id	sid	tid	token	lemma	pos
cana-3871	1	1	communications	communication	NOUN
cana-3871	1	2	on	on	ADP
cana-3871	1	3	applied	apply	VERB
cana-3871	1	4	nonlinear	nonlinear	ADJ
cana-3871	1	5	analysis	analysis	NOUN
cana-3871	1	6	issn	issn	NOUN
cana-3871	1	7	:	:	PUNCT
cana-3871	1	8	1074	1074	NUM
cana-3871	1	9	-	-	PUNCT
cana-3871	1	10	133x	133x	NUM
cana-3871	1	11	vol	vol	NOUN
cana-3871	1	12	32	32	NUM
cana-3871	1	13	no	no	NOUN
cana-3871	1	14	.	.	PUNCT
cana-3871	2	1	7s	7	NOUN
cana-3871	2	2	(	(	PUNCT
cana-3871	2	3	2025	2025	NUM
cana-3871	2	4	)	)	PUNCT
cana-3871	2	5	941	941	NUM
cana-3871	3	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	3	2	a	a	DET
cana-3871	3	3	generalized	generalized	ADJ
cana-3871	3	4	study	study	NOUN
cana-3871	3	5	of	of	ADP
cana-3871	3	6	zero	zero	NUM
cana-3871	3	7	divisor	divisor	NOUN
cana-3871	3	8	graphs	graph	NOUN
cana-3871	3	9	of	of	ADP
cana-3871	3	10	boolean	boolean	ADJ
cana-3871	3	11	rings	ring	NOUN
cana-3871	3	12	ℤ	ℤ	PROPN
cana-3871	3	13	2n	2n	NUM
cana-3871	3	14	=	=	SYM
cana-3871	3	15	ℤ2	ℤ2	PROPN
cana-3871	3	16	×	×	PROPN
cana-3871	3	17	ℤ	ℤ	PROPN
cana-3871	3	18	2	2	NUM
cana-3871	3	19	×	×	NOUN
cana-3871	3	20	·	·	PUNCT
cana-3871	3	21	·	·	PUNCT
cana-3871	3	22	·	·	PUNCT
cana-3871	4	1	×	×	NOUN
cana-3871	4	2	ℤ	ℤ	PROPN
cana-3871	4	3	2	2	NUM
cana-3871	4	4	s.	s.	PROPN
cana-3871	4	5	g.	g.	PROPN
cana-3871	4	6	jakkewad1	jakkewad1	PROPN
cana-3871	4	7	,	,	PUNCT
cana-3871	4	8	r.	r.	PROPN
cana-3871	4	9	g.	g.	PROPN
cana-3871	4	10	metkar2	metkar2	PROPN
cana-3871	4	11	,	,	PUNCT
cana-3871	4	12	g.	g.	PROPN
cana-3871	4	13	a.	a.	NOUN
cana-3871	4	14	dhanorkar3	dhanorkar3	PROPN
cana-3871	4	15	,	,	PUNCT
cana-3871	4	16	p.	p.	NOUN
cana-3871	4	17	n.tekalkar4	n.tekalkar4	NOUN
cana-3871	4	18	1rayat	1rayat	NUM
cana-3871	4	19	shikshan	shikshan	NOUN
cana-3871	4	20	sanstha	sanstha	PROPN
cana-3871	4	21	’s	’s	PROPN
cana-3871	5	1	k.	k.	PROPN
cana-3871	5	2	b.	b.	PROPN
cana-3871	6	1	p.	p.	PROPN
cana-3871	6	2	college	college	PROPN
cana-3871	6	3	vashi	vashi	PROPN
cana-3871	6	4	,	,	PUNCT
cana-3871	6	5	navi	navi	PROPN
cana-3871	6	6	mumbai	mumbai	PROPN
cana-3871	6	7	2indira	2indira	PROPN
cana-3871	6	8	gandhi	gandhi	PROPN
cana-3871	6	9	(	(	PUNCT
cana-3871	6	10	sr	sr	PROPN
cana-3871	6	11	)	)	PUNCT
cana-3871	6	12	college	college	PROPN
cana-3871	6	13	cidco	cidco	PROPN
cana-3871	6	14	,	,	PUNCT
cana-3871	6	15	nanded	nande	VERB
cana-3871	6	16	3rayat	3rayat	NUM
cana-3871	6	17	shikshan	shikshan	NOUN
cana-3871	6	18	sanstha	sanstha	PROPN
cana-3871	6	19	’s	’s	PROPN
cana-3871	7	1	k.	k.	PROPN
cana-3871	7	2	b.	b.	PROPN
cana-3871	8	1	p.	p.	PROPN
cana-3871	8	2	college	college	PROPN
cana-3871	8	3	vashi	vashi	PROPN
cana-3871	8	4	,	,	PUNCT
cana-3871	8	5	navi	navi	PROPN
cana-3871	8	6	mumbai	mumbai	PROPN
cana-3871	8	7	4rayat	4rayat	NUM
cana-3871	8	8	shikshan	shikshan	NOUN
cana-3871	8	9	sanstha	sanstha	PROPN
cana-3871	8	10	’s	’s	PROPN
cana-3871	9	1	k.	k.	PROPN
cana-3871	9	2	b.	b.	PROPN
cana-3871	10	1	p.	p.	PROPN
cana-3871	10	2	college	college	PROPN
cana-3871	10	3	vashi	vashi	PROPN
cana-3871	10	4	,	,	PUNCT
cana-3871	10	5	navi	navi	PROPN
cana-3871	10	6	mumbai	mumbai	PROPN
cana-3871	10	7	s.	s.	PROPN
cana-3871	10	8	g.	g.	PROPN
cana-3871	10	9	jakkewad	jakkewad	PROPN
cana-3871	10	10	:	:	PUNCT
cana-3871	10	11	shrikantjakkewad171991@gmail.com	shrikantjakkewad171991@gmail.com	PROPN
cana-3871	10	12	,	,	PUNCT
cana-3871	10	13	r.	r.	PROPN
cana-3871	10	14	g.	g.	PROPN
cana-3871	10	15	metkar	metkar	PROPN
cana-3871	10	16	:	:	PUNCT
cana-3871	11	1	rammetkarmath@gmail.com	rammetkarmath@gmail.com	X
cana-3871	11	2	.	.	PUNCT
cana-3871	12	1	article	article	NOUN
cana-3871	12	2	history	history	NOUN
cana-3871	12	3	:	:	PUNCT
cana-3871	12	4	received	receive	VERB
cana-3871	12	5	:	:	PUNCT
cana-3871	12	6	29	29	NUM
cana-3871	12	7	-	-	SYM
cana-3871	12	8	10	10	NUM
cana-3871	12	9	-	-	PUNCT
cana-3871	12	10	2024	2024	NUM
cana-3871	12	11	revised	revise	VERB
cana-3871	12	12	:	:	PUNCT
cana-3871	12	13	15	15	NUM
cana-3871	12	14	-	-	SYM
cana-3871	12	15	11	11	NUM
cana-3871	12	16	-	-	PUNCT
cana-3871	12	17	2024	2024	NUM
cana-3871	12	18	accepted	accept	VERB
cana-3871	12	19	:	:	PUNCT
cana-3871	12	20	19	19	NUM
cana-3871	12	21	-	-	SYM
cana-3871	12	22	12	12	NUM
cana-3871	12	23	-	-	PUNCT
cana-3871	12	24	2024	2024	NUM
cana-3871	12	25	abstract	abstract	NOUN
cana-3871	12	26	:	:	PUNCT
cana-3871	12	27	the	the	DET
cana-3871	12	28	zero	zero	NUM
cana-3871	12	29	-	-	PUNCT
cana-3871	12	30	divisor	divisor	NOUN
cana-3871	12	31	graph	graph	NOUN
cana-3871	12	32	of	of	ADP
cana-3871	12	33	a	a	DET
cana-3871	12	34	commutative	commutative	ADJ
cana-3871	12	35	ring	ring	NOUN
cana-3871	12	36	r	r	NOUN
cana-3871	12	37	is	be	AUX
cana-3871	12	38	defined	define	VERB
cana-3871	12	39	as	as	ADP
cana-3871	12	40	a	a	DET
cana-3871	12	41	graph	graph	NOUN
cana-3871	12	42	in	in	ADP
cana-3871	12	43	which	which	PRON
cana-3871	12	44	the	the	DET
cana-3871	12	45	vertices	vertex	NOUN
cana-3871	12	46	represent	represent	VERB
cana-3871	12	47	the	the	DET
cana-3871	12	48	non	non	ADJ
cana-3871	12	49	-	-	ADJ
cana-3871	12	50	zero	zero	ADJ
cana-3871	12	51	zero	zero	NUM
cana-3871	12	52	divisors	divisor	NOUN
cana-3871	12	53	of	of	ADP
cana-3871	12	54	r	r	NOUN
cana-3871	12	55	,	,	PUNCT
cana-3871	12	56	and	and	CCONJ
cana-3871	12	57	two	two	NUM
cana-3871	12	58	vertices	vertex	NOUN
cana-3871	12	59	x	x	PUNCT
cana-3871	12	60	and	and	CCONJ
cana-3871	12	61	y	y	PROPN
cana-3871	12	62	are	be	AUX
cana-3871	12	63	connected	connect	VERB
cana-3871	12	64	if	if	SCONJ
cana-3871	12	65	and	and	CCONJ
cana-3871	12	66	only	only	ADV
cana-3871	12	67	if	if	SCONJ
cana-3871	12	68	x×	x×	PROPN
cana-3871	12	69	y	y	PROPN
cana-3871	12	70	=	=	SYM
cana-3871	12	71	0	0	PROPN
cana-3871	12	72	.	.	PUNCT
cana-3871	13	1	in	in	ADP
cana-3871	13	2	this	this	DET
cana-3871	13	3	study	study	NOUN
cana-3871	13	4	,	,	PUNCT
cana-3871	13	5	we	we	PRON
cana-3871	13	6	focus	focus	VERB
cana-3871	13	7	on	on	ADP
cana-3871	13	8	examining	examine	VERB
cana-3871	13	9	the	the	DET
cana-3871	13	10	zero	zero	NUM
cana-3871	13	11	divisor	divisor	NOUN
cana-3871	13	12	graphs	graph	NOUN
cana-3871	13	13	of	of	ADP
cana-3871	13	14	boolean	boolean	ADJ
cana-3871	13	15	rings	ring	NOUN
cana-3871	13	16	and	and	CCONJ
cana-3871	13	17	deriving	derive	VERB
cana-3871	13	18	insights	insight	NOUN
cana-3871	13	19	from	from	ADP
cana-3871	13	20	their	their	PRON
cana-3871	13	21	graphical	graphical	ADJ
cana-3871	13	22	representations	representation	NOUN
cana-3871	13	23	.	.	PUNCT
cana-3871	14	1	keywords	keyword	NOUN
cana-3871	14	2	:	:	PUNCT
cana-3871	14	3	zero	zero	NUM
cana-3871	14	4	-	-	PUNCT
cana-3871	14	5	divisor	divisor	NOUN
cana-3871	14	6	graph	graph	NOUN
cana-3871	14	7	,	,	PUNCT
cana-3871	14	8	commutative	commutative	ADJ
cana-3871	14	9	ring	ring	NOUN
cana-3871	14	10	,	,	PUNCT
cana-3871	14	11	boolean	boolean	ADJ
cana-3871	14	12	ring	ring	NOUN
cana-3871	14	13	ℤ	ℤ	PROPN
cana-3871	14	14	2n	2n	NUM
cana-3871	14	15	=	=	SYM
cana-3871	14	16	ℤ	ℤ	PROPN
cana-3871	14	17	2	2	NUM
cana-3871	14	18	×	×	NOUN
cana-3871	14	19	ℤ	ℤ	PROPN
cana-3871	14	20	2	2	NUM
cana-3871	14	21	×	×	NOUN
cana-3871	14	22	ℤ	ℤ	PROPN
cana-3871	14	23	2	2	NUM
cana-3871	14	24	×	×	NOUN
cana-3871	14	25	...	...	PUNCT
cana-3871	14	26	×	×	NOUN
cana-3871	14	27	ℤ	ℤ	PROPN
cana-3871	14	28	2	2	NUM
cana-3871	14	29	,	,	PUNCT
cana-3871	14	30	girth	girth	NOUN
cana-3871	14	31	,	,	PUNCT
cana-3871	14	32	diameter	diameter	NOUN
cana-3871	14	33	.	.	PUNCT
cana-3871	14	34	1	1	NUM
cana-3871	14	35	introduction	introduction	NOUN
cana-3871	14	36	the	the	DET
cana-3871	14	37	roots	root	NOUN
cana-3871	14	38	of	of	ADP
cana-3871	14	39	graph	graph	NOUN
cana-3871	14	40	theory	theory	NOUN
cana-3871	14	41	can	can	AUX
cana-3871	14	42	be	be	AUX
cana-3871	14	43	traced	trace	VERB
cana-3871	14	44	back	back	ADV
cana-3871	14	45	to	to	ADP
cana-3871	14	46	1735	1735	NUM
cana-3871	14	47	when	when	SCONJ
cana-3871	14	48	the	the	DET
cana-3871	14	49	swiss	swiss	ADJ
cana-3871	14	50	mathematician	mathematician	NOUN
cana-3871	14	51	leonhard	leonhard	PROPN
cana-3871	14	52	euler	euler	PROPN
cana-3871	14	53	provided	provide	VERB
cana-3871	14	54	a	a	DET
cana-3871	14	55	groundbreaking	groundbreaking	ADJ
cana-3871	14	56	solution	solution	NOUN
cana-3871	14	57	to	to	ADP
cana-3871	14	58	the	the	DET
cana-3871	14	59	konigsberg	konigsberg	PROPN
cana-3871	14	60	bridge	bridge	PROPN
cana-3871	14	61	problem,1	problem,1	NOUN
cana-3871	14	62	introducing	introduce	VERB
cana-3871	14	63	a	a	DET
cana-3871	14	64	novel	novel	ADJ
cana-3871	14	65	conceptual	conceptual	ADJ
cana-3871	14	66	framework	framework	NOUN
cana-3871	14	67	.	.	PUNCT
cana-3871	15	1	euler	euler	PROPN
cana-3871	15	2	’s	’s	PART
cana-3871	15	3	subsequent	subsequent	ADJ
cana-3871	15	4	theorem	theorem	NOUN
cana-3871	15	5	marked	mark	VERB
cana-3871	15	6	a	a	DET
cana-3871	15	7	seminal	seminal	ADJ
cana-3871	15	8	moment	moment	NOUN
cana-3871	15	9	in	in	ADP
cana-3871	15	10	the	the	DET
cana-3871	15	11	field	field	NOUN
cana-3871	15	12	,	,	PUNCT
cana-3871	15	13	paving	pave	VERB
cana-3871	15	14	the	the	DET
cana-3871	15	15	way	way	NOUN
cana-3871	15	16	for	for	ADP
cana-3871	15	17	the	the	DET
cana-3871	15	18	development	development	NOUN
cana-3871	15	19	of	of	ADP
cana-3871	15	20	eulerian	eulerian	ADJ
cana-3871	15	21	graphs	graph	NOUN
cana-3871	15	22	.	.	PUNCT
cana-3871	16	1	the	the	DET
cana-3871	16	2	exploration	exploration	NOUN
cana-3871	16	3	of	of	ADP
cana-3871	16	4	cycles	cycle	NOUN
cana-3871	16	5	on	on	ADP
cana-3871	16	6	polyhedra	polyhedra	NOUN
cana-3871	16	7	by	by	ADP
cana-3871	16	8	the	the	DET
cana-3871	16	9	revd	revd	PROPN
cana-3871	16	10	.	.	PUNCT
cana-3871	17	1	thomas	thomas	PROPN
cana-3871	17	2	penyngton	penyngton	PROPN
cana-3871	17	3	kirkman	kirkman	PROPN
cana-3871	17	4	(	(	PUNCT
cana-3871	17	5	1806	1806	NUM
cana-3871	17	6	-	-	SYM
cana-3871	17	7	95	95	NUM
cana-3871	17	8	)	)	PUNCT
cana-3871	17	9	and	and	CCONJ
cana-3871	17	10	sir	sir	PROPN
cana-3871	17	11	william	william	PROPN
cana-3871	17	12	rowan	rowan	PROPN
cana-3871	17	13	hamilton	hamilton	PROPN
cana-3871	17	14	(	(	PUNCT
cana-3871	17	15	1805	1805	NUM
cana-3871	17	16	-	-	SYM
cana-3871	17	17	65	65	NUM
cana-3871	17	18	)	)	PUNCT
cana-3871	17	19	led	lead	VERB
cana-3871	17	20	to	to	ADP
cana-3871	17	21	the	the	DET
cana-3871	17	22	conception	conception	NOUN
cana-3871	17	23	of	of	ADP
cana-3871	17	24	hamiltonian	hamiltonian	ADJ
cana-3871	17	25	graphs	graph	NOUN
cana-3871	17	26	.	.	PUNCT
cana-3871	18	1	the	the	DET
cana-3871	18	2	foundational	foundational	ADJ
cana-3871	18	3	notion	notion	NOUN
cana-3871	18	4	of	of	ADP
cana-3871	18	5	a	a	DET
cana-3871	18	6	tree	tree	NOUN
cana-3871	18	7	,	,	PUNCT
cana-3871	18	8	defined	define	VERB
cana-3871	18	9	as	as	ADP
cana-3871	18	10	a	a	DET
cana-3871	18	11	connected	connected	ADJ
cana-3871	18	12	graph	graph	NOUN
cana-3871	18	13	devoid	devoid	ADJ
cana-3871	18	14	of	of	ADP
cana-3871	18	15	cycles	cycle	NOUN
cana-3871	18	16	,	,	PUNCT
cana-3871	18	17	first	first	ADV
cana-3871	18	18	emerged	emerge	VERB
cana-3871	18	19	implicitly	implicitly	ADV
cana-3871	18	20	in	in	ADP
cana-3871	18	21	the	the	DET
cana-3871	18	22	work	work	NOUN
cana-3871	18	23	of	of	ADP
cana-3871	18	24	gustav	gustav	PROPN
cana-3871	18	25	kirchho	kirchho	PROPN
cana-3871	18	26	(	(	PUNCT
cana-3871	18	27	1824	1824	NUM
cana-3871	18	28	-	-	SYM
cana-3871	18	29	87	87	NUM
cana-3871	18	30	)	)	PUNCT
cana-3871	18	31	,	,	PUNCT
cana-3871	18	32	who	who	PRON
cana-3871	18	33	applied	apply	VERB
cana-3871	18	34	graph	graph	NOUN
cana-3871	18	35	-	-	PUNCT
cana-3871	18	36	theoretical	theoretical	ADJ
cana-3871	18	37	principles	principle	NOUN
cana-3871	18	38	to	to	ADP
cana-3871	18	39	analyℤe	analyℤe	PROPN
cana-3871	18	40	currents	current	NOUN
cana-3871	18	41	in	in	ADP
cana-3871	18	42	electrical	electrical	ADJ
cana-3871	18	43	networks	network	NOUN
cana-3871	18	44	.	.	PUNCT
cana-3871	19	1	later	later	ADV
cana-3871	19	2	,	,	PUNCT
cana-3871	19	3	arthur	arthur	PROPN
cana-3871	19	4	cayley	cayley	PROPN
cana-3871	19	5	(	(	PUNCT
cana-3871	19	6	1821	1821	NUM
cana-3871	19	7	-	-	SYM
cana-3871	19	8	95	95	NUM
cana-3871	19	9	)	)	PUNCT
cana-3871	19	10	,	,	PUNCT
cana-3871	19	11	james	james	PROPN
cana-3871	19	12	joseph	joseph	PROPN
cana-3871	19	13	sylvester	sylvester	PROPN
cana-3871	19	14	(	(	PUNCT
cana-3871	19	15	180697	180697	NUM
cana-3871	19	16	)	)	PUNCT
cana-3871	19	17	,	,	PUNCT
cana-3871	19	18	georg	georg	NOUN
cana-3871	19	19	polya	polya	NOUN
cana-3871	19	20	(	(	PUNCT
cana-3871	19	21	1887	1887	NUM
cana-3871	19	22	-	-	SYM
cana-3871	19	23	1985	1985	NUM
cana-3871	19	24	)	)	PUNCT
cana-3871	19	25	,	,	PUNCT
cana-3871	19	26	and	and	CCONJ
cana-3871	19	27	others	other	NOUN
cana-3871	19	28	introduced	introduce	VERB
cana-3871	19	29	trees	tree	NOUN
cana-3871	19	30	in	in	ADP
cana-3871	19	31	connection	connection	NOUN
cana-3871	19	32	with	with	ADP
cana-3871	19	33	the	the	DET
cana-3871	19	34	enumeration	enumeration	NOUN
cana-3871	19	35	of	of	ADP
cana-3871	19	36	specific	specific	ADJ
cana-3871	19	37	chemical	chemical	NOUN
cana-3871	19	38	structures	structure	NOUN
cana-3871	19	39	.	.	PUNCT
cana-3871	20	1	i.	i.	PROPN
cana-3871	20	2	beck	beck	PROPN
cana-3871	20	3	introduced	introduce	VERB
cana-3871	20	4	the	the	DET
cana-3871	20	5	concept	concept	NOUN
cana-3871	20	6	of	of	ADP
cana-3871	20	7	a	a	DET
cana-3871	20	8	zero	zero	NUM
cana-3871	20	9	-	-	PUNCT
cana-3871	20	10	divisor	divisor	NOUN
cana-3871	20	11	graph	graph	NOUN
cana-3871	20	12	in	in	ADP
cana-3871	20	13	1988.2	1988.2	NUM
cana-3871	20	14	denoted	denote	VERB
cana-3871	20	15	by	by	ADP
cana-3871	20	16	γ(r	γ(r	PROPN
cana-3871	20	17	)	)	PUNCT
cana-3871	20	18	,	,	PUNCT
cana-3871	20	19	the	the	DET
cana-3871	20	20	zero	zero	NUM
cana-3871	20	21	divisor	divisor	NOUN
cana-3871	20	22	graph	graph	NOUN
cana-3871	20	23	of	of	ADP
cana-3871	20	24	a	a	DET
cana-3871	20	25	ring	ring	NOUN
cana-3871	20	26	r	r	NOUN
cana-3871	20	27	is	be	AUX
cana-3871	20	28	a	a	DET
cana-3871	20	29	simple	simple	ADJ
cana-3871	20	30	graph	graph	NOUN
cana-3871	20	31	whose	whose	DET
cana-3871	20	32	vertices	vertex	NOUN
cana-3871	20	33	represent	represent	VERB
cana-3871	20	34	elements	element	NOUN
cana-3871	20	35	of	of	ADP
cana-3871	20	36	r	r	NOUN
cana-3871	20	37	,	,	PUNCT
cana-3871	20	38	with	with	ADP
cana-3871	20	39	two	two	NUM
cana-3871	20	40	vertices	vertex	NOUN
cana-3871	20	41	x	x	PUNCT
cana-3871	20	42	and	and	CCONJ
cana-3871	20	43	y	y	PROPN
cana-3871	20	44	being	be	AUX
cana-3871	20	45	adjacent	adjacent	ADJ
cana-3871	20	46	if	if	SCONJ
cana-3871	20	47	and	and	CCONJ
cana-3871	20	48	only	only	ADV
cana-3871	20	49	if	if	SCONJ
cana-3871	20	50	their	their	PRON
cana-3871	20	51	product	product	NOUN
cana-3871	20	52	equals	equal	VERB
cana-3871	20	53	zero	zero	NUM
cana-3871	20	54	.	.	PUNCT
cana-3871	20	55	beck	beck	PROPN
cana-3871	20	56	’s	’s	PART
cana-3871	20	57	research	research	NOUN
cana-3871	20	58	focused	focus	VERB
cana-3871	20	59	on	on	ADP
cana-3871	20	60	colorings	coloring	NOUN
cana-3871	20	61	of	of	ADP
cana-3871	20	62	r.2	r.2	DET
cana-3871	20	63	this	this	DET
cana-3871	20	64	perspective	perspective	NOUN
cana-3871	20	65	originated	originate	VERB
cana-3871	20	66	in	in	ADP
cana-3871	20	67	a	a	DET
cana-3871	20	68	paper	paper	NOUN
cana-3871	20	69	by	by	ADP
cana-3871	20	70	d.f	d.f	PROPN
cana-3871	20	71	.	.	PROPN
cana-3871	20	72	anderson	anderson	PROPN
cana-3871	20	73	and	and	CCONJ
cana-3871	20	74	p.s	p.s	PROPN
cana-3871	20	75	.	.	PROPN
cana-3871	20	76	livingston4	livingston4	PROPN
cana-3871	20	77	and	and	CCONJ
cana-3871	20	78	has	have	AUX
cana-3871	20	79	since	since	SCONJ
cana-3871	20	80	seen	see	VERB
cana-3871	20	81	further	further	ADJ
cana-3871	20	82	development.6	development.6	NOUN
cana-3871	20	83	,	,	PUNCT
cana-3871	20	84	12	12	NUM
cana-3871	20	85	,	,	PUNCT
cana-3871	20	86	13	13	NUM
cana-3871	20	87	for	for	ADP
cana-3871	20	88	instance	instance	NOUN
cana-3871	20	89	,	,	PUNCT
cana-3871	20	90	it	it	PRON
cana-3871	20	91	is	be	AUX
cana-3871	20	92	established	establish	VERB
cana-3871	20	93	in15	in15	PROPN
cana-3871	20	94	that	that	SCONJ
cana-3871	20	95	all	all	DET
cana-3871	20	96	zero	zero	NUM
cana-3871	20	97	-	-	PUNCT
cana-3871	20	98	divisor	divisor	NOUN
cana-3871	20	99	graphs	graph	NOUN
cana-3871	20	100	are	be	AUX
cana-3871	20	101	connected	connect	VERB
cana-3871	20	102	,	,	PUNCT
cana-3871	20	103	meaning	mean	VERB
cana-3871	20	104	a	a	DET
cana-3871	20	105	path	path	NOUN
cana-3871	20	106	exists	exist	VERB
cana-3871	20	107	between	between	ADP
cana-3871	20	108	any	any	DET
cana-3871	20	109	pair	pair	NOUN
cana-3871	20	110	of	of	ADP
cana-3871	20	111	vertices	vertex	NOUN
cana-3871	20	112	.	.	PUNCT
cana-3871	21	1	communications	communication	NOUN
cana-3871	21	2	on	on	ADP
cana-3871	21	3	applied	apply	VERB
cana-3871	21	4	nonlinear	nonlinear	ADJ
cana-3871	21	5	analysis	analysis	NOUN
cana-3871	21	6	issn	issn	NOUN
cana-3871	21	7	:	:	PUNCT
cana-3871	21	8	1074	1074	NUM
cana-3871	21	9	-	-	PUNCT
cana-3871	21	10	133x	133x	NUM
cana-3871	21	11	vol	vol	NOUN
cana-3871	21	12	32	32	NUM
cana-3871	21	13	no	no	NOUN
cana-3871	21	14	.	.	PUNCT
cana-3871	22	1	7s	7	NOUN
cana-3871	22	2	(	(	PUNCT
cana-3871	22	3	2025	2025	NUM
cana-3871	22	4	)	)	PUNCT
cana-3871	22	5	942	942	NUM
cana-3871	22	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	22	7	a	a	DET
cana-3871	22	8	ring	ring	NOUN
cana-3871	22	9	r	r	NOUN
cana-3871	22	10	is	be	AUX
cana-3871	22	11	classified	classify	VERB
cana-3871	22	12	as	as	ADP
cana-3871	22	13	boolean	boolean	ADJ
cana-3871	22	14	if	if	SCONJ
cana-3871	22	15	every	every	DET
cana-3871	22	16	element	element	NOUN
cana-3871	22	17	r	r	NOUN
cana-3871	22	18	in	in	ADP
cana-3871	22	19	r	r	NOUN
cana-3871	22	20	satisfies	satisfie	NOUN
cana-3871	22	21	the	the	DET
cana-3871	22	22	condition	condition	NOUN
cana-3871	22	23	r2	r2	PROPN
cana-3871	22	24	=	=	SYM
cana-3871	22	25	r.	r.	PROPN
cana-3871	22	26	in	in	ADP
cana-3871	22	27	particular	particular	ADJ
cana-3871	22	28	,	,	PUNCT
cana-3871	22	29	a	a	DET
cana-3871	22	30	boolean	boolean	ADJ
cana-3871	22	31	ring	ring	NOUN
cana-3871	22	32	is	be	AUX
cana-3871	22	33	invariably	invariably	ADV
cana-3871	22	34	commutative	commutative	ADJ
cana-3871	22	35	with	with	ADP
cana-3871	22	36	a	a	DET
cana-3871	22	37	characteristic	characteristic	NOUN
cana-3871	22	38	of	of	ADP
cana-3871	22	39	2	2	NUM
cana-3871	22	40	.	.	PUNCT
cana-3871	23	1	a	a	DET
cana-3871	23	2	graph	graph	NOUN
cana-3871	23	3	is	be	AUX
cana-3871	23	4	deemed	deem	VERB
cana-3871	23	5	boolean	boolean	ADJ
cana-3871	23	6	if	if	SCONJ
cana-3871	23	7	it	it	PRON
cana-3871	23	8	exhibits	exhibit	VERB
cana-3871	23	9	isomorphism	isomorphism	NOUN
cana-3871	23	10	to	to	ADP
cana-3871	23	11	the	the	DET
cana-3871	23	12	zero	zero	NUM
cana-3871	23	13	-	-	PUNCT
cana-3871	23	14	divisor	divisor	NOUN
cana-3871	23	15	graph	graph	NOUN
cana-3871	23	16	of	of	ADP
cana-3871	23	17	a	a	DET
cana-3871	23	18	boolean	boolean	ADJ
cana-3871	23	19	ring.10–12	ring.10–12	NOUN
cana-3871	23	20	,	,	PUNCT
cana-3871	23	21	16	16	NUM
cana-3871	23	22	,	,	PUNCT
cana-3871	23	23	17	17	NUM
cana-3871	23	24	.	.	SYM
cana-3871	23	25	2	2	NUM
cana-3871	23	26	preliminaries	preliminary	NOUN
cana-3871	23	27	graph	graph	NOUN
cana-3871	23	28	theory	theory	NOUN
cana-3871	23	29	is	be	AUX
cana-3871	23	30	a	a	DET
cana-3871	23	31	branch	branch	NOUN
cana-3871	23	32	of	of	ADP
cana-3871	23	33	mathematics	mathematic	NOUN
cana-3871	23	34	concerned	concern	VERB
cana-3871	23	35	with	with	ADP
cana-3871	23	36	the	the	DET
cana-3871	23	37	study	study	NOUN
cana-3871	23	38	of	of	ADP
cana-3871	23	39	graphs	graph	NOUN
cana-3871	23	40	,	,	PUNCT
cana-3871	23	41	which	which	PRON
cana-3871	23	42	consist	consist	VERB
cana-3871	23	43	of	of	ADP
cana-3871	23	44	nodes	node	NOUN
cana-3871	23	45	and	and	CCONJ
cana-3871	23	46	edges	edge	NOUN
cana-3871	23	47	,	,	PUNCT
cana-3871	23	48	often	often	ADV
cana-3871	23	49	used	use	VERB
cana-3871	23	50	to	to	PART
cana-3871	23	51	represent	represent	VERB
cana-3871	23	52	mathematical	mathematical	ADJ
cana-3871	23	53	concepts	concept	NOUN
cana-3871	23	54	visually	visually	ADV
cana-3871	23	55	.	.	PUNCT
cana-3871	24	1	the	the	DET
cana-3871	24	2	field	field	NOUN
cana-3871	24	3	explores	explore	VERB
cana-3871	24	4	the	the	DET
cana-3871	24	5	connections	connection	NOUN
cana-3871	24	6	between	between	ADP
cana-3871	24	7	the	the	DET
cana-3871	24	8	vertices	vertex	NOUN
cana-3871	24	9	and	and	CCONJ
cana-3871	24	10	edges	edge	NOUN
cana-3871	24	11	within	within	ADP
cana-3871	24	12	these	these	DET
cana-3871	24	13	structures	structure	NOUN
cana-3871	24	14	.	.	PUNCT
cana-3871	25	1	below	below	ADV
cana-3871	25	2	,	,	PUNCT
cana-3871	25	3	we	we	PRON
cana-3871	25	4	will	will	AUX
cana-3871	25	5	delve	delve	VERB
cana-3871	25	6	into	into	ADP
cana-3871	25	7	fundamental	fundamental	ADJ
cana-3871	25	8	definitions	definition	NOUN
cana-3871	25	9	to	to	PART
cana-3871	25	10	facilitate	facilitate	VERB
cana-3871	25	11	comprehension	comprehension	NOUN
cana-3871	25	12	of	of	ADP
cana-3871	25	13	key	key	ADJ
cana-3871	25	14	terminologies	terminology	NOUN
cana-3871	25	15	.	.	PUNCT
cana-3871	26	1	a	a	DET
cana-3871	26	2	zero	zero	NUM
cana-3871	26	3	-	-	PUNCT
cana-3871	26	4	divisor	divisor	NOUN
cana-3871	26	5	graph	graph	NOUN
cana-3871	26	6	is	be	AUX
cana-3871	26	7	an	an	DET
cana-3871	26	8	undirected	undirected	ADJ
cana-3871	26	9	graph	graph	NOUN
cana-3871	26	10	representing	represent	VERB
cana-3871	26	11	the	the	DET
cana-3871	26	12	zero	zero	NUM
cana-3871	26	13	-	-	PUNCT
cana-3871	26	14	divisors	divisor	NOUN
cana-3871	26	15	of	of	ADP
cana-3871	26	16	a	a	DET
cana-3871	26	17	commutative	commutative	ADJ
cana-3871	26	18	ring	ring	NOUN
cana-3871	26	19	.	.	PUNCT
cana-3871	27	1	its	its	PRON
cana-3871	27	2	vertices	vertex	NOUN
cana-3871	27	3	correspond	correspond	VERB
cana-3871	27	4	to	to	ADP
cana-3871	27	5	elements	element	NOUN
cana-3871	27	6	of	of	ADP
cana-3871	27	7	the	the	DET
cana-3871	27	8	ring	ring	NOUN
cana-3871	27	9	,	,	PUNCT
cana-3871	27	10	and	and	CCONJ
cana-3871	27	11	its	its	PRON
cana-3871	27	12	edges	edge	NOUN
cana-3871	27	13	connect	connect	VERB
cana-3871	27	14	pairs	pair	NOUN
cana-3871	27	15	of	of	ADP
cana-3871	27	16	elements	element	NOUN
cana-3871	27	17	whose	whose	DET
cana-3871	27	18	product	product	NOUN
cana-3871	27	19	equals	equal	VERB
cana-3871	27	20	zero	zero	NUM
cana-3871	27	21	.	.	PUNCT
cana-3871	28	1	in	in	ADP
cana-3871	28	2	this	this	DET
cana-3871	28	3	context	context	NOUN
cana-3871	28	4	,	,	PUNCT
cana-3871	28	5	two	two	NUM
cana-3871	28	6	vertices	vertice	VERB
cana-3871	28	7	u	u	NOUN
cana-3871	28	8	and	and	CCONJ
cana-3871	28	9	v	v	NOUN
cana-3871	28	10	within	within	ADP
cana-3871	28	11	the	the	DET
cana-3871	28	12	graph	graph	NOUN
cana-3871	28	13	g	g	NOUN
cana-3871	28	14	are	be	AUX
cana-3871	28	15	considered	consider	VERB
cana-3871	28	16	connected	connect	VERB
cana-3871	28	17	if	if	SCONJ
cana-3871	28	18	there	there	PRON
cana-3871	28	19	exists	exist	VERB
cana-3871	28	20	a	a	DET
cana-3871	28	21	path	path	NOUN
cana-3871	28	22	from	from	ADP
cana-3871	28	23	u	u	PRON
cana-3871	28	24	to	to	ADP
cana-3871	28	25	v.	v.	ADP
cana-3871	28	26	this	this	DET
cana-3871	28	27	notion	notion	NOUN
cana-3871	28	28	of	of	ADP
cana-3871	28	29	connection	connection	NOUN
cana-3871	28	30	forms	form	VERB
cana-3871	28	31	an	an	DET
cana-3871	28	32	equivalence	equivalence	NOUN
cana-3871	28	33	relation	relation	NOUN
cana-3871	28	34	on	on	ADP
cana-3871	28	35	the	the	DET
cana-3871	28	36	vertex	vertex	NOUN
cana-3871	28	37	set	set	NOUN
cana-3871	28	38	v.	v.	ADP
cana-3871	28	39	consequently	consequently	ADV
cana-3871	28	40	,	,	PUNCT
cana-3871	28	41	the	the	DET
cana-3871	28	42	vertex	vertex	NOUN
cana-3871	28	43	set	set	NOUN
cana-3871	28	44	v	v	NOUN
cana-3871	28	45	can	can	AUX
cana-3871	28	46	be	be	AUX
cana-3871	28	47	partitioned	partition	VERB
cana-3871	28	48	into	into	ADP
cana-3871	28	49	nonempty	nonempty	ADJ
cana-3871	28	50	subsets	subset	NOUN
cana-3871	28	51	v1	v1	NOUN
cana-3871	28	52	,	,	PUNCT
cana-3871	28	53	v2	v2	PROPN
cana-3871	28	54	,	,	PUNCT
cana-3871	28	55	...	...	PUNCT
cana-3871	28	56	,	,	PUNCT
cana-3871	28	57	vw	vw	PROPN
cana-3871	28	58	,	,	PUNCT
cana-3871	28	59	where	where	SCONJ
cana-3871	28	60	two	two	NUM
cana-3871	28	61	vertices	vertice	VERB
cana-3871	28	62	u	u	NOUN
cana-3871	28	63	and	and	CCONJ
cana-3871	28	64	v	v	NOUN
cana-3871	28	65	are	be	AUX
cana-3871	28	66	connected	connect	VERB
cana-3871	28	67	if	if	SCONJ
cana-3871	28	68	and	and	CCONJ
cana-3871	28	69	only	only	ADV
cana-3871	28	70	if	if	SCONJ
cana-3871	28	71	they	they	PRON
cana-3871	28	72	both	both	PRON
cana-3871	28	73	belong	belong	VERB
cana-3871	28	74	to	to	ADP
cana-3871	28	75	the	the	DET
cana-3871	28	76	same	same	ADJ
cana-3871	28	77	subset	subset	NOUN
cana-3871	28	78	vi	vi	PROPN
cana-3871	28	79	.	.	PUNCT
cana-3871	29	1	the	the	DET
cana-3871	29	2	subgraphs	subgraphs	PROPN
cana-3871	29	3	g[v1	g[v1	PROPN
cana-3871	29	4	]	]	PUNCT
cana-3871	29	5	,	,	PUNCT
cana-3871	29	6	g[v2	g[v2	NOUN
cana-3871	29	7	]	]	X
cana-3871	29	8	,	,	PUNCT
cana-3871	29	9	...	...	PUNCT
cana-3871	29	10	,	,	PUNCT
cana-3871	29	11	g[vw	g[vw	NOUN
cana-3871	29	12	]	]	PUNCT
cana-3871	29	13	are	be	AUX
cana-3871	29	14	referred	refer	VERB
cana-3871	29	15	to	to	ADP
cana-3871	29	16	as	as	ADP
cana-3871	29	17	the	the	DET
cana-3871	29	18	components	component	NOUN
cana-3871	29	19	of	of	ADP
cana-3871	29	20	g.	g.	PROPN
cana-3871	29	21	if	if	SCONJ
cana-3871	29	22	g	g	PROPN
cana-3871	29	23	contains	contain	VERB
cana-3871	29	24	only	only	ADV
cana-3871	29	25	one	one	NUM
cana-3871	29	26	component	component	NOUN
cana-3871	29	27	,	,	PUNCT
cana-3871	29	28	it	it	PRON
cana-3871	29	29	is	be	AUX
cana-3871	29	30	termed	term	VERB
cana-3871	29	31	connected	connect	VERB
cana-3871	29	32	;	;	PUNCT
cana-3871	29	33	otherwise	otherwise	ADV
cana-3871	29	34	,	,	PUNCT
cana-3871	29	35	it	it	PRON
cana-3871	29	36	is	be	AUX
cana-3871	29	37	classified	classify	VERB
cana-3871	29	38	as	as	SCONJ
cana-3871	29	39	disconnected	disconnect	VERB
cana-3871	29	40	.	.	PUNCT
cana-3871	30	1	additionally	additionally	ADV
cana-3871	30	2	,	,	PUNCT
cana-3871	30	3	a	a	DET
cana-3871	30	4	graph	graph	NOUN
cana-3871	30	5	is	be	AUX
cana-3871	30	6	considered	consider	VERB
cana-3871	30	7	simple	simple	ADJ
cana-3871	30	8	when	when	SCONJ
cana-3871	30	9	it	it	PRON
cana-3871	30	10	does	do	AUX
cana-3871	30	11	not	not	PART
cana-3871	30	12	contain	contain	VERB
cana-3871	30	13	loops	loop	NOUN
cana-3871	30	14	,	,	PUNCT
cana-3871	30	15	meaning	mean	VERB
cana-3871	30	16	there	there	PRON
cana-3871	30	17	are	be	VERB
cana-3871	30	18	no	no	DET
cana-3871	30	19	edges	edge	NOUN
cana-3871	30	20	connecting	connect	VERB
cana-3871	30	21	a	a	DET
cana-3871	30	22	vertex	vertex	NOUN
cana-3871	30	23	to	to	ADP
cana-3871	30	24	itself	itself	PRON
cana-3871	30	25	,	,	PUNCT
cana-3871	30	26	and	and	CCONJ
cana-3871	30	27	when	when	SCONJ
cana-3871	30	28	each	each	DET
cana-3871	30	29	pair	pair	NOUN
cana-3871	30	30	of	of	ADP
cana-3871	30	31	vertices	vertex	NOUN
cana-3871	30	32	is	be	AUX
cana-3871	30	33	connected	connect	VERB
cana-3871	30	34	by	by	ADP
cana-3871	30	35	at	at	ADP
cana-3871	30	36	most	most	ADV
cana-3871	30	37	one	one	NUM
cana-3871	30	38	edge	edge	NOUN
cana-3871	30	39	,	,	PUNCT
cana-3871	30	40	ensuring	ensure	VERB
cana-3871	30	41	that	that	SCONJ
cana-3871	30	42	no	no	DET
cana-3871	30	43	two	two	NUM
cana-3871	30	44	edges	edge	NOUN
cana-3871	30	45	join	join	VERB
cana-3871	30	46	the	the	DET
cana-3871	30	47	same	same	ADJ
cana-3871	30	48	pair	pair	NOUN
cana-3871	30	49	of	of	ADP
cana-3871	30	50	vertices	vertex	NOUN
cana-3871	30	51	.	.	PUNCT
cana-3871	31	1	(	(	PUNCT
cana-3871	31	2	a	a	DET
cana-3871	31	3	self	self	NOUN
cana-3871	31	4	-	-	PUNCT
cana-3871	31	5	loop	loop	NOUN
cana-3871	31	6	is	be	AUX
cana-3871	31	7	an	an	DET
cana-3871	31	8	edge	edge	NOUN
cana-3871	31	9	that	that	PRON
cana-3871	31	10	joins	join	VERB
cana-3871	31	11	a	a	DET
cana-3871	31	12	single	single	ADJ
cana-3871	31	13	endpoint	endpoint	NOUN
cana-3871	31	14	to	to	ADP
cana-3871	31	15	itself	itself	PRON
cana-3871	31	16	)	)	PUNCT
cana-3871	32	1	[	[	X
cana-3871	32	2	refer	refer	VERB
cana-3871	32	3	figure1	figure1	X
cana-3871	32	4	]	]	PUNCT
cana-3871	32	5	fig	fig	NOUN
cana-3871	32	6	1	1	NUM
cana-3871	32	7	:	:	PUNCT
cana-3871	32	8	simple	simple	ADJ
cana-3871	32	9	graph	graph	NOUN
cana-3871	32	10	graph	graph	NOUN
cana-3871	32	11	theory	theory	NOUN
cana-3871	32	12	describes	describe	VERB
cana-3871	32	13	a	a	DET
cana-3871	32	14	walk	walk	NOUN
cana-3871	32	15	-	-	PUNCT
cana-3871	32	16	in	in	ADP
cana-3871	32	17	graph	graph	NOUN
cana-3871	32	18	g	g	NOUN
cana-3871	32	19	as	as	ADP
cana-3871	32	20	a	a	DET
cana-3871	32	21	finite	finite	NOUN
cana-3871	32	22	,	,	PUNCT
cana-3871	32	23	non	non	ADJ
cana-3871	32	24	-	-	ADJ
cana-3871	32	25	null	null	ADJ
cana-3871	32	26	sequence	sequence	NOUN
cana-3871	32	27	denoted	denote	VERB
cana-3871	32	28	by	by	ADP
cana-3871	32	29	w	w	PROPN
cana-3871	32	30	=	=	PUNCT
cana-3871	32	31	v0e1v1e2v2	v0e1v1e2v2	NUM
cana-3871	32	32	...	...	PUNCT
cana-3871	32	33	ekvk	ekvk	NOUN
cana-3871	32	34	.	.	PUNCT
cana-3871	33	1	this	this	DET
cana-3871	33	2	sequence	sequence	NOUN
cana-3871	33	3	alternates	alternate	NOUN
cana-3871	33	4	between	between	ADP
cana-3871	33	5	vertices	vertex	NOUN
cana-3871	33	6	and	and	CCONJ
cana-3871	33	7	edges	edge	NOUN
cana-3871	33	8	,	,	PUNCT
cana-3871	33	9	where	where	SCONJ
cana-3871	33	10	for	for	ADP
cana-3871	33	11	1	1	NUM
cana-3871	33	12	≤	≤	NOUN
cana-3871	33	13	i	i	NOUN
cana-3871	33	14	≤	≤	PROPN
cana-3871	34	1	k	k	X
cana-3871	34	2	,	,	PUNCT
cana-3871	34	3	the	the	DET
cana-3871	34	4	ends	end	NOUN
cana-3871	34	5	of	of	ADP
cana-3871	34	6	ei	ei	NOUN
cana-3871	34	7	are	be	AUX
cana-3871	34	8	vi−1	vi−1	PROPN
cana-3871	34	9	and	and	CCONJ
cana-3871	34	10	vi	vi	NOUN
cana-3871	34	11	.	.	PUNCT
cana-3871	35	1	this	this	DET
cana-3871	35	2	sequence	sequence	NOUN
cana-3871	35	3	is	be	AUX
cana-3871	35	4	called	call	VERB
cana-3871	35	5	a	a	DET
cana-3871	35	6	walk	walk	NOUN
cana-3871	35	7	from	from	ADP
cana-3871	35	8	v0	v0	NOUN
cana-3871	35	9	to	to	ADP
cana-3871	35	10	vk	vk	PROPN
cana-3871	35	11	,	,	PUNCT
cana-3871	35	12	or	or	CCONJ
cana-3871	35	13	a	a	DET
cana-3871	35	14	(	(	PUNCT
cana-3871	35	15	v0	v0	NOUN
cana-3871	35	16	,	,	PUNCT
cana-3871	35	17	vk	vk	NOUN
cana-3871	35	18	)	)	PUNCT
cana-3871	35	19	walk	walk	VERB
cana-3871	35	20	.	.	PUNCT
cana-3871	36	1	the	the	DET
cana-3871	36	2	vertices	vertex	NOUN
cana-3871	36	3	v0	v0	NOUN
cana-3871	36	4	and	and	CCONJ
cana-3871	36	5	vk	vk	PROPN
cana-3871	36	6	are	be	AUX
cana-3871	36	7	respectively	respectively	ADV
cana-3871	36	8	termed	term	VERB
cana-3871	36	9	the	the	DET
cana-3871	36	10	origin	origin	NOUN
cana-3871	36	11	and	and	CCONJ
cana-3871	36	12	terminus	terminus	NOUN
cana-3871	36	13	of	of	ADP
cana-3871	36	14	the	the	DET
cana-3871	36	15	walk	walk	NOUN
cana-3871	36	16	,	,	PUNCT
cana-3871	36	17	while	while	SCONJ
cana-3871	36	18	v1	v1	NOUN
cana-3871	36	19	,	,	PUNCT
cana-3871	36	20	v2	v2	NOUN
cana-3871	36	21	,	,	PUNCT
cana-3871	36	22	.	.	PUNCT
cana-3871	36	23	.	.	PUNCT
cana-3871	37	1	.	.	PUNCT
cana-3871	38	1	,	,	PUNCT
cana-3871	38	2	vk−1	vk−1	NOUN
cana-3871	38	3	are	be	AUX
cana-3871	38	4	its	its	PRON
cana-3871	38	5	internal	internal	ADJ
cana-3871	38	6	vertices	vertex	NOUN
cana-3871	38	7	.	.	PUNCT
cana-3871	39	1	the	the	DET
cana-3871	39	2	integer	integer	PROPN
cana-3871	39	3	k	k	PROPN
cana-3871	39	4	is	be	AUX
cana-3871	39	5	the	the	DET
cana-3871	39	6	length	length	NOUN
cana-3871	39	7	of	of	ADP
cana-3871	39	8	w.	w.	PROPN
cana-3871	39	9	example	example	PROPN
cana-3871	39	10	:	:	PUNCT
cana-3871	39	11	uavfyfvgyhwbv	uavfyfvgyhwbv	X
cana-3871	39	12	[	[	X
cana-3871	39	13	refer	refer	VERB
cana-3871	39	14	figure	figure	NOUN
cana-3871	39	15	2	2	NUM
cana-3871	39	16	]	]	PUNCT
cana-3871	39	17	communications	communication	NOUN
cana-3871	39	18	on	on	ADP
cana-3871	39	19	applied	apply	VERB
cana-3871	39	20	nonlinear	nonlinear	ADJ
cana-3871	39	21	analysis	analysis	NOUN
cana-3871	39	22	issn	issn	NOUN
cana-3871	39	23	:	:	PUNCT
cana-3871	39	24	1074	1074	NUM
cana-3871	39	25	-	-	PUNCT
cana-3871	39	26	133x	133x	NUM
cana-3871	39	27	vol	vol	NOUN
cana-3871	39	28	32	32	NUM
cana-3871	39	29	no	no	NOUN
cana-3871	39	30	.	.	PUNCT
cana-3871	40	1	7s	7	NOUN
cana-3871	40	2	(	(	PUNCT
cana-3871	40	3	2025	2025	NUM
cana-3871	40	4	)	)	PUNCT
cana-3871	40	5	943	943	NUM
cana-3871	40	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	40	7	fig	fig	NOUN
cana-3871	40	8	2	2	NUM
cana-3871	40	9	:	:	PUNCT
cana-3871	40	10	walk	walk	VERB
cana-3871	40	11	if	if	SCONJ
cana-3871	40	12	the	the	DET
cana-3871	40	13	edges	edge	NOUN
cana-3871	40	14	e1	e1	PROPN
cana-3871	40	15	,	,	PUNCT
cana-3871	40	16	e2	e2	PROPN
cana-3871	40	17	,	,	PUNCT
cana-3871	40	18	...	...	PUNCT
cana-3871	40	19	,	,	PUNCT
cana-3871	40	20	ek	ek	PROPN
cana-3871	40	21	of	of	ADP
cana-3871	40	22	a	a	DET
cana-3871	40	23	walk	walk	NOUN
cana-3871	40	24	w	w	NOUN
cana-3871	40	25	are	be	AUX
cana-3871	40	26	distinct	distinct	ADJ
cana-3871	40	27	,	,	PUNCT
cana-3871	40	28	w	w	PROPN
cana-3871	40	29	is	be	AUX
cana-3871	40	30	called	call	VERB
cana-3871	40	31	a	a	DET
cana-3871	40	32	trail	trail	NOUN
cana-3871	40	33	.	.	PUNCT
cana-3871	41	1	example	example	NOUN
cana-3871	41	2	:	:	PUNCT
cana-3871	41	3	wcxdyhwbvgy	wcxdyhwbvgy	PROPN
cana-3871	41	4	fig	fig	NOUN
cana-3871	41	5	3	3	NUM
cana-3871	41	6	:	:	PUNCT
cana-3871	41	7	trail	trail	NOUN
cana-3871	41	8	and	and	CCONJ
cana-3871	41	9	path	path	VERB
cana-3871	41	10	a	a	DET
cana-3871	41	11	path	path	NOUN
cana-3871	41	12	is	be	AUX
cana-3871	41	13	a	a	DET
cana-3871	41	14	trail	trail	NOUN
cana-3871	41	15	in	in	ADP
cana-3871	41	16	which	which	PRON
cana-3871	41	17	no	no	DET
cana-3871	41	18	vertices	vertex	NOUN
cana-3871	41	19	(	(	PUNCT
cana-3871	41	20	except	except	SCONJ
cana-3871	41	21	possibly	possibly	ADV
cana-3871	41	22	the	the	DET
cana-3871	41	23	end	end	NOUN
cana-3871	41	24	vertices	vertex	NOUN
cana-3871	41	25	)	)	PUNCT
cana-3871	41	26	are	be	AUX
cana-3871	41	27	repeated	repeat	VERB
cana-3871	41	28	i.e.	i.e.	X
cana-3871	41	29	the	the	DET
cana-3871	41	30	vertices	vertex	NOUN
cana-3871	41	31	v0	v0	NOUN
cana-3871	41	32	,	,	PUNCT
cana-3871	41	33	v1	v1	NOUN
cana-3871	41	34	,	,	PUNCT
cana-3871	41	35	...	...	PUNCT
cana-3871	41	36	,	,	PUNCT
cana-3871	41	37	vk	vk	NOUN
cana-3871	41	38	are	be	AUX
cana-3871	41	39	distinct	distinct	ADJ
cana-3871	41	40	,	,	PUNCT
cana-3871	41	41	w	w	PROPN
cana-3871	41	42	is	be	AUX
cana-3871	41	43	called	call	VERB
cana-3871	41	44	a	a	DET
cana-3871	41	45	path	path	NOUN
cana-3871	41	46	.	.	PUNCT
cana-3871	42	1	example	example	NOUN
cana-3871	42	2	:	:	PUNCT
cana-3871	42	3	xcwhyeuav	xcwhyeuav	PROPN
cana-3871	42	4	a	a	DET
cana-3871	42	5	circuit	circuit	NOUN
cana-3871	42	6	is	be	AUX
cana-3871	42	7	a	a	DET
cana-3871	42	8	closed	closed	ADJ
cana-3871	42	9	trail	trail	NOUN
cana-3871	42	10	(	(	PUNCT
cana-3871	42	11	that	that	PRON
cana-3871	42	12	is	be	AUX
cana-3871	42	13	end	end	NOUN
cana-3871	42	14	vertices	vertex	NOUN
cana-3871	42	15	are	be	AUX
cana-3871	42	16	the	the	DET
cana-3871	42	17	same	same	ADJ
cana-3871	42	18	)	)	PUNCT
cana-3871	42	19	with	with	ADP
cana-3871	42	20	at	at	ADV
cana-3871	42	21	least	least	ADV
cana-3871	42	22	one	one	NUM
cana-3871	42	23	edge	edge	NOUN
cana-3871	42	24	known	know	VERB
cana-3871	42	25	as	as	ADP
cana-3871	42	26	circuit	circuit	NOUN
cana-3871	42	27	.	.	PUNCT
cana-3871	43	1	fig	fig	NOUN
cana-3871	43	2	4	4	NUM
cana-3871	43	3	:	:	PUNCT
cana-3871	43	4	cycle	cycle	NOUN
cana-3871	43	5	a	a	DET
cana-3871	43	6	walk	walk	NOUN
cana-3871	43	7	is	be	AUX
cana-3871	43	8	closed	close	VERB
cana-3871	43	9	if	if	SCONJ
cana-3871	43	10	it	it	PRON
cana-3871	43	11	has	have	VERB
cana-3871	43	12	a	a	DET
cana-3871	43	13	positive	positive	ADJ
cana-3871	43	14	length	length	NOUN
cana-3871	43	15	and	and	CCONJ
cana-3871	43	16	its	its	PRON
cana-3871	43	17	origin	origin	NOUN
cana-3871	43	18	and	and	CCONJ
cana-3871	43	19	terminus	terminus	NOUN
cana-3871	43	20	are	be	AUX
cana-3871	43	21	the	the	DET
cana-3871	43	22	same	same	ADJ
cana-3871	43	23	.	.	PUNCT
cana-3871	44	1	a	a	DET
cana-3871	44	2	closed	closed	ADJ
cana-3871	44	3	trail	trail	NOUN
cana-3871	44	4	whose	whose	DET
cana-3871	44	5	origin	origin	NOUN
cana-3871	44	6	and	and	CCONJ
cana-3871	44	7	internal	internal	ADJ
cana-3871	44	8	vertices	vertex	NOUN
cana-3871	44	9	are	be	AUX
cana-3871	44	10	distinct	distinct	ADJ
cana-3871	44	11	is	be	AUX
cana-3871	44	12	a	a	DET
cana-3871	44	13	cycle	cycle	NOUN
cana-3871	44	14	.	.	PUNCT
cana-3871	45	1	the	the	DET
cana-3871	45	2	graph	graph	NOUN
cana-3871	45	3	’s	’s	PART
cana-3871	45	4	diameter	diameter	NOUN
cana-3871	45	5	is	be	AUX
cana-3871	45	6	the	the	DET
cana-3871	45	7	maximum	maximum	ADJ
cana-3871	45	8	distance	distance	NOUN
cana-3871	45	9	between	between	ADP
cana-3871	45	10	the	the	DET
cana-3871	45	11	pair	pair	NOUN
cana-3871	45	12	of	of	ADP
cana-3871	45	13	vertices	vertex	NOUN
cana-3871	45	14	.	.	PUNCT
cana-3871	46	1	it	it	PRON
cana-3871	46	2	can	can	AUX
cana-3871	46	3	also	also	ADV
cana-3871	46	4	be	be	AUX
cana-3871	46	5	defined	define	VERB
cana-3871	46	6	as	as	ADP
cana-3871	46	7	the	the	DET
cana-3871	46	8	maximal	maximal	ADJ
cana-3871	46	9	distance	distance	NOUN
cana-3871	46	10	between	between	ADP
cana-3871	46	11	the	the	DET
cana-3871	46	12	pair	pair	NOUN
cana-3871	46	13	of	of	ADP
cana-3871	46	14	vertices	vertex	NOUN
cana-3871	46	15	.	.	PUNCT
cana-3871	47	1	example	example	NOUN
cana-3871	47	2	:	:	PUNCT
cana-3871	47	3	bc	bc	PROPN
cana-3871	47	4	→	→	SYM
cana-3871	47	5	cf	cf	PROPN
cana-3871	47	6	→	→	SYM
cana-3871	47	7	fg	fg	PROPN
cana-3871	47	8	a	a	DET
cana-3871	47	9	radius	radius	NOUN
cana-3871	47	10	of	of	ADP
cana-3871	47	11	the	the	DET
cana-3871	47	12	graph	graph	NOUN
cana-3871	47	13	exists	exist	VERB
cana-3871	47	14	only	only	ADV
cana-3871	47	15	if	if	SCONJ
cana-3871	47	16	it	it	PRON
cana-3871	47	17	has	have	VERB
cana-3871	47	18	a	a	DET
cana-3871	47	19	diameter	diameter	NOUN
cana-3871	47	20	.	.	PUNCT
cana-3871	48	1	the	the	DET
cana-3871	48	2	minimum	minimum	NOUN
cana-3871	48	3	among	among	ADP
cana-3871	48	4	all	all	DET
cana-3871	48	5	the	the	DET
cana-3871	48	6	maximum	maximum	ADJ
cana-3871	48	7	distances	distance	NOUN
cana-3871	48	8	between	between	ADP
cana-3871	48	9	vertexes	vertex	NOUN
cana-3871	48	10	to	to	ADP
cana-3871	48	11	all	all	DET
cana-3871	48	12	other	other	ADJ
cana-3871	48	13	vertices	vertex	NOUN
cana-3871	48	14	is	be	AUX
cana-3871	48	15	considered	consider	VERB
cana-3871	48	16	as	as	ADP
cana-3871	48	17	the	the	DET
cana-3871	48	18	radius	radius	NOUN
cana-3871	48	19	of	of	ADP
cana-3871	48	20	graph	graph	NOUN
cana-3871	48	21	g.	g.	PROPN
cana-3871	48	22	it	it	PRON
cana-3871	48	23	is	be	AUX
cana-3871	48	24	denoted	denote	VERB
cana-3871	48	25	as	as	ADP
cana-3871	48	26	r(g	r(g	NUM
cana-3871	48	27	)	)	PUNCT
cana-3871	48	28	.	.	PUNCT
cana-3871	49	1	communications	communication	NOUN
cana-3871	49	2	on	on	ADP
