id	sid	tid	token	lemma	pos
cana-3842	1	1	communications	communication	NOUN
cana-3842	1	2	on	on	ADP
cana-3842	1	3	applied	apply	VERB
cana-3842	1	4	nonlinear	nonlinear	ADJ
cana-3842	1	5	analysis	analysis	NOUN
cana-3842	1	6	issn	issn	NOUN
cana-3842	1	7	:	:	PUNCT
cana-3842	1	8	1074	1074	NUM
cana-3842	1	9	-	-	PUNCT
cana-3842	1	10	133x	133x	NUM
cana-3842	1	11	vol	vol	NOUN
cana-3842	1	12	32	32	NUM
cana-3842	1	13	no	no	NOUN
cana-3842	1	14	.	.	PUNCT
cana-3842	2	1	9s	9s	NUM
cana-3842	2	2	(	(	PUNCT
cana-3842	2	3	2025	2025	NUM
cana-3842	2	4	)	)	PUNCT
cana-3842	2	5	115	115	NUM
cana-3842	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3842	2	7	changing	change	VERB
cana-3842	2	8	and	and	CCONJ
cana-3842	2	9	unchanging	unchanging	ADJ
cana-3842	2	10	secure	secure	ADJ
cana-3842	2	11	integer	integer	NOUN
cana-3842	2	12	domination	domination	NOUN
cana-3842	2	13	in	in	ADP
cana-3842	2	14	graphs	graph	NOUN
cana-3842	2	15	𝑮𝒐𝒘𝒕𝒉𝒂𝒎	𝑮𝒐𝒘𝒕𝒉𝒂𝒎	PROPN
cana-3842	2	16	𝑷𝒓𝒊𝒚𝒂	𝑷𝒓𝒊𝒚𝒂	PROPN
cana-3842	2	17	𝑳∗𝟏	𝑳∗𝟏	NOUN
cana-3842	2	18	,	,	PUNCT
cana-3842	2	19	𝑽𝒆𝒏𝒌𝒂𝒕𝒆𝒔𝒉	𝑽𝒆𝒏𝒌𝒂𝒕𝒆𝒔𝒉	PROPN
cana-3842	2	20	𝑲	𝑲	PROPN
cana-3842	2	21	𝑨𝟐	𝑨𝟐	NOUN
cana-3842	2	22	1	1	NUM
cana-3842	2	23	department	department	NOUN
cana-3842	2	24	of	of	ADP
cana-3842	2	25	mathematics	mathematics	PROPN
cana-3842	2	26	,	,	PUNCT
cana-3842	2	27	alliance	alliance	NOUN
cana-3842	2	28	university	university	PROPN
cana-3842	2	29	,	,	PUNCT
cana-3842	2	30	bengaluru	bengaluru	PROPN
cana-3842	2	31	,	,	PUNCT
cana-3842	2	32	karnataka	karnataka	PROPN
cana-3842	2	33	5621064	5621064	NUM
cana-3842	2	34	,	,	PUNCT
cana-3842	2	35	india	india	PROPN
cana-3842	2	36	.	.	PROPN
cana-3842	2	37	2	2	NUM
cana-3842	2	38	school	school	NOUN
cana-3842	2	39	of	of	ADP
cana-3842	2	40	advanced	advanced	ADJ
cana-3842	2	41	computing	computing	NOUN
cana-3842	2	42	,	,	PUNCT
cana-3842	2	43	alliance	alliance	NOUN
cana-3842	2	44	university	university	PROPN
cana-3842	2	45	,	,	PUNCT
cana-3842	2	46	bengaluru	bengaluru	PROPN
cana-3842	2	47	,	,	PUNCT
cana-3842	2	48	karnataka	karnataka	PROPN
cana-3842	2	49	5621064	5621064	NUM
cana-3842	2	50	,	,	PUNCT
cana-3842	2	51	india	india	PROPN
cana-3842	2	52	.	.	PUNCT
cana-3842	2	53	gowthampriya.28@gmail.com	gowthampriya.28@gmail.com	PROPN
cana-3842	2	54	article	article	PROPN
cana-3842	2	55	history	history	NOUN
cana-3842	2	56	:	:	PUNCT
cana-3842	2	57	received	receive	VERB
cana-3842	2	58	:	:	PUNCT
cana-3842	2	59	12	12	NUM
cana-3842	2	60	-	-	SYM
cana-3842	2	61	11	11	NUM
cana-3842	2	62	-	-	PUNCT
cana-3842	2	63	2024	2024	NUM
cana-3842	2	64	revised:24	revised:24	X
cana-3842	2	65	-	-	PUNCT
cana-3842	2	66	12	12	NUM
cana-3842	2	67	-	-	PUNCT
cana-3842	2	68	2024	2024	NUM
cana-3842	2	69	accepted:09	accepted:09	NOUN
cana-3842	2	70	-	-	PUNCT
cana-3842	2	71	01	01	NUM
cana-3842	2	72	-	-	PUNCT
cana-3842	2	73	2025	2025	NUM
cana-3842	2	74	abstract	abstract	NOUN
cana-3842	2	75	:	:	PUNCT
cana-3842	2	76	an	an	DET
cana-3842	2	77	integer	integer	NOUN
cana-3842	2	78	dominating	dominating	NOUN
cana-3842	2	79	function	function	NOUN
cana-3842	2	80	on	on	ADP
cana-3842	2	81	a	a	DET
cana-3842	2	82	graph	graph	NOUN
cana-3842	2	83	g	g	NOUN
cana-3842	2	84	is	be	AUX
cana-3842	2	85	a	a	DET
cana-3842	2	86	function	function	NOUN
cana-3842	3	1	f	f	NOUN
cana-3842	3	2	:	:	PUNCT
cana-3842	3	3	v	v	X
cana-3842	3	4	(	(	PUNCT
cana-3842	3	5	g	g	NOUN
cana-3842	3	6	)	)	PUNCT
cana-3842	3	7	→	→	PUNCT
cana-3842	3	8	w	w	ADP
cana-3842	3	9	such	such	ADJ
cana-3842	3	10	that	that	PRON
cana-3842	3	11	for	for	ADP
cana-3842	3	12	every	every	DET
cana-3842	3	13	vertex	vertex	NOUN
cana-3842	3	14	v	v	ADP
cana-3842	3	15	∈	∈	NOUN
cana-3842	3	16	v	v	NOUN
cana-3842	3	17	(	(	PUNCT
cana-3842	3	18	g	g	NOUN
cana-3842	3	19	)	)	PUNCT
cana-3842	3	20	,	,	PUNCT
cana-3842	3	21	∑	∑	PROPN
cana-3842	3	22	(	(	PUNCT
cana-3842	3	23	𝑁[𝑣	𝑁[𝑣	PROPN
cana-3842	3	24	]	]	X
cana-3842	3	25	)	)	PUNCT
cana-3842	3	26	≥	≥	NOUN
cana-3842	4	1	𝑘𝑣	𝑘𝑣	NOUN
cana-3842	4	2	∈	∈	PROPN
cana-3842	4	3	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	4	4	)	)	PUNCT
cana-3842	4	5	.	.	PUNCT
cana-3842	5	1	for	for	ADP
cana-3842	5	2	any	any	DET
cana-3842	5	3	function	function	NOUN
cana-3842	5	4	f	f	NOUN
cana-3842	5	5	:	:	PUNCT
cana-3842	5	6	v	v	X
cana-3842	5	7	(	(	PUNCT
cana-3842	5	8	g	g	NOUN
cana-3842	5	9	)	)	PUNCT
cana-3842	5	10	→	→	SYM
cana-3842	5	11	w	w	NOUN
cana-3842	5	12	and	and	CCONJ
cana-3842	5	13	any	any	DET
cana-3842	5	14	pair	pair	NOUN
cana-3842	5	15	of	of	ADP
cana-3842	5	16	adjacent	adjacent	ADJ
cana-3842	5	17	vertices	vertex	NOUN
cana-3842	5	18	with	with	ADP
cana-3842	5	19	f(v	f(v	NOUN
cana-3842	5	20	)	)	PUNCT
cana-3842	5	21	=	=	SYM
cana-3842	5	22	0	0	NUM
cana-3842	5	23	and	and	CCONJ
cana-3842	5	24	u	u	X
cana-3842	5	25	>	>	X
cana-3842	5	26	0	0	PROPN
cana-3842	5	27	,	,	PUNCT
cana-3842	5	28	the	the	DET
cana-3842	5	29	function	function	NOUN
cana-3842	5	30	guv	guv	NOUN
cana-3842	5	31	is	be	AUX
cana-3842	5	32	defined	define	VERB
cana-3842	5	33	by	by	ADP
cana-3842	5	34	𝑔𝑢𝑣	𝑔𝑢𝑣	PROPN
cana-3842	5	35	(	(	PUNCT
cana-3842	5	36	l	l	NOUN
cana-3842	5	37	)	)	PUNCT
cana-3842	5	38	=	=	SYM
cana-3842	5	39	1	1	NUM
cana-3842	5	40	,	,	PUNCT
cana-3842	5	41	𝑔𝑢𝑣	𝑔𝑢𝑣	X
cana-3842	5	42	(	(	PUNCT
cana-3842	5	43	l	l	NOUN
cana-3842	5	44	)	)	PUNCT
cana-3842	5	45	=	=	SYM
cana-3842	5	46	f(u	f(u	PROPN
cana-3842	5	47	)	)	PUNCT
cana-3842	6	1	−	−	PROPN
cana-3842	6	2	1	1	NUM
cana-3842	6	3	and	and	CCONJ
cana-3842	6	4	𝑔𝑢𝑣	𝑔𝑢𝑣	PROPN
cana-3842	6	5	(	(	PUNCT
cana-3842	6	6	l	l	NOUN
cana-3842	6	7	)	)	PUNCT
cana-3842	6	8	=	=	SYM
cana-3842	6	9	f(l	f(l	VERB
cana-3842	6	10	)	)	PUNCT
cana-3842	6	11	if	if	SCONJ
cana-3842	6	12	𝑙	𝑙	PROPN
cana-3842	6	13	∈	∈	PROPN
cana-3842	6	14	𝑉	𝑉	PROPN
cana-3842	6	15	−	−	PROPN
cana-3842	6	16	{	{	PUNCT
cana-3842	6	17	𝑢	𝑢	PROPN
cana-3842	6	18	,	,	PUNCT
cana-3842	6	19	𝑣	𝑣	NOUN
cana-3842	6	20	}	}	PUNCT
cana-3842	6	21	.	.	PUNCT
cana-3842	7	1	a	a	DET
cana-3842	7	2	secure	secure	ADJ
cana-3842	7	3	integer	integer	NOUN
cana-3842	7	4	dominating	dominating	NOUN
cana-3842	7	5	function	function	NOUN
cana-3842	7	6	on	on	ADP
cana-3842	7	7	a	a	DET
cana-3842	7	8	graph	graph	NOUN
cana-3842	7	9	g	g	NOUN
cana-3842	7	10	is	be	AUX
cana-3842	7	11	defined	define	VERB
cana-3842	7	12	as	as	ADP
cana-3842	7	13	an	an	DET
cana-3842	7	14	integer	integer	NOUN
cana-3842	7	15	dominating	dominating	NOUN
cana-3842	7	16	function	function	NOUN
cana-3842	7	17	g	g	NOUN
cana-3842	7	18	which	which	PRON
cana-3842	7	19	satisfies	satisfy	VERB
cana-3842	7	20	that	that	PRON
cana-3842	7	21	for	for	ADP
cana-3842	7	22	every	every	DET
cana-3842	7	23	vertex	vertex	NOUN
cana-3842	7	24	v	v	NOUN
cana-3842	7	25	with	with	ADP
cana-3842	7	26	f(v	f(v	NOUN
cana-3842	7	27	)	)	PUNCT
cana-3842	8	1	=	=	SYM
cana-3842	8	2	0	0	NUM
cana-3842	8	3	,	,	PUNCT
cana-3842	8	4	a	a	DET
cana-3842	8	5	neighbour	neighbour	ADJ
cana-3842	8	6	u	u	NOUN
cana-3842	8	7	with	with	ADP
cana-3842	8	8	f(u	f(u	PROPN
cana-3842	8	9	)	)	PUNCT
cana-3842	8	10	>	>	X
cana-3842	8	11	0	0	PUNCT
cana-3842	9	1	such	such	ADJ
cana-3842	9	2	that	that	SCONJ
cana-3842	9	3	𝑔𝑢𝑣	𝑔𝑢𝑣	PROPN
cana-3842	9	4	is	be	AUX
cana-3842	9	5	an	an	DET
cana-3842	9	6	integer	integer	NOUN
cana-3842	9	7	dominating	dominating	NOUN
cana-3842	9	8	function	function	NOUN
cana-3842	9	9	.	.	PUNCT
cana-3842	10	1	the	the	DET
cana-3842	10	2	weight	weight	NOUN
cana-3842	10	3	of	of	ADP
cana-3842	10	4	f	f	PROPN
cana-3842	10	5	is	be	AUX
cana-3842	10	6	w(f	w(f	ADJ
cana-3842	10	7	)	)	PUNCT
cana-3842	10	8	=	=	SYM
cana-3842	10	9	∑	∑	PUNCT
cana-3842	10	10	𝑓(𝑣)𝑣	𝑓(𝑣)𝑣	PROPN
cana-3842	10	11	∈	∈	PROPN
cana-3842	10	12	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	10	13	)	)	PUNCT
cana-3842	10	14	.	.	PUNCT
cana-3842	11	1	minimum	minimum	ADJ
cana-3842	11	2	weight	weight	NOUN
cana-3842	11	3	among	among	ADP
cana-3842	11	4	all	all	DET
cana-3842	11	5	the	the	DET
cana-3842	11	6	secure	secure	ADJ
cana-3842	11	7	integer	integer	NOUN
cana-3842	11	8	dominating	dominating	NOUN
cana-3842	11	9	function	function	NOUN
cana-3842	11	10	on	on	ADP
cana-3842	11	11	g	g	PROPN
cana-3842	11	12	is	be	AUX
cana-3842	11	13	secure	secure	ADJ
cana-3842	11	14	integer	integer	NOUN
cana-3842	11	15	domination	domination	NOUN
cana-3842	11	16	number	number	NOUN
cana-3842	11	17	on	on	ADP
cana-3842	11	18	g.	g.	PROPN
cana-3842	11	19	this	this	DET
cana-3842	11	20	paper	paper	NOUN
cana-3842	11	21	is	be	AUX
cana-3842	11	22	devoted	devote	VERB
cana-3842	11	23	to	to	ADP
cana-3842	11	24	initiating	initiate	VERB
cana-3842	11	25	the	the	DET
cana-3842	11	26	study	study	NOUN
cana-3842	11	27	of	of	ADP
cana-3842	11	28	sidf	sidf	NOUN
cana-3842	11	29	of	of	ADP
cana-3842	11	30	a	a	DET
cana-3842	11	31	graph	graph	NOUN
cana-3842	11	32	.	.	PUNCT
cana-3842	12	1	in	in	ADP
cana-3842	12	2	particular	particular	ADJ
cana-3842	12	3	,	,	PUNCT
cana-3842	12	4	we	we	PRON
cana-3842	12	5	have	have	AUX
cana-3842	12	6	studied	study	VERB
cana-3842	12	7	the	the	DET
cana-3842	12	8	changing	change	VERB
cana-3842	12	9	and	and	CCONJ
cana-3842	12	10	unchanging	unchanging	ADJ
cana-3842	12	11	behavior	behavior	NOUN
cana-3842	12	12	of	of	ADP
cana-3842	12	13	the	the	DET
cana-3842	12	14	graphs	graph	NOUN
cana-3842	12	15	.	.	PUNCT
cana-3842	13	1	objectives	objective	NOUN
cana-3842	13	2	:	:	PUNCT
cana-3842	13	3	we	we	PRON
cana-3842	13	4	propose	propose	VERB
cana-3842	13	5	a	a	DET
cana-3842	13	6	novel	novel	ADJ
cana-3842	13	7	generalization	generalization	NOUN
cana-3842	13	8	of	of	ADP
cana-3842	13	9	domination	domination	NOUN
cana-3842	13	10	,	,	PUNCT
cana-3842	13	11	which	which	PRON
cana-3842	13	12	incorporates	incorporate	VERB
cana-3842	13	13	additional	additional	ADJ
cana-3842	13	14	security	security	NOUN
cana-3842	13	15	and	and	CCONJ
cana-3842	13	16	broader	broad	ADJ
cana-3842	13	17	applicability	applicability	NOUN
cana-3842	13	18	.	.	PUNCT
cana-3842	14	1	this	this	DET
cana-3842	14	2	refined	refined	ADJ
cana-3842	14	3	framework	framework	NOUN
cana-3842	14	4	offers	offer	VERB
cana-3842	14	5	new	new	ADJ
cana-3842	14	6	possibilities	possibility	NOUN
cana-3842	14	7	for	for	ADP
