id	sid	tid	token	lemma	pos
ejpam-6307	1	1	european	european	PROPN
ejpam-6307	1	2	journal	journal	PROPN
ejpam-6307	1	3	of	of	ADP
ejpam-6307	1	4	pure	pure	ADJ
ejpam-6307	1	5	and	and	CCONJ
ejpam-6307	1	6	applied	applied	ADJ
ejpam-6307	1	7	mathematics	mathematic	NOUN
ejpam-6307	1	8	2025	2025	NUM
ejpam-6307	1	9	,	,	PUNCT
ejpam-6307	1	10	vol	vol	NOUN
ejpam-6307	1	11	.	.	PROPN
ejpam-6307	1	12	18	18	NUM
ejpam-6307	1	13	,	,	PUNCT
ejpam-6307	1	14	issue	issue	NOUN
ejpam-6307	1	15	4	4	NUM
ejpam-6307	1	16	,	,	PUNCT
ejpam-6307	1	17	article	article	NOUN
ejpam-6307	1	18	number	number	NOUN
ejpam-6307	1	19	6307	6307	NUM
ejpam-6307	1	20	issn	issn	PROPN
ejpam-6307	1	21	1307	1307	NUM
ejpam-6307	1	22	-	-	SYM
ejpam-6307	1	23	5543	5543	NUM
ejpam-6307	1	24	–	–	PUNCT
ejpam-6307	1	25	ejpam.com	ejpam.com	X
ejpam-6307	1	26	published	publish	VERB
ejpam-6307	1	27	by	by	ADP
ejpam-6307	1	28	new	new	PROPN
ejpam-6307	1	29	york	york	PROPN
ejpam-6307	1	30	business	business	PROPN
ejpam-6307	1	31	global	global	ADJ
ejpam-6307	1	32	fuzzy	fuzzy	ADJ
ejpam-6307	1	33	geodetic	geodetic	ADJ
ejpam-6307	1	34	and	and	CCONJ
ejpam-6307	1	35	detour	detour	NOUN
ejpam-6307	1	36	spectra	spectra	NOUN
ejpam-6307	1	37	:	:	PUNCT
ejpam-6307	1	38	geodetic	geodetic	ADJ
ejpam-6307	1	39	-	-	PUNCT
ejpam-6307	1	40	laplacian	laplacian	ADJ
ejpam-6307	1	41	energy	energy	NOUN
ejpam-6307	1	42	in	in	ADP
ejpam-6307	1	43	fuzzy	fuzzy	ADJ
ejpam-6307	1	44	graphs	graph	NOUN
ejpam-6307	1	45	r.	r.	PROPN
ejpam-6307	1	46	rajeshkumar1	rajeshkumar1	PROPN
ejpam-6307	1	47	,	,	PUNCT
ejpam-6307	1	48	a.	a.	NOUN
ejpam-6307	1	49	m.	m.	NOUN
ejpam-6307	1	50	anto2,∗	anto2,∗	PROPN
ejpam-6307	1	51	,	,	PUNCT
ejpam-6307	1	52	v.	v.	PROPN
ejpam-6307	1	53	mary	mary	PROPN
ejpam-6307	1	54	mettilda	mettilda	PROPN
ejpam-6307	1	55	rose3	rose3	PROPN
ejpam-6307	1	56	1	1	NUM
ejpam-6307	1	57	department	department	NOUN
ejpam-6307	1	58	of	of	ADP
ejpam-6307	1	59	mathematics	mathematic	NOUN
ejpam-6307	1	60	,	,	PUNCT
ejpam-6307	1	61	malankara	malankara	PROPN
ejpam-6307	1	62	catholic	catholic	PROPN
ejpam-6307	1	63	college	college	PROPN
ejpam-6307	1	64	,	,	PUNCT
ejpam-6307	1	65	affiliated	affiliate	VERB
ejpam-6307	1	66	to	to	ADP
ejpam-6307	1	67	manonmaniam	manonmaniam	PROPN
ejpam-6307	1	68	sundaranar	sundaranar	PROPN
ejpam-6307	1	69	university	university	PROPN
ejpam-6307	1	70	,	,	PUNCT
ejpam-6307	1	71	tirunelveli	tirunelveli	PROPN
ejpam-6307	1	72	,	,	PUNCT
ejpam-6307	1	73	627012	627012	NUM
ejpam-6307	1	74	,	,	PUNCT
ejpam-6307	1	75	tamil	tamil	PROPN
ejpam-6307	1	76	nadu	nadu	PROPN
ejpam-6307	1	77	,	,	PUNCT
ejpam-6307	1	78	india	india	PROPN
ejpam-6307	1	79	2	2	NUM
ejpam-6307	1	80	department	department	NOUN
ejpam-6307	1	81	of	of	ADP
ejpam-6307	1	82	mathematics	mathematics	PROPN
ejpam-6307	1	83	,	,	PUNCT
ejpam-6307	1	84	st	st	PROPN
ejpam-6307	1	85	.	.	PROPN
ejpam-6307	1	86	albert	albert	PROPN
ejpam-6307	1	87	’s	’s	PROPN
ejpam-6307	1	88	college	college	PROPN
ejpam-6307	1	89	(	(	PUNCT
ejpam-6307	1	90	autonomous	autonomous	ADJ
ejpam-6307	1	91	)	)	PUNCT
ejpam-6307	1	92	,	,	PUNCT
ejpam-6307	1	93	ernakulam	ernakulam	PROPN
ejpam-6307	1	94	,	,	PUNCT
ejpam-6307	1	95	682018	682018	NUM
ejpam-6307	1	96	,	,	PUNCT
ejpam-6307	1	97	kerala	kerala	PROPN
ejpam-6307	1	98	,	,	PUNCT
ejpam-6307	1	99	india	india	PROPN
ejpam-6307	1	100	3	3	PROPN
ejpam-6307	1	101	department	department	PROPN
ejpam-6307	1	102	of	of	ADP
ejpam-6307	1	103	mathematics	mathematics	PROPN
ejpam-6307	1	104	,	,	PUNCT
ejpam-6307	1	105	christ	christ	PROPN
ejpam-6307	1	106	nagar	nagar	PROPN
ejpam-6307	1	107	college	college	PROPN
ejpam-6307	1	108	,	,	PUNCT
ejpam-6307	1	109	affiliated	affiliate	VERB
ejpam-6307	1	110	to	to	ADP
ejpam-6307	1	111	university	university	PROPN
ejpam-6307	1	112	of	of	ADP
ejpam-6307	1	113	kerala	kerala	PROPN
ejpam-6307	1	114	,	,	PUNCT
ejpam-6307	1	115	maranalloor	maranalloor	NOUN
ejpam-6307	1	116	695512	695512	NUM
ejpam-6307	1	117	,	,	PUNCT
ejpam-6307	1	118	kerala	kerala	PROPN
ejpam-6307	1	119	,	,	PUNCT
ejpam-6307	1	120	india	india	PROPN
ejpam-6307	1	121	abstract	abstract	NOUN
ejpam-6307	1	122	.	.	PUNCT
ejpam-6307	2	1	this	this	DET
ejpam-6307	2	2	research	research	NOUN
ejpam-6307	2	3	study	study	NOUN
ejpam-6307	2	4	delves	delve	VERB
ejpam-6307	2	5	into	into	ADP
ejpam-6307	2	6	the	the	DET
ejpam-6307	2	7	spectral	spectral	ADJ
ejpam-6307	2	8	characteristics	characteristic	NOUN
ejpam-6307	2	9	and	and	CCONJ
ejpam-6307	2	10	energy	energy	NOUN
ejpam-6307	2	11	measures	measure	NOUN
ejpam-6307	2	12	associated	associate	VERB
ejpam-6307	2	13	with	with	ADP
ejpam-6307	2	14	fuzzy	fuzzy	ADJ
ejpam-6307	2	15	graphs	graph	NOUN
ejpam-6307	2	16	.	.	PUNCT
ejpam-6307	3	1	we	we	PRON
ejpam-6307	3	2	present	present	VERB
ejpam-6307	3	3	the	the	DET
ejpam-6307	3	4	fuzzy	fuzzy	ADJ
ejpam-6307	3	5	geodetic	geodetic	ADJ
ejpam-6307	3	6	spectrum	spectrum	NOUN
ejpam-6307	3	7	and	and	CCONJ
ejpam-6307	3	8	fuzzy	fuzzy	ADJ
ejpam-6307	3	9	detour	detour	NOUN
ejpam-6307	3	10	spectrum	spectrum	NOUN
ejpam-6307	3	11	,	,	PUNCT
ejpam-6307	3	12	which	which	PRON
ejpam-6307	3	13	capture	capture	VERB
ejpam-6307	3	14	the	the	DET
ejpam-6307	3	15	spectral	spectral	ADJ
ejpam-6307	3	16	properties	property	NOUN
ejpam-6307	3	17	of	of	ADP
ejpam-6307	3	18	fuzzy	fuzzy	ADJ
ejpam-6307	3	19	graphs	graph	NOUN
ejpam-6307	3	20	under	under	ADP
ejpam-6307	3	21	geodetic	geodetic	ADJ
ejpam-6307	3	22	and	and	CCONJ
ejpam-6307	3	23	detour	detour	NOUN
ejpam-6307	3	24	constraints	constraint	NOUN
ejpam-6307	3	25	.	.	PUNCT
ejpam-6307	4	1	in	in	ADP
ejpam-6307	4	2	addition	addition	NOUN
ejpam-6307	4	3	,	,	PUNCT
ejpam-6307	4	4	we	we	PRON
ejpam-6307	4	5	propose	propose	VERB
ejpam-6307	4	6	and	and	CCONJ
ejpam-6307	4	7	derive	derive	VERB
ejpam-6307	4	8	novel	novel	ADJ
ejpam-6307	4	9	expressions	expression	NOUN
ejpam-6307	4	10	for	for	ADP
ejpam-6307	4	11	the	the	DET
ejpam-6307	4	12	fuzzy	fuzzy	ADJ
ejpam-6307	4	13	geodetic	geodetic	ADJ
ejpam-6307	4	14	-	-	PUNCT
ejpam-6307	4	15	laplacian	laplacian	ADJ
ejpam-6307	4	16	and	and	CCONJ
ejpam-6307	4	17	detour	detour	NOUN
ejpam-6307	4	18	-	-	PUNCT
ejpam-6307	4	19	laplacian	laplacian	ADJ
ejpam-6307	4	20	energies	energy	NOUN
ejpam-6307	4	21	,	,	PUNCT
ejpam-6307	4	22	incorporating	incorporate	VERB
ejpam-6307	4	23	both	both	CCONJ
ejpam-6307	4	24	upper	upper	ADJ
ejpam-6307	4	25	and	and	CCONJ
ejpam-6307	4	26	lower	low	ADJ
ejpam-6307	4	27	bounds	bound	NOUN
ejpam-6307	4	28	.	.	PUNCT
ejpam-6307	5	1	towards	towards	ADP
ejpam-6307	5	2	the	the	DET
ejpam-6307	5	3	end	end	NOUN
ejpam-6307	5	4	,	,	PUNCT
ejpam-6307	5	5	a	a	DET
ejpam-6307	5	6	real	real	ADJ
ejpam-6307	5	7	-	-	PUNCT
ejpam-6307	5	8	world	world	NOUN
ejpam-6307	5	9	application	application	NOUN
ejpam-6307	5	10	of	of	ADP
ejpam-6307	5	11	fuzzy	fuzzy	ADJ
ejpam-6307	5	12	geodetic	geodetic	ADJ
ejpam-6307	5	13	-	-	PUNCT
ejpam-6307	5	14	laplacian	laplacian	ADJ
ejpam-6307	5	15	energy	energy	NOUN
ejpam-6307	5	16	pertaining	pertain	VERB
ejpam-6307	5	17	to	to	ADP
ejpam-6307	5	18	illegal	illegal	ADJ
ejpam-6307	5	19	immigration	immigration	NOUN
ejpam-6307	5	20	and	and	CCONJ
ejpam-6307	5	21	human	human	ADJ
ejpam-6307	5	22	trafficking	trafficking	NOUN
ejpam-6307	5	23	is	be	AUX
ejpam-6307	5	24	described	describe	VERB
ejpam-6307	5	25	.	.	PUNCT
ejpam-6307	6	1	it	it	PRON
ejpam-6307	6	2	emphasizes	emphasize	VERB
ejpam-6307	6	3	its	its	PRON
ejpam-6307	6	4	potential	potential	NOUN
ejpam-6307	6	5	to	to	PART
ejpam-6307	6	6	improve	improve	VERB
ejpam-6307	6	7	decision	decision	NOUN
ejpam-6307	6	8	-	-	PUNCT
ejpam-6307	6	9	making	make	VERB
ejpam-6307	6	10	measures	measure	NOUN
ejpam-6307	6	11	,	,	PUNCT
ejpam-6307	6	12	allowing	allow	VERB
ejpam-6307	6	13	more	more	ADV
ejpam-6307	6	14	effective	effective	ADJ
ejpam-6307	6	15	and	and	CCONJ
ejpam-6307	6	16	coordinated	coordinated	ADJ
ejpam-6307	6	17	crime	crime	NOUN
ejpam-6307	6	18	prevention	prevention	NOUN
ejpam-6307	6	19	and	and	CCONJ
ejpam-6307	6	20	resolution	resolution	NOUN
ejpam-6307	6	21	initiatives	initiative	NOUN
ejpam-6307	6	22	.	.	PUNCT
ejpam-6307	7	1	2020	2020	NUM
ejpam-6307	7	2	mathematics	mathematic	NOUN
ejpam-6307	7	3	subject	subject	NOUN
ejpam-6307	7	4	classifications	classification	NOUN
ejpam-6307	7	5	:	:	PUNCT
ejpam-6307	7	6	05c72	05c72	NOUN
ejpam-6307	7	7	,	,	PUNCT
ejpam-6307	7	8	05c50	05c50	NUM
ejpam-6307	7	9	,	,	PUNCT
ejpam-6307	7	10	05c20	05c20	NOUN
ejpam-6307	7	11	key	key	ADJ
ejpam-6307	7	12	words	word	NOUN
ejpam-6307	7	13	and	and	CCONJ
ejpam-6307	7	14	phrases	phrase	NOUN
ejpam-6307	7	15	:	:	PUNCT
ejpam-6307	7	16	fuzzy	fuzzy	ADJ
ejpam-6307	7	17	graphs	graph	NOUN
ejpam-6307	7	18	,	,	PUNCT
ejpam-6307	7	19	geodetic	geodetic	ADJ
ejpam-6307	7	20	spectrum	spectrum	NOUN
ejpam-6307	7	21	,	,	PUNCT
ejpam-6307	7	22	detour	detour	NOUN
ejpam-6307	7	23	spectrum	spectrum	NOUN
ejpam-6307	7	24	,	,	PUNCT
ejpam-6307	7	25	geodetic	geodetic	ADJ
ejpam-6307	7	26	-	-	PUNCT
ejpam-6307	7	27	laplacian	laplacian	ADJ
ejpam-6307	7	28	energy	energy	NOUN
ejpam-6307	7	29	1	1	NUM
ejpam-6307	7	30	.	.	PUNCT
ejpam-6307	8	1	introduction	introduction	NOUN
ejpam-6307	8	2	lotfi	lotfi	PROPN
ejpam-6307	8	3	a.	a.	PROPN
ejpam-6307	8	4	zadeh	zadeh	PROPN
ejpam-6307	8	5	set	set	VERB
ejpam-6307	8	6	forth	forth	ADP
ejpam-6307	8	7	the	the	DET
ejpam-6307	8	8	idea	idea	NOUN
ejpam-6307	8	9	of	of	ADP
ejpam-6307	8	10	fuzzy	fuzzy	ADJ
ejpam-6307	8	11	sets	set	NOUN
ejpam-6307	8	12	[	[	X
ejpam-6307	8	13	1	1	NUM
ejpam-6307	8	14	]	]	PUNCT
ejpam-6307	8	15	,	,	PUNCT
ejpam-6307	8	16	which	which	PRON
ejpam-6307	8	17	handle	handle	VERB
ejpam-6307	8	18	vagueness	vagueness	NOUN
ejpam-6307	8	19	and	and	CCONJ
ejpam-6307	8	20	unpredictability	unpredictability	NOUN
ejpam-6307	8	21	in	in	ADP
ejpam-6307	8	22	set	set	NOUN
ejpam-6307	8	23	theory	theory	NOUN
ejpam-6307	8	24	.	.	PUNCT
ejpam-6307	9	1	zadeh	zadeh	NOUN
ejpam-6307	10	1	[	[	X
ejpam-6307	10	2	2	2	NUM
ejpam-6307	10	3	]	]	PUNCT
ejpam-6307	10	4	explored	explore	VERB
ejpam-6307	10	5	fuzzy	fuzzy	ADJ
ejpam-6307	10	6	relations	relation	NOUN
ejpam-6307	10	7	and	and	CCONJ
ejpam-6307	10	8	their	their	PRON
ejpam-6307	10	9	underlying	underlie	VERB
ejpam-6307	10	10	mechanisms	mechanism	NOUN
ejpam-6307	10	11	,	,	PUNCT
ejpam-6307	10	12	aiming	aim	VERB
ejpam-6307	10	13	to	to	PART
ejpam-6307	10	14	address	address	VERB
ejpam-6307	10	15	the	the	DET
ejpam-6307	10	16	inherent	inherent	ADJ
ejpam-6307	10	17	vagueness	vagueness	NOUN
ejpam-6307	10	18	in	in	ADP
ejpam-6307	10	19	human	human	ADJ
ejpam-6307	10	20	reasoning	reasoning	NOUN
ejpam-6307	10	21	.	.	PUNCT
ejpam-6307	11	1	his	his	PRON
ejpam-6307	11	2	work	work	NOUN
ejpam-6307	11	3	laid	lay	VERB
ejpam-6307	11	4	the	the	DET
ejpam-6307	11	5	groundwork	groundwork	NOUN
ejpam-6307	11	6	for	for	ADP
ejpam-6307	11	7	applying	apply	VERB
ejpam-6307	11	8	fuzzy	fuzzy	ADJ
ejpam-6307	11	9	logic	logic	NOUN
ejpam-6307	11	10	to	to	PART
ejpam-6307	11	11	diverse	diverse	VERB
ejpam-6307	11	12	fields	field	NOUN
ejpam-6307	11	13	such	such	ADJ
ejpam-6307	11	14	as	as	ADP
ejpam-6307	11	15	abstraction	abstraction	NOUN
ejpam-6307	11	16	,	,	PUNCT
ejpam-6307	11	17	information	information	NOUN
ejpam-6307	11	18	technology	technology	NOUN
ejpam-6307	11	19	,	,	PUNCT
ejpam-6307	11	20	and	and	CCONJ
ejpam-6307	11	21	communication	communication	NOUN
ejpam-6307	11	22	.	.	PUNCT
ejpam-6307	12	1	inspired	inspire	VERB
ejpam-6307	12	2	by	by	ADP
ejpam-6307	12	3	his	his	PRON
ejpam-6307	12	4	notion	notion	NOUN
ejpam-6307	12	5	of	of	ADP
ejpam-6307	12	6	fuzzy	fuzzy	ADJ
ejpam-6307	12	7	sets	set	NOUN
ejpam-6307	12	8	,	,	PUNCT
ejpam-6307	12	9	azriel	azriel	PROPN
ejpam-6307	12	10	rosenfeld	rosenfeld	PROPN
ejpam-6307	13	1	[	[	X
ejpam-6307	13	2	3	3	NUM
ejpam-6307	13	3	]	]	PUNCT
ejpam-6307	13	4	instilled	instilled	ADJ
ejpam-6307	13	5	fuzzy	fuzzy	ADJ
ejpam-6307	13	6	set	set	NOUN
ejpam-6307	13	7	theory	theory	NOUN
ejpam-6307	13	8	into	into	ADP
ejpam-6307	13	9	fuzzy	fuzzy	ADJ
ejpam-6307	13	10	graph	graph	NOUN
ejpam-6307	13	11	theory	theory	NOUN
ejpam-6307	13	12	in	in	ADP
ejpam-6307	13	13	1975	1975	NUM
ejpam-6307	13	14	.	.	PUNCT
ejpam-6307	14	1	this	this	DET
ejpam-6307	14	2	state	state	NOUN
ejpam-6307	14	3	of	of	ADP
ejpam-6307	14	4	the	the	DET
ejpam-6307	14	5	art	art	NOUN
ejpam-6307	14	6	of	of	ADP
ejpam-6307	14	7	graph	graph	NOUN
ejpam-6307	14	8	theory	theory	NOUN
ejpam-6307	14	9	allowed	allow	VERB
ejpam-6307	14	10	us	we	PRON
ejpam-6307	14	11	to	to	PART
ejpam-6307	14	12	convey	convey	VERB
ejpam-6307	14	13	the	the	DET
ejpam-6307	14	14	strength	strength	NOUN
ejpam-6307	14	15	of	of	ADP
ejpam-6307	14	16	relationships	relationship	NOUN
ejpam-6307	14	17	within	within	ADP
ejpam-6307	14	18	the	the	DET
ejpam-6307	14	19	interval	interval	NOUN
ejpam-6307	14	20	[	[	X
ejpam-6307	14	21	0	0	NUM
ejpam-6307	14	22	,	,	PUNCT
ejpam-6307	14	23	1	1	NUM
ejpam-6307	14	24	]	]	PUNCT
ejpam-6307	14	25	.	.	PUNCT
ejpam-6307	15	1	different	different	ADJ
ejpam-6307	15	2	mathematicians	mathematician	NOUN
ejpam-6307	15	3	were	be	AUX
ejpam-6307	15	4	given	give	VERB
ejpam-6307	15	5	the	the	DET
ejpam-6307	15	6	freedom	freedom	NOUN
ejpam-6307	15	7	to	to	PART
ejpam-6307	15	8	experiment	experiment	VERB
ejpam-6307	15	9	after	after	ADP
ejpam-6307	15	10	being	be	AUX
ejpam-6307	15	11	inspired	inspire	VERB
ejpam-6307	15	12	by	by	ADP
ejpam-6307	15	13	∗corresponding	∗corresponde	VERB
ejpam-6307	15	14	author	author	NOUN
ejpam-6307	15	15	.	.	PUNCT
ejpam-6307	16	1	doi	doi	NOUN
ejpam-6307	16	2	:	:	PUNCT
ejpam-6307	16	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6307	https://doi.org/10.29020/nybg.ejpam.v18i4.6307	ADJ
ejpam-6307	16	4	email	email	NOUN
ejpam-6307	16	5	addresses	address	NOUN
ejpam-6307	16	6	:	:	PUNCT
ejpam-6307	16	7	rajeshrajendrakumar09@gmail.com	rajeshrajendrakumar09@gmail.com	X
ejpam-6307	16	8	(	(	PUNCT
ejpam-6307	16	9	r.	r.	NOUN
ejpam-6307	16	10	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	16	11	)	)	PUNCT
ejpam-6307	16	12	,	,	PUNCT
ejpam-6307	16	13	antoalexam@gmail.com	antoalexam@gmail.com	X
ejpam-6307	16	14	(	(	PUNCT
ejpam-6307	16	15	a.	a.	PROPN
ejpam-6307	16	16	m.	m.	PROPN
ejpam-6307	16	17	anto	anto	PROPN
ejpam-6307	16	18	)	)	PUNCT
ejpam-6307	16	19	,	,	PUNCT
ejpam-6307	16	20	marymettilda@cnc.ac.in	marymettilda@cnc.ac.in	PROPN
ejpam-6307	16	21	(	(	PUNCT
ejpam-6307	16	22	v.	v.	ADP
ejpam-6307	16	23	mary	mary	PROPN
ejpam-6307	16	24	mettilda	mettilda	PROPN
ejpam-6307	16	25	rose	rise	VERB
ejpam-6307	16	26	)	)	PUNCT
ejpam-6307	16	27	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6307	17	1	1	1	NUM
ejpam-6307	17	2	copyright	copyright	NOUN
ejpam-6307	17	3	:	:	PUNCT
ejpam-6307	17	4	©	©	PROPN
ejpam-6307	17	5	2025	2025	NUM
ejpam-6307	17	6	the	the	DET
ejpam-6307	17	7	author(s	author(s	NOUN
ejpam-6307	17	8	)	)	PUNCT
ejpam-6307	17	9	.	.	PUNCT
ejpam-6307	18	1	(	(	PUNCT
ejpam-6307	18	2	cc	cc	NOUN
ejpam-6307	18	3	by	by	ADP
ejpam-6307	18	4	-	-	PUNCT
ejpam-6307	18	5	nc	nc	PROPN
ejpam-6307	18	6	4.0	4.0	NUM
ejpam-6307	18	7	)	)	PUNCT
ejpam-6307	18	8	r.	r.	NOUN
ejpam-6307	18	9	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	18	10	,	,	PUNCT
ejpam-6307	18	11	a.	a.	NOUN
ejpam-6307	18	12	m.	m.	PROPN
ejpam-6307	18	13	anto	anto	PROPN
ejpam-6307	18	14	,	,	PUNCT
ejpam-6307	18	15	v.	v.	PROPN
ejpam-6307	18	16	mary	mary	PROPN
ejpam-6307	18	17	mettilda	mettilda	PROPN
ejpam-6307	18	18	rose	rise	VERB
ejpam-6307	18	19	/	/	SYM
ejpam-6307	18	20	eur	eur	PROPN
ejpam-6307	18	21	.	.	PUNCT
ejpam-6307	19	1	j.	j.	PROPN
ejpam-6307	19	2	pure	pure	PROPN
ejpam-6307	19	3	appl	appl	PROPN
ejpam-6307	19	4	.	.	PROPN
ejpam-6307	19	5	math	math	PROPN
ejpam-6307	19	6	,	,	PUNCT
ejpam-6307	19	7	18	18	NUM
ejpam-6307	19	8	(	(	PUNCT
ejpam-6307	19	9	4	4	NUM
ejpam-6307	19	10	)	)	PUNCT
ejpam-6307	19	11	(	(	PUNCT
ejpam-6307	19	12	2025	2025	NUM
ejpam-6307	19	13	)	)	PUNCT
ejpam-6307	19	14	,	,	PUNCT
ejpam-6307	19	15	6307	6307	NUM
ejpam-6307	19	16	2	2	NUM
ejpam-6307	19	17	of	of	ADP
ejpam-6307	19	18	25	25	NUM
ejpam-6307	19	19	rosenfeld	rosenfeld	PROPN
ejpam-6307	19	20	’s	’s	PART
ejpam-6307	19	21	papers	paper	NOUN
ejpam-6307	19	22	.	.	PUNCT
