id	sid	tid	token	lemma	pos
ejpam-3001	1	1	european	european	PROPN
ejpam-3001	1	2	journal	journal	PROPN
ejpam-3001	1	3	of	of	ADP
ejpam-3001	1	4	pure	pure	ADJ
ejpam-3001	1	5	and	and	CCONJ
ejpam-3001	1	6	applied	apply	VERB
ejpam-3001	1	7	mathematics	mathematic	NOUN
ejpam-3001	1	8	vol	vol	NOUN
ejpam-3001	1	9	.	.	PROPN
ejpam-3001	2	1	10	10	NUM
ejpam-3001	2	2	,	,	PUNCT
ejpam-3001	2	3	no	no	INTJ
ejpam-3001	2	4	.	.	NOUN
ejpam-3001	2	5	3	3	NUM
ejpam-3001	2	6	,	,	PUNCT
ejpam-3001	2	7	2017	2017	NUM
ejpam-3001	2	8	,	,	PUNCT
ejpam-3001	2	9	552	552	NUM
ejpam-3001	2	10	-	-	SYM
ejpam-3001	2	11	560	560	NUM
ejpam-3001	2	12	issn	issn	PROPN
ejpam-3001	2	13	1307	1307	NUM
ejpam-3001	2	14	-	-	SYM
ejpam-3001	2	15	5543	5543	NUM
ejpam-3001	2	16	–	–	PUNCT
ejpam-3001	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3001	2	18	published	publish	VERB
ejpam-3001	2	19	by	by	ADP
ejpam-3001	2	20	new	new	PROPN
ejpam-3001	2	21	york	york	PROPN
ejpam-3001	2	22	business	business	PROPN
ejpam-3001	2	23	global	global	ADJ
ejpam-3001	2	24	certain	certain	ADJ
ejpam-3001	2	25	classes	class	NOUN
ejpam-3001	2	26	of	of	ADP
ejpam-3001	2	27	fuzzy	fuzzy	ADJ
ejpam-3001	2	28	graphs	graph	NOUN
ejpam-3001	2	29	talal	talal	PROPN
ejpam-3001	2	30	al	al	PROPN
ejpam-3001	2	31	-	-	PUNCT
ejpam-3001	2	32	hawary	hawary	PROPN
ejpam-3001	2	33	department	department	NOUN
ejpam-3001	2	34	of	of	ADP
ejpam-3001	2	35	mathematics	mathematic	NOUN
ejpam-3001	2	36	,	,	PUNCT
ejpam-3001	2	37	faculty	faculty	NOUN
ejpam-3001	2	38	of	of	ADP
ejpam-3001	2	39	sciences	science	NOUN
ejpam-3001	2	40	,	,	PUNCT
ejpam-3001	2	41	yarmouk	yarmouk	PRON
ejpam-3001	2	42	university	university	NOUN
ejpam-3001	2	43	,	,	PUNCT
ejpam-3001	2	44	jordan	jordan	PROPN
ejpam-3001	2	45	abstract	abstract	PROPN
ejpam-3001	2	46	.	.	PUNCT
ejpam-3001	3	1	in	in	ADP
ejpam-3001	3	2	this	this	DET
ejpam-3001	3	3	paper	paper	NOUN
ejpam-3001	3	4	,	,	PUNCT
ejpam-3001	3	5	several	several	ADJ
ejpam-3001	3	6	classes	class	NOUN
ejpam-3001	3	7	of	of	ADP
ejpam-3001	3	8	fuzzy	fuzzy	ADJ
ejpam-3001	3	9	graphs	graph	NOUN
ejpam-3001	3	10	are	be	AUX
ejpam-3001	3	11	characterized	characterize	VERB
ejpam-3001	3	12	and	and	CCONJ
ejpam-3001	3	13	we	we	PRON
ejpam-3001	3	14	provide	provide	VERB
ejpam-3001	3	15	two	two	NUM
ejpam-3001	3	16	new	new	ADJ
ejpam-3001	3	17	operations	operation	NOUN
ejpam-3001	3	18	on	on	ADP
ejpam-3001	3	19	fuzzy	fuzzy	ADJ
ejpam-3001	3	20	graphs	graph	NOUN
ejpam-3001	3	21	;	;	PUNCT
ejpam-3001	3	22	namely	namely	ADV
ejpam-3001	3	23	parallel	parallel	ADJ
ejpam-3001	3	24	connection	connection	NOUN
ejpam-3001	3	25	and	and	CCONJ
ejpam-3001	3	26	series	series	NOUN
ejpam-3001	3	27	connection	connection	NOUN
ejpam-3001	3	28	.	.	PUNCT
ejpam-3001	4	1	we	we	PRON
ejpam-3001	4	2	show	show	VERB
ejpam-3001	4	3	that	that	SCONJ
ejpam-3001	4	4	parallel	parallel	ADJ
ejpam-3001	4	5	connection	connection	NOUN
ejpam-3001	4	6	and	and	CCONJ
ejpam-3001	4	7	series	series	NOUN
ejpam-3001	4	8	connection	connection	NOUN
ejpam-3001	4	9	of	of	ADP
ejpam-3001	4	10	balanced	balanced	ADJ
ejpam-3001	4	11	fuzzy	fuzzy	ADJ
ejpam-3001	4	12	graphs	graph	NOUN
ejpam-3001	4	13	need	need	AUX
ejpam-3001	4	14	not	not	PART
ejpam-3001	4	15	be	be	AUX
ejpam-3001	4	16	balanced	balance	VERB
ejpam-3001	4	17	and	and	CCONJ
ejpam-3001	4	18	they	they	PRON
ejpam-3001	4	19	are	be	AUX
ejpam-3001	4	20	balanced	balance	VERB
ejpam-3001	4	21	in	in	ADP
ejpam-3001	4	22	case	case	NOUN
ejpam-3001	4	23	the	the	DET
ejpam-3001	4	24	original	original	ADJ
ejpam-3001	4	25	graphs	graph	NOUN
ejpam-3001	4	26	are	be	AUX
ejpam-3001	4	27	induced	induce	VERB
ejpam-3001	4	28	by	by	ADP
ejpam-3001	4	29	cycles	cycle	NOUN
ejpam-3001	4	30	.	.	PUNCT
ejpam-3001	5	1	finally	finally	ADV
ejpam-3001	5	2	,	,	PUNCT
ejpam-3001	5	3	we	we	PRON
ejpam-3001	5	4	study	study	VERB
ejpam-3001	5	5	the	the	DET
ejpam-3001	5	6	notions	notion	NOUN
ejpam-3001	5	7	of	of	ADP
ejpam-3001	5	8	strong	strong	ADJ
ejpam-3001	5	9	and	and	CCONJ
ejpam-3001	5	10	complete	complete	ADJ
ejpam-3001	5	11	via	via	ADP
ejpam-3001	5	12	these	these	DET
ejpam-3001	5	13	operations	operation	NOUN
ejpam-3001	5	14	.	.	PUNCT
ejpam-3001	6	1	2010	2010	NUM
ejpam-3001	6	2	mathematics	mathematic	NOUN
ejpam-3001	6	3	subject	subject	NOUN
ejpam-3001	6	4	classifications	classification	NOUN
ejpam-3001	6	5	:	:	PUNCT
ejpam-3001	6	6	05c72	05c72	NOUN
ejpam-3001	6	7	1	1	X
ejpam-3001	6	8	.	.	X
ejpam-3001	6	9	introduction	introduction	NOUN
ejpam-3001	6	10	a	a	DET
ejpam-3001	6	11	graph	graph	NOUN
ejpam-3001	6	12	is	be	AUX
ejpam-3001	6	13	a	a	DET
ejpam-3001	6	14	nice	nice	ADJ
ejpam-3001	6	15	way	way	NOUN
ejpam-3001	6	16	of	of	ADP
ejpam-3001	6	17	representing	represent	VERB
ejpam-3001	6	18	information	information	NOUN
ejpam-3001	6	19	involving	involve	VERB
ejpam-3001	6	20	relationships	relationship	NOUN
ejpam-3001	6	21	between	between	ADP
ejpam-3001	6	22	objects	object	NOUN
ejpam-3001	6	23	where	where	SCONJ
ejpam-3001	6	24	objects	object	NOUN
ejpam-3001	6	25	are	be	AUX
ejpam-3001	6	26	represented	represent	VERB
ejpam-3001	6	27	by	by	ADP
ejpam-3001	6	28	vertices	vertex	NOUN
ejpam-3001	6	29	and	and	CCONJ
ejpam-3001	6	30	relations	relation	NOUN
ejpam-3001	6	31	by	by	ADP
ejpam-3001	6	32	edges	edge	NOUN
ejpam-3001	6	33	.	.	PUNCT
ejpam-3001	7	1	when	when	SCONJ
ejpam-3001	7	2	there	there	PRON
ejpam-3001	7	3	is	be	VERB
ejpam-3001	7	4	vagueness	vagueness	NOUN
ejpam-3001	7	5	in	in	ADP
ejpam-3001	7	6	the	the	DET
ejpam-3001	7	7	description	description	NOUN
ejpam-3001	7	8	of	of	ADP
ejpam-3001	7	9	the	the	DET
ejpam-3001	7	10	objects	object	NOUN
ejpam-3001	7	11	or	or	CCONJ
ejpam-3001	7	12	relationships	relationship	NOUN
ejpam-3001	7	13	,	,	PUNCT
ejpam-3001	7	14	it	it	PRON
ejpam-3001	7	15	is	be	AUX
ejpam-3001	7	16	natural	natural	ADJ
ejpam-3001	7	17	that	that	SCONJ
ejpam-3001	7	18	we	we	PRON
ejpam-3001	7	19	think	think	VERB
ejpam-3001	7	20	of	of	ADP
ejpam-3001	7	21	it	it	PRON
ejpam-3001	7	22	as	as	SCONJ
ejpam-3001	7	23	what	what	PRON
ejpam-3001	7	24	is	be	AUX
ejpam-3001	7	25	called	call	VERB
ejpam-3001	7	26	’	'	PUNCT
ejpam-3001	7	27	fuzzy	fuzzy	ADJ
ejpam-3001	7	28	graph	graph	NOUN
ejpam-3001	7	29	model	model	NOUN
ejpam-3001	7	30	’	'	PUNCT
ejpam-3001	7	31	.	.	PUNCT
ejpam-3001	8	1	applications	application	NOUN
ejpam-3001	8	2	of	of	ADP
ejpam-3001	8	3	fuzzy	fuzzy	ADJ
ejpam-3001	8	4	relations	relation	NOUN
ejpam-3001	8	5	are	be	AUX
ejpam-3001	8	6	widespread	widespread	ADJ
ejpam-3001	8	7	and	and	CCONJ
ejpam-3001	8	8	important	important	ADJ
ejpam-3001	8	9	in	in	ADP
ejpam-3001	8	10	many	many	ADJ
ejpam-3001	8	11	fields	field	NOUN
ejpam-3001	8	12	;	;	PUNCT
ejpam-3001	8	13	especially	especially	ADV
ejpam-3001	8	14	in	in	ADP
ejpam-3001	8	15	the	the	DET
ejpam-3001	8	16	field	field	NOUN
ejpam-3001	8	17	of	of	ADP
ejpam-3001	8	18	clustering	cluster	VERB
ejpam-3001	8	19	analysis	analysis	NOUN
ejpam-3001	8	20	,	,	PUNCT
ejpam-3001	8	21	neural	neural	ADJ
ejpam-3001	8	22	networks	network	NOUN
ejpam-3001	8	23	,	,	PUNCT
ejpam-3001	8	24	computer	computer	NOUN
ejpam-3001	8	25	networks	network	NOUN
ejpam-3001	8	26	,	,	PUNCT
ejpam-3001	8	27	pattern	pattern	NOUN
ejpam-3001	8	28	recognition	recognition	NOUN
ejpam-3001	8	29	,	,	PUNCT
ejpam-3001	8	30	decision	decision	NOUN
ejpam-3001	8	31	making	making	NOUN
ejpam-3001	8	32	and	and	CCONJ
ejpam-3001	8	33	expert	expert	NOUN
ejpam-3001	8	34	systems	system	NOUN
ejpam-3001	8	35	.	.	PUNCT
ejpam-3001	9	1	in	in	ADP
ejpam-3001	9	2	each	each	PRON
ejpam-3001	9	3	of	of	ADP
ejpam-3001	9	4	these	these	PRON
ejpam-3001	9	5	,	,	PUNCT
ejpam-3001	9	6	the	the	DET
ejpam-3001	9	7	basic	basic	ADJ
ejpam-3001	9	8	mathematical	mathematical	ADJ
ejpam-3001	9	9	structure	structure	NOUN
ejpam-3001	9	10	is	be	AUX
ejpam-3001	9	11	that	that	PRON
ejpam-3001	9	12	of	of	ADP
ejpam-3001	9	13	a	a	DET
ejpam-3001	9	14	fuzzy	fuzzy	ADJ
ejpam-3001	9	15	graph	graph	NOUN
ejpam-3001	9	16	.	.	PUNCT
ejpam-3001	10	1	the	the	DET
ejpam-3001	10	2	notion	notion	NOUN
ejpam-3001	10	3	of	of	ADP
ejpam-3001	10	4	fuzzy	fuzzy	ADJ
ejpam-3001	10	5	relation	relation	NOUN
ejpam-3001	10	6	was	be	AUX
ejpam-3001	10	7	introduced	introduce	VERB
ejpam-3001	10	8	by	by	ADP
ejpam-3001	10	9	zadeh	zadeh	PROPN
ejpam-3001	11	1	[	[	X
ejpam-3001	11	2	17	17	NUM
ejpam-3001	11	3	]	]	PUNCT
ejpam-3001	11	4	in	in	ADP
ejpam-3001	11	5	his	his	PRON
ejpam-3001	11	6	landmark	landmark	NOUN
ejpam-3001	11	7	paper	paper	NOUN
ejpam-3001	11	8	”	"	PUNCT
ejpam-3001	11	9	fuzzy	fuzzy	ADJ
ejpam-3001	11	10	sets	set	NOUN
ejpam-3001	11	11	”	"	PUNCT
ejpam-3001	11	12	in	in	ADP
ejpam-3001	11	13	1965	1965	NUM
ejpam-3001	11	14	.	.	PUNCT
ejpam-3001	12	1	fuzzy	fuzzy	ADJ
ejpam-3001	12	2	graph	graph	NOUN
ejpam-3001	12	3	and	and	CCONJ
ejpam-3001	12	4	several	several	ADJ
ejpam-3001	12	5	fuzzy	fuzzy	ADJ
ejpam-3001	12	6	analogs	analog	NOUN
ejpam-3001	12	7	of	of	ADP
ejpam-3001	12	8	graph	graph	NOUN
ejpam-3001	12	9	theoretic	theoretic	ADJ
ejpam-3001	12	10	concepts	concept	NOUN
ejpam-3001	12	11	were	be	AUX
ejpam-3001	12	12	introduced	introduce	VERB
ejpam-3001	12	13	by	by	ADP
ejpam-3001	12	14	rosenfeld	rosenfeld	PROPN
ejpam-3001	12	15	[	[	X
ejpam-3001	12	16	15	15	NUM
ejpam-3001	12	17	]	]	PUNCT
ejpam-3001	12	18	in	in	ADP
ejpam-3001	12	19	1975	1975	NUM
ejpam-3001	12	20	.	.	PUNCT
ejpam-3001	13	1	after	after	ADP
ejpam-3001	13	2	that	that	PRON
ejpam-3001	13	3	,	,	PUNCT
ejpam-3001	13	4	the	the	DET
ejpam-3001	13	5	theory	theory	NOUN
ejpam-3001	13	6	of	of	ADP
ejpam-3001	13	7	fuzzy	fuzzy	ADJ
ejpam-3001	13	8	graph	graph	NOUN
ejpam-3001	13	9	started	start	VERB
ejpam-3001	13	10	to	to	ADP
ejpam-3001	13	11	finding	find	VERB
ejpam-3001	13	12	an	an	DET
ejpam-3001	13	13	increasing	increase	VERB
ejpam-3001	13	14	number	number	NOUN
ejpam-3001	13	15	of	of	ADP
ejpam-3001	13	16	applications	application	NOUN
ejpam-3001	13	17	in	in	ADP
ejpam-3001	13	18	several	several	ADJ
ejpam-3001	13	19	fields	field	NOUN
ejpam-3001	13	20	.	.	PUNCT
ejpam-3001	14	1	mordeson	mordeson	NOUN
ejpam-3001	14	2	and	and	CCONJ
ejpam-3001	14	3	peng	peng	PROPN
ejpam-3001	15	1	[	[	X
ejpam-3001	15	2	9	9	NUM
ejpam-3001	15	3	]	]	PUNCT
ejpam-3001	15	4	defined	define	VERB
ejpam-3001	15	5	the	the	DET
ejpam-3001	15	6	concept	concept	NOUN
ejpam-3001	15	7	of	of	ADP
ejpam-3001	15	8	fuzzy	fuzzy	ADJ
ejpam-3001	15	9	graph	graph	NOUN
ejpam-3001	15	10	complement	complement	NOUN
ejpam-3001	15	11	and	and	CCONJ
ejpam-3001	15	12	introduced	introduce	VERB
ejpam-3001	15	13	several	several	ADJ
ejpam-3001	15	14	operations	operation	NOUN
ejpam-3001	15	15	on	on	ADP
ejpam-3001	15	16	fuzzy	fuzzy	ADJ
ejpam-3001	15	17	graphs	graph	NOUN
ejpam-3001	15	18	.	.	PUNCT
ejpam-3001	16	1	in	in	ADP
ejpam-3001	16	2	[	[	X
ejpam-3001	16	3	16	16	NUM
ejpam-3001	16	4	]	]	PUNCT
ejpam-3001	16	5	,	,	PUNCT
ejpam-3001	16	6	the	the	DET
ejpam-3001	16	7	definition	definition	NOUN
ejpam-3001	16	8	of	of	ADP
ejpam-3001	16	9	complement	complement	NOUN
ejpam-3001	16	10	of	of	ADP
ejpam-3001	16	11	a	a	DET
ejpam-3001	16	12	fuzzy	fuzzy	ADJ
ejpam-3001	16	13	graph	graph	NOUN
ejpam-3001	16	14	was	be	AUX
ejpam-3001	16	15	modified	modify	VERB
ejpam-3001	16	16	to	to	PART
ejpam-3001	16	17	agree	agree	VERB
ejpam-3001	16	18	with	with	ADP
ejpam-3001	16	19	the	the	DET
ejpam-3001	16	20	classical	classical	ADJ
ejpam-3001	16	21	graph	graph	NOUN
ejpam-3001	16	22	case	case	NOUN
ejpam-3001	16	23	.	.	PUNCT
ejpam-3001	17	1	moreover	moreover	ADV
ejpam-3001	17	2	,	,	PUNCT
ejpam-3001	17	3	some	some	DET
ejpam-3001	17	4	properties	property	NOUN
ejpam-3001	17	5	of	of	ADP
ejpam-3001	17	6	selfcomplementary	selfcomplementary	ADJ
ejpam-3001	17	7	fuzzy	fuzzy	ADJ
ejpam-3001	17	8	graphs	graph	NOUN
ejpam-3001	17	9	and	and	CCONJ
ejpam-3001	17	10	complements	complement	NOUN
ejpam-3001	17	11	of	of	ADP
ejpam-3001	17	12	several	several	ADJ
ejpam-3001	17	13	operations	operation	NOUN
ejpam-3001	17	14	of	of	ADP
ejpam-3001	17	15	fuzzy	fuzzy	ADJ
ejpam-3001	17	16	graphs	graph	NOUN
ejpam-3001	17	17	that	that	PRON
ejpam-3001	17	18	were	be	AUX
ejpam-3001	17	19	introduced	introduce	VERB
ejpam-3001	17	20	in	in	ADP
ejpam-3001	17	21	[	[	X
ejpam-3001	17	22	9	9	NUM
ejpam-3001	17	23	]	]	PUNCT
ejpam-3001	17	24	were	be	AUX
ejpam-3001	17	25	discussed	discuss	VERB
ejpam-3001	17	26	.	.	PUNCT
ejpam-3001	18	1	al	al	PROPN
ejpam-3001	18	2	-	-	PUNCT
ejpam-3001	18	3	hawary	hawary	PROPN
ejpam-3001	18	4	[	[	X
ejpam-3001	18	5	1	1	NUM
ejpam-3001	18	6	]	]	PUNCT
ejpam-3001	18	7	introduced	introduce	VERB
ejpam-3001	18	8	and	and	CCONJ
ejpam-3001	18	9	explored	explore	VERB
ejpam-3001	18	10	the	the	DET
ejpam-3001	18	11	new	new	ADJ
ejpam-3001	18	12	notion	notion	NOUN
ejpam-3001	18	13	of	of	ADP
ejpam-3001	18	14	balanced	balanced	ADJ
ejpam-3001	18	15	fuzzy	fuzzy	ADJ
ejpam-3001	18	16	graphs	graph	NOUN
ejpam-3001	18	17	and	and	CCONJ
ejpam-3001	18	18	several	several	ADJ
ejpam-3001	18	19	new	new	ADJ
ejpam-3001	18	20	operations	operation	NOUN
ejpam-3001	18	21	.	.	PUNCT
ejpam-3001	19	1	after	after	ADP
ejpam-3001	19	2	that	that	PRON
ejpam-3001	19	3	,	,	PUNCT
ejpam-3001	19	4	balanced	balanced	ADJ
ejpam-3001	19	5	concept	concept	NOUN
ejpam-3001	19	6	was	be	AUX
ejpam-3001	19	7	studied	study	VERB
ejpam-3001	19	8	by	by	ADP
ejpam-3001	19	9	many	many	ADJ
ejpam-3001	19	10	authors	author	NOUN
ejpam-3001	19	11	.	.	PUNCT
ejpam-3001	20	1	the	the	DET
ejpam-3001	20	2	idea	idea	NOUN
ejpam-3001	20	3	of	of	ADP
ejpam-3001	20	4	balanced	balanced	ADJ
ejpam-3001	20	5	came	come	VERB
ejpam-3001	20	6	from	from	ADP
ejpam-3001	20	7	matroids	matroid	NOUN
ejpam-3001	20	8	,	,	PUNCT
ejpam-3001	20	9	see	see	VERB
ejpam-3001	20	10	[	[	X
ejpam-3001	20	11	2	2	NUM
ejpam-3001	20	12	,	,	PUNCT
ejpam-3001	20	13	3	3	NUM
ejpam-3001	20	14	,	,	PUNCT
ejpam-3001	20	15	4	4	NUM
ejpam-3001	20	16	,	,	PUNCT
ejpam-3001	20	17	6	6	NUM
ejpam-3001	20	18	]	]	PUNCT
ejpam-3001	20	19	.	.	PUNCT
ejpam-3001	21	1	email	email	NOUN
ejpam-3001	21	2	addresses	address	NOUN
ejpam-3001	21	3	:	:	PUNCT
ejpam-3001	21	4	talalhawary@yahoo.com	talalhawary@yahoo.com	X
ejpam-3001	21	5	(	(	PUNCT
ejpam-3001	21	6	t.	t.	NOUN
ejpam-3001	21	7	a.	a.	PROPN
ejpam-3001	21	8	hawary	hawary	PROPN
ejpam-3001	21	9	)	)	PUNCT
ejpam-3001	22	1	this	this	DET
ejpam-3001	22	2	work	work	NOUN
ejpam-3001	22	3	has	have	AUX
ejpam-3001	22	4	been	be	AUX
ejpam-3001	22	5	done	do	VERB
ejpam-3001	22	6	during	during	ADP
ejpam-3001	22	7	the	the	DET
ejpam-3001	22	8	author	author	NOUN
ejpam-3001	22	9	’s	’s	PART
ejpam-3001	22	10	sabbatical	sabbatical	ADJ
ejpam-3001	22	11	leave	leave	NOUN
ejpam-3001	22	12	at	at	ADP
ejpam-3001	22	13	jordan	jordan	PROPN
ejpam-3001	22	14	university	university	PROPN
ejpam-3001	22	15	of	of	ADP
ejpam-3001	22	16	science	science	NOUN
ejpam-3001	22	17	and	and	CCONJ
ejpam-3001	22	18	technology	technology	NOUN
ejpam-3001	22	19	---	---	PUNCT
ejpam-3001	22	20	jordan	jordan	PROPN
ejpam-3001	22	21	.	.	PUNCT
ejpam-3001	23	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3001	24	1	552	552	NUM
ejpam-3001	24	2	c	c	X
ejpam-3001	24	3	©	©	PROPN
ejpam-3001	24	4	2017	2017	NUM
ejpam-3001	24	5	ejpam	ejpam	VERB
ejpam-3001	24	6	all	all	DET
ejpam-3001	24	7	rights	right	NOUN
ejpam-3001	24	8	reserved	reserve	VERB
ejpam-3001	24	9	.	.	PUNCT
ejpam-3001	25	1	t.	t.	NOUN
ejpam-3001	25	2	a.	a.	PROPN
ejpam-3001	25	3	hawary	hawary	PROPN
ejpam-3001	25	4	/	/	SYM
ejpam-3001	25	5	eur	eur	PROPN
ejpam-3001	25	6	.	.	PUNCT
ejpam-3001	26	1	j.	j.	PROPN
ejpam-3001	26	2	pure	pure	PROPN
ejpam-3001	26	3	appl	appl	PROPN
ejpam-3001	26	4	.	.	PROPN
ejpam-3001	26	5	math	math	PROPN
ejpam-3001	26	6	,	,	PUNCT
ejpam-3001	26	7	10	10	NUM
ejpam-3001	26	8	(	(	PUNCT
ejpam-3001	26	9	3	3	NUM
ejpam-3001	26	10	)	)	PUNCT
ejpam-3001	26	11	(	(	PUNCT
ejpam-3001	26	12	2017	2017	NUM
ejpam-3001	26	13	)	)	PUNCT
ejpam-3001	26	14	,	,	PUNCT
