	DET
cana-1652	220	20	network	network	NOUN
cana-1652	220	21	.	.	PUNCT
cana-1652	221	1	if	if	SCONJ
cana-1652	221	2	one	one	NUM
cana-1652	221	3	of	of	ADP
cana-1652	221	4	these	these	DET
cana-1652	221	5	methods	method	NOUN
cana-1652	221	6	causes	cause	VERB
cana-1652	221	7	a	a	DET
cana-1652	221	8	crash	crash	NOUN
cana-1652	221	9	or	or	CCONJ
cana-1652	221	10	shutdown	shutdown	NOUN
cana-1652	221	11	,	,	PUNCT
cana-1652	221	12	it	it	PRON
cana-1652	221	13	can	can	AUX
cana-1652	221	14	cause	cause	VERB
cana-1652	221	15	significant	significant	ADJ
cana-1652	221	16	network	network	NOUN
cana-1652	221	17	-	-	PUNCT
cana-1652	221	18	wide	wide	ADJ
cana-1652	221	19	delays	delay	NOUN
cana-1652	221	20	and	and	CCONJ
cana-1652	221	21	backups	backup	NOUN
cana-1652	221	22	.	.	PUNCT
cana-1652	222	1	we	we	PRON
cana-1652	222	2	can	can	AUX
cana-1652	222	3	optimize	optimize	VERB
cana-1652	222	4	routing	routing	NOUN
cana-1652	222	5	and	and	CCONJ
cana-1652	222	6	navigation	navigation	NOUN
cana-1652	222	7	in	in	ADP
cana-1652	222	8	the	the	DET
cana-1652	222	9	network	network	NOUN
cana-1652	222	10	using	use	VERB
cana-1652	222	11	other	other	ADJ
cana-1652	222	12	image	image	NOUN
cana-1652	222	13	technology	technology	NOUN
cana-1652	222	14	algorithms	algorithm	NOUN
cana-1652	222	15	such	such	ADJ
cana-1652	222	16	as	as	ADP
cana-1652	222	17	the	the	DET
cana-1652	222	18	shortest	short	ADJ
cana-1652	222	19	path	path	NOUN
cana-1652	222	20	algorithm	algorithm	NOUN
cana-1652	222	21	or	or	CCONJ
cana-1652	222	22	the	the	DET
cana-1652	222	23	maximum	maximum	ADJ
cana-1652	222	24	flow	flow	NOUN
cana-1652	222	25	algorithm	algorithm	NOUN
cana-1652	222	26	.	.	PUNCT
cana-1652	223	1	in	in	ADP
cana-1652	223	2	general	general	ADJ
cana-1652	223	3	,	,	PUNCT
cana-1652	223	4	graph	graph	NOUN
cana-1652	223	5	theory	theory	NOUN
cana-1652	223	6	provides	provide	VERB
cana-1652	223	7	a	a	DET
cana-1652	223	8	strong	strong	ADJ
cana-1652	223	9	foundation	foundation	NOUN
cana-1652	223	10	for	for	ADP
cana-1652	223	11	modeling	modeling	NOUN
cana-1652	223	12	and	and	CCONJ
cana-1652	223	13	analyzing	analyze	VERB
cana-1652	223	14	complex	complex	ADJ
cana-1652	223	15	networks	network	NOUN
cana-1652	223	16	such	such	ADJ
cana-1652	223	17	as	as	ADP
cana-1652	223	18	meshes	mesh	NOUN
cana-1652	223	19	,	,	PUNCT
cana-1652	223	20	but	but	CCONJ
cana-1652	223	21	these	these	DET
cana-1652	223	22	specific	specific	ADJ
cana-1652	223	23	theorems	theorem	NOUN
cana-1652	223	24	may	may	AUX
cana-1652	223	25	not	not	PART
cana-1652	223	26	be	be	AUX
cana-1652	223	27	directly	directly	ADV
cana-1652	223	28	applicable	applicable	ADJ
cana-1652	223	29	to	to	ADP
cana-1652	223	30	google	google	PROPN
cana-1652	223	31	maps	map	NOUN
cana-1652	223	32	itself	itself	PRON
cana-1652	223	33	.	.	PUNCT
cana-1652	224	1	by	by	ADP
cana-1652	224	2	identifying	identify	VERB
cana-1652	224	3	the	the	DET
cana-1652	224	4	key	key	ADJ
cana-1652	224	5	components	component	NOUN
cana-1652	224	6	in	in	ADP
cana-1652	224	7	these	these	DET
cana-1652	224	8	networks	network	NOUN
cana-1652	224	9	,	,	PUNCT
cana-1652	224	10	we	we	PRON
cana-1652	224	11	can	can	AUX
cana-1652	224	12	improve	improve	VERB
cana-1652	224	13	overall	overall	ADJ
cana-1652	224	14	efficiency	efficiency	NOUN
cana-1652	224	15	and	and	CCONJ
cana-1652	224	16	effectiveness	effectiveness	NOUN
cana-1652	224	17	.	.	PUNCT
cana-1652	225	1	4	4	X
cana-1652	225	2	.	.	X
cana-1652	225	3	conclusion	conclusion	NOUN
cana-1652	225	4	fuzzy	fuzzy	ADJ
cana-1652	225	5	graph	graph	NOUN
cana-1652	225	6	theory	theory	NOUN
cana-1652	225	7	is	be	AUX
cana-1652	225	8	one	one	NUM
cana-1652	225	9	of	of	ADP
cana-1652	225	10	the	the	DET
cana-1652	225	11	branch	branch	NOUN
cana-1652	225	12	of	of	ADP
cana-1652	225	13	fuzzy	fuzzy	ADJ
cana-1652	225	14	theoretical	theoretical	ADJ
cana-1652	225	15	area	area	NOUN
cana-1652	225	16	,	,	PUNCT
cana-1652	225	17	which	which	PRON
cana-1652	225	18	is	be	AUX
cana-1652	225	19	advanced	advanced	ADJ
cana-1652	225	20	with	with	ADP
cana-1652	225	21	many	many	ADJ
cana-1652	225	22	real	real	ADJ
cana-1652	225	23	life	life	NOUN
cana-1652	225	24	applications	application	NOUN
cana-1652	225	25	in	in	ADP
cana-1652	225	26	new	new	ADJ
cana-1652	225	27	mathematical	mathematical	ADJ
cana-1652	225	28	developments	development	NOUN
cana-1652	225	29	.	.	PUNCT
cana-1652	226	1	herein	herein	VERB
cana-1652	226	2	new	new	ADJ
cana-1652	226	3	theoretical	theoretical	ADJ
cana-1652	226	4	concepts	concept	NOUN
cana-1652	226	5	of	of	ADP
cana-1652	226	6	domination	domination	NOUN
cana-1652	226	7	in	in	ADP
cana-1652	226	8	fuzzy	fuzzy	ADJ
cana-1652	226	9	graphs	graph	NOUN
cana-1652	226	10	have	have	AUX
cana-1652	226	11	been	be	AUX
cana-1652	226	12	studied	study	VERB
cana-1652	226	13	and	and	CCONJ
cana-1652	226	14	examined	examine	VERB
cana-1652	226	15	.	.	PUNCT
cana-1652	227	1	some	some	DET
cana-1652	227	2	useful	useful	ADJ
cana-1652	227	3	application	application	NOUN
cana-1652	227	4	for	for	ADP
cana-1652	227	5	fuzzy	fuzzy	ADJ
cana-1652	227	6	graphs	graph	NOUN
cana-1652	227	7	had	have	AUX
cana-1652	227	8	been	be	AUX
cana-1652	227	9	given	give	VERB
cana-1652	227	10	in	in	ADP
cana-1652	227	11	this	this	DET
cana-1652	227	12	research	research	NOUN
cana-1652	227	13	article	article	NOUN
cana-1652	227	14	.	.	PUNCT
cana-1652	228	1	our	our	PRON
cana-1652	228	2	future	future	ADJ
cana-1652	228	3	extension	extension	NOUN
cana-1652	228	4	would	would	AUX
cana-1652	228	5	be	be	AUX
cana-1652	228	6	extending	extend	VERB
cana-1652	228	7	this	this	DET
cana-1652	228	8	study	study	NOUN
cana-1652	228	9	for	for	ADP
cana-1652	228	10	further	further	ADJ
cana-1652	228	11	extensions	extension	NOUN
cana-1652	228	12	of	of	ADP
cana-1652	228	13	fuzzy	fuzzy	ADJ
cana-1652	228	14	graphs	graph	NOUN
cana-1652	228	15	like	like	ADP
cana-1652	228	16	pythagorean	pythagorean	PROPN
cana-1652	228	17	fuzzy	fuzzy	ADJ
cana-1652	228	18	graphs	graph	NOUN
cana-1652	228	19	,	,	PUNCT
cana-1652	228	20	hesitant	hesitant	ADJ
cana-1652	228	21	fuzzy	fuzzy	ADJ
cana-1652	228	22	graphs	graph	NOUN
cana-1652	228	23	,	,	PUNCT
cana-1652	228	24	so	so	ADV
cana-1652	228	25	on	on	ADV
cana-1652	228	26	and	and	CCONJ
cana-1652	228	27	explore	explore	VERB
