id	sid	tid	token	lemma	pos
ejpam-5872	1	1	european	european	PROPN
ejpam-5872	1	2	journal	journal	PROPN
ejpam-5872	1	3	of	of	ADP
ejpam-5872	1	4	pure	pure	ADJ
ejpam-5872	1	5	and	and	CCONJ
ejpam-5872	1	6	applied	applied	ADJ
ejpam-5872	1	7	mathematics	mathematic	NOUN
ejpam-5872	1	8	2025	2025	NUM
ejpam-5872	1	9	,	,	PUNCT
ejpam-5872	1	10	vol	vol	NOUN
ejpam-5872	1	11	.	.	PROPN
ejpam-5872	1	12	18	18	NUM
ejpam-5872	1	13	,	,	PUNCT
ejpam-5872	1	14	issue	issue	NOUN
ejpam-5872	1	15	4	4	NUM
ejpam-5872	1	16	,	,	PUNCT
ejpam-5872	1	17	article	article	NOUN
ejpam-5872	1	18	number	number	NOUN
ejpam-5872	1	19	5872	5872	NUM
ejpam-5872	1	20	issn	issn	VERB
ejpam-5872	1	21	1307	1307	NUM
ejpam-5872	1	22	-	-	SYM
ejpam-5872	1	23	5543	5543	NUM
ejpam-5872	1	24	–	–	PUNCT
ejpam-5872	1	25	ejpam.com	ejpam.com	X
ejpam-5872	1	26	published	publish	VERB
ejpam-5872	1	27	by	by	ADP
ejpam-5872	1	28	new	new	PROPN
ejpam-5872	1	29	york	york	PROPN
ejpam-5872	1	30	business	business	PROPN
ejpam-5872	1	31	global	global	PROPN
ejpam-5872	1	32	signed	sign	VERB
ejpam-5872	1	33	fuzzy	fuzzy	ADJ
ejpam-5872	1	34	graphs	graph	NOUN
ejpam-5872	1	35	domination	domination	NOUN
ejpam-5872	1	36	in	in	ADP
ejpam-5872	1	37	environmental	environmental	ADJ
ejpam-5872	1	38	monitoring	monitoring	NOUN
ejpam-5872	1	39	wireless	wireless	ADJ
ejpam-5872	1	40	sensor	sensor	NOUN
ejpam-5872	1	41	networks	network	NOUN
ejpam-5872	1	42	chakaravarthy	chakaravarthy	ADJ
ejpam-5872	1	43	sankar1,∗	sankar1,∗	NOUN
ejpam-5872	1	44	,	,	PUNCT
ejpam-5872	1	45	mariappan	mariappan	ADJ
ejpam-5872	1	46	saravanan2	saravanan2	NOUN
ejpam-5872	1	47	,	,	PUNCT
ejpam-5872	1	48	ramalingam	ramalingam	ADJ
ejpam-5872	1	49	sujatha3	sujatha3	PROPN
ejpam-5872	1	50	,	,	PUNCT
ejpam-5872	1	51	gangatharan	gangatharan	NOUN
ejpam-5872	1	52	venkat	venkat	PROPN
ejpam-5872	1	53	narayanan1	narayanan1	PROPN
ejpam-5872	1	54	1	1	NUM
ejpam-5872	1	55	department	department	NOUN
ejpam-5872	1	56	of	of	ADP
ejpam-5872	1	57	mathematics	mathematics	PROPN
ejpam-5872	1	58	,	,	PUNCT
ejpam-5872	1	59	st	st	PROPN
ejpam-5872	1	60	.	.	PROPN
ejpam-5872	1	61	joseph	joseph	PROPN
ejpam-5872	1	62	’s	’s	PART
ejpam-5872	1	63	college	college	PROPN
ejpam-5872	1	64	of	of	ADP
ejpam-5872	1	65	engineering	engineering	PROPN
ejpam-5872	1	66	,	,	PUNCT
ejpam-5872	1	67	omr	omr	NOUN
ejpam-5872	1	68	,	,	PUNCT
ejpam-5872	1	69	chennai-600119	chennai-600119	ADJ
ejpam-5872	1	70	,	,	PUNCT
ejpam-5872	1	71	tamilnadu	tamilnadu	ADJ
ejpam-5872	1	72	,	,	PUNCT
ejpam-5872	1	73	india	india	PROPN
ejpam-5872	1	74	2	2	NUM
ejpam-5872	1	75	department	department	NOUN
ejpam-5872	1	76	of	of	ADP
ejpam-5872	1	77	mathematics	mathematic	NOUN
ejpam-5872	1	78	,	,	PUNCT
ejpam-5872	1	79	mannar	mannar	ADJ
ejpam-5872	1	80	thirumalai	thirumalai	PROPN
ejpam-5872	1	81	naicker	naicker	PROPN
ejpam-5872	1	82	college	college	PROPN
ejpam-5872	1	83	,	,	PUNCT
ejpam-5872	1	84	pasumalai	pasumalai	NOUN
ejpam-5872	1	85	,	,	PUNCT
ejpam-5872	1	86	madurai625004	madurai625004	PROPN
ejpam-5872	1	87	,	,	PUNCT
ejpam-5872	1	88	tamilnadu	tamilnadu	NOUN
ejpam-5872	1	89	,	,	PUNCT
ejpam-5872	1	90	india	india	PROPN
ejpam-5872	1	91	3	3	NUM
ejpam-5872	1	92	school	school	NOUN
ejpam-5872	1	93	of	of	ADP
ejpam-5872	1	94	science	science	NOUN
ejpam-5872	1	95	and	and	CCONJ
ejpam-5872	1	96	humanities(mathematics	humanities(mathematic	NOUN
ejpam-5872	1	97	)	)	PUNCT
ejpam-5872	1	98	,	,	PUNCT
ejpam-5872	1	99	shiv	shiv	PROPN
ejpam-5872	1	100	nadar	nadar	PROPN
ejpam-5872	1	101	university	university	PROPN
ejpam-5872	1	102	chennai	chennai	PROPN
ejpam-5872	1	103	,	,	PUNCT
ejpam-5872	1	104	omr	omr	NOUN
ejpam-5872	1	105	,	,	PUNCT
ejpam-5872	1	106	chennai-603110	chennai-603110	NOUN
ejpam-5872	1	107	,	,	PUNCT
ejpam-5872	1	108	tamilnadu	tamilnadu	NOUN
ejpam-5872	1	109	,	,	PUNCT
ejpam-5872	1	110	india	india	PROPN
ejpam-5872	1	111	abstract	abstract	PROPN
ejpam-5872	1	112	.	.	PUNCT
ejpam-5872	2	1	signed	sign	VERB
ejpam-5872	2	2	fuzzy	fuzzy	ADJ
ejpam-5872	2	3	graphs(signed	graphs(signe	VERB
ejpam-5872	2	4	-	-	PUNCT
ejpam-5872	2	5	fg	fg	PROPN
ejpam-5872	2	6	)	)	PUNCT
ejpam-5872	2	7	,	,	PUNCT
ejpam-5872	2	8	a	a	DET
ejpam-5872	2	9	mathematical	mathematical	ADJ
ejpam-5872	2	10	structure	structure	NOUN
ejpam-5872	2	11	having	have	VERB
ejpam-5872	2	12	nodes	node	NOUN
ejpam-5872	2	13	associated	associate	VERB
ejpam-5872	2	14	with	with	ADP
ejpam-5872	2	15	membership	membership	NOUN
ejpam-5872	2	16	values	value	NOUN
ejpam-5872	2	17	and	and	CCONJ
ejpam-5872	2	18	edges	edge	NOUN
ejpam-5872	2	19	consisting	consist	VERB
ejpam-5872	2	20	of	of	ADP
ejpam-5872	2	21	positive	positive	ADJ
ejpam-5872	2	22	and	and	CCONJ
ejpam-5872	2	23	negative	negative	ADJ
ejpam-5872	2	24	signs	sign	NOUN
ejpam-5872	2	25	,	,	PUNCT
ejpam-5872	2	26	present	present	VERB
ejpam-5872	2	27	a	a	DET
ejpam-5872	2	28	multi	multi	ADJ
ejpam-5872	2	29	-	-	ADJ
ejpam-5872	2	30	faceted	faceted	ADJ
ejpam-5872	2	31	mathematical	mathematical	ADJ
ejpam-5872	2	32	model	model	NOUN
ejpam-5872	2	33	to	to	PART
ejpam-5872	2	34	address	address	VERB
ejpam-5872	2	35	uncertainty	uncertainty	NOUN
ejpam-5872	2	36	and	and	CCONJ
ejpam-5872	2	37	polarity	polarity	NOUN
ejpam-5872	2	38	in	in	ADP
ejpam-5872	2	39	graph	graph	NOUN
ejpam-5872	2	40	-	-	PUNCT
ejpam-5872	2	41	based	base	VERB
ejpam-5872	2	42	networks	network	NOUN
ejpam-5872	2	43	.	.	PUNCT
ejpam-5872	3	1	exploring	explore	VERB
ejpam-5872	3	2	the	the	DET
ejpam-5872	3	3	theories	theory	NOUN
ejpam-5872	3	4	of	of	ADP
ejpam-5872	3	5	signed	sign	VERB
ejpam-5872	3	6	-	-	PUNCT
ejpam-5872	3	7	fg	fg	PROPN
ejpam-5872	3	8	and	and	CCONJ
ejpam-5872	3	9	its	its	PRON
ejpam-5872	3	10	applications	application	NOUN
ejpam-5872	3	11	helps	help	VERB
ejpam-5872	3	12	us	we	PRON
ejpam-5872	3	13	understand	understand	VERB
ejpam-5872	3	14	complex	complex	ADJ
ejpam-5872	3	15	networks	network	NOUN
ejpam-5872	3	16	and	and	CCONJ
ejpam-5872	3	17	their	their	PRON
ejpam-5872	3	18	characteristics	characteristic	NOUN
ejpam-5872	3	19	.	.	PUNCT
ejpam-5872	4	1	this	this	DET
ejpam-5872	4	2	study	study	NOUN
ejpam-5872	4	3	intends	intend	VERB
ejpam-5872	4	4	to	to	PART
ejpam-5872	4	5	examine	examine	VERB
ejpam-5872	4	6	the	the	DET
ejpam-5872	4	7	key	key	ADJ
ejpam-5872	4	8	theorems	theorem	NOUN
ejpam-5872	4	9	pertaining	pertain	VERB
ejpam-5872	4	10	to	to	ADP
ejpam-5872	4	11	vertex	vertex	NOUN
ejpam-5872	4	12	and	and	CCONJ
ejpam-5872	4	13	edge	edge	NOUN
ejpam-5872	4	14	degrees	degree	NOUN
ejpam-5872	4	15	and	and	CCONJ
ejpam-5872	4	16	their	their	PRON
ejpam-5872	4	17	membership	membership	NOUN
ejpam-5872	4	18	values	value	NOUN
ejpam-5872	4	19	by	by	ADP
ejpam-5872	4	20	highlighting	highlight	VERB
ejpam-5872	4	21	their	their	PRON
ejpam-5872	4	22	real	real	ADJ
ejpam-5872	4	23	-	-	PUNCT
ejpam-5872	4	24	time	time	NOUN
ejpam-5872	4	25	applications	application	NOUN
ejpam-5872	4	26	in	in	ADP
ejpam-5872	4	27	wireless	wireless	ADJ
ejpam-5872	4	28	sensor	sensor	NOUN
ejpam-5872	4	29	networks	network	NOUN
ejpam-5872	4	30	(	(	PUNCT
ejpam-5872	4	31	wsns	wsns	NOUN
ejpam-5872	4	32	)	)	PUNCT
ejpam-5872	4	33	and	and	CCONJ
ejpam-5872	4	34	environmental	environmental	ADJ
ejpam-5872	4	35	monitoring	monitoring	NOUN
ejpam-5872	4	36	systems	system	NOUN
ejpam-5872	4	37	(	(	PUNCT
ejpam-5872	4	38	emss	emss	NOUN
ejpam-5872	4	39	)	)	PUNCT
ejpam-5872	4	40	,	,	PUNCT
ejpam-5872	4	41	where	where	SCONJ
ejpam-5872	4	42	sensor	sensor	NOUN
ejpam-5872	4	43	nodes	node	NOUN
ejpam-5872	4	44	must	must	AUX
ejpam-5872	4	45	maintain	maintain	VERB
ejpam-5872	4	46	reliable	reliable	ADJ
ejpam-5872	4	47	communication	communication	NOUN
ejpam-5872	4	48	.	.	PUNCT
ejpam-5872	5	1	the	the	DET
ejpam-5872	5	2	main	main	ADJ
ejpam-5872	5	3	focus	focus	NOUN
ejpam-5872	5	4	of	of	ADP
ejpam-5872	5	5	this	this	DET
ejpam-5872	5	6	paper	paper	NOUN
ejpam-5872	5	7	shifts	shift	NOUN
ejpam-5872	5	8	from	from	ADP
ejpam-5872	5	9	the	the	DET
ejpam-5872	5	10	exploration	exploration	NOUN
ejpam-5872	5	11	of	of	ADP
ejpam-5872	5	12	theorems	theorem	NOUN
ejpam-5872	5	13	about	about	ADP
ejpam-5872	5	14	vertex	vertex	NOUN
ejpam-5872	5	15	and	and	CCONJ
ejpam-5872	5	16	edge	edge	NOUN
ejpam-5872	5	17	degree	degree	NOUN
ejpam-5872	5	18	and	and	CCONJ
ejpam-5872	5	19	their	their	PRON
ejpam-5872	5	20	membership	membership	NOUN
ejpam-5872	5	21	values	value	NOUN
ejpam-5872	5	22	to	to	ADP
ejpam-5872	5	23	the	the	DET
ejpam-5872	5	24	introduction	introduction	NOUN
ejpam-5872	5	25	of	of	ADP
ejpam-5872	5	26	new	new	ADJ
ejpam-5872	5	27	domination	domination	NOUN
ejpam-5872	5	28	metrics	metric	NOUN
ejpam-5872	5	29	tailored	tailor	VERB
ejpam-5872	5	30	for	for	ADP
ejpam-5872	5	31	signed	sign	VERB
ejpam-5872	5	32	-	-	PUNCT
ejpam-5872	5	33	fgs	fgs	NOUN
ejpam-5872	5	34	,	,	PUNCT
ejpam-5872	5	35	the	the	DET
ejpam-5872	5	36	domination	domination	NOUN
ejpam-5872	5	37	sets	set	NOUN
ejpam-5872	5	38	and	and	CCONJ
ejpam-5872	5	39	minimum	minimum	NOUN
ejpam-5872	5	40	domination	domination	NOUN
ejpam-5872	5	41	sets	set	NOUN
ejpam-5872	5	42	,	,	PUNCT
ejpam-5872	5	43	and	and	CCONJ
ejpam-5872	5	44	their	their	PRON
ejpam-5872	5	45	relevance	relevance	NOUN
ejpam-5872	5	46	to	to	ADP
ejpam-5872	5	47	efficient	efficient	ADJ
ejpam-5872	5	48	placement	placement	NOUN
ejpam-5872	5	49	and	and	CCONJ
ejpam-5872	5	50	the	the	DET
ejpam-5872	5	51	operation	operation	NOUN
ejpam-5872	5	52	of	of	ADP
ejpam-5872	5	53	wsns	wsns	NOUN
ejpam-5872	5	54	in	in	ADP
ejpam-5872	5	55	emss	emss	NOUN
ejpam-5872	5	56	.	.	PUNCT
ejpam-5872	6	1	signed	sign	VERB
ejpam-5872	6	2	-	-	PUNCT
ejpam-5872	6	3	fgs	fgs	NOUN
ejpam-5872	6	4	facilitate	facilitate	NOUN
ejpam-5872	6	5	effective	effective	ADJ
ejpam-5872	6	6	data	datum	NOUN
ejpam-5872	6	7	collection	collection	NOUN
ejpam-5872	6	8	by	by	ADP
ejpam-5872	6	9	ensuring	ensure	VERB
ejpam-5872	6	10	network	network	NOUN
ejpam-5872	6	11	coverage	coverage	NOUN
ejpam-5872	6	12	.	.	PUNCT
ejpam-5872	7	1	this	this	DET
ejpam-5872	7	2	study	study	NOUN
ejpam-5872	7	3	makes	make	VERB
ejpam-5872	7	4	a	a	DET
ejpam-5872	7	5	major	major	ADJ
ejpam-5872	7	6	contribution	contribution	NOUN
ejpam-5872	7	7	to	to	ADP
ejpam-5872	7	8	the	the	DET
ejpam-5872	7	9	field	field	NOUN
ejpam-5872	7	10	of	of	ADP
ejpam-5872	7	11	fuzzy	fuzzy	ADJ
ejpam-5872	7	12	mathematics	mathematic	NOUN
ejpam-5872	7	13	with	with	ADP
ejpam-5872	7	14	a	a	DET
ejpam-5872	7	15	comprehensive	comprehensive	ADJ
ejpam-5872	7	16	understanding	understanding	NOUN
ejpam-5872	7	17	of	of	ADP
ejpam-5872	7	18	complex	complex	ADJ
ejpam-5872	7	19	networks	network	NOUN
ejpam-5872	7	20	and	and	CCONJ
ejpam-5872	7	21	their	their	PRON
ejpam-5872	7	22	characteristics	characteristic	NOUN
ejpam-5872	7	23	.	.	PUNCT
ejpam-5872	8	1	2020	2020	NUM
ejpam-5872	8	2	mathematics	mathematic	NOUN
ejpam-5872	8	3	subject	subject	NOUN
ejpam-5872	8	4	classifications	classification	NOUN
ejpam-5872	8	5	:	:	PUNCT
ejpam-5872	8	6	05c72	05c72	NOUN
ejpam-5872	8	7	,	,	PUNCT
ejpam-5872	8	8	05c22	05c22	NOUN
ejpam-5872	8	9	,	,	PUNCT
ejpam-5872	8	10	05c69	05c69	NUM
ejpam-5872	8	11	,	,	PUNCT
ejpam-5872	8	12	05c12	05c12	NOUN
ejpam-5872	8	13	key	key	ADJ
ejpam-5872	8	14	words	word	NOUN
ejpam-5872	8	15	and	and	CCONJ
ejpam-5872	8	16	phrases	phrase	NOUN
ejpam-5872	8	17	:	:	PUNCT
ejpam-5872	8	18	signed	sign	VERB
ejpam-5872	8	19	fuzzy	fuzzy	ADJ
ejpam-5872	8	20	graphs	graph	NOUN
ejpam-5872	8	21	(	(	PUNCT
ejpam-5872	8	22	signed	sign	VERB
ejpam-5872	8	23	-	-	PUNCT
ejpam-5872	8	24	fg	fg	NOUN
ejpam-5872	8	25	)	)	PUNCT
ejpam-5872	8	26	,	,	PUNCT
ejpam-5872	8	27	wireless	wireless	ADJ
ejpam-5872	8	28	sensor	sensor	NOUN
ejpam-5872	8	29	networks	network	NOUN
ejpam-5872	8	30	(	(	PUNCT
ejpam-5872	8	31	wsn	wsn	PROPN
ejpam-5872	8	32	)	)	PUNCT
ejpam-5872	8	33	,	,	PUNCT
ejpam-5872	8	34	environmental	environmental	ADJ
ejpam-5872	8	35	monitoring	monitoring	NOUN
ejpam-5872	8	36	systems	system	NOUN
ejpam-5872	8	37	(	(	PUNCT
ejpam-5872	8	38	ems	ems	PROPN
ejpam-5872	8	39	)	)	PUNCT
ejpam-5872	8	40	1	1	NUM
ejpam-5872	8	41	.	.	PUNCT
ejpam-5872	9	1	introduction	introduction	NOUN
ejpam-5872	9	2	graphs	graph	NOUN
ejpam-5872	9	3	have	have	AUX
ejpam-5872	9	4	long	long	ADV
ejpam-5872	9	5	been	be	AUX
ejpam-5872	9	6	recognized	recognize	VERB
ejpam-5872	9	7	as	as	ADP
ejpam-5872	9	8	powerful	powerful	ADJ
ejpam-5872	9	9	tools	tool	NOUN
ejpam-5872	9	10	for	for	ADP
ejpam-5872	9	11	modeling	model	VERB
ejpam-5872	9	12	relationships	relationship	NOUN
ejpam-5872	9	13	,	,	PUNCT
ejpam-5872	9	14	providing	provide	VERB
ejpam-5872	9	15	a	a	DET
ejpam-5872	9	16	simple	simple	ADJ
ejpam-5872	9	17	way	way	NOUN
ejpam-5872	9	18	to	to	PART
ejpam-5872	9	19	represent	represent	VERB
ejpam-5872	9	20	connections	connection	NOUN
ejpam-5872	9	21	between	between	ADP
ejpam-5872	9	22	objects	object	NOUN
ejpam-5872	9	23	.	.	PUNCT
ejpam-5872	10	1	in	in	ADP
ejpam-5872	10	2	this	this	DET
ejpam-5872	10	3	model	model	NOUN
ejpam-5872	10	4	,	,	PUNCT
ejpam-5872	10	5	objects	object	NOUN
ejpam-5872	10	6	are	be	AUX
ejpam-5872	10	7	∗corresponding	∗corresponde	VERB
ejpam-5872	10	8	author	author	NOUN
ejpam-5872	10	9	.	.	PUNCT
ejpam-5872	11	1	doi	doi	NOUN
ejpam-5872	11	2	:	:	PUNCT
ejpam-5872	11	3	https://doi.org/10.29020/nybg.ejpam.v18i4.5872	https://doi.org/10.29020/nybg.ejpam.v18i4.5872	ADP
ejpam-5872	11	4	email	email	NOUN
ejpam-5872	11	5	addresses	address	NOUN
ejpam-5872	11	6	:	:	PUNCT
ejpam-5872	11	7	csankar26@gmail.com	csankar26@gmail.com	X
ejpam-5872	11	8	(	(	PUNCT
ejpam-5872	11	9	c.	c.	PROPN
ejpam-5872	11	10	sankar	sankar	PROPN
ejpam-5872	11	11	)	)	PUNCT
ejpam-5872	11	12	,	,	PUNCT
ejpam-5872	11	13	msaran81@gmail.com	msaran81@gmail.com	PROPN
ejpam-5872	11	14	(	(	PUNCT
ejpam-5872	11	15	m.	m.	PROPN
ejpam-5872	11	16	saravanan	saravanan	PROPN
ejpam-5872	11	17	)	)	PUNCT
ejpam-5872	11	18	,	,	PUNCT
ejpam-5872	11	19	sujathar@snuchennai.edu.in	sujathar@snuchennai.edu.in	NOUN
ejpam-5872	11	20	(	(	PUNCT
ejpam-5872	11	21	r.	r.	PROPN
ejpam-5872	11	22	sujatha	sujatha	PROPN
ejpam-5872	11	23	)	)	PUNCT
ejpam-5872	11	24	,	,	PUNCT
ejpam-5872	11	25	gvenkatnarayanan@gmail.com	gvenkatnarayanan@gmail.com	X
ejpam-5872	11	26	(	(	PUNCT
ejpam-5872	11	27	g.	g.	PROPN
ejpam-5872	11	28	venkat	venkat	PROPN
ejpam-5872	11	29	narayanan	narayanan	PROPN
ejpam-5872	11	30	)	)	PUNCT
ejpam-5872	11	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5872	12	1	1	1	NUM
ejpam-5872	12	2	copyright	copyright	NOUN
ejpam-5872	12	3	:	:	PUNCT
ejpam-5872	12	4	©	©	PROPN
ejpam-5872	12	5	2025	2025	NUM
ejpam-5872	12	6	the	the	DET
ejpam-5872	12	7	author(s	author(s	NOUN
ejpam-5872	12	8	)	)	PUNCT
ejpam-5872	12	9	.	.	PUNCT
ejpam-5872	13	1	(	(	PUNCT
ejpam-5872	13	2	cc	cc	NOUN
ejpam-5872	13	3	by	by	ADP
ejpam-5872	13	4	-	-	PUNCT
ejpam-5872	13	5	nc	nc	PROPN
ejpam-5872	13	6	4.0	4.0	NUM
ejpam-5872	13	7	)	)	PUNCT
ejpam-5872	13	8	c.	c.	NOUN
ejpam-5872	13	9	sankar	sankar	NOUN
ejpam-5872	13	10	et	et	PROPN
ejpam-5872	13	11	al	al	PROPN
ejpam-5872	13	12	.	.	PUNCT
ejpam-5872	13	13	/	/	SYM
ejpam-5872	13	14	eur	eur	PROPN
ejpam-5872	13	15	.	.	PUNCT
ejpam-5872	14	1	j.	j.	PROPN
ejpam-5872	14	2	pure	pure	PROPN
ejpam-5872	14	3	appl	appl	PROPN
ejpam-5872	14	4	.	.	PROPN
ejpam-5872	14	5	math	math	PROPN
ejpam-5872	14	6	,	,	PUNCT
ejpam-5872	14	7	18	18	NUM
ejpam-5872	14	8	(	(	PUNCT
ejpam-5872	14	9	4	4	NUM
ejpam-5872	14	10	)	)	PUNCT
ejpam-5872	14	11	(	(	PUNCT
ejpam-5872	14	12	2025	2025	NUM
ejpam-5872	14	13	)	)	PUNCT
ejpam-5872	14	14	,	,	PUNCT
ejpam-5872	14	15	5872	5872	NUM
ejpam-5872	14	16	2	2	NUM
ejpam-5872	14	17	of	of	ADP
ejpam-5872	14	18	17	17	NUM
ejpam-5872	14	19	represented	represent	VERB
ejpam-5872	14	20	as	as	ADP
ejpam-5872	14	21	vertices	vertex	NOUN
ejpam-5872	14	22	,	,	PUNCT
ejpam-5872	14	23	and	and	CCONJ
ejpam-5872	14	24	the	the	DET
ejpam-5872	14	25	relationships	relationship	NOUN
ejpam-5872	14	26	between	between	ADP
ejpam-5872	14	27	them	they	PRON
ejpam-5872	14	28	are	be	AUX
ejpam-5872	14	29	defined	define	VERB
ejpam-5872	14	30	as	as	ADP
ejpam-5872	14	31	edges	edge	NOUN
ejpam-5872	14	32	.	.	PUNCT
ejpam-5872	15	1	although	although	SCONJ
ejpam-5872	15	2	they	they	PRON
ejpam-5872	15	3	are	be	AUX
ejpam-5872	15	4	helpful	helpful	ADJ
ejpam-5872	15	5	in	in	ADP
ejpam-5872	15	6	many	many	ADJ
ejpam-5872	15	7	situations	situation	NOUN
ejpam-5872	15	8	,	,	PUNCT
ejpam-5872	15	9	traditional	traditional	ADJ
ejpam-5872	15	10	graph	graph	NOUN
ejpam-5872	15	11	models	model	NOUN
ejpam-5872	15	12	are	be	AUX
ejpam-5872	15	13	based	base	VERB
ejpam-5872	15	14	on	on	ADP
ejpam-5872	15	15	binary	binary	ADJ
ejpam-5872	15	16	relationships	relationship	NOUN
ejpam-5872	15	17	with	with	ADP
ejpam-5872	15	18	edges	edge	NOUN
ejpam-5872	15	19	that	that	PRON
ejpam-5872	15	20	may	may	AUX
ejpam-5872	15	21	or	or	CCONJ
ejpam-5872	15	22	may	may	AUX
ejpam-5872	15	23	not	not	PART
ejpam-5872	15	24	exist	exist	VERB
ejpam-5872	15	25	.	.	PUNCT
ejpam-5872	16	1	however	however	ADV
ejpam-5872	16	2	,	,	PUNCT
ejpam-5872	16	3	ambiguity	ambiguity	NOUN
ejpam-5872	16	4	or	or	CCONJ
ejpam-5872	16	5	confusion	confusion	NOUN
ejpam-5872	16	6	in	in	ADP
ejpam-5872	16	7	the	the	DET
ejpam-5872	16	8	definition	definition	NOUN
ejpam-5872	16	9	of	of	ADP
ejpam-5872	16	10	items	item	NOUN
ejpam-5872	16	11	,	,	PUNCT
ejpam-5872	16	12	their	their	PRON
ejpam-5872	16	13	relationships	relationship	NOUN
ejpam-5872	16	14	,	,	PUNCT
ejpam-5872	16	15	or	or	CCONJ
ejpam-5872	16	16	both	both	PRON
ejpam-5872	16	17	are	be	AUX
ejpam-5872	16	18	common	common	ADJ
ejpam-5872	16	19	in	in	ADP
ejpam-5872	16	20	the	the	DET
ejpam-5872	16	21	real	real	ADJ
ejpam-5872	16	22	world	world	NOUN
ejpam-5872	16	23	.	.	PUNCT
ejpam-5872	17	1	binary	binary	ADJ
ejpam-5872	17	2	edges	edge	NOUN
ejpam-5872	17	3	can	can	AUX
ejpam-5872	17	4	be	be	AUX
ejpam-5872	17	5	used	use	VERB
ejpam-5872	17	6	to	to	PART
ejpam-5872	17	7	make	make	VERB
ejpam-5872	17	8	things	thing	NOUN
ejpam-5872	17	9	like	like	ADP
ejpam-5872	17	10	the	the	DET
ejpam-5872	17	11	quality	quality	NOUN
ejpam-5872	17	12	of	of	ADP
ejpam-5872	17	13	sensor	sensor	NOUN
ejpam-5872	17	14	data	datum	NOUN
ejpam-5872	17	15	in	in	ADP
ejpam-5872	17	16	environmental	environmental	ADJ
ejpam-5872	17	17	monitoring	monitoring	NOUN
ejpam-5872	17	18	,	,	PUNCT
ejpam-5872	17	19	the	the	DET
ejpam-5872	17	20	strength	strength	NOUN
ejpam-5872	17	21	of	of	ADP
ejpam-5872	17	22	friendships	friendship	NOUN
ejpam-5872	17	23	in	in	ADP
ejpam-5872	17	24	social	social	ADJ
ejpam-5872	17	25	networks	network	NOUN
ejpam-5872	17	26	,	,	PUNCT
ejpam-5872	17	27	and	and	CCONJ
ejpam-5872	17	28	the	the	DET
ejpam-5872	17	29	dependability	dependability	NOUN
ejpam-5872	17	30	of	of	ADP
ejpam-5872	17	31	transportation	transportation	NOUN
ejpam-5872	17	32	routes	route	NOUN
ejpam-5872	17	33	sufficiently	sufficiently	ADV
ejpam-5872	17	34	variable	variable	ADJ
ejpam-5872	17	35	and	and	CCONJ
ejpam-5872	17	36	unexpected	unexpected	ADJ
ejpam-5872	17	37	.	.	PUNCT
ejpam-5872	18	1	by	by	ADP
ejpam-5872	18	2	giving	give	VERB
ejpam-5872	18	3	vertices	vertex	NOUN
ejpam-5872	18	4	and	and	CCONJ
ejpam-5872	18	5	edges	edge	VERB
ejpam-5872	18	6	membership	membership	NOUN
ejpam-5872	18	7	values	value	NOUN
ejpam-5872	18	8	,	,	PUNCT
ejpam-5872	18	9	fuzzy	fuzzy	ADJ
ejpam-5872	18	10	graphs	graph	NOUN
ejpam-5872	18	11	enable	enable	VERB
ejpam-5872	18	12	a	a	DET
ejpam-5872	18	13	more	more	ADV
ejpam-5872	18	14	accurate	accurate	ADJ
ejpam-5872	18	15	description	description	NOUN
ejpam-5872	18	16	of	of	ADP
ejpam-5872	18	17	relationships	relationship	NOUN
ejpam-5872	18	18	,	,	PUNCT
ejpam-5872	18	19	offering	offer	VERB
ejpam-5872	18	20	a	a	DET
ejpam-5872	18	21	more	more	ADV
ejpam-5872	18	22	reliable	reliable	ADJ
ejpam-5872	18	23	framework	framework	NOUN
ejpam-5872	18	24	in	in	ADP
ejpam-5872	18	25	this	this	DET
ejpam-5872	18	26	situation	situation	NOUN
ejpam-5872	18	27	.	.	PUNCT
ejpam-5872	19	1	they	they	PRON
ejpam-5872	19	2	do	do	AUX
ejpam-5872	19	3	not	not	PART
ejpam-5872	19	4	,	,	PUNCT
ejpam-5872	19	5	however	however	ADV
ejpam-5872	19	6	,	,	PUNCT
ejpam-5872	19	7	adequately	adequately	ADV
ejpam-5872	19	8	capture	capture	VERB
ejpam-5872	19	9	the	the	DET
ejpam-5872	19	10	dichotomous	dichotomous	ADJ
ejpam-5872	19	11	character	character	NOUN
ejpam-5872	19	12	of	of	ADP
ejpam-5872	19	13	relationships	relationship	NOUN
ejpam-5872	19	14	,	,	PUNCT
ejpam-5872	19	15	which	which	PRON
ejpam-5872	19	16	can	can	AUX
ejpam-5872	19	17	be	be	AUX
ejpam-5872	19	18	either	either	CCONJ
ejpam-5872	19	19	positive	positive	ADJ
ejpam-5872	19	20	(	(	PUNCT
ejpam-5872	19	21	supporting	support	VERB
ejpam-5872	19	22	)	)	PUNCT
ejpam-5872	19	23	or	or	CCONJ
ejpam-5872	19	24	negative	negative	ADJ
ejpam-5872	19	25	(	(	PUNCT
ejpam-5872	19	26	antagonistic	antagonistic	ADJ
ejpam-5872	19	27	)	)	PUNCT
ejpam-5872	19	28	.	.	PUNCT
ejpam-5872	20	1	relationships	relationship	NOUN
ejpam-5872	20	2	are	be	AUX
ejpam-5872	20	3	not	not	PART
ejpam-5872	20	4	just	just	ADV
ejpam-5872	20	5	ambiguous	ambiguous	ADJ
ejpam-5872	20	6	but	but	CCONJ
ejpam-5872	20	7	also	also	ADV
ejpam-5872	20	8	divisive	divisive	ADJ
ejpam-5872	20	9	in	in	ADP
ejpam-5872	20	10	many	many	ADJ
ejpam-5872	20	11	applications	application	NOUN
ejpam-5872	20	12	,	,	PUNCT
ejpam-5872	20	13	including	include	VERB
ejpam-5872	20	14	wireless	wireless	ADJ
ejpam-5872	20	15	sensor	sensor	NOUN
ejpam-5872	20	16	networks	network	NOUN
ejpam-5872	20	17	,	,	PUNCT
ejpam-5872	20	18	ecosystems	ecosystem	NOUN
ejpam-5872	20	19	,	,	PUNCT
ejpam-5872	20	20	and	and	CCONJ
ejpam-5872	20	21	conflict	conflict	NOUN
ejpam-5872	20	22	and	and	CCONJ
ejpam-5872	20	23	cooperation	cooperation	NOUN
ejpam-5872	20	24	studies	study	NOUN
ejpam-5872	20	25	.	.	PUNCT
ejpam-5872	21	1	examples	example	NOUN
ejpam-5872	21	2	of	of	ADP
ejpam-5872	21	3	connections	connection	NOUN
ejpam-5872	21	4	and	and	CCONJ
ejpam-5872	21	5	relationships	relationship	NOUN
ejpam-5872	21	6	include	include	VERB
ejpam-5872	21	7	support	support	NOUN
ejpam-5872	21	8	and	and	CCONJ
ejpam-5872	21	9	influence	influence	NOUN
ejpam-5872	21	10	in	in	ADP
ejpam-5872	21	11	social	social	ADJ
ejpam-5872	21	12	communication	communication	NOUN
ejpam-5872	21	13	,	,	PUNCT
ejpam-5872	21	14	relationships	relationship	NOUN
ejpam-5872	21	15	and	and	CCONJ
ejpam-5872	21	16	relationships	relationship	NOUN
ejpam-5872	21	17	in	in	ADP
ejpam-5872	21	18	ecosystems	ecosystem	NOUN
ejpam-5872	21	19	,	,	PUNCT
ejpam-5872	21	20	and	and	CCONJ
ejpam-5872	21	21	collaboration	collaboration	NOUN
ejpam-5872	21	22	and	and	CCONJ
ejpam-5872	21	23	competition	competition	NOUN
ejpam-5872	21	24	in	in	ADP
ejpam-5872	21	25	social	social	ADJ
ejpam-5872	21	26	or	or	CCONJ
ejpam-5872	21	27	political	political	ADJ
ejpam-5872	21	28	interactions	interaction	NOUN
ejpam-5872	21	29	.	.	PUNCT
ejpam-5872	22	1	by	by	ADP
ejpam-5872	22	2	adding	add	VERB
ejpam-5872	22	3	the	the	DET
ejpam-5872	22	4	idea	idea	NOUN
ejpam-5872	22	5	of	of	ADP
ejpam-5872	22	6	polarity	polarity	NOUN
ejpam-5872	22	7	,	,	PUNCT
ejpam-5872	22	8	signed	sign	VERB
ejpam-5872	22	9	-	-	PUNCT
ejpam-5872	22	10	fgs	fgs	NOUN
ejpam-5872	22	11	expand	expand	VERB
ejpam-5872	22	12	on	on	ADP
ejpam-5872	22	13	the	the	DET
ejpam-5872	22	14	notion	notion	NOUN
ejpam-5872	22	15	of	of	ADP
ejpam-5872	22	16	fuzzy	fuzzy	ADJ
ejpam-5872	22	17	graphs	graph	NOUN
ejpam-5872	22	18	.	.	PUNCT
ejpam-5872	23	1	a	a	DET
ejpam-5872	23	2	relationship	relationship	NOUN
ejpam-5872	23	3	value	value	NOUN
ejpam-5872	23	4	,	,	PUNCT
ejpam-5872	23	5	which	which	PRON
ejpam-5872	23	6	indicates	indicate	VERB
ejpam-5872	23	7	the	the	DET
ejpam-5872	23	8	strength	strength	NOUN
ejpam-5872	23	9	of	of	ADP
ejpam-5872	23	10	the	the	DET
ejpam-5872	23	11	link	link	NOUN
ejpam-5872	23	12	,	,	PUNCT
ejpam-5872	23	13	and	and	CCONJ
ejpam-5872	23	14	a	a	DET
ejpam-5872	23	15	sign	sign	NOUN
ejpam-5872	23	16	,	,	PUNCT
ejpam-5872	23	17	which	which	PRON
ejpam-5872	23	18	indicates	indicate	VERB
ejpam-5872	23	19	whether	whether	SCONJ
ejpam-5872	23	20	the	the	DET
ejpam-5872	23	21	relationship	relationship	NOUN
ejpam-5872	23	22	is	be	AUX
ejpam-5872	23	23	positive	positive	ADJ
ejpam-5872	23	24	or	or	CCONJ
ejpam-5872	23	25	negative	negative	ADJ
ejpam-5872	23	26	,	,	PUNCT
ejpam-5872	23	27	are	be	AUX
ejpam-5872	23	28	characteristics	characteristic	NOUN
ejpam-5872	23	29	of	of	ADP
ejpam-5872	23	30	each	each	DET
ejpam-5872	23	31	edge	edge	NOUN
ejpam-5872	23	32	in	in	ADP
ejpam-5872	23	33	a	a	DET
ejpam-5872	23	34	signed	sign	VERB
ejpam-5872	23	35	-	-	PUNCT
ejpam-5872	23	36	fg	fg	PROPN
ejpam-5872	23	37	.	.	PUNCT
ejpam-5872	23	38	signature	signature	NOUN
ejpam-5872	23	39	fuzzy	fuzzy	ADJ
ejpam-5872	23	40	images	image	NOUN
ejpam-5872	23	41	can	can	AUX
ejpam-5872	23	42	capture	capture	VERB
ejpam-5872	23	43	small	small	ADJ
ejpam-5872	23	44	changes	change	NOUN
ejpam-5872	23	45	in	in	ADP
ejpam-5872	23	46	systems	system	NOUN
ejpam-5872	23	47	where	where	SCONJ
ejpam-5872	23	48	the	the	DET
ejpam-5872	23	49	nature	nature	NOUN
ejpam-5872	23	50	of	of	ADP
ejpam-5872	23	51	the	the	DET
ejpam-5872	23	52	interaction	interaction	NOUN
ejpam-5872	23	53	and	and	CCONJ
ejpam-5872	23	54	uncertainty	uncertainty	NOUN
ejpam-5872	23	55	are	be	AUX
ejpam-5872	23	56	both	both	ADV
ejpam-5872	23	57	significant	significant	ADJ
ejpam-5872	23	58	thanks	thank	NOUN
ejpam-5872	23	59	to	to	ADP
ejpam-5872	23	60	this	this	DET
ejpam-5872	23	61	binary	binary	ADJ
ejpam-5872	23	62	representation	representation	NOUN
ejpam-5872	23	63	.	.	PUNCT
ejpam-5872	24	1	by	by	ADP
ejpam-5872	24	2	altering	alter	VERB
ejpam-5872	24	3	the	the	DET
ejpam-5872	24	4	polarity	polarity	NOUN
ejpam-5872	24	5	of	of	ADP
ejpam-5872	24	6	the	the	DET
ejpam-5872	24	7	interactions	interaction	NOUN
ejpam-5872	24	8	to	to	PART
ejpam-5872	24	9	produce	produce	VERB
ejpam-5872	24	10	a	a	DET
ejpam-5872	24	11	framework	framework	NOUN
ejpam-5872	24	12	,	,	PUNCT
ejpam-5872	24	13	signed	sign	VERB
ejpam-5872	24	14	-	-	PUNCT
ejpam-5872	24	15	fgs	fgs	NOUN
ejpam-5872	24	16	further	far	ADV
ejpam-5872	24	17	enhance	enhance	VERB
ejpam-5872	24	18	these	these	DET
ejpam-5872	24	19	properties	property	NOUN
ejpam-5872	24	20	.	.	PUNCT
ejpam-5872	25	1	when	when	SCONJ
ejpam-5872	25	2	combined	combine	VERB
ejpam-5872	25	3	,	,	PUNCT
ejpam-5872	25	4	these	these	DET
ejpam-5872	25	5	models	model	NOUN
ejpam-5872	25	6	offer	offer	VERB
ejpam-5872	25	7	a	a	DET
ejpam-5872	25	8	cohesive	cohesive	ADJ
ejpam-5872	25	9	framework	framework	NOUN
ejpam-5872	25	10	for	for	ADP
ejpam-5872	25	11	examining	examine	VERB
ejpam-5872	25	12	intricate	intricate	ADJ
ejpam-5872	25	13	communication	communication	NOUN
ejpam-5872	25	14	systems	system	NOUN
ejpam-5872	25	15	across	across	ADP
ejpam-5872	25	16	a	a	DET
ejpam-5872	25	17	range	range	NOUN
ejpam-5872	25	18	of	of	ADP
ejpam-5872	25	19	fields	field	NOUN
ejpam-5872	25	20	,	,	PUNCT
ejpam-5872	25	21	such	such	ADJ
ejpam-5872	25	22	as	as	ADP
ejpam-5872	25	23	wireless	wireless	ADJ
ejpam-5872	25	24	communications	communication	NOUN
ejpam-5872	25	25	,	,	PUNCT
ejpam-5872	25	26	social	social	ADJ
ejpam-5872	25	27	networks	network	NOUN
ejpam-5872	25	28	,	,	PUNCT
ejpam-5872	25	29	and	and	CCONJ
ejpam-5872	25	30	environmental	environmental	ADJ
ejpam-5872	25	31	monitoring	monitoring	NOUN
ejpam-5872	25	32	.	.	PUNCT
ejpam-5872	26	1	a	a	DET
ejpam-5872	26	2	more	more	ADV
ejpam-5872	26	3	accurate	accurate	ADJ
ejpam-5872	26	4	framework	framework	NOUN
ejpam-5872	26	5	for	for	ADP
ejpam-5872	26	6	simulating	simulate	VERB
ejpam-5872	26	7	environmental	environmental	ADJ
ejpam-5872	26	8	monitoring	monitoring	NOUN
ejpam-5872	26	9	networks	network	NOUN
ejpam-5872	26	10	is	be	AUX
ejpam-5872	26	11	offered	offer	VERB
ejpam-5872	26	12	by	by	ADP
ejpam-5872	26	13	signed	sign	VERB
ejpam-5872	26	14	-	-	PUNCT
ejpam-5872	26	15	fgs	fgs	NOUN
ejpam-5872	26	16	,	,	PUNCT
ejpam-5872	26	17	which	which	PRON
ejpam-5872	26	18	depict	depict	VERB
ejpam-5872	26	19	both	both	CCONJ
ejpam-5872	26	20	the	the	DET
ejpam-5872	26	21	type	type	NOUN
ejpam-5872	26	22	of	of	ADP
ejpam-5872	26	23	interaction	interaction	NOUN
ejpam-5872	26	24	(	(	PUNCT
ejpam-5872	26	25	positive	positive	ADJ
ejpam-5872	26	26	or	or	CCONJ
ejpam-5872	26	27	negative	negative	ADJ
ejpam-5872	26	28	signs	sign	NOUN
ejpam-5872	26	29	)	)	PUNCT
ejpam-5872	26	30	and	and	CCONJ
ejpam-5872	26	31	the	the	DET
ejpam-5872	26	32	degree	degree	NOUN
ejpam-5872	26	33	of	of	ADP
ejpam-5872	26	34	connectivity	connectivity	NOUN
ejpam-5872	26	35	(	(	PUNCT
ejpam-5872	26	36	fuzzy	fuzzy	ADJ
ejpam-5872	26	37	weights	weight	NOUN
ejpam-5872	26	38	)	)	PUNCT
ejpam-5872	26	39	between	between	ADP
ejpam-5872	26	40	sensor	sensor	NOUN
ejpam-5872	26	41	nodes	nod	VERB
ejpam-5872	26	42	.	.	PUNCT
ejpam-5872	27	1	they	they	PRON
ejpam-5872	27	2	outperform	outperform	VERB
ejpam-5872	27	3	traditional	traditional	ADJ
ejpam-5872	27	4	crisp	crisp	ADJ
ejpam-5872	27	5	graph	graph	NOUN
ejpam-5872	27	6	models	model	NOUN
ejpam-5872	27	7	for	for	ADP
ejpam-5872	27	8	real	real	ADJ
ejpam-5872	27	9	-	-	PUNCT
ejpam-5872	27	10	world	world	NOUN
ejpam-5872	27	11	monitoring	monitoring	NOUN
ejpam-5872	27	12	applications	application	NOUN
ejpam-5872	27	13	because	because	SCONJ
ejpam-5872	27	14	they	they	PRON
ejpam-5872	27	15	can	can	AUX
ejpam-5872	27	16	capture	capture	VERB
ejpam-5872	27	17	changes	change	NOUN
ejpam-5872	27	18	in	in	ADP
ejpam-5872	27	19	link	link	NOUN
ejpam-5872	27	20	quality	quality	NOUN
ejpam-5872	27	21	,	,	PUNCT
ejpam-5872	27	22	take	take	VERB
ejpam-5872	27	23	interference	interference	NOUN
ejpam-5872	27	24	or	or	CCONJ
ejpam-5872	27	25	malfunctioning	malfunction	VERB
ejpam-5872	27	26	nodes	node	NOUN
ejpam-5872	27	27	into	into	ADP
ejpam-5872	27	28	account	account	NOUN
ejpam-5872	27	29	,	,	PUNCT
ejpam-5872	27	30	adjust	adjust	VERB
ejpam-5872	27	31	to	to	ADP
ejpam-5872	27	32	shifting	shift	VERB
ejpam-5872	27	33	environmental	environmental	ADJ
ejpam-5872	27	34	conditions	condition	NOUN
ejpam-5872	27	35	,	,	PUNCT
ejpam-5872	27	36	and	and	CCONJ
ejpam-5872	27	37	support	support	VERB
ejpam-5872	27	38	richer	rich	ADJ
ejpam-5872	27	39	network	network	NOUN
ejpam-5872	27	40	analysis	analysis	NOUN
ejpam-5872	27	41	.	.	PUNCT
ejpam-5872	28	1	graph[1	graph[1	VERB
ejpam-5872	28	2	]	]	PUNCT
ejpam-5872	28	3	can	can	AUX
ejpam-5872	28	4	be	be	AUX
ejpam-5872	28	5	viewed	view	VERB
ejpam-5872	28	6	as	as	ADP
ejpam-5872	28	7	a	a	DET
ejpam-5872	28	8	binary	binary	ADJ
ejpam-5872	28	9	relation	relation	NOUN
ejpam-5872	28	10	between	between	ADP
ejpam-5872	28	11	nonempty	nonempty	NOUN
ejpam-5872	28	12	v.	v.	ADP
ejpam-5872	28	13	the	the	DET
ejpam-5872	28	14	basis	basis	NOUN
ejpam-5872	28	15	of	of	ADP
ejpam-5872	28	16	fuzzy	fuzzy	ADJ
ejpam-5872	28	17	graphs	graph	NOUN
ejpam-5872	28	18	in	in	ADP
ejpam-5872	28	19	the	the	DET
ejpam-5872	28	20	theory	theory	NOUN
ejpam-5872	28	21	of	of	ADP
ejpam-5872	28	22	fuzzy	fuzzy	ADJ
ejpam-5872	28	23	relations	relation	NOUN
ejpam-5872	28	24	and	and	CCONJ
ejpam-5872	28	25	fuzzy	fuzzy	ADJ
ejpam-5872	28	26	sets	set	NOUN
ejpam-5872	28	27	mentioned	mention	VERB
ejpam-5872	28	28	by	by	ADP
ejpam-5872	28	29	zadeh	zadeh	PROPN
ejpam-5872	28	30	in	in	ADP
ejpam-5872	28	31	1965	1965	NUM
ejpam-5872	28	32	[	[	X
ejpam-5872	28	33	2	2	NUM
ejpam-5872	28	34	]	]	PUNCT
ejpam-5872	28	35	.	.	PUNCT
ejpam-5872	29	1	this	this	DET
ejpam-5872	29	2	concept	concept	NOUN
ejpam-5872	29	3	was	be	AUX
ejpam-5872	29	4	introduced	introduce	VERB
ejpam-5872	29	5	by	by	ADP
ejpam-5872	29	6	rosenfeld	rosenfeld	PROPN
ejpam-5872	29	7	[	[	X
ejpam-5872	29	8	3	3	X
ejpam-5872	29	9	]	]	PUNCT
ejpam-5872	29	10	in	in	ADP
ejpam-5872	29	11	1975	1975	NUM
ejpam-5872	29	12	,	,	PUNCT
ejpam-5872	29	13	who	who	PRON
ejpam-5872	29	14	discovered	discover	VERB
ejpam-5872	29	15	the	the	DET
ejpam-5872	29	16	relationship	relationship	NOUN
ejpam-5872	29	17	between	between	ADP
ejpam-5872	29	18	fuzzy	fuzzy	ADJ
ejpam-5872	29	19	sets	set	NOUN
ejpam-5872	29	20	and	and	CCONJ
ejpam-5872	29	21	paved	pave	VERB
ejpam-5872	29	22	the	the	DET
ejpam-5872	29	23	way	way	NOUN
ejpam-5872	29	24	for	for	ADP
ejpam-5872	29	25	the	the	DET
ejpam-5872	29	26	research	research	NOUN
ejpam-5872	29	27	of	of	ADP
ejpam-5872	29	28	fuzzy	fuzzy	ADJ
ejpam-5872	29	29	trees	tree	NOUN
ejpam-5872	29	30	,	,	PUNCT
ejpam-5872	29	31	blocks	block	NOUN
ejpam-5872	29	32	,	,	PUNCT
ejpam-5872	29	33	bridges	bridge	NOUN
ejpam-5872	29	34	and	and	CCONJ
ejpam-5872	29	35	cutting	cutting	NOUN
ejpam-5872	29	36	nodes	node	NOUN
ejpam-5872	29	37	.	.	PUNCT
ejpam-5872	30	1	in	in	ADP
ejpam-5872	30	2	[	[	X
ejpam-5872	30	3	3	3	NUM
ejpam-5872	30	4	]	]	PUNCT
ejpam-5872	30	5	,	,	PUNCT
ejpam-5872	30	6	the	the	DET
ejpam-5872	30	7	ideas	idea	NOUN
ejpam-5872	30	8	of	of	ADP
ejpam-5872	30	9	blocks	block	NOUN
ejpam-5872	30	10	,	,	PUNCT
ejpam-5872	30	11	cut	cut	NOUN
ejpam-5872	30	12	nodes	node	NOUN
ejpam-5872	30	13	,	,	PUNCT
ejpam-5872	30	14	fuzzy	fuzzy	ADJ
ejpam-5872	30	15	trees	tree	NOUN
ejpam-5872	30	16	and	and	CCONJ
ejpam-5872	30	17	bridges	bridge	NOUN
ejpam-5872	30	18	,	,	PUNCT
ejpam-5872	30	19	in	in	ADP
ejpam-5872	30	20	fuzzy	fuzzy	ADJ
ejpam-5872	30	21	graphs	graph	NOUN
ejpam-5872	30	22	were	be	AUX
ejpam-5872	30	23	examined	examine	VERB
ejpam-5872	30	24	.	.	PUNCT
ejpam-5872	31	1	yeh	yeh	PROPN
ejpam-5872	32	1	[	[	X
ejpam-5872	32	2	4	4	X
ejpam-5872	32	3	]	]	PUNCT
ejpam-5872	32	4	established	establish	VERB
ejpam-5872	32	5	several	several	ADJ
ejpam-5872	32	6	concepts	concept	NOUN
ejpam-5872	32	7	of	of	ADP
ejpam-5872	32	8	connectedness	connectedness	NOUN
ejpam-5872	32	9	in	in	ADP
ejpam-5872	32	10	fuzzy	fuzzy	ADJ
ejpam-5872	32	11	graphs	graph	NOUN
ejpam-5872	32	12	around	around	ADP
ejpam-5872	32	13	the	the	DET
ejpam-5872	32	14	same	same	ADJ
ejpam-5872	32	15	period	period	NOUN
ejpam-5872	32	16	.	.	PUNCT
ejpam-5872	33	1	numerous	numerous	ADJ
ejpam-5872	33	2	academics	academic	NOUN
ejpam-5872	33	3	have	have	AUX
ejpam-5872	33	4	explored	explore	VERB
ejpam-5872	33	5	this	this	DET
ejpam-5872	33	6	area	area	NOUN
ejpam-5872	33	7	further	far	ADV
ejpam-5872	33	8	since	since	SCONJ
ejpam-5872	33	9	the	the	DET
ejpam-5872	33	10	seminal	seminal	ADJ
ejpam-5872	33	11	publications	publication	NOUN
ejpam-5872	33	12	of	of	ADP
ejpam-5872	33	13	rosenfeld	rosenfeld	PROPN
ejpam-5872	33	14	[	[	X
ejpam-5872	33	15	3	3	NUM
ejpam-5872	33	16	]	]	PUNCT
ejpam-5872	33	17	.	.	PUNCT
ejpam-5872	34	1	yeh	yeh	PROPN
ejpam-5872	35	1	[	[	X
ejpam-5872	35	2	4	4	X
ejpam-5872	35	3	]	]	PUNCT
ejpam-5872	35	4	in	in	ADP
ejpam-5872	35	5	1975	1975	NUM
ejpam-5872	35	6	,	,	PUNCT
ejpam-5872	35	7	which	which	PRON
ejpam-5872	35	8	described	describe	VERB
ejpam-5872	35	9	fundamental	fundamental	ADJ
ejpam-5872	35	10	theoretic	theoretic	ADJ
ejpam-5872	35	11	fuzzy	fuzzy	ADJ
ejpam-5872	35	12	graph	graph	NOUN
ejpam-5872	35	13	notions	notion	NOUN
ejpam-5872	35	14	and	and	CCONJ
ejpam-5872	35	15	applications	application	NOUN
ejpam-5872	35	16	.	.	PUNCT
ejpam-5872	36	1	they	they	PRON
ejpam-5872	36	2	have	have	AUX
ejpam-5872	36	3	discovered	discover	VERB
ejpam-5872	36	4	fuzzy	fuzzy	ADJ
ejpam-5872	36	5	analogues	analogue	NOUN
ejpam-5872	36	6	of	of	ADP
ejpam-5872	36	7	many	many	ADJ
ejpam-5872	36	8	theoreticgraph	theoreticgraph	NOUN
ejpam-5872	36	9	concepts	concept	NOUN
ejpam-5872	36	10	.	.	PUNCT
ejpam-5872	37	1	these	these	DET
ejpam-5872	37	2	consist	consist	NOUN
ejpam-5872	37	3	of	of	ADP
ejpam-5872	37	4	fuzzy	fuzzy	ADJ
ejpam-5872	37	5	interval	interval	NOUN
ejpam-5872	37	6	graphs	graph	NOUN
ejpam-5872	37	7	[	[	X
ejpam-5872	37	8	5	5	NUM
ejpam-5872	37	9	,	,	PUNCT
ejpam-5872	37	10	6	6	NUM
ejpam-5872	37	11	]	]	PUNCT
ejpam-5872	37	12	,	,	PUNCT
ejpam-5872	37	13	fuzzy	fuzzy	ADJ
ejpam-5872	37	14	trees	tree	NOUN
ejpam-5872	37	15	[	[	X
ejpam-5872	37	16	4	4	NUM
ejpam-5872	37	17	,	,	PUNCT
ejpam-5872	37	18	7	7	NUM
ejpam-5872	37	19	]	]	PUNCT
ejpam-5872	37	20	,	,	PUNCT
ejpam-5872	37	21	fuzzy	fuzzy	ADJ
ejpam-5872	37	22	line	line	NOUN
ejpam-5872	37	23	graphs	graph	NOUN
ejpam-5872	37	24	[	[	X
ejpam-5872	37	25	8	8	NUM
ejpam-5872	37	26	]	]	PUNCT
ejpam-5872	37	27	,	,	PUNCT
ejpam-5872	37	28	automorphisms	automorphism	NOUN
ejpam-5872	37	29	of	of	ADP
ejpam-5872	37	30	fuzzy	fuzzy	ADJ
ejpam-5872	37	31	graphs	graph	NOUN
ejpam-5872	37	32	[	[	X
ejpam-5872	37	33	9	9	NUM
ejpam-5872	37	34	]	]	PUNCT
ejpam-5872	37	35	,	,	PUNCT
ejpam-5872	37	36	and	and	CCONJ
ejpam-5872	37	37	cycles	cycle	NOUN
ejpam-5872	37	38	and	and	CCONJ
ejpam-5872	37	39	cocycles	cocycle	NOUN
ejpam-5872	37	40	of	of	ADP
ejpam-5872	37	41	fuzzy	fuzzy	ADJ
ejpam-5872	37	42	graphs	graph	NOUN
ejpam-5872	37	43	[	[	X
ejpam-5872	37	44	10	10	NUM
ejpam-5872	37	45	]	]	PUNCT
ejpam-5872	37	46	.	.	PUNCT
ejpam-5872	38	1	in	in	ADP
ejpam-5872	38	2	[	[	X
ejpam-5872	38	3	4	4	NUM
ejpam-5872	38	4	]	]	PUNCT
ejpam-5872	38	5	,	,	PUNCT
ejpam-5872	38	6	many	many	ADJ
ejpam-5872	38	7	definitions	definition	NOUN
ejpam-5872	38	8	of	of	ADP
ejpam-5872	38	9	fuzzy	fuzzy	ADJ
ejpam-5872	38	10	trees	tree	NOUN
ejpam-5872	38	11	that	that	PRON
ejpam-5872	38	12	are	be	AUX
ejpam-5872	38	13	compatible	compatible	ADJ
ejpam-5872	38	14	with	with	ADP
ejpam-5872	38	15	cut	cut	VERB
ejpam-5872	38	16	-	-	PUNCT
ejpam-5872	38	17	level	level	NOUN
ejpam-5872	38	18	represenc	represenc	NOUN
ejpam-5872	38	19	.	.	PUNCT
ejpam-5872	39	1	sankar	sankar	PROPN
ejpam-5872	39	2	et	et	PROPN
ejpam-5872	39	3	al	al	PROPN
ejpam-5872	39	4	.	.	PUNCT
ejpam-5872	39	5	/	/	SYM
ejpam-5872	39	6	eur	eur	PROPN
ejpam-5872	39	7	.	.	PUNCT
ejpam-5872	40	1	j.	j.	PROPN
ejpam-5872	40	2	pure	pure	PROPN
ejpam-5872	40	3	appl	appl	PROPN
ejpam-5872	40	4	.	.	PROPN
ejpam-5872	40	5	math	math	PROPN
ejpam-5872	40	6	,	,	PUNCT
ejpam-5872	40	7	18	18	NUM
ejpam-5872	40	8	(	(	PUNCT
ejpam-5872	40	9	4	4	NUM
ejpam-5872	40	10	)	)	PUNCT
ejpam-5872	40	11	(	(	PUNCT
ejpam-5872	40	12	2025	2025	NUM
ejpam-5872	40	13	)	)	PUNCT
ejpam-5872	40	14	,	,	PUNCT
ejpam-5872	40	15	5872	5872	NUM
ejpam-5872	40	16	3	3	NUM
ejpam-5872	40	17	of	of	ADP
ejpam-5872	40	18	17	17	NUM
ejpam-5872	40	19	tations	tation	NOUN
ejpam-5872	40	20	were	be	AUX
ejpam-5872	40	21	presented	present	VERB
ejpam-5872	40	22	,	,	PUNCT
ejpam-5872	40	23	along	along	ADP
ejpam-5872	40	24	with	with	ADP
ejpam-5872	40	25	the	the	DET
ejpam-5872	40	26	ideas	idea	NOUN
ejpam-5872	40	27	of	of	ADP
ejpam-5872	40	28	connectedness	connectedness	NOUN
ejpam-5872	40	29	and	and	CCONJ
ejpam-5872	40	30	acyclicity	acyclicity	NOUN
ejpam-5872	40	31	degrees	degree	NOUN
ejpam-5872	40	32	for	for	ADP
ejpam-5872	40	33	fuzzy	fuzzy	ADJ
ejpam-5872	40	34	graphs	graph	NOUN
ejpam-5872	40	35	.	.	PUNCT
ejpam-5872	41	1	the	the	DET
ejpam-5872	41	2	notions	notion	NOUN
ejpam-5872	41	3	of	of	ADP
ejpam-5872	41	4	dominance	dominance	NOUN
ejpam-5872	41	5	and	and	CCONJ
ejpam-5872	41	6	absolute	absolute	ADJ
ejpam-5872	41	7	domination	domination	NOUN
ejpam-5872	41	8	in	in	ADP
ejpam-5872	41	9	fuzzy	fuzzy	ADJ
ejpam-5872	41	10	graphs	graph	NOUN
ejpam-5872	41	11	were	be	AUX
ejpam-5872	41	12	developed	develop	VERB
ejpam-5872	41	13	by	by	ADP
ejpam-5872	41	14	somasundaram	somasundaram	NOUN
ejpam-5872	41	15	[	[	X
ejpam-5872	41	16	11	11	NUM
ejpam-5872	41	17	,	,	PUNCT
ejpam-5872	41	18	12	12	NUM
ejpam-5872	41	19	]	]	PUNCT
ejpam-5872	41	20	.	.	PUNCT
ejpam-5872	42	1	they	they	PRON
ejpam-5872	42	2	also	also	ADV
ejpam-5872	42	3	established	establish	VERB
ejpam-5872	42	4	boundaries	boundary	NOUN
ejpam-5872	42	5	and	and	CCONJ
ejpam-5872	42	6	calculated	calculate	VERB
ejpam-5872	42	7	the	the	DET
ejpam-5872	42	8	domination	domination	NOUN
ejpam-5872	42	9	number	number	NOUN
ejpam-5872	42	10	for	for	ADP
ejpam-5872	42	11	different	different	ADJ
ejpam-5872	42	12	sets	set	NOUN
ejpam-5872	42	13	of	of	ADP
ejpam-5872	42	14	fuzzy	fuzzy	ADJ
ejpam-5872	42	15	graphs	graph	NOUN
ejpam-5872	42	16	.	.	PUNCT
ejpam-5872	43	1	union	union	NOUN
ejpam-5872	43	2	,	,	PUNCT
ejpam-5872	43	3	join	join	NOUN
ejpam-5872	43	4	,	,	PUNCT
ejpam-5872	43	5	composition	composition	NOUN
ejpam-5872	43	6	,	,	PUNCT
ejpam-5872	43	7	and	and	CCONJ
ejpam-5872	43	8	cartesian	cartesian	ADJ
ejpam-5872	43	9	product	product	NOUN
ejpam-5872	43	10	are	be	AUX
ejpam-5872	43	11	among	among	ADP
ejpam-5872	43	12	the	the	DET
ejpam-5872	43	13	operations	operation	NOUN
ejpam-5872	43	14	on	on	ADP
ejpam-5872	43	15	fuzzy	fuzzy	ADJ
ejpam-5872	43	16	graphs	graph	NOUN
ejpam-5872	43	17	that	that	SCONJ
ejpam-5872	43	18	somasundaram	somasundaram	NOUN
ejpam-5872	44	1	[	[	X
ejpam-5872	44	2	13	13	NUM