cana-3842	14	8	research	research	NOUN
cana-3842	14	9	and	and	CCONJ
cana-3842	14	10	practical	practical	ADJ
cana-3842	14	11	implementation	implementation	NOUN
cana-3842	14	12	.	.	PUNCT
cana-3842	15	1	keywords	keyword	NOUN
cana-3842	15	2	:	:	PUNCT
cana-3842	15	3	domination	domination	NOUN
cana-3842	15	4	,	,	PUNCT
cana-3842	15	5	secure	secure	ADJ
cana-3842	15	6	domination	domination	NOUN
cana-3842	15	7	,	,	PUNCT
cana-3842	15	8	integer	integer	NOUN
cana-3842	15	9	domination	domination	NOUN
cana-3842	15	10	,	,	PUNCT
cana-3842	15	11	changing	change	VERB
cana-3842	15	12	and	and	CCONJ
cana-3842	15	13	unchanging	unchanging	ADJ
cana-3842	15	14	domination	domination	NOUN
cana-3842	15	15	.	.	PUNCT
cana-3842	16	1	1	1	X
cana-3842	16	2	.	.	X
cana-3842	16	3	introduction	introduction	NOUN
cana-3842	16	4	the	the	DET
cana-3842	16	5	study	study	NOUN
cana-3842	16	6	of	of	ADP
cana-3842	16	7	domination	domination	NOUN
cana-3842	16	8	can	can	AUX
cana-3842	16	9	be	be	AUX
cana-3842	16	10	traced	trace	VERB
cana-3842	16	11	back	back	ADV
cana-3842	16	12	to	to	ADP
cana-3842	16	13	1862	1862	NUM
cana-3842	16	14	,	,	PUNCT
cana-3842	16	15	when	when	SCONJ
cana-3842	16	16	de	de	X
cana-3842	16	17	jaenish	jaenish	PROPN
cana-3842	16	18	attempted	attempt	VERB
cana-3842	16	19	to	to	PART
cana-3842	16	20	determine	determine	VERB
cana-3842	16	21	the	the	DET
cana-3842	16	22	minimum	minimum	ADJ
cana-3842	16	23	number	number	NOUN
cana-3842	16	24	of	of	ADP
cana-3842	16	25	queens	queen	NOUN
cana-3842	16	26	required	require	VERB
cana-3842	16	27	to	to	PART
cana-3842	16	28	cover	cover	VERB
cana-3842	16	29	the	the	DET
cana-3842	16	30	n	n	NOUN
cana-3842	16	31	∗	∗	NOUN
cana-3842	16	32	n	n	PRON
cana-3842	16	33	chess	chess	NOUN
cana-3842	16	34	board	board	NOUN
cana-3842	16	35	.	.	PUNCT
cana-3842	17	1	the	the	DET
cana-3842	17	2	study	study	NOUN
cana-3842	17	3	of	of	ADP
cana-3842	17	4	domination	domination	NOUN
cana-3842	17	5	in	in	ADP
cana-3842	17	6	graphs	graph	NOUN
cana-3842	17	7	was	be	AUX
cana-3842	17	8	further	far	ADV
cana-3842	17	9	developed	develop	VERB
cana-3842	17	10	in	in	ADP
cana-3842	17	11	1958	1958	NUM
cana-3842	17	12	by	by	ADP
cana-3842	17	13	c.	c.	PROPN
cana-3842	17	14	berge	berge	PROPN
cana-3842	17	15	and	and	CCONJ
cana-3842	17	16	o.	o.	ADJ
cana-3842	17	17	ore	ore	NOUN
cana-3842	17	18	in	in	ADP
cana-3842	17	19	1962	1962	NUM
cana-3842	18	1	[	[	X
cana-3842	18	2	6	6	NUM
cana-3842	18	3	]	]	PUNCT
cana-3842	18	4	.	.	PUNCT
cana-3842	19	1	one	one	NUM
cana-3842	19	2	of	of	ADP
cana-3842	19	3	the	the	DET
cana-3842	19	4	variation	variation	NOUN
cana-3842	19	5	of	of	ADP
cana-3842	19	6	domination	domination	NOUN
cana-3842	19	7	is	be	AUX
cana-3842	19	8	secure	secure	ADJ
cana-3842	19	9	domination	domination	NOUN
cana-3842	19	10	in	in	ADP
cana-3842	19	11	graphs	graph	NOUN
cana-3842	19	12	.	.	PUNCT
cana-3842	20	1	this	this	PRON
cana-3842	20	2	was	be	AUX
cana-3842	20	3	studied	study	VERB
cana-3842	20	4	and	and	CCONJ
cana-3842	20	5	introduced	introduce	VERB
cana-3842	20	6	by	by	ADP
cana-3842	20	7	e.	e.	PROPN
cana-3842	20	8	j.	j.	PROPN
cana-3842	20	9	cockayne	cockayne	PROPN
cana-3842	20	10	et.al	et.al	PROPN
cana-3842	21	1	[	[	X
cana-3842	21	2	4	4	NUM
cana-3842	21	3	]	]	PUNCT
cana-3842	21	4	.	.	PUNCT
cana-3842	22	1	secure	secure	ADJ
cana-3842	22	2	dominating	dominating	NOUN
cana-3842	22	3	sets	set	NOUN
cana-3842	22	4	can	can	AUX
cana-3842	22	5	be	be	AUX
cana-3842	22	6	applied	apply	VERB
cana-3842	22	7	as	as	ADP
cana-3842	22	8	protection	protection	NOUN
cana-3842	22	9	strategies	strategy	NOUN
cana-3842	22	10	by	by	ADP
cana-3842	22	11	minimizing	minimize	VERB
cana-3842	22	12	the	the	DET
cana-3842	22	13	number	number	NOUN
cana-3842	22	14	of	of	ADP
cana-3842	22	15	guards	guard	NOUN
cana-3842	22	16	to	to	PART
cana-3842	22	17	secure	secure	VERB
cana-3842	22	18	a	a	DET
cana-3842	22	19	system	system	NOUN
cana-3842	22	20	so	so	SCONJ
cana-3842	22	21	as	as	SCONJ
cana-3842	22	22	to	to	PART
cana-3842	22	23	be	be	AUX
cana-3842	22	24	cost	cost	VERB
cana-3842	22	25	effective	effective	ADJ
cana-3842	22	26	as	as	ADP
cana-3842	22	27	possible	possible	ADJ
cana-3842	22	28	.	.	PUNCT
cana-3842	23	1	for	for	ADP
cana-3842	23	2	the	the	DET
cana-3842	23	3	general	general	ADJ
cana-3842	23	4	concepts	concept	NOUN
cana-3842	23	5	not	not	PART
cana-3842	23	6	mentioned	mention	VERB
cana-3842	23	7	,	,	PUNCT
cana-3842	23	8	the	the	DET
cana-3842	23	9	readers	reader	NOUN
cana-3842	23	10	may	may	AUX
cana-3842	23	11	be	be	AUX
cana-3842	23	12	referred	refer	VERB
cana-3842	23	13	to	to	ADP
cana-3842	23	14	[	[	X
cana-3842	23	15	11	11	NUM
cana-3842	23	16	]	]	PUNCT
cana-3842	23	17	.	.	PUNCT
cana-3842	24	1	a	a	DET
cana-3842	24	2	graph	graph	NOUN
cana-3842	24	3	g	g	NOUN
cana-3842	24	4	is	be	AUX
cana-3842	24	5	a	a	DET
cana-3842	24	6	pair	pair	NOUN
cana-3842	24	7	(	(	PUNCT
cana-3842	24	8	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	24	9	)	)	PUNCT
cana-3842	24	10	,	,	PUNCT
cana-3842	24	11	𝐸(𝐺	𝐸(𝐺	PROPN
cana-3842	24	12	)	)	PUNCT
cana-3842	24	13	)	)	PUNCT
cana-3842	24	14	,	,	PUNCT
cana-3842	24	15	where	where	SCONJ
cana-3842	24	16	v(g	v(g	VERB
cana-3842	24	17	)	)	PUNCT
cana-3842	24	18	is	be	AUX
cana-3842	24	19	a	a	DET
cana-3842	24	20	finite	finite	NOUN
cana-3842	24	21	nonempty	nonempty	ADV
cana-3842	24	22	set	set	NOUN
cana-3842	24	23	called	call	VERB
cana-3842	24	24	the	the	DET
cana-3842	24	25	vertex	vertex	NOUN
cana-3842	24	26	set	set	NOUN
cana-3842	24	27	of	of	ADP
cana-3842	24	28	g	g	PROPN
cana-3842	24	29	and	and	CCONJ
cana-3842	24	30	e(g	e(g	PROPN
cana-3842	24	31	)	)	PUNCT
cana-3842	24	32	is	be	AUX
cana-3842	24	33	a	a	DET
cana-3842	24	34	set	set	NOUN
cana-3842	24	35	of	of	ADP
cana-3842	24	36	unordered	unordered	ADJ
cana-3842	24	37	pairs	pair	NOUN
cana-3842	24	38	xy	xy	PROPN
cana-3842	24	39	of	of	ADP
cana-3842	24	40	distinct	distinct	ADJ
cana-3842	24	41	elements	element	NOUN
cana-3842	24	42	from	from	ADP
cana-3842	24	43	v(g	v(g	PROPN
cana-3842	24	44	)	)	PUNCT
cana-3842	24	45	called	call	VERB
cana-3842	24	46	the	the	DET
cana-3842	24	47	edge	edge	NOUN
cana-3842	24	48	set	set	NOUN
cana-3842	24	49	of	of	ADP
cana-3842	24	50	g.	g.	PROPN
cana-3842	24	51	the	the	DET
cana-3842	24	52	elements	element	NOUN
cana-3842	24	53	of	of	ADP
cana-3842	24	54	v(g	v(g	NUM
cana-3842	24	55	)	)	PUNCT
cana-3842	24	56	are	be	AUX
cana-3842	24	57	called	call	VERB
cana-3842	24	58	vertices	vertex	NOUN
cana-3842	24	59	.	.	PUNCT
cana-3842	25	1	the	the	DET
cana-3842	25	2	order	order	NOUN
cana-3842	25	3	of	of	ADP
cana-3842	25	4	g	g	PROPN
cana-3842	25	5	is	be	AUX
cana-3842	25	6	denoted	denote	VERB
cana-3842	25	7	by	by	ADP
cana-3842	25	8	n	n	CCONJ
cana-3842	25	9	=|	=|	X
cana-3842	25	10	v(g	v(g	ADJ
cana-3842	25	11	)	)	PUNCT
cana-3842	26	1	|	|	ADV
cana-3842	26	2	and	and	CCONJ
cana-3842	26	3	the	the	DET
cana-3842	26	4	size	size	NOUN
cana-3842	26	5	of	of	ADP
cana-3842	26	6	g	g	NOUN
cana-3842	26	7	by	by	ADP
cana-3842	26	8	m	m	PROPN
cana-3842	26	9	=|	=|	NOUN
cana-3842	26	10	e(g	e(g	NOUN
cana-3842	26	11	)	)	PUNCT
cana-3842	27	1	|	|	ADV
cana-3842	27	2	.	.	PUNCT
cana-3842	28	1	a	a	DET
cana-3842	28	2	subset	subset	NOUN
cana-3842	28	3	𝐻	𝐻	PROPN
cana-3842	28	4	∈	∈	PROPN
cana-3842	28	5	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	28	6	)	)	PUNCT
cana-3842	28	7	the	the	DET
cana-3842	28	8	subgraph	subgraph	NOUN
cana-3842	28	9	induced	induce	VERB
cana-3842	28	10	by	by	ADP
cana-3842	28	11	h	h	NOUN
cana-3842	28	12	is	be	AUX
cana-3842	28	13	the	the	DET
cana-3842	28	14	graph	graph	NOUN
cana-3842	28	15	g[h	g[h	PROPN
cana-3842	28	16	]	]	PUNCT
cana-3842	28	17	with	with	ADP
cana-3842	28	18	vertex	vertex	NOUN
cana-3842	28	19	set	set	VERB
cana-3842	28	20	h	h	NOUN
cana-3842	28	21	and	and	CCONJ
cana-3842	28	22	edge	edge	NOUN
cana-3842	28	23	set	set	NOUN
cana-3842	28	24	{	{	PUNCT
cana-3842	28	25	xy	xy	PROPN
cana-3842	28	26	∈	∈	PROPN
cana-3842	28	27	e(g	e(g	PROPN
cana-3842	28	28	)	)	PUNCT
cana-3842	29	1	|	|	ADV
cana-3842	29	2	x	x	X
cana-3842	29	3	,	,	PUNCT
cana-3842	29	4	y	y	PROPN
cana-3842	29	5	∈	∈	PROPN
cana-3842	29	6	h	h	NOUN
cana-3842	29	7	}	}	PUNCT
cana-3842	29	8	.	.	PUNCT
cana-3842	30	1	we	we	PRON
cana-3842	30	2	write	write	VERB
cana-3842	30	3	kn	kn	PROPN
cana-3842	30	4	for	for	ADP
cana-3842	30	5	complete	complete	ADJ
cana-3842	30	6	graph	graph	NOUN
cana-3842	30	7	of	of	ADP
cana-3842	30	8	order	order	NOUN
cana-3842	30	9	n	n	CCONJ
cana-3842	30	10	,	,	PUNCT
cana-3842	30	11	km	km	PROPN
cana-3842	30	12	,	,	PUNCT
cana-3842	30	13	n	n	NOUN
cana-3842	30	14	for	for	ADP
cana-3842	30	15	complete	complete	ADJ
cana-3842	30	16	bipartite	bipartite	NOUN
cana-3842	30	17	graph	graph	NOUN
cana-3842	30	18	with	with	ADP
cana-3842	30	19	partite	partite	ADJ
cana-3842	30	20	sets	set	NOUN
cana-3842	30	21	of	of	ADP
cana-3842	30	22	order	order	NOUN
cana-3842	30	23	n	n	NOUN
cana-3842	30	24	and	and	CCONJ
cana-3842	30	25	m	m	PROPN
cana-3842	30	26	,	,	PUNCT
cana-3842	30	27	pn	pn	VERB
cana-3842	30	28	for	for	ADP
cana-3842	30	29	the	the	DET
cana-3842	30	30	path	path	NOUN
cana-3842	30	31	on	on	ADP
cana-3842	30	32	n	n	DET
cana-3842	30	33	vertices	vertex	NOUN
cana-3842	30	34	and	and	CCONJ
cana-3842	30	35	cn	cn	VERB
cana-3842	30	36	for	for	ADP
cana-3842	30	37	the	the	DET
cana-3842	30	38	cycle	cycle	NOUN
cana-3842	30	39	of	of	ADP
cana-3842	30	40	length	length	NOUN
cana-3842	30	41	n.	n.	PROPN
cana-3842	30	42	a	a	DET
cana-3842	30	43	star	star	NOUN
cana-3842	30	44	is	be	AUX
cana-3842	30	45	the	the	DET
cana-3842	30	46	graph	graph	NOUN
cana-3842	30	47	𝑆1,𝑟	𝑆1,𝑟	NOUN
cana-3842	30	48	where	where	SCONJ
cana-3842	30	49	r	r	NOUN
cana-3842	30	50	≤	≤	NUM
cana-3842	30	51	1	1	NUM
cana-3842	30	52	.	.	PUNCT
cana-3842	31	1	for	for	ADP
cana-3842	31	2	any	any	DET
cana-3842	31	3	vertex	vertex	NOUN
cana-3842	31	4	v	v	ADP
cana-3842	31	5	∈	∈	PROPN
cana-3842	31	6	v(g	v(g	ADJ
cana-3842	31	7	)	)	PUNCT
cana-3842	31	8	open	open	ADJ
cana-3842	31	9	neighbourhood	neighbourhood	NOUN
cana-3842	31	10	of	of	ADP
cana-3842	31	11	v	v	NOUN
cana-3842	31	12	is	be	AUX
cana-3842	31	13	the	the	DET