cana-1652	228	28	more	more	ADJ
cana-1652	228	29	graph	graph	NOUN
cana-1652	228	30	theoretical	theoretical	ADJ
cana-1652	228	31	concepts	concept	NOUN
cana-1652	228	32	for	for	ADP
cana-1652	228	33	fuzzy	fuzzy	ADJ
cana-1652	228	34	graphs	graph	NOUN
cana-1652	228	35	and	and	CCONJ
cana-1652	228	36	its	its	PRON
cana-1652	228	37	extensions	extension	NOUN
cana-1652	228	38	.	.	PUNCT
cana-1652	229	1	references	reference	NOUN
cana-1652	229	2	[	[	X
cana-1652	229	3	1	1	NUM
cana-1652	229	4	]	]	X
cana-1652	229	5	bondy	bondy	PROPN
cana-1652	229	6	,	,	PUNCT
cana-1652	229	7	j.a	j.a	PROPN
cana-1652	229	8	.	.	PROPN
cana-1652	229	9	;	;	PUNCT
cana-1652	229	10	murty	murty	NOUN
cana-1652	229	11	,	,	PUNCT
cana-1652	229	12	u.s.r	u.s.r	NOUN
cana-1652	229	13	.	.	PROPN
cana-1652	229	14	graph	graph	NOUN
cana-1652	229	15	theory	theory	NOUN
cana-1652	229	16	with	with	ADP
cana-1652	229	17	applications	application	NOUN
cana-1652	229	18	;	;	PUNCT
cana-1652	229	19	macmillan	macmillan	PROPN
cana-1652	229	20	:	:	PUNCT
cana-1652	229	21	london	london	PROPN
cana-1652	229	22	,	,	PUNCT
cana-1652	229	23	uk	uk	PROPN
cana-1652	229	24	,	,	PUNCT
cana-1652	229	25	1976	1976	NUM
cana-1652	229	26	;	;	PUNCT
cana-1652	229	27	volume	volume	NOUN
cana-1652	229	28	290	290	NUM
cana-1652	229	29	.	.	PUNCT
cana-1652	230	1	[	[	X
cana-1652	230	2	2	2	NUM
cana-1652	230	3	]	]	SYM
cana-1652	230	4	chartrand	chartrand	NOUN
cana-1652	230	5	,	,	PUNCT
cana-1652	230	6	g.	g.	PROPN
cana-1652	230	7	;	;	PUNCT
cana-1652	230	8	zhang	zhang	PROPN
cana-1652	230	9	,	,	PUNCT
cana-1652	230	10	p.	p.	NOUN
cana-1652	230	11	a	a	DET
cana-1652	230	12	first	first	ADJ
cana-1652	230	13	course	course	NOUN
cana-1652	230	14	in	in	ADP
cana-1652	230	15	graph	graph	NOUN
cana-1652	230	16	theory	theory	NOUN
cana-1652	230	17	;	;	PUNCT
cana-1652	230	18	courier	courier	NOUN
cana-1652	230	19	corporation	corporation	NOUN
cana-1652	230	20	:	:	PUNCT
cana-1652	230	21	north	north	PROPN
cana-1652	230	22	chelmsford	chelmsford	PROPN
cana-1652	230	23	,	,	PUNCT
cana-1652	230	24	ma	ma	PROPN
cana-1652	230	25	,	,	PUNCT
cana-1652	230	26	usa	usa	PROPN
cana-1652	230	27	,	,	PUNCT
cana-1652	230	28	2013	2013	NUM
cana-1652	230	29	.	.	PUNCT
cana-1652	231	1	[	[	X
cana-1652	231	2	3	3	NUM
cana-1652	231	3	]	]	X
cana-1652	231	4	zadeh	zadeh	PROPN
cana-1652	231	5	,	,	PUNCT
cana-1652	231	6	l.a	l.a	PROPN
cana-1652	231	7	.	.	PROPN
cana-1652	231	8	fuzzy	fuzzy	ADJ
cana-1652	231	9	sets	set	NOUN
cana-1652	231	10	.	.	PUNCT
cana-1652	232	1	inf	inf	PROPN
cana-1652	232	2	.	.	PUNCT
cana-1652	232	3	control	control	PROPN
cana-1652	232	4	1965	1965	NUM
cana-1652	232	5	,	,	PUNCT
cana-1652	232	6	8	8	NUM
cana-1652	232	7	,	,	PUNCT
cana-1652	232	8	338	338	NUM
cana-1652	232	9	-	-	SYM
cana-1652	232	10	353	353	NUM
cana-1652	232	11	.	.	PUNCT
cana-1652	233	1	[	[	X
cana-1652	233	2	4	4	NUM
cana-1652	233	3	]	]	X
cana-1652	233	4	rosenfeld	rosenfeld	PROPN
cana-1652	233	5	,	,	PUNCT
cana-1652	233	6	a.	a.	NOUN
cana-1652	233	7	fuzzy	fuzzy	ADJ
cana-1652	233	8	graphs	graph	NOUN
cana-1652	233	9	.	.	PUNCT
cana-1652	234	1	in	in	ADP
cana-1652	234	2	fuzzy	fuzzy	ADJ
cana-1652	234	3	sets	set	NOUN
cana-1652	234	4	and	and	CCONJ
cana-1652	234	5	their	their	PRON
cana-1652	234	6	applications	application	NOUN
cana-1652	234	7	;	;	PUNCT
cana-1652	234	8	zadeh	zadeh	PROPN
cana-1652	234	9	,	,	PUNCT
cana-1652	234	10	l.a	l.a	PROPN
cana-1652	234	11	.	.	PROPN
cana-1652	234	12	,	,	PUNCT
cana-1652	234	13	fu	fu	PROPN
cana-1652	234	14	,	,	PUNCT
cana-1652	234	15	k.s	k.s	PROPN
cana-1652	234	16	.	.	PROPN
cana-1652	234	17	,	,	PUNCT
cana-1652	234	18	shimura	shimura	PROPN
cana-1652	234	19	,	,	PUNCT
cana-1652	234	20	m.	m.	NOUN
cana-1652	234	21	,	,	PUNCT
cana-1652	234	22	eds	eds	PROPN
cana-1652	234	23	.	.	PUNCT
cana-1652	234	24	;	;	PUNCT
cana-1652	234	25	academic	academic	ADJ
cana-1652	234	26	press	press	NOUN
cana-1652	234	27	:	:	PUNCT
cana-1652	234	28	new	new	PROPN
cana-1652	234	29	york	york	PROPN
cana-1652	234	30	,	,	PUNCT
cana-1652	234	31	ny	ny	PROPN
cana-1652	234	32	,	,	PUNCT
cana-1652	234	33	usa	usa	PROPN
cana-1652	234	34	,	,	PUNCT
cana-1652	234	35	1975	1975	NUM
cana-1652	234	36	;	;	PUNCT
cana-1652	234	37	pp	pp	ADP
cana-1652	234	38	.	.	PUNCT
cana-1652	235	1	77	77	NUM
cana-1652	235	2	-	-	SYM
cana-1652	235	3	95	95	NUM
cana-1652	235	4	.	.	PUNCT
cana-1652	236	1	[	[	X
cana-1652	236	2	5	5	NUM
cana-1652	236	3	]	]	X
cana-1652	236	4	mordeson	mordeson	NOUN
cana-1652	236	5	,	,	PUNCT
cana-1652	236	6	j.n	j.n	PROPN
cana-1652	236	7	.	.	PROPN
cana-1652	236	8	;	;	PUNCT
cana-1652	236	9	chang	chang	PROPN
cana-1652	236	10	-	-	PUNCT
cana-1652	236	11	shyh	shyh	PROPN
cana-1652	236	12	,	,	PUNCT
cana-1652	236	13	p.	p.	NOUN
cana-1652	236	14	operations	operation	NOUN
cana-1652	236	15	on	on	ADP
cana-1652	236	16	fuzzy	fuzzy	ADJ
cana-1652	236	17	graphs	graph	NOUN
cana-1652	236	18	.	.	PUNCT
cana-1652	237	1	inf	inf	PROPN
cana-1652	237	2	.	.	PUNCT
cana-1652	238	1	sci	sci	PROPN
cana-1652	238	2	.	.	PROPN
cana-1652	238	3	1994	1994	NUM
cana-1652	238	4	,	,	PUNCT
cana-1652	238	5	79	79	NUM
cana-1652	238	6	,	,	PUNCT
cana-1652	238	7	159	159	NUM
cana-1652	238	8	-	-	SYM
cana-1652	238	9	170	170	NUM
cana-1652	238	10	.	.	PUNCT
cana-1652	239	1	communications	communication	NOUN
cana-1652	239	2	on	on	ADP
cana-1652	239	3	applied	apply	VERB
cana-1652	239	4	nonlinear	nonlinear	ADJ
cana-1652	239	5	analysis	analysis	NOUN
cana-1652	239	6	issn	issn	NOUN
cana-1652	239	7	:	:	PUNCT
cana-1652	239	8	1074	1074	NUM
cana-1652	239	9	-	-	PUNCT
cana-1652	239	10	133x	133x	NUM
cana-1652	239	11	vol	vol	NOUN
cana-1652	239	12	32	32	NUM
cana-1652	239	13	no	no	NOUN
cana-1652	239	14	.	.	NOUN
cana-1652	239	15	1	1	NUM
cana-1652	239	16	(	(	PUNCT
cana-1652	239	17	2025	2025	NUM
cana-1652	239	18	)	)	PUNCT
cana-1652	240	1	333	333	NUM
cana-1652	240	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1652	240	3	[	[	X
cana-1652	240	4	6	6	NUM
cana-1652	240	5	]	]	SYM
cana-1652	240	6	mordeson	mordeson	NOUN
cana-1652	240	7	,	,	PUNCT
cana-1652	240	8	j.n	j.n	PROPN
cana-1652	240	9	.	.	PROPN
cana-1652	240	10	;	;	PUNCT
cana-1652	240	11	nair	nair	PROPN
cana-1652	240	12	,	,	PUNCT
cana-1652	240	13	p.s	p.s	PROPN
cana-1652	240	14	.	.	PROPN
cana-1652	240	15	fuzzy	fuzzy	ADJ
