id	sid	tid	token	lemma	pos
cana-1300	1	1	communications	communication	NOUN
cana-1300	1	2	on	on	ADP
cana-1300	1	3	applied	apply	VERB
cana-1300	1	4	nonlinear	nonlinear	ADJ
cana-1300	1	5	analysis	analysis	NOUN
cana-1300	1	6	issn	issn	NOUN
cana-1300	1	7	:	:	PUNCT
cana-1300	1	8	1074	1074	NUM
cana-1300	1	9	-	-	PUNCT
cana-1300	1	10	133x	133x	NUM
cana-1300	1	11	vol	vol	NOUN
cana-1300	1	12	31	31	NUM
cana-1300	1	13	no	no	NOUN
cana-1300	1	14	.	.	PUNCT
cana-1300	2	1	7s	7	NOUN
cana-1300	2	2	(	(	PUNCT
cana-1300	2	3	2024	2024	NUM
cana-1300	2	4	)	)	PUNCT
cana-1300	2	5	250	250	NUM
cana-1300	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1300	2	7	a	a	DET
cana-1300	2	8	collaboration	collaboration	NOUN
cana-1300	2	9	graph	graph	NOUN
cana-1300	2	10	of	of	ADP
cana-1300	2	11	the	the	DET
cana-1300	2	12	lilavati	lilavati	PROPN
cana-1300	2	13	prize	prize	PROPN
cana-1300	2	14	winners	winner	NOUN
cana-1300	2	15	with	with	ADP
cana-1300	2	16	certain	certain	ADJ
cana-1300	2	17	domination	domination	NOUN
cana-1300	2	18	parameters	parameter	NOUN
cana-1300	2	19	renuka	renuka	PROPN
cana-1300	2	20	lakshmi	lakshmi	PROPN
cana-1300	2	21	a1	a1	PROPN
cana-1300	2	22	,	,	PUNCT
cana-1300	2	23	vani	vani	PROPN
cana-1300	2	24	m2	m2	PROPN
cana-1300	2	25	,	,	PUNCT
cana-1300	2	26	koteswaramma	koteswaramma	PROPN
cana-1300	2	27	n	n	PROPN
cana-1300	2	28	3	3	PROPN
cana-1300	2	29	*	*	NOUN
cana-1300	2	30	,	,	PUNCT
cana-1300	2	31	ramprasad	ramprasad	ADJ
cana-1300	2	32	c4	c4	NOUN
cana-1300	2	33	*	*	PROPN
cana-1300	2	34	,	,	PUNCT
cana-1300	2	35	janardhana	janardhana	PROPN
cana-1300	2	36	rao	rao	PROPN
cana-1300	3	1	k	k	NOUN
cana-1300	3	2	5	5	NUM
cana-1300	3	3	1,2,3,4	1,2,3,4	NUM
cana-1300	3	4	department	department	NOUN
cana-1300	3	5	of	of	ADP
cana-1300	3	6	science	science	NOUN
cana-1300	3	7	and	and	CCONJ
cana-1300	3	8	humanities	humanity	NOUN
cana-1300	3	9	,	,	PUNCT
cana-1300	3	10	vasireddy	vasireddy	NOUN
cana-1300	3	11	venkatadri	venkatadri	PROPN
cana-1300	3	12	institute	institute	PROPN
cana-1300	3	13	of	of	ADP
cana-1300	3	14	technology	technology	PROPN
cana-1300	3	15	,	,	PUNCT
cana-1300	3	16	nambur	nambur	PROPN
cana-1300	3	17	,	,	PUNCT
cana-1300	3	18	guntur	guntur	PROPN
cana-1300	3	19	(	(	PUNCT
cana-1300	3	20	dt),a.p	dt),a.p	PROPN
cana-1300	3	21	,	,	PUNCT
cana-1300	3	22	india	india	PROPN
cana-1300	3	23	.	.	PUNCT
cana-1300	4	1	5research	5research	NUM
cana-1300	4	2	scholar	scholar	NOUN
cana-1300	4	3	and	and	CCONJ
cana-1300	4	4	lecturer	lecturer	NOUN
cana-1300	4	5	in	in	ADP
cana-1300	4	6	mathematics	mathematic	NOUN
cana-1300	4	7	,	,	PUNCT
cana-1300	4	8	government	government	NOUN
cana-1300	4	9	degree	degree	NOUN
cana-1300	4	10	college	college	NOUN
cana-1300	4	11	,	,	PUNCT
cana-1300	4	12	kovvur	kovvur	PROPN
cana-1300	4	13	,	,	PUNCT
cana-1300	4	14	east	east	PROPN
cana-1300	4	15	godavari	godavari	PROPN
cana-1300	4	16	(	(	PUNCT
cana-1300	4	17	dt	dt	PROPN
cana-1300	4	18	)	)	PUNCT
cana-1300	4	19	,	,	PUNCT
cana-1300	4	20	a.p	a.p	PROPN
cana-1300	4	21	,	,	PUNCT
cana-1300	4	22	india	india	PROPN
cana-1300	4	23	.	.	PUNCT
cana-1300	5	1	email	email	NOUN
cana-1300	6	1	i	i	PROPN
cana-1300	6	2	d	d	PROPN
cana-1300	6	3	:	:	PUNCT
cana-1300	6	4	renukalakshmiavvari@gmail.com	renukalakshmiavvari@gmail.com	PROPN
cana-1300	6	5	,	,	PUNCT
cana-1300	6	6	ramprasadchegu1984@gmail.com	ramprasadchegu1984@gmail.com	PROPN
cana-1300	6	7	,	,	PUNCT
cana-1300	6	8	koteswaramma@vvit.net	koteswaramma@vvit.net	PROPN
cana-1300	6	9	article	article	NOUN
cana-1300	6	10	history	history	NOUN
cana-1300	6	11	:	:	PUNCT
cana-1300	6	12	received	receive	VERB
cana-1300	6	13	:	:	PUNCT
cana-1300	6	14	01	01	NUM
cana-1300	6	15	-	-	PUNCT
cana-1300	6	16	06	06	NUM
cana-1300	6	17	-	-	PUNCT
cana-1300	6	18	2024	2024	NUM
cana-1300	6	19	revised	revise	VERB
cana-1300	6	20	:	:	PUNCT
cana-1300	6	21	03	03	NUM
cana-1300	6	22	-	-	PUNCT
cana-1300	6	23	07	07	NUM
cana-1300	6	24	-	-	PUNCT
cana-1300	6	25	2024	2024	NUM
cana-1300	6	26	accepted	accept	VERB
cana-1300	6	27	:	:	PUNCT
cana-1300	6	28	29	29	NUM
cana-1300	6	29	-	-	SYM
cana-1300	6	30	07	07	NUM
cana-1300	6	31	-	-	PUNCT
cana-1300	6	32	2024	2024	NUM
cana-1300	6	33	abstract	abstract	NOUN
cana-1300	6	34	:	:	PUNCT
cana-1300	6	35	the	the	DET
cana-1300	6	36	lilavati	lilavati	PROPN
cana-1300	6	37	prize	prize	PROPN
cana-1300	6	38	stands	stand	VERB
cana-1300	6	39	as	as	ADP
cana-1300	6	40	a	a	DET
cana-1300	6	41	hallmark	hallmark	NOUN
cana-1300	6	42	of	of	ADP
cana-1300	6	43	excellence	excellence	NOUN
cana-1300	6	44	in	in	ADP
cana-1300	6	45	the	the	DET
cana-1300	6	46	field	field	NOUN
cana-1300	6	47	of	of	ADP
cana-1300	6	48	mathematics	mathematic	NOUN
cana-1300	6	49	,	,	PUNCT
cana-1300	6	50	recognizing	recognize	VERB
cana-1300	6	51	outstanding	outstanding	ADJ
cana-1300	6	52	contributions	contribution	NOUN
cana-1300	6	53	to	to	ADP
cana-1300	6	54	the	the	DET
cana-1300	6	55	discipline	discipline	NOUN
cana-1300	6	56	.	.	PUNCT
cana-1300	7	1	this	this	DET
cana-1300	7	2	study	study	NOUN
cana-1300	7	3	delves	delve	VERB
cana-1300	7	4	into	into	ADP
cana-1300	7	5	the	the	DET
cana-1300	7	6	domination	domination	NOUN
cana-1300	7	7	parameters	parameter	NOUN
cana-1300	7	8	exhibited	exhibit	VERB
cana-1300	7	9	by	by	ADP
cana-1300	7	10	past	past	PROPN
cana-1300	7	11	lilavati	lilavati	PROPN
cana-1300	7	12	prize	prize	PROPN
cana-1300	7	13	winners	winner	NOUN
cana-1300	7	14	,	,	PUNCT
cana-1300	7	15	aiming	aim	VERB
cana-1300	7	16	to	to	PART
cana-1300	7	17	uncover	uncover	VERB
cana-1300	7	18	the	the	DET
cana-1300	7	19	underlying	underlie	VERB
cana-1300	7	20	factors	factor	NOUN
cana-1300	7	21	contributing	contribute	VERB
cana-1300	7	22	to	to	ADP
cana-1300	7	23	their	their	PRON
cana-1300	7	24	exceptional	exceptional	ADJ
cana-1300	7	25	achievements	achievement	NOUN
cana-1300	7	26	.	.	PUNCT
cana-1300	8	1	through	through	ADP
cana-1300	8	2	a	a	DET
cana-1300	8	3	meticulous	meticulous	ADJ
cana-1300	8	4	analysis	analysis	NOUN
cana-1300	8	5	of	of	ADP
cana-1300	8	6	their	their	PRON
cana-1300	8	7	mathematical	mathematical	ADJ
cana-1300	8	8	prowess	prowess	NOUN
cana-1300	8	9	,	,	PUNCT
cana-1300	8	10	academic	academic	ADJ
cana-1300	8	11	backgrounds	background	NOUN
cana-1300	8	12	,	,	PUNCT
cana-1300	8	13	research	research	NOUN
cana-1300	8	14	methodologies	methodology	NOUN
cana-1300	8	15	,	,	PUNCT
cana-1300	8	16	and	and	CCONJ
cana-1300	8	17	societal	societal	ADJ
cana-1300	8	18	impact	impact	NOUN
cana-1300	8	19	,	,	PUNCT
cana-1300	8	20	this	this	DET
cana-1300	8	21	research	research	NOUN
cana-1300	8	22	seeks	seek	VERB
cana-1300	8	23	to	to	PART
cana-1300	8	24	delineate	delineate	VERB
cana-1300	8	25	the	the	DET
cana-1300	8	26	common	common	ADJ
cana-1300	8	27	traits	trait	NOUN
cana-1300	8	28	and	and	CCONJ
cana-1300	8	29	strategies	strategy	NOUN
cana-1300	8	30	employed	employ	VERB
cana-1300	8	31	by	by	ADP
cana-1300	8	32	these	these	DET
cana-1300	8	33	laureates	laureate	NOUN
cana-1300	8	34	.	.	PUNCT
cana-1300	9	1	utilizing	utilize	VERB
cana-1300	9	2	a	a	DET
cana-1300	9	3	combination	combination	NOUN
cana-1300	9	4	of	of	ADP
cana-1300	9	5	quantitative	quantitative	ADJ
cana-1300	9	6	data	datum	NOUN
cana-1300	9	7	analysis	analysis	NOUN
cana-1300	9	8	and	and	CCONJ
cana-1300	9	9	qualitative	qualitative	ADJ
cana-1300	9	10	assessments	assessment	NOUN
cana-1300	9	11	,	,	PUNCT
cana-1300	9	12	we	we	PRON
cana-1300	9	13	aim	aim	VERB
cana-1300	9	14	to	to	PART
cana-1300	9	15	provide	provide	VERB
cana-1300	9	16	insights	insight	NOUN
cana-1300	9	17	into	into	ADP
cana-1300	9	18	the	the	DET
cana-1300	9	19	intricate	intricate	ADJ
cana-1300	9	20	interplay	interplay	NOUN
cana-1300	9	21	between	between	ADP
cana-1300	9	22	individual	individual	ADJ
cana-1300	9	23	brilliance	brilliance	NOUN
cana-1300	9	24	,	,	PUNCT
cana-1300	9	25	collaborative	collaborative	ADJ
cana-1300	9	26	endeavors	endeavor	NOUN
cana-1300	9	27	,	,	PUNCT
cana-1300	9	28	and	and	CCONJ
cana-1300	9	29	institutional	institutional	ADJ
cana-1300	9	30	support	support	NOUN
cana-1300	9	31	in	in	ADP
cana-1300	9	32	shaping	shape	VERB
cana-1300	9	33	mathematical	mathematical	ADJ
cana-1300	9	34	excellence	excellence	NOUN
cana-1300	9	35	.	.	PUNCT
cana-1300	10	1	by	by	ADP
cana-1300	10	2	identifying	identify	VERB
cana-1300	10	3	key	key	ADJ
cana-1300	10	4	domination	domination	NOUN
cana-1300	10	5	parameters	parameter	NOUN
cana-1300	10	6	among	among	ADP
cana-1300	10	7	lilavati	lilavati	PROPN
cana-1300	10	8	prize	prize	PROPN
cana-1300	10	9	winners	winner	NOUN
cana-1300	10	10	,	,	PUNCT
cana-1300	10	11	this	this	DET
cana-1300	10	12	study	study	NOUN
cana-1300	10	13	not	not	PART
cana-1300	10	14	only	only	ADV
cana-1300	10	15	offers	offer	VERB
cana-1300	10	16	valuable	valuable	ADJ
cana-1300	10	17	insights	insight	NOUN
cana-1300	10	18	into	into	ADP
cana-1300	10	19	the	the	DET
cana-1300	10	20	dynamics	dynamic	NOUN
cana-1300	10	21	of	of	ADP
cana-1300	10	22	mathematical	mathematical	ADJ
cana-1300	10	23	achievement	achievement	NOUN
cana-1300	10	24	but	but	CCONJ
cana-1300	10	25	also	also	ADV
cana-1300	10	26	provides	provide	VERB
cana-1300	10	27	guidance	guidance	NOUN
cana-1300	10	28	for	for	ADP
cana-1300	10	29	fostering	foster	VERB
cana-1300	10	30	future	future	ADJ
cana-1300	10	31	talent	talent	NOUN
cana-1300	10	32	in	in	ADP
cana-1300	10	33	the	the	DET
cana-1300	10	34	field	field	NOUN
cana-1300	10	35	.	.	PUNCT
cana-1300	11	1	in	in	ADP
cana-1300	11	2	this	this	DET
cana-1300	11	3	present	present	ADJ
cana-1300	11	4	article	article	NOUN
cana-1300	11	5	,	,	PUNCT
cana-1300	11	6	the	the	DET
cana-1300	11	7	collaboration	collaboration	NOUN
cana-1300	11	8	graph	graph	NOUN
cana-1300	11	9	of	of	ADP
cana-1300	11	10	lilavathi	lilavathi	ADJ
cana-1300	11	11	prize	prize	NOUN
cana-1300	11	12	winners	winner	NOUN
cana-1300	11	13	(	(	PUNCT
cana-1300	11	14	2010	2010	NUM
cana-1300	11	15	-	-	SYM
cana-1300	11	16	2022	2022	NUM
cana-1300	11	17	)	)	PUNCT
cana-1300	11	18	was	be	AUX
cana-1300	11	19	obtained	obtain	VERB
cana-1300	11	20	with	with	ADP
cana-1300	11	21	14	14	NUM
cana-1300	11	22	nodes	node	NOUN
cana-1300	11	23	and	and	CCONJ
cana-1300	11	24	78	78	NUM
cana-1300	11	25	links	link	NOUN
cana-1300	11	26	.	.	PUNCT
cana-1300	12	1	it	it	PRON
cana-1300	12	2	will	will	AUX
cana-1300	12	3	be	be	AUX
cana-1300	12	4	quite	quite	ADV
cana-1300	12	5	time	time	NOUN
cana-1300	12	6	consuming	consume	VERB
cana-1300	12	7	to	to	PART
cana-1300	12	8	share	share	VERB
cana-1300	12	9	a	a	DET
cana-1300	12	10	piece	piece	NOUN
cana-1300	12	11	of	of	ADP
cana-1300	12	12	information	information	NOUN
cana-1300	12	13	from	from	ADP
cana-1300	12	14	a	a	DET
cana-1300	12	15	given	give	VERB
cana-1300	12	16	node	node	NOUN
cana-1300	12	17	to	to	ADP
cana-1300	12	18	any	any	DET
cana-1300	12	19	other	other	ADJ
cana-1300	12	20	node	node	NOUN
cana-1300	12	21	even	even	ADV
cana-1300	12	22	though	though	SCONJ
cana-1300	12	23	the	the	DET
cana-1300	12	24	whole	whole	ADJ
cana-1300	12	25	network	network	NOUN
cana-1300	12	26	is	be	AUX
cana-1300	12	27	connected	connect	VERB
cana-1300	12	28	.	.	PUNCT
cana-1300	13	1	moreover	moreover	ADV
cana-1300	13	2	it	it	PRON
cana-1300	13	3	demands	demand	VERB
cana-1300	13	4	more	more	ADJ
cana-1300	13	5	resources	resource	NOUN
cana-1300	13	6	in	in	ADP
cana-1300	13	7	terms	term	NOUN
cana-1300	13	8	of	of	ADP
cana-1300	13	9	time	time	NOUN
cana-1300	13	10	,	,	PUNCT
cana-1300	13	11	memory	memory	NOUN
cana-1300	13	12	etc	etc	X
cana-1300	13	13	.	.	X
cana-1300	14	1	to	to	PART
cana-1300	14	2	optimize	optimize	VERB
cana-1300	14	3	the	the	DET
cana-1300	14	4	use	use	NOUN
cana-1300	14	5	of	of	ADP
cana-1300	14	6	above	above	ADJ
cana-1300	14	7	resources	resource	NOUN
cana-1300	14	8	the	the	DET
cana-1300	14	9	idea	idea	NOUN
cana-1300	14	10	of	of	ADP
cana-1300	14	11	computing	compute	VERB
cana-1300	14	12	the	the	DET
cana-1300	14	13	split	split	ADJ
cana-1300	14	14	domination	domination	NOUN
cana-1300	14	15	,	,	PUNCT
cana-1300	14	16	strong	strong	ADJ
cana-1300	14	17	split	split	ADJ
cana-1300	14	18	domination	domination	NOUN
cana-1300	14	19	,	,	PUNCT
cana-1300	14	20	strong	strong	ADJ
cana-1300	14	21	nonsplit	nonsplit	ADJ
cana-1300	14	22	domination	domination	NOUN
cana-1300	14	23	,	,	PUNCT
cana-1300	14	24	inverse	inverse	ADJ
cana-1300	14	25	domination	domination	NOUN
cana-1300	14	26	,	,	PUNCT
cana-1300	14	27	inverse	inverse	NOUN
cana-1300	14	28	non	non	NOUN
cana-1300	14	29	split	split	NOUN
cana-1300	14	30	domination	domination	NOUN
cana-1300	14	31	,	,	PUNCT
cana-1300	14	32	edge	edge	NOUN
cana-1300	14	33	,	,	PUNCT
cana-1300	14	34	outer	outer	ADV
cana-1300	14	35	connected	connect	VERB
cana-1300	14	36	,	,	PUNCT
cana-1300	14	37	total	total	ADJ
cana-1300	14	38	connected	connect	VERB
cana-1300	14	39	,	,	PUNCT
cana-1300	14	40	connected	connected	ADJ
cana-1300	14	41	edge	edge	NOUN
cana-1300	14	42	domination	domination	NOUN
cana-1300	14	43	number	number	NOUN
cana-1300	14	44	and	and	CCONJ
cana-1300	14	45	just	just	ADV
cana-1300	14	46	excellent	excellent	ADJ
cana-1300	14	47	assumes	assume	NOUN
cana-1300	14	48	significance	significance	NOUN
cana-1300	14	49	.	.	PUNCT
cana-1300	15	1	in	in	ADP
cana-1300	15	2	this	this	DET
cana-1300	15	3	paper	paper	NOUN
cana-1300	15	4	we	we	PRON
cana-1300	15	5	aimed	aim	VERB
cana-1300	15	6	to	to	PART
cana-1300	15	7	find	find	VERB
cana-1300	15	8	some	some	DET
cana-1300	15	9	particular	particular	ADJ
cana-1300	15	10	domination	domination	NOUN
cana-1300	15	11	parameters	parameter	NOUN
cana-1300	15	12	namely	namely	ADV
cana-1300	15	13	split	split	VERB
cana-1300	15	14	,	,	PUNCT
cana-1300	15	15	strong	strong	ADJ
cana-1300	15	16	,	,	PUNCT
cana-1300	15	17	strong	strong	ADJ
cana-1300	15	18	split	split	NOUN
cana-1300	15	19	,	,	PUNCT
cana-1300	15	20	inverse	inverse	NOUN
cana-1300	15	21	,	,	PUNCT
cana-1300	15	22	connected	connect	VERB
cana-1300	15	23	,	,	PUNCT
cana-1300	15	24	edge	edge	NOUN
cana-1300	15	25	connected	connect	VERB
cana-1300	15	26	,	,	PUNCT
cana-1300	15	27	outer	outer	ADV
cana-1300	15	28	connected	connected	ADJ
cana-1300	15	29	,	,	PUNCT
cana-1300	15	30	just	just	ADV
cana-1300	15	31	excellent	excellent	ADJ
cana-1300	15	32	;	;	PUNCT
cana-1300	15	33	domination	domination	NOUN
cana-1300	15	34	&	&	CCONJ
cana-1300	15	35	total	total	ADJ
cana-1300	15	36	domination	domination	NOUN
cana-1300	15	37	number	number	NOUN
cana-1300	15	38	for	for	ADP
cana-1300	15	39	the	the	DET
cana-1300	15	40	collaboration	collaboration	NOUN
cana-1300	15	41	graph	graph	NOUN
cana-1300	15	42	of	of	ADP
cana-1300	15	43	lilavathi	lilavathi	ADJ
cana-1300	15	44	prize	prize	NOUN
cana-1300	15	45	winners	winner	NOUN
cana-1300	15	46	.	.	PUNCT
cana-1300	16	1	keywords	keyword	NOUN
cana-1300	16	2	:	:	PUNCT
cana-1300	16	3	dominating	dominate	VERB
cana-1300	16	4	set	set	NOUN
cana-1300	16	5	,	,	PUNCT
cana-1300	16	6	erdӧsnumber	erdӧsnumber	PROPN
cana-1300	16	7	,	,	PUNCT
cana-1300	16	8	lilavati	lilavati	PROPN
cana-1300	16	9	award	award	PROPN
cana-1300	16	10	,	,	PUNCT
cana-1300	16	11	collaborative	collaborative	ADJ
cana-1300	16	12	graph	graph	NOUN
cana-1300	16	13	,	,	PUNCT
cana-1300	16	14	domination	domination	NOUN
cana-1300	16	15	parameters	parameter	NOUN
cana-1300	16	16	1.introduction	1.introduction	NUM
cana-1300	16	17	in	in	ADP
cana-1300	16	18	advanced	advanced	ADJ
cana-1300	16	19	era	era	NOUN
cana-1300	16	20	,	,	PUNCT
cana-1300	16	21	graphs	graph	NOUN
cana-1300	16	22	have	have	AUX
cana-1300	16	23	grown	grow	VERB
cana-1300	16	24	up	up	ADP
cana-1300	16	25	as	as	ADP
cana-1300	16	26	the	the	DET
cana-1300	16	27	most	most	ADV
cana-1300	16	28	effective	effective	ADJ
cana-1300	16	29	leading	lead	VERB
cana-1300	16	30	tool	tool	NOUN
cana-1300	16	31	of	of	ADP
cana-1300	16	32	mathematics	mathematic	NOUN
cana-1300	16	33	in	in	ADP
cana-1300	16	34	various	various	ADJ
cana-1300	16	35	subjects	subject	NOUN
cana-1300	16	36	.	.	PUNCT
cana-1300	17	1	in	in	ADP
cana-1300	17	2	the	the	DET
cana-1300	17	3	interim	interim	NOUN
cana-1300	17	4	it	it	PRON
cana-1300	17	5	has	have	AUX
cana-1300	17	6	also	also	ADV
cana-1300	17	7	turned	turn	VERB
cana-1300	17	8	out	out	ADP
cana-1300	17	9	as	as	ADP
cana-1300	17	10	a	a	DET
cana-1300	17	11	full	full	ADV
cana-1300	17	12	-	-	PUNCT
cana-1300	17	13	fledged	fledged	ADJ
cana-1300	17	14	substantial	substantial	ADJ
cana-1300	17	15	field	field	NOUN
cana-1300	17	16	of	of	ADP
cana-1300	17	17	mathematics	mathematic	NOUN
cana-1300	17	18	.	.	PUNCT
cana-1300	18	1	in	in	ADP
cana-1300	18	2	graphs	graph	NOUN
cana-1300	18	3	,	,	PUNCT
cana-1300	18	4	the	the	DET
cana-1300	18	5	domination	domination	NOUN
cana-1300	18	6	theory	theory	NOUN
cana-1300	18	7	has	have	VERB
cana-1300	18	8	extensive	extensive	ADJ
cana-1300	18	9	applications	application	NOUN
cana-1300	18	10	in	in	ADP
cana-1300	18	11	different	different	ADJ
cana-1300	18	12	fields	field	NOUN
cana-1300	18	13	.	.	PUNCT
cana-1300	19	1	now	now	ADV
cana-1300	19	2	days	day	NOUN
cana-1300	19	3	,	,	PUNCT
cana-1300	19	4	it	it	PRON
cana-1300	19	5	can	can	AUX
cana-1300	19	6	be	be	AUX
cana-1300	19	7	considered	consider	VERB
cana-1300	19	8	as	as	ADP
cana-1300	19	9	the	the	DET
cana-1300	19	10	most	most	ADV
cana-1300	19	11	basic	basic	ADJ
cana-1300	19	12	concepts	concept	NOUN
cana-1300	19	13	in	in	ADP
cana-1300	19	14	the	the	DET
cana-1300	19	15	theory	theory	NOUN
cana-1300	19	16	of	of	ADP
cana-1300	19	17	graphs	graph	NOUN
cana-1300	19	18	and	and	CCONJ
cana-1300	19	19	its	its	PRON
cana-1300	19	20	practical	practical	ADJ
cana-1300	19	21	significance	significance	NOUN
cana-1300	19	22	in	in	ADP
cana-1300	19	23	web	web	NOUN
cana-1300	19	24	graphs	graph	NOUN
cana-1300	19	25	,	,	PUNCT
cana-1300	19	26	social	social	ADJ
cana-1300	19	27	networks	network	NOUN
cana-1300	19	28	,	,	PUNCT
cana-1300	19	29	biological	biological	ADJ
cana-1300	19	30	patterns	pattern	NOUN
cana-1300	19	31	etc	etc	X
cana-1300	19	32	.	.	X
cana-1300	19	33	,	,	PUNCT
cana-1300	19	34	shows	show	VERB
cana-1300	19	35	the	the	DET
cana-1300	19	36	increased	increase	VERB
cana-1300	19	37	curiosity	curiosity	NOUN
cana-1300	19	38	towards	towards	ADP
cana-1300	19	39	the	the	DET
cana-1300	19	40	topic	topic	NOUN
cana-1300	19	41	.	.	PUNCT
cana-1300	20	1	in	in	ADP
cana-1300	20	2	general	general	ADJ
cana-1300	20	3	the	the	DET
cana-1300	20	4	domination	domination	NOUN
cana-1300	20	5	appears	appear	VERB
cana-1300	20	6	in	in	ADP
cana-1300	20	7	problems	problem	NOUN
cana-1300	20	8	like	like	ADP
cana-1300	20	9	locating	locate	VERB
cana-1300	20	10	the	the	DET
cana-1300	20	11	facilities	facility	NOUN
cana-1300	20	12	in	in	ADP
cana-1300	20	13	which	which	PRON
cana-1300	20	14	one	one	PRON
cana-1300	20	15	aims	aim	VERB
cana-1300	20	16	to	to	PART
cana-1300	20	17	reduce	reduce	VERB
cana-1300	20	18	the	the	DET
cana-1300	20	19	communications	communication	NOUN
cana-1300	20	20	on	on	ADP
cana-1300	20	21	applied	apply	VERB
cana-1300	20	22	nonlinear	nonlinear	ADJ
cana-1300	20	23	analysis	analysis	NOUN
cana-1300	20	24	issn	issn	NOUN
cana-1300	20	25	:	:	PUNCT
cana-1300	20	26	1074	1074	NUM
cana-1300	20	27	-	-	PUNCT
cana-1300	20	28	133x	133x	NUM
cana-1300	20	29	vol	vol	NOUN
cana-1300	20	30	31	31	NUM
cana-1300	20	31	no	no	NOUN
cana-1300	20	32	.	.	PUNCT
cana-1300	21	1	7s	7	NOUN
cana-1300	21	2	(	(	PUNCT
cana-1300	21	3	2024	2024	NUM
cana-1300	21	4	)	)	PUNCT
cana-1300	21	5	251	251	NUM
cana-1300	21	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1300	21	7	distance	distance	NOUN
cana-1300	21	8	a	a	DET
cana-1300	21	9	person	person	NOUN
cana-1300	21	10	requires	require	VERB
cana-1300	21	11	to	to	PART
cana-1300	21	12	reach	reach	VERB
cana-1300	21	13	the	the	DET
cana-1300	21	14	nearest	near	ADJ
cana-1300	21	15	facility	facility	NOUN
cana-1300	21	16	when	when	SCONJ
cana-1300	21	17	the	the	DET
cana-1300	21	18	facility	facility	NOUN
cana-1300	21	19	is	be	AUX
cana-1300	21	20	fixed	fix	VERB
cana-1300	21	21	.	.	PUNCT
cana-1300	22	1	a	a	DET
cana-1300	22	2	similar	similar	ADJ
cana-1300	22	3	kind	kind	NOUN
cana-1300	22	4	of	of	ADP
cana-1300	22	5	problem	problem	NOUN
cana-1300	22	6	arises	arise	VERB
cana-1300	22	7	where	where	SCONJ
cana-1300	22	8	the	the	DET
cana-1300	22	9	maximum	maximum	ADJ
cana-1300	22	10	distance	distance	NOUN
cana-1300	22	11	to	to	ADP
cana-1300	22	12	a	a	DET
cana-1300	22	13	particular	particular	ADJ
cana-1300	22	14	facility	facility	NOUN
cana-1300	22	15	remains	remain	VERB
cana-1300	22	16	constant	constant	ADJ
cana-1300	22	17	and	and	CCONJ
cana-1300	22	18	a	a	DET
cana-1300	22	19	person	person	NOUN
cana-1300	22	20	tries	try	VERB
cana-1300	22	21	to	to	PART
cana-1300	22	22	see	see	VERB
cana-1300	22	23	that	that	SCONJ
cana-1300	22	24	everyone	everyone	PRON
cana-1300	22	25	is	be	AUX
cana-1300	22	26	facilitated	facilitate	VERB
cana-1300	22	27	with	with	ADP
cana-1300	22	28	the	the	DET
cana-1300	22	29	minimum	minimum	ADJ
cana-1300	22	30	number	number	NOUN
cana-1300	22	31	of	of	ADP
cana-1300	22	32	facilities	facility	NOUN
cana-1300	22	33	.	.	PUNCT
cana-1300	23	1	also	also	ADV
cana-1300	23	2	the	the	DET
cana-1300	23	3	concept	concept	NOUN
cana-1300	23	4	of	of	ADP
cana-1300	23	5	domination	domination	NOUN
cana-1300	23	6	arises	arise	VERB
cana-1300	23	7	in	in	ADP
cana-1300	23	8	the	the	DET
cana-1300	23	9	problems	problem	NOUN
cana-1300	23	10	of	of	ADP
cana-1300	23	11	obtaining	obtain	VERB
cana-1300	23	12	a	a	DET
cana-1300	23	13	set	set	NOUN
cana-1300	23	14	of	of	ADP
cana-1300	23	15	representatives	representative	NOUN
cana-1300	23	16	,	,	PUNCT
cana-1300	23	17	in	in	ADP
cana-1300	23	18	electrical	electrical	ADJ
cana-1300	23	19	networks	network	NOUN
cana-1300	23	20	or	or	CCONJ
cana-1300	23	21	in	in	ADP
cana-1300	23	22	land	land	NOUN
cana-1300	23	23	survey	survey	NOUN
cana-1300	23	24	etc	etc	X
cana-1300	23	25	.	.	X
cana-1300	23	26	,	,	PUNCT
cana-1300	23	27	claude	claude	PROPN
cana-1300	23	28	berge	berge	NOUN
cana-1300	24	1	[	[	X
cana-1300	24	2	2	2	NUM
cana-1300	24	3	]	]	PUNCT
cana-1300	24	4	and	and	CCONJ
cana-1300	24	5	oystein	oystein	PROPN
cana-1300	24	6	ore[15	ore[15	PROPN
cana-1300	24	7	]	]	PUNCT
cana-1300	24	8	make	make	VERB
cana-1300	24	9	known	know	VERB
cana-1300	24	10	the	the	DET
cana-1300	24	11	concept	concept	NOUN
cana-1300	24	12	of	of	ADP
cana-1300	24	13	dominant	dominant	ADJ
cana-1300	24	14	sets	set	NOUN
cana-1300	24	15	in	in	ADP
cana-1300	24	16	graphs	graph	NOUN
cana-1300	24	17	as	as	ADP
cana-1300	24	18	the	the	DET
cana-1300	24	19	first	first	ADJ
cana-1300	24	20	time	time	NOUN
cana-1300	24	21	in	in	ADP
cana-1300	24	22	1958	1958	NUM
cana-1300	24	23	and	and	CCONJ
cana-1300	24	24	1962	1962	NUM
cana-1300	24	25	respectively	respectively	ADV
cana-1300	24	26	.	.	PUNCT
cana-1300	25	1	after	after	ADP
cana-1300	25	2	reading	read	VERB
cana-1300	25	3	write	write	VERB
cana-1300	25	4	-	-	PUNCT
cana-1300	25	5	up	up	NOUN
cana-1300	25	6	of	of	ADP
cana-1300	25	7	ernie	ernie	PROPN
cana-1300	25	8	cockayne	cockayne	PROPN
cana-1300	25	9	and	and	CCONJ
cana-1300	25	10	stephen	stephen	PROPN
cana-1300	25	11	hedetniemi	hedetniemi	PROPN
cana-1300	25	12	,	,	PUNCT
cana-1300	25	13	many	many	ADJ
cana-1300	25	14	academics	academic	NOUN
cana-1300	25	15	became	become	VERB
cana-1300	25	16	more	more	ADV
cana-1300	25	17	interested	interested	ADJ
cana-1300	25	18	in	in	ADP
cana-1300	25	19	the	the	DET
cana-1300	25	20	subject	subject	NOUN
cana-1300	25	21	of	of	ADP
cana-1300	25	22	domination	domination	NOUN
cana-1300	25	23	in	in	ADP
cana-1300	25	24	graphs	graph	NOUN
cana-1300	25	25	[	[	X
cana-1300	25	26	3	3	NUM
cana-1300	25	27	]	]	PUNCT
cana-1300	25	28	.	.	PUNCT
cana-1300	26	1	the	the	DET
cana-1300	26	2	dominating	dominating	NOUN
cana-1300	26	3	idea	idea	NOUN
cana-1300	26	4	is	be	AUX
cana-1300	26	5	also	also	ADV
cana-1300	26	6	useful	useful	ADJ
cana-1300	26	7	in	in	ADP
cana-1300	26	8	problems	problem	NOUN
cana-1300	26	9	with	with	ADP
cana-1300	26	10	land	land	NOUN
cana-1300	26	11	surveys	survey	NOUN
cana-1300	26	12	,	,	PUNCT
cana-1300	26	13	establishing	establish	VERB
cana-1300	26	14	representative	representative	ADJ
cana-1300	26	15	sets	set	NOUN
cana-1300	26	16	for	for	ADP
cana-1300	26	17	communications	communication	NOUN
cana-1300	26	18	or	or	CCONJ
cana-1300	26	19	power	power	NOUN
cana-1300	26	20	grid	grid	NOUN
cana-1300	26	21	monitoring	monitoring	NOUN
cana-1300	26	22	,	,	PUNCT
cana-1300	26	23	and	and	CCONJ
cana-1300	26	24	facility	facility	NOUN
cana-1300	26	25	placement	placement	NOUN
cana-1300	26	26	.	.	PUNCT
cana-1300	27	1	peter	peter	PROPN
cana-1300	27	2	j.	j.	PROPN
cana-1300	27	3	slater	slater	PROPN
cana-1300	27	4	,	,	PUNCT
cana-1300	27	5	stephen	stephen	PROPN
cana-1300	27	6	t.	t.	PROPN
cana-1300	27	7	hedetniemi	hedetniemi	PROPN
cana-1300	27	8	,	,	PUNCT
cana-1300	27	9	t.w	t.w	PROPN
cana-1300	27	10	.	.	PROPN
cana-1300	27	11	haynes	haynes	PROPN
cana-1300	27	12	,	,	PUNCT
cana-1300	27	13	v.r	v.r	PROPN
cana-1300	27	14	.	.	PROPN
cana-1300	27	15	kulli	kulli	PROPN
cana-1300	27	16	,	,	PUNCT
cana-1300	27	17	and	and	CCONJ
cana-1300	27	18	stephen	stephen	PROPN
cana-1300	27	19	t.	t.	PROPN
cana-1300	27	20	hedetniemi	hedetniemi	NOUN
cana-1300	27	21	are	be	AUX
cana-1300	27	22	cited	cite	VERB
cana-1300	27	23	as	as	ADV
cana-1300	27	24	well	well	ADV
cana-1300	27	25	as	as	ADP
cana-1300	27	26	their	their	PRON
cana-1300	27	27	works	work	NOUN
cana-1300	27	28	,	,	PUNCT
cana-1300	27	29	for	for	ADP
cana-1300	27	30	more	more	ADJ
cana-1300	27	31	information	information	NOUN
cana-1300	27	32	on	on	ADP
cana-1300	27	33	several	several	ADJ
cana-1300	27	34	dominant	dominant	ADJ
cana-1300	27	35	variations	variation	NOUN
cana-1300	27	36	depicted	depict	VERB
cana-1300	27	37	on	on	ADP
cana-1300	27	38	the	the	DET
cana-1300	27	39	graph	graph	NOUN
cana-1300	27	40	.	.	PUNCT
cana-1300	28	1	many	many	ADJ
cana-1300	28	2	graph	graph	NOUN
cana-1300	28	3	theorists	theorist	NOUN
cana-1300	28	4	ikonig	ikonig	ADJ
cana-1300	28	5	,	,	PUNCT
cana-1300	28	6	ore	ore	NOUN
cana-1300	28	7	,	,	PUNCT
cana-1300	28	8	bauer	bauer	PROPN
cana-1300	28	9	,	,	PUNCT
cana-1300	28	10	iharary	iharary	ADJ
cana-1300	28	11	,	,	PUNCT
cana-1300	28	12	ilasker	ilasker	PROPN
cana-1300	28	13	,	,	PUNCT
cana-1300	28	14	berge	berge	NOUN
cana-1300	28	15	,	,	PUNCT
cana-1300	28	16	icockayne	icockayne	PROPN
cana-1300	28	17	,	,	PUNCT
cana-1300	28	18	ihedetniemi	ihedetniemi	PROPN
cana-1300	28	19	,	,	PUNCT
cana-1300	28	20	ialavi	ialavi	PROPN
cana-1300	28	21	,	,	PUNCT
cana-1300	28	22	allan	allan	PROPN
cana-1300	28	23	,	,	PUNCT
cana-1300	28	24	ichartrand	ichartrand	NOUN
cana-1300	28	25	,	,	PUNCT
