id	sid	tid	token	lemma	pos
cana-2791	1	1	inverse	inverse	NOUN
cana-2791	1	2	independent	independent	ADJ
cana-2791	1	3	outer	outer	ADJ
cana-2791	1	4	connected	connected	ADJ
cana-2791	1	5	domination	domination	NOUN
cana-2791	1	6	number	number	NOUN
cana-2791	1	7	of	of	ADP
cana-2791	1	8	few	few	ADJ
cana-2791	1	9	classes	class	NOUN
cana-2791	1	10	of	of	ADP
cana-2791	1	11	graphs	graph	NOUN
cana-2791	1	12	g	g	PROPN
cana-2791	1	13	menon1	menon1	PROPN
cana-2791	1	14	,	,	PUNCT
cana-2791	1	15	mallikarjun	mallikarjun	PROPN
cana-2791	1	16	s	s	PART
cana-2791	1	17	biradar2	biradar2	NOUN
cana-2791	1	18	,	,	PUNCT
cana-2791	1	19	r	r	NOUN
cana-2791	1	20	r	r	NOUN
cana-2791	1	21	iyer3	iyer3	PROPN
cana-2791	1	22	,	,	PUNCT
cana-2791	1	23	and	and	CCONJ
cana-2791	1	24	k	k	PROPN
cana-2791	1	25	s	s	PROPN
cana-2791	1	26	sreeranjini4	sreeranjini4	PROPN
cana-2791	1	27	1,3,4	1,3,4	NUM
cana-2791	1	28	department	department	NOUN
cana-2791	1	29	of	of	ADP
cana-2791	1	30	mathematics	mathematic	NOUN
cana-2791	1	31	,	,	PUNCT
cana-2791	1	32	amrita	amrita	PROPN
cana-2791	1	33	school	school	PROPN
cana-2791	1	34	of	of	ADP
cana-2791	1	35	physical	physical	ADJ
cana-2791	1	36	sciences	sciences	PROPN
cana-2791	1	37	,	,	PUNCT
cana-2791	1	38	coimbatore	coimbatore	PROPN
cana-2791	1	39	,	,	PUNCT
cana-2791	1	40	amrita	amrita	PROPN
cana-2791	1	41	vishwa	vishwa	PROPN
cana-2791	1	42	vidyapeetham	vidyapeetham	PROPN
cana-2791	1	43	,	,	PUNCT
cana-2791	1	44	india	india	PROPN
cana-2791	1	45	.	.	PROPN
cana-2791	1	46	2	2	NUM
cana-2791	1	47	government	government	NOUN
cana-2791	1	48	first	first	ADJ
cana-2791	1	49	grade	grade	NOUN
cana-2791	1	50	college	college	NOUN
cana-2791	1	51	,	,	PUNCT
cana-2791	1	52	chittapur	chittapur	NOUN
cana-2791	1	53	,	,	PUNCT
cana-2791	1	54	karnataka	karnataka	PROPN
cana-2791	1	55	,	,	PUNCT
cana-2791	1	56	india	india	PROPN
cana-2791	1	57	.	.	PUNCT
cana-2791	2	1	1gopikamenon14009@gmail.com	1gopikamenon14009@gmail.com	NUM
cana-2791	2	2	,	,	PUNCT
cana-2791	2	3	2mallikarjunbiradar54@gmail.com	2mallikarjunbiradar54@gmail.com	NUM
cana-2791	2	4	,	,	PUNCT
cana-2791	2	5	3r	3r	NUM
cana-2791	2	6	radhaiyer@cb.amrita.edu	radhaiyer@cb.amrita.edu	NOUN
cana-2791	2	7	and	and	CCONJ
cana-2791	2	8	4ks	4ks	ADJ
cana-2791	2	9	sreeranjini@cb.amrita.edu	sreeranjini@cb.amrita.edu	PROPN
cana-2791	2	10	corresponding	correspond	VERB
cana-2791	2	11	author	author	NOUN
cana-2791	2	12	e	e	NOUN
cana-2791	2	13	-	-	NOUN
cana-2791	2	14	mail	mail	NOUN
cana-2791	2	15	:	:	PUNCT
cana-2791	3	1	mallikarjunbiradar54@gmail.com	mallikarjunbiradar54@gmail.com	X
cana-2791	3	2	abstract	abstract	ADJ
cana-2791	3	3	in	in	ADP
cana-2791	3	4	a	a	DET
cana-2791	3	5	graph	graph	NOUN
cana-2791	3	6	g	g	NOUN
cana-2791	3	7	=	=	SYM
cana-2791	3	8	(	(	PUNCT
cana-2791	3	9	v	v	NOUN
cana-2791	3	10	,	,	PUNCT
cana-2791	3	11	e	e	NOUN
cana-2791	3	12	)	)	PUNCT
cana-2791	3	13	,	,	PUNCT
cana-2791	3	14	a	a	DET
cana-2791	3	15	vertex	vertex	NOUN
cana-2791	3	16	set	set	NOUN
cana-2791	3	17	d	d	PROPN
cana-2791	3	18	⊆	⊆	PROPN
cana-2791	3	19	v	v	ADP
cana-2791	3	20	such	such	ADJ
cana-2791	3	21	that	that	PRON
cana-2791	3	22	for	for	ADP
cana-2791	3	23	every	every	DET
cana-2791	3	24	vertex	vertex	NOUN
cana-2791	3	25	v	v	ADP
cana-2791	3	26	∈/	∈/	PROPN
cana-2791	3	27	d	d	PROPN
cana-2791	3	28	the	the	DET
cana-2791	3	29	vertex	vertex	NOUN
cana-2791	3	30	v	v	NOUN
cana-2791	3	31	is	be	AUX
cana-2791	3	32	adjacent	adjacent	ADJ
cana-2791	3	33	to	to	PART
cana-2791	3	34	atleast	atleast	VERB
cana-2791	3	35	one	one	NUM
cana-2791	3	36	vertex	vertex	NOUN
cana-2791	3	37	in	in	ADP
cana-2791	3	38	d	d	NOUN
cana-2791	3	39	and	and	CCONJ
cana-2791	3	40	no	no	DET
cana-2791	3	41	vertex	vertex	NOUN
cana-2791	3	42	in	in	ADP
cana-2791	3	43	d	d	PROPN
cana-2791	3	44	is	be	AUX
cana-2791	3	45	adjacent	adjacent	ADJ
cana-2791	3	46	to	to	ADP
cana-2791	3	47	each	each	DET
cana-2791	3	48	other	other	ADJ
cana-2791	3	49	,	,	PUNCT
cana-2791	3	50	then	then	ADV
cana-2791	3	51	,	,	PUNCT
cana-2791	3	52	d	d	PROPN
cana-2791	3	53	is	be	AUX
cana-2791	3	54	the	the	DET
cana-2791	3	55	independent	independent	ADJ
cana-2791	3	56	dominating	dominating	NOUN
cana-2791	3	57	set.when	set.when	ADV
cana-2791	3	58	the	the	DET
cana-2791	3	59	vertex	vertex	NOUN
cana-2791	3	60	set	set	VERB
cana-2791	3	61	v	v	PROPN
cana-2791	3	62	d	d	PROPN
cana-2791	3	63	v	v	NOUN
cana-2791	3	64	con	con	PROPN
cana-2791	3	65	tains	tain	NOUN
cana-2791	3	66	a	a	DET
cana-2791	3	67	independent	independent	ADJ
cana-2791	3	68	dominating	dominating	NOUN
cana-2791	3	69	set	set	NOUN
cana-2791	3	70	,	,	PUNCT
cana-2791	3	71	say	say	VERB
cana-2791	3	72	d′	d′	NUM
cana-2791	3	73	,	,	PUNCT
cana-2791	3	74	then	then	ADV
cana-2791	3	75	d′	d′	PRON
cana-2791	3	76	is	be	AUX
cana-2791	3	77	called	call	VERB
cana-2791	3	78	the	the	DET
cana-2791	3	79	inverse	inverse	ADJ
cana-2791	3	80	independent	independent	ADJ
cana-2791	3	81	domiating	domiating	NOUN
cana-2791	3	82	set	set	NOUN
cana-2791	3	83	.	.	PUNCT
cana-2791	4	1	if	if	SCONJ
cana-2791	4	2	the	the	DET
cana-2791	4	3	subgraph	subgraph	NOUN
cana-2791	4	4	induced	induce	VERB
cana-2791	4	5	by	by	ADP
cana-2791	4	6	v	v	ADP
cana-2791	4	7	−	−	PROPN
cana-2791	4	8	d′	d′	PRON
cana-2791	4	9	is	be	AUX
cana-2791	4	10	connected	connect	VERB
cana-2791	4	11	then	then	ADV
cana-2791	4	12	d′	d′	PRON
cana-2791	4	13	is	be	AUX
cana-2791	4	14	called	call	VERB
cana-2791	4	15	the	the	DET
cana-2791	4	16	inverse	inverse	NOUN
cana-2791	4	17	independent	independent	ADJ
cana-2791	4	18	outer	outer	ADJ
cana-2791	4	19	connected	connected	ADJ
cana-2791	4	20	dominating	dominating	NOUN
cana-2791	4	21	set	set	NOUN
cana-2791	4	22	.	.	PUNCT
cana-2791	5	1	the	the	DET
cana-2791	5	2	minimum	minimum	ADJ
cana-2791	5	3	cardinality	cardinality	NOUN
cana-2791	5	4	of	of	ADP
cana-2791	5	5	such	such	ADJ
cana-2791	5	6	set	set	NOUN
cana-2791	5	7	of	of	ADP
cana-2791	5	8	vertices	vertex	NOUN
cana-2791	5	9	is	be	AUX
cana-2791	5	10	called	call	VERB
cana-2791	5	11	the	the	DET
cana-2791	5	12	inverse	inverse	NOUN
cana-2791	5	13	independent	independent	ADJ
cana-2791	5	14	outer	outer	ADJ
cana-2791	5	15	connected	connected	ADJ
cana-2791	5	16	domination	domination	NOUN
cana-2791	5	17	number	number	NOUN
cana-2791	5	18	denoted	denote	VERB
cana-2791	5	19	by	by	ADP
cana-2791	5	20	γ̃i	γ̃i	ADJ
cana-2791	5	21	−	−	PROPN
cana-2791	5	22	oc	oc	NOUN
cana-2791	5	23	(	(	PUNCT
cana-2791	5	24	g	g	NOUN
cana-2791	5	25	)	)	PUNCT
cana-2791	5	26	.	.	PUNCT
cana-2791	6	1	in	in	ADP
cana-2791	6	2	this	this	DET
cana-2791	6	3	paper	paper	NOUN
cana-2791	6	4	we	we	PRON
cana-2791	6	5	will	will	AUX
cana-2791	6	6	be	be	AUX
cana-2791	6	7	discussing	discuss	VERB
cana-2791	6	8	γ̃i	γ̃i	ADJ
cana-2791	6	9	−	−	NOUN
cana-2791	6	10	oc	oc	ADP
cana-2791	6	11	s(n	s(n	PROPN
cana-2791	6	12	,	,	PUNCT
cana-2791	6	13	k	k	NOUN
cana-2791	6	14	)	)	PUNCT
cana-2791	6	15	,	,	PUNCT
cana-2791	6	16	γ̃i	γ̃i	ADJ
cana-2791	6	17	−	−	ADP
cana-2791	6	18	oc	oc	X
cana-2791	6	19	s	s	PART
cana-2791	6	20	+	+	NOUN
cana-2791	6	21	(	(	PUNCT
cana-2791	6	22	n	n	X
cana-2791	6	23	,	,	PUNCT
cana-2791	6	24	k	k	NOUN
cana-2791	6	25	)	)	PUNCT
cana-2791	6	26	,	,	PUNCT
cana-2791	6	27	γ̃i	γ̃i	ADJ
cana-2791	6	28	−	−	ADP
cana-2791	6	29	oc	oc	X
cana-2791	6	30	s	s	PART
cana-2791	6	31	+	+	ADJ
cana-2791	6	32	+	+	ADJ
cana-2791	6	33	(	(	PUNCT
cana-2791	6	34	n	n	X
cana-2791	6	35	,	,	PUNCT
cana-2791	6	36	k	k	NOUN
cana-2791	6	37	)	)	PUNCT
cana-2791	6	38	,	,	PUNCT
cana-2791	6	39	γ̃i	γ̃i	ADJ
cana-2791	6	40	−	−	PROPN
cana-2791	6	41	oc	oc	NOUN
cana-2791	6	42	(	(	PUNCT
cana-2791	6	43	sn	sn	PROPN
cana-2791	6	44	)	)	PUNCT
cana-2791	6	45	,	,	PUNCT
cana-2791	6	46	γ̃i	γ̃i	ADJ
cana-2791	6	47	−	−	PROPN
cana-2791	6	48	oc	oc	NOUN
cana-2791	6	49	(	(	PUNCT
cana-2791	6	50	g1	g1	VERB
cana-2791	6	51	◦	◦	PROPN
cana-2791	6	52	g2	g2	PROPN
cana-2791	6	53	)	)	PUNCT
cana-2791	6	54	where	where	SCONJ
cana-2791	6	55	s(n	s(n	PROPN
cana-2791	6	56	,	,	PUNCT
cana-2791	6	57	k	k	NOUN
cana-2791	6	58	)	)	PUNCT
cana-2791	6	59	,	,	PUNCT
cana-2791	6	60	s+(n	s+(n	NOUN
cana-2791	6	61	,	,	PUNCT
cana-2791	6	62	k	k	NOUN
cana-2791	6	63	)	)	PUNCT
cana-2791	6	64	,	,	PUNCT
cana-2791	6	65	s++(n	s++(n	PROPN
cana-2791	6	66	,	,	PUNCT
cana-2791	6	67	k	k	NOUN
cana-2791	6	68	)	)	PUNCT
cana-2791	6	69	,	,	PUNCT
cana-2791	6	70	sn	sn	PROPN
cana-2791	6	71	are	be	AUX
cana-2791	6	72	sierpinski	sierpinski	ADJ
cana-2791	6	73	graph	graph	NOUN
cana-2791	6	74	,	,	PUNCT
cana-2791	6	75	extended	extend	VERB
cana-2791	6	76	sierpinski	sierpinski	ADJ
cana-2791	6	77	graphs	graph	NOUN
cana-2791	6	78	and	and	CCONJ
cana-2791	6	79	sierpinski	sierpinski	ADJ
cana-2791	6	80	gasket	gasket	NOUN
cana-2791	6	81	graph	graph	NOUN
cana-2791	6	82	respectively	respectively	ADV
cana-2791	6	83	and	and	CCONJ
cana-2791	6	84	g1	g1	PROPN
cana-2791	6	85	and	and	CCONJ
cana-2791	6	86	g2	g2	PROPN
cana-2791	6	87	are	be	AUX
cana-2791	6	88	two	two	NUM
cana-2791	6	89	standard	standard	ADJ
cana-2791	6	90	graphs	graph	NOUN
cana-2791	6	91	.	.	PUNCT
cana-2791	7	1	keywords	keyword	NOUN
cana-2791	7	2	inverse	inverse	VERB
cana-2791	7	3	independent	independent	ADJ
cana-2791	7	4	domination	domination	NOUN
cana-2791	7	5	,	,	PUNCT
cana-2791	7	6	outer	outer	ADJ
cana-2791	7	7	connected	connect	VERB
cana-2791	7	8	,	,	PUNCT
cana-2791	7	9	inverse	inverse	ADJ
cana-2791	7	10	independent	independent	ADJ
cana-2791	7	11	outer	outer	ADJ
cana-2791	7	12	connected	connected	ADJ
cana-2791	7	13	domination	domination	NOUN
cana-2791	7	14	number	number	NOUN
cana-2791	7	15	,	,	PUNCT
cana-2791	7	16	sierpinski	sierpinski	ADJ
cana-2791	7	17	graph	graph	NOUN
cana-2791	7	18	,	,	PUNCT
cana-2791	7	19	sierpinski	sierpinski	ADJ
cana-2791	7	20	-	-	PUNCT
cana-2791	7	21	like	like	ADJ
cana-2791	7	22	graphs	graph	NOUN
cana-2791	7	23	,	,	PUNCT
cana-2791	7	24	corona	corona	NOUN
cana-2791	7	25	of	of	ADP
cana-2791	7	26	graphs	graph	NOUN
cana-2791	7	27	1	1	NUM
cana-2791	7	28	introduction	introduction	NOUN
cana-2791	7	29	let	let	VERB
cana-2791	7	30	g	g	NOUN
cana-2791	7	31	=	=	SYM
cana-2791	7	32	(	(	PUNCT
cana-2791	7	33	v	v	NOUN
cana-2791	7	34	,	,	PUNCT
cana-2791	7	35	e	e	NOUN
cana-2791	7	36	)	)	PUNCT
cana-2791	7	37	be	be	AUX
cana-2791	7	38	a	a	DET
cana-2791	7	39	simple	simple	ADJ
cana-2791	7	40	,	,	PUNCT
cana-2791	7	41	finite	finite	ADJ
cana-2791	7	42	,	,	PUNCT
cana-2791	7	43	undirected	undirected	ADJ
cana-2791	7	44	graph	graph	NOUN
cana-2791	7	45	,	,	PUNCT
cana-2791	7	46	with	with	ADP
cana-2791	7	47	v	v	NOUN
cana-2791	7	48	(	(	PUNCT
cana-2791	7	49	g	g	NOUN
cana-2791	7	50	)	)	PUNCT
cana-2791	7	51	being	be	AUX
cana-2791	7	52	the	the	DET
cana-2791	7	53	vertex	vertex	NOUN
cana-2791	7	54	set	set	NOUN
cana-2791	7	55	and	and	CCONJ
cana-2791	7	56	e(g	e(g	PROPN
cana-2791	7	57	)	)	PUNCT
cana-2791	7	58	being	be	AUX
cana-2791	7	59	the	the	DET
cana-2791	7	60	edge	edge	NOUN
cana-2791	7	61	set	set	NOUN
cana-2791	7	62	of	of	ADP
cana-2791	7	63	the	the	DET
cana-2791	7	64	graph	graph	NOUN
cana-2791	7	65	.	.	PUNCT
cana-2791	8	1	we	we	PRON
cana-2791	8	2	we	we	PRON
cana-2791	8	3	will	will	AUX
cana-2791	8	4	be	be	AUX
cana-2791	8	5	using	use	VERB
cana-2791	8	6	v	v	NOUN
cana-2791	8	7	instead	instead	ADV
cana-2791	8	8	of	of	ADP
cana-2791	8	9	v	v	NOUN
cana-2791	8	10	(	(	PUNCT
cana-2791	8	11	g	g	NOUN
cana-2791	8	12	)	)	PUNCT
cana-2791	8	13	and	and	CCONJ
cana-2791	8	14	e	e	NOUN
cana-2791	8	15	instead	instead	ADV
cana-2791	8	16	of	of	ADP
cana-2791	8	17	e(g	e(g	PROPN
cana-2791	8	18	)	)	PUNCT
cana-2791	8	19	for	for	ADP
cana-2791	8	20	simplicity	simplicity	NOUN
cana-2791	8	21	.	.	PUNCT
cana-2791	9	1	as	as	SCONJ
cana-2791	9	2	the	the	DET
cana-2791	9	3	independent	independent	ADJ
cana-2791	9	4	inverse	inverse	NOUN
cana-2791	9	5	outer	outer	ADJ
cana-2791	9	6	connected	connect	VERB
cana-2791	9	7	domination	domination	NOUN
cana-2791	9	8	number	number	NOUN
cana-2791	9	9	does	do	AUX
cana-2791	9	10	not	not	PART
cana-2791	9	11	require	require	VERB
cana-2791	9	12	a	a	DET
cana-2791	9	13	graph	graph	NOUN
cana-2791	9	14	with	with	ADP
cana-2791	9	15	self	self	NOUN
cana-2791	9	16	-	-	PUNCT
cana-2791	9	17	loops	loop	NOUN
cana-2791	9	18	and	and	CCONJ
cana-2791	9	19	that	that	SCONJ
cana-2791	9	20	with	with	ADP
cana-2791	9	21	multiple	multiple	ADJ
cana-2791	9	22	edges	edge	NOUN
cana-2791	9	23	,	,	PUNCT
cana-2791	9	24	we	we	PRON
cana-2791	9	25	have	have	AUX
cana-2791	9	26	chosen	choose	VERB
cana-2791	9	27	only	only	ADV
cana-2791	9	28	the	the	DET
cana-2791	9	29	simple	simple	ADJ
cana-2791	9	30	graphs	graph	NOUN
cana-2791	9	31	.	.	PUNCT
cana-2791	10	1	for	for	ADP
cana-2791	10	2	any	any	DET
cana-2791	10	3	vertex	vertex	NOUN
cana-2791	10	4	v	v	ADP
cana-2791	10	5	∈	∈	PROPN
cana-2791	10	6	v	v	NOUN
cana-2791	10	7	and	and	CCONJ
cana-2791	10	8	set	set	VERB
cana-2791	10	9	s	s	PROPN
cana-2791	10	10	⊆	⊆	NUM
cana-2791	10	11	v	v	NOUN
cana-2791	10	12	,	,	PUNCT
cana-2791	10	13	t	t	PROPN
cana-2791	10	14	h	h	NOUN
cana-2791	10	15	e	e	NOUN
cana-2791	10	16	open	open	VERB
cana-2791	10	17	neighborhood	neighborhood	NOUN
cana-2791	10	18	of	of	ADP
cana-2791	10	19	v	v	NOUN
cana-2791	10	20	in	in	ADP
cana-2791	10	21	s	s	PROPN
cana-2791	10	22	is	be	AUX
cana-2791	10	23	the	the	DET
cana-2791	10	24	set	set	VERB
cana-2791	10	25	ns(v	ns(v	NOUN
cana-2791	10	26	)	)	PUNCT
cana-2791	10	27	=	=	SYM
cana-2791	10	28	u	u	NOUN
cana-2791	10	29	∈	∈	PROPN
cana-2791	10	30	s|uv	s|uv	PROPN
cana-2791	10	31	∈	∈	PROPN
cana-2791	10	32	e.	e.	PROPN
cana-2791	11	1	the	the	DET
cana-2791	11	2	closed	close	VERB
cana-2791	11	3	neighbourhood	neighbourhood	NOUN
cana-2791	11	4	of	of	ADP
cana-2791	11	5	v	v	NOUN
cana-2791	11	6	in	in	ADP
cana-2791	11	7	s	s	PROPN
cana-2791	11	8	is	be	AUX
cana-2791	11	9	ns[v	ns[v	NOUN
cana-2791	11	10	]	]	PUNCT
cana-2791	11	11	ns(v	ns(v	NOUN
cana-2791	11	12	)	)	PUNCT
cana-2791	11	13	∪	∪	NOUN
cana-2791	11	14	v.	v.	ADP
cana-2791	11	15	if	if	SCONJ
cana-2791	11	16	s	s	PART
cana-2791	11	17	=	=	SYM
cana-2791	11	18	v	v	NOUN
cana-2791	11	19	,	,	PUNCT
cana-2791	11	20	then	then	ADV
cana-2791	11	21	we	we	PRON
cana-2791	11	22	simply	simply	ADV
cana-2791	11	23	write	write	VERB
cana-2791	11	24	n	n	PROPN
cana-2791	11	25	(	(	PUNCT
cana-2791	11	26	v	v	NOUN
cana-2791	11	27	)	)	PUNCT
cana-2791	11	28	and	and	CCONJ
cana-2791	11	29	n	n	CCONJ
cana-2791	12	1	[	[	X
cana-2791	12	2	v	v	X
cana-2791	12	3	]	]	PUNCT
cana-2791	12	4	rather	rather	ADV
cana-2791	12	5	than	than	ADP
cana-2791	12	6	nv(v	nv(v	PUNCT
cana-2791	12	7	)	)	PUNCT
cana-2791	12	8	.	.	PUNCT
cana-2791	13	1	communications	communication	NOUN
cana-2791	13	2	on	on	ADP
cana-2791	13	3	applied	apply	VERB
cana-2791	13	4	nonlinear	nonlinear	ADJ
cana-2791	13	5	analysis	analysis	NOUN
cana-2791	13	6	issn	issn	NOUN
cana-2791	13	7	:	:	PUNCT
cana-2791	13	8	1074	1074	NUM
cana-2791	13	9	-	-	PUNCT
cana-2791	13	10	133x	133x	NUM
cana-2791	13	11	vol	vol	NOUN
cana-2791	13	12	32	32	NUM
cana-2791	13	13	no	no	NOUN
cana-2791	13	14	.	.	PUNCT
cana-2791	14	1	4s	4s	NUM
cana-2791	14	2	(	(	PUNCT
cana-2791	14	3	2025	2025	NUM
cana-2791	14	4	)	)	PUNCT
cana-2791	14	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2791	14	6	247	247	NUM
cana-2791	14	7	received	receive	VERB
cana-2791	14	8	:	:	PUNCT
cana-2791	14	9	20	20	NUM
cana-2791	14	10	-	-	SYM
cana-2791	14	11	09	09	NUM
cana-2791	14	12	-	-	PUNCT
cana-2791	14	13	2024	2024	NUM
cana-2791	14	14	revised	revise	VERB
cana-2791	14	15	:	:	PUNCT
cana-2791	14	16	24	24	NUM
cana-2791	14	17	-	-	SYM
cana-2791	14	18	11	11	NUM
cana-2791	14	19	-	-	PUNCT
cana-2791	14	20	2024	2024	NUM
cana-2791	14	21	accepted	accept	VERB
cana-2791	14	22	:	:	PUNCT
cana-2791	14	23	05	05	NUM
cana-2791	14	24	-	-	SYM
cana-2791	14	25	12	12	NUM
cana-2791	14	26	-	-	PUNCT
cana-2791	14	27	2024	2024	NUM
cana-2791	14	28	mailto:1gopikamenon14009@gmail.com	mailto:1gopikamenon14009@gmail.com	PROPN
cana-2791	14	29	mailto:2mallikarjunbiradar54@gmail.com	mailto:2mallikarjunbiradar54@gmail.com	X
cana-2791	14	30	mailto:radhaiyer@cb.amrita.edu	mailto:radhaiyer@cb.amrita.edu	PROPN
cana-2791	15	1	mailto:er@cb.amrita.edu	mailto:er@cb.amrita.edu	PROPN
cana-2791	15	2	mailto:sreeranjini@cb.amrita.edu	mailto:sreeranjini@cb.amrita.edu	PROPN
cana-2791	15	3	mailto:mallikarjunbiradar54@gmail.com	mailto:mallikarjunbiradar54@gmail.com	PROPN
cana-2791	15	4	∈	∈	PROPN
cana-2791	16	1	i	i	PRON
cana-2791	16	2	−	−	PROPN
cana-2791	16	3	—	—	PUNCT
cana-2791	16	4	⊆	⊆	NUM
cana-2791	16	5	ioc	ioc	X
cana-2791	16	6	≥	≥	NOUN
cana-2791	16	7	−	−	PROPN
cana-2791	16	8	−	−	PROPN
cana-2791	16	9	−	−	PROPN
cana-2791	16	10	≥	≥	X
cana-2791	16	11	≥	≥	NUM
cana-2791	16	12	≥	≥	PROPN
cana-2791	16	13	≥	≥	PROPN
cana-2791	16	14	≥	≥	PROPN
cana-2791	16	15	≥	≥	NUM
cana-2791	16	16	—	—	PUNCT
cana-2791	16	17	−	−	PROPN
cana-2791	16	18	|	|	ADV
cana-2791	16	19	|	|	ADV
cana-2791	16	20	◦	◦	VERB
cana-2791	16	21	for	for	ADP
cana-2791	16	22	a	a	DET
cana-2791	16	23	graph	graph	NOUN
cana-2791	16	24	g	g	NOUN
cana-2791	16	25	,	,	PUNCT
cana-2791	16	26	a	a	DET
cana-2791	16	27	set	set	NOUN
cana-2791	16	28	d	d	NOUN
cana-2791	16	29	⊆	⊆	NUM
cana-2791	16	30	v	v	NOUN
cana-2791	16	31	is	be	AUX
cana-2791	16	32	a	a	DET
cana-2791	16	33	dominating	dominating	NOUN
cana-2791	16	34	set	set	NOUN
cana-2791	16	35	if	if	SCONJ
cana-2791	16	36	every	every	DET
cana-2791	16	37	v	v	NOUN
cana-2791	16	38	∈/	∈/	PROPN
cana-2791	16	39	d	d	PROPN
cana-2791	16	40	is	be	AUX
cana-2791	16	41	adjacent	adjacent	ADJ
cana-2791	16	42	to	to	PART
cana-2791	16	43	atleast	atleast	VERB
cana-2791	16	44	one	one	NUM
cana-2791	16	45	element	element	NOUN
cana-2791	16	46	in	in	ADP
cana-2791	16	47	d.	d.	PROPN
cana-2791	16	48	the	the	DET
cana-2791	16	49	minimum	minimum	NOUN
cana-2791	16	50	domination	domination	NOUN
cana-2791	16	51	number	number	NOUN
cana-2791	16	52	is	be	AUX
cana-2791	16	53	denoted	denote	VERB
cana-2791	16	54	by	by	ADP
cana-2791	16	55	γ̃(g	γ̃(g	NOUN
cana-2791	16	56	)	)	PUNCT
cana-2791	16	57	.	.	PUNCT
cana-2791	17	1	if	if	SCONJ
cana-2791	17	2	no	no	INTJ
cana-2791	17	3	,	,	PUNCT
cana-2791	17	4	v	v	NOUN
cana-2791	17	5	d	d	NOUN
cana-2791	17	6	,	,	PUNCT
cana-2791	17	7	is	be	AUX
cana-2791	17	8	adjacent	adjacent	ADJ
cana-2791	17	9	to	to	ADP
cana-2791	17	10	each	each	DET
cana-2791	17	11	other	other	ADJ
cana-2791	17	12	,	,	PUNCT
cana-2791	17	13	then	then	ADV
cana-2791	17	14	d	d	PROPN
cana-2791	17	15	is	be	AUX
cana-2791	17	16	called	call	VERB
cana-2791	17	17	the	the	DET
cana-2791	17	18	independent	independent	ADJ
cana-2791	17	19	dominating	dominating	NOUN
cana-2791	17	20	set	set	NOUN
cana-2791	17	21	.	.	PUNCT
cana-2791	18	1	the	the	DET
cana-2791	18	2	minimum	minimum	ADJ
cana-2791	18	3	cardinality	cardinality	NOUN
cana-2791	18	4	of	of	ADP
cana-2791	18	5	the	the	DET
cana-2791	18	6	independent	independent	ADJ
cana-2791	18	7	dominating	dominating	NOUN
cana-2791	18	8	set	set	NOUN
cana-2791	18	9	is	be	AUX
cana-2791	18	10	called	call	VERB
cana-2791	18	11	the	the	DET
cana-2791	18	12	independent	independent	ADJ
cana-2791	18	13	domination	domination	NOUN
cana-2791	18	14	number	number	NOUN