ejpam-3001	26	15	552	552	NUM
ejpam-3001	26	16	-	-	SYM
ejpam-3001	26	17	560	560	NUM
ejpam-3001	26	18	553	553	NUM
ejpam-3001	26	19	for	for	ADP
ejpam-3001	26	20	a	a	DET
ejpam-3001	26	21	complete	complete	ADJ
ejpam-3001	26	22	background	background	NOUN
ejpam-3001	26	23	on	on	ADP
ejpam-3001	26	24	the	the	DET
ejpam-3001	26	25	previous	previous	ADJ
ejpam-3001	26	26	notions	notion	NOUN
ejpam-3001	26	27	and	and	CCONJ
ejpam-3001	26	28	the	the	DET
ejpam-3001	26	29	following	following	ADJ
ejpam-3001	26	30	ones	one	NOUN
ejpam-3001	26	31	,	,	PUNCT
ejpam-3001	26	32	the	the	DET
ejpam-3001	26	33	reader	reader	NOUN
ejpam-3001	26	34	is	be	AUX
ejpam-3001	26	35	referred	refer	VERB
ejpam-3001	26	36	to	to	ADP
ejpam-3001	26	37	[	[	X
ejpam-3001	26	38	1	1	NUM
ejpam-3001	26	39	,	,	PUNCT
ejpam-3001	26	40	5	5	NUM
ejpam-3001	26	41	,	,	PUNCT
ejpam-3001	26	42	7	7	NUM
ejpam-3001	26	43	,	,	PUNCT
ejpam-3001	26	44	9	9	NUM
ejpam-3001	26	45	,	,	PUNCT
ejpam-3001	26	46	10	10	NUM
ejpam-3001	26	47	,	,	PUNCT
ejpam-3001	26	48	11	11	NUM
ejpam-3001	26	49	,	,	PUNCT
ejpam-3001	26	50	12	12	NUM
ejpam-3001	26	51	,	,	PUNCT
ejpam-3001	26	52	13	13	NUM
ejpam-3001	26	53	,	,	PUNCT
ejpam-3001	26	54	14	14	NUM
ejpam-3001	26	55	,	,	PUNCT
ejpam-3001	26	56	15	15	NUM
ejpam-3001	26	57	,	,	PUNCT
ejpam-3001	26	58	16	16	NUM
ejpam-3001	26	59	]	]	PUNCT
ejpam-3001	26	60	.	.	PUNCT
ejpam-3001	27	1	a	a	DET
ejpam-3001	27	2	fuzzy	fuzzy	ADJ
ejpam-3001	27	3	subset	subset	NOUN
ejpam-3001	27	4	of	of	ADP
ejpam-3001	27	5	a	a	DET
ejpam-3001	27	6	non	non	ADJ
ejpam-3001	27	7	-	-	ADJ
ejpam-3001	27	8	empty	empty	ADJ
ejpam-3001	27	9	set	set	ADJ
ejpam-3001	27	10	v	v	NOUN
ejpam-3001	27	11	is	be	AUX
ejpam-3001	27	12	a	a	DET
ejpam-3001	27	13	mapping	mapping	NOUN
ejpam-3001	27	14	σ	σ	NOUN
ejpam-3001	27	15	:	:	PUNCT
ejpam-3001	27	16	v	v	X
ejpam-3001	27	17	→	→	SYM
ejpam-3001	27	18	[	[	X
ejpam-3001	27	19	0	0	NUM
ejpam-3001	27	20	,	,	PUNCT
ejpam-3001	27	21	1	1	NUM
ejpam-3001	27	22	]	]	PUNCT
ejpam-3001	27	23	and	and	CCONJ
ejpam-3001	27	24	a	a	DET
ejpam-3001	27	25	fuzzy	fuzzy	ADJ
ejpam-3001	27	26	relation	relation	NOUN
ejpam-3001	27	27	µ	µ	X
ejpam-3001	27	28	on	on	ADP
ejpam-3001	27	29	a	a	DET
ejpam-3001	27	30	fuzzy	fuzzy	ADJ
ejpam-3001	27	31	subset	subset	NOUN
ejpam-3001	27	32	σ	σ	NOUN
ejpam-3001	27	33	,	,	PUNCT
ejpam-3001	27	34	is	be	AUX
ejpam-3001	27	35	a	a	DET
ejpam-3001	27	36	fuzzy	fuzzy	ADJ
ejpam-3001	27	37	subset	subset	NOUN
ejpam-3001	27	38	of	of	ADP
ejpam-3001	27	39	v	v	NUM
ejpam-3001	27	40	×	×	NOUN
ejpam-3001	27	41	v.	v.	CCONJ
ejpam-3001	27	42	all	all	PRON
ejpam-3001	27	43	throughout	throughout	ADP
ejpam-3001	27	44	this	this	DET
ejpam-3001	27	45	paper	paper	NOUN
ejpam-3001	27	46	,	,	PUNCT
ejpam-3001	27	47	we	we	PRON
ejpam-3001	27	48	assume	assume	VERB
ejpam-3001	27	49	that	that	SCONJ
ejpam-3001	27	50	σ	σ	PROPN
ejpam-3001	27	51	is	be	AUX
ejpam-3001	27	52	reflexive	reflexive	ADJ
ejpam-3001	27	53	,	,	PUNCT
ejpam-3001	27	54	µ	µ	PRON
ejpam-3001	27	55	is	be	AUX
ejpam-3001	27	56	symmetric	symmetric	ADJ
ejpam-3001	27	57	and	and	CCONJ
ejpam-3001	27	58	v	v	NOUN
ejpam-3001	27	59	is	be	AUX
ejpam-3001	27	60	finite	finite	ADJ
ejpam-3001	27	61	.	.	PUNCT
ejpam-3001	28	1	definition	definition	NOUN
ejpam-3001	28	2	1	1	NUM
ejpam-3001	28	3	.	.	PUNCT
ejpam-3001	29	1	[	[	X
ejpam-3001	29	2	15	15	NUM
ejpam-3001	29	3	]	]	X
ejpam-3001	29	4	a	a	DET
ejpam-3001	29	5	fuzzy	fuzzy	ADJ
ejpam-3001	29	6	graph	graph	NOUN
ejpam-3001	29	7	with	with	ADP
ejpam-3001	29	8	v	v	NOUN
ejpam-3001	29	9	as	as	ADP
ejpam-3001	29	10	the	the	DET
ejpam-3001	29	11	underlying	underlying	ADJ
ejpam-3001	29	12	set	set	NOUN
ejpam-3001	29	13	is	be	AUX
ejpam-3001	29	14	a	a	DET
ejpam-3001	29	15	pair	pair	NOUN
ejpam-3001	29	16	g	g	NOUN
ejpam-3001	29	17	:	:	PUNCT
ejpam-3001	29	18	(	(	PUNCT
ejpam-3001	29	19	σ	σ	PROPN
ejpam-3001	29	20	,	,	PUNCT
ejpam-3001	29	21	µ	µ	NOUN
ejpam-3001	29	22	)	)	PUNCT
ejpam-3001	29	23	where	where	SCONJ
ejpam-3001	29	24	σ	σ	NOUN
ejpam-3001	29	25	:	:	PUNCT
ejpam-3001	29	26	v	v	X
ejpam-3001	29	27	→	→	SYM
ejpam-3001	29	28	[	[	X
ejpam-3001	29	29	0	0	NUM
ejpam-3001	29	30	,	,	PUNCT
ejpam-3001	29	31	1	1	NUM
ejpam-3001	29	32	]	]	PUNCT
ejpam-3001	29	33	is	be	AUX
ejpam-3001	29	34	a	a	DET
ejpam-3001	29	35	fuzzy	fuzzy	ADJ
ejpam-3001	29	36	subset	subset	NOUN
ejpam-3001	29	37	and	and	CCONJ
ejpam-3001	29	38	µ	µ	X
ejpam-3001	29	39	:	:	PUNCT
ejpam-3001	29	40	v	v	NUM
ejpam-3001	29	41	×	×	NOUN
ejpam-3001	29	42	v	v	NOUN
ejpam-3001	29	43	→	→	SYM
ejpam-3001	29	44	[	[	X
ejpam-3001	29	45	0	0	NUM
ejpam-3001	29	46	,	,	PUNCT
ejpam-3001	29	47	1	1	NUM
ejpam-3001	29	48	]	]	PUNCT
ejpam-3001	29	49	is	be	AUX
ejpam-3001	29	50	a	a	DET
ejpam-3001	29	51	fuzzy	fuzzy	ADJ
ejpam-3001	29	52	relation	relation	NOUN
ejpam-3001	29	53	on	on	ADP
ejpam-3001	29	54	σ	σ	NUM
ejpam-3001	29	55	such	such	ADJ
ejpam-3001	29	56	that	that	SCONJ
ejpam-3001	29	57	µ(x	µ(x	VERB
ejpam-3001	29	58	,	,	PUNCT
ejpam-3001	29	59	y	y	NOUN
ejpam-3001	29	60	)	)	PUNCT
ejpam-3001	29	61	≤	≤	NUM
ejpam-3001	29	62	σ(x)∧	σ(x)∧	NOUN
ejpam-3001	29	63	σ(y	σ(y	NOUN
ejpam-3001	29	64	)	)	PUNCT
ejpam-3001	29	65	for	for	ADP
ejpam-3001	29	66	all	all	DET
ejpam-3001	29	67	x	x	NOUN
ejpam-3001	29	68	,	,	PUNCT
ejpam-3001	29	69	y	y	PROPN
ejpam-3001	29	70	∈	∈	PROPN
ejpam-3001	29	71	v	v	NOUN
ejpam-3001	29	72	,	,	PUNCT
ejpam-3001	29	73	where	where	SCONJ
ejpam-3001	29	74	∧	∧	PROPN
ejpam-3001	29	75	stands	stand	VERB
ejpam-3001	29	76	for	for	ADP
ejpam-3001	29	77	minimum	minimum	NOUN
ejpam-3001	29	78	.	.	PUNCT
ejpam-3001	30	1	the	the	DET
ejpam-3001	30	2	underlying	underlie	VERB
ejpam-3001	30	3	crisp	crisp	ADJ
ejpam-3001	30	4	graph	graph	NOUN
ejpam-3001	30	5	of	of	ADP
ejpam-3001	30	6	g	g	PROPN
ejpam-3001	30	7	is	be	AUX
ejpam-3001	30	8	denoted	denote	VERB
ejpam-3001	30	9	by	by	ADP
ejpam-3001	30	10	g∗	g∗	PROPN
ejpam-3001	30	11	:	:	PUNCT
ejpam-3001	30	12	(	(	PUNCT
ejpam-3001	30	13	σ∗	σ∗	X
ejpam-3001	30	14	,	,	PUNCT
ejpam-3001	30	15	µ∗	µ∗	PROPN
ejpam-3001	30	16	)	)	PUNCT
ejpam-3001	30	17	where	where	SCONJ
ejpam-3001	30	18	σ∗	σ∗	NOUN
ejpam-3001	30	19	=	=	SYM
ejpam-3001	30	20	sup	sup	NOUN
ejpam-3001	30	21	p(σ	p(σ	NOUN
ejpam-3001	30	22	)	)	PUNCT
ejpam-3001	30	23	=	=	PRON
ejpam-3001	31	1	{	{	PUNCT
ejpam-3001	31	2	x	x	PUNCT
ejpam-3001	31	3	∈	∈	PROPN
ejpam-3001	31	4	v	v	NOUN
ejpam-3001	31	5	:	:	PUNCT
ejpam-3001	31	6	σ(x	σ(x	PROPN
ejpam-3001	31	7	)	)	PUNCT
ejpam-3001	31	8	>	>	X
ejpam-3001	31	9	0	0	X
ejpam-3001	31	10	}	}	PUNCT
ejpam-3001	31	11	and	and	CCONJ
ejpam-3001	31	12	µ∗	µ∗	VERB
ejpam-3001	31	13	=	=	SYM
ejpam-3001	31	14	sup	sup	NOUN
ejpam-3001	31	15	p(µ	p(µ	NOUN
ejpam-3001	31	16	)	)	PUNCT
ejpam-3001	31	17	=	=	PRON
ejpam-3001	31	18	{	{	PUNCT
ejpam-3001	31	19	(	(	PUNCT
ejpam-3001	31	20	x	x	NOUN
ejpam-3001	31	21	,	,	PUNCT
ejpam-3001	31	22	y	y	NOUN
ejpam-3001	31	23	)	)	PUNCT
ejpam-3001	31	24	∈	∈	PROPN
ejpam-3001	31	25	v	v	ADP
ejpam-3001	31	26	×	×	NOUN
ejpam-3001	31	27	v	v	NOUN
ejpam-3001	31	28	:	:	PUNCT
ejpam-3001	31	29	µ(x	µ(x	NUM
ejpam-3001	31	30	,	,	PUNCT
ejpam-3001	31	31	y	y	NOUN
ejpam-3001	31	32	)	)	PUNCT
ejpam-3001	31	33	>	>	X
ejpam-3001	31	34	0}.h	0}.h	PUNCT
ejpam-3001	32	1	=	=	PUNCT
ejpam-3001	32	2	(	(	PUNCT
ejpam-3001	32	3	σ′	σ′	PROPN
ejpam-3001	32	4	,	,	PUNCT
ejpam-3001	32	5	µ′	µ′	NUM
ejpam-3001	32	6	)	)	PUNCT
ejpam-3001	32	7	is	be	AUX
ejpam-3001	32	8	a	a	DET
ejpam-3001	32	9	fuzzy	fuzzy	ADJ
ejpam-3001	32	10	subgraph	subgraph	NOUN
ejpam-3001	32	11	of	of	ADP
ejpam-3001	32	12	g	g	PROPN
ejpam-3001	32	13	if	if	SCONJ
ejpam-3001	32	14	there	there	PRON
ejpam-3001	32	15	exists	exist	VERB
ejpam-3001	32	16	x	x	X
ejpam-3001	32	17	⊆	⊆	NUM
ejpam-3001	32	18	v	v	ADP
ejpam-3001	32	19	such	such	ADJ
ejpam-3001	32	20	that	that	PRON
ejpam-3001	32	21	,	,	PUNCT
ejpam-3001	32	22	σ′	σ′	PROPN
ejpam-3001	32	23	:	:	PUNCT
ejpam-3001	32	24	x	x	X
ejpam-3001	32	25	→	→	PUNCT
ejpam-3001	33	1	[	[	X
ejpam-3001	33	2	0	0	NUM
ejpam-3001	33	3	,	,	PUNCT
ejpam-3001	33	4	1	1	NUM
ejpam-3001	33	5	]	]	PUNCT
ejpam-3001	33	6	is	be	AUX
ejpam-3001	33	7	a	a	DET
ejpam-3001	33	8	fuzzy	fuzzy	ADJ
ejpam-3001	33	9	subset	subset	NOUN
ejpam-3001	33	10	and	and	CCONJ
ejpam-3001	33	11	µ′	µ′	PUNCT
ejpam-3001	33	12	:	:	PUNCT
ejpam-3001	33	13	x	x	X
ejpam-3001	33	14	×x	×x	X
ejpam-3001	33	15	→	→	SYM
ejpam-3001	33	16	[	[	X
ejpam-3001	33	17	0	0	NUM
ejpam-3001	33	18	,	,	PUNCT
ejpam-3001	33	19	1	1	NUM
ejpam-3001	33	20	]	]	PUNCT
ejpam-3001	33	21	is	be	AUX
ejpam-3001	33	22	a	a	DET
ejpam-3001	33	23	fuzzy	fuzzy	ADJ
ejpam-3001	33	24	relation	relation	NOUN
ejpam-3001	33	25	on	on	ADP
ejpam-3001	33	26	σ′	σ′	NOUN
ejpam-3001	33	27	such	such	ADJ
ejpam-3001	33	28	that	that	SCONJ
ejpam-3001	33	29	µ(x	µ(x	VERB
ejpam-3001	33	30	,	,	PUNCT
ejpam-3001	33	31	y	y	NOUN
ejpam-3001	33	32	)	)	PUNCT
ejpam-3001	33	33	≤	≤	NOUN
ejpam-3001	33	34	σ(x	σ(x	NOUN
ejpam-3001	33	35	)	)	PUNCT
ejpam-3001	33	36	∧	∧	NOUN
ejpam-3001	33	37	σ(y	σ(y	NOUN
ejpam-3001	33	38	)	)	PUNCT
ejpam-3001	33	39	for	for	ADP
ejpam-3001	33	40	all	all	DET
ejpam-3001	33	41	x	x	NOUN
ejpam-3001	33	42	,	,	PUNCT
ejpam-3001	33	43	y	y	PROPN
ejpam-3001	33	44	∈	∈	PROPN
ejpam-3001	33	45	x.	x.	NOUN
ejpam-3001	33	46	definition	definition	NOUN
ejpam-3001	33	47	2	2	NUM
ejpam-3001	33	48	.	.	PUNCT
ejpam-3001	34	1	[	[	X
ejpam-3001	34	2	14	14	NUM
ejpam-3001	34	3	]	]	X
ejpam-3001	34	4	a	a	DET
ejpam-3001	34	5	fuzzy	fuzzy	ADJ
ejpam-3001	34	6	graph	graph	NOUN
ejpam-3001	34	7	g	g	NOUN
ejpam-3001	34	8	:	:	PUNCT
ejpam-3001	34	9	(	(	PUNCT
ejpam-3001	34	10	σ	σ	PROPN
ejpam-3001	34	11	,	,	PUNCT
ejpam-3001	34	12	µ	µ	NOUN
ejpam-3001	34	13	)	)	PUNCT
ejpam-3001	34	14	with	with	ADP
ejpam-3001	34	15	underlying	underlie	VERB
ejpam-3001	34	16	graph	graph	NOUN
ejpam-3001	34	17	g	g	NOUN
ejpam-3001	34	18	:	:	PUNCT
ejpam-3001	34	19	(	(	PUNCT
ejpam-3001	34	20	v	v	NOUN
ejpam-3001	34	21	,	,	PUNCT
ejpam-3001	34	22	e	e	NOUN
ejpam-3001	34	23	)	)	PUNCT
ejpam-3001	34	24	is	be	AUX
ejpam-3001	34	25	complete	complete	ADJ
ejpam-3001	34	26	if	if	SCONJ
ejpam-3001	34	27	µ(x	µ(x	VERB
ejpam-3001	34	28	,	,	PUNCT
ejpam-3001	34	29	y	y	NOUN
ejpam-3001	34	30	)	)	PUNCT
ejpam-3001	34	31	=	=	SYM
ejpam-3001	34	32	σ(x	σ(x	X
ejpam-3001	34	33	)	)	PUNCT
ejpam-3001	34	34	∧	∧	NOUN
ejpam-3001	34	35	σ(y	σ(y	NOUN
ejpam-3001	34	36	)	)	PUNCT
ejpam-3001	34	37	for	for	ADP
ejpam-3001	34	38	all	all	DET
ejpam-3001	34	39	x	x	NOUN
ejpam-3001	34	40	,	,	PUNCT
ejpam-3001	34	41	y	y	PROPN
ejpam-3001	34	42	∈	∈	PROPN
ejpam-3001	34	43	v.	v.	ADP
ejpam-3001	34	44	definition	definition	NOUN
ejpam-3001	34	45	3	3	NUM
ejpam-3001	34	46	.	.	PUNCT
ejpam-3001	35	1	[	[	X
ejpam-3001	35	2	14	14	NUM
ejpam-3001	35	3	]	]	X
ejpam-3001	35	4	a	a	DET
ejpam-3001	35	5	fuzzy	fuzzy	ADJ
ejpam-3001	35	6	graph	graph	NOUN
ejpam-3001	35	7	g	g	NOUN
ejpam-3001	35	8	:	:	PUNCT
ejpam-3001	35	9	(	(	PUNCT
ejpam-3001	35	10	σ	σ	PROPN
ejpam-3001	35	11	,	,	PUNCT
ejpam-3001	35	12	µ	µ	NOUN
ejpam-3001	35	13	)	)	PUNCT
ejpam-3001	35	14	with	with	ADP
ejpam-3001	35	15	underlying	underlie	VERB
ejpam-3001	35	16	graph	graph	NOUN
ejpam-3001	35	17	g	g	NOUN
ejpam-3001	35	18	:	:	PUNCT
ejpam-3001	35	19	(	(	PUNCT
ejpam-3001	35	20	v	v	NOUN
ejpam-3001	35	21	,	,	PUNCT
ejpam-3001	35	22	e	e	NOUN
ejpam-3001	35	23	)	)	PUNCT
ejpam-3001	35	24	is	be	AUX
ejpam-3001	35	25	strong	strong	ADJ
ejpam-3001	35	26	if	if	SCONJ
ejpam-3001	35	27	µ(x	µ(x	VERB
ejpam-3001	35	28	,	,	PUNCT
ejpam-3001	35	29	y	y	NOUN
ejpam-3001	35	30	)	)	PUNCT
ejpam-3001	35	31	=	=	SYM
ejpam-3001	35	32	σ(x	σ(x	X
ejpam-3001	35	33	)	)	PUNCT
ejpam-3001	35	34	∧	∧	NOUN
ejpam-3001	35	35	σ(y	σ(y	NOUN
ejpam-3001	35	36	)	)	PUNCT
ejpam-3001	35	37	for	for	ADP
ejpam-3001	35	38	all	all	PRON
ejpam-3001	35	39	{	{	PUNCT
ejpam-3001	35	40	x	x	NOUN
ejpam-3001	35	41	,	,	PUNCT
ejpam-3001	35	42	y	y	PROPN
ejpam-3001	35	43	}	}	PUNCT
ejpam-3001	35	44	∈	∈	PROPN
ejpam-3001	35	45	e.	e.	PROPN
ejpam-3001	35	46	definition	definition	NOUN
ejpam-3001	35	47	4	4	NUM
ejpam-3001	35	48	.	.	PUNCT
ejpam-3001	36	1	[	[	X
ejpam-3001	36	2	8	8	NUM
ejpam-3001	36	3	]	]	SYM
ejpam-3001	36	4	two	two	NUM
ejpam-3001	36	5	fuzzy	fuzzy	ADJ
ejpam-3001	36	6	graphs	graph	NOUN
ejpam-3001	36	7	g1	g1	PROPN
ejpam-3001	36	8	:	:	PUNCT
ejpam-3001	36	9	(	(	PUNCT
ejpam-3001	36	10	σ1	σ1	PROPN
ejpam-3001	36	11	,	,	PUNCT
ejpam-3001	36	12	µ1	µ1	PROPN
ejpam-3001	36	13	)	)	PUNCT
ejpam-3001	36	14	with	with	ADP
ejpam-3001	36	15	crisp	crisp	ADJ
ejpam-3001	36	16	graph	graph	NOUN
ejpam-3001	36	17	g∗1	g∗1	NOUN
ejpam-3001	36	18	:	:	PUNCT
ejpam-3001	36	19	(	(	PUNCT
ejpam-3001	36	20	v1	v1	NOUN
ejpam-3001	36	21	,	,	PUNCT
ejpam-3001	36	22	e1	e1	NOUN
ejpam-3001	36	23	)	)	PUNCT
ejpam-3001	36	24	and	and	CCONJ
ejpam-3001	36	25	g2	g2	PROPN
ejpam-3001	36	26	:	:	PUNCT
ejpam-3001	36	27	(	(	PUNCT
ejpam-3001	36	28	σ2	σ2	NOUN
ejpam-3001	36	29	,	,	PUNCT
ejpam-3001	36	30	µ2	µ2	PROPN
ejpam-3001	36	31	)	)	PUNCT
ejpam-3001	36	32	with	with	ADP
ejpam-3001	36	33	crisp	crisp	ADJ
ejpam-3001	36	34	graph	graph	NOUN
ejpam-3001	36	35	g∗2	g∗2	NOUN
ejpam-3001	36	36	:	:	PUNCT
ejpam-3001	36	37	(	(	PUNCT
ejpam-3001	36	38	v2	v2	PROPN
ejpam-3001	36	39	,	,	PUNCT
ejpam-3001	36	40	e2	e2	PROPN
ejpam-3001	36	41	)	)	PUNCT
ejpam-3001	36	42	are	be	AUX
ejpam-3001	36	43	isomorphic	isomorphic	ADJ
ejpam-3001	36	44	if	if	SCONJ
ejpam-3001	36	45	there	there	PRON
ejpam-3001	36	46	exists	exist	VERB
ejpam-3001	36	47	a	a	DET
ejpam-3001	36	48	bijection	bijection	ADJ
ejpam-3001	36	49	h	h	NOUN
ejpam-3001	36	50	:	:	PUNCT
ejpam-3001	36	51	v1	v1	VERB
ejpam-3001	36	52	→	→	SYM
ejpam-3001	36	53	v2	v2	VERB
ejpam-3001	36	54	such	such	ADJ
ejpam-3001	36	55	that	that	DET
ejpam-3001	36	56	σ1(x	σ1(x	NOUN
ejpam-3001	36	57	)	)	PUNCT
ejpam-3001	36	58	=	=	SYM
ejpam-3001	36	59	σ2(h(x	σ2(h(x	NUM
ejpam-3001	36	60	)	)	PUNCT
ejpam-3001	36	61	)	)	PUNCT
ejpam-3001	37	1	and	and	CCONJ
ejpam-3001	37	2	µ1(x	µ1(x	PROPN
ejpam-3001	37	3	,	,	PUNCT
ejpam-3001	37	4	y	y	NOUN
ejpam-3001	37	5	)	)	PUNCT
ejpam-3001	37	6	=	=	SYM
ejpam-3001	37	7	µ2(h(x	µ2(h(x	PROPN
ejpam-3001	37	8	)	)	PUNCT
ejpam-3001	37	9	,	,	PUNCT
ejpam-3001	37	10	h(y	h(y	NOUN
ejpam-3001	37	11	)	)	PUNCT
ejpam-3001	37	12	)	)	PUNCT
ejpam-3001	37	13	for	for	ADP
ejpam-3001	37	14	all	all	DET
ejpam-3001	37	15	x	x	NOUN
ejpam-3001	37	16	,	,	PUNCT
ejpam-3001	37	17	y	y	PROPN
ejpam-3001	37	18	∈	∈	PROPN
ejpam-3001	37	19	v1	v1	NOUN
ejpam-3001	37	20	.	.	PUNCT
ejpam-3001	38	1	next	next	ADV
ejpam-3001	38	2	,	,	PUNCT
ejpam-3001	38	3	we	we	PRON
ejpam-3001	38	4	recall	recall	VERB
ejpam-3001	38	5	the	the	DET
ejpam-3001	38	6	following	follow	VERB
ejpam-3001	38	7	definition	definition	NOUN
ejpam-3001	38	8	of	of	ADP
ejpam-3001	38	9	balanced	balanced	ADJ
ejpam-3001	38	10	fuzzy	fuzzy	ADJ
ejpam-3001	38	11	graphs	graph	NOUN
ejpam-3001	38	12	that	that	PRON
ejpam-3001	38	13	will	will	AUX
ejpam-3001	38	14	be	be	AUX
ejpam-3001	38	15	our	our	PRON
ejpam-3001	38	16	main	main	ADJ
ejpam-3001	38	17	concern	concern	NOUN
ejpam-3001	38	18	in	in	ADP
ejpam-3001	38	19	this	this	DET
ejpam-3001	38	20	paper	paper	NOUN
ejpam-3001	38	21	.	.	PUNCT
ejpam-3001	39	1	it	it	PRON
ejpam-3001	39	2	was	be	AUX
ejpam-3001	39	3	motivated	motivate	VERB
ejpam-3001	39	4	and	and	CCONJ
ejpam-3001	39	5	deeply	deeply	ADV
ejpam-3001	39	6	studied	study	VERB
ejpam-3001	39	7	by	by	ADP
ejpam-3001	39	8	al	al	PROPN
ejpam-3001	39	9	-	-	PUNCT
ejpam-3001	39	10	hawary	hawary	NOUN
ejpam-3001	39	11	in	in	ADP
ejpam-3001	39	12	[	[	X
ejpam-3001	39	13	1	1	NUM
ejpam-3001	39	14	,	,	PUNCT
ejpam-3001	39	15	5	5	NUM
ejpam-3001	39	16	,	,	PUNCT
ejpam-3001	39	17	7	7	NUM
ejpam-3001	39	18	]	]	PUNCT
ejpam-3001	39	19	.	.	PUNCT
ejpam-3001	40	1	definition	definition	NOUN
ejpam-3001	40	2	5	5	NUM
ejpam-3001	40	3	.	.	PUNCT
ejpam-3001	41	1	[	[	X
ejpam-3001	41	2	1	1	X
ejpam-3001	41	3	]	]	PUNCT
ejpam-3001	41	4	the	the	DET
ejpam-3001	41	5	density	density	NOUN
