id	sid	tid	token	lemma	pos
cana-1399	1	1	communications	communication	NOUN
cana-1399	1	2	on	on	ADP
cana-1399	1	3	applied	apply	VERB
cana-1399	1	4	nonlinear	nonlinear	ADJ
cana-1399	1	5	analysis	analysis	NOUN
cana-1399	1	6	issn	issn	NOUN
cana-1399	1	7	:	:	PUNCT
cana-1399	1	8	1074	1074	NUM
cana-1399	1	9	-	-	PUNCT
cana-1399	1	10	133x	133x	NUM
cana-1399	1	11	vol	vol	NOUN
cana-1399	1	12	31	31	NUM
cana-1399	1	13	no	no	NOUN
cana-1399	1	14	.	.	PUNCT
cana-1399	2	1	7s	7	NOUN
cana-1399	2	2	(	(	PUNCT
cana-1399	2	3	2024	2024	NUM
cana-1399	2	4	)	)	PUNCT
cana-1399	2	5	574	574	NUM
cana-1399	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1399	2	7	on	on	ADP
cana-1399	2	8	decomposing	decompose	VERB
cana-1399	2	9	any	any	DET
cana-1399	2	10	graph	graph	NOUN
cana-1399	2	11	g	g	NOUN
cana-1399	2	12	into	into	ADP
cana-1399	2	13	vdt	vdt	PROPN
cana-1399	2	14	graphs	graphs	PROPN
cana-1399	2	15	m.	m.	NOUN
cana-1399	2	16	sivasankari	sivasankari	PROPN
cana-1399	2	17	1	1	NUM
cana-1399	2	18	,	,	PUNCT
cana-1399	2	19	m.	m.	NOUN
cana-1399	2	20	yamuna	yamuna	PROPN
cana-1399	2	21	2	2	NUM
cana-1399	2	22	1	1	NUM
cana-1399	2	23	department	department	NOUN
cana-1399	2	24	of	of	ADP
cana-1399	2	25	mathematics	mathematics	PROPN
cana-1399	2	26	,	,	PUNCT
cana-1399	2	27	sas	sas	PROPN
cana-1399	2	28	,	,	PUNCT
cana-1399	2	29	vit	vit	NOUN
cana-1399	2	30	,	,	PUNCT
cana-1399	2	31	vellore	vellore	NOUN
cana-1399	2	32	,	,	PUNCT
cana-1399	2	33	tamil	tamil	PROPN
cana-1399	2	34	nadu	nadu	PROPN
cana-1399	2	35	,	,	PUNCT
cana-1399	2	36	india	india	PROPN
cana-1399	2	37	.	.	PUNCT
cana-1399	2	38	email	email	NOUN
cana-1399	2	39	:	:	PUNCT
cana-1399	2	40	sivasankari.2019@vitstudent.ac.in	sivasankari.2019@vitstudent.ac.in	PROPN
cana-1399	2	41	2	2	NUM
cana-1399	2	42	department	department	NOUN
cana-1399	2	43	of	of	ADP
cana-1399	2	44	mathematics	mathematics	PROPN
cana-1399	2	45	,	,	PUNCT
cana-1399	2	46	sas	sas	PROPN
cana-1399	2	47	,	,	PUNCT
cana-1399	2	48	vit	vit	NOUN
cana-1399	2	49	,	,	PUNCT
cana-1399	2	50	vellore	vellore	NOUN
cana-1399	2	51	,	,	PUNCT
cana-1399	2	52	tamil	tamil	PROPN
cana-1399	2	53	nadu	nadu	PROPN
cana-1399	2	54	,	,	PUNCT
cana-1399	2	55	india	india	PROPN
cana-1399	2	56	.	.	PUNCT
cana-1399	2	57	email	email	PROPN
cana-1399	2	58	:	:	PUNCT
cana-1399	2	59	myamuna@vit.ac.in	myamuna@vit.ac.in	PROPN
cana-1399	2	60	corresponding	corresponding	PROPN
cana-1399	2	61	author	author	NOUN
cana-1399	2	62	:	:	PUNCT
cana-1399	2	63	myamuna@vit.ac.in	myamuna@vit.ac.in	PROPN
cana-1399	2	64	article	article	PROPN
cana-1399	2	65	history	history	NOUN
cana-1399	2	66	:	:	PUNCT
cana-1399	2	67	received	receive	VERB
cana-1399	2	68	:	:	PUNCT
cana-1399	2	69	04	04	NUM
cana-1399	2	70	-	-	PUNCT
cana-1399	2	71	06	06	NUM
cana-1399	2	72	-	-	PUNCT
cana-1399	2	73	2024	2024	NUM
cana-1399	2	74	revised	revise	VERB
cana-1399	2	75	:	:	PUNCT
cana-1399	2	76	03	03	NUM
cana-1399	2	77	-	-	PUNCT
cana-1399	2	78	07	07	NUM
cana-1399	2	79	-	-	PUNCT
cana-1399	2	80	2024	2024	NUM
cana-1399	2	81	accepted	accept	VERB
cana-1399	2	82	:	:	PUNCT
cana-1399	2	83	30	30	NUM
cana-1399	2	84	-	-	SYM
cana-1399	2	85	07	07	NUM
cana-1399	2	86	-	-	PUNCT
cana-1399	2	87	2024	2024	NUM
cana-1399	2	88	abstract	abstract	NOUN
cana-1399	2	89	:	:	PUNCT
cana-1399	2	90	this	this	DET
cana-1399	2	91	article	article	NOUN
cana-1399	2	92	targets	target	VERB
cana-1399	2	93	to	to	PART
cana-1399	2	94	develop	develop	VERB
cana-1399	2	95	an	an	DET
cana-1399	2	96	iterative	iterative	NOUN
cana-1399	2	97	procedure	procedure	NOUN
cana-1399	2	98	for	for	ADP
cana-1399	2	99	decomposing	decompose	VERB
cana-1399	2	100	any	any	DET
cana-1399	2	101	random	random	ADJ
cana-1399	2	102	graph	graph	NOUN
cana-1399	2	103	g	g	NOUN
cana-1399	2	104	into	into	ADP
cana-1399	2	105	subgraphs	subgraph	NOUN
cana-1399	2	106	1	1	NUM
cana-1399	2	107	2	2	NUM
cana-1399	2	108	kh	kh	NOUN
cana-1399	2	109	,	,	PUNCT
cana-1399	2	110	h	h	NOUN
cana-1399	2	111	,	,	PUNCT
cana-1399	2	112	...	...	PUNCT
cana-1399	2	113	,	,	PUNCT
cana-1399	2	114	h	h	NOUN
cana-1399	2	115	such	such	ADJ
cana-1399	2	116	that	that	SCONJ
cana-1399	2	117	each	each	DET
cana-1399	2	118	hi	hi	INTJ
cana-1399	2	119	is	be	AUX
cana-1399	2	120	a	a	DET
cana-1399	2	121	vdt	vdt	PROPN
cana-1399	2	122	graph	graph	NOUN
cana-1399	2	123	,	,	PUNCT
cana-1399	2	124	1	1	NUM
cana-1399	2	125	≤	≤	NUM
cana-1399	2	126	i	i	PRON
cana-1399	2	127	≤	≤	PROPN
cana-1399	2	128	k.	k.	INTJ
cana-1399	3	1	this	this	DET
cana-1399	3	2	iterative	iterative	NOUN
cana-1399	3	3	technique	technique	NOUN
cana-1399	3	4	is	be	AUX
cana-1399	3	5	based	base	VERB
cana-1399	3	6	on	on	ADP
cana-1399	3	7	developing	develop	VERB
cana-1399	3	8	a	a	DET
cana-1399	3	9	rooted	rooted	ADJ
cana-1399	3	10	tree	tree	NOUN
cana-1399	3	11	,	,	PUNCT
cana-1399	3	12	and	and	CCONJ
cana-1399	3	13	then	then	ADV
cana-1399	3	14	decompose	decompose	VERB
cana-1399	3	15	g	g	NOUN
cana-1399	3	16	into	into	ADP
cana-1399	3	17	vdt	vdt	PROPN
cana-1399	3	18	graphs	graph	NOUN
cana-1399	3	19	using	use	VERB
cana-1399	3	20	backtracking	backtrack	VERB
cana-1399	3	21	.	.	PUNCT
cana-1399	4	1	keywords	keyword	NOUN
cana-1399	4	2	:	:	PUNCT
cana-1399	4	3	decomposition	decomposition	NOUN
cana-1399	4	4	,	,	PUNCT
cana-1399	4	5	bfs	bfs	NOUN
cana-1399	4	6	,	,	PUNCT
cana-1399	4	7	tree	tree	NOUN
cana-1399	4	8	,	,	PUNCT
cana-1399	4	9	domination	domination	NOUN
cana-1399	4	10	.	.	PUNCT
cana-1399	5	1	1	1	X
cana-1399	5	2	.	.	X
cana-1399	5	3	introduction	introduction	NOUN
cana-1399	5	4	in	in	ADP
cana-1399	5	5	the	the	DET
cana-1399	5	6	literature	literature	NOUN
cana-1399	5	7	of	of	ADP
cana-1399	5	8	graph	graph	NOUN
cana-1399	5	9	theory	theory	NOUN
cana-1399	5	10	,	,	PUNCT
cana-1399	5	11	graph	graph	NOUN
cana-1399	5	12	decomposition	decomposition	NOUN
cana-1399	5	13	is	be	AUX
cana-1399	5	14	one	one	NUM
cana-1399	5	15	interesting	interesting	ADJ
cana-1399	5	16	problem	problem	NOUN
cana-1399	5	17	where	where	SCONJ
cana-1399	5	18	any	any	DET
cana-1399	5	19	graph	graph	NOUN
cana-1399	5	20	is	be	AUX
cana-1399	5	21	decomposed	decompose	VERB
cana-1399	5	22	into	into	ADP
cana-1399	5	23	subgraphs	subgraph	NOUN
cana-1399	5	24	[	[	X
cana-1399	5	25	1	1	NUM
cana-1399	5	26	]	]	PUNCT
cana-1399	5	27	.	.	PUNCT
cana-1399	6	1	researchers	researcher	NOUN
cana-1399	6	2	have	have	AUX
cana-1399	6	3	made	make	VERB
cana-1399	6	4	different	different	ADJ
cana-1399	6	5	contributions	contribution	NOUN
cana-1399	6	6	to	to	ADP
cana-1399	6	7	this	this	DET
cana-1399	6	8	domain	domain	NOUN
cana-1399	6	9	.	.	PUNCT
cana-1399	7	1	samuel	samuel	PROPN
cana-1399	7	2	issacraj	issacraj	PROPN
cana-1399	7	3	et	et	PROPN
cana-1399	7	4	al	al	PROPN
cana-1399	7	5	.	.	PROPN
cana-1399	7	6	studied	study	VERB
cana-1399	7	7	forks	fork	NOUN
cana-1399	7	8	,	,	PUNCT
cana-1399	7	9	trees	tree	NOUN
cana-1399	7	10	formed	form	VERB
cana-1399	7	11	by	by	ADP
cana-1399	7	12	subdividing	subdivide	VERB
cana-1399	7	13	a	a	DET
cana-1399	7	14	star	star	NOUN
cana-1399	7	15	of	of	ADP
cana-1399	7	16	size	size	NOUN
cana-1399	7	17	three	three	NUM
cana-1399	7	18	once	once	ADV
cana-1399	7	19	,	,	PUNCT
cana-1399	7	20	providing	provide	VERB
cana-1399	7	21	conditions	condition	NOUN
cana-1399	7	22	for	for	ADP
cana-1399	7	23	fork	fork	NOUN
cana-1399	7	24	-	-	PUNCT
cana-1399	7	25	decomposition	decomposition	NOUN
cana-1399	7	26	of	of	ADP
cana-1399	7	27	some	some	DET
cana-1399	7	28	total	total	ADJ
cana-1399	7	29	graphs	graph	NOUN
cana-1399	7	30	[	[	X
cana-1399	7	31	2	2	NUM
cana-1399	7	32	]	]	PUNCT
cana-1399	7	33	.	.	PUNCT
cana-1399	8	1	ganguly	ganguly	PROPN
cana-1399	8	2	et	et	PROPN
cana-1399	8	3	al	al	PROPN
cana-1399	8	4	.	.	PROPN
cana-1399	8	5	demonstrated	demonstrate	VERB
cana-1399	8	6	the	the	DET
cana-1399	8	7	decomposition	decomposition	NOUN
cana-1399	8	8	of	of	ADP
cana-1399	8	9	the	the	DET
cana-1399	8	10	real	real	ADJ
cana-1399	8	11	line	line	NOUN
cana-1399	8	12	r	r	NOUN
cana-1399	8	13	into	into	ADP
cana-1399	8	14	complementary	complementary	ADJ
cana-1399	8	15	sets	set	NOUN
cana-1399	8	16	with	with	ADP
cana-1399	8	17	empty	empty	ADJ
cana-1399	8	18	ratio	ratio	NOUN
cana-1399	8	19	sets	set	NOUN
cana-1399	8	20	[	[	X
cana-1399	8	21	3	3	NUM
cana-1399	8	22	]	]	PUNCT
cana-1399	8	23	.	.	PUNCT
cana-1399	9	1	hasan	hasan	PROPN
cana-1399	9	2	et	et	PROPN
cana-1399	9	3	al	al	PROPN
cana-1399	9	4	.	.	PROPN
cana-1399	9	5	explored	explore	VERB
cana-1399	9	6	properties	property	NOUN
cana-1399	9	7	of	of	ADP
cana-1399	9	8	stiff	stiff	ADJ
cana-1399	9	9	modules	module	NOUN
cana-1399	9	10	in	in	ADP
cana-1399	9	11	qt	qt	PROPN
cana-1399	9	12	ag	ag	PROPN
cana-1399	9	13	modules	module	NOUN
cana-1399	9	14	[	[	X
cana-1399	9	15	4	4	NUM
cana-1399	9	16	]	]	PUNCT
cana-1399	9	17	.	.	PUNCT
cana-1399	10	1	bhatt	bhatt	PROPN
cana-1399	10	2	et	et	PROPN
cana-1399	10	3	al	al	PROPN
cana-1399	10	4	.	.	PROPN
cana-1399	10	5	computed	compute	VERB
cana-1399	10	6	a	a	DET
cana-1399	10	7	rank-1	rank-1	NUM
cana-1399	10	8	tensor	tensor	NOUN
cana-1399	10	9	approximation	approximation	NOUN
cana-1399	10	10	[	[	X
cana-1399	10	11	5	5	NUM
cana-1399	10	12	]	]	PUNCT
cana-1399	10	13	.	.	PUNCT
cana-1399	11	1	gao	gao	PROPN
cana-1399	11	2	et	et	PROPN
cana-1399	11	3	al	al	PROPN
cana-1399	11	4	.	.	PROPN
cana-1399	11	5	applied	apply	VERB
cana-1399	11	6	graph	graph	NOUN
cana-1399	11	7	theory	theory	NOUN
cana-1399	11	8	to	to	ADP
cana-1399	11	9	crystal	crystal	NOUN
cana-1399	11	10	structure	structure	NOUN
cana-1399	11	11	prediction	prediction	NOUN
cana-1399	12	1	[	[	X
cana-1399	12	2	6	6	NUM
cana-1399	12	3	]	]	PUNCT
cana-1399	12	4	.	.	PUNCT
cana-1399	13	1	guo	guo	PROPN
cana-1399	13	2	et	et	PROPN
cana-1399	13	3	al	al	PROPN
cana-1399	13	4	.	.	PROPN
cana-1399	14	1	characterized	characterize	VERB
cana-1399	14	2	hereditary	hereditary	ADJ
cana-1399	14	3	vertex	vertex	NOUN
cana-1399	14	4	decomposable	decomposable	ADJ
cana-1399	14	5	graphs	graph	NOUN
cana-1399	14	6	,	,	PUNCT
cana-1399	14	7	including	include	VERB
cana-1399	14	8	well	well	ADV
cana-1399	14	9	-	-	PUNCT
cana-1399	14	10	known	know	VERB
cana-1399	14	11	examples	example	NOUN
cana-1399	15	1	[	[	X
cana-1399	15	2	7	7	NUM
cana-1399	15	3	]	]	PUNCT
cana-1399	15	4	.	.	PUNCT
cana-1399	16	1	bonizzoni	bonizzoni	PROPN
cana-1399	16	2	et	et	PROPN
cana-1399	17	1	al	al	PROPN
cana-1399	17	2	.	.	PROPN
cana-1399	17	3	developed	develop	VERB
cana-1399	17	4	efficient	efficient	ADJ
cana-1399	17	5	algorithms	algorithm	NOUN
cana-1399	17	6	for	for	ADP
cana-1399	17	7	hypergraph	hypergraph	NOUN
cana-1399	17	8	decomposition	decomposition	NOUN
cana-1399	17	9	[	[	X
cana-1399	17	10	8	8	NUM
cana-1399	17	11	]	]	PUNCT
cana-1399	17	12	.	.	PUNCT
cana-1399	18	1	grohe	grohe	PROPN
cana-1399	18	2	et	et	PROPN
cana-1399	18	3	al	al	PROPN
cana-1399	18	4	.	.	PROPN
cana-1399	18	5	contributed	contribute	VERB
cana-1399	18	6	to	to	PART
cana-1399	18	7	graph	graph	VERB
cana-1399	18	8	minor	minor	ADJ
cana-1399	18	9	decomposition	decomposition	NOUN
cana-1399	18	10	[	[	X
cana-1399	18	11	9	9	NUM
cana-1399	18	12	]	]	PUNCT
cana-1399	18	13	.	.	PUNCT
cana-1399	19	1	mesady	mesady	PROPN
cana-1399	19	2	et	et	PROPN
cana-1399	19	3	al	al	PROPN
cana-1399	19	4	.	.	PUNCT
cana-1399	20	1	[	[	X
cana-1399	20	2	10	10	NUM
cana-1399	20	3	]	]	PUNCT
cana-1399	20	4	studied	study	VERB
cana-1399	20	5	edge	edge	NOUN
cana-1399	20	6	decomposition	decomposition	NOUN
cana-1399	20	7	on	on	ADP
cana-1399	20	8	circulant	circulant	ADJ
cana-1399	20	9	graphs	graph	NOUN
cana-1399	20	10	while	while	SCONJ
cana-1399	20	11	dac	dac	PROPN
cana-1399	20	12	et	et	PROPN
cana-1399	20	13	al	al	PROPN
cana-1399	20	14	.	.	PUNCT
cana-1399	21	1	[	[	X
cana-1399	21	2	11	11	NUM
cana-1399	21	3	]	]	PUNCT
cana-1399	21	4	explored	explore	VERB
cana-1399	21	5	a	a	DET
cana-1399	21	6	conjecture	conjecture	NOUN
cana-1399	21	7	on	on	ADP
cana-1399	21	8	digraph	digraph	ADJ
cana-1399	21	9	cycles	cycle	NOUN
cana-1399	21	10	.	.	PUNCT
cana-1399	22	1	most	most	ADJ
cana-1399	22	2	researchers	researcher	NOUN
cana-1399	22	3	attempt	attempt	VERB
cana-1399	22	4	to	to	PART
cana-1399	22	5	decompose	decompose	VERB
cana-1399	22	6	specific	specific	ADJ
cana-1399	22	7	kind	kind	NOUN
cana-1399	22	8	of	of	ADP
cana-1399	22	9	graphs	graph	NOUN
cana-1399	22	10	.	.	PUNCT
cana-1399	23	1	the	the	DET
cana-1399	23	2	questions	question	NOUN
cana-1399	23	3	that	that	PRON
cana-1399	23	4	arise	arise	VERB
cana-1399	23	5	is	be	AUX
cana-1399	23	6	“	"	PUNCT
cana-1399	23	7	is	be	AUX
cana-1399	23	8	it	it	PRON
cana-1399	23	9	possible	possible	ADJ
cana-1399	23	10	to	to	PART
cana-1399	23	11	decompose	decompose	VERB
cana-1399	23	12	any	any	DET
cana-1399	23	13	given	give	VERB
cana-1399	23	14	graph	graph	NOUN
cana-1399	23	15	g	g	PROPN
cana-1399	23	16	?	?	PUNCT
cana-1399	24	1	can	can	AUX
cana-1399	24	2	we	we	PRON
cana-1399	24	3	decompose	decompose	VERB
cana-1399	24	4	a	a	DET
cana-1399	24	5	random	random	ADJ
cana-1399	24	6	graph	graph	NOUN
cana-1399	24	7	g	g	NOUN
cana-1399	24	8	into	into	ADP
cana-1399	24	9	predefined	predefined	ADJ
cana-1399	24	10	type	type	NOUN
cana-1399	24	11	of	of	ADP
cana-1399	24	12	graphs	graph	NOUN
cana-1399	24	13	”	"	PUNCT
cana-1399	24	14	.	.	PUNCT
cana-1399	25	1	in	in	ADP
cana-1399	25	2	this	this	DET
cana-1399	25	3	article	article	NOUN
cana-1399	25	4	we	we	PRON
cana-1399	25	5	develop	develop	VERB
cana-1399	25	6	an	an	DET
cana-1399	25	7	iterative	iterative	NOUN
cana-1399	25	8	technique	technique	NOUN
cana-1399	25	9	to	to	PART
cana-1399	25	10	decompose	decompose	VERB
cana-1399	25	11	any	any	DET
cana-1399	25	12	random	random	ADJ
