id	sid	tid	token	lemma	pos
cana-950	1	1	communications	communication	NOUN
cana-950	1	2	on	on	ADP
cana-950	1	3	applied	apply	VERB
cana-950	1	4	nonlinear	nonlinear	ADJ
cana-950	1	5	analysis	analysis	NOUN
cana-950	1	6	issn	issn	NOUN
cana-950	1	7	:	:	PUNCT
cana-950	1	8	1074	1074	NUM
cana-950	1	9	-	-	PUNCT
cana-950	1	10	133x	133x	NUM
cana-950	1	11	vol	vol	NOUN
cana-950	1	12	31	31	NUM
cana-950	1	13	no	no	NOUN
cana-950	1	14	.	.	PUNCT
cana-950	2	1	4s	4s	NUM
cana-950	2	2	(	(	PUNCT
cana-950	2	3	2024	2024	NUM
cana-950	2	4	)	)	PUNCT
cana-950	2	5	560	560	NUM
cana-950	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-950	2	7	secure	secure	ADJ
cana-950	2	8	vertex	vertex	NOUN
cana-950	2	9	edge	edge	NOUN
cana-950	2	10	domination	domination	NOUN
cana-950	2	11	of	of	ADP
cana-950	2	12	certain	certain	ADJ
cana-950	2	13	named	name	VERB
cana-950	2	14	special	special	ADJ
cana-950	2	15	graphs	graph	NOUN
cana-950	2	16	c.	c.	PROPN
cana-950	2	17	ruby	ruby	PROPN
cana-950	2	18	sharmila1	sharmila1	PROPN
cana-950	2	19	,	,	PUNCT
cana-950	2	20	s.	s.	PROPN
cana-950	2	21	meenakshi2	meenakshi2	PROPN
cana-950	2	22	1	1	NUM
cana-950	2	23	research	research	NOUN
cana-950	2	24	scholar	scholar	NOUN
cana-950	2	25	,	,	PUNCT
cana-950	2	26	department	department	NOUN
cana-950	2	27	of	of	ADP
cana-950	2	28	mathematics	mathematics	PROPN
cana-950	2	29	,	,	PUNCT
cana-950	2	30	vels	vels	PROPN
cana-950	2	31	institute	institute	PROPN
cana-950	2	32	of	of	ADP
cana-950	2	33	science	science	PROPN
cana-950	2	34	technology	technology	NOUN
cana-950	2	35	and	and	CCONJ
cana-950	2	36	advanced	advanced	ADJ
cana-950	2	37	studies	study	NOUN
cana-950	2	38	,	,	PUNCT
cana-950	2	39	chennai	chennai	PROPN
cana-950	2	40	,	,	PUNCT
cana-950	2	41	tamil	tamil	PROPN
cana-950	2	42	nadu	nadu	PROPN
cana-950	2	43	.	.	PUNCT
cana-950	3	1	mail	mail	NOUN
cana-950	3	2	i	i	PRON
cana-950	3	3	’d	’d	NOUN
cana-950	3	4	:	:	PUNCT
cana-950	4	1	sharmi.ruby2011@gmail.com	sharmi.ruby2011@gmail.com	NUM
cana-950	4	2	2associate	2associate	NUM
cana-950	4	3	professor	professor	NOUN
cana-950	4	4	&	&	CCONJ
cana-950	4	5	head	head	PROPN
cana-950	4	6	,	,	PUNCT
cana-950	4	7	department	department	NOUN
cana-950	4	8	of	of	ADP
cana-950	4	9	mathematics	mathematics	PROPN
cana-950	4	10	,	,	PUNCT
cana-950	4	11	vels	vels	PROPN
cana-950	4	12	institute	institute	PROPN
cana-950	4	13	of	of	ADP
cana-950	4	14	science	science	PROPN
cana-950	4	15	technology	technology	NOUN
cana-950	4	16	and	and	CCONJ
cana-950	4	17	advanced	advanced	ADJ
cana-950	4	18	studies	study	NOUN
cana-950	4	19	,	,	PUNCT
cana-950	4	20	chennai	chennai	PROPN
cana-950	4	21	,	,	PUNCT
cana-950	4	22	tamil	tamil	PROPN
cana-950	4	23	nadu	nadu	PROPN
cana-950	4	24	.	.	PUNCT
cana-950	5	1	mail	mail	NOUN
cana-950	5	2	i	i	PRON
cana-950	5	3	’d	’d	NOUN
cana-950	5	4	:	:	PUNCT
cana-950	5	5	meenakshikarthikeyan@yahoo.co.in	meenakshikarthikeyan@yahoo.co.in	PROPN
cana-950	5	6	article	article	NOUN
cana-950	5	7	history	history	NOUN
cana-950	5	8	:	:	PUNCT
cana-950	5	9	received	receive	VERB
cana-950	5	10	:	:	PUNCT
cana-950	5	11	20	20	NUM
cana-950	5	12	-	-	PUNCT
cana-950	5	13	04	04	NUM
cana-950	5	14	-	-	PUNCT
cana-950	5	15	2024	2024	NUM
cana-950	5	16	revised	revise	VERB
cana-950	5	17	:	:	PUNCT
cana-950	5	18	09	09	NUM
cana-950	5	19	-	-	SYM
cana-950	5	20	06	06	NUM
cana-950	5	21	-	-	PUNCT
cana-950	5	22	2024	2024	NUM
cana-950	5	23	accepted	accept	VERB
cana-950	5	24	:	:	PUNCT
cana-950	5	25	22	22	NUM
cana-950	5	26	-	-	SYM
cana-950	5	27	06	06	NUM
cana-950	5	28	-	-	PUNCT
cana-950	5	29	2024	2024	NUM
cana-950	5	30	abstract	abstract	NOUN
cana-950	5	31	:	:	PUNCT
cana-950	5	32	applications	application	NOUN
cana-950	5	33	using	use	VERB
cana-950	5	34	domination	domination	NOUN
cana-950	5	35	in	in	ADP
cana-950	5	36	graphs	graph	NOUN
cana-950	5	37	can	can	AUX
cana-950	5	38	be	be	AUX
cana-950	5	39	found	find	VERB
cana-950	5	40	across	across	ADP
cana-950	5	41	multiple	multiple	ADJ
cana-950	5	42	domains.when	domains.when	ADV
cana-950	5	43	there	there	PRON
cana-950	5	44	is	be	VERB
cana-950	5	45	a	a	DET
cana-950	5	46	set	set	ADJ
cana-950	5	47	number	number	NOUN
cana-950	5	48	of	of	ADP
cana-950	5	49	resources	resource	NOUN
cana-950	5	50	(	(	PUNCT
cana-950	5	51	such	such	ADJ
cana-950	5	52	as	as	ADP
cana-950	5	53	fire	fire	NOUN
cana-950	5	54	departments	department	NOUN
cana-950	5	55	and	and	CCONJ
cana-950	5	56	healthcare	healthcare	PROPN
cana-950	5	57	facilities	facility	NOUN
cana-950	5	58	)	)	PUNCT
cana-950	5	59	and	and	CCONJ
cana-950	5	60	the	the	DET
cana-950	5	61	goal	goal	NOUN
cana-950	5	62	is	be	AUX
cana-950	5	63	to	to	PART
cana-950	5	64	reduce	reduce	VERB
cana-950	5	65	the	the	DET
cana-950	5	66	distance	distance	NOUN
cana-950	5	67	that	that	SCONJ
cana-950	5	68	someone	someone	PRON
cana-950	5	69	must	must	AUX
cana-950	5	70	travel	travel	VERB
cana-950	5	71	in	in	ADP
cana-950	5	72	order	order	NOUN
cana-950	5	73	to	to	PART
cana-950	5	74	reach	reach	VERB
cana-950	5	75	the	the	DET
cana-950	5	76	most	most	ADV
cana-950	5	77	nearby	nearby	ADJ
cana-950	5	78	facility	facility	NOUN
cana-950	5	79	,	,	PUNCT
cana-950	5	80	domination	domination	NOUN
cana-950	5	81	emerges	emerge	VERB
cana-950	5	82	in	in	ADP
cana-950	5	83	facility	facility	NOUN
cana-950	5	84	positioning	positioning	NOUN
cana-950	5	85	problems.domination	problems.domination	NOUN
cana-950	5	86	notions	notion	NOUN
cana-950	5	87	can	can	AUX
cana-950	5	88	also	also	ADV
cana-950	5	89	be	be	AUX
cana-950	5	90	found	find	VERB
cana-950	5	91	in	in	ADP
cana-950	5	92	land	land	NOUN
cana-950	5	93	mapping	mapping	NOUN
cana-950	5	94	problems	problem	NOUN
cana-950	5	95	(	(	PUNCT
cana-950	5	96	e.g.	e.g.	ADV
cana-950	5	97	,	,	PUNCT
cana-950	5	98	limiting	limit	VERB
cana-950	5	99	the	the	DET
cana-950	5	100	quantity	quantity	NOUN
cana-950	5	101	of	of	ADP
cana-950	5	102	places	place	NOUN
cana-950	5	103	where	where	SCONJ
cana-950	5	104	an	an	DET
cana-950	5	105	assessor	assessor	NOUN
cana-950	5	106	has	have	VERB
cana-950	5	107	to	to	PART
cana-950	5	108	visit	visit	VERB
cana-950	5	109	in	in	ADP
cana-950	5	110	order	order	NOUN
cana-950	5	111	to	to	PART
cana-950	5	112	obtain	obtain	VERB
cana-950	5	113	measurements	measurement	NOUN
cana-950	5	114	of	of	ADP
cana-950	5	115	elevation	elevation	NOUN
cana-950	5	116	for	for	ADP
cana-950	5	117	an	an	DET
cana-950	5	118	entire	entire	ADJ
cana-950	5	119	region	region	NOUN
cana-950	5	120	)	)	PUNCT
cana-950	5	121	,	,	PUNCT
cana-950	5	122	tracking	track	VERB
cana-950	5	123	telecommunications	telecommunication	NOUN
cana-950	5	124	or	or	CCONJ
cana-950	5	125	electrical	electrical	ADJ
cana-950	5	126	infrastructure	infrastructure	NOUN
cana-950	5	127	,	,	PUNCT
cana-950	5	128	and	and	CCONJ
cana-950	5	129	tasks	task	NOUN
cana-950	5	130	involving	involve	VERB
cana-950	5	131	spotting	spot	VERB
cana-950	5	132	squads	squad	NOUN
cana-950	5	133	of	of	ADP
cana-950	5	134	senators	senator	NOUN
cana-950	5	135	.	.	PUNCT
cana-950	6	1	a	a	DET
cana-950	6	2	comparable	comparable	ADJ
cana-950	6	3	issue	issue	NOUN
cana-950	6	4	arises	arise	VERB
cana-950	6	5	when	when	SCONJ
cana-950	6	6	efforts	effort	NOUN
cana-950	6	7	are	be	AUX
cana-950	6	8	made	make	VERB
cana-950	6	9	to	to	PART
cana-950	6	10	minimize	minimize	VERB
cana-950	6	11	the	the	DET
cana-950	6	12	quantity	quantity	NOUN
cana-950	6	13	of	of	ADP
cana-950	6	14	facilities	facility	NOUN
cana-950	6	15	needed	need	VERB
cana-950	6	16	to	to	PART
cana-950	6	17	serve	serve	VERB
cana-950	6	18	every	every	DET
cana-950	6	19	individual	individual	NOUN
cana-950	6	20	and	and	CCONJ
cana-950	6	21	the	the	DET
cana-950	6	22	ideal	ideal	ADJ
cana-950	6	23	distance	distance	NOUN
cana-950	6	24	to	to	ADP
cana-950	6	25	service	service	NOUN
cana-950	6	26	is	be	AUX
cana-950	6	27	established	establish	VERB
cana-950	6	28	.	.	PUNCT
cana-950	7	1	considering	consider	VERB
cana-950	7	2	the	the	DET
cana-950	7	3	graph	graph	NOUN
cana-950	7	4	g	g	NOUN
cana-950	7	5	=	=	PUNCT
cana-950	7	6	[	[	PUNCT
cana-950	7	7	{	{	PUNCT
cana-950	7	8	v	v	NOUN
cana-950	7	9	}	}	PUNCT
cana-950	7	10	,	,	PUNCT
cana-950	7	11	{	{	PUNCT
cana-950	7	12	e	e	NOUN
cana-950	7	13	}	}	PUNCT
cana-950	7	14	]	]	PUNCT
cana-950	7	15	.	.	PUNCT
cana-950	8	1	let	let	VERB
cana-950	8	2	the	the	DET
cana-950	8	3	set	set	NOUN
cana-950	8	4	i	i	PRON
cana-950	8	5	v	v	X
cana-950	8	6	{	{	PUNCT
cana-950	8	7	g	g	NOUN
cana-950	8	8	}	}	PUNCT
cana-950	8	9	is	be	AUX
cana-950	8	10	a	a	DET
cana-950	8	11	secure	secure	ADJ
cana-950	8	12	vertex	vertex	NOUN
cana-950	8	13	edge	edge	NOUN
cana-950	8	14	dominating	dominating	NOUN
cana-950	8	15	set	set	NOUN
cana-950	8	16	of	of	ADP
cana-950	8	17	g	g	NOUN
cana-950	8	18	,	,	PUNCT
cana-950	8	19	suppose	suppose	VERB
cana-950	8	20	every	every	DET
cana-950	8	21	edge	edge	NOUN
cana-950	8	22	,	,	PUNCT
cana-950	8	23	y	y	PROPN
cana-950	8	24	e	e	PROPN
cana-950	9	1	[	[	X
cana-950	9	2	g	g	X
cana-950	9	3	]	]	PUNCT
cana-950	9	4	,	,	PUNCT
cana-950	9	5	then	then	ADV
cana-950	9	6	there	there	PRON
cana-950	9	7	exists	exist	VERB
cana-950	9	8	a	a	DET
cana-950	9	9	vertex	vertex	NOUN
cana-950	9	10	v	v	ADP
cana-950	9	11	i	i	PRON
cana-950	9	12	so	so	SCONJ
cana-950	9	13	that	that	SCONJ
cana-950	9	14	v	v	NOUN
cana-950	9	15	stands	stand	VERB
cana-950	9	16	up	up	ADP
cana-950	9	17	for	for	ADP
cana-950	9	18	y	y	PROPN
cana-950	9	19	.	.	PUNCT
cana-950	10	1	i.e.	i.e.	X
cana-950	10	2	,	,	PUNCT
cana-950	10	3	the	the	DET
cana-950	10	4	vertex	vertex	NOUN
cana-950	10	5	in	in	ADP
cana-950	10	6	i	i	PRON
cana-950	10	7	defends	defend	VERB
cana-950	10	8	the	the	DET
cana-950	10	9	edges	edge	NOUN
cana-950	10	10	incident	incident	NOUN
cana-950	10	11	on	on	ADP
cana-950	10	12	that	that	DET
cana-950	10	13	vertex	vertex	NOUN
cana-950	10	14	and	and	CCONJ
cana-950	10	15	the	the	DET
cana-950	10	16	edges	edge	NOUN
cana-950	10	17	which	which	PRON
cana-950	10	18	lie	lie	VERB
cana-950	10	19	next	next	ADV
cana-950	10	20	to	to	ADP
cana-950	10	21	the	the	DET
cana-950	10	22	incident	incident	NOUN
cana-950	10	23	edges	edge	VERB
cana-950	10	24	.	.	PUNCT
cana-950	11	1	a	a	DET
cana-950	11	2	secure	secure	ADJ
cana-950	11	3	vertex	vertex	NOUN
cana-950	11	4	edge	edge	NOUN
cana-950	11	5	dominating	dominating	NOUN
cana-950	11	6	set	set	NOUN
cana-950	11	7	i	i	PRON
cana-950	11	8	of	of	ADP
cana-950	11	9	a	a	DET
cana-950	11	10	graph	graph	NOUN
cana-950	11	11	g	g	NOUN
cana-950	11	12	has	have	VERB
cana-950	11	13	the	the	DET
cana-950	11	14	characteristic	characteristic	NOUN
cana-950	11	15	of	of	ADP
cana-950	11	16	being	be	AUX
cana-950	11	17	a	a	DET
cana-950	11	18	dominant	dominant	ADJ
cana-950	11	19	set	set	NOUN
cana-950	11	20	where	where	SCONJ
cana-950	11	21	every	every	DET
cana-950	11	22	vertex	vertex	NOUN
cana-950	11	23	z	z	NOUN
cana-950	11	24	v	v	NOUN
cana-950	11	25	–	–	PUNCT
cana-950	12	1	i	i	PRON
cana-950	12	2	either	either	CCONJ
cana-950	12	3	follows	follow	VERB
cana-950	12	4	a	a	DET
cana-950	12	5	vertex	vertex	NOUN
cana-950	12	6	or	or	CCONJ
cana-950	12	7	a	a	DET
cana-950	12	8	vertex	vertex	NOUN
cana-950	12	9	adjacent	adjacent	ADJ
cana-950	12	10	to	to	ADP
cana-950	12	11	the	the	DET
cana-950	12	12	incident	incident	NOUN
cana-950	12	13	edges	edge	NOUN
cana-950	12	14	of	of	ADP
cana-950	12	15	z	z	NOUN
cana-950	12	16	,	,	PUNCT
cana-950	12	17	x	x	VERB
cana-950	12	18	i	i	PRON
cana-950	12	19	such	such	ADJ
cana-950	12	20	that	that	SCONJ
cana-950	12	21	(	(	PUNCT
cana-950	12	22	i{x	i{x	NOUN
cana-950	12	23	}	}	PUNCT
cana-950	12	24	)	)	PUNCT
cana-950	12	25	{	{	PUNCT
cana-950	12	26	z	z	X
cana-950	12	27	}	}	PUNCT
cana-950	12	28	is	be	AUX
cana-950	12	29	a	a	DET
cana-950	12	30	dominating	dominating	NOUN
cana-950	12	31	set	set	NOUN
cana-950	12	32	.	.	PUNCT
cana-950	13	1	the	the	DET
cana-950	13	2	secure	secure	ADJ
cana-950	13	3	vertex	vertex	NOUN
cana-950	13	4	edge	edge	NOUN
cana-950	13	5	domination	domination	NOUN
cana-950	13	6	number	number	NOUN
cana-950	13	7	in	in	ADP
cana-950	13	8	g	g	PROPN
cana-950	13	9	is	be	AUX
cana-950	13	10	the	the	DET
cana-950	13	11	least	least	ADJ
cana-950	13	12	cardinality	cardinality	NOUN
cana-950	13	13	of	of	ADP
cana-950	13	14	secure	secure	ADJ
cana-950	13	15	vertex	vertex	NOUN
cana-950	13	16	edge	edge	NOUN
cana-950	13	17	domination	domination	NOUN
cana-950	13	18	and	and	CCONJ
cana-950	13	19	is	be	AUX
cana-950	13	20	depicted	depict	VERB
cana-950	13	21	by	by	ADP
cana-950	13	22	.	.	PUNCT
cana-950	14	1	we	we	PRON
cana-950	14	2	have	have	AUX
cana-950	14	3	commenced	commence	VERB
cana-950	14	4	researching	research	VERB
cana-950	14	5	this	this	DET
cana-950	14	6	new	new	ADJ
cana-950	14	7	parameter	parameter	NOUN
cana-950	14	8	and	and	CCONJ
cana-950	14	9	have	have	AUX
cana-950	14	10	found	find	VERB
cana-950	14	11	the	the	DET
cana-950	14	12	secure	secure	ADJ
cana-950	14	13	vertex	vertex	NOUN
cana-950	14	14	edge	edge	NOUN
cana-950	14	15	dominance	dominance	NOUN
cana-950	14	16	number	number	NOUN
cana-950	14	17	of	of	ADP
cana-950	14	18	several	several	ADJ
cana-950	14	19	standard	standard	ADJ
cana-950	14	20	graphs	graph	NOUN
cana-950	14	21	and	and	CCONJ
cana-950	14	22	the	the	DET
cana-950	14	23	middle	middle	ADJ
cana-950	14	24	graphs	graph	NOUN
cana-950	14	25	of	of	ADP
cana-950	14	26	some	some	DET
cana-950	14	27	standard	standard	ADJ
cana-950	14	28	graphs	graph	NOUN
cana-950	14	29	.	.	PUNCT
cana-950	15	1	in	in	ADP
cana-950	15	2	the	the	DET
cana-950	15	3	current	current	ADJ
cana-950	15	4	analysis	analysis	NOUN
cana-950	15	5	,	,	PUNCT
cana-950	15	6	the	the	DET
cana-950	15	7	secure	secure	ADJ
cana-950	15	8	vertex	vertex	NOUN
cana-950	15	9	edge	edge	NOUN
cana-950	15	10	dominance	dominance	NOUN
cana-950	15	11	number	number	NOUN
cana-950	15	12	of	of	ADP
cana-950	15	13	a	a	DET
cana-950	15	14	few	few	ADJ
cana-950	15	15	designated	designate	VERB
cana-950	15	16	specific	specific	ADJ
cana-950	15	17	graphs	graph	NOUN
cana-950	15	18	such	such	ADJ
cana-950	15	19	as	as	ADP
cana-950	15	20	bull	bull	NOUN
cana-950	15	21	graph	graph	NOUN
cana-950	15	22	,	,	PUNCT
cana-950	15	23	durer	durer	PROPN
cana-950	15	24	graph	graph	NOUN
cana-950	15	25	,	,	PUNCT
cana-950	15	26	heawood	heawood	NOUN
cana-950	15	27	graph	graph	NOUN
cana-950	15	28	,	,	PUNCT
cana-950	15	29	moser	moser	PROPN
cana-950	15	30	spindle	spindle	PROPN
cana-950	15	31	graph	graph	NOUN
cana-950	15	32	and	and	CCONJ
cana-950	15	33	etc	etc	X
cana-950	15	34	.	.	X
cana-950	15	35	,	,	PUNCT
cana-950	15	36	was	be	AUX
cana-950	15	37	discovered	discover	VERB
cana-950	15	38	.	.	PUNCT
cana-950	16	1	keywords	keyword	NOUN
cana-950	16	2	:	:	PUNCT
cana-950	16	3	dominating	dominate	VERB
cana-950	16	4	set	set	NOUN
cana-950	16	5	,	,	PUNCT
cana-950	16	6	secure	secure	ADJ
cana-950	16	7	vertex	vertex	NOUN
cana-950	16	8	edge	edge	NOUN
cana-950	16	9	dominating	dominating	NOUN
cana-950	16	10	set	set	NOUN
cana-950	16	11	,	,	PUNCT
cana-950	16	12	domination	domination	NOUN
cana-950	16	13	number	number	NOUN
cana-950	16	14	,	,	PUNCT
cana-950	16	15	bull	bull	NOUN
cana-950	16	16	graph	graph	NOUN
cana-950	16	17	,	,	PUNCT
cana-950	16	18	butterfly	butterfly	NOUN
cana-950	16	19	graph	graph	NOUN
cana-950	16	20	,	,	PUNCT
cana-950	16	21	durer	durer	PROPN
cana-950	16	22	graph	graph	NOUN
cana-950	16	23	,	,	PUNCT
cana-950	16	24	heawood	heawood	NOUN
cana-950	16	25	graph	graph	NOUN
cana-950	16	26	,	,	PUNCT
cana-950	16	27	moser	moser	PROPN
cana-950	16	28	spindle	spindle	PROPN
cana-950	16	29	graph	graph	NOUN
cana-950	16	30	.	.	PUNCT
cana-950	17	1	1	1	X
cana-950	17	2	.	.	X
cana-950	17	3	introduction	introduction	NOUN
cana-950	17	4	graph	graph	NOUN
cana-950	17	5	theory	theory	NOUN
cana-950	17	6	is	be	AUX
cana-950	17	7	one	one	NUM
cana-950	17	8	of	of	ADP
cana-950	17	9	a	a	DET
cana-950	17	10	great	great	ADJ
cana-950	17	11	deal	deal	NOUN
cana-950	17	12	of	of	ADP
cana-950	17	13	active	active	ADJ
cana-950	17	14	fields	field	NOUN
cana-950	17	15	in	in	ADP
cana-950	17	16	modern	modern	ADJ
cana-950	17	17	mathematics	mathematic	NOUN
cana-950	17	18	,	,	PUNCT
cana-950	17	19	having	having	AUX
cana-950	17	20	developed	develop	VERB
cana-950	17	21	during	during	ADP
cana-950	17	22	the	the	DET
cana-950	17	23	last	last	ADJ
cana-950	17	24	trilogy	trilogy	NOUN
cana-950	17	25	of	of	ADP
cana-950	17	26	decades	decade	NOUN
cana-950	17	27	.	.	PUNCT
cana-950	18	1	numerous	numerous	ADJ
cana-950	18	2	domains	domain	NOUN
cana-950	18	3	,	,	PUNCT
cana-950	18	4	including	include	VERB
cana-950	18	5	discrete	discrete	ADJ
cana-950	18	6	optimization	optimization	NOUN
cana-950	18	7	problems	problem	NOUN
cana-950	18	8	,	,	PUNCT
cana-950	18	9	sequential	sequential	ADJ
cana-950	18	10	problems	problem	NOUN
cana-950	18	11	,	,	PUNCT
cana-950	18	12	and	and	CCONJ
cana-950	18	13	ancient	ancient	ADJ
cana-950	18	14	algebraic	algebraic	ADJ
cana-950	18	15	challenges	challenge	NOUN
cana-950	18	16	are	be	AUX
cana-950	18	17	among	among	ADP
cana-950	18	18	its	its	PRON
cana-950	18	19	applications	application	NOUN
cana-950	18	20	.	.	PUNCT
cana-950	19	1	[	[	X
cana-950	19	2	1	1	NUM
cana-950	19	3	]	]	PUNCT
cana-950	19	4	.	.	PUNCT
cana-950	20	1	in	in	ADP
cana-950	20	2	addition	addition	NOUN
cana-950	20	3	,	,	PUNCT
cana-950	20	4	the	the	DET
cana-950	20	5	fields	field	NOUN
cana-950	20	6	of	of	ADP
cana-950	20	7	languages	language	NOUN
cana-950	20	8	,	,	PUNCT
cana-950	20	9	biology	biology	NOUN
cana-950	20	10	,	,	PUNCT
cana-950	20	11	physics	physics	NOUN
cana-950	20	12	,	,	PUNCT
cana-950	20	13	and	and	CCONJ
cana-950	20	14	sociological	sociological	ADJ
cana-950	20	15	studies	study	NOUN
cana-950	20	16	all	all	PRON
cana-950	20	17	bear	bear	VERB
cana-950	20	18	the	the	DET
cana-950	20	19	mark	mark	NOUN
cana-950	20	20	of	of	ADP
cana-950	20	21	graph	graph	NOUN
cana-950	20	22	theory	theory	NOUN
cana-950	20	23	's	's	PART
cana-950	20	24	imprint	imprint	NOUN
cana-950	20	25	.	.	PUNCT
cana-950	21	1	computational	computational	ADJ
cana-950	21	2	frameworks	framework	NOUN
cana-950	21	3	are	be	AUX
cana-950	21	4	in	in	ADP
cana-950	21	5	handy	handy	ADJ
cana-950	21	6	whenever	whenever	SCONJ
cana-950	21	7	an	an	DET
cana-950	21	8	extensive	extensive	ADJ
cana-950	21	9	issue	issue	NOUN
cana-950	21	10	arises	arise	VERB
cana-950	21	11	.	.	PUNCT
cana-950	22	1	one	one	NUM
cana-950	22	2	of	of	ADP
cana-950	22	3	the	the	DET
cana-950	22	4	easiest	easy	ADJ
cana-950	22	5	and	and	CCONJ
cana-950	22	6	most	most	ADV
cana-950	22	7	efficient	efficient	ADJ
cana-950	22	8	methods	method	NOUN
cana-950	22	9	to	to	PART
cana-950	22	10	approach	approach	VERB
cana-950	22	11	a	a	DET
cana-950	22	12	challenge	challenge	NOUN
cana-950	22	13	is	be	AUX
cana-950	22	14	to	to	PART
cana-950	22	15	lay	lay	VERB
cana-950	22	16	out	out	ADP
cana-950	22	17	it	it	PRON
cana-950	22	18	as	as	ADP
cana-950	22	19	a	a	DET
cana-950	22	20	visual	visual	ADJ
cana-950	22	21	representation	representation	NOUN
cana-950	22	22	graph	graph	NOUN
cana-950	22	23	.	.	PUNCT
cana-950	23	1	one	one	NUM
cana-950	23	2	of	of	ADP
cana-950	23	3	the	the	DET
cana-950	23	4	main	main	ADJ
cana-950	23	5	focuses	focus	NOUN
cana-950	23	6	of	of	ADP
cana-950	23	7	graph	graph	NOUN
cana-950	23	8	theory	theory	NOUN
cana-950	23	9	is	be	AUX
cana-950	23	10	exploration	exploration	NOUN
cana-950	23	11	the	the	DET
cana-950	23	12	concept	concept	NOUN
cana-950	23	13	of	of	ADP
cana-950	23	14	dominance	dominance	NOUN
cana-950	23	15	in	in	ADP
cana-950	23	16	graphs	graph	NOUN
cana-950	23	17	.	.	PUNCT
cana-950	24	1	the	the	DET
cana-950	24	2	goals	goal	NOUN
cana-950	24	3	of	of	ADP
cana-950	24	4	the	the	DET
cana-950	24	5	dominance	dominance	NOUN
cana-950	24	6	hypothesis	hypothesis	NOUN
cana-950	24	7	include	include	VERB
cana-950	24	8	identifying	identify	VERB
cana-950	24	9	dominant	dominant	ADJ
cana-950	24	10	groups	group	NOUN
cana-950	24	11	in	in	ADP
cana-950	24	12	graphs	graph	NOUN
cana-950	24	13	,	,	PUNCT
cana-950	24	14	investigating	investigate	VERB
cana-950	24	15	their	their	PRON
cana-950	24	16	characteristics	characteristic	NOUN
cana-950	24	17	,	,	PUNCT
cana-950	24	18	and	and	CCONJ
cana-950	24	19	comprehending	comprehend	VERB
cana-950	24	20	the	the	DET
cana-950	24	21	practical	practical	ADJ
cana-950	24	22	applications	application	NOUN
cana-950	24	23	associated	associate	VERB
cana-950	24	24	with	with	ADP
cana-950	24	25	those	those	DET
cana-950	24	26	collections	collection	NOUN
cana-950	24	27	.	.	PUNCT
cana-950	25	1	when	when	SCONJ
cana-950	25	2	de	de	PROPN
cana-950	25	3	jaenisch	jaenisch	PROPN
cana-950	25	4	examined	examine	VERB
cana-950	25	5	the	the	DET
cana-950	25	6	bare	bare	ADJ
cana-950	25	7	minimum	minimum	NOUN
cana-950	25	8	of	of	ADP
cana-950	25	9	monarchs	monarch	NOUN
cana-950	25	10	needed	need	VERB
cana-950	25	11	to	to	PART
cana-950	25	12	wrap	wrap	VERB
cana-950	25	13	around	around	ADV
cana-950	25	14	or	or	CCONJ
cana-950	25	15	rule	rule	VERB
cana-950	25	16	communications	communication	NOUN
cana-950	25	17	on	on	ADP
cana-950	25	18	applied	apply	VERB
cana-950	25	19	nonlinear	nonlinear	ADJ
cana-950	25	20	analysis	analysis	NOUN
cana-950	25	21	issn	issn	NOUN
cana-950	25	22	:	:	PUNCT
cana-950	25	23	1074	1074	NUM
cana-950	25	24	-	-	PUNCT
cana-950	25	25	133x	133x	NUM
cana-950	25	26	vol	vol	NOUN
cana-950	25	27	31	31	NUM
cana-950	25	28	no	no	NOUN
cana-950	25	29	.	.	PUNCT
cana-950	26	1	4s	4s	NUM
cana-950	26	2	(	(	PUNCT
cana-950	26	3	2024	2024	NUM
cana-950	26	4	)	)	PUNCT
cana-950	26	5	561	561	NUM
cana-950	26	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-950	26	7	an	an	DET
cana-950	26	8	nxn	nxn	PROPN
cana-950	26	9	checkers	checkers	PROPN
cana-950	26	10	board	board	NOUN
cana-950	26	11	in	in	ADP
cana-950	26	12	1862	1862	NUM
cana-950	26	13	,	,	PUNCT
cana-950	26	14	the	the	DET
cana-950	26	15	doctrine	doctrine	NOUN
cana-950	26	16	of	of	ADP
cana-950	26	17	domination	domination	NOUN
cana-950	26	18	originated	originate	VERB
cana-950	26	19	[	[	X
cana-950	26	20	2	2	NUM
cana-950	26	21	]	]	PUNCT
cana-950	26	22	.	.	PUNCT
cana-950	27	1	during	during	ADP
cana-950	27	2	1892	1892	NUM
cana-950	27	3	,	,	PUNCT
cana-950	27	4	chess	chess	NOUN
cana-950	27	5	players	player	NOUN
cana-950	27	6	studied	study	VERB