cana-3842	31	14	set	set	NOUN
cana-3842	31	15	n(v	n(v	PROPN
cana-3842	31	16	)	)	PUNCT
cana-3842	31	17	=	=	PRON
cana-3842	32	1	{	{	PUNCT
cana-3842	32	2	u	u	NOUN
cana-3842	32	3	∈	∈	PROPN
cana-3842	32	4	v	v	ADP
cana-3842	32	5	|	|	ADV
cana-3842	32	6	uv	uv	NOUN
cana-3842	32	7	∈	∈	NOUN
cana-3842	32	8	e	e	NOUN
cana-3842	32	9	}	}	PUNCT
cana-3842	32	10	and	and	CCONJ
cana-3842	32	11	the	the	DET
cana-3842	32	12	closed	closed	ADJ
cana-3842	32	13	neighbourhood	neighbourhood	NOUN
cana-3842	32	14	communications	communication	NOUN
cana-3842	32	15	on	on	ADP
cana-3842	32	16	applied	apply	VERB
cana-3842	32	17	nonlinear	nonlinear	ADJ
cana-3842	32	18	analysis	analysis	NOUN
cana-3842	32	19	issn	issn	NOUN
cana-3842	32	20	:	:	PUNCT
cana-3842	32	21	1074	1074	NUM
cana-3842	32	22	-	-	PUNCT
cana-3842	32	23	133x	133x	NUM
cana-3842	32	24	vol	vol	NOUN
cana-3842	32	25	32	32	NUM
cana-3842	33	1	no	no	NOUN
cana-3842	33	2	.	.	PUNCT
cana-3842	34	1	9s	9s	NUM
cana-3842	34	2	(	(	PUNCT
cana-3842	34	3	2025	2025	NUM
cana-3842	34	4	)	)	PUNCT
cana-3842	34	5	116	116	NUM
cana-3842	35	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3842	35	2	is	be	AUX
cana-3842	35	3	the	the	DET
cana-3842	35	4	set	set	NOUN
cana-3842	35	5	n[v	n[v	ADV
cana-3842	35	6	]	]	X
cana-3842	35	7	=	=	SYM
cana-3842	35	8	n(v	n(v	PROPN
cana-3842	35	9	)	)	PUNCT
cana-3842	35	10	∪	∪	NOUN
cana-3842	35	11	v.	v.	ADP
cana-3842	35	12	the	the	DET
cana-3842	35	13	private	private	ADJ
cana-3842	35	14	neighbor	neighbor	NOUN
cana-3842	35	15	set	set	VERB
cana-3842	35	16	of	of	ADP
cana-3842	35	17	a	a	DET
cana-3842	35	18	v	v	NOUN
cana-3842	35	19	∈	∈	PROPN
cana-3842	35	20	v(g	v(g	NOUN
cana-3842	35	21	)	)	PUNCT
cana-3842	35	22	with	with	ADP
cana-3842	35	23	respect	respect	NOUN
cana-3842	35	24	to	to	ADP
cana-3842	35	25	a	a	DET
cana-3842	35	26	set	set	NOUN
cana-3842	35	27	d	d	NOUN
cana-3842	35	28	,	,	PUNCT
cana-3842	35	29	denoted	denote	VERB
cana-3842	35	30	by	by	ADP
cana-3842	35	31	pn[v	pn[v	PROPN
cana-3842	35	32	,	,	PUNCT
cana-3842	35	33	d	d	X
cana-3842	35	34	]	]	X
cana-3842	35	35	is	be	AUX
cana-3842	35	36	n[v]n[sv	n[v]n[sv	ADJ
cana-3842	35	37	]	]	PUNCT
cana-3842	35	38	and	and	CCONJ
cana-3842	35	39	each	each	DET
cana-3842	35	40	u	u	PROPN
cana-3842	35	41	∈	∈	PROPN
cana-3842	35	42	pn[v	pn[v	PROPN
cana-3842	35	43	,	,	PUNCT
cana-3842	35	44	d	d	X
cana-3842	35	45	]	]	X
cana-3842	35	46	is	be	AUX
cana-3842	35	47	called	call	VERB
cana-3842	35	48	a	a	DET
cana-3842	35	49	private	private	ADJ
cana-3842	35	50	neighbor	neighbor	NOUN
cana-3842	35	51	of	of	ADP
cana-3842	35	52	v(g	v(g	PROPN
cana-3842	35	53	)	)	PUNCT
cana-3842	35	54	with	with	ADP
cana-3842	35	55	respect	respect	NOUN
cana-3842	35	56	to	to	ADP
cana-3842	35	57	d.	d.	PROPN
cana-3842	35	58	o.	o.	PROPN
cana-3842	35	59	ore	ore	PROPN
cana-3842	35	60	introduced	introduce	VERB
cana-3842	35	61	the	the	DET
cana-3842	35	62	concept	concept	NOUN
cana-3842	35	63	of	of	ADP
cana-3842	35	64	domination	domination	NOUN
cana-3842	35	65	theory	theory	NOUN
cana-3842	35	66	.	.	PUNCT
cana-3842	36	1	a	a	DET
cana-3842	36	2	set	set	NOUN
cana-3842	36	3	d	d	X
cana-3842	36	4	∈	∈	PROPN
cana-3842	36	5	v(g	v(g	PROPN
cana-3842	36	6	)	)	PUNCT
cana-3842	36	7	is	be	AUX
cana-3842	36	8	a	a	DET
cana-3842	36	9	dominating	dominating	NOUN
cana-3842	36	10	set	set	NOUN
cana-3842	36	11	if	if	SCONJ
cana-3842	36	12	every	every	DET
cana-3842	36	13	vertex	vertex	NOUN
cana-3842	36	14	in	in	ADP
cana-3842	36	15	v(g)is	v(g)i	NOUN
cana-3842	36	16	adjacent	adjacent	ADJ
cana-3842	36	17	to	to	ADP
cana-3842	36	18	at	at	ADV
cana-3842	36	19	least	least	ADV
cana-3842	36	20	one	one	NUM
cana-3842	36	21	vertex	vertex	NOUN
cana-3842	36	22	in	in	ADP
cana-3842	36	23	d.	d.	PROPN
cana-3842	36	24	the	the	DET
cana-3842	36	25	domination	domination	NOUN
cana-3842	36	26	number	number	PROPN
cana-3842	36	27	γ(g	γ(g	PROPN
cana-3842	36	28	)	)	PUNCT
cana-3842	36	29	is	be	AUX
cana-3842	36	30	the	the	DET
cana-3842	36	31	minimum	minimum	ADJ
cana-3842	36	32	cardinality	cardinality	NOUN
cana-3842	36	33	of	of	ADP
cana-3842	36	34	a	a	DET
cana-3842	36	35	dominating	dominating	NOUN
cana-3842	36	36	set	set	NOUN
cana-3842	36	37	of	of	ADP
cana-3842	36	38	g.	g.	PROPN
cana-3842	36	39	domination	domination	PROPN
cana-3842	36	40	theory	theory	NOUN
cana-3842	36	41	has	have	VERB
cana-3842	36	42	wide	wide	ADJ
cana-3842	36	43	application	application	NOUN
cana-3842	36	44	in	in	ADP
cana-3842	36	45	real	real	ADJ
cana-3842	36	46	life	life	NOUN
cana-3842	36	47	.	.	PUNCT
cana-3842	37	1	various	various	ADJ
cana-3842	37	2	kinds	kind	NOUN
cana-3842	37	3	of	of	ADP
cana-3842	37	4	domination	domination	NOUN
cana-3842	37	5	have	have	AUX
cana-3842	37	6	been	be	AUX
cana-3842	37	7	studied	study	VERB
cana-3842	37	8	in	in	ADP
cana-3842	37	9	recent	recent	ADJ
cana-3842	37	10	times	time	NOUN
cana-3842	37	11	,	,	PUNCT
cana-3842	37	12	one	one	NUM
cana-3842	37	13	of	of	ADP
cana-3842	37	14	the	the	DET
cana-3842	37	15	variation	variation	NOUN
cana-3842	37	16	is	be	AUX
cana-3842	37	17	integer	integer	NOUN
cana-3842	37	18	domination	domination	NOUN
cana-3842	37	19	.	.	PUNCT
cana-3842	38	1	domke	domke	PROPN
cana-3842	38	2	et	et	PROPN
cana-3842	38	3	al.[3	al.[3	PROPN
cana-3842	38	4	]	]	PUNCT
cana-3842	38	5	introduced	introduce	VERB
cana-3842	38	6	the	the	DET
cana-3842	38	7	concept	concept	NOUN
cana-3842	38	8	of	of	ADP
cana-3842	38	9	integer	integer	PROPN
cana-3842	38	10	k	k	PROPN
cana-3842	38	11	-	-	PUNCT
cana-3842	38	12	domination	domination	NOUN
cana-3842	38	13	and	and	CCONJ
cana-3842	38	14	further	further	ADJ
cana-3842	38	15	integer	integer	NOUN
cana-3842	38	16	domination	domination	NOUN
cana-3842	38	17	on	on	ADP
cana-3842	38	18	vizing	vizing	PROPN
cana-3842	38	19	’s	’s	PART
cana-3842	38	20	conjecture	conjecture	NOUN
cana-3842	38	21	was	be	AUX
cana-3842	38	22	studied	study	VERB
cana-3842	38	23	by	by	ADP
cana-3842	38	24	bresar	bresar	VERB
cana-3842	38	25	et	et	PROPN
cana-3842	38	26	al.[2	al.[2	PROPN
cana-3842	38	27	]	]	X
cana-3842	38	28	.	.	PUNCT
cana-3842	39	1	a	a	DET
cana-3842	39	2	function	function	NOUN
cana-3842	39	3	f	f	NOUN
cana-3842	39	4	:	:	PUNCT
cana-3842	39	5	v	v	X
cana-3842	39	6	(	(	PUNCT
cana-3842	39	7	g	g	NOUN
cana-3842	39	8	)	)	PUNCT
cana-3842	39	9	→	→	SYM
cana-3842	39	10	w	w	X
cana-3842	39	11	(	(	PUNCT
cana-3842	39	12	w	w	PROPN
cana-3842	39	13	is	be	AUX
cana-3842	39	14	the	the	DET
cana-3842	39	15	whole	whole	ADJ
cana-3842	39	16	number	number	NOUN
cana-3842	39	17	)	)	PUNCT
cana-3842	39	18	is	be	AUX
cana-3842	39	19	called	call	VERB
cana-3842	39	20	integer	integer	ADJ
cana-3842	39	21	k	k	ADJ
cana-3842	39	22	-	-	PUNCT
cana-3842	39	23	dominating	dominate	VERB
cana-3842	39	24	function	function	NOUN
cana-3842	39	25	if	if	SCONJ
cana-3842	39	26	the	the	DET
cana-3842	39	27	sum	sum	NOUN
cana-3842	39	28	of	of	ADP
cana-3842	39	29	functional	functional	ADJ
cana-3842	39	30	value	value	NOUN
cana-3842	39	31	over	over	ADP
cana-3842	39	32	any	any	DET
cana-3842	39	33	closed	closed	ADJ
cana-3842	39	34	neighbor	neighbor	NOUN
cana-3842	39	35	is	be	AUX
cana-3842	39	36	at	at	ADP
cana-3842	39	37	least	least	ADJ
cana-3842	39	38	k.	k.	VERB
cana-3842	40	1	the	the	DET
cana-3842	40	2	weight	weight	NOUN
cana-3842	40	3	of	of	ADP
cana-3842	40	4	integer	integer	PROPN
cana-3842	40	5	k	k	PROPN
cana-3842	40	6	-	-	PUNCT
cana-3842	40	7	dominating	dominate	VERB
cana-3842	40	8	function	function	NOUN
cana-3842	40	9	is	be	AUX
cana-3842	40	10	the	the	DET
cana-3842	40	11	value	value	NOUN
cana-3842	40	12	of	of	ADP
cana-3842	40	13	f(v	f(v	NOUN
cana-3842	40	14	)	)	PUNCT
cana-3842	41	1	=	=	X
cana-3842	41	2	∑	∑	PUNCT
cana-3842	41	3	𝑓(𝑣)𝑣	𝑓(𝑣)𝑣	PROPN
cana-3842	41	4	∈𝑉(𝐺	∈𝑉(𝐺	NUM
cana-3842	41	5	)	)	PUNCT
cana-3842	41	6	.	.	PUNCT
cana-3842	42	1	the	the	DET
cana-3842	42	2	minimum	minimum	ADJ
cana-3842	42	3	weight	weight	NOUN
cana-3842	42	4	of	of	ADP
cana-3842	42	5	integer	integer	NOUN
cana-3842	42	6	{	{	PUNCT
cana-3842	42	7	k}−	k}−	PROPN
cana-3842	42	8	dominating	dominating	NOUN
cana-3842	42	9	function	function	NOUN
cana-3842	42	10	is	be	AUX
cana-3842	42	11	denoted	denote	VERB
cana-3842	42	12	as	as	ADP
cana-3842	42	13	𝛾𝑘(g	𝛾𝑘(g	NOUN
cana-3842	42	14	)	)	PUNCT
cana-3842	42	15	and	and	CCONJ
cana-3842	42	16	is	be	AUX
cana-3842	42	17	called	call	VERB
cana-3842	42	18	integer	integer	NOUN
cana-3842	42	19	domination	domination	NOUN
cana-3842	42	20	number	number	NOUN
cana-3842	42	21	.	.	PUNCT
cana-3842	43	1	note	note	VERB
cana-3842	43	2	that	that	SCONJ
cana-3842	43	3	,	,	PUNCT
cana-3842	43	4	when	when	SCONJ
cana-3842	43	5	k	k	PROPN
cana-3842	43	6	=	=	SYM
cana-3842	43	7	1	1	NUM
cana-3842	43	8	its	its	PRON
cana-3842	43	9	a	a	DET
cana-3842	43	10	general	general	ADJ
cana-3842	43	11	domination	domination	NOUN
cana-3842	43	12	.	.	PUNCT
cana-3842	44	1	in	in	ADP
cana-3842	44	2	this	this	DET
cana-3842	44	3	article	article	NOUN
cana-3842	44	4	,	,	PUNCT
cana-3842	44	5	we	we	PRON
cana-3842	44	6	introduce	introduce	VERB
cana-3842	44	7	secure	secure	ADJ
cana-3842	44	8	integer	integer	NOUN
cana-3842	44	9	domination	domination	NOUN
cana-3842	44	10	and	and	CCONJ
cana-3842	44	11	study	study	NOUN
cana-3842	44	12	about	about	ADP
cana-3842	44	13	changing	change	VERB
cana-3842	44	14	and	and	CCONJ
cana-3842	44	15	unchanging	unchanging	ADJ
cana-3842	44	16	behavior	behavior	NOUN
cana-3842	44	17	of	of	ADP
cana-3842	44	18	graph	graph	NOUN
cana-3842	44	19	.	.	PUNCT
cana-3842	45	1	a	a	DET
cana-3842	45	2	function	function	NOUN
cana-3842	45	3	g	g	NOUN
cana-3842	45	4	:	:	PUNCT
cana-3842	45	5	v	v	NOUN
cana-3842	45	6	(	(	PUNCT
cana-3842	45	7	g	g	NOUN
cana-3842	45	8	)	)	PUNCT
cana-3842	45	9	→	→	SYM
cana-3842	45	10	{	{	PUNCT
cana-3842	45	11	0	0	NUM
cana-3842	45	12	,	,	PUNCT
cana-3842	45	13	1	1	NUM
cana-3842	45	14	,	,	PUNCT
cana-3842	45	15	2	2	NUM
cana-3842	45	16	,	,	PUNCT
cana-3842	45	17	..	..	PUNCT
cana-3842	45	18	,	,	PUNCT
cana-3842	45	19	k	k	X
cana-3842	45	20	}	}	PUNCT
cana-3842	45	21	is	be	AUX
cana-3842	45	22	called	call	VERB
cana-3842	45	23	secure	secure	ADJ
cana-3842	45	24	integer	integer	NOUN
cana-3842	45	25	dominating	dominating	NOUN