ejpam-6307	20	1	in	in	ADP
ejpam-6307	20	2	fuzzy	fuzzy	ADJ
ejpam-6307	20	3	graphs	graph	NOUN
ejpam-6307	20	4	,	,	PUNCT
ejpam-6307	20	5	he	he	PRON
ejpam-6307	20	6	developed	develop	VERB
ejpam-6307	20	7	fuzzy	fuzzy	ADJ
ejpam-6307	20	8	relations	relation	NOUN
ejpam-6307	20	9	on	on	ADP
ejpam-6307	20	10	fuzzy	fuzzy	ADJ
ejpam-6307	20	11	sets	set	NOUN
ejpam-6307	20	12	and	and	CCONJ
ejpam-6307	20	13	verified	verify	VERB
ejpam-6307	20	14	several	several	ADJ
ejpam-6307	20	15	fundamental	fundamental	ADJ
ejpam-6307	20	16	concepts	concept	NOUN
ejpam-6307	20	17	.	.	PUNCT
ejpam-6307	21	1	recent	recent	ADJ
ejpam-6307	21	2	works	work	NOUN
ejpam-6307	21	3	such	such	ADJ
ejpam-6307	21	4	as	as	ADP
ejpam-6307	21	5	platil	platil	PROPN
ejpam-6307	21	6	and	and	CCONJ
ejpam-6307	21	7	tanaka	tanaka	PROPN
ejpam-6307	22	1	[	[	X
ejpam-6307	22	2	4	4	NUM
ejpam-6307	22	3	]	]	PUNCT
ejpam-6307	22	4	developed	develop	VERB
ejpam-6307	22	5	multi	multi	ADJ
ejpam-6307	22	6	-	-	ADJ
ejpam-6307	22	7	criteria	criterion	NOUN
ejpam-6307	22	8	evaluation	evaluation	NOUN
ejpam-6307	22	9	frameworks	framework	NOUN
ejpam-6307	22	10	for	for	ADP
ejpam-6307	22	11	intuitionistic	intuitionistic	ADJ
ejpam-6307	22	12	fuzzy	fuzzy	ADJ
ejpam-6307	22	13	sets	set	NOUN
ejpam-6307	22	14	using	use	VERB
ejpam-6307	22	15	set	set	NOUN
ejpam-6307	22	16	-	-	PUNCT
ejpam-6307	22	17	relations	relation	NOUN
ejpam-6307	22	18	,	,	PUNCT
ejpam-6307	22	19	which	which	PRON
ejpam-6307	22	20	may	may	AUX
ejpam-6307	22	21	serve	serve	VERB
ejpam-6307	22	22	as	as	ADP
ejpam-6307	22	23	a	a	DET
ejpam-6307	22	24	useful	useful	ADJ
ejpam-6307	22	25	theoretical	theoretical	ADJ
ejpam-6307	22	26	backdrop	backdrop	NOUN
ejpam-6307	22	27	for	for	ADP
ejpam-6307	22	28	the	the	DET
ejpam-6307	22	29	spectral	spectral	ADJ
ejpam-6307	22	30	approaches	approach	NOUN
ejpam-6307	22	31	.	.	PUNCT
ejpam-6307	23	1	it	it	PRON
ejpam-6307	23	2	was	be	AUX
ejpam-6307	23	3	gary	gary	PROPN
ejpam-6307	23	4	chartrand	chartrand	PROPN
ejpam-6307	23	5	,	,	PUNCT
ejpam-6307	23	6	gamy	gamy	PROPN
ejpam-6307	23	7	l.	l.	PROPN
ejpam-6307	23	8	johns	johns	PROPN
ejpam-6307	23	9	,	,	PUNCT
ejpam-6307	23	10	and	and	CCONJ
ejpam-6307	23	11	songlin	songlin	PROPN
ejpam-6307	23	12	tian	tian	PROPN
ejpam-6307	23	13	who	who	PRON
ejpam-6307	23	14	presented	present	VERB
ejpam-6307	23	15	the	the	DET
ejpam-6307	23	16	notion	notion	NOUN
ejpam-6307	23	17	of	of	ADP
ejpam-6307	23	18	detour	detour	NOUN
ejpam-6307	23	19	distance	distance	NOUN
ejpam-6307	23	20	in	in	ADP
ejpam-6307	23	21	graphs	graph	NOUN
ejpam-6307	23	22	[	[	X
ejpam-6307	23	23	5	5	NUM
ejpam-6307	23	24	]	]	PUNCT
ejpam-6307	23	25	.	.	PUNCT
ejpam-6307	24	1	later	later	ADV
ejpam-6307	24	2	,	,	PUNCT
ejpam-6307	24	3	rosenfeld	rosenfeld	PROPN
ejpam-6307	24	4	,	,	PUNCT
ejpam-6307	24	5	who	who	PRON
ejpam-6307	24	6	developed	develop	VERB
ejpam-6307	24	7	a	a	DET
ejpam-6307	24	8	metric	metric	NOUN
ejpam-6307	24	9	called	call	VERB
ejpam-6307	24	10	the	the	DET
ejpam-6307	24	11	µ	µ	ADJ
ejpam-6307	24	12	distance	distance	NOUN
ejpam-6307	24	13	in	in	ADP
ejpam-6307	24	14	fuzzy	fuzzy	ADJ
ejpam-6307	24	15	graphs	graph	NOUN
ejpam-6307	24	16	.	.	PUNCT
ejpam-6307	25	1	several	several	ADJ
ejpam-6307	25	2	other	other	ADJ
ejpam-6307	25	3	researchers	researcher	NOUN
ejpam-6307	25	4	,	,	PUNCT
ejpam-6307	25	5	including	include	VERB
ejpam-6307	25	6	p.	p.	PROPN
ejpam-6307	25	7	s.	s.	PROPN
ejpam-6307	25	8	nair	nair	PROPN
ejpam-6307	26	1	[	[	X
ejpam-6307	26	2	6	6	NUM
ejpam-6307	26	3	]	]	PUNCT
ejpam-6307	26	4	,	,	PUNCT
ejpam-6307	26	5	mathew	mathew	PROPN
ejpam-6307	26	6	and	and	CCONJ
ejpam-6307	26	7	mordeson	mordeson	NOUN
ejpam-6307	26	8	[	[	X
ejpam-6307	26	9	7	7	NUM
ejpam-6307	26	10	,	,	PUNCT
ejpam-6307	26	11	8	8	NUM
ejpam-6307	26	12	]	]	PUNCT
ejpam-6307	26	13	presented	present	VERB
ejpam-6307	26	14	geodetic	geodetic	ADJ
ejpam-6307	26	15	distance	distance	NOUN
ejpam-6307	26	16	and	and	CCONJ
ejpam-6307	26	17	other	other	ADJ
ejpam-6307	26	18	properties	property	NOUN
ejpam-6307	26	19	in	in	ADP
ejpam-6307	26	20	fuzzy	fuzzy	ADJ
ejpam-6307	26	21	graphs	graph	NOUN
ejpam-6307	26	22	,	,	PUNCT
ejpam-6307	26	23	vijayakumar	vijayakumar	NOUN
ejpam-6307	26	24	and	and	CCONJ
ejpam-6307	26	25	sunitha	sunitha	ADJ
ejpam-6307	27	1	[	[	X
ejpam-6307	27	2	9	9	NUM
ejpam-6307	27	3	]	]	PUNCT
ejpam-6307	27	4	,	,	PUNCT
ejpam-6307	27	5	and	and	CCONJ
ejpam-6307	27	6	rajeshkumar	rajeshkumar	NOUN
ejpam-6307	27	7	and	and	CCONJ
ejpam-6307	27	8	anto	anto	PROPN
ejpam-6307	28	1	[	[	X
ejpam-6307	28	2	10	10	NUM
ejpam-6307	28	3	,	,	PUNCT
ejpam-6307	28	4	11	11	NUM
ejpam-6307	28	5	]	]	PUNCT
ejpam-6307	28	6	,	,	PUNCT
ejpam-6307	28	7	have	have	AUX
ejpam-6307	28	8	conducted	conduct	VERB
ejpam-6307	28	9	significant	significant	ADJ
ejpam-6307	28	10	studies	study	NOUN
ejpam-6307	28	11	within	within	ADP
ejpam-6307	28	12	the	the	DET
ejpam-6307	28	13	frameworks	framework	NOUN
ejpam-6307	28	14	of	of	ADP
ejpam-6307	28	15	fuzzy	fuzzy	ADJ
ejpam-6307	28	16	and	and	CCONJ
ejpam-6307	28	17	intuitionistic	intuitionistic	ADJ
ejpam-6307	28	18	fuzzy	fuzzy	ADJ
ejpam-6307	28	19	graph	graph	NOUN
ejpam-6307	28	20	theory	theory	NOUN
ejpam-6307	28	21	.	.	PUNCT
ejpam-6307	29	1	nagoorgani	nagoorgani	PROPN
ejpam-6307	29	2	and	and	CCONJ
ejpam-6307	29	3	umamaheswari	umamaheswari	PROPN
ejpam-6307	29	4	presented	present	VERB
ejpam-6307	29	5	the	the	DET
ejpam-6307	29	6	notion	notion	NOUN
ejpam-6307	29	7	of	of	ADP
ejpam-6307	29	8	fuzzy	fuzzy	ADJ
ejpam-6307	29	9	detour	detour	NOUN
ejpam-6307	29	10	µ-distance	µ-distance	NOUN
ejpam-6307	29	11	and	and	CCONJ
ejpam-6307	29	12	some	some	PRON
ejpam-6307	29	13	of	of	ADP
ejpam-6307	29	14	its	its	PRON
ejpam-6307	29	15	properties	property	NOUN
ejpam-6307	29	16	in	in	ADP
ejpam-6307	29	17	[	[	X
ejpam-6307	29	18	12	12	NUM
ejpam-6307	29	19	]	]	PUNCT
ejpam-6307	29	20	.	.	PUNCT
ejpam-6307	30	1	the	the	DET
ejpam-6307	30	2	concept	concept	NOUN
ejpam-6307	30	3	of	of	ADP
ejpam-6307	30	4	graph	graph	NOUN
ejpam-6307	30	5	energy	energy	NOUN
ejpam-6307	30	6	was	be	AUX
ejpam-6307	30	7	introduced	introduce	VERB
ejpam-6307	30	8	by	by	ADP
ejpam-6307	30	9	i.	i.	PROPN
ejpam-6307	30	10	gutman	gutman	PROPN
ejpam-6307	30	11	in	in	ADP
ejpam-6307	30	12	1978	1978	NUM
ejpam-6307	30	13	[	[	X
ejpam-6307	30	14	13	13	NUM
ejpam-6307	30	15	]	]	PUNCT
ejpam-6307	30	16	in	in	ADP
ejpam-6307	30	17	a	a	DET
ejpam-6307	30	18	concise	concise	ADJ
ejpam-6307	30	19	and	and	CCONJ
ejpam-6307	30	20	accessible	accessible	ADJ
ejpam-6307	30	21	form	form	NOUN
ejpam-6307	30	22	.	.	PUNCT
ejpam-6307	31	1	as	as	SCONJ
ejpam-6307	31	2	discussed	discuss	VERB
ejpam-6307	31	3	in	in	ADP
ejpam-6307	31	4	[	[	X
ejpam-6307	31	5	14–18	14–18	NUM
ejpam-6307	31	6	]	]	X
ejpam-6307	31	7	,	,	PUNCT
ejpam-6307	31	8	several	several	ADJ
ejpam-6307	31	9	energy	energy	NOUN
ejpam-6307	31	10	-	-	PUNCT
ejpam-6307	31	11	related	relate	VERB
ejpam-6307	31	12	concepts	concept	NOUN
ejpam-6307	31	13	have	have	AUX
ejpam-6307	31	14	been	be	AUX
ejpam-6307	31	15	proposed	propose	VERB
ejpam-6307	31	16	by	by	ADP
ejpam-6307	31	17	various	various	ADJ
ejpam-6307	31	18	researchers	researcher	NOUN
ejpam-6307	31	19	,	,	PUNCT
ejpam-6307	31	20	expanding	expand	VERB
ejpam-6307	31	21	the	the	DET
ejpam-6307	31	22	scope	scope	NOUN
ejpam-6307	31	23	of	of	ADP
ejpam-6307	31	24	graph	graph	NOUN
ejpam-6307	31	25	energy	energy	NOUN
ejpam-6307	31	26	studies	study	NOUN
ejpam-6307	31	27	.	.	PUNCT
ejpam-6307	32	1	however	however	ADV
ejpam-6307	32	2	,	,	PUNCT
ejpam-6307	32	3	most	most	ADJ
ejpam-6307	32	4	of	of	ADP
ejpam-6307	32	5	the	the	DET
ejpam-6307	32	6	existing	exist	VERB
ejpam-6307	32	7	studies	study	NOUN
ejpam-6307	32	8	on	on	ADP
ejpam-6307	32	9	graph	graph	NOUN
ejpam-6307	32	10	energy	energy	NOUN
ejpam-6307	32	11	have	have	AUX
ejpam-6307	32	12	focused	focus	VERB
ejpam-6307	32	13	primarily	primarily	ADV
ejpam-6307	32	14	on	on	ADP
ejpam-6307	32	15	crisp	crisp	ADJ
ejpam-6307	32	16	graphs	graph	NOUN
ejpam-6307	32	17	,	,	PUNCT
ejpam-6307	32	18	with	with	ADP
ejpam-6307	32	19	limited	limited	ADJ
ejpam-6307	32	20	extensions	extension	NOUN
ejpam-6307	32	21	into	into	ADP
ejpam-6307	32	22	fuzzy	fuzzy	ADJ
ejpam-6307	32	23	graphs	graph	NOUN
ejpam-6307	32	24	.	.	PUNCT
ejpam-6307	33	1	even	even	ADV
ejpam-6307	33	2	within	within	ADP
ejpam-6307	33	3	the	the	DET
ejpam-6307	33	4	fuzzy	fuzzy	ADJ
ejpam-6307	33	5	graph	graph	NOUN
ejpam-6307	33	6	domain	domain	NOUN
ejpam-6307	33	7	,	,	PUNCT
ejpam-6307	33	8	energyrelated	energyrelate	VERB
ejpam-6307	33	9	measures	measure	NOUN
ejpam-6307	33	10	have	have	AUX
ejpam-6307	33	11	largely	largely	ADV
ejpam-6307	33	12	overlooked	overlook	VERB
ejpam-6307	33	13	the	the	DET
ejpam-6307	33	14	roles	role	NOUN
ejpam-6307	33	15	of	of	ADP
ejpam-6307	33	16	alternative	alternative	ADJ
ejpam-6307	33	17	distance	distance	NOUN
ejpam-6307	33	18	metrics	metric	NOUN
ejpam-6307	33	19	such	such	ADJ
ejpam-6307	33	20	as	as	ADP
ejpam-6307	33	21	geodetic	geodetic	ADJ
ejpam-6307	33	22	and	and	CCONJ
ejpam-6307	33	23	detour	detour	NOUN
ejpam-6307	33	24	distances	distance	NOUN
ejpam-6307	33	25	.	.	PUNCT
ejpam-6307	34	1	the	the	DET
ejpam-6307	34	2	concept	concept	NOUN
ejpam-6307	34	3	of	of	ADP
ejpam-6307	34	4	fuzzy	fuzzy	ADJ
ejpam-6307	34	5	graph	graph	NOUN
ejpam-6307	34	6	energy	energy	NOUN
ejpam-6307	34	7	,	,	PUNCT
ejpam-6307	34	8	in	in	ADP
ejpam-6307	34	9	particular	particular	ADJ
ejpam-6307	34	10	,	,	PUNCT
ejpam-6307	34	11	introduces	introduce	VERB
ejpam-6307	34	12	additional	additional	ADJ
ejpam-6307	34	13	complexity	complexity	NOUN
ejpam-6307	34	14	,	,	PUNCT
ejpam-6307	34	15	as	as	SCONJ
ejpam-6307	34	16	the	the	DET
ejpam-6307	34	17	fuzziness	fuzziness	NOUN
ejpam-6307	34	18	of	of	ADP
ejpam-6307	34	19	both	both	DET
ejpam-6307	34	20	vertices	vertex	NOUN
ejpam-6307	34	21	and	and	CCONJ
ejpam-6307	34	22	edges	edge	NOUN
ejpam-6307	34	23	must	must	AUX
ejpam-6307	34	24	be	be	AUX
ejpam-6307	34	25	integrated	integrate	VERB
ejpam-6307	34	26	into	into	ADP
ejpam-6307	34	27	spectral	spectral	ADJ
ejpam-6307	34	28	computations	computation	NOUN
ejpam-6307	34	29	.	.	PUNCT
ejpam-6307	35	1	anjali	anjali	PROPN
ejpam-6307	35	2	and	and	CCONJ
ejpam-6307	35	3	mathew	mathew	PROPN
ejpam-6307	36	1	[	[	X
ejpam-6307	36	2	19	19	NUM
ejpam-6307	36	3	]	]	PUNCT
ejpam-6307	36	4	were	be	AUX
ejpam-6307	36	5	among	among	ADP
ejpam-6307	36	6	the	the	DET
ejpam-6307	36	7	first	first	ADJ
ejpam-6307	36	8	to	to	PART
ejpam-6307	36	9	explore	explore	VERB
ejpam-6307	36	10	this	this	DET
ejpam-6307	36	11	area	area	NOUN
ejpam-6307	36	12	,	,	PUNCT
ejpam-6307	36	13	proposing	propose	VERB
ejpam-6307	36	14	a	a	DET
ejpam-6307	36	15	method	method	NOUN
ejpam-6307	36	16	to	to	PART
ejpam-6307	36	17	derive	derive	VERB
ejpam-6307	36	18	spectral	spectral	ADJ
ejpam-6307	36	19	properties	property	NOUN
ejpam-6307	36	20	from	from	ADP
ejpam-6307	36	21	fuzzy	fuzzy	ADJ
ejpam-6307	36	22	adjacency	adjacency	NOUN
ejpam-6307	36	23	matrices	matrix	NOUN
ejpam-6307	36	24	and	and	CCONJ
ejpam-6307	36	25	generalizing	generalize	VERB
ejpam-6307	36	26	the	the	DET
ejpam-6307	36	27	classical	classical	ADJ
ejpam-6307	36	28	notion	notion	NOUN
ejpam-6307	36	29	of	of	ADP
ejpam-6307	36	30	graph	graph	NOUN
ejpam-6307	36	31	energy	energy	NOUN
ejpam-6307	36	32	to	to	PART
ejpam-6307	36	33	accommodate	accommodate	VERB
ejpam-6307	36	34	fuzzy	fuzzy	ADJ
ejpam-6307	36	35	structures	structure	NOUN
ejpam-6307	36	36	.	.	PUNCT
ejpam-6307	37	1	gutman	gutman	NOUN
ejpam-6307	37	2	and	and	CCONJ
ejpam-6307	37	3	zhou	zhou	PROPN
ejpam-6307	37	4	explored	explore	VERB
ejpam-6307	37	5	the	the	DET
ejpam-6307	37	6	laplacian	laplacian	ADJ
ejpam-6307	37	7	energy	energy	NOUN
ejpam-6307	37	8	in	in	ADP
ejpam-6307	37	9	classical	classical	ADJ
ejpam-6307	37	10	graph	graph	NOUN
ejpam-6307	37	11	theory	theory	NOUN
ejpam-6307	37	12	[	[	X
ejpam-6307	37	13	20	20	NUM
ejpam-6307	37	14	]	]	PUNCT
ejpam-6307	37	15	,	,	PUNCT
ejpam-6307	37	16	while	while	SCONJ
ejpam-6307	37	17	s.	s.	PROPN
ejpam-6307	37	18	rahimi	rahimi	PROPN
ejpam-6307	37	19	sharbaf	sharbaf	PROPN
ejpam-6307	37	20	and	and	CCONJ
ejpam-6307	37	21	f.	f.	PROPN
ejpam-6307	37	22	fayazi	fayazi	PROPN
ejpam-6307	37	23	introduced	introduce	VERB
ejpam-6307	37	24	the	the	DET
ejpam-6307	37	25	concept	concept	NOUN
ejpam-6307	37	26	of	of	ADP
ejpam-6307	37	27	laplacian	laplacian	ADJ
ejpam-6307	37	28	energy	energy	NOUN
ejpam-6307	37	29	for	for	ADP
ejpam-6307	37	30	fuzzy	fuzzy	ADJ
ejpam-6307	37	31	graphs	graph	NOUN
ejpam-6307	37	32	[	[	X
ejpam-6307	37	33	21	21	NUM
ejpam-6307	37	34	]	]	PUNCT
ejpam-6307	37	35	.	.	PUNCT
ejpam-6307	38	1	m.	m.	PROPN
ejpam-6307	38	2	nath	nath	PROPN
ejpam-6307	38	3	and	and	CCONJ
ejpam-6307	38	4	s.	s.	PROPN
ejpam-6307	38	5	paul	paul	PROPN
ejpam-6307	38	6	have	have	AUX
ejpam-6307	38	7	investigated	investigate	VERB
ejpam-6307	38	8	the	the	DET
ejpam-6307	38	9	distance	distance	NOUN
ejpam-6307	38	10	laplacian	laplacian	ADJ
ejpam-6307	38	11	spectra	spectra	NOUN
ejpam-6307	38	12	of	of	ADP
ejpam-6307	38	13	graphs	graph	NOUN
ejpam-6307	38	14	[	[	X
ejpam-6307	38	15	22	22	NUM
ejpam-6307	38	16	]	]	PUNCT
ejpam-6307	38	17	.	.	PUNCT
ejpam-6307	39	1	furthermore	furthermore	ADV
ejpam-6307	39	2	,	,	PUNCT
ejpam-6307	39	3	there	there	PRON
ejpam-6307	39	4	has	have	AUX
ejpam-6307	39	5	been	be	AUX
ejpam-6307	39	6	little	little	ADJ
ejpam-6307	39	7	exploration	exploration	NOUN
ejpam-6307	39	8	of	of	ADP
ejpam-6307	39	9	how	how	SCONJ
ejpam-6307	39	10	these	these	DET
ejpam-6307	39	11	distance	distance	NOUN
ejpam-6307	39	12	-	-	PUNCT
ejpam-6307	39	13	based	base	VERB
ejpam-6307	39	14	energies	energy	NOUN
ejpam-6307	39	15	interact	interact	VERB
ejpam-6307	39	16	with	with	ADP
ejpam-6307	39	17	structural	structural	ADJ
ejpam-6307	39	18	properties	property	NOUN
ejpam-6307	39	19	of	of	ADP
ejpam-6307	39	20	fuzzy	fuzzy	ADJ
ejpam-6307	39	21	graphs	graph	NOUN
ejpam-6307	39	22	,	,	PUNCT
ejpam-6307	39	23	especially	especially	ADV
ejpam-6307	39	24	in	in	ADP
ejpam-6307	39	25	terms	term	NOUN
ejpam-6307	39	26	of	of	ADP
ejpam-6307	39	27	spectral	spectral	ADJ
ejpam-6307	39	28	measures	measure	NOUN
ejpam-6307	39	29	like	like	ADP
ejpam-6307	39	30	the	the	DET
ejpam-6307	39	31	laplacian	laplacian	NOUN
ejpam-6307	39	32	.	.	PUNCT
ejpam-6307	40	1	the	the	DET
ejpam-6307	40	2	theoretical	theoretical	ADJ
ejpam-6307	40	3	foundation	foundation	NOUN
ejpam-6307	40	4	of	of	ADP
ejpam-6307	40	5	the	the	DET
ejpam-6307	40	6	present	present	ADJ
ejpam-6307	40	7	study	study	NOUN
ejpam-6307	40	8	draws	draw	VERB
ejpam-6307	40	9	inspiration	inspiration	NOUN
ejpam-6307	40	10	from	from	ADP
ejpam-6307	40	11	these	these	DET
ejpam-6307	40	12	key	key	ADJ
ejpam-6307	40	13	works	work	NOUN
ejpam-6307	40	14	.	.	PUNCT
ejpam-6307	41	1	the	the	DET
ejpam-6307	41	2	application	application	NOUN
ejpam-6307	41	3	-	-	PUNCT
ejpam-6307	41	4	oriented	orient	VERB
ejpam-6307	41	5	motivation	motivation	NOUN
ejpam-6307	41	6	for	for	ADP
ejpam-6307	41	7	this	this	DET
ejpam-6307	41	8	study	study	NOUN
ejpam-6307	41	9	stems	stem	VERB
ejpam-6307	41	10	from	from	ADP
ejpam-6307	41	11	the	the	DET
ejpam-6307	41	12	foundational	foundational	ADJ
ejpam-6307	41	13	work	work	NOUN
ejpam-6307	41	14	of	of	ADP
ejpam-6307	41	15	j.	j.	PROPN
ejpam-6307	41	16	n.	n.	PROPN
ejpam-6307	41	17	mordeson	mordeson	PROPN
ejpam-6307	41	18	and	and	CCONJ
ejpam-6307	41	19	s.	s.	PROPN
ejpam-6307	41	20	mathew	mathew	PROPN
ejpam-6307	41	21	on	on	ADP
ejpam-6307	41	22	distance	distance	NOUN
ejpam-6307	41	23	measures	measure	NOUN
ejpam-6307	41	24	and	and	CCONJ
ejpam-6307	41	25	energy	energy	NOUN
ejpam-6307	41	26	concepts	concept	NOUN
ejpam-6307	41	27	in	in	ADP
ejpam-6307	41	28	fuzzy	fuzzy	ADJ
ejpam-6307	41	29	graphs	graph	NOUN
ejpam-6307	41	30	[	[	X
ejpam-6307	41	31	8	8	NUM
ejpam-6307	41	32	]	]	PUNCT
ejpam-6307	41	33	,	,	PUNCT
ejpam-6307	41	34	as	as	ADV
ejpam-6307	41	35	well	well	ADV
ejpam-6307	41	36	as	as	ADP
ejpam-6307	41	37	the	the	DET
ejpam-6307	41	38	study	study	NOUN
ejpam-6307	41	39	by	by	ADP
ejpam-6307	41	40	binu	binu	NOUN
ejpam-6307	41	41	,	,	PUNCT
ejpam-6307	41	42	mathew	mathew	PROPN