cana-2791	18	15	,	,	PUNCT
cana-2791	18	16	denoted	denote	VERB
cana-2791	18	17	by	by	ADP
cana-2791	18	18	γ̃i(g	γ̃i(g	NOUN
cana-2791	18	19	)	)	PUNCT
cana-2791	18	20	.	.	PUNCT
cana-2791	19	1	if	if	SCONJ
cana-2791	19	2	v	v	NOUN
cana-2791	19	3	d	d	NOUN
cana-2791	19	4	contains	contain	VERB
cana-2791	19	5	an	an	DET
cana-2791	19	6	independent	independent	ADJ
cana-2791	19	7	dominating	dominating	NOUN
cana-2791	19	8	set	set	NOUN
cana-2791	19	9	say	say	VERB
cana-2791	19	10	d′	d′	NUM
cana-2791	19	11	v	v	NOUN
cana-2791	19	12	,	,	PUNCT
cana-2791	19	13	then	then	ADV
cana-2791	19	14	d′	d′	PRON
cana-2791	19	15	is	be	AUX
cana-2791	19	16	called	call	VERB
cana-2791	19	17	an	an	DET
cana-2791	19	18	inverse	inverse	NOUN
cana-2791	19	19	independent	independent	ADJ
cana-2791	19	20	dominating	dominating	NOUN
cana-2791	19	21	set	set	NOUN
cana-2791	19	22	of	of	ADP
cana-2791	19	23	g	g	NOUN
cana-2791	19	24	with	with	ADP
cana-2791	19	25	respect	respect	NOUN
cana-2791	19	26	to	to	ADP
cana-2791	19	27	d.	d.	NOUN
cana-2791	19	28	the	the	DET
cana-2791	19	29	number	number	NOUN
cana-2791	19	30	of	of	ADP
cana-2791	19	31	vertices	vertex	NOUN
cana-2791	19	32	in	in	ADP
cana-2791	19	33	the	the	DET
cana-2791	19	34	smallest	small	ADJ
cana-2791	19	35	inverse	inverse	NOUN
cana-2791	19	36	independent	independent	ADJ
cana-2791	19	37	dominating	dominating	NOUN
cana-2791	19	38	set	set	NOUN
cana-2791	19	39	is	be	AUX
cana-2791	19	40	called	call	VERB
cana-2791	19	41	the	the	DET
cana-2791	19	42	inverse	inverse	ADJ
cana-2791	19	43	independent	independent	ADJ
cana-2791	19	44	domination	domination	NOUN
cana-2791	19	45	number	number	NOUN
cana-2791	19	46	,	,	PUNCT
cana-2791	19	47	denoted	denote	VERB
cana-2791	19	48	by	by	ADP
cana-2791	19	49	γ̃−1(g	γ̃−1(g	NOUN
cana-2791	19	50	)	)	PUNCT
cana-2791	19	51	.	.	PUNCT
cana-2791	20	1	if	if	SCONJ
cana-2791	20	2	the	the	DET
cana-2791	20	3	set	set	NOUN
cana-2791	20	4	v	v	NOUN
cana-2791	20	5	d′	d′	PRON
cana-2791	20	6	induces	induce	VERB
cana-2791	20	7	a	a	DET
cana-2791	20	8	connected	connected	ADJ
cana-2791	20	9	subgraph	subgraph	NOUN
cana-2791	20	10	,	,	PUNCT
cana-2791	20	11	where	where	SCONJ
cana-2791	20	12	d′	d′	PRON
cana-2791	20	13	is	be	AUX
cana-2791	20	14	an	an	DET
cana-2791	20	15	inverse	inverse	NOUN
cana-2791	20	16	independent	independent	ADJ
cana-2791	20	17	dominating	dominating	NOUN
cana-2791	20	18	set	set	NOUN
cana-2791	20	19	of	of	ADP
cana-2791	20	20	the	the	DET
cana-2791	20	21	graph	graph	NOUN
cana-2791	20	22	g	g	NOUN
cana-2791	20	23	,	,	PUNCT
cana-2791	20	24	then	then	ADV
cana-2791	20	25	d′	d′	PRON
cana-2791	20	26	is	be	AUX
cana-2791	20	27	called	call	VERB
cana-2791	20	28	the	the	DET
cana-2791	20	29	inverse	inverse	NOUN
cana-2791	20	30	independent	independent	ADJ
cana-2791	20	31	outer	outer	ADJ
cana-2791	20	32	connected	connected	ADJ
cana-2791	20	33	dominating	dominating	NOUN
cana-2791	20	34	set	set	NOUN
cana-2791	20	35	,	,	PUNCT
cana-2791	20	36	abbreviated	abbreviate	VERB
cana-2791	20	37	as	as	ADP
cana-2791	20	38	iiocd	iiocd	NOUN
cana-2791	20	39	-	-	PUNCT
cana-2791	20	40	set	set	NOUN
cana-2791	20	41	.	.	PUNCT
cana-2791	21	1	the	the	DET
cana-2791	21	2	cardinality	cardinality	NOUN
cana-2791	21	3	of	of	ADP
cana-2791	21	4	the	the	DET
cana-2791	21	5	minimum	minimum	ADJ
cana-2791	21	6	iiocd	iiocd	ADV
cana-2791	21	7	-	-	PUNCT
cana-2791	21	8	set	set	NOUN
cana-2791	21	9	is	be	AUX
cana-2791	21	10	the	the	DET
cana-2791	21	11	iiocd	iiocd	ADJ
cana-2791	21	12	number	number	NOUN
cana-2791	21	13	which	which	PRON
cana-2791	21	14	is	be	AUX
cana-2791	21	15	denoted	denote	VERB
cana-2791	21	16	by	by	ADP
cana-2791	21	17	γ̃−1	γ̃−1	PROPN
cana-2791	21	18	(	(	PUNCT
cana-2791	21	19	g	g	NOUN
cana-2791	21	20	)	)	PUNCT
cana-2791	21	21	.	.	PUNCT
cana-2791	22	1	s.	s.	PROPN
cana-2791	22	2	klavzar	klavzar	PROPN
cana-2791	22	3	and	and	CCONJ
cana-2791	22	4	u.	u.	PROPN
cana-2791	22	5	milutinovic	milutinovic	PROPN
cana-2791	22	6	were	be	AUX
cana-2791	22	7	the	the	DET
cana-2791	22	8	first	first	ADJ
cana-2791	22	9	to	to	PART
cana-2791	22	10	introduce	introduce	VERB
cana-2791	22	11	the	the	DET
cana-2791	22	12	concept	concept	NOUN
cana-2791	22	13	of	of	ADP
cana-2791	22	14	sierpinski	sierpinski	ADJ
cana-2791	22	15	graphs	graph	NOUN
cana-2791	22	16	in	in	ADP
cana-2791	22	17	[	[	X
cana-2791	22	18	7	7	NUM
cana-2791	22	19	]	]	PUNCT
cana-2791	22	20	.	.	PUNCT
cana-2791	23	1	the	the	DET
cana-2791	23	2	sierpinski	sierpinski	ADJ
cana-2791	23	3	graphs	graph	NOUN
cana-2791	23	4	are	be	AUX
cana-2791	23	5	denoted	denote	VERB
cana-2791	23	6	as	as	ADP
cana-2791	23	7	s(n	s(n	PROPN
cana-2791	23	8	,	,	PUNCT
cana-2791	23	9	k	k	NOUN
cana-2791	23	10	)	)	PUNCT
cana-2791	23	11	.	.	PUNCT
cana-2791	24	1	as	as	ADP
cana-2791	24	2	per	per	ADP
cana-2791	24	3	the	the	DET
cana-2791	24	4	definition	definition	NOUN
cana-2791	24	5	in	in	ADP
cana-2791	24	6	[	[	X
cana-2791	24	7	8	8	NUM
cana-2791	24	8	]	]	PUNCT
cana-2791	24	9	,	,	PUNCT
cana-2791	24	10	the	the	DET
cana-2791	24	11	vertex	vertex	NOUN
cana-2791	24	12	set	set	NOUN
cana-2791	24	13	of	of	ADP
cana-2791	24	14	s(n	s(n	PROPN
cana-2791	24	15	,	,	PUNCT
cana-2791	24	16	k	k	NOUN
cana-2791	24	17	)	)	PUNCT
cana-2791	24	18	consists	consist	VERB
cana-2791	24	19	of	of	ADP
cana-2791	24	20	all	all	DET
cana-2791	24	21	n	n	NOUN
cana-2791	24	22	-	-	PUNCT
cana-2791	24	23	tuples	tuple	NOUN
cana-2791	24	24	of	of	ADP
cana-2791	24	25	integers	integer	NOUN
cana-2791	24	26	1,2,	1,2,	NUM
cana-2791	24	27	...	...	PUNCT
cana-2791	24	28	,k	,k	PUNCT
cana-2791	24	29	,	,	PUNCT
cana-2791	24	30	for	for	ADP
cana-2791	24	31	integers	integer	NOUN
cana-2791	24	32	n	n	CCONJ
cana-2791	24	33	1	1	NUM
cana-2791	24	34	and	and	CCONJ
cana-2791	24	35	k	k	PROPN
cana-2791	24	36	3	3	X
cana-2791	24	37	.	.	PUNCT
cana-2791	25	1	the	the	DET
cana-2791	25	2	cardinality	cardinality	NOUN
cana-2791	25	3	of	of	ADP
cana-2791	25	4	v	v	NOUN
cana-2791	25	5	(	(	PUNCT
cana-2791	25	6	g	g	NOUN
cana-2791	25	7	)	)	PUNCT
cana-2791	25	8	of	of	ADP
cana-2791	25	9	a	a	DET
cana-2791	25	10	sierpinski	sierpinski	ADJ
cana-2791	25	11	graph	graph	NOUN
cana-2791	25	12	will	will	AUX
cana-2791	25	13	be	be	AUX
cana-2791	25	14	kn	kn	PROPN
cana-2791	25	15	.	.	PUNCT
cana-2791	26	1	as	as	ADP
cana-2791	26	2	in	in	ADP
cana-2791	26	3	[	[	X
cana-2791	26	4	1	1	NUM
cana-2791	26	5	]	]	PUNCT
cana-2791	26	6	,	,	PUNCT
cana-2791	26	7	[	[	X
cana-2791	26	8	6	6	NUM
cana-2791	26	9	]	]	PUNCT
cana-2791	26	10	the	the	DET
cana-2791	26	11	sierpinski	sierpinski	ADJ
cana-2791	26	12	graphs	graph	NOUN
cana-2791	26	13	s(n	s(n	PROPN
cana-2791	26	14	,	,	PUNCT
cana-2791	26	15	k	k	NOUN
cana-2791	26	16	)	)	PUNCT
cana-2791	26	17	,	,	PUNCT
cana-2791	26	18	n	n	PROPN
cana-2791	26	19	1	1	NUM
cana-2791	26	20	,	,	PUNCT
cana-2791	26	21	are	be	AUX
cana-2791	26	22	defined	define	VERB
cana-2791	26	23	in	in	ADP
cana-2791	26	24	the	the	DET
cana-2791	26	25	following	following	ADJ
cana-2791	26	26	way	way	NOUN
cana-2791	26	27	:	:	PUNCT
cana-2791	26	28	v	v	X
cana-2791	26	29	(	(	PUNCT
cana-2791	26	30	s(n	s(n	PROPN
cana-2791	26	31	,	,	PUNCT
cana-2791	26	32	k	k	NOUN
cana-2791	26	33	)	)	PUNCT
cana-2791	26	34	)	)	PUNCT
cana-2791	27	1	=	=	SYM
cana-2791	27	2	1	1	NUM
cana-2791	27	3	,	,	PUNCT
cana-2791	27	4	2	2	NUM
cana-2791	27	5	,	,	PUNCT
cana-2791	27	6	...	...	PUNCT
cana-2791	27	7	,	,	PUNCT
cana-2791	27	8	kn	kn	PROPN
cana-2791	27	9	,	,	PUNCT
cana-2791	27	10	two	two	NUM
cana-2791	27	11	different	different	ADJ
cana-2791	27	12	vertices	vertex	NOUN
cana-2791	27	13	u	u	NOUN
cana-2791	27	14	=	=	PUNCT
cana-2791	27	15	(	(	PUNCT
cana-2791	27	16	u1	u1	PROPN
cana-2791	27	17	,	,	PUNCT
cana-2791	27	18	...	...	PUNCT
cana-2791	27	19	,	,	PUNCT
cana-2791	27	20	un	un	PROPN
cana-2791	27	21	)	)	PUNCT
cana-2791	27	22	and	and	CCONJ
cana-2791	27	23	v	v	NOUN
cana-2791	27	24	=	=	SYM
cana-2791	27	25	(	(	PUNCT
cana-2791	27	26	v1	v1	PROPN
cana-2791	27	27	,	,	PUNCT
cana-2791	27	28	...	...	PUNCT
cana-2791	27	29	,	,	PUNCT
cana-2791	27	30	vn	vn	X
cana-2791	27	31	)	)	PUNCT
cana-2791	27	32	being	be	AUX
cana-2791	27	33	adjacent	adjacent	ADJ
cana-2791	27	34	if	if	SCONJ
cana-2791	27	35	and	and	CCONJ
cana-2791	27	36	only	only	ADV
cana-2791	27	37	if	if	SCONJ
cana-2791	27	38	there	there	PRON
cana-2791	27	39	exists	exist	VERB
cana-2791	27	40	an	an	DET
cana-2791	27	41	h	h	NOUN
cana-2791	27	42	∈	∈	NOUN
cana-2791	27	43	1	1	NUM
cana-2791	27	44	,	,	PUNCT
cana-2791	27	45	...	...	PUNCT
cana-2791	27	46	,	,	PUNCT
cana-2791	27	47	n	n	PRON
cana-2791	27	48	such	such	ADJ
cana-2791	27	49	that	that	SCONJ
cana-2791	27	50	(	(	PUNCT
cana-2791	27	51	i	i	NOUN
cana-2791	27	52	)	)	PUNCT
cana-2791	27	53	ut	ut	PROPN
cana-2791	28	1	=	=	SYM
cana-2791	28	2	vt	vt	PROPN
cana-2791	28	3	,	,	PUNCT
cana-2791	28	4	for	for	ADP
cana-2791	28	5	t	t	NOUN
cana-2791	28	6	=	=	SYM
cana-2791	28	7	1	1	NUM
cana-2791	28	8	,	,	PUNCT
cana-2791	28	9	...	...	PUNCT
cana-2791	28	10	,	,	PUNCT
cana-2791	28	11	h	h	NOUN
cana-2791	29	1	−	−	PROPN
cana-2791	29	2	1	1	NUM
cana-2791	29	3	;	;	PUNCT
cana-2791	29	4	(	(	PUNCT
cana-2791	29	5	ii	ii	NOUN
cana-2791	29	6	)	)	PUNCT
cana-2791	29	7	uh	uh	INTJ
cana-2791	29	8	̸=	̸=	PROPN
cana-2791	29	9	vh	vh	PROPN
cana-2791	29	10	;	;	PUNCT
cana-2791	29	11	and	and	CCONJ
cana-2791	29	12	(	(	PUNCT
cana-2791	29	13	iii	iii	X
cana-2791	29	14	)	)	PUNCT
cana-2791	29	15	ut	ut	PROPN
cana-2791	29	16	=	=	PROPN
cana-2791	29	17	vh	vh	PROPN
cana-2791	29	18	and	and	CCONJ
cana-2791	29	19	vt	vt	PROPN
cana-2791	29	20	=	=	PROPN
cana-2791	29	21	uh	uh	INTJ
cana-2791	29	22	for	for	ADP
cana-2791	29	23	t	t	PROPN
cana-2791	29	24	=	=	SYM
cana-2791	29	25	h+1,	h+1,	NOUN
cana-2791	29	26	...	...	PUNCT
cana-2791	29	27	,n	,n	NOUN
cana-2791	29	28	.	.	PUNCT
cana-2791	30	1	for	for	ADP
cana-2791	30	2	the	the	DET
cana-2791	30	3	labelling	labelling	NOUN
cana-2791	30	4	of	of	ADP
cana-2791	30	5	a	a	DET
cana-2791	30	6	sieprinski	sieprinski	ADJ
cana-2791	30	7	graph	graph	NOUN
cana-2791	30	8	each	each	DET
cana-2791	30	9	n	n	CCONJ
cana-2791	30	10	-	-	PUNCT
cana-2791	30	11	tuple	tuple	NOUN
cana-2791	30	12	is	be	AUX
cana-2791	30	13	labelled	label	VERB
cana-2791	30	14	in	in	ADP
cana-2791	30	15	such	such	DET
cana-2791	30	16	a	a	DET
cana-2791	30	17	way	way	NOUN
cana-2791	30	18	that	that	PRON
cana-2791	30	19	the	the	DET
cana-2791	30	20	first	first	ADJ
cana-2791	30	21	′n	′n	NOUN
cana-2791	30	22	1′	1′	NUM
cana-2791	30	23	members	member	NOUN
cana-2791	30	24	of	of	ADP
cana-2791	30	25	the	the	DET
cana-2791	30	26	n	n	CCONJ
cana-2791	30	27	-	-	PUNCT
cana-2791	30	28	tuple	tuple	NOUN
cana-2791	30	29	denotes	denote	VERB
cana-2791	30	30	the	the	DET
cana-2791	30	31	level	level	NOUN
cana-2791	30	32	of	of	ADP
cana-2791	30	33	the	the	DET
cana-2791	30	34	subgraph	subgraph	NOUN
cana-2791	30	35	in	in	ADP
cana-2791	30	36	which	which	PRON
cana-2791	30	37	the	the	DET
cana-2791	30	38	vertex	vertex	NOUN
cana-2791	30	39	is	be	AUX
cana-2791	30	40	chosen	choose	VERB
cana-2791	30	41	.	.	PUNCT
cana-2791	31	1	for	for	ADP
cana-2791	31	2	instance	instance	NOUN
cana-2791	31	3	,	,	PUNCT
cana-2791	31	4	we	we	PRON
cana-2791	31	5	can	can	AUX
cana-2791	31	6	say	say	VERB
cana-2791	31	7	that	that	SCONJ
cana-2791	31	8	the	the	DET
cana-2791	31	9	first	first	ADJ
cana-2791	31	10	member	member	NOUN
cana-2791	31	11	denotes	denote	VERB
cana-2791	31	12	the	the	DET
cana-2791	31	13	subgraph	subgraph	NOUN
cana-2791	31	14	s(n	s(n	PROPN
cana-2791	31	15	1	1	NUM
cana-2791	31	16	,	,	PUNCT
cana-2791	31	17	k	k	NOUN
cana-2791	31	18	)	)	PUNCT
cana-2791	31	19	and	and	CCONJ
cana-2791	31	20	the	the	DET
cana-2791	31	21	(	(	PUNCT
cana-2791	31	22	n	n	PROPN
cana-2791	31	23	1)th	1)th	NUM
cana-2791	31	24	member	member	NOUN
cana-2791	31	25	denotes	denote	VERB
cana-2791	31	26	the	the	DET
cana-2791	31	27	subgraph	subgraph	PROPN
cana-2791	31	28	s(1	s(1	PROPN
cana-2791	31	29	,	,	PUNCT
cana-2791	31	30	k	k	PROPN
cana-2791	31	31	)	)	PUNCT
cana-2791	31	32	in	in	ADP
cana-2791	31	33	which	which	PRON
cana-2791	31	34	the	the	DET
cana-2791	31	35	vertex	vertex	NOUN
cana-2791	31	36	is	be	AUX
cana-2791	31	37	chosen	choose	VERB
cana-2791	31	38	.	.	PUNCT
cana-2791	32	1	the	the	DET
cana-2791	32	2	nth	nth	PROPN
cana-2791	32	3	member	member	NOUN
cana-2791	32	4	denotes	denote	VERB
cana-2791	32	5	the	the	DET
cana-2791	32	6	position	position	NOUN
cana-2791	32	7	of	of	ADP
cana-2791	32	8	the	the	DET
cana-2791	32	9	vertex	vertex	NOUN
cana-2791	32	10	in	in	ADP
cana-2791	32	11	the	the	DET
cana-2791	32	12	graph	graph	NOUN
cana-2791	32	13	.	.	PUNCT
cana-2791	33	1	the	the	DET
cana-2791	33	2	extended	extended	ADJ
cana-2791	33	3	sierpinski	sierpinski	ADJ
cana-2791	33	4	graph	graph	NOUN
cana-2791	33	5	s+(n	s+(n	NOUN
cana-2791	33	6	,	,	PUNCT
cana-2791	33	7	k	k	NOUN
cana-2791	33	8	)	)	PUNCT
cana-2791	33	9	for	for	ADP
cana-2791	33	10	n	n	ADV
cana-2791	33	11	1	1	NUM
cana-2791	33	12	and	and	CCONJ
cana-2791	33	13	k	k	PROPN
cana-2791	33	14	3	3	NUM
cana-2791	33	15	is	be	AUX
cana-2791	33	16	derived	derive	VERB
cana-2791	33	17	from	from	ADP
cana-2791	33	18	the	the	DET
cana-2791	33	19	sierpinski	sierpinski	ADJ
cana-2791	33	20	graph	graph	NOUN
cana-2791	33	21	s(n	s(n	PROPN
cana-2791	33	22	,	,	PUNCT
cana-2791	33	23	k	k	NOUN
cana-2791	33	24	)	)	PUNCT
cana-2791	33	25	by	by	ADP
cana-2791	33	26	the	the	DET
cana-2791	33	27	addition	addition	NOUN
cana-2791	33	28	of	of	ADP
cana-2791	33	29	an	an	DET
cana-2791	33	30	extra	extra	ADJ
cana-2791	33	31	vertex	vertex	NOUN
cana-2791	33	32	say	say	NOUN
cana-2791	33	33	,	,	PUNCT
cana-2791	33	34	′s′	′s′	NOUN
cana-2791	33	35	and	and	CCONJ
cana-2791	33	36	the	the	DET
cana-2791	33	37	vertex	vertex	NOUN
cana-2791	33	38	′s′	′s′	NOUN
cana-2791	33	39	is	be	AUX
cana-2791	33	40	adjacent	adjacent	ADJ
cana-2791	33	41	to	to	ADP
cana-2791	33	42	the	the	DET
cana-2791	33	43	end	end	NOUN
cana-2791	33	44	vertices	vertex	NOUN
cana-2791	33	45	of	of	ADP
cana-2791	33	46	the	the	DET
cana-2791	33	47	sierpinski	sierpinski	ADJ
cana-2791	33	48	graph	graph	NOUN
cana-2791	33	49	s(n	s(n	PROPN
cana-2791	33	50	,	,	PUNCT
cana-2791	33	51	k	k	NOUN
cana-2791	33	52	)	)	PUNCT
cana-2791	33	53	.	.	PUNCT
cana-2791	34	1	the	the	DET
cana-2791	34	2	extended	extended	ADJ
cana-2791	34	3	sierpinski	sierpinski	ADJ
cana-2791	34	4	graph	graph	NOUN
cana-2791	34	5	s++(n	s++(n	NOUN
cana-2791	34	6	,	,	PUNCT
cana-2791	34	7	k	k	NOUN
cana-2791	34	8	)	)	PUNCT
cana-2791	34	9	for	for	ADP
cana-2791	34	10	n	n	ADV
cana-2791	34	11	2	2	NUM
cana-2791	34	12	and	and	CCONJ
cana-2791	34	13	k	k	PROPN
cana-2791	34	14	3	3	NUM
cana-2791	34	15	is	be	AUX
cana-2791	34	16	derived	derive	VERB
cana-2791	34	17	from	from	ADP
cana-2791	34	18	the	the	DET
cana-2791	34	19	sierpinski	sierpinski	ADJ
cana-2791	34	20	graph	graph	NOUN
cana-2791	34	21	s(n	s(n	PROPN
cana-2791	34	22	,	,	PUNCT
cana-2791	34	23	k	k	NOUN
cana-2791	34	24	)	)	PUNCT
cana-2791	34	25	by	by	ADP
cana-2791	34	26	the	the	DET
cana-2791	34	27	addition	addition	NOUN
cana-2791	34	28	of	of	ADP
cana-2791	34	29	an	an	DET
cana-2791	34	30	extra	extra	ADJ
cana-2791	34	31	copy	copy	NOUN
cana-2791	34	32	of	of	ADP
cana-2791	34	33	the	the	DET
cana-2791	34	34	sierpinski	sierpinski	ADJ
cana-2791	34	35	graph	graph	NOUN
cana-2791	34	36	,	,	PUNCT
cana-2791	34	37	s(n	s(n	PROPN
cana-2791	34	38	1	1	NUM
cana-2791	34	39	,	,	PUNCT
cana-2791	34	40	k	k	NOUN
cana-2791	34	41	)	)	PUNCT
cana-2791	34	42	and	and	CCONJ
cana-2791	34	43	the	the	DET
cana-2791	34	44	end	end	NOUN
cana-2791	34	45	vertices	vertex	NOUN
cana-2791	34	46	of	of	ADP
cana-2791	34	47	this	this	DET
cana-2791	34	48	s(n	s(n	PROPN
cana-2791	34	49	1	1	NUM
cana-2791	34	50	,	,	PUNCT
cana-2791	34	51	k	k	NOUN
cana-2791	34	52	)	)	PUNCT
cana-2791	34	53	is	be	AUX
cana-2791	34	54	adjacent	adjacent	ADJ
cana-2791	34	55	to	to	ADP
cana-2791	34	56	the	the	DET
cana-2791	34	57	end	end	NOUN
cana-2791	34	58	vertices	vertex	NOUN
cana-2791	34	59	of	of	ADP
cana-2791	34	60	the	the	DET
cana-2791	34	61	sierpinski	sierpinski	ADJ
cana-2791	34	62	graph	graph	NOUN
cana-2791	34	63	s(n	s(n	PROPN
cana-2791	34	64	,	,	PUNCT
cana-2791	34	65	k	k	NOUN
cana-2791	34	66	)	)	PUNCT
cana-2791	34	67	.	.	PUNCT
cana-2791	35	1	now	now	ADV
cana-2791	35	2	the	the	DET
cana-2791	35	3	sierpinski	sierpinski	ADJ
cana-2791	35	4	gasket	gasket	NOUN
cana-2791	35	5	graphs	graph	NOUN
cana-2791	35	6	are	be	AUX
cana-2791	35	7	obtained	obtain	VERB
cana-2791	35	8	from	from	ADP
cana-2791	35	9	the	the	DET
cana-2791	35	10	sierpinski	sierpinski	ADJ
cana-2791	35	11	graph	graph	NOUN
cana-2791	35	12	s(n	s(n	PROPN
cana-2791	35	13	,	,	PUNCT
cana-2791	35	14	3	3	NUM
cana-2791	35	15	)	)	PUNCT
cana-2791	35	16	where	where	SCONJ
cana-2791	35	17	the	the	DET
cana-2791	35	18	edges	edge	NOUN
cana-2791	35	19	joining	join	VERB
cana-2791	35	20	each	each	DET
cana-2791	35	21	copy	copy	NOUN
cana-2791	35	22	is	be	AUX
cana-2791	35	23	removed	remove	VERB
cana-2791	35	24	.	.	PUNCT
cana-2791	36	1	a	a	DET
cana-2791	36	2	sierpinski	sierpinski	ADJ
cana-2791	36	3	gasket	gasket	NOUN
cana-2791	36	4	graph	graph	NOUN
cana-2791	36	5	is	be	AUX
cana-2791	36	6	denoted	denote	VERB
cana-2791	36	7	as	as	ADP
cana-2791	36	8	sn	sn	PROPN
cana-2791	36	9	.	.	PUNCT
cana-2791	37	1	in	in	ADP
cana-2791	37	2	the	the	DET
cana-2791	37	3	year	year	NOUN
cana-2791	37	4	1970	1970	NUM
cana-2791	37	5	frucht	frucht	NOUN
cana-2791	37	6	and	and	CCONJ
cana-2791	37	7	harary	harary	NOUN
cana-2791	37	8	in	in	ADP
cana-2791	37	9	[	[	X
cana-2791	37	10	5	5	NUM
cana-2791	37	11	]	]	PUNCT
cana-2791	37	12	had	have	AUX
cana-2791	37	13	introduced	introduce	VERB
cana-2791	37	14	the	the	DET
cana-2791	37	15	concept	concept	NOUN
cana-2791	37	16	of	of	ADP
cana-2791	37	17	corona	corona	NOUN
cana-2791	37	18	product	product	NOUN
cana-2791	37	19	of	of	ADP
cana-2791	37	20	two	two	NUM
cana-2791	37	21	graphs	graph	NOUN
cana-2791	37	22	g1	g1	NOUN
cana-2791	37	23	and	and	CCONJ
cana-2791	37	24	g2	g2	PROPN
cana-2791	37	25	denoted	denote	VERB
cana-2791	37	26	by	by	ADP
cana-2791	37	27	g1	g1	PROPN
cana-2791	37	28	g2	g2	PROPN
cana-2791	37	29	.	.	PUNCT
cana-2791	38	1	the	the	DET
cana-2791	38	2	corona	corona	NOUN
cana-2791	38	3	product	product	NOUN
cana-2791	38	4	is	be	AUX
cana-2791	38	5	obtained	obtain	VERB
cana-2791	38	6	by	by	ADP
cana-2791	38	7	taking	take	VERB
cana-2791	38	8	one	one	NUM
cana-2791	38	9	copy	copy	NOUN
cana-2791	38	10	of	of	ADP
cana-2791	38	11	center	center	NOUN
cana-2791	38	12	graph	graph	NOUN
cana-2791	38	13	g1	g1	NOUN
cana-2791	38	14	and	and	CCONJ
cana-2791	38	15	v	v	NOUN
cana-2791	38	16	(	(	PUNCT
cana-2791	38	17	g1	g1	PROPN
cana-2791	38	18	)	)	PUNCT
cana-2791	38	19	copies	copy	NOUN
cana-2791	38	20	of	of	ADP
cana-2791	38	21	the	the	DET
cana-2791	38	22	outer	outer	ADJ
cana-2791	38	23	graph	graph	NOUN
cana-2791	38	24	g2	g2	PROPN
cana-2791	38	25	,	,	PUNCT
cana-2791	38	26	where	where	SCONJ
cana-2791	38	27	the	the	DET
cana-2791	38	28	ith	ith	PROPN
cana-2791	38	29	vertex	vertex	NOUN
cana-2791	38	30	of	of	ADP
cana-2791	38	31	g1	g1	PROPN
cana-2791	38	32	is	be	AUX