cana-3842	45	26	function	function	NOUN
cana-3842	45	27	(	(	PUNCT
cana-3842	45	28	sidf	sidf	PROPN
cana-3842	45	29	)	)	PUNCT
cana-3842	45	30	of	of	ADP
cana-3842	45	31	g	g	PROPN
cana-3842	45	32	if	if	SCONJ
cana-3842	45	33	it	it	PRON
cana-3842	45	34	satisfies	satisfy	VERB
cana-3842	45	35	the	the	DET
cana-3842	45	36	following	follow	VERB
cana-3842	45	37	:	:	PUNCT
cana-3842	45	38	1	1	X
cana-3842	45	39	)	)	PUNCT
cana-3842	45	40	∀	∀	X
cana-3842	45	41	𝑦	𝑦	NOUN
cana-3842	45	42	∈	∈	NOUN
cana-3842	45	43	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	45	44	)	)	PUNCT
cana-3842	45	45	,	,	PUNCT
cana-3842	45	46	∑	∑	ADP
cana-3842	45	47	𝑔(𝑁[𝑦	𝑔(𝑁[𝑦	NOUN
cana-3842	45	48	]	]	PUNCT
cana-3842	45	49	)	)	PUNCT
cana-3842	45	50	≥	≥	NOUN
cana-3842	45	51	𝑘.𝑣∈𝑉(𝐺	𝑘.𝑣∈𝑉(𝐺	NOUN
cana-3842	45	52	)	)	PUNCT
cana-3842	45	53	2	2	NUM
cana-3842	45	54	)	)	PUNCT
cana-3842	45	55	∀	∀	X
cana-3842	46	1	𝑦	𝑦	NOUN
cana-3842	46	2	∈	∈	NOUN
cana-3842	46	3	𝑉0	𝑉0	NOUN
cana-3842	46	4	∃	∃	PROPN
cana-3842	46	5	𝑧	𝑧	PROPN
cana-3842	46	6	∈	∈	PROPN
cana-3842	46	7	𝑁(𝑦	𝑁(𝑦	PROPN
cana-3842	46	8	)	)	PUNCT
cana-3842	46	9	−	−	NOUN
cana-3842	46	10	𝑉0	𝑉0	NOUN
cana-3842	46	11	such	such	ADJ
cana-3842	46	12	that	that	SCONJ
cana-3842	46	13	𝑔𝑦𝑧	𝑔𝑦𝑧	NOUN
cana-3842	46	14	is	be	AUX
cana-3842	46	15	an	an	DET
cana-3842	46	16	integer	integer	NOUN
cana-3842	46	17	dominating	dominating	NOUN
cana-3842	46	18	function	function	NOUN
cana-3842	46	19	on	on	ADP
cana-3842	46	20	g.	g.	PROPN
cana-3842	46	21	the	the	DET
cana-3842	46	22	secure	secure	ADJ
cana-3842	46	23	integer	integer	NOUN
cana-3842	46	24	dominating	dominating	NOUN
cana-3842	46	25	function	function	NOUN
cana-3842	46	26	has	have	VERB
cana-3842	46	27	a	a	DET
cana-3842	46	28	weight	weight	NOUN
cana-3842	46	29	equal	equal	ADJ
cana-3842	46	30	to	to	ADP
cana-3842	46	31	the	the	DET
cana-3842	46	32	value	value	NOUN
cana-3842	46	33	of	of	ADP
cana-3842	46	34	w(y	w(y	NOUN
cana-3842	46	35	)	)	PUNCT
cana-3842	47	1	=	=	PROPN
cana-3842	47	2	∑	∑	PROPN
cana-3842	47	3	𝑔(𝑦)𝑦	𝑔(𝑦)𝑦	PROPN
cana-3842	47	4	∈𝑉(𝐺	∈𝑉(𝐺	NOUN
cana-3842	47	5	)	)	PUNCT
cana-3842	47	6	.	.	PUNCT
cana-3842	48	1	the	the	DET
cana-3842	48	2	minimum	minimum	ADJ
cana-3842	48	3	weight	weight	NOUN
cana-3842	48	4	of	of	ADP
cana-3842	48	5	secure	secure	ADJ
cana-3842	48	6	integer	integer	NOUN
cana-3842	48	7	dominating	dominating	NOUN
cana-3842	48	8	function	function	NOUN
cana-3842	48	9	is	be	AUX
cana-3842	48	10	denoted	denote	VERB
cana-3842	48	11	by	by	ADP
cana-3842	48	12	𝛾𝑘	𝛾𝑘	ADP
cana-3842	48	13	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	48	14	)	)	PUNCT
cana-3842	48	15	is	be	AUX
cana-3842	48	16	called	call	VERB
cana-3842	48	17	secure	secure	ADJ
cana-3842	48	18	integer	integer	NOUN
cana-3842	48	19	domination	domination	NOUN
cana-3842	48	20	number	number	NOUN
cana-3842	48	21	(	(	PUNCT
cana-3842	48	22	sidn	sidn	PROPN
cana-3842	48	23	)	)	PUNCT
cana-3842	48	24	.	.	PUNCT
cana-3842	49	1	for	for	ADP
cana-3842	49	2	a	a	DET
cana-3842	49	3	sidf	sidf	NOUN
cana-3842	49	4	g	g	NOUN
cana-3842	49	5	,	,	PUNCT
cana-3842	49	6	let	let	VERB
cana-3842	49	7	𝑉𝑖	𝑉𝑖	PROPN
cana-3842	49	8	𝑔	𝑔	PROPN
cana-3842	49	9	=	=	PUNCT
cana-3842	49	10	{	{	PUNCT
cana-3842	49	11	v	v	NUM
cana-3842	49	12	∈	∈	PROPN
cana-3842	49	13	v(g	v(g	NOUN
cana-3842	49	14	)	)	PUNCT
cana-3842	49	15	:	:	PUNCT
cana-3842	50	1	f	f	X
cana-3842	50	2	(	(	PUNCT
cana-3842	50	3	v	v	NOUN
cana-3842	50	4	)	)	PUNCT
cana-3842	50	5	=	=	PUNCT
cana-3842	51	1	i	i	PROPN
cana-3842	51	2	}	}	PUNCT
cana-3842	51	3	for	for	ADP
cana-3842	51	4	i	i	PROPN
cana-3842	51	5	=	=	SYM
cana-3842	51	6	0	0	NUM
cana-3842	51	7	,	,	PUNCT
cana-3842	51	8	1	1	NUM
cana-3842	51	9	,	,	PUNCT
cana-3842	51	10	2	2	NUM
cana-3842	51	11	,	,	PUNCT
cana-3842	51	12	...	...	PUNCT
cana-3842	51	13	,	,	PUNCT
cana-3842	51	14	k.	k.	PROPN
cana-3842	51	15	since	since	SCONJ
cana-3842	51	16	these	these	DET
cana-3842	51	17	k	k	PROPN
cana-3842	51	18	sets	set	NOUN
cana-3842	51	19	determine	determine	VERB
cana-3842	51	20	g	g	NOUN
cana-3842	51	21	,	,	PUNCT
cana-3842	51	22	we	we	PRON
cana-3842	51	23	can	can	AUX
cana-3842	51	24	equivalently	equivalently	ADV
cana-3842	51	25	write	write	VERB
cana-3842	51	26	𝑔	𝑔	PROPN
cana-3842	51	27	=	=	SYM
cana-3842	51	28	(	(	PUNCT
cana-3842	51	29	𝑉0	𝑉0	NOUN
cana-3842	51	30	𝑔	𝑔	PROPN
cana-3842	51	31	,	,	PUNCT
cana-3842	51	32	𝑉1	𝑉1	PROPN
cana-3842	51	33	𝑔	𝑔	PROPN
cana-3842	51	34	,	,	PUNCT
cana-3842	51	35	𝑉2	𝑉2	PROPN
cana-3842	51	36	𝑔	𝑔	PROPN
cana-3842	51	37	,	,	PUNCT
cana-3842	51	38	.	.	PUNCT
cana-3842	51	39	.	.	PUNCT
cana-3842	51	40	.	.	PUNCT
cana-3842	52	1	𝑉𝑘	𝑉𝑘	PROPN
cana-3842	52	2	𝑔	𝑔	PROPN
cana-3842	52	3	)	)	PUNCT
cana-3842	52	4	.	.	PUNCT
cana-3842	53	1	we	we	PRON
cana-3842	53	2	examine	examine	VERB
cana-3842	53	3	the	the	DET
cana-3842	53	4	effects	effect	NOUN
cana-3842	53	5	on	on	ADP
cana-3842	53	6	the	the	DET
cana-3842	53	7	domination	domination	NOUN
cana-3842	53	8	number	number	NOUN
cana-3842	53	9	when	when	SCONJ
cana-3842	53	10	the	the	DET
cana-3842	53	11	graph	graph	NOUN
cana-3842	53	12	is	be	AUX
cana-3842	53	13	modified	modify	VERB
cana-3842	53	14	by	by	ADP
cana-3842	53	15	deleting	delete	VERB
cana-3842	53	16	a	a	DET
cana-3842	53	17	vertex	vertex	NOUN
cana-3842	53	18	or	or	CCONJ
cana-3842	53	19	deleting	delete	VERB
cana-3842	53	20	or	or	CCONJ
cana-3842	53	21	adding	add	VERB
cana-3842	53	22	an	an	DET
cana-3842	53	23	edge	edge	NOUN
cana-3842	53	24	.	.	PUNCT
cana-3842	54	1	let	let	VERB
cana-3842	54	2	g	g	NOUN
cana-3842	54	3	-	-	PUNCT
cana-3842	54	4	v	v	NOUN
cana-3842	54	5	denote	denote	NOUN
cana-3842	54	6	the	the	DET
cana-3842	54	7	graph	graph	NOUN
cana-3842	54	8	formed	form	VERB
cana-3842	54	9	by	by	ADP
cana-3842	54	10	removing	remove	VERB
cana-3842	54	11	vertex	vertex	NOUN
cana-3842	54	12	v	v	NOUN
cana-3842	54	13	and	and	CCONJ
cana-3842	54	14	g	g	PROPN
cana-3842	54	15	−	−	PROPN
cana-3842	54	16	e	e	NOUN
cana-3842	54	17	denote	denote	VERB
cana-3842	54	18	the	the	DET
cana-3842	54	19	graph	graph	NOUN
cana-3842	54	20	formed	form	VERB
cana-3842	54	21	by	by	ADP
cana-3842	54	22	removing	remove	VERB
cana-3842	54	23	edge	edge	NOUN
cana-3842	54	24	e	e	NOUN
cana-3842	54	25	from	from	ADP
cana-3842	54	26	g.	g.	PROPN
cana-3842	54	27	we	we	PRON
cana-3842	54	28	use	use	VERB
cana-3842	54	29	acronyms	acronym	NOUN
cana-3842	54	30	to	to	PART
cana-3842	54	31	denote	denote	VERB
cana-3842	54	32	these	these	DET
cana-3842	54	33	classes	class	NOUN
cana-3842	54	34	(	(	PUNCT
cana-3842	54	35	v	v	NOUN
cana-3842	54	36	represents	represent	VERB
cana-3842	54	37	vertex	vertex	NOUN
cana-3842	54	38	;	;	PUNCT
cana-3842	54	39	e	e	NOUN
cana-3842	54	40	:	:	PUNCT
cana-3842	54	41	edge	edge	NOUN
cana-3842	54	42	;	;	PUNCT
cana-3842	54	43	r	r	NOUN
cana-3842	54	44	:	:	PUNCT
cana-3842	54	45	removal	removal	NOUN
cana-3842	54	46	;	;	PUNCT
cana-3842	54	47	a	a	DET
cana-3842	54	48	:	:	PUNCT
cana-3842	54	49	addition	addition	NOUN
cana-3842	54	50	)	)	PUNCT
cana-3842	54	51	.	.	PUNCT
cana-3842	55	1	note	note	VERB
cana-3842	55	2	that	that	SCONJ
cana-3842	55	3	,	,	PUNCT
cana-3842	55	4	there	there	PRON
cana-3842	55	5	are	be	VERB
cana-3842	55	6	six	six	NUM
cana-3842	55	7	class	class	NOUN
cana-3842	55	8	of	of	ADP
cana-3842	55	9	subgraphs	subgraph	NOUN
cana-3842	55	10	obtainted	obtainte	VERB
cana-3842	55	11	.	.	PUNCT
cana-3842	56	1	the	the	DET
cana-3842	56	2	following	follow	VERB
cana-3842	56	3	are	be	AUX
cana-3842	56	4	the	the	DET
cana-3842	56	5	class	class	NOUN
cana-3842	56	6	of	of	ADP
cana-3842	56	7	graphs	graph	NOUN
cana-3842	56	8	.	.	PUNCT
cana-3842	57	1	•	•	NUM
cana-3842	57	2	𝛾𝑘	𝛾𝑘	ADP
cana-3842	57	3	𝑠(𝐺	𝑠(𝐺	NOUN
cana-3842	57	4	−	−	PUNCT
cana-3842	57	5	𝑣	𝑣	X
cana-3842	57	6	)	)	PUNCT
cana-3842	57	7	≠	≠	PROPN
cana-3842	57	8	𝛾𝑘	𝛾𝑘	ADP
cana-3842	57	9	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	57	10	)	)	PUNCT
cana-3842	57	11	for	for	ADP
cana-3842	57	12	all	all	DET
cana-3842	57	13	𝑣	𝑣	PRON
cana-3842	57	14	∈	∈	PROPN
cana-3842	57	15	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	57	16	)	)	PUNCT
cana-3842	57	17	.	.	PUNCT
cana-3842	58	1	(	(	PUNCT
cana-3842	58	2	cvr	cvr	NOUN
cana-3842	58	3	)	)	PUNCT
cana-3842	58	4	•	•	NUM
cana-3842	58	5	𝛾𝑘	𝛾𝑘	ADP
cana-3842	58	6	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	58	7	−	−	NOUN
cana-3842	58	8	𝑣	𝑣	X
cana-3842	58	9	)	)	PUNCT
cana-3842	58	10	=	=	PUNCT
cana-3842	58	11	𝛾𝑘	𝛾𝑘	ADP
cana-3842	58	12	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	58	13	)	)	PUNCT
cana-3842	58	14	for	for	ADP
cana-3842	58	15	all	all	DET
cana-3842	58	16	𝑣	𝑣	PRON
cana-3842	58	17	∈	∈	PROPN
cana-3842	58	18	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	58	19	)	)	PUNCT
cana-3842	58	20	.	.	PUNCT
cana-3842	59	1	(	(	PUNCT
cana-3842	59	2	uvr	uvr	NOUN
cana-3842	59	3	)	)	PUNCT
cana-3842	59	4	•	•	NUM
cana-3842	59	5	𝛾𝑘	𝛾𝑘	ADP
cana-3842	59	6	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	59	7	−	−	NOUN
cana-3842	59	8	𝑒	𝑒	X
cana-3842	59	9	)	)	PUNCT
cana-3842	59	10	≠	≠	PROPN
cana-3842	59	11	𝛾𝑘	𝛾𝑘	ADP
cana-3842	59	12	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	59	13	)	)	PUNCT
cana-3842	59	14	for	for	ADP
cana-3842	59	15	all	all	DET
cana-3842	59	16	𝑒	𝑒	PROPN
cana-3842	59	17	∈	∈	PROPN
cana-3842	59	18	𝐸(𝐺	𝐸(𝐺	NOUN
cana-3842	59	19	)	)	PUNCT
cana-3842	59	20	.	.	PUNCT
cana-3842	60	1	(	(	PUNCT
cana-3842	60	2	cer	cer	PROPN
cana-3842	60	3	)	)	PUNCT
cana-3842	60	4	•	•	NUM
cana-3842	60	5	𝛾𝑘	𝛾𝑘	ADP
cana-3842	60	6	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	60	7	−	−	NOUN
cana-3842	60	8	𝑒	𝑒	X
cana-3842	60	9	)	)	PUNCT
cana-3842	60	10	=	=	PUNCT
cana-3842	60	11	𝛾𝑘	𝛾𝑘	ADP
cana-3842	60	12	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	60	13	)	)	PUNCT
cana-3842	60	14	for	for	ADP
cana-3842	60	15	all	all	DET
cana-3842	60	16	𝑒	𝑒	PROPN
cana-3842	60	17	∈	∈	PROPN
cana-3842	60	18	𝐸(𝐺	𝐸(𝐺	NOUN
cana-3842	60	19	)	)	PUNCT
cana-3842	60	20	.	.	PUNCT
cana-3842	61	1	(	(	PUNCT
cana-3842	61	2	uer	uer	PROPN
cana-3842	61	3	)	)	PUNCT
cana-3842	61	4	•	•	NUM
cana-3842	61	5	𝛾𝑘	𝛾𝑘	ADP
cana-3842	61	6	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	61	7	+	+	CCONJ