ejpam-5872	44	3	]	]	PUNCT
ejpam-5872	44	4	further	far	ADV
ejpam-5872	44	5	examined	examine	VERB
ejpam-5872	44	6	and	and	CCONJ
ejpam-5872	44	7	determined	determine	VERB
ejpam-5872	44	8	their	their	PRON
ejpam-5872	44	9	dominating	dominating	NOUN
ejpam-5872	44	10	parameters	parameter	NOUN
ejpam-5872	44	11	.	.	PUNCT
ejpam-5872	45	1	moderson[7	moderson[7	PROPN
ejpam-5872	45	2	]	]	X
ejpam-5872	45	3	examined	examine	VERB
ejpam-5872	45	4	fuzzy	fuzzy	ADJ
ejpam-5872	45	5	graphs	graph	NOUN
ejpam-5872	45	6	with	with	ADP
ejpam-5872	45	7	varying	vary	VERB
ejpam-5872	45	8	degrees	degree	NOUN
ejpam-5872	45	9	of	of	ADP
ejpam-5872	45	10	connectivity	connectivity	NOUN
ejpam-5872	45	11	.	.	PUNCT
ejpam-5872	46	1	it	it	PRON
ejpam-5872	46	2	was	be	AUX
ejpam-5872	46	3	demonstrated	demonstrate	VERB
ejpam-5872	46	4	how	how	SCONJ
ejpam-5872	46	5	the	the	DET
ejpam-5872	46	6	structural	structural	ADJ
ejpam-5872	46	7	characteristics	characteristic	NOUN
ejpam-5872	46	8	of	of	ADP
ejpam-5872	46	9	finite	finite	PROPN
ejpam-5872	46	10	fgs	fgs	PROPN
ejpam-5872	46	11	can	can	AUX
ejpam-5872	46	12	be	be	AUX
ejpam-5872	46	13	used	use	VERB
ejpam-5872	46	14	to	to	PART
ejpam-5872	46	15	solve	solve	VERB
ejpam-5872	46	16	operational	operational	ADJ
ejpam-5872	46	17	research	research	NOUN
ejpam-5872	46	18	issues	issue	NOUN
ejpam-5872	46	19	.	.	PUNCT
ejpam-5872	47	1	the	the	DET
ejpam-5872	47	2	authors	author	NOUN
ejpam-5872	47	3	of	of	ADP
ejpam-5872	47	4	the	the	DET
ejpam-5872	47	5	same	same	ADJ
ejpam-5872	47	6	work	work	NOUN
ejpam-5872	47	7	examined	examine	VERB
ejpam-5872	47	8	the	the	DET
ejpam-5872	47	9	properties	property	NOUN
ejpam-5872	47	10	of	of	ADP
ejpam-5872	47	11	cut	cut	NOUN
ejpam-5872	47	12	nodes	node	NOUN
ejpam-5872	47	13	,	,	PUNCT
ejpam-5872	47	14	bridges	bridge	NOUN
ejpam-5872	47	15	,	,	PUNCT
ejpam-5872	47	16	trees	tree	NOUN
ejpam-5872	47	17	,	,	PUNCT
ejpam-5872	47	18	and	and	CCONJ
ejpam-5872	47	19	fuzzy	fuzzy	ADJ
ejpam-5872	47	20	cycles	cycle	NOUN
ejpam-5872	47	21	in	in	ADP
ejpam-5872	47	22	fuzzy	fuzzy	ADJ
ejpam-5872	47	23	graphs	graph	NOUN
ejpam-5872	47	24	.	.	PUNCT
ejpam-5872	48	1	in	in	ADP
ejpam-5872	48	2	order	order	NOUN
ejpam-5872	48	3	to	to	PART
ejpam-5872	48	4	demonstrate	demonstrate	VERB
ejpam-5872	48	5	the	the	DET
ejpam-5872	48	6	interconnectedness	interconnectedness	NOUN
ejpam-5872	48	7	of	of	ADP
ejpam-5872	48	8	fgs	fgs	PROPN
ejpam-5872	48	9	,	,	PUNCT
ejpam-5872	48	10	nagoor	nagoor	NOUN
ejpam-5872	48	11	gani	gani	PROPN
ejpam-5872	48	12	[	[	X
ejpam-5872	48	13	14	14	NUM
ejpam-5872	48	14	]	]	PUNCT
ejpam-5872	48	15	looked	look	VERB
ejpam-5872	48	16	at	at	ADP
ejpam-5872	48	17	the	the	DET
ejpam-5872	48	18	interactions	interaction	NOUN
ejpam-5872	48	19	between	between	ADP
ejpam-5872	48	20	degree	degree	NOUN
ejpam-5872	48	21	,	,	PUNCT
ejpam-5872	48	22	order	order	NOUN
ejpam-5872	48	23	,	,	PUNCT
ejpam-5872	48	24	and	and	CCONJ
ejpam-5872	48	25	size	size	NOUN
ejpam-5872	48	26	.	.	PUNCT
ejpam-5872	49	1	bhutani	bhutani	NOUN
ejpam-5872	49	2	[	[	X
ejpam-5872	49	3	15	15	NUM
ejpam-5872	49	4	]	]	PUNCT
ejpam-5872	49	5	created	create	VERB
ejpam-5872	49	6	fuzzy	fuzzy	ADJ
ejpam-5872	49	7	end	end	NOUN
ejpam-5872	49	8	nodes	node	NOUN
ejpam-5872	49	9	in	in	ADP
ejpam-5872	49	10	fuzzy	fuzzy	ADJ
ejpam-5872	49	11	graphs	graph	NOUN
ejpam-5872	49	12	,	,	PUNCT
ejpam-5872	49	13	showing	show	VERB
ejpam-5872	49	14	that	that	SCONJ
ejpam-5872	49	15	no	no	DET
ejpam-5872	49	16	node	node	NOUN
ejpam-5872	49	17	could	could	AUX
ejpam-5872	49	18	be	be	AUX
ejpam-5872	49	19	both	both	CCONJ
ejpam-5872	49	20	a	a	DET
ejpam-5872	49	21	cut	cut	ADJ
ejpam-5872	49	22	node	node	NOUN
ejpam-5872	49	23	and	and	CCONJ
ejpam-5872	49	24	a	a	DET
ejpam-5872	49	25	fuzzy	fuzzy	ADJ
ejpam-5872	49	26	end	end	NOUN
ejpam-5872	49	27	node	node	NOUN
ejpam-5872	49	28	simultaneously	simultaneously	ADV
ejpam-5872	49	29	.	.	PUNCT
ejpam-5872	50	1	additionally	additionally	ADV
ejpam-5872	50	2	,	,	PUNCT
ejpam-5872	50	3	they	they	PRON
ejpam-5872	50	4	analyzed	analyze	VERB
ejpam-5872	50	5	fuzzy	fuzzy	ADJ
ejpam-5872	50	6	end	end	NOUN
ejpam-5872	50	7	node	node	ADJ
ejpam-5872	50	8	characteristics	characteristic	NOUN
ejpam-5872	50	9	in	in	ADP
ejpam-5872	50	10	fuzzy	fuzzy	ADJ
ejpam-5872	50	11	trees	tree	NOUN
ejpam-5872	50	12	and	and	CCONJ
ejpam-5872	50	13	described	describe	VERB
ejpam-5872	50	14	fuzzy	fuzzy	ADJ
ejpam-5872	50	15	cycles	cycle	NOUN
ejpam-5872	50	16	that	that	PRON
ejpam-5872	50	17	lacked	lack	VERB
ejpam-5872	50	18	fuzzy	fuzzy	ADJ
ejpam-5872	50	19	end	end	NOUN
ejpam-5872	50	20	nodes	node	NOUN
ejpam-5872	50	21	or	or	CCONJ
ejpam-5872	50	22	cut	cut	NOUN
ejpam-5872	50	23	nodes	node	NOUN
ejpam-5872	50	24	.	.	PUNCT
ejpam-5872	51	1	strong	strong	ADJ
ejpam-5872	51	2	arcs	arc	NOUN
ejpam-5872	51	3	and	and	CCONJ
ejpam-5872	51	4	strong	strong	ADJ
ejpam-5872	51	5	pathways	pathway	NOUN
ejpam-5872	51	6	in	in	ADP
ejpam-5872	51	7	fuzzy	fuzzy	ADJ
ejpam-5872	51	8	graphs	graph	NOUN
ejpam-5872	51	9	were	be	AUX
ejpam-5872	51	10	first	first	ADV
ejpam-5872	51	11	proposed	propose	VERB
ejpam-5872	51	12	in	in	ADP
ejpam-5872	51	13	[	[	X
ejpam-5872	51	14	16	16	NUM
ejpam-5872	51	15	]	]	PUNCT
ejpam-5872	51	16	,	,	PUNCT
ejpam-5872	51	17	where	where	SCONJ
ejpam-5872	51	18	it	it	PRON
ejpam-5872	51	19	was	be	AUX
ejpam-5872	51	20	shown	show	VERB
ejpam-5872	51	21	that	that	SCONJ
ejpam-5872	51	22	while	while	SCONJ
ejpam-5872	51	23	a	a	DET
ejpam-5872	51	24	strong	strong	ADJ
ejpam-5872	51	25	arc	arc	NOUN
ejpam-5872	51	26	is	be	AUX
ejpam-5872	51	27	not	not	PART
ejpam-5872	51	28	always	always	ADV
ejpam-5872	51	29	a	a	DET
ejpam-5872	51	30	fuzzy	fuzzy	ADJ
ejpam-5872	51	31	bridge	bridge	NOUN
ejpam-5872	51	32	,	,	PUNCT
ejpam-5872	51	33	a	a	DET
ejpam-5872	51	34	fuzzy	fuzzy	ADJ
ejpam-5872	51	35	bridge	bridge	NOUN
ejpam-5872	51	36	is	be	AUX
ejpam-5872	51	37	always	always	ADV
ejpam-5872	51	38	strong	strong	ADJ
ejpam-5872	51	39	.	.	PUNCT
ejpam-5872	52	1	furthermore	furthermore	ADV
ejpam-5872	52	2	,	,	PUNCT
ejpam-5872	52	3	the	the	DET
ejpam-5872	52	4	authors	author	NOUN
ejpam-5872	52	5	demonstrated	demonstrate	VERB
ejpam-5872	52	6	the	the	DET
ejpam-5872	52	7	characteristics	characteristic	NOUN
ejpam-5872	52	8	of	of	ADP
ejpam-5872	52	9	strong	strong	ADJ
ejpam-5872	52	10	arcs	arc	NOUN
ejpam-5872	52	11	in	in	ADP
ejpam-5872	52	12	fuzzy	fuzzy	ADJ
ejpam-5872	52	13	trees	tree	NOUN
ejpam-5872	52	14	and	and	CCONJ
ejpam-5872	52	15	characterized	characterize	VERB
ejpam-5872	52	16	fuzzy	fuzzy	ADJ
ejpam-5872	52	17	trees	tree	NOUN
ejpam-5872	52	18	using	use	VERB
ejpam-5872	52	19	strong	strong	ADJ
ejpam-5872	52	20	pathways	pathway	NOUN
ejpam-5872	52	21	.	.	PUNCT
ejpam-5872	53	1	assia	assia	PROPN
ejpam-5872	53	2	alaoui	alaoui	PROPN
ejpam-5872	54	1	[	[	X
ejpam-5872	54	2	17	17	NUM
ejpam-5872	54	3	]	]	PUNCT
ejpam-5872	54	4	expanded	expand	VERB
ejpam-5872	54	5	the	the	DET
ejpam-5872	54	6	concepts	concept	NOUN
ejpam-5872	54	7	of	of	ADP
ejpam-5872	54	8	external	external	ADJ
ejpam-5872	54	9	stability	stability	NOUN
ejpam-5872	54	10	,	,	PUNCT
ejpam-5872	54	11	external	external	ADJ
ejpam-5872	54	12	stability	stability	NOUN
ejpam-5872	54	13	,	,	PUNCT
ejpam-5872	54	14	external	external	ADJ
ejpam-5872	54	15	dominance	dominance	NOUN
ejpam-5872	54	16	,	,	PUNCT
ejpam-5872	54	17	and	and	CCONJ
ejpam-5872	54	18	their	their	PRON
ejpam-5872	54	19	combinations	combination	NOUN
ejpam-5872	54	20	to	to	ADP
ejpam-5872	54	21	fuzzy	fuzzy	ADJ
ejpam-5872	54	22	graphs	graph	NOUN
ejpam-5872	54	23	.	.	PUNCT
ejpam-5872	55	1	similarly	similarly	ADV
ejpam-5872	55	2	,	,	PUNCT
ejpam-5872	55	3	sameena	sameena	ADJ
ejpam-5872	55	4	and	and	CCONJ
ejpam-5872	55	5	sunitha	sunitha	PROPN
ejpam-5872	55	6	researched	research	VERB
ejpam-5872	55	7	the	the	DET
ejpam-5872	55	8	concept	concept	NOUN
ejpam-5872	55	9	of	of	ADP
ejpam-5872	55	10	strong	strong	ADJ
ejpam-5872	55	11	arcs	arc	NOUN
ejpam-5872	55	12	in	in	ADP
ejpam-5872	55	13	maximum	maximum	ADJ
ejpam-5872	55	14	spanning	span	VERB
ejpam-5872	55	15	trees	tree	NOUN
ejpam-5872	55	16	[	[	X
ejpam-5872	55	17	18	18	NUM
ejpam-5872	55	18	]	]	PUNCT
ejpam-5872	55	19	and	and	CCONJ
ejpam-5872	55	20	its	its	PRON
ejpam-5872	55	21	applications	application	NOUN
ejpam-5872	55	22	in	in	ADP
ejpam-5872	55	23	neural	neural	ADJ
ejpam-5872	55	24	networks	network	NOUN
ejpam-5872	55	25	[	[	X
ejpam-5872	55	26	19	19	NUM
ejpam-5872	55	27	,	,	PUNCT
ejpam-5872	55	28	20	20	NUM
ejpam-5872	55	29	]	]	PUNCT
ejpam-5872	55	30	.	.	PUNCT
ejpam-5872	56	1	fuzzy	fuzzy	ADJ
ejpam-5872	56	2	graphs	graph	NOUN
ejpam-5872	56	3	are	be	AUX
ejpam-5872	56	4	also	also	ADV
ejpam-5872	56	5	used	use	VERB
ejpam-5872	56	6	in	in	ADP
ejpam-5872	56	7	the	the	DET
ejpam-5872	56	8	literature	literature	NOUN
ejpam-5872	56	9	for	for	ADP
ejpam-5872	56	10	database	database	NOUN
ejpam-5872	56	11	theory	theory	NOUN
ejpam-5872	56	12	,	,	PUNCT
ejpam-5872	56	13	group	group	NOUN
ejpam-5872	56	14	structure	structure	NOUN
ejpam-5872	56	15	analysis	analysis	NOUN
ejpam-5872	56	16	,	,	PUNCT
ejpam-5872	56	17	and	and	CCONJ
ejpam-5872	56	18	chemical	chemical	NOUN
ejpam-5872	56	19	systems	system	NOUN
ejpam-5872	56	20	[	[	X
ejpam-5872	56	21	21	21	NUM
ejpam-5872	56	22	,	,	PUNCT
ejpam-5872	56	23	22	22	NUM
ejpam-5872	56	24	]	]	PUNCT
ejpam-5872	56	25	.	.	PUNCT
ejpam-5872	57	1	signed	sign	VERB
ejpam-5872	57	2	-	-	PUNCT
ejpam-5872	57	3	fg	fg	PROPN
ejpam-5872	57	4	was	be	AUX
ejpam-5872	57	5	introduced	introduce	VERB
ejpam-5872	57	6	by	by	ADP
ejpam-5872	57	7	[	[	X
ejpam-5872	57	8	23	23	NUM
ejpam-5872	57	9	]	]	PUNCT
ejpam-5872	57	10	,	,	PUNCT
ejpam-5872	57	11	its	its	PRON
ejpam-5872	57	12	integrity	integrity	NOUN
ejpam-5872	57	13	was	be	AUX
ejpam-5872	57	14	discussed	discuss	VERB
ejpam-5872	57	15	by	by	ADP
ejpam-5872	57	16	[	[	X
ejpam-5872	57	17	24	24	NUM
ejpam-5872	57	18	]	]	PUNCT
ejpam-5872	57	19	,	,	PUNCT
ejpam-5872	57	20	the	the	DET
ejpam-5872	57	21	domination	domination	NOUN
ejpam-5872	57	22	parameter	parameter	NOUN
ejpam-5872	57	23	was	be	AUX
ejpam-5872	57	24	examined	examine	VERB
ejpam-5872	57	25	by	by	ADP
ejpam-5872	57	26	[	[	X
ejpam-5872	57	27	25	25	NUM
ejpam-5872	57	28	]	]	PUNCT
ejpam-5872	57	29	,	,	PUNCT
ejpam-5872	57	30	and	and	CCONJ
ejpam-5872	57	31	the	the	DET
ejpam-5872	57	32	operations	operation	NOUN
ejpam-5872	57	33	of	of	ADP
ejpam-5872	57	34	signed	sign	VERB
ejpam-5872	57	35	-	-	PUNCT
ejpam-5872	57	36	fgs	fgs	NOUN
ejpam-5872	57	37	were	be	AUX
ejpam-5872	57	38	explored	explore	VERB
ejpam-5872	57	39	by	by	ADP
ejpam-5872	57	40	[	[	X
ejpam-5872	57	41	26	26	NUM
ejpam-5872	57	42	]	]	PUNCT
ejpam-5872	57	43	.	.	PUNCT
ejpam-5872	58	1	1.1	1.1	NUM
ejpam-5872	58	2	.	.	PUNCT
ejpam-5872	59	1	motivation	motivation	NOUN
ejpam-5872	59	2	conventional	conventional	ADJ
ejpam-5872	59	3	graph	graph	NOUN
ejpam-5872	59	4	theory	theory	NOUN
ejpam-5872	59	5	often	often	ADV
ejpam-5872	59	6	limits	limit	VERB
ejpam-5872	59	7	itself	itself	PRON
ejpam-5872	59	8	to	to	ADP
ejpam-5872	59	9	binary	binary	ADJ
ejpam-5872	59	10	relationships	relationship	NOUN
ejpam-5872	59	11	,	,	PUNCT
ejpam-5872	59	12	which	which	PRON
ejpam-5872	59	13	may	may	AUX
ejpam-5872	59	14	be	be	AUX
ejpam-5872	59	15	insufficient	insufficient	ADJ
ejpam-5872	59	16	to	to	PART
ejpam-5872	59	17	represent	represent	VERB
ejpam-5872	59	18	real	real	ADJ
ejpam-5872	59	19	-	-	PUNCT
ejpam-5872	59	20	world	world	NOUN
ejpam-5872	59	21	scenarios	scenario	NOUN
ejpam-5872	59	22	where	where	SCONJ
ejpam-5872	59	23	connections	connection	NOUN
ejpam-5872	59	24	are	be	AUX
ejpam-5872	59	25	ambiguous	ambiguous	ADJ
ejpam-5872	59	26	or	or	CCONJ
ejpam-5872	59	27	fuzzy	fuzzy	ADJ
ejpam-5872	59	28	.	.	PUNCT
ejpam-5872	60	1	this	this	DET
ejpam-5872	60	2	research	research	NOUN
ejpam-5872	60	3	aims	aim	VERB
ejpam-5872	60	4	to	to	PART
ejpam-5872	60	5	address	address	VERB
ejpam-5872	60	6	such	such	ADJ
ejpam-5872	60	7	complexities	complexity	NOUN
ejpam-5872	60	8	by	by	ADP
ejpam-5872	60	9	applying	apply	VERB
ejpam-5872	60	10	fuzzy	fuzzy	ADJ
ejpam-5872	60	11	graph	graph	NOUN
ejpam-5872	60	12	principles	principle	NOUN
ejpam-5872	60	13	.	.	PUNCT
ejpam-5872	61	1	the	the	DET
ejpam-5872	61	2	paper	paper	NOUN
ejpam-5872	61	3	emphasizes	emphasize	VERB
ejpam-5872	61	4	the	the	DET
ejpam-5872	61	5	importance	importance	NOUN
ejpam-5872	61	6	of	of	ADP
ejpam-5872	61	7	reliable	reliable	ADJ
ejpam-5872	61	8	communication	communication	NOUN
ejpam-5872	61	9	between	between	ADP
ejpam-5872	61	10	sensors	sensor	NOUN
ejpam-5872	61	11	used	use	VERB
ejpam-5872	61	12	in	in	ADP
ejpam-5872	61	13	environmental	environmental	ADJ
ejpam-5872	61	14	monitoring	monitoring	NOUN
ejpam-5872	61	15	and	and	CCONJ
ejpam-5872	61	16	explores	explore	VERB
ejpam-5872	61	17	the	the	DET
ejpam-5872	61	18	practical	practical	ADJ
ejpam-5872	61	19	need	need	NOUN
ejpam-5872	61	20	to	to	PART
ejpam-5872	61	21	maintain	maintain	VERB
ejpam-5872	61	22	network	network	NOUN
ejpam-5872	61	23	coverage	coverage	NOUN
ejpam-5872	61	24	.	.	PUNCT
ejpam-5872	62	1	by	by	ADP
ejpam-5872	62	2	leveraging	leverage	VERB
ejpam-5872	62	3	the	the	DET
ejpam-5872	62	4	principles	principle	NOUN
ejpam-5872	62	5	of	of	ADP
ejpam-5872	62	6	signed	sign	VERB
ejpam-5872	62	7	-	-	PUNCT
ejpam-5872	62	8	fgs	fgs	NOUN
ejpam-5872	62	9	,	,	PUNCT
ejpam-5872	62	10	it	it	PRON
ejpam-5872	62	11	ensures	ensure	VERB
ejpam-5872	62	12	efficient	efficient	ADJ
ejpam-5872	62	13	data	datum	NOUN
ejpam-5872	62	14	collection	collection	NOUN
ejpam-5872	62	15	despite	despite	SCONJ
ejpam-5872	62	16	potential	potential	ADJ
ejpam-5872	62	17	connectivity	connectivity	NOUN
ejpam-5872	62	18	issues	issue	NOUN
ejpam-5872	62	19	.	.	PUNCT
ejpam-5872	63	1	the	the	DET
ejpam-5872	63	2	study	study	NOUN
ejpam-5872	63	3	of	of	ADP
ejpam-5872	63	4	domination	domination	NOUN
ejpam-5872	63	5	sets	set	NOUN
ejpam-5872	63	6	,	,	PUNCT
ejpam-5872	63	7	minimum	minimum	ADJ
ejpam-5872	63	8	domination	domination	NOUN
ejpam-5872	63	9	numbers	number	NOUN
ejpam-5872	63	10	,	,	PUNCT
ejpam-5872	63	11	and	and	CCONJ
ejpam-5872	63	12	strong	strong	ADJ
ejpam-5872	63	13	and	and	CCONJ
ejpam-5872	63	14	effective	effective	ADJ
ejpam-5872	63	15	degrees	degree	NOUN
ejpam-5872	63	16	in	in	ADP
ejpam-5872	63	17	signed	sign	VERB
ejpam-5872	63	18	-	-	PUNCT
ejpam-5872	63	19	fgs	fgs	NOUN
ejpam-5872	63	20	contributes	contribute	VERB
ejpam-5872	63	21	to	to	ADP
ejpam-5872	63	22	the	the	DET
ejpam-5872	63	23	advancement	advancement	NOUN
ejpam-5872	63	24	of	of	ADP
ejpam-5872	63	25	fuzzy	fuzzy	ADJ
ejpam-5872	63	26	graph	graph	NOUN
ejpam-5872	63	27	theory	theory	NOUN
ejpam-5872	63	28	by	by	ADP
ejpam-5872	63	29	strengthening	strengthen	VERB
ejpam-5872	63	30	its	its	PRON
ejpam-5872	63	31	mathematical	mathematical	ADJ
ejpam-5872	63	32	foundations	foundation	NOUN
ejpam-5872	63	33	.	.	PUNCT
ejpam-5872	64	1	this	this	DET
ejpam-5872	64	2	theoretical	theoretical	ADJ
ejpam-5872	64	3	framework	framework	NOUN
ejpam-5872	64	4	is	be	AUX
ejpam-5872	64	5	essential	essential	ADJ
ejpam-5872	64	6	for	for	ADP
ejpam-5872	64	7	developing	develop	VERB
ejpam-5872	64	8	algorithms	algorithm	NOUN
ejpam-5872	64	9	that	that	PRON
ejpam-5872	64	10	optimize	optimize	VERB
ejpam-5872	64	11	network	network	NOUN
ejpam-5872	64	12	performance	performance	NOUN
ejpam-5872	64	13	.	.	PUNCT
ejpam-5872	65	1	c.	c.	PROPN
ejpam-5872	65	2	sankar	sankar	PROPN
ejpam-5872	65	3	et	et	PROPN
ejpam-5872	65	4	al	al	PROPN
ejpam-5872	65	5	.	.	PUNCT
ejpam-5872	65	6	/	/	SYM
ejpam-5872	65	7	eur	eur	PROPN
ejpam-5872	65	8	.	.	PUNCT
ejpam-5872	66	1	j.	j.	PROPN
ejpam-5872	66	2	pure	pure	PROPN
ejpam-5872	66	3	appl	appl	PROPN
ejpam-5872	66	4	.	.	PROPN
ejpam-5872	66	5	math	math	PROPN
ejpam-5872	66	6	,	,	PUNCT
ejpam-5872	66	7	18	18	NUM
ejpam-5872	66	8	(	(	PUNCT
ejpam-5872	66	9	4	4	NUM
ejpam-5872	66	10	)	)	PUNCT
ejpam-5872	66	11	(	(	PUNCT
ejpam-5872	66	12	2025	2025	NUM
ejpam-5872	66	13	)	)	PUNCT
ejpam-5872	66	14	,	,	PUNCT
ejpam-5872	66	15	5872	5872	NUM
ejpam-5872	66	16	4	4	NUM
ejpam-5872	66	17	of	of	ADP
ejpam-5872	66	18	17	17	NUM
ejpam-5872	66	19	1.2	1.2	NUM
ejpam-5872	66	20	.	.	PUNCT
ejpam-5872	67	1	organization	organization	NOUN
ejpam-5872	67	2	of	of	ADP
ejpam-5872	67	3	content	content	NOUN
ejpam-5872	67	4	the	the	DET
ejpam-5872	67	5	first	first	ADJ
ejpam-5872	67	6	section	section	NOUN
ejpam-5872	67	7	gives	give	VERB
ejpam-5872	67	8	a	a	DET
ejpam-5872	67	9	detailed	detailed	ADJ
ejpam-5872	67	10	introduction	introduction	NOUN
ejpam-5872	67	11	to	to	ADP
ejpam-5872	67	12	graph	graph	NOUN
ejpam-5872	67	13	theory	theory	NOUN
ejpam-5872	67	14	,	,	PUNCT
ejpam-5872	67	15	establishing	establish	VERB
ejpam-5872	67	16	a	a	DET
ejpam-5872	67	17	solid	solid	ADJ
ejpam-5872	67	18	foundation	foundation	NOUN
ejpam-5872	67	19	for	for	ADP
ejpam-5872	67	20	the	the	DET
ejpam-5872	67	21	discussions	discussion	NOUN
ejpam-5872	67	22	that	that	PRON
ejpam-5872	67	23	follow	follow	VERB
ejpam-5872	67	24	.	.	PUNCT
ejpam-5872	68	1	the	the	DET
ejpam-5872	68	2	second	second	ADJ
ejpam-5872	68	3	section	section	NOUN
ejpam-5872	68	4	introduces	introduce	VERB
ejpam-5872	68	5	the	the	DET
ejpam-5872	68	6	fundamentals	fundamental	NOUN
ejpam-5872	68	7	of	of	ADP
ejpam-5872	68	8	fuzzy	fuzzy	ADJ
ejpam-5872	68	9	graphs	graph	NOUN
ejpam-5872	68	10	and	and	CCONJ
ejpam-5872	68	11	signed	sign	VERB
ejpam-5872	68	12	fuzzy	fuzzy	ADJ
ejpam-5872	68	13	graphs	graph	NOUN
ejpam-5872	68	14	,	,	PUNCT
ejpam-5872	68	15	emphasizing	emphasize	VERB
ejpam-5872	68	16	key	key	ADJ
ejpam-5872	68	17	concepts	concept	NOUN
ejpam-5872	68	18	such	such	ADJ
ejpam-5872	68	19	as	as	ADP
ejpam-5872	68	20	minimum	minimum	NOUN
ejpam-5872	68	21	degree	degree	NOUN
ejpam-5872	68	22	,	,	PUNCT
ejpam-5872	68	23	maximum	maximum	ADJ
ejpam-5872	68	24	degree	degree	NOUN
ejpam-5872	68	25	,	,	PUNCT
ejpam-5872	68	26	effective	effective	ADJ
ejpam-5872	68	27	degree	degree	NOUN
ejpam-5872	68	28	,	,	PUNCT
ejpam-5872	68	29	and	and	CCONJ
ejpam-5872	68	30	standard	standard	ADJ
ejpam-5872	68	31	results	result	NOUN
ejpam-5872	68	32	relevant	relevant	ADJ
ejpam-5872	68	33	to	to	ADP
ejpam-5872	68	34	these	these	DET
ejpam-5872	68	35	structures	structure	NOUN
ejpam-5872	68	36	.	.	PUNCT
ejpam-5872	69	1	the	the	DET
ejpam-5872	69	2	third	third	ADJ
ejpam-5872	69	3	section	section	NOUN
ejpam-5872	69	4	,	,	PUNCT
ejpam-5872	69	5	titled	title	VERB
ejpam-5872	69	6	”	"	PUNCT
ejpam-5872	69	7	theoretical	theoretical	ADJ
ejpam-5872	69	8	framework	framework	NOUN
ejpam-5872	69	9	,	,	PUNCT
ejpam-5872	69	10	”	"	PUNCT
ejpam-5872	69	11	outlines	outline	VERB
ejpam-5872	69	12	the	the	DET
ejpam-5872	69	13	properties	property	NOUN
ejpam-5872	69	14	of	of	ADP
ejpam-5872	69	15	signed	sign	VERB
ejpam-5872	69	16	fuzzy	fuzzy	ADJ
ejpam-5872	69	17	graphs	graph	NOUN
ejpam-5872	69	18	and	and	CCONJ
ejpam-5872	69	19	explores	explore	VERB
ejpam-5872	69	20	the	the	DET
ejpam-5872	69	21	interrelationships	interrelationship	NOUN
ejpam-5872	69	22	between	between	ADP
ejpam-5872	69	23	strong	strong	ADJ
ejpam-5872	69	24	arcs	arc	NOUN
ejpam-5872	69	25	,	,	PUNCT
ejpam-5872	69	26	effective	effective	ADJ
ejpam-5872	69	27	degrees	degree	NOUN
ejpam-5872	69	28	,	,	PUNCT
ejpam-5872	69	29	and	and	CCONJ
ejpam-5872	69	30	membership	membership	NOUN
ejpam-5872	69	31	values	value	NOUN
ejpam-5872	69	32	,	,	PUNCT
ejpam-5872	69	33	thereby	thereby	ADV
ejpam-5872	69	34	providing	provide	VERB
ejpam-5872	69	35	a	a	DET
ejpam-5872	69	36	rigorous	rigorous	ADJ
ejpam-5872	69	37	mathematical	mathematical	ADJ
ejpam-5872	69	38	foundation	foundation	NOUN
ejpam-5872	69	39	for	for	ADP
ejpam-5872	69	40	analyzing	analyze	VERB
ejpam-5872	69	41	these	these	DET
ejpam-5872	69	42	graphs	graph	NOUN
ejpam-5872	69	43	.	.	PUNCT
ejpam-5872	70	1	in	in	ADP
ejpam-5872	70	2	addition	addition	NOUN
ejpam-5872	70	3	to	to	ADP
ejpam-5872	70	4	these	these	DET
ejpam-5872	70	5	foundational	foundational	ADJ
ejpam-5872	70	6	concepts	concept	NOUN
ejpam-5872	70	7	,	,	PUNCT
ejpam-5872	70	8	essential	essential	ADJ
ejpam-5872	70	9	terminology	terminology	NOUN
ejpam-5872	70	10	is	be	AUX
ejpam-5872	70	11	introduced	introduce	VERB
ejpam-5872	70	12	,	,	PUNCT
ejpam-5872	70	13	including	include	VERB
ejpam-5872	70	14	domination	domination	NOUN
ejpam-5872	70	15	,	,	PUNCT
ejpam-5872	70	16	domination	domination	NOUN
ejpam-5872	70	17	numbers	number	NOUN
ejpam-5872	70	18	,	,	PUNCT
ejpam-5872	70	19	and	and	CCONJ
ejpam-5872	70	20	the	the	DET
ejpam-5872	70	21	strong	strong	ADJ
ejpam-5872	70	22	domination	domination	NOUN
ejpam-5872	70	23	number	number	NOUN
ejpam-5872	70	24	,	,	PUNCT
ejpam-5872	70	25	to	to	PART
ejpam-5872	70	26	prepare	prepare	VERB
ejpam-5872	70	27	the	the	DET
ejpam-5872	70	28	reader	reader	NOUN
ejpam-5872	70	29	for	for	ADP
ejpam-5872	70	30	the	the	DET
ejpam-5872	70	31	analysis	analysis	NOUN
ejpam-5872	70	32	presented	present	VERB
ejpam-5872	70	33	in	in	ADP
ejpam-5872	70	34	the	the	DET
ejpam-5872	70	35	fourth	fourth	ADJ
ejpam-5872	70	36	section	section	NOUN
ejpam-5872	70	37	.	.	PUNCT
ejpam-5872	71	1	this	this	DET
ejpam-5872	71	2	section	section	NOUN
ejpam-5872	71	3	focuses	focus	VERB
ejpam-5872	71	4	on	on	ADP
ejpam-5872	71	5	results	result	NOUN
ejpam-5872	71	6	related	relate	VERB
ejpam-5872	71	7	to	to	ADP
ejpam-5872	71	8	domination	domination	NOUN
ejpam-5872	71	9	in	in	ADP
ejpam-5872	71	10	signed	sign	VERB
ejpam-5872	71	11	fuzzy	fuzzy	ADJ
ejpam-5872	71	12	graphs	graph	NOUN
ejpam-5872	71	13	.	.	PUNCT
ejpam-5872	72	1	the	the	DET
ejpam-5872	72	2	fifth	fifth	ADJ
ejpam-5872	72	3	section	section	NOUN
ejpam-5872	72	4	examines	examine	VERB
ejpam-5872	72	5	the	the	DET
ejpam-5872	72	6	application	application	NOUN
ejpam-5872	72	7	of	of	ADP
ejpam-5872	72	8	domination	domination	NOUN
ejpam-5872	72	9	in	in	ADP
ejpam-5872	72	10	signed	sign	VERB
ejpam-5872	72	11	fuzzy	fuzzy	ADJ
ejpam-5872	72	12	graphs	graph	NOUN
ejpam-5872	72	13	,	,	PUNCT
ejpam-5872	72	14	illustrated	illustrate	VERB
ejpam-5872	72	15	with	with	ADP
ejpam-5872	72	16	a	a	DET
ejpam-5872	72	17	numerical	numerical	ADJ
ejpam-5872	72	18	example	example	NOUN
ejpam-5872	72	19	that	that	SCONJ
ejpam-5872	72	20	highlights	highlight	VERB
ejpam-5872	72	21	its	its	PRON
ejpam-5872	72	22	relevance	relevance	NOUN
ejpam-5872	72	23	to	to	ADP
ejpam-5872	72	24	wireless	wireless	ADJ
ejpam-5872	72	25	sensor	sensor	NOUN
ejpam-5872	72	26	networks	network	NOUN
ejpam-5872	72	27	(	(	PUNCT
ejpam-5872	72	28	wsns	wsns	NOUN
ejpam-5872	72	29	)	)	PUNCT
ejpam-5872	72	30	for	for	ADP
ejpam-5872	72	31	environmental	environmental	ADJ
ejpam-5872	72	32	monitoring	monitoring	NOUN
ejpam-5872	72	33	systems	system	NOUN
ejpam-5872	72	34	.	.	PUNCT
ejpam-5872	73	1	this	this	DET
ejpam-5872	73	2	discussion	discussion	NOUN
ejpam-5872	73	3	demonstrates	demonstrate	VERB
ejpam-5872	73	4	how	how	SCONJ
ejpam-5872	73	5	domination	domination	NOUN
ejpam-5872	73	6	sets	set	NOUN
ejpam-5872	73	7	can	can	AUX
ejpam-5872	73	8	enhance	enhance	VERB
ejpam-5872	73	9	communication	communication	NOUN
ejpam-5872	73	10	within	within	ADP
ejpam-5872	73	11	a	a	DET
ejpam-5872	73	12	wsn	wsn	NOUN
ejpam-5872	73	13	consisting	consist	VERB
ejpam-5872	73	14	of	of	ADP
ejpam-5872	73	15	multiple	multiple	ADJ
ejpam-5872	73	16	sensors	sensor	NOUN
ejpam-5872	73	17	.	.	PUNCT
ejpam-5872	74	1	finally	finally	ADV
ejpam-5872	74	2	,	,	PUNCT
ejpam-5872	74	3	the	the	DET
ejpam-5872	74	4	document	document	NOUN
ejpam-5872	74	5	concludes	conclude	VERB
ejpam-5872	74	6	by	by	ADP
ejpam-5872	74	7	summarizing	summarize	VERB
ejpam-5872	74	8	the	the	DET
ejpam-5872	74	9	key	key	ADJ
ejpam-5872	74	10	findings	finding	NOUN
ejpam-5872	74	11	and	and	CCONJ
ejpam-5872	74	12	proposing	propose	VERB
ejpam-5872	74	13	directions	direction	NOUN
ejpam-5872	74	14	for	for	ADP
ejpam-5872	74	15	future	future	ADJ
ejpam-5872	74	16	research	research	NOUN
ejpam-5872	74	17	.	.	PUNCT
ejpam-5872	75	1	1.3	1.3	NUM
ejpam-5872	75	2	.	.	PUNCT
ejpam-5872	75	3	preliminary	preliminary	ADJ
ejpam-5872	75	4	concepts	concept	NOUN
ejpam-5872	75	5	and	and	CCONJ
ejpam-5872	75	6	results	result	NOUN
ejpam-5872	75	7	let	let	VERB
ejpam-5872	75	8	ℑ	ℑ	PRON
ejpam-5872	75	9	be	be	AUX
ejpam-5872	75	10	a	a	DET
ejpam-5872	75	11	nonempty	nonempty	ADJ
ejpam-5872	75	12	set	set	NOUN
ejpam-5872	75	13	of	of	ADP
ejpam-5872	75	14	nodes	node	NOUN
ejpam-5872	75	15	and	and	CCONJ
ejpam-5872	75	16	ξ	ξ	PRON
ejpam-5872	75	17	⊆	⊆	NUM
ejpam-5872	75	18	ℑ×ℑ	ℑ×ℑ	NOUN
ejpam-5872	75	19	a	a	DET
ejpam-5872	75	20	set	set	NOUN
ejpam-5872	75	21	of	of	ADP
ejpam-5872	75	22	edges	edge	NOUN
ejpam-5872	75	23	.	.	PUNCT
ejpam-5872	76	1	a	a	DET
ejpam-5872	76	2	crisp	crisp	ADJ
ejpam-5872	76	3	graph	graph	NOUN
ejpam-5872	76	4	is	be	AUX
ejpam-5872	76	5	σ∗	σ∗	ADJ
ejpam-5872	76	6	=	=	SYM
ejpam-5872	76	7	(	(	PUNCT
ejpam-5872	76	8	ℑ	ℑ	PROPN
ejpam-5872	76	9	,	,	PUNCT
ejpam-5872	76	10	ξ	ξ	NOUN
ejpam-5872	76	11	)	)	PUNCT
ejpam-5872	76	12	.	.	PUNCT
ejpam-5872	77	1	following	follow	VERB
ejpam-5872	77	2	rosenfeld	rosenfeld	PROPN
ejpam-5872	77	3	,	,	PUNCT
ejpam-5872	77	4	a	a	DET
ejpam-5872	77	5	fuzzy	fuzzy	ADJ
ejpam-5872	77	6	graph	graph	NOUN
ejpam-5872	77	7	on	on	ADP
ejpam-5872	77	8	ℑ	ℑ	PROPN
ejpam-5872	77	9	is	be	AUX
ejpam-5872	77	10	a	a	DET
ejpam-5872	77	11	pair	pair	NOUN
ejpam-5872	77	12	of	of	ADP
ejpam-5872	77	13	functions	function	NOUN
ejpam-5872	77	14	σ	σ	NOUN
ejpam-5872	77	15	=	=	SYM
ejpam-5872	77	16	(	(	PUNCT
ejpam-5872	77	17	σ	σ	PROPN
ejpam-5872	77	18	,	,	PUNCT
ejpam-5872	77	19	µ	µ	NOUN
ejpam-5872	77	20	)	)	PUNCT
ejpam-5872	77	21	,	,	PUNCT
ejpam-5872	77	22	σ	σ	PROPN
ejpam-5872	77	23	:	:	PUNCT
ejpam-5872	77	24	ℑ	ℑ	PROPN
ejpam-5872	77	25	→	→	SYM
ejpam-5872	77	26	[	[	X
ejpam-5872	77	27	0	0	NUM
ejpam-5872	77	28	,	,	PUNCT
ejpam-5872	77	29	1	1	NUM
ejpam-5872	77	30	]	]	PUNCT
ejpam-5872	77	31	,	,	PUNCT
ejpam-5872	77	32	µ	µ	X
ejpam-5872	77	33	:	:	PUNCT
ejpam-5872	77	34	ℑ	ℑ	PROPN
ejpam-5872	77	35	×	×	NOUN
ejpam-5872	77	36	ℑ	ℑ	NOUN
ejpam-5872	77	37	→	→	SYM
ejpam-5872	77	38	[	[	X
ejpam-5872	77	39	0	0	NUM
ejpam-5872	77	40	,	,	PUNCT
ejpam-5872	77	41	1	1	NUM
ejpam-5872	77	42	]	]	PUNCT
ejpam-5872	77	43	,	,	PUNCT
ejpam-5872	77	44	such	such	ADJ
ejpam-5872	77	45	that	that	SCONJ
ejpam-5872	77	46	,	,	PUNCT
ejpam-5872	77	47	for	for	ADP
ejpam-5872	77	48	all	all	PRON
ejpam-5872	77	49	,	,	PUNCT
ejpam-5872	77	50	1ג	1ג	NUM
ejpam-5872	77	51	2ג	2ג	NUM
ejpam-5872	77	52	∈	∈	PROPN
ejpam-5872	77	53	ℑ	ℑ	PROPN
ejpam-5872	77	54	,	,	PUNCT
ejpam-5872	77	55	µ(1ג	µ(1ג	PRON
ejpam-5872	77	56	,	,	PUNCT
ejpam-5872	77	57	(	(	PUNCT
ejpam-5872	77	58	2ג	2ג	NOUN
ejpam-5872	77	59	≤	≤	NOUN
ejpam-5872	77	60	σ(1ג	σ(1ג	NOUN
ejpam-5872	77	61	)	)	PUNCT
ejpam-5872	77	62	∧	∧	NOUN
ejpam-5872	77	63	σ(2ג	σ(2ג	NUM
ejpam-5872	77	64	)	)	PUNCT
ejpam-5872	77	65	.	.	PUNCT
ejpam-5872	78	1	(	(	PUNCT
ejpam-5872	78	2	when	when	SCONJ
ejpam-5872	78	3	the	the	DET
ejpam-5872	78	4	graph	graph	NOUN
ejpam-5872	78	5	is	be	AUX
ejpam-5872	78	6	undirected	undirected	ADJ
ejpam-5872	78	7	,	,	PUNCT
ejpam-5872	78	8	assume	assume	VERB
ejpam-5872	78	9	µ(1ג	µ(1ג	NOUN
ejpam-5872	78	10	,	,	PUNCT
ejpam-5872	78	11	(	(	PUNCT
ejpam-5872	78	12	2ג	2ג	NOUN
ejpam-5872	78	13	=	=	SYM
ejpam-5872	78	14	µ(2ג	µ(2ג	NOUN
ejpam-5872	78	15	,	,	PUNCT
ejpam-5872	78	16	(	(	PUNCT
ejpam-5872	78	17	1ג	1ג	NUM
ejpam-5872	78	18	and	and	CCONJ
ejpam-5872	78	19	µ(ג	µ(ג	NOUN
ejpam-5872	78	20	,	,	PUNCT
ejpam-5872	78	21	(	(	PUNCT
ejpam-5872	78	22	ג	ג	PROPN
ejpam-5872	78	23	=	=	SYM
ejpam-5872	78	24	0	0	NUM
ejpam-5872	78	25	.	.	PUNCT
ejpam-5872	78	26	)	)	PUNCT
ejpam-5872	79	1	a	a	DET
ejpam-5872	79	2	fuzzy	fuzzy	ADJ
ejpam-5872	79	3	subgraph	subgraph	NOUN
ejpam-5872	79	4	γ	γ	X
ejpam-5872	79	5	=	=	SYM
ejpam-5872	79	6	(	(	PUNCT
ejpam-5872	79	7	τ	τ	PROPN
ejpam-5872	79	8	,	,	PUNCT
ejpam-5872	79	9	ξ	ξ	NOUN
ejpam-5872	79	10	)	)	PUNCT
ejpam-5872	79	11	of	of	ADP
ejpam-5872	79	12	σ	σ	PROPN
ejpam-5872	79	13	=	=	SYM
ejpam-5872	79	14	(	(	PUNCT
ejpam-5872	79	15	σ	σ	PROPN
ejpam-5872	79	16	,	,	PUNCT
ejpam-5872	79	17	µ	µ	NOUN
ejpam-5872	79	18	)	)	PUNCT
ejpam-5872	79	19	satisfies	satisfie	NOUN
ejpam-5872	79	20	τ(ג	τ(ג	NOUN
ejpam-5872	79	21	)	)	PUNCT
ejpam-5872	79	22	≤	≤	NOUN
ejpam-5872	79	23	σ(ג	σ(ג	NOUN
ejpam-5872	79	24	)	)	PUNCT
ejpam-5872	79	25	for	for	ADP
ejpam-5872	79	26	all	all	DET
ejpam-5872	79	27	ג	ג	ADP
ejpam-5872	79	28	∈	∈	PROPN
ejpam-5872	79	29	ℑ	ℑ	PROPN
ejpam-5872	79	30	,	,	PUNCT
ejpam-5872	79	31	ξ(1ג	ξ(1ג	NUM
ejpam-5872	79	32	,	,	PUNCT
ejpam-5872	79	33	(	(	PUNCT
ejpam-5872	79	34	2ג	2ג	NOUN
ejpam-5872	79	35	≤	≤	NOUN
ejpam-5872	79	36	µ(1ג	µ(1ג	NOUN
ejpam-5872	79	37	,	,	PUNCT
ejpam-5872	79	38	(	(	PUNCT
ejpam-5872	79	39	2ג	2ג	NOUN
ejpam-5872	79	40	for	for	ADP
ejpam-5872	79	41	all	all	PRON
ejpam-5872	79	42	,	,	PUNCT
ejpam-5872	79	43	1ג	1ג	NUM
ejpam-5872	79	44	)	)	PUNCT
ejpam-5872	79	45	(	(	PUNCT
ejpam-5872	79	46	2ג	2ג	NOUN
ejpam-5872	79	47	∈	∈	NOUN
ejpam-5872	79	48	ℑ	ℑ	PROPN
ejpam-5872	79	49	×	×	PROPN
ejpam-5872	79	50	ℑ	ℑ	PROPN
ejpam-5872	79	51	,	,	PUNCT
ejpam-5872	79	52	together	together	ADV
ejpam-5872	79	53	with	with	ADP
ejpam-5872	79	54	ξ(1ג	ξ(1ג	NUM
ejpam-5872	79	55	,	,	PUNCT
ejpam-5872	79	56	(	(	PUNCT
ejpam-5872	79	57	2ג	2ג	NOUN
ejpam-5872	79	58	≤	≤	NOUN
ejpam-5872	79	59	τ(1ג	τ(1ג	NOUN
ejpam-5872	79	60	)	)	PUNCT
ejpam-5872	79	61	∧	∧	PROPN
ejpam-5872	79	62	τ(2ג	τ(2ג	NUM
ejpam-5872	79	63	)	)	PUNCT
ejpam-5872	79	64	.	.	PUNCT
ejpam-5872	80	1	it	it	PRON
ejpam-5872	80	2	is	be	AUX
ejpam-5872	80	3	spanning	span	VERB
ejpam-5872	80	4	if	if	SCONJ
ejpam-5872	80	5	τ	τ	PROPN
ejpam-5872	80	6	=	=	SYM
ejpam-5872	80	7	σ	σ	PROPN
ejpam-5872	80	8	(	(	PUNCT
ejpam-5872	80	9	i.e.	i.e.	X
ejpam-5872	80	10	,	,	PUNCT
ejpam-5872	80	11	both	both	DET
ejpam-5872	80	12	fuzzy	fuzzy	ADJ
ejpam-5872	80	13	graphs	graph	NOUN
ejpam-5872	80	14	have	have	VERB
ejpam-5872	80	15	the	the	DET
ejpam-5872	80	16	same	same	ADJ
ejpam-5872	80	17	vertex	vertex	NOUN
ejpam-5872	80	18	memberships	membership	NOUN
ejpam-5872	80	19	)	)	PUNCT
ejpam-5872	80	20	.	.	PUNCT
ejpam-5872	81	1	a	a	DET
ejpam-5872	81	2	simple	simple	ADJ
ejpam-5872	81	3	path	path	NOUN
ejpam-5872	81	4	of	of	ADP
ejpam-5872	81	5	length	length	NOUN
ejpam-5872	81	6	n	n	PROPN
ejpam-5872	81	7	is	be	AUX
ejpam-5872	81	8	a	a	DET
ejpam-5872	81	9	sequence	sequence	NOUN
ejpam-5872	81	10	of	of	ADP
ejpam-5872	81	11	distinct	distinct	ADJ
ejpam-5872	81	12	nodes	node	NOUN
ejpam-5872	81	13	,	,	PUNCT
ejpam-5872	81	14	0ג	0ג	NOUN
ejpam-5872	81	15	,	,	PUNCT
ejpam-5872	81	16	1ג	1ג	NUM
ejpam-5872	81	17	.	.	PUNCT
ejpam-5872	81	18	.	.	PUNCT
ejpam-5872	82	1	.	.	PUNCT
ejpam-5872	83	1	,	,	PUNCT
ejpam-5872	83	2	nג	nג	NOUN
ejpam-5872	83	3	with	with	ADP
ejpam-5872	83	4	µ(גi	µ(גi	NOUN
ejpam-5872	83	5	,	,	PUNCT
ejpam-5872	83	6	(	(	PUNCT
ejpam-5872	83	7	i+1ג	i+1ג	X
ejpam-5872	83	8	>	>	X
ejpam-5872	83	9	0	0	NUM
ejpam-5872	83	10	for	for	ADP
ejpam-5872	83	11	all	all	DET
ejpam-5872	83	12	i.	i.	NOUN
ejpam-5872	83	13	the	the	DET
ejpam-5872	83	14	strength	strength	NOUN
ejpam-5872	83	15	of	of	ADP
ejpam-5872	83	16	a	a	DET
ejpam-5872	83	17	path	path	NOUN
ejpam-5872	83	18	is	be	AUX
ejpam-5872	83	19	min	min	PROPN
ejpam-5872	83	20	0≤i	0≤i	PROPN
ejpam-5872	83	21	<	<	NOUN
ejpam-5872	83	22	n	n	PRON
ejpam-5872	83	23	µ(גi	µ(גi	NUM
ejpam-5872	83	24	,	,	PUNCT
ejpam-5872	83	25	.(i+1ג	.(i+1ג	PROPN
ejpam-5872	83	26	the	the	DET
ejpam-5872	83	27	connectedness	connectedness	NOUN
ejpam-5872	83	28	between	between	ADP
ejpam-5872	83	29	,	,	PUNCT
ejpam-5872	83	30	1ג	1ג	NUM
ejpam-5872	83	31	2ג	2ג	NOUN
ejpam-5872	83	32	∈	∈	PROPN
ejpam-5872	83	33	ℑ	ℑ	PROPN
ejpam-5872	83	34	is	be	AUX
ejpam-5872	83	35	connς(1ג	connς(1ג	NOUN
ejpam-5872	83	36	,	,	PUNCT
ejpam-5872	83	37	=(	=(	NOUN
ejpam-5872	83	38	2ג	2ג	NUM
ejpam-5872	83	39	max	max	PROPN
ejpam-5872	84	1	p	p	X
ejpam-5872	84	2	:	:	PUNCT
ejpam-5872	84	3	2ג	2ג	NUM
ejpam-5872	84	4	⇝	⇝	NOUN
ejpam-5872	84	5	1ג	1ג	NUM
ejpam-5872	84	6	min	min	NOUN
ejpam-5872	84	7	e∈p	e∈p	NOUN
ejpam-5872	84	8	µ(e	µ(e	PROPN
ejpam-5872	84	9	)	)	PUNCT
ejpam-5872	84	10	,	,	PUNCT
ejpam-5872	84	11	the	the	DET
ejpam-5872	84	12	max	max	PROPN
ejpam-5872	84	13	–	–	PUNCT
ejpam-5872	84	14	min	min	NOUN
ejpam-5872	84	15	strength	strength	NOUN
ejpam-5872	84	16	over	over	ADP
ejpam-5872	84	17	all	all	DET
ejpam-5872	84	18	paths	path	NOUN
ejpam-5872	84	19	p	p	NOUN
ejpam-5872	84	20	from	from	ADP
ejpam-5872	84	21	1ג	1ג	NUM
ejpam-5872	84	22	to	to	ADP
ejpam-5872	84	23	.2ג	.2ג	PROPN
ejpam-5872	84	24	σ	σ	PROPN
ejpam-5872	84	25	is	be	AUX
ejpam-5872	84	26	connected	connect	VERB
ejpam-5872	84	27	if	if	SCONJ
ejpam-5872	84	28	every	every	DET
ejpam-5872	84	29	pair	pair	NOUN
ejpam-5872	84	30	of	of	ADP
ejpam-5872	84	31	nodes	node	NOUN
ejpam-5872	84	32	has	have	VERB
ejpam-5872	84	33	connς(1ג	connς(1ג	NOUN
ejpam-5872	84	34	,	,	PUNCT
ejpam-5872	84	35	(	(	PUNCT
ejpam-5872	84	36	2ג	2ג	NOUN
ejpam-5872	84	37	>	>	X
ejpam-5872	84	38	0	0	NUM
ejpam-5872	84	39	.	.	PUNCT
ejpam-5872	85	1	σ	σ	NOUN
ejpam-5872	85	2	is	be	AUX
ejpam-5872	85	3	strong	strong	ADJ
ejpam-5872	85	4	if	if	SCONJ
ejpam-5872	85	5	,	,	PUNCT
ejpam-5872	85	6	for	for	ADP
ejpam-5872	85	7	every	every	DET
ejpam-5872	85	8	edge	edge	NOUN
ejpam-5872	85	9	(	(	PUNCT
ejpam-5872	85	10	i.e.	i.e.	X
ejpam-5872	85	11	,	,	PUNCT
ejpam-5872	85	12	for	for	ADP
ejpam-5872	85	13	every	every	DET
ejpam-5872	85	14	pair	pair	NOUN
ejpam-5872	85	15	with	with	ADP
ejpam-5872	85	16	positive	positive	ADJ
ejpam-5872	85	17	membership	membership	NOUN
ejpam-5872	85	18	)	)	PUNCT
ejpam-5872	85	19	,	,	PUNCT
ejpam-5872	85	20	µ(1ג	µ(1ג	NOUN
ejpam-5872	85	21	,	,	PUNCT
ejpam-5872	85	22	(	(	PUNCT
ejpam-5872	85	23	2ג	2ג	NOUN
ejpam-5872	85	24	=	=	X
ejpam-5872	85	25	σ(1ג)∧	σ(1ג)∧	ADP
ejpam-5872	85	26	σ(2ג	σ(2ג	NUM
ejpam-5872	85	27	)	)	PUNCT
ejpam-5872	85	28	.	.	PUNCT
ejpam-5872	86	1	it	it	PRON
ejpam-5872	86	2	is	be	AUX
ejpam-5872	86	3	complete	complete	ADJ
ejpam-5872	86	4	if	if	SCONJ
ejpam-5872	86	5	the	the	DET
ejpam-5872	86	6	above	above	ADJ
ejpam-5872	86	7	holds	hold	VERB
ejpam-5872	86	8	for	for	ADP
ejpam-5872	86	9	all	all	DET
ejpam-5872	86	10	unordered	unordered	ADJ
ejpam-5872	86	11	pairs	pair	NOUN
ejpam-5872	86	12	,	,	PUNCT
ejpam-5872	86	13	1ג	1ג	NUM
ejpam-5872	86	14	}	}	PUNCT
ejpam-5872	86	15	{	{	PUNCT
ejpam-5872	86	16	2ג	2ג	NOUN
ejpam-5872	86	17	with	with	ADP
ejpam-5872	86	18	1ג	1ג	NUM
ejpam-5872	86	19	̸=	̸=	PROPN
ejpam-5872	86	20	.2ג	.2ג	PUNCT
ejpam-5872	86	21	the	the	DET
ejpam-5872	86	22	order	order	NOUN
ejpam-5872	86	23	and	and	CCONJ
ejpam-5872	86	24	size	size	NOUN
ejpam-5872	86	25	of	of	ADP
ejpam-5872	86	26	σ	σ	PROPN
ejpam-5872	86	27	are	be	AUX
ejpam-5872	86	28	|σ|v	|σ|v	PROPN
ejpam-5872	86	29	=	=	PUNCT
ejpam-5872	86	30	∑	∑	PROPN
ejpam-5872	86	31	ℑ∋ג	ℑ∋ג	DET
ejpam-5872	86	32	σ(ג	σ(ג	PROPN
ejpam-5872	86	33	)	)	PUNCT
ejpam-5872	86	34	,	,	PUNCT
ejpam-5872	86	35	|σ|e	|σ|e	NOUN
ejpam-5872	86	36	=	=	SYM
ejpam-5872	86	37	∑	∑	PUNCT
ejpam-5872	86	38	ℑ⊇{2ג,1ג	ℑ⊇{2ג,1ג	PROPN
ejpam-5872	86	39	}	}	PUNCT
ejpam-5872	86	40	µ(1ג	µ(1ג	NUM
ejpam-5872	86	41	,	,	PUNCT
ejpam-5872	86	42	(	(	PUNCT
ejpam-5872	86	43	2ג	2ג	NOUN
ejpam-5872	86	44	.	.	PUNCT
ejpam-5872	87	1	the	the	DET
ejpam-5872	87	2	complement	complement	NOUN
ejpam-5872	87	3	σ	σ	X
ejpam-5872	87	4	=	=	SYM
ejpam-5872	87	5	(	(	PUNCT
ejpam-5872	87	6	σ	σ	PROPN
ejpam-5872	87	7	,	,	PUNCT
ejpam-5872	87	8	µ	µ	NOUN
ejpam-5872	87	9	)	)	PUNCT
ejpam-5872	87	10	is	be	AUX
ejpam-5872	87	11	given	give	VERB
ejpam-5872	87	12	by	by	ADP
ejpam-5872	87	13	σ	σ	PROPN
ejpam-5872	87	14	=	=	SYM
ejpam-5872	87	15	σ	σ	PROPN
ejpam-5872	87	16	,	,	PUNCT
ejpam-5872	87	17	µ(1ג	µ(1ג	NUM
ejpam-5872	87	18	,	,	PUNCT
ejpam-5872	87	19	(	(	PUNCT
ejpam-5872	87	20	2ג	2ג	NOUN
ejpam-5872	87	21	=	=	SYM
ejpam-5872	87	22	σ(1ג	σ(1ג	NOUN
ejpam-5872	87	23	)	)	PUNCT
ejpam-5872	87	24	∧	∧	NOUN
ejpam-5872	87	25	σ(2ג	σ(2ג	NUM
ejpam-5872	87	26	)	)	PUNCT
ejpam-5872	87	27	−	−	ADP
ejpam-5872	87	28	µ(1ג	µ(1ג	NOUN
ejpam-5872	87	29	,	,	PUNCT
ejpam-5872	87	30	(	(	PUNCT
ejpam-5872	87	31	2ג	2ג	NOUN
ejpam-5872	87	32	for	for	ADP
ejpam-5872	87	33	all	all	DET
ejpam-5872	87	34	distinct	distinct	ADJ
ejpam-5872	87	35	,	,	PUNCT
ejpam-5872	87	36	1ג	1ג	NUM
ejpam-5872	87	37	2ג	2ג	NOUN
ejpam-5872	87	38	∈	∈	ADJ
ejpam-5872	87	39	ℑ.	ℑ.	PROPN
ejpam-5872	87	40	a	a	DET
ejpam-5872	87	41	signed	sign	VERB
ejpam-5872	87	42	-	-	PUNCT
ejpam-5872	87	43	fg	fg	NOUN
ejpam-5872	87	44	is	be	AUX
ejpam-5872	87	45	a	a	DET
ejpam-5872	87	46	fuzzy	fuzzy	ADJ
ejpam-5872	87	47	graph	graph	NOUN
ejpam-5872	87	48	whose	whose	DET
ejpam-5872	87	49	memberships	membership	NOUN
ejpam-5872	87	50	can	can	AUX
ejpam-5872	87	51	be	be	AUX
ejpam-5872	87	52	positive	positive	ADJ
ejpam-5872	87	53	or	or	CCONJ
ejpam-5872	87	54	negative	negative	ADJ
ejpam-5872	87	55	.	.	PUNCT
ejpam-5872	88	1	formally	formally	ADV
ejpam-5872	88	2	,	,	PUNCT
ejpam-5872	88	3	let	let	VERB
ejpam-5872	88	4	σ±	σ±	NOUN
ejpam-5872	88	5	=	=	SYM
ejpam-5872	88	6	(	(	PUNCT
ejpam-5872	88	7	ℑ	ℑ	PROPN
ejpam-5872	88	8	,	,	PUNCT
ejpam-5872	88	9	σ	σ	PROPN
ejpam-5872	88	10	,	,	PUNCT
ejpam-5872	88	11	µ	µ	NOUN
ejpam-5872	88	12	)	)	PUNCT
ejpam-5872	88	13	,	,	PUNCT
ejpam-5872	88	14	σ	σ	PROPN
ejpam-5872	88	15	:	:	PUNCT
ejpam-5872	88	16	ℑ	ℑ	PROPN
ejpam-5872	88	17	→	→	SYM
ejpam-5872	89	1	[	[	X
ejpam-5872	89	2	−1	−1	NOUN
ejpam-5872	89	3	,	,	PUNCT
ejpam-5872	89	4	1	1	NUM
ejpam-5872	89	5	]	]	PUNCT
ejpam-5872	89	6	,	,	PUNCT
ejpam-5872	89	7	µ	µ	X
ejpam-5872	89	8	:	:	PUNCT
ejpam-5872	89	9	ℑ×	ℑ×	PROPN
ejpam-5872	89	10	ℑ	ℑ	PROPN
ejpam-5872	89	11	→	→	SYM
ejpam-5872	89	12	[	[	X
ejpam-5872	89	13	−1	−1	NOUN
ejpam-5872	89	14	,	,	PUNCT
ejpam-5872	89	15	1	1	NUM
ejpam-5872	89	16	]	]	PUNCT
ejpam-5872	89	17	,	,	PUNCT
ejpam-5872	89	18	c.	c.	PROPN
ejpam-5872	89	19	sankar	sankar	PROPN
ejpam-5872	89	20	et	et	PROPN
ejpam-5872	89	21	al	al	PROPN
ejpam-5872	89	22	.	.	PUNCT
ejpam-5872	89	23	/	/	SYM
ejpam-5872	89	24	eur	eur	PROPN
ejpam-5872	89	25	.	.	PUNCT
ejpam-5872	90	1	j.	j.	PROPN
ejpam-5872	90	2	pure	pure	PROPN
ejpam-5872	90	3	appl	appl	PROPN
ejpam-5872	90	4	.	.	PROPN
ejpam-5872	90	5	math	math	PROPN
ejpam-5872	90	6	,	,	PUNCT
ejpam-5872	90	7	18	18	NUM
ejpam-5872	90	8	(	(	PUNCT
ejpam-5872	90	9	4	4	NUM
ejpam-5872	90	10	)	)	PUNCT
ejpam-5872	90	11	(	(	PUNCT
ejpam-5872	90	12	2025	2025	NUM
ejpam-5872	90	13	)	)	PUNCT
ejpam-5872	90	14	,	,	PUNCT
ejpam-5872	90	15	5872	5872	NUM
ejpam-5872	90	16	5	5	NUM
ejpam-5872	90	17	of	of	ADP
ejpam-5872	90	18	17	17	NUM
ejpam-5872	90	19	(	(	PUNCT
ejpam-5872	90	20	0.7)3ג(0.3−)2ג	0.7)3ג(0.3−)2ג	NUM
ejpam-5872	90	21	(	(	PUNCT
ejpam-5872	90	22	0.4)1ג	0.4)1ג	NOUN
ejpam-5872	90	23	−0.3	−0.3	PROPN
ejpam-5872	91	1	−	−	ADP
ejpam-5872	91	2	0.50	0.50	NUM
ejpam-5872	91	3	.	.	PUNCT
ejpam-5872	92	1	4	4	NUM
ejpam-5872	92	2	figure	figure	NOUN
ejpam-5872	92	3	1	1	NUM
ejpam-5872	92	4	:	:	PUNCT
ejpam-5872	92	5	a	a	DET
ejpam-5872	92	6	signed	sign	VERB
ejpam-5872	92	7	-	-	PUNCT
ejpam-5872	92	8	fg	fg	PRON
ejpam-5872	92	9	example	example	NOUN
ejpam-5872	92	10	.	.	PUNCT
ejpam-5872	93	1	with	with	ADP
ejpam-5872	93	2	symmetry	symmetry	NOUN
ejpam-5872	93	3	and	and	CCONJ
ejpam-5872	93	4	zero	zero	NUM
ejpam-5872	93	5	diagonals	diagonal	NOUN
ejpam-5872	93	6	as	as	ADP
ejpam-5872	93	7	appropriate	appropriate	ADJ
ejpam-5872	93	8	,	,	PUNCT
ejpam-5872	93	9	and	and	CCONJ
ejpam-5872	93	10	satisfying	satisfy	VERB
ejpam-5872	93	11	the	the	DET
ejpam-5872	93	12	constraint	constraint	NOUN
ejpam-5872	93	13	µ(1ג	µ(1ג	NOUN
ejpam-5872	93	14	,	,	PUNCT
ejpam-5872	93	15	(	(	PUNCT
ejpam-5872	93	16	2ג	2ג	NOUN
ejpam-5872	93	17	≤	≤	NOUN
ejpam-5872	93	18	σ(1ג	σ(1ג	NOUN
ejpam-5872	93	19	)	)	PUNCT
ejpam-5872	93	20	∧	∧	NOUN
ejpam-5872	93	21	σ(2ג	σ(2ג	NUM
ejpam-5872	93	22	)	)	PUNCT
ejpam-5872	93	23	,	,	PUNCT
ejpam-5872	93	24	for	for	ADP
ejpam-5872	93	25	all	all	PRON
ejpam-5872	93	26	,	,	PUNCT
ejpam-5872	93	27	1ג	1ג	NUM
ejpam-5872	93	28	)	)	PUNCT
ejpam-5872	93	29	(	(	PUNCT
ejpam-5872	93	30	2ג	2ג	NOUN
ejpam-5872	93	31	∈	∈	NOUN
ejpam-5872	93	32	ℑ	ℑ	NOUN
ejpam-5872	93	33	×	×	VERB
ejpam-5872	93	34	ℑ.	ℑ.	NOUN
ejpam-5872	93	35	here	here	ADV
ejpam-5872	93	36	the	the	DET
ejpam-5872	93	37	sign	sign	NOUN
ejpam-5872	93	38	encodes	encode	VERB
ejpam-5872	93	39	the	the	DET
ejpam-5872	93	40	type	type	NOUN
ejpam-5872	93	41	of	of	ADP
ejpam-5872	93	42	relation	relation	NOUN
ejpam-5872	93	43	(	(	PUNCT
ejpam-5872	93	44	positive	positive	ADJ
ejpam-5872	93	45	or	or	CCONJ
ejpam-5872	93	46	negative	negative	ADJ
ejpam-5872	93	47	)	)	PUNCT
ejpam-5872	93	48	,	,	PUNCT
ejpam-5872	93	49	while	while	SCONJ
ejpam-5872	93	50	the	the	DET