cana-1652	240	16	graphs	graph	NOUN
cana-1652	240	17	and	and	CCONJ
cana-1652	240	18	fuzzy	fuzzy	ADJ
cana-1652	240	19	hypergraphs	hypergraph	NOUN
cana-1652	240	20	;	;	PUNCT
cana-1652	240	21	physica	physica	NOUN
cana-1652	240	22	-	-	PUNCT
cana-1652	240	23	verlag	verlag	NOUN
cana-1652	240	24	:	:	PUNCT
cana-1652	240	25	heidelberg	heidelberg	PROPN
cana-1652	240	26	,	,	PUNCT
cana-1652	240	27	germany	germany	PROPN
cana-1652	240	28	,	,	PUNCT
cana-1652	240	29	2012	2012	NUM
cana-1652	240	30	;	;	PUNCT
cana-1652	240	31	volume	volume	NOUN
cana-1652	240	32	46	46	NUM
cana-1652	240	33	.	.	PUNCT
cana-1652	241	1	[	[	X
cana-1652	241	2	7	7	NUM
cana-1652	241	3	]	]	PUNCT
cana-1652	241	4	bhutani	bhutani	NOUN
cana-1652	241	5	,	,	PUNCT
cana-1652	241	6	k.r	k.r	PROPN
cana-1652	241	7	.	.	PROPN
cana-1652	241	8	;	;	PUNCT
cana-1652	241	9	battou	battou	NOUN
cana-1652	241	10	,	,	PUNCT
cana-1652	241	11	a.	a.	NOUN
cana-1652	241	12	on	on	ADP
cana-1652	241	13	m	m	ADJ
cana-1652	241	14	-	-	ADJ
cana-1652	241	15	strong	strong	ADJ
cana-1652	241	16	fuzzy	fuzzy	ADJ
cana-1652	241	17	graphs	graph	NOUN
cana-1652	241	18	.	.	PUNCT
cana-1652	242	1	inf	inf	PROPN
cana-1652	242	2	.	.	PUNCT
cana-1652	243	1	sci	sci	PROPN
cana-1652	243	2	.	.	PROPN
cana-1652	243	3	2003	2003	NUM
cana-1652	243	4	,	,	PUNCT
cana-1652	243	5	155	155	NUM
cana-1652	243	6	,	,	PUNCT
cana-1652	243	7	103	103	NUM
cana-1652	243	8	-	-	SYM
cana-1652	243	9	109	109	NUM
cana-1652	243	10	.	.	PUNCT
cana-1652	244	1	[	[	X
cana-1652	244	2	8	8	NUM
cana-1652	244	3	]	]	X
cana-1652	244	4	parvathi	parvathi	PROPN
cana-1652	244	5	,	,	PUNCT
cana-1652	244	6	r.	r.	PROPN
cana-1652	244	7	;	;	PUNCT
cana-1652	244	8	karunambigai	karunambigai	PROPN
cana-1652	244	9	,	,	PUNCT
cana-1652	244	10	m.g	m.g	PROPN
cana-1652	244	11	.	.	PROPN
cana-1652	244	12	intuitionistic	intuitionistic	ADJ
cana-1652	244	13	fuzzy	fuzzy	ADJ
cana-1652	244	14	graphs	graph	NOUN
cana-1652	244	15	.	.	PUNCT
cana-1652	245	1	in	in	ADP
cana-1652	245	2	computational	computational	ADJ
cana-1652	245	3	intelligence	intelligence	NOUN
cana-1652	245	4	,	,	PUNCT
cana-1652	245	5	theory	theory	NOUN
cana-1652	245	6	and	and	CCONJ
cana-1652	245	7	applications	application	NOUN
cana-1652	245	8	;	;	PUNCT
cana-1652	245	9	springer	springer	NOUN
cana-1652	245	10	international	international	ADJ
cana-1652	245	11	publishing	publishing	NOUN
cana-1652	245	12	:	:	PUNCT
cana-1652	245	13	cham	cham	PROPN
cana-1652	245	14	,	,	PUNCT
cana-1652	245	15	switzerland	switzerland	PROPN
cana-1652	245	16	,	,	PUNCT
cana-1652	245	17	2006	2006	NUM
cana-1652	245	18	;	;	PUNCT
cana-1652	245	19	pp	pp	X
cana-1652	245	20	.	.	PUNCT
cana-1652	246	1	139	139	NUM
cana-1652	246	2	-	-	SYM
cana-1652	246	3	150	150	NUM
cana-1652	246	4	.	.	PUNCT
cana-1652	247	1	[	[	X
cana-1652	247	2	9	9	NUM
cana-1652	247	3	]	]	X
cana-1652	247	4	gani	gani	X
cana-1652	247	5	,	,	PUNCT
cana-1652	247	6	a.n	a.n	PROPN
cana-1652	247	7	.	.	PROPN
cana-1652	247	8	;	;	PUNCT
cana-1652	247	9	radha	radha	PROPN
cana-1652	247	10	,	,	PUNCT
cana-1652	247	11	k.	k.	PROPN
cana-1652	247	12	on	on	ADP
cana-1652	247	13	regular	regular	ADJ
cana-1652	247	14	fuzzy	fuzzy	ADJ
cana-1652	247	15	graphs	graph	NOUN
cana-1652	247	16	.	.	PUNCT
cana-1652	248	1	j.	j.	PROPN
cana-1652	248	2	phys	phys	PROPN
cana-1652	248	3	.	.	PUNCT
cana-1652	249	1	sci	sci	PROPN
cana-1652	249	2	.	.	PROPN
cana-1652	249	3	2012	2012	NUM
cana-1652	249	4	,	,	PUNCT
cana-1652	249	5	12	12	NUM
cana-1652	249	6	,	,	PUNCT
cana-1652	249	7	33	33	NUM
cana-1652	249	8	-	-	SYM
cana-1652	249	9	40	40	NUM
cana-1652	249	10	.	.	PUNCT
cana-1652	250	1	[	[	X
cana-1652	250	2	10	10	NUM
cana-1652	250	3	]	]	X
cana-1652	250	4	akram	akram	NOUN
cana-1652	250	5	,	,	PUNCT
cana-1652	250	6	m.	m.	NOUN
cana-1652	250	7	bipolar	bipolar	ADJ
cana-1652	250	8	fuzzy	fuzzy	ADJ
cana-1652	250	9	graphs	graph	NOUN
cana-1652	250	10	.	.	PUNCT
cana-1652	251	1	inf	inf	PROPN
cana-1652	251	2	.	.	PUNCT
cana-1652	252	1	sci	sci	PROPN
cana-1652	252	2	.	.	PROPN
cana-1652	252	3	2011	2011	NUM
cana-1652	252	4	,	,	PUNCT
cana-1652	252	5	181	181	NUM
cana-1652	252	6	,	,	PUNCT
cana-1652	252	7	5548	5548	NUM
cana-1652	252	8	-	-	SYM
cana-1652	252	9	5564	5564	NUM
cana-1652	252	10	.	.	PUNCT
cana-1652	253	1	[	[	X
cana-1652	253	2	11	11	NUM
cana-1652	253	3	]	]	X
cana-1652	253	4	akram	akram	NOUN
cana-1652	253	5	,	,	PUNCT
cana-1652	253	6	m.	m.	NOUN
cana-1652	253	7	;	;	PUNCT
cana-1652	253	8	dudek	dudek	PROPN
cana-1652	253	9	,	,	PUNCT
cana-1652	253	10	w.	w.	PROPN
cana-1652	253	11	interval	interval	NOUN
cana-1652	253	12	-	-	PUNCT
cana-1652	253	13	valued	value	VERB
cana-1652	253	14	fuzzy	fuzzy	ADJ
cana-1652	253	15	graphs	graph	NOUN
cana-1652	253	16	.	.	PUNCT
cana-1652	254	1	comput	comput	NOUN
cana-1652	254	2	.	.	PUNCT
cana-1652	255	1	math	math	NOUN
cana-1652	255	2	.	.	PUNCT
cana-1652	256	1	appl	appl	PROPN
cana-1652	256	2	.	.	PUNCT
cana-1652	257	1	2011	2011	NUM
cana-1652	257	2	,	,	PUNCT
cana-1652	257	3	61	61	NUM
cana-1652	257	4	,	,	PUNCT
cana-1652	257	5	289	289	NUM
cana-1652	257	6	-	-	SYM
cana-1652	257	7	299	299	NUM
cana-1652	257	8	.	.	PUNCT
cana-1652	258	1	[	[	X
cana-1652	258	2	12	12	NUM
cana-1652	258	3	]	]	PUNCT
cana-1652	258	4	ashraf	ashraf	NOUN
cana-1652	258	5	,	,	PUNCT
cana-1652	258	6	s.	s.	PROPN
cana-1652	258	7	;	;	PUNCT
cana-1652	258	8	naz	naz	PROPN
cana-1652	258	9	,	,	PUNCT
cana-1652	258	10	s.	s.	PROPN
cana-1652	258	11	;	;	PUNCT
cana-1652	258	12	kerre	kerre	PROPN
cana-1652	258	13	,	,	PUNCT
cana-1652	258	14	e.e	e.e	PROPN
cana-1652	258	15	.	.	PROPN
cana-1652	258	16	dombi	dombi	PROPN
cana-1652	258	17	fuzzy	fuzzy	ADJ
cana-1652	258	18	graphs	graph	NOUN
cana-1652	258	19	.	.	PUNCT
cana-1652	259	1	fuzzy	fuzzy	PROPN
cana-1652	259	2	inf	inf	PROPN
cana-1652	259	3	.	.	PUNCT
cana-1652	260	1	eng	eng	PROPN
cana-1652	260	2	.	.	PROPN
cana-1652	260	3	2018	2018	NUM
cana-1652	260	4	,	,	PUNCT
cana-1652	260	5	10	10	NUM
cana-1652	260	6	,	,	PUNCT
cana-1652	260	7	58	58	NUM
cana-1652	260	8	-	-	SYM
cana-1652	260	9	79	79	NUM
cana-1652	260	10	.	.	PUNCT
cana-1652	261	1	[	[	X
cana-1652	261	2	13	13	NUM
cana-1652	261	3	]	]	SYM
cana-1652	261	4	ore	ore	NOUN
cana-1652	261	5	,	,	PUNCT
cana-1652	261	6	o.	o.	PROPN
cana-1652	261	7	theory	theory	NOUN
cana-1652	261	8	of	of	ADP