cana-2791	38	33	adjacent	adjacent	ADJ
cana-2791	38	34	to	to	ADP
cana-2791	38	35	every	every	DET
cana-2791	38	36	vertex	vertex	NOUN
cana-2791	38	37	of	of	ADP
cana-2791	38	38	the	the	DET
cana-2791	38	39	ith	ith	PROPN
cana-2791	38	40	copy	copy	NOUN
cana-2791	38	41	of	of	ADP
cana-2791	38	42	g2	g2	PROPN
cana-2791	38	43	.	.	PUNCT
cana-2791	39	1	in	in	ADP
cana-2791	39	2	[	[	X
cana-2791	39	3	9	9	NUM
cana-2791	39	4	]	]	X
cana-2791	39	5	s.nada	s.nada	NOUN
cana-2791	39	6	,	,	PUNCT
cana-2791	39	7	a.elrokh	a.elrokh	ADJ
cana-2791	39	8	,	,	PUNCT
cana-2791	39	9	e.a.elsakhawi	e.a.elsakhawi	PROPN
cana-2791	39	10	,	,	PUNCT
cana-2791	39	11	d.e.sabrafollows	d.e.sabrafollow	NOUN
cana-2791	39	12	had	have	AUX
cana-2791	39	13	inferred	infer	VERB
cana-2791	39	14	from	from	ADP
cana-2791	39	15	the	the	DET
cana-2791	39	16	definition	definition	NOUN
cana-2791	39	17	of	of	ADP
cana-2791	39	18	the	the	DET
cana-2791	39	19	corona	corona	NOUN
cana-2791	39	20	that	that	PRON
cana-2791	39	21	g1	g1	VERB
cana-2791	39	22	◦	◦	PROPN
cana-2791	39	23	g2	g2	PROPN
cana-2791	39	24	has	have	VERB
cana-2791	39	25	n1	n1	NOUN
cana-2791	39	26	+	+	CCONJ
cana-2791	39	27	n1n2	n1n2	NUM
cana-2791	39	28	vertices	vertex	NOUN
cana-2791	39	29	.	.	PUNCT
cana-2791	40	1	it	it	PRON
cana-2791	40	2	is	be	AUX
cana-2791	40	3	easy	easy	ADJ
cana-2791	40	4	to	to	PART
cana-2791	40	5	see	see	VERB
cana-2791	40	6	that	that	SCONJ
cana-2791	40	7	g1	g1	PROPN
cana-2791	40	8	◦	◦	PROPN
cana-2791	40	9	g2	g2	PROPN
cana-2791	40	10	is	be	AUX
cana-2791	40	11	not	not	PART
cana-2791	40	12	in	in	ADP
cana-2791	40	13	general	general	ADJ
cana-2791	40	14	isomorphic	isomorphic	ADJ
cana-2791	40	15	to	to	ADP
cana-2791	40	16	g2	g2	PROPN
cana-2791	40	17	◦	◦	NOUN
cana-2791	40	18	g1	g1	PROPN
cana-2791	40	19	.	.	PUNCT
cana-2791	41	1	if	if	SCONJ
cana-2791	41	2	g1	g1	PROPN
cana-2791	41	3	and	and	CCONJ
cana-2791	41	4	g2	g2	PROPN
cana-2791	41	5	communications	communication	NOUN
cana-2791	41	6	on	on	ADP
cana-2791	41	7	applied	apply	VERB
cana-2791	41	8	nonlinear	nonlinear	ADJ
cana-2791	41	9	analysis	analysis	NOUN
cana-2791	41	10	issn	issn	NOUN
cana-2791	41	11	:	:	PUNCT
cana-2791	41	12	1074	1074	NUM
cana-2791	41	13	-	-	PUNCT
cana-2791	41	14	133x	133x	NUM
cana-2791	41	15	vol	vol	NOUN
cana-2791	41	16	32	32	NUM
cana-2791	41	17	no	no	NOUN
cana-2791	41	18	.	.	PUNCT
cana-2791	42	1	4s	4s	NUM
cana-2791	42	2	(	(	PUNCT
cana-2791	42	3	2025	2025	NUM
cana-2791	42	4	)	)	PUNCT
cana-2791	42	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2791	42	6	248	248	NUM
cana-2791	42	7	≤	≤	NUM
cana-2791	42	8	≤	≤	NUM
cana-2791	42	9	≥	≥	NUM
cana-2791	42	10	≥	≥	NUM
cana-2791	42	11	ioc	ioc	PROPN
cana-2791	42	12	ioc	ioc	PROPN
cana-2791	42	13	ioc	ioc	PROPN
cana-2791	42	14	ioc	ioc	PROPN
cana-2791	42	15	are	be	AUX
cana-2791	42	16	two	two	NUM
cana-2791	42	17	graphs	graph	NOUN
cana-2791	42	18	,	,	PUNCT
cana-2791	42	19	where	where	SCONJ
cana-2791	42	20	g1	g1	PROPN
cana-2791	42	21	has	have	VERB
cana-2791	42	22	n	n	NOUN
cana-2791	42	23	vertices	vertex	NOUN
cana-2791	42	24	,	,	PUNCT
cana-2791	42	25	the	the	DET
cana-2791	42	26	labeling	labeling	NOUN
cana-2791	42	27	of	of	ADP
cana-2791	42	28	the	the	DET
cana-2791	42	29	corona	corona	NOUN
cana-2791	42	30	g1	g1	PROPN
cana-2791	42	31	◦	◦	PROPN
cana-2791	42	32	g2	g2	PROPN
cana-2791	42	33	is	be	AUX
cana-2791	42	34	often	often	ADV
cana-2791	42	35	denoted	denote	VERB
cana-2791	42	36	by	by	ADP
cana-2791	42	37	[	[	PUNCT
cana-2791	42	38	a	a	DET
cana-2791	42	39	:	:	PUNCT
cana-2791	42	40	b1	b1	NOUN
cana-2791	42	41	,	,	PUNCT
cana-2791	42	42	b2	b2	NOUN
cana-2791	42	43	,	,	PUNCT
cana-2791	42	44	.	.	PUNCT
cana-2791	42	45	.	.	PUNCT
cana-2791	42	46	.	.	PUNCT
cana-2791	43	1	,	,	PUNCT
cana-2791	43	2	bn	bn	X
cana-2791	43	3	]	]	PUNCT
cana-2791	43	4	,	,	PUNCT
cana-2791	43	5	where	where	SCONJ
cana-2791	43	6	a	a	PRON
cana-2791	43	7	is	be	AUX
cana-2791	43	8	the	the	DET
cana-2791	43	9	labeling	labeling	NOUN
cana-2791	43	10	of	of	ADP
cana-2791	43	11	the	the	DET
cana-2791	43	12	n	n	DET
cana-2791	43	13	vertices	vertex	NOUN
cana-2791	43	14	of	of	ADP
cana-2791	43	15	g1	g1	NOUN
cana-2791	43	16	,	,	PUNCT
cana-2791	43	17	and	and	CCONJ
cana-2791	43	18	bi	bi	NOUN
cana-2791	43	19	,	,	PUNCT
cana-2791	43	20	1	1	NUM
cana-2791	43	21	i	i	PRON
cana-2791	43	22	n	n	VERB
cana-2791	43	23	is	be	AUX
cana-2791	43	24	the	the	DET
cana-2791	43	25	labeling	labeling	NOUN
cana-2791	43	26	of	of	ADP
cana-2791	43	27	the	the	DET
cana-2791	43	28	vertices	vertex	NOUN
cana-2791	43	29	of	of	ADP
cana-2791	43	30	the	the	DET
cana-2791	43	31	copy	copy	NOUN
cana-2791	43	32	of	of	ADP
cana-2791	43	33	g2	g2	PROPN
cana-2791	43	34	that	that	PRON
cana-2791	43	35	is	be	AUX
cana-2791	43	36	connected	connect	VERB
cana-2791	43	37	to	to	ADP
cana-2791	43	38	the	the	DET
cana-2791	43	39	ith	ith	PROPN
cana-2791	43	40	vertex	vertex	NOUN
cana-2791	43	41	of	of	ADP
cana-2791	43	42	g1	g1	PROPN
cana-2791	43	43	.	.	PUNCT
cana-2791	44	1	the	the	DET
cana-2791	44	2	corona	corona	NOUN
cana-2791	44	3	product	product	NOUN
cana-2791	44	4	is	be	AUX
cana-2791	44	5	not	not	PART
cana-2791	44	6	commutative	commutative	ADJ
cana-2791	44	7	as	as	ADV
cana-2791	44	8	well	well	ADV
cana-2791	44	9	as	as	ADV
cana-2791	44	10	associative	associative	ADJ
cana-2791	44	11	.	.	PUNCT
cana-2791	45	1	joanna	joanna	PROPN
cana-2791	45	2	cymann	cymann	PROPN
cana-2791	45	3	in	in	ADP
cana-2791	45	4	[	[	X
cana-2791	45	5	2	2	NUM
cana-2791	45	6	]	]	PUNCT
cana-2791	45	7	has	have	AUX
cana-2791	45	8	observed	observe	VERB
cana-2791	45	9	the	the	DET
cana-2791	45	10	outer	outer	ADJ
cana-2791	45	11	connected	connected	ADJ
cana-2791	45	12	domination	domination	NOUN
cana-2791	45	13	number	number	NOUN
cana-2791	45	14	of	of	ADP
cana-2791	45	15	the	the	DET
cana-2791	45	16	cycle	cycle	NOUN
cana-2791	45	17	graphs	graph	NOUN
cana-2791	45	18	and	and	CCONJ
cana-2791	45	19	the	the	DET
cana-2791	45	20	complete	complete	ADJ
cana-2791	45	21	graphs	graph	NOUN
cana-2791	45	22	.	.	PUNCT
cana-2791	46	1	in	in	ADP
cana-2791	46	2	[	[	X
cana-2791	46	3	4	4	X
cana-2791	46	4	]	]	PUNCT
cana-2791	46	5	renario	renario	PROPN
cana-2791	46	6	g.	g.	PROPN
cana-2791	46	7	hinampas	hinampas	PROPN
cana-2791	46	8	,	,	PUNCT
cana-2791	46	9	jr	jr	PROPN
cana-2791	46	10	.	.	PROPN
cana-2791	46	11	jocecar	jocecar	PROPN
cana-2791	46	12	lomarda	lomarda	PROPN
cana-2791	46	13	-	-	PUNCT
cana-2791	46	14	hinampas	hinampas	NOUN
cana-2791	46	15	,	,	PUNCT
cana-2791	46	16	analyn	analyn	X
cana-2791	46	17	dahunan	dahunan	PROPN
cana-2791	46	18	have	have	AUX
cana-2791	46	19	found	find	VERB
cana-2791	46	20	out	out	ADP
cana-2791	46	21	the	the	DET
cana-2791	46	22	independent	independent	ADJ
cana-2791	46	23	outer	outer	ADJ
cana-2791	46	24	connected	connected	ADJ
cana-2791	46	25	domination	domination	NOUN
cana-2791	46	26	number	number	NOUN
cana-2791	46	27	of	of	ADP
cana-2791	46	28	corona	corona	NOUN
cana-2791	46	29	product	product	NOUN
cana-2791	46	30	of	of	ADP
cana-2791	46	31	two	two	NUM
cana-2791	46	32	connected	connect	VERB
cana-2791	46	33	non	non	ADJ
cana-2791	46	34	trivial	trivial	ADJ
cana-2791	46	35	graphs	graph	NOUN
cana-2791	46	36	of	of	ADP
cana-2791	46	37	order	order	NOUN
cana-2791	46	38	m	m	VERB
cana-2791	46	39	2	2	NUM
cana-2791	46	40	and	and	CCONJ
cana-2791	46	41	n	n	PRON
cana-2791	46	42	2	2	NUM
cana-2791	46	43	.	.	PUNCT
cana-2791	46	44	taking	take	VERB
cana-2791	46	45	the	the	DET
cana-2791	46	46	corona	corona	NOUN
cana-2791	46	47	product	product	NOUN
cana-2791	46	48	of	of	ADP
cana-2791	46	49	the	the	DET
cana-2791	46	50	complete	complete	ADJ
cana-2791	46	51	graphs	graph	NOUN
cana-2791	46	52	and	and	CCONJ
cana-2791	46	53	the	the	DET
cana-2791	46	54	cycle	cycle	NOUN
cana-2791	46	55	graphs	graph	NOUN
cana-2791	46	56	in	in	ADP
cana-2791	46	57	different	different	ADJ
cana-2791	46	58	combinations	combination	NOUN
cana-2791	46	59	and	and	CCONJ
cana-2791	46	60	imposing	impose	VERB
cana-2791	46	61	two	two	NUM
cana-2791	46	62	more	more	ADJ
cana-2791	46	63	conditions	condition	NOUN
cana-2791	46	64	(	(	PUNCT
cana-2791	46	65	inverse	inverse	NOUN
cana-2791	46	66	and	and	CCONJ
cana-2791	46	67	independent	independent	ADJ
cana-2791	46	68	)	)	PUNCT
cana-2791	46	69	on	on	ADP
cana-2791	46	70	them	they	PRON
cana-2791	46	71	we	we	PRON
cana-2791	46	72	get	get	VERB
cana-2791	46	73	few	few	ADJ
cana-2791	46	74	new	new	ADJ
cana-2791	46	75	results	result	NOUN
cana-2791	46	76	.	.	PUNCT
cana-2791	47	1	we	we	PRON
cana-2791	47	2	will	will	AUX
cana-2791	47	3	be	be	AUX
cana-2791	47	4	discussing	discuss	VERB
cana-2791	47	5	the	the	DET
cana-2791	47	6	inverse	inverse	NOUN
cana-2791	47	7	independent	independent	ADJ
cana-2791	47	8	outer	outer	ADJ
cana-2791	47	9	connected	connected	ADJ
cana-2791	47	10	domination	domination	NOUN
cana-2791	47	11	number	number	NOUN
cana-2791	47	12	of	of	ADP
cana-2791	47	13	the	the	DET
cana-2791	47	14	corona	corona	NOUN
cana-2791	47	15	graph	graph	NOUN
cana-2791	47	16	when	when	SCONJ
cana-2791	47	17	g1	g1	PROPN
cana-2791	47	18	and	and	CCONJ
cana-2791	47	19	g2	g2	PROPN
cana-2791	47	20	both	both	PRON
cana-2791	47	21	are	be	AUX
cana-2791	47	22	complete	complete	ADJ
cana-2791	47	23	graphs	graph	NOUN
cana-2791	47	24	with	with	ADP
cana-2791	47	25	different	different	ADJ
cana-2791	47	26	number	number	NOUN
cana-2791	47	27	of	of	ADP
cana-2791	47	28	vertices	vertex	NOUN
cana-2791	47	29	;	;	PUNCT
cana-2791	47	30	inverse	inverse	NOUN
cana-2791	47	31	independent	independent	ADJ
cana-2791	47	32	outer	outer	ADJ
cana-2791	47	33	connected	connected	ADJ
cana-2791	47	34	domination	domination	NOUN
cana-2791	47	35	number	number	NOUN
cana-2791	47	36	of	of	ADP
cana-2791	47	37	the	the	DET
cana-2791	47	38	corona	corona	NOUN
cana-2791	47	39	graph	graph	NOUN
cana-2791	47	40	when	when	SCONJ
cana-2791	47	41	g1	g1	PROPN
cana-2791	47	42	is	be	AUX
cana-2791	47	43	a	a	DET
cana-2791	47	44	cycle	cycle	NOUN
cana-2791	47	45	graph	graph	NOUN
cana-2791	47	46	and	and	CCONJ
cana-2791	47	47	g2	g2	PROPN
cana-2791	47	48	is	be	AUX
cana-2791	47	49	a	a	DET
cana-2791	47	50	complete	complete	ADJ
cana-2791	47	51	graph	graph	NOUN
cana-2791	47	52	with	with	ADP
cana-2791	47	53	different	different	ADJ
cana-2791	47	54	number	number	NOUN
cana-2791	47	55	of	of	ADP
cana-2791	47	56	vertices	vertex	NOUN
cana-2791	47	57	;	;	PUNCT
cana-2791	47	58	inverse	inverse	NOUN
cana-2791	47	59	independent	independent	ADJ
cana-2791	47	60	outer	outer	ADJ
cana-2791	47	61	connected	connected	ADJ
cana-2791	47	62	domination	domination	NOUN
cana-2791	47	63	number	number	NOUN
cana-2791	47	64	of	of	ADP
cana-2791	47	65	the	the	DET
cana-2791	47	66	corona	corona	NOUN
cana-2791	47	67	graph	graph	NOUN
cana-2791	47	68	when	when	SCONJ
cana-2791	47	69	g1	g1	PROPN
cana-2791	47	70	is	be	AUX
cana-2791	47	71	a	a	DET
cana-2791	47	72	complete	complete	ADJ
cana-2791	47	73	graph	graph	NOUN
cana-2791	47	74	and	and	CCONJ
cana-2791	47	75	g2	g2	PROPN
cana-2791	47	76	is	be	AUX
cana-2791	47	77	a	a	DET
cana-2791	47	78	cycle	cycle	NOUN
cana-2791	47	79	graph	graph	NOUN
cana-2791	47	80	with	with	ADP
cana-2791	47	81	different	different	ADJ
cana-2791	47	82	number	number	NOUN
cana-2791	47	83	of	of	ADP
cana-2791	47	84	vertices	vertex	NOUN
cana-2791	47	85	.	.	PUNCT
cana-2791	48	1	2	2	NUM
cana-2791	48	2	inverse	inverse	NOUN
cana-2791	48	3	independent	independent	ADJ
cana-2791	48	4	outer	outer	ADJ
cana-2791	48	5	connected	connected	ADJ
cana-2791	48	6	domination	domination	NOUN
cana-2791	48	7	number	number	NOUN
cana-2791	48	8	of	of	ADP
cana-2791	48	9	the	the	DET
cana-2791	48	10	sierpinski	sierpinski	ADJ
cana-2791	48	11	graphs	graph	NOUN
cana-2791	48	12	theorem	theorem	VERB
cana-2791	48	13	2.1	2.1	NUM
cana-2791	48	14	.	.	PUNCT
cana-2791	49	1	let	let	VERB
cana-2791	49	2	s(n	s(n	PROPN
cana-2791	49	3	,	,	PUNCT
cana-2791	49	4	k	k	NOUN
cana-2791	49	5	)	)	PUNCT
cana-2791	49	6	be	be	VERB
cana-2791	49	7	a	a	DET
cana-2791	49	8	sierpinski	sierpinski	ADJ
cana-2791	49	9	graph	graph	NOUN
cana-2791	49	10	,	,	PUNCT
cana-2791	49	11	consisting	consist	VERB
cana-2791	49	12	of	of	ADP
cana-2791	49	13	k	k	PROPN
cana-2791	49	14	copies	copy	NOUN
cana-2791	49	15	of	of	ADP
cana-2791	49	16	s(n−1	s(n−1	PROPN
cana-2791	49	17	,	,	PUNCT
cana-2791	49	18	k	k	NOUN
cana-2791	49	19	)	)	PUNCT
cana-2791	49	20	for	for	ADP
cana-2791	49	21	n	n	PROPN
cana-2791	49	22	>	>	X
cana-2791	49	23	1	1	NUM
cana-2791	49	24	,	,	PUNCT
cana-2791	49	25	k	k	PROPN
cana-2791	49	26	is	be	AUX
cana-2791	49	27	the	the	DET
cana-2791	49	28	number	number	NOUN
cana-2791	49	29	of	of	ADP
cana-2791	49	30	vertices	vertex	NOUN
cana-2791	49	31	in	in	ADP
cana-2791	49	32	the	the	DET
cana-2791	49	33	complete	complete	ADJ
cana-2791	49	34	graph	graph	NOUN
cana-2791	49	35	,	,	PUNCT
cana-2791	49	36	then	then	ADV
cana-2791	49	37	γ−1	γ−1	PROPN
cana-2791	49	38	(	(	PUNCT
cana-2791	49	39	s(n	s(n	PROPN
cana-2791	49	40	,	,	PUNCT
cana-2791	49	41	k	k	NOUN
cana-2791	49	42	)	)	PUNCT
cana-2791	49	43	)	)	PUNCT
cana-2791	50	1	=	=	PUNCT
cana-2791	50	2	kn−1where	kn−1where	PROPN
cana-2791	50	3	k	k	PROPN
cana-2791	50	4	≥	≥	NUM
cana-2791	50	5	5	5	NUM
cana-2791	50	6	,	,	PUNCT
cana-2791	50	7	and	and	CCONJ
cana-2791	50	8	n	n	PRON
cana-2791	50	9	≥	≥	NOUN
cana-2791	50	10	1	1	NUM
cana-2791	50	11	proof	proof	NOUN
cana-2791	50	12	.	.	PUNCT
cana-2791	51	1	apply	apply	VERB
cana-2791	51	2	induction	induction	NOUN
cana-2791	51	3	on	on	ADP
cana-2791	51	4	′n′.	′n′.	PUNCT
cana-2791	51	5	for	for	ADP
cana-2791	51	6	the	the	DET
cana-2791	51	7	initial	initial	ADJ
cana-2791	51	8	value	value	NOUN
cana-2791	51	9	n	n	NOUN
cana-2791	51	10	=	=	SYM
cana-2791	51	11	1	1	NUM
cana-2791	51	12	γ̃−1	γ̃−1	PROPN
cana-2791	51	13	(	(	PUNCT
cana-2791	51	14	s(1	s(1	PROPN
cana-2791	51	15	,	,	PUNCT
cana-2791	51	16	k	k	NOUN
cana-2791	51	17	)	)	PUNCT
cana-2791	51	18	)	)	PUNCT
cana-2791	52	1	=	=	SYM
cana-2791	52	2	k0	k0	PROPN
cana-2791	52	3	=	=	PROPN
cana-2791	52	4	1	1	NUM
cana-2791	52	5	here	here	ADV
cana-2791	52	6	all	all	DET
cana-2791	52	7	the	the	DET
cana-2791	52	8	k′s	k′s	PROPN
cana-2791	52	9	are	be	AUX
cana-2791	52	10	the	the	DET
cana-2791	52	11	number	number	NOUN
cana-2791	52	12	of	of	ADP
cana-2791	52	13	vertices	vertex	NOUN
cana-2791	52	14	in	in	ADP
cana-2791	52	15	a	a	DET
cana-2791	52	16	complete	complete	ADJ
cana-2791	52	17	graph	graph	NOUN
cana-2791	52	18	.	.	PUNCT
cana-2791	53	1	we	we	PRON
cana-2791	53	2	know	know	VERB
cana-2791	53	3	the	the	DET
cana-2791	53	4	iiocd	iiocd	ADJ
cana-2791	53	5	number	number	NOUN
cana-2791	53	6	of	of	ADP
cana-2791	53	7	a	a	DET
cana-2791	53	8	complete	complete	ADJ
cana-2791	53	9	graph	graph	NOUN
cana-2791	53	10	is	be	AUX
cana-2791	53	11	1	1	NUM
cana-2791	53	12	.	.	PUNCT
cana-2791	54	1	the	the	DET
cana-2791	54	2	outer	outer	ADJ
cana-2791	54	3	connectedness	connectedness	NOUN
cana-2791	54	4	property	property	NOUN
cana-2791	54	5	:	:	PUNCT
cana-2791	54	6	after	after	ADP
cana-2791	54	7	the	the	DET
cana-2791	54	8	removal	removal	NOUN
cana-2791	54	9	of	of	ADP
cana-2791	54	10	one	one	NUM
cana-2791	54	11	vertex	vertex	NOUN
cana-2791	54	12	from	from	ADP
cana-2791	54	13	a	a	DET
cana-2791	54	14	complete	complete	ADJ
cana-2791	54	15	graph	graph	NOUN
cana-2791	54	16	with	with	ADP
cana-2791	54	17	k	k	PROPN
cana-2791	54	18	vertices	vertex	NOUN
cana-2791	54	19	,	,	PUNCT
cana-2791	54	20	the	the	DET
cana-2791	54	21	graph	graph	NOUN
cana-2791	54	22	will	will	AUX
cana-2791	54	23	still	still	ADV
cana-2791	54	24	be	be	AUX
cana-2791	54	25	a	a	DET
cana-2791	54	26	connected	connected	ADJ
cana-2791	54	27	graph	graph	NOUN
cana-2791	54	28	.	.	PUNCT
cana-2791	55	1	hence	hence	ADV
cana-2791	55	2	γ̃−1	γ̃−1	PUNCT
cana-2791	55	3	(	(	PUNCT
cana-2791	55	4	s(1	s(1	PROPN
cana-2791	55	5	,	,	PUNCT
cana-2791	55	6	k	k	PROPN
cana-2791	55	7	)	)	PUNCT
cana-2791	55	8	)	)	PUNCT
cana-2791	56	1	=	=	SYM
cana-2791	56	2	k0	k0	PROPN
cana-2791	56	3	,	,	PUNCT
cana-2791	56	4	k	k	PROPN
cana-2791	56	5	≥	≥	NUM
cana-2791	56	6	5	5	NUM
cana-2791	56	7	,	,	PUNCT
cana-2791	56	8	n	n	NOUN
cana-2791	56	9	=	=	SYM
cana-2791	56	10	1	1	NUM
cana-2791	56	11	holds	hold	VERB
cana-2791	56	12	true	true	ADJ
cana-2791	56	13	.	.	PUNCT
cana-2791	57	1	figure	figure	VERB
cana-2791	57	2	1	1	NUM
cana-2791	57	3	:	:	PUNCT
cana-2791	57	4	(	(	PUNCT
cana-2791	57	5	s(1	s(1	PROPN
cana-2791	57	6	,	,	PUNCT
cana-2791	57	7	5	5	NUM
cana-2791	57	8	)	)	PUNCT
cana-2791	57	9	)	)	PUNCT
cana-2791	58	1	γ̃−1	γ̃−1	PROPN
cana-2791	58	2	we	we	PRON
cana-2791	58	3	make	make	VERB
cana-2791	58	4	an	an	DET
cana-2791	58	5	assumption	assumption	NOUN
cana-2791	58	6	that	that	SCONJ
cana-2791	58	7	for	for	ADP
cana-2791	58	8	n	n	NOUN
cana-2791	58	9	=	=	PRON
cana-2791	58	10	i	i	PRON
cana-2791	58	11	the	the	DET
cana-2791	58	12	result	result	NOUN
cana-2791	58	13	holds	hold	VERB
cana-2791	58	14	true	true	ADJ
cana-2791	58	15	.	.	PUNCT
cana-2791	59	1	(	(	PUNCT
cana-2791	59	2	s(i	s(i	PROPN
cana-2791	59	3	,	,	PUNCT
cana-2791	59	4	k	k	NOUN
cana-2791	59	5	)	)	PUNCT
cana-2791	59	6	)	)	PUNCT
cana-2791	60	1	=	=	SYM
cana-2791	60	2	ki−1	ki−1	PROPN
cana-2791	60	3	,	,	PUNCT
cana-2791	60	4	k	k	PROPN
cana-2791	60	5	≥	≥	NUM
cana-2791	60	6	5	5	NUM
cana-2791	60	7	,	,	PUNCT
cana-2791	60	8	n	n	NOUN
cana-2791	60	9	=	=	NOUN
cana-2791	60	10	i.	i.	NOUN
cana-2791	60	11	communications	communication	NOUN
cana-2791	60	12	on	on	ADP
cana-2791	60	13	applied	apply	VERB
cana-2791	60	14	nonlinear	nonlinear	ADJ
cana-2791	60	15	analysis	analysis	NOUN
cana-2791	60	16	issn	issn	NOUN
cana-2791	60	17	:	:	PUNCT
cana-2791	60	18	1074	1074	NUM
cana-2791	60	19	-	-	PUNCT
cana-2791	60	20	133x	133x	NUM
cana-2791	60	21	vol	vol	NOUN
cana-2791	60	22	32	32	NUM
cana-2791	60	23	no	no	NOUN
cana-2791	60	24	.	.	PUNCT
cana-2791	61	1	4s	4s	NUM
cana-2791	61	2	(	(	PUNCT
cana-2791	61	3	2025	2025	NUM
cana-2791	61	4	)	)	PUNCT
cana-2791	62	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2791	62	2	249	249	NUM
cana-2791	62	3	ioc	ioc	PROPN
cana-2791	62	4	×	×	NOUN
cana-2791	62	5	ioc	ioc	NOUN
cana-2791	62	6	γ̃−	γ̃−	VERB
cana-2791	62	7	to	to	PART
cana-2791	62	8	be	be	AUX
cana-2791	62	9	proved	prove	VERB
cana-2791	62	10	that	that	SCONJ
cana-2791	62	11	for	for	ADP
cana-2791	62	12	n	n	NOUN
cana-2791	62	13	=	=	NOUN
cana-2791	62	14	i	i	PRON
cana-2791	62	15	+	+	NOUN
cana-2791	62	16	1	1	NUM
cana-2791	62	17	,	,	PUNCT
cana-2791	62	18	γ̃−1	γ̃−1	X
cana-2791	62	19	(	(	PUNCT
cana-2791	62	20	s(i	s(i	NOUN
cana-2791	62	21	+	+	NOUN
cana-2791	62	22	1	1	NUM
cana-2791	62	23	,	,	PUNCT
cana-2791	62	24	k	k	NOUN
cana-2791	62	25	)	)	PUNCT
cana-2791	62	26	)	)	PUNCT
cana-2791	63	1	=	=	SYM
cana-2791	63	2	k(i+1)−1	k(i+1)−1	PROPN
cana-2791	63	3	,	,	PUNCT
cana-2791	63	4	k	k	PROPN
cana-2791	63	5	≥	≥	NUM
cana-2791	63	6	5	5	NUM
cana-2791	63	7	,	,	PUNCT
cana-2791	63	8	n	n	NOUN
cana-2791	63	9	=	=	SYM
cana-2791	64	1	i	i	PRON
cana-2791	64	2	+	+	NOUN
cana-2791	64	3	1	1	NUM
cana-2791	64	4	figure	figure	NOUN
cana-2791	64	5	2	2	NUM
cana-2791	64	6	:	:	PUNCT
cana-2791	64	7	(	(	PUNCT
cana-2791	64	8	s(2	s(2	NOUN
cana-2791	64	9	,	,	PUNCT
