id	sid	tid	token	lemma	pos
cana-6073	1	1	communications	communication	NOUN
cana-6073	1	2	on	on	ADP
cana-6073	1	3	applied	apply	VERB
cana-6073	1	4	nonlinear	nonlinear	ADJ
cana-6073	1	5	analysis	analysis	NOUN
cana-6073	1	6	issn	issn	NOUN
cana-6073	1	7	:	:	PUNCT
cana-6073	1	8	1074	1074	NUM
cana-6073	1	9	-	-	PUNCT
cana-6073	1	10	133x	133x	NUM
cana-6073	1	11	vol	vol	NOUN
cana-6073	1	12	31	31	NUM
cana-6073	1	13	no	no	NOUN
cana-6073	1	14	.	.	PUNCT
cana-6073	2	1	8s	8s	PROPN
cana-6073	2	2	(	(	PUNCT
cana-6073	2	3	2024	2024	NUM
cana-6073	2	4	)	)	PUNCT
cana-6073	2	5	1184	1184	NUM
cana-6073	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6073	2	7	analyzing	analyze	VERB
cana-6073	2	8	detour	detour	NOUN
cana-6073	2	9	distance	distance	NOUN
cana-6073	2	10	and	and	CCONJ
cana-6073	2	11	domination	domination	NOUN
cana-6073	2	12	number	number	NOUN
cana-6073	2	13	in	in	ADP
cana-6073	2	14	special	special	ADJ
cana-6073	2	15	graph	graph	NOUN
cana-6073	2	16	classes	class	NOUN
cana-6073	2	17	n.	n.	PROPN
cana-6073	2	18	jeyasree1	jeyasree1	PROPN
cana-6073	2	19	and	and	CCONJ
cana-6073	2	20	dr	dr	PROPN
cana-6073	2	21	s.	s.	PROPN
cana-6073	2	22	chelliah2	chelliah2	PROPN
cana-6073	3	1	1research	1research	NUM
cana-6073	3	2	scholar	scholar	NOUN
cana-6073	3	3	,	,	PUNCT
cana-6073	3	4	register	register	VERB
cana-6073	3	5	number	number	NOUN
cana-6073	3	6	:	:	PUNCT
cana-6073	3	7	21121072092002	21121072092002	NUM
cana-6073	3	8	,	,	PUNCT
cana-6073	3	9	department	department	NOUN
cana-6073	3	10	of	of	ADP
cana-6073	3	11	mathematics	mathematic	NOUN
cana-6073	3	12	,	,	PUNCT
cana-6073	3	13	the	the	DET
cana-6073	3	14	m.d.t	m.d.t	ADJ
cana-6073	3	15	hindu	hindu	NOUN
cana-6073	3	16	college	college	NOUN
cana-6073	3	17	,	,	PUNCT
cana-6073	3	18	affiliated	affiliate	VERB
cana-6073	3	19	to	to	ADP
cana-6073	3	20	manonmaniam	manonmaniam	PROPN
cana-6073	3	21	sundaranar	sundaranar	PROPN
cana-6073	3	22	university	university	PROPN
cana-6073	3	23	,	,	PUNCT
cana-6073	3	24	abishekapatti	abishekapatti	PROPN
cana-6073	3	25	,	,	PUNCT
cana-6073	3	26	tirunelveli	tirunelveli	PROPN
cana-6073	3	27	,	,	PUNCT
cana-6073	3	28	india	india	PROPN
cana-6073	3	29	jeyasree1960@gmail.com	jeyasree1960@gmail.com	NOUN
cana-6073	3	30	2associate	2associate	NUM
cana-6073	3	31	professor	professor	NOUN
cana-6073	3	32	,	,	PUNCT
cana-6073	3	33	department	department	NOUN
cana-6073	3	34	of	of	ADP
cana-6073	3	35	mathematics	mathematic	NOUN
cana-6073	3	36	,	,	PUNCT
cana-6073	3	37	the	the	DET
cana-6073	3	38	m.d.t	m.d.t	ADJ
cana-6073	3	39	hindu	hindu	NOUN
cana-6073	3	40	college	college	NOUN
cana-6073	3	41	,	,	PUNCT
cana-6073	3	42	affiliated	affiliate	VERB
cana-6073	3	43	to	to	ADP
cana-6073	3	44	manonmaniam	manonmaniam	PROPN
cana-6073	3	45	sundaranar	sundaranar	PROPN
cana-6073	3	46	university	university	PROPN
cana-6073	3	47	,	,	PUNCT
cana-6073	3	48	abishekapatti	abishekapatti	PROPN
cana-6073	3	49	,	,	PUNCT
cana-6073	3	50	tirunelveli	tirunelveli	PROPN
cana-6073	3	51	,	,	PUNCT
cana-6073	3	52	india	india	PROPN
cana-6073	3	53	kscmdt@gmail.com	kscmdt@gmail.com	PROPN
cana-6073	3	54	article	article	NOUN
cana-6073	3	55	history	history	NOUN
cana-6073	3	56	:	:	PUNCT
cana-6073	3	57	received:01/10/2024	received:01/10/2024	NOUN
cana-6073	3	58	revised	revised	ADJ
cana-6073	3	59	:	:	PUNCT
cana-6073	3	60	06/11/2024	06/11/2024	NUM
cana-6073	3	61	accepted	accept	VERB
cana-6073	3	62	:	:	PUNCT
cana-6073	3	63	30/12/2024	30/12/2024	NUM
cana-6073	3	64	abstract	abstract	NOUN
cana-6073	3	65	:	:	PUNCT
cana-6073	3	66	in	in	ADP
cana-6073	3	67	this	this	DET
cana-6073	3	68	paper	paper	NOUN
cana-6073	3	69	,	,	PUNCT
cana-6073	3	70	we	we	PRON
cana-6073	3	71	investigate	investigate	VERB
cana-6073	3	72	the	the	DET
cana-6073	3	73	relationship	relationship	NOUN
cana-6073	3	74	between	between	ADP
cana-6073	3	75	detour	detour	NOUN
cana-6073	3	76	distance	distance	NOUN
cana-6073	3	77	and	and	CCONJ
cana-6073	3	78	domination	domination	NOUN
cana-6073	3	79	number	number	NOUN
cana-6073	3	80	within	within	ADP
cana-6073	3	81	various	various	ADJ
cana-6073	3	82	special	special	ADJ
cana-6073	3	83	classes	class	NOUN
cana-6073	3	84	of	of	ADP
cana-6073	3	85	graphs	graph	NOUN
cana-6073	3	86	.	.	PUNCT
cana-6073	4	1	the	the	DET
cana-6073	4	2	detour	detour	NOUN
cana-6073	4	3	distance	distance	NOUN
cana-6073	4	4	between	between	ADP
cana-6073	4	5	two	two	NUM
cana-6073	4	6	vertices	vertex	NOUN
cana-6073	4	7	is	be	AUX
cana-6073	4	8	defined	define	VERB
cana-6073	4	9	as	as	ADP
cana-6073	4	10	the	the	DET
cana-6073	4	11	length	length	NOUN
cana-6073	4	12	of	of	ADP
cana-6073	4	13	the	the	DET
cana-6073	4	14	longest	long	ADJ
cana-6073	4	15	path	path	NOUN
cana-6073	4	16	connecting	connect	VERB
cana-6073	4	17	them	they	PRON
cana-6073	4	18	,	,	PUNCT
cana-6073	4	19	and	and	CCONJ
cana-6073	4	20	it	it	PRON
cana-6073	4	21	provides	provide	VERB
cana-6073	4	22	an	an	DET
cana-6073	4	23	alternative	alternative	NOUN
cana-6073	4	24	metric	metric	ADJ
cana-6073	4	25	to	to	ADP
cana-6073	4	26	the	the	DET
cana-6073	4	27	traditional	traditional	ADJ
cana-6073	4	28	geodesic	geodesic	ADJ
cana-6073	4	29	distance	distance	NOUN
cana-6073	4	30	in	in	ADP
cana-6073	4	31	graph	graph	NOUN
cana-6073	4	32	theory	theory	NOUN
cana-6073	4	33	.	.	PUNCT
cana-6073	5	1	by	by	ADP
cana-6073	5	2	integrating	integrate	VERB
cana-6073	5	3	this	this	DET
cana-6073	5	4	concept	concept	NOUN
cana-6073	5	5	with	with	ADP
cana-6073	5	6	domination	domination	NOUN
cana-6073	5	7	theory	theory	NOUN
cana-6073	5	8	,	,	PUNCT
cana-6073	5	9	we	we	PRON
cana-6073	5	10	introduce	introduce	VERB
cana-6073	5	11	new	new	ADJ
cana-6073	5	12	structural	structural	ADJ
cana-6073	5	13	measures	measure	NOUN
cana-6073	5	14	that	that	PRON
cana-6073	5	15	capture	capture	VERB
cana-6073	5	16	the	the	DET
cana-6073	5	17	extended	extended	ADJ
cana-6073	5	18	influence	influence	NOUN
cana-6073	5	19	of	of	ADP
cana-6073	5	20	vertices	vertex	NOUN
cana-6073	5	21	beyond	beyond	ADP
cana-6073	5	22	their	their	PRON
cana-6073	5	23	immediate	immediate	ADJ
cana-6073	5	24	neighborhoods	neighborhood	NOUN
cana-6073	5	25	.	.	PUNCT
cana-6073	6	1	we	we	PRON
cana-6073	6	2	define	define	VERB
cana-6073	6	3	and	and	CCONJ
cana-6073	6	4	analyze	analyze	VERB
cana-6073	6	5	the	the	DET
cana-6073	6	6	detour	detour	NOUN
cana-6073	6	7	domination	domination	NOUN
cana-6073	6	8	number	number	NOUN
cana-6073	6	9	,	,	PUNCT
cana-6073	6	10	denoted	denote	VERB
cana-6073	6	11	as	as	ADP
cana-6073	6	12	γdd(g	γdd(g	PROPN
cana-6073	6	13	)	)	PUNCT
cana-6073	6	14	,	,	PUNCT
cana-6073	6	15	which	which	PRON
cana-6073	6	16	represents	represent	VERB
cana-6073	6	17	the	the	DET
cana-6073	6	18	minimum	minimum	ADJ
cana-6073	6	19	cardinality	cardinality	NOUN
cana-6073	6	20	of	of	ADP
cana-6073	6	21	a	a	DET
cana-6073	6	22	set	set	NOUN
cana-6073	6	23	of	of	ADP
cana-6073	6	24	vertices	vertex	NOUN
cana-6073	6	25	such	such	ADJ
cana-6073	6	26	that	that	SCONJ
cana-6073	6	27	every	every	DET
cana-6073	6	28	vertex	vertex	NOUN
cana-6073	6	29	in	in	ADP
cana-6073	6	30	the	the	DET
cana-6073	6	31	graph	graph	NOUN
cana-6073	6	32	lies	lie	VERB
cana-6073	6	33	on	on	ADP
cana-6073	6	34	a	a	DET
cana-6073	6	35	detour	detour	NOUN
cana-6073	6	36	path	path	NOUN
cana-6073	6	37	from	from	ADP
cana-6073	6	38	at	at	ADV
cana-6073	6	39	least	least	ADV
cana-6073	6	40	one	one	NUM
cana-6073	6	41	dominating	dominating	NOUN
cana-6073	6	42	vertex	vertex	NOUN
cana-6073	6	43	.	.	PUNCT
cana-6073	7	1	we	we	PRON
cana-6073	7	2	examine	examine	VERB
cana-6073	7	3	the	the	DET
cana-6073	7	4	behavior	behavior	NOUN
cana-6073	7	5	of	of	ADP
cana-6073	7	6	this	this	DET
cana-6073	7	7	parameter	parameter	NOUN
cana-6073	7	8	in	in	ADP
cana-6073	7	9	specific	specific	ADJ
cana-6073	7	10	graph	graph	NOUN
cana-6073	7	11	classes	class	NOUN
cana-6073	7	12	,	,	PUNCT
cana-6073	7	13	including	include	VERB
cana-6073	7	14	complete	complete	ADJ
cana-6073	7	15	graphs	graph	NOUN
cana-6073	7	16	,	,	PUNCT
cana-6073	7	17	paths	path	NOUN
cana-6073	7	18	,	,	PUNCT
cana-6073	7	19	cycles	cycle	NOUN
cana-6073	7	20	,	,	PUNCT
cana-6073	7	21	trees	tree	NOUN
cana-6073	7	22	,	,	PUNCT
cana-6073	7	23	and	and	CCONJ
cana-6073	7	24	grid	grid	NOUN
cana-6073	7	25	graphs	graph	NOUN
cana-6073	7	26	,	,	PUNCT
cana-6073	7	27	deriving	derive	VERB
cana-6073	7	28	exact	exact	ADJ
cana-6073	7	29	values	value	NOUN
cana-6073	7	30	or	or	CCONJ
cana-6073	7	31	bounds	bound	NOUN
cana-6073	7	32	where	where	SCONJ
cana-6073	7	33	applicable	applicable	ADJ
cana-6073	7	34	.	.	PUNCT
cana-6073	8	1	additionally	additionally	ADV
cana-6073	8	2	,	,	PUNCT
cana-6073	8	3	we	we	PRON
cana-6073	8	4	study	study	VERB
cana-6073	8	5	the	the	DET
cana-6073	8	6	upper	upper	ADJ
cana-6073	8	7	detour	detour	NOUN
cana-6073	8	8	domination	domination	NOUN
cana-6073	8	9	number	number	NOUN
cana-6073	8	10	,	,	PUNCT
cana-6073	8	11	investigate	investigate	VERB
cana-6073	8	12	its	its	PRON
cana-6073	8	13	extremal	extremal	ADJ
cana-6073	8	14	properties	property	NOUN
cana-6073	8	15	,	,	PUNCT
cana-6073	8	16	and	and	CCONJ
cana-6073	8	17	explore	explore	VERB
cana-6073	8	18	how	how	SCONJ
cana-6073	8	19	it	it	PRON
cana-6073	8	20	contrasts	contrast	VERB
cana-6073	8	21	with	with	ADP
cana-6073	8	22	traditional	traditional	ADJ
cana-6073	8	23	domination	domination	NOUN
cana-6073	8	24	metrics	metric	NOUN
cana-6073	8	25	.	.	PUNCT
cana-6073	9	1	we	we	PRON
cana-6073	9	2	also	also	ADV
cana-6073	9	3	characterize	characterize	VERB
cana-6073	9	4	graph	graph	NOUN
cana-6073	9	5	classes	class	NOUN
cana-6073	9	6	where	where	SCONJ
cana-6073	9	7	the	the	DET
cana-6073	9	8	detour	detour	NOUN
cana-6073	9	9	domination	domination	NOUN
cana-6073	9	10	number	number	NOUN
cana-6073	9	11	equals	equal	VERB
cana-6073	9	12	the	the	DET
cana-6073	9	13	classical	classical	ADJ
cana-6073	9	14	domination	domination	NOUN
cana-6073	9	15	number	number	NOUN
cana-6073	9	16	and	and	CCONJ
cana-6073	9	17	where	where	SCONJ
cana-6073	9	18	it	it	PRON
cana-6073	9	19	significantly	significantly	ADV
cana-6073	9	20	diverges	diverge	VERB
cana-6073	9	21	.	.	PUNCT
cana-6073	10	1	the	the	DET
cana-6073	10	2	results	result	NOUN
cana-6073	10	3	contribute	contribute	VERB
cana-6073	10	4	to	to	ADP
cana-6073	10	5	a	a	DET
cana-6073	10	6	deeper	deep	ADJ
cana-6073	10	7	understanding	understanding	NOUN
cana-6073	10	8	of	of	ADP
cana-6073	10	9	detour	detour	NOUN
cana-6073	10	10	-	-	PUNCT
cana-6073	10	11	based	base	VERB
cana-6073	10	12	influence	influence	NOUN
cana-6073	10	13	in	in	ADP
cana-6073	10	14	graphs	graph	NOUN
cana-6073	10	15	,	,	PUNCT
cana-6073	10	16	offering	offer	VERB
cana-6073	10	17	new	new	ADJ
cana-6073	10	18	perspectives	perspective	NOUN
cana-6073	10	19	for	for	ADP
cana-6073	10	20	applications	application	NOUN
cana-6073	10	21	in	in	ADP
cana-6073	10	22	network	network	NOUN
cana-6073	10	23	resilience	resilience	NOUN
cana-6073	10	24	,	,	PUNCT
cana-6073	10	25	transport	transport	NOUN
cana-6073	10	26	systems	system	NOUN
cana-6073	10	27	,	,	PUNCT
cana-6073	10	28	and	and	CCONJ
cana-6073	10	29	distributed	distributed	ADJ
cana-6073	10	30	computing	computing	NOUN
cana-6073	10	31	,	,	PUNCT
cana-6073	10	32	where	where	SCONJ
cana-6073	10	33	long	long	ADJ
cana-6073	10	34	-	-	PUNCT
cana-6073	10	35	range	range	NOUN
cana-6073	10	36	reachability	reachability	NOUN
cana-6073	10	37	and	and	CCONJ
cana-6073	10	38	control	control	NOUN
cana-6073	10	39	are	be	AUX
cana-6073	10	40	essential	essential	ADJ
cana-6073	10	41	.	.	PUNCT
cana-6073	11	1	keywords	keyword	NOUN
cana-6073	11	2	:	:	PUNCT
cana-6073	11	3	detour	detour	NOUN
cana-6073	11	4	distance	distance	NOUN
cana-6073	11	5	,	,	PUNCT
cana-6073	11	6	detour	detour	NOUN
cana-6073	11	7	dominating	dominating	NOUN
cana-6073	11	8	set	set	NOUN
cana-6073	11	9	,	,	PUNCT
cana-6073	11	10	domination	domination	NOUN
cana-6073	11	11	number	number	NOUN
cana-6073	11	12	,	,	PUNCT
cana-6073	11	13	upper	upper	ADJ
cana-6073	11	14	detour	detour	NOUN
cana-6073	11	15	domination	domination	NOUN
cana-6073	11	16	,	,	PUNCT
cana-6073	11	17	forcing	force	VERB
cana-6073	11	18	set	set	NOUN
cana-6073	11	19	in	in	ADP
cana-6073	11	20	graphs	graph	NOUN
cana-6073	11	21	,	,	PUNCT
cana-6073	11	22	special	special	ADJ
cana-6073	11	23	graph	graph	NOUN
cana-6073	11	24	classes	class	NOUN
cana-6073	11	25	.	.	PUNCT
cana-6073	12	1	introduction	introduction	NOUN
cana-6073	12	2	graph	graph	NOUN
cana-6073	12	3	theory	theory	NOUN
cana-6073	12	4	,	,	PUNCT
cana-6073	12	5	a	a	DET
cana-6073	12	6	foundational	foundational	ADJ
cana-6073	12	7	discipline	discipline	NOUN
cana-6073	12	8	in	in	ADP
cana-6073	12	9	discrete	discrete	ADJ
cana-6073	12	10	mathematics	mathematic	NOUN
cana-6073	12	11	,	,	PUNCT
cana-6073	12	12	has	have	AUX
cana-6073	12	13	evolved	evolve	VERB
cana-6073	12	14	to	to	PART
cana-6073	12	15	become	become	VERB
cana-6073	12	16	a	a	DET
cana-6073	12	17	powerful	powerful	ADJ
cana-6073	12	18	tool	tool	NOUN
cana-6073	12	19	for	for	ADP
cana-6073	12	20	modeling	model	VERB
cana-6073	12	21	a	a	DET
cana-6073	12	22	wide	wide	ADJ
cana-6073	12	23	variety	variety	NOUN
cana-6073	12	24	of	of	ADP
cana-6073	12	25	systems	system	NOUN
cana-6073	12	26	in	in	ADP
cana-6073	12	27	science	science	NOUN
cana-6073	12	28	,	,	PUNCT
cana-6073	12	29	engineering	engineering	NOUN
cana-6073	12	30	,	,	PUNCT
cana-6073	12	31	social	social	ADJ
cana-6073	12	32	networks	network	NOUN
cana-6073	12	33	,	,	PUNCT
cana-6073	12	34	computer	computer	NOUN
cana-6073	12	35	science	science	NOUN
cana-6073	12	36	,	,	PUNCT
cana-6073	12	37	and	and	CCONJ
cana-6073	12	38	operations	operation	NOUN
cana-6073	12	39	research	research	NOUN
cana-6073	12	40	.	.	PUNCT
cana-6073	13	1	one	one	NUM
cana-6073	13	2	of	of	ADP
cana-6073	13	3	the	the	DET
cana-6073	13	4	most	most	ADV
cana-6073	13	5	widely	widely	ADV
cana-6073	13	6	studied	study	VERB
cana-6073	13	7	problems	problem	NOUN
cana-6073	13	8	in	in	ADP
cana-6073	13	9	graph	graph	NOUN
cana-6073	13	10	theory	theory	NOUN
cana-6073	13	11	is	be	AUX
cana-6073	13	12	the	the	DET
cana-6073	13	13	domination	domination	NOUN
cana-6073	13	14	problem	problem	NOUN
cana-6073	13	15	,	,	PUNCT
cana-6073	13	16	which	which	PRON
cana-6073	13	17	seeks	seek	VERB
cana-6073	13	18	a	a	DET
cana-6073	13	19	subset	subset	NOUN
cana-6073	13	20	of	of	ADP
cana-6073	13	21	vertices	vertex	NOUN
cana-6073	13	22	that	that	PRON
cana-6073	13	23	exerts	exert	VERB
cana-6073	13	24	influence	influence	NOUN
cana-6073	13	25	or	or	CCONJ
cana-6073	13	26	control	control	NOUN
cana-6073	13	27	over	over	ADP
cana-6073	13	28	the	the	DET
cana-6073	13	29	entire	entire	ADJ
cana-6073	13	30	graph	graph	NOUN
cana-6073	13	31	.	.	PUNCT
cana-6073	14	1	traditional	traditional	ADJ
cana-6073	14	2	domination	domination	NOUN
cana-6073	14	3	theory	theory	NOUN
cana-6073	14	4	focuses	focus	VERB
cana-6073	14	5	on	on	ADP
cana-6073	14	6	minimum	minimum	ADJ
cana-6073	14	7	sets	set	NOUN
cana-6073	14	8	of	of	ADP
cana-6073	14	9	mailto:jeyasree1960@gmail.com	mailto:jeyasree1960@gmail.com	X
cana-6073	14	10	mailto:kscmdt@gmail.com	mailto:kscmdt@gmail.com	PROPN