cana-950	27	7	three	three	NUM
cana-950	27	8	basic	basic	ADJ
cana-950	27	9	types	type	NOUN
cana-950	27	10	of	of	ADP
cana-950	27	11	problems	problem	NOUN
cana-950	27	12	,	,	PUNCT
cana-950	27	13	according	accord	VERB
cana-950	27	14	to	to	ADP
cana-950	27	15	w.	w.	PROPN
cana-950	27	16	w.	w.	PROPN
cana-950	27	17	rouse	rouse	VERB
cana-950	27	18	ball	ball	PROPN
cana-950	28	1	[	[	X
cana-950	28	2	3	3	NUM
cana-950	28	3	]	]	PUNCT
cana-950	28	4	.	.	PUNCT
cana-950	29	1	[	[	X
cana-950	29	2	4	4	NUM
cana-950	29	3	]	]	PUNCT
cana-950	29	4	berge	berge	NOUN
cana-950	29	5	initially	initially	ADV
cana-950	29	6	introduced	introduce	VERB
cana-950	29	7	the	the	DET
cana-950	29	8	dominant	dominant	ADJ
cana-950	29	9	number	number	NOUN
cana-950	29	10	of	of	ADP
cana-950	29	11	a	a	DET
cana-950	29	12	graph	graph	NOUN
cana-950	29	13	in	in	ADP
cana-950	29	14	1958	1958	NUM
cana-950	29	15	;	;	PUNCT
cana-950	29	16	it	it	PRON
cana-950	29	17	was	be	AUX
cana-950	29	18	alternatively	alternatively	ADV
cana-950	29	19	known	know	VERB
cana-950	29	20	as	as	ADP
cana-950	29	21	the	the	DET
cana-950	29	22	"	"	PUNCT
cana-950	29	23	coefficient	coefficient	NOUN
cana-950	29	24	of	of	ADP
cana-950	29	25	external	external	ADJ
cana-950	29	26	stability	stability	NOUN
cana-950	29	27	.	.	PUNCT
cana-950	29	28	"	"	PUNCT
cana-950	30	1	in	in	ADP
cana-950	30	2	1962	1962	NUM
cana-950	30	3	,	,	PUNCT
cana-950	30	4	ore	ore	NOUN
cana-950	30	5	used	use	VERB
cana-950	30	6	the	the	DET
cana-950	30	7	phrases	phrase	NOUN
cana-950	30	8	"	"	PUNCT
cana-950	30	9	dominating	dominating	NOUN
cana-950	30	10	set	set	NOUN
cana-950	30	11	"	"	PUNCT
cana-950	30	12	and	and	CCONJ
cana-950	30	13	"	"	PUNCT
cana-950	30	14	domination	domination	NOUN
cana-950	30	15	number	number	NOUN
cana-950	30	16	"	"	PUNCT
cana-950	30	17	to	to	PART
cana-950	30	18	convey	convey	VERB
cana-950	30	19	a	a	DET
cana-950	30	20	similar	similar	ADJ
cana-950	30	21	concept	concept	NOUN
cana-950	30	22	[	[	X
cana-950	30	23	5	5	NUM
cana-950	30	24	]	]	PUNCT
cana-950	30	25	.	.	PUNCT
cana-950	31	1	nevertheless	nevertheless	ADV
cana-950	31	2	,	,	PUNCT
cana-950	31	3	dominating	dominating	NOUN
cana-950	31	4	sets	set	NOUN
cana-950	31	5	in	in	ADP
cana-950	31	6	graph	graph	NOUN
cana-950	31	7	theory	theory	NOUN
cana-950	31	8	were	be	AUX
cana-950	31	9	n't	not	PART
cana-950	31	10	well	well	ADV
cana-950	31	11	investigated	investigate	VERB
cana-950	31	12	until	until	ADP
cana-950	31	13	about	about	ADP
cana-950	31	14	1960	1960	NUM
cana-950	31	15	.	.	PUNCT
cana-950	32	1	once	once	ADV
cana-950	32	2	cockayne	cockayne	PROPN
cana-950	32	3	and	and	CCONJ
cana-950	32	4	hedetniemi	hedetniemi	ADV
cana-950	32	5	presented	present	VERB
cana-950	32	6	a	a	DET
cana-950	32	7	comprehensive	comprehensive	ADJ
cana-950	32	8	study	study	NOUN
cana-950	32	9	of	of	ADP
cana-950	32	10	the	the	DET
cana-950	32	11	research	research	NOUN
cana-950	32	12	on	on	ADP
cana-950	32	13	dominant	dominant	ADJ
cana-950	32	14	sets	set	NOUN
cana-950	32	15	in	in	ADP
cana-950	32	16	graphs	graph	NOUN
cana-950	32	17	at	at	ADP
cana-950	32	18	that	that	DET
cana-950	32	19	period	period	NOUN
cana-950	32	20	1977	1977	NUM
cana-950	33	1	[	[	X
cana-950	33	2	6	6	NUM
cana-950	33	3	]	]	PUNCT
cana-950	33	4	,	,	PUNCT
cana-950	33	5	they	they	PRON
cana-950	33	6	significantly	significantly	ADV
cana-950	33	7	advanced	advance	VERB
cana-950	33	8	the	the	DET
cana-950	33	9	discipline	discipline	NOUN
cana-950	33	10	's	's	PART
cana-950	33	11	understanding	understanding	NOUN
cana-950	33	12	of	of	ADP
cana-950	33	13	dominating	dominating	NOUN
cana-950	33	14	sets	set	NOUN
cana-950	33	15	.	.	PUNCT
cana-950	34	1	they	they	PRON
cana-950	34	2	created	create	VERB
cana-950	34	3	the	the	DET
cana-950	34	4	graph	graph	NOUN
cana-950	34	5	notation	notation	NOUN
cana-950	34	6	's	's	PART
cana-950	34	7	domination	domination	NOUN
cana-950	34	8	number	number	NOUN
cana-950	34	9	(	(	PUNCT
cana-950	34	10	g	g	NOUN
cana-950	34	11	)	)	PUNCT
cana-950	34	12	,	,	PUNCT
cana-950	34	13	which	which	PRON
cana-950	34	14	was	be	AUX
cana-950	34	15	subsequently	subsequently	ADV
cana-950	34	16	adopted	adopt	VERB
cana-950	34	17	by	by	ADP
cana-950	34	18	many	many	ADJ
cana-950	34	19	.	.	PUNCT
cana-950	35	1	the	the	DET
cana-950	35	2	pioneering	pioneering	ADJ
cana-950	35	3	poll	poll	NOUN
cana-950	35	4	results	result	NOUN
cana-950	35	5	by	by	ADP
cana-950	35	6	hedetniemi	hedetniemi	NOUN
cana-950	35	7	and	and	CCONJ
cana-950	35	8	cockayne	cockayne	NOUN
cana-950	35	9	caused	cause	VERB
cana-950	35	10	a	a	DET
cana-950	35	11	spike	spike	NOUN
cana-950	35	12	in	in	ADP
cana-950	35	13	the	the	DET
cana-950	35	14	amount	amount	NOUN
cana-950	35	15	of	of	ADP
cana-950	35	16	studies	study	NOUN
cana-950	35	17	being	be	AUX
cana-950	35	18	done	do	VERB
cana-950	35	19	on	on	ADP
cana-950	35	20	graph	graph	NOUN
cana-950	35	21	domination	domination	NOUN
cana-950	35	22	.	.	PUNCT
cana-950	36	1	over	over	ADP
cana-950	36	2	1200	1200	NUM
cana-950	36	3	academic	academic	ADJ
cana-950	36	4	papers	paper	NOUN
cana-950	36	5	on	on	ADP
cana-950	36	6	this	this	DET
cana-950	36	7	fascinating	fascinating	ADJ
cana-950	36	8	intricate	intricate	ADJ
cana-950	36	9	issue	issue	NOUN
cana-950	36	10	were	be	AUX
cana-950	36	11	produced	produce	VERB
cana-950	36	12	in	in	ADP
cana-950	36	13	the	the	DET
cana-950	36	14	two	two	NUM
cana-950	36	15	decades	decade	NOUN
cana-950	36	16	of	of	ADP
cana-950	36	17	which	which	PRON
cana-950	36	18	followed	follow	VERB
cana-950	36	19	the	the	DET
cana-950	36	20	research	research	NOUN
cana-950	36	21	study	study	NOUN
cana-950	36	22	.	.	PUNCT
cana-950	37	1	secure	secure	ADJ
cana-950	37	2	domination	domination	NOUN
cana-950	37	3	is	be	AUX
cana-950	37	4	a	a	DET
cana-950	37	5	theory	theory	NOUN
cana-950	37	6	that	that	PRON
cana-950	37	7	was	be	AUX
cana-950	37	8	developed	develop	VERB
cana-950	37	9	by	by	ADP
cana-950	37	10	cockayne	cockayne	PROPN
cana-950	37	11	et	et	PROPN
cana-950	37	12	al	al	PROPN
cana-950	37	13	.	.	PROPN
cana-950	38	1	in	in	ADP
cana-950	38	2	2003	2003	NUM
cana-950	38	3	,	,	PUNCT
cana-950	38	4	[	[	X
cana-950	38	5	7	7	NUM
cana-950	38	6	]	]	PUNCT
cana-950	38	7	.	.	PUNCT
cana-950	39	1	to	to	PART
cana-950	39	2	defend	defend	VERB
cana-950	39	3	an	an	DET
cana-950	39	4	unprotected	unprotected	ADJ
cana-950	39	5	vertex	vertex	NOUN
cana-950	39	6	u	u	NOUN
cana-950	39	7	,	,	PUNCT
cana-950	39	8	within	within	ADP
cana-950	39	9	a	a	DET
cana-950	39	10	graph	graph	NOUN
cana-950	39	11	g	g	NOUN
cana-950	39	12	=	=	PUNCT
cana-950	39	13	[	[	PUNCT
cana-950	39	14	{	{	PUNCT
cana-950	39	15	v	v	NOUN
cana-950	39	16	}	}	PUNCT
cana-950	39	17	,	,	PUNCT
cana-950	39	18	{	{	PUNCT
cana-950	39	19	e	e	NOUN
cana-950	39	20	}	}	PUNCT
cana-950	39	21	]	]	PUNCT
cana-950	39	22	,	,	PUNCT
cana-950	39	23	each	each	DET
cana-950	39	24	vertex	vertex	NOUN
cana-950	39	25	in	in	ADP
cana-950	39	26	a	a	DET
cana-950	39	27	subset	subset	NOUN
cana-950	39	28	s	s	NOUN
cana-950	39	29	of	of	ADP
cana-950	39	30	v	v	NOUN
cana-950	39	31	has	have	VERB
cana-950	39	32	to	to	PART
cana-950	39	33	have	have	VERB
cana-950	39	34	an	an	DET
cana-950	39	35	enforcer	enforcer	NOUN
cana-950	39	36	assigned	assign	VERB
cana-950	39	37	to	to	ADP
cana-950	39	38	it	it	PRON
cana-950	39	39	.	.	PUNCT
cana-950	40	1	this	this	DET
cana-950	40	2	thorough	thorough	ADJ
cana-950	40	3	analysis	analysis	NOUN
cana-950	40	4	seeks	seek	VERB
cana-950	40	5	to	to	PART
cana-950	40	6	explore	explore	VERB
cana-950	40	7	the	the	DET
cana-950	40	8	multifaceted	multifaceted	ADJ
cana-950	40	9	nature	nature	NOUN
cana-950	40	10	of	of	ADP
cana-950	40	11	vertex	vertex	NOUN
cana-950	40	12	dominations	domination	NOUN
cana-950	40	13	in	in	ADP
cana-950	40	14	graph	graph	NOUN
cana-950	40	15	theory	theory	NOUN
cana-950	40	16	,	,	PUNCT
cana-950	40	17	illuminating	illuminate	VERB
cana-950	40	18	several	several	ADJ
cana-950	40	19	topics	topic	NOUN
cana-950	40	20	like	like	ADP
cana-950	40	21	dominance	dominance	NOUN
cana-950	40	22	insets	inset	NOUN
cana-950	40	23	,	,	PUNCT
cana-950	40	24	different	different	ADJ
cana-950	40	25	kinds	kind	NOUN
cana-950	40	26	of	of	ADP
cana-950	40	27	dominance	dominance	NOUN
cana-950	40	28	,	,	PUNCT
cana-950	40	29	typical	typical	ADJ
cana-950	40	30	minimal	minimal	ADJ
cana-950	40	31	dominance	dominance	NOUN
cana-950	40	32	,	,	PUNCT
cana-950	40	33	theoretical	theoretical	ADJ
cana-950	40	34	findings	finding	NOUN
cana-950	40	35	,	,	PUNCT
cana-950	40	36	results	result	NOUN
cana-950	40	37	,	,	PUNCT
cana-950	40	38	and	and	CCONJ
cana-950	40	39	applications	application	NOUN
cana-950	40	40	of	of	ADP
cana-950	40	41	dominance	dominance	NOUN
cana-950	40	42	in	in	ADP
cana-950	40	43	graphs[8].several	graphs[8].several	ADJ
cana-950	40	44	results	result	NOUN
cana-950	40	45	on	on	ADP
cana-950	40	46	vertex	vertex	NOUN
cana-950	40	47	-	-	PUNCT
cana-950	40	48	edge	edge	NOUN
cana-950	40	49	and	and	CCONJ
cana-950	40	50	edge	edge	NOUN
cana-950	40	51	-	-	PUNCT
cana-950	40	52	vertex	vertex	NOUN
cana-950	40	53	properties	property	NOUN
cana-950	40	54	in	in	ADP
cana-950	40	55	graphs	graph	NOUN
cana-950	40	56	were	be	AUX
cana-950	40	57	put	put	VERB
cana-950	40	58	forth	forth	ADV
cana-950	40	59	in	in	ADP
cana-950	40	60	2007	2007	NUM
cana-950	40	61	by	by	ADP
cana-950	40	62	j.	j.	PROPN
cana-950	40	63	r.	r.	PROPN
cana-950	40	64	lewis	lewis	PROPN
cana-950	41	1	[	[	X
cana-950	41	2	9	9	NUM
cana-950	41	3	]	]	PUNCT
cana-950	41	4	in	in	ADP
cana-950	41	5	his	his	PRON
cana-950	41	6	dissertation	dissertation	NOUN
cana-950	41	7	for	for	ADP
cana-950	41	8	doctoral	doctoral	ADJ
cana-950	41	9	study	study	NOUN
cana-950	41	10	.	.	PUNCT
cana-950	42	1	the	the	DET
cana-950	42	2	cardinal	cardinal	ADJ
cana-950	42	3	value	value	NOUN
cana-950	42	4	of	of	ADP
cana-950	42	5	v	v	NOUN
cana-950	42	6	is	be	AUX
cana-950	42	7	represented	represent	VERB
cana-950	42	8	by	by	ADP
cana-950	42	9	𝑑𝑒g(v	𝑑𝑒g(v	PROPN
cana-950	42	10	)	)	PUNCT
cana-950	42	11	,	,	PUNCT
cana-950	42	12	which	which	PRON
cana-950	42	13	is	be	AUX
cana-950	42	14	the	the	DET
cana-950	42	15	degree	degree	NOUN
cana-950	42	16	of	of	ADP
cana-950	42	17	v.	v.	ADP
cana-950	42	18	an	an	DET
cana-950	42	19	independent	independent	ADJ
cana-950	42	20	vertex	vertex	NOUN
cana-950	42	21	or	or	CCONJ
cana-950	42	22	a	a	DET
cana-950	42	23	pendant	pendant	ADJ
cana-950	42	24	vertex	vertex	NOUN
cana-950	42	25	has	have	VERB
cana-950	42	26	a	a	DET
cana-950	42	27	degree	degree	NOUN
cana-950	42	28	of	of	ADP
cana-950	42	29	zero	zero	NUM
cana-950	42	30	or	or	CCONJ
cana-950	42	31	one	one	NUM
cana-950	42	32	,	,	PUNCT
cana-950	42	33	correspondingly	correspondingly	ADV
cana-950	42	34	.	.	PUNCT
cana-950	43	1	the	the	DET
cana-950	43	2	lowest	low	ADJ
cana-950	43	3	degree	degree	NOUN
cana-950	43	4	,	,	PUNCT
cana-950	43	5	𝛿	𝛿	PROPN
cana-950	43	6	(	(	PUNCT
cana-950	43	7	𝐺	𝐺	NOUN
cana-950	43	8	)	)	PUNCT
cana-950	43	9	,	,	PUNCT
cana-950	43	10	and	and	CCONJ
cana-950	43	11	highest	high	ADJ
cana-950	43	12	degree	degree	NOUN
cana-950	43	13	,	,	PUNCT
cana-950	43	14	δ	δ	PROPN
cana-950	43	15	(	(	PUNCT
cana-950	43	16	𝐺	𝐺	PROPN
cana-950	43	17	)	)	PUNCT
cana-950	43	18	,	,	PUNCT
cana-950	43	19	are	be	AUX
cana-950	43	20	depicted	depict	VERB
cana-950	43	21	correspondingly	correspondingly	ADV
cana-950	43	22	.	.	PUNCT
cana-950	44	1	a	a	DET
cana-950	44	2	regular	regular	ADJ
cana-950	44	3	graph	graph	NOUN
cana-950	44	4	is	be	AUX
cana-950	44	5	one	one	NUM
cana-950	44	6	where	where	SCONJ
cana-950	44	7	δ(𝐺	δ(𝐺	VERB
cana-950	44	8	)	)	PUNCT
cana-950	44	9	=	=	SYM
cana-950	45	1	𝛿(𝐺	𝛿(𝐺	X
cana-950	45	2	)	)	PUNCT
cana-950	46	1	were	be	AUX
cana-950	46	2	discussed	discuss	VERB
cana-950	46	3	in	in	ADP
cana-950	46	4	[	[	X
cana-950	46	5	10	10	NUM
cana-950	46	6	]	]	PUNCT
cana-950	46	7	.	.	PUNCT
cana-950	47	1	the	the	DET
cana-950	47	2	secure	secure	ADJ
cana-950	47	3	dominant	dominant	ADJ
cana-950	47	4	set	set	NOUN
cana-950	47	5	of	of	ADP
cana-950	47	6	graph	graph	NOUN
cana-950	47	7	g	g	PROPN
cana-950	47	8	is	be	AUX
cana-950	47	9	defined	define	VERB
cana-950	47	10	as	as	ADP
cana-950	47	11	a	a	DET
cana-950	47	12	collection	collection	NOUN
cana-950	47	13	of	of	ADP
cana-950	47	14	vertices	vertex	NOUN
cana-950	47	15	in	in	ADP
cana-950	47	16	v	v	NOUN
cana-950	47	17	-	-	PUNCT
cana-950	47	18	s	s	NOUN
cana-950	47	19	,	,	PUNCT
cana-950	47	20	where	where	SCONJ
cana-950	47	21	each	each	DET
cana-950	47	22	vertex	vertex	NOUN
cana-950	47	23	is	be	AUX
cana-950	47	24	secured	secure	VERB
cana-950	47	25	by	by	ADP
cana-950	47	26	a	a	DET
cana-950	47	27	vertex	vertex	NOUN
cana-950	47	28	in	in	ADP
cana-950	47	29	s.	s.	PROPN
cana-950	47	30	this	this	PRON
cana-950	47	31	is	be	AUX
cana-950	47	32	a	a	DET
cana-950	47	33	secure	secure	ADJ
cana-950	47	34	dominant	dominant	ADJ
cana-950	47	35	set	set	NOUN
cana-950	47	36	's	's	PART
cana-950	47	37	minimal	minimal	ADJ
cana-950	47	38	cardinality	cardinality	NOUN
cana-950	47	39	.	.	PUNCT
cana-950	48	1	arumugam	arumugam	ADJ
cana-950	48	2	et	et	PROPN
cana-950	48	3	al	al	PROPN
cana-950	48	4	.	.	PROPN
cana-950	49	1	(	(	PUNCT
cana-950	49	2	2014	2014	NUM
cana-950	49	3	)	)	PUNCT
cana-950	49	4	provide	provide	VERB
cana-950	49	5	some	some	DET
cana-950	49	6	conclusions	conclusion	NOUN
cana-950	49	7	regarding	regard	VERB
cana-950	49	8	co	co	NOUN
cana-950	49	9	-	-	ADJ
cana-950	49	10	secure	secure	ADJ
cana-950	49	11	and	and	CCONJ
cana-950	49	12	secure	secure	ADJ
cana-950	49	13	dominations	domination	NOUN
cana-950	49	14	in	in	ADP
cana-950	49	15	graphs	graph	NOUN
cana-950	49	16	[	[	X
cana-950	49	17	11	11	NUM
cana-950	49	18	]	]	PUNCT
cana-950	49	19	.	.	PUNCT
cana-950	50	1	additionally	additionally	ADV
cana-950	50	2	,	,	PUNCT
cana-950	50	3	this	this	DET
cana-950	50	4	new	new	ADJ
cana-950	50	5	guard	guard	NOUN
cana-950	50	6	arrangement	arrangement	NOUN
cana-950	50	7	forges	forge	VERB
cana-950	50	8	a	a	DET
cana-950	50	9	strong	strong	ADJ
cana-950	50	10	group	group	NOUN
cana-950	50	11	.	.	PUNCT
cana-950	51	1	motivated	motivate	VERB
cana-950	51	2	by	by	ADP
cana-950	51	3	all	all	DET
cana-950	51	4	these	these	DET
cana-950	51	5	results	result	NOUN
cana-950	51	6	,	,	PUNCT
cana-950	51	7	we	we	PRON
cana-950	51	8	have	have	AUX
cana-950	51	9	consequently	consequently	ADV
cana-950	51	10	developed	develop	VERB
cana-950	51	11	a	a	DET
cana-950	51	12	new	new	ADJ
cana-950	51	13	attribute	attribute	NOUN
cana-950	51	14	called	call	VERB
cana-950	51	15	secure	secure	ADJ
cana-950	51	16	vertex	vertex	NOUN
cana-950	51	17	edge	edge	NOUN
cana-950	51	18	domination	domination	NOUN
cana-950	51	19	of	of	ADP
cana-950	51	20	graphs	graph	NOUN
cana-950	51	21	[	[	X
cana-950	51	22	12	12	NUM
cana-950	51	23	]	]	PUNCT
cana-950	51	24	.	.	PUNCT
cana-950	52	1	[	[	X
cana-950	52	2	13	13	NUM
cana-950	52	3	]	]	PUNCT
cana-950	52	4	–	–	PUNCT
cana-950	53	1	[	[	X
cana-950	53	2	15	15	NUM
cana-950	53	3	]	]	PUNCT
cana-950	53	4	used	use	VERB
cana-950	53	5	some	some	DET
cana-950	53	6	special	special	ADJ
cana-950	53	7	graphs	graph	NOUN
cana-950	53	8	in	in	ADP
cana-950	53	9	their	their	PRON
cana-950	53	10	research	research	NOUN
cana-950	53	11	.	.	PUNCT
cana-950	54	1	we	we	PRON
cana-950	54	2	kick	kick	VERB
cana-950	54	3	off	off	ADP
cana-950	54	4	the	the	DET
cana-950	54	5	current	current	ADJ
cana-950	54	6	study	study	NOUN
cana-950	54	7	by	by	ADP
cana-950	54	8	investigating	investigate	VERB
cana-950	54	9	the	the	DET
cana-950	54	10	novel	novel	ADJ
cana-950	54	11	parameter	parameter	NOUN
cana-950	54	12	and	and	CCONJ
cana-950	54	13	ascertaining	ascertain	VERB
cana-950	54	14	the	the	DET
cana-950	54	15	secure	secure	ADJ
cana-950	54	16	vertex	vertex	NOUN
cana-950	54	17	edge	edge	NOUN
cana-950	54	18	domination	domination	NOUN
cana-950	54	19	number	number	NOUN
cana-950	54	20	of	of	ADP
cana-950	54	21	some	some	DET
cana-950	54	22	named	name	VERB
cana-950	54	23	special	special	ADJ
cana-950	54	24	graphs	graph	NOUN
cana-950	54	25	such	such	ADJ
cana-950	54	26	as	as	ADP
cana-950	54	27	bull	bull	NOUN
cana-950	54	28	graph	graph	NOUN
cana-950	54	29	,	,	PUNCT
cana-950	54	30	butterfly	butterfly	NOUN
cana-950	54	31	graph	graph	NOUN
cana-950	54	32	,	,	PUNCT
cana-950	54	33	diamond	diamond	NOUN
cana-950	54	34	graph	graph	NOUN
cana-950	54	35	,	,	PUNCT
cana-950	54	36	house	house	NOUN
cana-950	54	37	graph	graph	NOUN
cana-950	54	38	,	,	PUNCT
cana-950	54	39	wagner	wagner	NOUN
cana-950	54	40	graph	graph	NOUN
cana-950	54	41	,	,	PUNCT
cana-950	54	42	golomb	golomb	NOUN
cana-950	54	43	graph	graph	NOUN
cana-950	54	44	and	and	CCONJ
cana-950	54	45	etc	etc	X
cana-950	54	46	.	.	X
cana-950	54	47	,	,	PUNCT
cana-950	54	48	2	2	X
cana-950	54	49	.	.	PUNCT
cana-950	54	50	preludes	prelude	NOUN
cana-950	54	51	graph	graph	NOUN
cana-950	54	52	:	:	PUNCT
cana-950	54	53	a	a	DET
cana-950	54	54	graph	graph	NOUN
cana-950	54	55	g	g	NOUN
cana-950	54	56	=	=	PUNCT
cana-950	54	57	(	(	PUNCT
cana-950	54	58	{	{	PUNCT
cana-950	54	59	v},{e	v},{e	NOUN
cana-950	54	60	}	}	PUNCT
cana-950	54	61	)	)	PUNCT
cana-950	54	62	is	be	AUX
cana-950	54	63	composed	compose	VERB
cana-950	54	64	of	of	ADP
cana-950	54	65	a	a	DET
cana-950	54	66	collection	collection	NOUN
cana-950	54	67	of	of	ADP
cana-950	54	68	vertices	vertex	NOUN
cana-950	54	69	v(g	v(g	NOUN
cana-950	54	70	)	)	PUNCT
cana-950	54	71	and	and	CCONJ
cana-950	54	72	a	a	DET
cana-950	54	73	set	set	NOUN
cana-950	54	74	of	of	ADP
cana-950	54	75	edges	edge	NOUN
cana-950	54	76	e(g	e(g	PROPN
cana-950	54	77	)	)	PUNCT
cana-950	54	78	.	.	PUNCT
cana-950	55	1	let	let	AUX
cana-950	55	2	represent	represent	VERB
cana-950	55	3	the	the	DET
cana-950	55	4	order	order	NOUN
cana-950	55	5	of	of	ADP
cana-950	55	6	the	the	DET
cana-950	55	7	group	group	NOUN
cana-950	55	8	g.	g.	NOUN
cana-950	55	9	the	the	DET
cana-950	55	10	degree	degree	NOUN
cana-950	55	11	of	of	ADP
cana-950	55	12	a	a	DET
cana-950	55	13	vertex	vertex	NOUN
cana-950	55	14	in	in	ADP
cana-950	55	15	a	a	DET
cana-950	55	16	graph	graph	NOUN
cana-950	55	17	is	be	AUX
cana-950	55	18	determined	determine	VERB
cana-950	55	19	by	by	ADP
cana-950	55	20	the	the	DET
cana-950	55	21	number	number	NOUN
cana-950	55	22	of	of	ADP
cana-950	55	23	edges	edge	NOUN
cana-950	55	24	that	that	PRON
cana-950	55	25	are	be	AUX
cana-950	55	26	connected	connect	VERB
cana-950	55	27	to	to	ADP
cana-950	55	28	the	the	DET
cana-950	55	29	vertex	vertex	NOUN
cana-950	55	30	,	,	PUNCT
cana-950	55	31	taking	take	VERB
cana-950	55	32	into	into	ADP
cana-950	55	33	account	account	NOUN
cana-950	55	34	loops	loop	NOUN
cana-950	55	35	as	as	ADP
cana-950	55	36	two	two	NUM
cana-950	55	37	separate	separate	ADJ
cana-950	55	38	edges	edge	NOUN
cana-950	55	39	.	.	PUNCT
cana-950	56	1	the	the	DET
cana-950	56	2	degree	degree	NOUN
cana-950	56	3	of	of	ADP
cana-950	56	4	a	a	DET
cana-950	56	5	vertex	vertex	NOUN
cana-950	56	6	is	be	AUX
cana-950	56	7	represented	represent	VERB
cana-950	56	8	by	by	ADP
cana-950	56	9	the	the	DET
cana-950	56	10	notation	notation	NOUN
cana-950	56	11	deg(v	deg(v	PROPN
cana-950	56	12	)	)	PUNCT
cana-950	56	13	.	.	PUNCT
cana-950	57	1	the	the	DET
cana-950	57	2	maximum	maximum	ADJ
cana-950	57	3	and	and	CCONJ
cana-950	57	4	least	least	ADJ
cana-950	57	5	degree	degree	NOUN
cana-950	57	6	of	of	ADP
cana-950	57	7	a	a	DET
cana-950	57	8	graph	graph	NOUN
cana-950	57	9	are	be	AUX
cana-950	57	10	indicated	indicate	VERB
cana-950	57	11	by	by	ADP
cana-950	57	12	(	(	PUNCT
cana-950	57	13	)	)	PUNCT
cana-950	57	14	(	(	PUNCT
cana-950	57	15	)	)	PUNCT
cana-950	57	16	g	g	PROPN
cana-950	57	17	and	and	CCONJ
cana-950	57	18	g	g	PROPN
cana-950	57	19	respectively	respectively	ADV
cana-950	57	20	.	.	PUNCT
cana-950	58	1	neighborhood	neighborhood	NOUN
cana-950	58	2	:	:	PUNCT
cana-950	58	3	the	the	DET
cana-950	58	4	open	open	ADJ
cana-950	58	5	neighborhood	neighborhood	NOUN
cana-950	58	6	of	of	ADP
cana-950	58	7	a	a	DET
cana-950	58	8	vertex	vertex	NOUN
cana-950	58	9	w	w	NOUN
cana-950	58	10	v	v	PUNCT
cana-950	58	11	is	be	AUX
cana-950	58	12	denoted	denote	VERB
cana-950	58	13	by	by	ADP
cana-950	58	14	(	(	PUNCT
cana-950	58	15	w	w	NOUN
cana-950	58	16	)	)	PUNCT
cana-950	58	17	{	{	PUNCT
cana-950	58	18	:	:	PUNCT
cana-950	58	19	}	}	PUNCT
cana-950	58	20	n	n	CCONJ
cana-950	58	21	u	u	NOUN
cana-950	58	22	v	v	PROPN
cana-950	58	23	uw	uw	PROPN
cana-950	58	24	e=	e=	PROPN
cana-950	58	25			PROPN
cana-950	58	26			NOUN
cana-950	58	27	and	and	CCONJ
cana-950	58	28	its	its	PRON
cana-950	58	29	closed	closed	ADJ
cana-950	58	30	neighborhood	neighborhood	NOUN
cana-950	58	31	is	be	AUX
cana-950	58	32	[	[	X
cana-950	58	33	w	w	X
cana-950	58	34	]	]	X
cana-950	58	35	(	(	PUNCT
cana-950	58	36	w	w	NOUN
cana-950	58	37	)	)	PUNCT
cana-950	58	38	{	{	PUNCT
cana-950	58	39	w}n	w}n	PROPN
cana-950	58	40	n=	n=	PROPN
cana-950	58	41	.	.	PUNCT
cana-950	59	1	communications	communication	NOUN
cana-950	59	2	on	on	ADP
cana-950	59	3	applied	apply	VERB
cana-950	59	4	nonlinear	nonlinear	ADJ
cana-950	59	5	analysis	analysis	NOUN
cana-950	59	6	issn	issn	NOUN
cana-950	59	7	:	:	PUNCT
cana-950	59	8	1074	1074	NUM
cana-950	59	9	-	-	PUNCT
cana-950	59	10	133x	133x	NUM
cana-950	59	11	vol	vol	NOUN
cana-950	59	12	31	31	NUM
cana-950	59	13	no	no	NOUN
cana-950	59	14	.	.	PUNCT
cana-950	60	1	4s	4s	NUM
cana-950	60	2	(	(	PUNCT
cana-950	60	3	2024	2024	NUM
cana-950	60	4	)	)	PUNCT
cana-950	60	5	562	562	NUM
cana-950	60	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-950	60	7	floor	floor	NOUN
cana-950	60	8	function	function	NOUN
cana-950	60	9	:	:	PUNCT
cana-950	61	1	the	the	DET
cana-950	61	2	biggest	big	ADJ
cana-950	61	3	integer	integer	NOUN
cana-950	61	4	less	less	ADJ
cana-950	61	5	than	than	ADP
cana-950	61	6	or	or	CCONJ
cana-950	61	7	equal	equal	ADJ
cana-950	61	8	to	to	ADP
cana-950	61	9	l	l	NOUN
cana-950	61	10	is	be	AUX
cana-950	61	11	the	the	DET
cana-950	61	12	floor	floor	NOUN
cana-950	61	13	function	function	NOUN
cana-950	61	14	of	of	ADP
cana-950	61	15	a	a	DET
cana-950	61	16	real	real	ADJ
cana-950	61	17	number	number	NOUN
cana-950	61	18	l	l	NOUN
cana-950	61	19	,	,	PUNCT
cana-950	61	20	and	and	CCONJ
cana-950	61	21	it	it	PRON
cana-950	61	22	can	can	AUX
cana-950	61	23	be	be	AUX
cana-950	61	24	expressed	express	VERB