cana-1652	261	9	graphs	graph	NOUN
cana-1652	261	10	,	,	PUNCT
cana-1652	261	11	american	american	PROPN
cana-1652	261	12	mathematical	mathematical	ADJ
cana-1652	261	13	society	society	NOUN
cana-1652	261	14	colloquium	colloquium	NOUN
cana-1652	261	15	publications	publication	NOUN
cana-1652	261	16	.	.	PUNCT
cana-1652	262	1	am	be	AUX
cana-1652	262	2	.	.	PUNCT
cana-1652	263	1	math	math	NOUN
cana-1652	263	2	.	.	PUNCT
cana-1652	264	1	soc	soc	PROPN
cana-1652	264	2	.	.	PUNCT
cana-1652	265	1	provid	provid	PROPN
cana-1652	265	2	.	.	PUNCT
cana-1652	266	1	1962	1962	NUM
cana-1652	266	2	,	,	PUNCT
cana-1652	266	3	38	38	NUM
cana-1652	266	4	,	,	PUNCT
cana-1652	266	5	270	270	NUM
cana-1652	266	6	.	.	PUNCT
cana-1652	267	1	[	[	X
cana-1652	267	2	14	14	NUM
cana-1652	267	3	]	]	X
cana-1652	267	4	cockayne	cockayne	NOUN
cana-1652	267	5	,	,	PUNCT
cana-1652	267	6	e.j	e.j	PROPN
cana-1652	267	7	.	.	PROPN
cana-1652	267	8	;	;	PUNCT
cana-1652	267	9	hedetniemi	hedetniemi	PROPN
cana-1652	267	10	,	,	PUNCT
cana-1652	267	11	s.t	s.t	PROPN
cana-1652	267	12	.	.	PROPN
cana-1652	267	13	towards	towards	ADP
cana-1652	267	14	a	a	DET
cana-1652	267	15	theory	theory	NOUN
cana-1652	267	16	of	of	ADP
cana-1652	267	17	domination	domination	NOUN
cana-1652	267	18	in	in	ADP
cana-1652	267	19	graphs	graph	NOUN
cana-1652	267	20	.	.	PUNCT
cana-1652	268	1	networks	network	NOUN
cana-1652	268	2	1977	1977	NUM
cana-1652	268	3	,	,	PUNCT
cana-1652	268	4	7	7	NUM
cana-1652	268	5	,	,	PUNCT
cana-1652	268	6	247	247	NUM
cana-1652	268	7	-	-	SYM
cana-1652	268	8	261	261	NUM
cana-1652	268	9	.	.	PUNCT
cana-1652	269	1	[	[	X
cana-1652	269	2	15	15	NUM
cana-1652	269	3	]	]	X
cana-1652	269	4	haynes	hayne	NOUN
cana-1652	269	5	,	,	PUNCT
cana-1652	269	6	t.w	t.w	PROPN
cana-1652	269	7	.	.	PROPN
cana-1652	269	8	;	;	PUNCT
cana-1652	269	9	hedetniemi	hedetniemi	ADV
cana-1652	269	10	,	,	PUNCT
cana-1652	269	11	s.	s.	PROPN
cana-1652	269	12	;	;	PUNCT
cana-1652	269	13	slater	slater	NOUN
cana-1652	269	14	,	,	PUNCT
cana-1652	269	15	p.	p.	NOUN
cana-1652	269	16	fundamentals	fundamental	NOUN
cana-1652	269	17	of	of	ADP
cana-1652	269	18	domination	domination	NOUN
cana-1652	269	19	in	in	ADP
cana-1652	269	20	graphs	graph	NOUN
cana-1652	269	21	;	;	PUNCT
cana-1652	269	22	crc	crc	NOUN
cana-1652	269	23	press	press	PROPN
cana-1652	269	24	:	:	PUNCT
cana-1652	269	25	boca	boca	PROPN
cana-1652	269	26	raton	raton	PROPN
cana-1652	269	27	,	,	PUNCT
cana-1652	269	28	fl	fl	PROPN
cana-1652	269	29	,	,	PUNCT
cana-1652	269	30	usa	usa	PROPN
cana-1652	269	31	,	,	PUNCT
cana-1652	269	32	2013	2013	NUM
cana-1652	269	33	.	.	PUNCT
cana-1652	270	1	[	[	X
cana-1652	270	2	16	16	NUM
cana-1652	270	3	]	]	X
cana-1652	270	4	haynes	hayne	NOUN
cana-1652	270	5	,	,	PUNCT
cana-1652	270	6	t.	t.	NOUN
cana-1652	270	7	domination	domination	NOUN
cana-1652	270	8	in	in	ADP
cana-1652	270	9	graphs	graph	NOUN
cana-1652	270	10	:	:	PUNCT
cana-1652	270	11	volume	volume	NOUN
cana-1652	270	12	2	2	NUM
cana-1652	270	13	:	:	PUNCT
cana-1652	270	14	advanced	advanced	ADJ
cana-1652	270	15	topics	topic	NOUN
cana-1652	270	16	;	;	PUNCT
cana-1652	270	17	routledge	routledge	PROPN
cana-1652	270	18	:	:	PUNCT
cana-1652	270	19	london	london	PROPN
cana-1652	270	20	,	,	PUNCT
cana-1652	270	21	uk	uk	PROPN
cana-1652	270	22	,	,	PUNCT
cana-1652	270	23	2017	2017	NUM
cana-1652	270	24	.	.	PUNCT
cana-1652	271	1	[	[	X
cana-1652	271	2	17	17	NUM
cana-1652	271	3	]	]	X
cana-1652	271	4	d.	d.	PROPN
cana-1652	271	5	ajay	ajay	PROPN
cana-1652	271	6	and	and	CCONJ
cana-1652	271	7	p.	p.	PROPN
cana-1652	271	8	chellamani	chellamani	PROPN
cana-1652	271	9	,	,	PUNCT
cana-1652	271	10	“	"	PUNCT
cana-1652	271	11	pythagorean	pythagorean	PROPN
cana-1652	271	12	neutrosophic	neutrosophic	ADJ
cana-1652	271	13	fuzzy	fuzzy	ADJ
cana-1652	271	14	graphs	graph	NOUN
cana-1652	271	15	”	"	PUNCT
cana-1652	271	16	,	,	PUNCT
cana-1652	271	17	international	international	ADJ
cana-1652	271	18	journal	journal	NOUN
cana-1652	271	19	of	of	ADP
cana-1652	271	20	neutrosophic	neutrosophic	ADJ
cana-1652	271	21	science	science	NOUN
cana-1652	271	22	,	,	PUNCT
cana-1652	271	23	vol	vol	NOUN
cana-1652	271	24	.	.	PROPN
cana-1652	271	25	11	11	NUM
cana-1652	271	26	,	,	PUNCT
cana-1652	271	27	pp	pp	ADJ
cana-1652	271	28	.	.	PUNCT
cana-1652	272	1	108–114	108–114	NUM
cana-1652	272	2	,	,	PUNCT
cana-1652	272	3	(	(	PUNCT
cana-1652	272	4	2020	2020	NUM
cana-1652	272	5	)	)	PUNCT
cana-1652	272	6	.	.	PUNCT
cana-1652	273	1	[	[	X
cana-1652	273	2	18	18	NUM
cana-1652	273	3	]	]	X
cana-1652	273	4	haynes	hayne	NOUN
cana-1652	273	5	,	,	PUNCT
cana-1652	273	6	t.w	t.w	PROPN
cana-1652	273	7	.	.	PROPN
cana-1652	273	8	;	;	PUNCT
cana-1652	273	9	hedetniemi	hedetniemi	PROPN
cana-1652	273	10	,	,	PUNCT
cana-1652	273	11	s.t	s.t	PROPN
cana-1652	273	12	.	.	PROPN
cana-1652	273	13	;	;	PUNCT
cana-1652	273	14	henning	henning	PROPN
cana-1652	273	15	,	,	PUNCT
cana-1652	273	16	m.a	m.a	PROPN
cana-1652	273	17	.	.	PROPN
cana-1652	273	18	topics	topic	NOUN
cana-1652	273	19	in	in	ADP
cana-1652	273	20	domination	domination	NOUN
cana-1652	273	21	in	in	ADP
cana-1652	273	22	graphs	graph	NOUN
cana-1652	273	23	;	;	PUNCT
cana-1652	273	24	springer	springer	NOUN
cana-1652	273	25	international	international	ADJ
cana-1652	273	26	publishing	publishing	NOUN
cana-1652	273	27	:	:	PUNCT
cana-1652	273	28	cham	cham	PROPN
cana-1652	273	29	,	,	PUNCT
cana-1652	273	30	switzerland	switzerland	PROPN
cana-1652	273	31	,	,	PUNCT
cana-1652	273	32	2020	2020	NUM
cana-1652	273	33	.	.	PUNCT
cana-1652	274	1	[	[	X
cana-1652	274	2	19	19	NUM
cana-1652	274	3	]	]	PUNCT
cana-1652	274	4	p.	p.	NOUN
cana-1652	274	5	chellamani	chellamani	PROPN
cana-1652	274	6	and	and	CCONJ
cana-1652	274	7	d.	d.	PROPN
cana-1652	274	8	ajay	ajay	PROPN
cana-1652	274	9	,	,	PUNCT
cana-1652	274	10	“	"	PUNCT
cana-1652	274	11	pythagorean	pythagorean	PROPN
cana-1652	274	12	neutrosophic	neutrosophic	PROPN
cana-1652	274	13	dombi	dombi	NOUN
cana-1652	274	14	fuzzy	fuzzy	ADJ
cana-1652	274	15	graphs	graph	NOUN
cana-1652	274	16	with	with	ADP
cana-1652	274	17	an	an	DET
cana-1652	274	18	application	application	NOUN
cana-1652	274	19	to	to	ADP
cana-1652	274	20	mcdm	mcdm	PROPN
cana-1652	274	21	”	"	PUNCT
cana-1652	274	22	,	,	PUNCT