cana-6073	14	11	communications	communication	NOUN
cana-6073	14	12	on	on	ADP
cana-6073	14	13	applied	apply	VERB
cana-6073	14	14	nonlinear	nonlinear	ADJ
cana-6073	14	15	analysis	analysis	NOUN
cana-6073	14	16	issn	issn	NOUN
cana-6073	14	17	:	:	PUNCT
cana-6073	14	18	1074	1074	NUM
cana-6073	14	19	-	-	PUNCT
cana-6073	14	20	133x	133x	NUM
cana-6073	14	21	vol	vol	NOUN
cana-6073	14	22	31	31	NUM
cana-6073	14	23	no	no	NOUN
cana-6073	14	24	.	.	PUNCT
cana-6073	15	1	8s	8s	PROPN
cana-6073	15	2	(	(	PUNCT
cana-6073	15	3	2024	2024	NUM
cana-6073	15	4	)	)	PUNCT
cana-6073	15	5	1185	1185	NUM
cana-6073	16	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6073	16	2	vertices	vertice	VERB
cana-6073	16	3	that	that	PRON
cana-6073	16	4	are	be	AUX
cana-6073	16	5	adjacent	adjacent	ADJ
cana-6073	16	6	to	to	ADP
cana-6073	16	7	all	all	DET
cana-6073	16	8	other	other	ADJ
cana-6073	16	9	vertices	vertex	NOUN
cana-6073	16	10	either	either	CCONJ
cana-6073	16	11	directly	directly	ADV
cana-6073	16	12	or	or	CCONJ
cana-6073	16	13	indirectly	indirectly	ADV
cana-6073	16	14	.	.	PUNCT
cana-6073	17	1	however	however	ADV
cana-6073	17	2	,	,	PUNCT
cana-6073	17	3	in	in	ADP
cana-6073	17	4	many	many	ADJ
cana-6073	17	5	real	real	ADJ
cana-6073	17	6	-	-	PUNCT
cana-6073	17	7	world	world	NOUN
cana-6073	17	8	networks	network	NOUN
cana-6073	17	9	—	—	PUNCT
cana-6073	17	10	such	such	ADJ
cana-6073	17	11	as	as	ADP
cana-6073	17	12	communication	communication	NOUN
cana-6073	17	13	systems	system	NOUN
cana-6073	17	14	,	,	PUNCT
cana-6073	17	15	transportation	transportation	NOUN
cana-6073	17	16	grids	grid	NOUN
cana-6073	17	17	,	,	PUNCT
cana-6073	17	18	biological	biological	ADJ
cana-6073	17	19	systems	system	NOUN
cana-6073	17	20	,	,	PUNCT
cana-6073	17	21	and	and	CCONJ
cana-6073	17	22	social	social	ADJ
cana-6073	17	23	networks	network	NOUN
cana-6073	17	24	—	—	PUNCT
cana-6073	17	25	the	the	DET
cana-6073	17	26	shortest	short	ADJ
cana-6073	17	27	-	-	PUNCT
cana-6073	17	28	path	path	NOUN
cana-6073	17	29	assumption	assumption	NOUN
cana-6073	17	30	is	be	AUX
cana-6073	17	31	often	often	ADV
cana-6073	17	32	unrealistic	unrealistic	ADJ
cana-6073	17	33	.	.	PUNCT
cana-6073	18	1	this	this	PRON
cana-6073	18	2	motivates	motivate	VERB
cana-6073	18	3	the	the	DET
cana-6073	18	4	need	need	NOUN
cana-6073	18	5	for	for	ADP
cana-6073	18	6	domination	domination	NOUN
cana-6073	18	7	models	model	NOUN
cana-6073	18	8	that	that	PRON
cana-6073	18	9	incorporate	incorporate	VERB
cana-6073	18	10	longest	long	ADJ
cana-6073	18	11	-	-	PUNCT
cana-6073	18	12	path	path	NOUN
cana-6073	18	13	interactions	interaction	NOUN
cana-6073	18	14	,	,	PUNCT
cana-6073	18	15	leading	lead	VERB
cana-6073	18	16	to	to	ADP
cana-6073	18	17	the	the	DET
cana-6073	18	18	development	development	NOUN
cana-6073	18	19	of	of	ADP
cana-6073	18	20	detour	detour	NOUN
cana-6073	18	21	-	-	PUNCT
cana-6073	18	22	based	base	VERB
cana-6073	18	23	domination	domination	NOUN
cana-6073	18	24	concepts	concept	NOUN
cana-6073	18	25	.	.	PUNCT
cana-6073	19	1	this	this	DET
cana-6073	19	2	work	work	NOUN
cana-6073	19	3	introduces	introduce	NOUN
cana-6073	19	4	and	and	CCONJ
cana-6073	19	5	elaborates	elaborate	VERB
cana-6073	19	6	upon	upon	SCONJ
cana-6073	19	7	new	new	ADJ
cana-6073	19	8	graph	graph	NOUN
cana-6073	19	9	invariants	invariant	NOUN
cana-6073	19	10	based	base	VERB
cana-6073	19	11	on	on	ADP
cana-6073	19	12	detour	detour	NOUN
cana-6073	19	13	domination	domination	NOUN
cana-6073	19	14	and	and	CCONJ
cana-6073	19	15	detour	detour	NOUN
cana-6073	19	16	distances	distance	NOUN
cana-6073	19	17	.	.	PUNCT
cana-6073	20	1	first	first	ADV
cana-6073	20	2	,	,	PUNCT
cana-6073	20	3	we	we	PRON
cana-6073	20	4	formalize	formalize	VERB
cana-6073	20	5	the	the	DET
cana-6073	20	6	detour	detour	NOUN
cana-6073	20	7	dominating	dominating	NOUN
cana-6073	20	8	degree	degree	NOUN
cana-6073	20	9	set	set	NOUN
cana-6073	20	10	,	,	PUNCT
cana-6073	20	11	which	which	PRON
cana-6073	20	12	includes	include	VERB
cana-6073	20	13	sets	set	NOUN
cana-6073	20	14	that	that	SCONJ
cana-6073	20	15	not	not	PART
cana-6073	20	16	only	only	ADV
cana-6073	20	17	detourdominate	detourdominate	VERB
cana-6073	20	18	the	the	DET
cana-6073	20	19	graph	graph	NOUN
cana-6073	20	20	but	but	CCONJ
cana-6073	20	21	are	be	AUX
cana-6073	20	22	evaluated	evaluate	VERB
cana-6073	20	23	based	base	VERB
cana-6073	20	24	on	on	ADP
cana-6073	20	25	degree	degree	NOUN
cana-6073	20	26	-	-	PUNCT
cana-6073	20	27	based	base	VERB
cana-6073	20	28	metrics	metric	NOUN
cana-6073	20	29	of	of	ADP
cana-6073	20	30	influence	influence	NOUN
cana-6073	20	31	.	.	PUNCT
cana-6073	21	1	we	we	PRON
cana-6073	21	2	then	then	ADV
cana-6073	21	3	introduce	introduce	VERB
cana-6073	21	4	the	the	DET
cana-6073	21	5	upper	upper	ADJ
cana-6073	21	6	detour	detour	NOUN
cana-6073	21	7	dominating	dominating	NOUN
cana-6073	21	8	degree	degree	NOUN
cana-6073	21	9	set	set	NOUN
cana-6073	21	10	,	,	PUNCT
cana-6073	21	11	which	which	PRON
cana-6073	21	12	seeks	seek	VERB
cana-6073	21	13	to	to	PART
cana-6073	21	14	maximize	maximize	VERB
cana-6073	21	15	the	the	DET
cana-6073	21	16	local	local	ADJ
cana-6073	21	17	domination	domination	NOUN
cana-6073	21	18	measure	measure	NOUN
cana-6073	21	19	based	base	VERB
cana-6073	21	20	on	on	ADP
cana-6073	21	21	vertex	vertex	NOUN
cana-6073	21	22	degrees	degree	NOUN
cana-6073	21	23	involved	involve	VERB
cana-6073	21	24	in	in	ADP
cana-6073	21	25	the	the	DET
cana-6073	21	26	detour	detour	NOUN
cana-6073	21	27	structure	structure	NOUN
cana-6073	21	28	.	.	PUNCT
cana-6073	22	1	such	such	ADJ
cana-6073	22	2	sets	set	NOUN
cana-6073	22	3	provide	provide	VERB
cana-6073	22	4	insight	insight	NOUN
cana-6073	22	5	into	into	ADP
cana-6073	22	6	the	the	DET
cana-6073	22	7	maximum	maximum	ADJ
cana-6073	22	8	structural	structural	ADJ
cana-6073	22	9	influence	influence	NOUN
cana-6073	22	10	that	that	PRON
cana-6073	22	11	can	can	AUX
cana-6073	22	12	be	be	AUX
cana-6073	22	13	exerted	exert	VERB
cana-6073	22	14	through	through	ADP
cana-6073	22	15	longdistance	longdistance	NOUN
cana-6073	22	16	interactions	interaction	NOUN
cana-6073	22	17	in	in	ADP
cana-6073	22	18	the	the	DET
cana-6073	22	19	graph	graph	NOUN
cana-6073	22	20	.	.	PUNCT
cana-6073	23	1	the	the	DET
cana-6073	23	2	associated	associated	PROPN
cana-6073	23	3	invariant	invariant	PROPN
cana-6073	23	4	,	,	PUNCT
cana-6073	23	5	the	the	DET
cana-6073	23	6	upper	upper	ADJ
cana-6073	23	7	detour	detour	NOUN
cana-6073	23	8	domination	domination	NOUN
cana-6073	23	9	number	number	NOUN
cana-6073	23	10	𝛾𝑑𝑑	𝛾𝑑𝑑	VERB
cana-6073	23	11	+	+	CCONJ
cana-6073	23	12	(	(	PUNCT
cana-6073	23	13	𝐺	𝐺	NOUN
cana-6073	23	14	)	)	PUNCT
cana-6073	23	15	,	,	PUNCT
cana-6073	23	16	captures	capture	VERB
cana-6073	23	17	the	the	DET
cana-6073	23	18	maximum	maximum	NOUN
cana-6073	23	19	weighted	weight	VERB
cana-6073	23	20	detour	detour	NOUN
cana-6073	23	21	reachability	reachability	NOUN
cana-6073	23	22	.	.	PUNCT
cana-6073	24	1	preliminaries	preliminary	NOUN
cana-6073	24	2	definition	definition	NOUN
cana-6073	24	3	1	1	NUM
cana-6073	24	4	:	:	PUNCT
cana-6073	24	5	detour	detour	NOUN
cana-6073	24	6	distance	distance	NOUN
cana-6073	24	7	let	let	VERB
cana-6073	24	8	𝐺	𝐺	PROPN
cana-6073	24	9	=	=	SYM
cana-6073	24	10	(	(	PUNCT
cana-6073	24	11	𝑉	𝑉	PROPN
cana-6073	24	12	,	,	PUNCT
cana-6073	24	13	𝐸	𝐸	PROPN
cana-6073	24	14	)	)	PUNCT
cana-6073	24	15	be	be	VERB
cana-6073	24	16	a	a	DET
cana-6073	24	17	connected	connected	ADJ
cana-6073	24	18	graph	graph	NOUN
cana-6073	24	19	and	and	CCONJ
cana-6073	24	20	let	let	VERB
cana-6073	24	21	𝑢	𝑢	NOUN
cana-6073	24	22	,	,	PUNCT
cana-6073	24	23	𝑣	𝑣	PRON
cana-6073	24	24	∈	∈	PROPN
cana-6073	24	25	𝑉(𝐺	𝑉(𝐺	NOUN
cana-6073	24	26	)	)	PUNCT
cana-6073	24	27	.	.	PUNCT
cana-6073	25	1	the	the	DET
cana-6073	25	2	detour	detour	NOUN
cana-6073	25	3	distance	distance	NOUN
cana-6073	25	4	𝐷(𝑢	𝐷(𝑢	NOUN
cana-6073	25	5	,	,	PUNCT
cana-6073	25	6	𝑣	𝑣	NOUN
cana-6073	25	7	)	)	PUNCT
cana-6073	25	8	is	be	AUX
cana-6073	25	9	defined	define	VERB
cana-6073	25	10	as	as	ADP
cana-6073	25	11	the	the	DET
cana-6073	25	12	length	length	NOUN
cana-6073	25	13	of	of	ADP
cana-6073	25	14	the	the	DET
cana-6073	25	15	longest	long	ADJ
cana-6073	25	16	𝑢	𝑢	ADP
cana-6073	25	17	−	−	PROPN
cana-6073	25	18	𝑣	𝑣	DET
cana-6073	25	19	path	path	NOUN
cana-6073	25	20	in	in	ADP
cana-6073	25	21	the	the	DET
cana-6073	25	22	graph	graph	NOUN
cana-6073	25	23	𝐺.	𝐺.	NOUN
cana-6073	25	24	formally	formally	ADV
cana-6073	25	25	,	,	PUNCT
cana-6073	25	26	𝐷(𝑢	𝐷(𝑢	NOUN
cana-6073	25	27	,	,	PUNCT
cana-6073	25	28	𝑣	𝑣	NOUN
cana-6073	25	29	)	)	PUNCT
cana-6073	25	30	=	=	SYM
cana-6073	25	31	max	max	PROPN
cana-6073	25	32	{	{	PUNCT
cana-6073	25	33	length	length	NOUN
cana-6073	25	34	(	(	PUNCT
cana-6073	25	35	𝑃	𝑃	NOUN
cana-6073	25	36	)	)	PUNCT
cana-6073	25	37	∣	∣	ADJ
cana-6073	25	38	𝑃	𝑃	NOUN
cana-6073	25	39	is	be	AUX
cana-6073	25	40	a	a	DET
cana-6073	25	41	𝑢	𝑢	ADJ
cana-6073	25	42	−	−	NOUN
cana-6073	25	43	𝑣	𝑣	DET
cana-6073	25	44	path	path	NOUN
cana-6073	25	45	in	in	ADP
cana-6073	25	46	𝐺	𝐺	NOUN
cana-6073	25	47	}	}	PUNCT
cana-6073	25	48	this	this	DET
cana-6073	25	49	measure	measure	NOUN
cana-6073	25	50	contrasts	contrast	VERB
cana-6073	25	51	with	with	ADP
cana-6073	25	52	the	the	DET
cana-6073	25	53	usual	usual	ADJ
cana-6073	25	54	distance	distance	NOUN
cana-6073	25	55	𝑑(𝑢	𝑑(𝑢	ADJ
cana-6073	25	56	,	,	PUNCT
cana-6073	25	57	𝑣	𝑣	NOUN
cana-6073	25	58	)	)	PUNCT
cana-6073	25	59	,	,	PUNCT
cana-6073	25	60	which	which	PRON
cana-6073	25	61	considers	consider	VERB
cana-6073	25	62	the	the	DET
cana-6073	25	63	shortest	short	ADJ
cana-6073	25	64	path	path	NOUN
cana-6073	25	65	.	.	PUNCT
cana-6073	26	1	the	the	DET
cana-6073	26	2	detour	detour	NOUN
cana-6073	26	3	distance	distance	NOUN
cana-6073	26	4	captures	capture	VERB
cana-6073	26	5	long	long	ADJ
cana-6073	26	6	-	-	PUNCT
cana-6073	26	7	range	range	NOUN
cana-6073	26	8	connectivity	connectivity	NOUN
cana-6073	26	9	between	between	ADP
cana-6073	26	10	vertices	vertex	NOUN
cana-6073	26	11	and	and	CCONJ
cana-6073	26	12	is	be	AUX
cana-6073	26	13	particularly	particularly	ADV
cana-6073	26	14	relevant	relevant	ADJ
cana-6073	26	15	in	in	ADP
cana-6073	26	16	resilience	resilience	NOUN
cana-6073	26	17	and	and	CCONJ
cana-6073	26	18	influence	influence	NOUN
cana-6073	26	19	spread	spread	NOUN
cana-6073	26	20	models	model	NOUN
cana-6073	26	21	.	.	PUNCT
cana-6073	27	1	definition	definition	NOUN
cana-6073	27	2	2	2	NUM
cana-6073	27	3	:	:	PUNCT
cana-6073	27	4	detour	detour	NOUN
cana-6073	27	5	dominating	dominating	NOUN
cana-6073	27	6	set	set	VERB
cana-6073	27	7	a	a	DET
cana-6073	27	8	subset	subset	NOUN
cana-6073	27	9	𝑆	𝑆	PROPN
cana-6073	27	10	⊆	⊆	NUM
cana-6073	27	11	𝑉(𝐺	𝑉(𝐺	NOUN
cana-6073	27	12	)	)	PUNCT
cana-6073	27	13	is	be	AUX
cana-6073	27	14	called	call	VERB
cana-6073	27	15	a	a	DET
cana-6073	27	16	detour	detour	NOUN
cana-6073	27	17	dominating	dominating	NOUN
cana-6073	27	18	set	set	VERB
cana-6073	27	19	if	if	SCONJ
cana-6073	27	20	for	for	ADP
cana-6073	27	21	every	every	DET
cana-6073	27	22	vertex	vertex	NOUN
cana-6073	27	23	𝑣	𝑣	ADP
cana-6073	27	24	∈	∈	PROPN
cana-6073	27	25	𝑉(𝐺	𝑉(𝐺	NOUN
cana-6073	27	26	)	)	PUNCT
cana-6073	27	27	,	,	PUNCT
cana-6073	27	28	there	there	PRON
cana-6073	27	29	exists	exist	VERB
cana-6073	27	30	a	a	DET
cana-6073	27	31	vertex	vertex	NOUN
cana-6073	27	32	𝑢	𝑢	ADP
cana-6073	27	33	∈	∈	PROPN
cana-6073	27	34	𝑆	𝑆	PROPN
cana-6073	27	35	such	such	ADJ
cana-6073	27	36	that	that	SCONJ
cana-6073	27	37	𝑣	𝑣	PROPN
cana-6073	27	38	lies	lie	VERB
cana-6073	27	39	on	on	ADP
cana-6073	27	40	a	a	DET
cana-6073	27	41	detour	detour	NOUN
cana-6073	27	42	path	path	NOUN
cana-6073	27	43	originating	originate	VERB
cana-6073	27	44	from	from	ADP
cana-6073	27	45	𝑢.	𝑢.	PROPN
cana-6073	27	46	that	that	PRON
cana-6073	27	47	is	be	AUX
cana-6073	27	48	,	,	PUNCT
cana-6073	27	49	∀𝑣	∀𝑣	PROPN
cana-6073	27	50	∈	∈	PROPN
cana-6073	27	51	𝑉(𝐺	𝑉(𝐺	NOUN
cana-6073	27	52	)	)	PUNCT
cana-6073	27	53	,	,	PUNCT
cana-6073	27	54	∃𝑢	∃𝑢	PROPN
cana-6073	27	55	∈	∈	PROPN
cana-6073	27	56	𝑆	𝑆	PROPN
cana-6073	27	57	such	such	ADJ
cana-6073	27	58	that	that	SCONJ
cana-6073	27	59	𝑣	𝑣	PRON
cana-6073	27	60	∈	∈	PROPN
cana-6073	27	61	𝑉(𝑃𝑢𝑣	𝑉(𝑃𝑢𝑣	PROPN
cana-6073	27	62	)	)	PUNCT
cana-6073	27	63	,	,	PUNCT
cana-6073	27	64	where	where	SCONJ
cana-6073	27	65	𝑃𝑢𝑣	𝑃𝑢𝑣	PROPN
cana-6073	27	66	is	be	AUX
cana-6073	27	67	a	a	DET
cana-6073	27	68	detour	detour	NOUN
cana-6073	27	69	path	path	NOUN
cana-6073	27	70	from	from	ADP
cana-6073	27	71	𝑢	𝑢	PRON
cana-6073	27	72	to	to	ADP
cana-6073	27	73	𝑣	𝑣	ADP
cana-6073	27	74	this	this	DET
cana-6073	27	75	definition	definition	NOUN
cana-6073	27	76	implies	imply	VERB
cana-6073	27	77	that	that	SCONJ
cana-6073	27	78	𝑆	𝑆	PROPN
cana-6073	27	79	collectively	collectively	ADV
cana-6073	27	80	"	"	PUNCT
cana-6073	27	81	controls	control	VERB
cana-6073	27	82	"	"	PUNCT
cana-6073	27	83	the	the	DET
cana-6073	27	84	graph	graph	NOUN
cana-6073	27	85	via	via	ADP
cana-6073	27	86	its	its	PRON
cana-6073	27	87	longest	long	ADJ
cana-6073	27	88	internal	internal	ADJ
cana-6073	27	89	routes	route	NOUN
cana-6073	27	90	,	,	PUNCT
cana-6073	27	91	not	not	PART
cana-6073	27	92	just	just	ADV
cana-6073	27	93	the	the	DET
cana-6073	27	94	immediate	immediate	ADJ
cana-6073	27	95	neighborhoods	neighborhood	NOUN
cana-6073	27	96	.	.	PUNCT
cana-6073	28	1	definition	definition	NOUN
cana-6073	28	2	3	3	NUM
cana-6073	28	3	:	:	PUNCT
cana-6073	28	4	detour	detour	NOUN
cana-6073	28	5	dominating	dominating	NOUN
cana-6073	28	6	degree	degree	NOUN
cana-6073	28	7	set	set	NOUN
cana-6073	28	8	(	(	PUNCT
cana-6073	28	9	𝜸𝒅𝒅(𝑮	𝜸𝒅𝒅(𝑮	NUM
cana-6073	28	10	)	)	PUNCT
cana-6073	28	11	)	)	PUNCT
cana-6073	29	1	a	a	DET
cana-6073	29	2	detour	detour	NOUN
cana-6073	29	3	dominating	dominating	NOUN
cana-6073	29	4	degree	degree	NOUN
cana-6073	29	5	set	set	VERB
cana-6073	29	6	𝑆	𝑆	PROPN
cana-6073	29	7	⊆	⊆	NUM
cana-6073	29	8	𝑉(𝐺	𝑉(𝐺	NOUN
cana-6073	29	9	)	)	PUNCT
cana-6073	29	10	is	be	AUX
cana-6073	29	11	a	a	DET
cana-6073	29	12	detour	detour	NOUN
cana-6073	29	13	dominating	dominating	NOUN
cana-6073	29	14	set	set	VERB
cana-6073	29	15	with	with	ADP
cana-6073	29	16	minimum	minimum	ADJ
cana-6073	29	17	cardinality	cardinality	NOUN
cana-6073	29	18	.	.	PUNCT
cana-6073	30	1	the	the	DET
cana-6073	30	2	detour	detour	NOUN
cana-6073	30	3	domination	domination	NOUN
cana-6073	30	4	degree	degree	NOUN
cana-6073	30	5	number	number	NOUN
cana-6073	30	6	,	,	PUNCT
cana-6073	30	7	denoted	denote	VERB
cana-6073	30	8	by	by	ADP
cana-6073	30	9	𝛾𝑑𝑑(𝐺	𝛾𝑑𝑑(𝐺	PROPN
cana-6073	30	10	)	)	PUNCT
cana-6073	30	11	,	,	PUNCT
cana-6073	30	12	is	be	AUX
cana-6073	30	13	defined	define	VERB
cana-6073	30	14	as	as	ADP
cana-6073	30	15	:	:	PUNCT
cana-6073	30	16	𝛾𝑑𝑑(𝐺	𝛾𝑑𝑑(𝐺	PROPN
cana-6073	30	17	)	)	PUNCT
cana-6073	30	18	=	=	SYM
cana-6073	30	19	min{|𝑆|	min{|𝑆|	PROPN
cana-6073	30	20	∣	∣	ADJ
cana-6073	30	21	𝑆	𝑆	PROPN
cana-6073	30	22	⊆	⊆	NUM
cana-6073	30	23	𝑉(𝐺	𝑉(𝐺	NOUN
cana-6073	30	24	)	)	PUNCT
cana-6073	30	25	,	,	PUNCT
cana-6073	30	26	𝑆	𝑆	PROPN
cana-6073	30	27	is	be	AUX
cana-6073	30	28	a	a	DET
cana-6073	30	29	detour	detour	NOUN
cana-6073	30	30	dominating	dominating	NOUN