cana-1300	28	26	ikulli	ikulli	NOUN
cana-1300	28	27	,	,	PUNCT
cana-1300	28	28	imuddebihal	imuddebihal	ADJ
cana-1300	28	29	,	,	PUNCT
cana-1300	28	30	isampthkumar	isampthkumar	ADJ
cana-1300	28	31	,	,	PUNCT
cana-1300	28	32	iwalikar	iwalikar	NOUN
cana-1300	28	33	,	,	PUNCT
cana-1300	28	34	armugam	armugam	NUM
cana-1300	28	35	,	,	PUNCT
cana-1300	28	36	iacharya	iacharya	PROPN
cana-1300	28	37	,	,	PUNCT
cana-1300	28	38	ineeralgi	ineeralgi	PROPN
cana-1300	28	39	,	,	PUNCT
cana-1300	28	40	nagaraja	nagaraja	PROPN
cana-1300	28	41	rao	rao	PROPN
cana-1300	28	42	,	,	PUNCT
cana-1300	28	43	vangipuram	vangipuram	NOUN
cana-1300	28	44	putforth	putforth	NOUN
cana-1300	28	45	many	many	ADJ
cana-1300	28	46	interesting	interesting	ADJ
cana-1300	28	47	concepts	concept	NOUN
cana-1300	28	48	of	of	ADP
cana-1300	28	49	domination	domination	NOUN
cana-1300	28	50	theory	theory	NOUN
cana-1300	28	51	and	and	CCONJ
cana-1300	28	52	related	related	ADJ
cana-1300	28	53	topics	topic	NOUN
cana-1300	28	54	.	.	PUNCT
cana-1300	29	1	some	some	PRON
cana-1300	29	2	of	of	ADP
cana-1300	29	3	them	they	PRON
cana-1300	29	4	worked	work	VERB
cana-1300	29	5	in	in	ADP
cana-1300	29	6	introducing	introduce	VERB
cana-1300	29	7	a	a	DET
cana-1300	29	8	new	new	ADJ
cana-1300	29	9	domination	domination	NOUN
cana-1300	29	10	parameter	parameter	NOUN
cana-1300	29	11	and	and	CCONJ
cana-1300	29	12	obtaining	obtain	VERB
cana-1300	29	13	the	the	DET
cana-1300	29	14	boundaries	boundary	NOUN
cana-1300	29	15	of	of	ADP
cana-1300	29	16	the	the	DET
cana-1300	29	17	defined	define	VERB
cana-1300	29	18	variable	variable	NOUN
cana-1300	29	19	in	in	ADP
cana-1300	29	20	terms	term	NOUN
cana-1300	29	21	of	of	ADP
cana-1300	29	22	the	the	DET
cana-1300	29	23	graph	graph	NOUN
cana-1300	29	24	parameters	parameter	NOUN
cana-1300	29	25	.	.	PUNCT
cana-1300	30	1	and	and	CCONJ
cana-1300	30	2	some	some	PRON
cana-1300	30	3	of	of	ADP
cana-1300	30	4	them	they	PRON
cana-1300	30	5	worked	work	VERB
cana-1300	30	6	on	on	ADP
cana-1300	30	7	the	the	DET
cana-1300	30	8	graph	graph	NOUN
cana-1300	30	9	algorithms	algorithm	NOUN
cana-1300	30	10	to	to	PART
cana-1300	30	11	study	study	VERB
cana-1300	30	12	the	the	DET
cana-1300	30	13	complexity	complexity	NOUN
cana-1300	30	14	results	result	NOUN
cana-1300	30	15	of	of	ADP
cana-1300	30	16	domination	domination	NOUN
cana-1300	30	17	parameters	parameter	NOUN
cana-1300	30	18	.	.	PUNCT
cana-1300	31	1	the	the	DET
cana-1300	31	2	combination	combination	NOUN
cana-1300	31	3	of	of	ADP
cana-1300	31	4	domination	domination	NOUN
cana-1300	31	5	with	with	ADP
cana-1300	31	6	other	other	ADJ
cana-1300	31	7	graph	graph	NOUN
cana-1300	31	8	theoretical	theoretical	ADJ
cana-1300	31	9	properties	property	NOUN
cana-1300	31	10	resulted	result	VERB
cana-1300	31	11	in	in	ADP
cana-1300	31	12	several	several	ADJ
cana-1300	31	13	domination	domination	NOUN
cana-1300	31	14	parameters	parameter	NOUN
cana-1300	31	15	and	and	CCONJ
cana-1300	31	16	many	many	ADJ
cana-1300	31	17	of	of	ADP
cana-1300	31	18	them	they	PRON
cana-1300	31	19	are	be	AUX
cana-1300	31	20	defined	define	VERB
cana-1300	31	21	by	by	ADP
cana-1300	31	22	inflicting	inflict	VERB
cana-1300	31	23	an	an	DET
cana-1300	31	24	added	add	VERB
cana-1300	31	25	constraint	constraint	NOUN
cana-1300	31	26	on	on	ADP
cana-1300	31	27	the	the	DET
cana-1300	31	28	dominating	dominating	NOUN
cana-1300	31	29	set	set	NOUN
cana-1300	31	30	.	.	PUNCT
cana-1300	32	1	kulli	kulli	PROPN
cana-1300	32	2	and	and	CCONJ
cana-1300	32	3	janakiram	janakiram	PROPN
cana-1300	32	4	make	make	VERB
cana-1300	32	5	known	know	VERB
cana-1300	32	6	the	the	DET
cana-1300	32	7	idea	idea	NOUN
cana-1300	32	8	of	of	ADP
cana-1300	32	9	split	split	ADJ
cana-1300	32	10	domination	domination	NOUN
cana-1300	32	11	number[10	number[10	ADV
cana-1300	32	12	]	]	PUNCT
cana-1300	32	13	.	.	PUNCT
cana-1300	33	1	by	by	ADP
cana-1300	33	2	sampath	sampath	PROPN
cana-1300	33	3	kumar[16	kumar[16	PROPN
cana-1300	33	4	]	]	X
cana-1300	33	5	,	,	PUNCT
cana-1300	33	6	the	the	DET
cana-1300	33	7	idea	idea	NOUN
cana-1300	33	8	of	of	ADP
cana-1300	33	9	a	a	DET
cana-1300	33	10	strong	strong	ADJ
cana-1300	33	11	domination	domination	NOUN
cana-1300	33	12	number	number	NOUN
cana-1300	33	13	was	be	AUX
cana-1300	33	14	first	first	ADV
cana-1300	33	15	presented	present	VERB
cana-1300	33	16	.	.	PUNCT
cana-1300	34	1	by	by	ADP
cana-1300	34	2	kulli	kulli	PROPN
cana-1300	34	3	and	and	CCONJ
cana-1300	34	4	janakiram	janakiram	VERB
cana-1300	34	5	[	[	X
cana-1300	34	6	13	13	NUM
cana-1300	34	7	]	]	PUNCT
cana-1300	34	8	,	,	PUNCT
cana-1300	34	9	the	the	DET
cana-1300	34	10	idea	idea	NOUN
cana-1300	34	11	of	of	ADP
cana-1300	34	12	a	a	DET
cana-1300	34	13	strong	strong	ADJ
cana-1300	34	14	split	split	ADJ
cana-1300	34	15	domination	domination	NOUN
cana-1300	34	16	number	number	NOUN
cana-1300	34	17	was	be	AUX
cana-1300	34	18	first	first	ADV
cana-1300	34	19	presented	present	VERB
cana-1300	34	20	.	.	PUNCT
cana-1300	35	1	inverse	inverse	ADJ
cana-1300	35	2	domination	domination	NOUN
cana-1300	35	3	in	in	ADP
cana-1300	35	4	graphs	graph	NOUN
cana-1300	35	5	is	be	AUX
cana-1300	35	6	a	a	DET
cana-1300	35	7	notion	notion	NOUN
cana-1300	35	8	that	that	PRON
cana-1300	35	9	was	be	AUX
cana-1300	35	10	first	first	ADV
cana-1300	35	11	developed	develop	VERB
cana-1300	35	12	by	by	ADP
cana-1300	35	13	kulli	kulli	PROPN
cana-1300	35	14	v.r[9	v.r[9	NOUN
cana-1300	35	15	]	]	X
cana-1300	35	16	.	.	PUNCT
cana-1300	36	1	also	also	ADV
cana-1300	36	2	v.yegnanarayanan	v.yegnanarayanan	X
cana-1300	36	3	with	with	ADP
cana-1300	36	4	lokeswary	lokeswary	PROPN
cana-1300	36	5	and	and	CCONJ
cana-1300	36	6	renuka	renuka	PROPN
cana-1300	36	7	lakshmi	lakshmi	PROPN
cana-1300	36	8	a.	a.	PROPN
cana-1300	36	9	obtained	obtain	VERB
cana-1300	36	10	the	the	DET
cana-1300	36	11	domination	domination	NOUN
cana-1300	36	12	numbers	number	NOUN
cana-1300	36	13	for	for	ADP
cana-1300	36	14	the	the	DET
cana-1300	36	15	colloboration	colloboration	NOUN
cana-1300	36	16	graph	graph	NOUN
cana-1300	36	17	of	of	ADP
cana-1300	36	18	the	the	DET
cana-1300	36	19	rolf	rolf	PROPN
cana-1300	36	20	nevalinna	nevalinna	PROPN
cana-1300	36	21	prize	prize	PROPN
cana-1300	36	22	winners	winner	NOUN
cana-1300	36	23	[	[	X
cana-1300	36	24	18	18	NUM
cana-1300	36	25	&	&	CCONJ
cana-1300	36	26	19	19	NUM
cana-1300	36	27	]	]	PUNCT
cana-1300	36	28	.	.	PUNCT
cana-1300	37	1	a	a	DET
cana-1300	37	2	note	note	NOUN
cana-1300	37	3	on	on	ADP
cana-1300	37	4	inverse	inverse	NOUN
cana-1300	37	5	split	split	NOUN
cana-1300	37	6	and	and	CCONJ
cana-1300	37	7	nonsplit	nonsplit	VERB
cana-1300	37	8	domination	domination	NOUN
cana-1300	37	9	in	in	ADP
cana-1300	37	10	graphs	graph	NOUN
cana-1300	37	11	was	be	AUX
cana-1300	37	12	given	give	VERB
cana-1300	37	13	by	by	ADP
cana-1300	37	14	ameenal	ameenal	ADJ
cana-1300	37	15	bibi	bibi	NOUN
cana-1300	37	16	along	along	ADP
cana-1300	37	17	with	with	ADP
cana-1300	37	18	selvakumar[1].yamuna	selvakumar[1].yamuna	PROPN
cana-1300	37	19	in	in	ADP
cana-1300	37	20	colloboration	colloboration	NOUN
cana-1300	37	21	with	with	ADP
cana-1300	37	22	sridharan[17	sridharan[17	PROPN
cana-1300	37	23	]	]	PUNCT
cana-1300	37	24	worked	work	VERB
cana-1300	37	25	on	on	ADP
cana-1300	37	26	the	the	DET
cana-1300	37	27	just	just	ADV
cana-1300	37	28	excellent	excellent	ADJ
cana-1300	37	29	graphs	graph	NOUN
cana-1300	37	30	whereas	whereas	SCONJ
cana-1300	37	31	cockayne	cockayne	PROPN
cana-1300	37	32	e.j	e.j	PROPN
cana-1300	37	33	,	,	PUNCT
cana-1300	37	34	hartnell	hartnell	PROPN
cana-1300	37	35	b.l	b.l	PROPN
cana-1300	37	36	,	,	PUNCT
cana-1300	37	37	hedetniemi	hedetniemi	ADP
cana-1300	37	38	s.t	s.t	PROPN
cana-1300	37	39	,	,	PUNCT
cana-1300	37	40	and	and	CCONJ
cana-1300	37	41	laskar	laskar	PROPN
cana-1300	37	42	r[4	r[4	PROPN
cana-1300	37	43	]	]	PUNCT
cana-1300	37	44	has	have	AUX
cana-1300	37	45	given	give	VERB
cana-1300	37	46	an	an	DET
cana-1300	37	47	article	article	NOUN
cana-1300	37	48	on	on	ADP
cana-1300	37	49	“	"	PUNCT
cana-1300	37	50	efficient	efficient	ADJ
cana-1300	37	51	domination	domination	NOUN
cana-1300	37	52	in	in	ADP
cana-1300	37	53	graphs	graph	NOUN
cana-1300	37	54	”	"	PUNCT
cana-1300	37	55	.	.	PUNCT
cana-1300	38	1	a	a	DET
cana-1300	38	2	brief	brief	ADJ
cana-1300	38	3	study	study	NOUN
cana-1300	38	4	on	on	ADP
cana-1300	38	5	‘	'	PUNCT
cana-1300	38	6	the	the	DET
cana-1300	38	7	domatic	domatic	ADJ
cana-1300	38	8	number	number	NOUN
cana-1300	38	9	problem	problem	NOUN
cana-1300	38	10	’	'	PUNCT
cana-1300	38	11	was	be	AUX
cana-1300	38	12	given	give	VERB
cana-1300	38	13	by	by	ADP
cana-1300	38	14	gerald	gerald	PROPN
cana-1300	38	15	j.chang[5	j.chang[5	PROPN
cana-1300	38	16	]	]	PUNCT
cana-1300	38	17	and	and	CCONJ
cana-1300	38	18	joanna	joanna	PROPN
cana-1300	38	19	cyman[8	cyman[8	PRON
cana-1300	38	20	]	]	PUNCT
cana-1300	38	21	has	have	AUX
cana-1300	38	22	given	give	VERB
cana-1300	38	23	a	a	DET
cana-1300	38	24	discussion	discussion	NOUN
cana-1300	38	25	on	on	ADP
cana-1300	38	26	“	"	PUNCT
cana-1300	38	27	the	the	DET
cana-1300	38	28	outer	outer	ADJ
cana-1300	38	29	connected	connected	ADJ
cana-1300	38	30	domination	domination	NOUN
cana-1300	38	31	number	number	NOUN
cana-1300	38	32	of	of	ADP
cana-1300	38	33	a	a	DET
cana-1300	38	34	graph	graph	NOUN
cana-1300	38	35	”	"	PUNCT
cana-1300	38	36	1.1	1.1	NUM
cana-1300	38	37	statement	statement	NOUN
cana-1300	38	38	of	of	ADP
cana-1300	38	39	problem	problem	NOUN
cana-1300	38	40	attract	attract	VERB
cana-1300	38	41	collaboration	collaboration	NOUN
cana-1300	38	42	graph	graph	NOUN
cana-1300	38	43	of	of	ADP
cana-1300	38	44	lilavati	lilavati	PROPN
cana-1300	38	45	prize	prize	PROPN
cana-1300	38	46	winners	winner	NOUN
cana-1300	38	47	by	by	ADP
cana-1300	38	48	considering	consider	VERB
cana-1300	38	49	all	all	DET
cana-1300	38	50	the	the	DET
cana-1300	38	51	winners	winner	NOUN
cana-1300	38	52	from	from	ADP
cana-1300	38	53	the	the	DET
cana-1300	38	54	date	date	NOUN
cana-1300	38	55	of	of	ADP
cana-1300	38	56	establishment	establishment	NOUN
cana-1300	38	57	to	to	ADP
cana-1300	38	58	the	the	DET
cana-1300	38	59	present	present	NOUN
cana-1300	38	60	(	(	PUNCT
cana-1300	38	61	i.e	i.e	X
cana-1300	38	62	,	,	PUNCT
cana-1300	38	63	from	from	ADP
cana-1300	38	64	2010	2010	NUM
cana-1300	38	65	to	to	ADP
cana-1300	38	66	2022	2022	NUM
cana-1300	38	67	)	)	PUNCT
cana-1300	38	68	and	and	CCONJ
cana-1300	38	69	also	also	ADV
cana-1300	38	70	to	to	PART
cana-1300	38	71	determine	determine	VERB
cana-1300	38	72	its	its	PRON
cana-1300	38	73	domination	domination	NOUN
cana-1300	38	74	parameters	parameter	NOUN
cana-1300	38	75	such	such	ADJ
cana-1300	38	76	as	as	ADP
cana-1300	38	77	split	split	ADJ
cana-1300	38	78	,	,	PUNCT
cana-1300	38	79	strong	strong	ADJ
cana-1300	38	80	split	split	NOUN
cana-1300	38	81	,	,	PUNCT
cana-1300	38	82	strong	strong	ADJ
cana-1300	38	83	,	,	PUNCT
cana-1300	38	84	strong	strong	ADJ
cana-1300	38	85	non	non	NOUN
cana-1300	38	86	split	split	NOUN
cana-1300	38	87	,	,	PUNCT
cana-1300	38	88	inverse	inverse	NOUN
cana-1300	38	89	,	,	PUNCT
cana-1300	38	90	inverse	inverse	NOUN
cana-1300	38	91	non	non	NOUN
cana-1300	38	92	split	split	NOUN
cana-1300	38	93	edge	edge	NOUN
cana-1300	38	94	and	and	CCONJ
cana-1300	38	95	connected	connected	ADJ
cana-1300	38	96	edge	edge	NOUN
cana-1300	38	97	.	.	PUNCT
cana-1300	39	1	1.2	1.2	NUM
cana-1300	39	2	a	a	DET
cana-1300	39	3	brief	brief	NOUN
cana-1300	39	4	about	about	ADP
cana-1300	39	5	lilavati	lilavati	PROPN
cana-1300	39	6	ward	ward	PROPN
cana-1300	39	7	la	la	ADP
cana-1300	39	8	the	the	DET
cana-1300	39	9	lilavati	lilavati	PROPN
cana-1300	39	10	prize	prize	PROPN
cana-1300	39	11	is	be	AUX
cana-1300	39	12	a	a	DET
cana-1300	39	13	unique	unique	ADJ
cana-1300	39	14	international	international	ADJ
cana-1300	39	15	award	award	NOUN
cana-1300	39	16	that	that	PRON
cana-1300	39	17	recognizes	recognize	VERB
cana-1300	39	18	magnificent	magnificent	ADJ
cana-1300	39	19	hype	hype	NOUN
cana-1300	39	20	work	work	NOUN
cana-1300	39	21	in	in	ADP
cana-1300	39	22	mathematics	mathematic	NOUN
cana-1300	39	23	.	.	PUNCT
cana-1300	40	1	this	this	DET
cana-1300	40	2	award	award	NOUN
cana-1300	40	3	was	be	AUX
cana-1300	40	4	tremendously	tremendously	ADV
cana-1300	40	5	eulogized	eulogize	VERB
cana-1300	40	6	in	in	ADP
cana-1300	40	7	the	the	DET
cana-1300	40	8	conference	conference	NOUN
cana-1300	40	9	and	and	CCONJ
cana-1300	40	10	mathematical	mathematical	ADJ
cana-1300	40	11	media	medium	NOUN
cana-1300	40	12	,	,	PUNCT
cana-1300	40	13	the	the	DET
cana-1300	40	14	‘	'	PUNCT
cana-1300	40	15	international	international	ADJ
cana-1300	40	16	congress	congress	PROPN
cana-1300	40	17	of	of	ADP
cana-1300	40	18	mathematicians	mathematician	NOUN
cana-1300	40	19	'	'	PART
cana-1300	40	20	closing	closing	NOUN
cana-1300	40	21	ceremony	ceremony	NOUN
cana-1300	40	22	always	always	ADV
cana-1300	40	23	includes	include	VERB
cana-1300	40	24	an	an	DET
cana-1300	40	25	award	award	NOUN
cana-1300	40	26	ceremony	ceremony	NOUN
cana-1300	40	27	,	,	PUNCT
cana-1300	40	28	communications	communication	NOUN
cana-1300	40	29	on	on	ADP
cana-1300	40	30	applied	apply	VERB
cana-1300	40	31	nonlinear	nonlinear	ADJ
cana-1300	40	32	analysis	analysis	NOUN
cana-1300	40	33	issn	issn	NOUN
cana-1300	40	34	:	:	PUNCT
cana-1300	40	35	1074	1074	NUM
cana-1300	40	36	-	-	PUNCT
cana-1300	40	37	133x	133x	NUM
cana-1300	40	38	vol	vol	NOUN
cana-1300	40	39	31	31	NUM
cana-1300	40	40	no	no	NOUN
cana-1300	40	41	.	.	PUNCT
cana-1300	41	1	7s	7	NOUN
cana-1300	41	2	(	(	PUNCT
cana-1300	41	3	2024	2024	NUM
cana-1300	41	4	)	)	PUNCT
cana-1300	41	5	252	252	NUM
cana-1300	41	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1300	41	7	thus	thus	ADV
cana-1300	41	8	the	the	DET
cana-1300	41	9	imu	imu	NOUN
cana-1300	41	10	decided	decide	VERB
cana-1300	41	11	to	to	PART
cana-1300	41	12	make	make	VERB
cana-1300	41	13	it	it	PRON
cana-1300	41	14	a	a	DET
cana-1300	41	15	recrudescing	recrudesce	VERB
cana-1300	41	16	prize	prize	NOUN
cana-1300	41	17	that	that	PRON
cana-1300	41	18	is	be	AUX
cana-1300	41	19	given	give	VERB
cana-1300	41	20	out	out	ADP
cana-1300	41	21	once	once	SCONJ
cana-1300	41	22	every	every	DET
cana-1300	41	23	four	four	NUM
cana-1300	41	24	years	year	NOUN
cana-1300	41	25	.	.	PUNCT
cana-1300	42	1	instead	instead	ADV
cana-1300	42	2	of	of	ADP
cana-1300	42	3	honoring	honor	VERB
cana-1300	42	4	mathematical	mathematical	ADJ
cana-1300	42	5	research	research	NOUN
cana-1300	42	6	,	,	PUNCT
cana-1300	42	7	the	the	DET
cana-1300	42	8	lilavati	lilavati	PROPN
cana-1300	42	9	prize	prize	PROPN
cana-1300	42	10	seeks	seek	VERB
cana-1300	42	11	to	to	PART
cana-1300	42	12	promote	promote	VERB
cana-1300	42	13	endeavors	endeavor	NOUN
cana-1300	42	14	as	as	ADV
cana-1300	42	15	far	far	ADV
cana-1300	42	16	as	as	ADP
cana-1300	42	17	possible	possible	ADJ
cana-1300	42	18	.	.	PUNCT
cana-1300	43	1	1.3	1.3	NUM
cana-1300	43	2	brief	brief	ADJ
cana-1300	43	3	history	history	NOUN
cana-1300	43	4	of	of	ADP
cana-1300	43	5	lilavati	lilavati	PROPN
cana-1300	43	6	award	award	VERB
cana-1300	43	7	an	an	DET
cana-1300	43	8	award	award	NOUN
cana-1300	43	9	for	for	ADP
cana-1300	43	10	virtuoso	virtuoso	ADJ
cana-1300	43	11	contributions	contribution	NOUN
cana-1300	43	12	to	to	PART
cana-1300	43	13	poignant	poignant	VERB
cana-1300	43	14	in	in	ADP
cana-1300	43	15	the	the	DET
cana-1300	43	16	field	field	NOUN
cana-1300	43	17	of	of	ADP
cana-1300	43	18	public	public	ADJ
cana-1300	43	19	mathematics	mathematic	NOUN
cana-1300	43	20	is	be	AUX
cana-1300	43	21	lilavathi	lilavathi	ADJ
cana-1300	43	22	award	award	NOUN
cana-1300	43	23	.	.	PUNCT
cana-1300	44	1	after	after	ADP
cana-1300	44	2	the	the	DET
cana-1300	44	3	indian	indian	ADJ
cana-1300	44	4	mathematician	mathematician	NOUN
cana-1300	44	5	bhskara	bhskara	PROPN
cana-1300	44	6	ii	ii	PROPN
cana-1300	44	7	(	(	PUNCT
cana-1300	44	8	also	also	ADV
cana-1300	44	9	known	know	VERB
cana-1300	44	10	as	as	ADP
cana-1300	44	11	bhaskara	bhaskara	NOUN
cana-1300	44	12	achrya	achrya	PROPN
cana-1300	44	13	)	)	PUNCT
cana-1300	44	14	,	,	PUNCT
cana-1300	44	15	who	who	PRON
cana-1300	44	16	wrote	write	VERB
cana-1300	44	17	the	the	DET
cana-1300	44	18	algebra	algebra	NOUN
cana-1300	44	19	and	and	CCONJ
cana-1300	44	20	arithmetic	arithmetic	PROPN
cana-1300	44	21	mathematics	mathematics	PROPN
cana-1300	44	22	monograph	monograph	NOUN
cana-1300	44	23	"	"	PUNCT
cana-1300	44	24	lilavati	lilavati	PROPN
cana-1300	44	25	"	"	PUNCT
cana-1300	44	26	in	in	ADP
cana-1300	44	27	the	the	DET
cana-1300	44	28	12th	12th	ADJ
cana-1300	44	29	century	century	NOUN
cana-1300	44	30	,	,	PUNCT
cana-1300	44	31	the	the	DET
cana-1300	44	32	term	term	NOUN
cana-1300	44	33	"	"	PUNCT
cana-1300	44	34	lilavathi	lilavathi	ADJ
cana-1300	44	35	"	"	PUNCT
cana-1300	44	36	was	be	AUX
cana-1300	44	37	coined	coin	VERB
cana-1300	44	38	.	.	PUNCT
cana-1300	45	1	in	in	ADP
cana-1300	45	2	this	this	DET
cana-1300	45	3	volume	volume	NOUN
cana-1300	45	4	,	,	PUNCT
cana-1300	45	5	the	the	DET
cana-1300	45	6	author	author	NOUN
cana-1300	45	7	poses	pose	VERB
cana-1300	45	8	a	a	DET
cana-1300	45	9	series	series	NOUN
cana-1300	45	10	of	of	ADP
cana-1300	45	11	(	(	PUNCT
cana-1300	45	12	basic	basic	ADJ
cana-1300	45	13	)	)	PUNCT
cana-1300	45	14	arithmetic	arithmetic	ADJ
cana-1300	45	15	problems	problem	NOUN
cana-1300	45	16	to	to	ADP
cana-1300	45	17	lilavati	lilavati	PROPN
cana-1300	45	18	(	(	PUNCT
cana-1300	45	19	perhaps	perhaps	ADV
cana-1300	45	20	his	his	PRON
cana-1300	45	21	daughter	daughter	NOUN
cana-1300	45	22	)	)	PUNCT
cana-1300	45	23	in	in	ADP
cana-1300	45	24	the	the	DET
cana-1300	45	25	form	form	NOUN
cana-1300	45	26	of	of	ADP
cana-1300	45	27	verses	verse	NOUN
cana-1300	45	28	,	,	PUNCT
cana-1300	45	29	and	and	CCONJ
cana-1300	45	30	proposes	propose	VERB
cana-1300	45	31	elucidations	elucidation	NOUN
cana-1300	45	32	.	.	PUNCT
cana-1300	46	1	this	this	DET
cana-1300	46	2	work	work	NOUN
cana-1300	46	3	appears	appear	VERB
cana-1300	46	4	to	to	PART
cana-1300	46	5	have	have	AUX
cana-1300	46	6	evolved	evolve	VERB
cana-1300	46	7	into	into	ADP
cana-1300	46	8	the	the	DET
cana-1300	46	9	primary	primary	ADJ
cana-1300	46	10	resource	resource	NOUN
cana-1300	46	11	for	for	ADP
cana-1300	46	12	studying	study	VERB
cana-1300	46	13	algebra	algebra	NOUN
cana-1300	46	14	and	and	CCONJ
cana-1300	46	15	arithmetic	arithmetic	ADJ
cana-1300	46	16	in	in	ADP
cana-1300	46	17	medieval	medieval	PROPN
cana-1300	46	18	india	india	PROPN
cana-1300	46	19	.	.	PUNCT
cana-1300	47	1	the	the	DET
cana-1300	47	2	work	work	NOUN
cana-1300	47	3	has	have	AUX
cana-1300	47	4	been	be	AUX
cana-1300	47	5	rewritten	rewrite	VERB
cana-1300	47	6	in	in	ADP
cana-1300	47	7	persian	persian	PROPN
cana-1300	47	8	and	and	CCONJ
cana-1300	47	9	is	be	AUX
cana-1300	47	10	widely	widely	ADV
cana-1300	47	11	read	read	VERB
cana-1300	47	12	in	in	ADP
cana-1300	47	13	west	west	PROPN
cana-1300	47	14	asia	asia	PROPN
cana-1300	47	15	.	.	PUNCT
cana-1300	48	1	inaugurated	inaugurate	VERB
cana-1300	48	2	by	by	ADP
cana-1300	48	3	the	the	DET
cana-1300	48	4	executive	executive	ADJ
cana-1300	48	5	organising	organise	VERB
cana-1300	48	6	committee	committee	NOUN
cana-1300	48	7	(	(	PUNCT
cana-1300	48	8	eoc	eoc	PROPN
cana-1300	48	9	)	)	PUNCT
cana-1300	48	10	of	of	ADP
cana-1300	48	11	the	the	DET
cana-1300	48	12	international	international	ADJ
cana-1300	48	13	conference	conference	NOUN
cana-1300	48	14	of	of	ADP
cana-1300	48	15	mathematics	mathematics	PROPN
cana-1300	48	16	(	(	PUNCT
cana-1300	48	17	icm	icm	NOUN
cana-1300	48	18	)	)	PUNCT
cana-1300	48	19	with	with	ADP
cana-1300	48	20	the	the	DET
cana-1300	48	21	authorization	authorization	NOUN
cana-1300	48	22	of	of	ADP
cana-1300	48	23	the	the	DET
cana-1300	48	24	imu	imu	PROPN
cana-1300	48	25	executive	executive	PROPN
cana-1300	48	26	committee	committee	PROPN
cana-1300	48	27	(	(	PUNCT
cana-1300	48	28	ec	ec	PROPN
cana-1300	48	29	)	)	PUNCT
cana-1300	48	30	,	,	PUNCT
cana-1300	48	31	the	the	DET
cana-1300	48	32	lilavati	lilavati	PROPN
cana-1300	48	33	prize	prize	PROPN
cana-1300	48	34	was	be	AUX
cana-1300	48	35	presented	present	VERB
cana-1300	48	36	for	for	ADP
cana-1300	48	37	the	the	DET
cana-1300	48	38	first	first	ADJ
cana-1300	48	39	time	time	NOUN
cana-1300	48	40	at	at	ADP
cana-1300	48	41	the	the	DET
cana-1300	48	42	closing	closing	NOUN
cana-1300	48	43	ceremony	ceremony	NOUN
cana-1300	48	44	of	of	ADP
cana-1300	48	45	the	the	DET
cana-1300	48	46	icm	icm	NOUN
cana-1300	48	47	in	in	ADP
cana-1300	48	48	hyderabad	hyderabad	PROPN
cana-1300	48	49	,	,	PUNCT
cana-1300	48	50	india	india	PROPN
cana-1300	48	51	,	,	PUNCT
cana-1300	48	52	in	in	ADP
cana-1300	48	53	2010	2010	NUM
cana-1300	48	54	.	.	PUNCT
cana-1300	49	1	it	it	PRON
cana-1300	49	2	is	be	AUX
cana-1300	49	3	sponsored	sponsor	VERB
cana-1300	49	4	by	by	ADP
cana-1300	49	5	infosys	infosy	NOUN
cana-1300	49	6	and	and	CCONJ
cana-1300	49	7	includes	include	VERB
cana-1300	49	8	a	a	DET
cana-1300	49	9	cash	cash	NOUN
cana-1300	49	10	reward	reward	NOUN
cana-1300	49	11	of	of	ADP
cana-1300	49	12	10	10	NUM
cana-1300	49	13	lakh	lakh	NOUN
cana-1300	49	14	rupees	rupee	NOUN
cana-1300	49	15	as	as	ADV
cana-1300	49	16	well	well	ADV
cana-1300	49	17	as	as	ADP
cana-1300	49	18	a	a	DET
cana-1300	49	19	certificate	certificate	NOUN
cana-1300	49	20	.	.	PUNCT
cana-1300	50	1	1.4	1.4	NUM
cana-1300	50	2	details	detail	NOUN
cana-1300	50	3	about	about	ADP
cana-1300	50	4	lilavati	lilavati	PROPN
cana-1300	50	5	award	award	PROPN
cana-1300	50	6	(	(	PUNCT
cana-1300	50	7	la	la	ADJ
cana-1300	50	8	)	)	PUNCT
cana-1300	50	9	winners	winner	NOUN
cana-1300	50	10	(	(	PUNCT
cana-1300	50	11	2010	2010	NUM
cana-1300	50	12	to	to	ADP
cana-1300	50	13	2022	2022	NUM
cana-1300	50	14	)	)	PUNCT
cana-1300	50	15	s.no	s.no	VERB
cana-1300	50	16	name	name	NOUN
cana-1300	50	17	of	of	ADP
cana-1300	50	18	the	the	DET
cana-1300	50	19	prize	prize	NOUN
cana-1300	50	20	winner	winner	NOUN
cana-1300	50	21	year	year	NOUN
cana-1300	50	22	country	country	NOUN
cana-1300	50	23	1	1	NUM
cana-1300	50	24	simon	simon	PROPN
cana-1300	50	25	singh	singh	PROPN
cana-1300	50	26	2010	2010	NUM
cana-1300	50	27	indian	indian	PROPN
cana-1300	50	28	settled	settle	VERB
cana-1300	50	29	in	in	ADP
cana-1300	50	30	britain	britain	PROPN
cana-1300	50	31	2	2	NUM
cana-1300	50	32	adrián	adrián	NOUN
cana-1300	50	33	paenza	paenza	ADJ
cana-1300	50	34	2014	2014	NUM
cana-1300	50	35	argentina	argentina	PROPN
cana-1300	50	36	3	3	PROPN
cana-1300	50	37	ali	ali	PROPN
cana-1300	50	38	nesin	nesin	PROPN
cana-1300	50	39	2018	2018	NUM
cana-1300	50	40	turkey	turkey	PROPN
cana-1300	50	41	4	4	NUM
cana-1300	50	42	nikolai	nikolai	PROPN
cana-1300	50	43	andreev	andreev	VERB
cana-1300	50	44	2022	2022	NUM
cana-1300	50	45	table	table	NOUN
cana-1300	50	46	1	1	NUM
cana-1300	50	47	2	2	NUM
cana-1300	50	48	.	.	PUNCT
cana-1300	50	49	notations	notation	NOUN
cana-1300	50	50	and	and	CCONJ
cana-1300	50	51	terminology	terminology	NOUN
cana-1300	50	52	2.1	2.1	NUM
cana-1300	50	53	.	.	PUNCT
cana-1300	51	1	collaboration	collaboration	NOUN
cana-1300	51	2	graph	graph	NOUN
cana-1300	51	3	:	:	PUNCT
cana-1300	51	4	by	by	ADP
cana-1300	51	5	a	a	DET
cana-1300	51	6	collaboration	collaboration	NOUN
cana-1300	51	7	graph	graph	NOUN
cana-1300	51	8	𝐺	𝐺	NOUN
cana-1300	51	9	we	we	PRON
cana-1300	51	10	mean	mean	VERB
cana-1300	51	11	agraph	agraph	VERB
cana-1300	51	12	whose	whose	DET
cana-1300	51	13	vertex	vertex	NOUN
cana-1300	51	14	elements	element	NOUN
cana-1300	51	15	denote	denote	VERB
cana-1300	51	16	all	all	DET
cana-1300	51	17	research	research	NOUN
cana-1300	51	18	scientists	scientist	NOUN
cana-1300	51	19	(	(	PUNCT
cana-1300	51	20	either	either	CCONJ
cana-1300	51	21	presently	presently	ADV
cana-1300	51	22	alive	alive	ADJ
cana-1300	51	23	or	or	CCONJ
cana-1300	51	24	no	no	PRON
cana-1300	51	25	more	more	ADJ
cana-1300	51	26	and	and	CCONJ
cana-1300	51	27	we	we	PRON
cana-1300	51	28	introduce	introduce	VERB
cana-1300	51	29	an	an	DET
cana-1300	51	30	edge	edge	NOUN
cana-1300	51	31	between	between	ADP
cana-1300	51	32	two	two	NUM
cana-1300	51	33	vertex	vertex	NOUN
cana-1300	51	34	elements	element	NOUN
cana-1300	51	35	𝑢1	𝑢1	NOUN
cana-1300	51	36	and	and	CCONJ
cana-1300	51	37	𝑢2of	𝑢2of	NUM
cana-1300	51	38	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	51	39	)	)	PUNCT
cana-1300	51	40	,	,	PUNCT
cana-1300	51	41	if	if	SCONJ
cana-1300	51	42	they	they	PRON
cana-1300	51	43	are	be	AUX
cana-1300	51	44	joint	joint	ADJ
cana-1300	51	45	authors	author	NOUN
cana-1300	51	46	of	of	ADP
cana-1300	51	47	a	a	DET
cana-1300	51	48	published	publish	VERB
cana-1300	51	49	paper	paper	NOUN
cana-1300	51	50	or	or	CCONJ
cana-1300	51	51	a	a	DET
cana-1300	51	52	book	book	NOUN
cana-1300	51	53	.	.	PUNCT
cana-1300	52	1	2.2	2.2	NUM
cana-1300	52	2	.	.	PUNCT
cana-1300	53	1	erdӧs	erdӧs	NOUN
cana-1300	53	2	number	number	NOUN
cana-1300	53	3	:	:	PUNCT
cana-1300	53	4	by	by	ADP
cana-1300	53	5	an	an	DET
cana-1300	53	6	erdos	erdo	NOUN
cana-1300	53	7	number	number	NOUN
cana-1300	53	8	of	of	ADP
cana-1300	53	9	a	a	DET
cana-1300	53	10	research	research	NOUN
cana-1300	53	11	scientist	scientist	NOUN
cana-1300	53	12	𝑢	𝑢	PROPN
cana-1300	53	13	ina	ina	PROPN
cana-1300	53	14	collaboration	collaboration	NOUN
cana-1300	53	15	graph	graph	NOUN
cana-1300	53	16	,	,	PUNCT
cana-1300	53	17	we	we	PRON
cana-1300	53	18	mean	mean	VERB
cana-1300	53	19	the	the	DET
cana-1300	53	20	number	number	NOUN
cana-1300	53	21	𝑑(𝐸𝑟𝑑ӧ𝑠	𝑑(𝐸𝑟𝑑ӧ𝑠	NOUN
cana-1300	53	22	,	,	PUNCT
cana-1300	53	23	𝑢	𝑢	NOUN
cana-1300	53	24	)	)	PUNCT
cana-1300	53	25	.	.	PUNCT
cana-1300	54	1	(	(	PUNCT
cana-1300	54	2	by	by	ADP
cana-1300	54	3	𝑑(𝑥	𝑑(𝑥	PROPN
cana-1300	54	4	,	,	PUNCT
cana-1300	54	5	𝑦	𝑦	X
cana-1300	54	6	)	)	PUNCT
cana-1300	54	7	we	we	PRON
cana-1300	54	8	mean	mean	VERB
cana-1300	54	9	the	the	DET
cana-1300	54	10	smallest	small	ADJ
cana-1300	54	11	distance	distance	NOUN
cana-1300	54	12	between	between	ADP
cana-1300	54	13	x	x	PROPN
cana-1300	54	14	and	and	CCONJ
cana-1300	54	15	y	y	NOUN
cana-1300	54	16	)	)	PUNCT
cana-1300	54	17	note	note	VERB
cana-1300	54	18	2.1	2.1	NUM
cana-1300	54	19	:	:	PUNCT
cana-1300	54	20	paul	paul	PROPN
cana-1300	54	21	erdӧs	erdӧs	VERB
cana-1300	54	22	himself	himself	PRON
cana-1300	54	23	by	by	ADP
cana-1300	54	24	virtue	virtue	NOUN
cana-1300	54	25	of	of	ADP
cana-1300	54	26	the	the	DET
cana-1300	54	27	above	above	ADJ
cana-1300	54	28	definition	definition	NOUN
cana-1300	54	29	earns	earn	VERB
cana-1300	54	30	the	the	DET
cana-1300	54	31	erdӧs	erdӧs	NOUN
cana-1300	54	32	number	number	NOUN