cana-1399	25	13	graph	graph	NOUN
cana-1399	25	14	into	into	ADP
cana-1399	25	15	a	a	DET
cana-1399	25	16	specific	specific	ADJ
cana-1399	25	17	type	type	NOUN
cana-1399	25	18	of	of	ADP
cana-1399	25	19	graphs	graph	NOUN
cana-1399	25	20	called	call	VERB
cana-1399	25	21	vdt	vdt	PROPN
cana-1399	25	22	graphs	graph	NOUN
cana-1399	25	23	.	.	PUNCT
cana-1399	26	1	2	2	X
cana-1399	26	2	.	.	X
cana-1399	26	3	preliminary	preliminary	ADJ
cana-1399	26	4	note	note	NOUN
cana-1399	26	5	for	for	ADP
cana-1399	26	6	any	any	DET
cana-1399	26	7	set	set	NOUN
cana-1399	26	8	s	s	NOUN
cana-1399	26	9	of	of	ADP
cana-1399	26	10	vertices	vertex	NOUN
cana-1399	26	11	in	in	ADP
cana-1399	26	12	g	g	NOUN
cana-1399	26	13	,	,	PUNCT
cana-1399	26	14	the	the	DET
cana-1399	26	15	induced	induced	ADJ
cana-1399	26	16	subgraph	subgraph	NOUN
cana-1399	26	17	⟨s⟩	⟨s⟩	PROPN
cana-1399	26	18	is	be	AUX
cana-1399	26	19	the	the	DET
cana-1399	26	20	maximal	maximal	ADJ
cana-1399	26	21	subgraph	subgraph	NOUN
cana-1399	26	22	of	of	ADP
cana-1399	26	23	g	g	PROPN
cana-1399	26	24	with	with	ADP
cana-1399	26	25	vertex	vertex	NOUN
cana-1399	26	26	set	set	VERB
cana-1399	26	27	s.	s.	PROPN
cana-1399	26	28	a	a	DET
cana-1399	26	29	tree	tree	NOUN
cana-1399	26	30	is	be	AUX
cana-1399	26	31	a	a	DET
cana-1399	26	32	connected	connected	ADJ
cana-1399	26	33	graph	graph	NOUN
cana-1399	26	34	without	without	ADP
cana-1399	26	35	cycles	cycle	NOUN
cana-1399	26	36	.	.	PUNCT
cana-1399	27	1	forks	fork	NOUN
cana-1399	27	2	are	be	AUX
cana-1399	27	3	trees	tree	NOUN
cana-1399	27	4	formed	form	VERB
cana-1399	27	5	by	by	ADP
cana-1399	27	6	subdividing	subdivide	VERB
cana-1399	27	7	a	a	DET
cana-1399	27	8	star	star	NOUN
cana-1399	27	9	of	of	ADP
cana-1399	27	10	size	size	NOUN
cana-1399	27	11	three	three	NUM
cana-1399	27	12	exactly	exactly	ADV
cana-1399	27	13	once	once	ADV
cana-1399	27	14	.	.	PUNCT
cana-1399	28	1	a	a	DET
cana-1399	28	2	path	path	NOUN
cana-1399	28	3	is	be	AUX
cana-1399	28	4	a	a	DET
cana-1399	28	5	sequence	sequence	NOUN
cana-1399	28	6	of	of	ADP
cana-1399	28	7	connected	connected	ADJ
cana-1399	28	8	vertices	vertex	NOUN
cana-1399	28	9	.	.	PUNCT
cana-1399	29	1	a	a	DET
cana-1399	29	2	comb	comb	NOUN
cana-1399	29	3	is	be	AUX
cana-1399	29	4	a	a	DET
cana-1399	29	5	graph	graph	NOUN
cana-1399	29	6	shaped	shape	VERB
cana-1399	29	7	like	like	ADP
cana-1399	29	8	a	a	DET
cana-1399	29	9	comb	comb	NOUN
cana-1399	29	10	with	with	ADP
cana-1399	29	11	a	a	DET
cana-1399	29	12	central	central	ADJ
cana-1399	29	13	path	path	NOUN
cana-1399	29	14	and	and	CCONJ
cana-1399	29	15	hanging	hang	VERB
cana-1399	29	16	edges	edge	NOUN
cana-1399	29	17	.	.	PUNCT
cana-1399	30	1	graph	graph	NOUN
cana-1399	30	2	decomposition	decomposition	NOUN
cana-1399	30	3	involves	involve	VERB
cana-1399	30	4	dividing	divide	VERB
cana-1399	30	5	a	a	DET
cana-1399	30	6	graph	graph	NOUN
cana-1399	30	7	into	into	ADP
cana-1399	30	8	smaller	small	ADJ
cana-1399	30	9	graphs	graph	NOUN
cana-1399	30	10	such	such	ADJ
cana-1399	30	11	that	that	SCONJ
cana-1399	30	12	every	every	DET
cana-1399	30	13	edge	edge	NOUN
cana-1399	30	14	appears	appear	VERB
cana-1399	30	15	in	in	ADP
cana-1399	30	16	exactly	exactly	ADV
cana-1399	30	17	one	one	NUM
cana-1399	30	18	of	of	ADP
cana-1399	30	19	the	the	DET
cana-1399	30	20	smaller	small	ADJ
cana-1399	30	21	graphs	graph	NOUN
cana-1399	30	22	.	.	PUNCT
cana-1399	31	1	a	a	DET
cana-1399	31	2	dominating	dominating	NOUN
cana-1399	31	3	set	set	NOUN
cana-1399	31	4	d	d	NOUN
cana-1399	31	5	of	of	ADP
cana-1399	31	6	g	g	PROPN
cana-1399	31	7	is	be	AUX
cana-1399	31	8	a	a	DET
cana-1399	31	9	set	set	NOUN
cana-1399	31	10	of	of	ADP
cana-1399	31	11	vertices	vertex	NOUN
cana-1399	31	12	of	of	ADP
cana-1399	31	13	g	g	NOUN
cana-1399	31	14	such	such	ADJ
cana-1399	31	15	that	that	SCONJ
cana-1399	31	16	every	every	DET
cana-1399	31	17	vertex	vertex	NOUN
cana-1399	31	18	in	in	ADP
cana-1399	31	19	v	v	NUM
cana-1399	31	20	–	–	PUNCT
cana-1399	31	21	d	d	PRON
cana-1399	31	22	is	be	AUX
cana-1399	31	23	adjacent	adjacent	ADJ
cana-1399	31	24	to	to	ADP
cana-1399	31	25	a	a	DET
cana-1399	31	26	vertex	vertex	NOUN
cana-1399	31	27	in	in	ADP
cana-1399	31	28	d.	d.	PROPN
cana-1399	31	29	if	if	SCONJ
cana-1399	31	30	d	d	PROPN
cana-1399	31	31	has	have	VERB
cana-1399	31	32	the	the	DET
cana-1399	31	33	smallest	small	ADJ
cana-1399	31	34	possible	possible	ADJ
cana-1399	31	35	cardinality	cardinality	NOUN
cana-1399	31	36	of	of	ADP
cana-1399	31	37	any	any	DET
cana-1399	31	38	dominating	dominating	NOUN
cana-1399	31	39	set	set	NOUN
cana-1399	31	40	of	of	ADP
cana-1399	31	41	g	g	NOUN
cana-1399	31	42	,	,	PUNCT
cana-1399	31	43	then	then	ADV
cana-1399	31	44	d	d	PROPN
cana-1399	31	45	is	be	AUX
cana-1399	31	46	called	call	VERB
cana-1399	31	47	a	a	DET
cana-1399	31	48	minimum	minimum	ADJ
cana-1399	31	49	dominating	dominating	NOUN
cana-1399	31	50	set	set	NOUN
cana-1399	31	51	.	.	PUNCT
cana-1399	32	1	the	the	DET
cana-1399	32	2	cardinality	cardinality	NOUN
cana-1399	32	3	of	of	ADP
cana-1399	32	4	any	any	DET
cana-1399	32	5	minimum	minimum	ADJ
cana-1399	32	6	dominating	dominating	NOUN
cana-1399	32	7	set	set	NOUN
cana-1399	32	8	for	for	ADP
cana-1399	32	9	g	g	PROPN
cana-1399	32	10	is	be	AUX
cana-1399	32	11	called	call	VERB
cana-1399	32	12	a	a	DET
cana-1399	32	13	domination	domination	NOUN
cana-1399	32	14	number	number	NOUN
cana-1399	32	15	of	of	ADP
cana-1399	32	16	g	g	NOUN
cana-1399	32	17	and	and	CCONJ
cana-1399	32	18	is	be	AUX
cana-1399	32	19	denoted	denote	VERB
cana-1399	32	20	by	by	ADP
cana-1399	32	21	γ(g	γ(g	PROPN
cana-1399	32	22	)	)	PUNCT
cana-1399	32	23	.	.	PUNCT
cana-1399	33	1	a	a	DET
cana-1399	33	2	γ	γ	PROPN
cana-1399	33	3	−	−	PROPN
cana-1399	33	4	set	set	NOUN
cana-1399	33	5	denotes	denote	VERB
cana-1399	33	6	a	a	DET
cana-1399	33	7	dominating	dominating	NOUN
cana-1399	33	8	set	set	NOUN
cana-1399	33	9	for	for	ADP
cana-1399	33	10	g	g	NOUN
cana-1399	33	11	with	with	ADP
cana-1399	33	12	minimum	minimum	ADJ
cana-1399	33	13	cardinality	cardinality	NOUN
cana-1399	34	1	[	[	X
cana-1399	34	2	12	12	NUM
cana-1399	34	3	]	]	PUNCT
cana-1399	34	4	.	.	PUNCT
cana-1399	35	1	in	in	ADP
cana-1399	35	2	this	this	DET
cana-1399	35	3	communications	communication	NOUN
cana-1399	35	4	on	on	ADP
cana-1399	35	5	applied	apply	VERB
cana-1399	35	6	nonlinear	nonlinear	ADJ
cana-1399	35	7	analysis	analysis	NOUN
cana-1399	35	8	issn	issn	NOUN
cana-1399	35	9	:	:	PUNCT
cana-1399	35	10	1074	1074	NUM
cana-1399	35	11	-	-	PUNCT
cana-1399	35	12	133x	133x	NUM
cana-1399	35	13	vol	vol	NOUN
cana-1399	35	14	31	31	NUM
cana-1399	35	15	no	no	NOUN
cana-1399	35	16	.	.	PUNCT
cana-1399	36	1	7s	7	NOUN
cana-1399	36	2	(	(	PUNCT
cana-1399	36	3	2024	2024	NUM
cana-1399	36	4	)	)	PUNCT
cana-1399	36	5	575	575	NUM
cana-1399	36	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1399	36	7	article	article	NOUN
cana-1399	36	8	we	we	PRON
cana-1399	36	9	have	have	AUX
cana-1399	36	10	developed	develop	VERB
cana-1399	36	11	an	an	DET
cana-1399	36	12	iterative	iterative	NOUN
cana-1399	36	13	procedure	procedure	NOUN
cana-1399	36	14	for	for	ADP
cana-1399	36	15	decomposing	decompose	VERB
cana-1399	36	16	any	any	DET
cana-1399	36	17	random	random	ADJ
cana-1399	36	18	graph	graph	NOUN
cana-1399	36	19	g	g	NOUN
cana-1399	36	20	into	into	ADP
cana-1399	36	21	subgraphs	subgraph	NOUN
cana-1399	36	22	1	1	NUM
cana-1399	36	23	2	2	NUM
cana-1399	36	24	kh	kh	NOUN
cana-1399	36	25	,	,	PUNCT
cana-1399	36	26	h	h	NOUN
cana-1399	36	27	,	,	PUNCT
cana-1399	36	28	...	...	PUNCT
cana-1399	36	29	,	,	PUNCT
cana-1399	36	30	h	h	NOUN
cana-1399	36	31	such	such	ADJ
cana-1399	36	32	that	that	SCONJ
cana-1399	36	33	each	each	DET
cana-1399	36	34	hi	hi	INTJ
cana-1399	36	35	is	be	AUX
cana-1399	36	36	a	a	DET
cana-1399	36	37	vdt	vdt	PROPN
cana-1399	36	38	graphs	graph	NOUN
cana-1399	36	39	,	,	PUNCT
cana-1399	36	40	1	1	NUM
cana-1399	36	41	≤	≤	NUM
cana-1399	36	42	i	i	NOUN
cana-1399	36	43	≤	≤	PROPN
cana-1399	36	44	k.	k.	PROPN
cana-1399	37	1	3	3	X
cana-1399	37	2	.	.	PUNCT
cana-1399	38	1	vdt	vdt	PROPN
cana-1399	38	2	graph	graph	NOUN
cana-1399	38	3	a	a	DET
cana-1399	38	4	graph	graph	NOUN
cana-1399	38	5	g	g	NOUN
cana-1399	38	6	is	be	AUX
cana-1399	38	7	said	say	VERB
cana-1399	38	8	to	to	PART
cana-1399	38	9	be	be	AUX
cana-1399	38	10	vdt	vdt	PROPN
cana-1399	38	11	graph	graph	NOUN
cana-1399	38	12	if	if	SCONJ
cana-1399	38	13	g	g	PROPN
cana-1399	38	14	has	have	VERB
cana-1399	38	15	at	at	ADV
cana-1399	38	16	least	least	ADV
cana-1399	38	17	one	one	NUM
cana-1399	38	18	γ	γ	NOUN
cana-1399	38	19	–	–	PUNCT
cana-1399	38	20	set	set	ADJ
cana-1399	38	21	d	d	NOUN
cana-1399	38	22	such	such	ADJ
cana-1399	38	23	that	that	DET
cana-1399	38	24	⟨v	⟨v	NOUN
cana-1399	38	25	–	–	PUNCT
cana-1399	38	26	d⟩	d⟩	NOUN
cana-1399	38	27	is	be	AUX
cana-1399	38	28	a	a	DET
cana-1399	38	29	tree	tree	NOUN
cana-1399	38	30	.	.	PUNCT
cana-1399	39	1	we	we	PRON
cana-1399	39	2	shall	shall	AUX
cana-1399	39	3	denote	denote	VERB
cana-1399	39	4	such	such	ADJ
cana-1399	39	5	graphs	graph	NOUN
cana-1399	39	6	as	as	ADP
cana-1399	39	7	vdt	vdt	PROPN
cana-1399	39	8	graphs	graph	NOUN
cana-1399	39	9	and	and	CCONJ
cana-1399	39	10	the	the	DET
cana-1399	39	11	γ	γ	X
cana-1399	39	12	–	–	PUNCT
cana-1399	39	13	set	set	VERB
cana-1399	39	14	d	d	ADP
cana-1399	39	15	such	such	ADJ
cana-1399	39	16	that	that	DET
cana-1399	39	17	⟨v	⟨v	NOUN
cana-1399	39	18	–	–	PUNCT
cana-1399	39	19	d⟩	d⟩	NOUN
cana-1399	39	20	is	be	AUX
cana-1399	39	21	a	a	DET
cana-1399	39	22	tree	tree	NOUN
cana-1399	39	23	as	as	ADP
cana-1399	39	24	a	a	DET
cana-1399	39	25	vdt	vdt	PROPN
cana-1399	39	26	set.	set.	PROPN
cana-1399	39	27			NOUN
cana-1399	39	28	the	the	DET
cana-1399	39	29	graphs	graph	NOUN
cana-1399	39	30	in	in	ADP
cana-1399	39	31	figure	figure	NOUN
cana-1399	39	32	1	1	NUM
cana-1399	39	33	is	be	AUX
cana-1399	39	34	an	an	DET
cana-1399	39	35	example	example	NOUN
cana-1399	39	36	of	of	ADP
cana-1399	39	37	vdt	vdt	PROPN
cana-1399	39	38	and	and	CCONJ
cana-1399	39	39	non	non	ADJ
cana-1399	39	40	vdt	vdt	PROPN
cana-1399	39	41	graph	graph	NOUN
cana-1399	39	42	.	.	PUNCT
cana-1399	40	1	vdt	vdt	PROPN
cana-1399	40	2	graph	graph	NOUN
cana-1399	40	3	non	non	ADJ
cana-1399	40	4	–	–	PUNCT
cana-1399	40	5	vdt	vdt	PROPN
cana-1399	40	6	graph	graph	NOUN
cana-1399	40	7	fig	fig	NOUN
cana-1399	40	8	1	1	NUM
cana-1399	40	9	.	.	PUNCT
cana-1399	41	1	vdt	vdt	PROPN
cana-1399	41	2	and	and	CCONJ
cana-1399	41	3	non	non	ADJ
cana-1399	41	4	-	-	ADJ
cana-1399	41	5	vdt	vdt	ADJ
cana-1399	41	6	graphs	graph	NOUN
cana-1399	41	7	now	now	ADV
cana-1399	41	8	let	let	VERB
cana-1399	41	9	us	we	PRON
cana-1399	41	10	prove	prove	VERB
cana-1399	41	11	few	few	ADJ
cana-1399	41	12	observations	observation	NOUN
cana-1399	41	13	to	to	PART
cana-1399	41	14	decompose	decompose	VERB
cana-1399	41	15	g	g	NOUN
cana-1399	41	16	into	into	ADP
cana-1399	41	17	vdt	vdt	PROPN
cana-1399	41	18	graphs	graph	NOUN
cana-1399	41	19	.	.	PUNCT
cana-1399	42	1	in	in	ADP
cana-1399	42	2	all	all	DET
cana-1399	42	3	these	these	DET
cana-1399	42	4	observations	observation	NOUN
cana-1399	42	5	,	,	PUNCT
cana-1399	42	6	let	let	VERB
cana-1399	42	7	g	g	PRON
cana-1399	42	8	be	be	AUX
cana-1399	42	9	a	a	DET
cana-1399	42	10	vdt	vdt	PROPN
cana-1399	42	11	graph	graph	NOUN
cana-1399	42	12	and	and	CCONJ
cana-1399	42	13	d	d	X
cana-1399	42	14	a	a	DET
cana-1399	42	15	vdt	vdt	PROPN
cana-1399	42	16	set	set	PROPN
cana-1399	42	17			PROPN
cana-1399	42	18	for	for	ADP
cana-1399	42	19	g.	g.	PROPN
cana-1399	42	20	theorem	theorem	VERB
cana-1399	42	21	1	1	NUM
cana-1399	42	22	d	d	NOUN
cana-1399	42	23	contains	contain	VERB
cana-1399	42	24	all	all	DET
cana-1399	42	25	the	the	DET
cana-1399	42	26	pendant	pendant	ADJ
cana-1399	42	27	vertices	vertex	NOUN
cana-1399	42	28	.	.	PUNCT
cana-1399	43	1	proof	proof	NOUN
cana-1399	43	2	if	if	SCONJ
cana-1399	43	3	possible	possible	ADJ
cana-1399	43	4	,	,	PUNCT
cana-1399	43	5	let	let	VERB
cana-1399	43	6	v	v	NOUN
cana-1399	43	7	∈	∈	NOUN
cana-1399	43	8	d	d	SCONJ
cana-1399	43	9	such	such	ADJ
cana-1399	43	10	that	that	DET
cana-1399	43	11	v	v	NOUN
cana-1399	43	12	is	be	AUX
cana-1399	43	13	a	a	DET
cana-1399	43	14	pendant	pendant	ADJ
cana-1399	43	15	vertex	vertex	NOUN
cana-1399	43	16	.	.	PUNCT
cana-1399	44	1	let	let	VERB
cana-1399	44	2	u	u	PRON
cana-1399	44	3	be	be	AUX
cana-1399	44	4	a	a	DET
cana-1399	44	5	support	support	NOUN
cana-1399	44	6	vertex	vertex	NOUN
cana-1399	44	7	with	with	ADP
cana-1399	44	8	respect	respect	NOUN
cana-1399	44	9	to	to	ADP
cana-1399	44	10	d.	d.	NOUN
cana-1399	44	11	we	we	PRON
cana-1399	44	12	know	know	VERB
cana-1399	44	13	that	that	SCONJ
cana-1399	44	14	both	both	DET
cana-1399	44	15	u	u	NOUN
cana-1399	44	16	,	,	PUNCT
cana-1399	44	17	v	v	NOUN
cana-1399	44	18	can	can	AUX
cana-1399	44	19	not	not	PART
cana-1399	44	20	be	be	AUX
cana-1399	44	21	contained	contain	VERB
cana-1399	44	22	in	in	ADP
cana-1399	44	23	d	d	PROPN
cana-1399	44	24	since	since	SCONJ
cana-1399	44	25	d′	d′	NUM
cana-1399	45	1	=	=	SYM
cana-1399	46	1	d	d	ADP
cana-1399	46	2	−	−	NOUN
cana-1399	46	3	v	v	NOUN
cana-1399	46	4	itself	itself	PRON
cana-1399	46	5	is	be	AUX
cana-1399	46	6	a	a	DET
cana-1399	46	7	γ	γ	NOUN
cana-1399	46	8	set	set	VERB
cana-1399	46	9	for	for	ADP
cana-1399	46	10	g	g	NOUN
cana-1399	46	11	,	,	PUNCT
cana-1399	46	12	a	a	DET
cana-1399	46	13	contradiction	contradiction	NOUN
cana-1399	46	14	to	to	ADP
cana-1399	46	15	our	our	PRON
cana-1399	46	16	assumption	assumption	NOUN
cana-1399	46	17	that	that	SCONJ
cana-1399	46	18	d	d	NOUN
cana-1399	46	19	is	be	AUX
cana-1399	46	20	a	a	DET
cana-1399	46	21	vdt	vdt	PROPN