cana-6073	30	31	set	set	NOUN
cana-6073	30	32	}	}	PUNCT
cana-6073	30	33	this	this	DET
cana-6073	30	34	number	number	NOUN
cana-6073	30	35	reflects	reflect	VERB
cana-6073	30	36	the	the	DET
cana-6073	30	37	minimum	minimum	ADJ
cana-6073	30	38	number	number	NOUN
cana-6073	30	39	of	of	ADP
cana-6073	30	40	vertices	vertex	NOUN
cana-6073	30	41	required	require	VERB
cana-6073	30	42	to	to	AUX
cana-6073	30	43	detour	detour	VERB
cana-6073	30	44	-	-	PUNCT
cana-6073	30	45	dominate	dominate	VERB
cana-6073	30	46	the	the	DET
cana-6073	30	47	entire	entire	ADJ
cana-6073	30	48	graph	graph	NOUN
cana-6073	30	49	.	.	PUNCT
cana-6073	31	1	it	it	PRON
cana-6073	31	2	serves	serve	VERB
cana-6073	31	3	as	as	ADP
cana-6073	31	4	a	a	DET
cana-6073	31	5	generalization	generalization	NOUN
cana-6073	31	6	of	of	ADP
cana-6073	31	7	the	the	DET
cana-6073	31	8	classical	classical	ADJ
cana-6073	31	9	domination	domination	NOUN
cana-6073	31	10	number	number	NOUN
cana-6073	31	11	under	under	ADP
cana-6073	31	12	the	the	DET
cana-6073	31	13	lens	lens	NOUN
cana-6073	31	14	of	of	ADP
cana-6073	31	15	maximum	maximum	ADJ
cana-6073	31	16	connectivity	connectivity	NOUN
cana-6073	31	17	.	.	PUNCT
cana-6073	32	1	definition	definition	NOUN
cana-6073	32	2	4	4	NUM
cana-6073	32	3	:	:	PUNCT
cana-6073	32	4	upper	upper	ADJ
cana-6073	32	5	detour	detour	NOUN
cana-6073	32	6	dominating	dominating	NOUN
cana-6073	32	7	degree	degree	NOUN
cana-6073	32	8	set	set	NOUN
cana-6073	32	9	(	(	PUNCT
cana-6073	32	10	𝜸𝒅𝒅	𝜸𝒅𝒅	NOUN
cana-6073	32	11	+	+	CCONJ
cana-6073	32	12	(	(	PUNCT
cana-6073	32	13	𝑮	𝑮	PROPN
cana-6073	32	14	)	)	PUNCT
cana-6073	32	15	)	)	PUNCT
cana-6073	32	16	let	let	VERB
cana-6073	32	17	𝐺	𝐺	PRON
cana-6073	32	18	be	be	AUX
cana-6073	32	19	a	a	DET
cana-6073	32	20	graph	graph	NOUN
cana-6073	32	21	and	and	CCONJ
cana-6073	32	22	let	let	VERB
cana-6073	32	23	𝑆	𝑆	PROPN
cana-6073	32	24	⊆	⊆	NUM
cana-6073	32	25	𝑉(𝐺	𝑉(𝐺	NOUN
cana-6073	32	26	)	)	PUNCT
cana-6073	32	27	be	be	VERB
cana-6073	32	28	a	a	DET
cana-6073	32	29	detour	detour	NOUN
cana-6073	32	30	dominating	dominating	NOUN
cana-6073	32	31	set	set	NOUN
cana-6073	32	32	.	.	PUNCT
cana-6073	33	1	the	the	DET
cana-6073	33	2	set	set	NOUN
cana-6073	33	3	𝑆	𝑆	PROPN
cana-6073	33	4	is	be	AUX
cana-6073	33	5	called	call	VERB
cana-6073	33	6	an	an	DET
cana-6073	33	7	upper	upper	ADJ
cana-6073	33	8	detour	detour	NOUN
cana-6073	33	9	dominating	dominating	NOUN
cana-6073	33	10	degree	degree	NOUN
cana-6073	33	11	set	set	VERB
cana-6073	33	12	if	if	SCONJ
cana-6073	33	13	it	it	PRON
cana-6073	33	14	maximizes	maximize	VERB
cana-6073	33	15	a	a	DET
cana-6073	33	16	structural	structural	ADJ
cana-6073	33	17	parameter	parameter	NOUN
cana-6073	33	18	called	call	VERB
cana-6073	33	19	the	the	DET
cana-6073	33	20	local	local	ADJ
cana-6073	33	21	detour	detour	NOUN
cana-6073	33	22	communications	communication	NOUN
cana-6073	33	23	on	on	ADP
cana-6073	33	24	applied	apply	VERB
cana-6073	33	25	nonlinear	nonlinear	ADJ
cana-6073	33	26	analysis	analysis	NOUN
cana-6073	33	27	issn	issn	NOUN
cana-6073	33	28	:	:	PUNCT
cana-6073	33	29	1074	1074	NUM
cana-6073	33	30	-	-	PUNCT
cana-6073	33	31	133x	133x	NUM
cana-6073	33	32	vol	vol	NOUN
cana-6073	33	33	31	31	NUM
cana-6073	33	34	no	no	NOUN
cana-6073	33	35	.	.	PUNCT
cana-6073	34	1	8s	8s	PROPN
cana-6073	34	2	(	(	PUNCT
cana-6073	34	3	2024	2024	NUM
cana-6073	34	4	)	)	PUNCT
cana-6073	34	5	1186	1186	NUM
cana-6073	34	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6073	34	7	domination	domination	NOUN
cana-6073	34	8	degree	degree	NOUN
cana-6073	34	9	,	,	PUNCT
cana-6073	34	10	denoted	denote	VERB
cana-6073	34	11	𝑙𝑑(𝑠	𝑙𝑑(𝑠	NOUN
cana-6073	34	12	)	)	PUNCT
cana-6073	34	13	.	.	PUNCT
cana-6073	35	1	the	the	DET
cana-6073	35	2	upper	upper	ADJ
cana-6073	35	3	detour	detour	NOUN
cana-6073	35	4	domination	domination	NOUN
cana-6073	35	5	degree	degree	NOUN
cana-6073	35	6	number	number	NOUN
cana-6073	35	7	𝛾𝑑𝑑	𝛾𝑑𝑑	VERB
cana-6073	35	8	+	+	CCONJ
cana-6073	35	9	(	(	PUNCT
cana-6073	35	10	𝐺	𝐺	NOUN
cana-6073	35	11	)	)	PUNCT
cana-6073	35	12	is	be	AUX
cana-6073	35	13	given	give	VERB
cana-6073	35	14	by	by	ADP
cana-6073	35	15	:	:	PUNCT
cana-6073	35	16	𝛾𝑑𝑑	𝛾𝑑𝑑	NOUN
cana-6073	35	17	+	+	CCONJ
cana-6073	35	18	(	(	PUNCT
cana-6073	35	19	𝑢	𝑢	X
cana-6073	35	20	,	,	PUNCT
cana-6073	35	21	𝑣	𝑣	NOUN
cana-6073	35	22	)	)	PUNCT
cana-6073	35	23	=	=	SYM
cana-6073	35	24	max{𝑙𝑑(𝑠	max{𝑙𝑑(𝑠	X
cana-6073	35	25	)	)	PUNCT
cana-6073	35	26	}	}	PUNCT
cana-6073	35	27	=	=	SYM
cana-6073	35	28	max	max	X
cana-6073	35	29	{	{	PUNCT
cana-6073	35	30	deg(𝑢	deg(𝑢	PROPN
cana-6073	35	31	)	)	PUNCT
cana-6073	35	32	+	+	CCONJ
cana-6073	35	33	deg(𝑣	deg(𝑣	PROPN
cana-6073	35	34	)	)	PUNCT
cana-6073	35	35	+	+	CCONJ
cana-6073	35	36	∑	∑	PROPN
cana-6073	35	37	  	  	SPACE
cana-6073	35	38	𝑤∈𝑁(𝑢,𝑣	𝑤∈𝑁(𝑢,𝑣	PROPN
cana-6073	35	39	)	)	PUNCT
cana-6073	35	40	 	 	SPACE
cana-6073	35	41	deg(𝑤	deg(𝑤	PROPN
cana-6073	35	42	)	)	PUNCT
cana-6073	35	43	}	}	PUNCT
cana-6073	35	44	where	where	SCONJ
cana-6073	35	45	:	:	PUNCT
cana-6073	35	46	•	•	NUM
cana-6073	35	47	𝑢	𝑢	X
cana-6073	35	48	,	,	PUNCT
cana-6073	35	49	𝑣	𝑣	PRON
cana-6073	35	50	∈	∈	PROPN
cana-6073	35	51	𝑆	𝑆	PROPN
cana-6073	35	52	•	•	ADP
cana-6073	35	53	𝑁(𝑢	𝑁(𝑢	PROPN
cana-6073	35	54	,	,	PUNCT
cana-6073	35	55	𝑣	𝑣	NOUN
cana-6073	35	56	)	)	PUNCT
cana-6073	35	57	is	be	AUX
cana-6073	35	58	a	a	DET
cana-6073	35	59	neighborhood	neighborhood	NOUN
cana-6073	35	60	of	of	ADP
cana-6073	35	61	vertices	vertex	NOUN
cana-6073	35	62	lying	lie	VERB
cana-6073	35	63	on	on	ADP
cana-6073	35	64	the	the	DET
cana-6073	35	65	detour	detour	NOUN
cana-6073	35	66	path	path	NOUN
cana-6073	35	67	from	from	ADP
cana-6073	35	68	𝑢	𝑢	PRON
cana-6073	35	69	to	to	ADP
cana-6073	35	70	𝑣	𝑣	PRON
cana-6073	35	71	•	•	NUM
cana-6073	35	72	deg(𝑥	deg(𝑥	PROPN
cana-6073	35	73	)	)	PUNCT
cana-6073	35	74	denotes	denote	VERB
cana-6073	35	75	the	the	DET
cana-6073	35	76	degree	degree	NOUN
cana-6073	35	77	of	of	ADP
cana-6073	35	78	vertex	vertex	NOUN
cana-6073	35	79	𝑥	𝑥	INTJ
cana-6073	36	1	this	this	DET
cana-6073	36	2	definition	definition	NOUN
cana-6073	36	3	captures	capture	VERB
cana-6073	36	4	the	the	DET
cana-6073	36	5	strongest	strong	ADJ
cana-6073	36	6	detour	detour	NOUN
cana-6073	36	7	influence	influence	NOUN
cana-6073	36	8	a	a	DET
cana-6073	36	9	subset	subset	NOUN
cana-6073	36	10	can	can	AUX
cana-6073	36	11	exert	exert	VERB
cana-6073	36	12	in	in	ADP
cana-6073	36	13	terms	term	NOUN
cana-6073	36	14	of	of	ADP
cana-6073	36	15	degree	degree	NOUN
cana-6073	36	16	and	and	CCONJ
cana-6073	36	17	detour	detour	NOUN
cana-6073	36	18	structure	structure	NOUN
cana-6073	36	19	.	.	PUNCT
cana-6073	37	1	theorems	theorem	NOUN
cana-6073	37	2	theorem	theorem	VERB
cana-6073	37	3	1	1	NUM
cana-6073	37	4	:	:	PUNCT
cana-6073	37	5	detour	detour	NOUN
cana-6073	37	6	domination	domination	NOUN
cana-6073	37	7	number	number	NOUN
cana-6073	37	8	in	in	ADP
cana-6073	37	9	complete	complete	ADJ
cana-6073	37	10	graphs	graph	NOUN
cana-6073	37	11	theorem	theorem	VERB
cana-6073	37	12	:	:	PUNCT
cana-6073	37	13	let	let	VERB
cana-6073	37	14	𝐾𝑛	𝐾𝑛	PROPN
cana-6073	37	15	−	−	PROPN
cana-6073	37	16	(	(	PUNCT
cana-6073	37	17	𝑉	𝑉	PROPN
cana-6073	37	18	,	,	PUNCT
cana-6073	37	19	𝐸	𝐸	PROPN
cana-6073	37	20	)	)	PUNCT
cana-6073	37	21	be	be	VERB
cana-6073	37	22	a	a	DET
cana-6073	37	23	complete	complete	ADJ
cana-6073	37	24	graph	graph	NOUN
cana-6073	37	25	on	on	ADP
cana-6073	37	26	𝑛	𝑛	DET
cana-6073	37	27	≥	≥	NUM
cana-6073	37	28	2	2	NUM
cana-6073	37	29	vertices	vertex	NOUN
cana-6073	37	30	.	.	PUNCT
cana-6073	38	1	then	then	ADV
cana-6073	38	2	the	the	DET
cana-6073	38	3	detour	detour	NOUN
cana-6073	38	4	domination	domination	NOUN
cana-6073	38	5	number	number	NOUN
cana-6073	38	6	𝛾𝐷(𝐾𝑛	𝛾𝐷(𝐾𝑛	NOUN
cana-6073	38	7	)	)	PUNCT
cana-6073	38	8	is	be	AUX
cana-6073	38	9	1	1	NUM
cana-6073	38	10	,	,	PUNCT
cana-6073	38	11	i.e.	i.e.	X
cana-6073	38	12	,	,	PUNCT
cana-6073	38	13	𝛾𝐷(𝐾𝑛	𝛾𝐷(𝐾𝑛	NOUN
cana-6073	38	14	)	)	PUNCT
cana-6073	38	15	−	−	NOUN
cana-6073	38	16	1	1	NUM
cana-6073	38	17	proof	proof	NOUN
cana-6073	38	18	:	:	PUNCT
cana-6073	38	19	in	in	ADP
cana-6073	38	20	a	a	DET
cana-6073	38	21	complete	complete	ADJ
cana-6073	38	22	graph	graph	NOUN
cana-6073	38	23	𝐾𝑛	𝐾𝑛	PROPN
cana-6073	38	24	,	,	PUNCT
cana-6073	38	25	every	every	DET
cana-6073	38	26	pair	pair	NOUN
cana-6073	38	27	of	of	ADP
cana-6073	38	28	distinct	distinct	ADJ
cana-6073	38	29	vertices	vertex	NOUN
cana-6073	38	30	𝑢	𝑢	PART
cana-6073	38	31	,	,	PUNCT
cana-6073	38	32	𝑣	𝑣	PRON
cana-6073	38	33	∈	∈	PROPN
cana-6073	38	34	𝑉	𝑉	PROPN
cana-6073	38	35	is	be	AUX
cana-6073	38	36	connected	connect	VERB
cana-6073	38	37	by	by	ADP
cana-6073	38	38	a	a	DET
cana-6073	38	39	unique	unique	ADJ
cana-6073	38	40	edge	edge	NOUN
cana-6073	38	41	,	,	PUNCT
cana-6073	38	42	so	so	ADV
cana-6073	38	43	:	:	PUNCT
cana-6073	38	44	𝑑(𝑢	𝑑(𝑢	ADJ
cana-6073	38	45	,	,	PUNCT
cana-6073	38	46	𝑣	𝑣	NOUN
cana-6073	38	47	)	)	PUNCT
cana-6073	38	48	−	−	PROPN
cana-6073	38	49	1	1	NUM
cana-6073	38	50	∀𝑢	∀𝑢	DET
cana-6073	38	51	≠	≠	PROPN
cana-6073	38	52	𝑣	𝑣	ADP
cana-6073	38	53	however	however	ADV
cana-6073	38	54	,	,	PUNCT
cana-6073	38	55	the	the	DET
cana-6073	38	56	detour	detour	NOUN
cana-6073	38	57	distance	distance	NOUN
cana-6073	38	58	𝐷(𝑢	𝐷(𝑢	NOUN
cana-6073	38	59	,	,	PUNCT
cana-6073	38	60	𝑣	𝑣	NOUN
cana-6073	38	61	)	)	PUNCT
cana-6073	38	62	,	,	PUNCT
cana-6073	38	63	defined	define	VERB
cana-6073	38	64	as	as	ADP
cana-6073	38	65	the	the	DET
cana-6073	38	66	length	length	NOUN
cana-6073	38	67	of	of	ADP
cana-6073	38	68	the	the	DET
cana-6073	38	69	longest	long	ADJ
cana-6073	38	70	possible	possible	ADJ
cana-6073	38	71	path	path	NOUN
cana-6073	38	72	between	between	ADP
cana-6073	38	73	𝑢	𝑢	NOUN
cana-6073	38	74	and	and	CCONJ
cana-6073	38	75	𝑣	𝑣	X
cana-6073	38	76	without	without	ADP
cana-6073	38	77	repeating	repeat	VERB
cana-6073	38	78	any	any	DET
cana-6073	38	79	vertices	vertex	NOUN
cana-6073	38	80	,	,	PUNCT
cana-6073	38	81	is	be	AUX
cana-6073	38	82	:	:	PUNCT
cana-6073	38	83	𝐷(𝑢	𝐷(𝑢	PROPN
cana-6073	38	84	,	,	PUNCT
cana-6073	38	85	𝑣	𝑣	NOUN
cana-6073	38	86	)	)	PUNCT
cana-6073	38	87	−	−	NOUN
cana-6073	38	88	𝑛	𝑛	PRON
cana-6073	38	89	−	−	NUM
cana-6073	38	90	1	1	NUM
cana-6073	38	91	∀𝑢	∀𝑢	DET
cana-6073	38	92	≠	≠	PROPN
cana-6073	38	93	𝑣	𝑣	X
cana-6073	38	94	since	since	SCONJ
cana-6073	38	95	the	the	DET
cana-6073	38	96	longest	long	ADJ
cana-6073	38	97	path	path	NOUN
cana-6073	38	98	between	between	ADP
cana-6073	38	99	any	any	DET
cana-6073	38	100	two	two	NUM
cana-6073	38	101	vertices	vertex	NOUN
cana-6073	38	102	in	in	ADP
cana-6073	38	103	𝐾𝑛	𝐾𝑛	PROPN
cana-6073	38	104	must	must	AUX
cana-6073	38	105	visit	visit	VERB
cana-6073	38	106	all	all	DET
cana-6073	38	107	other	other	ADJ
cana-6073	38	108	𝑛	𝑛	DET
cana-6073	38	109	−	−	NUM
cana-6073	38	110	2	2	NUM
cana-6073	38	111	vertices	vertex	NOUN
cana-6073	38	112	exactly	exactly	ADV
cana-6073	38	113	once	once	ADV
cana-6073	38	114	before	before	ADP
cana-6073	38	115	reaching	reach	VERB
cana-6073	38	116	𝑣	𝑣	NOUN
cana-6073	38	117	,	,	PUNCT
cana-6073	38	118	utilizing	utilize	VERB
cana-6073	38	119	all	all	DET
cana-6073	38	120	𝑛	𝑛	DET
cana-6073	38	121	−	−	NUM
cana-6073	38	122	1	1	NUM
cana-6073	38	123	vertices	vertex	NOUN
cana-6073	38	124	(	(	PUNCT
cana-6073	38	125	including	include	VERB
cana-6073	38	126	𝑢	𝑢	NOUN
cana-6073	38	127	and	and	CCONJ
cana-6073	38	128	𝑣	𝑣	PRON
cana-6073	38	129	)	)	PUNCT
cana-6073	38	130	.	.	PUNCT
cana-6073	39	1	let	let	VERB
cana-6073	39	2	𝑆	𝑆	PROPN
cana-6073	39	3	⊆	⊆	PROPN
cana-6073	39	4	𝑉	𝑉	PROPN
cana-6073	39	5	be	be	AUX
cana-6073	39	6	a	a	DET
cana-6073	39	7	detour	detour	NOUN
cana-6073	39	8	dominating	dominating	NOUN
cana-6073	39	9	set	set	NOUN
cana-6073	39	10	,	,	PUNCT
cana-6073	39	11	i.e.	i.e.	X
cana-6073	39	12	,	,	PUNCT
cana-6073	39	13	every	every	DET
cana-6073	39	14	vertex	vertex	NOUN
cana-6073	39	15	𝑣	𝑣	ADP
cana-6073	39	16	∈	∈	PROPN
cana-6073	39	17	𝑉	𝑉	PROPN
cana-6073	39	18	∖	∖	NOUN
cana-6073	39	19	𝑆	𝑆	PROPN
cana-6073	39	20	must	must	AUX
cana-6073	39	21	lie	lie	VERB
cana-6073	39	22	on	on	ADP
cana-6073	39	23	a	a	DET
cana-6073	39	24	detour	detour	NOUN
cana-6073	39	25	path	path	NOUN
cana-6073	39	26	that	that	PRON
cana-6073	39	27	includes	include	VERB
cana-6073	39	28	some	some	DET
cana-6073	39	29	𝑢	𝑢	ADJ
cana-6073	39	30	∈	∈	NOUN
cana-6073	39	31	𝑆.	𝑆.	PROPN
cana-6073	39	32	due	due	ADP
cana-6073	39	33	to	to	ADP
cana-6073	39	34	the	the	DET
cana-6073	39	35	complete	complete	ADJ
cana-6073	39	36	connectivity	connectivity	NOUN
cana-6073	39	37	of	of	ADP
cana-6073	39	38	𝐾𝑛	𝐾𝑛	PROPN
cana-6073	39	39	,	,	PUNCT
cana-6073	39	40	from	from	ADP
cana-6073	39	41	any	any	DET
cana-6073	39	42	chosen	choose	VERB
cana-6073	39	43	vertex	vertex	NOUN
cana-6073	39	44	𝑢	𝑢	PROPN
cana-6073	39	45	∈	∈	PROPN
cana-6073	39	46	𝑉	𝑉	PROPN
cana-6073	39	47	,	,	PUNCT
cana-6073	39	48	there	there	PRON
cana-6073	39	49	exists	exist	VERB
cana-6073	39	50	a	a	DET
cana-6073	39	51	detour	detour	NOUN
cana-6073	39	52	path	path	NOUN
cana-6073	39	53	of	of	ADP
cana-6073	39	54	length	length	NOUN
cana-6073	39	55	𝑛	𝑛	PRON
cana-6073	39	56	−	−	PROPN
cana-6073	39	57	1	1	NUM
cana-6073	39	58	that	that	PRON
cana-6073	39	59	visits	visit	VERB
cana-6073	39	60	every	every	DET
cana-6073	39	61	other	other	ADJ
cana-6073	39	62	vertex	vertex	NOUN
cana-6073	39	63	𝑣	𝑣	ADP
cana-6073	39	64	∈	∈	PROPN
cana-6073	39	65	𝑉	𝑉	PROPN
cana-6073	39	66	∖	∖	X
cana-6073	39	67	{	{	PUNCT
cana-6073	39	68	𝑢	𝑢	X
cana-6073	39	69	}	}	PUNCT
cana-6073	39	70	.	.	PUNCT
cana-6073	40	1	hence	hence	ADV
cana-6073	40	2	,	,	PUNCT
cana-6073	40	3	one	one	NUM
cana-6073	40	4	vertex	vertex	NOUN
cana-6073	40	5	suffices	suffice	VERB
cana-6073	40	6	to	to	ADP
cana-6073	40	7	detour	detour	NOUN
cana-6073	40	8	dominate	dominate	VERB
cana-6073	40	9	the	the	DET
cana-6073	40	10	entire	entire	ADJ
cana-6073	40	11	graph	graph	NOUN
cana-6073	40	12	.	.	PUNCT
cana-6073	41	1	therefore	therefore	ADV
cana-6073	41	2	:	:	PUNCT
cana-6073	41	3	𝛾𝐷(𝐾𝑛	𝛾𝐷(𝐾𝑛	NOUN
cana-6073	41	4	)	)	PUNCT
cana-6073	41	5	−	−	PROPN
cana-6073	41	6	1	1	NUM
cana-6073	41	7	to	to	PART
cana-6073	41	8	formalize	formalize	VERB
cana-6073	41	9	this	this	PRON
cana-6073	41	10	in	in	ADP
cana-6073	41	11	matrix	matrix	NOUN
cana-6073	41	12	terms	term	NOUN
cana-6073	41	13	,	,	PUNCT
cana-6073	41	14	let	let	VERB
cana-6073	41	15	𝐴	𝐴	PROPN
cana-6073	41	16	∈	∈	PROPN
cana-6073	41	17	ℝ𝑛×𝑛	ℝ𝑛×𝑛	PROPN
cana-6073	41	18	be	be	VERB
cana-6073	41	19	the	the	DET
cana-6073	41	20	adjacency	adjacency	NOUN
cana-6073	41	21	matrix	matrix	NOUN
cana-6073	41	22	of	of	ADP
cana-6073	41	23	𝐾𝑛	𝐾𝑛	PROPN
cana-6073	41	24	,	,	PUNCT
cana-6073	41	25	defined	define	VERB
cana-6073	41	26	by	by	ADP
cana-6073	41	27	:	:	PUNCT
cana-6073	41	28	𝐴	𝐴	PROPN
cana-6073	41	29	−	−	PROPN
cana-6073	42	1	𝐽𝑛	𝐽𝑛	PROPN
cana-6073	42	2	−	−	PROPN
cana-6073	42	3	𝐼𝑛	𝐼𝑛	PROPN
cana-6073	42	4	where	where	SCONJ
cana-6073	42	5	𝐽𝑛	𝐽𝑛	PROPN
cana-6073	42	6	is	be	AUX
cana-6073	42	7	the	the	DET
cana-6073	42	8	all	all	DET
cana-6073	42	9	-	-	PUNCT
cana-6073	42	10	ones	one	NOUN
cana-6073	42	11	matrix	matrix	NOUN
cana-6073	42	12	and	and	CCONJ
cana-6073	42	13	𝐼𝑛	𝐼𝑛	PROPN