ejpam-6307	41	43	,	,	PUNCT
ejpam-6307	41	44	and	and	CCONJ
ejpam-6307	41	45	mordeson	mordeson	NOUN
ejpam-6307	41	46	,	,	PUNCT
ejpam-6307	41	47	which	which	PRON
ejpam-6307	41	48	applied	apply	VERB
ejpam-6307	41	49	the	the	DET
ejpam-6307	41	50	fuzzy	fuzzy	ADJ
ejpam-6307	41	51	wiener	wiener	NOUN
ejpam-6307	41	52	index	index	NOUN
ejpam-6307	41	53	to	to	PART
ejpam-6307	41	54	model	model	VERB
ejpam-6307	41	55	illegal	illegal	ADJ
ejpam-6307	41	56	immigration	immigration	NOUN
ejpam-6307	41	57	networks	network	NOUN
ejpam-6307	41	58	[	[	X
ejpam-6307	41	59	23	23	NUM
ejpam-6307	41	60	]	]	PUNCT
ejpam-6307	41	61	.	.	PUNCT
ejpam-6307	42	1	furthermore	furthermore	ADV
ejpam-6307	42	2	,	,	PUNCT
ejpam-6307	42	3	a	a	DET
ejpam-6307	42	4	recent	recent	ADJ
ejpam-6307	42	5	investigation	investigation	NOUN
ejpam-6307	42	6	into	into	ADP
ejpam-6307	42	7	the	the	DET
ejpam-6307	42	8	intuitionistic	intuitionistic	ADJ
ejpam-6307	42	9	fuzzy	fuzzy	ADJ
ejpam-6307	42	10	geodetic	geodetic	ADJ
ejpam-6307	42	11	wiener	wiener	NOUN
ejpam-6307	42	12	index	index	NOUN
ejpam-6307	42	13	for	for	ADP
ejpam-6307	42	14	global	global	ADJ
ejpam-6307	42	15	human	human	ADJ
ejpam-6307	42	16	trading	trading	NOUN
ejpam-6307	42	17	analysis	analysis	NOUN
ejpam-6307	42	18	[	[	X
ejpam-6307	42	19	24	24	NUM
ejpam-6307	42	20	]	]	PUNCT
ejpam-6307	42	21	has	have	AUX
ejpam-6307	42	22	highlighted	highlight	VERB
ejpam-6307	42	23	the	the	DET
ejpam-6307	42	24	relevance	relevance	NOUN
ejpam-6307	42	25	of	of	ADP
ejpam-6307	42	26	fuzzy	fuzzy	ADJ
ejpam-6307	42	27	distance	distance	NOUN
ejpam-6307	42	28	-	-	PUNCT
ejpam-6307	42	29	based	base	VERB
ejpam-6307	42	30	measures	measure	NOUN
ejpam-6307	42	31	in	in	ADP
ejpam-6307	42	32	addressing	address	VERB
ejpam-6307	42	33	complex	complex	ADJ
ejpam-6307	42	34	real	real	ADJ
ejpam-6307	42	35	-	-	PUNCT
ejpam-6307	42	36	world	world	NOUN
ejpam-6307	42	37	problems	problem	NOUN
ejpam-6307	42	38	.	.	PUNCT
ejpam-6307	43	1	these	these	DET
ejpam-6307	43	2	works	work	NOUN
ejpam-6307	43	3	collectively	collectively	ADV
ejpam-6307	43	4	inspired	inspire	VERB
ejpam-6307	43	5	the	the	DET
ejpam-6307	43	6	present	present	ADJ
ejpam-6307	43	7	study	study	NOUN
ejpam-6307	43	8	to	to	PART
ejpam-6307	43	9	explore	explore	VERB
ejpam-6307	43	10	novel	novel	ADJ
ejpam-6307	43	11	parameters	parameter	NOUN
ejpam-6307	43	12	for	for	ADP
ejpam-6307	43	13	evaluating	evaluate	VERB
ejpam-6307	43	14	uncertain	uncertain	ADJ
ejpam-6307	43	15	and	and	CCONJ
ejpam-6307	43	16	dynamic	dynamic	ADJ
ejpam-6307	43	17	network	network	NOUN
ejpam-6307	43	18	structures	structure	NOUN
ejpam-6307	43	19	.	.	PUNCT
ejpam-6307	44	1	additional	additional	ADJ
ejpam-6307	44	2	insights	insight	NOUN
ejpam-6307	44	3	from	from	ADP
ejpam-6307	44	4	related	related	ADJ
ejpam-6307	44	5	literature	literature	NOUN
ejpam-6307	44	6	[	[	X
ejpam-6307	44	7	25–27	25–27	NUM
ejpam-6307	44	8	]	]	PUNCT
ejpam-6307	44	9	have	have	AUX
ejpam-6307	44	10	also	also	ADV
ejpam-6307	44	11	enriched	enrich	VERB
ejpam-6307	44	12	the	the	DET
ejpam-6307	44	13	conceptual	conceptual	ADJ
ejpam-6307	44	14	and	and	CCONJ
ejpam-6307	44	15	methodological	methodological	ADJ
ejpam-6307	44	16	development	development	NOUN
ejpam-6307	44	17	of	of	ADP
ejpam-6307	44	18	this	this	DET
ejpam-6307	44	19	work	work	NOUN
ejpam-6307	44	20	.	.	PUNCT
ejpam-6307	45	1	this	this	DET
ejpam-6307	45	2	study	study	NOUN
ejpam-6307	45	3	addresses	address	VERB
ejpam-6307	45	4	these	these	DET
ejpam-6307	45	5	gaps	gap	NOUN
ejpam-6307	45	6	by	by	ADP
ejpam-6307	45	7	extending	extend	VERB
ejpam-6307	45	8	the	the	DET
ejpam-6307	45	9	concept	concept	NOUN
ejpam-6307	45	10	of	of	ADP
ejpam-6307	45	11	fuzzy	fuzzy	ADJ
ejpam-6307	45	12	graph	graph	NOUN
ejpam-6307	45	13	energy	energy	NOUN
ejpam-6307	45	14	to	to	PART
ejpam-6307	45	15	include	include	VERB
ejpam-6307	45	16	fuzzy	fuzzy	ADJ
ejpam-6307	45	17	geodetic	geodetic	ADJ
ejpam-6307	45	18	energy	energy	NOUN
ejpam-6307	45	19	,	,	PUNCT
ejpam-6307	45	20	fuzzy	fuzzy	ADJ
ejpam-6307	45	21	detour	detour	NOUN
ejpam-6307	45	22	energy	energy	NOUN
ejpam-6307	45	23	,	,	PUNCT
ejpam-6307	45	24	and	and	CCONJ
ejpam-6307	45	25	,	,	PUNCT
ejpam-6307	45	26	most	most	ADV
ejpam-6307	45	27	notably	notably	ADV
ejpam-6307	45	28	,	,	PUNCT
ejpam-6307	45	29	fuzzy	fuzzy	ADJ
ejpam-6307	45	30	geodeticlaplacian	geodeticlaplacian	ADJ
ejpam-6307	45	31	energy	energy	NOUN
ejpam-6307	45	32	and	and	CCONJ
ejpam-6307	45	33	fuzzy	fuzzy	ADJ
ejpam-6307	45	34	detour	detour	NOUN
ejpam-6307	45	35	-	-	PUNCT
ejpam-6307	45	36	laplacian	laplacian	ADJ
ejpam-6307	45	37	energy	energy	NOUN
ejpam-6307	45	38	.	.	PUNCT
ejpam-6307	46	1	these	these	DET
ejpam-6307	46	2	new	new	ADJ
ejpam-6307	46	3	energy	energy	NOUN
ejpam-6307	46	4	constructs	construct	NOUN
ejpam-6307	46	5	provide	provide	VERB
ejpam-6307	46	6	a	a	DET
ejpam-6307	46	7	more	more	ADV
ejpam-6307	46	8	comprehensive	comprehensive	ADJ
ejpam-6307	46	9	framework	framework	NOUN
ejpam-6307	46	10	for	for	ADP
ejpam-6307	46	11	analyzing	analyze	VERB
ejpam-6307	46	12	fuzzy	fuzzy	ADJ
ejpam-6307	46	13	graphs	graph	NOUN
ejpam-6307	46	14	,	,	PUNCT
ejpam-6307	46	15	as	as	SCONJ
ejpam-6307	46	16	they	they	PRON
ejpam-6307	46	17	integrate	integrate	VERB
ejpam-6307	46	18	distancer	distancer	NOUN
ejpam-6307	46	19	.	.	PUNCT
ejpam-6307	47	1	rajeshkumar	rajeshkumar	NOUN
ejpam-6307	47	2	,	,	PUNCT
ejpam-6307	47	3	a.	a.	NOUN
ejpam-6307	47	4	m.	m.	PROPN
ejpam-6307	47	5	anto	anto	PROPN
ejpam-6307	47	6	,	,	PUNCT
ejpam-6307	47	7	v.	v.	PROPN
ejpam-6307	47	8	mary	mary	PROPN
ejpam-6307	47	9	mettilda	mettilda	PROPN
ejpam-6307	47	10	rose	rise	VERB
ejpam-6307	47	11	/	/	SYM
ejpam-6307	47	12	eur	eur	PROPN
ejpam-6307	47	13	.	.	PUNCT
ejpam-6307	48	1	j.	j.	PROPN
ejpam-6307	48	2	pure	pure	PROPN
ejpam-6307	48	3	appl	appl	PROPN
ejpam-6307	48	4	.	.	PROPN
ejpam-6307	48	5	math	math	PROPN
ejpam-6307	48	6	,	,	PUNCT
ejpam-6307	48	7	18	18	NUM
ejpam-6307	48	8	(	(	PUNCT
ejpam-6307	48	9	4	4	NUM
ejpam-6307	48	10	)	)	PUNCT
ejpam-6307	48	11	(	(	PUNCT
ejpam-6307	48	12	2025	2025	NUM
ejpam-6307	48	13	)	)	PUNCT
ejpam-6307	48	14	,	,	PUNCT
ejpam-6307	48	15	6307	6307	NUM
ejpam-6307	48	16	3	3	NUM
ejpam-6307	48	17	of	of	ADP
ejpam-6307	48	18	25	25	NUM
ejpam-6307	48	19	based	base	VERB
ejpam-6307	48	20	information	information	NOUN
ejpam-6307	48	21	and	and	CCONJ
ejpam-6307	48	22	spectral	spectral	ADJ
ejpam-6307	48	23	properties	property	NOUN
ejpam-6307	48	24	.	.	PUNCT
ejpam-6307	49	1	the	the	DET
ejpam-6307	49	2	novelty	novelty	NOUN
ejpam-6307	49	3	of	of	ADP
ejpam-6307	49	4	the	the	DET
ejpam-6307	49	5	proposed	propose	VERB
ejpam-6307	49	6	fuzzy	fuzzy	ADJ
ejpam-6307	49	7	geodeticlaplacian	geodeticlaplacian	NOUN
ejpam-6307	49	8	and	and	CCONJ
ejpam-6307	49	9	detour	detour	NOUN
ejpam-6307	49	10	-	-	PUNCT
ejpam-6307	49	11	laplacian	laplacian	ADJ
ejpam-6307	49	12	energies	energy	NOUN
ejpam-6307	49	13	lies	lie	VERB
ejpam-6307	49	14	in	in	ADP
ejpam-6307	49	15	their	their	PRON
ejpam-6307	49	16	ability	ability	NOUN
ejpam-6307	49	17	to	to	PART
ejpam-6307	49	18	reflect	reflect	VERB
ejpam-6307	49	19	both	both	CCONJ
ejpam-6307	49	20	the	the	DET
ejpam-6307	49	21	topological	topological	ADJ
ejpam-6307	49	22	variation	variation	NOUN
ejpam-6307	49	23	and	and	CCONJ
ejpam-6307	49	24	fuzzy	fuzzy	ADJ
ejpam-6307	49	25	connectivity	connectivity	NOUN
ejpam-6307	49	26	of	of	ADP
ejpam-6307	49	27	the	the	DET
ejpam-6307	49	28	graph	graph	NOUN
ejpam-6307	49	29	—	—	PUNCT
ejpam-6307	49	30	features	feature	VERB
ejpam-6307	49	31	that	that	SCONJ
ejpam-6307	49	32	classical	classical	ADJ
ejpam-6307	49	33	energy	energy	NOUN
ejpam-6307	49	34	measures	measure	NOUN
ejpam-6307	49	35	do	do	AUX
ejpam-6307	49	36	not	not	PART
ejpam-6307	49	37	fully	fully	ADV
ejpam-6307	49	38	capture	capture	VERB
ejpam-6307	49	39	.	.	PUNCT
ejpam-6307	50	1	compared	compare	VERB
ejpam-6307	50	2	to	to	ADP
ejpam-6307	50	3	traditional	traditional	ADJ
ejpam-6307	50	4	graph	graph	NOUN
ejpam-6307	50	5	energies	energy	NOUN
ejpam-6307	50	6	,	,	PUNCT
ejpam-6307	50	7	these	these	DET
ejpam-6307	50	8	fuzzy	fuzzy	ADJ
ejpam-6307	50	9	spectral	spectral	ADJ
ejpam-6307	50	10	energies	energy	NOUN
ejpam-6307	50	11	offer	offer	VERB
ejpam-6307	50	12	greater	great	ADJ
ejpam-6307	50	13	flexibility	flexibility	NOUN
ejpam-6307	50	14	and	and	CCONJ
ejpam-6307	50	15	descriptive	descriptive	ADJ
ejpam-6307	50	16	power	power	NOUN
ejpam-6307	50	17	,	,	PUNCT
ejpam-6307	50	18	especially	especially	ADV
ejpam-6307	50	19	for	for	ADP
ejpam-6307	50	20	applications	application	NOUN
ejpam-6307	50	21	involving	involve	VERB
ejpam-6307	50	22	uncertainty	uncertainty	NOUN
ejpam-6307	50	23	and	and	CCONJ
ejpam-6307	50	24	imprecision	imprecision	NOUN
ejpam-6307	50	25	.	.	PUNCT
ejpam-6307	51	1	this	this	DET
ejpam-6307	51	2	paper	paper	NOUN
ejpam-6307	51	3	systematically	systematically	ADV
ejpam-6307	51	4	extends	extend	VERB
ejpam-6307	51	5	spectral	spectral	ADJ
ejpam-6307	51	6	concepts	concept	NOUN
ejpam-6307	51	7	to	to	ADP
ejpam-6307	51	8	the	the	DET
ejpam-6307	51	9	domain	domain	NOUN
ejpam-6307	51	10	of	of	ADP
ejpam-6307	51	11	fuzzy	fuzzy	ADJ
ejpam-6307	51	12	graphs	graph	NOUN
ejpam-6307	51	13	by	by	ADP
ejpam-6307	51	14	introducing	introduce	VERB
ejpam-6307	51	15	novel	novel	ADJ
ejpam-6307	51	16	distance	distance	NOUN
ejpam-6307	51	17	-	-	PUNCT
ejpam-6307	51	18	based	base	VERB
ejpam-6307	51	19	energies	energy	NOUN
ejpam-6307	51	20	and	and	CCONJ
ejpam-6307	51	21	exploring	explore	VERB
ejpam-6307	51	22	their	their	PRON
ejpam-6307	51	23	structural	structural	ADJ
ejpam-6307	51	24	implications	implication	NOUN
ejpam-6307	51	25	.	.	PUNCT
ejpam-6307	52	1	the	the	DET
ejpam-6307	52	2	core	core	ADJ
ejpam-6307	52	3	contributions	contribution	NOUN
ejpam-6307	52	4	are	be	AUX
ejpam-6307	52	5	organized	organize	VERB
ejpam-6307	52	6	across	across	ADP
ejpam-6307	52	7	seven	seven	NUM
ejpam-6307	52	8	sections	section	NOUN
ejpam-6307	52	9	.	.	PUNCT
ejpam-6307	53	1	section	section	NOUN
ejpam-6307	53	2	2	2	NUM
ejpam-6307	53	3	introduces	introduce	NOUN
ejpam-6307	53	4	foundational	foundational	ADJ
ejpam-6307	53	5	definitions	definition	NOUN
ejpam-6307	53	6	and	and	CCONJ
ejpam-6307	53	7	notations	notation	NOUN
ejpam-6307	53	8	relevant	relevant	ADJ
ejpam-6307	53	9	to	to	ADP
ejpam-6307	53	10	fuzzy	fuzzy	ADJ
ejpam-6307	53	11	graph	graph	NOUN
ejpam-6307	53	12	theory	theory	NOUN
ejpam-6307	53	13	.	.	PUNCT
ejpam-6307	54	1	section	section	NOUN
ejpam-6307	54	2	3	3	NUM
ejpam-6307	54	3	presents	present	VERB
ejpam-6307	54	4	the	the	DET
ejpam-6307	54	5	concept	concept	NOUN
ejpam-6307	54	6	of	of	ADP
ejpam-6307	54	7	fuzzy	fuzzy	ADJ
ejpam-6307	54	8	geodetic	geodetic	ADJ
ejpam-6307	54	9	energy	energy	NOUN
ejpam-6307	54	10	,	,	PUNCT
ejpam-6307	54	11	extending	extend	VERB
ejpam-6307	54	12	classical	classical	ADJ
ejpam-6307	54	13	spectral	spectral	ADJ
ejpam-6307	54	14	ideas	idea	NOUN
ejpam-6307	54	15	by	by	ADP
ejpam-6307	54	16	defining	define	VERB
ejpam-6307	54	17	the	the	DET
ejpam-6307	54	18	geodetic	geodetic	ADJ
ejpam-6307	54	19	spectrum	spectrum	NOUN
ejpam-6307	54	20	and	and	CCONJ
ejpam-6307	54	21	computing	compute	VERB
ejpam-6307	54	22	energy	energy	NOUN
ejpam-6307	54	23	based	base	VERB
ejpam-6307	54	24	on	on	ADP
ejpam-6307	54	25	fuzzy	fuzzy	ADJ
ejpam-6307	54	26	distances	distance	NOUN
ejpam-6307	54	27	.	.	PUNCT
ejpam-6307	55	1	in	in	ADP
ejpam-6307	55	2	addition	addition	NOUN
ejpam-6307	55	3	,	,	PUNCT
ejpam-6307	55	4	the	the	DET
ejpam-6307	55	5	study	study	NOUN
ejpam-6307	55	6	also	also	ADV
ejpam-6307	55	7	outlines	outline	VERB
ejpam-6307	55	8	an	an	DET
ejpam-6307	55	9	algorithm	algorithm	NOUN
ejpam-6307	55	10	for	for	ADP
ejpam-6307	55	11	computing	compute	VERB
ejpam-6307	55	12	geodetic	geodetic	ADJ
ejpam-6307	55	13	paths	path	NOUN
ejpam-6307	55	14	in	in	ADP
ejpam-6307	55	15	fuzzy	fuzzy	ADJ
ejpam-6307	55	16	graphs	graph	NOUN
ejpam-6307	55	17	,	,	PUNCT
ejpam-6307	55	18	thereby	thereby	ADV
ejpam-6307	55	19	complementing	complement	VERB
ejpam-6307	55	20	the	the	DET
ejpam-6307	55	21	theoretical	theoretical	ADJ
ejpam-6307	55	22	developments	development	NOUN
ejpam-6307	55	23	with	with	ADP
ejpam-6307	55	24	computational	computational	ADJ
ejpam-6307	55	25	techniques	technique	NOUN
ejpam-6307	55	26	that	that	PRON
ejpam-6307	55	27	ultimately	ultimately	ADV
ejpam-6307	55	28	lead	lead	VERB
ejpam-6307	55	29	to	to	ADP
ejpam-6307	55	30	the	the	DET
ejpam-6307	55	31	determination	determination	NOUN
ejpam-6307	55	32	of	of	ADP
ejpam-6307	55	33	the	the	DET
ejpam-6307	55	34	fuzzy	fuzzy	ADJ
ejpam-6307	55	35	geodetic	geodetic	ADJ
ejpam-6307	55	36	energy	energy	NOUN
ejpam-6307	55	37	.	.	PUNCT
ejpam-6307	56	1	section	section	NOUN
ejpam-6307	56	2	4	4	NUM
ejpam-6307	56	3	investigates	investigate	VERB
ejpam-6307	56	4	fuzzy	fuzzy	ADJ
ejpam-6307	56	5	detour	detour	NOUN
ejpam-6307	56	6	energy	energy	NOUN
ejpam-6307	56	7	derived	derive	VERB
ejpam-6307	56	8	from	from	ADP
ejpam-6307	56	9	the	the	DET
ejpam-6307	56	10	spectrum	spectrum	NOUN
ejpam-6307	56	11	of	of	ADP
ejpam-6307	56	12	the	the	DET
ejpam-6307	56	13	fuzzy	fuzzy	ADJ
ejpam-6307	56	14	detour	detour	NOUN
ejpam-6307	56	15	distance	distance	NOUN
ejpam-6307	56	16	matrix	matrix	NOUN
ejpam-6307	56	17	,	,	PUNCT
ejpam-6307	56	18	offering	offer	VERB
ejpam-6307	56	19	new	new	ADJ
ejpam-6307	56	20	structural	structural	ADJ
ejpam-6307	56	21	insights	insight	NOUN
ejpam-6307	56	22	using	use	VERB
ejpam-6307	56	23	long	long	ADJ
ejpam-6307	56	24	-	-	PUNCT
ejpam-6307	56	25	path	path	NOUN
ejpam-6307	56	26	distance	distance	NOUN
ejpam-6307	56	27	measures	measure	NOUN
ejpam-6307	56	28	.	.	PUNCT
ejpam-6307	57	1	section	section	NOUN
ejpam-6307	57	2	5	5	NUM
ejpam-6307	57	3	defines	define	NOUN
ejpam-6307	57	4	fuzzy	fuzzy	ADJ
ejpam-6307	57	5	geodetic	geodetic	ADJ
ejpam-6307	57	6	-	-	PUNCT
ejpam-6307	57	7	laplacian	laplacian	ADJ
ejpam-6307	57	8	energy	energy	NOUN
ejpam-6307	57	9	,	,	PUNCT
ejpam-6307	57	10	a	a	DET
ejpam-6307	57	11	novel	novel	ADJ
ejpam-6307	57	12	spectral	spectral	ADJ
ejpam-6307	57	13	invariant	invariant	NOUN
ejpam-6307	57	14	based	base	VERB
ejpam-6307	57	15	on	on	ADP
ejpam-6307	57	16	the	the	DET
ejpam-6307	57	17	fuzzy	fuzzy	ADJ
ejpam-6307	57	18	geodetic	geodetic	ADJ
ejpam-6307	57	19	-	-	PUNCT
ejpam-6307	57	20	distance	distance	NOUN
ejpam-6307	57	21	matrix	matrix	NOUN
ejpam-6307	57	22	,	,	PUNCT
ejpam-6307	57	23	representing	represent	VERB
ejpam-6307	57	24	a	a	DET
ejpam-6307	57	25	new	new	ADJ
ejpam-6307	57	26	innovation	innovation	NOUN
ejpam-6307	57	27	within	within	ADP
ejpam-6307	57	28	the	the	DET
ejpam-6307	57	29	framework	framework	NOUN
ejpam-6307	57	30	of	of	ADP
ejpam-6307	57	31	laplacian	laplacian	ADJ
ejpam-6307	57	32	energy	energy	NOUN
ejpam-6307	57	33	concepts	concept	NOUN
ejpam-6307	57	34	..	..	PUNCT
ejpam-6307	57	35	section	section	NOUN
ejpam-6307	57	36	6	6	NUM
ejpam-6307	57	37	introduces	introduce	NOUN
ejpam-6307	57	38	fuzzy	fuzzy	ADJ
ejpam-6307	57	39	detour	detour	NOUN
ejpam-6307	57	40	-	-	PUNCT
ejpam-6307	57	41	laplacian	laplacian	ADJ
ejpam-6307	57	42	energy	energy	NOUN
ejpam-6307	57	43	by	by	ADP
ejpam-6307	57	44	applying	apply	VERB
ejpam-6307	57	45	spectral	spectral	ADJ
ejpam-6307	57	46	analysis	analysis	NOUN
ejpam-6307	57	47	to	to	ADP
ejpam-6307	57	48	the	the	DET
ejpam-6307	57	49	detour	detour	NOUN
ejpam-6307	57	50	-	-	PUNCT
ejpam-6307	57	51	distance	distance	NOUN
ejpam-6307	57	52	laplacian	laplacian	ADJ
ejpam-6307	57	53	matrix	matrix	NOUN
ejpam-6307	57	54	,	,	PUNCT
ejpam-6307	57	55	bridging	bridge	VERB
ejpam-6307	57	56	classical	classical	ADJ
ejpam-6307	57	57	laplacian	laplacian	ADJ
ejpam-6307	57	58	energy	energy	NOUN
ejpam-6307	57	59	and	and	CCONJ
ejpam-6307	57	60	detour	detour	NOUN
ejpam-6307	57	61	-	-	PUNCT
ejpam-6307	57	62	based	base	VERB
ejpam-6307	57	63	metrics	metric	NOUN
ejpam-6307	57	64	.	.	PUNCT
ejpam-6307	58	1	finally	finally	ADV
ejpam-6307	58	2	,	,	PUNCT
ejpam-6307	58	3	section	section	NOUN
ejpam-6307	58	4	7	7	NUM
ejpam-6307	58	5	explores	explore	VERB
ejpam-6307	58	6	the	the	DET
ejpam-6307	58	7	application	application	NOUN