ejpam-5872	93	51	magnitude	magnitude	NOUN
ejpam-5872	93	52	encodes	encode	VERB
ejpam-5872	93	53	its	its	PRON
ejpam-5872	93	54	strength	strength	NOUN
ejpam-5872	93	55	.	.	PUNCT
ejpam-5872	94	1	definition	definition	NOUN
ejpam-5872	94	2	1	1	NUM
ejpam-5872	94	3	.	.	PUNCT
ejpam-5872	95	1	an	an	DET
ejpam-5872	95	2	arc	arc	NOUN
ejpam-5872	95	3	,	,	PUNCT
ejpam-5872	95	4	1ג	1ג	NUM
ejpam-5872	95	5	)	)	PUNCT
ejpam-5872	95	6	(	(	PUNCT
ejpam-5872	95	7	2ג	2ג	NOUN
ejpam-5872	95	8	in	in	ADP
ejpam-5872	95	9	a	a	DET
ejpam-5872	95	10	signed	sign	VERB
ejpam-5872	95	11	-	-	PUNCT
ejpam-5872	95	12	fg	fg	PROPN
ejpam-5872	95	13	∑	∑	PROPN
ejpam-5872	95	14	±	±	NUM
ejpam-5872	95	15	=	=	SYM
ejpam-5872	95	16	(	(	PUNCT
ejpam-5872	95	17	ℑ	ℑ	PROPN
ejpam-5872	95	18	,	,	PUNCT
ejpam-5872	95	19	σ	σ	PROPN
ejpam-5872	95	20	,	,	PUNCT
ejpam-5872	95	21	µ	µ	NOUN
ejpam-5872	95	22	)	)	PUNCT
ejpam-5872	95	23	is	be	AUX
ejpam-5872	95	24	•	•	ADV
ejpam-5872	95	25	α	α	ADV
ejpam-5872	95	26	-	-	PUNCT
ejpam-5872	95	27	strong	strong	ADJ
ejpam-5872	95	28	if	if	SCONJ
ejpam-5872	95	29	µ(1ג	µ(1ג	NOUN
ejpam-5872	95	30	,	,	PUNCT
ejpam-5872	95	31	(	(	PUNCT
ejpam-5872	95	32	2ג	2ג	NOUN
ejpam-5872	95	33	>	>	X
ejpam-5872	95	34	conn∑	conn∑	PROPN
ejpam-5872	95	35	±	±	PROPN
ejpam-5872	95	36	,	,	PUNCT
ejpam-5872	95	37	1ג)(2ג,1ג)−	1ג)(2ג,1ג)−	NUM
ejpam-5872	95	38	.(2ג	.(2ג	SYM
ejpam-5872	95	39	•	•	NUM
ejpam-5872	95	40	β	β	X
ejpam-5872	95	41	-	-	ADJ
ejpam-5872	95	42	strong	strong	ADJ
ejpam-5872	95	43	if	if	SCONJ
ejpam-5872	95	44	µ(1ג	µ(1ג	NOUN
ejpam-5872	95	45	,	,	PUNCT
ejpam-5872	95	46	(	(	PUNCT
ejpam-5872	95	47	2ג	2ג	NOUN
ejpam-5872	95	48	=	=	SYM
ejpam-5872	95	49	conn∑	conn∑	PROPN
ejpam-5872	95	50	±	±	NUM
ejpam-5872	95	51	,	,	PUNCT
ejpam-5872	95	52	1ג)(2ג,1ג)−	1ג)(2ג,1ג)−	NUM
ejpam-5872	95	53	.(2ג	.(2ג	PUNCT
ejpam-5872	96	1	•	•	NUM
ejpam-5872	96	2	δ	δ	NOUN
ejpam-5872	96	3	-	-	PUNCT
ejpam-5872	96	4	arc	arc	NOUN
ejpam-5872	96	5	if	if	SCONJ
ejpam-5872	96	6	µ(1ג	µ(1ג	NOUN
ejpam-5872	96	7	,	,	PUNCT
ejpam-5872	96	8	(	(	PUNCT
ejpam-5872	96	9	2ג	2ג	NOUN
ejpam-5872	96	10	<	<	X
ejpam-5872	96	11	conn∑	conn∑	X
ejpam-5872	96	12	±	±	PROPN
ejpam-5872	96	13	,	,	PUNCT
ejpam-5872	96	14	1ג)(2ג,1ג)−	1ג)(2ג,1ג)−	NUM
ejpam-5872	96	15	.(2ג	.(2ג	PUNCT
ejpam-5872	96	16	definition	definition	NOUN
ejpam-5872	96	17	2	2	NUM
ejpam-5872	96	18	.	.	PUNCT
ejpam-5872	97	1	an	an	DET
ejpam-5872	97	2	arc	arc	NOUN
ejpam-5872	97	3	in	in	ADP
ejpam-5872	97	4	signed	sign	VERB
ejpam-5872	97	5	-	-	PUNCT
ejpam-5872	97	6	fg	fg	PROPN
ejpam-5872	97	7	is	be	AUX
ejpam-5872	97	8	a	a	DET
ejpam-5872	97	9	strong	strong	ADJ
ejpam-5872	97	10	arc	arc	NOUN
ejpam-5872	97	11	if	if	SCONJ
ejpam-5872	97	12	it	it	PRON
ejpam-5872	97	13	is	be	AUX
ejpam-5872	97	14	either	either	CCONJ
ejpam-5872	97	15	an	an	DET
ejpam-5872	97	16	α−strong	α−strong	NOUN
ejpam-5872	97	17	or	or	CCONJ
ejpam-5872	97	18	a	a	DET
ejpam-5872	97	19	β−strong	β−strong	NOUN
ejpam-5872	97	20	arc	arc	NOUN
ejpam-5872	97	21	.	.	PUNCT
ejpam-5872	98	1	definition	definition	NOUN
ejpam-5872	98	2	3	3	NUM
ejpam-5872	98	3	.	.	PUNCT
ejpam-5872	99	1	in	in	ADP
ejpam-5872	99	2	a	a	DET
ejpam-5872	99	3	signed	sign	VERB
ejpam-5872	99	4	-	-	PUNCT
ejpam-5872	99	5	fg	fg	ADP
ejpam-5872	99	6	,	,	PUNCT
ejpam-5872	99	7	if	if	SCONJ
ejpam-5872	99	8	µ(1ג	µ(1ג	NOUN
ejpam-5872	99	9	,	,	PUNCT
ejpam-5872	99	10	(	(	PUNCT
ejpam-5872	99	11	2ג	2ג	NOUN
ejpam-5872	99	12	=	=	SYM
ejpam-5872	99	13	σ(1ג	σ(1ג	NOUN
ejpam-5872	99	14	)	)	PUNCT
ejpam-5872	99	15	∧	∧	NOUN
ejpam-5872	99	16	σ(2ג	σ(2ג	NUM
ejpam-5872	99	17	)	)	PUNCT
ejpam-5872	99	18	for	for	ADP
ejpam-5872	99	19	,	,	PUNCT
ejpam-5872	99	20	1ג	1ג	NUM
ejpam-5872	99	21	)	)	PUNCT
ejpam-5872	99	22	(	(	PUNCT
ejpam-5872	99	23	2ג	2ג	NUM
ejpam-5872	99	24	∈	∈	PROPN
ejpam-5872	99	25	ξ	ξ	PROPN
ejpam-5872	99	26	,	,	PUNCT
ejpam-5872	99	27	then	then	ADV
ejpam-5872	99	28	it	it	PRON
ejpam-5872	99	29	is	be	AUX
ejpam-5872	99	30	a	a	DET
ejpam-5872	99	31	effective	effective	ADJ
ejpam-5872	99	32	arc	arc	NOUN
ejpam-5872	99	33	.	.	PUNCT
ejpam-5872	100	1	definition	definition	NOUN
ejpam-5872	100	2	4	4	NUM
ejpam-5872	100	3	.	.	PUNCT
ejpam-5872	101	1	this	this	DET
ejpam-5872	101	2	vertex	vertex	NOUN
ejpam-5872	101	3	1ג	1ג	NUM
ejpam-5872	101	4	has	have	VERB
ejpam-5872	101	5	degree	degree	NOUN
ejpam-5872	101	6	∑	∑	PUNCT
ejpam-5872	101	7	1ג	1ג	NUM
ejpam-5872	101	8	2ג≠	2ג≠	NUM
ejpam-5872	101	9	µ(1ג	µ(1ג	NOUN
ejpam-5872	101	10	,	,	PUNCT
ejpam-5872	101	11	.(2ג	.(2ג	PUNCT
ejpam-5872	101	12	the	the	DET
ejpam-5872	101	13	sum	sum	NOUN
ejpam-5872	101	14	∑	∑	PROPN
ejpam-5872	101	15	±	±	PROPN
ejpam-5872	101	16	has	have	VERB
ejpam-5872	101	17	minimal	minimal	ADJ
ejpam-5872	101	18	degree	degree	NOUN
ejpam-5872	101	19	δ±(ג	δ±(ג	NOUN
ejpam-5872	101	20	)	)	PUNCT
ejpam-5872	101	21	=	=	SYM
ejpam-5872	101	22	∧{d±(ג)/ג	∧{d±(ג)/ג	NUM
ejpam-5872	101	23	∈	∈	PROPN
ejpam-5872	101	24	ℑ	ℑ	PROPN
ejpam-5872	101	25	}	}	PUNCT
ejpam-5872	101	26	and	and	CCONJ
ejpam-5872	101	27	maximum	maximum	ADJ
ejpam-5872	101	28	degree	degree	NOUN
ejpam-5872	101	29	(	(	PUNCT
ejpam-5872	101	30	ג)±∆	ג)±∆	X
ejpam-5872	101	31	=	=	PUNCT
ejpam-5872	101	32	∨{d±(ג)/ג	∨{d±(ג)/ג	PROPN
ejpam-5872	101	33	∈	∈	PROPN
ejpam-5872	101	34	ℑ	ℑ	PROPN
ejpam-5872	101	35	}	}	PUNCT
ejpam-5872	101	36	.	.	PUNCT
ejpam-5872	102	1	example	example	NOUN
ejpam-5872	103	1	1	1	NUM
ejpam-5872	103	2	.	.	X
ejpam-5872	103	3	consider	consider	VERB
ejpam-5872	103	4	the	the	DET
ejpam-5872	103	5	signed	sign	VERB
ejpam-5872	103	6	-	-	PUNCT
ejpam-5872	103	7	fg	fg	PRON
ejpam-5872	103	8	σ±	σ±	NOUN
ejpam-5872	103	9	=	=	SYM
ejpam-5872	103	10	(	(	PUNCT
ejpam-5872	103	11	ℑ	ℑ	PROPN
ejpam-5872	103	12	,	,	PUNCT
ejpam-5872	103	13	σ	σ	PROPN
ejpam-5872	103	14	,	,	PUNCT
ejpam-5872	103	15	µ	µ	NOUN
ejpam-5872	103	16	)	)	PUNCT
ejpam-5872	103	17	,	,	PUNCT
ejpam-5872	103	18	where	where	SCONJ
ejpam-5872	103	19	the	the	DET
ejpam-5872	103	20	vertex	vertex	NOUN
ejpam-5872	103	21	set	set	VERB
ejpam-5872	103	22	ℑ	ℑ	PROPN
ejpam-5872	103	23	=	=	PRON
ejpam-5872	103	24	,	,	PUNCT
ejpam-5872	103	25	1ג	1ג	NUM
ejpam-5872	103	26	}	}	PUNCT
ejpam-5872	103	27	,	,	PUNCT
ejpam-5872	103	28	2ג	2ג	NUM
ejpam-5872	103	29	{	{	PUNCT
ejpam-5872	103	30	3ג	3ג	NOUN
ejpam-5872	103	31	together	together	ADV
ejpam-5872	103	32	with	with	ADP
ejpam-5872	103	33	the	the	DET
ejpam-5872	103	34	edge	edge	NOUN
ejpam-5872	103	35	set	set	VERB
ejpam-5872	103	36	ℑ	ℑ	PROPN
ejpam-5872	103	37	×	×	PROPN
ejpam-5872	103	38	ℑ	ℑ	PROPN
ejpam-5872	103	39	=	=	PUNCT
ejpam-5872	103	40	,	,	PUNCT
ejpam-5872	103	41	1ג	1ג	NUM
ejpam-5872	103	42	)	)	PUNCT
ejpam-5872	103	43	}	}	PUNCT
ejpam-5872	103	44	,	,	PUNCT
ejpam-5872	103	45	(	(	PUNCT
ejpam-5872	103	46	2ג	2ג	NOUN
ejpam-5872	103	47	,	,	PUNCT
ejpam-5872	103	48	2ג	2ג	NUM
ejpam-5872	103	49	)	)	PUNCT
ejpam-5872	103	50	,	,	PUNCT
ejpam-5872	103	51	(	(	PUNCT
ejpam-5872	103	52	3ג	3ג	NUM
ejpam-5872	103	53	,	,	PUNCT
ejpam-5872	103	54	1ג	1ג	NUM
ejpam-5872	103	55	)	)	PUNCT
ejpam-5872	103	56	{	{	PUNCT
ejpam-5872	103	57	(	(	PUNCT
ejpam-5872	103	58	3ג	3ג	NOUN
ejpam-5872	103	59	whose	whose	DET
ejpam-5872	103	60	vertex	vertex	NOUN
ejpam-5872	103	61	values	value	NOUN
ejpam-5872	103	62	are	be	AUX
ejpam-5872	103	63	as	as	SCONJ
ejpam-5872	103	64	follows	follow	VERB
ejpam-5872	103	65	:	:	PUNCT
ejpam-5872	103	66	σ(1ג	σ(1ג	NUM
ejpam-5872	103	67	)	)	PUNCT
ejpam-5872	103	68	=	=	SYM
ejpam-5872	103	69	0.4	0.4	NUM
ejpam-5872	103	70	,	,	PUNCT
ejpam-5872	103	71	σ(2ג	σ(2ג	NUM
ejpam-5872	103	72	)	)	PUNCT
ejpam-5872	103	73	=	=	SYM
ejpam-5872	103	74	−0.3	−0.3	PROPN
ejpam-5872	103	75	,	,	PUNCT
ejpam-5872	103	76	and	and	CCONJ
ejpam-5872	103	77	σ(3ג	σ(3ג	NOUN
ejpam-5872	103	78	)	)	PUNCT
ejpam-5872	103	79	=	=	PUNCT
ejpam-5872	103	80	0.7	0.7	NUM
ejpam-5872	103	81	each	each	DET
ejpam-5872	103	82	.	.	PUNCT
ejpam-5872	104	1	figure	figure	NOUN
ejpam-5872	104	2	1	1	NUM
ejpam-5872	104	3	illustrates	illustrate	VERB
ejpam-5872	104	4	the	the	DET
ejpam-5872	104	5	edge	edge	NOUN
ejpam-5872	104	6	values	value	NOUN
ejpam-5872	104	7	,	,	PUNCT
ejpam-5872	104	8	which	which	PRON
ejpam-5872	104	9	are	be	AUX
ejpam-5872	104	10	µ(1ג	µ(1ג	NOUN
ejpam-5872	104	11	,	,	PUNCT
ejpam-5872	104	12	(	(	PUNCT
ejpam-5872	104	13	2ג	2ג	NOUN
ejpam-5872	104	14	=	=	SYM
ejpam-5872	104	15	−0.5	−0.5	PROPN
ejpam-5872	104	16	,	,	PUNCT
ejpam-5872	104	17	µ(2ג	µ(2ג	VERB
ejpam-5872	104	18	,	,	PUNCT
ejpam-5872	104	19	(	(	PUNCT
ejpam-5872	104	20	3ג	3ג	NUM
ejpam-5872	104	21	=	=	SYM
ejpam-5872	104	22	−0.3	−0.3	PROPN
ejpam-5872	104	23	,	,	PUNCT
ejpam-5872	104	24	and	and	CCONJ
ejpam-5872	104	25	µ(1ג	µ(1ג	NUM
ejpam-5872	104	26	,	,	PUNCT
ejpam-5872	104	27	(	(	PUNCT
ejpam-5872	104	28	3ג	3ג	NUM
ejpam-5872	104	29	=	=	SYM
ejpam-5872	104	30	0.4	0.4	NUM
ejpam-5872	104	31	.	.	PUNCT
ejpam-5872	105	1	these	these	DET
ejpam-5872	105	2	degrees	degree	NOUN
ejpam-5872	105	3	are	be	AUX
ejpam-5872	105	4	d±(1ג	d±(1ג	NOUN
ejpam-5872	105	5	)	)	PUNCT
ejpam-5872	106	1	=	=	SYM
ejpam-5872	107	1	−0.1	−0.1	PROPN
ejpam-5872	107	2	,	,	PUNCT
ejpam-5872	107	3	d±(2ג	d±(2ג	PROPN
ejpam-5872	107	4	)	)	PUNCT
ejpam-5872	107	5	=	=	SYM
ejpam-5872	107	6	−0.8	−0.8	PROPN
ejpam-5872	107	7	,	,	PUNCT
ejpam-5872	107	8	and	and	CCONJ
ejpam-5872	107	9	d±(3ג	d±(3ג	NOUN
ejpam-5872	107	10	)	)	PUNCT
ejpam-5872	107	11	=	=	SYM
ejpam-5872	107	12	0.1	0.1	NUM
ejpam-5872	107	13	for	for	ADP
ejpam-5872	107	14	∑	∑	PUNCT
ejpam-5872	107	15	±.	±.	NOUN
ejpam-5872	107	16	the	the	DET
ejpam-5872	107	17	degree	degree	NOUN
ejpam-5872	107	18	ranges	range	VERB
ejpam-5872	107	19	from	from	ADP
ejpam-5872	107	20	δ±	δ±	PROPN
ejpam-5872	107	21	(	(	PUNCT
ejpam-5872	107	22	∑	∑	NOUN
ejpam-5872	107	23	±	±	NUM
ejpam-5872	107	24	)	)	PUNCT
ejpam-5872	107	25	=	=	SYM
ejpam-5872	108	1	−0.8	−0.8	CCONJ
ejpam-5872	108	2	at	at	ADP
ejpam-5872	108	3	the	the	DET
ejpam-5872	108	4	minimum	minimum	NOUN
ejpam-5872	108	5	to	to	PART
ejpam-5872	108	6	∆±	∆±	X
ejpam-5872	108	7	(	(	PUNCT
ejpam-5872	108	8	∑	∑	PROPN
ejpam-5872	108	9	±	±	NUM
ejpam-5872	108	10	)	)	PUNCT
ejpam-5872	108	11	=	=	SYM
ejpam-5872	108	12	0.1	0.1	NUM
ejpam-5872	108	13	at	at	ADP
ejpam-5872	108	14	the	the	DET
ejpam-5872	108	15	maximum	maximum	NOUN
ejpam-5872	108	16	.	.	PUNCT
ejpam-5872	109	1	definition	definition	NOUN
ejpam-5872	109	2	5	5	NUM
ejpam-5872	109	3	.	.	PUNCT
ejpam-5872	109	4	d±ξ(ג	d±ξ(ג	NOUN
ejpam-5872	109	5	)	)	PUNCT
ejpam-5872	109	6	represents	represent	VERB
ejpam-5872	109	7	the	the	DET
ejpam-5872	109	8	effective	effective	ADJ
ejpam-5872	109	9	degree	degree	NOUN
ejpam-5872	109	10	of	of	ADP
ejpam-5872	109	11	a	a	DET
ejpam-5872	109	12	vertex	vertex	NOUN
ejpam-5872	109	13	,	,	PUNCT
ejpam-5872	109	14	ג	ג	PROPN
ejpam-5872	109	15	which	which	PRON
ejpam-5872	109	16	is	be	AUX
ejpam-5872	109	17	the	the	DET
ejpam-5872	109	18	sum	sum	NOUN
ejpam-5872	109	19	of	of	ADP
ejpam-5872	109	20	the	the	DET
ejpam-5872	109	21	weights	weight	NOUN
ejpam-5872	109	22	of	of	ADP
ejpam-5872	109	23	the	the	DET
ejpam-5872	109	24	effective	effective	ADJ
ejpam-5872	109	25	arcs	arcs	NOUN
ejpam-5872	109	26	incident	incident	NOUN
ejpam-5872	109	27	to	to	PART
ejpam-5872	109	28	.ג	.ג	PUNCT
ejpam-5872	110	1	δ±ξ	δ±ξ	PROPN
ejpam-5872	110	2	(	(	PUNCT
ejpam-5872	110	3	∑	∑	PROPN
ejpam-5872	110	4	±	±	NUM
ejpam-5872	110	5	)	)	PUNCT
ejpam-5872	110	6	=	=	SYM
ejpam-5872	110	7	∧{d±ξ(ג)/ג	∧{d±ξ(ג)/ג	PROPN
ejpam-5872	110	8	∈	∈	PROPN
ejpam-5872	110	9	ℑ	ℑ	PROPN
ejpam-5872	110	10	}	}	PUNCT
ejpam-5872	110	11	gives	give	VERB
ejpam-5872	110	12	the	the	DET
ejpam-5872	110	13	minimum	minimum	ADJ
ejpam-5872	110	14	sum	sum	NOUN
ejpam-5872	110	15	of	of	ADP
ejpam-5872	110	16	the	the	DET
ejpam-5872	110	17	degree	degree	NOUN
ejpam-5872	110	18	∑	∑	PROPN
ejpam-5872	110	19	±	±	NUM
ejpam-5872	110	20	,	,	PUNCT
ejpam-5872	110	21	and	and	CCONJ
ejpam-5872	110	22	∆±ξ	∆±ξ	PROPN
ejpam-5872	110	23	(	(	PUNCT
ejpam-5872	110	24	∑	∑	PROPN
ejpam-5872	110	25	±	±	NUM
ejpam-5872	110	26	)	)	PUNCT
ejpam-5872	110	27	=	=	PUNCT
ejpam-5872	110	28	∨{d±ξ(ג)/ג	∨{d±ξ(ג)/ג	NUM
ejpam-5872	110	29	∈	∈	PROPN
ejpam-5872	110	30	ℑ	ℑ	PROPN
ejpam-5872	110	31	}	}	PUNCT
ejpam-5872	110	32	gives	give	VERB
ejpam-5872	110	33	the	the	DET
ejpam-5872	110	34	maximum	maximum	ADJ
ejpam-5872	110	35	degree	degree	NOUN
ejpam-5872	110	36	.	.	PUNCT
ejpam-5872	111	1	c.	c.	PROPN
ejpam-5872	111	2	sankar	sankar	PROPN
ejpam-5872	111	3	et	et	PROPN
ejpam-5872	111	4	al	al	PROPN
ejpam-5872	111	5	.	.	PUNCT
ejpam-5872	111	6	/	/	SYM
ejpam-5872	111	7	eur	eur	PROPN
ejpam-5872	111	8	.	.	PUNCT
ejpam-5872	112	1	j.	j.	PROPN
ejpam-5872	112	2	pure	pure	PROPN
ejpam-5872	112	3	appl	appl	PROPN
ejpam-5872	112	4	.	.	PROPN
ejpam-5872	112	5	math	math	PROPN
ejpam-5872	112	6	,	,	PUNCT
ejpam-5872	112	7	18	18	NUM
ejpam-5872	112	8	(	(	PUNCT
ejpam-5872	112	9	4	4	NUM
ejpam-5872	112	10	)	)	PUNCT
ejpam-5872	112	11	(	(	PUNCT
ejpam-5872	112	12	2025	2025	NUM
ejpam-5872	112	13	)	)	PUNCT
ejpam-5872	112	14	,	,	PUNCT
ejpam-5872	112	15	5872	5872	NUM
ejpam-5872	112	16	6	6	NUM
ejpam-5872	112	17	of	of	ADP
ejpam-5872	112	18	17	17	NUM
ejpam-5872	112	19	example	example	NOUN
ejpam-5872	112	20	2	2	NUM
ejpam-5872	112	21	.	.	PUNCT
ejpam-5872	113	1	the	the	DET
ejpam-5872	113	2	effective	effective	ADJ
ejpam-5872	113	3	arcs	arc	NOUN
ejpam-5872	113	4	in	in	ADP
ejpam-5872	113	5	figure	figure	NOUN
ejpam-5872	113	6	1	1	NUM
ejpam-5872	113	7	are	be	AUX
ejpam-5872	113	8	,	,	PUNCT
ejpam-5872	113	9	1ג	1ג	NUM
ejpam-5872	113	10	)	)	PUNCT
ejpam-5872	113	11	(	(	PUNCT
ejpam-5872	113	12	3ג	3ג	NUM
ejpam-5872	113	13	and	and	CCONJ
ejpam-5872	113	14	,	,	PUNCT
ejpam-5872	113	15	2ג	2ג	NUM
ejpam-5872	113	16	)	)	PUNCT
ejpam-5872	113	17	.(3ג	.(3ג	PUNCT
ejpam-5872	113	18	d±ξ(1ג	d±ξ(1ג	PROPN
ejpam-5872	113	19	)	)	PUNCT
ejpam-5872	114	1	=	=	SYM
ejpam-5872	114	2	0.4	0.4	NUM
ejpam-5872	114	3	,	,	PUNCT
ejpam-5872	114	4	d±ξ(2ג	d±ξ(2ג	ADJ
ejpam-5872	114	5	)	)	PUNCT
ejpam-5872	114	6	=	=	SYM
ejpam-5872	115	1	−0.3	−0.3	PROPN
ejpam-5872	115	2	,	,	PUNCT
ejpam-5872	115	3	and	and	CCONJ
ejpam-5872	115	4	d±ξ(3ג	d±ξ(3ג	NOUN
ejpam-5872	115	5	)	)	PUNCT
ejpam-5872	115	6	=	=	SYM
ejpam-5872	115	7	0.1	0.1	NUM
ejpam-5872	115	8	are	be	AUX
ejpam-5872	115	9	the	the	DET
ejpam-5872	115	10	effective	effective	ADJ
ejpam-5872	115	11	degrees	degree	NOUN
ejpam-5872	115	12	of	of	ADP
ejpam-5872	115	13	∑	∑	PUNCT
ejpam-5872	115	14	±.	±.	NOUN
ejpam-5872	115	15	δ±ξ	δ±ξ	PROPN
ejpam-5872	115	16	(	(	PUNCT
ejpam-5872	115	17	∑	∑	PROPN
ejpam-5872	115	18	±	±	NUM
ejpam-5872	115	19	)	)	PUNCT
ejpam-5872	115	20	=	=	SYM
ejpam-5872	116	1	−0.3	−0.3	PROPN
ejpam-5872	116	2	is	be	AUX
ejpam-5872	116	3	the	the	DET
ejpam-5872	116	4	minimum	minimum	ADJ
ejpam-5872	116	5	effective	effective	ADJ
ejpam-5872	116	6	degree	degree	NOUN
ejpam-5872	116	7	,	,	PUNCT
ejpam-5872	116	8	while	while	SCONJ
ejpam-5872	116	9	∆±ξ	∆±ξ	PROPN
ejpam-5872	116	10	(	(	PUNCT
ejpam-5872	116	11	∑	∑	PROPN
ejpam-5872	116	12	±	±	NUM
ejpam-5872	116	13	)	)	PUNCT
ejpam-5872	116	14	=	=	PUNCT
ejpam-5872	116	15	0.4	0.4	NUM
ejpam-5872	116	16	is	be	AUX
ejpam-5872	116	17	the	the	DET
ejpam-5872	116	18	maximum	maximum	ADJ
ejpam-5872	116	19	effective	effective	ADJ
ejpam-5872	116	20	degree	degree	NOUN
ejpam-5872	116	21	.	.	PUNCT
ejpam-5872	117	1	definition	definition	NOUN
ejpam-5872	117	2	6	6	NUM
ejpam-5872	117	3	.	.	PUNCT
ejpam-5872	118	1	the	the	DET
ejpam-5872	118	2	cumulative	cumulative	ADJ
ejpam-5872	118	3	membership	membership	NOUN
ejpam-5872	118	4	values	value	NOUN
ejpam-5872	118	5	of	of	ADP
ejpam-5872	118	6	all	all	DET
ejpam-5872	118	7	strong	strong	ADJ
ejpam-5872	118	8	arcs	arc	NOUN
ejpam-5872	118	9	occurring	occur	VERB
ejpam-5872	118	10	to	to	ADP
ejpam-5872	118	11	a	a	DET
ejpam-5872	118	12	node	node	NOUN
ejpam-5872	118	13	ג	ג	PROPN
ejpam-5872	118	14	determine	determine	VERB
ejpam-5872	118	15	its	its	PRON
ejpam-5872	118	16	strong	strong	ADJ
ejpam-5872	118	17	degree	degree	NOUN
ejpam-5872	118	18	.	.	PUNCT
ejpam-5872	119	1	d±s(ג	d±s(ג	NOUN
ejpam-5872	119	2	)	)	PUNCT
ejpam-5872	119	3	=	=	PUNCT
ejpam-5872	120	1	∑	∑	PUNCT
ejpam-5872	120	2	(	(	PUNCT
ejpam-5872	120	3	ג)ns∋ג	ג)ns∋ג	PROPN
ejpam-5872	120	4	µ(ג	µ(ג	VERB
ejpam-5872	120	5	,	,	PUNCT
ejpam-5872	120	6	(	(	PUNCT
ejpam-5872	120	7	iג	iג	NOUN
ejpam-5872	120	8	is	be	AUX
ejpam-5872	120	9	the	the	DET
ejpam-5872	120	10	representation	representation	NOUN
ejpam-5872	120	11	for	for	ADP
ejpam-5872	120	12	it	it	PRON
ejpam-5872	120	13	.	.	PUNCT
ejpam-5872	121	1	δ±s	δ±s	X
ejpam-5872	121	2	(	(	PUNCT
ejpam-5872	121	3	∑	∑	PROPN
ejpam-5872	121	4	±	±	NUM
ejpam-5872	121	5	)	)	PUNCT
ejpam-5872	121	6	=	=	SYM
ejpam-5872	122	1	∧{d±s(ג)/ג	∧{d±s(ג)/ג	PROPN
ejpam-5872	122	2	∈	∈	PROPN
ejpam-5872	122	3	ℑ	ℑ	PROPN
ejpam-5872	122	4	}	}	PUNCT
ejpam-5872	122	5	is	be	AUX
ejpam-5872	122	6	the	the	DET
ejpam-5872	122	7	minimum	minimum	ADJ
ejpam-5872	122	8	strong	strong	ADJ
ejpam-5872	122	9	degree	degree	NOUN
ejpam-5872	122	10	of	of	ADP
ejpam-5872	122	11	the	the	DET
ejpam-5872	122	12	sum	sum	NOUN
ejpam-5872	122	13	∑	∑	PROPN
ejpam-5872	122	14	±	±	PROPN
ejpam-5872	122	15	,	,	PUNCT
ejpam-5872	122	16	and	and	CCONJ
ejpam-5872	122	17	∆±s	∆±s	NUM
ejpam-5872	122	18	(	(	PUNCT
ejpam-5872	122	19	∑	∑	PROPN
ejpam-5872	122	20	±	±	NUM
ejpam-5872	122	21	)	)	PUNCT
ejpam-5872	122	22	=	=	PUNCT
ejpam-5872	122	23	∨{d±s(ג)/ג	∨{d±s(ג)/ג	NUM
ejpam-5872	122	24	∈	∈	PROPN
ejpam-5872	122	25	ℑ	ℑ	PROPN
ejpam-5872	122	26	}	}	PUNCT
ejpam-5872	122	27	is	be	AUX
ejpam-5872	122	28	the	the	DET
ejpam-5872	122	29	maximum	maximum	ADJ
ejpam-5872	122	30	strong	strong	ADJ
ejpam-5872	122	31	degree	degree	NOUN
ejpam-5872	122	32	.	.	PUNCT
ejpam-5872	123	1	example	example	NOUN
ejpam-5872	124	1	3	3	NUM
ejpam-5872	124	2	.	.	PUNCT
ejpam-5872	125	1	the	the	DET
ejpam-5872	125	2	strong	strong	ADJ
ejpam-5872	125	3	arcs	arc	NOUN
ejpam-5872	125	4	in	in	ADP
ejpam-5872	125	5	figure	figure	NOUN
ejpam-5872	125	6	1	1	NUM
ejpam-5872	125	7	are	be	AUX
ejpam-5872	125	8	,	,	PUNCT
ejpam-5872	125	9	1ג	1ג	NUM
ejpam-5872	125	10	)	)	PUNCT
ejpam-5872	125	11	(	(	PUNCT
ejpam-5872	125	12	3ג	3ג	NUM
ejpam-5872	125	13	and	and	CCONJ
ejpam-5872	125	14	,	,	PUNCT
ejpam-5872	125	15	2ג	2ג	NUM
ejpam-5872	125	16	)	)	PUNCT
ejpam-5872	125	17	.(3ג	.(3ג	PUNCT
ejpam-5872	126	1	∑	∑	PUNCT
ejpam-5872	126	2	±	±	NOUN
ejpam-5872	126	3	has	have	VERB
ejpam-5872	126	4	the	the	DET
ejpam-5872	126	5	following	follow	VERB
ejpam-5872	126	6	strong	strong	ADJ
ejpam-5872	126	7	degrees	degree	NOUN
ejpam-5872	126	8	:	:	PUNCT
ejpam-5872	126	9	d±s(1ג	d±s(1ג	NOUN
ejpam-5872	126	10	)	)	PUNCT
ejpam-5872	126	11	=	=	SYM
ejpam-5872	126	12	0.4	0.4	NUM
ejpam-5872	126	13	,	,	PUNCT
ejpam-5872	126	14	d±s(2ג	d±s(2ג	VERB
ejpam-5872	126	15	)	)	PUNCT
ejpam-5872	126	16	=	=	SYM
ejpam-5872	126	17	−0.3	−0.3	PROPN
ejpam-5872	126	18	,	,	PUNCT
ejpam-5872	126	19	and	and	CCONJ
ejpam-5872	126	20	d±s(3ג	d±s(3ג	NOUN
ejpam-5872	126	21	)	)	PUNCT
ejpam-5872	126	22	=	=	SYM
ejpam-5872	126	23	0.1	0.1	NUM
ejpam-5872	126	24	.	.	PUNCT
ejpam-5872	127	1	strong	strong	ADJ
ejpam-5872	127	2	degrees	degree	NOUN
ejpam-5872	127	3	range	range	VERB
ejpam-5872	127	4	from	from	ADP
ejpam-5872	127	5	δ±s	δ±s	PROPN
ejpam-5872	127	6	(	(	PUNCT
ejpam-5872	127	7	∑	∑	PROPN
ejpam-5872	127	8	±	±	NUM
ejpam-5872	127	9	)	)	PUNCT
ejpam-5872	127	10	=	=	SYM
ejpam-5872	127	11	−0.3	−0.3	PROPN
ejpam-5872	127	12	at	at	ADP
ejpam-5872	127	13	the	the	DET
ejpam-5872	127	14	minimum	minimum	NOUN
ejpam-5872	127	15	to	to	ADP
ejpam-5872	127	16	∆±s	∆±s	NUM
ejpam-5872	127	17	(	(	PUNCT
ejpam-5872	127	18	∑	∑	PROPN
ejpam-5872	127	19	±	±	NUM
ejpam-5872	127	20	)	)	PUNCT
ejpam-5872	127	21	=	=	SYM
ejpam-5872	127	22	0.4	0.4	NUM
ejpam-5872	127	23	at	at	ADP
ejpam-5872	127	24	the	the	DET
ejpam-5872	127	25	maximum	maximum	NOUN
ejpam-5872	127	26	.	.	PUNCT
ejpam-5872	128	1	definition	definition	NOUN
ejpam-5872	128	2	7	7	NUM
ejpam-5872	128	3	.	.	PUNCT
ejpam-5872	129	1	the	the	DET
ejpam-5872	129	2	definition	definition	NOUN
ejpam-5872	129	3	of	of	ADP
ejpam-5872	129	4	a	a	DET
ejpam-5872	129	5	vertex	vertex	NOUN
ejpam-5872	129	6	s’ג	s’ג	VERB
ejpam-5872	129	7	neighborhood	neighborhood	NOUN
ejpam-5872	129	8	degree	degree	NOUN
ejpam-5872	129	9	is	be	AUX
ejpam-5872	129	10	d±n	d±n	PROPN
ejpam-5872	129	11	(	(	PUNCT
ejpam-5872	129	12	ג	ג	PROPN
ejpam-5872	129	13	)	)	PUNCT
ejpam-5872	129	14	=	=	PUNCT
ejpam-5872	129	15	∑	∑	PUNCT
ejpam-5872	129	16	(	(	PUNCT
ejpam-5872	129	17	ג)n∋ג	ג)n∋ג	X
ejpam-5872	129	18	σ(ג	σ(ג	PROPN
ejpam-5872	129	19	)	)	PUNCT
ejpam-5872	129	20	.	.	PUNCT
ejpam-5872	130	1	the	the	DET
ejpam-5872	130	2	sum	sum	NOUN
ejpam-5872	130	3	∑	∑	PROPN
ejpam-5872	130	4	±	±	PROPN
ejpam-5872	130	5	has	have	VERB
ejpam-5872	130	6	a	a	DET
ejpam-5872	130	7	minimum	minimum	ADJ
ejpam-5872	130	8	neighborhood	neighborhood	NOUN
ejpam-5872	130	9	degree	degree	NOUN
ejpam-5872	130	10	:	:	PUNCT
ejpam-5872	130	11	δ±n	δ±n	PROPN
ejpam-5872	130	12	(	(	PUNCT
ejpam-5872	130	13	∑	∑	NOUN
ejpam-5872	130	14	±	±	NUM
ejpam-5872	130	15	)	)	PUNCT
ejpam-5872	130	16	=	=	SYM
ejpam-5872	130	17	∧{d±n	∧{d±n	X
ejpam-5872	130	18	ג/(ג	ג/(ג	NUM
ejpam-5872	130	19	)	)	PUNCT
ejpam-5872	130	20	∈	∈	PROPN
ejpam-5872	130	21	ℑ	ℑ	PROPN
ejpam-5872	130	22	}	}	PUNCT
ejpam-5872	130	23	,	,	PUNCT
ejpam-5872	130	24	and	and	CCONJ
ejpam-5872	130	25	a	a	DET
ejpam-5872	130	26	maximum	maximum	ADJ
ejpam-5872	130	27	neighborhood	neighborhood	NOUN
ejpam-5872	130	28	degree	degree	NOUN
ejpam-5872	130	29	:	:	PUNCT
ejpam-5872	130	30	∆±n	∆±n	NUM
ejpam-5872	130	31	(	(	PUNCT
ejpam-5872	130	32	∑	∑	PUNCT
ejpam-5872	130	33	±	±	NUM
ejpam-5872	130	34	)	)	PUNCT
ejpam-5872	130	35	=	=	SYM
ejpam-5872	130	36	∨{d±n	∨{d±n	NUM
ejpam-5872	130	37	ג/(ג	ג/(ג	NUM
ejpam-5872	130	38	)	)	PUNCT
ejpam-5872	130	39	∈	∈	PROPN
ejpam-5872	130	40	ℑ	ℑ	PROPN
ejpam-5872	130	41	}	}	PUNCT
ejpam-5872	130	42	.	.	PUNCT
ejpam-5872	131	1	example	example	NOUN
ejpam-5872	132	1	4	4	NUM
ejpam-5872	132	2	.	.	PUNCT
ejpam-5872	133	1	the	the	DET
ejpam-5872	133	2	neighborhood	neighborhood	NOUN
ejpam-5872	133	3	degrees	degree	NOUN
ejpam-5872	133	4	of	of	ADP
ejpam-5872	133	5	∑	∑	PUNCT
ejpam-5872	133	6	±	±	PROPN
ejpam-5872	133	7	in	in	ADP
ejpam-5872	133	8	figure	figure	NOUN
ejpam-5872	133	9	1	1	NUM
ejpam-5872	133	10	are	be	AUX
ejpam-5872	133	11	d±n	d±n	PROPN
ejpam-5872	133	12	(	(	PUNCT
ejpam-5872	133	13	1ג	1ג	NOUN
ejpam-5872	133	14	)	)	PUNCT
ejpam-5872	133	15	=	=	SYM
ejpam-5872	133	16	0.4	0.4	NUM
ejpam-5872	133	17	,	,	PUNCT
ejpam-5872	133	18	d±n	d±n	PROPN
ejpam-5872	133	19	(	(	PUNCT
ejpam-5872	133	20	2ג	2ג	NUM
ejpam-5872	133	21	)	)	PUNCT
ejpam-5872	133	22	=	=	NOUN
ejpam-5872	133	23	1.1	1.1	NUM
ejpam-5872	133	24	,	,	PUNCT
ejpam-5872	133	25	and	and	CCONJ
ejpam-5872	133	26	d±n	d±n	PROPN
ejpam-5872	133	27	(	(	PUNCT
ejpam-5872	133	28	3ג	3ג	NUM
ejpam-5872	133	29	)	)	PUNCT
ejpam-5872	133	30	=	=	SYM
ejpam-5872	133	31	0.1	0.1	NUM
ejpam-5872	133	32	.	.	PUNCT
ejpam-5872	134	1	neighborhood	neighborhood	NOUN
ejpam-5872	134	2	degree	degree	NOUN
ejpam-5872	134	3	is	be	AUX
ejpam-5872	134	4	minimum	minimum	ADJ
ejpam-5872	134	5	δ±n	δ±n	PROPN
ejpam-5872	135	1	(	(	PUNCT
ejpam-5872	135	2	∑	∑	PUNCT
ejpam-5872	135	3	±	±	NUM
ejpam-5872	135	4	)	)	PUNCT
ejpam-5872	135	5	=	=	SYM
ejpam-5872	135	6	0.1	0.1	NUM
ejpam-5872	135	7	,	,	PUNCT
ejpam-5872	135	8	and	and	CCONJ
ejpam-5872	135	9	effective	effective	ADJ
ejpam-5872	135	10	degree	degree	NOUN
ejpam-5872	135	11	is	be	AUX
ejpam-5872	135	12	maximum	maximum	ADJ
ejpam-5872	135	13	∆±n	∆±n	NUM
ejpam-5872	135	14	(	(	PUNCT
ejpam-5872	135	15	∑	∑	PUNCT
ejpam-5872	135	16	±	±	NUM
ejpam-5872	135	17	)	)	PUNCT
ejpam-5872	135	18	=	=	NOUN
ejpam-5872	136	1	1.1	1.1	NUM
ejpam-5872	136	2	.	.	PUNCT
ejpam-5872	137	1	definition	definition	NOUN
ejpam-5872	137	2	8	8	NUM
ejpam-5872	137	3	.	.	PUNCT
ejpam-5872	138	1	the	the	DET
ejpam-5872	138	2	formula	formula	NOUN
ejpam-5872	138	3	for	for	ADP
ejpam-5872	138	4	a	a	DET
ejpam-5872	138	5	vertex	vertex	NOUN
ejpam-5872	138	6	s’ג	s’ג	PUNCT
ejpam-5872	138	7	effective	effective	ADJ
ejpam-5872	138	8	neighborhood	neighborhood	NOUN
ejpam-5872	138	9	degree	degree	NOUN
ejpam-5872	138	10	is	be	AUX
ejpam-5872	138	11	d±en	d±en	PROPN
ejpam-5872	138	12	(	(	PUNCT
ejpam-5872	138	13	ג	ג	NOUN
ejpam-5872	138	14	)	)	PUNCT
ejpam-5872	138	15	=	=	NOUN
ejpam-5872	138	16	∑	∑	PROPN
ejpam-5872	138	17	(	(	PUNCT
ejpam-5872	138	18	ג)en∋ג	ג)en∋ג	NOUN
ejpam-5872	138	19	σ(ג	σ(ג	PROPN
ejpam-5872	138	20	)	)	PUNCT
ejpam-5872	138	21	.	.	PUNCT
ejpam-5872	139	1	the	the	DET
ejpam-5872	139	2	sum	sum	NOUN
ejpam-5872	139	3	∑	∑	PROPN
ejpam-5872	139	4	±	±	PROPN
ejpam-5872	139	5	has	have	VERB
ejpam-5872	139	6	a	a	DET
ejpam-5872	139	7	minimum	minimum	ADJ
ejpam-5872	139	8	effective	effective	ADJ
ejpam-5872	139	9	neighborhood	neighborhood	NOUN
ejpam-5872	139	10	degree	degree	NOUN
ejpam-5872	139	11	of	of	ADP
ejpam-5872	139	12	δ±en	δ±en	ADJ
ejpam-5872	139	13	(	(	PUNCT
ejpam-5872	139	14	∑	∑	PROPN
ejpam-5872	139	15	±	±	NUM
ejpam-5872	139	16	)	)	PUNCT
ejpam-5872	139	17	=	=	SYM
ejpam-5872	139	18	∧{d±en	∧{d±en	NUM
ejpam-5872	139	19	ג/(ג	ג/(ג	PROPN
ejpam-5872	139	20	)	)	PUNCT
ejpam-5872	139	21	∈	∈	PROPN
ejpam-5872	139	22	ℑ	ℑ	PROPN
ejpam-5872	139	23	}	}	PUNCT
ejpam-5872	139	24	,	,	PUNCT
ejpam-5872	139	25	and	and	CCONJ
ejpam-5872	139	26	a	a	DET
ejpam-5872	139	27	maximum	maximum	ADJ
ejpam-5872	139	28	effective	effective	ADJ
ejpam-5872	139	29	neighborhood	neighborhood	NOUN
ejpam-5872	139	30	degree	degree	NOUN
ejpam-5872	139	31	of	of	ADP
ejpam-5872	139	32	∆±en	∆±en	PROPN
ejpam-5872	139	33	(	(	PUNCT
ejpam-5872	139	34	∑	∑	PROPN
ejpam-5872	139	35	±	±	NUM
ejpam-5872	139	36	)	)	PUNCT
ejpam-5872	139	37	=	=	SYM
ejpam-5872	139	38	∨	∨	X
ejpam-5872	139	39	{	{	PUNCT
ejpam-5872	139	40	d±en	d±en	PROPN
ejpam-5872	139	41	ג/(ג	ג/(ג	PROPN
ejpam-5872	139	42	)	)	PUNCT
ejpam-5872	139	43	∈	∈	PROPN
ejpam-5872	139	44	ℑ	ℑ	PROPN
ejpam-5872	139	45	}	}	PUNCT
ejpam-5872	139	46	.	.	PUNCT
ejpam-5872	140	1	example	example	NOUN
ejpam-5872	141	1	5	5	NUM
ejpam-5872	141	2	.	.	PUNCT
ejpam-5872	142	1	the	the	DET
ejpam-5872	142	2	effective	effective	ADJ
ejpam-5872	142	3	arcs	arc	NOUN
ejpam-5872	142	4	in	in	ADP
ejpam-5872	142	5	figure	figure	NOUN
ejpam-5872	142	6	1	1	NUM
ejpam-5872	142	7	are	be	AUX
ejpam-5872	142	8	,	,	PUNCT
ejpam-5872	142	9	1ג	1ג	NUM
ejpam-5872	142	10	)	)	PUNCT
ejpam-5872	142	11	(	(	PUNCT
ejpam-5872	142	12	3ג	3ג	NUM
ejpam-5872	142	13	and	and	CCONJ
ejpam-5872	142	14	,	,	PUNCT
ejpam-5872	142	15	2ג	2ג	NUM
ejpam-5872	142	16	)	)	PUNCT
ejpam-5872	142	17	.(3ג	.(3ג	PUNCT
ejpam-5872	143	1	d±en	d±en	PROPN
ejpam-5872	143	2	(	(	PUNCT
ejpam-5872	143	3	1ג	1ג	NOUN
ejpam-5872	143	4	)	)	PUNCT
ejpam-5872	143	5	=	=	SYM
ejpam-5872	143	6	0.7	0.7	NUM
ejpam-5872	143	7	,	,	PUNCT
ejpam-5872	143	8	d±en	d±en	PROPN
ejpam-5872	143	9	(	(	PUNCT
ejpam-5872	143	10	2ג	2ג	NUM
ejpam-5872	143	11	)	)	PUNCT
ejpam-5872	143	12	=	=	SYM
ejpam-5872	143	13	0.7	0.7	NUM
ejpam-5872	143	14	,	,	PUNCT
ejpam-5872	143	15	and	and	CCONJ
ejpam-5872	143	16	d±en	d±en	PROPN
ejpam-5872	143	17	(	(	PUNCT
ejpam-5872	143	18	3ג	3ג	NUM
ejpam-5872	143	19	)	)	PUNCT
ejpam-5872	143	20	=	=	SYM
ejpam-5872	143	21	0.1	0.1	NUM
ejpam-5872	143	22	are	be	AUX
ejpam-5872	143	23	the	the	DET
ejpam-5872	143	24	effective	effective	ADJ
ejpam-5872	143	25	neighborhood	neighborhood	NOUN
ejpam-5872	143	26	degrees	degree	NOUN
ejpam-5872	143	27	of	of	ADP
ejpam-5872	143	28	∑	∑	PUNCT
ejpam-5872	143	29	±.	±.	PROPN
ejpam-5872	143	30	δ±en	δ±en	PROPN
ejpam-5872	143	31	(	(	PUNCT
ejpam-5872	143	32	∑	∑	PROPN
ejpam-5872	143	33	±	±	NUM
ejpam-5872	143	34	)	)	PUNCT
ejpam-5872	143	35	=	=	SYM
ejpam-5872	143	36	0.1	0.1	NUM
ejpam-5872	143	37	is	be	AUX
ejpam-5872	143	38	the	the	DET
ejpam-5872	143	39	smallest	small	ADJ
ejpam-5872	143	40	effective	effective	ADJ
ejpam-5872	143	41	neighborhood	neighborhood	NOUN
ejpam-5872	143	42	degree	degree	NOUN
ejpam-5872	143	43	,	,	PUNCT
ejpam-5872	143	44	while	while	SCONJ
ejpam-5872	143	45	∆±en	∆±en	PROPN
ejpam-5872	143	46	(	(	PUNCT
ejpam-5872	143	47	∑	∑	NOUN
ejpam-5872	143	48	±	±	NUM
ejpam-5872	143	49	)	)	PUNCT
ejpam-5872	143	50	=	=	SYM
ejpam-5872	143	51	0.7	0.7	NUM
ejpam-5872	143	52	is	be	AUX
ejpam-5872	143	53	the	the	DET
ejpam-5872	143	54	maximum	maximum	ADJ
ejpam-5872	143	55	.	.	PUNCT
ejpam-5872	144	1	definition	definition	NOUN
ejpam-5872	144	2	9	9	NUM
ejpam-5872	144	3	.	.	PUNCT
ejpam-5872	145	1	the	the	DET
ejpam-5872	145	2	definition	definition	NOUN
ejpam-5872	145	3	of	of	ADP
ejpam-5872	145	4	a	a	DET
ejpam-5872	145	5	vertex	vertex	NOUN
ejpam-5872	145	6	s’ג	s’ג	PUNCT
ejpam-5872	145	7	strong	strong	ADJ
ejpam-5872	145	8	neighborhood	neighborhood	NOUN
ejpam-5872	145	9	degree	degree	NOUN
ejpam-5872	145	10	is	be	AUX
ejpam-5872	145	11	d±sn	d±sn	PROPN
ejpam-5872	145	12	(	(	PUNCT
ejpam-5872	145	13	ג	ג	X
ejpam-5872	145	14	)	)	PUNCT
ejpam-5872	145	15	=	=	NOUN
ejpam-5872	145	16	∑	∑	PROPN
ejpam-5872	145	17	(	(	PUNCT
ejpam-5872	145	18	ג)ns∋ג	ג)ns∋ג	PROPN
ejpam-5872	145	19	σ(ג	σ(ג	PROPN
ejpam-5872	145	20	)	)	PUNCT
ejpam-5872	145	21	.	.	PUNCT
ejpam-5872	146	1	the	the	DET
ejpam-5872	146	2	sum	sum	NOUN
ejpam-5872	146	3	∑	∑	PROPN
ejpam-5872	146	4	±	±	PROPN
ejpam-5872	146	5	has	have	VERB
ejpam-5872	146	6	a	a	DET
ejpam-5872	146	7	minimum	minimum	ADJ
ejpam-5872	146	8	strong	strong	ADJ
ejpam-5872	146	9	neighborhood	neighborhood	NOUN
ejpam-5872	146	10	degree	degree	NOUN
ejpam-5872	146	11	of	of	ADP
ejpam-5872	146	12	δ±sn	δ±sn	PROPN
ejpam-5872	146	13	(	(	PUNCT
ejpam-5872	146	14	∑	∑	NOUN
ejpam-5872	146	15	±	±	NUM
ejpam-5872	146	16	)	)	PUNCT
ejpam-5872	146	17	=	=	SYM
ejpam-5872	146	18	∧{d±sn	∧{d±sn	PROPN
ejpam-5872	146	19	ג/(ג	ג/(ג	NUM
ejpam-5872	146	20	)	)	PUNCT
ejpam-5872	146	21	∈	∈	PROPN
ejpam-5872	146	22	ℑ	ℑ	PROPN
ejpam-5872	146	23	}	}	PUNCT
ejpam-5872	146	24	,	,	PUNCT
ejpam-5872	146	25	and	and	CCONJ
ejpam-5872	146	26	a	a	DET
ejpam-5872	146	27	maximum	maximum	ADJ
ejpam-5872	146	28	strong	strong	ADJ
ejpam-5872	146	29	neighborhood	neighborhood	NOUN
ejpam-5872	146	30	degree	degree	NOUN
ejpam-5872	146	31	of	of	ADP
ejpam-5872	146	32	∆±sn	∆±sn	PROPN
ejpam-5872	146	33	(	(	PUNCT
ejpam-5872	146	34	∑	∑	PROPN
ejpam-5872	146	35	±	±	NUM
ejpam-5872	146	36	)	)	PUNCT
ejpam-5872	146	37	=	=	VERB
ejpam-5872	146	38	∨{d±sn	∨{d±sn	ADJ
ejpam-5872	146	39	ג/(ג	ג/(ג	PROPN
ejpam-5872	146	40	)	)	PUNCT
ejpam-5872	146	41	∈	∈	PROPN
ejpam-5872	146	42	ℑ	ℑ	PROPN
ejpam-5872	146	43	}	}	PUNCT
ejpam-5872	146	44	.	.	PUNCT
ejpam-5872	147	1	example	example	NOUN
ejpam-5872	147	2	6	6	NUM
ejpam-5872	147	3	.	.	NUM
ejpam-5872	147	4	,	,	PUNCT
ejpam-5872	147	5	1ג	1ג	NUM
ejpam-5872	147	6	)	)	PUNCT
ejpam-5872	147	7	(	(	PUNCT
ejpam-5872	147	8	3ג	3ג	NUM
ejpam-5872	147	9	and	and	CCONJ
ejpam-5872	147	10	,	,	PUNCT
ejpam-5872	147	11	2ג	2ג	NUM
ejpam-5872	147	12	)	)	PUNCT
ejpam-5872	147	13	(	(	PUNCT
ejpam-5872	147	14	3ג	3ג	NOUN
ejpam-5872	147	15	are	be	AUX
ejpam-5872	147	16	the	the	DET
ejpam-5872	147	17	strong	strong	ADJ
ejpam-5872	147	18	arcs	arc	NOUN
ejpam-5872	147	19	in	in	ADP
ejpam-5872	147	20	figure	figure	NOUN
ejpam-5872	147	21	1	1	NUM
ejpam-5872	147	22	.	.	PUNCT
ejpam-5872	148	1	d±sn	d±sn	PROPN
ejpam-5872	148	2	(	(	PUNCT
ejpam-5872	148	3	1ג	1ג	NUM
ejpam-5872	148	4	)	)	PUNCT
ejpam-5872	148	5	=	=	SYM
ejpam-5872	148	6	0.7	0.7	NUM
ejpam-5872	148	7	,	,	PUNCT
ejpam-5872	148	8	d±sn	d±sn	PROPN
ejpam-5872	148	9	(	(	PUNCT
ejpam-5872	148	10	2ג	2ג	NUM
ejpam-5872	148	11	)	)	PUNCT
ejpam-5872	148	12	=	=	SYM
ejpam-5872	148	13	0.7	0.7	NUM
ejpam-5872	148	14	,	,	PUNCT
ejpam-5872	148	15	and	and	CCONJ
ejpam-5872	148	16	d±sn	d±sn	PROPN
ejpam-5872	148	17	(	(	PUNCT
ejpam-5872	148	18	3ג	3ג	NUM
ejpam-5872	148	19	)	)	PUNCT
ejpam-5872	148	20	=	=	SYM
ejpam-5872	148	21	0.1	0.1	NUM
ejpam-5872	148	22	are	be	AUX
ejpam-5872	148	23	the	the	DET
ejpam-5872	148	24	strong	strong	ADJ
ejpam-5872	148	25	neighborhood	neighborhood	NOUN
ejpam-5872	148	26	degrees	degree	NOUN
ejpam-5872	148	27	of	of	ADP
ejpam-5872	148	28	∑	∑	PUNCT
ejpam-5872	148	29	±.	±.	NOUN
ejpam-5872	148	30	δ±sn	δ±sn	PROPN
ejpam-5872	148	31	(	(	PUNCT
ejpam-5872	148	32	∑	∑	PROPN
ejpam-5872	148	33	±	±	NUM
ejpam-5872	148	34	)	)	PUNCT
ejpam-5872	148	35	=	=	SYM
ejpam-5872	148	36	0.1	0.1	NUM
ejpam-5872	148	37	is	be	AUX
ejpam-5872	148	38	the	the	DET
ejpam-5872	148	39	smallest	small	ADJ
ejpam-5872	148	40	strong	strong	ADJ
ejpam-5872	148	41	neighborhood	neighborhood	NOUN
ejpam-5872	148	42	degree	degree	NOUN
ejpam-5872	148	43	,	,	PUNCT
ejpam-5872	148	44	while	while	SCONJ
ejpam-5872	148	45	∆±sn	∆±sn	PROPN
ejpam-5872	148	46	(	(	PUNCT
ejpam-5872	148	47	∑	∑	PROPN
ejpam-5872	148	48	±	±	NUM
ejpam-5872	148	49	)	)	PUNCT
ejpam-5872	148	50	=	=	SYM
ejpam-5872	148	51	0.7	0.7	NUM
ejpam-5872	148	52	is	be	AUX
ejpam-5872	148	53	the	the	DET
ejpam-5872	148	54	maximum	maximum	ADJ
ejpam-5872	148	55	.	.	PUNCT
ejpam-5872	149	1	theorem	theorem	NOUN
ejpam-5872	149	2	1	1	NUM
ejpam-5872	149	3	.	.	PUNCT
ejpam-5872	150	1	in	in	ADP
ejpam-5872	150	2	a	a	DET
ejpam-5872	150	3	signed	sign	VERB
ejpam-5872	150	4	-	-	PUNCT
ejpam-5872	150	5	fg	fg	PROPN
ejpam-5872	150	6	∑	∑	PROPN
ejpam-5872	150	7	±	±	NUM
ejpam-5872	150	8	=	=	SYM
ejpam-5872	150	9	(	(	PUNCT
ejpam-5872	150	10	ℑ	ℑ	PROPN
ejpam-5872	150	11	,	,	PUNCT
ejpam-5872	150	12	σ	σ	PROPN
ejpam-5872	150	13	,	,	PUNCT
ejpam-5872	150	14	µ	µ	NOUN
ejpam-5872	150	15	)	)	PUNCT
ejpam-5872	150	16	,	,	PUNCT
ejpam-5872	150	17	(	(	PUNCT
ejpam-5872	150	18	i	i	NOUN
ejpam-5872	150	19	)	)	PUNCT
ejpam-5872	150	20	d±e(ג	d±e(ג	PROPN
ejpam-5872	150	21	)	)	PUNCT
ejpam-5872	150	22	≤	≤	NOUN
ejpam-5872	150	23	d±s(ג	d±s(ג	NOUN
ejpam-5872	150	24	)	)	PUNCT
ejpam-5872	150	25	≤	≤	NOUN
ejpam-5872	150	26	d±(ג	d±(ג	PROPN
ejpam-5872	150	27	)	)	PUNCT
ejpam-5872	150	28	,	,	PUNCT
ejpam-5872	150	29	∀	∀	PUNCT
ejpam-5872	150	30	ג	ג	ADP
ejpam-5872	150	31	∈	∈	PROPN
ejpam-5872	150	32	ℑ.	ℑ.	PROPN
ejpam-5872	150	33	c.	c.	NOUN
ejpam-5872	150	34	sankar	sankar	NOUN
ejpam-5872	150	35	et	et	PROPN
ejpam-5872	150	36	al	al	PROPN
ejpam-5872	150	37	.	.	PUNCT
ejpam-5872	150	38	/	/	SYM
ejpam-5872	150	39	eur	eur	PROPN
ejpam-5872	150	40	.	.	PUNCT
ejpam-5872	151	1	j.	j.	PROPN
ejpam-5872	151	2	pure	pure	PROPN
ejpam-5872	151	3	appl	appl	PROPN
ejpam-5872	151	4	.	.	PROPN
ejpam-5872	151	5	math	math	PROPN
ejpam-5872	151	6	,	,	PUNCT
ejpam-5872	151	7	18	18	NUM
ejpam-5872	151	8	(	(	PUNCT
ejpam-5872	151	9	4	4	NUM
ejpam-5872	151	10	)	)	PUNCT
ejpam-5872	151	11	(	(	PUNCT
ejpam-5872	151	12	2025	2025	NUM
ejpam-5872	151	13	)	)	PUNCT
ejpam-5872	151	14	,	,	PUNCT
ejpam-5872	151	15	5872	5872	NUM
ejpam-5872	151	16	7	7	NUM
ejpam-5872	151	17	of	of	ADP
ejpam-5872	151	18	17	17	NUM
ejpam-5872	151	19	(	(	PUNCT
ejpam-5872	151	20	ii	ii	NOUN
ejpam-5872	151	21	)	)	PUNCT
ejpam-5872	151	22	d±en	d±en	PROPN
ejpam-5872	151	23	(	(	PUNCT
ejpam-5872	151	24	ג	ג	NOUN
ejpam-5872	151	25	)	)	PUNCT
ejpam-5872	151	26	≤	≤	NOUN
ejpam-5872	151	27	d±sn	d±sn	PROPN
ejpam-5872	151	28	(	(	PUNCT
ejpam-5872	151	29	ג	ג	PROPN
ejpam-5872	151	30	)	)	PUNCT
ejpam-5872	151	31	≤	≤	NOUN
ejpam-5872	151	32	d±n	d±n	PROPN
ejpam-5872	151	33	,	,	PUNCT
ejpam-5872	151	34	(	(	PUNCT
ejpam-5872	151	35	ג	ג	X
ejpam-5872	151	36	)	)	PUNCT
ejpam-5872	151	37	∀	∀	PUNCT
ejpam-5872	152	1	ג	ג	ADP
ejpam-5872	152	2	∈	∈	ADJ
ejpam-5872	152	3	ℑ.	ℑ.	NOUN
ejpam-5872	152	4	proof	proof	NOUN
ejpam-5872	152	5	.	.	PUNCT
ejpam-5872	153	1	the	the	DET
ejpam-5872	153	2	total	total	NOUN
ejpam-5872	153	3	of	of	ADP
ejpam-5872	153	4	the	the	DET
ejpam-5872	153	5	edge	edge	NOUN
ejpam-5872	153	6	membership	membership	NOUN
ejpam-5872	153	7	values	value	NOUN
ejpam-5872	153	8	of	of	ADP
ejpam-5872	153	9	the	the	DET
ejpam-5872	153	10	effective	effective	ADJ
ejpam-5872	153	11	arcs	arcs	NOUN
ejpam-5872	153	12	incident	incident	NOUN
ejpam-5872	153	13	to	to	ADP
ejpam-5872	153	14	ג	ג	PROPN
ejpam-5872	153	15	and	and	CCONJ
ejpam-5872	153	16	the	the	DET
ejpam-5872	153	17	total	total	NOUN
ejpam-5872	153	18	of	of	ADP
ejpam-5872	153	19	the	the	DET
ejpam-5872	153	20	strong	strong	ADJ
ejpam-5872	153	21	edge	edge	NOUN
ejpam-5872	153	22	membership	membership	NOUN
ejpam-5872	153	23	values	value	NOUN
ejpam-5872	153	24	of	of	ADP
ejpam-5872	153	25	the	the	DET
ejpam-5872	153	26	strong	strong	ADJ
ejpam-5872	153	27	arcs	arcs	NOUN
ejpam-5872	153	28	incident	incident	NOUN
ejpam-5872	153	29	to	to	ADP
ejpam-5872	153	30	ג	ג	PROPN
ejpam-5872	153	31	makes	make	VERB
ejpam-5872	153	32	up	up	ADP
ejpam-5872	153	33	the	the	DET
ejpam-5872	153	34	effective	effective	ADJ
ejpam-5872	153	35	degree	degree	NOUN
ejpam-5872	153	36	of	of	ADP
ejpam-5872	153	37	vertex	vertex	NOUN
ejpam-5872	153	38	.ג	.ג	PUNCT
ejpam-5872	154	1	d±e(ג	d±e(ג	PROPN
ejpam-5872	154	2	)	)	PUNCT
ejpam-5872	154	3	≤	≤	NOUN
ejpam-5872	154	4	d±s(ג	d±s(ג	PROPN
ejpam-5872	154	5	)	)	PUNCT
ejpam-5872	154	6	indicates	indicate	VERB
ejpam-5872	154	7	that	that	SCONJ
ejpam-5872	154	8	strong	strong	ADJ
ejpam-5872	154	9	arcs	arc	NOUN
ejpam-5872	154	10	do	do	AUX
ejpam-5872	154	11	not	not	PART
ejpam-5872	154	12	necessarily	necessarily	ADV
ejpam-5872	154	13	have	have	VERB
ejpam-5872	154	14	to	to	PART
ejpam-5872	154	15	be	be	AUX
ejpam-5872	154	16	effective	effective	ADJ
ejpam-5872	154	17	arcs	arc	NOUN
ejpam-5872	154	18	,	,	PUNCT
ejpam-5872	154	19	but	but	CCONJ
ejpam-5872	154	20	effective	effective	ADJ
ejpam-5872	154	21	arcs	arc	NOUN
ejpam-5872	154	22	can	can	AUX
ejpam-5872	154	23	be	be	AUX
ejpam-5872	154	24	strong	strong	ADJ
ejpam-5872	154	25	arcs	arc	NOUN
ejpam-5872	154	26	.	.	PUNCT
ejpam-5872	155	1	in	in	ADP
ejpam-5872	155	2	a	a	DET
ejpam-5872	155	3	similar	similar	ADJ
ejpam-5872	155	4	vein	vein	NOUN
ejpam-5872	155	5	,	,	PUNCT
ejpam-5872	155	6	not	not	PART
ejpam-5872	155	7	every	every	DET
ejpam-5872	155	8	arc	arc	NOUN
ejpam-5872	155	9	that	that	PRON
ejpam-5872	155	10	intersects	intersect	VERB
ejpam-5872	155	11	a	a	DET
ejpam-5872	155	12	vertex	vertex	NOUN
ejpam-5872	155	13	must	must	AUX
ejpam-5872	155	14	be	be	AUX
ejpam-5872	155	15	a	a	DET
ejpam-5872	155	16	strong	strong	ADJ
ejpam-5872	155	17	one	one	NOUN
ejpam-5872	155	18	.	.	PUNCT
ejpam-5872	156	1	because	because	SCONJ
ejpam-5872	156	2	of	of	ADP
ejpam-5872	156	3	this	this	PRON
ejpam-5872	156	4	,	,	PUNCT
ejpam-5872	156	5	d±e(ג	d±e(ג	PROPN
ejpam-5872	156	6	)	)	PUNCT
ejpam-5872	156	7	≤	≤	NOUN
ejpam-5872	156	8	d±s(ג	d±s(ג	NOUN
ejpam-5872	156	9	)	)	PUNCT
ejpam-5872	156	10	≤	≤	NOUN
ejpam-5872	156	11	d±(ג).the	d±(ג).the	DET
ejpam-5872	156	12	same	same	ADJ
ejpam-5872	156	13	is	be	AUX
ejpam-5872	156	14	true	true	ADJ
ejpam-5872	156	15	for	for	ADP
ejpam-5872	156	16	all	all	DET
ejpam-5872	156	17	ג	ג	ADP
ejpam-5872	156	18	∈	∈	PROPN
ejpam-5872	156	19	ℑ	ℑ	PROPN
ejpam-5872	156	20	:	:	PUNCT
ejpam-5872	156	21	d±en	d±en	PROPN
ejpam-5872	156	22	(	(	PUNCT
ejpam-5872	156	23	ג	ג	NOUN
ejpam-5872	156	24	)	)	PUNCT
ejpam-5872	156	25	≤	≤	NOUN
ejpam-5872	156	26	d±sn	d±sn	PROPN
ejpam-5872	156	27	(	(	PUNCT
ejpam-5872	156	28	ג	ג	PROPN
ejpam-5872	156	29	)	)	PUNCT
ejpam-5872	156	30	≤	≤	NUM
ejpam-5872	156	31	d±n	d±n	PROPN
ejpam-5872	156	32	.(ג	.(ג	PUNCT
ejpam-5872	156	33	)	)	PUNCT
ejpam-5872	156	34	theorem	theorem	VERB
ejpam-5872	156	35	2	2	NUM
ejpam-5872	156	36	.	.	PUNCT
ejpam-5872	156	37	in	in	ADP
ejpam-5872	156	38	a	a	DET
ejpam-5872	156	39	signed	sign	VERB
ejpam-5872	156	40	-	-	PUNCT
ejpam-5872	156	41	fg	fg	PROPN
ejpam-5872	156	42	∑	∑	PROPN
ejpam-5872	156	43	±	±	NUM
ejpam-5872	156	44	=	=	SYM
ejpam-5872	156	45	(	(	PUNCT
ejpam-5872	156	46	ℑ	ℑ	PROPN
ejpam-5872	156	47	,	,	PUNCT
ejpam-5872	156	48	σ	σ	PROPN
ejpam-5872	156	49	,	,	PUNCT
ejpam-5872	156	50	µ	µ	NOUN
ejpam-5872	156	51	)	)	PUNCT
ejpam-5872	156	52	,	,	PUNCT
ejpam-5872	156	53	(	(	PUNCT
ejpam-5872	156	54	i	i	NOUN
ejpam-5872	156	55	)	)	PUNCT
ejpam-5872	156	56	d±e(ג	d±e(ג	PROPN
ejpam-5872	156	57	)	)	PUNCT
ejpam-5872	156	58	≤	≤	PUNCT
ejpam-5872	156	59	d±en	d±en	PROPN
ejpam-5872	156	60	,	,	PUNCT
ejpam-5872	156	61	(	(	PUNCT
ejpam-5872	156	62	ג	ג	X
ejpam-5872	156	63	)	)	PUNCT
ejpam-5872	156	64	∀	∀	PUNCT
ejpam-5872	156	65	ג	ג	ADP
ejpam-5872	156	66	∈	∈	ADJ
ejpam-5872	156	67	ℑ.	ℑ.	PROPN
ejpam-5872	156	68	(	(	PUNCT
ejpam-5872	156	69	ii	ii	NOUN
ejpam-5872	156	70	)	)	PUNCT
ejpam-5872	156	71	d±(ג	d±(ג	PROPN
ejpam-5872	156	72	)	)	PUNCT
ejpam-5872	156	73	≤	≤	NUM
ejpam-5872	156	74	d±n	d±n	PROPN
ejpam-5872	156	75	,	,	PUNCT
ejpam-5872	156	76	(	(	PUNCT
ejpam-5872	156	77	ג	ג	X
ejpam-5872	156	78	)	)	PUNCT
ejpam-5872	156	79	∀	∀	PUNCT
ejpam-5872	156	80	ג	ג	ADP
ejpam-5872	156	81	∈	∈	ADJ
ejpam-5872	156	82	ℑ.	ℑ.	PROPN
ejpam-5872	156	83	(	(	PUNCT
ejpam-5872	156	84	iii	iii	NOUN