cana-950	61	25	as	as	ADP
cana-950	61	26	l	l	PROPN
cana-950	61	27			PROPN
cana-950	61	28			PROPN
cana-950	61	29	.	.	PUNCT
cana-950	62	1	suppose	suppose	VERB
cana-950	62	2	that	that	SCONJ
cana-950	62	3	1	1	NUM
cana-950	62	4	m	m	NOUN
cana-950	62	5	l	l	NOUN
cana-950	62	6	m	m	NOUN
cana-950	62	7			PROPN
cana-950	63	1	+	+	CCONJ
cana-950	63	2	,	,	PUNCT
cana-950	63	3	where	where	SCONJ
cana-950	63	4	m	m	NOUN
cana-950	63	5	is	be	AUX
cana-950	63	6	an	an	DET
cana-950	63	7	integer	integer	NOUN
cana-950	63	8	,	,	PUNCT
cana-950	63	9	then	then	ADV
cana-950	63	10	l	l	NOUN
cana-950	63	11	m=	m=	PROPN
cana-950	63	12			PROPN
cana-950	63	13			PROPN
cana-950	63	14	.	.	PUNCT
cana-950	64	1	ceiling	ceiling	NOUN
cana-950	64	2	function	function	PROPN
cana-950	64	3	:	:	PUNCT
cana-950	64	4	the	the	DET
cana-950	64	5	smallest	small	ADJ
cana-950	64	6	integer	integer	NOUN
cana-950	64	7	larger	large	ADJ
cana-950	64	8	than	than	ADP
cana-950	64	9	or	or	CCONJ
cana-950	64	10	equal	equal	ADJ
cana-950	64	11	to	to	ADP
cana-950	64	12	a	a	DET
cana-950	64	13	real	real	ADJ
cana-950	64	14	number	number	NOUN
cana-950	64	15	l	l	NOUN
cana-950	64	16	is	be	AUX
cana-950	64	17	its	its	PRON
cana-950	64	18	ceiling	ceiling	NOUN
cana-950	64	19	function	function	NOUN
cana-950	64	20	,	,	PUNCT
cana-950	64	21	and	and	CCONJ
cana-950	64	22	it	it	PRON
cana-950	64	23	is	be	AUX
cana-950	64	24	symbolized	symbolize	VERB
cana-950	64	25	by	by	ADP
cana-950	64	26	l	l	NOUN
cana-950	64	27			NOUN
cana-950	64	28			PROPN
cana-950	64	29	.	.	PUNCT
cana-950	65	1	suppose	suppose	VERB
cana-950	65	2	that	that	SCONJ
cana-950	65	3	1	1	NUM
cana-950	65	4	m	m	VERB
cana-950	65	5	l	l	NOUN
cana-950	65	6	m−	m−	PROPN
cana-950	65	7			PROPN
cana-950	65	8			PROPN
cana-950	65	9	,	,	PUNCT
cana-950	65	10	where	where	SCONJ
cana-950	65	11	n	n	PRON
cana-950	65	12	is	be	AUX
cana-950	65	13	an	an	DET
cana-950	65	14	integer	integer	NOUN
cana-950	65	15	,	,	PUNCT
cana-950	65	16	then	then	ADV
cana-950	65	17	l	l	NOUN
cana-950	65	18	m=	m=	X
cana-950	65	19			NOUN
cana-950	65	20			NOUN
cana-950	65	21	.	.	PUNCT
cana-950	66	1	domination	domination	NOUN
cana-950	66	2	:	:	PUNCT
cana-950	66	3	a	a	DET
cana-950	66	4	dominating	dominating	NOUN
cana-950	66	5	group	group	NOUN
cana-950	66	6	in	in	ADP
cana-950	66	7	which	which	PRON
cana-950	66	8	,	,	PUNCT
cana-950	66	9	each	each	DET
cana-950	66	10	vertex	vertex	NOUN
cana-950	66	11	of	of	ADP
cana-950	66	12	g	g	PROPN
cana-950	66	13	is	be	AUX
cana-950	66	14	either	either	CCONJ
cana-950	66	15	in	in	ADP
cana-950	66	16	d	d	NOUN
cana-950	66	17	or	or	CCONJ
cana-950	66	18	has	have	VERB
cana-950	66	19	at	at	ADV
cana-950	66	20	least	least	ADV
cana-950	66	21	one	one	NUM
cana-950	66	22	neighbor	neighbor	NOUN
cana-950	66	23	who	who	PRON
cana-950	66	24	is	be	AUX
cana-950	66	25	also	also	ADV
cana-950	66	26	in	in	ADP
cana-950	66	27	d.	d.	PROPN
cana-950	66	28	d	d	PROPN
cana-950	66	29	is	be	AUX
cana-950	66	30	a	a	DET
cana-950	66	31	set	set	NOUN
cana-950	66	32	of	of	ADP
cana-950	66	33	vertices	vertex	NOUN
cana-950	66	34	.	.	PUNCT
cana-950	67	1	the	the	DET
cana-950	67	2	dominance	dominance	NOUN
cana-950	67	3	number	number	NOUN
cana-950	67	4	of	of	ADP
cana-950	67	5	g	g	NOUN
cana-950	67	6	,	,	PUNCT
cana-950	67	7	)	)	PUNCT
cana-950	67	8	(	(	PUNCT
cana-950	67	9	g	g	NOUN
cana-950	67	10	is	be	AUX
cana-950	67	11	the	the	DET
cana-950	67	12	minimal	minimal	ADJ
cana-950	67	13	cardinality	cardinality	NOUN
cana-950	67	14	of	of	ADP
cana-950	67	15	such	such	DET
cana-950	67	16	a	a	DET
cana-950	67	17	set	set	NOUN
cana-950	67	18	.	.	PUNCT
cana-950	68	1	secure	secure	ADJ
cana-950	68	2	domination	domination	NOUN
cana-950	68	3	:	:	PUNCT
cana-950	68	4	assume	assume	VERB
cana-950	68	5	that	that	SCONJ
cana-950	68	6	g	g	NOUN
cana-950	68	7	=	=	PUNCT
cana-950	69	1	[	[	X
cana-950	69	2	{	{	PUNCT
cana-950	69	3	v	v	NOUN
cana-950	69	4	}	}	PUNCT
cana-950	69	5	,	,	PUNCT
cana-950	69	6	{	{	PUNCT
cana-950	69	7	e	e	X
cana-950	69	8	}	}	PUNCT
cana-950	69	9	]	]	PUNCT
cana-950	69	10	is	be	AUX
cana-950	69	11	an	an	DET
cana-950	69	12	elementary	elementary	ADJ
cana-950	69	13	graph	graph	NOUN
cana-950	69	14	of	of	ADP
cana-950	69	15	order	order	NOUN
cana-950	69	16	n.	n.	NOUN
cana-950	69	17	if	if	SCONJ
cana-950	69	18	every	every	DET
cana-950	69	19	vertex	vertex	NOUN
cana-950	69	20	in	in	ADP
cana-950	69	21	vs	vs	ADP
cana-950	69	22	is	be	AUX
cana-950	69	23	next	next	ADJ
cana-950	69	24	to	to	ADP
cana-950	69	25	a	a	DET
cana-950	69	26	vertex	vertex	NOUN
cana-950	69	27	in	in	ADP
cana-950	69	28	s	s	PROPN
cana-950	69	29	,	,	PUNCT
cana-950	69	30	then	then	ADV
cana-950	69	31	set	set	VERB
cana-950	69	32	s	s	PRON
cana-950	69	33			PROPN
cana-950	69	34	v	v	PROPN
cana-950	69	35	is	be	AUX
cana-950	69	36	a	a	DET
cana-950	69	37	dominant	dominant	ADJ
cana-950	69	38	set	set	NOUN
cana-950	69	39	of	of	ADP
cana-950	69	40	set	set	NOUN
cana-950	69	41	g.	g.	PROPN
cana-950	69	42	a	a	DET
cana-950	69	43	secure	secure	ADJ
cana-950	69	44	dominating	dominating	NOUN
cana-950	69	45	set	set	NOUN
cana-950	69	46	s	s	VERB
cana-950	69	47	inside	inside	ADP
cana-950	69	48	a	a	DET
cana-950	69	49	graph	graph	NOUN
cana-950	69	50	g	g	NOUN
cana-950	69	51	is	be	AUX
cana-950	69	52	characterized	characterize	VERB
cana-950	69	53	by	by	ADP
cana-950	69	54	its	its	PRON
cana-950	69	55	ability	ability	NOUN
cana-950	69	56	to	to	PART
cana-950	69	57	include	include	VERB
cana-950	69	58	all	all	DET
cana-950	69	59	vertices	vertice	VERB
cana-950	69	60	u	u	PRON
cana-950	69	61			NOUN
cana-950	69	62	v	v	ADP
cana-950	69	63	s	s	VERB
cana-950	69	64	close	close	ADJ
cana-950	69	65	to	to	ADP
cana-950	69	66	a	a	DET
cana-950	69	67	vertex	vertex	NOUN
cana-950	69	68	v	v	NOUN
cana-950	69	69	s	s	NOUN
cana-950	69	70	,	,	PUNCT
cana-950	69	71	so	so	SCONJ
cana-950	69	72	that	that	SCONJ
cana-950	69	73	[	[	X
cana-950	69	74	(	(	PUNCT
cana-950	69	75	s	s	X
cana-950	69	76	{	{	PUNCT
cana-950	69	77	u})	u})	NOUN
cana-950	69	78	{	{	PUNCT
cana-950	69	79	v	v	NOUN
cana-950	69	80	}	}	PUNCT
cana-950	69	81	]	]	PUNCT
cana-950	69	82	is	be	AUX
cana-950	69	83	moreover	moreover	ADV
cana-950	69	84	a	a	DET
cana-950	69	85	dominating	dominating	NOUN
cana-950	69	86	set	set	NOUN
cana-950	69	87	.	.	PUNCT
cana-950	70	1	the	the	DET
cana-950	70	2	secure	secure	ADJ
cana-950	70	3	domination	domination	NOUN
cana-950	70	4	number	number	NOUN
cana-950	70	5	,	,	PUNCT
cana-950	70	6	represented	represent	VERB
cana-950	70	7	by	by	ADP
cana-950	70	8	(	(	PUNCT
cana-950	70	9	)	)	PUNCT
cana-950	70	10	s	s	PART
cana-950	70	11	g	g	NOUN
cana-950	70	12	,	,	PUNCT
cana-950	70	13	is	be	AUX
cana-950	70	14	the	the	DET
cana-950	70	15	minimal	minimal	ADJ
cana-950	70	16	cardinality	cardinality	NOUN
cana-950	70	17	of	of	ADP
cana-950	70	18	a	a	DET
cana-950	70	19	secure	secure	ADJ
cana-950	70	20	dominating	dominating	NOUN
cana-950	70	21	set	set	NOUN
cana-950	70	22	of	of	ADP
cana-950	70	23	g.	g.	PROPN
cana-950	70	24	secure	secure	ADJ
cana-950	70	25	vertex	vertex	NOUN
cana-950	70	26	edge	edge	NOUN
cana-950	70	27	domination	domination	NOUN
cana-950	70	28	:	:	PUNCT
cana-950	70	29	if	if	SCONJ
cana-950	70	30	for	for	ADP
cana-950	70	31	every	every	DET
cana-950	70	32	edge	edge	NOUN
cana-950	70	33	,	,	PUNCT
cana-950	70	34	y	y	PROPN
cana-950	70	35	e	e	X
cana-950	70	36	(	(	PUNCT
cana-950	70	37	g	g	NOUN
cana-950	70	38	)	)	PUNCT
cana-950	70	39	,	,	PUNCT
cana-950	70	40	there	there	PRON
cana-950	70	41	is	be	VERB
cana-950	70	42	a	a	DET
cana-950	70	43	vertex	vertex	NOUN
cana-950	70	44	v	v	NOUN
cana-950	70	45	i	i	PRON
cana-950	70	46	such	such	ADJ
cana-950	70	47	that	that	SCONJ
cana-950	70	48	v	v	NOUN
cana-950	70	49	defends	defend	VERB
cana-950	70	50	y	y	PROPN
cana-950	70	51	,	,	PUNCT
cana-950	70	52	then	then	ADV
cana-950	70	53	the	the	DET
cana-950	70	54	collection	collection	NOUN
cana-950	71	1	i	i	X
cana-950	71	2	v	v	NOUN
cana-950	71	3	(	(	PUNCT
cana-950	71	4	g	g	NOUN
cana-950	71	5	)	)	PUNCT
cana-950	71	6	is	be	AUX
cana-950	71	7	a	a	DET
cana-950	71	8	safe	safe	ADJ
cana-950	71	9	vertex	vertex	NOUN
cana-950	71	10	edge	edge	NOUN
cana-950	71	11	dominating	dominating	NOUN
cana-950	71	12	set	set	NOUN
cana-950	71	13	of	of	ADP
cana-950	71	14	g.	g.	PROPN
cana-950	71	15	in	in	ADP
cana-950	71	16	this	this	DET
cana-950	71	17	regard	regard	NOUN
cana-950	71	18	,	,	PUNCT
cana-950	71	19	an	an	DET
cana-950	71	20	edge	edge	NOUN
cana-950	71	21	that	that	PRON
cana-950	71	22	is	be	AUX
cana-950	71	23	incident	incident	NOUN
cana-950	71	24	on	on	ADP
cana-950	71	25	a	a	DET
cana-950	71	26	vertex	vertex	NOUN
cana-950	71	27	in	in	ADP
cana-950	71	28	i	i	PRON
cana-950	71	29	defends	defend	VERB
cana-950	71	30	that	that	SCONJ
cana-950	71	31	vertex	vertex	NOUN
cana-950	71	32	's	's	PART
cana-950	71	33	surrounding	surround	VERB
cana-950	71	34	edges	edge	NOUN
cana-950	71	35	as	as	ADV
cana-950	71	36	well	well	ADV
cana-950	71	37	as	as	ADP
cana-950	71	38	the	the	DET
cana-950	71	39	incident	incident	NOUN
cana-950	71	40	edges	edge	VERB
cana-950	71	41	themselves	themselves	PRON
cana-950	71	42	.	.	PUNCT
cana-950	72	1	the	the	DET
cana-950	72	2	dominant	dominant	ADJ
cana-950	72	3	set	set	NOUN
cana-950	72	4	i	i	PRON
cana-950	72	5	of	of	ADP
cana-950	72	6	a	a	DET
cana-950	72	7	graph	graph	NOUN
cana-950	72	8	g	g	NOUN
cana-950	72	9	is	be	AUX
cana-950	72	10	defined	define	VERB
cana-950	72	11	as	as	ADP
cana-950	72	12	a	a	DET
cana-950	72	13	collection	collection	NOUN
cana-950	72	14	of	of	ADP
cana-950	72	15	vertices	vertex	NOUN
cana-950	72	16	such	such	ADJ
cana-950	72	17	that	that	SCONJ
cana-950	72	18	every	every	DET
cana-950	72	19	vertex	vertex	NOUN
cana-950	72	20	z	z	NOUN
cana-950	72	21	in	in	ADP
cana-950	72	22	v	v	NOUN
cana-950	72	23	i	i	PRON
cana-950	72	24	is	be	AUX
cana-950	72	25	either	either	ADV
cana-950	72	26	adjacent	adjacent	ADJ
cana-950	72	27	to	to	ADP
cana-950	72	28	a	a	DET
cana-950	72	29	vertex	vertex	NOUN
cana-950	72	30	in	in	ADP
cana-950	72	31	i	i	PRON
cana-950	72	32	or	or	CCONJ
cana-950	72	33	has	have	VERB
cana-950	72	34	a	a	DET
cana-950	72	35	vertex	vertex	NOUN
cana-950	72	36	in	in	ADP
cana-950	72	37	i	i	PRON
cana-950	72	38	adjacent	adjacent	ADJ
cana-950	72	39	to	to	ADP
cana-950	72	40	its	its	PRON
cana-950	72	41	incident	incident	NOUN
cana-950	72	42	edges	edge	NOUN
cana-950	72	43	,	,	PUNCT
cana-950	72	44	such	such	ADJ
cana-950	72	45	that	that	SCONJ
cana-950	72	46	removing	remove	VERB
cana-950	72	47	any	any	DET
cana-950	72	48	vertex	vertex	NOUN
cana-950	72	49	x	x	PUNCT
cana-950	72	50	from	from	ADP
cana-950	72	51	i	i	PRON
cana-950	72	52	and	and	CCONJ
cana-950	72	53	adding	add	VERB
cana-950	72	54	z	z	PROPN
cana-950	72	55	to	to	ADP
cana-950	72	56	the	the	DET
cana-950	72	57	resulting	result	VERB
cana-950	72	58	set	set	NOUN
cana-950	72	59	,	,	PUNCT
cana-950	72	60	[	[	X
cana-950	72	61	(	(	PUNCT
cana-950	72	62	i	i	PRON
cana-950	72	63	{	{	PUNCT
cana-950	72	64	x})	x})	PROPN
cana-950	73	1	z	z	X
cana-950	73	2	]	]	X
cana-950	73	3	forms	form	VERB
cana-950	73	4	another	another	DET
cana-950	73	5	dominating	dominating	NOUN
cana-950	73	6	set	set	NOUN
cana-950	73	7	.	.	PUNCT
cana-950	74	1	the	the	DET
cana-950	74	2	secure	secure	ADJ
cana-950	74	3	vertex	vertex	NOUN
cana-950	74	4	edge	edge	NOUN
cana-950	74	5	domination	domination	NOUN
cana-950	74	6	number	number	NOUN
cana-950	74	7	,	,	PUNCT
cana-950	74	8	indicated	indicate	VERB
cana-950	74	9	as	as	ADP
cana-950	74	10	)	)	PUNCT
cana-950	74	11	(	(	PUNCT
cana-950	74	12	gsve	gsve	PROPN
cana-950	74	13	,	,	PUNCT
cana-950	74	14	refers	refer	VERB
cana-950	74	15	to	to	ADP
cana-950	74	16	the	the	DET
cana-950	74	17	lowest	low	ADJ
cana-950	74	18	cardinality	cardinality	NOUN
cana-950	74	19	of	of	ADP
cana-950	74	20	secure	secure	ADJ
cana-950	74	21	vertex	vertex	NOUN
cana-950	74	22	edge	edge	NOUN
cana-950	74	23	domination	domination	NOUN
cana-950	74	24	in	in	ADP
cana-950	74	25	graph	graph	NOUN
cana-950	74	26	g.	g.	PROPN
cana-950	74	27	bull	bull	NOUN
cana-950	74	28	graph	graph	NOUN
cana-950	74	29	:	:	PUNCT
cana-950	74	30	the	the	DET
cana-950	74	31	bull	bull	NOUN
cana-950	74	32	graph	graph	NOUN
cana-950	74	33	is	be	AUX
cana-950	74	34	a	a	DET
cana-950	74	35	planar	planar	ADJ
cana-950	74	36	undirected	undirected	ADJ
cana-950	74	37	network	network	NOUN
cana-950	74	38	consisting	consist	VERB
cana-950	74	39	of	of	ADP
cana-950	74	40	five	five	NUM
cana-950	74	41	vertices	vertex	NOUN
cana-950	74	42	and	and	CCONJ
cana-950	74	43	five	five	NUM
cana-950	74	44	edges	edge	NOUN
cana-950	74	45	.	.	PUNCT
cana-950	75	1	its	its	PRON
cana-950	75	2	form	form	NOUN
cana-950	75	3	resembles	resemble	VERB
cana-950	75	4	a	a	DET
cana-950	75	5	triangle	triangle	NOUN
cana-950	75	6	with	with	ADP
cana-950	75	7	two	two	NUM
cana-950	75	8	additional	additional	ADJ
cana-950	75	9	edges	edge	NOUN
cana-950	75	10	attached	attach	VERB
cana-950	75	11	to	to	ADP
cana-950	75	12	other	other	ADJ
cana-950	75	13	vertices	vertex	NOUN
cana-950	75	14	.	.	PUNCT
cana-950	76	1	butterfly	butterfly	NOUN
cana-950	76	2	graph	graph	NOUN
cana-950	76	3	:	:	PUNCT
cana-950	76	4	the	the	DET
cana-950	76	5	butterfly	butterfly	NOUN
cana-950	76	6	graph	graph	NOUN
cana-950	76	7	is	be	AUX
cana-950	76	8	a	a	DET
cana-950	76	9	planar	planar	ADJ
cana-950	76	10	,	,	PUNCT
cana-950	76	11	undirected	undirected	ADJ
cana-950	76	12	graph	graph	NOUN
cana-950	76	13	having	have	VERB
cana-950	76	14	six	six	NUM
cana-950	76	15	edges	edge	NOUN
cana-950	76	16	and	and	CCONJ
cana-950	76	17	five	five	NUM
cana-950	76	18	vertices	vertex	NOUN
cana-950	76	19	.	.	PUNCT
cana-950	77	1	the	the	DET
cana-950	77	2	graph	graph	NOUN
cana-950	77	3	is	be	AUX
cana-950	77	4	created	create	VERB
cana-950	77	5	by	by	ADP
cana-950	77	6	linking	link	VERB
cana-950	77	7	two	two	NUM
cana-950	77	8	duplicates	duplicate	NOUN
cana-950	77	9	of	of	ADP
cana-950	77	10	the	the	DET
cana-950	77	11	cycle	cycle	NOUN
cana-950	77	12	graph	graph	NOUN
cana-950	77	13	c3	c3	PROPN
cana-950	77	14	at	at	ADP
cana-950	77	15	a	a	DET
cana-950	77	16	shared	share	VERB
cana-950	77	17	vertex	vertex	NOUN
cana-950	77	18	and	and	CCONJ
cana-950	77	19	is	be	AUX
cana-950	77	20	identical	identical	ADJ
cana-950	77	21	to	to	ADP
cana-950	77	22	the	the	DET
cana-950	77	23	friendship	friendship	NOUN
cana-950	77	24	graph	graph	NOUN
cana-950	77	25	f2	f2	PROPN
cana-950	77	26	.	.	PUNCT
cana-950	78	1	diamond	diamond	NOUN
cana-950	78	2	graph	graph	NOUN
cana-950	78	3	:	:	PUNCT
cana-950	78	4	a	a	DET
cana-950	78	5	diamond	diamond	NOUN
cana-950	78	6	graph	graph	NOUN
cana-950	78	7	refers	refer	VERB
cana-950	78	8	to	to	ADP
cana-950	78	9	a	a	DET
cana-950	78	10	planar	planar	ADJ
cana-950	78	11	,	,	PUNCT
cana-950	78	12	undirected	undirected	ADJ
cana-950	78	13	network	network	NOUN
cana-950	78	14	that	that	PRON
cana-950	78	15	consists	consist	VERB
cana-950	78	16	of	of	ADP
cana-950	78	17	four	four	NUM
cana-950	78	18	vertices	vertex	NOUN
cana-950	78	19	and	and	CCONJ
cana-950	78	20	five	five	NUM
cana-950	78	21	edges	edge	NOUN
cana-950	78	22	.	.	PUNCT
cana-950	79	1	it	it	PRON
cana-950	79	2	is	be	AUX
cana-950	79	3	comprised	comprise	VERB
cana-950	79	4	of	of	ADP
cana-950	79	5	a	a	DET
cana-950	79	6	complete	complete	ADJ
cana-950	79	7	k4	k4	NOUN
cana-950	79	8	graph	graph	NOUN
cana-950	79	9	with	with	ADP
cana-950	79	10	one	one	NUM
cana-950	79	11	edge	edge	NOUN
cana-950	79	12	eradicated	eradicate	VERB
cana-950	79	13	.	.	PUNCT
cana-950	80	1	durer	durer	PROPN
cana-950	80	2	graph	graph	NOUN
cana-950	80	3	:	:	PUNCT
cana-950	80	4	with	with	ADP
cana-950	80	5	twelve	twelve	NUM
cana-950	80	6	vertices	vertex	NOUN
cana-950	80	7	and	and	CCONJ
cana-950	80	8	eighteen	eighteen	NUM
cana-950	80	9	edges	edge	NOUN
cana-950	80	10	,	,	PUNCT
cana-950	80	11	the	the	DET
cana-950	80	12	durer	durer	PROPN
cana-950	80	13	graph	graph	NOUN
cana-950	80	14	is	be	AUX
cana-950	80	15	a	a	DET
cana-950	80	16	free	free	ADJ
cana-950	80	17	hexagonal	hexagonal	ADJ
cana-950	80	18	graph	graph	NOUN
cana-950	80	19	.	.	PUNCT
cana-950	81	1	six	six	NUM
cana-950	81	2	vertices	vertex	NOUN
cana-950	81	3	create	create	VERB
cana-950	81	4	an	an	DET
cana-950	81	5	exterior	exterior	ADJ
cana-950	81	6	hexagon	hexagon	NOUN
cana-950	81	7	in	in	ADP
cana-950	81	8	the	the	DET
cana-950	81	9	durer	durer	PROPN
cana-950	81	10	graph	graph	NOUN
cana-950	81	11	,	,	PUNCT
cana-950	81	12	despite	despite	SCONJ
cana-950	81	13	the	the	DET
cana-950	81	14	other	other	ADJ
cana-950	81	15	six	six	NUM
cana-950	81	16	vertices	vertex	NOUN
cana-950	81	17	which	which	PRON
cana-950	81	18	compose	compose	VERB
cana-950	81	19	an	an	DET
cana-950	81	20	inverted	inverted	ADJ
cana-950	81	21	2	2	NUM
cana-950	81	22	triangle	triangle	NOUN
cana-950	81	23	region	region	NOUN
cana-950	81	24	.	.	PUNCT
cana-950	82	1	only	only	ADV
cana-950	82	2	one	one	NUM
cana-950	82	3	vertex	vertex	NOUN
cana-950	82	4	on	on	ADP
cana-950	82	5	the	the	DET
cana-950	82	6	hexagon	hexagon	NOUN
cana-950	82	7	is	be	AUX
cana-950	82	8	next	next	ADJ
cana-950	82	9	to	to	ADP
cana-950	82	10	any	any	PRON
cana-950	82	11	of	of	ADP
cana-950	82	12	the	the	DET
cana-950	82	13	six	six	NUM
cana-950	82	14	vertices	vertex	NOUN
cana-950	82	15	of	of	ADP
cana-950	82	16	the	the	DET
cana-950	82	17	interior	interior	ADJ
cana-950	82	18	triangles	triangle	NOUN
cana-950	82	19	.	.	PUNCT
cana-950	83	1	franklin	franklin	PROPN
cana-950	83	2	graph	graph	NOUN
cana-950	83	3	:	:	PUNCT
cana-950	83	4	eighteen	eighteen	NUM
cana-950	83	5	edges	edge	NOUN
cana-950	83	6	and	and	CCONJ
cana-950	83	7	twelve	twelve	NUM
cana-950	83	8	vertices	vertex	NOUN
cana-950	83	9	make	make	VERB
cana-950	83	10	up	up	ADP
cana-950	83	11	the	the	DET
cana-950	83	12	three	three	NUM
cana-950	83	13	-	-	PUNCT
cana-950	83	14	regular	regular	ADJ
cana-950	83	15	franklin	franklin	PROPN
cana-950	83	16	graph	graph	NOUN
cana-950	83	17	.	.	PUNCT
cana-950	84	1	in	in	ADP
cana-950	84	2	addition	addition	NOUN
cana-950	84	3	,	,	PUNCT
cana-950	84	4	the	the	DET
cana-950	84	5	graph	graph	NOUN
cana-950	84	6	has	have	VERB
cana-950	84	7	three	three	NUM
cana-950	84	8	edges	edge	NOUN
cana-950	84	9	and	and	CCONJ
cana-950	84	10	three	three	NUM
cana-950	84	11	vertices	vertex	NOUN
cana-950	84	12	that	that	PRON
cana-950	84	13	are	be	AUX
cana-950	84	14	connected	connect	VERB
cana-950	84	15	.	.	PUNCT
cana-950	85	1	golomb	golomb	NOUN
cana-950	85	2	graph	graph	NOUN
cana-950	85	3	:	:	PUNCT
cana-950	85	4	the	the	DET
cana-950	85	5	golomb	golomb	NOUN
cana-950	85	6	graph	graph	NOUN
cana-950	85	7	is	be	AUX
cana-950	85	8	a	a	DET
cana-950	85	9	non	non	ADJ
cana-950	85	10	-	-	ADJ
cana-950	85	11	planar	planar	ADJ
cana-950	85	12	polyhedral	polyhedral	ADJ
cana-950	85	13	shape	shape	NOUN
cana-950	85	14	graph	graph	NOUN
cana-950	85	15	that	that	PRON
cana-950	85	16	may	may	AUX
cana-950	85	17	be	be	AUX
cana-950	85	18	represented	represent	VERB
cana-950	85	19	as	as	ADP
cana-950	85	20	a	a	DET
cana-950	85	21	unit	unit	NOUN
cana-950	85	22	distance	distance	NOUN
cana-950	85	23	graph	graph	NOUN
cana-950	85	24	.	.	PUNCT
cana-950	86	1	it	it	PRON
cana-950	86	2	is	be	AUX
cana-950	86	3	composed	compose	VERB
cana-950	86	4	of	of	ADP
cana-950	86	5	10	10	NUM
cana-950	86	6	vertices	vertex	NOUN
cana-950	86	7	and	and	CCONJ
cana-950	86	8	18	18	NUM
cana-950	86	9	edges	edge	NOUN
cana-950	86	10	.	.	PUNCT
cana-950	87	1	communications	communication	NOUN
cana-950	87	2	on	on	ADP
cana-950	87	3	applied	apply	VERB
cana-950	87	4	nonlinear	nonlinear	ADJ
cana-950	87	5	analysis	analysis	NOUN
cana-950	87	6	issn	issn	NOUN
cana-950	87	7	:	:	PUNCT
cana-950	87	8	1074	1074	NUM
cana-950	87	9	-	-	PUNCT
cana-950	87	10	133x	133x	NUM
cana-950	87	11	vol	vol	NOUN
cana-950	87	12	31	31	NUM
cana-950	87	13	no	no	NOUN
cana-950	87	14	.	.	PUNCT
cana-950	88	1	4s	4s	NUM
cana-950	88	2	(	(	PUNCT
cana-950	88	3	2024	2024	NUM
cana-950	88	4	)	)	PUNCT
cana-950	88	5	563	563	NUM
cana-950	88	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-950	88	7	moser	moser	PROPN
cana-950	88	8	spindle	spindle	PROPN
cana-950	88	9	graph	graph	NOUN
cana-950	88	10	:	:	PUNCT
cana-950	88	11	the	the	DET
cana-950	88	12	moser	moser	PROPN
cana-950	88	13	spindle	spindle	PROPN
cana-950	88	14	is	be	AUX
cana-950	88	15	a	a	DET
cana-950	88	16	seven	seven	NUM
cana-950	88	17	-	-	PUNCT
cana-950	88	18	vertex	vertex	NOUN
cana-950	88	19	,	,	PUNCT
cana-950	88	20	eleven	eleven	NUM
cana-950	88	21	-	-	PUNCT
cana-950	88	22	edge	edge	NOUN
cana-950	88	23	undirected	undirected	ADJ
cana-950	88	24	graph	graph	NOUN
cana-950	88	25	.	.	PUNCT
cana-950	89	1	the	the	DET
cana-950	89	2	shape	shape	NOUN
cana-950	89	3	of	of	ADP
cana-950	89	4	it	it	PRON
cana-950	89	5	resembles	resemble	VERB
cana-950	89	6	a	a	DET
cana-950	89	7	triangle	triangle	NOUN
cana-950	89	8	that	that	PRON
cana-950	89	9	is	be	AUX
cana-950	89	10	enclosed	enclose	VERB
cana-950	89	11	in	in	ADP
cana-950	89	12	a	a	DET
cana-950	89	13	hexagon	hexagon	NOUN
cana-950	89	14	.	.	PUNCT
cana-950	90	1	the	the	DET
cana-950	90	2	hajos	hajos	ADJ
cana-950	90	3	graph	graph	NOUN
cana-950	90	4	is	be	AUX
cana-950	90	5	another	another	DET
cana-950	90	6	name	name	NOUN
cana-950	90	7	for	for	ADP
cana-950	90	8	the	the	DET
cana-950	90	9	moser	moser	PROPN
cana-950	90	10	spindle	spindle	PROPN
cana-950	90	11	.	.	PUNCT
cana-950	91	1	herschel	herschel	PROPN
cana-950	91	2	graph	graph	PROPN
cana-950	91	3	:	:	PUNCT
cana-950	91	4	the	the	DET
cana-950	91	5	bipartite	bipartite	ADJ
cana-950	91	6	,	,	PUNCT
cana-950	91	7	undirected	undirected	ADJ
cana-950	91	8	herschel	herschel	PROPN
cana-950	91	9	graph	graph	NOUN
cana-950	91	10	has	have	VERB
cana-950	91	11	eighteen	eighteen	NUM
cana-950	91	12	edges	edge	NOUN
cana-950	91	13	and	and	CCONJ
cana-950	91	14	eleven	eleven	NUM
cana-950	91	15	vertices	vertex	NOUN
cana-950	91	16	.	.	PUNCT
cana-950	92	1	the	the	DET
cana-950	92	2	smallest	small	ADJ
cana-950	92	3	polyhedral	polyhedral	ADJ
cana-950	92	4	graph	graph	NOUN
cana-950	92	5	without	without	ADP
cana-950	92	6	a	a	DET
cana-950	92	7	hamiltonian	hamiltonian	ADJ
cana-950	92	8	cycle	cycle	NOUN
cana-950	92	9	is	be	AUX
cana-950	92	10	this	this	DET
cana-950	92	11	one	one	NUM
cana-950	92	12	,	,	PUNCT