cana-3871	49	3	applied	apply	VERB
cana-3871	49	4	nonlinear	nonlinear	ADJ
cana-3871	49	5	analysis	analysis	NOUN
cana-3871	49	6	issn	issn	NOUN
cana-3871	49	7	:	:	PUNCT
cana-3871	49	8	1074	1074	NUM
cana-3871	49	9	-	-	PUNCT
cana-3871	49	10	133x	133x	NUM
cana-3871	49	11	vol	vol	NOUN
cana-3871	49	12	32	32	NUM
cana-3871	49	13	no	no	NOUN
cana-3871	49	14	.	.	PUNCT
cana-3871	50	1	7s	7	NOUN
cana-3871	50	2	(	(	PUNCT
cana-3871	50	3	2025	2025	NUM
cana-3871	50	4	)	)	PUNCT
cana-3871	50	5	944	944	NUM
cana-3871	50	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	50	7	example	example	NOUN
cana-3871	50	8	:	:	PUNCT
cana-3871	50	9	bc	bc	PROPN
cana-3871	50	10	→	→	X
cana-3871	50	11	ca	can	AUX
cana-3871	50	12	the	the	DET
cana-3871	50	13	girth	girth	NOUN
cana-3871	50	14	of	of	ADP
cana-3871	50	15	a	a	DET
cana-3871	50	16	graph	graph	NOUN
cana-3871	50	17	is	be	AUX
cana-3871	50	18	the	the	DET
cana-3871	50	19	length	length	NOUN
cana-3871	50	20	of	of	ADP
cana-3871	50	21	the	the	DET
cana-3871	50	22	shortest	short	ADJ
cana-3871	50	23	cycle	cycle	NOUN
cana-3871	50	24	contained	contain	VERB
cana-3871	50	25	in	in	ADP
cana-3871	50	26	the	the	DET
cana-3871	50	27	graph	graph	NOUN
cana-3871	50	28	.	.	PUNCT
cana-3871	51	1	if	if	SCONJ
cana-3871	51	2	the	the	DET
cana-3871	51	3	graph	graph	NOUN
cana-3871	51	4	does	do	AUX
cana-3871	51	5	not	not	PART
cana-3871	51	6	contain	contain	VERB
cana-3871	51	7	any	any	DET
cana-3871	51	8	cycles	cycle	NOUN
cana-3871	51	9	(	(	PUNCT
cana-3871	51	10	i.e.	i.e.	X
cana-3871	51	11	,	,	PUNCT
cana-3871	51	12	it	it	PRON
cana-3871	51	13	’s	’	VERB
cana-3871	51	14	an	an	DET
cana-3871	51	15	acyclic	acyclic	ADJ
cana-3871	51	16	graph	graph	NOUN
cana-3871	51	17	)	)	PUNCT
cana-3871	51	18	,	,	PUNCT
cana-3871	51	19	its	its	PRON
cana-3871	51	20	girth	girth	NOUN
cana-3871	51	21	is	be	AUX
cana-3871	51	22	defined	define	VERB
cana-3871	51	23	as	as	ADP
cana-3871	51	24	infinity	infinity	NOUN
cana-3871	51	25	.	.	PUNCT
cana-3871	52	1	•	•	NUM
cana-3871	52	2	a	a	DET
cana-3871	52	3	4	4	NUM
cana-3871	52	4	-	-	PUNCT
cana-3871	52	5	cycle	cycle	NOUN
cana-3871	52	6	(	(	PUNCT
cana-3871	52	7	square	square	NOUN
cana-3871	52	8	)	)	PUNCT
cana-3871	52	9	has	have	AUX
cana-3871	52	10	girth	girth	NOUN
cana-3871	52	11	4	4	NUM
cana-3871	52	12	.	.	PUNCT
cana-3871	53	1	a	a	DET
cana-3871	53	2	grid	grid	NOUN
cana-3871	53	3	also	also	ADV
cana-3871	53	4	has	have	VERB
cana-3871	53	5	a	a	DET
cana-3871	53	6	girth	girth	NOUN
cana-3871	53	7	4	4	NUM
cana-3871	53	8	,	,	PUNCT
cana-3871	53	9	and	and	CCONJ
cana-3871	53	10	a	a	DET
cana-3871	53	11	triangular	triangular	NOUN
cana-3871	53	12	mesh	mesh	NOUN
cana-3871	53	13	has	have	VERB
cana-3871	53	14	a	a	DET
cana-3871	53	15	girth	girth	NOUN
cana-3871	53	16	3	3	NUM
cana-3871	53	17	.	.	PUNCT
cana-3871	54	1	a	a	DET
cana-3871	54	2	graph	graph	NOUN
cana-3871	54	3	with	with	ADP
cana-3871	54	4	a	a	DET
cana-3871	54	5	girth	girth	NOUN
cana-3871	54	6	of	of	ADP
cana-3871	54	7	four	four	NUM
cana-3871	54	8	or	or	CCONJ
cana-3871	54	9	more	more	ADJ
cana-3871	54	10	is	be	AUX
cana-3871	54	11	triangle	triangle	NOUN
cana-3871	54	12	-	-	PUNCT
cana-3871	54	13	free	free	ADJ
cana-3871	54	14	.	.	PUNCT
cana-3871	55	1	3	3	NUM
cana-3871	55	2	main	main	ADJ
cana-3871	55	3	results	result	NOUN
cana-3871	55	4	3.1	3.1	NUM
cana-3871	55	5	theorem	theorem	ADJ
cana-3871	55	6	statement	statement	NOUN
cana-3871	55	7	:	:	PUNCT
cana-3871	55	8	let	let	VERB
cana-3871	55	9	ℤ	ℤ	PROPN
cana-3871	55	10	2	2	NUM
cana-3871	55	11	n	n	NOUN
cana-3871	55	12	=	=	SYM
cana-3871	55	13	ℤ	ℤ	PROPN
cana-3871	55	14	2	2	NUM
cana-3871	55	15	×	×	NOUN
cana-3871	55	16	ℤ	ℤ	PROPN
cana-3871	55	17	2	2	NUM
cana-3871	55	18	×	×	NOUN
cana-3871	55	19	ℤ	ℤ	PROPN
cana-3871	55	20	2	2	NUM
cana-3871	55	21	×	×	NOUN
cana-3871	55	22	...	...	PUNCT
cana-3871	55	23	×	×	NOUN
cana-3871	55	24	ℤ	ℤ	PROPN
cana-3871	55	25	2	2	NUM
cana-3871	55	26	be	be	AUX
cana-3871	55	27	a	a	DET
cana-3871	55	28	boolean	boolean	ADJ
cana-3871	55	29	ring	ring	NOUN
cana-3871	55	30	and	and	CCONJ
cana-3871	55	31	ℤ	ℤ	PROPN
cana-3871	55	32	2	2	PROPN
cana-3871	55	33	n	n	PRON
cana-3871	55	34	has	have	VERB
cana-3871	55	35	(	(	PUNCT
cana-3871	55	36	2n	2n	NUM
cana-3871	55	37	−	−	NOUN
cana-3871	55	38	2	2	X
cana-3871	55	39	)	)	PUNCT
cana-3871	55	40	zero	zero	NUM
cana-3871	55	41	divisors	divisor	NOUN
cana-3871	55	42	i.e	i.e	X
cana-3871	55	43	|	|	ADV
cana-3871	55	44	ℤ	ℤ	PROPN
cana-3871	55	45	2	2	NUM
cana-3871	55	46	n|	n|	NOUN
cana-3871	55	47	=	=	SYM
cana-3871	55	48	2n	2n	NUM
cana-3871	55	49	and	and	CCONJ
cana-3871	55	50	|	|	ADV
cana-3871	55	51	ℤ	ℤ	PROPN
cana-3871	55	52	(	(	PUNCT
cana-3871	55	53	ℤ	ℤ	PROPN
cana-3871	55	54	2	2	NUM
cana-3871	55	55	n)|	n)|	NOUN
cana-3871	55	56	=	=	SYM
cana-3871	55	57	2n	2n	NUM
cana-3871	55	58	−	−	NOUN
cana-3871	55	59	2	2	NUM
cana-3871	55	60	,	,	PUNCT
cana-3871	55	61	then	then	ADV
cana-3871	55	62	n	n	PRON
cana-3871	55	63	vertices	vertice	VERB
cana-3871	55	64	in	in	ADP
cana-3871	55	65	zero	zero	NUM
cana-3871	55	66	divisor	divisor	NOUN
cana-3871	55	67	graph	graph	NOUN
cana-3871	55	68	γ(ℤ	γ(ℤ	NUM
cana-3871	55	69	n	n	CCONJ
cana-3871	55	70	)	)	PUNCT
cana-3871	55	71	have	have	VERB
cana-3871	55	72	2n−1	2n−1	NUM
cana-3871	55	73	–	–	PUNCT
cana-3871	55	74	degree	degree	NOUN
cana-3871	55	75	.	.	PUNCT
cana-3871	56	1	proof	proof	NOUN
cana-3871	56	2	let	let	VERB
cana-3871	56	3	ℤ	ℤ	PROPN
cana-3871	56	4	2	2	NUM
cana-3871	56	5	n	n	NOUN
cana-3871	56	6	=	=	SYM
cana-3871	56	7	ℤ	ℤ	PROPN
cana-3871	56	8	2	2	NUM
cana-3871	56	9	×	×	NOUN
cana-3871	56	10	ℤ	ℤ	PROPN
cana-3871	56	11	2	2	NUM
cana-3871	56	12	×	×	NOUN
cana-3871	56	13	ℤ	ℤ	PROPN
cana-3871	56	14	2	2	NUM
cana-3871	56	15	×	×	NOUN
cana-3871	56	16	...	...	PUNCT
cana-3871	56	17	×	×	NOUN
cana-3871	56	18	ℤ	ℤ	PROPN
cana-3871	56	19	2	2	NUM
cana-3871	56	20	,	,	PUNCT
cana-3871	56	21	be	be	AUX
cana-3871	56	22	a	a	DET
cana-3871	56	23	boolean	boolean	ADJ
cana-3871	56	24	ring	ring	NOUN
cana-3871	56	25	and	and	CCONJ
cana-3871	56	26	ℤ	ℤ	PROPN
cana-3871	56	27	2	2	PROPN
cana-3871	56	28	n	n	PRON
cana-3871	56	29	has	have	VERB
cana-3871	56	30	(	(	PUNCT
cana-3871	56	31	2n	2n	NUM
cana-3871	56	32	–	–	PUNCT
cana-3871	56	33	2	2	NUM
cana-3871	56	34	)	)	PUNCT
cana-3871	56	35	zero	zero	NUM
cana-3871	56	36	divisors	divisor	NOUN
cana-3871	56	37	i.e.	i.e.	X
cana-3871	56	38	zero	zero	NUM
cana-3871	56	39	divisors	divisor	NOUN
cana-3871	56	40	and	and	CCONJ
cana-3871	56	41	ℤ	ℤ	PROPN
cana-3871	56	42	2	2	PROPN
cana-3871	56	43	n	n	NOUN
cana-3871	56	44	is	be	AUX
cana-3871	56	45	given	give	VERB
cana-3871	56	46	by	by	ADP
cana-3871	56	47	,	,	PUNCT
cana-3871	56	48	ℤ	ℤ	PROPN
cana-3871	56	49	2	2	NUM
cana-3871	56	50	n	n	NOUN
cana-3871	56	51	=	=	PRON
cana-3871	56	52	{	{	PUNCT
cana-3871	56	53	(	(	PUNCT
cana-3871	56	54	b1	b1	NOUN
cana-3871	56	55	,	,	PUNCT
cana-3871	56	56	b2	b2	NOUN
cana-3871	56	57	,	,	PUNCT
cana-3871	56	58	b3	b3	PROPN
cana-3871	56	59	,	,	PUNCT
cana-3871	56	60	...	...	PUNCT
cana-3871	56	61	,	,	PUNCT
cana-3871	56	62	bn	bn	X
cana-3871	56	63	)	)	PUNCT
cana-3871	56	64	|	|	ADV
cana-3871	56	65	bi′s	bi′s	NOUN
cana-3871	56	66	∈	∈	PROPN
cana-3871	56	67	{	{	PUNCT
cana-3871	56	68	0	0	NUM
cana-3871	56	69	,	,	PUNCT
cana-3871	56	70	1	1	NUM
cana-3871	56	71	}	}	PUNCT
cana-3871	56	72	,	,	PUNCT
cana-3871	56	73	i	i	PRON
cana-3871	56	74	=	=	NOUN
cana-3871	56	75	1	1	NUM
cana-3871	56	76	,	,	PUNCT
cana-3871	56	77	2	2	NUM
cana-3871	56	78	,	,	PUNCT
cana-3871	56	79	...	...	PUNCT
cana-3871	56	80	,	,	PUNCT
cana-3871	56	81	n	n	CCONJ
cana-3871	56	82	}	}	PUNCT
cana-3871	56	83	since	since	ADV
cana-3871	56	84	,	,	PUNCT
cana-3871	56	85	each	each	DET
cana-3871	56	86	bis	bis	X
cana-3871	56	87	has	have	VERB
cana-3871	56	88	two	two	NUM
cana-3871	56	89	choices	choice	NOUN
cana-3871	56	90	0	0	NUM
cana-3871	56	91	and	and	CCONJ
cana-3871	56	92	1	1	NUM
cana-3871	56	93	,	,	PUNCT
cana-3871	56	94	so	so	SCONJ
cana-3871	56	95	there	there	PRON
cana-3871	56	96	are	be	VERB
cana-3871	56	97	2n	2n	NUM
cana-3871	56	98	elements	element	NOUN
cana-3871	56	99	in	in	ADP
cana-3871	56	100	ℤ	ℤ	PROPN
cana-3871	56	101	2	2	NUM
cana-3871	56	102	n	n	NOUN
cana-3871	57	1	|	|	ADV
cana-3871	57	2	ℤ	ℤ	PROPN
cana-3871	57	3	2	2	NUM
cana-3871	57	4	n	n	NOUN
cana-3871	57	5	|	|	NOUN
cana-3871	57	6	=	=	SYM
cana-3871	57	7	2n	2n	NUM
cana-3871	57	8	the	the	DET
cana-3871	57	9	set	set	NOUN
cana-3871	57	10	of	of	ADP
cana-3871	57	11	zero	zero	NUM
cana-3871	57	12	divisors	divisor	NOUN
cana-3871	57	13	of	of	ADP
cana-3871	57	14	ℤ	ℤ	PROPN
cana-3871	57	15	2	2	PROPN
cana-3871	57	16	n	n	NOUN
cana-3871	57	17	is	be	AUX
cana-3871	57	18	denoted	denote	VERB
cana-3871	57	19	by	by	ADP
cana-3871	57	20	ℤ	ℤ	PROPN
cana-3871	57	21	(	(	PUNCT
cana-3871	57	22	ℤ	ℤ	PROPN
cana-3871	57	23	2	2	NUM
cana-3871	57	24	n	n	CCONJ
cana-3871	57	25	)	)	PUNCT
cana-3871	57	26	and	and	CCONJ
cana-3871	57	27	is	be	AUX
cana-3871	57	28	given	give	VERB
cana-3871	57	29	by	by	ADP
cana-3871	57	30	,	,	PUNCT
cana-3871	57	31	ℤ	ℤ	PROPN
cana-3871	57	32	(	(	PUNCT
cana-3871	57	33	ℤ	ℤ	PROPN
cana-3871	57	34	2	2	NUM
cana-3871	57	35	n	n	CCONJ
cana-3871	57	36	)	)	PUNCT
cana-3871	58	1	=	=	PRON
cana-3871	58	2	{	{	PUNCT
cana-3871	58	3	(	(	PUNCT
cana-3871	58	4	b1	b1	NOUN
cana-3871	58	5	,	,	PUNCT
cana-3871	58	6	b2	b2	NOUN
cana-3871	58	7	,	,	PUNCT
cana-3871	58	8	b3	b3	PROPN
cana-3871	58	9	,	,	PUNCT
cana-3871	58	10	...	...	PUNCT
cana-3871	58	11	,	,	PUNCT
cana-3871	58	12	bn	bn	X
cana-3871	58	13	)	)	PUNCT
cana-3871	58	14	|	|	ADV
cana-3871	58	15	bis	bi	VERB
cana-3871	58	16	∈	∈	NOUN
cana-3871	58	17	{	{	PUNCT
cana-3871	58	18	0	0	NUM
cana-3871	58	19	,	,	PUNCT
cana-3871	58	20	1	1	NUM
cana-3871	58	21	}	}	PUNCT
cana-3871	58	22	,	,	PUNCT
cana-3871	58	23	all	all	DET
cana-3871	58	24	bi	bi	ADJ
cana-3871	58	25	≠	≠	PROPN
cana-3871	58	26	0	0	NUM
cana-3871	58	27	,	,	PUNCT
cana-3871	58	28	and	and	CCONJ
cana-3871	58	29	all	all	DET
cana-3871	58	30	bi≠1	bi≠1	ADJ
cana-3871	58	31	,	,	PUNCT
cana-3871	58	32	i	i	PRON
cana-3871	58	33	=	=	NOUN
cana-3871	58	34	1	1	NUM
cana-3871	58	35	,	,	PUNCT
cana-3871	58	36	2	2	NUM
cana-3871	58	37	,	,	PUNCT
cana-3871	58	38	...	...	PUNCT
cana-3871	58	39	,	,	PUNCT
cana-3871	58	40	n	n	CCONJ
cana-3871	58	41	}	}	PUNCT
cana-3871	58	42	∴	∴	PROPN
cana-3871	58	43	|ℤ	|ℤ	PUNCT
cana-3871	58	44	(	(	PUNCT
cana-3871	58	45	ℤ	ℤ	PROPN
cana-3871	58	46	2	2	NUM
cana-3871	58	47	n	n	CCONJ
cana-3871	58	48	)	)	PUNCT
cana-3871	58	49	|	|	ADV
cana-3871	58	50	=	=	SYM
cana-3871	58	51	2n	2n	NUM
cana-3871	59	1	−	−	ADP
cana-3871	59	2	2	2	NUM
cana-3871	59	3	the	the	DET
cana-3871	59	4	vertices	vertex	NOUN
cana-3871	59	5	(	(	PUNCT
cana-3871	59	6	1	1	NUM
cana-3871	59	7	,	,	PUNCT
cana-3871	59	8	0	0	NUM
cana-3871	59	9	,	,	PUNCT
cana-3871	59	10	0	0	NUM
cana-3871	59	11	,	,	PUNCT
cana-3871	59	12	...	...	PUNCT
cana-3871	59	13	,	,	PUNCT
cana-3871	59	14	0	0	NUM
cana-3871	59	15	)	)	PUNCT
cana-3871	59	16	,	,	PUNCT
cana-3871	59	17	(	(	PUNCT
cana-3871	59	18	0	0	NUM
cana-3871	59	19	,	,	PUNCT
cana-3871	59	20	1	1	NUM
cana-3871	59	21	,	,	PUNCT
cana-3871	59	22	0	0	NUM
cana-3871	59	23	,	,	PUNCT
cana-3871	59	24	...	...	PUNCT
cana-3871	59	25	,	,	PUNCT
cana-3871	59	26	0	0	NUM
cana-3871	59	27	)	)	PUNCT
cana-3871	59	28	,	,	PUNCT
cana-3871	59	29	(	(	PUNCT
cana-3871	59	30	0	0	NUM
cana-3871	59	31	,	,	PUNCT
cana-3871	59	32	0	0	NUM
cana-3871	59	33	,	,	PUNCT
cana-3871	59	34	1	1	NUM
cana-3871	59	35	,	,	PUNCT
cana-3871	59	36	0	0	NUM
cana-3871	59	37	,	,	PUNCT
cana-3871	59	38	…	…	PUNCT
cana-3871	59	39	,	,	PUNCT
cana-3871	59	40	0	0	NUM
cana-3871	59	41	)	)	PUNCT
cana-3871	59	42	,	,	PUNCT
cana-3871	59	43	...	...	PUNCT
cana-3871	59	44	,	,	PUNCT
cana-3871	59	45	(	(	PUNCT
cana-3871	59	46	0	0	NUM
cana-3871	59	47	,	,	PUNCT
cana-3871	59	48	0	0	NUM
cana-3871	59	49	,	,	PUNCT
cana-3871	59	50	0	0	NUM
cana-3871	59	51	,	,	PUNCT
cana-3871	59	52	..	..	PUNCT
cana-3871	59	53	,	,	PUNCT
cana-3871	59	54	1	1	X
cana-3871	59	55	)	)	PUNCT
cana-3871	59	56	are	be	AUX
cana-3871	59	57	adjacent	adjacent	ADJ
cana-3871	59	58	to	to	ADP
cana-3871	59	59	(	(	PUNCT
cana-3871	59	60	0	0	NUM
cana-3871	59	61	,	,	PUNCT
cana-3871	59	62	b2	b2	NOUN
cana-3871	59	63	,	,	PUNCT
cana-3871	59	64	b3	b3	PROPN
cana-3871	59	65	,	,	PUNCT
cana-3871	59	66	...	...	PUNCT
cana-3871	59	67	,	,	PUNCT
cana-3871	59	68	bn	bn	NOUN
cana-3871	59	69	)	)	PUNCT
cana-3871	59	70	,	,	PUNCT
cana-3871	59	71	(	(	PUNCT
cana-3871	59	72	b1	b1	NOUN
cana-3871	59	73	,	,	PUNCT
cana-3871	59	74	0	0	NUM
cana-3871	59	75	,	,	PUNCT
cana-3871	59	76	b3	b3	PROPN
cana-3871	59	77	,	,	PUNCT
cana-3871	59	78	...	...	PUNCT
cana-3871	59	79	,	,	PUNCT
cana-3871	59	80	bn	bn	NOUN
cana-3871	59	81	)	)	PUNCT
cana-3871	59	82	,	,	PUNCT
cana-3871	59	83	...	...	PUNCT
cana-3871	59	84	,	,	PUNCT
cana-3871	59	85	(	(	PUNCT
cana-3871	59	86	b1	b1	NOUN
cana-3871	59	87	,	,	PUNCT
cana-3871	59	88	b2	b2	NOUN
cana-3871	59	89	,	,	PUNCT
cana-3871	59	90	b3	b3	PROPN
cana-3871	59	91	,	,	PUNCT
cana-3871	59	92	...	...	PUNCT
cana-3871	59	93	,	,	PUNCT
cana-3871	59	94	0	0	X
cana-3871	59	95	)	)	PUNCT
cana-3871	59	96	respectively	respectively	ADV
cana-3871	59	97	.	.	PUNCT
cana-3871	60	1	the	the	DET
cana-3871	60	2	vertex	vertex	NOUN
cana-3871	60	3	(	(	PUNCT
cana-3871	60	4	1	1	NUM
cana-3871	60	5	,	,	PUNCT
cana-3871	60	6	0	0	NUM
cana-3871	60	7	,	,	PUNCT
cana-3871	60	8	0	0	NUM
cana-3871	60	9	,	,	PUNCT
cana-3871	60	10	..	..	PUNCT
cana-3871	60	11	,	,	PUNCT
cana-3871	60	12	0	0	NUM
cana-3871	60	13	)	)	PUNCT
cana-3871	60	14	is	be	AUX
cana-3871	60	15	adjacent	adjacent	ADJ
cana-3871	60	16	to	to	ADP
cana-3871	60	17	(	(	PUNCT
cana-3871	60	18	0	0	NUM
cana-3871	60	19	,	,	PUNCT
cana-3871	60	20	b2	b2	NOUN
cana-3871	60	21	,	,	PUNCT
cana-3871	60	22	b3	b3	PROPN
cana-3871	60	23	,	,	PUNCT
cana-3871	60	24	..	..	PUNCT
cana-3871	60	25	,	,	PUNCT
cana-3871	60	26	bn	bn	ADJ
cana-3871	60	27	)	)	PUNCT
cana-3871	60	28	and	and	CCONJ
cana-3871	60	29	ℤ	ℤ	PROPN
cana-3871	60	30	2	2	PROPN
cana-3871	60	31	n	n	PRON
cana-3871	60	32	has	have	VERB
cana-3871	60	33	two	two	NUM
cana-3871	60	34	choices	choice	NOUN
cana-3871	60	35	0	0	NUM
cana-3871	60	36	or	or	CCONJ
cana-3871	60	37	1	1	NUM
cana-3871	60	38	but	but	CCONJ
cana-3871	60	39	all	all	DET
cana-3871	60	40	bi	bi	ADJ
cana-3871	60	41	≠0	≠0	NOUN
cana-3871	60	42	,	,	PUNCT
cana-3871	60	43	∀i	∀i	NOUN
cana-3871	60	44	=	=	SYM
cana-3871	60	45	1	1	NUM
cana-3871	60	46	,	,	PUNCT
cana-3871	60	47	2	2	NUM
cana-3871	60	48	,	,	PUNCT
cana-3871	60	49	...	...	PUNCT
cana-3871	60	50	,	,	PUNCT
cana-3871	60	51	n.	n.	NOUN
cana-3871	60	52	i.e	i.e	VERB
cana-3871	60	53	the	the	DET
cana-3871	60	54	vertex	vertex	NOUN
cana-3871	60	55	(	(	PUNCT
cana-3871	60	56	1	1	NUM
cana-3871	60	57	,	,	PUNCT
cana-3871	60	58	0	0	NUM
cana-3871	60	59	,	,	PUNCT
cana-3871	60	60	0	0	NUM
cana-3871	60	61	,	,	PUNCT
cana-3871	60	62	...	...	PUNCT
cana-3871	60	63	,	,	PUNCT
cana-3871	60	64	0	0	X
cana-3871	60	65	)	)	PUNCT
cana-3871	60	66	is	be	AUX
cana-3871	60	67	adjacent	adjacent	ADJ
cana-3871	60	68	to	to	ADP
cana-3871	60	69	(	(	PUNCT
cana-3871	60	70	0	0	NUM
cana-3871	60	71	,	,	PUNCT
cana-3871	60	72	b2	b2	NOUN
cana-3871	60	73	,	,	PUNCT
cana-3871	60	74	b3	b3	PROPN
cana-3871	60	75	,	,	PUNCT
cana-3871	60	76	...	...	PUNCT
cana-3871	60	77	,	,	PUNCT
cana-3871	60	78	bn	bn	X
cana-3871	60	79	)	)	PUNCT
cana-3871	60	80	except	except	SCONJ
cana-3871	60	81	(	(	PUNCT
cana-3871	60	82	0	0	NUM
cana-3871	60	83	,	,	PUNCT
cana-3871	60	84	0	0	NUM
cana-3871	60	85	,	,	PUNCT
cana-3871	60	86	0	0	NUM
cana-3871	60	87	,	,	PUNCT
cana-3871	60	88	...	...	PUNCT
cana-3871	60	89	,	,	PUNCT
cana-3871	60	90	0	0	NUM
cana-3871	60	91	)	)	PUNCT
cana-3871	60	92	.	.	PUNCT
cana-3871	61	1	i.e	i.e	PRON
cana-3871	61	2	the	the	DET
cana-3871	61	3	degree	degree	NOUN
cana-3871	61	4	of	of	ADP
cana-3871	61	5	(	(	PUNCT
cana-3871	61	6	1	1	NUM
cana-3871	61	7	,	,	PUNCT
cana-3871	61	8	0	0	NUM
cana-3871	61	9	,	,	PUNCT
cana-3871	61	10	0	0	NUM
cana-3871	61	11	,	,	PUNCT
cana-3871	61	12	...	...	PUNCT
cana-3871	61	13	,	,	PUNCT
cana-3871	61	14	0	0	X
cana-3871	61	15	)	)	PUNCT
cana-3871	61	16	is	be	AUX
cana-3871	61	17	2n−1	2n−1	NUM
cana-3871	61	18	−	−	NOUN
cana-3871	61	19	1	1	NUM
cana-3871	61	20	since	since	SCONJ
cana-3871	61	21	(	(	PUNCT
cana-3871	61	22	1	1	NUM
cana-3871	61	23	,	,	PUNCT
cana-3871	61	24	0	0	NUM
cana-3871	61	25	,	,	PUNCT
cana-3871	61	26	0	0	NUM
cana-3871	61	27	,	,	PUNCT
cana-3871	61	28	...	...	PUNCT
cana-3871	61	29	,	,	PUNCT
cana-3871	61	30	0	0	X
cana-3871	61	31	)	)	PUNCT
cana-3871	61	32	is	be	AUX
cana-3871	61	33	adjacent	adjacent	ADJ
cana-3871	61	34	with	with	ADP
cana-3871	61	35	2n−1	2n−1	NUM
cana-3871	61	36	−	−	NUM
cana-3871	61	37	1	1	NUM
cana-3871	61	38	number	number	NOUN
cana-3871	61	39	of	of	ADP
cana-3871	61	40	vertices	vertex	NOUN
cana-3871	61	41	.	.	PUNCT
cana-3871	62	1	similarly	similarly	ADV
cana-3871	62	2	,	,	PUNCT
cana-3871	62	3	the	the	DET
cana-3871	62	4	degree	degree	NOUN
cana-3871	62	5	of	of	ADP
cana-3871	62	6	(	(	PUNCT
cana-3871	62	7	0	0	NUM
cana-3871	62	8	,	,	PUNCT
cana-3871	62	9	1	1	NUM
cana-3871	62	10	,	,	PUNCT
cana-3871	62	11	0	0	NUM
cana-3871	62	12	,	,	PUNCT
cana-3871	62	13	...	...	PUNCT
cana-3871	62	14	,	,	PUNCT
cana-3871	62	15	0	0	NUM
cana-3871	62	16	)	)	PUNCT
cana-3871	62	17	,	,	PUNCT
cana-3871	62	18	(	(	PUNCT
cana-3871	62	19	0	0	NUM
cana-3871	62	20	,	,	PUNCT
cana-3871	62	21	0	0	NUM
cana-3871	62	22	,	,	PUNCT
cana-3871	62	23	1	1	NUM
cana-3871	62	24	,	,	PUNCT
cana-3871	62	25	0	0	NUM
cana-3871	62	26	,	,	PUNCT
cana-3871	62	27	...	...	PUNCT
cana-3871	62	28	,	,	PUNCT
cana-3871	62	29	0	0	NUM
cana-3871	62	30	)	)	PUNCT
cana-3871	62	31	,	,	PUNCT
cana-3871	62	32	(	(	PUNCT
cana-3871	62	33	0	0	NUM
cana-3871	62	34	,	,	PUNCT
cana-3871	62	35	0	0	NUM
cana-3871	62	36	,	,	PUNCT
cana-3871	62	37	0	0	NUM
cana-3871	62	38	,	,	PUNCT
cana-3871	62	39	1	1	NUM
cana-3871	62	40	,	,	PUNCT
cana-3871	62	41	0	0	NUM
cana-3871	62	42	,	,	PUNCT
cana-3871	62	43	...	...	PUNCT
cana-3871	62	44	,	,	PUNCT
cana-3871	62	45	0	0	NUM
cana-3871	62	46	)	)	PUNCT
cana-3871	62	47	,	,	PUNCT
cana-3871	62	48	.....	.....	PUNCT
cana-3871	62	49	,	,	PUNCT
cana-3871	62	50	(	(	PUNCT
cana-3871	62	51	0	0	NUM
cana-3871	62	52	,	,	PUNCT
cana-3871	62	53	0	0	NUM
cana-3871	62	54	,	,	PUNCT
cana-3871	62	55	0	0	NUM
cana-3871	62	56	,	,	PUNCT
cana-3871	62	57	...	...	PUNCT
cana-3871	62	58	,	,	PUNCT
cana-3871	62	59	1	1	X
cana-3871	62	60	)	)	PUNCT
cana-3871	62	61	is	be	AUX
cana-3871	62	62	2n−1	2n−1	NUM
cana-3871	62	63	−	−	NOUN
cana-3871	62	64	1	1	NUM
cana-3871	62	65	.	.	PUNCT
cana-3871	63	1	∴	∴	VERB
cana-3871	63	2	these	these	DET
cana-3871	63	3	n	n	PRON
cana-3871	63	4	elements	element	NOUN
cana-3871	63	5	have	have	VERB
cana-3871	63	6	2n−1	2n−1	NUM
cana-3871	63	7	−	−	NUM
cana-3871	63	8	1	1	NUM
cana-3871	63	9	degree	degree	NOUN
cana-3871	63	10	.	.	PUNCT
cana-3871	64	1	∴	∴	NOUN
cana-3871	64	2	the	the	DET
cana-3871	64	3	n	n	NOUN
cana-3871	64	4	vertices	vertice	VERB
cana-3871	64	5	in	in	ADP
cana-3871	64	6	the	the	DET
cana-3871	64	7	zero	zero	NUM
cana-3871	64	8	divisor	divisor	NOUN
cana-3871	64	9	graph	graph	NOUN
cana-3871	64	10	of	of	ADP
cana-3871	64	11	ℤ	ℤ	PROPN
cana-3871	64	12	2	2	NUM
cana-3871	64	13	n	n	CCONJ
cana-3871	64	14	,	,	PUNCT
cana-3871	64	15	γ(ℤ	γ(ℤ	NUM
cana-3871	64	16	2	2	NUM
cana-3871	64	17	n	n	CCONJ
cana-3871	64	18	)	)	PUNCT
cana-3871	64	19	have	have	VERB
cana-3871	64	20	2n−1	2n−1	NUM
cana-3871	64	21	−	−	NUM
cana-3871	64	22	1	1	NUM
cana-3871	64	23	degree	degree	NOUN
cana-3871	64	24	.	.	PUNCT
cana-3871	65	1	3.1.1	3.1.1	NUM
cana-3871	65	2	example	example	NOUN
cana-3871	65	3	b3	b3	PROPN
cana-3871	65	4	=	=	SYM
cana-3871	65	5	ℤ2	ℤ2	PROPN
cana-3871	65	6	3	3	NUM
cana-3871	65	7	=	=	SYM
cana-3871	65	8	ℤ2	ℤ2	PROPN
cana-3871	65	9	×	×	NOUN
cana-3871	65	10	ℤ2	ℤ2	PROPN
cana-3871	65	11	×	×	PROPN
cana-3871	65	12	ℤ2	ℤ2	PROPN
cana-3871	65	13	communications	communication	NOUN
cana-3871	65	14	on	on	ADP
cana-3871	65	15	applied	apply	VERB
cana-3871	65	16	nonlinear	nonlinear	ADJ
cana-3871	65	17	analysis	analysis	NOUN
cana-3871	65	18	issn	issn	NOUN
cana-3871	65	19	:	:	PUNCT
cana-3871	65	20	1074	1074	NUM
cana-3871	65	21	-	-	PUNCT
cana-3871	65	22	133x	133x	NUM
cana-3871	65	23	vol	vol	NOUN
cana-3871	65	24	32	32	NUM
cana-3871	65	25	no	no	NOUN
cana-3871	65	26	.	.	PUNCT
cana-3871	66	1	7s	7	NOUN
cana-3871	66	2	(	(	PUNCT
cana-3871	66	3	2025	2025	NUM
cana-3871	66	4	)	)	PUNCT
cana-3871	66	5	945	945	NUM
cana-3871	66	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	66	7	fig	fig	NOUN
cana-3871	66	8	5	5	NUM
cana-3871	66	9	:	:	PUNCT
cana-3871	66	10	γ(ℤ2	γ(ℤ2	PROPN
cana-3871	66	11	×	×	NOUN
cana-3871	66	12	ℤ2	ℤ2	PROPN
cana-3871	66	13	×	×	PROPN
cana-3871	66	14	ℤ2	ℤ2	PROPN
cana-3871	66	15	)	)	PUNCT
cana-3871	67	1	ℤ	ℤ	PROPN
cana-3871	67	2	2	2	NUM
cana-3871	67	3	n	n	NOUN
cana-3871	67	4	=	=	NOUN
cana-3871	67	5	ℤ2	ℤ2	PROPN
cana-3871	67	6	×ℤ2	×ℤ2	PROPN
cana-3871	67	7	×ℤ2	×ℤ2	NOUN
cana-3871	67	8	=	=	SYM
cana-3871	67	9	{	{	PUNCT
cana-3871	67	10	(	(	PUNCT
cana-3871	67	11	0	0	NUM
cana-3871	67	12	,	,	PUNCT
cana-3871	67	13	0	0	NUM
cana-3871	67	14	,	,	PUNCT
cana-3871	67	15	0	0	NUM
cana-3871	67	16	)	)	PUNCT
cana-3871	67	17	,	,	PUNCT
cana-3871	67	18	(	(	PUNCT
cana-3871	67	19	0	0	NUM
cana-3871	67	20	,	,	PUNCT
cana-3871	67	21	0	0	NUM
cana-3871	67	22	,	,	PUNCT
cana-3871	67	23	1	1	NUM
cana-3871	67	24	)	)	PUNCT
cana-3871	67	25	,	,	PUNCT
cana-3871	67	26	(	(	PUNCT
cana-3871	67	27	0	0	NUM
cana-3871	67	28	,	,	PUNCT
cana-3871	67	29	1	1	NUM
cana-3871	67	30	,	,	PUNCT
cana-3871	67	31	0	0	NUM
cana-3871	67	32	)	)	PUNCT
cana-3871	67	33	,	,	PUNCT
cana-3871	67	34	(	(	PUNCT
cana-3871	67	35	0	0	NUM
cana-3871	67	36	,	,	PUNCT
cana-3871	67	37	1	1	NUM
cana-3871	67	38	,	,	PUNCT
cana-3871	67	39	1	1	NUM
cana-3871	67	40	)	)	PUNCT
cana-3871	67	41	,	,	PUNCT
cana-3871	67	42	(	(	PUNCT
cana-3871	67	43	1	1	NUM
cana-3871	67	44	,	,	PUNCT
cana-3871	67	45	0	0	NUM
cana-3871	67	46	,	,	PUNCT
cana-3871	67	47	1	1	NUM
cana-3871	67	48	)	)	PUNCT
cana-3871	67	49	,	,	PUNCT
cana-3871	67	50	(	(	PUNCT
cana-3871	67	51	1	1	NUM
cana-3871	67	52	,	,	PUNCT
cana-3871	67	53	1	1	NUM
cana-3871	67	54	,	,	PUNCT
cana-3871	67	55	0	0	NUM
cana-3871	67	56	)	)	PUNCT
cana-3871	67	57	,	,	PUNCT
cana-3871	67	58	(	(	PUNCT
cana-3871	67	59	1	1	NUM
cana-3871	67	60	,	,	PUNCT
cana-3871	67	61	0	0	NUM
cana-3871	67	62	,	,	PUNCT
cana-3871	67	63	0	0	NUM
cana-3871	67	64	)	)	PUNCT
cana-3871	67	65	,	,	PUNCT
cana-3871	67	66	(	(	PUNCT
cana-3871	67	67	1	1	NUM
cana-3871	67	68	,	,	PUNCT
cana-3871	67	69	1	1	NUM
cana-3871	67	70	,	,	PUNCT
cana-3871	67	71	1	1	NUM
cana-3871	67	72	)	)	PUNCT
cana-3871	67	73	}	}	PUNCT
cana-3871	67	74	ℤ	ℤ	PROPN
cana-3871	67	75	(	(	PUNCT
cana-3871	67	76	ℤ2	ℤ2	PROPN
cana-3871	67	77	×	×	PROPN
cana-3871	67	78	ℤ2	ℤ2	PROPN
cana-3871	67	79	×	×	PROPN
cana-3871	67	80	ℤ2	ℤ2	PROPN
cana-3871	67	81	)	)	PUNCT
cana-3871	67	82	=	=	PRON
cana-3871	67	83	{	{	PUNCT
cana-3871	67	84	(	(	PUNCT
cana-3871	67	85	0	0	NUM
cana-3871	67	86	,	,	PUNCT
cana-3871	67	87	0	0	NUM
cana-3871	67	88	,	,	PUNCT
cana-3871	67	89	1	1	NUM
cana-3871	67	90	)	)	PUNCT
cana-3871	67	91	,	,	PUNCT
cana-3871	67	92	(	(	PUNCT
cana-3871	67	93	0	0	NUM
cana-3871	67	94	,	,	PUNCT
cana-3871	67	95	1	1	NUM
cana-3871	67	96	,	,	PUNCT
cana-3871	67	97	0	0	NUM
cana-3871	67	98	)	)	PUNCT
cana-3871	67	99	,	,	PUNCT
cana-3871	67	100	(	(	PUNCT
cana-3871	67	101	0	0	NUM
cana-3871	67	102	,	,	PUNCT
cana-3871	67	103	1	1	NUM
cana-3871	67	104	,	,	PUNCT
cana-3871	67	105	1	1	NUM
cana-3871	67	106	)	)	PUNCT
cana-3871	67	107	,	,	PUNCT
cana-3871	67	108	(	(	PUNCT
cana-3871	67	109	1	1	NUM
cana-3871	67	110	,	,	PUNCT
cana-3871	67	111	0	0	NUM
cana-3871	67	112	,	,	PUNCT
cana-3871	67	113	1	1	NUM
cana-3871	67	114	)	)	PUNCT
cana-3871	67	115	,	,	PUNCT
cana-3871	67	116	(	(	PUNCT
cana-3871	67	117	1	1	NUM
cana-3871	67	118	,	,	PUNCT
cana-3871	67	119	1	1	NUM
cana-3871	67	120	,	,	PUNCT
cana-3871	67	121	0	0	NUM
cana-3871	67	122	)	)	PUNCT
cana-3871	67	123	,	,	PUNCT
cana-3871	67	124	(	(	PUNCT
cana-3871	67	125	1	1	NUM
cana-3871	67	126	,	,	PUNCT
cana-3871	67	127	0	0	NUM
cana-3871	67	128	,	,	PUNCT
cana-3871	67	129	0	0	NUM
cana-3871	67	130	)	)	PUNCT
cana-3871	67	131	}	}	PUNCT
cana-3871	67	132	the	the	DET
cana-3871	67	133	zero	zero	NUM
cana-3871	67	134	-	-	PUNCT
cana-3871	67	135	divisor	divisor	NOUN
cana-3871	67	136	graph	graph	NOUN
cana-3871	67	137	of	of	ADP
cana-3871	67	138	ℤ2	ℤ2	PROPN
cana-3871	67	139	×	×	PROPN
cana-3871	67	140	ℤ2	ℤ2	PROPN
cana-3871	67	141	×	×	PROPN
cana-3871	67	142	ℤ2	ℤ2	PROPN
cana-3871	67	143	is	be	AUX
cana-3871	67	144	given	give	VERB
cana-3871	67	145	in	in	ADP
cana-3871	67	146	the	the	DET
cana-3871	67	147	figure	figure	NOUN
cana-3871	67	148	above	above	ADV
cana-3871	67	149	.	.	PUNCT
cana-3871	68	1	here	here	ADV
cana-3871	68	2	,	,	PUNCT
cana-3871	68	3	n	n	PROPN
cana-3871	68	4	=	=	SYM
cana-3871	68	5	3	3	X
cana-3871	68	6	.	.	NOUN
cana-3871	68	7	number	number	NOUN
cana-3871	68	8	of	of	ADP
cana-3871	68	9	vertices	vertex	NOUN
cana-3871	68	10	in	in	ADP
cana-3871	68	11	the	the	DET
cana-3871	68	12	graph	graph	NOUN
cana-3871	68	13	of	of	ADP
cana-3871	68	14	ℤ	ℤ	PROPN
cana-3871	68	15	(	(	PUNCT
cana-3871	68	16	ℤ2	ℤ2	PROPN
cana-3871	68	17	×	×	PROPN
cana-3871	68	18	ℤ2	ℤ2	PROPN
cana-3871	68	19	×	×	PROPN
cana-3871	68	20	ℤ2	ℤ2	PROPN
cana-3871	68	21	)	)	PUNCT
cana-3871	68	22	=	=	NOUN
cana-3871	69	1	23	23	NUM
cana-3871	69	2	−	−	NUM
cana-3871	69	3	2	2	NUM
cana-3871	69	4	=	=	SYM
cana-3871	69	5	6	6	NUM
cana-3871	69	6	degree	degree	NOUN
cana-3871	69	7	of	of	ADP
cana-3871	69	8	vertex	vertex	NOUN
cana-3871	69	9	(	(	PUNCT
cana-3871	69	10	0	0	NUM
cana-3871	69	11	,	,	PUNCT
cana-3871	69	12	0	0	NUM
cana-3871	69	13	,	,	PUNCT
cana-3871	69	14	1	1	NUM
cana-3871	69	15	)	)	PUNCT
cana-3871	69	16	=	=	SYM
cana-3871	70	1	23−1	23−1	NUM
cana-3871	70	2	−	−	NOUN
cana-3871	70	3	1	1	NUM
cana-3871	71	1	=	=	SYM
cana-3871	71	2	22	22	NUM
cana-3871	71	3	−	−	NOUN
cana-3871	71	4	1	1	NUM
cana-3871	71	5	=	=	SYM
cana-3871	71	6	3	3	NUM
cana-3871	71	7	degree	degree	NOUN
cana-3871	71	8	of	of	ADP
cana-3871	71	9	vertex	vertex	NOUN
cana-3871	71	10	(	(	PUNCT
cana-3871	71	11	0	0	NUM
cana-3871	71	12	,	,	PUNCT
cana-3871	71	13	1	1	NUM
cana-3871	71	14	,	,	PUNCT
cana-3871	71	15	0	0	NUM
cana-3871	71	16	)	)	PUNCT
cana-3871	71	17	=	=	SYM
cana-3871	72	1	23−1	23−1	NUM
cana-3871	72	2	−	−	NOUN
cana-3871	72	3	1	1	NUM
cana-3871	73	1	=	=	SYM
cana-3871	73	2	22	22	NUM
cana-3871	73	3	−	−	NOUN
cana-3871	73	4	1	1	NUM
cana-3871	73	5	=	=	SYM
cana-3871	73	6	3	3	NUM
cana-3871	73	7	degree	degree	NOUN
cana-3871	73	8	of	of	ADP
cana-3871	73	9	vertex	vertex	NOUN
cana-3871	73	10	(	(	PUNCT
cana-3871	73	11	0	0	NUM
cana-3871	73	12	,	,	PUNCT
cana-3871	73	13	0	0	NUM
cana-3871	73	14	,	,	PUNCT
cana-3871	73	15	1	1	NUM
cana-3871	73	16	)	)	PUNCT
cana-3871	73	17	=	=	SYM
cana-3871	74	1	23−1	23−1	NUM
cana-3871	74	2	−	−	NOUN
cana-3871	74	3	1	1	NUM
cana-3871	75	1	=	=	SYM
cana-3871	75	2	22	22	NUM
cana-3871	75	3	−	−	NOUN
cana-3871	75	4	1	1	NUM
cana-3871	75	5	=	=	SYM
cana-3871	75	6	3	3	NUM
cana-3871	75	7	∴	∴	NOUN
cana-3871	75	8	3	3	NUM
cana-3871	75	9	vertices	vertex	NOUN
cana-3871	75	10	have	have	VERB
cana-3871	75	11	degree	degree	NOUN
cana-3871	75	12	3	3	NUM
cana-3871	75	13	.	.	PUNCT
cana-3871	76	1	∴	∴	PROPN
cana-3871	76	2	the	the	DET
cana-3871	76	3	theorem	theorem	NOUN
cana-3871	76	4	holds	hold	VERB
cana-3871	76	5	.	.	PUNCT
cana-3871	77	1	3.1.2	3.1.2	NUM
cana-3871	77	2	example	example	NOUN
cana-3871	77	3	ℤ2	ℤ2	PROPN
cana-3871	77	4	4	4	NUM
cana-3871	77	5	=	=	SYM
cana-3871	77	6	ℤ2	ℤ2	PROPN
cana-3871	77	7	×	×	NOUN
cana-3871	77	8	ℤ2	ℤ2	PROPN
cana-3871	77	9	×	×	PROPN
cana-3871	77	10	ℤ2	ℤ2	PROPN
cana-3871	77	11	×	×	PROPN
cana-3871	77	12	ℤ2	ℤ2	PROPN
cana-3871	77	13	fig	fig	NOUN
cana-3871	77	14	6	6	NUM
cana-3871	77	15	:	:	PUNCT
cana-3871	77	16	γ(ℤ2	γ(ℤ2	PROPN
cana-3871	77	17	×	×	NOUN
cana-3871	77	18	ℤ2	ℤ2	PROPN
cana-3871	77	19	×	×	PROPN
cana-3871	77	20	ℤ2	ℤ2	PROPN
cana-3871	77	21	×	×	PROPN
cana-3871	77	22	ℤ2	ℤ2	PROPN
cana-3871	77	23	)	)	PUNCT
cana-3871	77	24	the	the	DET
cana-3871	77	25	zero	zero	NUM
cana-3871	77	26	-	-	PUNCT
cana-3871	77	27	divisor	divisor	NOUN
cana-3871	77	28	graph	graph	NOUN
cana-3871	77	29	of	of	ADP
cana-3871	77	30	ℤ2	ℤ2	PROPN
cana-3871	77	31	×	×	PROPN
cana-3871	77	32	ℤ2	ℤ2	PROPN
cana-3871	77	33	×	×	PROPN
cana-3871	77	34	ℤ2	ℤ2	PROPN
cana-3871	77	35	×	×	PROPN
cana-3871	77	36	ℤ2	ℤ2	PROPN
cana-3871	77	37	is	be	AUX
cana-3871	77	38	shown	show	VERB
cana-3871	77	39	in	in	ADP
cana-3871	77	40	the	the	DET
cana-3871	77	41	figure	figure	NOUN
cana-3871	77	42	above	above	ADV
cana-3871	77	43	.	.	PUNCT
cana-3871	78	1	here	here	ADV
cana-3871	78	2	,	,	PUNCT
cana-3871	78	3	n	n	PROPN
cana-3871	78	4	=	=	SYM
cana-3871	78	5	4	4	NUM
cana-3871	78	6	.	.	PUNCT
cana-3871	79	1	the	the	DET
cana-3871	79	2	number	number	NOUN
cana-3871	79	3	of	of	ADP
cana-3871	79	4	vertices	vertex	NOUN
cana-3871	79	5	in	in	ADP
cana-3871	79	6	the	the	DET
cana-3871	79	7	graph	graph	NOUN
cana-3871	79	8	of	of	ADP
cana-3871	79	9	zero	zero	NUM
cana-3871	79	10	divisors	divisor	NOUN
cana-3871	79	11	of	of	ADP
cana-3871	79	12	ℤ2	ℤ2	PROPN
cana-3871	79	13	×	×	PROPN
cana-3871	79	14	ℤ2	ℤ2	PROPN
cana-3871	79	15	×	×	PROPN
cana-3871	79	16	ℤ2	ℤ2	PROPN
cana-3871	79	17	×	×	PROPN
cana-3871	79	18	ℤ2	ℤ2	PROPN
cana-3871	79	19	is	be	AUX
cana-3871	79	20	:	:	PUNCT
cana-3871	79	21	24	24	NUM
cana-3871	79	22	−	−	NUM
cana-3871	79	23	2	2	NUM
cana-3871	79	24	=	=	SYM
cana-3871	79	25	14	14	NUM
cana-3871	79	26	.	.	PUNCT
cana-3871	80	1	the	the	DET
cana-3871	80	2	degree	degree	NOUN
cana-3871	80	3	of	of	ADP
cana-3871	80	4	the	the	DET
cana-3871	80	5	vertices	vertex	NOUN
cana-3871	80	6	is	be	AUX
cana-3871	80	7	computed	compute	VERB
cana-3871	80	8	as	as	SCONJ
cana-3871	80	9	follows	follow	VERB
cana-3871	80	10	:	:	PUNCT
cana-3871	80	11	degree	degree	NOUN
cana-3871	80	12	of	of	ADP
cana-3871	80	13	vertex	vertex	NOUN
cana-3871	80	14	(	(	PUNCT
cana-3871	80	15	0	0	NUM
cana-3871	80	16	,	,	PUNCT
cana-3871	80	17	0	0	NUM
cana-3871	80	18	,	,	PUNCT
cana-3871	80	19	0	0	NUM
cana-3871	80	20	,	,	PUNCT
cana-3871	80	21	1	1	X
cana-3871	80	22	)	)	PUNCT
cana-3871	80	23	=	=	SYM
cana-3871	81	1	24−1	24−1	NUM
cana-3871	81	2	−	−	NOUN
cana-3871	81	3	1	1	NUM
cana-3871	81	4	=	=	SYM
cana-3871	81	5	22	22	NUM
cana-3871	81	6	−	−	NOUN
cana-3871	81	7	1	1	NUM
cana-3871	81	8	=	=	SYM
cana-3871	81	9	7	7	NUM
cana-3871	81	10	degree	degree	NOUN
cana-3871	81	11	of	of	ADP
cana-3871	81	12	vertex	vertex	NOUN
cana-3871	81	13	(	(	PUNCT
cana-3871	81	14	0	0	NUM
cana-3871	81	15	,	,	PUNCT
cana-3871	81	16	0	0	NUM
cana-3871	81	17	,	,	PUNCT
cana-3871	81	18	1	1	NUM
cana-3871	81	19	,	,	PUNCT
cana-3871	81	20	0	0	NUM
cana-3871	81	21	)	)	PUNCT
cana-3871	81	22	=	=	SYM
cana-3871	81	23	24−1	24−1	NUM
cana-3871	81	24	−	−	NOUN
cana-3871	81	25	1	1	NUM
cana-3871	81	26	=	=	SYM
cana-3871	81	27	22	22	NUM
cana-3871	81	28	−	−	NOUN
cana-3871	81	29	1	1	NUM
cana-3871	81	30	=	=	SYM
cana-3871	81	31	7	7	NUM
cana-3871	81	32	communications	communication	NOUN
cana-3871	81	33	on	on	ADP
cana-3871	81	34	applied	apply	VERB
cana-3871	81	35	nonlinear	nonlinear	ADJ
cana-3871	81	36	analysis	analysis	NOUN
cana-3871	81	37	issn	issn	NOUN
cana-3871	81	38	:	:	PUNCT
cana-3871	81	39	1074	1074	NUM
cana-3871	81	40	-	-	PUNCT
cana-3871	81	41	133x	133x	NUM
cana-3871	81	42	vol	vol	NOUN
cana-3871	81	43	32	32	NUM
cana-3871	81	44	no	no	NOUN
cana-3871	81	45	.	.	PUNCT
cana-3871	82	1	7s	7	NOUN
cana-3871	82	2	(	(	PUNCT
cana-3871	82	3	2025	2025	NUM
cana-3871	82	4	)	)	PUNCT
cana-3871	82	5	946	946	NUM
cana-3871	82	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-3871	82	7	2	2	NUM
cana-3871	82	8	degree	degree	NOUN
cana-3871	82	9	of	of	ADP
cana-3871	82	10	vertex	vertex	NOUN
cana-3871	82	11	(	(	PUNCT
cana-3871	82	12	0	0	NUM
cana-3871	82	13	,	,	PUNCT
cana-3871	82	14	1	1	NUM
cana-3871	82	15	,	,	PUNCT
cana-3871	82	16	0	0	NUM
cana-3871	82	17	,	,	PUNCT
cana-3871	82	18	0	0	NUM
cana-3871	82	19	)	)	PUNCT
cana-3871	82	20	=	=	SYM
cana-3871	83	1	24−1	24−1	NUM
cana-3871	83	2	−	−	NOUN
cana-3871	83	3	1	1	NUM
cana-3871	83	4	=	=	SYM
cana-3871	83	5	22	22	NUM
cana-3871	83	6	−	−	NOUN
cana-3871	83	7	1	1	NUM
cana-3871	83	8	=	=	SYM
cana-3871	83	9	7	7	NUM
cana-3871	83	10	degree	degree	NOUN
cana-3871	83	11	of	of	ADP
cana-3871	83	12	vertex	vertex	NOUN
cana-3871	83	13	(	(	PUNCT
cana-3871	83	14	1	1	NUM
cana-3871	83	15	,	,	PUNCT
cana-3871	83	16	0	0	NUM
cana-3871	83	17	,	,	PUNCT
cana-3871	83	18	0	0	NUM
cana-3871	83	19	,	,	PUNCT
cana-3871	83	20	0	0	NUM
cana-3871	83	21	)	)	PUNCT
cana-3871	83	22	=	=	SYM
cana-3871	83	23	24−1	24−1	NUM
cana-3871	83	24	−	−	NOUN
cana-3871	83	25	1	1	NUM
cana-3871	83	26	=	=	SYM
cana-3871	83	27	22	22	NUM
cana-3871	83	28	−	−	NOUN
cana-3871	83	29	1	1	NUM
cana-3871	83	30	=	=	SYM
cana-3871	83	31	7	7	NUM
cana-3871	83	32	∴	∴	NOUN
cana-3871	83	33	4	4	NUM
cana-3871	83	34	vertices	vertex	NOUN
cana-3871	83	35	have	have	VERB
cana-3871	83	36	degree	degree	NOUN
cana-3871	83	37	7	7	NUM
cana-3871	83	38	,	,	PUNCT
cana-3871	83	39	and	and	CCONJ
cana-3871	83	40	the	the	DET
cana-3871	83	41	theorem	theorem	NOUN
cana-3871	83	42	holds	hold	VERB
cana-3871	83	43	.	.	PUNCT
cana-3871	84	1	3.1.3	3.1.3	NUM
cana-3871	84	2	example	example	NOUN
cana-3871	84	3	let	let	VERB
cana-3871	84	4	ℤ5	ℤ5	NOUN
cana-3871	84	5	=	=	VERB
cana-3871	84	6	ℤ2	ℤ2	PROPN
cana-3871	84	7	×	×	NOUN
cana-3871	84	8	ℤ2	ℤ2	PROPN
cana-3871	84	9	×	×	PROPN
cana-3871	84	10	ℤ2	ℤ2	PROPN
cana-3871	84	11	×	×	PROPN
cana-3871	84	12	ℤ2	ℤ2	PROPN
cana-3871	84	13	×	×	PROPN
cana-3871	84	14	ℤ2	ℤ2	PROPN
cana-3871	84	15	.	.	PUNCT
cana-3871	85	1	ℤ2	ℤ2	PROPN
cana-3871	85	2	×ℤ2	×ℤ2	PROPN
cana-3871	85	3	×ℤ2	×ℤ2	NOUN
cana-3871	85	4	×ℤ2	×ℤ2	NOUN
cana-3871	85	5	×ℤ2	×ℤ2	NOUN
cana-3871	85	6	=	=	SYM
cana-3871	85	7	{	{	PUNCT
cana-3871	85	8	(	(	PUNCT
cana-3871	85	9	0	0	NUM
cana-3871	85	10	,	,	PUNCT
cana-3871	85	11	0	0	NUM
cana-3871	85	12	,	,	PUNCT
cana-3871	85	13	0	0	NUM
cana-3871	85	14	,	,	PUNCT
cana-3871	85	15	0	0	NUM
cana-3871	85	16	,	,	PUNCT
cana-3871	85	17	0	0	NUM
cana-3871	85	18	)	)	PUNCT
cana-3871	85	19	,	,	PUNCT
cana-3871	85	20	(	(	PUNCT
cana-3871	85	21	0	0	NUM
cana-3871	85	22	,	,	PUNCT
cana-3871	85	23	0	0	NUM
cana-3871	85	24	,	,	PUNCT
cana-3871	85	25	0	0	NUM
cana-3871	85	26	,	,	PUNCT
cana-3871	85	27	0	0	NUM
cana-3871	85	28	,	,	PUNCT
cana-3871	85	29	1	1	NUM
cana-3871	85	30	)	)	PUNCT
cana-3871	85	31	,	,	PUNCT
cana-3871	85	32	(	(	PUNCT
cana-3871	85	33	0	0	NUM
cana-3871	85	34	,	,	PUNCT
cana-3871	85	35	0	0	NUM
cana-3871	85	36	,	,	PUNCT
cana-3871	85	37	0	0	NUM
cana-3871	85	38	,	,	PUNCT
cana-3871	85	39	1	1	NUM
cana-3871	85	40	,	,	PUNCT
cana-3871	85	41	0	0	NUM
cana-3871	85	42	)	)	PUNCT
cana-3871	85	43	,	,	PUNCT
cana-3871	85	44	(	(	PUNCT
cana-3871	85	45	0	0	NUM
cana-3871	85	46	,	,	PUNCT
cana-3871	85	47	0	0	NUM
cana-3871	85	48	,	,	PUNCT
cana-3871	85	49	0	0	NUM
cana-3871	85	50	,	,	PUNCT
cana-3871	85	51	1	1	NUM
cana-3871	85	52	,	,	PUNCT
cana-3871	85	53	1	1	NUM
cana-3871	85	54	)	)	PUNCT
cana-3871	85	55	,	,	PUNCT
cana-3871	85	56	(	(	PUNCT
cana-3871	85	57	0	0	NUM
cana-3871	85	58	,	,	PUNCT
cana-3871	85	59	0	0	NUM
cana-3871	85	60	,	,	PUNCT
cana-3871	85	61	1	1	NUM
cana-3871	85	62	,	,	PUNCT
cana-3871	85	63	0	0	NUM
cana-3871	85	64	,	,	PUNCT
cana-3871	85	65	0	0	NUM
cana-3871	85	66	)	)	PUNCT
cana-3871	85	67	,	,	PUNCT
cana-3871	85	68	(	(	PUNCT
cana-3871	85	69	0	0	NUM
cana-3871	85	70	,	,	PUNCT
cana-3871	85	71	0	0	NUM
cana-3871	85	72	,	,	PUNCT
cana-3871	85	73	1	1	NUM
cana-3871	85	74	,	,	PUNCT
cana-3871	85	75	0	0	NUM
cana-3871	85	76	,	,	PUNCT
cana-3871	85	77	1	1	NUM
cana-3871	85	78	)	)	PUNCT
cana-3871	85	79	,	,	PUNCT
cana-3871	85	80	(	(	PUNCT
cana-3871	85	81	0	0	NUM
cana-3871	85	82	,	,	PUNCT
cana-3871	85	83	0	0	NUM
cana-3871	85	84	,	,	PUNCT
cana-3871	85	85	1	1	NUM
cana-3871	85	86	,	,	PUNCT
cana-3871	85	87	1	1	NUM
cana-3871	85	88	,	,	PUNCT
cana-3871	85	89	0	0	NUM
cana-3871	85	90	)	)	PUNCT
cana-3871	85	91	,	,	PUNCT
cana-3871	85	92	(	(	PUNCT
cana-3871	85	93	0	0	NUM
cana-3871	85	94	,	,	PUNCT
cana-3871	85	95	0	0	NUM
cana-3871	85	96	,	,	PUNCT
cana-3871	85	97	1	1	NUM
cana-3871	85	98	,	,	PUNCT
cana-3871	85	99	1	1	NUM
cana-3871	85	100	,	,	PUNCT
cana-3871	85	101	1	1	NUM
cana-3871	85	102	)	)	PUNCT
cana-3871	85	103	,	,	PUNCT
cana-3871	85	104	(	(	PUNCT
cana-3871	85	105	0	0	NUM
cana-3871	85	106	,	,	PUNCT
cana-3871	85	107	1	1	NUM
cana-3871	85	108	,	,	PUNCT
cana-3871	85	109	0	0	NUM
cana-3871	85	110	,	,	PUNCT
cana-3871	85	111	0	0	NUM
cana-3871	85	112	,	,	PUNCT
cana-3871	85	113	0	0	NUM
cana-3871	85	114	)	)	PUNCT
cana-3871	85	115	,	,	PUNCT
cana-3871	85	116	(	(	PUNCT
cana-3871	85	117	0	0	NUM
cana-3871	85	118	,	,	PUNCT
cana-3871	85	119	1	1	NUM
cana-3871	85	120	,	,	PUNCT
cana-3871	85	121	0	0	NUM
cana-3871	85	122	,	,	PUNCT
cana-3871	85	123	0	0	NUM
cana-3871	85	124	,	,	PUNCT
cana-3871	85	125	1	1	NUM
cana-3871	85	126	)	)	PUNCT
cana-3871	85	127	,	,	PUNCT
cana-3871	85	128	(	(	PUNCT
cana-3871	85	129	0	0	NUM
cana-3871	85	130	,	,	PUNCT
cana-3871	85	131	1	1	NUM
cana-3871	85	132	,	,	PUNCT
cana-3871	85	133	0	0	NUM
cana-3871	85	134	,	,	PUNCT
cana-3871	85	135	1	1	NUM
cana-3871	85	136	,	,	PUNCT
cana-3871	85	137	0	0	NUM
cana-3871	85	138	)	)	PUNCT
cana-3871	85	139	,	,	PUNCT
cana-3871	85	140	(	(	PUNCT
cana-3871	85	141	0	0	NUM
cana-3871	85	142	,	,	PUNCT
cana-3871	85	143	1	1	NUM
cana-3871	85	144	,	,	PUNCT
cana-3871	85	145	0	0	NUM
cana-3871	85	146	,	,	PUNCT
cana-3871	85	147	1	1	NUM
cana-3871	85	148	,	,	PUNCT
cana-3871	85	149	1	1	NUM
cana-3871	85	150	)	)	PUNCT
cana-3871	85	151	,	,	PUNCT
cana-3871	85	152	(	(	PUNCT
cana-3871	85	153	0	0	NUM
cana-3871	85	154	,	,	PUNCT
cana-3871	85	155	1	1	NUM
cana-3871	85	156	,	,	PUNCT
cana-3871	85	157	1	1	NUM
cana-3871	85	158	,	,	PUNCT
cana-3871	85	159	0	0	NUM
cana-3871	85	160	,	,	PUNCT
cana-3871	85	161	0	0	NUM
cana-3871	85	162	)	)	PUNCT
cana-3871	85	163	,	,	PUNCT
cana-3871	85	164	(	(	PUNCT
cana-3871	85	165	0	0	NUM
cana-3871	85	166	,	,	PUNCT
cana-3871	85	167	1	1	NUM
cana-3871	85	168	,	,	PUNCT
cana-3871	85	169	1	1	NUM
cana-3871	85	170	,	,	PUNCT
cana-3871	85	171	0	0	NUM
cana-3871	85	172	,	,	PUNCT
cana-3871	85	173	1	1	NUM
cana-3871	85	174	)	)	PUNCT
cana-3871	85	175	,	,	PUNCT
cana-3871	85	176	(	(	PUNCT
cana-3871	85	177	0	0	NUM
cana-3871	85	178	,	,	PUNCT
cana-3871	85	179	1	1	NUM
cana-3871	85	180	,	,	PUNCT
cana-3871	85	181	1	1	NUM
cana-3871	85	182	,	,	PUNCT
cana-3871	85	183	1	1	NUM
cana-3871	85	184	,	,	PUNCT
cana-3871	85	185	0	0	NUM
cana-3871	85	186	)	)	PUNCT
cana-3871	85	187	,	,	PUNCT
cana-3871	85	188	(	(	PUNCT
cana-3871	85	189	0	0	NUM
cana-3871	85	190	,	,	PUNCT
cana-3871	85	191	1	1	NUM
cana-3871	85	192	,	,	PUNCT
cana-3871	85	193	1	1	NUM
cana-3871	85	194	,	,	PUNCT
cana-3871	85	195	1	1	NUM
cana-3871	85	196	,	,	PUNCT
cana-3871	85	197	1	1	NUM
cana-3871	85	198	)	)	PUNCT
cana-3871	85	199	,	,	PUNCT
cana-3871	85	200	(	(	PUNCT
cana-3871	85	201	1	1	NUM
cana-3871	85	202	,	,	PUNCT
cana-3871	85	203	0	0	NUM
cana-3871	85	204	,	,	PUNCT
cana-3871	85	205	0	0	NUM
cana-3871	85	206	,	,	PUNCT
cana-3871	85	207	0	0	NUM
cana-3871	85	208	,	,	PUNCT
cana-3871	85	209	0	0	NUM
cana-3871	85	210	)	)	PUNCT
cana-3871	85	211	,	,	PUNCT
cana-3871	85	212	(	(	PUNCT
cana-3871	85	213	1	1	NUM
cana-3871	85	214	,	,	PUNCT