cana-2791	64	10	5	5	NUM
cana-2791	64	11	)	)	PUNCT
cana-2791	64	12	)	)	PUNCT
cana-2791	64	13	figure	figure	NOUN
cana-2791	64	14	3	3	NUM
cana-2791	64	15	:	:	PUNCT
cana-2791	64	16	(	(	PUNCT
cana-2791	64	17	s(3	s(3	PROPN
cana-2791	64	18	,	,	PUNCT
cana-2791	64	19	5	5	NUM
cana-2791	64	20	)	)	PUNCT
cana-2791	64	21	)	)	PUNCT
cana-2791	64	22	by	by	ADP
cana-2791	64	23	the	the	DET
cana-2791	64	24	definition	definition	NOUN
cana-2791	64	25	of	of	ADP
cana-2791	64	26	sierpinski	sierpinski	ADJ
cana-2791	64	27	graphs	graph	NOUN
cana-2791	64	28	,	,	PUNCT
cana-2791	64	29	there	there	PRON
cana-2791	64	30	will	will	AUX
cana-2791	64	31	be	be	AUX
cana-2791	64	32	′k′	′k′	NOUN
cana-2791	64	33	copies	copy	NOUN
cana-2791	64	34	of	of	ADP
cana-2791	64	35	s(n	s(n	PROPN
cana-2791	64	36	,	,	PUNCT
cana-2791	64	37	k	k	NOUN
cana-2791	64	38	)	)	PUNCT
cana-2791	64	39	incorporated	incorporate	VERB
cana-2791	64	40	inside	inside	ADP
cana-2791	64	41	s(n	s(n	PROPN
cana-2791	64	42	+	+	CCONJ
cana-2791	64	43	1	1	NUM
cana-2791	64	44	,	,	PUNCT
cana-2791	64	45	k	k	NOUN
cana-2791	64	46	)	)	PUNCT
cana-2791	64	47	and	and	CCONJ
cana-2791	64	48	the	the	DET
cana-2791	64	49	unit	unit	NOUN
cana-2791	64	50	graphs	graph	NOUN
cana-2791	64	51	will	will	AUX
cana-2791	64	52	always	always	ADV
cana-2791	64	53	be	be	AUX
cana-2791	64	54	complete	complete	ADJ
cana-2791	64	55	graphs	graph	NOUN
cana-2791	64	56	and	and	CCONJ
cana-2791	64	57	hence	hence	ADV
cana-2791	64	58	we	we	PRON
cana-2791	64	59	take	take	VERB
cana-2791	64	60	kn−1	kn−1	PROPN
cana-2791	64	61	number	number	NOUN
cana-2791	64	62	of	of	ADP
cana-2791	64	63	vertices	vertex	NOUN
cana-2791	64	64	from	from	ADP
cana-2791	64	65	each	each	DET
cana-2791	64	66	copy	copy	NOUN
cana-2791	64	67	.	.	PUNCT
cana-2791	65	1	figure	figure	NOUN
cana-2791	65	2	2	2	NUM
cana-2791	65	3	and	and	CCONJ
cana-2791	65	4	figure	figure	VERB
cana-2791	65	5	3	3	NUM
cana-2791	65	6	show	show	VERB
cana-2791	65	7	the	the	DET
cana-2791	65	8	sierpinski	sierpinski	ADJ
cana-2791	65	9	graphs	graph	NOUN
cana-2791	65	10	for	for	ADP
cana-2791	65	11	k=5	k=5	PROPN
cana-2791	65	12	and	and	CCONJ
cana-2791	65	13	n=2	n=2	ADV
cana-2791	65	14	and	and	CCONJ
cana-2791	65	15	n=3	n=3	PUNCT
cana-2791	65	16	respectively	respectively	ADV
cana-2791	65	17	.	.	PUNCT
cana-2791	66	1	finally	finally	ADV
cana-2791	66	2	we	we	PRON
cana-2791	66	3	will	will	AUX
cana-2791	66	4	be	be	AUX
cana-2791	66	5	left	leave	VERB
cana-2791	66	6	with	with	ADP
cana-2791	66	7	k	k	PROPN
cana-2791	66	8	kn−1	kn−1	PROPN
cana-2791	66	9	number	number	NOUN
cana-2791	66	10	of	of	ADP
cana-2791	66	11	vertices	vertex	NOUN
cana-2791	66	12	that	that	PRON
cana-2791	66	13	dominates	dominate	VERB
cana-2791	66	14	all	all	DET
cana-2791	66	15	the	the	DET
cana-2791	66	16	edges	edge	NOUN
cana-2791	66	17	of	of	ADP
cana-2791	66	18	s(n	s(n	PROPN
cana-2791	66	19	+	+	CCONJ
cana-2791	66	20	1	1	NUM
cana-2791	66	21	,	,	PUNCT
cana-2791	66	22	k	k	NOUN
cana-2791	66	23	)	)	PUNCT
cana-2791	66	24	.	.	PUNCT
cana-2791	67	1	therefore	therefore	ADV
cana-2791	67	2	,	,	PUNCT
cana-2791	67	3	γ̃−1	γ̃−1	X
cana-2791	67	4	(	(	PUNCT
cana-2791	67	5	s(n	s(n	PROPN
cana-2791	67	6	,	,	PUNCT
cana-2791	67	7	k	k	NOUN
cana-2791	67	8	)	)	PUNCT
cana-2791	67	9	)	)	PUNCT
cana-2791	67	10	=	=	PUNCT
cana-2791	68	1	k	k	PROPN
cana-2791	68	2	×	×	PROPN
cana-2791	68	3	ki−1	ki−1	PROPN
cana-2791	68	4	=	=	PUNCT
cana-2791	68	5	ki	ki	PROPN
cana-2791	68	6	=	=	PROPN
cana-2791	68	7	k(i+1)−1	k(i+1)−1	PROPN
cana-2791	68	8	,	,	PUNCT
cana-2791	68	9	k	k	PROPN
cana-2791	68	10	≥	≥	NUM
cana-2791	68	11	5	5	NUM
cana-2791	68	12	,	,	PUNCT
cana-2791	68	13	n	n	NOUN
cana-2791	68	14	=	=	SYM
cana-2791	69	1	i	i	PRON
cana-2791	69	2	+	+	NOUN
cana-2791	69	3	1	1	NUM
cana-2791	69	4	the	the	DET
cana-2791	69	5	outer	outer	ADJ
cana-2791	69	6	connectedness	connectedness	NOUN
cana-2791	69	7	property	property	NOUN
cana-2791	69	8	:	:	PUNCT
cana-2791	69	9	to	to	PART
cana-2791	69	10	ensure	ensure	VERB
cana-2791	69	11	the	the	DET
cana-2791	69	12	outer	outer	ADJ
cana-2791	69	13	connectedness	connectedness	NOUN
cana-2791	69	14	,	,	PUNCT
cana-2791	69	15	vertex	vertex	NOUN
cana-2791	69	16	chosen	choose	VERB
cana-2791	69	17	must	must	AUX
cana-2791	69	18	be	be	AUX
cana-2791	69	19	such	such	ADJ
cana-2791	69	20	that	that	SCONJ
cana-2791	69	21	,	,	PUNCT
cana-2791	69	22	they	they	PRON
cana-2791	69	23	do	do	AUX
cana-2791	69	24	nt	not	PART
cana-2791	69	25	engulf	engulf	VERB
cana-2791	69	26	one	one	NUM
cana-2791	69	27	unit	unit	NOUN
cana-2791	69	28	and	and	CCONJ
cana-2791	69	29	isolate	isolate	VERB
cana-2791	69	30	it	it	PRON
cana-2791	69	31	after	after	ADP
cana-2791	69	32	the	the	DET
cana-2791	69	33	vertex	vertex	NOUN
cana-2791	69	34	deletion	deletion	NOUN
cana-2791	69	35	as	as	SCONJ
cana-2791	69	36	the	the	DET
cana-2791	69	37	induced	induced	ADJ
cana-2791	69	38	subgraph	subgraph	NOUN
cana-2791	69	39	must	must	AUX
cana-2791	69	40	be	be	AUX
cana-2791	69	41	connected	connect	VERB
cana-2791	69	42	.	.	PUNCT
cana-2791	70	1	hence	hence	ADV
cana-2791	70	2	the	the	DET
cana-2791	70	3	result	result	NOUN
cana-2791	70	4	1	1	NUM
cana-2791	70	5	ioc	ioc	X
cana-2791	70	6	(	(	PUNCT
cana-2791	70	7	s(n	s(n	PROPN
cana-2791	70	8	,	,	PUNCT
cana-2791	70	9	k	k	NOUN
cana-2791	70	10	)	)	PUNCT
cana-2791	70	11	)	)	PUNCT
cana-2791	71	1	=	=	SYM
cana-2791	71	2	kn−1	kn−1	PROPN
cana-2791	71	3	,	,	PUNCT
cana-2791	71	4	k	k	PROPN
cana-2791	71	5	≥	≥	NUM
cana-2791	71	6	5	5	NUM
cana-2791	71	7	,	,	PUNCT
cana-2791	71	8	n	n	PRON
cana-2791	71	9	≥	≥	NOUN
cana-2791	71	10	1	1	NUM
cana-2791	71	11	.	.	PUNCT
cana-2791	72	1	communications	communication	NOUN
cana-2791	72	2	on	on	ADP
cana-2791	72	3	applied	apply	VERB
cana-2791	72	4	nonlinear	nonlinear	ADJ
cana-2791	72	5	analysis	analysis	NOUN
cana-2791	72	6	issn	issn	NOUN
cana-2791	72	7	:	:	PUNCT
cana-2791	72	8	1074	1074	NUM
cana-2791	72	9	-	-	PUNCT
cana-2791	72	10	133x	133x	NUM
cana-2791	72	11	vol	vol	NOUN
cana-2791	72	12	32	32	NUM
cana-2791	72	13	no	no	NOUN
cana-2791	72	14	.	.	PUNCT
cana-2791	73	1	4s	4s	NUM
cana-2791	73	2	(	(	PUNCT
cana-2791	73	3	2025	2025	NUM
cana-2791	73	4	)	)	PUNCT
cana-2791	74	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2791	74	2	250	250	NUM
cana-2791	74	3	γ̃−	γ̃−	ADJ
cana-2791	74	4	ioc	ioc	PROPN
cana-2791	74	5	ioc	ioc	PROPN
cana-2791	74	6	ioc	ioc	AUX
cana-2791	74	7	×	×	NOUN
cana-2791	74	8	γ̃−	γ̃−	ADJ
cana-2791	74	9	γ̃−	γ̃−	CCONJ
cana-2791	74	10	γ̃−	γ̃−	NUM
cana-2791	74	11	ioc	ioc	NOUN
cana-2791	74	12	3	3	NUM
cana-2791	74	13	inverse	inverse	NOUN
cana-2791	74	14	independent	independent	ADJ
cana-2791	74	15	outer	outer	ADJ
cana-2791	74	16	connected	connected	ADJ
cana-2791	74	17	domination	domination	NOUN
cana-2791	74	18	number	number	NOUN
cana-2791	74	19	of	of	ADP
cana-2791	74	20	extended	extended	ADJ
cana-2791	74	21	sierpinski	sierpinski	ADJ
cana-2791	74	22	graph	graph	NOUN
cana-2791	74	23	s+(n	s+(n	NOUN
cana-2791	74	24	,	,	PUNCT
cana-2791	74	25	k	k	NOUN
cana-2791	74	26	)	)	PUNCT
cana-2791	74	27	theorem	theorem	VERB
cana-2791	74	28	3.1	3.1	NUM
cana-2791	74	29	.	.	PUNCT
cana-2791	75	1	let	let	VERB
cana-2791	75	2	s+(n	s+(n	NOUN
cana-2791	75	3	,	,	PUNCT
cana-2791	75	4	k	k	NOUN
cana-2791	75	5	)	)	PUNCT
cana-2791	75	6	be	be	AUX
cana-2791	75	7	a	a	DET
cana-2791	75	8	sierpinski	sierpinski	ADJ
cana-2791	75	9	-	-	PUNCT
cana-2791	75	10	like	like	ADJ
cana-2791	75	11	graph	graph	NOUN
cana-2791	75	12	,	,	PUNCT
cana-2791	75	13	where	where	SCONJ
cana-2791	75	14	the	the	DET
cana-2791	75	15	end	end	NOUN
cana-2791	75	16	vertices	vertex	NOUN
cana-2791	75	17	of	of	ADP
cana-2791	75	18	the	the	DET
cana-2791	75	19	sier	sier	ADJ
cana-2791	75	20	pinski	pinski	ADJ
cana-2791	75	21	graph	graph	NOUN
cana-2791	75	22	s(n	s(n	PROPN
cana-2791	75	23	,	,	PUNCT
cana-2791	75	24	k	k	NOUN
cana-2791	75	25	)	)	PUNCT
cana-2791	75	26	is	be	AUX
cana-2791	75	27	connected	connect	VERB
cana-2791	75	28	to	to	ADP
cana-2791	75	29	an	an	DET
cana-2791	75	30	extra	extra	ADJ
cana-2791	75	31	vertex	vertex	NOUN
cana-2791	75	32	then	then	ADV
cana-2791	75	33	,	,	PUNCT
cana-2791	75	34	1	1	NUM
cana-2791	75	35	ioc	ioc	NOUN
cana-2791	75	36	(	(	PUNCT
cana-2791	75	37	s+(n	s+(n	NOUN
cana-2791	75	38	,	,	PUNCT
cana-2791	75	39	k	k	NOUN
cana-2791	75	40	)	)	PUNCT
cana-2791	75	41	)	)	PUNCT
cana-2791	76	1	=	=	SYM
cana-2791	76	2	kn−1	kn−1	PROPN
cana-2791	76	3	,	,	PUNCT
cana-2791	76	4	where	where	SCONJ
cana-2791	76	5	k	k	PROPN
cana-2791	76	6	≥	≥	NUM
cana-2791	76	7	5	5	NUM
cana-2791	76	8	,	,	PUNCT
cana-2791	76	9	and	and	CCONJ
cana-2791	76	10	n	n	PRON
cana-2791	76	11	≥	≥	NOUN
cana-2791	76	12	1	1	NUM
cana-2791	76	13	proof	proof	NOUN
cana-2791	76	14	.	.	PUNCT
cana-2791	77	1	apply	apply	VERB
cana-2791	77	2	induction	induction	NOUN
cana-2791	77	3	on	on	ADP
cana-2791	77	4	′n′.	′n′.	PUNCT
cana-2791	77	5	for	for	ADP
cana-2791	77	6	the	the	DET
cana-2791	77	7	initial	initial	ADJ
cana-2791	77	8	value	value	NOUN
cana-2791	77	9	n	n	NOUN
cana-2791	77	10	=	=	SYM
cana-2791	77	11	1	1	NUM
cana-2791	77	12	γ̃−1	γ̃−1	PROPN
cana-2791	77	13	(	(	PUNCT
cana-2791	77	14	s+(1	s+(1	NOUN
cana-2791	77	15	,	,	PUNCT
cana-2791	77	16	k	k	NOUN
cana-2791	77	17	)	)	PUNCT
cana-2791	77	18	)	)	PUNCT
cana-2791	78	1	=	=	SYM
cana-2791	78	2	k0	k0	PROPN
cana-2791	78	3	=	=	PROPN
cana-2791	78	4	1	1	NUM
cana-2791	78	5	here	here	ADV
cana-2791	78	6	all	all	DET
cana-2791	78	7	the	the	DET
cana-2791	78	8	k′s	k′s	PROPN
cana-2791	78	9	are	be	AUX
cana-2791	78	10	the	the	DET
cana-2791	78	11	number	number	NOUN
cana-2791	78	12	of	of	ADP
cana-2791	78	13	vertices	vertex	NOUN
cana-2791	78	14	in	in	ADP
cana-2791	78	15	a	a	DET
cana-2791	78	16	complete	complete	ADJ
cana-2791	78	17	graph	graph	NOUN
cana-2791	78	18	.	.	PUNCT
cana-2791	79	1	we	we	PRON
cana-2791	79	2	know	know	VERB
cana-2791	79	3	the	the	DET
cana-2791	79	4	iiocd	iiocd	ADJ
cana-2791	79	5	number	number	NOUN
cana-2791	79	6	of	of	ADP
cana-2791	79	7	a	a	DET
cana-2791	79	8	complete	complete	ADJ
cana-2791	79	9	graph	graph	NOUN
cana-2791	79	10	is	be	AUX
cana-2791	79	11	1,and	1,and	NUM
cana-2791	79	12	also	also	ADV
cana-2791	79	13	the	the	DET
cana-2791	79	14	end	end	NOUN
cana-2791	79	15	vertices	vertex	NOUN
cana-2791	79	16	of	of	ADP
cana-2791	79	17	s(1	s(1	PROPN
cana-2791	79	18	,	,	PUNCT
cana-2791	79	19	k	k	PROPN
cana-2791	79	20	)	)	PUNCT
cana-2791	79	21	are	be	AUX
cana-2791	79	22	connected	connect	VERB
cana-2791	79	23	to	to	ADP
cana-2791	79	24	an	an	DET
cana-2791	79	25	extra	extra	ADJ
cana-2791	79	26	vertex	vertex	NOUN
cana-2791	79	27	’s	’s	NOUN
cana-2791	79	28	’	'	PUNCT
cana-2791	79	29	.	.	PUNCT
cana-2791	80	1	the	the	DET
cana-2791	80	2	outer	outer	ADJ
cana-2791	80	3	connectedness	connectedness	NOUN
cana-2791	80	4	property	property	NOUN
cana-2791	80	5	:	:	PUNCT
cana-2791	80	6	after	after	ADP
cana-2791	80	7	the	the	DET
cana-2791	80	8	removal	removal	NOUN
cana-2791	80	9	of	of	ADP
cana-2791	80	10	one	one	NUM
cana-2791	80	11	vertex	vertex	NOUN
cana-2791	80	12	from	from	ADP
cana-2791	80	13	a	a	DET
cana-2791	80	14	complete	complete	ADJ
cana-2791	80	15	graph	graph	NOUN
cana-2791	80	16	with	with	ADP
cana-2791	80	17	k	k	PROPN
cana-2791	80	18	vertices	vertex	NOUN
cana-2791	80	19	,	,	PUNCT
cana-2791	80	20	the	the	DET
cana-2791	80	21	graph	graph	NOUN
cana-2791	80	22	will	will	AUX
cana-2791	80	23	still	still	ADV
cana-2791	80	24	be	be	AUX
cana-2791	80	25	a	a	DET
cana-2791	80	26	connected	connected	ADJ
cana-2791	80	27	graph	graph	NOUN
cana-2791	80	28	.	.	PUNCT
cana-2791	81	1	hence	hence	ADV
cana-2791	81	2	γ̃−1	γ̃−1	PROPN
cana-2791	81	3	(	(	PUNCT
cana-2791	81	4	s+(1	s+(1	NOUN
cana-2791	81	5	,	,	PUNCT
cana-2791	81	6	k	k	NOUN
cana-2791	81	7	)	)	PUNCT
cana-2791	81	8	)	)	PUNCT
cana-2791	82	1	=	=	SYM
cana-2791	82	2	k0	k0	PROPN
cana-2791	82	3	,	,	PUNCT
cana-2791	82	4	k	k	PROPN
cana-2791	82	5	≥	≥	NUM
cana-2791	82	6	5	5	NUM
cana-2791	82	7	,	,	PUNCT
cana-2791	82	8	n	n	NOUN
cana-2791	82	9	=	=	SYM
cana-2791	82	10	1	1	NUM
cana-2791	82	11	holds	hold	VERB
cana-2791	82	12	true	true	ADJ
cana-2791	82	13	.	.	PUNCT
cana-2791	83	1	γ̃−1	γ̃−1	PROPN
cana-2791	83	2	we	we	PRON
cana-2791	83	3	make	make	VERB
cana-2791	83	4	an	an	DET
cana-2791	83	5	assumption	assumption	NOUN
cana-2791	83	6	that	that	SCONJ
cana-2791	83	7	for	for	ADP
cana-2791	83	8	n	n	NOUN
cana-2791	83	9	=	=	PRON
cana-2791	83	10	i	i	PRON
cana-2791	83	11	the	the	DET
cana-2791	83	12	result	result	NOUN
cana-2791	83	13	holds	hold	VERB
cana-2791	83	14	good	good	ADJ
cana-2791	83	15	.	.	PUNCT
cana-2791	84	1	(	(	PUNCT
cana-2791	84	2	s+(i	s+(i	PROPN
cana-2791	84	3	,	,	PUNCT
cana-2791	84	4	k	k	NOUN
cana-2791	84	5	)	)	PUNCT
cana-2791	84	6	)	)	PUNCT
cana-2791	85	1	=	=	SYM
cana-2791	85	2	ki−1	ki−1	PROPN
cana-2791	85	3	,	,	PUNCT
cana-2791	85	4	k	k	PROPN
cana-2791	85	5	≥	≥	NUM
cana-2791	85	6	5	5	NUM
cana-2791	85	7	,	,	PUNCT
cana-2791	85	8	n	n	PROPN
cana-2791	85	9	=	=	PROPN
cana-2791	85	10	i.	i.	PROPN
cana-2791	85	11	ioc	ioc	PROPN
cana-2791	85	12	to	to	PART
cana-2791	85	13	be	be	AUX
cana-2791	85	14	proved	prove	VERB
cana-2791	85	15	that	that	SCONJ
cana-2791	85	16	for	for	ADP
cana-2791	85	17	n	n	NOUN
cana-2791	85	18	=	=	SYM
cana-2791	86	1	i	i	PRON
cana-2791	86	2	+	+	NOUN
cana-2791	86	3	1	1	NUM
cana-2791	86	4	γ̃−1	γ̃−1	PROPN
cana-2791	86	5	(	(	PUNCT
cana-2791	86	6	s+(i	s+(i	PROPN
cana-2791	86	7	+	+	CCONJ
cana-2791	86	8	1	1	NUM
cana-2791	86	9	,	,	PUNCT
cana-2791	86	10	k	k	NOUN
cana-2791	86	11	)	)	PUNCT
cana-2791	86	12	)	)	PUNCT
cana-2791	87	1	=	=	SYM
cana-2791	87	2	k(i+1)−1	k(i+1)−1	PROPN
cana-2791	87	3	,	,	PUNCT
cana-2791	87	4	k	k	PROPN
cana-2791	87	5	≥	≥	NUM
cana-2791	87	6	5	5	NUM
cana-2791	87	7	,	,	PUNCT
cana-2791	87	8	n	n	NOUN
cana-2791	87	9	=	=	SYM
cana-2791	88	1	i	i	PRON
cana-2791	88	2	+	+	NOUN
cana-2791	88	3	1	1	NUM
cana-2791	88	4	by	by	ADP
cana-2791	88	5	the	the	DET
cana-2791	88	6	definition	definition	NOUN
cana-2791	88	7	of	of	ADP
cana-2791	88	8	the	the	DET
cana-2791	88	9	extended	extended	ADJ
cana-2791	88	10	sierpinski	sierpinski	ADJ
cana-2791	88	11	graphs	graph	NOUN
cana-2791	88	12	s+(n	s+(n	NOUN
cana-2791	88	13	,	,	PUNCT
cana-2791	88	14	k	k	NOUN
cana-2791	88	15	)	)	PUNCT
cana-2791	88	16	is	be	AUX
cana-2791	88	17	obtained	obtain	VERB
cana-2791	88	18	from	from	ADP
cana-2791	88	19	s(n	s(n	PROPN
cana-2791	88	20	,	,	PUNCT
cana-2791	88	21	k	k	NOUN
cana-2791	88	22	)	)	PUNCT
cana-2791	88	23	by	by	ADP
cana-2791	88	24	adding	add	VERB
cana-2791	88	25	an	an	DET
cana-2791	88	26	extra	extra	ADJ
cana-2791	88	27	vertex	vertex	NOUN
cana-2791	88	28	′s′,and	′s′,and	PROPN
cana-2791	88	29	edges	edge	NOUN
cana-2791	88	30	joining	join	VERB
cana-2791	88	31	s	s	PRON
cana-2791	88	32	to	to	ADP
cana-2791	88	33	all	all	DET
cana-2791	88	34	extreme	extreme	ADJ
cana-2791	88	35	vertices	vertex	NOUN
cana-2791	88	36	of	of	ADP
cana-2791	88	37	s(n	s(n	PROPN
cana-2791	88	38	,	,	PUNCT
cana-2791	88	39	k	k	NOUN
cana-2791	88	40	)	)	PUNCT
cana-2791	88	41	.	.	PUNCT
cana-2791	89	1	the	the	DET
cana-2791	89	2	unit	unit	NOUN
cana-2791	89	3	graphs	graph	NOUN
cana-2791	89	4	will	will	AUX
cana-2791	89	5	always	always	ADV
cana-2791	89	6	be	be	AUX
cana-2791	89	7	complete	complete	ADJ
cana-2791	89	8	graphs	graph	NOUN
cana-2791	89	9	and	and	CCONJ
cana-2791	89	10	hence	hence	ADV
cana-2791	89	11	we	we	PRON
cana-2791	89	12	take	take	VERB
cana-2791	89	13	kn−1	kn−1	PROPN
cana-2791	89	14	number	number	NOUN
cana-2791	89	15	of	of	ADP
cana-2791	89	16	vertices	vertex	NOUN
cana-2791	89	17	from	from	ADP
cana-2791	89	18	each	each	DET
cana-2791	89	19	copy	copy	NOUN
cana-2791	89	20	and	and	CCONJ
cana-2791	89	21	any	any	DET
cana-2791	89	22	one	one	NUM
cana-2791	89	23	of	of	ADP
cana-2791	89	24	these	these	DET
cana-2791	89	25	vertices	vertex	NOUN
cana-2791	89	26	will	will	AUX
cana-2791	89	27	be	be	AUX
cana-2791	89	28	an	an	DET
cana-2791	89	29	end	end	NOUN
cana-2791	89	30	vertex	vertex	NOUN
cana-2791	89	31	and	and	CCONJ
cana-2791	89	32	hence	hence	ADV
cana-2791	89	33	these	these	DET
cana-2791	89	34	vertices	vertex	NOUN
cana-2791	89	35	will	will	AUX
cana-2791	89	36	dominate	dominate	VERB
cana-2791	89	37	all	all	DET
cana-2791	89	38	the	the	DET
cana-2791	89	39	vertices	vertex	NOUN
cana-2791	89	40	in	in	ADP
cana-2791	89	41	the	the	DET
cana-2791	89	42	graph	graph	NOUN
cana-2791	89	43	.	.	PUNCT
cana-2791	90	1	finally	finally	ADV
cana-2791	90	2	we	we	PRON
cana-2791	90	3	will	will	AUX
cana-2791	90	4	be	be	AUX
cana-2791	90	5	left	leave	VERB
cana-2791	90	6	with	with	ADP
cana-2791	90	7	k	k	PROPN
cana-2791	90	8	kn−1	kn−1	PROPN
cana-2791	90	9	number	number	NOUN
cana-2791	90	10	of	of	ADP
cana-2791	90	11	vertices	vertex	NOUN
cana-2791	90	12	that	that	PRON
cana-2791	90	13	dominates	dominate	VERB
cana-2791	90	14	all	all	DET
cana-2791	90	15	the	the	DET
cana-2791	90	16	edges	edge	NOUN
cana-2791	90	17	of	of	ADP
cana-2791	90	18	s+(n	s+(n	NOUN
cana-2791	90	19	+	+	X
cana-2791	90	20	1	1	NUM
cana-2791	90	21	,	,	PUNCT
cana-2791	90	22	k	k	NOUN
cana-2791	90	23	)	)	PUNCT
cana-2791	90	24	.	.	PUNCT
cana-2791	91	1	1	1	NUM
cana-2791	91	2	ioc	ioc	PROPN
cana-2791	91	3	(	(	PUNCT
cana-2791	91	4	s+(n	s+(n	NOUN
cana-2791	91	5	,	,	PUNCT
cana-2791	91	6	k	k	NOUN
cana-2791	91	7	)	)	PUNCT
cana-2791	91	8	)	)	PUNCT
cana-2791	92	1	=	=	PUNCT
cana-2791	93	1	k	k	PROPN
cana-2791	93	2	×	×	PROPN
cana-2791	93	3	ki−1	ki−1	PROPN
cana-2791	93	4	=	=	PUNCT
cana-2791	93	5	ki	ki	PROPN
cana-2791	93	6	=	=	PROPN
cana-2791	93	7	k(i+1)−1	k(i+1)−1	PROPN
cana-2791	93	8	,	,	PUNCT
cana-2791	93	9	k	k	PROPN
cana-2791	93	10	≥	≥	NUM
cana-2791	93	11	5	5	NUM
cana-2791	93	12	,	,	PUNCT
cana-2791	93	13	n	n	NOUN
cana-2791	93	14	=	=	SYM
cana-2791	94	1	i	i	PRON
cana-2791	94	2	+	+	NOUN
cana-2791	94	3	1	1	NUM
cana-2791	94	4	the	the	DET
cana-2791	94	5	outer	outer	ADJ
cana-2791	94	6	connectedness	connectedness	NOUN
cana-2791	94	7	property	property	NOUN
cana-2791	94	8	:	:	PUNCT
cana-2791	94	9	to	to	PART
cana-2791	94	10	ensure	ensure	VERB
cana-2791	94	11	the	the	DET
cana-2791	94	12	outer	outer	ADJ
cana-2791	94	13	connectedness	connectedness	NOUN
cana-2791	94	14	,	,	PUNCT
cana-2791	94	15	vertex	vertex	NOUN
cana-2791	94	16	chosen	choose	VERB
cana-2791	94	17	must	must	AUX
cana-2791	94	18	be	be	AUX
cana-2791	94	19	such	such	ADJ
cana-2791	94	20	that	that	SCONJ
cana-2791	94	21	,	,	PUNCT
cana-2791	94	22	they	they	PRON
cana-2791	94	23	do	do	AUX
cana-2791	94	24	not	not	PART
cana-2791	94	25	engulf	engulf	VERB
cana-2791	94	26	one	one	NUM
cana-2791	94	27	unit	unit	NOUN
cana-2791	94	28	and	and	CCONJ
cana-2791	94	29	isolate	isolate	VERB
cana-2791	94	30	it	it	PRON
cana-2791	94	31	after	after	ADP
cana-2791	94	32	the	the	DET
cana-2791	94	33	vertex	vertex	NOUN
cana-2791	94	34	deletion	deletion	NOUN
cana-2791	94	35	as	as	SCONJ
cana-2791	94	36	the	the	DET
cana-2791	94	37	induced	induced	ADJ
cana-2791	94	38	subgraph	subgraph	NOUN
cana-2791	94	39	must	must	AUX
cana-2791	94	40	be	be	AUX
cana-2791	94	41	connected	connect	VERB
cana-2791	94	42	.	.	PUNCT
cana-2791	95	1	hence	hence	ADV
cana-2791	95	2	the	the	DET