cana-1652	274	23	neutrosophic	neutrosophic	ADJ
cana-1652	274	24	sets	set	NOUN
cana-1652	274	25	and	and	CCONJ
cana-1652	274	26	systems	system	NOUN
cana-1652	274	27	,	,	PUNCT
cana-1652	274	28	vol	vol	NOUN
cana-1652	274	29	.	.	PROPN
cana-1652	275	1	47	47	NUM
cana-1652	275	2	,	,	PUNCT
cana-1652	275	3	pp	pp	ADJ
cana-1652	275	4	.	.	PUNCT
cana-1652	276	1	411–431	411–431	NUM
cana-1652	276	2	,	,	PUNCT
cana-1652	276	3	(	(	PUNCT
cana-1652	276	4	2021	2021	NUM
cana-1652	276	5	)	)	PUNCT
cana-1652	276	6	.	.	PUNCT
cana-1652	277	1	[	[	X
cana-1652	277	2	20	20	NUM
cana-1652	277	3	]	]	X
cana-1652	277	4	d.	d.	PROPN
cana-1652	277	5	ajay	ajay	PROPN
cana-1652	277	6	,	,	PUNCT
cana-1652	277	7	s.	s.	PROPN
cana-1652	277	8	john	john	PROPN
cana-1652	277	9	borg	borg	PROPN
cana-1652	277	10	and	and	CCONJ
cana-1652	277	11	p.	p.	PROPN
cana-1652	277	12	chellamani	chellamani	PROPN
cana-1652	277	13	,	,	PUNCT
cana-1652	277	14	“	"	PUNCT
cana-1652	277	15	domination	domination	NOUN
cana-1652	277	16	in	in	ADP
cana-1652	277	17	pythagorean	pythagorean	PROPN
cana-1652	277	18	neutrosophic	neutrosophic	ADJ
cana-1652	277	19	graphs	graph	NOUN
cana-1652	277	20	with	with	ADP
cana-1652	277	21	an	an	DET
cana-1652	277	22	application	application	NOUN
cana-1652	277	23	in	in	ADP
cana-1652	277	24	fuzzy	fuzzy	ADJ
cana-1652	277	25	intelligent	intelligent	ADJ
cana-1652	277	26	decision	decision	NOUN
cana-1652	277	27	making	make	VERB
cana-1652	277	28	”	"	PUNCT
cana-1652	277	29	,	,	PUNCT
cana-1652	277	30	international	international	ADJ
cana-1652	277	31	conference	conference	NOUN
cana-1652	277	32	on	on	ADP
cana-1652	277	33	intelligent	intelligent	ADJ
cana-1652	277	34	and	and	CCONJ
cana-1652	277	35	fuzzy	fuzzy	ADJ
cana-1652	277	36	systems	system	NOUN
cana-1652	277	37	.	.	PUNCT
cana-1652	278	1	cham	cham	PROPN
cana-1652	278	2	:	:	PUNCT
cana-1652	278	3	springer	springer	NOUN
cana-1652	278	4	international	international	ADJ
cana-1652	278	5	publishing	publishing	NOUN
cana-1652	278	6	.	.	PUNCT
cana-1652	278	7	,	,	PUNCT
cana-1652	279	1	pp	pp	PROPN
cana-1652	279	2	.	.	PUNCT
cana-1652	280	1	667	667	NUM
cana-1652	280	2	-	-	SYM
cana-1652	280	3	675	675	NUM
cana-1652	280	4	,	,	PUNCT
cana-1652	280	5	(	(	PUNCT
cana-1652	280	6	2022	2022	NUM
cana-1652	280	7	)	)	PUNCT
cana-1652	280	8	.	.	PUNCT
cana-1652	281	1	[	[	X
cana-1652	281	2	21	21	NUM
cana-1652	281	3	]	]	X
cana-1652	281	4	henning	henning	PROPN
cana-1652	281	5	,	,	PUNCT
cana-1652	281	6	m.a	m.a	PROPN
cana-1652	281	7	.	.	PROPN
cana-1652	281	8	;	;	PUNCT
cana-1652	281	9	macgillivray	macgillivray	PROPN
cana-1652	281	10	,	,	PUNCT
cana-1652	281	11	g.	g.	PROPN
cana-1652	281	12	;	;	PUNCT
cana-1652	281	13	yang	yang	PROPN
cana-1652	281	14	,	,	PUNCT
cana-1652	281	15	f.	f.	PROPN
cana-1652	281	16	broadcast	broadcast	PROPN
cana-1652	281	17	domination	domination	NOUN
cana-1652	281	18	in	in	ADP
cana-1652	281	19	graphs	graph	NOUN
cana-1652	281	20	.	.	PUNCT
cana-1652	282	1	in	in	ADP
cana-1652	282	2	structures	structure	NOUN
cana-1652	282	3	of	of	ADP
cana-1652	282	4	domination	domination	NOUN
cana-1652	282	5	in	in	ADP
cana-1652	282	6	graphs	graph	NOUN
cana-1652	282	7	;	;	PUNCT
cana-1652	282	8	haynes	hayne	NOUN
cana-1652	282	9	,	,	PUNCT
cana-1652	282	10	t.w	t.w	PROPN
cana-1652	282	11	.	.	PROPN
cana-1652	282	12	,	,	PUNCT
cana-1652	282	13	hedetniemi	hedetniemi	PROPN
cana-1652	282	14	,	,	PUNCT
cana-1652	282	15	s.t	s.t	PROPN
cana-1652	282	16	.	.	PROPN
cana-1652	282	17	,	,	PUNCT
cana-1652	282	18	henning	henning	PROPN
cana-1652	282	19	,	,	PUNCT
cana-1652	282	20	m.a	m.a	PROPN
cana-1652	282	21	.	.	PROPN
cana-1652	282	22	,	,	PUNCT
cana-1652	282	23	eds	eds	PROPN
cana-1652	282	24	.	.	PUNCT
cana-1652	282	25	;	;	PUNCT
cana-1652	282	26	springer	springer	NOUN
cana-1652	282	27	international	international	ADJ
cana-1652	282	28	publishing	publishing	NOUN
cana-1652	282	29	:	:	PUNCT
cana-1652	282	30	cham	cham	PROPN
cana-1652	282	31	,	,	PUNCT
cana-1652	282	32	switzerland	switzerland	PROPN
cana-1652	282	33	,	,	PUNCT
cana-1652	282	34	2021	2021	NUM
cana-1652	282	35	;	;	PUNCT
cana-1652	282	36	pp	pp	X
cana-1652	282	37	.	.	PUNCT
cana-1652	282	38	15	15	NUM
cana-1652	282	39	-	-	SYM
cana-1652	282	40	46	46	NUM
cana-1652	282	41	.	.	PUNCT
cana-1652	283	1	[	[	X
cana-1652	283	2	22	22	NUM
cana-1652	283	3	]	]	X
cana-1652	283	4	al	al	PROPN
cana-1652	283	5	-	-	PUNCT
cana-1652	283	6	harere	harere	PROPN
cana-1652	283	7	,	,	PUNCT
cana-1652	283	8	m.n	m.n	PROPN
cana-1652	283	9	.	.	PROPN
cana-1652	283	10	;	;	PUNCT
cana-1652	283	11	abdlhusein	abdlhusein	PROPN
cana-1652	283	12	,	,	PUNCT
cana-1652	283	13	m.a	m.a	PROPN
cana-1652	283	14	.	.	PROPN
cana-1652	283	15	pitchfork	pitchfork	NOUN
cana-1652	283	16	domination	domination	NOUN
cana-1652	283	17	in	in	ADP
cana-1652	283	18	graphs	graph	NOUN
cana-1652	283	19	.	.	PUNCT
cana-1652	284	1	discret	discret	PROPN
cana-1652	284	2	.	.	PUNCT
cana-1652	284	3	math	math	NOUN
cana-1652	284	4	.	.	PUNCT
cana-1652	285	1	algorithms	algorithms	PROPN
cana-1652	285	2	appl	appl	PROPN
cana-1652	285	3	.	.	PUNCT
cana-1652	286	1	2020	2020	NUM
cana-1652	286	2	,	,	PUNCT
cana-1652	286	3	12	12	NUM
cana-1652	286	4	,	,	PUNCT
cana-1652	286	5	2050025	2050025	NUM
cana-1652	286	6	.	.	PUNCT
cana-1652	287	1	[	[	X
cana-1652	287	2	23	23	NUM
cana-1652	287	3	]	]	X
cana-1652	287	4	d.	d.	PROPN
cana-1652	287	5	ajay	ajay	PROPN
cana-1652	287	6	,	,	PUNCT
cana-1652	287	7	p.	p.	NOUN
cana-1652	287	8	chellamani	chellamani	PROPN
cana-1652	287	9	,	,	PUNCT
cana-1652	287	10	g.	g.	PROPN
cana-1652	287	11	rajchakit	rajchakit	PROPN
cana-1652	287	12	,	,	PUNCT
cana-1652	287	13	n.	n.	NOUN
cana-1652	287	14	boonsatit	boonsatit	NOUN
cana-1652	287	15	,	,	PUNCT
cana-1652	287	16	and	and	CCONJ
cana-1652	287	17	p.	p.	NOUN
cana-1652	287	18	hammachukiattikul	hammachukiattikul	NOUN
cana-1652	287	19	.	.	PUNCT
cana-1652	288	1	“	"	PUNCT
cana-1652	288	2	regularity	regularity	NOUN
cana-1652	288	3	of	of	ADP
cana-1652	288	4	pythagorean	pythagorean	PROPN
cana-1652	288	5	neutrosophic	neutrosophic	ADJ
cana-1652	288	6	graphs	graph	NOUN
cana-1652	288	7	with	with	ADP
cana-1652	288	8	an	an	DET
cana-1652	288	9	illustration	illustration	NOUN
cana-1652	288	10	in	in	ADP
cana-1652	288	11	mcdm	mcdm	PROPN
cana-1652	288	12	”	"	PUNCT