cana-1399	46	22	set	set	PROPN
cana-1399	46	23			PROPN
cana-1399	46	24	.	.	PUNCT
cana-1399	47	1	so	so	ADV
cana-1399	47	2	,	,	PUNCT
cana-1399	47	3	if	if	SCONJ
cana-1399	47	4	v	v	ADP
cana-1399	47	5	∈	∈	PROPN
cana-1399	47	6	d	d	NOUN
cana-1399	47	7	,	,	PUNCT
cana-1399	47	8	u	u	PROPN
cana-1399	47	9			PROPN
cana-1399	47	10	d	d	PROPN
cana-1399	47	11	,	,	PUNCT
cana-1399	47	12	implies	imply	VERB
cana-1399	47	13	⟨v	⟨v	NOUN
cana-1399	47	14	−	−	PRON
cana-1399	47	15	d⟩	d⟩	NOUN
cana-1399	47	16	is	be	AUX
cana-1399	47	17	disconnected	disconnect	VERB
cana-1399	47	18	,	,	PUNCT
cana-1399	47	19	a	a	DET
cana-1399	47	20	contradiction	contradiction	NOUN
cana-1399	47	21	to	to	ADP
cana-1399	47	22	our	our	PRON
cana-1399	47	23	assumption	assumption	NOUN
cana-1399	47	24	that	that	SCONJ
cana-1399	47	25	d	d	NOUN
cana-1399	47	26	is	be	AUX
cana-1399	47	27	a	a	DET
cana-1399	47	28	vdt	vdt	PROPN
cana-1399	47	29	set	set	PROPN
cana-1399	47	30			PROPN
cana-1399	47	31	.	.	PUNCT
cana-1399	48	1	hence	hence	ADV
cana-1399	48	2	d	d	PROPN
cana-1399	48	3	contains	contain	VERB
cana-1399	48	4	all	all	DET
cana-1399	48	5	the	the	DET
cana-1399	48	6	pendant	pendant	ADJ
cana-1399	48	7	vertices	vertex	NOUN
cana-1399	48	8	of	of	ADP
cana-1399	48	9	g.	g.	PROPN
cana-1399	48	10	theorem	theorem	VERB
cana-1399	48	11	2	2	NUM
cana-1399	48	12	for	for	ADP
cana-1399	48	13	any	any	DET
cana-1399	48	14	support	support	NOUN
cana-1399	48	15	vertex	vertex	NOUN
cana-1399	48	16	u	u	NOUN
cana-1399	48	17	∈	∈	PROPN
cana-1399	48	18	g	g	PROPN
cana-1399	48	19	,	,	PUNCT
cana-1399	48	20	|n(u	|n(u	NOUN
cana-1399	48	21	)	)	PUNCT
cana-1399	48	22	∩	∩	NOUN
cana-1399	48	23	x	x	SYM
cana-1399	48	24	|	|	NOUN
cana-1399	48	25	=	=	SYM
cana-1399	48	26	1	1	NUM
cana-1399	48	27	,	,	PUNCT
cana-1399	48	28	where	where	SCONJ
cana-1399	48	29	x	x	PRON
cana-1399	48	30	is	be	AUX
cana-1399	48	31	the	the	DET
cana-1399	48	32	set	set	NOUN
cana-1399	48	33	of	of	ADP
cana-1399	48	34	all	all	DET
cana-1399	48	35	pendant	pendant	ADJ
cana-1399	48	36	vertices	vertex	NOUN
cana-1399	48	37	of	of	ADP
cana-1399	48	38	g.	g.	NOUN
cana-1399	48	39	proof	proof	NOUN
cana-1399	48	40	if	if	SCONJ
cana-1399	48	41	possible	possible	ADJ
cana-1399	48	42	,	,	PUNCT
cana-1399	48	43	let	let	VERB
cana-1399	48	44	u	u	PRON
cana-1399	48	45	∈	∈	PROPN
cana-1399	48	46	g	g	PROPN
cana-1399	48	47	such	such	ADJ
cana-1399	48	48	that	that	DET
cana-1399	48	49	|n(u	|n(u	NOUN
cana-1399	48	50	)	)	PUNCT
cana-1399	48	51	∩	∩	NOUN
cana-1399	48	52	x	x	SYM
cana-1399	48	53	|	|	ADV
cana-1399	48	54	≥	≥	NOUN
cana-1399	48	55	2	2	NUM
cana-1399	48	56	.	.	PUNCT
cana-1399	48	57	without	without	ADP
cana-1399	48	58	loss	loss	NOUN
cana-1399	48	59	of	of	ADP
cana-1399	48	60	generality	generality	NOUN
cana-1399	48	61	let	let	VERB
cana-1399	48	62	|n(u	|n(u	NOUN
cana-1399	48	63	)	)	PUNCT
cana-1399	48	64	∩	∩	NOUN
cana-1399	48	65	x	x	SYM
cana-1399	48	66	|	|	ADV
cana-1399	48	67	=	=	SYM
cana-1399	48	68	k	k	PROPN
cana-1399	48	69	,	,	PUNCT
cana-1399	48	70	k	k	PROPN
cana-1399	48	71	≥	≥	NUM
cana-1399	48	72	2	2	X
cana-1399	48	73	.	.	PUNCT
cana-1399	49	1	let	let	VERB
cana-1399	49	2	x1	x1	NOUN
cana-1399	49	3	⊆	⊆	NUM
cana-1399	49	4	x	x	SYM
cana-1399	49	5	=	=	SYM
cana-1399	49	6	1	1	NUM
cana-1399	49	7	2	2	NUM
cana-1399	49	8	k{v	k{v	NOUN
cana-1399	49	9	,	,	PUNCT
cana-1399	49	10	v	v	INTJ
cana-1399	49	11	,	,	PUNCT
cana-1399	49	12	...	...	PUNCT
cana-1399	49	13	,	,	PUNCT
cana-1399	49	14	v	v	X
cana-1399	49	15	}	}	PUNCT
cana-1399	49	16	be	be	AUX
cana-1399	49	17	the	the	DET
cana-1399	49	18	set	set	NOUN
cana-1399	49	19	of	of	ADP
cana-1399	49	20	all	all	DET
cana-1399	49	21	pendant	pendant	ADJ
cana-1399	49	22	vertices	vertex	NOUN
cana-1399	49	23	adjacent	adjacent	ADJ
cana-1399	49	24	to	to	PART
cana-1399	49	25	u.	u.	VERB
cana-1399	49	26	then	then	ADV
cana-1399	49	27	⟨v	⟨v	NOUN
cana-1399	49	28	−	−	PROPN
cana-1399	49	29	d⟩	d⟩	NOUN
cana-1399	49	30	is	be	AUX
cana-1399	49	31	a	a	DET
cana-1399	49	32	disconnected	disconnected	ADJ
cana-1399	49	33	graph	graph	NOUN
cana-1399	49	34	with	with	ADP
cana-1399	49	35	at	at	ADP
cana-1399	49	36	least	least	ADJ
cana-1399	49	37	k	k	NOUN
cana-1399	49	38	+	+	CCONJ
cana-1399	49	39	1	1	NUM
cana-1399	49	40	components	component	NOUN
cana-1399	49	41	,	,	PUNCT
cana-1399	49	42	a	a	DET
cana-1399	49	43	contradiction	contradiction	NOUN
cana-1399	49	44	to	to	ADP
cana-1399	49	45	our	our	PRON
cana-1399	49	46	assumption	assumption	NOUN
cana-1399	49	47	that	that	SCONJ
cana-1399	49	48	d	d	NOUN
cana-1399	49	49	is	be	AUX
cana-1399	49	50	a	a	DET
cana-1399	49	51	vdt	vdt	PROPN
cana-1399	49	52	set	set	PROPN
cana-1399	49	53			PROPN
cana-1399	49	54	with	with	ADP
cana-1399	49	55	respect	respect	NOUN
cana-1399	49	56	to	to	ADP
cana-1399	49	57	g	g	NOUN
cana-1399	49	58	,	,	PUNCT
cana-1399	49	59	which	which	PRON
cana-1399	49	60	implies	imply	VERB
cana-1399	49	61	|n(u	|n(u	NOUN
cana-1399	49	62	)	)	PUNCT
cana-1399	49	63	∩	∩	NOUN
cana-1399	49	64	x	x	SYM
cana-1399	49	65	|	|	ADV
cana-1399	49	66	=	=	SYM
cana-1399	49	67	1	1	X
cana-1399	49	68	.	.	PUNCT
cana-1399	49	69	theorem	theorem	VERB
cana-1399	49	70	3	3	NUM
cana-1399	49	71	the	the	DET
cana-1399	49	72	corona	corona	NOUN
cana-1399	49	73	graph	graph	NOUN
cana-1399	49	74	g	g	PROPN
cana-1399	49	75	◦	◦	NOUN
cana-1399	49	76	k1	k1	NOUN
cana-1399	49	77	is	be	AUX
cana-1399	49	78	a	a	DET
cana-1399	49	79	vdt	vdt	PROPN
cana-1399	49	80	graph	graph	NOUN
cana-1399	49	81	if	if	SCONJ
cana-1399	49	82	g	g	PROPN
cana-1399	49	83	is	be	AUX
cana-1399	49	84	a	a	DET
cana-1399	49	85	tree	tree	NOUN
cana-1399	49	86	.	.	PUNCT
cana-1399	50	1	proof	proof	NOUN
cana-1399	50	2	let	let	VERB
cana-1399	50	3	g	g	NOUN
cana-1399	50	4	be	be	AUX
cana-1399	50	5	a	a	DET
cana-1399	50	6	tree	tree	NOUN
cana-1399	50	7	.	.	PUNCT
cana-1399	51	1	consider	consider	VERB
cana-1399	51	2	t	t	NOUN
cana-1399	51	3	◦	◦	NOUN
cana-1399	51	4	k1	k1	PROPN
cana-1399	51	5	.	.	PUNCT
cana-1399	52	1	let	let	VERB
cana-1399	52	2	t	t	NOUN
cana-1399	52	3	◦	◦	VERB
cana-1399	52	4	k1	k1	NOUN
cana-1399	52	5	=	=	SYM
cana-1399	52	6	y1	y1	NOUN
cana-1399	52	7	∪	∪	NOUN
cana-1399	52	8	y2	y2	NOUN
cana-1399	52	9	=	=	SYM
cana-1399	52	10	1	1	NUM
cana-1399	52	11	2	2	NUM
cana-1399	52	12	k{u	k{u	NOUN
cana-1399	52	13	,	,	PUNCT
cana-1399	52	14	u	u	NOUN
cana-1399	52	15	,	,	PUNCT
cana-1399	52	16	...	...	PUNCT
cana-1399	52	17	,	,	PUNCT
cana-1399	52	18	u	u	NOUN
cana-1399	52	19	}	}	PUNCT
cana-1399	52	20	∪	∪	VERB
cana-1399	52	21	1	1	NUM
cana-1399	52	22	2	2	NUM
cana-1399	52	23	k{v	k{v	NOUN
cana-1399	52	24	,	,	PUNCT
cana-1399	52	25	v	v	INTJ
cana-1399	52	26	,	,	PUNCT
cana-1399	52	27	...	...	PUNCT
cana-1399	52	28	,	,	PUNCT
cana-1399	52	29	v	v	X
cana-1399	52	30	}	}	PUNCT
cana-1399	52	31	where	where	SCONJ
cana-1399	52	32	⟨y1⟩	⟨y1⟩	NOUN
cana-1399	52	33	is	be	AUX
cana-1399	52	34	a	a	DET
cana-1399	52	35	tree	tree	NOUN
cana-1399	52	36	and	and	CCONJ
cana-1399	52	37	⟨y2⟩	⟨y2⟩	NOUN
cana-1399	52	38	is	be	AUX
cana-1399	52	39	a	a	DET
cana-1399	52	40	null	null	ADJ
cana-1399	52	41	graph	graph	NOUN
cana-1399	52	42	.	.	PUNCT
cana-1399	53	1	from	from	ADP
cana-1399	53	2	theorem	theorem	NOUN
cana-1399	53	3	1	1	NUM
cana-1399	53	4	,	,	PUNCT
cana-1399	53	5	we	we	PRON
cana-1399	53	6	know	know	VERB
cana-1399	53	7	that	that	SCONJ
cana-1399	53	8	d	d	PROPN
cana-1399	53	9	contains	contain	VERB
cana-1399	53	10	all	all	DET
cana-1399	53	11	the	the	DET
cana-1399	53	12	pendant	pendant	ADJ
cana-1399	53	13	vertices	vertex	NOUN
cana-1399	53	14	,	,	PUNCT
cana-1399	53	15	implies	imply	VERB
cana-1399	53	16	y2	y2	PROPN
cana-1399	53	17	∈	∈	PROPN
cana-1399	53	18	d.	d.	PROPN
cana-1399	53	19	also	also	ADV
cana-1399	53	20	,	,	PUNCT
cana-1399	53	21	by	by	ADP
cana-1399	53	22	theorem	theorem	NOUN
cana-1399	53	23	2	2	NUM
cana-1399	53	24	,	,	PUNCT
cana-1399	53	25	we	we	PRON
cana-1399	53	26	know	know	VERB
cana-1399	53	27	that	that	SCONJ
cana-1399	53	28	every	every	DET
cana-1399	53	29	ui	ui	PROPN
cana-1399	53	30	,	,	PUNCT
cana-1399	53	31	1	1	NUM
cana-1399	53	32	≤	≤	NUM
cana-1399	53	33	i	i	NOUN
cana-1399	53	34	≤	≤	PUNCT
cana-1399	54	1	k	k	X
cana-1399	54	2	,	,	PUNCT
cana-1399	54	3	is	be	AUX
cana-1399	54	4	a	a	DET
cana-1399	54	5	support	support	NOUN
cana-1399	54	6	vertex	vertex	NOUN
cana-1399	54	7	.	.	PUNCT
cana-1399	55	1	by	by	ADP
cana-1399	55	2	theorem	theorem	NOUN
cana-1399	55	3	2	2	NUM
cana-1399	55	4	,	,	PUNCT
cana-1399	55	5	we	we	PRON
cana-1399	55	6	know	know	VERB
cana-1399	55	7	that	that	SCONJ
cana-1399	55	8	y1	y1	NOUN
cana-1399	55	9	does	do	AUX
cana-1399	55	10	not	not	PART
cana-1399	55	11	belong	belong	VERB
cana-1399	55	12	to	to	ADP
cana-1399	55	13	d.	d.	PROPN
cana-1399	55	14	also	also	ADV
cana-1399	55	15	,	,	PUNCT
cana-1399	55	16	⟨y1⟩	⟨y1⟩	NOUN
cana-1399	55	17	is	be	AUX
cana-1399	55	18	a	a	DET
cana-1399	55	19	tree	tree	NOUN
cana-1399	55	20	,	,	PUNCT
cana-1399	55	21	implies	imply	VERB
cana-1399	55	22	g	g	PROPN
cana-1399	55	23	◦	◦	NOUN
cana-1399	55	24	k1	k1	PROPN
cana-1399	55	25	is	be	AUX
cana-1399	55	26	a	a	DET
cana-1399	55	27	vdt	vdt	PROPN
cana-1399	55	28	graph	graph	NOUN
cana-1399	55	29	if	if	SCONJ
cana-1399	55	30	g	g	PROPN
cana-1399	55	31	is	be	AUX
cana-1399	55	32	tree	tree	NOUN
cana-1399	55	33	.	.	PUNCT
cana-1399	56	1	communications	communication	NOUN
cana-1399	56	2	on	on	ADP
cana-1399	56	3	applied	apply	VERB
cana-1399	56	4	nonlinear	nonlinear	ADJ
cana-1399	56	5	analysis	analysis	NOUN
cana-1399	56	6	issn	issn	NOUN
cana-1399	56	7	:	:	PUNCT
cana-1399	56	8	1074	1074	NUM
cana-1399	56	9	-	-	PUNCT
cana-1399	56	10	133x	133x	NUM
cana-1399	56	11	vol	vol	NOUN
cana-1399	56	12	31	31	NUM
cana-1399	56	13	no	no	NOUN
cana-1399	56	14	.	.	PUNCT
cana-1399	57	1	7s	7	NOUN
cana-1399	57	2	(	(	PUNCT
cana-1399	57	3	2024	2024	NUM
cana-1399	57	4	)	)	PUNCT
cana-1399	57	5	576	576	NUM
cana-1399	57	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1399	57	7	in	in	ADP
cana-1399	57	8	general	general	ADJ
cana-1399	57	9	g	g	PROPN
cana-1399	57	10	◦	◦	NOUN
cana-1399	57	11	k1	k1	NOUN
cana-1399	57	12	need	need	AUX
cana-1399	57	13	not	not	PART
cana-1399	57	14	be	be	AUX
cana-1399	57	15	a	a	DET
cana-1399	57	16	vdt	vdt	PROPN
cana-1399	57	17	graph	graph	NOUN
cana-1399	57	18	for	for	ADP
cana-1399	57	19	any	any	DET
cana-1399	57	20	graph	graph	NOUN
cana-1399	57	21	g.	g.	NOUN
cana-1399	57	22	the	the	DET
cana-1399	57	23	graph	graph	NOUN
cana-1399	57	24	in	in	ADP
cana-1399	57	25	figure	figure	NOUN
cana-1399	57	26	2	2	NUM
cana-1399	57	27	is	be	AUX
cana-1399	57	28	an	an	DET
cana-1399	57	29	example	example	NOUN
cana-1399	57	30	of	of	ADP
cana-1399	57	31	corona	corona	NOUN
cana-1399	57	32	graph	graph	NOUN
cana-1399	57	33	that	that	PRON
cana-1399	57	34	is	be	AUX
cana-1399	57	35	not	not	PART
cana-1399	57	36	vdt	vdt	PROPN
cana-1399	57	37	.	.	PROPN
cana-1399	58	1	from	from	ADP
cana-1399	58	2	these	these	DET
cana-1399	58	3	observations	observation	NOUN
cana-1399	58	4	we	we	PRON
cana-1399	58	5	know	know	VERB
cana-1399	58	6	that	that	SCONJ
cana-1399	58	7	there	there	PRON
cana-1399	58	8	exist	exist	VERB
cana-1399	58	9	a	a	DET
cana-1399	58	10	family	family	NOUN
cana-1399	58	11	of	of	ADP
cana-1399	58	12	graphs	graph	NOUN
cana-1399	58	13	t	t	PROPN
cana-1399	58	14	◦	◦	NOUN
cana-1399	58	15	k1	k1	NOUN
cana-1399	58	16	that	that	PRON
cana-1399	58	17	are	be	AUX
cana-1399	58	18	vdt	vdt	PROPN
cana-1399	58	19	for	for	ADP
cana-1399	58	20	any	any	DET
cana-1399	58	21	tree	tree	NOUN
cana-1399	58	22	t.	t.	NOUN
cana-1399	58	23	for	for	ADP
cana-1399	58	24	our	our	PRON
cana-1399	58	25	purpose	purpose	NOUN
cana-1399	58	26	of	of	ADP
cana-1399	58	27	decomposition	decomposition	NOUN
cana-1399	58	28	,	,	PUNCT
cana-1399	58	29	we	we	PRON
cana-1399	58	30	shall	shall	AUX
cana-1399	58	31	choose	choose	VERB
cana-1399	58	32	the	the	DET
cana-1399	58	33	vdt	vdt	PROPN
cana-1399	58	34	trees	tree	NOUN
cana-1399	58	35	p2	p2	NOUN
cana-1399	58	36	,	,	PUNCT
cana-1399	58	37	p4	p4	ADJ
cana-1399	58	38	,	,	PUNCT
cana-1399	58	39	comb	comb	NOUN
cana-1399	58	40	graphs	graph	NOUN
cana-1399	58	41	.	.	PUNCT
cana-1399	59	1	now	now	ADV
cana-1399	59	2	we	we	PRON
cana-1399	59	3	continue	continue	VERB
cana-1399	59	4	further	far	ADV
cana-1399	59	5	to	to	PART
cana-1399	59	6	determine	determine	VERB
cana-1399	59	7	a	a	DET
cana-1399	59	8	decomposition	decomposition	NOUN
cana-1399	59	9	of	of	ADP
cana-1399	59	10	any	any	DET
cana-1399	59	11	given	give	VERB
cana-1399	59	12	graph	graph	NOUN
cana-1399	59	13	into	into	ADP
cana-1399	59	14	p2	p2	PROPN
cana-1399	59	15	,	,	PUNCT
cana-1399	59	16	p4	p4	ADJ
cana-1399	59	17	,	,	PUNCT
cana-1399	59	18	comb	comb	NOUN
cana-1399	59	19	graphs	graph	NOUN
cana-1399	59	20	.	.	PUNCT
cana-1399	60	1	fig	fig	NOUN
cana-1399	60	2	2	2	NUM
cana-1399	60	3	.	.	PUNCT
cana-1399	60	4	non	non	PROPN
cana-1399	61	1	vdt	vdt	PROPN
cana-1399	61	2	corona	corona	PROPN
cana-1399	61	3	graph	graph	NOUN
cana-1399	61	4	4	4	NUM
cana-1399	61	5	.	.	PUNCT
cana-1399	62	1	vdt	vdt	PROPN
cana-1399	62	2	graph	graph	NOUN
cana-1399	62	3	decomposition	decomposition	NOUN
cana-1399	62	4	let	let	VERB
cana-1399	62	5	g	g	NOUN
cana-1399	62	6	be	be	AUX
cana-1399	62	7	any	any	DET
cana-1399	62	8	graph	graph	NOUN
cana-1399	62	9	with	with	ADP
cana-1399	62	10	n	n	ADP
cana-1399	62	11	vertices	vertex	NOUN
cana-1399	62	12	.	.	PUNCT
cana-1399	63	1	for	for	ADP
cana-1399	63	2	our	our	PRON
cana-1399	63	3	iteration	iteration	NOUN
cana-1399	63	4	procedure	procedure	NOUN
cana-1399	63	5	let	let	VERB
cana-1399	63	6	us	we	PRON
cana-1399	63	7	consider	consider	VERB
cana-1399	63	8	the	the	DET
cana-1399	63	9	graph	graph	NOUN