ejpam-3001	41	6	of	of	ADP
ejpam-3001	41	7	a	a	DET
ejpam-3001	41	8	fuzzy	fuzzy	ADJ
ejpam-3001	41	9	graph	graph	NOUN
ejpam-3001	41	10	g	g	NOUN
ejpam-3001	41	11	:	:	PUNCT
ejpam-3001	41	12	(	(	PUNCT
ejpam-3001	41	13	σ	σ	PROPN
ejpam-3001	41	14	,	,	PUNCT
ejpam-3001	41	15	µ	µ	NOUN
ejpam-3001	41	16	)	)	PUNCT
ejpam-3001	41	17	is	be	AUX
ejpam-3001	41	18	d(g	d(g	PROPN
ejpam-3001	41	19	)	)	PUNCT
ejpam-3001	41	20	=	=	SYM
ejpam-3001	42	1	2	2	NUM
ejpam-3001	42	2	(	(	PUNCT
ejpam-3001	42	3	∑	∑	NOUN
ejpam-3001	42	4	u	u	NOUN
ejpam-3001	42	5	,	,	PUNCT
ejpam-3001	42	6	v∈v	v∈v	ADJ
ejpam-3001	42	7	µ(u	µ(u	NOUN
ejpam-3001	42	8	,	,	PUNCT
ejpam-3001	42	9	v))/	v))/	ADP
ejpam-3001	42	10	(	(	PUNCT
ejpam-3001	42	11	∑	∑	PROPN
ejpam-3001	42	12	u	u	PROPN
ejpam-3001	42	13	,	,	PUNCT
ejpam-3001	42	14	v∈v	v∈v	ADJ
ejpam-3001	42	15	u6	u6	NOUN
ejpam-3001	42	16	=	=	SYM
ejpam-3001	42	17	v	v	NOUN
ejpam-3001	42	18	(	(	PUNCT
ejpam-3001	42	19	σ(u	σ(u	NOUN
ejpam-3001	42	20	)	)	PUNCT
ejpam-3001	42	21	∧	∧	NOUN
ejpam-3001	42	22	σ(v	σ(v	NOUN
ejpam-3001	42	23	)	)	PUNCT
ejpam-3001	42	24	)	)	PUNCT
ejpam-3001	42	25	)	)	PUNCT
ejpam-3001	42	26	.	.	PUNCT
ejpam-3001	43	1	g	g	PROPN
ejpam-3001	43	2	is	be	AUX
ejpam-3001	43	3	balanced	balance	VERB
ejpam-3001	43	4	if	if	SCONJ
ejpam-3001	43	5	.	.	PUNCT
ejpam-3001	44	1	d(h	d(h	PROPN
ejpam-3001	44	2	)	)	PUNCT
ejpam-3001	45	1	≤	≤	NUM
ejpam-3001	45	2	d(g	d(g	PROPN
ejpam-3001	45	3	)	)	PUNCT
ejpam-3001	45	4	for	for	ADP
ejpam-3001	45	5	all	all	DET
ejpam-3001	45	6	fuzzy	fuzzy	ADJ
ejpam-3001	45	7	non	non	ADJ
ejpam-3001	45	8	-	-	ADJ
ejpam-3001	45	9	empty	empty	ADJ
ejpam-3001	45	10	subgraphs	subgraphs	ADJ
ejpam-3001	45	11	h	h	NOUN
ejpam-3001	45	12	of	of	ADP
ejpam-3001	45	13	g.	g.	PROPN
ejpam-3001	45	14	in	in	ADP
ejpam-3001	45	15	this	this	DET
ejpam-3001	45	16	paper	paper	NOUN
ejpam-3001	45	17	,	,	PUNCT
ejpam-3001	45	18	several	several	ADJ
ejpam-3001	45	19	classes	class	NOUN
ejpam-3001	45	20	of	of	ADP
ejpam-3001	45	21	balanced	balanced	ADJ
ejpam-3001	45	22	fuzzy	fuzzy	ADJ
ejpam-3001	45	23	graphs	graph	NOUN
ejpam-3001	45	24	are	be	AUX
ejpam-3001	45	25	characterized	characterize	VERB
ejpam-3001	45	26	;	;	PUNCT
ejpam-3001	45	27	namely	namely	ADV
ejpam-3001	45	28	the	the	DET
ejpam-3001	45	29	classes	class	NOUN
ejpam-3001	45	30	of	of	ADP
ejpam-3001	45	31	complete	complete	ADJ
ejpam-3001	45	32	fuzzy	fuzzy	ADJ
ejpam-3001	45	33	graphs	graph	NOUN
ejpam-3001	45	34	,	,	PUNCT
ejpam-3001	45	35	fuzzy	fuzzy	ADJ
ejpam-3001	45	36	graphs	graph	NOUN
ejpam-3001	45	37	induced	induce	VERB
ejpam-3001	45	38	by	by	ADP
ejpam-3001	45	39	the	the	DET
ejpam-3001	45	40	complete	complete	ADJ
ejpam-3001	45	41	graph	graph	NOUN
ejpam-3001	45	42	,	,	PUNCT
ejpam-3001	45	43	fuzzy	fuzzy	ADJ
ejpam-3001	45	44	graphs	graph	NOUN
ejpam-3001	45	45	with	with	ADP
ejpam-3001	45	46	balanced	balanced	ADJ
ejpam-3001	45	47	components	component	NOUN
ejpam-3001	45	48	,	,	PUNCT
ejpam-3001	45	49	fuzzy	fuzzy	ADJ
ejpam-3001	45	50	graphs	graph	NOUN
ejpam-3001	45	51	induced	induce	VERB
ejpam-3001	45	52	by	by	ADP
ejpam-3001	45	53	trees	tree	NOUN
ejpam-3001	45	54	and	and	CCONJ
ejpam-3001	45	55	fuzzy	fuzzy	ADJ
ejpam-3001	45	56	graphs	graph	NOUN
ejpam-3001	45	57	induced	induce	VERB
ejpam-3001	45	58	by	by	ADP
ejpam-3001	45	59	cycles	cycle	NOUN
ejpam-3001	45	60	.	.	PUNCT
ejpam-3001	46	1	moreover	moreover	ADV
ejpam-3001	46	2	,	,	PUNCT
ejpam-3001	46	3	we	we	PRON
ejpam-3001	46	4	provide	provide	VERB
ejpam-3001	46	5	two	two	NUM
ejpam-3001	46	6	new	new	ADJ
ejpam-3001	46	7	operations	operation	NOUN
ejpam-3001	46	8	on	on	ADP
ejpam-3001	46	9	fuzzy	fuzzy	ADJ
ejpam-3001	46	10	graphs	graph	NOUN
ejpam-3001	46	11	,	,	PUNCT
ejpam-3001	46	12	namely	namely	ADV
ejpam-3001	46	13	parallel	parallel	ADJ
ejpam-3001	46	14	connection	connection	NOUN
ejpam-3001	46	15	and	and	CCONJ
ejpam-3001	46	16	series	series	NOUN
ejpam-3001	46	17	connection	connection	NOUN
ejpam-3001	46	18	.	.	PUNCT
ejpam-3001	47	1	we	we	PRON
ejpam-3001	47	2	show	show	VERB
ejpam-3001	47	3	that	that	SCONJ
ejpam-3001	47	4	parallel	parallel	ADJ
ejpam-3001	47	5	connection	connection	NOUN
ejpam-3001	47	6	and	and	CCONJ
ejpam-3001	47	7	series	series	NOUN
ejpam-3001	47	8	connection	connection	NOUN
ejpam-3001	47	9	of	of	ADP
ejpam-3001	47	10	balanced	balanced	ADJ
ejpam-3001	47	11	fuzzy	fuzzy	ADJ
ejpam-3001	47	12	graphs	graph	NOUN
ejpam-3001	47	13	need	need	AUX
ejpam-3001	47	14	not	not	PART
ejpam-3001	47	15	be	be	AUX
ejpam-3001	47	16	balanced	balance	VERB
ejpam-3001	47	17	and	and	CCONJ
ejpam-3001	47	18	they	they	PRON
ejpam-3001	47	19	are	be	AUX
ejpam-3001	47	20	balanced	balance	VERB
ejpam-3001	47	21	in	in	ADP
ejpam-3001	47	22	case	case	NOUN
ejpam-3001	47	23	the	the	DET
ejpam-3001	47	24	original	original	ADJ
ejpam-3001	47	25	graphs	graph	NOUN
ejpam-3001	47	26	are	be	AUX
ejpam-3001	47	27	induced	induce	VERB
ejpam-3001	47	28	by	by	ADP
ejpam-3001	47	29	cycles	cycle	NOUN
ejpam-3001	47	30	.	.	PUNCT
ejpam-3001	48	1	finally	finally	ADV
ejpam-3001	48	2	,	,	PUNCT
ejpam-3001	48	3	we	we	PRON
ejpam-3001	48	4	study	study	VERB
ejpam-3001	48	5	the	the	DET
ejpam-3001	48	6	notions	notion	NOUN
ejpam-3001	48	7	of	of	ADP
ejpam-3001	48	8	strong	strong	ADJ
ejpam-3001	48	9	and	and	CCONJ
ejpam-3001	48	10	complete	complete	ADJ
ejpam-3001	48	11	via	via	ADP
ejpam-3001	48	12	these	these	DET
ejpam-3001	48	13	operations	operation	NOUN
ejpam-3001	48	14	.	.	PUNCT
ejpam-3001	49	1	t.	t.	NOUN
ejpam-3001	49	2	a.	a.	PROPN
ejpam-3001	49	3	hawary	hawary	PROPN
ejpam-3001	49	4	/	/	SYM
ejpam-3001	49	5	eur	eur	PROPN
ejpam-3001	49	6	.	.	PUNCT
ejpam-3001	50	1	j.	j.	PROPN
ejpam-3001	50	2	pure	pure	PROPN
ejpam-3001	50	3	appl	appl	PROPN
ejpam-3001	50	4	.	.	PROPN
ejpam-3001	50	5	math	math	PROPN
ejpam-3001	50	6	,	,	PUNCT
ejpam-3001	50	7	10	10	NUM
ejpam-3001	50	8	(	(	PUNCT
ejpam-3001	50	9	3	3	NUM
ejpam-3001	50	10	)	)	PUNCT
ejpam-3001	50	11	(	(	PUNCT
ejpam-3001	50	12	2017	2017	NUM
ejpam-3001	50	13	)	)	PUNCT
ejpam-3001	50	14	,	,	PUNCT
ejpam-3001	50	15	552	552	NUM
ejpam-3001	50	16	-	-	SYM
ejpam-3001	50	17	560	560	NUM
ejpam-3001	50	18	554	554	NUM
ejpam-3001	50	19	2	2	NUM
ejpam-3001	50	20	.	.	PUNCT
ejpam-3001	50	21	classes	class	NOUN
ejpam-3001	50	22	of	of	ADP
ejpam-3001	50	23	balanced	balanced	ADJ
ejpam-3001	50	24	fuzzy	fuzzy	ADJ
ejpam-3001	50	25	graphs	graph	NOUN
ejpam-3001	50	26	in	in	ADP
ejpam-3001	50	27	this	this	DET
ejpam-3001	50	28	section	section	NOUN
ejpam-3001	50	29	,	,	PUNCT
ejpam-3001	50	30	several	several	ADJ
ejpam-3001	50	31	classes	class	NOUN
ejpam-3001	50	32	of	of	ADP
ejpam-3001	50	33	balanced	balanced	ADJ
ejpam-3001	50	34	fuzzy	fuzzy	ADJ
ejpam-3001	50	35	graphs	graph	NOUN
ejpam-3001	50	36	are	be	AUX
ejpam-3001	50	37	provided	provide	VERB
ejpam-3001	50	38	.	.	PUNCT
ejpam-3001	51	1	the	the	DET
ejpam-3001	51	2	first	first	ADJ
ejpam-3001	51	3	class	class	NOUN
ejpam-3001	51	4	of	of	ADP
ejpam-3001	51	5	balanced	balanced	ADJ
ejpam-3001	51	6	fuzzy	fuzzy	ADJ
ejpam-3001	51	7	graphs	graph	NOUN
ejpam-3001	51	8	is	be	AUX
ejpam-3001	51	9	the	the	DET
ejpam-3001	51	10	class	class	NOUN
ejpam-3001	51	11	of	of	ADP
ejpam-3001	51	12	complete	complete	ADJ
ejpam-3001	51	13	fuzzy	fuzzy	ADJ
ejpam-3001	51	14	graphs	graph	NOUN
ejpam-3001	51	15	.	.	PUNCT
ejpam-3001	52	1	theorem	theorem	NOUN
ejpam-3001	52	2	1	1	NUM
ejpam-3001	52	3	.	.	PUNCT
ejpam-3001	53	1	[	[	X
ejpam-3001	53	2	1	1	X
ejpam-3001	53	3	]	]	PUNCT
ejpam-3001	53	4	any	any	DET
ejpam-3001	53	5	complete	complete	ADJ
ejpam-3001	53	6	fuzzy	fuzzy	ADJ
ejpam-3001	53	7	graph	graph	NOUN
ejpam-3001	53	8	is	be	AUX
ejpam-3001	53	9	balanced	balanced	ADJ
ejpam-3001	53	10	.	.	PUNCT
ejpam-3001	54	1	by	by	ADP
ejpam-3001	54	2	a	a	DET
ejpam-3001	54	3	fuzzy	fuzzy	ADJ
ejpam-3001	54	4	graph	graph	NOUN
ejpam-3001	54	5	g	g	NOUN
ejpam-3001	54	6	:	:	PUNCT
ejpam-3001	54	7	(	(	PUNCT
ejpam-3001	54	8	σ	σ	PROPN
ejpam-3001	54	9	,	,	PUNCT
ejpam-3001	54	10	µ	µ	NOUN
ejpam-3001	54	11	)	)	PUNCT
ejpam-3001	54	12	induced	induce	VERB
ejpam-3001	54	13	by	by	ADP
ejpam-3001	54	14	a	a	DET
ejpam-3001	54	15	graph	graph	NOUN
ejpam-3001	54	16	g	g	NOUN
ejpam-3001	54	17	:	:	PUNCT
ejpam-3001	54	18	(	(	PUNCT
ejpam-3001	54	19	v	v	NOUN
ejpam-3001	54	20	,	,	PUNCT
ejpam-3001	54	21	e	e	NOUN
ejpam-3001	54	22	)	)	PUNCT
ejpam-3001	54	23	,	,	PUNCT
ejpam-3001	54	24	we	we	PRON
ejpam-3001	54	25	mean	mean	VERB
ejpam-3001	54	26	the	the	DET
ejpam-3001	54	27	the	the	DET
ejpam-3001	54	28	graph	graph	NOUN
ejpam-3001	54	29	g	g	NOUN
ejpam-3001	54	30	after	after	ADP
ejpam-3001	54	31	assigning	assign	VERB
ejpam-3001	54	32	values	value	NOUN
ejpam-3001	54	33	σ(x	σ(x	NOUN
ejpam-3001	54	34	)	)	PUNCT
ejpam-3001	54	35	for	for	ADP
ejpam-3001	54	36	all	all	DET
ejpam-3001	54	37	x	x	SYM
ejpam-3001	54	38	∈	∈	PROPN
ejpam-3001	54	39	v	v	NOUN
ejpam-3001	54	40	and	and	CCONJ
ejpam-3001	54	41	µ(x	µ(x	ADJ
ejpam-3001	54	42	,	,	PUNCT
ejpam-3001	54	43	y	y	NOUN
ejpam-3001	54	44	)	)	PUNCT
ejpam-3001	54	45	for	for	ADP
ejpam-3001	54	46	all	all	PRON
ejpam-3001	54	47	{	{	PUNCT
ejpam-3001	54	48	x	x	NOUN
ejpam-3001	54	49	,	,	PUNCT
ejpam-3001	54	50	y	y	PROPN
ejpam-3001	54	51	}	}	PUNCT
ejpam-3001	54	52	∈	∈	PROPN
ejpam-3001	54	53	e	e	X
ejpam-3001	54	54	where	where	SCONJ
ejpam-3001	54	55	each	each	DET
ejpam-3001	54	56	σ(x	σ(x	PROPN
ejpam-3001	54	57	)	)	PUNCT
ejpam-3001	54	58	and	and	CCONJ
ejpam-3001	54	59	µ(x	µ(x	PROPN
ejpam-3001	54	60	,	,	PUNCT
ejpam-3001	54	61	y	y	NOUN
ejpam-3001	54	62	)	)	PUNCT
ejpam-3001	54	63	are	be	AUX
ejpam-3001	54	64	in	in	ADP
ejpam-3001	54	65	the	the	DET
ejpam-3001	54	66	interval	interval	NOUN
ejpam-3001	54	67	[	[	X
ejpam-3001	54	68	0	0	NUM
ejpam-3001	54	69	,	,	PUNCT
ejpam-3001	54	70	1	1	NUM
ejpam-3001	54	71	]	]	PUNCT
ejpam-3001	54	72	.	.	PUNCT
ejpam-3001	55	1	theorem	theorem	NOUN
ejpam-3001	55	2	2	2	NUM
ejpam-3001	55	3	.	.	PUNCT
ejpam-3001	55	4	a	a	DET
ejpam-3001	55	5	fuzzy	fuzzy	ADJ
ejpam-3001	55	6	graph	graph	NOUN
ejpam-3001	55	7	g	g	NOUN
ejpam-3001	55	8	induced	induce	VERB
ejpam-3001	55	9	by	by	ADP
ejpam-3001	55	10	the	the	DET
ejpam-3001	55	11	complete	complete	ADJ
ejpam-3001	55	12	graph	graph	NOUN
ejpam-3001	55	13	kn	kn	PROPN
ejpam-3001	55	14	is	be	AUX
ejpam-3001	55	15	balanced	balanced	ADJ
ejpam-3001	55	16	.	.	PUNCT
ejpam-3001	56	1	proof	proof	NOUN
ejpam-3001	56	2	.	.	PUNCT
ejpam-3001	57	1	let	let	VERB
ejpam-3001	57	2	h	h	PRON
ejpam-3001	57	3	be	be	AUX
ejpam-3001	57	4	a	a	DET
ejpam-3001	57	5	fuzzy	fuzzy	ADJ
ejpam-3001	57	6	subgraph	subgraph	NOUN
ejpam-3001	57	7	of	of	ADP
ejpam-3001	57	8	g	g	PROPN
ejpam-3001	57	9	with	with	ADP
ejpam-3001	57	10	m	m	PROPN
ejpam-3001	57	11	vertices	vertex	NOUN
ejpam-3001	57	12	.	.	PUNCT
ejpam-3001	58	1	we	we	PRON
ejpam-3001	58	2	claim	claim	VERB
ejpam-3001	58	3	that	that	SCONJ
ejpam-3001	58	4	the	the	DET
ejpam-3001	58	5	many	many	ADJ
ejpam-3001	58	6	possible	possible	ADJ
ejpam-3001	58	7	cases	case	NOUN
ejpam-3001	58	8	of	of	ADP
ejpam-3001	58	9	h	h	NOUN
ejpam-3001	58	10	reduce	reduce	VERB
ejpam-3001	58	11	to	to	ADP
ejpam-3001	58	12	the	the	DET
ejpam-3001	58	13	case	case	NOUN
ejpam-3001	58	14	that	that	SCONJ
ejpam-3001	58	15	h	h	NOUN
ejpam-3001	58	16	is	be	AUX
ejpam-3001	58	17	is	be	AUX
ejpam-3001	58	18	induced	induce	VERB
ejpam-3001	58	19	by	by	ADP
ejpam-3001	58	20	a	a	DET
ejpam-3001	58	21	complete	complete	ADJ
ejpam-3001	58	22	graph	graph	NOUN
ejpam-3001	58	23	km	km	NOUN
ejpam-3001	58	24	.	.	PUNCT
ejpam-3001	59	1	if	if	SCONJ
ejpam-3001	59	2	this	this	PRON
ejpam-3001	59	3	is	be	AUX
ejpam-3001	59	4	true	true	ADJ
ejpam-3001	59	5	,	,	PUNCT
ejpam-3001	59	6	then	then	ADV
ejpam-3001	59	7	as	as	ADP
ejpam-3001	59	8	∑	∑	PROPN
ejpam-3001	59	9	x	x	PROPN
ejpam-3001	59	10	,	,	PUNCT
ejpam-3001	59	11	y∈v	y∈v	PROPN
ejpam-3001	59	12	(	(	PUNCT
ejpam-3001	59	13	km	km	NOUN
ejpam-3001	59	14	)	)	PUNCT
ejpam-3001	59	15	µ(x	µ(x	PROPN
ejpam-3001	59	16	,	,	PUNCT
ejpam-3001	59	17	y	y	NOUN
ejpam-3001	59	18	)	)	PUNCT
ejpam-3001	59	19	≤	≤	NOUN
ejpam-3001	59	20	∑	∑	PUNCT
ejpam-3001	59	21	x	x	X
ejpam-3001	59	22	,	,	PUNCT
ejpam-3001	59	23	y∈v	y∈v	PROPN
ejpam-3001	59	24	(	(	PUNCT
ejpam-3001	59	25	kn	kn	PROPN
ejpam-3001	59	26	)	)	PUNCT
ejpam-3001	59	27	µ(x	µ(x	PROPN
ejpam-3001	59	28	,	,	PUNCT
ejpam-3001	59	29	y	y	NOUN
ejpam-3001	59	30	)	)	PUNCT
ejpam-3001	59	31	and	and	CCONJ
ejpam-3001	59	32	∑	∑	ADP
ejpam-3001	59	33	x	x	NOUN
ejpam-3001	59	34	,	,	PUNCT
ejpam-3001	59	35	y∈v	y∈v	PROPN
ejpam-3001	59	36	(	(	PUNCT
ejpam-3001	59	37	kn	kn	PROPN
ejpam-3001	59	38	)	)	PUNCT
ejpam-3001	59	39	(	(	PUNCT
ejpam-3001	59	40	σ	σ	NOUN
ejpam-3001	59	41	′	′	NUM
ejpam-3001	59	42	2(x)∧σ′	2(x)∧σ′	NUM
ejpam-3001	59	43	2(y	2(y	NUM
ejpam-3001	59	44	)	)	PUNCT
ejpam-3001	59	45	)	)	PUNCT
ejpam-3001	59	46	≤∑	≤∑	PROPN
ejpam-3001	59	47	x	x	NOUN
ejpam-3001	59	48	,	,	PUNCT
ejpam-3001	59	49	y∈v	y∈v	PROPN
ejpam-3001	59	50	(	(	PUNCT
ejpam-3001	59	51	km)(σ	km)(σ	NOUN
ejpam-3001	59	52	′	′	NOUN
ejpam-3001	59	53	2(x	2(x	NUM
ejpam-3001	59	54	)	)	PUNCT
ejpam-3001	60	1	∧	∧	NOUN
ejpam-3001	60	2	σ′	σ′	NOUN
ejpam-3001	60	3	2(y	2(y	NUM
ejpam-3001	60	4	)	)	PUNCT
ejpam-3001	60	5	)	)	PUNCT
ejpam-3001	61	1	,	,	PUNCT
ejpam-3001	61	2	we	we	PRON
ejpam-3001	61	3	have	have	VERB
ejpam-3001	61	4	d(h	d(h	PROPN
ejpam-3001	61	5	)	)	PUNCT
ejpam-3001	62	1	=	=	SYM
ejpam-3001	63	1	2	2	NUM
ejpam-3001	63	2	∑	∑	PUNCT
ejpam-3001	63	3	x	x	PROPN
ejpam-3001	63	4	,	,	PUNCT
ejpam-3001	63	5	y∈v	y∈v	NOUN
ejpam-3001	63	6	(	(	PUNCT
ejpam-3001	63	7	km	km	NOUN
ejpam-3001	63	8	)	)	PUNCT
ejpam-3001	63	9	µ(x	µ(x	VERB
ejpam-3001	63	10	,	,	PUNCT
ejpam-3001	63	11	y)∑	y)∑	PROPN
ejpam-3001	63	12	x	x	NOUN
ejpam-3001	63	13	,	,	PUNCT
ejpam-3001	63	14	y∈v	y∈v	NOUN
ejpam-3001	63	15	(	(	PUNCT
ejpam-3001	63	16	km)(σ	km)(σ	NOUN
ejpam-3001	63	17	′	′	NOUN
ejpam-3001	63	18	2(x	2(x	NUM
ejpam-3001	63	19	)	)	PUNCT
ejpam-3001	64	1	∧	∧	NOUN
ejpam-3001	64	2	σ′	σ′	NOUN
ejpam-3001	64	3	2(y	2(y	NUM
ejpam-3001	64	4	)	)	PUNCT
ejpam-3001	64	5	)	)	PUNCT
ejpam-3001	65	1	≤	≤	ADV
ejpam-3001	65	2	2	2	NUM
ejpam-3001	65	3	∑	∑	PUNCT
ejpam-3001	65	4	x	x	PROPN
ejpam-3001	65	5	,	,	PUNCT
ejpam-3001	65	6	y∈v	y∈v	PROPN
ejpam-3001	65	7	(	(	PUNCT
ejpam-3001	65	8	kn	kn	PROPN
ejpam-3001	65	9	)	)	PUNCT
ejpam-3001	65	10	µ(x	µ(x	PROPN
ejpam-3001	65	11	,	,	PUNCT
ejpam-3001	65	12	y)∑	y)∑	PROPN
ejpam-3001	65	13	x	x	NOUN
ejpam-3001	65	14	,	,	PUNCT
ejpam-3001	65	15	y∈v	y∈v	PROPN
ejpam-3001	65	16	(	(	PUNCT
ejpam-3001	65	17	kn	kn	PROPN
ejpam-3001	65	18	)	)	PUNCT
ejpam-3001	65	19	(	(	PUNCT
ejpam-3001	65	20	σ	σ	NOUN
ejpam-3001	65	21	′	′	NUM
ejpam-3001	65	22	2(x	2(x	NUM
ejpam-3001	65	23	)	)	PUNCT
ejpam-3001	65	24	∧	∧	NOUN
ejpam-3001	65	25	σ′	σ′	NOUN
ejpam-3001	65	26	2(y	2(y	NUM
ejpam-3001	65	27	)	)	PUNCT
ejpam-3001	65	28	)	)	PUNCT
ejpam-3001	66	1	=	=	PUNCT
ejpam-3001	66	2	d(g	d(g	PROPN
ejpam-3001	66	3	)	)	PUNCT
ejpam-3001	66	4	.	.	PUNCT
ejpam-3001	67	1	therefore	therefore	ADV
ejpam-3001	67	2	,	,	PUNCT
ejpam-3001	67	3	g	g	PROPN
ejpam-3001	67	4	is	be	AUX
ejpam-3001	67	5	balanced	balanced	ADJ
ejpam-3001	67	6	.	.	PUNCT
ejpam-3001	68	1	to	to	PART
ejpam-3001	68	2	show	show	VERB
ejpam-3001	68	3	the	the	DET
ejpam-3001	68	4	claim	claim	NOUN
ejpam-3001	68	5	is	be	AUX
ejpam-3001	68	6	true	true	ADJ
ejpam-3001	68	7	,	,	PUNCT
ejpam-3001	68	8	let	let	VERB
ejpam-3001	68	9	h′	h′	PROPN
ejpam-3001	68	10	be	be	AUX
ejpam-3001	68	11	a	a	DET
ejpam-3001	68	12	fuzzy	fuzzy	ADJ
ejpam-3001	68	13	subgraph	subgraph	NOUN
ejpam-3001	68	14	of	of	ADP
ejpam-3001	68	15	with	with	ADP
ejpam-3001	68	16	k	k	PROPN
ejpam-3001	68	17	vertices	vertex	NOUN
ejpam-3001	68	18	.	.	PUNCT
ejpam-3001	69	1	obviously	obviously	ADV
ejpam-3001	69	2	,	,	PUNCT
ejpam-3001	69	3	d(h′	d(h′	PROPN
ejpam-3001	69	4	)	)	PUNCT
ejpam-3001	69	5	≤	≤	NUM
ejpam-3001	69	6	d(h	d(h	PROPN
ejpam-3001	69	7	)	)	PUNCT
ejpam-3001	69	8	since	since	SCONJ