cana-1300	54	33	zero	zero	NUM
cana-1300	54	34	.	.	PUNCT
cana-1300	55	1	all	all	DET
cana-1300	55	2	coauthors	coauthor	NOUN
cana-1300	55	3	directly	directly	ADV
cana-1300	55	4	related	relate	VERB
cana-1300	55	5	with	with	ADP
cana-1300	55	6	erdӧs	erdӧs	NOUN
cana-1300	55	7	has	have	VERB
cana-1300	55	8	erdӧs	erdӧs	ADJ
cana-1300	55	9	number	number	NOUN
cana-1300	55	10	1	1	NUM
cana-1300	55	11	.	.	PUNCT
cana-1300	56	1	interestingly	interestingly	ADV
cana-1300	56	2	there	there	PRON
cana-1300	56	3	are	be	VERB
cana-1300	56	4	511	511	NUM
cana-1300	56	5	such	such	ADJ
cana-1300	56	6	people	people	NOUN
cana-1300	56	7	with	with	ADP
cana-1300	56	8	erdӧs	erdӧs	NOUN
cana-1300	56	9	number	number	NOUN
cana-1300	56	10	1	1	NUM
cana-1300	56	11	.	.	PUNCT
cana-1300	57	1	unfortunately	unfortunately	ADV
cana-1300	57	2	this	this	DET
cana-1300	57	3	number	number	NOUN
cana-1300	57	4	has	have	AUX
cana-1300	57	5	become	become	VERB
cana-1300	57	6	a	a	DET
cana-1300	57	7	fixed	fix	VERB
cana-1300	57	8	number	number	NOUN
cana-1300	57	9	as	as	SCONJ
cana-1300	57	10	erdӧs	erdӧs	NOUN
cana-1300	57	11	is	be	AUX
cana-1300	57	12	no	no	PRON
cana-1300	57	13	more	more	ADJ
cana-1300	57	14	.	.	PUNCT
cana-1300	58	1	the	the	DET
cana-1300	58	2	coauthors	coauthor	NOUN
cana-1300	58	3	of	of	ADP
cana-1300	58	4	co	co	NOUN
cana-1300	58	5	-	-	NOUN
cana-1300	58	6	authors	author	NOUN
cana-1300	58	7	of	of	ADP
cana-1300	58	8	erdӧs	erdӧs	NOUN
cana-1300	58	9	earns	earn	VERB
cana-1300	58	10	the	the	DET
cana-1300	58	11	erdӧs	erdӧs	NOUN
cana-1300	58	12	number	number	NOUN
cana-1300	58	13	two	two	NUM
cana-1300	58	14	and	and	CCONJ
cana-1300	58	15	so	so	ADV
cana-1300	58	16	on	on	ADV
cana-1300	58	17	.	.	PUNCT
cana-1300	59	1	2.3	2.3	NUM
cana-1300	59	2	.	.	PUNCT
cana-1300	60	1	domination	domination	NOUN
cana-1300	60	2	number	number	NOUN
cana-1300	60	3	:	:	PUNCT
cana-1300	61	1	if	if	SCONJ
cana-1300	61	2	every	every	DET
cana-1300	61	3	element	element	NOUN
cana-1300	61	4	selected	select	VERB
cana-1300	61	5	from	from	ADP
cana-1300	61	6	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	61	7	)	)	PUNCT
cana-1300	61	8	−	−	PROPN
cana-1300	61	9	𝐴	𝐴	PROPN
cana-1300	61	10	is	be	AUX
cana-1300	61	11	connected	connect	VERB
cana-1300	61	12	by	by	ADP
cana-1300	61	13	a	a	DET
cana-1300	61	14	path	path	NOUN
cana-1300	61	15	of	of	ADP
cana-1300	61	16	distance	distance	NOUN
cana-1300	61	17	one	one	NUM
cana-1300	61	18	to	to	ADP
cana-1300	61	19	some	some	DET
cana-1300	61	20	element	element	NOUN
cana-1300	61	21	in	in	ADP
cana-1300	61	22	𝐴	𝐴	PROPN
cana-1300	61	23	,	,	PUNCT
cana-1300	61	24	then	then	ADV
cana-1300	61	25	we	we	PRON
cana-1300	61	26	say	say	VERB
cana-1300	61	27	that	that	SCONJ
cana-1300	61	28	set	set	PROPN
cana-1300	61	29	𝐴	𝐴	PROPN
cana-1300	61	30	,	,	PUNCT
cana-1300	61	31	whose	whose	DET
cana-1300	61	32	elements	element	NOUN
cana-1300	61	33	come	come	VERB
cana-1300	61	34	from	from	ADP
cana-1300	61	35	the	the	DET
cana-1300	61	36	vertex	vertex	NOUN
cana-1300	61	37	set	set	NOUN
cana-1300	61	38	of	of	ADP
cana-1300	61	39	a	a	DET
cana-1300	61	40	graph	graph	NOUN
cana-1300	61	41	𝐺	𝐺	NOUN
cana-1300	61	42	=	=	SYM
cana-1300	61	43	(	(	PUNCT
cana-1300	61	44	𝑉	𝑉	PROPN
cana-1300	61	45	,	,	PUNCT
cana-1300	61	46	𝐸	𝐸	PROPN
cana-1300	61	47	)	)	PUNCT
cana-1300	61	48	,	,	PUNCT
cana-1300	61	49	is	be	AUX
cana-1300	61	50	a	a	DET
cana-1300	61	51	dominant	dominant	ADJ
cana-1300	61	52	set	set	NOUN
cana-1300	61	53	.	.	PUNCT
cana-1300	62	1	we	we	PRON
cana-1300	62	2	use	use	VERB
cana-1300	62	3	the	the	DET
cana-1300	62	4	symbol	symbol	NOUN
cana-1300	62	5	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1300	62	6	)	)	PUNCT
cana-1300	62	7	to	to	PART
cana-1300	62	8	denote	denote	VERB
cana-1300	62	9	the	the	DET
cana-1300	62	10	domination	domination	NOUN
cana-1300	62	11	number	number	NOUN
cana-1300	62	12	of	of	ADP
cana-1300	62	13	𝐺	𝐺	PROPN
cana-1300	62	14	and	and	CCONJ
cana-1300	62	15	(	(	PUNCT
cana-1300	62	16	𝐺	𝐺	NOUN
cana-1300	62	17	)	)	PUNCT
cana-1300	62	18	=	=	SYM
cana-1300	62	19	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-1300	62	20	|	|	ADV
cana-1300	62	21	𝐴|	𝐴|	PROPN
cana-1300	62	22	.	.	PUNCT
cana-1300	63	1	2.4	2.4	NUM
cana-1300	63	2	.	.	PUNCT
cana-1300	64	1	induced	induce	VERB
cana-1300	64	2	subgraph	subgraph	NOUN
cana-1300	64	3	:	:	PUNCT
cana-1300	64	4	a	a	DET
cana-1300	64	5	subgraph	subgraph	NOUN
cana-1300	64	6	formed	form	VERB
cana-1300	64	7	by	by	ADP
cana-1300	64	8	the	the	DET
cana-1300	64	9	subset	subset	NOUN
cana-1300	64	10	𝐷vertices	𝐷vertices	PROPN
cana-1300	64	11	of	of	ADP
cana-1300	64	12	a	a	DET
cana-1300	64	13	graph	graph	NOUN
cana-1300	64	14	𝐺	𝐺	NOUN
cana-1300	64	15	whose	whose	DET
cana-1300	64	16	edges	edge	NOUN
cana-1300	64	17	are	be	AUX
cana-1300	64	18	all	all	DET
cana-1300	64	19	the	the	DET
cana-1300	64	20	connecting	connect	VERB
cana-1300	64	21	edges	edge	NOUN
cana-1300	64	22	of	of	ADP
cana-1300	64	23	the	the	DET
cana-1300	64	24	respective	respective	ADJ
cana-1300	64	25	vertices	vertex	NOUN
cana-1300	64	26	,	,	PUNCT
cana-1300	64	27	denoted	denote	VERB
cana-1300	64	28	by	by	ADP
cana-1300	64	29	〈	〈	PROPN
cana-1300	64	30	𝐷	𝐷	NOUN
cana-1300	64	31	〉	〉	NOUN
cana-1300	64	32	.	.	PUNCT
cana-1300	65	1	communications	communication	NOUN
cana-1300	65	2	on	on	ADP
cana-1300	65	3	applied	apply	VERB
cana-1300	65	4	nonlinear	nonlinear	ADJ
cana-1300	65	5	analysis	analysis	NOUN
cana-1300	65	6	issn	issn	NOUN
cana-1300	65	7	:	:	PUNCT
cana-1300	65	8	1074	1074	NUM
cana-1300	65	9	-	-	PUNCT
cana-1300	65	10	133x	133x	NUM
cana-1300	65	11	vol	vol	NOUN
cana-1300	65	12	31	31	NUM
cana-1300	65	13	no	no	NOUN
cana-1300	65	14	.	.	PUNCT
cana-1300	66	1	7s	7	NOUN
cana-1300	66	2	(	(	PUNCT
cana-1300	66	3	2024	2024	NUM
cana-1300	66	4	)	)	PUNCT
cana-1300	66	5	253	253	NUM
cana-1300	66	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1300	66	7	2.5	2.5	NUM
cana-1300	66	8	.	.	PUNCT
cana-1300	67	1	split	split	VERB
cana-1300	67	2	domination	domination	NOUN
cana-1300	67	3	number	number	NOUN
cana-1300	67	4	:	:	PUNCT
cana-1300	67	5	if	if	SCONJ
cana-1300	67	6	the	the	DET
cana-1300	67	7	subgraph	subgraph	NOUN
cana-1300	67	8	(	(	PUNCT
cana-1300	67	9	𝑉	𝑉	PROPN
cana-1300	67	10	(	(	PUNCT
cana-1300	67	11	𝐺	𝐺	NOUN
cana-1300	67	12	)	)	PUNCT
cana-1300	67	13	−	−	PROPN
cana-1300	67	14	𝐷	𝐷	NOUN
cana-1300	67	15	)	)	PUNCT
cana-1300	67	16	is	be	AUX
cana-1300	67	17	disconnected	disconnect	VERB
cana-1300	67	18	,	,	PUNCT
cana-1300	67	19	the	the	DET
cana-1300	67	20	dominating	dominating	NOUN
cana-1300	67	21	set	set	VERB
cana-1300	67	22	𝐷	𝐷	PROPN
cana-1300	67	23	⊆	⊆	NUM
cana-1300	67	24	𝑉(𝐺)is	𝑉(𝐺)i	NOUN
cana-1300	67	25	a	a	DET
cana-1300	67	26	split	split	ADJ
cana-1300	67	27	dominating	dominating	NOUN
cana-1300	67	28	set	set	NOUN
cana-1300	67	29	.	.	PUNCT
cana-1300	68	1	split	split	ADJ
cana-1300	68	2	domination	domination	NOUN
cana-1300	68	3	number	number	NOUN
cana-1300	68	4	in	in	ADP
cana-1300	68	5	g	g	NOUN
cana-1300	68	6	,	,	PUNCT
cana-1300	68	7	is	be	AUX
cana-1300	68	8	denoted	denote	VERB
cana-1300	68	9	by	by	ADP
cana-1300	68	10	aγs(g	aγs(g	PROPN
cana-1300	68	11	)	)	PUNCT
cana-1300	68	12	and	and	CCONJ
cana-1300	68	13	γs(g	γs(g	NUM
cana-1300	68	14	)	)	PUNCT
cana-1300	68	15	=	=	SYM
cana-1300	68	16	min|d|	min|d|	PROPN
cana-1300	68	17	.	.	PUNCT
cana-1300	69	1	2.6	2.6	NUM
cana-1300	69	2	.	.	PUNCT
cana-1300	70	1	strong	strong	ADJ
cana-1300	70	2	domination	domination	NOUN
cana-1300	70	3	number	number	NOUN
cana-1300	70	4	:	:	PUNCT
cana-1300	70	5	a	a	DET
cana-1300	70	6	set	set	NOUN
cana-1300	70	7	𝐷	𝐷	NOUN
cana-1300	70	8	⊆	⊆	NUM
cana-1300	70	9	𝑉(𝐺)is	𝑉(𝐺)i	NOUN
cana-1300	70	10	a	a	DET
cana-1300	70	11	strong	strong	ADJ
cana-1300	70	12	dominating	dominating	NOUN
cana-1300	70	13	set	set	NOUN
cana-1300	70	14	of	of	ADP
cana-1300	70	15	𝐺	𝐺	PROPN
cana-1300	70	16	if	if	SCONJ
cana-1300	70	17	for	for	ADP
cana-1300	70	18	each	each	DET
cana-1300	70	19	vertex	vertex	NOUN
cana-1300	70	20	𝑥	𝑥	DET
cana-1300	70	21	∈	∈	PROPN
cana-1300	70	22	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	70	23	)	)	PUNCT
cana-1300	70	24	−	−	PROPN
cana-1300	70	25	𝐷	𝐷	PROPN
cana-1300	70	26	there	there	PRON
cana-1300	70	27	is	be	VERB
cana-1300	70	28	a	a	DET
cana-1300	70	29	vertex	vertex	NOUN
cana-1300	70	30	𝑦	𝑦	NOUN
cana-1300	70	31	∈	∈	PROPN
cana-1300	70	32	𝐷	𝐷	NOUN
cana-1300	70	33	with	with	ADP
cana-1300	70	34	𝑥𝑦	𝑥𝑦	PROPN
cana-1300	70	35	∈	∈	PROPN
cana-1300	70	36	𝐸(𝐺	𝐸(𝐺	NOUN
cana-1300	70	37	)	)	PUNCT
cana-1300	70	38	and	and	CCONJ
cana-1300	70	39	𝑑𝑒𝑔(𝑥	𝑑𝑒𝑔(𝑥	PROPN
cana-1300	70	40	,	,	PUNCT
cana-1300	70	41	𝐺	𝐺	NOUN
cana-1300	70	42	)	)	PUNCT
cana-1300	70	43	<	<	X
cana-1300	70	44	𝑑𝑒𝑔(𝑦	𝑑𝑒𝑔(𝑦	PROPN
cana-1300	70	45	,	,	PUNCT
cana-1300	70	46	𝐺).strong	𝐺).strong	PRON
cana-1300	70	47	domination	domination	NOUN
cana-1300	70	48	number	number	NOUN
cana-1300	70	49	in	in	ADP
cana-1300	70	50	𝐺	𝐺	PROPN
cana-1300	70	51	,	,	PUNCT
cana-1300	70	52	is	be	AUX
cana-1300	70	53	denoted	denote	VERB
cana-1300	70	54	by	by	ADP
cana-1300	70	55	𝛾𝑠𝑡(𝐺	𝛾𝑠𝑡(𝐺	PROPN
cana-1300	70	56	)	)	PUNCT
cana-1300	70	57	and	and	CCONJ
cana-1300	70	58	𝛾𝑠𝑡(𝐺	𝛾𝑠𝑡(𝐺	NUM
cana-1300	70	59	)	)	PUNCT
cana-1300	71	1	=	=	SYM
cana-1300	71	2	min|d|	min|d|	PROPN
cana-1300	71	3	.	.	PUNCT
cana-1300	72	1	2.7	2.7	NUM
cana-1300	72	2	.	.	PUNCT
cana-1300	73	1	strong	strong	ADJ
cana-1300	73	2	split	split	ADJ
cana-1300	73	3	domination	domination	NOUN
cana-1300	73	4	number	number	NOUN
cana-1300	73	5	:	:	PUNCT
cana-1300	73	6	a	a	DET
cana-1300	73	7	dominating	dominating	NOUN
cana-1300	73	8	set	set	NOUN
cana-1300	73	9	if	if	SCONJ
cana-1300	73	10	the	the	DET
cana-1300	73	11	induced	induced	ADJ
cana-1300	73	12	subgraph	subgraph	NOUN
cana-1300	73	13	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	73	14	)	)	PUNCT
cana-1300	73	15	−	−	PROPN
cana-1300	73	16	𝐷	𝐷	PROPN
cana-1300	73	17	is	be	AUX
cana-1300	73	18	completely	completely	ADV
cana-1300	73	19	disconnected	disconnected	ADJ
cana-1300	73	20	with	with	ADP
cana-1300	73	21	at	at	ADV
cana-1300	73	22	least	least	ADV
cana-1300	73	23	two	two	NUM
cana-1300	73	24	vertices	vertex	NOUN
cana-1300	73	25	,	,	PUNCT
cana-1300	73	26	then	then	ADV
cana-1300	73	27	𝐷	𝐷	PROPN
cana-1300	73	28	⊆	⊆	NUM
cana-1300	73	29	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	73	30	)	)	PUNCT
cana-1300	73	31	is	be	AUX
cana-1300	73	32	a	a	DET
cana-1300	73	33	strong	strong	ADJ
cana-1300	73	34	split	split	ADJ
cana-1300	73	35	dominating	dominating	NOUN
cana-1300	73	36	set	set	NOUN
cana-1300	73	37	.	.	PUNCT
cana-1300	74	1	strong	strong	ADJ
cana-1300	74	2	split	split	ADJ
cana-1300	74	3	domination	domination	NOUN
cana-1300	74	4	number	number	NOUN
cana-1300	74	5	of	of	ADP
cana-1300	74	6	𝐺	𝐺	PROPN
cana-1300	74	7	,	,	PUNCT
cana-1300	74	8	is	be	AUX
cana-1300	74	9	denoted	denote	VERB
cana-1300	74	10	by	by	ADP
cana-1300	74	11	𝛾𝑠𝑠(𝐺	𝛾𝑠𝑠(𝐺	NUM
cana-1300	74	12	)	)	PUNCT
cana-1300	74	13	and	and	CCONJ
cana-1300	74	14	𝛾𝑠𝑠(𝐺	𝛾𝑠𝑠(𝐺	NUM
cana-1300	74	15	)	)	PUNCT
cana-1300	74	16	=	=	SYM
cana-1300	74	17	𝑚𝑖𝑛|𝐷|	𝑚𝑖𝑛|𝐷|	NOUN
cana-1300	74	18	.	.	PUNCT
cana-1300	75	1	2.8	2.8	NUM
cana-1300	75	2	.	.	PUNCT
cana-1300	75	3	inverse	inverse	ADJ
cana-1300	75	4	domination	domination	NOUN
cana-1300	75	5	number	number	NOUN
cana-1300	75	6	:	:	PUNCT
cana-1300	75	7	assume	assume	VERB
cana-1300	75	8	that	that	SCONJ
cana-1300	75	9	set	set	NOUN
cana-1300	75	10	𝐷	𝐷	PROPN
cana-1300	75	11	is	be	AUX
cana-1300	75	12	the	the	DET
cana-1300	75	13	least	least	ADJ
cana-1300	75	14	domination	domination	NOUN
cana-1300	75	15	set	set	VERB
cana-1300	75	16	in	in	ADP
cana-1300	75	17	g.the	g.the	DET
cana-1300	75	18	set	set	NOUN
cana-1300	75	19	𝐷′	𝐷′	NOUN
cana-1300	75	20	is	be	AUX
cana-1300	75	21	referred	refer	VERB
cana-1300	75	22	to	to	ADP
cana-1300	75	23	as	as	ADP
cana-1300	75	24	an	an	DET
cana-1300	75	25	inverse	inverse	NOUN
cana-1300	75	26	dominating	dominating	NOUN
cana-1300	75	27	set	set	VERB
cana-1300	75	28	if	if	SCONJ
cana-1300	75	29	,	,	PUNCT
cana-1300	75	30	with	with	ADP
cana-1300	75	31	regard	regard	NOUN
cana-1300	75	32	to	to	ADP
cana-1300	75	33	𝐷	𝐷	PROPN
cana-1300	75	34	,	,	PUNCT
cana-1300	75	35	a	a	DET
cana-1300	75	36	set	set	NOUN
cana-1300	75	37	,	,	PUNCT
cana-1300	75	38	let	let	VERB
cana-1300	75	39	's	us	PRON
cana-1300	75	40	say	say	VERB
cana-1300	75	41	𝐷′	𝐷′	PROPN
cana-1300	75	42	in	in	ADP
cana-1300	75	43	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	75	44	)	)	PUNCT
cana-1300	75	45	−	−	PROPN
cana-1300	75	46	𝐷	𝐷	PROPN
cana-1300	75	47	,	,	PUNCT
cana-1300	75	48	which	which	PRON
cana-1300	75	49	is	be	AUX
cana-1300	75	50	a	a	DET
cana-1300	75	51	dominating	dominating	NOUN
cana-1300	75	52	set	set	NOUN
cana-1300	75	53	in	in	ADP
cana-1300	75	54	g	g	NOUN
cana-1300	75	55	,	,	PUNCT
cana-1300	75	56	corresponds	correspond	VERB
cana-1300	75	57	.	.	PUNCT
cana-1300	76	1	the	the	DET
cana-1300	76	2	symbol	symbol	NOUN
cana-1300	76	3	for	for	ADP
cana-1300	76	4	g	g	PROPN
cana-1300	76	5	's	's	PART
cana-1300	76	6	inverse	inverse	ADJ
cana-1300	76	7	domination	domination	NOUN
cana-1300	76	8	number	number	NOUN
cana-1300	76	9	is	be	AUX
cana-1300	76	10	𝛾−1(𝐺	𝛾−1(𝐺	NOUN
cana-1300	76	11	)	)	PUNCT
cana-1300	76	12	.	.	PUNCT
cana-1300	77	1	inverse	inverse	ADJ
cana-1300	77	2	domination	domination	NOUN
cana-1300	77	3	number	number	NOUN
cana-1300	77	4	of	of	ADP
cana-1300	77	5	𝐺	𝐺	PROPN
cana-1300	77	6	,	,	PUNCT
cana-1300	77	7	is	be	AUX
cana-1300	77	8	denoted	denote	VERB
cana-1300	77	9	by	by	ADP
cana-1300	77	10	𝛾−1(𝐺	𝛾−1(𝐺	NOUN
cana-1300	77	11	)	)	PUNCT
cana-1300	77	12	and	and	CCONJ
cana-1300	77	13	𝛾−1(𝐺	𝛾−1(𝐺	NOUN
cana-1300	77	14	)	)	PUNCT
cana-1300	77	15	=	=	PUNCT
cana-1300	77	16	𝑚𝑖𝑛|𝐷|	𝑚𝑖𝑛|𝐷|	PROPN
cana-1300	77	17	.	.	PROPN
cana-1300	78	1	2.9	2.9	NUM
cana-1300	78	2	.	.	PUNCT
cana-1300	79	1	strong	strong	ADJ
cana-1300	79	2	non	non	NOUN
cana-1300	79	3	split	split	NOUN
cana-1300	79	4	domination	domination	NOUN
cana-1300	79	5	number	number	NOUN
cana-1300	79	6	:	:	PUNCT
cana-1300	79	7	a	a	DET
cana-1300	79	8	dominating	dominating	NOUN
cana-1300	79	9	set	set	VERB
cana-1300	79	10	𝐷	𝐷	NOUN
cana-1300	79	11	of	of	ADP
cana-1300	79	12	a	a	DET
cana-1300	79	13	graph	graph	NOUN
cana-1300	79	14	𝐺	𝐺	NOUN
cana-1300	79	15	=	=	SYM
cana-1300	79	16	(	(	PUNCT
cana-1300	79	17	𝑉	𝑉	PROPN
cana-1300	79	18	,	,	PUNCT
cana-1300	79	19	𝐸	𝐸	PROPN
cana-1300	79	20	)	)	PUNCT
cana-1300	79	21	is	be	AUX
cana-1300	79	22	a	a	DET
cana-1300	79	23	strong	strong	ADJ
cana-1300	79	24	non	non	NOUN
cana-1300	79	25	split	split	NOUN
cana-1300	79	26	dominating	dominating	NOUN
cana-1300	79	27	set	set	NOUN
cana-1300	79	28	if	if	SCONJ
cana-1300	79	29	the	the	DET
cana-1300	79	30	induced	induced	ADJ
cana-1300	79	31	sub	sub	NOUN
cana-1300	79	32	graph	graph	NOUN
cana-1300	79	33	(	(	PUNCT
cana-1300	79	34	𝑉	𝑉	PROPN
cana-1300	79	35	–	–	PUNCT
cana-1300	79	36	𝐷	𝐷	NOUN
cana-1300	79	37	)	)	PUNCT
cana-1300	79	38	is	be	AUX
cana-1300	79	39	complete	complete	ADJ
cana-1300	79	40	.	.	PUNCT
cana-1300	80	1	strong	strong	ADJ
cana-1300	80	2	non	non	NOUN
cana-1300	80	3	split	split	NOUN
cana-1300	80	4	domination	domination	NOUN
cana-1300	80	5	number	number	NOUN
cana-1300	80	6	in	in	ADP
cana-1300	80	7	𝐺	𝐺	PROPN
cana-1300	80	8	,	,	PUNCT
cana-1300	80	9	is	be	AUX
cana-1300	80	10	denoted	denote	VERB
cana-1300	80	11	by	by	ADP
cana-1300	80	12	aγns(g	aγns(g	PROPN
cana-1300	80	13	)	)	PUNCT
cana-1300	80	14	and	and	CCONJ
cana-1300	80	15	γns(g	γns(g	PROPN
cana-1300	80	16	)	)	PUNCT
cana-1300	80	17	=	=	SYM
cana-1300	80	18	min|d|	min|d|	PROPN
cana-1300	80	19	.	.	PUNCT
cana-1300	81	1	2.10	2.10	NUM
cana-1300	81	2	.	.	PUNCT
cana-1300	81	3	inverse	inverse	PROPN
cana-1300	81	4	non	non	NOUN
cana-1300	81	5	split	split	NOUN
cana-1300	81	6	domination	domination	NOUN
cana-1300	81	7	number	number	NOUN
cana-1300	81	8	:	:	PUNCT
cana-1300	81	9	let	let	VERB
cana-1300	81	10	𝐷	𝐷	NOUN
cana-1300	81	11	be	be	AUX
cana-1300	81	12	the	the	DET
cana-1300	81	13	smallest	small	ADJ
cana-1300	81	14	non	non	ADJ
cana-1300	81	15	-	-	ADJ
cana-1300	81	16	split	split	ADJ
cana-1300	81	17	dominating	dominating	NOUN
cana-1300	81	18	set	set	VERB
cana-1300	81	19	in	in	ADP
cana-1300	81	20	𝐺.	𝐺.	PROPN
cana-1300	81	21	if	if	SCONJ
cana-1300	81	22	a	a	DET
cana-1300	81	23	set	set	NOUN
cana-1300	81	24	𝐷′	𝐷′	NOUN
cana-1300	81	25	in	in	ADP
cana-1300	81	26	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	81	27	)	)	PUNCT
cana-1300	81	28	−	−	PROPN
cana-1300	81	29	𝐷	𝐷	NOUN
cana-1300	81	30	corresponds	correspond	VERB
cana-1300	81	31	to	to	ADP
cana-1300	81	32	a	a	DET
cana-1300	81	33	non	non	NOUN
cana-1300	81	34	split	split	NOUN
cana-1300	81	35	dominating	dominating	NOUN
cana-1300	81	36	set	set	VERB
cana-1300	81	37	in	in	ADP
cana-1300	81	38	g	g	PROPN
cana-1300	81	39	,	,	PUNCT
cana-1300	81	40	then	then	ADV
cana-1300	81	41	the	the	DET
cana-1300	81	42	set	set	PROPN
cana-1300	81	43	𝐷	𝐷	NOUN
cana-1300	81	44	'	'	PUNCT
cana-1300	81	45	is	be	AUX
cana-1300	81	46	termed	term	VERB
cana-1300	81	47	the	the	DET
cana-1300	81	48	inverse	inverse	NOUN
cana-1300	81	49	non	non	NOUN
cana-1300	81	50	split	split	NOUN
cana-1300	81	51	dominating	dominating	NOUN
cana-1300	81	52	set	set	NOUN
cana-1300	81	53	,	,	PUNCT
cana-1300	81	54	and	and	CCONJ
cana-1300	81	55	the	the	DET
cana-1300	81	56	inverse	inverse	NOUN
cana-1300	81	57	non	non	NOUN
cana-1300	81	58	split	split	VERB
cana-1300	81	59	dominating	dominating	NOUN
cana-1300	81	60	number	number	NOUN
cana-1300	81	61	of	of	ADP
cana-1300	81	62	𝐺	𝐺	PROPN
cana-1300	81	63	,	,	PUNCT
cana-1300	81	64	is	be	AUX
cana-1300	81	65	denoted	denote	VERB
cana-1300	81	66	by	by	ADP
cana-1300	81	67	𝛾𝑛𝑠	𝛾𝑛𝑠	PROPN
cana-1300	81	68	−1(𝐺	−1(𝐺	NOUN
cana-1300	81	69	)	)	PUNCT
cana-1300	81	70	and	and	CCONJ
cana-1300	81	71	𝛾𝑛𝑠	𝛾𝑛𝑠	VERB
cana-1300	81	72	−1(𝐺	−1(𝐺	NOUN
cana-1300	81	73	)	)	PUNCT
cana-1300	81	74	=	=	SYM
cana-1300	81	75	𝑚𝑖𝑛|𝐷|	𝑚𝑖𝑛|𝐷|	NOUN
cana-1300	81	76	.	.	PUNCT
cana-1300	82	1	2.11	2.11	NUM
cana-1300	82	2	.	.	PUNCT
cana-1300	83	1	total	total	ADJ
cana-1300	83	2	domination	domination	NOUN
cana-1300	83	3	set	set	NOUN
cana-1300	83	4	:	:	PUNCT
cana-1300	83	5	by	by	ADP
cana-1300	83	6	a	a	DET
cana-1300	83	7	total	total	ADJ
cana-1300	83	8	dominating	dominating	NOUN
cana-1300	83	9	set	set	NOUN
cana-1300	83	10	𝐵	𝐵	NOUN
cana-1300	83	11	of	of	ADP
cana-1300	83	12	a	a	DET
cana-1300	83	13	graph	graph	NOUN
cana-1300	83	14	𝐺we	𝐺we	PROPN
cana-1300	83	15	mean	mean	VERB
cana-1300	83	16	a	a	DET
cana-1300	83	17	set	set	NOUN
cana-1300	83	18	with	with	ADP
cana-1300	83	19	the	the	DET
cana-1300	83	20	ensuing	ensue	VERB
cana-1300	83	21	properties	property	NOUN
cana-1300	83	22	:	:	PUNCT
cana-1300	83	23	(	(	PUNCT
cana-1300	83	24	a	a	X
cana-1300	83	25	)	)	PUNCT
cana-1300	83	26	𝐵	𝐵	NOUN
cana-1300	83	27	is	be	AUX
cana-1300	83	28	a	a	DET
cana-1300	83	29	dominating	dominating	NOUN
cana-1300	83	30	set	set	NOUN
cana-1300	83	31	;	;	PUNCT
cana-1300	83	32	(	(	PUNCT
cana-1300	83	33	b	b	X
cana-1300	83	34	)	)	PUNCT
cana-1300	83	35	𝐵	𝐵	NOUN
cana-1300	83	36	is	be	AUX
cana-1300	83	37	connected	connect	VERB
cana-1300	83	38	(	(	PUNCT
cana-1300	83	39	by	by	ADP
cana-1300	83	40	𝐵	𝐵	NOUN
cana-1300	83	41	we	we	PRON
cana-1300	83	42	mean	mean	VERB
cana-1300	83	43	the	the	DET
cana-1300	83	44	subgraph	subgraph	NOUN
cana-1300	83	45	induced	induce	VERB
cana-1300	83	46	by	by	ADP
cana-1300	83	47	𝐵	𝐵	PROPN
cana-1300	83	48	)	)	PUNCT
cana-1300	83	49	.	.	PUNCT
cana-1300	84	1	the	the	DET
cana-1300	84	2	property	property	NOUN
cana-1300	84	3	(	(	PUNCT
cana-1300	84	4	b	b	NOUN
cana-1300	84	5	)	)	PUNCT
cana-1300	84	6	can	can	AUX
cana-1300	84	7	also	also	ADV
cana-1300	84	8	be	be	AUX
cana-1300	84	9	stated	state	VERB
cana-1300	84	10	as	as	SCONJ
cana-1300	84	11	follows	follow	VERB
cana-1300	84	12	:	:	PUNCT
cana-1300	84	13	every	every	DET
cana-1300	84	14	element	element	NOUN
cana-1300	84	15	of	of	ADP
cana-1300	84	16	𝐵	𝐵	NOUN
cana-1300	84	17	must	must	AUX
cana-1300	84	18	be	be	AUX
cana-1300	84	19	connected	connect	VERB
cana-1300	84	20	with	with	ADP
cana-1300	84	21	at	at	ADV
cana-1300	84	22	least	least	ADV
cana-1300	84	23	one	one	NUM
cana-1300	84	24	element	element	NOUN
cana-1300	84	25	in	in	ADP
cana-1300	84	26	𝐵	𝐵	NOUN
cana-1300	84	27	by	by	ADP
cana-1300	84	28	a	a	DET
cana-1300	84	29	path	path	NOUN
cana-1300	84	30	length	length	NOUN
cana-1300	84	31	one	one	NUM
cana-1300	84	32	.	.	PUNCT
cana-1300	85	1	total	total	ADJ
cana-1300	85	2	domination	domination	NOUN
cana-1300	85	3	number	number	NOUN
cana-1300	85	4	of	of	ADP
cana-1300	85	5	𝐺	𝐺	PROPN
cana-1300	85	6	is	be	AUX
cana-1300	85	7	denoted	denote	VERB
cana-1300	85	8	by	by	ADP
cana-1300	85	9	𝛾𝑡(𝐺	𝛾𝑡(𝐺	PROPN
cana-1300	85	10	)	)	PUNCT
cana-1300	85	11	and	and	CCONJ
cana-1300	85	12	𝛾𝑡(𝐺	𝛾𝑡(𝐺	PROPN
cana-1300	85	13	)	)	PUNCT
cana-1300	85	14	=	=	SYM
cana-1300	85	15	𝑚𝑖𝑛|	𝑚𝑖𝑛|	PROPN
cana-1300	85	16	𝐵|	𝐵|	NOUN
cana-1300	85	17	.	.	PUNCT
cana-1300	86	1	2.12	2.12	X
cana-1300	86	2	.	.	X
cana-1300	86	3	private	private	ADJ
cana-1300	86	4	neighborhood	neighborhood	NOUN
cana-1300	86	5	:	:	PUNCT
cana-1300	86	6	let	let	VERB
cana-1300	86	7	𝐴	𝐴	PROPN
cana-1300	86	8	⊆	⊆	NUM
cana-1300	86	9	𝑉(𝐺)&𝑣	𝑉(𝐺)&𝑣	NUM
cana-1300	86	10	∈	∈	NOUN
cana-1300	86	11	𝐴.	𝐴.	NOUN
cana-1300	86	12	then	then	ADV
cana-1300	86	13	byprivate	byprivate	VERB
cana-1300	86	14	neighbourhood	neighbourhood	NOUN
cana-1300	86	15	of	of	ADP
cana-1300	86	16	𝑣	𝑣	NOUN
cana-1300	86	17	with	with	ADP
cana-1300	86	18	respect	respect	NOUN
cana-1300	86	19	to	to	ADP
cana-1300	86	20	𝐴	𝐴	PROPN
cana-1300	86	21	,	,	PUNCT
cana-1300	86	22	denoted	denote	VERB
cana-1300	86	23	𝑃𝑟(𝑣	𝑃𝑟(𝑣	NOUN
cana-1300	86	24	,	,	PUNCT
cana-1300	86	25	𝐴	𝐴	PROPN
cana-1300	86	26	)	)	PUNCT
cana-1300	86	27	,	,	PUNCT
cana-1300	86	28	we	we	PRON
cana-1300	86	29	mean	mean	VERB
cana-1300	86	30	𝑃𝑟(𝑣	𝑃𝑟(𝑣	NOUN
cana-1300	86	31	,	,	PUNCT
cana-1300	86	32	𝐴	𝐴	PROPN
cana-1300	86	33	)	)	PUNCT
cana-1300	86	34	=	=	PRON
cana-1300	86	35	{	{	PUNCT
cana-1300	86	36	𝑤	𝑤	PRON
cana-1300	86	37	∈	∈	PROPN
cana-1300	86	38	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	86	39	)	)	PUNCT
cana-1300	86	40	∶	∶	NOUN
cana-1300	86	41	𝑁	𝑁	PROPN
cana-1300	86	42	(	(	PUNCT
cana-1300	86	43	𝑤	𝑤	NOUN
cana-1300	86	44	)	)	PUNCT
cana-1300	86	45	∩	∩	ADJ
cana-1300	86	46	𝐴	𝐴	NOUN
cana-1300	86	47	=	=	SYM
cana-1300	86	48	{	{	PUNCT
cana-1300	86	49	𝑣	𝑣	NOUN
cana-1300	86	50	}	}	PUNCT
cana-1300	86	51	}	}	PUNCT
cana-1300	86	52	.	.	PUNCT
cana-1300	87	1	note	note	VERB
cana-1300	87	2	2.2	2.2	NUM
cana-1300	87	3	:	:	PUNCT
cana-1300	87	4	easily	easily	ADV
cana-1300	87	5	we	we	PRON
cana-1300	87	6	can	can	AUX
cana-1300	87	7	see	see	VERB
cana-1300	87	8	that	that	PRON
cana-1300	87	9	(	(	PUNCT
cana-1300	87	10	i	i	NOUN
cana-1300	87	11	)	)	PUNCT
cana-1300	87	12	if	if	SCONJ
cana-1300	87	13	𝑤	𝑤	PUNCT
cana-1300	87	14	∈	∈	PROPN
cana-1300	87	15	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	87	16	)	)	PUNCT
cana-1300	87	17	–	–	PUNCT
cana-1300	87	18	𝐴	𝐴	PROPN
cana-1300	87	19	and	and	CCONJ
cana-1300	87	20	𝑤	𝑤	NOUN
cana-1300	87	21	is	be	AUX
cana-1300	87	22	adjacent	adjacent	ADJ
cana-1300	87	23	to	to	ADP
cana-1300	87	24	𝑣in𝐴	𝑣in𝐴	ADV
cana-1300	87	25	the	the	DET
cana-1300	87	26	𝑤	𝑤	ADP
cana-1300	87	27	∈	∈	PROPN
cana-1300	87	28	𝑃𝑟(𝑣	𝑃𝑟(𝑣	NOUN
cana-1300	87	29	,	,	PUNCT
cana-1300	87	30	𝐴	𝐴	PROPN
cana-1300	87	31	)	)	PUNCT
cana-1300	87	32	(	(	PUNCT
cana-1300	87	33	ii	ii	NOUN
cana-1300	87	34	)	)	PUNCT
cana-1300	87	35	if	if	SCONJ
cana-1300	87	36	𝑤	𝑤	PRON
cana-1300	87	37	∈	∈	PROPN
cana-1300	87	38	𝐴	𝐴	PROPN
cana-1300	87	39	and	and	CCONJ
cana-1300	87	40	𝑤	𝑤	ADP
cana-1300	87	41	≠	≠	PROPN
cana-1300	87	42	𝑣	𝑣	PRON
cana-1300	87	43	then	then	ADV
cana-1300	87	44	𝑤	𝑤	X
cana-1300	87	45	is	be	AUX
cana-1300	87	46	not	not	PART
cana-1300	87	47	in	in	ADP
cana-1300	87	48	𝑃𝑟(𝑣	𝑃𝑟(𝑣	NOUN
cana-1300	87	49	,	,	PUNCT
cana-1300	87	50	𝐴	𝐴	PROPN
cana-1300	87	51	)	)	PUNCT
cana-1300	87	52	;	;	PUNCT
cana-1300	87	53	(	(	PUNCT
cana-1300	87	54	iii	iii	X
cana-1300	87	55	)	)	PUNCT
cana-1300	87	56	if	if	SCONJ
cana-1300	87	57	𝑤	𝑤	X
cana-1300	87	58	=	=	VERB
cana-1300	87	59	𝑣	𝑣	NOUN
cana-1300	87	60	is	be	AUX
cana-1300	87	61	not	not	PART
cana-1300	87	62	adjacent	adjacent	ADJ
cana-1300	87	63	to	to	ADP
cana-1300	87	64	a	a	DET
cana-1300	87	65	vertex	vertex	NOUN
cana-1300	87	66	of	of	ADP
cana-1300	87	67	𝐴	𝐴	PROPN
cana-1300	87	68	then	then	ADV
cana-1300	87	69	𝑤	𝑤	ADP
cana-1300	87	70	∈	∈	NOUN
cana-1300	87	71	𝑃𝑟(𝑣	𝑃𝑟(𝑣	NOUN
cana-1300	87	72	,	,	PUNCT
cana-1300	87	73	𝐴	𝐴	PROPN
cana-1300	87	74	)	)	PUNCT
cana-1300	87	75	.	.	PUNCT
cana-1300	88	1	2.13	2.13	NUM
cana-1300	88	2	.	.	X
cana-1300	88	3	minimal	minimal	ADJ
cana-1300	88	4	dominating	dominating	NOUN
cana-1300	88	5	set	set	NOUN
cana-1300	88	6	:	:	PUNCT
cana-1300	88	7	a	a	DET
cana-1300	88	8	dominating	dominating	NOUN
cana-1300	88	9	set	set	NOUN
cana-1300	88	10	𝐴	𝐴	PROPN
cana-1300	88	11	is	be	AUX
cana-1300	88	12	called	call	VERB
cana-1300	88	13	a	a	DET
cana-1300	88	14	minimal	minimal	ADJ
cana-1300	88	15	dominating	dominating	NOUN
cana-1300	88	16	set	set	VERB
cana-1300	88	17	iff	iff	PROPN
cana-1300	88	18	∀	∀	PUNCT
cana-1300	88	19	𝑣	𝑣	ADP
cana-1300	88	20	∈	∈	PROPN
cana-1300	88	21	𝐴	𝐴	PROPN
cana-1300	88	22	𝑃𝑟(𝑣	𝑃𝑟(𝑣	NOUN
cana-1300	88	23	,	,	PUNCT
cana-1300	88	24	𝐴	𝐴	PROPN
cana-1300	88	25	)	)	PUNCT
cana-1300	88	26	≠	≠	PROPN
cana-1300	88	27	∅.	∅.	VERB
cana-1300	88	28	2.14	2.14	NUM
cana-1300	88	29	.	.	PUNCT
cana-1300	89	1	outer	outer	ADJ
cana-1300	89	2	–	–	PUNCT
cana-1300	89	3	connected	connect	VERB
cana-1300	89	4	dominating	dominating	NOUN
cana-1300	89	5	set	set	NOUN
cana-1300	89	6	:	:	PUNCT
cana-1300	89	7	in	in	ADP
cana-1300	89	8	a	a	DET
cana-1300	89	9	graph	graph	NOUN
cana-1300	89	10	𝐺	𝐺	NOUN
cana-1300	89	11	=	=	SYM
cana-1300	89	12	(	(	PUNCT
cana-1300	89	13	𝑉	𝑉	PROPN
cana-1300	89	14	,	,	PUNCT
cana-1300	89	15	𝐸	𝐸	PROPN
cana-1300	89	16	)	)	PUNCT
cana-1300	89	17	,	,	PUNCT
cana-1300	89	18	an	an	DET
cana-1300	89	19	outer	outer	ADV
cana-1300	89	20	-	-	PUNCT
cana-1300	89	21	connected	connect	VERB
cana-1300	89	22	dominant	dominant	ADJ
cana-1300	89	23	set	set	NOUN
cana-1300	89	24	is	be	AUX
cana-1300	89	25	a	a	DET
cana-1300	89	26	set	set	ADJ
cana-1300	89	27	𝐷	𝐷	PROPN
cana-1300	89	28	⊆	⊆	NUM
cana-1300	89	29	𝑉	𝑉	PROPN
cana-1300	89	30	in	in	ADP
cana-1300	89	31	which	which	PRON
cana-1300	89	32	each	each	DET
cana-1300	89	33	vertex	vertex	NOUN
cana-1300	89	34	that	that	PRON
cana-1300	89	35	is	be	AUX
cana-1300	89	36	not	not	PART
cana-1300	89	37	in	in	ADP
cana-1300	89	38	𝐷	𝐷	PROPN
cana-1300	89	39	is	be	AUX
cana-1300	89	40	adjacent	adjacent	ADJ
cana-1300	89	41	to	to	ADP
cana-1300	89	42	at	at	ADV