cana-3871	85	215	0	0	NUM
cana-3871	85	216	,	,	PUNCT
cana-3871	85	217	0	0	NUM
cana-3871	85	218	,	,	PUNCT
cana-3871	85	219	0	0	NUM
cana-3871	85	220	,	,	PUNCT
cana-3871	85	221	1	1	NUM
cana-3871	85	222	)	)	PUNCT
cana-3871	85	223	,	,	PUNCT
cana-3871	85	224	(	(	PUNCT
cana-3871	85	225	1	1	NUM
cana-3871	85	226	,	,	PUNCT
cana-3871	85	227	0	0	NUM
cana-3871	85	228	,	,	PUNCT
cana-3871	85	229	0	0	NUM
cana-3871	85	230	,	,	PUNCT
cana-3871	85	231	1	1	NUM
cana-3871	85	232	,	,	PUNCT
cana-3871	85	233	0	0	NUM
cana-3871	85	234	)	)	PUNCT
cana-3871	85	235	,	,	PUNCT
cana-3871	85	236	(	(	PUNCT
cana-3871	85	237	1	1	NUM
cana-3871	85	238	,	,	PUNCT
cana-3871	85	239	0	0	NUM
cana-3871	85	240	,	,	PUNCT
cana-3871	85	241	0	0	NUM
cana-3871	85	242	,	,	PUNCT
cana-3871	85	243	1	1	NUM
cana-3871	85	244	,	,	PUNCT
cana-3871	85	245	1	1	NUM
cana-3871	85	246	)	)	PUNCT
cana-3871	85	247	,	,	PUNCT
cana-3871	85	248	(	(	PUNCT
cana-3871	85	249	1	1	NUM
cana-3871	85	250	,	,	PUNCT
cana-3871	85	251	0	0	NUM
cana-3871	85	252	,	,	PUNCT
cana-3871	85	253	1	1	NUM
cana-3871	85	254	,	,	PUNCT
cana-3871	85	255	0	0	NUM
cana-3871	85	256	,	,	PUNCT
cana-3871	85	257	0	0	NUM
cana-3871	85	258	)	)	PUNCT
cana-3871	85	259	,	,	PUNCT
cana-3871	85	260	(	(	PUNCT
cana-3871	85	261	1	1	NUM
cana-3871	85	262	,	,	PUNCT
cana-3871	85	263	0	0	NUM
cana-3871	85	264	,	,	PUNCT
cana-3871	85	265	1	1	NUM
cana-3871	85	266	,	,	PUNCT
cana-3871	85	267	0	0	NUM
cana-3871	85	268	,	,	PUNCT
cana-3871	85	269	1	1	NUM
cana-3871	85	270	)	)	PUNCT
cana-3871	85	271	,	,	PUNCT
cana-3871	85	272	(	(	PUNCT
cana-3871	85	273	1	1	NUM
cana-3871	85	274	,	,	PUNCT
cana-3871	85	275	0	0	NUM
cana-3871	85	276	,	,	PUNCT
cana-3871	85	277	1	1	NUM
cana-3871	85	278	,	,	PUNCT
cana-3871	85	279	1	1	NUM
cana-3871	85	280	,	,	PUNCT
cana-3871	85	281	0	0	NUM
cana-3871	85	282	)	)	PUNCT
cana-3871	85	283	,	,	PUNCT
cana-3871	85	284	(	(	PUNCT
cana-3871	85	285	1	1	NUM
cana-3871	85	286	,	,	PUNCT
cana-3871	85	287	0	0	NUM
cana-3871	85	288	,	,	PUNCT
cana-3871	85	289	1	1	NUM
cana-3871	85	290	,	,	PUNCT
cana-3871	85	291	1	1	NUM
cana-3871	85	292	,	,	PUNCT
cana-3871	85	293	1	1	NUM
cana-3871	85	294	)	)	PUNCT
cana-3871	85	295	,	,	PUNCT
cana-3871	85	296	(	(	PUNCT
cana-3871	85	297	1	1	NUM
cana-3871	85	298	,	,	PUNCT
cana-3871	85	299	1	1	NUM
cana-3871	85	300	,	,	PUNCT
cana-3871	85	301	0	0	NUM
cana-3871	85	302	,	,	PUNCT
cana-3871	85	303	0	0	NUM
cana-3871	85	304	,	,	PUNCT
cana-3871	85	305	0	0	NUM
cana-3871	85	306	)	)	PUNCT
cana-3871	85	307	,	,	PUNCT
cana-3871	85	308	(	(	PUNCT
cana-3871	85	309	1	1	NUM
cana-3871	85	310	,	,	PUNCT
cana-3871	85	311	1	1	NUM
cana-3871	85	312	,	,	PUNCT
cana-3871	85	313	0	0	NUM
cana-3871	85	314	,	,	PUNCT
cana-3871	85	315	0	0	NUM
cana-3871	85	316	,	,	PUNCT
cana-3871	85	317	1	1	NUM
cana-3871	85	318	)	)	PUNCT
cana-3871	85	319	,	,	PUNCT
cana-3871	85	320	(	(	PUNCT
cana-3871	85	321	1	1	NUM
cana-3871	85	322	,	,	PUNCT
cana-3871	85	323	1	1	NUM
cana-3871	85	324	,	,	PUNCT
cana-3871	85	325	0	0	NUM
cana-3871	85	326	,	,	PUNCT
cana-3871	85	327	1	1	NUM
cana-3871	85	328	,	,	PUNCT
cana-3871	85	329	0	0	NUM
cana-3871	85	330	)	)	PUNCT
cana-3871	85	331	,	,	PUNCT
cana-3871	85	332	(	(	PUNCT
cana-3871	85	333	1	1	NUM
cana-3871	85	334	,	,	PUNCT
cana-3871	85	335	1	1	NUM
cana-3871	85	336	,	,	PUNCT
cana-3871	85	337	0	0	NUM
cana-3871	85	338	,	,	PUNCT
cana-3871	85	339	1	1	NUM
cana-3871	85	340	,	,	PUNCT
cana-3871	85	341	1	1	NUM
cana-3871	85	342	)	)	PUNCT
cana-3871	85	343	,	,	PUNCT
cana-3871	85	344	(	(	PUNCT
cana-3871	85	345	1	1	NUM
cana-3871	85	346	,	,	PUNCT
cana-3871	85	347	1	1	NUM
cana-3871	85	348	,	,	PUNCT
cana-3871	85	349	1	1	NUM
cana-3871	85	350	,	,	PUNCT
cana-3871	85	351	0	0	NUM
cana-3871	85	352	,	,	PUNCT
cana-3871	85	353	0	0	NUM
cana-3871	85	354	)	)	PUNCT
cana-3871	85	355	,	,	PUNCT
cana-3871	85	356	(	(	PUNCT
cana-3871	85	357	1	1	NUM
cana-3871	85	358	,	,	PUNCT
cana-3871	85	359	1	1	NUM
cana-3871	85	360	,	,	PUNCT
cana-3871	85	361	1	1	NUM
cana-3871	85	362	,	,	PUNCT
cana-3871	85	363	0	0	NUM
cana-3871	85	364	,	,	PUNCT
cana-3871	85	365	1	1	NUM
cana-3871	85	366	)	)	PUNCT
cana-3871	85	367	,	,	PUNCT
cana-3871	85	368	(	(	PUNCT
cana-3871	85	369	1	1	NUM
cana-3871	85	370	,	,	PUNCT
cana-3871	85	371	1	1	NUM
cana-3871	85	372	,	,	PUNCT
cana-3871	85	373	1	1	NUM
cana-3871	85	374	,	,	PUNCT
cana-3871	85	375	1	1	NUM
cana-3871	85	376	,	,	PUNCT
cana-3871	85	377	0	0	NUM
cana-3871	85	378	)	)	PUNCT
cana-3871	85	379	,	,	PUNCT
cana-3871	85	380	(	(	PUNCT
cana-3871	85	381	1	1	NUM
cana-3871	85	382	,	,	PUNCT
cana-3871	85	383	1	1	NUM
cana-3871	85	384	,	,	PUNCT
cana-3871	85	385	1	1	NUM
cana-3871	85	386	,	,	PUNCT
cana-3871	85	387	1	1	NUM
cana-3871	85	388	,	,	PUNCT
cana-3871	85	389	1	1	NUM
cana-3871	85	390	)	)	PUNCT
cana-3871	85	391	}	}	PUNCT
cana-3871	85	392	ℤ(ℤ2×ℤ2×ℤ2×ℤ2×ℤ2	ℤ(ℤ2×ℤ2×ℤ2×ℤ2×ℤ2	PROPN
cana-3871	85	393	)	)	PUNCT
cana-3871	85	394	=	=	PRON
cana-3871	85	395	{	{	PUNCT
cana-3871	85	396	(	(	PUNCT
cana-3871	85	397	0	0	NUM
cana-3871	85	398	,	,	PUNCT
cana-3871	85	399	0	0	NUM
cana-3871	85	400	,	,	PUNCT
cana-3871	85	401	0	0	NUM
cana-3871	85	402	,	,	PUNCT
cana-3871	85	403	0	0	NUM
cana-3871	85	404	,	,	PUNCT
cana-3871	85	405	1	1	NUM
cana-3871	85	406	)	)	PUNCT
cana-3871	85	407	,	,	PUNCT
cana-3871	85	408	(	(	PUNCT
cana-3871	85	409	0	0	NUM
cana-3871	85	410	,	,	PUNCT
cana-3871	85	411	0	0	NUM
cana-3871	85	412	,	,	PUNCT
cana-3871	85	413	0	0	NUM
cana-3871	85	414	,	,	PUNCT
cana-3871	85	415	1	1	NUM
cana-3871	85	416	,	,	PUNCT
cana-3871	85	417	0	0	NUM
cana-3871	85	418	)	)	PUNCT
cana-3871	85	419	,	,	PUNCT
cana-3871	85	420	(	(	PUNCT
cana-3871	85	421	0	0	NUM
cana-3871	85	422	,	,	PUNCT
cana-3871	85	423	0	0	NUM
cana-3871	85	424	,	,	PUNCT
cana-3871	85	425	0	0	NUM
cana-3871	85	426	,	,	PUNCT
cana-3871	85	427	1	1	NUM
cana-3871	85	428	,	,	PUNCT
cana-3871	85	429	1	1	NUM
cana-3871	85	430	)	)	PUNCT
cana-3871	85	431	,	,	PUNCT
cana-3871	85	432	(	(	PUNCT
cana-3871	85	433	0	0	NUM
cana-3871	85	434	,	,	PUNCT
cana-3871	85	435	0	0	NUM
cana-3871	85	436	,	,	PUNCT
cana-3871	85	437	1	1	NUM
cana-3871	85	438	,	,	PUNCT
cana-3871	85	439	0	0	NUM
cana-3871	85	440	,	,	PUNCT
cana-3871	85	441	0	0	NUM
cana-3871	85	442	)	)	PUNCT
cana-3871	85	443	,	,	PUNCT
cana-3871	85	444	(	(	PUNCT
cana-3871	85	445	0	0	NUM
cana-3871	85	446	,	,	PUNCT
cana-3871	85	447	0	0	NUM
cana-3871	85	448	,	,	PUNCT
cana-3871	85	449	1	1	NUM
cana-3871	85	450	,	,	PUNCT
cana-3871	85	451	0	0	NUM
cana-3871	85	452	,	,	PUNCT
cana-3871	85	453	1	1	NUM
cana-3871	85	454	)	)	PUNCT
cana-3871	85	455	,	,	PUNCT
cana-3871	85	456	(	(	PUNCT
cana-3871	85	457	0	0	NUM
cana-3871	85	458	,	,	PUNCT
cana-3871	85	459	0	0	NUM
cana-3871	85	460	,	,	PUNCT
cana-3871	85	461	1	1	NUM
cana-3871	85	462	,	,	PUNCT
cana-3871	85	463	1	1	NUM
cana-3871	85	464	,	,	PUNCT
cana-3871	85	465	0	0	NUM
cana-3871	85	466	)	)	PUNCT
cana-3871	85	467	,	,	PUNCT
cana-3871	85	468	(	(	PUNCT
cana-3871	85	469	0	0	NUM
cana-3871	85	470	,	,	PUNCT
cana-3871	85	471	0	0	NUM
cana-3871	85	472	,	,	PUNCT
cana-3871	85	473	1	1	NUM
cana-3871	85	474	,	,	PUNCT
cana-3871	85	475	1	1	NUM
cana-3871	85	476	,	,	PUNCT
cana-3871	85	477	1	1	NUM
cana-3871	85	478	)	)	PUNCT
cana-3871	85	479	,	,	PUNCT
cana-3871	85	480	(	(	PUNCT
cana-3871	85	481	0	0	NUM
cana-3871	85	482	,	,	PUNCT
cana-3871	85	483	1	1	NUM
cana-3871	85	484	,	,	PUNCT
cana-3871	85	485	0	0	NUM
cana-3871	85	486	,	,	PUNCT
cana-3871	85	487	0	0	NUM
cana-3871	85	488	,	,	PUNCT
cana-3871	85	489	0	0	NUM
cana-3871	85	490	)	)	PUNCT
cana-3871	85	491	,	,	PUNCT
cana-3871	85	492	(	(	PUNCT
cana-3871	85	493	0	0	NUM
cana-3871	85	494	,	,	PUNCT
cana-3871	85	495	1	1	NUM
cana-3871	85	496	,	,	PUNCT
cana-3871	85	497	0	0	NUM
cana-3871	85	498	,	,	PUNCT
cana-3871	85	499	0	0	NUM
cana-3871	85	500	,	,	PUNCT
cana-3871	85	501	1	1	NUM
cana-3871	85	502	)	)	PUNCT
cana-3871	85	503	,	,	PUNCT
cana-3871	85	504	(	(	PUNCT
cana-3871	85	505	0	0	NUM
cana-3871	85	506	,	,	PUNCT
cana-3871	85	507	1	1	NUM
cana-3871	85	508	,	,	PUNCT
cana-3871	85	509	0	0	NUM
cana-3871	85	510	,	,	PUNCT
cana-3871	85	511	1	1	NUM
cana-3871	85	512	,	,	PUNCT
cana-3871	85	513	0	0	NUM
cana-3871	85	514	)	)	PUNCT
cana-3871	85	515	,	,	PUNCT
cana-3871	85	516	(	(	PUNCT
cana-3871	85	517	0	0	NUM
cana-3871	85	518	,	,	PUNCT
cana-3871	85	519	1	1	NUM
cana-3871	85	520	,	,	PUNCT
cana-3871	85	521	0	0	NUM
cana-3871	85	522	,	,	PUNCT
cana-3871	85	523	1	1	NUM
cana-3871	85	524	,	,	PUNCT
cana-3871	85	525	1	1	NUM
cana-3871	85	526	)	)	PUNCT
cana-3871	85	527	,	,	PUNCT
cana-3871	85	528	(	(	PUNCT
cana-3871	85	529	0	0	NUM
cana-3871	85	530	,	,	PUNCT
cana-3871	85	531	1	1	NUM
cana-3871	85	532	,	,	PUNCT
cana-3871	85	533	1	1	NUM
cana-3871	85	534	,	,	PUNCT
cana-3871	85	535	0	0	NUM
cana-3871	85	536	,	,	PUNCT
cana-3871	85	537	0	0	NUM
cana-3871	85	538	)	)	PUNCT
cana-3871	85	539	,	,	PUNCT
cana-3871	85	540	(	(	PUNCT
cana-3871	85	541	0	0	NUM
cana-3871	85	542	,	,	PUNCT
cana-3871	85	543	1	1	NUM
cana-3871	85	544	,	,	PUNCT
cana-3871	85	545	1	1	NUM
cana-3871	85	546	,	,	PUNCT
cana-3871	85	547	0	0	NUM
cana-3871	85	548	,	,	PUNCT
cana-3871	85	549	1	1	NUM
cana-3871	85	550	)	)	PUNCT
cana-3871	85	551	,	,	PUNCT
cana-3871	85	552	(	(	PUNCT
cana-3871	85	553	0	0	NUM
cana-3871	85	554	,	,	PUNCT
cana-3871	85	555	1	1	NUM
cana-3871	85	556	,	,	PUNCT
cana-3871	85	557	1	1	NUM
cana-3871	85	558	,	,	PUNCT
cana-3871	85	559	1	1	NUM
cana-3871	85	560	,	,	PUNCT
cana-3871	85	561	0	0	NUM
cana-3871	85	562	)	)	PUNCT
cana-3871	85	563	,	,	PUNCT
cana-3871	85	564	(	(	PUNCT
cana-3871	85	565	0	0	NUM
cana-3871	85	566	,	,	PUNCT
cana-3871	85	567	1	1	NUM
cana-3871	85	568	,	,	PUNCT
cana-3871	85	569	1	1	NUM
cana-3871	85	570	,	,	PUNCT
cana-3871	85	571	1	1	NUM
cana-3871	85	572	,	,	PUNCT
cana-3871	85	573	1	1	NUM
cana-3871	85	574	)	)	PUNCT
cana-3871	85	575	,	,	PUNCT
cana-3871	85	576	(	(	PUNCT
cana-3871	85	577	1	1	NUM
cana-3871	85	578	,	,	PUNCT
cana-3871	85	579	0	0	NUM
cana-3871	85	580	,	,	PUNCT
cana-3871	85	581	0	0	NUM
cana-3871	85	582	,	,	PUNCT
cana-3871	85	583	0	0	NUM
cana-3871	85	584	,	,	PUNCT
cana-3871	85	585	0	0	NUM
cana-3871	85	586	)	)	PUNCT
cana-3871	85	587	,	,	PUNCT
cana-3871	85	588	(	(	PUNCT
cana-3871	85	589	1	1	NUM
cana-3871	85	590	,	,	PUNCT
cana-3871	85	591	0	0	NUM
cana-3871	85	592	,	,	PUNCT
cana-3871	85	593	0	0	NUM
cana-3871	85	594	,	,	PUNCT
cana-3871	85	595	0	0	NUM
cana-3871	85	596	,	,	PUNCT
cana-3871	85	597	1	1	NUM
cana-3871	85	598	)	)	PUNCT
cana-3871	85	599	,	,	PUNCT
cana-3871	85	600	(	(	PUNCT
cana-3871	85	601	1	1	NUM
cana-3871	85	602	,	,	PUNCT
cana-3871	85	603	0	0	NUM
cana-3871	85	604	,	,	PUNCT
cana-3871	85	605	0	0	NUM
cana-3871	85	606	,	,	PUNCT
cana-3871	85	607	1	1	NUM
cana-3871	85	608	,	,	PUNCT
cana-3871	85	609	0	0	NUM
cana-3871	85	610	)	)	PUNCT
cana-3871	85	611	,	,	PUNCT
cana-3871	85	612	(	(	PUNCT
cana-3871	85	613	1	1	NUM
cana-3871	85	614	,	,	PUNCT
cana-3871	85	615	0	0	NUM
cana-3871	85	616	,	,	PUNCT
cana-3871	85	617	0	0	NUM
cana-3871	85	618	,	,	PUNCT
cana-3871	85	619	1	1	NUM
cana-3871	85	620	,	,	PUNCT
cana-3871	85	621	1	1	NUM
cana-3871	85	622	)	)	PUNCT
cana-3871	85	623	,	,	PUNCT
cana-3871	85	624	(	(	PUNCT
cana-3871	85	625	1	1	NUM
cana-3871	85	626	,	,	PUNCT
cana-3871	85	627	0	0	NUM
cana-3871	85	628	,	,	PUNCT
cana-3871	85	629	1	1	NUM
cana-3871	85	630	,	,	PUNCT
cana-3871	85	631	0	0	NUM
cana-3871	85	632	,	,	PUNCT
cana-3871	85	633	0	0	NUM
cana-3871	85	634	)	)	PUNCT
cana-3871	85	635	,	,	PUNCT
cana-3871	85	636	(	(	PUNCT
cana-3871	85	637	1	1	NUM
cana-3871	85	638	,	,	PUNCT
cana-3871	85	639	0	0	NUM
cana-3871	85	640	,	,	PUNCT
cana-3871	85	641	1	1	NUM
cana-3871	85	642	,	,	PUNCT
cana-3871	85	643	0	0	NUM
cana-3871	85	644	,	,	PUNCT
cana-3871	85	645	1	1	NUM
cana-3871	85	646	)	)	PUNCT
cana-3871	85	647	,	,	PUNCT
cana-3871	85	648	(	(	PUNCT
cana-3871	85	649	1	1	NUM
cana-3871	85	650	,	,	PUNCT
cana-3871	85	651	0	0	NUM
cana-3871	85	652	,	,	PUNCT
cana-3871	85	653	1	1	NUM
cana-3871	85	654	,	,	PUNCT
cana-3871	85	655	1	1	NUM
cana-3871	85	656	,	,	PUNCT
cana-3871	85	657	0	0	NUM
cana-3871	85	658	)	)	PUNCT
cana-3871	85	659	,	,	PUNCT
cana-3871	85	660	(	(	PUNCT
cana-3871	85	661	1	1	NUM
cana-3871	85	662	,	,	PUNCT
cana-3871	85	663	0	0	NUM
cana-3871	85	664	,	,	PUNCT
cana-3871	85	665	1	1	NUM
cana-3871	85	666	,	,	PUNCT
cana-3871	85	667	1	1	NUM
cana-3871	85	668	,	,	PUNCT
cana-3871	85	669	1	1	NUM
cana-3871	85	670	)	)	PUNCT
cana-3871	85	671	,	,	PUNCT
cana-3871	85	672	(	(	PUNCT
cana-3871	85	673	1	1	NUM
cana-3871	85	674	,	,	PUNCT
cana-3871	85	675	1	1	NUM
cana-3871	85	676	,	,	PUNCT
cana-3871	85	677	0	0	NUM
cana-3871	85	678	,	,	PUNCT
cana-3871	85	679	0	0	NUM
cana-3871	85	680	,	,	PUNCT
cana-3871	85	681	0	0	NUM
cana-3871	85	682	)	)	PUNCT
cana-3871	85	683	,	,	PUNCT
cana-3871	85	684	(	(	PUNCT
cana-3871	85	685	1	1	NUM
cana-3871	85	686	,	,	PUNCT
cana-3871	85	687	1	1	NUM
cana-3871	85	688	,	,	PUNCT
cana-3871	85	689	0	0	NUM
cana-3871	85	690	,	,	PUNCT
cana-3871	85	691	0	0	NUM
cana-3871	85	692	,	,	PUNCT
cana-3871	85	693	1	1	NUM
cana-3871	85	694	)	)	PUNCT
cana-3871	85	695	,	,	PUNCT
cana-3871	85	696	(	(	PUNCT
cana-3871	85	697	1	1	NUM
cana-3871	85	698	,	,	PUNCT
cana-3871	85	699	1	1	NUM
cana-3871	85	700	,	,	PUNCT
cana-3871	85	701	0	0	NUM
cana-3871	85	702	,	,	PUNCT
cana-3871	85	703	1	1	NUM
cana-3871	85	704	,	,	PUNCT
cana-3871	85	705	0	0	NUM
cana-3871	85	706	)	)	PUNCT
cana-3871	85	707	,	,	PUNCT
cana-3871	85	708	(	(	PUNCT
cana-3871	85	709	1	1	NUM
cana-3871	85	710	,	,	PUNCT
cana-3871	85	711	1	1	NUM
cana-3871	85	712	,	,	PUNCT
cana-3871	85	713	0	0	NUM
cana-3871	85	714	,	,	PUNCT
cana-3871	85	715	1	1	NUM
cana-3871	85	716	,	,	PUNCT
cana-3871	85	717	1	1	NUM
cana-3871	85	718	)	)	PUNCT
cana-3871	85	719	,	,	PUNCT
cana-3871	85	720	(	(	PUNCT
cana-3871	85	721	1	1	NUM
cana-3871	85	722	,	,	PUNCT
cana-3871	85	723	1	1	NUM
cana-3871	85	724	,	,	PUNCT
cana-3871	85	725	1	1	NUM
cana-3871	85	726	,	,	PUNCT
cana-3871	85	727	0	0	NUM
cana-3871	85	728	,	,	PUNCT
cana-3871	85	729	0	0	NUM
cana-3871	85	730	)	)	PUNCT
cana-3871	85	731	,	,	PUNCT
cana-3871	85	732	(	(	PUNCT
cana-3871	85	733	1	1	NUM
cana-3871	85	734	,	,	PUNCT
cana-3871	85	735	1	1	NUM
cana-3871	85	736	,	,	PUNCT
cana-3871	85	737	1	1	NUM
cana-3871	85	738	,	,	PUNCT
cana-3871	85	739	0	0	NUM
cana-3871	85	740	,	,	PUNCT
cana-3871	85	741	1	1	NUM
cana-3871	85	742	)	)	PUNCT
cana-3871	85	743	,	,	PUNCT
cana-3871	85	744	(	(	PUNCT
cana-3871	85	745	1	1	NUM
cana-3871	85	746	,	,	PUNCT
cana-3871	85	747	1	1	NUM
cana-3871	85	748	,	,	PUNCT
cana-3871	85	749	1	1	NUM
cana-3871	85	750	,	,	PUNCT
cana-3871	85	751	1	1	NUM
cana-3871	85	752	,	,	PUNCT
cana-3871	85	753	0	0	NUM
cana-3871	85	754	)	)	PUNCT
cana-3871	85	755	}	}	PUNCT
cana-3871	85	756	the	the	DET
cana-3871	85	757	zero	zero	NUM
cana-3871	85	758	-	-	PUNCT
cana-3871	85	759	divisor	divisor	NOUN
cana-3871	85	760	graph	graph	NOUN
cana-3871	85	761	of	of	ADP
cana-3871	85	762	ℤ2	ℤ2	PROPN
cana-3871	85	763	×	×	PROPN
cana-3871	85	764	ℤ2	ℤ2	PROPN
cana-3871	85	765	×	×	PROPN
cana-3871	85	766	ℤ2	ℤ2	PROPN
cana-3871	85	767	×	×	PROPN
cana-3871	85	768	ℤ2	ℤ2	PROPN
cana-3871	85	769	×	×	PROPN
cana-3871	85	770	ℤ2	ℤ2	PROPN
cana-3871	85	771	is	be	AUX
cana-3871	85	772	given	give	VERB
cana-3871	85	773	in	in	ADP
cana-3871	85	774	the	the	DET
cana-3871	85	775	figure	figure	NOUN
cana-3871	85	776	below	below	ADV
cana-3871	85	777	,	,	PUNCT
cana-3871	85	778	fig	fig	NOUN
cana-3871	85	779	7	7	NUM
cana-3871	85	780	:	:	PUNCT
cana-3871	85	781	γ	γ	X
cana-3871	85	782	(	(	PUNCT
cana-3871	85	783	ℤ2	ℤ2	PROPN
cana-3871	85	784	×	×	PROPN
cana-3871	85	785	ℤ2	ℤ2	PROPN
cana-3871	85	786	×	×	PROPN
cana-3871	85	787	ℤ2	ℤ2	PROPN
cana-3871	85	788	×	×	PROPN
cana-3871	85	789	ℤ2	ℤ2	PROPN
cana-3871	85	790	×	×	PROPN
cana-3871	85	791	ℤ2	ℤ2	PROPN
cana-3871	85	792	)	)	PUNCT
cana-3871	85	793	here	here	ADV
cana-3871	85	794	,	,	PUNCT
cana-3871	85	795	n	n	NOUN
cana-3871	85	796	=	=	SYM
cana-3871	85	797	5	5	NUM
cana-3871	85	798	number	number	NOUN
cana-3871	85	799	of	of	ADP
cana-3871	85	800	vertices	vertex	NOUN
cana-3871	85	801	in	in	ADP
cana-3871	85	802	ℤ	ℤ	PROPN
cana-3871	85	803	(	(	PUNCT
cana-3871	85	804	ℤ2	ℤ2	PROPN
cana-3871	85	805	×	×	PROPN
cana-3871	85	806	ℤ2	ℤ2	PROPN
cana-3871	85	807	×	×	PROPN
cana-3871	85	808	ℤ2	ℤ2	PROPN
cana-3871	85	809	×	×	PROPN
cana-3871	85	810	ℤ2	ℤ2	PROPN
cana-3871	85	811	×	×	PROPN
cana-3871	85	812	ℤ2	ℤ2	PROPN
cana-3871	85	813	)	)	PUNCT
cana-3871	85	814	=	=	PUNCT
cana-3871	86	1	25	25	NUM
cana-3871	86	2	−	−	NUM
cana-3871	86	3	2	2	NUM
cana-3871	86	4	=	=	SYM
cana-3871	86	5	30	30	NUM
cana-3871	86	6	communications	communication	NOUN
cana-3871	86	7	on	on	ADP
cana-3871	86	8	applied	apply	VERB
cana-3871	86	9	nonlinear	nonlinear	ADJ
cana-3871	86	10	analysis	analysis	NOUN
cana-3871	86	11	issn	issn	NOUN
cana-3871	86	12	:	:	PUNCT
cana-3871	86	13	1074	1074	NUM
cana-3871	86	14	-	-	PUNCT
cana-3871	86	15	133x	133x	NUM
cana-3871	86	16	vol	vol	NOUN
cana-3871	86	17	32	32	NUM
cana-3871	86	18	no	no	NOUN
cana-3871	86	19	.	.	PUNCT
cana-3871	87	1	7s	7	NOUN
cana-3871	87	2	(	(	PUNCT
cana-3871	87	3	2025	2025	NUM
cana-3871	87	4	)	)	PUNCT
cana-3871	87	5	947	947	NUM
cana-3871	87	6	https://internationalpubls.com	https://internationalpubls.com	NOUN
cana-3871	87	7	degree	degree	NOUN
cana-3871	87	8	of	of	ADP
cana-3871	87	9	vertex	vertex	NOUN
cana-3871	87	10	(	(	PUNCT
cana-3871	87	11	0	0	NUM
cana-3871	87	12	,	,	PUNCT
cana-3871	87	13	0	0	NUM
cana-3871	87	14	,	,	PUNCT
cana-3871	87	15	0	0	NUM
cana-3871	87	16	,	,	PUNCT
cana-3871	87	17	0	0	NUM
cana-3871	87	18	,	,	PUNCT
cana-3871	87	19	1	1	NUM
cana-3871	87	20	)	)	PUNCT
cana-3871	87	21	=	=	SYM
cana-3871	87	22	25−1	25−1	NUM
cana-3871	87	23	−	−	NUM
cana-3871	87	24	1	1	NUM
cana-3871	87	25	=	=	SYM
cana-3871	87	26	24	24	NUM
cana-3871	87	27	−	−	NOUN
cana-3871	87	28	1	1	NUM
cana-3871	87	29	=	=	SYM
cana-3871	87	30	15	15	NUM
cana-3871	87	31	degree	degree	NOUN
cana-3871	87	32	of	of	ADP
cana-3871	87	33	vertex	vertex	NOUN
cana-3871	87	34	(	(	PUNCT
cana-3871	87	35	0	0	NUM
cana-3871	87	36	,	,	PUNCT
cana-3871	87	37	0	0	NUM
cana-3871	87	38	,	,	PUNCT
cana-3871	87	39	0	0	NUM
cana-3871	87	40	,	,	PUNCT
cana-3871	87	41	1	1	NUM
cana-3871	87	42	,	,	PUNCT
cana-3871	87	43	0	0	NUM
cana-3871	87	44	)	)	PUNCT
cana-3871	87	45	=	=	SYM
cana-3871	88	1	25−1	25−1	NUM
cana-3871	88	2	−	−	NUM
cana-3871	88	3	1	1	NUM
cana-3871	88	4	=	=	SYM
cana-3871	88	5	24	24	NUM
cana-3871	88	6	−	−	NOUN
cana-3871	88	7	1	1	NUM
cana-3871	88	8	=	=	SYM
cana-3871	88	9	15	15	NUM
cana-3871	88	10	degree	degree	NOUN
cana-3871	88	11	of	of	ADP
cana-3871	88	12	vertex	vertex	NOUN
cana-3871	88	13	(	(	PUNCT
cana-3871	88	14	0	0	NUM
cana-3871	88	15	,	,	PUNCT
cana-3871	88	16	0	0	NUM
cana-3871	88	17	,	,	PUNCT
cana-3871	88	18	1	1	NUM
cana-3871	88	19	,	,	PUNCT
cana-3871	88	20	0	0	NUM
cana-3871	88	21	,	,	PUNCT
cana-3871	88	22	0	0	NUM
cana-3871	88	23	)	)	PUNCT
cana-3871	88	24	=	=	SYM
cana-3871	89	1	25−1	25−1	NUM
cana-3871	89	2	−	−	NUM
cana-3871	89	3	1	1	NUM
cana-3871	89	4	=	=	SYM
cana-3871	89	5	24	24	NUM
cana-3871	89	6	−	−	NOUN
cana-3871	89	7	1	1	NUM
cana-3871	89	8	=	=	SYM
cana-3871	89	9	15	15	NUM
cana-3871	89	10	degree	degree	NOUN
cana-3871	89	11	of	of	ADP
cana-3871	89	12	vertex	vertex	NOUN
cana-3871	89	13	(	(	PUNCT
cana-3871	89	14	0	0	NUM
cana-3871	89	15	,	,	PUNCT
cana-3871	89	16	1	1	NUM
cana-3871	89	17	,	,	PUNCT
cana-3871	89	18	0	0	NUM
cana-3871	89	19	,	,	PUNCT
cana-3871	89	20	0	0	NUM
cana-3871	89	21	,	,	PUNCT
cana-3871	89	22	0	0	NUM
cana-3871	89	23	)	)	PUNCT
cana-3871	89	24	=	=	SYM
cana-3871	90	1	25−1	25−1	NUM
cana-3871	90	2	−	−	NUM
cana-3871	90	3	1	1	NUM
cana-3871	90	4	=	=	SYM
cana-3871	90	5	24	24	NUM
cana-3871	90	6	−	−	NOUN
cana-3871	90	7	1	1	NUM
cana-3871	90	8	=	=	SYM
cana-3871	90	9	15	15	NUM
cana-3871	90	10	degree	degree	NOUN
cana-3871	90	11	of	of	ADP
cana-3871	90	12	vertex	vertex	NOUN
cana-3871	90	13	(	(	PUNCT
cana-3871	90	14	1	1	NUM
cana-3871	90	15	,	,	PUNCT
cana-3871	90	16	0	0	NUM
cana-3871	90	17	,	,	PUNCT
cana-3871	90	18	0	0	NUM
cana-3871	90	19	,	,	PUNCT
cana-3871	90	20	0	0	NUM
cana-3871	90	21	,	,	PUNCT
cana-3871	90	22	0	0	NUM
cana-3871	90	23	)	)	PUNCT
cana-3871	90	24	=	=	SYM
cana-3871	91	1	25−1	25−1	NUM
cana-3871	91	2	−	−	NUM
cana-3871	91	3	1	1	NUM
cana-3871	91	4	=	=	SYM
cana-3871	91	5	24	24	NUM
cana-3871	91	6	−	−	NOUN
cana-3871	91	7	1	1	NUM
cana-3871	91	8	=	=	SYM
cana-3871	91	9	15	15	NUM
cana-3871	91	10	∴	∴	NOUN
cana-3871	91	11	5	5	NUM
cana-3871	91	12	vertices	vertex	NOUN
cana-3871	91	13	have	have	VERB
cana-3871	91	14	degree	degree	NOUN
cana-3871	91	15	15	15	NUM
cana-3871	91	16	.	.	PUNCT
cana-3871	92	1	∴	∴	NOUN
cana-3871	92	2	the	the	DET
cana-3871	92	3	theorem	theorem	NOUN
cana-3871	92	4	holds	hold	VERB
cana-3871	92	5	true	true	ADJ
cana-3871	92	6	.	.	PUNCT
cana-3871	93	1	3.2	3.2	NUM
cana-3871	93	2	theorem	theorem	ADJ
cana-3871	93	3	statement	statement	NOUN
cana-3871	93	4	:	:	PUNCT
cana-3871	93	5	let	let	VERB
cana-3871	93	6	ℤ2	ℤ2	PROPN
cana-3871	93	7	n	n	PROPN
cana-3871	93	8	=	=	SYM
cana-3871	93	9	ℤ2	ℤ2	PROPN
cana-3871	93	10	×	×	NOUN
cana-3871	93	11	ℤ2	ℤ2	PROPN
cana-3871	93	12	×	×	PROPN
cana-3871	93	13	ℤ2	ℤ2	PROPN
cana-3871	93	14	×	×	PROPN
cana-3871	93	15	ℤ2	ℤ2	PROPN
cana-3871	93	16	×	×	NOUN
cana-3871	93	17	...	...	PUNCT
cana-3871	93	18	×	×	NOUN
cana-3871	93	19	ℤ2	ℤ2	PROPN
cana-3871	93	20	be	be	VERB
cana-3871	93	21	a	a	DET
cana-3871	93	22	boolean	boolean	ADJ
cana-3871	93	23	ring	ring	NOUN
cana-3871	93	24	then	then	ADV
cana-3871	93	25	n	n	DET
cana-3871	93	26	vertices	vertex	NOUN
cana-3871	93	27	of	of	ADP
cana-3871	93	28	zero	zero	NUM
cana-3871	93	29	divisor	divisor	NOUN
cana-3871	93	30	graph	graph	NOUN
cana-3871	93	31	γ(ℤ2	γ(ℤ2	PROPN
cana-3871	93	32	n	n	CCONJ
cana-3871	93	33	)	)	PUNCT
cana-3871	93	34	have	have	VERB
cana-3871	93	35	degree	degree	NOUN
cana-3871	93	36	1	1	NUM
cana-3871	93	37	.	.	PUNCT
cana-3871	94	1	proof	proof	NOUN
cana-3871	94	2	:	:	PUNCT
cana-3871	94	3	let	let	VERB
cana-3871	94	4	ℤ2	ℤ2	PROPN
cana-3871	94	5	n	n	PROPN
cana-3871	94	6	=	=	SYM
cana-3871	94	7	ℤ2	ℤ2	PROPN
cana-3871	94	8	×	×	NOUN
cana-3871	94	9	ℤ2	ℤ2	PROPN
cana-3871	94	10	×	×	PROPN
cana-3871	94	11	ℤ2	ℤ2	PROPN
cana-3871	94	12	×	×	PROPN
cana-3871	94	13	ℤ2	ℤ2	PROPN
cana-3871	94	14	...	...	PUNCT
cana-3871	94	15	ℤ2	ℤ2	PROPN
cana-3871	94	16	,	,	PUNCT
cana-3871	94	17	be	be	VERB
cana-3871	94	18	a	a	DET
cana-3871	94	19	boolean	boolean	ADJ
cana-3871	94	20	ring	ring	NOUN
cana-3871	94	21	ℤ2	ℤ2	PROPN
cana-3871	94	22	n	n	PART
cana-3871	94	23	has	have	AUX
cana-3871	94	24	(	(	PUNCT
cana-3871	94	25	2n	2n	NUM
cana-3871	94	26	−	−	NOUN
cana-3871	94	27	2	2	X
cana-3871	94	28	)	)	PUNCT
cana-3871	94	29	zero	zero	NUM
cana-3871	94	30	divisors	divisor	NOUN
cana-3871	94	31	and	and	CCONJ
cana-3871	94	32	ℤ2	ℤ2	NOUN
cana-3871	94	33	n	n	AUX
cana-3871	94	34	is	be	AUX
cana-3871	94	35	given	give	VERB
cana-3871	94	36	by	by	ADP
cana-3871	94	37	,	,	PUNCT
cana-3871	94	38	ℤ2	ℤ2	PROPN
cana-3871	94	39	n	n	NOUN
cana-3871	94	40	=	=	SYM
cana-3871	94	41	{	{	PUNCT
cana-3871	94	42	(	(	PUNCT
cana-3871	94	43	b1	b1	NOUN
cana-3871	94	44	,	,	PUNCT
cana-3871	94	45	b2	b2	NOUN
cana-3871	94	46	,	,	PUNCT
cana-3871	94	47	b3	b3	PROPN
cana-3871	94	48	,	,	PUNCT
cana-3871	94	49	...	...	PUNCT
cana-3871	94	50	,	,	PUNCT
cana-3871	94	51	bn	bn	X
cana-3871	94	52	)	)	PUNCT
cana-3871	94	53	|	|	ADV
cana-3871	94	54	bis	bi	VERB
cana-3871	94	55	∈	∈	NOUN
cana-3871	94	56	{	{	PUNCT
cana-3871	94	57	0	0	NUM
cana-3871	94	58	,	,	PUNCT
cana-3871	94	59	1	1	NUM
cana-3871	94	60	}	}	PUNCT
cana-3871	94	61	,	,	PUNCT
cana-3871	94	62	∀i	∀i	NOUN
cana-3871	94	63	=	=	SYM
cana-3871	94	64	1	1	NUM
cana-3871	94	65	,	,	PUNCT
cana-3871	94	66	2	2	NUM
cana-3871	94	67	,	,	PUNCT
cana-3871	94	68	...	...	PUNCT
cana-3871	94	69	,	,	PUNCT
cana-3871	94	70	n	n	CCONJ
cana-3871	94	71	}	}	PUNCT
cana-3871	94	72	since	since	ADV
cana-3871	94	73	,	,	PUNCT
cana-3871	94	74	each	each	DET
cana-3871	94	75	bis	bis	X
cana-3871	94	76	has	have	VERB
cana-3871	94	77	two	two	NUM
cana-3871	94	78	choices	choice	NOUN
cana-3871	94	79	0	0	NUM
cana-3871	94	80	and	and	CCONJ
cana-3871	94	81	1	1	NUM
cana-3871	94	82	,	,	PUNCT
cana-3871	94	83	so	so	SCONJ
cana-3871	94	84	there	there	PRON
cana-3871	94	85	are	be	VERB
cana-3871	94	86	2n	2n	NUM
cana-3871	94	87	elements	element	NOUN
cana-3871	94	88	in	in	ADP
cana-3871	94	89	ℤ2	ℤ2	PROPN
cana-3871	94	90	n	n	PART
cana-3871	94	91	|ℤ2	|ℤ2	X
cana-3871	94	92	n|	n|	NOUN
cana-3871	94	93	=	=	SYM
cana-3871	94	94	2n	2n	NUM
cana-3871	94	95	the	the	DET
cana-3871	94	96	set	set	NOUN
cana-3871	94	97	of	of	ADP
cana-3871	94	98	zero	zero	NUM
cana-3871	94	99	divisors	divisor	NOUN
cana-3871	94	100	of	of	ADP
cana-3871	94	101	ℤ2	ℤ2	PROPN
cana-3871	94	102	n	n	X
cana-3871	94	103	is	be	AUX
cana-3871	94	104	denoted	denote	VERB
cana-3871	94	105	by	by	ADP
cana-3871	94	106	ℤ(ℤ2	ℤ(ℤ2	NOUN
cana-3871	94	107	n	n	CCONJ
cana-3871	94	108	)	)	PUNCT
cana-3871	94	109	and	and	CCONJ
cana-3871	94	110	is	be	AUX
cana-3871	94	111	given	give	VERB
cana-3871	94	112	by	by	ADP
cana-3871	94	113	,	,	PUNCT
cana-3871	94	114	ℤ(ℤ2	ℤ(ℤ2	PROPN
cana-3871	94	115	n	n	CCONJ
cana-3871	94	116	)	)	PUNCT
cana-3871	94	117	=	=	PRON
cana-3871	94	118	{	{	PUNCT
cana-3871	94	119	(	(	PUNCT
cana-3871	94	120	b1	b1	NOUN
cana-3871	94	121	,	,	PUNCT
cana-3871	94	122	b2	b2	NOUN
cana-3871	94	123	,	,	PUNCT
cana-3871	94	124	b3	b3	PROPN
cana-3871	94	125	,	,	PUNCT
cana-3871	94	126	...	...	PUNCT
cana-3871	94	127	,	,	PUNCT
cana-3871	94	128	bn	bn	X
cana-3871	94	129	)	)	PUNCT
cana-3871	94	130	|	|	ADV
cana-3871	94	131	bis	bi	VERB
cana-3871	94	132	∈	∈	NOUN
cana-3871	94	133	{	{	PUNCT
cana-3871	94	134	0	0	NUM
cana-3871	94	135	,	,	PUNCT
cana-3871	94	136	1	1	NUM
cana-3871	94	137	}	}	PUNCT
cana-3871	94	138	,	,	PUNCT
cana-3871	94	139	all	all	PRON
cana-3871	94	140	bi≠	bi≠	PROPN
cana-3871	94	141	0	0	NUM
cana-3871	94	142	,	,	PUNCT
cana-3871	94	143	all	all	DET
cana-3871	94	144	bi	bi	NOUN
cana-3871	94	145	≠1	≠1	NOUN
cana-3871	94	146	,	,	PUNCT
cana-3871	94	147	i	i	NOUN
cana-3871	94	148	=	=	NOUN
cana-3871	94	149	1	1	NUM
cana-3871	94	150	,	,	PUNCT
cana-3871	94	151	2	2	NUM
cana-3871	94	152	,	,	PUNCT
cana-3871	94	153	...	...	PUNCT
cana-3871	94	154	,	,	PUNCT
cana-3871	94	155	n	n	CCONJ
cana-3871	94	156	}	}	PUNCT
cana-3871	94	157	|ℤ(ℤ2	|ℤ(ℤ2	PROPN
cana-3871	94	158	n	n	CCONJ
cana-3871	94	159	)	)	PUNCT
cana-3871	94	160	|	|	ADV
cana-3871	94	161	=	=	SYM
cana-3871	94	162	2n	2n	NUM
cana-3871	95	1	−	−	ADP
cana-3871	95	2	2	2	NUM
cana-3871	95	3	the	the	DET
cana-3871	95	4	vertices	vertex	NOUN
cana-3871	95	5	(	(	PUNCT
cana-3871	95	6	0	0	NUM
cana-3871	95	7	,	,	PUNCT
cana-3871	95	8	1	1	NUM
cana-3871	95	9	,	,	PUNCT
cana-3871	95	10	1	1	NUM
cana-3871	95	11	,	,	PUNCT
cana-3871	95	12	...	...	PUNCT
cana-3871	95	13	,	,	PUNCT
cana-3871	95	14	1	1	X
cana-3871	95	15	)	)	PUNCT
cana-3871	95	16	,	,	PUNCT
cana-3871	95	17	(	(	PUNCT
cana-3871	95	18	1	1	NUM
cana-3871	95	19	,	,	PUNCT
cana-3871	95	20	0	0	NUM
cana-3871	95	21	,	,	PUNCT
cana-3871	95	22	1	1	NUM
cana-3871	95	23	,	,	PUNCT
cana-3871	95	24	1	1	NUM
cana-3871	95	25	,	,	PUNCT
cana-3871	95	26	...	...	PUNCT
cana-3871	95	27	,	,	PUNCT
cana-3871	95	28	1	1	X
cana-3871	95	29	)	)	PUNCT
cana-3871	95	30	,	,	PUNCT
cana-3871	95	31	(	(	PUNCT
cana-3871	95	32	1	1	NUM
cana-3871	95	33	,	,	PUNCT
cana-3871	95	34	1	1	NUM
cana-3871	95	35	,	,	PUNCT
cana-3871	95	36	0	0	NUM
cana-3871	95	37	,	,	PUNCT
cana-3871	95	38	1	1	NUM
cana-3871	95	39	,	,	PUNCT
cana-3871	95	40	...	...	PUNCT
cana-3871	95	41	,	,	PUNCT
cana-3871	95	42	1	1	X
cana-3871	95	43	)	)	PUNCT
cana-3871	95	44	,	,	PUNCT
cana-3871	95	45	...	...	PUNCT
cana-3871	95	46	,	,	PUNCT
cana-3871	95	47	(	(	PUNCT
cana-3871	95	48	1	1	NUM
cana-3871	95	49	,	,	PUNCT
cana-3871	95	50	1	1	NUM
cana-3871	95	51	,	,	PUNCT
cana-3871	95	52	1	1	NUM
cana-3871	95	53	,	,	PUNCT
cana-3871	95	54	...	...	PUNCT
cana-3871	95	55	,	,	PUNCT
cana-3871	95	56	0	0	X
cana-3871	95	57	)	)	PUNCT
cana-3871	95	58	are	be	AUX
cana-3871	95	59	adjacent	adjacent	ADJ
cana-3871	95	60	to	to	ADP
cana-3871	95	61	(	(	PUNCT
cana-3871	95	62	1	1	NUM
cana-3871	95	63	,	,	PUNCT
cana-3871	95	64	b2	b2	NOUN
cana-3871	95	65	,	,	PUNCT
cana-3871	95	66	b3	b3	PROPN
cana-3871	95	67	,	,	PUNCT
cana-3871	95	68	...	...	PUNCT
cana-3871	95	69	,	,	PUNCT
cana-3871	95	70	bn	bn	NOUN
cana-3871	95	71	)	)	PUNCT
cana-3871	95	72	,	,	PUNCT
cana-3871	95	73	(	(	PUNCT
cana-3871	95	74	b1	b1	NOUN
cana-3871	95	75	,	,	PUNCT
cana-3871	95	76	1	1	NUM
cana-3871	95	77	,	,	PUNCT
cana-3871	95	78	b3	b3	NOUN
cana-3871	95	79	,	,	PUNCT
cana-3871	95	80	...	...	PUNCT
cana-3871	95	81	,	,	PUNCT
cana-3871	95	82	bn	bn	NOUN
cana-3871	95	83	)	)	PUNCT
cana-3871	95	84	,	,	PUNCT
cana-3871	95	85	(	(	PUNCT
cana-3871	95	86	b1	b1	NOUN
cana-3871	95	87	,	,	PUNCT
cana-3871	95	88	b2	b2	NOUN
cana-3871	95	89	,	,	PUNCT
cana-3871	95	90	1	1	NUM
cana-3871	95	91	,	,	PUNCT
cana-3871	95	92	b4	b4	NOUN
cana-3871	95	93	,	,	PUNCT
cana-3871	95	94	...	...	PUNCT
cana-3871	95	95	,	,	PUNCT
cana-3871	95	96	bn	bn	NOUN
cana-3871	95	97	)	)	PUNCT
cana-3871	95	98	,	,	PUNCT
cana-3871	95	99	...	...	PUNCT
cana-3871	95	100	,	,	PUNCT
cana-3871	95	101	(	(	PUNCT
cana-3871	95	102	b1	b1	NOUN
cana-3871	95	103	,	,	PUNCT
cana-3871	95	104	b2	b2	NOUN
cana-3871	95	105	,	,	PUNCT
cana-3871	95	106	b3	b3	PROPN
cana-3871	95	107	,	,	PUNCT
cana-3871	95	108	...	...	PUNCT
cana-3871	95	109	,	,	PUNCT
cana-3871	95	110	1	1	X
cana-3871	95	111	)	)	PUNCT
cana-3871	95	112	respectively	respectively	ADV
cana-3871	95	113	.	.	PUNCT
cana-3871	96	1	clearly	clearly	ADV
cana-3871	96	2	the	the	DET
cana-3871	96	3	vertex	vertex	NOUN
cana-3871	96	4	(	(	PUNCT
cana-3871	96	5	0	0	NUM
cana-3871	96	6	,	,	PUNCT
cana-3871	96	7	1	1	NUM
cana-3871	96	8	,	,	PUNCT
cana-3871	96	9	1	1	NUM
cana-3871	96	10	,	,	PUNCT
cana-3871	96	11	...	...	PUNCT
cana-3871	96	12	,	,	PUNCT
cana-3871	96	13	1	1	X
cana-3871	96	14	)	)	PUNCT
cana-3871	96	15	is	be	AUX
cana-3871	96	16	adjacent	adjacent	ADJ
cana-3871	96	17	to	to	ADP
cana-3871	96	18	(	(	PUNCT
cana-3871	96	19	1	1	NUM
cana-3871	96	20	,	,	PUNCT
cana-3871	96	21	b2	b2	NOUN
cana-3871	96	22	,	,	PUNCT
cana-3871	96	23	b3	b3	PROPN
cana-3871	96	24	,	,	PUNCT
cana-3871	96	25	...	...	PUNCT
cana-3871	96	26	,	,	PUNCT
cana-3871	96	27	bn	bn	ADJ
cana-3871	96	28	)	)	PUNCT
cana-3871	96	29	and	and	CCONJ
cana-3871	96	30	b2	b2	NOUN
cana-3871	96	31	,	,	PUNCT
cana-3871	96	32	b3	b3	PROPN
cana-3871	96	33	,	,	PUNCT
cana-3871	96	34	...	...	PUNCT
cana-3871	96	35	,	,	PUNCT
cana-3871	96	36	bn	bn	PART
cana-3871	96	37	have	have	VERB
cana-3871	96	38	only	only	ADV
cana-3871	96	39	one	one	NUM
cana-3871	96	40	choice	choice	NOUN
cana-3871	96	41	which	which	PRON
cana-3871	96	42	is	be	AUX
cana-3871	96	43	0	0	NUM
cana-3871	96	44	.	.	PUNCT
cana-3871	97	1	∴	∴	NOUN
cana-3871	97	2	the	the	DET
cana-3871	97	3	vertex	vertex	NOUN
cana-3871	97	4	(	(	PUNCT
cana-3871	97	5	0	0	NUM
cana-3871	97	6	,	,	PUNCT
cana-3871	97	7	1	1	NUM
cana-3871	97	8	,	,	PUNCT
cana-3871	97	9	1	1	NUM
cana-3871	97	10	,	,	PUNCT
cana-3871	97	11	...	...	PUNCT
cana-3871	97	12	,	,	PUNCT
cana-3871	97	13	1	1	X
cana-3871	97	14	)	)	PUNCT
cana-3871	97	15	is	be	AUX
cana-3871	97	16	adjacent	adjacent	ADJ
cana-3871	97	17	to	to	ADP
cana-3871	97	18	(	(	PUNCT
cana-3871	97	19	1	1	NUM
cana-3871	97	20	,	,	PUNCT
cana-3871	97	21	0	0	NUM
cana-3871	97	22	,	,	PUNCT
cana-3871	97	23	0	0	NUM
cana-3871	97	24	,	,	PUNCT
cana-3871	97	25	...	...	PUNCT
cana-3871	97	26	,	,	PUNCT
cana-3871	97	27	0	0	NUM
cana-3871	97	28	)	)	PUNCT
cana-3871	97	29	only	only	ADV
cana-3871	97	30	.	.	PUNCT
cana-3871	98	1	∴	∴	VERB
cana-3871	98	2	the	the	DET
cana-3871	98	3	degree	degree	NOUN
cana-3871	98	4	of	of	ADP
cana-3871	98	5	(	(	PUNCT
cana-3871	98	6	0	0	NUM
cana-3871	98	7	,	,	PUNCT
cana-3871	98	8	1	1	NUM
cana-3871	98	9	,	,	PUNCT
cana-3871	98	10	1	1	NUM
cana-3871	98	11	,	,	PUNCT
cana-3871	98	12	...	...	PUNCT
cana-3871	98	13	,	,	PUNCT
cana-3871	98	14	1	1	X
cana-3871	98	15	)	)	PUNCT
cana-3871	98	16	is	be	AUX
cana-3871	98	17	1	1	NUM
cana-3871	98	18	.	.	PUNCT
cana-3871	99	1	similarly	similarly	ADV
cana-3871	99	2	,	,	PUNCT
cana-3871	99	3	the	the	DET
cana-3871	99	4	degree	degree	NOUN
cana-3871	99	5	of	of	ADP
cana-3871	99	6	(	(	PUNCT
cana-3871	99	7	1	1	NUM
cana-3871	99	8	,	,	PUNCT
cana-3871	99	9	0	0	NUM
cana-3871	99	10	,	,	PUNCT
cana-3871	99	11	1	1	NUM
cana-3871	99	12	,	,	PUNCT
cana-3871	99	13	1	1	NUM
cana-3871	99	14	,	,	PUNCT
cana-3871	99	15	...	...	PUNCT
cana-3871	99	16	,	,	PUNCT
cana-3871	99	17	1	1	X
cana-3871	99	18	)	)	PUNCT
cana-3871	99	19	,	,	PUNCT
cana-3871	99	20	(	(	PUNCT
cana-3871	99	21	1	1	NUM
cana-3871	99	22	,	,	PUNCT
cana-3871	99	23	1	1	NUM
cana-3871	99	24	,	,	PUNCT
cana-3871	99	25	0	0	NUM
cana-3871	99	26	,	,	PUNCT
cana-3871	99	27	1	1	NUM
cana-3871	99	28	,	,	PUNCT
cana-3871	99	29	...	...	PUNCT
cana-3871	99	30	,	,	PUNCT
cana-3871	99	31	1	1	X
cana-3871	99	32	)	)	PUNCT
cana-3871	99	33	,	,	PUNCT
cana-3871	99	34	...	...	PUNCT
cana-3871	99	35	,	,	PUNCT
cana-3871	99	36	(	(	PUNCT
cana-3871	99	37	1	1	NUM
cana-3871	99	38	,	,	PUNCT
cana-3871	99	39	1	1	NUM
cana-3871	99	40	,	,	PUNCT
cana-3871	99	41	1	1	NUM
cana-3871	99	42	,	,	PUNCT
cana-3871	99	43	...	...	PUNCT
cana-3871	99	44	,	,	PUNCT
cana-3871	99	45	0	0	X
cana-3871	99	46	)	)	PUNCT
cana-3871	99	47	is	be	AUX
cana-3871	99	48	1	1	NUM
cana-3871	99	49	.	.	PUNCT
cana-3871	100	1	∴	∴	VERB
cana-3871	100	2	these	these	DET
cana-3871	100	3	n	n	PRON
cana-3871	100	4	elements	element	NOUN
cana-3871	100	5	have	have	VERB
cana-3871	100	6	degree	degree	NOUN
cana-3871	100	7	1	1	NUM
cana-3871	100	8	.	.	PUNCT
cana-3871	101	1	∴	∴	VERB
cana-3871	101	2	the	the	DET
cana-3871	101	3	n	n	NUM
cana-3871	101	4	vertices	vertex	NOUN
cana-3871	101	5	of	of	ADP
cana-3871	101	6	the	the	DET
cana-3871	101	7	zero	zero	NUM
cana-3871	101	8	divisor	divisor	NOUN
cana-3871	101	9	graph	graph	NOUN
cana-3871	101	10	of	of	ADP
cana-3871	101	11	ℤ2	ℤ2	PROPN
cana-3871	101	12	n	n	PRON
cana-3871	101	13	have	have	VERB
cana-3871	101	14	degree	degree	NOUN
cana-3871	101	15	1	1	NUM
cana-3871	101	16	3.2.1	3.2.1	NUM
cana-3871	101	17	example	example	NOUN
cana-3871	101	18	ℤ2	ℤ2	PROPN
cana-3871	101	19	2	2	NUM
cana-3871	101	20	=	=	SYM
cana-3871	101	21	ℤ2	ℤ2	PROPN
cana-3871	101	22	×	×	NOUN
cana-3871	101	23	ℤ2	ℤ2	NOUN
cana-3871	101	24	=	=	SYM
cana-3871	101	25	{	{	PUNCT
cana-3871	101	26	(	(	PUNCT
cana-3871	101	27	0	0	NUM
cana-3871	101	28	,	,	PUNCT
cana-3871	101	29	0	0	NUM
cana-3871	101	30	)	)	PUNCT
cana-3871	101	31	,	,	PUNCT
cana-3871	101	32	(	(	PUNCT
cana-3871	101	33	0	0	NUM
cana-3871	101	34	,	,	PUNCT
cana-3871	101	35	1	1	NUM
cana-3871	101	36	)	)	PUNCT
cana-3871	101	37	,	,	PUNCT
cana-3871	101	38	(	(	PUNCT
cana-3871	101	39	1	1	NUM
cana-3871	101	40	,	,	PUNCT
cana-3871	101	41	0	0	NUM
cana-3871	101	42	)	)	PUNCT
cana-3871	101	43	,	,	PUNCT
cana-3871	101	44	(	(	PUNCT
cana-3871	101	45	1	1	NUM
cana-3871	101	46	,	,	PUNCT
cana-3871	101	47	1	1	NUM
cana-3871	101	48	)	)	PUNCT
cana-3871	101	49	}	}	PUNCT
cana-3871	101	50	ℤ	ℤ	PROPN
cana-3871	101	51	(	(	PUNCT
cana-3871	101	52	ℤ2	ℤ2	PROPN
cana-3871	101	53	×	×	PROPN
cana-3871	101	54	ℤ2	ℤ2	PROPN
cana-3871	101	55	)	)	PUNCT
cana-3871	101	56	=	=	PRON
cana-3871	101	57	{	{	PUNCT
cana-3871	101	58	(	(	PUNCT
cana-3871	101	59	0	0	NUM
cana-3871	101	60	,	,	PUNCT
cana-3871	101	61	1	1	NUM
cana-3871	101	62	)	)	PUNCT
cana-3871	101	63	,	,	PUNCT
cana-3871	101	64	(	(	PUNCT
cana-3871	101	65	1	1	NUM
cana-3871	101	66	,	,	PUNCT
cana-3871	101	67	0	0	NUM
cana-3871	101	68	)	)	PUNCT
cana-3871	101	69	}	}	PUNCT
cana-3871	101	70	communications	communication	NOUN
cana-3871	101	71	on	on	ADP
cana-3871	101	72	applied	apply	VERB
cana-3871	101	73	nonlinear	nonlinear	ADJ
cana-3871	101	74	analysis	analysis	NOUN
cana-3871	101	75	issn	issn	NOUN
cana-3871	101	76	:	:	PUNCT
cana-3871	101	77	1074	1074	NUM
cana-3871	101	78	-	-	PUNCT
cana-3871	101	79	133x	133x	NUM
cana-3871	101	80	vol	vol	NOUN
cana-3871	101	81	32	32	NUM
cana-3871	101	82	no	no	NOUN
cana-3871	101	83	.	.	PUNCT
cana-3871	102	1	7s	7	NOUN
cana-3871	102	2	(	(	PUNCT
cana-3871	102	3	2025	2025	NUM
cana-3871	102	4	)	)	PUNCT
cana-3871	102	5	948	948	NUM
cana-3871	102	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	102	7	number	number	NOUN
cana-3871	102	8	of	of	ADP
cana-3871	102	9	vertices	vertex	NOUN
cana-3871	102	10	in	in	ADP
cana-3871	102	11	ℤ	ℤ	PROPN
cana-3871	102	12	(	(	PUNCT
cana-3871	102	13	ℤ2	ℤ2	PROPN
cana-3871	102	14	×	×	PROPN
cana-3871	102	15	ℤ2	ℤ2	PROPN
cana-3871	102	16	)	)	PUNCT
cana-3871	102	17	=	=	SYM
cana-3871	103	1	22	22	NUM
cana-3871	103	2	−	−	NUM
cana-3871	103	3	2	2	NUM
cana-3871	103	4	=	=	SYM
cana-3871	103	5	2	2	NUM
cana-3871	103	6	degree	degree	NOUN
cana-3871	103	7	of	of	ADP
cana-3871	103	8	vertex	vertex	NOUN
cana-3871	103	9	(	(	PUNCT
cana-3871	103	10	0,1	0,1	NUM
cana-3871	103	11	)	)	PUNCT
cana-3871	103	12	=	=	SYM
cana-3871	103	13	1	1	NUM
cana-3871	103	14	degree	degree	NOUN
cana-3871	103	15	of	of	ADP
cana-3871	103	16	vertex	vertex	NOUN
cana-3871	103	17	(	(	PUNCT
cana-3871	103	18	1,0	1,0	NUM
cana-3871	103	19	)	)	PUNCT
cana-3871	103	20	=	=	SYM
cana-3871	103	21	1	1	NUM
cana-3871	103	22	∴	∴	NOUN
cana-3871	103	23	2	2	NUM
cana-3871	103	24	vertices	vertex	NOUN
cana-3871	103	25	have	have	VERB
cana-3871	103	26	degree	degree	NOUN
cana-3871	103	27	1	1	NUM
cana-3871	103	28	.	.	PUNCT
cana-3871	103	29	3.2.2	3.2.2	NUM
cana-3871	103	30	example	example	NOUN
cana-3871	103	31	fig	fig	NOUN
cana-3871	103	32	8	8	NUM
cana-3871	103	33	:	:	PUNCT
cana-3871	103	34	γ(ℤ2	γ(ℤ2	PROPN
cana-3871	103	35	×	×	NOUN
cana-3871	103	36	ℤ2	ℤ2	PROPN
cana-3871	103	37	×	×	PROPN
cana-3871	103	38	ℤ2	ℤ2	PROPN
cana-3871	103	39	)	)	PUNCT
cana-3871	103	40	ℤ2	ℤ2	PROPN
cana-3871	103	41	3	3	NUM
cana-3871	103	42	=	=	SYM
cana-3871	103	43	ℤ2	ℤ2	PROPN
cana-3871	103	44	×	×	NOUN
cana-3871	103	45	ℤ2	ℤ2	PROPN
cana-3871	103	46	×	×	PROPN
cana-3871	103	47	ℤ2	ℤ2	PROPN
cana-3871	103	48	ℤ2	ℤ2	PROPN
cana-3871	103	49	×	×	PROPN
cana-3871	103	50	ℤ2	ℤ2	PROPN
cana-3871	103	51	×	×	NOUN
cana-3871	103	52	ℤ2	ℤ2	NOUN
cana-3871	103	53	=	=	SYM
cana-3871	103	54	{	{	PUNCT
cana-3871	103	55	(	(	PUNCT
cana-3871	103	56	0	0	NUM
cana-3871	103	57	,	,	PUNCT
cana-3871	103	58	0	0	NUM
cana-3871	103	59	,	,	PUNCT
cana-3871	103	60	0	0	NUM
cana-3871	103	61	)	)	PUNCT
cana-3871	103	62	,	,	PUNCT
cana-3871	103	63	(	(	PUNCT
cana-3871	103	64	0	0	NUM
cana-3871	103	65	,	,	PUNCT
cana-3871	103	66	0	0	NUM
cana-3871	103	67	,	,	PUNCT
cana-3871	103	68	1	1	NUM
cana-3871	103	69	)	)	PUNCT
cana-3871	103	70	,	,	PUNCT
cana-3871	103	71	(	(	PUNCT
cana-3871	103	72	0	0	NUM
cana-3871	103	73	,	,	PUNCT
cana-3871	103	74	1	1	NUM
cana-3871	103	75	,	,	PUNCT
cana-3871	103	76	0	0	NUM
cana-3871	103	77	)	)	PUNCT
cana-3871	103	78	,	,	PUNCT
cana-3871	103	79	(	(	PUNCT
cana-3871	103	80	0	0	NUM
cana-3871	103	81	,	,	PUNCT
cana-3871	103	82	1	1	NUM
cana-3871	103	83	,	,	PUNCT
cana-3871	103	84	1	1	NUM
cana-3871	103	85	)	)	PUNCT
cana-3871	103	86	,	,	PUNCT
cana-3871	103	87	(	(	PUNCT
cana-3871	103	88	1	1	NUM
cana-3871	103	89	,	,	PUNCT
cana-3871	103	90	0	0	NUM
cana-3871	103	91	,	,	PUNCT
cana-3871	103	92	1	1	NUM
cana-3871	103	93	)	)	PUNCT
cana-3871	103	94	,	,	PUNCT
cana-3871	103	95	(	(	PUNCT
cana-3871	103	96	1	1	NUM
cana-3871	103	97	,	,	PUNCT
cana-3871	103	98	1	1	NUM
cana-3871	103	99	,	,	PUNCT
cana-3871	103	100	0	0	NUM
cana-3871	103	101	)	)	PUNCT