cana-950	92	13	which	which	PRON
cana-950	92	14	is	be	AUX
cana-950	92	15	also	also	ADV
cana-950	92	16	polyhedral	polyhedral	ADJ
cana-950	92	17	.	.	PUNCT
cana-950	93	1	petersen	petersen	NOUN
cana-950	93	2	graph	graph	NOUN
cana-950	93	3	:	:	PUNCT
cana-950	93	4	the	the	DET
cana-950	93	5	petersen	petersen	NOUN
cana-950	93	6	graph	graph	NOUN
cana-950	93	7	is	be	AUX
cana-950	93	8	an	an	DET
cana-950	93	9	untamed	untamed	ADJ
cana-950	93	10	graph	graph	NOUN
cana-950	93	11	that	that	PRON
cana-950	93	12	holds	hold	VERB
cana-950	93	13	ten	ten	NUM
cana-950	93	14	vertices	vertex	NOUN
cana-950	93	15	and	and	CCONJ
cana-950	93	16	fifteen	fifteen	NUM
cana-950	93	17	edges	edge	NOUN
cana-950	93	18	.	.	PUNCT
cana-950	94	1	it	it	PRON
cana-950	94	2	is	be	AUX
cana-950	94	3	the	the	DET
cana-950	94	4	complement	complement	NOUN
cana-950	94	5	of	of	ADP
cana-950	94	6	the	the	DET
cana-950	94	7	k5	k5	PROPN
cana-950	94	8	line	line	NOUN
cana-950	94	9	graph	graph	NOUN
cana-950	94	10	.	.	PUNCT
cana-950	95	1	fish	fish	NOUN
cana-950	95	2	graph	graph	NOUN
cana-950	95	3	:	:	PUNCT
cana-950	95	4	a	a	DET
cana-950	95	5	unique	unique	ADJ
cana-950	95	6	type	type	NOUN
cana-950	95	7	of	of	ADP
cana-950	95	8	graph	graph	NOUN
cana-950	95	9	that	that	PRON
cana-950	95	10	is	be	AUX
cana-950	95	11	comprised	comprise	VERB
cana-950	95	12	of	of	ADP
cana-950	95	13	six	six	NUM
cana-950	95	14	vertices	vertex	NOUN
cana-950	95	15	and	and	CCONJ
cana-950	95	16	seven	seven	NUM
cana-950	95	17	edges	edge	NOUN
cana-950	95	18	could	could	AUX
cana-950	95	19	be	be	AUX
cana-950	95	20	referred	refer	VERB
cana-950	95	21	to	to	ADP
cana-950	95	22	as	as	ADP
cana-950	95	23	a	a	DET
cana-950	95	24	fish	fish	NOUN
cana-950	95	25	graph	graph	NOUN
cana-950	95	26	.	.	PUNCT
cana-950	96	1	wagner	wagner	NOUN
cana-950	96	2	graph	graph	NOUN
cana-950	96	3	:	:	PUNCT
cana-950	96	4	there	there	PRON
cana-950	96	5	are	be	VERB
cana-950	96	6	just	just	ADV
cana-950	96	7	eight	eight	NUM
cana-950	96	8	vertices	vertex	NOUN
cana-950	96	9	and	and	CCONJ
cana-950	96	10	twelve	twelve	NUM
cana-950	96	11	edges	edge	NOUN
cana-950	96	12	in	in	ADP
cana-950	96	13	the	the	DET
cana-950	96	14	three	three	NUM
cana-950	96	15	-	-	PUNCT
cana-950	96	16	regular	regular	ADJ
cana-950	96	17	wagner	wagner	NOUN
cana-950	96	18	graph	graph	NOUN
cana-950	96	19	.	.	PUNCT
cana-950	97	1	this	this	PRON
cana-950	97	2	is	be	AUX
cana-950	97	3	an	an	DET
cana-950	97	4	octahedral	octahedral	ADJ
cana-950	97	5	mobius	mobius	NOUN
cana-950	97	6	ladder	ladder	NOUN
cana-950	97	7	graph	graph	NOUN
cana-950	97	8	.	.	PUNCT
cana-950	98	1	the	the	DET
cana-950	98	2	wagner	wagner	PROPN
cana-950	98	3	graph	graph	NOUN
cana-950	98	4	,	,	PUNCT
cana-950	98	5	a	a	DET
cana-950	98	6	particular	particular	ADJ
cana-950	98	7	kind	kind	NOUN
cana-950	98	8	of	of	ADP
cana-950	98	9	circulant	circulant	ADJ
cana-950	98	10	graph	graph	NOUN
cana-950	98	11	in	in	ADP
cana-950	98	12	which	which	PRON
cana-950	98	13	the	the	DET
cana-950	98	14	vertices	vertex	NOUN
cana-950	98	15	can	can	AUX
cana-950	98	16	be	be	AUX
cana-950	98	17	organized	organize	VERB
cana-950	98	18	in	in	ADP
cana-950	98	19	a	a	DET
cana-950	98	20	cycle	cycle	NOUN
cana-950	98	21	,	,	PUNCT
cana-950	98	22	is	be	AUX
cana-950	98	23	a	a	DET
cana-950	98	24	cubic	cubic	ADJ
cana-950	98	25	hamiltonian	hamiltonian	ADJ
cana-950	98	26	graph	graph	NOUN
cana-950	98	27	.	.	PUNCT
cana-950	99	1	heawood	heawood	NOUN
cana-950	99	2	graph	graph	NOUN
cana-950	99	3	:	:	PUNCT
cana-950	99	4	having	have	VERB
cana-950	99	5	21	21	NUM
cana-950	99	6	edges	edge	NOUN
cana-950	99	7	and	and	CCONJ
cana-950	99	8	14	14	NUM
cana-950	99	9	vertices	vertex	NOUN
cana-950	99	10	,	,	PUNCT
cana-950	99	11	the	the	DET
cana-950	99	12	heawood	heawood	NOUN
cana-950	99	13	graph	graph	NOUN
cana-950	99	14	is	be	AUX
cana-950	99	15	an	an	DET
cana-950	99	16	undirected	undirected	ADJ
cana-950	99	17	graph	graph	NOUN
cana-950	99	18	.	.	PUNCT
cana-950	100	1	there	there	PRON
cana-950	100	2	are	be	VERB
cana-950	100	3	six	six	NUM
cana-950	100	4	edges	edge	NOUN
cana-950	100	5	or	or	CCONJ
cana-950	100	6	more	more	ADJ
cana-950	100	7	on	on	ADP
cana-950	100	8	each	each	DET
cana-950	100	9	cycle	cycle	NOUN
cana-950	100	10	in	in	ADP
cana-950	100	11	the	the	DET
cana-950	100	12	cubic	cubic	ADJ
cana-950	100	13	graph	graph	NOUN
cana-950	100	14	.	.	PUNCT
cana-950	101	1	this	this	DET
cana-950	101	2	graph	graph	NOUN
cana-950	101	3	is	be	AUX
cana-950	101	4	6	6	NUM
cana-950	101	5	-	-	PUNCT
cana-950	101	6	cage	cage	NOUN
cana-950	101	7	because	because	SCONJ
cana-950	101	8	the	the	DET
cana-950	101	9	cycles	cycle	NOUN
cana-950	101	10	of	of	ADP
cana-950	101	11	any	any	DET
cana-950	101	12	smaller	small	ADJ
cana-950	101	13	cubic	cubic	ADJ
cana-950	101	14	graph	graph	NOUN
cana-950	101	15	are	be	AUX
cana-950	101	16	shorter	short	ADJ
cana-950	101	17	.	.	PUNCT
cana-950	102	1	pappus	pappus	PROPN
cana-950	102	2	graph	graph	NOUN
cana-950	102	3	:	:	PUNCT
cana-950	102	4	pappus	pappus	ADJ
cana-950	102	5	graph	graph	NOUN
cana-950	102	6	is	be	AUX
cana-950	102	7	a	a	DET
cana-950	102	8	bipartite	bipartite	ADJ
cana-950	102	9	3	3	NUM
cana-950	102	10	-	-	PUNCT
cana-950	102	11	regular	regular	ADJ
cana-950	102	12	graph	graph	NOUN
cana-950	102	13	featuring	feature	VERB
cana-950	102	14	18	18	NUM
cana-950	102	15	vertices	vertex	NOUN
cana-950	102	16	and	and	CCONJ
cana-950	102	17	27	27	NUM
cana-950	102	18	edges	edge	NOUN
cana-950	102	19	.	.	PUNCT
cana-950	103	1	house	house	NOUN
cana-950	103	2	graph	graph	NOUN
cana-950	103	3	:	:	PUNCT
cana-950	103	4	the	the	DET
cana-950	103	5	graph	graph	NOUN
cana-950	103	6	consists	consist	VERB
cana-950	103	7	of	of	ADP
cana-950	103	8	five	five	NUM
cana-950	103	9	nodes	node	NOUN
cana-950	103	10	and	and	CCONJ
cana-950	103	11	six	six	NUM
cana-950	103	12	edges	edge	NOUN
cana-950	103	13	.	.	PUNCT
cana-950	104	1	the	the	DET
cana-950	104	2	term	term	NOUN
cana-950	104	3	"	"	PUNCT
cana-950	104	4	house	house	NOUN
cana-950	104	5	graph	graph	NOUN
cana-950	104	6	"	"	PUNCT
cana-950	104	7	is	be	AUX
cana-950	104	8	derived	derive	VERB
cana-950	104	9	from	from	ADP
cana-950	104	10	its	its	PRON
cana-950	104	11	resemblance	resemblance	NOUN
cana-950	104	12	to	to	ADP
cana-950	104	13	a	a	DET
cana-950	104	14	schematic	schematic	ADJ
cana-950	104	15	illustration	illustration	NOUN
cana-950	104	16	of	of	ADP
cana-950	104	17	a	a	DET
cana-950	104	18	home	home	NOUN
cana-950	104	19	with	with	ADP
cana-950	104	20	a	a	DET
cana-950	104	21	roof	roof	NOUN
cana-950	104	22	.	.	PUNCT
cana-950	105	1	cricket	cricket	NOUN
cana-950	105	2	graph	graph	NOUN
cana-950	105	3	:	:	PUNCT
cana-950	105	4	the	the	DET
cana-950	105	5	cricket	cricket	NOUN
cana-950	105	6	graph	graph	NOUN
cana-950	105	7	is	be	AUX
cana-950	105	8	a	a	DET
cana-950	105	9	triangular	triangular	NOUN
cana-950	105	10	-	-	PUNCT
cana-950	105	11	shaped	shape	VERB
cana-950	105	12	planar	planar	ADJ
cana-950	105	13	free	free	ADJ
cana-950	105	14	graph	graph	NOUN
cana-950	105	15	.	.	PUNCT
cana-950	106	1	it	it	PRON
cana-950	106	2	has	have	VERB
cana-950	106	3	five	five	NUM
cana-950	106	4	vertices	vertex	NOUN
cana-950	106	5	and	and	CCONJ
cana-950	106	6	five	five	NUM
cana-950	106	7	edges	edge	NOUN
cana-950	106	8	.	.	PUNCT
cana-950	107	1	these	these	DET
cana-950	107	2	edges	edge	NOUN
cana-950	107	3	are	be	AUX
cana-950	107	4	linked	link	VERB
cana-950	107	5	to	to	ADP
cana-950	107	6	a	a	DET
cana-950	107	7	unique	unique	ADJ
cana-950	107	8	node	node	NOUN
cana-950	107	9	by	by	ADP
cana-950	107	10	two	two	NUM
cana-950	107	11	different	different	ADJ
cana-950	107	12	pendant	pendant	ADJ
cana-950	107	13	vertices	vertex	NOUN
cana-950	107	14	.	.	PUNCT
cana-950	108	1	3	3	X
cana-950	108	2	.	.	X
cana-950	108	3	main	main	ADJ
cana-950	108	4	results	result	NOUN
cana-950	108	5	theorem	theorem	VERB
cana-950	108	6	1	1	NUM
cana-950	108	7	:	:	PUNCT
cana-950	108	8	the	the	DET
cana-950	108	9	secure	secure	ADJ
cana-950	108	10	vertex	vertex	NOUN
cana-950	108	11	edge	edge	NOUN
cana-950	108	12	domination	domination	NOUN
cana-950	108	13	of	of	ADP
cana-950	108	14	a	a	DET
cana-950	108	15	bull	bull	NOUN
cana-950	108	16	graph	graph	NOUN
cana-950	108	17	is	be	AUX
cana-950	108	18	1	1	NUM
cana-950	108	19	.	.	PUNCT
cana-950	109	1	proof	proof	NOUN
cana-950	109	2	:	:	PUNCT
cana-950	109	3	the	the	DET
cana-950	109	4	bull	bull	NOUN
cana-950	109	5	graph	graph	NOUN
cana-950	109	6	is	be	AUX
cana-950	109	7	a	a	DET
cana-950	109	8	graph	graph	NOUN
cana-950	109	9	comprised	comprise	VERB
cana-950	109	10	of	of	ADP
cana-950	109	11	5	5	NUM
cana-950	109	12	vertices	vertex	NOUN
cana-950	109	13	and	and	CCONJ
cana-950	109	14	5	5	NUM
cana-950	109	15	edges	edge	NOUN
cana-950	109	16	.	.	PUNCT
cana-950	110	1	it	it	PRON
cana-950	110	2	is	be	AUX
cana-950	110	3	shaped	shape	VERB
cana-950	110	4	like	like	ADP
cana-950	110	5	a	a	DET
cana-950	110	6	triangle	triangle	NOUN
cana-950	110	7	with	with	ADP
cana-950	110	8	two	two	NUM
cana-950	110	9	separate	separate	ADJ
cana-950	110	10	pendant	pendant	ADJ
cana-950	110	11	edges	edge	NOUN
cana-950	110	12	.	.	PUNCT
cana-950	111	1	two	two	NUM
cana-950	111	2	vertices	vertex	NOUN
cana-950	111	3	possess	possess	VERB
cana-950	111	4	a	a	DET
cana-950	111	5	degree	degree	NOUN
cana-950	111	6	of	of	ADP
cana-950	111	7	3	3	NUM
cana-950	111	8	,	,	PUNCT
cana-950	111	9	while	while	SCONJ
cana-950	111	10	one	one	NUM
cana-950	111	11	vertex	vertex	NOUN
cana-950	111	12	possesses	possess	VERB
cana-950	111	13	a	a	DET
cana-950	111	14	degree	degree	NOUN
cana-950	111	15	of	of	ADP
cana-950	111	16	2	2	NUM
cana-950	111	17	.	.	PUNCT
cana-950	112	1	the	the	DET
cana-950	112	2	remaining	remain	VERB
cana-950	112	3	vertices	vertex	NOUN
cana-950	112	4	possess	possess	VERB
cana-950	112	5	a	a	DET
cana-950	112	6	degree	degree	NOUN
cana-950	112	7	of	of	ADP
cana-950	112	8	1	1	NUM
cana-950	112	9	.	.	PUNCT
cana-950	113	1	the	the	DET
cana-950	113	2	secure	secure	ADJ
cana-950	113	3	vertex	vertex	NOUN
cana-950	113	4	edge	edge	NOUN
cana-950	113	5	dominating	dominating	NOUN
cana-950	113	6	set	set	NOUN
cana-950	113	7	i=	i=	PROPN
cana-950	113	8	{	{	PUNCT
cana-950	113	9	x2	x2	ADJ
cana-950	113	10	}	}	PUNCT
cana-950	113	11	or{x3	or{x3	NUM
cana-950	113	12	}	}	PUNCT
cana-950	113	13	.	.	PUNCT
cana-950	114	1	the	the	DET
cana-950	114	2	vertex	vertex	NOUN
cana-950	114	3	in	in	ADP
cana-950	114	4	the	the	DET
cana-950	114	5	set	set	NOUN
cana-950	114	6	i	i	PRON
cana-950	114	7	have	have	VERB
cana-950	114	8	degree	degree	NOUN
cana-950	114	9	three	three	NUM
cana-950	114	10	,	,	PUNCT
cana-950	114	11	which	which	PRON
cana-950	114	12	defends	defend	VERB
cana-950	114	13	the	the	DET
cana-950	114	14	edges	edge	NOUN
cana-950	114	15	that	that	PRON
cana-950	114	16	are	be	AUX
cana-950	114	17	connected	connect	VERB
cana-950	114	18	to	to	ADP
cana-950	114	19	this	this	DET
cana-950	114	20	particular	particular	ADJ
cana-950	114	21	apex	apex	NOUN
cana-950	114	22	and	and	CCONJ
cana-950	114	23	the	the	DET
cana-950	114	24	edges	edge	NOUN
cana-950	114	25	that	that	PRON
cana-950	114	26	’s	’	VERB
cana-950	114	27	are	be	AUX
cana-950	114	28	adjacent	adjacent	ADJ
cana-950	114	29	to	to	ADP
cana-950	114	30	that	that	DET
cana-950	114	31	incident	incident	NOUN
cana-950	114	32	edges	edge	NOUN
cana-950	114	33	.	.	PUNCT
cana-950	115	1	so	so	ADV
cana-950	115	2	,	,	PUNCT
cana-950	115	3	all	all	DET
cana-950	115	4	the	the	DET
cana-950	115	5	edges	edge	NOUN
cana-950	115	6	of	of	ADP
cana-950	115	7	the	the	DET
cana-950	115	8	bull	bull	NOUN
cana-950	115	9	communications	communication	NOUN
cana-950	115	10	on	on	ADP
cana-950	115	11	applied	apply	VERB
cana-950	115	12	nonlinear	nonlinear	ADJ
cana-950	115	13	analysis	analysis	NOUN
cana-950	115	14	issn	issn	NOUN
cana-950	115	15	:	:	PUNCT
cana-950	115	16	1074	1074	NUM
cana-950	115	17	-	-	PUNCT
cana-950	115	18	133x	133x	NUM
cana-950	115	19	vol	vol	NOUN
cana-950	115	20	31	31	NUM
cana-950	115	21	no	no	NOUN
cana-950	115	22	.	.	PUNCT
cana-950	116	1	4s	4s	NUM
cana-950	116	2	(	(	PUNCT
cana-950	116	3	2024	2024	NUM
cana-950	116	4	)	)	PUNCT
cana-950	116	5	564	564	NUM
cana-950	116	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-950	116	7	graph	graph	NOUN
cana-950	116	8	will	will	AUX
cana-950	116	9	be	be	AUX
cana-950	116	10	defended	defend	VERB
cana-950	116	11	by	by	ADP
cana-950	116	12	the	the	DET
cana-950	116	13	set	set	NOUN
cana-950	116	14	i.	i.	NOUN
cana-950	116	15	hence	hence	ADV
cana-950	116	16	the	the	DET
cana-950	116	17	secure	secure	ADJ
cana-950	116	18	vertex	vertex	NOUN
cana-950	116	19	edge	edge	NOUN
cana-950	116	20	domination	domination	NOUN
cana-950	116	21	number	number	NOUN
cana-950	116	22	of	of	ADP
cana-950	116	23	the	the	DET
cana-950	116	24	bull	bull	NOUN
cana-950	116	25	graph	graph	NOUN
cana-950	116	26	is	be	AUX
cana-950	116	27	one	one	NUM
cana-950	116	28	.	.	PUNCT
cana-950	117	1	theorem	theorem	NOUN
cana-950	117	2	2	2	NUM
cana-950	117	3	:	:	PUNCT
cana-950	117	4	let	let	VERB
cana-950	117	5	byg	byg	NOUN
cana-950	117	6	be	be	AUX
cana-950	117	7	the	the	DET
cana-950	117	8	butterfly	butterfly	NOUN
cana-950	117	9	graph	graph	NOUN
cana-950	117	10	,	,	PUNCT
cana-950	117	11	the	the	DET
cana-950	117	12	secure	secure	ADJ
cana-950	117	13	vertex	vertex	NOUN
cana-950	117	14	edge	edge	NOUN
cana-950	117	15	domination	domination	NOUN
cana-950	117	16	number	number	NOUN
cana-950	117	17	of	of	ADP
cana-950	117	18	the	the	DET
cana-950	117	19	graph	graph	NOUN
cana-950	117	20	byg	byg	NOUN
cana-950	117	21	is	be	AUX
cana-950	117	22	one	one	NUM
cana-950	117	23	.	.	PUNCT
cana-950	118	1	proof	proof	NOUN
cana-950	118	2	:	:	PUNCT
cana-950	118	3	the	the	DET
cana-950	118	4	butterfly	butterfly	NOUN
cana-950	118	5	graph	graph	NOUN
cana-950	118	6	is	be	AUX
cana-950	118	7	a	a	DET
cana-950	118	8	planar	planar	ADJ
cana-950	118	9	graph	graph	NOUN
cana-950	118	10	made	make	VERB
cana-950	118	11	up	up	ADP
cana-950	118	12	of	of	ADP
cana-950	118	13	five	five	NUM
cana-950	118	14	vertices	vertex	NOUN
cana-950	118	15	and	and	CCONJ
cana-950	118	16	six	six	NUM
cana-950	118	17	edges	edge	NOUN
cana-950	118	18	.	.	PUNCT
cana-950	119	1	the	the	DET
cana-950	119	2	structure	structure	NOUN
cana-950	119	3	is	be	AUX
cana-950	119	4	formed	form	VERB
cana-950	119	5	by	by	ADP
cana-950	119	6	combining	combine	VERB
cana-950	119	7	two	two	NUM
cana-950	119	8	instances	instance	NOUN
cana-950	119	9	of	of	ADP
cana-950	119	10	the	the	DET
cana-950	119	11	cycle	cycle	NOUN
cana-950	119	12	graph	graph	NOUN
cana-950	119	13	c3	c3	PROPN
cana-950	119	14	,	,	PUNCT
cana-950	119	15	with	with	ADP
cana-950	119	16	a	a	DET
cana-950	119	17	shared	share	VERB
cana-950	119	18	vertex	vertex	NOUN
cana-950	119	19	.	.	PUNCT
cana-950	120	1	the	the	DET
cana-950	120	2	common	common	ADJ
cana-950	120	3	vertex	vertex	NOUN
cana-950	120	4	has	have	AUX
cana-950	120	5	degree	degree	NOUN
cana-950	120	6	four	four	NUM
cana-950	120	7	and	and	CCONJ
cana-950	120	8	all	all	DET
cana-950	120	9	the	the	DET
cana-950	120	10	remaining	remain	VERB
cana-950	120	11	vertices	vertex	NOUN
cana-950	120	12	have	have	VERB
cana-950	120	13	degree	degree	NOUN
cana-950	120	14	two	two	NUM
cana-950	120	15	.	.	PUNCT
cana-950	121	1	the	the	DET
cana-950	121	2	secure	secure	ADJ
cana-950	121	3	vertex	vertex	NOUN
cana-950	121	4	edge	edge	NOUN
cana-950	121	5	dominating	dominating	NOUN
cana-950	121	6	set	set	NOUN
cana-950	121	7	i	i	PRON
cana-950	121	8	=	=	PUNCT
cana-950	121	9	{	{	PUNCT
cana-950	121	10	x1	x1	PROPN
cana-950	121	11	}	}	PUNCT
cana-950	121	12	,	,	PUNCT
cana-950	121	13	which	which	PRON
cana-950	121	14	is	be	AUX
cana-950	121	15	the	the	DET
cana-950	121	16	common	common	ADJ
cana-950	121	17	vertex	vertex	NOUN
cana-950	121	18	with	with	ADP
cana-950	121	19	highest	high	ADJ
cana-950	121	20	degree	degree	NOUN
cana-950	121	21	.	.	PUNCT
cana-950	122	1	this	this	DET
cana-950	122	2	common	common	ADJ
cana-950	122	3	vertex	vertex	NOUN
cana-950	122	4	protects	protect	VERB
cana-950	122	5	all	all	DET
cana-950	122	6	the	the	DET
cana-950	122	7	incident	incident	NOUN
cana-950	122	8	edges	edge	NOUN
cana-950	122	9	and	and	CCONJ
cana-950	122	10	the	the	DET
cana-950	122	11	edges	edge	NOUN
cana-950	122	12	adjacent	adjacent	ADJ
cana-950	122	13	to	to	ADP
cana-950	122	14	that	that	DET
cana-950	122	15	incident	incident	NOUN
cana-950	122	16	edges	edge	NOUN
cana-950	122	17	,	,	PUNCT
cana-950	122	18	so	so	SCONJ
cana-950	122	19	that	that	SCONJ
cana-950	122	20	all	all	DET
cana-950	122	21	the	the	DET
cana-950	122	22	edges	edge	NOUN
cana-950	122	23	of	of	ADP
cana-950	122	24	the	the	DET
cana-950	122	25	graph	graph	NOUN
cana-950	122	26	are	be	AUX
cana-950	122	27	protected	protect	VERB
cana-950	122	28	by	by	ADP
cana-950	122	29	the	the	DET
cana-950	122	30	vertex	vertex	NOUN
cana-950	122	31	x1	x1	NUM
cana-950	122	32	.	.	PUNCT
cana-950	123	1	hence	hence	ADV
cana-950	123	2	the	the	DET
cana-950	123	3	secure	secure	ADJ
cana-950	123	4	vertex	vertex	NOUN
cana-950	123	5	edge	edge	NOUN
cana-950	123	6	domination	domination	NOUN
cana-950	123	7	number	number	NOUN
cana-950	123	8	of	of	ADP
cana-950	123	9	the	the	DET
cana-950	123	10	butterfly	butterfly	NOUN
cana-950	123	11	graph	graph	NOUN
cana-950	123	12	is	be	AUX
cana-950	123	13	one	one	NUM
cana-950	123	14	.	.	PUNCT
cana-950	124	1	theorem	theorem	VERB
cana-950	124	2	3	3	NUM
cana-950	124	3	:	:	PUNCT
cana-950	124	4	let	let	VERB
cana-950	124	5	dg	dg	PART
cana-950	124	6	be	be	AUX
cana-950	124	7	the	the	DET
cana-950	124	8	diamond	diamond	NOUN
cana-950	124	9	graph	graph	NOUN
cana-950	124	10	whose	whose	DET
cana-950	124	11	secure	secure	ADJ
cana-950	124	12	vertex	vertex	NOUN
cana-950	124	13	edge	edge	NOUN
cana-950	124	14	domination	domination	NOUN
cana-950	124	15	number	number	NOUN
cana-950	124	16	is	be	AUX
cana-950	124	17	one	one	NUM
cana-950	124	18	.	.	PUNCT
cana-950	125	1	proof	proof	NOUN
cana-950	125	2	:	:	PUNCT
cana-950	125	3	a	a	DET
cana-950	125	4	graph	graph	NOUN
cana-950	125	5	with	with	ADP
cana-950	125	6	four	four	NUM
cana-950	125	7	vertices	vertex	NOUN
cana-950	125	8	and	and	CCONJ
cana-950	125	9	five	five	NUM
cana-950	125	10	edges	edge	NOUN
cana-950	125	11	constitute	constitute	VERB
cana-950	125	12	a	a	DET
cana-950	125	13	diamond	diamond	NOUN
cana-950	125	14	graph	graph	NOUN
cana-950	125	15	.	.	PUNCT
cana-950	126	1	in	in	ADP
cana-950	126	2	that	that	DET
cana-950	126	3	four	four	NUM
cana-950	126	4	vertices	vertex	NOUN
cana-950	126	5	,	,	PUNCT
cana-950	126	6	two	two	NUM
cana-950	126	7	vertices	vertex	NOUN
cana-950	126	8	have	have	VERB
cana-950	126	9	their	their	PRON
cana-950	126	10	degree	degree	NOUN
cana-950	126	11	three	three	NUM
cana-950	126	12	and	and	CCONJ
cana-950	126	13	the	the	DET
cana-950	126	14	remaining	remain	VERB
cana-950	126	15	two	two	NUM
cana-950	126	16	vertices	vertex	NOUN
cana-950	126	17	of	of	ADP
cana-950	126	18	degree	degree	NOUN
cana-950	126	19	two	two	NUM
cana-950	126	20	.	.	PUNCT
cana-950	127	1	secure	secure	ADJ
cana-950	127	2	vertex	vertex	NOUN
cana-950	127	3	edge	edge	NOUN
cana-950	127	4	dominating	dominating	NOUN
cana-950	127	5	set	set	NOUN
cana-950	127	6	i	i	PRON
cana-950	127	7	=	=	PUNCT
cana-950	127	8	{	{	PUNCT
cana-950	127	9	x1	x1	PROPN
cana-950	127	10	}	}	PUNCT
cana-950	127	11	or	or	CCONJ
cana-950	127	12	{	{	PUNCT
cana-950	127	13	x3	x3	ADJ
cana-950	127	14	}	}	PUNCT
cana-950	127	15	.	.	PUNCT
cana-950	128	1	the	the	DET
cana-950	128	2	vertices	vertex	NOUN
cana-950	128	3	x1	x1	PROPN
cana-950	128	4	and	and	CCONJ
cana-950	128	5	x3	x3	ADJ
cana-950	128	6	are	be	AUX
cana-950	128	7	having	have	VERB
cana-950	128	8	the	the	DET
cana-950	128	9	highest	high	ADJ
cana-950	128	10	degree	degree	NOUN
cana-950	128	11	,	,	PUNCT
cana-950	128	12	one	one	NUM
cana-950	128	13	of	of	ADP
cana-950	128	14	these	these	DET
cana-950	128	15	two	two	NUM
cana-950	128	16	vertices	vertex	NOUN
cana-950	128	17	can	can	AUX
cana-950	128	18	secure	secure	VERB
cana-950	128	19	all	all	DET
cana-950	128	20	the	the	DET
cana-950	128	21	incident	incident	NOUN
cana-950	128	22	edges	edge	NOUN
cana-950	128	23	and	and	CCONJ
cana-950	128	24	the	the	DET
cana-950	128	25	adjacent	adjacent	ADJ
cana-950	128	26	edges	edge	NOUN
cana-950	128	27	of	of	ADP
cana-950	128	28	that	that	DET
cana-950	128	29	two	two	NUM
cana-950	128	30	vertices	vertex	NOUN
cana-950	128	31	.	.	PUNCT
cana-950	129	1	so	so	ADV
cana-950	129	2	that	that	SCONJ
cana-950	129	3	,	,	PUNCT
cana-950	129	4	all	all	DET
cana-950	129	5	the	the	DET
cana-950	129	6	edges	edge	NOUN
cana-950	129	7	of	of	ADP
cana-950	129	8	the	the	DET
cana-950	129	9	graph	graph	NOUN
cana-950	129	10	are	be	AUX
cana-950	129	11	secured	secure	VERB
cana-950	129	12	.	.	PUNCT
cana-950	130	1	thus	thus	ADV
cana-950	130	2	,	,	PUNCT
cana-950	130	3	the	the	DET
cana-950	130	4	secure	secure	ADJ
cana-950	130	5	vertex	vertex	NOUN
cana-950	130	6	edge	edge	NOUN
cana-950	130	7	domination	domination	NOUN
cana-950	130	8	number	number	NOUN
cana-950	130	9	of	of	ADP
cana-950	130	10	the	the	DET
cana-950	130	11	diamond	diamond	NOUN
cana-950	130	12	graph	graph	NOUN
cana-950	130	13	is	be	AUX
cana-950	130	14	one	one	NUM
cana-950	130	15	.	.	PUNCT
cana-950	131	1	theorem	theorem	VERB
cana-950	131	2	4	4	NUM
cana-950	131	3	:	:	PUNCT
cana-950	131	4	the	the	DET
cana-950	131	5	secure	secure	ADJ
cana-950	131	6	vertex	vertex	NOUN
cana-950	131	7	edge	edge	NOUN
cana-950	131	8	domination	domination	NOUN
cana-950	131	9	number	number	NOUN
cana-950	131	10	of	of	ADP
cana-950	131	11	the	the	DET
cana-950	131	12	durer	durer	PROPN
cana-950	131	13	graph	graph	NOUN
cana-950	131	14	is	be	AUX
cana-950	131	15	calculated	calculate	VERB
cana-950	131	16	through	through	ADP
cana-950	131	17	communications	communication	NOUN
cana-950	131	18	on	on	ADP
cana-950	131	19	applied	apply	VERB
cana-950	131	20	nonlinear	nonlinear	ADJ
cana-950	131	21	analysis	analysis	NOUN
cana-950	131	22	issn	issn	NOUN
cana-950	131	23	:	:	PUNCT
cana-950	131	24	1074	1074	NUM
cana-950	131	25	-	-	PUNCT
cana-950	131	26	133x	133x	NUM
cana-950	131	27	vol	vol	NOUN
cana-950	131	28	31	31	NUM
cana-950	131	29	no	no	NOUN
cana-950	131	30	.	.	PUNCT