cana-6073	42	14	is	be	AUX
cana-6073	42	15	the	the	DET
cana-6073	42	16	identity	identity	NOUN
cana-6073	42	17	matrix	matrix	NOUN
cana-6073	42	18	.	.	PUNCT
cana-6073	43	1	the	the	DET
cana-6073	43	2	entries	entry	NOUN
cana-6073	43	3	of	of	ADP
cana-6073	43	4	𝐴	𝐴	PROPN
cana-6073	43	5	are	be	AUX
cana-6073	43	6	given	give	VERB
cana-6073	43	7	by	by	ADP
cana-6073	43	8	:	:	PUNCT
cana-6073	43	9	communications	communication	NOUN
cana-6073	43	10	on	on	ADP
cana-6073	43	11	applied	apply	VERB
cana-6073	43	12	nonlinear	nonlinear	ADJ
cana-6073	43	13	analysis	analysis	NOUN
cana-6073	43	14	issn	issn	NOUN
cana-6073	43	15	:	:	PUNCT
cana-6073	43	16	1074	1074	NUM
cana-6073	43	17	-	-	PUNCT
cana-6073	43	18	133x	133x	NUM
cana-6073	43	19	vol	vol	NOUN
cana-6073	43	20	31	31	NUM
cana-6073	43	21	no	no	NOUN
cana-6073	43	22	.	.	PUNCT
cana-6073	44	1	8s	8s	PROPN
cana-6073	44	2	(	(	PUNCT
cana-6073	44	3	2024	2024	NUM
cana-6073	44	4	)	)	PUNCT
cana-6073	44	5	1187	1187	NUM
cana-6073	44	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6073	45	1	𝐴𝑖𝑗	𝐴𝑖𝑗	NUM
cana-6073	45	2	=	=	PUNCT
cana-6073	45	3	{	{	PUNCT
cana-6073	45	4	1	1	NUM
cana-6073	45	5	if	if	SCONJ
cana-6073	45	6	𝑖	𝑖	PRON
cana-6073	45	7	≠	≠	PROPN
cana-6073	45	8	𝑗	𝑗	INTJ
cana-6073	45	9	0	0	NUM
cana-6073	46	1	if	if	SCONJ
cana-6073	46	2	𝑖	𝑖	PRON
cana-6073	46	3	−	−	NOUN
cana-6073	46	4	𝑗	𝑗	INTJ
cana-6073	46	5	let	let	VERB
cana-6073	46	6	𝑥	𝑥	PRON
cana-6073	46	7	−	−	PROPN
cana-6073	46	8	(	(	PUNCT
cana-6073	46	9	𝑥1	𝑥1	NOUN
cana-6073	46	10	,	,	PUNCT
cana-6073	46	11	𝑥2	𝑥2	NOUN
cana-6073	46	12	,	,	PUNCT
cana-6073	46	13	…	…	PUNCT
cana-6073	46	14	,	,	PUNCT
cana-6073	46	15	𝑥𝑛)𝑇	𝑥𝑛)𝑇	ADP
cana-6073	46	16	be	be	AUX
cana-6073	46	17	the	the	DET
cana-6073	46	18	characteristic	characteristic	ADJ
cana-6073	46	19	vector	vector	NOUN
cana-6073	46	20	of	of	ADP
cana-6073	46	21	the	the	DET
cana-6073	46	22	detour	detour	NOUN
cana-6073	46	23	dominating	dominating	NOUN
cana-6073	46	24	set	set	VERB
cana-6073	46	25	𝑆	𝑆	PROPN
cana-6073	46	26	⊆	⊆	NUM
cana-6073	46	27	𝑉	𝑉	PROPN
cana-6073	46	28	,	,	PUNCT
cana-6073	46	29	where	where	SCONJ
cana-6073	46	30	:	:	PUNCT
cana-6073	47	1	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	47	2	−	−	PROPN
cana-6073	47	3	{	{	PUNCT
cana-6073	47	4	1	1	NUM
cana-6073	47	5	if	if	SCONJ
cana-6073	47	6	𝑣𝑖	𝑣𝑖	ADP
cana-6073	47	7	∈	∈	PROPN
cana-6073	47	8	𝑆	𝑆	PROPN
cana-6073	47	9	0	0	PUNCT
cana-6073	48	1	otherwise	otherwise	ADV
cana-6073	48	2	then	then	ADV
cana-6073	48	3	the	the	DET
cana-6073	48	4	detour	detour	NOUN
cana-6073	48	5	domination	domination	NOUN
cana-6073	48	6	constraint	constraint	NOUN
cana-6073	48	7	requires	require	VERB
cana-6073	48	8	that	that	SCONJ
cana-6073	48	9	for	for	ADP
cana-6073	48	10	each	each	PRON
cana-6073	48	11	𝑗	𝑗	NOUN
cana-6073	48	12	−	−	PROPN
cana-6073	48	13	1,2	1,2	NUM
cana-6073	48	14	,	,	PUNCT
cana-6073	48	15	…	…	PUNCT
cana-6073	48	16	,	,	PUNCT
cana-6073	48	17	𝑛	𝑛	PROPN
cana-6073	48	18	,	,	PUNCT
cana-6073	48	19	there	there	PRON
cana-6073	48	20	must	must	AUX
cana-6073	48	21	exist	exist	VERB
cana-6073	48	22	at	at	ADV
cana-6073	48	23	least	least	ADJ
cana-6073	48	24	one	one	NUM
cana-6073	48	25	𝑖	𝑖	SYM
cana-6073	48	26	≠	≠	PROPN
cana-6073	48	27	𝑗	𝑗	PRON
cana-6073	48	28	such	such	ADJ
cana-6073	48	29	that	that	PRON
cana-6073	48	30	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	49	1	−	−	NOUN
cana-6073	49	2	1	1	X
cana-6073	49	3	.	.	PUNCT
cana-6073	50	1	this	this	PRON
cana-6073	50	2	is	be	AUX
cana-6073	50	3	equivalent	equivalent	ADJ
cana-6073	50	4	to	to	ADP
cana-6073	50	5	:	:	PUNCT
cana-6073	50	6	∑	∑	PART
cana-6073	50	7	  	  	SPACE
cana-6073	50	8	𝑛	𝑛	PRON
cana-6073	50	9	𝑖=1	𝑖=1	PROPN
cana-6073	50	10	𝑖≠𝑗	𝑖≠𝑗	NUM
cana-6073	50	11	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	50	12	≥	≥	NOUN
cana-6073	50	13	1	1	NUM
cana-6073	50	14	however	however	ADV
cana-6073	50	15	,	,	PUNCT
cana-6073	50	16	since	since	SCONJ
cana-6073	50	17	𝐾𝑛	𝐾𝑛	PROPN
cana-6073	50	18	allows	allow	VERB
cana-6073	50	19	for	for	SCONJ
cana-6073	50	20	each	each	DET
cana-6073	50	21	vertex	vertex	NOUN
cana-6073	50	22	to	to	PART
cana-6073	50	23	lie	lie	VERB
cana-6073	50	24	on	on	ADP
cana-6073	50	25	a	a	DET
cana-6073	50	26	detour	detour	NOUN
cana-6073	50	27	path	path	NOUN
cana-6073	50	28	from	from	ADP
cana-6073	50	29	any	any	DET
cana-6073	50	30	other	other	ADJ
cana-6073	50	31	vertex	vertex	NOUN
cana-6073	50	32	,	,	PUNCT
cana-6073	50	33	and	and	CCONJ
cana-6073	50	34	since	since	SCONJ
cana-6073	50	35	every	every	DET
cana-6073	50	36	vertex	vertex	NOUN
cana-6073	50	37	is	be	AUX
cana-6073	50	38	adjacent	adjacent	ADJ
cana-6073	50	39	to	to	ADP
cana-6073	50	40	all	all	DET
cana-6073	50	41	others	other	NOUN
cana-6073	50	42	,	,	PUNCT
cana-6073	50	43	a	a	DET
cana-6073	50	44	single	single	ADJ
cana-6073	50	45	vertex	vertex	NOUN
cana-6073	50	46	suffices	suffice	NOUN
cana-6073	50	47	for	for	ADP
cana-6073	50	48	detour	detour	NOUN
cana-6073	50	49	domination	domination	NOUN
cana-6073	50	50	.	.	PUNCT
cana-6073	51	1	thus	thus	ADV
cana-6073	51	2	,	,	PUNCT
cana-6073	51	3	the	the	DET
cana-6073	51	4	integer	integer	NOUN
cana-6073	51	5	program	program	NOUN
cana-6073	51	6	becomes	become	VERB
cana-6073	51	7	:	:	PUNCT
cana-6073	51	8	minimize	minimize	VERB
cana-6073	51	9	∑	∑	DET
cana-6073	51	10	  	  	SPACE
cana-6073	51	11	𝑛	𝑛	PRON
cana-6073	51	12	𝑖=1	𝑖=1	PUNCT
cana-6073	51	13	 	 	SPACE
cana-6073	51	14	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	51	15	subject	subject	VERB
cana-6073	51	16	to	to	ADP
cana-6073	51	17	∑	∑	PROPN
cana-6073	51	18	  	  	SPACE
cana-6073	51	19	𝑛	𝑛	PRON
cana-6073	51	20	𝑖=1	𝑖=1	PROPN
cana-6073	51	21	𝑖≠𝑗	𝑖≠𝑗	PUNCT
cana-6073	51	22	 	 	SPACE
cana-6073	52	1	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	52	2	≥	≥	NUM
cana-6073	52	3	1	1	NUM
cana-6073	52	4	for	for	ADP
cana-6073	52	5	all	all	PRON
cana-6073	52	6	𝑗	𝑗	PRON
cana-6073	52	7	−	−	NOUN
cana-6073	52	8	1,2	1,2	NUM
cana-6073	52	9	,	,	PUNCT
cana-6073	52	10	…	…	PUNCT
cana-6073	52	11	,	,	PUNCT
cana-6073	52	12	𝑛	𝑛	PRON
cana-6073	52	13	𝑥𝑖	𝑥𝑖	X
cana-6073	52	14	∈	∈	PROPN
cana-6073	52	15	{	{	PUNCT
cana-6073	52	16	0,1	0,1	NOUN
cana-6073	52	17	}	}	PUNCT
cana-6073	52	18	,	,	PUNCT
cana-6073	52	19	𝑖	𝑖	ADP
cana-6073	52	20	−	−	PROPN
cana-6073	52	21	1,2	1,2	NUM
cana-6073	52	22	,	,	PUNCT
cana-6073	52	23	…	…	PUNCT
cana-6073	52	24	,	,	PUNCT
cana-6073	53	1	𝑛	𝑛	PRON
cana-6073	53	2	setting	set	VERB
cana-6073	53	3	any	any	DET
cana-6073	53	4	one	one	NUM
cana-6073	53	5	𝑥𝑘	𝑥𝑘	NOUN
cana-6073	53	6	−	−	PROPN
cana-6073	53	7	1	1	NUM
cana-6073	53	8	and	and	CCONJ
cana-6073	53	9	all	all	DET
cana-6073	53	10	others	other	NOUN
cana-6073	53	11	𝑥𝑖	𝑥𝑖	ADP
cana-6073	53	12	−	−	NOUN
cana-6073	53	13	0	0	NUM
cana-6073	53	14	for	for	ADP
cana-6073	53	15	𝑖	𝑖	PRON
cana-6073	53	16	≠	≠	PROPN
cana-6073	53	17	𝑘	𝑘	DET
cana-6073	53	18	satisfies	satisfie	NOUN
cana-6073	53	19	all	all	DET
cana-6073	53	20	constraints	constraint	NOUN
cana-6073	53	21	,	,	PUNCT
cana-6073	53	22	yielding	yield	VERB
cana-6073	53	23	the	the	DET
cana-6073	53	24	minimum	minimum	ADJ
cana-6073	53	25	value	value	NOUN
cana-6073	53	26	:	:	PUNCT
cana-6073	53	27	𝛾𝐷(𝐾𝑛	𝛾𝐷(𝐾𝑛	NOUN
cana-6073	53	28	)	)	PUNCT
cana-6073	53	29	−	−	PUNCT
cana-6073	53	30	∑	∑	ADP
cana-6073	53	31	  	  	SPACE
cana-6073	53	32	𝑛	𝑛	PRON
cana-6073	53	33	𝑖=1	𝑖=1	PROPN
cana-6073	53	34	𝑥𝑖	𝑥𝑖	ADP
cana-6073	53	35	−	−	NUM
cana-6073	53	36	1	1	NUM
cana-6073	53	37	this	this	PRON
cana-6073	53	38	completes	complete	VERB
cana-6073	53	39	the	the	DET
cana-6073	53	40	proof	proof	NOUN
cana-6073	53	41	.	.	PUNCT
cana-6073	54	1	theorem	theorem	VERB
cana-6073	54	2	2	2	NUM
cana-6073	54	3	:	:	PUNCT
cana-6073	54	4	detour	detour	NOUN
cana-6073	54	5	domination	domination	NOUN
cana-6073	54	6	number	number	NOUN
cana-6073	54	7	in	in	ADP
cana-6073	54	8	path	path	NOUN
cana-6073	54	9	graphs	graph	NOUN
cana-6073	54	10	𝑃𝑛	𝑃𝑛	PROPN
cana-6073	54	11	theorem	theorem	VERB
cana-6073	54	12	:	:	PUNCT
cana-6073	54	13	let	let	VERB
cana-6073	54	14	𝑃𝑛	𝑃𝑛	PROPN
cana-6073	54	15	−	−	PROPN
cana-6073	54	16	(	(	PUNCT
cana-6073	54	17	𝑉	𝑉	PROPN
cana-6073	54	18	,	,	PUNCT
cana-6073	54	19	𝐸	𝐸	PROPN
cana-6073	54	20	)	)	PUNCT
cana-6073	54	21	denote	denote	VERB
cana-6073	54	22	a	a	DET
cana-6073	54	23	simple	simple	ADJ
cana-6073	54	24	undirected	undirected	ADJ
cana-6073	54	25	path	path	NOUN
cana-6073	54	26	graph	graph	NOUN
cana-6073	54	27	on	on	ADP
cana-6073	54	28	𝑛	𝑛	DET
cana-6073	54	29	≥	≥	NUM
cana-6073	54	30	1	1	NUM
cana-6073	54	31	vertices	vertex	NOUN
cana-6073	54	32	with	with	ADP
cana-6073	54	33	consecutive	consecutive	ADJ
cana-6073	54	34	edges	edge	NOUN
cana-6073	54	35	.	.	PUNCT
cana-6073	55	1	then	then	ADV
cana-6073	55	2	the	the	DET
cana-6073	55	3	detour	detour	NOUN
cana-6073	55	4	domination	domination	NOUN
cana-6073	55	5	number	number	NOUN
cana-6073	55	6	𝛾𝐷(𝑃𝑛	𝛾𝐷(𝑃𝑛	NOUN
cana-6073	55	7	)	)	PUNCT
cana-6073	55	8	satisfies	satisfie	NOUN
cana-6073	55	9	:	:	PUNCT
cana-6073	55	10	𝛾𝐷(𝑃𝑛	𝛾𝐷(𝑃𝑛	NOUN
cana-6073	55	11	)	)	PUNCT
cana-6073	55	12	−	−	PROPN
cana-6073	55	13	⌈	⌈	SYM
cana-6073	55	14	𝑛	𝑛	DET
cana-6073	55	15	3	3	NUM
cana-6073	55	16	⌉	⌉	DET
cana-6073	55	17	proof	proof	NOUN
cana-6073	55	18	:	:	PUNCT
cana-6073	55	19	let	let	VERB
cana-6073	55	20	𝑉	𝑉	PROPN
cana-6073	55	21	−	−	PROPN
cana-6073	55	22	{	{	PUNCT
cana-6073	55	23	𝑣1	𝑣1	PROPN
cana-6073	55	24	,	,	PUNCT
cana-6073	55	25	𝑣2	𝑣2	PROPN
cana-6073	55	26	,	,	PUNCT
cana-6073	55	27	…	…	PUNCT
cana-6073	55	28	,	,	PUNCT
cana-6073	55	29	𝑣𝑛	𝑣𝑛	NOUN
cana-6073	55	30	}	}	PUNCT
cana-6073	55	31	,	,	PUNCT
cana-6073	55	32	and	and	CCONJ
cana-6073	55	33	let	let	VERB
cana-6073	55	34	edges	edge	NOUN
cana-6073	55	35	𝐸	𝐸	PRON
cana-6073	55	36	−	−	PROPN
cana-6073	55	37	{	{	PUNCT
cana-6073	55	38	(	(	PUNCT
cana-6073	55	39	𝑣𝑖	𝑣𝑖	PROPN
cana-6073	55	40	,	,	PUNCT
cana-6073	55	41	𝑣𝑖+1	𝑣𝑖+1	X
cana-6073	55	42	)	)	PUNCT
cana-6073	55	43	∣	∣	ADJ
cana-6073	55	44	1	1	NUM
cana-6073	55	45	≤	≤	NUM
cana-6073	55	46	𝑖	𝑖	ADP
cana-6073	55	47	<	<	AUX
cana-6073	55	48	𝑛	𝑛	PROPN
cana-6073	55	49	}	}	PUNCT
cana-6073	55	50	connect	connect	VERB
cana-6073	55	51	consecutive	consecutive	ADJ
cana-6073	55	52	communications	communication	NOUN
cana-6073	55	53	on	on	ADP
cana-6073	55	54	applied	apply	VERB
cana-6073	55	55	nonlinear	nonlinear	ADJ
cana-6073	55	56	analysis	analysis	NOUN
cana-6073	55	57	issn	issn	NOUN
cana-6073	55	58	:	:	PUNCT
cana-6073	55	59	1074	1074	NUM
cana-6073	55	60	-	-	PUNCT
cana-6073	55	61	133x	133x	NUM
cana-6073	55	62	vol	vol	NOUN
cana-6073	55	63	31	31	NUM
cana-6073	55	64	no	no	NOUN
cana-6073	55	65	.	.	PUNCT
cana-6073	56	1	8s	8s	PROPN
cana-6073	56	2	(	(	PUNCT
cana-6073	56	3	2024	2024	NUM
cana-6073	56	4	)	)	PUNCT
cana-6073	56	5	1188	1188	NUM
cana-6073	56	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-6073	56	7	vertices	vertice	VERB
cana-6073	56	8	.	.	PUNCT
cana-6073	57	1	then	then	ADV
cana-6073	57	2	𝑃𝑛	𝑃𝑛	PROPN
cana-6073	57	3	is	be	AUX
cana-6073	57	4	a	a	DET
cana-6073	57	5	path	path	NOUN
cana-6073	57	6	of	of	ADP
cana-6073	57	7	length	length	NOUN
cana-6073	57	8	𝑛	𝑛	PRON
cana-6073	57	9	−	−	PROPN
cana-6073	57	10	1	1	NUM
cana-6073	57	11	.	.	PUNCT
cana-6073	58	1	the	the	DET
cana-6073	58	2	distance	distance	NOUN
cana-6073	58	3	𝑑(𝑣𝑖	𝑑(𝑣𝑖	VERB
cana-6073	58	4	,	,	PUNCT
cana-6073	58	5	𝑣𝑗	𝑣𝑗	ADP
cana-6073	58	6	)	)	PUNCT
cana-6073	58	7	between	between	ADP
cana-6073	58	8	any	any	DET
cana-6073	58	9	two	two	NUM
cana-6073	58	10	vertices	vertex	NOUN
cana-6073	58	11	𝑣𝑖	𝑣𝑖	ADV
cana-6073	58	12	and	and	CCONJ
cana-6073	58	13	𝑣𝑗	𝑣𝑗	ADP
cana-6073	58	14	is	be	AUX
cana-6073	58	15	:	:	PUNCT
cana-6073	58	16	𝑑(𝑣𝑖	𝑑(𝑣𝑖	VERB
cana-6073	58	17	,	,	PUNCT
cana-6073	58	18	𝑣𝑗	𝑣𝑗	NOUN
cana-6073	58	19	)	)	PUNCT
cana-6073	58	20	−	−	NOUN
cana-6073	58	21	|𝑖	|𝑖	NOUN
cana-6073	58	22	−	−	NOUN
cana-6073	58	23	𝑗|	𝑗|	PROPN
cana-6073	58	24	the	the	DET
cana-6073	58	25	detour	detour	NOUN
cana-6073	58	26	distance	distance	NOUN
cana-6073	58	27	𝐷(𝑣𝑖	𝐷(𝑣𝑖	NOUN
cana-6073	58	28	,	,	PUNCT
cana-6073	58	29	𝑣𝑗	𝑣𝑗	ADP
cana-6073	58	30	)	)	PUNCT
cana-6073	58	31	,	,	PUNCT
cana-6073	58	32	defined	define	VERB
cana-6073	58	33	as	as	ADP
cana-6073	58	34	the	the	DET
cana-6073	58	35	length	length	NOUN
cana-6073	58	36	of	of	ADP
cana-6073	58	37	the	the	DET
cana-6073	58	38	longest	long	ADJ
cana-6073	58	39	simple	simple	ADJ
cana-6073	58	40	path	path	NOUN
cana-6073	58	41	between	between	ADP
cana-6073	58	42	𝑣𝑖	𝑣𝑖	NOUN
cana-6073	58	43	and	and	CCONJ
cana-6073	58	44	𝑣𝑗	𝑣𝑗	NOUN
cana-6073	58	45	,	,	PUNCT
cana-6073	58	46	equals	equal	VERB
cana-6073	58	47	:	:	PUNCT
cana-6073	58	48	𝐷(𝑣𝑖	𝐷(𝑣𝑖	INTJ
cana-6073	58	49	,	,	PUNCT
cana-6073	58	50	𝑣𝑗	𝑣𝑗	NOUN
cana-6073	58	51	)	)	PUNCT
cana-6073	58	52	−	−	NOUN
cana-6073	58	53	𝑛	𝑛	PRON
cana-6073	58	54	−	−	PROPN
cana-6073	58	55	1	1	NUM
cana-6073	58	56	,	,	PUNCT
cana-6073	58	57	for	for	ADP
cana-6073	58	58	(	(	PUNCT
cana-6073	58	59	𝑣𝑖	𝑣𝑖	NOUN
cana-6073	58	60	,	,	PUNCT
cana-6073	58	61	𝑣𝑗	𝑣𝑗	NOUN
cana-6073	58	62	)	)	PUNCT
cana-6073	58	63	−	−	PROPN
cana-6073	58	64	(	(	PUNCT
cana-6073	58	65	𝑣1	𝑣1	PROPN
cana-6073	58	66	,	,	PUNCT
cana-6073	58	67	𝑣𝑛	𝑣𝑛	NOUN
cana-6073	58	68	)	)	PUNCT
cana-6073	58	69	let	let	VERB
cana-6073	58	70	𝑆	𝑆	PROPN
cana-6073	58	71	⊆	⊆	PROPN
cana-6073	58	72	𝑉	𝑉	PROPN
cana-6073	58	73	be	be	AUX
cana-6073	58	74	a	a	DET
cana-6073	58	75	detour	detour	NOUN
cana-6073	58	76	dominating	dominating	NOUN
cana-6073	58	77	set	set	VERB
cana-6073	58	78	such	such	ADJ
cana-6073	58	79	that	that	PRON
cana-6073	58	80	for	for	ADP
cana-6073	58	81	every	every	DET
cana-6073	58	82	vertex	vertex	NOUN
cana-6073	58	83	𝑣𝑘	𝑣𝑘	PROPN
cana-6073	58	84	∈	∈	PROPN
cana-6073	58	85	𝑉	𝑉	PROPN
cana-6073	58	86	,	,	PUNCT
cana-6073	58	87	there	there	PRON
cana-6073	58	88	exists	exist	VERB
cana-6073	58	89	𝑣𝑖	𝑣𝑖	ADP
cana-6073	58	90	∈	∈	PROPN
cana-6073	58	91	𝑆	𝑆	PROPN
cana-6073	58	92	for	for	ADP
cana-6073	58	93	which	which	PRON
cana-6073	58	94	𝑣𝑘	𝑣𝑘	ADV
cana-6073	58	95	lies	lie	VERB
cana-6073	58	96	on	on	ADP
cana-6073	58	97	a	a	DET
cana-6073	58	98	detour	detour	NOUN
cana-6073	58	99	path	path	NOUN
cana-6073	58	100	(	(	PUNCT
cana-6073	58	101	of	of	ADP
cana-6073	58	102	length	length	NOUN
cana-6073	58	103	𝑛	𝑛	DET
cana-6073	58	104	−	−	PROPN
cana-6073	58	105	1	1	NUM
cana-6073	58	106	)	)	PUNCT
cana-6073	58	107	beginning	begin	VERB
cana-6073	58	108	at	at	ADP
cana-6073	58	109	𝑣𝑖.	𝑣𝑖.	NOUN
cana-6073	58	110	that	that	PRON
cana-6073	58	111	is	be	AUX
cana-6073	58	112	:	:	PUNCT
cana-6073	58	113	∀𝑣𝑘	∀𝑣𝑘	PROPN
cana-6073	58	114	∈	∈	PROPN
cana-6073	58	115	𝑉	𝑉	PROPN
cana-6073	58	116	,	,	PUNCT
cana-6073	58	117	∃𝑣𝑖	∃𝑣𝑖	NOUN
cana-6073	58	118	∈	∈	PROPN
cana-6073	58	119	𝑆	𝑆	PROPN
cana-6073	58	120	such	such	ADJ
cana-6073	58	121	that	that	SCONJ
cana-6073	58	122	𝑣𝑘	𝑣𝑘	PROPN
cana-6073	58	123	∈	∈	PROPN
cana-6073	58	124	pathdetour	pathdetour	NOUN
cana-6073	58	125	(	(	PUNCT
cana-6073	58	126	𝑣𝑖	𝑣𝑖	NOUN
cana-6073	58	127	)	)	PUNCT
cana-6073	58	128	we	we	PRON
cana-6073	58	129	construct	construct	VERB
cana-6073	58	130	such	such	DET
cana-6073	58	131	a	a	DET
cana-6073	58	132	set	set	ADJ
cana-6073	58	133	𝑆	𝑆	PROPN
cana-6073	58	134	by	by	ADP
cana-6073	58	135	selecting	select	VERB