cana-3871	103	102	,	,	PUNCT
cana-3871	103	103	(	(	PUNCT
cana-3871	103	104	1	1	NUM
cana-3871	103	105	,	,	PUNCT
cana-3871	103	106	0	0	NUM
cana-3871	103	107	,	,	PUNCT
cana-3871	103	108	0	0	NUM
cana-3871	103	109	)	)	PUNCT
cana-3871	103	110	,	,	PUNCT
cana-3871	103	111	(	(	PUNCT
cana-3871	103	112	1	1	NUM
cana-3871	103	113	,	,	PUNCT
cana-3871	103	114	1	1	NUM
cana-3871	103	115	,	,	PUNCT
cana-3871	103	116	1	1	NUM
cana-3871	103	117	)	)	PUNCT
cana-3871	103	118	}	}	PUNCT
cana-3871	103	119	ℤ	ℤ	PROPN
cana-3871	103	120	(	(	PUNCT
cana-3871	103	121	ℤ2	ℤ2	PROPN
cana-3871	103	122	×	×	PROPN
cana-3871	103	123	ℤ2	ℤ2	PROPN
cana-3871	103	124	×	×	PROPN
cana-3871	103	125	ℤ2	ℤ2	PROPN
cana-3871	103	126	)	)	PUNCT
cana-3871	103	127	=	=	PUNCT
cana-3871	103	128	(	(	PUNCT
cana-3871	103	129	0	0	NUM
cana-3871	103	130	,	,	PUNCT
cana-3871	103	131	0	0	NUM
cana-3871	103	132	,	,	PUNCT
cana-3871	103	133	1	1	NUM
cana-3871	103	134	)	)	PUNCT
cana-3871	103	135	,	,	PUNCT
cana-3871	103	136	(	(	PUNCT
cana-3871	103	137	0	0	NUM
cana-3871	103	138	,	,	PUNCT
cana-3871	103	139	1	1	NUM
cana-3871	103	140	,	,	PUNCT
cana-3871	103	141	0	0	NUM
cana-3871	103	142	)	)	PUNCT
cana-3871	103	143	,	,	PUNCT
cana-3871	103	144	(	(	PUNCT
cana-3871	103	145	0	0	NUM
cana-3871	103	146	,	,	PUNCT
cana-3871	103	147	1	1	NUM
cana-3871	103	148	,	,	PUNCT
cana-3871	103	149	1	1	NUM
cana-3871	103	150	)	)	PUNCT
cana-3871	103	151	,	,	PUNCT
cana-3871	103	152	(	(	PUNCT
cana-3871	103	153	1	1	NUM
cana-3871	103	154	,	,	PUNCT
cana-3871	103	155	0	0	NUM
cana-3871	103	156	,	,	PUNCT
cana-3871	103	157	1	1	NUM
cana-3871	103	158	)	)	PUNCT
cana-3871	103	159	,	,	PUNCT
cana-3871	103	160	(	(	PUNCT
cana-3871	103	161	1	1	NUM
cana-3871	103	162	,	,	PUNCT
cana-3871	103	163	1	1	NUM
cana-3871	103	164	,	,	PUNCT
cana-3871	103	165	0	0	NUM
cana-3871	103	166	)	)	PUNCT
cana-3871	103	167	,	,	PUNCT
cana-3871	103	168	(	(	PUNCT
cana-3871	103	169	1	1	NUM
cana-3871	103	170	,	,	PUNCT
cana-3871	103	171	0	0	NUM
cana-3871	103	172	,	,	PUNCT
cana-3871	103	173	0	0	NUM
cana-3871	103	174	)	)	PUNCT
cana-3871	103	175	the	the	DET
cana-3871	103	176	zero	zero	NUM
cana-3871	103	177	-	-	PUNCT
cana-3871	103	178	divisor	divisor	NOUN
cana-3871	103	179	graph	graph	NOUN
cana-3871	103	180	of	of	ADP
cana-3871	103	181	ℤ2	ℤ2	PROPN
cana-3871	103	182	×	×	PROPN
cana-3871	103	183	ℤ2	ℤ2	PROPN
cana-3871	103	184	×	×	PROPN
cana-3871	103	185	ℤ2	ℤ2	PROPN
cana-3871	103	186	is	be	AUX
cana-3871	103	187	given	give	VERB
cana-3871	103	188	in	in	ADP
cana-3871	103	189	the	the	DET
cana-3871	103	190	figure	figure	NOUN
cana-3871	103	191	above	above	ADV
cana-3871	103	192	.	.	PUNCT
cana-3871	104	1	number	number	NOUN
cana-3871	104	2	of	of	ADP
cana-3871	104	3	vertices	vertex	NOUN
cana-3871	104	4	in	in	ADP
cana-3871	104	5	the	the	DET
cana-3871	104	6	graph	graph	NOUN
cana-3871	104	7	of	of	ADP
cana-3871	104	8	ℤ	ℤ	PROPN
cana-3871	104	9	(	(	PUNCT
cana-3871	104	10	ℤ2	ℤ2	PROPN
cana-3871	104	11	×	×	PROPN
cana-3871	104	12	ℤ2	ℤ2	PROPN
cana-3871	104	13	×	×	PROPN
cana-3871	104	14	ℤ2	ℤ2	PROPN
cana-3871	104	15	)	)	PUNCT
cana-3871	105	1	=	=	NOUN
cana-3871	106	1	23	23	NUM
cana-3871	106	2	−	−	NUM
cana-3871	106	3	2	2	NUM
cana-3871	106	4	=	=	SYM
cana-3871	106	5	6	6	NUM
cana-3871	106	6	degree	degree	NOUN
cana-3871	106	7	of	of	ADP
cana-3871	106	8	vertex	vertex	NOUN
cana-3871	106	9	(	(	PUNCT
cana-3871	106	10	0	0	NUM
cana-3871	106	11	,	,	PUNCT
cana-3871	106	12	1	1	NUM
cana-3871	106	13	,	,	PUNCT
cana-3871	106	14	1	1	NUM
cana-3871	106	15	)	)	PUNCT
cana-3871	106	16	=	=	SYM
cana-3871	106	17	1	1	NUM
cana-3871	106	18	degree	degree	NOUN
cana-3871	106	19	of	of	ADP
cana-3871	106	20	vertex	vertex	NOUN
cana-3871	106	21	(	(	PUNCT
cana-3871	106	22	1	1	NUM
cana-3871	106	23	,	,	PUNCT
cana-3871	106	24	0	0	NUM
cana-3871	106	25	,	,	PUNCT
cana-3871	106	26	1	1	NUM
cana-3871	106	27	)	)	PUNCT
cana-3871	106	28	=	=	SYM
cana-3871	106	29	1	1	NUM
cana-3871	106	30	degree	degree	NOUN
cana-3871	106	31	of	of	ADP
cana-3871	106	32	vertex	vertex	NOUN
cana-3871	106	33	(	(	PUNCT
cana-3871	106	34	1	1	NUM
cana-3871	106	35	,	,	PUNCT
cana-3871	106	36	1	1	NUM
cana-3871	106	37	,	,	PUNCT
cana-3871	106	38	0	0	NUM
cana-3871	106	39	)	)	PUNCT
cana-3871	106	40	=	=	SYM
cana-3871	106	41	1	1	NUM
cana-3871	106	42	∴	∴	NOUN
cana-3871	106	43	3	3	NUM
cana-3871	106	44	vertices	vertex	NOUN
cana-3871	106	45	have	have	VERB
cana-3871	106	46	degree	degree	NOUN
cana-3871	106	47	1	1	NUM
cana-3871	106	48	.	.	PUNCT
cana-3871	106	49	3.2.3	3.2.3	NUM
cana-3871	106	50	example	example	NOUN
cana-3871	106	51	ℤ2	ℤ2	PROPN
cana-3871	106	52	4	4	NUM
cana-3871	106	53	=	=	SYM
cana-3871	106	54	ℤ2×ℤ2×ℤ2×ℤ2	ℤ2×ℤ2×ℤ2×ℤ2	NOUN
cana-3871	106	55	=	=	SYM
cana-3871	106	56	{	{	PUNCT
cana-3871	106	57	(	(	PUNCT
cana-3871	106	58	0	0	NUM
cana-3871	106	59	,	,	PUNCT
cana-3871	106	60	0	0	NUM
cana-3871	106	61	,	,	PUNCT
cana-3871	106	62	0	0	NUM
cana-3871	106	63	,	,	PUNCT
cana-3871	106	64	0	0	NUM
cana-3871	106	65	)	)	PUNCT
cana-3871	106	66	,	,	PUNCT
cana-3871	106	67	(	(	PUNCT
cana-3871	106	68	0	0	NUM
cana-3871	106	69	,	,	PUNCT
cana-3871	106	70	0	0	NUM
cana-3871	106	71	,	,	PUNCT
cana-3871	106	72	0	0	NUM
cana-3871	106	73	,	,	PUNCT
cana-3871	106	74	1	1	NUM
cana-3871	106	75	)	)	PUNCT
cana-3871	106	76	,	,	PUNCT
cana-3871	106	77	(	(	PUNCT
cana-3871	106	78	0	0	NUM
cana-3871	106	79	,	,	PUNCT
cana-3871	106	80	0	0	NUM
cana-3871	106	81	,	,	PUNCT
cana-3871	106	82	1	1	NUM
cana-3871	106	83	,	,	PUNCT
cana-3871	106	84	0	0	NUM
cana-3871	106	85	)	)	PUNCT
cana-3871	106	86	,	,	PUNCT
cana-3871	106	87	(	(	PUNCT
cana-3871	106	88	0	0	NUM
cana-3871	106	89	,	,	PUNCT
cana-3871	106	90	1	1	NUM
cana-3871	106	91	,	,	PUNCT
cana-3871	106	92	0	0	NUM
cana-3871	106	93	,	,	PUNCT
cana-3871	106	94	0	0	NUM
cana-3871	106	95	)	)	PUNCT
cana-3871	106	96	,	,	PUNCT
cana-3871	106	97	(	(	PUNCT
cana-3871	106	98	0	0	NUM
cana-3871	106	99	,	,	PUNCT
cana-3871	106	100	0	0	NUM
cana-3871	106	101	,	,	PUNCT
cana-3871	106	102	1	1	NUM
cana-3871	106	103	,	,	PUNCT
cana-3871	106	104	1	1	NUM
cana-3871	106	105	)	)	PUNCT
cana-3871	106	106	,	,	PUNCT
cana-3871	106	107	(	(	PUNCT
cana-3871	106	108	0	0	NUM
cana-3871	106	109	,	,	PUNCT
cana-3871	106	110	1	1	NUM
cana-3871	106	111	,	,	PUNCT
cana-3871	106	112	0	0	NUM
cana-3871	106	113	,	,	PUNCT
cana-3871	106	114	1	1	NUM
cana-3871	106	115	)	)	PUNCT
cana-3871	106	116	,	,	PUNCT
cana-3871	106	117	(	(	PUNCT
cana-3871	106	118	(	(	PUNCT
cana-3871	106	119	0	0	NUM
cana-3871	106	120	,	,	PUNCT
cana-3871	106	121	1	1	NUM
cana-3871	106	122	,	,	PUNCT
cana-3871	106	123	1	1	NUM
cana-3871	106	124	,	,	PUNCT
cana-3871	106	125	0	0	NUM
cana-3871	106	126	)	)	PUNCT
cana-3871	106	127	,	,	PUNCT
cana-3871	106	128	(	(	PUNCT
cana-3871	106	129	0	0	NUM
cana-3871	106	130	,	,	PUNCT
cana-3871	106	131	1	1	NUM
cana-3871	106	132	,	,	PUNCT
cana-3871	106	133	1	1	NUM
cana-3871	106	134	,	,	PUNCT
cana-3871	106	135	1	1	NUM
cana-3871	106	136	)	)	PUNCT
cana-3871	106	137	,	,	PUNCT
cana-3871	106	138	(	(	PUNCT
cana-3871	106	139	1	1	NUM
cana-3871	106	140	,	,	PUNCT
cana-3871	106	141	0	0	NUM
cana-3871	106	142	,	,	PUNCT
cana-3871	106	143	0	0	NUM
cana-3871	106	144	,	,	PUNCT
cana-3871	106	145	0	0	NUM
cana-3871	106	146	)	)	PUNCT
cana-3871	106	147	,	,	PUNCT
cana-3871	106	148	(	(	PUNCT
cana-3871	106	149	1	1	NUM
cana-3871	106	150	,	,	PUNCT
cana-3871	106	151	0	0	NUM
cana-3871	106	152	,	,	PUNCT
cana-3871	106	153	0	0	NUM
cana-3871	106	154	,	,	PUNCT
cana-3871	106	155	1	1	NUM
cana-3871	106	156	)	)	PUNCT
cana-3871	106	157	,	,	PUNCT
cana-3871	106	158	(	(	PUNCT
cana-3871	106	159	1	1	NUM
cana-3871	106	160	,	,	PUNCT
cana-3871	106	161	0	0	NUM
cana-3871	106	162	,	,	PUNCT
cana-3871	106	163	1	1	NUM
cana-3871	106	164	,	,	PUNCT
cana-3871	106	165	0	0	NUM
cana-3871	106	166	)	)	PUNCT
cana-3871	106	167	,	,	PUNCT
cana-3871	106	168	(	(	PUNCT
cana-3871	106	169	1	1	NUM
cana-3871	106	170	,	,	PUNCT
cana-3871	106	171	0	0	NUM
cana-3871	106	172	,	,	PUNCT
cana-3871	106	173	1	1	NUM
cana-3871	106	174	,	,	PUNCT
cana-3871	106	175	1	1	NUM
cana-3871	106	176	)	)	PUNCT
cana-3871	106	177	,	,	PUNCT
cana-3871	106	178	(	(	PUNCT
cana-3871	106	179	1	1	NUM
cana-3871	106	180	,	,	PUNCT
cana-3871	106	181	1	1	NUM
cana-3871	106	182	,	,	PUNCT
cana-3871	106	183	0	0	NUM
cana-3871	106	184	,	,	PUNCT
cana-3871	106	185	0	0	NUM
cana-3871	106	186	)	)	PUNCT
cana-3871	106	187	,	,	PUNCT
cana-3871	106	188	(	(	PUNCT
cana-3871	106	189	1	1	NUM
cana-3871	106	190	,	,	PUNCT
cana-3871	106	191	1	1	NUM
cana-3871	106	192	,	,	PUNCT
cana-3871	106	193	0	0	NUM
cana-3871	106	194	,	,	PUNCT
cana-3871	106	195	1	1	NUM
cana-3871	106	196	)	)	PUNCT
cana-3871	106	197	,	,	PUNCT
cana-3871	106	198	(	(	PUNCT
cana-3871	106	199	1	1	NUM
cana-3871	106	200	,	,	PUNCT
cana-3871	106	201	1	1	NUM
cana-3871	106	202	,	,	PUNCT
cana-3871	106	203	1	1	NUM
cana-3871	106	204	,	,	PUNCT
cana-3871	106	205	0	0	NUM
cana-3871	106	206	)	)	PUNCT
cana-3871	106	207	,	,	PUNCT
cana-3871	106	208	(	(	PUNCT
cana-3871	106	209	1	1	NUM
cana-3871	106	210	,	,	PUNCT
cana-3871	106	211	1	1	NUM
cana-3871	106	212	,	,	PUNCT
cana-3871	106	213	1	1	NUM
cana-3871	106	214	,	,	PUNCT
cana-3871	106	215	1	1	NUM
cana-3871	106	216	)	)	PUNCT
cana-3871	106	217	}	}	PUNCT
cana-3871	106	218	ℤ(ℤ2×ℤ2×ℤ2×ℤ2	ℤ(ℤ2×ℤ2×ℤ2×ℤ2	NOUN
cana-3871	106	219	)	)	PUNCT
cana-3871	106	220	=	=	SYM
cana-3871	106	221	{	{	PUNCT
cana-3871	106	222	(	(	PUNCT
cana-3871	106	223	0	0	NUM
cana-3871	106	224	,	,	PUNCT
cana-3871	106	225	0	0	NUM
cana-3871	106	226	,	,	PUNCT
cana-3871	106	227	0	0	NUM
cana-3871	106	228	,	,	PUNCT
cana-3871	106	229	1	1	NUM
cana-3871	106	230	)	)	PUNCT
cana-3871	106	231	,	,	PUNCT
cana-3871	106	232	(	(	PUNCT
cana-3871	106	233	0	0	NUM
cana-3871	106	234	,	,	PUNCT
cana-3871	106	235	0	0	NUM
cana-3871	106	236	,	,	PUNCT
cana-3871	106	237	1	1	NUM
cana-3871	106	238	,	,	PUNCT
cana-3871	106	239	0	0	NUM
cana-3871	106	240	)	)	PUNCT
cana-3871	106	241	,	,	PUNCT
cana-3871	106	242	(	(	PUNCT
cana-3871	106	243	0	0	NUM
cana-3871	106	244	,	,	PUNCT
cana-3871	106	245	1	1	NUM
cana-3871	106	246	,	,	PUNCT
cana-3871	106	247	0	0	NUM
cana-3871	106	248	,	,	PUNCT
cana-3871	106	249	0	0	NUM
cana-3871	106	250	)	)	PUNCT
cana-3871	106	251	,	,	PUNCT
cana-3871	106	252	(	(	PUNCT
cana-3871	106	253	0	0	NUM
cana-3871	106	254	,	,	PUNCT
cana-3871	106	255	0	0	NUM
cana-3871	106	256	,	,	PUNCT
cana-3871	106	257	1	1	NUM
cana-3871	106	258	,	,	PUNCT
cana-3871	106	259	1	1	NUM
cana-3871	106	260	)	)	PUNCT
cana-3871	106	261	,	,	PUNCT
cana-3871	106	262	(	(	PUNCT
cana-3871	106	263	0	0	NUM
cana-3871	106	264	,	,	PUNCT
cana-3871	106	265	1	1	NUM
cana-3871	106	266	,	,	PUNCT
cana-3871	106	267	0	0	NUM
cana-3871	106	268	,	,	PUNCT
cana-3871	106	269	1	1	NUM
cana-3871	106	270	)	)	PUNCT
cana-3871	106	271	,	,	PUNCT
cana-3871	106	272	(	(	PUNCT
cana-3871	106	273	0	0	NUM
cana-3871	106	274	,	,	PUNCT
cana-3871	106	275	1	1	NUM
cana-3871	106	276	,	,	PUNCT
cana-3871	106	277	1	1	NUM
cana-3871	106	278	,	,	PUNCT
cana-3871	106	279	0	0	NUM
cana-3871	106	280	)	)	PUNCT
cana-3871	106	281	,	,	PUNCT
cana-3871	106	282	(	(	PUNCT
cana-3871	106	283	0	0	NUM
cana-3871	106	284	,	,	PUNCT
cana-3871	106	285	1	1	NUM
cana-3871	106	286	,	,	PUNCT
cana-3871	106	287	1	1	NUM
cana-3871	106	288	,	,	PUNCT
cana-3871	106	289	1	1	NUM
cana-3871	106	290	)	)	PUNCT
cana-3871	106	291	,	,	PUNCT
cana-3871	106	292	(	(	PUNCT
cana-3871	106	293	1	1	NUM
cana-3871	106	294	,	,	PUNCT
cana-3871	106	295	0	0	NUM
cana-3871	106	296	,	,	PUNCT
cana-3871	106	297	0	0	NUM
cana-3871	106	298	,	,	PUNCT
cana-3871	106	299	0	0	NUM
cana-3871	106	300	)	)	PUNCT
cana-3871	106	301	,	,	PUNCT
cana-3871	106	302	(	(	PUNCT
cana-3871	106	303	1	1	NUM
cana-3871	106	304	,	,	PUNCT
cana-3871	106	305	0	0	NUM
cana-3871	106	306	,	,	PUNCT
cana-3871	106	307	0	0	NUM
cana-3871	106	308	,	,	PUNCT
cana-3871	106	309	1	1	NUM
cana-3871	106	310	)	)	PUNCT
cana-3871	106	311	,	,	PUNCT
cana-3871	106	312	(	(	PUNCT
cana-3871	106	313	1	1	NUM
cana-3871	106	314	,	,	PUNCT
cana-3871	106	315	0	0	NUM
cana-3871	106	316	,	,	PUNCT
cana-3871	106	317	1	1	NUM
cana-3871	106	318	,	,	PUNCT
cana-3871	106	319	0	0	NUM
cana-3871	106	320	)	)	PUNCT
cana-3871	106	321	,	,	PUNCT
cana-3871	106	322	(	(	PUNCT
cana-3871	106	323	1	1	NUM
cana-3871	106	324	,	,	PUNCT
cana-3871	106	325	0	0	NUM
cana-3871	106	326	,	,	PUNCT
cana-3871	106	327	1	1	NUM
cana-3871	106	328	,	,	PUNCT
cana-3871	106	329	1	1	NUM
cana-3871	106	330	)	)	PUNCT
cana-3871	106	331	,	,	PUNCT
cana-3871	106	332	(	(	PUNCT
cana-3871	106	333	1	1	NUM
cana-3871	106	334	,	,	PUNCT
cana-3871	106	335	1	1	NUM
cana-3871	106	336	,	,	PUNCT
cana-3871	106	337	0	0	NUM
cana-3871	106	338	,	,	PUNCT
cana-3871	106	339	0	0	NUM
cana-3871	106	340	)	)	PUNCT
cana-3871	106	341	,	,	PUNCT
cana-3871	106	342	(	(	PUNCT
cana-3871	106	343	1	1	NUM
cana-3871	106	344	,	,	PUNCT
cana-3871	106	345	1	1	NUM
cana-3871	106	346	,	,	PUNCT
cana-3871	106	347	0	0	NUM
cana-3871	106	348	,	,	PUNCT
cana-3871	106	349	1	1	NUM
cana-3871	106	350	)	)	PUNCT
cana-3871	106	351	,	,	PUNCT
cana-3871	106	352	(	(	PUNCT
cana-3871	106	353	1	1	NUM
cana-3871	106	354	,	,	PUNCT
cana-3871	106	355	1	1	NUM
cana-3871	106	356	,	,	PUNCT
cana-3871	106	357	1	1	NUM
cana-3871	106	358	,	,	PUNCT
cana-3871	106	359	0	0	NUM
cana-3871	106	360	)	)	PUNCT
cana-3871	106	361	}	}	PUNCT
cana-3871	106	362	the	the	DET
cana-3871	106	363	zero	zero	NUM
cana-3871	106	364	-	-	PUNCT
cana-3871	106	365	divisor	divisor	NOUN
cana-3871	106	366	graph	graph	NOUN
cana-3871	106	367	of	of	ADP
cana-3871	106	368	ℤ2	ℤ2	PROPN
cana-3871	106	369	×	×	PROPN
cana-3871	106	370	ℤ2	ℤ2	PROPN
cana-3871	106	371	×	×	PROPN
cana-3871	106	372	ℤ2	ℤ2	PROPN
cana-3871	106	373	×	×	PROPN
cana-3871	106	374	ℤ2	ℤ2	PROPN
cana-3871	106	375	is	be	AUX
cana-3871	106	376	given	give	VERB
cana-3871	106	377	in	in	ADP
cana-3871	106	378	the	the	DET
cana-3871	106	379	figure	figure	NOUN
cana-3871	106	380	below	below	ADV
cana-3871	106	381	.	.	PUNCT
cana-3871	107	1	communications	communication	NOUN
cana-3871	107	2	on	on	ADP
cana-3871	107	3	applied	apply	VERB
cana-3871	107	4	nonlinear	nonlinear	ADJ
cana-3871	107	5	analysis	analysis	NOUN
cana-3871	107	6	issn	issn	NOUN
cana-3871	107	7	:	:	PUNCT
cana-3871	107	8	1074	1074	NUM
cana-3871	107	9	-	-	PUNCT
cana-3871	107	10	133x	133x	NUM
cana-3871	107	11	vol	vol	NOUN
cana-3871	107	12	32	32	NUM
cana-3871	107	13	no	no	NOUN
cana-3871	107	14	.	.	PUNCT
cana-3871	108	1	7s	7	NOUN
cana-3871	108	2	(	(	PUNCT
cana-3871	108	3	2025	2025	NUM
cana-3871	108	4	)	)	PUNCT
cana-3871	108	5	949	949	NUM
cana-3871	108	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	108	7	fig	fig	NOUN
cana-3871	108	8	9	9	NUM
cana-3871	108	9	:	:	PUNCT
cana-3871	108	10	γ	γ	X
cana-3871	108	11	(	(	PUNCT
cana-3871	108	12	ℤ2	ℤ2	PROPN
cana-3871	108	13	×	×	PROPN
cana-3871	108	14	ℤ2	ℤ2	PROPN
cana-3871	108	15	×	×	PROPN
cana-3871	108	16	ℤ2	ℤ2	PROPN
cana-3871	108	17	×	×	PROPN
cana-3871	108	18	ℤ2	ℤ2	PROPN
cana-3871	108	19	)	)	PUNCT
cana-3871	108	20	here	here	ADV
cana-3871	108	21	,	,	PUNCT
cana-3871	108	22	n	n	PROPN
cana-3871	108	23	=	=	SYM
cana-3871	108	24	4	4	NUM
cana-3871	108	25	.	.	NOUN
cana-3871	108	26	number	number	NOUN
cana-3871	108	27	of	of	ADP
cana-3871	108	28	vertices	vertex	NOUN
cana-3871	108	29	in	in	ADP
cana-3871	108	30	the	the	DET
cana-3871	108	31	graph	graph	NOUN
cana-3871	108	32	of	of	ADP
cana-3871	108	33	ℤ	ℤ	PROPN
cana-3871	108	34	(	(	PUNCT
cana-3871	108	35	ℤ2	ℤ2	PROPN
cana-3871	108	36	×	×	PROPN
cana-3871	108	37	ℤ2	ℤ2	PROPN
cana-3871	108	38	×	×	PROPN
cana-3871	108	39	ℤ2	ℤ2	PROPN
cana-3871	108	40	×	×	PROPN
cana-3871	108	41	ℤ2	ℤ2	PROPN
cana-3871	108	42	)	)	PUNCT
cana-3871	109	1	=	=	SYM
cana-3871	109	2	24	24	NUM
cana-3871	109	3	−	−	NUM
cana-3871	109	4	2	2	NUM
cana-3871	109	5	=	=	SYM
cana-3871	109	6	14	14	NUM
cana-3871	109	7	degree	degree	NOUN
cana-3871	109	8	of	of	ADP
cana-3871	109	9	vertex	vertex	NOUN
cana-3871	109	10	(	(	PUNCT
cana-3871	109	11	0	0	NUM
cana-3871	109	12	,	,	PUNCT
cana-3871	109	13	1	1	NUM
cana-3871	109	14	,	,	PUNCT
cana-3871	109	15	1	1	NUM
cana-3871	109	16	,	,	PUNCT
cana-3871	109	17	1	1	NUM
cana-3871	109	18	)	)	PUNCT
cana-3871	109	19	=	=	SYM
cana-3871	109	20	1	1	NUM
cana-3871	109	21	degree	degree	NOUN
cana-3871	109	22	of	of	ADP
cana-3871	109	23	vertex	vertex	NOUN
cana-3871	109	24	(	(	PUNCT
cana-3871	109	25	1	1	NUM
cana-3871	109	26	,	,	PUNCT
cana-3871	109	27	0	0	NUM
cana-3871	109	28	,	,	PUNCT
cana-3871	109	29	1	1	NUM
cana-3871	109	30	,	,	PUNCT
cana-3871	109	31	1	1	NUM
cana-3871	109	32	)	)	PUNCT
cana-3871	109	33	=	=	SYM
cana-3871	109	34	1	1	NUM
cana-3871	109	35	degree	degree	NOUN
cana-3871	109	36	of	of	ADP
cana-3871	109	37	vertex	vertex	NOUN
cana-3871	109	38	(	(	PUNCT
cana-3871	109	39	1	1	NUM
cana-3871	109	40	,	,	PUNCT
cana-3871	109	41	1	1	NUM
cana-3871	109	42	,	,	PUNCT
cana-3871	109	43	0	0	NUM
cana-3871	109	44	,	,	PUNCT
cana-3871	109	45	1	1	NUM
cana-3871	109	46	)	)	PUNCT
cana-3871	109	47	=	=	SYM
cana-3871	109	48	1	1	NUM
cana-3871	109	49	degree	degree	NOUN
cana-3871	109	50	of	of	ADP
cana-3871	109	51	vertex	vertex	NOUN
cana-3871	109	52	(	(	PUNCT
cana-3871	109	53	1	1	NUM
cana-3871	109	54	,	,	PUNCT
cana-3871	109	55	1	1	NUM
cana-3871	109	56	,	,	PUNCT
cana-3871	109	57	1	1	NUM
cana-3871	109	58	,	,	PUNCT
cana-3871	109	59	0	0	NUM
cana-3871	109	60	)	)	PUNCT
cana-3871	109	61	=	=	SYM
cana-3871	109	62	1	1	NUM
cana-3871	109	63	∴	∴	NOUN
cana-3871	109	64	4	4	NUM
cana-3871	109	65	vertices	vertex	NOUN
cana-3871	109	66	have	have	VERB
cana-3871	109	67	degree	degree	NOUN
cana-3871	109	68	1	1	NUM
cana-3871	109	69	and	and	CCONJ
cana-3871	109	70	the	the	DET
cana-3871	109	71	theorem	theorem	NOUN
cana-3871	109	72	holds	hold	VERB
cana-3871	109	73	true	true	ADJ
cana-3871	109	74	.	.	PUNCT
cana-3871	110	1	3.2.4	3.2.4	NUM
cana-3871	110	2	example	example	NOUN
cana-3871	110	3	ℤ2	ℤ2	NOUN
cana-3871	110	4	5	5	NUM
cana-3871	110	5	=	=	SYM
cana-3871	110	6	ℤ2	ℤ2	PROPN
cana-3871	110	7	×	×	NOUN
cana-3871	110	8	ℤ2	ℤ2	PROPN
cana-3871	110	9	×	×	PROPN
cana-3871	110	10	ℤ2	ℤ2	PROPN
cana-3871	110	11	×	×	PROPN
cana-3871	110	12	ℤ2	ℤ2	PROPN
cana-3871	110	13	×	×	PROPN
cana-3871	110	14	ℤ2	ℤ2	PROPN
cana-3871	110	15	ℤ2	ℤ2	PROPN
cana-3871	110	16	×	×	PROPN
cana-3871	110	17	ℤ2	ℤ2	PROPN
cana-3871	110	18	×	×	PROPN
cana-3871	110	19	ℤ2	ℤ2	PROPN
cana-3871	110	20	×	×	PROPN
cana-3871	110	21	ℤ2	ℤ2	PROPN
cana-3871	110	22	×	×	NOUN
cana-3871	110	23	ℤ2	ℤ2	NOUN
cana-3871	110	24	=	=	SYM
cana-3871	110	25	{	{	PUNCT
cana-3871	110	26	(	(	PUNCT
cana-3871	110	27	0	0	NUM
cana-3871	110	28	,	,	PUNCT
cana-3871	110	29	0	0	NUM
cana-3871	110	30	,	,	PUNCT
cana-3871	110	31	0	0	NUM
cana-3871	110	32	,	,	PUNCT
cana-3871	110	33	0	0	NUM
cana-3871	110	34	,	,	PUNCT
cana-3871	110	35	0	0	NUM
cana-3871	110	36	)	)	PUNCT
cana-3871	110	37	,	,	PUNCT
cana-3871	110	38	(	(	PUNCT
cana-3871	110	39	0	0	NUM
cana-3871	110	40	,	,	PUNCT
cana-3871	110	41	0	0	NUM
cana-3871	110	42	,	,	PUNCT
cana-3871	110	43	0	0	NUM
cana-3871	110	44	,	,	PUNCT
cana-3871	110	45	0	0	NUM
cana-3871	110	46	,	,	PUNCT
cana-3871	110	47	1	1	NUM
cana-3871	110	48	)	)	PUNCT
cana-3871	110	49	,	,	PUNCT
cana-3871	110	50	(	(	PUNCT
cana-3871	110	51	0	0	NUM
cana-3871	110	52	,	,	PUNCT
cana-3871	110	53	0	0	NUM
cana-3871	110	54	,	,	PUNCT
cana-3871	110	55	0	0	NUM
cana-3871	110	56	,	,	PUNCT
cana-3871	110	57	1	1	NUM
cana-3871	110	58	,	,	PUNCT
cana-3871	110	59	0	0	NUM
cana-3871	110	60	)	)	PUNCT
cana-3871	110	61	,	,	PUNCT
cana-3871	110	62	(	(	PUNCT
cana-3871	110	63	0	0	NUM
cana-3871	110	64	,	,	PUNCT
cana-3871	110	65	0	0	NUM
cana-3871	110	66	,	,	PUNCT
cana-3871	110	67	0	0	NUM
cana-3871	110	68	,	,	PUNCT
cana-3871	110	69	1	1	NUM
cana-3871	110	70	,	,	PUNCT
cana-3871	110	71	1	1	NUM
cana-3871	110	72	)	)	PUNCT
cana-3871	110	73	,	,	PUNCT
cana-3871	110	74	(	(	PUNCT
cana-3871	110	75	0	0	NUM
cana-3871	110	76	,	,	PUNCT
cana-3871	110	77	0	0	NUM
cana-3871	110	78	,	,	PUNCT
cana-3871	110	79	1	1	NUM
cana-3871	110	80	,	,	PUNCT
cana-3871	110	81	0	0	NUM
cana-3871	110	82	,	,	PUNCT
cana-3871	110	83	0	0	NUM
cana-3871	110	84	)	)	PUNCT
cana-3871	110	85	,	,	PUNCT
cana-3871	110	86	(	(	PUNCT
cana-3871	110	87	0	0	NUM
cana-3871	110	88	,	,	PUNCT
cana-3871	110	89	0	0	NUM
cana-3871	110	90	,	,	PUNCT
cana-3871	110	91	1	1	NUM
cana-3871	110	92	,	,	PUNCT
cana-3871	110	93	0	0	NUM
cana-3871	110	94	,	,	PUNCT
cana-3871	110	95	1	1	NUM
cana-3871	110	96	)	)	PUNCT
cana-3871	110	97	,	,	PUNCT
cana-3871	110	98	(	(	PUNCT
cana-3871	110	99	0	0	NUM
cana-3871	110	100	,	,	PUNCT
cana-3871	110	101	0	0	NUM
cana-3871	110	102	,	,	PUNCT
cana-3871	110	103	1	1	NUM
cana-3871	110	104	,	,	PUNCT
cana-3871	110	105	1	1	NUM
cana-3871	110	106	,	,	PUNCT
cana-3871	110	107	0	0	NUM
cana-3871	110	108	)	)	PUNCT
cana-3871	110	109	,	,	PUNCT
cana-3871	110	110	(	(	PUNCT
cana-3871	110	111	0	0	NUM
cana-3871	110	112	,	,	PUNCT
cana-3871	110	113	0	0	NUM
cana-3871	110	114	,	,	PUNCT
cana-3871	110	115	1	1	NUM
cana-3871	110	116	,	,	PUNCT
cana-3871	110	117	1	1	NUM
cana-3871	110	118	,	,	PUNCT
cana-3871	110	119	1	1	NUM
cana-3871	110	120	)	)	PUNCT
cana-3871	110	121	,	,	PUNCT
cana-3871	110	122	(	(	PUNCT
cana-3871	110	123	0	0	NUM
cana-3871	110	124	,	,	PUNCT
cana-3871	110	125	1	1	NUM
cana-3871	110	126	,	,	PUNCT
cana-3871	110	127	0	0	NUM
cana-3871	110	128	,	,	PUNCT
cana-3871	110	129	0	0	NUM
cana-3871	110	130	,	,	PUNCT
cana-3871	110	131	0	0	NUM
cana-3871	110	132	)	)	PUNCT
cana-3871	110	133	,	,	PUNCT
cana-3871	110	134	(	(	PUNCT
cana-3871	110	135	0	0	NUM
cana-3871	110	136	,	,	PUNCT
cana-3871	110	137	1	1	NUM
cana-3871	110	138	,	,	PUNCT
cana-3871	110	139	0	0	NUM
cana-3871	110	140	,	,	PUNCT
cana-3871	110	141	0	0	NUM
cana-3871	110	142	,	,	PUNCT
cana-3871	110	143	1	1	NUM
cana-3871	110	144	)	)	PUNCT
cana-3871	110	145	,	,	PUNCT
cana-3871	110	146	(	(	PUNCT
cana-3871	110	147	0	0	NUM
cana-3871	110	148	,	,	PUNCT
cana-3871	110	149	1	1	NUM
cana-3871	110	150	,	,	PUNCT
cana-3871	110	151	0	0	NUM
cana-3871	110	152	,	,	PUNCT
cana-3871	110	153	1	1	NUM
cana-3871	110	154	,	,	PUNCT
cana-3871	110	155	0	0	NUM
cana-3871	110	156	)	)	PUNCT
cana-3871	110	157	,	,	PUNCT
cana-3871	110	158	(	(	PUNCT
cana-3871	110	159	0	0	NUM
cana-3871	110	160	,	,	PUNCT
cana-3871	110	161	1	1	NUM
cana-3871	110	162	,	,	PUNCT
cana-3871	110	163	0	0	NUM
cana-3871	110	164	,	,	PUNCT
cana-3871	110	165	1	1	NUM
cana-3871	110	166	,	,	PUNCT
cana-3871	110	167	1	1	NUM
cana-3871	110	168	)	)	PUNCT
cana-3871	110	169	,	,	PUNCT
cana-3871	110	170	(	(	PUNCT
cana-3871	110	171	0	0	NUM
cana-3871	110	172	,	,	PUNCT
cana-3871	110	173	1	1	NUM
cana-3871	110	174	,	,	PUNCT
cana-3871	110	175	1	1	NUM
cana-3871	110	176	,	,	PUNCT
cana-3871	110	177	0	0	NUM
cana-3871	110	178	,	,	PUNCT
cana-3871	110	179	0	0	NUM
cana-3871	110	180	)	)	PUNCT
cana-3871	110	181	,	,	PUNCT
cana-3871	110	182	(	(	PUNCT
cana-3871	110	183	0	0	NUM
cana-3871	110	184	,	,	PUNCT
cana-3871	110	185	1	1	NUM
cana-3871	110	186	,	,	PUNCT
cana-3871	110	187	1	1	NUM
cana-3871	110	188	,	,	PUNCT
cana-3871	110	189	0	0	NUM
cana-3871	110	190	,	,	PUNCT
cana-3871	110	191	1	1	NUM
cana-3871	110	192	)	)	PUNCT
cana-3871	110	193	,	,	PUNCT
cana-3871	110	194	(	(	PUNCT
cana-3871	110	195	0	0	NUM
cana-3871	110	196	,	,	PUNCT
cana-3871	110	197	1	1	NUM
cana-3871	110	198	,	,	PUNCT
cana-3871	110	199	1	1	NUM
cana-3871	110	200	,	,	PUNCT
cana-3871	110	201	1	1	NUM
cana-3871	110	202	,	,	PUNCT
cana-3871	110	203	0	0	NUM
cana-3871	110	204	)	)	PUNCT
cana-3871	110	205	,	,	PUNCT
cana-3871	110	206	(	(	PUNCT
cana-3871	110	207	0	0	NUM
cana-3871	110	208	,	,	PUNCT
cana-3871	110	209	1	1	NUM
cana-3871	110	210	,	,	PUNCT
cana-3871	110	211	1	1	NUM
cana-3871	110	212	,	,	PUNCT
cana-3871	110	213	1	1	NUM
cana-3871	110	214	,	,	PUNCT
cana-3871	110	215	1	1	NUM
cana-3871	110	216	)	)	PUNCT
cana-3871	110	217	,	,	PUNCT
cana-3871	110	218	(	(	PUNCT
cana-3871	110	219	1	1	NUM
cana-3871	110	220	,	,	PUNCT
cana-3871	110	221	0	0	NUM
cana-3871	110	222	,	,	PUNCT
cana-3871	110	223	0	0	NUM
cana-3871	110	224	,	,	PUNCT
cana-3871	110	225	0	0	NUM
cana-3871	110	226	,	,	PUNCT
cana-3871	110	227	0	0	NUM
cana-3871	110	228	)	)	PUNCT
cana-3871	110	229	,	,	PUNCT
cana-3871	110	230	(	(	PUNCT
cana-3871	110	231	1	1	NUM
cana-3871	110	232	,	,	PUNCT
cana-3871	110	233	0	0	NUM
cana-3871	110	234	,	,	PUNCT
cana-3871	110	235	0	0	NUM
cana-3871	110	236	,	,	PUNCT
cana-3871	110	237	0	0	NUM
cana-3871	110	238	,	,	PUNCT
cana-3871	110	239	1	1	NUM
cana-3871	110	240	)	)	PUNCT
cana-3871	110	241	,	,	PUNCT
cana-3871	110	242	(	(	PUNCT
cana-3871	110	243	1	1	NUM
cana-3871	110	244	,	,	PUNCT
cana-3871	110	245	0	0	NUM
cana-3871	110	246	,	,	PUNCT
cana-3871	110	247	0	0	NUM
cana-3871	110	248	,	,	PUNCT
cana-3871	110	249	1	1	NUM
cana-3871	110	250	,	,	PUNCT
cana-3871	110	251	0	0	NUM
cana-3871	110	252	)	)	PUNCT
cana-3871	110	253	,	,	PUNCT
cana-3871	110	254	(	(	PUNCT
cana-3871	110	255	1	1	NUM
cana-3871	110	256	,	,	PUNCT
cana-3871	110	257	0	0	NUM
cana-3871	110	258	,	,	PUNCT
cana-3871	110	259	0	0	NUM
cana-3871	110	260	,	,	PUNCT
cana-3871	110	261	1	1	NUM
cana-3871	110	262	,	,	PUNCT
cana-3871	110	263	1	1	NUM
cana-3871	110	264	)	)	PUNCT
cana-3871	110	265	,	,	PUNCT
cana-3871	110	266	(	(	PUNCT
cana-3871	110	267	1	1	NUM
cana-3871	110	268	,	,	PUNCT
cana-3871	110	269	0	0	NUM
cana-3871	110	270	,	,	PUNCT
cana-3871	110	271	1	1	NUM
cana-3871	110	272	,	,	PUNCT
cana-3871	110	273	0	0	NUM
cana-3871	110	274	,	,	PUNCT
cana-3871	110	275	0	0	NUM
cana-3871	110	276	)	)	PUNCT
cana-3871	110	277	,	,	PUNCT
cana-3871	110	278	(	(	PUNCT
cana-3871	110	279	1	1	NUM
cana-3871	110	280	,	,	PUNCT
cana-3871	110	281	0	0	NUM
cana-3871	110	282	,	,	PUNCT
cana-3871	110	283	1	1	NUM
cana-3871	110	284	,	,	PUNCT
cana-3871	110	285	0	0	NUM
cana-3871	110	286	,	,	PUNCT
cana-3871	110	287	1	1	NUM
cana-3871	110	288	)	)	PUNCT
cana-3871	110	289	,	,	PUNCT
cana-3871	110	290	(	(	PUNCT
cana-3871	110	291	1	1	NUM
cana-3871	110	292	,	,	PUNCT
cana-3871	110	293	0	0	NUM
cana-3871	110	294	,	,	PUNCT
cana-3871	110	295	1	1	NUM
cana-3871	110	296	,	,	PUNCT
cana-3871	110	297	1	1	NUM
cana-3871	110	298	,	,	PUNCT
cana-3871	110	299	0	0	NUM
cana-3871	110	300	)	)	PUNCT
cana-3871	110	301	,	,	PUNCT
cana-3871	110	302	(	(	PUNCT
cana-3871	110	303	1	1	NUM
cana-3871	110	304	,	,	PUNCT
cana-3871	110	305	0	0	NUM
cana-3871	110	306	,	,	PUNCT
cana-3871	110	307	1	1	NUM
cana-3871	110	308	,	,	PUNCT
cana-3871	110	309	1	1	NUM
cana-3871	110	310	,	,	PUNCT
cana-3871	110	311	1	1	NUM
cana-3871	110	312	)	)	PUNCT
cana-3871	110	313	,	,	PUNCT
cana-3871	110	314	(	(	PUNCT
cana-3871	110	315	1	1	NUM
cana-3871	110	316	,	,	PUNCT
cana-3871	110	317	1	1	NUM
cana-3871	110	318	,	,	PUNCT
cana-3871	110	319	0	0	NUM
cana-3871	110	320	,	,	PUNCT
cana-3871	110	321	0	0	NUM
cana-3871	110	322	,	,	PUNCT
cana-3871	110	323	0	0	NUM
cana-3871	110	324	)	)	PUNCT
cana-3871	110	325	,	,	PUNCT
cana-3871	110	326	(	(	PUNCT
cana-3871	110	327	1	1	NUM
cana-3871	110	328	,	,	PUNCT
cana-3871	110	329	1	1	NUM
cana-3871	110	330	,	,	PUNCT
cana-3871	110	331	0	0	NUM
cana-3871	110	332	,	,	PUNCT
cana-3871	110	333	0	0	NUM
cana-3871	110	334	,	,	PUNCT
cana-3871	110	335	1	1	NUM
cana-3871	110	336	)	)	PUNCT
cana-3871	110	337	,	,	PUNCT
cana-3871	110	338	(	(	PUNCT
cana-3871	110	339	1	1	NUM
cana-3871	110	340	,	,	PUNCT
cana-3871	110	341	1	1	NUM
cana-3871	110	342	,	,	PUNCT
cana-3871	110	343	0	0	NUM
cana-3871	110	344	,	,	PUNCT
cana-3871	110	345	1	1	NUM
cana-3871	110	346	,	,	PUNCT
cana-3871	110	347	0	0	NUM
cana-3871	110	348	)	)	PUNCT
cana-3871	110	349	,	,	PUNCT
cana-3871	110	350	(	(	PUNCT
cana-3871	110	351	1	1	NUM
cana-3871	110	352	,	,	PUNCT
cana-3871	110	353	1	1	NUM
cana-3871	110	354	,	,	PUNCT
cana-3871	110	355	0	0	NUM
cana-3871	110	356	,	,	PUNCT
cana-3871	110	357	1	1	NUM
cana-3871	110	358	,	,	PUNCT
cana-3871	110	359	1	1	NUM
cana-3871	110	360	)	)	PUNCT
cana-3871	110	361	,	,	PUNCT
cana-3871	110	362	(	(	PUNCT
cana-3871	110	363	1	1	NUM
cana-3871	110	364	,	,	PUNCT
cana-3871	110	365	1	1	NUM
cana-3871	110	366	,	,	PUNCT
cana-3871	110	367	1	1	NUM
cana-3871	110	368	,	,	PUNCT
cana-3871	110	369	0	0	NUM
cana-3871	110	370	,	,	PUNCT
cana-3871	110	371	0	0	NUM
cana-3871	110	372	)	)	PUNCT
cana-3871	110	373	,	,	PUNCT
cana-3871	110	374	(	(	PUNCT
cana-3871	110	375	1	1	NUM
cana-3871	110	376	,	,	PUNCT
cana-3871	110	377	1	1	NUM
cana-3871	110	378	,	,	PUNCT
cana-3871	110	379	1	1	NUM
cana-3871	110	380	,	,	PUNCT
cana-3871	110	381	0	0	NUM
cana-3871	110	382	,	,	PUNCT
cana-3871	110	383	1	1	NUM
cana-3871	110	384	)	)	PUNCT
cana-3871	110	385	,	,	PUNCT
cana-3871	110	386	(	(	PUNCT
cana-3871	110	387	1	1	NUM
cana-3871	110	388	,	,	PUNCT
cana-3871	110	389	1	1	NUM
cana-3871	110	390	,	,	PUNCT
cana-3871	110	391	1	1	NUM
cana-3871	110	392	,	,	PUNCT
cana-3871	110	393	1	1	NUM
cana-3871	110	394	,	,	PUNCT
cana-3871	110	395	0	0	NUM
cana-3871	110	396	)	)	PUNCT
cana-3871	110	397	,	,	PUNCT
cana-3871	110	398	(	(	PUNCT
cana-3871	110	399	1	1	NUM
cana-3871	110	400	,	,	PUNCT
cana-3871	110	401	1	1	NUM
cana-3871	110	402	,	,	PUNCT
cana-3871	110	403	1	1	NUM
cana-3871	110	404	,	,	PUNCT
cana-3871	110	405	1	1	NUM
cana-3871	110	406	,	,	PUNCT
cana-3871	110	407	1	1	NUM
cana-3871	110	408	)	)	PUNCT
cana-3871	110	409	}	}	PUNCT
cana-3871	110	410	ℤ(ℤ2×ℤ2×ℤ2×ℤ2×ℤ2	ℤ(ℤ2×ℤ2×ℤ2×ℤ2×ℤ2	PROPN
cana-3871	110	411	)	)	PUNCT
cana-3871	110	412	=	=	PRON
cana-3871	110	413	{	{	PUNCT
cana-3871	110	414	(	(	PUNCT
cana-3871	110	415	0	0	NUM
cana-3871	110	416	,	,	PUNCT
cana-3871	110	417	0	0	NUM
cana-3871	110	418	,	,	PUNCT
cana-3871	110	419	0	0	NUM
cana-3871	110	420	,	,	PUNCT
cana-3871	110	421	0	0	NUM
cana-3871	110	422	,	,	PUNCT
cana-3871	110	423	1	1	NUM
cana-3871	110	424	)	)	PUNCT
cana-3871	110	425	,	,	PUNCT
cana-3871	110	426	(	(	PUNCT
cana-3871	110	427	0	0	NUM
cana-3871	110	428	,	,	PUNCT
cana-3871	110	429	0	0	NUM
cana-3871	110	430	,	,	PUNCT
cana-3871	110	431	0	0	NUM
cana-3871	110	432	,	,	PUNCT
cana-3871	110	433	1	1	NUM
cana-3871	110	434	,	,	PUNCT
cana-3871	110	435	0	0	NUM
cana-3871	110	436	)	)	PUNCT
cana-3871	110	437	,	,	PUNCT
cana-3871	110	438	(	(	PUNCT
cana-3871	110	439	0	0	NUM
cana-3871	110	440	,	,	PUNCT
cana-3871	110	441	0	0	NUM
cana-3871	110	442	,	,	PUNCT
cana-3871	110	443	0	0	NUM
cana-3871	110	444	,	,	PUNCT
cana-3871	110	445	1	1	NUM
cana-3871	110	446	,	,	PUNCT
cana-3871	110	447	1	1	NUM
cana-3871	110	448	)	)	PUNCT
cana-3871	110	449	(	(	PUNCT
cana-3871	110	450	0	0	NUM
cana-3871	110	451	,	,	PUNCT
cana-3871	110	452	0	0	NUM
cana-3871	110	453	,	,	PUNCT
cana-3871	110	454	1	1	NUM
cana-3871	110	455	,	,	PUNCT
cana-3871	110	456	0	0	NUM
cana-3871	110	457	,	,	PUNCT
cana-3871	110	458	0	0	NUM
cana-3871	110	459	)	)	PUNCT
cana-3871	110	460	,	,	PUNCT
cana-3871	110	461	(	(	PUNCT
cana-3871	110	462	0	0	NUM
cana-3871	110	463	,	,	PUNCT
cana-3871	110	464	0	0	NUM
cana-3871	110	465	,	,	PUNCT
cana-3871	110	466	1	1	NUM
cana-3871	110	467	,	,	PUNCT
cana-3871	110	468	0	0	NUM
cana-3871	110	469	,	,	PUNCT
cana-3871	110	470	1	1	NUM
cana-3871	110	471	)	)	PUNCT
cana-3871	110	472	,	,	PUNCT
cana-3871	110	473	(	(	PUNCT
cana-3871	110	474	0	0	NUM
cana-3871	110	475	,	,	PUNCT
cana-3871	110	476	0	0	NUM
cana-3871	110	477	,	,	PUNCT
cana-3871	110	478	1	1	NUM
cana-3871	110	479	,	,	PUNCT
cana-3871	110	480	1	1	NUM
cana-3871	110	481	,	,	PUNCT
cana-3871	110	482	0	0	NUM
cana-3871	110	483	)	)	PUNCT
cana-3871	110	484	,	,	PUNCT
cana-3871	110	485	(	(	PUNCT
cana-3871	110	486	0	0	NUM
cana-3871	110	487	,	,	PUNCT
cana-3871	110	488	0	0	NUM
cana-3871	110	489	,	,	PUNCT
cana-3871	110	490	1	1	NUM
cana-3871	110	491	,	,	PUNCT
cana-3871	110	492	1	1	NUM
cana-3871	110	493	,	,	PUNCT
cana-3871	110	494	1	1	NUM
cana-3871	110	495	)	)	PUNCT
cana-3871	110	496	,	,	PUNCT
cana-3871	110	497	(	(	PUNCT
cana-3871	110	498	0	0	NUM
cana-3871	110	499	,	,	PUNCT
cana-3871	110	500	1	1	NUM
cana-3871	110	501	,	,	PUNCT
cana-3871	110	502	0	0	NUM
cana-3871	110	503	,	,	PUNCT
cana-3871	110	504	0	0	NUM
cana-3871	110	505	,	,	PUNCT
cana-3871	110	506	0	0	NUM
cana-3871	110	507	)	)	PUNCT
cana-3871	110	508	,	,	PUNCT
cana-3871	110	509	(	(	PUNCT
cana-3871	110	510	0	0	NUM
cana-3871	110	511	,	,	PUNCT
cana-3871	110	512	1	1	NUM
cana-3871	110	513	,	,	PUNCT
cana-3871	110	514	0	0	NUM
cana-3871	110	515	,	,	PUNCT
cana-3871	110	516	0	0	NUM
cana-3871	110	517	,	,	PUNCT
cana-3871	110	518	1	1	NUM
cana-3871	110	519	)	)	PUNCT
cana-3871	110	520	,	,	PUNCT
cana-3871	110	521	(	(	PUNCT
cana-3871	110	522	0	0	NUM
cana-3871	110	523	,	,	PUNCT
cana-3871	110	524	1	1	NUM
cana-3871	110	525	,	,	PUNCT
cana-3871	110	526	0	0	NUM
cana-3871	110	527	,	,	PUNCT
cana-3871	110	528	1	1	NUM
cana-3871	110	529	,	,	PUNCT
cana-3871	110	530	0	0	NUM
cana-3871	110	531	)	)	PUNCT
cana-3871	110	532	,	,	PUNCT
cana-3871	110	533	(	(	PUNCT
cana-3871	110	534	0	0	NUM
cana-3871	110	535	,	,	PUNCT
cana-3871	110	536	1	1	NUM
cana-3871	110	537	,	,	PUNCT
cana-3871	110	538	0	0	NUM
cana-3871	110	539	,	,	PUNCT
cana-3871	110	540	1	1	NUM
cana-3871	110	541	,	,	PUNCT
cana-3871	110	542	1	1	NUM
cana-3871	110	543	)	)	PUNCT
cana-3871	110	544	,	,	PUNCT
cana-3871	110	545	(	(	PUNCT
cana-3871	110	546	0	0	NUM
cana-3871	110	547	,	,	PUNCT
cana-3871	110	548	1	1	NUM
cana-3871	110	549	,	,	PUNCT
cana-3871	110	550	1	1	NUM
cana-3871	110	551	,	,	PUNCT
cana-3871	110	552	0	0	NUM
cana-3871	110	553	,	,	PUNCT
cana-3871	110	554	0	0	NUM
cana-3871	110	555	)	)	PUNCT
cana-3871	110	556	,	,	PUNCT
cana-3871	110	557	(	(	PUNCT
cana-3871	110	558	0	0	NUM
cana-3871	110	559	,	,	PUNCT
cana-3871	110	560	1	1	NUM
cana-3871	110	561	,	,	PUNCT
cana-3871	110	562	1	1	NUM
cana-3871	110	563	,	,	PUNCT
cana-3871	110	564	0	0	NUM
cana-3871	110	565	,	,	PUNCT
cana-3871	110	566	1	1	NUM
cana-3871	110	567	)	)	PUNCT
cana-3871	110	568	,	,	PUNCT
cana-3871	110	569	(	(	PUNCT
cana-3871	110	570	0	0	NUM
cana-3871	110	571	,	,	PUNCT
cana-3871	110	572	1	1	NUM
cana-3871	110	573	,	,	PUNCT
cana-3871	110	574	1	1	NUM
cana-3871	110	575	,	,	PUNCT
cana-3871	110	576	1	1	NUM
cana-3871	110	577	,	,	PUNCT
cana-3871	110	578	0	0	NUM
cana-3871	110	579	)	)	PUNCT
cana-3871	110	580	,	,	PUNCT
cana-3871	110	581	(	(	PUNCT
cana-3871	110	582	0	0	NUM
cana-3871	110	583	,	,	PUNCT
cana-3871	110	584	1	1	NUM
cana-3871	110	585	,	,	PUNCT
cana-3871	110	586	1	1	NUM
cana-3871	110	587	,	,	PUNCT
cana-3871	110	588	1	1	NUM
cana-3871	110	589	,	,	PUNCT
cana-3871	110	590	1	1	NUM
cana-3871	110	591	)	)	PUNCT
cana-3871	110	592	,	,	PUNCT
cana-3871	110	593	(	(	PUNCT
cana-3871	110	594	1	1	NUM
cana-3871	110	595	,	,	PUNCT
cana-3871	110	596	0	0	NUM
cana-3871	110	597	,	,	PUNCT
cana-3871	110	598	0	0	NUM
cana-3871	110	599	,	,	PUNCT
cana-3871	110	600	0	0	NUM
cana-3871	110	601	,	,	PUNCT
cana-3871	110	602	0	0	NUM
cana-3871	110	603	)	)	PUNCT
cana-3871	110	604	,	,	PUNCT
cana-3871	110	605	(	(	PUNCT
cana-3871	110	606	1	1	NUM
cana-3871	110	607	,	,	PUNCT
cana-3871	110	608	0	0	NUM
cana-3871	110	609	,	,	PUNCT
cana-3871	110	610	0	0	NUM
cana-3871	110	611	,	,	PUNCT
cana-3871	110	612	0	0	NUM
cana-3871	110	613	,	,	PUNCT
cana-3871	110	614	1	1	NUM
cana-3871	110	615	)	)	PUNCT
cana-3871	110	616	,	,	PUNCT
cana-3871	110	617	(	(	PUNCT
cana-3871	110	618	1	1	NUM
cana-3871	110	619	,	,	PUNCT
cana-3871	110	620	0	0	NUM
cana-3871	110	621	,	,	PUNCT
cana-3871	110	622	0	0	NUM
cana-3871	110	623	,	,	PUNCT
cana-3871	110	624	1	1	NUM
cana-3871	110	625	,	,	PUNCT
cana-3871	110	626	0	0	NUM
cana-3871	110	627	)	)	PUNCT
cana-3871	110	628	,	,	PUNCT
cana-3871	110	629	(	(	PUNCT
cana-3871	110	630	1	1	NUM
cana-3871	110	631	,	,	PUNCT
cana-3871	110	632	0	0	NUM
cana-3871	110	633	,	,	PUNCT
cana-3871	110	634	0	0	NUM
cana-3871	110	635	,	,	PUNCT
cana-3871	110	636	1	1	NUM
cana-3871	110	637	,	,	PUNCT
cana-3871	110	638	1	1	NUM
cana-3871	110	639	)	)	PUNCT
cana-3871	110	640	,	,	PUNCT
cana-3871	110	641	(	(	PUNCT
cana-3871	110	642	1	1	NUM
cana-3871	110	643	,	,	PUNCT
cana-3871	110	644	0	0	NUM
cana-3871	110	645	,	,	PUNCT
cana-3871	110	646	1	1	NUM
cana-3871	110	647	,	,	PUNCT
cana-3871	110	648	0	0	NUM
cana-3871	110	649	,	,	PUNCT
cana-3871	110	650	0	0	NUM
cana-3871	110	651	)	)	PUNCT
cana-3871	110	652	,	,	PUNCT
cana-3871	110	653	(	(	PUNCT
cana-3871	110	654	1	1	NUM
cana-3871	110	655	,	,	PUNCT
cana-3871	110	656	0	0	NUM
cana-3871	110	657	,	,	PUNCT
cana-3871	110	658	1	1	NUM
cana-3871	110	659	,	,	PUNCT
cana-3871	110	660	0	0	NUM
cana-3871	110	661	,	,	PUNCT
cana-3871	110	662	1	1	NUM
cana-3871	110	663	)	)	PUNCT
cana-3871	110	664	,	,	PUNCT
cana-3871	110	665	(	(	PUNCT
cana-3871	110	666	1	1	NUM
cana-3871	110	667	,	,	PUNCT
cana-3871	110	668	0	0	NUM
cana-3871	110	669	,	,	PUNCT
cana-3871	110	670	1	1	NUM
cana-3871	110	671	,	,	PUNCT
cana-3871	110	672	1	1	NUM
cana-3871	110	673	,	,	PUNCT
cana-3871	110	674	0	0	NUM
cana-3871	110	675	)	)	PUNCT
cana-3871	110	676	,	,	PUNCT
cana-3871	110	677	(	(	PUNCT
cana-3871	110	678	1	1	NUM
cana-3871	110	679	,	,	PUNCT
cana-3871	110	680	0	0	NUM
cana-3871	110	681	,	,	PUNCT
cana-3871	110	682	1	1	NUM
cana-3871	110	683	,	,	PUNCT
cana-3871	110	684	1	1	NUM
cana-3871	110	685	,	,	PUNCT
cana-3871	110	686	1	1	NUM
cana-3871	110	687	)	)	PUNCT
cana-3871	110	688	,	,	PUNCT
cana-3871	110	689	(	(	PUNCT
cana-3871	110	690	1	1	NUM
cana-3871	110	691	,	,	PUNCT
cana-3871	110	692	1	1	NUM
cana-3871	110	693	,	,	PUNCT
cana-3871	110	694	0	0	NUM
cana-3871	110	695	,	,	PUNCT
cana-3871	110	696	0	0	NUM
cana-3871	110	697	,	,	PUNCT
cana-3871	110	698	0	0	NUM
cana-3871	110	699	)	)	PUNCT
cana-3871	110	700	,	,	PUNCT
cana-3871	110	701	(	(	PUNCT
cana-3871	110	702	1	1	NUM
cana-3871	110	703	,	,	PUNCT
cana-3871	110	704	1	1	NUM
cana-3871	110	705	,	,	PUNCT
cana-3871	110	706	0	0	NUM
cana-3871	110	707	,	,	PUNCT
cana-3871	110	708	0	0	NUM
cana-3871	110	709	,	,	PUNCT
cana-3871	110	710	1	1	NUM
cana-3871	110	711	)	)	PUNCT
cana-3871	110	712	,	,	PUNCT
cana-3871	110	713	(	(	PUNCT
cana-3871	110	714	1	1	NUM
cana-3871	110	715	,	,	PUNCT
cana-3871	110	716	1	1	NUM
cana-3871	110	717	,	,	PUNCT
cana-3871	110	718	0	0	NUM
cana-3871	110	719	,	,	PUNCT
cana-3871	110	720	1	1	NUM
cana-3871	110	721	,	,	PUNCT
cana-3871	110	722	0	0	NUM
cana-3871	110	723	)	)	PUNCT
cana-3871	110	724	,	,	PUNCT
cana-3871	110	725	(	(	PUNCT
cana-3871	110	726	1	1	NUM
cana-3871	110	727	,	,	PUNCT
cana-3871	110	728	1	1	NUM
cana-3871	110	729	,	,	PUNCT
cana-3871	110	730	0	0	NUM
cana-3871	110	731	,	,	PUNCT
cana-3871	110	732	1	1	NUM
cana-3871	110	733	,	,	PUNCT
cana-3871	110	734	1	1	NUM
cana-3871	110	735	)	)	PUNCT
cana-3871	110	736	,	,	PUNCT
cana-3871	110	737	(	(	PUNCT
cana-3871	110	738	1	1	NUM
cana-3871	110	739	,	,	PUNCT
cana-3871	110	740	1	1	NUM
cana-3871	110	741	,	,	PUNCT
cana-3871	110	742	1	1	NUM
cana-3871	110	743	,	,	PUNCT
cana-3871	110	744	0	0	NUM
cana-3871	110	745	,	,	PUNCT
cana-3871	110	746	0	0	NUM
cana-3871	110	747	)	)	PUNCT
cana-3871	110	748	,	,	PUNCT
cana-3871	110	749	(	(	PUNCT
cana-3871	110	750	1	1	NUM
cana-3871	110	751	,	,	PUNCT
cana-3871	110	752	1	1	NUM
cana-3871	110	753	,	,	PUNCT
cana-3871	110	754	1	1	NUM
cana-3871	110	755	,	,	PUNCT
cana-3871	110	756	0	0	NUM
cana-3871	110	757	,	,	PUNCT
cana-3871	110	758	1	1	NUM
cana-3871	110	759	)	)	PUNCT
cana-3871	110	760	,	,	PUNCT
cana-3871	110	761	(	(	PUNCT
cana-3871	110	762	1	1	NUM
cana-3871	110	763	,	,	PUNCT
cana-3871	110	764	1	1	NUM
cana-3871	110	765	,	,	PUNCT
cana-3871	110	766	1	1	NUM
cana-3871	110	767	,	,	PUNCT
cana-3871	110	768	1	1	NUM
cana-3871	110	769	,	,	PUNCT
cana-3871	110	770	0	0	NUM
cana-3871	110	771	)	)	PUNCT
cana-3871	110	772	}	}	PUNCT
cana-3871	110	773	the	the	DET
cana-3871	110	774	zero	zero	NUM