cana-950	132	1	4s	4s	NUM
cana-950	132	2	(	(	PUNCT
cana-950	132	3	2024	2024	NUM
cana-950	132	4	)	)	PUNCT
cana-950	132	5	565	565	NUM
cana-950	132	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-950	132	7	.	.	PUNCT
cana-950	133	1	3	3	X
cana-950	133	2	)	)	PUNCT
cana-950	133	3	(	(	PUNCT
cana-950	133	4	n	n	CCONJ
cana-950	133	5	drgsve	drgsve	VERB
cana-950	133	6	=	=	NOUN
cana-950	133	7			NUM
cana-950	133	8	proof	proof	NOUN
cana-950	133	9	:	:	PUNCT
cana-950	133	10	the	the	DET
cana-950	133	11	durer	durer	PROPN
cana-950	133	12	graph	graph	NOUN
cana-950	133	13	is	be	AUX
cana-950	133	14	a	a	DET
cana-950	133	15	graph	graph	NOUN
cana-950	133	16	that	that	PRON
cana-950	133	17	is	be	AUX
cana-950	133	18	not	not	PART
cana-950	133	19	directed	direct	VERB
cana-950	133	20	and	and	CCONJ
cana-950	133	21	has	have	VERB
cana-950	133	22	a	a	DET
cana-950	133	23	total	total	NOUN
cana-950	133	24	of	of	ADP
cana-950	133	25	12	12	NUM
cana-950	133	26	vertices	vertex	NOUN
cana-950	133	27	and	and	CCONJ
cana-950	133	28	18	18	NUM
cana-950	133	29	edges	edge	NOUN
cana-950	133	30	.	.	PUNCT
cana-950	134	1	every	every	DET
cana-950	134	2	single	single	ADJ
cana-950	134	3	vertex	vertex	NOUN
cana-950	134	4	in	in	ADP
cana-950	134	5	the	the	DET
cana-950	134	6	graph	graph	NOUN
cana-950	134	7	has	have	VERB
cana-950	134	8	a	a	DET
cana-950	134	9	degree	degree	NOUN
cana-950	134	10	of	of	ADP
cana-950	134	11	3	3	NUM
cana-950	134	12	.	.	PUNCT
cana-950	135	1	it	it	PRON
cana-950	135	2	is	be	AUX
cana-950	135	3	a	a	DET
cana-950	135	4	well	well	ADV
cana-950	135	5	covered	cover	VERB
cana-950	135	6	3connected	3connected	NUM
cana-950	135	7	cubic	cubic	ADJ
cana-950	135	8	graphs	graph	NOUN
cana-950	135	9	.	.	PUNCT
cana-950	136	1	the	the	DET
cana-950	136	2	secure	secure	ADJ
cana-950	136	3	vertex	vertex	NOUN
cana-950	136	4	edge	edge	NOUN
cana-950	136	5	domination	domination	NOUN
cana-950	136	6	number	number	NOUN
cana-950	136	7	of	of	ADP
cana-950	136	8	the	the	DET
cana-950	136	9	graph	graph	NOUN
cana-950	136	10	that	that	PRON
cana-950	136	11	comes	come	VERB
cana-950	136	12	from	from	ADP
cana-950	136	13	3	3	NUM
cana-950	136	14	n	n	NOUN
cana-950	136	15	,	,	PUNCT
cana-950	136	16	i.e.	i.e.	X
cana-950	136	17	4	4	NUM
cana-950	136	18	3	3	NUM
cana-950	136	19	12	12	NUM
cana-950	136	20	=	=	NOUN
cana-950	136	21	.	.	PUNCT
cana-950	137	1	the	the	DET
cana-950	137	2	set	set	NOUN
cana-950	137	3	i	i	PRON
cana-950	137	4	=	=	PUNCT
cana-950	137	5	{	{	PUNCT
cana-950	137	6	x1	x1	PROPN
cana-950	137	7	,	,	PUNCT
cana-950	137	8	x2	x2	PROPN
cana-950	137	9	,	,	PUNCT
cana-950	137	10	x9	x9	PROPN
cana-950	137	11	,	,	PUNCT
cana-950	137	12	x11	x11	PRON
cana-950	137	13	}	}	PUNCT
cana-950	137	14	is	be	AUX
cana-950	137	15	the	the	DET
cana-950	137	16	secure	secure	ADJ
cana-950	137	17	vertex	vertex	NOUN
cana-950	137	18	edge	edge	NOUN
cana-950	137	19	dominating	dominate	VERB
cana-950	137	20	set	set	NOUN
cana-950	137	21	of	of	ADP
cana-950	137	22	this	this	DET
cana-950	137	23	durer	durer	PROPN
cana-950	137	24	graph	graph	NOUN
cana-950	137	25	which	which	PRON
cana-950	137	26	protects	protect	VERB
cana-950	137	27	all	all	DET
cana-950	137	28	the	the	DET
cana-950	137	29	edges	edge	NOUN
cana-950	137	30	which	which	PRON
cana-950	137	31	are	be	AUX
cana-950	137	32	incident	incident	NOUN
cana-950	137	33	on	on	ADP
cana-950	137	34	the	the	DET
cana-950	137	35	vertices	vertex	NOUN
cana-950	137	36	of	of	ADP
cana-950	137	37	the	the	DET
cana-950	137	38	set	set	NOUN
cana-950	137	39	i	i	PRON
cana-950	137	40	and	and	CCONJ
cana-950	137	41	the	the	DET
cana-950	137	42	edges	edge	NOUN
cana-950	137	43	which	which	PRON
cana-950	137	44	are	be	AUX
cana-950	137	45	adjacent	adjacent	ADJ
cana-950	137	46	to	to	ADP
cana-950	137	47	that	that	DET
cana-950	137	48	incident	incident	NOUN
cana-950	137	49	edges	edge	NOUN
cana-950	137	50	of	of	ADP
cana-950	137	51	that	that	DET
cana-950	137	52	vertices	vertex	NOUN
cana-950	137	53	.	.	PUNCT
cana-950	138	1	we	we	PRON
cana-950	138	2	can	can	AUX
cana-950	138	3	select	select	VERB
cana-950	138	4	any	any	DET
cana-950	138	5	four	four	NUM
cana-950	138	6	vertices	vertex	NOUN
cana-950	138	7	of	of	ADP
cana-950	138	8	the	the	DET
cana-950	138	9	graph	graph	NOUN
cana-950	138	10	to	to	ADP
cana-950	138	11	the	the	DET
cana-950	138	12	set	set	NOUN
cana-950	138	13	i	i	PRON
cana-950	138	14	so	so	SCONJ
cana-950	138	15	that	that	SCONJ
cana-950	138	16	it	it	PRON
cana-950	138	17	will	will	AUX
cana-950	138	18	conserve	conserve	VERB
cana-950	138	19	every	every	DET
cana-950	138	20	edge	edge	NOUN
cana-950	138	21	of	of	ADP
cana-950	138	22	the	the	DET
cana-950	138	23	graph	graph	NOUN
cana-950	138	24	.	.	PUNCT
cana-950	139	1	hence	hence	ADV
cana-950	139	2	.	.	PUNCT
cana-950	140	1	3	3	X
cana-950	140	2	)	)	PUNCT
cana-950	140	3	(	(	PUNCT
cana-950	140	4	n	n	CCONJ
cana-950	140	5	drgsve	drgsve	NOUN
cana-950	140	6	=	=	SYM
cana-950	140	7			NUM
cana-950	140	8	theorem	theorem	VERB
cana-950	140	9	5	5	NUM
cana-950	140	10	:	:	PUNCT
cana-950	140	11	if	if	SCONJ
cana-950	140	12	fkg	fkg	NOUN
cana-950	140	13	is	be	AUX
cana-950	140	14	the	the	DET
cana-950	140	15	franklin	franklin	PROPN
cana-950	140	16	graph	graph	NOUN
cana-950	140	17	then	then	ADV
cana-950	140	18	the	the	DET
cana-950	140	19	secure	secure	ADJ
cana-950	140	20	vertex	vertex	NOUN
cana-950	140	21	edge	edge	NOUN
cana-950	140	22	domination	domination	NOUN
cana-950	140	23	number	number	NOUN
cana-950	140	24	of	of	ADP
cana-950	140	25	the	the	DET
cana-950	140	26	graph	graph	NOUN
cana-950	140	27	is	be	AUX
cana-950	140	28	3	3	NUM
cana-950	140	29	.	.	PUNCT
cana-950	141	1	proof	proof	NOUN
cana-950	141	2	:	:	PUNCT
cana-950	141	3	the	the	DET
cana-950	141	4	franklin	franklin	PROPN
cana-950	141	5	graph	graph	NOUN
cana-950	141	6	is	be	AUX
cana-950	141	7	a	a	DET
cana-950	141	8	graph	graph	NOUN
cana-950	141	9	that	that	PRON
cana-950	141	10	consists	consist	VERB
cana-950	141	11	of	of	ADP
cana-950	141	12	twelve	twelve	NUM
cana-950	141	13	nodes	node	NOUN
cana-950	141	14	and	and	CCONJ
cana-950	141	15	18	18	NUM
cana-950	141	16	lines	line	NOUN
cana-950	141	17	.	.	PUNCT
cana-950	142	1	the	the	DET
cana-950	142	2	graph	graph	NOUN
cana-950	142	3	is	be	AUX
cana-950	142	4	trivalent	trivalent	ADJ
cana-950	142	5	.	.	PUNCT
cana-950	143	1	the	the	DET
cana-950	143	2	set	set	NOUN
cana-950	143	3	i	i	PRON
cana-950	143	4	=	=	PUNCT
cana-950	143	5	{	{	PUNCT
cana-950	143	6	x2	x2	PROPN
cana-950	143	7	,	,	PUNCT
cana-950	143	8	x4	x4	PROPN
cana-950	143	9	,	,	PUNCT
cana-950	143	10	x6	x6	PROPN
cana-950	143	11	}	}	PUNCT
cana-950	143	12	contains	contain	VERB
cana-950	143	13	three	three	NUM
cana-950	143	14	vertices	vertex	NOUN
cana-950	143	15	,	,	PUNCT
cana-950	143	16	which	which	PRON
cana-950	143	17	will	will	AUX
cana-950	143	18	protect	protect	VERB
cana-950	143	19	the	the	DET
cana-950	143	20	edges	edge	NOUN
cana-950	143	21	which	which	PRON
cana-950	143	22	are	be	AUX
cana-950	143	23	incident	incident	NOUN
cana-950	143	24	on	on	ADP
cana-950	143	25	the	the	DET
cana-950	143	26	vertices	vertex	NOUN
cana-950	143	27	and	and	CCONJ
cana-950	143	28	the	the	DET
cana-950	143	29	edges	edge	NOUN
cana-950	143	30	which	which	PRON
cana-950	143	31	are	be	AUX
cana-950	143	32	adjacent	adjacent	ADJ
cana-950	143	33	to	to	ADP
cana-950	143	34	that	that	DET
cana-950	143	35	incident	incident	NOUN
cana-950	143	36	edges	edge	NOUN
cana-950	143	37	.	.	PUNCT
cana-950	144	1	the	the	DET
cana-950	144	2	vertex	vertex	NOUN
cana-950	144	3	x2	x2	PROPN
cana-950	144	4	protects	protect	VERB
cana-950	144	5	the	the	DET
cana-950	144	6	edges	edge	NOUN
cana-950	144	7	y1	y1	NOUN
cana-950	144	8	,	,	PUNCT
cana-950	144	9	y2	y2	INTJ
cana-950	144	10	,	,	PUNCT
cana-950	144	11	y3	y3	NOUN
cana-950	144	12	and	and	CCONJ
cana-950	144	13	the	the	DET
cana-950	144	14	adjacent	adjacent	ADJ
cana-950	144	15	edges	edge	NOUN
cana-950	144	16	y8	y8	PROPN
cana-950	144	17	,	,	PUNCT
cana-950	144	18	y13	y13	PROPN
cana-950	144	19	,	,	PUNCT
cana-950	144	20	y9	y9	PROPN
cana-950	144	21	,	,	PUNCT
cana-950	144	22	y10	y10	NOUN
cana-950	144	23	,	,	PUNCT
cana-950	144	24	y14	y14	PROPN
cana-950	144	25	,	,	PUNCT
cana-950	144	26	y12	y12	PROPN
cana-950	144	27	.	.	PUNCT
cana-950	145	1	the	the	DET
cana-950	145	2	vertex	vertex	NOUN
cana-950	145	3	x4	x4	PROPN
cana-950	145	4	defend	defend	VERB
cana-950	145	5	the	the	DET
cana-950	145	6	following	follow	VERB
cana-950	145	7	edges	edge	NOUN
cana-950	145	8	y6	y6	ADJ
cana-950	145	9	,	,	PUNCT
cana-950	145	10	y7	y7	PROPN
cana-950	145	11	,	,	PUNCT
cana-950	145	12	y8	y8	PROPN
cana-950	145	13	which	which	PRON
cana-950	145	14	are	be	AUX
cana-950	145	15	incident	incident	NOUN
cana-950	145	16	and	and	CCONJ
cana-950	145	17	the	the	DET
cana-950	145	18	adjacent	adjacent	ADJ
cana-950	145	19	edges	edge	NOUN
cana-950	145	20	y1	y1	PROPN
cana-950	145	21	,	,	PUNCT
cana-950	145	22	y4	y4	PROPN
cana-950	145	23	,	,	PUNCT
cana-950	145	24	y5	y5	PROPN
cana-950	145	25	,	,	PUNCT
cana-950	145	26	y12	y12	PROPN
cana-950	145	27	,	,	PUNCT
cana-950	145	28	y15	y15	NOUN
cana-950	145	29	,	,	PUNCT
cana-950	145	30	y16	y16	NOUN
cana-950	145	31	and	and	CCONJ
cana-950	145	32	the	the	DET
cana-950	145	33	vertex	vertex	NOUN
cana-950	145	34	x6	x6	PROPN
cana-950	145	35	safeguards	safeguard	VERB
cana-950	145	36	the	the	DET
cana-950	145	37	edges	edge	NOUN
cana-950	145	38	y4	y4	NOUN
cana-950	145	39	,	,	PUNCT
cana-950	145	40	y11	y11	NOUN
cana-950	145	41	,	,	PUNCT
cana-950	145	42	y10	y10	NOUN
cana-950	145	43	,	,	PUNCT
cana-950	145	44	adjacent	adjacent	ADJ
cana-950	145	45	edges	edge	NOUN
cana-950	145	46	y5	y5	NOUN
cana-950	145	47	,	,	PUNCT
cana-950	145	48	y6	y6	ADJ
cana-950	145	49	,	,	PUNCT
cana-950	145	50	y17	y17	NOUN
cana-950	145	51	,	,	PUNCT
cana-950	145	52	y18	y18	NUM
cana-950	145	53	,	,	PUNCT
cana-950	145	54	y9	y9	PROPN
cana-950	145	55	,	,	PUNCT
cana-950	145	56	y2	y2	INTJ
cana-950	145	57	.	.	PUNCT
cana-950	146	1	hence	hence	ADV
cana-950	146	2	the	the	DET
cana-950	146	3	set	set	NOUN
cana-950	146	4	i	i	PRON
cana-950	146	5	will	will	AUX
cana-950	146	6	communications	communication	NOUN
cana-950	146	7	on	on	ADP
cana-950	146	8	applied	apply	VERB
cana-950	146	9	nonlinear	nonlinear	ADJ
cana-950	146	10	analysis	analysis	NOUN
cana-950	146	11	issn	issn	NOUN
cana-950	146	12	:	:	PUNCT
cana-950	146	13	1074	1074	NUM
cana-950	146	14	-	-	PUNCT
cana-950	146	15	133x	133x	NUM
cana-950	146	16	vol	vol	NOUN
cana-950	146	17	31	31	NUM
cana-950	146	18	no	no	NOUN
cana-950	146	19	.	.	PUNCT
cana-950	147	1	4s	4s	NUM
cana-950	147	2	(	(	PUNCT
cana-950	147	3	2024	2024	NUM
cana-950	147	4	)	)	PUNCT
cana-950	147	5	566	566	NUM
cana-950	147	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-950	147	7	defend	defend	VERB
cana-950	147	8	all	all	DET
cana-950	147	9	the	the	DET
cana-950	147	10	edges	edge	NOUN
cana-950	147	11	of	of	ADP
cana-950	147	12	the	the	DET
cana-950	147	13	graph	graph	NOUN
cana-950	147	14	.	.	PUNCT
cana-950	148	1	thus	thus	ADV
cana-950	148	2	,	,	PUNCT
cana-950	148	3	the	the	DET
cana-950	148	4	secure	secure	ADJ
cana-950	148	5	vertex	vertex	NOUN
cana-950	148	6	edge	edge	NOUN
cana-950	148	7	domination	domination	NOUN
cana-950	148	8	of	of	ADP
cana-950	148	9	the	the	DET
cana-950	148	10	franklin	franklin	PROPN
cana-950	148	11	graph	graph	NOUN
cana-950	148	12	(	(	PUNCT
cana-950	148	13	)	)	PUNCT
cana-950	148	14	3.sve	3.sve	NUM
cana-950	149	1	fkg	fkg	NOUN
cana-950	149	2	=	=	NOUN
cana-950	149	3	hence	hence	ADV
cana-950	149	4	the	the	DET
cana-950	149	5	proof	proof	NOUN
cana-950	149	6	.	.	PUNCT
cana-950	150	1	theorem	theorem	VERB
cana-950	150	2	6	6	NUM
cana-950	150	3	:	:	PUNCT
cana-950	150	4	the	the	DET
cana-950	150	5	secure	secure	ADJ
cana-950	150	6	vertex	vertex	NOUN
cana-950	150	7	edge	edge	NOUN
cana-950	150	8	domination	domination	NOUN
cana-950	150	9	number	number	NOUN
cana-950	150	10	of	of	ADP
cana-950	150	11	the	the	DET
cana-950	150	12	golomb	golomb	NOUN
cana-950	150	13	graph	graph	NOUN
cana-950	150	14	is	be	AUX
cana-950	150	15	two	two	NUM
cana-950	150	16	.	.	PUNCT
cana-950	151	1	proof	proof	NOUN
cana-950	151	2	:	:	PUNCT
cana-950	151	3	a	a	DET
cana-950	151	4	graph	graph	NOUN
cana-950	151	5	that	that	PRON
cana-950	151	6	involves	involve	VERB
cana-950	151	7	10	10	NUM
cana-950	151	8	vertices	vertex	NOUN
cana-950	151	9	and	and	CCONJ
cana-950	151	10	eighteen	eighteen	NUM
cana-950	151	11	edges	edge	NOUN
cana-950	151	12	has	have	AUX
cana-950	151	13	been	be	AUX
cana-950	151	14	referred	refer	VERB
cana-950	151	15	to	to	ADP
cana-950	151	16	as	as	ADP
cana-950	151	17	a	a	DET
cana-950	151	18	golomb	golomb	NOUN
cana-950	151	19	graph	graph	NOUN
cana-950	151	20	.	.	PUNCT
cana-950	152	1	the	the	DET
cana-950	152	2	middle	middle	ADJ
cana-950	152	3	vertex	vertex	NOUN
cana-950	152	4	of	of	ADP
cana-950	152	5	the	the	DET
cana-950	152	6	graph	graph	NOUN
cana-950	152	7	has	have	VERB
cana-950	152	8	a	a	DET
cana-950	152	9	degree	degree	NOUN
cana-950	152	10	of	of	ADP
cana-950	152	11	six	six	NUM
cana-950	152	12	.	.	PUNCT
cana-950	153	1	the	the	DET
cana-950	153	2	outer	outer	ADJ
cana-950	153	3	vertices	vertex	NOUN
cana-950	153	4	have	have	VERB
cana-950	153	5	a	a	DET
cana-950	153	6	degree	degree	NOUN
cana-950	153	7	of	of	ADP
cana-950	153	8	four	four	NUM
cana-950	153	9	,	,	PUNCT
cana-950	153	10	whereas	whereas	SCONJ
cana-950	153	11	the	the	DET
cana-950	153	12	inner	inner	ADJ
cana-950	153	13	three	three	NUM
cana-950	153	14	vertices	vertex	NOUN
cana-950	153	15	have	have	VERB
cana-950	153	16	a	a	DET
cana-950	153	17	degree	degree	NOUN
cana-950	153	18	of	of	ADP
cana-950	153	19	three	three	NUM
cana-950	153	20	.	.	PUNCT
cana-950	154	1	the	the	DET
cana-950	154	2	remaining	remain	VERB
cana-950	154	3	three	three	NUM
cana-950	154	4	vertices	vertex	NOUN
cana-950	154	5	also	also	ADV
cana-950	154	6	have	have	VERB
cana-950	154	7	a	a	DET
cana-950	154	8	degree	degree	NOUN
cana-950	154	9	of	of	ADP
cana-950	154	10	four	four	NUM
cana-950	154	11	.	.	PUNCT
cana-950	155	1	a	a	DET
cana-950	155	2	set	set	NOUN
cana-950	155	3	i	i	PRON
cana-950	155	4	=	=	PUNCT
cana-950	155	5	{	{	PUNCT
cana-950	155	6	x	x	PROPN
cana-950	155	7	,	,	PUNCT
cana-950	155	8	x8	x8	PROPN
cana-950	155	9	}	}	PUNCT
cana-950	155	10	is	be	AUX
cana-950	155	11	a	a	DET
cana-950	155	12	secure	secure	ADJ
cana-950	155	13	vertex	vertex	NOUN
cana-950	155	14	edge	edge	NOUN
cana-950	155	15	dominating	dominating	NOUN
cana-950	155	16	set	set	NOUN
cana-950	155	17	which	which	PRON
cana-950	155	18	contains	contain	VERB
cana-950	155	19	two	two	NUM
cana-950	155	20	vertices	vertex	NOUN
cana-950	155	21	;	;	PUNCT
cana-950	155	22	these	these	DET
cana-950	155	23	two	two	NUM
cana-950	155	24	vertices	vertex	NOUN
cana-950	155	25	will	will	AUX
cana-950	155	26	defend	defend	VERB
cana-950	155	27	all	all	DET
cana-950	155	28	the	the	DET
cana-950	155	29	edges	edge	NOUN
cana-950	155	30	of	of	ADP
cana-950	155	31	the	the	DET
cana-950	155	32	golomb	golomb	NOUN
cana-950	155	33	graph	graph	NOUN
cana-950	155	34	.	.	PUNCT
cana-950	156	1	the	the	DET
cana-950	156	2	set	set	NOUN
cana-950	156	3	i	i	PRON
cana-950	156	4	should	should	AUX
cana-950	156	5	contain	contain	VERB
cana-950	156	6	the	the	DET
cana-950	156	7	centre	centre	NOUN
cana-950	156	8	vertex	vertex	NOUN
cana-950	156	9	and	and	CCONJ
cana-950	156	10	any	any	PRON
cana-950	156	11	of	of	ADP
cana-950	156	12	the	the	DET
cana-950	156	13	outer	outer	ADJ
cana-950	156	14	vertex	vertex	NOUN
cana-950	156	15	,	,	PUNCT
cana-950	156	16	then	then	ADV
cana-950	156	17	only	only	ADV
cana-950	156	18	the	the	DET
cana-950	156	19	vertices	vertex	NOUN
cana-950	156	20	in	in	ADP
cana-950	156	21	i	i	PRON
cana-950	156	22	can	can	AUX
cana-950	156	23	protect	protect	VERB
cana-950	156	24	all	all	DET
cana-950	156	25	the	the	DET
cana-950	156	26	edges	edge	NOUN
cana-950	156	27	of	of	ADP
cana-950	156	28	the	the	DET
cana-950	156	29	graph	graph	NOUN
cana-950	156	30	.	.	PUNCT
cana-950	157	1	thus	thus	ADV
cana-950	157	2	,	,	PUNCT
cana-950	157	3	the	the	DET
cana-950	157	4	secure	secure	ADJ
cana-950	157	5	vertex	vertex	NOUN
cana-950	157	6	edge	edge	NOUN
cana-950	157	7	domination	domination	NOUN
cana-950	157	8	number	number	NOUN
cana-950	157	9	of	of	ADP
cana-950	157	10	the	the	DET
cana-950	157	11	golomb	golomb	NOUN
cana-950	157	12	graph	graph	NOUN
cana-950	157	13	is	be	AUX
cana-950	157	14	two	two	NUM
cana-950	157	15	.	.	PUNCT
cana-950	158	1	hence	hence	ADV
cana-950	158	2	the	the	DET
cana-950	158	3	proof	proof	NOUN
cana-950	158	4	.	.	PUNCT
cana-950	159	1	theorem	theorem	ADJ
cana-950	159	2	7	7	NUM
cana-950	159	3	:	:	PUNCT
cana-950	159	4	let	let	VERB
cana-950	159	5	msg	msg	PART
cana-950	159	6	be	be	AUX
cana-950	159	7	the	the	DET
cana-950	159	8	moser	moser	PROPN
cana-950	159	9	spindle	spindle	PROPN
cana-950	159	10	graph	graph	NOUN
cana-950	159	11	with	with	ADP
cana-950	159	12	seven	seven	NUM
cana-950	159	13	vertices	vertex	NOUN
cana-950	159	14	,	,	PUNCT
cana-950	159	15	the	the	DET
cana-950	159	16	secure	secure	ADJ
cana-950	159	17	vertex	vertex	NOUN
cana-950	159	18	edge	edge	NOUN
cana-950	159	19	domination	domination	NOUN
cana-950	159	20	number	number	NOUN
cana-950	159	21	of	of	ADP
cana-950	159	22	the	the	DET
cana-950	159	23	graph	graph	NOUN
cana-950	159	24	2	2	NUM
cana-950	159	25	)	)	PUNCT
cana-950	159	26	(	(	PUNCT
cana-950	160	1	=	=	PROPN
cana-950	160	2	msgsve	msgsve	PROPN
cana-950	160	3	.	.	PUNCT
cana-950	161	1	proof	proof	NOUN
cana-950	161	2	:	:	PUNCT
cana-950	161	3	a	a	DET
cana-950	161	4	moser	moser	PROPN
cana-950	161	5	spindle	spindle	PROPN
cana-950	161	6	graph	graph	NOUN
cana-950	161	7	may	may	AUX
cana-950	161	8	be	be	AUX
cana-950	161	9	constructed	construct	VERB
cana-950	161	10	by	by	ADP
cana-950	161	11	using	use	VERB
cana-950	161	12	a	a	DET
cana-950	161	13	graph	graph	NOUN
cana-950	161	14	that	that	PRON
cana-950	161	15	has	have	VERB
cana-950	161	16	no	no	DET
cana-950	161	17	direction	direction	NOUN
cana-950	161	18	comprising	comprise	VERB
cana-950	161	19	seven	seven	NUM
cana-950	161	20	vertices	vertex	NOUN
cana-950	161	21	and	and	CCONJ
cana-950	161	22	11	11	NUM
cana-950	161	23	edges	edge	NOUN
cana-950	161	24	.	.	PUNCT
cana-950	162	1	msg	msg	NOUN
cana-950	162	2	is	be	AUX
cana-950	162	3	of	of	ADP
cana-950	162	4	the	the	DET
cana-950	162	5	form	form	NOUN
cana-950	162	6	of	of	ADP
cana-950	162	7	a	a	DET
cana-950	162	8	triangle	triangle	NOUN
cana-950	162	9	which	which	PRON
cana-950	162	10	is	be	AUX
cana-950	162	11	inscribed	inscribe	VERB
cana-950	162	12	within	within	ADP
cana-950	162	13	a	a	DET
cana-950	162	14	hexagon	hexagon	NOUN
cana-950	162	15	.	.	PUNCT
cana-950	163	1	the	the	DET
cana-950	163	2	centre	centre	ADJ
cana-950	163	3	vertex	vertex	NOUN
cana-950	163	4	of	of	ADP
cana-950	163	5	the	the	DET
cana-950	163	6	graph	graph	NOUN
cana-950	163	7	having	have	VERB
cana-950	163	8	the	the	DET
cana-950	163	9	degree	degree	NOUN
cana-950	163	10	4	4	NUM
cana-950	163	11	and	and	CCONJ
cana-950	163	12	all	all	DET
cana-950	163	13	the	the	DET
cana-950	163	14	other	other	ADJ
cana-950	163	15	vertices	vertex	NOUN
cana-950	163	16	having	have	VERB
cana-950	163	17	degree	degree	NOUN
cana-950	163	18	3	3	NUM
cana-950	163	19	.	.	PUNCT
cana-950	164	1	the	the	DET
cana-950	164	2	set	set	NOUN
cana-950	164	3	i	i	PRON
cana-950	164	4	=	=	PUNCT
cana-950	164	5	{	{	PUNCT
cana-950	164	6	x	x	NOUN
cana-950	164	7	,	,	PUNCT
cana-950	164	8	x3	x3	ADJ
cana-950	164	9	}	}	PUNCT
cana-950	164	10	be	be	VERB
cana-950	164	11	the	the	DET
cana-950	164	12	secure	secure	ADJ
cana-950	164	13	vertex	vertex	NOUN
cana-950	164	14	edge	edge	NOUN
cana-950	164	15	dominating	dominating	NOUN
cana-950	164	16	set	set	NOUN
cana-950	164	17	which	which	PRON
cana-950	164	18	will	will	AUX
cana-950	164	19	defend	defend	VERB
cana-950	164	20	all	all	DET
cana-950	164	21	the	the	DET
cana-950	164	22	edges	edge	NOUN
cana-950	164	23	which	which	PRON
cana-950	164	24	are	be	AUX
cana-950	164	25	incident	incident	NOUN
cana-950	164	26	and	and	CCONJ
cana-950	164	27	the	the	DET
cana-950	164	28	edges	edge	NOUN
cana-950	164	29	which	which	PRON
cana-950	164	30	are	be	AUX
cana-950	164	31	adjacent	adjacent	ADJ
cana-950	164	32	to	to	ADP
cana-950	164	33	that	that	DET
cana-950	164	34	incident	incident	NOUN
cana-950	164	35	edges	edge	NOUN
cana-950	164	36	.	.	PUNCT
cana-950	165	1	in	in	ADP
cana-950	165	2	the	the	DET
cana-950	165	3	set	set	NOUN
cana-950	165	4	i	i	PRON
cana-950	165	5	there	there	PRON
cana-950	165	6	should	should	AUX
cana-950	165	7	be	be	AUX
cana-950	165	8	a	a	DET
cana-950	165	9	centre	centre	ADJ
cana-950	165	10	vertex	vertex	NOUN
cana-950	165	11	which	which	PRON
cana-950	165	12	has	have	VERB
cana-950	165	13	the	the	DET
cana-950	165	14	highest	high	ADJ
cana-950	165	15	degree	degree	NOUN
cana-950	165	16	and	and	CCONJ
cana-950	165	17	the	the	DET
cana-950	165	18	other	other	ADJ
cana-950	165	19	vertex	vertex	NOUN
cana-950	165	20	can	can	AUX
cana-950	165	21	be	be	AUX
cana-950	165	22	any	any	DET
cana-950	165	23	one	one	NOUN
cana-950	165	24	from	from	ADP
cana-950	165	25	the	the	DET
cana-950	165	26	remaining	remain	VERB
cana-950	165	27	vertices	vertex	NOUN
cana-950	165	28	.	.	PUNCT
cana-950	166	1	therefore	therefore	ADV
cana-950	166	2	,	,	PUNCT
cana-950	166	3	these	these	DET
cana-950	166	4	two	two	NUM
cana-950	166	5	vertices	vertex	NOUN
cana-950	166	6	guarantee	guarantee	VERB
cana-950	166	7	the	the	DET
cana-950	166	8	safety	safety	NOUN
cana-950	166	9	of	of	ADP
cana-950	166	10	every	every	DET
cana-950	166	11	edge	edge	NOUN
cana-950	166	12	in	in	ADP
cana-950	166	13	the	the	DET
cana-950	166	14	graph	graph	NOUN
cana-950	166	15	.	.	PUNCT
cana-950	167	1	thus	thus	ADV
cana-950	167	2	,	,	PUNCT
cana-950	167	3	the	the	DET
cana-950	167	4	secure	secure	ADJ
cana-950	167	5	vertex	vertex	NOUN
cana-950	167	6	edge	edge	NOUN
cana-950	167	7	domination	domination	NOUN
cana-950	167	8	number	number	NOUN
cana-950	167	9	of	of	ADP
cana-950	167	10	the	the	DET
cana-950	167	11	msg	msg	NOUN
cana-950	167	12	is	be	AUX
cana-950	167	13	2	2	NUM
cana-950	167	14	.	.	PUNCT
cana-950	167	15	communications	communication	NOUN
cana-950	167	16	on	on	ADP