ejpam-5872	156	85	)	)	PUNCT
ejpam-5872	156	86	d±s(ג	d±s(ג	PROPN
ejpam-5872	156	87	)	)	PUNCT
ejpam-5872	156	88	≤	≤	NOUN
ejpam-5872	156	89	d±sn	d±sn	PROPN
ejpam-5872	156	90	,	,	PUNCT
ejpam-5872	156	91	(	(	PUNCT
ejpam-5872	156	92	ג	ג	X
ejpam-5872	156	93	)	)	PUNCT
ejpam-5872	156	94	∀	∀	PUNCT
ejpam-5872	157	1	ג	ג	ADP
ejpam-5872	157	2	∈	∈	ADJ
ejpam-5872	157	3	ℑ.	ℑ.	NOUN
ejpam-5872	157	4	proof	proof	NOUN
ejpam-5872	157	5	.	.	PUNCT
ejpam-5872	158	1	effective	effective	ADJ
ejpam-5872	158	2	arcs	arc	NOUN
ejpam-5872	158	3	are	be	AUX
ejpam-5872	158	4	defined	define	VERB
ejpam-5872	158	5	as	as	ADP
ejpam-5872	158	6	the	the	DET
ejpam-5872	158	7	total	total	ADJ
ejpam-5872	158	8	membership	membership	NOUN
ejpam-5872	158	9	values	value	NOUN
ejpam-5872	158	10	of	of	ADP
ejpam-5872	158	11	the	the	DET
ejpam-5872	158	12	effective	effective	ADJ
ejpam-5872	158	13	arcs	arcs	NOUN
ejpam-5872	158	14	incident	incident	NOUN
ejpam-5872	158	15	to	to	AUX
ejpam-5872	158	16	,	,	PUNCT
ejpam-5872	158	17	ג	ג	ADP
ejpam-5872	158	18	while	while	SCONJ
ejpam-5872	158	19	the	the	DET
ejpam-5872	158	20	vertex	vertex	NOUN
ejpam-5872	158	21	membership	membership	NOUN
ejpam-5872	158	22	values	value	NOUN
ejpam-5872	158	23	of	of	ADP
ejpam-5872	158	24	the	the	DET
ejpam-5872	158	25	end	end	NOUN
ejpam-5872	158	26	vertices	vertex	NOUN
ejpam-5872	158	27	of	of	ADP
ejpam-5872	158	28	these	these	DET
ejpam-5872	158	29	effective	effective	ADJ
ejpam-5872	158	30	edges	edge	NOUN
ejpam-5872	158	31	constitute	constitute	VERB
ejpam-5872	158	32	the	the	DET
ejpam-5872	158	33	effective	effective	ADJ
ejpam-5872	158	34	neighborhood	neighborhood	NOUN
ejpam-5872	158	35	degree	degree	NOUN
ejpam-5872	158	36	of	of	ADP
ejpam-5872	158	37	the	the	DET
ejpam-5872	158	38	vertex	vertex	NOUN
ejpam-5872	158	39	.ג	.ג	NOUN
ejpam-5872	159	1	it	it	PRON
ejpam-5872	159	2	follows	follow	VERB
ejpam-5872	159	3	that	that	SCONJ
ejpam-5872	159	4	d±e(ג	d±e(ג	PROPN
ejpam-5872	159	5	)	)	PUNCT
ejpam-5872	159	6	≤	≤	NOUN
ejpam-5872	159	7	d±en	d±en	PROPN
ejpam-5872	159	8	(	(	PUNCT
ejpam-5872	159	9	ג	ג	PROPN
ejpam-5872	159	10	)	)	PUNCT
ejpam-5872	159	11	for	for	ADP
ejpam-5872	159	12	all	all	DET
ejpam-5872	159	13	ג	ג	PROPN
ejpam-5872	159	14	∈	∈	PROPN
ejpam-5872	159	15	ℑ	ℑ	PROPN
ejpam-5872	159	16	,	,	PUNCT
ejpam-5872	159	17	since	since	SCONJ
ejpam-5872	159	18	the	the	DET
ejpam-5872	159	19	edge	edge	NOUN
ejpam-5872	159	20	membership	membership	NOUN
ejpam-5872	159	21	value	value	NOUN
ejpam-5872	159	22	is	be	AUX
ejpam-5872	159	23	less	less	ADJ
ejpam-5872	159	24	than	than	ADP
ejpam-5872	159	25	or	or	CCONJ
ejpam-5872	159	26	equal	equal	ADJ
ejpam-5872	159	27	to	to	ADP
ejpam-5872	159	28	the	the	DET
ejpam-5872	159	29	membership	membership	NOUN
ejpam-5872	159	30	values	value	NOUN
ejpam-5872	159	31	of	of	ADP
ejpam-5872	159	32	its	its	PRON
ejpam-5872	159	33	end	end	NOUN
ejpam-5872	159	34	vertices	vertex	NOUN
ejpam-5872	159	35	.	.	PUNCT
ejpam-5872	160	1	similarly	similarly	ADV
ejpam-5872	160	2	,	,	PUNCT
ejpam-5872	160	3	for	for	ADP
ejpam-5872	160	4	every	every	DET
ejpam-5872	160	5	ג	ג	PROPN
ejpam-5872	160	6	∈	∈	PROPN
ejpam-5872	160	7	ℑ	ℑ	PROPN
ejpam-5872	160	8	,	,	PUNCT
ejpam-5872	160	9	we	we	PRON
ejpam-5872	160	10	have	have	VERB
ejpam-5872	160	11	d±(ג	d±(ג	PROPN
ejpam-5872	160	12	)	)	PUNCT
ejpam-5872	160	13	≤	≤	NUM
ejpam-5872	161	1	d±n	d±n	PROPN
ejpam-5872	161	2	(	(	PUNCT
ejpam-5872	161	3	ג	ג	PROPN
ejpam-5872	161	4	)	)	PUNCT
ejpam-5872	161	5	and	and	CCONJ
ejpam-5872	161	6	d±s(ג	d±s(ג	PROPN
ejpam-5872	161	7	)	)	PUNCT
ejpam-5872	161	8	≤	≤	NOUN
ejpam-5872	161	9	d±sn	d±sn	PROPN
ejpam-5872	161	10	.(ג	.(ג	PUNCT
ejpam-5872	161	11	)	)	PUNCT
ejpam-5872	162	1	hence	hence	ADV
ejpam-5872	162	2	,	,	PUNCT
ejpam-5872	162	3	the	the	DET
ejpam-5872	162	4	stated	state	VERB
ejpam-5872	162	5	results	result	NOUN
ejpam-5872	162	6	hold	hold	VERB
ejpam-5872	162	7	.	.	PUNCT
ejpam-5872	163	1	theorem	theorem	NOUN
ejpam-5872	163	2	3	3	NUM
ejpam-5872	163	3	.	.	PUNCT
ejpam-5872	164	1	in	in	ADP
ejpam-5872	164	2	a	a	DET
ejpam-5872	164	3	signed	sign	VERB
ejpam-5872	164	4	-	-	PUNCT
ejpam-5872	164	5	fg	fg	PROPN
ejpam-5872	164	6	∑	∑	PROPN
ejpam-5872	164	7	±	±	NUM
ejpam-5872	164	8	=	=	SYM
ejpam-5872	164	9	(	(	PUNCT
ejpam-5872	164	10	ℑ	ℑ	PROPN
ejpam-5872	164	11	,	,	PUNCT
ejpam-5872	164	12	σ	σ	PROPN
ejpam-5872	164	13	,	,	PUNCT
ejpam-5872	164	14	µ	µ	NOUN
ejpam-5872	164	15	)	)	PUNCT
ejpam-5872	164	16	,	,	PUNCT
ejpam-5872	164	17	the	the	DET
ejpam-5872	164	18	total	total	ADJ
ejpam-5872	164	19	degrees	degree	NOUN
ejpam-5872	164	20	of	of	ADP
ejpam-5872	164	21	all	all	DET
ejpam-5872	164	22	nodes	node	NOUN
ejpam-5872	164	23	are	be	AUX
ejpam-5872	164	24	equal	equal	ADJ
ejpam-5872	164	25	to	to	ADP
ejpam-5872	164	26	twice	twice	DET
ejpam-5872	164	27	the	the	DET
ejpam-5872	164	28	total	total	ADJ
ejpam-5872	164	29	membership	membership	NOUN
ejpam-5872	164	30	values	value	NOUN
ejpam-5872	164	31	of	of	ADP
ejpam-5872	164	32	all	all	DET
ejpam-5872	164	33	arcs	arc	NOUN
ejpam-5872	164	34	in	in	ADP
ejpam-5872	164	35	∑	∑	PUNCT
ejpam-5872	164	36	±.	±.	NOUN
ejpam-5872	164	37	proof	proof	NOUN
ejpam-5872	164	38	.	.	PUNCT
ejpam-5872	165	1	let	let	VERB
ejpam-5872	165	2	σ±	σ±	NOUN
ejpam-5872	165	3	=	=	SYM
ejpam-5872	165	4	(	(	PUNCT
ejpam-5872	165	5	ℑ	ℑ	PROPN
ejpam-5872	165	6	,	,	PUNCT
ejpam-5872	165	7	σ	σ	PROPN
ejpam-5872	165	8	,	,	PUNCT
ejpam-5872	165	9	µ	µ	NOUN
ejpam-5872	165	10	)	)	PUNCT
ejpam-5872	165	11	be	be	VERB
ejpam-5872	165	12	a	a	DET
ejpam-5872	165	13	signed	sign	VERB
ejpam-5872	165	14	fuzzy	fuzzy	ADJ
ejpam-5872	165	15	graph	graph	NOUN
ejpam-5872	165	16	,	,	PUNCT
ejpam-5872	165	17	where	where	SCONJ
ejpam-5872	165	18	ℑ	ℑ	PROPN
ejpam-5872	165	19	=	=	SYM
ejpam-5872	165	20	,	,	PUNCT
ejpam-5872	165	21	1ג	1ג	NUM
ejpam-5872	165	22	}	}	PUNCT
ejpam-5872	165	23	,	,	PUNCT
ejpam-5872	165	24	2ג	2ג	NOUN
ejpam-5872	165	25	.	.	PUNCT
ejpam-5872	165	26	.	.	PUNCT
ejpam-5872	165	27	.	.	PUNCT
ejpam-5872	166	1	,	,	PUNCT
ejpam-5872	166	2	,	,	PUNCT
ejpam-5872	166	3	{	{	PUNCT
ejpam-5872	166	4	nג	nג	NOUN
ejpam-5872	166	5	σ	σ	PROPN
ejpam-5872	166	6	is	be	AUX
ejpam-5872	166	7	a	a	DET
ejpam-5872	166	8	signed	sign	VERB
ejpam-5872	166	9	fuzzy	fuzzy	ADJ
ejpam-5872	166	10	subset	subset	NOUN
ejpam-5872	166	11	of	of	ADP
ejpam-5872	166	12	ℑ	ℑ	PROPN
ejpam-5872	166	13	,	,	PUNCT
ejpam-5872	166	14	and	and	CCONJ
ejpam-5872	166	15	µ	µ	NOUN
ejpam-5872	166	16	is	be	AUX
ejpam-5872	166	17	a	a	DET
ejpam-5872	166	18	signed	sign	VERB
ejpam-5872	166	19	fuzzy	fuzzy	ADJ
ejpam-5872	166	20	subset	subset	NOUN
ejpam-5872	166	21	of	of	ADP
ejpam-5872	166	22	ℑ×	ℑ×	NOUN
ejpam-5872	166	23	ℑ.	ℑ.	NOUN
ejpam-5872	166	24	by	by	ADP
ejpam-5872	166	25	definition	definition	NOUN
ejpam-5872	166	26	4	4	NUM
ejpam-5872	166	27	,	,	PUNCT
ejpam-5872	166	28	the	the	DET
ejpam-5872	166	29	degree	degree	NOUN
ejpam-5872	166	30	of	of	ADP
ejpam-5872	166	31	a	a	DET
ejpam-5872	166	32	vertex	vertex	NOUN
ejpam-5872	166	33	ג	ג	ADP
ejpam-5872	166	34	∈	∈	NOUN
ejpam-5872	166	35	ℑ	ℑ	PROPN
ejpam-5872	166	36	is	be	AUX
ejpam-5872	166	37	d(ג	d(ג	PROPN
ejpam-5872	166	38	)	)	PUNCT
ejpam-5872	166	39	=	=	PUNCT
ejpam-5872	166	40	∑	∑	PUNCT
ejpam-5872	166	41	i∈ℑג	i∈ℑג	VERB
ejpam-5872	166	42	iג	iג	ADP
ejpam-5872	166	43	ג≠	ג≠	PROPN
ejpam-5872	166	44	µ(ג	µ(ג	NOUN
ejpam-5872	166	45	,	,	PUNCT
ejpam-5872	166	46	,	,	PUNCT
ejpam-5872	166	47	i).henceג	i).henceג	PROPN
ejpam-5872	166	48	∑	∑	PUNCT
ejpam-5872	166	49	ℑ∋ג	ℑ∋ג	ADP
ejpam-5872	166	50	d(ג	d(ג	NOUN
ejpam-5872	166	51	)	)	PUNCT
ejpam-5872	167	1	=	=	NOUN
ejpam-5872	167	2	∑n	∑n	PROPN
ejpam-5872	167	3	i=1	i=1	PROPN
ejpam-5872	167	4	d(גi).now	d(גi).now	PROPN
ejpam-5872	167	5	,	,	PUNCT
ejpam-5872	167	6	expanding	expand	VERB
ejpam-5872	167	7	each	each	DET
ejpam-5872	167	8	degree	degree	NOUN
ejpam-5872	167	9	:	:	PUNCT
ejpam-5872	167	10	d(1ג	d(1ג	X
ejpam-5872	167	11	)	)	PUNCT
ejpam-5872	167	12	=	=	SYM
ejpam-5872	168	1	∑n	∑n	PROPN
ejpam-5872	168	2	j=1	j=1	PROPN
ejpam-5872	168	3	µ(1ג	µ(1ג	NOUN
ejpam-5872	168	4	,	,	PUNCT
ejpam-5872	168	5	,	,	PUNCT
ejpam-5872	168	6	(	(	PUNCT
ejpam-5872	168	7	jג	jג	PROPN
ejpam-5872	168	8	d(2ג	d(2ג	PROPN
ejpam-5872	168	9	)	)	PUNCT
ejpam-5872	168	10	=	=	SYM
ejpam-5872	169	1	∑n	∑n	PROPN
ejpam-5872	169	2	j=1	j=1	PROPN
ejpam-5872	169	3	µ(2ג	µ(2ג	VERB
ejpam-5872	169	4	,	,	PUNCT
ejpam-5872	169	5	,	,	PUNCT
ejpam-5872	169	6	(	(	PUNCT
ejpam-5872	169	7	jג	jג	PROPN
ejpam-5872	169	8	.	.	PUNCT
ejpam-5872	169	9	.	.	PUNCT
ejpam-5872	169	10	.	.	PUNCT
ejpam-5872	170	1	,	,	PUNCT
ejpam-5872	170	2	d(גn	d(גn	NOUN
ejpam-5872	170	3	)	)	PUNCT
ejpam-5872	170	4	=	=	SYM
ejpam-5872	171	1	∑n	∑n	PROPN
ejpam-5872	171	2	j=1	j=1	PROPN
ejpam-5872	171	3	µ(גn	µ(גn	PROPN
ejpam-5872	171	4	,	,	PUNCT
ejpam-5872	171	5	.(jג	.(jג	PROPN
ejpam-5872	171	6	thus	thus	ADV
ejpam-5872	171	7	,	,	PUNCT
ejpam-5872	171	8	∑n	∑n	PROPN
ejpam-5872	171	9	i=1	i=1	PROPN
ejpam-5872	171	10	d(גi	d(גi	PROPN
ejpam-5872	171	11	)	)	PUNCT
ejpam-5872	171	12	=	=	SYM
ejpam-5872	172	1	∑n	∑n	PROPN
ejpam-5872	172	2	i=1	i=1	PROPN
ejpam-5872	172	3	∑n	∑n	PROPN
ejpam-5872	172	4	j=1	j=1	ADJ
ejpam-5872	172	5	µ(גi	µ(גi	NOUN
ejpam-5872	172	6	,	,	PUNCT
ejpam-5872	172	7	.(jג	.(jג	PROPN
ejpam-5872	172	8	since	since	SCONJ
ejpam-5872	172	9	every	every	DET
ejpam-5872	172	10	arc	arc	NOUN
ejpam-5872	172	11	jגiג	jגiג	NOUN
ejpam-5872	172	12	contributes	contribute	VERB
ejpam-5872	172	13	to	to	ADP
ejpam-5872	172	14	the	the	DET
ejpam-5872	172	15	degree	degree	NOUN
ejpam-5872	172	16	of	of	ADP
ejpam-5872	172	17	both	both	PRON
ejpam-5872	172	18	iג	iג	NOUN
ejpam-5872	172	19	and	and	CCONJ
ejpam-5872	172	20	jג	jג	PROPN
ejpam-5872	172	21	,	,	PUNCT
ejpam-5872	172	22	each	each	DET
ejpam-5872	172	23	membership	membership	NOUN
ejpam-5872	172	24	value	value	VERB
ejpam-5872	172	25	µ(גi	µ(גi	NOUN
ejpam-5872	172	26	,	,	PUNCT
ejpam-5872	172	27	(	(	PUNCT
ejpam-5872	172	28	jג	jג	PROPN
ejpam-5872	172	29	is	be	AUX
ejpam-5872	172	30	counted	count	VERB
ejpam-5872	172	31	twice	twice	ADV
ejpam-5872	172	32	in	in	ADP
ejpam-5872	172	33	the	the	DET
ejpam-5872	172	34	above	above	ADJ
ejpam-5872	172	35	sum	sum	NOUN
ejpam-5872	172	36	.	.	PUNCT
ejpam-5872	173	1	therefore	therefore	ADV
ejpam-5872	173	2	,	,	PUNCT
ejpam-5872	173	3	∑	∑	ADV
ejpam-5872	173	4	ℑ∋ג	ℑ∋ג	ADP
ejpam-5872	173	5	d(ג	d(ג	PROPN
ejpam-5872	173	6	)	)	PUNCT
ejpam-5872	173	7	=	=	SYM
ejpam-5872	173	8	2	2	NUM
ejpam-5872	173	9	∑	∑	PUNCT
ejpam-5872	173	10	j∈ℑג	j∈ℑג	PROPN
ejpam-5872	173	11	,	,	PUNCT
ejpam-5872	173	12	iג	iג	ADP
ejpam-5872	173	13	i	i	PROPN
ejpam-5872	173	14	<	<	X
ejpam-5872	173	15	j	j	PROPN
ejpam-5872	173	16	µ(גi	µ(גi	PROPN
ejpam-5872	173	17	,	,	PUNCT
ejpam-5872	173	18	.(jג	.(jג	PROPN
ejpam-5872	173	19	that	that	ADV
ejpam-5872	173	20	is	is	ADV
ejpam-5872	173	21	,	,	PUNCT
ejpam-5872	173	22	the	the	DET
ejpam-5872	173	23	total	total	ADJ
ejpam-5872	173	24	degree	degree	NOUN
ejpam-5872	173	25	of	of	ADP
ejpam-5872	173	26	all	all	DET
ejpam-5872	173	27	vertices	vertex	NOUN
ejpam-5872	173	28	is	be	AUX
ejpam-5872	173	29	equal	equal	ADJ
ejpam-5872	173	30	to	to	ADP
ejpam-5872	173	31	twice	twice	DET
ejpam-5872	173	32	the	the	DET
ejpam-5872	173	33	total	total	ADJ
ejpam-5872	173	34	membership	membership	NOUN
ejpam-5872	173	35	value	value	NOUN
ejpam-5872	173	36	of	of	ADP
ejpam-5872	173	37	all	all	DET
ejpam-5872	173	38	arcs	arc	NOUN
ejpam-5872	173	39	in	in	ADP
ejpam-5872	173	40	σ±.	σ±.	PUNCT
ejpam-5872	173	41	theorem	theorem	VERB
ejpam-5872	173	42	4	4	NUM
ejpam-5872	173	43	.	.	PUNCT
ejpam-5872	174	1	a	a	DET
ejpam-5872	174	2	signed	sign	VERB
ejpam-5872	174	3	-	-	PUNCT
ejpam-5872	174	4	fg	fg	PROPN
ejpam-5872	174	5	∑	∑	PROPN
ejpam-5872	174	6	±.	±.	VERB
ejpam-5872	174	7	the	the	DET
ejpam-5872	174	8	sum	sum	NOUN
ejpam-5872	174	9	of	of	ADP
ejpam-5872	174	10	the	the	DET
ejpam-5872	174	11	strong	strong	ADJ
ejpam-5872	174	12	degrees	degree	NOUN
ejpam-5872	174	13	of	of	ADP
ejpam-5872	174	14	all	all	DET
ejpam-5872	174	15	vertex	vertex	NOUN
ejpam-5872	174	16	is	be	AUX
ejpam-5872	174	17	twice	twice	DET
ejpam-5872	174	18	the	the	DET
ejpam-5872	174	19	total	total	ADJ
ejpam-5872	174	20	membership	membership	NOUN
ejpam-5872	174	21	values	value	NOUN
ejpam-5872	174	22	of	of	ADP
ejpam-5872	174	23	all	all	DET
ejpam-5872	174	24	strong	strong	ADJ
ejpam-5872	174	25	edges	edge	NOUN
ejpam-5872	174	26	,	,	PUNCT
ejpam-5872	174	27	∑	∑	PUNCT
ejpam-5872	174	28	±	±	NUM
ejpam-5872	174	29	=	=	SYM
ejpam-5872	174	30	(	(	PUNCT
ejpam-5872	174	31	ℑ	ℑ	PROPN
ejpam-5872	174	32	,	,	PUNCT
ejpam-5872	174	33	σ	σ	PROPN
ejpam-5872	174	34	,	,	PUNCT
ejpam-5872	174	35	µ	µ	NOUN
ejpam-5872	174	36	)	)	PUNCT
ejpam-5872	174	37	.	.	PUNCT
ejpam-5872	175	1	proof	proof	NOUN
ejpam-5872	175	2	.	.	PUNCT
ejpam-5872	176	1	we	we	PRON
ejpam-5872	176	2	give	give	VERB
ejpam-5872	176	3	a	a	DET
ejpam-5872	176	4	formal	formal	ADJ
ejpam-5872	176	5	,	,	PUNCT
ejpam-5872	176	6	stepwise	stepwise	ADJ
ejpam-5872	176	7	argument	argument	NOUN
ejpam-5872	176	8	.	.	PUNCT
ejpam-5872	177	1	let	let	VERB
ejpam-5872	177	2	ℑ	ℑ	PROPN
ejpam-5872	177	3	=	=	PRON
ejpam-5872	177	4	,	,	PUNCT
ejpam-5872	177	5	1ג	1ג	NUM
ejpam-5872	177	6	}	}	PUNCT
ejpam-5872	177	7	.	.	PUNCT
ejpam-5872	177	8	.	.	PUNCT
ejpam-5872	178	1	.	.	PUNCT
ejpam-5872	179	1	,	,	PUNCT
ejpam-5872	179	2	.{nג	.{nג	PROPN
ejpam-5872	180	1	for	for	SCONJ
ejpam-5872	180	2	ordered	order	VERB
ejpam-5872	180	3	indices	index	NOUN
ejpam-5872	180	4	write	write	VERB
ejpam-5872	180	5	φij	φij	NOUN
ejpam-5872	180	6	=	=	SYM
ejpam-5872	180	7	µ(גi	µ(גi	NOUN
ejpam-5872	180	8	,	,	PUNCT
ejpam-5872	180	9	.(jג	.(jג	PROPN
ejpam-5872	180	10	denote	denote	VERB
ejpam-5872	180	11	by	by	ADP
ejpam-5872	180	12	s	s	PRON
ejpam-5872	180	13	the	the	DET
ejpam-5872	180	14	set	set	NOUN
ejpam-5872	180	15	of	of	ADP
ejpam-5872	180	16	unordered	unordered	ADJ
ejpam-5872	180	17	strong	strong	ADJ
ejpam-5872	180	18	edges	edge	NOUN
ejpam-5872	180	19	:	:	PUNCT
ejpam-5872	180	20	s	s	X
ejpam-5872	180	21	=	=	PUNCT
ejpam-5872	180	22	,	,	PUNCT
ejpam-5872	180	23	iג	iג	NOUN
ejpam-5872	180	24	}	}	PUNCT
ejpam-5872	180	25	}	}	PUNCT
ejpam-5872	180	26	{	{	PUNCT
ejpam-5872	180	27	jג	jג	NOUN
ejpam-5872	180	28	:	:	PUNCT
ejpam-5872	180	29	1	1	NUM
ejpam-5872	180	30	≤	≤	PUNCT
ejpam-5872	181	1	i	i	PRON
ejpam-5872	181	2	<	<	X
ejpam-5872	181	3	j	j	PROPN
ejpam-5872	181	4	≤	≤	PROPN
ejpam-5872	181	5	n	n	CCONJ
ejpam-5872	181	6	,	,	PUNCT
ejpam-5872	181	7	φij	φij	ADV
ejpam-5872	181	8	̸=	̸=	PROPN
ejpam-5872	181	9	0	0	NUM
ejpam-5872	181	10	}	}	PUNCT
ejpam-5872	181	11	.	.	PUNCT
ejpam-5872	182	1	for	for	ADP
ejpam-5872	182	2	each	each	DET
ejpam-5872	182	3	vertex	vertex	NOUN
ejpam-5872	182	4	iג	iג	ADP
ejpam-5872	182	5	the	the	DET
ejpam-5872	182	6	strong	strong	ADJ
ejpam-5872	182	7	degree	degree	NOUN
ejpam-5872	182	8	is	be	AUX
ejpam-5872	182	9	ds(גi	ds(גi	PROPN
ejpam-5872	182	10	)	)	PUNCT
ejpam-5872	183	1	=	=	PUNCT
ejpam-5872	184	1	n∑	n∑	NOUN
ejpam-5872	184	2	j=1,j	j=1,j	NOUN
ejpam-5872	184	3	̸=i	̸=i	INTJ
ejpam-5872	184	4	φij	φij	INTJ
ejpam-5872	184	5	,	,	PUNCT
ejpam-5872	184	6	where	where	SCONJ
ejpam-5872	184	7	the	the	DET
ejpam-5872	184	8	sum	sum	NOUN
ejpam-5872	184	9	ranges	range	VERB
ejpam-5872	184	10	only	only	ADV
ejpam-5872	184	11	over	over	ADP
ejpam-5872	184	12	j	j	PROPN
ejpam-5872	184	13	such	such	ADJ
ejpam-5872	184	14	that	that	PRON
ejpam-5872	184	15	,	,	PUNCT
ejpam-5872	184	16	iג	iג	NOUN
ejpam-5872	184	17	}	}	PUNCT
ejpam-5872	184	18	{	{	PUNCT
ejpam-5872	184	19	jג	jג	PROPN
ejpam-5872	184	20	∈	∈	PROPN
ejpam-5872	184	21	s	s	PART
ejpam-5872	184	22	(	(	PUNCT
ejpam-5872	184	23	and	and	CCONJ
ejpam-5872	184	24	φii	φii	NOUN
ejpam-5872	184	25	=	=	SYM
ejpam-5872	184	26	0	0	NUM
ejpam-5872	184	27	by	by	ADP
ejpam-5872	184	28	assumption	assumption	NOUN
ejpam-5872	184	29	)	)	PUNCT
ejpam-5872	184	30	.	.	PUNCT
ejpam-5872	185	1	c.	c.	PROPN
ejpam-5872	185	2	sankar	sankar	PROPN
ejpam-5872	185	3	et	et	PROPN
ejpam-5872	185	4	al	al	PROPN
ejpam-5872	185	5	.	.	PUNCT
ejpam-5872	185	6	/	/	SYM
ejpam-5872	185	7	eur	eur	PROPN
ejpam-5872	185	8	.	.	PUNCT
ejpam-5872	186	1	j.	j.	PROPN
ejpam-5872	186	2	pure	pure	PROPN
ejpam-5872	186	3	appl	appl	PROPN
ejpam-5872	186	4	.	.	PROPN
ejpam-5872	186	5	math	math	PROPN
ejpam-5872	186	6	,	,	PUNCT
ejpam-5872	186	7	18	18	NUM
ejpam-5872	186	8	(	(	PUNCT
ejpam-5872	186	9	4	4	NUM
ejpam-5872	186	10	)	)	PUNCT
ejpam-5872	186	11	(	(	PUNCT
ejpam-5872	186	12	2025	2025	NUM
ejpam-5872	186	13	)	)	PUNCT
ejpam-5872	186	14	,	,	PUNCT
ejpam-5872	186	15	5872	5872	NUM
ejpam-5872	186	16	8	8	NUM
ejpam-5872	186	17	of	of	ADP
ejpam-5872	186	18	17	17	NUM
ejpam-5872	186	19	summing	sum	VERB
ejpam-5872	186	20	over	over	ADP
ejpam-5872	186	21	all	all	DET
ejpam-5872	186	22	vertices	vertex	NOUN
ejpam-5872	186	23	yields	yield	NOUN
ejpam-5872	186	24	n∑	n∑	PROPN
ejpam-5872	186	25	i=1	i=1	PROPN
ejpam-5872	186	26	ds(גi	ds(גi	PROPN
ejpam-5872	186	27	)	)	PUNCT
ejpam-5872	187	1	=	=	PUNCT
ejpam-5872	187	2	n∑	n∑	NOUN
ejpam-5872	187	3	i=1	i=1	PROPN
ejpam-5872	188	1	n∑	n∑	PROPN
ejpam-5872	189	1	j=1	j=1	PROPN
ejpam-5872	190	1	j	j	PROPN
ejpam-5872	190	2	̸=i	̸=i	PROPN
ejpam-5872	190	3	φij	φij	INTJ
ejpam-5872	190	4	=	=	PUNCT
ejpam-5872	190	5	∑	∑	PUNCT
ejpam-5872	190	6	1≤i	1≤i	INTJ
ejpam-5872	190	7	,	,	PUNCT
ejpam-5872	190	8	j≤n	j≤n	PROPN
ejpam-5872	190	9	i̸=j	i̸=j	NOUN
ejpam-5872	190	10	φij	φij	VERB
ejpam-5872	190	11	.	.	PUNCT
ejpam-5872	191	1	by	by	ADP
ejpam-5872	191	2	symmetry	symmetry	NOUN
ejpam-5872	191	3	φij	φij	NOUN
ejpam-5872	191	4	=	=	PUNCT
ejpam-5872	191	5	φji	φji	PROPN
ejpam-5872	191	6	for	for	ADP
ejpam-5872	191	7	every	every	DET
ejpam-5872	191	8	i	i	PROPN
ejpam-5872	191	9	̸=	̸=	PROPN
ejpam-5872	191	10	j.	j.	PROPN
ejpam-5872	191	11	hence	hence	ADV
ejpam-5872	191	12	each	each	DET
ejpam-5872	191	13	unordered	unordered	ADJ
ejpam-5872	191	14	strong	strong	ADJ
ejpam-5872	191	15	edge	edge	NOUN
ejpam-5872	191	16	,	,	PUNCT
ejpam-5872	191	17	iג	iג	NOUN
ejpam-5872	191	18	}	}	PUNCT
ejpam-5872	191	19	{	{	PUNCT
ejpam-5872	191	20	jג	jג	PROPN
ejpam-5872	191	21	∈	∈	PROPN
ejpam-5872	191	22	s	s	PART
ejpam-5872	191	23	contributes	contribute	VERB
ejpam-5872	191	24	the	the	DET
ejpam-5872	191	25	two	two	NUM
ejpam-5872	191	26	equal	equal	ADJ
ejpam-5872	191	27	terms	term	NOUN
ejpam-5872	191	28	φij	φij	VERB
ejpam-5872	191	29	and	and	CCONJ
ejpam-5872	191	30	φji	φji	VERB
ejpam-5872	191	31	to	to	ADP
ejpam-5872	191	32	the	the	DET
ejpam-5872	191	33	double	double	ADJ
ejpam-5872	191	34	sum	sum	NOUN
ejpam-5872	191	35	.	.	PUNCT
ejpam-5872	192	1	therefore	therefore	ADV
ejpam-5872	192	2	∑	∑	ADV
ejpam-5872	192	3	1≤i	1≤i	INTJ
ejpam-5872	192	4	,	,	PUNCT
ejpam-5872	192	5	j≤n	j≤n	PROPN
ejpam-5872	192	6	i̸=j	i̸=j	PROPN
ejpam-5872	192	7	φij	φij	X
ejpam-5872	192	8	=	=	SYM
ejpam-5872	192	9	2	2	NUM
ejpam-5872	192	10	∑	∑	PUNCT
ejpam-5872	192	11	1≤i	1≤i	PROPN
ejpam-5872	192	12	<	<	X
ejpam-5872	192	13	j≤n	j≤n	NOUN
ejpam-5872	192	14	s∋{jג	s∋{jג	PROPN
ejpam-5872	192	15	,	,	PUNCT
ejpam-5872	192	16	iג	iג	NOUN
ejpam-5872	192	17	}	}	PUNCT
ejpam-5872	192	18	φij	φij	NOUN
ejpam-5872	193	1	=	=	SYM
ejpam-5872	193	2	2	2	NUM
ejpam-5872	193	3	∑	∑	PUNCT
ejpam-5872	193	4	1≤i	1≤i	PROPN
ejpam-5872	193	5	<	<	X
ejpam-5872	193	6	j≤n	j≤n	NOUN
ejpam-5872	193	7	φij	φij	NOUN
ejpam-5872	193	8	,	,	PUNCT
ejpam-5872	193	9	the	the	DET
ejpam-5872	193	10	latter	latter	ADJ
ejpam-5872	193	11	equality	equality	NOUN
ejpam-5872	193	12	since	since	SCONJ
ejpam-5872	193	13	φij	φij	NOUN
ejpam-5872	193	14	=	=	SYM
ejpam-5872	193	15	0	0	PUNCT
ejpam-5872	193	16	when	when	SCONJ
ejpam-5872	193	17	,	,	PUNCT
ejpam-5872	193	18	iג	iג	NOUN
ejpam-5872	193	19	}	}	PUNCT
ejpam-5872	193	20	{	{	PUNCT
ejpam-5872	193	21	jג	jג	PROPN
ejpam-5872	193	22	/∈	/∈	PUNCT
ejpam-5872	193	23	s.	s.	PROPN
ejpam-5872	193	24	combining	combine	VERB
ejpam-5872	193	25	the	the	DET
ejpam-5872	193	26	above	above	ADJ
ejpam-5872	193	27	gives	give	VERB
ejpam-5872	193	28	n∑	n∑	PROPN
ejpam-5872	193	29	i=1	i=1	PROPN
ejpam-5872	193	30	ds(גi	ds(גi	PROPN
ejpam-5872	193	31	)	)	PUNCT
ejpam-5872	194	1	=	=	SYM
ejpam-5872	194	2	2	2	NUM
ejpam-5872	194	3	∑	∑	PUNCT
ejpam-5872	194	4	1≤i	1≤i	NUM
ejpam-5872	194	5	<	<	X
ejpam-5872	194	6	j≤n	j≤n	NOUN
ejpam-5872	194	7	φij	φij	NOUN
ejpam-5872	194	8	,	,	PUNCT
ejpam-5872	194	9	which	which	PRON
ejpam-5872	194	10	is	be	AUX
ejpam-5872	194	11	the	the	DET
ejpam-5872	194	12	claimed	claim	VERB
ejpam-5872	194	13	identity	identity	NOUN
ejpam-5872	194	14	.	.	PUNCT
ejpam-5872	195	1	theorem	theorem	NOUN
ejpam-5872	195	2	5	5	NUM
ejpam-5872	195	3	.	.	PUNCT
ejpam-5872	196	1	in	in	ADP
ejpam-5872	196	2	a	a	DET
ejpam-5872	196	3	signed	sign	VERB
ejpam-5872	196	4	-	-	PUNCT
ejpam-5872	196	5	fg	fg	PRON
ejpam-5872	196	6	σ±	σ±	NOUN
ejpam-5872	196	7	=	=	SYM
ejpam-5872	196	8	(	(	PUNCT
ejpam-5872	196	9	ℑ	ℑ	PROPN
ejpam-5872	196	10	,	,	PUNCT
ejpam-5872	196	11	σ	σ	PROPN
ejpam-5872	196	12	,	,	PUNCT
ejpam-5872	196	13	µ	µ	NOUN
ejpam-5872	196	14	)	)	PUNCT
ejpam-5872	196	15	,	,	PUNCT
ejpam-5872	196	16	the	the	DET
ejpam-5872	196	17	sum	sum	NOUN
ejpam-5872	196	18	of	of	ADP
ejpam-5872	196	19	the	the	DET
ejpam-5872	196	20	effective	effective	ADJ
ejpam-5872	196	21	degrees	degree	NOUN
ejpam-5872	196	22	of	of	ADP
ejpam-5872	196	23	all	all	DET
ejpam-5872	196	24	nodes	node	NOUN
ejpam-5872	196	25	is	be	AUX
ejpam-5872	196	26	equal	equal	ADJ
ejpam-5872	196	27	to	to	ADP
ejpam-5872	196	28	twice	twice	DET
ejpam-5872	196	29	the	the	DET
ejpam-5872	196	30	total	total	ADJ
ejpam-5872	196	31	membership	membership	NOUN
ejpam-5872	196	32	value	value	NOUN
ejpam-5872	196	33	of	of	ADP
ejpam-5872	196	34	all	all	DET
ejpam-5872	196	35	effective	effective	ADJ
ejpam-5872	196	36	arcs	arc	NOUN
ejpam-5872	196	37	.	.	PUNCT
ejpam-5872	197	1	that	that	PRON
ejpam-5872	197	2	is	be	AUX
ejpam-5872	197	3	,	,	PUNCT
ejpam-5872	197	4	∑	∑	ADV
ejpam-5872	197	5	ℑ∋ג	ℑ∋ג	PROPN
ejpam-5872	197	6	d±(ג	d±(ג	PROPN
ejpam-5872	197	7	)	)	PUNCT
ejpam-5872	197	8	=	=	SYM
ejpam-5872	197	9	2	2	NUM
ejpam-5872	197	10	∑	∑	NOUN
ejpam-5872	197	11	ℑ⊇{2ג,1ג	ℑ⊇{2ג,1ג	NOUN
ejpam-5872	197	12	}	}	PUNCT
ejpam-5872	197	13	µ(1ג	µ(1ג	NUM
ejpam-5872	197	14	,	,	PUNCT
ejpam-5872	197	15	,	,	PUNCT
ejpam-5872	197	16	(	(	PUNCT
ejpam-5872	197	17	2ג	2ג	NUM
ejpam-5872	197	18	where	where	SCONJ
ejpam-5872	197	19	the	the	DET
ejpam-5872	197	20	effective	effective	ADJ
ejpam-5872	197	21	degree	degree	NOUN
ejpam-5872	197	22	of	of	ADP
ejpam-5872	197	23	a	a	DET
ejpam-5872	197	24	vertex	vertex	NOUN
ejpam-5872	197	25	ג	ג	ADP
ejpam-5872	197	26	∈	∈	NOUN
ejpam-5872	197	27	ℑ	ℑ	PROPN
ejpam-5872	197	28	is	be	AUX
ejpam-5872	197	29	defined	define	VERB
ejpam-5872	197	30	as	as	ADP
ejpam-5872	197	31	d±(ג	d±(ג	PROPN
ejpam-5872	197	32	)	)	PUNCT
ejpam-5872	197	33	=	=	PUNCT
ejpam-5872	197	34	∑	∑	PUNCT
ejpam-5872	197	35	i∈ℑג	i∈ℑג	VERB
ejpam-5872	197	36	iג	iג	ADP
ejpam-5872	197	37	ג≠	ג≠	PROPN
ejpam-5872	197	38	µ(ג	µ(ג	NOUN
ejpam-5872	197	39	,	,	PUNCT
ejpam-5872	197	40	.(iג	.(iג	PROPN
ejpam-5872	197	41	2	2	NUM
ejpam-5872	197	42	.	.	X
ejpam-5872	197	43	domination	domination	NOUN
ejpam-5872	197	44	of	of	ADP
ejpam-5872	197	45	signed	sign	VERB
ejpam-5872	197	46	fuzzy	fuzzy	ADJ
ejpam-5872	197	47	graphs	graph	NOUN
ejpam-5872	197	48	in	in	ADP
ejpam-5872	197	49	this	this	DET
ejpam-5872	197	50	section	section	NOUN
ejpam-5872	197	51	,	,	PUNCT
ejpam-5872	197	52	we	we	PRON
ejpam-5872	197	53	delve	delve	VERB
ejpam-5872	197	54	into	into	ADP
ejpam-5872	197	55	the	the	DET
ejpam-5872	197	56	theoretical	theoretical	ADJ
ejpam-5872	197	57	foundations	foundation	NOUN
ejpam-5872	197	58	of	of	ADP
ejpam-5872	197	59	signed	sign	VERB
ejpam-5872	197	60	fuzzy	fuzzy	ADJ
ejpam-5872	197	61	graphs	graph	NOUN
ejpam-5872	197	62	(	(	PUNCT
ejpam-5872	197	63	signedfgs	signedfgs	NOUN
ejpam-5872	197	64	)	)	PUNCT
ejpam-5872	197	65	,	,	PUNCT
ejpam-5872	197	66	emphasizing	emphasize	VERB
ejpam-5872	197	67	key	key	ADJ
ejpam-5872	197	68	concepts	concept	NOUN
ejpam-5872	197	69	such	such	ADJ
ejpam-5872	197	70	as	as	ADP
ejpam-5872	197	71	domination	domination	NOUN
ejpam-5872	197	72	sets	set	NOUN
ejpam-5872	197	73	and	and	CCONJ
ejpam-5872	197	74	the	the	DET
ejpam-5872	197	75	properties	property	NOUN
ejpam-5872	197	76	that	that	PRON
ejpam-5872	197	77	govern	govern	VERB
ejpam-5872	197	78	their	their	PRON
ejpam-5872	197	79	behavior	behavior	NOUN
ejpam-5872	197	80	.	.	PUNCT
ejpam-5872	198	1	critical	critical	ADJ
ejpam-5872	198	2	terminology	terminology	NOUN
ejpam-5872	198	3	relevant	relevant	ADJ
ejpam-5872	198	4	to	to	ADP
ejpam-5872	198	5	understanding	understand	VERB
ejpam-5872	198	6	the	the	DET
ejpam-5872	198	7	dynamics	dynamic	NOUN
ejpam-5872	198	8	of	of	ADP
ejpam-5872	198	9	interactions	interaction	NOUN
ejpam-5872	198	10	within	within	ADP
ejpam-5872	198	11	signed	sign	VERB
ejpam-5872	198	12	-	-	PUNCT
ejpam-5872	198	13	fgs	fgs	NOUN
ejpam-5872	198	14	,	,	PUNCT
ejpam-5872	198	15	including	include	VERB
ejpam-5872	198	16	the	the	DET
ejpam-5872	198	17	strong	strong	ADJ
ejpam-5872	198	18	domination	domination	NOUN
ejpam-5872	198	19	number	number	NOUN
ejpam-5872	198	20	and	and	CCONJ
ejpam-5872	198	21	effective	effective	ADJ
ejpam-5872	198	22	degrees	degree	NOUN
ejpam-5872	198	23	of	of	ADP
ejpam-5872	198	24	nodes	node	NOUN
ejpam-5872	198	25	,	,	PUNCT
ejpam-5872	198	26	is	be	AUX
ejpam-5872	198	27	clearly	clearly	ADV
ejpam-5872	198	28	defined	define	VERB
ejpam-5872	198	29	.	.	PUNCT
ejpam-5872	199	1	by	by	ADP
ejpam-5872	199	2	presenting	present	VERB
ejpam-5872	199	3	key	key	ADJ
ejpam-5872	199	4	theorems	theorem	NOUN
ejpam-5872	199	5	and	and	CCONJ
ejpam-5872	199	6	assertions	assertion	NOUN
ejpam-5872	199	7	,	,	PUNCT
ejpam-5872	199	8	we	we	PRON
ejpam-5872	199	9	establish	establish	VERB
ejpam-5872	199	10	a	a	DET
ejpam-5872	199	11	structured	structured	ADJ
ejpam-5872	199	12	framework	framework	NOUN
ejpam-5872	199	13	for	for	ADP
ejpam-5872	199	14	studying	study	VERB
ejpam-5872	199	15	domination	domination	NOUN
ejpam-5872	199	16	in	in	ADP
ejpam-5872	199	17	these	these	DET
ejpam-5872	199	18	fuzzy	fuzzy	ADJ
ejpam-5872	199	19	graphs	graph	NOUN
ejpam-5872	199	20	,	,	PUNCT
ejpam-5872	199	21	paving	pave	VERB
ejpam-5872	199	22	the	the	DET
ejpam-5872	199	23	way	way	NOUN
ejpam-5872	199	24	for	for	ADP
ejpam-5872	199	25	investigating	investigate	VERB
ejpam-5872	199	26	their	their	PRON
ejpam-5872	199	27	applications	application	NOUN
ejpam-5872	199	28	in	in	ADP
ejpam-5872	199	29	complex	complex	ADJ
ejpam-5872	199	30	network	network	NOUN
ejpam-5872	199	31	systems	system	NOUN
ejpam-5872	199	32	.	.	PUNCT
ejpam-5872	200	1	definition	definition	NOUN
ejpam-5872	200	2	10	10	NUM
ejpam-5872	200	3	.	.	PUNCT
ejpam-5872	201	1	let	let	VERB
ejpam-5872	201	2	σ±	σ±	NOUN
ejpam-5872	201	3	=	=	SYM
ejpam-5872	201	4	(	(	PUNCT
ejpam-5872	201	5	ℑ	ℑ	PROPN
ejpam-5872	201	6	,	,	PUNCT
ejpam-5872	201	7	σ	σ	PROPN
ejpam-5872	201	8	,	,	PUNCT
ejpam-5872	201	9	µ	µ	NOUN
ejpam-5872	201	10	)	)	PUNCT
ejpam-5872	201	11	be	be	VERB
ejpam-5872	201	12	a	a	DET
ejpam-5872	201	13	signed	sign	VERB
ejpam-5872	201	14	-	-	PUNCT
ejpam-5872	201	15	fg	fg	NOUN
ejpam-5872	201	16	,	,	PUNCT
ejpam-5872	201	17	and	and	CCONJ
ejpam-5872	201	18	let	let	VERB
ejpam-5872	201	19	,	,	PUNCT
ejpam-5872	201	20	1ג	1ג	NUM
ejpam-5872	201	21	2ג	2ג	NOUN
ejpam-5872	201	22	∈	∈	ADJ
ejpam-5872	201	23	ℑ.	ℑ.	NOUN
ejpam-5872	201	24	we	we	PRON
ejpam-5872	201	25	say	say	VERB
ejpam-5872	201	26	that	that	SCONJ
ejpam-5872	201	27	1ג	1ג	NOUN
ejpam-5872	201	28	dominates	dominate	VERB
ejpam-5872	201	29	2ג	2ג	NUM
ejpam-5872	201	30	in	in	ADP
ejpam-5872	201	31	σ±	σ±	NOUN
ejpam-5872	201	32	if	if	SCONJ
ejpam-5872	201	33	the	the	DET
ejpam-5872	201	34	ordered	order	VERB
ejpam-5872	201	35	pair	pair	NOUN
ejpam-5872	201	36	,	,	PUNCT
ejpam-5872	201	37	1ג	1ג	NUM
ejpam-5872	201	38	)	)	PUNCT
ejpam-5872	201	39	(	(	PUNCT
ejpam-5872	201	40	2ג	2ג	NOUN
ejpam-5872	201	41	is	be	AUX
ejpam-5872	201	42	a	a	DET
ejpam-5872	201	43	strong	strong	ADJ
ejpam-5872	201	44	arc	arc	NOUN
ejpam-5872	201	45	of	of	ADP
ejpam-5872	201	46	σ±.	σ±.	X
ejpam-5872	201	47	a	a	DET
ejpam-5872	201	48	subset	subset	NOUN
ejpam-5872	201	49	d	d	X
ejpam-5872	201	50	⊆	⊆	NUM
ejpam-5872	201	51	ℑ	ℑ	PROPN
ejpam-5872	201	52	is	be	AUX
ejpam-5872	201	53	a	a	DET
ejpam-5872	201	54	domination	domination	NOUN
ejpam-5872	201	55	set	set	NOUN
ejpam-5872	201	56	of	of	ADP
ejpam-5872	201	57	σ±	σ±	NOUN
ejpam-5872	201	58	if	if	SCONJ
ejpam-5872	201	59	∀	∀	NOUN
ejpam-5872	201	60	2ג	2ג	NUM
ejpam-5872	201	61	∈	∈	PROPN
ejpam-5872	201	62	ℑ−d	ℑ−d	PROPN
ejpam-5872	201	63	,	,	PUNCT
ejpam-5872	201	64	∃	∃	PROPN
ejpam-5872	201	65	1ג	1ג	NUM
ejpam-5872	201	66	∈	∈	PROPN
ejpam-5872	201	67	d	d	NOUN
ejpam-5872	201	68	,	,	PUNCT
ejpam-5872	201	69	such	such	ADJ
ejpam-5872	201	70	that	that	SCONJ
ejpam-5872	201	71	,	,	PUNCT
ejpam-5872	201	72	1ג	1ג	NUM
ejpam-5872	201	73	)	)	PUNCT
ejpam-5872	201	74	(	(	PUNCT
ejpam-5872	201	75	2ג	2ג	NOUN
ejpam-5872	201	76	is	be	AUX
ejpam-5872	201	77	a	a	DET
ejpam-5872	201	78	strong	strong	ADJ
ejpam-5872	201	79	arc	arc	NOUN
ejpam-5872	201	80	of	of	ADP
ejpam-5872	201	81	σ±.	σ±.	NOUN
ejpam-5872	201	82	definition	definition	NOUN
ejpam-5872	201	83	11	11	NUM
ejpam-5872	201	84	.	.	PUNCT
ejpam-5872	202	1	let	let	VERB
ejpam-5872	202	2	σ±	σ±	NOUN
ejpam-5872	202	3	=	=	SYM
ejpam-5872	202	4	(	(	PUNCT
ejpam-5872	202	5	ℑ	ℑ	PROPN
ejpam-5872	202	6	,	,	PUNCT
ejpam-5872	202	7	σ	σ	PROPN
ejpam-5872	202	8	,	,	PUNCT
ejpam-5872	202	9	µ	µ	NOUN
ejpam-5872	202	10	)	)	PUNCT
ejpam-5872	202	11	be	be	VERB
ejpam-5872	202	12	a	a	DET
ejpam-5872	202	13	signed	sign	VERB
ejpam-5872	202	14	-	-	PUNCT
ejpam-5872	202	15	fg	fg	NOUN
ejpam-5872	202	16	.	.	PUNCT
ejpam-5872	203	1	a	a	DET
ejpam-5872	203	2	domination	domination	NOUN
ejpam-5872	203	3	set	set	VERB
ejpam-5872	203	4	d	d	PROPN
ejpam-5872	203	5	⊆	⊆	NUM
ejpam-5872	203	6	ℑ	ℑ	PROPN
ejpam-5872	203	7	is	be	AUX
ejpam-5872	203	8	called	call	VERB
ejpam-5872	203	9	a	a	DET
ejpam-5872	203	10	minimum	minimum	ADJ
ejpam-5872	203	11	domination	domination	NOUN
ejpam-5872	203	12	set	set	VERB
ejpam-5872	203	13	if	if	SCONJ
ejpam-5872	203	14	no	no	DET
ejpam-5872	203	15	proper	proper	ADJ
ejpam-5872	203	16	subset	subset	NOUN
ejpam-5872	203	17	of	of	ADP
ejpam-5872	203	18	d	d	PROPN
ejpam-5872	203	19	is	be	AUX
ejpam-5872	203	20	also	also	ADV
ejpam-5872	203	21	a	a	DET
ejpam-5872	203	22	domination	domination	NOUN
ejpam-5872	203	23	set	set	NOUN
ejpam-5872	203	24	of	of	ADP
ejpam-5872	203	25	σ±.	σ±.	PUNCT
ejpam-5872	203	26	the	the	DET
ejpam-5872	203	27	domination	domination	NOUN
ejpam-5872	203	28	number	number	NOUN
ejpam-5872	203	29	of	of	ADP
ejpam-5872	203	30	σ±	σ±	NOUN
ejpam-5872	203	31	,	,	PUNCT
ejpam-5872	203	32	denoted	denote	VERB
ejpam-5872	203	33	γ(σ±	γ(σ±	NOUN
ejpam-5872	203	34	)	)	PUNCT
ejpam-5872	203	35	,	,	PUNCT
ejpam-5872	203	36	is	be	AUX
ejpam-5872	203	37	defined	define	VERB
ejpam-5872	203	38	as	as	ADP
ejpam-5872	203	39	γ(σ±	γ(σ±	NOUN
ejpam-5872	203	40	)	)	PUNCT
ejpam-5872	203	41	=	=	SYM
ejpam-5872	203	42	min	min	X
ejpam-5872	203	43	{	{	PUNCT
ejpam-5872	203	44	|d|	|d|	NOUN
ejpam-5872	203	45	:	:	PUNCT
ejpam-5872	204	1	d	d	X
ejpam-5872	204	2	is	be	AUX
ejpam-5872	204	3	a	a	DET
ejpam-5872	204	4	domination	domination	NOUN
ejpam-5872	204	5	set	set	NOUN
ejpam-5872	204	6	of	of	ADP
ejpam-5872	204	7	σ±	σ±	NOUN
ejpam-5872	204	8	}	}	PUNCT
ejpam-5872	204	9	.	.	PUNCT
ejpam-5872	205	1	any	any	DET
ejpam-5872	205	2	domination	domination	NOUN
ejpam-5872	205	3	set	set	VERB
ejpam-5872	205	4	d	d	PROPN
ejpam-5872	205	5	of	of	ADP
ejpam-5872	205	6	size	size	NOUN
ejpam-5872	205	7	|d|	|d|	PROPN
ejpam-5872	205	8	=	=	PUNCT
ejpam-5872	205	9	γ(σ±	γ(σ±	PROPN
ejpam-5872	205	10	)	)	PUNCT
ejpam-5872	205	11	is	be	AUX
ejpam-5872	205	12	called	call	VERB
ejpam-5872	205	13	a	a	DET
ejpam-5872	205	14	minimum	minimum	ADJ
ejpam-5872	205	15	domination	domination	NOUN
ejpam-5872	205	16	set	set	NOUN
ejpam-5872	205	17	.	.	PUNCT
ejpam-5872	205	18	example	example	NOUN
ejpam-5872	206	1	7	7	X
ejpam-5872	206	2	.	.	X
ejpam-5872	206	3	consider	consider	VERB
ejpam-5872	206	4	the	the	DET
ejpam-5872	206	5	signed	sign	VERB
ejpam-5872	206	6	-	-	PUNCT
ejpam-5872	206	7	fg	fg	PRON
ejpam-5872	206	8	σ±	σ±	NOUN
ejpam-5872	206	9	=	=	SYM
ejpam-5872	206	10	(	(	PUNCT
ejpam-5872	206	11	ℑ	ℑ	PROPN
ejpam-5872	206	12	,	,	PUNCT
ejpam-5872	206	13	σ	σ	PROPN
ejpam-5872	206	14	,	,	PUNCT
ejpam-5872	206	15	µ	µ	NOUN
ejpam-5872	206	16	)	)	PUNCT
ejpam-5872	206	17	with	with	ADP
ejpam-5872	206	18	vertex	vertex	NOUN
ejpam-5872	206	19	set	set	VERB
ejpam-5872	206	20	ℑ	ℑ	PROPN
ejpam-5872	206	21	=	=	PRON
ejpam-5872	206	22	,	,	PUNCT
ejpam-5872	206	23	1ג	1ג	NUM
ejpam-5872	206	24	}	}	PUNCT
ejpam-5872	206	25	,	,	PUNCT
ejpam-5872	206	26	2ג	2ג	NUM
ejpam-5872	206	27	,	,	PUNCT
ejpam-5872	206	28	3ג	3ג	NUM
ejpam-5872	206	29	,	,	PUNCT
ejpam-5872	206	30	4ג	4ג	NOUN
ejpam-5872	206	31	{	{	PUNCT
ejpam-5872	206	32	5ג	5ג	NOUN
ejpam-5872	206	33	and	and	CCONJ
ejpam-5872	206	34	edge	edge	NOUN
ejpam-5872	206	35	set	set	VERB
ejpam-5872	206	36	e	e	NOUN
ejpam-5872	206	37	=	=	PRON
ejpam-5872	206	38	,	,	PUNCT
ejpam-5872	206	39	1ג	1ג	NUM
ejpam-5872	206	40	)	)	PUNCT
ejpam-5872	206	41	}	}	PUNCT
ejpam-5872	206	42	,	,	PUNCT
ejpam-5872	206	43	(	(	PUNCT
ejpam-5872	206	44	2ג	2ג	NOUN
ejpam-5872	206	45	,	,	PUNCT
ejpam-5872	206	46	2ג	2ג	NUM
ejpam-5872	206	47	)	)	PUNCT
ejpam-5872	206	48	,	,	PUNCT
ejpam-5872	206	49	(	(	PUNCT
ejpam-5872	206	50	3ג	3ג	NUM
ejpam-5872	206	51	,	,	PUNCT
ejpam-5872	206	52	2ג	2ג	NUM
ejpam-5872	206	53	)	)	PUNCT
ejpam-5872	206	54	,	,	PUNCT
ejpam-5872	206	55	(	(	PUNCT
ejpam-5872	206	56	4ג	4ג	NOUN
ejpam-5872	206	57	,	,	PUNCT
ejpam-5872	206	58	4ג	4ג	PROPN
ejpam-5872	206	59	)	)	PUNCT
ejpam-5872	206	60	,	,	PUNCT
ejpam-5872	206	61	(	(	PUNCT
ejpam-5872	206	62	5ג	5ג	NOUN
ejpam-5872	206	63	,	,	PUNCT
ejpam-5872	206	64	1ג	1ג	NUM
ejpam-5872	206	65	)	)	PUNCT
ejpam-5872	206	66	,	,	PUNCT
ejpam-5872	206	67	(	(	PUNCT
ejpam-5872	206	68	5ג	5ג	NOUN
ejpam-5872	206	69	,	,	PUNCT
ejpam-5872	206	70	2ג	2ג	NUM
ejpam-5872	206	71	)	)	PUNCT
ejpam-5872	206	72	.{(5ג	.{(5ג	NOUN
ejpam-5872	207	1	the	the	DET
ejpam-5872	207	2	vertex	vertex	NOUN
ejpam-5872	207	3	membership	membership	NOUN
ejpam-5872	207	4	values	value	NOUN
ejpam-5872	207	5	are	be	AUX
ejpam-5872	207	6	σ(1ג	σ(1ג	NOUN
ejpam-5872	207	7	)	)	PUNCT
ejpam-5872	207	8	=	=	SYM
ejpam-5872	208	1	−0.3	−0.3	NOUN
ejpam-5872	208	2	,	,	PUNCT
ejpam-5872	208	3	σ(2ג	σ(2ג	NUM
ejpam-5872	208	4	)	)	PUNCT
ejpam-5872	208	5	=	=	SYM
ejpam-5872	208	6	0.4	0.4	NUM
ejpam-5872	208	7	,	,	PUNCT
ejpam-5872	208	8	σ(3ג	σ(3ג	NUM
ejpam-5872	208	9	)	)	PUNCT
ejpam-5872	208	10	=	=	SYM
ejpam-5872	208	11	−0.3	−0.3	NOUN
ejpam-5872	208	12	,	,	PUNCT
ejpam-5872	208	13	σ(4ג	σ(4ג	NOUN
ejpam-5872	208	14	)	)	PUNCT
ejpam-5872	208	15	=	=	NUM
ejpam-5872	208	16	0.5	0.5	NUM
ejpam-5872	208	17	,	,	PUNCT
ejpam-5872	208	18	σ(5ג	σ(5ג	NUM
ejpam-5872	208	19	)	)	PUNCT
ejpam-5872	208	20	=	=	SYM
ejpam-5872	208	21	0.2	0.2	NUM
ejpam-5872	208	22	.	.	PUNCT
ejpam-5872	209	1	the	the	DET
ejpam-5872	209	2	c.	c.	PROPN
ejpam-5872	209	3	sankar	sankar	PROPN
ejpam-5872	209	4	et	et	PROPN
ejpam-5872	209	5	al	al	PROPN
ejpam-5872	209	6	.	.	PUNCT
ejpam-5872	209	7	/	/	SYM
ejpam-5872	209	8	eur	eur	PROPN
ejpam-5872	209	9	.	.	PUNCT
ejpam-5872	210	1	j.	j.	PROPN
ejpam-5872	210	2	pure	pure	PROPN
ejpam-5872	210	3	appl	appl	PROPN
ejpam-5872	210	4	.	.	PROPN
ejpam-5872	210	5	math	math	PROPN
ejpam-5872	210	6	,	,	PUNCT
ejpam-5872	210	7	18	18	NUM
ejpam-5872	210	8	(	(	PUNCT
ejpam-5872	210	9	4	4	NUM
ejpam-5872	210	10	)	)	PUNCT
ejpam-5872	210	11	(	(	PUNCT
ejpam-5872	210	12	2025	2025	NUM
ejpam-5872	210	13	)	)	PUNCT
ejpam-5872	210	14	,	,	PUNCT
ejpam-5872	210	15	5872	5872	NUM
ejpam-5872	210	16	9	9	NUM
ejpam-5872	210	17	of	of	ADP
ejpam-5872	210	18	17	17	NUM
ejpam-5872	210	19	edge	edge	NOUN
ejpam-5872	210	20	membership	membership	NOUN
ejpam-5872	210	21	values	value	NOUN
ejpam-5872	210	22	are	be	AUX
ejpam-5872	210	23	µ(1ג	µ(1ג	NOUN
ejpam-5872	210	24	,	,	PUNCT
ejpam-5872	210	25	(	(	PUNCT
ejpam-5872	210	26	2ג	2ג	NOUN
ejpam-5872	210	27	=	=	SYM
ejpam-5872	210	28	−0.4	−0.4	NUM
ejpam-5872	210	29	,	,	PUNCT
ejpam-5872	210	30	µ(1ג	µ(1ג	NUM
ejpam-5872	210	31	,	,	PUNCT
ejpam-5872	210	32	(	(	PUNCT
ejpam-5872	210	33	5ג	5ג	NOUN
ejpam-5872	210	34	=	=	SYM
ejpam-5872	210	35	−0.3	−0.3	PROPN
ejpam-5872	210	36	,	,	PUNCT
ejpam-5872	210	37	µ(2ג	µ(2ג	VERB
ejpam-5872	210	38	,	,	PUNCT
ejpam-5872	210	39	(	(	PUNCT
ejpam-5872	210	40	4ג	4ג	NOUN
ejpam-5872	210	41	=	=	SYM
ejpam-5872	210	42	0.4	0.4	NUM
ejpam-5872	210	43	,	,	PUNCT
ejpam-5872	210	44	µ(2ג	µ(2ג	VERB
ejpam-5872	210	45	,	,	PUNCT
ejpam-5872	210	46	(	(	PUNCT
ejpam-5872	210	47	3ג	3ג	NUM
ejpam-5872	210	48	=	=	SYM
ejpam-5872	210	49	−0.3	−0.3	PROPN
ejpam-5872	210	50	,	,	PUNCT
ejpam-5872	210	51	µ(2ג	µ(2ג	VERB
ejpam-5872	210	52	,	,	PUNCT
ejpam-5872	210	53	(	(	PUNCT
ejpam-5872	210	54	5ג	5ג	NOUN
ejpam-5872	210	55	=	=	SYM
ejpam-5872	210	56	0.2	0.2	NUM
ejpam-5872	210	57	,	,	PUNCT
ejpam-5872	210	58	µ(4ג	µ(4ג	PROPN
ejpam-5872	210	59	,	,	PUNCT
ejpam-5872	210	60	(	(	PUNCT
ejpam-5872	210	61	5ג	5ג	NOUN
ejpam-5872	210	62	=	=	NOUN
ejpam-5872	210	63	0.1	0.1	NUM
ejpam-5872	210	64	.	.	PUNCT
ejpam-5872	211	1	the	the	DET
ejpam-5872	211	2	strong	strong	ADJ
ejpam-5872	211	3	arcs	arc	NOUN
ejpam-5872	211	4	in	in	ADP
ejpam-5872	211	5	σ±	σ±	NOUN
ejpam-5872	211	6	are	be	AUX
ejpam-5872	211	7	,	,	PUNCT
ejpam-5872	211	8	1ג	1ג	NUM
ejpam-5872	211	9	)	)	PUNCT
ejpam-5872	211	10	,	,	PUNCT
ejpam-5872	211	11	(	(	PUNCT
ejpam-5872	211	12	5ג	5ג	NOUN
ejpam-5872	211	13	,	,	PUNCT
ejpam-5872	211	14	2ג	2ג	NUM
ejpam-5872	211	15	)	)	PUNCT
ejpam-5872	211	16	,	,	PUNCT
ejpam-5872	211	17	(	(	PUNCT
ejpam-5872	211	18	5ג	5ג	NOUN
ejpam-5872	211	19	,	,	PUNCT
ejpam-5872	211	20	2ג	2ג	NUM
ejpam-5872	211	21	)	)	PUNCT
ejpam-5872	211	22	,	,	PUNCT
ejpam-5872	211	23	(	(	PUNCT
ejpam-5872	211	24	4ג	4ג	NOUN
ejpam-5872	211	25	,	,	PUNCT
ejpam-5872	211	26	2ג	2ג	NUM
ejpam-5872	211	27	)	)	PUNCT
ejpam-5872	211	28	.(3ג	.(3ג	PUNCT
ejpam-5872	211	29	possible	possible	ADJ
ejpam-5872	211	30	dominating	dominating	NOUN
ejpam-5872	211	31	sets	set	NOUN
ejpam-5872	211	32	include	include	VERB
ejpam-5872	211	33	,	,	PUNCT
ejpam-5872	211	34	1ג	1ג	NOUN
ejpam-5872	211	35	}	}	PUNCT
ejpam-5872	211	36	,	,	PUNCT
ejpam-5872	211	37	{	{	PUNCT
ejpam-5872	211	38	2ג	2ג	NOUN
ejpam-5872	211	39	,	,	PUNCT
ejpam-5872	211	40	2ג	2ג	NOUN
ejpam-5872	211	41	}	}	PUNCT
ejpam-5872	211	42	,	,	PUNCT
ejpam-5872	211	43	{	{	PUNCT
ejpam-5872	211	44	5ג	5ג	NOUN
ejpam-5872	211	45	,	,	PUNCT
ejpam-5872	211	46	1ג	1ג	NUM
ejpam-5872	211	47	}	}	PUNCT
ejpam-5872	211	48	,	,	PUNCT
ejpam-5872	211	49	3ג	3ג	NUM
ejpam-5872	211	50	,	,	PUNCT
ejpam-5872	211	51	{	{	PUNCT
ejpam-5872	211	52	4ג	4ג	NOUN
ejpam-5872	211	53	,	,	PUNCT
ejpam-5872	211	54	3ג	3ג	NOUN
ejpam-5872	211	55	}	}	PUNCT
ejpam-5872	211	56	,	,	PUNCT
ejpam-5872	211	57	4ג	4ג	NOUN
ejpam-5872	211	58	.{5ג	.{5ג	X
ejpam-5872	212	1	among	among	ADP
ejpam-5872	212	2	these	these	PRON
ejpam-5872	212	3	,	,	PUNCT
ejpam-5872	212	4	the	the	DET
ejpam-5872	212	5	smallest	small	ADJ
ejpam-5872	212	6	domination	domination	NOUN
ejpam-5872	212	7	set	set	NOUN
ejpam-5872	212	8	is	be	AUX
ejpam-5872	212	9	,	,	PUNCT
ejpam-5872	212	10	1ג	1ג	NUM
ejpam-5872	212	11	}	}	PUNCT
ejpam-5872	212	12	,	,	PUNCT
ejpam-5872	212	13	3ג	3ג	NUM
ejpam-5872	212	14	.{4ג	.{4ג	PUNCT
ejpam-5872	213	1	therefore	therefore	ADV
ejpam-5872	213	2	,	,	PUNCT
ejpam-5872	213	3	the	the	DET
ejpam-5872	213	4	domination	domination	NOUN
ejpam-5872	213	5	number	number	NOUN
ejpam-5872	213	6	of	of	ADP
ejpam-5872	213	7	σ±	σ±	NOUN
ejpam-5872	213	8	is	be	AUX
ejpam-5872	213	9	γ(σ±	γ(σ±	NOUN
ejpam-5872	213	10	)	)	PUNCT
ejpam-5872	213	11	=	=	X
ejpam-5872	213	12	min{|d|	min{|d|	NOUN
ejpam-5872	213	13	:	:	PUNCT
ejpam-5872	214	1	d	d	PRON
ejpam-5872	214	2	is	be	AUX
ejpam-5872	214	3	a	a	DET
ejpam-5872	214	4	domination	domination	NOUN
ejpam-5872	214	5	set	set	NOUN
ejpam-5872	214	6	of	of	ADP
ejpam-5872	214	7	σ±	σ±	NOUN
ejpam-5872	214	8	}	}	PUNCT
ejpam-5872	214	9	=	=	SYM
ejpam-5872	214	10	3	3	X
ejpam-5872	214	11	.	.	PUNCT
ejpam-5872	215	1	(	(	PUNCT
ejpam-5872	215	2	0.3−)1ג	0.3−)1ג	NUM
ejpam-5872	215	3	(	(	PUNCT
ejpam-5872	215	4	0.2)5ג	0.2)5ג	NUM
ejpam-5872	215	5	(	(	PUNCT
ejpam-5872	215	6	0.5)4ג	0.5)4ג	NOUN
ejpam-5872	215	7	(	(	PUNCT
ejpam-5872	215	8	0.4)2ג	0.4)2ג	NUM
ejpam-5872	215	9	(	(	PUNCT
ejpam-5872	215	10	0.3−)3ג	0.3−)3ג	NOUN
ejpam-5872	215	11	0.1	0.1	NUM
ejpam-5872	215	12	−0.4	−0.4	NUM
ejpam-5872	215	13	0	0	NUM