cana-2791	95	3	result	result	NOUN
cana-2791	95	4	1	1	NUM
cana-2791	95	5	ioc	ioc	X
cana-2791	95	6	(	(	PUNCT
cana-2791	95	7	s(n	s(n	PROPN
cana-2791	95	8	,	,	PUNCT
cana-2791	95	9	k	k	NOUN
cana-2791	95	10	)	)	PUNCT
cana-2791	95	11	)	)	PUNCT
cana-2791	96	1	=	=	SYM
cana-2791	96	2	kn−1	kn−1	PROPN
cana-2791	96	3	,	,	PUNCT
cana-2791	96	4	k	k	PROPN
cana-2791	96	5	≥	≥	NUM
cana-2791	96	6	5	5	NUM
cana-2791	96	7	,	,	PUNCT
cana-2791	96	8	n	n	PRON
cana-2791	96	9	≥	≥	NOUN
cana-2791	96	10	1	1	NUM
cana-2791	96	11	holds	hold	VERB
cana-2791	96	12	good	good	ADJ
cana-2791	96	13	.	.	PUNCT
cana-2791	97	1	4	4	NUM
cana-2791	97	2	inverse	inverse	NOUN
cana-2791	97	3	independent	independent	ADJ
cana-2791	97	4	outer	outer	ADJ
cana-2791	97	5	connected	connected	ADJ
cana-2791	97	6	domination	domination	NOUN
cana-2791	97	7	number	number	NOUN
cana-2791	97	8	of	of	ADP
cana-2791	97	9	extended	extended	ADJ
cana-2791	97	10	sierpinski	sierpinski	ADJ
cana-2791	97	11	graph	graph	NOUN
cana-2791	97	12	s++(n	s++(n	NOUN
cana-2791	97	13	,	,	PUNCT
cana-2791	97	14	k	k	NOUN
cana-2791	97	15	)	)	PUNCT
cana-2791	97	16	theorem	theorem	VERB
cana-2791	97	17	4.1	4.1	NUM
cana-2791	97	18	.	.	PUNCT
cana-2791	98	1	let	let	VERB
cana-2791	98	2	s++(n	s++(n	NOUN
cana-2791	98	3	,	,	PUNCT
cana-2791	98	4	k	k	NOUN
cana-2791	98	5	)	)	PUNCT
cana-2791	98	6	be	be	VERB
cana-2791	98	7	a	a	DET
cana-2791	98	8	sierpinski	sierpinski	ADJ
cana-2791	98	9	-	-	PUNCT
cana-2791	98	10	like	like	ADJ
cana-2791	98	11	graph	graph	NOUN
cana-2791	98	12	obtained	obtain	VERB
cana-2791	98	13	from	from	ADP
cana-2791	98	14	s(n	s(n	PROPN
cana-2791	98	15	,	,	PUNCT
cana-2791	98	16	k	k	NOUN
cana-2791	98	17	)	)	PUNCT
cana-2791	98	18	by	by	ADP
cana-2791	98	19	adding	add	VERB
cana-2791	98	20	a	a	DET
cana-2791	98	21	new	new	ADJ
cana-2791	98	22	copy	copy	NOUN
cana-2791	98	23	of	of	ADP
cana-2791	98	24	s(n	s(n	PROPN
cana-2791	98	25	−	−	PROPN
cana-2791	98	26	1	1	NUM
cana-2791	98	27	,	,	PUNCT
cana-2791	98	28	k	k	NOUN
cana-2791	98	29	)	)	PUNCT
cana-2791	98	30	,	,	PUNCT
cana-2791	98	31	denoted	denote	VERB
cana-2791	98	32	by	by	ADP
cana-2791	98	33	sk+1(n	sk+1(n	NOUN
cana-2791	98	34	−	−	PROPN
cana-2791	98	35	1	1	NUM
cana-2791	98	36	,	,	PUNCT
cana-2791	98	37	k	k	NOUN
cana-2791	98	38	)	)	PUNCT
cana-2791	98	39	and	and	CCONJ
cana-2791	98	40	joining	join	VERB
cana-2791	98	41	the	the	DET
cana-2791	98	42	jth	jth	PROPN
cana-2791	98	43	extreme	extreme	ADJ
cana-2791	98	44	vertices	vertex	NOUN
cana-2791	98	45	of	of	ADP
cana-2791	98	46	s(n	s(n	PROPN
cana-2791	98	47	,	,	PUNCT
cana-2791	98	48	k	k	NOUN
cana-2791	98	49	)	)	PUNCT
cana-2791	98	50	and	and	CCONJ
cana-2791	98	51	sk+1(n	sk+1(n	NOUN
cana-2791	98	52	−	−	PROPN
cana-2791	98	53	1	1	NUM
cana-2791	98	54	,	,	PUNCT
cana-2791	98	55	k	k	NOUN
cana-2791	98	56	)	)	PUNCT
cana-2791	98	57	with	with	ADP
cana-2791	98	58	an	an	DET
cana-2791	98	59	edge	edge	NOUN
cana-2791	98	60	,	,	PUNCT
cana-2791	98	61	then	then	ADV
cana-2791	98	62	,	,	PUNCT
cana-2791	98	63	1	1	NUM
cana-2791	98	64	ioc	ioc	X
cana-2791	98	65	(	(	PUNCT
cana-2791	98	66	s++(n	s++(n	PROPN
cana-2791	98	67	,	,	PUNCT
cana-2791	98	68	k	k	NOUN
cana-2791	98	69	)	)	PUNCT
cana-2791	98	70	)	)	PUNCT
cana-2791	99	1	=	=	PUNCT
cana-2791	99	2	kn−1	kn−1	PROPN
cana-2791	99	3	+	+	CCONJ
cana-2791	99	4	kn−2	kn−2	PROPN
cana-2791	99	5	,	,	PUNCT
cana-2791	99	6	where	where	SCONJ
cana-2791	99	7	k	k	PROPN
cana-2791	99	8	≥	≥	NUM
cana-2791	99	9	5	5	NUM
cana-2791	99	10	,	,	PUNCT
cana-2791	99	11	and	and	CCONJ
cana-2791	99	12	n	n	PRON
cana-2791	99	13	≥	≥	NOUN
cana-2791	99	14	2	2	NUM
cana-2791	99	15	proof	proof	NOUN
cana-2791	99	16	.	.	PUNCT
cana-2791	100	1	apply	apply	VERB
cana-2791	100	2	induction	induction	NOUN
cana-2791	100	3	on	on	ADP
cana-2791	100	4	′n′.	′n′.	PUNCT
cana-2791	100	5	for	for	ADP
cana-2791	100	6	the	the	DET
cana-2791	100	7	initial	initial	ADJ
cana-2791	100	8	value	value	NOUN
cana-2791	100	9	n	n	NOUN
cana-2791	100	10	=	=	SYM
cana-2791	100	11	1	1	NUM
cana-2791	100	12	;	;	PUNCT
cana-2791	100	13	γ̃−1	γ̃−1	PROPN
cana-2791	100	14	(	(	PUNCT
cana-2791	100	15	s+(1	s+(1	NOUN
cana-2791	100	16	,	,	PUNCT
cana-2791	100	17	k	k	NOUN
cana-2791	100	18	)	)	PUNCT
cana-2791	100	19	)	)	PUNCT
cana-2791	101	1	=	=	SYM
cana-2791	101	2	k0	k0	PROPN
cana-2791	101	3	=	=	PROPN
cana-2791	101	4	1	1	NUM
cana-2791	101	5	here	here	ADV
cana-2791	101	6	all	all	DET
cana-2791	101	7	the	the	DET
cana-2791	101	8	k′s	k′s	PROPN
cana-2791	101	9	are	be	AUX
cana-2791	101	10	the	the	DET
cana-2791	101	11	number	number	NOUN
cana-2791	101	12	of	of	ADP
cana-2791	101	13	vertices	vertex	NOUN
cana-2791	101	14	in	in	ADP
cana-2791	101	15	a	a	DET
cana-2791	101	16	complete	complete	ADJ
cana-2791	101	17	graph	graph	NOUN
cana-2791	101	18	.	.	PUNCT
cana-2791	102	1	we	we	PRON
cana-2791	102	2	know	know	VERB
cana-2791	102	3	the	the	DET
cana-2791	102	4	iiocd	iiocd	ADJ
cana-2791	102	5	number	number	NOUN
cana-2791	102	6	of	of	ADP
cana-2791	102	7	a	a	DET
cana-2791	102	8	complete	complete	ADJ
cana-2791	102	9	graph	graph	NOUN
cana-2791	102	10	is	be	AUX
cana-2791	102	11	1,and	1,and	NUM
cana-2791	102	12	also	also	ADV
cana-2791	102	13	the	the	DET
cana-2791	102	14	end	end	NOUN
cana-2791	102	15	vertices	vertex	NOUN
cana-2791	102	16	of	of	ADP
cana-2791	102	17	s(1	s(1	PROPN
cana-2791	102	18	,	,	PUNCT
cana-2791	102	19	k	k	PROPN
cana-2791	102	20	)	)	PUNCT
cana-2791	102	21	are	be	AUX
cana-2791	102	22	connected	connect	VERB
cana-2791	102	23	to	to	ADP
cana-2791	102	24	an	an	DET
cana-2791	102	25	extra	extra	ADJ
cana-2791	102	26	vertex	vertex	NOUN
cana-2791	102	27	’s	’s	PART
cana-2791	102	28	’	'	PUNCT
cana-2791	102	29	.	.	PUNCT
cana-2791	103	1	communications	communication	NOUN
cana-2791	103	2	on	on	ADP
cana-2791	103	3	applied	apply	VERB
cana-2791	103	4	nonlinear	nonlinear	ADJ
cana-2791	103	5	analysis	analysis	NOUN
cana-2791	103	6	issn	issn	NOUN
cana-2791	103	7	:	:	PUNCT
cana-2791	103	8	1074	1074	NUM
cana-2791	103	9	-	-	PUNCT
cana-2791	103	10	133x	133x	NUM
cana-2791	103	11	vol	vol	NOUN
cana-2791	103	12	32	32	NUM
cana-2791	103	13	no	no	NOUN
cana-2791	103	14	.	.	PUNCT
cana-2791	104	1	4s	4s	NUM
cana-2791	104	2	(	(	PUNCT
cana-2791	104	3	2025	2025	NUM
cana-2791	104	4	)	)	PUNCT
cana-2791	104	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2791	104	6	251	251	NUM
cana-2791	104	7	ioc	ioc	PROPN
cana-2791	104	8	ioc	ioc	PROPN
cana-2791	104	9	×	×	NOUN
cana-2791	104	10	γ̃−	γ̃−	ADJ
cana-2791	104	11	γ̃−	γ̃−	NUM
cana-2791	104	12	ioc	ioc	X
cana-2791	104	13	(	(	PUNCT
cana-2791	104	14	γ̃−	γ̃−	X
cana-2791	104	15	∈	∈	PROPN
cana-2791	104	16	{	{	PUNCT
cana-2791	104	17	}	}	PUNCT
cana-2791	104	18	{	{	PUNCT
cana-2791	104	19	}	}	PUNCT
cana-2791	104	20	{	{	PUNCT
cana-2791	104	21	}	}	PUNCT
cana-2791	104	22	the	the	DET
cana-2791	104	23	outer	outer	ADJ
cana-2791	104	24	connectedness	connectedness	NOUN
cana-2791	104	25	property	property	NOUN
cana-2791	104	26	:	:	PUNCT
cana-2791	104	27	after	after	ADP
cana-2791	104	28	the	the	DET
cana-2791	104	29	removal	removal	NOUN
cana-2791	104	30	of	of	ADP
cana-2791	104	31	one	one	NUM
cana-2791	104	32	vertex	vertex	NOUN
cana-2791	104	33	from	from	ADP
cana-2791	104	34	a	a	DET
cana-2791	104	35	complete	complete	ADJ
cana-2791	104	36	graph	graph	NOUN
cana-2791	104	37	with	with	ADP
cana-2791	104	38	k	k	PROPN
cana-2791	104	39	vertices	vertex	NOUN
cana-2791	104	40	,	,	PUNCT
cana-2791	104	41	the	the	DET
cana-2791	104	42	graph	graph	NOUN
cana-2791	104	43	will	will	AUX
cana-2791	104	44	still	still	ADV
cana-2791	104	45	be	be	AUX
cana-2791	104	46	a	a	DET
cana-2791	104	47	connected	connected	ADJ
cana-2791	104	48	graph	graph	NOUN
cana-2791	104	49	.	.	PUNCT
cana-2791	105	1	hence	hence	ADV
cana-2791	105	2	γ̃−1	γ̃−1	PROPN
cana-2791	105	3	(	(	PUNCT
cana-2791	105	4	s+(1	s+(1	NOUN
cana-2791	105	5	,	,	PUNCT
cana-2791	105	6	k	k	NOUN
cana-2791	105	7	)	)	PUNCT
cana-2791	105	8	)	)	PUNCT
cana-2791	106	1	=	=	SYM
cana-2791	106	2	k0	k0	PROPN
cana-2791	106	3	,	,	PUNCT
cana-2791	106	4	k	k	PROPN
cana-2791	106	5	≥	≥	NUM
cana-2791	106	6	5	5	NUM
cana-2791	106	7	,	,	PUNCT
cana-2791	106	8	n	n	NOUN
cana-2791	106	9	=	=	SYM
cana-2791	106	10	1	1	NUM
cana-2791	106	11	holds	hold	VERB
cana-2791	106	12	true	true	ADJ
cana-2791	106	13	.	.	PUNCT
cana-2791	107	1	γ̃−1	γ̃−1	PROPN
cana-2791	107	2	we	we	PRON
cana-2791	107	3	make	make	VERB
cana-2791	107	4	an	an	DET
cana-2791	107	5	assumption	assumption	NOUN
cana-2791	107	6	that	that	SCONJ
cana-2791	107	7	for	for	ADP
cana-2791	107	8	n	n	NOUN
cana-2791	107	9	=	=	PRON
cana-2791	107	10	i	i	PRON
cana-2791	107	11	the	the	DET
cana-2791	107	12	result	result	NOUN
cana-2791	107	13	holds	hold	VERB
cana-2791	107	14	good	good	ADJ
cana-2791	107	15	.	.	PUNCT
cana-2791	108	1	(	(	PUNCT
cana-2791	108	2	s+(i	s+(i	PROPN
cana-2791	108	3	,	,	PUNCT
cana-2791	108	4	k	k	NOUN
cana-2791	108	5	)	)	PUNCT
cana-2791	108	6	)	)	PUNCT
cana-2791	109	1	=	=	SYM
cana-2791	109	2	ki−1	ki−1	PROPN
cana-2791	109	3	,	,	PUNCT
cana-2791	109	4	k	k	PROPN
cana-2791	109	5	≥	≥	NUM
cana-2791	109	6	5	5	NUM
cana-2791	109	7	,	,	PUNCT
cana-2791	109	8	n	n	PROPN
cana-2791	109	9	=	=	PROPN
cana-2791	109	10	i.	i.	PROPN
cana-2791	109	11	ioc	ioc	PROPN
cana-2791	109	12	to	to	PART
cana-2791	109	13	be	be	AUX
cana-2791	109	14	proved	prove	VERB
cana-2791	109	15	that	that	SCONJ
cana-2791	109	16	for	for	ADP
cana-2791	109	17	n	n	NOUN
cana-2791	109	18	=	=	SYM
cana-2791	110	1	i	i	PRON
cana-2791	110	2	+	+	NOUN
cana-2791	110	3	1	1	NUM
cana-2791	110	4	γ̃−1	γ̃−1	PROPN
cana-2791	110	5	(	(	PUNCT
cana-2791	110	6	s+(i	s+(i	PROPN
cana-2791	110	7	+	+	CCONJ
cana-2791	110	8	1	1	NUM
cana-2791	110	9	,	,	PUNCT
cana-2791	110	10	k	k	NOUN
cana-2791	110	11	)	)	PUNCT
cana-2791	110	12	)	)	PUNCT
cana-2791	111	1	=	=	SYM
cana-2791	111	2	k(i+1)−1	k(i+1)−1	PROPN
cana-2791	111	3	,	,	PUNCT
cana-2791	111	4	k	k	PROPN
cana-2791	111	5	≥	≥	NUM
cana-2791	111	6	5	5	NUM
cana-2791	111	7	,	,	PUNCT
cana-2791	111	8	n	n	NOUN
cana-2791	111	9	=	=	SYM
cana-2791	112	1	i	i	PRON
cana-2791	112	2	+	+	NOUN
cana-2791	112	3	1	1	NUM
cana-2791	112	4	by	by	ADP
cana-2791	112	5	the	the	DET
cana-2791	112	6	definition	definition	NOUN
cana-2791	112	7	of	of	ADP
cana-2791	112	8	the	the	DET
cana-2791	112	9	extended	extended	ADJ
cana-2791	112	10	sierpinski	sierpinski	ADJ
cana-2791	112	11	graphs	graph	NOUN
cana-2791	112	12	s+(n	s+(n	NOUN
cana-2791	112	13	,	,	PUNCT
cana-2791	112	14	k	k	NOUN
cana-2791	112	15	)	)	PUNCT
cana-2791	112	16	is	be	AUX
cana-2791	112	17	obtained	obtain	VERB
cana-2791	112	18	from	from	ADP
cana-2791	112	19	s(n	s(n	PROPN
cana-2791	112	20	,	,	PUNCT
cana-2791	112	21	k	k	NOUN
cana-2791	112	22	)	)	PUNCT
cana-2791	112	23	by	by	ADP
cana-2791	112	24	adding	add	VERB
cana-2791	112	25	an	an	DET
cana-2791	112	26	extra	extra	ADJ
cana-2791	112	27	vertex	vertex	NOUN
cana-2791	112	28	′s′,and	′s′,and	PROPN
cana-2791	112	29	edges	edge	NOUN
cana-2791	112	30	joining	join	VERB
cana-2791	112	31	s	s	PRON
cana-2791	112	32	to	to	ADP
cana-2791	112	33	all	all	DET
cana-2791	112	34	extreme	extreme	ADJ
cana-2791	112	35	vertices	vertex	NOUN
cana-2791	112	36	of	of	ADP
cana-2791	112	37	s(n	s(n	PROPN
cana-2791	112	38	,	,	PUNCT
cana-2791	112	39	k	k	NOUN
cana-2791	112	40	)	)	PUNCT
cana-2791	112	41	.	.	PUNCT
cana-2791	113	1	the	the	DET
cana-2791	113	2	unit	unit	NOUN
cana-2791	113	3	graphs	graph	NOUN
cana-2791	113	4	will	will	AUX
cana-2791	113	5	always	always	ADV
cana-2791	113	6	be	be	AUX
cana-2791	113	7	complete	complete	ADJ
cana-2791	113	8	graphs	graph	NOUN
cana-2791	113	9	and	and	CCONJ
cana-2791	113	10	hence	hence	ADV
cana-2791	113	11	we	we	PRON
cana-2791	113	12	take	take	VERB
cana-2791	113	13	kn−1	kn−1	PROPN
cana-2791	113	14	number	number	NOUN
cana-2791	113	15	of	of	ADP
cana-2791	113	16	vertices	vertex	NOUN
cana-2791	113	17	from	from	ADP
cana-2791	113	18	each	each	DET
cana-2791	113	19	copy	copy	NOUN
cana-2791	113	20	and	and	CCONJ
cana-2791	113	21	any	any	DET
cana-2791	113	22	one	one	NUM
cana-2791	113	23	of	of	ADP
cana-2791	113	24	these	these	DET
cana-2791	113	25	vertices	vertex	NOUN
cana-2791	113	26	will	will	AUX
cana-2791	113	27	be	be	AUX
cana-2791	113	28	an	an	DET
cana-2791	113	29	end	end	NOUN
cana-2791	113	30	vertex	vertex	NOUN
cana-2791	113	31	and	and	CCONJ
cana-2791	113	32	hence	hence	ADV
cana-2791	113	33	these	these	DET
cana-2791	113	34	vertices	vertex	NOUN
cana-2791	113	35	will	will	AUX
cana-2791	113	36	dominate	dominate	VERB
cana-2791	113	37	all	all	DET
cana-2791	113	38	the	the	DET
cana-2791	113	39	vertices	vertex	NOUN
cana-2791	113	40	in	in	ADP
cana-2791	113	41	the	the	DET
cana-2791	113	42	graph	graph	NOUN
cana-2791	113	43	.	.	PUNCT
cana-2791	114	1	finally	finally	ADV
cana-2791	114	2	we	we	PRON
cana-2791	114	3	will	will	AUX
cana-2791	114	4	be	be	AUX
cana-2791	114	5	left	leave	VERB
cana-2791	114	6	with	with	ADP
cana-2791	114	7	k	k	PROPN
cana-2791	114	8	kn−1	kn−1	PROPN
cana-2791	114	9	number	number	NOUN
cana-2791	114	10	of	of	ADP
cana-2791	114	11	vertices	vertex	NOUN
cana-2791	114	12	that	that	PRON
cana-2791	114	13	dominates	dominate	VERB
cana-2791	114	14	all	all	DET
cana-2791	114	15	the	the	DET
cana-2791	114	16	edges	edge	NOUN
cana-2791	114	17	of	of	ADP
cana-2791	114	18	s+(n	s+(n	NOUN
cana-2791	114	19	+	+	X
cana-2791	114	20	1	1	NUM
cana-2791	114	21	,	,	PUNCT
cana-2791	114	22	k	k	NOUN
cana-2791	114	23	)	)	PUNCT
cana-2791	114	24	.	.	PUNCT
cana-2791	115	1	1	1	NUM
cana-2791	115	2	ioc	ioc	PROPN
cana-2791	115	3	(	(	PUNCT
cana-2791	115	4	s+(n	s+(n	NOUN
cana-2791	115	5	,	,	PUNCT
cana-2791	115	6	k	k	NOUN
cana-2791	115	7	)	)	PUNCT
cana-2791	115	8	)	)	PUNCT
cana-2791	116	1	=	=	PUNCT
cana-2791	117	1	k	k	PROPN
cana-2791	117	2	×	×	PROPN
cana-2791	117	3	ki−1	ki−1	PROPN
cana-2791	117	4	=	=	PUNCT
cana-2791	117	5	ki	ki	PROPN
cana-2791	117	6	=	=	PROPN
cana-2791	117	7	k(i+1)−1	k(i+1)−1	PROPN
cana-2791	117	8	,	,	PUNCT
cana-2791	117	9	k	k	PROPN
cana-2791	117	10	≥	≥	NUM
cana-2791	117	11	5	5	NUM
cana-2791	117	12	,	,	PUNCT
cana-2791	117	13	n	n	NOUN
cana-2791	117	14	=	=	SYM
cana-2791	118	1	i	i	PRON
cana-2791	118	2	+	+	NOUN
cana-2791	118	3	1	1	NUM
cana-2791	118	4	the	the	DET
cana-2791	118	5	outer	outer	ADJ
cana-2791	118	6	connectedness	connectedness	NOUN
cana-2791	118	7	property	property	NOUN
cana-2791	118	8	:	:	PUNCT
cana-2791	118	9	to	to	PART
cana-2791	118	10	ensure	ensure	VERB
cana-2791	118	11	the	the	DET
cana-2791	118	12	outer	outer	ADJ
cana-2791	118	13	connectedness	connectedness	NOUN
cana-2791	118	14	,	,	PUNCT
cana-2791	118	15	vertex	vertex	NOUN
cana-2791	118	16	chosen	choose	VERB
cana-2791	118	17	must	must	AUX
cana-2791	118	18	be	be	AUX
cana-2791	118	19	such	such	ADJ
cana-2791	118	20	that	that	SCONJ
cana-2791	118	21	,	,	PUNCT
cana-2791	118	22	they	they	PRON
cana-2791	118	23	do	do	AUX
cana-2791	118	24	not	not	PART
cana-2791	118	25	engulf	engulf	VERB
cana-2791	118	26	one	one	NUM
cana-2791	118	27	unit	unit	NOUN
cana-2791	118	28	and	and	CCONJ
cana-2791	118	29	isolate	isolate	VERB
cana-2791	118	30	it	it	PRON
cana-2791	118	31	after	after	ADP
cana-2791	118	32	the	the	DET
cana-2791	118	33	vertex	vertex	NOUN
cana-2791	118	34	deletion	deletion	NOUN
cana-2791	118	35	as	as	SCONJ
cana-2791	118	36	the	the	DET
cana-2791	118	37	induced	induced	ADJ
cana-2791	118	38	subgraph	subgraph	NOUN
cana-2791	118	39	must	must	AUX
cana-2791	118	40	be	be	AUX
cana-2791	118	41	connected	connect	VERB
cana-2791	118	42	.	.	PUNCT
cana-2791	119	1	hence	hence	ADV
cana-2791	119	2	the	the	DET
cana-2791	119	3	result	result	NOUN
cana-2791	119	4	1	1	NUM
cana-2791	119	5	ioc	ioc	X
cana-2791	119	6	(	(	PUNCT
cana-2791	119	7	s(n	s(n	PROPN
cana-2791	119	8	,	,	PUNCT
cana-2791	119	9	k	k	NOUN
cana-2791	119	10	)	)	PUNCT
cana-2791	119	11	)	)	PUNCT
cana-2791	120	1	=	=	SYM
cana-2791	120	2	kn−1	kn−1	PROPN
cana-2791	120	3	,	,	PUNCT
cana-2791	120	4	k	k	PROPN
cana-2791	120	5	≥	≥	NUM
cana-2791	120	6	5	5	NUM
cana-2791	120	7	,	,	PUNCT
cana-2791	120	8	n	n	PRON
cana-2791	120	9	≥	≥	NOUN
cana-2791	120	10	1	1	NUM
cana-2791	120	11	holds	hold	VERB
cana-2791	120	12	good	good	ADJ
cana-2791	120	13	.	.	PUNCT
cana-2791	121	1	5	5	NUM
cana-2791	121	2	inverse	inverse	NOUN
cana-2791	121	3	independent	independent	ADJ
cana-2791	121	4	outer	outer	ADJ
cana-2791	121	5	connected	connected	ADJ
cana-2791	121	6	domination	domination	NOUN
cana-2791	121	7	number	number	NOUN
cana-2791	121	8	of	of	ADP
cana-2791	121	9	sierpinki	sierpinki	ADJ
cana-2791	121	10	gasket	gasket	NOUN
cana-2791	121	11	graph	graph	NOUN
cana-2791	121	12	theorem	theorem	VERB
cana-2791	121	13	5.1	5.1	NUM
cana-2791	121	14	.	.	PUNCT
cana-2791	122	1	let	let	VERB
cana-2791	122	2	sn	sn	PROPN
cana-2791	122	3	be	be	AUX
cana-2791	122	4	the	the	DET
cana-2791	122	5	sierpinski	sierpinski	ADJ
cana-2791	122	6	gasket	gasket	NOUN
cana-2791	122	7	graph	graph	NOUN
cana-2791	122	8	,	,	PUNCT
cana-2791	122	9	a	a	DET
cana-2791	122	10	variant	variant	NOUN
cana-2791	122	11	of	of	ADP
cana-2791	122	12	the	the	DET
cana-2791	122	13	sierpinski	sierpinski	ADJ
cana-2791	122	14	graph	graph	NOUN
cana-2791	122	15	s(n	s(n	PROPN
cana-2791	122	16	,	,	PUNCT
cana-2791	122	17	3	3	NUM
cana-2791	122	18	)	)	PUNCT
cana-2791	122	19	,	,	PUNCT
cana-2791	122	20	then	then	ADV
cana-2791	122	21	,	,	PUNCT
cana-2791	122	22	γ−1	γ−1	PROPN
cana-2791	122	23	(	(	PUNCT
cana-2791	122	24	sn	sn	PROPN
cana-2791	122	25	)	)	PUNCT
cana-2791	122	26	=	=	SYM
cana-2791	123	1	3n−2	3n−2	NUM
cana-2791	123	2	,	,	PUNCT
cana-2791	123	3	(	(	PUNCT
cana-2791	123	4	n	n	CCONJ
cana-2791	123	5	≥	≥	NOUN
cana-2791	123	6	3	3	NUM
cana-2791	123	7	)	)	PUNCT
cana-2791	123	8	n	n	CCONJ
cana-2791	123	9	,	,	PUNCT
cana-2791	123	10	n	n	NOUN
cana-2791	123	11	=	=	SYM
cana-2791	123	12	1	1	NUM
cana-2791	123	13	,	,	PUNCT
cana-2791	123	14	2	2	NUM
cana-2791	123	15	proof	proof	NOUN
cana-2791	123	16	.	.	PUNCT
cana-2791	124	1	the	the	DET
cana-2791	124	2	graph	graph	NOUN
cana-2791	124	3	sn	sn	PROPN
cana-2791	124	4	can	can	AUX
cana-2791	124	5	be	be	AUX
cana-2791	124	6	obtained	obtain	VERB
cana-2791	124	7	from	from	ADP
cana-2791	124	8	s(n	s(n	PROPN
cana-2791	124	9	,	,	PUNCT
cana-2791	124	10	3	3	NUM
cana-2791	124	11	)	)	PUNCT
cana-2791	124	12	by	by	ADP
cana-2791	124	13	contracting	contract	VERB
cana-2791	124	14	every	every	DET
cana-2791	124	15	edge	edge	NOUN
cana-2791	124	16	of	of	ADP
cana-2791	124	17	s(n	s(n	PROPN
cana-2791	124	18	,	,	PUNCT
cana-2791	124	19	3	3	NUM
cana-2791	124	20	)	)	PUNCT
cana-2791	124	21	that	that	PRON
cana-2791	124	22	lies	lie	VERB
cana-2791	124	23	in	in	ADP
cana-2791	124	24	no	no	DET
cana-2791	124	25	triangle	triangle	NOUN
cana-2791	124	26	.	.	PUNCT
cana-2791	125	1	an	an	DET
cana-2791	125	2	induction	induction	NOUN
cana-2791	125	3	on	on	ADP
cana-2791	125	4	′n′	′n′	PROPN
cana-2791	125	5	is	be	AUX
cana-2791	125	6	applied	apply	VERB
cana-2791	125	7	.	.	PUNCT
cana-2791	126	1	for	for	ADP
cana-2791	126	2	n	n	NOUN
cana-2791	126	3	=	=	SYM
cana-2791	126	4	1	1	NUM
cana-2791	126	5	the	the	DET
cana-2791	126	6	sierpinski	sierpinski	ADJ
cana-2791	126	7	gasket	gasket	NOUN