cana-950	167	17	applied	apply	VERB
cana-950	167	18	nonlinear	nonlinear	ADJ
cana-950	167	19	analysis	analysis	NOUN
cana-950	167	20	issn	issn	NOUN
cana-950	167	21	:	:	PUNCT
cana-950	167	22	1074	1074	NUM
cana-950	167	23	-	-	PUNCT
cana-950	167	24	133x	133x	NUM
cana-950	167	25	vol	vol	NOUN
cana-950	167	26	31	31	NUM
cana-950	167	27	no	no	NOUN
cana-950	167	28	.	.	PUNCT
cana-950	168	1	4s	4s	NUM
cana-950	168	2	(	(	PUNCT
cana-950	168	3	2024	2024	NUM
cana-950	168	4	)	)	PUNCT
cana-950	168	5	567	567	NUM
cana-950	168	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-950	168	7	theorem	theorem	ADJ
cana-950	168	8	8	8	NUM
cana-950	168	9	:	:	PUNCT
cana-950	168	10	the	the	DET
cana-950	168	11	secure	secure	ADJ
cana-950	168	12	vertex	vertex	NOUN
cana-950	168	13	edge	edge	NOUN
cana-950	168	14	domination	domination	NOUN
cana-950	168	15	number	number	NOUN
cana-950	168	16	of	of	ADP
cana-950	168	17	the	the	DET
cana-950	168	18	herschel	herschel	PROPN
cana-950	168	19	graph	graph	NOUN
cana-950	168	20	is	be	AUX
cana-950	168	21	two	two	NUM
cana-950	168	22	.	.	PUNCT
cana-950	169	1	proof	proof	NOUN
cana-950	169	2	:	:	PUNCT
cana-950	169	3	the	the	DET
cana-950	169	4	herschel	herschel	PROPN
cana-950	169	5	graph	graph	NOUN
cana-950	169	6	is	be	AUX
cana-950	169	7	a	a	DET
cana-950	169	8	bipartite	bipartite	ADJ
cana-950	169	9	graph	graph	NOUN
cana-950	169	10	with	with	ADP
cana-950	169	11	eleven	eleven	NUM
cana-950	169	12	vertices	vertex	NOUN
cana-950	169	13	and	and	CCONJ
cana-950	169	14	eighteen	eighteen	NUM
cana-950	169	15	edges	edge	NOUN
cana-950	169	16	,	,	PUNCT
cana-950	169	17	and	and	CCONJ
cana-950	169	18	it	it	PRON
cana-950	169	19	is	be	AUX
cana-950	169	20	free	free	ADJ
cana-950	169	21	of	of	ADP
cana-950	169	22	direction	direction	NOUN
cana-950	169	23	.	.	PUNCT
cana-950	170	1	the	the	DET
cana-950	170	2	network	network	NOUN
cana-950	170	3	consists	consist	VERB
cana-950	170	4	of	of	ADP
cana-950	170	5	three	three	NUM
cana-950	170	6	vertices	vertex	NOUN
cana-950	170	7	with	with	ADP
cana-950	170	8	a	a	DET
cana-950	170	9	degree	degree	NOUN
cana-950	170	10	of	of	ADP
cana-950	170	11	4	4	NUM
cana-950	170	12	,	,	PUNCT
cana-950	170	13	while	while	SCONJ
cana-950	170	14	the	the	DET
cana-950	170	15	remaining	remain	VERB
cana-950	170	16	eight	eight	NUM
cana-950	170	17	vertices	vertex	NOUN
cana-950	170	18	have	have	VERB
cana-950	170	19	a	a	DET
cana-950	170	20	degree	degree	NOUN
cana-950	170	21	of	of	ADP
cana-950	170	22	3	3	NUM
cana-950	170	23	.	.	PUNCT
cana-950	171	1	the	the	DET
cana-950	171	2	secure	secure	ADJ
cana-950	171	3	vertex	vertex	NOUN
cana-950	171	4	edge	edge	NOUN
cana-950	171	5	dominating	dominating	NOUN
cana-950	171	6	set	set	NOUN
cana-950	171	7	i	i	PRON
cana-950	171	8	=	=	PUNCT
cana-950	171	9	{	{	PUNCT
cana-950	171	10	x5	x5	PROPN
cana-950	171	11	,	,	PUNCT
cana-950	171	12	x10	x10	NOUN
cana-950	171	13	}	}	PUNCT
cana-950	171	14	.	.	PUNCT
cana-950	172	1	the	the	DET
cana-950	172	2	vertex	vertex	NOUN
cana-950	172	3	x5	x5	PROPN
cana-950	172	4	will	will	AUX
cana-950	172	5	safeguard	safeguard	VERB
cana-950	172	6	the	the	DET
cana-950	172	7	following	follow	VERB
cana-950	172	8	edges	edge	NOUN
cana-950	172	9	y7	y7	ADJ
cana-950	172	10	,	,	PUNCT
cana-950	172	11	y8	y8	PROPN
cana-950	172	12	,	,	PUNCT
cana-950	172	13	y14	y14	PROPN
cana-950	172	14	,	,	PUNCT
cana-950	172	15	y15	y15	NOUN
cana-950	172	16	,	,	PUNCT
cana-950	172	17	y3	y3	PROPN
cana-950	172	18	,	,	PUNCT
cana-950	172	19	y13	y13	PROPN
cana-950	172	20	,	,	PUNCT
cana-950	172	21	y9	y9	PROPN
cana-950	172	22	,	,	PUNCT
cana-950	172	23	y5	y5	PROPN
cana-950	172	24	,	,	PUNCT
cana-950	172	25	y10	y10	NOUN
cana-950	172	26	,	,	PUNCT
cana-950	172	27	y6	y6	ADJ
cana-950	172	28	,	,	PUNCT
cana-950	172	29	y4	y4	PROPN
cana-950	172	30	,	,	PUNCT
cana-950	172	31	y16	y16	NOUN
cana-950	172	32	and	and	CCONJ
cana-950	172	33	the	the	DET
cana-950	172	34	vertex	vertex	NOUN
cana-950	172	35	x10	x10	PRON
cana-950	172	36	will	will	AUX
cana-950	172	37	be	be	AUX
cana-950	172	38	a	a	DET
cana-950	172	39	defender	defender	NOUN
cana-950	172	40	to	to	ADP
cana-950	172	41	the	the	DET
cana-950	172	42	following	follow	VERB
cana-950	172	43	edges	edge	NOUN
cana-950	172	44	y18	y18	NOUN
cana-950	172	45	,	,	PUNCT
cana-950	172	46	y11	y11	NOUN
cana-950	172	47	,	,	PUNCT
cana-950	172	48	y5	y5	PROPN
cana-950	172	49	,	,	PUNCT
cana-950	172	50	y6	y6	ADJ
cana-950	172	51	,	,	PUNCT
cana-950	172	52	y2	y2	PROPN
cana-950	172	53	,	,	PUNCT
cana-950	172	54	y1	y1	PROPN
cana-950	172	55	,	,	PUNCT
cana-950	172	56	y17	y17	NOUN
cana-950	172	57	,	,	PUNCT
cana-950	172	58	y12	y12	PROPN
cana-950	172	59	,	,	PUNCT
cana-950	172	60	y9	y9	PROPN
cana-950	172	61	,	,	PUNCT
cana-950	172	62	y8	y8	PROPN
cana-950	172	63	,	,	PUNCT
cana-950	172	64	y10	y10	NOUN
cana-950	172	65	,	,	PUNCT
cana-950	172	66	y7	y7	PROPN
cana-950	172	67	.	.	PUNCT
cana-950	173	1	hence	hence	ADV
cana-950	173	2	these	these	DET
cana-950	173	3	two	two	NUM
cana-950	173	4	vertices	vertex	NOUN
cana-950	173	5	in	in	ADP
cana-950	173	6	set	set	NOUN
cana-950	173	7	i	i	PRON
cana-950	173	8	defend	defend	VERB
cana-950	173	9	all	all	DET
cana-950	173	10	the	the	DET
cana-950	173	11	edges	edge	NOUN
cana-950	173	12	which	which	PRON
cana-950	173	13	are	be	AUX
cana-950	173	14	incident	incident	NOUN
cana-950	173	15	and	and	CCONJ
cana-950	173	16	the	the	DET
cana-950	173	17	edges	edge	NOUN
cana-950	173	18	which	which	PRON
cana-950	173	19	are	be	AUX
cana-950	173	20	adjacent	adjacent	ADJ
cana-950	173	21	to	to	ADP
cana-950	173	22	that	that	DET
cana-950	173	23	incident	incident	NOUN
cana-950	173	24	edges	edge	NOUN
cana-950	173	25	.	.	PUNCT
cana-950	174	1	thus	thus	ADV
cana-950	174	2	,	,	PUNCT
cana-950	174	3	all	all	DET
cana-950	174	4	the	the	DET
cana-950	174	5	edges	edge	NOUN
cana-950	174	6	of	of	ADP
cana-950	174	7	the	the	DET
cana-950	174	8	hlg	hlg	PROPN
cana-950	174	9	are	be	AUX
cana-950	174	10	protected	protect	VERB
cana-950	174	11	.	.	PUNCT
cana-950	175	1	so	so	ADV
cana-950	175	2	,	,	PUNCT
cana-950	175	3	the	the	DET
cana-950	175	4	secure	secure	ADJ
cana-950	175	5	vertex	vertex	NOUN
cana-950	175	6	edge	edge	NOUN
cana-950	175	7	domination	domination	NOUN
cana-950	175	8	number	number	NOUN
cana-950	175	9	of	of	ADP
cana-950	175	10	the	the	DET
cana-950	175	11	herschel	herschel	PROPN
cana-950	175	12	graph	graph	NOUN
cana-950	175	13	2	2	NUM
cana-950	175	14	)	)	PUNCT
cana-950	175	15	(	(	PUNCT
cana-950	176	1	=	=	NOUN
cana-950	176	2	hlgsve	hlgsve	X
cana-950	176	3	.	.	PUNCT
cana-950	177	1	theorem	theorem	VERB
cana-950	177	2	9	9	NUM
cana-950	177	3	:	:	PUNCT
cana-950	177	4	let	let	VERB
cana-950	177	5	png	png	PROPN
cana-950	177	6	be	be	AUX
cana-950	177	7	the	the	DET
cana-950	177	8	petersen	petersen	NOUN
cana-950	177	9	graph	graph	NOUN
cana-950	177	10	with	with	ADP
cana-950	177	11	n	n	PRON
cana-950	177	12	=	=	NOUN
cana-950	177	13	10	10	NUM
cana-950	177	14	vertices	vertex	NOUN
cana-950	177	15	for	for	ADP
cana-950	177	16	which	which	PRON
cana-950	177	17	the	the	DET
cana-950	177	18	secure	secure	ADJ
cana-950	177	19	vertex	vertex	NOUN
cana-950	177	20	edge	edge	NOUN
cana-950	177	21	domination	domination	NOUN
cana-950	177	22	number	number	NOUN
cana-950	177	23	is	be	AUX
cana-950	177	24	given	give	VERB
cana-950	177	25	by	by	ADP
cana-950	177	26			PROPN
cana-950	177	27			NOUN
cana-950	177	28			X
cana-950	177	29			NOUN
cana-950	177	30			X
cana-950	177	31			PROPN
cana-950	177	32	3	3	NUM
cana-950	177	33	n	n	NOUN
cana-950	177	34	.	.	PUNCT
cana-950	178	1	proof	proof	NOUN
cana-950	178	2	:	:	PUNCT
cana-950	178	3	a	a	DET
cana-950	178	4	graph	graph	NOUN
cana-950	178	5	formed	form	VERB
cana-950	178	6	by	by	ADP
cana-950	178	7	10	10	NUM
cana-950	178	8	vertices	vertex	NOUN
cana-950	178	9	and	and	CCONJ
cana-950	178	10	fifteen	fifteen	NUM
cana-950	178	11	edges	edge	NOUN
cana-950	178	12	is	be	AUX
cana-950	178	13	referred	refer	VERB
cana-950	178	14	to	to	ADP
cana-950	178	15	as	as	ADP
cana-950	178	16	a	a	DET
cana-950	178	17	petersen	petersen	NOUN
cana-950	178	18	graph	graph	NOUN
cana-950	178	19	.	.	PUNCT
cana-950	179	1	the	the	DET
cana-950	179	2	petersen	petersen	PROPN
cana-950	179	3	graph	graph	NOUN
cana-950	179	4	is	be	AUX
cana-950	179	5	of	of	ADP
cana-950	179	6	the	the	DET
cana-950	179	7	form	form	NOUN
cana-950	179	8	of	of	ADP
cana-950	179	9	a	a	DET
cana-950	179	10	star	star	NOUN
cana-950	179	11	inscribed	inscribe	VERB
cana-950	179	12	in	in	ADP
cana-950	179	13	a	a	DET
cana-950	179	14	pentagon	pentagon	PROPN
cana-950	179	15	.	.	PUNCT
cana-950	180	1	the	the	DET
cana-950	180	2	degree	degree	NOUN
cana-950	180	3	of	of	ADP
cana-950	180	4	each	each	DET
cana-950	180	5	vertex	vertex	NOUN
cana-950	180	6	in	in	ADP
cana-950	180	7	the	the	DET
cana-950	180	8	petersen	petersen	NOUN
cana-950	180	9	graph	graph	NOUN
cana-950	180	10	is	be	AUX
cana-950	180	11	three	three	NUM
cana-950	180	12	.	.	PUNCT
cana-950	181	1	the	the	DET
cana-950	181	2	secure	secure	ADJ
cana-950	181	3	vertex	vertex	NOUN
cana-950	181	4	edge	edge	NOUN
cana-950	181	5	domination	domination	NOUN
cana-950	181	6	number	number	NOUN
cana-950	181	7	of	of	ADP
cana-950	181	8	the	the	DET
cana-950	181	9	png	png	PROPN
cana-950	181	10	is	be	AUX
cana-950	181	11	given	give	VERB
cana-950	181	12	by	by	ADP
cana-950	181	13	.3	.3	NUM
cana-950	181	14	3	3	NUM
cana-950	181	15	10	10	NUM
cana-950	181	16	3	3	NUM
cana-950	181	17	=	=	NOUN
cana-950	181	18			NOUN
cana-950	181	19			NOUN
cana-950	181	20			X
cana-950	181	21			NOUN
cana-950	181	22			X
cana-950	181	23			PROPN
cana-950	181	24	=	=	NOUN
cana-950	181	25			NOUN
cana-950	181	26			NOUN
cana-950	181	27			NOUN
cana-950	181	28			NOUN
cana-950	181	29			X
cana-950	181	30	n	n	NOUN
cana-950	181	31	let	let	VERB
cana-950	181	32	i	i	PRON
cana-950	181	33	=	=	PUNCT
cana-950	181	34	{	{	PUNCT
cana-950	181	35	x1	x1	PROPN
cana-950	181	36	,	,	PUNCT
cana-950	181	37	x5	x5	PROPN
cana-950	181	38	,	,	PUNCT
cana-950	181	39	x9	x9	NOUN
cana-950	181	40	}	}	PUNCT
cana-950	181	41	be	be	VERB
cana-950	181	42	the	the	DET
cana-950	181	43	secure	secure	ADJ
cana-950	181	44	vertex	vertex	NOUN
cana-950	181	45	edge	edge	NOUN
cana-950	181	46	dominating	dominating	NOUN
cana-950	181	47	set	set	NOUN
cana-950	181	48	,	,	PUNCT
cana-950	181	49	in	in	ADP
cana-950	181	50	which	which	PRON
cana-950	181	51	x1	x1	DET
cana-950	181	52	vertex	vertex	NOUN
cana-950	181	53	protects	protect	VERB
cana-950	181	54	the	the	DET
cana-950	181	55	edges	edge	NOUN
cana-950	181	56	y2	y2	NOUN
cana-950	181	57	,	,	PUNCT
cana-950	181	58	y5	y5	PROPN
cana-950	181	59	,	,	PUNCT
cana-950	181	60	y3	y3	NOUN
cana-950	181	61	,	,	PUNCT
cana-950	181	62	y8	y8	PROPN
cana-950	181	63	,	,	PUNCT
cana-950	181	64	y4	y4	PROPN
cana-950	181	65	,	,	PUNCT
cana-950	181	66	y11	y11	NOUN
cana-950	181	67	,	,	PUNCT
cana-950	181	68	y7	y7	PROPN
cana-950	181	69	,	,	PUNCT
cana-950	181	70	y10	y10	NOUN
cana-950	181	71	,	,	PUNCT
cana-950	181	72	y15	y15	NOUN
cana-950	181	73	the	the	DET
cana-950	181	74	vertex	vertex	NOUN
cana-950	181	75	x5	x5	PROPN
cana-950	181	76	defends	defend	VERB
cana-950	181	77	the	the	DET
cana-950	181	78	edges	edge	NOUN
cana-950	181	79	y1	y1	NOUN
cana-950	181	80	,	,	PUNCT
cana-950	181	81	y4,y2	y4,y2	PROPN
cana-950	181	82	,	,	PUNCT
cana-950	181	83	y9,y3	y9,y3	PROPN
cana-950	181	84	,	,	PUNCT
cana-950	181	85	y6	y6	PROPN
cana-950	181	86	,	,	PUNCT
cana-950	181	87	y14	y14	PROPN
cana-950	181	88	,	,	PUNCT
cana-950	181	89	y7,y15	y7,y15	PROPN
cana-950	181	90	and	and	CCONJ
cana-950	181	91	the	the	DET
cana-950	181	92	vertex	vertex	NOUN
cana-950	181	93	x9	x9	NOUN
cana-950	181	94	protects	protect	VERB
cana-950	181	95	the	the	DET
cana-950	181	96	edges	edge	NOUN
cana-950	181	97	y5	y5	PROPN
cana-950	181	98	,	,	PUNCT
cana-950	181	99	y12,y7	y12,y7	PROPN
cana-950	181	100	,	,	PUNCT
cana-950	181	101	y14,y8	y14,y8	PROPN
cana-950	181	102	,	,	PUNCT
cana-950	181	103	y2,y9	y2,y9	PROPN
cana-950	181	104	,	,	PUNCT
cana-950	181	105	y13	y13	PROPN
cana-950	181	106	,	,	PUNCT
cana-950	181	107	y15	y15	NOUN
cana-950	181	108	.	.	PUNCT
cana-950	182	1	thus	thus	ADV
cana-950	182	2	,	,	PUNCT
cana-950	182	3	all	all	DET
cana-950	182	4	the	the	DET
cana-950	182	5	edges	edge	NOUN
cana-950	182	6	communications	communication	NOUN
cana-950	182	7	on	on	ADP
cana-950	182	8	applied	apply	VERB
cana-950	182	9	nonlinear	nonlinear	ADJ
cana-950	182	10	analysis	analysis	NOUN
cana-950	182	11	issn	issn	NOUN
cana-950	182	12	:	:	PUNCT
cana-950	182	13	1074	1074	NUM
cana-950	182	14	-	-	PUNCT
cana-950	182	15	133x	133x	NUM
cana-950	182	16	vol	vol	NOUN
cana-950	182	17	31	31	NUM
cana-950	182	18	no	no	NOUN
cana-950	182	19	.	.	PUNCT
cana-950	183	1	4s	4s	NUM
cana-950	183	2	(	(	PUNCT
cana-950	183	3	2024	2024	NUM
cana-950	183	4	)	)	PUNCT
cana-950	183	5	568	568	NUM
cana-950	183	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-950	183	7	of	of	ADP
cana-950	183	8	the	the	DET
cana-950	183	9	graph	graph	NOUN
cana-950	183	10	are	be	AUX
cana-950	183	11	protected	protect	VERB
cana-950	183	12	.	.	PUNCT
cana-950	184	1	hence	hence	ADV
cana-950	184	2	the	the	DET
cana-950	184	3	secure	secure	ADJ
cana-950	184	4	vertex	vertex	NOUN
cana-950	184	5	edge	edge	NOUN
cana-950	184	6	domination	domination	NOUN
cana-950	184	7	number	number	NOUN
cana-950	184	8	of	of	ADP
cana-950	184	9	the	the	DET
cana-950	184	10	petersen	petersen	NOUN
cana-950	184	11	graph	graph	NOUN
cana-950	184	12	is	be	AUX
cana-950	184	13			ADJ
cana-950	184	14			NOUN
cana-950	184	15			X
cana-950	184	16			NOUN
cana-950	184	17			X
cana-950	184	18			NOUN
cana-950	184	19	=	=	SYM
cana-950	184	20	3	3	NUM
cana-950	184	21	)	)	PUNCT
cana-950	184	22	(	(	PUNCT
cana-950	184	23	n	n	CCONJ
cana-950	184	24	pngsve	pngsve	PROPN
cana-950	184	25	.	.	PUNCT
cana-950	185	1	theorem	theorem	VERB
cana-950	185	2	10	10	NUM
cana-950	185	3	:	:	PUNCT
cana-950	185	4	the	the	DET
cana-950	185	5	fish	fish	NOUN
cana-950	185	6	graph	graph	NOUN
cana-950	185	7	possesses	possess	VERB
cana-950	185	8	a	a	DET
cana-950	185	9	secure	secure	ADJ
cana-950	185	10	vertex	vertex	NOUN
cana-950	185	11	-	-	PUNCT
cana-950	185	12	edge	edge	NOUN
cana-950	185	13	dominance	dominance	NOUN
cana-950	185	14	number	number	NOUN
cana-950	185	15	as	as	ADP
cana-950	185	16	one	one	NUM
cana-950	185	17	.	.	PUNCT
cana-950	186	1	proof	proof	NOUN
cana-950	186	2	:	:	PUNCT
cana-950	186	3	fish	fish	NOUN
cana-950	186	4	graph	graph	NOUN
cana-950	186	5	comprises	comprise	VERB
cana-950	186	6	six	six	NUM
cana-950	186	7	vertices	vertex	NOUN
cana-950	186	8	and	and	CCONJ
cana-950	186	9	7	7	NUM
cana-950	186	10	edges	edge	NOUN
cana-950	186	11	in	in	ADP
cana-950	186	12	which	which	PRON
cana-950	186	13	one	one	NUM
cana-950	186	14	vertex	vertex	NOUN
cana-950	186	15	has	have	VERB
cana-950	186	16	its	its	PRON
cana-950	186	17	degree	degree	NOUN
cana-950	186	18	4	4	NUM
cana-950	186	19	and	and	CCONJ
cana-950	186	20	the	the	DET
cana-950	186	21	other	other	ADJ
cana-950	186	22	vertices	vertex	NOUN
cana-950	186	23	has	have	VERB
cana-950	186	24	degree	degree	NOUN
cana-950	186	25	2	2	NUM
cana-950	186	26	.	.	PUNCT
cana-950	187	1	the	the	DET
cana-950	187	2	secure	secure	ADJ
cana-950	187	3	vertex	vertex	NOUN
cana-950	187	4	-	-	PUNCT
cana-950	187	5	edge	edge	NOUN
cana-950	187	6	dominant	dominant	NOUN
cana-950	187	7	set	set	NOUN
cana-950	187	8	i	i	PRON
cana-950	187	9	=	=	PUNCT
cana-950	187	10	{	{	PUNCT
cana-950	187	11	x3	x3	ADJ
cana-950	187	12	}	}	PUNCT
cana-950	187	13	,	,	PUNCT
cana-950	187	14	where	where	SCONJ
cana-950	187	15	x3	x3	PROPN
cana-950	187	16	is	be	AUX
cana-950	187	17	the	the	DET
cana-950	187	18	vertex	vertex	NOUN
cana-950	187	19	with	with	ADP
cana-950	187	20	the	the	DET
cana-950	187	21	greatest	great	ADJ
cana-950	187	22	degree	degree	NOUN
cana-950	187	23	,	,	PUNCT
cana-950	187	24	will	will	AUX
cana-950	187	25	safeguard	safeguard	VERB
cana-950	187	26	the	the	DET
cana-950	187	27	edges	edge	NOUN
cana-950	187	28	that	that	PRON
cana-950	187	29	are	be	AUX
cana-950	187	30	connected	connect	VERB
cana-950	187	31	to	to	PART
cana-950	187	32	x3	x3	VERB
cana-950	187	33	as	as	ADV
cana-950	187	34	well	well	ADV
cana-950	187	35	as	as	ADP
cana-950	187	36	the	the	DET
cana-950	187	37	edges	edge	NOUN
cana-950	187	38	next	next	ADV
cana-950	187	39	to	to	ADP
cana-950	187	40	those	those	PRON
cana-950	187	41	connected	connect	VERB
cana-950	187	42	to	to	PART
cana-950	187	43	x3	x3	VERB
cana-950	187	44	.	.	PUNCT
cana-950	188	1	so	so	ADV
cana-950	188	2	that	that	SCONJ
cana-950	188	3	,	,	PUNCT
cana-950	188	4	every	every	DET
cana-950	188	5	edge	edge	NOUN
cana-950	188	6	of	of	ADP
cana-950	188	7	the	the	DET
cana-950	188	8	fish	fish	NOUN
cana-950	188	9	graph	graph	NOUN
cana-950	188	10	is	be	AUX
cana-950	188	11	safe	safe	ADJ
cana-950	188	12	.	.	PUNCT
cana-950	189	1	thus	thus	ADV
cana-950	189	2	,	,	PUNCT
cana-950	189	3	the	the	DET
cana-950	189	4	secure	secure	ADJ
cana-950	189	5	vertex	vertex	NOUN
cana-950	189	6	edge	edge	NOUN
cana-950	189	7	domination	domination	NOUN
cana-950	189	8	of	of	ADP
cana-950	189	9	the	the	DET
cana-950	189	10	fish	fish	NOUN
cana-950	189	11	graph	graph	NOUN
cana-950	189	12	is	be	AUX
cana-950	189	13	given	give	VERB
cana-950	189	14	by	by	ADP
cana-950	189	15	1	1	NUM
cana-950	189	16	)	)	PUNCT
cana-950	189	17	(	(	PUNCT
cana-950	189	18	=	=	NUM
cana-950	189	19	figsve	figsve	PROPN
cana-950	189	20	.	.	PUNCT
cana-950	190	1	hence	hence	ADV
cana-950	190	2	the	the	DET
cana-950	190	3	proof	proof	NOUN
cana-950	190	4	.	.	PUNCT
cana-950	191	1	theorem	theorem	VERB
cana-950	191	2	11	11	NUM
cana-950	191	3	:	:	PUNCT
cana-950	191	4	the	the	DET
cana-950	191	5	wagner	wagner	PROPN
cana-950	191	6	graph	graph	NOUN
cana-950	191	7	,	,	PUNCT
cana-950	191	8	designated	designate	VERB
cana-950	191	9	as	as	ADP
cana-950	191	10	wrg	wrg	PROPN
cana-950	191	11	,	,	PUNCT
cana-950	191	12	has	have	VERB
cana-950	191	13	a	a	DET
cana-950	191	14	secure	secure	ADJ
cana-950	191	15	vertex	vertex	NOUN
cana-950	191	16	-	-	PUNCT
cana-950	191	17	edge	edge	NOUN
cana-950	191	18	dominance	dominance	NOUN
cana-950	191	19	number	number	NOUN
cana-950	191	20	as	as	ADP
cana-950	191	21	2	2	NUM
cana-950	191	22	.	.	PUNCT
cana-950	192	1	proof	proof	NOUN
cana-950	192	2	:	:	PUNCT
cana-950	192	3	wagner	wagner	PROPN
cana-950	192	4	graph	graph	NOUN
cana-950	192	5	is	be	AUX
cana-950	192	6	a	a	DET
cana-950	192	7	graph	graph	NOUN
cana-950	192	8	which	which	PRON
cana-950	192	9	consists	consist	VERB
cana-950	192	10	of	of	ADP
cana-950	192	11	eight	eight	NUM
cana-950	192	12	vertices	vertex	NOUN
cana-950	192	13	and	and	CCONJ
cana-950	192	14	12	12	NUM
cana-950	192	15	edges	edge	NOUN
cana-950	192	16	.	.	PUNCT
cana-950	193	1	the	the	DET
cana-950	193	2	graph	graph	NOUN
cana-950	193	3	is	be	AUX
cana-950	193	4	a	a	DET
cana-950	193	5	regular	regular	ADJ
cana-950	193	6	graph	graph	NOUN
cana-950	193	7	with	with	ADP
cana-950	193	8	a	a	DET
cana-950	193	9	degree	degree	NOUN
cana-950	193	10	of	of	ADP
cana-950	193	11	3	3	NUM
cana-950	193	12	.	.	PUNCT
cana-950	194	1	since	since	SCONJ
cana-950	194	2	it	it	PRON
cana-950	194	3	is	be	AUX
cana-950	194	4	symmetric	symmetric	ADJ
cana-950	194	5	,	,	PUNCT
cana-950	194	6	one	one	NUM
cana-950	194	7	vertex	vertex	NOUN
cana-950	194	8	from	from	ADP
cana-950	194	9	each	each	DET
cana-950	194	10	side	side	NOUN
cana-950	194	11	will	will	AUX
cana-950	194	12	safeguard	safeguard	VERB
cana-950	194	13	each	each	PRON
cana-950	194	14	of	of	ADP
cana-950	194	15	the	the	DET
cana-950	194	16	edges	edge	NOUN
cana-950	194	17	of	of	ADP
cana-950	194	18	the	the	DET
cana-950	194	19	graph	graph	NOUN
cana-950	194	20	.	.	PUNCT
cana-950	195	1	two	two	NUM
cana-950	195	2	vertices	vertex	NOUN
cana-950	195	3	in	in	ADP
cana-950	195	4	i	i	PRON
cana-950	195	5	should	should	AUX
cana-950	195	6	not	not	PART
cana-950	195	7	be	be	AUX
cana-950	195	8	in	in	ADP
cana-950	195	9	the	the	DET
cana-950	195	10	same	same	ADJ
cana-950	195	11	straight	straight	ADJ
cana-950	195	12	line	line	NOUN
cana-950	195	13	.	.	PUNCT
cana-950	196	1	the	the	DET
cana-950	196	2	secure	secure	ADJ
cana-950	196	3	vertex	vertex	NOUN
cana-950	196	4	edge	edge	NOUN
cana-950	196	5	dominating	dominating	NOUN
cana-950	196	6	set	set	NOUN
cana-950	196	7	i	i	PRON
cana-950	196	8	=	=	PUNCT
cana-950	196	9	{	{	PUNCT
cana-950	196	10	x1	x1	PROPN
cana-950	196	11	,	,	PUNCT
cana-950	196	12	x3	x3	ADJ
cana-950	196	13	}	}	PUNCT
cana-950	196	14	,	,	PUNCT
cana-950	196	15	which	which	PRON
cana-950	196	16	will	will	AUX
cana-950	196	17	protect	protect	VERB
cana-950	196	18	all	all	DET
cana-950	196	19	the	the	DET
cana-950	196	20	12	12	NUM
cana-950	196	21	edges	edge	NOUN
cana-950	196	22	of	of	ADP
cana-950	196	23	the	the	DET
cana-950	196	24	graph	graph	NOUN
cana-950	196	25	.	.	PUNCT
cana-950	197	1	thus	thus	ADV
cana-950	197	2	,	,	PUNCT
cana-950	197	3	the	the	DET
cana-950	197	4	secure	secure	ADJ
cana-950	197	5	vertex	vertex	NOUN
cana-950	197	6	edge	edge	NOUN
cana-950	197	7	domination	domination	NOUN
cana-950	197	8	of	of	ADP
cana-950	197	9	wagner	wagner	PROPN
cana-950	197	10	graph	graph	NOUN
cana-950	197	11	is	be	AUX
cana-950	197	12	2	2	NUM
cana-950	197	13	)	)	PUNCT
cana-950	197	14	(	(	PUNCT
cana-950	197	15	=	=	NOUN
cana-950	197	16	wrgsve	wrgsve	X
cana-950	197	17	.	.	PUNCT
cana-950	198	1	communications	communication	NOUN
cana-950	198	2	on	on	ADP
cana-950	198	3	applied	apply	VERB
cana-950	198	4	nonlinear	nonlinear	ADJ
cana-950	198	5	analysis	analysis	NOUN
cana-950	198	6	issn	issn	NOUN
cana-950	198	7	:	:	PUNCT
cana-950	198	8	1074	1074	NUM
cana-950	198	9	-	-	PUNCT
cana-950	198	10	133x	133x	NUM
cana-950	198	11	vol	vol	NOUN
cana-950	198	12	31	31	NUM
cana-950	198	13	no	no	NOUN
cana-950	198	14	.	.	PUNCT
cana-950	199	1	4s	4s	NUM
cana-950	199	2	(	(	PUNCT
cana-950	199	3	2024	2024	NUM
cana-950	199	4	)	)	PUNCT
cana-950	199	5	569	569	NUM
cana-950	199	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-950	199	7	hence	hence	ADV
cana-950	199	8	the	the	DET
cana-950	199	9	proof	proof	NOUN
cana-950	199	10	.	.	PUNCT
cana-950	200	1	theorem	theorem	NOUN
cana-950	200	2	12	12	NUM
cana-950	200	3	:	:	PUNCT
cana-950	200	4	the	the	DET