cana-3871	110	775	-	-	PUNCT
cana-3871	110	776	divisor	divisor	NOUN
cana-3871	110	777	graph	graph	NOUN
cana-3871	110	778	of	of	ADP
cana-3871	110	779	ℤ2	ℤ2	PROPN
cana-3871	110	780	×	×	PROPN
cana-3871	110	781	ℤ2	ℤ2	PROPN
cana-3871	110	782	×	×	PROPN
cana-3871	110	783	ℤ2	ℤ2	PROPN
cana-3871	110	784	×	×	PROPN
cana-3871	110	785	ℤ2	ℤ2	PROPN
cana-3871	110	786	×	×	PROPN
cana-3871	110	787	ℤ2	ℤ2	PROPN
cana-3871	110	788	is	be	AUX
cana-3871	110	789	given	give	VERB
cana-3871	110	790	in	in	ADP
cana-3871	110	791	the	the	DET
cana-3871	110	792	figure	figure	NOUN
cana-3871	110	793	below	below	ADV
cana-3871	110	794	,	,	PUNCT
cana-3871	110	795	communications	communication	NOUN
cana-3871	110	796	on	on	ADP
cana-3871	110	797	applied	apply	VERB
cana-3871	110	798	nonlinear	nonlinear	ADJ
cana-3871	110	799	analysis	analysis	NOUN
cana-3871	110	800	issn	issn	NOUN
cana-3871	110	801	:	:	PUNCT
cana-3871	110	802	1074	1074	NUM
cana-3871	110	803	-	-	PUNCT
cana-3871	110	804	133x	133x	NUM
cana-3871	110	805	vol	vol	NOUN
cana-3871	110	806	32	32	NUM
cana-3871	110	807	no	no	NOUN
cana-3871	110	808	.	.	PUNCT
cana-3871	111	1	7s	7	NOUN
cana-3871	111	2	(	(	PUNCT
cana-3871	111	3	2025	2025	NUM
cana-3871	111	4	)	)	PUNCT
cana-3871	111	5	950	950	NUM
cana-3871	111	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	111	7	fig	fig	NOUN
cana-3871	111	8	10	10	NUM
cana-3871	111	9	:	:	PUNCT
cana-3871	111	10	γ	γ	X
cana-3871	111	11	(	(	PUNCT
cana-3871	111	12	ℤ2	ℤ2	PROPN
cana-3871	111	13	×	×	PROPN
cana-3871	111	14	ℤ2	ℤ2	PROPN
cana-3871	111	15	×	×	PROPN
cana-3871	111	16	ℤ2	ℤ2	PROPN
cana-3871	111	17	×	×	PROPN
cana-3871	111	18	ℤ2	ℤ2	PROPN
cana-3871	111	19	×	×	PROPN
cana-3871	111	20	ℤ2	ℤ2	PROPN
cana-3871	111	21	)	)	PUNCT
cana-3871	111	22	here	here	ADV
cana-3871	111	23	,	,	PUNCT
cana-3871	111	24	n	n	NOUN
cana-3871	111	25	=	=	SYM
cana-3871	111	26	5	5	NUM
cana-3871	111	27	number	number	NOUN
cana-3871	111	28	of	of	ADP
cana-3871	111	29	vertices	vertex	NOUN
cana-3871	111	30	in	in	ADP
cana-3871	111	31	ℤ	ℤ	PROPN
cana-3871	111	32	(	(	PUNCT
cana-3871	111	33	ℤ2	ℤ2	PROPN
cana-3871	111	34	×	×	PROPN
cana-3871	111	35	ℤ2	ℤ2	PROPN
cana-3871	111	36	×	×	PROPN
cana-3871	111	37	ℤ2	ℤ2	PROPN
cana-3871	111	38	×	×	PROPN
cana-3871	111	39	ℤ2	ℤ2	PROPN
cana-3871	111	40	×	×	PROPN
cana-3871	111	41	ℤ2	ℤ2	PROPN
cana-3871	111	42	)	)	PUNCT
cana-3871	111	43	=	=	PUNCT
cana-3871	112	1	25	25	NUM
cana-3871	112	2	−	−	NUM
cana-3871	112	3	2	2	NUM
cana-3871	112	4	=	=	SYM
cana-3871	112	5	30	30	NUM
cana-3871	112	6	degree	degree	NOUN
cana-3871	112	7	of	of	ADP
cana-3871	112	8	vertex	vertex	NOUN
cana-3871	112	9	(	(	PUNCT
cana-3871	112	10	0	0	NUM
cana-3871	112	11	,	,	PUNCT
cana-3871	112	12	1	1	NUM
cana-3871	112	13	,	,	PUNCT
cana-3871	112	14	1	1	NUM
cana-3871	112	15	,	,	PUNCT
cana-3871	112	16	1	1	NUM
cana-3871	112	17	,	,	PUNCT
cana-3871	112	18	1	1	NUM
cana-3871	112	19	)	)	PUNCT
cana-3871	112	20	=	=	SYM
cana-3871	112	21	1	1	NUM
cana-3871	112	22	degree	degree	NOUN
cana-3871	112	23	of	of	ADP
cana-3871	112	24	vertex	vertex	NOUN
cana-3871	112	25	(	(	PUNCT
cana-3871	112	26	1	1	NUM
cana-3871	112	27	,	,	PUNCT
cana-3871	112	28	0	0	NUM
cana-3871	112	29	,	,	PUNCT
cana-3871	112	30	1	1	NUM
cana-3871	112	31	,	,	PUNCT
cana-3871	112	32	1	1	NUM
cana-3871	112	33	,	,	PUNCT
cana-3871	112	34	1	1	NUM
cana-3871	112	35	)	)	PUNCT
cana-3871	112	36	=	=	SYM
cana-3871	112	37	1	1	NUM
cana-3871	112	38	degree	degree	NOUN
cana-3871	112	39	of	of	ADP
cana-3871	112	40	vertex	vertex	NOUN
cana-3871	112	41	(	(	PUNCT
cana-3871	112	42	1	1	NUM
cana-3871	112	43	,	,	PUNCT
cana-3871	112	44	1	1	NUM
cana-3871	112	45	,	,	PUNCT
cana-3871	112	46	0	0	NUM
cana-3871	112	47	,	,	PUNCT
cana-3871	112	48	1	1	NUM
cana-3871	112	49	,	,	PUNCT
cana-3871	112	50	1	1	NUM
cana-3871	112	51	)	)	PUNCT
cana-3871	112	52	=	=	SYM
cana-3871	112	53	1	1	NUM
cana-3871	112	54	degree	degree	NOUN
cana-3871	112	55	of	of	ADP
cana-3871	112	56	vertex	vertex	NOUN
cana-3871	112	57	(	(	PUNCT
cana-3871	112	58	1	1	NUM
cana-3871	112	59	,	,	PUNCT
cana-3871	112	60	1	1	NUM
cana-3871	112	61	,	,	PUNCT
cana-3871	112	62	1	1	NUM
cana-3871	112	63	,	,	PUNCT
cana-3871	112	64	0	0	NUM
cana-3871	112	65	,	,	PUNCT
cana-3871	112	66	1	1	NUM
cana-3871	112	67	)	)	PUNCT
cana-3871	112	68	=	=	SYM
cana-3871	112	69	1	1	NUM
cana-3871	112	70	degree	degree	NOUN
cana-3871	112	71	of	of	ADP
cana-3871	112	72	vertex	vertex	NOUN
cana-3871	112	73	(	(	PUNCT
cana-3871	112	74	1	1	NUM
cana-3871	112	75	,	,	PUNCT
cana-3871	112	76	1	1	NUM
cana-3871	112	77	,	,	PUNCT
cana-3871	112	78	1	1	NUM
cana-3871	112	79	,	,	PUNCT
cana-3871	112	80	1	1	NUM
cana-3871	112	81	,	,	PUNCT
cana-3871	112	82	0	0	NUM
cana-3871	112	83	)	)	PUNCT
cana-3871	112	84	=	=	SYM
cana-3871	112	85	1	1	NUM
cana-3871	112	86	∴	∴	NOUN
cana-3871	112	87	5	5	NUM
cana-3871	112	88	vertices	vertex	NOUN
cana-3871	112	89	have	have	VERB
cana-3871	112	90	degree	degree	NOUN
cana-3871	112	91	1	1	NUM
cana-3871	112	92	.	.	PUNCT
cana-3871	113	1	∴	∴	PROPN
cana-3871	113	2	the	the	DET
cana-3871	113	3	theorem	theorem	NOUN
cana-3871	113	4	holds	hold	VERB
cana-3871	113	5	.	.	PUNCT
cana-3871	114	1	3.3	3.3	NUM
cana-3871	114	2	corollary	corollary	NOUN
cana-3871	114	3	:	:	PUNCT
cana-3871	114	4	all	all	DET
cana-3871	114	5	vertices	vertex	NOUN
cana-3871	114	6	of	of	ADP
cana-3871	114	7	the	the	DET
cana-3871	114	8	zero	zero	NUM
cana-3871	114	9	divisor	divisor	NOUN
cana-3871	114	10	graph	graph	NOUN
cana-3871	114	11	γ(ℤ2	γ(ℤ2	PROPN
cana-3871	114	12	n	n	CCONJ
cana-3871	114	13	)	)	PUNCT
cana-3871	114	14	have	have	VERB
cana-3871	114	15	odd	odd	ADJ
cana-3871	114	16	degrees	degree	NOUN
cana-3871	114	17	.	.	PUNCT
cana-3871	115	1	3.3.1	3.3.1	NUM
cana-3871	115	2	example	example	NOUN
cana-3871	115	3	fig	fig	NOUN
cana-3871	115	4	11	11	NUM
cana-3871	115	5	:	:	PUNCT
cana-3871	115	6	γ	γ	X
cana-3871	115	7	(	(	PUNCT
cana-3871	115	8	ℤ2	ℤ2	PROPN
cana-3871	115	9	×	×	PROPN
cana-3871	115	10	ℤ2	ℤ2	PROPN
cana-3871	115	11	×	×	PROPN
cana-3871	115	12	ℤ2	ℤ2	PROPN
cana-3871	115	13	)	)	PUNCT
cana-3871	115	14	ℤ2	ℤ2	PROPN
cana-3871	115	15	3	3	NUM
cana-3871	115	16	=	=	SYM
cana-3871	115	17	ℤ2	ℤ2	PROPN
cana-3871	115	18	×	×	NOUN
cana-3871	115	19	ℤ2	ℤ2	PROPN
cana-3871	115	20	×	×	PROPN
cana-3871	115	21	ℤ2	ℤ2	PROPN
cana-3871	115	22	ℤ2	ℤ2	PROPN
cana-3871	115	23	×	×	PROPN
cana-3871	115	24	ℤ2	ℤ2	PROPN
cana-3871	115	25	×	×	NOUN
cana-3871	115	26	ℤ2	ℤ2	NOUN
cana-3871	115	27	=	=	SYM
cana-3871	115	28	{	{	PUNCT
cana-3871	115	29	(	(	PUNCT
cana-3871	115	30	0	0	NUM
cana-3871	115	31	,	,	PUNCT
cana-3871	115	32	0	0	NUM
cana-3871	115	33	,	,	PUNCT
cana-3871	115	34	0	0	NUM
cana-3871	115	35	)	)	PUNCT
cana-3871	115	36	,	,	PUNCT
cana-3871	115	37	(	(	PUNCT
cana-3871	115	38	0	0	NUM
cana-3871	115	39	,	,	PUNCT
cana-3871	115	40	0	0	NUM
cana-3871	115	41	,	,	PUNCT
cana-3871	115	42	1	1	NUM
cana-3871	115	43	)	)	PUNCT
cana-3871	115	44	,	,	PUNCT
cana-3871	115	45	(	(	PUNCT
cana-3871	115	46	0	0	NUM
cana-3871	115	47	,	,	PUNCT
cana-3871	115	48	1	1	NUM
cana-3871	115	49	,	,	PUNCT
cana-3871	115	50	0	0	NUM
cana-3871	115	51	)	)	PUNCT
cana-3871	115	52	,	,	PUNCT
cana-3871	115	53	(	(	PUNCT
cana-3871	115	54	0	0	NUM
cana-3871	115	55	,	,	PUNCT
cana-3871	115	56	1	1	NUM
cana-3871	115	57	,	,	PUNCT
cana-3871	115	58	1	1	NUM
cana-3871	115	59	)	)	PUNCT
cana-3871	115	60	,	,	PUNCT
cana-3871	115	61	(	(	PUNCT
cana-3871	115	62	1	1	NUM
cana-3871	115	63	,	,	PUNCT
cana-3871	115	64	0	0	NUM
cana-3871	115	65	,	,	PUNCT
cana-3871	115	66	1	1	NUM
cana-3871	115	67	)	)	PUNCT
cana-3871	115	68	,	,	PUNCT
cana-3871	115	69	(	(	PUNCT
cana-3871	115	70	1	1	NUM
cana-3871	115	71	,	,	PUNCT
cana-3871	115	72	1	1	NUM
cana-3871	115	73	,	,	PUNCT
cana-3871	115	74	0	0	NUM
cana-3871	115	75	)	)	PUNCT
cana-3871	115	76	,	,	PUNCT
cana-3871	115	77	(	(	PUNCT
cana-3871	115	78	1	1	NUM
cana-3871	115	79	,	,	PUNCT
cana-3871	115	80	0	0	NUM
cana-3871	115	81	,	,	PUNCT
cana-3871	115	82	0	0	NUM
cana-3871	115	83	)	)	PUNCT
cana-3871	115	84	,	,	PUNCT
cana-3871	115	85	(	(	PUNCT
cana-3871	115	86	1	1	NUM
cana-3871	115	87	,	,	PUNCT
cana-3871	115	88	1	1	NUM
cana-3871	115	89	,	,	PUNCT
cana-3871	115	90	1	1	NUM
cana-3871	115	91	)	)	PUNCT
cana-3871	115	92	}	}	PUNCT
cana-3871	115	93	communications	communication	NOUN
cana-3871	115	94	on	on	ADP
cana-3871	115	95	applied	apply	VERB
cana-3871	115	96	nonlinear	nonlinear	ADJ
cana-3871	115	97	analysis	analysis	NOUN
cana-3871	115	98	issn	issn	NOUN
cana-3871	115	99	:	:	PUNCT
cana-3871	115	100	1074	1074	NUM
cana-3871	115	101	-	-	PUNCT
cana-3871	115	102	133x	133x	NUM
cana-3871	115	103	vol	vol	NOUN
cana-3871	115	104	32	32	NUM
cana-3871	115	105	no	no	NOUN
cana-3871	115	106	.	.	PUNCT
cana-3871	116	1	7s	7	NOUN
cana-3871	116	2	(	(	PUNCT
cana-3871	116	3	2025	2025	NUM
cana-3871	116	4	)	)	PUNCT
cana-3871	116	5	951	951	NUM
cana-3871	116	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	116	7	ℤ	ℤ	PROPN
cana-3871	116	8	(	(	PUNCT
cana-3871	116	9	ℤ2	ℤ2	PROPN
cana-3871	116	10	×	×	PROPN
cana-3871	116	11	ℤ2	ℤ2	PROPN
cana-3871	116	12	×	×	PROPN
cana-3871	116	13	ℤ2	ℤ2	PROPN
cana-3871	116	14	)	)	PUNCT
cana-3871	116	15	=	=	PUNCT
cana-3871	116	16	(	(	PUNCT
cana-3871	116	17	0	0	NUM
cana-3871	116	18	,	,	PUNCT
cana-3871	116	19	0	0	NUM
cana-3871	116	20	,	,	PUNCT
cana-3871	116	21	1	1	NUM
cana-3871	116	22	)	)	PUNCT
cana-3871	116	23	,	,	PUNCT
cana-3871	116	24	(	(	PUNCT
cana-3871	116	25	0	0	NUM
cana-3871	116	26	,	,	PUNCT
cana-3871	116	27	1	1	NUM
cana-3871	116	28	,	,	PUNCT
cana-3871	116	29	0	0	NUM
cana-3871	116	30	)	)	PUNCT
cana-3871	116	31	,	,	PUNCT
cana-3871	116	32	(	(	PUNCT
cana-3871	116	33	0	0	NUM
cana-3871	116	34	,	,	PUNCT
cana-3871	116	35	1	1	NUM
cana-3871	116	36	,	,	PUNCT
cana-3871	116	37	1	1	NUM
cana-3871	116	38	)	)	PUNCT
cana-3871	116	39	,	,	PUNCT
cana-3871	116	40	(	(	PUNCT
cana-3871	116	41	1	1	NUM
cana-3871	116	42	,	,	PUNCT
cana-3871	116	43	0	0	NUM
cana-3871	116	44	,	,	PUNCT
cana-3871	116	45	1	1	NUM
cana-3871	116	46	)	)	PUNCT
cana-3871	116	47	,	,	PUNCT
cana-3871	116	48	(	(	PUNCT
cana-3871	116	49	1	1	NUM
cana-3871	116	50	,	,	PUNCT
cana-3871	116	51	1	1	NUM
cana-3871	116	52	,	,	PUNCT
cana-3871	116	53	0	0	NUM
cana-3871	116	54	)	)	PUNCT
cana-3871	116	55	,	,	PUNCT
cana-3871	116	56	(	(	PUNCT
cana-3871	116	57	1	1	NUM
cana-3871	116	58	,	,	PUNCT
cana-3871	116	59	0	0	NUM
cana-3871	116	60	,	,	PUNCT
cana-3871	116	61	0	0	NUM
cana-3871	116	62	)	)	PUNCT
cana-3871	116	63	the	the	DET
cana-3871	116	64	zero	zero	NUM
cana-3871	116	65	-	-	PUNCT
cana-3871	116	66	divisor	divisor	NOUN
cana-3871	116	67	graph	graph	NOUN
cana-3871	116	68	of	of	ADP
cana-3871	116	69	ℤ2	ℤ2	PROPN
cana-3871	116	70	×	×	PROPN
cana-3871	116	71	ℤ2	ℤ2	PROPN
cana-3871	116	72	×	×	PROPN
cana-3871	116	73	ℤ2	ℤ2	PROPN
cana-3871	116	74	is	be	AUX
cana-3871	116	75	given	give	VERB
cana-3871	116	76	in	in	ADP
cana-3871	116	77	the	the	DET
cana-3871	116	78	figure	figure	NOUN
cana-3871	116	79	above	above	ADV
cana-3871	116	80	.	.	PUNCT
cana-3871	117	1	number	number	NOUN
cana-3871	117	2	of	of	ADP
cana-3871	117	3	vertices	vertex	NOUN
cana-3871	117	4	in	in	ADP
cana-3871	117	5	the	the	DET
cana-3871	117	6	graph	graph	NOUN
cana-3871	117	7	of	of	ADP
cana-3871	117	8	ℤ	ℤ	PROPN
cana-3871	117	9	(	(	PUNCT
cana-3871	117	10	ℤ2	ℤ2	PROPN
cana-3871	117	11	×	×	PROPN
cana-3871	117	12	ℤ2	ℤ2	PROPN
cana-3871	117	13	×	×	PROPN
cana-3871	117	14	ℤ2	ℤ2	PROPN
cana-3871	117	15	)	)	PUNCT
cana-3871	118	1	=	=	NOUN
cana-3871	119	1	23	23	NUM
cana-3871	119	2	−	−	NUM
cana-3871	119	3	2	2	NUM
cana-3871	119	4	=	=	SYM
cana-3871	119	5	6	6	NUM
cana-3871	119	6	the	the	DET
cana-3871	119	7	degree	degree	NOUN
cana-3871	119	8	of	of	ADP
cana-3871	119	9	(	(	PUNCT
cana-3871	119	10	0,1,1	0,1,1	NUM
cana-3871	119	11	)	)	PUNCT
cana-3871	119	12	,	,	PUNCT
cana-3871	119	13	(	(	PUNCT
cana-3871	119	14	1,0,1	1,0,1	NUM
cana-3871	119	15	)	)	PUNCT
cana-3871	119	16	,	,	PUNCT
cana-3871	119	17	(	(	PUNCT
cana-3871	119	18	1,1,0	1,1,0	NUM
cana-3871	119	19	)	)	PUNCT
cana-3871	119	20	is	be	AUX
cana-3871	119	21	1	1	NUM
cana-3871	119	22	.	.	PUNCT
cana-3871	120	1	the	the	DET
cana-3871	120	2	degree	degree	NOUN
cana-3871	120	3	of	of	ADP
cana-3871	120	4	(	(	PUNCT
cana-3871	120	5	0,0,1	0,0,1	NOUN
cana-3871	120	6	)	)	PUNCT
cana-3871	120	7	,	,	PUNCT
cana-3871	120	8	(	(	PUNCT
cana-3871	120	9	0,1,0	0,1,0	NUM
cana-3871	120	10	)	)	PUNCT
cana-3871	120	11	,	,	PUNCT
cana-3871	120	12	(	(	PUNCT
cana-3871	120	13	1,0,0	1,0,0	NUM
cana-3871	120	14	)	)	PUNCT
cana-3871	120	15	is	be	AUX
cana-3871	120	16	3	3	NUM
cana-3871	120	17	.	.	PUNCT
cana-3871	121	1	∴	∴	NOUN
cana-3871	121	2	all	all	DET
cana-3871	121	3	vertices	vertex	NOUN
cana-3871	121	4	of	of	ADP
cana-3871	121	5	ℤ2	ℤ2	PROPN
cana-3871	121	6	×	×	PROPN
cana-3871	121	7	ℤ2	ℤ2	PROPN
cana-3871	121	8	×	×	PROPN
cana-3871	121	9	ℤ2	ℤ2	PROPN
cana-3871	121	10	have	have	VERB
cana-3871	121	11	odd	odd	ADJ
cana-3871	121	12	degrees	degree	NOUN
cana-3871	121	13	.	.	PUNCT
cana-3871	122	1	3.3.2	3.3.2	NUM
cana-3871	122	2	example	example	NOUN
cana-3871	122	3	ℤ2	ℤ2	PROPN
cana-3871	122	4	4	4	NUM
cana-3871	122	5	=	=	SYM
cana-3871	122	6	ℤ2	ℤ2	PROPN
cana-3871	122	7	×	×	NOUN
cana-3871	122	8	ℤ2	ℤ2	PROPN
cana-3871	122	9	×	×	PROPN
cana-3871	122	10	ℤ2	ℤ2	PROPN
cana-3871	122	11	×	×	PROPN
cana-3871	122	12	ℤ2	ℤ2	PROPN
cana-3871	122	13	ℤ2×ℤ2×ℤ2×ℤ2	ℤ2×ℤ2×ℤ2×ℤ2	PROPN
cana-3871	122	14	=	=	SYM
cana-3871	122	15	{	{	PUNCT
cana-3871	122	16	(	(	PUNCT
cana-3871	122	17	0	0	NUM
cana-3871	122	18	,	,	PUNCT
cana-3871	122	19	0	0	NUM
cana-3871	122	20	,	,	PUNCT
cana-3871	122	21	0	0	NUM
cana-3871	122	22	,	,	PUNCT
cana-3871	122	23	0	0	NUM
cana-3871	122	24	)	)	PUNCT
cana-3871	122	25	,	,	PUNCT
cana-3871	122	26	(	(	PUNCT
cana-3871	122	27	0	0	NUM
cana-3871	122	28	,	,	PUNCT
cana-3871	122	29	0	0	NUM
cana-3871	122	30	,	,	PUNCT
cana-3871	122	31	0	0	NUM
cana-3871	122	32	,	,	PUNCT
cana-3871	122	33	1	1	NUM
cana-3871	122	34	)	)	PUNCT
cana-3871	122	35	,	,	PUNCT
cana-3871	122	36	(	(	PUNCT
cana-3871	122	37	0	0	NUM
cana-3871	122	38	,	,	PUNCT
cana-3871	122	39	0	0	NUM
cana-3871	122	40	,	,	PUNCT
cana-3871	122	41	1	1	NUM
cana-3871	122	42	,	,	PUNCT
cana-3871	122	43	0	0	NUM
cana-3871	122	44	)	)	PUNCT
cana-3871	122	45	,	,	PUNCT
cana-3871	122	46	(	(	PUNCT
cana-3871	122	47	0	0	NUM
cana-3871	122	48	,	,	PUNCT
cana-3871	122	49	1	1	NUM
cana-3871	122	50	,	,	PUNCT
cana-3871	122	51	0	0	NUM
cana-3871	122	52	,	,	PUNCT
cana-3871	122	53	0	0	NUM
cana-3871	122	54	)	)	PUNCT
cana-3871	122	55	,	,	PUNCT
cana-3871	122	56	(	(	PUNCT
cana-3871	122	57	0	0	NUM
cana-3871	122	58	,	,	PUNCT
cana-3871	122	59	0	0	NUM
cana-3871	122	60	,	,	PUNCT
cana-3871	122	61	1	1	NUM
cana-3871	122	62	,	,	PUNCT
cana-3871	122	63	1	1	NUM
cana-3871	122	64	)	)	PUNCT
cana-3871	122	65	,	,	PUNCT
cana-3871	122	66	(	(	PUNCT
cana-3871	122	67	0	0	NUM
cana-3871	122	68	,	,	PUNCT
cana-3871	122	69	1	1	NUM
cana-3871	122	70	,	,	PUNCT
cana-3871	122	71	0	0	NUM
cana-3871	122	72	,	,	PUNCT
cana-3871	122	73	1	1	NUM
cana-3871	122	74	)	)	PUNCT
cana-3871	122	75	,	,	PUNCT
cana-3871	122	76	(	(	PUNCT
cana-3871	122	77	(	(	PUNCT
cana-3871	122	78	0	0	NUM
cana-3871	122	79	,	,	PUNCT
cana-3871	122	80	1	1	NUM
cana-3871	122	81	,	,	PUNCT
cana-3871	122	82	1	1	NUM
cana-3871	122	83	,	,	PUNCT
cana-3871	122	84	0	0	NUM
cana-3871	122	85	)	)	PUNCT
cana-3871	122	86	,	,	PUNCT
cana-3871	122	87	(	(	PUNCT
cana-3871	122	88	0	0	NUM
cana-3871	122	89	,	,	PUNCT
cana-3871	122	90	1	1	NUM
cana-3871	122	91	,	,	PUNCT
cana-3871	122	92	1	1	NUM
cana-3871	122	93	,	,	PUNCT
cana-3871	122	94	1	1	NUM
cana-3871	122	95	)	)	PUNCT
cana-3871	122	96	,	,	PUNCT
cana-3871	122	97	(	(	PUNCT
cana-3871	122	98	1	1	NUM
cana-3871	122	99	,	,	PUNCT
cana-3871	122	100	0	0	NUM
cana-3871	122	101	,	,	PUNCT
cana-3871	122	102	0	0	NUM
cana-3871	122	103	,	,	PUNCT
cana-3871	122	104	0	0	NUM
cana-3871	122	105	)	)	PUNCT
cana-3871	122	106	,	,	PUNCT
cana-3871	122	107	(	(	PUNCT
cana-3871	122	108	1	1	NUM
cana-3871	122	109	,	,	PUNCT
cana-3871	122	110	0	0	NUM
cana-3871	122	111	,	,	PUNCT
cana-3871	122	112	0	0	NUM
cana-3871	122	113	,	,	PUNCT
cana-3871	122	114	1	1	NUM
cana-3871	122	115	)	)	PUNCT
cana-3871	122	116	,	,	PUNCT
cana-3871	122	117	(	(	PUNCT
cana-3871	122	118	1	1	NUM
cana-3871	122	119	,	,	PUNCT
cana-3871	122	120	0	0	NUM
cana-3871	122	121	,	,	PUNCT
cana-3871	122	122	1	1	NUM
cana-3871	122	123	,	,	PUNCT
cana-3871	122	124	0	0	NUM
cana-3871	122	125	)	)	PUNCT
cana-3871	122	126	,	,	PUNCT
cana-3871	122	127	(	(	PUNCT
cana-3871	122	128	1	1	NUM
cana-3871	122	129	,	,	PUNCT
cana-3871	122	130	0	0	NUM
cana-3871	122	131	,	,	PUNCT
cana-3871	122	132	1	1	NUM
cana-3871	122	133	,	,	PUNCT
cana-3871	122	134	1	1	NUM
cana-3871	122	135	)	)	PUNCT
cana-3871	122	136	,	,	PUNCT
cana-3871	122	137	(	(	PUNCT
cana-3871	122	138	1	1	NUM
cana-3871	122	139	,	,	PUNCT
cana-3871	122	140	1	1	NUM
cana-3871	122	141	,	,	PUNCT
cana-3871	122	142	0	0	NUM
cana-3871	122	143	,	,	PUNCT
cana-3871	122	144	0	0	NUM
cana-3871	122	145	)	)	PUNCT
cana-3871	122	146	,	,	PUNCT
cana-3871	122	147	(	(	PUNCT
cana-3871	122	148	1	1	NUM
cana-3871	122	149	,	,	PUNCT
cana-3871	122	150	1	1	NUM
cana-3871	122	151	,	,	PUNCT
cana-3871	122	152	0	0	NUM
cana-3871	122	153	,	,	PUNCT
cana-3871	122	154	1	1	NUM
cana-3871	122	155	)	)	PUNCT
cana-3871	122	156	,	,	PUNCT
cana-3871	122	157	(	(	PUNCT
cana-3871	122	158	1	1	NUM
cana-3871	122	159	,	,	PUNCT
cana-3871	122	160	1	1	NUM
cana-3871	122	161	,	,	PUNCT
cana-3871	122	162	1	1	NUM
cana-3871	122	163	,	,	PUNCT
cana-3871	122	164	0	0	NUM
cana-3871	122	165	)	)	PUNCT
cana-3871	122	166	,	,	PUNCT
cana-3871	122	167	(	(	PUNCT
cana-3871	122	168	1	1	NUM
cana-3871	122	169	,	,	PUNCT
cana-3871	122	170	1	1	NUM
cana-3871	122	171	,	,	PUNCT
cana-3871	122	172	1	1	NUM
cana-3871	122	173	,	,	PUNCT
cana-3871	122	174	1	1	NUM
cana-3871	122	175	)	)	PUNCT
cana-3871	122	176	}	}	PUNCT
cana-3871	122	177	ℤ(ℤ2×ℤ2×ℤ2×ℤ2	ℤ(ℤ2×ℤ2×ℤ2×ℤ2	NOUN
cana-3871	122	178	)	)	PUNCT
cana-3871	122	179	=	=	SYM
cana-3871	122	180	{	{	PUNCT
cana-3871	122	181	(	(	PUNCT
cana-3871	122	182	0	0	NUM
cana-3871	122	183	,	,	PUNCT
cana-3871	122	184	0	0	NUM
cana-3871	122	185	,	,	PUNCT
cana-3871	122	186	0	0	NUM
cana-3871	122	187	,	,	PUNCT
cana-3871	122	188	1	1	NUM
cana-3871	122	189	)	)	PUNCT
cana-3871	122	190	,	,	PUNCT
cana-3871	122	191	(	(	PUNCT
cana-3871	122	192	0	0	NUM
cana-3871	122	193	,	,	PUNCT
cana-3871	122	194	0	0	NUM
cana-3871	122	195	,	,	PUNCT
cana-3871	122	196	1	1	NUM
cana-3871	122	197	,	,	PUNCT
cana-3871	122	198	0	0	NUM
cana-3871	122	199	)	)	PUNCT
cana-3871	122	200	,	,	PUNCT
cana-3871	122	201	(	(	PUNCT
cana-3871	122	202	0	0	NUM
cana-3871	122	203	,	,	PUNCT
cana-3871	122	204	1	1	NUM
cana-3871	122	205	,	,	PUNCT
cana-3871	122	206	0	0	NUM
cana-3871	122	207	,	,	PUNCT
cana-3871	122	208	0	0	NUM
cana-3871	122	209	)	)	PUNCT
cana-3871	122	210	,	,	PUNCT
cana-3871	122	211	(	(	PUNCT
cana-3871	122	212	0	0	NUM
cana-3871	122	213	,	,	PUNCT
cana-3871	122	214	0	0	NUM
cana-3871	122	215	,	,	PUNCT
cana-3871	122	216	1	1	NUM
cana-3871	122	217	,	,	PUNCT
cana-3871	122	218	1	1	NUM
cana-3871	122	219	)	)	PUNCT
cana-3871	122	220	,	,	PUNCT
cana-3871	122	221	(	(	PUNCT
cana-3871	122	222	0	0	NUM
cana-3871	122	223	,	,	PUNCT
cana-3871	122	224	1	1	NUM
cana-3871	122	225	,	,	PUNCT
cana-3871	122	226	0	0	NUM
cana-3871	122	227	,	,	PUNCT
cana-3871	122	228	1	1	NUM
cana-3871	122	229	)	)	PUNCT
cana-3871	122	230	,	,	PUNCT
cana-3871	122	231	(	(	PUNCT
cana-3871	122	232	0	0	NUM
cana-3871	122	233	,	,	PUNCT
cana-3871	122	234	1	1	NUM
cana-3871	122	235	,	,	PUNCT
cana-3871	122	236	1	1	NUM
cana-3871	122	237	,	,	PUNCT
cana-3871	122	238	0	0	NUM
cana-3871	122	239	)	)	PUNCT
cana-3871	122	240	,	,	PUNCT
cana-3871	122	241	(	(	PUNCT
cana-3871	122	242	0	0	NUM
cana-3871	122	243	,	,	PUNCT
cana-3871	122	244	1	1	NUM
cana-3871	122	245	,	,	PUNCT
cana-3871	122	246	1	1	NUM
cana-3871	122	247	,	,	PUNCT
cana-3871	122	248	1	1	NUM
cana-3871	122	249	)	)	PUNCT
cana-3871	122	250	,	,	PUNCT
cana-3871	122	251	(	(	PUNCT
cana-3871	122	252	1	1	NUM
cana-3871	122	253	,	,	PUNCT
cana-3871	122	254	0	0	NUM
cana-3871	122	255	,	,	PUNCT
cana-3871	122	256	0	0	NUM
cana-3871	122	257	,	,	PUNCT
cana-3871	122	258	0	0	NUM
cana-3871	122	259	)	)	PUNCT
cana-3871	122	260	,	,	PUNCT
cana-3871	122	261	(	(	PUNCT
cana-3871	122	262	1	1	NUM
cana-3871	122	263	,	,	PUNCT
cana-3871	122	264	0	0	NUM
cana-3871	122	265	,	,	PUNCT
cana-3871	122	266	0	0	NUM
cana-3871	122	267	,	,	PUNCT
cana-3871	122	268	1	1	NUM
cana-3871	122	269	)	)	PUNCT
cana-3871	122	270	,	,	PUNCT
cana-3871	122	271	(	(	PUNCT
cana-3871	122	272	1	1	NUM
cana-3871	122	273	,	,	PUNCT
cana-3871	122	274	0	0	NUM
cana-3871	122	275	,	,	PUNCT
cana-3871	122	276	1	1	NUM
cana-3871	122	277	,	,	PUNCT
cana-3871	122	278	0	0	NUM
cana-3871	122	279	)	)	PUNCT
cana-3871	122	280	,	,	PUNCT
cana-3871	122	281	(	(	PUNCT
cana-3871	122	282	1	1	NUM
cana-3871	122	283	,	,	PUNCT
cana-3871	122	284	0	0	NUM
cana-3871	122	285	,	,	PUNCT
cana-3871	122	286	1	1	NUM
cana-3871	122	287	,	,	PUNCT
cana-3871	122	288	1	1	NUM
cana-3871	122	289	)	)	PUNCT
cana-3871	122	290	,	,	PUNCT
cana-3871	122	291	(	(	PUNCT
cana-3871	122	292	1	1	NUM
cana-3871	122	293	,	,	PUNCT
cana-3871	122	294	1	1	NUM
cana-3871	122	295	,	,	PUNCT
cana-3871	122	296	0	0	NUM
cana-3871	122	297	,	,	PUNCT
cana-3871	122	298	0	0	NUM
cana-3871	122	299	)	)	PUNCT
cana-3871	122	300	,	,	PUNCT
cana-3871	122	301	(	(	PUNCT
cana-3871	122	302	1	1	NUM
cana-3871	122	303	,	,	PUNCT
cana-3871	122	304	1	1	NUM
cana-3871	122	305	,	,	PUNCT
cana-3871	122	306	0	0	NUM
cana-3871	122	307	,	,	PUNCT
cana-3871	122	308	1	1	NUM
cana-3871	122	309	)	)	PUNCT
cana-3871	122	310	,	,	PUNCT
cana-3871	122	311	(	(	PUNCT
cana-3871	122	312	1	1	NUM
cana-3871	122	313	,	,	PUNCT
cana-3871	122	314	1	1	NUM
cana-3871	122	315	,	,	PUNCT
cana-3871	122	316	1	1	NUM
cana-3871	122	317	,	,	PUNCT
cana-3871	122	318	0	0	NUM
cana-3871	122	319	)	)	PUNCT
cana-3871	122	320	}	}	PUNCT
cana-3871	122	321	the	the	DET
cana-3871	122	322	zero	zero	NUM
cana-3871	122	323	-	-	PUNCT
cana-3871	122	324	divisor	divisor	NOUN
cana-3871	122	325	graph	graph	NOUN
cana-3871	122	326	of	of	ADP
cana-3871	122	327	ℤ2	ℤ2	PROPN
cana-3871	122	328	×	×	PROPN
cana-3871	122	329	ℤ2	ℤ2	PROPN
cana-3871	122	330	×	×	PROPN
cana-3871	122	331	ℤ2	ℤ2	PROPN
cana-3871	122	332	×	×	PROPN
cana-3871	122	333	ℤ2	ℤ2	PROPN
cana-3871	122	334	is	be	AUX
cana-3871	122	335	given	give	VERB
cana-3871	122	336	in	in	ADP
cana-3871	122	337	the	the	DET
cana-3871	122	338	figure	figure	NOUN
cana-3871	122	339	below	below	ADV
cana-3871	122	340	.	.	PUNCT
cana-3871	123	1	fig	fig	NOUN
cana-3871	123	2	12	12	NUM
cana-3871	123	3	:	:	PUNCT
cana-3871	123	4	γ	γ	X
cana-3871	123	5	(	(	PUNCT
cana-3871	123	6	ℤ2	ℤ2	PROPN
cana-3871	123	7	×	×	PROPN
cana-3871	123	8	ℤ2	ℤ2	PROPN
cana-3871	123	9	×	×	PROPN
cana-3871	123	10	ℤ2	ℤ2	PROPN
cana-3871	123	11	×	×	PROPN
cana-3871	123	12	ℤ2	ℤ2	PROPN
cana-3871	123	13	)	)	PUNCT
cana-3871	123	14	here	here	ADV
cana-3871	123	15	,	,	PUNCT
cana-3871	123	16	n	n	PROPN
cana-3871	123	17	=	=	SYM
cana-3871	123	18	4	4	NUM
cana-3871	123	19	.	.	NOUN
cana-3871	123	20	number	number	NOUN
cana-3871	123	21	of	of	ADP
cana-3871	123	22	vertices	vertex	NOUN
cana-3871	123	23	in	in	ADP
cana-3871	123	24	the	the	DET
cana-3871	123	25	graph	graph	NOUN
cana-3871	123	26	of	of	ADP
cana-3871	123	27	ℤ	ℤ	PROPN
cana-3871	123	28	(	(	PUNCT
cana-3871	123	29	ℤ2	ℤ2	PROPN
cana-3871	123	30	×	×	PROPN
cana-3871	123	31	ℤ2	ℤ2	PROPN
cana-3871	123	32	×	×	PROPN
cana-3871	123	33	ℤ2	ℤ2	PROPN
cana-3871	123	34	×	×	PROPN
cana-3871	123	35	ℤ2	ℤ2	PROPN
cana-3871	123	36	)	)	PUNCT
cana-3871	124	1	=	=	SYM
cana-3871	124	2	24	24	NUM
cana-3871	124	3	−	−	NUM
cana-3871	124	4	2	2	NUM
cana-3871	124	5	=	=	SYM
cana-3871	124	6	14	14	NUM
cana-3871	124	7	degree	degree	NOUN
cana-3871	124	8	of	of	ADP
cana-3871	124	9	vertices	vertex	NOUN
cana-3871	124	10	(	(	PUNCT
cana-3871	124	11	0	0	NUM
cana-3871	124	12	,	,	PUNCT
cana-3871	124	13	0	0	NUM
cana-3871	124	14	,	,	PUNCT
cana-3871	124	15	0	0	NUM
cana-3871	124	16	,	,	PUNCT
cana-3871	124	17	1	1	NUM
cana-3871	124	18	)	)	PUNCT
cana-3871	124	19	,	,	PUNCT
cana-3871	124	20	(	(	PUNCT
cana-3871	124	21	0	0	NUM
cana-3871	124	22	,	,	PUNCT
cana-3871	124	23	0	0	NUM
cana-3871	124	24	,	,	PUNCT
cana-3871	124	25	1	1	NUM
cana-3871	124	26	,	,	PUNCT
cana-3871	124	27	0	0	NUM
cana-3871	124	28	)	)	PUNCT
cana-3871	124	29	,	,	PUNCT
cana-3871	124	30	(	(	PUNCT
cana-3871	124	31	0	0	NUM
cana-3871	124	32	,	,	PUNCT
cana-3871	124	33	1	1	NUM
cana-3871	124	34	,	,	PUNCT
cana-3871	124	35	0	0	NUM
cana-3871	124	36	,	,	PUNCT
cana-3871	124	37	0	0	NUM
cana-3871	124	38	)	)	PUNCT
cana-3871	124	39	,	,	PUNCT
cana-3871	124	40	(	(	PUNCT
cana-3871	124	41	1	1	NUM
cana-3871	124	42	,	,	PUNCT
cana-3871	124	43	0	0	NUM
cana-3871	124	44	,	,	PUNCT
cana-3871	124	45	0	0	NUM
cana-3871	124	46	,	,	PUNCT
cana-3871	124	47	0	0	NUM
cana-3871	124	48	)	)	PUNCT
cana-3871	124	49	is	be	AUX
cana-3871	124	50	7	7	NUM
cana-3871	124	51	degree	degree	NOUN
cana-3871	124	52	of	of	ADP
cana-3871	124	53	vertices	vertex	NOUN
cana-3871	124	54	(	(	PUNCT
cana-3871	124	55	0	0	NUM
cana-3871	124	56	,	,	PUNCT
cana-3871	124	57	0	0	NUM
cana-3871	124	58	,	,	PUNCT
cana-3871	124	59	1	1	NUM
cana-3871	124	60	,	,	PUNCT
cana-3871	124	61	1	1	NUM
cana-3871	124	62	)	)	PUNCT
cana-3871	124	63	,	,	PUNCT
cana-3871	124	64	(	(	PUNCT
cana-3871	124	65	0	0	NUM
cana-3871	124	66	,	,	PUNCT
cana-3871	124	67	1	1	NUM
cana-3871	124	68	,	,	PUNCT
cana-3871	124	69	0	0	NUM
cana-3871	124	70	,	,	PUNCT
cana-3871	124	71	1	1	NUM
cana-3871	124	72	)	)	PUNCT
cana-3871	124	73	,	,	PUNCT
cana-3871	124	74	(	(	PUNCT
cana-3871	124	75	0	0	NUM
cana-3871	124	76	,	,	PUNCT
cana-3871	124	77	1	1	NUM
cana-3871	124	78	,	,	PUNCT
cana-3871	124	79	1	1	NUM
cana-3871	124	80	,	,	PUNCT
cana-3871	124	81	0	0	NUM
cana-3871	124	82	)	)	PUNCT
cana-3871	124	83	,	,	PUNCT
cana-3871	124	84	(	(	PUNCT
cana-3871	124	85	1	1	NUM
cana-3871	124	86	,	,	PUNCT
cana-3871	124	87	0	0	NUM
cana-3871	124	88	,	,	PUNCT
cana-3871	124	89	0	0	NUM
cana-3871	124	90	,	,	PUNCT
cana-3871	124	91	1	1	NUM
cana-3871	124	92	)	)	PUNCT
cana-3871	124	93	,	,	PUNCT
cana-3871	124	94	(	(	PUNCT
cana-3871	124	95	1	1	NUM
cana-3871	124	96	,	,	PUNCT
cana-3871	124	97	0	0	NUM
cana-3871	124	98	,	,	PUNCT
cana-3871	124	99	1	1	NUM
cana-3871	124	100	,	,	PUNCT
cana-3871	124	101	0	0	NUM
cana-3871	124	102	)	)	PUNCT
cana-3871	124	103	,	,	PUNCT
cana-3871	124	104	(	(	PUNCT
cana-3871	124	105	1	1	NUM
cana-3871	124	106	,	,	PUNCT
cana-3871	124	107	1	1	NUM
cana-3871	124	108	,	,	PUNCT
cana-3871	124	109	0	0	NUM
cana-3871	124	110	,	,	PUNCT
cana-3871	124	111	0	0	NUM
cana-3871	124	112	)	)	PUNCT
cana-3871	124	113	is	be	AUX
cana-3871	124	114	3	3	NUM
cana-3871	124	115	.	.	NOUN
cana-3871	124	116	degree	degree	NOUN
cana-3871	124	117	of	of	ADP
cana-3871	124	118	vertices	vertex	NOUN
cana-3871	124	119	(	(	PUNCT
cana-3871	124	120	0	0	NUM
cana-3871	124	121	,	,	PUNCT
cana-3871	124	122	1	1	NUM
cana-3871	124	123	,	,	PUNCT
cana-3871	124	124	1	1	NUM
cana-3871	124	125	,	,	PUNCT
cana-3871	124	126	1	1	NUM
cana-3871	124	127	)	)	PUNCT
cana-3871	124	128	,	,	PUNCT
cana-3871	124	129	(	(	PUNCT
cana-3871	124	130	1	1	NUM
cana-3871	124	131	,	,	PUNCT
cana-3871	124	132	0	0	NUM
cana-3871	124	133	,	,	PUNCT
cana-3871	124	134	1	1	NUM
cana-3871	124	135	,	,	PUNCT
cana-3871	124	136	1	1	NUM
cana-3871	124	137	)	)	PUNCT
cana-3871	124	138	,	,	PUNCT
cana-3871	124	139	(	(	PUNCT
cana-3871	124	140	1	1	NUM
cana-3871	124	141	,	,	PUNCT
cana-3871	124	142	1	1	NUM
cana-3871	124	143	,	,	PUNCT
cana-3871	124	144	0	0	NUM
cana-3871	124	145	,	,	PUNCT
cana-3871	124	146	1	1	NUM
cana-3871	124	147	)	)	PUNCT
cana-3871	124	148	,	,	PUNCT
cana-3871	124	149	(	(	PUNCT
cana-3871	124	150	1	1	NUM
cana-3871	124	151	,	,	PUNCT
cana-3871	124	152	1	1	NUM
cana-3871	124	153	,	,	PUNCT
cana-3871	124	154	1	1	NUM
cana-3871	124	155	,	,	PUNCT
cana-3871	124	156	0	0	NUM
cana-3871	124	157	)	)	PUNCT
cana-3871	124	158	is	be	AUX
cana-3871	124	159	1	1	NUM
cana-3871	124	160	.	.	PUNCT
cana-3871	125	1	∴	∴	NOUN
cana-3871	125	2	all	all	DET
cana-3871	125	3	vertices	vertex	NOUN
cana-3871	125	4	of	of	ADP
cana-3871	125	5	zero	zero	NUM
cana-3871	125	6	divisor	divisor	NOUN
cana-3871	125	7	graph	graph	NOUN
cana-3871	125	8	of	of	ADP
cana-3871	125	9	ℤ2	ℤ2	PROPN
cana-3871	125	10	×	×	PROPN
cana-3871	125	11	ℤ2	ℤ2	PROPN
cana-3871	125	12	×	×	PROPN
cana-3871	125	13	ℤ2	ℤ2	PROPN
cana-3871	125	14	×	×	PROPN
cana-3871	125	15	ℤ2	ℤ2	PROPN
cana-3871	125	16	have	have	VERB
cana-3871	125	17	odd	odd	ADJ
cana-3871	125	18	degree	degree	NOUN
cana-3871	125	19	.	.	PUNCT
cana-3871	126	1	3.4	3.4	NUM
cana-3871	126	2	theorem	theorem	ADJ
cana-3871	126	3	statement	statement	NOUN
cana-3871	126	4	:	:	PUNCT
cana-3871	126	5	let	let	VERB
cana-3871	126	6	ℤ2	ℤ2	PROPN
cana-3871	126	7	n	n	PROPN
cana-3871	126	8	=	=	SYM
cana-3871	126	9	ℤ2	ℤ2	PROPN
cana-3871	126	10	×	×	NOUN
cana-3871	126	11	ℤ2	ℤ2	PROPN
cana-3871	126	12	×	×	PROPN
cana-3871	126	13	ℤ2	ℤ2	PROPN
cana-3871	126	14	×	×	PROPN
cana-3871	126	15	ℤ2	ℤ2	PROPN
cana-3871	126	16	×	×	NOUN
cana-3871	126	17	...	...	PUNCT
cana-3871	126	18	×	×	NOUN
cana-3871	126	19	ℤ2	ℤ2	PROPN
cana-3871	126	20	be	be	VERB
cana-3871	126	21	any	any	DET
cana-3871	126	22	boolean	boolean	ADJ
cana-3871	126	23	ring	ring	NOUN
cana-3871	126	24	then	then	ADV
cana-3871	126	25	the	the	DET
cana-3871	126	26	zero	zero	NUM
cana-3871	126	27	divisor	divisor	NOUN
cana-3871	126	28	graph	graph	NOUN
cana-3871	126	29	of	of	ADP
cana-3871	126	30	the	the	DET
cana-3871	126	31	boolean	boolean	ADJ
cana-3871	126	32	ring	ring	NOUN
cana-3871	126	33	γ(ℤ2	γ(ℤ2	PROPN
cana-3871	126	34	n	n	CCONJ
cana-3871	126	35	)	)	PUNCT
cana-3871	126	36	has	have	VERB
cana-3871	126	37	a	a	DET
cana-3871	126	38	cycle	cycle	NOUN
cana-3871	126	39	of	of	ADP
cana-3871	126	40	length	length	NOUN
cana-3871	126	41	n.	n.	NOUN
cana-3871	126	42	proof	proof	NOUN
cana-3871	126	43	:	:	PUNCT
cana-3871	126	44	let	let	VERB
cana-3871	126	45	ℤ2	ℤ2	PROPN
cana-3871	126	46	n	n	PROPN
cana-3871	126	47	=	=	SYM
cana-3871	126	48	ℤ2	ℤ2	PROPN
cana-3871	126	49	×	×	NOUN
cana-3871	126	50	ℤ2	ℤ2	PROPN
cana-3871	126	51	×	×	PROPN
cana-3871	126	52	ℤ2	ℤ2	PROPN
cana-3871	126	53	×	×	PROPN
cana-3871	126	54	ℤ2	ℤ2	PROPN
cana-3871	126	55	×	×	NOUN
cana-3871	126	56	...	...	PUNCT
cana-3871	126	57	×	×	NOUN
cana-3871	126	58	ℤ2	ℤ2	PROPN
cana-3871	126	59	be	be	VERB
cana-3871	126	60	a	a	DET
cana-3871	126	61	boolean	boolean	ADJ
cana-3871	126	62	ring	ring	NOUN
cana-3871	126	63	ℤ2	ℤ2	PROPN
cana-3871	126	64	n	n	PART
cana-3871	126	65	has	have	AUX
cana-3871	126	66	(	(	PUNCT
cana-3871	126	67	2n	2n	NUM
cana-3871	126	68	−	−	NOUN
cana-3871	126	69	2	2	X
cana-3871	126	70	)	)	PUNCT
cana-3871	126	71	zero	zero	NUM
cana-3871	126	72	divisors	divisor	NOUN
cana-3871	126	73	communications	communication	NOUN
cana-3871	126	74	on	on	ADP
cana-3871	126	75	applied	apply	VERB
cana-3871	126	76	nonlinear	nonlinear	ADJ
cana-3871	126	77	analysis	analysis	NOUN
cana-3871	126	78	issn	issn	NOUN
cana-3871	126	79	:	:	PUNCT
cana-3871	126	80	1074	1074	NUM
cana-3871	126	81	-	-	PUNCT
cana-3871	126	82	133x	133x	NUM
cana-3871	126	83	vol	vol	NOUN
cana-3871	126	84	32	32	NUM
cana-3871	126	85	no	no	NOUN
cana-3871	126	86	.	.	PUNCT
cana-3871	127	1	7s	7	NOUN
cana-3871	127	2	(	(	PUNCT
cana-3871	127	3	2025	2025	NUM
cana-3871	127	4	)	)	PUNCT
cana-3871	127	5	952	952	NUM
cana-3871	127	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	127	7	and	and	CCONJ
cana-3871	127	8	ℤ2	ℤ2	PROPN
cana-3871	127	9	n	n	AUX
cana-3871	127	10	is	be	AUX
cana-3871	127	11	given	give	VERB
cana-3871	127	12	by	by	ADP
cana-3871	127	13	,	,	PUNCT
cana-3871	127	14	bn	bn	NOUN
cana-3871	127	15	=	=	SYM
cana-3871	127	16	{	{	PUNCT
cana-3871	127	17	(	(	PUNCT
cana-3871	127	18	b1	b1	NOUN
cana-3871	127	19	,	,	PUNCT
cana-3871	127	20	b2	b2	NOUN
cana-3871	127	21	,	,	PUNCT
cana-3871	127	22	b3	b3	PROPN
cana-3871	127	23	,	,	PUNCT
cana-3871	127	24	...	...	PUNCT
cana-3871	127	25	,	,	PUNCT
cana-3871	127	26	bn	bn	X
cana-3871	127	27	)	)	PUNCT
cana-3871	127	28	|	|	ADV
cana-3871	127	29	bi′s	bi′s	NOUN
cana-3871	127	30	∈	∈	PROPN
cana-3871	127	31	{	{	PUNCT
cana-3871	127	32	0	0	NUM
cana-3871	127	33	,	,	PUNCT
cana-3871	127	34	1	1	NUM
cana-3871	127	35	}	}	PUNCT
cana-3871	127	36	,	,	PUNCT
cana-3871	127	37	i	i	PRON
cana-3871	127	38	=	=	NOUN
cana-3871	127	39	1	1	NUM
cana-3871	127	40	,	,	PUNCT
cana-3871	127	41	2	2	NUM
cana-3871	127	42	,	,	PUNCT
cana-3871	127	43	...	...	PUNCT
cana-3871	127	44	,	,	PUNCT
cana-3871	127	45	n	n	CCONJ
cana-3871	127	46	}	}	PUNCT
cana-3871	127	47	since	since	SCONJ
cana-3871	127	48	each	each	DET
cana-3871	127	49	bis	bis	NOUN
cana-3871	127	50	has	have	VERB
cana-3871	127	51	two	two	NUM
cana-3871	127	52	choices	choice	NOUN
cana-3871	127	53	0	0	NUM
cana-3871	127	54	and	and	CCONJ
cana-3871	127	55	1	1	NUM
cana-3871	127	56	,	,	PUNCT
cana-3871	127	57	there	there	PRON
cana-3871	127	58	are	be	VERB
cana-3871	127	59	2n	2n	NUM
cana-3871	127	60	elements	element	NOUN
cana-3871	127	61	in	in	ADP
cana-3871	127	62	ℤ2	ℤ2	PROPN
cana-3871	127	63	n.	n.	PROPN
cana-3871	127	64	|ℤ2	|ℤ2	PUNCT
cana-3871	127	65	n|	n|	NOUN
cana-3871	127	66	=	=	SYM
cana-3871	127	67	2n	2n	NUM
cana-3871	127	68	the	the	DET
cana-3871	127	69	set	set	NOUN
cana-3871	127	70	of	of	ADP
cana-3871	127	71	zero	zero	NUM
cana-3871	127	72	divisors	divisor	NOUN
cana-3871	127	73	of	of	ADP
cana-3871	127	74	ℤ2	ℤ2	PROPN
cana-3871	127	75	n	n	X
cana-3871	127	76	is	be	AUX
cana-3871	127	77	denoted	denote	VERB
cana-3871	127	78	by	by	ADP
cana-3871	127	79	ℤ(ℤ2	ℤ(ℤ2	NOUN
cana-3871	127	80	n	n	CCONJ
cana-3871	127	81	)	)	PUNCT
cana-3871	127	82	and	and	CCONJ
cana-3871	127	83	is	be	AUX
cana-3871	127	84	given	give	VERB
cana-3871	127	85	by	by	ADP
cana-3871	127	86	,	,	PUNCT
cana-3871	127	87	ℤ(ℤ2	ℤ(ℤ2	PROPN
cana-3871	127	88	n	n	CCONJ
cana-3871	127	89	)	)	PUNCT
cana-3871	127	90	=	=	SYM
cana-3871	127	91	{	{	PUNCT
cana-3871	127	92	(	(	PUNCT
cana-3871	127	93	b1	b1	NOUN
cana-3871	127	94	,	,	PUNCT
cana-3871	127	95	b2	b2	NOUN
cana-3871	127	96	,	,	PUNCT
cana-3871	127	97	b3	b3	PROPN
cana-3871	127	98	,	,	PUNCT
cana-3871	127	99	...	...	PUNCT
cana-3871	127	100	,	,	PUNCT
cana-3871	127	101	bn	bn	X
cana-3871	127	102	)	)	PUNCT
cana-3871	127	103	|	|	ADV
cana-3871	127	104	bis	bi	VERB
cana-3871	127	105	∈	∈	NOUN
cana-3871	127	106	{	{	PUNCT
cana-3871	127	107	0	0	NUM
cana-3871	127	108	,	,	PUNCT
cana-3871	127	109	1},all	1},all	NUM
cana-3871	127	110	bi	bi	NOUN
cana-3871	127	111	≠0	≠0	NOUN
cana-3871	127	112	,	,	PUNCT
cana-3871	127	113	and	and	CCONJ
cana-3871	127	114	all	all	DET
cana-3871	127	115	bi	bi	ADJ
cana-3871	127	116	≠	≠	PROPN
cana-3871	127	117	1	1	NUM
cana-3871	127	118	,	,	PUNCT
cana-3871	127	119	i	i	PRON
cana-3871	127	120	=	=	NOUN
cana-3871	127	121	1	1	NUM
cana-3871	127	122	,	,	PUNCT
cana-3871	127	123	2	2	NUM
cana-3871	127	124	,	,	PUNCT
cana-3871	127	125	...	...	PUNCT
cana-3871	127	126	,	,	PUNCT
cana-3871	127	127	n	n	CCONJ
cana-3871	127	128	}	}	PUNCT
cana-3871	127	129	∴	∴	PROPN
cana-3871	127	130	|ℤ(ℤ2	|ℤ(ℤ2	NOUN
cana-3871	127	131	n	n	CCONJ
cana-3871	127	132	)	)	PUNCT
cana-3871	128	1	|	|	ADV
cana-3871	128	2	=	=	SYM
cana-3871	128	3	2n	2n	NUM
cana-3871	129	1	−	−	ADP
cana-3871	129	2	2	2	NUM
cana-3871	129	3	the	the	DET
cana-3871	129	4	n	n	NOUN
cana-3871	129	5	vertices	vertex	NOUN
cana-3871	129	6	(	(	PUNCT
cana-3871	129	7	1	1	NUM
cana-3871	129	8	,	,	PUNCT
cana-3871	129	9	0	0	NUM
cana-3871	129	10	,	,	PUNCT
cana-3871	129	11	0	0	NUM
cana-3871	129	12	,	,	PUNCT
cana-3871	129	13	...	...	PUNCT
cana-3871	129	14	,	,	PUNCT
cana-3871	129	15	0	0	NUM
cana-3871	129	16	)	)	PUNCT
cana-3871	129	17	,	,	PUNCT
cana-3871	129	18	(	(	PUNCT
cana-3871	129	19	0	0	NUM
cana-3871	129	20	,	,	PUNCT
cana-3871	129	21	1	1	NUM
cana-3871	129	22	,	,	PUNCT
cana-3871	129	23	0	0	NUM
cana-3871	129	24	,	,	PUNCT
cana-3871	129	25	...	...	PUNCT
cana-3871	129	26	,	,	PUNCT
cana-3871	129	27	0	0	NUM
cana-3871	129	28	)	)	PUNCT
cana-3871	129	29	,	,	PUNCT
cana-3871	129	30	(	(	PUNCT
cana-3871	129	31	0	0	NUM
cana-3871	129	32	,	,	PUNCT
cana-3871	129	33	0	0	NUM
cana-3871	129	34	,	,	PUNCT
cana-3871	129	35	1	1	NUM
cana-3871	129	36	,	,	PUNCT
cana-3871	129	37	0	0	NUM
cana-3871	129	38	,	,	PUNCT
cana-3871	129	39	...	...	PUNCT
cana-3871	129	40	,	,	PUNCT
cana-3871	129	41	0	0	NUM
cana-3871	129	42	)	)	PUNCT
cana-3871	129	43	,	,	PUNCT
cana-3871	129	44	...	...	PUNCT
cana-3871	129	45	,	,	PUNCT
cana-3871	129	46	(	(	PUNCT
cana-3871	129	47	0	0	NUM
cana-3871	129	48	,	,	PUNCT
cana-3871	129	49	0	0	NUM
cana-3871	129	50	,	,	PUNCT
cana-3871	129	51	0	0	NUM
cana-3871	129	52	,	,	PUNCT
cana-3871	129	53	...	...	PUNCT
cana-3871	129	54	,	,	PUNCT
cana-3871	129	55	1	1	X
cana-3871	129	56	)	)	PUNCT
cana-3871	129	57	are	be	AUX
cana-3871	129	58	adjacent	adjacent	ADJ
cana-3871	129	59	to	to	ADP
cana-3871	129	60	each	each	DET
cana-3871	129	61	other	other	ADJ
cana-3871	129	62	.	.	PUNCT
cana-3871	130	1	but	but	CCONJ
cana-3871	130	2	we	we	PRON
cana-3871	130	3	consider	consider	VERB
cana-3871	130	4	the	the	DET
cana-3871	130	5	case	case	NOUN
cana-3871	130	6	where	where	SCONJ
cana-3871	130	7	these	these	DET
cana-3871	130	8	vertices	vertex	NOUN
cana-3871	130	9	are	be	AUX
cana-3871	130	10	only	only	ADV
cana-3871	130	11	adjacent	adjacent	ADJ
cana-3871	130	12	to	to	ADP
cana-3871	130	13	its	its	PRON
cana-3871	130	14	consecutive	consecutive	ADJ
cana-3871	130	15	elements	element	NOUN
cana-3871	130	16	i.e.	i.e.	X
cana-3871	130	17	(	(	PUNCT
cana-3871	130	18	1	1	NUM
cana-3871	130	19	,	,	PUNCT
cana-3871	130	20	0	0	NUM
cana-3871	130	21	,	,	PUNCT
cana-3871	130	22	0	0	NUM
cana-3871	130	23	,	,	PUNCT
cana-3871	130	24	...	...	PUNCT
cana-3871	130	25	,	,	PUNCT
cana-3871	130	26	0	0	X
cana-3871	130	27	)	)	PUNCT
cana-3871	130	28	is	be	AUX
cana-3871	130	29	adjacent	adjacent	ADJ
cana-3871	130	30	to	to	ADP
cana-3871	130	31	(	(	PUNCT
cana-3871	130	32	0	0	NUM
cana-3871	130	33	,	,	PUNCT
cana-3871	130	34	1	1	NUM
cana-3871	130	35	,	,	PUNCT
cana-3871	130	36	0	0	NUM
cana-3871	130	37	,	,	PUNCT
cana-3871	130	38	...	...	PUNCT
cana-3871	130	39	,	,	PUNCT
cana-3871	130	40	0	0	NUM
cana-3871	130	41	)	)	PUNCT
cana-3871	130	42	;	;	PUNCT
cana-3871	130	43	(	(	PUNCT
cana-3871	130	44	0	0	NUM
cana-3871	130	45	,	,	PUNCT
cana-3871	130	46	1	1	NUM
cana-3871	130	47	,	,	PUNCT
cana-3871	130	48	0	0	NUM
cana-3871	130	49	,	,	PUNCT
cana-3871	130	50	...	...	PUNCT
cana-3871	130	51	,	,	PUNCT
cana-3871	130	52	0	0	X
cana-3871	130	53	)	)	PUNCT
cana-3871	130	54	is	be	AUX
cana-3871	130	55	adjacent	adjacent	ADJ
cana-3871	130	56	to	to	ADP
cana-3871	130	57	(	(	PUNCT
cana-3871	130	58	0	0	NUM
cana-3871	130	59	,	,	PUNCT
cana-3871	130	60	0	0	NUM
cana-3871	130	61	,	,	PUNCT
cana-3871	130	62	1	1	NUM
cana-3871	130	63	,	,	PUNCT
cana-3871	130	64	0	0	NUM
cana-3871	130	65	,	,	PUNCT
cana-3871	130	66	...	...	PUNCT
cana-3871	130	67	,	,	PUNCT
cana-3871	130	68	0	0	NUM
cana-3871	130	69	)	)	PUNCT
cana-3871	130	70	;	;	PUNCT
cana-3871	130	71	and	and	CCONJ
cana-3871	130	72	so	so	ADV
cana-3871	130	73	on	on	ADP
cana-3871	130	74	till	till	SCONJ
cana-3871	130	75	(	(	PUNCT
cana-3871	130	76	0	0	NUM
cana-3871	130	77	,	,	PUNCT
cana-3871	130	78	0	0	NUM
cana-3871	130	79	,	,	PUNCT
cana-3871	130	80	0	0	NUM
cana-3871	130	81	,	,	PUNCT
cana-3871	130	82	...	...	PUNCT
cana-3871	130	83	,	,	PUNCT
cana-3871	130	84	1	1	NUM