cana-1300	89	43	least	least	ADV
cana-1300	89	44	one	one	NUM
cana-1300	89	45	vertex	vertex	NOUN
cana-1300	89	46	in	in	ADP
cana-1300	89	47	𝐷	𝐷	PROPN
cana-1300	89	48	and	and	CCONJ
cana-1300	89	49	the	the	DET
cana-1300	89	50	subgraph	subgraph	NOUN
cana-1300	89	51	induced	induce	VERB
cana-1300	89	52	by	by	ADP
cana-1300	89	53	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1300	89	54	is	be	AUX
cana-1300	89	55	connected	connect	VERB
cana-1300	89	56	.	.	PUNCT
cana-1300	90	1	outer	outer	ADJ
cana-1300	90	2	connected	connected	ADJ
cana-1300	90	3	domination	domination	NOUN
cana-1300	90	4	number	number	NOUN
cana-1300	90	5	is	be	AUX
cana-1300	90	6	denoted	denote	VERB
cana-1300	90	7	by	by	ADP
cana-1300	90	8	𝛾𝑐	𝛾𝑐	NOUN
cana-1300	90	9	~(𝐺	~(𝐺	NUM
cana-1300	90	10	)	)	PUNCT
cana-1300	90	11	and	and	CCONJ
cana-1300	90	12	𝛾𝑐	𝛾𝑐	VERB
cana-1300	90	13	~(𝐺	~(𝐺	NUM
cana-1300	90	14	)	)	PUNCT
cana-1300	91	1	=	=	NOUN
cana-1300	92	1	𝑚𝑖𝑛|	𝑚𝑖𝑛|	PRON
cana-1300	92	2	𝐷|	𝐷|	NOUN
cana-1300	92	3	2.15	2.15	NUM
cana-1300	92	4	.	.	PUNCT
cana-1300	93	1	excellent	excellent	ADJ
cana-1300	93	2	graph	graph	NOUN
cana-1300	93	3	:	:	PUNCT
cana-1300	93	4	an	an	DET
cana-1300	93	5	excellent	excellent	ADJ
cana-1300	93	6	graph	graph	NOUN
cana-1300	93	7	is	be	AUX
cana-1300	93	8	one	one	NUM
cana-1300	93	9	where	where	SCONJ
cana-1300	93	10	every	every	DET
cana-1300	93	11	vertex	vertex	NOUN
cana-1300	93	12	of	of	ADP
cana-1300	93	13	the	the	DET
cana-1300	93	14	graph	graph	NOUN
cana-1300	93	15	g	g	PROPN
cana-1300	93	16	belongs	belong	VERB
cana-1300	93	17	to	to	ADP
cana-1300	93	18	𝛾	𝛾	PROPN
cana-1300	93	19	set	set	NOUN
cana-1300	93	20	.	.	PUNCT
cana-1300	94	1	2.16	2.16	NUM
cana-1300	94	2	.	.	PUNCT
cana-1300	95	1	domatic	domatic	ADJ
cana-1300	95	2	number	number	NOUN
cana-1300	95	3	:	:	PUNCT
cana-1300	95	4	the	the	DET
cana-1300	95	5	domatic	domatic	ADJ
cana-1300	95	6	number	number	NOUN
cana-1300	95	7	𝑑(𝐺	𝑑(𝐺	NUM
cana-1300	95	8	)	)	PUNCT
cana-1300	95	9	of	of	ADP
cana-1300	95	10	a	a	DET
cana-1300	95	11	graph	graph	NOUN
cana-1300	95	12	𝐺	𝐺	NOUN
cana-1300	95	13	is	be	AUX
cana-1300	95	14	the	the	DET
cana-1300	95	15	maximum	maximum	ADJ
cana-1300	95	16	number	number	NOUN
cana-1300	95	17	of	of	ADP
cana-1300	95	18	communications	communication	NOUN
cana-1300	95	19	on	on	ADP
cana-1300	95	20	applied	apply	VERB
cana-1300	95	21	nonlinear	nonlinear	ADJ
cana-1300	95	22	analysis	analysis	NOUN
cana-1300	95	23	issn	issn	NOUN
cana-1300	95	24	:	:	PUNCT
cana-1300	95	25	1074	1074	NUM
cana-1300	95	26	-	-	PUNCT
cana-1300	95	27	133x	133x	NUM
cana-1300	95	28	vol	vol	NOUN
cana-1300	95	29	31	31	NUM
cana-1300	95	30	no	no	NOUN
cana-1300	95	31	.	.	PUNCT
cana-1300	96	1	7s	7	NOUN
cana-1300	96	2	(	(	PUNCT
cana-1300	96	3	2024	2024	NUM
cana-1300	96	4	)	)	PUNCT
cana-1300	96	5	254	254	NUM
cana-1300	96	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1300	96	7	elements	element	NOUN
cana-1300	96	8	in	in	ADP
cana-1300	96	9	a	a	DET
cana-1300	96	10	partition	partition	NOUN
cana-1300	96	11	of	of	ADP
cana-1300	96	12	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	96	13	)	)	PUNCT
cana-1300	96	14	into	into	ADP
cana-1300	96	15	dominating	dominating	NOUN
cana-1300	96	16	sets	set	NOUN
cana-1300	96	17	.	.	PUNCT
cana-1300	97	1	2.17	2.17	NUM
cana-1300	97	2	.	.	PUNCT
cana-1300	98	1	just	just	ADV
cana-1300	98	2	excellent	excellent	ADJ
cana-1300	98	3	:	:	PUNCT
cana-1300	98	4	a	a	DET
cana-1300	98	5	excellent	excellent	ADJ
cana-1300	98	6	graph	graph	NOUN
cana-1300	98	7	if	if	SCONJ
cana-1300	98	8	for	for	ADP
cana-1300	98	9	every	every	DET
cana-1300	98	10	𝑣,there	𝑣,there	NOUN
cana-1300	98	11	is	be	AUX
cana-1300	98	12	precisely	precisely	ADV
cana-1300	98	13	one	one	NUM
cana-1300	98	14	𝛾	𝛾	NOUN
cana-1300	98	15	−	−	NOUN
cana-1300	98	16	𝑠𝑒𝑡	𝑠𝑒𝑡	NOUN
cana-1300	98	17	of	of	ADP
cana-1300	98	18	𝐺	𝐺	PROPN
cana-1300	98	19	that	that	PRON
cana-1300	98	20	contains	contain	VERB
cana-1300	98	21	𝑣	𝑣	ADP
cana-1300	98	22	then	then	ADV
cana-1300	98	23	𝐺	𝐺	PROPN
cana-1300	98	24	is	be	AUX
cana-1300	98	25	said	say	VERB
cana-1300	98	26	to	to	PART
cana-1300	98	27	be	be	AUX
cana-1300	98	28	just	just	ADV
cana-1300	98	29	exellent	exellent	NOUN
cana-1300	98	30	.	.	PUNCT
cana-1300	99	1	3.materials	3.material	NOUN
cana-1300	99	2	and	and	CCONJ
cana-1300	99	3	methods	method	NOUN
cana-1300	99	4	3.1	3.1	NUM
cana-1300	99	5	construction	construction	NOUN
cana-1300	99	6	of	of	ADP
cana-1300	99	7	collaboration	collaboration	NOUN
cana-1300	99	8	graph	graph	NOUN
cana-1300	100	1	[	[	X
cana-1300	100	2	13	13	NUM
cana-1300	100	3	]	]	PUNCT
cana-1300	100	4	:	:	PUNCT
cana-1300	100	5	by	by	ADP
cana-1300	100	6	𝐺	𝐺	PROPN
cana-1300	100	7	we	we	PRON
cana-1300	100	8	mean	mean	VERB
cana-1300	100	9	graph	graph	NOUN
cana-1300	100	10	of	of	ADP
cana-1300	100	11	collaboration	collaboration	NOUN
cana-1300	100	12	graph	graph	NOUN
cana-1300	100	13	for	for	ADP
cana-1300	100	14	the	the	DET
cana-1300	100	15	prize	prize	NOUN
cana-1300	100	16	winners	winner	NOUN
cana-1300	100	17	from	from	ADP
cana-1300	100	18	2010	2010	NUM
cana-1300	100	19	to	to	ADP
cana-1300	100	20	2022	2022	NUM
cana-1300	100	21	.	.	PUNCT
cana-1300	101	1	3.2	3.2	NUM
cana-1300	101	2	vertex	vertex	NOUN
cana-1300	101	3	set	set	NOUN
cana-1300	101	4	of	of	ADP
cana-1300	101	5	𝑮	𝑮	PROPN
cana-1300	101	6	:	:	PUNCT
cana-1300	101	7	firstly	firstly	ADV
cana-1300	101	8	,	,	PUNCT
cana-1300	101	9	notice	notice	VERB
cana-1300	101	10	the	the	DET
cana-1300	101	11	mammoth	mammoth	ADJ
cana-1300	101	12	erdӧs	erdӧs	NOUN
cana-1300	101	13	is	be	AUX
cana-1300	101	14	just	just	ADV
cana-1300	101	15	number	number	NOUN
cana-1300	101	16	three	three	NUM
cana-1300	101	17	among	among	ADP
cana-1300	101	18	all	all	DET
cana-1300	101	19	the	the	DET
cana-1300	101	20	winners	winner	NOUN
cana-1300	101	21	and	and	CCONJ
cana-1300	101	22	collaborators	collaborator	NOUN
cana-1300	101	23	.	.	PUNCT
cana-1300	102	1	this	this	PRON
cana-1300	102	2	signifies	signify	VERB
cana-1300	102	3	that	that	SCONJ
cana-1300	102	4	the	the	DET
cana-1300	102	5	partnership	partnership	NOUN
cana-1300	102	6	has	have	AUX
cana-1300	102	7	progressed	progress	VERB
cana-1300	102	8	from	from	ADP
cana-1300	102	9	erdӧs	erdӧs	NOUN
cana-1300	102	10	at	at	ADP
cana-1300	102	11	stage	stage	NOUN
cana-1300	102	12	0	0	NUM
cana-1300	102	13	through	through	ADP
cana-1300	102	14	stage	stage	NOUN
cana-1300	102	15	3	3	NUM
cana-1300	102	16	and	and	CCONJ
cana-1300	102	17	eventually	eventually	ADV
cana-1300	102	18	to	to	PART
cana-1300	102	19	stage	stage	VERB
cana-1300	102	20	4	4	NUM
cana-1300	102	21	.	.	PUNCT
cana-1300	102	22	by	by	ADP
cana-1300	102	23	stage	stage	NOUN
cana-1300	102	24	𝑖	𝑖	X
cana-1300	102	25	,	,	PUNCT
cana-1300	102	26	we	we	PRON
cana-1300	102	27	refer	refer	VERB
cana-1300	102	28	to	to	ADP
cana-1300	102	29	collaborators	collaborator	NOUN
cana-1300	102	30	with	with	ADP
cana-1300	102	31	erdӧs	erdӧs	ADJ
cana-1300	102	32	number	number	NOUN
cana-1300	102	33	𝑖.	𝑖.	ADV
cana-1300	102	34	14	14	NUM
cana-1300	102	35	vertices	vertex	NOUN
cana-1300	102	36	are	be	AUX
cana-1300	102	37	produced	produce	VERB
cana-1300	102	38	for	for	ADP
cana-1300	102	39	the	the	DET
cana-1300	102	40	vertex	vertex	NOUN
cana-1300	102	41	set	set	NOUN
cana-1300	102	42	of	of	ADP
cana-1300	102	43	𝐺	𝐺	PROPN
cana-1300	102	44	by	by	ADP
cana-1300	102	45	the	the	DET
cana-1300	102	46	procedure	procedure	NOUN
cana-1300	102	47	outlined	outline	VERB
cana-1300	102	48	below	below	ADV
cana-1300	102	49	.	.	PUNCT
cana-1300	103	1	let	let	VERB
cana-1300	103	2	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	103	3	)	)	PUNCT
cana-1300	103	4	=	=	PRON
cana-1300	103	5	{	{	PUNCT
cana-1300	103	6	𝑤1	𝑤1	PROPN
cana-1300	103	7	,	,	PUNCT
cana-1300	103	8	𝑤2	𝑤2	NOUN
cana-1300	103	9	,	,	PUNCT
cana-1300	103	10	𝑤3	𝑤3	PROPN
cana-1300	103	11	,	,	PUNCT
cana-1300	103	12	…	…	PUNCT
cana-1300	103	13	…	…	PUNCT
cana-1300	103	14	…	…	PUNCT
cana-1300	103	15	,	,	PUNCT
cana-1300	103	16	𝑤14	𝑤14	ADV
cana-1300	103	17	}	}	PUNCT
cana-1300	103	18	.	.	PUNCT
cana-1300	104	1	𝑤𝑖′𝑠	𝑤𝑖′𝑠	PROPN
cana-1300	104	2	are	be	AUX
cana-1300	104	3	the	the	DET
cana-1300	104	4	following	follow	VERB
cana-1300	104	5	𝑤1	𝑤1	NOUN
cana-1300	104	6	=	=	SYM
cana-1300	104	7	paul	paul	PROPN
cana-1300	104	8	erdos	erdo	NOUN
cana-1300	104	9	,	,	PUNCT
cana-1300	104	10	𝑤2=	𝑤2=	ADJ
cana-1300	104	11	simon	simon	PROPN
cana-1300	104	12	singh	singh	PROPN
cana-1300	104	13	,	,	PUNCT
cana-1300	105	1	𝑤3	𝑤3	PROPN
cana-1300	105	2	=	=	SYM
cana-1300	105	3	adrian	adrian	PROPN
cana-1300	105	4	paenza	paenza	ADJ
cana-1300	105	5	,	,	PUNCT
cana-1300	105	6	𝑤4	𝑤4	NOUN
cana-1300	105	7	=	=	SYM
cana-1300	105	8	ali	ali	PROPN
cana-1300	105	9	nesin	nesin	PROPN
cana-1300	105	10	,	,	PUNCT
cana-1300	105	11	𝑤5	𝑤5	PROPN
cana-1300	105	12	=	=	SYM
cana-1300	105	13	nikolai	nikolai	PROPN
cana-1300	105	14	andreev	andreev	PROPN
cana-1300	105	15	,	,	PUNCT
cana-1300	105	16	𝑤6	𝑤6	PROPN
cana-1300	105	17	=	=	SYM
cana-1300	105	18	peter	peter	PROPN
cana-1300	105	19	komjath	komjath	PROPN
cana-1300	105	20	,	,	PUNCT
cana-1300	105	21	𝑤7	𝑤7	PROPN
cana-1300	105	22	=	=	PROPN
cana-1300	105	23	gregory	gregory	PROPN
cana-1300	105	24	l.	l.	PROPN
cana-1300	105	25	cherlin	cherlin	PROPN
cana-1300	105	26	,	,	PUNCT
cana-1300	105	27	𝑤8	𝑤8	PROPN
cana-1300	105	28	=	=	PROPN
cana-1300	105	29	melvyn	melvyn	PROPN
cana-1300	105	30	b.nathanson	b.nathanson	PROPN
cana-1300	105	31	,	,	PUNCT
cana-1300	105	32	𝑤9	𝑤9	PROPN
cana-1300	105	33	=	=	SYM
cana-1300	105	34	sergei	sergei	PROPN
cana-1300	105	35	vladimirovich	vladimirovich	PROPN
cana-1300	105	36	konyagin	konyagin	NOUN
cana-1300	105	37	,	,	PUNCT
cana-1300	105	38	𝑤10	𝑤10	PROPN
cana-1300	105	39	=	=	PROPN
cana-1300	105	40	anand	anand	PROPN
cana-1300	105	41	pillay	pillay	PROPN
cana-1300	105	42	,	,	PUNCT
cana-1300	105	43	𝑤11	𝑤11	PROPN
cana-1300	105	44	=	=	PROPN
cana-1300	105	45	david	david	PROPN
cana-1300	105	46	william	william	PROPN
cana-1300	105	47	masser	masser	PROPN
cana-1300	105	48	,	,	PUNCT
cana-1300	105	49	𝑤12	𝑤12	PROPN
cana-1300	105	50	=	=	PROPN
cana-1300	105	51	enrico	enrico	PROPN
cana-1300	105	52	bombieri	bombieri	NOUN
cana-1300	105	53	,	,	PUNCT
cana-1300	105	54	𝑤13	𝑤13	NOUN
cana-1300	105	55	=	=	SYM
cana-1300	105	56	d.r.heath	d.r.heath	NOUN
cana-1300	105	57	brown	brown	NOUN
cana-1300	105	58	,	,	PUNCT
cana-1300	105	59	𝑤14	𝑤14	ADV
cana-1300	105	60	=	=	SYM
cana-1300	105	61	angus	angus	PROPN
cana-1300	105	62	j.	j.	PROPN
cana-1300	105	63	macntyre	macntyre	PROPN
cana-1300	105	64	.	.	PUNCT
cana-1300	106	1	3.3	3.3	NUM
cana-1300	106	2	edge	edge	NOUN
cana-1300	106	3	set	set	NOUN
cana-1300	106	4	of	of	ADP
cana-1300	106	5	𝑮	𝑮	PROPN
cana-1300	106	6	:	:	PUNCT
cana-1300	106	7	let	let	VERB
cana-1300	106	8	us	we	PRON
cana-1300	106	9	represent	represent	VERB
cana-1300	106	10	the	the	DET
cana-1300	106	11	edge	edge	NOUN
cana-1300	106	12	set	set	NOUN
cana-1300	106	13	of	of	ADP
cana-1300	106	14	𝐺	𝐺	PROPN
cana-1300	106	15	by	by	ADP
cana-1300	106	16	𝐸(𝐺	𝐸(𝐺	PROPN
cana-1300	106	17	)	)	PUNCT
cana-1300	106	18	.	.	PUNCT
cana-1300	107	1	the	the	DET
cana-1300	107	2	step	step	NOUN
cana-1300	107	3	by	by	ADP
cana-1300	107	4	step	step	NOUN
cana-1300	107	5	procedure	procedure	NOUN
cana-1300	107	6	to	to	PART
cana-1300	107	7	be	be	AUX
cana-1300	107	8	outlined	outline	VERB
cana-1300	107	9	below	below	ADV
cana-1300	107	10	reveals	reveal	VERB
cana-1300	107	11	that	that	SCONJ
cana-1300	107	12	e(𝐺	e(𝐺	NUM
cana-1300	107	13	)	)	PUNCT
cana-1300	108	1	=	=	PRON
cana-1300	108	2	{	{	PUNCT
cana-1300	108	3	𝑓1,𝑓2,	𝑓1,𝑓2,	NOUN
cana-1300	108	4	...	...	PUNCT
cana-1300	108	5	,𝑓78	,𝑓78	PUNCT
cana-1300	108	6	}	}	PUNCT
cana-1300	108	7	.	.	PUNCT
cana-1300	109	1	the	the	DET
cana-1300	109	2	𝑓i	𝑓i	PROPN
cana-1300	109	3	’s	’	NOUN
cana-1300	109	4	are	be	AUX
cana-1300	109	5	described	describe	VERB
cana-1300	109	6	as	as	SCONJ
cana-1300	109	7	follows	follow	VERB
cana-1300	109	8	:	:	PUNCT
cana-1300	109	9	𝑓1	𝑓1	PROPN
cana-1300	109	10	=	=	SYM
cana-1300	109	11	(	(	PUNCT
cana-1300	109	12	𝑤1	𝑤1	VERB
cana-1300	109	13	,	,	PUNCT
cana-1300	109	14	𝑖𝑤2	𝑖𝑤2	NOUN
cana-1300	109	15	)	)	PUNCT
cana-1300	109	16	;	;	PUNCT
cana-1300	109	17	𝑓2	𝑓2	NOUN
cana-1300	109	18	=	=	SYM
cana-1300	109	19	(	(	PUNCT
cana-1300	109	20	𝑤1,𝑤3	𝑤1,𝑤3	PROPN
cana-1300	109	21	)	)	PUNCT
cana-1300	109	22	;	;	PUNCT
cana-1300	109	23	𝑓3	𝑓3	NOUN
cana-1300	109	24	=	=	SYM
cana-1300	109	25	(	(	PUNCT
cana-1300	109	26	𝑤1,𝑤4	𝑤1,𝑤4	PROPN
cana-1300	109	27	)	)	PUNCT
cana-1300	109	28	;	;	PUNCT
cana-1300	109	29	𝑓4	𝑓4	NOUN
cana-1300	109	30	=	=	SYM
cana-1300	109	31	(	(	PUNCT
cana-1300	109	32	𝑤1,𝑤5	𝑤1,𝑤5	PROPN
cana-1300	109	33	)	)	PUNCT
cana-1300	109	34	;	;	PUNCT
cana-1300	109	35	𝑓5	𝑓5	NOUN
cana-1300	109	36	=	=	SYM
cana-1300	109	37	(	(	PUNCT
cana-1300	109	38	𝑤1,𝑤7	𝑤1,𝑤7	PROPN
cana-1300	109	39	)	)	PUNCT
cana-1300	109	40	;	;	PUNCT
cana-1300	109	41	𝑓6	𝑓6	NOUN
cana-1300	109	42	=	=	SYM
cana-1300	109	43	(	(	PUNCT
cana-1300	109	44	𝑤1,𝑤9	𝑤1,𝑤9	PROPN
cana-1300	109	45	)	)	PUNCT
cana-1300	109	46	;	;	PUNCT
cana-1300	109	47	𝑓7	𝑓7	PROPN
cana-1300	109	48	=	=	SYM
cana-1300	109	49	(	(	PUNCT
cana-1300	109	50	𝑤1,𝑤10	𝑤1,𝑤10	NOUN
cana-1300	109	51	)	)	PUNCT
cana-1300	109	52	;	;	PUNCT
cana-1300	110	1	𝑓8	𝑓8	PROPN
cana-1300	110	2	=	=	SYM
cana-1300	110	3	(	(	PUNCT
cana-1300	110	4	𝑤1	𝑤1	VERB
cana-1300	110	5	,	,	PUNCT
cana-1300	110	6	𝑤11	𝑤11	NOUN
cana-1300	110	7	)	)	PUNCT
cana-1300	110	8	;	;	PUNCT
cana-1300	110	9	𝑓9	𝑓9	NOUN
cana-1300	110	10	=	=	SYM
cana-1300	110	11	(	(	PUNCT
cana-1300	110	12	𝑤1,𝑤12	𝑤1,𝑤12	PROPN
cana-1300	110	13	)	)	PUNCT
cana-1300	110	14	;	;	PUNCT
cana-1300	110	15	𝑓10	𝑓10	NOUN
cana-1300	110	16	=	=	SYM
cana-1300	110	17	(	(	PUNCT
cana-1300	110	18	𝑤1,𝑤13	𝑤1,𝑤13	NOUN
cana-1300	110	19	)	)	PUNCT
cana-1300	110	20	;	;	PUNCT
cana-1300	110	21	𝑓11	𝑓11	NOUN
cana-1300	110	22	=	=	SYM
cana-1300	110	23	(	(	PUNCT
cana-1300	110	24	𝑤1,𝑤14	𝑤1,𝑤14	PROPN
cana-1300	110	25	)	)	PUNCT
cana-1300	110	26	;	;	PUNCT
cana-1300	110	27	𝑓12	𝑓12	NOUN
cana-1300	110	28	=	=	SYM
cana-1300	110	29	(	(	PUNCT
cana-1300	110	30	𝑤2,𝑤3	𝑤2,𝑤3	PROPN
cana-1300	110	31	)	)	PUNCT
cana-1300	110	32	;	;	PUNCT
cana-1300	110	33	𝑓13	𝑓13	PROPN
cana-1300	110	34	=	=	SYM
cana-1300	110	35	(	(	PUNCT
cana-1300	110	36	𝑤2,𝑤4	𝑤2,𝑤4	PROPN
cana-1300	110	37	)	)	PUNCT
cana-1300	110	38	;	;	PUNCT
cana-1300	110	39	𝑓14	𝑓14	NOUN
cana-1300	110	40	=	=	SYM
cana-1300	110	41	(	(	PUNCT
cana-1300	110	42	𝑤2,𝑤5	𝑤2,𝑤5	PROPN
cana-1300	110	43	)	)	PUNCT
cana-1300	110	44	;	;	PUNCT
cana-1300	110	45	𝑓15	𝑓15	NOUN
cana-1300	110	46	=	=	SYM
cana-1300	110	47	(	(	PUNCT
cana-1300	110	48	𝑤2,𝑤6	𝑤2,𝑤6	PROPN
cana-1300	110	49	)	)	PUNCT
cana-1300	110	50	;	;	PUNCT
cana-1300	110	51	𝑓16	𝑓16	NOUN
cana-1300	110	52	=	=	SYM
cana-1300	110	53	(	(	PUNCT
cana-1300	110	54	𝑤2,𝑤7	𝑤2,𝑤7	PROPN
cana-1300	110	55	)	)	PUNCT
cana-1300	110	56	;	;	PUNCT
cana-1300	110	57	𝑓17	𝑓17	NOUN
cana-1300	110	58	=	=	SYM
cana-1300	110	59	(	(	PUNCT
cana-1300	110	60	𝑤2,𝑤8	𝑤2,𝑤8	PROPN
cana-1300	110	61	)	)	PUNCT
cana-1300	110	62	;	;	PUNCT
cana-1300	110	63	𝑓18	𝑓18	NOUN
cana-1300	110	64	=	=	SYM
cana-1300	110	65	(	(	PUNCT
cana-1300	110	66	𝑤2,𝑤9	𝑤2,𝑤9	PROPN
cana-1300	110	67	)	)	PUNCT
cana-1300	110	68	;	;	PUNCT
cana-1300	110	69	𝑓19	𝑓19	NOUN
cana-1300	110	70	=	=	SYM
cana-1300	110	71	(	(	PUNCT
cana-1300	110	72	𝑤2,𝑤10	𝑤2,𝑤10	NOUN
cana-1300	110	73	)	)	PUNCT
cana-1300	110	74	;	;	PUNCT
cana-1300	110	75	𝑓20	𝑓20	NOUN
cana-1300	110	76	=	=	SYM
cana-1300	110	77	(	(	PUNCT
cana-1300	110	78	𝑤2,𝑤11	𝑤2,𝑤11	PROPN
cana-1300	110	79	)	)	PUNCT
cana-1300	110	80	;	;	PUNCT
cana-1300	110	81	𝑓21	𝑓21	NOUN
cana-1300	110	82	=	=	SYM
cana-1300	110	83	(	(	PUNCT
cana-1300	110	84	𝑤2,𝑤12	𝑤2,𝑤12	NOUN
cana-1300	110	85	)	)	PUNCT
cana-1300	110	86	;	;	PUNCT
cana-1300	110	87	𝑓22	𝑓22	NOUN
cana-1300	110	88	=	=	SYM
cana-1300	110	89	(	(	PUNCT
cana-1300	110	90	𝑤2,𝑤13	𝑤2,𝑤13	NOUN
cana-1300	110	91	)	)	PUNCT
cana-1300	110	92	;	;	PUNCT
cana-1300	110	93	𝑓23	𝑓23	NOUN
cana-1300	110	94	=	=	SYM
cana-1300	110	95	(	(	PUNCT
cana-1300	110	96	𝑤2,𝑤14	𝑤2,𝑤14	PROPN
cana-1300	110	97	)	)	PUNCT
cana-1300	110	98	;	;	PUNCT
cana-1300	110	99	𝑓24=	𝑓24=	PROPN
cana-1300	110	100	(	(	PUNCT
cana-1300	110	101	𝑤3,𝑤4	𝑤3,𝑤4	PROPN
cana-1300	110	102	)	)	PUNCT
cana-1300	110	103	;	;	PUNCT
cana-1300	110	104	𝑓25	𝑓25	NOUN
cana-1300	110	105	=	=	SYM
cana-1300	110	106	(	(	PUNCT
cana-1300	110	107	𝑤3,𝑤5	𝑤3,𝑤5	PROPN
cana-1300	110	108	)	)	PUNCT
cana-1300	110	109	;	;	PUNCT
cana-1300	110	110	𝑓26	𝑓26	NOUN
cana-1300	110	111	=	=	SYM
cana-1300	110	112	(	(	PUNCT
cana-1300	110	113	𝑤3,𝑤6	𝑤3,𝑤6	PROPN
cana-1300	110	114	)	)	PUNCT
cana-1300	110	115	;	;	PUNCT
cana-1300	110	116	𝑓27	𝑓27	NOUN
cana-1300	110	117	=	=	SYM
cana-1300	110	118	(	(	PUNCT
cana-1300	110	119	𝑤3,𝑤7	𝑤3,𝑤7	PROPN
cana-1300	110	120	)	)	PUNCT
cana-1300	110	121	;	;	PUNCT
cana-1300	110	122	𝑓28	𝑓28	ADJ
cana-1300	110	123	=	=	SYM
cana-1300	110	124	(	(	PUNCT
cana-1300	110	125	𝑤3,𝑤8	𝑤3,𝑤8	NUM
cana-1300	110	126	)	)	PUNCT
cana-1300	110	127	;	;	PUNCT
cana-1300	110	128	𝑓29	𝑓29	NOUN
cana-1300	110	129	=	=	SYM
cana-1300	110	130	(	(	PUNCT
cana-1300	110	131	𝑤3,𝑤9	𝑤3,𝑤9	PROPN
cana-1300	110	132	)	)	PUNCT
cana-1300	110	133	;	;	PUNCT
cana-1300	110	134	𝑓30	𝑓30	NOUN
cana-1300	110	135	=	=	SYM
cana-1300	110	136	(	(	PUNCT
cana-1300	110	137	𝑤3,𝑤10	𝑤3,𝑤10	NOUN
cana-1300	110	138	)	)	PUNCT
cana-1300	110	139	;	;	PUNCT
cana-1300	110	140	𝑓31	𝑓31	NOUN
cana-1300	110	141	=	=	SYM
cana-1300	110	142	(	(	PUNCT
cana-1300	110	143	𝑤3,𝑤11);𝑓32=(𝑤3,𝑤12);𝑓33	𝑤3,𝑤11);𝑓32=(𝑤3,𝑤12);𝑓33	ADJ
cana-1300	110	144	=	=	SYM
cana-1300	110	145	(	(	PUNCT
cana-1300	110	146	𝑤3,𝑤13	𝑤3,𝑤13	PROPN
cana-1300	110	147	)	)	PUNCT
cana-1300	110	148	;	;	PUNCT
cana-1300	110	149	𝑓34	𝑓34	NOUN
cana-1300	110	150	=	=	SYM
cana-1300	110	151	(	(	PUNCT
cana-1300	110	152	𝑤3,𝑤14	𝑤3,𝑤14	PROPN
cana-1300	110	153	)	)	PUNCT
cana-1300	110	154	;	;	PUNCT
cana-1300	110	155	𝑓35	𝑓35	NOUN
cana-1300	110	156	=	=	SYM
cana-1300	110	157	(	(	PUNCT
cana-1300	110	158	𝑤4	𝑤4	NOUN
cana-1300	110	159	,	,	PUNCT
cana-1300	110	160	𝑤5);𝑓36	𝑤5);𝑓36	NOUN
cana-1300	110	161	=	=	PUNCT
cana-1300	110	162	(	(	PUNCT
cana-1300	110	163	𝑤4	𝑤4	NOUN
cana-1300	110	164	,	,	PUNCT
cana-1300	110	165	𝑤6);𝑓37	𝑤6);𝑓37	NOUN
cana-1300	110	166	=	=	SYM
cana-1300	110	167	(	(	PUNCT
cana-1300	110	168	𝑤4	𝑤4	NOUN
cana-1300	110	169	,	,	PUNCT
cana-1300	110	170	𝑤8	𝑤8	NUM
cana-1300	110	171	)	)	PUNCT
cana-1300	110	172	;	;	PUNCT
cana-1300	110	173	𝑓38	𝑓38	NOUN
cana-1300	110	174	=	=	SYM
cana-1300	110	175	(	(	PUNCT
cana-1300	110	176	𝑤4	𝑤4	NOUN
cana-1300	110	177	,	,	PUNCT
cana-1300	110	178	𝑤9);𝑓39	𝑤9);𝑓39	NOUN
cana-1300	110	179	=	=	SYM
cana-1300	110	180	(	(	PUNCT
cana-1300	110	181	𝑤4	𝑤4	NOUN
cana-1300	110	182	,	,	PUNCT
cana-1300	110	183	𝑤11);𝑓40	𝑤11);𝑓40	NOUN
cana-1300	110	184	=	=	SYM
cana-1300	110	185	(	(	PUNCT
cana-1300	110	186	𝑤4	𝑤4	PROPN
cana-1300	110	187	,	,	PUNCT
cana-1300	110	188	𝑤12	𝑤12	PROPN
cana-1300	110	189	)	)	PUNCT
cana-1300	110	190	;	;	PUNCT
cana-1300	110	191	𝑓41	𝑓41	NOUN
cana-1300	110	192	=	=	SYM
cana-1300	110	193	(	(	PUNCT
cana-1300	110	194	𝑤4	𝑤4	NOUN
cana-1300	110	195	,	,	PUNCT
cana-1300	110	196	𝑤13);𝑓42	𝑤13);𝑓42	NOUN
cana-1300	110	197	=	=	SYM
cana-1300	110	198	(	(	PUNCT
cana-1300	110	199	𝑤4	𝑤4	PROPN
cana-1300	110	200	,	,	PUNCT
cana-1300	110	201	𝑤14	𝑤14	PROPN
cana-1300	110	202	)	)	PUNCT
cana-1300	110	203	;	;	PUNCT
cana-1300	110	204	𝑓43	𝑓43	NOUN
cana-1300	110	205	=	=	SYM
cana-1300	110	206	(	(	PUNCT
cana-1300	110	207	𝑤5	𝑤5	PROPN
cana-1300	110	208	,	,	PUNCT
cana-1300	110	209	𝑤6	𝑤6	PROPN
cana-1300	110	210	)	)	PUNCT
cana-1300	110	211	;	;	PUNCT
cana-1300	110	212	𝑓44	𝑓44	VERB
cana-1300	110	213	=	=	SYM
cana-1300	110	214	(	(	PUNCT
cana-1300	110	215	𝑤5	𝑤5	PROPN
cana-1300	110	216	,	,	PUNCT
cana-1300	110	217	𝑤7	𝑤7	PROPN
cana-1300	110	218	)	)	PUNCT
cana-1300	110	219	;	;	PUNCT
cana-1300	110	220	𝑓45	𝑓45	PROPN
cana-1300	110	221	=	=	SYM
cana-1300	110	222	(	(	PUNCT
cana-1300	110	223	𝑤5	𝑤5	PROPN
cana-1300	110	224	,	,	PUNCT
cana-1300	110	225	𝑤8	𝑤8	NUM
cana-1300	110	226	)	)	PUNCT
cana-1300	110	227	;	;	PUNCT
cana-1300	110	228	𝑓46	𝑓46	NOUN
cana-1300	110	229	=	=	SYM
cana-1300	110	230	(	(	PUNCT
cana-1300	110	231	𝑤5	𝑤5	PROPN
cana-1300	110	232	,	,	PUNCT
cana-1300	110	233	𝑤10	𝑤10	NOUN
cana-1300	110	234	)	)	PUNCT
cana-1300	110	235	;	;	PUNCT
cana-1300	110	236	𝑓47	𝑓47	NOUN
cana-1300	110	237	=	=	SYM
cana-1300	110	238	(	(	PUNCT
cana-1300	110	239	𝑤5	𝑤5	PROPN
cana-1300	110	240	,	,	PUNCT
cana-1300	110	241	𝑤11	𝑤11	NOUN
cana-1300	110	242	)	)	PUNCT
cana-1300	110	243	;	;	PUNCT
cana-1300	110	244	𝑓48	𝑓48	NOUN
cana-1300	110	245	=	=	SYM
cana-1300	110	246	(	(	PUNCT
cana-1300	110	247	𝑤5	𝑤5	NOUN
cana-1300	110	248	,	,	PUNCT
cana-1300	110	249	𝑤13	𝑤13	NOUN
cana-1300	110	250	)	)	PUNCT
cana-1300	110	251	;	;	PUNCT
cana-1300	110	252	𝑓49	𝑓49	NOUN
cana-1300	110	253	=	=	SYM
cana-1300	110	254	(	(	PUNCT
cana-1300	110	255	𝑤5	𝑤5	PROPN
cana-1300	110	256	,	,	PUNCT
cana-1300	110	257	𝑤14	𝑤14	ADV
cana-1300	110	258	)	)	PUNCT
cana-1300	110	259	;	;	PUNCT
cana-1300	110	260	𝑓50=	𝑓50=	PROPN
cana-1300	110	261	(	(	PUNCT
cana-1300	110	262	𝑤6,𝑤8	𝑤6,𝑤8	PROPN
cana-1300	110	263	)	)	PUNCT
cana-1300	110	264	;	;	PUNCT
cana-1300	110	265	𝑓51	𝑓51	NOUN
cana-1300	110	266	=	=	SYM
cana-1300	110	267	(	(	PUNCT
cana-1300	110	268	𝑤6,𝑤9	𝑤6,𝑤9	PROPN
cana-1300	110	269	)	)	PUNCT
cana-1300	110	270	;	;	PUNCT
cana-1300	110	271	𝑓52	𝑓52	VERB
cana-1300	110	272	=	=	SYM
cana-1300	110	273	(	(	PUNCT
cana-1300	110	274	𝑤6,𝑤10	𝑤6,𝑤10	NOUN
cana-1300	110	275	)	)	PUNCT
cana-1300	110	276	;	;	PUNCT
cana-1300	110	277	𝑓53	𝑓53	NOUN
cana-1300	110	278	=	=	SYM
cana-1300	110	279	(	(	PUNCT
cana-1300	110	280	𝑤6,𝑤11	𝑤6,𝑤11	NOUN
cana-1300	110	281	)	)	PUNCT
cana-1300	110	282	;	;	PUNCT
cana-1300	110	283	𝑓54	𝑓54	NOUN
cana-1300	110	284	=	=	SYM
cana-1300	110	285	(	(	PUNCT
cana-1300	110	286	𝑤6,𝑤12	𝑤6,𝑤12	PROPN
cana-1300	110	287	)	)	PUNCT
cana-1300	110	288	;	;	PUNCT
cana-1300	110	289	𝑓55	𝑓55	NOUN
cana-1300	110	290	=	=	SYM
cana-1300	110	291	(	(	PUNCT
cana-1300	110	292	𝑤6,𝑤13	𝑤6,𝑤13	PROPN
cana-1300	110	293	)	)	PUNCT
cana-1300	110	294	;	;	PUNCT
cana-1300	110	295	𝑓56	𝑓56	NOUN
cana-1300	110	296	=	=	SYM
cana-1300	110	297	(	(	PUNCT
cana-1300	110	298	𝑤6,𝑤14	𝑤6,𝑤14	PROPN
cana-1300	110	299	)	)	PUNCT
cana-1300	110	300	;	;	PUNCT
cana-1300	110	301	𝑓57	𝑓57	ADJ
cana-1300	110	302	=	=	SYM
cana-1300	110	303	(	(	PUNCT
cana-1300	110	304	𝑤7,𝑤8	𝑤7,𝑤8	PROPN
cana-1300	110	305	)	)	PUNCT
cana-1300	110	306	;	;	PUNCT
cana-1300	110	307	𝑓58	𝑓58	NOUN
cana-1300	110	308	=	=	SYM
cana-1300	110	309	(	(	PUNCT
cana-1300	110	310	𝑤7,𝑤9	𝑤7,𝑤9	PROPN
cana-1300	110	311	)	)	PUNCT
cana-1300	110	312	;	;	PUNCT
cana-1300	110	313	𝑓59	𝑓59	PROPN
cana-1300	110	314	=	=	SYM
cana-1300	110	315	(	(	PUNCT
cana-1300	110	316	𝑤7,𝑤10	𝑤7,𝑤10	NOUN
cana-1300	110	317	)	)	PUNCT
cana-1300	110	318	;	;	PUNCT
cana-1300	110	319	𝑓60	𝑓60	PROPN
cana-1300	110	320	=	=	SYM
cana-1300	110	321	(	(	PUNCT
cana-1300	110	322	𝑤7,𝑤11	𝑤7,𝑤11	PROPN
cana-1300	110	323	)	)	PUNCT
cana-1300	110	324	;	;	PUNCT
cana-1300	110	325	𝑓61	𝑓61	NOUN
cana-1300	110	326	=	=	SYM
cana-1300	110	327	(	(	PUNCT
cana-1300	110	328	𝑤7,𝑤12	𝑤7,𝑤12	PROPN
cana-1300	110	329	)	)	PUNCT
cana-1300	110	330	;	;	PUNCT
cana-1300	110	331	𝑓62	𝑓62	NOUN
cana-1300	110	332	=	=	SYM
cana-1300	110	333	(	(	PUNCT
cana-1300	110	334	𝑤7,𝑤13	𝑤7,𝑤13	PROPN
cana-1300	110	335	)	)	PUNCT
cana-1300	110	336	;	;	PUNCT
cana-1300	110	337	𝑓63	𝑓63	PROPN
cana-1300	110	338	=	=	SYM
cana-1300	110	339	(	(	PUNCT
cana-1300	110	340	𝑤8,𝑤10	𝑤8,𝑤10	PROPN
cana-1300	110	341	)	)	PUNCT
cana-1300	110	342	;	;	PUNCT
cana-1300	110	343	𝑓64	𝑓64	ADV
cana-1300	110	344	=	=	SYM
cana-1300	110	345	(	(	PUNCT
cana-1300	110	346	𝑤8,𝑤11	𝑤8,𝑤11	PROPN
cana-1300	110	347	)	)	PUNCT
cana-1300	110	348	;	;	PUNCT
cana-1300	110	349	𝑓65	𝑓65	NOUN
cana-1300	110	350	=	=	SYM
cana-1300	110	351	(	(	PUNCT
cana-1300	110	352	𝑤8,𝑤12	𝑤8,𝑤12	PROPN
cana-1300	110	353	)	)	PUNCT
cana-1300	110	354	;	;	PUNCT
cana-1300	110	355	𝑓66	𝑓66	NOUN
cana-1300	110	356	=	=	SYM
cana-1300	110	357	(	(	PUNCT
cana-1300	110	358	𝑤8,𝑤13	𝑤8,𝑤13	PROPN
cana-1300	110	359	)	)	PUNCT
cana-1300	110	360	;	;	PUNCT
cana-1300	110	361	𝑓67	𝑓67	NOUN
cana-1300	110	362	=	=	SYM
cana-1300	110	363	(	(	PUNCT
cana-1300	110	364	𝑤8,𝑤14	𝑤8,𝑤14	PROPN
cana-1300	110	365	)	)	PUNCT
cana-1300	110	366	;	;	PUNCT
cana-1300	110	367	𝑓68	𝑓68	NOUN
cana-1300	110	368	=	=	SYM
cana-1300	110	369	(	(	PUNCT
cana-1300	110	370	𝑤9,𝑤10	𝑤9,𝑤10	NOUN
cana-1300	110	371	)	)	PUNCT
cana-1300	110	372	;	;	PUNCT
cana-1300	110	373	𝑓69	𝑓69	NOUN
cana-1300	110	374	=	=	SYM
cana-1300	110	375	(	(	PUNCT
cana-1300	110	376	𝑤9,𝑤11	𝑤9,𝑤11	PROPN
cana-1300	110	377	)	)	PUNCT
cana-1300	110	378	;	;	PUNCT
cana-1300	110	379	𝑓70=(𝑤9,𝑤12);𝑓71=(𝑤9,𝑤14);𝑓72	𝑓70=(𝑤9,𝑤12);𝑓71=(𝑤9,𝑤14);𝑓72	X
cana-1300	110	380	=	=	SYM
cana-1300	110	381	(	(	PUNCT
cana-1300	110	382	𝑤10	𝑤10	PROPN
cana-1300	110	383	,	,	PUNCT
cana-1300	110	384	𝑤12	𝑤12	PROPN
cana-1300	110	385	)	)	PUNCT
cana-1300	110	386	;	;	PUNCT
cana-1300	110	387	𝑓73	𝑓73	PROPN
cana-1300	110	388	=	=	SYM
cana-1300	110	389	(	(	PUNCT
cana-1300	110	390	𝑤10	𝑤10	PROPN
cana-1300	110	391	,	,	PUNCT
cana-1300	110	392	𝑤13);𝑓74	𝑤13);𝑓74	PROPN
cana-1300	110	393	=	=	SYM
cana-1300	110	394	(	(	PUNCT
cana-1300	110	395	𝑤10	𝑤10	PROPN
cana-1300	110	396	,	,	PUNCT
cana-1300	110	397	𝑤14	𝑤14	PROPN
cana-1300	110	398	)	)	PUNCT
cana-1300	110	399	;	;	PUNCT
cana-1300	110	400	𝑓75	𝑓75	NOUN
cana-1300	110	401	=	=	SYM
cana-1300	110	402	(	(	PUNCT
cana-1300	110	403	𝑤11	𝑤11	NOUN
cana-1300	110	404	,	,	PUNCT
cana-1300	110	405	𝑤13);𝑓76	𝑤13);𝑓76	X
cana-1300	110	406	=	=	SYM
cana-1300	110	407	(	(	PUNCT
cana-1300	110	408	𝑤11	𝑤11	PROPN
cana-1300	110	409	,	,	PUNCT
cana-1300	110	410	𝑤14	𝑤14	ADV
cana-1300	110	411	)	)	PUNCT
cana-1300	110	412	;	;	PUNCT
cana-1300	110	413	𝑓77	𝑓77	NOUN
cana-1300	110	414	=	=	SYM
cana-1300	110	415	(	(	PUNCT
cana-1300	110	416	𝑤12,𝑤13	𝑤12,𝑤13	NOUN
cana-1300	110	417	)	)	PUNCT
cana-1300	110	418	;	;	PUNCT
cana-1300	110	419	𝑓78	𝑓78	VERB
cana-1300	110	420	=	=	SYM
cana-1300	110	421	(	(	PUNCT
cana-1300	110	422	𝑤12,𝑤14	𝑤12,𝑤14	ADV
cana-1300	110	423	)	)	PUNCT
cana-1300	110	424	;	;	PUNCT
cana-1300	110	425	3.4	3.4	NUM
cana-1300	110	426	number	number	NOUN
cana-1300	110	427	of	of	ADP
cana-1300	110	428	prize	prize	NOUN
cana-1300	110	429	winners	winner	NOUN
cana-1300	110	430	at	at	ADP
cana-1300	110	431	each	each	DET
cana-1300	110	432	level	level	NOUN
cana-1300	110	433	:	:	PUNCT
cana-1300	110	434	note	note	VERB
cana-1300	110	435	that	that	SCONJ
cana-1300	110	436	at	at	ADP
cana-1300	110	437	level	level	NOUN
cana-1300	110	438	0	0	NUM
cana-1300	110	439	erdӧs	erdӧs	NOUN
cana-1300	110	440	sits	sit	VERB
cana-1300	110	441	alone	alone	ADV
cana-1300	110	442	.	.	PUNCT
cana-1300	111	1	at	at	ADP