cana-6073	58	136	every	every	DET
cana-6073	58	137	third	third	ADJ
cana-6073	58	138	vertex	vertex	NOUN
cana-6073	58	139	,	,	PUNCT
cana-6073	59	1	i.e.	i.e.	X
cana-6073	59	2	,	,	PUNCT
cana-6073	59	3	𝑆	𝑆	PROPN
cana-6073	59	4	−	−	PROPN
cana-6073	59	5	{	{	PUNCT
cana-6073	59	6	𝑣𝑖	𝑣𝑖	NOUN
cana-6073	59	7	∈	∈	PROPN
cana-6073	59	8	𝑉	𝑉	PROPN
cana-6073	59	9	∣	∣	NOUN
cana-6073	59	10	𝑖	𝑖	NUM
cana-6073	59	11	≡	≡	PROPN
cana-6073	59	12	2(mod3	2(mod3	NUM
cana-6073	59	13	)	)	PUNCT
cana-6073	59	14	}	}	PUNCT
cana-6073	60	1	each	each	DET
cana-6073	60	2	such	such	ADJ
cana-6073	60	3	𝑣𝑖	𝑣𝑖	ADP
cana-6073	60	4	∈	∈	PROPN
cana-6073	60	5	𝑆	𝑆	PROPN
cana-6073	60	6	can	can	AUX
cana-6073	60	7	detour	detour	AUX
cana-6073	60	8	-	-	PUNCT
cana-6073	60	9	dominate	dominate	VERB
cana-6073	60	10	its	its	PRON
cana-6073	60	11	neighbors	neighbor	NOUN
cana-6073	60	12	:	:	PUNCT
cana-6073	60	13	𝑁𝐷[𝑣𝑖	𝑁𝐷[𝑣𝑖	PROPN
cana-6073	60	14	]	]	X
cana-6073	60	15	−	−	X
cana-6073	60	16	{	{	PUNCT
cana-6073	60	17	𝑣𝑖−1	𝑣𝑖−1	NOUN
cana-6073	60	18	,	,	PUNCT
cana-6073	60	19	𝑣𝑖	𝑣𝑖	ADV
cana-6073	60	20	,	,	PUNCT
cana-6073	60	21	𝑣𝑖+1	𝑣𝑖+1	NOUN
cana-6073	60	22	}	}	PUNCT
cana-6073	60	23	∩	∩	X
cana-6073	60	24	𝑉	𝑉	PROPN
cana-6073	60	25	thus	thus	ADV
cana-6073	60	26	,	,	PUNCT
cana-6073	60	27	the	the	DET
cana-6073	60	28	total	total	ADJ
cana-6073	60	29	detour	detour	NOUN
cana-6073	60	30	coverage	coverage	NOUN
cana-6073	60	31	from	from	ADP
cana-6073	60	32	all	all	DET
cana-6073	60	33	selected	select	VERB
cana-6073	60	34	dominators	dominator	NOUN
cana-6073	60	35	is	be	AUX
cana-6073	60	36	:	:	PUNCT
cana-6073	60	37	⋃	⋃	PROPN
cana-6073	60	38	  	  	SPACE
cana-6073	60	39	𝑣𝑖∈𝑆	𝑣𝑖∈𝑆	PROPN
cana-6073	60	40	𝑁𝐷[𝑣𝑖	𝑁𝐷[𝑣𝑖	PROPN
cana-6073	60	41	]	]	X
cana-6073	60	42	−	−	PROPN
cana-6073	60	43	𝑉	𝑉	PROPN
cana-6073	60	44	and	and	CCONJ
cana-6073	60	45	the	the	DET
cana-6073	60	46	size	size	NOUN
cana-6073	60	47	of	of	ADP
cana-6073	60	48	such	such	DET
cana-6073	60	49	a	a	DET
cana-6073	60	50	set	set	NOUN
cana-6073	60	51	is	be	AUX
cana-6073	60	52	:	:	PUNCT
cana-6073	60	53	|𝑆|	|𝑆|	ADJ
cana-6073	60	54	=	=	SYM
cana-6073	60	55	⌈	⌈	ADP
cana-6073	60	56	𝑛	𝑛	DET
cana-6073	60	57	3	3	NUM
cana-6073	60	58	⌉	⌉	SCONJ
cana-6073	60	59	now	now	ADV
cana-6073	60	60	,	,	PUNCT
cana-6073	60	61	to	to	PART
cana-6073	60	62	formulate	formulate	VERB
cana-6073	60	63	the	the	DET
cana-6073	60	64	problem	problem	NOUN
cana-6073	60	65	algebraically	algebraically	ADV
cana-6073	60	66	,	,	PUNCT
cana-6073	60	67	define	define	VERB
cana-6073	60	68	indicator	indicator	NOUN
cana-6073	60	69	variables	variable	NOUN
cana-6073	60	70	:	:	PUNCT
cana-6073	60	71	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	61	1	=	=	PUNCT
cana-6073	61	2	{	{	PUNCT
cana-6073	61	3	1	1	NUM
cana-6073	61	4	if	if	SCONJ
cana-6073	61	5	𝑣𝑖	𝑣𝑖	ADP
cana-6073	61	6	∈	∈	PROPN
cana-6073	61	7	𝑆	𝑆	PROPN
cana-6073	61	8	0	0	PUNCT
cana-6073	61	9	otherwise	otherwise	ADV
cana-6073	61	10	for	for	ADP
cana-6073	61	11	𝑖	𝑖	X
cana-6073	61	12	−	−	PROPN
cana-6073	61	13	1,2	1,2	NUM
cana-6073	61	14	,	,	PUNCT
cana-6073	61	15	…	…	PUNCT
cana-6073	61	16	,	,	PUNCT
cana-6073	61	17	𝑛	𝑛	PRON
cana-6073	61	18	then	then	ADV
cana-6073	61	19	,	,	PUNCT
cana-6073	61	20	for	for	ADP
cana-6073	61	21	each	each	DET
cana-6073	61	22	vertex	vertex	NOUN
cana-6073	61	23	𝑣𝑘	𝑣𝑘	PROPN
cana-6073	61	24	∈	∈	PROPN
cana-6073	61	25	𝑉	𝑉	PROPN
cana-6073	61	26	,	,	PUNCT
cana-6073	61	27	the	the	DET
cana-6073	61	28	domination	domination	NOUN
cana-6073	61	29	constraint	constraint	NOUN
cana-6073	61	30	is	be	AUX
cana-6073	61	31	:	:	PUNCT
cana-6073	61	32	𝑥𝑘−1	𝑥𝑘−1	PROPN
cana-6073	61	33	+	+	NUM
cana-6073	61	34	𝑥𝑘	𝑥𝑘	X
cana-6073	61	35	+	+	CCONJ
cana-6073	61	36	𝑥𝑘+1	𝑥𝑘+1	NUM
cana-6073	61	37	≥	≥	NUM
cana-6073	61	38	1	1	NUM
cana-6073	61	39	∀1	∀1	PUNCT
cana-6073	61	40	≤	≤	NOUN
cana-6073	61	41	𝑘	𝑘	DET
cana-6073	61	42	≤	≤	NOUN
cana-6073	61	43	𝑛	𝑛	PRON
cana-6073	61	44	with	with	ADP
cana-6073	61	45	boundary	boundary	ADJ
cana-6073	61	46	conditions	condition	NOUN
cana-6073	61	47	handled	handle	VERB
cana-6073	61	48	by	by	ADP
cana-6073	61	49	setting	set	VERB
cana-6073	61	50	:	:	PUNCT
cana-6073	61	51	𝑥0	𝑥0	VERB
cana-6073	61	52	−	−	PROPN
cana-6073	61	53	𝑥𝑛+1	𝑥𝑛+1	NOUN
cana-6073	61	54	−	−	NOUN
cana-6073	61	55	0	0	NUM
cana-6073	62	1	the	the	DET
cana-6073	62	2	optimization	optimization	NOUN
cana-6073	62	3	problem	problem	NOUN
cana-6073	62	4	becomes	become	VERB
cana-6073	62	5	:	:	PUNCT
cana-6073	62	6	minimize	minimize	VERB
cana-6073	62	7	:	:	PUNCT
cana-6073	62	8	𝑧	𝑧	PROPN
cana-6073	62	9	−	−	PROPN
cana-6073	62	10	∑	∑	INTJ
cana-6073	62	11	  	  	SPACE
cana-6073	62	12	𝑛	𝑛	PRON
cana-6073	62	13	𝑖=1	𝑖=1	PROPN
cana-6073	62	14	  	  	SPACE
cana-6073	62	15	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	62	16	subject	subject	ADJ
cana-6073	62	17	to	to	ADP
cana-6073	62	18	:	:	PUNCT
cana-6073	62	19	𝑥𝑖−1	𝑥𝑖−1	PROPN
cana-6073	62	20	+	+	NOUN
cana-6073	62	21	𝑥𝑖	𝑥𝑖	PRON
cana-6073	62	22	+	+	CCONJ
cana-6073	62	23	𝑥𝑖+1	𝑥𝑖+1	PROPN
cana-6073	62	24	≥	≥	NOUN
cana-6073	62	25	1	1	NUM
cana-6073	62	26	,	,	PUNCT
cana-6073	62	27	∀𝑖	∀𝑖	PROPN
cana-6073	62	28	−	−	PROPN
cana-6073	62	29	1	1	NUM
cana-6073	62	30	,	,	PUNCT
cana-6073	62	31	…	…	PUNCT
cana-6073	62	32	,	,	PUNCT
cana-6073	62	33	𝑛	𝑛	DET
cana-6073	62	34	𝑥0	𝑥0	NOUN
cana-6073	62	35	−	−	PROPN
cana-6073	62	36	𝑥𝑛+1	𝑥𝑛+1	NOUN
cana-6073	62	37	−	−	NOUN
cana-6073	62	38	0	0	NUM
cana-6073	63	1	𝑥𝑖	𝑥𝑖	ADP
cana-6073	63	2	∈	∈	PROPN
cana-6073	63	3	{	{	PUNCT
cana-6073	63	4	0,1	0,1	NOUN
cana-6073	63	5	}	}	PUNCT
cana-6073	63	6	,	,	PUNCT
cana-6073	63	7	∀𝑖	∀𝑖	PROPN
cana-6073	63	8	communications	communication	NOUN
cana-6073	63	9	on	on	ADP
cana-6073	63	10	applied	apply	VERB
cana-6073	63	11	nonlinear	nonlinear	ADJ
cana-6073	63	12	analysis	analysis	NOUN
cana-6073	63	13	issn	issn	NOUN
cana-6073	63	14	:	:	PUNCT
cana-6073	63	15	1074	1074	NUM
cana-6073	63	16	-	-	PUNCT
cana-6073	63	17	133x	133x	NUM
cana-6073	63	18	vol	vol	NOUN
cana-6073	63	19	31	31	NUM
cana-6073	63	20	no	no	NOUN
cana-6073	63	21	.	.	PUNCT
cana-6073	64	1	8s	8s	PROPN
cana-6073	64	2	(	(	PUNCT
cana-6073	64	3	2024	2024	NUM
cana-6073	64	4	)	)	PUNCT
cana-6073	64	5	1189	1189	NUM
cana-6073	64	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6073	64	7	this	this	PRON
cana-6073	64	8	is	be	AUX
cana-6073	64	9	an	an	DET
cana-6073	64	10	instance	instance	NOUN
cana-6073	64	11	of	of	ADP
cana-6073	64	12	a	a	DET
cana-6073	64	13	binary	binary	ADJ
cana-6073	64	14	integer	integer	NOUN
cana-6073	64	15	programming	programming	NOUN
cana-6073	64	16	problem	problem	NOUN
cana-6073	64	17	.	.	PUNCT
cana-6073	65	1	thus	thus	ADV
cana-6073	65	2	,	,	PUNCT
cana-6073	65	3	the	the	DET
cana-6073	65	4	solution	solution	NOUN
cana-6073	65	5	gives	give	VERB
cana-6073	65	6	the	the	DET
cana-6073	65	7	detour	detour	NOUN
cana-6073	65	8	domination	domination	NOUN
cana-6073	65	9	number	number	NOUN
cana-6073	65	10	:	:	PUNCT
cana-6073	65	11	𝛾𝐷(𝑃𝑛	𝛾𝐷(𝑃𝑛	NOUN
cana-6073	65	12	)	)	PUNCT
cana-6073	65	13	−	−	PROPN
cana-6073	65	14	min	min	NOUN
cana-6073	65	15	{	{	PUNCT
cana-6073	65	16	∑	∑	PROPN
cana-6073	65	17	  	  	SPACE
cana-6073	65	18	𝑛	𝑛	PRON
cana-6073	65	19	𝑖=1	𝑖=1	PROPN
cana-6073	65	20	  	  	SPACE
cana-6073	65	21	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	65	22	∣	∣	PROPN
cana-6073	65	23	𝑥𝑖−1	𝑥𝑖−1	PROPN
cana-6073	65	24	+	+	CCONJ
cana-6073	65	25	𝑥𝑖	𝑥𝑖	PRON
cana-6073	65	26	+	+	CCONJ
cana-6073	65	27	𝑥𝑖+1	𝑥𝑖+1	PROPN
cana-6073	65	28	≥	≥	NOUN
cana-6073	65	29	1	1	NUM
cana-6073	65	30	,	,	PUNCT
cana-6073	65	31	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	65	32	∈	∈	PROPN
cana-6073	65	33	{	{	PUNCT
cana-6073	65	34	0,1	0,1	NOUN
cana-6073	65	35	}	}	PUNCT
cana-6073	65	36	,	,	PUNCT
cana-6073	65	37	𝑖	𝑖	ADP
cana-6073	65	38	−	−	PROPN
cana-6073	65	39	1	1	NUM
cana-6073	65	40	,	,	PUNCT
cana-6073	65	41	…	…	PUNCT
cana-6073	65	42	,	,	PUNCT
cana-6073	65	43	𝑛	𝑛	ADJ
cana-6073	65	44	}	}	PUNCT
cana-6073	65	45	in	in	ADP
cana-6073	65	46	compact	compact	ADJ
cana-6073	65	47	set	set	NOUN
cana-6073	65	48	-	-	PUNCT
cana-6073	65	49	theoretic	theoretic	NOUN
cana-6073	65	50	optimization	optimization	NOUN
cana-6073	65	51	form	form	NOUN
cana-6073	65	52	,	,	PUNCT
cana-6073	65	53	the	the	DET
cana-6073	65	54	detour	detour	NOUN
cana-6073	65	55	domination	domination	NOUN
cana-6073	65	56	number	number	NOUN
cana-6073	65	57	can	can	AUX
cana-6073	65	58	also	also	ADV
cana-6073	65	59	be	be	AUX
cana-6073	65	60	written	write	VERB
cana-6073	65	61	as	as	ADP
cana-6073	65	62	:	:	PUNCT
cana-6073	65	63	𝛾𝐷(𝑃𝑛	𝛾𝐷(𝑃𝑛	NOUN
cana-6073	65	64	)	)	PUNCT
cana-6073	65	65	=	=	SYM
cana-6073	65	66	min	min	NOUN
cana-6073	65	67	𝑥∈{0,1}a	𝑥∈{0,1}a	NOUN
cana-6073	65	68	 	 	SPACE
cana-6073	65	69	{	{	PUNCT
cana-6073	65	70	∑	∑	PROPN
cana-6073	65	71	  	  	SPACE
cana-6073	65	72	𝑛	𝑛	PRON
cana-6073	65	73	𝑖=1	𝑖=1	PUNCT
cana-6073	65	74	 	 	SPACE
cana-6073	65	75	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	65	76	∣	∣	VERB
cana-6073	65	77	⋃	⋃	NOUN
cana-6073	65	78	  	  	SPACE
cana-6073	65	79	𝑖:𝑥𝑖−1	𝑖:𝑥𝑖−1	ADJ
cana-6073	65	80	 	 	SPACE
cana-6073	65	81	𝑁𝐷[𝑖	𝑁𝐷[𝑖	ADJ
cana-6073	65	82	]	]	X
cana-6073	65	83	−	−	PROPN
cana-6073	65	84	𝑉(𝑃𝑛	𝑉(𝑃𝑛	NOUN
cana-6073	65	85	)	)	PUNCT
cana-6073	65	86	}	}	PUNCT
cana-6073	66	1	where	where	SCONJ
cana-6073	66	2	:	:	PUNCT
cana-6073	66	3	𝑁𝐷[𝑖	𝑁𝐷[𝑖	NUM
cana-6073	66	4	]	]	X
cana-6073	66	5	−	−	PROPN
cana-6073	66	6	{	{	PUNCT
cana-6073	66	7	𝑖	𝑖	SYM
cana-6073	66	8	−	−	PROPN
cana-6073	66	9	1	1	NUM
cana-6073	66	10	,	,	PUNCT
cana-6073	66	11	𝑖	𝑖	CCONJ
cana-6073	66	12	,	,	PUNCT
cana-6073	66	13	𝑖	𝑖	X
cana-6073	66	14	+	+	NOUN
cana-6073	66	15	1	1	NUM
cana-6073	66	16	}	}	PUNCT
cana-6073	66	17	∩	∩	NOUN
cana-6073	66	18	[	[	X
cana-6073	66	19	1	1	NUM
cana-6073	66	20	,	,	PUNCT
cana-6073	66	21	𝑛	𝑛	PROPN
cana-6073	66	22	]	]	X
cana-6073	66	23	this	this	PRON
cana-6073	66	24	completes	complete	VERB
cana-6073	66	25	the	the	DET
cana-6073	66	26	proof	proof	NOUN
cana-6073	66	27	.	.	PUNCT
cana-6073	67	1	theorem	theorem	VERB
cana-6073	67	2	3	3	NUM
cana-6073	67	3	:	:	PUNCT
cana-6073	67	4	detour	detour	NOUN
cana-6073	67	5	domination	domination	NOUN
cana-6073	67	6	number	number	NOUN
cana-6073	67	7	in	in	ADP
cana-6073	67	8	cycle	cycle	NOUN
cana-6073	67	9	graphs	graph	NOUN
cana-6073	67	10	cn	cn	PROPN
cana-6073	67	11	theorem	theorem	PROPN
cana-6073	67	12	:	:	PUNCT
cana-6073	67	13	for	for	ADP
cana-6073	67	14	the	the	DET
cana-6073	67	15	cycle	cycle	NOUN
cana-6073	67	16	graph	graph	NOUN
cana-6073	67	17	𝐶𝑛	𝐶𝑛	PROPN
cana-6073	67	18	on	on	ADP
cana-6073	67	19	𝑛	𝑛	DET
cana-6073	67	20	≥	≥	NUM
cana-6073	67	21	3	3	NUM
cana-6073	67	22	vertices	vertex	NOUN
cana-6073	67	23	,	,	PUNCT
cana-6073	67	24	the	the	DET
cana-6073	67	25	detour	detour	NOUN
cana-6073	67	26	domination	domination	NOUN
cana-6073	67	27	number	number	NOUN
cana-6073	67	28	satisfies	satisfie	NOUN
cana-6073	67	29	:	:	PUNCT
cana-6073	67	30	𝛾𝐷𝐷(𝐶𝑛	𝛾𝐷𝐷(𝐶𝑛	X
cana-6073	67	31	)	)	PUNCT
cana-6073	67	32	−	−	ADP
cana-6073	67	33	⌈	⌈	SYM
cana-6073	67	34	𝑛	𝑛	DET
cana-6073	67	35	3	3	NUM
cana-6073	67	36	⌉	⌉	DET
cana-6073	67	37	proof	proof	NOUN
cana-6073	67	38	:	:	PUNCT
cana-6073	67	39	let	let	VERB
cana-6073	67	40	𝐶𝑛	𝐶𝑛	INTJ
cana-6073	67	41	−	−	PROPN
cana-6073	67	42	(	(	PUNCT
cana-6073	67	43	𝑉	𝑉	PROPN
cana-6073	67	44	,	,	PUNCT
cana-6073	67	45	𝐸	𝐸	PROPN
cana-6073	67	46	)	)	PUNCT
cana-6073	67	47	be	be	VERB
cana-6073	67	48	the	the	DET
cana-6073	67	49	cycle	cycle	NOUN
cana-6073	67	50	graph	graph	NOUN
cana-6073	67	51	with	with	ADP
cana-6073	67	52	vertex	vertex	NOUN
cana-6073	67	53	set	set	VERB
cana-6073	68	1	𝑉	𝑉	PROPN
cana-6073	68	2	−	−	PROPN
cana-6073	68	3	{	{	PUNCT
cana-6073	68	4	𝑣1	𝑣1	PROPN
cana-6073	68	5	,	,	PUNCT
cana-6073	68	6	𝑣2	𝑣2	PROPN
cana-6073	68	7	,	,	PUNCT
cana-6073	68	8	…	…	PUNCT
cana-6073	68	9	,	,	PUNCT
cana-6073	68	10	𝑣𝑛	𝑣𝑛	NOUN
cana-6073	68	11	}	}	PUNCT
cana-6073	68	12	and	and	CCONJ
cana-6073	68	13	edge	edge	NOUN
cana-6073	68	14	set	set	VERB
cana-6073	68	15	defined	define	VERB
cana-6073	68	16	by	by	ADP
cana-6073	68	17	:	:	PUNCT
cana-6073	68	18	𝐸	𝐸	PROPN
cana-6073	68	19	−	−	PROPN
cana-6073	68	20	{	{	PUNCT
cana-6073	68	21	(	(	PUNCT
cana-6073	68	22	𝑣𝑖	𝑣𝑖	PROPN
cana-6073	68	23	,	,	PUNCT
cana-6073	68	24	𝑣𝑖+1	𝑣𝑖+1	X
cana-6073	68	25	)	)	PUNCT
cana-6073	68	26	∣	∣	ADJ
cana-6073	68	27	1	1	NUM
cana-6073	68	28	≤	≤	NUM
cana-6073	68	29	𝑖	𝑖	ADP
cana-6073	68	30	<	<	X
cana-6073	68	31	𝑛	𝑛	X
cana-6073	68	32	}	}	PUNCT
cana-6073	68	33	∪	∪	X
cana-6073	68	34	{	{	PUNCT
cana-6073	68	35	(	(	PUNCT
cana-6073	68	36	𝑣𝑛	𝑣𝑛	NOUN
cana-6073	68	37	,	,	PUNCT
cana-6073	68	38	𝑣1	𝑣1	NOUN
cana-6073	68	39	)	)	PUNCT
cana-6073	68	40	}	}	PUNCT
cana-6073	68	41	the	the	DET
cana-6073	68	42	distance	distance	NOUN
cana-6073	68	43	between	between	ADP
cana-6073	68	44	any	any	DET
cana-6073	68	45	two	two	NUM
cana-6073	68	46	vertices	vertex	NOUN
cana-6073	68	47	𝑣𝑖	𝑣𝑖	ADV
cana-6073	68	48	and	and	CCONJ
cana-6073	68	49	𝑣𝑗	𝑣𝑗	ADP
cana-6073	68	50	on	on	ADP
cana-6073	68	51	the	the	DET
cana-6073	68	52	cycle	cycle	NOUN
cana-6073	68	53	is	be	AUX
cana-6073	68	54	given	give	VERB
cana-6073	68	55	by	by	ADP
cana-6073	68	56	:	:	PUNCT
cana-6073	68	57	𝑑(𝑣𝑖	𝑑(𝑣𝑖	PROPN
cana-6073	68	58	,	,	PUNCT
cana-6073	68	59	𝑣𝑗	𝑣𝑗	NOUN
cana-6073	68	60	)	)	PUNCT
cana-6073	68	61	−	−	NOUN
cana-6073	68	62	min(|𝑖	min(|𝑖	NOUN
cana-6073	68	63	−	−	PROPN
cana-6073	68	64	𝑗|	𝑗|	PROPN
cana-6073	68	65	,	,	PUNCT
cana-6073	68	66	𝑛	𝑛	DET
cana-6073	68	67	−	−	PROPN
cana-6073	68	68	|𝑖	|𝑖	NOUN
cana-6073	68	69	−	−	PROPN
cana-6073	68	70	𝑗|	𝑗|	PROPN
cana-6073	68	71	)	)	PUNCT
cana-6073	68	72	the	the	DET
cana-6073	68	73	detour	detour	NOUN
cana-6073	68	74	distance	distance	NOUN
cana-6073	68	75	(	(	PUNCT
cana-6073	68	76	longest	long	ADJ
cana-6073	68	77	simple	simple	ADJ
cana-6073	68	78	path	path	NOUN
cana-6073	68	79	)	)	PUNCT
cana-6073	68	80	between	between	ADP
cana-6073	68	81	𝑣𝑖	𝑣𝑖	ADV
cana-6073	68	82	and	and	CCONJ
cana-6073	68	83	𝑣𝑗	𝑣𝑗	ADP
cana-6073	68	84	is	be	AUX
cana-6073	68	85	:	:	PUNCT
cana-6073	68	86	𝐷(𝑣𝑖	𝐷(𝑣𝑖	INTJ
cana-6073	68	87	,	,	PUNCT
cana-6073	68	88	𝑣𝑗	𝑣𝑗	NOUN
cana-6073	68	89	)	)	PUNCT
cana-6073	68	90	−	−	NOUN
cana-6073	69	1	⌊	⌊	VERB
cana-6073	69	2	𝑛	𝑛	DET
cana-6073	69	3	2	2	NUM
cana-6073	69	4	⌋	⌋	NOUN
cana-6073	69	5	to	to	PART
cana-6073	69	6	construct	construct	VERB
cana-6073	69	7	a	a	DET
cana-6073	69	8	detour	detour	NOUN
cana-6073	69	9	dominating	dominating	NOUN
cana-6073	69	10	set	set	VERB
cana-6073	69	11	𝑆	𝑆	PROPN
cana-6073	69	12	⊆	⊆	NUM
cana-6073	69	13	𝑉	𝑉	PROPN
cana-6073	69	14	,	,	PUNCT
cana-6073	69	15	we	we	PRON
cana-6073	69	16	require	require	VERB
cana-6073	69	17	that	that	SCONJ
cana-6073	69	18	for	for	ADP
cana-6073	69	19	all	all	PRON
cana-6073	69	20	𝑣	𝑣	PRON
cana-6073	69	21	∈	∈	PROPN
cana-6073	69	22	𝑉	𝑉	PROPN
cana-6073	69	23	,	,	PUNCT
cana-6073	69	24	there	there	PRON
cana-6073	69	25	exists	exist	VERB
cana-6073	69	26	some	some	DET
cana-6073	69	27	𝑣𝑘	𝑣𝑘	NOUN
cana-6073	69	28	∈	∈	PROPN
cana-6073	69	29	𝑆	𝑆	PROPN
cana-6073	69	30	such	such	ADJ
cana-6073	69	31	that	that	SCONJ
cana-6073	69	32	𝑣	𝑣	DET
cana-6073	69	33	∈	∈	PROPN
cana-6073	69	34	pathdetour	pathdetour	NOUN
cana-6073	69	35	(	(	PUNCT
cana-6073	69	36	𝑣𝑘	𝑣𝑘	NOUN
cana-6073	69	37	)	)	PUNCT