cana-3842	61	8	𝑒	𝑒	X
cana-3842	61	9	)	)	PUNCT
cana-3842	61	10	≠	≠	PROPN
cana-3842	61	11	𝛾𝑘	𝛾𝑘	ADP
cana-3842	61	12	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	61	13	)	)	PUNCT
cana-3842	61	14	for	for	ADP
cana-3842	61	15	all	all	DET
cana-3842	61	16	𝑒	𝑒	PROPN
cana-3842	61	17	∈	∈	PROPN
cana-3842	61	18	𝐸(𝐺	𝐸(𝐺	NOUN
cana-3842	61	19	)	)	PUNCT
cana-3842	61	20	.	.	PUNCT
cana-3842	62	1	(	(	PUNCT
cana-3842	62	2	cea	cea	PROPN
cana-3842	62	3	)	)	PUNCT
cana-3842	62	4	•	•	NUM
cana-3842	62	5	𝛾𝑘	𝛾𝑘	ADP
cana-3842	62	6	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	62	7	−	−	NOUN
cana-3842	62	8	𝑒	𝑒	X
cana-3842	62	9	)	)	PUNCT
cana-3842	62	10	=	=	PUNCT
cana-3842	62	11	𝛾𝑘	𝛾𝑘	ADP
cana-3842	62	12	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	62	13	)	)	PUNCT
cana-3842	62	14	for	for	ADP
cana-3842	62	15	all	all	DET
cana-3842	62	16	𝑒	𝑒	PROPN
cana-3842	62	17	∈	∈	PROPN
cana-3842	62	18	𝐸(𝐺	𝐸(𝐺	NOUN
cana-3842	62	19	)	)	PUNCT
cana-3842	62	20	.	.	PUNCT
cana-3842	63	1	(	(	PUNCT
cana-3842	63	2	uea	uea	PROPN
cana-3842	63	3	)	)	PUNCT
cana-3842	63	4	communications	communication	NOUN
cana-3842	63	5	on	on	ADP
cana-3842	63	6	applied	apply	VERB
cana-3842	63	7	nonlinear	nonlinear	ADJ
cana-3842	63	8	analysis	analysis	NOUN
cana-3842	63	9	issn	issn	NOUN
cana-3842	63	10	:	:	PUNCT
cana-3842	63	11	1074	1074	NUM
cana-3842	63	12	-	-	PUNCT
cana-3842	63	13	133x	133x	NUM
cana-3842	63	14	vol	vol	NOUN
cana-3842	63	15	32	32	NUM
cana-3842	63	16	no	no	NOUN
cana-3842	63	17	.	.	PUNCT
cana-3842	64	1	9s	9s	NUM
cana-3842	64	2	(	(	PUNCT
cana-3842	64	3	2025	2025	NUM
cana-3842	64	4	)	)	PUNCT
cana-3842	64	5	117	117	NUM
cana-3842	64	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3842	64	7	here	here	ADV
cana-3842	64	8	we	we	PRON
cana-3842	64	9	examine	examine	VERB
cana-3842	64	10	two	two	NUM
cana-3842	64	11	cases	case	NOUN
cana-3842	64	12	that	that	PRON
cana-3842	64	13	is	be	AUX
cana-3842	64	14	,	,	PUNCT
cana-3842	64	15	𝛾𝑘	𝛾𝑘	ADP
cana-3842	64	16	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	64	17	−	−	PUNCT
cana-3842	64	18	𝑣	𝑣	X
cana-3842	64	19	)	)	PUNCT
cana-3842	64	20	≠	≠	PROPN
cana-3842	64	21	𝛾𝑘	𝛾𝑘	ADP
cana-3842	64	22	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	64	23	)	)	PUNCT
cana-3842	64	24	for	for	ADP
cana-3842	64	25	all	all	DET
cana-3842	64	26	𝑣	𝑣	PRON
cana-3842	64	27	∈	∈	PROPN
cana-3842	64	28	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	64	29	)	)	PUNCT
cana-3842	64	30	.	.	PUNCT
cana-3842	65	1	we	we	PRON
cana-3842	65	2	partition	partition	VERB
cana-3842	65	3	the	the	DET
cana-3842	65	4	vertex	vertex	NOUN
cana-3842	65	5	set	set	NOUN
cana-3842	65	6	of	of	ADP
cana-3842	65	7	g	g	NOUN
cana-3842	65	8	into	into	ADP
cana-3842	65	9	three	three	NUM
cana-3842	65	10	sets	set	NOUN
cana-3842	65	11	according	accord	VERB
cana-3842	65	12	to	to	ADP
cana-3842	65	13	their	their	PRON
cana-3842	65	14	removal	removal	NOUN
cana-3842	65	15	affects	affect	VERB
cana-3842	65	16	𝛾𝑘	𝛾𝑘	ADP
cana-3842	65	17	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	65	18	)	)	PUNCT
cana-3842	65	19	.	.	PUNCT
cana-3842	66	1	let	let	VERB
cana-3842	66	2	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	66	3	)	)	PUNCT
cana-3842	67	1	=	=	PRON
cana-3842	67	2	{	{	PUNCT
cana-3842	67	3	𝑉0	𝑉0	NOUN
cana-3842	67	4	∪	∪	ADP
cana-3842	67	5	𝑉+	𝑉+	PROPN
cana-3842	67	6	∪	∪	ADP
cana-3842	67	7	𝑉−	𝑉−	NOUN
cana-3842	67	8	}	}	PUNCT
cana-3842	67	9	where	where	SCONJ
cana-3842	67	10	𝑉0	𝑉0	NOUN
cana-3842	67	11	=	=	PRON
cana-3842	67	12	{	{	PUNCT
cana-3842	67	13	𝑢	𝑢	PRON
cana-3842	67	14	∈	∈	PROPN
cana-3842	67	15	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	67	16	):	):	PUNCT
cana-3842	67	17	𝛾𝑘	𝛾𝑘	ADP
cana-3842	67	18	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	67	19	−	−	PUNCT
cana-3842	67	20	𝑣	𝑣	X
cana-3842	67	21	)	)	PUNCT
cana-3842	67	22	=	=	PUNCT
cana-3842	67	23	𝛾𝑘	𝛾𝑘	ADP
cana-3842	67	24	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	67	25	)	)	PUNCT
cana-3842	67	26	}	}	PUNCT
cana-3842	67	27	,	,	PUNCT
cana-3842	67	28	𝑉+	𝑉+	X
cana-3842	67	29	=	=	PUNCT
cana-3842	67	30	{	{	PUNCT
cana-3842	67	31	𝑢	𝑢	X
cana-3842	67	32	∈	∈	PROPN
cana-3842	67	33	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	67	34	):	):	PUNCT
cana-3842	67	35	𝛾𝑘	𝛾𝑘	ADP
cana-3842	67	36	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	67	37	−	−	NOUN
cana-3842	67	38	𝑣	𝑣	X
cana-3842	67	39	)	)	PUNCT
cana-3842	67	40	>	>	X
cana-3842	67	41	𝛾𝑘	𝛾𝑘	ADP
cana-3842	67	42	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	67	43	)	)	PUNCT
cana-3842	67	44	}	}	PUNCT
cana-3842	67	45	and	and	CCONJ
cana-3842	67	46	𝑉−	𝑉−	X
cana-3842	67	47	=	=	X
cana-3842	67	48	{	{	PUNCT
cana-3842	67	49	𝑢	𝑢	PRON
cana-3842	67	50	∈	∈	PROPN
cana-3842	67	51	𝑉(𝐺	𝑉(𝐺	NOUN
cana-3842	67	52	):	):	PUNCT
cana-3842	67	53	𝛾𝑘	𝛾𝑘	ADP
cana-3842	67	54	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	67	55	−	−	NOUN
cana-3842	67	56	𝑣	𝑣	X
cana-3842	67	57	)	)	PUNCT
cana-3842	67	58	<	<	X
cana-3842	67	59	𝛾𝑘	𝛾𝑘	ADP
cana-3842	67	60	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	67	61	)	)	PUNCT
cana-3842	67	62	}	}	PUNCT
cana-3842	67	63	.	.	PUNCT
cana-3842	68	1	similarly	similarly	ADV
cana-3842	68	2	,	,	PUNCT
cana-3842	68	3	the	the	DET
cana-3842	68	4	edge	edge	NOUN
cana-3842	68	5	set	set	NOUN
cana-3842	68	6	can	can	AUX
cana-3842	68	7	be	be	AUX
cana-3842	68	8	partitioned	partition	VERB
cana-3842	68	9	into	into	ADP
cana-3842	68	10	𝐸0	𝐸0	ADJ
cana-3842	68	11	=	=	SYM
cana-3842	68	12	{	{	PUNCT
cana-3842	68	13	𝑥𝑦	𝑥𝑦	PROPN
cana-3842	68	14	∈	∈	PROPN
cana-3842	68	15	𝐸(𝐺	𝐸(𝐺	NOUN
cana-3842	68	16	)	)	PUNCT
cana-3842	68	17	∶	∶	NOUN
cana-3842	68	18	𝛾𝑘	𝛾𝑘	ADP
cana-3842	68	19	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	68	20	−	−	PUNCT
cana-3842	68	21	𝑥𝑦	𝑥𝑦	NOUN
cana-3842	68	22	)	)	PUNCT
cana-3842	68	23	=	=	PUNCT
cana-3842	68	24	𝛾𝑘	𝛾𝑘	ADP
cana-3842	68	25	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	68	26	)	)	PUNCT
cana-3842	68	27	}	}	PUNCT
cana-3842	68	28	and	and	CCONJ
cana-3842	68	29	𝐸+	𝐸+	PUNCT
cana-3842	68	30	=	=	NOUN
cana-3842	68	31	{	{	PUNCT
cana-3842	68	32	𝑥𝑦	𝑥𝑦	PROPN
cana-3842	68	33	∈	∈	PROPN
cana-3842	68	34	𝐸(𝐺	𝐸(𝐺	NOUN
cana-3842	68	35	):	):	PUNCT
cana-3842	68	36	𝛾𝑘	𝛾𝑘	ADP
cana-3842	68	37	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	68	38	−	−	PUNCT
cana-3842	68	39	𝑥𝑦	𝑥𝑦	NOUN
cana-3842	68	40	)	)	PUNCT
cana-3842	68	41	>	>	X
cana-3842	68	42	𝛾𝑘	𝛾𝑘	ADP
cana-3842	68	43	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	68	44	)	)	PUNCT
cana-3842	68	45	}	}	PUNCT
cana-3842	68	46	.	.	PUNCT
cana-3842	69	1	2	2	X
cana-3842	69	2	.	.	X
cana-3842	69	3	results	result	NOUN
cana-3842	69	4	:	:	PUNCT
cana-3842	69	5	theorem	theorem	VERB
cana-3842	69	6	2.1	2.1	NUM
cana-3842	69	7	.	.	PUNCT
cana-3842	70	1	for	for	ADP
cana-3842	70	2	every	every	DET
cana-3842	70	3	vertex	vertex	NOUN
cana-3842	70	4	v	v	NOUN
cana-3842	70	5	in	in	ADP
cana-3842	70	6	kn	kn	PROPN
cana-3842	70	7	,	,	PUNCT
cana-3842	70	8	𝛾𝑘	𝛾𝑘	ADP
cana-3842	70	9	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	70	10	−	−	PUNCT
cana-3842	70	11	𝑣	𝑣	X
cana-3842	70	12	)	)	PUNCT
cana-3842	70	13	=	=	PUNCT
cana-3842	70	14	𝛾𝑘	𝛾𝑘	ADP
cana-3842	70	15	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	70	16	)	)	PUNCT
cana-3842	70	17	.	.	PUNCT
cana-3842	71	1	proof	proof	NOUN
cana-3842	71	2	.	.	PUNCT
cana-3842	72	1	let	let	VERB
cana-3842	72	2	g	g	PROPN
cana-3842	72	3	=	=	PROPN
cana-3842	72	4	kn	kn	PROPN
cana-3842	72	5	be	be	AUX
cana-3842	72	6	a	a	DET
cana-3842	72	7	complete	complete	ADJ
cana-3842	72	8	graph	graph	NOUN
cana-3842	72	9	with	with	ADP
cana-3842	72	10	n	n	ADP
cana-3842	72	11	vertices	vertex	NOUN
cana-3842	72	12	.	.	PUNCT
cana-3842	73	1	on	on	ADP
cana-3842	73	2	contrary	contrary	ADV
cana-3842	73	3	,	,	PUNCT
cana-3842	73	4	assume	assume	VERB
cana-3842	73	5	that	that	SCONJ
cana-3842	73	6	𝛾𝑘	𝛾𝑘	ADP
cana-3842	73	7	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	73	8	−	−	PUNCT
cana-3842	73	9	𝑣	𝑣	X
cana-3842	73	10	)	)	PUNCT
cana-3842	73	11	≠	≠	PROPN
cana-3842	73	12	𝛾𝑘	𝛾𝑘	ADP
cana-3842	73	13	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	73	14	)	)	PUNCT
cana-3842	73	15	.	.	PUNCT
cana-3842	74	1	since	since	SCONJ
cana-3842	74	2	every	every	DET
cana-3842	74	3	vertex	vertex	NOUN
cana-3842	74	4	is	be	AUX
cana-3842	74	5	of	of	ADP
cana-3842	74	6	degree	degree	NOUN
cana-3842	74	7	𝑛	𝑛	PRON
cana-3842	74	8	−	−	NOUN
cana-3842	74	9	1	1	X
cana-3842	74	10	.	.	PUNCT
cana-3842	75	1	𝐺	𝐺	NOUN
cana-3842	75	2	−	−	PROPN
cana-3842	76	1	𝑣	𝑣	PRON
cana-3842	76	2	will	will	AUX
cana-3842	76	3	be	be	AUX
cana-3842	76	4	a	a	DET
cana-3842	76	5	graph	graph	NOUN
cana-3842	76	6	with	with	ADP
cana-3842	76	7	𝑛	𝑛	DET
cana-3842	76	8	−	−	NUM
cana-3842	76	9	1	1	NUM
cana-3842	76	10	vertices	vertex	NOUN
cana-3842	76	11	and	and	CCONJ
cana-3842	76	12	degree	degree	NOUN
cana-3842	76	13	𝑛	𝑛	DET
cana-3842	76	14	−	−	PROPN
cana-3842	76	15	2	2	NUM
cana-3842	76	16	,	,	PUNCT
cana-3842	76	17	which	which	PRON
cana-3842	76	18	will	will	AUX
cana-3842	76	19	be	be	AUX
cana-3842	76	20	a	a	DET
cana-3842	76	21	complete	complete	ADJ
cana-3842	76	22	graph	graph	NOUN
cana-3842	76	23	with	with	ADP
cana-3842	76	24	kn−1	kn−1	PROPN
cana-3842	76	25	.	.	PROPN
cana-3842	76	26	removal	removal	NOUN
cana-3842	76	27	of	of	ADP
cana-3842	76	28	vertex	vertex	NOUN
cana-3842	76	29	in	in	ADP
cana-3842	76	30	g	g	NOUN
cana-3842	76	31	,	,	PUNCT
cana-3842	76	32	does	do	AUX
cana-3842	76	33	not	not	PART
cana-3842	76	34	affect	affect	VERB
cana-3842	76	35	secure	secure	ADJ
cana-3842	76	36	domination	domination	NOUN
cana-3842	76	37	number	number	NOUN
cana-3842	76	38	.	.	PUNCT
cana-3842	77	1	therefore	therefore	ADV
cana-3842	77	2	,	,	PUNCT
cana-3842	77	3	our	our	PRON
cana-3842	77	4	assumption	assumption	NOUN
cana-3842	77	5	is	be	AUX
cana-3842	77	6	wrong	wrong	ADJ
cana-3842	77	7	.	.	PUNCT
cana-3842	78	1	theorem	theorem	VERB
cana-3842	78	2	2.2	2.2	NUM
cana-3842	78	3	.	.	PUNCT
cana-3842	79	1	let	let	VERB
cana-3842	79	2	𝐺	𝐺	PROPN
cana-3842	79	3	=	=	PUNCT
cana-3842	79	4	𝑆1,𝑟	𝑆1,𝑟	PROPN