cana-1300	111	2	level	level	NOUN
cana-1300	111	3	3	3	NUM
cana-1300	111	4	two	two	NUM
cana-1300	111	5	mathematicians	mathematician	NOUN
cana-1300	111	6	are	be	AUX
cana-1300	111	7	there	there	ADV
cana-1300	111	8	,	,	PUNCT
cana-1300	111	9	they	they	PRON
cana-1300	111	10	are	be	AUX
cana-1300	111	11	w4	w4	NOUN
cana-1300	111	12	and	and	CCONJ
cana-1300	111	13	w5	w5	PROPN
cana-1300	111	14	3.5	3.5	NUM
cana-1300	111	15	the	the	DET
cana-1300	111	16	lapw	lapw	NOUN
cana-1300	111	17	’s	’s	PART
cana-1300	111	18	at	at	ADP
cana-1300	111	19	various	various	ADJ
cana-1300	111	20	levels	level	NOUN
cana-1300	111	21	:	:	PUNCT
cana-1300	111	22	obviously	obviously	ADV
cana-1300	111	23	there	there	PRON
cana-1300	111	24	is	be	VERB
cana-1300	111	25	none	none	NOUN
cana-1300	111	26	at	at	ADP
cana-1300	111	27	level	level	NOUN
cana-1300	111	28	0.interestingly	0.interestingly	NUM
cana-1300	111	29	,	,	PUNCT
cana-1300	111	30	none	none	NOUN
cana-1300	111	31	of	of	ADP
cana-1300	111	32	the	the	DET
cana-1300	111	33	direct	direct	ADJ
cana-1300	111	34	collaborators	collaborator	NOUN
cana-1300	111	35	of	of	ADP
cana-1300	111	36	paul	paul	PROPN
cana-1300	111	37	erdӧs	erdӧs	PROPN
cana-1300	111	38	have	have	AUX
cana-1300	111	39	won	win	VERB
cana-1300	111	40	leelavati	leelavati	PROPN
cana-1300	111	41	award	award	NOUN
cana-1300	111	42	and	and	CCONJ
cana-1300	111	43	hence	hence	ADV
cana-1300	111	44	at	at	ADP
cana-1300	111	45	level	level	NOUN
cana-1300	111	46	1	1	NUM
cana-1300	111	47	it	it	PRON
cana-1300	111	48	is	be	AUX
cana-1300	111	49	0.at	0.at	NUM
cana-1300	111	50	level	level	NOUN
cana-1300	111	51	3	3	NUM
cana-1300	111	52	,	,	PUNCT
cana-1300	111	53	we	we	PRON
cana-1300	111	54	have	have	VERB
cana-1300	111	55	two	two	NUM
cana-1300	111	56	prize	prize	NOUN
cana-1300	111	57	winners	winner	NOUN
cana-1300	111	58	w4	w4	PROPN
cana-1300	111	59	=	=	SYM
cana-1300	111	60	ali	ali	PROPN
cana-1300	111	61	nesin	nesin	PROPN
cana-1300	111	62	and	and	CCONJ
cana-1300	111	63	𝑤5	𝑤5	NOUN
cana-1300	111	64	=	=	SYM
cana-1300	111	65	nikolai	nikolai	PROPN
cana-1300	111	66	andreev	andreev	VERB
cana-1300	111	67	.	.	PUNCT
cana-1300	112	1	3.6	3.6	NUM
cana-1300	112	2	procedure	procedure	NOUN
cana-1300	112	3	to	to	PART
cana-1300	112	4	obtain	obtain	VERB
cana-1300	112	5	collaboration	collaboration	NOUN
cana-1300	112	6	graph	graph	NOUN
cana-1300	112	7	:	:	PUNCT
cana-1300	112	8	step	step	NOUN
cana-1300	112	9	1	1	NUM
cana-1300	112	10	:	:	PUNCT
cana-1300	112	11	click	click	VERB
cana-1300	112	12	on	on	ADP
cana-1300	112	13	the	the	DET
cana-1300	112	14	link	link	NOUN
cana-1300	112	15	http://www.ams.org/mathscinet/collaborationdistance.html	http://www.ams.org/mathscinet/collaborationdistance.html	PROPN
cana-1300	112	16	.	.	PUNCT
cana-1300	113	1	it	it	PRON
cana-1300	113	2	will	will	AUX
cana-1300	113	3	direct	direct	VERB
cana-1300	113	4	us	we	PRON
cana-1300	113	5	to	to	ADP
cana-1300	113	6	the	the	DET
cana-1300	113	7	following	follow	VERB
cana-1300	113	8	screen	screen	NOUN
cana-1300	113	9	from	from	ADP
cana-1300	113	10	mathscinet	mathscinet	NOUN
cana-1300	113	11	.	.	PUNCT
cana-1300	114	1	communications	communication	NOUN
cana-1300	114	2	on	on	ADP
cana-1300	114	3	applied	apply	VERB
cana-1300	114	4	nonlinear	nonlinear	ADJ
cana-1300	114	5	analysis	analysis	NOUN
cana-1300	114	6	issn	issn	NOUN
cana-1300	114	7	:	:	PUNCT
cana-1300	114	8	1074	1074	NUM
cana-1300	114	9	-	-	PUNCT
cana-1300	114	10	133x	133x	NUM
cana-1300	114	11	vol	vol	NOUN
cana-1300	114	12	31	31	NUM
cana-1300	114	13	no	no	NOUN
cana-1300	114	14	.	.	PUNCT
cana-1300	115	1	7s	7	NOUN
cana-1300	115	2	(	(	PUNCT
cana-1300	115	3	2024	2024	NUM
cana-1300	115	4	)	)	PUNCT
cana-1300	115	5	255	255	NUM
cana-1300	116	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1300	116	2	figure	figure	NOUN
cana-1300	116	3	1	1	NUM
cana-1300	116	4	:	:	PUNCT
cana-1300	116	5	collaboration	collaboration	NOUN
cana-1300	116	6	distance	distance	NOUN
cana-1300	116	7	description	description	NOUN
cana-1300	116	8	page	page	NOUN
cana-1300	116	9	step	step	NOUN
cana-1300	116	10	2	2	NUM
cana-1300	116	11	:	:	PUNCT
cana-1300	116	12	enter	enter	VERB
cana-1300	116	13	the	the	DET
cana-1300	116	14	name	name	NOUN
cana-1300	116	15	of	of	ADP
cana-1300	116	16	the	the	DET
cana-1300	116	17	author	author	NOUN
cana-1300	116	18	and	and	CCONJ
cana-1300	116	19	then	then	ADV
cana-1300	116	20	enter	enter	VERB
cana-1300	116	21	the	the	DET
cana-1300	116	22	names	name	NOUN
cana-1300	116	23	of	of	ADP
cana-1300	116	24	other	other	ADJ
cana-1300	116	25	authors	author	NOUN
cana-1300	116	26	or	or	CCONJ
cana-1300	116	27	press	press	VERB
cana-1300	116	28	the	the	DET
cana-1300	116	29	"	"	PUNCT
cana-1300	116	30	use	use	NOUN
cana-1300	116	31	erdӧs	erdӧs	NOUN
cana-1300	116	32	"	"	PUNCT
cana-1300	116	33	icon	icon	NOUN
cana-1300	116	34	.	.	PUNCT
cana-1300	117	1	for	for	ADP
cana-1300	117	2	example	example	NOUN
cana-1300	117	3	,	,	PUNCT
cana-1300	117	4	if	if	SCONJ
cana-1300	117	5	one	one	NUM
cana-1300	117	6	of	of	ADP
cana-1300	117	7	the	the	DET
cana-1300	117	8	authors	author	NOUN
cana-1300	117	9	is	be	AUX
cana-1300	117	10	ali	ali	PROPN
cana-1300	117	11	nesin	nesin	PROPN
cana-1300	117	12	and	and	CCONJ
cana-1300	117	13	the	the	DET
cana-1300	117	14	other	other	ADJ
cana-1300	117	15	is	be	AUX
cana-1300	117	16	paul	paul	PROPN
cana-1300	117	17	erdos	erdo	NOUN
cana-1300	117	18	,	,	PUNCT
cana-1300	117	19	the	the	DET
cana-1300	117	20	outcome	outcome	NOUN
cana-1300	117	21	of	of	ADP
cana-1300	117	22	our	our	PRON
cana-1300	117	23	action	action	NOUN
cana-1300	117	24	is	be	AUX
cana-1300	117	25	depicted	depict	VERB
cana-1300	117	26	in	in	ADP
cana-1300	117	27	figure	figure	NOUN
cana-1300	117	28	2	2	NUM
cana-1300	117	29	.	.	PUNCT
cana-1300	117	30	figure	figure	NOUN
cana-1300	117	31	2	2	NUM
cana-1300	117	32	:	:	PUNCT
cana-1300	117	33	respective	respective	ADJ
cana-1300	117	34	author	author	NOUN
cana-1300	117	35	’s	’s	PART
cana-1300	117	36	collaboration	collaboration	NOUN
cana-1300	117	37	details	detail	NOUN
cana-1300	117	38	with	with	ADP
cana-1300	117	39	erdӧs	erdӧs	NOUN
cana-1300	117	40	number	number	NOUN
cana-1300	117	41	step	step	NOUN
cana-1300	117	42	3	3	NUM
cana-1300	117	43	:	:	PUNCT
cana-1300	117	44	to	to	PART
cana-1300	117	45	acquaint	acquaint	VERB
cana-1300	117	46	with	with	ADP
cana-1300	117	47	further	further	ADJ
cana-1300	117	48	details	detail	NOUN
cana-1300	117	49	regarding	regard	VERB
cana-1300	117	50	the	the	DET
cana-1300	117	51	collaborative	collaborative	ADJ
cana-1300	117	52	work	work	NOUN
cana-1300	117	53	of	of	ADP
cana-1300	117	54	the	the	DET
cana-1300	117	55	above	above	ADJ
cana-1300	117	56	said	say	VERB
cana-1300	117	57	authors	author	NOUN
cana-1300	117	58	in	in	ADP
cana-1300	117	59	step	step	NOUN
cana-1300	117	60	b	b	PROPN
cana-1300	117	61	just	just	ADV
cana-1300	117	62	act	act	VERB
cana-1300	117	63	on	on	ADP
cana-1300	117	64	the	the	DET
cana-1300	117	65	appropriate	appropriate	ADJ
cana-1300	117	66	mr	mr	PROPN
cana-1300	117	67	number	number	NOUN
cana-1300	117	68	blue	blue	ADJ
cana-1300	117	69	link	link	NOUN
cana-1300	117	70	.	.	PUNCT
cana-1300	118	1	it	it	PRON
cana-1300	118	2	will	will	AUX
cana-1300	118	3	take	take	VERB
cana-1300	118	4	us	we	PRON
cana-1300	118	5	to	to	ADP
cana-1300	118	6	figure.3	figure.3	PROPN
cana-1300	118	7	figure	figure	NOUN
cana-1300	118	8	3	3	NUM
cana-1300	118	9	:	:	PUNCT
cana-1300	118	10	data	datum	NOUN
cana-1300	118	11	screen	screen	NOUN
cana-1300	118	12	of	of	ADP
cana-1300	118	13	required	require	VERB
cana-1300	118	14	mathscinet	mathscinet	NOUN
cana-1300	118	15	bibliography	bibliography	NOUN
cana-1300	118	16	.	.	PUNCT
cana-1300	119	1	step	step	NOUN
cana-1300	119	2	4	4	NUM
cana-1300	119	3	:	:	PUNCT
cana-1300	119	4	repeat	repeat	VERB
cana-1300	119	5	steps	step	NOUN
cana-1300	119	6	1	1	NUM
cana-1300	119	7	to	to	ADP
cana-1300	119	8	3	3	NUM
cana-1300	119	9	until	until	SCONJ
cana-1300	119	10	all	all	DET
cana-1300	119	11	three	three	NUM
cana-1300	119	12	prize	prize	NOUN
cana-1300	119	13	winners	winner	NOUN
cana-1300	119	14	collaboration	collaboration	NOUN
cana-1300	119	15	details	detail	NOUN
cana-1300	119	16	are	be	AUX
cana-1300	119	17	acquired	acquire	VERB
cana-1300	119	18	one	one	NUM
cana-1300	119	19	after	after	ADP
cana-1300	119	20	the	the	DET
cana-1300	119	21	other	other	ADJ
cana-1300	119	22	.	.	PUNCT
cana-1300	120	1	step	step	NOUN
cana-1300	120	2	5	5	NUM
cana-1300	120	3	:	:	PUNCT
cana-1300	120	4	stop	stop	VERB
cana-1300	120	5	if	if	SCONJ
cana-1300	120	6	steps	step	NOUN
cana-1300	120	7	1	1	NUM
cana-1300	120	8	to	to	PART
cana-1300	120	9	5	5	NUM
cana-1300	120	10	are	be	AUX
cana-1300	120	11	well	well	ADV
cana-1300	120	12	implemented	implement	VERB
cana-1300	120	13	.	.	PUNCT
cana-1300	121	1	3.7	3.7	NUM
cana-1300	121	2	collaboration	collaboration	NOUN
cana-1300	121	3	graph	graph	NOUN
cana-1300	121	4	of	of	ADP
cana-1300	121	5	lilavati	lilavati	PROPN
cana-1300	121	6	prize	prize	PROPN
cana-1300	121	7	winners	winner	NOUN
cana-1300	121	8	:	:	PUNCT
cana-1300	121	9	we	we	PRON
cana-1300	121	10	create	create	VERB
cana-1300	121	11	the	the	DET
cana-1300	121	12	collaborative	collaborative	ADJ
cana-1300	121	13	graph	graph	NOUN
cana-1300	121	14	using	use	VERB
cana-1300	121	15	the	the	DET
cana-1300	121	16	program	program	NOUN
cana-1300	121	17	graphtea	graphtea	NOUN
cana-1300	121	18	because	because	SCONJ
cana-1300	121	19	the	the	DET
cana-1300	121	20	number	number	NOUN
cana-1300	121	21	of	of	ADP
cana-1300	121	22	vertices	vertex	NOUN
cana-1300	121	23	and	and	CCONJ
cana-1300	121	24	communications	communication	NOUN
cana-1300	121	25	on	on	ADP
cana-1300	121	26	applied	apply	VERB
cana-1300	121	27	nonlinear	nonlinear	ADJ
cana-1300	121	28	analysis	analysis	NOUN
cana-1300	121	29	issn	issn	NOUN
cana-1300	121	30	:	:	PUNCT
cana-1300	121	31	1074	1074	NUM
cana-1300	121	32	-	-	PUNCT
cana-1300	121	33	133x	133x	NUM
cana-1300	121	34	vol	vol	NOUN
cana-1300	121	35	31	31	NUM
cana-1300	121	36	no	no	NOUN
cana-1300	121	37	.	.	PUNCT
cana-1300	122	1	7s	7	NOUN
cana-1300	122	2	(	(	PUNCT
cana-1300	122	3	2024	2024	NUM
cana-1300	122	4	)	)	PUNCT
cana-1300	122	5	256	256	NUM
cana-1300	122	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1300	122	7	edges	edge	NOUN
cana-1300	122	8	is	be	AUX
cana-1300	122	9	constrained	constrain	VERB
cana-1300	122	10	.	.	PUNCT
cana-1300	123	1	figure	figure	VERB
cana-1300	123	2	4	4	NUM
cana-1300	123	3	:	:	PUNCT
cana-1300	123	4	collaboration	collaboration	NOUN
cana-1300	123	5	graph	graph	NOUN
cana-1300	123	6	3.8	3.8	NUM
cana-1300	123	7	some	some	DET
cana-1300	123	8	observations	observation	NOUN
cana-1300	123	9	:	:	PUNCT
cana-1300	123	10	as	as	SCONJ
cana-1300	123	11	the	the	DET
cana-1300	123	12	count	count	NOUN
cana-1300	123	13	of	of	ADP
cana-1300	123	14	la	la	PROPN
cana-1300	123	15	winners	winner	NOUN
cana-1300	123	16	is	be	AUX
cana-1300	123	17	a	a	DET
cana-1300	123	18	single	single	ADJ
cana-1300	123	19	digit	digit	NOUN
cana-1300	123	20	,	,	PUNCT
cana-1300	123	21	the	the	DET
cana-1300	123	22	foregoing	forego	VERB
cana-1300	123	23	technique	technique	NOUN
cana-1300	123	24	can	can	AUX
cana-1300	123	25	be	be	AUX
cana-1300	123	26	handled	handle	VERB
cana-1300	123	27	manually	manually	ADV
cana-1300	123	28	.	.	PUNCT
cana-1300	124	1	but	but	CCONJ
cana-1300	124	2	alternative	alternative	ADJ
cana-1300	124	3	strategies	strategy	NOUN
cana-1300	124	4	have	have	VERB
cana-1300	124	5	to	to	PART
cana-1300	124	6	be	be	AUX
cana-1300	124	7	worked	work	VERB
cana-1300	124	8	out	out	ADP
cana-1300	124	9	to	to	PART
cana-1300	124	10	construct	construct	VERB
cana-1300	124	11	the	the	DET
cana-1300	124	12	collaboration	collaboration	NOUN
cana-1300	124	13	graphs	graph	NOUN
cana-1300	124	14	of	of	ADP
cana-1300	124	15	other	other	ADJ
cana-1300	124	16	popular	popular	ADJ
cana-1300	124	17	prizes	prize	NOUN
cana-1300	124	18	like	like	ADP
cana-1300	124	19	the	the	DET
cana-1300	124	20	nobel	nobel	PROPN
cana-1300	124	21	prize	prize	PROPN
cana-1300	124	22	;	;	PUNCT
cana-1300	124	23	fields	field	NOUN
cana-1300	124	24	medal	medal	NOUN
cana-1300	124	25	etc	etc	X
cana-1300	124	26	where	where	SCONJ
cana-1300	124	27	the	the	DET
cana-1300	124	28	number	number	NOUN
cana-1300	124	29	of	of	ADP
cana-1300	124	30	prize	prize	NOUN
cana-1300	124	31	winners	winner	NOUN
cana-1300	124	32	is	be	AUX
cana-1300	124	33	more	more	ADJ
cana-1300	124	34	than	than	ADP
cana-1300	124	35	50	50	NUM
cana-1300	124	36	.	.	PUNCT
cana-1300	125	1	if	if	SCONJ
cana-1300	125	2	there	there	PRON
cana-1300	125	3	is	be	VERB
cana-1300	125	4	no	no	DET
cana-1300	125	5	co	co	NOUN
cana-1300	125	6	-	-	NOUN
cana-1300	125	7	author	author	NOUN
cana-1300	125	8	correlation	correlation	NOUN
cana-1300	125	9	between	between	ADP
cana-1300	125	10	two	two	NUM
cana-1300	125	11	arbitrary	arbitrary	ADJ
cana-1300	125	12	mathematicians	mathematician	NOUN
cana-1300	125	13	𝑥	𝑥	PROPN
cana-1300	125	14	&	&	CCONJ
cana-1300	125	15	𝑦	𝑦	PROPN
cana-1300	125	16	,	,	PUNCT
cana-1300	125	17	our	our	PRON
cana-1300	125	18	implementation	implementation	NOUN
cana-1300	125	19	of	of	ADP
cana-1300	125	20	step	step	NOUN
cana-1300	125	21	b	b	NOUN
cana-1300	125	22	will	will	AUX
cana-1300	125	23	return	return	VERB
cana-1300	125	24	"	"	PUNCT
cana-1300	125	25	no	no	DET
cana-1300	125	26	path	path	NOUN
cana-1300	125	27	found	find	VERB
cana-1300	125	28	.	.	PUNCT
cana-1300	125	29	"	"	PUNCT
cana-1300	126	1	4	4	NUM
cana-1300	126	2	.	.	NUM
cana-1300	126	3	results	result	NOUN
cana-1300	126	4	and	and	CCONJ
cana-1300	126	5	discussion	discussion	NOUN
cana-1300	126	6	theorem	theorem	VERB
cana-1300	126	7	4.1	4.1	NUM
cana-1300	126	8	:	:	SYM
cana-1300	126	9	𝛾𝑠𝑠(𝐺	𝛾𝑠𝑠(𝐺	NUM
cana-1300	126	10	)	)	PUNCT
cana-1300	126	11	=	=	SYM
cana-1300	126	12	12	12	NUM
cana-1300	126	13	proof	proof	NOUN
cana-1300	126	14	:	:	PUNCT
cana-1300	126	15	the	the	DET
cana-1300	126	16	lilavati	lilavati	PROPN
cana-1300	126	17	award	award	PROPN
cana-1300	126	18	winners	winner	NOUN
cana-1300	126	19	and	and	CCONJ
cana-1300	126	20	collaborators	collaborator	NOUN
cana-1300	126	21	of	of	ADP
cana-1300	126	22	prize	prize	NOUN
cana-1300	126	23	winners	winner	NOUN
cana-1300	126	24	are	be	AUX
cana-1300	126	25	represented	represent	VERB
cana-1300	126	26	by	by	ADP
cana-1300	126	27	the	the	DET
cana-1300	126	28	vertex	vertex	NOUN
cana-1300	126	29	set	set	NOUN
cana-1300	126	30	,	,	PUNCT
cana-1300	126	31	which	which	PRON
cana-1300	126	32	has	have	VERB
cana-1300	126	33	14	14	NUM
cana-1300	126	34	elements	element	NOUN
cana-1300	126	35	and	and	CCONJ
cana-1300	126	36	is	be	AUX
cana-1300	126	37	provided	provide	VERB
cana-1300	126	38	by	by	ADP
cana-1300	126	39	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	126	40	)	)	PUNCT
cana-1300	126	41	=	=	PRON
cana-1300	126	42	{	{	PUNCT
cana-1300	126	43	𝑤1	𝑤1	VERB
cana-1300	126	44	,	,	PUNCT
cana-1300	126	45	𝑤2	𝑤2	NOUN
cana-1300	126	46	,	,	PUNCT
cana-1300	126	47	…	…	PUNCT
cana-1300	126	48	…	…	PUNCT
cana-1300	126	49	.	.	PUNCT
cana-1300	127	1	,	,	PUNCT
cana-1300	127	2	𝑤14	𝑤14	ADV
cana-1300	127	3	}	}	PUNCT
cana-1300	127	4	.	.	PUNCT
cana-1300	128	1	notice	notice	VERB
cana-1300	128	2	that	that	SCONJ
cana-1300	128	3	𝑤2	𝑤2	NOUN
cana-1300	128	4	&	&	CCONJ
cana-1300	128	5	𝑤3	𝑤3	PROPN
cana-1300	128	6	are	be	AUX
cana-1300	128	7	the	the	DET
cana-1300	128	8	highest	high	ADJ
cana-1300	128	9	degree	degree	NOUN
cana-1300	128	10	vertices	vertex	NOUN
cana-1300	128	11	in	in	ADP
cana-1300	128	12	graph	graph	NOUN
cana-1300	128	13	and	and	CCONJ
cana-1300	128	14	𝑁(𝑤2	𝑁(𝑤2	PROPN
cana-1300	128	15	)	)	PUNCT
cana-1300	128	16	∩	∩	X
cana-1300	128	17	𝑁(𝑤3	𝑁(𝑤3	X
cana-1300	128	18	)	)	PUNCT
cana-1300	128	19	≠	≠	PROPN
cana-1300	128	20	∅	∅	NOUN
cana-1300	128	21	gains	gain	NOUN
cana-1300	128	22	entry	entry	NOUN
cana-1300	128	23	as	as	ADP
cana-1300	128	24	elements	element	NOUN
cana-1300	128	25	to	to	ADP
cana-1300	128	26	the	the	DET
cana-1300	128	27	dominating	dominating	NOUN
cana-1300	128	28	set	set	VERB
cana-1300	128	29	𝐷.	𝐷.	PROPN
cana-1300	128	30	𝐷	𝐷	NOUN
cana-1300	128	31	is	be	AUX
cana-1300	128	32	not	not	PART
cana-1300	128	33	a	a	DET
cana-1300	128	34	strong	strong	ADJ
cana-1300	128	35	split	split	NOUN
cana-1300	128	36	since	since	SCONJ
cana-1300	128	37	the	the	DET
cana-1300	128	38	subgraph	subgraph	NOUN
cana-1300	128	39	that	that	PRON
cana-1300	128	40	the	the	DET
cana-1300	128	41	remaining	remain	VERB
cana-1300	128	42	vertices	vertex	NOUN
cana-1300	128	43	trace	trace	NOUN
cana-1300	128	44	is	be	AUX
cana-1300	128	45	apical	apical	ADJ
cana-1300	128	46	.	.	PUNCT
cana-1300	129	1	as	as	SCONJ
cana-1300	129	2	the	the	DET
cana-1300	129	3	subgraph	subgraph	NOUN
cana-1300	129	4	traced	trace	VERB
cana-1300	129	5	by	by	ADP
cana-1300	129	6	the	the	DET
cana-1300	129	7	remaining	remain	VERB
cana-1300	129	8	vertices	vertex	NOUN
cana-1300	129	9	is	be	AUX
cana-1300	129	10	connected	connect	VERB
cana-1300	129	11	and	and	CCONJ
cana-1300	129	12	𝐷	𝐷	NOUN
cana-1300	129	13	is	be	AUX
cana-1300	129	14	not	not	PART
cana-1300	129	15	a	a	DET
cana-1300	129	16	strong	strong	ADJ
cana-1300	129	17	split	split	NOUN
cana-1300	129	18	.	.	PUNCT
cana-1300	130	1	to	to	PART
cana-1300	130	2	make	make	VERB
cana-1300	130	3	𝐷	𝐷	PROPN
cana-1300	130	4	a	a	DET
cana-1300	130	5	strong	strong	ADJ
cana-1300	130	6	split	split	NOUN
cana-1300	130	7	,	,	PUNCT
cana-1300	130	8	let	let	VERB
cana-1300	130	9	us	we	PRON
cana-1300	130	10	look	look	VERB
cana-1300	130	11	forward	forward	ADV
cana-1300	130	12	for	for	ADP
cana-1300	130	13	other	other	ADJ
cana-1300	130	14	vertices	vertex	NOUN
cana-1300	130	15	with	with	ADP
cana-1300	130	16	next	next	ADJ
cana-1300	130	17	highest	high	ADJ
cana-1300	130	18	degrees	degree	NOUN
cana-1300	130	19	such	such	ADJ
cana-1300	130	20	vertices	vertex	NOUN
cana-1300	130	21	are	be	AUX
cana-1300	130	22	𝑤1and𝑤13	𝑤1and𝑤13	PUNCT
cana-1300	130	23	the	the	DET
cana-1300	130	24	subgraph	subgraph	NOUN
cana-1300	130	25	traced	trace	VERB
cana-1300	130	26	by	by	ADP
cana-1300	130	27	remaining	remain	VERB
cana-1300	130	28	vertices	vertex	NOUN
cana-1300	130	29	turns	turn	VERB
cana-1300	130	30	a	a	DET
cana-1300	130	31	regular	regular	ADJ
cana-1300	130	32	graph	graph	NOUN
cana-1300	130	33	with	with	ADP
cana-1300	130	34	degree	degree	NOUN
cana-1300	130	35	eight	eight	NUM
cana-1300	130	36	.	.	PUNCT
cana-1300	131	1	hence	hence	ADV
cana-1300	131	2	the	the	DET
cana-1300	131	3	dominating	dominating	NOUN
cana-1300	131	4	set	set	VERB
cana-1300	131	5	with	with	ADP
cana-1300	131	6	elements	element	NOUN
cana-1300	131	7	{	{	PUNCT
cana-1300	131	8	𝑤1	𝑤1	VERB
cana-1300	131	9	,	,	PUNCT
cana-1300	131	10	𝑤2	𝑤2	NOUN
cana-1300	131	11	,	,	PUNCT
cana-1300	131	12	𝑤3	𝑤3	PROPN
cana-1300	131	13	,	,	PUNCT
cana-1300	131	14	𝑤13	𝑤13	NOUN
cana-1300	131	15	}	}	PUNCT
cana-1300	131	16	are	be	AUX
cana-1300	131	17	again	again	ADV
cana-1300	131	18	not	not	PART
cana-1300	131	19	a	a	DET
cana-1300	131	20	strong	strong	ADJ
cana-1300	131	21	split	split	NOUN
cana-1300	131	22	.	.	PUNCT
cana-1300	132	1	again	again	ADV
cana-1300	132	2	to	to	PART
cana-1300	132	3	make	make	VERB
cana-1300	132	4	𝐷	𝐷	PROPN
cana-1300	132	5	a	a	DET
cana-1300	132	6	strong	strong	ADJ
cana-1300	132	7	split	split	NOUN
cana-1300	132	8	dominating	dominating	NOUN
cana-1300	132	9	set	set	VERB
cana-1300	132	10	the	the	DET
cana-1300	132	11	choice	choice	NOUN
cana-1300	132	12	of	of	ADP
cana-1300	132	13	vertices	vertex	NOUN
cana-1300	132	14	{	{	PUNCT
cana-1300	132	15	𝑤4	𝑤4	NOUN
cana-1300	132	16	,	,	PUNCT
cana-1300	132	17	𝑤6	𝑤6	PROPN
cana-1300	132	18	,	,	PUNCT
cana-1300	132	19	𝑤9	𝑤9	PROPN
cana-1300	132	20	,	,	PUNCT
cana-1300	132	21	𝑤11	𝑤11	NOUN
cana-1300	132	22	}	}	PUNCT
cana-1300	132	23	along	along	ADP
cana-1300	132	24	with	with	ADP
cana-1300	132	25	𝐷	𝐷	PROPN
cana-1300	132	26	leads	lead	VERB
cana-1300	132	27	to	to	ADP
cana-1300	132	28	a	a	DET
cana-1300	132	29	regular	regular	ADJ
cana-1300	132	30	graph	graph	NOUN
cana-1300	132	31	with	with	ADP
cana-1300	132	32	degree	degree	NOUN
cana-1300	132	33	five	five	NUM
cana-1300	132	34	.	.	PUNCT
cana-1300	133	1	so	so	ADV
cana-1300	133	2	,	,	PUNCT
cana-1300	133	3	the	the	DET
cana-1300	133	4	cardinality	cardinality	NOUN
cana-1300	133	5	of	of	ADP
cana-1300	133	6	𝐷	𝐷	PROPN
cana-1300	133	7	must	must	AUX
cana-1300	133	8	be	be	AUX
cana-1300	133	9	altered	alter	VERB
cana-1300	133	10	continuously	continuously	ADV
cana-1300	133	11	to	to	PART
cana-1300	133	12	get	get	VERB
cana-1300	133	13	a	a	DET
cana-1300	133	14	disconnected	disconnected	ADJ
cana-1300	133	15	graph	graph	NOUN
cana-1300	133	16	with	with	ADP
cana-1300	133	17	atleast	atleast	ADJ
cana-1300	133	18	two	two	NUM
cana-1300	133	19	vertices	vertex	NOUN
cana-1300	133	20	.	.	PUNCT
cana-1300	134	1	finally	finally	ADV
cana-1300	134	2	this	this	PRON
cana-1300	134	3	yielded	yield	VERB
cana-1300	134	4	to	to	ADP
cana-1300	134	5	a	a	DET
cana-1300	134	6	dominating	dominating	NOUN
cana-1300	134	7	set	set	NOUN
cana-1300	134	8	becomes	become	VERB
cana-1300	134	9	strong	strong	ADJ
cana-1300	134	10	split	split	NOUN
cana-1300	134	11	with	with	ADP
cana-1300	134	12	12	12	NUM
cana-1300	134	13	elements	element	NOUN
cana-1300	134	14	given	give	VERB
cana-1300	134	15	by	by	ADP
cana-1300	134	16	𝐷	𝐷	PROPN
cana-1300	134	17	=	=	SYM
cana-1300	134	18	{	{	PUNCT
cana-1300	134	19	𝑤1	𝑤1	PROPN
cana-1300	134	20	,	,	PUNCT
cana-1300	134	21	𝑤2	𝑤2	NOUN
cana-1300	134	22	,	,	PUNCT
cana-1300	134	23	𝑤3	𝑤3	PROPN
cana-1300	134	24	,	,	PUNCT
cana-1300	134	25	𝑤4	𝑤4	NOUN
cana-1300	134	26	,	,	PUNCT
cana-1300	134	27	𝑤5	𝑤5	NOUN
cana-1300	134	28	,	,	PUNCT
cana-1300	134	29	𝑤6	𝑤6	PROPN
cana-1300	134	30	,	,	PUNCT
cana-1300	134	31	𝑤8	𝑤8	PROPN
cana-1300	134	32	,	,	PUNCT
cana-1300	134	33	𝑤9	𝑤9	PROPN
cana-1300	134	34	,	,	PUNCT
cana-1300	134	35	𝑤10	𝑤10	NOUN
cana-1300	134	36	,	,	PUNCT
cana-1300	134	37	𝑤11	𝑤11	NOUN
cana-1300	134	38	,	,	PUNCT
cana-1300	134	39	𝑤12	𝑤12	NOUN
cana-1300	134	40	,	,	PUNCT
cana-1300	134	41	𝑤13	𝑤13	NOUN
cana-1300	134	42	}	}	PUNCT
cana-1300	134	43	.	.	PUNCT
cana-1300	135	1	since	since	SCONJ
cana-1300	135	2	,	,	PUNCT
cana-1300	135	3	the	the	DET
cana-1300	135	4	cardinality	cardinality	NOUN
cana-1300	135	5	of	of	ADP
cana-1300	135	6	𝐷	𝐷	PROPN
cana-1300	135	7	forms	form	NOUN
cana-1300	135	8	strong	strong	ADJ
cana-1300	135	9	split	split	ADJ
cana-1300	135	10	domination	domination	NOUN
cana-1300	135	11	number	number	NOUN
cana-1300	135	12	.	.	PUNCT
cana-1300	135	13	therefore	therefore	ADV
cana-1300	135	14	𝛾𝑠𝑠(𝐺	𝛾𝑠𝑠(𝐺	NUM
cana-1300	135	15	)	)	PUNCT
cana-1300	135	16	=	=	SYM
cana-1300	136	1	12	12	NUM
cana-1300	136	2	.	.	PUNCT
cana-1300	137	1	□	□	PUNCT
cana-1300	137	2	observation	observation	NOUN
cana-1300	137	3	4.1	4.1	NUM
cana-1300	137	4	:	:	PUNCT
cana-1300	137	5	observed	observe	VERB
cana-1300	137	6	from	from	ADP
cana-1300	137	7	graph	graph	NOUN
cana-1300	137	8	that	that	SCONJ
cana-1300	137	9	𝛾𝑠(𝐺	𝛾𝑠(𝐺	NOUN
cana-1300	137	10	)	)	PUNCT
cana-1300	137	11	=	=	SYM
cana-1300	137	12	𝛾𝑠𝑠(𝐺	𝛾𝑠𝑠(𝐺	NUM
cana-1300	137	13	)	)	PUNCT
cana-1300	137	14	theorem	theorem	VERB
cana-1300	137	15	4.2	4.2	NUM
cana-1300	137	16	:	:	PUNCT
cana-1300	137	17	𝛾𝑠𝑛𝑠(𝐺	𝛾𝑠𝑛𝑠(𝐺	NOUN
cana-1300	137	18	)	)	PUNCT
cana-1300	137	19	=	=	SYM
cana-1300	137	20	7	7	NUM
cana-1300	137	21	proof	proof	NOUN
cana-1300	137	22	:	:	PUNCT
cana-1300	137	23	from	from	ADP
cana-1300	137	24	the	the	DET
cana-1300	137	25	collaboration	collaboration	NOUN
cana-1300	137	26	graph	graph	NOUN
cana-1300	137	27	the	the	DET
cana-1300	137	28	vertex	vertex	NOUN
cana-1300	137	29	set	set	VERB
cana-1300	137	30	with	with	ADP
cana-1300	137	31	14	14	NUM
cana-1300	137	32	elements	element	NOUN
cana-1300	137	33	is	be	AUX
cana-1300	137	34	given	give	VERB
cana-1300	137	35	by	by	ADP
cana-1300	137	36	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	137	37	)	)	PUNCT
cana-1300	137	38	=	=	PRON
cana-1300	137	39	{	{	PUNCT
cana-1300	137	40	𝑤1	𝑤1	VERB
cana-1300	137	41	,	,	PUNCT
cana-1300	137	42	𝑤2	𝑤2	NOUN
cana-1300	137	43	,	,	PUNCT
cana-1300	137	44	…	…	PUNCT
cana-1300	137	45	…	…	PUNCT
cana-1300	137	46	,	,	PUNCT
cana-1300	137	47	𝑤14	𝑤14	ADV
cana-1300	137	48	}	}	PUNCT
cana-1300	137	49	which	which	PRON
cana-1300	137	50	denotes	denote	VERB
cana-1300	137	51	the	the	DET
cana-1300	137	52	lilavati	lilavati	PROPN
cana-1300	137	53	prize	prize	PROPN
cana-1300	137	54	winners	winner	NOUN
cana-1300	137	55	and	and	CCONJ
cana-1300	137	56	collaborators	collaborator	NOUN
cana-1300	137	57	of	of	ADP
cana-1300	137	58	prize	prize	NOUN
cana-1300	137	59	winners	winner	NOUN
cana-1300	137	60	.	.	PUNCT
cana-1300	138	1	to	to	PART
cana-1300	138	2	make	make	VERB
cana-1300	138	3	vertex	vertex	NOUN
cana-1300	138	4	set	set	VERB
cana-1300	138	5	a	a	DET
cana-1300	138	6	strong	strong	ADJ
cana-1300	138	7	non	non	NOUN
cana-1300	138	8	split	split	NOUN
cana-1300	138	9	dominating	dominating	NOUN
cana-1300	138	10	set	set	NOUN
cana-1300	138	11	,	,	PUNCT
cana-1300	138	12	first	first	ADV
cana-1300	138	13	we	we	PRON
cana-1300	138	14	begin	begin	VERB
cana-1300	138	15	our	our	PRON
cana-1300	138	16	argument	argument	NOUN
cana-1300	138	17	with	with	ADP
cana-1300	138	18	the	the	DET
cana-1300	138	19	dominating	dominating	NOUN
cana-1300	138	20	set	set	NOUN
cana-1300	138	21	of	of	ADP
cana-1300	138	22	vertices	vertex	NOUN
cana-1300	138	23	in	in	ADP
cana-1300	138	24	a	a	DET
cana-1300	138	25	collaboration	collaboration	NOUN
cana-1300	138	26	network	network	NOUN
cana-1300	138	27	{	{	PUNCT
cana-1300	138	28	𝑤1	𝑤1	PROPN
cana-1300	138	29	,	,	PUNCT
cana-1300	138	30	𝑤6}however	𝑤6}however	PROPN
cana-1300	138	31	,	,	PUNCT
cana-1300	138	32	the	the	DET
cana-1300	138	33	subgraph	subgraph	NOUN
cana-1300	138	34	formed	form	VERB
cana-1300	138	35	by	by	ADP
cana-1300	138	36	these	these	DET
cana-1300	138	37	vertices	vertex	NOUN
cana-1300	138	38	does	do	AUX
cana-1300	138	39	not	not	PART
cana-1300	138	40	form	form	VERB
cana-1300	138	41	a	a	DET
cana-1300	138	42	complete	complete	ADJ
cana-1300	138	43	graph	graph	NOUN
cana-1300	138	44	.	.	PUNCT
cana-1300	139	1	to	to	PART
cana-1300	139	2	make	make	VERB
cana-1300	139	3	the	the	DET
cana-1300	139	4	subgraph	subgraph	NOUN
cana-1300	139	5	complete	complete	VERB
cana-1300	139	6	the	the	DET
cana-1300	139	7	cardinality	cardinality	NOUN
cana-1300	139	8	of	of	ADP
cana-1300	139	9	𝐷	𝐷	PROPN
cana-1300	139	10	must	must	AUX
cana-1300	139	11	alter	alter	VERB
cana-1300	139	12	continuously	continuously	ADV
cana-1300	139	13	.	.	PUNCT
cana-1300	140	1	finally	finally	ADV
cana-1300	140	2	this	this	PRON
cana-1300	140	3	give	give	VERB
cana-1300	140	4	rise	rise	NOUN