cana-1399	63	10	g	g	NOUN
cana-1399	63	11	in	in	ADP
cana-1399	63	12	figure	figure	NOUN
cana-1399	63	13	3	3	NUM
cana-1399	63	14	as	as	ADP
cana-1399	63	15	illustration	illustration	NOUN
cana-1399	63	16	.	.	PUNCT
cana-1399	64	1	fig	fig	NOUN
cana-1399	64	2	3	3	NUM
cana-1399	64	3	.	.	PUNCT
cana-1399	64	4	graph	graph	VERB
cana-1399	64	5	g	g	NOUN
cana-1399	64	6	for	for	ADP
cana-1399	64	7	vdt	vdt	PROPN
cana-1399	64	8	graph	graph	NOUN
cana-1399	64	9	decomposition	decomposition	NOUN
cana-1399	64	10	step	step	NOUN
cana-1399	64	11	1	1	NUM
cana-1399	64	12	determine	determine	VERB
cana-1399	64	13	the	the	DET
cana-1399	64	14	rooted	rooted	ADJ
cana-1399	64	15	tree	tree	NOUN
cana-1399	64	16	t1	t1	NOUN
cana-1399	64	17	for	for	ADP
cana-1399	64	18	g	g	NOUN
cana-1399	64	19	from	from	ADP
cana-1399	64	20	any	any	DET
cana-1399	64	21	arbitrary	arbitrary	ADJ
cana-1399	64	22	vertex	vertex	NOUN
cana-1399	64	23	using	use	VERB
cana-1399	64	24	bfs	bfs	NOUN
cana-1399	64	25	algorithm	algorithm	NOUN
cana-1399	64	26	.	.	PUNCT
cana-1399	65	1	for	for	ADP
cana-1399	65	2	our	our	PRON
cana-1399	65	3	example	example	NOUN
cana-1399	65	4	the	the	DET
cana-1399	65	5	rooted	rooted	ADJ
cana-1399	65	6	tree	tree	NOUN
cana-1399	65	7	is	be	AUX
cana-1399	65	8	seen	see	VERB
cana-1399	65	9	in	in	ADP
cana-1399	65	10	figure	figure	NOUN
cana-1399	65	11	4	4	NUM
cana-1399	65	12	.	.	NOUN
cana-1399	65	13	step	step	NOUN
cana-1399	65	14	2	2	NUM
cana-1399	65	15	vertex	vertex	NOUN
cana-1399	65	16	labelling	labelling	NOUN
cana-1399	65	17	of	of	ADP
cana-1399	65	18	tree	tree	NOUN
cana-1399	65	19	t1	t1	NOUN
cana-1399	65	20	let	let	VERB
cana-1399	65	21	us	we	PRON
cana-1399	65	22	label	label	VERB
cana-1399	65	23	the	the	DET
cana-1399	65	24	tree	tree	NOUN
cana-1399	65	25	t1	t1	NOUN
cana-1399	65	26	obtained	obtain	VERB
cana-1399	65	27	by	by	ADP
cana-1399	65	28	bfs	bfs	NOUN
cana-1399	65	29	algorithm	algorithm	NOUN
cana-1399	65	30	.	.	PUNCT
cana-1399	66	1	1	1	X
cana-1399	66	2	.	.	X
cana-1399	66	3	label	label	VERB
cana-1399	66	4	the	the	DET
cana-1399	66	5	root	root	NOUN
cana-1399	66	6	vertex	vertex	NOUN
cana-1399	66	7	as	as	ADP
cana-1399	66	8	v11	v11	NOUN
cana-1399	66	9	.	.	PUNCT
cana-1399	67	1	2	2	X
cana-1399	67	2	.	.	X
cana-1399	67	3	label	label	VERB
cana-1399	67	4	the	the	DET
cana-1399	67	5	vertices	vertex	NOUN
cana-1399	67	6	in	in	ADP
cana-1399	67	7	level	level	NOUN
cana-1399	67	8	2	2	NUM
cana-1399	67	9	as	as	ADP
cana-1399	67	10	v21	v21	NOUN
cana-1399	67	11	,	,	PUNCT
cana-1399	67	12	v22	v22	NOUN
cana-1399	67	13	,	,	PUNCT
cana-1399	67	14	...	...	PUNCT
cana-1399	67	15	,	,	PUNCT
cana-1399	67	16	v2r2	v2r2	ADP
cana-1399	67	17	from	from	ADP
cana-1399	67	18	left	left	NOUN
cana-1399	67	19	to	to	ADP
cana-1399	67	20	right	right	NOUN
cana-1399	67	21	.	.	PUNCT
cana-1399	68	1	3	3	X
cana-1399	68	2	.	.	X
cana-1399	68	3	label	label	VERB
cana-1399	68	4	the	the	DET
cana-1399	68	5	vertices	vertex	NOUN
cana-1399	68	6	in	in	ADP
cana-1399	68	7	level	level	NOUN
cana-1399	68	8	3	3	NUM
cana-1399	68	9	as	as	ADP
cana-1399	68	10	v31	v31	PROPN
cana-1399	68	11	,	,	PUNCT
cana-1399	68	12	v32	v32	PROPN
cana-1399	68	13	,	,	PUNCT
cana-1399	68	14	...	...	PUNCT
cana-1399	68	15	,	,	PUNCT
cana-1399	68	16	v3r3	v3r3	X
cana-1399	68	17	from	from	ADP
cana-1399	68	18	left	leave	VERB
cana-1399	68	19	to	to	ADP
cana-1399	68	20	right	right	NOUN
cana-1399	68	21	.	.	PUNCT
cana-1399	69	1	4	4	X
cana-1399	69	2	.	.	X
cana-1399	69	3	continue	continue	VERB
cana-1399	69	4	this	this	DET
cana-1399	69	5	pattern	pattern	NOUN
cana-1399	69	6	and	and	CCONJ
cana-1399	69	7	label	label	VERB
cana-1399	69	8	the	the	DET
cana-1399	69	9	vertices	vertex	NOUN
cana-1399	69	10	at	at	ADP
cana-1399	69	11	level	level	NOUN
cana-1399	69	12	k	k	PROPN
cana-1399	69	13	as	as	ADP
cana-1399	69	14	vk1	vk1	ADJ
cana-1399	69	15	,	,	PUNCT
cana-1399	69	16	vk2	vk2	NOUN
cana-1399	69	17	,	,	PUNCT
cana-1399	69	18	...	...	PUNCT
cana-1399	69	19	,	,	PUNCT
cana-1399	69	20	vkrk	vkrk	NOUN
cana-1399	69	21	from	from	ADP
cana-1399	69	22	left	left	ADJ
cana-1399	69	23	to	to	ADP
cana-1399	69	24	right	right	NOUN
cana-1399	69	25	.	.	PUNCT
cana-1399	70	1	communications	communication	NOUN
cana-1399	70	2	on	on	ADP
cana-1399	70	3	applied	apply	VERB
cana-1399	70	4	nonlinear	nonlinear	ADJ
cana-1399	70	5	analysis	analysis	NOUN
cana-1399	70	6	issn	issn	NOUN
cana-1399	70	7	:	:	PUNCT
cana-1399	70	8	1074	1074	NUM
cana-1399	70	9	-	-	PUNCT
cana-1399	70	10	133x	133x	NUM
cana-1399	70	11	vol	vol	NOUN
cana-1399	70	12	31	31	NUM
cana-1399	70	13	no	no	NOUN
cana-1399	70	14	.	.	PUNCT
cana-1399	71	1	7s	7	NOUN
cana-1399	71	2	(	(	PUNCT
cana-1399	71	3	2024	2024	NUM
cana-1399	71	4	)	)	PUNCT
cana-1399	71	5	577	577	NUM
cana-1399	71	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1399	71	7	fig	fig	NOUN
cana-1399	71	8	4	4	NUM
cana-1399	71	9	.	.	PUNCT
cana-1399	72	1	tree	tree	NOUN
cana-1399	72	2	t1	t1	NOUN
cana-1399	72	3	using	use	VERB
cana-1399	72	4	bfs	bfs	NOUN
cana-1399	72	5	algorithm	algorithm	PROPN
cana-1399	72	6	step	step	NOUN
cana-1399	72	7	3	3	NUM
cana-1399	72	8	include	include	VERB
cana-1399	72	9	the	the	DET
cana-1399	72	10	remaining	remain	VERB
cana-1399	72	11	edges	edge	NOUN
cana-1399	72	12	to	to	ADP
cana-1399	72	13	the	the	DET
cana-1399	72	14	tree	tree	NOUN
cana-1399	72	15	t1	t1	NOUN
cana-1399	72	16	as	as	SCONJ
cana-1399	72	17	seen	see	VERB
cana-1399	72	18	in	in	ADP
cana-1399	72	19	figure	figure	NOUN
cana-1399	72	20	5	5	NUM
cana-1399	72	21	.	.	PUNCT
cana-1399	72	22	fig	fig	NOUN
cana-1399	72	23	5	5	NUM
cana-1399	72	24	.	.	PUNCT
cana-1399	72	25	t1	t1	NOUN
cana-1399	72	26	with	with	ADP
cana-1399	72	27	remaining	remain	VERB
cana-1399	72	28	edges	edge	NOUN
cana-1399	72	29	added	add	VERB
cana-1399	72	30	step	step	NOUN
cana-1399	72	31	4	4	NUM
cana-1399	72	32	edge	edge	NOUN
cana-1399	72	33	labelling	label	VERB
cana-1399	72	34	any	any	DET
cana-1399	72	35	edge	edge	NOUN
cana-1399	73	1	e	e	NOUN
cana-1399	73	2	=	=	SYM
cana-1399	73	3	ij	ij	X
cana-1399	73	4	ik(v	ik(v	ADJ
cana-1399	73	5	,	,	PUNCT
cana-1399	73	6	v	v	NOUN
cana-1399	73	7	)	)	PUNCT
cana-1399	73	8	is	be	AUX
cana-1399	73	9	labelled	label	VERB
cana-1399	73	10	as	as	ADP
cana-1399	73	11	ij	ij	NUM
cana-1399	73	12	ike	ike	PROPN
cana-1399	73	13	.	.	PUNCT
cana-1399	74	1	note	note	VERB
cana-1399	74	2	that	that	SCONJ
cana-1399	74	3	here	here	ADV
cana-1399	74	4	i	i	PRON
cana-1399	74	5	represents	represent	VERB
cana-1399	74	6	the	the	DET
cana-1399	74	7	level	level	NOUN
cana-1399	74	8	of	of	ADP
cana-1399	74	9	the	the	DET
cana-1399	74	10	vertices	vertex	NOUN
cana-1399	74	11	.	.	PUNCT
cana-1399	75	1	11	11	NUM
cana-1399	75	2	32e	32e	NOUN
cana-1399	75	3	denotes	denote	VERB
cana-1399	75	4	an	an	DET
cana-1399	75	5	edge	edge	NOUN
cana-1399	75	6	between	between	ADP
cana-1399	75	7	vertices	vertex	NOUN
cana-1399	75	8	11v	11v	NOUN
cana-1399	75	9	and	and	CCONJ
cana-1399	75	10	32v	32v	NOUN
cana-1399	75	11	,	,	PUNCT
cana-1399	75	12	the	the	DET
cana-1399	75	13	edge	edge	NOUN
cana-1399	75	14	is	be	AUX
cana-1399	75	15	between	between	ADP
cana-1399	75	16	vertices	vertex	NOUN
cana-1399	75	17	in	in	ADP
cana-1399	75	18	level	level	NOUN
cana-1399	75	19	1	1	NUM
cana-1399	75	20	and	and	CCONJ
cana-1399	75	21	level	level	NOUN
cana-1399	75	22	3	3	NUM
cana-1399	75	23	.	.	PUNCT
cana-1399	76	1	the	the	DET
cana-1399	76	2	partial	partial	ADJ
cana-1399	76	3	structure	structure	NOUN
cana-1399	76	4	of	of	ADP
cana-1399	76	5	the	the	DET
cana-1399	76	6	tree	tree	NOUN
cana-1399	76	7	t1	t1	NOUN
cana-1399	76	8	labelling	labelling	NOUN
cana-1399	76	9	is	be	AUX
cana-1399	76	10	as	as	SCONJ
cana-1399	76	11	seen	see	VERB
cana-1399	76	12	in	in	ADP
cana-1399	76	13	figure	figure	NOUN
cana-1399	76	14	6	6	NUM
cana-1399	76	15	.	.	PUNCT
cana-1399	76	16	communications	communication	NOUN
cana-1399	76	17	on	on	ADP
cana-1399	76	18	applied	apply	VERB
cana-1399	76	19	nonlinear	nonlinear	ADJ
cana-1399	76	20	analysis	analysis	NOUN
cana-1399	76	21	issn	issn	NOUN
cana-1399	76	22	:	:	PUNCT
cana-1399	76	23	1074	1074	NUM
cana-1399	76	24	-	-	PUNCT
cana-1399	76	25	133x	133x	NUM
cana-1399	76	26	vol	vol	NOUN
cana-1399	76	27	31	31	NUM
cana-1399	76	28	no	no	NOUN
cana-1399	76	29	.	.	PUNCT
cana-1399	77	1	7s	7	NOUN
cana-1399	77	2	(	(	PUNCT
cana-1399	77	3	2024	2024	NUM
cana-1399	77	4	)	)	PUNCT
cana-1399	77	5	578	578	NUM
cana-1399	77	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1399	77	7	fig	fig	NOUN
cana-1399	77	8	6	6	NUM
cana-1399	77	9	.	.	PUNCT
cana-1399	78	1	labelling	labelling	NOUN
cana-1399	78	2	of	of	ADP
cana-1399	78	3	t1	t1	NUM
cana-1399	78	4	step	step	NOUN
cana-1399	78	5	5	5	NUM
cana-1399	78	6	starting	start	VERB
cana-1399	78	7	from	from	ADP
cana-1399	78	8	vertex	vertex	NOUN
cana-1399	78	9	k1v	k1v	PROPN
cana-1399	78	10	trace	trace	VERB
cana-1399	78	11	a	a	DET
cana-1399	78	12	longest	long	ADJ
cana-1399	78	13	possible	possible	ADJ
cana-1399	78	14	path	path	NOUN
cana-1399	78	15	by	by	ADP
cana-1399	78	16	back	back	NOUN
cana-1399	78	17	tracking	tracking	NOUN
cana-1399	78	18	along	along	ADP
cana-1399	78	19	the	the	DET
cana-1399	78	20	tree	tree	NOUN
cana-1399	78	21	t1	t1	NOUN
cana-1399	78	22	by	by	ADP
cana-1399	78	23	choosing	choose	VERB
cana-1399	78	24	a	a	DET
cana-1399	78	25	new	new	ADJ
cana-1399	78	26	edge	edge	NOUN
cana-1399	78	27	each	each	DET
cana-1399	78	28	time	time	NOUN
cana-1399	78	29	.	.	PUNCT
cana-1399	79	1	label	label	VERB
cana-1399	79	2	the	the	DET
cana-1399	79	3	resulting	result	VERB
cana-1399	79	4	path	path	NOUN
cana-1399	79	5	as	as	ADP
cana-1399	79	6	k1	k1	PROPN
cana-1399	79	7	k1	k1	PROPN
cana-1399	79	8	k1p	k1p	NUM
cana-1399	79	9	:	:	PUNCT
cana-1399	79	10	v	v	X
cana-1399	79	11	,	,	PUNCT
cana-1399	79	12	pred(v	pred(v	INTJ
cana-1399	79	13	)	)	PUNCT
cana-1399	79	14	,	,	PUNCT
cana-1399	79	15	k1	k1	PROPN
cana-1399	79	16	11pred(pred(v	11pred(pred(v	PROPN
cana-1399	79	17	)	)	PUNCT
cana-1399	79	18	)	)	PUNCT
cana-1399	79	19	,	,	PUNCT
cana-1399	79	20	...	...	PUNCT
cana-1399	79	21	,	,	PUNCT
cana-1399	79	22	v	v	X
cana-1399	79	23	.	.	PUNCT
cana-1399	80	1	let	let	VERB
cana-1399	80	2	us	we	PRON
cana-1399	80	3	now	now	ADV
cana-1399	80	4	attempt	attempt	VERB
cana-1399	80	5	to	to	PART
cana-1399	80	6	include	include	VERB
cana-1399	80	7	edges	edge	NOUN
cana-1399	80	8	to	to	ADP
cana-1399	80	9	the	the	DET
cana-1399	80	10	path	path	NOUN
cana-1399	80	11	k1p	k1p	PART
cana-1399	80	12	to	to	PART
cana-1399	80	13	generate	generate	VERB
cana-1399	80	14	a	a	DET
cana-1399	80	15	comb	comb	NOUN
cana-1399	80	16	graph	graph	NOUN
cana-1399	80	17	if	if	SCONJ
cana-1399	80	18	possible	possible	ADJ
cana-1399	80	19	.	.	PUNCT
cana-1399	81	1	step	step	NOUN
cana-1399	81	2	6	6	NUM
cana-1399	81	3	let	let	VERB
cana-1399	81	4	ijv	ijv	PROPN
cana-1399	81	5	be	be	AUX
cana-1399	81	6	any	any	DET
cana-1399	81	7	random	random	ADJ
cana-1399	81	8	vertex	vertex	NOUN
cana-1399	81	9	in	in	ADP
cana-1399	81	10	path	path	NOUN
cana-1399	81	11	k1p	k1p	ADJ
cana-1399	81	12	.	.	PUNCT
cana-1399	82	1	a.	a.	NOUN
cana-1399	82	2	1	1	NUM
cana-1399	82	3	.	.	PROPN
cana-1399	82	4	include	include	VERB
cana-1399	82	5	a	a	DET
cana-1399	82	6	new	new	ADJ
cana-1399	82	7	edge	edge	NOUN
cana-1399	82	8	ij	ij	X
cana-1399	82	9	ike	ike	NOUN
cana-1399	82	10	to	to	ADP
cana-1399	82	11	k1p	k1p	PRON
cana-1399	82	12	where	where	SCONJ
cana-1399	82	13	k	k	PROPN
cana-1399	82	14	is	be	AUX
cana-1399	82	15	the	the	DET
cana-1399	82	16	smallest	small	ADJ
cana-1399	82	17	possible	possible	ADJ
cana-1399	82	18	value	value	NOUN
cana-1399	82	19	,	,	PUNCT
cana-1399	82	20	i	i	PRON
cana-1399	82	21	r	r	VERB
cana-1399	82	22	i	i	NOUN
cana-1399	83	1	2	2	NUM
cana-1399	83	2	k	k	NOUN
cana-1399	83	3	v	v	ADP
cana-1399	83	4			NUM
cana-1399	83	5			NOUN
cana-1399	83	6	(	(	PUNCT
cana-1399	83	7	if	if	SCONJ
cana-1399	83	8	it	it	PRON
cana-1399	83	9	exists	exist	VERB
cana-1399	83	10	)	)	PUNCT
cana-1399	83	11	such	such	ADJ
cana-1399	83	12	that	that	SCONJ
cana-1399	83	13	ijv	ijv	PROPN
cana-1399	83	14	is	be	AUX
cana-1399	83	15	adjacent	adjacent	ADJ
cana-1399	83	16	to	to	PART
cana-1399	83	17	ikv	ikv	VERB
cana-1399	83	18	.	.	PUNCT
cana-1399	83	19	include	include	VERB
cana-1399	83	20	ikv	ikv	ADJ
cana-1399	83	21	and	and	CCONJ
cana-1399	83	22	ij	ij	INTJ
cana-1399	83	23	ike	ike	NOUN
cana-1399	83	24	to	to	ADP
cana-1399	83	25	k1p	k1p	PRON
cana-1399	83	26	.	.	PUNCT
cana-1399	84	1	else	else	ADV
cana-1399	84	2	2	2	NUM
cana-1399	84	3	.	.	PUNCT
cana-1399	84	4	choose	choose	VERB
cana-1399	84	5	the	the	DET
cana-1399	84	6	smallest	small	ADJ
cana-1399	84	7	possible	possible	ADJ
cana-1399	84	8	p	p	X
cana-1399	84	9	,	,	PUNCT
cana-1399	84	10	i	i	PRON
cana-1399	84	11	r	r	VERB
cana-1399	85	1	i	i	PRON
cana-1399	85	2	+	+	NOUN
cana-1399	85	3	1	1	NUM
cana-1399	85	4	2	2	NUM
cana-1399	85	5	p	p	NOUN
cana-1399	85	6	v	v	ADP
cana-1399	85	7			NOUN
cana-1399	85	8			NOUN
cana-1399	85	9	(	(	PUNCT
cana-1399	85	10	if	if	SCONJ
cana-1399	85	11	it	it	PRON
cana-1399	85	12	exists	exist	VERB
cana-1399	85	13	)	)	PUNCT
cana-1399	85	14	such	such	ADJ
cana-1399	85	15	that	that	SCONJ
cana-1399	85	16	ijv	ijv	PROPN
cana-1399	85	17	is	be	AUX
cana-1399	85	18	adjacent	adjacent	ADJ
cana-1399	85	19	to	to	ADP
cana-1399	85	20	i	i	PRON
cana-1399	85	21	+	+	NOUN
cana-1399	85	22	1	1	NUM
cana-1399	85	23	pv	pv	NOUN
cana-1399	85	24	.	.	PUNCT
cana-1399	86	1	include	include	VERB
cana-1399	86	2	i	i	PRON
cana-1399	86	3	+	+	CCONJ
cana-1399	86	4	1	1	NUM
cana-1399	86	5	pv	pv	NOUN
cana-1399	87	1	and	and	CCONJ
cana-1399	87	2	ij	ij	INTJ
cana-1399	87	3	i	i	PRON
cana-1399	87	4	+	+	CCONJ