ejpam-6307	58	8	of	of	ADP
ejpam-6307	58	9	fuzzy	fuzzy	ADJ
ejpam-6307	58	10	geodetic	geodetic	ADJ
ejpam-6307	58	11	-	-	PUNCT
ejpam-6307	58	12	laplacian	laplacian	ADJ
ejpam-6307	58	13	energy	energy	NOUN
ejpam-6307	58	14	in	in	ADP
ejpam-6307	58	15	optimizing	optimize	VERB
ejpam-6307	58	16	decision	decision	NOUN
ejpam-6307	58	17	-	-	PUNCT
ejpam-6307	58	18	making	make	VERB
ejpam-6307	58	19	processes	process	NOUN
ejpam-6307	58	20	,	,	PUNCT
ejpam-6307	58	21	particularly	particularly	ADV
ejpam-6307	58	22	in	in	ADP
ejpam-6307	58	23	areas	area	NOUN
ejpam-6307	58	24	such	such	ADJ
ejpam-6307	58	25	as	as	ADP
ejpam-6307	58	26	modern	modern	ADJ
ejpam-6307	58	27	-	-	PUNCT
ejpam-6307	58	28	day	day	NOUN
ejpam-6307	58	29	slavery	slavery	NOUN
ejpam-6307	58	30	[	[	X
ejpam-6307	58	31	28	28	NUM
ejpam-6307	58	32	]	]	X
ejpam-6307	58	33	prevention	prevention	NOUN
ejpam-6307	58	34	and	and	CCONJ
ejpam-6307	58	35	law	law	NOUN
ejpam-6307	58	36	enforcement	enforcement	NOUN
ejpam-6307	58	37	modeling	modeling	NOUN
ejpam-6307	58	38	.	.	PUNCT
ejpam-6307	59	1	2	2	X
ejpam-6307	59	2	.	.	X
ejpam-6307	59	3	preliminaries	preliminary	NOUN
ejpam-6307	59	4	this	this	DET
ejpam-6307	59	5	section	section	NOUN
ejpam-6307	59	6	presents	present	VERB
ejpam-6307	59	7	the	the	DET
ejpam-6307	59	8	foundational	foundational	ADJ
ejpam-6307	59	9	definitions	definition	NOUN
ejpam-6307	59	10	necessary	necessary	ADJ
ejpam-6307	59	11	for	for	ADP
ejpam-6307	59	12	the	the	DET
ejpam-6307	59	13	study	study	NOUN
ejpam-6307	59	14	.	.	PUNCT
ejpam-6307	60	1	fuzzy	fuzzy	ADJ
ejpam-6307	60	2	graphs	graph	NOUN
ejpam-6307	60	3	and	and	CCONJ
ejpam-6307	60	4	fuzzy	fuzzy	ADJ
ejpam-6307	60	5	relations	relation	NOUN
ejpam-6307	60	6	were	be	AUX
ejpam-6307	60	7	first	first	ADV
ejpam-6307	60	8	introduced	introduce	VERB
ejpam-6307	60	9	by	by	ADP
ejpam-6307	60	10	rosenfeld	rosenfeld	PROPN
ejpam-6307	60	11	[	[	X
ejpam-6307	60	12	3	3	NUM
ejpam-6307	60	13	]	]	PUNCT
ejpam-6307	60	14	.	.	PUNCT
ejpam-6307	61	1	the	the	DET
ejpam-6307	61	2	algebraic	algebraic	ADJ
ejpam-6307	61	3	underpinnings	underpinning	NOUN
ejpam-6307	61	4	of	of	ADP
ejpam-6307	61	5	fuzzy	fuzzy	ADJ
ejpam-6307	61	6	graph	graph	NOUN
ejpam-6307	61	7	structures	structure	NOUN
ejpam-6307	61	8	may	may	AUX
ejpam-6307	61	9	be	be	AUX
ejpam-6307	61	10	further	far	ADV
ejpam-6307	61	11	contextualized	contextualize	VERB
ejpam-6307	61	12	by	by	ADP
ejpam-6307	61	13	fuzzy	fuzzy	ADJ
ejpam-6307	61	14	γ	γ	PROPN
ejpam-6307	61	15	-	-	PUNCT
ejpam-6307	61	16	semimodule	semimodule	NOUN
ejpam-6307	61	17	theory	theory	NOUN
ejpam-6307	61	18	,	,	PUNCT
ejpam-6307	61	19	as	as	SCONJ
ejpam-6307	61	20	discussed	discuss	VERB
ejpam-6307	61	21	by	by	ADP
ejpam-6307	61	22	platil	platil	NOUN
ejpam-6307	61	23	and	and	CCONJ
ejpam-6307	61	24	petalcorin	petalcorin	NOUN
ejpam-6307	61	25	[	[	X
ejpam-6307	61	26	29	29	NUM
ejpam-6307	61	27	]	]	PUNCT
ejpam-6307	61	28	,	,	PUNCT
ejpam-6307	61	29	which	which	PRON
ejpam-6307	61	30	enriches	enrich	VERB
ejpam-6307	61	31	the	the	DET
ejpam-6307	61	32	mathematical	mathematical	ADJ
ejpam-6307	61	33	modeling	modeling	NOUN
ejpam-6307	61	34	of	of	ADP
ejpam-6307	61	35	generalized	generalized	ADJ
ejpam-6307	61	36	fuzzy	fuzzy	ADJ
ejpam-6307	61	37	relationships	relationship	NOUN
ejpam-6307	61	38	.	.	PUNCT
ejpam-6307	62	1	in	in	ADP
ejpam-6307	62	2	this	this	DET
ejpam-6307	62	3	work	work	NOUN
ejpam-6307	62	4	,	,	PUNCT
ejpam-6307	62	5	we	we	PRON
ejpam-6307	62	6	adopt	adopt	VERB
ejpam-6307	62	7	the	the	DET
ejpam-6307	62	8	notion	notion	NOUN
ejpam-6307	62	9	of	of	ADP
ejpam-6307	62	10	fuzzy	fuzzy	ADJ
ejpam-6307	62	11	graphs	graph	NOUN
ejpam-6307	62	12	(	(	PUNCT
ejpam-6307	62	13	fgs	fgs	PROPN
ejpam-6307	62	14	)	)	PUNCT
ejpam-6307	62	15	as	as	SCONJ
ejpam-6307	62	16	discussed	discuss	VERB
ejpam-6307	62	17	in	in	ADP
ejpam-6307	62	18	[	[	X
ejpam-6307	62	19	7	7	NUM
ejpam-6307	62	20	,	,	PUNCT
ejpam-6307	62	21	8	8	NUM
ejpam-6307	62	22	]	]	PUNCT
ejpam-6307	62	23	,	,	PUNCT
ejpam-6307	62	24	along	along	ADP
ejpam-6307	62	25	with	with	ADP
ejpam-6307	62	26	other	other	ADJ
ejpam-6307	62	27	related	relate	VERB
ejpam-6307	62	28	concepts	concept	NOUN
ejpam-6307	62	29	from	from	ADP
ejpam-6307	62	30	existing	exist	VERB
ejpam-6307	62	31	literature	literature	NOUN
ejpam-6307	62	32	.	.	PUNCT
ejpam-6307	63	1	definition	definition	NOUN
ejpam-6307	63	2	1	1	NUM
ejpam-6307	63	3	.	.	PUNCT
ejpam-6307	64	1	[	[	X
ejpam-6307	64	2	7	7	X
ejpam-6307	64	3	]	]	X
ejpam-6307	64	4	a	a	DET
ejpam-6307	64	5	fuzzy	fuzzy	ADJ
ejpam-6307	64	6	graph	graph	NOUN
ejpam-6307	64	7	g	g	NOUN
ejpam-6307	64	8	:	:	PUNCT
ejpam-6307	64	9	(	(	PUNCT
ejpam-6307	64	10	v	v	NOUN
ejpam-6307	64	11	,	,	PUNCT
ejpam-6307	64	12	σ	σ	PROPN
ejpam-6307	64	13	,	,	PUNCT
ejpam-6307	64	14	µ	µ	NOUN
ejpam-6307	64	15	)	)	PUNCT
ejpam-6307	64	16	consists	consist	VERB
ejpam-6307	64	17	of	of	ADP
ejpam-6307	64	18	a	a	DET
ejpam-6307	64	19	non	non	ADJ
ejpam-6307	64	20	-	-	ADJ
ejpam-6307	64	21	empty	empty	ADJ
ejpam-6307	64	22	set	set	VERB
ejpam-6307	64	23	v	v	NOUN
ejpam-6307	64	24	along	along	ADP
ejpam-6307	64	25	with	with	ADP
ejpam-6307	64	26	a	a	DET
ejpam-6307	64	27	pair	pair	NOUN
ejpam-6307	64	28	of	of	ADP
ejpam-6307	64	29	functions	function	NOUN
ejpam-6307	64	30	σ	σ	NOUN
ejpam-6307	64	31	:	:	PUNCT
ejpam-6307	64	32	v→	v→	X
ejpam-6307	65	1	[	[	X
ejpam-6307	65	2	0	0	NUM
ejpam-6307	65	3	,	,	PUNCT
ejpam-6307	65	4	1	1	NUM
ejpam-6307	65	5	]	]	PUNCT
ejpam-6307	65	6	and	and	CCONJ
ejpam-6307	65	7	µ	µ	PRON
ejpam-6307	65	8	:	:	PUNCT
ejpam-6307	65	9	e	e	X
ejpam-6307	65	10	→	→	SYM
ejpam-6307	65	11	[	[	X
ejpam-6307	65	12	0	0	NUM
ejpam-6307	65	13	,	,	PUNCT
ejpam-6307	65	14	1	1	NUM
ejpam-6307	65	15	]	]	PUNCT
ejpam-6307	65	16	such	such	ADJ
ejpam-6307	65	17	that	that	SCONJ
ejpam-6307	65	18	∀u	∀u	NOUN
ejpam-6307	65	19	,	,	PUNCT
ejpam-6307	65	20	v	v	ADP
ejpam-6307	65	21	∈	∈	PROPN
ejpam-6307	65	22	v	v	NOUN
ejpam-6307	65	23	,	,	PUNCT
ejpam-6307	65	24	with	with	ADP
ejpam-6307	65	25	µ(u	µ(u	NOUN
ejpam-6307	65	26	,	,	PUNCT
ejpam-6307	65	27	v	v	NOUN
ejpam-6307	65	28	)	)	PUNCT
ejpam-6307	65	29	≤	≤	NOUN
ejpam-6307	65	30	σ(u)∧σ(v	σ(u)∧σ(v	NOUN
ejpam-6307	65	31	)	)	PUNCT
ejpam-6307	65	32	.	.	PUNCT
ejpam-6307	66	1	where	where	SCONJ
ejpam-6307	66	2	the	the	DET
ejpam-6307	66	3	elements	element	NOUN
ejpam-6307	66	4	in	in	ADP
ejpam-6307	66	5	v	v	NUM
ejpam-6307	66	6	are	be	AUX
ejpam-6307	66	7	the	the	DET
ejpam-6307	66	8	vertices	vertex	NOUN
ejpam-6307	66	9	and	and	CCONJ
ejpam-6307	66	10	the	the	DET
ejpam-6307	66	11	elements	element	NOUN
ejpam-6307	66	12	in	in	ADP
ejpam-6307	66	13	e	e	NOUN
ejpam-6307	66	14	are	be	AUX
ejpam-6307	66	15	edges	edge	NOUN
ejpam-6307	66	16	of	of	ADP
ejpam-6307	66	17	the	the	DET
ejpam-6307	66	18	fuzzy	fuzzy	ADJ
ejpam-6307	66	19	graph	graph	NOUN
ejpam-6307	66	20	.	.	PUNCT
ejpam-6307	67	1	definition	definition	NOUN
ejpam-6307	67	2	2	2	NUM
ejpam-6307	67	3	.	.	PUNCT
ejpam-6307	68	1	[	[	X
ejpam-6307	68	2	8	8	NUM
ejpam-6307	68	3	]	]	PUNCT
ejpam-6307	68	4	let	let	VERB
ejpam-6307	68	5	g	g	NOUN
ejpam-6307	68	6	:	:	PUNCT
ejpam-6307	68	7	(	(	PUNCT
ejpam-6307	68	8	v	v	NOUN
ejpam-6307	68	9	,	,	PUNCT
ejpam-6307	68	10	σ	σ	PROPN
ejpam-6307	68	11	,	,	PUNCT
ejpam-6307	68	12	µ	µ	NOUN
ejpam-6307	68	13	)	)	PUNCT
ejpam-6307	68	14	is	be	AUX
ejpam-6307	68	15	a	a	DET
ejpam-6307	68	16	fuzzy	fuzzy	ADJ
ejpam-6307	68	17	graph	graph	NOUN
ejpam-6307	68	18	,	,	PUNCT
ejpam-6307	68	19	then	then	ADV
ejpam-6307	68	20	h	h	NOUN
ejpam-6307	68	21	:	:	PUNCT
ejpam-6307	68	22	(	(	PUNCT
ejpam-6307	68	23	v	v	NOUN
ejpam-6307	68	24	,	,	PUNCT
ejpam-6307	68	25	τ	τ	PROPN
ejpam-6307	68	26	,	,	PUNCT
ejpam-6307	68	27	ϑ	ϑ	X
ejpam-6307	68	28	)	)	PUNCT
ejpam-6307	68	29	is	be	AUX
ejpam-6307	68	30	called	call	VERB
ejpam-6307	68	31	a	a	DET
ejpam-6307	68	32	partial	partial	ADJ
ejpam-6307	68	33	fuzzy	fuzzy	ADJ
ejpam-6307	68	34	subgraph	subgraph	NOUN
ejpam-6307	68	35	of	of	ADP
ejpam-6307	68	36	g	g	PROPN
ejpam-6307	68	37	if	if	SCONJ
ejpam-6307	68	38	τ	τ	PROPN
ejpam-6307	68	39	⊆	⊆	NUM
ejpam-6307	68	40	σ	σ	NOUN
ejpam-6307	68	41	and	and	CCONJ
ejpam-6307	68	42	ϑ	ϑ	X
ejpam-6307	68	43	⊆	⊆	NUM
ejpam-6307	68	44	µ	µ	NOUN
ejpam-6307	68	45	.	.	PUNCT
ejpam-6307	69	1	similarly	similarly	ADV
ejpam-6307	69	2	,	,	PUNCT
ejpam-6307	69	3	a	a	DET
ejpam-6307	69	4	fuzzy	fuzzy	ADJ
ejpam-6307	69	5	subgraph	subgraph	NOUN
ejpam-6307	69	6	h	h	NOUN
ejpam-6307	69	7	:	:	PUNCT
ejpam-6307	69	8	(	(	PUNCT
ejpam-6307	69	9	v	v	NOUN
ejpam-6307	69	10	′	′	NUM
ejpam-6307	69	11	,	,	PUNCT
ejpam-6307	69	12	τ	τ	PROPN
ejpam-6307	69	13	,	,	PUNCT
ejpam-6307	69	14	ϑ	ϑ	NOUN
ejpam-6307	69	15	)	)	PUNCT
ejpam-6307	69	16	of	of	ADP
ejpam-6307	69	17	g	g	PROPN
ejpam-6307	69	18	is	be	AUX
ejpam-6307	69	19	induced	induce	VERB
ejpam-6307	69	20	by	by	ADP
ejpam-6307	69	21	v	v	NUM
ejpam-6307	69	22	′	′	NOUN
ejpam-6307	69	23	if	if	SCONJ
ejpam-6307	69	24	v	v	ADJ
ejpam-6307	69	25	′	′	NUM
ejpam-6307	69	26	⊆	⊆	NUM
ejpam-6307	69	27	v	v	NOUN
ejpam-6307	69	28	,	,	PUNCT
ejpam-6307	69	29	τ	τ	PROPN
ejpam-6307	69	30	(	(	PUNCT
ejpam-6307	69	31	u	u	NOUN
ejpam-6307	69	32	)	)	PUNCT
ejpam-6307	69	33	=	=	SYM
ejpam-6307	69	34	σ(u	σ(u	NOUN
ejpam-6307	69	35	)	)	PUNCT
ejpam-6307	69	36	∀	∀	NOUN
ejpam-6307	70	1	u	u	NOUN
ejpam-6307	71	1	ϵv	ϵv	INTJ
ejpam-6307	71	2	′	′	NUM
ejpam-6307	71	3	and	and	CCONJ
ejpam-6307	71	4	ϑ	ϑ	X
ejpam-6307	71	5	(	(	PUNCT
ejpam-6307	71	6	u	u	NOUN
ejpam-6307	71	7	,	,	PUNCT
ejpam-6307	71	8	v	v	NOUN
ejpam-6307	71	9	)	)	PUNCT
ejpam-6307	71	10	=	=	SYM
ejpam-6307	71	11	µ(u	µ(u	NOUN
ejpam-6307	71	12	,	,	PUNCT
ejpam-6307	71	13	v	v	NOUN
ejpam-6307	71	14	)	)	PUNCT
ejpam-6307	71	15	∀u	∀u	NOUN
ejpam-6307	71	16	,	,	PUNCT
ejpam-6307	71	17	v	v	ADP
ejpam-6307	71	18	ϵ	ϵ	X
ejpam-6307	71	19	p.	p.	NOUN
ejpam-6307	71	20	definition	definition	NOUN
ejpam-6307	71	21	3	3	NUM
ejpam-6307	71	22	.	.	PUNCT
ejpam-6307	72	1	[	[	X
ejpam-6307	72	2	8	8	X
ejpam-6307	72	3	]	]	X
ejpam-6307	72	4	the	the	DET
ejpam-6307	72	5	support	support	NOUN
ejpam-6307	72	6	of	of	ADP
ejpam-6307	72	7	σ	σ	PROPN
ejpam-6307	72	8	is	be	AUX
ejpam-6307	72	9	described	describe	VERB
ejpam-6307	72	10	as	as	ADP
ejpam-6307	72	11	,	,	PUNCT
ejpam-6307	72	12	supp	supp	PROPN
ejpam-6307	72	13	(	(	PUNCT
ejpam-6307	72	14	σ	σ	NOUN
ejpam-6307	72	15	)	)	PUNCT
ejpam-6307	72	16	=	=	SYM
ejpam-6307	72	17	u	u	PROPN
ejpam-6307	72	18	ϵ	ϵ	X
ejpam-6307	72	19	v	v	NOUN
ejpam-6307	72	20	:	:	PUNCT
ejpam-6307	72	21	σ	σ	PROPN
ejpam-6307	72	22	(	(	PUNCT
ejpam-6307	72	23	u	u	NOUN
ejpam-6307	72	24	)	)	PUNCT
ejpam-6307	72	25	>	>	X
ejpam-6307	72	26	0	0	PUNCT
ejpam-6307	72	27	and	and	CCONJ
ejpam-6307	72	28	is	be	AUX
ejpam-6307	72	29	denoted	denote	VERB
ejpam-6307	72	30	as	as	ADP
ejpam-6307	72	31	σ∗.	σ∗.	NOUN
ejpam-6307	72	32	the	the	DET
ejpam-6307	72	33	definitions	definition	NOUN
ejpam-6307	72	34	and	and	CCONJ
ejpam-6307	72	35	additional	additional	ADJ
ejpam-6307	72	36	findings	finding	NOUN
ejpam-6307	72	37	that	that	PRON
ejpam-6307	72	38	we	we	PRON
ejpam-6307	72	39	utilize	utilize	VERB
ejpam-6307	72	40	later	later	ADV
ejpam-6307	72	41	in	in	ADP
ejpam-6307	72	42	our	our	PRON
ejpam-6307	72	43	r.	r.	PROPN
ejpam-6307	72	44	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	72	45	,	,	PUNCT
ejpam-6307	72	46	a.	a.	NOUN
ejpam-6307	72	47	m.	m.	PROPN
ejpam-6307	72	48	anto	anto	PROPN
ejpam-6307	72	49	,	,	PUNCT
ejpam-6307	72	50	v.	v.	PROPN
ejpam-6307	72	51	mary	mary	PROPN
ejpam-6307	72	52	mettilda	mettilda	PROPN
ejpam-6307	72	53	rose	rise	VERB
ejpam-6307	72	54	/	/	SYM
ejpam-6307	72	55	eur	eur	PROPN
ejpam-6307	72	56	.	.	PUNCT
ejpam-6307	73	1	j.	j.	PROPN
ejpam-6307	73	2	pure	pure	PROPN
ejpam-6307	73	3	appl	appl	PROPN
ejpam-6307	73	4	.	.	PROPN
ejpam-6307	73	5	math	math	PROPN
ejpam-6307	73	6	,	,	PUNCT
ejpam-6307	73	7	18	18	NUM
ejpam-6307	73	8	(	(	PUNCT
ejpam-6307	73	9	4	4	NUM
ejpam-6307	73	10	)	)	PUNCT
ejpam-6307	73	11	(	(	PUNCT
ejpam-6307	73	12	2025	2025	NUM
ejpam-6307	73	13	)	)	PUNCT
ejpam-6307	73	14	,	,	PUNCT
ejpam-6307	73	15	6307	6307	NUM
ejpam-6307	73	16	4	4	NUM
ejpam-6307	73	17	of	of	ADP
ejpam-6307	73	18	25	25	NUM
ejpam-6307	73	19	discussion	discussion	NOUN
ejpam-6307	73	20	are	be	AUX
ejpam-6307	73	21	listed	list	VERB
ejpam-6307	73	22	below	below	ADV
ejpam-6307	73	23	.	.	PUNCT
ejpam-6307	74	1	definition	definition	NOUN
ejpam-6307	74	2	4	4	NUM
ejpam-6307	74	3	.	.	PUNCT
ejpam-6307	75	1	[	[	X
ejpam-6307	75	2	12	12	NUM
ejpam-6307	75	3	]	]	PUNCT
ejpam-6307	75	4	in	in	ADP
ejpam-6307	75	5	a	a	DET
ejpam-6307	75	6	fuzzy	fuzzy	ADJ
ejpam-6307	75	7	graph	graph	NOUN
ejpam-6307	75	8	g	g	NOUN
ejpam-6307	75	9	:	:	PUNCT
ejpam-6307	75	10	(	(	PUNCT
ejpam-6307	75	11	v	v	NOUN
ejpam-6307	75	12	,	,	PUNCT
ejpam-6307	75	13	σ	σ	PROPN
ejpam-6307	75	14	,	,	PUNCT
ejpam-6307	75	15	µ	µ	NOUN
ejpam-6307	75	16	)	)	PUNCT
ejpam-6307	75	17	a	a	DET
ejpam-6307	75	18	path	path	NOUN
ejpam-6307	75	19	p	p	NOUN
ejpam-6307	75	20	is	be	AUX
ejpam-6307	75	21	a	a	DET
ejpam-6307	75	22	chain	chain	NOUN
ejpam-6307	75	23	of	of	ADP
ejpam-6307	75	24	distinct	distinct	ADJ
ejpam-6307	75	25	vertices	vertex	NOUN
ejpam-6307	75	26	v0	v0	NOUN
ejpam-6307	75	27	,	,	PUNCT
ejpam-6307	75	28	v1	v1	NOUN
ejpam-6307	75	29	,	,	PUNCT
ejpam-6307	75	30	.	.	PUNCT
ejpam-6307	75	31	.	.	PUNCT
ejpam-6307	75	32	.	.	PUNCT
ejpam-6307	75	33	.	.	PUNCT
ejpam-6307	75	34	.	.	PUNCT
ejpam-6307	76	1	.	.	PUNCT
ejpam-6307	77	1	vn	vn	VERB
ejpam-6307	77	2	such	such	ADJ
ejpam-6307	77	3	that	that	PRON
ejpam-6307	77	4	(	(	PUNCT
ejpam-6307	77	5	vi−1	vi−1	PROPN
ejpam-6307	77	6	,	,	PUNCT
ejpam-6307	77	7	vi	vi	NOUN
ejpam-6307	77	8	)	)	PUNCT
ejpam-6307	77	9	>	>	X
ejpam-6307	77	10	0	0	NUM
ejpam-6307	77	11	,	,	PUNCT
ejpam-6307	77	12	1	1	NUM
ejpam-6307	77	13	≤	≤	NUM
ejpam-6307	77	14	i	i	PRON
ejpam-6307	77	15	≤	≤	NOUN
ejpam-6307	77	16	n	n	CCONJ
ejpam-6307	77	17	,	,	PUNCT
ejpam-6307	77	18	where	where	SCONJ
ejpam-6307	77	19	n	n	PRON
ejpam-6307	77	20	denotes	denote	VERB
ejpam-6307	77	21	the	the	DET
ejpam-6307	77	22	length	length	NOUN
ejpam-6307	77	23	of	of	ADP
ejpam-6307	77	24	the	the	DET
ejpam-6307	77	25	path	path	NOUN
ejpam-6307	77	26	.	.	PUNCT
ejpam-6307	78	1	definition	definition	NOUN
ejpam-6307	78	2	5	5	NUM
ejpam-6307	78	3	.	.	PUNCT
ejpam-6307	79	1	[	[	X
ejpam-6307	79	2	8	8	NUM
ejpam-6307	79	3	]	]	PUNCT
ejpam-6307	79	4	every	every	DET
ejpam-6307	79	5	path	path	NOUN
ejpam-6307	79	6	has	have	VERB
ejpam-6307	79	7	a	a	DET
ejpam-6307	79	8	strength	strength	NOUN
ejpam-6307	79	9	and	and	CCONJ
ejpam-6307	79	10	is	be	AUX
ejpam-6307	79	11	defined	define	VERB
ejpam-6307	79	12	to	to	PART
ejpam-6307	79	13	be	be	AUX
ejpam-6307	79	14	∧n	∧n	ADP
ejpam-6307	79	15	i=1{µ	i=1{µ	ADJ
ejpam-6307	79	16	(	(	PUNCT
ejpam-6307	79	17	vi−1	vi−1	PROPN
ejpam-6307	79	18	,	,	PUNCT
ejpam-6307	79	19	vi	vi	NOUN
ejpam-6307	79	20	)	)	PUNCT
ejpam-6307	79	21	}	}	PUNCT
ejpam-6307	79	22	.	.	PUNCT
ejpam-6307	80	1	the	the	DET
ejpam-6307	80	2	symbol	symbol	NOUN
ejpam-6307	80	3	∧	∧	PROPN
ejpam-6307	80	4	denotes	denote	VERB
ejpam-6307	80	5	the	the	DET
ejpam-6307	80	6	minimum	minimum	NOUN
ejpam-6307	80	7	.	.	PUNCT
ejpam-6307	81	1	definition	definition	NOUN
ejpam-6307	81	2	6	6	NUM
ejpam-6307	81	3	.	.	PUNCT
ejpam-6307	82	1	[	[	X
ejpam-6307	82	2	7	7	X
ejpam-6307	82	3	]	]	X
ejpam-6307	82	4	the	the	DET
ejpam-6307	82	5	strength	strength	NOUN
ejpam-6307	82	6	of	of	ADP
ejpam-6307	82	7	connectedness	connectedness	NOUN
ejpam-6307	82	8	between	between	ADP
ejpam-6307	82	9	two	two	NUM
ejpam-6307	82	10	vertices	vertex	NOUN
ejpam-6307	82	11	is	be	AUX
ejpam-6307	82	12	the	the	DET
ejpam-6307	82	13	maximum	maximum	ADJ
ejpam-6307	82	14	strength	strength	NOUN
ejpam-6307	82	15	among	among	ADP
ejpam-6307	82	16	all	all	DET
ejpam-6307	82	17	paths	path	NOUN
ejpam-6307	82	18	connecting	connect	VERB
ejpam-6307	82	19	them	they	PRON
ejpam-6307	82	20	and	and	CCONJ
ejpam-6307	82	21	is	be	AUX
ejpam-6307	82	22	represented	represent	VERB
ejpam-6307	82	23	as	as	ADP
ejpam-6307	82	24	µ	µ	NOUN
ejpam-6307	82	25	∞	∞	PROPN
ejpam-6307	82	26	(	(	PUNCT
ejpam-6307	82	27	vi−1	vi−1	PROPN
ejpam-6307	82	28	,	,	PUNCT
ejpam-6307	82	29	vi	vi	NOUN
ejpam-6307	82	30	)	)	PUNCT