cana-1300	140	5	to	to	ADP
cana-1300	140	6	strong	strong	ADJ
cana-1300	140	7	non	non	NOUN
cana-1300	140	8	split	split	NOUN
cana-1300	140	9	dominating	dominate	VERB
cana-1300	140	10	set	set	VERB
cana-1300	140	11	𝐷	𝐷	NOUN
cana-1300	140	12	with	with	ADP
cana-1300	140	13	seven	seven	NUM
cana-1300	140	14	elements	element	NOUN
cana-1300	140	15	{	{	PUNCT
cana-1300	140	16	𝑤1	𝑤1	VERB
cana-1300	140	17	,	,	PUNCT
cana-1300	140	18	𝑤6	𝑤6	PROPN
cana-1300	140	19	,	,	PUNCT
cana-1300	140	20	𝑤7	𝑤7	PROPN
cana-1300	140	21	,	,	PUNCT
cana-1300	140	22	𝑤9	𝑤9	PROPN
cana-1300	140	23	,	,	PUNCT
cana-1300	140	24	𝑤10	𝑤10	NOUN
cana-1300	140	25	,	,	PUNCT
cana-1300	140	26	𝑤12	𝑤12	PROPN
cana-1300	140	27	,	,	PUNCT
cana-1300	140	28	𝑤14	𝑤14	ADV
cana-1300	140	29	}	}	PUNCT
cana-1300	140	30	.	.	PUNCT
cana-1300	141	1	since	since	SCONJ
cana-1300	141	2	,	,	PUNCT
cana-1300	141	3	|𝐷|	|𝐷|	NOUN
cana-1300	141	4	forms	form	VERB
cana-1300	141	5	a	a	DET
cana-1300	141	6	𝛾𝑠𝑛𝑠(𝐺)set	𝛾𝑠𝑛𝑠(𝐺)set	PROPN
cana-1300	141	7	.	.	PUNCT
cana-1300	141	8	therefore	therefore	ADV
cana-1300	141	9	𝛾𝑠𝑛𝑠(𝐺	𝛾𝑠𝑛𝑠(𝐺	PROPN
cana-1300	141	10	)	)	PUNCT
cana-1300	141	11	=	=	SYM
cana-1300	141	12	7	7	NUM
cana-1300	141	13	□	□	PUNCT
cana-1300	141	14	communications	communication	NOUN
cana-1300	141	15	on	on	ADP
cana-1300	141	16	applied	apply	VERB
cana-1300	141	17	nonlinear	nonlinear	ADJ
cana-1300	141	18	analysis	analysis	NOUN
cana-1300	141	19	issn	issn	NOUN
cana-1300	141	20	:	:	PUNCT
cana-1300	141	21	1074	1074	NUM
cana-1300	141	22	-	-	PUNCT
cana-1300	141	23	133x	133x	NUM
cana-1300	141	24	vol	vol	NOUN
cana-1300	141	25	31	31	NUM
cana-1300	141	26	no	no	NOUN
cana-1300	141	27	.	.	PUNCT
cana-1300	142	1	7s	7	NOUN
cana-1300	142	2	(	(	PUNCT
cana-1300	142	3	2024	2024	NUM
cana-1300	142	4	)	)	PUNCT
cana-1300	142	5	257	257	NUM
cana-1300	142	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1300	142	7	figure	figure	NOUN
cana-1300	142	8	5	5	NUM
cana-1300	142	9	:	:	PUNCT
cana-1300	142	10	complete	complete	ADJ
cana-1300	142	11	graph	graph	NOUN
cana-1300	142	12	theorem	theorem	VERB
cana-1300	142	13	4.3	4.3	NUM
cana-1300	142	14	:	:	PUNCT
cana-1300	142	15	𝜸𝒏𝒔	𝜸𝒏𝒔	PROPN
cana-1300	142	16	−𝟏(𝑮	−𝟏(𝑮	NOUN
cana-1300	142	17	)	)	PUNCT
cana-1300	142	18	=	=	SYM
cana-1300	143	1	𝟏	𝟏	NUM
cana-1300	143	2	proof	proof	NOUN
cana-1300	143	3	:	:	PUNCT
cana-1300	143	4	we	we	PRON
cana-1300	143	5	begin	begin	VERB
cana-1300	143	6	with	with	ADP
cana-1300	143	7	a	a	DET
cana-1300	143	8	non	non	ADJ
cana-1300	143	9	-	-	ADJ
cana-1300	143	10	split	split	ADJ
cana-1300	143	11	dominating	dominating	NOUN
cana-1300	143	12	set	set	VERB
cana-1300	143	13	𝐷	𝐷	NOUN
cana-1300	143	14	=	=	SYM
cana-1300	143	15	{	{	PUNCT
cana-1300	143	16	𝑤2	𝑤2	NOUN
cana-1300	143	17	}	}	PUNCT
cana-1300	143	18	,	,	PUNCT
cana-1300	143	19	where	where	SCONJ
cana-1300	143	20	each	each	PRON
cana-1300	143	21	and	and	CCONJ
cana-1300	143	22	every	every	PRON
cana-1300	143	23	vertex	vertex	NOUN
cana-1300	143	24	in	in	ADP
cana-1300	143	25	𝑉	𝑉	PROPN
cana-1300	143	26	−	−	PROPN
cana-1300	143	27	𝐷	𝐷	PROPN
cana-1300	143	28	is	be	AUX
cana-1300	143	29	adjacent	adjacent	ADJ
cana-1300	143	30	to	to	ADP
cana-1300	143	31	a	a	DET
cana-1300	143	32	vertex	vertex	NOUN
cana-1300	143	33	in	in	ADP
cana-1300	143	34	𝐷.	𝐷.	PROPN
cana-1300	143	35	if	if	SCONJ
cana-1300	143	36	a	a	DET
cana-1300	143	37	set	set	NOUN
cana-1300	143	38	,	,	PUNCT
cana-1300	143	39	say	say	VERB
cana-1300	143	40	𝐷′	𝐷′	NOUN
cana-1300	143	41	=	=	NOUN
cana-1300	143	42	{	{	PUNCT
cana-1300	143	43	𝑤3	𝑤3	PROPN
cana-1300	143	44	}	}	PUNCT
cana-1300	143	45	,	,	PUNCT
cana-1300	143	46	corresponds	correspond	VERB
cana-1300	143	47	to	to	ADP
cana-1300	143	48	𝐷	𝐷	NOUN
cana-1300	143	49	,	,	PUNCT
cana-1300	143	50	then	then	ADV
cana-1300	143	51	𝑉	𝑉	PROPN
cana-1300	143	52	−	−	PROPN
cana-1300	143	53	𝐷	𝐷	PROPN
cana-1300	143	54	forms	form	VERB
cana-1300	143	55	a	a	DET
cana-1300	143	56	non	non	NOUN
cana-1300	143	57	split	split	NOUN
cana-1300	143	58	dominating	dominate	VERB
cana-1300	143	59	set	set	NOUN
cana-1300	143	60	of	of	ADP
cana-1300	143	61	g.	g.	PROPN
cana-1300	143	62	the	the	DET
cana-1300	143	63	inverse	inverse	NOUN
cana-1300	143	64	non	non	NOUN
cana-1300	143	65	split	split	NOUN
cana-1300	143	66	domination	domination	NOUN
cana-1300	143	67	number	number	NOUN
cana-1300	143	68	has	have	VERB
cana-1300	143	69	a	a	DET
cana-1300	143	70	cardinality	cardinality	NOUN
cana-1300	143	71	one	one	NUM
cana-1300	143	72	.	.	PUNCT
cana-1300	144	1	as	as	ADP
cana-1300	144	2	a	a	DET
cana-1300	144	3	result	result	NOUN
cana-1300	144	4	,	,	PUNCT
cana-1300	144	5	𝛾𝑛𝑠	𝛾𝑛𝑠	NOUN
cana-1300	144	6	−1(𝐺	−1(𝐺	NOUN
cana-1300	144	7	)	)	PUNCT
cana-1300	144	8	=	=	SYM
cana-1300	145	1	1	1	X
cana-1300	145	2	.	.	PUNCT
cana-1300	145	3	□	□	PUNCT
cana-1300	145	4	observation	observation	NOUN
cana-1300	145	5	4.2	4.2	NUM
cana-1300	145	6	:	:	PUNCT
cana-1300	145	7	for	for	ADP
cana-1300	145	8	a	a	DET
cana-1300	145	9	collaboration	collaboration	NOUN
cana-1300	145	10	graph	graph	NOUN
cana-1300	145	11	𝛾−1(𝐺	𝛾−1(𝐺	NOUN
cana-1300	145	12	)	)	PUNCT
cana-1300	145	13	=	=	PUNCT
cana-1300	145	14	𝛾𝑛𝑠	𝛾𝑛𝑠	NOUN
cana-1300	145	15	−1(𝐺	−1(𝐺	NOUN
cana-1300	145	16	)	)	PUNCT
cana-1300	145	17	theorem	theorem	VERB
cana-1300	145	18	4.3	4.3	NUM
cana-1300	145	19	:	:	PUNCT
cana-1300	145	20	𝜸𝒔(𝑮	𝜸𝒔(𝑮	NUM
cana-1300	145	21	)	)	PUNCT
cana-1300	146	1	=	=	SYM
cana-1300	147	1	𝟏	𝟏	NUM
cana-1300	147	2	proof	proof	NOUN
cana-1300	147	3	:	:	PUNCT
cana-1300	147	4	we	we	PRON
cana-1300	147	5	begin	begin	VERB
cana-1300	147	6	our	our	PRON
cana-1300	147	7	proof	proof	NOUN
cana-1300	147	8	by	by	ADP
cana-1300	147	9	stating	state	VERB
cana-1300	147	10	that	that	SCONJ
cana-1300	147	11	𝐷	𝐷	PROPN
cana-1300	147	12	is	be	AUX
cana-1300	147	13	a	a	DET
cana-1300	147	14	minimal	minimal	ADJ
cana-1300	147	15	dominant	dominant	NOUN
cana-1300	147	16	set.close	set.close	ADP
cana-1300	147	17	examination	examination	NOUN
cana-1300	147	18	of	of	ADP
cana-1300	147	19	the	the	DET
cana-1300	147	20	vertex	vertex	NOUN
cana-1300	147	21	's	's	PART
cana-1300	147	22	surroundings	surrounding	NOUN
cana-1300	147	23	𝑤2	𝑤2	NOUN
cana-1300	147	24	reveals	reveal	VERB
cana-1300	147	25	that	that	SCONJ
cana-1300	147	26	n(𝑤2	n(𝑤2	NOUN
cana-1300	147	27	)	)	PUNCT
cana-1300	147	28	∩	∩	NOUN
cana-1300	147	29	𝑉	𝑉	PROPN
cana-1300	147	30	=	=	PUNCT
cana-1300	147	31	{	{	PUNCT
cana-1300	147	32	𝑤3	𝑤3	PROPN
cana-1300	147	33	}	}	PUNCT
cana-1300	147	34	.	.	PUNCT
cana-1300	148	1	we	we	PRON
cana-1300	148	2	conclude	conclude	VERB
cana-1300	148	3	that	that	SCONJ
cana-1300	148	4	𝐷	𝐷	NOUN
cana-1300	148	5	is	be	AUX
cana-1300	148	6	a	a	DET
cana-1300	148	7	least	least	ADJ
cana-1300	148	8	dominating	dominating	NOUN
cana-1300	148	9	set	set	NOUN
cana-1300	148	10	.	.	PUNCT
cana-1300	149	1	the	the	DET
cana-1300	149	2	cardinality	cardinality	NOUN
cana-1300	149	3	should	should	AUX
cana-1300	149	4	be	be	AUX
cana-1300	149	5	least	least	ADJ
cana-1300	149	6	therefore	therefore	ADV
cana-1300	149	7	either	either	CCONJ
cana-1300	149	8	𝑤2	𝑤2	NOUN
cana-1300	149	9	or	or	CCONJ
cana-1300	149	10	𝑤3	𝑤3	PROPN
cana-1300	149	11	be	be	AUX
cana-1300	149	12	a	a	DET
cana-1300	149	13	dominating	dominating	NOUN
cana-1300	149	14	set	set	NOUN
cana-1300	149	15	.	.	PUNCT
cana-1300	150	1	let	let	VERB
cana-1300	150	2	𝐷	𝐷	NOUN
cana-1300	150	3	=	=	SYM
cana-1300	150	4	{	{	PUNCT
cana-1300	150	5	𝑤2	𝑤2	NOUN
cana-1300	150	6	}	}	PUNCT
cana-1300	150	7	⊂	⊂	NOUN
cana-1300	150	8	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	150	9	)	)	PUNCT
cana-1300	150	10	that	that	PRON
cana-1300	150	11	dominates	dominate	VERB
cana-1300	150	12	the	the	DET
cana-1300	150	13	every	every	DET
cana-1300	150	14	vertex	vertex	NOUN
cana-1300	150	15	in	in	ADP
cana-1300	150	16	𝑉	𝑉	PROPN
cana-1300	150	17	–	–	PUNCT
cana-1300	150	18	𝐷.	𝐷.	PROPN
cana-1300	150	19	if	if	SCONJ
cana-1300	150	20	𝑒	𝑒	PROPN
cana-1300	150	21	is	be	AUX
cana-1300	150	22	an	an	DET
cana-1300	150	23	edge	edge	NOUN
cana-1300	150	24	with	with	ADP
cana-1300	150	25	vertices	vertex	NOUN
cana-1300	150	26	𝑥	𝑥	NOUN
cana-1300	150	27	and	and	CCONJ
cana-1300	150	28	𝑦	𝑦	NOUN
cana-1300	150	29	at	at	ADV
cana-1300	150	30	both	both	DET
cana-1300	150	31	ends	end	NOUN
cana-1300	150	32	,	,	PUNCT
cana-1300	150	33	the	the	DET
cana-1300	150	34	degree	degree	NOUN
cana-1300	150	35	of	of	ADP
cana-1300	150	36	𝑤2is	𝑤2is	PUNCT
cana-1300	150	37	larger	large	ADJ
cana-1300	150	38	than	than	ADP
cana-1300	150	39	or	or	CCONJ
cana-1300	150	40	equal	equal	ADJ
cana-1300	150	41	to	to	ADP
cana-1300	150	42	the	the	DET
cana-1300	150	43	degree	degree	NOUN
cana-1300	150	44	of	of	ADP
cana-1300	150	45	all	all	DET
cana-1300	150	46	other	other	ADJ
cana-1300	150	47	vertices	vertex	NOUN
cana-1300	150	48	in	in	ADP
cana-1300	150	49	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	150	50	)	)	PUNCT
cana-1300	150	51	.	.	PUNCT
cana-1300	151	1	i.e	i.e	PRON
cana-1300	151	2	,	,	PUNCT
cana-1300	151	3	𝑑𝑒𝑔(𝑥	𝑑𝑒𝑔(𝑥	PROPN
cana-1300	151	4	,	,	PUNCT
cana-1300	151	5	𝐺	𝐺	NOUN
cana-1300	151	6	)	)	PUNCT
cana-1300	151	7	≤	≤	NUM
cana-1300	151	8	deg	deg	X
cana-1300	151	9	(	(	PUNCT
cana-1300	151	10	𝑦	𝑦	NOUN
cana-1300	151	11	,	,	PUNCT
cana-1300	151	12	𝐺	𝐺	PROPN
cana-1300	151	13	)	)	PUNCT
cana-1300	151	14	.	.	PUNCT
cana-1300	152	1	then	then	ADV
cana-1300	152	2	we	we	PRON
cana-1300	152	3	can	can	AUX
cana-1300	152	4	say	say	VERB
cana-1300	152	5	that	that	SCONJ
cana-1300	152	6	𝑤2	𝑤2	NOUN
cana-1300	152	7	strongly	strongly	ADV
cana-1300	152	8	dominates	dominate	VERB
cana-1300	152	9	.	.	PUNCT
cana-1300	153	1	since	since	SCONJ
cana-1300	153	2	each	each	DET
cana-1300	153	3	vertex	vertex	NOUN
cana-1300	153	4	𝑉	𝑉	PROPN
cana-1300	153	5	–	–	PUNCT
cana-1300	153	6	𝐷	𝐷	PROPN
cana-1300	153	7	is	be	AUX
cana-1300	153	8	strongly	strongly	ADV
cana-1300	153	9	dominated	dominate	VERB
cana-1300	153	10	by	by	ADP
cana-1300	153	11	the	the	DET
cana-1300	153	12	vertex	vertex	NOUN
cana-1300	153	13	𝑤2	𝑤2	NOUN
cana-1300	153	14	,	,	PUNCT
cana-1300	153	15	𝐷	𝐷	NOUN
cana-1300	153	16	=	=	SYM
cana-1300	153	17	{	{	PUNCT
cana-1300	153	18	𝑤2	𝑤2	NOUN
cana-1300	153	19	}	}	PUNCT
cana-1300	153	20	becomes	become	VERB
cana-1300	153	21	a	a	DET
cana-1300	153	22	strong	strong	ADJ
cana-1300	153	23	dominating	dominating	NOUN
cana-1300	153	24	set	set	NOUN
cana-1300	153	25	of	of	ADP
cana-1300	153	26	𝐺.	𝐺.	NOUN
cana-1300	153	27	∴	∴	NOUN
cana-1300	153	28	min|𝛾𝑠(𝐺)|	min|𝛾𝑠(𝐺)|	NOUN
cana-1300	153	29	=	=	SYM
cana-1300	153	30	1	1	NUM
cana-1300	153	31	and	and	CCONJ
cana-1300	153	32	so	so	ADV
cana-1300	153	33	𝛾𝑠(𝐺	𝛾𝑠(𝐺	ADJ
cana-1300	153	34	)	)	PUNCT
cana-1300	153	35	=	=	SYM
cana-1300	153	36	1	1	X
cana-1300	153	37	.	.	PUNCT
cana-1300	153	38	□	□	PUNCT
cana-1300	153	39	theorem	theorem	ADJ
cana-1300	153	40	4.4	4.4	NUM
cana-1300	153	41	:	:	PUNCT
cana-1300	153	42	𝜸′	𝜸′	PUNCT
cana-1300	153	43	𝒔	𝒔	X
cana-1300	153	44	(	(	PUNCT
cana-1300	153	45	𝑮	𝑮	PROPN
cana-1300	153	46	)	)	PUNCT
cana-1300	153	47	=	=	SYM
cana-1300	153	48	𝜸′	𝜸′	PUNCT
cana-1300	153	49	𝒄𝒔	𝒄𝒔	X
cana-1300	153	50	(	(	PUNCT
cana-1300	153	51	𝑮	𝑮	NOUN
cana-1300	153	52	)	)	PUNCT
cana-1300	153	53	=	=	SYM
cana-1300	153	54	𝟔	𝟔	NUM
cana-1300	153	55	proof	proof	NOUN
cana-1300	153	56	:	:	PUNCT
cana-1300	153	57	from	from	ADP
cana-1300	153	58	the	the	DET
cana-1300	153	59	construction	construction	NOUN
cana-1300	153	60	of	of	ADP
cana-1300	153	61	the	the	DET
cana-1300	153	62	collaboration	collaboration	NOUN
cana-1300	153	63	graph	graph	NOUN
cana-1300	153	64	of	of	ADP
cana-1300	153	65	the	the	DET
cana-1300	153	66	lilavathi	lilavathi	ADJ
cana-1300	153	67	prize	prize	NOUN
cana-1300	153	68	winners	winner	NOUN
cana-1300	153	69	,	,	PUNCT
cana-1300	153	70	we	we	PRON
cana-1300	153	71	have	have	VERB
cana-1300	153	72	|𝑉(𝐺)|	|𝑉(𝐺)|	NOUN
cana-1300	153	73	=	=	SYM
cana-1300	153	74	14	14	NUM
cana-1300	153	75	and	and	CCONJ
cana-1300	153	76	|𝐸(𝐺)|	|𝐸(𝐺)|	SYM
cana-1300	154	1	=	=	NOUN
cana-1300	154	2	78	78	NUM
cana-1300	154	3	as	as	SCONJ
cana-1300	154	4	the	the	DET
cana-1300	154	5	edge	edge	NOUN
cana-1300	154	6	set	set	VERB
cana-1300	154	7	e(𝐺	e(𝐺	NOUN
cana-1300	154	8	)	)	PUNCT
cana-1300	155	1	=	=	PRON
cana-1300	155	2	{	{	PUNCT
cana-1300	155	3	𝑓1,𝑓2,	𝑓1,𝑓2,	NOUN
cana-1300	155	4	...	...	PUNCT
cana-1300	155	5	,𝑓78	,𝑓78	PUNCT
cana-1300	155	6	}	}	PUNCT
cana-1300	155	7	.	.	PUNCT
cana-1300	156	1	to	to	PART
cana-1300	156	2	arrive	arrive	VERB
cana-1300	156	3	at	at	ADP
cana-1300	156	4	an	an	DET
cana-1300	156	5	edge	edge	NOUN
cana-1300	156	6	dominating	dominating	NOUN
cana-1300	156	7	set	set	NOUN
cana-1300	156	8	for	for	ADP
cana-1300	156	9	the	the	DET
cana-1300	156	10	graph	graph	NOUN
cana-1300	156	11	,	,	PUNCT
cana-1300	156	12	we	we	PRON
cana-1300	156	13	start	start	VERB
cana-1300	156	14	our	our	PRON
cana-1300	156	15	assertion	assertion	NOUN
cana-1300	156	16	with	with	ADP
cana-1300	156	17	an	an	DET
cana-1300	156	18	edge	edge	NOUN
cana-1300	156	19	𝑓1	𝑓1	PROPN
cana-1300	156	20	=	=	PUNCT
cana-1300	156	21	(	(	PUNCT
cana-1300	156	22	𝑤1	𝑤1	VERB
cana-1300	156	23	,	,	PUNCT
cana-1300	156	24	𝑤2	𝑤2	NOUN
cana-1300	156	25	)	)	PUNCT
cana-1300	156	26	∈	∈	PROPN
cana-1300	156	27	𝐸(𝐺	𝐸(𝐺	NOUN
cana-1300	156	28	)	)	PUNCT
cana-1300	156	29	.	.	PUNCT
cana-1300	157	1	if	if	SCONJ
cana-1300	157	2	the	the	DET
cana-1300	157	3	considered	consider	VERB
cana-1300	157	4	edge	edge	NOUN
cana-1300	157	5	𝑓1	𝑓1	PROPN
cana-1300	157	6	covers	cover	VERB
cana-1300	157	7	all	all	DET
cana-1300	157	8	the	the	DET
cana-1300	157	9	edges	edge	NOUN
cana-1300	157	10	of	of	ADP
cana-1300	157	11	the	the	DET
cana-1300	157	12	graph	graph	NOUN
cana-1300	157	13	then	then	ADV
cana-1300	157	14	the	the	DET
cana-1300	157	15	set	set	NOUN
cana-1300	157	16	𝐷	𝐷	NOUN
cana-1300	157	17	=	=	PUNCT
cana-1300	157	18	{	{	PUNCT
cana-1300	157	19	𝑓1	𝑓1	NOUN
cana-1300	157	20	}	}	PUNCT
cana-1300	157	21	becomes	become	VERB
cana-1300	157	22	an	an	DET
cana-1300	157	23	edge	edge	NOUN
cana-1300	157	24	dominating	dominating	NOUN
cana-1300	157	25	set	set	NOUN
cana-1300	157	26	for	for	ADP
cana-1300	157	27	𝐺.	𝐺.	PROPN
cana-1300	157	28	but	but	CCONJ
cana-1300	157	29	𝑓1	𝑓1	PROPN
cana-1300	157	30	covers	cover	VERB
cana-1300	157	31	only	only	ADV
cana-1300	157	32	23	23	NUM
cana-1300	157	33	of	of	ADP
cana-1300	157	34	the	the	DET
cana-1300	157	35	edges	edge	NOUN
cana-1300	157	36	of	of	ADP
cana-1300	157	37	.	.	PUNCT
cana-1300	158	1	so	so	ADV
cana-1300	158	2	the	the	DET
cana-1300	158	3	set	set	NOUN
cana-1300	158	4	𝐷	𝐷	NOUN
cana-1300	158	5	must	must	AUX
cana-1300	158	6	be	be	AUX
cana-1300	158	7	altered	alter	VERB
cana-1300	158	8	.	.	PUNCT
cana-1300	159	1	let	let	VERB
cana-1300	159	2	us	we	PRON
cana-1300	159	3	consider	consider	VERB
cana-1300	159	4	another	another	DET
cana-1300	159	5	edge	edge	NOUN
cana-1300	159	6	𝑓24=	𝑓24=	PROPN
cana-1300	159	7	(	(	PUNCT
cana-1300	159	8	𝑤3,𝑤4	𝑤3,𝑤4	PROPN
cana-1300	159	9	)	)	PUNCT
cana-1300	159	10	.	.	PUNCT
cana-1300	160	1	if	if	SCONJ
cana-1300	160	2	the	the	DET
cana-1300	160	3	set	set	NOUN
cana-1300	160	4	𝐷	𝐷	PROPN
cana-1300	160	5	along	along	ADP
cana-1300	160	6	with	with	ADP
cana-1300	160	7	𝑓24	𝑓24	NOUN
cana-1300	160	8	covers	cover	VERB
cana-1300	160	9	all	all	DET
cana-1300	160	10	the	the	DET
cana-1300	160	11	edges	edge	NOUN
cana-1300	160	12	of	of	ADP
cana-1300	160	13	𝐺	𝐺	PROPN
cana-1300	160	14	then	then	ADV
cana-1300	160	15	the	the	DET
cana-1300	160	16	set	set	NOUN
cana-1300	160	17	𝐷	𝐷	PROPN
cana-1300	160	18	=	=	PUNCT
cana-1300	160	19	{	{	PUNCT
cana-1300	160	20	𝑓1	𝑓1	PROPN
cana-1300	160	21	,	,	PUNCT
cana-1300	160	22	𝑓24	𝑓24	PROPN
cana-1300	160	23	}	}	PUNCT
cana-1300	160	24	becomes	become	VERB
cana-1300	160	25	an	an	DET
cana-1300	160	26	edge	edge	NOUN
cana-1300	160	27	dominating	dominating	NOUN
cana-1300	160	28	set	set	NOUN
cana-1300	160	29	for	for	ADP
cana-1300	160	30	𝐺.	𝐺.	PROPN
cana-1300	160	31	but	but	CCONJ
cana-1300	160	32	𝐷	𝐷	NOUN
cana-1300	160	33	covers	cover	VERB
cana-1300	160	34	only	only	ADV
cana-1300	160	35	a	a	DET
cana-1300	160	36	partial	partial	ADJ
cana-1300	160	37	part	part	NOUN
cana-1300	160	38	of	of	ADP
cana-1300	160	39	edges	edge	NOUN
cana-1300	160	40	of	of	ADP
cana-1300	160	41	𝐺.	𝐺.	NOUN
cana-1300	160	42	continuously	continuously	ADV
cana-1300	160	43	altering	alter	VERB
cana-1300	160	44	the	the	DET
cana-1300	160	45	set	set	NOUN
cana-1300	160	46	𝐷	𝐷	NOUN
cana-1300	160	47	by	by	ADP
cana-1300	160	48	including	include	VERB
cana-1300	160	49	the	the	DET
cana-1300	160	50	required	require	VERB
cana-1300	160	51	number	number	NOUN
cana-1300	160	52	of	of	ADP
cana-1300	160	53	edges	edge	NOUN
cana-1300	160	54	,	,	PUNCT
cana-1300	160	55	finally	finally	ADV
cana-1300	160	56	we	we	PRON
cana-1300	160	57	arrive	arrive	VERB
cana-1300	160	58	at	at	ADP
cana-1300	160	59	a	a	DET
cana-1300	160	60	stage	stage	NOUN
cana-1300	160	61	where	where	SCONJ
cana-1300	160	62	the	the	DET
cana-1300	160	63	set	set	NOUN
cana-1300	160	64	𝐷	𝐷	NOUN
cana-1300	160	65	becomes	become	VERB
cana-1300	160	66	an	an	DET
cana-1300	160	67	edge	edge	NOUN
cana-1300	160	68	dominating	dominating	NOUN
cana-1300	160	69	set	set	NOUN
cana-1300	160	70	given	give	VERB
cana-1300	160	71	by	by	ADP
cana-1300	160	72	𝐷	𝐷	PROPN
cana-1300	160	73	=	=	SYM
cana-1300	160	74	{	{	PUNCT
cana-1300	160	75	𝑓1	𝑓1	PROPN
cana-1300	160	76	,	,	PUNCT
cana-1300	160	77	𝑓24	𝑓24	PROPN
cana-1300	160	78	,	,	PUNCT
cana-1300	160	79	𝑓43	𝑓43	NOUN
cana-1300	160	80	,	,	PUNCT
cana-1300	160	81	𝑓57	𝑓57	NOUN
cana-1300	160	82	,	,	PUNCT
cana-1300	160	83	𝑓68	𝑓68	NUM
cana-1300	160	84	,	,	PUNCT
cana-1300	160	85	𝑓77	𝑓77	PROPN
cana-1300	160	86	}	}	PUNCT
cana-1300	160	87	.	.	PUNCT
cana-1300	161	1	therefore	therefore	ADV
cana-1300	161	2	𝛾′𝑠(𝐺	𝛾′𝑠(𝐺	VERB
cana-1300	161	3	)	)	PUNCT
cana-1300	161	4	=	=	SYM
cana-1300	161	5	6	6	NUM
cana-1300	161	6	.	.	PUNCT
cana-1300	162	1	𝐷	𝐷	PROPN
cana-1300	162	2	also	also	ADV
cana-1300	162	3	induces	induce	VERB
cana-1300	162	4	a	a	DET
cana-1300	162	5	apical	apical	ADJ
cana-1300	162	6	subgraph	subgraph	NOUN
cana-1300	162	7	.	.	PUNCT
cana-1300	163	1	as	as	ADP
cana-1300	163	2	a	a	DET
cana-1300	163	3	result	result	NOUN
cana-1300	163	4	,	,	PUNCT
cana-1300	163	5	set	set	VERB
cana-1300	163	6	𝐷	𝐷	PROPN
cana-1300	163	7	is	be	AUX
cana-1300	163	8	also	also	ADV
cana-1300	163	9	a	a	DET
cana-1300	163	10	connected	connected	ADJ
cana-1300	163	11	edge	edge	NOUN
cana-1300	163	12	dominating	dominating	NOUN
cana-1300	163	13	set	set	NOUN
cana-1300	163	14	.	.	PUNCT
cana-1300	164	1	therefore	therefore	ADV
cana-1300	164	2	we	we	PRON
cana-1300	164	3	can	can	AUX
cana-1300	164	4	conclude	conclude	VERB
cana-1300	164	5	that	that	PRON
cana-1300	164	6	𝛾′𝑠(𝐺	𝛾′𝑠(𝐺	PROPN
cana-1300	164	7	)	)	PUNCT
cana-1300	164	8	=	=	SYM
cana-1300	164	9	𝛾′𝑐𝑠(𝐺	𝛾′𝑐𝑠(𝐺	NOUN
cana-1300	164	10	)	)	PUNCT
cana-1300	164	11	=	=	SYM
cana-1300	164	12	6	6	NUM
cana-1300	164	13	.	.	PUNCT
cana-1300	164	14	□	□	PUNCT
cana-1300	164	15	theorem	theorem	ADJ
cana-1300	164	16	4.5	4.5	NUM
cana-1300	164	17	:	:	PUNCT
cana-1300	164	18	the	the	DET
cana-1300	164	19	following	follow	VERB
cana-1300	164	20	conditions	condition	NOUN
cana-1300	164	21	must	must	AUX
cana-1300	164	22	apply	apply	VERB
cana-1300	164	23	for	for	ADP
cana-1300	164	24	each	each	DET
cana-1300	164	25	vertex	vertex	NOUN
cana-1300	164	26	𝑣	𝑣	ADP
cana-1300	164	27	∈	∈	PROPN
cana-1300	164	28	𝐷	𝐷	NOUN
cana-1300	164	29	in	in	ADP
cana-1300	164	30	order	order	NOUN
cana-1300	164	31	for	for	SCONJ
cana-1300	164	32	an	an	DET
cana-1300	164	33	outer	outer	ADJ
cana-1300	164	34	connected	connected	ADJ
cana-1300	164	35	dominating	dominating	NOUN
cana-1300	164	36	set	set	VERB
cana-1300	164	37	𝐷	𝐷	PROPN
cana-1300	164	38	of	of	ADP
cana-1300	164	39	𝐺	𝐺	PROPN
cana-1300	164	40	to	to	PART
cana-1300	164	41	be	be	AUX
cana-1300	164	42	minimal	minimal	ADJ
cana-1300	164	43	:	:	PUNCT
cana-1300	164	44	a	a	X
cana-1300	164	45	)	)	PUNCT
cana-1300	164	46	𝑃𝑟[𝑣	𝑃𝑟[𝑣	NOUN
cana-1300	164	47	,	,	PUNCT
cana-1300	164	48	𝐷	𝐷	PROPN
cana-1300	164	49	]	]	PUNCT
cana-1300	164	50	≠	≠	PROPN
cana-1300	164	51	∅	∅	NOUN
cana-1300	164	52	communications	communication	NOUN
cana-1300	164	53	on	on	ADP
cana-1300	164	54	applied	apply	VERB
cana-1300	164	55	nonlinear	nonlinear	ADJ
cana-1300	164	56	analysis	analysis	NOUN
cana-1300	164	57	issn	issn	NOUN
cana-1300	164	58	:	:	PUNCT
cana-1300	164	59	1074	1074	NUM
cana-1300	164	60	-	-	PUNCT
cana-1300	164	61	133x	133x	NUM
cana-1300	164	62	vol	vol	NOUN
cana-1300	164	63	31	31	NUM
cana-1300	164	64	no	no	NOUN
cana-1300	164	65	.	.	PUNCT
cana-1300	165	1	7s	7	NOUN
cana-1300	165	2	(	(	PUNCT
cana-1300	165	3	2024	2024	NUM
cana-1300	165	4	)	)	PUNCT
cana-1300	165	5	258	258	NUM
cana-1300	165	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-1300	165	7	b	b	X
cana-1300	165	8	)	)	PUNCT
cana-1300	165	9	in	in	ADP
cana-1300	165	10	the	the	DET
cana-1300	165	11	graph	graph	NOUN
cana-1300	165	12	that	that	PRON
cana-1300	165	13	𝐷	𝐷	NOUN
cana-1300	165	14	induced	induce	VERB
cana-1300	165	15	,	,	PUNCT
cana-1300	165	16	𝑣	𝑣	PRON
cana-1300	165	17	is	be	AUX
cana-1300	165	18	a	a	DET
cana-1300	165	19	isolated	isolated	ADJ
cana-1300	165	20	vertex	vertex	NOUN
cana-1300	165	21	.	.	PUNCT
cana-1300	166	1	c	c	X
cana-1300	166	2	)	)	PUNCT
cana-1300	166	3	𝑁(𝑣	𝑁(𝑣	X
cana-1300	166	4	)	)	PUNCT
cana-1300	166	5	∩	∩	NOUN
cana-1300	166	6	(	(	PUNCT
cana-1300	166	7	𝑉	𝑉	PROPN
cana-1300	166	8	∖	∖	PROPN
cana-1300	166	9	𝐷	𝐷	NOUN
cana-1300	166	10	)	)	PUNCT
cana-1300	166	11	=	=	NOUN
cana-1300	166	12	∅	∅	NOUN
cana-1300	166	13	proof	proof	NOUN
cana-1300	166	14	:	:	PUNCT
cana-1300	166	15	firstly	firstly	ADV
cana-1300	166	16	,	,	PUNCT
cana-1300	166	17	prove	prove	VERB
cana-1300	166	18	sufficiency	sufficiency	NOUN
cana-1300	166	19	.	.	PUNCT
cana-1300	167	1	if	if	SCONJ
cana-1300	167	2	none	none	NOUN
cana-1300	167	3	of	of	ADP
cana-1300	167	4	the	the	DET
cana-1300	167	5	three	three	NUM
cana-1300	167	6	conditions	condition	NOUN
cana-1300	167	7	are	be	AUX
cana-1300	167	8	true	true	ADJ
cana-1300	167	9	under	under	ADP
cana-1300	167	10	the	the	DET
cana-1300	167	11	assumption	assumption	NOUN
cana-1300	167	12	of	of	ADP
cana-1300	167	13	the	the	DET
cana-1300	167	14	necessity	necessity	NOUN
cana-1300	167	15	part	part	NOUN
cana-1300	167	16	,	,	PUNCT
cana-1300	167	17	then	then	ADV
cana-1300	167	18	there	there	PRON
cana-1300	167	19	is	be	VERB
cana-1300	167	20	a	a	DET
cana-1300	167	21	vertex	vertex	NOUN
cana-1300	167	22	𝑣	𝑣	PRON
cana-1300	167	23	∈	∈	NOUN
cana-1300	167	24	𝐷in	𝐷in	PROPN
cana-1300	167	25	order	order	NOUN
cana-1300	167	26	to𝐷′	to𝐷′	NOUN
cana-1300	167	27	=	=	SYM
cana-1300	167	28	𝐷	𝐷	PROPN
cana-1300	167	29	∖	∖	NOUN
cana-1300	167	30	{	{	PUNCT
cana-1300	167	31	𝑣	𝑣	NOUN
cana-1300	167	32	}	}	PUNCT
cana-1300	167	33	is	be	AUX
cana-1300	167	34	the	the	DET
cana-1300	167	35	dominating	dominating	NOUN
cana-1300	167	36	set	set	NOUN
cana-1300	167	37	of	of	ADP
cana-1300	167	38	𝐺.the	𝐺.the	DET
cana-1300	167	39	(	(	PUNCT
cana-1300	167	40	𝑉	𝑉	PROPN
cana-1300	167	41	∖	∖	NOUN
cana-1300	167	42	𝐷′)induced	𝐷′)induce	VERB
cana-1300	167	43	graph	graph	NOUN
cana-1300	167	44	is	be	AUX
cana-1300	167	45	connected	connect	VERB
cana-1300	167	46	when	when	SCONJ
cana-1300	167	47	𝑁(𝑣	𝑁(𝑣	X
cana-1300	167	48	)	)	PUNCT
cana-1300	167	49	∩	∩	NOUN
cana-1300	167	50	(	(	PUNCT
cana-1300	167	51	𝑉	𝑉	PROPN
cana-1300	167	52	∖	∖	NOUN
cana-1300	167	53	𝐷′	𝐷′	NOUN
cana-1300	167	54	)	)	PUNCT
cana-1300	167	55	≠	≠	PROPN
cana-1300	167	56	∅.	∅.	PRON
cana-1300	167	57	this	this	PRON
cana-1300	167	58	implies	imply	VERB
cana-1300	167	59	𝐷′	𝐷′	PROPN
cana-1300	167	60	is	be	AUX
cana-1300	167	61	an	an	DET
cana-1300	167	62	outer	outer	ADJ
cana-1300	167	63	connected	connected	ADJ
cana-1300	167	64	dominating	dominating	NOUN
cana-1300	167	65	set	set	NOUN
cana-1300	167	66	of	of	ADP
cana-1300	167	67	𝐺	𝐺	PROPN
cana-1300	167	68	with	with	ADP
cana-1300	167	69	inconsiderable	inconsiderable	ADJ
cana-1300	167	70	number	number	NOUN
cana-1300	167	71	of	of	ADP
cana-1300	167	72	elements	element	NOUN
cana-1300	167	73	than	than	ADP
cana-1300	167	74	𝐷	𝐷	PROPN
cana-1300	167	75	,	,	PUNCT
cana-1300	167	76	which	which	PRON
cana-1300	167	77	is	be	AUX
cana-1300	167	78	a	a	DET
cana-1300	167	79	paradox	paradox	NOUN
cana-1300	167	80	.	.	PUNCT
cana-1300	168	1	next	next	ADV
cana-1300	168	2	,	,	PUNCT
cana-1300	168	3	it	it	PRON
cana-1300	168	4	is	be	AUX
cana-1300	168	5	easy	easy	ADJ
cana-1300	168	6	to	to	PART
cana-1300	168	7	prove	prove	VERB
cana-1300	168	8	the	the	DET
cana-1300	168	9	necessary	necessary	ADJ
cana-1300	168	10	condition	condition	NOUN
cana-1300	168	11	under	under	ADP
cana-1300	168	12	the	the	DET
cana-1300	168	13	assumption	assumption	NOUN
cana-1300	168	14	of	of	ADP
cana-1300	168	15	the	the	DET
cana-1300	168	16	sufficiency	sufficiency	NOUN
cana-1300	168	17	condition	condition	NOUN
cana-1300	168	18	.	.	PUNCT
cana-1300	169	1	□	□	PUNCT
cana-1300	169	2	theorem	theorem	ADJ
cana-1300	169	3	4.6	4.6	NUM
cana-1300	169	4	:	:	PUNCT
cana-1300	169	5	for	for	ADP
cana-1300	169	6	a	a	DET
cana-1300	169	7	graph,𝛾𝑐	graph,𝛾𝑐	NOUN
cana-1300	169	8	~(𝐺	~(𝐺	NUM
cana-1300	169	9	)	)	PUNCT
cana-1300	169	10	≤	≤	NUM
cana-1300	169	11	𝑛	𝑛	DET
cana-1300	169	12	−	−	PROPN
cana-1300	169	13	𝑤(𝐺	𝑤(𝐺	NOUN
cana-1300	169	14	)	)	PUNCT
cana-1300	170	1	+	+	CCONJ
cana-1300	170	2	1where	1where	NUM
cana-1300	170	3	𝑤(𝐺	𝑤(𝐺	NOUN
cana-1300	170	4	)	)	PUNCT
cana-1300	170	5	,	,	PUNCT
cana-1300	170	6	clique	clique	ADJ
cana-1300	170	7	number	number	NOUN
cana-1300	170	8	.	.	PUNCT
cana-1300	171	1	proof	proof	NOUN
cana-1300	171	2	:	:	PUNCT
cana-1300	171	3	assume	assume	VERB
cana-1300	171	4	vertex	vertex	NOUN
cana-1300	171	5	set	set	NOUN
cana-1300	171	6	𝐴	𝐴	PROPN
cana-1300	171	7	is	be	AUX
cana-1300	171	8	such	such	ADJ
cana-1300	171	9	that	that	SCONJ
cana-1300	171	10	|𝐴|	|𝐴|	NOUN
cana-1300	171	11	=	=	SYM
cana-1300	171	12	𝑤(𝐺	𝑤(𝐺	NOUN
cana-1300	171	13	)	)	PUNCT
cana-1300	171	14	and	and	CCONJ
cana-1300	171	15	the	the	DET
cana-1300	171	16	subgraph	subgraph	NOUN
cana-1300	171	17	𝐴	𝐴	PROPN
cana-1300	171	18	is	be	AUX
cana-1300	171	19	complete	complete	ADJ
cana-1300	171	20	.	.	PUNCT
cana-1300	172	1	now	now	ADV
cana-1300	172	2	,	,	PUNCT
cana-1300	172	3	since	since	SCONJ
cana-1300	172	4	(	(	PUNCT
cana-1300	172	5	𝑉	𝑉	PROPN
cana-1300	172	6	∖	∖	PROPN
cana-1300	172	7	𝐴	𝐴	PROPN
cana-1300	172	8	)	)	PUNCT
cana-1300	172	9	∪	∪	VERB
cana-1300	172	10	{	{	PUNCT
cana-1300	172	11	𝑢}is	𝑢}is	PROPN
cana-1300	172	12	an	an	DET
cana-1300	172	13	outer	outer	ADJ
cana-1300	172	14	connected	connected	ADJ
cana-1300	172	15	dominating	dominating	NOUN
cana-1300	172	16	set	set	NOUN
cana-1300	172	17	of	of	ADP
cana-1300	172	18	𝐺	𝐺	PROPN