cana-2791	126	8	graph	graph	NOUN
cana-2791	126	9	will	will	AUX
cana-2791	126	10	be	be	AUX
cana-2791	126	11	a	a	DET
cana-2791	126	12	complete	complete	ADJ
cana-2791	126	13	graph	graph	NOUN
cana-2791	126	14	with	with	ADP
cana-2791	126	15	3	3	NUM
cana-2791	126	16	vertices	vertex	NOUN
cana-2791	126	17	,	,	PUNCT
cana-2791	126	18	which	which	PRON
cana-2791	126	19	is	be	AUX
cana-2791	126	20	a	a	DET
cana-2791	126	21	triangle	triangle	NOUN
cana-2791	126	22	.	.	PUNCT
cana-2791	127	1	inverse	inverse	ADJ
cana-2791	127	2	independent	independent	ADJ
cana-2791	127	3	domination	domination	NOUN
cana-2791	127	4	number	number	NOUN
cana-2791	127	5	of	of	ADP
cana-2791	127	6	a	a	DET
cana-2791	127	7	complete	complete	ADJ
cana-2791	127	8	graph	graph	NOUN
cana-2791	127	9	with	with	ADP
cana-2791	127	10	3	3	NUM
cana-2791	127	11	vertices	vertex	NOUN
cana-2791	127	12	will	will	AUX
cana-2791	127	13	be	be	AUX
cana-2791	127	14	one	one	NUM
cana-2791	127	15	.	.	PUNCT
cana-2791	128	1	the	the	DET
cana-2791	128	2	outer	outer	ADJ
cana-2791	128	3	connectedness	connectedness	NOUN
cana-2791	128	4	property	property	NOUN
cana-2791	128	5	:	:	PUNCT
cana-2791	128	6	if	if	SCONJ
cana-2791	128	7	that	that	DET
cana-2791	128	8	one	one	NUM
cana-2791	128	9	vertex	vertex	NOUN
cana-2791	128	10	is	be	AUX
cana-2791	128	11	deleted	delete	VERB
cana-2791	128	12	the	the	DET
cana-2791	128	13	subgraph	subgraph	NOUN
cana-2791	128	14	induced	induce	VERB
cana-2791	128	15	by	by	ADP
cana-2791	128	16	it	it	PRON
cana-2791	128	17	still	still	ADV
cana-2791	128	18	remains	remain	VERB
cana-2791	128	19	connected	connect	VERB
cana-2791	128	20	.	.	PUNCT
cana-2791	129	1	1	1	NUM
cana-2791	129	2	ioc	ioc	PROPN
cana-2791	129	3	(	(	PUNCT
cana-2791	129	4	s1	s1	NOUN
cana-2791	129	5	)	)	PUNCT
cana-2791	129	6	=	=	SYM
cana-2791	129	7	1	1	NUM
cana-2791	129	8	in	in	ADP
cana-2791	129	9	(	(	PUNCT
cana-2791	129	10	s2	s2	PROPN
cana-2791	129	11	)	)	PUNCT
cana-2791	129	12	,	,	PUNCT
cana-2791	129	13	see	see	VERB
cana-2791	129	14	figure	figure	NOUN
cana-2791	129	15	4	4	NUM
cana-2791	129	16	,	,	PUNCT
cana-2791	129	17	the	the	DET
cana-2791	129	18	inverse	inverse	ADJ
cana-2791	129	19	independent	independent	ADJ
cana-2791	129	20	dominating	dominating	NOUN
cana-2791	129	21	sets	set	NOUN
cana-2791	129	22	are	be	AUX
cana-2791	129	23	chosen	choose	VERB
cana-2791	129	24	by	by	ADP
cana-2791	129	25	selecting	select	VERB
cana-2791	129	26	the	the	DET
cana-2791	129	27	vertex	vertex	NOUN
cana-2791	129	28	with	with	ADP
cana-2791	129	29	maximum	maximum	ADJ
cana-2791	129	30	degree	degree	NOUN
cana-2791	129	31	.	.	PUNCT
cana-2791	130	1	vertex	vertex	NOUN
cana-2791	130	2	labelled	label	VERB
cana-2791	130	3	p	p	PROPN
cana-2791	130	4	,	,	PUNCT
cana-2791	130	5	q	q	X
cana-2791	130	6	is	be	AUX
cana-2791	130	7	chosen	choose	VERB
cana-2791	130	8	since	since	SCONJ
cana-2791	130	9	the	the	DET
cana-2791	130	10	degree	degree	NOUN
cana-2791	130	11	of	of	ADP
cana-2791	130	12	such	such	ADJ
cana-2791	130	13	vertex	vertex	NOUN
cana-2791	130	14	is	be	AUX
cana-2791	130	15	maximum	maximum	ADJ
cana-2791	130	16	.	.	PUNCT
cana-2791	131	1	this	this	DET
cana-2791	131	2	vertex	vertex	NOUN
cana-2791	131	3	dominates	dominate	VERB
cana-2791	131	4	5	5	NUM
cana-2791	131	5	out	out	ADP
cana-2791	131	6	of	of	ADP
cana-2791	131	7	6	6	NUM
cana-2791	131	8	vertices	vertex	NOUN
cana-2791	131	9	.	.	PUNCT
cana-2791	132	1	now	now	ADV
cana-2791	132	2	the	the	DET
cana-2791	132	3	left	leave	VERB
cana-2791	132	4	out	out	ADP
cana-2791	132	5	end	end	NOUN
cana-2791	132	6	vertex	vertex	PROPN
cana-2791	132	7	rr	rr	PROPN
cana-2791	132	8	is	be	AUX
cana-2791	132	9	chosen	choose	VERB
cana-2791	132	10	,	,	PUNCT
cana-2791	132	11	where	where	SCONJ
cana-2791	132	12	p	p	X
cana-2791	132	13	,	,	PUNCT
cana-2791	132	14	q	q	ADJ
cana-2791	132	15	,	,	PUNCT
cana-2791	132	16	r	r	NOUN
cana-2791	132	17	1	1	NUM
cana-2791	132	18	,	,	PUNCT
cana-2791	132	19	2	2	NUM
cana-2791	132	20	,	,	PUNCT
cana-2791	132	21	3	3	NUM
cana-2791	132	22	respectively	respectively	ADV
cana-2791	132	23	.	.	PUNCT
cana-2791	133	1	hence	hence	ADV
cana-2791	133	2	the	the	DET
cana-2791	133	3	inverse	inverse	ADJ
cana-2791	133	4	independent	independent	ADJ
cana-2791	133	5	domination	domination	NOUN
cana-2791	133	6	number	number	NOUN
cana-2791	133	7	is	be	AUX
cana-2791	133	8	2	2	NUM
cana-2791	133	9	.	.	PUNCT
cana-2791	133	10	communications	communication	NOUN
cana-2791	133	11	on	on	ADP
cana-2791	133	12	applied	apply	VERB
cana-2791	133	13	nonlinear	nonlinear	ADJ
cana-2791	133	14	analysis	analysis	NOUN
cana-2791	133	15	issn	issn	NOUN
cana-2791	133	16	:	:	PUNCT
cana-2791	133	17	1074	1074	NUM
cana-2791	133	18	-	-	PUNCT
cana-2791	133	19	133x	133x	NUM
cana-2791	133	20	vol	vol	NOUN
cana-2791	133	21	32	32	NUM
cana-2791	133	22	no	no	NOUN
cana-2791	133	23	.	.	PUNCT
cana-2791	134	1	4s	4s	NUM
cana-2791	134	2	(	(	PUNCT
cana-2791	134	3	2025	2025	NUM
cana-2791	134	4	)	)	PUNCT
cana-2791	134	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2791	134	6	252	252	NUM
cana-2791	134	7	ioc	ioc	NOUN
cana-2791	134	8	figure	figure	NOUN
cana-2791	134	9	4	4	NUM
cana-2791	134	10	:	:	PUNCT
cana-2791	134	11	s2	s2	VERB
cana-2791	134	12	γ̃−1	γ̃−1	PUNCT
cana-2791	134	13	the	the	DET
cana-2791	134	14	graph	graph	NOUN
cana-2791	134	15	induced	induce	VERB
cana-2791	134	16	by	by	ADP
cana-2791	134	17	the	the	DET
cana-2791	134	18	remaining	remain	VERB
cana-2791	134	19	vertices	vertex	NOUN
cana-2791	134	20	is	be	AUX
cana-2791	134	21	a	a	DET
cana-2791	134	22	connected	connected	ADJ
cana-2791	134	23	graph	graph	NOUN
cana-2791	134	24	.	.	PUNCT
cana-2791	135	1	(	(	PUNCT
cana-2791	135	2	s2	s2	PROPN
cana-2791	135	3	)	)	PUNCT
cana-2791	135	4	=	=	SYM
cana-2791	135	5	2	2	NUM
cana-2791	135	6	ioc	ioc	NOUN
cana-2791	135	7	now	now	ADV
cana-2791	135	8	we	we	PRON
cana-2791	135	9	use	use	VERB
cana-2791	135	10	induction	induction	NOUN
cana-2791	135	11	hypothesis	hypothesis	NOUN
cana-2791	135	12	.	.	PUNCT
cana-2791	136	1	for	for	ADP
cana-2791	136	2	n	n	NOUN
cana-2791	136	3	=	=	SYM
cana-2791	136	4	3	3	NUM
cana-2791	136	5	,	,	PUNCT
cana-2791	136	6	to	to	PART
cana-2791	136	7	choose	choose	VERB
cana-2791	136	8	the	the	DET
cana-2791	136	9	inverse	inverse	NOUN
cana-2791	136	10	independent	independent	ADJ
cana-2791	136	11	dominating	dominating	NOUN
cana-2791	136	12	set	set	NOUN
cana-2791	136	13	,	,	PUNCT
cana-2791	136	14	from	from	ADP
cana-2791	136	15	the	the	DET
cana-2791	136	16	first	first	ADJ
cana-2791	136	17	copy	copy	NOUN
cana-2791	136	18	of	of	ADP
cana-2791	136	19	(	(	PUNCT
cana-2791	136	20	s2	s2	PROPN
cana-2791	136	21	)	)	PUNCT
cana-2791	136	22	one	one	NUM
cana-2791	136	23	vertex	vertex	NOUN
cana-2791	136	24	is	be	AUX
cana-2791	136	25	chosen	choose	VERB
cana-2791	136	26	which	which	PRON
cana-2791	136	27	has	have	VERB
cana-2791	136	28	the	the	DET
cana-2791	136	29	maximum	maximum	ADJ
cana-2791	136	30	degree	degree	NOUN
cana-2791	136	31	.	.	PUNCT
cana-2791	137	1	max	max	PROPN
cana-2791	137	2	imum	imum	PROPN
cana-2791	137	3	degree	degree	NOUN
cana-2791	137	4	in	in	ADP
cana-2791	137	5	a	a	DET
cana-2791	137	6	sierpinski	sierpinski	ADJ
cana-2791	137	7	gasket	gasket	NOUN
cana-2791	137	8	graph	graph	NOUN
cana-2791	137	9	is	be	AUX
cana-2791	137	10	4	4	NUM
cana-2791	137	11	.	.	PUNCT
cana-2791	138	1	there	there	PRON
cana-2791	138	2	are	be	VERB
cana-2791	138	3	15	15	NUM
cana-2791	138	4	vertices	vertex	NOUN
cana-2791	138	5	in	in	ADP
cana-2791	138	6	(	(	PUNCT
cana-2791	138	7	s3	s3	PROPN
cana-2791	138	8	)	)	PUNCT
cana-2791	138	9	.	.	PUNCT
cana-2791	139	1	if	if	SCONJ
cana-2791	139	2	we	we	PRON
cana-2791	139	3	choose	choose	VERB
cana-2791	139	4	one	one	NUM
cana-2791	139	5	vertex	vertex	NOUN
cana-2791	139	6	from	from	ADP
cana-2791	139	7	each	each	DET
cana-2791	139	8	copy	copy	NOUN
cana-2791	139	9	of	of	ADP
cana-2791	139	10	(	(	PUNCT
cana-2791	139	11	s2	s2	PROPN
cana-2791	139	12	)	)	PUNCT
cana-2791	139	13	we	we	PRON
cana-2791	139	14	will	will	AUX
cana-2791	139	15	get	get	VERB
cana-2791	139	16	three	three	NUM
cana-2791	139	17	vertices	vertex	NOUN
cana-2791	139	18	that	that	PRON
cana-2791	139	19	will	will	AUX
cana-2791	139	20	dominate	dominate	VERB
cana-2791	139	21	the	the	DET
cana-2791	139	22	rest	rest	NOUN
cana-2791	139	23	of	of	ADP
cana-2791	139	24	the	the	DET
cana-2791	139	25	twelve	twelve	NUM
cana-2791	139	26	vertices	vertex	NOUN
cana-2791	139	27	.	.	PUNCT
cana-2791	140	1	refer	refer	VERB
cana-2791	140	2	figure	figure	NOUN
cana-2791	140	3	5	5	NUM
cana-2791	140	4	for	for	ADP
cana-2791	140	5	s3	s3	PROPN
cana-2791	140	6	therefore	therefore	ADV
cana-2791	140	7	,	,	PUNCT
cana-2791	140	8	γ̃−1	γ̃−1	X
cana-2791	140	9	(	(	PUNCT
cana-2791	140	10	s3	s3	PROPN
cana-2791	140	11	)	)	PUNCT
cana-2791	140	12	=	=	PUNCT
cana-2791	141	1	3	3	X
cana-2791	141	2	.	.	PUNCT
cana-2791	142	1	the	the	DET
cana-2791	142	2	outer	outer	ADJ
cana-2791	142	3	connectedness	connectedness	NOUN
cana-2791	142	4	property	property	NOUN
cana-2791	142	5	:	:	PUNCT
cana-2791	142	6	(	(	PUNCT
cana-2791	142	7	s2	s2	PROPN
cana-2791	142	8	)	)	PUNCT
cana-2791	142	9	is	be	AUX
cana-2791	142	10	inverse	inverse	ADJ
cana-2791	142	11	outer	outer	NOUN
cana-2791	142	12	connected	connect	VERB
cana-2791	142	13	.	.	PUNCT
cana-2791	143	1	three	three	NUM
cana-2791	143	2	copies	copy	NOUN
cana-2791	143	3	of	of	ADP
cana-2791	143	4	(	(	PUNCT
cana-2791	143	5	s2	s2	PROPN
cana-2791	143	6	)	)	PUNCT
cana-2791	143	7	is	be	AUX
cana-2791	143	8	incorporated	incorporate	VERB
cana-2791	143	9	in	in	ADP
cana-2791	143	10	(	(	PUNCT
cana-2791	143	11	s3	s3	PROPN
cana-2791	143	12	)	)	PUNCT
cana-2791	143	13	.	.	PUNCT
cana-2791	144	1	we	we	PRON
cana-2791	144	2	have	have	AUX
cana-2791	144	3	chosen	choose	VERB
cana-2791	144	4	one	one	NUM
cana-2791	144	5	vertex	vertex	NOUN
cana-2791	144	6	less	less	ADJ
cana-2791	144	7	in	in	ADP
cana-2791	144	8	(	(	PUNCT
cana-2791	144	9	s3	s3	PROPN
cana-2791	144	10	)	)	PUNCT
cana-2791	144	11	than	than	ADP
cana-2791	144	12	the	the	DET
cana-2791	144	13	number	number	NOUN
cana-2791	144	14	of	of	ADP
cana-2791	144	15	vertices	vertex	NOUN
cana-2791	144	16	chosen	choose	VERB
cana-2791	144	17	in	in	ADP
cana-2791	144	18	(	(	PUNCT
cana-2791	144	19	s2	s2	PROPN
cana-2791	144	20	)	)	PUNCT
cana-2791	144	21	to	to	PART
cana-2791	144	22	satisfy	satisfy	VERB
cana-2791	144	23	the	the	DET
cana-2791	144	24	inverse	inverse	ADJ
cana-2791	144	25	independent	independent	ADJ
cana-2791	144	26	domination	domination	NOUN
cana-2791	144	27	.	.	PUNCT
cana-2791	145	1	hence	hence	ADV
cana-2791	145	2	the	the	DET
cana-2791	145	3	graph	graph	NOUN
cana-2791	145	4	induced	induce	VERB
cana-2791	145	5	by	by	ADP
cana-2791	145	6	the	the	DET
cana-2791	145	7	vertices	vertex	NOUN
cana-2791	145	8	excluding	exclude	VERB
cana-2791	145	9	the	the	DET
cana-2791	145	10	inverse	inverse	NOUN
cana-2791	145	11	independent	independent	ADJ
cana-2791	145	12	dominating	dominating	NOUN
cana-2791	145	13	set	set	NOUN
cana-2791	145	14	is	be	AUX
cana-2791	145	15	connected	connect	VERB
cana-2791	145	16	.	.	PUNCT
cana-2791	146	1	figure	figure	VERB
cana-2791	146	2	6	6	NUM
cana-2791	146	3	shows	show	VERB
cana-2791	146	4	that	that	SCONJ
cana-2791	146	5	s3	s3	PROPN
cana-2791	146	6	is	be	AUX
cana-2791	146	7	inverse	inverse	ADJ
cana-2791	146	8	outer	outer	ADV
cana-2791	146	9	connected	connect	VERB
cana-2791	146	10	.	.	PUNCT
cana-2791	147	1	figure	figure	VERB
cana-2791	147	2	5	5	NUM
cana-2791	147	3	:	:	PUNCT
cana-2791	147	4	(	(	PUNCT
cana-2791	147	5	s3	s3	NOUN
cana-2791	147	6	)	)	PUNCT
cana-2791	147	7	figure	figure	NOUN
cana-2791	147	8	6	6	NUM
cana-2791	147	9	:	:	PUNCT
cana-2791	147	10	s3	s3	PROPN
cana-2791	147	11	is	be	AUX
cana-2791	147	12	outer	outer	ADJ
cana-2791	147	13	connected	connect	VERB
cana-2791	147	14	communications	communication	NOUN
cana-2791	147	15	on	on	ADP
cana-2791	147	16	applied	apply	VERB
cana-2791	147	17	nonlinear	nonlinear	ADJ
cana-2791	147	18	analysis	analysis	NOUN
cana-2791	147	19	issn	issn	NOUN
cana-2791	147	20	:	:	PUNCT
cana-2791	147	21	1074	1074	NUM
cana-2791	147	22	-	-	PUNCT
cana-2791	147	23	133x	133x	NUM
cana-2791	147	24	vol	vol	NOUN
cana-2791	147	25	32	32	NUM
cana-2791	147	26	no	no	NOUN
cana-2791	147	27	.	.	PUNCT
cana-2791	148	1	4s	4s	NUM
cana-2791	148	2	(	(	PUNCT
cana-2791	148	3	2025	2025	NUM
cana-2791	148	4	)	)	PUNCT
cana-2791	149	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2791	149	2	253	253	NUM
cana-2791	149	3	γ̃−	γ̃−	ADJ
cana-2791	149	4	ioc	ioc	PROPN
cana-2791	149	5	ioc	ioc	PROPN
cana-2791	149	6	γ−	γ−	PROPN
cana-2791	149	7	ioc	ioc	PROPN
cana-2791	149	8	ioc	ioc	PROPN
cana-2791	149	9	ioc	ioc	NOUN
cana-2791	149	10	we	we	PRON
cana-2791	149	11	make	make	VERB
cana-2791	149	12	the	the	DET
cana-2791	149	13	assumption	assumption	NOUN
cana-2791	149	14	that	that	SCONJ
cana-2791	149	15	the	the	DET
cana-2791	149	16	result	result	NOUN
cana-2791	149	17	is	be	AUX
cana-2791	149	18	true	true	ADJ
cana-2791	149	19	for	for	ADP
cana-2791	149	20	any	any	DET
cana-2791	149	21	n	n	NOUN
cana-2791	149	22	=	=	NOUN
cana-2791	149	23	i	i	PRON
cana-2791	149	24	where	where	SCONJ
cana-2791	149	25	i	i	PRON
cana-2791	149	26	≥	≥	VERB
cana-2791	149	27	3	3	NUM
cana-2791	149	28	,	,	PUNCT
cana-2791	149	29	then	then	ADV
cana-2791	149	30	1	1	NUM
cana-2791	149	31	ioc	ioc	NOUN
cana-2791	149	32	(	(	PUNCT
cana-2791	149	33	si	si	NOUN
cana-2791	149	34	)	)	PUNCT
cana-2791	149	35	=	=	NOUN
cana-2791	149	36	3i−2	3i−2	NUM
cana-2791	149	37	for	for	ADP
cana-2791	149	38	n	n	NOUN
cana-2791	149	39	=	=	SYM
cana-2791	150	1	i	i	PRON
cana-2791	150	2	+	+	NOUN
cana-2791	150	3	1	1	NUM
cana-2791	150	4	,	,	PUNCT
cana-2791	150	5	the	the	DET
cana-2791	150	6	sierpinski	sierpinski	ADJ
cana-2791	150	7	gasket	gasket	NOUN
cana-2791	150	8	graph	graph	NOUN
cana-2791	150	9	si+1	si+1	NOUN
cana-2791	150	10	is	be	AUX
cana-2791	150	11	obtained	obtain	VERB
cana-2791	150	12	by	by	ADP
cana-2791	150	13	taking	take	VERB
cana-2791	150	14	three	three	NUM
cana-2791	150	15	copies	copy	NOUN
cana-2791	150	16	of	of	ADP
cana-2791	150	17	si	si	X
cana-2791	150	18	.	.	PUNCT
cana-2791	151	1	we	we	PRON
cana-2791	151	2	take	take	VERB
cana-2791	151	3	3i−2	3i−2	NUM
cana-2791	151	4	vertices	vertex	NOUN
cana-2791	151	5	in	in	ADP
cana-2791	151	6	each	each	DET
cana-2791	151	7	jth	jth	PROPN
cana-2791	151	8	copy	copy	NOUN
cana-2791	151	9	of	of	ADP
cana-2791	151	10	si	si	PROPN
cana-2791	151	11	of	of	ADP
cana-2791	151	12	si+1	si+1	PROPN
cana-2791	151	13	.	.	PUNCT
cana-2791	152	1	then	then	ADV
cana-2791	152	2	γ̃−1	γ̃−1	PUNCT
cana-2791	152	3	(	(	PUNCT
cana-2791	152	4	si+1	si+1	NOUN
cana-2791	152	5	)	)	PUNCT
cana-2791	152	6	=	=	SYM
cana-2791	152	7	3	3	NUM
cana-2791	152	8	×	×	NOUN
cana-2791	152	9	3i−2	3i−2	NUM
cana-2791	152	10	=	=	PUNCT
cana-2791	152	11	3(i+1)−2	3(i+1)−2	NUM
cana-2791	152	12	the	the	DET
cana-2791	152	13	outer	outer	ADJ
cana-2791	152	14	connectedness	connectedness	NOUN
cana-2791	152	15	property	property	NOUN
cana-2791	152	16	:	:	PUNCT
cana-2791	152	17	(	(	PUNCT
cana-2791	152	18	si	si	X
cana-2791	152	19	)	)	PUNCT
cana-2791	152	20	is	be	AUX
cana-2791	152	21	inverse	inverse	ADJ
cana-2791	152	22	independent	independent	ADJ
cana-2791	152	23	outer	outer	NOUN
cana-2791	152	24	connected	connect	VERB
cana-2791	152	25	and	and	CCONJ
cana-2791	152	26	hence	hence	ADV
cana-2791	152	27	(	(	PUNCT
cana-2791	152	28	si+1	si+1	NOUN
cana-2791	152	29	)	)	PUNCT
cana-2791	152	30	is	be	AUX
cana-2791	152	31	also	also	ADV
cana-2791	152	32	inverse	inverse	ADJ
cana-2791	152	33	independent	independent	ADJ
cana-2791	152	34	outer	outer	NOUN
cana-2791	152	35	connected	connect	VERB
cana-2791	152	36	as	as	ADP
cana-2791	152	37	(	(	PUNCT
cana-2791	152	38	s1	s1	NOUN
cana-2791	152	39	)	)	PUNCT
cana-2791	152	40	is	be	AUX
cana-2791	152	41	contained	contain	VERB
cana-2791	152	42	inside	inside	ADV
cana-2791	152	43	(	(	PUNCT
cana-2791	152	44	si+1	si+1	NOUN
cana-2791	152	45	)	)	PUNCT
cana-2791	152	46	.	.	PUNCT
cana-2791	153	1	to	to	PART
cana-2791	153	2	up	up	ADP
cana-2791	153	3	hold	hold	VERB
cana-2791	153	4	this	this	DET
cana-2791	153	5	property	property	NOUN
cana-2791	153	6	we	we	PRON
cana-2791	153	7	have	have	VERB
cana-2791	153	8	to	to	PART
cana-2791	153	9	restrain	restrain	VERB
cana-2791	153	10	ourselves	ourselves	PRON
cana-2791	153	11	from	from	ADP
cana-2791	153	12	choosing	choose	VERB
cana-2791	153	13	vertices	vertex	NOUN
cana-2791	153	14	labelled	label	VERB
cana-2791	153	15	{	{	PUNCT
cana-2791	153	16	p	p	X
cana-2791	153	17	,	,	PUNCT
cana-2791	153	18	q	q	NOUN
cana-2791	153	19	}	}	PUNCT
cana-2791	153	20	,	,	PUNCT
cana-2791	153	21	{	{	PUNCT
cana-2791	153	22	q	q	X
cana-2791	153	23	,	,	PUNCT
cana-2791	153	24	r	r	NOUN
cana-2791	153	25	}	}	PUNCT
cana-2791	153	26	,	,	PUNCT
cana-2791	153	27	{	{	PUNCT
cana-2791	153	28	p	p	X
cana-2791	153	29	,	,	PUNCT
cana-2791	153	30	r	r	NOUN
cana-2791	153	31	}	}	PUNCT
cana-2791	153	32	where	where	SCONJ
cana-2791	153	33	{	{	PUNCT
cana-2791	153	34	p	p	X
cana-2791	153	35	,	,	PUNCT
cana-2791	153	36	q	q	ADJ
cana-2791	153	37	,	,	PUNCT
cana-2791	153	38	r	r	NOUN
cana-2791	153	39	}	}	PUNCT
cana-2791	153	40	=	=	PUNCT
cana-2791	153	41	{	{	PUNCT
cana-2791	153	42	1	1	NUM
cana-2791	153	43	,	,	PUNCT
cana-2791	153	44	2	2	NUM
cana-2791	153	45	,	,	PUNCT
cana-2791	153	46	3	3	NUM
cana-2791	153	47	}	}	PUNCT
cana-2791	153	48	respectively	respectively	ADV
cana-2791	153	49	.	.	PUNCT
cana-2791	154	1	therefore	therefore	ADV
cana-2791	154	2	γ̃−1	γ̃−1	PUNCT
cana-2791	154	3	(	(	PUNCT
cana-2791	154	4	sn	sn	PROPN
cana-2791	154	5	)	)	PUNCT
cana-2791	154	6	=	=	SYM
cana-2791	154	7	3n−2	3n−2	NUM
cana-2791	154	8	,	,	PUNCT
cana-2791	154	9	n	n	PRON
cana-2791	154	10	≥	≥	NOUN
cana-2791	154	11	3	3	NUM
cana-2791	154	12	6	6	NUM
cana-2791	154	13	inverse	inverse	NOUN
cana-2791	154	14	independent	independent	ADJ
cana-2791	154	15	outer	outer	ADJ
cana-2791	154	16	connected	connected	ADJ
cana-2791	154	17	domination	domination	NOUN
cana-2791	154	18	number	number	NOUN
cana-2791	154	19	of	of	ADP
cana-2791	154	20	corona	corona	NOUN
cana-2791	154	21	of	of	ADP
cana-2791	154	22	a	a	DET
cana-2791	154	23	finite	finite	ADJ
cana-2791	154	24	simple	simple	ADJ
cana-2791	154	25	undirected	undirected	ADJ
cana-2791	154	26	con	con	NOUN
cana-2791	154	27	nected	necte	VERB
cana-2791	154	28	graph	graph	NOUN
cana-2791	154	29	and	and	CCONJ
cana-2791	154	30	complete	complete	ADJ
cana-2791	154	31	graph	graph	NOUN
cana-2791	154	32	theorem	theorem	VERB
cana-2791	154	33	6.1	6.1	NUM
cana-2791	154	34	.	.	PUNCT
cana-2791	155	1	g1	g1	PROPN
cana-2791	155	2	is	be	AUX
cana-2791	155	3	a	a	DET
cana-2791	155	4	complete	complete	ADJ
cana-2791	155	5	graph	graph	NOUN
cana-2791	155	6	with	with	ADP
cana-2791	155	7	′n′	′n′	NOUN
cana-2791	155	8	vertices	vertex	NOUN
cana-2791	155	9	and	and	CCONJ
cana-2791	155	10	g2	g2	PROPN
cana-2791	155	11	is	be	AUX
cana-2791	155	12	a	a	DET
cana-2791	155	13	complete	complete	ADJ
cana-2791	155	14	graph	graph	NOUN
cana-2791	155	15	with	with	ADP