ejpam-3001	69	9	the	the	DET
ejpam-3001	69	10	corresponding	correspond	VERB
ejpam-3001	69	11	graphs	graph	NOUN
ejpam-3001	69	12	of	of	ADP
ejpam-3001	69	13	both	both	PRON
ejpam-3001	69	14	have	have	VERB
ejpam-3001	69	15	same	same	ADJ
ejpam-3001	69	16	vertices	vertex	NOUN
ejpam-3001	69	17	and	and	CCONJ
ejpam-3001	69	18	that	that	PRON
ejpam-3001	69	19	of	of	ADP
ejpam-3001	69	20	h	h	NOUN
ejpam-3001	69	21	has	have	VERB
ejpam-3001	69	22	more	more	ADJ
ejpam-3001	69	23	edges	edge	NOUN
ejpam-3001	69	24	.	.	PUNCT
ejpam-3001	70	1	lemma	lemma	PROPN
ejpam-3001	70	2	3	3	NUM
ejpam-3001	70	3	.	.	PUNCT
ejpam-3001	71	1	the	the	DET
ejpam-3001	71	2	union	union	NOUN
ejpam-3001	71	3	of	of	ADP
ejpam-3001	71	4	two	two	NUM
ejpam-3001	71	5	balanced	balanced	ADJ
ejpam-3001	71	6	fuzzy	fuzzy	ADJ
ejpam-3001	71	7	graphs	graph	NOUN
ejpam-3001	71	8	is	be	AUX
ejpam-3001	71	9	balanced	balanced	ADJ
ejpam-3001	71	10	.	.	PUNCT
ejpam-3001	72	1	proof	proof	NOUN
ejpam-3001	72	2	.	.	PUNCT
ejpam-3001	73	1	if	if	SCONJ
ejpam-3001	73	2	g1	g1	PROPN
ejpam-3001	73	3	:	:	PUNCT
ejpam-3001	73	4	(	(	PUNCT
ejpam-3001	73	5	σ1	σ1	PROPN
ejpam-3001	73	6	,	,	PUNCT
ejpam-3001	73	7	µ1	µ1	PROPN
ejpam-3001	73	8	)	)	PUNCT
ejpam-3001	73	9	is	be	AUX
ejpam-3001	73	10	a	a	DET
ejpam-3001	73	11	fuzzy	fuzzy	ADJ
ejpam-3001	73	12	balanced	balanced	ADJ
ejpam-3001	73	13	graph	graph	NOUN
ejpam-3001	73	14	with	with	ADP
ejpam-3001	73	15	crisp	crisp	ADJ
ejpam-3001	73	16	graph	graph	NOUN
ejpam-3001	73	17	g∗1	g∗1	NOUN
ejpam-3001	73	18	:	:	PUNCT
ejpam-3001	73	19	(	(	PUNCT
ejpam-3001	73	20	v1	v1	NOUN
ejpam-3001	73	21	,	,	PUNCT
ejpam-3001	73	22	e1	e1	NOUN
ejpam-3001	73	23	)	)	PUNCT
ejpam-3001	73	24	and	and	CCONJ
ejpam-3001	73	25	g2	g2	PROPN
ejpam-3001	73	26	:	:	PUNCT
ejpam-3001	73	27	(	(	PUNCT
ejpam-3001	73	28	σ2	σ2	NOUN
ejpam-3001	73	29	,	,	PUNCT
ejpam-3001	73	30	µ2	µ2	PROPN
ejpam-3001	73	31	)	)	PUNCT
ejpam-3001	73	32	is	be	AUX
ejpam-3001	73	33	a	a	DET
ejpam-3001	73	34	fuzzy	fuzzy	ADJ
ejpam-3001	73	35	balanced	balanced	ADJ
ejpam-3001	73	36	graph	graph	NOUN
ejpam-3001	73	37	with	with	ADP
ejpam-3001	73	38	crisp	crisp	ADJ
ejpam-3001	73	39	graph	graph	NOUN
ejpam-3001	73	40	g∗2	g∗2	NOUN
ejpam-3001	73	41	:	:	PUNCT
ejpam-3001	73	42	(	(	PUNCT
ejpam-3001	73	43	v2	v2	NOUN
ejpam-3001	73	44	,	,	PUNCT
ejpam-3001	73	45	e2),where	e2),where	X
ejpam-3001	74	1	we	we	PRON
ejpam-3001	74	2	assume	assume	VERB
ejpam-3001	74	3	that	that	SCONJ
ejpam-3001	74	4	v1	v1	NOUN
ejpam-3001	74	5	∩	∩	ADJ
ejpam-3001	74	6	v2	v2	NOUN
ejpam-3001	74	7	=	=	NOUN
ejpam-3001	74	8	∅	∅	NOUN
ejpam-3001	74	9	,	,	PUNCT
ejpam-3001	74	10	then	then	ADV
ejpam-3001	74	11	for	for	ADP
ejpam-3001	74	12	any	any	DET
ejpam-3001	74	13	fuzzy	fuzzy	ADJ
ejpam-3001	74	14	subgraph	subgraph	NOUN
ejpam-3001	74	15	h	h	NOUN
ejpam-3001	74	16	of	of	ADP
ejpam-3001	74	17	g1	g1	PROPN
ejpam-3001	74	18	∪g2	∪g2	PROPN
ejpam-3001	74	19	,	,	PUNCT
ejpam-3001	74	20	h	h	NOUN
ejpam-3001	74	21	'	'	PUNCT
ejpam-3001	74	22	h1	h1	PROPN
ejpam-3001	74	23	∪h2	∪h2	NOUN
ejpam-3001	74	24	for	for	ADP
ejpam-3001	74	25	some	some	DET
ejpam-3001	74	26	fuzzy	fuzzy	ADJ
ejpam-3001	74	27	subgraphs	subgraphs	NOUN
ejpam-3001	74	28	h1	h1	NOUN
ejpam-3001	74	29	of	of	ADP
ejpam-3001	74	30	g1	g1	NOUN
ejpam-3001	74	31	and	and	CCONJ
ejpam-3001	74	32	h2	h2	NOUN
ejpam-3001	74	33	of	of	ADP
ejpam-3001	74	34	g2	g2	PROPN
ejpam-3001	74	35	.	.	PUNCT
ejpam-3001	75	1	now	now	ADV
ejpam-3001	75	2	∑	∑	ADP
ejpam-3001	75	3	x	x	X
ejpam-3001	75	4	,	,	PUNCT
ejpam-3001	75	5	y∈v	y∈v	NOUN
ejpam-3001	75	6	(	(	PUNCT
ejpam-3001	75	7	h1)∪v	h1)∪v	PROPN
ejpam-3001	75	8	(	(	PUNCT
ejpam-3001	75	9	h2	h2	NOUN
ejpam-3001	75	10	)	)	PUNCT
ejpam-3001	75	11	µ(x	µ(x	PROPN
ejpam-3001	75	12	,	,	PUNCT
ejpam-3001	75	13	y	y	NOUN
ejpam-3001	75	14	)	)	PUNCT
ejpam-3001	75	15	≤	≤	NOUN
ejpam-3001	75	16	∑	∑	PUNCT
ejpam-3001	75	17	x	x	X
ejpam-3001	75	18	,	,	PUNCT
ejpam-3001	75	19	y∈v1∪v2	y∈v1∪v2	X
ejpam-3001	75	20	µ(x	µ(x	X
ejpam-3001	75	21	,	,	PUNCT
ejpam-3001	75	22	y	y	NOUN
ejpam-3001	75	23	)	)	PUNCT
ejpam-3001	75	24	and	and	CCONJ
ejpam-3001	75	25	∑	∑	ADP
ejpam-3001	75	26	x	x	X
ejpam-3001	75	27	,	,	PUNCT
ejpam-3001	75	28	y∈v1∪v2	y∈v1∪v2	PROPN
ejpam-3001	75	29	(	(	PUNCT
ejpam-3001	75	30	σ	σ	NOUN
ejpam-3001	75	31	′	′	NUM
ejpam-3001	75	32	2(x	2(x	NUM
ejpam-3001	75	33	)	)	PUNCT
ejpam-3001	75	34	∧	∧	NOUN
ejpam-3001	75	35	σ′	σ′	NOUN
ejpam-3001	75	36	2(y	2(y	NUM
ejpam-3001	75	37	)	)	PUNCT
ejpam-3001	75	38	)	)	PUNCT
ejpam-3001	76	1	≤	≤	ADV
ejpam-3001	76	2	∑	∑	PUNCT
ejpam-3001	76	3	x	x	X
ejpam-3001	76	4	,	,	PUNCT
ejpam-3001	76	5	y∈v	y∈v	NOUN
ejpam-3001	76	6	(	(	PUNCT
ejpam-3001	76	7	h1)∪v	h1)∪v	PROPN
ejpam-3001	76	8	(	(	PUNCT
ejpam-3001	76	9	h2	h2	PROPN
ejpam-3001	76	10	)	)	PUNCT
ejpam-3001	76	11	)	)	PUNCT
ejpam-3001	77	1	(	(	PUNCT
ejpam-3001	77	2	σ	σ	NOUN
ejpam-3001	77	3	′	′	NUM
ejpam-3001	77	4	2(x	2(x	NUM
ejpam-3001	77	5	)	)	PUNCT
ejpam-3001	77	6	∧	∧	NOUN
ejpam-3001	77	7	σ′	σ′	NOUN
ejpam-3001	77	8	2(y	2(y	NUM
ejpam-3001	77	9	)	)	PUNCT
ejpam-3001	77	10	)	)	PUNCT
ejpam-3001	78	1	and	and	CCONJ
ejpam-3001	78	2	so	so	ADV
ejpam-3001	78	3	d(h	d(h	PROPN
ejpam-3001	78	4	)	)	PUNCT
ejpam-3001	79	1	=	=	SYM
ejpam-3001	79	2	2	2	NUM
ejpam-3001	79	3	∑	∑	PUNCT
ejpam-3001	79	4	x	x	PROPN
ejpam-3001	79	5	,	,	PUNCT
ejpam-3001	79	6	y∈v	y∈v	NOUN
ejpam-3001	79	7	(	(	PUNCT
ejpam-3001	79	8	h1)∪v	h1)∪v	PROPN
ejpam-3001	79	9	(	(	PUNCT
ejpam-3001	79	10	h2	h2	NOUN
ejpam-3001	79	11	)	)	PUNCT
ejpam-3001	79	12	µ(x	µ(x	NOUN
ejpam-3001	79	13	,	,	PUNCT
ejpam-3001	79	14	y)∑	y)∑	PROPN
ejpam-3001	79	15	x	x	NOUN
ejpam-3001	79	16	,	,	PUNCT
ejpam-3001	79	17	y∈v	y∈v	NOUN
ejpam-3001	79	18	(	(	PUNCT
ejpam-3001	79	19	h1)∪v	h1)∪v	PROPN
ejpam-3001	79	20	(	(	PUNCT
ejpam-3001	79	21	h2	h2	PROPN
ejpam-3001	79	22	)	)	PUNCT
ejpam-3001	79	23	)	)	PUNCT
ejpam-3001	80	1	(	(	PUNCT
ejpam-3001	80	2	σ	σ	NOUN
ejpam-3001	80	3	′	′	NUM
ejpam-3001	80	4	2(x	2(x	NUM
ejpam-3001	80	5	)	)	PUNCT
ejpam-3001	80	6	∧	∧	NOUN
ejpam-3001	80	7	σ′	σ′	NOUN
ejpam-3001	80	8	2(y	2(y	NUM
ejpam-3001	80	9	)	)	PUNCT
ejpam-3001	80	10	)	)	PUNCT
ejpam-3001	81	1	≤	≤	ADV
ejpam-3001	81	2	2	2	NUM
ejpam-3001	81	3	∑	∑	PUNCT
ejpam-3001	81	4	x	x	PROPN
ejpam-3001	81	5	,	,	PUNCT
ejpam-3001	81	6	y∈v1∪v2	y∈v1∪v2	X
ejpam-3001	81	7	µ(x	µ(x	NOUN
ejpam-3001	81	8	,	,	PUNCT
ejpam-3001	81	9	y)∑	y)∑	PROPN
ejpam-3001	81	10	x	x	NOUN
ejpam-3001	81	11	,	,	PUNCT
ejpam-3001	81	12	y∈v1∪v2	y∈v1∪v2	PROPN
ejpam-3001	81	13	(	(	PUNCT
ejpam-3001	81	14	σ	σ	NOUN
ejpam-3001	81	15	′	′	NUM
ejpam-3001	81	16	2(x	2(x	NUM
ejpam-3001	81	17	)	)	PUNCT
ejpam-3001	81	18	∧	∧	NOUN
ejpam-3001	81	19	σ′	σ′	NOUN
ejpam-3001	81	20	2(y	2(y	NUM
ejpam-3001	81	21	)	)	PUNCT
ejpam-3001	81	22	)	)	PUNCT
ejpam-3001	82	1	=	=	PUNCT
ejpam-3001	82	2	d(g1	d(g1	NOUN
ejpam-3001	82	3	∪g2	∪g2	PROPN
ejpam-3001	82	4	)	)	PUNCT
ejpam-3001	82	5	.	.	PUNCT
ejpam-3001	83	1	therefore	therefore	ADV
ejpam-3001	83	2	,	,	PUNCT
ejpam-3001	83	3	g1	g1	PROPN
ejpam-3001	83	4	∪g2	∪g2	PROPN
ejpam-3001	83	5	is	be	AUX
ejpam-3001	83	6	balanced	balanced	ADJ
ejpam-3001	83	7	.	.	PUNCT
ejpam-3001	84	1	although	although	SCONJ
ejpam-3001	84	2	the	the	DET
ejpam-3001	84	3	union	union	NOUN
ejpam-3001	84	4	of	of	ADP
ejpam-3001	84	5	two	two	NUM
ejpam-3001	84	6	balanced	balanced	ADJ
ejpam-3001	84	7	fuzzy	fuzzy	ADJ
ejpam-3001	84	8	graphs	graph	NOUN
ejpam-3001	84	9	is	be	AUX
ejpam-3001	84	10	balanced	balance	VERB
ejpam-3001	84	11	,	,	PUNCT
ejpam-3001	84	12	the	the	DET
ejpam-3001	84	13	intersection	intersection	NOUN
ejpam-3001	84	14	(	(	PUNCT
ejpam-3001	84	15	join	join	NOUN
ejpam-3001	84	16	)	)	PUNCT
ejpam-3001	84	17	of	of	ADP
ejpam-3001	84	18	two	two	NUM
ejpam-3001	84	19	balanced	balanced	ADJ
ejpam-3001	84	20	fuzzy	fuzzy	ADJ
ejpam-3001	84	21	graphs	graph	NOUN
ejpam-3001	84	22	needs	needs	AUX
ejpam-3001	84	23	not	not	PART
ejpam-3001	84	24	be	be	AUX
ejpam-3001	84	25	balanced	balance	VERB
ejpam-3001	84	26	.	.	PUNCT
ejpam-3001	85	1	example	example	NOUN
ejpam-3001	86	1	1	1	NUM
ejpam-3001	86	2	.	.	X
ejpam-3001	86	3	consider	consider	VERB
ejpam-3001	86	4	the	the	DET
ejpam-3001	86	5	fuzzy	fuzzy	ADJ
ejpam-3001	86	6	graphs	graph	NOUN
ejpam-3001	86	7	g1	g1	PROPN
ejpam-3001	86	8	:	:	PUNCT
ejpam-3001	86	9	(	(	PUNCT
ejpam-3001	86	10	σ1	σ1	PROPN
ejpam-3001	86	11	,	,	PUNCT
ejpam-3001	86	12	µ1	µ1	PROPN
ejpam-3001	86	13	)	)	PUNCT
ejpam-3001	86	14	with	with	ADP
ejpam-3001	86	15	crisp	crisp	ADJ
ejpam-3001	86	16	graph	graph	NOUN
ejpam-3001	86	17	g∗1	g∗1	NOUN
ejpam-3001	86	18	:	:	PUNCT
ejpam-3001	86	19	(	(	PUNCT
ejpam-3001	86	20	v1	v1	NOUN
ejpam-3001	86	21	,	,	PUNCT
ejpam-3001	86	22	e1	e1	PROPN
ejpam-3001	86	23	)	)	PUNCT
ejpam-3001	86	24	where	where	SCONJ
ejpam-3001	86	25	v1	v1	NOUN
ejpam-3001	86	26	=	=	SYM
ejpam-3001	86	27	{	{	PUNCT
ejpam-3001	86	28	v1	v1	NOUN
ejpam-3001	86	29	,	,	PUNCT
ejpam-3001	86	30	v2	v2	PROPN
ejpam-3001	86	31	}	}	PUNCT
ejpam-3001	86	32	,	,	PUNCT
ejpam-3001	86	33	σ1(v1	σ1(v1	NOUN
ejpam-3001	86	34	)	)	PUNCT
ejpam-3001	86	35	=	=	SYM
ejpam-3001	86	36	1/2	1/2	NUM
ejpam-3001	86	37	,	,	PUNCT
ejpam-3001	86	38	σ1(v2	σ1(v2	NOUN
ejpam-3001	86	39	)	)	PUNCT
ejpam-3001	86	40	=	=	SYM
ejpam-3001	86	41	1/3	1/3	NUM
ejpam-3001	86	42	and	and	CCONJ
ejpam-3001	86	43	µ1(v1	µ1(v1	NOUN
ejpam-3001	86	44	,	,	PUNCT
ejpam-3001	86	45	v2	v2	NOUN
ejpam-3001	86	46	)	)	PUNCT
ejpam-3001	86	47	=	=	SYM
ejpam-3001	86	48	1/3	1/3	PROPN
ejpam-3001	86	49	and	and	CCONJ
ejpam-3001	86	50	g2	g2	PROPN
ejpam-3001	86	51	:	:	PUNCT
ejpam-3001	86	52	(	(	PUNCT
ejpam-3001	86	53	σ2	σ2	NOUN
ejpam-3001	86	54	,	,	PUNCT
ejpam-3001	86	55	µ2	µ2	PROPN
ejpam-3001	86	56	)	)	PUNCT
ejpam-3001	86	57	with	with	ADP
ejpam-3001	86	58	crisp	crisp	ADJ
ejpam-3001	86	59	graph	graph	NOUN
ejpam-3001	86	60	g∗2	g∗2	NOUN
ejpam-3001	86	61	:	:	PUNCT
ejpam-3001	86	62	(	(	PUNCT
ejpam-3001	86	63	v2	v2	PROPN
ejpam-3001	86	64	,	,	PUNCT
ejpam-3001	86	65	e2	e2	PROPN
ejpam-3001	86	66	)	)	PUNCT
ejpam-3001	86	67	where	where	SCONJ
ejpam-3001	86	68	v2	v2	NOUN
ejpam-3001	86	69	=	=	SYM
ejpam-3001	86	70	{	{	PUNCT
ejpam-3001	86	71	w1	w1	NOUN
ejpam-3001	86	72	,	,	PUNCT
ejpam-3001	86	73	w2	w2	NOUN
ejpam-3001	86	74	}	}	PUNCT
ejpam-3001	86	75	,	,	PUNCT
ejpam-3001	86	76	σ2(w1	σ2(w1	NOUN
ejpam-3001	86	77	)	)	PUNCT
ejpam-3001	86	78	=	=	SYM
ejpam-3001	86	79	1	1	NUM
ejpam-3001	86	80	,	,	PUNCT
ejpam-3001	86	81	σ2(w2	σ2(w2	NOUN
ejpam-3001	86	82	)	)	PUNCT
ejpam-3001	86	83	=	=	SYM
ejpam-3001	86	84	1	1	NUM
ejpam-3001	86	85	and	and	CCONJ
ejpam-3001	86	86	µ2(w1	µ2(w1	NOUN
ejpam-3001	86	87	,	,	PUNCT
ejpam-3001	86	88	w2	w2	NOUN
ejpam-3001	86	89	)	)	PUNCT
ejpam-3001	86	90	=	=	SYM
ejpam-3001	87	1	1	1	X
ejpam-3001	87	2	.	.	PUNCT
ejpam-3001	87	3	then	then	ADV
ejpam-3001	87	4	g1	g1	PROPN
ejpam-3001	87	5	and	and	CCONJ
ejpam-3001	87	6	g2	g2	PROPN
ejpam-3001	87	7	are	be	AUX
ejpam-3001	87	8	balanced	balanced	ADJ
ejpam-3001	87	9	,	,	PUNCT
ejpam-3001	87	10	while	while	SCONJ
ejpam-3001	87	11	the	the	DET
ejpam-3001	87	12	intersection	intersection	NOUN
ejpam-3001	87	13	(	(	PUNCT
ejpam-3001	87	14	join	join	NOUN
ejpam-3001	87	15	)	)	PUNCT
ejpam-3001	87	16	of	of	ADP
ejpam-3001	87	17	g1	g1	PROPN
ejpam-3001	87	18	and	and	CCONJ
ejpam-3001	87	19	g2	g2	PROPN
ejpam-3001	87	20	is	be	AUX
ejpam-3001	87	21	not	not	PART
ejpam-3001	87	22	balanced	balance	VERB
ejpam-3001	87	23	as	as	SCONJ
ejpam-3001	87	24	the	the	DET
ejpam-3001	87	25	join	join	NOUN
ejpam-3001	87	26	has	have	VERB
ejpam-3001	87	27	density	density	NOUN
ejpam-3001	87	28	equals	equal	VERB
ejpam-3001	87	29	to	to	ADP
ejpam-3001	87	30	71/90	71/90	NUM
ejpam-3001	87	31	while	while	SCONJ
ejpam-3001	87	32	the	the	DET
ejpam-3001	87	33	fuzzy	fuzzy	ADJ
ejpam-3001	87	34	subgraph	subgraph	NOUN
ejpam-3001	87	35	g1	g1	PROPN
ejpam-3001	87	36	of	of	ADP
ejpam-3001	87	37	the	the	DET
ejpam-3001	87	38	join	join	NOUN
ejpam-3001	87	39	has	have	VERB
ejpam-3001	87	40	density	density	NOUN
ejpam-3001	87	41	equals	equal	VERB
ejpam-3001	87	42	to	to	ADP
ejpam-3001	87	43	2	2	NUM
ejpam-3001	87	44	.	.	PUNCT
ejpam-3001	88	1	t.	t.	NOUN
ejpam-3001	88	2	a.	a.	PROPN
ejpam-3001	88	3	hawary	hawary	PROPN
ejpam-3001	88	4	/	/	SYM
ejpam-3001	88	5	eur	eur	PROPN
ejpam-3001	88	6	.	.	PUNCT
ejpam-3001	89	1	j.	j.	PROPN
ejpam-3001	89	2	pure	pure	PROPN
ejpam-3001	89	3	appl	appl	PROPN
ejpam-3001	89	4	.	.	PROPN
ejpam-3001	89	5	math	math	PROPN
ejpam-3001	89	6	,	,	PUNCT
ejpam-3001	89	7	10	10	NUM
ejpam-3001	89	8	(	(	PUNCT
ejpam-3001	89	9	3	3	NUM
ejpam-3001	89	10	)	)	PUNCT
ejpam-3001	89	11	(	(	PUNCT
ejpam-3001	89	12	2017	2017	NUM
ejpam-3001	89	13	)	)	PUNCT
ejpam-3001	89	14	,	,	PUNCT
ejpam-3001	89	15	552	552	NUM
ejpam-3001	89	16	-	-	SYM
ejpam-3001	89	17	560	560	NUM
ejpam-3001	89	18	555	555	NUM
ejpam-3001	89	19	the	the	DET
ejpam-3001	89	20	following	following	ADJ
ejpam-3001	89	21	result	result	NOUN
ejpam-3001	89	22	can	can	AUX
ejpam-3001	89	23	be	be	AUX
ejpam-3001	89	24	proved	prove	VERB
ejpam-3001	89	25	by	by	ADP
ejpam-3001	89	26	induction	induction	NOUN
ejpam-3001	89	27	on	on	ADP
ejpam-3001	89	28	the	the	DET
ejpam-3001	89	29	number	number	NOUN
ejpam-3001	89	30	of	of	ADP
ejpam-3001	89	31	components	component	NOUN
ejpam-3001	89	32	of	of	ADP
ejpam-3001	89	33	a	a	DET
ejpam-3001	89	34	fuzzy	fuzzy	ADJ
ejpam-3001	89	35	graph	graph	NOUN
ejpam-3001	89	36	g.	g.	PROPN
ejpam-3001	89	37	corollary	corollary	NOUN
ejpam-3001	89	38	1	1	NUM
ejpam-3001	89	39	.	.	PUNCT
ejpam-3001	90	1	if	if	SCONJ
ejpam-3001	90	2	g	g	NOUN
ejpam-3001	90	3	:	:	PUNCT
ejpam-3001	90	4	(	(	PUNCT
ejpam-3001	90	5	σ	σ	PROPN
ejpam-3001	90	6	,	,	PUNCT
ejpam-3001	90	7	µ	µ	NOUN
ejpam-3001	90	8	)	)	PUNCT
ejpam-3001	90	9	is	be	AUX
ejpam-3001	90	10	a	a	DET
ejpam-3001	90	11	fuzzy	fuzzy	ADJ
ejpam-3001	90	12	graph	graph	NOUN
ejpam-3001	90	13	with	with	ADP
ejpam-3001	90	14	each	each	PRON
ejpam-3001	90	15	of	of	ADP
ejpam-3001	90	16	its	its	PRON
ejpam-3001	90	17	component	component	NOUN
ejpam-3001	90	18	is	be	AUX
ejpam-3001	90	19	balanced	balanced	ADJ
ejpam-3001	90	20	,	,	PUNCT
ejpam-3001	90	21	then	then	ADV
ejpam-3001	90	22	g	g	PROPN
ejpam-3001	90	23	is	be	AUX
ejpam-3001	90	24	balanced	balanced	ADJ
ejpam-3001	90	25	.	.	PUNCT
ejpam-3001	91	1	theorem	theorem	ADJ
ejpam-3001	91	2	4	4	NUM
ejpam-3001	91	3	.	.	PUNCT
ejpam-3001	92	1	a	a	DET
ejpam-3001	92	2	fuzzy	fuzzy	ADJ
ejpam-3001	92	3	graph	graph	NOUN
ejpam-3001	92	4	g	g	NOUN
ejpam-3001	92	5	induced	induce	VERB
ejpam-3001	92	6	by	by	ADP
ejpam-3001	92	7	a	a	DET
ejpam-3001	92	8	tree	tree	NOUN
ejpam-3001	92	9	with	with	ADP
ejpam-3001	92	10	n	n	DET
ejpam-3001	92	11	vertices	vertex	NOUN
ejpam-3001	92	12	is	be	AUX
ejpam-3001	92	13	balanced	balanced	ADJ
ejpam-3001	92	14	.	.	PUNCT
ejpam-3001	93	1	proof	proof	NOUN
ejpam-3001	93	2	.	.	PUNCT
ejpam-3001	94	1	let	let	VERB
ejpam-3001	94	2	h	h	PRON
ejpam-3001	94	3	be	be	AUX
ejpam-3001	94	4	a	a	DET
ejpam-3001	94	5	fuzzy	fuzzy	ADJ
ejpam-3001	94	6	subgraph	subgraph	NOUN
ejpam-3001	94	7	of	of	ADP
ejpam-3001	94	8	g	g	PROPN
ejpam-3001	94	9	with	with	ADP
ejpam-3001	94	10	m	m	PROPN
ejpam-3001	94	11	vertices	vertex	NOUN
ejpam-3001	94	12	.	.	PUNCT
ejpam-3001	95	1	since	since	SCONJ
ejpam-3001	95	2	all	all	DET
ejpam-3001	95	3	subgraphs	subgraph	NOUN
ejpam-3001	95	4	of	of	ADP
ejpam-3001	95	5	trees	tree	NOUN
ejpam-3001	95	6	are	be	AUX
ejpam-3001	95	7	forests	forest	NOUN
ejpam-3001	95	8	,	,	PUNCT
ejpam-3001	95	9	we	we	PRON
ejpam-3001	95	10	have	have	VERB
ejpam-3001	95	11	the	the	DET
ejpam-3001	95	12	following	follow	VERB
ejpam-3001	95	13	two	two	NUM
ejpam-3001	95	14	case	case	NOUN
ejpam-3001	95	15	:	:	PUNCT
ejpam-3001	95	16	case	case	NOUN
ejpam-3001	95	17	1	1	NUM
ejpam-3001	95	18	:	:	PUNCT
ejpam-3001	95	19	h	h	NOUN
ejpam-3001	95	20	is	be	AUX
ejpam-3001	95	21	induced	induce	VERB
ejpam-3001	95	22	by	by	ADP
ejpam-3001	95	23	a	a	DET
ejpam-3001	95	24	tree	tree	NOUN