cana-6073	69	38	.	.	PUNCT
cana-6073	70	1	since	since	SCONJ
cana-6073	70	2	each	each	DET
cana-6073	70	3	detour	detour	NOUN
cana-6073	70	4	in	in	ADP
cana-6073	70	5	the	the	DET
cana-6073	70	6	cycle	cycle	NOUN
cana-6073	70	7	is	be	AUX
cana-6073	70	8	symmetric	symmetric	ADJ
cana-6073	70	9	and	and	CCONJ
cana-6073	70	10	spans	span	NOUN
cana-6073	70	11	up	up	ADP
cana-6073	70	12	to	to	PART
cana-6073	70	13	half	half	DET
cana-6073	70	14	the	the	DET
cana-6073	70	15	cycle	cycle	NOUN
cana-6073	70	16	,	,	PUNCT
cana-6073	70	17	it	it	PRON
cana-6073	70	18	suffices	suffice	VERB
cana-6073	70	19	to	to	PART
cana-6073	70	20	place	place	VERB
cana-6073	70	21	dominators	dominator	NOUN
cana-6073	70	22	every	every	DET
cana-6073	70	23	3	3	NUM
cana-6073	70	24	vertices	vertex	NOUN
cana-6073	70	25	.	.	PUNCT
cana-6073	71	1	construct	construct	VERB
cana-6073	71	2	𝑆	𝑆	PROPN
cana-6073	71	3	as	as	ADP
cana-6073	71	4	:	:	PUNCT
cana-6073	71	5	𝑆	𝑆	PROPN
cana-6073	71	6	−	−	PROPN
cana-6073	71	7	{	{	PUNCT
cana-6073	71	8	𝑣𝑘	𝑣𝑘	NOUN
cana-6073	71	9	∈	∈	PROPN
cana-6073	71	10	𝑉	𝑉	PROPN
cana-6073	71	11	∣	∣	VERB
cana-6073	71	12	𝑘	𝑘	PRON
cana-6073	71	13	≡	≡	PROPN
cana-6073	71	14	1(mod3	1(mod3	NUM
cana-6073	71	15	)	)	PUNCT
cana-6073	71	16	}	}	PUNCT
cana-6073	71	17	using	use	VERB
cana-6073	71	18	modular	modular	ADJ
cana-6073	71	19	arithmetic	arithmetic	NOUN
cana-6073	71	20	on	on	ADP
cana-6073	71	21	indices	index	NOUN
cana-6073	71	22	,	,	PUNCT
cana-6073	71	23	each	each	DET
cana-6073	71	24	dominator	dominator	NOUN
cana-6073	71	25	𝑣𝑘	𝑣𝑘	NOUN
cana-6073	71	26	∈	∈	PROPN
cana-6073	71	27	𝑆	𝑆	PROPN
cana-6073	71	28	covers	cover	VERB
cana-6073	71	29	:	:	PUNCT
cana-6073	71	30	communications	communication	NOUN
cana-6073	71	31	on	on	ADP
cana-6073	71	32	applied	apply	VERB
cana-6073	71	33	nonlinear	nonlinear	ADJ
cana-6073	71	34	analysis	analysis	NOUN
cana-6073	71	35	issn	issn	NOUN
cana-6073	71	36	:	:	PUNCT
cana-6073	71	37	1074	1074	NUM
cana-6073	71	38	-	-	PUNCT
cana-6073	71	39	133x	133x	NUM
cana-6073	71	40	vol	vol	NOUN
cana-6073	71	41	31	31	NUM
cana-6073	71	42	no	no	NOUN
cana-6073	71	43	.	.	PUNCT
cana-6073	72	1	8s	8s	PROPN
cana-6073	72	2	(	(	PUNCT
cana-6073	72	3	2024	2024	NUM
cana-6073	72	4	)	)	PUNCT
cana-6073	72	5	1190	1190	NUM
cana-6073	72	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6073	72	7	𝑁𝐷[𝑣𝑘	𝑁𝐷[𝑣𝑘	X
cana-6073	72	8	]	]	X
cana-6073	72	9	−	−	X
cana-6073	72	10	{	{	PUNCT
cana-6073	72	11	𝑣𝑘−1	𝑣𝑘−1	PROPN
cana-6073	72	12	,	,	PUNCT
cana-6073	72	13	𝑣𝑘	𝑣𝑘	INTJ
cana-6073	72	14	,	,	PUNCT
cana-6073	72	15	𝑣𝑘+1	𝑣𝑘+1	ADP
cana-6073	72	16	}	}	PUNCT
cana-6073	72	17	with	with	ADP
cana-6073	72	18	indices	index	NOUN
cana-6073	72	19	modulo	modulo	VERB
cana-6073	72	20	𝑛	𝑛	ADP
cana-6073	72	21	therefore	therefore	ADV
cana-6073	72	22	,	,	PUNCT
cana-6073	72	23	the	the	DET
cana-6073	72	24	union	union	NOUN
cana-6073	72	25	of	of	ADP
cana-6073	72	26	closed	closed	ADJ
cana-6073	72	27	detour	detour	NOUN
cana-6073	72	28	neighborhoods	neighborhood	NOUN
cana-6073	72	29	satisfies	satisfie	NOUN
cana-6073	72	30	:	:	PUNCT
cana-6073	72	31	⋃	⋃	NOUN
cana-6073	72	32	  	  	SPACE
cana-6073	72	33	𝑣𝑘∈𝑆	𝑣𝑘∈𝑆	SYM
cana-6073	72	34	𝑁𝐷[𝑣𝑘	𝑁𝐷[𝑣𝑘	X
cana-6073	72	35	]	]	X
cana-6073	72	36	−	−	PROPN
cana-6073	72	37	𝑉	𝑉	PROPN
cana-6073	72	38	and	and	CCONJ
cana-6073	72	39	the	the	DET
cana-6073	72	40	size	size	NOUN
cana-6073	72	41	of	of	ADP
cana-6073	72	42	such	such	DET
cana-6073	72	43	a	a	DET
cana-6073	72	44	set	set	NOUN
cana-6073	72	45	is	be	AUX
cana-6073	72	46	:	:	PUNCT
cana-6073	72	47	|𝑆|	|𝑆|	ADJ
cana-6073	72	48	−	−	NOUN
cana-6073	72	49	⌈	⌈	NOUN
cana-6073	72	50	𝑛	𝑛	ADP
cana-6073	72	51	3	3	NUM
cana-6073	72	52	⌉	⌉	PUNCT
cana-6073	72	53	to	to	PART
cana-6073	72	54	express	express	VERB
cana-6073	72	55	this	this	PRON
cana-6073	72	56	algebraically	algebraically	ADV
cana-6073	72	57	,	,	PUNCT
cana-6073	72	58	define	define	VERB
cana-6073	72	59	indicator	indicator	NOUN
cana-6073	72	60	variables	variable	NOUN
cana-6073	72	61	:	:	PUNCT
cana-6073	73	1	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	73	2	−	−	PROPN
cana-6073	73	3	{	{	PUNCT
cana-6073	73	4	1	1	NUM
cana-6073	73	5	if	if	SCONJ
cana-6073	73	6	𝑣𝑖	𝑣𝑖	ADP
cana-6073	73	7	∈	∈	PROPN
cana-6073	73	8	𝑆	𝑆	PROPN
cana-6073	73	9	0	0	PUNCT
cana-6073	74	1	otherwise	otherwise	ADV
cana-6073	74	2	∀𝑖	∀𝑖	PRON
cana-6073	74	3	−	−	PROPN
cana-6073	74	4	1	1	NUM
cana-6073	74	5	,	,	PUNCT
cana-6073	74	6	…	…	PUNCT
cana-6073	74	7	,	,	PUNCT
cana-6073	74	8	𝑛	𝑛	DET
cana-6073	74	9	the	the	DET
cana-6073	74	10	domination	domination	NOUN
cana-6073	74	11	constraint	constraint	NOUN
cana-6073	74	12	for	for	ADP
cana-6073	74	13	each	each	DET
cana-6073	74	14	vertex	vertex	NOUN
cana-6073	74	15	𝑣𝑗	𝑣𝑗	ADP
cana-6073	74	16	∈	∈	PROPN
cana-6073	74	17	𝑉	𝑉	PROPN
cana-6073	74	18	is	be	AUX
cana-6073	74	19	:	:	PUNCT
cana-6073	74	20	𝑥𝑗−1	𝑥𝑗−1	PROPN
cana-6073	74	21	+	+	CCONJ
cana-6073	74	22	𝑥𝑗	𝑥𝑗	PROPN
cana-6073	74	23	+	+	X
cana-6073	74	24	𝑥𝑗+1	𝑥𝑗+1	ADP
cana-6073	74	25	≥	≥	NOUN
cana-6073	74	26	1	1	NUM
cana-6073	74	27	,	,	PUNCT
cana-6073	74	28	for	for	ADP
cana-6073	74	29	𝑗	𝑗	INTJ
cana-6073	74	30	−	−	PROPN
cana-6073	74	31	1	1	NUM
cana-6073	74	32	,	,	PUNCT
cana-6073	74	33	…	…	PUNCT
cana-6073	74	34	,	,	PUNCT
cana-6073	74	35	𝑛	𝑛	X
cana-6073	74	36	with	with	ADP
cana-6073	74	37	cyclic	cyclic	ADJ
cana-6073	74	38	(	(	PUNCT
cana-6073	74	39	modular	modular	ADJ
cana-6073	74	40	)	)	PUNCT
cana-6073	74	41	indexing	indexing	NOUN
cana-6073	74	42	:	:	PUNCT
cana-6073	74	43	𝑥0	𝑥0	PROPN
cana-6073	74	44	−	−	PROPN
cana-6073	74	45	𝑥𝑛	𝑥𝑛	NOUN
cana-6073	74	46	,	,	PUNCT
cana-6073	74	47	𝑥𝑛+1	𝑥𝑛+1	ADP
cana-6073	74	48	−	−	PROPN
cana-6073	74	49	𝑥1	𝑥1	NOUN
cana-6073	74	50	minimize	minimize	VERB
cana-6073	74	51	:	:	PUNCT
cana-6073	74	52	∑	∑	PART
cana-6073	74	53	  	  	SPACE
cana-6073	74	54	𝑛	𝑛	PRON
cana-6073	74	55	𝑖=1	𝑖=1	PROPN
cana-6073	74	56	  	  	SPACE
cana-6073	74	57	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	74	58	subject	subject	ADJ
cana-6073	74	59	to	to	ADP
cana-6073	74	60	:	:	PUNCT
cana-6073	74	61	𝑥𝑖−1	𝑥𝑖−1	PROPN
cana-6073	74	62	+	+	NOUN
cana-6073	74	63	𝑥𝑖	𝑥𝑖	PRON
cana-6073	75	1	+	+	CCONJ
cana-6073	75	2	𝑥𝑖+1	𝑥𝑖+1	PROPN
cana-6073	75	3	≥	≥	NOUN
cana-6073	75	4	1	1	NUM
cana-6073	75	5	∀𝑖	∀𝑖	PRON
cana-6073	75	6	−	−	NUM
cana-6073	75	7	1	1	NUM
cana-6073	75	8	,	,	PUNCT
cana-6073	75	9	…	…	PUNCT
cana-6073	75	10	,	,	PUNCT
cana-6073	75	11	𝑛	𝑛	PRON
cana-6073	75	12	𝑥𝑖	𝑥𝑖	X
cana-6073	75	13	∈	∈	PROPN
cana-6073	75	14	{	{	PUNCT
cana-6073	75	15	0,1	0,1	NOUN
cana-6073	75	16	}	}	PUNCT
cana-6073	75	17	∀𝑖	∀𝑖	PROPN
cana-6073	75	18	thus	thus	ADV
cana-6073	75	19	,	,	PUNCT
cana-6073	75	20	𝛾𝐷𝐷(𝐶𝑛	𝛾𝐷𝐷(𝐶𝑛	PROPN
cana-6073	75	21	)	)	PUNCT
cana-6073	75	22	−	−	PROPN
cana-6073	75	23	min	min	NOUN
cana-6073	75	24	{	{	PUNCT
cana-6073	75	25	∑	∑	PROPN
cana-6073	75	26	  	  	SPACE
cana-6073	75	27	𝑛	𝑛	PRON
cana-6073	75	28	𝑖=1	𝑖=1	PROPN
cana-6073	75	29	 	 	SPACE
cana-6073	75	30	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	75	31	∣	∣	PROPN
cana-6073	75	32	𝑥𝑖−1	𝑥𝑖−1	PROPN
cana-6073	75	33	+	+	CCONJ
cana-6073	75	34	𝑥𝑖	𝑥𝑖	PRON
cana-6073	75	35	+	+	CCONJ
cana-6073	75	36	𝑥𝑖+1	𝑥𝑖+1	PROPN
cana-6073	75	37	≥	≥	NOUN
cana-6073	75	38	1	1	NUM
cana-6073	75	39	,	,	PUNCT
cana-6073	75	40	𝑥𝑖	𝑥𝑖	PROPN
cana-6073	75	41	∈	∈	PROPN
cana-6073	75	42	{	{	PUNCT
cana-6073	75	43	0,1	0,1	NOUN
cana-6073	75	44	}	}	PUNCT
cana-6073	75	45	}	}	PUNCT
cana-6073	75	46	−	−	PROPN
cana-6073	75	47	⌈	⌈	SYM
cana-6073	75	48	𝑛	𝑛	ADP
cana-6073	75	49	3	3	NUM
cana-6073	75	50	⌉	⌉	NOUN
cana-6073	75	51	theorem	theorem	VERB
cana-6073	75	52	4	4	NUM
cana-6073	75	53	:	:	PUNCT
cana-6073	75	54	detour	detour	PRON
cana-6073	75	55	domination	domination	NOUN
cana-6073	75	56	in	in	ADP
cana-6073	75	57	trees	tree	NOUN
cana-6073	75	58	via	via	ADP
cana-6073	75	59	branch	branch	NOUN
cana-6073	75	60	decomposition	decomposition	NOUN
cana-6073	75	61	theorem	theorem	NOUN
cana-6073	75	62	:	:	PUNCT
cana-6073	75	63	let	let	VERB
cana-6073	75	64	𝑇	𝑇	PROPN
cana-6073	75	65	−	−	PROPN
cana-6073	75	66	(	(	PUNCT
cana-6073	75	67	𝑉	𝑉	PROPN
cana-6073	75	68	,	,	PUNCT
cana-6073	75	69	𝐸	𝐸	PROPN
cana-6073	75	70	)	)	PUNCT
cana-6073	75	71	be	be	VERB
cana-6073	75	72	a	a	DET
cana-6073	75	73	tree	tree	NOUN
cana-6073	75	74	of	of	ADP
cana-6073	75	75	order	order	NOUN
cana-6073	75	76	𝑛	𝑛	NOUN
cana-6073	75	77	,	,	PUNCT
cana-6073	75	78	rooted	root	VERB
cana-6073	75	79	at	at	ADP
cana-6073	75	80	a	a	DET
cana-6073	75	81	vertex	vertex	NOUN
cana-6073	75	82	𝑟	𝑟	NOUN
cana-6073	75	83	,	,	PUNCT
cana-6073	75	84	and	and	CCONJ
cana-6073	75	85	let	let	VERB
cana-6073	75	86	it	it	PRON
cana-6073	75	87	branch	branch	VERB
cana-6073	75	88	into	into	ADP
cana-6073	75	89	𝑘	𝑘	DET
cana-6073	75	90	major	major	ADJ
cana-6073	75	91	paths	path	NOUN
cana-6073	75	92	𝐵1	𝐵1	PROPN
cana-6073	75	93	,	,	PUNCT
cana-6073	75	94	𝐵2	𝐵2	NOUN
cana-6073	75	95	,	,	PUNCT
cana-6073	75	96	…	…	PUNCT
cana-6073	75	97	,	,	PUNCT
cana-6073	75	98	𝐵𝑘	𝐵𝑘	PROPN
cana-6073	75	99	,	,	PUNCT
cana-6073	75	100	with	with	ADP
cana-6073	75	101	each	each	DET
cana-6073	75	102	branch	branch	NOUN
cana-6073	75	103	𝐵𝑖	𝐵𝑖	PROPN
cana-6073	75	104	of	of	ADP
cana-6073	75	105	height	height	NOUN
cana-6073	76	1	ℎ𝑖.	ℎ𝑖.	NOUN
cana-6073	76	2	then	then	ADV
cana-6073	76	3	,	,	PUNCT
cana-6073	76	4	𝛾𝐷𝐷(𝑇	𝛾𝐷𝐷(𝑇	PROPN
cana-6073	76	5	)	)	PUNCT
cana-6073	76	6	≤	≤	NOUN
cana-6073	76	7	∑	∑	ADP
cana-6073	76	8	  	  	SPACE
cana-6073	76	9	𝑘	𝑘	PRON
cana-6073	76	10	𝑖=1	𝑖=1	PROPN
cana-6073	76	11	⌈	⌈	ADJ
cana-6073	76	12	ℎ𝑖	ℎ𝑖	ADP
cana-6073	76	13	2	2	NUM
cana-6073	77	1	⌉	⌉	NOUN
cana-6073	77	2	proof	proof	NOUN
cana-6073	77	3	:	:	PUNCT
cana-6073	77	4	in	in	ADP
cana-6073	77	5	a	a	DET
cana-6073	77	6	tree	tree	NOUN
cana-6073	77	7	,	,	PUNCT
cana-6073	77	8	the	the	DET
cana-6073	77	9	path	path	NOUN
cana-6073	77	10	between	between	ADP
cana-6073	77	11	any	any	DET
cana-6073	77	12	two	two	NUM
cana-6073	77	13	vertices	vertex	NOUN
cana-6073	77	14	is	be	AUX
cana-6073	77	15	unique	unique	ADJ
cana-6073	77	16	.	.	PUNCT
cana-6073	78	1	let	let	VERB
cana-6073	78	2	𝑑(𝑢	𝑑(𝑢	ADJ
cana-6073	78	3	,	,	PUNCT
cana-6073	78	4	𝑣	𝑣	NOUN
cana-6073	78	5	)	)	PUNCT
cana-6073	78	6	denote	denote	VERB
cana-6073	78	7	the	the	DET
cana-6073	78	8	number	number	NOUN
cana-6073	78	9	of	of	ADP
cana-6073	78	10	edges	edge	NOUN
cana-6073	78	11	in	in	ADP
cana-6073	78	12	the	the	DET
cana-6073	78	13	unique	unique	ADJ
cana-6073	78	14	𝑢	𝑢	NOUN
cana-6073	78	15	→	→	SYM
cana-6073	78	16	𝑣	𝑣	DET
cana-6073	78	17	path	path	NOUN
cana-6073	78	18	.	.	PUNCT
cana-6073	79	1	then	then	ADV
cana-6073	79	2	,	,	PUNCT
cana-6073	79	3	𝐷(𝑢	𝐷(𝑢	PROPN
cana-6073	79	4	,	,	PUNCT
cana-6073	79	5	𝑣	𝑣	NOUN
cana-6073	79	6	)	)	PUNCT
cana-6073	79	7	−	−	PROPN
cana-6073	79	8	𝑑(𝑢	𝑑(𝑢	PROPN
cana-6073	79	9	,	,	PUNCT
cana-6073	79	10	𝑣	𝑣	NOUN
cana-6073	79	11	)	)	PUNCT
cana-6073	79	12	,	,	PUNCT
cana-6073	79	13	∀𝑢	∀𝑢	NOUN
cana-6073	79	14	,	,	PUNCT
cana-6073	79	15	𝑣	𝑣	PRON
cana-6073	79	16	∈	∈	NOUN
cana-6073	79	17	𝑉(𝑇	𝑉(𝑇	NOUN
cana-6073	79	18	)	)	PUNCT
cana-6073	79	19	let	let	VERB
cana-6073	79	20	the	the	DET
cana-6073	79	21	root	root	NOUN
cana-6073	79	22	be	be	AUX
cana-6073	79	23	𝑟	𝑟	NOUN
cana-6073	79	24	,	,	PUNCT
cana-6073	79	25	and	and	CCONJ
cana-6073	79	26	decompose	decompose	VERB
cana-6073	79	27	the	the	DET
cana-6073	79	28	tree	tree	NOUN
cana-6073	79	29	into	into	ADP
cana-6073	79	30	disjoint	disjoint	NOUN
cana-6073	79	31	branches	branch	NOUN
cana-6073	79	32	from	from	ADP
cana-6073	79	33	𝑟	𝑟	NOUN
cana-6073	79	34	as	as	ADP
cana-6073	79	35	:	:	PUNCT
cana-6073	79	36	communications	communication	NOUN
cana-6073	79	37	on	on	ADP
cana-6073	79	38	applied	apply	VERB
cana-6073	79	39	nonlinear	nonlinear	ADJ
cana-6073	79	40	analysis	analysis	NOUN
cana-6073	79	41	issn	issn	NOUN
cana-6073	79	42	:	:	PUNCT
cana-6073	79	43	1074	1074	NUM
cana-6073	79	44	-	-	PUNCT
cana-6073	79	45	133x	133x	NUM
cana-6073	79	46	vol	vol	NOUN
cana-6073	79	47	31	31	NUM
cana-6073	79	48	no	no	NOUN
cana-6073	79	49	.	.	PUNCT
cana-6073	80	1	8s	8s	PROPN
cana-6073	80	2	(	(	PUNCT
cana-6073	80	3	2024	2024	NUM
cana-6073	80	4	)	)	PUNCT
cana-6073	80	5	1191	1191	NUM
cana-6073	80	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6073	80	7	𝑇	𝑇	PROPN
cana-6073	80	8	−	−	PROPN
cana-6073	80	9	⋃	⋃	NOUN
cana-6073	80	10	  	  	SPACE
cana-6073	80	11	𝑘	𝑘	PRON
cana-6073	80	12	𝑖=1	𝑖=1	PROPN
cana-6073	80	13	𝐵𝑖	𝐵𝑖	PROPN
cana-6073	80	14	each	each	DET
cana-6073	80	15	branch	branch	NOUN
cana-6073	81	1	𝐵𝑖	𝐵𝑖	PROPN
cana-6073	81	2	is	be	AUX
cana-6073	81	3	a	a	DET
cana-6073	81	4	path	path	NOUN
cana-6073	81	5	of	of	ADP
cana-6073	81	6	height	height	NOUN
cana-6073	81	7	ℎ𝑖.	ℎ𝑖.	NOUN
cana-6073	81	8	to	to	ADP
cana-6073	81	9	detour	detour	NOUN
cana-6073	81	10	-	-	PUNCT
cana-6073	81	11	dominate	dominate	VERB
cana-6073	81	12	each	each	DET
cana-6073	81	13	𝐵𝑖	𝐵𝑖	PROPN
cana-6073	81	14	,	,	PUNCT
cana-6073	81	15	we	we	PRON
cana-6073	81	16	select	select	VERB
cana-6073	81	17	vertices	vertex	NOUN
cana-6073	81	18	at	at	ADP
cana-6073	81	19	intervals	interval	NOUN
cana-6073	81	20	of	of	ADP
cana-6073	81	21	2	2	NUM
cana-6073	81	22	along	along	ADP
cana-6073	81	23	the	the	DET
cana-6073	81	24	path	path	NOUN
cana-6073	81	25	from	from	ADP
cana-6073	81	26	root	root	NOUN
cana-6073	81	27	to	to	ADP
cana-6073	81	28	leaves	leave	NOUN
cana-6073	81	29	.	.	PUNCT
cana-6073	82	1	thus	thus	ADV
cana-6073	82	2	,	,	PUNCT
cana-6073	82	3	each	each	DET
cana-6073	82	4	branch	branch	NOUN
cana-6073	82	5	requires	require	VERB
cana-6073	82	6	:	:	PUNCT
cana-6073	82	7	|𝑆𝑖|	|𝑆𝑖|	NOUN
cana-6073	82	8	=	=	SYM
cana-6073	82	9	⌈	⌈	NOUN
cana-6073	82	10	ℎ𝑖	ℎ𝑖	ADP
cana-6073	82	11	2	2	NUM
cana-6073	82	12	⌉	⌉	ADP
cana-6073	82	13	dominators	dominator	NOUN
cana-6073	82	14	summing	sum	VERB
cana-6073	82	15	over	over	ADP
cana-6073	82	16	all	all	DET
cana-6073	82	17	branches	branch	NOUN
cana-6073	82	18	:	:	PUNCT
cana-6073	82	19	𝛾𝐷𝐷(𝑇	𝛾𝐷𝐷(𝑇	NUM
cana-6073	82	20	)	)	PUNCT
cana-6073	82	21	≤	≤	NOUN
cana-6073	82	22	∑	∑	ADP
cana-6073	82	23	  	  	SPACE
cana-6073	82	24	𝑘	𝑘	PRON
cana-6073	82	25	𝑖=1	𝑖=1	PROPN
cana-6073	82	26	⌈	⌈	ADJ
cana-6073	82	27	ℎ𝑖	ℎ𝑖	ADP
cana-6073	82	28	2	2	NUM
cana-6073	82	29	⌉	⌉	VERB
cana-6073	82	30	define	define	VERB
cana-6073	82	31	binary	binary	ADJ
cana-6073	82	32	variables	variable	NOUN
cana-6073	82	33	𝑥𝑣	𝑥𝑣	ADP
cana-6073	82	34	∈	∈	PROPN
cana-6073	82	35	{	{	PUNCT
cana-6073	82	36	0,1	0,1	NOUN
cana-6073	82	37	}	}	PUNCT
cana-6073	82	38	for	for	ADP
cana-6073	82	39	all	all	PRON
cana-6073	82	40	𝑣	𝑣	DET
cana-6073	82	41	∈	∈	NOUN
cana-6073	82	42	𝑉(𝑇	𝑉(𝑇	NOUN
cana-6073	82	43	)	)	PUNCT
cana-6073	82	44	where	where	SCONJ
cana-6073	82	45	:	:	PUNCT
cana-6073	82	46	𝑥𝑣	𝑥𝑣	PROPN
cana-6073	82	47	−	−	PROPN
cana-6073	82	48	{	{	PUNCT
cana-6073	82	49	1	1	NUM
cana-6073	82	50	if	if	SCONJ
cana-6073	82	51	𝑣	𝑣	PRON
cana-6073	82	52	∈	∈	PROPN
cana-6073	82	53	𝑆	𝑆	PROPN
cana-6073	82	54	0	0	PUNCT
cana-6073	82	55	otherwise	otherwise	ADV
cana-6073	82	56	each	each	DET
cana-6073	82	57	vertex	vertex	NOUN
cana-6073	82	58	𝑢	𝑢	ADP
cana-6073	82	59	∈	∈	PROPN
cana-6073	82	60	𝑉	𝑉	PROPN
cana-6073	82	61	must	must	AUX
cana-6073	82	62	lie	lie	VERB
cana-6073	82	63	on	on	ADP
cana-6073	82	64	a	a	DET