ejpam-6307	82	31	.	.	PUNCT
ejpam-6307	83	1	definition	definition	NOUN
ejpam-6307	83	2	7	7	NUM
ejpam-6307	83	3	.	.	PUNCT
ejpam-6307	84	1	[	[	X
ejpam-6307	84	2	8	8	NUM
ejpam-6307	84	3	]	]	X
ejpam-6307	84	4	a	a	DET
ejpam-6307	84	5	fuzzy	fuzzy	ADJ
ejpam-6307	84	6	graph	graph	NOUN
ejpam-6307	84	7	g	g	NOUN
ejpam-6307	84	8	:	:	PUNCT
ejpam-6307	84	9	(	(	PUNCT
ejpam-6307	84	10	v	v	NOUN
ejpam-6307	84	11	,	,	PUNCT
ejpam-6307	84	12	σ	σ	PROPN
ejpam-6307	84	13	,	,	PUNCT
ejpam-6307	84	14	µ	µ	NOUN
ejpam-6307	84	15	)	)	PUNCT
ejpam-6307	84	16	is	be	AUX
ejpam-6307	84	17	defined	define	VERB
ejpam-6307	84	18	to	to	PART
ejpam-6307	84	19	be	be	AUX
ejpam-6307	84	20	a	a	DET
ejpam-6307	84	21	complete	complete	ADJ
ejpam-6307	84	22	fuzzy	fuzzy	ADJ
ejpam-6307	84	23	graph	graph	NOUN
ejpam-6307	84	24	if	if	SCONJ
ejpam-6307	84	25	µ	µ	X
ejpam-6307	84	26	(	(	PUNCT
ejpam-6307	84	27	vi	vi	PROPN
ejpam-6307	84	28	,	,	PUNCT
ejpam-6307	84	29	vj	vj	ADJ
ejpam-6307	84	30	)	)	PUNCT
ejpam-6307	84	31	=	=	SYM
ejpam-6307	84	32	σ	σ	PROPN
ejpam-6307	84	33	(	(	PUNCT
ejpam-6307	84	34	vi	vi	NOUN
ejpam-6307	84	35	)	)	PUNCT
ejpam-6307	84	36	∧	∧	NOUN
ejpam-6307	84	37	σ(vj	σ(vj	NOUN
ejpam-6307	84	38	)	)	PUNCT
ejpam-6307	84	39	∀	∀	PUNCT
ejpam-6307	84	40	vi	vi	PROPN
ejpam-6307	84	41	,	,	PUNCT
ejpam-6307	84	42	vj	vj	INTJ
ejpam-6307	84	43	ϵ	ϵ	NOUN
ejpam-6307	84	44	σ∗.	σ∗.	NOUN
ejpam-6307	84	45	definition	definition	NOUN
ejpam-6307	84	46	8	8	NUM
ejpam-6307	84	47	.	.	PUNCT
ejpam-6307	85	1	[	[	X
ejpam-6307	85	2	7	7	X
ejpam-6307	85	3	]	]	PUNCT
ejpam-6307	85	4	a	a	DET
ejpam-6307	85	5	connected	connected	ADJ
ejpam-6307	85	6	fuzzy	fuzzy	ADJ
ejpam-6307	85	7	graph	graph	NOUN
ejpam-6307	85	8	is	be	AUX
ejpam-6307	85	9	called	call	VERB
ejpam-6307	85	10	a	a	DET
ejpam-6307	85	11	fuzzy	fuzzy	ADJ
ejpam-6307	85	12	tree	tree	NOUN
ejpam-6307	85	13	if	if	SCONJ
ejpam-6307	85	14	it	it	PRON
ejpam-6307	85	15	has	have	VERB
ejpam-6307	85	16	a	a	DET
ejpam-6307	85	17	fuzzy	fuzzy	ADJ
ejpam-6307	85	18	spanning	span	VERB
ejpam-6307	85	19	subgraph	subgraph	NOUN
ejpam-6307	85	20	h:(v	h:(v	PROPN
ejpam-6307	85	21	,	,	PUNCT
ejpam-6307	85	22	σ	σ	PROPN
ejpam-6307	85	23	,	,	PUNCT
ejpam-6307	85	24	τ	τ	PROPN
ejpam-6307	85	25	)	)	PUNCT
ejpam-6307	85	26	,	,	PUNCT
ejpam-6307	85	27	which	which	PRON
ejpam-6307	85	28	is	be	AUX
ejpam-6307	85	29	a	a	DET
ejpam-6307	85	30	tree	tree	NOUN
ejpam-6307	85	31	where	where	SCONJ
ejpam-6307	85	32	for	for	ADP
ejpam-6307	85	33	all	all	DET
ejpam-6307	85	34	vivj	vivj	NOUN
ejpam-6307	85	35	not	not	PART
ejpam-6307	85	36	in	in	ADP
ejpam-6307	85	37	h	h	NOUN
ejpam-6307	85	38	,	,	PUNCT
ejpam-6307	85	39	µ	µ	X
ejpam-6307	85	40	(	(	PUNCT
ejpam-6307	85	41	vi	vi	PROPN
ejpam-6307	85	42	,	,	PUNCT
ejpam-6307	85	43	vj	vj	NOUN
ejpam-6307	85	44	)	)	PUNCT
ejpam-6307	85	45	<	<	X
ejpam-6307	85	46	τ∞(vi	τ∞(vi	PROPN
ejpam-6307	85	47	,	,	PUNCT
ejpam-6307	85	48	vj	vj	PROPN
ejpam-6307	85	49	)	)	PUNCT
ejpam-6307	85	50	.	.	PUNCT
ejpam-6307	86	1	definition	definition	NOUN
ejpam-6307	86	2	9	9	NUM
ejpam-6307	86	3	.	.	PUNCT
ejpam-6307	87	1	[	[	X
ejpam-6307	87	2	8	8	NUM
ejpam-6307	87	3	]	]	PUNCT
ejpam-6307	87	4	in	in	ADP
ejpam-6307	87	5	a	a	DET
ejpam-6307	87	6	fuzzy	fuzzy	ADJ
ejpam-6307	87	7	graph	graph	NOUN
ejpam-6307	87	8	(	(	PUNCT
ejpam-6307	87	9	fg	fg	PROPN
ejpam-6307	87	10	)	)	PUNCT
ejpam-6307	87	11	,	,	PUNCT
ejpam-6307	87	12	the	the	DET
ejpam-6307	87	13	fuzzy	fuzzy	ADJ
ejpam-6307	87	14	distance	distance	NOUN
ejpam-6307	87	15	between	between	ADP
ejpam-6307	87	16	any	any	DET
ejpam-6307	87	17	two	two	NUM
ejpam-6307	87	18	nodes	node	NOUN
ejpam-6307	87	19	is	be	AUX
ejpam-6307	87	20	defined	define	VERB
ejpam-6307	87	21	and	and	CCONJ
ejpam-6307	87	22	denoted	denote	VERB
ejpam-6307	87	23	as	as	ADP
ejpam-6307	87	24	df	df	PROPN
ejpam-6307	87	25	(	(	PUNCT
ejpam-6307	87	26	u	u	NOUN
ejpam-6307	87	27	,	,	PUNCT
ejpam-6307	87	28	v	v	NOUN
ejpam-6307	87	29	)	)	PUNCT
ejpam-6307	87	30	=	=	PUNCT
ejpam-6307	87	31	∧	∧	PROPN
ejpam-6307	87	32	p{l(p)∗s(p	p{l(p)∗s(p	PROPN
ejpam-6307	87	33	)	)	PUNCT
ejpam-6307	87	34	}	}	PUNCT
ejpam-6307	87	35	,	,	PUNCT
ejpam-6307	87	36	where	where	SCONJ
ejpam-6307	87	37	the	the	DET
ejpam-6307	87	38	length	length	NOUN
ejpam-6307	87	39	of	of	ADP
ejpam-6307	87	40	the	the	DET
ejpam-6307	87	41	path	path	NOUN
ejpam-6307	87	42	is	be	AUX
ejpam-6307	87	43	denoted	denote	VERB
ejpam-6307	87	44	as	as	ADP
ejpam-6307	87	45	l(p	l(p	NOUN
ejpam-6307	87	46	)	)	PUNCT
ejpam-6307	87	47	and	and	CCONJ
ejpam-6307	87	48	the	the	DET
ejpam-6307	87	49	strength	strength	NOUN
ejpam-6307	87	50	of	of	ADP
ejpam-6307	87	51	the	the	DET
ejpam-6307	87	52	path	path	NOUN
ejpam-6307	87	53	is	be	AUX
ejpam-6307	87	54	denoted	denote	VERB
ejpam-6307	87	55	as	as	ADP
ejpam-6307	87	56	s(p	s(p	PROPN
ejpam-6307	87	57	)	)	PUNCT
ejpam-6307	87	58	,	,	PUNCT
ejpam-6307	87	59	while	while	SCONJ
ejpam-6307	87	60	the	the	DET
ejpam-6307	87	61	symbol	symbol	NOUN
ejpam-6307	87	62	∧	∧	PROPN
ejpam-6307	87	63	denotes	denote	VERB
ejpam-6307	87	64	the	the	DET
ejpam-6307	87	65	minimum	minimum	NOUN
ejpam-6307	87	66	over	over	ADP
ejpam-6307	87	67	all	all	DET
ejpam-6307	87	68	such	such	ADJ
ejpam-6307	87	69	paths	path	NOUN
ejpam-6307	87	70	.	.	PUNCT
ejpam-6307	88	1	moreover	moreover	ADV
ejpam-6307	88	2	,	,	PUNCT
ejpam-6307	88	3	a	a	DET
ejpam-6307	88	4	vi−	vi−	NUM
ejpam-6307	88	5	vj	vj	PROPN
ejpam-6307	88	6	path	path	NOUN
ejpam-6307	88	7	is	be	AUX
ejpam-6307	88	8	called	call	VERB
ejpam-6307	88	9	a	a	DET
ejpam-6307	88	10	fuzzy	fuzzy	ADJ
ejpam-6307	88	11	vi−	vi−	PROPN
ejpam-6307	88	12	vj	vj	INTJ
ejpam-6307	88	13	geodesic	geodesic	NOUN
ejpam-6307	88	14	if	if	SCONJ
ejpam-6307	88	15	df	df	PROPN
ejpam-6307	88	16	(	(	PUNCT
ejpam-6307	88	17	vi	vi	PROPN
ejpam-6307	88	18	,	,	PUNCT
ejpam-6307	88	19	vj	vj	ADJ
ejpam-6307	88	20	)	)	PUNCT
ejpam-6307	88	21	=	=	SYM
ejpam-6307	88	22	l(p	l(p	PROPN
ejpam-6307	88	23	)	)	PUNCT
ejpam-6307	88	24	∗	∗	NOUN
ejpam-6307	88	25	s(p	s(p	PROPN
ejpam-6307	88	26	)	)	PUNCT
ejpam-6307	88	27	.	.	PUNCT
ejpam-6307	89	1	definition	definition	NOUN
ejpam-6307	89	2	10	10	NUM
ejpam-6307	89	3	.	.	PUNCT
ejpam-6307	90	1	[	[	X
ejpam-6307	90	2	12	12	NUM
ejpam-6307	90	3	]	]	PUNCT
ejpam-6307	90	4	a	a	DET
ejpam-6307	90	5	u	u	NOUN
ejpam-6307	90	6	–	–	PUNCT
ejpam-6307	90	7	v	v	ADP
ejpam-6307	90	8	path	path	NOUN
ejpam-6307	90	9	is	be	AUX
ejpam-6307	90	10	called	call	VERB
ejpam-6307	90	11	a	a	DET
ejpam-6307	90	12	fuzzy	fuzzy	ADJ
ejpam-6307	90	13	detour	detour	NOUN
ejpam-6307	90	14	if	if	SCONJ
ejpam-6307	90	15	its	its	PRON
ejpam-6307	90	16	length	length	NOUN
ejpam-6307	90	17	is	be	AUX
ejpam-6307	90	18	∆(u	∆(u	ADJ
ejpam-6307	90	19	,	,	PUNCT
ejpam-6307	90	20	v	v	NOUN
ejpam-6307	90	21	)	)	PUNCT
ejpam-6307	90	22	,	,	PUNCT
ejpam-6307	90	23	where	where	SCONJ
ejpam-6307	90	24	∆(u	∆(u	NOUN
ejpam-6307	90	25	,	,	PUNCT
ejpam-6307	90	26	v	v	NOUN
ejpam-6307	90	27	)	)	PUNCT
ejpam-6307	90	28	is	be	AUX
ejpam-6307	90	29	the	the	DET
ejpam-6307	90	30	fuzzy	fuzzy	ADJ
ejpam-6307	90	31	detour	detour	NOUN
ejpam-6307	90	32	µ	µ	ADJ
ejpam-6307	90	33	–	–	PUNCT
ejpam-6307	90	34	distance	distance	NOUN
ejpam-6307	90	35	between	between	ADP
ejpam-6307	90	36	pair	pair	NOUN
ejpam-6307	90	37	of	of	ADP
ejpam-6307	90	38	vertices	vertex	NOUN
ejpam-6307	90	39	u	u	NOUN
ejpam-6307	90	40	and	and	CCONJ
ejpam-6307	90	41	v	v	NOUN
ejpam-6307	90	42	and	and	CCONJ
ejpam-6307	90	43	is	be	AUX
ejpam-6307	90	44	defined	define	VERB
ejpam-6307	90	45	by	by	ADP
ejpam-6307	90	46	the	the	DET
ejpam-6307	90	47	maximum	maximum	ADJ
ejpam-6307	90	48	µ-length	µ-length	NOUN
ejpam-6307	90	49	of	of	ADP
ejpam-6307	90	50	any	any	DET
ejpam-6307	90	51	u	u	NOUN
ejpam-6307	90	52	–	–	PUNCT
ejpam-6307	90	53	v	v	NUM
ejpam-6307	90	54	path	path	NOUN
ejpam-6307	90	55	,	,	PUNCT
ejpam-6307	90	56	where	where	SCONJ
ejpam-6307	90	57	the	the	DET
ejpam-6307	90	58	µlength	µlength	NOUN
ejpam-6307	90	59	of	of	ADP
ejpam-6307	90	60	a	a	DET
ejpam-6307	90	61	path	path	NOUN
ejpam-6307	90	62	p	p	NOUN
ejpam-6307	90	63	:	:	PUNCT
ejpam-6307	90	64	u	u	PROPN
ejpam-6307	90	65	=	=	PROPN
ejpam-6307	90	66	v0	v0	PROPN
ejpam-6307	90	67	,	,	PUNCT
ejpam-6307	90	68	v1	v1	NOUN
ejpam-6307	90	69	,	,	PUNCT
ejpam-6307	90	70	.	.	PUNCT
ejpam-6307	90	71	.	.	PUNCT
ejpam-6307	90	72	.	.	PUNCT
ejpam-6307	90	73	.	.	PUNCT
ejpam-6307	90	74	.	.	PUNCT
ejpam-6307	91	1	.	.	PUNCT
ejpam-6307	92	1	,	,	PUNCT
ejpam-6307	92	2	vn	vn	PROPN
ejpam-6307	92	3	=	=	SYM
ejpam-6307	92	4	v	v	PROPN
ejpam-6307	92	5	is	be	AUX
ejpam-6307	92	6	l	l	NOUN
ejpam-6307	92	7	(	(	PUNCT
ejpam-6307	92	8	p	p	NOUN
ejpam-6307	92	9	)	)	PUNCT
ejpam-6307	93	1	=	=	SYM
ejpam-6307	94	1	∑n	∑n	PROPN
ejpam-6307	94	2	i=1	i=1	PROPN
ejpam-6307	94	3	1	1	NUM
ejpam-6307	94	4	µ(vi−1	µ(vi−1	PROPN
ejpam-6307	94	5	,	,	PUNCT
ejpam-6307	94	6	vi	vi	NOUN
ejpam-6307	94	7	)	)	PUNCT
ejpam-6307	94	8	.	.	PUNCT
ejpam-6307	95	1	definition	definition	NOUN
ejpam-6307	95	2	11	11	NUM
ejpam-6307	95	3	.	.	PUNCT
ejpam-6307	96	1	[	[	X
ejpam-6307	96	2	20	20	NUM
ejpam-6307	96	3	]	]	PUNCT
ejpam-6307	96	4	an	an	DET
ejpam-6307	96	5	m×m	m×m	ADJ
ejpam-6307	96	6	matrix	matrix	NOUN
ejpam-6307	96	7	fdg	fdg	NOUN
ejpam-6307	96	8	=	=	PUNCT
ejpam-6307	97	1	[	[	X
ejpam-6307	97	2	aij	aij	X
ejpam-6307	97	3	]	]	X
ejpam-6307	97	4	,	,	PUNCT
ejpam-6307	97	5	where	where	SCONJ
ejpam-6307	97	6	aij	aij	PROPN
ejpam-6307	97	7	=	=	SYM
ejpam-6307	97	8	dfg(si	dfg(si	PROPN
ejpam-6307	97	9	)	)	PUNCT
ejpam-6307	97	10	,	,	PUNCT
ejpam-6307	97	11	if	if	SCONJ
ejpam-6307	97	12	i	i	PRON
ejpam-6307	97	13	=	=	SYM
ejpam-6307	97	14	j	j	PROPN
ejpam-6307	97	15	and	and	CCONJ
ejpam-6307	97	16	0	0	NUM
ejpam-6307	97	17	otherwise	otherwise	ADV
ejpam-6307	97	18	,	,	PUNCT
ejpam-6307	97	19	is	be	AUX
ejpam-6307	97	20	called	call	VERB
ejpam-6307	97	21	the	the	DET
ejpam-6307	97	22	degree	degree	NOUN
ejpam-6307	97	23	matrix	matrix	NOUN
ejpam-6307	97	24	of	of	ADP
ejpam-6307	97	25	fuzzy	fuzzy	ADJ
ejpam-6307	97	26	graph	graph	NOUN
ejpam-6307	97	27	g	g	NOUN
ejpam-6307	97	28	:	:	PUNCT
ejpam-6307	97	29	(	(	PUNCT
ejpam-6307	97	30	v	v	NOUN
ejpam-6307	97	31	,	,	PUNCT
ejpam-6307	97	32	σ	σ	PROPN
ejpam-6307	97	33	,	,	PUNCT
ejpam-6307	97	34	µ	µ	NOUN
ejpam-6307	97	35	)	)	PUNCT
ejpam-6307	97	36	.	.	PUNCT
ejpam-6307	98	1	definition	definition	NOUN
ejpam-6307	98	2	12	12	NUM
ejpam-6307	98	3	.	.	PUNCT
ejpam-6307	99	1	[	[	X
ejpam-6307	99	2	20	20	NUM
ejpam-6307	99	3	]	]	PUNCT
ejpam-6307	99	4	let	let	AUX
ejpam-6307	99	5	g	g	NOUN
ejpam-6307	99	6	:	:	PUNCT
ejpam-6307	99	7	(	(	PUNCT
ejpam-6307	99	8	v	v	NOUN
ejpam-6307	99	9	,	,	PUNCT
ejpam-6307	99	10	σ	σ	PROPN
ejpam-6307	99	11	,	,	PUNCT
ejpam-6307	99	12	µ	µ	NOUN
ejpam-6307	99	13	)	)	PUNCT
ejpam-6307	99	14	be	be	VERB
ejpam-6307	99	15	an	an	DET
ejpam-6307	99	16	fg	fg	NOUN
ejpam-6307	99	17	with	with	ADP
ejpam-6307	99	18	|v|	|v|	PROPN
ejpam-6307	99	19	=	=	SYM
ejpam-6307	99	20	n	n	PROPN
ejpam-6307	99	21	and	and	CCONJ
ejpam-6307	99	22	µ1	µ1	PROPN
ejpam-6307	99	23	≥	≥	NOUN
ejpam-6307	99	24	µ2	µ2	PROPN
ejpam-6307	99	25	≥	≥	NUM
ejpam-6307	99	26	......	......	PUNCT
ejpam-6307	99	27	≥	≥	NUM
ejpam-6307	99	28	µn	µn	NOUN
ejpam-6307	99	29	be	be	AUX
ejpam-6307	99	30	the	the	DET
ejpam-6307	99	31	laplacian	laplacian	ADJ
ejpam-6307	99	32	eigenvalues	eigenvalue	NOUN
ejpam-6307	99	33	.	.	PUNCT
ejpam-6307	100	1	then	then	ADV
ejpam-6307	100	2	le(g	le(g	PUNCT
ejpam-6307	100	3	)	)	PUNCT
ejpam-6307	101	1	=	=	PUNCT
ejpam-6307	102	1	|µi	|µi	NUM
ejpam-6307	102	2	−	−	NUM
ejpam-6307	102	3	2	2	NUM
ejpam-6307	102	4	∑	∑	PUNCT
ejpam-6307	102	5	1≤i	1≤i	PROPN
ejpam-6307	102	6	<	<	X
ejpam-6307	102	7	j≤n	j≤n	NOUN
ejpam-6307	102	8	µ(vi	µ(vi	NOUN
ejpam-6307	102	9	,	,	PUNCT
ejpam-6307	102	10	vj	vj	NOUN
ejpam-6307	102	11	)	)	PUNCT
ejpam-6307	102	12	n	n	CCONJ
ejpam-6307	102	13	|	|	ADV
ejpam-6307	102	14	.	.	PUNCT
ejpam-6307	103	1	theorem	theorem	NOUN
ejpam-6307	103	2	1	1	NUM
ejpam-6307	103	3	.	.	PUNCT
ejpam-6307	104	1	[	[	X
ejpam-6307	104	2	18	18	NUM
ejpam-6307	104	3	]	]	PUNCT
ejpam-6307	104	4	let	let	VERB
ejpam-6307	104	5	g	g	PRON
ejpam-6307	104	6	be	be	AUX
ejpam-6307	104	7	a	a	DET
ejpam-6307	104	8	weighted	weight	VERB
ejpam-6307	104	9	graph	graph	NOUN
ejpam-6307	104	10	of	of	ADP
ejpam-6307	104	11	order	order	NOUN
ejpam-6307	104	12	n	n	PRON
ejpam-6307	104	13	each	each	PRON
ejpam-6307	104	14	of	of	ADP
ejpam-6307	104	15	whose	whose	DET
ejpam-6307	104	16	edges	edge	NOUN
ejpam-6307	104	17	has	have	VERB
ejpam-6307	104	18	nonzero	nonzero	NOUN
ejpam-6307	104	19	weight	weight	NOUN
ejpam-6307	104	20	and	and	CCONJ
ejpam-6307	104	21	e1	e1	NOUN
ejpam-6307	104	22	,	,	PUNCT
ejpam-6307	104	23	.	.	PUNCT
ejpam-6307	104	24	.	.	PUNCT
ejpam-6307	105	1	.	.	PUNCT
ejpam-6307	106	1	,	,	PUNCT
ejpam-6307	106	2	em	em	PRON
ejpam-6307	106	3	be	be	VERB
ejpam-6307	106	4	all	all	DET
ejpam-6307	106	5	the	the	DET
ejpam-6307	106	6	edges	edge	NOUN
ejpam-6307	106	7	of	of	ADP
ejpam-6307	106	8	g.	g.	PROPN
ejpam-6307	106	9	then	then	ADV
ejpam-6307	106	10	e(g	e(g	PROPN
ejpam-6307	106	11	)	)	PUNCT
ejpam-6307	106	12	≤	≤	NOUN
ejpam-6307	106	13	2	2	NUM
ejpam-6307	106	14	∑m	∑m	PROPN
ejpam-6307	106	15	i=1	i=1	PROPN
ejpam-6307	106	16	|w(ei)|	|w(ei)|	NOUN
ejpam-6307	106	17	,	,	PUNCT
ejpam-6307	106	18	where	where	SCONJ
ejpam-6307	106	19	equality	equality	NOUN
ejpam-6307	106	20	holds	hold	VERB
ejpam-6307	106	21	if	if	SCONJ
ejpam-6307	106	22	and	and	CCONJ
ejpam-6307	106	23	only	only	ADV
ejpam-6307	106	24	if	if	SCONJ
ejpam-6307	106	25	each	each	DET
ejpam-6307	106	26	connected	connected	ADJ
ejpam-6307	106	27	component	component	NOUN
ejpam-6307	106	28	of	of	ADP
ejpam-6307	106	29	g	g	PROPN
ejpam-6307	106	30	has	have	VERB
ejpam-6307	106	31	at	at	ADP
ejpam-6307	106	32	most	most	ADV
ejpam-6307	106	33	two	two	NUM
ejpam-6307	106	34	vertices	vertex	NOUN
ejpam-6307	106	35	.	.	PUNCT
ejpam-6307	107	1	theorem	theorem	NOUN
ejpam-6307	107	2	2	2	NUM
ejpam-6307	107	3	.	.	PUNCT
ejpam-6307	108	1	[	[	X
ejpam-6307	108	2	8	8	NUM
ejpam-6307	108	3	]	]	PUNCT
ejpam-6307	108	4	let	let	AUX
ejpam-6307	108	5	g	g	NOUN
ejpam-6307	108	6	:	:	PUNCT
ejpam-6307	108	7	(	(	PUNCT
ejpam-6307	108	8	v	v	NOUN
ejpam-6307	108	9	,	,	PUNCT
ejpam-6307	108	10	σ	σ	PROPN
ejpam-6307	108	11	,	,	PUNCT
ejpam-6307	108	12	µ	µ	NOUN
ejpam-6307	108	13	)	)	PUNCT
ejpam-6307	108	14	be	be	VERB
ejpam-6307	108	15	fg	fg	PROPN
ejpam-6307	108	16	with	with	ADP
ejpam-6307	108	17	|v|	|v|	NOUN
ejpam-6307	108	18	=	=	SYM
ejpam-6307	108	19	n	n	NOUN
ejpam-6307	108	20	and	and	CCONJ
ejpam-6307	108	21	µ∗	µ∗	VERB
ejpam-6307	108	22	=	=	SYM
ejpam-6307	108	23	{	{	PUNCT
ejpam-6307	108	24	e1	e1	PROPN
ejpam-6307	108	25	,	,	PUNCT
ejpam-6307	108	26	...	...	PUNCT
ejpam-6307	108	27	,	,	PUNCT
ejpam-6307	108	28	em	em	PRON
ejpam-6307	108	29	}	}	PUNCT
ejpam-6307	108	30	.	.	PUNCT
ejpam-6307	109	1	then	then	ADV
ejpam-6307	109	2	,	,	PUNCT
ejpam-6307	109	3	e(g	e(g	PROPN
ejpam-6307	109	4	)	)	PUNCT
ejpam-6307	109	5	≤	≤	NOUN
ejpam-6307	109	6	2	2	NUM
ejpam-6307	109	7	∑m	∑m	PROPN
ejpam-6307	109	8	i=1	i=1	PRON
ejpam-6307	109	9	µ(ei	µ(ei	NOUN
ejpam-6307	109	10	)	)	PUNCT
ejpam-6307	109	11	.	.	PUNCT
ejpam-6307	110	1	theorem	theorem	NOUN
ejpam-6307	110	2	3	3	NUM
ejpam-6307	110	3	.	.	PUNCT
ejpam-6307	111	1	[	[	X
ejpam-6307	111	2	8	8	NUM
ejpam-6307	111	3	]	]	PUNCT
ejpam-6307	111	4	let	let	AUX
ejpam-6307	111	5	h	h	NOUN
ejpam-6307	111	6	:	:	PUNCT
ejpam-6307	111	7	(	(	PUNCT
ejpam-6307	111	8	v	v	NOUN
ejpam-6307	111	9	,	,	PUNCT
ejpam-6307	111	10	σ	σ	PROPN
ejpam-6307	111	11	,	,	PUNCT
ejpam-6307	111	12	µ	µ	NOUN
ejpam-6307	111	13	)	)	PUNCT
ejpam-6307	111	14	be	be	AUX
ejpam-6307	111	15	a	a	DET
ejpam-6307	111	16	complete	complete	ADJ
ejpam-6307	111	17	fuzzy	fuzzy	ADJ
ejpam-6307	111	18	subgraph	subgraph	NOUN
ejpam-6307	111	19	of	of	ADP
ejpam-6307	111	20	g.	g.	PROPN
ejpam-6307	111	21	then	then	ADV
ejpam-6307	111	22	,	,	PUNCT
ejpam-6307	111	23	h	h	NOUN
ejpam-6307	111	24	is	be	AUX
ejpam-6307	111	25	a	a	DET
ejpam-6307	111	26	fuzzy	fuzzy	ADJ
ejpam-6307	111	27	geodetic	geodetic	ADJ
ejpam-6307	111	28	block	block	NOUN
ejpam-6307	111	29	(	(	PUNCT
ejpam-6307	111	30	fgb	fgb	NOUN
ejpam-6307	111	31	)	)	PUNCT
ejpam-6307	112	1	if	if	SCONJ