cana-1399	87	5	1	1	NUM
cana-1399	87	6	pe	pe	INTJ
cana-1399	87	7	to	to	ADP
cana-1399	87	8	k1p	k1p	PRON
cana-1399	87	9	.	.	PUNCT
cana-1399	88	1	else	else	ADV
cana-1399	88	2	3	3	X
cana-1399	88	3	.	.	PUNCT
cana-1399	88	4	choose	choose	VERB
cana-1399	88	5	the	the	DET
cana-1399	88	6	smallest	small	ADJ
cana-1399	88	7	possible	possible	ADJ
cana-1399	88	8	q	q	NOUN
cana-1399	88	9	,	,	PUNCT
cana-1399	88	10	i	i	PRON
cana-1399	88	11	r	r	VERB
cana-1399	88	12	i	i	NOUN
cana-1399	88	13	1	1	NUM
cana-1399	88	14	2	2	NUM
cana-1399	88	15	q	q	NOUN
cana-1399	88	16	v	v	NOUN
cana-1399	88	17			NOUN
cana-1399	88	18			NOUN
cana-1399	88	19	(	(	PUNCT
cana-1399	88	20	if	if	SCONJ
cana-1399	88	21	it	it	PRON
cana-1399	88	22	exists	exist	VERB
cana-1399	88	23	)	)	PUNCT
cana-1399	88	24	such	such	ADJ
cana-1399	88	25	that	that	SCONJ
cana-1399	88	26	vij	vij	PROPN
cana-1399	88	27	is	be	AUX
cana-1399	88	28	adjacent	adjacent	ADJ
cana-1399	88	29	to	to	ADP
cana-1399	88	30	i	i	PRON
cana-1399	88	31	1	1	NUM
cana-1399	88	32	qv	qv	ADV
cana-1399	88	33	.	.	PUNCT
cana-1399	89	1	include	include	VERB
cana-1399	89	2	i	i	PRON
cana-1399	89	3	1	1	NUM
cana-1399	89	4	qv	qv	ADV
cana-1399	90	1	and	and	CCONJ
cana-1399	90	2	ij	ij	INTJ
cana-1399	90	3	i	i	NOUN
cana-1399	90	4	1	1	NUM
cana-1399	90	5	qe	qe	NOUN
cana-1399	90	6	to	to	ADP
cana-1399	90	7	k1p	k1p	PRON
cana-1399	90	8	.	.	PUNCT
cana-1399	91	1	repeat	repeat	VERB
cana-1399	91	2	1	1	NUM
cana-1399	91	3	,	,	PUNCT
cana-1399	91	4	2	2	NUM
cana-1399	91	5	or	or	CCONJ
cana-1399	91	6	3	3	NUM
cana-1399	91	7	for	for	ADP
cana-1399	91	8	every	every	DET
cana-1399	91	9	vertex	vertex	NOUN
cana-1399	91	10	in	in	ADP
cana-1399	91	11	k1p	k1p	PUNCT
cana-1399	91	12	starting	start	VERB
cana-1399	91	13	from	from	ADP
cana-1399	91	14	k1v	k1v	PROPN
cana-1399	91	15	.	.	PUNCT
cana-1399	92	1	if	if	SCONJ
cana-1399	92	2	there	there	PRON
cana-1399	92	3	is	be	VERB
cana-1399	92	4	at	at	ADV
cana-1399	92	5	least	least	ADV
cana-1399	92	6	one	one	NUM
cana-1399	92	7	vertex	vertex	NOUN
cana-1399	92	8	say	say	VERB
cana-1399	92	9	ijv	ijv	PROPN
cana-1399	92	10	for	for	ADP
cana-1399	92	11	which	which	DET
cana-1399	92	12	step	step	NOUN
cana-1399	92	13	6a	6a	NOUN
cana-1399	92	14	fails	fail	VERB
cana-1399	92	15	,	,	PUNCT
cana-1399	92	16	we	we	PRON
cana-1399	92	17	terminate	terminate	VERB
cana-1399	92	18	step	step	NOUN
cana-1399	92	19	6a	6a	NOUN
cana-1399	92	20	.	.	PUNCT
cana-1399	93	1	else	else	ADV
cana-1399	93	2	we	we	PRON
cana-1399	93	3	continue	continue	VERB
cana-1399	93	4	step	step	NOUN
cana-1399	93	5	6	6	NUM
cana-1399	93	6	until	until	SCONJ
cana-1399	93	7	we	we	PRON
cana-1399	93	8	reach	reach	VERB
cana-1399	93	9	vertex	vertex	NOUN
cana-1399	93	10	11v	11v	NOUN
cana-1399	93	11	.	.	PUNCT
cana-1399	94	1	if	if	SCONJ
cana-1399	94	2	step	step	NOUN
cana-1399	94	3	6a	6a	NOUN
cana-1399	94	4	is	be	AUX
cana-1399	94	5	true	true	ADJ
cana-1399	94	6	for	for	ADP
cana-1399	94	7	every	every	DET
cana-1399	94	8	vertex	vertex	NOUN
cana-1399	94	9	in	in	ADP
cana-1399	94	10	k1p	k1p	ADJ
cana-1399	94	11	,	,	PUNCT
cana-1399	94	12	then	then	ADV
cana-1399	94	13	we	we	PRON
cana-1399	94	14	include	include	VERB
cana-1399	94	15	w	w	NOUN
cana-1399	94	16	vertices	vertex	NOUN
cana-1399	94	17	and	and	CCONJ
cana-1399	94	18	w	w	NOUN
cana-1399	94	19	edges	edge	NOUN
cana-1399	94	20	to	to	AUX
cana-1399	94	21	k1p	k1p	ADV
cana-1399	94	22	generated	generate	VERB
cana-1399	94	23	by	by	ADP
cana-1399	94	24	step	step	NOUN
cana-1399	94	25	6a	6a	NOUN
cana-1399	94	26	where	where	SCONJ
cana-1399	94	27	|w|	|w|	ADJ
cana-1399	94	28	=	=	SYM
cana-1399	94	29	|v	|v	X
cana-1399	94	30	(	(	PUNCT
cana-1399	94	31	k1p	k1p	X
cana-1399	94	32	)	)	PUNCT
cana-1399	94	33	|	|	ADV
cana-1399	94	34	,	,	PUNCT
cana-1399	94	35	1	1	NUM
cana-1399	94	36	≤	≤	NUM
cana-1399	94	37	w	w	NOUN
cana-1399	94	38	≤	≤	PROPN
cana-1399	94	39	k.	k.	NOUN
cana-1399	95	1	the	the	DET
cana-1399	95	2	resulting	result	VERB
cana-1399	95	3	graph	graph	NOUN
cana-1399	95	4	is	be	AUX
cana-1399	95	5	a	a	DET
cana-1399	95	6	comb	comb	NOUN
cana-1399	95	7	say	say	VERB
cana-1399	95	8	k1	k1	NOUN
cana-1399	95	9	1(p	1(p	NUM
cana-1399	95	10	k	k	PROPN
cana-1399	95	11	)	)	PUNCT
cana-1399	95	12	.	.	PUNCT
cana-1399	96	1	else	else	PROPN
cana-1399	96	2	b.	b.	PROPN
cana-1399	96	3	retain	retain	VERB
cana-1399	96	4	the	the	DET
cana-1399	96	5	path	path	NOUN
cana-1399	96	6	k1p	k1p	ADJ
cana-1399	96	7	.	.	PUNCT
cana-1399	97	1	step	step	VERB
cana-1399	97	2	7	7	NUM
cana-1399	97	3	starting	start	VERB
cana-1399	97	4	from	from	ADP
cana-1399	97	5	vertex	vertex	NOUN
cana-1399	97	6	k2v	k2v	NOUN
cana-1399	97	7	trace	trace	VERB
cana-1399	97	8	a	a	DET
cana-1399	97	9	longest	long	ADJ
cana-1399	97	10	path	path	NOUN
cana-1399	97	11	by	by	ADP
cana-1399	97	12	back	back	NOUN
cana-1399	97	13	tracking	tracking	NOUN
cana-1399	97	14	along	along	ADP
cana-1399	97	15	the	the	DET
cana-1399	97	16	tree	tree	NOUN
cana-1399	97	17	t1	t1	NOUN
cana-1399	97	18	by	by	ADP
cana-1399	97	19	choosing	choose	VERB
cana-1399	97	20	a	a	DET
cana-1399	97	21	new	new	ADJ
cana-1399	97	22	edge	edge	NOUN
cana-1399	97	23	each	each	DET
cana-1399	97	24	time	time	NOUN
cana-1399	97	25	.	.	PUNCT
cana-1399	98	1	label	label	VERB
cana-1399	98	2	the	the	DET
cana-1399	98	3	resulting	result	VERB
cana-1399	98	4	path	path	NOUN
cana-1399	98	5	as	as	ADP
cana-1399	98	6	k2	k2	PROPN
cana-1399	98	7	k2	k2	PROPN
cana-1399	98	8	k2	k2	PROPN
cana-1399	98	9	k2p	k2p	PROPN
cana-1399	98	10	:	:	PUNCT
cana-1399	98	11	v	v	X
cana-1399	98	12	,	,	PUNCT
cana-1399	98	13	pred(v	pred(v	INTJ
cana-1399	98	14	)	)	PUNCT
cana-1399	98	15	,	,	PUNCT
cana-1399	98	16	pred(pred(v	pred(pred(v	NOUN
cana-1399	98	17	)	)	PUNCT
cana-1399	98	18	)	)	PUNCT
cana-1399	98	19	,	,	PUNCT
cana-1399	98	20	ij	ij	INTJ
cana-1399	98	21	...	...	PUNCT
cana-1399	98	22	,	,	PUNCT
cana-1399	98	23	v	v	X
cana-1399	98	24	.	.	PUNCT
cana-1399	99	1	repeat	repeat	NOUN
cana-1399	99	2	step	step	NOUN
cana-1399	99	3	6a	6a	NOUN
cana-1399	99	4	for	for	ADP
cana-1399	99	5	path	path	NOUN
cana-1399	99	6	k2p	k2p	PROPN
cana-1399	99	7	to	to	PART
cana-1399	99	8	generate	generate	VERB
cana-1399	99	9	a	a	DET
cana-1399	99	10	comb	comb	NOUN
cana-1399	99	11	k2	k2	NOUN
cana-1399	99	12	1(p	1(p	NUM
cana-1399	99	13	k	k	PROPN
cana-1399	99	14	)	)	PUNCT
cana-1399	100	1	if	if	SCONJ
cana-1399	100	2	it	it	PRON
cana-1399	100	3	exists	exist	VERB
cana-1399	100	4	or	or	CCONJ
cana-1399	100	5	retain	retain	VERB
cana-1399	100	6	k2p	k2p	NOUN
cana-1399	100	7	(	(	PUNCT
cana-1399	100	8	step	step	NOUN
cana-1399	100	9	6b	6b	NOUN
cana-1399	100	10	)	)	PUNCT
cana-1399	100	11	.	.	PUNCT
cana-1399	101	1	communications	communication	NOUN
cana-1399	101	2	on	on	ADP
cana-1399	101	3	applied	apply	VERB
cana-1399	101	4	nonlinear	nonlinear	ADJ
cana-1399	101	5	analysis	analysis	NOUN
cana-1399	101	6	issn	issn	NOUN
cana-1399	101	7	:	:	PUNCT
cana-1399	101	8	1074	1074	NUM
cana-1399	101	9	-	-	PUNCT
cana-1399	101	10	133x	133x	NUM
cana-1399	101	11	vol	vol	NOUN
cana-1399	101	12	31	31	NUM
cana-1399	101	13	no	no	NOUN
cana-1399	101	14	.	.	PUNCT
cana-1399	102	1	7s	7	NOUN
cana-1399	102	2	(	(	PUNCT
cana-1399	102	3	2024	2024	NUM
cana-1399	102	4	)	)	PUNCT
cana-1399	102	5	579	579	NUM
cana-1399	102	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1399	103	1	step	step	NOUN
cana-1399	103	2	8	8	NUM
cana-1399	103	3	repeat	repeat	NOUN
cana-1399	103	4	step	step	NOUN
cana-1399	103	5	5	5	NUM
cana-1399	103	6	for	for	ADP
cana-1399	103	7	every	every	DET
cana-1399	103	8	kiv	kiv	NOUN
cana-1399	103	9	,	,	PUNCT
cana-1399	103	10	k3	k3	VERB
cana-1399	103	11	i	i	PRON
cana-1399	103	12	r	r	NOUN
cana-1399	103	13			NOUN
cana-1399	103	14			NOUN
cana-1399	103	15	to	to	PART
cana-1399	103	16	generate	generate	VERB
cana-1399	103	17	a	a	DET
cana-1399	103	18	sequence	sequence	NOUN
cana-1399	103	19	1	1	NUM
cana-1399	103	20	2	2	NUM
cana-1399	103	21	rx	rx	NOUN
cana-1399	103	22	,	,	PUNCT
cana-1399	103	23	x	x	INTJ
cana-1399	103	24	,	,	PUNCT
cana-1399	103	25	...	...	PUNCT
cana-1399	103	26	,	,	PUNCT
cana-1399	103	27	x	x	X
cana-1399	103	28	where	where	SCONJ
cana-1399	103	29	ki	ki	PROPN
cana-1399	103	30	1	1	NUM
cana-1399	103	31	i	i	PRON
cana-1399	103	32	ki	ki	PROPN
cana-1399	103	33	p	p	PROPN
cana-1399	103	34	k	k	PROPN
cana-1399	103	35	or	or	CCONJ
cana-1399	103	36	x	x	X
cana-1399	103	37	p	p	NOUN
cana-1399	104	1			ADV
cana-1399	104	2			NOUN
cana-1399	105	1			NUM
cana-1399	105	2			NUM
cana-1399	105	3	fig	fig	NOUN
cana-1399	105	4	7	7	NUM
cana-1399	105	5	.	.	PUNCT
cana-1399	105	6	iteration	iteration	NOUN
cana-1399	105	7	1	1	NUM
cana-1399	105	8	step	step	NOUN
cana-1399	105	9	9	9	NUM
cana-1399	105	10	repeat	repeat	NOUN
cana-1399	105	11	step	step	NOUN
cana-1399	105	12	5	5	NUM
cana-1399	105	13	to	to	PART
cana-1399	105	14	step	step	VERB
cana-1399	105	15	8	8	NUM
cana-1399	105	16	for	for	ADP
cana-1399	105	17	all	all	DET
cana-1399	105	18	the	the	DET
cana-1399	105	19	vertices	vertex	NOUN
cana-1399	105	20	in	in	ADP
cana-1399	105	21	the	the	DET
cana-1399	105	22	level	level	NOUN
cana-1399	105	23	k	k	PROPN
cana-1399	105	24	–	–	PUNCT
cana-1399	105	25	1	1	NUM
cana-1399	105	26	,	,	PUNCT
cana-1399	105	27	k	k	PROPN
cana-1399	105	28	–	–	PUNCT
cana-1399	105	29	2	2	NUM
cana-1399	105	30	,	,	PUNCT
cana-1399	105	31	.	.	PUNCT
cana-1399	105	32	.	.	PUNCT
cana-1399	106	1	.	.	PUNCT
cana-1399	107	1	,	,	PUNCT
cana-1399	107	2	2	2	X
cana-1399	107	3	.	.	X
cana-1399	107	4	executing	execute	VERB
cana-1399	107	5	step	step	NOUN
cana-1399	107	6	5	5	NUM
cana-1399	107	7	to	to	PART
cana-1399	107	8	step	step	VERB
cana-1399	107	9	8	8	NUM
cana-1399	107	10	once	once	ADV
cana-1399	107	11	,	,	PUNCT
cana-1399	107	12	we	we	PRON
cana-1399	107	13	finally	finally	ADV
cana-1399	107	14	generate	generate	VERB
cana-1399	107	15	a	a	DET
cana-1399	107	16	sequence	sequence	NOUN
cana-1399	107	17	of	of	ADP
cana-1399	107	18	subgraphs	subgraph	NOUN
cana-1399	108	1			PROPN
cana-1399	108	2	1	1	ADJ
cana-1399	108	3	2	2	NUM
cana-1399	108	4	sh	sh	INTJ
cana-1399	108	5	,	,	PUNCT
cana-1399	108	6	h	h	NOUN
cana-1399	108	7	,	,	PUNCT
cana-1399	108	8	...	...	PUNCT
cana-1399	108	9	,	,	PUNCT
cana-1399	108	10	h	h	VERB
cana-1399	109	1	where	where	SCONJ
cana-1399	109	2	each	each	DET
cana-1399	109	3	ki	ki	PROPN
cana-1399	109	4	1	1	NUM
cana-1399	109	5	i	i	PRON
cana-1399	109	6	ki	ki	PROPN
cana-1399	109	7	p	p	PROPN
cana-1399	109	8	k	k	PROPN
cana-1399	109	9	or	or	CCONJ
cana-1399	109	10	h	h	NOUN
cana-1399	109	11	p	p	NOUN
cana-1399	109	12			ADP
cana-1399	109	13			NUM
cana-1399	110	1			NOUN
cana-1399	110	2			INTJ
cana-1399	110	3	.	.	PUNCT
cana-1399	111	1	for	for	ADP
cana-1399	111	2	our	our	PRON
cana-1399	111	3	example	example	NOUN
cana-1399	111	4	iteration	iteration	NOUN
cana-1399	111	5	1	1	NUM
cana-1399	111	6	is	be	AUX
cana-1399	111	7	given	give	VERB
cana-1399	111	8	in	in	ADP
cana-1399	111	9	figure	figure	NOUN
cana-1399	111	10	7	7	NUM
cana-1399	111	11	.	.	PUNCT
cana-1399	112	1	if	if	SCONJ
cana-1399	112	2	all	all	DET
cana-1399	112	3	the	the	DET
cana-1399	112	4	edges	edge	NOUN
cana-1399	112	5	of	of	ADP
cana-1399	112	6	g	g	NOUN
cana-1399	112	7	are	be	AUX
cana-1399	112	8	covered	cover	VERB
cana-1399	112	9	then	then	ADV
cana-1399	112	10	terminate	terminate	VERB
cana-1399	112	11	the	the	DET
cana-1399	112	12	procedure	procedure	NOUN
cana-1399	112	13	here	here	ADV
cana-1399	112	14	.	.	PUNCT
cana-1399	113	1	else	else	ADV
cana-1399	113	2	step	step	NOUN
cana-1399	113	3	10	10	NUM
cana-1399	113	4	let	let	VERB
cana-1399	113	5	1	1	NUM
cana-1399	113	6	2	2	NUM
cana-1399	113	7	sl	sl	NOUN
cana-1399	113	8	g	g	NOUN
cana-1399	113	9	–	–	PUNCT
cana-1399	113	10	{	{	PUNCT
cana-1399	113	11	h	h	NOUN
cana-1399	113	12	h	h	NOUN
cana-1399	113	13	...	...	PUNCT
cana-1399	114	1	h	h	NOUN
cana-1399	114	2	}	}	PUNCT
cana-1399	114	3	.	.	NOUN
cana-1399	114	4			PROPN
cana-1399	114	5			PROPN
cana-1399	114	6			PROPN
cana-1399	114	7	if	if	SCONJ
cana-1399	114	8	l	l	NOUN
cana-1399	114	9	is	be	AUX
cana-1399	114	10	a	a	DET
cana-1399	114	11	connected	connected	ADJ
cana-1399	114	12	graph	graph	NOUN
cana-1399	114	13	,	,	PUNCT
cana-1399	114	14	then	then	ADV
cana-1399	114	15	repeat	repeat	VERB
cana-1399	114	16	step	step	NOUN
cana-1399	114	17	1	1	NUM
cana-1399	114	18	to	to	PART
cana-1399	114	19	step	step	VERB
cana-1399	114	20	9	9	NUM
cana-1399	114	21	.	.	PUNCT
cana-1399	115	1	else	else	ADV
cana-1399	115	2	if	if	SCONJ
cana-1399	115	3	l	l	NOUN
cana-1399	115	4	is	be	AUX
cana-1399	115	5	disconnected	disconnected	ADJ
cana-1399	115	6	graph	graph	NOUN
cana-1399	115	7	,	,	PUNCT
cana-1399	115	8	then	then	ADV
cana-1399	115	9	repeat	repeat	VERB
cana-1399	115	10	step	step	NOUN
cana-1399	115	11	1	1	NUM
cana-1399	115	12	to	to	PART
cana-1399	115	13	step	step	VERB
cana-1399	115	14	9	9	NUM
cana-1399	115	15	on	on	ADP
cana-1399	115	16	all	all	DET
cana-1399	115	17	the	the	DET
cana-1399	115	18	x	x	NOUN
cana-1399	115	19	components	component	NOUN
cana-1399	115	20	say	say	VERB
cana-1399	115	21	1	1	NUM
cana-1399	115	22	2	2	NUM
cana-1399	115	23	xg	xg	NOUN
cana-1399	115	24	,	,	PUNCT
cana-1399	115	25	g	g	PROPN
cana-1399	115	26	,	,	PUNCT
cana-1399	115	27	...	...	PUNCT
cana-1399	115	28	,	,	PUNCT
cana-1399	115	29	g	g	PROPN
cana-1399	115	30	.	.	PUNCT
cana-1399	116	1	for	for	ADP
cana-1399	116	2	our	our	PRON
cana-1399	116	3	example	example	NOUN
cana-1399	116	4	the	the	DET
cana-1399	116	5	graph	graph	NOUN
cana-1399	116	6	g	g	NOUN
cana-1399	116	7	is	be	AUX
cana-1399	116	8	disconnected	disconnect	VERB
cana-1399	116	9	as	as	SCONJ
cana-1399	116	10	seen	see	VERB
cana-1399	116	11	in	in	ADP