ejpam-5872	215	14	.	.	NOUN
ejpam-5872	215	15	2	2	NUM
ejpam-5872	215	16	−	−	NOUN
ejpam-5872	215	17	0	0	NUM
ejpam-5872	215	18	.	.	NOUN
ejpam-5872	215	19	3	3	NUM
ejpam-5872	215	20	−0.3	−0.3	PROPN
ejpam-5872	215	21	0	0	NUM
ejpam-5872	215	22	.	.	X
ejpam-5872	215	23	4	4	NUM
ejpam-5872	215	24	figure	figure	NOUN
ejpam-5872	215	25	2	2	NUM
ejpam-5872	215	26	:	:	PUNCT
ejpam-5872	215	27	domination	domination	NOUN
ejpam-5872	215	28	in	in	ADP
ejpam-5872	215	29	a	a	DET
ejpam-5872	215	30	signed	sign	VERB
ejpam-5872	215	31	-	-	PUNCT
ejpam-5872	215	32	fg	fg	PRON
ejpam-5872	215	33	example	example	NOUN
ejpam-5872	215	34	.	.	PUNCT
ejpam-5872	216	1	definition	definition	NOUN
ejpam-5872	216	2	12	12	NUM
ejpam-5872	216	3	.	.	PUNCT
ejpam-5872	217	1	consider	consider	VERB
ejpam-5872	217	2	the	the	DET
ejpam-5872	217	3	signed	sign	VERB
ejpam-5872	217	4	-	-	PUNCT
ejpam-5872	217	5	fg	fg	PROPN
ejpam-5872	217	6	∑	∑	PROPN
ejpam-5872	217	7	±	±	PROPN
ejpam-5872	217	8	,	,	PUNCT
ejpam-5872	217	9	which	which	PRON
ejpam-5872	217	10	has	have	VERB
ejpam-5872	217	11	no	no	DET
ejpam-5872	217	12	isolated	isolated	ADJ
ejpam-5872	217	13	vertices	vertex	NOUN
ejpam-5872	217	14	.	.	PUNCT
ejpam-5872	218	1	if	if	SCONJ
ejpam-5872	218	2	all	all	PRON
ejpam-5872	218	3	of	of	ADP
ejpam-5872	218	4	the	the	DET
ejpam-5872	218	5	vertices	vertex	NOUN
ejpam-5872	218	6	in	in	ADP
ejpam-5872	218	7	ℑ	ℑ	NOUN
ejpam-5872	218	8	are	be	AUX
ejpam-5872	218	9	dominated	dominate	VERB
ejpam-5872	218	10	by	by	ADP
ejpam-5872	218	11	a	a	DET
ejpam-5872	218	12	single	single	ADJ
ejpam-5872	218	13	vertex	vertex	NOUN
ejpam-5872	218	14	in	in	ADP
ejpam-5872	218	15	d	d	PROPN
ejpam-5872	218	16	,	,	PUNCT
ejpam-5872	218	17	then	then	ADV
ejpam-5872	218	18	subset	subset	VERB
ejpam-5872	218	19	d	d	NOUN
ejpam-5872	218	20	of	of	ADP
ejpam-5872	218	21	ℑ	ℑ	PROPN
ejpam-5872	218	22	is	be	AUX
ejpam-5872	218	23	referred	refer	VERB
ejpam-5872	218	24	to	to	ADP
ejpam-5872	218	25	as	as	ADP
ejpam-5872	218	26	a	a	DET
ejpam-5872	218	27	total	total	ADJ
ejpam-5872	218	28	domination	domination	NOUN
ejpam-5872	218	29	set	set	NOUN
ejpam-5872	218	30	.	.	PUNCT
ejpam-5872	219	1	a	a	DET
ejpam-5872	219	2	total	total	ADJ
ejpam-5872	219	3	domination	domination	NOUN
ejpam-5872	219	4	set	set	NOUN
ejpam-5872	219	5	’s	’s	PART
ejpam-5872	219	6	minimal	minimal	ADJ
ejpam-5872	219	7	fuzzy	fuzzy	ADJ
ejpam-5872	219	8	cardinality	cardinality	NOUN
ejpam-5872	219	9	is	be	AUX
ejpam-5872	219	10	γt	γt	NOUN
ejpam-5872	219	11	,	,	PUNCT
ejpam-5872	219	12	which	which	PRON
ejpam-5872	219	13	is	be	AUX
ejpam-5872	219	14	the	the	DET
ejpam-5872	219	15	total	total	ADJ
ejpam-5872	219	16	domination	domination	NOUN
ejpam-5872	219	17	number	number	NOUN
ejpam-5872	219	18	of	of	ADP
ejpam-5872	219	19	∑	∑	PUNCT
ejpam-5872	219	20	±.	±.	NOUN
ejpam-5872	219	21	theorem	theorem	NOUN
ejpam-5872	219	22	6	6	NUM
ejpam-5872	219	23	.	.	PUNCT
ejpam-5872	220	1	let	let	AUX
ejpam-5872	220	2	σ±	σ±	NOUN
ejpam-5872	220	3	=	=	SYM
ejpam-5872	220	4	(	(	PUNCT
ejpam-5872	220	5	ℑ	ℑ	PROPN
ejpam-5872	220	6	,	,	PUNCT
ejpam-5872	220	7	σ	σ	PROPN
ejpam-5872	220	8	,	,	PUNCT
ejpam-5872	220	9	µ	µ	NOUN
ejpam-5872	220	10	)	)	PUNCT
ejpam-5872	220	11	be	be	AUX
ejpam-5872	220	12	a	a	DET
ejpam-5872	220	13	non	non	ADJ
ejpam-5872	220	14	-	-	ADJ
ejpam-5872	220	15	trivial	trivial	ADJ
ejpam-5872	220	16	signed	sign	VERB
ejpam-5872	220	17	-	-	PUNCT
ejpam-5872	220	18	fg	fg	NOUN
ejpam-5872	220	19	,	,	PUNCT
ejpam-5872	220	20	and	and	CCONJ
ejpam-5872	220	21	let	let	VERB
ejpam-5872	220	22	d	d	PRON
ejpam-5872	220	23	be	be	AUX
ejpam-5872	220	24	a	a	DET
ejpam-5872	220	25	dominating	dominating	NOUN
ejpam-5872	220	26	set	set	NOUN
ejpam-5872	220	27	of	of	ADP
ejpam-5872	220	28	σ±.	σ±.	NOUN
ejpam-5872	220	29	then	then	ADV
ejpam-5872	220	30	ℑ−d	ℑ−d	PROPN
ejpam-5872	220	31	is	be	AUX
ejpam-5872	220	32	also	also	ADV
ejpam-5872	220	33	a	a	DET
ejpam-5872	220	34	dominating	dominating	NOUN
ejpam-5872	220	35	set	set	NOUN
ejpam-5872	220	36	.	.	PUNCT
ejpam-5872	221	1	proof	proof	NOUN
ejpam-5872	221	2	.	.	PUNCT
ejpam-5872	222	1	let	let	VERB
ejpam-5872	222	2	f±	f±	PROPN
ejpam-5872	222	3	be	be	AUX
ejpam-5872	222	4	a	a	DET
ejpam-5872	222	5	spanning	span	VERB
ejpam-5872	222	6	tree	tree	NOUN
ejpam-5872	222	7	of	of	ADP
ejpam-5872	222	8	σ±	σ±	NOUN
ejpam-5872	222	9	,	,	PUNCT
ejpam-5872	222	10	and	and	CCONJ
ejpam-5872	222	11	let	let	VERB
ejpam-5872	222	12	ג	ג	PART
ejpam-5872	222	13	be	be	AUX
ejpam-5872	222	14	any	any	DET
ejpam-5872	222	15	vertex	vertex	NOUN
ejpam-5872	222	16	of	of	ADP
ejpam-5872	222	17	f±.	f±.	PUNCT
ejpam-5872	222	18	we	we	PRON
ejpam-5872	222	19	can	can	AUX
ejpam-5872	222	20	partition	partition	VERB
ejpam-5872	222	21	the	the	DET
ejpam-5872	222	22	vertex	vertex	NOUN
ejpam-5872	222	23	set	set	VERB
ejpam-5872	222	24	ℑ	ℑ	PROPN
ejpam-5872	222	25	into	into	ADP
ejpam-5872	222	26	two	two	NUM
ejpam-5872	222	27	disjoint	disjoint	ADJ
ejpam-5872	222	28	subsets	subset	NOUN
ejpam-5872	222	29	according	accord	VERB
ejpam-5872	222	30	to	to	ADP
ejpam-5872	222	31	the	the	DET
ejpam-5872	222	32	parity	parity	NOUN
ejpam-5872	222	33	of	of	ADP
ejpam-5872	222	34	the	the	DET
ejpam-5872	222	35	distance	distance	NOUN
ejpam-5872	222	36	from	from	ADP
ejpam-5872	222	37	ג	ג	PROPN
ejpam-5872	222	38	in	in	ADP
ejpam-5872	222	39	f±	f±	ADJ
ejpam-5872	222	40	:	:	PUNCT
ejpam-5872	222	41	vertices	vertice	VERB
ejpam-5872	222	42	at	at	ADP
ejpam-5872	222	43	even	even	ADJ
ejpam-5872	222	44	distance	distance	NOUN
ejpam-5872	222	45	from	from	ADP
ejpam-5872	222	46	ג	ג	PROPN
ejpam-5872	222	47	form	form	NOUN
ejpam-5872	222	48	the	the	DET
ejpam-5872	222	49	set	set	PROPN
ejpam-5872	222	50	d	d	PROPN
ejpam-5872	222	51	,	,	PUNCT
ejpam-5872	222	52	vertices	vertice	VERB
ejpam-5872	222	53	at	at	ADP
ejpam-5872	222	54	odd	odd	ADJ
ejpam-5872	222	55	distance	distance	NOUN
ejpam-5872	222	56	from	from	ADP
ejpam-5872	222	57	ג	ג	PROPN
ejpam-5872	222	58	form	form	NOUN
ejpam-5872	222	59	the	the	DET
ejpam-5872	222	60	set	set	NOUN
ejpam-5872	222	61	ℑ−d	ℑ−d	NOUN
ejpam-5872	222	62	.	.	PUNCT
ejpam-5872	223	1	by	by	ADP
ejpam-5872	223	2	the	the	DET
ejpam-5872	223	3	properties	property	NOUN
ejpam-5872	223	4	of	of	ADP
ejpam-5872	223	5	a	a	DET
ejpam-5872	223	6	tree	tree	NOUN
ejpam-5872	223	7	,	,	PUNCT
ejpam-5872	223	8	every	every	DET
ejpam-5872	223	9	vertex	vertex	NOUN
ejpam-5872	223	10	in	in	ADP
ejpam-5872	223	11	d	d	PROPN
ejpam-5872	223	12	is	be	AUX
ejpam-5872	223	13	adjacent	adjacent	ADJ
ejpam-5872	223	14	to	to	ADP
ejpam-5872	223	15	at	at	ADV
ejpam-5872	223	16	least	least	ADV
ejpam-5872	223	17	one	one	NUM
ejpam-5872	223	18	vertex	vertex	NOUN
ejpam-5872	223	19	in	in	ADP
ejpam-5872	223	20	ℑ−d	ℑ−d	NOUN
ejpam-5872	223	21	,	,	PUNCT
ejpam-5872	223	22	and	and	CCONJ
ejpam-5872	223	23	vice	vice	ADV
ejpam-5872	223	24	versa	versa	ADV
ejpam-5872	223	25	.	.	PUNCT
ejpam-5872	224	1	hence	hence	ADV
ejpam-5872	224	2	,	,	PUNCT
ejpam-5872	224	3	each	each	PRON
ejpam-5872	224	4	of	of	ADP
ejpam-5872	224	5	d	d	PROPN
ejpam-5872	224	6	and	and	CCONJ
ejpam-5872	224	7	ℑ−d	ℑ−d	PRON
ejpam-5872	224	8	dominates	dominate	VERB
ejpam-5872	224	9	the	the	DET
ejpam-5872	224	10	graph	graph	NOUN
ejpam-5872	224	11	.	.	PUNCT
ejpam-5872	225	1	therefore	therefore	ADV
ejpam-5872	225	2	,	,	PUNCT
ejpam-5872	225	3	both	both	PRON
ejpam-5872	225	4	d	d	PROPN
ejpam-5872	225	5	and	and	CCONJ
ejpam-5872	225	6	its	its	PRON
ejpam-5872	225	7	complement	complement	NOUN
ejpam-5872	225	8	are	be	AUX
ejpam-5872	225	9	dominating	dominate	VERB
ejpam-5872	225	10	sets	set	NOUN
ejpam-5872	225	11	in	in	ADP
ejpam-5872	225	12	σ±.	σ±.	PUNCT
ejpam-5872	225	13	theorem	theorem	NOUN
ejpam-5872	225	14	7	7	NUM
ejpam-5872	225	15	.	.	PUNCT
ejpam-5872	226	1	if	if	SCONJ
ejpam-5872	226	2	d	d	PROPN
ejpam-5872	226	3	is	be	AUX
ejpam-5872	226	4	a	a	DET
ejpam-5872	226	5	minimal	minimal	ADJ
ejpam-5872	226	6	dominating	dominating	NOUN
ejpam-5872	226	7	set	set	NOUN
ejpam-5872	226	8	and	and	CCONJ
ejpam-5872	226	9	σ±	σ±	NOUN
ejpam-5872	226	10	=	=	SYM
ejpam-5872	226	11	(	(	PUNCT
ejpam-5872	226	12	ℑ	ℑ	PROPN
ejpam-5872	226	13	,	,	PUNCT
ejpam-5872	226	14	σ	σ	PROPN
ejpam-5872	226	15	,	,	PUNCT
ejpam-5872	226	16	µ	µ	NOUN
ejpam-5872	226	17	)	)	PUNCT
ejpam-5872	226	18	is	be	AUX
ejpam-5872	226	19	a	a	DET
ejpam-5872	226	20	signed	sign	VERB
ejpam-5872	226	21	-	-	PUNCT
ejpam-5872	226	22	fg	fg	NOUN
ejpam-5872	226	23	without	without	ADP
ejpam-5872	226	24	isolated	isolated	ADJ
ejpam-5872	226	25	nodes	node	NOUN
ejpam-5872	226	26	,	,	PUNCT
ejpam-5872	226	27	then	then	ADV
ejpam-5872	226	28	ℑ−d	ℑ−d	PROPN
ejpam-5872	226	29	is	be	AUX
ejpam-5872	226	30	also	also	ADV
ejpam-5872	226	31	a	a	DET
ejpam-5872	226	32	dominating	dominating	NOUN
ejpam-5872	226	33	set	set	NOUN
ejpam-5872	226	34	.	.	PUNCT
ejpam-5872	227	1	proof	proof	NOUN
ejpam-5872	227	2	.	.	PUNCT
ejpam-5872	228	1	let	let	VERB
ejpam-5872	228	2	d	d	PRON
ejpam-5872	228	3	be	be	AUX
ejpam-5872	228	4	a	a	DET
ejpam-5872	228	5	minimal	minimal	ADJ
ejpam-5872	228	6	dominating	dominating	NOUN
ejpam-5872	228	7	set	set	NOUN
ejpam-5872	228	8	of	of	ADP
ejpam-5872	228	9	σ±.	σ±.	NOUN
ejpam-5872	228	10	suppose	suppose	VERB
ejpam-5872	228	11	,	,	PUNCT
ejpam-5872	228	12	for	for	ADP
ejpam-5872	228	13	the	the	DET
ejpam-5872	228	14	sake	sake	NOUN
ejpam-5872	228	15	of	of	ADP
ejpam-5872	228	16	contradiction	contradiction	NOUN
ejpam-5872	228	17	,	,	PUNCT
ejpam-5872	228	18	that	that	SCONJ
ejpam-5872	228	19	ℑ	ℑ	NOUN
ejpam-5872	228	20	−d	−d	VERB
ejpam-5872	228	21	is	be	AUX
ejpam-5872	228	22	not	not	PART
ejpam-5872	228	23	a	a	DET
ejpam-5872	228	24	dominating	dominating	NOUN
ejpam-5872	228	25	set	set	NOUN
ejpam-5872	228	26	.	.	PUNCT
ejpam-5872	229	1	then	then	ADV
ejpam-5872	229	2	there	there	PRON
ejpam-5872	229	3	exists	exist	VERB
ejpam-5872	229	4	a	a	DET
ejpam-5872	229	5	vertex	vertex	NOUN
ejpam-5872	229	6	ג	ג	ADP
ejpam-5872	229	7	∈	∈	PROPN
ejpam-5872	229	8	d	d	X
ejpam-5872	229	9	which	which	PRON
ejpam-5872	229	10	is	be	AUX
ejpam-5872	229	11	not	not	PART
ejpam-5872	229	12	adjacent	adjacent	ADJ
ejpam-5872	229	13	to	to	ADP
ejpam-5872	229	14	any	any	DET
ejpam-5872	229	15	vertex	vertex	NOUN
ejpam-5872	229	16	in	in	ADP
ejpam-5872	229	17	ℑ−d	ℑ−d	NOUN
ejpam-5872	229	18	.	.	PUNCT
ejpam-5872	230	1	this	this	PRON
ejpam-5872	230	2	means	mean	VERB
ejpam-5872	230	3	that	that	SCONJ
ejpam-5872	230	4	ג	ג	PROPN
ejpam-5872	230	5	is	be	AUX
ejpam-5872	230	6	adjacent	adjacent	ADJ
ejpam-5872	230	7	only	only	ADV
ejpam-5872	230	8	to	to	ADP
ejpam-5872	230	9	vertices	vertex	NOUN
ejpam-5872	230	10	in	in	ADP
ejpam-5872	230	11	d.	d.	PROPN
ejpam-5872	230	12	c.	c.	PROPN
ejpam-5872	230	13	sankar	sankar	PROPN
ejpam-5872	230	14	et	et	PROPN
ejpam-5872	230	15	al	al	PROPN
ejpam-5872	230	16	.	.	PUNCT
ejpam-5872	230	17	/	/	SYM
ejpam-5872	230	18	eur	eur	PROPN
ejpam-5872	230	19	.	.	PUNCT
ejpam-5872	231	1	j.	j.	PROPN
ejpam-5872	231	2	pure	pure	PROPN
ejpam-5872	231	3	appl	appl	PROPN
ejpam-5872	231	4	.	.	PROPN
ejpam-5872	231	5	math	math	PROPN
ejpam-5872	231	6	,	,	PUNCT
ejpam-5872	231	7	18	18	NUM
ejpam-5872	231	8	(	(	PUNCT
ejpam-5872	231	9	4	4	NUM
ejpam-5872	231	10	)	)	PUNCT
ejpam-5872	231	11	(	(	PUNCT
ejpam-5872	231	12	2025	2025	NUM
ejpam-5872	231	13	)	)	PUNCT
ejpam-5872	231	14	,	,	PUNCT
ejpam-5872	231	15	5872	5872	NUM
ejpam-5872	231	16	10	10	NUM
ejpam-5872	231	17	of	of	ADP
ejpam-5872	231	18	17	17	NUM
ejpam-5872	231	19	since	since	SCONJ
ejpam-5872	231	20	σ±	σ±	NOUN
ejpam-5872	231	21	has	have	VERB
ejpam-5872	231	22	no	no	DET
ejpam-5872	231	23	isolated	isolated	ADJ
ejpam-5872	231	24	vertices	vertex	NOUN
ejpam-5872	231	25	,	,	PUNCT
ejpam-5872	231	26	ג	ג	PROPN
ejpam-5872	231	27	must	must	AUX
ejpam-5872	231	28	be	be	AUX
ejpam-5872	231	29	a	a	DET
ejpam-5872	231	30	strong	strong	ADJ
ejpam-5872	231	31	neighbor	neighbor	NOUN
ejpam-5872	231	32	of	of	ADP
ejpam-5872	231	33	at	at	ADV
ejpam-5872	231	34	least	least	ADV
ejpam-5872	231	35	one	one	NUM
ejpam-5872	231	36	vertex	vertex	NOUN
ejpam-5872	231	37	in	in	ADP
ejpam-5872	231	38	d−{ג	d−{ג	PROPN
ejpam-5872	231	39	}	}	PUNCT
ejpam-5872	231	40	.	.	PUNCT
ejpam-5872	232	1	therefore	therefore	ADV
ejpam-5872	232	2	,	,	PUNCT
ejpam-5872	232	3	d−{ג	d−{ג	PROPN
ejpam-5872	232	4	}	}	PUNCT
ejpam-5872	232	5	would	would	AUX
ejpam-5872	232	6	still	still	ADV
ejpam-5872	232	7	be	be	AUX
ejpam-5872	232	8	a	a	DET
ejpam-5872	232	9	dominating	dominating	NOUN
ejpam-5872	232	10	set	set	NOUN
ejpam-5872	232	11	,	,	PUNCT
ejpam-5872	232	12	contradicting	contradict	VERB
ejpam-5872	232	13	the	the	DET
ejpam-5872	232	14	minimality	minimality	NOUN
ejpam-5872	232	15	of	of	ADP
ejpam-5872	232	16	d.	d.	PROPN
ejpam-5872	232	17	hence	hence	ADV
ejpam-5872	232	18	,	,	PUNCT
ejpam-5872	232	19	every	every	DET
ejpam-5872	232	20	vertex	vertex	NOUN
ejpam-5872	232	21	in	in	ADP
ejpam-5872	232	22	d	d	PROPN
ejpam-5872	232	23	has	have	VERB
ejpam-5872	232	24	at	at	ADV
ejpam-5872	232	25	least	least	ADJ
ejpam-5872	232	26	one	one	NUM
ejpam-5872	232	27	strong	strong	ADJ
ejpam-5872	232	28	neighbor	neighbor	NOUN
ejpam-5872	232	29	in	in	ADP
ejpam-5872	232	30	ℑ	ℑ	PROPN
ejpam-5872	232	31	−	−	PROPN
ejpam-5872	232	32	d	d	NOUN
ejpam-5872	232	33	,	,	PUNCT
ejpam-5872	232	34	implying	imply	VERB
ejpam-5872	232	35	that	that	SCONJ
ejpam-5872	232	36	ℑ−d	ℑ−d	PRON
ejpam-5872	232	37	is	be	AUX
ejpam-5872	232	38	indeed	indeed	ADV
ejpam-5872	232	39	a	a	DET
ejpam-5872	232	40	dominating	dominating	NOUN
ejpam-5872	232	41	set	set	NOUN
ejpam-5872	232	42	.	.	PUNCT
ejpam-5872	233	1	theorem	theorem	VERB
ejpam-5872	233	2	8	8	NUM
ejpam-5872	233	3	.	.	PUNCT
ejpam-5872	234	1	if	if	SCONJ
ejpam-5872	234	2	σ±	σ±	NOUN
ejpam-5872	234	3	=	=	SYM
ejpam-5872	234	4	(	(	PUNCT
ejpam-5872	234	5	ℑ	ℑ	PROPN
ejpam-5872	234	6	,	,	PUNCT
ejpam-5872	234	7	σ	σ	PROPN
ejpam-5872	234	8	,	,	PUNCT
ejpam-5872	234	9	µ	µ	NOUN
ejpam-5872	234	10	)	)	PUNCT
ejpam-5872	234	11	is	be	AUX
ejpam-5872	234	12	a	a	DET
ejpam-5872	234	13	complete	complete	ADJ
ejpam-5872	234	14	signed	sign	VERB
ejpam-5872	234	15	-	-	PUNCT
ejpam-5872	234	16	fg	fg	NOUN
ejpam-5872	234	17	,	,	PUNCT
ejpam-5872	234	18	then	then	ADV
ejpam-5872	234	19	γ	γ	PROPN
ejpam-5872	234	20	(	(	PUNCT
ejpam-5872	234	21	∑	∑	PROPN
ejpam-5872	234	22	±	±	NUM
ejpam-5872	234	23	)	)	PUNCT
ejpam-5872	235	1	=	=	SYM
ejpam-5872	235	2	min	min	PROPN
ejpam-5872	235	3	{	{	PUNCT
ejpam-5872	235	4	σ(ג	σ(ג	NOUN
ejpam-5872	235	5	)	)	PUNCT
ejpam-5872	235	6	}	}	PUNCT
ejpam-5872	235	7	ג∀	ג∀	PROPN
ejpam-5872	235	8	,	,	PUNCT
ejpam-5872	235	9	∈	∈	PROPN
ejpam-5872	235	10	ℑ.	ℑ.	NOUN
ejpam-5872	235	11	proof	proof	NOUN
ejpam-5872	235	12	.	.	PUNCT
ejpam-5872	236	1	all	all	PRON
ejpam-5872	236	2	of	of	ADP
ejpam-5872	236	3	the	the	DET
ejpam-5872	236	4	arcs	arcs	NOUN
ejpam-5872	236	5	in	in	ADP
ejpam-5872	236	6	∑	∑	PROPN
ejpam-5872	236	7	±	±	NOUN
ejpam-5872	236	8	are	be	AUX
ejpam-5872	236	9	strong	strong	ADJ
ejpam-5872	236	10	,	,	PUNCT
ejpam-5872	236	11	and	and	CCONJ
ejpam-5872	236	12	since	since	SCONJ
ejpam-5872	236	13	∑	∑	PROPN
ejpam-5872	236	14	±	±	PROPN
ejpam-5872	236	15	is	be	AUX
ejpam-5872	236	16	a	a	DET
ejpam-5872	236	17	complete	complete	ADJ
ejpam-5872	236	18	signed	sign	VERB
ejpam-5872	236	19	-	-	PUNCT
ejpam-5872	236	20	fg	fg	NOUN
ejpam-5872	236	21	,	,	PUNCT
ejpam-5872	236	22	every	every	DET
ejpam-5872	236	23	node	node	NOUN
ejpam-5872	236	24	in	in	ADP
ejpam-5872	236	25	∑	∑	PROPN
ejpam-5872	236	26	±	±	PROPN
ejpam-5872	236	27	is	be	AUX
ejpam-5872	236	28	incident	incident	NOUN
ejpam-5872	236	29	to	to	ADP
ejpam-5872	236	30	every	every	DET
ejpam-5872	236	31	other	other	ADJ
ejpam-5872	236	32	node	node	NOUN
ejpam-5872	236	33	.	.	PUNCT
ejpam-5872	237	1	every	every	DET
ejpam-5872	237	2	ג	ג	PROPN
ejpam-5872	237	3	∈	∈	PROPN
ejpam-5872	237	4	ℑ	ℑ	PROPN
ejpam-5872	237	5	has	have	VERB
ejpam-5872	237	6	a	a	DET
ejpam-5872	237	7	domination	domination	NOUN
ejpam-5872	237	8	set	set	VERB
ejpam-5872	237	9	d	d	NOUN
ejpam-5872	237	10	=	=	SYM
ejpam-5872	237	11	.{ג	.{ג	PUNCT
ejpam-5872	237	12	}	}	PUNCT
ejpam-5872	237	13	this	this	PRON
ejpam-5872	237	14	means	mean	VERB
ejpam-5872	237	15	that	that	SCONJ
ejpam-5872	237	16	γ	γ	PROPN
ejpam-5872	237	17	(	(	PUNCT
ejpam-5872	237	18	∑	∑	PROPN
ejpam-5872	237	19	±	±	NUM
ejpam-5872	237	20	)	)	PUNCT
ejpam-5872	237	21	=	=	SYM
ejpam-5872	237	22	min	min	PROPN
ejpam-5872	237	23	{	{	PUNCT
ejpam-5872	237	24	σ(ג	σ(ג	NOUN
ejpam-5872	237	25	)	)	PUNCT
ejpam-5872	237	26	}	}	PUNCT
ejpam-5872	237	27	ג∀	ג∀	PROPN
ejpam-5872	237	28	,	,	PUNCT
ejpam-5872	237	29	∈	∈	PROPN
ejpam-5872	237	30	ℑ.	ℑ.	NOUN
ejpam-5872	237	31	theorem	theorem	VERB
ejpam-5872	237	32	9	9	NUM
ejpam-5872	237	33	.	.	PUNCT
ejpam-5872	238	1	let	let	VERB
ejpam-5872	238	2	σ±	σ±	NOUN
ejpam-5872	238	3	=	=	SYM
ejpam-5872	238	4	(	(	PUNCT
ejpam-5872	238	5	ℑ	ℑ	PROPN
ejpam-5872	238	6	,	,	PUNCT
ejpam-5872	238	7	σ	σ	PROPN
ejpam-5872	238	8	,	,	PUNCT
ejpam-5872	238	9	µ	µ	NOUN
ejpam-5872	238	10	)	)	PUNCT
ejpam-5872	238	11	be	be	AUX
ejpam-5872	238	12	a	a	DET
ejpam-5872	238	13	nontrivial	nontrivial	NOUN
ejpam-5872	238	14	signed	sign	VERB
ejpam-5872	238	15	-	-	PUNCT
ejpam-5872	238	16	fg	fg	PROPN
ejpam-5872	238	17	of	of	ADP
ejpam-5872	238	18	order	order	NOUN
ejpam-5872	238	19	.ג	.ג	PUNCT
ejpam-5872	239	1	γ	γ	X
ejpam-5872	239	2	(	(	PUNCT
ejpam-5872	239	3	∑	∑	PROPN
ejpam-5872	239	4	±	±	NUM
ejpam-5872	239	5	)	)	PUNCT
ejpam-5872	239	6	is	be	AUX
ejpam-5872	239	7	ג	ג	PROPN
ejpam-5872	239	8	if	if	SCONJ
ejpam-5872	239	9	all	all	DET
ejpam-5872	239	10	nodes	node	NOUN
ejpam-5872	239	11	are	be	AUX
ejpam-5872	239	12	isolated	isolate	VERB
ejpam-5872	239	13	.	.	PUNCT
ejpam-5872	240	1	proof	proof	NOUN
ejpam-5872	240	2	.	.	PUNCT
ejpam-5872	241	1	if	if	SCONJ
ejpam-5872	241	2	each	each	DET
ejpam-5872	241	3	node	node	NOUN
ejpam-5872	241	4	is	be	AUX
ejpam-5872	241	5	isolated	isolate	VERB
ejpam-5872	241	6	,	,	PUNCT
ejpam-5872	241	7	it	it	PRON
ejpam-5872	241	8	is	be	AUX
ejpam-5872	241	9	clear	clear	ADJ
ejpam-5872	241	10	that	that	SCONJ
ejpam-5872	241	11	γ	γ	PROPN
ejpam-5872	241	12	(	(	PUNCT
ejpam-5872	241	13	∑	∑	PROPN
ejpam-5872	241	14	±	±	NUM
ejpam-5872	241	15	)	)	PUNCT
ejpam-5872	241	16	=	=	VERB
ejpam-5872	242	1	.ג	.ג	X
ejpam-5872	242	2	however	however	ADV
ejpam-5872	242	3	,	,	PUNCT
ejpam-5872	242	4	to	to	PART
ejpam-5872	242	5	show	show	VERB
ejpam-5872	242	6	that	that	SCONJ
ejpam-5872	242	7	each	each	DET
ejpam-5872	242	8	node	node	NOUN
ejpam-5872	242	9	is	be	AUX
ejpam-5872	242	10	isolated	isolate	VERB
ejpam-5872	242	11	,	,	PUNCT
ejpam-5872	242	12	suppose	suppose	VERB
ejpam-5872	242	13	that	that	SCONJ
ejpam-5872	242	14	γ	γ	PROPN
ejpam-5872	242	15	(	(	PUNCT
ejpam-5872	242	16	∑	∑	PROPN
ejpam-5872	242	17	±	±	NUM
ejpam-5872	242	18	)	)	PUNCT
ejpam-5872	242	19	=	=	PUNCT
ejpam-5872	243	1	.ג	.ג	PUNCT
ejpam-5872	243	2	if	if	SCONJ
ejpam-5872	243	3	at	at	ADV
ejpam-5872	243	4	all	all	ADV
ejpam-5872	243	5	feasible	feasible	ADJ
ejpam-5872	243	6	,	,	PUNCT
ejpam-5872	243	7	let	let	VERB
ejpam-5872	243	8	1ג	1ג	PRON
ejpam-5872	243	9	be	be	AUX
ejpam-5872	243	10	a	a	DET
ejpam-5872	243	11	non	non	ADJ
ejpam-5872	243	12	-	-	ADJ
ejpam-5872	243	13	isolated	isolated	ADJ
ejpam-5872	243	14	node	node	NOUN
ejpam-5872	243	15	of	of	ADP
ejpam-5872	243	16	∑	∑	PUNCT
ejpam-5872	243	17	±.	±.	VERB
ejpam-5872	243	18	the	the	DET
ejpam-5872	243	19	arc	arc	NOUN
ejpam-5872	243	20	,	,	PUNCT
ejpam-5872	243	21	1ג	1ג	NUM
ejpam-5872	243	22	)	)	PUNCT
ejpam-5872	243	23	(	(	PUNCT
ejpam-5872	243	24	2ג	2ג	NOUN
ejpam-5872	243	25	is	be	AUX
ejpam-5872	243	26	then	then	ADV
ejpam-5872	243	27	strong	strong	ADJ
ejpam-5872	243	28	due	due	ADP
ejpam-5872	243	29	to	to	ADP
ejpam-5872	243	30	a	a	DET
ejpam-5872	243	31	node	node	NOUN
ejpam-5872	243	32	.ג	.ג	NOUN
ejpam-5872	243	33	therefore	therefore	ADV
ejpam-5872	243	34	,	,	PUNCT
ejpam-5872	243	35	there	there	PRON
ejpam-5872	243	36	are	be	VERB
ejpam-5872	243	37	a	a	DET
ejpam-5872	243	38	maximum	maximum	NOUN
ejpam-5872	243	39	of	of	ADP
ejpam-5872	243	40	(	(	PUNCT
ejpam-5872	243	41	n	n	CCONJ
ejpam-5872	243	42	−	−	PROPN
ejpam-5872	243	43	1	1	NUM
ejpam-5872	243	44	)	)	PUNCT
ejpam-5872	243	45	nodes	node	NOUN
ejpam-5872	243	46	for	for	ADP
ejpam-5872	243	47	each	each	DET
ejpam-5872	243	48	dominant	dominant	ADJ
ejpam-5872	243	49	set	set	NOUN
ejpam-5872	243	50	of	of	ADP
ejpam-5872	243	51	∑	∑	PROPN
ejpam-5872	243	52	±	±	PROPN
ejpam-5872	243	53	,	,	PUNCT
ejpam-5872	243	54	where	where	SCONJ
ejpam-5872	243	55	n	n	PRON
ejpam-5872	243	56	is	be	AUX
ejpam-5872	243	57	the	the	DET
ejpam-5872	243	58	number	number	NOUN
ejpam-5872	243	59	of	of	ADP
ejpam-5872	243	60	nodes	node	NOUN
ejpam-5872	243	61	in	in	ADP
ejpam-5872	243	62	∑	∑	PROPN
ejpam-5872	243	63	±.	±.	NOUN
ejpam-5872	243	64	consequently	consequently	ADV
ejpam-5872	243	65	,	,	PUNCT
ejpam-5872	243	66	γ	γ	PROPN
ejpam-5872	243	67	(	(	PUNCT
ejpam-5872	243	68	∑	∑	PROPN
ejpam-5872	243	69	±	±	NUM
ejpam-5872	243	70	)	)	PUNCT
ejpam-5872	243	71	<	<	X
ejpam-5872	243	72	ג	ג	X
ejpam-5872	243	73	is	be	AUX
ejpam-5872	243	74	a	a	DET
ejpam-5872	243	75	contradiction	contradiction	NOUN
ejpam-5872	243	76	.	.	PUNCT
ejpam-5872	244	1	thus	thus	ADV
ejpam-5872	244	2	,	,	PUNCT
ejpam-5872	244	3	each	each	DET
ejpam-5872	244	4	node	node	NOUN
ejpam-5872	244	5	is	be	AUX
ejpam-5872	244	6	segregated	segregate	VERB
ejpam-5872	244	7	.	.	PUNCT
ejpam-5872	245	1	theorem	theorem	ADJ
ejpam-5872	245	2	10	10	NUM
ejpam-5872	245	3	.	.	PUNCT
ejpam-5872	246	1	if	if	SCONJ
ejpam-5872	246	2	∑	∑	PROPN
ejpam-5872	246	3	±	±	PROPN
ejpam-5872	246	4	is	be	AUX
ejpam-5872	246	5	a	a	DET
ejpam-5872	246	6	complete	complete	ADJ
ejpam-5872	246	7	bipartite	bipartite	NOUN
ejpam-5872	246	8	signed	sign	VERB
ejpam-5872	246	9	-	-	PUNCT
ejpam-5872	246	10	fg	fg	PROPN
ejpam-5872	246	11	,	,	PUNCT
ejpam-5872	246	12	then	then	ADV
ejpam-5872	246	13	γ(kσ±1,σ±2	γ(kσ±1,σ±2	PROPN
ejpam-5872	246	14	)	)	PUNCT
ejpam-5872	246	15	=	=	SYM
ejpam-5872	246	16	min	min	NOUN
ejpam-5872	246	17	{	{	PUNCT
ejpam-5872	246	18	|ℑ1|	|ℑ1|	PROPN
ejpam-5872	246	19	,	,	PUNCT
ejpam-5872	246	20	|ℑ2|,min	|ℑ2|,min	X
ejpam-5872	246	21	ℑ1∋ג	ℑ1∋ג	X
ejpam-5872	246	22	σ(ג	σ(ג	PROPN
ejpam-5872	246	23	)	)	PUNCT
ejpam-5872	247	1	+	+	NUM
ejpam-5872	247	2	min	min	NOUN
ejpam-5872	247	3	ℑ2∋ג	ℑ2∋ג	PROPN
ejpam-5872	247	4	σ(ג	σ(ג	PROPN
ejpam-5872	247	5	)	)	PUNCT
ejpam-5872	247	6	}	}	PUNCT
ejpam-5872	247	7	.	.	PUNCT
ejpam-5872	248	1	proof	proof	NOUN
ejpam-5872	248	2	.	.	PUNCT
ejpam-5872	249	1	they	they	PRON
ejpam-5872	249	2	are	be	AUX
ejpam-5872	249	3	all	all	ADV
ejpam-5872	249	4	strong	strong	ADJ
ejpam-5872	249	5	arcs	arc	NOUN
ejpam-5872	249	6	in	in	ADP
ejpam-5872	249	7	kσ±1,σ±2	kσ±1,σ±2	NOUN
ejpam-5872	249	8	.	.	PUNCT
ejpam-5872	250	1	all	all	DET
ejpam-5872	250	2	nodes	node	NOUN
ejpam-5872	250	3	in	in	ADP
ejpam-5872	250	4	ℑ1	ℑ1	NOUN
ejpam-5872	250	5	are	be	AUX
ejpam-5872	250	6	also	also	ADV
ejpam-5872	250	7	connected	connect	VERB
ejpam-5872	250	8	to	to	ADP
ejpam-5872	250	9	all	all	DET
ejpam-5872	250	10	nodes	node	NOUN
ejpam-5872	250	11	in	in	ADP
ejpam-5872	250	12	ℑ2	ℑ2	PROPN
ejpam-5872	250	13	.	.	PUNCT
ejpam-5872	251	1	therefore	therefore	ADV
ejpam-5872	251	2	,	,	PUNCT
ejpam-5872	251	3	the	the	DET
ejpam-5872	251	4	domination	domination	NOUN
ejpam-5872	251	5	set	set	VERB
ejpam-5872	251	6	in	in	ADP
ejpam-5872	251	7	kσ±1,σ±2	kσ±1,σ±2	PROPN
ejpam-5872	251	8	are	be	AUX
ejpam-5872	251	9	ℑ1	ℑ1	NOUN
ejpam-5872	251	10	and	and	CCONJ
ejpam-5872	251	11	ℑ2	ℑ2	VERB
ejpam-5872	251	12	,	,	PUNCT
ejpam-5872	251	13	and	and	CCONJ
ejpam-5872	251	14	any	any	DET
ejpam-5872	251	15	set	set	NOUN
ejpam-5872	251	16	that	that	PRON
ejpam-5872	251	17	has	have	VERB
ejpam-5872	251	18	two	two	NUM
ejpam-5872	251	19	nodes	node	NOUN
ejpam-5872	251	20	,	,	PUNCT
ejpam-5872	251	21	one	one	NUM
ejpam-5872	251	22	in	in	ADP
ejpam-5872	251	23	ℑ1	ℑ1	NOUN
ejpam-5872	251	24	and	and	CCONJ
ejpam-5872	251	25	the	the	DET
ejpam-5872	251	26	other	other	ADJ
ejpam-5872	251	27	in	in	ADP
ejpam-5872	251	28	ℑ2	ℑ2	PROPN
ejpam-5872	251	29	,	,	PUNCT
ejpam-5872	251	30	do	do	VERB
ejpam-5872	251	31	so	so	ADV
ejpam-5872	251	32	.	.	PUNCT
ejpam-5872	252	1	therefore	therefore	ADV
ejpam-5872	252	2	,	,	PUNCT
ejpam-5872	252	3	γ(kσ±1,σ±2	γ(kσ±1,σ±2	PROPN
ejpam-5872	252	4	)	)	PUNCT
ejpam-5872	252	5	=	=	SYM
ejpam-5872	252	6	min	min	NOUN
ejpam-5872	252	7	{	{	PUNCT
ejpam-5872	252	8	|ℑ1|	|ℑ1|	PROPN
ejpam-5872	252	9	,	,	PUNCT
ejpam-5872	252	10	|ℑ2|,min	|ℑ2|,min	X
ejpam-5872	252	11	ℑ1∋ג	ℑ1∋ג	X
ejpam-5872	252	12	σ(ג	σ(ג	PROPN
ejpam-5872	252	13	)	)	PUNCT
ejpam-5872	252	14	+	+	NUM
ejpam-5872	252	15	min	min	NOUN
ejpam-5872	252	16	ℑ2∋ג	ℑ2∋ג	PROPN
ejpam-5872	252	17	σ(ג	σ(ג	PROPN
ejpam-5872	252	18	)	)	PUNCT
ejpam-5872	252	19	}	}	PUNCT
ejpam-5872	252	20	.	.	PUNCT
ejpam-5872	253	1	theorem	theorem	ADJ
ejpam-5872	253	2	11	11	NUM
ejpam-5872	253	3	.	.	PUNCT
ejpam-5872	254	1	for	for	ADP
ejpam-5872	254	2	any	any	DET
ejpam-5872	254	3	nontrivial	nontrivial	NOUN
ejpam-5872	254	4	signed	sign	VERB
ejpam-5872	254	5	-	-	PUNCT
ejpam-5872	254	6	fg	fg	PROPN
ejpam-5872	254	7	∑	∑	PROPN
ejpam-5872	254	8	±	±	PROPN
ejpam-5872	254	9	,	,	PUNCT
ejpam-5872	254	10	γ	γ	X
ejpam-5872	254	11	(	(	PUNCT
ejpam-5872	254	12	∑	∑	PROPN
ejpam-5872	254	13	±	±	NUM
ejpam-5872	254	14	)	)	PUNCT
ejpam-5872	254	15	+	+	CCONJ
ejpam-5872	254	16	γ	γ	X
ejpam-5872	254	17	(	(	PUNCT
ejpam-5872	254	18	∑	∑	PROPN
ejpam-5872	254	19	±	±	NUM
ejpam-5872	254	20	)	)	PUNCT
ejpam-5872	254	21	<	<	X
ejpam-5872	254	22	.ג2	.ג2	PUNCT
ejpam-5872	255	1	proof	proof	NOUN
ejpam-5872	255	2	.	.	PUNCT
ejpam-5872	256	1	a	a	DET
ejpam-5872	256	2	domination	domination	NOUN
ejpam-5872	256	3	set	set	VERB
ejpam-5872	256	4	in	in	ADP
ejpam-5872	256	5	∑	∑	PROPN
ejpam-5872	256	6	±	±	PROPN
ejpam-5872	256	7	has	have	VERB
ejpam-5872	256	8	a	a	DET
ejpam-5872	256	9	minimum	minimum	ADJ
ejpam-5872	256	10	scalar	scalar	ADJ
ejpam-5872	256	11	cardinality	cardinality	NOUN
ejpam-5872	256	12	of	of	ADP
ejpam-5872	256	13	γ	γ	PROPN
ejpam-5872	256	14	,	,	PUNCT
ejpam-5872	256	15	therefore	therefore	ADV
ejpam-5872	256	16	γ	γ	PROPN
ejpam-5872	256	17	≤	≤	PROPN
ejpam-5872	256	18	.ג	.ג	NOUN
ejpam-5872	257	1	likewise	likewise	ADV
ejpam-5872	257	2	,	,	PUNCT
ejpam-5872	257	3	the	the	DET
ejpam-5872	257	4	smallest	small	ADJ
ejpam-5872	257	5	scalar	scalar	ADJ
ejpam-5872	257	6	cardinality	cardinality	NOUN
ejpam-5872	257	7	for	for	ADP
ejpam-5872	257	8	∑	∑	PROPN
ejpam-5872	257	9	±	±	PROPN
ejpam-5872	257	10	is	be	AUX
ejpam-5872	257	11	γ	γ	NOUN
ejpam-5872	257	12	≤	≤	NUM
ejpam-5872	257	13	.ג	.ג	NOUN
ejpam-5872	258	1	γ	γ	X
ejpam-5872	258	2	+	+	X
ejpam-5872	258	3	γ	γ	PROPN
ejpam-5872	258	4	≤	≤	NOUN
ejpam-5872	258	5	ג	ג	ADP
ejpam-5872	258	6	+	+	CCONJ
ejpam-5872	258	7	ג	ג	PROPN
ejpam-5872	258	8	=	=	PUNCT
ejpam-5872	258	9	,	,	PUNCT
ejpam-5872	258	10	ג2	ג2	NOUN
ejpam-5872	258	11	as	as	ADP
ejpam-5872	258	12	a	a	DET
ejpam-5872	258	13	result	result	NOUN
ejpam-5872	258	14	.	.	PUNCT
ejpam-5872	259	1	assume	assume	VERB
ejpam-5872	259	2	that	that	SCONJ
ejpam-5872	259	3	γ	γ	PROPN
ejpam-5872	259	4	+	+	CCONJ
ejpam-5872	259	5	γ	γ	PROPN
ejpam-5872	259	6	̸=	̸=	PROPN
ejpam-5872	259	7	ג2	ג2	NOUN
ejpam-5872	259	8	in	in	ADP
ejpam-5872	259	9	order	order	NOUN
ejpam-5872	259	10	to	to	PART
ejpam-5872	259	11	demonstrate	demonstrate	VERB
ejpam-5872	259	12	that	that	SCONJ
ejpam-5872	259	13	γ	γ	PROPN
ejpam-5872	259	14	+	+	X
ejpam-5872	259	15	γ	γ	X
ejpam-5872	259	16	=	=	SYM
ejpam-5872	259	17	.ג2	.ג2	PROPN
ejpam-5872	259	18	since	since	SCONJ
ejpam-5872	259	19	maximal	maximal	ADJ
ejpam-5872	259	20	scalar	scalar	ADJ
ejpam-5872	259	21	cardinality	cardinality	NOUN
ejpam-5872	259	22	equals	equal	VERB
ejpam-5872	259	23	,	,	PUNCT
ejpam-5872	259	24	ג	ג	PROPN
ejpam-5872	259	25	if	if	SCONJ
ejpam-5872	259	26	γ	γ	X
ejpam-5872	259	27	<	<	X
ejpam-5872	259	28	,	,	PUNCT
ejpam-5872	259	29	ג	ג	PROPN
ejpam-5872	259	30	then	then	ADV
ejpam-5872	259	31	γ	γ	X
ejpam-5872	259	32	>	>	X
ejpam-5872	259	33	,	,	PUNCT
ejpam-5872	259	34	ג	ג	ADP
ejpam-5872	259	35	preventing	prevent	VERB
ejpam-5872	259	36	the	the	DET
ejpam-5872	259	37	possibility	possibility	NOUN
ejpam-5872	259	38	of	of	ADP
ejpam-5872	259	39	reaching	reach	VERB
ejpam-5872	259	40	γ	γ	NOUN
ejpam-5872	259	41	+	+	X
ejpam-5872	259	42	γ	γ	X
ejpam-5872	259	43	=	=	X
ejpam-5872	259	44	.ג2	.ג2	PUNCT
ejpam-5872	259	45	consequently	consequently	ADV
ejpam-5872	259	46	,	,	PUNCT
ejpam-5872	259	47	both	both	PRON
ejpam-5872	259	48	γ	γ	NOUN
ejpam-5872	259	49	=	=	SYM
ejpam-5872	259	50	ג	ג	PROPN
ejpam-5872	259	51	and	and	CCONJ
ejpam-5872	259	52	γ	γ	X
ejpam-5872	259	53	=	=	SYM
ejpam-5872	259	54	.ג	.ג	NOUN
ejpam-5872	260	1	it	it	PRON
ejpam-5872	260	2	is	be	AUX
ejpam-5872	260	3	claimed	claim	VERB
ejpam-5872	260	4	that	that	SCONJ
ejpam-5872	260	5	each	each	DET
ejpam-5872	260	6	node	node	NOUN
ejpam-5872	260	7	is	be	AUX
ejpam-5872	260	8	isolated	isolate	VERB
ejpam-5872	260	9	if	if	SCONJ
ejpam-5872	260	10	γ	γ	X
ejpam-5872	260	11	=	=	PUNCT
ejpam-5872	260	12	.ג	.ג	NOUN
ejpam-5872	260	13	by	by	ADP
ejpam-5872	260	14	this	this	DET
ejpam-5872	260	15	definition	definition	NOUN
ejpam-5872	260	16	,	,	PUNCT
ejpam-5872	260	17	∑	∑	PUNCT
ejpam-5872	260	18	±	±	NOUN
ejpam-5872	260	19	is	be	AUX
ejpam-5872	260	20	a	a	DET
ejpam-5872	260	21	complete	complete	ADJ
ejpam-5872	260	22	signed	sign	VERB
ejpam-5872	260	23	-	-	PUNCT
ejpam-5872	260	24	fg	fg	NOUN
ejpam-5872	260	25	.	.	PUNCT
ejpam-5872	261	1	this	this	PRON
ejpam-5872	261	2	leads	lead	VERB
ejpam-5872	261	3	to	to	ADP
ejpam-5872	261	4	the	the	DET
ejpam-5872	261	5	failure	failure	NOUN
ejpam-5872	261	6	of	of	ADP
ejpam-5872	261	7	γ	γ	X
ejpam-5872	261	8	=	=	SYM
ejpam-5872	261	9	min	min	PROPN
ejpam-5872	261	10	v∋1ג	v∋1ג	NOUN
ejpam-5872	261	11	σ(1ג	σ(1ג	NOUN
ejpam-5872	261	12	)	)	PUNCT
ejpam-5872	261	13	<	<	X
ejpam-5872	261	14	.ג	.ג	X
ejpam-5872	262	1	likewise	likewise	ADV
ejpam-5872	262	2	,	,	PUNCT
ejpam-5872	262	3	a	a	DET
ejpam-5872	262	4	contradiction	contradiction	NOUN
ejpam-5872	262	5	exists	exist	VERB
ejpam-5872	262	6	:	:	PUNCT
ejpam-5872	262	7	γ	γ	X
ejpam-5872	262	8	=	=	SYM
ejpam-5872	262	9	min	min	PROPN
ejpam-5872	262	10	v∋1ג	v∋1ג	NOUN
ejpam-5872	262	11	σ(1ג	σ(1ג	NOUN
ejpam-5872	262	12	)	)	PUNCT
ejpam-5872	262	13	<	<	X
ejpam-5872	262	14	,	,	PUNCT
ejpam-5872	262	15	ג	ג	PROPN
ejpam-5872	262	16	as	as	SCONJ
ejpam-5872	262	17	γ	γ	PROPN
ejpam-5872	262	18	=	=	SYM
ejpam-5872	262	19	ג	ג	PROPN
ejpam-5872	262	20	suggests	suggest	VERB
ejpam-5872	262	21	.	.	PUNCT
ejpam-5872	263	1	therefore	therefore	ADV
ejpam-5872	263	2	,	,	PUNCT
ejpam-5872	263	3	our	our	PRON
ejpam-5872	263	4	claim	claim	NOUN
ejpam-5872	263	5	is	be	AUX
ejpam-5872	263	6	accurate	accurate	ADJ
ejpam-5872	263	7	.	.	PUNCT
ejpam-5872	264	1	thus	thus	ADV
ejpam-5872	264	2	,	,	PUNCT
ejpam-5872	264	3	γ	γ	X
ejpam-5872	264	4	+	+	X
ejpam-5872	264	5	γ	γ	X
ejpam-5872	264	6	<	<	X
ejpam-5872	264	7	ג2	ג2	PROPN
ejpam-5872	264	8	for	for	ADP
ejpam-5872	264	9	every	every	DET
ejpam-5872	264	10	nontrivial	nontrivial	NOUN
ejpam-5872	264	11	signed	sign	VERB
ejpam-5872	264	12	-	-	PUNCT
ejpam-5872	264	13	fg	fg	PROPN
ejpam-5872	264	14	∑	∑	PROPN
ejpam-5872	264	15	±.	±.	PROPN
ejpam-5872	264	16	c.	c.	PROPN
ejpam-5872	264	17	sankar	sankar	PROPN
ejpam-5872	264	18	et	et	PROPN
ejpam-5872	264	19	al	al	PROPN
ejpam-5872	264	20	.	.	PUNCT
ejpam-5872	264	21	/	/	SYM
ejpam-5872	264	22	eur	eur	PROPN
ejpam-5872	264	23	.	.	PUNCT
ejpam-5872	265	1	j.	j.	PROPN
ejpam-5872	265	2	pure	pure	PROPN
ejpam-5872	265	3	appl	appl	PROPN
ejpam-5872	265	4	.	.	PROPN
ejpam-5872	265	5	math	math	PROPN
ejpam-5872	265	6	,	,	PUNCT
ejpam-5872	265	7	18	18	NUM
ejpam-5872	265	8	(	(	PUNCT
ejpam-5872	265	9	4	4	NUM
ejpam-5872	265	10	)	)	PUNCT
ejpam-5872	265	11	(	(	PUNCT
ejpam-5872	265	12	2025	2025	NUM
ejpam-5872	265	13	)	)	PUNCT
ejpam-5872	265	14	,	,	PUNCT
ejpam-5872	265	15	5872	5872	NUM
ejpam-5872	265	16	11	11	NUM
ejpam-5872	265	17	of	of	ADP
ejpam-5872	265	18	17	17	NUM
ejpam-5872	265	19	theorem	theorem	NOUN
ejpam-5872	265	20	12	12	NUM
ejpam-5872	265	21	.	.	PUNCT
ejpam-5872	266	1	if	if	SCONJ
ejpam-5872	266	2	∑	∑	PROPN
ejpam-5872	266	3	±	±	PROPN
ejpam-5872	266	4	is	be	AUX
ejpam-5872	266	5	any	any	DET
ejpam-5872	266	6	signed	sign	VERB
ejpam-5872	266	7	-	-	PUNCT
ejpam-5872	266	8	fg	fg	NOUN
ejpam-5872	266	9	without	without	ADP
ejpam-5872	266	10	isolated	isolated	ADJ
ejpam-5872	266	11	nodes	node	NOUN
ejpam-5872	266	12	,	,	PUNCT
ejpam-5872	266	13	then	then	ADV
ejpam-5872	266	14	γ	γ	PROPN
ejpam-5872	266	15	≤	≤	NOUN
ejpam-5872	266	16	ג	ג	ADP
ejpam-5872	266	17	2	2	NUM
ejpam-5872	266	18	.	.	PUNCT
ejpam-5872	266	19	proof	proof	NOUN
ejpam-5872	266	20	.	.	PUNCT
ejpam-5872	267	1	in	in	ADP
ejpam-5872	267	2	∑	∑	PROPN
ejpam-5872	267	3	±	±	NUM
ejpam-5872	267	4	,	,	PUNCT
ejpam-5872	267	5	d	d	PROPN
ejpam-5872	267	6	would	would	AUX
ejpam-5872	267	7	be	be	AUX
ejpam-5872	267	8	the	the	DET
ejpam-5872	267	9	smallest	small	ADJ
ejpam-5872	267	10	dominant	dominant	ADJ
ejpam-5872	267	11	set	set	NOUN
ejpam-5872	267	12	.	.	PUNCT
ejpam-5872	268	1	consequently	consequently	ADV
ejpam-5872	268	2	,	,	PUNCT
ejpam-5872	268	3	theorem	theorem	VERB
ejpam-5872	268	4	7	7	NUM
ejpam-5872	268	5	states	state	NOUN
ejpam-5872	268	6	that	that	SCONJ
ejpam-5872	268	7	v	v	ADP
ejpam-5872	268	8	−	−	PROPN
ejpam-5872	268	9	d	d	NOUN
ejpam-5872	268	10	is	be	AUX
ejpam-5872	268	11	a	a	DET
ejpam-5872	268	12	dominant	dominant	ADJ
ejpam-5872	268	13	set	set	NOUN
ejpam-5872	268	14	of	of	ADP
ejpam-5872	268	15	∑	∑	PUNCT
ejpam-5872	268	16	±	±	PROPN
ejpam-5872	268	17	itself	itself	PRON
ejpam-5872	268	18	.	.	PUNCT
ejpam-5872	269	1	it	it	PRON
ejpam-5872	269	2	follows	follow	VERB
ejpam-5872	269	3	that	that	SCONJ
ejpam-5872	269	4	γ	γ	PROPN
ejpam-5872	269	5	≤	≤	PROPN
ejpam-5872	269	6	|d|	|d|	PROPN
ejpam-5872	269	7	and	and	CCONJ
ejpam-5872	269	8	γ	γ	PROPN
ejpam-5872	269	9	≤	≤	X
ejpam-5872	269	10	|ℑ	|ℑ	NOUN
ejpam-5872	269	11	−	−	PROPN
ejpam-5872	269	12	d|	d|	PROPN
ejpam-5872	269	13	.	.	PUNCT
ejpam-5872	270	1	therefore	therefore	ADV
ejpam-5872	270	2	,	,	PUNCT
ejpam-5872	270	3	γ	γ	PROPN
ejpam-5872	270	4	≤	≤	NOUN
ejpam-5872	270	5	ג	ג	DET
ejpam-5872	270	6	2	2	NUM
ejpam-5872	270	7	results	result	NOUN
ejpam-5872	270	8	from	from	ADP
ejpam-5872	270	9	2γ	2γ	NOUN
ejpam-5872	270	10	≤	≤	NUM
ejpam-5872	270	11	|d|+	|d|+	NOUN
ejpam-5872	270	12	|ℑ	|ℑ	NOUN
ejpam-5872	270	13	−d|	−d|	X
ejpam-5872	270	14	=	=	SYM
ejpam-5872	270	15	.ג	.ג	SYM
ejpam-5872	270	16	corollary	corollary	ADJ
ejpam-5872	270	17	1	1	NUM
ejpam-5872	270	18	.	.	PUNCT
ejpam-5872	270	19	assume	assume	VERB
ejpam-5872	270	20	that	that	SCONJ
ejpam-5872	270	21	∑	∑	PROPN
ejpam-5872	270	22	±	±	PROPN
ejpam-5872	270	23	is	be	AUX
ejpam-5872	270	24	a	a	DET
ejpam-5872	270	25	signed	sign	VERB
ejpam-5872	270	26	-	-	PUNCT
ejpam-5872	270	27	fg	fg	NOUN
ejpam-5872	270	28	that	that	PRON
ejpam-5872	270	29	contains	contain	VERB
ejpam-5872	270	30	neither	neither	CCONJ
ejpam-5872	270	31	∑	∑	PROPN
ejpam-5872	270	32	±	±	NOUN
ejpam-5872	270	33	nor	nor	CCONJ
ejpam-5872	270	34	∑	∑	PUNCT
ejpam-5872	270	35	±	±	NOUN
ejpam-5872	270	36	isolated	isolate	VERB
ejpam-5872	270	37	nodes	node	NOUN
ejpam-5872	270	38	.	.	PUNCT
ejpam-5872	271	1	thus	thus	ADV
ejpam-5872	271	2	,	,	PUNCT
ejpam-5872	271	3	γ+	γ+	PUNCT
ejpam-5872	271	4	γ	γ	PROPN
ejpam-5872	271	5	≤	≤	X
ejpam-5872	271	6	.ג	.ג	VERB
ejpam-5872	272	1	if	if	SCONJ
ejpam-5872	272	2	and	and	CCONJ
ejpam-5872	272	3	only	only	ADV
ejpam-5872	272	4	if	if	SCONJ
ejpam-5872	272	5	γ	γ	X
ejpam-5872	272	6	=	=	SYM
ejpam-5872	272	7	γ	γ	X
ejpam-5872	272	8	=	=	SYM
ejpam-5872	272	9	ג	ג	ADP
ejpam-5872	272	10	2	2	NUM
ejpam-5872	272	11	,	,	PUNCT
ejpam-5872	272	12	then	then	ADV
ejpam-5872	272	13	additional	additional	ADJ
ejpam-5872	272	14	equality	equality	NOUN
ejpam-5872	272	15	is	be	AUX
ejpam-5872	272	16	preserved	preserve	VERB
ejpam-5872	272	17	.	.	PUNCT
ejpam-5872	273	1	proof	proof	NOUN
ejpam-5872	273	2	.	.	PUNCT
ejpam-5872	274	1	with	with	ADP
ejpam-5872	274	2	no	no	DET
ejpam-5872	274	3	isolated	isolated	ADJ
ejpam-5872	274	4	nodes	node	NOUN
ejpam-5872	274	5	,	,	PUNCT
ejpam-5872	274	6	∑	∑	PUNCT
ejpam-5872	274	7	±	±	NOUN
ejpam-5872	274	8	is	be	AUX
ejpam-5872	274	9	a	a	DET
ejpam-5872	274	10	signed	sign	VERB
ejpam-5872	274	11	-	-	PUNCT
ejpam-5872	274	12	fg	fg	PROPN
ejpam-5872	274	13	.	.	PUNCT
ejpam-5872	274	14	theorem	theorem	VERB
ejpam-5872	274	15	12	12	NUM
ejpam-5872	274	16	thus	thus	ADV
ejpam-5872	274	17	states	state	VERB
ejpam-5872	274	18	that	that	SCONJ
ejpam-5872	274	19	γ	γ	NOUN
ejpam-5872	274	20	≤	≤	NOUN
ejpam-5872	274	21	ג	ג	ADP
ejpam-5872	274	22	2	2	NUM
ejpam-5872	274	23	and	and	CCONJ
ejpam-5872	274	24	γ	γ	NOUN
ejpam-5872	274	25	≤	≤	NOUN
ejpam-5872	274	26	ג	ג	ADP
ejpam-5872	274	27	2	2	NUM
ejpam-5872	274	28	.	.	PUNCT
ejpam-5872	275	1	this	this	PRON
ejpam-5872	275	2	means	mean	VERB
ejpam-5872	275	3	that	that	SCONJ
ejpam-5872	275	4	γ+	γ+	PUNCT
ejpam-5872	275	5	γ	γ	PROPN
ejpam-5872	275	6	≤	≤	NOUN
ejpam-5872	275	7	ג	ג	ADP
ejpam-5872	275	8	2	2	NUM
ejpam-5872	275	9	+	+	CCONJ
ejpam-5872	275	10	ג	ג	SYM
ejpam-5872	275	11	2	2	NUM
ejpam-5872	275	12	=	=	PUNCT
ejpam-5872	275	13	+	+	NOUN
ejpam-5872	275	14	γ	γ	X
ejpam-5872	275	15	.	.	PUNCT
ejpam-5872	275	16	ג	ג	ADP
ejpam-5872	275	17	γ	γ	X
ejpam-5872	275	18	=	=	SYM
ejpam-5872	275	19	ג	ג	PROPN
ejpam-5872	275	20	if	if	SCONJ
ejpam-5872	275	21	γ	γ	X
ejpam-5872	275	22	=	=	SYM
ejpam-5872	275	23	γ	γ	X
ejpam-5872	275	24	=	=	SYM
ejpam-5872	275	25	ג	ג	PROPN
ejpam-5872	275	26	2	2	NUM
ejpam-5872	275	27	.	.	PUNCT
ejpam-5872	276	1	if	if	SCONJ
ejpam-5872	276	2	γ+	γ+	PUNCT
ejpam-5872	276	3	γ	γ	X
ejpam-5872	276	4	=	=	X
ejpam-5872	276	5	,	,	PUNCT
ejpam-5872	276	6	ג	ג	PROPN
ejpam-5872	276	7	on	on	ADP
ejpam-5872	276	8	the	the	DET
ejpam-5872	276	9	other	other	ADJ
ejpam-5872	276	10	hand	hand	NOUN
ejpam-5872	276	11	.	.	PUNCT
ejpam-5872	277	1	γ	γ	NOUN
ejpam-5872	277	2	≤	≤	NOUN
ejpam-5872	277	3	ג	ג	ADP
ejpam-5872	277	4	2	2	NUM
ejpam-5872	277	5	and	and	CCONJ
ejpam-5872	277	6	γ	γ	PROPN
ejpam-5872	277	7	≤	≤	NOUN
ejpam-5872	277	8	ג	ג	ADP
ejpam-5872	277	9	2	2	NUM
ejpam-5872	277	10	according	accord	VERB
ejpam-5872	277	11	to	to	ADP
ejpam-5872	277	12	theorem	theorem	NOUN
ejpam-5872	277	13	12	12	NUM
ejpam-5872	277	14	.	.	PUNCT
ejpam-5872	278	1	γ+	γ+	X
ejpam-5872	278	2	γ	γ	X
ejpam-5872	278	3	<	<	X
ejpam-5872	278	4	,	,	PUNCT
ejpam-5872	278	5	ג	ג	PROPN
ejpam-5872	278	6	which	which	PRON
ejpam-5872	278	7	is	be	AUX
ejpam-5872	278	8	contrary	contrary	ADJ
ejpam-5872	278	9	to	to	ADP
ejpam-5872	278	10	our	our	PRON
ejpam-5872	278	11	premise	premise	NOUN
ejpam-5872	278	12	,	,	PUNCT
ejpam-5872	278	13	if	if	SCONJ
ejpam-5872	278	14	γ	γ	NOUN
ejpam-5872	278	15	≤	≤	X
ejpam-5872	278	16	ג	ג	ADP
ejpam-5872	278	17	2	2	NUM
ejpam-5872	278	18	or	or	CCONJ
ejpam-5872	278	19	γ	γ	NOUN
ejpam-5872	278	20	≤	≤	NOUN
ejpam-5872	278	21	ג	ג	ADP
ejpam-5872	278	22	2	2	NUM
ejpam-5872	278	23	.	.	PUNCT
ejpam-5872	279	1	γ	γ	X
ejpam-5872	279	2	=	=	SYM
ejpam-5872	279	3	γ	γ	X
ejpam-5872	279	4	=	=	SYM
ejpam-5872	279	5	ג	ג	ADP
ejpam-5872	279	6	2	2	NUM
ejpam-5872	279	7	,	,	PUNCT
ejpam-5872	279	8	as	as	ADP
ejpam-5872	279	9	a	a	DET
ejpam-5872	279	10	result	result	NOUN
ejpam-5872	279	11	.	.	PUNCT
ejpam-5872	280	1	theorem	theorem	ADJ
ejpam-5872	280	2	13	13	NUM
ejpam-5872	280	3	.	.	PUNCT
ejpam-5872	281	1	let	let	VERB
ejpam-5872	281	2	σ±	σ±	NOUN
ejpam-5872	281	3	=	=	SYM
ejpam-5872	281	4	(	(	PUNCT
ejpam-5872	281	5	ℑ	ℑ	PROPN
ejpam-5872	281	6	,	,	PUNCT
ejpam-5872	281	7	σ	σ	PROPN
ejpam-5872	281	8	,	,	PUNCT
ejpam-5872	281	9	µ	µ	NOUN
ejpam-5872	281	10	)	)	PUNCT
ejpam-5872	281	11	be	be	VERB
ejpam-5872	281	12	a	a	DET
ejpam-5872	281	13	signed	sign	VERB
ejpam-5872	281	14	-	-	PUNCT
ejpam-5872	281	15	fg	fg	NOUN
ejpam-5872	281	16	of	of	ADP
ejpam-5872	281	17	order	order	NOUN
ejpam-5872	281	18	℘.	℘.	PROPN
ejpam-5872	281	19	then	then	ADV
ejpam-5872	281	20	min	min	PROPN
ejpam-5872	281	21	ℑ∋ג	ℑ∋ג	PROPN
ejpam-5872	281	22	σ(ג	σ(ג	PROPN
ejpam-5872	281	23	)	)	PUNCT
ejpam-5872	281	24	≤	≤	NUM
ejpam-5872	281	25	γ	γ	X
ejpam-5872	281	26	≤	≤	PROPN
ejpam-5872	281	27	℘−∆sn	℘−∆sn	PROPN
ejpam-5872	281	28	(	(	PUNCT
ejpam-5872	281	29	∑	∑	PROPN
ejpam-5872	281	30	±	±	NUM
ejpam-5872	281	31	)	)	PUNCT
ejpam-5872	281	32	.	.	PUNCT
ejpam-5872	282	1	proof	proof	NOUN
ejpam-5872	282	2	.	.	PUNCT
ejpam-5872	283	1	suppose	suppose	VERB
ejpam-5872	283	2	that	that	SCONJ
ejpam-5872	283	3	the	the	DET
ejpam-5872	283	4	initial	initial	ADJ
ejpam-5872	283	5	component	component	NOUN
ejpam-5872	283	6	min	min	NOUN