cana-1300	172	19	,	,	PUNCT
cana-1300	172	20	for	for	ADP
cana-1300	172	21	any	any	DET
cana-1300	172	22	𝑢	𝑢	PROPN
cana-1300	172	23	∈	∈	NOUN
cana-1300	172	24	𝐴.	𝐴.	NOUN
cana-1300	172	25	thus	thus	ADV
cana-1300	172	26	result	result	NOUN
cana-1300	172	27	follows	follow	VERB
cana-1300	172	28	.	.	PUNCT
cana-1300	173	1	theorem	theorem	VERB
cana-1300	173	2	4.7	4.7	NUM
cana-1300	173	3	:	:	PUNCT
cana-1300	173	4	if	if	SCONJ
cana-1300	173	5	𝐿(𝐺	𝐿(𝐺	PROPN
cana-1300	173	6	)	)	PUNCT
cana-1300	173	7	>	>	X
cana-1300	174	1	𝛽0(𝐺	𝛽0(𝐺	PROPN
cana-1300	174	2	)	)	PUNCT
cana-1300	174	3	,	,	PUNCT
cana-1300	174	4	then	then	ADV
cana-1300	174	5	𝛾𝑐	𝛾𝑐	VERB
cana-1300	174	6	~(𝐺	~(𝐺	NUM
cana-1300	174	7	)	)	PUNCT
cana-1300	174	8	≥	≥	NOUN
cana-1300	174	9	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1300	174	10	)	)	PUNCT
cana-1300	174	11	where	where	SCONJ
cana-1300	174	12	l(𝐺	l(𝐺	PROPN
cana-1300	174	13	)	)	PUNCT
cana-1300	174	14	is	be	AUX
cana-1300	174	15	the	the	DET
cana-1300	174	16	vertex	vertex	NOUN
cana-1300	174	17	connectivity	connectivity	NOUN
cana-1300	174	18	of	of	ADP
cana-1300	174	19	𝐺	𝐺	PROPN
cana-1300	174	20	and	and	CCONJ
cana-1300	174	21	𝛽0(𝐺)is	𝛽0(𝐺)is	PROPN
cana-1300	174	22	vertex	vertex	NOUN
cana-1300	174	23	independence	independence	NOUN
cana-1300	174	24	number	number	NOUN
cana-1300	174	25	of	of	ADP
cana-1300	174	26	𝐺	𝐺	PROPN
cana-1300	174	27	proof	proof	NOUN
cana-1300	174	28	:	:	PUNCT
cana-1300	174	29	let	let	VERB
cana-1300	174	30	dominating	dominating	NOUN
cana-1300	174	31	set	set	NOUN
cana-1300	174	32	be	be	AUX
cana-1300	174	33	𝐷in	𝐷in	PROPN
cana-1300	174	34	𝐺.	𝐺.	PROPN
cana-1300	174	35	since𝛾(𝐺	since𝛾(𝐺	PROPN
cana-1300	174	36	)	)	PUNCT
cana-1300	174	37	≤	≤	PUNCT
cana-1300	174	38	𝛽0(𝐺	𝛽0(𝐺	PROPN
cana-1300	174	39	)	)	PUNCT
cana-1300	174	40	≤	≤	PUNCT
cana-1300	175	1	𝐿(𝐺)	𝐿(𝐺)	PROPN
cana-1300	175	2	................	................	PUNCT
cana-1300	175	3	(1	(1	PROPN
cana-1300	175	4	)	)	PUNCT
cana-1300	176	1	it	it	PRON
cana-1300	176	2	follows	follow	VERB
cana-1300	176	3	that	that	SCONJ
cana-1300	176	4	𝑉	𝑉	PROPN
cana-1300	176	5	∖	∖	PUNCT
cana-1300	176	6	𝐷	𝐷	NOUN
cana-1300	176	7	is	be	AUX
cana-1300	176	8	connected	connect	VERB
cana-1300	176	9	.	.	PUNCT
cana-1300	177	1	we	we	PRON
cana-1300	177	2	have	have	VERB
cana-1300	177	3	𝛾𝑐	𝛾𝑐	NUM
cana-1300	177	4	~(𝐺	~(𝐺	NUM
cana-1300	177	5	)	)	PUNCT
cana-1300	177	6	≤	≤	PUNCT
cana-1300	178	1	𝐿(𝐺)	𝐿(𝐺)	PROPN
cana-1300	178	2	...............	...............	PUNCT
cana-1300	178	3	(2	(2	PROPN
cana-1300	178	4	)	)	PUNCT
cana-1300	178	5	.	.	PUNCT
cana-1300	179	1	subtracting	subtract	VERB
cana-1300	179	2	(	(	PUNCT
cana-1300	179	3	2	2	NUM
cana-1300	179	4	)	)	PUNCT
cana-1300	179	5	from	from	ADP
cana-1300	179	6	(	(	PUNCT
cana-1300	179	7	1	1	NUM
cana-1300	179	8	)	)	PUNCT
cana-1300	179	9	𝛾(𝐺	𝛾(𝐺	NOUN
cana-1300	179	10	)	)	PUNCT
cana-1300	180	1	−	−	NOUN
cana-1300	180	2	𝛾𝑐	𝛾𝑐	NOUN
cana-1300	180	3	~(𝐺	~(𝐺	NUM
cana-1300	180	4	)	)	PUNCT
cana-1300	180	5	≤	≤	NOUN
cana-1300	180	6	0	0	NUM
cana-1300	180	7	.	.	PUNCT
cana-1300	181	1	thus	thus	ADV
cana-1300	181	2	𝛾𝑐	𝛾𝑐	ADP
cana-1300	181	3	~(𝐺	~(𝐺	NUM
cana-1300	181	4	)	)	PUNCT
cana-1300	181	5	≥	≥	NOUN
cana-1300	181	6	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1300	181	7	)	)	PUNCT
cana-1300	181	8	.	.	PUNCT
cana-1300	182	1	□	□	PUNCT
cana-1300	182	2	theorem	theorem	ADJ
cana-1300	182	3	4.8	4.8	NUM
cana-1300	182	4	:	:	PUNCT
cana-1300	182	5	for	for	ADP
cana-1300	182	6	each	each	DET
cana-1300	182	7	graph𝒢	graph𝒢	PROPN
cana-1300	182	8	,	,	PUNCT
cana-1300	182	9	𝛾𝑐	𝛾𝑐	ADP
cana-1300	182	10	~(𝐺	~(𝐺	NUM
cana-1300	182	11	)	)	PUNCT
cana-1300	182	12	≤	≤	NUM
cana-1300	183	1	|𝑉(𝐺)|	|𝑉(𝐺)|	ADP
cana-1300	183	2	−	−	NOUN
cana-1300	183	3	𝑑𝑖𝑎𝑚(𝐺	𝑑𝑖𝑎𝑚(𝐺	PRON
cana-1300	183	4	)	)	PUNCT
cana-1300	183	5	+	+	CCONJ
cana-1300	183	6	𝑠	𝑠	PROPN
cana-1300	184	1	+	+	NOUN
cana-1300	184	2	1	1	NUM
cana-1300	184	3	where	where	SCONJ
cana-1300	184	4	𝑠	𝑠	PROPN
cana-1300	184	5	is	be	AUX
cana-1300	184	6	a	a	DET
cana-1300	184	7	𝛾𝑐	𝛾𝑐	NOUN
cana-1300	184	8	~set	~set	NOUN
cana-1300	184	9	𝐷	𝐷	PROPN
cana-1300	184	10	of	of	ADP
cana-1300	184	11	's	's	PART
cana-1300	184	12	minimal	minimal	ADJ
cana-1300	184	13	number	number	NOUN
cana-1300	184	14	of	of	ADP
cana-1300	184	15	vertices	vertex	NOUN
cana-1300	184	16	.	.	PUNCT
cana-1300	185	1	proof	proof	NOUN
cana-1300	185	2	:	:	PUNCT
cana-1300	185	3	let	let	VERB
cana-1300	185	4	𝑑𝑖𝑎𝑚(𝐺	𝑑𝑖𝑎𝑚(𝐺	PRON
cana-1300	185	5	)	)	PUNCT
cana-1300	186	1	=	=	PUNCT
cana-1300	186	2	𝑡.	𝑡.	NOUN
cana-1300	186	3	then	then	ADV
cana-1300	186	4	there	there	PRON
cana-1300	186	5	are	be	VERB
cana-1300	186	6	three	three	NUM
cana-1300	186	7	possibilities	possibility	NOUN
cana-1300	186	8	.	.	PUNCT
cana-1300	187	1	first	first	ADV
cana-1300	187	2	,	,	PUNCT
cana-1300	187	3	it	it	PRON
cana-1300	187	4	may	may	AUX
cana-1300	187	5	occur	occur	VERB
cana-1300	187	6	that	that	SCONJ
cana-1300	187	7	𝑥	𝑥	PROPN
cana-1300	187	8	,	,	PUNCT
cana-1300	187	9	𝑦	𝑦	NOUN
cana-1300	187	10	∈	∈	PROPN
cana-1300	187	11	𝑉\𝐷.	𝑉\𝐷.	PROPN
cana-1300	187	12	then	then	ADV
cana-1300	187	13	note	note	VERB
cana-1300	187	14	that	that	SCONJ
cana-1300	187	15	in	in	ADP
cana-1300	187	16	this	this	DET
cana-1300	187	17	case	case	NOUN
cana-1300	187	18	,	,	PUNCT
cana-1300	187	19	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1300	187	20	has	have	AUX
cana-1300	187	21	atleast	atleast	VERB
cana-1300	187	22	𝑡	𝑡	ADP
cana-1300	187	23	+	+	NOUN
cana-1300	187	24	1	1	NUM
cana-1300	187	25	vertices	vertex	NOUN
cana-1300	187	26	.	.	PUNCT
cana-1300	188	1	second	second	ADV
cana-1300	188	2	it	it	PRON
cana-1300	188	3	may	may	AUX
cana-1300	188	4	be	be	AUX
cana-1300	188	5	the	the	DET
cana-1300	188	6	case	case	NOUN
cana-1300	188	7	that	that	SCONJ
cana-1300	188	8	𝑥	𝑥	PRON
cana-1300	188	9	∈	∈	PROPN
cana-1300	188	10	𝐷	𝐷	PROPN
cana-1300	188	11	&	&	CCONJ
cana-1300	188	12	𝑦	𝑦	NOUN
cana-1300	188	13	∈	∈	PROPN
cana-1300	188	14	𝑉\𝐷.	𝑉\𝐷.	PROPN
cana-1300	189	1	if	if	SCONJ
cana-1300	189	2	there	there	PRON
cana-1300	189	3	is	be	VERB
cana-1300	189	4	a	a	DET
cana-1300	189	5	vertex	vertex	NOUN
cana-1300	189	6	𝑥1	𝑥1	NOUN
cana-1300	189	7	∈	∈	PROPN
cana-1300	189	8	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1300	189	9	such	such	ADJ
cana-1300	189	10	that	that	SCONJ
cana-1300	189	11	𝑥1	𝑥1	NOUN
cana-1300	189	12	is	be	AUX
cana-1300	189	13	connected	connect	VERB
cana-1300	189	14	to	to	ADP
cana-1300	189	15	x	x	PUNCT
cana-1300	189	16	by	by	ADP
cana-1300	189	17	way	way	NOUN
cana-1300	189	18	of	of	ADP
cana-1300	189	19	the	the	DET
cana-1300	189	20	vertices	vertex	NOUN
cana-1300	189	21	in	in	ADP
cana-1300	189	22	𝐷.	𝐷.	PROPN
cana-1300	189	23	then	then	ADV
cana-1300	189	24	this	this	PRON
cana-1300	189	25	implies	imply	VERB
cana-1300	189	26	that	that	SCONJ
cana-1300	189	27	𝑑(𝑥	𝑑(𝑥	PROPN
cana-1300	189	28	,	,	PUNCT
cana-1300	189	29	𝑦	𝑦	NOUN
cana-1300	189	30	)	)	PUNCT
cana-1300	189	31	≥	≥	NOUN
cana-1300	189	32	𝑘	𝑘	ADV
cana-1300	189	33	−	−	PROPN
cana-1300	189	34	(	(	PUNCT
cana-1300	189	35	𝑡	𝑡	X
cana-1300	189	36	+	+	NOUN
cana-1300	189	37	1	1	NUM
cana-1300	189	38	)	)	PUNCT
cana-1300	189	39	and	and	CCONJ
cana-1300	189	40	hence	hence	ADV
cana-1300	189	41	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1300	189	42	has	have	AUX
cana-1300	189	43	atleast	atleast	VERB
cana-1300	189	44	𝑡	𝑡	ADP
cana-1300	189	45	−	−	NOUN
cana-1300	189	46	𝑠	𝑠	PROPN
cana-1300	189	47	vertices	vertex	NOUN
cana-1300	189	48	.	.	PUNCT
cana-1300	190	1	this	this	PRON
cana-1300	190	2	is	be	AUX
cana-1300	190	3	because	because	SCONJ
cana-1300	190	4	in	in	ADP
cana-1300	190	5	the	the	DET
cana-1300	190	6	opposite	opposite	ADJ
cana-1300	190	7	case	case	NOUN
cana-1300	190	8	,	,	PUNCT
cana-1300	190	9	there	there	PRON
cana-1300	190	10	is	be	VERB
cana-1300	190	11	an	an	DET
cana-1300	190	12	adjacent	adjacent	ADJ
cana-1300	190	13	vertex	vertex	NOUN
cana-1300	190	14	z	z	NOUN
cana-1300	190	15	to	to	ADP
cana-1300	190	16	each	each	DET
cana-1300	190	17	𝑥1	𝑥1	NOUN
cana-1300	190	18	∈	∈	PROPN
cana-1300	190	19	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1300	190	20	such	such	ADJ
cana-1300	190	21	that	that	SCONJ
cana-1300	190	22	𝑑(𝑥	𝑑(𝑥	PROPN
cana-1300	190	23	,	,	PUNCT
cana-1300	190	24	𝑧	𝑧	NOUN
cana-1300	190	25	)	)	PUNCT
cana-1300	190	26	=	=	SYM
cana-1300	190	27	𝑑(𝑥	𝑑(𝑥	PROPN
cana-1300	190	28	,	,	PUNCT
cana-1300	190	29	𝑦	𝑦	NOUN
cana-1300	190	30	)	)	PUNCT
cana-1300	190	31	+	+	CCONJ
cana-1300	190	32	𝑑(𝑦	𝑑(𝑦	NOUN
cana-1300	190	33	,	,	PUNCT
cana-1300	190	34	𝑥1	𝑥1	NOUN
cana-1300	190	35	)	)	PUNCT
cana-1300	190	36	+	+	X
cana-1300	190	37	𝑑(𝑥1	𝑑(𝑥1	ADV
cana-1300	190	38	,	,	PUNCT
cana-1300	190	39	𝑧	𝑧	NOUN
cana-1300	190	40	)	)	PUNCT
cana-1300	190	41	≥	≥	NOUN
cana-1300	190	42	𝑡	𝑡	X
cana-1300	190	43	+	+	NOUN
cana-1300	190	44	1	1	NUM
cana-1300	190	45	,	,	PUNCT
cana-1300	190	46	which	which	PRON
cana-1300	190	47	is	be	AUX
cana-1300	190	48	a	a	DET
cana-1300	190	49	contradiction	contradiction	NOUN
cana-1300	190	50	.	.	PUNCT
cana-1300	191	1	in	in	ADP
cana-1300	191	2	this	this	DET
cana-1300	191	3	incident	incident	NOUN
cana-1300	191	4	,	,	PUNCT
cana-1300	191	5	we	we	PRON
cana-1300	191	6	have	have	VERB
cana-1300	191	7	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1300	191	8	=	=	SYM
cana-1300	191	9	{	{	PUNCT
cana-1300	191	10	𝑦	𝑦	NOUN
cana-1300	191	11	}	}	PUNCT
cana-1300	191	12	.	.	PUNCT
cana-1300	192	1	finally	finally	ADV
cana-1300	192	2	,	,	PUNCT
cana-1300	192	3	it	it	PRON
cana-1300	192	4	may	may	AUX
cana-1300	192	5	be	be	AUX
cana-1300	192	6	an	an	DET
cana-1300	192	7	instance	instance	NOUN
cana-1300	192	8	of	of	ADP
cana-1300	192	9	𝑥	𝑥	PROPN
cana-1300	192	10	,	,	PUNCT
cana-1300	192	11	𝑦	𝑦	PROPN
cana-1300	192	12	∈	∈	PROPN
cana-1300	192	13	𝐷.	𝐷.	NOUN
cana-1300	192	14	assume	assume	VERB
cana-1300	192	15	that	that	SCONJ
cana-1300	192	16	there	there	PRON
cana-1300	192	17	is	be	VERB
cana-1300	192	18	𝑥1	𝑥1	NOUN
cana-1300	192	19	,	,	PUNCT
cana-1300	192	20	𝑦1	𝑦1	PROPN
cana-1300	192	21	∈	∈	PROPN
cana-1300	192	22	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1300	192	23	such	such	ADJ
cana-1300	192	24	that	that	SCONJ
cana-1300	192	25	𝑥	𝑥	PROPN
cana-1300	192	26	is	be	AUX
cana-1300	192	27	connected	connect	VERB
cana-1300	192	28	to	to	ADP
cana-1300	192	29	𝑥1	𝑥1	NOUN
cana-1300	192	30	and	and	CCONJ
cana-1300	192	31	𝑦	𝑦	NOUN
cana-1300	192	32	is	be	AUX
cana-1300	192	33	connected	connect	VERB
cana-1300	192	34	to	to	ADP
cana-1300	192	35	𝑦1	𝑦1	PROPN
cana-1300	192	36	by	by	ADP
cana-1300	192	37	way	way	NOUN
cana-1300	192	38	of	of	ADP
cana-1300	192	39	the	the	DET
cana-1300	192	40	vertices	vertex	NOUN
cana-1300	192	41	of	of	ADP
cana-1300	192	42	𝐷.	𝐷.	PROPN
cana-1300	192	43	then	then	ADV
cana-1300	192	44	𝑑(𝑥1	𝑑(𝑥1	ADV
cana-1300	192	45	,	,	PUNCT
cana-1300	192	46	𝑦1	𝑦1	PROPN
cana-1300	192	47	)	)	PUNCT
cana-1300	192	48	is	be	AUX
cana-1300	192	49	atleast	atleast	VERB
cana-1300	192	50	𝑡	𝑡	X
cana-1300	192	51	−	−	PROPN
cana-1300	193	1	(	(	PUNCT
cana-1300	193	2	𝑠	𝑠	PROPN
cana-1300	193	3	+	+	PROPN
cana-1300	193	4	2	2	NUM
cana-1300	193	5	)	)	PUNCT
cana-1300	193	6	and	and	CCONJ
cana-1300	193	7	hence	hence	ADV
cana-1300	193	8	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1300	193	9	has	have	AUX
cana-1300	193	10	atleast	atleast	VERB
cana-1300	193	11	(	(	PUNCT
cana-1300	193	12	𝑡	𝑡	X
cana-1300	193	13	−	−	NOUN
cana-1300	193	14	𝑠	𝑠	INTJ
cana-1300	193	15	−	−	PROPN
cana-1300	193	16	1	1	NUM
cana-1300	193	17	)	)	PUNCT
cana-1300	193	18	vertices	vertex	NOUN
cana-1300	193	19	.	.	PUNCT
cana-1300	194	1	this	this	PRON
cana-1300	194	2	is	be	AUX
cana-1300	194	3	because	because	SCONJ
cana-1300	194	4	,	,	PUNCT
cana-1300	194	5	otherwise	otherwise	ADV
cana-1300	194	6	there	there	PRON
cana-1300	194	7	is	be	VERB
cana-1300	194	8	exactly	exactly	ADV
cana-1300	194	9	one	one	NUM
cana-1300	194	10	vertex	vertex	NOUN
cana-1300	194	11	𝑥1	𝑥1	NOUN
cana-1300	194	12	∈	∈	PROPN
cana-1300	194	13	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1300	194	14	that	that	PRON
cana-1300	194	15	is	be	AUX
cana-1300	194	16	adjacent	adjacent	ADJ
cana-1300	194	17	to	to	ADP
cana-1300	194	18	both	both	PRON
cana-1300	194	19	x	x	PROPN
cana-1300	194	20	and	and	CCONJ
cana-1300	194	21	y	y	PROPN
cana-1300	194	22	and	and	CCONJ
cana-1300	194	23	𝑣\𝐷={x1	𝑣\𝐷={x1	PROPN
cana-1300	194	24	}	}	PUNCT
cana-1300	194	25	and	and	CCONJ
cana-1300	194	26	as	as	ADP
cana-1300	194	27	a	a	DET
cana-1300	194	28	consequence	consequence	NOUN
cana-1300	194	29	it	it	PRON
cana-1300	194	30	has	have	VERB
cana-1300	194	31	𝐺	𝐺	PROPN
cana-1300	194	32	≅	≅	PROPN
cana-1300	194	33	𝐾1,3	𝐾1,3	PROPN
cana-1300	194	34	.	.	PUNCT
cana-1300	195	1	so	so	ADV
cana-1300	195	2	in	in	ADP
cana-1300	195	3	all	all	DET
cana-1300	195	4	three	three	NUM
cana-1300	195	5	instances	instance	NOUN
cana-1300	195	6	𝑉\𝐷	𝑉\𝐷	NOUN
cana-1300	195	7	has	have	AUX
cana-1300	195	8	at	at	ADV
cana-1300	195	9	least	least	ADJ
cana-1300	195	10	(	(	PUNCT
cana-1300	195	11	𝑡	𝑡	X
cana-1300	195	12	−	−	NOUN
cana-1300	195	13	𝑠	𝑠	INTJ
cana-1300	195	14	−	−	PROPN
cana-1300	195	15	1	1	NUM
cana-1300	195	16	)	)	PUNCT
cana-1300	195	17	vertices	vertex	NOUN
cana-1300	195	18	.	.	PUNCT
cana-1300	196	1	theorem	theorem	VERB
cana-1300	196	2	4.9	4.9	NUM
cana-1300	196	3	:	:	PUNCT
cana-1300	196	4	if	if	SCONJ
cana-1300	196	5	𝐺	𝐺	PROPN
cana-1300	196	6	is	be	AUX
cana-1300	196	7	just	just	ADV
cana-1300	196	8	excellent	excellent	ADJ
cana-1300	196	9	,	,	PUNCT
cana-1300	196	10	then	then	ADV
cana-1300	196	11	𝛿(𝑣	𝛿(𝑣	PROPN
cana-1300	196	12	)	)	PUNCT
cana-1300	196	13	≥	≥	NOUN
cana-1300	196	14	𝑛	𝑛	DET
cana-1300	196	15	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1300	196	16	)	)	PUNCT
cana-1300	197	1	−	−	NOUN
cana-1300	197	2	1	1	NUM
cana-1300	197	3	proof	proof	NOUN
cana-1300	197	4	:	:	PUNCT
cana-1300	197	5	let	let	VERB
cana-1300	197	6	𝑉	𝑉	PROPN
cana-1300	197	7	=	=	NOUN
cana-1300	197	8	𝑆1	𝑆1	NOUN
cana-1300	197	9	∪	∪	ADJ
cana-1300	197	10	𝑆2	𝑆2	PROPN
cana-1300	197	11	∪	∪	X
cana-1300	197	12	…	…	PUNCT
cana-1300	197	13	…	…	PUNCT
cana-1300	197	14	…	…	PUNCT
cana-1300	197	15	.∪	.∪	X
cana-1300	198	1	𝑆𝑚	𝑆𝑚	NOUN
cana-1300	198	2	be	be	AUX
cana-1300	198	3	the	the	DET
cana-1300	198	4	phyletic	phyletic	NOUN
cana-1300	198	5	of	of	ADP
cana-1300	198	6	𝑉	𝑉	PROPN
cana-1300	198	7	into	into	ADP
cana-1300	198	8	𝛾	𝛾	PROPN
cana-1300	198	9	−	−	PROPN
cana-1300	198	10	𝑠𝑒𝑡	𝑠𝑒𝑡	NOUN
cana-1300	198	11	of	of	ADP
cana-1300	198	12	𝐺.	𝐺.	NOUN
cana-1300	198	13	set	set	VERB
cana-1300	198	14	up	up	ADP
cana-1300	198	15	a	a	DET
cana-1300	198	16	vertex	vertex	NOUN
cana-1300	198	17	𝑢	𝑢	ADP
cana-1300	198	18	∈	∈	PROPN
cana-1300	198	19	𝑉.	𝑉.	NOUN
cana-1300	198	20	assume	assume	VERB
cana-1300	198	21	that	that	SCONJ
cana-1300	198	22	𝑢	𝑢	PROPN
cana-1300	198	23	∈	∈	PROPN
cana-1300	198	24	𝑆𝑗	𝑆𝑗	PROPN
cana-1300	198	25	since	since	SCONJ
cana-1300	198	26	each	each	DET
cana-1300	198	27	𝑆𝑖	𝑆𝑖	PROPN
cana-1300	198	28	is	be	AUX
cana-1300	198	29	a	a	DET
cana-1300	198	30	−𝑠𝑒𝑡	−𝑠𝑒𝑡	NOUN
cana-1300	198	31	,	,	PUNCT
cana-1300	198	32	𝑢	𝑢	X
cana-1300	198	33	is	be	AUX
cana-1300	198	34	adjacent	adjacent	ADJ
cana-1300	198	35	to	to	ADP
cana-1300	198	36	not	not	PART
cana-1300	198	37	less	less	ADJ
cana-1300	198	38	than	than	ADP
cana-1300	198	39	a	a	DET
cana-1300	198	40	vertex	vertex	NOUN
cana-1300	198	41	of	of	ADP
cana-1300	198	42	𝑆𝑖,𝑖	𝑆𝑖,𝑖	NOUN
cana-1300	198	43	≠	≠	PROPN
cana-1300	198	44	𝑗.	𝑗.	NOUN
cana-1300	198	45	hence	hence	ADV
cana-1300	198	46	𝛿(𝑣	𝛿(𝑣	PROPN
cana-1300	198	47	)	)	PUNCT
cana-1300	198	48	≥	≥	NOUN
cana-1300	198	49	𝑚	𝑚	ADP
cana-1300	198	50	−	−	NUM
cana-1300	198	51	1	1	NUM
cana-1300	198	52	≥	≥	NOUN
cana-1300	198	53	𝑛	𝑛	DET
cana-1300	198	54	𝛾(𝐺	𝛾(𝐺	PROPN
cana-1300	198	55	)	)	PUNCT
cana-1300	198	56	theorem	theorem	VERB
cana-1300	198	57	4.10:𝛾(𝐺	4.10:𝛾(𝐺	NOUN
cana-1300	198	58	)	)	PUNCT
cana-1300	198	59	=	=	SYM
cana-1300	198	60	1	1	NUM
cana-1300	198	61	communications	communication	NOUN
cana-1300	198	62	on	on	ADP
cana-1300	198	63	applied	apply	VERB
cana-1300	198	64	nonlinear	nonlinear	ADJ
cana-1300	198	65	analysis	analysis	NOUN
cana-1300	198	66	issn	issn	NOUN
cana-1300	198	67	:	:	PUNCT
cana-1300	198	68	1074	1074	NUM
cana-1300	198	69	-	-	PUNCT
cana-1300	198	70	133x	133x	NUM
cana-1300	198	71	vol	vol	NOUN
cana-1300	198	72	31	31	NUM
cana-1300	198	73	no	no	NOUN
cana-1300	198	74	.	.	PUNCT
cana-1300	199	1	7s	7	NOUN
cana-1300	199	2	(	(	PUNCT
cana-1300	199	3	2024	2024	NUM
cana-1300	199	4	)	)	PUNCT
cana-1300	199	5	259	259	NUM
cana-1300	200	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1300	200	2	proof	proof	NOUN
cana-1300	200	3	:	:	PUNCT
cana-1300	200	4	we	we	PRON
cana-1300	200	5	begin	begin	VERB
cana-1300	200	6	our	our	PRON
cana-1300	200	7	assertion	assertion	NOUN
cana-1300	200	8	with	with	ADP
cana-1300	200	9	a	a	DET
cana-1300	200	10	claim	claim	NOUN
cana-1300	200	11	that	that	SCONJ
cana-1300	200	12	a	a	DET
cana-1300	200	13	dominating	dominating	NOUN
cana-1300	200	14	set	set	NOUN
cana-1300	200	15	of	of	ADP
cana-1300	200	16	𝐺	𝐺	PROPN
cana-1300	200	17	must	must	AUX
cana-1300	200	18	have	have	AUX
cana-1300	200	19	one	one	NUM
cana-1300	200	20	element	element	NOUN
cana-1300	200	21	.	.	PUNCT
cana-1300	201	1	let	let	VERB
cana-1300	201	2	us	we	PRON
cana-1300	201	3	deem	deem	VERB
cana-1300	201	4	that	that	SCONJ
cana-1300	201	5	it	it	PRON
cana-1300	201	6	is	be	AUX
cana-1300	201	7	not	not	PART
cana-1300	201	8	so	so	ADV
cana-1300	201	9	.	.	PUNCT
cana-1300	202	1	this	this	PRON
cana-1300	202	2	implies	imply	VERB
cana-1300	202	3	that	that	SCONJ
cana-1300	202	4	𝐺	𝐺	PROPN
cana-1300	202	5	has	have	VERB
cana-1300	202	6	a	a	DET
cana-1300	202	7	dominating	dominating	NOUN
cana-1300	202	8	set	set	VERB
cana-1300	202	9	𝐴	𝐴	PROPN
cana-1300	202	10	with	with	ADP
cana-1300	202	11	atleast	atleast	ADJ
cana-1300	202	12	two	two	NUM
cana-1300	202	13	elements	element	NOUN
cana-1300	202	14	.	.	PUNCT
cana-1300	203	1	notice	notice	VERB
cana-1300	203	2	that	that	SCONJ
cana-1300	203	3	𝑤2	𝑤2	NOUN
cana-1300	203	4	and	and	CCONJ
cana-1300	203	5	𝑤3	𝑤3	PROPN
cana-1300	203	6	has	have	VERB
cana-1300	203	7	the	the	DET
cana-1300	203	8	highest	high	ADJ
cana-1300	203	9	degree	degree	NOUN
cana-1300	203	10	vertices	vertex	NOUN
cana-1300	203	11	in	in	ADP
cana-1300	203	12	that	that	DET
cana-1300	203	13	order	order	NOUN
cana-1300	203	14	automatically	automatically	ADV
cana-1300	203	15	gains	gain	VERB
cana-1300	203	16	entry	entry	NOUN
cana-1300	203	17	as	as	SCONJ
cana-1300	203	18	the	the	DET
cana-1300	203	19	elements	element	NOUN
cana-1300	203	20	of	of	ADP
cana-1300	203	21	𝐷	𝐷	NOUN
cana-1300	203	22	and	and	CCONJ
cana-1300	203	23	degree	degree	NOUN
cana-1300	203	24	of	of	ADP
cana-1300	203	25	𝑤2	𝑤2	NOUN
cana-1300	203	26	and	and	CCONJ
cana-1300	203	27	𝑤3	𝑤3	PROPN
cana-1300	203	28	are	be	AUX
cana-1300	203	29	same	same	ADJ
cana-1300	203	30	.	.	PUNCT
cana-1300	204	1	moreover	moreover	ADV
cana-1300	204	2	𝑁(𝑤2	𝑁(𝑤2	PROPN
cana-1300	204	3	)	)	PUNCT
cana-1300	204	4	∩	∩	X
cana-1300	204	5	𝑁(𝑤3	𝑁(𝑤3	X
cana-1300	204	6	)	)	PUNCT
cana-1300	204	7	≠	≠	PROPN
cana-1300	204	8	∅	∅	NOUN
cana-1300	204	9	is	be	AUX
cana-1300	204	10	the	the	DET
cana-1300	204	11	reason	reason	NOUN
cana-1300	204	12	for	for	ADP
cana-1300	204	13	having	have	VERB
cana-1300	204	14	either	either	CCONJ
cana-1300	204	15	𝑤2	𝑤2	NOUN
cana-1300	204	16	or	or	CCONJ
cana-1300	204	17	𝑤3	𝑤3	PROPN
cana-1300	204	18	in	in	ADP
cana-1300	204	19	𝐷	𝐷	PROPN
cana-1300	204	20	as	as	ADP
cana-1300	204	21	compulsory	compulsory	ADJ
cana-1300	204	22	elements	element	NOUN
cana-1300	204	23	.	.	PUNCT
cana-1300	205	1	in	in	ADP
cana-1300	205	2	order	order	NOUN
cana-1300	205	3	to	to	PART
cana-1300	205	4	explore	explore	VERB
cana-1300	205	5	the	the	DET
cana-1300	205	6	possibility	possibility	NOUN
cana-1300	205	7	of	of	ADP
cana-1300	205	8	having	have	VERB
cana-1300	205	9	any	any	DET
cana-1300	205	10	other	other	ADJ
cana-1300	205	11	indispensable	indispensable	ADJ
cana-1300	205	12	elements	element	NOUN
cana-1300	205	13	in	in	ADP
cana-1300	205	14	𝐴.	𝐴.	PROPN
cana-1300	205	15	we	we	PRON
cana-1300	205	16	analysed	analyse	VERB
cana-1300	205	17	the	the	DET
cana-1300	205	18	carefully	carefully	ADV
cana-1300	205	19	the	the	DET
cana-1300	205	20	degree	degree	NOUN
cana-1300	205	21	distribution	distribution	NOUN
cana-1300	205	22	of	of	ADP
cana-1300	205	23	other	other	ADJ
cana-1300	205	24	vertices	vertex	NOUN
cana-1300	205	25	of	of	ADP
cana-1300	205	26	𝐺.	𝐺.	NOUN
cana-1300	205	27	we	we	PRON
cana-1300	205	28	found	find	VERB
cana-1300	205	29	it	it	PRON
cana-1300	205	30	wise	wise	ADJ
cana-1300	205	31	to	to	PART
cana-1300	205	32	look	look	VERB
cana-1300	205	33	at	at	ADP
cana-1300	205	34	the	the	DET
cana-1300	205	35	least	least	ADJ
cana-1300	205	36	degree	degree	NOUN
cana-1300	205	37	vertices	vertex	NOUN
cana-1300	205	38	of	of	ADP
cana-1300	205	39	𝐺.	𝐺.	NOUN
cana-1300	205	40	such	such	ADJ
cana-1300	205	41	vertices	vertex	NOUN
cana-1300	205	42	include	include	VERB
cana-1300	205	43	the	the	DET
cana-1300	205	44	following	follow	VERB
cana-1300	205	45	two	two	NUM
cana-1300	205	46	𝑤5	𝑤5	NOUN
cana-1300	205	47	and	and	CCONJ
cana-1300	205	48	𝑤6	𝑤6	PROPN
cana-1300	205	49	.	.	PUNCT
cana-1300	206	1	out	out	ADP
cana-1300	206	2	of	of	ADP
cana-1300	206	3	these	these	DET
cana-1300	206	4	vertices	vertex	NOUN
cana-1300	206	5	𝑤5	𝑤5	NOUN
cana-1300	206	6	and	and	CCONJ
cana-1300	206	7	𝑤6	𝑤6	NOUN
cana-1300	206	8	are	be	AUX
cana-1300	206	9	taken	take	VERB
cana-1300	206	10	by	by	ADP
cana-1300	206	11	𝑤2	𝑤2	NOUN
cana-1300	206	12	itself	itself	PRON
cana-1300	206	13	involving	involve	VERB
cana-1300	206	14	of	of	ADP
cana-1300	206	15	any	any	DET
cana-1300	206	16	other	other	ADJ
cana-1300	206	17	vertices	vertex	NOUN
cana-1300	206	18	in	in	ADP
cana-1300	206	19	𝐷	𝐷	PROPN
cana-1300	206	20	leads	lead	VERB
cana-1300	206	21	to	to	ADP
cana-1300	206	22	a	a	DET
cana-1300	206	23	contradiction	contradiction	NOUN
cana-1300	206	24	to	to	ADP
cana-1300	206	25	the	the	DET
cana-1300	206	26	definition	definition	NOUN
cana-1300	206	27	.	.	PUNCT
cana-1300	207	1	therefore	therefore	ADV
cana-1300	207	2	𝛾(𝐺	𝛾(𝐺	NUM
cana-1300	207	3	)	)	PUNCT
cana-1300	208	1	=	=	SYM
cana-1300	208	2	1	1	NUM
cana-1300	208	3	□	□	PUNCT
cana-1300	208	4	theorem	theorem	ADJ
cana-1300	208	5	4.11:𝛾𝑡(𝐺	4.11:𝛾𝑡(𝐺	NOUN
cana-1300	208	6	)	)	PUNCT
cana-1300	208	7	=	=	SYM
cana-1300	208	8	2	2	NUM
cana-1300	208	9	proof	proof	NOUN
cana-1300	208	10	:	:	PUNCT
cana-1300	208	11	let	let	VERB
cana-1300	208	12	𝐵	𝐵	PRON
cana-1300	208	13	⊆	⊆	NUM
cana-1300	208	14	𝑉(𝐺	𝑉(𝐺	NOUN
cana-1300	208	15	)	)	PUNCT
cana-1300	208	16	be	be	VERB
cana-1300	208	17	any	any	DET
cana-1300	208	18	total	total	ADJ
cana-1300	208	19	dominating	dominating	NOUN
cana-1300	208	20	set	set	NOUN
cana-1300	208	21	.	.	PUNCT
cana-1300	209	1	we	we	PRON
cana-1300	209	2	assert	assert	VERB
cana-1300	209	3	that𝐵	that𝐵	PROPN
cana-1300	209	4	≥	≥	NOUN
cana-1300	209	5	1	1	NUM
cana-1300	209	6	.	.	PUNCT
cana-1300	210	1	since𝐵	since𝐵	PROPN
cana-1300	210	2	is	be	AUX
cana-1300	210	3	a	a	DET
cana-1300	210	4	dominating	dominating	NOUN
cana-1300	210	5	set	set	VERB
cana-1300	210	6	by	by	ADP
cana-1300	210	7	theorem	theorem	NOUN
cana-1300	210	8	3.2.7	3.2.7	NUM
cana-1300	210	9	it	it	PRON
cana-1300	210	10	follows	follow	VERB
cana-1300	210	11	that	that	SCONJ
cana-1300	211	1	𝐵	𝐵	NOUN
cana-1300	211	2	≥	≥	NOUN
cana-1300	211	3	1	1	NUM
cana-1300	211	4	.	.	PUNCT
cana-1300	211	5	further	far	ADV
cana-1300	211	6	we	we	PRON
cana-1300	211	7	establishedin	establishedin	NOUN
cana-1300	211	8	theorem	theorem	VERB
cana-1300	211	9	3.2.7	3.2.7	NUM
cana-1300	211	10	guided	guide	VERB
cana-1300	211	11	by	by	ADP
cana-1300	211	12	the	the	DET
cana-1300	211	13	structure	structure	NOUN
cana-1300	211	14	of	of	ADP
cana-1300	211	15	𝐺that	𝐺that	PRON
cana-1300	211	16	any	any	DET
cana-1300	211	17	dominating	dominating	NOUN
cana-1300	211	18	set	set	VERB
cana-1300	211	19	of𝐺mustcompulsorily	of𝐺mustcompulsorily	ADV
cana-1300	211	20	contain	contain	VERB
cana-1300	211	21	the	the	DET
cana-1300	211	22	elements	element	NOUN
cana-1300	211	23	𝑤2	𝑤2	NOUN
cana-1300	211	24	∈	∈	NOUN
cana-1300	211	25	𝐵.	𝐵.	NOUN
cana-1300	211	26	let	let	VERB
cana-1300	211	27	𝐵	𝐵	PRON
cana-1300	211	28	=	=	SYM
cana-1300	211	29	{	{	PUNCT
cana-1300	211	30	𝑤1	𝑤1	PROPN
cana-1300	211	31	,	,	PUNCT
cana-1300	211	32	𝑤2	𝑤2	NOUN
cana-1300	211	33	}	}	PUNCT
cana-1300	211	34	be	be	VERB
cana-1300	211	35	any	any	DET
cana-1300	211	36	dominating	dominating	NOUN
cana-1300	211	37	set	set	NOUN
cana-1300	211	38	of	of	ADP
cana-1300	211	39	𝐺.	𝐺.	NOUN
cana-1300	211	40	now	now	ADV
cana-1300	211	41	𝐵	𝐵	PRON
cana-1300	211	42	must	must	AUX
cana-1300	211	43	be	be	AUX
cana-1300	211	44	adjacent	adjacent	ADJ
cana-1300	211	45	to	to	ADP
cana-1300	211	46	at	at	ADV
cana-1300	211	47	least	least	ADV
cana-1300	211	48	one	one	NUM
cana-1300	211	49	element	element	NOUN
cana-1300	211	50	of	of	ADP
cana-1300	211	51	the	the	DET
cana-1300	211	52	set	set	NOUN
cana-1300	211	53	,	,	PUNCT
cana-1300	211	54	finally	finally	ADV
cana-1300	211	55	𝐵	𝐵	NOUN
cana-1300	211	56	become	become	VERB
cana-1300	211	57	a	a	DET
cana-1300	211	58	total	total	ADJ
cana-1300	211	59	dominating	dominating	NOUN
cana-1300	211	60	set	set	NOUN
cana-1300	211	61	.	.	PUNCT
cana-1300	212	1	concluding	conclude	VERB
cana-1300	212	2	remarks	remark	NOUN
cana-1300	212	3	and	and	CCONJ
cana-1300	212	4	open	open	ADJ
cana-1300	212	5	problems	problem	NOUN
cana-1300	212	6	the	the	DET
cana-1300	212	7	collaboration	collaboration	NOUN
cana-1300	212	8	graph	graph	NOUN
cana-1300	212	9	of	of	ADP
cana-1300	212	10	lilavathi	lilavathi	ADJ
cana-1300	212	11	prize	prize	NOUN
cana-1300	212	12	winners	winner	NOUN
cana-1300	212	13	from	from	ADP
cana-1300	212	14	2010	2010	NUM
cana-1300	212	15	-	-	SYM
cana-1300	212	16	2022	2022	NUM
cana-1300	212	17	was	be	AUX
cana-1300	212	18	obtained	obtain	VERB
cana-1300	212	19	which	which	PRON
cana-1300	212	20	is	be	AUX
cana-1300	212	21	a	a	DET
cana-1300	212	22	huge	huge	ADJ
cana-1300	212	23	network	network	NOUN
cana-1300	212	24	with	with	ADP
cana-1300	212	25	14	14	NUM
cana-1300	212	26	nodes	node	NOUN
cana-1300	212	27	and	and	CCONJ
cana-1300	212	28	78	78	NUM
cana-1300	212	29	links	link	NOUN
cana-1300	212	30	.	.	PUNCT
cana-1300	213	1	as	as	SCONJ
cana-1300	213	2	the	the	DET
cana-1300	213	3	number	number	NOUN
cana-1300	213	4	of	of	ADP
cana-1300	213	5	vertices	vertex	NOUN
cana-1300	213	6	and	and	CCONJ
cana-1300	213	7	edges	edge	NOUN
cana-1300	213	8	is	be	AUX
cana-1300	213	9	limited	limit	VERB
cana-1300	213	10	in	in	ADP
cana-1300	213	11	number	number	NOUN