cana-2791	155	16	′m′	′m′	PUNCT
cana-2791	155	17	vertices	vertex	NOUN
cana-2791	155	18	,	,	PUNCT
cana-2791	155	19	then	then	ADV
cana-2791	155	20	1	1	NUM
cana-2791	155	21	ioc	ioc	NOUN
cana-2791	155	22	(	(	PUNCT
cana-2791	155	23	kn	kn	NOUN
cana-2791	155	24	◦	◦	PROPN
cana-2791	155	25	km	km	PROPN
cana-2791	155	26	)	)	PUNCT
cana-2791	155	27	=	=	SYM
cana-2791	156	1	n	n	PROPN
cana-2791	156	2	where	where	SCONJ
cana-2791	156	3	n	n	PRON
cana-2791	156	4	≥	≥	X
cana-2791	156	5	2	2	NUM
cana-2791	156	6	and	and	CCONJ
cana-2791	156	7	m	m	PROPN
cana-2791	156	8	≥	≥	NOUN
cana-2791	156	9	2	2	NUM
cana-2791	156	10	proof	proof	NOUN
cana-2791	156	11	.	.	PUNCT
cana-2791	157	1	the	the	DET
cana-2791	157	2	inverse	inverse	ADJ
cana-2791	157	3	independent	independent	ADJ
cana-2791	157	4	dominating	dominating	NOUN
cana-2791	157	5	set	set	NOUN
cana-2791	157	6	for	for	ADP
cana-2791	157	7	such	such	ADJ
cana-2791	157	8	corona	corona	NOUN
cana-2791	157	9	graphs	graph	NOUN
cana-2791	157	10	can	can	AUX
cana-2791	157	11	be	be	AUX
cana-2791	157	12	chosen	choose	VERB
cana-2791	157	13	from	from	ADP
cana-2791	157	14	g2	g2	PROPN
cana-2791	157	15	.	.	PUNCT
cana-2791	158	1	since	since	SCONJ
cana-2791	158	2	g1	g1	PROPN
cana-2791	158	3	and	and	CCONJ
cana-2791	158	4	g2	g2	PROPN
cana-2791	158	5	are	be	AUX
cana-2791	158	6	complete	complete	ADJ
cana-2791	158	7	graphs	graph	NOUN
cana-2791	158	8	,	,	PUNCT
cana-2791	158	9	choosing	choose	VERB
cana-2791	158	10	one	one	NUM
cana-2791	158	11	vertex	vertex	NOUN
cana-2791	158	12	from	from	ADP
cana-2791	158	13	the	the	DET
cana-2791	158	14	ith	ith	PROPN
cana-2791	158	15	copy	copy	NOUN
cana-2791	158	16	of	of	ADP
cana-2791	158	17	g2	g2	PROPN
cana-2791	158	18	will	will	AUX
cana-2791	158	19	dominate	dominate	VERB
cana-2791	158	20	all	all	DET
cana-2791	158	21	the	the	DET
cana-2791	158	22	vertex	vertex	NOUN
cana-2791	158	23	in	in	ADP
cana-2791	158	24	the	the	DET
cana-2791	158	25	ith	ith	PROPN
cana-2791	158	26	copy	copy	NOUN
cana-2791	158	27	of	of	ADP
cana-2791	158	28	g2	g2	PROPN
cana-2791	158	29	and	and	CCONJ
cana-2791	158	30	the	the	DET
cana-2791	158	31	ith	ith	PROPN
cana-2791	158	32	vertex	vertex	NOUN
cana-2791	158	33	of	of	ADP
cana-2791	158	34	g1	g1	PROPN
cana-2791	158	35	.	.	PUNCT
cana-2791	159	1	hence	hence	ADV
cana-2791	159	2	we	we	PRON
cana-2791	159	3	choose	choose	VERB
cana-2791	159	4	one	one	NUM
cana-2791	159	5	vertex	vertex	NOUN
cana-2791	159	6	each	each	PRON
cana-2791	159	7	from	from	ADP
cana-2791	159	8	the	the	DET
cana-2791	159	9	g2	g2	PROPN
cana-2791	159	10	graphs	graph	NOUN
cana-2791	159	11	.	.	PUNCT
cana-2791	160	1	the	the	DET
cana-2791	160	2	total	total	ADJ
cana-2791	160	3	number	number	NOUN
cana-2791	160	4	of	of	ADP
cana-2791	160	5	g2	g2	PROPN
cana-2791	160	6	graphs	graph	NOUN
cana-2791	160	7	is	be	AUX
cana-2791	160	8	equal	equal	ADJ
cana-2791	160	9	to	to	ADP
cana-2791	160	10	the	the	DET
cana-2791	160	11	number	number	NOUN
cana-2791	160	12	of	of	ADP
cana-2791	160	13	vertices	vertex	NOUN
cana-2791	160	14	in	in	ADP
cana-2791	160	15	g1	g1	NOUN
cana-2791	160	16	.	.	PUNCT
cana-2791	161	1	therefore	therefore	ADV
cana-2791	161	2	γ−1	γ−1	PROPN
cana-2791	161	3	(	(	PUNCT
cana-2791	161	4	kn	kn	NOUN
cana-2791	161	5	◦	◦	PROPN
cana-2791	161	6	km	km	PROPN
cana-2791	161	7	)	)	PUNCT
cana-2791	161	8	=	=	SYM
cana-2791	161	9	n	n	PRON
cana-2791	161	10	a	a	DET
cana-2791	161	11	k6	k6	NOUN
cana-2791	161	12	◦	◦	NOUN
cana-2791	161	13	k4	k4	ADJ
cana-2791	161	14	graph	graph	NOUN
cana-2791	161	15	is	be	AUX
cana-2791	161	16	shown	show	VERB
cana-2791	161	17	in	in	ADP
cana-2791	161	18	figure	figure	NOUN
cana-2791	161	19	7	7	NUM
cana-2791	161	20	and	and	CCONJ
cana-2791	161	21	the	the	DET
cana-2791	161	22	γ−1	γ−1	PROPN
cana-2791	161	23	(	(	PUNCT
cana-2791	161	24	k6	k6	PROPN
cana-2791	161	25	◦	◦	NOUN
cana-2791	161	26	k4	k4	NOUN
cana-2791	161	27	)	)	PUNCT
cana-2791	161	28	=	=	SYM
cana-2791	161	29	6	6	NUM
cana-2791	161	30	figure	figure	NOUN
cana-2791	161	31	7	7	NUM
cana-2791	161	32	:	:	PUNCT
cana-2791	161	33	γ−1	γ−1	PROPN
cana-2791	161	34	(	(	PUNCT
cana-2791	161	35	k6	k6	PROPN
cana-2791	161	36	◦	◦	NOUN
cana-2791	161	37	k4	k4	PROPN
cana-2791	161	38	)	)	PUNCT
cana-2791	161	39	the	the	DET
cana-2791	161	40	outer	outer	ADJ
cana-2791	161	41	connectedness	connectedness	NOUN
cana-2791	161	42	property	property	NOUN
cana-2791	161	43	:	:	PUNCT
cana-2791	161	44	removing	remove	VERB
cana-2791	161	45	one	one	NUM
cana-2791	161	46	vertex	vertex	NOUN
cana-2791	161	47	from	from	ADP
cana-2791	161	48	a	a	DET
cana-2791	161	49	complete	complete	ADJ
cana-2791	161	50	graph	graph	NOUN
cana-2791	161	51	will	will	AUX
cana-2791	161	52	not	not	PART
cana-2791	161	53	affect	affect	VERB
cana-2791	161	54	the	the	DET
cana-2791	161	55	connectedness	connectedness	NOUN
cana-2791	161	56	of	of	ADP
cana-2791	161	57	the	the	DET
cana-2791	161	58	graph	graph	NOUN
cana-2791	161	59	since	since	SCONJ
cana-2791	161	60	all	all	DET
cana-2791	161	61	the	the	DET
cana-2791	161	62	vertices	vertex	NOUN
cana-2791	161	63	in	in	ADP
cana-2791	161	64	g2	g2	PROPN
cana-2791	161	65	are	be	AUX
cana-2791	161	66	connected	connect	VERB
cana-2791	161	67	to	to	ADP
cana-2791	161	68	all	all	DET
cana-2791	161	69	other	other	ADJ
cana-2791	161	70	vertices	vertex	NOUN
cana-2791	161	71	in	in	ADP
cana-2791	161	72	g2	g2	PROPN
cana-2791	161	73	and	and	CCONJ
cana-2791	161	74	also	also	ADV
cana-2791	161	75	it	it	PRON
cana-2791	161	76	is	be	AUX
cana-2791	161	77	connected	connect	VERB
cana-2791	161	78	to	to	AUX
cana-2791	161	79	g1	g1	VERB
cana-2791	161	80	in	in	ADP
cana-2791	161	81	one	one	NUM
cana-2791	161	82	way	way	NOUN
cana-2791	161	83	or	or	CCONJ
cana-2791	161	84	the	the	DET
cana-2791	161	85	other	other	ADJ
cana-2791	161	86	.	.	PUNCT
cana-2791	162	1	choosing	choose	VERB
cana-2791	162	2	a	a	DET
cana-2791	162	3	vertex	vertex	NOUN
cana-2791	162	4	from	from	ADP
cana-2791	162	5	the	the	DET
cana-2791	162	6	graph	graph	NOUN
cana-2791	162	7	g1	g1	NOUN
cana-2791	162	8	must	must	AUX
cana-2791	162	9	be	be	AUX
cana-2791	162	10	restricted	restrict	VERB
cana-2791	162	11	.	.	PUNCT
cana-2791	163	1	communications	communication	NOUN
cana-2791	163	2	on	on	ADP
cana-2791	163	3	applied	apply	VERB
cana-2791	163	4	nonlinear	nonlinear	ADJ
cana-2791	163	5	analysis	analysis	NOUN
cana-2791	163	6	issn	issn	NOUN
cana-2791	163	7	:	:	PUNCT
cana-2791	163	8	1074	1074	NUM
cana-2791	163	9	-	-	PUNCT
cana-2791	163	10	133x	133x	NUM
cana-2791	163	11	vol	vol	NOUN
cana-2791	163	12	32	32	NUM
cana-2791	163	13	no	no	NOUN
cana-2791	163	14	.	.	PUNCT
cana-2791	164	1	4s	4s	NUM
cana-2791	164	2	(	(	PUNCT
cana-2791	164	3	2025	2025	NUM
cana-2791	164	4	)	)	PUNCT
cana-2791	165	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2791	165	2	254	254	NUM
cana-2791	165	3	γ−	γ−	NUM
cana-2791	165	4	ioc	ioc	NOUN
cana-2791	165	5	γ−	γ−	NUM
cana-2791	165	6	i	i	PRON
cana-2791	165	7	ioc	ioc	PROPN
cana-2791	166	1	i	i	PRON
cana-2791	166	2	theorem	theorem	VERB
cana-2791	166	3	6.2	6.2	NUM
cana-2791	166	4	.	.	PUNCT
cana-2791	167	1	g1	g1	PROPN
cana-2791	167	2	is	be	AUX
cana-2791	167	3	a	a	DET
cana-2791	167	4	cycle	cycle	NOUN
cana-2791	167	5	graph	graph	NOUN
cana-2791	167	6	with	with	ADP
cana-2791	167	7	′n′	′n′	NOUN
cana-2791	167	8	vertices	vertex	NOUN
cana-2791	167	9	and	and	CCONJ
cana-2791	167	10	g2	g2	PROPN
cana-2791	167	11	is	be	AUX
cana-2791	167	12	a	a	DET
cana-2791	167	13	complete	complete	ADJ
cana-2791	167	14	graph	graph	NOUN
cana-2791	167	15	with	with	ADP
cana-2791	167	16	′m′	′m′	PUNCT
cana-2791	167	17	vertices	vertex	NOUN
cana-2791	167	18	,	,	PUNCT
cana-2791	167	19	then	then	ADV
cana-2791	167	20	1	1	NUM
cana-2791	167	21	ioc	ioc	NOUN
cana-2791	167	22	(	(	PUNCT
cana-2791	167	23	cn	cn	NOUN
cana-2791	167	24	◦	◦	PROPN
cana-2791	167	25	km	km	PROPN
cana-2791	167	26	)	)	PUNCT
cana-2791	167	27	=	=	SYM
cana-2791	168	1	n	n	PROPN
cana-2791	168	2	where	where	SCONJ
cana-2791	168	3	n	n	PRON
cana-2791	168	4	≥	≥	X
cana-2791	168	5	3	3	NUM
cana-2791	168	6	and	and	CCONJ
cana-2791	168	7	m	m	PROPN
cana-2791	168	8	≥	≥	NOUN
cana-2791	168	9	2	2	NUM
cana-2791	168	10	proof	proof	NOUN
cana-2791	168	11	.	.	PUNCT
cana-2791	169	1	the	the	DET
cana-2791	169	2	first	first	ADJ
cana-2791	169	3	graph	graph	NOUN
cana-2791	169	4	is	be	AUX
cana-2791	169	5	a	a	DET
cana-2791	169	6	cycle	cycle	NOUN
cana-2791	169	7	graph	graph	NOUN
cana-2791	169	8	and	and	CCONJ
cana-2791	169	9	the	the	DET
cana-2791	169	10	second	second	ADJ
cana-2791	169	11	graph	graph	NOUN
cana-2791	169	12	is	be	AUX
cana-2791	169	13	a	a	DET
cana-2791	169	14	complete	complete	ADJ
cana-2791	169	15	graph	graph	NOUN
cana-2791	169	16	.	.	PUNCT
cana-2791	170	1	we	we	PRON
cana-2791	170	2	choose	choose	VERB
cana-2791	170	3	one	one	NUM
cana-2791	170	4	vertex	vertex	NOUN
cana-2791	170	5	from	from	ADP
cana-2791	170	6	each	each	DET
cana-2791	170	7	copy	copy	NOUN
cana-2791	170	8	of	of	ADP
cana-2791	170	9	g2	g2	PROPN
cana-2791	170	10	which	which	PRON
cana-2791	170	11	will	will	AUX
cana-2791	170	12	dominate	dominate	VERB
cana-2791	170	13	all	all	DET
cana-2791	170	14	vertices	vertex	NOUN
cana-2791	170	15	of	of	ADP
cana-2791	170	16	that	that	DET
cana-2791	170	17	particular	particular	ADJ
cana-2791	170	18	graph	graph	NOUN
cana-2791	170	19	and	and	CCONJ
cana-2791	170	20	also	also	ADV
cana-2791	170	21	one	one	NUM
cana-2791	170	22	vertex	vertex	NOUN
cana-2791	170	23	each	each	PRON
cana-2791	170	24	of	of	ADP
cana-2791	170	25	the	the	DET
cana-2791	170	26	graph	graph	NOUN
cana-2791	170	27	g1	g1	NOUN
cana-2791	170	28	.	.	PUNCT
cana-2791	171	1	since	since	SCONJ
cana-2791	171	2	we	we	PRON
cana-2791	171	3	choose	choose	VERB
cana-2791	171	4	one	one	NUM
cana-2791	171	5	vertex	vertex	NOUN
cana-2791	171	6	from	from	ADP
cana-2791	171	7	different	different	ADJ
cana-2791	171	8	copies	copy	NOUN
cana-2791	171	9	the	the	DET
cana-2791	171	10	vertices	vertex	NOUN
cana-2791	171	11	will	will	AUX
cana-2791	171	12	be	be	AUX
cana-2791	171	13	independent	independent	ADJ
cana-2791	171	14	.	.	PUNCT
cana-2791	172	1	therefore	therefore	ADV
cana-2791	172	2	γ−1	γ−1	PROPN
cana-2791	172	3	(	(	PUNCT
cana-2791	172	4	cn	cn	PROPN
cana-2791	172	5	◦	◦	PROPN
cana-2791	172	6	km	km	PROPN
cana-2791	172	7	)	)	PUNCT
cana-2791	172	8	=	=	SYM
cana-2791	172	9	n	n	CCONJ
cana-2791	172	10	the	the	DET
cana-2791	172	11	outer	outer	ADJ
cana-2791	172	12	connectedness	connectedness	NOUN
cana-2791	172	13	property	property	NOUN
cana-2791	172	14	:	:	PUNCT
cana-2791	172	15	choosing	choose	VERB
cana-2791	172	16	a	a	DET
cana-2791	172	17	vertex	vertex	NOUN
cana-2791	172	18	from	from	ADP
cana-2791	172	19	g1	g1	PROPN
cana-2791	172	20	must	must	AUX
cana-2791	172	21	be	be	AUX
cana-2791	172	22	restricted	restrict	VERB
cana-2791	172	23	.	.	PUNCT
cana-2791	173	1	it	it	PRON
cana-2791	173	2	will	will	AUX
cana-2791	173	3	be	be	AUX
cana-2791	173	4	inverse	inverse	ADJ
cana-2791	173	5	independent	independent	ADJ
cana-2791	173	6	outer	outer	NOUN
cana-2791	173	7	connected	connect	VERB
cana-2791	173	8	as	as	ADP
cana-2791	173	9	the	the	DET
cana-2791	173	10	complete	complete	ADJ
cana-2791	173	11	graphs	graph	NOUN
cana-2791	173	12	after	after	ADP
cana-2791	173	13	removing	remove	VERB
cana-2791	173	14	a	a	DET
cana-2791	173	15	vertex	vertex	NOUN
cana-2791	173	16	will	will	AUX
cana-2791	173	17	be	be	AUX
cana-2791	173	18	still	still	ADV
cana-2791	173	19	connected	connect	VERB
cana-2791	173	20	and	and	CCONJ
cana-2791	173	21	all	all	DET
cana-2791	173	22	the	the	DET
cana-2791	173	23	vertices	vertex	NOUN
cana-2791	173	24	of	of	ADP
cana-2791	173	25	each	each	DET
cana-2791	173	26	g2	g2	NOUN
cana-2791	173	27	are	be	AUX
cana-2791	173	28	connected	connect	VERB
cana-2791	173	29	to	to	AUX
cana-2791	173	30	g1	g1	VERB
cana-2791	173	31	.	.	PUNCT
cana-2791	174	1	note	note	NOUN
cana-2791	174	2	:	:	PUNCT
cana-2791	174	3	from	from	ADP
cana-2791	174	4	theorem	theorem	ADJ
cana-2791	174	5	6.1	6.1	NUM
cana-2791	174	6	and	and	CCONJ
cana-2791	174	7	theorem	theorem	VERB
cana-2791	174	8	6.2	6.2	NUM
cana-2791	174	9	,	,	PUNCT
cana-2791	174	10	whenever	whenever	SCONJ
cana-2791	174	11	g1	g1	PROPN
cana-2791	174	12	is	be	AUX
cana-2791	174	13	a	a	DET
cana-2791	174	14	finite	finite	ADJ
cana-2791	174	15	simple	simple	ADJ
cana-2791	174	16	undirected	undirected	ADJ
cana-2791	174	17	connected	connected	ADJ
cana-2791	174	18	graph	graph	NOUN
cana-2791	174	19	and	and	CCONJ
cana-2791	174	20	g2	g2	PROPN
cana-2791	174	21	is	be	AUX
cana-2791	174	22	a	a	DET
cana-2791	174	23	complete	complete	ADJ
cana-2791	174	24	graph	graph	NOUN
cana-2791	174	25	,	,	PUNCT
cana-2791	174	26	then	then	ADV
cana-2791	174	27	the	the	DET
cana-2791	174	28	inverse	inverse	ADJ
cana-2791	174	29	independent	independent	ADJ
cana-2791	174	30	outer	outer	ADJ
cana-2791	174	31	connected	connected	ADJ
cana-2791	174	32	domi	domi	NOUN
cana-2791	174	33	nation	nation	NOUN
cana-2791	174	34	number	number	NOUN
cana-2791	174	35	of	of	ADP
cana-2791	174	36	the	the	DET
cana-2791	174	37	corona	corona	NOUN
cana-2791	174	38	of	of	ADP
cana-2791	174	39	these	these	DET
cana-2791	174	40	two	two	NUM
cana-2791	174	41	graphs	graph	NOUN
cana-2791	174	42	will	will	AUX
cana-2791	174	43	be	be	AUX
cana-2791	174	44	equal	equal	ADJ
cana-2791	174	45	to	to	ADP
cana-2791	174	46	the	the	DET
cana-2791	174	47	number	number	NOUN
cana-2791	174	48	of	of	ADP
cana-2791	174	49	vertices	vertex	NOUN
cana-2791	174	50	in	in	ADP
cana-2791	174	51	g1	g1	NOUN
cana-2791	174	52	.	.	PUNCT
cana-2791	175	1	since	since	SCONJ
cana-2791	175	2	we	we	PRON
cana-2791	175	3	are	be	AUX
cana-2791	175	4	choosing	choose	VERB
cana-2791	175	5	the	the	DET
cana-2791	175	6	vertices	vertex	NOUN
cana-2791	175	7	from	from	ADP
cana-2791	175	8	the	the	DET
cana-2791	175	9	complete	complete	ADJ
cana-2791	175	10	graph	graph	NOUN
cana-2791	175	11	g2	g2	PROPN
cana-2791	175	12	which	which	PRON
cana-2791	175	13	is	be	AUX
cana-2791	175	14	connected	connect	VERB
cana-2791	175	15	to	to	ADP
cana-2791	175	16	g1	g1	VERB
cana-2791	175	17	always	always	ADV
cana-2791	175	18	.	.	PUNCT
cana-2791	176	1	the	the	DET
cana-2791	176	2	type	type	NOUN
cana-2791	176	3	of	of	ADP
cana-2791	176	4	the	the	DET
cana-2791	176	5	graph	graph	NOUN
cana-2791	176	6	g1	g1	NOUN
cana-2791	176	7	need	need	AUX
cana-2791	176	8	not	not	PART
cana-2791	176	9	be	be	AUX
cana-2791	176	10	considered	consider	VERB
cana-2791	176	11	except	except	SCONJ
cana-2791	176	12	that	that	SCONJ
cana-2791	176	13	it	it	PRON
cana-2791	176	14	is	be	AUX
cana-2791	176	15	connected	connect	VERB
cana-2791	176	16	.	.	PUNCT
cana-2791	177	1	the	the	DET
cana-2791	177	2	outer	outer	ADJ
cana-2791	177	3	connectedness	connectedness	NOUN
cana-2791	177	4	property	property	NOUN
cana-2791	177	5	:	:	PUNCT
cana-2791	177	6	choosing	choose	VERB
cana-2791	177	7	a	a	DET
cana-2791	177	8	vertex	vertex	NOUN
cana-2791	177	9	from	from	ADP
cana-2791	177	10	g1	g1	PROPN
cana-2791	177	11	must	must	AUX
cana-2791	177	12	be	be	AUX
cana-2791	177	13	restricted	restrict	VERB
cana-2791	177	14	.	.	PUNCT
cana-2791	178	1	7	7	NUM
cana-2791	178	2	inverse	inverse	NOUN
cana-2791	178	3	independent	independent	ADJ
cana-2791	178	4	outer	outer	ADJ
cana-2791	178	5	connected	connected	ADJ
cana-2791	178	6	domination	domination	NOUN
cana-2791	178	7	number	number	NOUN
cana-2791	178	8	of	of	ADP
cana-2791	178	9	corona	corona	NOUN
cana-2791	178	10	of	of	ADP
cana-2791	178	11	complete	complete	ADJ
cana-2791	178	12	graph	graph	NOUN
cana-2791	178	13	and	and	CCONJ
cana-2791	178	14	cycle	cycle	NOUN
cana-2791	178	15	graph	graph	NOUN
cana-2791	178	16	theorem	theorem	VERB
cana-2791	178	17	7.1	7.1	NUM
cana-2791	178	18	.	.	PUNCT
cana-2791	179	1	g1	g1	PROPN
cana-2791	179	2	is	be	AUX
cana-2791	179	3	a	a	DET
cana-2791	179	4	complete	complete	ADJ
cana-2791	179	5	graph	graph	NOUN
cana-2791	179	6	with	with	ADP
cana-2791	179	7	′m′	′m′	ADV
cana-2791	179	8	vertices	vertex	NOUN
cana-2791	179	9	and	and	CCONJ
cana-2791	179	10	g2	g2	PROPN
cana-2791	179	11	is	be	AUX
cana-2791	179	12	a	a	DET
cana-2791	179	13	cycle	cycle	NOUN
cana-2791	179	14	graph	graph	NOUN
cana-2791	179	15	with	with	ADP
cana-2791	179	16	′n′	′n′	NOUN
cana-2791	179	17	vertices	vertex	NOUN
cana-2791	179	18	,	,	PUNCT
cana-2791	180	1	then	then	ADV
cana-2791	180	2	1	1	NUM
cana-2791	180	3	ioc	ioc	NOUN
cana-2791	180	4	(	(	PUNCT
cana-2791	180	5	km	km	NOUN
cana-2791	180	6	◦	◦	NOUN
cana-2791	180	7	cn	cn	ADJ
cana-2791	180	8	)	)	PUNCT
cana-2791	180	9	=	=	SYM
cana-2791	180	10	mγ−1(cn	mγ−1(cn	X
cana-2791	180	11	)	)	PUNCT
cana-2791	180	12	where	where	SCONJ
cana-2791	180	13	m	m	PROPN
cana-2791	180	14	≥	≥	VERB
cana-2791	180	15	2	2	NUM
cana-2791	180	16	and	and	CCONJ
cana-2791	180	17	n	n	PRON
cana-2791	180	18	≥	≥	NOUN
cana-2791	180	19	3	3	NUM
cana-2791	180	20	proof	proof	NOUN
cana-2791	180	21	.	.	PUNCT
cana-2791	181	1	g1	g1	PROPN
cana-2791	181	2	is	be	AUX
cana-2791	181	3	a	a	DET
cana-2791	181	4	complete	complete	ADJ
cana-2791	181	5	graph	graph	NOUN
cana-2791	181	6	and	and	CCONJ
cana-2791	181	7	g2	g2	PROPN
cana-2791	181	8	is	be	AUX
cana-2791	181	9	a	a	DET
cana-2791	181	10	cycle	cycle	NOUN
cana-2791	181	11	graph	graph	NOUN
cana-2791	181	12	,	,	PUNCT
cana-2791	181	13	the	the	DET
cana-2791	181	14	inverse	inverse	ADJ
cana-2791	181	15	independent	independent	ADJ
cana-2791	181	16	outer	outer	ADJ
cana-2791	181	17	connected	connected	ADJ
cana-2791	181	18	dominating	dominating	NOUN
cana-2791	181	19	set	set	NOUN
cana-2791	181	20	of	of	ADP
cana-2791	181	21	the	the	DET
cana-2791	181	22	corona	corona	NOUN
cana-2791	181	23	of	of	ADP
cana-2791	181	24	two	two	NUM
cana-2791	181	25	graphs	graph	NOUN
cana-2791	181	26	can	can	AUX
cana-2791	181	27	be	be	AUX
cana-2791	181	28	found	find	VERB
cana-2791	181	29	out	out	ADP
cana-2791	181	30	by	by	ADP
cana-2791	181	31	choosing	choose	VERB
cana-2791	181	32	the	the	DET
cana-2791	181	33	inverse	inverse	NOUN
cana-2791	181	34	independent	independent	ADJ
cana-2791	181	35	dominating	dominating	NOUN
cana-2791	181	36	set	set	NOUN
cana-2791	181	37	of	of	ADP
cana-2791	181	38	the	the	DET
cana-2791	181	39	cycle	cycle	NOUN
cana-2791	181	40	graph	graph	NOUN
cana-2791	181	41	.	.	PUNCT
cana-2791	182	1	in	in	ADP
cana-2791	182	2	the	the	DET
cana-2791	182	3	corona	corona	NOUN
cana-2791	182	4	graphs	graph	VERB
cana-2791	182	5	the	the	DET
cana-2791	182	6	inverse	inverse	ADJ
cana-2791	182	7	independent	independent	ADJ
cana-2791	182	8	outer	outer	ADJ
cana-2791	182	9	connected	connected	ADJ
cana-2791	182	10	dominating	dominating	NOUN
cana-2791	182	11	set	set	NOUN
cana-2791	182	12	is	be	AUX
cana-2791	182	13	chosen	choose	VERB
cana-2791	182	14	from	from	ADP
cana-2791	182	15	the	the	DET
cana-2791	182	16	second	second	ADJ
cana-2791	182	17	graph	graph	NOUN
cana-2791	182	18	as	as	SCONJ
cana-2791	182	19	it	it	PRON
cana-2791	182	20	will	will	AUX
cana-2791	182	21	dominate	dominate	VERB
cana-2791	182	22	the	the	DET
cana-2791	182	23	vertices	vertex	NOUN
cana-2791	182	24	in	in	ADP
cana-2791	182	25	g2	g2	PROPN