cana-3871	130	85	,	,	PUNCT
cana-3871	130	86	0	0	NUM
cana-3871	130	87	)	)	PUNCT
cana-3871	130	88	is	be	AUX
cana-3871	130	89	adjacent	adjacent	ADJ
cana-3871	130	90	to	to	ADP
cana-3871	130	91	(	(	PUNCT
cana-3871	130	92	0	0	NUM
cana-3871	130	93	,	,	PUNCT
cana-3871	130	94	0	0	NUM
cana-3871	130	95	,	,	PUNCT
cana-3871	130	96	0	0	NUM
cana-3871	130	97	,	,	PUNCT
cana-3871	130	98	...	...	PUNCT
cana-3871	130	99	,	,	PUNCT
cana-3871	130	100	1	1	X
cana-3871	130	101	)	)	PUNCT
cana-3871	130	102	and	and	CCONJ
cana-3871	130	103	(	(	PUNCT
cana-3871	130	104	0	0	NUM
cana-3871	130	105	,	,	PUNCT
cana-3871	130	106	0	0	NUM
cana-3871	130	107	,	,	PUNCT
cana-3871	130	108	0	0	NUM
cana-3871	130	109	,	,	PUNCT
cana-3871	130	110	...	...	PUNCT
cana-3871	130	111	,	,	PUNCT
cana-3871	130	112	1	1	X
cana-3871	130	113	)	)	PUNCT
cana-3871	130	114	is	be	AUX
cana-3871	130	115	adjacent	adjacent	ADJ
cana-3871	130	116	to	to	ADP
cana-3871	130	117	(	(	PUNCT
cana-3871	130	118	1	1	NUM
cana-3871	130	119	,	,	PUNCT
cana-3871	130	120	0	0	NUM
cana-3871	130	121	,	,	PUNCT
cana-3871	130	122	0	0	NUM
cana-3871	130	123	,	,	PUNCT
cana-3871	130	124	...	...	PUNCT
cana-3871	130	125	,	,	PUNCT
cana-3871	130	126	0	0	NUM
cana-3871	130	127	)	)	PUNCT
cana-3871	130	128	.	.	PUNCT
cana-3871	131	1	so	so	ADV
cana-3871	131	2	,	,	PUNCT
cana-3871	131	3	we	we	PRON
cana-3871	131	4	get	get	VERB
cana-3871	131	5	these	these	DET
cana-3871	131	6	n	n	ADP
cana-3871	131	7	vertices	vertice	VERB
cana-3871	131	8	forming	form	VERB
cana-3871	131	9	edges	edge	NOUN
cana-3871	131	10	between	between	ADP
cana-3871	131	11	them	they	PRON
cana-3871	131	12	.	.	PUNCT
cana-3871	132	1	these	these	DET
cana-3871	132	2	n	n	ADP
cana-3871	132	3	vertices	vertice	VERB
cana-3871	132	4	form	form	NOUN
cana-3871	132	5	“	"	PUNCT
cana-3871	132	6	n	n	CCONJ
cana-3871	132	7	”	"	PUNCT
cana-3871	132	8	edges	edge	NOUN
cana-3871	132	9	between	between	ADP
cana-3871	132	10	them	they	PRON
cana-3871	132	11	.	.	PUNCT
cana-3871	133	1	hence	hence	ADV
cana-3871	133	2	,	,	PUNCT
cana-3871	133	3	we	we	PRON
cana-3871	133	4	get	get	VERB
cana-3871	133	5	a	a	DET
cana-3871	133	6	closed	closed	ADJ
cana-3871	133	7	loop	loop	NOUN
cana-3871	133	8	formed	form	VERB
cana-3871	133	9	by	by	ADP
cana-3871	133	10	these	these	DET
cana-3871	133	11	n	n	NOUN
cana-3871	133	12	edges	edge	NOUN
cana-3871	133	13	.	.	PUNCT
cana-3871	134	1	∴	∴	VERB
cana-3871	134	2	the	the	DET
cana-3871	134	3	zero	zero	NUM
cana-3871	134	4	-	-	PUNCT
cana-3871	134	5	divisor	divisor	NOUN
cana-3871	134	6	graph	graph	NOUN
cana-3871	134	7	of	of	ADP
cana-3871	134	8	ℤ2	ℤ2	PROPN
cana-3871	134	9	×	×	PROPN
cana-3871	134	10	ℤ2	ℤ2	PROPN
cana-3871	134	11	×	×	PROPN
cana-3871	134	12	ℤ2	ℤ2	PROPN
cana-3871	134	13	×	×	PROPN
cana-3871	134	14	ℤ2	ℤ2	PROPN
cana-3871	134	15	has	have	VERB
cana-3871	134	16	a	a	DET
cana-3871	134	17	cycle	cycle	NOUN
cana-3871	134	18	of	of	ADP
cana-3871	134	19	length	length	NOUN
cana-3871	134	20	n.	n.	PROPN
cana-3871	134	21	3.4.1	3.4.1	PROPN
cana-3871	134	22	example	example	NOUN
cana-3871	134	23	ℤ2	ℤ2	PROPN
cana-3871	134	24	3	3	NUM
cana-3871	134	25	=	=	SYM
cana-3871	134	26	ℤ2	ℤ2	PROPN
cana-3871	134	27	×	×	NOUN
cana-3871	134	28	ℤ2	ℤ2	PROPN
cana-3871	134	29	×	×	PROPN
cana-3871	134	30	ℤ2	ℤ2	PROPN
cana-3871	134	31	ℤ2	ℤ2	PROPN
cana-3871	134	32	×	×	PROPN
cana-3871	134	33	ℤ2	ℤ2	PROPN
cana-3871	134	34	×	×	NOUN
cana-3871	134	35	ℤ2	ℤ2	NOUN
cana-3871	134	36	=	=	SYM
cana-3871	134	37	{	{	PUNCT
cana-3871	134	38	(	(	PUNCT
cana-3871	134	39	0	0	NUM
cana-3871	134	40	,	,	PUNCT
cana-3871	134	41	0	0	NUM
cana-3871	134	42	,	,	PUNCT
cana-3871	134	43	0	0	NUM
cana-3871	134	44	)	)	PUNCT
cana-3871	134	45	,	,	PUNCT
cana-3871	134	46	(	(	PUNCT
cana-3871	134	47	0	0	NUM
cana-3871	134	48	,	,	PUNCT
cana-3871	134	49	0	0	NUM
cana-3871	134	50	,	,	PUNCT
cana-3871	134	51	1	1	NUM
cana-3871	134	52	)	)	PUNCT
cana-3871	134	53	,	,	PUNCT
cana-3871	134	54	(	(	PUNCT
cana-3871	134	55	0	0	NUM
cana-3871	134	56	,	,	PUNCT
cana-3871	134	57	1	1	NUM
cana-3871	134	58	,	,	PUNCT
cana-3871	134	59	0	0	NUM
cana-3871	134	60	)	)	PUNCT
cana-3871	134	61	,	,	PUNCT
cana-3871	134	62	(	(	PUNCT
cana-3871	134	63	0	0	NUM
cana-3871	134	64	,	,	PUNCT
cana-3871	134	65	1	1	NUM
cana-3871	134	66	,	,	PUNCT
cana-3871	134	67	1	1	NUM
cana-3871	134	68	)	)	PUNCT
cana-3871	134	69	,	,	PUNCT
cana-3871	134	70	(	(	PUNCT
cana-3871	134	71	1	1	NUM
cana-3871	134	72	,	,	PUNCT
cana-3871	134	73	0	0	NUM
cana-3871	134	74	,	,	PUNCT
cana-3871	134	75	1	1	NUM
cana-3871	134	76	)	)	PUNCT
cana-3871	134	77	,	,	PUNCT
cana-3871	134	78	(	(	PUNCT
cana-3871	134	79	1	1	NUM
cana-3871	134	80	,	,	PUNCT
cana-3871	134	81	1	1	NUM
cana-3871	134	82	,	,	PUNCT
cana-3871	134	83	0	0	NUM
cana-3871	134	84	)	)	PUNCT
cana-3871	134	85	,	,	PUNCT
cana-3871	134	86	(	(	PUNCT
cana-3871	134	87	1	1	NUM
cana-3871	134	88	,	,	PUNCT
cana-3871	134	89	0	0	NUM
cana-3871	134	90	,	,	PUNCT
cana-3871	134	91	0	0	NUM
cana-3871	134	92	)	)	PUNCT
cana-3871	134	93	,	,	PUNCT
cana-3871	134	94	(	(	PUNCT
cana-3871	134	95	1	1	NUM
cana-3871	134	96	,	,	PUNCT
cana-3871	134	97	1	1	NUM
cana-3871	134	98	,	,	PUNCT
cana-3871	134	99	1	1	NUM
cana-3871	134	100	)	)	PUNCT
cana-3871	134	101	}	}	PUNCT
cana-3871	134	102	ℤ	ℤ	PROPN
cana-3871	134	103	(	(	PUNCT
cana-3871	134	104	ℤ2	ℤ2	PROPN
cana-3871	134	105	×	×	PROPN
cana-3871	134	106	ℤ2	ℤ2	PROPN
cana-3871	134	107	×	×	PROPN
cana-3871	134	108	ℤ2	ℤ2	PROPN
cana-3871	134	109	)	)	PUNCT
cana-3871	134	110	=	=	PRON
cana-3871	134	111	{	{	PUNCT
cana-3871	134	112	(	(	PUNCT
cana-3871	134	113	0	0	NUM
cana-3871	134	114	,	,	PUNCT
cana-3871	134	115	0	0	NUM
cana-3871	134	116	,	,	PUNCT
cana-3871	134	117	1	1	NUM
cana-3871	134	118	)	)	PUNCT
cana-3871	134	119	,	,	PUNCT
cana-3871	134	120	(	(	PUNCT
cana-3871	134	121	0	0	NUM
cana-3871	134	122	,	,	PUNCT
cana-3871	134	123	1	1	NUM
cana-3871	134	124	,	,	PUNCT
cana-3871	134	125	0	0	NUM
cana-3871	134	126	)	)	PUNCT
cana-3871	134	127	,	,	PUNCT
cana-3871	134	128	(	(	PUNCT
cana-3871	134	129	0	0	NUM
cana-3871	134	130	,	,	PUNCT
cana-3871	134	131	1	1	NUM
cana-3871	134	132	,	,	PUNCT
cana-3871	134	133	1	1	NUM
cana-3871	134	134	)	)	PUNCT
cana-3871	134	135	,	,	PUNCT
cana-3871	134	136	(	(	PUNCT
cana-3871	134	137	1	1	NUM
cana-3871	134	138	,	,	PUNCT
cana-3871	134	139	0	0	NUM
cana-3871	134	140	,	,	PUNCT
cana-3871	134	141	1	1	NUM
cana-3871	134	142	)	)	PUNCT
cana-3871	134	143	,	,	PUNCT
cana-3871	134	144	(	(	PUNCT
cana-3871	134	145	1	1	NUM
cana-3871	134	146	,	,	PUNCT
cana-3871	134	147	1	1	NUM
cana-3871	134	148	,	,	PUNCT
cana-3871	134	149	0	0	NUM
cana-3871	134	150	)	)	PUNCT
cana-3871	134	151	,	,	PUNCT
cana-3871	134	152	(	(	PUNCT
cana-3871	134	153	1	1	NUM
cana-3871	134	154	,	,	PUNCT
cana-3871	134	155	0	0	NUM
cana-3871	134	156	,	,	PUNCT
cana-3871	134	157	0	0	NUM
cana-3871	134	158	)	)	PUNCT
cana-3871	134	159	}	}	PUNCT
cana-3871	134	160	fig	fig	NOUN
cana-3871	134	161	13	13	NUM
cana-3871	134	162	:	:	PUNCT
cana-3871	134	163	γ(ℤ2	γ(ℤ2	PROPN
cana-3871	134	164	×	×	NOUN
cana-3871	134	165	ℤ2	ℤ2	PROPN
cana-3871	134	166	×	×	PROPN
cana-3871	134	167	ℤ2	ℤ2	PROPN
cana-3871	134	168	)	)	PUNCT
cana-3871	134	169	the	the	DET
cana-3871	134	170	zero	zero	NUM
cana-3871	134	171	-	-	PUNCT
cana-3871	134	172	divisor	divisor	NOUN
cana-3871	134	173	graph	graph	NOUN
cana-3871	134	174	of	of	ADP
cana-3871	134	175	ℤ2	ℤ2	PROPN
cana-3871	134	176	×	×	PROPN
cana-3871	134	177	ℤ2	ℤ2	PROPN
cana-3871	134	178	×	×	PROPN
cana-3871	134	179	ℤ2	ℤ2	PROPN
cana-3871	134	180	is	be	AUX
cana-3871	134	181	given	give	VERB
cana-3871	134	182	in	in	ADP
cana-3871	134	183	the	the	DET
cana-3871	134	184	figure	figure	NOUN
cana-3871	134	185	10	10	NUM
cana-3871	134	186	above	above	ADV
cana-3871	134	187	.	.	PUNCT
cana-3871	135	1	number	number	NOUN
cana-3871	135	2	of	of	ADP
cana-3871	135	3	vertices	vertex	NOUN
cana-3871	135	4	in	in	ADP
cana-3871	135	5	the	the	DET
cana-3871	135	6	graph	graph	NOUN
cana-3871	135	7	of	of	ADP
cana-3871	135	8	ℤ	ℤ	PROPN
cana-3871	135	9	(	(	PUNCT
cana-3871	135	10	ℤ2	ℤ2	PROPN
cana-3871	135	11	×	×	PROPN
cana-3871	135	12	ℤ2	ℤ2	PROPN
cana-3871	135	13	×	×	PROPN
cana-3871	135	14	ℤ2	ℤ2	PROPN
cana-3871	135	15	)	)	PUNCT
cana-3871	136	1	=	=	NOUN
cana-3871	137	1	23	23	NUM
cana-3871	137	2	−	−	NUM
cana-3871	137	3	2	2	NUM
cana-3871	137	4	=	=	SYM
cana-3871	137	5	6	6	NUM
cana-3871	137	6	the	the	DET
cana-3871	137	7	vertices	vertex	NOUN
cana-3871	137	8	(	(	PUNCT
cana-3871	137	9	0	0	NUM
cana-3871	137	10	,	,	PUNCT
cana-3871	137	11	0	0	NUM
cana-3871	137	12	,	,	PUNCT
cana-3871	137	13	1	1	NUM
cana-3871	137	14	)	)	PUNCT
cana-3871	137	15	,	,	PUNCT
cana-3871	137	16	(	(	PUNCT
cana-3871	137	17	0	0	NUM
cana-3871	137	18	,	,	PUNCT
cana-3871	137	19	1	1	NUM
cana-3871	137	20	,	,	PUNCT
cana-3871	137	21	0	0	NUM
cana-3871	137	22	)	)	PUNCT
cana-3871	137	23	and	and	CCONJ
cana-3871	137	24	(	(	PUNCT
cana-3871	137	25	1	1	NUM
cana-3871	137	26	,	,	PUNCT
cana-3871	137	27	0	0	NUM
cana-3871	137	28	,	,	PUNCT
cana-3871	137	29	0	0	NUM
cana-3871	137	30	)	)	PUNCT
cana-3871	137	31	form	form	VERB
cana-3871	137	32	a	a	DET
cana-3871	137	33	cycle	cycle	NOUN
cana-3871	137	34	.	.	PUNCT
cana-3871	138	1	∴	∴	PROPN
cana-3871	138	2	ℤ2	ℤ2	PROPN
cana-3871	138	3	3	3	NUM
cana-3871	138	4	has	have	VERB
cana-3871	138	5	a	a	DET
cana-3871	138	6	cycle	cycle	NOUN
cana-3871	138	7	of	of	ADP
cana-3871	138	8	length	length	NOUN
cana-3871	138	9	3	3	NUM
cana-3871	138	10	.	.	PUNCT
cana-3871	139	1	∴	∴	PROPN
cana-3871	139	2	the	the	DET
cana-3871	139	3	theorem	theorem	NOUN
cana-3871	139	4	holds	hold	VERB
cana-3871	139	5	.	.	PUNCT
cana-3871	140	1	3.4.2	3.4.2	NUM
cana-3871	140	2	example	example	NOUN
cana-3871	140	3	communications	communication	NOUN
cana-3871	140	4	on	on	ADP
cana-3871	140	5	applied	apply	VERB
cana-3871	140	6	nonlinear	nonlinear	ADJ
cana-3871	140	7	analysis	analysis	NOUN
cana-3871	140	8	issn	issn	NOUN
cana-3871	140	9	:	:	PUNCT
cana-3871	140	10	1074	1074	NUM
cana-3871	140	11	-	-	PUNCT
cana-3871	140	12	133x	133x	NUM
cana-3871	140	13	vol	vol	NOUN
cana-3871	140	14	32	32	NUM
cana-3871	140	15	no	no	NOUN
cana-3871	140	16	.	.	PUNCT
cana-3871	141	1	7s	7	NOUN
cana-3871	141	2	(	(	PUNCT
cana-3871	141	3	2025	2025	NUM
cana-3871	141	4	)	)	PUNCT
cana-3871	141	5	953	953	NUM
cana-3871	141	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	141	7	ℤ2	ℤ2	PROPN
cana-3871	141	8	4	4	NUM
cana-3871	141	9	=	=	SYM
cana-3871	141	10	ℤ2	ℤ2	PROPN
cana-3871	141	11	×	×	NOUN
cana-3871	141	12	ℤ2	ℤ2	PROPN
cana-3871	141	13	×	×	PROPN
cana-3871	141	14	ℤ2	ℤ2	PROPN
cana-3871	141	15	×	×	PROPN
cana-3871	141	16	ℤ2	ℤ2	PROPN
cana-3871	141	17	ℤ2×ℤ2×ℤ2×ℤ2	ℤ2×ℤ2×ℤ2×ℤ2	PROPN
cana-3871	141	18	=	=	SYM
cana-3871	141	19	{	{	PUNCT
cana-3871	141	20	(	(	PUNCT
cana-3871	141	21	0	0	NUM
cana-3871	141	22	,	,	PUNCT
cana-3871	141	23	0	0	NUM
cana-3871	141	24	,	,	PUNCT
cana-3871	141	25	0	0	NUM
cana-3871	141	26	,	,	PUNCT
cana-3871	141	27	0	0	NUM
cana-3871	141	28	)	)	PUNCT
cana-3871	141	29	,	,	PUNCT
cana-3871	141	30	(	(	PUNCT
cana-3871	141	31	0	0	NUM
cana-3871	141	32	,	,	PUNCT
cana-3871	141	33	0	0	NUM
cana-3871	141	34	,	,	PUNCT
cana-3871	141	35	0	0	NUM
cana-3871	141	36	,	,	PUNCT
cana-3871	141	37	1	1	NUM
cana-3871	141	38	)	)	PUNCT
cana-3871	141	39	,	,	PUNCT
cana-3871	141	40	(	(	PUNCT
cana-3871	141	41	0	0	NUM
cana-3871	141	42	,	,	PUNCT
cana-3871	141	43	0	0	NUM
cana-3871	141	44	,	,	PUNCT
cana-3871	141	45	1	1	NUM
cana-3871	141	46	,	,	PUNCT
cana-3871	141	47	0	0	NUM
cana-3871	141	48	)	)	PUNCT
cana-3871	141	49	,	,	PUNCT
cana-3871	141	50	(	(	PUNCT
cana-3871	141	51	0	0	NUM
cana-3871	141	52	,	,	PUNCT
cana-3871	141	53	1	1	NUM
cana-3871	141	54	,	,	PUNCT
cana-3871	141	55	0	0	NUM
cana-3871	141	56	,	,	PUNCT
cana-3871	141	57	0	0	NUM
cana-3871	141	58	)	)	PUNCT
cana-3871	141	59	,	,	PUNCT
cana-3871	141	60	(	(	PUNCT
cana-3871	141	61	0	0	NUM
cana-3871	141	62	,	,	PUNCT
cana-3871	141	63	0	0	NUM
cana-3871	141	64	,	,	PUNCT
cana-3871	141	65	1	1	NUM
cana-3871	141	66	,	,	PUNCT
cana-3871	141	67	1	1	NUM
cana-3871	141	68	)	)	PUNCT
cana-3871	141	69	,	,	PUNCT
cana-3871	141	70	(	(	PUNCT
cana-3871	141	71	0	0	NUM
cana-3871	141	72	,	,	PUNCT
cana-3871	141	73	1	1	NUM
cana-3871	141	74	,	,	PUNCT
cana-3871	141	75	0	0	NUM
cana-3871	141	76	,	,	PUNCT
cana-3871	141	77	1	1	NUM
cana-3871	141	78	)	)	PUNCT
cana-3871	141	79	,	,	PUNCT
cana-3871	141	80	(	(	PUNCT
cana-3871	141	81	(	(	PUNCT
cana-3871	141	82	0	0	NUM
cana-3871	141	83	,	,	PUNCT
cana-3871	141	84	1	1	NUM
cana-3871	141	85	,	,	PUNCT
cana-3871	141	86	1	1	NUM
cana-3871	141	87	,	,	PUNCT
cana-3871	141	88	0	0	NUM
cana-3871	141	89	)	)	PUNCT
cana-3871	141	90	,	,	PUNCT
cana-3871	141	91	(	(	PUNCT
cana-3871	141	92	0	0	NUM
cana-3871	141	93	,	,	PUNCT
cana-3871	141	94	1	1	NUM
cana-3871	141	95	,	,	PUNCT
cana-3871	141	96	1	1	NUM
cana-3871	141	97	,	,	PUNCT
cana-3871	141	98	1	1	NUM
cana-3871	141	99	)	)	PUNCT
cana-3871	141	100	,	,	PUNCT
cana-3871	141	101	(	(	PUNCT
cana-3871	141	102	1	1	NUM
cana-3871	141	103	,	,	PUNCT
cana-3871	141	104	0	0	NUM
cana-3871	141	105	,	,	PUNCT
cana-3871	141	106	0	0	NUM
cana-3871	141	107	,	,	PUNCT
cana-3871	141	108	0	0	NUM
cana-3871	141	109	)	)	PUNCT
cana-3871	141	110	,	,	PUNCT
cana-3871	141	111	(	(	PUNCT
cana-3871	141	112	1	1	NUM
cana-3871	141	113	,	,	PUNCT
cana-3871	141	114	0	0	NUM
cana-3871	141	115	,	,	PUNCT
cana-3871	141	116	0	0	NUM
cana-3871	141	117	,	,	PUNCT
cana-3871	141	118	1	1	NUM
cana-3871	141	119	)	)	PUNCT
cana-3871	141	120	,	,	PUNCT
cana-3871	141	121	(	(	PUNCT
cana-3871	141	122	1	1	NUM
cana-3871	141	123	,	,	PUNCT
cana-3871	141	124	0	0	NUM
cana-3871	141	125	,	,	PUNCT
cana-3871	141	126	1	1	NUM
cana-3871	141	127	,	,	PUNCT
cana-3871	141	128	0	0	NUM
cana-3871	141	129	)	)	PUNCT
cana-3871	141	130	,	,	PUNCT
cana-3871	141	131	(	(	PUNCT
cana-3871	141	132	1	1	NUM
cana-3871	141	133	,	,	PUNCT
cana-3871	141	134	0	0	NUM
cana-3871	141	135	,	,	PUNCT
cana-3871	141	136	1	1	NUM
cana-3871	141	137	,	,	PUNCT
cana-3871	141	138	1	1	NUM
cana-3871	141	139	)	)	PUNCT
cana-3871	141	140	,	,	PUNCT
cana-3871	141	141	(	(	PUNCT
cana-3871	141	142	1	1	NUM
cana-3871	141	143	,	,	PUNCT
cana-3871	141	144	1	1	NUM
cana-3871	141	145	,	,	PUNCT
cana-3871	141	146	0	0	NUM
cana-3871	141	147	,	,	PUNCT
cana-3871	141	148	0	0	NUM
cana-3871	141	149	)	)	PUNCT
cana-3871	141	150	,	,	PUNCT
cana-3871	141	151	(	(	PUNCT
cana-3871	141	152	1	1	NUM
cana-3871	141	153	,	,	PUNCT
cana-3871	141	154	1	1	NUM
cana-3871	141	155	,	,	PUNCT
cana-3871	141	156	0	0	NUM
cana-3871	141	157	,	,	PUNCT
cana-3871	141	158	1	1	NUM
cana-3871	141	159	)	)	PUNCT
cana-3871	141	160	,	,	PUNCT
cana-3871	141	161	(	(	PUNCT
cana-3871	141	162	1	1	NUM
cana-3871	141	163	,	,	PUNCT
cana-3871	141	164	1	1	NUM
cana-3871	141	165	,	,	PUNCT
cana-3871	141	166	1	1	NUM
cana-3871	141	167	,	,	PUNCT
cana-3871	141	168	0	0	NUM
cana-3871	141	169	)	)	PUNCT
cana-3871	141	170	,	,	PUNCT
cana-3871	141	171	(	(	PUNCT
cana-3871	141	172	1	1	NUM
cana-3871	141	173	,	,	PUNCT
cana-3871	141	174	1	1	NUM
cana-3871	141	175	,	,	PUNCT
cana-3871	141	176	1	1	NUM
cana-3871	141	177	,	,	PUNCT
cana-3871	141	178	1	1	NUM
cana-3871	141	179	)	)	PUNCT
cana-3871	141	180	}	}	PUNCT
cana-3871	141	181	γ(ℤ2×ℤ2×ℤ2×ℤ2	γ(ℤ2×ℤ2×ℤ2×ℤ2	PROPN
cana-3871	141	182	)	)	PUNCT
cana-3871	141	183	=	=	PRON
cana-3871	141	184	{	{	PUNCT
cana-3871	141	185	(	(	PUNCT
cana-3871	141	186	0	0	NUM
cana-3871	141	187	,	,	PUNCT
cana-3871	141	188	0	0	NUM
cana-3871	141	189	,	,	PUNCT
cana-3871	141	190	0	0	NUM
cana-3871	141	191	,	,	PUNCT
cana-3871	141	192	1	1	NUM
cana-3871	141	193	)	)	PUNCT
cana-3871	141	194	,	,	PUNCT
cana-3871	141	195	(	(	PUNCT
cana-3871	141	196	0	0	NUM
cana-3871	141	197	,	,	PUNCT
cana-3871	141	198	0	0	NUM
cana-3871	141	199	,	,	PUNCT
cana-3871	141	200	1	1	NUM
cana-3871	141	201	,	,	PUNCT
cana-3871	141	202	0	0	NUM
cana-3871	141	203	)	)	PUNCT
cana-3871	141	204	,	,	PUNCT
cana-3871	141	205	(	(	PUNCT
cana-3871	141	206	0	0	NUM
cana-3871	141	207	,	,	PUNCT
cana-3871	141	208	1	1	NUM
cana-3871	141	209	,	,	PUNCT
cana-3871	141	210	0	0	NUM
cana-3871	141	211	,	,	PUNCT
cana-3871	141	212	0	0	NUM
cana-3871	141	213	)	)	PUNCT
cana-3871	141	214	,	,	PUNCT
cana-3871	141	215	(	(	PUNCT
cana-3871	141	216	0	0	NUM
cana-3871	141	217	,	,	PUNCT
cana-3871	141	218	0	0	NUM
cana-3871	141	219	,	,	PUNCT
cana-3871	141	220	1	1	NUM
cana-3871	141	221	,	,	PUNCT
cana-3871	141	222	1	1	NUM
cana-3871	141	223	)	)	PUNCT
cana-3871	141	224	,	,	PUNCT
cana-3871	141	225	(	(	PUNCT
cana-3871	141	226	0	0	NUM
cana-3871	141	227	,	,	PUNCT
cana-3871	141	228	1	1	NUM
cana-3871	141	229	,	,	PUNCT
cana-3871	141	230	0	0	NUM
cana-3871	141	231	,	,	PUNCT
cana-3871	141	232	1	1	NUM
cana-3871	141	233	)	)	PUNCT
cana-3871	141	234	,	,	PUNCT
cana-3871	141	235	(	(	PUNCT
cana-3871	141	236	0	0	NUM
cana-3871	141	237	,	,	PUNCT
cana-3871	141	238	1	1	NUM
cana-3871	141	239	,	,	PUNCT
cana-3871	141	240	1	1	NUM
cana-3871	141	241	,	,	PUNCT
cana-3871	141	242	0	0	NUM
cana-3871	141	243	)	)	PUNCT
cana-3871	141	244	,	,	PUNCT
cana-3871	141	245	(	(	PUNCT
cana-3871	141	246	0	0	NUM
cana-3871	141	247	,	,	PUNCT
cana-3871	141	248	1	1	NUM
cana-3871	141	249	,	,	PUNCT
cana-3871	141	250	1	1	NUM
cana-3871	141	251	,	,	PUNCT
cana-3871	141	252	1	1	NUM
cana-3871	141	253	)	)	PUNCT
cana-3871	141	254	,	,	PUNCT
cana-3871	141	255	(	(	PUNCT
cana-3871	141	256	1	1	NUM
cana-3871	141	257	,	,	PUNCT
cana-3871	141	258	0	0	NUM
cana-3871	141	259	,	,	PUNCT
cana-3871	141	260	0	0	NUM
cana-3871	141	261	,	,	PUNCT
cana-3871	141	262	0	0	NUM
cana-3871	141	263	)	)	PUNCT
cana-3871	141	264	,	,	PUNCT
cana-3871	141	265	(	(	PUNCT
cana-3871	141	266	1	1	NUM
cana-3871	141	267	,	,	PUNCT
cana-3871	141	268	0	0	NUM
cana-3871	141	269	,	,	PUNCT
cana-3871	141	270	0	0	NUM
cana-3871	141	271	,	,	PUNCT
cana-3871	141	272	1	1	NUM
cana-3871	141	273	)	)	PUNCT
cana-3871	141	274	,	,	PUNCT
cana-3871	141	275	(	(	PUNCT
cana-3871	141	276	1	1	NUM
cana-3871	141	277	,	,	PUNCT
cana-3871	141	278	0	0	NUM
cana-3871	141	279	,	,	PUNCT
cana-3871	141	280	1	1	NUM
cana-3871	141	281	,	,	PUNCT
cana-3871	141	282	0	0	NUM
cana-3871	141	283	)	)	PUNCT
cana-3871	141	284	,	,	PUNCT
cana-3871	141	285	(	(	PUNCT
cana-3871	141	286	1	1	NUM
cana-3871	141	287	,	,	PUNCT
cana-3871	141	288	0	0	NUM
cana-3871	141	289	,	,	PUNCT
cana-3871	141	290	1	1	NUM
cana-3871	141	291	,	,	PUNCT
cana-3871	141	292	1	1	NUM
cana-3871	141	293	)	)	PUNCT
cana-3871	141	294	,	,	PUNCT
cana-3871	141	295	(	(	PUNCT
cana-3871	141	296	1	1	NUM
cana-3871	141	297	,	,	PUNCT
cana-3871	141	298	1	1	NUM
cana-3871	141	299	,	,	PUNCT
cana-3871	141	300	0	0	NUM
cana-3871	141	301	,	,	PUNCT
cana-3871	141	302	0	0	NUM
cana-3871	141	303	)	)	PUNCT
cana-3871	141	304	,	,	PUNCT
cana-3871	141	305	(	(	PUNCT
cana-3871	141	306	1	1	NUM
cana-3871	141	307	,	,	PUNCT
cana-3871	141	308	1	1	NUM
cana-3871	141	309	,	,	PUNCT
cana-3871	141	310	0	0	NUM
cana-3871	141	311	,	,	PUNCT
cana-3871	141	312	1	1	NUM
cana-3871	141	313	)	)	PUNCT
cana-3871	141	314	,	,	PUNCT
cana-3871	141	315	(	(	PUNCT
cana-3871	141	316	1	1	NUM
cana-3871	141	317	,	,	PUNCT
cana-3871	141	318	1	1	NUM
cana-3871	141	319	,	,	PUNCT
cana-3871	141	320	1	1	NUM
cana-3871	141	321	,	,	PUNCT
cana-3871	141	322	0	0	NUM
cana-3871	141	323	)	)	PUNCT
cana-3871	141	324	}	}	PUNCT
cana-3871	141	325	the	the	DET
cana-3871	141	326	zero	zero	NUM
cana-3871	141	327	-	-	PUNCT
cana-3871	141	328	divisor	divisor	NOUN
cana-3871	141	329	graph	graph	NOUN
cana-3871	141	330	of	of	ADP
cana-3871	141	331	ℤ2	ℤ2	PROPN
cana-3871	141	332	×	×	PROPN
cana-3871	141	333	ℤ2	ℤ2	PROPN
cana-3871	141	334	×	×	PROPN
cana-3871	141	335	ℤ2	ℤ2	PROPN
cana-3871	141	336	×	×	PROPN
cana-3871	141	337	ℤ2	ℤ2	PROPN
cana-3871	141	338	is	be	AUX
cana-3871	141	339	given	give	VERB
cana-3871	141	340	in	in	ADP
cana-3871	141	341	the	the	DET
cana-3871	141	342	figure	figure	NOUN
cana-3871	141	343	below	below	ADV
cana-3871	141	344	.	.	PUNCT
cana-3871	142	1	fig	fig	NOUN
cana-3871	142	2	14	14	NUM
cana-3871	142	3	:	:	PUNCT
cana-3871	142	4	γ	γ	X
cana-3871	142	5	(	(	PUNCT
cana-3871	142	6	ℤ2	ℤ2	PROPN
cana-3871	142	7	×	×	PROPN
cana-3871	142	8	ℤ2	ℤ2	PROPN
cana-3871	142	9	×	×	PROPN
cana-3871	142	10	ℤ2	ℤ2	PROPN
cana-3871	142	11	×	×	PROPN
cana-3871	142	12	ℤ2	ℤ2	PROPN
cana-3871	142	13	)	)	PUNCT
cana-3871	142	14	number	number	NOUN
cana-3871	142	15	of	of	ADP
cana-3871	142	16	vertices	vertex	NOUN
cana-3871	142	17	in	in	ADP
cana-3871	142	18	the	the	DET
cana-3871	142	19	graph	graph	NOUN
cana-3871	142	20	of	of	ADP
cana-3871	142	21	ℤ	ℤ	PROPN
cana-3871	142	22	(	(	PUNCT
cana-3871	142	23	ℤ2	ℤ2	PROPN
cana-3871	142	24	×	×	PROPN
cana-3871	142	25	ℤ2	ℤ2	PROPN
cana-3871	142	26	×	×	PROPN
cana-3871	142	27	ℤ2	ℤ2	PROPN
cana-3871	142	28	×	×	PROPN
cana-3871	142	29	ℤ2	ℤ2	PROPN
cana-3871	142	30	)	)	PUNCT
cana-3871	142	31	=	=	SYM
cana-3871	143	1	24	24	NUM
cana-3871	143	2	−	−	NUM
cana-3871	143	3	2	2	NUM
cana-3871	143	4	=	=	SYM
cana-3871	143	5	14	14	NUM
cana-3871	143	6	the	the	DET
cana-3871	143	7	vertices	vertex	NOUN
cana-3871	143	8	(	(	PUNCT
cana-3871	143	9	0	0	NUM
cana-3871	143	10	,	,	PUNCT
cana-3871	143	11	0	0	NUM
cana-3871	143	12	,	,	PUNCT
cana-3871	143	13	0	0	NUM
cana-3871	143	14	,	,	PUNCT
cana-3871	143	15	1	1	NUM
cana-3871	143	16	)	)	PUNCT
cana-3871	143	17	,	,	PUNCT
cana-3871	143	18	(	(	PUNCT
cana-3871	143	19	0	0	NUM
cana-3871	143	20	,	,	PUNCT
cana-3871	143	21	0	0	NUM
cana-3871	143	22	,	,	PUNCT
cana-3871	143	23	1	1	NUM
cana-3871	143	24	,	,	PUNCT
cana-3871	143	25	0	0	NUM
cana-3871	143	26	)	)	PUNCT
cana-3871	143	27	,	,	PUNCT
cana-3871	143	28	(	(	PUNCT
cana-3871	143	29	0	0	NUM
cana-3871	143	30	,	,	PUNCT
cana-3871	143	31	1	1	NUM
cana-3871	143	32	,	,	PUNCT
cana-3871	143	33	0	0	NUM
cana-3871	143	34	,	,	PUNCT
cana-3871	143	35	0	0	NUM
cana-3871	143	36	)	)	PUNCT
cana-3871	143	37	,	,	PUNCT
cana-3871	143	38	(	(	PUNCT
cana-3871	143	39	1	1	NUM
cana-3871	143	40	,	,	PUNCT
cana-3871	143	41	0	0	NUM
cana-3871	143	42	,	,	PUNCT
cana-3871	143	43	0	0	NUM
cana-3871	143	44	,	,	PUNCT
cana-3871	143	45	0	0	NUM
cana-3871	143	46	)	)	PUNCT
cana-3871	143	47	form	form	VERB
cana-3871	143	48	a	a	DET
cana-3871	143	49	cycle	cycle	NOUN
cana-3871	143	50	of	of	ADP
cana-3871	143	51	length	length	NOUN
cana-3871	143	52	4	4	NUM
cana-3871	143	53	.	.	PUNCT
cana-3871	144	1	the	the	DET
cana-3871	144	2	vertices	vertex	NOUN
cana-3871	144	3	(	(	PUNCT
cana-3871	144	4	0	0	NUM
cana-3871	144	5	,	,	PUNCT
cana-3871	144	6	1	1	NUM
cana-3871	144	7	,	,	PUNCT
cana-3871	144	8	1	1	NUM
cana-3871	144	9	,	,	PUNCT
cana-3871	144	10	0	0	NUM
cana-3871	144	11	)	)	PUNCT
cana-3871	144	12	,	,	PUNCT
cana-3871	144	13	(	(	PUNCT
cana-3871	144	14	1	1	NUM
cana-3871	144	15	,	,	PUNCT
cana-3871	144	16	0	0	NUM
cana-3871	144	17	,	,	PUNCT
cana-3871	144	18	0	0	NUM
cana-3871	144	19	,	,	PUNCT
cana-3871	144	20	0	0	NUM
cana-3871	144	21	)	)	PUNCT
cana-3871	144	22	,	,	PUNCT
cana-3871	144	23	(	(	PUNCT
cana-3871	144	24	0	0	NUM
cana-3871	144	25	,	,	PUNCT
cana-3871	144	26	1	1	NUM
cana-3871	144	27	,	,	PUNCT
cana-3871	144	28	0	0	NUM
cana-3871	144	29	,	,	PUNCT
cana-3871	144	30	0	0	NUM
cana-3871	144	31	)	)	PUNCT
cana-3871	144	32	,	,	PUNCT
cana-3871	144	33	(	(	PUNCT
cana-3871	144	34	0	0	NUM
cana-3871	144	35	,	,	PUNCT
cana-3871	144	36	0	0	NUM
cana-3871	144	37	,	,	PUNCT
cana-3871	144	38	0	0	NUM
cana-3871	144	39	,	,	PUNCT
cana-3871	144	40	1	1	X
cana-3871	144	41	)	)	PUNCT
cana-3871	144	42	form	form	VERB
cana-3871	144	43	a	a	DET
cana-3871	144	44	cycle	cycle	NOUN
cana-3871	144	45	of	of	ADP
cana-3871	144	46	length	length	NOUN
cana-3871	144	47	4	4	NUM
cana-3871	144	48	.	.	PUNCT
cana-3871	145	1	the	the	DET
cana-3871	145	2	vertices	vertex	NOUN
cana-3871	145	3	(	(	PUNCT
cana-3871	145	4	1	1	NUM
cana-3871	145	5	,	,	PUNCT
cana-3871	145	6	0	0	NUM
cana-3871	145	7	,	,	PUNCT
cana-3871	145	8	0	0	NUM
cana-3871	145	9	,	,	PUNCT
cana-3871	145	10	0	0	NUM
cana-3871	145	11	)	)	PUNCT
cana-3871	145	12	,	,	PUNCT
cana-3871	145	13	(	(	PUNCT
cana-3871	145	14	0	0	NUM
cana-3871	145	15	,	,	PUNCT
cana-3871	145	16	1	1	NUM
cana-3871	145	17	,	,	PUNCT
cana-3871	145	18	0	0	NUM
cana-3871	145	19	,	,	PUNCT
cana-3871	145	20	1	1	NUM
cana-3871	145	21	)	)	PUNCT
cana-3871	145	22	,	,	PUNCT
cana-3871	145	23	(	(	PUNCT
cana-3871	145	24	1	1	NUM
cana-3871	145	25	,	,	PUNCT
cana-3871	145	26	0	0	NUM
cana-3871	145	27	,	,	PUNCT
cana-3871	145	28	1	1	NUM
cana-3871	145	29	,	,	PUNCT
cana-3871	145	30	0	0	NUM
cana-3871	145	31	)	)	PUNCT
cana-3871	145	32	,	,	PUNCT
cana-3871	145	33	(	(	PUNCT
cana-3871	145	34	0	0	NUM
cana-3871	145	35	,	,	PUNCT
cana-3871	145	36	1	1	NUM
cana-3871	145	37	,	,	PUNCT
cana-3871	145	38	0	0	NUM
cana-3871	145	39	,	,	PUNCT
cana-3871	145	40	0	0	NUM
cana-3871	145	41	)	)	PUNCT
cana-3871	145	42	form	form	VERB
cana-3871	145	43	a	a	DET
cana-3871	145	44	cycle	cycle	NOUN
cana-3871	145	45	of	of	ADP
cana-3871	145	46	length	length	NOUN
cana-3871	145	47	4	4	NUM
cana-3871	145	48	and	and	CCONJ
cana-3871	145	49	etc	etc	X
cana-3871	145	50	.	.	PUNCT
cana-3871	146	1	∴	∴	PROPN
cana-3871	146	2	ℤ2	ℤ2	PROPN
cana-3871	147	1	n	n	PART
cana-3871	147	2	has	have	VERB
cana-3871	147	3	a	a	DET
cana-3871	147	4	cycle	cycle	NOUN
cana-3871	147	5	of	of	ADP
cana-3871	147	6	length	length	NOUN
cana-3871	147	7	4	4	NUM
cana-3871	147	8	and	and	CCONJ
cana-3871	147	9	the	the	DET
cana-3871	147	10	theorem	theorem	NOUN
cana-3871	147	11	holds	hold	VERB
cana-3871	147	12	.	.	PUNCT
cana-3871	148	1	3.4.3	3.4.3	NUM
cana-3871	148	2	example	example	NOUN
cana-3871	148	3	:	:	PUNCT
cana-3871	148	4	b5	b5	PROPN
cana-3871	148	5	=	=	SYM
cana-3871	148	6	ℤ2	ℤ2	PROPN
cana-3871	148	7	5	5	NUM
cana-3871	148	8	=	=	SYM
cana-3871	148	9	ℤ2	ℤ2	PROPN
cana-3871	148	10	×	×	NOUN
cana-3871	148	11	ℤ2	ℤ2	PROPN
cana-3871	148	12	×	×	PROPN
cana-3871	148	13	ℤ2	ℤ2	PROPN
cana-3871	148	14	×	×	PROPN
cana-3871	148	15	ℤ2	ℤ2	PROPN
cana-3871	148	16	×	×	PROPN
cana-3871	148	17	ℤ2	ℤ2	PROPN
cana-3871	148	18	ℤ2	ℤ2	PROPN
cana-3871	148	19	×	×	PROPN
cana-3871	148	20	ℤ2	ℤ2	PROPN
cana-3871	148	21	×	×	PROPN
cana-3871	148	22	ℤ2	ℤ2	PROPN
cana-3871	148	23	×	×	PROPN
cana-3871	148	24	ℤ2	ℤ2	PROPN
cana-3871	148	25	×	×	NOUN
cana-3871	148	26	ℤ2	ℤ2	NOUN
cana-3871	148	27	=	=	SYM
cana-3871	148	28	{	{	PUNCT
cana-3871	148	29	(	(	PUNCT
cana-3871	148	30	0	0	NUM
cana-3871	148	31	,	,	PUNCT
cana-3871	148	32	0	0	NUM
cana-3871	148	33	,	,	PUNCT
cana-3871	148	34	0	0	NUM
cana-3871	148	35	,	,	PUNCT
cana-3871	148	36	0	0	NUM
cana-3871	148	37	,	,	PUNCT
cana-3871	148	38	0	0	NUM
cana-3871	148	39	)	)	PUNCT
cana-3871	148	40	,	,	PUNCT
cana-3871	148	41	(	(	PUNCT
cana-3871	148	42	0	0	NUM
cana-3871	148	43	,	,	PUNCT
cana-3871	148	44	0	0	NUM
cana-3871	148	45	,	,	PUNCT
cana-3871	148	46	0	0	NUM
cana-3871	148	47	,	,	PUNCT
cana-3871	148	48	0	0	NUM
cana-3871	148	49	,	,	PUNCT
cana-3871	148	50	1	1	NUM
cana-3871	148	51	)	)	PUNCT
cana-3871	148	52	,	,	PUNCT
cana-3871	148	53	(	(	PUNCT
cana-3871	148	54	0	0	NUM
cana-3871	148	55	,	,	PUNCT
cana-3871	148	56	0	0	NUM
cana-3871	148	57	,	,	PUNCT
cana-3871	148	58	0	0	NUM
cana-3871	148	59	,	,	PUNCT
cana-3871	148	60	1	1	NUM
cana-3871	148	61	,	,	PUNCT
cana-3871	148	62	0	0	NUM
cana-3871	148	63	)	)	PUNCT
cana-3871	148	64	,	,	PUNCT
cana-3871	148	65	(	(	PUNCT
cana-3871	148	66	0	0	NUM
cana-3871	148	67	,	,	PUNCT
cana-3871	148	68	0	0	NUM
cana-3871	148	69	,	,	PUNCT
cana-3871	148	70	0	0	NUM
cana-3871	148	71	,	,	PUNCT
cana-3871	148	72	1	1	NUM
cana-3871	148	73	,	,	PUNCT
cana-3871	148	74	1	1	NUM
cana-3871	148	75	)	)	PUNCT
cana-3871	148	76	,	,	PUNCT
cana-3871	148	77	(	(	PUNCT
cana-3871	148	78	0	0	NUM
cana-3871	148	79	,	,	PUNCT
cana-3871	148	80	0	0	NUM
cana-3871	148	81	,	,	PUNCT
cana-3871	148	82	1	1	NUM
cana-3871	148	83	,	,	PUNCT
cana-3871	148	84	0	0	NUM
cana-3871	148	85	,	,	PUNCT
cana-3871	148	86	0	0	NUM
cana-3871	148	87	)	)	PUNCT
cana-3871	148	88	,	,	PUNCT
cana-3871	148	89	(	(	PUNCT
cana-3871	148	90	0	0	NUM
cana-3871	148	91	,	,	PUNCT
cana-3871	148	92	0	0	NUM
cana-3871	148	93	,	,	PUNCT
cana-3871	148	94	1	1	NUM
cana-3871	148	95	,	,	PUNCT
cana-3871	148	96	0	0	NUM
cana-3871	148	97	,	,	PUNCT
cana-3871	148	98	1	1	NUM
cana-3871	148	99	)	)	PUNCT
cana-3871	148	100	,	,	PUNCT
cana-3871	148	101	(	(	PUNCT
cana-3871	148	102	0	0	NUM
cana-3871	148	103	,	,	PUNCT
cana-3871	148	104	0	0	NUM
cana-3871	148	105	,	,	PUNCT
cana-3871	148	106	1	1	NUM
cana-3871	148	107	,	,	PUNCT
cana-3871	148	108	1	1	NUM
cana-3871	148	109	,	,	PUNCT
cana-3871	148	110	0	0	NUM
cana-3871	148	111	)	)	PUNCT
cana-3871	148	112	,	,	PUNCT
cana-3871	148	113	(	(	PUNCT
cana-3871	148	114	0	0	NUM
cana-3871	148	115	,	,	PUNCT
cana-3871	148	116	0	0	NUM
cana-3871	148	117	,	,	PUNCT
cana-3871	148	118	1	1	NUM
cana-3871	148	119	,	,	PUNCT
cana-3871	148	120	1	1	NUM
cana-3871	148	121	,	,	PUNCT
cana-3871	148	122	1	1	NUM
cana-3871	148	123	)	)	PUNCT
cana-3871	148	124	,	,	PUNCT
cana-3871	148	125	(	(	PUNCT
cana-3871	148	126	0	0	NUM
cana-3871	148	127	,	,	PUNCT
cana-3871	148	128	1	1	NUM
cana-3871	148	129	,	,	PUNCT
cana-3871	148	130	0	0	NUM
cana-3871	148	131	,	,	PUNCT
cana-3871	148	132	0	0	NUM
cana-3871	148	133	,	,	PUNCT
cana-3871	148	134	0	0	NUM
cana-3871	148	135	)	)	PUNCT
cana-3871	148	136	,	,	PUNCT
cana-3871	148	137	(	(	PUNCT
cana-3871	148	138	0	0	NUM
cana-3871	148	139	,	,	PUNCT
cana-3871	148	140	1	1	NUM
cana-3871	148	141	,	,	PUNCT
cana-3871	148	142	0	0	NUM
cana-3871	148	143	,	,	PUNCT
cana-3871	148	144	0	0	NUM
cana-3871	148	145	,	,	PUNCT
cana-3871	148	146	1	1	NUM
cana-3871	148	147	)	)	PUNCT
cana-3871	148	148	,	,	PUNCT
cana-3871	148	149	(	(	PUNCT
cana-3871	148	150	0	0	NUM
cana-3871	148	151	,	,	PUNCT
cana-3871	148	152	1	1	NUM
cana-3871	148	153	,	,	PUNCT
cana-3871	148	154	0	0	NUM
cana-3871	148	155	,	,	PUNCT
cana-3871	148	156	1	1	NUM
cana-3871	148	157	,	,	PUNCT
cana-3871	148	158	0	0	NUM
cana-3871	148	159	)	)	PUNCT
cana-3871	148	160	,	,	PUNCT
cana-3871	148	161	(	(	PUNCT
cana-3871	148	162	0	0	NUM
cana-3871	148	163	,	,	PUNCT
cana-3871	148	164	1	1	NUM
cana-3871	148	165	,	,	PUNCT
cana-3871	148	166	0	0	NUM
cana-3871	148	167	,	,	PUNCT
cana-3871	148	168	1	1	NUM
cana-3871	148	169	,	,	PUNCT
cana-3871	148	170	1	1	NUM
cana-3871	148	171	)	)	PUNCT
cana-3871	148	172	,	,	PUNCT
cana-3871	148	173	(	(	PUNCT
cana-3871	148	174	0	0	NUM
cana-3871	148	175	,	,	PUNCT
cana-3871	148	176	1	1	NUM
cana-3871	148	177	,	,	PUNCT
cana-3871	148	178	1	1	NUM
cana-3871	148	179	,	,	PUNCT
cana-3871	148	180	0	0	NUM
cana-3871	148	181	,	,	PUNCT
cana-3871	148	182	0	0	NUM
cana-3871	148	183	)	)	PUNCT
cana-3871	148	184	,	,	PUNCT
cana-3871	148	185	(	(	PUNCT
cana-3871	148	186	0	0	NUM
cana-3871	148	187	,	,	PUNCT
cana-3871	148	188	1	1	NUM
cana-3871	148	189	,	,	PUNCT
cana-3871	148	190	1	1	NUM
cana-3871	148	191	,	,	PUNCT
cana-3871	148	192	0	0	NUM
cana-3871	148	193	,	,	PUNCT
cana-3871	148	194	1	1	NUM
cana-3871	148	195	)	)	PUNCT
cana-3871	148	196	,	,	PUNCT
cana-3871	148	197	(	(	PUNCT
cana-3871	148	198	0	0	NUM
cana-3871	148	199	,	,	PUNCT
cana-3871	148	200	1	1	NUM
cana-3871	148	201	,	,	PUNCT
cana-3871	148	202	1	1	NUM
cana-3871	148	203	,	,	PUNCT
cana-3871	148	204	1	1	NUM
cana-3871	148	205	,	,	PUNCT
cana-3871	148	206	0	0	NUM
cana-3871	148	207	)	)	PUNCT
cana-3871	148	208	,	,	PUNCT
cana-3871	148	209	(	(	PUNCT
cana-3871	148	210	0	0	NUM
cana-3871	148	211	,	,	PUNCT
cana-3871	148	212	1	1	NUM
cana-3871	148	213	,	,	PUNCT
cana-3871	148	214	1	1	NUM
cana-3871	148	215	,	,	PUNCT
cana-3871	148	216	1	1	NUM
cana-3871	148	217	,	,	PUNCT
cana-3871	148	218	1	1	NUM
cana-3871	148	219	)	)	PUNCT
cana-3871	148	220	,	,	PUNCT
cana-3871	148	221	(	(	PUNCT
cana-3871	148	222	1	1	NUM
cana-3871	148	223	,	,	PUNCT
cana-3871	148	224	0	0	NUM
cana-3871	148	225	,	,	PUNCT
cana-3871	148	226	0	0	NUM
cana-3871	148	227	,	,	PUNCT
cana-3871	148	228	0	0	NUM
cana-3871	148	229	,	,	PUNCT
cana-3871	148	230	0	0	NUM
cana-3871	148	231	)	)	PUNCT
cana-3871	148	232	,	,	PUNCT
cana-3871	148	233	(	(	PUNCT
cana-3871	148	234	1	1	NUM
cana-3871	148	235	,	,	PUNCT
cana-3871	148	236	0	0	NUM
cana-3871	148	237	,	,	PUNCT
cana-3871	148	238	0	0	NUM
cana-3871	148	239	,	,	PUNCT
cana-3871	148	240	0	0	NUM
cana-3871	148	241	,	,	PUNCT
cana-3871	148	242	1	1	NUM
cana-3871	148	243	)	)	PUNCT
cana-3871	148	244	,	,	PUNCT
cana-3871	148	245	(	(	PUNCT
cana-3871	148	246	1	1	NUM
cana-3871	148	247	,	,	PUNCT
cana-3871	148	248	0	0	NUM
cana-3871	148	249	,	,	PUNCT
cana-3871	148	250	0	0	NUM
cana-3871	148	251	,	,	PUNCT
cana-3871	148	252	1	1	NUM
cana-3871	148	253	,	,	PUNCT
cana-3871	148	254	0	0	NUM
cana-3871	148	255	)	)	PUNCT
cana-3871	148	256	,	,	PUNCT
cana-3871	148	257	(	(	PUNCT
cana-3871	148	258	1	1	NUM
cana-3871	148	259	,	,	PUNCT
cana-3871	148	260	0	0	NUM
cana-3871	148	261	,	,	PUNCT
cana-3871	148	262	0	0	NUM
cana-3871	148	263	,	,	PUNCT
cana-3871	148	264	1	1	NUM
cana-3871	148	265	,	,	PUNCT
cana-3871	148	266	1	1	NUM
cana-3871	148	267	)	)	PUNCT
cana-3871	148	268	,	,	PUNCT
cana-3871	148	269	(	(	PUNCT
cana-3871	148	270	1	1	NUM
cana-3871	148	271	,	,	PUNCT
cana-3871	148	272	0	0	NUM
cana-3871	148	273	,	,	PUNCT
cana-3871	148	274	1	1	NUM
cana-3871	148	275	,	,	PUNCT
cana-3871	148	276	0	0	NUM
cana-3871	148	277	,	,	PUNCT
cana-3871	148	278	0	0	NUM
cana-3871	148	279	)	)	PUNCT
cana-3871	148	280	,	,	PUNCT
cana-3871	148	281	(	(	PUNCT
cana-3871	148	282	1	1	NUM
cana-3871	148	283	,	,	PUNCT
cana-3871	148	284	0	0	NUM
cana-3871	148	285	,	,	PUNCT
cana-3871	148	286	1	1	NUM
cana-3871	148	287	,	,	PUNCT
cana-3871	148	288	0	0	NUM
cana-3871	148	289	,	,	PUNCT
cana-3871	148	290	1	1	NUM
cana-3871	148	291	)	)	PUNCT
cana-3871	148	292	,	,	PUNCT
cana-3871	148	293	(	(	PUNCT
cana-3871	148	294	1	1	NUM
cana-3871	148	295	,	,	PUNCT
cana-3871	148	296	0	0	NUM
cana-3871	148	297	,	,	PUNCT
cana-3871	148	298	1	1	NUM
cana-3871	148	299	,	,	PUNCT
cana-3871	148	300	1	1	NUM
cana-3871	148	301	,	,	PUNCT
cana-3871	148	302	0	0	NUM
cana-3871	148	303	)	)	PUNCT
cana-3871	148	304	,	,	PUNCT
cana-3871	148	305	(	(	PUNCT
cana-3871	148	306	1	1	NUM
cana-3871	148	307	,	,	PUNCT
cana-3871	148	308	0	0	NUM
cana-3871	148	309	,	,	PUNCT
cana-3871	148	310	1	1	NUM
cana-3871	148	311	,	,	PUNCT
cana-3871	148	312	1	1	NUM
cana-3871	148	313	,	,	PUNCT
cana-3871	148	314	1	1	NUM
cana-3871	148	315	)	)	PUNCT
cana-3871	148	316	,	,	PUNCT
cana-3871	148	317	(	(	PUNCT
cana-3871	148	318	1	1	NUM
cana-3871	148	319	,	,	PUNCT
cana-3871	148	320	1	1	NUM
cana-3871	148	321	,	,	PUNCT
cana-3871	148	322	0	0	NUM
cana-3871	148	323	,	,	PUNCT
cana-3871	148	324	0	0	NUM
cana-3871	148	325	,	,	PUNCT
cana-3871	148	326	0	0	NUM
cana-3871	148	327	)	)	PUNCT
cana-3871	148	328	,	,	PUNCT
cana-3871	148	329	(	(	PUNCT
cana-3871	148	330	1	1	NUM
cana-3871	148	331	,	,	PUNCT
cana-3871	148	332	1	1	NUM
cana-3871	148	333	,	,	PUNCT
cana-3871	148	334	0	0	NUM
cana-3871	148	335	,	,	PUNCT
cana-3871	148	336	0	0	NUM
cana-3871	148	337	,	,	PUNCT
cana-3871	148	338	1	1	NUM
cana-3871	148	339	)	)	PUNCT
cana-3871	148	340	,	,	PUNCT
cana-3871	148	341	(	(	PUNCT
cana-3871	148	342	1	1	NUM
cana-3871	148	343	,	,	PUNCT
cana-3871	148	344	1	1	NUM
cana-3871	148	345	,	,	PUNCT
cana-3871	148	346	0	0	NUM
cana-3871	148	347	,	,	PUNCT
cana-3871	148	348	1	1	NUM
cana-3871	148	349	,	,	PUNCT
cana-3871	148	350	0	0	NUM
cana-3871	148	351	)	)	PUNCT
cana-3871	148	352	,	,	PUNCT
cana-3871	148	353	(	(	PUNCT
cana-3871	148	354	1	1	NUM
cana-3871	148	355	,	,	PUNCT
cana-3871	148	356	1	1	NUM
cana-3871	148	357	,	,	PUNCT
cana-3871	148	358	0	0	NUM
cana-3871	148	359	,	,	PUNCT
cana-3871	148	360	1	1	NUM
cana-3871	148	361	,	,	PUNCT
cana-3871	148	362	1	1	NUM
cana-3871	148	363	)	)	PUNCT
cana-3871	148	364	,	,	PUNCT
cana-3871	148	365	(	(	PUNCT
cana-3871	148	366	1	1	NUM
cana-3871	148	367	,	,	PUNCT
cana-3871	148	368	1	1	NUM
cana-3871	148	369	,	,	PUNCT
cana-3871	148	370	1	1	NUM
cana-3871	148	371	,	,	PUNCT
cana-3871	148	372	0	0	NUM
cana-3871	148	373	,	,	PUNCT
cana-3871	148	374	0	0	NUM
cana-3871	148	375	)	)	PUNCT
cana-3871	148	376	,	,	PUNCT
cana-3871	148	377	(	(	PUNCT
cana-3871	148	378	1	1	NUM
cana-3871	148	379	,	,	PUNCT
cana-3871	148	380	1	1	NUM
cana-3871	148	381	,	,	PUNCT
cana-3871	148	382	1	1	NUM
cana-3871	148	383	,	,	PUNCT
cana-3871	148	384	0	0	NUM
cana-3871	148	385	,	,	PUNCT
cana-3871	148	386	1	1	NUM
cana-3871	148	387	)	)	PUNCT
cana-3871	148	388	,	,	PUNCT
cana-3871	148	389	(	(	PUNCT
cana-3871	148	390	1	1	NUM
cana-3871	148	391	,	,	PUNCT
cana-3871	148	392	1	1	NUM
cana-3871	148	393	,	,	PUNCT
cana-3871	148	394	1	1	NUM
cana-3871	148	395	,	,	PUNCT
cana-3871	148	396	1	1	NUM
cana-3871	148	397	,	,	PUNCT
cana-3871	148	398	0	0	NUM
cana-3871	148	399	)	)	PUNCT
cana-3871	148	400	,	,	PUNCT
cana-3871	148	401	(	(	PUNCT
cana-3871	148	402	1	1	NUM
cana-3871	148	403	,	,	PUNCT
cana-3871	148	404	1	1	NUM
cana-3871	148	405	,	,	PUNCT
cana-3871	148	406	1	1	NUM
cana-3871	148	407	,	,	PUNCT
cana-3871	148	408	1	1	NUM
cana-3871	148	409	,	,	PUNCT
cana-3871	148	410	1	1	NUM
cana-3871	148	411	)	)	PUNCT
cana-3871	148	412	}	}	PUNCT
cana-3871	148	413	ℤ(ℤ2×ℤ2×ℤ2×ℤ2×ℤ2	ℤ(ℤ2×ℤ2×ℤ2×ℤ2×ℤ2	PROPN
cana-3871	148	414	)	)	PUNCT
cana-3871	148	415	=	=	PRON
cana-3871	148	416	{	{	PUNCT
cana-3871	148	417	(	(	PUNCT
cana-3871	148	418	0	0	NUM
cana-3871	148	419	,	,	PUNCT
cana-3871	148	420	0	0	NUM
cana-3871	148	421	,	,	PUNCT
cana-3871	148	422	0	0	NUM
cana-3871	148	423	,	,	PUNCT
cana-3871	148	424	0	0	NUM
cana-3871	148	425	,	,	PUNCT
cana-3871	148	426	1	1	NUM
cana-3871	148	427	)	)	PUNCT
cana-3871	148	428	,	,	PUNCT
cana-3871	148	429	(	(	PUNCT
cana-3871	148	430	0	0	NUM
cana-3871	148	431	,	,	PUNCT
cana-3871	148	432	0	0	NUM
cana-3871	148	433	,	,	PUNCT
cana-3871	148	434	0	0	NUM
cana-3871	148	435	,	,	PUNCT
cana-3871	148	436	1	1	NUM
cana-3871	148	437	,	,	PUNCT
cana-3871	148	438	0	0	NUM
cana-3871	148	439	)	)	PUNCT
cana-3871	148	440	,	,	PUNCT
cana-3871	148	441	(	(	PUNCT
cana-3871	148	442	0	0	NUM
cana-3871	148	443	,	,	PUNCT
cana-3871	148	444	0	0	NUM
cana-3871	148	445	,	,	PUNCT
cana-3871	148	446	0	0	NUM
cana-3871	148	447	,	,	PUNCT
cana-3871	148	448	1	1	NUM
cana-3871	148	449	,	,	PUNCT
cana-3871	148	450	1	1	NUM
cana-3871	148	451	)	)	PUNCT
cana-3871	148	452	(	(	PUNCT
cana-3871	148	453	0	0	NUM
cana-3871	148	454	,	,	PUNCT
cana-3871	148	455	0	0	NUM
cana-3871	148	456	,	,	PUNCT
cana-3871	148	457	1	1	NUM
cana-3871	148	458	,	,	PUNCT
cana-3871	148	459	0	0	NUM
cana-3871	148	460	,	,	PUNCT
cana-3871	148	461	0	0	NUM
cana-3871	148	462	)	)	PUNCT
cana-3871	148	463	,	,	PUNCT
cana-3871	148	464	(	(	PUNCT
cana-3871	148	465	0	0	NUM
cana-3871	148	466	,	,	PUNCT
cana-3871	148	467	0	0	NUM
cana-3871	148	468	,	,	PUNCT
cana-3871	148	469	1	1	NUM
cana-3871	148	470	,	,	PUNCT
cana-3871	148	471	0	0	NUM
cana-3871	148	472	,	,	PUNCT
cana-3871	148	473	1	1	NUM
cana-3871	148	474	)	)	PUNCT
cana-3871	148	475	,	,	PUNCT
cana-3871	148	476	(	(	PUNCT
cana-3871	148	477	0	0	NUM
cana-3871	148	478	,	,	PUNCT
cana-3871	148	479	0	0	NUM
cana-3871	148	480	,	,	PUNCT
cana-3871	148	481	1	1	NUM
cana-3871	148	482	,	,	PUNCT
cana-3871	148	483	1	1	NUM
cana-3871	148	484	,	,	PUNCT
cana-3871	148	485	0	0	NUM
cana-3871	148	486	)	)	PUNCT
cana-3871	148	487	,	,	PUNCT
cana-3871	148	488	communications	communication	NOUN
cana-3871	148	489	on	on	ADP
cana-3871	148	490	applied	apply	VERB
cana-3871	148	491	nonlinear	nonlinear	ADJ
cana-3871	148	492	analysis	analysis	NOUN
cana-3871	148	493	issn	issn	NOUN
cana-3871	148	494	:	:	PUNCT
cana-3871	148	495	1074	1074	NUM
cana-3871	148	496	-	-	PUNCT
cana-3871	148	497	133x	133x	NUM
cana-3871	148	498	vol	vol	NOUN
cana-3871	148	499	32	32	NUM
cana-3871	148	500	no	no	NOUN