cana-1399	116	12	figure	figure	NOUN
cana-1399	116	13	8	8	NUM
cana-1399	116	14	.	.	PUNCT
cana-1399	117	1	summarizing	summarize	VERB
cana-1399	117	2	we	we	PRON
cana-1399	117	3	repeat	repeat	VERB
cana-1399	117	4	bfs	bfs	NOUN
cana-1399	117	5	algorithm	algorithm	PROPN
cana-1399	117	6	multiple	multiple	ADJ
cana-1399	117	7	times	time	NOUN
cana-1399	117	8	to	to	PART
cana-1399	117	9	generate	generate	VERB
cana-1399	117	10	a	a	DET
cana-1399	117	11	sequence	sequence	NOUN
cana-1399	117	12	of	of	ADP
cana-1399	117	13	trees	tree	NOUN
cana-1399	117	14	1	1	NUM
cana-1399	117	15	2	2	NUM
cana-1399	117	16	zt	zt	PROPN
cana-1399	117	17	,	,	PUNCT
cana-1399	117	18	t	t	PROPN
cana-1399	117	19	,	,	PUNCT
cana-1399	117	20	...	...	PUNCT
cana-1399	117	21	,	,	PUNCT
cana-1399	117	22	t	t	PROPN
cana-1399	117	23	as	as	SCONJ
cana-1399	117	24	seen	see	VERB
cana-1399	117	25	in	in	ADP
cana-1399	117	26	figure	figure	NOUN
cana-1399	117	27	9	9	NUM
cana-1399	117	28	.	.	PUNCT
cana-1399	117	29	from	from	ADP
cana-1399	117	30	these	these	DET
cana-1399	117	31	trees	tree	NOUN
cana-1399	117	32	we	we	PRON
cana-1399	117	33	then	then	ADV
cana-1399	117	34	decompose	decompose	VERB
cana-1399	117	35	graph	graph	NOUN
cana-1399	117	36	g	g	NOUN
cana-1399	117	37	into	into	ADP
cana-1399	117	38	subgraphs	subgraph	NOUN
cana-1399	117	39	1	1	NUM
cana-1399	117	40	2	2	NUM
cana-1399	117	41	sh	sh	NOUN
cana-1399	117	42	,	,	PUNCT
cana-1399	117	43	h	h	NOUN
cana-1399	117	44	,	,	PUNCT
cana-1399	117	45	...	...	PUNCT
cana-1399	117	46	,	,	PUNCT
cana-1399	117	47	h	h	VERB
cana-1399	118	1	where	where	SCONJ
cana-1399	118	2	each	each	DET
cana-1399	118	3	ki	ki	PROPN
cana-1399	118	4	1	1	NUM
cana-1399	118	5	i	i	PRON
cana-1399	118	6	ki	ki	PROPN
cana-1399	118	7	p	p	PROPN
cana-1399	118	8	k	k	PROPN
cana-1399	118	9	or	or	CCONJ
cana-1399	118	10	h	h	NOUN
cana-1399	118	11	p	p	NOUN
cana-1399	118	12			ADP
cana-1399	118	13			NUM
cana-1399	119	1			NUM
cana-1399	119	2			INTJ
cana-1399	119	3	.	.	PUNCT
cana-1399	120	1	communications	communication	NOUN
cana-1399	120	2	on	on	ADP
cana-1399	120	3	applied	apply	VERB
cana-1399	120	4	nonlinear	nonlinear	ADJ
cana-1399	120	5	analysis	analysis	NOUN
cana-1399	120	6	issn	issn	NOUN
cana-1399	120	7	:	:	PUNCT
cana-1399	120	8	1074	1074	NUM
cana-1399	120	9	-	-	PUNCT
cana-1399	120	10	133x	133x	NUM
cana-1399	120	11	vol	vol	NOUN
cana-1399	120	12	31	31	NUM
cana-1399	120	13	no	no	NOUN
cana-1399	120	14	.	.	PUNCT
cana-1399	121	1	7s	7	NOUN
cana-1399	121	2	(	(	PUNCT
cana-1399	121	3	2024	2024	NUM
cana-1399	121	4	)	)	PUNCT
cana-1399	121	5	580	580	NUM
cana-1399	121	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1399	121	7	fig	fig	NOUN
cana-1399	121	8	8	8	NUM
cana-1399	121	9	.	.	PUNCT
cana-1399	122	1	subgraphs	subgraph	NOUN
cana-1399	122	2	of	of	ADP
cana-1399	122	3	graph	graph	NOUN
cana-1399	122	4	g	g	PROPN
cana-1399	122	5	for	for	ADP
cana-1399	122	6	vdt	vdt	PROPN
cana-1399	122	7	graph	graph	NOUN
cana-1399	122	8	decomposition	decomposition	NOUN
cana-1399	122	9	fig	fig	NOUN
cana-1399	122	10	9	9	NUM
cana-1399	122	11	.	.	PUNCT
cana-1399	123	1	rooted	root	VERB
cana-1399	123	2	trees	tree	NOUN
cana-1399	123	3	t2	t2	PROPN
cana-1399	123	4	,	,	PUNCT
cana-1399	123	5	t3	t3	PROPN
cana-1399	123	6	,	,	PUNCT
cana-1399	123	7	t4	t4	PROPN
cana-1399	123	8	using	use	VERB
cana-1399	123	9	step	step	NOUN
cana-1399	123	10	1	1	NUM
cana-1399	123	11	figure	figure	NOUN
cana-1399	123	12	10	10	NUM
cana-1399	123	13	shows	show	VERB
cana-1399	123	14	the	the	DET
cana-1399	123	15	decomposition	decomposition	NOUN
cana-1399	123	16	for	for	ADP
cana-1399	123	17	our	our	PRON
cana-1399	123	18	example	example	NOUN
cana-1399	123	19	in	in	ADP
cana-1399	123	20	iteration	iteration	NOUN
cana-1399	123	21	2	2	NUM
cana-1399	123	22	.	.	PUNCT
cana-1399	123	23	fig	fig	NOUN
cana-1399	123	24	11	11	NUM
cana-1399	123	25	.	.	PUNCT
cana-1399	124	1	iteration	iteration	NOUN
cana-1399	124	2	2	2	NUM
cana-1399	124	3	step	step	NOUN
cana-1399	124	4	11	11	NUM
cana-1399	124	5	if	if	SCONJ
cana-1399	124	6	step	step	NOUN
cana-1399	124	7	10	10	NUM
cana-1399	124	8	covers	cover	VERB
cana-1399	124	9	all	all	DET
cana-1399	124	10	the	the	DET
cana-1399	124	11	edges	edge	NOUN
cana-1399	124	12	of	of	ADP
cana-1399	124	13	g	g	NOUN
cana-1399	124	14	,	,	PUNCT
cana-1399	124	15	then	then	ADV
cana-1399	124	16	terminate	terminate	VERB
cana-1399	124	17	the	the	DET
cana-1399	124	18	iterative	iterative	NOUN
cana-1399	124	19	procedure	procedure	NOUN
cana-1399	124	20	.	.	PUNCT
cana-1399	125	1	else	else	ADV
cana-1399	125	2	repeat	repeat	NOUN
cana-1399	125	3	step	step	NOUN
cana-1399	125	4	1	1	NUM
cana-1399	125	5	to	to	PART
cana-1399	125	6	step	step	VERB
cana-1399	125	7	9	9	NUM
cana-1399	125	8	on	on	ADP
cana-1399	125	9	all	all	DET
cana-1399	125	10	the	the	DET
cana-1399	125	11	resulting	result	VERB
cana-1399	125	12	graphs	graph	NOUN
cana-1399	125	13	until	until	SCONJ
cana-1399	125	14	all	all	DET
cana-1399	125	15	the	the	DET
cana-1399	125	16	edges	edge	NOUN
cana-1399	125	17	of	of	ADP
cana-1399	125	18	g	g	NOUN
cana-1399	125	19	are	be	AUX
cana-1399	125	20	covered	cover	VERB
cana-1399	125	21	.	.	PUNCT
cana-1399	126	1	our	our	PRON
cana-1399	126	2	example	example	NOUN
cana-1399	126	3	terminates	terminate	VERB
cana-1399	126	4	in	in	ADP
cana-1399	126	5	iteration	iteration	NOUN
cana-1399	126	6	3	3	NUM
cana-1399	126	7	as	as	SCONJ
cana-1399	126	8	seen	see	VERB
cana-1399	126	9	in	in	ADP
cana-1399	126	10	figure	figure	NOUN
cana-1399	126	11	11	11	NUM
cana-1399	126	12	and	and	CCONJ
cana-1399	126	13	1	1	NUM
cana-1399	126	14	2	2	NUM
cana-1399	126	15	3	3	NUM
cana-1399	126	16	4	4	NUM
cana-1399	126	17	5	5	NUM
cana-1399	126	18	6	6	NUM
cana-1399	126	19	7	7	NUM
cana-1399	126	20	8	8	NUM
cana-1399	126	21	9	9	NUM
cana-1399	126	22	10	10	NUM
cana-1399	126	23	11	11	NUM
cana-1399	126	24	12	12	NUM
cana-1399	126	25	13	13	NUM
cana-1399	126	26	14	14	NUM
cana-1399	126	27	15	15	NUM
cana-1399	126	28	16	16	NUM
cana-1399	126	29	17	17	NUM
cana-1399	126	30	18	18	NUM
cana-1399	126	31	19	19	NUM
cana-1399	126	32	20h	20h	NOUN
cana-1399	126	33	,	,	PUNCT
cana-1399	126	34	h	h	NOUN
cana-1399	126	35	,	,	PUNCT
cana-1399	126	36	h	h	NOUN
cana-1399	126	37	,	,	PUNCT
cana-1399	126	38	h	h	NOUN
cana-1399	126	39	,	,	PUNCT
cana-1399	126	40	h	h	NOUN
cana-1399	126	41	,	,	PUNCT
cana-1399	126	42	h	h	NOUN
cana-1399	126	43	,	,	PUNCT
cana-1399	126	44	h	h	NOUN
cana-1399	126	45	,	,	PUNCT
cana-1399	126	46	h	h	NOUN
cana-1399	126	47	,	,	PUNCT
cana-1399	126	48	h	h	NOUN
cana-1399	126	49	,	,	PUNCT
cana-1399	126	50	h	h	NOUN
cana-1399	126	51	,	,	PUNCT
cana-1399	126	52	h	h	NOUN
cana-1399	126	53	,	,	PUNCT
cana-1399	126	54	h	h	NOUN
cana-1399	126	55	,	,	PUNCT
cana-1399	126	56	h	h	NOUN
cana-1399	126	57	,	,	PUNCT
cana-1399	126	58	h	h	NOUN
cana-1399	126	59	,	,	PUNCT
cana-1399	126	60	h	h	NOUN
cana-1399	126	61	,	,	PUNCT
cana-1399	126	62	h	h	NOUN
cana-1399	126	63	,	,	PUNCT
cana-1399	126	64	h	h	NOUN
cana-1399	126	65	,	,	PUNCT
cana-1399	126	66	h	h	NOUN
cana-1399	126	67	,	,	PUNCT
cana-1399	126	68	h	h	NOUN
cana-1399	126	69	,	,	PUNCT
cana-1399	126	70	h	h	PROPN
cana-1399	126	71	are	be	AUX
cana-1399	126	72	the	the	DET
cana-1399	126	73	decompositions	decomposition	NOUN
cana-1399	126	74	of	of	ADP
cana-1399	126	75	graph	graph	NOUN
cana-1399	126	76	g.	g.	PROPN
cana-1399	126	77	hence	hence	ADV
cana-1399	126	78	,	,	PUNCT
cana-1399	126	79	we	we	PRON
cana-1399	126	80	conclude	conclude	VERB
cana-1399	126	81	the	the	DET
cana-1399	126	82	following	follow	VERB
cana-1399	126	83	theorem	theorem	PROPN
cana-1399	126	84	.	.	PUNCT
cana-1399	126	85	theorem	theorem	NOUN
cana-1399	126	86	4	4	NUM
cana-1399	126	87	given	give	VERB
cana-1399	126	88	any	any	DET
cana-1399	126	89	graph	graph	NOUN
cana-1399	126	90	g	g	NOUN
cana-1399	126	91	,	,	PUNCT
cana-1399	126	92	there	there	PRON
cana-1399	126	93	exist	exist	VERB
cana-1399	126	94	a	a	DET
cana-1399	126	95	decomposition	decomposition	NOUN
cana-1399	126	96	1	1	NUM
cana-1399	126	97	2	2	NUM
cana-1399	126	98	sh	sh	NOUN
cana-1399	126	99	,	,	PUNCT
cana-1399	126	100	h	h	NOUN
cana-1399	126	101	,	,	PUNCT
cana-1399	126	102	.	.	PUNCT
cana-1399	126	103	.	.	PUNCT
cana-1399	127	1	.	.	PUNCT
cana-1399	128	1	,	,	PUNCT
cana-1399	128	2	h	h	NOUN
cana-1399	128	3	such	such	ADJ
cana-1399	128	4	that	that	SCONJ
cana-1399	128	5	each	each	DET
cana-1399	128	6	ih	ih	NOUN
cana-1399	128	7	,	,	PUNCT
cana-1399	128	8	1	1	NUM
cana-1399	128	9	i	i	PRON
cana-1399	128	10	s	s	VERB
cana-1399	128	11			NOUN
cana-1399	128	12	is	be	AUX
cana-1399	128	13	either	either	CCONJ
cana-1399	128	14	comb	comb	NOUN
cana-1399	128	15	graph	graph	NOUN
cana-1399	128	16	or	or	CCONJ
cana-1399	128	17	path	path	NOUN
cana-1399	128	18	.	.	PUNCT
cana-1399	129	1	theorem	theorem	NOUN
cana-1399	129	2	5	5	NUM
cana-1399	129	3	given	give	VERB
cana-1399	129	4	any	any	DET
cana-1399	129	5	graph	graph	NOUN
cana-1399	129	6	g	g	NOUN
cana-1399	129	7	there	there	ADV
cana-1399	129	8	exist	exist	VERB
cana-1399	129	9	a	a	DET
cana-1399	129	10	decomposition	decomposition	NOUN
cana-1399	130	1			PRON
cana-1399	130	2	1	1	NOUN
cana-1399	130	3	2	2	NUM
cana-1399	130	4	kh	kh	INTJ
cana-1399	130	5	,	,	PUNCT
cana-1399	130	6	h	h	NOUN
cana-1399	130	7	,	,	PUNCT
cana-1399	130	8	...	...	PUNCT
cana-1399	130	9	,	,	PUNCT
cana-1399	130	10	h	h	NOUN
cana-1399	130	11	for	for	ADP
cana-1399	130	12	g	g	PROPN
cana-1399	130	13	such	such	ADJ
cana-1399	130	14	that	that	SCONJ
cana-1399	130	15	each	each	DET
cana-1399	130	16	ih	ih	NOUN
cana-1399	130	17	is	be	AUX
cana-1399	130	18	a	a	DET
cana-1399	130	19	vdt	vdt	PROPN
cana-1399	130	20	graph	graph	NOUN
cana-1399	130	21	.	.	PUNCT
cana-1399	131	1	communications	communication	NOUN
cana-1399	131	2	on	on	ADP
cana-1399	131	3	applied	apply	VERB
cana-1399	131	4	nonlinear	nonlinear	ADJ
cana-1399	131	5	analysis	analysis	NOUN
cana-1399	131	6	issn	issn	NOUN
cana-1399	131	7	:	:	PUNCT
cana-1399	131	8	1074	1074	NUM
cana-1399	131	9	-	-	PUNCT
cana-1399	131	10	133x	133x	NUM
cana-1399	131	11	vol	vol	NOUN
cana-1399	131	12	31	31	NUM
cana-1399	131	13	no	no	NOUN
cana-1399	131	14	.	.	PUNCT
cana-1399	132	1	7s	7	NOUN
cana-1399	132	2	(	(	PUNCT
cana-1399	132	3	2024	2024	NUM
cana-1399	132	4	)	)	PUNCT
cana-1399	132	5	581	581	NUM
cana-1399	132	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1399	132	7	proof	proof	NOUN
cana-1399	132	8	let	let	VERB
cana-1399	132	9	g	g	NOUN
cana-1399	132	10	be	be	AUX
cana-1399	132	11	any	any	DET
cana-1399	132	12	given	give	VERB
cana-1399	132	13	graph	graph	NOUN
cana-1399	132	14	.	.	PUNCT
cana-1399	133	1	determine	determine	VERB
cana-1399	133	2	a	a	DET
cana-1399	133	3	decomposition	decomposition	NOUN
cana-1399	133	4	1	1	NUM
cana-1399	133	5	2	2	NUM
cana-1399	133	6	sx	sx	NOUN
cana-1399	133	7	h	h	NOUN
cana-1399	133	8	,	,	PUNCT
cana-1399	133	9	h	h	NOUN
cana-1399	133	10	,	,	PUNCT
cana-1399	133	11	.	.	PUNCT
cana-1399	133	12	.	.	PUNCT
cana-1399	134	1	.	.	PUNCT
cana-1399	135	1	,	,	PUNCT
cana-1399	135	2	h	h	NOUN
cana-1399	135	3	for	for	ADP
cana-1399	135	4	g	g	NOUN
cana-1399	135	5	using	use	VERB
cana-1399	135	6	theorem	theorem	NOUN
cana-1399	135	7	4	4	NUM
cana-1399	135	8	.	.	PUNCT
cana-1399	136	1	we	we	PRON
cana-1399	136	2	know	know	VERB
cana-1399	136	3	that	that	SCONJ
cana-1399	136	4	each	each	DET
cana-1399	136	5	ih	ih	NOUN
cana-1399	136	6	is	be	AUX
cana-1399	136	7	either	either	CCONJ
cana-1399	136	8	a	a	DET
cana-1399	136	9	comb	comb	NOUN
cana-1399	136	10	or	or	CCONJ
cana-1399	136	11	a	a	DET
cana-1399	136	12	path	path	NOUN
cana-1399	136	13	.	.	PUNCT
cana-1399	137	1	if	if	SCONJ
cana-1399	137	2	ih	ih	NOUN
cana-1399	137	3	is	be	AUX
cana-1399	137	4	a	a	DET
cana-1399	137	5	comb	comb	NOUN
cana-1399	137	6	then	then	ADV
cana-1399	137	7	it	it	PRON
cana-1399	137	8	is	be	AUX
cana-1399	137	9	a	a	DET
cana-1399	137	10	vdt	vdt	PROPN
cana-1399	137	11	graph	graph	NOUN
cana-1399	137	12	.	.	PUNCT
cana-1399	138	1	if	if	SCONJ
cana-1399	138	2	ih	ih	NOUN
cana-1399	138	3	is	be	AUX
cana-1399	138	4	a	a	DET
cana-1399	138	5	path	path	NOUN
cana-1399	138	6	np	np	INTJ
cana-1399	138	7	then	then	ADV
cana-1399	138	8	we	we	PRON
cana-1399	138	9	continue	continue	VERB
cana-1399	138	10	as	as	SCONJ
cana-1399	138	11	follows	follow	VERB
cana-1399	138	12	.	.	PUNCT
cana-1399	139	1	fig	fig	NOUN
cana-1399	139	2	12	12	NUM
cana-1399	139	3	.	.	PUNCT
cana-1399	140	1	iteration	iteration	NOUN
cana-1399	140	2	3	3	NUM
cana-1399	140	3	i.	i.	NOUN
cana-1399	140	4	let	let	VERB
cana-1399	140	5	n	n	NOUN
cana-1399	140	6	1	1	NUM
cana-1399	140	7	1	1	NUM
cana-1399	140	8	2	2	NUM
cana-1399	140	9	2	2	NUM
cana-1399	140	10	3	3	NUM
cana-1399	140	11	n	n	SYM
cana-1399	140	12	1	1	NUM
cana-1399	140	13	n	n	NUM
cana-1399	140	14	1	1	NUM
cana-1399	140	15	np	np	NOUN
cana-1399	140	16	v	v	PART
cana-1399	140	17	e	e	X
cana-1399	140	18	v	v	X
cana-1399	140	19	e	e	X
cana-1399	140	20	v	v	NOUN
cana-1399	140	21	...	...	PUNCT
cana-1399	140	22	v	v	NUM
cana-1399	140	23	e	e	PROPN
cana-1399	140	24	v	v	ADP
cana-1399	140	25			PROPN
cana-1399	140	26			PROPN
cana-1399	140	27	where	where	SCONJ
cana-1399	140	28	n	n	PRON
cana-1399	140	29	1e	1e	NOUN
cana-1399	140	30	0mod3	0mod3	NUM
cana-1399	141	1			PROPN
cana-1399	141	2	.	.	PUNCT
cana-1399	142	1	let	let	VERB
cana-1399	142	2	us	we	PRON
cana-1399	142	3	decompose	decompose	VERB
cana-1399	142	4	np	np	INTJ
cana-1399	142	5	into	into	ADP
cana-1399	142	6	paths	path	NOUN
cana-1399	142	7	1	1	NUM
cana-1399	142	8	2	2	NUM
cana-1399	142	9	k1p	k1p	X
cana-1399	142	10	,	,	PUNCT
cana-1399	142	11	p	p	X
cana-1399	142	12	,	,	PUNCT
cana-1399	142	13	...	...	PUNCT