ejpam-3001	95	25	tm	tm	NOUN
ejpam-3001	95	26	.	.	PUNCT
ejpam-3001	96	1	then	then	ADV
ejpam-3001	96	2	as	as	ADP
ejpam-3001	96	3	∑	∑	PROPN
ejpam-3001	96	4	x	x	PROPN
ejpam-3001	96	5	,	,	PUNCT
ejpam-3001	96	6	y∈v	y∈v	PROPN
ejpam-3001	96	7	(	(	PUNCT
ejpam-3001	96	8	tm	tm	NOUN
ejpam-3001	96	9	)	)	PUNCT
ejpam-3001	96	10	µ(x	µ(x	PROPN
ejpam-3001	96	11	,	,	PUNCT
ejpam-3001	96	12	y	y	NOUN
ejpam-3001	96	13	)	)	PUNCT
ejpam-3001	96	14	≤	≤	NOUN
ejpam-3001	96	15	∑	∑	PUNCT
ejpam-3001	96	16	x	x	X
ejpam-3001	96	17	,	,	PUNCT
ejpam-3001	96	18	y∈v	y∈v	PROPN
ejpam-3001	96	19	(	(	PUNCT
ejpam-3001	96	20	tn	tn	NOUN
ejpam-3001	96	21	)	)	PUNCT
ejpam-3001	96	22	µ(x	µ(x	PROPN
ejpam-3001	96	23	,	,	PUNCT
ejpam-3001	96	24	y	y	NOUN
ejpam-3001	96	25	)	)	PUNCT
ejpam-3001	96	26	and	and	CCONJ
ejpam-3001	96	27	∑	∑	ADP
ejpam-3001	96	28	x	x	NOUN
ejpam-3001	96	29	,	,	PUNCT
ejpam-3001	96	30	y∈v	y∈v	PROPN
ejpam-3001	96	31	(	(	PUNCT
ejpam-3001	96	32	tn	tn	NOUN
ejpam-3001	96	33	)	)	PUNCT
ejpam-3001	96	34	(	(	PUNCT
ejpam-3001	96	35	σ	σ	NOUN
ejpam-3001	96	36	′	′	NUM
ejpam-3001	96	37	2(x	2(x	NUM
ejpam-3001	96	38	)	)	PUNCT
ejpam-3001	96	39	∧	∧	NOUN
ejpam-3001	96	40	σ′	σ′	NOUN
ejpam-3001	96	41	2(y	2(y	NUM
ejpam-3001	96	42	)	)	PUNCT
ejpam-3001	96	43	)	)	PUNCT
ejpam-3001	96	44	≤	≤	ADV
ejpam-3001	96	45	∑	∑	PUNCT
ejpam-3001	96	46	x	x	X
ejpam-3001	96	47	,	,	PUNCT
ejpam-3001	96	48	y∈v	y∈v	NOUN
ejpam-3001	96	49	(	(	PUNCT
ejpam-3001	96	50	tm)(σ	tm)(σ	NOUN
ejpam-3001	96	51	′	′	NUM
ejpam-3001	96	52	2(x	2(x	NUM
ejpam-3001	96	53	)	)	PUNCT
ejpam-3001	96	54	∧	∧	NOUN
ejpam-3001	96	55	σ′	σ′	NOUN
ejpam-3001	96	56	2(y	2(y	NUM
ejpam-3001	96	57	)	)	PUNCT
ejpam-3001	96	58	)	)	PUNCT
ejpam-3001	96	59	,	,	PUNCT
ejpam-3001	96	60	we	we	PRON
ejpam-3001	96	61	have	have	VERB
ejpam-3001	96	62	d(h	d(h	PROPN
ejpam-3001	96	63	)	)	PUNCT
ejpam-3001	97	1	=	=	SYM
ejpam-3001	97	2	2	2	NUM
ejpam-3001	97	3	∑	∑	PUNCT
ejpam-3001	97	4	x	x	PROPN
ejpam-3001	97	5	,	,	PUNCT
ejpam-3001	97	6	y∈v	y∈v	PROPN
ejpam-3001	97	7	(	(	PUNCT
ejpam-3001	97	8	tm	tm	NOUN
ejpam-3001	97	9	)	)	PUNCT
ejpam-3001	97	10	µ(x	µ(x	NOUN
ejpam-3001	97	11	,	,	PUNCT
ejpam-3001	97	12	y)∑	y)∑	PROPN
ejpam-3001	97	13	x	x	NOUN
ejpam-3001	97	14	,	,	PUNCT
ejpam-3001	97	15	y∈v	y∈v	NUM
ejpam-3001	97	16	(	(	PUNCT
ejpam-3001	97	17	tm)(σ	tm)(σ	NOUN
ejpam-3001	97	18	′	′	NUM
ejpam-3001	97	19	2(x	2(x	NUM
ejpam-3001	97	20	)	)	PUNCT
ejpam-3001	98	1	∧	∧	NOUN
ejpam-3001	98	2	σ′	σ′	NOUN
ejpam-3001	98	3	2(y	2(y	NUM
ejpam-3001	98	4	)	)	PUNCT
ejpam-3001	98	5	)	)	PUNCT
ejpam-3001	99	1	≤	≤	ADV
ejpam-3001	99	2	2	2	NUM
ejpam-3001	99	3	∑	∑	PUNCT
ejpam-3001	99	4	x	x	PROPN
ejpam-3001	99	5	,	,	PUNCT
ejpam-3001	99	6	y∈v	y∈v	PROPN
ejpam-3001	99	7	(	(	PUNCT
ejpam-3001	99	8	tn	tn	NOUN
ejpam-3001	99	9	)	)	PUNCT
ejpam-3001	99	10	µ(x	µ(x	PROPN
ejpam-3001	99	11	,	,	PUNCT
ejpam-3001	99	12	y)∑	y)∑	PROPN
ejpam-3001	99	13	x	x	NOUN
ejpam-3001	99	14	,	,	PUNCT
ejpam-3001	99	15	y∈v	y∈v	PROPN
ejpam-3001	99	16	(	(	PUNCT
ejpam-3001	99	17	tn	tn	NOUN
ejpam-3001	99	18	)	)	PUNCT
ejpam-3001	99	19	(	(	PUNCT
ejpam-3001	99	20	σ	σ	NOUN
ejpam-3001	99	21	′	′	NUM
ejpam-3001	99	22	2(x	2(x	NUM
ejpam-3001	99	23	)	)	PUNCT
ejpam-3001	99	24	∧	∧	NOUN
ejpam-3001	99	25	σ′	σ′	NOUN
ejpam-3001	99	26	2(y	2(y	NUM
ejpam-3001	99	27	)	)	PUNCT
ejpam-3001	99	28	)	)	PUNCT
ejpam-3001	100	1	=	=	PUNCT
ejpam-3001	100	2	d(g	d(g	PROPN
ejpam-3001	100	3	)	)	PUNCT
ejpam-3001	100	4	.	.	PUNCT
ejpam-3001	101	1	case	case	NOUN
ejpam-3001	101	2	2	2	NUM
ejpam-3001	101	3	:	:	PUNCT
ejpam-3001	101	4	h	h	NOUN
ejpam-3001	101	5	is	be	AUX
ejpam-3001	101	6	induced	induce	VERB
ejpam-3001	101	7	by	by	ADP
ejpam-3001	101	8	a	a	DET
ejpam-3001	101	9	forest	forest	NOUN
ejpam-3001	101	10	k	k	PROPN
ejpam-3001	101	11	with	with	ADP
ejpam-3001	101	12	m	m	PROPN
ejpam-3001	101	13	vertices	vertex	NOUN
ejpam-3001	101	14	and	and	CCONJ
ejpam-3001	101	15	p	p	PRON
ejpam-3001	101	16	≥	≥	NUM
ejpam-3001	101	17	2	2	NUM
ejpam-3001	101	18	components	component	NOUN
ejpam-3001	101	19	.	.	PUNCT
ejpam-3001	102	1	let	let	VERB
ejpam-3001	102	2	the	the	DET
ejpam-3001	102	3	number	number	NOUN
ejpam-3001	102	4	of	of	ADP
ejpam-3001	102	5	vertices	vertex	NOUN
ejpam-3001	102	6	in	in	ADP
ejpam-3001	102	7	each	each	DET
ejpam-3001	102	8	tree	tree	NOUN
ejpam-3001	102	9	be	be	AUX
ejpam-3001	102	10	ni	ni	PROPN
ejpam-3001	102	11	for	for	ADP
ejpam-3001	102	12	i	i	PRON
ejpam-3001	102	13	=	=	NOUN
ejpam-3001	102	14	1	1	NUM
ejpam-3001	102	15	,	,	PUNCT
ejpam-3001	102	16	2	2	NUM
ejpam-3001	102	17	,	,	PUNCT
ejpam-3001	102	18	...	...	PUNCT
ejpam-3001	102	19	,	,	PUNCT
ejpam-3001	102	20	p.	p.	NOUN
ejpam-3001	102	21	since	since	SCONJ
ejpam-3001	102	22	a	a	DET
ejpam-3001	102	23	forest	forest	NOUN
ejpam-3001	102	24	is	be	AUX
ejpam-3001	102	25	a	a	DET
ejpam-3001	102	26	disjoint	disjoint	ADJ
ejpam-3001	102	27	union	union	NOUN
ejpam-3001	102	28	of	of	ADP
ejpam-3001	102	29	trees	tree	NOUN
ejpam-3001	102	30	,	,	PUNCT
ejpam-3001	102	31	by	by	ADP
ejpam-3001	102	32	lemma	lemma	PROPN
ejpam-3001	102	33	3	3	NUM
ejpam-3001	102	34	,	,	PUNCT
ejpam-3001	102	35	g	g	PROPN
ejpam-3001	102	36	is	be	AUX
ejpam-3001	102	37	balanced	balanced	ADJ
ejpam-3001	102	38	.	.	PUNCT
ejpam-3001	103	1	corollary	corollary	ADJ
ejpam-3001	103	2	2	2	NUM
ejpam-3001	103	3	.	.	PUNCT
ejpam-3001	103	4	a	a	DET
ejpam-3001	103	5	fuzzy	fuzzy	ADJ
ejpam-3001	103	6	graph	graph	NOUN
ejpam-3001	103	7	g	g	NOUN
ejpam-3001	103	8	induced	induce	VERB
ejpam-3001	103	9	by	by	ADP
ejpam-3001	103	10	a	a	DET
ejpam-3001	103	11	forest	forest	NOUN
ejpam-3001	103	12	is	be	AUX
ejpam-3001	103	13	balanced	balance	VERB
ejpam-3001	103	14	.	.	PUNCT
ejpam-3001	104	1	theorem	theorem	ADJ
ejpam-3001	104	2	5	5	NUM
ejpam-3001	104	3	.	.	PUNCT
ejpam-3001	105	1	a	a	DET
ejpam-3001	105	2	fuzzy	fuzzy	ADJ
ejpam-3001	105	3	graph	graph	NOUN
ejpam-3001	105	4	g	g	NOUN
ejpam-3001	105	5	induced	induce	VERB
ejpam-3001	105	6	by	by	ADP
ejpam-3001	105	7	the	the	DET
ejpam-3001	105	8	cycle	cycle	NOUN
ejpam-3001	105	9	cn	cn	PROPN
ejpam-3001	105	10	is	be	AUX
ejpam-3001	105	11	balanced	balanced	ADJ
ejpam-3001	105	12	.	.	PUNCT
ejpam-3001	106	1	proof	proof	NOUN
ejpam-3001	106	2	.	.	PUNCT
ejpam-3001	107	1	let	let	VERB
ejpam-3001	107	2	h	h	PRON
ejpam-3001	107	3	be	be	AUX
ejpam-3001	107	4	a	a	DET
ejpam-3001	107	5	proper	proper	ADJ
ejpam-3001	107	6	fuzzy	fuzzy	ADJ
ejpam-3001	107	7	subgraph	subgraph	NOUN
ejpam-3001	107	8	of	of	ADP
ejpam-3001	107	9	g	g	PROPN
ejpam-3001	107	10	.	.	PUNCT
ejpam-3001	108	1	it	it	PRON
ejpam-3001	108	2	is	be	AUX
ejpam-3001	108	3	easy	easy	ADJ
ejpam-3001	108	4	to	to	PART
ejpam-3001	108	5	see	see	VERB
ejpam-3001	108	6	that	that	SCONJ
ejpam-3001	108	7	h	h	NOUN
ejpam-3001	108	8	is	be	AUX
ejpam-3001	108	9	induced	induce	VERB
ejpam-3001	108	10	by	by	ADP
ejpam-3001	108	11	forests	forest	NOUN
ejpam-3001	108	12	.	.	PUNCT
ejpam-3001	109	1	now	now	ADV
ejpam-3001	109	2	by	by	ADP
ejpam-3001	109	3	corollary	corollary	ADJ
ejpam-3001	109	4	2	2	NUM
ejpam-3001	109	5	,	,	PUNCT
ejpam-3001	109	6	forests	forest	NOUN
ejpam-3001	109	7	are	be	AUX
ejpam-3001	109	8	balanced	balanced	ADJ
ejpam-3001	109	9	and	and	CCONJ
ejpam-3001	109	10	by	by	ADP
ejpam-3001	109	11	lemma	lemma	PROPN
ejpam-3001	109	12	3	3	NUM
ejpam-3001	109	13	,	,	PUNCT
ejpam-3001	109	14	g	g	PROPN
ejpam-3001	109	15	is	be	AUX
ejpam-3001	109	16	balanced	balance	VERB
ejpam-3001	109	17	as	as	ADP
ejpam-3001	109	18	a	a	DET
ejpam-3001	109	19	a	a	DET
ejpam-3001	109	20	union	union	NOUN
ejpam-3001	109	21	of	of	ADP
ejpam-3001	109	22	balanced	balanced	ADJ
ejpam-3001	109	23	fuzzy	fuzzy	ADJ
ejpam-3001	109	24	graphs	graph	NOUN
ejpam-3001	109	25	.	.	PUNCT
ejpam-3001	110	1	3	3	X
ejpam-3001	110	2	.	.	X
ejpam-3001	110	3	series	series	NOUN
ejpam-3001	110	4	and	and	CCONJ
ejpam-3001	110	5	parallel	parallel	ADJ
ejpam-3001	110	6	connections	connection	NOUN
ejpam-3001	110	7	the	the	DET
ejpam-3001	110	8	operations	operation	NOUN
ejpam-3001	110	9	of	of	ADP
ejpam-3001	110	10	joining	join	VERB
ejpam-3001	110	11	electrical	electrical	ADJ
ejpam-3001	110	12	components	component	NOUN
ejpam-3001	110	13	in	in	ADP
ejpam-3001	110	14	parallel	parallel	ADJ
ejpam-3001	110	15	and	and	CCONJ
ejpam-3001	110	16	in	in	ADP
ejpam-3001	110	17	series	series	NOUN
ejpam-3001	110	18	are	be	AUX
ejpam-3001	110	19	very	very	ADV
ejpam-3001	110	20	important	important	ADJ
ejpam-3001	110	21	in	in	ADP
ejpam-3001	110	22	electrical	electrical	ADJ
ejpam-3001	110	23	network	network	NOUN
ejpam-3001	110	24	theory	theory	NOUN
ejpam-3001	110	25	.	.	PUNCT
ejpam-3001	111	1	graphs	graph	NOUN
ejpam-3001	111	2	may	may	AUX
ejpam-3001	111	3	be	be	AUX
ejpam-3001	111	4	also	also	ADV
ejpam-3001	111	5	constructed	construct	VERB
ejpam-3001	111	6	through	through	ADP
ejpam-3001	111	7	an	an	DET
ejpam-3001	111	8	operation	operation	NOUN
ejpam-3001	111	9	known	know	VERB
ejpam-3001	111	10	as	as	ADP
ejpam-3001	111	11	the	the	DET
ejpam-3001	111	12	parallel	parallel	ADJ
ejpam-3001	111	13	connection	connection	NOUN
ejpam-3001	111	14	.	.	PUNCT
ejpam-3001	112	1	this	this	PRON
ejpam-3001	112	2	can	can	AUX
ejpam-3001	112	3	be	be	AUX
ejpam-3001	112	4	defined	define	VERB
ejpam-3001	112	5	as	as	ADP
ejpam-3001	112	6	adding	add	VERB
ejpam-3001	112	7	elements	element	NOUN
ejpam-3001	112	8	in	in	ADP
ejpam-3001	112	9	parallel	parallel	NOUN
ejpam-3001	112	10	to	to	ADP
ejpam-3001	112	11	some	some	DET
ejpam-3001	112	12	existing	exist	VERB
ejpam-3001	112	13	element	element	NOUN
ejpam-3001	112	14	.	.	PUNCT
ejpam-3001	113	1	that	that	PRON
ejpam-3001	113	2	is	be	AUX
ejpam-3001	113	3	as	as	SCONJ
ejpam-3001	113	4	doubling	double	VERB
ejpam-3001	113	5	one	one	NUM
ejpam-3001	113	6	or	or	CCONJ
ejpam-3001	113	7	more	more	ADJ
ejpam-3001	113	8	elements	element	NOUN
ejpam-3001	113	9	.	.	PUNCT
ejpam-3001	114	1	it	it	PRON
ejpam-3001	114	2	is	be	AUX
ejpam-3001	114	3	also	also	ADV
ejpam-3001	114	4	can	can	AUX
ejpam-3001	114	5	be	be	AUX
ejpam-3001	114	6	constructed	construct	VERB
ejpam-3001	114	7	through	through	ADP
ejpam-3001	114	8	an	an	DET
ejpam-3001	114	9	operation	operation	NOUN
ejpam-3001	114	10	known	know	VERB
ejpam-3001	114	11	as	as	ADP
ejpam-3001	114	12	the	the	DET
ejpam-3001	114	13	series	series	NOUN
ejpam-3001	114	14	connection	connection	NOUN
ejpam-3001	114	15	.	.	PUNCT
ejpam-3001	115	1	analogously	analogously	ADV
ejpam-3001	115	2	,	,	PUNCT
ejpam-3001	115	3	in	in	ADP
ejpam-3001	115	4	this	this	DET
ejpam-3001	115	5	section	section	NOUN
ejpam-3001	115	6	,	,	PUNCT
ejpam-3001	115	7	we	we	PRON
ejpam-3001	115	8	introduce	introduce	VERB
ejpam-3001	115	9	two	two	NUM
ejpam-3001	115	10	new	new	ADJ
ejpam-3001	115	11	operations	operation	NOUN
ejpam-3001	115	12	on	on	ADP
ejpam-3001	115	13	fuzzy	fuzzy	ADJ
ejpam-3001	115	14	graphs	graph	NOUN
ejpam-3001	115	15	;	;	PUNCT
ejpam-3001	115	16	namely	namely	ADV
ejpam-3001	115	17	series	series	NOUN
ejpam-3001	115	18	and	and	CCONJ
ejpam-3001	115	19	parallel	parallel	ADJ
ejpam-3001	115	20	connections	connection	NOUN
ejpam-3001	115	21	.	.	PUNCT
ejpam-3001	116	1	to	to	PART
ejpam-3001	116	2	describe	describe	VERB
ejpam-3001	116	3	these	these	DET
ejpam-3001	116	4	operations	operation	NOUN
ejpam-3001	116	5	,	,	PUNCT
ejpam-3001	116	6	let	let	VERB
ejpam-3001	116	7	g1	g1	PROPN
ejpam-3001	116	8	:	:	PUNCT
ejpam-3001	116	9	(	(	PUNCT
ejpam-3001	116	10	σ1	σ1	PROPN
ejpam-3001	116	11	,	,	PUNCT
ejpam-3001	116	12	µ1	µ1	PROPN
ejpam-3001	116	13	)	)	PUNCT
ejpam-3001	116	14	be	be	VERB
ejpam-3001	116	15	a	a	DET
ejpam-3001	116	16	fuzzy	fuzzy	ADJ
ejpam-3001	116	17	graph	graph	NOUN
ejpam-3001	116	18	with	with	ADP
ejpam-3001	116	19	crisp	crisp	ADJ
ejpam-3001	116	20	graph	graph	NOUN
ejpam-3001	116	21	g∗1	g∗1	NOUN
ejpam-3001	116	22	:	:	PUNCT
ejpam-3001	116	23	(	(	PUNCT
ejpam-3001	116	24	v1	v1	NOUN
ejpam-3001	116	25	,	,	PUNCT
ejpam-3001	116	26	e1	e1	NOUN
ejpam-3001	116	27	)	)	PUNCT
ejpam-3001	116	28	and	and	CCONJ
ejpam-3001	116	29	g2	g2	PROPN
ejpam-3001	116	30	:	:	PUNCT
ejpam-3001	116	31	(	(	PUNCT
ejpam-3001	116	32	σ2	σ2	NOUN
ejpam-3001	116	33	,	,	PUNCT
ejpam-3001	116	34	µ2	µ2	PROPN
ejpam-3001	116	35	)	)	PUNCT
ejpam-3001	116	36	be	be	VERB
ejpam-3001	116	37	a	a	DET
ejpam-3001	116	38	fuzzy	fuzzy	ADJ
ejpam-3001	116	39	graph	graph	NOUN
ejpam-3001	116	40	with	with	ADP
ejpam-3001	116	41	crisp	crisp	ADJ
ejpam-3001	116	42	graph	graph	NOUN
ejpam-3001	116	43	g∗2	g∗2	NOUN
ejpam-3001	116	44	:	:	PUNCT
ejpam-3001	116	45	(	(	PUNCT
ejpam-3001	116	46	v2	v2	PROPN
ejpam-3001	116	47	,	,	PUNCT
ejpam-3001	116	48	e2	e2	PROPN
ejpam-3001	116	49	)	)	PUNCT
ejpam-3001	116	50	and	and	CCONJ
ejpam-3001	116	51	let	let	VERB
ejpam-3001	116	52	e1	e1	NOUN
ejpam-3001	116	53	=	=	SYM
ejpam-3001	116	54	{	{	PUNCT
ejpam-3001	116	55	v1	v1	PROPN
ejpam-3001	116	56	,	,	PUNCT
ejpam-3001	116	57	v′1	v′1	ADJ
ejpam-3001	116	58	}	}	PUNCT
ejpam-3001	116	59	∈	∈	PROPN
ejpam-3001	116	60	e1	e1	NOUN
ejpam-3001	116	61	and	and	CCONJ
ejpam-3001	116	62	e2	e2	PROPN
ejpam-3001	116	63	=	=	PUNCT
ejpam-3001	116	64	{	{	PUNCT
ejpam-3001	116	65	v2	v2	PROPN
ejpam-3001	116	66	,	,	PUNCT
ejpam-3001	116	67	v′2	v′2	ADJ
ejpam-3001	116	68	}	}	PUNCT
ejpam-3001	116	69	∈	∈	PROPN
ejpam-3001	116	70	e2	e2	PROPN
ejpam-3001	116	71	.	.	PUNCT
ejpam-3001	117	1	for	for	ADP
ejpam-3001	117	2	i	i	PRON
ejpam-3001	117	3	=	=	NOUN
ejpam-3001	117	4	1	1	NUM
ejpam-3001	117	5	,	,	PUNCT
ejpam-3001	117	6	2	2	NUM
ejpam-3001	117	7	,	,	PUNCT
ejpam-3001	117	8	arbitrary	arbitrary	ADJ
ejpam-3001	117	9	assign	assign	VERB
ejpam-3001	117	10	a	a	DET
ejpam-3001	117	11	direction	direction	NOUN
ejpam-3001	117	12	to	to	PART
ejpam-3001	117	13	ei	ei	VERB
ejpam-3001	117	14	and	and	CCONJ
ejpam-3001	117	15	say	say	VERB
ejpam-3001	117	16	its	its	PRON
ejpam-3001	117	17	tail	tail	NOUN
ejpam-3001	117	18	vi	vi	NOUN
ejpam-3001	117	19	and	and	CCONJ
ejpam-3001	117	20	its	its	PRON
ejpam-3001	117	21	head	head	NOUN
ejpam-3001	117	22	v′i	v′i	ADV
ejpam-3001	117	23	.	.	PUNCT
ejpam-3001	118	1	definition	definition	NOUN
ejpam-3001	118	2	6	6	NUM
ejpam-3001	118	3	.	.	PUNCT
ejpam-3001	119	1	let	let	VERB
ejpam-3001	119	2	g1	g1	PROPN
ejpam-3001	119	3	:	:	PUNCT
ejpam-3001	119	4	(	(	PUNCT
ejpam-3001	119	5	σ1	σ1	PROPN
ejpam-3001	119	6	,	,	PUNCT
ejpam-3001	119	7	µ1	µ1	PROPN
ejpam-3001	119	8	)	)	PUNCT
ejpam-3001	119	9	be	be	VERB
ejpam-3001	119	10	a	a	DET
ejpam-3001	119	11	fuzzy	fuzzy	ADJ
ejpam-3001	119	12	graph	graph	NOUN
ejpam-3001	119	13	with	with	ADP
ejpam-3001	119	14	crisp	crisp	ADJ
ejpam-3001	119	15	graph	graph	NOUN
ejpam-3001	119	16	g∗1	g∗1	NOUN
ejpam-3001	119	17	:	:	PUNCT
ejpam-3001	119	18	(	(	PUNCT
ejpam-3001	119	19	v1	v1	NOUN
ejpam-3001	119	20	,	,	PUNCT
ejpam-3001	119	21	e1	e1	NOUN
ejpam-3001	119	22	)	)	PUNCT
ejpam-3001	119	23	and	and	CCONJ
ejpam-3001	119	24	g2	g2	PROPN
ejpam-3001	119	25	:	:	PUNCT
ejpam-3001	119	26	(	(	PUNCT
ejpam-3001	119	27	σ2	σ2	NOUN
ejpam-3001	119	28	,	,	PUNCT
ejpam-3001	119	29	µ2	µ2	PROPN
ejpam-3001	119	30	)	)	PUNCT
ejpam-3001	119	31	be	be	VERB
ejpam-3001	119	32	a	a	DET
ejpam-3001	119	33	fuzzy	fuzzy	ADJ
ejpam-3001	119	34	graph	graph	NOUN
ejpam-3001	119	35	with	with	ADP
ejpam-3001	119	36	crisp	crisp	ADJ
ejpam-3001	119	37	graph	graph	NOUN
ejpam-3001	119	38	g∗2	g∗2	NOUN
ejpam-3001	119	39	:	:	PUNCT
ejpam-3001	119	40	(	(	PUNCT
ejpam-3001	119	41	v2	v2	PROPN
ejpam-3001	119	42	,	,	PUNCT
ejpam-3001	119	43	e2	e2	PROPN
ejpam-3001	119	44	)	)	PUNCT
ejpam-3001	119	45	.	.	PUNCT
ejpam-3001	120	1	the	the	DET
ejpam-3001	120	2	parallel	parallel	ADJ
ejpam-3001	120	3	connection	connection	NOUN
ejpam-3001	120	4	of	of	ADP
ejpam-3001	120	5	g1	g1	PROPN
ejpam-3001	120	6	and	and	CCONJ
ejpam-3001	120	7	g2	g2	PROPN
ejpam-3001	120	8	with	with	ADP
ejpam-3001	120	9	respect	respect	NOUN
ejpam-3001	120	10	to	to	ADP
ejpam-3001	120	11	the	the	DET
ejpam-3001	120	12	directed	direct	VERB