cana-3842	79	5	and	and	CCONJ
cana-3842	79	6	v	v	NOUN
cana-3842	79	7	=	=	PUNCT
cana-3842	79	8	δ(g	δ(g	X
cana-3842	79	9	)	)	PUNCT
cana-3842	79	10	−	−	PROPN
cana-3842	79	11	1	1	NUM
cana-3842	79	12	,	,	PUNCT
cana-3842	79	13	then	then	ADV
cana-3842	79	14	𝛾𝑘	𝛾𝑘	ADP
cana-3842	79	15	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	79	16	−	−	PROPN
cana-3842	79	17	𝑣	𝑣	X
cana-3842	79	18	)	)	PUNCT
cana-3842	79	19	>	>	X
cana-3842	79	20	𝛾𝑘	𝛾𝑘	ADP
cana-3842	79	21	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	79	22	)	)	PUNCT
cana-3842	79	23	.	.	PUNCT
cana-3842	80	1	proof	proof	NOUN
cana-3842	80	2	.	.	PUNCT
cana-3842	81	1	let	let	VERB
cana-3842	81	2	g	g	PROPN
cana-3842	81	3	=	=	SYM
cana-3842	81	4	s1,r	s1,r	PROPN
cana-3842	81	5	be	be	AUX
cana-3842	81	6	a	a	DET
cana-3842	81	7	star	star	NOUN
cana-3842	81	8	graph	graph	NOUN
cana-3842	81	9	,	,	PUNCT
cana-3842	81	10	where	where	SCONJ
cana-3842	81	11	r	r	NOUN
cana-3842	81	12	=	=	SYM
cana-3842	81	13	{	{	PUNCT
cana-3842	81	14	𝑟1	𝑟1	NOUN
cana-3842	81	15	,	,	PUNCT
cana-3842	81	16	𝑟2	𝑟2	NOUN
cana-3842	81	17	,	,	PUNCT
cana-3842	81	18	.	.	PUNCT
cana-3842	81	19	.	.	PUNCT
cana-3842	81	20	.	.	PUNCT
cana-3842	82	1	𝑟𝑛−1	𝑟𝑛−1	NOUN
cana-3842	82	2	}	}	PUNCT
cana-3842	82	3	.	.	PUNCT
cana-3842	83	1	on	on	ADP
cana-3842	83	2	contrary	contrary	ADV
cana-3842	83	3	,	,	PUNCT
cana-3842	83	4	assume	assume	VERB
cana-3842	83	5	that	that	SCONJ
cana-3842	83	6	𝛾𝑘	𝛾𝑘	ADP
cana-3842	83	7	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	83	8	−	−	PUNCT
cana-3842	83	9	𝑣	𝑣	X
cana-3842	83	10	)	)	PUNCT
cana-3842	83	11	<	<	X
cana-3842	83	12	𝛾𝑘	𝛾𝑘	ADP
cana-3842	83	13	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	83	14	)	)	PUNCT
cana-3842	83	15	.	.	PUNCT
cana-3842	84	1	let	let	VERB
cana-3842	84	2	v	v	PART
cana-3842	84	3	be	be	AUX
cana-3842	84	4	a	a	DET
cana-3842	84	5	vertex	vertex	NOUN
cana-3842	84	6	with	with	ADP
cana-3842	84	7	degree	degree	NOUN
cana-3842	84	8	𝑛	𝑛	DET
cana-3842	84	9	−	−	PROPN
cana-3842	84	10	1	1	NUM
cana-3842	84	11	,	,	PUNCT
cana-3842	84	12	removal	removal	NOUN
cana-3842	84	13	of	of	ADP
cana-3842	84	14	vertex	vertex	NOUN
cana-3842	84	15	v	v	NOUN
cana-3842	84	16	,	,	PUNCT
cana-3842	84	17	will	will	AUX
cana-3842	84	18	disconnect	disconnect	VERB
cana-3842	84	19	the	the	DET
cana-3842	84	20	graph	graph	NOUN
cana-3842	84	21	.	.	PUNCT
cana-3842	85	1	we	we	PRON
cana-3842	85	2	obtain	obtain	VERB
cana-3842	85	3	a	a	DET
cana-3842	85	4	graph	graph	NOUN
cana-3842	85	5	with	with	ADP
cana-3842	85	6	𝑛	𝑛	DET
cana-3842	85	7	−	−	NUM
cana-3842	85	8	1	1	NUM
cana-3842	85	9	vertices	vertex	NOUN
cana-3842	85	10	and	and	CCONJ
cana-3842	85	11	𝑛	𝑛	DET
cana-3842	85	12	−	−	PROPN
cana-3842	85	13	1	1	NUM
cana-3842	85	14	component	component	NOUN
cana-3842	85	15	,	,	PUNCT
cana-3842	85	16	which	which	PRON
cana-3842	85	17	increase	increase	VERB
cana-3842	85	18	sidn	sidn	NOUN
cana-3842	85	19	.	.	PUNCT
cana-3842	86	1	therefore	therefore	ADV
cana-3842	86	2	,	,	PUNCT
cana-3842	86	3	our	our	PRON
cana-3842	86	4	assumption	assumption	NOUN
cana-3842	86	5	is	be	AUX
cana-3842	86	6	wrong	wrong	ADJ
cana-3842	86	7	.	.	PUNCT
cana-3842	87	1	theorem	theorem	VERB
cana-3842	87	2	2.3	2.3	NUM
cana-3842	87	3	.	.	PUNCT
cana-3842	88	1	a	a	DET
cana-3842	88	2	vertex	vertex	NOUN
cana-3842	88	3	v	v	NOUN
cana-3842	88	4	in	in	ADP
cana-3842	88	5	𝑉−	𝑉−	PROPN
cana-3842	88	6	iff	iff	PROPN
cana-3842	88	7	pn[v	pn[v	PROPN
cana-3842	88	8	,	,	PUNCT
cana-3842	88	9	d	d	X
cana-3842	88	10	]	]	X
cana-3842	88	11	=	=	SYM
cana-3842	88	12	v	v	NOUN
cana-3842	88	13	for	for	ADP
cana-3842	88	14	some	some	PRON
cana-3842	88	15	𝛾𝑘	𝛾𝑘	ADP
cana-3842	88	16	𝑠	𝑠	PROPN
cana-3842	88	17	set	set	VERB
cana-3842	88	18	d	d	NOUN
cana-3842	88	19	containing	contain	VERB
cana-3842	88	20	v.	v.	ADP
cana-3842	88	21	proof	proof	NOUN
cana-3842	88	22	.	.	PUNCT
cana-3842	89	1	let	let	VERB
cana-3842	89	2	v	v	X
cana-3842	89	3	∈	∈	NOUN
cana-3842	89	4	𝑉−and	𝑉−and	X
cana-3842	89	5	s	s	AUX
cana-3842	89	6	be	be	AUX
cana-3842	89	7	a	a	DET
cana-3842	89	8	𝛾𝑘	𝛾𝑘	ADP
cana-3842	89	9	𝑠	𝑠	PROPN
cana-3842	89	10	set	set	NOUN
cana-3842	89	11	of	of	ADP
cana-3842	89	12	g	g	PROPN
cana-3842	89	13	−	−	PROPN
cana-3842	90	1	v.	v.	CCONJ
cana-3842	90	2	then	then	ADV
cana-3842	90	3	d	d	PROPN
cana-3842	90	4	=	=	SYM
cana-3842	90	5	s	s	X
cana-3842	90	6	∪	∪	X
cana-3842	90	7	{	{	PUNCT
cana-3842	90	8	v	v	NOUN
cana-3842	90	9	}	}	PUNCT
cana-3842	90	10	is	be	AUX
cana-3842	90	11	a	a	DET
cana-3842	90	12	𝛾𝑘	𝛾𝑘	ADP
cana-3842	90	13	𝑠	𝑠	PROPN
cana-3842	90	14	set	set	NOUN
cana-3842	90	15	of	of	ADP
cana-3842	90	16	g.	g.	PROPN
cana-3842	90	17	if	if	SCONJ
cana-3842	90	18	s	s	PROPN
cana-3842	90	19	contains	contain	VERB
cana-3842	90	20	a	a	DET
cana-3842	90	21	vertex	vertex	NOUN
cana-3842	90	22	of	of	ADP
cana-3842	90	23	n(v	n(v	PROPN
cana-3842	90	24	)	)	PUNCT
cana-3842	90	25	,	,	PUNCT
cana-3842	90	26	then	then	ADV
cana-3842	90	27	s	s	VERB
cana-3842	90	28	is	be	AUX
cana-3842	90	29	a	a	DET
cana-3842	90	30	dominating	dominating	NOUN
cana-3842	90	31	set	set	NOUN
cana-3842	90	32	of	of	ADP
cana-3842	90	33	g	g	NOUN
cana-3842	90	34	,	,	PUNCT
cana-3842	90	35	which	which	PRON
cana-3842	90	36	contradicts	contradict	VERB
cana-3842	90	37	our	our	PRON
cana-3842	90	38	assumption	assumption	NOUN
cana-3842	90	39	.	.	PUNCT
cana-3842	91	1	thus	thus	ADV
cana-3842	91	2	,	,	PUNCT
cana-3842	91	3	pn[v	pn[v	PROPN
cana-3842	91	4	,	,	PUNCT
cana-3842	91	5	d	d	X
cana-3842	91	6	]	]	X
cana-3842	91	7	=	=	PUNCT
cana-3842	91	8	{	{	PUNCT
cana-3842	91	9	v	v	NOUN
cana-3842	91	10	}	}	PUNCT
cana-3842	91	11	.	.	PUNCT
cana-3842	92	1	conversely	conversely	ADV
cana-3842	92	2	,	,	PUNCT
cana-3842	92	3	d	d	PRON
cana-3842	92	4	−	−	PROPN
cana-3842	92	5	{	{	PUNCT
cana-3842	92	6	v	v	NOUN
cana-3842	92	7	}	}	PUNCT
cana-3842	92	8	dominates	dominate	VERB
cana-3842	92	9	𝐺	𝐺	PROPN
cana-3842	92	10	−	−	PROPN
cana-3842	92	11	𝑣	𝑣	NOUN
cana-3842	92	12	,	,	PUNCT
cana-3842	92	13	therefore	therefore	ADV
cana-3842	92	14	v	v	ADP
cana-3842	92	15	∈	∈	PROPN
cana-3842	92	16	𝑉−.	𝑉−.	NUM
cana-3842	92	17	theorem	theorem	VERB
cana-3842	92	18	2.4	2.4	NUM
cana-3842	92	19	.	.	PUNCT
cana-3842	93	1	for	for	ADP
cana-3842	93	2	any	any	DET
cana-3842	93	3	tree	tree	NOUN
cana-3842	93	4	t	t	NOUN
cana-3842	93	5	with	with	ADP
cana-3842	93	6	n	n	PRON
cana-3842	93	7	≥	≥	NUM
cana-3842	93	8	2	2	NUM
cana-3842	93	9	,	,	PUNCT
cana-3842	93	10	there	there	PRON
cana-3842	93	11	exists	exist	VERB
cana-3842	93	12	a	a	DET
cana-3842	93	13	vertex	vertex	NOUN
cana-3842	93	14	v	v	ADP
cana-3842	93	15	∈	∈	PROPN
cana-3842	93	16	v	v	NOUN
cana-3842	93	17	(	(	PUNCT
cana-3842	93	18	g	g	NOUN
cana-3842	93	19	)	)	PUNCT
cana-3842	93	20	such	such	ADJ
cana-3842	93	21	that	that	SCONJ
cana-3842	93	22	𝛾𝑘	𝛾𝑘	ADP
cana-3842	93	23	𝑠(𝑇	𝑠(𝑇	ADJ
cana-3842	93	24	−	−	ADP
cana-3842	93	25	𝑣	𝑣	NOUN
cana-3842	93	26	)	)	PUNCT
cana-3842	93	27	=	=	PUNCT
cana-3842	93	28	𝛾𝑘	𝛾𝑘	ADP
cana-3842	93	29	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	93	30	)	)	PUNCT
cana-3842	93	31	.	.	PUNCT
cana-3842	94	1	proof	proof	NOUN
cana-3842	94	2	.	.	PUNCT
cana-3842	95	1	assume	assume	VERB
cana-3842	95	2	that	that	SCONJ
cana-3842	95	3	t	t	PROPN
cana-3842	95	4	has	have	AUX
cana-3842	95	5	atleast	atleast	VERB
cana-3842	95	6	one	one	NUM
cana-3842	95	7	vertex	vertex	NOUN
cana-3842	95	8	v	v	NOUN
cana-3842	95	9	with	with	ADP
cana-3842	95	10	deg(v	deg(v	PROPN
cana-3842	95	11	)	)	PUNCT
cana-3842	95	12	≥	≥	NOUN
cana-3842	95	13	2	2	NUM
cana-3842	95	14	that	that	PRON
cana-3842	95	15	is	be	AUX
cana-3842	95	16	adjacent	adjacent	ADJ
cana-3842	95	17	to	to	AUX
cana-3842	95	18	atleast	atleast	VERB
cana-3842	95	19	one	one	NUM
cana-3842	95	20	endvertex	endvertex	NOUN
cana-3842	95	21	and	and	CCONJ
cana-3842	95	22	at	at	ADP
cana-3842	95	23	most	most	ADJ
cana-3842	95	24	one	one	NUM
cana-3842	95	25	non	non	NOUN
cana-3842	95	26	endvertex	endvertex	NOUN
cana-3842	95	27	.	.	PUNCT
cana-3842	96	1	if	if	SCONJ
cana-3842	96	2	v	v	NOUN
cana-3842	96	3	is	be	AUX
cana-3842	96	4	adjacent	adjacent	ADJ
cana-3842	96	5	to	to	ADP
cana-3842	96	6	two	two	NUM
cana-3842	96	7	or	or	CCONJ
cana-3842	96	8	more	more	ADJ
cana-3842	96	9	endvertices	endvertice	NOUN
cana-3842	96	10	𝑟1	𝑟1	NOUN
cana-3842	96	11	and	and	CCONJ
cana-3842	96	12	𝑟2	𝑟2	NOUN
cana-3842	96	13	,	,	PUNCT
cana-3842	96	14	then	then	ADV
cana-3842	96	15	v	v	NOUN
cana-3842	96	16	is	be	AUX
cana-3842	96	17	in	in	ADP
cana-3842	96	18	every	every	DET
cana-3842	96	19	𝛾𝑘	𝛾𝑘	ADP
cana-3842	96	20	𝑠	𝑠	PROPN
cana-3842	96	21	set	set	VERB
cana-3842	96	22	for	for	ADP
cana-3842	96	23	t	t	PROPN
cana-3842	96	24	and	and	CCONJ
cana-3842	96	25	𝛾𝑘	𝛾𝑘	ADP
cana-3842	96	26	𝑠(𝑇	𝑠(𝑇	PROPN
cana-3842	96	27	−	−	PROPN
cana-3842	96	28	𝑟1	𝑟1	NOUN
cana-3842	96	29	)	)	PUNCT
cana-3842	96	30	=	=	SYM
cana-3842	96	31	𝛾𝑘	𝛾𝑘	ADP
cana-3842	96	32	𝑠(𝑇	𝑠(𝑇	NOUN
cana-3842	96	33	)	)	PUNCT
cana-3842	96	34	.	.	PUNCT
cana-3842	97	1	if	if	SCONJ
cana-3842	97	2	not	not	PART
cana-3842	97	3	,	,	PUNCT
cana-3842	97	4	then	then	ADV
cana-3842	97	5	v	v	NOUN
cana-3842	97	6	is	be	AUX
cana-3842	97	7	adjacent	adjacent	ADJ
cana-3842	97	8	to	to	ADP
cana-3842	97	9	one	one	NUM
cana-3842	97	10	endvertex	endvertex	NOUN
cana-3842	97	11	r	r	NOUN
cana-3842	97	12	and	and	CCONJ
cana-3842	97	13	deg	deg	NOUN
cana-3842	97	14	=	=	NOUN
cana-3842	98	1	2	2	X
cana-3842	98	2	.	.	PUNCT
cana-3842	98	3	let	let	VERB
cana-3842	98	4	𝑇′=	𝑇′=	PROPN
cana-3842	98	5	t	t	ADP
cana-3842	98	6	−	−	NOUN
cana-3842	98	7	v	v	ADP
cana-3842	98	8	−	−	PROPN
cana-3842	98	9	r.	r.	NOUN
cana-3842	98	10	for	for	ADP
cana-3842	98	11	any	any	DET
cana-3842	98	12	graph	graph	NOUN
cana-3842	98	13	g	g	NOUN
cana-3842	98	14	,	,	PUNCT
cana-3842	98	15	if	if	SCONJ
cana-3842	98	16	deg(r	deg(r	PROPN
cana-3842	98	17	)	)	PUNCT
cana-3842	98	18	−	−	PROPN
cana-3842	98	19	1	1	NUM
cana-3842	98	20	,	,	PUNCT
cana-3842	98	21	then	then	ADV
cana-3842	98	22	𝛾𝑘	𝛾𝑘	ADP
cana-3842	98	23	𝑠(𝐺	𝑠(𝐺	PROPN
cana-3842	98	24	−	−	PROPN
cana-3842	98	25	𝑟	𝑟	X
cana-3842	98	26	)	)	PUNCT
cana-3842	98	27	≤	≤	NOUN
cana-3842	98	28	𝛾𝑘	𝛾𝑘	ADP
cana-3842	98	29	𝑠(𝐺	𝑠(𝐺	NUM
cana-3842	98	30	)	)	PUNCT