cana-1300	213	12	,	,	PUNCT
cana-1300	213	13	a	a	DET
cana-1300	213	14	software	software	NOUN
cana-1300	213	15	graph	graph	NOUN
cana-1300	213	16	tea	tea	NOUN
cana-1300	213	17	is	be	AUX
cana-1300	213	18	used	use	VERB
cana-1300	213	19	to	to	PART
cana-1300	213	20	construct	construct	VERB
cana-1300	213	21	the	the	DET
cana-1300	213	22	collaboration	collaboration	NOUN
cana-1300	213	23	graph	graph	NOUN
cana-1300	213	24	.	.	PUNCT
cana-1300	214	1	now	now	ADV
cana-1300	214	2	to	to	PART
cana-1300	214	3	improve	improve	VERB
cana-1300	214	4	the	the	DET
cana-1300	214	5	more	more	ADJ
cana-1300	214	6	connectedness	connectedness	NOUN
cana-1300	214	7	among	among	ADP
cana-1300	214	8	the	the	DET
cana-1300	214	9	winners	winner	NOUN
cana-1300	214	10	in	in	ADP
cana-1300	214	11	a	a	DET
cana-1300	214	12	connected	connected	ADJ
cana-1300	214	13	network	network	NOUN
cana-1300	214	14	the	the	DET
cana-1300	214	15	concept	concept	NOUN
cana-1300	214	16	of	of	ADP
cana-1300	214	17	domination	domination	NOUN
cana-1300	214	18	in	in	ADP
cana-1300	214	19	graphs	graph	NOUN
cana-1300	214	20	will	will	AUX
cana-1300	214	21	be	be	AUX
cana-1300	214	22	more	more	ADV
cana-1300	214	23	helpful	helpful	ADJ
cana-1300	214	24	.	.	PUNCT
cana-1300	215	1	so	so	ADV
cana-1300	215	2	,	,	PUNCT
cana-1300	215	3	a	a	DET
cana-1300	215	4	few	few	ADJ
cana-1300	215	5	prominent	prominent	ADJ
cana-1300	215	6	variants	variant	NOUN
cana-1300	215	7	of	of	ADP
cana-1300	215	8	domination	domination	NOUN
cana-1300	215	9	in	in	ADP
cana-1300	215	10	graphs	graph	NOUN
cana-1300	215	11	like	like	ADP
cana-1300	215	12	split	split	ADJ
cana-1300	215	13	domination	domination	NOUN
cana-1300	215	14	,	,	PUNCT
cana-1300	215	15	strong	strong	ADJ
cana-1300	215	16	split	split	ADJ
cana-1300	215	17	domination	domination	NOUN
cana-1300	215	18	,	,	PUNCT
cana-1300	215	19	strong	strong	ADJ
cana-1300	215	20	non	non	NOUN
cana-1300	215	21	split	split	NOUN
cana-1300	215	22	domination	domination	NOUN
cana-1300	215	23	,	,	PUNCT
cana-1300	215	24	inverse	inverse	ADJ
cana-1300	215	25	domination	domination	NOUN
cana-1300	215	26	,	,	PUNCT
cana-1300	215	27	inverse	inverse	NOUN
cana-1300	215	28	non	non	NOUN
cana-1300	215	29	split	split	NOUN
cana-1300	215	30	domination	domination	NOUN
cana-1300	215	31	,	,	PUNCT
cana-1300	215	32	edge	edge	NOUN
cana-1300	215	33	,	,	PUNCT
cana-1300	215	34	outer	outer	ADV
cana-1300	215	35	connected	connect	VERB
cana-1300	215	36	,	,	PUNCT
cana-1300	215	37	total	total	ADJ
cana-1300	215	38	connected	connect	VERB
cana-1300	215	39	,	,	PUNCT
cana-1300	215	40	connected	connected	ADJ
cana-1300	215	41	edge	edge	NOUN
cana-1300	215	42	domination	domination	NOUN
cana-1300	215	43	number	number	NOUN
cana-1300	215	44	and	and	CCONJ
cana-1300	215	45	just	just	ADV
cana-1300	215	46	excellent	excellent	ADJ
cana-1300	215	47	were	be	AUX
cana-1300	215	48	calculated	calculate	VERB
cana-1300	215	49	to	to	PART
cana-1300	215	50	serve	serve	VERB
cana-1300	215	51	the	the	DET
cana-1300	215	52	above	above	ADJ
cana-1300	215	53	purpose	purpose	NOUN
cana-1300	215	54	.	.	PUNCT
cana-1300	216	1	the	the	DET
cana-1300	216	2	calculation	calculation	NOUN
cana-1300	216	3	of	of	ADP
cana-1300	216	4	the	the	DET
cana-1300	216	5	domination	domination	NOUN
cana-1300	216	6	parameters	parameter	NOUN
cana-1300	216	7	of	of	ADP
cana-1300	216	8	the	the	DET
cana-1300	216	9	collaboration	collaboration	NOUN
cana-1300	216	10	graph	graph	NOUN
cana-1300	216	11	helps	help	VERB
cana-1300	216	12	to	to	PART
cana-1300	216	13	reach	reach	VERB
cana-1300	216	14	very	very	ADJ
cana-1300	216	15	member	member	NOUN
cana-1300	216	16	of	of	ADP
cana-1300	216	17	the	the	DET
cana-1300	216	18	graph	graph	NOUN
cana-1300	216	19	with	with	ADP
cana-1300	216	20	minimum	minimum	NOUN
cana-1300	216	21	connected	connect	VERB
cana-1300	216	22	ness	ness	NOUN
cana-1300	216	23	.	.	PUNCT
cana-1300	217	1	so	so	ADV
cana-1300	217	2	the	the	DET
cana-1300	217	3	idea	idea	NOUN
cana-1300	217	4	of	of	ADP
cana-1300	217	5	computing	compute	VERB
cana-1300	217	6	the	the	DET
cana-1300	217	7	split	split	ADJ
cana-1300	217	8	domination	domination	NOUN
cana-1300	217	9	,	,	PUNCT
cana-1300	217	10	strong	strong	ADJ
cana-1300	217	11	split	split	ADJ
cana-1300	217	12	domination	domination	NOUN
cana-1300	217	13	,	,	PUNCT
cana-1300	217	14	strong	strong	ADJ
cana-1300	217	15	non	non	NOUN
cana-1300	217	16	split	split	NOUN
cana-1300	217	17	domination	domination	NOUN
cana-1300	217	18	,	,	PUNCT
cana-1300	217	19	inverse	inverse	ADJ
cana-1300	217	20	domination	domination	NOUN
cana-1300	217	21	,	,	PUNCT
cana-1300	217	22	inverse	inverse	NOUN
cana-1300	217	23	non	non	NOUN
cana-1300	217	24	split	split	NOUN
cana-1300	217	25	domination	domination	NOUN
cana-1300	217	26	,	,	PUNCT
cana-1300	217	27	edge	edge	NOUN
cana-1300	217	28	,	,	PUNCT
cana-1300	217	29	outer	outer	ADV
cana-1300	217	30	connected	connect	VERB
cana-1300	217	31	,	,	PUNCT
cana-1300	217	32	total	total	ADJ
cana-1300	217	33	connected	connect	VERB
cana-1300	217	34	,	,	PUNCT
cana-1300	217	35	connected	connected	ADJ
cana-1300	217	36	edge	edge	NOUN
cana-1300	217	37	domination	domination	NOUN
cana-1300	217	38	number	number	NOUN
cana-1300	217	39	and	and	CCONJ
cana-1300	217	40	just	just	ADV
cana-1300	217	41	excellent	excellent	ADJ
cana-1300	217	42	assumes	assume	NOUN
cana-1300	217	43	significance	significance	NOUN
cana-1300	217	44	.	.	PUNCT
cana-1300	218	1	open	open	ADJ
cana-1300	218	2	problem	problem	NOUN
cana-1300	218	3	obtain	obtain	VERB
cana-1300	218	4	erdӧs	erdӧs	NOUN
cana-1300	218	5	centred	centre	VERB
cana-1300	218	6	collaboration	collaboration	NOUN
cana-1300	218	7	graph	graph	NOUN
cana-1300	218	8	for	for	ADP
cana-1300	218	9	nobel	nobel	PROPN
cana-1300	218	10	prize	prize	PROPN
cana-1300	218	11	,	,	PUNCT
cana-1300	218	12	fields	field	NOUN
cana-1300	218	13	medal	medal	NOUN
cana-1300	218	14	,	,	PUNCT
cana-1300	218	15	steel	steel	NOUN
cana-1300	218	16	’s	’s	PART
cana-1300	218	17	prize	prize	PROPN
cana-1300	218	18	and	and	CCONJ
cana-1300	218	19	abel	abel	PROPN
cana-1300	218	20	prize	prize	PROPN
cana-1300	218	21	etc	etc	X
cana-1300	218	22	and	and	CCONJ
cana-1300	218	23	compute	compute	VERB
cana-1300	218	24	its	its	PRON
cana-1300	218	25	dominating	dominating	NOUN
cana-1300	218	26	and	and	CCONJ
cana-1300	218	27	total	total	ADJ
cana-1300	218	28	dominating	dominating	NOUN
cana-1300	218	29	numbers	number	NOUN
cana-1300	218	30	.	.	PUNCT
cana-1300	219	1	references	reference	NOUN
cana-1300	219	2	[	[	X
cana-1300	219	3	1	1	NUM
cana-1300	219	4	]	]	X
cana-1300	219	5	ameenal	ameenal	ADJ
cana-1300	219	6	bibi	bibi	PROPN
cana-1300	219	7	k.	k.	PROPN
cana-1300	219	8	,	,	PUNCT
cana-1300	219	9	selvakumar	selvakumar	PROPN
cana-1300	219	10	r.	r.	PROPN
cana-1300	219	11	,	,	PUNCT
cana-1300	219	12	“	"	PUNCT
cana-1300	219	13	the	the	DET
cana-1300	219	14	inverse	inverse	NOUN
cana-1300	219	15	split	split	NOUN
cana-1300	219	16	and	and	CCONJ
cana-1300	219	17	nonsplit	nonsplit	VERB
cana-1300	219	18	domination	domination	NOUN
cana-1300	219	19	in	in	ADP
cana-1300	219	20	graphs	graph	NOUN
cana-1300	219	21	”	"	PUNCT
cana-1300	219	22	,	,	PUNCT
cana-1300	219	23	international	international	ADJ
cana-1300	219	24	journal	journal	NOUN
cana-1300	219	25	of	of	ADP
cana-1300	219	26	computer	computer	NOUN
cana-1300	219	27	applications	application	NOUN
cana-1300	219	28	,	,	PUNCT
cana-1300	219	29	volume	volume	NOUN
cana-1300	219	30	8	8	NUM
cana-1300	219	31	–	–	PUNCT
cana-1300	219	32	no.7	no.7	PROPN
cana-1300	219	33	october	october	PROPN
cana-1300	219	34	2010,pp:21	2010,pp:21	NUM
cana-1300	219	35	-	-	SYM
cana-1300	219	36	29	29	NUM
cana-1300	219	37	.	.	PUNCT
cana-1300	220	1	[	[	X
cana-1300	220	2	2	2	NUM
cana-1300	220	3	]	]	PUNCT
cana-1300	220	4	berge	berge	NOUN
cana-1300	220	5	c.	c.	PROPN
cana-1300	220	6	(	(	PUNCT
cana-1300	220	7	1962	1962	NUM
cana-1300	220	8	)	)	PUNCT
cana-1300	220	9	,	,	PUNCT
cana-1300	220	10	theory	theory	NOUN
cana-1300	220	11	of	of	ADP
cana-1300	220	12	graphs	graph	NOUN
cana-1300	220	13	and	and	CCONJ
cana-1300	220	14	its	its	PRON
cana-1300	220	15	applications	application	NOUN
cana-1300	220	16	,	,	PUNCT
cana-1300	220	17	methuen	methuen	PROPN
cana-1300	220	18	,	,	PUNCT
cana-1300	220	19	london	london	PROPN
cana-1300	220	20	.	.	PUNCT
cana-1300	221	1	[	[	X
cana-1300	221	2	3	3	X
cana-1300	221	3	]	]	X
cana-1300	221	4	cockayne	cockayne	PROPN
cana-1300	221	5	e.j	e.j	PROPN
cana-1300	221	6	.	.	PROPN
cana-1300	221	7	,	,	PUNCT
cana-1300	221	8	and	and	CCONJ
cana-1300	221	9	hedetniemi	hedetniemi	ADP
cana-1300	221	10	s.t	s.t	PROPN
cana-1300	221	11	.	.	PROPN
cana-1300	221	12	towards	towards	ADP
cana-1300	221	13	a	a	DET
cana-1300	221	14	theory	theory	NOUN
cana-1300	221	15	of	of	ADP
cana-1300	221	16	domination	domination	NOUN
cana-1300	221	17	in	in	ADP
cana-1300	221	18	graphs	graph	NOUN
cana-1300	221	19	,	,	PUNCT
cana-1300	221	20	networks	network	NOUN
cana-1300	221	21	,	,	PUNCT
cana-1300	221	22	(	(	PUNCT
cana-1300	221	23	1977	1977	NUM
cana-1300	221	24	)	)	PUNCT
cana-1300	222	1	[	[	X
cana-1300	222	2	4	4	NUM
cana-1300	222	3	]	]	PUNCT
cana-1300	222	4	cockayne	cockayne	PROPN
cana-1300	222	5	e.j	e.j	PROPN
cana-1300	222	6	,	,	PUNCT
cana-1300	222	7	hartnell	hartnell	PROPN
cana-1300	222	8	b.l	b.l	PROPN
cana-1300	222	9	,	,	PUNCT
cana-1300	222	10	hedetniemi	hedetniemi	ADP
cana-1300	222	11	s.t	s.t	PROPN
cana-1300	222	12	,	,	PUNCT
cana-1300	222	13	and	and	CCONJ
cana-1300	222	14	laskar	laskar	PROPN
cana-1300	222	15	r	r	PROPN
cana-1300	222	16	,	,	PUNCT
cana-1300	222	17	“	"	PUNCT
cana-1300	222	18	efficient	efficient	ADJ
cana-1300	222	19	domination	domination	NOUN
cana-1300	222	20	in	in	ADP
cana-1300	222	21	graphs	graph	NOUN
cana-1300	222	22	”	"	PUNCT
cana-1300	222	23	,	,	PUNCT
cana-1300	222	24	clemson	clemson	NOUN
cana-1300	222	25	university	university	NOUN
cana-1300	222	26	dept.of	dept.of	PROPN
cana-1300	222	27	mathematical	mathematical	ADJ
cana-1300	222	28	sciences	science	NOUN
cana-1300	222	29	,	,	PUNCT
cana-1300	222	30	technical	technical	ADJ
cana-1300	222	31	report	report	NOUN
cana-1300	222	32	1998	1998	NUM
cana-1300	222	33	,	,	PUNCT
cana-1300	222	34	558	558	NUM
cana-1300	222	35	.	.	PUNCT
cana-1300	223	1	[	[	X
cana-1300	223	2	5	5	X
cana-1300	223	3	]	]	X
cana-1300	223	4	gerald	gerald	PROPN
cana-1300	223	5	j.chang	j.chang	PROPN
cana-1300	223	6	,	,	PUNCT
cana-1300	223	7	the	the	DET
cana-1300	223	8	domatic	domatic	ADJ
cana-1300	223	9	number	number	NOUN
cana-1300	223	10	problem	problem	NOUN
cana-1300	223	11	,	,	PUNCT
cana-1300	223	12	discrete	discrete	ADJ
cana-1300	223	13	mathematics	mathematic	NOUN
cana-1300	223	14	,	,	PUNCT
cana-1300	223	15	volume	volume	NOUN
cana-1300	223	16	125	125	NUM
cana-1300	223	17	,	,	PUNCT
cana-1300	223	18	issue	issue	NOUN
cana-1300	223	19	1	1	NUM
cana-1300	223	20	-	-	SYM
cana-1300	223	21	3	3	NUM
cana-1300	223	22	,	,	PUNCT
cana-1300	223	23	feb	feb	NOUN
cana-1300	223	24	1994	1994	NUM
cana-1300	223	25	,	,	PUNCT
cana-1300	223	26	pp:115	pp:115	PROPN
cana-1300	223	27	-	-	SYM
cana-1300	223	28	122	122	NUM
cana-1300	223	29	.	.	PUNCT
cana-1300	224	1	communications	communication	NOUN
cana-1300	224	2	on	on	ADP
cana-1300	224	3	applied	apply	VERB
cana-1300	224	4	nonlinear	nonlinear	ADJ
cana-1300	224	5	analysis	analysis	NOUN
cana-1300	224	6	issn	issn	NOUN
cana-1300	224	7	:	:	PUNCT
cana-1300	224	8	1074	1074	NUM
cana-1300	224	9	-	-	PUNCT
cana-1300	224	10	133x	133x	NUM
cana-1300	224	11	vol	vol	NOUN
cana-1300	224	12	31	31	NUM
cana-1300	224	13	no	no	NOUN
cana-1300	224	14	.	.	PUNCT
cana-1300	225	1	7s	7	NOUN
cana-1300	225	2	(	(	PUNCT
cana-1300	225	3	2024	2024	NUM
cana-1300	225	4	)	)	PUNCT
cana-1300	225	5	260	260	NUM
cana-1300	225	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1300	226	1	[	[	X
cana-1300	226	2	6	6	NUM
cana-1300	226	3	]	]	PUNCT
cana-1300	226	4	haynes	haynes	PROPN
cana-1300	226	5	t.w	t.w	PROPN
cana-1300	226	6	.	.	PROPN
cana-1300	226	7	,	,	PUNCT
cana-1300	226	8	hedetniemi	hedetniemi	ADP
cana-1300	226	9	s.t	s.t	PROPN
cana-1300	226	10	.	.	PROPN
cana-1300	226	11	and	and	CCONJ
cana-1300	226	12	slater	slater	PROPN
cana-1300	226	13	p.j	p.j	PROPN
cana-1300	226	14	.	.	PROPN
cana-1300	226	15	,	,	PUNCT
cana-1300	226	16	fundamentals	fundamental	NOUN
cana-1300	226	17	of	of	ADP
cana-1300	226	18	domination	domination	NOUN
cana-1300	226	19	in	in	ADP
cana-1300	226	20	graph	graph	NOUN
cana-1300	226	21	,	,	PUNCT
cana-1300	226	22	new	new	PROPN
cana-1300	226	23	york	york	PROPN
cana-1300	226	24	,	,	PUNCT
cana-1300	226	25	marcel	marcel	PROPN
cana-1300	226	26	dekker	dekker	PROPN
cana-1300	226	27	,	,	PUNCT
cana-1300	226	28	inc	inc	PROPN
cana-1300	226	29	.	.	PROPN
cana-1300	226	30	,1998	,1998	PROPN
cana-1300	226	31	.	.	PUNCT
cana-1300	227	1	[	[	X
cana-1300	227	2	7	7	X
cana-1300	227	3	]	]	X
cana-1300	227	4	haynes	haynes	PROPN
cana-1300	227	5	t.w	t.w	PROPN
cana-1300	227	6	.	.	PROPN
cana-1300	227	7	,	,	PUNCT
cana-1300	227	8	hedetniemi	hedetniemi	ADP
cana-1300	227	9	s.t	s.t	PROPN
cana-1300	227	10	.	.	PROPN
cana-1300	227	11	and	and	CCONJ
cana-1300	227	12	slater	slater	PROPN
cana-1300	227	13	p.j	p.j	PROPN
cana-1300	227	14	.	.	PROPN
cana-1300	227	15	,	,	PUNCT
cana-1300	227	16	domination	domination	NOUN
cana-1300	227	17	in	in	ADP
cana-1300	227	18	graph	graph	NOUN
cana-1300	227	19	,	,	PUNCT
cana-1300	227	20	advanced	advanced	ADJ
cana-1300	227	21	topics	topic	NOUN
cana-1300	227	22	,	,	PUNCT
cana-1300	227	23	new	new	PROPN
cana-1300	227	24	york	york	PROPN
cana-1300	227	25	,	,	PUNCT
cana-1300	227	26	marcel	marcel	PROPN
cana-1300	227	27	dekker	dekker	PROPN
cana-1300	227	28	,	,	PUNCT
cana-1300	227	29	inc	inc	PROPN
cana-1300	227	30	.	.	PROPN
cana-1300	227	31	,1998	,1998	PROPN
cana-1300	227	32	.	.	PUNCT
cana-1300	228	1	[	[	X
cana-1300	228	2	8	8	NUM
cana-1300	228	3	]	]	X
cana-1300	228	4	joanna	joanna	PROPN
cana-1300	228	5	cyman	cyman	PROPN
cana-1300	228	6	,	,	PUNCT
cana-1300	228	7	“	"	PUNCT
cana-1300	228	8	the	the	DET
cana-1300	228	9	outer	outer	ADJ
cana-1300	228	10	connected	connected	ADJ
cana-1300	228	11	domination	domination	NOUN
cana-1300	228	12	number	number	NOUN
cana-1300	228	13	of	of	ADP
cana-1300	228	14	a	a	DET
cana-1300	228	15	graph	graph	NOUN
cana-1300	228	16	”	"	PUNCT
cana-1300	228	17	,	,	PUNCT
cana-1300	228	18	australisian	australisian	PROPN
cana-1300	228	19	journal	journal	PROPN
cana-1300	228	20	of	of	ADP
cana-1300	228	21	combinatorics	combinatorics	PROPN
cana-1300	228	22	,	,	PUNCT
cana-1300	228	23	volume	volume	NOUN
cana-1300	228	24	38	38	NUM
cana-1300	228	25	,	,	PUNCT
cana-1300	228	26	2007	2007	NUM
cana-1300	228	27	,	,	PUNCT
cana-1300	228	28	pp	pp	CCONJ
cana-1300	228	29	:	:	PUNCT
cana-1300	228	30	35	35	NUM
cana-1300	228	31	-	-	SYM
cana-1300	228	32	46	46	NUM
cana-1300	228	33	.	.	PUNCT
cana-1300	229	1	[	[	X
cana-1300	229	2	9	9	NUM
cana-1300	229	3	]	]	X
cana-1300	229	4	kulli	kulli	PROPN
cana-1300	229	5	v.r.and	v.r.and	PROPN
cana-1300	229	6	sigarkanti	sigarkanti	PROPN
cana-1300	229	7	s.c	s.c	PROPN
cana-1300	229	8	.	.	PROPN
cana-1300	229	9	,	,	PUNCT
cana-1300	229	10	inverse	inverse	ADJ
cana-1300	229	11	domination	domination	NOUN
cana-1300	229	12	in	in	ADP
cana-1300	229	13	graphs	graph	NOUN
cana-1300	229	14	,	,	PUNCT
cana-1300	229	15	research	research	NOUN
cana-1300	229	16	gate	gate	NOUN
cana-1300	229	17	,	,	PUNCT
cana-1300	229	18	n.a.sci.letters	n.a.sci.letter	NOUN
cana-1300	229	19	,	,	PUNCT
cana-1300	229	20	1991	1991	NUM
cana-1300	229	21	[	[	X
cana-1300	229	22	10	10	NUM
cana-1300	229	23	]	]	X
cana-1300	229	24	kulli	kulli	PROPN
cana-1300	229	25	v.r	v.r	PROPN
cana-1300	229	26	.	.	PROPN
cana-1300	229	27	and	and	CCONJ
cana-1300	229	28	janakiram	janakiram	PROPN
cana-1300	229	29	b.	b.	PROPN
cana-1300	229	30	,	,	PUNCT
cana-1300	229	31	“	"	PUNCT
cana-1300	229	32	the	the	DET
cana-1300	229	33	split	split	ADJ
cana-1300	229	34	domination	domination	NOUN
cana-1300	229	35	number	number	NOUN
cana-1300	229	36	of	of	ADP
cana-1300	229	37	a	a	DET
cana-1300	229	38	graph	graph	NOUN
cana-1300	229	39	”	"	PUNCT
cana-1300	229	40	,	,	PUNCT
cana-1300	229	41	graph	graph	NOUN
cana-1300	229	42	theory	theory	NOUN
cana-1300	229	43	notes	note	NOUN
cana-1300	229	44	of	of	ADP
cana-1300	229	45	new	new	PROPN
cana-1300	229	46	york	york	PROPN
cana-1300	229	47	,	,	PUNCT
cana-1300	229	48	new	new	PROPN
cana-1300	229	49	york	york	PROPN
cana-1300	229	50	academy	academy	PROPN
cana-1300	229	51	of	of	ADP
cana-1300	229	52	sciences	sciences	PROPN
cana-1300	229	53	,	,	PUNCT
cana-1300	229	54	xxxii	xxxii	PROPN
cana-1300	229	55	,	,	PUNCT
cana-1300	229	56	1997	1997	NUM
cana-1300	229	57	.	.	PUNCT
cana-1300	230	1	[	[	X
cana-1300	230	2	11	11	NUM
cana-1300	230	3	]	]	X
cana-1300	230	4	kulli	kulli	PROPN
cana-1300	230	5	v.r	v.r	PROPN
cana-1300	230	6	.	.	PROPN
cana-1300	230	7	and	and	CCONJ
cana-1300	230	8	janakiram	janakiram	PROPN
cana-1300	230	9	,	,	PUNCT
cana-1300	230	10	“	"	PUNCT
cana-1300	230	11	the	the	DET
cana-1300	230	12	nonsplit	nonsplit	ADJ
cana-1300	230	13	domination	domination	NOUN
cana-1300	230	14	number	number	NOUN
cana-1300	230	15	of	of	ADP
cana-1300	230	16	a	a	DET
cana-1300	230	17	graph”,indian	graph”,indian	ADJ
cana-1300	230	18	journal	journal	NOUN
cana-1300	230	19	of	of	ADP
cana-1300	230	20	pure	pure	ADJ
cana-1300	230	21	&	&	CCONJ
cana-1300	230	22	applied	applied	ADJ
cana-1300	230	23	mathemtics	mathemtic	NOUN
cana-1300	230	24	,	,	PUNCT
cana-1300	230	25	31	31	NUM
cana-1300	230	26	2000,pp:545	2000,pp:545	NUM
cana-1300	230	27	-	-	SYM
cana-1300	230	28	550	550	NUM
cana-1300	231	1	[	[	X
cana-1300	231	2	12	12	NUM
cana-1300	231	3	]	]	X
cana-1300	231	4	kulli	kulli	PROPN
cana-1300	231	5	v.r	v.r	PROPN
cana-1300	231	6	.	.	PROPN
cana-1300	231	7	and	and	CCONJ
cana-1300	231	8	janakiram	janakiram	PROPN
cana-1300	231	9	b.	b.	PROPN
cana-1300	231	10	,	,	PUNCT
cana-1300	231	11	“	"	PUNCT
cana-1300	231	12	the	the	DET
cana-1300	231	13	strong	strong	ADJ
cana-1300	231	14	nonsplit	nonsplit	ADJ
cana-1300	231	15	domination	domination	NOUN
cana-1300	231	16	number	number	NOUN
cana-1300	231	17	of	of	ADP
cana-1300	231	18	a	a	DET
cana-1300	231	19	graph	graph	NOUN
cana-1300	231	20	”	"	PUNCT
cana-1300	231	21	,	,	PUNCT
cana-1300	231	22	international	international	ADJ
cana-1300	231	23	journal	journal	NOUN
cana-1300	231	24	of	of	ADP
cana-1300	231	25	management	management	NOUN
cana-1300	231	26	and	and	CCONJ
cana-1300	231	27	systems	system	NOUN
cana-1300	231	28	,	,	PUNCT
cana-1300	231	29	vol	vol	NOUN
cana-1300	231	30	19	19	NUM
cana-1300	231	31	no-2	no-2	NOUN
cana-1300	231	32	,	,	PUNCT
cana-1300	231	33	mayaugust	mayaugust	NOUN
cana-1300	231	34	2003	2003	NUM
cana-1300	231	35	,	,	PUNCT
cana-1300	231	36	pp:145	pp:145	NOUN
cana-1300	231	37	-	-	PUNCT
cana-1300	231	38	156	156	NUM
cana-1300	231	39	.	.	PUNCT
cana-1300	232	1	[	[	X
cana-1300	232	2	13	13	NUM
cana-1300	232	3	]	]	X
cana-1300	232	4	kulli	kulli	PROPN
cana-1300	232	5	v.r	v.r	PROPN
cana-1300	232	6	.	.	PROPN
cana-1300	232	7	and	and	CCONJ
cana-1300	232	8	janakiram	janakiram	PROPN
cana-1300	232	9	b.	b.	PROPN
cana-1300	232	10	,	,	PUNCT
cana-1300	232	11	“	"	PUNCT
cana-1300	232	12	the	the	DET
cana-1300	232	13	strong	strong	ADJ
cana-1300	232	14	split	split	ADJ
cana-1300	232	15	domination	domination	NOUN
cana-1300	232	16	number	number	NOUN
cana-1300	232	17	of	of	ADP
cana-1300	232	18	a	a	DET
cana-1300	232	19	graph	graph	NOUN
cana-1300	232	20	,	,	PUNCT
cana-1300	232	21	acta	acta	PROPN
cana-1300	232	22	ciencia	ciencia	PROPN
cana-1300	232	23	indica	indica	PROPN
cana-1300	232	24	,	,	PUNCT
cana-1300	232	25	vol	vol	NOUN
cana-1300	232	26	xxxii	xxxii	PROPN
cana-1300	232	27	m	m	PROPN
cana-1300	232	28	,	,	PUNCT
cana-1300	232	29	no.2	no.2	PROPN
cana-1300	232	30	,	,	PUNCT
cana-1300	232	31	715(2006	715(2006	NOUN
cana-1300	232	32	)	)	PUNCT
cana-1300	232	33	.	.	PUNCT
cana-1300	233	1	[	[	X
cana-1300	233	2	14	14	NUM
cana-1300	233	3	]	]	X
cana-1300	233	4	kulli	kulli	PROPN
cana-1300	233	5	v.r	v.r	PROPN
cana-1300	233	6	.	.	PROPN
cana-1300	233	7	,	,	PUNCT
cana-1300	233	8	theory	theory	NOUN
cana-1300	233	9	of	of	ADP
cana-1300	233	10	domination	domination	NOUN
cana-1300	233	11	in	in	ADP
cana-1300	233	12	graphs	graph	NOUN
cana-1300	233	13	,	,	PUNCT
cana-1300	233	14	vishwa	vishwa	PROPN
cana-1300	233	15	inter	inter	PROPN
cana-1300	233	16	.	.	PUNCT
cana-1300	234	1	publ	publ	PROPN
cana-1300	234	2	.	.	PUNCT
cana-1300	235	1	gulbarga	gulbarga	PROPN
cana-1300	235	2	(	(	PUNCT
cana-1300	235	3	2010	2010	NUM
cana-1300	235	4	)	)	PUNCT
cana-1300	235	5	,	,	PUNCT
cana-1300	235	6	india	india	PROPN
cana-1300	235	7	.	.	PUNCT
cana-1300	236	1	[	[	X
cana-1300	236	2	15	15	NUM
cana-1300	236	3	]	]	X
cana-1300	236	4	ore	ore	NOUN
cana-1300	236	5	o.	o.	NOUN
cana-1300	236	6	,theory	,theory	PUNCT
cana-1300	236	7	of	of	ADP
cana-1300	236	8	graphs	graph	NOUN
cana-1300	236	9	,	,	PUNCT
cana-1300	236	10	amer	amer	PROPN
cana-1300	236	11	,	,	PUNCT
cana-1300	236	12	math	math	NOUN
cana-1300	236	13	,	,	PUNCT
cana-1300	236	14	soc	soc	NOUN
cana-1300	236	15	,	,	PUNCT
cana-1300	236	16	colloq	colloq	PROPN
cana-1300	236	17	,	,	PUNCT
cana-1300	236	18	publ	publ	NOUN
cana-1300	236	19	,	,	PUNCT
cana-1300	236	20	1962	1962	NUM
cana-1300	236	21	.	.	PUNCT
cana-1300	237	1	[	[	X
cana-1300	237	2	16	16	NUM
cana-1300	237	3	]	]	X
cana-1300	237	4	vaidya	vaidya	PROPN
cana-1300	237	5	s.k	s.k	PROPN
cana-1300	237	6	.	.	PROPN
cana-1300	237	7	&	&	CCONJ
cana-1300	237	8	karkar	karkar	PROPN
cana-1300	237	9	s.h	s.h	PROPN
cana-1300	237	10	.	.	PROPN
cana-1300	237	11	,	,	PUNCT
cana-1300	237	12	“	"	PUNCT
cana-1300	237	13	on	on	ADP
cana-1300	237	14	strong	strong	ADJ
cana-1300	237	15	domination	domination	NOUN
cana-1300	237	16	number	number	NOUN
cana-1300	237	17	of	of	ADP
cana-1300	237	18	graphs	graph	NOUN
cana-1300	237	19	”	"	PUNCT
cana-1300	237	20	,	,	PUNCT
cana-1300	237	21	applications	application	NOUN
cana-1300	237	22	and	and	CCONJ
cana-1300	237	23	applied	apply	VERB
cana-1300	237	24	mathematics	mathematic	NOUN
cana-1300	237	25	:	:	PUNCT
cana-1300	237	26	an	an	DET
cana-1300	237	27	international	international	ADJ
cana-1300	237	28	journal	journal	NOUN
cana-1300	237	29	,	,	PUNCT
cana-1300	237	30	issn	issn	PROPN
cana-1300	237	31	:	:	PUNCT
cana-1300	237	32	1932	1932	NUM
cana-1300	237	33	-	-	SYM
cana-1300	237	34	9466	9466	NUM
cana-1300	237	35	,	,	PUNCT
cana-1300	237	36	vol	vol	NOUN
cana-1300	237	37	12	12	NUM
cana-1300	237	38	,	,	PUNCT
cana-1300	237	39	issue	issue	NOUN
cana-1300	237	40	i	i	PRON
cana-1300	237	41	pp	pp	ADJ
cana-1300	237	42	:	:	PUNCT
cana-1300	237	43	604	604	NUM
cana-1300	237	44	-	-	NUM
cana-1300	237	45	612	612	NUM
cana-1300	237	46	,	,	PUNCT
cana-1300	237	47	2017	2017	NUM
cana-1300	237	48	.	.	PUNCT
cana-1300	238	1	[	[	X
cana-1300	238	2	17	17	NUM
cana-1300	238	3	]	]	X
cana-1300	238	4	yamuna	yamuna	PROPN
cana-1300	238	5	m.	m.	NOUN
cana-1300	238	6	and	and	CCONJ
cana-1300	238	7	sridharan	sridharan	ADJ
cana-1300	238	8	n.	n.	NOUN
cana-1300	238	9	,	,	PUNCT
cana-1300	238	10	just	just	ADV
cana-1300	238	11	excellent	excellent	ADJ
cana-1300	238	12	graphs	graph	NOUN
cana-1300	238	13	,	,	PUNCT
cana-1300	238	14	“	"	PUNCT
cana-1300	238	15	international	international	ADJ
cana-1300	238	16	journal	journal	NOUN
cana-1300	238	17	of	of	ADP
cana-1300	238	18	engineering	engineering	NOUN
cana-1300	238	19	science	science	NOUN
cana-1300	238	20	,	,	PUNCT
cana-1300	238	21	advanced	advanced	ADJ
cana-1300	238	22	computing	computing	NOUN
cana-1300	238	23	and	and	CCONJ
cana-1300	238	24	bio	bio	NOUN
cana-1300	238	25	-	-	NOUN
cana-1300	238	26	technology	technology	NOUN
cana-1300	238	27	”	"	PUNCT
cana-1300	238	28	vol	vol	NOUN
cana-1300	238	29	.	.	PROPN
cana-1300	238	30	1	1	NUM
cana-1300	238	31	,	,	PUNCT
cana-1300	238	32	no	no	INTJ
cana-1300	238	33	.	.	NOUN
cana-1300	238	34	3	3	NUM
cana-1300	238	35	,	,	PUNCT
cana-1300	238	36	july	july	PROPN
cana-1300	238	37	–	–	PUNCT
cana-1300	238	38	september	september	PROPN
cana-1300	238	39	2010	2010	NUM
cana-1300	238	40	,	,	PUNCT
cana-1300	238	41	pp	pp	ADP
cana-1300	238	42	.	.	PUNCT
cana-1300	239	1	129	129	NUM
cana-1300	239	2	-	-	SYM
cana-1300	239	3	136	136	NUM
cana-1300	239	4	.	.	PUNCT
cana-1300	240	1	[	[	X
cana-1300	240	2	18	18	NUM
cana-1300	240	3	]	]	X
cana-1300	240	4	yegnanarayanan	yegnanarayanan	PROPN
cana-1300	240	5	,	,	PUNCT
cana-1300	240	6	v.	v.	PROPN
cana-1300	240	7	&	&	CCONJ
cana-1300	240	8	lokeshwary	lokeshwary	PROPN
cana-1300	240	9	,	,	PUNCT
cana-1300	240	10	b.	b.	PROPN
cana-1300	240	11	,	,	PUNCT
cana-1300	240	12	on	on	ADP
cana-1300	240	13	graph	graph	NOUN
cana-1300	240	14	domination	domination	NOUN
cana-1300	240	15	numbers	number	NOUN
cana-1300	240	16	,	,	PUNCT
cana-1300	240	17	international	international	ADJ
cana-1300	240	18	journal	journal	NOUN
cana-1300	240	19	of	of	ADP
cana-1300	240	20	pure	pure	ADJ
cana-1300	240	21	and	and	CCONJ
cana-1300	240	22	applied	applied	ADJ
cana-1300	240	23	mathematics	mathematic	NOUN
cana-1300	240	24	,	,	PUNCT
cana-1300	240	25	(	(	PUNCT
cana-1300	240	26	2015	2015	NUM
cana-1300	240	27	)	)	PUNCT
cana-1300	240	28	,	,	PUNCT
cana-1300	240	29	105(4	105(4	NUM
cana-1300	240	30	)	)	PUNCT
cana-1300	240	31	,	,	PUNCT
cana-1300	240	32	751	751	NUM
cana-1300	240	33	-	-	SYM
cana-1300	240	34	761	761	NUM
cana-1300	240	35	.	.	PUNCT
cana-1300	241	1	[	[	X
cana-1300	241	2	19	19	NUM
cana-1300	241	3	]	]	X
cana-1300	241	4	yegnanarayanan	yegnanarayanan	PROPN
cana-1300	241	5	,	,	PUNCT
cana-1300	241	6	v.	v.	PROPN
cana-1300	241	7	&	&	CCONJ
cana-1300	241	8	renuka	renuka	PROPN
cana-1300	241	9	lakshmi	lakshmi	PROPN
cana-1300	241	10	,	,	PUNCT
cana-1300	241	11	a.	a.	NOUN
cana-1300	241	12	,	,	PUNCT
cana-1300	241	13	on	on	ADP
cana-1300	241	14	domination	domination	NOUN
cana-1300	241	15	and	and	CCONJ
cana-1300	241	16	total	total	ADJ
cana-1300	241	17	domination	domination	NOUN
cana-1300	241	18	number	number	NOUN
cana-1300	241	19	of	of	ADP
cana-1300	241	20	a	a	DET
cana-1300	241	21	collaboration	collaboration	NOUN
cana-1300	241	22	graph	graph	NOUN
cana-1300	241	23	,	,	PUNCT
cana-1300	241	24	international	international	ADJ
cana-1300	241	25	journal	journal	NOUN
cana-1300	241	26	of	of	ADP
cana-1300	241	27	advanced	advanced	ADJ
cana-1300	241	28	intelligence	intelligence	NOUN
cana-1300	241	29	paradigms	paradigm	NOUN
cana-1300	241	30	,	,	PUNCT
cana-1300	241	31	2017	2017	NUM
cana-1300	241	32	,	,	PUNCT
cana-1300	241	33	9(5/6	9(5/6	NUM
cana-1300	241	34	)	)	PUNCT
cana-1300	241	35	,	,	PUNCT
cana-1300	241	36	541	541	NUM
cana-1300	241	37	-	-	SYM
cana-1300	241	38	557	557	NUM
cana-1300	241	39	.	.	PUNCT