ejpam-3001	120	13	edges	edge	NOUN
ejpam-3001	120	14	e1	e1	PROPN
ejpam-3001	120	15	and	and	CCONJ
ejpam-3001	120	16	e2	e2	PROPN
ejpam-3001	120	17	is	be	AUX
ejpam-3001	120	18	the	the	DET
ejpam-3001	120	19	fuzzy	fuzzy	ADJ
ejpam-3001	120	20	graph	graph	NOUN
ejpam-3001	120	21	p	p	X
ejpam-3001	120	22	(	(	PUNCT
ejpam-3001	120	23	(	(	PUNCT
ejpam-3001	120	24	g1	g1	PROPN
ejpam-3001	120	25	,	,	PUNCT
ejpam-3001	120	26	e1	e1	NOUN
ejpam-3001	120	27	)	)	PUNCT
ejpam-3001	120	28	;	;	PUNCT
ejpam-3001	120	29	(	(	PUNCT
ejpam-3001	120	30	g2	g2	PROPN
ejpam-3001	120	31	,	,	PUNCT
ejpam-3001	120	32	e2	e2	PROPN
ejpam-3001	120	33	)	)	PUNCT
ejpam-3001	120	34	)	)	PUNCT
ejpam-3001	121	1	t.	t.	NOUN
ejpam-3001	121	2	a.	a.	PROPN
ejpam-3001	121	3	hawary	hawary	PROPN
ejpam-3001	121	4	/	/	SYM
ejpam-3001	121	5	eur	eur	PROPN
ejpam-3001	121	6	.	.	PUNCT
ejpam-3001	122	1	j.	j.	PROPN
ejpam-3001	122	2	pure	pure	PROPN
ejpam-3001	122	3	appl	appl	PROPN
ejpam-3001	122	4	.	.	PROPN
ejpam-3001	122	5	math	math	PROPN
ejpam-3001	122	6	,	,	PUNCT
ejpam-3001	122	7	10	10	NUM
ejpam-3001	122	8	(	(	PUNCT
ejpam-3001	122	9	3	3	NUM
ejpam-3001	122	10	)	)	PUNCT
ejpam-3001	122	11	(	(	PUNCT
ejpam-3001	122	12	2017	2017	NUM
ejpam-3001	122	13	)	)	PUNCT
ejpam-3001	122	14	,	,	PUNCT
ejpam-3001	122	15	552	552	NUM
ejpam-3001	122	16	-	-	SYM
ejpam-3001	122	17	560	560	NUM
ejpam-3001	122	18	556	556	NUM
ejpam-3001	122	19	obtained	obtain	VERB
ejpam-3001	122	20	by	by	ADP
ejpam-3001	122	21	deleting	delete	VERB
ejpam-3001	122	22	the	the	DET
ejpam-3001	122	23	edge	edge	NOUN
ejpam-3001	122	24	e1	e1	PROPN
ejpam-3001	122	25	from	from	ADP
ejpam-3001	122	26	g1	g1	NOUN
ejpam-3001	122	27	and	and	CCONJ
ejpam-3001	122	28	the	the	DET
ejpam-3001	122	29	edge	edge	NOUN
ejpam-3001	122	30	e2	e2	PROPN
ejpam-3001	122	31	from	from	ADP
ejpam-3001	122	32	g2	g2	PROPN
ejpam-3001	123	1	and	and	CCONJ
ejpam-3001	123	2	then	then	ADV
ejpam-3001	123	3	identify	identify	VERB
ejpam-3001	123	4	the	the	DET
ejpam-3001	123	5	vertices	vertex	NOUN
ejpam-3001	123	6	v1	v1	NOUN
ejpam-3001	123	7	,	,	PUNCT
ejpam-3001	123	8	v2	v2	PROPN
ejpam-3001	123	9	as	as	ADP
ejpam-3001	123	10	the	the	DET
ejpam-3001	123	11	vertex	vertex	NOUN
ejpam-3001	123	12	v	v	NOUN
ejpam-3001	123	13	with	with	ADP
ejpam-3001	123	14	σ(v	σ(v	NOUN
ejpam-3001	123	15	)	)	PUNCT
ejpam-3001	123	16	=	=	SYM
ejpam-3001	123	17	σ1(v1	σ1(v1	NOUN
ejpam-3001	123	18	)	)	PUNCT
ejpam-3001	123	19	∧	∧	PROPN
ejpam-3001	123	20	σ2(v2	σ2(v2	NOUN
ejpam-3001	123	21	)	)	PUNCT
ejpam-3001	123	22	and	and	CCONJ
ejpam-3001	123	23	v′1	v′1	VERB
ejpam-3001	123	24	,	,	PUNCT
ejpam-3001	123	25	v′2	v′2	NOUN
ejpam-3001	123	26	as	as	ADP
ejpam-3001	123	27	the	the	DET
ejpam-3001	123	28	vertex	vertex	NOUN
ejpam-3001	123	29	v′	v′	NOUN
ejpam-3001	123	30	with	with	ADP
ejpam-3001	123	31	σ(v′	σ(v′	PROPN
ejpam-3001	123	32	)	)	PUNCT
ejpam-3001	124	1	=	=	PUNCT
ejpam-3001	124	2	σ1(v	σ1(v	PUNCT
ejpam-3001	125	1	′	′	NUM
ejpam-3001	125	2	1	1	NUM
ejpam-3001	125	3	)	)	PUNCT
ejpam-3001	125	4	∧	∧	PROPN
ejpam-3001	125	5	σ2(v′2	σ2(v′2	PROPN
ejpam-3001	125	6	)	)	PUNCT
ejpam-3001	125	7	and	and	CCONJ
ejpam-3001	125	8	finally	finally	ADV
ejpam-3001	125	9	adding	add	VERB
ejpam-3001	125	10	a	a	DET
ejpam-3001	125	11	new	new	ADJ
ejpam-3001	125	12	edge	edge	NOUN
ejpam-3001	125	13	e	e	NOUN
ejpam-3001	125	14	joining	join	VERB
ejpam-3001	125	15	v	v	PRON
ejpam-3001	125	16	and	and	CCONJ
ejpam-3001	125	17	v′	v′	NOUN
ejpam-3001	125	18	with	with	ADP
ejpam-3001	125	19	µ(v	µ(v	PROPN
ejpam-3001	125	20	,	,	PUNCT
ejpam-3001	125	21	v′	v′	NUM
ejpam-3001	125	22	)	)	PUNCT
ejpam-3001	125	23	=	=	SYM
ejpam-3001	125	24	µ1(v1	µ1(v1	NOUN
ejpam-3001	125	25	,	,	PUNCT
ejpam-3001	125	26	v	v	ADJ
ejpam-3001	125	27	′	′	NUM
ejpam-3001	125	28	1	1	NUM
ejpam-3001	125	29	)	)	PUNCT
ejpam-3001	125	30	∧	∧	PROPN
ejpam-3001	125	31	µ2(v2	µ2(v2	NOUN
ejpam-3001	125	32	,	,	PUNCT
ejpam-3001	125	33	v′2	v′2	NOUN
ejpam-3001	125	34	)	)	PUNCT
ejpam-3001	125	35	.	.	PUNCT
ejpam-3001	126	1	definition	definition	NOUN
ejpam-3001	126	2	7	7	NUM
ejpam-3001	126	3	.	.	PUNCT
ejpam-3001	127	1	let	let	VERB
ejpam-3001	127	2	g1	g1	PROPN
ejpam-3001	127	3	:	:	PUNCT
ejpam-3001	127	4	(	(	PUNCT
ejpam-3001	127	5	σ1	σ1	PROPN
ejpam-3001	127	6	,	,	PUNCT
ejpam-3001	127	7	µ1	µ1	PROPN
ejpam-3001	127	8	)	)	PUNCT
ejpam-3001	127	9	be	be	VERB
ejpam-3001	127	10	a	a	DET
ejpam-3001	127	11	fuzzy	fuzzy	ADJ
ejpam-3001	127	12	graph	graph	NOUN
ejpam-3001	127	13	with	with	ADP
ejpam-3001	127	14	crisp	crisp	ADJ
ejpam-3001	127	15	graph	graph	NOUN
ejpam-3001	127	16	g∗1	g∗1	NOUN
ejpam-3001	127	17	:	:	PUNCT
ejpam-3001	127	18	(	(	PUNCT
ejpam-3001	127	19	v1	v1	NOUN
ejpam-3001	127	20	,	,	PUNCT
ejpam-3001	127	21	e1	e1	NOUN
ejpam-3001	127	22	)	)	PUNCT
ejpam-3001	127	23	and	and	CCONJ
ejpam-3001	127	24	g2	g2	PROPN
ejpam-3001	127	25	:	:	PUNCT
ejpam-3001	127	26	(	(	PUNCT
ejpam-3001	127	27	σ2	σ2	NOUN
ejpam-3001	127	28	,	,	PUNCT
ejpam-3001	127	29	µ2	µ2	PROPN
ejpam-3001	127	30	)	)	PUNCT
ejpam-3001	127	31	be	be	VERB
ejpam-3001	127	32	a	a	DET
ejpam-3001	127	33	fuzzy	fuzzy	ADJ
ejpam-3001	127	34	graph	graph	NOUN
ejpam-3001	127	35	with	with	ADP
ejpam-3001	127	36	crisp	crisp	ADJ
ejpam-3001	127	37	graph	graph	NOUN
ejpam-3001	127	38	g∗2	g∗2	NOUN
ejpam-3001	127	39	:	:	PUNCT
ejpam-3001	127	40	(	(	PUNCT
ejpam-3001	127	41	v2	v2	PROPN
ejpam-3001	127	42	,	,	PUNCT
ejpam-3001	127	43	e2	e2	PROPN
ejpam-3001	127	44	)	)	PUNCT
ejpam-3001	127	45	.	.	PUNCT
ejpam-3001	128	1	the	the	DET
ejpam-3001	128	2	series	series	PROPN
ejpam-3001	128	3	connection	connection	NOUN
ejpam-3001	128	4	of	of	ADP
ejpam-3001	128	5	g1	g1	PROPN
ejpam-3001	128	6	and	and	CCONJ
ejpam-3001	128	7	g2	g2	PROPN
ejpam-3001	128	8	with	with	ADP
ejpam-3001	128	9	respect	respect	NOUN
ejpam-3001	128	10	to	to	ADP
ejpam-3001	128	11	the	the	DET
ejpam-3001	128	12	directed	direct	VERB
ejpam-3001	128	13	edges	edge	NOUN
ejpam-3001	128	14	e1	e1	PROPN
ejpam-3001	128	15	and	and	CCONJ
ejpam-3001	128	16	e2	e2	PROPN
ejpam-3001	128	17	is	be	AUX
ejpam-3001	128	18	the	the	DET
ejpam-3001	128	19	fuzzy	fuzzy	ADJ
ejpam-3001	128	20	graph	graph	NOUN
ejpam-3001	128	21	s((g1	s((g1	NOUN
ejpam-3001	128	22	,	,	PUNCT
ejpam-3001	128	23	e1	e1	PROPN
ejpam-3001	128	24	)	)	PUNCT
ejpam-3001	128	25	;	;	PUNCT
ejpam-3001	128	26	(	(	PUNCT
ejpam-3001	128	27	g2	g2	PROPN
ejpam-3001	128	28	,	,	PUNCT
ejpam-3001	128	29	e2	e2	PROPN
ejpam-3001	128	30	)	)	PUNCT
ejpam-3001	128	31	)	)	PUNCT
ejpam-3001	128	32	obtained	obtain	VERB
ejpam-3001	128	33	by	by	ADP
ejpam-3001	128	34	deleting	delete	VERB
ejpam-3001	128	35	the	the	DET
ejpam-3001	128	36	edge	edge	NOUN
ejpam-3001	128	37	e1	e1	PROPN
ejpam-3001	128	38	from	from	ADP
ejpam-3001	128	39	g1	g1	NOUN
ejpam-3001	128	40	and	and	CCONJ
ejpam-3001	128	41	the	the	DET
ejpam-3001	128	42	edge	edge	NOUN
ejpam-3001	128	43	e2	e2	PROPN
ejpam-3001	128	44	from	from	ADP
ejpam-3001	128	45	g2	g2	PROPN
ejpam-3001	128	46	and	and	CCONJ
ejpam-3001	128	47	then	then	ADV
ejpam-3001	128	48	identify	identify	VERB
ejpam-3001	128	49	the	the	DET
ejpam-3001	128	50	vertices	vertex	NOUN
ejpam-3001	128	51	v1	v1	NOUN
ejpam-3001	128	52	,	,	PUNCT
ejpam-3001	128	53	v2	v2	PROPN
ejpam-3001	128	54	as	as	ADP
ejpam-3001	128	55	the	the	DET
ejpam-3001	128	56	vertex	vertex	NOUN
ejpam-3001	128	57	v	v	NOUN
ejpam-3001	128	58	with	with	ADP
ejpam-3001	128	59	σ(v	σ(v	NOUN
ejpam-3001	128	60	)	)	PUNCT
ejpam-3001	128	61	=	=	SYM
ejpam-3001	128	62	σ1(v1	σ1(v1	NOUN
ejpam-3001	128	63	)	)	PUNCT
ejpam-3001	128	64	∧	∧	PROPN
ejpam-3001	128	65	σ2(v2	σ2(v2	NOUN
ejpam-3001	128	66	)	)	PUNCT
ejpam-3001	128	67	and	and	CCONJ
ejpam-3001	128	68	finally	finally	ADV
ejpam-3001	128	69	adding	add	VERB
ejpam-3001	128	70	a	a	DET
ejpam-3001	128	71	new	new	ADJ
ejpam-3001	128	72	edge	edge	NOUN
ejpam-3001	128	73	e	e	NOUN
ejpam-3001	128	74	joining	join	VERB
ejpam-3001	128	75	v′1	v′1	NOUN
ejpam-3001	128	76	,	,	PUNCT
ejpam-3001	128	77	v′2	v′2	NOUN
ejpam-3001	128	78	with	with	ADP
ejpam-3001	128	79	µ(v′1	µ(v′1	NOUN
ejpam-3001	128	80	,	,	PUNCT
ejpam-3001	128	81	v	v	ADJ
ejpam-3001	128	82	′	′	NUM
ejpam-3001	128	83	2	2	NUM
ejpam-3001	128	84	)	)	PUNCT
ejpam-3001	128	85	=	=	SYM
ejpam-3001	128	86	µ1(v1	µ1(v1	NOUN
ejpam-3001	128	87	,	,	PUNCT
ejpam-3001	128	88	v	v	ADJ
ejpam-3001	128	89	′	′	NUM
ejpam-3001	128	90	1	1	NUM
ejpam-3001	128	91	)	)	PUNCT
ejpam-3001	128	92	∧	∧	PROPN
ejpam-3001	128	93	µ2(v2	µ2(v2	NOUN
ejpam-3001	128	94	,	,	PUNCT
ejpam-3001	128	95	v′2	v′2	NOUN
ejpam-3001	128	96	)	)	PUNCT
ejpam-3001	128	97	.	.	PUNCT
ejpam-3001	129	1	the	the	DET
ejpam-3001	129	2	connecting	connect	VERB
ejpam-3001	129	3	edges	edge	NOUN
ejpam-3001	129	4	in	in	ADP
ejpam-3001	129	5	p	p	X
ejpam-3001	129	6	(	(	PUNCT
ejpam-3001	129	7	(	(	PUNCT
ejpam-3001	129	8	g1	g1	PROPN
ejpam-3001	129	9	,	,	PUNCT
ejpam-3001	129	10	e1	e1	NOUN
ejpam-3001	129	11	)	)	PUNCT
ejpam-3001	129	12	;	;	PUNCT
ejpam-3001	129	13	(	(	PUNCT
ejpam-3001	129	14	g2	g2	PROPN
ejpam-3001	129	15	,	,	PUNCT
ejpam-3001	129	16	e2	e2	PROPN
ejpam-3001	129	17	)	)	PUNCT
ejpam-3001	129	18	)	)	PUNCT
ejpam-3001	129	19	and	and	CCONJ
ejpam-3001	129	20	s((g1	s((g1	NOUN
ejpam-3001	129	21	,	,	PUNCT
ejpam-3001	129	22	e1	e1	PROPN
ejpam-3001	129	23	)	)	PUNCT
ejpam-3001	129	24	;	;	PUNCT
ejpam-3001	129	25	(	(	PUNCT
ejpam-3001	129	26	g2	g2	PROPN
ejpam-3001	129	27	,	,	PUNCT
ejpam-3001	129	28	e2	e2	PROPN
ejpam-3001	129	29	)	)	PUNCT
ejpam-3001	129	30	)	)	PUNCT
ejpam-3001	129	31	are	be	AUX
ejpam-3001	129	32	usually	usually	ADV
ejpam-3001	129	33	arbitrary	arbitrary	ADJ
ejpam-3001	129	34	and	and	CCONJ
ejpam-3001	129	35	so	so	ADV
ejpam-3001	129	36	we	we	PRON
ejpam-3001	129	37	instead	instead	ADV
ejpam-3001	129	38	write	write	VERB
ejpam-3001	129	39	p	p	PROPN
ejpam-3001	129	40	(	(	PUNCT
ejpam-3001	129	41	g1;g2	g1;g2	PROPN
ejpam-3001	129	42	)	)	PUNCT
ejpam-3001	129	43	and	and	CCONJ
ejpam-3001	129	44	s(g1;g2	s(g1;g2	NOUN
ejpam-3001	129	45	)	)	PUNCT
ejpam-3001	129	46	,	,	PUNCT
ejpam-3001	129	47	respectively	respectively	ADV
ejpam-3001	129	48	.	.	PUNCT
ejpam-3001	130	1	to	to	PART
ejpam-3001	130	2	illustrate	illustrate	VERB
ejpam-3001	130	3	these	these	DET
ejpam-3001	130	4	definitions	definition	NOUN
ejpam-3001	130	5	,	,	PUNCT
ejpam-3001	130	6	we	we	PRON
ejpam-3001	130	7	offer	offer	VERB
ejpam-3001	130	8	the	the	DET
ejpam-3001	130	9	following	follow	VERB
ejpam-3001	130	10	example	example	NOUN
ejpam-3001	130	11	:	:	PUNCT
ejpam-3001	130	12	example	example	NOUN
ejpam-3001	130	13	2	2	X
ejpam-3001	130	14	.	.	X
ejpam-3001	130	15	consider	consider	VERB
ejpam-3001	130	16	the	the	DET
ejpam-3001	130	17	fuzzy	fuzzy	ADJ
ejpam-3001	130	18	graphs	graph	NOUN
ejpam-3001	130	19	g1	g1	NOUN
ejpam-3001	130	20	,	,	PUNCT
ejpam-3001	130	21	g2	g2	PROPN
ejpam-3001	130	22	,	,	PUNCT
ejpam-3001	130	23	p	p	X
ejpam-3001	130	24	(	(	PUNCT
ejpam-3001	130	25	g1;g2	g1;g2	PROPN
ejpam-3001	130	26	)	)	PUNCT
ejpam-3001	130	27	and	and	CCONJ
ejpam-3001	130	28	s(g1;g2	s(g1;g2	NOUN
ejpam-3001	130	29	)	)	PUNCT
ejpam-3001	130	30	in	in	ADP
ejpam-3001	130	31	figure	figure	NOUN
ejpam-3001	130	32	1	1	NUM
ejpam-3001	130	33	.	.	PUNCT
ejpam-3001	131	1	t.	t.	NOUN
ejpam-3001	131	2	a.	a.	PROPN
ejpam-3001	131	3	hawary	hawary	PROPN
ejpam-3001	131	4	/	/	SYM
ejpam-3001	131	5	eur	eur	PROPN
ejpam-3001	131	6	.	.	PUNCT
ejpam-3001	132	1	j.	j.	PROPN
ejpam-3001	132	2	pure	pure	PROPN
ejpam-3001	132	3	appl	appl	PROPN
ejpam-3001	132	4	.	.	PROPN
ejpam-3001	132	5	math	math	PROPN
ejpam-3001	132	6	,	,	PUNCT
ejpam-3001	132	7	10	10	NUM
ejpam-3001	132	8	(	(	PUNCT
ejpam-3001	132	9	3	3	NUM
ejpam-3001	132	10	)	)	PUNCT
ejpam-3001	132	11	(	(	PUNCT
ejpam-3001	132	12	2017	2017	NUM
ejpam-3001	132	13	)	)	PUNCT
ejpam-3001	132	14	,	,	PUNCT
ejpam-3001	132	15	552	552	NUM
ejpam-3001	132	16	-	-	SYM
ejpam-3001	132	17	560	560	NUM
ejpam-3001	132	18	557	557	NUM
ejpam-3001	132	19	as	as	ADP
ejpam-3001	132	20	an	an	DET
ejpam-3001	132	21	application	application	NOUN
ejpam-3001	132	22	,	,	PUNCT
ejpam-3001	132	23	we	we	PRON
ejpam-3001	132	24	provide	provide	VERB
ejpam-3001	132	25	the	the	DET
ejpam-3001	132	26	following	following	ADJ
ejpam-3001	132	27	result	result	NOUN
ejpam-3001	132	28	which	which	PRON
ejpam-3001	132	29	is	be	AUX
ejpam-3001	132	30	immediate	immediate	ADJ
ejpam-3001	132	31	on	on	ADP
ejpam-3001	132	32	the	the	DET
ejpam-3001	132	33	operation	operation	NOUN
ejpam-3001	132	34	of	of	ADP
ejpam-3001	132	35	union	union	NOUN
ejpam-3001	132	36	that	that	PRON
ejpam-3001	132	37	was	be	AUX
ejpam-3001	132	38	defined	define	VERB
ejpam-3001	132	39	in	in	ADP
ejpam-3001	132	40	[	[	X
ejpam-3001	132	41	16	16	NUM
ejpam-3001	132	42	]	]	X
ejpam-3001	132	43	:	:	PUNCT
ejpam-3001	132	44	theorem	theorem	NOUN
ejpam-3001	132	45	6	6	NUM
ejpam-3001	132	46	.	.	PUNCT
ejpam-3001	133	1	let	let	VERB
ejpam-3001	133	2	g1	g1	PROPN
ejpam-3001	133	3	:	:	PUNCT
ejpam-3001	133	4	(	(	PUNCT
ejpam-3001	133	5	σ1	σ1	PROPN
ejpam-3001	133	6	,	,	PUNCT
ejpam-3001	133	7	µ1	µ1	PROPN
ejpam-3001	133	8	)	)	PUNCT
ejpam-3001	133	9	be	be	VERB
ejpam-3001	133	10	a	a	DET
ejpam-3001	133	11	fuzzy	fuzzy	ADJ
ejpam-3001	133	12	graph	graph	NOUN
ejpam-3001	133	13	with	with	ADP
ejpam-3001	133	14	crisp	crisp	ADJ
ejpam-3001	133	15	graph	graph	NOUN
ejpam-3001	133	16	g∗1	g∗1	NOUN
ejpam-3001	133	17	:	:	PUNCT
ejpam-3001	133	18	(	(	PUNCT
ejpam-3001	133	19	v1	v1	NOUN
ejpam-3001	133	20	,	,	PUNCT
ejpam-3001	133	21	e1	e1	NOUN
ejpam-3001	133	22	)	)	PUNCT
ejpam-3001	133	23	and	and	CCONJ
ejpam-3001	133	24	g2	g2	PROPN
ejpam-3001	133	25	:	:	PUNCT
ejpam-3001	133	26	(	(	PUNCT
ejpam-3001	133	27	σ2	σ2	NOUN
ejpam-3001	133	28	,	,	PUNCT
ejpam-3001	133	29	µ2	µ2	PROPN
ejpam-3001	133	30	)	)	PUNCT
ejpam-3001	133	31	be	be	VERB
ejpam-3001	133	32	a	a	DET
ejpam-3001	133	33	fuzzy	fuzzy	ADJ
ejpam-3001	133	34	graph	graph	NOUN
ejpam-3001	133	35	with	with	ADP
ejpam-3001	133	36	crisp	crisp	ADJ
ejpam-3001	133	37	graph	graph	NOUN
ejpam-3001	133	38	g∗2	g∗2	NOUN
ejpam-3001	133	39	:	:	PUNCT
ejpam-3001	133	40	(	(	PUNCT
ejpam-3001	133	41	v2	v2	PROPN
ejpam-3001	133	42	,	,	PUNCT
ejpam-3001	133	43	e2	e2	PROPN
ejpam-3001	133	44	)	)	PUNCT
ejpam-3001	133	45	.	.	PUNCT
ejpam-3001	134	1	then	then	ADV
ejpam-3001	134	2	a	a	X
ejpam-3001	134	3	)	)	PUNCT
ejpam-3001	134	4	if	if	SCONJ
ejpam-3001	134	5	e1	e1	NOUN
ejpam-3001	134	6	∩	∩	ADJ
ejpam-3001	134	7	e2	e2	NOUN
ejpam-3001	134	8	=	=	VERB
ejpam-3001	134	9	∅	∅	NOUN
ejpam-3001	134	10	,	,	PUNCT
ejpam-3001	134	11	then	then	ADV
ejpam-3001	134	12	g1	g1	VERB
ejpam-3001	134	13	∪g2	∪g2	PROPN
ejpam-3001	134	14	=	=	SYM
ejpam-3001	134	15	g1	g1	PROPN
ejpam-3001	134	16	⊕g2	⊕g2	PROPN
ejpam-3001	134	17	.	.	PROPN
ejpam-3001	135	1	b	b	X
ejpam-3001	135	2	)	)	PUNCT
ejpam-3001	135	3	if	if	SCONJ
ejpam-3001	135	4	e1	e1	NOUN
ejpam-3001	135	5	∩	∩	ADJ
ejpam-3001	135	6	e2	e2	NOUN
ejpam-3001	135	7	=	=	SYM
ejpam-3001	135	8	{	{	PUNCT
ejpam-3001	135	9	e	e	NOUN
ejpam-3001	135	10	}	}	PUNCT
ejpam-3001	135	11	,	,	PUNCT
ejpam-3001	135	12	then	then	ADV
ejpam-3001	135	13	g1	g1	VERB
ejpam-3001	135	14	∪g2	∪g2	PROPN
ejpam-3001	135	15	=	=	SYM
ejpam-3001	135	16	s(g1;g2	s(g1;g2	PROPN
ejpam-3001	135	17	)	)	PUNCT
ejpam-3001	135	18	.	.	PUNCT
ejpam-3001	136	1	in	in	ADP
ejpam-3001	136	2	general	general	ADJ
ejpam-3001	136	3	,	,	PUNCT
ejpam-3001	136	4	the	the	DET
ejpam-3001	136	5	series	series	NOUN
ejpam-3001	136	6	connection	connection	NOUN
ejpam-3001	136	7	of	of	ADP
ejpam-3001	136	8	two	two	NUM
ejpam-3001	136	9	fuzzy	fuzzy	ADJ
ejpam-3001	136	10	graphs	graph	NOUN
ejpam-3001	136	11	needs	needs	AUX
ejpam-3001	136	12	not	not	PART
ejpam-3001	136	13	be	be	AUX
ejpam-3001	136	14	balanced	balance	VERB
ejpam-3001	136	15	.	.	PUNCT
ejpam-3001	137	1	example	example	NOUN
ejpam-3001	138	1	3	3	X
ejpam-3001	138	2	.	.	X
ejpam-3001	138	3	consider	consider	VERB
ejpam-3001	138	4	the	the	DET
ejpam-3001	138	5	fuzzy	fuzzy	ADJ