cana-3842	98	31	.	.	PUNCT
cana-3842	99	1	hence	hence	ADV
cana-3842	99	2	𝛾𝑘	𝛾𝑘	ADP
cana-3842	99	3	𝑠(𝑇′	𝑠(𝑇′	PROPN
cana-3842	99	4	)	)	PUNCT
cana-3842	99	5	≤	≤	NOUN
cana-3842	99	6	𝛾𝑘	𝛾𝑘	ADP
cana-3842	99	7	𝑠(𝑇	𝑠(𝑇	NOUN
cana-3842	99	8	)	)	PUNCT
cana-3842	99	9	.	.	PUNCT
cana-3842	100	1	however	however	ADV
cana-3842	100	2	,	,	PUNCT
cana-3842	100	3	𝛾𝑘	𝛾𝑘	ADP
cana-3842	100	4	𝑠(𝑇′	𝑠(𝑇′	PROPN
cana-3842	100	5	)	)	PUNCT
cana-3842	100	6	≤	≤	NOUN
cana-3842	100	7	𝛾𝑘	𝛾𝑘	ADP
cana-3842	100	8	𝑠(𝑇	𝑠(𝑇	NOUN
cana-3842	100	9	)	)	PUNCT
cana-3842	100	10	−	−	PROPN
cana-3842	100	11	1	1	X
cana-3842	100	12	.	.	PUNCT
cana-3842	101	1	if	if	SCONJ
cana-3842	101	2	𝛾𝑘	𝛾𝑘	ADP
cana-3842	101	3	𝑠(𝑇′	𝑠(𝑇′	PROPN
cana-3842	101	4	)	)	PUNCT
cana-3842	102	1	=	=	SYM
cana-3842	102	2	𝛾𝑘	𝛾𝑘	ADP
cana-3842	102	3	𝑠(𝑇	𝑠(𝑇	NOUN
cana-3842	102	4	)	)	PUNCT
cana-3842	102	5	−	−	PROPN
cana-3842	102	6	1	1	NUM
cana-3842	102	7	,	,	PUNCT
cana-3842	102	8	then	then	ADV
cana-3842	102	9	𝛾𝑘	𝛾𝑘	ADP
cana-3842	102	10	𝑠(𝑇	𝑠(𝑇	NOUN
cana-3842	102	11	)	)	PUNCT
cana-3842	102	12	≤	≤	NOUN
cana-3842	102	13	𝛾𝑘	𝛾𝑘	ADP
cana-3842	102	14	𝑠(𝑇	𝑠(𝑇	PROPN
cana-3842	102	15	−	−	PROPN
cana-3842	102	16	𝑣	𝑣	NOUN
cana-3842	102	17	)	)	PUNCT
cana-3842	102	18	.	.	PUNCT
cana-3842	103	1	otherwise	otherwise	ADV
cana-3842	103	2	,	,	PUNCT
cana-3842	103	3	𝛾𝑘	𝛾𝑘	ADP
cana-3842	103	4	𝑠(𝑇′	𝑠(𝑇′	PROPN
cana-3842	103	5	)	)	PUNCT
cana-3842	104	1	=	=	SYM
cana-3842	104	2	𝛾𝑘	𝛾𝑘	ADP
cana-3842	104	3	𝑠(𝑇	𝑠(𝑇	NOUN
cana-3842	104	4	)	)	PUNCT
cana-3842	104	5	=	=	SYM
cana-3842	104	6	𝛾𝑘	𝛾𝑘	ADP
cana-3842	104	7	𝑠(𝑇	𝑠(𝑇	NOUN
cana-3842	104	8	−	−	NOUN
cana-3842	104	9	𝑣	𝑣	NOUN
cana-3842	104	10	)	)	PUNCT
cana-3842	104	11	.	.	PUNCT
cana-3842	105	1	3	3	X
cana-3842	105	2	.	.	X
cana-3842	105	3	conclusions	conclusion	NOUN
cana-3842	105	4	in	in	ADP
cana-3842	105	5	this	this	DET
cana-3842	105	6	article	article	NOUN
cana-3842	105	7	,	,	PUNCT
cana-3842	105	8	we	we	PRON
cana-3842	105	9	have	have	VERB
cana-3842	105	10	studies	study	NOUN
cana-3842	105	11	introduced	introduce	VERB
cana-3842	105	12	the	the	DET
cana-3842	105	13	concept	concept	NOUN
cana-3842	105	14	of	of	ADP
cana-3842	105	15	secure	secure	ADJ
cana-3842	105	16	integer	integer	NOUN
cana-3842	105	17	domination	domination	NOUN
cana-3842	105	18	in	in	ADP
cana-3842	105	19	graphs	graph	NOUN
cana-3842	105	20	.	.	PUNCT
cana-3842	106	1	we	we	PRON
cana-3842	106	2	have	have	AUX
cana-3842	106	3	observed	observe	VERB
cana-3842	106	4	the	the	DET
cana-3842	106	5	changing	change	VERB
cana-3842	106	6	and	and	CCONJ
cana-3842	106	7	unchanging	unchanging	ADJ
cana-3842	106	8	behavior	behavior	NOUN
cana-3842	106	9	of	of	ADP
cana-3842	106	10	secure	secure	ADJ
cana-3842	106	11	integer	integer	NOUN
cana-3842	106	12	domination	domination	NOUN
cana-3842	106	13	in	in	ADP
cana-3842	106	14	some	some	DET
cana-3842	106	15	graphs	graph	NOUN
cana-3842	106	16	.	.	PUNCT
cana-3842	107	1	to	to	PART
cana-3842	107	2	generalize	generalize	VERB
cana-3842	107	3	,	,	PUNCT
cana-3842	107	4	the	the	DET
cana-3842	107	5	changing	change	VERB
cana-3842	107	6	and	and	CCONJ
cana-3842	107	7	unchanging	unchanging	ADJ
cana-3842	107	8	secure	secure	ADJ
cana-3842	107	9	integer	integer	NOUN
cana-3842	107	10	domination	domination	NOUN
cana-3842	107	11	in	in	ADP
cana-3842	107	12	graph	graph	NOUN
cana-3842	107	13	is	be	AUX
cana-3842	107	14	open	open	ADJ
cana-3842	107	15	.	.	PUNCT
cana-3842	108	1	funding	fund	VERB
cana-3842	108	2	this	this	DET
cana-3842	108	3	research	research	NOUN
cana-3842	108	4	received	receive	VERB
cana-3842	108	5	no	no	DET
cana-3842	108	6	specific	specific	ADJ
cana-3842	108	7	grant	grant	NOUN
cana-3842	108	8	from	from	ADP
cana-3842	108	9	public	public	ADJ
cana-3842	108	10	,	,	PUNCT
cana-3842	108	11	commercial	commercial	ADJ
cana-3842	108	12	,	,	PUNCT
cana-3842	108	13	or	or	CCONJ
cana-3842	108	14	not	not	PART
cana-3842	108	15	-	-	PUNCT
cana-3842	108	16	for	for	ADP
cana-3842	108	17	-	-	PUNCT
cana-3842	108	18	profit	profit	NOUN
cana-3842	108	19	funding	funding	NOUN
cana-3842	108	20	communications	communication	NOUN
cana-3842	108	21	on	on	ADP
cana-3842	108	22	applied	apply	VERB
cana-3842	108	23	nonlinear	nonlinear	ADJ
cana-3842	108	24	analysis	analysis	NOUN
cana-3842	108	25	issn	issn	NOUN
cana-3842	108	26	:	:	PUNCT
cana-3842	108	27	1074	1074	NUM
cana-3842	108	28	-	-	PUNCT
cana-3842	108	29	133x	133x	NUM
cana-3842	108	30	vol	vol	NOUN
cana-3842	108	31	32	32	NUM
cana-3842	108	32	no	no	NOUN
cana-3842	108	33	.	.	PUNCT
cana-3842	109	1	9s	9s	NUM
cana-3842	109	2	(	(	PUNCT
cana-3842	109	3	2025	2025	NUM
cana-3842	109	4	)	)	PUNCT
cana-3842	110	1	118	118	NUM
cana-3842	110	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-3842	110	3	agencies	agency	NOUN
cana-3842	110	4	.	.	PUNCT
cana-3842	111	1	acknowledgments	acknowledgment	NOUN
cana-3842	111	2	the	the	DET
cana-3842	111	3	authors	author	NOUN
cana-3842	111	4	wish	wish	VERB
cana-3842	111	5	to	to	PART
cana-3842	111	6	thank	thank	VERB
cana-3842	111	7	the	the	DET
cana-3842	111	8	management	management	NOUN
cana-3842	111	9	of	of	ADP
cana-3842	111	10	alliance	alliance	NOUN
cana-3842	111	11	university	university	PROPN
cana-3842	111	12	,	,	PUNCT
cana-3842	111	13	bengaluru	bengaluru	PROPN
cana-3842	111	14	,	,	PUNCT
cana-3842	111	15	karnataka	karnataka	PROPN
cana-3842	111	16	562106	562106	NUM
cana-3842	111	17	,	,	PUNCT
cana-3842	111	18	india	india	PROPN
cana-3842	111	19	.	.	PROPN
cana-3842	111	20	,	,	PUNCT
cana-3842	111	21	for	for	ADP
cana-3842	111	22	their	their	PRON
cana-3842	111	23	continuous	continuous	ADJ
cana-3842	111	24	support	support	NOUN
cana-3842	111	25	and	and	CCONJ
cana-3842	111	26	encouragement	encouragement	NOUN
cana-3842	111	27	to	to	PART
cana-3842	111	28	carry	carry	VERB
cana-3842	111	29	out	out	ADP
cana-3842	111	30	this	this	DET
cana-3842	111	31	research	research	NOUN
cana-3842	111	32	work	work	NOUN
cana-3842	111	33	.	.	PUNCT
cana-3842	112	1	conflicts	conflict	NOUN
cana-3842	112	2	of	of	ADP
cana-3842	112	3	interest	interest	NOUN
cana-3842	112	4	the	the	DET
cana-3842	112	5	authors	author	NOUN
cana-3842	112	6	declare	declare	VERB
cana-3842	112	7	that	that	SCONJ
cana-3842	112	8	none	none	NOUN
cana-3842	112	9	of	of	ADP
cana-3842	112	10	the	the	DET
cana-3842	112	11	work	work	NOUN
cana-3842	112	12	reported	report	VERB
cana-3842	112	13	in	in	ADP
cana-3842	112	14	this	this	DET
cana-3842	112	15	study	study	NOUN
cana-3842	112	16	could	could	AUX
cana-3842	112	17	have	have	AUX
cana-3842	112	18	been	be	AUX
cana-3842	112	19	influenced	influence	VERB
cana-3842	112	20	by	by	ADP
cana-3842	112	21	any	any	DET
cana-3842	112	22	known	known	ADJ
cana-3842	112	23	competing	compete	VERB
cana-3842	112	24	financial	financial	ADJ
cana-3842	112	25	interests	interest	NOUN
cana-3842	112	26	or	or	CCONJ
cana-3842	112	27	personal	personal	ADJ
cana-3842	112	28	relationships	relationship	NOUN
cana-3842	112	29	.	.	PUNCT
cana-3842	113	1	references	reference	NOUN
cana-3842	113	2	[	[	X
cana-3842	113	3	1	1	NUM
cana-3842	113	4	]	]	PUNCT
cana-3842	113	5	w.	w.	PROPN
cana-3842	113	6	goddard	goddard	PROPN
cana-3842	113	7	and	and	CCONJ
cana-3842	113	8	m.	m.	PROPN
cana-3842	113	9	a.	a.	PROPN
cana-3842	113	10	henning	henning	PROPN
cana-3842	113	11	,	,	PUNCT
cana-3842	113	12	“	"	PUNCT
cana-3842	113	13	real	real	ADJ
cana-3842	113	14	and	and	CCONJ
cana-3842	113	15	integer	integer	NOUN
cana-3842	113	16	domination	domination	NOUN
cana-3842	113	17	in	in	ADP
cana-3842	113	18	graphs	graph	NOUN
cana-3842	113	19	”	"	PUNCT
cana-3842	113	20	,	,	PUNCT
cana-3842	113	21	discrete	discrete	ADJ
cana-3842	113	22	math	math	NOUN
cana-3842	113	23	,	,	PUNCT
cana-3842	113	24	pp	pp	ADP
cana-3842	113	25	.	.	PUNCT
cana-3842	114	1	61	61	NUM
cana-3842	114	2	-	-	SYM
cana-3842	114	3	75	75	NUM
cana-3842	114	4	,	,	PUNCT
cana-3842	114	5	1999	1999	NUM
cana-3842	114	6	.	.	PUNCT
cana-3842	115	1	[	[	X
cana-3842	115	2	2	2	NUM
cana-3842	115	3	]	]	X
cana-3842	115	4	b.	b.	PROPN
cana-3842	115	5	bresar	bresar	PROPN
cana-3842	115	6	,	,	PUNCT
cana-3842	115	7	m.	m.	NOUN
cana-3842	115	8	a.	a.	PROPN
cana-3842	115	9	henning	henning	PROPN
cana-3842	115	10	and	and	CCONJ
cana-3842	115	11	s.	s.	PROPN
cana-3842	115	12	klavzar	klavzar	PROPN
cana-3842	115	13	,	,	PUNCT
cana-3842	115	14	“	"	PUNCT
cana-3842	115	15	on	on	ADP
cana-3842	115	16	integer	integer	NOUN
cana-3842	115	17	domination	domination	NOUN
cana-3842	115	18	in	in	ADP
cana-3842	115	19	graphs	graph	NOUN
cana-3842	115	20	and	and	CCONJ
cana-3842	115	21	vizing	vize	VERB
cana-3842	115	22	like	like	ADP
cana-3842	115	23	problem	problem	NOUN
cana-3842	115	24	”	"	PUNCT
cana-3842	115	25	,	,	PUNCT
cana-3842	115	26	taiwanese	taiwanese	ADJ
cana-3842	115	27	journal	journal	NOUN
cana-3842	115	28	of	of	ADP
cana-3842	115	29	math	math	NOUN
cana-3842	115	30	,	,	PUNCT
cana-3842	115	31	pp	pp	ADJ
cana-3842	115	32	.	.	PUNCT
cana-3842	116	1	1317	1317	NUM
cana-3842	116	2	-	-	SYM
cana-3842	116	3	1328	1328	NUM
cana-3842	116	4	,	,	PUNCT
cana-3842	116	5	2006	2006	NUM
cana-3842	116	6	.	.	PUNCT
cana-3842	117	1	[	[	X
cana-3842	117	2	3	3	X
cana-3842	117	3	]	]	X
cana-3842	117	4	g.	g.	PROPN
cana-3842	117	5	s.	s.	PROPN
cana-3842	117	6	domke	domke	PROPN
cana-3842	117	7	,	,	PUNCT
cana-3842	117	8	s.	s.	PROPN
cana-3842	117	9	t.	t.	PROPN
cana-3842	117	10	hedetniemi	hedetniemi	PROPN
cana-3842	117	11	,	,	PUNCT
cana-3842	117	12	r.	r.	PROPN
cana-3842	117	13	c	c	PROPN
cana-3842	117	14	.laskarandg	.laskarandg	PROPN
cana-3842	117	15	,	,	PUNCT
cana-3842	117	16	h.	h.	PROPN
cana-3842	117	17	fricke	fricke	PROPN
cana-3842	117	18	,	,	PUNCT
cana-3842	117	19	“	"	PUNCT
cana-3842	117	20	relationships	relationship	NOUN
cana-3842	117	21	between	between	ADP
cana-3842	117	22	integer	integer	NOUN
cana-3842	117	23	and	and	CCONJ
cana-3842	117	24	fractional	fractional	ADJ
cana-3842	117	25	parameters	parameter	NOUN
cana-3842	117	26	of	of	ADP
cana-3842	117	27	graphs	graph	NOUN
cana-3842	117	28	”	"	PUNCT
cana-3842	117	29	,	,	PUNCT
cana-3842	117	30	.	.	PUNCT
cana-3842	118	1	in	in	ADP
cana-3842	118	2	y.	y.	PROPN
cana-3842	118	3	alavi	alavi	PROPN