cana-3871	148	501	.	.	PUNCT
cana-3871	149	1	7s	7	NOUN
cana-3871	149	2	(	(	PUNCT
cana-3871	149	3	2025	2025	NUM
cana-3871	149	4	)	)	PUNCT
cana-3871	149	5	954	954	NUM
cana-3871	149	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	149	7	(	(	PUNCT
cana-3871	149	8	0	0	NUM
cana-3871	149	9	,	,	PUNCT
cana-3871	149	10	0	0	NUM
cana-3871	149	11	,	,	PUNCT
cana-3871	149	12	1	1	NUM
cana-3871	149	13	,	,	PUNCT
cana-3871	149	14	1	1	NUM
cana-3871	149	15	,	,	PUNCT
cana-3871	149	16	1	1	NUM
cana-3871	149	17	)	)	PUNCT
cana-3871	149	18	,	,	PUNCT
cana-3871	149	19	(	(	PUNCT
cana-3871	149	20	0	0	NUM
cana-3871	149	21	,	,	PUNCT
cana-3871	149	22	1	1	NUM
cana-3871	149	23	,	,	PUNCT
cana-3871	149	24	0	0	NUM
cana-3871	149	25	,	,	PUNCT
cana-3871	149	26	0	0	NUM
cana-3871	149	27	,	,	PUNCT
cana-3871	149	28	0	0	NUM
cana-3871	149	29	)	)	PUNCT
cana-3871	149	30	,	,	PUNCT
cana-3871	149	31	(	(	PUNCT
cana-3871	149	32	0	0	NUM
cana-3871	149	33	,	,	PUNCT
cana-3871	149	34	1	1	NUM
cana-3871	149	35	,	,	PUNCT
cana-3871	149	36	0	0	NUM
cana-3871	149	37	,	,	PUNCT
cana-3871	149	38	0	0	NUM
cana-3871	149	39	,	,	PUNCT
cana-3871	149	40	1	1	NUM
cana-3871	149	41	)	)	PUNCT
cana-3871	149	42	,	,	PUNCT
cana-3871	149	43	(	(	PUNCT
cana-3871	149	44	0	0	NUM
cana-3871	149	45	,	,	PUNCT
cana-3871	149	46	1	1	NUM
cana-3871	149	47	,	,	PUNCT
cana-3871	149	48	0	0	NUM
cana-3871	149	49	,	,	PUNCT
cana-3871	149	50	1	1	NUM
cana-3871	149	51	,	,	PUNCT
cana-3871	149	52	0	0	NUM
cana-3871	149	53	)	)	PUNCT
cana-3871	149	54	,	,	PUNCT
cana-3871	149	55	(	(	PUNCT
cana-3871	149	56	0	0	NUM
cana-3871	149	57	,	,	PUNCT
cana-3871	149	58	1	1	NUM
cana-3871	149	59	,	,	PUNCT
cana-3871	149	60	0	0	NUM
cana-3871	149	61	,	,	PUNCT
cana-3871	149	62	1	1	NUM
cana-3871	149	63	,	,	PUNCT
cana-3871	149	64	1	1	NUM
cana-3871	149	65	)	)	PUNCT
cana-3871	149	66	,	,	PUNCT
cana-3871	149	67	(	(	PUNCT
cana-3871	149	68	0	0	NUM
cana-3871	149	69	,	,	PUNCT
cana-3871	149	70	1	1	NUM
cana-3871	149	71	,	,	PUNCT
cana-3871	149	72	1	1	NUM
cana-3871	149	73	,	,	PUNCT
cana-3871	149	74	0	0	NUM
cana-3871	149	75	,	,	PUNCT
cana-3871	149	76	0	0	NUM
cana-3871	149	77	)	)	PUNCT
cana-3871	149	78	,	,	PUNCT
cana-3871	149	79	(	(	PUNCT
cana-3871	149	80	0	0	NUM
cana-3871	149	81	,	,	PUNCT
cana-3871	149	82	1	1	NUM
cana-3871	149	83	,	,	PUNCT
cana-3871	149	84	1	1	NUM
cana-3871	149	85	,	,	PUNCT
cana-3871	149	86	0	0	NUM
cana-3871	149	87	,	,	PUNCT
cana-3871	149	88	1	1	NUM
cana-3871	149	89	)	)	PUNCT
cana-3871	149	90	,	,	PUNCT
cana-3871	149	91	(	(	PUNCT
cana-3871	149	92	0	0	NUM
cana-3871	149	93	,	,	PUNCT
cana-3871	149	94	1	1	NUM
cana-3871	149	95	,	,	PUNCT
cana-3871	149	96	1	1	NUM
cana-3871	149	97	,	,	PUNCT
cana-3871	149	98	1	1	NUM
cana-3871	149	99	,	,	PUNCT
cana-3871	149	100	0	0	NUM
cana-3871	149	101	)	)	PUNCT
cana-3871	149	102	,	,	PUNCT
cana-3871	149	103	(	(	PUNCT
cana-3871	149	104	0	0	NUM
cana-3871	149	105	,	,	PUNCT
cana-3871	149	106	1	1	NUM
cana-3871	149	107	,	,	PUNCT
cana-3871	149	108	1	1	NUM
cana-3871	149	109	,	,	PUNCT
cana-3871	149	110	1	1	NUM
cana-3871	149	111	,	,	PUNCT
cana-3871	149	112	1	1	NUM
cana-3871	149	113	)	)	PUNCT
cana-3871	149	114	,	,	PUNCT
cana-3871	149	115	(	(	PUNCT
cana-3871	149	116	1	1	NUM
cana-3871	149	117	,	,	PUNCT
cana-3871	149	118	0	0	NUM
cana-3871	149	119	,	,	PUNCT
cana-3871	149	120	0	0	NUM
cana-3871	149	121	,	,	PUNCT
cana-3871	149	122	0	0	NUM
cana-3871	149	123	,	,	PUNCT
cana-3871	149	124	0	0	NUM
cana-3871	149	125	)	)	PUNCT
cana-3871	149	126	,	,	PUNCT
cana-3871	149	127	(	(	PUNCT
cana-3871	149	128	1	1	NUM
cana-3871	149	129	,	,	PUNCT
cana-3871	149	130	0	0	NUM
cana-3871	149	131	,	,	PUNCT
cana-3871	149	132	0	0	NUM
cana-3871	149	133	,	,	PUNCT
cana-3871	149	134	0	0	NUM
cana-3871	149	135	,	,	PUNCT
cana-3871	149	136	1	1	NUM
cana-3871	149	137	)	)	PUNCT
cana-3871	149	138	,	,	PUNCT
cana-3871	149	139	(	(	PUNCT
cana-3871	149	140	1	1	NUM
cana-3871	149	141	,	,	PUNCT
cana-3871	149	142	0	0	NUM
cana-3871	149	143	,	,	PUNCT
cana-3871	149	144	0	0	NUM
cana-3871	149	145	,	,	PUNCT
cana-3871	149	146	1	1	NUM
cana-3871	149	147	,	,	PUNCT
cana-3871	149	148	0	0	NUM
cana-3871	149	149	)	)	PUNCT
cana-3871	149	150	,	,	PUNCT
cana-3871	149	151	(	(	PUNCT
cana-3871	149	152	1	1	NUM
cana-3871	149	153	,	,	PUNCT
cana-3871	149	154	0	0	NUM
cana-3871	149	155	,	,	PUNCT
cana-3871	149	156	0	0	NUM
cana-3871	149	157	,	,	PUNCT
cana-3871	149	158	1	1	NUM
cana-3871	149	159	,	,	PUNCT
cana-3871	149	160	1	1	NUM
cana-3871	149	161	)	)	PUNCT
cana-3871	149	162	,	,	PUNCT
cana-3871	149	163	(	(	PUNCT
cana-3871	149	164	1	1	NUM
cana-3871	149	165	,	,	PUNCT
cana-3871	149	166	0	0	NUM
cana-3871	149	167	,	,	PUNCT
cana-3871	149	168	1	1	NUM
cana-3871	149	169	,	,	PUNCT
cana-3871	149	170	0	0	NUM
cana-3871	149	171	,	,	PUNCT
cana-3871	149	172	0	0	NUM
cana-3871	149	173	)	)	PUNCT
cana-3871	149	174	,	,	PUNCT
cana-3871	149	175	(	(	PUNCT
cana-3871	149	176	1	1	NUM
cana-3871	149	177	,	,	PUNCT
cana-3871	149	178	0	0	NUM
cana-3871	149	179	,	,	PUNCT
cana-3871	149	180	1	1	NUM
cana-3871	149	181	,	,	PUNCT
cana-3871	149	182	0	0	NUM
cana-3871	149	183	,	,	PUNCT
cana-3871	149	184	1	1	NUM
cana-3871	149	185	)	)	PUNCT
cana-3871	149	186	,	,	PUNCT
cana-3871	149	187	(	(	PUNCT
cana-3871	149	188	1	1	NUM
cana-3871	149	189	,	,	PUNCT
cana-3871	149	190	0	0	NUM
cana-3871	149	191	,	,	PUNCT
cana-3871	149	192	1	1	NUM
cana-3871	149	193	,	,	PUNCT
cana-3871	149	194	1	1	NUM
cana-3871	149	195	,	,	PUNCT
cana-3871	149	196	0	0	NUM
cana-3871	149	197	)	)	PUNCT
cana-3871	149	198	,	,	PUNCT
cana-3871	149	199	(	(	PUNCT
cana-3871	149	200	1	1	NUM
cana-3871	149	201	,	,	PUNCT
cana-3871	149	202	0	0	NUM
cana-3871	149	203	,	,	PUNCT
cana-3871	149	204	1	1	NUM
cana-3871	149	205	,	,	PUNCT
cana-3871	149	206	1	1	NUM
cana-3871	149	207	,	,	PUNCT
cana-3871	149	208	1	1	NUM
cana-3871	149	209	)	)	PUNCT
cana-3871	149	210	,	,	PUNCT
cana-3871	149	211	(	(	PUNCT
cana-3871	149	212	1	1	NUM
cana-3871	149	213	,	,	PUNCT
cana-3871	149	214	1	1	NUM
cana-3871	149	215	,	,	PUNCT
cana-3871	149	216	0	0	NUM
cana-3871	149	217	,	,	PUNCT
cana-3871	149	218	0	0	NUM
cana-3871	149	219	,	,	PUNCT
cana-3871	149	220	0	0	NUM
cana-3871	149	221	)	)	PUNCT
cana-3871	149	222	,	,	PUNCT
cana-3871	149	223	(	(	PUNCT
cana-3871	149	224	1	1	NUM
cana-3871	149	225	,	,	PUNCT
cana-3871	149	226	1	1	NUM
cana-3871	149	227	,	,	PUNCT
cana-3871	149	228	0	0	NUM
cana-3871	149	229	,	,	PUNCT
cana-3871	149	230	0	0	NUM
cana-3871	149	231	,	,	PUNCT
cana-3871	149	232	1	1	NUM
cana-3871	149	233	)	)	PUNCT
cana-3871	149	234	,	,	PUNCT
cana-3871	149	235	(	(	PUNCT
cana-3871	149	236	1	1	NUM
cana-3871	149	237	,	,	PUNCT
cana-3871	149	238	1	1	NUM
cana-3871	149	239	,	,	PUNCT
cana-3871	149	240	0	0	NUM
cana-3871	149	241	,	,	PUNCT
cana-3871	149	242	1	1	NUM
cana-3871	149	243	,	,	PUNCT
cana-3871	149	244	0	0	NUM
cana-3871	149	245	)	)	PUNCT
cana-3871	149	246	,	,	PUNCT
cana-3871	149	247	(	(	PUNCT
cana-3871	149	248	1	1	NUM
cana-3871	149	249	,	,	PUNCT
cana-3871	149	250	1	1	NUM
cana-3871	149	251	,	,	PUNCT
cana-3871	149	252	0	0	NUM
cana-3871	149	253	,	,	PUNCT
cana-3871	149	254	1	1	NUM
cana-3871	149	255	,	,	PUNCT
cana-3871	149	256	1	1	NUM
cana-3871	149	257	)	)	PUNCT
cana-3871	149	258	,	,	PUNCT
cana-3871	149	259	(	(	PUNCT
cana-3871	149	260	1	1	NUM
cana-3871	149	261	,	,	PUNCT
cana-3871	149	262	1	1	NUM
cana-3871	149	263	,	,	PUNCT
cana-3871	149	264	1	1	NUM
cana-3871	149	265	,	,	PUNCT
cana-3871	149	266	0	0	NUM
cana-3871	149	267	,	,	PUNCT
cana-3871	149	268	0	0	NUM
cana-3871	149	269	)	)	PUNCT
cana-3871	149	270	,	,	PUNCT
cana-3871	149	271	(	(	PUNCT
cana-3871	149	272	1	1	NUM
cana-3871	149	273	,	,	PUNCT
cana-3871	149	274	1	1	NUM
cana-3871	149	275	,	,	PUNCT
cana-3871	149	276	1	1	NUM
cana-3871	149	277	,	,	PUNCT
cana-3871	149	278	0	0	NUM
cana-3871	149	279	,	,	PUNCT
cana-3871	149	280	1	1	NUM
cana-3871	149	281	)	)	PUNCT
cana-3871	149	282	,	,	PUNCT
cana-3871	149	283	(	(	PUNCT
cana-3871	149	284	1	1	NUM
cana-3871	149	285	,	,	PUNCT
cana-3871	149	286	1	1	NUM
cana-3871	149	287	,	,	PUNCT
cana-3871	149	288	1	1	NUM
cana-3871	149	289	,	,	PUNCT
cana-3871	149	290	1	1	NUM
cana-3871	149	291	,	,	PUNCT
cana-3871	149	292	0	0	NUM
cana-3871	149	293	)	)	PUNCT
cana-3871	149	294	}	}	PUNCT
cana-3871	149	295	the	the	DET
cana-3871	149	296	zero	zero	NUM
cana-3871	149	297	-	-	PUNCT
cana-3871	149	298	divisor	divisor	NOUN
cana-3871	149	299	graph	graph	NOUN
cana-3871	149	300	of	of	ADP
cana-3871	149	301	ℤ2	ℤ2	PROPN
cana-3871	149	302	×	×	PROPN
cana-3871	149	303	ℤ2	ℤ2	PROPN
cana-3871	149	304	×	×	PROPN
cana-3871	149	305	ℤ2	ℤ2	PROPN
cana-3871	149	306	×	×	PROPN
cana-3871	149	307	ℤ2	ℤ2	PROPN
cana-3871	149	308	×	×	PROPN
cana-3871	149	309	ℤ2	ℤ2	PROPN
cana-3871	149	310	is	be	AUX
cana-3871	149	311	given	give	VERB
cana-3871	149	312	in	in	ADP
cana-3871	149	313	the	the	DET
cana-3871	149	314	figure	figure	NOUN
cana-3871	149	315	below	below	ADV
cana-3871	149	316	,	,	PUNCT
cana-3871	149	317	fig	fig	NOUN
cana-3871	149	318	15	15	NUM
cana-3871	149	319	:	:	PUNCT
cana-3871	149	320	γ	γ	X
cana-3871	149	321	(	(	PUNCT
cana-3871	149	322	ℤ2	ℤ2	PROPN
cana-3871	149	323	×	×	PROPN
cana-3871	149	324	ℤ2	ℤ2	PROPN
cana-3871	149	325	×	×	PROPN
cana-3871	149	326	ℤ2	ℤ2	PROPN
cana-3871	149	327	×	×	PROPN
cana-3871	149	328	ℤ2	ℤ2	PROPN
cana-3871	149	329	×	×	PROPN
cana-3871	149	330	ℤ2	ℤ2	PROPN
cana-3871	149	331	)	)	PUNCT
cana-3871	149	332	here	here	ADV
cana-3871	149	333	,	,	PUNCT
cana-3871	149	334	n	n	NOUN
cana-3871	149	335	=	=	SYM
cana-3871	149	336	5	5	NUM
cana-3871	149	337	number	number	NOUN
cana-3871	149	338	of	of	ADP
cana-3871	149	339	vertices	vertex	NOUN
cana-3871	149	340	in	in	ADP
cana-3871	149	341	ℤ	ℤ	PROPN
cana-3871	149	342	(	(	PUNCT
cana-3871	149	343	ℤ2	ℤ2	PROPN
cana-3871	149	344	×	×	PROPN
cana-3871	149	345	ℤ2	ℤ2	PROPN
cana-3871	149	346	×	×	PROPN
cana-3871	149	347	ℤ2	ℤ2	PROPN
cana-3871	149	348	×	×	PROPN
cana-3871	149	349	ℤ2	ℤ2	PROPN
cana-3871	149	350	×	×	PROPN
cana-3871	149	351	ℤ2	ℤ2	PROPN
cana-3871	149	352	)	)	PUNCT
cana-3871	149	353	=	=	PUNCT
cana-3871	150	1	25	25	NUM
cana-3871	150	2	−	−	NUM
cana-3871	150	3	2	2	NUM
cana-3871	150	4	=	=	SYM
cana-3871	150	5	30	30	NUM
cana-3871	150	6	the	the	DET
cana-3871	150	7	vertices	vertex	NOUN
cana-3871	150	8	(	(	PUNCT
cana-3871	150	9	0	0	NUM
cana-3871	150	10	,	,	PUNCT
cana-3871	150	11	0	0	NUM
cana-3871	150	12	,	,	PUNCT
cana-3871	150	13	0	0	NUM
cana-3871	150	14	,	,	PUNCT
cana-3871	150	15	0	0	NUM
cana-3871	150	16	,	,	PUNCT
cana-3871	150	17	1	1	NUM
cana-3871	150	18	)	)	PUNCT
cana-3871	150	19	,	,	PUNCT
cana-3871	150	20	(	(	PUNCT
cana-3871	150	21	0	0	NUM
cana-3871	150	22	,	,	PUNCT
cana-3871	150	23	0	0	NUM
cana-3871	150	24	,	,	PUNCT
cana-3871	150	25	0	0	NUM
cana-3871	150	26	,	,	PUNCT
cana-3871	150	27	1	1	NUM
cana-3871	150	28	,	,	PUNCT
cana-3871	150	29	0	0	NUM
cana-3871	150	30	)	)	PUNCT
cana-3871	150	31	,	,	PUNCT
cana-3871	150	32	(	(	PUNCT
cana-3871	150	33	0	0	NUM
cana-3871	150	34	,	,	PUNCT
cana-3871	150	35	1	1	NUM
cana-3871	150	36	,	,	PUNCT
cana-3871	150	37	0	0	NUM
cana-3871	150	38	,	,	PUNCT
cana-3871	150	39	0	0	NUM
cana-3871	150	40	,	,	PUNCT
cana-3871	150	41	0	0	NUM
cana-3871	150	42	)	)	PUNCT
cana-3871	150	43	,	,	PUNCT
cana-3871	150	44	(	(	PUNCT
cana-3871	150	45	1	1	NUM
cana-3871	150	46	,	,	PUNCT
cana-3871	150	47	0	0	NUM
cana-3871	150	48	,	,	PUNCT
cana-3871	150	49	0	0	NUM
cana-3871	150	50	,	,	PUNCT
cana-3871	150	51	0	0	NUM
cana-3871	150	52	,	,	PUNCT
cana-3871	150	53	0	0	NUM
cana-3871	150	54	)	)	PUNCT
cana-3871	150	55	,	,	PUNCT
cana-3871	150	56	(	(	PUNCT
cana-3871	150	57	0	0	NUM
cana-3871	150	58	,	,	PUNCT
cana-3871	150	59	0	0	NUM
cana-3871	150	60	,	,	PUNCT
cana-3871	150	61	1	1	NUM
cana-3871	150	62	,	,	PUNCT
cana-3871	150	63	0	0	NUM
cana-3871	150	64	,	,	PUNCT
cana-3871	150	65	0	0	NUM
cana-3871	150	66	)	)	PUNCT
cana-3871	150	67	form	form	VERB
cana-3871	150	68	a	a	DET
cana-3871	150	69	cycle	cycle	NOUN
cana-3871	150	70	of	of	ADP
cana-3871	150	71	length	length	NOUN
cana-3871	150	72	5	5	NUM
cana-3871	150	73	.	.	PUNCT
cana-3871	151	1	the	the	DET
cana-3871	151	2	vertices	vertex	NOUN
cana-3871	151	3	(	(	PUNCT
cana-3871	151	4	1	1	NUM
cana-3871	151	5	,	,	PUNCT
cana-3871	151	6	0	0	NUM
cana-3871	151	7	,	,	PUNCT
cana-3871	151	8	1	1	NUM
cana-3871	151	9	,	,	PUNCT
cana-3871	151	10	1	1	NUM
cana-3871	151	11	,	,	PUNCT
cana-3871	151	12	0	0	NUM
cana-3871	151	13	,	,	PUNCT
cana-3871	151	14	0	0	NUM
cana-3871	151	15	)	)	PUNCT
cana-3871	151	16	,	,	PUNCT
cana-3871	151	17	(	(	PUNCT
cana-3871	151	18	0	0	NUM
cana-3871	151	19	,	,	PUNCT
cana-3871	151	20	0	0	NUM
cana-3871	151	21	,	,	PUNCT
cana-3871	151	22	1	1	NUM
cana-3871	151	23	,	,	PUNCT
cana-3871	151	24	0	0	NUM
cana-3871	151	25	,	,	PUNCT
cana-3871	151	26	0	0	NUM
cana-3871	151	27	)	)	PUNCT
cana-3871	151	28	,	,	PUNCT
cana-3871	151	29	(	(	PUNCT
cana-3871	151	30	0	0	NUM
cana-3871	151	31	,	,	PUNCT
cana-3871	151	32	1	1	NUM
cana-3871	151	33	,	,	PUNCT
cana-3871	151	34	0	0	NUM
cana-3871	151	35	,	,	PUNCT
cana-3871	151	36	0	0	NUM
cana-3871	151	37	,	,	PUNCT
cana-3871	151	38	0	0	NUM
cana-3871	151	39	)	)	PUNCT
cana-3871	151	40	,	,	PUNCT
cana-3871	151	41	(	(	PUNCT
cana-3871	151	42	0	0	NUM
cana-3871	151	43	,	,	PUNCT
cana-3871	151	44	0	0	NUM
cana-3871	151	45	,	,	PUNCT
cana-3871	151	46	0	0	NUM
cana-3871	151	47	,	,	PUNCT
cana-3871	151	48	0	0	NUM
cana-3871	151	49	,	,	PUNCT
cana-3871	151	50	1	1	NUM
cana-3871	151	51	)	)	PUNCT
cana-3871	151	52	,	,	PUNCT
cana-3871	151	53	(	(	PUNCT
cana-3871	151	54	0	0	NUM
cana-3871	151	55	,	,	PUNCT
cana-3871	151	56	0	0	NUM
cana-3871	151	57	,	,	PUNCT
cana-3871	151	58	0	0	NUM
cana-3871	151	59	,	,	PUNCT
cana-3871	151	60	1	1	NUM
cana-3871	151	61	,	,	PUNCT
cana-3871	151	62	0	0	NUM
cana-3871	151	63	)	)	PUNCT
cana-3871	151	64	form	form	VERB
cana-3871	151	65	a	a	DET
cana-3871	151	66	cycle	cycle	NOUN
cana-3871	151	67	of	of	ADP
cana-3871	151	68	length	length	NOUN
cana-3871	151	69	5	5	NUM
cana-3871	151	70	,	,	PUNCT
cana-3871	151	71	etc	etc	X
cana-3871	151	72	.	.	X
cana-3871	152	1	∴	∴	PROPN
cana-3871	152	2	ℤ2	ℤ2	PROPN
cana-3871	152	3	5	5	NUM
cana-3871	152	4	has	have	VERB
cana-3871	152	5	a	a	DET
cana-3871	152	6	cycle	cycle	NOUN
cana-3871	152	7	of	of	ADP
cana-3871	152	8	length	length	NOUN
cana-3871	152	9	5	5	NUM
cana-3871	152	10	.	.	PUNCT
cana-3871	153	1	∴	∴	PROPN
cana-3871	153	2	the	the	DET
cana-3871	153	3	theorem	theorem	NOUN
cana-3871	153	4	holds	hold	VERB
cana-3871	153	5	.	.	PUNCT
cana-3871	154	1	3.5	3.5	NUM
cana-3871	154	2	theorem	theorem	ADJ
cana-3871	154	3	statement	statement	NOUN
cana-3871	154	4	:	:	PUNCT
cana-3871	154	5	let	let	VERB
cana-3871	154	6	ℤ2	ℤ2	PROPN
cana-3871	154	7	n	n	PROPN
cana-3871	154	8	=	=	SYM
cana-3871	154	9	ℤ2	ℤ2	PROPN
cana-3871	154	10	×	×	NOUN
cana-3871	154	11	ℤ2	ℤ2	PROPN
cana-3871	154	12	×	×	PROPN
cana-3871	154	13	ℤ2	ℤ2	PROPN
cana-3871	154	14	×	×	PROPN
cana-3871	154	15	ℤ2	ℤ2	PROPN
cana-3871	154	16	...	...	PUNCT
cana-3871	154	17	ℤ2	ℤ2	PROPN
cana-3871	154	18	be	be	VERB
cana-3871	154	19	a	a	DET
cana-3871	154	20	boolean	boolean	ADJ
cana-3871	154	21	ring	ring	NOUN
cana-3871	154	22	.	.	PUNCT
cana-3871	155	1	for	for	ADP
cana-3871	155	2	n	n	X
cana-3871	155	3	≥	≥	NUM
cana-3871	155	4	3	3	NUM
cana-3871	155	5	,	,	PUNCT
cana-3871	155	6	the	the	DET
cana-3871	155	7	girth	girth	NOUN
cana-3871	155	8	of	of	ADP
cana-3871	155	9	the	the	DET
cana-3871	155	10	zerodivisor	zerodivisor	NOUN
cana-3871	155	11	graph	graph	NOUN
cana-3871	155	12	γ(ℤ2	γ(ℤ2	PROPN
cana-3871	155	13	n	n	CCONJ
cana-3871	155	14	)	)	PUNCT
cana-3871	155	15	is	be	AUX
cana-3871	155	16	3	3	NUM
cana-3871	155	17	.	.	PUNCT
cana-3871	156	1	proof	proof	NOUN
cana-3871	156	2	:	:	PUNCT
cana-3871	156	3	let	let	VERB
cana-3871	156	4	ℤ2	ℤ2	PROPN
cana-3871	156	5	n	n	PROPN
cana-3871	156	6	=	=	SYM
cana-3871	156	7	ℤ2	ℤ2	PROPN
cana-3871	156	8	×	×	NOUN
cana-3871	156	9	ℤ2	ℤ2	PROPN
cana-3871	156	10	×	×	PROPN
cana-3871	156	11	ℤ2	ℤ2	PROPN
cana-3871	156	12	×	×	PROPN
cana-3871	156	13	ℤ2	ℤ2	PROPN
cana-3871	156	14	...	...	PUNCT
cana-3871	156	15	ℤ2	ℤ2	PROPN
cana-3871	156	16	be	be	VERB
cana-3871	156	17	a	a	DET
cana-3871	156	18	boolean	boolean	ADJ
cana-3871	156	19	ring	ring	NOUN
cana-3871	156	20	then	then	ADV
cana-3871	156	21	ℤ2	ℤ2	PROPN
cana-3871	156	22	n	n	PART
cana-3871	156	23	has	have	AUX
cana-3871	156	24	(	(	PUNCT
cana-3871	156	25	2n	2n	NUM
cana-3871	156	26	−	−	NOUN
cana-3871	156	27	2	2	X
cana-3871	156	28	)	)	PUNCT
cana-3871	156	29	zero	zero	NUM
cana-3871	156	30	divisors	divisor	NOUN
cana-3871	156	31	and	and	CCONJ
cana-3871	156	32	ℤ2	ℤ2	NOUN
cana-3871	156	33	n	n	AUX
cana-3871	156	34	is	be	AUX
cana-3871	156	35	given	give	VERB
cana-3871	156	36	by	by	ADP
cana-3871	156	37	,	,	PUNCT
cana-3871	156	38	ℤ2	ℤ2	PROPN
cana-3871	156	39	n	n	NOUN
cana-3871	156	40	=	=	SYM
cana-3871	156	41	{	{	PUNCT
cana-3871	156	42	(	(	PUNCT
cana-3871	156	43	b1	b1	NOUN
cana-3871	156	44	,	,	PUNCT
cana-3871	156	45	b2	b2	NOUN
cana-3871	156	46	,	,	PUNCT
cana-3871	156	47	b3	b3	PROPN
cana-3871	156	48	,	,	PUNCT
cana-3871	156	49	...	...	PUNCT
cana-3871	156	50	,	,	PUNCT
cana-3871	156	51	bn	bn	X
cana-3871	156	52	)	)	PUNCT
cana-3871	156	53	|	|	ADV
cana-3871	156	54	bi′s	bi′s	NOUN
cana-3871	156	55	∈	∈	PROPN
cana-3871	156	56	{	{	PUNCT
cana-3871	156	57	0	0	NUM
cana-3871	156	58	,	,	PUNCT
cana-3871	156	59	1	1	NUM
cana-3871	156	60	}	}	PUNCT
cana-3871	156	61	,	,	PUNCT
cana-3871	156	62	i	i	PRON
cana-3871	156	63	=	=	NOUN
cana-3871	156	64	1	1	NUM
cana-3871	156	65	,	,	PUNCT
cana-3871	156	66	2	2	NUM
cana-3871	156	67	,	,	PUNCT
cana-3871	156	68	...	...	PUNCT
cana-3871	156	69	,	,	PUNCT
cana-3871	156	70	n	n	CCONJ
cana-3871	156	71	}	}	PUNCT
cana-3871	156	72	since	since	SCONJ
cana-3871	156	73	each	each	DET
cana-3871	156	74	bis	bis	NOUN
cana-3871	156	75	has	have	VERB
cana-3871	156	76	two	two	NUM
cana-3871	156	77	choices	choice	NOUN
cana-3871	156	78	0	0	NUM
cana-3871	156	79	and	and	CCONJ
cana-3871	156	80	1	1	NUM
cana-3871	156	81	,	,	PUNCT
cana-3871	156	82	so	so	SCONJ
cana-3871	156	83	there	there	PRON
cana-3871	156	84	are	be	VERB
cana-3871	156	85	2n	2n	NUM
cana-3871	156	86	elements	element	NOUN
cana-3871	156	87	in	in	ADP
cana-3871	156	88	ℤ2	ℤ2	PROPN
cana-3871	156	89	n.	n.	PROPN
cana-3871	156	90	communications	communication	NOUN
cana-3871	156	91	on	on	ADP
cana-3871	156	92	applied	apply	VERB
cana-3871	156	93	nonlinear	nonlinear	ADJ
cana-3871	156	94	analysis	analysis	NOUN
cana-3871	156	95	issn	issn	NOUN
cana-3871	156	96	:	:	PUNCT
cana-3871	156	97	1074	1074	NUM
cana-3871	156	98	-	-	PUNCT
cana-3871	156	99	133x	133x	NUM
cana-3871	156	100	vol	vol	NOUN
cana-3871	156	101	32	32	NUM
cana-3871	156	102	no	no	NOUN
cana-3871	156	103	.	.	PUNCT
cana-3871	157	1	7s	7	NOUN
cana-3871	157	2	(	(	PUNCT
cana-3871	157	3	2025	2025	NUM
cana-3871	157	4	)	)	PUNCT
cana-3871	157	5	955	955	NUM
cana-3871	157	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	157	7	|ℤ2	|ℤ2	PUNCT
cana-3871	157	8	n|	n|	NOUN
cana-3871	157	9	=	=	SYM
cana-3871	157	10	2n	2n	NUM
cana-3871	157	11	the	the	DET
cana-3871	157	12	set	set	NOUN
cana-3871	157	13	of	of	ADP
cana-3871	157	14	zero	zero	NUM
cana-3871	157	15	divisors	divisor	NOUN
cana-3871	157	16	of	of	ADP
cana-3871	157	17	ℤ2	ℤ2	PROPN
cana-3871	157	18	n	n	X
cana-3871	157	19	is	be	AUX
cana-3871	157	20	denoted	denote	VERB
cana-3871	157	21	by	by	ADP
cana-3871	157	22	ℤ(ℤ2	ℤ(ℤ2	NOUN
cana-3871	157	23	n	n	CCONJ
cana-3871	157	24	)	)	PUNCT
cana-3871	157	25	and	and	CCONJ
cana-3871	157	26	is	be	AUX
cana-3871	157	27	given	give	VERB
cana-3871	157	28	by	by	ADP
cana-3871	157	29	,	,	PUNCT
cana-3871	157	30	ℤ	ℤ	PROPN
cana-3871	157	31	(	(	PUNCT
cana-3871	157	32	ℤ2	ℤ2	PROPN
cana-3871	157	33	n	n	CCONJ
cana-3871	157	34	)	)	PUNCT
cana-3871	158	1	=	=	PRON
cana-3871	158	2	{	{	PUNCT
cana-3871	158	3	(	(	PUNCT
cana-3871	158	4	b1	b1	NOUN
cana-3871	158	5	,	,	PUNCT
cana-3871	158	6	b2	b2	NOUN
cana-3871	158	7	,	,	PUNCT
cana-3871	158	8	b3	b3	PROPN
cana-3871	158	9	,	,	PUNCT
cana-3871	158	10	...	...	PUNCT
cana-3871	158	11	,	,	PUNCT
cana-3871	158	12	bn	bn	X
cana-3871	158	13	)	)	PUNCT
cana-3871	158	14	|	|	ADV
cana-3871	158	15	bis	bi	VERB
cana-3871	158	16	∈	∈	NOUN
cana-3871	158	17	{	{	PUNCT
cana-3871	158	18	0	0	NUM
cana-3871	158	19	,	,	PUNCT
cana-3871	158	20	1	1	NUM
cana-3871	158	21	}	}	PUNCT
cana-3871	158	22	,	,	PUNCT
cana-3871	158	23	all	all	PRON
cana-3871	158	24	bi≠	bi≠	ADJ
cana-3871	158	25	0	0	NUM
cana-3871	158	26	,	,	PUNCT
cana-3871	158	27	and	and	CCONJ
cana-3871	158	28	all	all	DET
cana-3871	158	29	bi	bi	ADJ
cana-3871	158	30	≠	≠	PROPN
cana-3871	158	31	1	1	NUM
cana-3871	158	32	,	,	PUNCT
cana-3871	158	33	i	i	PRON
cana-3871	158	34	=	=	NOUN
cana-3871	158	35	1	1	NUM
cana-3871	158	36	,	,	PUNCT
cana-3871	158	37	2	2	NUM
cana-3871	158	38	,	,	PUNCT
cana-3871	158	39	...	...	PUNCT
cana-3871	158	40	,	,	PUNCT
cana-3871	158	41	n	n	CCONJ
cana-3871	158	42	}	}	PUNCT
cana-3871	158	43	∴	∴	PROPN
cana-3871	158	44	|ℤ(ℤ2	|ℤ(ℤ2	NOUN
cana-3871	158	45	n	n	CCONJ
cana-3871	158	46	)	)	PUNCT
cana-3871	158	47	|	|	ADV
cana-3871	158	48	=	=	SYM
cana-3871	158	49	2n	2n	NUM
cana-3871	158	50	−	−	NOUN
cana-3871	158	51	2	2	NUM
cana-3871	158	52	consider	consider	VERB
cana-3871	158	53	the	the	DET
cana-3871	158	54	vertices	vertex	NOUN
cana-3871	158	55	(	(	PUNCT
cana-3871	158	56	1	1	NUM
cana-3871	158	57	,	,	PUNCT
cana-3871	158	58	0	0	NUM
cana-3871	158	59	,	,	PUNCT
cana-3871	158	60	0	0	NUM
cana-3871	158	61	,	,	PUNCT
cana-3871	158	62	...	...	PUNCT
cana-3871	158	63	,	,	PUNCT
cana-3871	158	64	0	0	NUM
cana-3871	158	65	)	)	PUNCT
cana-3871	158	66	,	,	PUNCT
cana-3871	158	67	(	(	PUNCT
cana-3871	158	68	0	0	NUM
cana-3871	158	69	,	,	PUNCT
cana-3871	158	70	1	1	NUM
cana-3871	158	71	,	,	PUNCT
cana-3871	158	72	0	0	NUM
cana-3871	158	73	,	,	PUNCT
cana-3871	158	74	...	...	PUNCT
cana-3871	158	75	,	,	PUNCT
cana-3871	158	76	0	0	NUM
cana-3871	158	77	)	)	PUNCT
cana-3871	158	78	,	,	PUNCT
cana-3871	158	79	(	(	PUNCT
cana-3871	158	80	0	0	NUM
cana-3871	158	81	,	,	PUNCT
cana-3871	158	82	0	0	NUM
cana-3871	158	83	,	,	PUNCT
cana-3871	158	84	1	1	NUM
cana-3871	158	85	,	,	PUNCT
cana-3871	158	86	...	...	PUNCT
cana-3871	158	87	,	,	PUNCT
cana-3871	158	88	0	0	NUM
cana-3871	158	89	)	)	PUNCT
cana-3871	158	90	,	,	PUNCT
cana-3871	158	91	...	...	PUNCT
cana-3871	158	92	,	,	PUNCT
cana-3871	158	93	(	(	PUNCT
cana-3871	158	94	0	0	NUM
cana-3871	158	95	,	,	PUNCT
cana-3871	158	96	0	0	NUM
cana-3871	158	97	,	,	PUNCT
cana-3871	158	98	0	0	NUM
cana-3871	158	99	,	,	PUNCT
cana-3871	158	100	...	...	PUNCT
cana-3871	158	101	,	,	PUNCT
cana-3871	158	102	1	1	X
cana-3871	158	103	)	)	PUNCT
cana-3871	158	104	,	,	PUNCT
cana-3871	158	105	they	they	PRON
cana-3871	158	106	all	all	PRON
cana-3871	158	107	form	form	VERB
cana-3871	158	108	their	their	PRON
cana-3871	158	109	edges	edge	NOUN
cana-3871	158	110	between	between	ADP
cana-3871	158	111	them	they	PRON
cana-3871	158	112	.	.	PUNCT
cana-3871	159	1	by	by	ADP
cana-3871	159	2	theorem	theorem	NOUN
cana-3871	159	3	(	(	PUNCT
cana-3871	159	4	2.1	2.1	NUM
cana-3871	159	5	)	)	PUNCT
cana-3871	159	6	,	,	PUNCT
cana-3871	159	7	the	the	DET
cana-3871	159	8	above	above	ADJ
cana-3871	159	9	elements	element	NOUN
cana-3871	159	10	have	have	AUX
cana-3871	159	11	degree	degree	NOUN
cana-3871	159	12	2n−1	2n−1	NUM
cana-3871	159	13	−	−	NOUN
cana-3871	159	14	1	1	NUM
cana-3871	159	15	for	for	ADP
cana-3871	159	16	n	n	X
cana-3871	159	17	≥	≥	NOUN
cana-3871	159	18	3	3	NUM
cana-3871	159	19	,	,	PUNCT
cana-3871	159	20	the	the	DET
cana-3871	159	21	degree	degree	NOUN
cana-3871	159	22	of	of	ADP
cana-3871	159	23	the	the	DET
cana-3871	159	24	above	above	ADJ
cana-3871	159	25	elements	element	NOUN
cana-3871	159	26	would	would	AUX
cana-3871	159	27	be	be	AUX
cana-3871	159	28	greater	great	ADJ
cana-3871	159	29	than	than	ADP
cana-3871	159	30	or	or	CCONJ
cana-3871	159	31	equal	equal	ADJ
cana-3871	159	32	to	to	ADP
cana-3871	159	33	3	3	NUM
cana-3871	159	34	.	.	PUNCT
cana-3871	160	1	any	any	DET
cana-3871	160	2	combination	combination	NOUN
cana-3871	160	3	of	of	ADP
cana-3871	160	4	3	3	NUM
cana-3871	160	5	elements	element	NOUN
cana-3871	160	6	between	between	ADP
cana-3871	160	7	these	these	DET
cana-3871	160	8	vertices	vertex	NOUN
cana-3871	160	9	will	will	AUX
cana-3871	160	10	form	form	VERB
cana-3871	160	11	a	a	DET
cana-3871	160	12	cycle	cycle	NOUN
cana-3871	160	13	,	,	PUNCT
cana-3871	160	14	and	and	CCONJ
cana-3871	160	15	the	the	DET
cana-3871	160	16	length	length	NOUN
cana-3871	160	17	of	of	ADP
cana-3871	160	18	that	that	DET
cana-3871	160	19	cycle	cycle	NOUN
cana-3871	160	20	will	will	AUX
cana-3871	160	21	be	be	AUX
cana-3871	160	22	3	3	NUM
cana-3871	160	23	.	.	PUNCT
cana-3871	161	1	the	the	DET
cana-3871	161	2	cycle	cycle	NOUN
cana-3871	161	3	formed	form	VERB
cana-3871	161	4	will	will	AUX
cana-3871	161	5	be	be	AUX
cana-3871	161	6	the	the	DET
cana-3871	161	7	shortest	short	ADJ
cana-3871	161	8	cycle	cycle	NOUN
cana-3871	161	9	of	of	ADP
cana-3871	161	10	the	the	DET
cana-3871	161	11	graph	graph	NOUN
cana-3871	161	12	.	.	PUNCT
cana-3871	162	1	we	we	PRON
cana-3871	162	2	know	know	VERB
cana-3871	162	3	,	,	PUNCT
cana-3871	162	4	the	the	DET
cana-3871	162	5	girth	girth	NOUN
cana-3871	162	6	of	of	ADP
cana-3871	162	7	the	the	DET
cana-3871	162	8	graph	graph	NOUN
cana-3871	162	9	is	be	AUX
cana-3871	162	10	the	the	DET
cana-3871	162	11	length	length	NOUN
cana-3871	162	12	of	of	ADP
cana-3871	162	13	the	the	DET
cana-3871	162	14	shortest	short	ADJ
cana-3871	162	15	cycle	cycle	NOUN
cana-3871	162	16	in	in	ADP
cana-3871	162	17	the	the	DET
cana-3871	162	18	graph	graph	NOUN
cana-3871	162	19	.	.	PUNCT
cana-3871	163	1	∴	∴	NOUN
cana-3871	163	2	the	the	DET
cana-3871	163	3	girth	girth	NOUN
cana-3871	163	4	of	of	ADP
cana-3871	163	5	the	the	DET
cana-3871	163	6	zero	zero	NUM
cana-3871	163	7	-	-	PUNCT
cana-3871	163	8	divisor	divisor	NOUN
cana-3871	163	9	graph	graph	NOUN
cana-3871	163	10	γ(ℤ2	γ(ℤ2	PROPN
cana-3871	163	11	n	n	CCONJ
cana-3871	163	12	)	)	PUNCT
cana-3871	163	13	is	be	AUX
cana-3871	163	14	3	3	NUM
cana-3871	163	15	.	.	PUNCT
cana-3871	164	1	(	(	PUNCT
cana-3871	164	2	for	for	ADP
cana-3871	164	3	n≥3	n≥3	NOUN
cana-3871	164	4	)	)	PUNCT
cana-3871	164	5	.	.	PUNCT
cana-3871	165	1	3.5.1	3.5.1	NUM
cana-3871	165	2	example	example	NOUN
cana-3871	165	3	ℤ2	ℤ2	PROPN
cana-3871	165	4	3	3	NUM
cana-3871	165	5	=	=	SYM
cana-3871	165	6	ℤ2	ℤ2	PROPN
cana-3871	165	7	×	×	NOUN
cana-3871	165	8	ℤ2	ℤ2	PROPN
cana-3871	165	9	×	×	PROPN
cana-3871	165	10	ℤ2	ℤ2	PROPN
cana-3871	165	11	ℤ2	ℤ2	PROPN
cana-3871	165	12	×	×	PROPN
cana-3871	165	13	ℤ2	ℤ2	PROPN
cana-3871	165	14	×	×	NOUN
cana-3871	165	15	ℤ2	ℤ2	NOUN
cana-3871	165	16	=	=	SYM
cana-3871	165	17	{	{	PUNCT
cana-3871	165	18	(	(	PUNCT
cana-3871	165	19	0	0	NUM
cana-3871	165	20	,	,	PUNCT
cana-3871	165	21	0	0	NUM
cana-3871	165	22	,	,	PUNCT
cana-3871	165	23	0	0	NUM
cana-3871	165	24	)	)	PUNCT
cana-3871	165	25	,	,	PUNCT
cana-3871	165	26	(	(	PUNCT
cana-3871	165	27	0	0	NUM
cana-3871	165	28	,	,	PUNCT
cana-3871	165	29	0	0	NUM
cana-3871	165	30	,	,	PUNCT
cana-3871	165	31	1	1	NUM
cana-3871	165	32	)	)	PUNCT
cana-3871	165	33	,	,	PUNCT
cana-3871	165	34	(	(	PUNCT
cana-3871	165	35	0	0	NUM
cana-3871	165	36	,	,	PUNCT
cana-3871	165	37	1	1	NUM
cana-3871	165	38	,	,	PUNCT
cana-3871	165	39	0	0	NUM
cana-3871	165	40	)	)	PUNCT
cana-3871	165	41	,	,	PUNCT
cana-3871	165	42	(	(	PUNCT
cana-3871	165	43	0	0	NUM
cana-3871	165	44	,	,	PUNCT
cana-3871	165	45	1	1	NUM
cana-3871	165	46	,	,	PUNCT
cana-3871	165	47	1	1	NUM
cana-3871	165	48	)	)	PUNCT
cana-3871	165	49	,	,	PUNCT
cana-3871	165	50	(	(	PUNCT
cana-3871	165	51	1	1	NUM
cana-3871	165	52	,	,	PUNCT
cana-3871	165	53	0	0	NUM
cana-3871	165	54	,	,	PUNCT
cana-3871	165	55	1	1	NUM
cana-3871	165	56	)	)	PUNCT
cana-3871	165	57	,	,	PUNCT
cana-3871	165	58	(	(	PUNCT
cana-3871	165	59	1	1	NUM
cana-3871	165	60	,	,	PUNCT
cana-3871	165	61	1	1	NUM
cana-3871	165	62	,	,	PUNCT
cana-3871	165	63	0	0	NUM
cana-3871	165	64	)	)	PUNCT
cana-3871	165	65	,	,	PUNCT
cana-3871	165	66	(	(	PUNCT
cana-3871	165	67	1	1	NUM
cana-3871	165	68	,	,	PUNCT
cana-3871	165	69	0	0	NUM
cana-3871	165	70	,	,	PUNCT
cana-3871	165	71	0	0	NUM
cana-3871	165	72	)	)	PUNCT
cana-3871	165	73	,	,	PUNCT
cana-3871	165	74	(	(	PUNCT
cana-3871	165	75	1	1	NUM
cana-3871	165	76	,	,	PUNCT
cana-3871	165	77	1	1	NUM
cana-3871	165	78	,	,	PUNCT
cana-3871	165	79	1	1	NUM
cana-3871	165	80	)	)	PUNCT
cana-3871	165	81	}	}	PUNCT
cana-3871	165	82	ℤ	ℤ	PROPN
cana-3871	165	83	(	(	PUNCT
cana-3871	165	84	ℤ2	ℤ2	PROPN
cana-3871	165	85	×	×	PROPN
cana-3871	165	86	ℤ2	ℤ2	PROPN
cana-3871	165	87	×	×	PROPN
cana-3871	165	88	ℤ2	ℤ2	PROPN
cana-3871	165	89	)	)	PUNCT
cana-3871	165	90	=	=	PUNCT
cana-3871	165	91	(	(	PUNCT
cana-3871	165	92	0	0	NUM
cana-3871	165	93	,	,	PUNCT
cana-3871	165	94	0	0	NUM
cana-3871	165	95	,	,	PUNCT
cana-3871	165	96	1	1	NUM
cana-3871	165	97	)	)	PUNCT
cana-3871	165	98	,	,	PUNCT
cana-3871	165	99	(	(	PUNCT
cana-3871	165	100	0	0	NUM
cana-3871	165	101	,	,	PUNCT
cana-3871	165	102	1	1	NUM
cana-3871	165	103	,	,	PUNCT
cana-3871	165	104	0	0	NUM
cana-3871	165	105	)	)	PUNCT
cana-3871	165	106	,	,	PUNCT
cana-3871	165	107	(	(	PUNCT
cana-3871	165	108	0	0	NUM
cana-3871	165	109	,	,	PUNCT
cana-3871	165	110	1	1	NUM
cana-3871	165	111	,	,	PUNCT
cana-3871	165	112	1	1	NUM
cana-3871	165	113	)	)	PUNCT
cana-3871	165	114	,	,	PUNCT
cana-3871	165	115	(	(	PUNCT
cana-3871	165	116	1	1	NUM
cana-3871	165	117	,	,	PUNCT
cana-3871	165	118	0	0	NUM
cana-3871	165	119	,	,	PUNCT
cana-3871	165	120	1	1	NUM
cana-3871	165	121	)	)	PUNCT
cana-3871	165	122	,	,	PUNCT
cana-3871	165	123	(	(	PUNCT
cana-3871	165	124	1	1	NUM
cana-3871	165	125	,	,	PUNCT
cana-3871	165	126	1	1	NUM
cana-3871	165	127	,	,	PUNCT
cana-3871	165	128	0	0	NUM
cana-3871	165	129	)	)	PUNCT
cana-3871	165	130	,	,	PUNCT
cana-3871	165	131	(	(	PUNCT
cana-3871	165	132	1	1	NUM
cana-3871	165	133	,	,	PUNCT
cana-3871	165	134	0	0	NUM
cana-3871	165	135	,	,	PUNCT
cana-3871	165	136	0	0	NUM
cana-3871	165	137	)	)	PUNCT
cana-3871	165	138	fig	fig	NOUN
cana-3871	165	139	16	16	NUM
cana-3871	165	140	:	:	PUNCT
cana-3871	165	141	γ(ℤ2	γ(ℤ2	PROPN
cana-3871	165	142	×	×	NOUN
cana-3871	165	143	ℤ2	ℤ2	PROPN
cana-3871	165	144	×	×	PROPN
cana-3871	165	145	ℤ2	ℤ2	PROPN
cana-3871	165	146	)	)	PUNCT
cana-3871	165	147	the	the	DET
cana-3871	165	148	zero	zero	NUM
cana-3871	165	149	-	-	PUNCT
cana-3871	165	150	divisor	divisor	NOUN
cana-3871	165	151	graph	graph	NOUN
cana-3871	165	152	of	of	ADP
cana-3871	165	153	ℤ2	ℤ2	PROPN
cana-3871	165	154	×	×	PROPN
cana-3871	165	155	ℤ2	ℤ2	PROPN
cana-3871	165	156	×	×	PROPN
cana-3871	165	157	ℤ2	ℤ2	PROPN
cana-3871	165	158	is	be	AUX
cana-3871	165	159	given	give	VERB
cana-3871	165	160	in	in	ADP
cana-3871	165	161	the	the	DET
cana-3871	165	162	figure	figure	NOUN
cana-3871	165	163	above	above	ADV
cana-3871	165	164	.	.	PUNCT
cana-3871	166	1	number	number	NOUN
cana-3871	166	2	of	of	ADP
cana-3871	166	3	vertices	vertex	NOUN
cana-3871	166	4	in	in	ADP
cana-3871	166	5	the	the	DET
cana-3871	166	6	graph	graph	NOUN
cana-3871	166	7	of	of	ADP
cana-3871	166	8	ℤ	ℤ	PROPN
cana-3871	166	9	(	(	PUNCT
cana-3871	166	10	ℤ2	ℤ2	PROPN
cana-3871	166	11	×	×	PROPN
cana-3871	166	12	ℤ2	ℤ2	PROPN
cana-3871	166	13	×	×	PROPN
cana-3871	166	14	ℤ2	ℤ2	PROPN
cana-3871	166	15	)	)	PUNCT
cana-3871	167	1	=	=	NOUN
cana-3871	168	1	23	23	NUM
cana-3871	168	2	−	−	NUM
cana-3871	168	3	2	2	NUM
cana-3871	168	4	=	=	SYM
cana-3871	168	5	6	6	NUM
cana-3871	168	6	the	the	DET
cana-3871	168	7	vertices	vertex	NOUN
cana-3871	168	8	(	(	PUNCT
cana-3871	168	9	0,0,1	0,0,1	NOUN
cana-3871	168	10	)	)	PUNCT
cana-3871	168	11	,	,	PUNCT
cana-3871	168	12	(	(	PUNCT
cana-3871	168	13	0,1,0	0,1,0	NUM
cana-3871	168	14	)	)	PUNCT
cana-3871	168	15	and	and	CCONJ
cana-3871	168	16	(	(	PUNCT
cana-3871	168	17	1,0,0	1,0,0	NUM
cana-3871	168	18	)	)	PUNCT
cana-3871	168	19	form	form	NOUN
cana-3871	168	20	a	a	DET
cana-3871	168	21	cycle	cycle	NOUN
cana-3871	168	22	.	.	PUNCT
cana-3871	169	1	∴	∴	PROPN
cana-3871	169	2	ℤ2	ℤ2	PROPN
cana-3871	169	3	3	3	NUM
cana-3871	169	4	has	have	VERB
cana-3871	169	5	a	a	DET
cana-3871	169	6	cycle	cycle	NOUN
cana-3871	169	7	of	of	ADP
cana-3871	169	8	length	length	NOUN
cana-3871	169	9	3	3	NUM
cana-3871	169	10	.	.	PUNCT
cana-3871	170	1	∴the	∴the	DET
cana-3871	170	2	girth	girth	NOUN
cana-3871	170	3	of	of	ADP
cana-3871	170	4	ℤ2	ℤ2	PROPN
cana-3871	170	5	3	3	NUM
cana-3871	170	6	is	be	AUX
cana-3871	170	7	3	3	NUM
cana-3871	170	8	.	.	PUNCT
cana-3871	171	1	∴	∴	PROPN
cana-3871	171	2	the	the	DET
cana-3871	171	3	theorem	theorem	NOUN
cana-3871	171	4	holds	hold	VERB
cana-3871	171	5	.	.	PUNCT
cana-3871	172	1	3.5.2	3.5.2	NUM
cana-3871	172	2	example	example	NOUN
cana-3871	172	3	ℤ2	ℤ2	PROPN
cana-3871	172	4	4	4	NUM
cana-3871	172	5	=	=	SYM
cana-3871	172	6	ℤ2	ℤ2	PROPN
cana-3871	172	7	×	×	NOUN
cana-3871	172	8	ℤ2	ℤ2	PROPN
cana-3871	172	9	×	×	PROPN
cana-3871	172	10	ℤ2	ℤ2	PROPN
cana-3871	172	11	×	×	PROPN
cana-3871	172	12	ℤ2	ℤ2	PROPN
cana-3871	172	13	communications	communication	NOUN
cana-3871	172	14	on	on	ADP
cana-3871	172	15	applied	apply	VERB
cana-3871	172	16	nonlinear	nonlinear	ADJ
cana-3871	172	17	analysis	analysis	NOUN
cana-3871	172	18	issn	issn	NOUN
cana-3871	172	19	:	:	PUNCT
cana-3871	172	20	1074	1074	NUM
cana-3871	172	21	-	-	PUNCT
cana-3871	172	22	133x	133x	NUM
cana-3871	172	23	vol	vol	NOUN
cana-3871	172	24	32	32	NUM
cana-3871	172	25	no	no	NOUN
cana-3871	172	26	.	.	PUNCT
cana-3871	173	1	7s	7	NOUN
cana-3871	173	2	(	(	PUNCT
cana-3871	173	3	2025	2025	NUM
cana-3871	173	4	)	)	PUNCT
cana-3871	173	5	956	956	NUM
cana-3871	173	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	173	7	ℤ2×ℤ2×ℤ2×ℤ2	ℤ2×ℤ2×ℤ2×ℤ2	NOUN
cana-3871	173	8	=	=	SYM
cana-3871	173	9	{	{	PUNCT
cana-3871	173	10	(	(	PUNCT
cana-3871	173	11	0	0	NUM
cana-3871	173	12	,	,	PUNCT
cana-3871	173	13	0	0	NUM
cana-3871	173	14	,	,	PUNCT
cana-3871	173	15	0	0	NUM
cana-3871	173	16	,	,	PUNCT
cana-3871	173	17	0	0	NUM
cana-3871	173	18	)	)	PUNCT
cana-3871	173	19	,	,	PUNCT
cana-3871	173	20	(	(	PUNCT
cana-3871	173	21	0	0	NUM
cana-3871	173	22	,	,	PUNCT
cana-3871	173	23	0	0	NUM
cana-3871	173	24	,	,	PUNCT
cana-3871	173	25	0	0	NUM
cana-3871	173	26	,	,	PUNCT
cana-3871	173	27	1	1	NUM
cana-3871	173	28	)	)	PUNCT
cana-3871	173	29	,	,	PUNCT
cana-3871	173	30	(	(	PUNCT
cana-3871	173	31	0	0	NUM
cana-3871	173	32	,	,	PUNCT
cana-3871	173	33	0	0	NUM
cana-3871	173	34	,	,	PUNCT
cana-3871	173	35	1	1	NUM
cana-3871	173	36	,	,	PUNCT
cana-3871	173	37	0	0	NUM
cana-3871	173	38	)	)	PUNCT
cana-3871	173	39	,	,	PUNCT
cana-3871	173	40	(	(	PUNCT
cana-3871	173	41	0	0	NUM
cana-3871	173	42	,	,	PUNCT
cana-3871	173	43	1	1	NUM
cana-3871	173	44	,	,	PUNCT
cana-3871	173	45	0	0	NUM
cana-3871	173	46	,	,	PUNCT
cana-3871	173	47	0	0	NUM
cana-3871	173	48	)	)	PUNCT
cana-3871	173	49	,	,	PUNCT
cana-3871	173	50	(	(	PUNCT
cana-3871	173	51	0	0	NUM
cana-3871	173	52	,	,	PUNCT
cana-3871	173	53	0	0	NUM
cana-3871	173	54	,	,	PUNCT
cana-3871	173	55	1	1	NUM
cana-3871	173	56	,	,	PUNCT
cana-3871	173	57	1	1	NUM
cana-3871	173	58	)	)	PUNCT
cana-3871	173	59	,	,	PUNCT
cana-3871	173	60	(	(	PUNCT
cana-3871	173	61	0	0	NUM
cana-3871	173	62	,	,	PUNCT
cana-3871	173	63	1	1	NUM
cana-3871	173	64	,	,	PUNCT
cana-3871	173	65	0	0	NUM
cana-3871	173	66	,	,	PUNCT
cana-3871	173	67	1	1	NUM
cana-3871	173	68	)	)	PUNCT
cana-3871	173	69	,	,	PUNCT
cana-3871	173	70	(	(	PUNCT
cana-3871	173	71	(	(	PUNCT
cana-3871	173	72	0	0	NUM
cana-3871	173	73	,	,	PUNCT
cana-3871	173	74	1	1	NUM
cana-3871	173	75	,	,	PUNCT
cana-3871	173	76	1	1	NUM
cana-3871	173	77	,	,	PUNCT
cana-3871	173	78	0	0	NUM
cana-3871	173	79	)	)	PUNCT
cana-3871	173	80	,	,	PUNCT
cana-3871	173	81	(	(	PUNCT
cana-3871	173	82	0	0	NUM
cana-3871	173	83	,	,	PUNCT
cana-3871	173	84	1	1	NUM
cana-3871	173	85	,	,	PUNCT
cana-3871	173	86	1	1	NUM
cana-3871	173	87	,	,	PUNCT
cana-3871	173	88	1	1	NUM
cana-3871	173	89	)	)	PUNCT
cana-3871	173	90	,	,	PUNCT
cana-3871	173	91	(	(	PUNCT
cana-3871	173	92	1	1	NUM
cana-3871	173	93	,	,	PUNCT
cana-3871	173	94	0	0	NUM
cana-3871	173	95	,	,	PUNCT
cana-3871	173	96	0	0	NUM
cana-3871	173	97	,	,	PUNCT
cana-3871	173	98	0	0	NUM
cana-3871	173	99	)	)	PUNCT
cana-3871	173	100	,	,	PUNCT
cana-3871	173	101	(	(	PUNCT
cana-3871	173	102	1	1	NUM
cana-3871	173	103	,	,	PUNCT
cana-3871	173	104	0	0	NUM
cana-3871	173	105	,	,	PUNCT
cana-3871	173	106	0	0	NUM
cana-3871	173	107	,	,	PUNCT
cana-3871	173	108	1	1	NUM
cana-3871	173	109	)	)	PUNCT
cana-3871	173	110	,	,	PUNCT
cana-3871	173	111	(	(	PUNCT
cana-3871	173	112	1	1	NUM
cana-3871	173	113	,	,	PUNCT
cana-3871	173	114	0	0	NUM
cana-3871	173	115	,	,	PUNCT
cana-3871	173	116	1	1	NUM
cana-3871	173	117	,	,	PUNCT
cana-3871	173	118	0	0	NUM
cana-3871	173	119	)	)	PUNCT
cana-3871	173	120	,	,	PUNCT
cana-3871	173	121	(	(	PUNCT
cana-3871	173	122	1	1	NUM
cana-3871	173	123	,	,	PUNCT
cana-3871	173	124	0	0	NUM
cana-3871	173	125	,	,	PUNCT
cana-3871	173	126	1	1	NUM
cana-3871	173	127	,	,	PUNCT
cana-3871	173	128	1	1	NUM
cana-3871	173	129	)	)	PUNCT
cana-3871	173	130	,	,	PUNCT
cana-3871	173	131	(	(	PUNCT
cana-3871	173	132	1	1	NUM
cana-3871	173	133	,	,	PUNCT
cana-3871	173	134	1	1	NUM
cana-3871	173	135	,	,	PUNCT
cana-3871	173	136	0	0	NUM
cana-3871	173	137	,	,	PUNCT
cana-3871	173	138	0	0	NUM
cana-3871	173	139	)	)	PUNCT
cana-3871	173	140	,	,	PUNCT
cana-3871	173	141	(	(	PUNCT
cana-3871	173	142	1	1	NUM
cana-3871	173	143	,	,	PUNCT
cana-3871	173	144	1	1	NUM
cana-3871	173	145	,	,	PUNCT
cana-3871	173	146	0	0	NUM
cana-3871	173	147	,	,	PUNCT
cana-3871	173	148	1	1	NUM
cana-3871	173	149	)	)	PUNCT
cana-3871	173	150	,	,	PUNCT
cana-3871	173	151	(	(	PUNCT
cana-3871	173	152	1	1	NUM
cana-3871	173	153	,	,	PUNCT
cana-3871	173	154	1	1	NUM
cana-3871	173	155	,	,	PUNCT
cana-3871	173	156	1	1	NUM
cana-3871	173	157	,	,	PUNCT
cana-3871	173	158	0	0	NUM
cana-3871	173	159	)	)	PUNCT
cana-3871	173	160	,	,	PUNCT
cana-3871	173	161	(	(	PUNCT
cana-3871	173	162	1	1	NUM
cana-3871	173	163	,	,	PUNCT
cana-3871	173	164	1	1	NUM
cana-3871	173	165	,	,	PUNCT
cana-3871	173	166	1	1	NUM
cana-3871	173	167	,	,	PUNCT
cana-3871	173	168	1	1	NUM
cana-3871	173	169	)	)	PUNCT
cana-3871	173	170	}	}	PUNCT
cana-3871	173	171	ℤ(ℤ2×ℤ2×ℤ2×ℤ2	ℤ(ℤ2×ℤ2×ℤ2×ℤ2	NOUN
cana-3871	173	172	)	)	PUNCT
cana-3871	173	173	=	=	SYM
cana-3871	173	174	{	{	PUNCT
cana-3871	173	175	(	(	PUNCT
cana-3871	173	176	0	0	NUM
cana-3871	173	177	,	,	PUNCT
cana-3871	173	178	0	0	NUM
cana-3871	173	179	,	,	PUNCT
cana-3871	173	180	0	0	NUM
cana-3871	173	181	,	,	PUNCT
cana-3871	173	182	1	1	NUM
cana-3871	173	183	)	)	PUNCT
cana-3871	173	184	,	,	PUNCT
cana-3871	173	185	(	(	PUNCT
cana-3871	173	186	0	0	NUM
cana-3871	173	187	,	,	PUNCT
cana-3871	173	188	0	0	NUM
cana-3871	173	189	,	,	PUNCT
cana-3871	173	190	1	1	NUM
cana-3871	173	191	,	,	PUNCT
cana-3871	173	192	0	0	NUM
cana-3871	173	193	)	)	PUNCT
cana-3871	173	194	,	,	PUNCT
cana-3871	173	195	(	(	PUNCT
cana-3871	173	196	0	0	NUM
cana-3871	173	197	,	,	PUNCT
cana-3871	173	198	1	1	NUM
cana-3871	173	199	,	,	PUNCT
cana-3871	173	200	0	0	NUM
cana-3871	173	201	,	,	PUNCT
cana-3871	173	202	0	0	NUM
cana-3871	173	203	)	)	PUNCT
cana-3871	173	204	,	,	PUNCT
cana-3871	173	205	(	(	PUNCT
cana-3871	173	206	0	0	NUM
cana-3871	173	207	,	,	PUNCT
cana-3871	173	208	0	0	NUM
cana-3871	173	209	,	,	PUNCT
cana-3871	173	210	1	1	NUM
cana-3871	173	211	,	,	PUNCT
cana-3871	173	212	1	1	NUM
cana-3871	173	213	)	)	PUNCT
cana-3871	173	214	,	,	PUNCT