ejpam-3001	138	6	graphs	graph	NOUN
ejpam-3001	138	7	g1	g1	NOUN
ejpam-3001	138	8	,	,	PUNCT
ejpam-3001	138	9	g2	g2	PROPN
ejpam-3001	138	10	and	and	CCONJ
ejpam-3001	138	11	s(g1;g2	s(g1;g2	NOUN
ejpam-3001	138	12	)	)	PUNCT
ejpam-3001	138	13	in	in	ADP
ejpam-3001	138	14	figure	figure	NOUN
ejpam-3001	138	15	2	2	NUM
ejpam-3001	138	16	.	.	PUNCT
ejpam-3001	139	1	the	the	DET
ejpam-3001	139	2	first	first	ADJ
ejpam-3001	139	3	graph	graph	NOUN
ejpam-3001	139	4	with	with	ADP
ejpam-3001	139	5	one	one	NUM
ejpam-3001	139	6	edge	edge	NOUN
ejpam-3001	139	7	removed	remove	VERB
ejpam-3001	139	8	is	be	AUX
ejpam-3001	139	9	subgraph	subgraph	NOUN
ejpam-3001	139	10	of	of	ADP
ejpam-3001	139	11	s(g1;g2	s(g1;g2	NOUN
ejpam-3001	139	12	)	)	PUNCT
ejpam-3001	139	13	that	that	PRON
ejpam-3001	139	14	has	have	VERB
ejpam-3001	139	15	density	density	NOUN
ejpam-3001	139	16	1	1	NUM
ejpam-3001	139	17	which	which	PRON
ejpam-3001	139	18	is	be	AUX
ejpam-3001	139	19	greater	great	ADJ
ejpam-3001	139	20	than10	than10	ADJ
ejpam-3001	139	21	12	12	NUM
ejpam-3001	139	22	=	=	PUNCT
ejpam-3001	139	23	d(s(g1;g2)).thus	d(s(g1;g2)).thu	NOUN
ejpam-3001	139	24	s(g1;g2	s(g1;g2	NOUN
ejpam-3001	139	25	)	)	PUNCT
ejpam-3001	139	26	is	be	AUX
ejpam-3001	139	27	not	not	PART
ejpam-3001	139	28	balanced	balanced	ADJ
ejpam-3001	139	29	.	.	PUNCT
ejpam-3001	140	1	we	we	PRON
ejpam-3001	140	2	remark	remark	VERB
ejpam-3001	140	3	that	that	SCONJ
ejpam-3001	140	4	in	in	ADP
ejpam-3001	140	5	the	the	DET
ejpam-3001	140	6	preceding	precede	VERB
ejpam-3001	140	7	example	example	NOUN
ejpam-3001	140	8	,	,	PUNCT
ejpam-3001	140	9	g1	g1	PROPN
ejpam-3001	140	10	and	and	CCONJ
ejpam-3001	140	11	g2	g2	PROPN
ejpam-3001	140	12	are	be	AUX
ejpam-3001	140	13	balanced	balanced	ADJ
ejpam-3001	140	14	.	.	PUNCT
ejpam-3001	141	1	thus	thus	ADV
ejpam-3001	141	2	the	the	DET
ejpam-3001	141	3	series	series	NOUN
ejpam-3001	141	4	connection	connection	NOUN
ejpam-3001	141	5	of	of	ADP
ejpam-3001	141	6	two	two	NUM
ejpam-3001	141	7	balanced	balanced	ADJ
ejpam-3001	141	8	fuzzy	fuzzy	ADJ
ejpam-3001	141	9	graphs	graph	NOUN
ejpam-3001	141	10	needs	needs	AUX
ejpam-3001	141	11	not	not	PART
ejpam-3001	141	12	be	be	AUX
ejpam-3001	141	13	balanced	balance	VERB
ejpam-3001	141	14	.	.	PUNCT
ejpam-3001	142	1	theorem	theorem	ADJ
ejpam-3001	142	2	7	7	NUM
ejpam-3001	142	3	.	.	PUNCT
ejpam-3001	143	1	the	the	DET
ejpam-3001	143	2	series	series	PROPN
ejpam-3001	143	3	connection	connection	NOUN
ejpam-3001	143	4	of	of	ADP
ejpam-3001	143	5	a	a	DET
ejpam-3001	143	6	fuzzy	fuzzy	ADJ
ejpam-3001	143	7	graph	graph	NOUN
ejpam-3001	143	8	g1	g1	PROPN
ejpam-3001	143	9	:	:	PUNCT
ejpam-3001	143	10	(	(	PUNCT
ejpam-3001	143	11	σ1	σ1	PROPN
ejpam-3001	143	12	,	,	PUNCT
ejpam-3001	143	13	µ1	µ1	PROPN
ejpam-3001	143	14	)	)	PUNCT
ejpam-3001	143	15	induced	induce	VERB
ejpam-3001	143	16	by	by	ADP
ejpam-3001	143	17	cn	cn	PROPN
ejpam-3001	143	18	and	and	CCONJ
ejpam-3001	143	19	a	a	DET
ejpam-3001	143	20	fuzzy	fuzzy	ADJ
ejpam-3001	143	21	graph	graph	NOUN
ejpam-3001	143	22	g2	g2	PROPN
ejpam-3001	143	23	:	:	PUNCT
ejpam-3001	143	24	(	(	PUNCT
ejpam-3001	143	25	σ2	σ2	NOUN
ejpam-3001	143	26	,	,	PUNCT
ejpam-3001	143	27	µ2	µ2	PROPN
ejpam-3001	143	28	)	)	PUNCT
ejpam-3001	143	29	induced	induce	VERB
ejpam-3001	143	30	by	by	ADP
ejpam-3001	143	31	cm	cm	PROPN
ejpam-3001	143	32	is	be	AUX
ejpam-3001	143	33	balanced	balanced	ADJ
ejpam-3001	143	34	.	.	PUNCT
ejpam-3001	144	1	t.	t.	NOUN
ejpam-3001	144	2	a.	a.	PROPN
ejpam-3001	144	3	hawary	hawary	PROPN
ejpam-3001	144	4	/	/	SYM
ejpam-3001	144	5	eur	eur	PROPN
ejpam-3001	144	6	.	.	PUNCT
ejpam-3001	145	1	j.	j.	PROPN
ejpam-3001	145	2	pure	pure	PROPN
ejpam-3001	145	3	appl	appl	PROPN
ejpam-3001	145	4	.	.	PROPN
ejpam-3001	145	5	math	math	PROPN
ejpam-3001	145	6	,	,	PUNCT
ejpam-3001	145	7	10	10	NUM
ejpam-3001	145	8	(	(	PUNCT
ejpam-3001	145	9	3	3	NUM
ejpam-3001	145	10	)	)	PUNCT
ejpam-3001	145	11	(	(	PUNCT
ejpam-3001	145	12	2017	2017	NUM
ejpam-3001	145	13	)	)	PUNCT
ejpam-3001	145	14	,	,	PUNCT
ejpam-3001	145	15	552	552	NUM
ejpam-3001	145	16	-	-	SYM
ejpam-3001	145	17	560	560	NUM
ejpam-3001	145	18	558	558	NUM
ejpam-3001	145	19	proof	proof	NOUN
ejpam-3001	145	20	.	.	PUNCT
ejpam-3001	146	1	from	from	ADP
ejpam-3001	146	2	the	the	DET
ejpam-3001	146	3	definition	definition	NOUN
ejpam-3001	146	4	of	of	ADP
ejpam-3001	146	5	series	series	NOUN
ejpam-3001	146	6	connection	connection	NOUN
ejpam-3001	146	7	of	of	ADP
ejpam-3001	146	8	two	two	NUM
ejpam-3001	146	9	fuzzy	fuzzy	ADJ
ejpam-3001	146	10	graphs	graph	NOUN
ejpam-3001	146	11	,	,	PUNCT
ejpam-3001	146	12	it	it	PRON
ejpam-3001	146	13	is	be	AUX
ejpam-3001	146	14	obvious	obvious	ADJ
ejpam-3001	146	15	that	that	SCONJ
ejpam-3001	146	16	s(g1;g2	s(g1;g2	NOUN
ejpam-3001	146	17	)	)	PUNCT
ejpam-3001	146	18	is	be	AUX
ejpam-3001	146	19	isomorphic	isomorphic	ADJ
ejpam-3001	146	20	to	to	ADP
ejpam-3001	146	21	a	a	DET
ejpam-3001	146	22	fuzzy	fuzzy	ADJ
ejpam-3001	146	23	graph	graph	NOUN
ejpam-3001	146	24	induced	induce	VERB
ejpam-3001	146	25	by	by	ADP
ejpam-3001	146	26	the	the	DET
ejpam-3001	146	27	cycle	cycle	NOUN
ejpam-3001	146	28	cn+m−1	cn+m−1	NOUN
ejpam-3001	146	29	.	.	PUNCT
ejpam-3001	147	1	hence	hence	ADV
ejpam-3001	147	2	by	by	ADP
ejpam-3001	147	3	theorem	theorem	ADJ
ejpam-3001	147	4	5	5	NUM
ejpam-3001	147	5	,	,	PUNCT
ejpam-3001	147	6	s(g1;g2	s(g1;g2	NOUN
ejpam-3001	147	7	)	)	PUNCT
ejpam-3001	147	8	is	be	AUX
ejpam-3001	147	9	balanced	balanced	ADJ
ejpam-3001	147	10	.	.	PUNCT
ejpam-3001	148	1	we	we	PRON
ejpam-3001	148	2	remark	remark	VERB
ejpam-3001	148	3	that	that	SCONJ
ejpam-3001	148	4	the	the	DET
ejpam-3001	148	5	above	above	ADJ
ejpam-3001	148	6	result	result	NOUN
ejpam-3001	148	7	needs	needs	AUX
ejpam-3001	148	8	not	not	PART
ejpam-3001	148	9	be	be	AUX
ejpam-3001	148	10	true	true	ADJ
ejpam-3001	148	11	in	in	ADP
ejpam-3001	148	12	the	the	DET
ejpam-3001	148	13	case	case	NOUN
ejpam-3001	148	14	of	of	ADP
ejpam-3001	148	15	parallel	parallel	ADJ
ejpam-3001	148	16	connection	connection	NOUN
ejpam-3001	148	17	.	.	PUNCT
ejpam-3001	149	1	example	example	NOUN
ejpam-3001	150	1	4	4	NUM
ejpam-3001	150	2	.	.	X
ejpam-3001	150	3	consider	consider	VERB
ejpam-3001	150	4	the	the	DET
ejpam-3001	150	5	fuzzy	fuzzy	ADJ
ejpam-3001	150	6	graphs	graph	NOUN
ejpam-3001	150	7	g1	g1	NOUN
ejpam-3001	150	8	,	,	PUNCT
ejpam-3001	150	9	g2	g2	PROPN
ejpam-3001	150	10	and	and	CCONJ
ejpam-3001	150	11	p	p	PROPN
ejpam-3001	150	12	(	(	PUNCT
ejpam-3001	150	13	g1;g2	g1;g2	PROPN
ejpam-3001	150	14	)	)	PUNCT
ejpam-3001	150	15	in	in	ADP
ejpam-3001	150	16	figure	figure	NOUN
ejpam-3001	150	17	3	3	NUM
ejpam-3001	150	18	.	.	PUNCT
ejpam-3001	151	1	now	now	ADV
ejpam-3001	151	2	g1	g1	PROPN
ejpam-3001	151	3	is	be	AUX
ejpam-3001	151	4	a	a	DET
ejpam-3001	151	5	subgraph	subgraph	NOUN
ejpam-3001	151	6	of	of	ADP
ejpam-3001	151	7	p	p	PROPN
ejpam-3001	151	8	(	(	PUNCT
ejpam-3001	151	9	g1;g2	g1;g2	PROPN
ejpam-3001	151	10	)	)	PUNCT
ejpam-3001	151	11	and	and	CCONJ
ejpam-3001	151	12	d(g1	d(g1	NOUN
ejpam-3001	151	13	)	)	PUNCT
ejpam-3001	151	14	=	=	SYM
ejpam-3001	151	15	2	2	X
ejpam-3001	151	16	>	>	X
ejpam-3001	151	17	.8	.8	PUNCT
ejpam-3001	152	1	=	=	SYM
ejpam-3001	152	2	d(p	d(p	PROPN
ejpam-3001	152	3	(	(	PUNCT
ejpam-3001	152	4	g1;g2	g1;g2	PROPN
ejpam-3001	152	5	)	)	PUNCT
ejpam-3001	152	6	)	)	PUNCT
ejpam-3001	152	7	.	.	PUNCT
ejpam-3001	153	1	thus	thus	ADV
ejpam-3001	153	2	p	p	X
ejpam-3001	153	3	(	(	PUNCT
ejpam-3001	153	4	g1;g2	g1;g2	PROPN
ejpam-3001	153	5	)	)	PUNCT
ejpam-3001	153	6	is	be	AUX
ejpam-3001	153	7	not	not	PART
ejpam-3001	153	8	balanced	balanced	ADJ
ejpam-3001	153	9	.	.	PUNCT
ejpam-3001	154	1	note	note	VERB
ejpam-3001	154	2	that	that	SCONJ
ejpam-3001	154	3	in	in	ADP
ejpam-3001	154	4	the	the	DET
ejpam-3001	154	5	preceding	precede	VERB
ejpam-3001	154	6	example	example	NOUN
ejpam-3001	154	7	,	,	PUNCT
ejpam-3001	154	8	g1	g1	PROPN
ejpam-3001	154	9	and	and	CCONJ
ejpam-3001	154	10	g2	g2	PROPN
ejpam-3001	154	11	are	be	AUX
ejpam-3001	154	12	complete	complete	ADJ
ejpam-3001	154	13	and	and	CCONJ
ejpam-3001	154	14	balanced	balanced	ADJ
ejpam-3001	154	15	while	while	SCONJ
ejpam-3001	154	16	s(g1;g2	s(g1;g2	NOUN
ejpam-3001	154	17	)	)	PUNCT
ejpam-3001	154	18	is	be	AUX
ejpam-3001	154	19	not	not	PART
ejpam-3001	154	20	complete	complete	ADJ
ejpam-3001	154	21	and	and	CCONJ
ejpam-3001	154	22	not	not	PART
ejpam-3001	154	23	balanced	balanced	ADJ
ejpam-3001	154	24	.	.	PUNCT
ejpam-3001	155	1	theorem	theorem	ADJ
ejpam-3001	155	2	8	8	NUM
ejpam-3001	155	3	.	.	PUNCT
ejpam-3001	156	1	let	let	VERB
ejpam-3001	156	2	g1	g1	PROPN
ejpam-3001	156	3	:	:	PUNCT
ejpam-3001	156	4	(	(	PUNCT
ejpam-3001	156	5	σ1	σ1	PROPN
ejpam-3001	156	6	,	,	PUNCT
ejpam-3001	156	7	µ1	µ1	PROPN
ejpam-3001	156	8	)	)	PUNCT
ejpam-3001	156	9	be	be	VERB
ejpam-3001	156	10	a	a	DET
ejpam-3001	156	11	strong	strong	ADJ
ejpam-3001	156	12	fuzzy	fuzzy	ADJ
ejpam-3001	156	13	graph	graph	NOUN
ejpam-3001	156	14	with	with	ADP
ejpam-3001	156	15	crisp	crisp	ADJ
ejpam-3001	156	16	graph	graph	NOUN
ejpam-3001	156	17	g∗1	g∗1	NOUN
ejpam-3001	156	18	:	:	PUNCT
ejpam-3001	156	19	(	(	PUNCT
ejpam-3001	156	20	v1	v1	NOUN
ejpam-3001	156	21	,	,	PUNCT
ejpam-3001	156	22	e1	e1	NOUN
ejpam-3001	156	23	)	)	PUNCT
ejpam-3001	156	24	and	and	CCONJ
ejpam-3001	156	25	g2	g2	PROPN
ejpam-3001	156	26	:	:	PUNCT
ejpam-3001	156	27	(	(	PUNCT
ejpam-3001	156	28	σ2	σ2	NOUN
ejpam-3001	156	29	,	,	PUNCT
ejpam-3001	156	30	µ2	µ2	PROPN
ejpam-3001	156	31	)	)	PUNCT
ejpam-3001	156	32	be	be	VERB
ejpam-3001	156	33	a	a	DET
ejpam-3001	156	34	strong	strong	ADJ
ejpam-3001	156	35	fuzzy	fuzzy	ADJ
ejpam-3001	156	36	graph	graph	NOUN
ejpam-3001	156	37	with	with	ADP
ejpam-3001	156	38	crisp	crisp	ADJ
ejpam-3001	156	39	graph	graph	NOUN
ejpam-3001	156	40	g∗2	g∗2	NOUN
ejpam-3001	156	41	:	:	PUNCT
ejpam-3001	156	42	(	(	PUNCT
ejpam-3001	156	43	v2	v2	INTJ
ejpam-3001	156	44	,	,	PUNCT
ejpam-3001	156	45	e2).then	e2).then	SCONJ
ejpam-3001	156	46	p	p	X
ejpam-3001	156	47	(	(	PUNCT
ejpam-3001	156	48	g1;g2	g1;g2	PROPN
ejpam-3001	156	49	)	)	PUNCT
ejpam-3001	156	50	and	and	CCONJ
ejpam-3001	156	51	s(g1;g2	s(g1;g2	NOUN
ejpam-3001	156	52	)	)	PUNCT
ejpam-3001	156	53	are	be	AUX
ejpam-3001	156	54	strong	strong	ADJ
ejpam-3001	156	55	.	.	PUNCT
ejpam-3001	157	1	proof	proof	NOUN
ejpam-3001	157	2	.	.	PUNCT
ejpam-3001	158	1	we	we	PRON
ejpam-3001	158	2	only	only	ADV
ejpam-3001	158	3	prove	prove	VERB
ejpam-3001	158	4	the	the	DET
ejpam-3001	158	5	case	case	NOUN
ejpam-3001	158	6	of	of	ADP
ejpam-3001	158	7	parallel	parallel	ADJ
ejpam-3001	158	8	connection	connection	NOUN
ejpam-3001	158	9	.	.	PUNCT
ejpam-3001	159	1	the	the	DET
ejpam-3001	159	2	case	case	NOUN
ejpam-3001	159	3	of	of	ADP
ejpam-3001	159	4	series	series	NOUN
ejpam-3001	159	5	connection	connection	NOUN
ejpam-3001	159	6	is	be	AUX
ejpam-3001	159	7	similar	similar	ADJ
ejpam-3001	159	8	.	.	PUNCT
ejpam-3001	160	1	references	reference	NOUN
ejpam-3001	160	2	559	559	NUM
ejpam-3001	160	3	any	any	DET
ejpam-3001	160	4	edge	edge	NOUN
ejpam-3001	160	5	{	{	PUNCT
ejpam-3001	160	6	x	x	NOUN
ejpam-3001	160	7	,	,	PUNCT
ejpam-3001	160	8	y	y	NOUN
ejpam-3001	160	9	}	}	PUNCT
ejpam-3001	160	10	in	in	ADP
ejpam-3001	160	11	p	p	PROPN
ejpam-3001	160	12	(	(	PUNCT
ejpam-3001	160	13	g1;g2	g1;g2	PROPN
ejpam-3001	160	14	)	)	PUNCT
ejpam-3001	160	15	is	be	AUX
ejpam-3001	160	16	either	either	CCONJ
ejpam-3001	160	17	an	an	DET
ejpam-3001	160	18	edge	edge	NOUN
ejpam-3001	160	19	from	from	ADP
ejpam-3001	160	20	g1	g1	NOUN
ejpam-3001	160	21	or	or	CCONJ
ejpam-3001	160	22	an	an	DET
ejpam-3001	160	23	edge	edge	NOUN
ejpam-3001	160	24	from	from	ADP
ejpam-3001	160	25	g2	g2	PROPN
ejpam-3001	160	26	or	or	CCONJ
ejpam-3001	160	27	it	it	PRON
ejpam-3001	160	28	is	be	AUX
ejpam-3001	160	29	the	the	DET
ejpam-3001	160	30	new	new	ADJ
ejpam-3001	160	31	edge	edge	NOUN
ejpam-3001	160	32	.	.	PUNCT
ejpam-3001	161	1	in	in	ADP
ejpam-3001	161	2	the	the	DET
ejpam-3001	161	3	first	first	ADJ
ejpam-3001	161	4	two	two	NUM
ejpam-3001	161	5	cases	case	NOUN
ejpam-3001	161	6	,	,	PUNCT
ejpam-3001	161	7	the	the	DET
ejpam-3001	161	8	result	result	NOUN
ejpam-3001	161	9	is	be	AUX
ejpam-3001	161	10	obvious	obvious	ADJ
ejpam-3001	161	11	.	.	PUNCT
ejpam-3001	162	1	in	in	ADP
ejpam-3001	162	2	the	the	DET
ejpam-3001	162	3	third	third	ADJ
ejpam-3001	162	4	case	case	NOUN
ejpam-3001	162	5	,	,	PUNCT
ejpam-3001	162	6	µ(x	µ(x	PROPN
ejpam-3001	162	7	,	,	PUNCT
ejpam-3001	162	8	y	y	NOUN
ejpam-3001	162	9	)	)	PUNCT
ejpam-3001	162	10	=	=	SYM
ejpam-3001	162	11	µ1(x1	µ1(x1	PROPN
ejpam-3001	162	12	,	,	PUNCT
ejpam-3001	162	13	x2	x2	PROPN
ejpam-3001	162	14	)	)	PUNCT
ejpam-3001	162	15	∧	∧	PROPN
ejpam-3001	162	16	µ2(y1	µ2(y1	PROPN
ejpam-3001	162	17	,	,	PUNCT
ejpam-3001	162	18	y2	y2	PROPN
ejpam-3001	162	19	)	)	PUNCT
ejpam-3001	162	20	for	for	ADP
ejpam-3001	162	21	some	some	DET
ejpam-3001	162	22	{	{	PUNCT
ejpam-3001	162	23	x1	x1	PROPN
ejpam-3001	162	24	,	,	PUNCT
ejpam-3001	162	25	x2	x2	ADJ
ejpam-3001	162	26	}	}	PUNCT
ejpam-3001	162	27	∈	∈	PROPN
ejpam-3001	162	28	e1	e1	NOUN
ejpam-3001	162	29	and	and	CCONJ
ejpam-3001	162	30	{	{	PUNCT
ejpam-3001	162	31	y1	y1	NOUN
ejpam-3001	162	32	,	,	PUNCT
ejpam-3001	162	33	y2	y2	NOUN
ejpam-3001	162	34	}	}	PUNCT
ejpam-3001	162	35	∈	∈	PROPN
ejpam-3001	162	36	e2	e2	PROPN
ejpam-3001	162	37	.	.	PUNCT
ejpam-3001	163	1	thus	thus	ADV
ejpam-3001	163	2	µ(x	µ(x	VERB
ejpam-3001	163	3	,	,	PUNCT
ejpam-3001	163	4	y	y	NOUN
ejpam-3001	163	5	)	)	PUNCT
ejpam-3001	163	6	=	=	SYM
ejpam-3001	164	1	σ1(x1	σ1(x1	ADJ
ejpam-3001	164	2	)	)	PUNCT
ejpam-3001	164	3	∧	∧	NOUN
ejpam-3001	164	4	σ1(x2	σ1(x2	NOUN
ejpam-3001	164	5	)	)	PUNCT
ejpam-3001	164	6	∧	∧	PROPN
ejpam-3001	164	7	σ2(y1	σ2(y1	VERB
ejpam-3001	164	8	)	)	PUNCT
ejpam-3001	164	9	∧	∧	NOUN
ejpam-3001	164	10	σ2(y2	σ2(y2	NOUN
ejpam-3001	164	11	)	)	PUNCT
ejpam-3001	164	12	.	.	PUNCT
ejpam-3001	165	1	as	as	SCONJ
ejpam-3001	165	2	x1	x1	PROPN
ejpam-3001	165	3	and	and	CCONJ
ejpam-3001	165	4	x2	x2	PROPN
ejpam-3001	165	5	are	be	AUX
ejpam-3001	165	6	identified	identify	VERB
ejpam-3001	165	7	by	by	ADP
ejpam-3001	165	8	x	x	PUNCT
ejpam-3001	165	9	and	and	CCONJ
ejpam-3001	165	10	y1	y1	INTJ
ejpam-3001	165	11	and	and	CCONJ
ejpam-3001	165	12	y2	y2	PROPN
ejpam-3001	165	13	are	be	AUX
ejpam-3001	165	14	identified	identify	VERB
ejpam-3001	165	15	by	by	ADP
ejpam-3001	165	16	y	y	PROPN
ejpam-3001	165	17	and	and	CCONJ
ejpam-3001	165	18	by	by	ADP
ejpam-3001	165	19	definition	definition	NOUN
ejpam-3001	165	20	of	of	ADP
ejpam-3001	165	21	p	p	PROPN
ejpam-3001	165	22	(	(	PUNCT
ejpam-3001	165	23	g1;g2	g1;g2	PROPN
ejpam-3001	165	24	)	)	PUNCT
ejpam-3001	165	25	,	,	PUNCT
ejpam-3001	165	26	µ(x	µ(x	PROPN
ejpam-3001	165	27	,	,	PUNCT
ejpam-3001	165	28	y	y	NOUN
ejpam-3001	165	29	)	)	PUNCT
ejpam-3001	166	1	=	=	SYM
ejpam-3001	166	2	σ(x	σ(x	PROPN
ejpam-3001	166	3	)	)	PUNCT
ejpam-3001	166	4	∧σ(y	∧σ(y	NUM
ejpam-3001	166	5	)	)	PUNCT
ejpam-3001	166	6	.	.	PUNCT
ejpam-3001	167	1	therefore	therefore	ADV
ejpam-3001	167	2	,	,	PUNCT
ejpam-3001	167	3	p	p	X
ejpam-3001	167	4	(	(	PUNCT
ejpam-3001	167	5	g1;g2	g1;g2	PROPN
ejpam-3001	167	6	)	)	PUNCT
ejpam-3001	167	7	is	be	AUX
ejpam-3001	167	8	strong	strong	ADJ
ejpam-3001	167	9	.	.	PUNCT
ejpam-3001	168	1	we	we	PRON
ejpam-3001	168	2	end	end	VERB
ejpam-3001	168	3	this	this	DET
ejpam-3001	168	4	section	section	NOUN
ejpam-3001	168	5	with	with	ADP
ejpam-3001	168	6	the	the	DET
ejpam-3001	168	7	following	follow	VERB
ejpam-3001	168	8	immediate	immediate	ADJ
ejpam-3001	168	9	result	result	NOUN
ejpam-3001	168	10	:	:	PUNCT
ejpam-3001	168	11	corollary	corollary	ADJ
ejpam-3001	168	12	3	3	X
ejpam-3001	168	13	.	.	PUNCT
ejpam-3001	169	1	let	let	VERB
ejpam-3001	169	2	g1	g1	PROPN
ejpam-3001	169	3	and	and	CCONJ
ejpam-3001	169	4	g2	g2	PROPN