cana-3842	118	4	,	,	PUNCT
cana-3842	118	5	g.	g.	PROPN
cana-3842	118	6	chartrand	chartrand	PROPN
cana-3842	118	7	,	,	PUNCT
cana-3842	118	8	o.	o.	PROPN
cana-3842	118	9	r.	r.	PROPN
cana-3842	118	10	oellermann	oellermann	PROPN
cana-3842	118	11	,	,	PUNCT
cana-3842	118	12	and	and	CCONJ
cana-3842	118	13	a.	a.	PROPN
cana-3842	118	14	j.	j.	PROPN
cana-3842	118	15	schwenk	schwenk	PROPN
cana-3842	118	16	,	,	PUNCT
cana-3842	118	17	editors	editor	NOUN
cana-3842	118	18	,	,	PUNCT
cana-3842	118	19	graph	graph	NOUN
cana-3842	118	20	theory	theory	NOUN
cana-3842	118	21	,	,	PUNCT
cana-3842	118	22	combinatorics	combinatoric	NOUN
cana-3842	118	23	,	,	PUNCT
cana-3842	118	24	and	and	CCONJ
cana-3842	118	25	applications	application	NOUN
cana-3842	118	26	,	,	PUNCT
cana-3842	118	27	proc	proc	NOUN
cana-3842	118	28	.	.	PUNCT
cana-3842	118	29	sixth	sixth	ADJ
cana-3842	118	30	quad	quad	ADJ
cana-3842	118	31	.	.	PUNCT
cana-3842	118	32	conf	conf	PROPN
cana-3842	118	33	.	.	PUNCT
cana-3842	119	1	on	on	ADP
cana-3842	119	2	the	the	DET
cana-3842	119	3	theory	theory	NOUN
cana-3842	119	4	and	and	CCONJ
cana-3842	119	5	applications	application	NOUN
cana-3842	119	6	of	of	ADP
cana-3842	119	7	graphs	graph	NOUN
cana-3842	119	8	,	,	PUNCT
cana-3842	119	9	(	(	PUNCT
cana-3842	119	10	kalamazoo	kalamazoo	PROPN
cana-3842	119	11	,	,	PUNCT
cana-3842	119	12	mi	mi	PROPN
cana-3842	119	13	1988	1988	NUM
cana-3842	119	14	)	)	PUNCT
cana-3842	119	15	,	,	PUNCT
cana-3842	119	16	wiley	wiley	NOUN
cana-3842	119	17	,	,	PUNCT
cana-3842	119	18	vol	vol	NOUN
cana-3842	119	19	.	.	PROPN
cana-3842	119	20	2	2	NUM
cana-3842	119	21	,	,	PUNCT
cana-3842	119	22	pp	pp	ADJ
cana-3842	119	23	.	.	PUNCT
cana-3842	119	24	371	371	NUM
cana-3842	119	25	-	-	SYM
cana-3842	119	26	387	387	NUM
cana-3842	119	27	,	,	PUNCT
cana-3842	119	28	1991	1991	NUM
cana-3842	119	29	.	.	PUNCT
cana-3842	120	1	[	[	X
cana-3842	120	2	4	4	X
cana-3842	120	3	]	]	PUNCT
cana-3842	120	4	e.	e.	PROPN
cana-3842	120	5	j.	j.	PROPN
cana-3842	120	6	cockayne	cockayne	PROPN
cana-3842	120	7	,	,	PUNCT
cana-3842	120	8	p.	p.	NOUN
cana-3842	120	9	j.	j.	PROPN
cana-3842	121	1	p.	p.	PROPN
cana-3842	121	2	grobler	grobler	NOUN
cana-3842	121	3	,	,	PUNCT
cana-3842	121	4	w.	w.	PROPN
cana-3842	121	5	r.	r.	PROPN
cana-3842	121	6	grundlingh	grundlingh	PROPN
cana-3842	121	7	,	,	PUNCT
cana-3842	121	8	j.	j.	PROPN
cana-3842	121	9	munganga	munganga	PROPN
cana-3842	121	10	and	and	CCONJ
cana-3842	121	11	j.	j.	PROPN
cana-3842	121	12	h.	h.	PROPN
cana-3842	121	13	van	van	PROPN
cana-3842	121	14	vuuren	vuuren	PROPN
cana-3842	121	15	,	,	PUNCT
cana-3842	121	16	“	"	PUNCT
cana-3842	121	17	protection	protection	NOUN
cana-3842	121	18	of	of	ADP
cana-3842	121	19	a	a	DET
cana-3842	121	20	graph	graph	NOUN
cana-3842	121	21	”	"	PUNCT
cana-3842	121	22	,	,	PUNCT
cana-3842	121	23	util	util	PROPN
cana-3842	121	24	.	.	PUNCT
cana-3842	121	25	math	math	NOUN
cana-3842	121	26	.	.	PUNCT
cana-3842	121	27	,	,	PUNCT
cana-3842	121	28	67	67	NUM
cana-3842	121	29	,	,	PUNCT
cana-3842	121	30	pp	pp	ADJ
cana-3842	121	31	.	.	PUNCT
cana-3842	122	1	19	19	NUM
cana-3842	122	2	-	-	SYM
cana-3842	122	3	32	32	NUM
cana-3842	122	4	,	,	PUNCT
cana-3842	122	5	2005	2005	NUM
cana-3842	122	6	.	.	PUNCT
cana-3842	123	1	[	[	X
cana-3842	123	2	5	5	X
cana-3842	123	3	]	]	PUNCT
cana-3842	123	4	e.	e.	PROPN
cana-3842	123	5	j.	j.	PROPN
cana-3842	123	6	cockayne	cockayne	PROPN
cana-3842	123	7	,	,	PUNCT
cana-3842	123	8	o.	o.	PROPN
cana-3842	123	9	favaron	favaron	PROPN
cana-3842	123	10	and	and	CCONJ
cana-3842	123	11	c.	c.	PROPN
cana-3842	123	12	mynhardt	mynhardt	PROPN
cana-3842	123	13	,	,	PUNCT
cana-3842	123	14	“	"	PUNCT
cana-3842	123	15	secure	secure	ADJ
cana-3842	123	16	domination	domination	NOUN
cana-3842	123	17	,	,	PUNCT
cana-3842	123	18	weak	weak	ADJ
cana-3842	123	19	roman	roman	ADJ
cana-3842	123	20	domination	domination	NOUN
cana-3842	123	21	and	and	CCONJ
cana-3842	123	22	forbidden	forbid	VERB
cana-3842	123	23	subgraphs	subgraph	NOUN
cana-3842	123	24	”	"	PUNCT
cana-3842	123	25	,	,	PUNCT
cana-3842	123	26	bulletin	bulletin	NOUN
cana-3842	123	27	of	of	ADP
cana-3842	123	28	the	the	DET
cana-3842	123	29	institute	institute	PROPN
cana-3842	123	30	of	of	ADP
cana-3842	123	31	combinatorics	combinatoric	NOUN
cana-3842	123	32	and	and	CCONJ
cana-3842	123	33	its	its	PRON
cana-3842	123	34	applications	application	NOUN
cana-3842	123	35	39	39	NUM
cana-3842	123	36	,	,	PUNCT
cana-3842	123	37	2003	2003	NUM
cana-3842	123	38	.	.	PUNCT
cana-3842	124	1	[	[	X
cana-3842	124	2	6	6	NUM
cana-3842	124	3	]	]	X
cana-3842	124	4	o.	o.	NOUN
cana-3842	124	5	ore	ore	NOUN
cana-3842	124	6	,	,	PUNCT
cana-3842	124	7	“	"	PUNCT
cana-3842	124	8	theory	theory	NOUN
cana-3842	124	9	of	of	ADP
cana-3842	124	10	graphs	graph	NOUN
cana-3842	124	11	,	,	PUNCT
cana-3842	124	12	”	"	PUNCT
cana-3842	124	13	amer	amer	PROPN
cana-3842	124	14	.	.	PUNCT
cana-3842	124	15	math	math	PROPN
cana-3842	124	16	.	.	PUNCT
cana-3842	125	1	soc	soc	PROPN
cana-3842	125	2	.	.	PUNCT
cana-3842	126	1	colloq	colloq	PROPN
cana-3842	126	2	.	.	PUNCT
cana-3842	127	1	publ	publ	PROPN
cana-3842	127	2	.	.	PUNCT
cana-3842	127	3	,	,	PUNCT
cana-3842	127	4	providence	providence	NOUN
cana-3842	127	5	ri	ri	PROPN
cana-3842	127	6	,	,	PUNCT
cana-3842	127	7	1962	1962	NUM
cana-3842	127	8	.	.	PUNCT
cana-3842	128	1	[	[	X
cana-3842	128	2	7	7	X
cana-3842	128	3	]	]	X
cana-3842	128	4	m.	m.	NOUN
cana-3842	128	5	dettlaff	dettlaff	NOUN
cana-3842	128	6	,	,	PUNCT
cana-3842	128	7	m.	m.	NOUN
cana-3842	128	8	lemanska1	lemanska1	PROPN
cana-3842	128	9	and	and	CCONJ
cana-3842	128	10	j	j	PROPN
cana-3842	128	11	.	.	PUNCT
cana-3842	129	1	a.	a.	PROPN
cana-3842	129	2	rodr´ıguez	rodr´ıguez	PROPN
cana-3842	129	3	vel	vel	PROPN
cana-3842	129	4	ázquez	ázquez	PROPN
cana-3842	129	5	,	,	PUNCT
cana-3842	129	6	“	"	PUNCT
cana-3842	129	7	secure	secure	ADJ
cana-3842	129	8	italian	italian	ADJ
cana-3842	129	9	domination	domination	NOUN
cana-3842	129	10	in	in	ADP
cana-3842	129	11	graphs	graph	NOUN
cana-3842	129	12	”	"	PUNCT
cana-3842	129	13	,	,	PUNCT
cana-3842	129	14	journal	journal	NOUN
cana-3842	129	15	of	of	ADP
cana-3842	129	16	combinatorial	combinatorial	ADJ
cana-3842	129	17	optimization	optimization	NOUN
cana-3842	129	18	,	,	PUNCT
cana-3842	129	19	pp	pp	ADJ
cana-3842	129	20	.	.	PUNCT
cana-3842	130	1	56–72	56–72	NUM
cana-3842	130	2	,	,	PUNCT
cana-3842	130	3	2021	2021	NUM
cana-3842	130	4	.	.	PUNCT
cana-3842	131	1	[	[	X
cana-3842	131	2	8	8	NUM
cana-3842	131	3	]	]	PUNCT
cana-3842	131	4	s.	s.	PROPN
cana-3842	131	5	t.	t.	PROPN
cana-3842	131	6	hedetniemi	hedetniemi	PROPN
cana-3842	131	7	and	and	CCONJ
cana-3842	131	8	m.	m.	PROPN
cana-3842	131	9	a.	a.	PROPN
cana-3842	131	10	henning	henning	PROPN
cana-3842	131	11	,	,	PUNCT
cana-3842	131	12	“	"	PUNCT
cana-3842	131	13	defending	defend	VERB
cana-3842	131	14	the	the	DET
cana-3842	131	15	roman	roman	ADJ
cana-3842	131	16	empire	empire	NOUN
cana-3842	131	17	a	a	DET
cana-3842	131	18	new	new	ADJ
cana-3842	131	19	strategy	strategy	NOUN
cana-3842	131	20	”	"	PUNCT
cana-3842	131	21	,	,	PUNCT
cana-3842	131	22	discrete	discrete	ADJ
cana-3842	131	23	math	math	NOUN
cana-3842	131	24	.	.	PUNCT
cana-3842	132	1	266	266	NUM
cana-3842	132	2	pp	pp	ADJ
cana-3842	132	3	.	.	PUNCT
cana-3842	133	1	239–251	239–251	NUM
cana-3842	133	2	,	,	PUNCT
cana-3842	133	3	2003	2003	NUM
cana-3842	133	4	.	.	PUNCT
cana-3842	134	1	[	[	X
cana-3842	134	2	9	9	NUM
cana-3842	134	3	]	]	X
cana-3842	134	4	liu	liu	PROPN
cana-3842	134	5	and	and	CCONJ
cana-3842	134	6	g.	g.	PROPN
cana-3842	134	7	j	j	PROPN
cana-3842	134	8	chang	chang	PROPN
cana-3842	134	9	“	"	PUNCT
cana-3842	134	10	roman	roman	ADJ
cana-3842	134	11	domination	domination	NOUN
cana-3842	134	12	on	on	ADP
cana-3842	134	13	strongly	strongly	ADV
cana-3842	134	14	chordal	chordal	ADJ
cana-3842	134	15	graphs	graph	NOUN
cana-3842	134	16	”	"	PUNCT
cana-3842	134	17	,	,	PUNCT
cana-3842	134	18	j.	j.	PROPN
cana-3842	134	19	comb	comb	PROPN
cana-3842	134	20	.	.	PUNCT
cana-3842	135	1	optim	optim	ADJ
cana-3842	135	2	.	.	PUNCT
cana-3842	136	1	26	26	NUM
cana-3842	136	2	,	,	PUNCT
cana-3842	136	3	pp	pp	ADJ
cana-3842	136	4	.	.	PUNCT
cana-3842	137	1	608–619	608–619	NUM
cana-3842	137	2	,	,	PUNCT
cana-3842	137	3	2013	2013	NUM
cana-3842	137	4	.	.	PUNCT
cana-3842	138	1	[	[	X
cana-3842	138	2	10	10	NUM
cana-3842	138	3	]	]	PUNCT
cana-3842	138	4	a.	a.	PROPN
cana-3842	138	5	cabrera	cabrera	PROPN
cana-3842	138	6	martınez	martınez	PROPN
cana-3842	138	7	,	,	PUNCT
cana-3842	138	8	a.	a.	PROPN
cana-3842	138	9	estrada	estrada	PROPN
cana-3842	138	10	moreno	moreno	PROPN
cana-3842	138	11	and	and	CCONJ
cana-3842	138	12	juan	juan	PROPN
cana-3842	138	13	a.	a.	PROPN
cana-3842	138	14	rodrıguez	rodrıguez	PROPN
cana-3842	138	15	velazquez	velazquez	PROPN
cana-3842	138	16	,	,	PUNCT
cana-3842	138	17	“	"	PUNCT
cana-3842	138	18	secure	secure	ADJ
cana-3842	138	19	w	w	NOUN
cana-3842	138	20	-	-	PUNCT
cana-3842	138	21	domination	domination	NOUN
cana-3842	138	22	in	in	ADP
cana-3842	138	23	graphs	graph	NOUN
cana-3842	138	24	”	"	PUNCT
cana-3842	138	25	,	,	PUNCT
cana-3842	138	26	symmetry	symmetry	NOUN
cana-3842	138	27	12	12	NUM
cana-3842	138	28	,	,	PUNCT
cana-3842	138	29	2020	2020	NUM
cana-3842	138	30	.	.	PUNCT
cana-3842	139	1	[	[	X
cana-3842	139	2	11	11	NUM
cana-3842	139	3	]	]	X
cana-3842	139	4	douglas	douglas	PROPN
cana-3842	139	5	b.	b.	PROPN
cana-3842	139	6	west	west	PROPN
cana-3842	139	7	,	,	PUNCT
cana-3842	139	8	“	"	PUNCT
cana-3842	139	9	introduction	introduction	NOUN
cana-3842	139	10	to	to	AUX
cana-3842	139	11	graph	graph	NOUN
cana-3842	139	12	theory	theory	NOUN
cana-3842	139	13	”	"	PUNCT
cana-3842	139	14	,	,	PUNCT
cana-3842	139	15	pearson	pearson	PROPN
cana-3842	139	16	education	education	PROPN
cana-3842	139	17	,	,	PUNCT
cana-3842	139	18	inc	inc	PROPN
cana-3842	139	19	.	.	PROPN
cana-3842	139	20	,	,	PUNCT
cana-3842	139	21	2nd	2nd	PROPN
cana-3842	139	22	ed	ed	NOUN
cana-3842	139	23	,	,	PUNCT
cana-3842	139	24	india	india	PROPN
cana-3842	139	25	,	,	PUNCT
cana-3842	139	26	2001	2001	NUM
cana-3842	139	27	.	.	PUNCT