ejpam-5872	283	7	ℑ∋ג	ℑ∋ג	PROPN
ejpam-5872	283	8	σ(ג	σ(ג	PROPN
ejpam-5872	283	9	)	)	PUNCT
ejpam-5872	283	10	≤	≤	NOUN
ejpam-5872	283	11	γ	γ	PROPN
ejpam-5872	283	12	.	.	PROPN
ejpam-5872	284	1	if	if	SCONJ
ejpam-5872	284	2	min	min	PROPN
ejpam-5872	284	3	ℑ∋ג	ℑ∋ג	PROPN
ejpam-5872	284	4	σ(ג	σ(ג	PROPN
ejpam-5872	284	5	)	)	PUNCT
ejpam-5872	284	6	is	be	AUX
ejpam-5872	284	7	true	true	ADJ
ejpam-5872	284	8	,	,	PUNCT
ejpam-5872	284	9	then	then	ADV
ejpam-5872	284	10	if	if	SCONJ
ejpam-5872	284	11	ג	ג	PROPN
ejpam-5872	284	12	are	be	AUX
ejpam-5872	284	13	any	any	DET
ejpam-5872	284	14	vertices	vertex	NOUN
ejpam-5872	284	15	in	in	ADP
ejpam-5872	284	16	∑	∑	PROPN
ejpam-5872	284	17	±	±	PROPN
ejpam-5872	284	18	,	,	PUNCT
ejpam-5872	284	19	then	then	ADV
ejpam-5872	284	20	dsn	dsn	PROPN
ejpam-5872	284	21	(	(	PUNCT
ejpam-5872	284	22	ג	ג	PROPN
ejpam-5872	284	23	)	)	PUNCT
ejpam-5872	284	24	=	=	PUNCT
ejpam-5872	284	25	∆sn	∆sn	NOUN
ejpam-5872	284	26	(	(	PUNCT
ejpam-5872	284	27	∑	∑	NUM
ejpam-5872	284	28	±	±	NUM
ejpam-5872	284	29	)	)	PUNCT
ejpam-5872	284	30	.	.	PUNCT
ejpam-5872	285	1	ℑ−ns(ג	ℑ−ns(ג	PROPN
ejpam-5872	285	2	)	)	PUNCT
ejpam-5872	285	3	is	be	AUX
ejpam-5872	285	4	a	a	DET
ejpam-5872	285	5	domination	domination	NOUN
ejpam-5872	285	6	set	set	NOUN
ejpam-5872	285	7	of	of	ADP
ejpam-5872	285	8	∑	∑	PROPN
ejpam-5872	285	9	±	±	PROPN
ejpam-5872	285	10	,	,	PUNCT
ejpam-5872	285	11	in	in	ADP
ejpam-5872	285	12	this	this	DET
ejpam-5872	285	13	case	case	NOUN
ejpam-5872	285	14	.	.	PUNCT
ejpam-5872	286	1	it	it	PRON
ejpam-5872	286	2	follows	follow	VERB
ejpam-5872	286	3	that	that	SCONJ
ejpam-5872	286	4	γ	γ	PROPN
ejpam-5872	286	5	(	(	PUNCT
ejpam-5872	286	6	∑	∑	PROPN
ejpam-5872	286	7	±	±	NUM
ejpam-5872	286	8	)	)	PUNCT
ejpam-5872	286	9	≤	≤	NOUN
ejpam-5872	286	10	℘−∆sn	℘−∆sn	PROPN
ejpam-5872	286	11	(	(	PUNCT
ejpam-5872	286	12	∑	∑	PROPN
ejpam-5872	286	13	±	±	NUM
ejpam-5872	286	14	)	)	PUNCT
ejpam-5872	286	15	.	.	PUNCT
ejpam-5872	287	1	remark	remark	PROPN
ejpam-5872	287	2	1	1	NUM
ejpam-5872	287	3	.	.	PUNCT
ejpam-5872	288	1	if	if	SCONJ
ejpam-5872	288	2	σ±	σ±	NOUN
ejpam-5872	288	3	=	=	SYM
ejpam-5872	288	4	(	(	PUNCT
ejpam-5872	288	5	µ	µ	X
ejpam-5872	288	6	,	,	PUNCT
ejpam-5872	288	7	σ	σ	PROPN
ejpam-5872	288	8	,	,	PUNCT
ejpam-5872	288	9	µ	µ	NOUN
ejpam-5872	288	10	)	)	PUNCT
ejpam-5872	288	11	is	be	AUX
ejpam-5872	288	12	a	a	DET
ejpam-5872	288	13	complete	complete	ADJ
ejpam-5872	288	14	signed	sign	VERB
ejpam-5872	288	15	-	-	PUNCT
ejpam-5872	288	16	fg	fg	NOUN
ejpam-5872	288	17	of	of	ADP
ejpam-5872	288	18	order	order	NOUN
ejpam-5872	288	19	℘.	℘.	PROPN
ejpam-5872	288	20	then	then	ADV
ejpam-5872	288	21	min(σ(ג	min(σ(ג	PROPN
ejpam-5872	288	22	)	)	PUNCT
ejpam-5872	288	23	)	)	PUNCT
ejpam-5872	289	1	=	=	SYM
ejpam-5872	289	2	γ	γ	X
ejpam-5872	289	3	=	=	SYM
ejpam-5872	289	4	℘−∆sn	℘−∆sn	PROPN
ejpam-5872	289	5	(	(	PUNCT
ejpam-5872	289	6	∑	∑	PROPN
ejpam-5872	289	7	±	±	NUM
ejpam-5872	289	8	)	)	PUNCT
ejpam-5872	289	9	.	.	PUNCT
ejpam-5872	290	1	remark	remark	PROPN
ejpam-5872	290	2	2	2	NUM
ejpam-5872	290	3	.	.	PUNCT
ejpam-5872	291	1	clearly	clearly	ADV
ejpam-5872	291	2	∆s	∆s	PROPN
ejpam-5872	291	3	(	(	PUNCT
ejpam-5872	291	4	∑	∑	PROPN
ejpam-5872	291	5	±	±	NUM
ejpam-5872	291	6	)	)	PUNCT
ejpam-5872	291	7	≤	≤	NUM
ejpam-5872	291	8	∆sn	∆sn	NOUN
ejpam-5872	291	9	(	(	PUNCT
ejpam-5872	291	10	∑	∑	NUM
ejpam-5872	291	11	±	±	NUM
ejpam-5872	291	12	)	)	PUNCT
ejpam-5872	291	13	.	.	PUNCT
ejpam-5872	292	1	3	3	X
ejpam-5872	292	2	.	.	X
ejpam-5872	292	3	domination	domination	NOUN
ejpam-5872	292	4	in	in	ADP
ejpam-5872	292	5	signed	sign	VERB
ejpam-5872	292	6	fuzzy	fuzzy	ADJ
ejpam-5872	292	7	trees	tree	NOUN
ejpam-5872	292	8	the	the	DET
ejpam-5872	292	9	notion	notion	NOUN
ejpam-5872	292	10	of	of	ADP
ejpam-5872	292	11	domination	domination	NOUN
ejpam-5872	292	12	in	in	ADP
ejpam-5872	292	13	signed	sign	VERB
ejpam-5872	292	14	fuzzy	fuzzy	ADJ
ejpam-5872	292	15	trees	tree	NOUN
ejpam-5872	292	16	,	,	PUNCT
ejpam-5872	292	17	a	a	DET
ejpam-5872	292	18	particular	particular	ADJ
ejpam-5872	292	19	class	class	NOUN
ejpam-5872	292	20	of	of	ADP
ejpam-5872	292	21	signed	sign	VERB
ejpam-5872	292	22	fuzzy	fuzzy	ADJ
ejpam-5872	292	23	graphs	graph	NOUN
ejpam-5872	292	24	distinguished	distinguish	VERB
ejpam-5872	292	25	by	by	ADP
ejpam-5872	292	26	their	their	PRON
ejpam-5872	292	27	hierarchical	hierarchical	ADJ
ejpam-5872	292	28	structure	structure	NOUN
ejpam-5872	292	29	and	and	CCONJ
ejpam-5872	292	30	lack	lack	NOUN
ejpam-5872	292	31	of	of	ADP
ejpam-5872	292	32	cycles	cycle	NOUN
ejpam-5872	292	33	,	,	PUNCT
ejpam-5872	292	34	is	be	AUX
ejpam-5872	292	35	explored	explore	VERB
ejpam-5872	292	36	in	in	ADP
ejpam-5872	292	37	this	this	DET
ejpam-5872	292	38	section	section	NOUN
ejpam-5872	292	39	.	.	PUNCT
ejpam-5872	293	1	the	the	DET
ejpam-5872	293	2	discussion	discussion	NOUN
ejpam-5872	293	3	is	be	AUX
ejpam-5872	293	4	on	on	ADP
ejpam-5872	293	5	the	the	DET
ejpam-5872	293	6	distinctive	distinctive	ADJ
ejpam-5872	293	7	characteristics	characteristic	NOUN
ejpam-5872	293	8	of	of	ADP
ejpam-5872	293	9	signed	sign	VERB
ejpam-5872	293	10	fuzzy	fuzzy	ADJ
ejpam-5872	293	11	trees	tree	NOUN
ejpam-5872	293	12	,	,	PUNCT
ejpam-5872	293	13	such	such	ADJ
ejpam-5872	293	14	as	as	ADP
ejpam-5872	293	15	their	their	PRON
ejpam-5872	293	16	dominating	dominating	NOUN
ejpam-5872	293	17	sets	set	NOUN
ejpam-5872	293	18	,	,	PUNCT
ejpam-5872	293	19	signed	sign	VERB
ejpam-5872	293	20	fuzzy	fuzzy	ADJ
ejpam-5872	293	21	cut	cut	NOUN
ejpam-5872	293	22	nodes	node	NOUN
ejpam-5872	293	23	,	,	PUNCT
ejpam-5872	293	24	and	and	CCONJ
ejpam-5872	293	25	signed	sign	VERB
ejpam-5872	293	26	fuzzy	fuzzy	ADJ
ejpam-5872	293	27	end	end	NOUN
ejpam-5872	293	28	nodes	node	NOUN
ejpam-5872	293	29	,	,	PUNCT
ejpam-5872	293	30	building	build	VERB
ejpam-5872	293	31	on	on	ADP
ejpam-5872	293	32	the	the	DET
ejpam-5872	293	33	fundamental	fundamental	ADJ
ejpam-5872	293	34	ideas	idea	NOUN
ejpam-5872	293	35	of	of	ADP
ejpam-5872	293	36	signed	sign	VERB
ejpam-5872	293	37	fuzzy	fuzzy	ADJ
ejpam-5872	293	38	graphs	graph	NOUN
ejpam-5872	293	39	and	and	CCONJ
ejpam-5872	293	40	dominance	dominance	NOUN
ejpam-5872	293	41	.	.	PUNCT
ejpam-5872	294	1	to	to	PART
ejpam-5872	294	2	demonstrate	demonstrate	VERB
ejpam-5872	294	3	how	how	SCONJ
ejpam-5872	294	4	dominance	dominance	NOUN
ejpam-5872	294	5	ensures	ensure	VERB
ejpam-5872	294	6	connectedness	connectedness	NOUN
ejpam-5872	294	7	and	and	CCONJ
ejpam-5872	294	8	effective	effective	ADJ
ejpam-5872	294	9	representation	representation	NOUN
ejpam-5872	294	10	of	of	ADP
ejpam-5872	294	11	these	these	DET
ejpam-5872	294	12	trees	tree	NOUN
ejpam-5872	294	13	,	,	PUNCT
ejpam-5872	294	14	theorems	theorem	NOUN
ejpam-5872	294	15	and	and	CCONJ
ejpam-5872	294	16	proofs	proof	NOUN
ejpam-5872	294	17	are	be	AUX
ejpam-5872	294	18	provided	provide	VERB
ejpam-5872	294	19	.	.	PUNCT
ejpam-5872	295	1	analyzing	analyze	VERB
ejpam-5872	295	2	the	the	DET
ejpam-5872	295	3	interactions	interaction	NOUN
ejpam-5872	295	4	between	between	ADP
ejpam-5872	295	5	signed	sign	VERB
ejpam-5872	295	6	fuzzy	fuzzy	ADJ
ejpam-5872	295	7	trees	tree	NOUN
ejpam-5872	295	8	and	and	CCONJ
ejpam-5872	295	9	their	their	PRON
ejpam-5872	295	10	uses	use	NOUN
ejpam-5872	295	11	in	in	ADP
ejpam-5872	295	12	structured	structured	ADJ
ejpam-5872	295	13	network	network	NOUN
ejpam-5872	295	14	environments	environment	NOUN
ejpam-5872	295	15	is	be	AUX
ejpam-5872	295	16	made	make	VERB
ejpam-5872	295	17	easier	easy	ADJ
ejpam-5872	295	18	by	by	ADP
ejpam-5872	295	19	these	these	DET
ejpam-5872	295	20	revelations	revelation	NOUN
ejpam-5872	295	21	.	.	PUNCT
ejpam-5872	296	1	definition	definition	NOUN
ejpam-5872	296	2	13	13	NUM
ejpam-5872	296	3	.	.	PUNCT
ejpam-5872	297	1	if	if	SCONJ
ejpam-5872	297	2	removing	remove	VERB
ejpam-5872	297	3	,	,	PUNCT
ejpam-5872	297	4	1ג	1ג	NUM
ejpam-5872	297	5	)	)	PUNCT
ejpam-5872	297	6	(	(	PUNCT
ejpam-5872	297	7	2ג	2ג	NOUN
ejpam-5872	297	8	reduces	reduce	VERB
ejpam-5872	297	9	the	the	DET
ejpam-5872	297	10	strength	strength	NOUN
ejpam-5872	297	11	between	between	ADP
ejpam-5872	297	12	some	some	DET
ejpam-5872	297	13	node	node	NOUN
ejpam-5872	297	14	pairs	pair	NOUN
ejpam-5872	297	15	,	,	PUNCT
ejpam-5872	297	16	then	then	ADV
ejpam-5872	297	17	an	an	DET
ejpam-5872	297	18	arc	arc	NOUN
ejpam-5872	297	19	,	,	PUNCT
ejpam-5872	297	20	1ג	1ג	NUM
ejpam-5872	297	21	)	)	PUNCT
ejpam-5872	297	22	(	(	PUNCT
ejpam-5872	297	23	2ג	2ג	NOUN
ejpam-5872	297	24	is	be	AUX
ejpam-5872	297	25	a	a	DET
ejpam-5872	297	26	signed	sign	VERB
ejpam-5872	297	27	fuzzy	fuzzy	ADJ
ejpam-5872	297	28	bridge	bridge	NOUN
ejpam-5872	297	29	of	of	ADP
ejpam-5872	297	30	σ±	σ±	NOUN
ejpam-5872	297	31	=	=	SYM
ejpam-5872	297	32	(	(	PUNCT
ejpam-5872	297	33	ℑ	ℑ	PROPN
ejpam-5872	297	34	,	,	PUNCT
ejpam-5872	297	35	σ	σ	PROPN
ejpam-5872	297	36	,	,	PUNCT
ejpam-5872	297	37	µ	µ	NOUN
ejpam-5872	297	38	)	)	PUNCT
ejpam-5872	297	39	.	.	PUNCT
ejpam-5872	298	1	definition	definition	NOUN
ejpam-5872	298	2	14	14	NUM
ejpam-5872	298	3	.	.	PUNCT
ejpam-5872	299	1	in	in	ADP
ejpam-5872	299	2	σ±	σ±	NOUN
ejpam-5872	299	3	=	=	SYM
ejpam-5872	299	4	(	(	PUNCT
ejpam-5872	299	5	ℑ	ℑ	PROPN
ejpam-5872	299	6	,	,	PUNCT
ejpam-5872	299	7	σ	σ	PROPN
ejpam-5872	299	8	,	,	PUNCT
ejpam-5872	299	9	µ	µ	NOUN
ejpam-5872	299	10	)	)	PUNCT
ejpam-5872	299	11	,	,	PUNCT
ejpam-5872	299	12	a	a	DET
ejpam-5872	299	13	node	node	NOUN
ejpam-5872	299	14	is	be	AUX
ejpam-5872	299	15	a	a	DET
ejpam-5872	299	16	signed	sign	VERB
ejpam-5872	299	17	fuzzy	fuzzy	ADJ
ejpam-5872	299	18	cutnode	cutnode	NOUN
ejpam-5872	299	19	if	if	SCONJ
ejpam-5872	299	20	its	its	PRON
ejpam-5872	299	21	removal	removal	NOUN
ejpam-5872	299	22	reduces	reduce	VERB
ejpam-5872	299	23	the	the	DET
ejpam-5872	299	24	strength	strength	NOUN
ejpam-5872	299	25	between	between	ADP
ejpam-5872	299	26	some	some	DET
ejpam-5872	299	27	pair	pair	NOUN
ejpam-5872	299	28	of	of	ADP
ejpam-5872	299	29	nodes	node	NOUN
ejpam-5872	299	30	.	.	PUNCT
ejpam-5872	300	1	definition	definition	NOUN
ejpam-5872	300	2	15	15	NUM
ejpam-5872	300	3	.	.	PUNCT
ejpam-5872	301	1	a	a	DET
ejpam-5872	301	2	connected	connect	VERB
ejpam-5872	301	3	signed	sign	VERB
ejpam-5872	301	4	-	-	PUNCT
ejpam-5872	301	5	fg	fg	PRON
ejpam-5872	301	6	σ±	σ±	NOUN
ejpam-5872	301	7	=	=	SYM
ejpam-5872	301	8	(	(	PUNCT
ejpam-5872	301	9	ℑ	ℑ	PROPN
ejpam-5872	301	10	,	,	PUNCT
ejpam-5872	301	11	σ	σ	PROPN
ejpam-5872	301	12	,	,	PUNCT
ejpam-5872	301	13	µ	µ	NOUN
ejpam-5872	301	14	)	)	PUNCT
ejpam-5872	301	15	has	have	VERB
ejpam-5872	301	16	a	a	DET
ejpam-5872	301	17	signed	sign	VERB
ejpam-5872	301	18	fuzzy	fuzzy	ADJ
ejpam-5872	301	19	spanning	span	VERB
ejpam-5872	301	20	subgraph	subgraph	NOUN
ejpam-5872	301	21	f±	f±	PROPN
ejpam-5872	301	22	=	=	SYM
ejpam-5872	301	23	(	(	PUNCT
ejpam-5872	301	24	ζ	ζ	PROPN
ejpam-5872	301	25	,	,	PUNCT
ejpam-5872	301	26	σ	σ	PROPN
ejpam-5872	301	27	,	,	PUNCT
ejpam-5872	301	28	µ	µ	NOUN
ejpam-5872	301	29	)	)	PUNCT
ejpam-5872	301	30	,	,	PUNCT
ejpam-5872	301	31	such	such	ADJ
ejpam-5872	301	32	that	that	SCONJ
ejpam-5872	301	33	µ(1ג	µ(1ג	NOUN
ejpam-5872	301	34	,	,	PUNCT
ejpam-5872	301	35	(	(	PUNCT
ejpam-5872	301	36	2ג	2ג	NOUN
ejpam-5872	301	37	<	<	X
ejpam-5872	301	38	conn(1ג	conn(1ג	PROPN
ejpam-5872	301	39	,	,	PUNCT
ejpam-5872	301	40	(	(	PUNCT
ejpam-5872	301	41	2ג	2ג	NOUN
ejpam-5872	301	42	for	for	ADP
ejpam-5872	301	43	all	all	DET
ejpam-5872	301	44	edges	edge	NOUN
ejpam-5872	301	45	,	,	PUNCT
ejpam-5872	301	46	1ג	1ג	NUM
ejpam-5872	301	47	)	)	PUNCT
ejpam-5872	301	48	(	(	PUNCT
ejpam-5872	301	49	2ג	2ג	NOUN
ejpam-5872	301	50	not	not	PART
ejpam-5872	301	51	included	include	VERB
ejpam-5872	301	52	in	in	ADP
ejpam-5872	301	53	f±	f±	PROPN
ejpam-5872	301	54	=	=	SYM
ejpam-5872	301	55	(	(	PUNCT
ejpam-5872	301	56	ζ	ζ	PROPN
ejpam-5872	301	57	,	,	PUNCT
ejpam-5872	301	58	σ	σ	PROPN
ejpam-5872	301	59	,	,	PUNCT
ejpam-5872	301	60	µ	µ	NOUN
ejpam-5872	301	61	)	)	PUNCT
ejpam-5872	301	62	.	.	PUNCT
ejpam-5872	302	1	in	in	ADP
ejpam-5872	302	2	this	this	DET
ejpam-5872	302	3	case	case	NOUN
ejpam-5872	302	4	,	,	PUNCT
ejpam-5872	302	5	σ±	σ±	NOUN
ejpam-5872	302	6	=	=	SYM
ejpam-5872	302	7	(	(	PUNCT
ejpam-5872	302	8	ℑ	ℑ	PROPN
ejpam-5872	302	9	,	,	PUNCT
ejpam-5872	302	10	σ	σ	PROPN
ejpam-5872	302	11	,	,	PUNCT
ejpam-5872	302	12	µ	µ	NOUN
ejpam-5872	302	13	)	)	PUNCT
ejpam-5872	302	14	is	be	AUX
ejpam-5872	302	15	classified	classify	VERB
ejpam-5872	302	16	as	as	ADP
ejpam-5872	302	17	a	a	DET
ejpam-5872	302	18	signed	sign	VERB
ejpam-5872	302	19	fuzzy	fuzzy	ADJ
ejpam-5872	302	20	tree	tree	NOUN
ejpam-5872	302	21	.	.	PUNCT
ejpam-5872	303	1	c.	c.	PROPN
ejpam-5872	303	2	sankar	sankar	PROPN
ejpam-5872	303	3	et	et	PROPN
ejpam-5872	303	4	al	al	PROPN
ejpam-5872	303	5	.	.	PUNCT
ejpam-5872	303	6	/	/	SYM
ejpam-5872	303	7	eur	eur	PROPN
ejpam-5872	303	8	.	.	PUNCT
ejpam-5872	304	1	j.	j.	PROPN
ejpam-5872	304	2	pure	pure	PROPN
ejpam-5872	304	3	appl	appl	PROPN
ejpam-5872	304	4	.	.	PROPN
ejpam-5872	304	5	math	math	PROPN
ejpam-5872	304	6	,	,	PUNCT
ejpam-5872	304	7	18	18	NUM
ejpam-5872	304	8	(	(	PUNCT
ejpam-5872	304	9	4	4	NUM
ejpam-5872	304	10	)	)	PUNCT
ejpam-5872	304	11	(	(	PUNCT
ejpam-5872	304	12	2025	2025	NUM
ejpam-5872	304	13	)	)	PUNCT
ejpam-5872	304	14	,	,	PUNCT
ejpam-5872	304	15	5872	5872	NUM
ejpam-5872	304	16	12	12	NUM
ejpam-5872	304	17	of	of	ADP
ejpam-5872	304	18	17	17	NUM
ejpam-5872	304	19	theorem	theorem	VERB
ejpam-5872	304	20	14	14	NUM
ejpam-5872	304	21	.	.	PUNCT
ejpam-5872	304	22	σ±	σ±	NOUN
ejpam-5872	304	23	=	=	SYM
ejpam-5872	304	24	(	(	PUNCT
ejpam-5872	304	25	ℑ	ℑ	PROPN
ejpam-5872	304	26	,	,	PUNCT
ejpam-5872	304	27	σ	σ	PROPN
ejpam-5872	304	28	,	,	PUNCT
ejpam-5872	304	29	µ	µ	NOUN
ejpam-5872	304	30	)	)	PUNCT
ejpam-5872	304	31	involves	involve	VERB
ejpam-5872	304	32	a	a	DET
ejpam-5872	304	33	signed	sign	VERB
ejpam-5872	304	34	fuzzy	fuzzy	ADJ
ejpam-5872	304	35	bridge	bridge	NOUN
ejpam-5872	304	36	connecting	connect	VERB
ejpam-5872	304	37	each	each	DET
ejpam-5872	304	38	node	node	NOUN
ejpam-5872	304	39	in	in	ADP
ejpam-5872	304	40	a	a	DET
ejpam-5872	304	41	domination	domination	NOUN
ejpam-5872	304	42	set	set	NOUN
ejpam-5872	304	43	of	of	ADP
ejpam-5872	304	44	a	a	DET
ejpam-5872	304	45	non	non	NOUN
ejpam-5872	304	46	isolated	isolate	VERB
ejpam-5872	304	47	signed	sign	VERB
ejpam-5872	304	48	fuzzy	fuzzy	ADJ
ejpam-5872	304	49	tree	tree	NOUN
ejpam-5872	304	50	∑	∑	PUNCT
ejpam-5872	304	51	±.	±.	NOUN
ejpam-5872	304	52	proof	proof	NOUN
ejpam-5872	304	53	.	.	PUNCT
ejpam-5872	305	1	it	it	PRON
ejpam-5872	305	2	is	be	AUX
ejpam-5872	305	3	assumed	assume	VERB
ejpam-5872	305	4	that	that	SCONJ
ejpam-5872	305	5	1ג	1ג	NOUN
ejpam-5872	305	6	is	be	AUX
ejpam-5872	305	7	an	an	DET
ejpam-5872	305	8	element	element	NOUN
ejpam-5872	305	9	of	of	ADP
ejpam-5872	305	10	d	d	PROPN
ejpam-5872	305	11	and	and	CCONJ
ejpam-5872	305	12	that	that	SCONJ
ejpam-5872	305	13	∑	∑	PUNCT
ejpam-5872	305	14	±	±	PROPN
ejpam-5872	305	15	is	be	AUX
ejpam-5872	305	16	a	a	DET
ejpam-5872	305	17	dominanting	dominanting	NOUN
ejpam-5872	305	18	set	set	NOUN
ejpam-5872	305	19	.	.	PUNCT
ejpam-5872	306	1	due	due	ADP
ejpam-5872	306	2	to	to	ADP
ejpam-5872	306	3	the	the	DET
ejpam-5872	306	4	fact	fact	NOUN
ejpam-5872	306	5	that	that	SCONJ
ejpam-5872	306	6	,	,	PUNCT
ejpam-5872	306	7	1ג	1ג	NUM
ejpam-5872	306	8	)	)	PUNCT
ejpam-5872	306	9	(	(	PUNCT
ejpam-5872	306	10	2ג	2ג	NOUN
ejpam-5872	306	11	is	be	AUX
ejpam-5872	306	12	a	a	DET
ejpam-5872	306	13	strong	strong	ADJ
ejpam-5872	306	14	arc	arc	NOUN
ejpam-5872	306	15	since	since	SCONJ
ejpam-5872	306	16	2ג	2ג	NOUN
ejpam-5872	306	17	∈	∈	PROPN
ejpam-5872	306	18	ℑ−d	ℑ−d	PROPN
ejpam-5872	306	19	.	.	PUNCT
ejpam-5872	306	20	arc,(1ג	arc,(1ג	PROPN
ejpam-5872	306	21	,	,	PUNCT
ejpam-5872	306	22	,	,	PUNCT
ejpam-5872	306	23	(	(	PUNCT
ejpam-5872	306	24	2ג	2ג	NOUN
ejpam-5872	306	25	denotes	denote	VERB
ejpam-5872	306	26	a	a	DET
ejpam-5872	306	27	unique	unique	ADJ
ejpam-5872	306	28	mst	mst	PROPN
ejpam-5872	306	29	f±	f±	PROPN
ejpam-5872	306	30	of	of	ADP
ejpam-5872	306	31	∑	∑	PROPN
ejpam-5872	306	32	±.	±.	NOUN
ejpam-5872	306	33	the	the	DET
ejpam-5872	306	34	signed	sign	VERB
ejpam-5872	306	35	fuzzy	fuzzy	ADJ
ejpam-5872	306	36	bridge	bridge	NOUN
ejpam-5872	306	37	,	,	PUNCT
ejpam-5872	306	38	1ג	1ג	NUM
ejpam-5872	306	39	)	)	PUNCT
ejpam-5872	306	40	(	(	PUNCT
ejpam-5872	306	41	2ג	2ג	NOUN
ejpam-5872	306	42	is	be	AUX
ejpam-5872	306	43	therefore	therefore	ADV
ejpam-5872	306	44	an	an	DET
ejpam-5872	306	45	example	example	NOUN
ejpam-5872	306	46	.	.	PUNCT
ejpam-5872	307	1	because	because	SCONJ
ejpam-5872	307	2	1ג	1ג	NOUN
ejpam-5872	307	3	is	be	AUX
ejpam-5872	307	4	arbitrary	arbitrary	ADJ
ejpam-5872	307	5	,	,	PUNCT
ejpam-5872	307	6	every	every	DET
ejpam-5872	307	7	node	node	NOUN
ejpam-5872	307	8	in	in	ADP
ejpam-5872	307	9	the	the	DET
ejpam-5872	307	10	domination	domination	NOUN
ejpam-5872	307	11	set	set	NOUN
ejpam-5872	307	12	of	of	ADP
ejpam-5872	307	13	∑	∑	PROPN
ejpam-5872	307	14	±	±	PROPN
ejpam-5872	307	15	has	have	VERB
ejpam-5872	307	16	this	this	DET
ejpam-5872	307	17	attribute	attribute	NOUN
ejpam-5872	307	18	.	.	PUNCT
ejpam-5872	308	1	theorem	theorem	VERB
ejpam-5872	308	2	15	15	NUM
ejpam-5872	308	3	.	.	PUNCT
ejpam-5872	309	1	in	in	ADP
ejpam-5872	309	2	a	a	DET
ejpam-5872	309	3	non	non	NOUN
ejpam-5872	309	4	isolated	isolate	VERB
ejpam-5872	309	5	signed	sign	VERB
ejpam-5872	309	6	fuzzy	fuzzy	ADJ
ejpam-5872	309	7	tree	tree	NOUN
ejpam-5872	309	8	,	,	PUNCT
ejpam-5872	309	9	f±	f±	PROPN
ejpam-5872	309	10	=	=	SYM
ejpam-5872	309	11	(	(	PUNCT
ejpam-5872	309	12	ℑ	ℑ	PROPN
ejpam-5872	309	13	,	,	PUNCT
ejpam-5872	309	14	σ	σ	PROPN
ejpam-5872	309	15	,	,	PUNCT
ejpam-5872	309	16	µ	µ	NOUN
ejpam-5872	309	17	)	)	PUNCT
ejpam-5872	309	18	,	,	PUNCT
ejpam-5872	309	19	the	the	DET
ejpam-5872	309	20	set	set	NOUN
ejpam-5872	309	21	of	of	ADP
ejpam-5872	309	22	all	all	DET
ejpam-5872	309	23	signed	sign	VERB
ejpam-5872	309	24	fuzzy	fuzzy	ADJ
ejpam-5872	309	25	cut	cut	NOUN
ejpam-5872	309	26	nodes	node	NOUN
ejpam-5872	309	27	is	be	AUX
ejpam-5872	309	28	a	a	DET
ejpam-5872	309	29	dominant	dominant	ADJ
ejpam-5872	309	30	set	set	NOUN
ejpam-5872	309	31	of	of	ADP
ejpam-5872	309	32	σ±	σ±	NOUN
ejpam-5872	309	33	=	=	SYM
ejpam-5872	309	34	(	(	PUNCT
ejpam-5872	309	35	ℑ	ℑ	PROPN
ejpam-5872	309	36	,	,	PUNCT
ejpam-5872	309	37	σ	σ	PROPN
ejpam-5872	309	38	,	,	PUNCT
ejpam-5872	309	39	µ	µ	NOUN
ejpam-5872	309	40	)	)	PUNCT
ejpam-5872	309	41	.	.	PUNCT
ejpam-5872	310	1	proof	proof	NOUN
ejpam-5872	310	2	.	.	PUNCT
ejpam-5872	311	1	the	the	DET
ejpam-5872	311	2	set	set	NOUN
ejpam-5872	311	3	of	of	ADP
ejpam-5872	311	4	all	all	DET
ejpam-5872	311	5	the	the	DET
ejpam-5872	311	6	signed	sign	VERB
ejpam-5872	311	7	fuzzy	fuzzy	ADJ
ejpam-5872	311	8	cut	cut	NOUN
ejpam-5872	311	9	nodes	node	NOUN
ejpam-5872	311	10	of	of	ADP
ejpam-5872	311	11	∑	∑	PROPN
ejpam-5872	311	12	±	±	PROPN
ejpam-5872	311	13	is	be	AUX
ejpam-5872	311	14	represented	represent	VERB
ejpam-5872	311	15	by	by	ADP
ejpam-5872	311	16	d.	d.	PROPN
ejpam-5872	311	17	the	the	DET
ejpam-5872	311	18	set	set	NOUN
ejpam-5872	311	19	of	of	ADP
ejpam-5872	311	20	all	all	PRON
ejpam-5872	311	21	∑	∑	PROPN
ejpam-5872	311	22	±	±	NOUN
ejpam-5872	311	23	signed	sign	VERB
ejpam-5872	311	24	fuzzy	fuzzy	ADJ
ejpam-5872	311	25	end	end	NOUN
ejpam-5872	311	26	nodes	node	NOUN
ejpam-5872	311	27	is	be	AUX
ejpam-5872	311	28	then	then	ADV
ejpam-5872	311	29	ℑ	ℑ	PROPN
ejpam-5872	311	30	−d	−d	VERB
ejpam-5872	311	31	.	.	PUNCT
ejpam-5872	312	1	every	every	DET
ejpam-5872	312	2	ג	ג	PROPN
ejpam-5872	312	3	∈	∈	PROPN
ejpam-5872	312	4	ℑ	ℑ	PROPN
ejpam-5872	312	5	−d	−d	VERB
ejpam-5872	312	6	has	have	VERB
ejpam-5872	312	7	a	a	DET
ejpam-5872	312	8	strong	strong	ADJ
ejpam-5872	312	9	neighbor	neighbor	NOUN
ejpam-5872	312	10	h	h	PROPN
ejpam-5872	312	11	∈	∈	PROPN
ejpam-5872	312	12	d.	d.	PROPN
ejpam-5872	312	13	each	each	DET
ejpam-5872	312	14	ג	ג	PROPN
ejpam-5872	312	15	∈	∈	PROPN
ejpam-5872	312	16	ℑ−d	ℑ−d	PROPN
ejpam-5872	312	17	is	be	AUX
ejpam-5872	312	18	therefore	therefore	ADV
ejpam-5872	312	19	dominated	dominate	VERB
ejpam-5872	312	20	by	by	ADP
ejpam-5872	312	21	a	a	DET
ejpam-5872	312	22	node	node	NOUN
ejpam-5872	312	23	in	in	ADP
ejpam-5872	312	24	d.	d.	PROPN
ejpam-5872	312	25	d	d	PROPN
ejpam-5872	312	26	is	be	AUX
ejpam-5872	312	27	therefore	therefore	ADV
ejpam-5872	312	28	a	a	DET
ejpam-5872	312	29	dominant	dominant	ADJ
ejpam-5872	312	30	set	set	NOUN
ejpam-5872	312	31	of	of	ADP
ejpam-5872	312	32	∑	∑	PUNCT
ejpam-5872	312	33	±.	±.	NOUN
ejpam-5872	312	34	theorem	theorem	VERB
ejpam-5872	312	35	16	16	NUM
ejpam-5872	312	36	.	.	PUNCT
ejpam-5872	313	1	a	a	DET
ejpam-5872	313	2	nontrivial	nontrivial	NOUN
ejpam-5872	313	3	signed	sign	VERB
ejpam-5872	313	4	fuzzy	fuzzy	ADJ
ejpam-5872	313	5	tree	tree	NOUN
ejpam-5872	313	6	,	,	PUNCT
ejpam-5872	313	7	ignoring	ignore	VERB
ejpam-5872	313	8	k2	k2	NOUN
ejpam-5872	313	9	,	,	PUNCT
ejpam-5872	313	10	is	be	AUX
ejpam-5872	313	11	σ±	σ±	NOUN
ejpam-5872	313	12	=	=	SYM
ejpam-5872	313	13	(	(	PUNCT
ejpam-5872	313	14	ℑ	ℑ	PROPN
ejpam-5872	313	15	,	,	PUNCT
ejpam-5872	313	16	σ	σ	PROPN
ejpam-5872	313	17	,	,	PUNCT
ejpam-5872	313	18	µ).there	µ).there	PROPN
ejpam-5872	313	19	must	must	AUX
ejpam-5872	313	20	be	be	AUX
ejpam-5872	313	21	at	at	ADV
ejpam-5872	313	22	least	least	ADJ
ejpam-5872	313	23	one	one	NUM
ejpam-5872	313	24	fuzzy	fuzzy	ADJ
ejpam-5872	313	25	end	end	NOUN
ejpam-5872	313	26	node	node	NOUN
ejpam-5872	313	27	as	as	ADP
ejpam-5872	313	28	a	a	DET
ejpam-5872	313	29	strong	strong	ADJ
ejpam-5872	313	30	neighbor	neighbor	NOUN
ejpam-5872	313	31	for	for	ADP
ejpam-5872	313	32	every	every	DET
ejpam-5872	313	33	fuzzy	fuzzy	ADJ
ejpam-5872	313	34	cut	cut	VERB
ejpam-5872	313	35	node	node	NOUN
ejpam-5872	313	36	for	for	ADP
ejpam-5872	313	37	the	the	DET
ejpam-5872	313	38	set	set	NOUN
ejpam-5872	313	39	of	of	ADP
ejpam-5872	313	40	all	all	DET
ejpam-5872	313	41	fuzzy	fuzzy	ADJ
ejpam-5872	313	42	end	end	NOUN
ejpam-5872	313	43	nodes	node	NOUN
ejpam-5872	313	44	to	to	PART
ejpam-5872	313	45	be	be	AUX
ejpam-5872	313	46	a	a	DET
ejpam-5872	313	47	dominant	dominant	ADJ
ejpam-5872	313	48	set	set	NOUN
ejpam-5872	313	49	.	.	PUNCT
ejpam-5872	314	1	proof	proof	NOUN
ejpam-5872	314	2	.	.	PUNCT
ejpam-5872	315	1	assume	assume	VERB
ejpam-5872	315	2	for	for	ADP
ejpam-5872	315	3	the	the	DET
ejpam-5872	315	4	moment	moment	NOUN
ejpam-5872	315	5	that	that	SCONJ
ejpam-5872	315	6	every	every	DET
ejpam-5872	315	7	signed	sign	VERB
ejpam-5872	315	8	fuzzy	fuzzy	ADJ
ejpam-5872	315	9	cut	cut	VERB
ejpam-5872	315	10	node	node	NOUN
ejpam-5872	315	11	in	in	ADP
ejpam-5872	315	12	∑	∑	PROPN
ejpam-5872	315	13	±	±	PROPN
ejpam-5872	315	14	has	have	VERB
ejpam-5872	315	15	at	at	ADV
ejpam-5872	315	16	least	least	ADV
ejpam-5872	315	17	one	one	NUM
ejpam-5872	315	18	signed	sign	VERB
ejpam-5872	315	19	fuzzy	fuzzy	ADJ
ejpam-5872	315	20	end	end	NOUN
ejpam-5872	315	21	node	node	NOUN
ejpam-5872	315	22	as	as	ADP
ejpam-5872	315	23	a	a	DET
ejpam-5872	315	24	strong	strong	ADJ
ejpam-5872	315	25	neighbor	neighbor	NOUN
ejpam-5872	315	26	.	.	PUNCT
ejpam-5872	316	1	let	let	VERB
ejpam-5872	316	2	d	d	PART
ejpam-5872	316	3	represent	represent	VERB
ejpam-5872	316	4	the	the	DET
ejpam-5872	316	5	set	set	NOUN
ejpam-5872	316	6	of	of	ADP
ejpam-5872	316	7	all	all	DET
ejpam-5872	316	8	signed	sign	VERB
ejpam-5872	316	9	fuzzy	fuzzy	ADJ
ejpam-5872	316	10	end	end	NOUN
ejpam-5872	316	11	nodes	node	NOUN
ejpam-5872	316	12	in	in	ADP
ejpam-5872	316	13	∑	∑	PROPN
ejpam-5872	316	14	±.	±.	NOUN
ejpam-5872	316	15	after	after	ADP
ejpam-5872	316	16	that	that	PRON
ejpam-5872	316	17	,	,	PUNCT
ejpam-5872	316	18	ℑ−d	ℑ−d	PRON
ejpam-5872	316	19	represents	represent	VERB
ejpam-5872	316	20	the	the	DET
ejpam-5872	316	21	set	set	NOUN
ejpam-5872	316	22	of	of	ADP
ejpam-5872	316	23	signed	sign	VERB
ejpam-5872	316	24	fuzzy	fuzzy	ADJ
ejpam-5872	316	25	cut	cut	NOUN
ejpam-5872	316	26	nodes	node	NOUN
ejpam-5872	316	27	of	of	ADP
ejpam-5872	316	28	∑	∑	PUNCT
ejpam-5872	316	29	±.	±.	NOUN
ejpam-5872	316	30	it	it	PRON
ejpam-5872	316	31	is	be	AUX
ejpam-5872	316	32	assumed	assume	VERB
ejpam-5872	316	33	that	that	SCONJ
ejpam-5872	316	34	for	for	ADP
ejpam-5872	316	35	each	each	DET
ejpam-5872	316	36	1ג	1ג	NUM
ejpam-5872	316	37	∈	∈	PROPN
ejpam-5872	316	38	ℑ−d	ℑ−d	NOUN
ejpam-5872	316	39	,	,	PUNCT
ejpam-5872	316	40	there	there	PRON
ejpam-5872	316	41	is	be	VERB
ejpam-5872	316	42	a	a	DET
ejpam-5872	316	43	2ג	2ג	NUM
ejpam-5872	316	44	∈	∈	NOUN
ejpam-5872	316	45	d	d	SCONJ
ejpam-5872	316	46	such	such	ADJ
ejpam-5872	316	47	that	that	PRON
ejpam-5872	316	48	(	(	PUNCT
ejpam-5872	316	49	β1	β1	NOUN
ejpam-5872	316	50	,	,	PUNCT
ejpam-5872	316	51	β2	β2	PROPN
ejpam-5872	316	52	)	)	PUNCT
ejpam-5872	316	53	is	be	AUX
ejpam-5872	316	54	a	a	DET
ejpam-5872	316	55	strong	strong	ADJ
ejpam-5872	316	56	arc	arc	NOUN
ejpam-5872	316	57	.	.	PUNCT
ejpam-5872	317	1	consequently	consequently	ADV
ejpam-5872	317	2	,	,	PUNCT
ejpam-5872	317	3	by	by	ADP
ejpam-5872	317	4	definition	definition	NOUN
ejpam-5872	317	5	of	of	ADP
ejpam-5872	317	6	a	a	DET
ejpam-5872	317	7	domination	domination	NOUN
ejpam-5872	317	8	set	set	NOUN
ejpam-5872	317	9	,	,	PUNCT
ejpam-5872	317	10	d	d	PROPN
ejpam-5872	317	11	is	be	AUX
ejpam-5872	317	12	a	a	DET
ejpam-5872	317	13	domination	domination	NOUN
ejpam-5872	317	14	set	set	NOUN
ejpam-5872	317	15	of	of	ADP
ejpam-5872	317	16	∑	∑	PUNCT
ejpam-5872	317	17	±.	±.	NOUN
ejpam-5872	317	18	conversely	conversely	ADV
ejpam-5872	317	19	,	,	PUNCT
ejpam-5872	317	20	let	let	VERB
ejpam-5872	317	21	’s	’s	PRON
ejpam-5872	317	22	say	say	VERB
ejpam-5872	317	23	that	that	SCONJ
ejpam-5872	317	24	the	the	DET
ejpam-5872	317	25	set	set	PROPN
ejpam-5872	317	26	d	d	PROPN
ejpam-5872	317	27	,	,	PUNCT
ejpam-5872	317	28	which	which	PRON
ejpam-5872	317	29	includes	include	VERB
ejpam-5872	317	30	all	all	DET
ejpam-5872	317	31	fuzzy	fuzzy	ADJ
ejpam-5872	317	32	end	end	NOUN
ejpam-5872	317	33	nodes	node	NOUN
ejpam-5872	317	34	,	,	PUNCT
ejpam-5872	317	35	is	be	AUX
ejpam-5872	317	36	a	a	DET
ejpam-5872	317	37	dominant	dominant	ADJ
ejpam-5872	317	38	set	set	NOUN
ejpam-5872	317	39	of	of	ADP
ejpam-5872	317	40	∑	∑	PUNCT
ejpam-5872	317	41	±.	±.	NOUN
ejpam-5872	317	42	consider	consider	VERB
ejpam-5872	317	43	a	a	DET
ejpam-5872	317	44	signed	sign	VERB
ejpam-5872	317	45	fuzzy	fuzzy	ADJ
ejpam-5872	317	46	cut	cut	VERB
ejpam-5872	317	47	node	node	NOUN
ejpam-5872	317	48	of	of	ADP
ejpam-5872	317	49	∑	∑	PROPN
ejpam-5872	317	50	±	±	PROPN
ejpam-5872	317	51	,	,	PUNCT
ejpam-5872	317	52	.1ג	.1ג	NOUN
ejpam-5872	317	53	1ג	1ג	NUM
ejpam-5872	317	54	∈	∈	PROPN
ejpam-5872	317	55	ℑ−d	ℑ−d	NOUN
ejpam-5872	317	56	,	,	PUNCT
ejpam-5872	317	57	therefore	therefore	ADV
ejpam-5872	317	58	.	.	PUNCT
ejpam-5872	318	1	since	since	SCONJ
ejpam-5872	318	2	d	d	PROPN
ejpam-5872	318	3	is	be	AUX
ejpam-5872	318	4	a	a	DET
ejpam-5872	318	5	domination	domination	NOUN
ejpam-5872	318	6	set	set	NOUN
ejpam-5872	318	7	of	of	ADP
ejpam-5872	318	8	∑	∑	PROPN
ejpam-5872	318	9	±	±	PROPN
ejpam-5872	318	10	,	,	PUNCT
ejpam-5872	318	11	there	there	PRON
ejpam-5872	318	12	exists	exist	VERB
ejpam-5872	318	13	1ג	1ג	NUM
ejpam-5872	318	14	∈	∈	NOUN
ejpam-5872	318	15	d	d	X
ejpam-5872	318	16	such	such	ADJ
ejpam-5872	318	17	that	that	PRON
ejpam-5872	318	18	,	,	PUNCT
ejpam-5872	318	19	1ג	1ג	NUM
ejpam-5872	318	20	)	)	PUNCT
ejpam-5872	318	21	(	(	PUNCT
ejpam-5872	318	22	2ג	2ג	NOUN
ejpam-5872	318	23	is	be	AUX
ejpam-5872	318	24	a	a	DET
ejpam-5872	318	25	strong	strong	ADJ
ejpam-5872	318	26	arc	arc	NOUN
ejpam-5872	318	27	.	.	PUNCT
ejpam-5872	319	1	consequently	consequently	ADV
ejpam-5872	319	2	,	,	PUNCT
ejpam-5872	319	3	2ג	2ג	NOUN
ejpam-5872	319	4	is	be	AUX
ejpam-5872	319	5	a	a	DET
ejpam-5872	319	6	strong	strong	ADJ
ejpam-5872	319	7	neighbor	neighbor	NOUN
ejpam-5872	319	8	of	of	ADP
ejpam-5872	319	9	.1ג	.1ג	ADV
ejpam-5872	319	10	furthermore	furthermore	ADV
ejpam-5872	319	11	,	,	PUNCT
ejpam-5872	319	12	since	since	SCONJ
ejpam-5872	319	13	2ג	2ג	NUM
ejpam-5872	319	14	∈	∈	PROPN
ejpam-5872	319	15	d	d	PROPN
ejpam-5872	319	16	,	,	PUNCT
ejpam-5872	319	17	2ג	2ג	NOUN
ejpam-5872	319	18	is	be	AUX
ejpam-5872	319	19	a	a	DET
ejpam-5872	319	20	signed	sign	VERB
ejpam-5872	319	21	fuzzy	fuzzy	ADJ
ejpam-5872	319	22	end	end	NOUN
ejpam-5872	319	23	node	node	NOUN
ejpam-5872	319	24	of	of	ADP
ejpam-5872	319	25	∑	∑	PROPN
ejpam-5872	319	26	±.	±.	PROPN
ejpam-5872	319	27	thus	thus	ADV
ejpam-5872	319	28	,	,	PUNCT
ejpam-5872	319	29	the	the	DET
ejpam-5872	319	30	signed	sign	VERB
ejpam-5872	319	31	fuzzy	fuzzy	ADJ
ejpam-5872	319	32	end	end	VERB
ejpam-5872	319	33	node	node	NOUN
ejpam-5872	319	34	of	of	ADP
ejpam-5872	319	35	1ג	1ג	NUM
ejpam-5872	319	36	has	have	VERB
ejpam-5872	319	37	a	a	DET
ejpam-5872	319	38	strong	strong	ADJ
ejpam-5872	319	39	neighbor	neighbor	NOUN
ejpam-5872	319	40	in	in	ADP
ejpam-5872	319	41	.2ג	.2ג	PROPN
ejpam-5872	319	42	since	since	SCONJ
ejpam-5872	319	43	1ג	1ג	NUM
ejpam-5872	319	44	is	be	AUX
ejpam-5872	319	45	random	random	ADJ
ejpam-5872	319	46	,	,	PUNCT
ejpam-5872	319	47	every	every	DET
ejpam-5872	319	48	signed	sign	VERB
ejpam-5872	319	49	fuzzy	fuzzy	ADJ
ejpam-5872	319	50	cut	cut	VERB
ejpam-5872	319	51	node	node	NOUN
ejpam-5872	319	52	in	in	ADP
ejpam-5872	319	53	∑	∑	PROPN
ejpam-5872	319	54	±	±	PROPN
ejpam-5872	319	55	has	have	VERB
ejpam-5872	319	56	at	at	ADV
ejpam-5872	319	57	least	least	ADV
ejpam-5872	319	58	one	one	NUM
ejpam-5872	319	59	signed	sign	VERB
ejpam-5872	319	60	fuzzy	fuzzy	ADJ
ejpam-5872	319	61	end	end	NOUN
ejpam-5872	319	62	node	node	NOUN
ejpam-5872	319	63	that	that	PRON
ejpam-5872	319	64	is	be	AUX
ejpam-5872	319	65	a	a	DET
ejpam-5872	319	66	strong	strong	ADJ
ejpam-5872	319	67	neighbor	neighbor	NOUN
ejpam-5872	319	68	.	.	PUNCT
ejpam-5872	320	1	theorem	theorem	VERB
ejpam-5872	320	2	17	17	NUM
ejpam-5872	320	3	.	.	PUNCT
ejpam-5872	321	1	let	let	VERB
ejpam-5872	321	2	σ±	σ±	NOUN
ejpam-5872	321	3	=	=	SYM
ejpam-5872	321	4	(	(	PUNCT
ejpam-5872	321	5	ℑ	ℑ	PROPN
ejpam-5872	321	6	,	,	PUNCT
ejpam-5872	321	7	σ	σ	PROPN
ejpam-5872	321	8	,	,	PUNCT
ejpam-5872	321	9	µ	µ	NOUN
ejpam-5872	321	10	)	)	PUNCT
ejpam-5872	321	11	be	be	VERB
ejpam-5872	321	12	a	a	DET
ejpam-5872	321	13	signed	sign	VERB
ejpam-5872	321	14	fuzzy	fuzzy	ADJ
ejpam-5872	321	15	tree	tree	NOUN
ejpam-5872	321	16	that	that	PRON
ejpam-5872	321	17	is	be	AUX
ejpam-5872	321	18	not	not	PART
ejpam-5872	321	19	trivial	trivial	ADJ
ejpam-5872	321	20	.	.	PUNCT
ejpam-5872	322	1	an	an	DET
ejpam-5872	322	2	∑	∑	PROPN
ejpam-5872	322	3	±	±	NUM
ejpam-5872	322	4	fuzzy	fuzzy	ADJ
ejpam-5872	322	5	bridge	bridge	NOUN
ejpam-5872	322	6	is	be	AUX
ejpam-5872	322	7	then	then	ADV
ejpam-5872	322	8	connected	connect	VERB
ejpam-5872	322	9	to	to	ADP
ejpam-5872	322	10	each	each	DET
ejpam-5872	322	11	node	node	NOUN
ejpam-5872	322	12	in	in	ADP
ejpam-5872	322	13	a	a	DET
ejpam-5872	322	14	domination	domination	NOUN
ejpam-5872	322	15	set	set	NOUN
ejpam-5872	322	16	.	.	PUNCT
ejpam-5872	323	1	proof	proof	NOUN
ejpam-5872	323	2	.	.	PUNCT
ejpam-5872	324	1	let	let	VERB
ejpam-5872	325	1	1ג	1ג	NUM
ejpam-5872	325	2	∈	∈	PROPN
ejpam-5872	325	3	d	d	NOUN
ejpam-5872	326	1	and	and	CCONJ
ejpam-5872	326	2	d	d	NOUN
ejpam-5872	326	3	be	be	AUX
ejpam-5872	326	4	a	a	DET
ejpam-5872	326	5	dominant	dominant	ADJ
ejpam-5872	326	6	set	set	NOUN
ejpam-5872	326	7	of	of	ADP
ejpam-5872	326	8	∑	∑	PUNCT
ejpam-5872	326	9	±.	±.	PROPN
ejpam-5872	326	10	there	there	PRON
ejpam-5872	326	11	is	be	VERB
ejpam-5872	326	12	2ג	2ג	NUM
ejpam-5872	326	13	∈	∈	PROPN
ejpam-5872	326	14	ℑ	ℑ	NOUN
ejpam-5872	326	15	−	−	PROPN
ejpam-5872	327	1	d	d	PRON
ejpam-5872	327	2	such	such	ADJ
ejpam-5872	327	3	that	that	PRON
ejpam-5872	327	4	,	,	PUNCT
ejpam-5872	327	5	1ג	1ג	NUM
ejpam-5872	327	6	)	)	PUNCT
ejpam-5872	327	7	(	(	PUNCT
ejpam-5872	327	8	2ג	2ג	NOUN
ejpam-5872	327	9	is	be	AUX
ejpam-5872	327	10	a	a	DET
ejpam-5872	327	11	strong	strong	ADJ
ejpam-5872	327	12	arc	arc	NOUN
ejpam-5872	327	13	sinced	since	VERB
ejpam-5872	327	14	is	be	AUX
ejpam-5872	327	15	a	a	DET
ejpam-5872	327	16	domination	domination	NOUN
ejpam-5872	327	17	set	set	NOUN
ejpam-5872	327	18	.	.	PUNCT
ejpam-5872	328	1	this	this	PRON
ejpam-5872	328	2	means	mean	VERB
ejpam-5872	328	3	that	that	SCONJ
ejpam-5872	328	4	in	in	ADP
ejpam-5872	328	5	the	the	DET
ejpam-5872	328	6	special	special	ADJ
ejpam-5872	328	7	minimum	minimum	NOUN
ejpam-5872	328	8	spanning	span	VERB
ejpam-5872	328	9	tree	tree	NOUN
ejpam-5872	328	10	f±	f±	PROPN
ejpam-5872	328	11	of	of	ADP
ejpam-5872	328	12	∑	∑	PROPN
ejpam-5872	328	13	±	±	PROPN
ejpam-5872	328	14	,	,	PUNCT
ejpam-5872	328	15	,	,	PUNCT
ejpam-5872	328	16	1ג	1ג	NUM
ejpam-5872	328	17	)	)	PUNCT
ejpam-5872	328	18	(	(	PUNCT
ejpam-5872	328	19	2ג	2ג	NOUN
ejpam-5872	328	20	is	be	AUX
ejpam-5872	328	21	an	an	DET
ejpam-5872	328	22	arc	arc	NOUN
ejpam-5872	328	23	.	.	PUNCT
ejpam-5872	329	1	the	the	DET
ejpam-5872	329	2	signed	sign	VERB
ejpam-5872	329	3	fuzzy	fuzzy	ADJ
ejpam-5872	329	4	bridge	bridge	NOUN
ejpam-5872	329	5	of	of	ADP
ejpam-5872	329	6	∑	∑	PROPN
ejpam-5872	329	7	±	±	PROPN
ejpam-5872	329	8	is	be	AUX
ejpam-5872	329	9	thus	thus	ADV
ejpam-5872	329	10	,	,	PUNCT
ejpam-5872	329	11	1ג	1ג	NUM
ejpam-5872	329	12	)	)	PUNCT
ejpam-5872	329	13	.(2ג	.(2ג	PUNCT
ejpam-5872	330	1	as	as	SCONJ
ejpam-5872	330	2	1ג	1ג	NUM
ejpam-5872	330	3	was	be	AUX
ejpam-5872	330	4	selected	select	VERB
ejpam-5872	330	5	at	at	ADP
ejpam-5872	330	6	random	random	ADJ
ejpam-5872	330	7	,	,	PUNCT
ejpam-5872	330	8	this	this	PRON
ejpam-5872	330	9	is	be	AUX
ejpam-5872	330	10	true	true	ADJ
ejpam-5872	330	11	for	for	ADP
ejpam-5872	330	12	all	all	DET
ejpam-5872	330	13	nodes	node	NOUN
ejpam-5872	330	14	in	in	ADP
ejpam-5872	330	15	the	the	DET
ejpam-5872	330	16	domination	domination	NOUN
ejpam-5872	330	17	set	set	NOUN
ejpam-5872	330	18	of	of	ADP
ejpam-5872	330	19	∑	∑	PUNCT
ejpam-5872	330	20	±.	±.	PROPN
ejpam-5872	330	21	c.	c.	PROPN
ejpam-5872	330	22	sankar	sankar	PROPN
ejpam-5872	330	23	et	et	PROPN
ejpam-5872	330	24	al	al	PROPN
ejpam-5872	330	25	.	.	PUNCT
ejpam-5872	330	26	/	/	SYM
ejpam-5872	330	27	eur	eur	PROPN
ejpam-5872	330	28	.	.	PUNCT
ejpam-5872	331	1	j.	j.	PROPN
ejpam-5872	331	2	pure	pure	PROPN
ejpam-5872	331	3	appl	appl	PROPN
ejpam-5872	331	4	.	.	PROPN
ejpam-5872	331	5	math	math	PROPN
ejpam-5872	331	6	,	,	PUNCT
ejpam-5872	331	7	18	18	NUM
ejpam-5872	331	8	(	(	PUNCT
ejpam-5872	331	9	4	4	NUM
ejpam-5872	331	10	)	)	PUNCT
ejpam-5872	331	11	(	(	PUNCT
ejpam-5872	331	12	2025	2025	NUM
ejpam-5872	331	13	)	)	PUNCT
ejpam-5872	331	14	,	,	PUNCT
ejpam-5872	331	15	5872	5872	NUM
ejpam-5872	331	16	13	13	NUM
ejpam-5872	331	17	of	of	ADP
ejpam-5872	331	18	17	17	NUM
ejpam-5872	331	19	4	4	NUM
ejpam-5872	331	20	.	.	PUNCT
ejpam-5872	332	1	domination	domination	NOUN
ejpam-5872	332	2	in	in	ADP
ejpam-5872	332	3	signed	sign	VERB
ejpam-5872	332	4	fuzzy	fuzzy	ADJ
ejpam-5872	332	5	graphs	graph	NOUN
ejpam-5872	332	6	applied	apply	VERB
ejpam-5872	332	7	to	to	ADP
ejpam-5872	332	8	wireless	wireless	ADJ
ejpam-5872	332	9	sensor	sensor	NOUN
ejpam-5872	332	10	networks	network	NOUN
ejpam-5872	332	11	for	for	ADP
ejpam-5872	332	12	environmental	environmental	ADJ
ejpam-5872	332	13	monitoring	monitoring	NOUN
ejpam-5872	332	14	systems	system	NOUN
ejpam-5872	332	15	signed	sign	VERB
ejpam-5872	332	16	-	-	PUNCT
ejpam-5872	332	17	fgs	fgs	NOUN
ejpam-5872	332	18	are	be	AUX
ejpam-5872	332	19	incredibly	incredibly	ADV
ejpam-5872	332	20	helpful	helpful	ADJ
ejpam-5872	332	21	tools	tool	NOUN
ejpam-5872	332	22	for	for	ADP
ejpam-5872	332	23	using	use	VERB
ejpam-5872	332	24	dominance	dominance	NOUN
ejpam-5872	332	25	sets	set	NOUN
ejpam-5872	332	26	in	in	ADP
ejpam-5872	332	27	wireless	wireless	ADJ
ejpam-5872	332	28	sensor	sensor	NOUN
ejpam-5872	332	29	networks	network	NOUN
ejpam-5872	332	30	,	,	PUNCT
ejpam-5872	332	31	especially	especially	ADV
ejpam-5872	332	32	in	in	ADP
ejpam-5872	332	33	real	real	ADJ
ejpam-5872	332	34	-	-	PUNCT
ejpam-5872	332	35	time	time	NOUN
ejpam-5872	332	36	applications	application	NOUN
ejpam-5872	332	37	where	where	SCONJ
ejpam-5872	332	38	the	the	DET
ejpam-5872	332	39	network	network	NOUN
ejpam-5872	332	40	must	must	AUX
ejpam-5872	332	41	be	be	AUX
ejpam-5872	332	42	dependable	dependable	ADJ
ejpam-5872	332	43	,	,	PUNCT
ejpam-5872	332	44	adaptive	adaptive	ADJ
ejpam-5872	332	45	,	,	PUNCT
ejpam-5872	332	46	and	and	CCONJ
ejpam-5872	332	47	efficient	efficient	ADJ
ejpam-5872	332	48	.	.	PUNCT
ejpam-5872	333	1	an	an	DET
ejpam-5872	333	2	outline	outline	NOUN
ejpam-5872	333	3	of	of	ADP
ejpam-5872	333	4	a	a	DET
ejpam-5872	333	5	real	real	ADJ
ejpam-5872	333	6	-	-	PUNCT
ejpam-5872	333	7	world	world	NOUN
ejpam-5872	333	8	use	use	NOUN
ejpam-5872	333	9	of	of	ADP
ejpam-5872	333	10	this	this	DET
ejpam-5872	333	11	combination	combination	NOUN
ejpam-5872	333	12	is	be	AUX
ejpam-5872	333	13	provided	provide	VERB
ejpam-5872	333	14	below	below	ADP
ejpam-5872	333	15	:	:	PUNCT
ejpam-5872	333	16	when	when	SCONJ
ejpam-5872	333	17	people	people	NOUN
ejpam-5872	333	18	are	be	AUX
ejpam-5872	333	19	unable	unable	ADJ
ejpam-5872	333	20	to	to	PART
ejpam-5872	333	21	attend	attend	VERB
ejpam-5872	333	22	events	event	NOUN
ejpam-5872	333	23	that	that	PRON
ejpam-5872	333	24	need	need	VERB
ejpam-5872	333	25	the	the	DET
ejpam-5872	333	26	movement	movement	NOUN
ejpam-5872	333	27	and	and	CCONJ
ejpam-5872	333	28	transmission	transmission	NOUN
ejpam-5872	333	29	of	of	ADP
ejpam-5872	333	30	data	datum	NOUN
ejpam-5872	333	31	,	,	PUNCT
ejpam-5872	333	32	networks	network	NOUN
ejpam-5872	333	33	of	of	ADP
ejpam-5872	333	34	sensors	sensor	NOUN
ejpam-5872	333	35	are	be	AUX
ejpam-5872	333	36	dispersed	disperse	VERB
ejpam-5872	333	37	throughout	throughout	ADP
ejpam-5872	333	38	different	different	ADJ
ejpam-5872	333	39	regions	region	NOUN
ejpam-5872	333	40	.	.	PUNCT
ejpam-5872	334	1	real	real	ADJ
ejpam-5872	334	2	-	-	PUNCT
ejpam-5872	334	3	time	time	NOUN
ejpam-5872	334	4	communication	communication	NOUN
ejpam-5872	334	5	,	,	PUNCT
ejpam-5872	334	6	fault	fault	VERB
ejpam-5872	334	7	tolerance	tolerance	NOUN
ejpam-5872	334	8	,	,	PUNCT
ejpam-5872	334	9	power	power	NOUN
ejpam-5872	334	10	efficiency	efficiency	NOUN
ejpam-5872	334	11	,	,	PUNCT
ejpam-5872	334	12	and	and	CCONJ
ejpam-5872	334	13	data	datum	NOUN
ejpam-5872	334	14	quality	quality	NOUN
ejpam-5872	334	15	are	be	AUX
ejpam-5872	334	16	issues	issue	NOUN
ejpam-5872	334	17	for	for	ADP
ejpam-5872	334	18	wsns	wsns	NOUN
ejpam-5872	334	19	.	.	PUNCT
ejpam-5872	335	1	in	in	ADP
ejpam-5872	335	2	a	a	DET
ejpam-5872	335	3	wsn	wsn	NOUN
ejpam-5872	335	4	,	,	PUNCT
ejpam-5872	335	5	the	the	DET
ejpam-5872	335	6	domination	domination	NOUN
ejpam-5872	335	7	set	set	NOUN
ejpam-5872	335	8	,	,	PUNCT
ejpam-5872	335	9	which	which	PRON
ejpam-5872	335	10	is	be	AUX
ejpam-5872	335	11	a	a	DET
ejpam-5872	335	12	subset	subset	NOUN
ejpam-5872	335	13	of	of	ADP
ejpam-5872	335	14	sensor	sensor	NOUN
ejpam-5872	335	15	nodes	node	NOUN
ejpam-5872	335	16	,	,	PUNCT
ejpam-5872	335	17	ensures	ensure	VERB
ejpam-5872	335	18	that	that	SCONJ
ejpam-5872	335	19	each	each	DET
ejpam-5872	335	20	non	non	ADJ
ejpam-5872	335	21	-	-	ADJ
ejpam-5872	335	22	set	set	ADJ
ejpam-5872	335	23	node	node	NOUN
ejpam-5872	335	24	is	be	AUX
ejpam-5872	335	25	connected	connect	VERB
ejpam-5872	335	26	to	to	ADP
ejpam-5872	335	27	at	at	ADV
ejpam-5872	335	28	least	least	ADV
ejpam-5872	335	29	one	one	NUM
ejpam-5872	335	30	set	set	VERB
ejpam-5872	335	31	node	node	NOUN
ejpam-5872	335	32	.	.	PUNCT
ejpam-5872	336	1	as	as	ADP
ejpam-5872	336	2	global	global	ADJ
ejpam-5872	336	3	communication	communication	NOUN
ejpam-5872	336	4	hubs	hub	NOUN
ejpam-5872	336	5	,	,	PUNCT
ejpam-5872	336	6	domination	domination	NOUN
ejpam-5872	336	7	set	set	NOUN
ejpam-5872	336	8	nodes	node	NOUN
ejpam-5872	336	9	use	use	VERB
ejpam-5872	336	10	less	less	ADJ
ejpam-5872	336	11	energy	energy	NOUN
ejpam-5872	336	12	than	than	ADP
ejpam-5872	336	13	other	other	ADJ
ejpam-5872	336	14	nodes	node	NOUN
ejpam-5872	336	15	by	by	ADP
ejpam-5872	336	16	accepting	accept	VERB
ejpam-5872	336	17	data	datum	NOUN
ejpam-5872	336	18	from	from	ADP
ejpam-5872	336	19	other	other	ADJ
ejpam-5872	336	20	nodes	node	NOUN
ejpam-5872	336	21	and	and	CCONJ
ejpam-5872	336	22	sending	send	VERB
ejpam-5872	336	23	it	it	PRON
ejpam-5872	336	24	to	to	ADP
ejpam-5872	336	25	the	the	DET
ejpam-5872	336	26	main	main	ADJ
ejpam-5872	336	27	station	station	NOUN