cana-6073	82	65	longest	long	ADJ
cana-6073	82	66	path	path	NOUN
cana-6073	82	67	from	from	ADP
cana-6073	82	68	some	some	DET
cana-6073	82	69	dominator	dominator	NOUN
cana-6073	82	70	:	:	PUNCT
cana-6073	82	71	∃𝑣	∃𝑣	NOUN
cana-6073	82	72	∈	∈	NOUN
cana-6073	82	73	𝑉(𝑇	𝑉(𝑇	NOUN
cana-6073	82	74	)	)	PUNCT
cana-6073	82	75	with	with	ADP
cana-6073	82	76	𝑥𝑣	𝑥𝑣	PROPN
cana-6073	82	77	−	−	NUM
cana-6073	82	78	1	1	NUM
cana-6073	82	79	such	such	ADJ
cana-6073	82	80	that	that	SCONJ
cana-6073	82	81	𝑢	𝑢	PROPN
cana-6073	82	82	∈	∈	PROPN
cana-6073	82	83	𝑃𝑣,𝑢	𝑃𝑣,𝑢	PROPN
cana-6073	82	84	max	max	PROPN
cana-6073	82	85	encode	encode	VERB
cana-6073	82	86	this	this	PRON
cana-6073	82	87	as	as	ADP
cana-6073	82	88	constraints	constraint	NOUN
cana-6073	82	89	:	:	PUNCT
cana-6073	82	90	∑	∑	PUNCT
cana-6073	82	91	  	  	SPACE
cana-6073	82	92	𝑣∈𝑉	𝑣∈𝑉	PROPN
cana-6073	82	93	𝑢∈𝑃𝑣,𝑢	𝑢∈𝑃𝑣,𝑢	PROPN
cana-6073	82	94	max	max	PROPN
cana-6073	82	95	𝑥𝑣	𝑥𝑣	X
cana-6073	82	96	≥	≥	PROPN
cana-6073	82	97	1	1	NUM
cana-6073	82	98	,	,	PUNCT
cana-6073	82	99	∀𝑢	∀𝑢	DET
cana-6073	82	100	∈	∈	PROPN
cana-6073	82	101	𝑉	𝑉	PROPN
cana-6073	82	102	optimization	optimization	NOUN
cana-6073	82	103	problem	problem	NOUN
cana-6073	82	104	:	:	PUNCT
cana-6073	82	105	minimize	minimize	VERB
cana-6073	82	106	:	:	PUNCT
cana-6073	82	107	∑	∑	PART
cana-6073	82	108	  	  	SPACE
cana-6073	82	109	𝑣∈𝑉	𝑣∈𝑉	PROPN
cana-6073	82	110	 	 	SPACE
cana-6073	82	111	𝑥𝑣	𝑥𝑣	PROPN
cana-6073	82	112	subject	subject	NOUN
cana-6073	82	113	to	to	ADP
cana-6073	82	114	:	:	PUNCT
cana-6073	82	115	∑	∑	PUNCT
cana-6073	82	116	  	  	SPACE
cana-6073	82	117	𝑣:𝑢∈𝐼toa	𝑣:𝑢∈𝐼toa	PROPN
cana-6073	82	118	max	max	PROPN
cana-6073	82	119	 	 	SPACE
cana-6073	82	120	𝑥𝑣	𝑥𝑣	PROPN
cana-6073	82	121	≥	≥	NUM
cana-6073	82	122	1	1	NUM
cana-6073	82	123	,	,	PUNCT
cana-6073	82	124	∀𝑢	∀𝑢	DET
cana-6073	82	125	∈	∈	PROPN
cana-6073	82	126	𝑉	𝑉	PROPN
cana-6073	82	127	𝑥𝑣	𝑥𝑣	PROPN
cana-6073	82	128	∈	∈	PROPN
cana-6073	82	129	{	{	PUNCT
cana-6073	82	130	0,1	0,1	NOUN
cana-6073	82	131	}	}	PUNCT
cana-6073	82	132	,	,	PUNCT
cana-6073	82	133	∀𝑣	∀𝑣	PROPN
cana-6073	82	134	∈	∈	PROPN
cana-6073	82	135	𝑉	𝑉	PROPN
cana-6073	82	136	hence	hence	ADV
cana-6073	82	137	,	,	PUNCT
cana-6073	82	138	𝛾𝐷𝐷(𝑇	𝛾𝐷𝐷(𝑇	PROPN
cana-6073	82	139	)	)	PUNCT
cana-6073	82	140	≤	≤	NOUN
cana-6073	82	141	∑	∑	ADP
cana-6073	82	142	  	  	SPACE
cana-6073	82	143	𝑘	𝑘	PRON
cana-6073	82	144	𝑖=1	𝑖=1	PROPN
cana-6073	82	145	⌈	⌈	ADJ
cana-6073	82	146	ℎ𝑖	ℎ𝑖	ADP
cana-6073	82	147	2	2	NUM
cana-6073	82	148	⌉	⌉	NOUN
cana-6073	82	149	reference	reference	NOUN
cana-6073	82	150	1	1	NUM
cana-6073	82	151	.	.	PUNCT
cana-6073	83	1	chartrand	chartrand	PROPN
cana-6073	83	2	,	,	PUNCT
cana-6073	83	3	g.	g.	PROPN
cana-6073	83	4	,	,	PUNCT
cana-6073	83	5	&	&	CCONJ
cana-6073	83	6	zhang	zhang	PROPN
cana-6073	83	7	,	,	PUNCT
cana-6073	83	8	p.	p.	PROPN
cana-6073	83	9	(	(	PUNCT
cana-6073	83	10	2004	2004	NUM
cana-6073	83	11	)	)	PUNCT
cana-6073	83	12	.	.	PUNCT
cana-6073	84	1	detour	detour	PRON
cana-6073	84	2	domination	domination	NOUN
cana-6073	84	3	in	in	ADP
cana-6073	84	4	graphs	graph	NOUN
cana-6073	84	5	.	.	PUNCT
cana-6073	85	1	utilitas	utilitas	PROPN
cana-6073	85	2	mathematica	mathematica	PROPN
cana-6073	85	3	,	,	PUNCT
cana-6073	85	4	65	65	NUM
cana-6073	85	5	,	,	PUNCT
cana-6073	85	6	169–179.this	169–179.this	NUM
cana-6073	85	7	foundational	foundational	ADJ
cana-6073	85	8	paper	paper	NOUN
cana-6073	85	9	introduces	introduce	VERB
cana-6073	85	10	the	the	DET
cana-6073	85	11	concept	concept	NOUN
cana-6073	85	12	of	of	ADP
cana-6073	85	13	detour	detour	NOUN
cana-6073	85	14	domination	domination	NOUN
cana-6073	85	15	and	and	CCONJ
cana-6073	85	16	investigates	investigate	VERB
cana-6073	85	17	it	it	PRON
cana-6073	85	18	across	across	ADP
cana-6073	85	19	various	various	ADJ
cana-6073	85	20	graph	graph	NOUN
cana-6073	85	21	classes	class	NOUN
cana-6073	85	22	.	.	PUNCT
cana-6073	86	1	2	2	X
cana-6073	86	2	.	.	X
cana-6073	86	3	mahalakshmi	mahalakshmi	PROPN
cana-6073	86	4	,	,	PUNCT
cana-6073	86	5	a.	a.	PROPN
cana-6073	86	6	,	,	PUNCT
cana-6073	86	7	&	&	CCONJ
cana-6073	86	8	palani	palani	PROPN
cana-6073	86	9	,	,	PUNCT
cana-6073	86	10	k.	k.	PROPN
cana-6073	86	11	(	(	PUNCT
cana-6073	86	12	2020	2020	NUM
cana-6073	86	13	)	)	PUNCT
cana-6073	86	14	.	.	PUNCT
cana-6073	87	1	total	total	ADJ
cana-6073	87	2	restrained	restrain	VERB
cana-6073	87	3	detour	detour	NOUN
cana-6073	87	4	domination	domination	NOUN
cana-6073	87	5	number	number	NOUN
cana-6073	87	6	of	of	ADP
cana-6073	87	7	a	a	DET
cana-6073	87	8	graph	graph	NOUN
cana-6073	87	9	.	.	PUNCT
cana-6073	88	1	malaya	malaya	PROPN
cana-6073	88	2	journal	journal	PROPN
cana-6073	88	3	of	of	ADP
cana-6073	88	4	matematik	matematik	PROPN
cana-6073	88	5	,	,	PUNCT
cana-6073	88	6	8(3	8(3	NUM
cana-6073	88	7	)	)	PUNCT
cana-6073	88	8	,	,	PUNCT
cana-6073	88	9	950–955.this	950–955.this	NUM
cana-6073	88	10	article	article	NOUN
cana-6073	88	11	explores	explore	VERB
cana-6073	88	12	a	a	DET
cana-6073	88	13	variation	variation	NOUN
cana-6073	88	14	of	of	ADP
cana-6073	88	15	communications	communication	NOUN
cana-6073	88	16	on	on	ADP
cana-6073	88	17	applied	apply	VERB
cana-6073	88	18	nonlinear	nonlinear	ADJ
cana-6073	88	19	analysis	analysis	NOUN
cana-6073	88	20	issn	issn	NOUN
cana-6073	88	21	:	:	PUNCT
cana-6073	88	22	1074	1074	NUM
cana-6073	88	23	-	-	PUNCT
cana-6073	88	24	133x	133x	NUM
cana-6073	88	25	vol	vol	NOUN
cana-6073	88	26	31	31	NUM
cana-6073	88	27	no	no	NOUN
cana-6073	88	28	.	.	PUNCT
cana-6073	89	1	8s	8s	PROPN
cana-6073	89	2	(	(	PUNCT
cana-6073	89	3	2024	2024	NUM
cana-6073	89	4	)	)	PUNCT
cana-6073	89	5	1192	1192	NUM
cana-6073	89	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6073	89	7	detour	detour	NOUN
cana-6073	89	8	domination	domination	NOUN
cana-6073	89	9	that	that	PRON
cana-6073	89	10	includes	include	VERB
cana-6073	89	11	restraining	restraining	NOUN
cana-6073	89	12	conditions	condition	NOUN
cana-6073	89	13	,	,	PUNCT
cana-6073	89	14	relevant	relevant	ADJ
cana-6073	89	15	to	to	ADP
cana-6073	89	16	constrained	constrain	VERB
cana-6073	89	17	domination	domination	NOUN
cana-6073	89	18	models	model	NOUN
cana-6073	89	19	.	.	PUNCT
cana-6073	90	1	3	3	X
cana-6073	90	2	.	.	X
cana-6073	90	3	shanthi	shanthi	PROPN
cana-6073	90	4	,	,	PUNCT
cana-6073	90	5	p.	p.	PROPN
cana-6073	90	6	,	,	PUNCT
cana-6073	90	7	nagarajan	nagarajan	PROPN
cana-6073	90	8	,	,	PUNCT
cana-6073	90	9	a.	a.	NOUN
cana-6073	90	10	,	,	PUNCT
cana-6073	90	11	&	&	CCONJ
cana-6073	90	12	mahalakshmi	mahalakshmi	PROPN
cana-6073	90	13	,	,	PUNCT
cana-6073	90	14	a.	a.	NOUN
cana-6073	90	15	(	(	PUNCT
cana-6073	90	16	2020	2020	NUM
cana-6073	90	17	)	)	PUNCT
cana-6073	90	18	.	.	PUNCT
cana-6073	91	1	total	total	ADJ
cana-6073	91	2	restrained	restrain	VERB
cana-6073	91	3	detour	detour	NOUN
cana-6073	91	4	domination	domination	NOUN
cana-6073	91	5	number	number	NOUN
cana-6073	91	6	of	of	ADP
cana-6073	91	7	a	a	DET
cana-6073	91	8	graph	graph	NOUN
cana-6073	91	9	.	.	PUNCT
cana-6073	92	1	malaya	malaya	PROPN
cana-6073	92	2	journal	journal	PROPN
cana-6073	92	3	of	of	ADP
cana-6073	92	4	matematik	matematik	PROPN
cana-6073	92	5	,	,	PUNCT
cana-6073	92	6	8(s1	8(s1	NUM
cana-6073	92	7	)	)	PUNCT
cana-6073	92	8	,	,	PUNCT
cana-6073	92	9	361–365.an	361–365.an	NUM
cana-6073	92	10	in	in	ADP
cana-6073	92	11	-	-	PUNCT
cana-6073	92	12	depth	depth	NOUN
cana-6073	92	13	extension	extension	NOUN
cana-6073	92	14	to	to	ADP
cana-6073	92	15	the	the	DET
cana-6073	92	16	concept	concept	NOUN
cana-6073	92	17	of	of	ADP
cana-6073	92	18	restrained	restrained	ADJ
cana-6073	92	19	domination	domination	NOUN
cana-6073	92	20	specifically	specifically	ADV
cana-6073	92	21	applied	apply	VERB
cana-6073	92	22	to	to	ADP
cana-6073	92	23	detour	detour	NOUN
cana-6073	92	24	domination	domination	NOUN
cana-6073	92	25	.	.	PUNCT
cana-6073	93	1	4	4	X
cana-6073	93	2	.	.	X
cana-6073	93	3	vaidya	vaidya	PROPN
cana-6073	93	4	,	,	PUNCT
cana-6073	93	5	s.	s.	PROPN
cana-6073	93	6	k.	k.	PROPN
cana-6073	93	7	,	,	PUNCT
cana-6073	93	8	&	&	CCONJ
cana-6073	93	9	mehta	mehta	PROPN
cana-6073	93	10	,	,	PUNCT
cana-6073	93	11	r.	r.	PROPN
cana-6073	93	12	n.	n.	PROPN
cana-6073	93	13	(	(	PUNCT
cana-6073	93	14	2015	2015	NUM
cana-6073	93	15	)	)	PUNCT
cana-6073	93	16	.	.	PUNCT
cana-6073	94	1	on	on	ADP
cana-6073	94	2	detour	detour	PRON
cana-6073	94	3	domination	domination	NOUN
cana-6073	94	4	in	in	ADP
cana-6073	94	5	graphs	graph	NOUN
cana-6073	94	6	.	.	PUNCT
cana-6073	95	1	international	international	ADJ
cana-6073	95	2	journal	journal	NOUN
cana-6073	95	3	of	of	ADP
cana-6073	95	4	mathematics	mathematic	NOUN
cana-6073	95	5	and	and	CCONJ
cana-6073	95	6	scientific	scientific	ADJ
cana-6073	95	7	computing	computing	NOUN
cana-6073	95	8	,	,	PUNCT
cana-6073	95	9	5(2	5(2	NUM
cana-6073	95	10	)	)	PUNCT
cana-6073	95	11	,	,	PUNCT
cana-6073	95	12	89–102.this	89–102.this	NUM
cana-6073	95	13	work	work	NOUN
cana-6073	95	14	analyzes	analyze	VERB
cana-6073	95	15	detour	detour	NOUN
cana-6073	95	16	domination	domination	NOUN
cana-6073	95	17	across	across	ADP
cana-6073	95	18	different	different	ADJ
cana-6073	95	19	structured	structured	ADJ
cana-6073	95	20	graphs	graph	NOUN
cana-6073	95	21	including	include	VERB
cana-6073	95	22	trees	tree	NOUN
cana-6073	95	23	,	,	PUNCT
cana-6073	95	24	grids	grid	NOUN
cana-6073	95	25	,	,	PUNCT
cana-6073	95	26	and	and	CCONJ
cana-6073	95	27	more	more	ADJ
cana-6073	95	28	.	.	PUNCT
cana-6073	96	1	5	5	X
cana-6073	96	2	.	.	X
cana-6073	96	3	mahalakshmi	mahalakshmi	PROPN
cana-6073	96	4	,	,	PUNCT
cana-6073	96	5	a.	a.	PROPN
cana-6073	96	6	,	,	PUNCT
cana-6073	96	7	&	&	CCONJ
cana-6073	96	8	priya	priya	PROPN
cana-6073	96	9	,	,	PUNCT
cana-6073	96	10	t.	t.	PROPN
cana-6073	96	11	(	(	PUNCT
cana-6073	96	12	2021	2021	NUM
cana-6073	96	13	)	)	PUNCT
cana-6073	96	14	.	.	PUNCT
cana-6073	97	1	detour	detour	PRON
cana-6073	97	2	global	global	ADJ
cana-6073	97	3	domination	domination	NOUN
cana-6073	97	4	number	number	NOUN
cana-6073	97	5	of	of	ADP
cana-6073	97	6	some	some	DET
cana-6073	97	7	graphs	graph	NOUN
cana-6073	97	8	.	.	PUNCT
cana-6073	98	1	malaya	malaya	PROPN
cana-6073	98	2	journal	journal	PROPN
cana-6073	98	3	of	of	ADP
cana-6073	98	4	matematik	matematik	PROPN
cana-6073	98	5	,	,	PUNCT
cana-6073	98	6	s-200105	s-200105	PROPN
cana-6073	98	7	,	,	PUNCT
cana-6073	98	8	1–8.the	1–8.the	PRON
cana-6073	98	9	paper	paper	NOUN
cana-6073	98	10	introduces	introduce	VERB
cana-6073	98	11	the	the	DET
cana-6073	98	12	concept	concept	NOUN
cana-6073	98	13	of	of	ADP
cana-6073	98	14	global	global	ADJ
cana-6073	98	15	detour	detour	NOUN
cana-6073	98	16	domination	domination	NOUN
cana-6073	98	17	,	,	PUNCT
cana-6073	98	18	relevant	relevant	ADJ
cana-6073	98	19	for	for	ADP
cana-6073	98	20	network	network	NOUN
cana-6073	98	21	-	-	PUNCT
cana-6073	98	22	wide	wide	ADJ
cana-6073	98	23	reachability	reachability	NOUN
cana-6073	98	24	.	.	PUNCT
cana-6073	99	1	6	6	X
cana-6073	99	2	.	.	X
cana-6073	99	3	prasanna	prasanna	PROPN
cana-6073	99	4	,	,	PUNCT
cana-6073	99	5	a.	a.	PROPN
cana-6073	99	6	,	,	PUNCT
cana-6073	99	7	&	&	CCONJ
cana-6073	99	8	mohamedazarudeen	mohamedazarudeen	PROPN
cana-6073	99	9	,	,	PUNCT
cana-6073	99	10	n.	n.	NOUN
cana-6073	99	11	(	(	PUNCT
cana-6073	99	12	2022	2022	NUM
cana-6073	99	13	)	)	PUNCT
cana-6073	99	14	.	.	PUNCT
cana-6073	100	1	detour	detour	PRON
cana-6073	100	2	d	d	ADJ
cana-6073	100	3	-	-	ADJ
cana-6073	100	4	eccentric	eccentric	ADJ
cana-6073	100	5	domination	domination	NOUN
cana-6073	100	6	in	in	ADP
cana-6073	100	7	graphs	graph	NOUN
cana-6073	100	8	.	.	PUNCT
cana-6073	101	1	journal	journal	NOUN
cana-6073	101	2	of	of	ADP
cana-6073	101	3	algebraic	algebraic	PROPN
cana-6073	101	4	statistics	statistic	NOUN
cana-6073	101	5	,	,	PUNCT
cana-6073	101	6	13(2	13(2	PROPN
cana-6073	101	7	)	)	PUNCT
cana-6073	101	8	,	,	PUNCT
cana-6073	101	9	3218–3225.presents	3218–3225.presents	NUM
cana-6073	101	10	a	a	DET
cana-6073	101	11	new	new	ADJ
cana-6073	101	12	domination	domination	NOUN
cana-6073	101	13	parameter	parameter	NOUN
cana-6073	101	14	combining	combine	VERB
cana-6073	101	15	detour	detour	NOUN
cana-6073	101	16	and	and	CCONJ
cana-6073	101	17	eccentricity	eccentricity	NOUN
cana-6073	101	18	,	,	PUNCT
cana-6073	101	19	suitable	suitable	ADJ
cana-6073	101	20	for	for	ADP
cana-6073	101	21	identifying	identify	VERB
cana-6073	101	22	distant	distant	ADJ
cana-6073	101	23	control	control	NOUN
cana-6073	101	24	centers	center	NOUN
cana-6073	101	25	.	.	PUNCT
cana-6073	102	1	7	7	X
cana-6073	102	2	.	.	X
cana-6073	102	3	jayasekaran	jayasekaran	PROPN
cana-6073	102	4	,	,	PUNCT
cana-6073	102	5	c.	c.	NOUN
cana-6073	102	6	,	,	PUNCT
cana-6073	102	7	palani	palani	PROPN
cana-6073	102	8	,	,	PUNCT
cana-6073	102	9	k.	k.	PROPN
cana-6073	102	10	,	,	PUNCT
cana-6073	102	11	&	&	CCONJ
cana-6073	102	12	mahalakshmi	mahalakshmi	PROPN
cana-6073	102	13	,	,	PUNCT
cana-6073	102	14	a.	a.	NOUN
cana-6073	102	15	(	(	PUNCT
cana-6073	102	16	2020	2020	NUM
cana-6073	102	17	)	)	PUNCT
cana-6073	102	18	.	.	PUNCT
cana-6073	103	1	on	on	ADP
cana-6073	103	2	detour	detour	NOUN
cana-6073	103	3	domination	domination	NOUN
cana-6073	103	4	number	number	NOUN
cana-6073	103	5	of	of	ADP
cana-6073	103	6	a	a	DET
cana-6073	103	7	graph	graph	NOUN
cana-6073	103	8	.	.	PUNCT
cana-6073	103	9	journal	journal	NOUN
cana-6073	103	10	of	of	ADP
cana-6073	103	11	graph	graph	NOUN
cana-6073	103	12	theory	theory	NOUN
cana-6073	103	13	and	and	CCONJ
cana-6073	103	14	algorithms	algorithm	NOUN
cana-6073	103	15	,	,	PUNCT
cana-6073	103	16	34(7	34(7	NUM
cana-6073	103	17	)	)	PUNCT
cana-6073	103	18	,	,	PUNCT
cana-6073	103	19	100–120.analyzes	100–120.analyzes	NUM
cana-6073	103	20	detour	detour	NOUN
cana-6073	103	21	domination	domination	NOUN
cana-6073	103	22	in	in	ADP
cana-6073	103	23	classic	classic	ADJ
cana-6073	103	24	graphs	graph	NOUN
cana-6073	103	25	including	include	VERB
cana-6073	103	26	paths	path	NOUN
cana-6073	103	27	and	and	CCONJ
cana-6073	103	28	cycles	cycle	NOUN
cana-6073	103	29	with	with	ADP
cana-6073	103	30	proof	proof	ADJ
cana-6073	103	31	constructions	construction	NOUN
cana-6073	103	32	.	.	PUNCT
cana-6073	104	1	8	8	NUM
cana-6073	104	2	.	.	X
cana-6073	104	3	chartrand	chartrand	PROPN
cana-6073	104	4	,	,	PUNCT
cana-6073	104	5	g.	g.	PROPN
cana-6073	104	6	,	,	PUNCT
cana-6073	104	7	lesniak	lesniak	PROPN
cana-6073	104	8	,	,	PUNCT
cana-6073	104	9	l.	l.	PROPN
cana-6073	104	10	,	,	PUNCT
cana-6073	104	11	&	&	CCONJ
cana-6073	104	12	zhang	zhang	PROPN
cana-6073	104	13	,	,	PUNCT
cana-6073	104	14	p.	p.	PROPN
cana-6073	104	15	(	(	PUNCT
cana-6073	104	16	2018	2018	NUM
cana-6073	104	17	)	)	PUNCT
cana-6073	104	18	.	.	PUNCT
cana-6073	105	1	perfect	perfect	ADJ
cana-6073	105	2	independent	independent	ADJ
cana-6073	105	3	detour	detour	NOUN
cana-6073	105	4	domination	domination	NOUN
cana-6073	105	5	number	number	NOUN
cana-6073	105	6	of	of	ADP
cana-6073	105	7	some	some	DET
cana-6073	105	8	special	special	ADJ
cana-6073	105	9	graphs	graph	NOUN
cana-6073	105	10	.	.	PUNCT
cana-6073	106	1	journal	journal	NOUN
cana-6073	106	2	of	of	ADP
cana-6073	106	3	combinatorics	combinatoric	NOUN