ejpam-6307	112	2	and	and	CCONJ
ejpam-6307	112	3	only	only	ADV
ejpam-6307	112	4	if	if	SCONJ
ejpam-6307	112	5	{	{	PUNCT
ejpam-6307	112	6	vivj	vivj	NOUN
ejpam-6307	112	7	}	}	PUNCT
ejpam-6307	112	8	is	be	AUX
ejpam-6307	112	9	geodetic	geodetic	ADJ
ejpam-6307	112	10	convex	convex	NOUN
ejpam-6307	112	11	for	for	ADP
ejpam-6307	112	12	any	any	DET
ejpam-6307	112	13	two	two	NUM
ejpam-6307	112	14	vertices	vertex	NOUN
ejpam-6307	112	15	.	.	PUNCT
ejpam-6307	113	1	the	the	DET
ejpam-6307	113	2	key	key	ADJ
ejpam-6307	113	3	symbols	symbol	NOUN
ejpam-6307	113	4	,	,	PUNCT
ejpam-6307	113	5	notations	notation	NOUN
ejpam-6307	113	6	and	and	CCONJ
ejpam-6307	113	7	abbreviations	abbreviation	NOUN
ejpam-6307	113	8	employed	employ	VERB
ejpam-6307	113	9	throughout	throughout	ADP
ejpam-6307	113	10	this	this	DET
ejpam-6307	113	11	paper	paper	NOUN
ejpam-6307	113	12	are	be	AUX
ejpam-6307	113	13	summarized	summarize	VERB
ejpam-6307	113	14	in	in	ADP
ejpam-6307	113	15	table	table	NOUN
ejpam-6307	113	16	1	1	NUM
ejpam-6307	113	17	.	.	PUNCT
ejpam-6307	113	18	r.	r.	PROPN
ejpam-6307	113	19	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	113	20	,	,	PUNCT
ejpam-6307	113	21	a.	a.	NOUN
ejpam-6307	113	22	m.	m.	PROPN
ejpam-6307	113	23	anto	anto	PROPN
ejpam-6307	113	24	,	,	PUNCT
ejpam-6307	113	25	v.	v.	PROPN
ejpam-6307	113	26	mary	mary	PROPN
ejpam-6307	113	27	mettilda	mettilda	PROPN
ejpam-6307	113	28	rose	rise	VERB
ejpam-6307	113	29	/	/	SYM
ejpam-6307	113	30	eur	eur	PROPN
ejpam-6307	113	31	.	.	PUNCT
ejpam-6307	114	1	j.	j.	PROPN
ejpam-6307	114	2	pure	pure	PROPN
ejpam-6307	114	3	appl	appl	PROPN
ejpam-6307	114	4	.	.	PROPN
ejpam-6307	114	5	math	math	PROPN
ejpam-6307	114	6	,	,	PUNCT
ejpam-6307	114	7	18	18	NUM
ejpam-6307	114	8	(	(	PUNCT
ejpam-6307	114	9	4	4	NUM
ejpam-6307	114	10	)	)	PUNCT
ejpam-6307	114	11	(	(	PUNCT
ejpam-6307	114	12	2025	2025	NUM
ejpam-6307	114	13	)	)	PUNCT
ejpam-6307	114	14	,	,	PUNCT
ejpam-6307	114	15	6307	6307	NUM
ejpam-6307	114	16	5	5	NUM
ejpam-6307	114	17	of	of	ADP
ejpam-6307	114	18	25	25	NUM
ejpam-6307	114	19	table	table	NOUN
ejpam-6307	114	20	1	1	NUM
ejpam-6307	114	21	:	:	PUNCT
ejpam-6307	114	22	symbols	symbol	NOUN
ejpam-6307	114	23	,	,	PUNCT
ejpam-6307	114	24	notations	notation	NOUN
ejpam-6307	114	25	and	and	CCONJ
ejpam-6307	114	26	abbreviations	abbreviation	NOUN
ejpam-6307	114	27	.	.	PUNCT
ejpam-6307	115	1	symbols	symbol	NOUN
ejpam-6307	115	2	/	/	SYM
ejpam-6307	115	3	notations	notation	NOUN
ejpam-6307	115	4	definition	definition	NOUN
ejpam-6307	115	5	g	g	NOUN
ejpam-6307	115	6	:	:	PUNCT
ejpam-6307	115	7	(	(	PUNCT
ejpam-6307	115	8	v	v	NOUN
ejpam-6307	115	9	,	,	PUNCT
ejpam-6307	115	10	σ	σ	PROPN
ejpam-6307	115	11	,	,	PUNCT
ejpam-6307	115	12	µ	µ	NOUN
ejpam-6307	115	13	)	)	PUNCT
ejpam-6307	115	14	a	a	DET
ejpam-6307	115	15	fuzzy	fuzzy	ADJ
ejpam-6307	115	16	graph	graph	NOUN
ejpam-6307	115	17	(	(	PUNCT
ejpam-6307	115	18	fg	fg	NOUN
ejpam-6307	115	19	)	)	PUNCT
ejpam-6307	115	20	with	with	ADP
ejpam-6307	115	21	membership	membership	NOUN
ejpam-6307	115	22	functions	function	NOUN
ejpam-6307	115	23	σ	σ	PROPN
ejpam-6307	115	24	and	and	CCONJ
ejpam-6307	115	25	µ.	µ.	PROPN
ejpam-6307	115	26	h	h	NOUN
ejpam-6307	115	27	:	:	PUNCT
ejpam-6307	115	28	(	(	PUNCT
ejpam-6307	115	29	v	v	NOUN
ejpam-6307	115	30	,	,	PUNCT
ejpam-6307	115	31	τ	τ	PROPN
ejpam-6307	115	32	,	,	PUNCT
ejpam-6307	115	33	ϑ	ϑ	ADJ
ejpam-6307	115	34	)	)	PUNCT
ejpam-6307	115	35	partial	partial	ADJ
ejpam-6307	115	36	fuzzy	fuzzy	ADJ
ejpam-6307	115	37	subgraph	subgraph	NOUN
ejpam-6307	115	38	of	of	ADP
ejpam-6307	115	39	an	an	DET
ejpam-6307	115	40	fg	fg	PROPN
ejpam-6307	115	41	.	.	PROPN
ejpam-6307	115	42	µ	µ	X
ejpam-6307	115	43	fuzzy	fuzzy	ADJ
ejpam-6307	115	44	edge	edge	NOUN
ejpam-6307	115	45	membership	membership	NOUN
ejpam-6307	115	46	function	function	NOUN
ejpam-6307	115	47	.	.	PUNCT
ejpam-6307	116	1	σ	σ	NOUN
ejpam-6307	116	2	fuzzy	fuzzy	ADJ
ejpam-6307	116	3	vertex	vertex	NOUN
ejpam-6307	116	4	membership	membership	NOUN
ejpam-6307	116	5	function	function	NOUN
ejpam-6307	116	6	.	.	PUNCT
ejpam-6307	117	1	p	p	X
ejpam-6307	117	2	a	a	DET
ejpam-6307	117	3	path	path	NOUN
ejpam-6307	117	4	in	in	ADP
ejpam-6307	117	5	an	an	DET
ejpam-6307	117	6	fg.∧	fg.∧	NOUN
ejpam-6307	117	7	symbol	symbol	NOUN
ejpam-6307	117	8	for	for	ADP
ejpam-6307	117	9	minimum	minimum	NOUN
ejpam-6307	117	10	.	.	PUNCT
ejpam-6307	118	1	min	min	NOUN
ejpam-6307	118	2	minimum	minimum	NOUN
ejpam-6307	118	3	.	.	PUNCT
ejpam-6307	119	1	max	max	PROPN
ejpam-6307	119	2	maximum	maximum	PROPN
ejpam-6307	119	3	.	.	PUNCT
ejpam-6307	119	4	fgb	fgb	ADJ
ejpam-6307	119	5	fuzzy	fuzzy	ADJ
ejpam-6307	119	6	geodetic	geodetic	ADJ
ejpam-6307	119	7	block	block	NOUN
ejpam-6307	119	8	.	.	PUNCT
ejpam-6307	120	1	df	df	PROPN
ejpam-6307	120	2	(	(	PUNCT
ejpam-6307	120	3	vi	vi	PROPN
ejpam-6307	120	4	,	,	PUNCT
ejpam-6307	120	5	vj	vj	ADJ
ejpam-6307	120	6	)	)	PUNCT
ejpam-6307	120	7	fuzzy	fuzzy	ADJ
ejpam-6307	120	8	vi	vi	PROPN
ejpam-6307	120	9	−	−	PROPN
ejpam-6307	120	10	vj	vj	INTJ
ejpam-6307	120	11	geodesic	geodesic	NOUN
ejpam-6307	120	12	∆	∆	PROPN
ejpam-6307	120	13	(	(	PUNCT
ejpam-6307	120	14	u	u	NOUN
ejpam-6307	120	15	,	,	PUNCT
ejpam-6307	120	16	v	v	NOUN
ejpam-6307	120	17	)	)	PUNCT
ejpam-6307	120	18	fuzzy	fuzzy	ADJ
ejpam-6307	120	19	detour	detour	PRON
ejpam-6307	120	20	µ	µ	ADJ
ejpam-6307	120	21	–	–	PUNCT
ejpam-6307	120	22	distance	distance	NOUN
ejpam-6307	120	23	.	.	PUNCT
ejpam-6307	121	1	e(g	e(g	NOUN
ejpam-6307	121	2	)	)	PUNCT
ejpam-6307	122	1	energy	energy	NOUN
ejpam-6307	122	2	of	of	ADP
ejpam-6307	122	3	an	an	DET
ejpam-6307	122	4	fg	fg	PROPN
ejpam-6307	122	5	.	.	PROPN
ejpam-6307	122	6	le(g	le(g	PROPN
ejpam-6307	122	7	)	)	PUNCT
ejpam-6307	122	8	laplacian	laplacian	ADJ
ejpam-6307	122	9	energy	energy	NOUN
ejpam-6307	122	10	of	of	ADP
ejpam-6307	122	11	an	an	DET
ejpam-6307	122	12	fg	fg	NOUN
ejpam-6307	122	13	.	.	PUNCT
ejpam-6307	122	14	fge(g	fge(g	PROPN
ejpam-6307	122	15	)	)	PUNCT
ejpam-6307	122	16	)	)	PUNCT
ejpam-6307	122	17	fuzzy	fuzzy	ADJ
ejpam-6307	122	18	geodetic	geodetic	ADJ
ejpam-6307	122	19	energy	energy	NOUN
ejpam-6307	122	20	(	(	PUNCT
ejpam-6307	122	21	fg	fg	NOUN
ejpam-6307	122	22	-	-	NOUN
ejpam-6307	122	23	energy	energy	NOUN
ejpam-6307	122	24	)	)	PUNCT
ejpam-6307	122	25	.	.	PUNCT
ejpam-6307	123	1	fde(g	fde(g	NOUN
ejpam-6307	123	2	)	)	PUNCT
ejpam-6307	123	3	)	)	PUNCT
ejpam-6307	124	1	fuzzy	fuzzy	ADJ
ejpam-6307	124	2	detour	detour	NOUN
ejpam-6307	124	3	energy	energy	NOUN
ejpam-6307	124	4	(	(	PUNCT
ejpam-6307	124	5	fd	fd	NOUN
ejpam-6307	124	6	-	-	PUNCT
ejpam-6307	124	7	energy	energy	NOUN
ejpam-6307	124	8	)	)	PUNCT
ejpam-6307	124	9	.	.	PUNCT
ejpam-6307	125	1	gle(g	gle(g	X
ejpam-6307	125	2	)	)	PUNCT
ejpam-6307	125	3	geodetic	geodetic	ADJ
ejpam-6307	125	4	laplacian	laplacian	ADJ
ejpam-6307	125	5	energy	energy	NOUN
ejpam-6307	125	6	.	.	PUNCT
ejpam-6307	126	1	dle(g	dle(g	PROPN
ejpam-6307	126	2	)	)	PUNCT
ejpam-6307	126	3	detour	detour	NOUN
ejpam-6307	126	4	laplacian	laplacian	ADJ
ejpam-6307	126	5	energy	energy	NOUN
ejpam-6307	126	6	.	.	PUNCT
ejpam-6307	127	1	mfgd	mfgd	ADJ
ejpam-6307	127	2	fuzzy	fuzzy	ADJ
ejpam-6307	127	3	geodetic	geodetic	ADJ
ejpam-6307	127	4	distance	distance	NOUN
ejpam-6307	127	5	matrix	matrix	NOUN
ejpam-6307	127	6	(	(	PUNCT
ejpam-6307	127	7	fg	fg	NOUN
ejpam-6307	127	8	-	-	NOUN
ejpam-6307	127	9	matrix	matrix	NOUN
ejpam-6307	127	10	)	)	PUNCT
ejpam-6307	127	11	.	.	PUNCT
ejpam-6307	128	1	tfgd	tfgd	ADJ
ejpam-6307	128	2	fuzzy	fuzzy	ADJ
ejpam-6307	128	3	geodetic	geodetic	ADJ
ejpam-6307	128	4	transmission	transmission	NOUN
ejpam-6307	128	5	matrix	matrix	NOUN
ejpam-6307	128	6	.	.	PUNCT
ejpam-6307	129	1	mfgld	mfgld	ADJ
ejpam-6307	129	2	fuzzy	fuzzy	ADJ
ejpam-6307	129	3	geodetic	geodetic	ADJ
ejpam-6307	129	4	-	-	PUNCT
ejpam-6307	129	5	laplacian	laplacian	ADJ
ejpam-6307	129	6	distance	distance	NOUN
ejpam-6307	129	7	matrix	matrix	NOUN
ejpam-6307	129	8	.	.	PUNCT
ejpam-6307	130	1	mfdd	mfdd	NOUN
ejpam-6307	130	2	fuzzy	fuzzy	ADJ
ejpam-6307	130	3	detour	detour	NOUN
ejpam-6307	130	4	distance	distance	NOUN
ejpam-6307	130	5	matrix	matrix	NOUN
ejpam-6307	130	6	(	(	PUNCT
ejpam-6307	130	7	fd	fd	NOUN
ejpam-6307	130	8	-	-	PUNCT
ejpam-6307	130	9	matrix	matrix	NOUN
ejpam-6307	130	10	)	)	PUNCT
ejpam-6307	130	11	.	.	PUNCT
ejpam-6307	131	1	tfdd	tfdd	PROPN
ejpam-6307	131	2	fuzzy	fuzzy	ADJ
ejpam-6307	131	3	detour	detour	NOUN
ejpam-6307	131	4	transmission	transmission	NOUN
ejpam-6307	131	5	matrix	matrix	NOUN
ejpam-6307	131	6	.	.	PUNCT
ejpam-6307	132	1	mfdld	mfdld	NOUN
ejpam-6307	132	2	fuzzy	fuzzy	ADJ
ejpam-6307	132	3	detour	detour	PRON
ejpam-6307	132	4	laplacian	laplacian	ADJ
ejpam-6307	132	5	-	-	PUNCT
ejpam-6307	132	6	distance	distance	NOUN
ejpam-6307	132	7	matrix	matrix	NOUN
ejpam-6307	132	8	.	.	PUNCT
ejpam-6307	133	1	fgsr	fgsr	VERB
ejpam-6307	133	2	fuzzy	fuzzy	ADJ
ejpam-6307	133	3	geodetic	geodetic	ADJ
ejpam-6307	133	4	spectral	spectral	ADJ
ejpam-6307	133	5	radius	radius	NOUN
ejpam-6307	133	6	.	.	PUNCT
ejpam-6307	134	1	fdsr	fdsr	PROPN
ejpam-6307	134	2	fuzzy	fuzzy	ADJ
ejpam-6307	134	3	detour	detour	PRON
ejpam-6307	134	4	spectral	spectral	ADJ
ejpam-6307	134	5	radius	radius	NOUN
ejpam-6307	134	6	.	.	PUNCT
ejpam-6307	135	1	3	3	X
ejpam-6307	135	2	.	.	X
ejpam-6307	135	3	fuzzy	fuzzy	ADJ
ejpam-6307	135	4	geodetic	geodetic	ADJ
ejpam-6307	135	5	spectrum	spectrum	NOUN
ejpam-6307	135	6	in	in	ADP
ejpam-6307	135	7	classical	classical	ADJ
ejpam-6307	135	8	graph	graph	NOUN
ejpam-6307	135	9	theory	theory	NOUN
ejpam-6307	135	10	,	,	PUNCT
ejpam-6307	135	11	the	the	DET
ejpam-6307	135	12	distance	distance	NOUN
ejpam-6307	135	13	spectrum	spectrum	NOUN
ejpam-6307	135	14	focuses	focus	VERB
ejpam-6307	135	15	on	on	ADP
ejpam-6307	135	16	the	the	DET
ejpam-6307	135	17	lengths	length	NOUN
ejpam-6307	135	18	of	of	ADP
ejpam-6307	135	19	paths	path	NOUN
ejpam-6307	135	20	between	between	ADP
ejpam-6307	135	21	pairs	pair	NOUN
ejpam-6307	135	22	of	of	ADP
ejpam-6307	135	23	vertices	vertex	NOUN
ejpam-6307	135	24	.	.	PUNCT
ejpam-6307	136	1	in	in	ADP
ejpam-6307	136	2	recent	recent	ADJ
ejpam-6307	136	3	years	year	NOUN
ejpam-6307	136	4	,	,	PUNCT
ejpam-6307	136	5	researchers	researcher	NOUN
ejpam-6307	136	6	have	have	AUX
ejpam-6307	136	7	extended	extend	VERB
ejpam-6307	136	8	spectral	spectral	ADJ
ejpam-6307	136	9	concepts	concept	NOUN
ejpam-6307	136	10	to	to	ADP
ejpam-6307	136	11	fuzzy	fuzzy	ADJ
ejpam-6307	136	12	graphs	graph	NOUN
ejpam-6307	136	13	,	,	PUNCT
ejpam-6307	136	14	where	where	SCONJ
ejpam-6307	136	15	uncertainty	uncertainty	NOUN
ejpam-6307	136	16	in	in	ADP
ejpam-6307	136	17	connections	connection	NOUN
ejpam-6307	136	18	must	must	AUX
ejpam-6307	136	19	be	be	AUX
ejpam-6307	136	20	taken	take	VERB
ejpam-6307	136	21	into	into	ADP
ejpam-6307	136	22	account	account	NOUN
ejpam-6307	136	23	.	.	PUNCT
ejpam-6307	137	1	the	the	DET
ejpam-6307	137	2	concept	concept	NOUN
ejpam-6307	137	3	of	of	ADP
ejpam-6307	137	4	fuzzy	fuzzy	ADJ
ejpam-6307	137	5	graph	graph	NOUN
ejpam-6307	137	6	energy	energy	NOUN
ejpam-6307	137	7	by	by	ADP
ejpam-6307	137	8	anjali	anjali	NOUN
ejpam-6307	137	9	and	and	CCONJ
ejpam-6307	137	10	mathew	mathew	PROPN
ejpam-6307	137	11	in	in	ADP
ejpam-6307	137	12	[	[	X
ejpam-6307	137	13	19	19	NUM
ejpam-6307	137	14	]	]	PUNCT
ejpam-6307	137	15	,	,	PUNCT
ejpam-6307	137	16	involves	involve	VERB
ejpam-6307	137	17	deriving	derive	VERB
ejpam-6307	137	18	spectral	spectral	ADJ
ejpam-6307	137	19	properties	property	NOUN
ejpam-6307	137	20	from	from	ADP
ejpam-6307	137	21	fuzzy	fuzzy	ADJ
ejpam-6307	137	22	adjacency	adjacency	NOUN
ejpam-6307	137	23	matrices	matrix	NOUN
ejpam-6307	137	24	to	to	PART
ejpam-6307	137	25	extend	extend	VERB
ejpam-6307	137	26	classical	classical	ADJ
ejpam-6307	137	27	graph	graph	NOUN
ejpam-6307	137	28	energy	energy	NOUN
ejpam-6307	137	29	to	to	ADP
ejpam-6307	137	30	fuzzy	fuzzy	ADJ
ejpam-6307	137	31	structures	structure	NOUN
ejpam-6307	137	32	.	.	PUNCT
ejpam-6307	138	1	motivated	motivate	VERB
ejpam-6307	138	2	by	by	ADP
ejpam-6307	138	3	the	the	DET
ejpam-6307	138	4	mathematical	mathematical	ADJ
ejpam-6307	138	5	richness	richness	NOUN
ejpam-6307	138	6	of	of	ADP
ejpam-6307	138	7	graph	graph	NOUN
ejpam-6307	138	8	energy	energy	NOUN
ejpam-6307	138	9	and	and	CCONJ
ejpam-6307	138	10	its	its	PRON
ejpam-6307	138	11	variants	variant	NOUN
ejpam-6307	138	12	,	,	PUNCT
ejpam-6307	138	13	we	we	PRON
ejpam-6307	138	14	take	take	VERB
ejpam-6307	138	15	the	the	DET
ejpam-6307	138	16	helm	helm	NOUN
ejpam-6307	138	17	in	in	ADP
ejpam-6307	138	18	this	this	DET
ejpam-6307	138	19	context	context	NOUN
ejpam-6307	138	20	by	by	ADP
ejpam-6307	138	21	introducing	introduce	VERB
ejpam-6307	138	22	the	the	DET
ejpam-6307	138	23	fuzzy	fuzzy	ADJ
ejpam-6307	138	24	geodetic	geodetic	ADJ
ejpam-6307	138	25	spectrum	spectrum	NOUN
ejpam-6307	138	26	and	and	CCONJ
ejpam-6307	138	27	investigating	investigate	VERB
ejpam-6307	138	28	its	its	PRON
ejpam-6307	138	29	mathematical	mathematical	ADJ
ejpam-6307	138	30	properties	property	NOUN
ejpam-6307	138	31	.	.	PUNCT
ejpam-6307	139	1	furthermore	furthermore	ADV
ejpam-6307	139	2	,	,	PUNCT
ejpam-6307	139	3	we	we	PRON
ejpam-6307	139	4	define	define	VERB
ejpam-6307	139	5	and	and	CCONJ
ejpam-6307	139	6	compute	compute	VERB
ejpam-6307	139	7	the	the	DET
ejpam-6307	139	8	fuzzy	fuzzy	ADJ
ejpam-6307	139	9	geodetic	geodetic	ADJ
ejpam-6307	139	10	energy	energy	NOUN
ejpam-6307	139	11	of	of	ADP
ejpam-6307	139	12	fuzzy	fuzzy	ADJ
ejpam-6307	139	13	graphs	graph	NOUN
ejpam-6307	139	14	,	,	PUNCT
ejpam-6307	139	15	thereby	thereby	ADV
ejpam-6307	139	16	extending	extend	VERB
ejpam-6307	139	17	classical	classical	ADJ
ejpam-6307	139	18	spectral	spectral	ADJ
ejpam-6307	139	19	concepts	concept	NOUN
ejpam-6307	139	20	into	into	ADP
ejpam-6307	139	21	the	the	DET
ejpam-6307	139	22	fuzzy	fuzzy	ADJ
ejpam-6307	139	23	domain	domain	NOUN
ejpam-6307	139	24	.	.	PUNCT
ejpam-6307	140	1	definition	definition	NOUN
ejpam-6307	140	2	13	13	NUM
ejpam-6307	140	3	.	.	PUNCT
ejpam-6307	141	1	let	let	VERB
ejpam-6307	141	2	g	g	PRON
ejpam-6307	141	3	be	be	AUX
ejpam-6307	141	4	a	a	DET
ejpam-6307	141	5	fuzzy	fuzzy	ADJ
ejpam-6307	141	6	graph	graph	NOUN
ejpam-6307	141	7	with	with	ADP
ejpam-6307	141	8	vertex	vertex	NOUN
ejpam-6307	141	9	set	set	VERB
ejpam-6307	141	10	σ∗	σ∗	NOUN
ejpam-6307	141	11	=	=	SYM
ejpam-6307	141	12	v1	v1	NOUN
ejpam-6307	141	13	,	,	PUNCT
ejpam-6307	141	14	v2	v2	NOUN
ejpam-6307	141	15	,	,	PUNCT
ejpam-6307	141	16	.	.	PUNCT
ejpam-6307	141	17	.	.	PUNCT
ejpam-6307	142	1	.	.	PUNCT
ejpam-6307	143	1	,	,	PUNCT
ejpam-6307	143	2	vm	vm	PROPN
ejpam-6307	143	3	.	.	PUNCT
ejpam-6307	144	1	the	the	DET
ejpam-6307	144	2	fuzzy	fuzzy	ADJ
ejpam-6307	144	3	geodetic	geodetic	ADJ
ejpam-6307	144	4	distance	distance	NOUN
ejpam-6307	144	5	matrix	matrix	NOUN
ejpam-6307	144	6	(	(	PUNCT
ejpam-6307	144	7	fg	fg	NOUN
ejpam-6307	144	8	-	-	NOUN
ejpam-6307	144	9	matrix	matrix	NOUN
ejpam-6307	144	10	)	)	PUNCT
ejpam-6307	144	11	of	of	ADP
ejpam-6307	144	12	g	g	PROPN
ejpam-6307	144	13	is	be	AUX
ejpam-6307	144	14	the	the	PRON
ejpam-6307	144	15	n	n	NUM
ejpam-6307	144	16	×	×	NOUN
ejpam-6307	144	17	n	n	CCONJ
ejpam-6307	144	18	matrix	matrix	NOUN
ejpam-6307	144	19	mfgd	mfgd	NOUN
ejpam-6307	144	20	=	=	PUNCT
ejpam-6307	145	1	[	[	X
ejpam-6307	145	2	bij	bij	NOUN
ejpam-6307	145	3	]	]	X
ejpam-6307	145	4	,	,	PUNCT
ejpam-6307	145	5	where	where	SCONJ
ejpam-6307	145	6	bij	bij	NOUN
ejpam-6307	145	7	=	=	SYM
ejpam-6307	145	8	df	df	PROPN
ejpam-6307	145	9	(	(	PUNCT
ejpam-6307	145	10	vi	vi	PROPN
ejpam-6307	145	11	,	,	PUNCT
ejpam-6307	145	12	vj	vj	ADJ
ejpam-6307	145	13	)	)	PUNCT
ejpam-6307	145	14	denotes	denote	VERB
ejpam-6307	145	15	the	the	DET
ejpam-6307	145	16	fuzzy	fuzzy	ADJ
ejpam-6307	145	17	geodetic	geodetic	ADJ
ejpam-6307	145	18	distance	distance	NOUN
ejpam-6307	145	19	between	between	ADP
ejpam-6307	145	20	vi	vi	PROPN
ejpam-6307	145	21	and	and	CCONJ
ejpam-6307	145	22	vj	vj	NOUN
ejpam-6307	145	23	.	.	PUNCT
ejpam-6307	146	1	the	the	DET
ejpam-6307	146	2	set	set	NOUN
ejpam-6307	146	3	of	of	ADP