cana-2791	182	26	as	as	ADV
cana-2791	182	27	well	well	ADV
cana-2791	182	28	as	as	ADP
cana-2791	182	29	in	in	ADP
cana-2791	182	30	g1	g1	PROPN
cana-2791	182	31	.	.	PUNCT
cana-2791	183	1	inverse	inverse	NOUN
cana-2791	183	2	independent	independent	ADJ
cana-2791	183	3	dominating	dominating	NOUN
cana-2791	183	4	set	set	NOUN
cana-2791	183	5	in	in	ADP
cana-2791	183	6	each	each	DET
cana-2791	183	7	copy	copy	NOUN
cana-2791	183	8	will	will	AUX
cana-2791	183	9	be	be	AUX
cana-2791	183	10	the	the	DET
cana-2791	183	11	same	same	ADJ
cana-2791	183	12	as	as	ADP
cana-2791	183	13	the	the	DET
cana-2791	183	14	number	number	NOUN
cana-2791	183	15	of	of	ADP
cana-2791	183	16	copies	copy	NOUN
cana-2791	183	17	of	of	ADP
cana-2791	183	18	g2	g2	PROPN
cana-2791	183	19	,	,	PUNCT
cana-2791	183	20	that	that	PRON
cana-2791	183	21	is	be	AUX
cana-2791	183	22	same	same	ADJ
cana-2791	183	23	as	as	ADP
cana-2791	183	24	the	the	DET
cana-2791	183	25	number	number	NOUN
cana-2791	183	26	of	of	ADP
cana-2791	183	27	vertices	vertex	NOUN
cana-2791	183	28	in	in	ADP
cana-2791	183	29	g1	g1	NOUN
cana-2791	183	30	.	.	PUNCT
cana-2791	184	1	therefore	therefore	ADV
cana-2791	184	2	γ−1	γ−1	PROPN
cana-2791	184	3	(	(	PUNCT
cana-2791	184	4	km	km	NOUN
cana-2791	184	5	◦	◦	NOUN
cana-2791	184	6	cn	cn	ADJ
cana-2791	184	7	)	)	PUNCT
cana-2791	184	8	=	=	SYM
cana-2791	184	9	mγ−1(cn	mγ−1(cn	ADJ
cana-2791	184	10	)	)	PUNCT
cana-2791	184	11	communications	communication	NOUN
cana-2791	184	12	on	on	ADP
cana-2791	184	13	applied	apply	VERB
cana-2791	184	14	nonlinear	nonlinear	ADJ
cana-2791	184	15	analysis	analysis	NOUN
cana-2791	184	16	issn	issn	NOUN
cana-2791	184	17	:	:	PUNCT
cana-2791	184	18	1074	1074	NUM
cana-2791	184	19	-	-	PUNCT
cana-2791	184	20	133x	133x	NUM
cana-2791	184	21	vol	vol	NOUN
cana-2791	184	22	32	32	NUM
cana-2791	184	23	no	no	NOUN
cana-2791	184	24	.	.	PUNCT
cana-2791	185	1	4s	4s	NUM
cana-2791	185	2	(	(	PUNCT
cana-2791	185	3	2025	2025	NUM
cana-2791	185	4	)	)	PUNCT
cana-2791	185	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2791	185	6	255	255	NUM
cana-2791	185	7	ioc	ioc	PROPN
cana-2791	185	8	ioc	ioc	PROPN
cana-2791	185	9	figure	figure	VERB
cana-2791	185	10	8	8	NUM
cana-2791	185	11	:	:	PUNCT
cana-2791	185	12	γ−1	γ−1	PROPN
cana-2791	185	13	(	(	PUNCT
cana-2791	185	14	k6	k6	PROPN
cana-2791	185	15	◦	◦	PROPN
cana-2791	185	16	c5	c5	PROPN
cana-2791	185	17	)	)	PUNCT
cana-2791	185	18	the	the	DET
cana-2791	185	19	k6	k6	PROPN
cana-2791	185	20	◦	◦	PROPN
cana-2791	185	21	c5	c5	PROPN
cana-2791	185	22	graph	graph	NOUN
cana-2791	185	23	is	be	AUX
cana-2791	185	24	shown	show	VERB
cana-2791	185	25	in	in	ADP
cana-2791	185	26	figure	figure	NOUN
cana-2791	185	27	8	8	NUM
cana-2791	185	28	and	and	CCONJ
cana-2791	185	29	the	the	DET
cana-2791	185	30	γ−1	γ−1	PROPN
cana-2791	185	31	(	(	PUNCT
cana-2791	185	32	k6	k6	PROPN
cana-2791	185	33	◦	◦	PROPN
cana-2791	185	34	c5	c5	PROPN
cana-2791	185	35	)	)	PUNCT
cana-2791	186	1	=	=	PUNCT
cana-2791	186	2	6	6	NUM
cana-2791	186	3	×	×	NOUN
cana-2791	186	4	2	2	NUM
cana-2791	186	5	=	=	SYM
cana-2791	186	6	12	12	NUM
cana-2791	186	7	the	the	DET
cana-2791	186	8	outer	outer	ADJ
cana-2791	186	9	connected	connected	ADJ
cana-2791	186	10	property	property	NOUN
cana-2791	186	11	:	:	PUNCT
cana-2791	186	12	all	all	DET
cana-2791	186	13	the	the	DET
cana-2791	186	14	vertices	vertex	NOUN
cana-2791	186	15	in	in	ADP
cana-2791	186	16	g2	g2	PROPN
cana-2791	186	17	are	be	AUX
cana-2791	186	18	connected	connect	VERB
cana-2791	186	19	to	to	ADP
cana-2791	186	20	g1	g1	VERB
cana-2791	186	21	and	and	CCONJ
cana-2791	186	22	g1	g1	PROPN
cana-2791	186	23	is	be	AUX
cana-2791	186	24	a	a	DET
cana-2791	186	25	complete	complete	ADJ
cana-2791	186	26	graph	graph	NOUN
cana-2791	186	27	.	.	PUNCT
cana-2791	187	1	after	after	ADP
cana-2791	187	2	deleting	delete	VERB
cana-2791	187	3	the	the	DET
cana-2791	187	4	inverse	inverse	NOUN
cana-2791	187	5	independent	independent	ADJ
cana-2791	187	6	dominating	dominating	NOUN
cana-2791	187	7	set	set	VERB
cana-2791	187	8	from	from	ADP
cana-2791	187	9	the	the	DET
cana-2791	187	10	graph	graph	NOUN
cana-2791	187	11	,	,	PUNCT
cana-2791	187	12	the	the	DET
cana-2791	187	13	subgraph	subgraph	NOUN
cana-2791	187	14	will	will	AUX
cana-2791	187	15	again	again	ADV
cana-2791	187	16	be	be	AUX
cana-2791	187	17	a	a	DET
cana-2791	187	18	connected	connected	ADJ
cana-2791	187	19	graph	graph	NOUN
cana-2791	187	20	.	.	PUNCT
cana-2791	188	1	a	a	DET
cana-2791	188	2	vertex	vertex	NOUN
cana-2791	188	3	from	from	ADP
cana-2791	188	4	g1	g1	PROPN
cana-2791	188	5	must	must	AUX
cana-2791	188	6	be	be	AUX
cana-2791	188	7	restricted	restrict	VERB
cana-2791	188	8	to	to	PART
cana-2791	188	9	be	be	AUX
cana-2791	188	10	chosen	choose	VERB
cana-2791	188	11	.	.	PUNCT
cana-2791	189	1	references	reference	NOUN
cana-2791	189	2	[	[	X
cana-2791	189	3	1	1	NUM
cana-2791	189	4	]	]	X
cana-2791	189	5	hong	hong	PROPN
cana-2791	189	6	-	-	PUNCT
cana-2791	189	7	yong	yong	PROPN
cana-2791	189	8	fu	fu	PROPN
cana-2791	189	9	,	,	PUNCT
cana-2791	189	10	dezheng	dezheng	PROPN
cana-2791	189	11	xie	xie	PROPN
cana-2791	189	12	(	(	PUNCT
cana-2791	189	13	2010	2010	NUM
cana-2791	189	14	)	)	PUNCT
cana-2791	189	15	equitable	equitable	ADJ
cana-2791	189	16	l(2,1)-labelings	l(2,1)-labeling	NOUN
cana-2791	189	17	of	of	ADP
cana-2791	189	18	sierpi	sierpi	ADJ
cana-2791	189	19	nski	nski	PROPN
cana-2791	189	20	graph	graph	PROPN
cana-2791	189	21	aus	aus	PROPN
cana-2791	189	22	tralasian	tralasian	PROPN
cana-2791	189	23	journal	journal	PROPN
cana-2791	189	24	of	of	ADP
cana-2791	189	25	combinatorics	combinatoric	NOUN
cana-2791	189	26	volume	volume	NOUN
cana-2791	189	27	46	46	NUM
cana-2791	189	28	(	(	PUNCT
cana-2791	189	29	2010	2010	NUM
cana-2791	189	30	)	)	PUNCT
cana-2791	189	31	,	,	PUNCT
cana-2791	189	32	pages	page	NOUN
cana-2791	189	33	147	147	NUM
cana-2791	189	34	-	-	SYM
cana-2791	189	35	156	156	NUM
cana-2791	190	1	[	[	X
cana-2791	190	2	2	2	NUM
cana-2791	190	3	]	]	PUNCT
cana-2791	190	4	joanna	joanna	PROPN
cana-2791	190	5	cyman	cyman	NOUN
cana-2791	190	6	(	(	PUNCT
cana-2791	190	7	2007	2007	NUM
cana-2791	190	8	)	)	PUNCT
cana-2791	190	9	the	the	DET
cana-2791	190	10	outer	outer	ADV
cana-2791	190	11	-	-	PUNCT
cana-2791	190	12	connected	connect	VERB
cana-2791	190	13	domination	domination	NOUN
cana-2791	190	14	of	of	ADP
cana-2791	190	15	a	a	DET
cana-2791	190	16	graph	graph	NOUN
cana-2791	190	17	australasian	australasian	ADJ
cana-2791	190	18	jour	jour	ADJ
cana-2791	190	19	nal	nal	PROPN
cana-2791	190	20	of	of	ADP
cana-2791	190	21	combinatorics	combinatoric	NOUN
cana-2791	190	22	volume	volume	NOUN
cana-2791	190	23	38(2007	38(2007	NUM
cana-2791	190	24	)	)	PUNCT
cana-2791	190	25	pages	page	NOUN
cana-2791	190	26	35	35	NUM
cana-2791	190	27	-	-	SYM
cana-2791	190	28	46	46	NUM
cana-2791	190	29	[	[	X
cana-2791	190	30	3	3	X
cana-2791	190	31	]	]	X
cana-2791	190	32	m.h	m.h	PROPN
cana-2791	190	33	.	.	PROPN
cana-2791	190	34	akhbari	akhbari	PROPN
cana-2791	190	35	,	,	PUNCT
cana-2791	190	36	r.	r.	PROPN
cana-2791	190	37	hasni	hasni	PROPN
cana-2791	190	38	,	,	PUNCT
cana-2791	190	39	o.	o.	PROPN
cana-2791	190	40	favaron	favaron	PROPN
cana-2791	190	41	,	,	PUNCT
cana-2791	190	42	h.	h.	PROPN
cana-2791	190	43	karami	karami	PROPN
cana-2791	190	44	,	,	PUNCT
cana-2791	190	45	s.m	s.m	PROPN
cana-2791	190	46	.	.	PROPN
cana-2791	190	47	sheikholeslami	sheikholeslami	PROPN
cana-2791	190	48	(	(	PUNCT
cana-2791	190	49	2011	2011	NUM
cana-2791	190	50	)	)	PUNCT
cana-2791	190	51	on	on	ADP
cana-2791	190	52	the	the	DET
cana-2791	190	53	outer	outer	ADV
cana-2791	190	54	-	-	PUNCT
cana-2791	190	55	connected	connect	VERB
cana-2791	190	56	domination	domination	NOUN
cana-2791	190	57	in	in	ADP
cana-2791	190	58	graphs	graph	NOUN
cana-2791	190	59	springer	springer	NOUN
cana-2791	190	60	science+business	science+business	NOUN
cana-2791	190	61	media	medium	NOUN
cana-2791	190	62	,	,	PUNCT
cana-2791	190	63	llc	llc	PROPN
cana-2791	190	64	2011	2011	NUM
cana-2791	190	65	26:10–18	26:10–18	NUM
cana-2791	191	1	[	[	X
cana-2791	191	2	4	4	NUM
cana-2791	191	3	]	]	PUNCT
cana-2791	191	4	renario	renario	PROPN
cana-2791	191	5	g.	g.	PROPN
cana-2791	191	6	hinampas	hinampas	PROPN
cana-2791	191	7	,	,	PUNCT
cana-2791	191	8	jr	jr	PROPN
cana-2791	191	9	.	.	PROPN
cana-2791	191	10	jocecar	jocecar	PROPN
cana-2791	191	11	lomarda	lomarda	PROPN
cana-2791	191	12	-	-	PUNCT
cana-2791	191	13	hinampas	hinampas	NOUN
cana-2791	191	14	,	,	PUNCT
cana-2791	191	15	analyn	analyn	X
cana-2791	191	16	dahunan	dahunan	X
cana-2791	191	17	(	(	PUNCT
cana-2791	191	18	2017	2017	NUM
cana-2791	191	19	)	)	PUNCT
cana-2791	191	20	inde	inde	PROPN
cana-2791	191	21	pendent	pendent	NOUN
cana-2791	191	22	outer	outer	ADV
cana-2791	191	23	-	-	PUNCT
cana-2791	191	24	connected	connect	VERB
cana-2791	191	25	domination	domination	NOUN
cana-2791	191	26	in	in	ADP
cana-2791	191	27	graphs	graph	NOUN
cana-2791	191	28	global	global	ADJ
cana-2791	191	29	journal	journal	NOUN
cana-2791	191	30	of	of	ADP
cana-2791	191	31	pure	pure	ADJ
cana-2791	191	32	and	and	CCONJ
cana-2791	191	33	applied	applied	ADJ
cana-2791	191	34	mathematics	mathematic	NOUN
cana-2791	191	35	.	.	PUNCT
cana-2791	192	1	issn	issn	PROPN
cana-2791	192	2	0973	0973	NUM
cana-2791	192	3	-	-	SYM
cana-2791	192	4	1768	1768	NUM
cana-2791	192	5	volume	volume	NOUN
cana-2791	192	6	13	13	NUM
cana-2791	192	7	,	,	PUNCT
cana-2791	192	8	number	number	NOUN
cana-2791	192	9	1	1	NUM
cana-2791	192	10	(	(	PUNCT
cana-2791	192	11	2017	2017	NUM
cana-2791	192	12	)	)	PUNCT
cana-2791	192	13	,	,	PUNCT
cana-2791	192	14	pp	pp	PROPN
cana-2791	192	15	.	.	PUNCT
cana-2791	193	1	1	1	NUM
cana-2791	193	2	-	-	SYM
cana-2791	193	3	7	7	NUM
cana-2791	193	4	[	[	X
cana-2791	193	5	5	5	NUM
cana-2791	193	6	]	]	PUNCT
cana-2791	193	7	r.frucht	r.frucht	NOUN
cana-2791	193	8	,	,	PUNCT
cana-2791	193	9	f.	f.	PROPN
cana-2791	193	10	harary	harary	PROPN
cana-2791	193	11	,	,	PUNCT
cana-2791	193	12	on	on	ADP
cana-2791	193	13	the	the	DET
cana-2791	193	14	corona	corona	NOUN
cana-2791	193	15	of	of	ADP
cana-2791	193	16	two	two	NUM
cana-2791	193	17	graphs	graph	NOUN
cana-2791	193	18	,	,	PUNCT
cana-2791	193	19	aequationes	aequatione	VERB
cana-2791	193	20	math	math	NOUN
cana-2791	193	21	.	.	PUNCT
cana-2791	194	1	4	4	NUM
cana-2791	194	2	(	(	PUNCT
cana-2791	194	3	1970	1970	NUM
cana-2791	194	4	)	)	PUNCT
cana-2791	194	5	,	,	PUNCT
cana-2791	194	6	322325	322325	NUM
cana-2791	194	7	[	[	X
cana-2791	194	8	6	6	NUM
cana-2791	194	9	]	]	PUNCT
cana-2791	194	10	sandi	sandi	PROPN
cana-2791	194	11	klavzar	klavzar	PROPN
cana-2791	194	12	(	(	PUNCT
cana-2791	194	13	2008	2008	NUM
cana-2791	194	14	)	)	PUNCT
cana-2791	194	15	coloring	color	VERB
cana-2791	194	16	sierpinski	sierpinski	ADJ
cana-2791	194	17	graphs	graph	NOUN
cana-2791	194	18	and	and	CCONJ
cana-2791	194	19	sierpinski	sierpinski	ADJ
cana-2791	194	20	gasket	gasket	NOUN
cana-2791	194	21	graphs	graph	NOUN
cana-2791	194	22	taiwanese	taiwanese	PROPN
cana-2791	194	23	j.	j.	PROPN
cana-2791	194	24	math	math	PROPN
cana-2791	194	25	.	.	PUNCT
cana-2791	195	1	volume	volume	NOUN
cana-2791	195	2	12	12	NUM
cana-2791	195	3	,	,	PUNCT
cana-2791	195	4	number	number	NOUN
cana-2791	195	5	2	2	NUM
cana-2791	195	6	(	(	PUNCT
cana-2791	195	7	2008	2008	NUM
cana-2791	195	8	)	)	PUNCT
cana-2791	195	9	,	,	PUNCT
cana-2791	195	10	513	513	NUM
cana-2791	195	11	-	-	SYM
cana-2791	195	12	522	522	NUM
cana-2791	195	13	communications	communication	NOUN
cana-2791	195	14	on	on	ADP
cana-2791	195	15	applied	apply	VERB
cana-2791	195	16	nonlinear	nonlinear	ADJ
cana-2791	195	17	analysis	analysis	NOUN
cana-2791	195	18	issn	issn	NOUN
cana-2791	195	19	:	:	PUNCT
cana-2791	195	20	1074	1074	NUM
cana-2791	195	21	-	-	PUNCT
cana-2791	195	22	133x	133x	NUM
cana-2791	195	23	vol	vol	NOUN
cana-2791	195	24	32	32	NUM
cana-2791	195	25	no	no	NOUN
cana-2791	195	26	.	.	PUNCT
cana-2791	196	1	4s	4s	NUM
cana-2791	196	2	(	(	PUNCT
cana-2791	196	3	2025	2025	NUM
cana-2791	196	4	)	)	PUNCT
cana-2791	197	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2791	197	2	256	256	NUM
cana-2791	197	3	[	[	X
cana-2791	197	4	7	7	X
cana-2791	197	5	]	]	X
cana-2791	197	6	sandi	sandi	PROPN
cana-2791	197	7	klavzar	klavzar	PROPN
cana-2791	197	8	,	,	PUNCT
cana-2791	197	9	uros	uros	PROPN
cana-2791	197	10	milutinovic	milutinovic	PROPN
cana-2791	197	11	(	(	PUNCT
cana-2791	197	12	1997	1997	NUM
cana-2791	197	13	)	)	PUNCT
cana-2791	197	14	graphs	graph	NOUN
cana-2791	197	15	s(n	s(n	PROPN
cana-2791	197	16	,	,	PUNCT
cana-2791	197	17	k	k	NOUN
cana-2791	197	18	)	)	PUNCT
cana-2791	197	19	and	and	CCONJ
cana-2791	197	20	a	a	DET
cana-2791	197	21	variant	variant	NOUN
cana-2791	197	22	of	of	ADP
cana-2791	197	23	the	the	DET
cana-2791	197	24	tower	tower	NOUN
cana-2791	197	25	of	of	ADP
cana-2791	197	26	hanoi	hanoi	PROPN
cana-2791	197	27	problem	problem	PROPN
cana-2791	197	28	czechoslovak	czechoslovak	PROPN
cana-2791	197	29	mathematical	mathematical	ADJ
cana-2791	197	30	journal	journal	NOUN
cana-2791	197	31	,	,	PUNCT
cana-2791	197	32	volume	volume	NOUN
cana-2791	197	33	47	47	NUM
cana-2791	197	34	,	,	PUNCT
cana-2791	197	35	issue	issue	NOUN
cana-2791	197	36	1	1	NUM
cana-2791	197	37	,	,	PUNCT
cana-2791	197	38	pp	pp	ADV
cana-2791	198	1	95–104	95–104	PROPN
cana-2791	199	1	[	[	X
cana-2791	199	2	8	8	NUM
cana-2791	199	3	]	]	X
cana-2791	199	4	shun	shun	PROPN
cana-2791	199	5	-	-	PUNCT
cana-2791	199	6	chieh	chieh	PROPN
cana-2791	199	7	chang	chang	PROPN
cana-2791	199	8	,	,	PUNCT
cana-2791	199	9	jia	jia	PROPN
cana-2791	199	10	-	-	PUNCT
cana-2791	199	11	jie	jie	PROPN
cana-2791	199	12	liu	liu	PROPN
cana-2791	199	13	,	,	PUNCT
cana-2791	199	14	yue	yue	PROPN
cana-2791	199	15	-	-	PUNCT
cana-2791	199	16	li	li	PROPN
cana-2791	199	17	wang	wang	PROPN
cana-2791	199	18	(	(	PUNCT
cana-2791	199	19	2015	2015	NUM
cana-2791	199	20	)	)	PUNCT
cana-2791	199	21	the	the	DET
cana-2791	199	22	outer	outer	ADV
cana-2791	199	23	-	-	PUNCT
cana-2791	199	24	connected	connect	VERB
cana-2791	199	25	domination	domination	NOUN
cana-2791	199	26	number	number	NOUN
cana-2791	199	27	of	of	ADP
cana-2791	199	28	sierpinski	sierpinski	ADJ
cana-2791	199	29	-	-	PUNCT
cana-2791	199	30	like	like	ADJ
cana-2791	199	31	graphs	graph	NOUN
cana-2791	199	32	springer	springer	NOUN
cana-2791	199	33	science+business	science+business	NOUN
cana-2791	199	34	media	medium	NOUN
cana-2791	199	35	new	new	PROPN
cana-2791	199	36	york	york	PROPN
cana-2791	199	37	2015	2015	NUM
cana-2791	199	38	theory	theory	NOUN
cana-2791	199	39	comput	comput	ADP
cana-2791	199	40	syst(2016)58:345	syst(2016)58:345	NOUN
cana-2791	199	41	-	-	PUNCT
cana-2791	199	42	356	356	NUM
cana-2791	199	43	[	[	X
cana-2791	199	44	9	9	NUM
cana-2791	199	45	]	]	X
cana-2791	199	46	s.nada	s.nada	NOUN
cana-2791	199	47	,	,	PUNCT
cana-2791	199	48	a.elrokh	a.elrokh	ADJ
cana-2791	199	49	,	,	PUNCT
cana-2791	199	50	e.a.elsakhawi	e.a.elsakhawi	NOUN
cana-2791	199	51	,	,	PUNCT
cana-2791	199	52	d.e.sabra	d.e.sabra	NOUN
cana-2791	199	53	(	(	PUNCT
cana-2791	199	54	2017	2017	NUM
cana-2791	199	55	)	)	PUNCT
cana-2791	199	56	the	the	DET
cana-2791	199	57	corona	corona	NOUN
cana-2791	199	58	between	between	ADP
cana-2791	199	59	cycles	cycle	NOUN
cana-2791	199	60	and	and	CCONJ
cana-2791	199	61	paths	path	NOUN
cana-2791	199	62	journal	journal	NOUN
cana-2791	199	63	of	of	ADP
cana-2791	199	64	the	the	DET
cana-2791	199	65	egyptian	egyptian	PROPN
cana-2791	199	66	mathematical	mathematical	ADJ
cana-2791	199	67	society	society	NOUN
cana-2791	199	68	111	111	NUM
cana-2791	199	69	-	-	SYM
cana-2791	199	70	118	118	NUM
cana-2791	199	71	[	[	SYM
cana-2791	199	72	10	10	NUM
cana-2791	199	73	]	]	X
cana-2791	199	74	r.r.iyer	r.r.iyer	NOUN
cana-2791	199	75	,	,	PUNCT
cana-2791	199	76	k.somasundaram	k.somasundaram	NOUN
cana-2791	199	77	,	,	PUNCT
cana-2791	199	78	irregular	irregular	ADJ
cana-2791	199	79	colorings	coloring	NOUN
cana-2791	199	80	of	of	ADP
cana-2791	199	81	certain	certain	ADJ
cana-2791	199	82	classes	class	NOUN
cana-2791	199	83	of	of	ADP
cana-2791	199	84	corona	corona	NOUN
cana-2791	199	85	product	product	NOUN
cana-2791	199	86	and	and	CCONJ
cana-2791	199	87	sierpinski	sierpinski	ADJ
cana-2791	199	88	graphs.j.discrete.math.sci.cryptogr.25(1)(2022)97	graphs.j.discrete.math.sci.cryptogr.25(1)(2022)97	PROPN
cana-2791	199	89	-	-	PUNCT
cana-2791	199	90	105	105	NUM
cana-2791	199	91	.	.	PUNCT
cana-2791	200	1	[	[	X
cana-2791	200	2	11	11	NUM
cana-2791	200	3	]	]	PUNCT
cana-2791	200	4	shyama.s	shyama.s	PROPN
cana-2791	200	5	,	,	PUNCT
cana-2791	200	6	radha	radha	PROPN
cana-2791	200	7	r	r	PROPN
cana-2791	200	8	iyer	iyer	PROPN
cana-2791	200	9	,	,	PUNCT
cana-2791	200	10	unraveling	unravel	VERB
cana-2791	200	11	the	the	DET
cana-2791	200	12	enigmatic	enigmatic	ADJ
cana-2791	200	13	irregular	irregular	ADJ
cana-2791	200	14	coloring	coloring	NOUN
cana-2791	200	15	of	of	ADP
cana-2791	200	16	honeycomb	honeycomb	NOUN
cana-2791	200	17	networks.discrete	networks.discrete	ADJ
cana-2791	200	18	applied	apply	VERB
cana-2791	200	19	mathematics	mathematic	NOUN
cana-2791	200	20	360	360	NUM
cana-2791	200	21	(	(	PUNCT
cana-2791	200	22	2025	2025	NUM
cana-2791	200	23	)	)	PUNCT
cana-2791	200	24	282–296	282–296	NUM
cana-2791	200	25	.	.	PUNCT
cana-2791	201	1	[	[	X
cana-2791	201	2	12	12	NUM
cana-2791	201	3	]	]	PUNCT
cana-2791	201	4	shyama.s	shyama.s	PUNCT
cana-2791	201	5	,	,	PUNCT
cana-2791	201	6	radha	radha	PROPN
cana-2791	201	7	r	r	PROPN
cana-2791	201	8	iyer	iyer	PROPN
cana-2791	201	9	,	,	PUNCT
cana-2791	201	10	irregular	irregular	ADJ
cana-2791	201	11	chromatic	chromatic	ADJ
cana-2791	201	12	number	number	NOUN
cana-2791	201	13	for	for	ADP
cana-2791	201	14	hypercube	hypercube	NOUN
cana-2791	201	15	graphs	graph	NOUN
cana-2791	201	16	and	and	CCONJ
cana-2791	201	17	its	its	PRON
cana-2791	201	18	vari	vari	ADJ
cana-2791	201	19	ants	ant	NOUN
cana-2791	201	20	,	,	PUNCT
cana-2791	201	21	j.intell.fuzzy	j.intell.fuzzy	PROPN
cana-2791	201	22	syst.45(5)(2023)8907	syst.45(5)(2023)8907	PROPN
cana-2791	201	23	-	-	PUNCT
cana-2791	201	24	8913,http://dx.doi.org/10.3233	8913,http://dx.doi.org/10.3233	NOUN
cana-2791	201	25	/	/	SYM
cana-2791	201	26	jifs-232471	jifs-232471	NOUN
cana-2791	201	27	.	.	PUNCT
cana-2791	202	1	communications	communication	NOUN
cana-2791	202	2	on	on	ADP
cana-2791	202	3	applied	apply	VERB
cana-2791	202	4	nonlinear	nonlinear	ADJ
cana-2791	202	5	analysis	analysis	NOUN
cana-2791	202	6	issn	issn	NOUN
cana-2791	202	7	:	:	PUNCT
cana-2791	202	8	1074	1074	NUM
cana-2791	202	9	-	-	PUNCT
cana-2791	202	10	133x	133x	NUM
cana-2791	202	11	vol	vol	NOUN
cana-2791	202	12	32	32	NUM
cana-2791	202	13	no	no	NOUN
cana-2791	202	14	.	.	PUNCT
cana-2791	203	1	4s	4s	NUM
cana-2791	203	2	(	(	PUNCT
cana-2791	203	3	2025	2025	NUM
cana-2791	203	4	)	)	PUNCT
cana-2791	204	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2791	204	2	257	257	NUM
cana-2791	204	3	http://dx.doi.org/10.3233/jifs-232471	http://dx.doi.org/10.3233/jifs-232471	NOUN