cana-1399	142	14	,	,	PUNCT
cana-1399	142	15	p	p	X
cana-1399	142	16	where	where	SCONJ
cana-1399	142	17	1	1	NUM
cana-1399	142	18	1	1	NUM
cana-1399	142	19	1	1	NUM
cana-1399	142	20	2	2	NUM
cana-1399	142	21	2	2	NUM
cana-1399	142	22	3	3	NUM
cana-1399	142	23	3	3	NUM
cana-1399	142	24	4	4	NUM
cana-1399	142	25	2	2	NUM
cana-1399	142	26	4	4	NUM
cana-1399	142	27	4	4	NUM
cana-1399	142	28	5	5	NUM
cana-1399	142	29	5	5	NUM
cana-1399	142	30	6	6	NUM
cana-1399	142	31	6	6	NUM
cana-1399	142	32	7p	7p	NOUN
cana-1399	142	33	v	v	ADP
cana-1399	142	34	e	e	NOUN
cana-1399	142	35	v	v	ADP
cana-1399	142	36	e	e	X
cana-1399	142	37	v	v	NOUN
cana-1399	142	38	e	e	NOUN
cana-1399	142	39	v	v	NOUN
cana-1399	142	40	;	;	PUNCT
cana-1399	143	1	p	p	X
cana-1399	143	2	v	v	X
cana-1399	143	3	e	e	X
cana-1399	143	4	v	v	NOUN
cana-1399	143	5	e	e	X
cana-1399	143	6	v	v	NOUN
cana-1399	143	7	e	e	NOUN
cana-1399	143	8	v	v	NOUN
cana-1399	143	9	;	;	PUNCT
cana-1399	143	10			NUM
cana-1399	143	11			NOUN
cana-1399	143	12	…	…	PUNCT
cana-1399	143	13	k1	k1	NOUN
cana-1399	143	14	n	n	CCONJ
cana-1399	143	15	3	3	NUM
cana-1399	143	16	n	n	CCONJ
cana-1399	143	17	3p	3p	NUM
cana-1399	143	18	v	v	NOUN
cana-1399	143	19	e	e	NOUN
cana-1399	143	20			NOUN
cana-1399	143	21	n	n	CCONJ
cana-1399	143	22	2	2	NUM
cana-1399	143	23	n	n	NUM
cana-1399	143	24	2	2	NUM
cana-1399	143	25	n	n	NUM
cana-1399	143	26	1	1	NUM
cana-1399	143	27	n	n	NUM
cana-1399	143	28	1	1	NUM
cana-1399	143	29	nv	nv	PROPN
cana-1399	143	30	e	e	X
cana-1399	143	31	v	v	ADP
cana-1399	143	32	e	e	PROPN
cana-1399	143	33	v	v	NUM
cana-1399	143	34	.	.	PUNCT
cana-1399	143	35			PROPN
cana-1399	143	36			PROPN
cana-1399	143	37			PROPN
cana-1399	143	38	ii	ii	NOUN
cana-1399	143	39	.	.	PUNCT
cana-1399	144	1	if	if	SCONJ
cana-1399	144	2	n	n	PROPN
cana-1399	144	3	1e	1e	NOUN
cana-1399	144	4	1mod3	1mod3	PROPN
cana-1399	144	5			PROPN
cana-1399	144	6	then	then	ADV
cana-1399	144	7	let	let	VERB
cana-1399	144	8	us	we	PRON
cana-1399	144	9	decompose	decompose	VERB
cana-1399	144	10	np	np	INTJ
cana-1399	144	11	into	into	ADP
cana-1399	144	12	paths	path	NOUN
cana-1399	144	13	1	1	NUM
cana-1399	144	14	2	2	NUM
cana-1399	144	15	k2p	k2p	NOUN
cana-1399	144	16	,	,	PUNCT
cana-1399	144	17	p	p	X
cana-1399	144	18	,	,	PUNCT
cana-1399	144	19	...	...	PUNCT
cana-1399	144	20	,	,	PUNCT
cana-1399	144	21	p	p	X
cana-1399	144	22	where	where	SCONJ
cana-1399	144	23	1	1	NUM
cana-1399	144	24	1	1	NUM
cana-1399	144	25	1	1	NUM
cana-1399	144	26	2	2	NUM
cana-1399	144	27	2	2	NUM
cana-1399	144	28	3p	3p	NUM
cana-1399	144	29	v	v	ADP
cana-1399	144	30	e	e	NOUN
cana-1399	144	31	v	v	ADP
cana-1399	144	32	e	e	X
cana-1399	144	33	v	v	NOUN
cana-1399	144	34	3	3	NUM
cana-1399	144	35	4	4	NUM
cana-1399	144	36	2	2	NUM
cana-1399	144	37	4	4	NUM
cana-1399	144	38	4	4	NUM
cana-1399	144	39	5	5	NUM
cana-1399	144	40	5	5	NUM
cana-1399	144	41	6	6	NUM
cana-1399	144	42	6	6	NUM
cana-1399	144	43	7	7	NUM
cana-1399	144	44	k2	k2	NOUN
cana-1399	144	45	n	n	CCONJ
cana-1399	144	46	1	1	NUM
cana-1399	144	47	n	n	NUM
cana-1399	144	48	1	1	NUM
cana-1399	144	49	ne	ne	NOUN
cana-1399	144	50	v	v	NOUN
cana-1399	144	51	;	;	PUNCT
cana-1399	144	52	p	p	X
cana-1399	144	53	v	v	X
cana-1399	144	54	e	e	X
cana-1399	144	55	v	v	NOUN
cana-1399	144	56	e	e	X
cana-1399	144	57	v	v	NOUN
cana-1399	144	58	e	e	NOUN
cana-1399	144	59	v	v	NOUN
cana-1399	144	60	;	;	PUNCT
cana-1399	144	61	....	....	PUNCT
cana-1399	145	1	p	p	X
cana-1399	145	2	v	v	X
cana-1399	145	3	e	e	X
cana-1399	145	4	v	v	NOUN
cana-1399	145	5	.	.	PUNCT
cana-1399	145	6			PROPN
cana-1399	145	7			PROPN
cana-1399	145	8	iii	iii	PROPN
cana-1399	145	9	.	.	PUNCT
cana-1399	146	1	if	if	SCONJ
cana-1399	146	2	n	n	PRON
cana-1399	146	3	1e	1e	NOUN
cana-1399	146	4	2mod3	2mod3	NUM
cana-1399	147	1			NOUN
cana-1399	147	2	let	let	VERB
cana-1399	147	3	us	we	PRON
cana-1399	147	4	decompose	decompose	VERB
cana-1399	147	5	np	np	INTJ
cana-1399	147	6	into	into	ADP
cana-1399	147	7	paths	path	NOUN
cana-1399	147	8	1	1	NUM
cana-1399	147	9	2	2	NUM
cana-1399	147	10	k3p	k3p	NOUN
cana-1399	147	11	,	,	PUNCT
cana-1399	147	12	p	p	X
cana-1399	147	13	,	,	PUNCT
cana-1399	147	14	...	...	PUNCT
cana-1399	147	15	,	,	PUNCT
cana-1399	147	16	p	p	X
cana-1399	147	17	where	where	SCONJ
cana-1399	147	18	1	1	NUM
cana-1399	147	19	1	1	NUM
cana-1399	147	20	1	1	NUM
cana-1399	147	21	2	2	NUM
cana-1399	147	22	2	2	NUM
cana-1399	147	23	3	3	NUM
cana-1399	147	24	3p	3p	NUM
cana-1399	147	25	v	v	ADP
cana-1399	147	26	e	e	NOUN
cana-1399	147	27	v	v	ADP
cana-1399	147	28	e	e	PROPN
cana-1399	147	29	v	v	ADP
cana-1399	147	30	e	e	ADJ
cana-1399	147	31	4	4	NUM
cana-1399	147	32	2	2	NUM
cana-1399	147	33	4	4	NUM
cana-1399	147	34	4	4	NUM
cana-1399	147	35	5	5	NUM
cana-1399	147	36	5	5	NUM
cana-1399	147	37	6	6	NUM
cana-1399	147	38	6	6	NUM
cana-1399	147	39	7	7	NUM
cana-1399	147	40	k3	k3	VERB
cana-1399	147	41	2	2	NUM
cana-1399	147	42	n	n	NUM
cana-1399	147	43	5	5	NUM
cana-1399	147	44	n	n	SYM
cana-1399	147	45	5	5	NUM
cana-1399	147	46	n	n	SYM
cana-1399	147	47	4	4	NUM
cana-1399	147	48	n	n	SYM
cana-1399	147	49	4	4	NUM
cana-1399	147	50	n	n	SYM
cana-1399	147	51	3	3	NUM
cana-1399	147	52	n	n	SYM
cana-1399	147	53	3	3	NUM
cana-1399	147	54	n	n	SYM
cana-1399	147	55	2	2	NUM
cana-1399	147	56	k3	k3	VERB
cana-1399	147	57	1	1	NUM
cana-1399	147	58	n	n	SYM
cana-1399	147	59	2	2	NUM
cana-1399	147	60	n	n	NUM
cana-1399	147	61	2v	2v	NUM
cana-1399	147	62	;	;	PUNCT
cana-1399	147	63	p	p	X
cana-1399	147	64	v	v	X
cana-1399	147	65	e	e	X
cana-1399	147	66	v	v	NOUN
cana-1399	147	67	e	e	X
cana-1399	147	68	v	v	NOUN
cana-1399	147	69	e	e	NOUN
cana-1399	147	70	v	v	NOUN
cana-1399	147	71	;	;	PUNCT
cana-1399	147	72	....	....	PUNCT
cana-1399	148	1	p	p	NOUN
cana-1399	148	2	v	v	X
cana-1399	148	3	e	e	X
cana-1399	148	4	v	v	NOUN
cana-1399	148	5	e	e	X
cana-1399	148	6	v	v	NOUN
cana-1399	148	7	e	e	NOUN
cana-1399	148	8	v	v	NOUN
cana-1399	148	9	;	;	PUNCT
cana-1399	148	10	p	p	NOUN
cana-1399	148	11	=	=	SYM
cana-1399	148	12	v	v	NOUN
cana-1399	148	13	e	e	NOUN
cana-1399	148	14			PROPN
cana-1399	148	15			PROPN
cana-1399	148	16			PROPN
cana-1399	148	17			PROPN
cana-1399	148	18			PROPN
cana-1399	148	19			PROPN
cana-1399	148	20			PROPN
cana-1399	148	21			PROPN
cana-1399	148	22			ADP
cana-1399	148	23			PROPN
cana-1399	148	24	n	n	NOUN
cana-1399	148	25	1	1	NUM
cana-1399	148	26	k3	k3	VERB
cana-1399	148	27	n	n	PRON
cana-1399	148	28	1	1	NUM
cana-1399	148	29	n	n	NUM
cana-1399	148	30	1	1	NUM
cana-1399	148	31	nv	nv	PROPN
cana-1399	148	32	;	;	PUNCT
cana-1399	148	33	p	p	X
cana-1399	148	34	=	=	X
cana-1399	148	35	v	v	PROPN
cana-1399	148	36	e	e	NOUN
cana-1399	148	37	v	v	NOUN
cana-1399	148	38	.	.	PUNCT
cana-1399	149	1			NOUN
cana-1399	149	2			PROPN
cana-1399	149	3			PROPN
cana-1399	149	4	hence	hence	ADV
cana-1399	149	5	from	from	ADP
cana-1399	149	6	the	the	DET
cana-1399	149	7	decomposition	decomposition	NOUN
cana-1399	149	8	x	x	PUNCT
cana-1399	149	9	we	we	PRON
cana-1399	149	10	obtain	obtain	VERB
cana-1399	149	11	a	a	DET
cana-1399	149	12	new	new	ADJ
cana-1399	149	13	decomposition	decomposition	NOUN
cana-1399	150	1	y	y	NOUN
cana-1399	150	2	=	=	SYM
cana-1399	150	3			NOUN
cana-1399	150	4	1	1	NOUN
cana-1399	151	1	2	2	NUM
cana-1399	151	2	kh	kh	INTJ
cana-1399	151	3	,	,	PUNCT
cana-1399	151	4	h	h	NOUN
cana-1399	151	5	,	,	PUNCT
cana-1399	151	6	...	...	PUNCT
cana-1399	151	7	,	,	PUNCT
cana-1399	151	8	h	h	NOUN
cana-1399	151	9	,	,	PUNCT
cana-1399	151	10	k	k	PROPN
cana-1399	151	11	s	s	PROPN
cana-1399	151	12			NUM
cana-1399	151	13	such	such	ADJ
cana-1399	151	14	that	that	SCONJ
cana-1399	151	15	each	each	DET
cana-1399	151	16	ih	ih	NOUN
cana-1399	151	17	is	be	AUX
cana-1399	151	18	either	either	CCONJ
cana-1399	151	19	2	2	NUM
cana-1399	151	20	4	4	NUM
cana-1399	151	21	n	n	NUM
cana-1399	151	22	1p	1p	NUM
cana-1399	151	23	,	,	PUNCT
cana-1399	151	24	p	p	X
cana-1399	151	25	,	,	PUNCT
cana-1399	151	26	p	p	PROPN
cana-1399	151	27	k	k	PROPN
cana-1399	151	28	,	,	PUNCT
cana-1399	151	29	implies	imply	VERB
cana-1399	151	30	g	g	NOUN
cana-1399	151	31	can	can	AUX
cana-1399	151	32	be	be	AUX
cana-1399	151	33	decomposed	decompose	VERB
cana-1399	151	34	into	into	ADP
cana-1399	151	35	vdt	vdt	PROPN
cana-1399	151	36	graphs	graph	NOUN
cana-1399	151	37	.	.	PUNCT
cana-1399	152	1	5	5	X
cana-1399	152	2	.	.	X
cana-1399	152	3	conclusion	conclusion	NOUN
cana-1399	152	4	graph	graph	NOUN
cana-1399	152	5	decomposition	decomposition	NOUN
cana-1399	152	6	has	have	VERB
cana-1399	152	7	several	several	ADJ
cana-1399	152	8	significant	significant	ADJ
cana-1399	152	9	applications	application	NOUN
cana-1399	152	10	.	.	PUNCT
cana-1399	153	1	it	it	PRON
cana-1399	153	2	reveals	reveal	VERB
cana-1399	153	3	patterns	pattern	NOUN
cana-1399	153	4	and	and	CCONJ
cana-1399	153	5	connectivity	connectivity	NOUN
cana-1399	153	6	between	between	ADP
cana-1399	153	7	vertices	vertex	NOUN
cana-1399	153	8	within	within	ADP
cana-1399	153	9	graphs	graph	NOUN
cana-1399	153	10	by	by	ADP
cana-1399	153	11	revealing	reveal	VERB
cana-1399	153	12	hierarchical	hierarchical	ADJ
cana-1399	153	13	relationships	relationship	NOUN
cana-1399	153	14	and	and	CCONJ
cana-1399	153	15	substructures	substructure	NOUN
cana-1399	153	16	.	.	PUNCT
cana-1399	154	1	different	different	ADJ
cana-1399	154	2	methods	method	NOUN
cana-1399	154	3	and	and	CCONJ
cana-1399	154	4	algorithms	algorithm	NOUN
cana-1399	154	5	exist	exist	VERB
cana-1399	154	6	for	for	ADP
cana-1399	154	7	graph	graph	NOUN
cana-1399	154	8	decomposition	decomposition	NOUN
cana-1399	154	9	.	.	PUNCT
cana-1399	155	1	according	accord	VERB
cana-1399	155	2	to	to	ADP
cana-1399	155	3	the	the	DET
cana-1399	155	4	graph	graph	NOUN
cana-1399	155	5	,	,	PUNCT
cana-1399	155	6	each	each	DET
cana-1399	155	7	approach	approach	NOUN
cana-1399	155	8	offers	offer	VERB
cana-1399	155	9	unique	unique	ADJ
cana-1399	155	10	insights	insight	NOUN
cana-1399	155	11	and	and	CCONJ
cana-1399	155	12	advantages	advantage	NOUN
cana-1399	155	13	.	.	PUNCT
cana-1399	156	1	in	in	ADP
cana-1399	156	2	this	this	DET
cana-1399	156	3	article	article	NOUN
cana-1399	156	4	,	,	PUNCT
cana-1399	156	5	we	we	PRON
cana-1399	156	6	presented	present	VERB
cana-1399	156	7	an	an	DET
cana-1399	156	8	algorithm	algorithm	NOUN
cana-1399	156	9	for	for	ADP
cana-1399	156	10	determining	determine	VERB
cana-1399	156	11	a	a	DET
cana-1399	156	12	decomposition	decomposition	NOUN
cana-1399	156	13	for	for	ADP
cana-1399	156	14	any	any	DET
cana-1399	156	15	given	give	VERB
cana-1399	156	16	graph	graph	NOUN
cana-1399	156	17	into	into	ADP
cana-1399	156	18	comb	comb	NOUN
cana-1399	156	19	graphs	graph	NOUN
cana-1399	156	20	,	,	PUNCT
cana-1399	156	21	p4	p4	ADJ
cana-1399	156	22	and	and	CCONJ
cana-1399	156	23	p2	p2	PROPN
cana-1399	156	24	which	which	PRON
cana-1399	156	25	are	be	AUX
cana-1399	156	26	vdt	vdt	PROPN
cana-1399	156	27	graphs	graph	NOUN
cana-1399	156	28	.	.	PUNCT
cana-1399	157	1	this	this	DET
cana-1399	157	2	algorithm	algorithm	NOUN
cana-1399	157	3	can	can	AUX
cana-1399	157	4	be	be	AUX
cana-1399	157	5	used	use	VERB
cana-1399	157	6	to	to	PART
cana-1399	157	7	study	study	VERB
cana-1399	157	8	graph	graph	NOUN
cana-1399	157	9	decomposition	decomposition	NOUN
cana-1399	157	10	in	in	ADP
cana-1399	157	11	a	a	DET
cana-1399	157	12	variety	variety	NOUN
cana-1399	157	13	of	of	ADP
cana-1399	157	14	contexts	contexts	NOUN
cana-1399	157	15	.	.	PUNCT
cana-1399	158	1	it	it	PRON
cana-1399	158	2	can	can	AUX
cana-1399	158	3	help	help	AUX
cana-1399	158	4	identify	identify	VERB
cana-1399	158	5	and	and	CCONJ
cana-1399	158	6	understand	understand	VERB
cana-1399	158	7	the	the	DET
cana-1399	158	8	underlying	underlie	VERB
cana-1399	158	9	structures	structure	NOUN
cana-1399	158	10	of	of	ADP
cana-1399	158	11	complex	complex	ADJ
cana-1399	158	12	networks	network	NOUN
cana-1399	158	13	.	.	PUNCT
cana-1399	159	1	furthermore	furthermore	ADV
cana-1399	159	2	,	,	PUNCT
cana-1399	159	3	it	it	PRON
cana-1399	159	4	can	can	AUX
cana-1399	159	5	be	be	AUX
cana-1399	159	6	used	use	VERB
cana-1399	159	7	to	to	PART
cana-1399	159	8	solve	solve	VERB
cana-1399	159	9	problems	problem	NOUN
cana-1399	159	10	related	relate	VERB
cana-1399	159	11	to	to	AUX
cana-1399	159	12	graph	graph	VERB
cana-1399	159	13	decomposition	decomposition	NOUN
cana-1399	159	14	in	in	ADP
cana-1399	159	15	an	an	DET
cana-1399	159	16	efficient	efficient	ADJ
cana-1399	159	17	manner	manner	NOUN
cana-1399	159	18	.	.	PUNCT
cana-1399	160	1	communications	communication	NOUN
cana-1399	160	2	on	on	ADP
cana-1399	160	3	applied	apply	VERB
cana-1399	160	4	nonlinear	nonlinear	ADJ
cana-1399	160	5	analysis	analysis	NOUN
cana-1399	160	6	issn	issn	NOUN
cana-1399	160	7	:	:	PUNCT
cana-1399	160	8	1074	1074	NUM
cana-1399	160	9	-	-	PUNCT
cana-1399	160	10	133x	133x	NUM
cana-1399	160	11	vol	vol	NOUN
cana-1399	160	12	31	31	NUM
cana-1399	160	13	no	no	NOUN
cana-1399	160	14	.	.	PUNCT
cana-1399	161	1	7s	7	NOUN
cana-1399	161	2	(	(	PUNCT
cana-1399	161	3	2024	2024	NUM
cana-1399	161	4	)	)	PUNCT
cana-1399	161	5	582	582	NUM
cana-1399	161	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1399	161	7	references	reference	NOUN
cana-1399	161	8	[	[	X
cana-1399	161	9	1	1	NUM
cana-1399	161	10	]	]	X
cana-1399	161	11	narsingh	narsingh	NOUN
cana-1399	161	12	deo	deo	NOUN
cana-1399	161	13	,	,	PUNCT
cana-1399	161	14	graph	graph	NOUN
cana-1399	161	15	theory	theory	NOUN
cana-1399	161	16	with	with	ADP
cana-1399	161	17	applications	application	NOUN
cana-1399	161	18	to	to	ADP
cana-1399	161	19	engineering	engineering	NOUN
cana-1399	161	20	and	and	CCONJ
cana-1399	161	21	computer	computer	NOUN