cana-6073	106	4	and	and	CCONJ
cana-6073	106	5	applications	application	NOUN
cana-6073	106	6	,	,	PUNCT
cana-6073	106	7	28(4	28(4	NUM
cana-6073	106	8	)	)	PUNCT
cana-6073	106	9	,	,	PUNCT
cana-6073	106	10	389	389	NUM
cana-6073	106	11	–	–	PUNCT
cana-6073	106	12	404.deals	404.deal	NOUN
cana-6073	106	13	with	with	ADP
cana-6073	106	14	independence	independence	NOUN
cana-6073	106	15	in	in	ADP
cana-6073	106	16	detour	detour	NOUN
cana-6073	106	17	dominating	dominating	NOUN
cana-6073	106	18	sets	set	NOUN
cana-6073	106	19	,	,	PUNCT
cana-6073	106	20	offering	offer	VERB
cana-6073	106	21	insights	insight	NOUN
cana-6073	106	22	into	into	ADP
cana-6073	106	23	optimization	optimization	NOUN
cana-6073	106	24	.	.	PUNCT
cana-6073	107	1	9	9	X
cana-6073	107	2	.	.	X
cana-6073	107	3	prasanna	prasanna	PROPN
cana-6073	107	4	,	,	PUNCT
cana-6073	107	5	a.	a.	PROPN
cana-6073	107	6	,	,	PUNCT
cana-6073	107	7	&	&	CCONJ
cana-6073	107	8	priyadharshini	priyadharshini	PROPN
cana-6073	107	9	,	,	PUNCT
cana-6073	107	10	r.	r.	PROPN
cana-6073	107	11	(	(	PUNCT
cana-6073	107	12	2019	2019	NUM
cana-6073	107	13	)	)	PUNCT
cana-6073	107	14	.	.	PUNCT
cana-6073	108	1	detour	detour	PRON
cana-6073	108	2	d	d	ADJ
cana-6073	108	3	-	-	ADJ
cana-6073	108	4	eccentric	eccentric	ADJ
cana-6073	108	5	dominating	dominating	NOUN
cana-6073	108	6	set	set	NOUN
cana-6073	108	7	.	.	PUNCT
cana-6073	109	1	journal	journal	NOUN
cana-6073	109	2	of	of	ADP
cana-6073	109	3	algebraic	algebraic	PROPN
cana-6073	109	4	statistics	statistic	NOUN
cana-6073	109	5	,	,	PUNCT
cana-6073	109	6	10(2	10(2	NUM
cana-6073	109	7	)	)	PUNCT
cana-6073	109	8	,	,	PUNCT
cana-6073	109	9	2101–2107.merges	2101–2107.merges	NUM
cana-6073	109	10	eccentric	eccentric	ADJ
cana-6073	109	11	and	and	CCONJ
cana-6073	109	12	detour	detour	NOUN
cana-6073	109	13	domination	domination	NOUN
cana-6073	109	14	concepts	concept	NOUN
cana-6073	109	15	for	for	ADP
cana-6073	109	16	specific	specific	ADJ
cana-6073	109	17	applications	application	NOUN
cana-6073	109	18	in	in	ADP
cana-6073	109	19	resilient	resilient	ADJ
cana-6073	109	20	graph	graph	NOUN
cana-6073	109	21	structures	structure	NOUN
cana-6073	109	22	.	.	PUNCT
cana-6073	110	1	10	10	NUM
cana-6073	110	2	.	.	X
cana-6073	110	3	sundaram	sundaram	PROPN
cana-6073	110	4	,	,	PUNCT
cana-6073	110	5	a.	a.	PROPN
cana-6073	110	6	,	,	PUNCT
cana-6073	110	7	&	&	CCONJ
cana-6073	110	8	suganthi	suganthi	PROPN
cana-6073	110	9	,	,	PUNCT
cana-6073	110	10	m.	m.	NOUN
cana-6073	110	11	(	(	PUNCT
cana-6073	110	12	2020	2020	NUM
cana-6073	110	13	)	)	PUNCT
cana-6073	110	14	.	.	PUNCT
cana-6073	111	1	detour	detour	PRON
cana-6073	111	2	domination	domination	NOUN
cana-6073	111	3	in	in	ADP
cana-6073	111	4	path	path	NOUN
cana-6073	111	5	and	and	CCONJ
cana-6073	111	6	cycle	cycle	NOUN
cana-6073	111	7	graphs	graph	NOUN
cana-6073	111	8	.	.	PUNCT
cana-6073	112	1	international	international	ADJ
cana-6073	112	2	journal	journal	PROPN
cana-6073	112	3	of	of	ADP
cana-6073	112	4	mathematics	mathematics	NOUN
cana-6073	112	5	trends	trend	NOUN
cana-6073	112	6	and	and	CCONJ
cana-6073	112	7	technology	technology	NOUN
cana-6073	112	8	,	,	PUNCT
cana-6073	112	9	66(4	66(4	NUM
cana-6073	112	10	)	)	PUNCT
cana-6073	112	11	,	,	PUNCT
cana-6073	112	12	24–30.provides	24–30.provides	NUM
cana-6073	112	13	exact	exact	ADJ
cana-6073	112	14	values	value	NOUN
cana-6073	112	15	for	for	ADP
cana-6073	112	16	detour	detour	NOUN
cana-6073	112	17	domination	domination	NOUN
cana-6073	112	18	numbers	number	NOUN
cana-6073	112	19	in	in	ADP
cana-6073	112	20	paths	path	NOUN
cana-6073	112	21	and	and	CCONJ
cana-6073	112	22	cycles	cycle	NOUN
cana-6073	112	23	with	with	ADP
cana-6073	112	24	generalized	generalized	ADJ
cana-6073	112	25	proofs	proof	NOUN
cana-6073	112	26	.	.	PUNCT
cana-6073	113	1	11	11	NUM
cana-6073	113	2	.	.	X
cana-6073	114	1	nandhini	nandhini	PROPN
cana-6073	114	2	,	,	PUNCT
cana-6073	114	3	b.	b.	PROPN
cana-6073	114	4	,	,	PUNCT
cana-6073	114	5	&	&	CCONJ
cana-6073	114	6	rajesh	rajesh	PROPN
cana-6073	114	7	,	,	PUNCT
cana-6073	114	8	s.	s.	PROPN
cana-6073	114	9	(	(	PUNCT
cana-6073	114	10	2020	2020	NUM
cana-6073	114	11	)	)	PUNCT
cana-6073	114	12	.	.	PUNCT
cana-6073	115	1	detour	detour	NOUN
cana-6073	115	2	domination	domination	NOUN
cana-6073	115	3	number	number	NOUN
cana-6073	115	4	in	in	ADP
cana-6073	115	5	grid	grid	NOUN
cana-6073	115	6	graphs	graph	NOUN
cana-6073	115	7	.	.	PUNCT
cana-6073	116	1	international	international	ADJ
cana-6073	116	2	journal	journal	PROPN
cana-6073	116	3	of	of	ADP
cana-6073	116	4	scientific	scientific	ADJ
cana-6073	116	5	research	research	NOUN
cana-6073	116	6	in	in	ADP
cana-6073	116	7	mathematical	mathematical	ADJ
cana-6073	116	8	and	and	CCONJ
cana-6073	116	9	statistical	statistical	ADJ
cana-6073	116	10	sciences	science	NOUN
cana-6073	116	11	,	,	PUNCT
cana-6073	116	12	7(2	7(2	NUM
cana-6073	116	13	)	)	PUNCT
cana-6073	116	14	,	,	PUNCT
cana-6073	116	15	67	67	NUM
cana-6073	116	16	–	–	PUNCT
cana-6073	116	17	73.focuses	73.focuses	PROPN
cana-6073	116	18	on	on	ADP
cana-6073	116	19	2d	2d	NUM
cana-6073	116	20	grid	grid	NOUN
cana-6073	116	21	graphs	graph	NOUN
cana-6073	116	22	,	,	PUNCT
cana-6073	116	23	giving	give	VERB
cana-6073	116	24	bounds	bound	NOUN
cana-6073	116	25	and	and	CCONJ
cana-6073	116	26	strategies	strategy	NOUN
cana-6073	116	27	for	for	ADP
cana-6073	116	28	efficient	efficient	ADJ
cana-6073	116	29	detour	detour	NOUN
cana-6073	116	30	coverage	coverage	NOUN
cana-6073	116	31	.	.	PUNCT
cana-6073	117	1	12	12	NUM
cana-6073	117	2	.	.	PUNCT
cana-6073	118	1	ranjini	ranjini	PROPN
cana-6073	118	2	,	,	PUNCT
cana-6073	118	3	r.	r.	PROPN
cana-6073	118	4	,	,	PUNCT
cana-6073	118	5	&	&	CCONJ
cana-6073	118	6	sundararajan	sundararajan	PROPN
cana-6073	118	7	,	,	PUNCT
cana-6073	118	8	d.	d.	PROPN
cana-6073	118	9	(	(	PUNCT
cana-6073	118	10	2018	2018	NUM
cana-6073	118	11	)	)	PUNCT
cana-6073	118	12	.	.	PUNCT
cana-6073	119	1	on	on	ADP
cana-6073	119	2	detour	detour	PRON
cana-6073	119	3	connected	connect	VERB
cana-6073	119	4	domination	domination	NOUN
cana-6073	119	5	in	in	ADP
cana-6073	119	6	graphs	graph	NOUN
cana-6073	119	7	.	.	PUNCT
cana-6073	120	1	international	international	ADJ
cana-6073	120	2	journal	journal	NOUN
cana-6073	120	3	of	of	ADP
cana-6073	120	4	pure	pure	ADJ
cana-6073	120	5	and	and	CCONJ
cana-6073	120	6	applied	applied	ADJ
cana-6073	120	7	mathematics	mathematic	NOUN
cana-6073	120	8	,	,	PUNCT
cana-6073	120	9	119(17	119(17	NUM
cana-6073	120	10	)	)	PUNCT
cana-6073	120	11	,	,	PUNCT
cana-6073	120	12	1681–1692.introduces	1681–1692.introduces	NUM
cana-6073	120	13	detour	detour	NOUN
cana-6073	120	14	-	-	PUNCT
cana-6073	120	15	connected	connect	VERB
cana-6073	120	16	domination	domination	NOUN
cana-6073	120	17	,	,	PUNCT
cana-6073	120	18	which	which	PRON
cana-6073	120	19	combines	combine	VERB
cana-6073	120	20	connectivity	connectivity	NOUN
cana-6073	120	21	with	with	ADP
cana-6073	120	22	long	long	ADJ
cana-6073	120	23	-	-	PUNCT
cana-6073	120	24	path	path	NOUN
cana-6073	120	25	reach	reach	NOUN
cana-6073	120	26	.	.	PUNCT
cana-6073	121	1	13	13	NUM
cana-6073	121	2	.	.	X
cana-6073	121	3	davila	davila	PROPN
cana-6073	121	4	,	,	PUNCT
cana-6073	121	5	r.	r.	PROPN
cana-6073	121	6	,	,	PUNCT
cana-6073	121	7	fast	fast	ADV
cana-6073	121	8	,	,	PUNCT
cana-6073	121	9	c.	c.	PROPN
cana-6073	121	10	,	,	PUNCT
cana-6073	121	11	henning	henning	PROPN
cana-6073	121	12	,	,	PUNCT
cana-6073	121	13	m.	m.	NOUN
cana-6073	121	14	a.	a.	PROPN
cana-6073	121	15	,	,	PUNCT
cana-6073	121	16	&	&	CCONJ
cana-6073	121	17	kenter	kenter	PROPN
cana-6073	121	18	,	,	PUNCT
cana-6073	121	19	f.	f.	PROPN
cana-6073	121	20	(	(	PUNCT
cana-6073	121	21	2015	2015	NUM
cana-6073	121	22	)	)	PUNCT
cana-6073	121	23	.	.	PUNCT
cana-6073	122	1	lower	low	ADJ
cana-6073	122	2	bounds	bound	NOUN
cana-6073	122	3	on	on	ADP
cana-6073	122	4	the	the	DET
cana-6073	122	5	distance	distance	NOUN
cana-6073	122	6	domination	domination	NOUN
cana-6073	122	7	number	number	NOUN
cana-6073	122	8	.	.	PUNCT
cana-6073	123	1	arxiv	arxiv	PROPN
cana-6073	123	2	preprint	preprint	NOUN
cana-6073	123	3	,	,	PUNCT
cana-6073	123	4	arxiv:1507.08745.although	arxiv:1507.08745.although	ADP
cana-6073	123	5	focused	focus	VERB
cana-6073	123	6	on	on	ADP
cana-6073	123	7	distance	distance	NOUN
cana-6073	123	8	domination	domination	NOUN
cana-6073	123	9	,	,	PUNCT
cana-6073	123	10	this	this	DET
cana-6073	123	11	paper	paper	NOUN
cana-6073	123	12	informs	inform	VERB
cana-6073	123	13	bounds	bound	NOUN
cana-6073	123	14	relevant	relevant	ADJ
cana-6073	123	15	to	to	ADP
cana-6073	123	16	detour	detour	NOUN
cana-6073	123	17	domination	domination	NOUN
cana-6073	123	18	.	.	PUNCT
cana-6073	124	1	communications	communication	NOUN
cana-6073	124	2	on	on	ADP
cana-6073	124	3	applied	apply	VERB
cana-6073	124	4	nonlinear	nonlinear	ADJ
cana-6073	124	5	analysis	analysis	NOUN
cana-6073	124	6	issn	issn	NOUN
cana-6073	124	7	:	:	PUNCT
cana-6073	124	8	1074	1074	NUM
cana-6073	124	9	-	-	PUNCT
cana-6073	124	10	133x	133x	NUM
cana-6073	124	11	vol	vol	NOUN
cana-6073	124	12	31	31	NUM
cana-6073	124	13	no	no	NOUN
cana-6073	124	14	.	.	PUNCT
cana-6073	125	1	8s	8s	PROPN
cana-6073	125	2	(	(	PUNCT
cana-6073	125	3	2024	2024	NUM
cana-6073	125	4	)	)	PUNCT
cana-6073	125	5	1193	1193	NUM
cana-6073	125	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6073	125	7	14	14	NUM
cana-6073	125	8	.	.	PUNCT
cana-6073	126	1	mojdeh	mojdeh	PROPN
cana-6073	126	2	,	,	PUNCT
cana-6073	126	3	d.	d.	PROPN
cana-6073	126	4	a.	a.	PROPN
cana-6073	126	5	,	,	PUNCT
cana-6073	126	6	musawi	musawi	PROPN
cana-6073	126	7	,	,	PUNCT
cana-6073	126	8	s.	s.	PROPN
cana-6073	126	9	r.	r.	PROPN
cana-6073	126	10	,	,	PUNCT
cana-6073	126	11	&	&	CCONJ
cana-6073	126	12	nazari	nazari	PROPN
cana-6073	126	13	,	,	PUNCT
cana-6073	126	14	e.	e.	PROPN
cana-6073	126	15	(	(	PUNCT
cana-6073	126	16	2018	2018	NUM
cana-6073	126	17	)	)	PUNCT
cana-6073	126	18	.	.	PUNCT
cana-6073	127	1	on	on	ADP
cana-6073	127	2	the	the	DET
cana-6073	127	3	distance	distance	NOUN
cana-6073	127	4	domination	domination	NOUN
cana-6073	127	5	number	number	NOUN
cana-6073	127	6	of	of	ADP
cana-6073	127	7	bipartite	bipartite	NOUN
cana-6073	127	8	graphs	graph	NOUN
cana-6073	127	9	.	.	PUNCT
cana-6073	128	1	arxiv	arxiv	PROPN
cana-6073	128	2	preprint	preprint	NOUN
cana-6073	128	3	,	,	PUNCT
cana-6073	128	4	arxiv:1805.01280.applies	arxiv:1805.01280.applies	PROPN
cana-6073	128	5	domination	domination	NOUN
cana-6073	128	6	parameters	parameter	NOUN
cana-6073	128	7	in	in	ADP
cana-6073	128	8	bipartite	bipartite	NOUN
cana-6073	128	9	graphs	graph	NOUN
cana-6073	128	10	and	and	CCONJ
cana-6073	128	11	provides	provide	VERB
cana-6073	128	12	insight	insight	NOUN
cana-6073	128	13	into	into	ADP
cana-6073	128	14	layered	layered	ADJ
cana-6073	128	15	detour	detour	NOUN
cana-6073	128	16	structures	structure	NOUN
cana-6073	128	17	.	.	PUNCT
cana-6073	129	1	15	15	NUM
cana-6073	129	2	.	.	X
cana-6073	130	1	kang	kang	PROPN
cana-6073	130	2	,	,	PUNCT
cana-6073	130	3	c.	c.	PROPN
cana-6073	130	4	x.	x.	PROPN
cana-6073	130	5	(	(	PUNCT
cana-6073	130	6	2014	2014	NUM
cana-6073	130	7	)	)	PUNCT
cana-6073	130	8	.	.	PUNCT
cana-6073	131	1	on	on	ADP
cana-6073	131	2	domination	domination	NOUN
cana-6073	131	3	number	number	NOUN
cana-6073	131	4	and	and	CCONJ
cana-6073	131	5	distance	distance	NOUN
cana-6073	131	6	in	in	ADP
cana-6073	131	7	graphs	graph	NOUN
cana-6073	131	8	.	.	PUNCT
cana-6073	132	1	arxiv	arxiv	PROPN
cana-6073	132	2	preprint	preprint	NOUN
cana-6073	132	3	,	,	PUNCT
cana-6073	132	4	arxiv:1409.4116.investigates	arxiv:1409.4116.investigate	VERB
cana-6073	132	5	distance	distance	NOUN
cana-6073	132	6	-	-	PUNCT
cana-6073	132	7	based	base	VERB
cana-6073	132	8	domination	domination	NOUN
cana-6073	132	9	relationships	relationship	NOUN
cana-6073	132	10	that	that	PRON
cana-6073	132	11	parallel	parallel	VERB
cana-6073	132	12	detour	detour	NOUN
cana-6073	132	13	domination	domination	NOUN
cana-6073	132	14	logic	logic	NOUN
cana-6073	132	15	.	.	PUNCT
cana-6073	133	1	16	16	NUM
cana-6073	133	2	.	.	PUNCT
cana-6073	134	1	bessy	bessy	PROPN
cana-6073	134	2	,	,	PUNCT
cana-6073	134	3	s.	s.	PROPN
cana-6073	134	4	,	,	PUNCT
cana-6073	134	5	ochem	ochem	PROPN
cana-6073	134	6	,	,	PUNCT
cana-6073	134	7	p.	p.	NOUN
cana-6073	134	8	,	,	PUNCT
cana-6073	134	9	&	&	CCONJ
cana-6073	134	10	rautenbach	rautenbach	NOUN
cana-6073	134	11	,	,	PUNCT
cana-6073	134	12	d.	d.	PROPN
cana-6073	134	13	(	(	PUNCT
cana-6073	134	14	2015	2015	NUM
cana-6073	134	15	)	)	PUNCT
cana-6073	134	16	.	.	PUNCT
cana-6073	135	1	bounds	bound	NOUN
cana-6073	135	2	on	on	ADP
cana-6073	135	3	the	the	DET
cana-6073	135	4	exponential	exponential	ADJ
cana-6073	135	5	domination	domination	NOUN
cana-6073	135	6	number	number	NOUN
cana-6073	135	7	.	.	PUNCT
cana-6073	136	1	arxiv	arxiv	PROPN
cana-6073	136	2	preprint	preprint	NOUN
cana-6073	136	3	,	,	PUNCT
cana-6073	136	4	arxiv:1510.08749.deals	arxiv:1510.08749.deal	NOUN
cana-6073	136	5	with	with	ADP
cana-6073	136	6	extended	extended	ADJ
cana-6073	136	7	influence	influence	NOUN
cana-6073	136	8	models	model	NOUN
cana-6073	136	9	in	in	ADP
cana-6073	136	10	graphs	graph	NOUN
cana-6073	136	11	akin	akin	ADJ
cana-6073	136	12	to	to	ADP
cana-6073	136	13	the	the	DET
cana-6073	136	14	reach	reach	NOUN
cana-6073	136	15	in	in	ADP
cana-6073	136	16	detour	detour	NOUN
cana-6073	136	17	domination	domination	NOUN
cana-6073	136	18	.	.	PUNCT
cana-6073	137	1	17	17	NUM
cana-6073	137	2	.	.	X
cana-6073	138	1	veni	veni	PROPN
cana-6073	138	2	,	,	PUNCT
cana-6073	138	3	k.	k.	PROPN
cana-6073	138	4	,	,	PUNCT
cana-6073	138	5	&	&	CCONJ
cana-6073	138	6	mahalakshmi	mahalakshmi	PROPN
cana-6073	138	7	,	,	PUNCT
cana-6073	138	8	a.	a.	NOUN
cana-6073	138	9	(	(	PUNCT
cana-6073	138	10	2021	2021	NUM
cana-6073	138	11	)	)	PUNCT
cana-6073	138	12	.	.	PUNCT
cana-6073	139	1	edge	edge	NOUN
cana-6073	139	2	-	-	PUNCT
cana-6073	139	3	detour	detour	NOUN
cana-6073	139	4	domination	domination	NOUN
cana-6073	139	5	in	in	ADP
cana-6073	139	6	generalized	generalized	ADJ
cana-6073	139	7	petersen	petersen	NOUN
cana-6073	139	8	graphs	graph	NOUN
cana-6073	139	9	.	.	PUNCT
cana-6073	140	1	international	international	ADJ
cana-6073	140	2	journal	journal	NOUN
cana-6073	140	3	of	of	ADP
cana-6073	140	4	applied	apply	VERB
cana-6073	140	5	mathematics	mathematic	NOUN
cana-6073	140	6	and	and	CCONJ
cana-6073	140	7	informatics	informatic	NOUN
cana-6073	140	8	,	,	PUNCT
cana-6073	140	9	15(2	15(2	NUM
cana-6073	140	10	)	)	PUNCT
cana-6073	140	11	,	,	PUNCT
cana-6073	140	12	55	55	NUM
cana-6073	140	13	–	–	PUNCT
cana-6073	140	14	68.explores	68.explores	DET
cana-6073	140	15	domination	domination	NOUN
cana-6073	140	16	based	base	VERB
cana-6073	140	17	on	on	ADP
cana-6073	140	18	edge	edge	NOUN
cana-6073	140	19	inclusion	inclusion	NOUN
cana-6073	140	20	,	,	PUNCT
cana-6073	140	21	expanding	expand	VERB
cana-6073	140	22	detour	detour	NOUN
cana-6073	140	23	considerations	consideration	NOUN
cana-6073	140	24	to	to	PART
cana-6073	140	25	edgebased	edgebase	VERB
cana-6073	140	26	influence	influence	NOUN
cana-6073	140	27	.	.	PUNCT