cana-950	200	5	heawood	heawood	NOUN
cana-950	200	6	graph	graph	NOUN
cana-950	200	7	's	's	PART
cana-950	200	8	secure	secure	ADJ
cana-950	200	9	-	-	PUNCT
cana-950	200	10	vertex	vertex	NOUN
cana-950	200	11	-	-	PUNCT
cana-950	200	12	edge	edge	NOUN
cana-950	200	13	dominance	dominance	NOUN
cana-950	200	14	number	number	NOUN
cana-950	200	15	is	be	AUX
cana-950	200	16	identified	identify	VERB
cana-950	200	17	by	by	ADP
cana-950	200	18			PROPN
cana-950	200	19			NOUN
cana-950	200	20			X
cana-950	200	21			NOUN
cana-950	200	22			X
cana-950	200	23			NOUN
cana-950	200	24	=	=	SYM
cana-950	200	25	3	3	NUM
cana-950	200	26	)	)	PUNCT
cana-950	200	27	(	(	PUNCT
cana-950	200	28	n	n	X
cana-950	200	29	hdgsve	hdgsve	PROPN
cana-950	200	30	.	.	PUNCT
cana-950	201	1	proof	proof	NOUN
cana-950	201	2	:	:	PUNCT
cana-950	201	3	the	the	DET
cana-950	201	4	heawood	heawood	NOUN
cana-950	201	5	graph	graph	NOUN
cana-950	201	6	(	(	PUNCT
cana-950	201	7	hdg	hdg	NOUN
cana-950	201	8	)	)	PUNCT
cana-950	201	9	is	be	AUX
cana-950	201	10	a	a	DET
cana-950	201	11	graph	graph	NOUN
cana-950	201	12	featuring	feature	VERB
cana-950	201	13	fourteen	fourteen	NUM
cana-950	201	14	nodes	node	NOUN
cana-950	201	15	and	and	CCONJ
cana-950	201	16	twenty	twenty	NUM
cana-950	201	17	-	-	PUNCT
cana-950	201	18	one	one	NUM
cana-950	201	19	edges	edge	NOUN
cana-950	201	20	,	,	PUNCT
cana-950	201	21	where	where	SCONJ
cana-950	201	22	all	all	DET
cana-950	201	23	vertices	vertex	NOUN
cana-950	201	24	are	be	AUX
cana-950	201	25	linked	link	VERB
cana-950	201	26	.	.	PUNCT
cana-950	202	1	it	it	PRON
cana-950	202	2	is	be	AUX
cana-950	202	3	a	a	DET
cana-950	202	4	3regular	3regular	NUM
cana-950	202	5	graph	graph	NOUN
cana-950	202	6	.	.	PUNCT
cana-950	203	1	the	the	DET
cana-950	203	2	secure	secure	ADJ
cana-950	203	3	vertex	vertex	NOUN
cana-950	203	4	edge	edge	NOUN
cana-950	203	5	domination	domination	NOUN
cana-950	203	6	number	number	NOUN
cana-950	203	7	of	of	ADP
cana-950	203	8	this	this	DET
cana-950	203	9	heawood	heawood	NOUN
cana-950	203	10	graph	graph	NOUN
cana-950	203	11	is	be	AUX
cana-950	203	12	determined	determine	VERB
cana-950	203	13	through	through	ADP
cana-950	203	14			PROPN
cana-950	203	15			NOUN
cana-950	203	16	.56.4	.56.4	PROPN
cana-950	203	17	3	3	NUM
cana-950	203	18	14	14	NUM
cana-950	203	19	3	3	NUM
cana-950	203	20	=	=	SYM
cana-950	203	21	=	=	NOUN
cana-950	203	22			NOUN
cana-950	203	23			NOUN
cana-950	203	24			X
cana-950	204	1			NOUN
cana-950	204	2			X
cana-950	204	3			PROPN
cana-950	204	4	=	=	NOUN
cana-950	204	5			NOUN
cana-950	204	6			NOUN
cana-950	204	7			NOUN
cana-950	204	8			NOUN
cana-950	204	9			X
cana-950	204	10	n	n	NOUN
cana-950	204	11	the	the	DET
cana-950	204	12	set	set	NOUN
cana-950	204	13	i	i	PRON
cana-950	204	14	contains	contain	VERB
cana-950	204	15	five	five	NUM
cana-950	204	16	vertices	vertex	NOUN
cana-950	204	17	namely	namely	ADV
cana-950	204	18	x3	x3	ADJ
cana-950	204	19	,	,	PUNCT
cana-950	204	20	x7	x7	NOUN
cana-950	204	21	,	,	PUNCT
cana-950	204	22	x8	x8	PROPN
cana-950	204	23	,	,	PUNCT
cana-950	204	24	x10	x10	NUM
cana-950	204	25	,	,	PUNCT
cana-950	204	26	x14	x14	PROPN
cana-950	204	27	.	.	PUNCT
cana-950	205	1	these	these	DET
cana-950	205	2	five	five	NUM
cana-950	205	3	vertices	vertex	NOUN
cana-950	205	4	secure	secure	VERB
cana-950	205	5	all	all	DET
cana-950	205	6	the	the	DET
cana-950	205	7	twenty	twenty	NUM
cana-950	205	8	-	-	PUNCT
cana-950	205	9	one	one	NUM
cana-950	205	10	edges	edge	NOUN
cana-950	205	11	of	of	ADP
cana-950	205	12	the	the	DET
cana-950	205	13	graph	graph	NOUN
cana-950	205	14	.	.	PUNCT
cana-950	206	1	the	the	DET
cana-950	206	2	condition	condition	NOUN
cana-950	206	3	to	to	PART
cana-950	206	4	select	select	VERB
cana-950	206	5	these	these	DET
cana-950	206	6	vertices	vertex	NOUN
cana-950	206	7	is	be	AUX
cana-950	206	8	that	that	SCONJ
cana-950	206	9	the	the	DET
cana-950	206	10	vertices	vertex	NOUN
cana-950	206	11	in	in	ADP
cana-950	206	12	the	the	DET
cana-950	206	13	set	set	NOUN
cana-950	206	14	i	i	PRON
cana-950	206	15	should	should	AUX
cana-950	206	16	not	not	PART
cana-950	206	17	be	be	AUX
cana-950	206	18	in	in	ADP
cana-950	206	19	the	the	DET
cana-950	206	20	same	same	ADJ
cana-950	206	21	line	line	NOUN
cana-950	206	22	.	.	PUNCT
cana-950	207	1	i.e.	i.e.	X
cana-950	207	2	,	,	PUNCT
cana-950	207	3	in	in	ADP
cana-950	207	4	a	a	DET
cana-950	207	5	straight	straight	ADJ
cana-950	207	6	line	line	NOUN
cana-950	207	7	there	there	PRON
cana-950	207	8	will	will	AUX
cana-950	207	9	be	be	AUX
cana-950	207	10	two	two	NUM
cana-950	207	11	vertices	vertex	NOUN
cana-950	207	12	at	at	ADP
cana-950	207	13	each	each	DET
cana-950	207	14	end	end	NOUN
cana-950	207	15	of	of	ADP
cana-950	207	16	the	the	DET
cana-950	207	17	line	line	NOUN
cana-950	207	18	,	,	PUNCT
cana-950	207	19	no	no	DET
cana-950	207	20	two	two	NUM
cana-950	207	21	vertices	vertex	NOUN
cana-950	207	22	of	of	ADP
cana-950	207	23	this	this	DET
cana-950	207	24	straight	straight	ADJ
cana-950	207	25	line	line	NOUN
cana-950	207	26	should	should	AUX
cana-950	207	27	be	be	AUX
cana-950	207	28	in	in	ADP
cana-950	207	29	the	the	DET
cana-950	207	30	set	set	NOUN
cana-950	207	31	i.	i.	NOUN
cana-950	207	32	therefore	therefore	ADV
cana-950	207	33	,	,	PUNCT
cana-950	207	34	all	all	DET
cana-950	207	35	the	the	DET
cana-950	207	36	edges	edge	NOUN
cana-950	207	37	that	that	PRON
cana-950	207	38	are	be	AUX
cana-950	207	39	connected	connect	VERB
cana-950	207	40	to	to	ADP
cana-950	207	41	the	the	DET
cana-950	207	42	vertices	vertex	NOUN
cana-950	207	43	and	and	CCONJ
cana-950	207	44	the	the	DET
cana-950	207	45	edges	edge	NOUN
cana-950	207	46	that	that	PRON
cana-950	207	47	are	be	AUX
cana-950	207	48	connected	connect	VERB
cana-950	207	49	to	to	ADP
cana-950	207	50	the	the	DET
cana-950	207	51	connected	connected	ADJ
cana-950	207	52	edges	edge	NOUN
cana-950	207	53	will	will	AUX
cana-950	207	54	be	be	AUX
cana-950	207	55	safeguarded	safeguard	VERB
cana-950	207	56	.	.	PUNCT
cana-950	208	1	hence	hence	ADV
cana-950	208	2	the	the	DET
cana-950	208	3	secure	secure	ADJ
cana-950	208	4	vertex	vertex	NOUN
cana-950	208	5	edge	edge	NOUN
cana-950	208	6	domination	domination	NOUN
cana-950	208	7	number	number	NOUN
cana-950	208	8	of	of	ADP
cana-950	208	9	the	the	DET
cana-950	208	10	heawood	heawood	NOUN
cana-950	208	11	graph	graph	NOUN
cana-950	208	12	is	be	AUX
cana-950	208	13			ADJ
cana-950	208	14			NOUN
cana-950	208	15			X
cana-950	208	16			NOUN
cana-950	208	17			X
cana-950	208	18			NOUN
cana-950	208	19	=	=	SYM
cana-950	208	20	3	3	NUM
cana-950	208	21	)	)	PUNCT
cana-950	208	22	(	(	PUNCT
cana-950	208	23	n	n	X
cana-950	208	24	hdgsve	hdgsve	PROPN
cana-950	208	25	.	.	PUNCT
cana-950	209	1	theorem	theorem	VERB
cana-950	209	2	13	13	NUM
cana-950	209	3	:	:	PUNCT
cana-950	209	4	consider	consider	VERB
cana-950	209	5	a	a	DET
cana-950	209	6	network	network	NOUN
cana-950	209	7	with	with	ADP
cana-950	209	8	n	n	NOUN
cana-950	209	9	=	=	SYM
cana-950	209	10	18	18	NUM
cana-950	209	11	vertices	vertex	NOUN
cana-950	209	12	that	that	PRON
cana-950	209	13	is	be	AUX
cana-950	209	14	a	a	DET
cana-950	209	15	pappus	pappus	ADJ
cana-950	209	16	graph	graph	NOUN
cana-950	209	17	.	.	PUNCT
cana-950	210	1	the	the	DET
cana-950	210	2	secure	secure	ADJ
cana-950	210	3	-	-	PUNCT
cana-950	210	4	vertex	vertex	NOUN
cana-950	210	5	-	-	PUNCT
cana-950	210	6	edge	edge	NOUN
cana-950	210	7	dominance	dominance	NOUN
cana-950	210	8	number	number	NOUN
cana-950	210	9	of	of	ADP
cana-950	210	10	this	this	DET
cana-950	210	11	graph	graph	NOUN
cana-950	210	12	is	be	AUX
cana-950	210	13	given	give	VERB
cana-950	210	14	by	by	ADP
cana-950	210	15			PROPN
cana-950	210	16			NOUN
cana-950	210	17			X
cana-950	210	18			NOUN
cana-950	210	19			X
cana-950	210	20			PROPN
cana-950	210	21	3	3	NUM
cana-950	210	22	n	n	NOUN
cana-950	210	23	.	.	PUNCT
cana-950	211	1	proof	proof	NOUN
cana-950	211	2	:	:	PUNCT
cana-950	211	3	communications	communication	NOUN
cana-950	211	4	on	on	ADP
cana-950	211	5	applied	apply	VERB
cana-950	211	6	nonlinear	nonlinear	ADJ
cana-950	211	7	analysis	analysis	NOUN
cana-950	211	8	issn	issn	NOUN
cana-950	211	9	:	:	PUNCT
cana-950	211	10	1074	1074	NUM
cana-950	211	11	-	-	PUNCT
cana-950	211	12	133x	133x	NUM
cana-950	211	13	vol	vol	NOUN
cana-950	211	14	31	31	NUM
cana-950	211	15	no	no	NOUN
cana-950	211	16	.	.	PUNCT
cana-950	212	1	4s	4s	NUM
cana-950	212	2	(	(	PUNCT
cana-950	212	3	2024	2024	NUM
cana-950	212	4	)	)	PUNCT
cana-950	212	5	570	570	NUM
cana-950	212	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-950	212	7	the	the	DET
cana-950	212	8	pappus	pappus	PROPN
cana-950	212	9	graph	graph	NOUN
cana-950	212	10	is	be	AUX
cana-950	212	11	a	a	DET
cana-950	212	12	graph	graph	NOUN
cana-950	212	13	that	that	PRON
cana-950	212	14	has	have	VERB
cana-950	212	15	a	a	DET
cana-950	212	16	degree	degree	NOUN
cana-950	212	17	of	of	ADP
cana-950	212	18	3	3	NUM
cana-950	212	19	,	,	PUNCT
cana-950	212	20	meaning	mean	VERB
cana-950	212	21	that	that	SCONJ
cana-950	212	22	each	each	DET
cana-950	212	23	vertex	vertex	NOUN
cana-950	212	24	is	be	AUX
cana-950	212	25	connected	connect	VERB
cana-950	212	26	to	to	ADP
cana-950	212	27	exactly	exactly	ADV
cana-950	212	28	3	3	NUM
cana-950	212	29	other	other	ADJ
cana-950	212	30	vertices	vertex	NOUN
cana-950	212	31	.	.	PUNCT
cana-950	213	1	it	it	PRON
cana-950	213	2	consists	consist	VERB
cana-950	213	3	of	of	ADP
cana-950	213	4	18	18	NUM
cana-950	213	5	vertices	vertex	NOUN
cana-950	213	6	and	and	CCONJ
cana-950	213	7	27	27	NUM
cana-950	213	8	edges	edge	NOUN
cana-950	213	9	.	.	PUNCT
cana-950	214	1	the	the	DET
cana-950	214	2	pappus	pappus	PROPN
cana-950	214	3	graph	graph	NOUN
cana-950	214	4	resembles	resemble	NOUN
cana-950	214	5	like	like	ADP
cana-950	214	6	a	a	DET
cana-950	214	7	flower	flower	NOUN
cana-950	214	8	with	with	ADP
cana-950	214	9	3	3	NUM
cana-950	214	10	layer	layer	NOUN
cana-950	214	11	and	and	CCONJ
cana-950	214	12	6	6	NUM
cana-950	214	13	petals	petal	NOUN
cana-950	214	14	.	.	PUNCT
cana-950	215	1	the	the	DET
cana-950	215	2	secure	secure	ADJ
cana-950	215	3	vertex	vertex	NOUN
cana-950	215	4	edge	edge	NOUN
cana-950	215	5	domination	domination	NOUN
cana-950	215	6	number	number	NOUN
cana-950	215	7	of	of	ADP
cana-950	215	8	the	the	DET
cana-950	215	9	pappus	pappus	ADJ
cana-950	215	10	graph	graph	NOUN
cana-950	215	11	provided	provide	VERB
cana-950	215	12	by	by	ADP
cana-950	215	13	.6	.6	NUM
cana-950	215	14	3	3	NUM
cana-950	215	15	18	18	NUM
cana-950	215	16	3	3	NUM
cana-950	215	17	=	=	NOUN
cana-950	215	18			NOUN
cana-950	215	19			NOUN
cana-950	215	20			X
cana-950	215	21			NOUN
cana-950	215	22			X
cana-950	215	23			PROPN
cana-950	215	24	=	=	NOUN
cana-950	215	25			NOUN
cana-950	215	26			NOUN
cana-950	215	27			NOUN
cana-950	215	28			NOUN
cana-950	215	29			X
cana-950	215	30	n	n	NOUN
cana-950	215	31	the	the	DET
cana-950	215	32	set	set	NOUN
cana-950	215	33	i	i	PRON
cana-950	215	34	contains	contain	VERB
cana-950	215	35	6	6	NUM
cana-950	215	36	vertices	vertex	NOUN
cana-950	215	37	in	in	ADP
cana-950	215	38	which	which	PRON
cana-950	215	39	,	,	PUNCT
cana-950	215	40	any	any	DET
cana-950	215	41	two	two	NUM
cana-950	215	42	vertices	vertex	NOUN
cana-950	215	43	of	of	ADP
cana-950	215	44	each	each	DET
cana-950	215	45	layer	layer	NOUN
cana-950	215	46	can	can	AUX
cana-950	215	47	be	be	AUX
cana-950	215	48	in	in	ADP
cana-950	215	49	the	the	DET
cana-950	215	50	set	set	NOUN
cana-950	215	51	i	i	PRON
cana-950	215	52	or	or	CCONJ
cana-950	215	53	3	3	NUM
cana-950	215	54	vertices	vertex	NOUN
cana-950	215	55	of	of	ADP
cana-950	215	56	the	the	DET
cana-950	215	57	inner	inner	ADJ
cana-950	215	58	two	two	NUM
cana-950	215	59	layers	layer	NOUN
cana-950	215	60	.	.	PUNCT
cana-950	216	1	these	these	DET
cana-950	216	2	6	6	NUM
cana-950	216	3	vertices	vertex	NOUN
cana-950	216	4	will	will	AUX
cana-950	216	5	defend	defend	VERB
cana-950	216	6	all	all	DET
cana-950	216	7	the	the	DET
cana-950	216	8	27	27	NUM
cana-950	216	9	edges	edge	NOUN
cana-950	216	10	of	of	ADP
cana-950	216	11	the	the	DET
cana-950	216	12	graph	graph	NOUN
cana-950	216	13	.	.	PUNCT
cana-950	217	1	let	let	VERB
cana-950	217	2	i	i	PRON
cana-950	217	3	=	=	PUNCT
cana-950	217	4	{	{	PUNCT
cana-950	217	5	x1	x1	PROPN
cana-950	217	6	,	,	PUNCT
cana-950	217	7	x2	x2	PROPN
cana-950	217	8	,	,	PUNCT
cana-950	217	9	x6	x6	PROPN
cana-950	217	10	,	,	PUNCT
cana-950	217	11	x8	x8	PROPN
cana-950	217	12	,	,	PUNCT
cana-950	217	13	x10	x10	NUM
cana-950	217	14	,	,	PUNCT
cana-950	217	15	x12	x12	PROPN
cana-950	217	16	}	}	PUNCT
cana-950	217	17	be	be	VERB
cana-950	217	18	the	the	DET
cana-950	217	19	secure	secure	ADJ
cana-950	217	20	vertex	vertex	NOUN
cana-950	217	21	edge	edge	NOUN
cana-950	217	22	dominating	dominate	VERB
cana-950	217	23	set	set	NOUN
cana-950	217	24	of	of	ADP
cana-950	217	25	the	the	DET
cana-950	217	26	pappus	pappus	ADJ
cana-950	217	27	graph	graph	NOUN
cana-950	217	28	which	which	PRON
cana-950	217	29	secures	secure	VERB
cana-950	217	30	all	all	DET
cana-950	217	31	the	the	DET
cana-950	217	32	incident	incident	NOUN
cana-950	217	33	edges	edge	NOUN
cana-950	217	34	of	of	ADP
cana-950	217	35	that	that	DET
cana-950	217	36	vertices	vertex	NOUN
cana-950	217	37	and	and	CCONJ
cana-950	217	38	the	the	DET
cana-950	217	39	edges	edge	NOUN
cana-950	217	40	which	which	PRON
cana-950	217	41	are	be	AUX
cana-950	217	42	adjacent	adjacent	ADJ
cana-950	217	43	to	to	ADP
cana-950	217	44	that	that	DET
cana-950	217	45	incident	incident	NOUN
cana-950	217	46	edges	edge	NOUN
cana-950	217	47	.	.	PUNCT
cana-950	218	1	therefore	therefore	ADV
cana-950	218	2	,	,	PUNCT
cana-950	218	3	every	every	DET
cana-950	218	4	edge	edge	NOUN
cana-950	218	5	in	in	ADP
cana-950	218	6	the	the	DET
cana-950	218	7	graph	graph	NOUN
cana-950	218	8	is	be	AUX
cana-950	218	9	protected	protect	VERB
cana-950	218	10	.	.	PUNCT
cana-950	219	1	therefore	therefore	ADV
cana-950	219	2	,	,	PUNCT
cana-950	219	3	the	the	DET
cana-950	219	4	pappus	pappus	ADJ
cana-950	219	5	graph	graph	NOUN
cana-950	219	6	has	have	VERB
cana-950	219	7	a	a	DET
cana-950	219	8	secure	secure	ADJ
cana-950	219	9	-	-	PUNCT
cana-950	219	10	vertex	vertex	NOUN
cana-950	219	11	-	-	PUNCT
cana-950	219	12	edge	edge	NOUN
cana-950	219	13	dominance	dominance	NOUN
cana-950	219	14	number	number	NOUN
cana-950	219	15	is	be	AUX
cana-950	219	16	(	(	PUNCT
cana-950	219	17	)	)	PUNCT
cana-950	219	18	3	3	NUM
cana-950	219	19	sve	sve	NOUN
cana-950	219	20	n	n	PROPN
cana-950	219	21	ppsg	ppsg	NOUN
cana-950	220	1			PROPN
cana-950	220	2			NOUN
cana-950	220	3	=	=	SYM
cana-950	220	4			NOUN
cana-950	220	5			NOUN
cana-950	220	6			NOUN
cana-950	220	7			PROPN
cana-950	220	8	.	.	PUNCT
cana-950	221	1	theorem	theorem	ADJ
cana-950	221	2	14	14	NUM
cana-950	221	3	:	:	PUNCT
cana-950	221	4	the	the	DET
cana-950	221	5	secure	secure	ADJ
cana-950	221	6	vertex	vertex	NOUN
cana-950	221	7	edge	edge	NOUN
cana-950	221	8	domination	domination	NOUN
cana-950	221	9	number	number	NOUN
cana-950	221	10	of	of	ADP
cana-950	221	11	the	the	DET
cana-950	221	12	house	house	NOUN
cana-950	221	13	graph	graph	NOUN
cana-950	221	14	is	be	AUX
cana-950	221	15	one	one	NUM
cana-950	221	16	.	.	PUNCT
cana-950	222	1	proof	proof	NOUN
cana-950	222	2	:	:	PUNCT
cana-950	222	3	the	the	DET
cana-950	222	4	house	house	NOUN
cana-950	222	5	graph	graph	NOUN
cana-950	222	6	is	be	AUX
cana-950	222	7	composed	compose	VERB
cana-950	222	8	of	of	ADP
cana-950	222	9	five	five	NUM
cana-950	222	10	vertices	vertex	NOUN
cana-950	222	11	labeled	label	VERB
cana-950	222	12	x1	x1	PROPN
cana-950	222	13	,	,	PUNCT
cana-950	222	14	x2	x2	PROPN
cana-950	222	15	,	,	PUNCT
cana-950	222	16	x3	x3	PROPN
cana-950	222	17	,	,	PUNCT
cana-950	222	18	x4	x4	PROPN
cana-950	222	19	,	,	PUNCT
cana-950	222	20	and	and	CCONJ
cana-950	222	21	x5	x5	NOUN
cana-950	222	22	,	,	PUNCT
cana-950	222	23	and	and	CCONJ
cana-950	222	24	six	six	NUM
cana-950	222	25	edges	edge	NOUN
cana-950	222	26	labeled	label	VERB
cana-950	222	27	y1	y1	NOUN
cana-950	222	28	,	,	PUNCT
cana-950	222	29	y2	y2	PROPN
cana-950	222	30	,	,	PUNCT
cana-950	222	31	y3	y3	PROPN
cana-950	222	32	,	,	PUNCT
cana-950	222	33	y4	y4	NOUN
cana-950	222	34	,	,	PUNCT
cana-950	222	35	y5	y5	NOUN
cana-950	222	36	,	,	PUNCT
cana-950	222	37	and	and	CCONJ
cana-950	222	38	y6	y6	ADJ
cana-950	222	39	.	.	PUNCT
cana-950	223	1	two	two	NUM
cana-950	223	2	vertices	vertex	NOUN
cana-950	223	3	,	,	PUNCT
cana-950	223	4	x2	x2	NOUN
cana-950	223	5	and	and	CCONJ
cana-950	223	6	x5	x5	PROPN
cana-950	223	7	,	,	PUNCT
cana-950	223	8	have	have	VERB
cana-950	223	9	a	a	DET
cana-950	223	10	degree	degree	NOUN
cana-950	223	11	of	of	ADP
cana-950	223	12	three	three	NUM
cana-950	223	13	,	,	PUNCT
cana-950	223	14	whereas	whereas	SCONJ
cana-950	223	15	all	all	PRON
cana-950	223	16	of	of	ADP
cana-950	223	17	the	the	DET
cana-950	223	18	rest	rest	NOUN
cana-950	223	19	have	have	VERB
cana-950	223	20	a	a	DET
cana-950	223	21	degree	degree	NOUN
cana-950	223	22	of	of	ADP
cana-950	223	23	two	two	NUM
cana-950	223	24	.	.	PUNCT
cana-950	224	1	the	the	DET
cana-950	224	2	secure	secure	ADJ
cana-950	224	3	vertex	vertex	NOUN
cana-950	224	4	edge	edge	NOUN
cana-950	224	5	dominating	dominating	NOUN
cana-950	224	6	set	set	NOUN
cana-950	224	7	i	i	PRON
cana-950	224	8	=	=	NOUN
cana-950	224	9	{	{	PUNCT
cana-950	224	10	x2	x2	ADJ
cana-950	224	11	}	}	PUNCT
cana-950	224	12	or{x5	or{x5	NOUN
cana-950	224	13	}	}	PUNCT
cana-950	224	14	.	.	PUNCT
cana-950	225	1	since	since	SCONJ
cana-950	225	2	x2	x2	PROPN
cana-950	225	3	and	and	CCONJ
cana-950	225	4	x5	x5	PROPN
cana-950	225	5	have	have	VERB
cana-950	225	6	the	the	DET
cana-950	225	7	maximum	maximum	ADJ
cana-950	225	8	degree	degree	NOUN
cana-950	225	9	,	,	PUNCT
cana-950	225	10	these	these	DET
cana-950	225	11	vertices	vertex	NOUN
cana-950	225	12	may	may	AUX
cana-950	225	13	effectively	effectively	ADV
cana-950	225	14	secure	secure	VERB
cana-950	225	15	all	all	DET
cana-950	225	16	the	the	DET
cana-950	225	17	incident	incident	NOUN
cana-950	225	18	edges	edge	NOUN
cana-950	225	19	and	and	CCONJ
cana-950	225	20	the	the	DET
cana-950	225	21	neighboring	neighboring	NOUN
cana-950	225	22	edges	edge	NOUN
cana-950	225	23	connected	connect	VERB
cana-950	225	24	to	to	ADP
cana-950	225	25	those	those	DET
cana-950	225	26	incident	incident	NOUN
cana-950	225	27	edges	edge	NOUN
cana-950	225	28	in	in	ADP
cana-950	225	29	the	the	DET
cana-950	225	30	graph	graph	NOUN
cana-950	225	31	.	.	PUNCT
cana-950	226	1	therefore	therefore	ADV
cana-950	226	2	,	,	PUNCT
cana-950	226	3	all	all	DET
cana-950	226	4	the	the	DET
cana-950	226	5	edges	edge	NOUN
cana-950	226	6	in	in	ADP
cana-950	226	7	the	the	DET
cana-950	226	8	graph	graph	NOUN
cana-950	226	9	are	be	AUX
cana-950	226	10	safeguarded	safeguard	VERB
cana-950	226	11	.	.	PUNCT
cana-950	227	1	hence	hence	ADV
cana-950	227	2	the	the	DET
cana-950	227	3	secure	secure	ADJ
cana-950	227	4	vertex	vertex	NOUN
cana-950	227	5	edge	edge	NOUN
cana-950	227	6	domination	domination	NOUN
cana-950	227	7	number	number	NOUN
cana-950	227	8	of	of	ADP
cana-950	227	9	the	the	DET
cana-950	227	10	house	house	NOUN
cana-950	227	11	graph	graph	NOUN
cana-950	227	12	is	be	AUX
cana-950	227	13	one	one	NUM
cana-950	227	14	.	.	PUNCT
cana-950	228	1	theorem	theorem	VERB
cana-950	228	2	15	15	NUM
cana-950	228	3	:	:	PUNCT
cana-950	228	4	the	the	DET
cana-950	228	5	cricket	cricket	NOUN
cana-950	228	6	graph	graph	NOUN
cana-950	228	7	,	,	PUNCT
cana-950	228	8	denoted	denote	VERB
cana-950	228	9	as	as	ADP
cana-950	228	10	cg	cg	NOUN
cana-950	228	11	,	,	PUNCT
cana-950	228	12	has	have	VERB
cana-950	228	13	a	a	DET
cana-950	228	14	secure	secure	ADJ
cana-950	228	15	-	-	PUNCT
cana-950	228	16	vertex	vertex	NOUN
cana-950	228	17	-	-	PUNCT
cana-950	228	18	edge	edge	NOUN
cana-950	228	19	dominance	dominance	NOUN
cana-950	228	20	number	number	NOUN
cana-950	228	21	as	as	ADP
cana-950	228	22	one	one	NUM
cana-950	228	23	.	.	PUNCT
cana-950	229	1	proof	proof	NOUN
cana-950	229	2	:	:	PUNCT
cana-950	229	3	communications	communication	NOUN
cana-950	229	4	on	on	ADP
cana-950	229	5	applied	apply	VERB
cana-950	229	6	nonlinear	nonlinear	ADJ
cana-950	229	7	analysis	analysis	NOUN
cana-950	229	8	issn	issn	NOUN
cana-950	229	9	:	:	PUNCT
cana-950	229	10	1074	1074	NUM
cana-950	229	11	-	-	PUNCT
cana-950	229	12	133x	133x	NUM
cana-950	229	13	vol	vol	NOUN
cana-950	229	14	31	31	NUM
cana-950	229	15	no	no	NOUN
cana-950	229	16	.	.	PUNCT
cana-950	230	1	4s	4s	NUM
cana-950	230	2	(	(	PUNCT
cana-950	230	3	2024	2024	NUM
cana-950	230	4	)	)	PUNCT
cana-950	230	5	571	571	NUM
cana-950	230	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-950	230	7	the	the	DET
cana-950	230	8	cricket	cricket	NOUN
cana-950	230	9	graph	graph	NOUN
cana-950	230	10	consists	consist	VERB
cana-950	230	11	of	of	ADP
cana-950	230	12	five	five	NUM
cana-950	230	13	vertices	vertex	NOUN
cana-950	230	14	labeled	label	VERB
cana-950	230	15	as	as	ADP
cana-950	230	16	x1	x1	PROPN
cana-950	230	17	to	to	ADP
cana-950	230	18	x5	x5	PROPN
cana-950	230	19	,	,	PUNCT
cana-950	230	20	and	and	CCONJ
cana-950	230	21	five	five	NUM
cana-950	230	22	edges	edge	NOUN
cana-950	230	23	labeled	label	VERB
cana-950	230	24	as	as	ADP
cana-950	230	25	y1	y1	NOUN
cana-950	230	26	to	to	ADP
cana-950	230	27	y5	y5	NOUN
cana-950	230	28	,	,	PUNCT
cana-950	230	29	in	in	ADP
cana-950	230	30	which	which	PRON
cana-950	230	31	one	one	NUM
cana-950	230	32	vertex	vertex	NOUN
cana-950	230	33	x2	x2	PRON
cana-950	230	34	has	have	VERB
cana-950	230	35	the	the	DET
cana-950	230	36	highest	high	ADJ
cana-950	230	37	degree	degree	NOUN
cana-950	230	38	four	four	NUM
cana-950	230	39	,	,	PUNCT
cana-950	230	40	two	two	NUM
cana-950	230	41	vertices	vertex	NOUN
cana-950	230	42	x4	x4	PROPN
cana-950	230	43	,	,	PUNCT
cana-950	230	44	x5	x5	PROPN
cana-950	230	45	with	with	ADP
cana-950	230	46	degree	degree	NOUN
cana-950	230	47	two	two	NUM
cana-950	230	48	and	and	CCONJ
cana-950	230	49	the	the	DET
cana-950	230	50	remaining	remain	VERB
cana-950	230	51	vertices	vertex	NOUN
cana-950	230	52	x1	x1	PROPN
cana-950	230	53	and	and	CCONJ
cana-950	230	54	x3	x3	ADJ
cana-950	230	55	having	have	VERB