ejpam-3001	169	5	be	be	AUX
ejpam-3001	169	6	complete	complete	ADJ
ejpam-3001	169	7	fuzzy	fuzzy	ADJ
ejpam-3001	169	8	graphs	graph	NOUN
ejpam-3001	169	9	.	.	PUNCT
ejpam-3001	170	1	then	then	ADV
ejpam-3001	170	2	p	p	X
ejpam-3001	170	3	(	(	PUNCT
ejpam-3001	170	4	g1;g2	g1;g2	PROPN
ejpam-3001	170	5	)	)	PUNCT
ejpam-3001	170	6	and	and	CCONJ
ejpam-3001	170	7	s(g1;g2	s(g1;g2	NOUN
ejpam-3001	170	8	)	)	PUNCT
ejpam-3001	170	9	are	be	AUX
ejpam-3001	170	10	complete	complete	ADJ
ejpam-3001	170	11	.	.	PUNCT
ejpam-3001	171	1	acknowledgement	acknowledgement	NOUN
ejpam-3001	171	2	the	the	DET
ejpam-3001	171	3	author	author	NOUN
ejpam-3001	171	4	would	would	AUX
ejpam-3001	171	5	like	like	VERB
ejpam-3001	171	6	to	to	PART
ejpam-3001	171	7	thank	thank	VERB
ejpam-3001	171	8	the	the	DET
ejpam-3001	171	9	referee	referee	NOUN
ejpam-3001	171	10	for	for	ADP
ejpam-3001	171	11	useful	useful	ADJ
ejpam-3001	171	12	comments	comment	NOUN
ejpam-3001	171	13	and	and	CCONJ
ejpam-3001	171	14	suggestions	suggestion	NOUN
ejpam-3001	171	15	.	.	PUNCT
ejpam-3001	172	1	references	reference	NOUN
ejpam-3001	172	2	[	[	X
ejpam-3001	172	3	1	1	X
ejpam-3001	172	4	]	]	PUNCT
ejpam-3001	172	5	t.	t.	PROPN
ejpam-3001	172	6	al	al	PROPN
ejpam-3001	172	7	-	-	PUNCT
ejpam-3001	172	8	hawary	hawary	PROPN
ejpam-3001	172	9	,	,	PUNCT
ejpam-3001	172	10	complete	complete	ADJ
ejpam-3001	172	11	fuzzy	fuzzy	ADJ
ejpam-3001	172	12	graphs	graph	NOUN
ejpam-3001	172	13	,	,	PUNCT
ejpam-3001	172	14	international	international	ADJ
ejpam-3001	172	15	j.	j.	PROPN
ejpam-3001	172	16	math	math	PROPN
ejpam-3001	172	17	comb	comb	NOUN
ejpam-3001	172	18	.	.	PUNCT
ejpam-3001	173	1	4(2011	4(2011	NUM
ejpam-3001	173	2	)	)	PUNCT
ejpam-3001	173	3	,	,	PUNCT
ejpam-3001	173	4	26	26	NUM
ejpam-3001	173	5	-	-	SYM
ejpam-3001	173	6	34	34	NUM
ejpam-3001	173	7	.	.	PUNCT
ejpam-3001	174	1	[	[	X
ejpam-3001	174	2	2	2	X
ejpam-3001	174	3	]	]	PUNCT
ejpam-3001	174	4	t.	t.	PROPN
ejpam-3001	174	5	al	al	PROPN
ejpam-3001	174	6	-	-	PUNCT
ejpam-3001	174	7	hawary	hawary	ADJ
ejpam-3001	174	8	,	,	PUNCT
ejpam-3001	174	9	fuzzy	fuzzy	ADJ
ejpam-3001	174	10	closure	closure	NOUN
ejpam-3001	174	11	matroids	matroid	NOUN
ejpam-3001	174	12	,	,	PUNCT
ejpam-3001	174	13	matematika	matematika	NOUN
ejpam-3001	174	14	32(1)(2016	32(1)(2016	NUM
ejpam-3001	174	15	)	)	PUNCT
ejpam-3001	174	16	,	,	PUNCT
ejpam-3001	174	17	69	69	NUM
ejpam-3001	174	18	-	-	SYM
ejpam-3001	174	19	74	74	NUM
ejpam-3001	174	20	.	.	PUNCT
ejpam-3001	175	1	[	[	X
ejpam-3001	175	2	3	3	NUM
ejpam-3001	175	3	]	]	X
ejpam-3001	175	4	t.al	t.al	ADJ
ejpam-3001	175	5	-	-	ADJ
ejpam-3001	175	6	hawary	hawary	ADJ
ejpam-3001	175	7	,	,	PUNCT
ejpam-3001	175	8	fuzzy	fuzzy	ADJ
ejpam-3001	175	9	flats	flat	NOUN
ejpam-3001	175	10	,	,	PUNCT
ejpam-3001	175	11	indian	indian	ADJ
ejpam-3001	175	12	j.	j.	PROPN
ejpam-3001	175	13	mathematics	mathematics	PROPN
ejpam-3001	175	14	55(2)(2013	55(2)(2013	NUM
ejpam-3001	175	15	)	)	PUNCT
ejpam-3001	175	16	,	,	PUNCT
ejpam-3001	175	17	223	223	NUM
ejpam-3001	175	18	-	-	SYM
ejpam-3001	175	19	236	236	NUM
ejpam-3001	175	20	.	.	PUNCT
ejpam-3001	176	1	[	[	X
ejpam-3001	176	2	4	4	NUM
ejpam-3001	176	3	]	]	X
ejpam-3001	176	4	t.al	t.al	ADJ
ejpam-3001	176	5	-	-	NOUN
ejpam-3001	176	6	hawary	hawary	ADJ
ejpam-3001	176	7	,	,	PUNCT
ejpam-3001	176	8	on	on	ADP
ejpam-3001	176	9	balanced	balanced	ADJ
ejpam-3001	176	10	graphs	graph	NOUN
ejpam-3001	176	11	and	and	CCONJ
ejpam-3001	176	12	balanced	balanced	ADJ
ejpam-3001	176	13	matroids	matroid	NOUN
ejpam-3001	176	14	,	,	PUNCT
ejpam-3001	176	15	math.sci.res.hotline,4(7)(2000	math.sci.res.hotline,4(7)(2000	NOUN
ejpam-3001	176	16	)	)	PUNCT
ejpam-3001	176	17	,	,	PUNCT
ejpam-3001	176	18	pp	pp	PROPN
ejpam-3001	176	19	.	.	PUNCT
ejpam-3001	177	1	35	35	NUM
ejpam-3001	177	2	-	-	SYM
ejpam-3001	177	3	45	45	NUM
ejpam-3001	177	4	.	.	PUNCT
ejpam-3001	178	1	[	[	X
ejpam-3001	178	2	5	5	X
ejpam-3001	178	3	]	]	PUNCT
ejpam-3001	178	4	t.	t.	PROPN
ejpam-3001	178	5	al	al	PROPN
ejpam-3001	178	6	-	-	PUNCT
ejpam-3001	178	7	hawary	hawary	PROPN
ejpam-3001	178	8	and	and	CCONJ
ejpam-3001	178	9	bayan	bayan	PROPN
ejpam-3001	178	10	horani	horani	PROPN
ejpam-3001	178	11	,	,	PUNCT
ejpam-3001	178	12	on	on	ADP
ejpam-3001	178	13	intuitionistic	intuitionistic	ADJ
ejpam-3001	178	14	product	product	NOUN
ejpam-3001	178	15	fuzzy	fuzzy	ADJ
ejpam-3001	178	16	graphs	graph	NOUN
ejpam-3001	178	17	,	,	PUNCT
ejpam-3001	178	18	to	to	PART
ejpam-3001	178	19	appear	appear	VERB
ejpam-3001	178	20	in	in	ADP
ejpam-3001	178	21	ital	ital	PROPN
ejpam-3001	178	22	.	.	PUNCT
ejpam-3001	179	1	j.	j.	PROPN
ejpam-3001	179	2	pure	pure	PROPN
ejpam-3001	179	3	.	.	PROPN
ejpam-3001	180	1	&	&	CCONJ
ejpam-3001	181	1	appl	appl	PROPN
ejpam-3001	181	2	.	.	PROPN
ejpam-3001	181	3	math	math	NOUN
ejpam-3001	181	4	.	.	PUNCT
ejpam-3001	182	1	[	[	X
ejpam-3001	182	2	6	6	NUM
ejpam-3001	182	3	]	]	X
ejpam-3001	182	4	t.al	t.al	ADJ
ejpam-3001	182	5	-	-	NOUN
ejpam-3001	182	6	hawary	hawary	ADJ
ejpam-3001	182	7	,	,	PUNCT
ejpam-3001	182	8	on	on	ADP
ejpam-3001	182	9	k	k	ADJ
ejpam-3001	182	10	-	-	PUNCT
ejpam-3001	182	11	balanced	balanced	ADJ
ejpam-3001	182	12	matroids	matroid	NOUN
ejpam-3001	182	13	,	,	PUNCT
ejpam-3001	182	14	mu’tah	mu’tah	PROPN
ejpam-3001	182	15	lil	lil	NOUN
ejpam-3001	182	16	-	-	PUNCT
ejpam-3001	182	17	buhuth	buhuth	NOUN
ejpam-3001	182	18	waddirasat,16(1),2001,pp	waddirasat,16(1),2001,pp	X
ejpam-3001	182	19	.	.	PUNCT
ejpam-3001	183	1	15	15	NUM
ejpam-3001	183	2	-	-	SYM
ejpam-3001	183	3	23	23	NUM
ejpam-3001	183	4	.	.	PUNCT
ejpam-3001	184	1	[	[	X
ejpam-3001	184	2	7	7	X
ejpam-3001	184	3	]	]	PUNCT
ejpam-3001	184	4	t.	t.	PROPN
ejpam-3001	184	5	al	al	PROPN
ejpam-3001	184	6	-	-	PUNCT
ejpam-3001	184	7	hawary	hawary	PROPN
ejpam-3001	184	8	and	and	CCONJ
ejpam-3001	184	9	bayan	bayan	PROPN
ejpam-3001	184	10	horani	horani	PROPN
ejpam-3001	184	11	,	,	PUNCT
ejpam-3001	184	12	on	on	ADP
ejpam-3001	184	13	product	product	NOUN
ejpam-3001	184	14	fuzzy	fuzzy	ADJ
ejpam-3001	184	15	graphs	graph	NOUN
ejpam-3001	184	16	,	,	PUNCT
ejpam-3001	184	17	annals	annal	NOUN
ejpam-3001	184	18	of	of	ADP
ejpam-3001	184	19	fuzzy	fuzzy	ADJ
ejpam-3001	184	20	mathematics	mathematic	NOUN
ejpam-3001	184	21	and	and	CCONJ
ejpam-3001	184	22	informatics	informatic	NOUN
ejpam-3001	184	23	12(2)(2016	12(2)(2016	NUM
ejpam-3001	184	24	)	)	PUNCT
ejpam-3001	184	25	,	,	PUNCT
ejpam-3001	184	26	279	279	NUM
ejpam-3001	184	27	-	-	SYM
ejpam-3001	184	28	294	294	NUM
ejpam-3001	184	29	.	.	PUNCT
ejpam-3001	185	1	[	[	X
ejpam-3001	185	2	8	8	X
ejpam-3001	185	3	]	]	PUNCT
ejpam-3001	185	4	k.	k.	PROPN
ejpam-3001	185	5	r.	r.	PROPN
ejpam-3001	185	6	bhutani	bhutani	PROPN
ejpam-3001	185	7	,	,	PUNCT
ejpam-3001	185	8	on	on	ADP
ejpam-3001	185	9	automorphism	automorphism	NOUN
ejpam-3001	185	10	of	of	ADP
ejpam-3001	185	11	fuzzy	fuzzy	ADJ
ejpam-3001	185	12	graphs	graph	NOUN
ejpam-3001	185	13	,	,	PUNCT
ejpam-3001	185	14	pattern	pattern	NOUN
ejpam-3001	185	15	recognition	recognition	NOUN
ejpam-3001	185	16	letter	letter	NOUN
ejpam-3001	185	17	9(1989	9(1989	NUM
ejpam-3001	185	18	)	)	PUNCT
ejpam-3001	185	19	,	,	PUNCT
ejpam-3001	185	20	159–162	159–162	NUM
ejpam-3001	185	21	.	.	PUNCT
ejpam-3001	186	1	[	[	X
ejpam-3001	186	2	9	9	NUM
ejpam-3001	186	3	]	]	PUNCT
ejpam-3001	186	4	j.	j.	PROPN
ejpam-3001	186	5	n.	n.	PROPN
ejpam-3001	186	6	mordeson	mordeson	PROPN
ejpam-3001	186	7	and	and	CCONJ
ejpam-3001	186	8	c.	c.	PROPN
ejpam-3001	186	9	s.	s.	PROPN
ejpam-3001	186	10	peng	peng	PROPN
ejpam-3001	186	11	,	,	PUNCT
ejpam-3001	186	12	operations	operation	NOUN
ejpam-3001	186	13	on	on	ADP
ejpam-3001	186	14	fuzzy	fuzzy	ADJ
ejpam-3001	186	15	graphs	graph	NOUN
ejpam-3001	186	16	,	,	PUNCT
ejpam-3001	186	17	information	information	NOUN
ejpam-3001	186	18	sciences	science	NOUN
ejpam-3001	186	19	79(1994	79(1994	NUM
ejpam-3001	186	20	)	)	PUNCT
ejpam-3001	186	21	,	,	PUNCT
ejpam-3001	186	22	381	381	NUM
ejpam-3001	186	23	-	-	SYM
ejpam-3001	186	24	384	384	NUM
ejpam-3001	186	25	.	.	PUNCT
ejpam-3001	187	1	[	[	X
ejpam-3001	187	2	10	10	NUM
ejpam-3001	187	3	]	]	PUNCT
ejpam-3001	187	4	m.	m.	NOUN
ejpam-3001	187	5	akram	akram	PROPN
ejpam-3001	187	6	,	,	PUNCT
ejpam-3001	187	7	bipolar	bipolar	ADJ
ejpam-3001	187	8	fuzzy	fuzzy	ADJ
ejpam-3001	187	9	graphs	graph	NOUN
ejpam-3001	187	10	,	,	PUNCT
ejpam-3001	187	11	information	information	NOUN
ejpam-3001	187	12	sciences	science	NOUN
ejpam-3001	187	13	181	181	NUM
ejpam-3001	187	14	(	(	PUNCT
ejpam-3001	187	15	24	24	NUM
ejpam-3001	187	16	)	)	PUNCT
ejpam-3001	187	17	,	,	PUNCT
ejpam-3001	187	18	5548	5548	NUM
ejpam-3001	187	19	-	-	SYM
ejpam-3001	187	20	5564	5564	NUM
ejpam-3001	187	21	.	.	PUNCT
ejpam-3001	188	1	[	[	X
ejpam-3001	188	2	11	11	NUM
ejpam-3001	188	3	]	]	PUNCT
ejpam-3001	188	4	m.	m.	NOUN
ejpam-3001	188	5	akram	akram	PROPN
ejpam-3001	188	6	and	and	CCONJ
ejpam-3001	188	7	w.a	w.a	PROPN
ejpam-3001	188	8	.	.	PROPN
ejpam-3001	188	9	dudek	dudek	PROPN
ejpam-3001	188	10	,	,	PUNCT
ejpam-3001	188	11	interval	interval	NOUN
ejpam-3001	188	12	-	-	PUNCT
ejpam-3001	188	13	valued	value	VERB
ejpam-3001	188	14	fuzzy	fuzzy	ADJ
ejpam-3001	188	15	graphs	graph	NOUN
ejpam-3001	188	16	,	,	PUNCT
ejpam-3001	188	17	computers	computer	NOUN
ejpam-3001	188	18	and	and	CCONJ
ejpam-3001	188	19	mathematics	mathematic	NOUN
ejpam-3001	188	20	with	with	ADP
ejpam-3001	188	21	applications	application	NOUN
ejpam-3001	188	22	61	61	NUM
ejpam-3001	188	23	(	(	PUNCT
ejpam-3001	188	24	2	2	NUM
ejpam-3001	188	25	)	)	PUNCT
ejpam-3001	188	26	,	,	PUNCT
ejpam-3001	188	27	289	289	NUM
ejpam-3001	188	28	-	-	SYM
ejpam-3001	188	29	299	299	NUM
ejpam-3001	188	30	.	.	PUNCT
ejpam-3001	189	1	[	[	X
ejpam-3001	189	2	12	12	NUM
ejpam-3001	189	3	]	]	PUNCT
ejpam-3001	189	4	a.nagoor	a.nagoor	ADV
ejpam-3001	189	5	gani	gani	PROPN
ejpam-3001	189	6	and	and	CCONJ
ejpam-3001	189	7	j.	j.	PROPN
ejpam-3001	189	8	malarvizhi	malarvizhi	PROPN
ejpam-3001	189	9	,	,	PUNCT
ejpam-3001	189	10	isomorphism	isomorphism	NOUN
ejpam-3001	189	11	on	on	ADP
ejpam-3001	189	12	fuzzy	fuzzy	ADJ
ejpam-3001	189	13	graphs	graph	NOUN
ejpam-3001	189	14	,	,	PUNCT
ejpam-3001	189	15	int	int	NOUN
ejpam-3001	189	16	.	.	PUNCT
ejpam-3001	190	1	j.	j.	PROPN
ejpam-3001	190	2	comp	comp	PROPN
ejpam-3001	190	3	.	.	PUNCT
ejpam-3001	190	4	and	and	CCONJ
ejpam-3001	190	5	math	math	NOUN
ejpam-3001	190	6	.	.	PUNCT
ejpam-3001	191	1	sci	sci	PROPN
ejpam-3001	191	2	.	.	PUNCT
ejpam-3001	192	1	2(4)(2008	2(4)(2008	NUM
ejpam-3001	192	2	)	)	PUNCT
ejpam-3001	192	3	,	,	PUNCT
ejpam-3001	192	4	190	190	NUM
ejpam-3001	192	5	-	-	SYM
ejpam-3001	192	6	196	196	NUM
ejpam-3001	192	7	.	.	PUNCT
ejpam-3001	193	1	references	reference	NOUN
ejpam-3001	193	2	560	560	NUM
ejpam-3001	193	3	[	[	X
ejpam-3001	193	4	13	13	NUM
ejpam-3001	193	5	]	]	PUNCT
ejpam-3001	193	6	a.nagoor	a.nagoor	ADV
ejpam-3001	193	7	gani	gani	PROPN
ejpam-3001	193	8	and	and	CCONJ
ejpam-3001	193	9	j.	j.	PROPN
ejpam-3001	193	10	malarvizhi	malarvizhi	PROPN
ejpam-3001	193	11	,	,	PUNCT
ejpam-3001	193	12	isomorphism	isomorphism	NOUN
ejpam-3001	193	13	properties	property	NOUN
ejpam-3001	193	14	on	on	ADP
ejpam-3001	193	15	strong	strong	ADJ
ejpam-3001	193	16	fuzzy	fuzzy	ADJ
ejpam-3001	193	17	graphs	graph	NOUN
ejpam-3001	193	18	,	,	PUNCT
ejpam-3001	193	19	int	int	NOUN
ejpam-3001	193	20	.	.	PUNCT
ejpam-3001	194	1	j.	j.	PROPN
ejpam-3001	194	2	algorithms	algorithms	PROPN
ejpam-3001	194	3	,	,	PUNCT
ejpam-3001	194	4	comp	comp	NOUN
ejpam-3001	194	5	.	.	PUNCT
ejpam-3001	194	6	and	and	CCONJ
ejpam-3001	194	7	math	math	NOUN
ejpam-3001	194	8	.	.	PUNCT
ejpam-3001	195	1	2	2	NUM
ejpam-3001	195	2	(	(	PUNCT
ejpam-3001	195	3	1)(2009	1)(2009	NUM
ejpam-3001	195	4	)	)	PUNCT
ejpam-3001	195	5	,	,	PUNCT
ejpam-3001	195	6	39	39	NUM
ejpam-3001	195	7	-	-	SYM
ejpam-3001	195	8	47	47	NUM
ejpam-3001	195	9	.	.	PUNCT
ejpam-3001	196	1	[	[	X
ejpam-3001	196	2	14	14	NUM
ejpam-3001	196	3	]	]	PUNCT
ejpam-3001	196	4	a.nagoor	a.nagoor	ADV
ejpam-3001	196	5	gani	gani	PROPN
ejpam-3001	196	6	and	and	CCONJ
ejpam-3001	196	7	k.	k.	PROPN
ejpam-3001	196	8	radha	radha	PROPN
ejpam-3001	196	9	,	,	PUNCT
ejpam-3001	196	10	on	on	ADP
ejpam-3001	196	11	regular	regular	ADJ
ejpam-3001	196	12	fuzzy	fuzzy	ADJ
ejpam-3001	196	13	graphs	graph	NOUN
ejpam-3001	196	14	,	,	PUNCT
ejpam-3001	196	15	j.	j.	PROPN
ejpam-3001	196	16	physical	physical	PROPN
ejpam-3001	196	17	sciences	sciences	PROPN
ejpam-3001	196	18	12(2008	12(2008	NUM
ejpam-3001	196	19	)	)	PUNCT
ejpam-3001	196	20	,	,	PUNCT
ejpam-3001	196	21	33	33	NUM
ejpam-3001	196	22	-	-	SYM
ejpam-3001	196	23	40	40	NUM
ejpam-3001	196	24	.	.	PUNCT
ejpam-3001	197	1	[	[	X
ejpam-3001	197	2	15	15	NUM
ejpam-3001	197	3	]	]	PUNCT
ejpam-3001	197	4	a.	a.	NOUN
ejpam-3001	197	5	rosenfeld	rosenfeld	PROPN
ejpam-3001	197	6	,	,	PUNCT
ejpam-3001	197	7	fuzzy	fuzzy	ADJ
ejpam-3001	197	8	graphs	graph	NOUN
ejpam-3001	197	9	,	,	PUNCT
ejpam-3001	197	10	in	in	ADP
ejpam-3001	197	11	l.a	l.a	PROPN
ejpam-3001	197	12	.	.	PROPN
ejpam-3001	197	13	zadeh	zadeh	PROPN
ejpam-3001	197	14	,	,	PUNCT
ejpam-3001	197	15	k.s	k.s	PROPN
ejpam-3001	197	16	.	.	PROPN
ejpam-3001	197	17	fu	fu	PROPN
ejpam-3001	197	18	,	,	PUNCT
ejpam-3001	197	19	k.	k.	PROPN
ejpam-3001	197	20	tanaka	tanaka	PROPN
ejpam-3001	197	21	and	and	CCONJ
ejpam-3001	197	22	m.	m.	NOUN
ejpam-3001	197	23	shirmura	shirmura	PROPN
ejpam-3001	197	24	(	(	PUNCT
ejpam-3001	197	25	eds	eds	PROPN
ejpam-3001	197	26	.	.	PUNCT
ejpam-3001	197	27	)	)	PUNCT
ejpam-3001	197	28	,	,	PUNCT
ejpam-3001	197	29	fuzzy	fuzzy	ADJ
ejpam-3001	197	30	and	and	CCONJ
ejpam-3001	197	31	their	their	PRON
ejpam-3001	197	32	applications	application	NOUN
ejpam-3001	197	33	to	to	PART
ejpam-3001	197	34	cognitive	cognitive	VERB
ejpam-3001	197	35	and	and	CCONJ
ejpam-3001	197	36	decision	decision	NOUN
ejpam-3001	197	37	processes	process	NOUN
ejpam-3001	197	38	,	,	PUNCT
ejpam-3001	197	39	academic	academic	ADJ
ejpam-3001	197	40	press	press	NOUN
ejpam-3001	197	41	,	,	PUNCT
ejpam-3001	197	42	new	new	PROPN
ejpam-3001	197	43	york	york	PROPN
ejpam-3001	197	44	,	,	PUNCT
ejpam-3001	197	45	1975	1975	NUM
ejpam-3001	197	46	,	,	PUNCT
ejpam-3001	197	47	77	77	NUM
ejpam-3001	197	48	-	-	SYM
ejpam-3001	197	49	95	95	NUM
ejpam-3001	197	50	.	.	PUNCT
ejpam-3001	198	1	[	[	X
ejpam-3001	198	2	16	16	NUM
ejpam-3001	198	3	]	]	X
ejpam-3001	198	4	m.s	m.s	PROPN
ejpam-3001	198	5	.	.	PROPN
ejpam-3001	198	6	sunitha	sunitha	PROPN
ejpam-3001	198	7	and	and	CCONJ
ejpam-3001	198	8	a.	a.	PROPN
ejpam-3001	198	9	v.	v.	PROPN
ejpam-3001	198	10	kumar	kumar	PROPN
ejpam-3001	198	11	,	,	PUNCT
ejpam-3001	198	12	complements	complement	NOUN
ejpam-3001	198	13	of	of	ADP
ejpam-3001	198	14	fuzzy	fuzzy	ADJ
ejpam-3001	198	15	graphs	graph	NOUN
ejpam-3001	198	16	,	,	PUNCT
ejpam-3001	198	17	indian	indian	ADJ
ejpam-3001	198	18	j.	j.	PROPN
ejpam-3001	198	19	pure	pure	PROPN
ejpam-3001	198	20	appl	appl	PROPN
ejpam-3001	198	21	.	.	PUNCT
ejpam-3001	198	22	math	math	NOUN
ejpam-3001	198	23	.	.	PUNCT
ejpam-3001	199	1	33(9)(2002	33(9)(2002	NUM
ejpam-3001	199	2	)	)	PUNCT
ejpam-3001	199	3	,	,	PUNCT
ejpam-3001	199	4	1451	1451	NUM
ejpam-3001	199	5	-	-	SYM
ejpam-3001	199	6	1464	1464	NUM
ejpam-3001	199	7	.	.	PUNCT
ejpam-3001	200	1	[	[	X
ejpam-3001	200	2	17	17	NUM
ejpam-3001	200	3	]	]	X
ejpam-3001	200	4	l.a	l.a	PROPN
ejpam-3001	200	5	.	.	PROPN
ejpam-3001	200	6	zadeh	zadeh	PROPN
ejpam-3001	200	7	,	,	PUNCT
ejpam-3001	200	8	fuzzy	fuzzy	ADJ
ejpam-3001	200	9	sets	set	NOUN
ejpam-3001	200	10	,	,	PUNCT
ejpam-3001	200	11	inform	inform	NOUN
ejpam-3001	200	12	.	.	PUNCT
ejpam-3001	201	1	control	control	NOUN
ejpam-3001	201	2	.	.	PUNCT
ejpam-3001	202	1	8(1965	8(1965	NUM
ejpam-3001	202	2	)	)	PUNCT
ejpam-3001	202	3	,	,	PUNCT
ejpam-3001	202	4	338	338	NUM
ejpam-3001	202	5	-	-	SYM
ejpam-3001	202	6	353	353	NUM
ejpam-3001	202	7	.	.	PUNCT