cana-1652	288	13	,	,	PUNCT
cana-1652	288	14	aims	aim	VERB
cana-1652	288	15	mathematics	mathematic	NOUN
cana-1652	288	16	,	,	PUNCT
cana-1652	288	17	vol	vol	NOUN
cana-1652	288	18	.	.	PROPN
cana-1652	288	19	5	5	NUM
cana-1652	288	20	,	,	PUNCT
cana-1652	288	21	pp	pp	ADJ
cana-1652	288	22	.	.	PUNCT
cana-1652	288	23	9424	9424	NUM
cana-1652	288	24	–	–	PUNCT
cana-1652	288	25	9442	9442	NUM
cana-1652	288	26	,	,	PUNCT
cana-1652	288	27	(	(	PUNCT
cana-1652	288	28	2022	2022	NUM
cana-1652	288	29	)	)	PUNCT
cana-1652	288	30	.	.	PUNCT
cana-1652	289	1	[	[	X
cana-1652	289	2	24	24	NUM
cana-1652	289	3	]	]	X
cana-1652	289	4	chellali	chellali	PROPN
cana-1652	289	5	,	,	PUNCT
cana-1652	289	6	m.	m.	NOUN
cana-1652	289	7	;	;	PUNCT
cana-1652	289	8	rad	rad	PROPN
cana-1652	289	9	,	,	PUNCT
cana-1652	289	10	n.j	n.j	PROPN
cana-1652	289	11	.	.	PROPN
cana-1652	289	12	;	;	PUNCT
cana-1652	289	13	sheikholeslami	sheikholeslami	PROPN
cana-1652	289	14	,	,	PUNCT
cana-1652	289	15	s.m	s.m	PROPN
cana-1652	289	16	.	.	PROPN
cana-1652	289	17	;	;	PUNCT
cana-1652	289	18	volkmann	volkmann	PROPN
cana-1652	289	19	,	,	PUNCT
cana-1652	289	20	l.	l.	PROPN
cana-1652	289	21	roman	roman	PROPN
cana-1652	289	22	domination	domination	NOUN
cana-1652	289	23	in	in	ADP
cana-1652	289	24	graphs	graph	NOUN
cana-1652	289	25	.	.	PUNCT
cana-1652	290	1	in	in	ADP
cana-1652	290	2	topics	topic	NOUN
cana-1652	290	3	in	in	ADP
cana-1652	290	4	domination	domination	NOUN
cana-1652	290	5	in	in	ADP
cana-1652	290	6	graphs	graph	NOUN
cana-1652	290	7	;	;	PUNCT
cana-1652	290	8	springer	springer	NOUN
cana-1652	290	9	international	international	ADJ
cana-1652	290	10	publishing	publishing	NOUN
cana-1652	290	11	:	:	PUNCT
cana-1652	290	12	cham	cham	PROPN
cana-1652	290	13	,	,	PUNCT
cana-1652	290	14	switzerland	switzerland	PROPN
cana-1652	290	15	,	,	PUNCT
cana-1652	290	16	2020	2020	NUM
cana-1652	290	17	;	;	PUNCT
cana-1652	290	18	pp	pp	X
cana-1652	290	19	.	.	PUNCT
cana-1652	291	1	365	365	NUM
cana-1652	291	2	-	-	SYM
cana-1652	291	3	409	409	NUM
cana-1652	291	4	.	.	PUNCT
cana-1652	292	1	[	[	X
cana-1652	292	2	25	25	NUM
cana-1652	292	3	]	]	X
cana-1652	292	4	d.	d.	PROPN
cana-1652	292	5	ajay	ajay	PROPN
cana-1652	292	6	and	and	CCONJ
cana-1652	292	7	p.	p.	PROPN
cana-1652	292	8	chellamani	chellamani	PROPN
cana-1652	292	9	,	,	PUNCT
cana-1652	292	10	“	"	PUNCT
cana-1652	292	11	operations	operation	NOUN
cana-1652	292	12	on	on	ADP
cana-1652	292	13	pythagorean	pythagorean	PROPN
cana-1652	292	14	neutrosophic	neutrosophic	ADJ
cana-1652	292	15	graphs	graph	NOUN
cana-1652	292	16	”	"	PUNCT
cana-1652	292	17	,	,	PUNCT
cana-1652	292	18	aip	aip	PROPN
cana-1652	292	19	conference	conference	NOUN
cana-1652	292	20	proceedings	proceeding	NOUN
cana-1652	292	21	,	,	PUNCT
cana-1652	292	22	vol	vol	NOUN
cana-1652	292	23	.	.	PROPN
cana-1652	292	24	2516	2516	NUM
cana-1652	292	25	,	,	PUNCT
cana-1652	292	26	pp	pp	ADJ
cana-1652	292	27	.	.	PUNCT
cana-1652	292	28	200028	200028	NUM
cana-1652	292	29	,	,	PUNCT
cana-1652	292	30	(	(	PUNCT
cana-1652	292	31	2022	2022	NUM
cana-1652	292	32	)	)	PUNCT
cana-1652	292	33	.	.	PUNCT
cana-1652	293	1	[	[	X
cana-1652	293	2	26	26	NUM
cana-1652	293	3	]	]	X
cana-1652	293	4	yue	yue	PROPN
cana-1652	293	5	,	,	PUNCT
cana-1652	293	6	j.	j.	PROPN
cana-1652	293	7	;	;	PUNCT
cana-1652	293	8	wei	wei	PROPN
cana-1652	293	9	,	,	PUNCT
cana-1652	293	10	m.	m.	NOUN
cana-1652	293	11	;	;	PUNCT
cana-1652	293	12	li	li	PROPN
cana-1652	293	13	,	,	PUNCT
cana-1652	293	14	m.	m.	NOUN
cana-1652	293	15	;	;	PUNCT
cana-1652	293	16	liu	liu	PROPN
cana-1652	293	17	,	,	PUNCT
cana-1652	293	18	g.	g.	PROPN
cana-1652	293	19	on	on	ADP
cana-1652	293	20	the	the	DET
cana-1652	293	21	double	double	ADJ
cana-1652	293	22	roman	roman	ADJ
cana-1652	293	23	domination	domination	NOUN
cana-1652	293	24	of	of	ADP
cana-1652	293	25	graphs	graph	NOUN
cana-1652	293	26	.	.	PUNCT
cana-1652	294	1	appl	appl	PROPN
cana-1652	294	2	.	.	PROPN
cana-1652	294	3	math	math	PROPN
cana-1652	294	4	.	.	PUNCT
cana-1652	295	1	comput	comput	NOUN
cana-1652	295	2	.	.	PUNCT
cana-1652	296	1	2018	2018	NUM
cana-1652	296	2	,	,	PUNCT
cana-1652	296	3	338	338	NUM
cana-1652	296	4	,	,	PUNCT
cana-1652	296	5	669675	669675	NUM
cana-1652	296	6	.	.	PUNCT
cana-1652	297	1	[	[	X
cana-1652	297	2	27	27	NUM
cana-1652	297	3	]	]	SYM
cana-1652	297	4	ahangar	ahangar	NOUN
cana-1652	297	5	,	,	PUNCT
cana-1652	297	6	h.a	h.a	PROPN
cana-1652	297	7	.	.	PROPN
cana-1652	297	8	;	;	PUNCT
cana-1652	297	9	álvarez	álvarez	PROPN
cana-1652	297	10	,	,	PUNCT
cana-1652	297	11	m.	m.	NOUN
cana-1652	297	12	;	;	PUNCT
cana-1652	297	13	chellali	chellali	PROPN
cana-1652	297	14	,	,	PUNCT
cana-1652	297	15	m.	m.	NOUN
cana-1652	297	16	;	;	PUNCT
cana-1652	297	17	sheikholeslami	sheikholeslami	NOUN
cana-1652	297	18	,	,	PUNCT
cana-1652	297	19	s.	s.	PROPN
cana-1652	297	20	;	;	PUNCT
cana-1652	297	21	valenzuela	valenzuela	PROPN
cana-1652	297	22	-	-	PUNCT
cana-1652	297	23	tripodoro	tripodoro	PROPN
cana-1652	297	24	,	,	PUNCT
cana-1652	297	25	j.	j.	PROPN
cana-1652	297	26	triple	triple	ADJ
cana-1652	297	27	roman	roman	ADJ
cana-1652	297	28	domination	domination	NOUN
cana-1652	297	29	in	in	ADP
cana-1652	297	30	graphs	graph	NOUN
cana-1652	297	31	.	.	PUNCT
cana-1652	298	1	appl	appl	PROPN
cana-1652	298	2	.	.	PROPN
cana-1652	298	3	math	math	PROPN
cana-1652	298	4	.	.	PUNCT
cana-1652	299	1	comput	comput	NOUN
cana-1652	299	2	.	.	PUNCT
cana-1652	300	1	2021	2021	NUM
cana-1652	300	2	,	,	PUNCT
cana-1652	300	3	391	391	NUM
cana-1652	300	4	,	,	PUNCT
cana-1652	300	5	125444	125444	NUM
cana-1652	300	6	.	.	PUNCT
cana-1652	301	1	[	[	X
cana-1652	301	2	28	28	NUM
cana-1652	301	3	]	]	X
cana-1652	301	4	al	al	PROPN
cana-1652	301	5	-	-	PUNCT
cana-1652	301	6	harere	harere	PROPN
cana-1652	301	7	,	,	PUNCT
cana-1652	301	8	m.n	m.n	PROPN
cana-1652	301	9	.	.	PROPN
cana-1652	301	10	;	;	PUNCT
cana-1652	301	11	omran	omran	PROPN
cana-1652	301	12	,	,	PUNCT
cana-1652	301	13	a.a	a.a	PROPN
cana-1652	301	14	.	.	PROPN
cana-1652	301	15	;	;	PUNCT
cana-1652	301	16	breesam	breesam	PROPN
cana-1652	301	17	,	,	PUNCT
cana-1652	301	18	a.t	a.t	PROPN
cana-1652	301	19	.	.	PROPN
cana-1652	301	20	captive	captive	ADJ
cana-1652	301	21	domination	domination	NOUN
cana-1652	301	22	in	in	ADP