cana-950	230	56	their	their	PRON
cana-950	230	57	degree	degree	NOUN
cana-950	230	58	one	one	NUM
cana-950	230	59	.	.	PUNCT
cana-950	231	1	the	the	DET
cana-950	231	2	secure	secure	ADJ
cana-950	231	3	vertex	vertex	NOUN
cana-950	231	4	edge	edge	NOUN
cana-950	231	5	dominating	dominating	NOUN
cana-950	231	6	set	set	NOUN
cana-950	231	7	i	i	PRON
cana-950	231	8	=	=	NOUN
cana-950	231	9	{	{	PUNCT
cana-950	231	10	x2	x2	NOUN
cana-950	231	11	}	}	PUNCT
cana-950	231	12	.	.	PUNCT
cana-950	232	1	since	since	SCONJ
cana-950	232	2	x2	x2	PROPN
cana-950	232	3	has	have	VERB
cana-950	232	4	the	the	DET
cana-950	232	5	highest	high	ADJ
cana-950	232	6	degree	degree	NOUN
cana-950	232	7	,	,	PUNCT
cana-950	232	8	it	it	PRON
cana-950	232	9	can	can	AUX
cana-950	232	10	safeguard	safeguard	VERB
cana-950	232	11	all	all	DET
cana-950	232	12	the	the	DET
cana-950	232	13	incident	incident	NOUN
cana-950	232	14	edges	edge	VERB
cana-950	232	15	y1	y1	NOUN
cana-950	232	16	,	,	PUNCT
cana-950	232	17	y2	y2	PROPN
cana-950	232	18	,	,	PUNCT
cana-950	232	19	y3	y3	PROPN
cana-950	232	20	,	,	PUNCT
cana-950	232	21	y4	y4	PROPN
cana-950	232	22	of	of	ADP
cana-950	232	23	x2	x2	PROPN
cana-950	232	24	and	and	CCONJ
cana-950	232	25	the	the	DET
cana-950	232	26	edges	edge	NOUN
cana-950	232	27	which	which	PRON
cana-950	232	28	are	be	AUX
cana-950	232	29	adjacent	adjacent	ADJ
cana-950	232	30	to	to	ADP
cana-950	232	31	that	that	DET
cana-950	232	32	incident	incident	NOUN
cana-950	232	33	edges	edge	VERB
cana-950	232	34	y5	y5	NOUN
cana-950	232	35	.	.	PUNCT
cana-950	233	1	so	so	ADV
cana-950	233	2	that	that	SCONJ
cana-950	233	3	,	,	PUNCT
cana-950	233	4	all	all	DET
cana-950	233	5	the	the	DET
cana-950	233	6	edges	edge	NOUN
cana-950	233	7	of	of	ADP
cana-950	233	8	the	the	DET
cana-950	233	9	graph	graph	NOUN
cana-950	233	10	are	be	AUX
cana-950	233	11	protected	protect	VERB
cana-950	233	12	.	.	PUNCT
cana-950	234	1	hence	hence	ADV
cana-950	234	2	the	the	DET
cana-950	234	3	secure	secure	ADJ
cana-950	234	4	vertex	vertex	NOUN
cana-950	234	5	edge	edge	NOUN
cana-950	234	6	domination	domination	NOUN
cana-950	234	7	number	number	NOUN
cana-950	234	8	of	of	ADP
cana-950	234	9	the	the	DET
cana-950	234	10	cricket	cricket	NOUN
cana-950	234	11	graph	graph	NOUN
cana-950	234	12	is	be	AUX
cana-950	234	13	one	one	NUM
cana-950	234	14	,	,	PUNCT
cana-950	234	15	i.e.	i.e.	X
cana-950	234	16	,	,	PUNCT
cana-950	234	17	(	(	PUNCT
cana-950	234	18	)	)	PUNCT
cana-950	234	19	1sve	1sve	NUM
cana-950	234	20	cg	cg	NOUN
cana-950	235	1	=	=	PUNCT
cana-950	235	2	.	.	PUNCT
cana-950	236	1	4	4	X
cana-950	236	2	.	.	X
cana-950	236	3	conclusion	conclusion	NOUN
cana-950	236	4	in	in	ADP
cana-950	236	5	graph	graph	NOUN
cana-950	236	6	theory	theory	NOUN
cana-950	236	7	,	,	PUNCT
cana-950	236	8	the	the	DET
cana-950	236	9	idea	idea	NOUN
cana-950	236	10	of	of	ADP
cana-950	236	11	dominance	dominance	NOUN
cana-950	236	12	states	state	VERB
cana-950	236	13	that	that	SCONJ
cana-950	236	14	a	a	DET
cana-950	236	15	group	group	NOUN
cana-950	236	16	of	of	ADP
cana-950	236	17	vertices	vertex	NOUN
cana-950	236	18	s	s	PART
cana-950	236	19	dominates	dominate	VERB
cana-950	236	20	a	a	DET
cana-950	236	21	graph	graph	NOUN
cana-950	236	22	g	g	NOUN
cana-950	236	23	if	if	SCONJ
cana-950	236	24	every	every	DET
cana-950	236	25	vertex	vertex	NOUN
cana-950	236	26	in	in	ADP
cana-950	236	27	the	the	DET
cana-950	236	28	graph	graph	NOUN
cana-950	236	29	is	be	AUX
cana-950	236	30	either	either	CCONJ
cana-950	236	31	a	a	DET
cana-950	236	32	member	member	NOUN
cana-950	236	33	of	of	ADP
cana-950	236	34	s	s	NOUN
cana-950	236	35	or	or	CCONJ
cana-950	236	36	adjacent	adjacent	ADJ
cana-950	236	37	to	to	ADP
cana-950	236	38	a	a	DET
cana-950	236	39	vertex	vertex	NOUN
cana-950	236	40	in	in	ADP
cana-950	236	41	s.	s.	PROPN
cana-950	236	42	the	the	DET
cana-950	236	43	dominance	dominance	NOUN
cana-950	236	44	number	number	NOUN
cana-950	236	45	of	of	ADP
cana-950	236	46	g	g	PROPN
cana-950	236	47	is	be	AUX
cana-950	236	48	determined	determine	VERB
cana-950	236	49	by	by	ADP
cana-950	236	50	the	the	DET
cana-950	236	51	size	size	NOUN
cana-950	236	52	of	of	ADP
cana-950	236	53	the	the	DET
cana-950	236	54	smallest	small	ADJ
cana-950	236	55	dominating	dominating	NOUN
cana-950	236	56	set	set	NOUN
cana-950	236	57	.	.	PUNCT
cana-950	237	1	this	this	PRON
cana-950	237	2	led	lead	VERB
cana-950	237	3	to	to	ADP
cana-950	237	4	the	the	DET
cana-950	237	5	introduction	introduction	NOUN
cana-950	237	6	of	of	ADP
cana-950	237	7	a	a	DET
cana-950	237	8	new	new	ADJ
cana-950	237	9	dominance	dominance	NOUN
cana-950	237	10	parameter	parameter	NOUN
cana-950	237	11	"	"	PUNCT
cana-950	237	12	secure	secure	ADJ
cana-950	237	13	vertex	vertex	NOUN
cana-950	237	14	edge	edge	NOUN
cana-950	237	15	domination	domination	NOUN
cana-950	237	16	"	"	PUNCT
cana-950	237	17	before	before	ADV
cana-950	237	18	.	.	PUNCT
cana-950	238	1	these	these	DET
cana-950	238	2	pervasive	pervasive	ADJ
cana-950	238	3	concepts	concept	NOUN
cana-950	238	4	may	may	AUX
cana-950	238	5	be	be	AUX
cana-950	238	6	used	use	VERB
cana-950	238	7	to	to	ADP
cana-950	238	8	numerous	numerous	ADJ
cana-950	238	9	industries	industry	NOUN
cana-950	238	10	,	,	PUNCT
cana-950	238	11	such	such	ADJ
cana-950	238	12	as	as	ADP
cana-950	238	13	radio	radio	NOUN
cana-950	238	14	programming	programming	NOUN
cana-950	238	15	,	,	PUNCT
cana-950	238	16	computer	computer	NOUN
cana-950	238	17	communication	communication	NOUN
cana-950	238	18	networks	network	NOUN
cana-950	238	19	,	,	PUNCT
cana-950	238	20	school	school	NOUN
cana-950	238	21	bus	bus	NOUN
cana-950	238	22	routing	routing	NOUN
cana-950	238	23	,	,	PUNCT
cana-950	238	24	social	social	ADJ
cana-950	238	25	networks	network	NOUN
cana-950	238	26	,	,	PUNCT
cana-950	238	27	and	and	CCONJ
cana-950	238	28	interconnection	interconnection	NOUN
cana-950	238	29	systems	system	NOUN
cana-950	238	30	.	.	PUNCT
cana-950	239	1	this	this	DET
cana-950	239	2	paper	paper	NOUN
cana-950	239	3	's	's	PART
cana-950	239	4	significant	significant	ADJ
cana-950	239	5	contribution	contribution	NOUN
cana-950	239	6	is	be	AUX
cana-950	239	7	its	its	PRON
cana-950	239	8	investigation	investigation	NOUN
cana-950	239	9	of	of	ADP
cana-950	239	10	the	the	DET
cana-950	239	11	secure	secure	ADJ
cana-950	239	12	vertex	vertex	NOUN
cana-950	239	13	edge	edge	NOUN
cana-950	239	14	dominance	dominance	NOUN
cana-950	239	15	number	number	NOUN
cana-950	239	16	of	of	ADP
cana-950	239	17	a	a	DET
cana-950	239	18	few	few	ADJ
cana-950	239	19	designated	designate	VERB
cana-950	239	20	specific	specific	ADJ
cana-950	239	21	graphs	graph	NOUN
cana-950	239	22	,	,	PUNCT
cana-950	239	23	including	include	VERB
cana-950	239	24	bull	bull	NOUN
cana-950	239	25	graph	graph	NOUN
cana-950	239	26	,	,	PUNCT
cana-950	239	27	butterfly	butterfly	NOUN
cana-950	239	28	graph	graph	NOUN
cana-950	239	29	,	,	PUNCT
cana-950	239	30	diamond	diamond	NOUN
cana-950	239	31	graph	graph	NOUN
cana-950	239	32	,	,	PUNCT
cana-950	239	33	durer	durer	PROPN
cana-950	239	34	graph	graph	NOUN
cana-950	239	35	,	,	PUNCT
cana-950	239	36	franklin	franklin	PROPN
cana-950	239	37	graph	graph	NOUN
cana-950	239	38	,	,	PUNCT
cana-950	239	39	golomb	golomb	NOUN
cana-950	239	40	graph	graph	NOUN
cana-950	239	41	,	,	PUNCT
cana-950	239	42	moser	moser	PROPN
cana-950	239	43	spindle	spindle	PROPN
cana-950	239	44	graph	graph	NOUN
cana-950	239	45	,	,	PUNCT
cana-950	239	46	herschel	herschel	PROPN
cana-950	239	47	graph	graph	NOUN
cana-950	239	48	,	,	PUNCT
cana-950	239	49	petersen	petersen	NOUN
cana-950	239	50	graph	graph	NOUN
cana-950	239	51	,	,	PUNCT
cana-950	239	52	fish	fish	NOUN
cana-950	239	53	graph	graph	NOUN
cana-950	239	54	,	,	PUNCT
cana-950	239	55	wagner	wagner	NOUN
cana-950	239	56	graph	graph	NOUN
cana-950	239	57	,	,	PUNCT
cana-950	239	58	heawood	heawood	NOUN
cana-950	239	59	graph	graph	NOUN
cana-950	239	60	,	,	PUNCT
cana-950	239	61	pappus	pappus	PROPN
cana-950	239	62	graph	graph	NOUN
cana-950	239	63	,	,	PUNCT
cana-950	239	64	house	house	NOUN
cana-950	239	65	graph	graph	NOUN
cana-950	239	66	and	and	CCONJ
cana-950	239	67	cricket	cricket	NOUN
cana-950	239	68	graph	graph	NOUN
cana-950	239	69	.	.	PUNCT
cana-950	240	1	references	reference	NOUN
cana-950	240	2	[	[	X
cana-950	240	3	1	1	NUM
cana-950	240	4	]	]	PUNCT
cana-950	240	5	d.	d.	NOUN
cana-950	240	6	guichard	guichard	PROPN
cana-950	240	7	,	,	PUNCT
cana-950	240	8	“	"	PUNCT
cana-950	240	9	an	an	DET
cana-950	240	10	introduction	introduction	NOUN
cana-950	240	11	to	to	ADP
cana-950	240	12	combinatorics	combinatoric	NOUN
cana-950	240	13	,	,	PUNCT
cana-950	240	14	”	"	PUNCT
cana-950	240	15	choice	choice	NOUN
cana-950	240	16	rev	rev	PROPN
cana-950	240	17	.	.	PROPN
cana-950	241	1	online	online	PROPN
cana-950	241	2	,	,	PUNCT
cana-950	241	3	vol	vol	NOUN
cana-950	241	4	.	.	PUNCT
cana-950	242	1	29,no	29,no	PROPN
cana-950	242	2	.	.	PROPN
cana-950	242	3	06	06	NUM
cana-950	242	4	,	,	PUNCT
cana-950	242	5	pp	pp	ADJ
cana-950	242	6	.	.	PUNCT
cana-950	243	1	29	29	NUM
cana-950	243	2	-	-	SYM
cana-950	243	3	3354	3354	NUM
cana-950	243	4	-	-	SYM
cana-950	243	5	29–3354	29–3354	NUM
cana-950	243	6	,	,	PUNCT
cana-950	243	7	1992	1992	NUM
cana-950	243	8	,	,	PUNCT
cana-950	243	9	doi	doi	NOUN
cana-950	243	10	:	:	PUNCT
cana-950	243	11	10.5860	10.5860	NUM
cana-950	243	12	/	/	SYM
cana-950	243	13	choice.29	choice.29	NOUN
cana-950	243	14	-	-	PUNCT
cana-950	243	15	3354	3354	NUM
cana-950	243	16	.	.	PUNCT
cana-950	244	1	[	[	X
cana-950	244	2	2	2	X
cana-950	244	3	]	]	PUNCT
cana-950	244	4	p.	p.	NOUN
cana-950	244	5	a.	a.	NOUN
cana-950	244	6	burchett	burchett	PROPN
cana-950	244	7	,	,	PUNCT
cana-950	244	8	“	"	PUNCT
cana-950	244	9	digital	digital	ADJ
cana-950	244	10	commons	common	NOUN
cana-950	244	11	@	@	ADP
cana-950	244	12	east	east	PROPN
cana-950	244	13	tennessee	tennessee	PROPN
cana-950	244	14	state	state	PROPN
cana-950	244	15	university	university	PROPN
cana-950	244	16	paired	pair	VERB
cana-950	244	17	and	and	CCONJ
cana-950	244	18	total	total	ADJ
cana-950	244	19	domination	domination	NOUN
cana-950	244	20	on	on	ADP
cana-950	244	21	the	the	DET
cana-950	244	22	queen	queen	NOUN
cana-950	244	23	’	'	PUNCT
cana-950	244	24	s	s	PART
cana-950	244	25	graph	graph	NOUN
cana-950	244	26	.	.	PUNCT
cana-950	245	1	,	,	PUNCT
cana-950	245	2	”	"	PUNCT
cana-950	245	3	2005	2005	NUM
cana-950	245	4	.	.	PUNCT
cana-950	246	1	[	[	X
cana-950	246	2	3	3	X
cana-950	246	3	]	]	X
cana-950	246	4	w.	w.	PROPN
cana-950	246	5	w.	w.	PROPN
cana-950	246	6	rouse	rouse	PROPN
cana-950	246	7	ball	ball	PROPN
cana-950	246	8	,	,	PUNCT
cana-950	246	9	mathematical	mathematical	ADJ
cana-950	246	10	recreation	recreation	NOUN
cana-950	246	11	and	and	CCONJ
cana-950	246	12	problems	problem	NOUN
cana-950	246	13	of	of	ADP
cana-950	246	14	past	past	NOUN
cana-950	246	15	and	and	CCONJ
cana-950	246	16	present	present	ADJ
cana-950	246	17	times,1892	times,1892	NOUN
cana-950	246	18	.	.	PUNCT
cana-950	247	1	[	[	X
cana-950	247	2	4	4	NUM
cana-950	247	3	]	]	X
cana-950	247	4	c.	c.	PROPN
cana-950	247	5	berge	berge	PROPN
cana-950	247	6	,	,	PUNCT
cana-950	247	7	theory	theory	NOUN
cana-950	247	8	of	of	ADP
cana-950	247	9	graphs	graph	NOUN
cana-950	247	10	and	and	CCONJ
cana-950	247	11	its	its	PRON
cana-950	247	12	applications	application	NOUN
cana-950	247	13	.	.	PUNCT
cana-950	248	1	methuen	methuen	PROPN
cana-950	248	2	,	,	PUNCT
cana-950	248	3	london	london	PROPN
cana-950	248	4	,	,	PUNCT
cana-950	248	5	1962	1962	NUM
cana-950	248	6	.	.	PUNCT
cana-950	249	1	[	[	X
cana-950	249	2	5	5	NUM
cana-950	249	3	]	]	X
cana-950	249	4	o.	o.	ADJ
cana-950	249	5	ore	ore	PROPN
cana-950	249	6	,	,	PUNCT
cana-950	249	7	theory	theory	NOUN
cana-950	249	8	of	of	ADP
cana-950	249	9	graphs	graph	NOUN
cana-950	249	10	.	.	PUNCT
cana-950	250	1	amer	amer	PROPN
cana-950	250	2	.	.	PUNCT
cana-950	250	3	math	math	PROPN
cana-950	250	4	.	.	PUNCT
cana-950	251	1	soc	soc	PROPN
cana-950	251	2	.	.	PUNCT
cana-950	252	1	colloq	colloq	PROPN
cana-950	252	2	.	.	PUNCT
cana-950	253	1	publ	publ	PROPN
cana-950	253	2	.	.	PUNCT
cana-950	253	3	,	,	PUNCT
cana-950	253	4	38	38	NUM
cana-950	253	5	(	(	PUNCT
cana-950	253	6	amer	amer	PROPN
cana-950	253	7	.	.	PROPN
cana-950	253	8	math	math	PROPN
cana-950	253	9	.	.	PUNCT
cana-950	254	1	soc	soc	PROPN
cana-950	254	2	.	.	PUNCT
cana-950	254	3	,	,	PUNCT
cana-950	254	4	providenceri	providenceri	NOUN
cana-950	254	5	)	)	PUNCT
cana-950	254	6	,	,	PUNCT
cana-950	254	7	1962	1962	NUM
cana-950	254	8	.	.	PUNCT
cana-950	255	1	[	[	X
cana-950	255	2	6	6	NUM
cana-950	255	3	]	]	PUNCT
cana-950	255	4	e.	e.	PROPN
cana-950	255	5	j.	j.	PROPN
cana-950	255	6	cockayne	cockayne	PROPN
cana-950	255	7	and	and	CCONJ
cana-950	255	8	s.	s.	PROPN
cana-950	255	9	t.	t.	PROPN
cana-950	255	10	hedetniemi	hedetniemi	PROPN
cana-950	255	11	,	,	PUNCT
cana-950	255	12	towards	towards	ADP
cana-950	255	13	a	a	DET
cana-950	255	14	theory	theory	NOUN
cana-950	255	15	of	of	ADP
cana-950	255	16	domination	domination	NOUN
cana-950	255	17	in	in	ADP
cana-950	255	18	graphs	graph	NOUN
cana-950	255	19	.	.	PUNCT
cana-950	256	1	networks,7:247	networks,7:247	NUM
cana-950	256	2	-	-	SYM
cana-950	256	3	261	261	NUM
cana-950	256	4	,	,	PUNCT
cana-950	256	5	1977.e	1977.e	PROPN
cana-950	256	6	.	.	PUNCT
cana-950	256	7	j.	j.	PROPN
cana-950	257	1	[	[	X
cana-950	257	2	7	7	NUM
cana-950	257	3	]	]	X
cana-950	257	4	e.j	e.j	PROPN
cana-950	257	5	.	.	PROPN
cana-950	257	6	cockayne	cockayne	NOUN
cana-950	257	7	,	,	PUNCT
cana-950	257	8	o.	o.	PROPN
cana-950	257	9	favaron	favaron	PROPN
cana-950	257	10	and	and	CCONJ
cana-950	257	11	c.	c.	PROPN
cana-950	257	12	m.	m.	PROPN
cana-950	257	13	mynhardt	mynhardt	ADJ
cana-950	257	14	,	,	PUNCT
cana-950	257	15	secure	secure	ADJ
cana-950	257	16	domination	domination	NOUN
cana-950	257	17	and	and	CCONJ
cana-950	257	18	weak	weak	ADJ
cana-950	257	19	roman	roman	ADJ
cana-950	257	20	domination	domination	NOUN
cana-950	257	21	and	and	CCONJ
cana-950	257	22	forbidden	forbid	VERB
cana-950	257	23	sub	sub	NOUN
cana-950	257	24	graphs	graph	NOUN
cana-950	257	25	,	,	PUNCT
cana-950	257	26	bull	bull	NOUN
cana-950	257	27	.	.	PUNCT
cana-950	258	1	inst.combin	inst.combin	PROPN
cana-950	258	2	.	.	PROPN
cana-950	258	3	appl	appl	PROPN
cana-950	258	4	.	.	PROPN
cana-950	258	5	,	,	PUNCT
cana-950	258	6	39(2003	39(2003	NOUN
cana-950	258	7	)	)	PUNCT
cana-950	258	8	,	,	PUNCT
cana-950	258	9	87	87	NUM
cana-950	258	10	-100	-100	NOUN
cana-950	258	11	.	.	PUNCT
cana-950	259	1	[	[	X
cana-950	259	2	8	8	NUM
cana-950	259	3	]	]	X
cana-950	259	4	r.	r.	PROPN
cana-950	259	5	brigham	brigham	PROPN
cana-950	259	6	,	,	PUNCT
cana-950	259	7	p.	p.	PROPN
cana-950	259	8	chinn	chinn	PROPN
cana-950	259	9	,	,	PUNCT
cana-950	259	10	and	and	CCONJ
cana-950	259	11	r.	r.	PROPN
cana-950	259	12	dutton	dutton	PROPN
cana-950	259	13	,	,	PUNCT
cana-950	259	14	“	"	PUNCT
cana-950	259	15	vertex	vertex	X
cana-950	259	16	domination‐critical	domination‐critical	ADJ
cana-950	259	17	graphs,”networks	graphs,”network	NOUN
cana-950	259	18	,	,	PUNCT
cana-950	259	19	vol	vol	NOUN
cana-950	259	20	.	.	PROPN
cana-950	259	21	18	18	NUM
cana-950	259	22	,	,	PUNCT
cana-950	259	23	pp	pp	ADJ
cana-950	259	24	.	.	PUNCT
cana-950	260	1	173–179	173–179	NUM
cana-950	260	2	,	,	PUNCT
cana-950	260	3	oct	oct	PROPN
cana-950	260	4	.	.	PROPN
cana-950	260	5	2006	2006	NUM
cana-950	260	6	.	.	PUNCT
cana-950	261	1	[	[	X
cana-950	261	2	9	9	X
cana-950	261	3	]	]	PUNCT
cana-950	261	4	j.	j.	PROPN
cana-950	261	5	r.	r.	PROPN
cana-950	261	6	lewis	lewis	PROPN
cana-950	261	7	,	,	PUNCT
cana-950	261	8	vertex	vertex	NOUN
cana-950	261	9	-	-	PUNCT
cana-950	261	10	edge	edge	NOUN
cana-950	261	11	and	and	CCONJ
cana-950	261	12	edge	edge	NOUN
cana-950	261	13	-	-	PUNCT
cana-950	261	14	vertex	vertex	NOUN
cana-950	261	15	domination	domination	NOUN
cana-950	261	16	in	in	ADP
cana-950	261	17	graphs	graph	NOUN
cana-950	261	18	,	,	PUNCT
cana-950	261	19	ph.d	ph.d	PROPN
cana-950	261	20	.	.	PUNCT
cana-950	262	1	thesis	thesis	NOUN
cana-950	262	2	(	(	PUNCT
cana-950	262	3	clemson	clemson	NOUN
cana-950	262	4	university	university	PROPN
cana-950	262	5	,	,	PUNCT
cana-950	262	6	clemson	clemson	NOUN
cana-950	262	7	,	,	PUNCT
cana-950	262	8	2007	2007	NUM
cana-950	262	9	)	)	PUNCT
cana-950	262	10	.	.	PUNCT
cana-950	263	1	[	[	X
cana-950	263	2	10	10	NUM
cana-950	263	3	]	]	X
cana-950	263	4	j.a	j.a	PROPN
cana-950	263	5	.	.	PROPN
cana-950	263	6	bondy	bondy	PROPN
cana-950	263	7	and	and	CCONJ
cana-950	263	8	u.s.r	u.s.r	ADJ
cana-950	263	9	.	.	PROPN
cana-950	263	10	murty	murty	PROPN
cana-950	263	11	,	,	PUNCT
cana-950	263	12	graph	graph	NOUN
cana-950	263	13	theory	theory	NOUN
cana-950	263	14	with	with	ADP
cana-950	263	15	applications	application	NOUN
cana-950	263	16	.	.	PUNCT
cana-950	264	1	new	new	PROPN
cana-950	264	2	york	york	PROPN
cana-950	264	3	(	(	PUNCT
cana-950	264	4	1976	1976	NUM
cana-950	264	5	)	)	PUNCT
cana-950	264	6	.	.	PUNCT
cana-950	265	1	[	[	X
cana-950	265	2	11	11	NUM
cana-950	265	3	]	]	PUNCT
cana-950	265	4	s.arumugam	s.arumugam	NOUN
cana-950	265	5	et	et	PROPN
cana-950	265	6	al	al	PROPN
cana-950	265	7	.	.	PROPN
cana-950	265	8	,	,	PUNCT
cana-950	265	9	co	co	ADJ
cana-950	265	10	-	-	ADJ
cana-950	265	11	secure	secure	ADJ
cana-950	265	12	and	and	CCONJ
cana-950	265	13	secure	secure	ADJ
cana-950	265	14	dominations	domination	NOUN
cana-950	265	15	in	in	ADP
cana-950	265	16	graphs	graph	NOUN
cana-950	265	17	,	,	PUNCT
cana-950	265	18	utilitas	utilitas	PROPN
cana-950	265	19	mathematica	mathematica	PROPN
cana-950	265	20	94	94	NUM
cana-950	265	21	,	,	PUNCT
cana-950	265	22	(	(	PUNCT
cana-950	265	23	2014	2014	NUM
cana-950	265	24	)	)	PUNCT
cana-950	265	25	,	,	PUNCT
cana-950	265	26	pp.167	pp.167	NOUN
cana-950	265	27	-	-	X
cana-950	265	28	182	182	NUM
cana-950	265	29	.	.	PUNCT
cana-950	266	1	[	[	X
cana-950	266	2	12	12	NUM
cana-950	266	3	]	]	X
cana-950	266	4	c.	c.	PROPN
cana-950	266	5	ruby	ruby	PROPN
cana-950	266	6	sharmila	sharmila	PROPN
cana-950	266	7	and	and	CCONJ
cana-950	266	8	s.	s.	PROPN
cana-950	266	9	meenakshi,“secure	meenakshi,“secure	VERB
cana-950	266	10	vertex	vertex	NOUN
cana-950	266	11	edge	edge	NOUN
cana-950	266	12	domination	domination	NOUN
cana-950	266	13	of	of	ADP
cana-950	266	14	graphs	graph	NOUN
cana-950	266	15	”	"	PUNCT
cana-950	266	16	,	,	PUNCT
cana-950	266	17	the	the	DET
cana-950	266	18	journal	journal	NOUN
cana-950	266	19	of	of	ADP
cana-950	266	20	balkan	balkan	PROPN
cana-950	266	21	tribological	tribological	ADJ
cana-950	266	22	association	association	NOUN
cana-950	266	23	vol.30	vol.30	NOUN
cana-950	266	24	(	(	PUNCT
cana-950	266	25	2024	2024	NUM
cana-950	266	26	)	)	PUNCT
cana-950	266	27	,	,	PUNCT
cana-950	266	28	issue	issue	NOUN
cana-950	266	29	–	–	PUNCT
cana-950	266	30	1	1	NUM
cana-950	266	31	,	,	PUNCT
cana-950	266	32	21	21	NUM
cana-950	266	33	-	-	SYM
cana-950	266	34	30	30	NUM
cana-950	266	35	.	.	PUNCT
cana-950	267	1	[	[	X
cana-950	267	2	13	13	NUM
cana-950	267	3	]	]	X
cana-950	267	4	latha	latha	PROPN
cana-950	267	5	s	s	PROPN
cana-950	267	6	,	,	PUNCT
cana-950	267	7	sandhya	sandhya	PROPN
cana-950	267	8	s	s	PROPN
cana-950	267	9	s	s	PROPN
cana-950	267	10	,	,	PUNCT
cana-950	267	11	heinz	heinz	ADJ
cana-950	267	12	quarter	quarter	NOUN
cana-950	267	13	mean	mean	VERB
cana-950	267	14	labeling	labeling	NOUN
cana-950	267	15	of	of	ADP
cana-950	267	16	some	some	DET
cana-950	267	17	named	name	VERB
cana-950	267	18	graphs	graph	NOUN
cana-950	267	19	,	,	PUNCT
cana-950	267	20	jetir	jetir	VERB
cana-950	267	21	april	april	PROPN
cana-950	267	22	2024	2024	NUM
cana-950	267	23	,	,	PUNCT
cana-950	267	24	volume	volume	NOUN
cana-950	267	25	11	11	NUM
cana-950	267	26	,	,	PUNCT
cana-950	267	27	issue	issue	NOUN
cana-950	267	28	4	4	NUM
cana-950	267	29	,	,	PUNCT
cana-950	267	30	i1	i1	PROPN
cana-950	267	31	–	–	PUNCT
cana-950	267	32	i5	i5	ADJ
cana-950	267	33	.	.	PUNCT
cana-950	268	1	[	[	X
cana-950	268	2	14	14	NUM
cana-950	268	3	]	]	X
cana-950	268	4	g.	g.	PROPN
cana-950	268	5	mahadevan	mahadevan	PROPN
cana-950	268	6	,	,	PUNCT
cana-950	268	7	et	et	PROPN
cana-950	268	8	al	al	PROPN
cana-950	268	9	,	,	PUNCT
cana-950	268	10	neighborhood	neighborhood	NOUN
cana-950	268	11	triple	triple	ADV
cana-950	268	12	connected	connect	VERB
cana-950	268	13	domination	domination	NOUN
cana-950	268	14	number	number	NOUN
cana-950	268	15	of	of	ADP
cana-950	268	16	a	a	DET
cana-950	268	17	graph	graph	NOUN
cana-950	268	18	,	,	PUNCT
cana-950	268	19	international	international	ADJ
cana-950	268	20	journal	journal	NOUN
cana-950	268	21	of	of	ADP
cana-950	268	22	computational	computational	ADJ
cana-950	268	23	engineering	engineering	NOUN
cana-950	268	24	research	research	NOUN
cana-950	268	25	,	,	PUNCT
cana-950	268	26	vol04	vol04	PROPN
cana-950	268	27	,	,	PUNCT
cana-950	268	28	issue	issue	NOUN
cana-950	268	29	-3	-3	INTJ
cana-950	268	30	,	,	PUNCT
cana-950	268	31	38	38	NUM
cana-950	268	32	–	–	SYM
cana-950	268	33	48	48	NUM
cana-950	268	34	.	.	PUNCT
cana-950	269	1	[	[	X
cana-950	269	2	15	15	NUM
cana-950	269	3	]	]	X
cana-950	269	4	m.	m.	NOUN
cana-950	269	5	pavithra	pavithra	PROPN
cana-950	269	6	and	and	CCONJ
cana-950	269	7	b.	b.	PROPN
cana-950	269	8	sharada	sharada	PROPN
cana-950	269	9	,	,	PUNCT
cana-950	269	10	miscellaneous	miscellaneous	ADJ
cana-950	269	11	results	result	NOUN
cana-950	269	12	on	on	ADP
cana-950	269	13	pendant	pendant	ADJ
cana-950	269	14	domination	domination	NOUN
cana-950	269	15	of	of	ADP
cana-950	269	16	graphs	graph	NOUN
cana-950	269	17	,	,	PUNCT
cana-950	269	18	advances	advance	NOUN
cana-950	269	19	and	and	CCONJ
cana-950	269	20	applications	application	NOUN
cana-950	269	21	in	in	ADP
cana-950	269	22	mathematical	mathematical	ADJ
cana-950	269	23	sciences	science	NOUN
cana-950	269	24	volume	volume	NOUN
cana-950	269	25	18	18	NUM
cana-950	269	26	,	,	PUNCT
cana-950	269	27	issue	issue	NOUN
cana-950	269	28	10	10	NUM
cana-950	269	29	,	,	PUNCT
cana-950	269	30	august	august	PROPN
cana-950	269	31	2019	2019	NUM
cana-950	269	32	,	,	PUNCT
cana-950	269	33	pages	page	NOUN
cana-950	269	34	1027	1027	NUM
cana-950	269	35	-	-	SYM
cana-950	269	36	1038	1038	NUM
cana-950	269	37	.	.	PUNCT