cana-3871	173	215	(	(	PUNCT
cana-3871	173	216	0	0	NUM
cana-3871	173	217	,	,	PUNCT
cana-3871	173	218	1	1	NUM
cana-3871	173	219	,	,	PUNCT
cana-3871	173	220	0	0	NUM
cana-3871	173	221	,	,	PUNCT
cana-3871	173	222	1	1	NUM
cana-3871	173	223	)	)	PUNCT
cana-3871	173	224	,	,	PUNCT
cana-3871	173	225	(	(	PUNCT
cana-3871	173	226	0	0	NUM
cana-3871	173	227	,	,	PUNCT
cana-3871	173	228	1	1	NUM
cana-3871	173	229	,	,	PUNCT
cana-3871	173	230	1	1	NUM
cana-3871	173	231	,	,	PUNCT
cana-3871	173	232	0	0	NUM
cana-3871	173	233	)	)	PUNCT
cana-3871	173	234	,	,	PUNCT
cana-3871	173	235	(	(	PUNCT
cana-3871	173	236	0	0	NUM
cana-3871	173	237	,	,	PUNCT
cana-3871	173	238	1	1	NUM
cana-3871	173	239	,	,	PUNCT
cana-3871	173	240	1	1	NUM
cana-3871	173	241	,	,	PUNCT
cana-3871	173	242	1	1	NUM
cana-3871	173	243	)	)	PUNCT
cana-3871	173	244	,	,	PUNCT
cana-3871	173	245	(	(	PUNCT
cana-3871	173	246	1	1	NUM
cana-3871	173	247	,	,	PUNCT
cana-3871	173	248	0	0	NUM
cana-3871	173	249	,	,	PUNCT
cana-3871	173	250	0	0	NUM
cana-3871	173	251	,	,	PUNCT
cana-3871	173	252	0	0	NUM
cana-3871	173	253	)	)	PUNCT
cana-3871	173	254	,	,	PUNCT
cana-3871	173	255	(	(	PUNCT
cana-3871	173	256	1	1	NUM
cana-3871	173	257	,	,	PUNCT
cana-3871	173	258	0	0	NUM
cana-3871	173	259	,	,	PUNCT
cana-3871	173	260	0	0	NUM
cana-3871	173	261	,	,	PUNCT
cana-3871	173	262	1	1	NUM
cana-3871	173	263	)	)	PUNCT
cana-3871	173	264	,	,	PUNCT
cana-3871	173	265	(	(	PUNCT
cana-3871	173	266	1	1	NUM
cana-3871	173	267	,	,	PUNCT
cana-3871	173	268	0	0	NUM
cana-3871	173	269	,	,	PUNCT
cana-3871	173	270	1	1	NUM
cana-3871	173	271	,	,	PUNCT
cana-3871	173	272	0	0	NUM
cana-3871	173	273	)	)	PUNCT
cana-3871	173	274	,	,	PUNCT
cana-3871	173	275	(	(	PUNCT
cana-3871	173	276	1	1	NUM
cana-3871	173	277	,	,	PUNCT
cana-3871	173	278	0	0	NUM
cana-3871	173	279	,	,	PUNCT
cana-3871	173	280	1	1	NUM
cana-3871	173	281	,	,	PUNCT
cana-3871	173	282	1	1	NUM
cana-3871	173	283	)	)	PUNCT
cana-3871	173	284	,	,	PUNCT
cana-3871	173	285	(	(	PUNCT
cana-3871	173	286	1	1	NUM
cana-3871	173	287	,	,	PUNCT
cana-3871	173	288	1	1	NUM
cana-3871	173	289	,	,	PUNCT
cana-3871	173	290	0	0	NUM
cana-3871	173	291	,	,	PUNCT
cana-3871	173	292	0	0	NUM
cana-3871	173	293	)	)	PUNCT
cana-3871	173	294	,	,	PUNCT
cana-3871	173	295	(	(	PUNCT
cana-3871	173	296	1	1	NUM
cana-3871	173	297	,	,	PUNCT
cana-3871	173	298	1	1	NUM
cana-3871	173	299	,	,	PUNCT
cana-3871	173	300	0	0	NUM
cana-3871	173	301	,	,	PUNCT
cana-3871	173	302	1	1	NUM
cana-3871	173	303	)	)	PUNCT
cana-3871	173	304	,	,	PUNCT
cana-3871	173	305	(	(	PUNCT
cana-3871	173	306	1	1	NUM
cana-3871	173	307	,	,	PUNCT
cana-3871	173	308	1	1	NUM
cana-3871	173	309	,	,	PUNCT
cana-3871	173	310	1	1	NUM
cana-3871	173	311	,	,	PUNCT
cana-3871	173	312	0	0	NUM
cana-3871	173	313	)	)	PUNCT
cana-3871	173	314	}	}	PUNCT
cana-3871	173	315	the	the	DET
cana-3871	173	316	zero	zero	NUM
cana-3871	173	317	-	-	PUNCT
cana-3871	173	318	divisor	divisor	NOUN
cana-3871	173	319	graph	graph	NOUN
cana-3871	173	320	of	of	ADP
cana-3871	173	321	ℤ2	ℤ2	PROPN
cana-3871	173	322	×	×	PROPN
cana-3871	173	323	ℤ2	ℤ2	PROPN
cana-3871	174	1	×	×	PROPN
cana-3871	174	2	ℤ2	ℤ2	PROPN
cana-3871	174	3	×	×	PROPN
cana-3871	174	4	ℤ2	ℤ2	PROPN
cana-3871	174	5	is	be	AUX
cana-3871	174	6	given	give	VERB
cana-3871	174	7	in	in	ADP
cana-3871	174	8	the	the	DET
cana-3871	174	9	figure	figure	NOUN
cana-3871	174	10	.	.	PUNCT
cana-3871	175	1	fig	fig	NOUN
cana-3871	175	2	17	17	NUM
cana-3871	175	3	:	:	PUNCT
cana-3871	175	4	γ	γ	X
cana-3871	175	5	(	(	PUNCT
cana-3871	175	6	ℤ2	ℤ2	PROPN
cana-3871	175	7	×	×	PROPN
cana-3871	175	8	ℤ2	ℤ2	PROPN
cana-3871	175	9	×	×	PROPN
cana-3871	175	10	ℤ2	ℤ2	PROPN
cana-3871	175	11	×	×	PROPN
cana-3871	175	12	ℤ2	ℤ2	PROPN
cana-3871	175	13	)	)	PUNCT
cana-3871	175	14	number	number	NOUN
cana-3871	175	15	of	of	ADP
cana-3871	175	16	vertices	vertex	NOUN
cana-3871	175	17	in	in	ADP
cana-3871	175	18	the	the	DET
cana-3871	175	19	graph	graph	NOUN
cana-3871	175	20	of	of	ADP
cana-3871	175	21	ℤ	ℤ	PROPN
cana-3871	175	22	(	(	PUNCT
cana-3871	175	23	ℤ2	ℤ2	PROPN
cana-3871	175	24	×	×	PROPN
cana-3871	175	25	ℤ2	ℤ2	PROPN
cana-3871	175	26	×	×	PROPN
cana-3871	175	27	ℤ2	ℤ2	PROPN
cana-3871	175	28	×	×	PROPN
cana-3871	175	29	ℤ2	ℤ2	PROPN
cana-3871	175	30	)	)	PUNCT
cana-3871	175	31	=	=	SYM
cana-3871	176	1	24	24	NUM
cana-3871	176	2	−	−	NUM
cana-3871	176	3	2	2	NUM
cana-3871	176	4	=	=	SYM
cana-3871	176	5	14	14	NUM
cana-3871	176	6	the	the	DET
cana-3871	176	7	vertices	vertex	NOUN
cana-3871	176	8	(	(	PUNCT
cana-3871	176	9	0	0	NUM
cana-3871	176	10	,	,	PUNCT
cana-3871	176	11	0	0	NUM
cana-3871	176	12	,	,	PUNCT
cana-3871	176	13	0	0	NUM
cana-3871	176	14	,	,	PUNCT
cana-3871	176	15	1	1	NUM
cana-3871	176	16	)	)	PUNCT
cana-3871	176	17	,	,	PUNCT
cana-3871	176	18	(	(	PUNCT
cana-3871	176	19	0	0	NUM
cana-3871	176	20	,	,	PUNCT
cana-3871	176	21	0	0	NUM
cana-3871	176	22	,	,	PUNCT
cana-3871	176	23	1	1	NUM
cana-3871	176	24	,	,	PUNCT
cana-3871	176	25	0	0	NUM
cana-3871	176	26	)	)	PUNCT
cana-3871	176	27	,	,	PUNCT
cana-3871	176	28	(	(	PUNCT
cana-3871	176	29	0	0	NUM
cana-3871	176	30	,	,	PUNCT
cana-3871	176	31	1	1	NUM
cana-3871	176	32	,	,	PUNCT
cana-3871	176	33	0	0	NUM
cana-3871	176	34	,	,	PUNCT
cana-3871	176	35	0	0	NUM
cana-3871	176	36	)	)	PUNCT
cana-3871	176	37	form	form	VERB
cana-3871	176	38	a	a	DET
cana-3871	176	39	cycle	cycle	NOUN
cana-3871	176	40	of	of	ADP
cana-3871	176	41	length	length	NOUN
cana-3871	176	42	3	3	NUM
cana-3871	176	43	.	.	PUNCT
cana-3871	177	1	the	the	DET
cana-3871	177	2	vertices	vertex	NOUN
cana-3871	177	3	(	(	PUNCT
cana-3871	177	4	0	0	NUM
cana-3871	177	5	,	,	PUNCT
cana-3871	177	6	1	1	NUM
cana-3871	177	7	,	,	PUNCT
cana-3871	177	8	1	1	NUM
cana-3871	177	9	,	,	PUNCT
cana-3871	177	10	0	0	NUM
cana-3871	177	11	)	)	PUNCT
cana-3871	177	12	,	,	PUNCT
cana-3871	177	13	(	(	PUNCT
cana-3871	177	14	1	1	NUM
cana-3871	177	15	,	,	PUNCT
cana-3871	177	16	0	0	NUM
cana-3871	177	17	,	,	PUNCT
cana-3871	177	18	0	0	NUM
cana-3871	177	19	,	,	PUNCT
cana-3871	177	20	0	0	NUM
cana-3871	177	21	)	)	PUNCT
cana-3871	177	22	,	,	PUNCT
cana-3871	177	23	(	(	PUNCT
cana-3871	177	24	0	0	NUM
cana-3871	177	25	,	,	PUNCT
cana-3871	177	26	0	0	NUM
cana-3871	177	27	,	,	PUNCT
cana-3871	177	28	0	0	NUM
cana-3871	177	29	,	,	PUNCT
cana-3871	177	30	1	1	X
cana-3871	177	31	)	)	PUNCT
cana-3871	177	32	form	form	VERB
cana-3871	177	33	a	a	DET
cana-3871	177	34	cycle	cycle	NOUN
cana-3871	177	35	of	of	ADP
cana-3871	177	36	length	length	NOUN
cana-3871	177	37	3	3	NUM
cana-3871	177	38	.	.	PUNCT
cana-3871	178	1	the	the	DET
cana-3871	178	2	vertices	vertex	NOUN
cana-3871	178	3	(	(	PUNCT
cana-3871	178	4	1	1	NUM
cana-3871	178	5	,	,	PUNCT
cana-3871	178	6	0	0	NUM
cana-3871	178	7	,	,	PUNCT
cana-3871	178	8	0	0	NUM
cana-3871	178	9	,	,	PUNCT
cana-3871	178	10	0	0	NUM
cana-3871	178	11	)	)	PUNCT
cana-3871	178	12	,	,	PUNCT
cana-3871	178	13	(	(	PUNCT
cana-3871	178	14	0	0	NUM
cana-3871	178	15	,	,	PUNCT
cana-3871	178	16	1	1	NUM
cana-3871	178	17	,	,	PUNCT
cana-3871	178	18	0	0	NUM
cana-3871	178	19	,	,	PUNCT
cana-3871	178	20	1	1	NUM
cana-3871	178	21	)	)	PUNCT
cana-3871	178	22	,	,	PUNCT
cana-3871	178	23	(	(	PUNCT
cana-3871	178	24	0	0	NUM
cana-3871	178	25	,	,	PUNCT
cana-3871	178	26	0	0	NUM
cana-3871	178	27	,	,	PUNCT
cana-3871	178	28	1	1	NUM
cana-3871	178	29	,	,	PUNCT
cana-3871	178	30	0	0	NUM
cana-3871	178	31	)	)	PUNCT
cana-3871	178	32	form	form	VERB
cana-3871	178	33	a	a	DET
cana-3871	178	34	cycle	cycle	NOUN
cana-3871	178	35	of	of	ADP
cana-3871	178	36	length	length	NOUN
cana-3871	178	37	3	3	NUM
cana-3871	178	38	and	and	CCONJ
cana-3871	178	39	etc	etc	X
cana-3871	178	40	.	.	PUNCT
cana-3871	179	1	∴	∴	PROPN
cana-3871	179	2	ℤ2	ℤ2	PROPN
cana-3871	179	3	4	4	NUM
cana-3871	179	4	has	have	VERB
cana-3871	179	5	the	the	DET
cana-3871	179	6	shortest	short	ADJ
cana-3871	179	7	cycle	cycle	NOUN
cana-3871	179	8	of	of	ADP
cana-3871	179	9	order	order	NOUN
cana-3871	179	10	3	3	X
cana-3871	179	11	.	.	PUNCT
cana-3871	179	12	∴the	∴the	DET
cana-3871	179	13	girth	girth	NOUN
cana-3871	179	14	of	of	ADP
cana-3871	179	15	ℤ2	ℤ2	PROPN
cana-3871	179	16	3	3	NUM
cana-3871	179	17	is	be	AUX
cana-3871	179	18	3	3	NUM
cana-3871	179	19	and	and	CCONJ
cana-3871	179	20	the	the	DET
cana-3871	179	21	theorem	theorem	NOUN
cana-3871	179	22	holds	hold	VERB
cana-3871	179	23	.	.	PUNCT
cana-3871	179	24	4	4	NUM
cana-3871	179	25	conclusion	conclusion	NOUN
cana-3871	179	26	an	an	DET
cana-3871	179	27	attempt	attempt	NOUN
cana-3871	179	28	has	have	AUX
cana-3871	179	29	been	be	AUX
cana-3871	179	30	made	make	VERB
cana-3871	179	31	to	to	PART
cana-3871	179	32	generalize	generalize	VERB
cana-3871	179	33	the	the	DET
cana-3871	179	34	zero	zero	NUM
cana-3871	179	35	divisor	divisor	NOUN
cana-3871	179	36	graphs	graph	NOUN
cana-3871	179	37	of	of	ADP
cana-3871	179	38	boolean	boolean	ADJ
cana-3871	179	39	rings	ring	NOUN
cana-3871	179	40	.	.	PUNCT
cana-3871	180	1	in	in	ADP
cana-3871	180	2	this	this	DET
cana-3871	180	3	project	project	NOUN
cana-3871	180	4	,	,	PUNCT
cana-3871	180	5	we	we	PRON
cana-3871	180	6	have	have	AUX
cana-3871	180	7	tried	try	VERB
cana-3871	180	8	to	to	PART
cana-3871	180	9	prove	prove	VERB
cana-3871	180	10	the	the	DET
cana-3871	180	11	results	result	NOUN
cana-3871	180	12	regarding	regard	VERB
cana-3871	180	13	the	the	DET
cana-3871	180	14	degree	degree	NOUN
cana-3871	180	15	of	of	ADP
cana-3871	180	16	vertices	vertex	NOUN
cana-3871	180	17	,	,	PUNCT
cana-3871	180	18	length	length	NOUN
cana-3871	180	19	of	of	ADP
cana-3871	180	20	cycles	cycle	NOUN
cana-3871	180	21	,	,	PUNCT
cana-3871	180	22	and	and	CCONJ
cana-3871	180	23	girth	girth	NOUN
cana-3871	180	24	of	of	ADP
cana-3871	180	25	the	the	DET
cana-3871	180	26	graph	graph	NOUN
cana-3871	180	27	for	for	ADP
cana-3871	180	28	the	the	DET
cana-3871	180	29	zero	zero	NUM
cana-3871	180	30	divisor	divisor	NOUN
cana-3871	180	31	graphs	graph	NOUN
cana-3871	180	32	of	of	ADP
cana-3871	180	33	these	these	DET
cana-3871	180	34	boolean	boolean	ADJ
cana-3871	180	35	rings	ring	NOUN
cana-3871	180	36	.	.	PUNCT
cana-3871	181	1	by	by	ADP
cana-3871	181	2	studying	study	VERB
cana-3871	181	3	the	the	DET
cana-3871	181	4	graphs	graph	NOUN
cana-3871	181	5	for	for	ADP
cana-3871	181	6	different	different	ADJ
cana-3871	181	7	values	value	NOUN
cana-3871	181	8	of	of	ADP
cana-3871	181	9	n	n	CCONJ
cana-3871	181	10	,	,	PUNCT
cana-3871	181	11	we	we	PRON
cana-3871	181	12	could	could	AUX
cana-3871	181	13	develop	develop	VERB
cana-3871	181	14	these	these	DET
cana-3871	181	15	results	result	NOUN
cana-3871	181	16	and	and	CCONJ
cana-3871	181	17	hence	hence	ADV
cana-3871	181	18	form	form	VERB
cana-3871	181	19	the	the	DET
cana-3871	181	20	proofs	proof	NOUN
cana-3871	181	21	of	of	ADP
cana-3871	181	22	the	the	DET
cana-3871	181	23	theorems	theorem	NOUN
cana-3871	181	24	stated	state	VERB
cana-3871	181	25	in	in	ADP
cana-3871	181	26	the	the	DET
cana-3871	181	27	project	project	NOUN
cana-3871	181	28	before	before	ADV
cana-3871	181	29	.	.	PUNCT
cana-3871	182	1	the	the	DET
cana-3871	182	2	ultimate	ultimate	ADJ
cana-3871	182	3	goal	goal	NOUN
cana-3871	182	4	of	of	ADP
cana-3871	182	5	this	this	DET
cana-3871	182	6	project	project	NOUN
cana-3871	182	7	is	be	AUX
cana-3871	182	8	to	to	PART
cana-3871	182	9	understand	understand	VERB
cana-3871	182	10	the	the	DET
cana-3871	182	11	relationship	relationship	NOUN
cana-3871	182	12	between	between	ADP
cana-3871	182	13	different	different	ADJ
cana-3871	182	14	aspects	aspect	NOUN
cana-3871	182	15	of	of	ADP
cana-3871	182	16	the	the	DET
cana-3871	182	17	zerodivisor	zerodivisor	NOUN
cana-3871	182	18	graphs	graph	NOUN
cana-3871	182	19	of	of	ADP
cana-3871	182	20	boolean	boolean	ADJ
cana-3871	182	21	rings	ring	NOUN
cana-3871	182	22	and	and	CCONJ
cana-3871	182	23	their	their	PRON
cana-3871	182	24	various	various	ADJ
cana-3871	182	25	properties	property	NOUN
cana-3871	182	26	.	.	PUNCT
cana-3871	183	1	5	5	NUM
cana-3871	183	2	sage	sage	NOUN
cana-3871	183	3	sage	sage	NOUN
cana-3871	183	4	is	be	AUX
cana-3871	183	5	free	free	ADJ
cana-3871	183	6	,	,	PUNCT
cana-3871	183	7	open	open	ADJ
cana-3871	183	8	-	-	PUNCT
cana-3871	183	9	source	source	NOUN
cana-3871	183	10	mathematics	mathematic	NOUN
cana-3871	183	11	software	software	NOUN
cana-3871	183	12	that	that	PRON
cana-3871	183	13	can	can	AUX
cana-3871	183	14	be	be	AUX
cana-3871	183	15	used	use	VERB
cana-3871	183	16	alternatively	alternatively	ADV
cana-3871	183	17	to	to	ADP
cana-3871	183	18	mathematica	mathematica	PROPN
cana-3871	183	19	or	or	CCONJ
cana-3871	183	20	matlab	matlab	PROPN
cana-3871	183	21	.	.	PUNCT
cana-3871	184	1	sage	sage	NOUN
cana-3871	184	2	math	math	NOUN
cana-3871	184	3	(	(	PUNCT
cana-3871	184	4	previously	previously	ADV
cana-3871	184	5	sage	sage	VERB
cana-3871	184	6	or	or	CCONJ
cana-3871	184	7	sage	sage	NOUN
cana-3871	184	8	,	,	PUNCT
cana-3871	184	9	”	"	PUNCT
cana-3871	184	10	system	system	NOUN
cana-3871	184	11	for	for	ADP
cana-3871	184	12	algebra	algebra	NOUN
cana-3871	184	13	and	and	CCONJ
cana-3871	184	14	geometry	geometry	NOUN
cana-3871	184	15	experimentation	experimentation	NOUN
cana-3871	184	16	”	"	PUNCT
cana-3871	184	17	)	)	PUNCT
cana-3871	184	18	is	be	AUX
cana-3871	184	19	a	a	DET
cana-3871	184	20	computer	computer	NOUN
cana-3871	184	21	algebra	algebra	NOUN
cana-3871	184	22	system	system	NOUN
cana-3871	184	23	(	(	PUNCT
cana-3871	184	24	cas	cas	PROPN
cana-3871	184	25	)	)	PUNCT
cana-3871	184	26	with	with	ADP
cana-3871	184	27	features	feature	NOUN
cana-3871	184	28	covering	cover	VERB
cana-3871	184	29	many	many	ADJ
cana-3871	184	30	aspects	aspect	NOUN
cana-3871	184	31	of	of	ADP
cana-3871	184	32	mathematics	mathematic	NOUN
cana-3871	184	33	,	,	PUNCT
cana-3871	184	34	including	include	VERB
cana-3871	184	35	algebra	algebra	NOUN
cana-3871	184	36	,	,	PUNCT
cana-3871	184	37	combinatorics	combinatoric	NOUN
cana-3871	184	38	,	,	PUNCT
cana-3871	184	39	graph	graph	NOUN
cana-3871	184	40	theory	theory	NOUN
cana-3871	184	41	,	,	PUNCT
cana-3871	184	42	numerical	numerical	ADJ
cana-3871	184	43	analysis	analysis	NOUN
cana-3871	184	44	,	,	PUNCT
cana-3871	184	45	number	number	NOUN
cana-3871	184	46	theory	theory	NOUN
cana-3871	184	47	,	,	PUNCT
cana-3871	184	48	calculus	calculus	NOUN
cana-3871	184	49	,	,	PUNCT
cana-3871	184	50	and	and	CCONJ
cana-3871	184	51	statistics	statistic	NOUN
cana-3871	184	52	.	.	PUNCT
cana-3871	185	1	we	we	PRON
cana-3871	185	2	have	have	AUX
cana-3871	185	3	been	be	AUX
cana-3871	185	4	using	use	VERB
cana-3871	185	5	this	this	DET
cana-3871	185	6	tool	tool	NOUN
cana-3871	185	7	to	to	PART
cana-3871	185	8	form	form	VERB
cana-3871	185	9	graphs	graph	NOUN
cana-3871	185	10	.	.	PUNCT
cana-3871	186	1	commands	command	NOUN
cana-3871	186	2	that	that	PRON
cana-3871	186	3	that	that	PRON
cana-3871	186	4	been	be	AUX
cana-3871	186	5	used	use	VERB
cana-3871	186	6	to	to	PART
cana-3871	186	7	form	form	VERB
cana-3871	186	8	a	a	DET
cana-3871	186	9	zero	zero	NUM
cana-3871	186	10	-	-	PUNCT
cana-3871	186	11	divisor	divisor	NOUN
cana-3871	186	12	graph	graph	NOUN
cana-3871	186	13	of	of	ADP
cana-3871	186	14	ℤ2	ℤ2	PROPN
cana-3871	186	15	3	3	NUM
cana-3871	186	16	are	be	AUX
cana-3871	186	17	:	:	PUNCT
cana-3871	186	18	communications	communication	NOUN
cana-3871	186	19	on	on	ADP
cana-3871	186	20	applied	apply	VERB
cana-3871	186	21	nonlinear	nonlinear	ADJ
cana-3871	186	22	analysis	analysis	NOUN
cana-3871	186	23	issn	issn	NOUN
cana-3871	186	24	:	:	PUNCT
cana-3871	186	25	1074	1074	NUM
cana-3871	186	26	-	-	PUNCT
cana-3871	186	27	133x	133x	NUM
cana-3871	186	28	vol	vol	NOUN
cana-3871	186	29	32	32	NUM
cana-3871	186	30	no	no	NOUN
cana-3871	186	31	.	.	PUNCT
cana-3871	187	1	7s	7	NOUN
cana-3871	187	2	(	(	PUNCT
cana-3871	187	3	2025	2025	NUM
cana-3871	187	4	)	)	PUNCT
cana-3871	187	5	957	957	NUM
cana-3871	187	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3871	188	1	we	we	PRON
cana-3871	188	2	have	have	AUX
cana-3871	188	3	defined	define	VERB
cana-3871	188	4	the	the	DET
cana-3871	188	5	function	function	NOUN
cana-3871	188	6	g1	g1	NOUN
cana-3871	188	7	=	=	NOUN
cana-3871	188	8	graph	graph	NOUN
cana-3871	188	9	(	(	PUNCT
cana-3871	188	10	)	)	PUNCT
cana-3871	188	11	g1.add_vertex(′(0	g1.add_vertex(′(0	NOUN
cana-3871	188	12	,	,	PUNCT
cana-3871	188	13	0	0	NUM
cana-3871	188	14	,	,	PUNCT
cana-3871	188	15	1)′	1)′	NOUN
cana-3871	188	16	)	)	PUNCT
cana-3871	188	17	g1.add_edge(′(0	g1.add_edge(′(0	NOUN
cana-3871	188	18	,	,	PUNCT
cana-3871	188	19	1	1	NUM
cana-3871	188	20	,	,	PUNCT
cana-3871	188	21	0)′,′	0)′,′	NUM
cana-3871	188	22	(	(	PUNCT
cana-3871	188	23	1	1	NUM
cana-3871	188	24	,	,	PUNCT
cana-3871	188	25	0	0	NUM
cana-3871	188	26	,	,	PUNCT
cana-3871	188	27	0)′	0)′	NOUN
cana-3871	188	28	)	)	PUNCT
cana-3871	188	29	g1.add_vertices([′(1	g1.add_vertices([′(1	PROPN
cana-3871	188	30	,	,	PUNCT
cana-3871	188	31	1	1	NUM
cana-3871	188	32	,	,	PUNCT
cana-3871	188	33	0)′,′	0)′,′	NUM
cana-3871	188	34	(	(	PUNCT
cana-3871	188	35	1	1	NUM
cana-3871	188	36	,	,	PUNCT
cana-3871	188	37	0	0	NUM
cana-3871	188	38	,	,	PUNCT
cana-3871	188	39	1)′,′	1)′,′	NUM
cana-3871	188	40	(	(	PUNCT
cana-3871	188	41	0	0	NUM
cana-3871	188	42	,	,	PUNCT
cana-3871	188	43	1	1	NUM
cana-3871	188	44	,	,	PUNCT
cana-3871	188	45	1)′	1)′	NOUN
cana-3871	188	46	]	]	X
cana-3871	188	47	)	)	PUNCT
cana-3871	188	48	g1.add	g1.add	VERB
cana-3871	188	49	_	_	SYM
cana-3871	188	50	edges([(′(0	edges([(′(0	NOUN
cana-3871	188	51	,	,	PUNCT
cana-3871	188	52	1	1	NUM
cana-3871	188	53	,	,	PUNCT
cana-3871	188	54	0)′,′	0)′,′	NUM
cana-3871	188	55	(	(	PUNCT
cana-3871	188	56	0	0	NUM
cana-3871	188	57	,	,	PUNCT
cana-3871	188	58	0	0	NUM
cana-3871	188	59	,	,	PUNCT
cana-3871	188	60	1)′	1)′	NOUN
cana-3871	188	61	)	)	PUNCT
cana-3871	188	62	,	,	PUNCT
cana-3871	188	63	(	(	PUNCT
cana-3871	188	64	′(0	′(0	PROPN
cana-3871	188	65	,	,	PUNCT
cana-3871	188	66	0	0	NUM
cana-3871	188	67	,	,	PUNCT
cana-3871	188	68	1)′,′	1)′,′	NUM
cana-3871	188	69	(	(	PUNCT
cana-3871	188	70	1	1	NUM
cana-3871	188	71	,	,	PUNCT
cana-3871	188	72	0	0	NUM
cana-3871	188	73	,	,	PUNCT
cana-3871	188	74	0)′	0)′	NOUN
cana-3871	188	75	)	)	PUNCT
cana-3871	188	76	,	,	PUNCT
cana-3871	188	77	(	(	PUNCT
cana-3871	188	78	′(1	′(1	PROPN
cana-3871	188	79	,	,	PUNCT
cana-3871	188	80	1	1	NUM
cana-3871	188	81	,	,	PUNCT
cana-3871	188	82	0)′,′	0)′,′	NUM
cana-3871	188	83	(	(	PUNCT
cana-3871	188	84	0	0	NUM
cana-3871	188	85	,	,	PUNCT
cana-3871	188	86	0	0	NUM
cana-3871	188	87	,	,	PUNCT
cana-3871	188	88	1)′	1)′	NOUN
cana-3871	188	89	)	)	PUNCT
cana-3871	188	90	,	,	PUNCT
cana-3871	188	91	(	(	PUNCT
cana-3871	188	92	′(1	′(1	PROPN
cana-3871	188	93	,	,	PUNCT
cana-3871	188	94	0	0	NUM
cana-3871	188	95	,	,	PUNCT
cana-3871	188	96	1)′,′	1)′,′	NUM
cana-3871	188	97	(	(	PUNCT
cana-3871	188	98	0	0	NUM
cana-3871	188	99	,	,	PUNCT
cana-3871	188	100	1	1	NUM
cana-3871	188	101	,	,	PUNCT
cana-3871	188	102	0)′	0)′	NOUN
cana-3871	188	103	)	)	PUNCT
cana-3871	188	104	,	,	PUNCT
cana-3871	188	105	(	(	PUNCT
cana-3871	188	106	′(0	′(0	NOUN
cana-3871	188	107	,	,	PUNCT
cana-3871	188	108	1	1	NUM
cana-3871	188	109	,	,	PUNCT
cana-3871	188	110	1)′,′	1)′,′	NUM
cana-3871	188	111	(	(	PUNCT
cana-3871	188	112	1	1	NUM
cana-3871	188	113	,	,	PUNCT
cana-3871	188	114	0	0	NUM
cana-3871	188	115	,	,	PUNCT
cana-3871	188	116	0)′	0)′	NOUN
cana-3871	188	117	)	)	PUNCT
cana-3871	188	118	]	]	PUNCT
cana-3871	188	119	)	)	PUNCT
cana-3871	188	120	g1	g1	NOUN
cana-3871	188	121	.	.	PUNCT
cana-3871	189	1	show	show	NOUN
cana-3871	189	2	(	(	PUNCT
cana-3871	189	3	)	)	PUNCT
cana-3871	189	4	similarly	similarly	ADV
cana-3871	189	5	,	,	PUNCT
cana-3871	189	6	we	we	PRON
cana-3871	189	7	have	have	AUX
cana-3871	189	8	used	use	VERB
cana-3871	189	9	the	the	DET
cana-3871	189	10	commands	command	NOUN
cana-3871	189	11	for	for	ADP
cana-3871	189	12	generating	generate	VERB
cana-3871	189	13	graphs	graph	NOUN
cana-3871	189	14	of	of	ADP
cana-3871	189	15	ℤ2	ℤ2	PROPN
cana-3871	189	16	4	4	NUM
cana-3871	189	17	and	and	CCONJ
cana-3871	189	18	ℤ2	ℤ2	PROPN
cana-3871	189	19	5	5	NUM
cana-3871	189	20	.	.	NOUN
cana-3871	189	21	6	6	NUM
cana-3871	189	22	acknowledgement	acknowledgement	NOUN
cana-3871	189	23	the	the	DET
cana-3871	189	24	authors	author	NOUN
cana-3871	189	25	thank	thank	VERB
cana-3871	189	26	k.b.p	k.b.p	PROPN
cana-3871	189	27	.	.	PUNCT
cana-3871	190	1	college	college	PROPN
cana-3871	190	2	vashi	vashi	PROPN
cana-3871	190	3	,	,	PUNCT
cana-3871	190	4	navi	navi	PROPN
cana-3871	190	5	mumbai	mumbai	PROPN
cana-3871	190	6	for	for	ADP
cana-3871	190	7	providing	provide	VERB
cana-3871	190	8	financial	financial	ADJ
cana-3871	190	9	support	support	NOUN
cana-3871	190	10	for	for	ADP
cana-3871	190	11	the	the	DET
cana-3871	190	12	mrp	mrp	NOUN
cana-3871	190	13	under	under	ADP
cana-3871	190	14	institutional	institutional	ADJ
cana-3871	190	15	seed	seed	NOUN
cana-3871	190	16	money	money	NOUN
cana-3871	190	17	ref.no.:1643/2024	ref.no.:1643/2024	NOUN
cana-3871	190	18	-	-	NOUN
cana-3871	190	19	2025	2025	NUM
cana-3871	190	20	/	/	SYM
cana-3871	190	21	sr	sr	PROPN
cana-3871	190	22	.	.	PUNCT
cana-3871	191	1	references	reference	NOUN
cana-3871	191	2	[	[	X
cana-3871	191	3	1	1	NUM
cana-3871	191	4	]	]	PUNCT
cana-3871	191	5	euler	euler	PROPN
cana-3871	191	6	l.	l.	PROPN
cana-3871	191	7	leonhard	leonhard	PROPN
cana-3871	191	8	euler	euler	PROPN
cana-3871	191	9	and	and	CCONJ
cana-3871	191	10	the	the	DET
cana-3871	191	11	königsberg	königsberg	PROPN
cana-3871	191	12	bridges	bridge	NOUN
cana-3871	191	13	.	.	PUNCT
cana-3871	192	1	scientific	scientific	ADJ
cana-3871	192	2	american	american	PROPN
cana-3871	192	3	.	.	PUNCT
cana-3871	193	1	1953	1953	NUM
cana-3871	193	2	jul	jul	PROPN
cana-3871	193	3	1;189(1):66	1;189(1):66	PROPN
cana-3871	193	4	-	-	SYM
cana-3871	193	5	72	72	NUM
cana-3871	193	6	.	.	PUNCT
cana-3871	194	1	[	[	X
cana-3871	194	2	2	2	NUM
cana-3871	194	3	]	]	PUNCT
cana-3871	194	4	m.	m.	PROPN
cana-3871	194	5	behzad	behzad	PROPN
cana-3871	194	6	and	and	CCONJ
cana-3871	194	7	a.	a.	PROPN
cana-3871	194	8	chartrand	chartrand	PROPN
cana-3871	194	9	,	,	PUNCT
cana-3871	194	10	introduction	introduction	NOUN
cana-3871	194	11	to	to	ADP
cana-3871	194	12	the	the	DET
cana-3871	194	13	theory	theory	NOUN
cana-3871	194	14	of	of	ADP
cana-3871	194	15	graphs	graph	NOUN
cana-3871	194	16	,	,	PUNCT
cana-3871	194	17	allyn	allyn	PROPN
cana-3871	194	18	and	and	CCONJ
cana-3871	194	19	becon	becon	PROPN
cana-3871	194	20	inc	inc	PROPN
cana-3871	194	21	.	.	PROPN
cana-3871	194	22	,	,	PUNCT
cana-3871	194	23	boston	boston	PROPN
cana-3871	194	24	,	,	PUNCT
cana-3871	194	25	1971	1971	NUM
cana-3871	194	26	.	.	PUNCT
cana-3871	195	1	[	[	X
cana-3871	195	2	3	3	NUM
cana-3871	195	3	]	]	X
cana-3871	195	4	i.	i.	PROPN
cana-3871	195	5	beck	beck	PROPN
cana-3871	195	6	(	(	PUNCT
cana-3871	195	7	1988	1988	NUM
cana-3871	195	8	)	)	PUNCT
cana-3871	195	9	.	.	PUNCT
cana-3871	196	1	coloring	coloring	NOUN
cana-3871	196	2	of	of	ADP
cana-3871	196	3	commutative	commutative	ADJ
cana-3871	196	4	rings	ring	NOUN
cana-3871	196	5	,	,	PUNCT
cana-3871	196	6	j.	j.	PROPN
cana-3871	196	7	algebra	algebra	PROPN
cana-3871	196	8	,	,	PUNCT
cana-3871	196	9	116	116	NUM
cana-3871	196	10	,	,	PUNCT
cana-3871	196	11	208–226	208–226	NUM
cana-3871	196	12	.	.	PUNCT
cana-3871	197	1	[	[	X
cana-3871	197	2	4	4	NUM
cana-3871	197	3	]	]	X
cana-3871	197	4	d.f	d.f	PROPN
cana-3871	197	5	.	.	PROPN
cana-3871	197	6	anderson	anderson	PROPN
cana-3871	197	7	,	,	PUNCT
cana-3871	197	8	a.	a.	PROPN
cana-3871	197	9	frazier	frazier	PROPN
cana-3871	197	10	,	,	PUNCT
cana-3871	197	11	a.	a.	NOUN
cana-3871	197	12	lauve	lauve	PROPN
cana-3871	197	13	,	,	PUNCT
cana-3871	197	14	p.	p.	PROPN
cana-3871	197	15	livingston	livingston	PROPN
cana-3871	197	16	,	,	PUNCT
cana-3871	197	17	the	the	DET
cana-3871	197	18	zero	zero	NUM
cana-3871	197	19	-	-	PUNCT
cana-3871	197	20	divisor	divisor	NOUN
cana-3871	197	21	graph	graph	NOUN
cana-3871	197	22	of	of	ADP
cana-3871	197	23	a	a	DET
cana-3871	197	24	commutative	commutative	ADJ
cana-3871	197	25	ring	ring	NOUN
cana-3871	197	26	,	,	PUNCT
cana-3871	197	27	ii	ii	PROPN
cana-3871	197	28	,	,	PUNCT
cana-3871	197	29	lecture	lecture	NOUN
cana-3871	197	30	notes	note	NOUN
cana-3871	197	31	in	in	ADP
cana-3871	197	32	pure	pure	ADJ
cana-3871	197	33	and	and	CCONJ
cana-3871	197	34	applied	applied	ADJ
cana-3871	197	35	mathematics	mathematic	NOUN
cana-3871	197	36	,	,	PUNCT
cana-3871	197	37	vol	vol	NOUN
cana-3871	197	38	.	.	PROPN
cana-3871	197	39	220	220	NUM
cana-3871	197	40	,	,	PUNCT
cana-3871	197	41	marcel	marcel	PROPN
cana-3871	197	42	dekker	dekker	PROPN
cana-3871	197	43	,	,	PUNCT
cana-3871	197	44	new	new	PROPN
cana-3871	197	45	york	york	PROPN
cana-3871	197	46	,	,	PUNCT
cana-3871	197	47	basel	basel	PROPN
cana-3871	197	48	,	,	PUNCT
cana-3871	197	49	2001	2001	NUM
cana-3871	197	50	,	,	PUNCT
cana-3871	197	51	pp	pp	ADJ
cana-3871	197	52	.	.	PUNCT
cana-3871	198	1	61–72	61–72	NUM
cana-3871	198	2	.	.	PUNCT
cana-3871	199	1	[	[	X
cana-3871	199	2	5	5	NUM
cana-3871	199	3	]	]	PUNCT
cana-3871	199	4	mulay	mulay	NOUN
cana-3871	199	5	,	,	PUNCT
cana-3871	199	6	s.	s.	PROPN
cana-3871	199	7	b.	b.	PROPN
cana-3871	199	8	(	(	PUNCT
cana-3871	199	9	2002	2002	NUM
cana-3871	199	10	)	)	PUNCT
cana-3871	199	11	.	.	PUNCT
cana-3871	200	1	cycles	cycle	NOUN
cana-3871	200	2	and	and	CCONJ
cana-3871	200	3	symmetries	symmetry	NOUN
cana-3871	200	4	of	of	ADP
cana-3871	200	5	zero	zero	NUM
cana-3871	200	6	-	-	PUNCT
cana-3871	200	7	divisors	divisor	NOUN
cana-3871	200	8	,	,	PUNCT
cana-3871	200	9	comm	comm	NOUN
cana-3871	200	10	.	.	PUNCT
cana-3871	201	1	algebra	algebra	NOUN
cana-3871	201	2	,	,	PUNCT
cana-3871	201	3	30	30	NUM
cana-3871	201	4	,	,	PUNCT
cana-3871	201	5	3533–3558	3533–3558	NUM
cana-3871	201	6	.	.	PUNCT
cana-3871	202	1	[	[	X
cana-3871	202	2	6	6	NUM
cana-3871	202	3	]	]	PUNCT
cana-3871	202	4	d.	d.	PROPN
cana-3871	202	5	f.	f.	PROPN
cana-3871	202	6	anderson	anderson	PROPN
cana-3871	202	7	,	,	PUNCT
cana-3871	202	8	r.	r.	PROPN
cana-3871	202	9	levy	levy	PROPN
cana-3871	202	10	,	,	PUNCT
cana-3871	202	11	and	and	CCONJ
cana-3871	202	12	j.	j.	PROPN
cana-3871	202	13	shapiro	shapiro	PROPN
cana-3871	202	14	,	,	PUNCT
cana-3871	202	15	“	"	PUNCT
cana-3871	202	16	zero	zero	NUM
cana-3871	202	17	-	-	PUNCT
cana-3871	202	18	divisor	divisor	NOUN
cana-3871	202	19	graphs	graph	NOUN
cana-3871	202	20	,	,	PUNCT
cana-3871	202	21	von	von	PROPN
cana-3871	202	22	neumann	neumann	PROPN
cana-3871	202	23	regular	regular	PROPN
cana-3871	202	24	rings	ring	NOUN
cana-3871	202	25	,	,	PUNCT
cana-3871	202	26	and	and	CCONJ
cana-3871	202	27	boolean	boolean	ADJ
cana-3871	202	28	algebras	algebra	NOUN
cana-3871	202	29	”	"	PUNCT
cana-3871	202	30	,	,	PUNCT
cana-3871	202	31	j.	j.	PROPN
cana-3871	202	32	pure	pure	PROPN
cana-3871	202	33	appl	appl	PROPN
cana-3871	202	34	.	.	PUNCT
cana-3871	203	1	algebra	algebra	PROPN
cana-3871	203	2	180:3	180:3	NUM
cana-3871	203	3	(	(	PUNCT
cana-3871	203	4	2003	2003	NUM
cana-3871	203	5	)	)	PUNCT
cana-3871	203	6	,	,	PUNCT
cana-3871	203	7	221–241	221–241	NUM
cana-3871	203	8	.	.	PUNCT
cana-3871	204	1	[	[	X
cana-3871	204	2	7	7	NUM
cana-3871	204	3	]	]	X
cana-3871	204	4	anderson	anderson	PROPN
cana-3871	204	5	,	,	PUNCT
cana-3871	204	6	david	david	PROPN
cana-3871	204	7	f.	f.	PROPN
cana-3871	204	8	,	,	PUNCT
cana-3871	204	9	ron	ron	PROPN
cana-3871	204	10	levy	levy	PROPN
cana-3871	204	11	,	,	PUNCT
cana-3871	204	12	and	and	CCONJ
cana-3871	204	13	jay	jay	PROPN
cana-3871	204	14	shapiro	shapiro	PROPN
cana-3871	204	15	.	.	PUNCT
cana-3871	205	1	“	"	PUNCT
cana-3871	205	2	zero	zero	NUM
cana-3871	205	3	-	-	PUNCT
cana-3871	205	4	divisor	divisor	NOUN
cana-3871	205	5	graphs	graph	NOUN
cana-3871	205	6	,	,	PUNCT
cana-3871	205	7	von	von	PROPN
cana-3871	205	8	neumann	neumann	PROPN
cana-3871	205	9	regular	regular	PROPN
cana-3871	205	10	rings	ring	NOUN
cana-3871	205	11	,	,	PUNCT
cana-3871	205	12	and	and	CCONJ
cana-3871	205	13	boolean	boolean	ADJ
cana-3871	205	14	algebras	algebra	NOUN
cana-3871	205	15	.	.	PUNCT
cana-3871	205	16	”	"	PUNCT
cana-3871	205	17	journal	journal	NOUN
cana-3871	205	18	of	of	ADP
cana-3871	205	19	pure	pure	ADJ
cana-3871	205	20	and	and	CCONJ
cana-3871	205	21	applied	applied	ADJ
cana-3871	205	22	algebra	algebra	NOUN
cana-3871	205	23	180.3	180.3	NUM
cana-3871	205	24	(	(	PUNCT
cana-3871	205	25	2003	2003	NUM
cana-3871	205	26	):	):	PUNCT
cana-3871	205	27	221	221	NUM
cana-3871	205	28	-	-	SYM
cana-3871	205	29	241	241	NUM
cana-3871	205	30	.	.	PUNCT
cana-3871	206	1	[	[	X
cana-3871	206	2	8	8	NUM
cana-3871	206	3	]	]	PUNCT
cana-3871	206	4	redmond	redmond	PROPN
cana-3871	206	5	s.	s.	PROPN
cana-3871	206	6	p.	p.	PROPN
cana-3871	206	7	(	(	PUNCT
cana-3871	206	8	2003	2003	NUM
cana-3871	206	9	)	)	PUNCT
cana-3871	206	10	.	.	PUNCT
cana-3871	207	1	a	a	DET
cana-3871	207	2	deal	deal	NOUN
cana-3871	207	3	-	-	PUNCT
cana-3871	207	4	based	base	VERB
cana-3871	207	5	zero	zero	NUM
cana-3871	207	6	-	-	PUNCT
cana-3871	207	7	divisor	divisor	NOUN
cana-3871	207	8	graph	graph	NOUN
cana-3871	207	9	of	of	ADP
cana-3871	207	10	a	a	DET
cana-3871	207	11	commutative	commutative	ADJ
cana-3871	207	12	ring	ring	NOUN
cana-3871	207	13	,	,	PUNCT
cana-3871	207	14	comm	comm	NOUN
cana-3871	207	15	.	.	PUNCT
cana-3871	208	1	algebra	algebra	NOUN
cana-3871	208	2	,	,	PUNCT
cana-3871	208	3	31	31	NUM
cana-3871	208	4	,	,	PUNCT
cana-3871	208	5	4425–4443	4425–4443	NUM
cana-3871	208	6	.	.	PUNCT
cana-3871	209	1	[	[	X
cana-3871	209	2	9	9	NUM
cana-3871	209	3	]	]	X
cana-3871	209	4	akbari	akbari	PROPN
cana-3871	209	5	,	,	PUNCT
cana-3871	209	6	s.	s.	PROPN
cana-3871	209	7	,	,	PUNCT
cana-3871	209	8	and	and	CCONJ
cana-3871	209	9	a.	a.	NOUN
cana-3871	209	10	mohammadian	mohammadian	NOUN
cana-3871	209	11	.	.	PUNCT
cana-3871	210	1	“	"	PUNCT
cana-3871	210	2	on	on	ADP
cana-3871	210	3	the	the	DET
cana-3871	210	4	zero	zero	NUM
cana-3871	210	5	-	-	PUNCT
cana-3871	210	6	divisor	divisor	NOUN
cana-3871	210	7	graph	graph	NOUN
cana-3871	210	8	of	of	ADP
cana-3871	210	9	a	a	DET
cana-3871	210	10	commutative	commutative	ADJ
cana-3871	210	11	ring	ring	NOUN
cana-3871	210	12	.	.	PUNCT
cana-3871	210	13	”	"	PUNCT
cana-3871	210	14	journal	journal	NOUN
cana-3871	210	15	of	of	ADP
cana-3871	210	16	algebra	algebra	PROPN
cana-3871	210	17	274.2	274.2	NUM
cana-3871	210	18	(	(	PUNCT
cana-3871	210	19	2004	2004	NUM
cana-3871	210	20	):	):	PUNCT
cana-3871	210	21	847	847	NUM
cana-3871	210	22	-	-	SYM
cana-3871	210	23	855	855	NUM
cana-3871	210	24	.	.	PUNCT
cana-3871	211	1	[	[	X
cana-3871	211	2	10	10	NUM
cana-3871	211	3	]	]	PUNCT
cana-3871	211	4	j.	j.	PROPN
cana-3871	211	5	d.	d.	PROPN
cana-3871	211	6	lagrange	lagrange	PROPN
cana-3871	211	7	,	,	PUNCT
cana-3871	211	8	“	"	PUNCT
cana-3871	211	9	complemented	complemented	ADJ
cana-3871	211	10	zero	zero	NUM
cana-3871	211	11	-	-	PUNCT
cana-3871	211	12	divisor	divisor	NOUN
cana-3871	211	13	graphs	graph	NOUN
cana-3871	211	14	and	and	CCONJ
cana-3871	211	15	boolean	boolean	ADJ
cana-3871	211	16	rings	ring	NOUN
cana-3871	211	17	”	"	PUNCT
cana-3871	211	18	,	,	PUNCT
cana-3871	211	19	j.	j.	PROPN
cana-3871	211	20	algebra	algebra	PROPN
cana-3871	211	21	315:2	315:2	NUM
cana-3871	211	22	(	(	PUNCT
cana-3871	211	23	2007	2007	NUM
cana-3871	211	24	)	)	PUNCT
cana-3871	211	25	,	,	PUNCT
cana-3871	211	26	600–611	600–611	NUM
cana-3871	211	27	.	.	PUNCT
cana-3871	212	1	mr	mr	PROPN
cana-3871	212	2	2008h:13012	2008h:13012	NUM
cana-3871	212	3	zbl	zbl	PROPN
cana-3871	212	4	1133.13005	1133.13005	NUM
cana-3871	213	1	[	[	X
cana-3871	213	2	11	11	NUM
cana-3871	213	3	]	]	X
cana-3871	213	4	mohammadian	mohammadian	NOUN
cana-3871	213	5	,	,	PUNCT
cana-3871	213	6	ali	ali	PROPN
cana-3871	213	7	.	.	PUNCT
cana-3871	214	1	“	"	PUNCT
cana-3871	214	2	on	on	ADP
cana-3871	214	3	zero	zero	NUM
cana-3871	214	4	-	-	PUNCT
cana-3871	214	5	divisor	divisor	NOUN
cana-3871	214	6	graphs	graph	NOUN
cana-3871	214	7	of	of	ADP
cana-3871	214	8	boolean	boolean	ADJ
cana-3871	214	9	rings	ring	NOUN
cana-3871	214	10	.	.	PUNCT
cana-3871	214	11	”	"	PUNCT
cana-3871	214	12	pacific	pacific	PROPN
cana-3871	214	13	journal	journal	PROPN
cana-3871	214	14	of	of	ADP
cana-3871	214	15	mathematics	mathematics	PROPN
cana-3871	214	16	251.2	251.2	NUM
cana-3871	214	17	(	(	PUNCT
cana-3871	214	18	2011	2011	NUM
cana-3871	214	19	):	):	PUNCT
cana-3871	214	20	375383	375383	NUM
cana-3871	214	21	.	.	PUNCT
cana-3871	215	1	[	[	X
cana-3871	215	2	12	12	NUM
cana-3871	215	3	]	]	X
cana-3871	215	4	anderson	anderson	PROPN
cana-3871	215	5	,	,	PUNCT
cana-3871	215	6	david	david	PROPN
cana-3871	215	7	f.	f.	PROPN
cana-3871	215	8	,	,	PUNCT
cana-3871	215	9	and	and	CCONJ
cana-3871	215	10	john	john	PROPN
cana-3871	215	11	d.	d.	PROPN
cana-3871	215	12	lagrange	lagrange	PROPN
cana-3871	215	13	.	.	PUNCT
cana-3871	216	1	“	"	PUNCT
cana-3871	216	2	commutative	commutative	ADJ
cana-3871	216	3	boolean	boolean	ADJ
cana-3871	216	4	monoids	monoid	NOUN
cana-3871	216	5	,	,	PUNCT
cana-3871	216	6	reduced	reduced	ADJ
cana-3871	216	7	rings	ring	NOUN
cana-3871	216	8	,	,	PUNCT
cana-3871	216	9	and	and	CCONJ
cana-3871	216	10	the	the	DET
cana-3871	216	11	compressed	compressed	ADJ
cana-3871	216	12	zero	zero	NUM
cana-3871	216	13	-	-	PUNCT
cana-3871	216	14	divisor	divisor	NOUN
cana-3871	216	15	graph	graph	NOUN
cana-3871	216	16	.	.	PUNCT
cana-3871	216	17	”	"	PUNCT
cana-3871	216	18	journal	journal	NOUN
cana-3871	216	19	of	of	ADP
cana-3871	216	20	pure	pure	ADJ
cana-3871	216	21	and	and	CCONJ
cana-3871	216	22	applied	applied	ADJ
cana-3871	216	23	algebra	algebra	NOUN
cana-3871	216	24	216.7	216.7	NUM
cana-3871	216	25	(	(	PUNCT
cana-3871	216	26	2012	2012	NUM
cana-3871	216	27	):	):	PUNCT
cana-3871	216	28	1626	1626	NUM
cana-3871	216	29	-	-	SYM
cana-3871	216	30	1636	1636	NUM
cana-3871	216	31	.	.	PUNCT
cana-3871	217	1	[	[	X
cana-3871	217	2	13	13	NUM
cana-3871	217	3	]	]	X
cana-3871	217	4	lagrange	lagrange	NOUN
cana-3871	217	5	,	,	PUNCT
cana-3871	217	6	john	john	PROPN
cana-3871	217	7	d.	d.	PROPN
cana-3871	217	8	“	"	PUNCT
cana-3871	217	9	boolean	boolean	ADJ
cana-3871	217	10	rings	ring	NOUN
cana-3871	217	11	and	and	CCONJ
cana-3871	217	12	reciprocal	reciprocal	ADJ
cana-3871	217	13	eigenvalue	eigenvalue	PROPN
cana-3871	217	14	properties	property	NOUN
cana-3871	217	15	.	.	PUNCT
cana-3871	217	16	”	"	PUNCT
cana-3871	218	1	linear	linear	ADJ
cana-3871	218	2	algebra	algebra	NOUN
cana-3871	218	3	and	and	CCONJ
cana-3871	218	4	its	its	PRON
cana-3871	218	5	applications	application	NOUN
cana-3871	218	6	436.7	436.7	NUM
cana-3871	218	7	(	(	PUNCT
cana-3871	218	8	2012	2012	NUM
cana-3871	218	9	):	):	PUNCT
cana-3871	218	10	1863	1863	NUM
cana-3871	218	11	-	-	SYM
cana-3871	218	12	1871	1871	NUM
cana-3871	218	13	.	.	PUNCT
cana-3871	219	1	[	[	X
cana-3871	219	2	14	14	NUM
cana-3871	219	3	]	]	PUNCT
cana-3871	219	4	muneshwar	muneshwar	PROPN
cana-3871	219	5	,	,	PUNCT
cana-3871	219	6	r.	r.	PROPN
cana-3871	219	7	a.	a.	PROPN
cana-3871	219	8	,	,	PUNCT
cana-3871	219	9	s.	s.	PROPN
cana-3871	219	10	s.	s.	PROPN
cana-3871	219	11	agrawal	agrawal	PROPN
cana-3871	219	12	,	,	PUNCT
cana-3871	219	13	and	and	CCONJ
cana-3871	219	14	s.	s.	PROPN
cana-3871	219	15	g.	g.	PROPN
cana-3871	219	16	jakkewad	jakkewad	PROPN
cana-3871	219	17	.	.	PUNCT
cana-3871	220	1	“	"	PUNCT
cana-3871	220	2	some	some	DET
cana-3871	220	3	properties	property	NOUN
cana-3871	220	4	of	of	ADP
cana-3871	220	5	graph	graph	NOUN
cana-3871	220	6	of	of	ADP
cana-3871	220	7	a	a	DET
cana-3871	220	8	finite	finite	ADJ
cana-3871	220	9	group	group	NOUN
cana-3871	220	10	.	.	PUNCT
cana-3871	220	11	”	"	PUNCT
cana-3871	220	12	2278	2278	NUM
cana-3871	220	13	-	-	SYM
cana-3871	220	14	5728	5728	NUM
cana-3871	220	15	,	,	PUNCT
cana-3871	220	16	volume	volume	NOUN
cana-3871	220	17	10	10	NUM
cana-3871	220	18	,	,	PUNCT
cana-3871	220	19	(	(	PUNCT
cana-3871	220	20	nov	nov	PROPN
cana-3871	220	21	dec	dec	PROPN
cana-3871	220	22	.	.	PROPN
cana-3871	220	23	2014	2014	NUM
cana-3871	220	24	)	)	PUNCT
cana-3871	220	25	,	,	PUNCT
cana-3871	220	26	pp	pp	ADP
cana-3871	220	27	55	55	NUM
cana-3871	220	28	-	-	SYM
cana-3871	220	29	58	58	NUM
cana-3871	220	30	)	)	PUNCT
cana-3871	220	31	.	.	PUNCT
cana-3871	221	1	[	[	X
cana-3871	221	2	15	15	NUM
cana-3871	221	3	]	]	X
cana-3871	221	4	deepa	deepa	PROPN
cana-3871	221	5	sinha	sinha	NOUN
cana-3871	221	6	and	and	CCONJ
cana-3871	221	7	baleen	baleen	NOUN
cana-3871	221	8	kaur	kaur	NOUN
cana-3871	221	9	,	,	PUNCT
cana-3871	221	10	on	on	ADP
cana-3871	221	11	beck	beck	PROPN
cana-3871	221	12	’s	’s	PART
cana-3871	221	13	zero	zero	NUM
cana-3871	221	14	-	-	PUNCT
cana-3871	221	15	divisor	divisor	NOUN
cana-3871	221	16	graph	graph	NOUN
cana-3871	221	17	,	,	PUNCT
cana-3871	221	18	vol	vol	NOUN
cana-3871	221	19	.	.	PROPN
cana-3871	221	20	25	25	NUM
cana-3871	221	21	,	,	PUNCT
cana-3871	221	22	2019	2019	NUM
cana-3871	221	23	,	,	PUNCT
cana-3871	221	24	no	no	INTJ
cana-3871	221	25	.	.	NOUN
cana-3871	221	26	4	4	NUM
cana-3871	221	27	,	,	PUNCT
cana-3871	221	28	150–157	150–157	NUM
cana-3871	221	29	.	.	PUNCT
cana-3871	222	1	[	[	X
cana-3871	222	2	16	16	NUM
cana-3871	222	3	]	]	X
cana-3871	222	4	anderson	anderson	PROPN
cana-3871	222	5	,	,	PUNCT
cana-3871	222	6	david	david	PROPN
cana-3871	222	7	f.	f.	PROPN
cana-3871	222	8	,	,	PUNCT
cana-3871	222	9	and	and	CCONJ
cana-3871	222	10	grace	grace	NOUN
cana-3871	222	11	mcclurkin	mcclurkin	PROPN
cana-3871	222	12	.	.	PUNCT
cana-3871	223	1	“	"	PUNCT
cana-3871	223	2	generalizations	generalization	NOUN
cana-3871	223	3	of	of	ADP
cana-3871	223	4	the	the	DET
cana-3871	223	5	zero	zero	NUM
cana-3871	223	6	-	-	PUNCT
cana-3871	223	7	divisor	divisor	NOUN
cana-3871	223	8	graph	graph	NOUN
cana-3871	223	9	.	.	PUNCT
cana-3871	223	10	”	"	PUNCT
cana-3871	224	1	international	international	ADJ
cana-3871	224	2	electronic	electronic	ADJ
cana-3871	224	3	journal	journal	NOUN
cana-3871	224	4	of	of	ADP
cana-3871	224	5	algebra	algebra	PROPN
cana-3871	224	6	27.27	27.27	NUM
cana-3871	224	7	(	(	PUNCT
cana-3871	224	8	2020	2020	NUM
cana-3871	224	9	):	):	PUNCT
cana-3871	224	10	237	237	NUM
cana-3871	224	11	-	-	SYM
cana-3871	224	12	262	262	NUM
cana-3871	224	13	.	.	PUNCT
cana-3871	225	1	[	[	X
cana-3871	225	2	17	17	NUM
cana-3871	225	3	]	]	SYM
cana-3871	225	4	wu	wu	PROPN
cana-3871	225	5	,	,	PUNCT
cana-3871	225	6	tongsuo	tongsuo	PROPN
cana-3871	225	7	.	.	PUNCT
cana-3871	226	1	“	"	PUNCT
cana-3871	226	2	boolean	boolean	ADJ
cana-3871	226	3	graphs	graph	NOUN
cana-3871	226	4	-	-	PUNCT
cana-3871	226	5	a	a	DET
cana-3871	226	6	survey	survey	NOUN
cana-3871	226	7	.	.	PUNCT
cana-3871	226	8	”	"	PUNCT
cana-3871	227	1	ring	ring	NOUN
cana-3871	227	2	theory	theory	NOUN
cana-3871	227	3	2019	2019	NUM
cana-3871	227	4	:	:	PUNCT
cana-3871	227	5	proceedings	proceeding	NOUN
cana-3871	227	6	of	of	ADP
cana-3871	227	7	the	the	DET
cana-3871	227	8	eighth	eighth	ADJ
cana-3871	227	9	china	china	PROPN
cana-3871	227	10	–	–	PUNCT
cana-3871	227	11	japan	japan	PROPN
cana-3871	227	12	–	–	PUNCT
cana-3871	227	13	korea	korea	PROPN
cana-3871	227	14	international	international	ADJ
cana-3871	227	15	symposium	symposium	NOUN
cana-3871	227	16	on	on	ADP
cana-3871	227	17	ring	ring	NOUN
cana-3871	227	18	theory	theory	NOUN
cana-3871	227	19	2021	2021	NUM
cana-3871	227	20	.	.	PUNCT