cana-1652	301	23	graphs	graph	NOUN
cana-1652	301	24	.	.	PUNCT
cana-1652	302	1	discret	discret	PROPN
cana-1652	302	2	.	.	PUNCT
cana-1652	302	3	math	math	NOUN
cana-1652	302	4	.	.	PUNCT
cana-1652	303	1	algorithms	algorithms	PROPN
cana-1652	303	2	appl	appl	PROPN
cana-1652	303	3	.	.	PUNCT
cana-1652	304	1	2020	2020	NUM
cana-1652	304	2	,	,	PUNCT
cana-1652	304	3	12	12	NUM
cana-1652	304	4	,	,	PUNCT
cana-1652	304	5	2050076	2050076	NUM
cana-1652	304	6	.	.	PUNCT
cana-1652	305	1	[	[	X
cana-1652	305	2	29	29	NUM
cana-1652	305	3	]	]	X
cana-1652	305	4	p.	p.	NOUN
cana-1652	305	5	chellamani	chellamani	PROPN
cana-1652	305	6	,	,	PUNCT
cana-1652	305	7	d.	d.	PROPN
cana-1652	305	8	ajay	ajay	PROPN
cana-1652	305	9	,	,	PUNCT
cana-1652	305	10	mohammed	mohammed	PROPN
cana-1652	305	11	m.	m.	PROPN
cana-1652	305	12	al	al	PROPN
cana-1652	305	13	-	-	PUNCT
cana-1652	305	14	shamiri	shamiri	PROPN
cana-1652	305	15	,	,	PUNCT
cana-1652	305	16	and	and	CCONJ
cana-1652	305	17	rashad	rashad	VERB
cana-1652	305	18	ismail	ismail	PROPN
cana-1652	305	19	,	,	PUNCT
cana-1652	305	20	“	"	PUNCT
cana-1652	305	21	pythagorean	pythagorean	PROPN
cana-1652	305	22	neutrosophic	neutrosophic	ADJ
cana-1652	305	23	planar	planar	ADJ
cana-1652	305	24	graphs	graph	NOUN
cana-1652	305	25	with	with	ADP
cana-1652	305	26	an	an	DET
cana-1652	305	27	application	application	NOUN
cana-1652	305	28	in	in	ADP
cana-1652	305	29	decision	decision	NOUN
cana-1652	305	30	-	-	PUNCT
cana-1652	305	31	making	making	NOUN
cana-1652	305	32	”	"	PUNCT
cana-1652	305	33	,	,	PUNCT
cana-1652	305	34	computers	computer	NOUN
cana-1652	305	35	,	,	PUNCT
cana-1652	305	36	materials	material	NOUN
cana-1652	305	37	&	&	CCONJ
cana-1652	305	38	continua	continua	PROPN
cana-1652	305	39	,	,	PUNCT
cana-1652	305	40	vol	vol	NOUN
cana-1652	305	41	.	.	PROPN
cana-1652	305	42	75	75	NUM
cana-1652	305	43	,	,	PUNCT
cana-1652	305	44	(	(	PUNCT
cana-1652	305	45	2023	2023	NUM
cana-1652	305	46	)	)	PUNCT
cana-1652	305	47	.	.	PUNCT
cana-1652	306	1	[	[	X
cana-1652	306	2	30	30	NUM
cana-1652	306	3	]	]	SYM
cana-1652	306	4	dayap	dayap	NOUN
cana-1652	306	5	,	,	PUNCT
cana-1652	306	6	j.a	j.a	PROPN
cana-1652	306	7	.	.	PROPN
cana-1652	306	8	;	;	PUNCT
cana-1652	306	9	enriquez	enriquez	PROPN
cana-1652	306	10	,	,	PUNCT
cana-1652	306	11	e.l	e.l	PROPN
cana-1652	306	12	.	.	PROPN
cana-1652	306	13	outer	outer	ADJ
cana-1652	306	14	-	-	PUNCT
cana-1652	306	15	convex	convex	NOUN
cana-1652	306	16	domination	domination	NOUN
cana-1652	306	17	in	in	ADP
cana-1652	306	18	graphs	graph	NOUN
cana-1652	306	19	.	.	PUNCT
cana-1652	307	1	discret	discret	PROPN
cana-1652	307	2	.	.	PUNCT
cana-1652	307	3	math	math	NOUN
cana-1652	307	4	.	.	PUNCT
cana-1652	308	1	algorithms	algorithms	PROPN
cana-1652	308	2	appl	appl	PROPN
cana-1652	308	3	.	.	PROPN
cana-1652	309	1	2019	2019	NUM
cana-1652	309	2	,	,	PUNCT
cana-1652	309	3	12	12	NUM
cana-1652	309	4	,	,	PUNCT
cana-1652	309	5	2050008	2050008	NUM
cana-1652	309	6	.	.	PUNCT
cana-1652	310	1	[	[	X
cana-1652	310	2	31	31	NUM
cana-1652	310	3	]	]	X
cana-1652	310	4	desormeaux	desormeaux	NOUN
cana-1652	310	5	,	,	PUNCT
cana-1652	310	6	w.j	w.j	PROPN
cana-1652	310	7	.	.	PROPN
cana-1652	310	8	;	;	PUNCT
cana-1652	310	9	haynes	haynes	PROPN
cana-1652	310	10	,	,	PUNCT
cana-1652	310	11	t.w	t.w	PROPN
cana-1652	310	12	.	.	PROPN
cana-1652	310	13	;	;	PUNCT
cana-1652	310	14	henning	henning	PROPN
cana-1652	310	15	,	,	PUNCT
cana-1652	310	16	m.a	m.a	PROPN
cana-1652	310	17	.	.	PROPN
cana-1652	310	18	paired	pair	VERB
cana-1652	310	19	domination	domination	NOUN
cana-1652	310	20	in	in	ADP
cana-1652	310	21	graphs	graph	NOUN
cana-1652	310	22	.	.	PUNCT
cana-1652	311	1	in	in	ADP
cana-1652	311	2	topics	topic	NOUN
cana-1652	311	3	in	in	ADP
cana-1652	311	4	domination	domination	NOUN
cana-1652	311	5	in	in	ADP
cana-1652	311	6	graphs	graph	NOUN
cana-1652	311	7	;	;	PUNCT
cana-1652	311	8	springer	springer	NOUN
cana-1652	311	9	international	international	ADJ
cana-1652	311	10	publishing	publishing	NOUN
cana-1652	311	11	:	:	PUNCT
cana-1652	311	12	cham	cham	PROPN
cana-1652	311	13	,	,	PUNCT
cana-1652	311	14	switzerland	switzerland	PROPN
cana-1652	311	15	,	,	PUNCT
cana-1652	311	16	2020	2020	NUM
cana-1652	311	17	;	;	PUNCT
cana-1652	311	18	pp	pp	X
cana-1652	311	19	.	.	PUNCT
cana-1652	312	1	31	31	NUM
cana-1652	312	2	-	-	SYM
cana-1652	312	3	77	77	NUM
cana-1652	312	4	.	.	PUNCT
cana-1652	313	1	[	[	X
cana-1652	313	2	32	32	NUM
cana-1652	313	3	]	]	SYM
cana-1652	313	4	somasundaram	somasundaram	PROPN
cana-1652	313	5	,	,	PUNCT
cana-1652	313	6	a.	a.	NOUN
cana-1652	313	7	;	;	PUNCT
cana-1652	313	8	somasundaram	somasundaram	PROPN
cana-1652	313	9	,	,	PUNCT
cana-1652	313	10	s.	s.	PROPN
cana-1652	313	11	domination	domination	PROPN
cana-1652	313	12	in	in	ADP
cana-1652	313	13	fuzzy	fuzzy	ADJ
cana-1652	313	14	graphs	graph	NOUN
cana-1652	313	15	–	–	PUNCT
cana-1652	313	16	i.	i.	NOUN
cana-1652	313	17	pattern	pattern	NOUN
cana-1652	313	18	recognit	recognit	VERB
cana-1652	313	19	.	.	PUNCT
cana-1652	314	1	lett	lett	PROPN
cana-1652	314	2	.	.	PUNCT
cana-1652	315	1	1998	1998	NUM
cana-1652	315	2	,	,	PUNCT
cana-1652	315	3	19	19	NUM
cana-1652	315	4	,	,	PUNCT
cana-1652	315	5	787	787	NUM
cana-1652	315	6	-	-	SYM
cana-1652	315	7	791	791	NUM
cana-1652	315	8	.	.	PUNCT
cana-1652	316	1	[	[	X
cana-1652	316	2	33	33	NUM
cana-1652	316	3	]	]	SYM
cana-1652	316	4	mordeson	mordeson	NOUN
cana-1652	316	5	,	,	PUNCT
cana-1652	316	6	j.	j.	PROPN
cana-1652	316	7	;	;	PUNCT
cana-1652	316	8	nair	nair	PROPN
cana-1652	316	9	,	,	PUNCT
cana-1652	316	10	p.	p.	NOUN
cana-1652	316	11	successor	successor	NOUN
cana-1652	316	12	and	and	CCONJ
cana-1652	316	13	source	source	NOUN
cana-1652	316	14	of	of	ADP
cana-1652	316	15	(	(	PUNCT
cana-1652	316	16	fuzzy	fuzzy	ADJ
cana-1652	316	17	)	)	PUNCT
cana-1652	316	18	finite	finite	PROPN
cana-1652	316	19	state	state	NOUN
cana-1652	316	20	machines	machine	NOUN
cana-1652	316	21	and	and	CCONJ
cana-1652	316	22	(	(	PUNCT
cana-1652	316	23	fuzzy	fuzzy	ADJ
cana-1652	316	24	)	)	PUNCT
cana-1652	316	25	directed	direct	VERB
cana-1652	316	26	graphs	graph	NOUN
cana-1652	316	27	.	.	PUNCT
cana-1652	317	1	inf	inf	PROPN
cana-1652	317	2	.	.	PUNCT
cana-1652	318	1	sci	sci	PROPN
cana-1652	318	2	.	.	PROPN