ejpam-6307	146	4	eigenvalues	eigenvalue	NOUN
ejpam-6307	146	5	of	of	ADP
ejpam-6307	146	6	r.	r.	PROPN
ejpam-6307	146	7	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	146	8	,	,	PUNCT
ejpam-6307	146	9	a.	a.	NOUN
ejpam-6307	146	10	m.	m.	PROPN
ejpam-6307	146	11	anto	anto	PROPN
ejpam-6307	146	12	,	,	PUNCT
ejpam-6307	146	13	v.	v.	PROPN
ejpam-6307	146	14	mary	mary	PROPN
ejpam-6307	146	15	mettilda	mettilda	PROPN
ejpam-6307	146	16	rose	rise	VERB
ejpam-6307	146	17	/	/	SYM
ejpam-6307	146	18	eur	eur	PROPN
ejpam-6307	146	19	.	.	PUNCT
ejpam-6307	147	1	j.	j.	PROPN
ejpam-6307	147	2	pure	pure	PROPN
ejpam-6307	147	3	appl	appl	PROPN
ejpam-6307	147	4	.	.	PROPN
ejpam-6307	147	5	math	math	PROPN
ejpam-6307	147	6	,	,	PUNCT
ejpam-6307	147	7	18	18	NUM
ejpam-6307	147	8	(	(	PUNCT
ejpam-6307	147	9	4	4	NUM
ejpam-6307	147	10	)	)	PUNCT
ejpam-6307	147	11	(	(	PUNCT
ejpam-6307	147	12	2025	2025	NUM
ejpam-6307	147	13	)	)	PUNCT
ejpam-6307	147	14	,	,	PUNCT
ejpam-6307	147	15	6307	6307	NUM
ejpam-6307	147	16	6	6	NUM
ejpam-6307	147	17	of	of	ADP
ejpam-6307	147	18	25	25	NUM
ejpam-6307	147	19	mfgd	mfgd	ADJ
ejpam-6307	147	20	is	be	AUX
ejpam-6307	147	21	referred	refer	VERB
ejpam-6307	147	22	to	to	ADP
ejpam-6307	147	23	as	as	ADP
ejpam-6307	147	24	the	the	DET
ejpam-6307	147	25	fuzzy	fuzzy	ADJ
ejpam-6307	147	26	geodetic	geodetic	ADJ
ejpam-6307	147	27	spectrum	spectrum	NOUN
ejpam-6307	147	28	(	(	PUNCT
ejpam-6307	147	29	fg	fg	NOUN
ejpam-6307	147	30	-	-	NOUN
ejpam-6307	147	31	spectrum	spectrum	NOUN
ejpam-6307	147	32	)	)	PUNCT
ejpam-6307	147	33	of	of	ADP
ejpam-6307	147	34	g.	g.	PROPN
ejpam-6307	147	35	definition	definition	NOUN
ejpam-6307	147	36	14	14	NUM
ejpam-6307	147	37	.	.	PUNCT
ejpam-6307	148	1	the	the	PRON
ejpam-6307	148	2	fuzzy	fuzzy	ADJ
ejpam-6307	148	3	geodetic	geodetic	ADJ
ejpam-6307	148	4	spectral	spectral	ADJ
ejpam-6307	148	5	radius	radius	NOUN
ejpam-6307	148	6	(	(	PUNCT
ejpam-6307	148	7	fgsr	fgsr	NOUN
ejpam-6307	148	8	)	)	PUNCT
ejpam-6307	148	9	of	of	ADP
ejpam-6307	148	10	the	the	DET
ejpam-6307	148	11	matrixmfg	matrixmfg	NOUN
ejpam-6307	148	12	is	be	AUX
ejpam-6307	148	13	defined	define	VERB
ejpam-6307	148	14	as	as	ADP
ejpam-6307	148	15	the	the	DET
ejpam-6307	148	16	maximum	maximum	PROPN
ejpam-6307	148	17	eigenvalue	eigenvalue	NOUN
ejpam-6307	148	18	in	in	ADP
ejpam-6307	148	19	the	the	DET
ejpam-6307	148	20	fg	fg	NOUN
ejpam-6307	148	21	-	-	NOUN
ejpam-6307	148	22	spectrum	spectrum	NOUN
ejpam-6307	148	23	of	of	ADP
ejpam-6307	148	24	g.	g.	PROPN
ejpam-6307	148	25	definition	definition	NOUN
ejpam-6307	148	26	15	15	NUM
ejpam-6307	148	27	.	.	PUNCT
ejpam-6307	149	1	the	the	DET
ejpam-6307	149	2	fuzzy	fuzzy	ADJ
ejpam-6307	149	3	geodetic	geodetic	ADJ
ejpam-6307	149	4	energy	energy	NOUN
ejpam-6307	149	5	(	(	PUNCT
ejpam-6307	149	6	fg	fg	NOUN
ejpam-6307	149	7	-	-	NOUN
ejpam-6307	149	8	energy	energy	NOUN
ejpam-6307	149	9	or	or	CCONJ
ejpam-6307	149	10	fge(g	fge(g	PROPN
ejpam-6307	149	11	)	)	PUNCT
ejpam-6307	149	12	)	)	PUNCT
ejpam-6307	149	13	is	be	AUX
ejpam-6307	149	14	defined	define	VERB
ejpam-6307	149	15	as	as	ADP
ejpam-6307	149	16	the	the	DET
ejpam-6307	149	17	sum	sum	NOUN
ejpam-6307	149	18	of	of	ADP
ejpam-6307	149	19	the	the	DET
ejpam-6307	149	20	absolute	absolute	ADJ
ejpam-6307	149	21	values	value	NOUN
ejpam-6307	149	22	of	of	ADP
ejpam-6307	149	23	the	the	DET
ejpam-6307	149	24	fg	fg	NOUN
ejpam-6307	149	25	-	-	PUNCT
ejpam-6307	149	26	eigenvalues	eigenvalue	NOUN
ejpam-6307	149	27	of	of	ADP
ejpam-6307	149	28	the	the	DET
ejpam-6307	149	29	matrixmfgd	matrixmfgd	PROPN
ejpam-6307	149	30	.	.	PUNCT
ejpam-6307	150	1	example	example	NOUN
ejpam-6307	151	1	1	1	NUM
ejpam-6307	151	2	.	.	X
ejpam-6307	151	3	consider	consider	VERB
ejpam-6307	151	4	the	the	DET
ejpam-6307	151	5	fg	fg	PROPN
ejpam-6307	151	6	g	g	PROPN
ejpam-6307	151	7	=	=	SYM
ejpam-6307	151	8	(	(	PUNCT
ejpam-6307	151	9	v	v	NOUN
ejpam-6307	151	10	,	,	PUNCT
ejpam-6307	151	11	σ	σ	PROPN
ejpam-6307	151	12	,	,	PUNCT
ejpam-6307	151	13	µ	µ	NOUN
ejpam-6307	151	14	)	)	PUNCT
ejpam-6307	151	15	as	as	SCONJ
ejpam-6307	151	16	shown	show	VERB
ejpam-6307	151	17	in	in	ADP
ejpam-6307	151	18	figure	figure	NOUN
ejpam-6307	151	19	1	1	NUM
ejpam-6307	151	20	.	.	PUNCT
ejpam-6307	152	1	let	let	VERB
ejpam-6307	152	2	the	the	DET
ejpam-6307	152	3	fg	fg	NOUN
ejpam-6307	152	4	-	-	NOUN
ejpam-6307	152	5	matrix	matrix	NOUN
ejpam-6307	152	6	of	of	ADP
ejpam-6307	152	7	g	g	NOUN
ejpam-6307	152	8	,	,	PUNCT
ejpam-6307	152	9	corresponding	correspond	VERB
ejpam-6307	152	10	to	to	ADP
ejpam-6307	152	11	the	the	DET
ejpam-6307	152	12	vertex	vertex	NOUN
ejpam-6307	152	13	set	set	VERB
ejpam-6307	152	14	σ∗	σ∗	NOUN
ejpam-6307	152	15	=	=	SYM
ejpam-6307	152	16	{	{	PUNCT
ejpam-6307	152	17	v1	v1	PROPN
ejpam-6307	152	18	,	,	PUNCT
ejpam-6307	152	19	v2	v2	PROPN
ejpam-6307	152	20	,	,	PUNCT
ejpam-6307	152	21	v3	v3	PROPN
ejpam-6307	152	22	,	,	PUNCT
ejpam-6307	152	23	v4	v4	PROPN
ejpam-6307	152	24	}	}	PUNCT
ejpam-6307	152	25	,	,	PUNCT
ejpam-6307	152	26	be	be	AUX
ejpam-6307	152	27	given	give	VERB
ejpam-6307	152	28	as	as	SCONJ
ejpam-6307	152	29	follows:	follows:	NOUN
ejpam-6307	152	30	0.0	0.0	NUM
ejpam-6307	152	31	0.2	0.2	NUM
ejpam-6307	152	32	0.1	0.1	NUM
ejpam-6307	152	33	0.2	0.2	NUM
ejpam-6307	152	34	0.2	0.2	NUM
ejpam-6307	152	35	0.0	0.0	NUM
ejpam-6307	152	36	0.2	0.2	NUM
ejpam-6307	152	37	0.3	0.3	NUM
ejpam-6307	152	38	0.1	0.1	NUM
ejpam-6307	152	39	0.2	0.2	NUM
ejpam-6307	152	40	0.0	0.0	NUM
ejpam-6307	152	41	0.2	0.2	NUM
ejpam-6307	152	42	0.2	0.2	NUM
ejpam-6307	152	43	0.3	0.3	NUM
ejpam-6307	152	44	0.2	0.2	NUM
ejpam-6307	152	45	0.0	0.0	NUM
ejpam-6307	152	46	.	.	NOUN
ejpam-6307	152	47	figure	figure	NOUN
ejpam-6307	152	48	1	1	NUM
ejpam-6307	152	49	:	:	PUNCT
ejpam-6307	152	50	a	a	DET
ejpam-6307	152	51	fuzzy	fuzzy	ADJ
ejpam-6307	152	52	graph	graph	NOUN
ejpam-6307	152	53	with	with	ADP
ejpam-6307	152	54	fg	fg	NOUN
ejpam-6307	152	55	-	-	NOUN
ejpam-6307	152	56	spectrum	spectrum	NOUN
ejpam-6307	152	57	{	{	PUNCT
ejpam-6307	152	58	0.6123	0.6123	NUM
ejpam-6307	152	59	,	,	PUNCT
ejpam-6307	152	60	−0.3	−0.3	NUM
ejpam-6307	152	61	,	,	PUNCT
ejpam-6307	152	62	−0.2123	−0.2123	PROPN
ejpam-6307	152	63	,	,	PUNCT
ejpam-6307	152	64	−0.1	−0.1	PROPN
ejpam-6307	152	65	}	}	PUNCT
ejpam-6307	152	66	.	.	PUNCT
ejpam-6307	153	1	to	to	PART
ejpam-6307	153	2	compute	compute	VERB
ejpam-6307	153	3	the	the	DET
ejpam-6307	153	4	fg	fg	NOUN
ejpam-6307	153	5	-	-	NOUN
ejpam-6307	153	6	spectrum	spectrum	NOUN
ejpam-6307	153	7	of	of	ADP
ejpam-6307	153	8	g	g	NOUN
ejpam-6307	153	9	,	,	PUNCT
ejpam-6307	153	10	we	we	PRON
ejpam-6307	153	11	employ	employ	VERB
ejpam-6307	153	12	the	the	DET
ejpam-6307	153	13	classical	classical	ADJ
ejpam-6307	153	14	matrix	matrix	NOUN
ejpam-6307	153	15	theory	theory	NOUN
ejpam-6307	153	16	approach	approach	NOUN
ejpam-6307	153	17	:	:	PUNCT
ejpam-6307	153	18	the	the	DET
ejpam-6307	153	19	eigenvalues	eigenvalue	NOUN
ejpam-6307	153	20	of	of	ADP
ejpam-6307	153	21	the	the	DET
ejpam-6307	153	22	fg	fg	ADJ
ejpam-6307	153	23	-	-	PUNCT
ejpam-6307	153	24	matrix	matrix	NOUN
ejpam-6307	153	25	mfgd	mfgd	NOUN
ejpam-6307	153	26	are	be	AUX
ejpam-6307	153	27	obtained	obtain	VERB
ejpam-6307	153	28	by	by	ADP
ejpam-6307	153	29	solving	solve	VERB
ejpam-6307	153	30	the	the	DET
ejpam-6307	153	31	characteristic	characteristic	ADJ
ejpam-6307	153	32	polynomial	polynomial	ADJ
ejpam-6307	153	33	equation	equation	NOUN
ejpam-6307	153	34	det(λi	det(λi	VERB
ejpam-6307	153	35	−mfgd	−mfgd	X
ejpam-6307	153	36	)	)	PUNCT
ejpam-6307	154	1	=	=	SYM
ejpam-6307	154	2	0	0	NUM
ejpam-6307	154	3	,	,	PUNCT
ejpam-6307	154	4	(	(	PUNCT
ejpam-6307	154	5	1	1	X
ejpam-6307	154	6	)	)	PUNCT
ejpam-6307	154	7	where	where	SCONJ
ejpam-6307	154	8	i	i	PRON
ejpam-6307	154	9	denotes	denote	VERB
ejpam-6307	154	10	the	the	DET
ejpam-6307	154	11	identity	identity	NOUN
ejpam-6307	154	12	matrix	matrix	NOUN
ejpam-6307	154	13	of	of	ADP
ejpam-6307	154	14	order	order	NOUN
ejpam-6307	154	15	|σ∗|	|σ∗|	NUM
ejpam-6307	154	16	.	.	PUNCT
ejpam-6307	155	1	for	for	ADP
ejpam-6307	155	2	the	the	DET
ejpam-6307	155	3	present	present	ADJ
ejpam-6307	155	4	case	case	NOUN
ejpam-6307	155	5	,	,	PUNCT
ejpam-6307	155	6	solving	solve	VERB
ejpam-6307	155	7	(	(	PUNCT
ejpam-6307	155	8	1	1	X
ejpam-6307	155	9	)	)	PUNCT
ejpam-6307	155	10	yields	yield	VERB
ejpam-6307	155	11	the	the	DET
ejpam-6307	155	12	eigenvalues	eigenvalue	NOUN
ejpam-6307	155	13	,	,	PUNCT
ejpam-6307	155	14	λ1	λ1	PROPN
ejpam-6307	155	15	=	=	SYM
ejpam-6307	155	16	0.6123	0.6123	PROPN
ejpam-6307	155	17	,	,	PUNCT
ejpam-6307	155	18	λ2	λ2	NOUN
ejpam-6307	155	19	=	=	SYM
ejpam-6307	155	20	−0.3	−0.3	PROPN
ejpam-6307	155	21	,	,	PUNCT
ejpam-6307	155	22	λ3	λ3	PROPN
ejpam-6307	155	23	=	=	SYM
ejpam-6307	155	24	−0.2123	−0.2123	NOUN
ejpam-6307	155	25	,	,	PUNCT
ejpam-6307	155	26	λ4	λ4	PROPN
ejpam-6307	155	27	=	=	PUNCT
ejpam-6307	156	1	−0.1	−0.1	PROPN
ejpam-6307	156	2	.	.	PUNCT
ejpam-6307	157	1	thus	thus	ADV
ejpam-6307	157	2	,	,	PUNCT
ejpam-6307	157	3	the	the	DET
ejpam-6307	157	4	fg	fg	NOUN
ejpam-6307	157	5	-	-	NOUN
ejpam-6307	157	6	spectrum	spectrum	NOUN
ejpam-6307	157	7	of	of	ADP
ejpam-6307	157	8	g	g	PROPN
ejpam-6307	157	9	is	be	AUX
ejpam-6307	157	10	{	{	PUNCT
ejpam-6307	157	11	0.6123	0.6123	NUM
ejpam-6307	157	12	,	,	PUNCT
ejpam-6307	157	13	−0.3	−0.3	NUM
ejpam-6307	157	14	,	,	PUNCT
ejpam-6307	157	15	−0.2123	−0.2123	PROPN
ejpam-6307	157	16	,	,	PUNCT
ejpam-6307	157	17	−0.1	−0.1	PROPN
ejpam-6307	157	18	}	}	PUNCT
ejpam-6307	157	19	.	.	PUNCT
ejpam-6307	158	1	accordingly	accordingly	ADV
ejpam-6307	158	2	,	,	PUNCT
ejpam-6307	158	3	the	the	DET
ejpam-6307	158	4	fg	fg	NOUN
ejpam-6307	158	5	-	-	NOUN
ejpam-6307	158	6	energy	energy	NOUN
ejpam-6307	158	7	of	of	ADP
ejpam-6307	158	8	g	g	PROPN
ejpam-6307	158	9	is	be	AUX
ejpam-6307	158	10	evaluated	evaluate	VERB
ejpam-6307	158	11	as	as	ADP
ejpam-6307	158	12	,	,	PUNCT
ejpam-6307	158	13	fge(g	fge(g	PROPN
ejpam-6307	158	14	)	)	PUNCT
ejpam-6307	159	1	=	=	PUNCT
ejpam-6307	159	2	4∑	4∑	NUM
ejpam-6307	159	3	i=1	i=1	PROPN
ejpam-6307	159	4	|λi|	|λi|	X
ejpam-6307	159	5	=	=	SYM
ejpam-6307	159	6	0.6123	0.6123	NUM
ejpam-6307	159	7	+	+	CCONJ
ejpam-6307	159	8	0.3	0.3	NUM
ejpam-6307	159	9	+	+	NUM
ejpam-6307	159	10	0.2123	0.2123	NUM
ejpam-6307	159	11	+	+	CCONJ
ejpam-6307	159	12	0.1	0.1	NUM
ejpam-6307	159	13	=	=	SYM
ejpam-6307	159	14	1.2246	1.2246	NUM
ejpam-6307	159	15	.	.	PUNCT
ejpam-6307	160	1	r.	r.	PROPN
ejpam-6307	160	2	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	160	3	,	,	PUNCT
ejpam-6307	160	4	a.	a.	NOUN
ejpam-6307	160	5	m.	m.	PROPN
ejpam-6307	160	6	anto	anto	PROPN
ejpam-6307	160	7	,	,	PUNCT
ejpam-6307	160	8	v.	v.	PROPN
ejpam-6307	160	9	mary	mary	PROPN
ejpam-6307	160	10	mettilda	mettilda	PROPN
ejpam-6307	160	11	rose	rise	VERB
ejpam-6307	160	12	/	/	SYM
ejpam-6307	160	13	eur	eur	PROPN
ejpam-6307	160	14	.	.	PUNCT
ejpam-6307	161	1	j.	j.	PROPN
ejpam-6307	161	2	pure	pure	PROPN
ejpam-6307	161	3	appl	appl	PROPN
ejpam-6307	161	4	.	.	PROPN
ejpam-6307	161	5	math	math	PROPN
ejpam-6307	161	6	,	,	PUNCT
ejpam-6307	161	7	18	18	NUM
ejpam-6307	161	8	(	(	PUNCT
ejpam-6307	161	9	4	4	NUM
ejpam-6307	161	10	)	)	PUNCT
ejpam-6307	161	11	(	(	PUNCT
ejpam-6307	161	12	2025	2025	NUM
ejpam-6307	161	13	)	)	PUNCT
ejpam-6307	161	14	,	,	PUNCT
ejpam-6307	161	15	6307	6307	NUM
ejpam-6307	161	16	7	7	NUM
ejpam-6307	161	17	of	of	ADP
ejpam-6307	161	18	25	25	NUM
ejpam-6307	161	19	theorem	theorem	NOUN
ejpam-6307	161	20	4	4	NUM
ejpam-6307	161	21	.	.	PUNCT
ejpam-6307	162	1	let	let	VERB
ejpam-6307	162	2	g	g	PRON
ejpam-6307	162	3	be	be	AUX
ejpam-6307	162	4	an	an	DET
ejpam-6307	162	5	fg	fg	NOUN
ejpam-6307	162	6	with	with	ADP
ejpam-6307	162	7	|v|	|v|	PROPN
ejpam-6307	162	8	=	=	NOUN
ejpam-6307	162	9	m	m	NOUN
ejpam-6307	162	10	and	and	CCONJ
ejpam-6307	162	11	|e|	|e|	ADJ
ejpam-6307	162	12	=	=	PUNCT
ejpam-6307	162	13	n.	n.	PROPN
ejpam-6307	162	14	suppose	suppose	VERB
ejpam-6307	162	15	the	the	DET
ejpam-6307	162	16	fuzzy	fuzzy	ADJ
ejpam-6307	162	17	geodetic	geodetic	ADJ
ejpam-6307	162	18	distance	distance	NOUN
ejpam-6307	162	19	between	between	ADP
ejpam-6307	162	20	vertices	vertex	NOUN
ejpam-6307	162	21	vi	vi	PROPN
ejpam-6307	162	22	and	and	CCONJ
ejpam-6307	162	23	vj	vj	PROPN
ejpam-6307	162	24	is	be	AUX
ejpam-6307	162	25	given	give	VERB
ejpam-6307	162	26	by	by	ADP
ejpam-6307	162	27	df	df	PROPN
ejpam-6307	162	28	(	(	PUNCT
ejpam-6307	162	29	vi	vi	PROPN
ejpam-6307	162	30	,	,	PUNCT
ejpam-6307	162	31	vj	vj	ADJ
ejpam-6307	162	32	)	)	PUNCT
ejpam-6307	162	33	=	=	SYM
ejpam-6307	162	34	l(p	l(p	PROPN
ejpam-6307	162	35	)	)	PUNCT
ejpam-6307	162	36	×	×	NOUN
ejpam-6307	162	37	s(p	s(p	PROPN
ejpam-6307	162	38	)	)	PUNCT
ejpam-6307	163	1	=	=	SYM
ejpam-6307	163	2	dij	dij	VERB
ejpam-6307	163	3	,	,	PUNCT
ejpam-6307	163	4	and	and	CCONJ
ejpam-6307	163	5	let	let	VERB
ejpam-6307	163	6	mfgd	mfgd	PROPN
ejpam-6307	163	7	denote	denote	VERB
ejpam-6307	163	8	the	the	DET
ejpam-6307	163	9	fuzzy	fuzzy	ADJ
ejpam-6307	163	10	geodetic	geodetic	ADJ
ejpam-6307	163	11	distance	distance	NOUN
ejpam-6307	163	12	matrix	matrix	NOUN
ejpam-6307	163	13	.	.	PUNCT
ejpam-6307	164	1	then	then	ADV
ejpam-6307	164	2	,	,	PUNCT
ejpam-6307	164	3	the	the	DET
ejpam-6307	164	4	fuzzy	fuzzy	ADJ
ejpam-6307	164	5	geodetic	geodetic	ADJ
ejpam-6307	164	6	energy	energy	NOUN
ejpam-6307	164	7	fge(g	fge(g	PROPN
ejpam-6307	164	8	)	)	PUNCT
ejpam-6307	164	9	satisfies	satisfy	VERB
ejpam-6307	164	10	the	the	DET
ejpam-6307	164	11	following	follow	VERB
ejpam-6307	164	12	bounds	bound	NOUN
ejpam-6307	164	13	:	:	PUNCT
ejpam-6307	164	14	√	√	PROPN
ejpam-6307	164	15	2	2	NUM
ejpam-6307	164	16	∑	∑	PUNCT
ejpam-6307	164	17	i	i	PRON
ejpam-6307	164	18	<	<	X
ejpam-6307	164	19	j	j	X
ejpam-6307	164	20	(	(	PUNCT
ejpam-6307	164	21	dij)2	dij)2	PROPN
ejpam-6307	164	22	+	+	PROPN
ejpam-6307	164	23	m(m−	m(m−	PROPN
ejpam-6307	164	24	1)|mfgd	1)|mfgd	NUM
ejpam-6307	165	1	|	|	ADV
ejpam-6307	165	2	2	2	NUM
ejpam-6307	165	3	m	m	NOUN
ejpam-6307	165	4	≤	≤	NUM
ejpam-6307	165	5	fge(g	fge(g	PROPN
ejpam-6307	165	6	)	)	PUNCT
ejpam-6307	165	7	≤	≤	NOUN
ejpam-6307	165	8	√√√√√2	√√√√√2	ADV
ejpam-6307	165	9	∑	∑	VERB
ejpam-6307	165	10	i	i	X
ejpam-6307	165	11	<	<	X
ejpam-6307	165	12	j	j	X
ejpam-6307	165	13	(	(	PUNCT
ejpam-6307	165	14	dij)2	dij)2	PROPN
ejpam-6307	165	15	m	m	PROPN
ejpam-6307	165	16	.	.	PUNCT
ejpam-6307	166	1	proof	proof	NOUN
ejpam-6307	166	2	.	.	PUNCT
ejpam-6307	167	1	by	by	ADP
ejpam-6307	167	2	applying	apply	VERB
ejpam-6307	167	3	the	the	DET
ejpam-6307	167	4	cauchy	cauchy	NOUN
ejpam-6307	167	5	–	–	PUNCT
ejpam-6307	167	6	schwarz	schwarz	PROPN
ejpam-6307	167	7	inequality	inequality	NOUN
ejpam-6307	167	8	to	to	ADP
ejpam-6307	167	9	the	the	DET
ejpam-6307	167	10	number	number	NOUN
ejpam-6307	167	11	of	of	ADP
ejpam-6307	167	12	vertices	vertex	NOUN
ejpam-6307	167	13	and	and	CCONJ
ejpam-6307	167	14	the	the	DET
ejpam-6307	167	15	set	set	NOUN
ejpam-6307	167	16	of	of	ADP
ejpam-6307	167	17	absolute	absolute	ADJ
ejpam-6307	167	18	values	value	NOUN
ejpam-6307	167	19	of	of	ADP
ejpam-6307	167	20	the	the	DET
ejpam-6307	167	21	eigenvalues	eigenvalue	NOUN
ejpam-6307	167	22	,	,	PUNCT
ejpam-6307	167	23	m∑	m∑	CCONJ
ejpam-6307	167	24	i=1	i=1	PRON
ejpam-6307	167	25	|θi|	|θi|	PROPN
ejpam-6307	167	26	≤	≤	NOUN
ejpam-6307	167	27	√	√	PUNCT
ejpam-6307	167	28	m	m	NOUN
ejpam-6307	167	29	√√√√	√√√√	NOUN
ejpam-6307	167	30	m∑	m∑	NOUN
ejpam-6307	167	31	i=1	i=1	PROPN
ejpam-6307	167	32	|θi|2	|θi|2	PUNCT
ejpam-6307	167	33	.	.	PUNCT
ejpam-6307	168	1	(	(	PUNCT
ejpam-6307	168	2	2	2	X
ejpam-6307	168	3	)	)	PUNCT
ejpam-6307	168	4	(	(	PUNCT
ejpam-6307	168	5	m∑	m∑	INTJ
ejpam-6307	168	6	i=1	i=1	PROPN
ejpam-6307	168	7	θi	θi	NUM
ejpam-6307	168	8	)	)	PUNCT
ejpam-6307	168	9	2	2	NUM
ejpam-6307	168	10	=	=	SYM
ejpam-6307	168	11	m∑	m∑	NOUN
ejpam-6307	168	12	i=1	i=1	PRON
ejpam-6307	168	13	|θi|2	|θi|2	PUNCT
ejpam-6307	169	1	+	+	CCONJ
ejpam-6307	169	2	2	2	NUM
ejpam-6307	169	3	∑	∑	PROPN
ejpam-6307	169	4	i	i	PROPN
ejpam-6307	169	5	<	<	X
ejpam-6307	169	6	j	j	PROPN
ejpam-6307	169	7	θiθj	θiθj	PROPN
ejpam-6307	169	8	.	.	PUNCT
ejpam-6307	170	1	(	(	PUNCT
ejpam-6307	170	2	3	3	X