ejpam-5872	336	28	.	.	PUNCT
ejpam-5872	337	1	fuzzy	fuzzy	ADJ
ejpam-5872	337	2	and	and	CCONJ
ejpam-5872	337	3	signed	sign	VERB
ejpam-5872	337	4	graphs	graph	NOUN
ejpam-5872	337	5	with	with	ADP
ejpam-5872	337	6	degrees	degree	NOUN
ejpam-5872	337	7	of	of	ADP
ejpam-5872	337	8	membership	membership	NOUN
ejpam-5872	337	9	and	and	CCONJ
ejpam-5872	337	10	edge	edge	NOUN
ejpam-5872	337	11	signs	sign	NOUN
ejpam-5872	337	12	combined	combine	VERB
ejpam-5872	337	13	.	.	PUNCT
ejpam-5872	338	1	therefore	therefore	ADV
ejpam-5872	338	2	,	,	PUNCT
ejpam-5872	338	3	complicated	complicated	ADJ
ejpam-5872	338	4	node	node	ADJ
ejpam-5872	338	5	interactions	interaction	NOUN
ejpam-5872	338	6	,	,	PUNCT
ejpam-5872	338	7	including	include	VERB
ejpam-5872	338	8	varying	vary	VERB
ejpam-5872	338	9	degrees	degree	NOUN
ejpam-5872	338	10	of	of	ADP
ejpam-5872	338	11	trust	trust	NOUN
ejpam-5872	338	12	,	,	PUNCT
ejpam-5872	338	13	depending	depend	VERB
ejpam-5872	338	14	on	on	ADP
ejpam-5872	338	15	one	one	NUM
ejpam-5872	338	16	another	another	DET
ejpam-5872	338	17	for	for	ADP
ejpam-5872	338	18	vital	vital	ADJ
ejpam-5872	338	19	information	information	NOUN
ejpam-5872	338	20	about	about	ADP
ejpam-5872	338	21	the	the	DET
ejpam-5872	338	22	task	task	NOUN
ejpam-5872	338	23	being	be	AUX
ejpam-5872	338	24	done	do	VERB
ejpam-5872	338	25	,	,	PUNCT
ejpam-5872	338	26	or	or	CCONJ
ejpam-5872	338	27	conversing	converse	VERB
ejpam-5872	338	28	amongst	amongst	ADP
ejpam-5872	338	29	themselves	themselves	PRON
ejpam-5872	338	30	,	,	PUNCT
ejpam-5872	338	31	can	can	AUX
ejpam-5872	338	32	be	be	AUX
ejpam-5872	338	33	simulated	simulate	VERB
ejpam-5872	338	34	using	use	VERB
ejpam-5872	338	35	these	these	DET
ejpam-5872	338	36	graphs	graph	NOUN
ejpam-5872	338	37	.	.	PUNCT
ejpam-5872	339	1	for	for	ADP
ejpam-5872	339	2	example	example	NOUN
ejpam-5872	339	3	,	,	PUNCT
ejpam-5872	339	4	to	to	PART
ejpam-5872	339	5	track	track	VERB
ejpam-5872	339	6	temperature	temperature	NOUN
ejpam-5872	339	7	,	,	PUNCT
ejpam-5872	339	8	air	air	NOUN
ejpam-5872	339	9	quality	quality	NOUN
ejpam-5872	339	10	,	,	PUNCT
ejpam-5872	339	11	and	and	CCONJ
ejpam-5872	339	12	humidity	humidity	NOUN
ejpam-5872	339	13	,	,	PUNCT
ejpam-5872	339	14	a	a	DET
ejpam-5872	339	15	wsn	wsn	NOUN
ejpam-5872	339	16	should	should	AUX
ejpam-5872	339	17	be	be	AUX
ejpam-5872	339	18	placed	place	VERB
ejpam-5872	339	19	in	in	ADP
ejpam-5872	339	20	a	a	DET
ejpam-5872	339	21	far	far	ADV
ejpam-5872	339	22	-	-	PUNCT
ejpam-5872	339	23	off	off	ADP
ejpam-5872	339	24	forest	forest	NOUN
ejpam-5872	339	25	.	.	PUNCT
ejpam-5872	340	1	this	this	DET
ejpam-5872	340	2	network	network	NOUN
ejpam-5872	340	3	must	must	AUX
ejpam-5872	340	4	be	be	AUX
ejpam-5872	340	5	adaptable	adaptable	ADJ
ejpam-5872	340	6	enough	enough	ADV
ejpam-5872	340	7	to	to	PART
ejpam-5872	340	8	guarantee	guarantee	VERB
ejpam-5872	340	9	dependable	dependable	ADJ
ejpam-5872	340	10	data	data	NOUN
ejpam-5872	340	11	transfer	transfer	NOUN
ejpam-5872	340	12	and	and	CCONJ
ejpam-5872	340	13	strong	strong	ADJ
ejpam-5872	340	14	performance	performance	NOUN
ejpam-5872	340	15	in	in	ADP
ejpam-5872	340	16	a	a	DET
ejpam-5872	340	17	variety	variety	NOUN
ejpam-5872	340	18	of	of	ADP
ejpam-5872	340	19	environmental	environmental	ADJ
ejpam-5872	340	20	circumstances	circumstance	NOUN
ejpam-5872	340	21	.	.	PUNCT
ejpam-5872	341	1	sensor	sensor	NOUN
ejpam-5872	341	2	nodes	node	NOUN
ejpam-5872	341	3	are	be	AUX
ejpam-5872	341	4	dispersed	disperse	VERB
ejpam-5872	341	5	throughout	throughout	ADP
ejpam-5872	341	6	the	the	DET
ejpam-5872	341	7	forest	forest	NOUN
ejpam-5872	341	8	.	.	PUNCT
ejpam-5872	342	1	a	a	DET
ejpam-5872	342	2	fuzzy	fuzzy	ADJ
ejpam-5872	342	3	membership	membership	NOUN
ejpam-5872	342	4	value	value	NOUN
ejpam-5872	342	5	that	that	PRON
ejpam-5872	342	6	reflects	reflect	VERB
ejpam-5872	342	7	the	the	DET
ejpam-5872	342	8	nodes	node	NOUN
ejpam-5872	342	9	’	'	PUNCT
ejpam-5872	342	10	initial	initial	ADJ
ejpam-5872	342	11	positions	position	NOUN
ejpam-5872	342	12	,	,	PUNCT
ejpam-5872	342	13	energy	energy	NOUN
ejpam-5872	342	14	levels	level	NOUN
ejpam-5872	342	15	,	,	PUNCT
ejpam-5872	342	16	and	and	CCONJ
ejpam-5872	342	17	trustworthiness	trustworthiness	NOUN
ejpam-5872	342	18	is	be	AUX
ejpam-5872	342	19	used	use	VERB
ejpam-5872	342	20	to	to	PART
ejpam-5872	342	21	create	create	VERB
ejpam-5872	342	22	a	a	DET
ejpam-5872	342	23	domination	domination	NOUN
ejpam-5872	342	24	set	set	NOUN
ejpam-5872	342	25	.	.	PUNCT
ejpam-5872	343	1	these	these	DET
ejpam-5872	343	2	nodes	node	NOUN
ejpam-5872	343	3	are	be	AUX
ejpam-5872	343	4	known	know	VERB
ejpam-5872	343	5	as	as	ADP
ejpam-5872	343	6	dominant	dominant	ADJ
ejpam-5872	343	7	nodes	node	NOUN
ejpam-5872	343	8	because	because	SCONJ
ejpam-5872	343	9	they	they	PRON
ejpam-5872	343	10	have	have	VERB
ejpam-5872	343	11	the	the	DET
ejpam-5872	343	12	ability	ability	NOUN
ejpam-5872	343	13	to	to	PART
ejpam-5872	343	14	aggregate	aggregate	VERB
ejpam-5872	343	15	data	datum	NOUN
ejpam-5872	343	16	by	by	ADP
ejpam-5872	343	17	collecting	collect	VERB
ejpam-5872	343	18	it	it	PRON
ejpam-5872	343	19	from	from	ADP
ejpam-5872	343	20	neighboring	neighboring	NOUN
ejpam-5872	343	21	sensors	sensor	NOUN
ejpam-5872	343	22	and	and	CCONJ
ejpam-5872	343	23	then	then	ADV
ejpam-5872	343	24	transmitting	transmit	VERB
ejpam-5872	343	25	it	it	PRON
ejpam-5872	343	26	to	to	ADP
ejpam-5872	343	27	a	a	DET
ejpam-5872	343	28	base	base	NOUN
ejpam-5872	343	29	station	station	NOUN
ejpam-5872	343	30	or	or	CCONJ
ejpam-5872	343	31	central	central	ADJ
ejpam-5872	343	32	station	station	NOUN
ejpam-5872	343	33	.	.	PUNCT
ejpam-5872	344	1	the	the	DET
ejpam-5872	344	2	network	network	NOUN
ejpam-5872	344	3	’s	’s	PART
ejpam-5872	344	4	lifespan	lifespan	NOUN
ejpam-5872	344	5	is	be	AUX
ejpam-5872	344	6	extended	extend	VERB
ejpam-5872	344	7	by	by	ADP
ejpam-5872	344	8	lowering	lower	VERB
ejpam-5872	344	9	the	the	DET
ejpam-5872	344	10	energy	energy	NOUN
ejpam-5872	344	11	usage	usage	NOUN
ejpam-5872	344	12	of	of	ADP
ejpam-5872	344	13	non	non	ADJ
ejpam-5872	344	14	-	-	ADJ
ejpam-5872	344	15	dominant	dominant	ADJ
ejpam-5872	344	16	nodes	node	NOUN
ejpam-5872	344	17	.	.	PUNCT
ejpam-5872	345	1	a	a	DET
ejpam-5872	345	2	signed	sign	VERB
ejpam-5872	345	3	-	-	PUNCT
ejpam-5872	345	4	fg	fg	NOUN
ejpam-5872	345	5	uses	use	VERB
ejpam-5872	345	6	edges	edge	NOUN
ejpam-5872	345	7	to	to	PART
ejpam-5872	345	8	show	show	VERB
ejpam-5872	345	9	the	the	DET
ejpam-5872	345	10	connections	connection	NOUN
ejpam-5872	345	11	between	between	ADP
ejpam-5872	345	12	its	its	PRON
ejpam-5872	345	13	nodes	node	NOUN
ejpam-5872	345	14	.	.	PUNCT
ejpam-5872	346	1	positive	positive	ADJ
ejpam-5872	346	2	edges	edge	NOUN
ejpam-5872	346	3	indicate	indicate	VERB
ejpam-5872	346	4	relationships	relationship	NOUN
ejpam-5872	346	5	that	that	PRON
ejpam-5872	346	6	are	be	AUX
ejpam-5872	346	7	going	go	VERB
ejpam-5872	346	8	well	well	ADV
ejpam-5872	346	9	,	,	PUNCT
ejpam-5872	346	10	whereas	whereas	SCONJ
ejpam-5872	346	11	negative	negative	ADJ
ejpam-5872	346	12	edges	edge	NOUN
ejpam-5872	346	13	indicate	indicate	VERB
ejpam-5872	346	14	potential	potential	ADJ
ejpam-5872	346	15	issues	issue	NOUN
ejpam-5872	346	16	like	like	ADP
ejpam-5872	346	17	interference	interference	NOUN
ejpam-5872	346	18	or	or	CCONJ
ejpam-5872	346	19	mistrust	mistrust	NOUN
ejpam-5872	346	20	.	.	PUNCT
ejpam-5872	347	1	the	the	DET
ejpam-5872	347	2	strength	strength	NOUN
ejpam-5872	347	3	or	or	CCONJ
ejpam-5872	347	4	dependability	dependability	NOUN
ejpam-5872	347	5	of	of	ADP
ejpam-5872	347	6	the	the	DET
ejpam-5872	347	7	associations	association	NOUN
ejpam-5872	347	8	is	be	AUX
ejpam-5872	347	9	demonstrated	demonstrate	VERB
ejpam-5872	347	10	by	by	ADP
ejpam-5872	347	11	the	the	DET
ejpam-5872	347	12	membership	membership	NOUN
ejpam-5872	347	13	degree	degree	NOUN
ejpam-5872	347	14	,	,	PUNCT
ejpam-5872	347	15	which	which	PRON
ejpam-5872	347	16	is	be	AUX
ejpam-5872	347	17	impacted	impact	VERB
ejpam-5872	347	18	by	by	ADP
ejpam-5872	347	19	variables	variable	NOUN
ejpam-5872	347	20	such	such	ADJ
ejpam-5872	347	21	as	as	ADP
ejpam-5872	347	22	energy	energy	NOUN
ejpam-5872	347	23	levels	level	NOUN
ejpam-5872	347	24	and	and	CCONJ
ejpam-5872	347	25	signal	signal	ADJ
ejpam-5872	347	26	intensity	intensity	NOUN
ejpam-5872	347	27	.	.	PUNCT
ejpam-5872	348	1	the	the	DET
ejpam-5872	348	2	fuzzy	fuzzy	ADJ
ejpam-5872	348	3	values	value	NOUN
ejpam-5872	348	4	on	on	ADP
ejpam-5872	348	5	the	the	DET
ejpam-5872	348	6	edges	edge	NOUN
ejpam-5872	348	7	can	can	AUX
ejpam-5872	348	8	be	be	AUX
ejpam-5872	348	9	quickly	quickly	ADV
ejpam-5872	348	10	changed	change	VERB
ejpam-5872	348	11	by	by	ADP
ejpam-5872	348	12	changes	change	NOUN
ejpam-5872	348	13	in	in	ADP
ejpam-5872	348	14	the	the	DET
ejpam-5872	348	15	surroundings	surrounding	NOUN
ejpam-5872	348	16	.	.	PUNCT
ejpam-5872	349	1	lower	low	ADJ
ejpam-5872	349	2	fuzzy	fuzzy	ADJ
ejpam-5872	349	3	membership	membership	NOUN
ejpam-5872	349	4	in	in	ADP
ejpam-5872	349	5	connections	connection	NOUN
ejpam-5872	349	6	can	can	AUX
ejpam-5872	349	7	result	result	VERB
ejpam-5872	349	8	from	from	ADP
ejpam-5872	349	9	an	an	DET
ejpam-5872	349	10	external	external	ADJ
ejpam-5872	349	11	interference	interference	NOUN
ejpam-5872	349	12	source	source	NOUN
ejpam-5872	349	13	that	that	PRON
ejpam-5872	349	14	lowers	lower	VERB
ejpam-5872	349	15	a	a	DET
ejpam-5872	349	16	node	node	NOUN
ejpam-5872	349	17	’s	’s	PART
ejpam-5872	349	18	energy	energy	NOUN
ejpam-5872	349	19	level	level	NOUN
ejpam-5872	349	20	or	or	CCONJ
ejpam-5872	349	21	adds	add	VERB
ejpam-5872	349	22	a	a	DET
ejpam-5872	349	23	negative	negative	ADJ
ejpam-5872	349	24	sign	sign	NOUN
ejpam-5872	349	25	to	to	ADP
ejpam-5872	349	26	some	some	DET
ejpam-5872	349	27	edges	edge	NOUN
ejpam-5872	349	28	in	in	ADP
ejpam-5872	349	29	some	some	PRON
ejpam-5872	349	30	of	of	ADP
ejpam-5872	349	31	these	these	DET
ejpam-5872	349	32	interactions	interaction	NOUN
ejpam-5872	349	33	.	.	PUNCT
ejpam-5872	350	1	accordingly	accordingly	ADV
ejpam-5872	350	2	,	,	PUNCT
ejpam-5872	350	3	only	only	ADV
ejpam-5872	350	4	the	the	DET
ejpam-5872	350	5	most	most	ADV
ejpam-5872	350	6	dependable	dependable	ADJ
ejpam-5872	350	7	and	and	CCONJ
ejpam-5872	350	8	low	low	ADJ
ejpam-5872	350	9	-	-	PUNCT
ejpam-5872	350	10	energy	energy	NOUN
ejpam-5872	350	11	nodes	node	NOUN
ejpam-5872	350	12	will	will	AUX
ejpam-5872	350	13	be	be	AUX
ejpam-5872	350	14	included	include	VERB
ejpam-5872	350	15	in	in	ADP
ejpam-5872	350	16	the	the	DET
ejpam-5872	350	17	dominance	dominance	NOUN
ejpam-5872	350	18	set	set	VERB
ejpam-5872	350	19	for	for	ADP
ejpam-5872	350	20	any	any	DET
ejpam-5872	350	21	modifications	modification	NOUN
ejpam-5872	350	22	to	to	ADP
ejpam-5872	350	23	the	the	DET
ejpam-5872	350	24	signed	sign	VERB
ejpam-5872	350	25	-	-	PUNCT
ejpam-5872	350	26	fg	fg	NOUN
ejpam-5872	350	27	.	.	PUNCT
ejpam-5872	351	1	the	the	DET
ejpam-5872	351	2	signed	sign	VERB
ejpam-5872	351	3	-	-	PUNCT
ejpam-5872	351	4	fg	fg	PROPN
ejpam-5872	351	5	has	have	AUX
ejpam-5872	351	6	been	be	AUX
ejpam-5872	351	7	utilized	utilize	VERB
ejpam-5872	351	8	to	to	PART
ejpam-5872	351	9	ensure	ensure	VERB
ejpam-5872	351	10	network	network	NOUN
ejpam-5872	351	11	integrity	integrity	NOUN
ejpam-5872	351	12	by	by	ADP
ejpam-5872	351	13	reducing	reduce	VERB
ejpam-5872	351	14	the	the	DET
ejpam-5872	351	15	time	time	NOUN
ejpam-5872	351	16	required	require	VERB
ejpam-5872	351	17	to	to	PART
ejpam-5872	351	18	identify	identify	VERB
ejpam-5872	351	19	a	a	DET
ejpam-5872	351	20	replacement	replacement	NOUN
ejpam-5872	351	21	node	node	NOUN
ejpam-5872	351	22	in	in	ADP
ejpam-5872	351	23	the	the	DET
ejpam-5872	351	24	event	event	NOUN
ejpam-5872	351	25	that	that	SCONJ
ejpam-5872	351	26	one	one	NUM
ejpam-5872	351	27	of	of	ADP
ejpam-5872	351	28	the	the	DET
ejpam-5872	351	29	sensor	sensor	NOUN
ejpam-5872	351	30	nodes	node	NOUN
ejpam-5872	351	31	in	in	ADP
ejpam-5872	351	32	the	the	DET
ejpam-5872	351	33	dominance	dominance	NOUN
ejpam-5872	351	34	set	set	VERB
ejpam-5872	351	35	fails	fail	VERB
ejpam-5872	351	36	or	or	CCONJ
ejpam-5872	351	37	becomes	become	VERB
ejpam-5872	351	38	unreliable	unreliable	ADJ
ejpam-5872	351	39	.	.	PUNCT
ejpam-5872	352	1	depending	depend	VERB
ejpam-5872	352	2	on	on	ADP
ejpam-5872	352	3	how	how	SCONJ
ejpam-5872	352	4	dependable	dependable	ADJ
ejpam-5872	352	5	their	their	PRON
ejpam-5872	352	6	connections	connection	NOUN
ejpam-5872	352	7	with	with	ADP
ejpam-5872	352	8	other	other	ADJ
ejpam-5872	352	9	devices	device	NOUN
ejpam-5872	352	10	are	be	AUX
ejpam-5872	352	11	,	,	PUNCT
ejpam-5872	352	12	nodes	node	NOUN
ejpam-5872	352	13	can	can	AUX
ejpam-5872	352	14	alter	alter	VERB
ejpam-5872	352	15	their	their	PRON
ejpam-5872	352	16	communication	communication	NOUN
ejpam-5872	352	17	patterns	pattern	NOUN
ejpam-5872	352	18	in	in	ADP
ejpam-5872	352	19	the	the	DET
ejpam-5872	352	20	signed	sign	VERB
ejpam-5872	352	21	-	-	PUNCT
ejpam-5872	352	22	fg	fg	NOUN
ejpam-5872	352	23	.	.	PUNCT
ejpam-5872	353	1	this	this	PRON
ejpam-5872	353	2	is	be	AUX
ejpam-5872	353	3	relevant	relevant	ADJ
ejpam-5872	353	4	when	when	SCONJ
ejpam-5872	353	5	specific	specific	ADJ
ejpam-5872	353	6	sensors	sensor	NOUN
ejpam-5872	353	7	are	be	AUX
ejpam-5872	353	8	vulnerable	vulnerable	ADJ
ejpam-5872	353	9	to	to	ADP
ejpam-5872	353	10	hacking	hack	VERB
ejpam-5872	353	11	or	or	CCONJ
ejpam-5872	353	12	when	when	SCONJ
ejpam-5872	353	13	unstable	unstable	ADJ
ejpam-5872	353	14	data	data	NOUN
ejpam-5872	353	15	transfer	transfer	NOUN
ejpam-5872	353	16	results	result	NOUN
ejpam-5872	353	17	from	from	ADP
ejpam-5872	353	18	environmental	environmental	ADJ
ejpam-5872	353	19	factors	factor	NOUN
ejpam-5872	353	20	.	.	PUNCT
ejpam-5872	354	1	because	because	SCONJ
ejpam-5872	354	2	dominant	dominant	ADJ
ejpam-5872	354	3	sets	set	NOUN
ejpam-5872	354	4	minimize	minimize	VERB
ejpam-5872	354	5	the	the	DET
ejpam-5872	354	6	number	number	NOUN
ejpam-5872	354	7	of	of	ADP
ejpam-5872	354	8	active	active	ADJ
ejpam-5872	354	9	nodes	node	NOUN
ejpam-5872	354	10	,	,	PUNCT
ejpam-5872	354	11	they	they	PRON
ejpam-5872	354	12	conserve	conserve	VERB
ejpam-5872	354	13	energy	energy	NOUN
ejpam-5872	354	14	in	in	ADP
ejpam-5872	354	15	c.	c.	PROPN
ejpam-5872	354	16	sankar	sankar	PROPN
ejpam-5872	354	17	et	et	PROPN
ejpam-5872	354	18	al	al	PROPN
ejpam-5872	354	19	.	.	PUNCT
ejpam-5872	354	20	/	/	SYM
ejpam-5872	354	21	eur	eur	PROPN
ejpam-5872	354	22	.	.	PUNCT
ejpam-5872	355	1	j.	j.	PROPN
ejpam-5872	355	2	pure	pure	PROPN
ejpam-5872	355	3	appl	appl	PROPN
ejpam-5872	355	4	.	.	PROPN
ejpam-5872	355	5	math	math	PROPN
ejpam-5872	355	6	,	,	PUNCT
ejpam-5872	355	7	18	18	NUM
ejpam-5872	355	8	(	(	PUNCT
ejpam-5872	355	9	4	4	NUM
ejpam-5872	355	10	)	)	PUNCT
ejpam-5872	355	11	(	(	PUNCT
ejpam-5872	355	12	2025	2025	NUM
ejpam-5872	355	13	)	)	PUNCT
ejpam-5872	355	14	,	,	PUNCT
ejpam-5872	355	15	5872	5872	NUM
ejpam-5872	355	16	14	14	NUM
ejpam-5872	355	17	of	of	ADP
ejpam-5872	355	18	17	17	NUM
ejpam-5872	355	19	long	long	ADJ
ejpam-5872	355	20	-	-	PUNCT
ejpam-5872	355	21	distance	distance	NOUN
ejpam-5872	355	22	communication	communication	NOUN
ejpam-5872	355	23	.	.	PUNCT
ejpam-5872	356	1	to	to	PART
ejpam-5872	356	2	provide	provide	VERB
ejpam-5872	356	3	real	real	ADJ
ejpam-5872	356	4	-	-	PUNCT
ejpam-5872	356	5	time	time	NOUN
ejpam-5872	356	6	energy	energy	NOUN
ejpam-5872	356	7	management	management	NOUN
ejpam-5872	356	8	,	,	PUNCT
ejpam-5872	356	9	nodes	node	NOUN
ejpam-5872	356	10	with	with	ADP
ejpam-5872	356	11	limited	limited	ADJ
ejpam-5872	356	12	energy	energy	NOUN
ejpam-5872	356	13	reserves	reserve	NOUN
ejpam-5872	356	14	can	can	AUX
ejpam-5872	356	15	gradually	gradually	ADV
ejpam-5872	356	16	reduce	reduce	VERB
ejpam-5872	356	17	their	their	PRON
ejpam-5872	356	18	involvement	involvement	NOUN
ejpam-5872	356	19	in	in	ADP
ejpam-5872	356	20	the	the	DET
ejpam-5872	356	21	fuzzy	fuzzy	ADJ
ejpam-5872	356	22	aspect	aspect	NOUN
ejpam-5872	356	23	domination	domination	NOUN
ejpam-5872	356	24	set	set	NOUN
ejpam-5872	356	25	.	.	PUNCT
ejpam-5872	357	1	in	in	ADP
ejpam-5872	357	2	order	order	NOUN
ejpam-5872	357	3	to	to	PART
ejpam-5872	357	4	achieve	achieve	VERB
ejpam-5872	357	5	a	a	DET
ejpam-5872	357	6	balanced	balanced	ADJ
ejpam-5872	357	7	network	network	NOUN
ejpam-5872	357	8	energy	energy	NOUN
ejpam-5872	357	9	consumption	consumption	NOUN
ejpam-5872	357	10	and	and	CCONJ
ejpam-5872	357	11	a	a	DET
ejpam-5872	357	12	longer	long	ADV
ejpam-5872	357	13	lifespan	lifespan	NOUN
ejpam-5872	357	14	for	for	ADP
ejpam-5872	357	15	the	the	DET
ejpam-5872	357	16	wsn	wsn	NOUN
ejpam-5872	357	17	,	,	PUNCT
ejpam-5872	357	18	the	the	DET
ejpam-5872	357	19	domination	domination	NOUN
ejpam-5872	357	20	set	set	NOUN
ejpam-5872	357	21	is	be	AUX
ejpam-5872	357	22	constantly	constantly	ADV
ejpam-5872	357	23	adjusted	adjust	VERB
ejpam-5872	357	24	in	in	ADP
ejpam-5872	357	25	reaction	reaction	NOUN
ejpam-5872	357	26	to	to	ADP
ejpam-5872	357	27	real	real	ADJ
ejpam-5872	357	28	-	-	PUNCT
ejpam-5872	357	29	time	time	NOUN
ejpam-5872	357	30	data	datum	NOUN
ejpam-5872	357	31	.	.	PUNCT
ejpam-5872	358	1	since	since	SCONJ
ejpam-5872	358	2	the	the	DET
ejpam-5872	358	3	signed	sign	VERB
ejpam-5872	358	4	-	-	PUNCT
ejpam-5872	358	5	fg	fg	PROPN
ejpam-5872	358	6	is	be	AUX
ejpam-5872	358	7	dynamic	dynamic	ADJ
ejpam-5872	358	8	,	,	PUNCT
ejpam-5872	358	9	data	datum	NOUN
ejpam-5872	358	10	is	be	AUX
ejpam-5872	358	11	sent	send	VERB
ejpam-5872	358	12	through	through	ADP
ejpam-5872	358	13	the	the	DET
ejpam-5872	358	14	most	most	ADV
ejpam-5872	358	15	reliable	reliable	ADJ
ejpam-5872	358	16	and	and	CCONJ
ejpam-5872	358	17	accurate	accurate	ADJ
ejpam-5872	358	18	pathways	pathway	NOUN
ejpam-5872	358	19	,	,	PUNCT
ejpam-5872	358	20	enhancing	enhance	VERB
ejpam-5872	358	21	data	datum	NOUN
ejpam-5872	358	22	quality	quality	NOUN
ejpam-5872	358	23	.	.	PUNCT
ejpam-5872	359	1	in	in	ADP
ejpam-5872	359	2	order	order	NOUN
ejpam-5872	359	3	to	to	PART
ejpam-5872	359	4	respond	respond	VERB
ejpam-5872	359	5	to	to	ADP
ejpam-5872	359	6	real	real	ADJ
ejpam-5872	359	7	-	-	PUNCT
ejpam-5872	359	8	time	time	NOUN
ejpam-5872	359	9	environmental	environmental	ADJ
ejpam-5872	359	10	changes	change	NOUN
ejpam-5872	359	11	,	,	PUNCT
ejpam-5872	359	12	the	the	DET
ejpam-5872	359	13	network	network	NOUN
ejpam-5872	359	14	can	can	AUX
ejpam-5872	359	15	adjust	adjust	VERB
ejpam-5872	359	16	sample	sample	NOUN
ejpam-5872	359	17	rates	rate	NOUN
ejpam-5872	359	18	by	by	ADP
ejpam-5872	359	19	focusing	focus	VERB
ejpam-5872	359	20	resources	resource	NOUN
ejpam-5872	359	21	where	where	SCONJ
ejpam-5872	359	22	they	they	PRON
ejpam-5872	359	23	are	be	AUX
ejpam-5872	359	24	most	most	ADV
ejpam-5872	359	25	needed	need	VERB
ejpam-5872	359	26	,	,	PUNCT
ejpam-5872	359	27	such	such	ADJ
ejpam-5872	359	28	as	as	ADP
ejpam-5872	359	29	increasing	increase	VERB
ejpam-5872	359	30	sampling	sample	VERB
ejpam-5872	359	31	during	during	ADP
ejpam-5872	359	32	a	a	DET
ejpam-5872	359	33	suspected	suspect	VERB
ejpam-5872	359	34	fire	fire	NOUN
ejpam-5872	359	35	outbreak	outbreak	NOUN
ejpam-5872	359	36	.	.	PUNCT
ejpam-5872	360	1	5	5	NUM
ejpam-5872	360	2	.	.	X
ejpam-5872	360	3	numerical	numerical	ADJ
ejpam-5872	360	4	illustration	illustration	NOUN
ejpam-5872	360	5	of	of	ADP
ejpam-5872	360	6	domination	domination	NOUN
ejpam-5872	360	7	in	in	ADP
ejpam-5872	360	8	signed	sign	VERB
ejpam-5872	360	9	fuzzy	fuzzy	ADJ
ejpam-5872	360	10	graphs	graph	NOUN
ejpam-5872	360	11	wireless	wireless	ADJ
ejpam-5872	360	12	sensor	sensor	NOUN
ejpam-5872	360	13	networks	network	NOUN
ejpam-5872	360	14	are	be	AUX
ejpam-5872	360	15	widely	widely	ADV
ejpam-5872	360	16	used	use	VERB
ejpam-5872	360	17	in	in	ADP
ejpam-5872	360	18	environmental	environmental	ADJ
ejpam-5872	360	19	monitoring	monitoring	NOUN
ejpam-5872	360	20	systems	system	NOUN
ejpam-5872	360	21	to	to	PART
ejpam-5872	360	22	collect	collect	VERB
ejpam-5872	360	23	data	datum	NOUN
ejpam-5872	360	24	from	from	ADP
ejpam-5872	360	25	a	a	DET
ejpam-5872	360	26	range	range	NOUN
ejpam-5872	360	27	of	of	ADP
ejpam-5872	360	28	sensors	sensor	NOUN
ejpam-5872	360	29	positioned	position	VERB
ejpam-5872	360	30	around	around	ADP
ejpam-5872	360	31	an	an	DET
ejpam-5872	360	32	area	area	NOUN
ejpam-5872	360	33	.	.	PUNCT
ejpam-5872	361	1	in	in	ADP
ejpam-5872	361	2	a	a	DET
ejpam-5872	361	3	signed	sign	VERB
ejpam-5872	361	4	-	-	PUNCT
ejpam-5872	361	5	fg	fg	NOUN
ejpam-5872	361	6	model	model	NOUN
ejpam-5872	361	7	of	of	ADP
ejpam-5872	361	8	such	such	DET
ejpam-5872	361	9	a	a	DET
ejpam-5872	361	10	network	network	NOUN
ejpam-5872	361	11	,	,	PUNCT
ejpam-5872	361	12	sensors	sensor	NOUN
ejpam-5872	361	13	are	be	AUX
ejpam-5872	361	14	the	the	DET
ejpam-5872	361	15	vertices	vertex	NOUN
ejpam-5872	361	16	,	,	PUNCT
ejpam-5872	361	17	and	and	CCONJ
ejpam-5872	361	18	communication	communication	NOUN
ejpam-5872	361	19	links	link	NOUN
ejpam-5872	361	20	are	be	AUX
ejpam-5872	361	21	the	the	DET
ejpam-5872	361	22	edges	edge	NOUN
ejpam-5872	361	23	.	.	PUNCT
ejpam-5872	362	1	signs	sign	NOUN
ejpam-5872	362	2	indicate	indicate	VERB
ejpam-5872	362	3	the	the	DET
ejpam-5872	362	4	quality	quality	NOUN
ejpam-5872	362	5	of	of	ADP
ejpam-5872	362	6	the	the	DET
ejpam-5872	362	7	connection	connection	NOUN
ejpam-5872	362	8	(	(	PUNCT
ejpam-5872	362	9	negative	negative	ADJ
ejpam-5872	362	10	for	for	ADP
ejpam-5872	362	11	poor	poor	ADJ
ejpam-5872	362	12	quality	quality	NOUN
ejpam-5872	362	13	,	,	PUNCT
ejpam-5872	362	14	and	and	CCONJ
ejpam-5872	362	15	positive	positive	ADJ
ejpam-5872	362	16	for	for	ADP
ejpam-5872	362	17	high	high	ADJ
ejpam-5872	362	18	quality	quality	NOUN
ejpam-5872	362	19	)	)	PUNCT
ejpam-5872	362	20	,	,	PUNCT
ejpam-5872	362	21	while	while	SCONJ
ejpam-5872	362	22	membership	membership	NOUN
ejpam-5872	362	23	values	value	NOUN
ejpam-5872	362	24	indicate	indicate	VERB
ejpam-5872	362	25	the	the	DET
ejpam-5872	362	26	reliability	reliability	NOUN
ejpam-5872	362	27	of	of	ADP
ejpam-5872	362	28	the	the	DET
ejpam-5872	362	29	connection	connection	NOUN
ejpam-5872	362	30	.	.	PUNCT
ejpam-5872	363	1	consider	consider	VERB
ejpam-5872	363	2	a	a	DET
ejpam-5872	363	3	system	system	NOUN
ejpam-5872	363	4	that	that	PRON
ejpam-5872	363	5	is	be	AUX
ejpam-5872	363	6	placed	place	VERB
ejpam-5872	363	7	in	in	ADP
ejpam-5872	363	8	a	a	DET
ejpam-5872	363	9	forest	forest	NOUN
ejpam-5872	363	10	to	to	PART
ejpam-5872	363	11	monitor	monitor	VERB
ejpam-5872	363	12	the	the	DET
ejpam-5872	363	13	temperature	temperature	NOUN
ejpam-5872	363	14	,	,	PUNCT
ejpam-5872	363	15	humidity	humidity	NOUN
ejpam-5872	363	16	,	,	PUNCT
ejpam-5872	363	17	and	and	CCONJ
ejpam-5872	363	18	air	air	NOUN
ejpam-5872	363	19	quality	quality	NOUN
ejpam-5872	363	20	.	.	PUNCT
ejpam-5872	364	1	in	in	ADP
ejpam-5872	364	2	the	the	DET
ejpam-5872	364	3	wsn	wsn	NOUN
ejpam-5872	364	4	,	,	PUNCT
ejpam-5872	364	5	there	there	PRON
ejpam-5872	364	6	are	be	VERB
ejpam-5872	364	7	five	five	NUM
ejpam-5872	364	8	sensors	sensor	NOUN
ejpam-5872	364	9	:	:	PUNCT
ejpam-5872	364	10	,	,	PUNCT
ejpam-5872	364	11	1ג	1ג	NUM
ejpam-5872	364	12	,	,	PUNCT
ejpam-5872	364	13	2ג	2ג	NUM
ejpam-5872	364	14	,	,	PUNCT
ejpam-5872	364	15	3ג	3ג	NUM
ejpam-5872	364	16	,	,	PUNCT
ejpam-5872	364	17	4ג	4ג	NOUN
ejpam-5872	364	18	and	and	CCONJ
ejpam-5872	364	19	.5ג	.5ג	NOUN
ejpam-5872	364	20	the	the	DET
ejpam-5872	364	21	identification	identification	NOUN
ejpam-5872	364	22	of	of	ADP
ejpam-5872	364	23	a	a	DET
ejpam-5872	364	24	dominance	dominance	NOUN
ejpam-5872	364	25	set	set	NOUN
ejpam-5872	364	26	of	of	ADP
ejpam-5872	364	27	sensors	sensor	NOUN
ejpam-5872	364	28	is	be	AUX
ejpam-5872	364	29	necessary	necessary	ADJ
ejpam-5872	364	30	to	to	PART
ejpam-5872	364	31	ensure	ensure	VERB
ejpam-5872	364	32	that	that	SCONJ
ejpam-5872	364	33	each	each	DET
ejpam-5872	364	34	sensor	sensor	NOUN
ejpam-5872	364	35	in	in	ADP
ejpam-5872	364	36	the	the	DET
ejpam-5872	364	37	network	network	NOUN
ejpam-5872	364	38	is	be	AUX
ejpam-5872	364	39	either	either	CCONJ
ejpam-5872	364	40	a	a	DET
ejpam-5872	364	41	member	member	NOUN
ejpam-5872	364	42	of	of	ADP
ejpam-5872	364	43	the	the	DET
ejpam-5872	364	44	domination	domination	NOUN
ejpam-5872	364	45	set	set	VERB
ejpam-5872	364	46	or	or	CCONJ
ejpam-5872	364	47	has	have	VERB
ejpam-5872	364	48	a	a	DET
ejpam-5872	364	49	robust	robust	ADJ
ejpam-5872	364	50	,	,	PUNCT
ejpam-5872	364	51	reliable	reliable	ADJ
ejpam-5872	364	52	link	link	NOUN
ejpam-5872	364	53	to	to	ADP
ejpam-5872	364	54	a	a	DET
ejpam-5872	364	55	sensor	sensor	NOUN
ejpam-5872	364	56	in	in	ADP
ejpam-5872	364	57	the	the	DET
ejpam-5872	364	58	domination	domination	NOUN
ejpam-5872	364	59	set	set	NOUN
ejpam-5872	364	60	.	.	PUNCT
ejpam-5872	365	1	let	let	VERB
ejpam-5872	365	2	σ±	σ±	NOUN
ejpam-5872	365	3	=	=	SYM
ejpam-5872	365	4	(	(	PUNCT
ejpam-5872	365	5	ℑ	ℑ	PROPN
ejpam-5872	365	6	,	,	PUNCT
ejpam-5872	365	7	σ	σ	PROPN
ejpam-5872	365	8	,	,	PUNCT
ejpam-5872	365	9	µ	µ	NOUN
ejpam-5872	365	10	)	)	PUNCT
ejpam-5872	365	11	be	be	VERB
ejpam-5872	365	12	a	a	DET
ejpam-5872	365	13	signed	sign	VERB
ejpam-5872	365	14	-	-	PUNCT
ejpam-5872	365	15	fg	fg	NOUN
ejpam-5872	365	16	,	,	PUNCT
ejpam-5872	365	17	where	where	SCONJ
ejpam-5872	365	18	the	the	DET
ejpam-5872	365	19	vertex	vertex	NOUN
ejpam-5872	365	20	set	set	VERB
ejpam-5872	365	21	ℑ	ℑ	PROPN
ejpam-5872	365	22	=	=	PRON
ejpam-5872	365	23	,	,	PUNCT
ejpam-5872	365	24	1ג	1ג	NUM
ejpam-5872	365	25	}	}	PUNCT
ejpam-5872	365	26	,	,	PUNCT
ejpam-5872	365	27	2ג	2ג	NUM
ejpam-5872	365	28	,	,	PUNCT
ejpam-5872	365	29	3ג	3ג	NUM
ejpam-5872	365	30	,	,	PUNCT
ejpam-5872	365	31	4ג	4ג	NOUN
ejpam-5872	365	32	{	{	PUNCT
ejpam-5872	365	33	5ג	5ג	NOUN
ejpam-5872	365	34	and	and	CCONJ
ejpam-5872	365	35	edge	edge	NOUN
ejpam-5872	365	36	set	set	VERB
ejpam-5872	365	37	ℑ×ℑ	ℑ×ℑ	PROPN
ejpam-5872	365	38	=	=	SYM
ejpam-5872	365	39	,	,	PUNCT
ejpam-5872	365	40	1ג	1ג	NUM
ejpam-5872	365	41	)	)	PUNCT
ejpam-5872	365	42	}	}	PUNCT
ejpam-5872	365	43	,	,	PUNCT
ejpam-5872	365	44	(	(	PUNCT
ejpam-5872	365	45	2ג	2ג	NOUN
ejpam-5872	365	46	,	,	PUNCT
ejpam-5872	365	47	1ג	1ג	NUM
ejpam-5872	365	48	)	)	PUNCT
ejpam-5872	365	49	,	,	PUNCT
ejpam-5872	365	50	(	(	PUNCT
ejpam-5872	365	51	3ג	3ג	NUM
ejpam-5872	365	52	,	,	PUNCT
ejpam-5872	365	53	1ג	1ג	NUM
ejpam-5872	365	54	)	)	PUNCT
ejpam-5872	365	55	,	,	PUNCT
ejpam-5872	365	56	(	(	PUNCT
ejpam-5872	365	57	4ג	4ג	NOUN
ejpam-5872	365	58	,	,	PUNCT
ejpam-5872	365	59	1ג	1ג	NUM
ejpam-5872	365	60	)	)	PUNCT
ejpam-5872	365	61	,	,	PUNCT
ejpam-5872	365	62	(	(	PUNCT
ejpam-5872	365	63	4ג	4ג	NOUN
ejpam-5872	365	64	,	,	PUNCT
ejpam-5872	365	65	2ג	2ג	NUM
ejpam-5872	365	66	)	)	PUNCT
ejpam-5872	365	67	,	,	PUNCT
ejpam-5872	365	68	(	(	PUNCT
ejpam-5872	365	69	3ג	3ג	NUM
ejpam-5872	365	70	,	,	PUNCT
ejpam-5872	365	71	2ג	2ג	NUM
ejpam-5872	365	72	)	)	PUNCT
ejpam-5872	365	73	,	,	PUNCT
ejpam-5872	365	74	(	(	PUNCT
ejpam-5872	365	75	4ג	4ג	NOUN
ejpam-5872	365	76	,	,	PUNCT
ejpam-5872	365	77	2ג	2ג	NUM
ejpam-5872	365	78	)	)	PUNCT
ejpam-5872	365	79	,	,	PUNCT
ejpam-5872	365	80	(	(	PUNCT
ejpam-5872	365	81	5ג	5ג	NOUN
ejpam-5872	365	82	,	,	PUNCT
ejpam-5872	365	83	3ג	3ג	NUM
ejpam-5872	365	84	)	)	PUNCT
ejpam-5872	365	85	,	,	PUNCT
ejpam-5872	365	86	(	(	PUNCT
ejpam-5872	365	87	4ג	4ג	NOUN
ejpam-5872	365	88	,	,	PUNCT
ejpam-5872	365	89	3ג	3ג	NUM
ejpam-5872	365	90	)	)	PUNCT
ejpam-5872	365	91	,	,	PUNCT
ejpam-5872	365	92	(	(	PUNCT
ejpam-5872	365	93	5ג	5ג	NOUN
ejpam-5872	365	94	,	,	PUNCT
ejpam-5872	365	95	4ג	4ג	NOUN
ejpam-5872	365	96	)	)	PUNCT
ejpam-5872	365	97	{	{	PUNCT
ejpam-5872	365	98	(	(	PUNCT
ejpam-5872	365	99	5ג	5ג	NOUN
ejpam-5872	365	100	with	with	ADP
ejpam-5872	365	101	the	the	DET
ejpam-5872	365	102	following	follow	VERB
ejpam-5872	365	103	vertex	vertex	NOUN
ejpam-5872	365	104	values	value	NOUN
ejpam-5872	365	105	σ(1ג	σ(1ג	NOUN
ejpam-5872	365	106	)	)	PUNCT
ejpam-5872	365	107	=	=	SYM
ejpam-5872	365	108	0.8	0.8	NUM
ejpam-5872	365	109	,	,	PUNCT
ejpam-5872	365	110	σ(2ג	σ(2ג	NUM
ejpam-5872	365	111	)	)	PUNCT
ejpam-5872	365	112	=	=	SYM
ejpam-5872	365	113	0.7	0.7	NUM
ejpam-5872	365	114	,	,	PUNCT
ejpam-5872	365	115	σ(3ג	σ(3ג	NUM
ejpam-5872	365	116	)	)	PUNCT
ejpam-5872	365	117	=	=	SYM
ejpam-5872	365	118	0.6	0.6	NUM
ejpam-5872	365	119	,	,	PUNCT
ejpam-5872	365	120	σ(4ג	σ(4ג	NOUN
ejpam-5872	365	121	)	)	PUNCT
ejpam-5872	365	122	=	=	SYM
ejpam-5872	365	123	0.5	0.5	NUM
ejpam-5872	365	124	and	and	CCONJ
ejpam-5872	365	125	σ(5ג	σ(5ג	NOUN
ejpam-5872	365	126	)	)	PUNCT
ejpam-5872	365	127	=	=	PUNCT
ejpam-5872	366	1	0.7	0.7	NUM
ejpam-5872	366	2	.	.	PUNCT
ejpam-5872	367	1	the	the	DET
ejpam-5872	367	2	edge	edge	NOUN
ejpam-5872	367	3	values	value	NOUN
ejpam-5872	367	4	are	be	AUX
ejpam-5872	367	5	µ(1ג	µ(1ג	NOUN
ejpam-5872	367	6	,	,	PUNCT
ejpam-5872	367	7	(	(	PUNCT
ejpam-5872	367	8	2ג	2ג	NOUN
ejpam-5872	367	9	=	=	SYM
ejpam-5872	367	10	0.5	0.5	NUM
ejpam-5872	367	11	,	,	PUNCT
ejpam-5872	367	12	µ(1ג	µ(1ג	NUM
ejpam-5872	367	13	,	,	PUNCT
ejpam-5872	367	14	(	(	PUNCT
ejpam-5872	367	15	3ג	3ג	NUM
ejpam-5872	367	16	=	=	SYM
ejpam-5872	367	17	−0.3	−0.3	PROPN
ejpam-5872	367	18	,	,	PUNCT
ejpam-5872	367	19	µ(1ג	µ(1ג	NUM
ejpam-5872	367	20	,	,	PUNCT
ejpam-5872	367	21	(	(	PUNCT
ejpam-5872	367	22	4ג	4ג	NOUN
ejpam-5872	367	23	=	=	SYM
ejpam-5872	367	24	0.5	0.5	NUM
ejpam-5872	367	25	,	,	PUNCT
ejpam-5872	367	26	,	,	PUNCT
ejpam-5872	367	27	µ(1ג	µ(1ג	NOUN
ejpam-5872	367	28	,	,	PUNCT
ejpam-5872	367	29	(	(	PUNCT
ejpam-5872	367	30	5ג	5ג	NOUN
ejpam-5872	367	31	=	=	SYM
ejpam-5872	367	32	0.2	0.2	NUM
ejpam-5872	367	33	,	,	PUNCT
ejpam-5872	367	34	µ(2ג	µ(2ג	VERB
ejpam-5872	367	35	,	,	PUNCT
ejpam-5872	367	36	(	(	PUNCT
ejpam-5872	367	37	3ג	3ג	NUM
ejpam-5872	367	38	=	=	SYM
ejpam-5872	367	39	0.4	0.4	NUM
ejpam-5872	367	40	,	,	PUNCT
ejpam-5872	367	41	µ(2ג	µ(2ג	VERB
ejpam-5872	367	42	,	,	PUNCT
ejpam-5872	367	43	(	(	PUNCT
ejpam-5872	367	44	4ג	4ג	NOUN
ejpam-5872	367	45	=	=	SYM
ejpam-5872	367	46	−0.5	−0.5	PROPN
ejpam-5872	367	47	,	,	PUNCT
ejpam-5872	367	48	µ(2ג	µ(2ג	VERB
ejpam-5872	367	49	,	,	PUNCT
ejpam-5872	367	50	(	(	PUNCT
ejpam-5872	367	51	5ג	5ג	NOUN
ejpam-5872	367	52	=	=	SYM
ejpam-5872	367	53	0.5	0.5	NUM
ejpam-5872	367	54	,	,	PUNCT
ejpam-5872	367	55	µ(3ג	µ(3ג	NOUN
ejpam-5872	367	56	,	,	PUNCT
ejpam-5872	367	57	(	(	PUNCT
ejpam-5872	367	58	4ג	4ג	NOUN
ejpam-5872	367	59	=	=	SYM
ejpam-5872	367	60	−0.3	−0.3	PROPN
ejpam-5872	367	61	,	,	PUNCT
ejpam-5872	367	62	µ(3ג	µ(3ג	NOUN
ejpam-5872	367	63	,	,	PUNCT
ejpam-5872	367	64	(	(	PUNCT
ejpam-5872	367	65	5ג	5ג	NOUN
ejpam-5872	367	66	=	=	SYM
ejpam-5872	367	67	0.6	0.6	NUM
ejpam-5872	367	68	and	and	CCONJ
ejpam-5872	367	69	µ(4ג	µ(4ג	NOUN
ejpam-5872	367	70	,	,	PUNCT
ejpam-5872	367	71	(	(	PUNCT
ejpam-5872	367	72	5ג	5ג	NOUN
ejpam-5872	367	73	=	=	SYM
ejpam-5872	367	74	−0.4	−0.4	PROPN
ejpam-5872	367	75	as	as	SCONJ
ejpam-5872	367	76	shown	show	VERB
ejpam-5872	367	77	in	in	ADP
ejpam-5872	367	78	figure	figure	NOUN
ejpam-5872	367	79	3	3	NUM
ejpam-5872	367	80	.	.	PUNCT
ejpam-5872	368	1	the	the	DET
ejpam-5872	368	2	strong	strong	ADJ
ejpam-5872	368	3	arcs	arc	NOUN
ejpam-5872	368	4	are	be	AUX
ejpam-5872	368	5	,	,	PUNCT
ejpam-5872	368	6	1ג	1ג	NUM
ejpam-5872	368	7	)	)	PUNCT
ejpam-5872	368	8	,	,	PUNCT
ejpam-5872	368	9	(	(	PUNCT
ejpam-5872	368	10	3ג	3ג	NUM
ejpam-5872	368	11	,	,	PUNCT
ejpam-5872	368	12	1ג	1ג	NUM
ejpam-5872	368	13	)	)	PUNCT
ejpam-5872	368	14	,	,	PUNCT
ejpam-5872	368	15	(	(	PUNCT
ejpam-5872	368	16	4ג	4ג	NOUN
ejpam-5872	368	17	,	,	PUNCT
ejpam-5872	368	18	2ג	2ג	NUM
ejpam-5872	368	19	)	)	PUNCT
ejpam-5872	368	20	(	(	PUNCT
ejpam-5872	368	21	5ג	5ג	NOUN
ejpam-5872	368	22	and	and	CCONJ
ejpam-5872	368	23	,	,	PUNCT
ejpam-5872	368	24	3ג	3ג	NUM
ejpam-5872	368	25	)	)	PUNCT
ejpam-5872	368	26	.(5ג	.(5ג	PUNCT
ejpam-5872	369	1	the	the	DET
ejpam-5872	369	2	possible	possible	ADJ
ejpam-5872	369	3	domination	domination	NOUN
ejpam-5872	369	4	sets	set	NOUN
ejpam-5872	369	5	are	be	AUX
ejpam-5872	369	6	,	,	PUNCT
ejpam-5872	369	7	1ג	1ג	NOUN
ejpam-5872	369	8	}	}	PUNCT
ejpam-5872	369	9	,	,	PUNCT
ejpam-5872	369	10	{	{	PUNCT
ejpam-5872	369	11	3ג	3ג	NUM
ejpam-5872	369	12	,	,	PUNCT
ejpam-5872	369	13	1ג	1ג	NUM
ejpam-5872	369	14	}	}	PUNCT
ejpam-5872	369	15	,	,	PUNCT
ejpam-5872	369	16	{	{	PUNCT
ejpam-5872	369	17	5ג	5ג	NOUN
ejpam-5872	369	18	,	,	PUNCT
ejpam-5872	369	19	1ג	1ג	NUM
ejpam-5872	369	20	}	}	PUNCT
ejpam-5872	369	21	,	,	PUNCT
ejpam-5872	369	22	5ג	5ג	NOUN
ejpam-5872	369	23	{	{	PUNCT
ejpam-5872	369	24	2ג	2ג	NOUN
ejpam-5872	369	25	and	and	CCONJ
ejpam-5872	369	26	,	,	PUNCT
ejpam-5872	369	27	3ג	3ג	NOUN
ejpam-5872	369	28	}	}	PUNCT
ejpam-5872	369	29	,	,	PUNCT
ejpam-5872	369	30	2ג	2ג	NOUN
ejpam-5872	369	31	.{4ג	.{4ג	PUNCT
ejpam-5872	370	1	the	the	DET
ejpam-5872	370	2	minimum	minimum	ADJ
ejpam-5872	370	3	domination	domination	NOUN
ejpam-5872	370	4	set	set	NOUN
ejpam-5872	370	5	is	be	AUX
ejpam-5872	370	6	,	,	PUNCT
ejpam-5872	370	7	2ג	2ג	NUM
ejpam-5872	370	8	}	}	PUNCT
ejpam-5872	370	9	{	{	PUNCT
ejpam-5872	370	10	4ג	4ג	NOUN
ejpam-5872	370	11	and	and	CCONJ
ejpam-5872	370	12	the	the	DET
ejpam-5872	370	13	domination	domination	NOUN
ejpam-5872	370	14	number	number	NOUN
ejpam-5872	370	15	is	be	AUX
ejpam-5872	370	16	γ	γ	X
ejpam-5872	370	17	(	(	PUNCT
ejpam-5872	370	18	∑	∑	PROPN
ejpam-5872	370	19	±	±	NUM
ejpam-5872	370	20	)	)	PUNCT
ejpam-5872	370	21	=	=	NOUN
ejpam-5872	370	22	1.2	1.2	NUM
ejpam-5872	370	23	.	.	PUNCT
ejpam-5872	371	1	(	(	PUNCT
ejpam-5872	371	2	0.8)1ג	0.8)1ג	NUM
ejpam-5872	371	3	(	(	PUNCT
ejpam-5872	371	4	0.7)5ג	0.7)5ג	NOUN
ejpam-5872	371	5	(	(	PUNCT
ejpam-5872	371	6	0.5)4ג	0.5)4ג	NOUN
ejpam-5872	371	7	(	(	PUNCT
ejpam-5872	371	8	0.7)2ג	0.7)2ג	NUM
ejpam-5872	371	9	(	(	PUNCT
ejpam-5872	371	10	0.6)3ג	0.6)3ג	PROPN
ejpam-5872	371	11	−0.4	−0.4	NUM
ejpam-5872	371	12	0.5	0.5	NUM
ejpam-5872	371	13	0	0	NUM
ejpam-5872	371	14	.	.	NOUN
ejpam-5872	371	15	5	5	NUM
ejpam-5872	371	16	0	0	NUM
ejpam-5872	371	17	.	.	NOUN
ejpam-5872	371	18	2	2	NUM
ejpam-5872	371	19	0.4	0.4	NUM
ejpam-5872	371	20	−	−	NOUN
ejpam-5872	371	21	0	0	NUM
ejpam-5872	371	22	.5	.5	NUM
ejpam-5872	371	23	−0	−0	NOUN
ejpam-5872	371	24	.	.	PUNCT
ejpam-5872	372	1	30.6	30.6	NUM
ejpam-5872	372	2	−0.3	−0.3	NUM
ejpam-5872	372	3	0.5	0.5	NUM
ejpam-5872	372	4	figure	figure	NOUN
ejpam-5872	372	5	3	3	NUM
ejpam-5872	372	6	:	:	PUNCT
ejpam-5872	372	7	domination	domination	NOUN
ejpam-5872	372	8	in	in	ADP
ejpam-5872	372	9	a	a	DET
ejpam-5872	372	10	signed	sign	VERB
ejpam-5872	372	11	-	-	PUNCT
ejpam-5872	372	12	fg	fg	NOUN
ejpam-5872	372	13	in	in	ADP
ejpam-5872	372	14	wsn	wsn	PROPN
ejpam-5872	372	15	is	be	AUX
ejpam-5872	372	16	demonstrated	demonstrate	VERB
ejpam-5872	372	17	.	.	PUNCT
ejpam-5872	373	1	c.	c.	PROPN
ejpam-5872	373	2	sankar	sankar	PROPN
ejpam-5872	373	3	et	et	PROPN
ejpam-5872	373	4	al	al	PROPN
ejpam-5872	373	5	.	.	PUNCT
ejpam-5872	373	6	/	/	SYM
ejpam-5872	373	7	eur	eur	PROPN
ejpam-5872	373	8	.	.	PUNCT
ejpam-5872	374	1	j.	j.	PROPN
ejpam-5872	374	2	pure	pure	PROPN
ejpam-5872	374	3	appl	appl	PROPN
ejpam-5872	374	4	.	.	PROPN
ejpam-5872	374	5	math	math	PROPN
ejpam-5872	374	6	,	,	PUNCT
ejpam-5872	374	7	18	18	NUM
ejpam-5872	374	8	(	(	PUNCT
ejpam-5872	374	9	4	4	NUM
ejpam-5872	374	10	)	)	PUNCT
ejpam-5872	374	11	(	(	PUNCT
ejpam-5872	374	12	2025	2025	NUM
ejpam-5872	374	13	)	)	PUNCT
ejpam-5872	374	14	,	,	PUNCT
ejpam-5872	374	15	5872	5872	NUM
ejpam-5872	374	16	15	15	NUM
ejpam-5872	374	17	of	of	ADP
ejpam-5872	374	18	17	17	NUM
ejpam-5872	374	19	for	for	ADP
ejpam-5872	374	20	this	this	DET
ejpam-5872	374	21	environmental	environmental	ADJ
ejpam-5872	374	22	monitoring	monitoring	NOUN
ejpam-5872	374	23	system	system	NOUN
ejpam-5872	374	24	,	,	PUNCT
ejpam-5872	374	25	a	a	DET
ejpam-5872	374	26	dominant	dominant	ADJ
ejpam-5872	374	27	collection	collection	NOUN
ejpam-5872	374	28	of	of	ADP
ejpam-5872	374	29	sensors	sensor	NOUN
ejpam-5872	374	30	that	that	PRON
ejpam-5872	374	31	can	can	AUX
ejpam-5872	374	32	cover	cover	VERB
ejpam-5872	374	33	the	the	DET
ejpam-5872	374	34	entire	entire	ADJ
ejpam-5872	374	35	network	network	NOUN
ejpam-5872	374	36	is	be	AUX
ejpam-5872	374	37	essential	essential	ADJ
ejpam-5872	374	38	to	to	PART
ejpam-5872	374	39	guarantee	guarantee	VERB
ejpam-5872	374	40	that	that	SCONJ
ejpam-5872	374	41	data	datum	NOUN
ejpam-5872	374	42	from	from	ADP
ejpam-5872	374	43	every	every	DET
ejpam-5872	374	44	place	place	NOUN
ejpam-5872	374	45	is	be	AUX
ejpam-5872	374	46	sent	send	VERB
ejpam-5872	374	47	efficiently	efficiently	ADV
ejpam-5872	374	48	,	,	PUNCT
ejpam-5872	374	49	even	even	ADV
ejpam-5872	374	50	in	in	ADP
ejpam-5872	374	51	the	the	DET
ejpam-5872	374	52	case	case	NOUN
ejpam-5872	374	53	that	that	SCONJ
ejpam-5872	374	54	certain	certain	ADJ
ejpam-5872	374	55	links	link	NOUN
ejpam-5872	374	56	are	be	AUX
ejpam-5872	374	57	defective	defective	ADJ
ejpam-5872	374	58	or	or	CCONJ
ejpam-5872	374	59	of	of	ADP
ejpam-5872	374	60	low	low	ADJ
ejpam-5872	374	61	quality.whether	quality.whether	PROPN
ejpam-5872	374	62	directly	directly	ADV
ejpam-5872	374	63	or	or	CCONJ
ejpam-5872	374	64	through	through	ADP
ejpam-5872	374	65	reliable	reliable	ADJ
ejpam-5872	374	66	linkages	linkage	NOUN
ejpam-5872	374	67	,	,	PUNCT
ejpam-5872	374	68	the	the	DET
ejpam-5872	374	69	objective	objective	NOUN
ejpam-5872	374	70	is	be	AUX
ejpam-5872	374	71	to	to	PART
ejpam-5872	374	72	determine	determine	VERB
ejpam-5872	374	73	the	the	DET
ejpam-5872	374	74	bare	bare	ADJ
ejpam-5872	374	75	minimum	minimum	NOUN
ejpam-5872	374	76	of	of	ADP
ejpam-5872	374	77	sensors	sensor	NOUN
ejpam-5872	374	78	needed	need	VERB
ejpam-5872	374	79	to	to	PART
ejpam-5872	374	80	monitor	monitor	VERB
ejpam-5872	374	81	the	the	DET
ejpam-5872	374	82	entire	entire	ADJ
ejpam-5872	374	83	network	network	NOUN
ejpam-5872	374	84	.	.	PUNCT
ejpam-5872	375	1	start	start	VERB
ejpam-5872	375	2	by	by	ADP
ejpam-5872	375	3	figuring	figure	VERB
ejpam-5872	375	4	out	out	ADP
ejpam-5872	375	5	whether	whether	SCONJ
ejpam-5872	375	6	one	one	NUM
ejpam-5872	375	7	sensor	sensor	NOUN
ejpam-5872	375	8	is	be	AUX
ejpam-5872	375	9	enough	enough	ADJ
ejpam-5872	375	10	to	to	PART
ejpam-5872	375	11	cover	cover	VERB
ejpam-5872	375	12	the	the	DET
ejpam-5872	375	13	entire	entire	ADJ
ejpam-5872	375	14	network	network	NOUN
ejpam-5872	375	15	.	.	PUNCT
ejpam-5872	376	1	one	one	NUM
ejpam-5872	376	2	sensor	sensor	NOUN
ejpam-5872	376	3	is	be	AUX
ejpam-5872	376	4	not	not	PART
ejpam-5872	376	5	enough	enough	ADJ
ejpam-5872	376	6	since	since	SCONJ
ejpam-5872	376	7	no	no	DET
ejpam-5872	376	8	single	single	ADJ
ejpam-5872	376	9	sensor	sensor	NOUN
ejpam-5872	376	10	has	have	VERB
ejpam-5872	376	11	links	link	NOUN
ejpam-5872	376	12	to	to	ADP
ejpam-5872	376	13	all	all	DET
ejpam-5872	376	14	other	other	ADJ
ejpam-5872	376	15	sensors	sensor	NOUN
ejpam-5872	376	16	with	with	ADP
ejpam-5872	376	17	high	high	ADJ
ejpam-5872	376	18	membership	membership	NOUN
ejpam-5872	376	19	levels	level	NOUN
ejpam-5872	376	20	.	.	PUNCT
ejpam-5872	377	1	then	then	ADV
ejpam-5872	377	2	examine	examine	VERB
ejpam-5872	377	3	a	a	DET
ejpam-5872	377	4	pair	pair	NOUN
ejpam-5872	377	5	of	of	ADP
ejpam-5872	377	6	sensors	sensor	NOUN
ejpam-5872	377	7	;	;	PUNCT
ejpam-5872	377	8	the	the	DET
ejpam-5872	377	9	potential	potential	ADJ
ejpam-5872	377	10	dominant	dominant	ADJ
ejpam-5872	377	11	sets	set	NOUN
ejpam-5872	377	12	are	be	AUX
ejpam-5872	377	13	,	,	PUNCT
ejpam-5872	377	14	1ג	1ג	NOUN
ejpam-5872	377	15	}	}	PUNCT
ejpam-5872	377	16	,	,	PUNCT
ejpam-5872	377	17	{	{	PUNCT
ejpam-5872	377	18	3ג	3ג	NUM
ejpam-5872	377	19	,	,	PUNCT
ejpam-5872	377	20	1ג	1ג	NUM
ejpam-5872	377	21	}	}	PUNCT
ejpam-5872	377	22	,	,	PUNCT
ejpam-5872	377	23	{	{	PUNCT
ejpam-5872	377	24	5ג	5ג	NOUN
ejpam-5872	377	25	,	,	PUNCT
ejpam-5872	377	26	1ג	1ג	NUM
ejpam-5872	377	27	}	}	PUNCT
ejpam-5872	377	28	,	,	PUNCT
ejpam-5872	377	29	5ג	5ג	NOUN
ejpam-5872	377	30	,	,	PUNCT
ejpam-5872	377	31	{	{	PUNCT
ejpam-5872	377	32	2ג	2ג	NOUN
ejpam-5872	377	33	and	and	CCONJ
ejpam-5872	377	34	,	,	PUNCT
ejpam-5872	377	35	3ג	3ג	NOUN
ejpam-5872	377	36	}	}	PUNCT
ejpam-5872	377	37	,	,	PUNCT
ejpam-5872	377	38	2ג	2ג	NOUN
ejpam-5872	377	39	.{4ג	.{4ג	PUNCT
ejpam-5872	378	1	the	the	DET
ejpam-5872	378	2	minimum	minimum	ADJ
ejpam-5872	378	3	domination	domination	NOUN
ejpam-5872	378	4	set	set	NOUN
ejpam-5872	378	5	is	be	AUX
ejpam-5872	378	6	,	,	PUNCT