cana-1652	318	3	1996	1996	NUM
cana-1652	318	4	,	,	PUNCT
cana-1652	318	5	95	95	NUM
cana-1652	318	6	,	,	PUNCT
cana-1652	318	7	113	113	NUM
cana-1652	318	8	-	-	SYM
cana-1652	318	9	124	124	NUM
cana-1652	318	10	.	.	PUNCT
cana-1652	319	1	communications	communication	NOUN
cana-1652	319	2	on	on	ADP
cana-1652	319	3	applied	apply	VERB
cana-1652	319	4	nonlinear	nonlinear	ADJ
cana-1652	319	5	analysis	analysis	NOUN
cana-1652	319	6	issn	issn	NOUN
cana-1652	319	7	:	:	PUNCT
cana-1652	319	8	1074	1074	NUM
cana-1652	319	9	-	-	PUNCT
cana-1652	319	10	133x	133x	NUM
cana-1652	319	11	vol	vol	NOUN
cana-1652	319	12	32	32	NUM
cana-1652	319	13	no	no	NOUN
cana-1652	319	14	.	.	NOUN
cana-1652	319	15	1	1	NUM
cana-1652	319	16	(	(	PUNCT
cana-1652	319	17	2025	2025	NUM
cana-1652	319	18	)	)	PUNCT
cana-1652	320	1	334	334	NUM
cana-1652	320	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1652	321	1	[	[	X
cana-1652	321	2	34	34	NUM
cana-1652	321	3	]	]	PUNCT
cana-1652	321	4	s.	s.	PROPN
cana-1652	321	5	broumi	broumi	PROPN
cana-1652	321	6	,	,	PUNCT
cana-1652	321	7	r.	r.	PROPN
cana-1652	321	8	sundareswaran	sundareswaran	PROPN
cana-1652	321	9	,	,	PUNCT
cana-1652	321	10	m.	m.	NOUN
cana-1652	321	11	shanmugapriya	shanmugapriya	PROPN
cana-1652	321	12	,	,	PUNCT
cana-1652	321	13	p.	p.	NOUN
cana-1652	321	14	chellamani	chellamani	PROPN
cana-1652	321	15	,	,	PUNCT
cana-1652	321	16	a.	a.	NOUN
cana-1652	321	17	bakali	bakali	PROPN
cana-1652	321	18	and	and	CCONJ
cana-1652	321	19	m.	m.	NOUN
cana-1652	321	20	talea	talea	ADV
cana-1652	321	21	,	,	PUNCT
cana-1652	321	22	“	"	PUNCT
cana-1652	321	23	determination	determination	NOUN
cana-1652	321	24	of	of	ADP
cana-1652	321	25	various	various	ADJ
cana-1652	321	26	factors	factor	NOUN
cana-1652	321	27	to	to	PART
cana-1652	321	28	evaluate	evaluate	VERB
cana-1652	321	29	a	a	DET
cana-1652	321	30	successful	successful	ADJ
cana-1652	321	31	curriculum	curriculum	NOUN
cana-1652	321	32	design	design	NOUN
cana-1652	321	33	using	use	VERB
cana-1652	321	34	interval	interval	NOUN
cana-1652	321	35	-	-	PUNCT
cana-1652	321	36	valued	value	VERB
cana-1652	321	37	pythagorean	pythagorean	PROPN
cana-1652	321	38	neutrosophic	neutrosophic	ADJ
cana-1652	321	39	graphs	graph	NOUN
cana-1652	321	40	”	"	PUNCT
cana-1652	321	41	,	,	PUNCT
cana-1652	321	42	soft	soft	ADJ
cana-1652	321	43	computing	computing	NOUN
cana-1652	321	44	,	,	PUNCT
cana-1652	321	45	pp	pp	ADJ
cana-1652	321	46	.	.	PUNCT
cana-1652	322	1	1–20	1–20	NUM
cana-1652	322	2	,	,	PUNCT
cana-1652	322	3	(	(	PUNCT
cana-1652	322	4	2023	2023	NUM
cana-1652	322	5	)	)	PUNCT
cana-1652	322	6	.	.	PUNCT
cana-1652	323	1	[	[	X
cana-1652	323	2	35	35	NUM
cana-1652	323	3	]	]	X
cana-1652	323	4	kumar	kumar	PROPN
cana-1652	323	5	,	,	PUNCT
cana-1652	323	6	p.k.k	p.k.k	NOUN
cana-1652	323	7	.	.	PUNCT
cana-1652	323	8	;	;	PUNCT
cana-1652	323	9	lavanya	lavanya	PROPN
cana-1652	323	10	,	,	PUNCT
cana-1652	323	11	s.	s.	PROPN
cana-1652	323	12	on	on	ADP
cana-1652	323	13	fuzzy	fuzzy	ADJ
cana-1652	323	14	digraphs	digraph	NOUN
cana-1652	323	15	.	.	PUNCT
cana-1652	324	1	int	int	NOUN
cana-1652	324	2	.	.	PUNCT
cana-1652	325	1	j.	j.	PROPN
cana-1652	325	2	pure	pure	PROPN
cana-1652	325	3	appl	appl	PROPN
cana-1652	325	4	.	.	PUNCT
cana-1652	325	5	math	math	PROPN
cana-1652	325	6	.	.	PUNCT
cana-1652	326	1	2017	2017	NUM
cana-1652	326	2	,	,	PUNCT
cana-1652	326	3	115	115	NUM
cana-1652	326	4	,	,	PUNCT
cana-1652	326	5	599-606.mathematics	599-606.mathematics	NUM
cana-1652	326	6	2021	2021	NUM
cana-1652	326	7	,	,	PUNCT
cana-1652	326	8	9	9	NUM
cana-1652	326	9	,	,	PUNCT
cana-1652	326	10	2143	2143	NUM
cana-1652	326	11	.	.	PUNCT
cana-1652	327	1	[	[	X
cana-1652	327	2	36	36	NUM
cana-1652	327	3	]	]	X
cana-1652	327	4	lin	lin	PROPN
cana-1652	327	5	,	,	PUNCT
cana-1652	327	6	c.j	c.j	PROPN
cana-1652	327	7	.	.	PROPN
cana-1652	327	8	;	;	PUNCT
cana-1652	327	9	wu	wu	PROPN
cana-1652	327	10	,	,	PUNCT
cana-1652	327	11	w.w	w.w	PROPN
cana-1652	327	12	.	.	PROPN
cana-1652	327	13	a	a	DET
cana-1652	327	14	causal	causal	ADJ
cana-1652	327	15	analytical	analytical	ADJ
cana-1652	327	16	method	method	NOUN
cana-1652	327	17	for	for	ADP
cana-1652	327	18	group	group	NOUN
cana-1652	327	19	decision	decision	NOUN
cana-1652	327	20	-	-	PUNCT
cana-1652	327	21	making	making	NOUN
cana-1652	327	22	under	under	ADP
cana-1652	327	23	fuzzy	fuzzy	ADJ
cana-1652	327	24	environment	environment	NOUN
cana-1652	327	25	.	.	PUNCT
cana-1652	328	1	expert	expert	NOUN
cana-1652	328	2	syst	syst	PROPN
cana-1652	328	3	.	.	PUNCT
cana-1652	329	1	appl	appl	PROPN
cana-1652	329	2	.	.	PROPN
cana-1652	329	3	2008	2008	NUM
cana-1652	329	4	,	,	PUNCT
cana-1652	329	5	34	34	NUM
cana-1652	329	6	,	,	PUNCT
cana-1652	329	7	205	205	NUM
cana-1652	329	8	-	-	SYM
cana-1652	329	9	213	213	NUM
cana-1652	329	10	.	.	PUNCT
cana-1652	330	1	[	[	X
cana-1652	330	2	37	37	NUM
cana-1652	330	3	]	]	X
cana-1652	330	4	kosko	kosko	PROPN
cana-1652	330	5	,	,	PUNCT
cana-1652	330	6	b.	b.	PROPN
cana-1652	330	7	fuzzy	fuzzy	ADJ
cana-1652	330	8	cognitive	cognitive	ADJ
cana-1652	330	9	maps	map	NOUN
cana-1652	330	10	.	.	PUNCT
cana-1652	331	1	int	int	NOUN
cana-1652	331	2	.	.	PUNCT
cana-1652	332	1	j.	j.	PROPN
cana-1652	332	2	man	man	PROPN
cana-1652	332	3	-	-	PUNCT
cana-1652	332	4	mach	mach	NOUN
cana-1652	332	5	.	.	PUNCT
cana-1652	333	1	stud	stud	PROPN
cana-1652	333	2	.	.	PUNCT
cana-1652	334	1	1986	1986	NUM
cana-1652	334	2	,	,	PUNCT
cana-1652	334	3	24	24	NUM
cana-1652	334	4	,	,	PUNCT
cana-1652	334	5	65	65	NUM
cana-1652	334	6	-	-	SYM
cana-1652	334	7	75	75	NUM
cana-1652	334	8	.	.	PUNCT
cana-1652	335	1	[	[	X
cana-1652	335	2	38	38	NUM
cana-1652	335	3	]	]	PUNCT
cana-1652	335	4	ragade	ragade	NOUN
cana-1652	335	5	,	,	PUNCT
cana-1652	335	6	r.k	r.k	PROPN
cana-1652	335	7	.	.	PROPN
cana-1652	335	8	fuzzy	fuzzy	ADJ
cana-1652	335	9	interpretive	interpretive	ADJ
cana-1652	335	10	structural	structural	ADJ
cana-1652	335	11	modeling	modeling	NOUN
cana-1652	335	12	.	.	PUNCT
cana-1652	336	1	j.	j.	PROPN
cana-1652	336	2	cybern	cybern	PROPN
cana-1652	336	3	.	.	PUNCT
cana-1652	337	1	1976	1976	NUM
cana-1652	337	2	,	,	PUNCT
cana-1652	337	3	6	6	NUM
cana-1652	337	4	,	,	PUNCT
cana-1652	337	5	189	189	NUM
cana-1652	337	6	-	-	SYM
cana-1652	337	7	211	211	NUM
cana-1652	337	8	.	.	PUNCT