cana-1399	161	22	sciences	science	NOUN
cana-1399	161	23	,	,	PUNCT
cana-1399	161	24	prentice	prentice	PROPN
cana-1399	161	25	hall	hall	PROPN
cana-1399	161	26	india	india	PROPN
cana-1399	161	27	,	,	PUNCT
cana-1399	161	28	2016	2016	NUM
cana-1399	161	29	.	.	PUNCT
cana-1399	162	1	[	[	X
cana-1399	162	2	2	2	NUM
cana-1399	162	3	]	]	PUNCT
cana-1399	162	4	samuel	samuel	PROPN
cana-1399	162	5	issacraj	issacraj	PROPN
cana-1399	162	6	,	,	PUNCT
cana-1399	162	7	a	a	PRON
cana-1399	162	8	and	and	CCONJ
cana-1399	162	9	paulraj	paulraj	ADJ
cana-1399	162	10	joseph.j	joseph.j	PROPN
cana-1399	162	11	,	,	PUNCT
cana-1399	162	12	fork	fork	NOUN
cana-1399	162	13	decomposition	decomposition	NOUN
cana-1399	162	14	of	of	ADP
cana-1399	162	15	some	some	DET
cana-1399	162	16	total	total	ADJ
cana-1399	162	17	graphs	graph	NOUN
cana-1399	162	18	,	,	PUNCT
cana-1399	162	19	palestine	palestine	PROPN
cana-1399	162	20	journal	journal	PROPN
cana-1399	162	21	of	of	ADP
cana-1399	162	22	mathematics	mathematics	PROPN
cana-1399	162	23	,	,	PUNCT
cana-1399	162	24	vol	vol	NOUN
cana-1399	162	25	.	.	PROPN
cana-1399	162	26	12(special	12(special	NUM
cana-1399	162	27	issue	issue	PROPN
cana-1399	162	28	ii	ii	PROPN
cana-1399	162	29	)	)	PUNCT
cana-1399	162	30	(	(	PUNCT
cana-1399	162	31	2023	2023	NUM
cana-1399	162	32	)	)	PUNCT
cana-1399	162	33	,	,	PUNCT
cana-1399	162	34	65–72	65–72	NUM
cana-1399	162	35	.	.	PUNCT
cana-1399	163	1	[	[	X
cana-1399	163	2	3	3	X
cana-1399	163	3	]	]	X
cana-1399	163	4	ganguly.d	ganguly.d	PROPN
cana-1399	163	5	.	.	PUNCT
cana-1399	164	1	k.	k.	PROPN
cana-1399	164	2	and	and	CCONJ
cana-1399	164	3	dhananjoy	dhananjoy	PROPN
cana-1399	164	4	halder	halder	PROPN
cana-1399	164	5	,	,	PUNCT
cana-1399	164	6	on	on	ADP
cana-1399	164	7	decomposition	decomposition	NOUN
cana-1399	164	8	of	of	ADP
cana-1399	164	9	the	the	DET
cana-1399	164	10	real	real	ADJ
cana-1399	164	11	line	line	NOUN
cana-1399	164	12	in	in	ADP
cana-1399	164	13	terms	term	NOUN
cana-1399	164	14	of	of	ADP
cana-1399	164	15	ratio	ratio	NOUN
cana-1399	164	16	sets	set	NOUN
cana-1399	164	17	,	,	PUNCT
cana-1399	164	18	palestine	palestine	PROPN
cana-1399	164	19	journal	journal	PROPN
cana-1399	164	20	of	of	ADP
cana-1399	164	21	mathematics	mathematics	PROPN
cana-1399	164	22	,	,	PUNCT
cana-1399	164	23	vol	vol	NOUN
cana-1399	164	24	.	.	PUNCT
cana-1399	164	25	7(2	7(2	NUM
cana-1399	164	26	)	)	PUNCT
cana-1399	164	27	(	(	PUNCT
cana-1399	164	28	2018	2018	NUM
cana-1399	164	29	)	)	PUNCT
cana-1399	164	30	,	,	PUNCT
cana-1399	164	31	624–627	624–627	NUM
cana-1399	164	32	.	.	PUNCT
cana-1399	165	1	[	[	X
cana-1399	165	2	4	4	X
cana-1399	165	3	]	]	X
cana-1399	165	4	ayazul	ayazul	PROPN
cana-1399	165	5	hasan	hasan	PROPN
cana-1399	165	6	,	,	PUNCT
cana-1399	165	7	jules	jules	PROPN
cana-1399	165	8	clement	clement	PROPN
cana-1399	165	9	mba	mba	PROPN
cana-1399	165	10	and	and	CCONJ
cana-1399	165	11	rafiquddin	rafiquddin	VERB
cana-1399	165	12	,	,	PUNCT
cana-1399	165	13	recent	recent	ADJ
cana-1399	165	14	decomposition	decomposition	NOUN
cana-1399	165	15	results	result	NOUN
cana-1399	165	16	on	on	ADP
cana-1399	165	17	qt	qt	PROPN
cana-1399	165	18	ag	ag	PROPN
cana-1399	165	19	-	-	PUNCT
cana-1399	165	20	modules	module	NOUN
cana-1399	165	21	,	,	PUNCT
cana-1399	165	22	palestine	palestine	PROPN
cana-1399	165	23	journal	journal	PROPN
cana-1399	165	24	of	of	ADP
cana-1399	165	25	mathematics	mathematics	PROPN
cana-1399	165	26	,	,	PUNCT
cana-1399	165	27	vol	vol	NOUN
cana-1399	165	28	.	.	PUNCT
cana-1399	165	29	7(2	7(2	NUM
cana-1399	165	30	)	)	PUNCT
cana-1399	165	31	(	(	PUNCT
cana-1399	165	32	2018	2018	NUM
cana-1399	165	33	)	)	PUNCT
cana-1399	165	34	,	,	PUNCT
cana-1399	166	1	633–640	633–640	NUM
cana-1399	166	2	.	.	PUNCT
cana-1399	167	1	[	[	X
cana-1399	167	2	5	5	X
cana-1399	167	3	]	]	X
cana-1399	167	4	vineet	vineet	PROPN
cana-1399	167	5	bhatt	bhatt	PROPN
cana-1399	167	6	and	and	CCONJ
cana-1399	167	7	kumar	kumar	PROPN
cana-1399	167	8	.	.	PUNCT
cana-1399	168	1	s.	s.	PROPN
cana-1399	168	2	,	,	PUNCT
cana-1399	168	3	a	a	DET
cana-1399	168	4	cas	cas	NOUN
cana-1399	168	5	aided	aid	VERB
cana-1399	168	6	survey	survey	NOUN
cana-1399	168	7	of	of	ADP
cana-1399	168	8	cp	cp	NUM
cana-1399	168	9	decomposition	decomposition	NOUN
cana-1399	168	10	and	and	CCONJ
cana-1399	168	11	rank-1	rank-1	NUM
cana-1399	168	12	approxition	approxition	NOUN
cana-1399	168	13	of	of	ADP
cana-1399	168	14	a	a	DET
cana-1399	168	15	3rd	3rd	ADJ
cana-1399	168	16	-	-	PUNCT
cana-1399	168	17	order	order	NOUN
cana-1399	168	18	tensor	tensor	NOUN
cana-1399	168	19	,	,	PUNCT
cana-1399	168	20	vol	vol	NOUN
cana-1399	168	21	.	.	PUNCT
cana-1399	168	22	3(2	3(2	NUM
cana-1399	168	23	)	)	PUNCT
cana-1399	168	24	(	(	PUNCT
cana-1399	168	25	2014	2014	NUM
cana-1399	168	26	)	)	PUNCT
cana-1399	168	27	,	,	PUNCT
cana-1399	168	28	299–319	299–319	NUM
cana-1399	168	29	.	.	PUNCT
cana-1399	169	1	[	[	X
cana-1399	169	2	6	6	NUM
cana-1399	169	3	]	]	PUNCT
cana-1399	169	4	hao	hao	PROPN
cana-1399	169	5	gao	gao	PROPN
cana-1399	169	6	,	,	PUNCT
cana-1399	169	7	junjie	junjie	PROPN
cana-1399	169	8	wang	wang	PROPN
cana-1399	169	9	,	,	PUNCT
cana-1399	169	10	yu	yu	PROPN
cana-1399	169	11	han	han	PROPN
cana-1399	169	12	and	and	CCONJ
cana-1399	169	13	jian	jian	PROPN
cana-1399	169	14	sun	sun	PROPN
cana-1399	169	15	,	,	PUNCT
cana-1399	169	16	enhancing	enhance	VERB
cana-1399	169	17	crystal	crystal	NOUN
cana-1399	169	18	structure	structure	NOUN
cana-1399	169	19	prediction	prediction	NOUN
cana-1399	169	20	by	by	ADP
cana-1399	169	21	decomposition	decomposition	NOUN
cana-1399	169	22	and	and	CCONJ
cana-1399	169	23	evolution	evolution	NOUN
cana-1399	169	24	schemes	scheme	NOUN
cana-1399	169	25	based	base	VERB
cana-1399	169	26	on	on	ADP
cana-1399	169	27	graph	graph	NOUN
cana-1399	169	28	theory	theory	NOUN
cana-1399	169	29	,	,	PUNCT
cana-1399	169	30	fundamental	fundamental	ADJ
cana-1399	169	31	research	research	NOUN
cana-1399	169	32	,	,	PUNCT
cana-1399	169	33	vol	vol	NOUN
cana-1399	169	34	1(4	1(4	NUM
cana-1399	169	35	)	)	PUNCT
cana-1399	169	36	(	(	PUNCT
cana-1399	169	37	2021	2021	NUM
cana-1399	169	38	)	)	PUNCT
cana-1399	169	39	,	,	PUNCT
cana-1399	169	40	466	466	NUM
cana-1399	169	41	-	-	SYM
cana-1399	169	42	471	471	NUM
cana-1399	169	43	.	.	PUNCT
cana-1399	170	1	[	[	X
cana-1399	170	2	7	7	X
cana-1399	170	3	]	]	X
cana-1399	170	4	jin	jin	NOUN
cana-1399	170	5	guo	guo	PROPN
cana-1399	170	6	,	,	PUNCT
cana-1399	170	7	meiyan	meiyan	ADJ
cana-1399	170	8	li	li	PROPN
cana-1399	170	9	and	and	CCONJ
cana-1399	170	10	tongsuo	tongsuo	PROPN
cana-1399	170	11	wu	wu	PROPN
cana-1399	170	12	,	,	PUNCT
cana-1399	170	13	a	a	DET
cana-1399	170	14	new	new	ADJ
cana-1399	170	15	view	view	NOUN
cana-1399	170	16	toward	toward	ADP
cana-1399	170	17	vertex	vertex	NOUN
cana-1399	170	18	decomposable	decomposable	ADJ
cana-1399	170	19	graphs	graph	NOUN
cana-1399	170	20	,	,	PUNCT
cana-1399	170	21	discrete	discrete	ADJ
cana-1399	170	22	mathematics	mathematic	NOUN
cana-1399	170	23	,	,	PUNCT
cana-1399	170	24	vol	vol	NOUN
cana-1399	170	25	345(9	345(9	NUM
cana-1399	170	26	)	)	PUNCT
cana-1399	170	27	(	(	PUNCT
cana-1399	170	28	2022	2022	NUM
cana-1399	170	29	)	)	PUNCT
cana-1399	170	30	,	,	PUNCT
cana-1399	170	31	112953	112953	NUM
cana-1399	170	32	.	.	PUNCT
cana-1399	171	1	[	[	X
cana-1399	171	2	8	8	NUM
cana-1399	171	3	]	]	X
cana-1399	171	4	paola	paola	NOUN
cana-1399	171	5	bonizzoni	bonizzoni	NOUN
cana-1399	171	6	and	and	CCONJ
cana-1399	171	7	gianluca	gianluca	PROPN
cana-1399	171	8	della	della	PROPN
cana-1399	171	9	vedova	vedova	PROPN
cana-1399	171	10	,	,	PUNCT
cana-1399	171	11	an	an	DET
cana-1399	171	12	algorithm	algorithm	NOUN
cana-1399	171	13	for	for	ADP
cana-1399	171	14	the	the	DET
cana-1399	171	15	modular	modular	ADJ
cana-1399	171	16	decomposition	decomposition	NOUN
cana-1399	171	17	of	of	ADP
cana-1399	171	18	hypergraphs	hypergraph	NOUN
cana-1399	171	19	,	,	PUNCT
cana-1399	171	20	journal	journal	NOUN
cana-1399	171	21	of	of	ADP
cana-1399	171	22	algorithms	algorithm	NOUN
cana-1399	171	23	,	,	PUNCT
cana-1399	171	24	vol	vol	NOUN
cana-1399	171	25	32(2	32(2	NUM
cana-1399	171	26	)	)	PUNCT
cana-1399	171	27	(	(	PUNCT
cana-1399	171	28	1999	1999	NUM
cana-1399	171	29	)	)	PUNCT
cana-1399	171	30	,	,	PUNCT
cana-1399	171	31	65	65	NUM
cana-1399	171	32	-	-	SYM
cana-1399	171	33	86	86	NUM
cana-1399	171	34	.	.	PUNCT
cana-1399	172	1	[	[	X
cana-1399	172	2	9	9	NUM
cana-1399	172	3	]	]	X
cana-1399	172	4	martin	martin	PROPN
cana-1399	172	5	grohe	grohe	PROPN
cana-1399	172	6	,	,	PUNCT
cana-1399	172	7	ken	ken	PROPN
cana-1399	172	8	-	-	PUNCT
cana-1399	172	9	ichi	ichi	PROPN
cana-1399	172	10	kawarabayashi	kawarabayashi	PROPN
cana-1399	172	11	,	,	PUNCT
cana-1399	172	12	and	and	CCONJ
cana-1399	172	13	bruce	bruce	PROPN
cana-1399	172	14	reed	reed	PROPN
cana-1399	172	15	,	,	PUNCT
cana-1399	172	16	a	a	DET
cana-1399	172	17	simple	simple	ADJ
cana-1399	172	18	algorithm	algorithm	NOUN
cana-1399	172	19	for	for	ADP
cana-1399	172	20	the	the	DET
cana-1399	172	21	graph	graph	NOUN
cana-1399	172	22	minor	minor	ADJ
cana-1399	172	23	decomposition	decomposition	NOUN
cana-1399	172	24	logic	logic	NOUN
cana-1399	172	25	meets	meet	VERB
cana-1399	172	26	structural	structural	ADJ
cana-1399	172	27	graph	graph	NOUN
cana-1399	172	28	theory	theory	NOUN
cana-1399	172	29	,	,	PUNCT
cana-1399	172	30	proceedings	proceeding	NOUN
cana-1399	172	31	of	of	ADP
cana-1399	172	32	the	the	DET
cana-1399	172	33	2013	2013	NUM
cana-1399	172	34	annual	annual	ADJ
cana-1399	172	35	acm	acm	NOUN
cana-1399	172	36	siam	siam	NOUN
cana-1399	172	37	symposium	symposium	NOUN
cana-1399	172	38	on	on	ADP
cana-1399	172	39	discrete	discrete	ADJ
cana-1399	172	40	algorithms	algorithm	NOUN
cana-1399	172	41	(	(	PUNCT
cana-1399	172	42	soda	soda	NOUN
cana-1399	172	43	)	)	PUNCT
cana-1399	172	44	,	,	PUNCT
cana-1399	172	45	(	(	PUNCT
cana-1399	172	46	2013	2013	NUM
cana-1399	172	47	)	)	PUNCT
cana-1399	172	48	,	,	PUNCT
cana-1399	172	49	414431	414431	NUM
cana-1399	172	50	.	.	PUNCT
cana-1399	173	1	[	[	X
cana-1399	173	2	10	10	NUM
cana-1399	173	3	]	]	X
cana-1399	173	4	a.	a.	PROPN
cana-1399	173	5	el	el	PROPN
cana-1399	173	6	-	-	PROPN
cana-1399	173	7	mesady	mesady	PROPN
cana-1399	173	8	,	,	PUNCT
cana-1399	173	9	y.s	y.s	PROPN
cana-1399	173	10	.	.	PROPN
cana-1399	173	11	hamed	hamed	PROPN
cana-1399	173	12	,	,	PUNCT
cana-1399	173	13	h.	h.	PROPN
cana-1399	173	14	shabana	shabana	PROPN
cana-1399	173	15	,	,	PUNCT
cana-1399	173	16	on	on	ADP
cana-1399	173	17	the	the	DET
cana-1399	173	18	decomposition	decomposition	NOUN
cana-1399	173	19	of	of	ADP
cana-1399	173	20	circulant	circulant	ADJ
cana-1399	173	21	graphs	graph	NOUN
cana-1399	173	22	using	use	VERB
cana-1399	173	23	algorithmic	algorithmic	ADJ
cana-1399	173	24	approaches	approach	NOUN
cana-1399	173	25	,	,	PUNCT
cana-1399	173	26	alexandria	alexandria	PROPN
cana-1399	173	27	engineering	engineering	PROPN
cana-1399	173	28	journal	journal	PROPN
cana-1399	173	29	,	,	PUNCT
cana-1399	173	30	vol	vol	NOUN
cana-1399	173	31	61(10	61(10	NUM
cana-1399	173	32	)	)	PUNCT
cana-1399	173	33	(	(	PUNCT
cana-1399	173	34	2022	2022	NUM
cana-1399	173	35	)	)	PUNCT
cana-1399	173	36	8263	8263	NUM
cana-1399	173	37	-	-	SYM
cana-1399	173	38	8275	8275	NUM
cana-1399	173	39	.	.	PUNCT
cana-1399	174	1	[	[	X
cana-1399	174	2	11	11	NUM
cana-1399	174	3	]	]	PUNCT
cana-1399	174	4	ngo	ngo	PROPN
cana-1399	174	5	dac	dac	PROPN
cana-1399	174	6	tan	tan	PROPN
cana-1399	174	7	,	,	PUNCT
cana-1399	174	8	a	a	DET
cana-1399	174	9	decomposition	decomposition	NOUN
cana-1399	174	10	for	for	ADP
cana-1399	174	11	digraphs	digraph	NOUN
cana-1399	174	12	with	with	ADP
cana-1399	174	13	minimum	minimum	ADJ
cana-1399	174	14	outdegree	outdegree	NOUN
cana-1399	174	15	3	3	NUM
cana-1399	174	16	having	have	VERB
cana-1399	174	17	no	no	DET
cana-1399	174	18	vertex	vertex	NOUN
cana-1399	174	19	disjoint	disjoint	NOUN
cana-1399	174	20	cycles	cycle	NOUN
cana-1399	174	21	of	of	ADP
cana-1399	174	22	different	different	ADJ
cana-1399	174	23	lengths	length	NOUN
cana-1399	174	24	,	,	PUNCT
cana-1399	174	25	discussiones	discussione	VERB
cana-1399	174	26	mathematicae	mathematicae	PROPN
cana-1399	174	27	graph	graph	NOUN
cana-1399	174	28	theory	theory	NOUN
cana-1399	174	29	,	,	PUNCT
cana-1399	174	30	vol	vol	NOUN
cana-1399	174	31	43	43	NUM
cana-1399	174	32	(	(	PUNCT
cana-1399	174	33	2023	2023	NUM
cana-1399	174	34	)	)	PUNCT
cana-1399	174	35	,	,	PUNCT
cana-1399	174	36	573	573	NUM
cana-1399	174	37	–	–	PUNCT
cana-1399	174	38	581	581	NUM
cana-1399	174	39	.	.	PUNCT
cana-1399	175	1	[	[	X
cana-1399	175	2	12	12	NUM
cana-1399	175	3	]	]	PUNCT
cana-1399	175	4	t.	t.	PROPN
cana-1399	175	5	w.	w.	PROPN
cana-1399	175	6	haynes	haynes	PROPN
cana-1399	175	7	,	,	PUNCT
cana-1399	175	8	s.	s.	PROPN
cana-1399	175	9	t.	t.	PROPN
cana-1399	175	10	hedetniemi	hedetniemi	PROPN
cana-1399	175	11	,	,	PUNCT
cana-1399	175	12	p.	p.	PROPN
cana-1399	175	13	j.	j.	PROPN
cana-1399	175	14	slater	slater	PROPN
cana-1399	175	15	,	,	PUNCT
cana-1399	175	16	fundamentals	fundamental	NOUN
cana-1399	175	17	of	of	ADP
cana-1399	175	18	domination	domination	NOUN
cana-1399	175	19	in	in	ADP
cana-1399	175	20	graphs	graph	NOUN
cana-1399	175	21	,	,	PUNCT
cana-1399	175	22	marcel	marcel	PROPN
cana-1399	175	23	dekker	dekker	PROPN
cana-1399	175	24	,	,	PUNCT
cana-1399	175	25	inc	inc	PROPN
cana-1399	175	26	.	.	PROPN
cana-1399	175	27	,	,	PUNCT
cana-1399	175	28	new	new	PROPN
cana-1399	175	29	york	york	PROPN
cana-1399	175	30	,	,	PUNCT
cana-1399	175	31	1998	1998	NUM
cana-1399	175	32	.	.	PUNCT