ejpam-5872	378	7	2ג	2ג	NUM
ejpam-5872	378	8	}	}	PUNCT
ejpam-5872	378	9	{	{	PUNCT
ejpam-5872	378	10	4ג	4ג	NOUN
ejpam-5872	378	11	and	and	CCONJ
ejpam-5872	378	12	the	the	DET
ejpam-5872	378	13	domination	domination	NOUN
ejpam-5872	378	14	number	number	NOUN
ejpam-5872	378	15	is	be	AUX
ejpam-5872	378	16	γ	γ	X
ejpam-5872	378	17	(	(	PUNCT
ejpam-5872	378	18	∑	∑	PROPN
ejpam-5872	378	19	±	±	NUM
ejpam-5872	378	20	)	)	PUNCT
ejpam-5872	378	21	=	=	NOUN
ejpam-5872	378	22	1.2	1.2	NUM
ejpam-5872	378	23	.	.	PUNCT
ejpam-5872	379	1	in	in	ADP
ejpam-5872	379	2	this	this	DET
ejpam-5872	379	3	scenario	scenario	NOUN
ejpam-5872	379	4	,	,	PUNCT
ejpam-5872	379	5	maintaining	maintain	VERB
ejpam-5872	379	6	the	the	DET
ejpam-5872	379	7	functionality	functionality	NOUN
ejpam-5872	379	8	of	of	ADP
ejpam-5872	379	9	sensors	sensor	NOUN
ejpam-5872	379	10	2ג	2ג	NUM
ejpam-5872	379	11	and	and	CCONJ
ejpam-5872	379	12	4ג	4ג	NOUN
ejpam-5872	379	13	ensures	ensure	VERB
ejpam-5872	379	14	that	that	SCONJ
ejpam-5872	379	15	the	the	DET
ejpam-5872	379	16	entire	entire	ADJ
ejpam-5872	379	17	network	network	NOUN
ejpam-5872	379	18	is	be	AUX
ejpam-5872	379	19	covered	cover	VERB
ejpam-5872	379	20	,	,	PUNCT
ejpam-5872	379	21	even	even	ADV
ejpam-5872	379	22	if	if	SCONJ
ejpam-5872	379	23	certain	certain	ADJ
ejpam-5872	379	24	connections	connection	NOUN
ejpam-5872	379	25	are	be	AUX
ejpam-5872	379	26	not	not	PART
ejpam-5872	379	27	ideal	ideal	ADJ
ejpam-5872	379	28	(	(	PUNCT
ejpam-5872	379	29	such	such	ADJ
ejpam-5872	379	30	as	as	ADP
ejpam-5872	379	31	the	the	DET
ejpam-5872	379	32	negative	negative	ADJ
ejpam-5872	379	33	connections	connection	NOUN
ejpam-5872	379	34	)	)	PUNCT
ejpam-5872	379	35	.	.	PUNCT
ejpam-5872	380	1	since	since	SCONJ
ejpam-5872	380	2	environmental	environmental	ADJ
ejpam-5872	380	3	factors	factor	NOUN
ejpam-5872	380	4	may	may	AUX
ejpam-5872	380	5	have	have	VERB
ejpam-5872	380	6	an	an	DET
ejpam-5872	380	7	impact	impact	NOUN
ejpam-5872	380	8	on	on	ADP
ejpam-5872	380	9	sensor	sensor	NOUN
ejpam-5872	380	10	dependability	dependability	NOUN
ejpam-5872	380	11	and	and	CCONJ
ejpam-5872	380	12	connection	connection	NOUN
ejpam-5872	380	13	strength	strength	NOUN
ejpam-5872	380	14	,	,	PUNCT
ejpam-5872	380	15	this	this	PRON
ejpam-5872	380	16	is	be	AUX
ejpam-5872	380	17	particularly	particularly	ADV
ejpam-5872	380	18	useful	useful	ADJ
ejpam-5872	380	19	for	for	ADP
ejpam-5872	380	20	environmental	environmental	ADJ
ejpam-5872	380	21	monitoring	monitoring	NOUN
ejpam-5872	380	22	.	.	PUNCT
ejpam-5872	381	1	the	the	DET
ejpam-5872	381	2	majority	majority	NOUN
ejpam-5872	381	3	of	of	ADP
ejpam-5872	381	4	the	the	DET
ejpam-5872	381	5	sensors	sensor	NOUN
ejpam-5872	381	6	are	be	AUX
ejpam-5872	381	7	kept	keep	VERB
ejpam-5872	381	8	in	in	ADP
ejpam-5872	381	9	operation	operation	NOUN
ejpam-5872	381	10	to	to	PART
ejpam-5872	381	11	enable	enable	VERB
ejpam-5872	381	12	efficient	efficient	ADJ
ejpam-5872	381	13	monitoring	monitoring	NOUN
ejpam-5872	381	14	and	and	CCONJ
ejpam-5872	381	15	data	datum	NOUN
ejpam-5872	381	16	collection	collection	NOUN
ejpam-5872	381	17	throughout	throughout	ADP
ejpam-5872	381	18	the	the	DET
ejpam-5872	381	19	entire	entire	ADJ
ejpam-5872	381	20	region	region	NOUN
ejpam-5872	381	21	.	.	PUNCT
ejpam-5872	382	1	to	to	PART
ejpam-5872	382	2	ensure	ensure	VERB
ejpam-5872	382	3	full	full	ADJ
ejpam-5872	382	4	network	network	NOUN
ejpam-5872	382	5	coverage	coverage	NOUN
ejpam-5872	382	6	,	,	PUNCT
ejpam-5872	382	7	the	the	DET
ejpam-5872	382	8	dominance	dominance	NOUN
ejpam-5872	382	9	number	number	NOUN
ejpam-5872	382	10	helps	help	VERB
ejpam-5872	382	11	determine	determine	VERB
ejpam-5872	382	12	the	the	DET
ejpam-5872	382	13	minimum	minimum	ADJ
ejpam-5872	382	14	number	number	NOUN
ejpam-5872	382	15	of	of	ADP
ejpam-5872	382	16	sensors	sensor	NOUN
ejpam-5872	382	17	needed	need	VERB
ejpam-5872	382	18	in	in	ADP
ejpam-5872	382	19	an	an	DET
ejpam-5872	382	20	environmental	environmental	ADJ
ejpam-5872	382	21	monitoring	monitoring	NOUN
ejpam-5872	382	22	system	system	NOUN
ejpam-5872	382	23	.	.	PUNCT
ejpam-5872	383	1	keeping	keep	VERB
ejpam-5872	383	2	the	the	DET
ejpam-5872	383	3	sensors	sensor	NOUN
ejpam-5872	383	4	in	in	ADP
ejpam-5872	383	5	the	the	DET
ejpam-5872	383	6	domination	domination	NOUN
ejpam-5872	383	7	set	set	NOUN
ejpam-5872	383	8	,	,	PUNCT
ejpam-5872	383	9	which	which	PRON
ejpam-5872	383	10	in	in	ADP
ejpam-5872	383	11	this	this	DET
ejpam-5872	383	12	case	case	NOUN
ejpam-5872	383	13	comprises	comprise	NOUN
ejpam-5872	383	14	of	of	ADP
ejpam-5872	383	15	2ג	2ג	NUM
ejpam-5872	383	16	and	and	CCONJ
ejpam-5872	383	17	,	,	PUNCT
ejpam-5872	383	18	4ג	4ג	NOUN
ejpam-5872	383	19	allows	allow	VERB
ejpam-5872	383	20	for	for	ADP
ejpam-5872	383	21	whole	whole	ADJ
ejpam-5872	383	22	-	-	PUNCT
ejpam-5872	383	23	region	region	NOUN
ejpam-5872	383	24	monitoring	monitoring	NOUN
ejpam-5872	383	25	and	and	CCONJ
ejpam-5872	383	26	data	datum	NOUN
ejpam-5872	383	27	collection	collection	NOUN
ejpam-5872	383	28	even	even	ADV
ejpam-5872	383	29	when	when	SCONJ
ejpam-5872	383	30	certain	certain	ADJ
ejpam-5872	383	31	links	link	NOUN
ejpam-5872	383	32	are	be	AUX
ejpam-5872	383	33	weak	weak	ADJ
ejpam-5872	383	34	or	or	CCONJ
ejpam-5872	383	35	unreliable	unreliable	ADJ
ejpam-5872	383	36	.	.	PUNCT
ejpam-5872	384	1	6	6	X
ejpam-5872	384	2	.	.	X
ejpam-5872	384	3	conclusion	conclusion	NOUN
ejpam-5872	384	4	bounds	bound	VERB
ejpam-5872	384	5	for	for	ADP
ejpam-5872	384	6	the	the	DET
ejpam-5872	384	7	concept	concept	NOUN
ejpam-5872	384	8	of	of	ADP
ejpam-5872	384	9	domination	domination	NOUN
ejpam-5872	384	10	in	in	ADP
ejpam-5872	384	11	signed	sign	VERB
ejpam-5872	384	12	-	-	PUNCT
ejpam-5872	384	13	fgs	fgs	NOUN
ejpam-5872	384	14	are	be	AUX
ejpam-5872	384	15	examined	examine	VERB
ejpam-5872	384	16	across	across	ADP
ejpam-5872	384	17	different	different	ADJ
ejpam-5872	384	18	classes	class	NOUN
ejpam-5872	384	19	of	of	ADP
ejpam-5872	384	20	such	such	ADJ
ejpam-5872	384	21	graphs	graph	NOUN
ejpam-5872	384	22	,	,	PUNCT
ejpam-5872	384	23	and	and	CCONJ
ejpam-5872	384	24	the	the	DET
ejpam-5872	384	25	notion	notion	NOUN
ejpam-5872	384	26	is	be	AUX
ejpam-5872	384	27	introduced	introduce	VERB
ejpam-5872	384	28	with	with	ADP
ejpam-5872	384	29	illustrative	illustrative	ADJ
ejpam-5872	384	30	examples	example	NOUN
ejpam-5872	384	31	.	.	PUNCT
ejpam-5872	385	1	in	in	ADP
ejpam-5872	385	2	particular	particular	ADJ
ejpam-5872	385	3	,	,	PUNCT
ejpam-5872	385	4	bounds	bound	VERB
ejpam-5872	385	5	for	for	ADP
ejpam-5872	385	6	the	the	DET
ejpam-5872	385	7	domination	domination	NOUN
ejpam-5872	385	8	number	number	NOUN
ejpam-5872	385	9	of	of	ADP
ejpam-5872	385	10	signed	sign	VERB
ejpam-5872	385	11	-	-	PUNCT
ejpam-5872	385	12	fgs	fgs	NOUN
ejpam-5872	385	13	,	,	PUNCT
ejpam-5872	385	14	complete	complete	ADJ
ejpam-5872	385	15	signed	sign	VERB
ejpam-5872	385	16	-	-	PUNCT
ejpam-5872	385	17	fgs	fgs	NOUN
ejpam-5872	385	18	,	,	PUNCT
ejpam-5872	385	19	and	and	CCONJ
ejpam-5872	385	20	complete	complete	ADJ
ejpam-5872	385	21	bipartite	bipartite	NOUN
ejpam-5872	385	22	signed	sign	VERB
ejpam-5872	385	23	-	-	PUNCT
ejpam-5872	385	24	fgs	fgs	NOUN
ejpam-5872	385	25	are	be	AUX
ejpam-5872	385	26	established	establish	VERB
ejpam-5872	385	27	.	.	PUNCT
ejpam-5872	386	1	the	the	DET
ejpam-5872	386	2	strong	strong	ADJ
ejpam-5872	386	3	domination	domination	NOUN
ejpam-5872	386	4	number	number	NOUN
ejpam-5872	386	5	is	be	AUX
ejpam-5872	386	6	further	far	ADV
ejpam-5872	386	7	defined	define	VERB
ejpam-5872	386	8	in	in	ADP
ejpam-5872	386	9	terms	term	NOUN
ejpam-5872	386	10	of	of	ADP
ejpam-5872	386	11	strong	strong	ADJ
ejpam-5872	386	12	arc	arc	NOUN
ejpam-5872	386	13	membership	membership	NOUN
ejpam-5872	386	14	values	value	NOUN
ejpam-5872	386	15	.	.	PUNCT
ejpam-5872	387	1	in	in	ADP
ejpam-5872	387	2	addition	addition	NOUN
ejpam-5872	387	3	,	,	PUNCT
ejpam-5872	387	4	the	the	DET
ejpam-5872	387	5	relationship	relationship	NOUN
ejpam-5872	387	6	between	between	ADP
ejpam-5872	387	7	the	the	DET
ejpam-5872	387	8	domination	domination	NOUN
ejpam-5872	387	9	number	number	NOUN
ejpam-5872	387	10	of	of	ADP
ejpam-5872	387	11	a	a	DET
ejpam-5872	387	12	signed	sign	VERB
ejpam-5872	387	13	fg	fg	NOUN
ejpam-5872	387	14	and	and	CCONJ
ejpam-5872	387	15	that	that	PRON
ejpam-5872	387	16	of	of	ADP
ejpam-5872	387	17	its	its	PRON
ejpam-5872	387	18	complement	complement	NOUN
ejpam-5872	387	19	is	be	AUX
ejpam-5872	387	20	investigated	investigate	VERB
ejpam-5872	387	21	.	.	PUNCT
ejpam-5872	388	1	the	the	DET
ejpam-5872	388	2	study	study	NOUN
ejpam-5872	388	3	also	also	ADV
ejpam-5872	388	4	identifies	identify	VERB
ejpam-5872	388	5	the	the	DET
ejpam-5872	388	6	classes	class	NOUN
ejpam-5872	388	7	of	of	ADP
ejpam-5872	388	8	signed	sign	VERB
ejpam-5872	388	9	-	-	PUNCT
ejpam-5872	388	10	fgs	fgs	NOUN
ejpam-5872	388	11	that	that	PRON
ejpam-5872	388	12	admit	admit	VERB
ejpam-5872	388	13	strong	strong	ADJ
ejpam-5872	388	14	domination	domination	NOUN
ejpam-5872	388	15	and	and	CCONJ
ejpam-5872	388	16	employs	employ	VERB
ejpam-5872	388	17	strong	strong	ADJ
ejpam-5872	388	18	arcs	arc	NOUN
ejpam-5872	388	19	to	to	PART
ejpam-5872	388	20	explore	explore	VERB
ejpam-5872	388	21	domination	domination	NOUN
ejpam-5872	388	22	in	in	ADP
ejpam-5872	388	23	greater	great	ADJ
ejpam-5872	388	24	depth	depth	NOUN
ejpam-5872	388	25	.	.	PUNCT
ejpam-5872	389	1	the	the	DET
ejpam-5872	389	2	investigation	investigation	NOUN
ejpam-5872	389	3	is	be	AUX
ejpam-5872	389	4	extended	extend	VERB
ejpam-5872	389	5	to	to	ADP
ejpam-5872	389	6	strong	strong	ADJ
ejpam-5872	389	7	domination	domination	NOUN
ejpam-5872	389	8	in	in	ADP
ejpam-5872	389	9	signed	sign	VERB
ejpam-5872	389	10	fuzzy	fuzzy	ADJ
ejpam-5872	389	11	trees	tree	NOUN
ejpam-5872	389	12	,	,	PUNCT
ejpam-5872	389	13	where	where	SCONJ
ejpam-5872	389	14	an	an	DET
ejpam-5872	389	15	upper	upper	ADJ
ejpam-5872	389	16	bound	bind	VERB
ejpam-5872	389	17	for	for	ADP
ejpam-5872	389	18	the	the	DET
ejpam-5872	389	19	strong	strong	ADJ
ejpam-5872	389	20	domination	domination	NOUN
ejpam-5872	389	21	number	number	NOUN
ejpam-5872	389	22	is	be	AUX
ejpam-5872	389	23	determined	determine	VERB
ejpam-5872	389	24	.	.	PUNCT
ejpam-5872	390	1	it	it	PRON
ejpam-5872	390	2	is	be	AUX
ejpam-5872	390	3	shown	show	VERB
ejpam-5872	390	4	that	that	SCONJ
ejpam-5872	390	5	every	every	DET
ejpam-5872	390	6	node	node	NOUN
ejpam-5872	390	7	belonging	belong	VERB
ejpam-5872	390	8	to	to	ADP
ejpam-5872	390	9	a	a	DET
ejpam-5872	390	10	strong	strong	ADJ
ejpam-5872	390	11	dominating	dominating	NOUN
ejpam-5872	390	12	set	set	VERB
ejpam-5872	390	13	in	in	ADP
ejpam-5872	390	14	a	a	DET
ejpam-5872	390	15	signed	sign	VERB
ejpam-5872	390	16	fuzzy	fuzzy	ADJ
ejpam-5872	390	17	tree	tree	NOUN
ejpam-5872	390	18	is	be	AUX
ejpam-5872	390	19	either	either	CCONJ
ejpam-5872	390	20	a	a	DET
ejpam-5872	390	21	signed	sign	VERB
ejpam-5872	390	22	fuzzy	fuzzy	ADJ
ejpam-5872	390	23	cut	cut	VERB
ejpam-5872	390	24	node	node	NOUN
ejpam-5872	390	25	or	or	CCONJ
ejpam-5872	390	26	a	a	DET
ejpam-5872	390	27	signed	sign	VERB
ejpam-5872	390	28	fuzzy	fuzzy	ADJ
ejpam-5872	390	29	end	end	NOUN
ejpam-5872	390	30	node	node	NOUN
ejpam-5872	390	31	.	.	PUNCT
ejpam-5872	391	1	moreover	moreover	ADV
ejpam-5872	391	2	,	,	PUNCT
ejpam-5872	391	3	each	each	DET
ejpam-5872	391	4	such	such	ADJ
ejpam-5872	391	5	node	node	NOUN
ejpam-5872	391	6	has	have	VERB
ejpam-5872	391	7	a	a	DET
ejpam-5872	391	8	signed	sign	VERB
ejpam-5872	391	9	fuzzy	fuzzy	ADJ
ejpam-5872	391	10	bridge	bridge	PROPN
ejpam-5872	391	11	incident	incident	NOUN
ejpam-5872	391	12	with	with	ADP
ejpam-5872	391	13	it	it	PRON
ejpam-5872	391	14	.	.	PUNCT
ejpam-5872	392	1	we	we	PRON
ejpam-5872	392	2	also	also	ADV
ejpam-5872	392	3	establish	establish	VERB
ejpam-5872	392	4	the	the	DET
ejpam-5872	392	5	unique	unique	ADJ
ejpam-5872	392	6	properties	property	NOUN
ejpam-5872	392	7	of	of	ADP
ejpam-5872	392	8	a	a	DET
ejpam-5872	392	9	strong	strong	ADJ
ejpam-5872	392	10	dominating	dominating	NOUN
ejpam-5872	392	11	set	set	NOUN
ejpam-5872	392	12	and	and	CCONJ
ejpam-5872	392	13	its	its	PRON
ejpam-5872	392	14	counterpart	counterpart	NOUN
ejpam-5872	392	15	in	in	ADP
ejpam-5872	392	16	a	a	DET
ejpam-5872	392	17	signed	sign	VERB
ejpam-5872	392	18	fuzzy	fuzzy	ADJ
ejpam-5872	392	19	graph	graph	NOUN
ejpam-5872	392	20	.	.	PUNCT
ejpam-5872	393	1	with	with	ADP
ejpam-5872	393	2	promising	promising	ADJ
ejpam-5872	393	3	implications	implication	NOUN
ejpam-5872	393	4	for	for	ADP
ejpam-5872	393	5	broader	broad	ADJ
ejpam-5872	393	6	applications	application	NOUN
ejpam-5872	393	7	in	in	ADP
ejpam-5872	393	8	intelligent	intelligent	ADJ
ejpam-5872	393	9	systems	system	NOUN
ejpam-5872	393	10	,	,	PUNCT
ejpam-5872	393	11	these	these	DET
ejpam-5872	393	12	findings	finding	NOUN
ejpam-5872	393	13	demonstrate	demonstrate	VERB
ejpam-5872	393	14	the	the	DET
ejpam-5872	393	15	potential	potential	NOUN
ejpam-5872	393	16	of	of	ADP
ejpam-5872	393	17	signed	sign	VERB
ejpam-5872	393	18	fuzzy	fuzzy	ADJ
ejpam-5872	393	19	graph	graph	NOUN
ejpam-5872	393	20	–	–	PUNCT
ejpam-5872	393	21	based	base	VERB
ejpam-5872	393	22	approaches	approach	NOUN
ejpam-5872	393	23	in	in	ADP
ejpam-5872	393	24	the	the	DET
ejpam-5872	393	25	design	design	NOUN
ejpam-5872	393	26	of	of	ADP
ejpam-5872	393	27	reliable	reliable	ADJ
ejpam-5872	393	28	and	and	CCONJ
ejpam-5872	393	29	energy	energy	NOUN
ejpam-5872	393	30	-	-	PUNCT
ejpam-5872	393	31	efficient	efficient	ADJ
ejpam-5872	393	32	wireless	wireless	ADJ
ejpam-5872	393	33	sensor	sensor	NOUN
ejpam-5872	393	34	networks	network	NOUN
ejpam-5872	393	35	(	(	PUNCT
ejpam-5872	393	36	wsns	wsns	PROPN
ejpam-5872	393	37	)	)	PUNCT
ejpam-5872	393	38	.	.	PUNCT
ejpam-5872	394	1	references	reference	NOUN
ejpam-5872	394	2	[	[	X
ejpam-5872	394	3	1	1	NUM
ejpam-5872	394	4	]	]	PUNCT
ejpam-5872	394	5	béla	béla	NOUN
ejpam-5872	394	6	bollobás	bollobás	NOUN
ejpam-5872	394	7	and	and	CCONJ
ejpam-5872	394	8	vladimir	vladimir	PROPN
ejpam-5872	394	9	nikiforov	nikiforov	PROPN
ejpam-5872	394	10	.	.	PUNCT
ejpam-5872	395	1	books	book	NOUN
ejpam-5872	395	2	in	in	ADP
ejpam-5872	395	3	graphs	graph	NOUN
ejpam-5872	395	4	.	.	PUNCT
ejpam-5872	396	1	european	european	ADJ
ejpam-5872	396	2	journal	journal	PROPN
ejpam-5872	396	3	of	of	ADP
ejpam-5872	396	4	combinatorics	combinatoric	NOUN
ejpam-5872	396	5	,	,	PUNCT
ejpam-5872	396	6	26(2):259–270	26(2):259–270	NUM
ejpam-5872	396	7	,	,	PUNCT
ejpam-5872	396	8	2005	2005	NUM
ejpam-5872	396	9	.	.	PUNCT
ejpam-5872	397	1	c.	c.	PROPN
ejpam-5872	397	2	sankar	sankar	PROPN
ejpam-5872	397	3	et	et	PROPN
ejpam-5872	397	4	al	al	PROPN
ejpam-5872	397	5	.	.	PUNCT
ejpam-5872	397	6	/	/	SYM
ejpam-5872	397	7	eur	eur	PROPN
ejpam-5872	397	8	.	.	PUNCT
ejpam-5872	398	1	j.	j.	PROPN
ejpam-5872	398	2	pure	pure	PROPN
ejpam-5872	398	3	appl	appl	PROPN
ejpam-5872	398	4	.	.	PROPN
ejpam-5872	398	5	math	math	PROPN
ejpam-5872	398	6	,	,	PUNCT
ejpam-5872	398	7	18	18	NUM
ejpam-5872	398	8	(	(	PUNCT
ejpam-5872	398	9	4	4	NUM
ejpam-5872	398	10	)	)	PUNCT
ejpam-5872	398	11	(	(	PUNCT
ejpam-5872	398	12	2025	2025	NUM
ejpam-5872	398	13	)	)	PUNCT
ejpam-5872	398	14	,	,	PUNCT
ejpam-5872	398	15	5872	5872	NUM
ejpam-5872	398	16	16	16	NUM
ejpam-5872	398	17	of	of	ADP
ejpam-5872	398	18	17	17	NUM
ejpam-5872	398	19	[	[	SYM
ejpam-5872	398	20	2	2	NUM
ejpam-5872	398	21	]	]	PUNCT
ejpam-5872	398	22	lotfi	lotfi	PROPN
ejpam-5872	398	23	a.	a.	PROPN
ejpam-5872	398	24	zadeh	zadeh	PROPN
ejpam-5872	398	25	.	.	PUNCT
ejpam-5872	399	1	fuzzy	fuzzy	ADJ
ejpam-5872	399	2	sets	set	NOUN
ejpam-5872	399	3	.	.	PUNCT
ejpam-5872	400	1	information	information	NOUN
ejpam-5872	400	2	and	and	CCONJ
ejpam-5872	400	3	control	control	NOUN
ejpam-5872	400	4	,	,	PUNCT
ejpam-5872	400	5	8(3):338–353	8(3):338–353	NUM
ejpam-5872	400	6	,	,	PUNCT
ejpam-5872	400	7	1965	1965	NUM
ejpam-5872	400	8	.	.	PUNCT
ejpam-5872	401	1	[	[	X
ejpam-5872	401	2	3	3	X
ejpam-5872	401	3	]	]	X
ejpam-5872	401	4	azriel	azriel	PROPN
ejpam-5872	401	5	rosenfeld	rosenfeld	PROPN
ejpam-5872	401	6	.	.	PUNCT
ejpam-5872	402	1	fuzzy	fuzzy	ADJ
ejpam-5872	402	2	graphs	graph	NOUN
ejpam-5872	402	3	.	.	PUNCT
ejpam-5872	403	1	in	in	ADP
ejpam-5872	403	2	fuzzy	fuzzy	ADJ
ejpam-5872	403	3	sets	set	NOUN
ejpam-5872	403	4	and	and	CCONJ
ejpam-5872	403	5	their	their	PRON
ejpam-5872	403	6	applications	application	NOUN
ejpam-5872	403	7	to	to	PART
ejpam-5872	403	8	cognitive	cognitive	VERB
ejpam-5872	403	9	and	and	CCONJ
ejpam-5872	403	10	decision	decision	NOUN
ejpam-5872	403	11	processes	process	NOUN
ejpam-5872	403	12	,	,	PUNCT
ejpam-5872	403	13	pages	page	NOUN
ejpam-5872	403	14	77–95	77–95	NUM
ejpam-5872	403	15	.	.	PUNCT
ejpam-5872	404	1	elsevier	elsevier	NOUN
ejpam-5872	404	2	,	,	PUNCT
ejpam-5872	404	3	1975	1975	NUM
ejpam-5872	404	4	.	.	PUNCT
ejpam-5872	405	1	[	[	X
ejpam-5872	405	2	4	4	X
ejpam-5872	405	3	]	]	X
ejpam-5872	405	4	raymond	raymond	PROPN
ejpam-5872	405	5	t.	t.	PROPN
ejpam-5872	405	6	yeh	yeh	PROPN
ejpam-5872	405	7	and	and	CCONJ
ejpam-5872	405	8	s.	s.	PROPN
ejpam-5872	405	9	y.	y.	PROPN
ejpam-5872	405	10	bang	bang	PROPN
ejpam-5872	405	11	.	.	PUNCT
ejpam-5872	406	1	fuzzy	fuzzy	ADJ
ejpam-5872	406	2	relations	relation	NOUN
ejpam-5872	406	3	,	,	PUNCT
ejpam-5872	406	4	fuzzy	fuzzy	ADJ
ejpam-5872	406	5	graphs	graph	NOUN
ejpam-5872	406	6	,	,	PUNCT
ejpam-5872	406	7	and	and	CCONJ
ejpam-5872	406	8	their	their	PRON
ejpam-5872	406	9	applications	application	NOUN
ejpam-5872	406	10	to	to	ADP
ejpam-5872	406	11	clustering	cluster	VERB
ejpam-5872	406	12	analysis	analysis	NOUN
ejpam-5872	406	13	.	.	PUNCT
ejpam-5872	407	1	in	in	ADP
ejpam-5872	407	2	fuzzy	fuzzy	ADJ
ejpam-5872	407	3	sets	set	NOUN
ejpam-5872	407	4	and	and	CCONJ
ejpam-5872	407	5	their	their	PRON
ejpam-5872	407	6	applications	application	NOUN
ejpam-5872	407	7	to	to	PART
ejpam-5872	407	8	cognitive	cognitive	VERB
ejpam-5872	407	9	and	and	CCONJ
ejpam-5872	407	10	decision	decision	NOUN
ejpam-5872	407	11	processes	process	NOUN
ejpam-5872	407	12	,	,	PUNCT
ejpam-5872	407	13	pages	page	NOUN
ejpam-5872	407	14	125–149	125–149	NUM
ejpam-5872	407	15	.	.	PUNCT
ejpam-5872	407	16	elsevier	elsevier	PROPN
ejpam-5872	407	17	,	,	PUNCT
ejpam-5872	407	18	1975	1975	NUM
ejpam-5872	407	19	.	.	PUNCT
ejpam-5872	408	1	[	[	X
ejpam-5872	408	2	5	5	X
ejpam-5872	408	3	]	]	PUNCT
ejpam-5872	408	4	john	john	PROPN
ejpam-5872	408	5	n.	n.	PROPN
ejpam-5872	408	6	mordeson	mordeson	PROPN
ejpam-5872	408	7	.	.	PUNCT
ejpam-5872	409	1	fuzzy	fuzzy	ADJ
ejpam-5872	409	2	line	line	NOUN
ejpam-5872	409	3	graphs	graph	NOUN
ejpam-5872	409	4	.	.	PUNCT
ejpam-5872	410	1	pattern	pattern	NOUN
ejpam-5872	410	2	recognition	recognition	NOUN
ejpam-5872	410	3	letters	letter	NOUN
ejpam-5872	410	4	,	,	PUNCT
ejpam-5872	410	5	14(5):381–384	14(5):381–384	NUM
ejpam-5872	410	6	,	,	PUNCT
ejpam-5872	410	7	1993	1993	NUM
ejpam-5872	410	8	.	.	PUNCT
ejpam-5872	411	1	[	[	X
ejpam-5872	411	2	6	6	NUM
ejpam-5872	411	3	]	]	PUNCT
ejpam-5872	411	4	m.	m.	NOUN
ejpam-5872	411	5	l.	l.	PROPN
ejpam-5872	411	6	n.	n.	PROPN
ejpam-5872	411	7	mcallister	mcallister	PROPN
ejpam-5872	411	8	.	.	PUNCT
ejpam-5872	412	1	fuzzy	fuzzy	ADJ
ejpam-5872	412	2	intersection	intersection	NOUN
ejpam-5872	412	3	graphs	graph	NOUN
ejpam-5872	412	4	.	.	PUNCT
ejpam-5872	413	1	computers	computer	NOUN
ejpam-5872	413	2	&	&	CCONJ
ejpam-5872	413	3	mathematics	mathematics	PROPN
ejpam-5872	413	4	with	with	ADP
ejpam-5872	413	5	applications	application	NOUN
ejpam-5872	413	6	,	,	PUNCT
ejpam-5872	413	7	15(10):871–886	15(10):871–886	NUM
ejpam-5872	413	8	,	,	PUNCT
ejpam-5872	413	9	1988	1988	NUM
ejpam-5872	413	10	.	.	PUNCT
ejpam-5872	414	1	[	[	X
ejpam-5872	414	2	7	7	X
ejpam-5872	414	3	]	]	X
ejpam-5872	414	4	john	john	PROPN
ejpam-5872	414	5	n.	n.	PROPN
ejpam-5872	414	6	mordeson	mordeson	PROPN
ejpam-5872	414	7	and	and	CCONJ
ejpam-5872	414	8	y.	y.	PROPN
ejpam-5872	414	9	y.	y.	PROPN
ejpam-5872	414	10	yao	yao	PROPN
ejpam-5872	414	11	.	.	PUNCT
ejpam-5872	415	1	fuzzy	fuzzy	ADJ
ejpam-5872	415	2	cycles	cycle	NOUN
ejpam-5872	415	3	and	and	CCONJ
ejpam-5872	415	4	fuzzy	fuzzy	ADJ
ejpam-5872	415	5	trees	tree	NOUN
ejpam-5872	415	6	.	.	PUNCT
ejpam-5872	416	1	journal	journal	NOUN
ejpam-5872	416	2	of	of	ADP
ejpam-5872	416	3	fuzzy	fuzzy	ADJ
ejpam-5872	416	4	mathematics	mathematic	NOUN
ejpam-5872	416	5	,	,	PUNCT
ejpam-5872	416	6	10(1):189–202	10(1):189–202	PROPN
ejpam-5872	416	7	,	,	PUNCT
ejpam-5872	416	8	2002	2002	NUM
ejpam-5872	416	9	.	.	PUNCT
ejpam-5872	417	1	[	[	X
ejpam-5872	417	2	8	8	NUM
ejpam-5872	417	3	]	]	X
ejpam-5872	417	4	saibal	saibal	ADJ
ejpam-5872	417	5	banerjee	banerjee	PROPN
ejpam-5872	417	6	.	.	PUNCT
ejpam-5872	418	1	an	an	DET
ejpam-5872	418	2	optimal	optimal	ADJ
ejpam-5872	418	3	algorithm	algorithm	NOUN
ejpam-5872	418	4	to	to	PART
ejpam-5872	418	5	find	find	VERB
ejpam-5872	418	6	the	the	DET
ejpam-5872	418	7	degrees	degree	NOUN
ejpam-5872	418	8	of	of	ADP
ejpam-5872	418	9	connectedness	connectedness	NOUN
ejpam-5872	418	10	in	in	ADP
ejpam-5872	418	11	an	an	DET
ejpam-5872	418	12	undirected	undirected	ADJ
ejpam-5872	418	13	edge	edge	NOUN
ejpam-5872	418	14	-	-	PUNCT
ejpam-5872	418	15	weighted	weight	VERB
ejpam-5872	418	16	graph	graph	NOUN
ejpam-5872	418	17	.	.	PUNCT
ejpam-5872	419	1	pattern	pattern	NOUN
ejpam-5872	419	2	recognition	recognition	NOUN
ejpam-5872	419	3	letters	letter	NOUN
ejpam-5872	419	4	,	,	PUNCT
ejpam-5872	419	5	12(7):421–424	12(7):421–424	NUM
ejpam-5872	419	6	,	,	PUNCT
ejpam-5872	419	7	1991	1991	NUM
ejpam-5872	419	8	.	.	PUNCT
ejpam-5872	420	1	[	[	X
ejpam-5872	420	2	9	9	NUM
ejpam-5872	420	3	]	]	X
ejpam-5872	420	4	kiran	kiran	PROPN
ejpam-5872	420	5	r.	r.	PROPN
ejpam-5872	420	6	bhutani	bhutani	PROPN
ejpam-5872	420	7	.	.	PUNCT
ejpam-5872	421	1	on	on	ADP
ejpam-5872	421	2	automorphisms	automorphism	NOUN
ejpam-5872	421	3	of	of	ADP
ejpam-5872	421	4	fuzzy	fuzzy	ADJ
ejpam-5872	421	5	graphs	graph	NOUN
ejpam-5872	421	6	.	.	PUNCT
ejpam-5872	422	1	pattern	pattern	NOUN
ejpam-5872	422	2	recognition	recognition	NOUN
ejpam-5872	422	3	letters	letter	NOUN
ejpam-5872	422	4	,	,	PUNCT
ejpam-5872	422	5	9(3):159–162	9(3):159–162	NOUN
ejpam-5872	422	6	,	,	PUNCT
ejpam-5872	422	7	1989	1989	NUM
ejpam-5872	422	8	.	.	PUNCT
ejpam-5872	423	1	[	[	X
ejpam-5872	423	2	10	10	NUM
ejpam-5872	423	3	]	]	PUNCT
ejpam-5872	423	4	p.	p.	PROPN
ejpam-5872	423	5	s.	s.	PROPN
ejpam-5872	423	6	nair	nair	PROPN
ejpam-5872	423	7	.	.	PUNCT
ejpam-5872	424	1	triangle	triangle	NOUN
ejpam-5872	424	2	and	and	CCONJ
ejpam-5872	424	3	parallelogram	parallelogram	NOUN
ejpam-5872	424	4	laws	law	NOUN
ejpam-5872	424	5	on	on	ADP
ejpam-5872	424	6	fuzzy	fuzzy	ADJ
ejpam-5872	424	7	graphs	graph	NOUN
ejpam-5872	424	8	.	.	PUNCT
ejpam-5872	425	1	pattern	pattern	NOUN
ejpam-5872	425	2	recognition	recognition	NOUN
ejpam-5872	425	3	letters	letter	NOUN
ejpam-5872	425	4	,	,	PUNCT
ejpam-5872	425	5	15(8):803–805	15(8):803–805	PROPN
ejpam-5872	425	6	,	,	PUNCT
ejpam-5872	425	7	1994	1994	NUM
ejpam-5872	425	8	.	.	PUNCT
ejpam-5872	426	1	[	[	X
ejpam-5872	426	2	11	11	NUM
ejpam-5872	426	3	]	]	PUNCT
ejpam-5872	426	4	a.	a.	NOUN
ejpam-5872	426	5	somasundaram	somasundaram	PROPN
ejpam-5872	426	6	and	and	CCONJ
ejpam-5872	426	7	s.	s.	PROPN
ejpam-5872	426	8	somasundaram	somasundaram	PROPN
ejpam-5872	426	9	.	.	PUNCT
ejpam-5872	427	1	domination	domination	NOUN
ejpam-5872	427	2	in	in	ADP
ejpam-5872	427	3	fuzzy	fuzzy	ADJ
ejpam-5872	427	4	graphs	graph	NOUN
ejpam-5872	427	5	–	–	PUNCT
ejpam-5872	427	6	i.	i.	NOUN
ejpam-5872	427	7	pattern	pattern	NOUN
ejpam-5872	427	8	recognition	recognition	NOUN
ejpam-5872	427	9	letters	letter	NOUN
ejpam-5872	427	10	,	,	PUNCT
ejpam-5872	427	11	19(9):787–791	19(9):787–791	NUM
ejpam-5872	427	12	,	,	PUNCT
ejpam-5872	427	13	1998	1998	NUM
ejpam-5872	427	14	.	.	PUNCT
ejpam-5872	428	1	[	[	X
ejpam-5872	428	2	12	12	NUM
ejpam-5872	428	3	]	]	PUNCT
ejpam-5872	428	4	a.	a.	NOUN
ejpam-5872	428	5	somasundaram	somasundaram	PROPN
ejpam-5872	428	6	.	.	PUNCT
ejpam-5872	429	1	domination	domination	NOUN
ejpam-5872	429	2	in	in	ADP
ejpam-5872	429	3	fuzzy	fuzzy	ADJ
ejpam-5872	429	4	graphs	graph	NOUN
ejpam-5872	429	5	-	-	PUNCT
ejpam-5872	429	6	ii	ii	NOUN
ejpam-5872	429	7	.	.	PUNCT
ejpam-5872	429	8	journal	journal	PROPN
ejpam-5872	429	9	of	of	ADP
ejpam-5872	429	10	fuzzy	fuzzy	ADJ
ejpam-5872	429	11	mathematics	mathematic	NOUN
ejpam-5872	429	12	,	,	PUNCT
ejpam-5872	429	13	13(2):281	13(2):281	NUM
ejpam-5872	429	14	,	,	PUNCT
ejpam-5872	429	15	2005	2005	NUM
ejpam-5872	429	16	.	.	PUNCT
ejpam-5872	430	1	[	[	X
ejpam-5872	430	2	13	13	NUM
ejpam-5872	430	3	]	]	PUNCT
ejpam-5872	430	4	a.	a.	NOUN
ejpam-5872	430	5	somasundaram	somasundaram	PROPN
ejpam-5872	430	6	.	.	PUNCT
ejpam-5872	431	1	domination	domination	NOUN
ejpam-5872	431	2	in	in	ADP
ejpam-5872	431	3	products	product	NOUN
ejpam-5872	431	4	of	of	ADP
ejpam-5872	431	5	fuzzy	fuzzy	ADJ
ejpam-5872	431	6	graphs	graph	NOUN
ejpam-5872	431	7	.	.	PUNCT
ejpam-5872	432	1	international	international	ADJ
ejpam-5872	432	2	journal	journal	NOUN
ejpam-5872	432	3	of	of	ADP
ejpam-5872	432	4	uncertainty	uncertainty	NOUN
ejpam-5872	432	5	,	,	PUNCT
ejpam-5872	432	6	fuzziness	fuzziness	NOUN
ejpam-5872	432	7	&	&	CCONJ
ejpam-5872	432	8	knowledge	knowledge	NOUN
ejpam-5872	432	9	-	-	PUNCT
ejpam-5872	432	10	based	base	VERB
ejpam-5872	432	11	systems	system	NOUN
ejpam-5872	432	12	,	,	PUNCT
ejpam-5872	432	13	13(2	13(2	PROPN
ejpam-5872	432	14	)	)	PUNCT
ejpam-5872	432	15	,	,	PUNCT
ejpam-5872	432	16	2005	2005	NUM
ejpam-5872	432	17	.	.	PUNCT
ejpam-5872	433	1	[	[	X
ejpam-5872	433	2	14	14	NUM
ejpam-5872	433	3	]	]	PUNCT
ejpam-5872	433	4	a.	a.	NOUN
ejpam-5872	433	5	nagoor	nagoor	PROPN
ejpam-5872	433	6	gani	gani	PROPN
ejpam-5872	433	7	and	and	CCONJ
ejpam-5872	433	8	m.	m.	NOUN
ejpam-5872	433	9	basheer	basheer	PROPN
ejpam-5872	433	10	ahamed	ahamed	PROPN
ejpam-5872	433	11	.	.	PUNCT
ejpam-5872	434	1	order	order	NOUN
ejpam-5872	434	2	and	and	CCONJ
ejpam-5872	434	3	size	size	NOUN
ejpam-5872	434	4	in	in	ADP
ejpam-5872	434	5	fuzzy	fuzzy	ADJ
ejpam-5872	434	6	graphs	graph	NOUN
ejpam-5872	434	7	.	.	PUNCT
ejpam-5872	435	1	bulletin	bulletin	NOUN
ejpam-5872	435	2	of	of	ADP
ejpam-5872	435	3	pure	pure	ADJ
ejpam-5872	435	4	and	and	CCONJ
ejpam-5872	435	5	applied	applied	ADJ
ejpam-5872	435	6	sciences	science	NOUN
ejpam-5872	435	7	,	,	PUNCT
ejpam-5872	435	8	22(1):145–148	22(1):145–148	PROPN
ejpam-5872	435	9	,	,	PUNCT
ejpam-5872	435	10	2003	2003	NUM
ejpam-5872	435	11	.	.	PUNCT
ejpam-5872	436	1	[	[	X
ejpam-5872	436	2	15	15	NUM
ejpam-5872	436	3	]	]	X
ejpam-5872	436	4	kiran	kiran	PROPN
ejpam-5872	436	5	r.	r.	PROPN
ejpam-5872	436	6	bhutani	bhutani	PROPN
ejpam-5872	436	7	and	and	CCONJ
ejpam-5872	436	8	azriel	azriel	PROPN
ejpam-5872	436	9	rosenfeld	rosenfeld	PROPN
ejpam-5872	436	10	.	.	PUNCT
ejpam-5872	437	1	fuzzy	fuzzy	ADJ
ejpam-5872	437	2	end	end	NOUN
ejpam-5872	437	3	nodes	node	NOUN
ejpam-5872	437	4	in	in	ADP
ejpam-5872	437	5	fuzzy	fuzzy	ADJ
ejpam-5872	437	6	graphs	graph	NOUN
ejpam-5872	437	7	.	.	PUNCT
ejpam-5872	438	1	information	information	NOUN
ejpam-5872	438	2	sciences	science	NOUN
ejpam-5872	438	3	,	,	PUNCT
ejpam-5872	438	4	152:323–326	152:323–326	NUM
ejpam-5872	438	5	,	,	PUNCT
ejpam-5872	438	6	2003	2003	NUM
ejpam-5872	438	7	.	.	PUNCT
ejpam-5872	439	1	[	[	X
ejpam-5872	439	2	16	16	NUM
ejpam-5872	439	3	]	]	X
ejpam-5872	439	4	kiran	kiran	PROPN
ejpam-5872	439	5	r.	r.	PROPN
ejpam-5872	439	6	bhutani	bhutani	PROPN
ejpam-5872	439	7	and	and	CCONJ
ejpam-5872	439	8	azriel	azriel	PROPN
ejpam-5872	439	9	rosenfeld	rosenfeld	PROPN
ejpam-5872	439	10	.	.	PUNCT
ejpam-5872	440	1	strong	strong	ADJ
ejpam-5872	440	2	arcs	arc	NOUN
ejpam-5872	440	3	in	in	ADP
ejpam-5872	440	4	fuzzy	fuzzy	ADJ
ejpam-5872	440	5	graphs	graph	NOUN
ejpam-5872	440	6	.	.	PUNCT
ejpam-5872	441	1	information	information	NOUN
ejpam-5872	441	2	sciences	sciences	PROPN
ejpam-5872	441	3	,	,	PUNCT
ejpam-5872	441	4	152:319–322	152:319–322	NUM
ejpam-5872	441	5	,	,	PUNCT
ejpam-5872	441	6	2003	2003	NUM
ejpam-5872	441	7	.	.	PUNCT
ejpam-5872	442	1	[	[	X
ejpam-5872	442	2	17	17	NUM
ejpam-5872	442	3	]	]	X
ejpam-5872	442	4	assia	assia	PROPN
ejpam-5872	442	5	alaoui	alaoui	PROPN
ejpam-5872	442	6	.	.	PUNCT
ejpam-5872	443	1	on	on	ADP
ejpam-5872	443	2	fuzzification	fuzzification	NOUN
ejpam-5872	443	3	of	of	ADP
ejpam-5872	443	4	some	some	DET
ejpam-5872	443	5	concepts	concept	NOUN
ejpam-5872	443	6	of	of	ADP
ejpam-5872	443	7	graphs	graph	NOUN
ejpam-5872	443	8	.	.	PUNCT
ejpam-5872	444	1	fuzzy	fuzzy	ADJ
ejpam-5872	444	2	sets	set	NOUN
ejpam-5872	444	3	and	and	CCONJ
ejpam-5872	444	4	systems	system	NOUN
ejpam-5872	444	5	,	,	PUNCT
ejpam-5872	444	6	101(3):363–389	101(3):363–389	NUM
ejpam-5872	444	7	,	,	PUNCT
ejpam-5872	444	8	1999	1999	NUM
ejpam-5872	444	9	.	.	PUNCT
ejpam-5872	445	1	[	[	X
ejpam-5872	445	2	18	18	NUM
ejpam-5872	445	3	]	]	PUNCT
ejpam-5872	445	4	k.	k.	PROPN
ejpam-5872	445	5	sameena	sameena	PROPN
ejpam-5872	445	6	and	and	CCONJ
ejpam-5872	445	7	m.	m.	PROPN
ejpam-5872	445	8	s.	s.	PROPN
ejpam-5872	445	9	sunitha	sunitha	PROPN
ejpam-5872	445	10	.	.	PUNCT
ejpam-5872	446	1	strong	strong	ADJ
ejpam-5872	446	2	arcs	arc	NOUN
ejpam-5872	446	3	and	and	CCONJ
ejpam-5872	446	4	maximum	maximum	ADJ
ejpam-5872	446	5	spanning	span	VERB
ejpam-5872	446	6	trees	tree	NOUN
ejpam-5872	446	7	in	in	ADP
ejpam-5872	446	8	fuzzy	fuzzy	ADJ
ejpam-5872	446	9	graphs	graph	NOUN
ejpam-5872	446	10	.	.	PUNCT
ejpam-5872	447	1	international	international	ADJ
ejpam-5872	447	2	journal	journal	PROPN
ejpam-5872	447	3	of	of	ADP
ejpam-5872	447	4	mathematical	mathematical	ADJ
ejpam-5872	447	5	sciences	science	NOUN
ejpam-5872	447	6	,	,	PUNCT
ejpam-5872	447	7	5(1):17–20	5(1):17–20	NUM
ejpam-5872	447	8	,	,	PUNCT
ejpam-5872	447	9	2006	2006	NUM
ejpam-5872	447	10	.	.	PUNCT
ejpam-5872	448	1	[	[	X
ejpam-5872	448	2	19	19	NUM
ejpam-5872	448	3	]	]	PUNCT
ejpam-5872	448	4	k.	k.	PROPN
ejpam-5872	448	5	sameena	sameena	PROPN
ejpam-5872	448	6	and	and	CCONJ
ejpam-5872	448	7	m.	m.	PROPN
ejpam-5872	448	8	s.	s.	PROPN
ejpam-5872	448	9	sunitha	sunitha	VERB
ejpam-5872	448	10	.	.	PUNCT
ejpam-5872	449	1	on	on	ADP
ejpam-5872	449	2	g	g	NOUN
ejpam-5872	449	3	-	-	PUNCT
ejpam-5872	449	4	distance	distance	NOUN
ejpam-5872	449	5	in	in	ADP
ejpam-5872	449	6	fuzzy	fuzzy	ADJ
ejpam-5872	449	7	trees	tree	NOUN
ejpam-5872	449	8	.	.	PUNCT
ejpam-5872	450	1	journal	journal	NOUN
ejpam-5872	450	2	of	of	ADP
ejpam-5872	450	3	fuzzy	fuzzy	ADJ
ejpam-5872	450	4	mathematics	mathematic	NOUN
ejpam-5872	450	5	,	,	PUNCT
ejpam-5872	450	6	19:787–791	19:787–791	NUM
ejpam-5872	450	7	,	,	PUNCT
ejpam-5872	450	8	2011	2011	NUM
ejpam-5872	450	9	.	.	PUNCT
ejpam-5872	451	1	[	[	X
ejpam-5872	451	2	20	20	NUM
ejpam-5872	451	3	]	]	X
ejpam-5872	451	4	john	john	PROPN
ejpam-5872	451	5	n.	n.	PROPN
ejpam-5872	451	6	mordeson	mordeson	PROPN
ejpam-5872	451	7	and	and	CCONJ
ejpam-5872	451	8	premchand	premchand	NOUN
ejpam-5872	451	9	s.	s.	PROPN
ejpam-5872	451	10	nair	nair	PROPN
ejpam-5872	451	11	.	.	PUNCT
ejpam-5872	452	1	fuzzy	fuzzy	ADJ
ejpam-5872	452	2	graphs	graph	NOUN
ejpam-5872	452	3	.	.	PUNCT
ejpam-5872	453	1	fuzzy	fuzzy	ADJ
ejpam-5872	453	2	mathematics	mathematic	NOUN
ejpam-5872	453	3	:	:	PUNCT
ejpam-5872	453	4	an	an	DET
ejpam-5872	453	5	introduction	introduction	NOUN
ejpam-5872	453	6	for	for	ADP
ejpam-5872	453	7	engineers	engineer	NOUN
ejpam-5872	453	8	and	and	CCONJ
ejpam-5872	453	9	scientists	scientist	NOUN
ejpam-5872	453	10	,	,	PUNCT
ejpam-5872	453	11	pages	page	NOUN
ejpam-5872	453	12	21–65	21–65	NUM
ejpam-5872	453	13	,	,	PUNCT
ejpam-5872	453	14	2001	2001	NUM
ejpam-5872	453	15	.	.	PUNCT
ejpam-5872	454	1	[	[	X
ejpam-5872	454	2	21	21	NUM
ejpam-5872	454	3	]	]	X
ejpam-5872	454	4	john	john	PROPN
ejpam-5872	454	5	n.	n.	PROPN
ejpam-5872	454	6	mordeson	mordeson	PROPN
ejpam-5872	454	7	and	and	CCONJ
ejpam-5872	454	8	premchand	premchand	NOUN
ejpam-5872	454	9	s.	s.	PROPN
ejpam-5872	454	10	nair	nair	PROPN
ejpam-5872	454	11	.	.	PUNCT
ejpam-5872	455	1	fuzzy	fuzzy	ADJ
ejpam-5872	455	2	graphs	graph	NOUN
ejpam-5872	455	3	and	and	CCONJ
ejpam-5872	455	4	fuzzy	fuzzy	ADJ
ejpam-5872	455	5	hypergraphs	hypergraph	NOUN
ejpam-5872	455	6	,	,	PUNCT
ejpam-5872	455	7	volume	volume	NOUN
ejpam-5872	455	8	46	46	NUM
ejpam-5872	455	9	.	.	PUNCT
ejpam-5872	456	1	physica	physica	NOUN
ejpam-5872	456	2	,	,	PUNCT
ejpam-5872	456	3	2012	2012	NUM
ejpam-5872	456	4	.	.	PUNCT
ejpam-5872	457	1	[	[	X
ejpam-5872	457	2	22	22	NUM
ejpam-5872	457	3	]	]	PUNCT
ejpam-5872	457	4	cigdem	cigdem	ADJ
ejpam-5872	457	5	gunduz	gunduz	NOUN
ejpam-5872	457	6	,	,	PUNCT
ejpam-5872	457	7	bülent	bülent	NOUN
ejpam-5872	457	8	yener	yener	NOUN
ejpam-5872	457	9	,	,	PUNCT
ejpam-5872	457	10	and	and	CCONJ
ejpam-5872	457	11	s.	s.	PROPN
ejpam-5872	457	12	humayun	humayun	PROPN
ejpam-5872	457	13	gultekin	gultekin	PROPN
ejpam-5872	457	14	.	.	PUNCT
ejpam-5872	458	1	the	the	DET
ejpam-5872	458	2	cell	cell	NOUN
ejpam-5872	458	3	graphs	graph	NOUN
ejpam-5872	458	4	of	of	ADP
ejpam-5872	458	5	cancer	cancer	NOUN
ejpam-5872	458	6	.	.	PUNCT
ejpam-5872	459	1	bioinformatics	bioinformatic	NOUN
ejpam-5872	459	2	,	,	PUNCT
ejpam-5872	459	3	20(suppl	20(suppl	NUM
ejpam-5872	459	4	1):i145	1):i145	NUM
ejpam-5872	459	5	–	–	PUNCT
ejpam-5872	459	6	i151	i151	PROPN
ejpam-5872	459	7	,	,	PUNCT
ejpam-5872	459	8	2004	2004	NUM
ejpam-5872	459	9	.	.	PUNCT
ejpam-5872	460	1	[	[	X
ejpam-5872	460	2	23	23	NUM
ejpam-5872	460	3	]	]	X
ejpam-5872	460	4	r.	r.	PROPN
ejpam-5872	460	5	sundareswaran	sundareswaran	PROPN
ejpam-5872	460	6	,	,	PUNCT
ejpam-5872	460	7	r.	r.	PROPN
ejpam-5872	460	8	sujatha	sujatha	PROPN
ejpam-5872	460	9	,	,	PUNCT
ejpam-5872	460	10	and	and	CCONJ
ejpam-5872	460	11	goksen	goksen	VERB
ejpam-5872	460	12	bacak	bacak	NOUN
ejpam-5872	460	13	-	-	PUNCT
ejpam-5872	460	14	turan	turan	NOUN
ejpam-5872	460	15	.	.	PUNCT
ejpam-5872	461	1	a	a	DET
ejpam-5872	461	2	study	study	NOUN
ejpam-5872	461	3	on	on	ADP
ejpam-5872	461	4	vulnerability	vulnerability	NOUN
ejpam-5872	461	5	c.	c.	PROPN
ejpam-5872	461	6	sankar	sankar	PROPN
ejpam-5872	461	7	et	et	PROPN
ejpam-5872	461	8	al	al	PROPN
ejpam-5872	461	9	.	.	PUNCT
ejpam-5872	461	10	/	/	SYM
ejpam-5872	461	11	eur	eur	PROPN
ejpam-5872	461	12	.	.	PUNCT
ejpam-5872	462	1	j.	j.	PROPN
ejpam-5872	462	2	pure	pure	PROPN
ejpam-5872	462	3	appl	appl	PROPN
ejpam-5872	462	4	.	.	PROPN
ejpam-5872	462	5	math	math	PROPN
ejpam-5872	462	6	,	,	PUNCT
ejpam-5872	462	7	18	18	NUM
ejpam-5872	462	8	(	(	PUNCT
ejpam-5872	462	9	4	4	NUM
ejpam-5872	462	10	)	)	PUNCT
ejpam-5872	462	11	(	(	PUNCT
ejpam-5872	462	12	2025	2025	NUM
ejpam-5872	462	13	)	)	PUNCT
ejpam-5872	462	14	,	,	PUNCT
ejpam-5872	462	15	5872	5872	NUM
ejpam-5872	462	16	17	17	NUM
ejpam-5872	462	17	of	of	ADP
ejpam-5872	462	18	17	17	NUM
ejpam-5872	462	19	parameters	parameter	NOUN
ejpam-5872	462	20	of	of	ADP
ejpam-5872	462	21	signed	sign	VERB
ejpam-5872	462	22	fuzzy	fuzzy	ADJ
ejpam-5872	462	23	graphs	graph	NOUN
ejpam-5872	462	24	.	.	PUNCT
ejpam-5872	463	1	in	in	ADP
ejpam-5872	463	2	intelligent	intelligent	ADJ
ejpam-5872	463	3	and	and	CCONJ
ejpam-5872	463	4	fuzzy	fuzzy	ADJ
ejpam-5872	463	5	techniques	technique	NOUN
ejpam-5872	463	6	in	in	ADP
ejpam-5872	463	7	big	big	ADJ
ejpam-5872	463	8	data	datum	NOUN
ejpam-5872	463	9	analytics	analytic	NOUN
ejpam-5872	463	10	and	and	CCONJ
ejpam-5872	463	11	decision	decision	NOUN
ejpam-5872	463	12	making	making	NOUN
ejpam-5872	463	13	:	:	PUNCT
ejpam-5872	463	14	proceedings	proceeding	NOUN
ejpam-5872	463	15	of	of	ADP
ejpam-5872	463	16	the	the	DET
ejpam-5872	463	17	infus	infus	PROPN
ejpam-5872	463	18	2019	2019	NUM
ejpam-5872	463	19	conference	conference	NOUN
ejpam-5872	463	20	,	,	PUNCT
ejpam-5872	463	21	istanbul	istanbul	PROPN
ejpam-5872	463	22	,	,	PUNCT
ejpam-5872	463	23	turkey	turkey	PROPN
ejpam-5872	463	24	,	,	PUNCT
ejpam-5872	463	25	july	july	PROPN
ejpam-5872	463	26	23	23	NUM
ejpam-5872	463	27	-	-	SYM
ejpam-5872	463	28	25	25	NUM
ejpam-5872	463	29	,	,	PUNCT
ejpam-5872	463	30	2019	2019	NUM
ejpam-5872	463	31	,	,	PUNCT
ejpam-5872	463	32	pages	page	NOUN
ejpam-5872	463	33	24–32	24–32	NUM
ejpam-5872	463	34	.	.	PUNCT
ejpam-5872	463	35	springer	springer	NOUN
ejpam-5872	463	36	,	,	PUNCT
ejpam-5872	463	37	2020	2020	NUM
ejpam-5872	463	38	.	.	PUNCT
ejpam-5872	464	1	[	[	X
ejpam-5872	464	2	24	24	NUM
ejpam-5872	464	3	]	]	PUNCT
ejpam-5872	464	4	sankar	sankar	NOUN
ejpam-5872	464	5	chakaravarthy	chakaravarthy	NOUN
ejpam-5872	464	6	,	,	PUNCT
ejpam-5872	464	7	kalaivani	kalaivani	PROPN
ejpam-5872	464	8	chandran	chandran	PROPN
ejpam-5872	464	9	,	,	PUNCT
ejpam-5872	464	10	saravanan	saravanan	PROPN
ejpam-5872	464	11	mariappan	mariappan	PROPN
ejpam-5872	464	12	,	,	PUNCT
ejpam-5872	464	13	and	and	CCONJ
ejpam-5872	464	14	sujatha	sujatha	PROPN
ejpam-5872	464	15	ramalingam	ramalingam	PROPN
ejpam-5872	464	16	.	.	PUNCT
ejpam-5872	465	1	edge	edge	NOUN
ejpam-5872	465	2	integrity	integrity	NOUN
ejpam-5872	465	3	for	for	ADP
ejpam-5872	465	4	signed	sign	VERB
ejpam-5872	465	5	fuzzy	fuzzy	ADJ
ejpam-5872	465	6	graphs	graph	NOUN
ejpam-5872	465	7	.	.	PUNCT
ejpam-5872	466	1	journal	journal	NOUN
ejpam-5872	466	2	of	of	ADP
ejpam-5872	466	3	intelligent	intelligent	ADJ
ejpam-5872	466	4	&	&	CCONJ
ejpam-5872	466	5	fuzzy	fuzzy	ADJ
ejpam-5872	466	6	systems	system	NOUN
ejpam-5872	466	7	,	,	PUNCT
ejpam-5872	466	8	43(4):4681–4690	43(4):4681–4690	NOUN
ejpam-5872	466	9	,	,	PUNCT
ejpam-5872	466	10	2022	2022	NUM
ejpam-5872	466	11	.	.	PUNCT
ejpam-5872	467	1	[	[	X
ejpam-5872	467	2	25	25	NUM
ejpam-5872	467	3	]	]	X
ejpam-5872	467	4	chakaravarthy	chakaravarthy	ADJ
ejpam-5872	467	5	sankar	sankar	NOUN
ejpam-5872	467	6	,	,	PUNCT
ejpam-5872	467	7	chandran	chandran	PROPN
ejpam-5872	467	8	kalaivani	kalaivani	PROPN
ejpam-5872	467	9	,	,	PUNCT
ejpam-5872	467	10	perumal	perumal	NOUN
ejpam-5872	467	11	chellamani	chellamani	NOUN
ejpam-5872	467	12	,	,	PUNCT
ejpam-5872	467	13	and	and	CCONJ
ejpam-5872	467	14	gangatharan	gangatharan	PROPN
ejpam-5872	467	15	venkat	venkat	PROPN
ejpam-5872	467	16	narayanan	narayanan	PROPN
ejpam-5872	467	17	.	.	PUNCT
ejpam-5872	468	1	analyzing	analyze	VERB
ejpam-5872	468	2	network	network	NOUN
ejpam-5872	468	3	stability	stability	NOUN
ejpam-5872	468	4	via	via	ADP
ejpam-5872	468	5	symmetric	symmetric	ADJ
ejpam-5872	468	6	structures	structure	NOUN
ejpam-5872	468	7	and	and	CCONJ
ejpam-5872	468	8	domination	domination	NOUN
ejpam-5872	468	9	integrity	integrity	NOUN
ejpam-5872	468	10	in	in	ADP
ejpam-5872	468	11	signed	sign	VERB
ejpam-5872	468	12	fuzzy	fuzzy	ADJ
ejpam-5872	468	13	graphs	graph	NOUN
ejpam-5872	468	14	.	.	PUNCT
ejpam-5872	469	1	symmetry	symmetry	NOUN
ejpam-5872	469	2	,	,	PUNCT
ejpam-5872	469	3	17(5):766	17(5):766	NUM
ejpam-5872	469	4	,	,	PUNCT
ejpam-5872	469	5	2025	2025	NUM
ejpam-5872	469	6	.	.	PUNCT
ejpam-5872	470	1	[	[	X
ejpam-5872	470	2	26	26	NUM
ejpam-5872	470	3	]	]	X
ejpam-5872	470	4	chakaravarthy	chakaravarthy	ADJ
ejpam-5872	470	5	sankar	sankar	NOUN
ejpam-5872	470	6	,	,	PUNCT
ejpam-5872	470	7	chandran	chandran	PROPN
ejpam-5872	470	8	kalaivani	kalaivani	PROPN
ejpam-5872	470	9	,	,	PUNCT
ejpam-5872	470	10	mariappan	mariappan	PROPN
ejpam-5872	470	11	saravanan	saravanan	PROPN
ejpam-5872	470	12	,	,	PUNCT
ejpam-5872	470	13	and	and	CCONJ
ejpam-5872	470	14	ramalingam	ramalingam	PROPN
ejpam-5872	470	15	sujatha	sujatha	PROPN
ejpam-5872	470	16	.	.	PUNCT
ejpam-5872	471	1	an	an	DET
ejpam-5872	471	2	algorithmic	algorithmic	ADJ
ejpam-5872	471	3	approach	approach	NOUN
ejpam-5872	471	4	to	to	ADP
ejpam-5872	471	5	signed	sign	VERB
ejpam-5872	471	6	fuzzy	fuzzy	ADJ
ejpam-5872	471	7	graph	graph	NOUN
ejpam-5872	471	8	integrity	integrity	NOUN
ejpam-5872	471	9	:	:	PUNCT
ejpam-5872	471	10	complexity	complexity	NOUN
ejpam-5872	471	11	,	,	PUNCT
ejpam-5872	471	12	graph	graph	NOUN
ejpam-5872	471	13	operations	operation	NOUN
ejpam-5872	471	14	,	,	PUNCT
ejpam-5872	471	15	and	and	CCONJ
ejpam-5872	471	16	metro	metro	PROPN
ejpam-5872	471	17	rail	rail	NOUN
ejpam-5872	471	18	network	network	NOUN
ejpam-5872	471	19	applications	application	NOUN
ejpam-5872	471	20	.	.	PUNCT
ejpam-5872	472	1	ain	ain	PROPN
ejpam-5872	472	2	shams	sham	VERB
ejpam-5872	472	3	engineering	engineering	NOUN
ejpam-5872	472	4	journal	journal	NOUN
ejpam-5872	472	5	,	,	PUNCT
ejpam-5872	472	6	16(9):103509	16(9):103509	NUM
ejpam-5872	472	7	,	,	PUNCT
ejpam-5872	472	8	2025	2025	NUM
ejpam-5872	472	9	.	.	PUNCT