ejpam-6307	170	3	)	)	PUNCT
ejpam-6307	170	4	next	next	ADV
ejpam-6307	170	5	,	,	PUNCT
ejpam-6307	170	6	we	we	PRON
ejpam-6307	170	7	analyze	analyze	VERB
ejpam-6307	170	8	the	the	DET
ejpam-6307	170	9	coefficients	coefficient	NOUN
ejpam-6307	170	10	of	of	ADP
ejpam-6307	170	11	∏m	∏m	NOUN
ejpam-6307	170	12	i=1(θ	i=1(θ	PROPN
ejpam-6307	170	13	−	−	PROPN
ejpam-6307	170	14	θi	θi	NUM
ejpam-6307	170	15	)	)	PUNCT
ejpam-6307	170	16	=	=	SYM
ejpam-6307	170	17	|mfgd	|mfgd	ADJ
ejpam-6307	170	18	−	−	PROPN
ejpam-6307	170	19	θi|	θi|	PROPN
ejpam-6307	171	1	implies∑	implies∑	NOUN
ejpam-6307	171	2	i	i	PROPN
ejpam-6307	171	3	<	<	X
ejpam-6307	171	4	j	j	PROPN
ejpam-6307	171	5	θiθj	θiθj	PROPN
ejpam-6307	171	6	=	=	PUNCT
ejpam-6307	172	1	−	−	PROPN
ejpam-6307	172	2	∑	∑	PUNCT
ejpam-6307	173	1	i	i	PRON
ejpam-6307	173	2	<	<	X
ejpam-6307	173	3	j	j	PROPN
ejpam-6307	173	4	d	d	PROPN
ejpam-6307	173	5	2	2	NUM
ejpam-6307	173	6	ij	ij	NOUN
ejpam-6307	173	7	.	.	PUNCT
ejpam-6307	174	1	(	(	PUNCT
ejpam-6307	174	2	4	4	X
ejpam-6307	174	3	)	)	PUNCT
ejpam-6307	174	4	now	now	ADV
ejpam-6307	174	5	,	,	PUNCT
ejpam-6307	174	6	in	in	ADP
ejpam-6307	174	7	light	light	NOUN
ejpam-6307	174	8	of	of	ADP
ejpam-6307	174	9	equation	equation	NOUN
ejpam-6307	174	10	(	(	PUNCT
ejpam-6307	174	11	3	3	NUM
ejpam-6307	174	12	)	)	PUNCT
ejpam-6307	174	13	m∑	m∑	NOUN
ejpam-6307	174	14	i=1	i=1	PROPN
ejpam-6307	174	15	|θi|2	|θi|2	PUNCT
ejpam-6307	174	16	=	=	SYM
ejpam-6307	174	17	2	2	NUM
ejpam-6307	174	18	∑	∑	PUNCT
ejpam-6307	174	19	i	i	PRON
ejpam-6307	174	20	<	<	X
ejpam-6307	174	21	j	j	PROPN
ejpam-6307	174	22	(	(	PUNCT
ejpam-6307	174	23	dij	dij	PROPN
ejpam-6307	174	24	)	)	PUNCT
ejpam-6307	174	25	2	2	NUM
ejpam-6307	174	26	.	.	PUNCT
ejpam-6307	175	1	(	(	PUNCT
ejpam-6307	175	2	5	5	X
ejpam-6307	175	3	)	)	PUNCT
ejpam-6307	175	4	substituting	substitute	VERB
ejpam-6307	175	5	equation	equation	NOUN
ejpam-6307	175	6	(	(	PUNCT
ejpam-6307	175	7	5	5	NUM
ejpam-6307	175	8	)	)	PUNCT
ejpam-6307	175	9	into	into	ADP
ejpam-6307	175	10	equation	equation	NOUN
ejpam-6307	175	11	(	(	PUNCT
ejpam-6307	175	12	2	2	X
ejpam-6307	175	13	)	)	PUNCT
ejpam-6307	175	14	yields	yield	NOUN
ejpam-6307	175	15	m∑	m∑	VERB
ejpam-6307	175	16	i=1	i=1	PRON
ejpam-6307	175	17	|θi|	|θi|	PROPN
ejpam-6307	175	18	≤	≤	NUM
ejpam-6307	175	19	√	√	NUM
ejpam-6307	175	20	m	m	NOUN
ejpam-6307	175	21	√	√	NOUN
ejpam-6307	175	22	2	2	NUM
ejpam-6307	175	23	∑	∑	PROPN
ejpam-6307	175	24	i	i	PRON
ejpam-6307	175	25	<	<	X
ejpam-6307	175	26	j	j	PROPN
ejpam-6307	175	27	d	d	PROPN
ejpam-6307	175	28	2	2	NUM
ejpam-6307	175	29	ij	ij	NOUN
ejpam-6307	175	30	=	=	PUNCT
ejpam-6307	175	31	√√√√√2	√√√√√2	ADV
ejpam-6307	175	32	∑	∑	VERB
ejpam-6307	176	1	i	i	X
ejpam-6307	176	2	<	<	X
ejpam-6307	176	3	j	j	PROPN
ejpam-6307	176	4	d	d	PROPN
ejpam-6307	176	5	2	2	NUM
ejpam-6307	176	6	ij	ij	NOUN
ejpam-6307	176	7	m	m	PROPN
ejpam-6307	176	8	fge(g	fge(g	PROPN
ejpam-6307	176	9	)	)	PUNCT
ejpam-6307	176	10	≤	≤	NOUN
ejpam-6307	176	11	√√√√√2	√√√√√2	ADV
ejpam-6307	176	12	∑	∑	VERB
ejpam-6307	176	13	i	i	X
ejpam-6307	176	14	<	<	X
ejpam-6307	176	15	j	j	X
ejpam-6307	176	16	(	(	PUNCT
ejpam-6307	176	17	dij)2	dij)2	PROPN
ejpam-6307	176	18	m	m	PROPN
ejpam-6307	176	19	.	.	PUNCT
ejpam-6307	177	1	r.	r.	PROPN
ejpam-6307	177	2	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	177	3	,	,	PUNCT
ejpam-6307	177	4	a.	a.	NOUN
ejpam-6307	177	5	m.	m.	PROPN
ejpam-6307	177	6	anto	anto	PROPN
ejpam-6307	177	7	,	,	PUNCT
ejpam-6307	177	8	v.	v.	PROPN
ejpam-6307	177	9	mary	mary	PROPN
ejpam-6307	177	10	mettilda	mettilda	PROPN
ejpam-6307	177	11	rose	rise	VERB
ejpam-6307	177	12	/	/	SYM
ejpam-6307	177	13	eur	eur	PROPN
ejpam-6307	177	14	.	.	PUNCT
ejpam-6307	178	1	j.	j.	PROPN
ejpam-6307	178	2	pure	pure	PROPN
ejpam-6307	178	3	appl	appl	PROPN
ejpam-6307	178	4	.	.	PROPN
ejpam-6307	178	5	math	math	PROPN
ejpam-6307	178	6	,	,	PUNCT
ejpam-6307	178	7	18	18	NUM
ejpam-6307	178	8	(	(	PUNCT
ejpam-6307	178	9	4	4	NUM
ejpam-6307	178	10	)	)	PUNCT
ejpam-6307	178	11	(	(	PUNCT
ejpam-6307	178	12	2025	2025	NUM
ejpam-6307	178	13	)	)	PUNCT
ejpam-6307	178	14	,	,	PUNCT
ejpam-6307	178	15	6307	6307	NUM
ejpam-6307	178	16	8	8	NUM
ejpam-6307	178	17	of	of	ADP
ejpam-6307	178	18	25	25	NUM
ejpam-6307	178	19	regarding	regard	VERB
ejpam-6307	178	20	the	the	DET
ejpam-6307	178	21	second	second	ADJ
ejpam-6307	178	22	inequality	inequality	NOUN
ejpam-6307	178	23	,	,	PUNCT
ejpam-6307	178	24	we	we	PRON
ejpam-6307	178	25	have	have	VERB
ejpam-6307	178	26	[	[	X
ejpam-6307	178	27	fge(g)]2	fge(g)]2	X
ejpam-6307	179	1	=	=	SYM
ejpam-6307	180	1	(	(	PUNCT
ejpam-6307	180	2	m∑	m∑	INTJ
ejpam-6307	180	3	i=1	i=1	PROPN
ejpam-6307	180	4	θi	θi	NUM
ejpam-6307	180	5	)	)	PUNCT
ejpam-6307	180	6	2	2	NUM
ejpam-6307	180	7	=	=	SYM
ejpam-6307	180	8	m∑	m∑	NOUN
ejpam-6307	180	9	i=1	i=1	PRON
ejpam-6307	180	10	|θi|2	|θi|2	PUNCT
ejpam-6307	181	1	+	+	CCONJ
ejpam-6307	181	2	2	2	NUM
ejpam-6307	181	3	∑	∑	PROPN
ejpam-6307	181	4	i	i	PROPN
ejpam-6307	181	5	<	<	PROPN
ejpam-6307	181	6	j	j	PROPN
ejpam-6307	181	7	θiθj	θiθj	PROPN
ejpam-6307	181	8	≥	≥	NUM
ejpam-6307	181	9	2	2	NUM
ejpam-6307	181	10	∑	∑	PROPN
ejpam-6307	181	11	i	i	PRON
ejpam-6307	181	12	<	<	X
ejpam-6307	181	13	j	j	PROPN
ejpam-6307	181	14	(	(	PUNCT
ejpam-6307	181	15	dij	dij	PROPN
ejpam-6307	181	16	)	)	PUNCT
ejpam-6307	181	17	2	2	NUM
ejpam-6307	182	1	+	+	ADP
ejpam-6307	182	2	m(m−	m(m−	X
ejpam-6307	182	3	1)gm{|θiθj	1)gm{|θiθj	NUM
ejpam-6307	182	4	|	|	NOUN
ejpam-6307	182	5	}	}	PUNCT
ejpam-6307	182	6	=	=	VERB
ejpam-6307	182	7	⇒	⇒	NOUN
ejpam-6307	182	8	fge(g	fge(g	PROPN
ejpam-6307	182	9	)	)	PUNCT
ejpam-6307	182	10	≥	≥	NOUN
ejpam-6307	182	11	√	√	NUM
ejpam-6307	182	12	2	2	NUM
ejpam-6307	182	13	∑	∑	PROPN
ejpam-6307	182	14	i	i	PRON
ejpam-6307	182	15	<	<	X
ejpam-6307	182	16	j	j	X
ejpam-6307	182	17	(	(	PUNCT
ejpam-6307	182	18	dij)2	dij)2	PROPN
ejpam-6307	182	19	+	+	PROPN
ejpam-6307	182	20	m(m−	m(m−	X
ejpam-6307	182	21	1)gm{|θiθj	1)gm{|θiθj	NUM
ejpam-6307	182	22	|	|	ADV
ejpam-6307	182	23	}	}	PUNCT
ejpam-6307	182	24	.	.	PUNCT
ejpam-6307	183	1	but	but	CCONJ
ejpam-6307	183	2	,	,	PUNCT
ejpam-6307	183	3	gm{|θiθj	gm{|θiθj	PROPN
ejpam-6307	183	4	|	|	NOUN
ejpam-6307	183	5	}	}	PUNCT
ejpam-6307	183	6	=	=	SYM
ejpam-6307	183	7	∏	∏	NOUN
ejpam-6307	184	1	i	i	PRON
ejpam-6307	184	2	<	<	X
ejpam-6307	184	3	j	j	PROPN
ejpam-6307	184	4	|θiθj	|θiθj	VERB
ejpam-6307	184	5	|	|	INTJ
ejpam-6307	184	6			PROPN
ejpam-6307	184	7	2	2	NUM
ejpam-6307	184	8	m(m−1	m(m−1	NOUN
ejpam-6307	184	9	)	)	PUNCT
ejpam-6307	185	1	=	=	SYM
ejpam-6307	185	2	∏	∏	NOUN
ejpam-6307	186	1	i	i	PRON
ejpam-6307	186	2	<	<	X
ejpam-6307	186	3	j	j	PROPN
ejpam-6307	186	4	|θi|	|θi|	PROPN
ejpam-6307	186	5			PROPN
ejpam-6307	186	6	2	2	NUM
ejpam-6307	186	7	m	m	NOUN
ejpam-6307	186	8	=	=	NOUN
ejpam-6307	186	9	|mdf	|mdf	PROPN
ejpam-6307	186	10	|	|	NOUN
ejpam-6307	186	11	2	2	NUM
ejpam-6307	186	12	m	m	NOUN
ejpam-6307	186	13	.	.	PUNCT
ejpam-6307	187	1	now	now	ADV
ejpam-6307	187	2	,	,	PUNCT
ejpam-6307	187	3	fge(g	fge(g	PROPN
ejpam-6307	187	4	)	)	PUNCT
ejpam-6307	187	5	≥	≥	NOUN
ejpam-6307	188	1	√	√	NUM
ejpam-6307	188	2	2	2	NUM
ejpam-6307	188	3	∑	∑	PROPN
ejpam-6307	188	4	i	i	PRON
ejpam-6307	188	5	<	<	X
ejpam-6307	188	6	j	j	X
ejpam-6307	188	7	(	(	PUNCT
ejpam-6307	188	8	dij)2	dij)2	PROPN
ejpam-6307	188	9	+	+	PROPN
ejpam-6307	188	10	m(m−	m(m−	PROPN
ejpam-6307	188	11	1)|mfgd	1)|mfgd	NUM
ejpam-6307	188	12	|	|	ADV
ejpam-6307	188	13	2	2	NUM
ejpam-6307	188	14	m	m	NOUN
ejpam-6307	188	15	.	.	PUNCT
ejpam-6307	189	1	this	this	PRON
ejpam-6307	189	2	completes	complete	VERB
ejpam-6307	189	3	the	the	DET
ejpam-6307	189	4	proof	proof	NOUN
ejpam-6307	189	5	.	.	PUNCT
ejpam-6307	190	1	upper	upper	ADJ
ejpam-6307	190	2	bounds	bound	NOUN
ejpam-6307	190	3	for	for	ADP
ejpam-6307	190	4	the	the	DET
ejpam-6307	190	5	fg	fg	NOUN
ejpam-6307	190	6	-	-	NOUN
ejpam-6307	190	7	energy	energy	NOUN
ejpam-6307	190	8	of	of	ADP
ejpam-6307	190	9	an	an	DET
ejpam-6307	190	10	fg	fg	NOUN
ejpam-6307	190	11	can	can	AUX
ejpam-6307	190	12	be	be	AUX
ejpam-6307	190	13	derived	derive	VERB
ejpam-6307	190	14	using	use	VERB
ejpam-6307	190	15	the	the	DET
ejpam-6307	190	16	spectral	spectral	ADJ
ejpam-6307	190	17	radius	radius	NOUN
ejpam-6307	190	18	.	.	PUNCT
ejpam-6307	191	1	theorem	theorem	NOUN
ejpam-6307	191	2	5	5	NUM
ejpam-6307	191	3	.	.	PUNCT
ejpam-6307	192	1	let	let	VERB
ejpam-6307	192	2	g	g	PRON
ejpam-6307	192	3	be	be	AUX
ejpam-6307	192	4	an	an	DET
ejpam-6307	192	5	fg	fg	NOUN
ejpam-6307	192	6	with	with	ADP
ejpam-6307	192	7	m	m	PROPN
ejpam-6307	192	8	vertices	vertex	NOUN
ejpam-6307	192	9	,	,	PUNCT
ejpam-6307	192	10	and	and	CCONJ
ejpam-6307	192	11	let	let	VERB
ejpam-6307	192	12	ri	ri	PRON
ejpam-6307	192	13	denote	denote	VERB
ejpam-6307	192	14	the	the	DET
ejpam-6307	192	15	sum	sum	NOUN
ejpam-6307	192	16	of	of	ADP
ejpam-6307	192	17	the	the	DET
ejpam-6307	192	18	entries	entry	NOUN
ejpam-6307	192	19	in	in	ADP
ejpam-6307	192	20	the	the	DET
ejpam-6307	192	21	ith	ith	PROPN
ejpam-6307	192	22	row	row	NOUN
ejpam-6307	192	23	of	of	ADP
ejpam-6307	192	24	the	the	DET
ejpam-6307	192	25	fg	fg	NOUN
ejpam-6307	192	26	-	-	NOUN
ejpam-6307	192	27	matrix	matrix	NOUN
ejpam-6307	192	28	.	.	PUNCT
ejpam-6307	193	1	then	then	ADV
ejpam-6307	193	2	,	,	PUNCT
ejpam-6307	193	3	fge(g	fge(g	PROPN
ejpam-6307	193	4	)	)	PUNCT
ejpam-6307	193	5	≤	≤	NUM
ejpam-6307	193	6	m	m	VERB
ejpam-6307	193	7	max{ri	max{ri	ADV
ejpam-6307	193	8	}	}	PUNCT
ejpam-6307	193	9	,	,	PUNCT
ejpam-6307	193	10	1	1	NUM
ejpam-6307	193	11	≤	≤	NUM
ejpam-6307	193	12	i	i	PRON
ejpam-6307	193	13	≤	≤	ADJ
ejpam-6307	193	14	m.	m.	NOUN
ejpam-6307	193	15	proof	proof	NOUN
ejpam-6307	193	16	.	.	PUNCT
ejpam-6307	194	1	the	the	DET
ejpam-6307	194	2	fg	fg	NOUN
ejpam-6307	194	3	-	-	NOUN
ejpam-6307	194	4	matrix	matrix	NOUN
ejpam-6307	194	5	is	be	AUX
ejpam-6307	194	6	a	a	DET
ejpam-6307	194	7	non	non	ADJ
ejpam-6307	194	8	-	-	ADJ
ejpam-6307	194	9	negative	negative	ADJ
ejpam-6307	194	10	square	square	ADJ
ejpam-6307	194	11	matrix	matrix	NOUN
ejpam-6307	194	12	with	with	ADP
ejpam-6307	194	13	zero	zero	NUM
ejpam-6307	194	14	diagonal	diagonal	ADJ
ejpam-6307	194	15	entries	entry	NOUN
ejpam-6307	194	16	.	.	PUNCT
ejpam-6307	195	1	by	by	ADP
ejpam-6307	195	2	the	the	DET
ejpam-6307	195	3	properties	property	NOUN
ejpam-6307	195	4	of	of	ADP
ejpam-6307	195	5	non	non	ADJ
ejpam-6307	195	6	-	-	ADJ
ejpam-6307	195	7	negative	negative	ADJ
ejpam-6307	195	8	matrices	matrix	NOUN
ejpam-6307	195	9	,	,	PUNCT
ejpam-6307	195	10	the	the	DET
ejpam-6307	195	11	spectral	spectral	ADJ
ejpam-6307	195	12	radius	radius	NOUN
ejpam-6307	195	13	fgsr	fgsr	PROPN
ejpam-6307	195	14	satisfies	satisfy	VERB
ejpam-6307	195	15	min	min	PROPN
ejpam-6307	195	16	1≤i≤m	1≤i≤m	NUM
ejpam-6307	195	17	ri	ri	PROPN
ejpam-6307	195	18	≤	≤	PROPN
ejpam-6307	195	19	fgsr	fgsr	NOUN
ejpam-6307	195	20	≤	≤	PROPN
ejpam-6307	195	21	max	max	PROPN
ejpam-6307	195	22	1≤i≤m	1≤i≤m	NUM
ejpam-6307	195	23	ri	ri	NOUN
ejpam-6307	195	24	,	,	PUNCT
ejpam-6307	195	25	where	where	SCONJ
ejpam-6307	195	26	ri	ri	PROPN
ejpam-6307	195	27	is	be	AUX
ejpam-6307	195	28	the	the	DET
ejpam-6307	195	29	sum	sum	NOUN
ejpam-6307	195	30	of	of	ADP
ejpam-6307	195	31	the	the	DET
ejpam-6307	195	32	ith	ith	PROPN
ejpam-6307	195	33	row	row	NOUN
ejpam-6307	195	34	of	of	ADP
ejpam-6307	195	35	the	the	DET
ejpam-6307	195	36	fg	fg	NOUN
ejpam-6307	195	37	-	-	NOUN
ejpam-6307	195	38	matrix	matrix	NOUN
ejpam-6307	195	39	.	.	PUNCT
ejpam-6307	196	1	thus	thus	ADV
ejpam-6307	196	2	,	,	PUNCT
ejpam-6307	196	3	fgsr	fgsr	VERB
ejpam-6307	196	4	≤	≤	NUM
ejpam-6307	196	5	max	max	PROPN
ejpam-6307	196	6	1≤i≤m	1≤i≤m	NUM
ejpam-6307	196	7	ri	ri	NOUN
ejpam-6307	196	8	.	.	PUNCT
ejpam-6307	197	1	since	since	SCONJ
ejpam-6307	197	2	fge(g	fge(g	PROPN
ejpam-6307	197	3	)	)	PUNCT
ejpam-6307	197	4	is	be	AUX
ejpam-6307	197	5	the	the	DET
ejpam-6307	197	6	sum	sum	NOUN
ejpam-6307	197	7	of	of	ADP
ejpam-6307	197	8	the	the	DET
ejpam-6307	197	9	absolute	absolute	ADJ
ejpam-6307	197	10	values	value	NOUN
ejpam-6307	197	11	of	of	ADP
ejpam-6307	197	12	the	the	DET
ejpam-6307	197	13	eigenvalues	eigenvalue	NOUN
ejpam-6307	197	14	,	,	PUNCT
ejpam-6307	197	15	and	and	CCONJ
ejpam-6307	197	16	the	the	DET
ejpam-6307	197	17	spectral	spectral	ADJ
ejpam-6307	197	18	radius	radius	NOUN
ejpam-6307	197	19	bounds	bound	VERB
ejpam-6307	197	20	the	the	DET
ejpam-6307	197	21	largest	large	ADJ
ejpam-6307	197	22	absolute	absolute	ADJ
ejpam-6307	197	23	eigenvalue	eigenvalue	NOUN
ejpam-6307	197	24	,	,	PUNCT
ejpam-6307	197	25	it	it	PRON
ejpam-6307	197	26	follows	follow	VERB
ejpam-6307	197	27	that	that	SCONJ
ejpam-6307	197	28	fge(g	fge(g	PROPN
ejpam-6307	197	29	)	)	PUNCT
ejpam-6307	197	30	≤	≤	NUM
ejpam-6307	197	31	m	m	VERB
ejpam-6307	198	1	max	max	PROPN
ejpam-6307	198	2	1≤i≤m	1≤i≤m	NUM
ejpam-6307	198	3	ri	ri	PROPN
ejpam-6307	198	4	,	,	PUNCT
ejpam-6307	198	5	completing	complete	VERB
ejpam-6307	198	6	the	the	DET
ejpam-6307	198	7	proof	proof	NOUN
ejpam-6307	198	8	.	.	PUNCT
ejpam-6307	199	1	to	to	PART
ejpam-6307	199	2	establish	establish	VERB
ejpam-6307	199	3	a	a	DET
ejpam-6307	199	4	lower	low	ADJ
ejpam-6307	199	5	bound	bind	VERB
ejpam-6307	199	6	for	for	ADP
ejpam-6307	199	7	fge(g	fge(g	PROPN
ejpam-6307	199	8	)	)	PUNCT
ejpam-6307	199	9	,	,	PUNCT
ejpam-6307	199	10	a	a	DET
ejpam-6307	199	11	similar	similar	ADJ
ejpam-6307	199	12	approach	approach	NOUN
ejpam-6307	199	13	can	can	AUX
ejpam-6307	199	14	be	be	AUX
ejpam-6307	199	15	applied	apply	VERB
ejpam-6307	199	16	.	.	PUNCT
ejpam-6307	200	1	the	the	DET
ejpam-6307	200	2	following	follow	VERB
ejpam-6307	200	3	theorem	theorem	NOUN
ejpam-6307	200	4	presents	present	VERB
ejpam-6307	200	5	the	the	DET
ejpam-6307	200	6	equivalence	equivalence	NOUN
ejpam-6307	200	7	of	of	ADP
ejpam-6307	200	8	adjacency	adjacency	PROPN
ejpam-6307	200	9	energy	energy	NOUN
ejpam-6307	200	10	and	and	CCONJ
ejpam-6307	200	11	geodetic	geodetic	ADJ
ejpam-6307	200	12	energy	energy	NOUN
ejpam-6307	200	13	within	within	ADP
ejpam-6307	200	14	fuzzy	fuzzy	ADJ
ejpam-6307	200	15	geodetic	geodetic	ADJ
ejpam-6307	200	16	blocks	block	NOUN
ejpam-6307	200	17	.	.	PUNCT
ejpam-6307	201	1	r.	r.	PROPN
ejpam-6307	201	2	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	201	3	,	,	PUNCT
ejpam-6307	201	4	a.	a.	NOUN
ejpam-6307	201	5	m.	m.	PROPN
ejpam-6307	201	6	anto	anto	PROPN
ejpam-6307	201	7	,	,	PUNCT
ejpam-6307	201	8	v.	v.	PROPN
ejpam-6307	201	9	mary	mary	PROPN
ejpam-6307	201	10	mettilda	mettilda	PROPN
ejpam-6307	201	11	rose	rise	VERB
ejpam-6307	201	12	/	/	SYM
ejpam-6307	201	13	eur	eur	PROPN
ejpam-6307	201	14	.	.	PUNCT
ejpam-6307	202	1	j.	j.	PROPN
ejpam-6307	202	2	pure	pure	PROPN
ejpam-6307	202	3	appl	appl	PROPN
ejpam-6307	202	4	.	.	PROPN
ejpam-6307	202	5	math	math	PROPN
ejpam-6307	202	6	,	,	PUNCT
ejpam-6307	202	7	18	18	NUM
ejpam-6307	202	8	(	(	PUNCT
ejpam-6307	202	9	4	4	NUM
ejpam-6307	202	10	)	)	PUNCT
ejpam-6307	202	11	(	(	PUNCT
ejpam-6307	202	12	2025	2025	NUM
ejpam-6307	202	13	)	)	PUNCT
ejpam-6307	202	14	,	,	PUNCT
ejpam-6307	202	15	6307	6307	NUM
ejpam-6307	202	16	9	9	NUM
ejpam-6307	202	17	of	of	ADP
ejpam-6307	202	18	25	25	NUM
ejpam-6307	202	19	theorem	theorem	NOUN
ejpam-6307	202	20	6	6	NUM
ejpam-6307	202	21	.	.	PUNCT
ejpam-6307	203	1	let	let	VERB
ejpam-6307	203	2	g	g	PRON
ejpam-6307	203	3	be	be	AUX
ejpam-6307	203	4	a	a	DET
ejpam-6307	203	5	fuzzy	fuzzy	ADJ
ejpam-6307	203	6	geodetic	geodetic	ADJ
ejpam-6307	203	7	block	block	NOUN
ejpam-6307	203	8	graph	graph	NOUN
ejpam-6307	203	9	(	(	PUNCT
ejpam-6307	203	10	fgb	fgb	NOUN
ejpam-6307	203	11	)	)	PUNCT
ejpam-6307	203	12	.	.	PUNCT
ejpam-6307	204	1	then	then	ADV
ejpam-6307	204	2	,	,	PUNCT
ejpam-6307	204	3	the	the	DET
ejpam-6307	204	4	spectra	spectra	NOUN
ejpam-6307	204	5	of	of	ADP
ejpam-6307	204	6	the	the	DET
ejpam-6307	204	7	fgmatrix	fgmatrix	NOUN
ejpam-6307	204	8	and	and	CCONJ
ejpam-6307	204	9	the	the	DET
ejpam-6307	204	10	adjacency	adjacency	NOUN
ejpam-6307	204	11	matrix	matrix	NOUN
ejpam-6307	204	12	a	a	PRON
ejpam-6307	204	13	of	of	ADP
ejpam-6307	204	14	g	g	PROPN
ejpam-6307	204	15	coincide	coincide	NOUN
ejpam-6307	204	16	,	,	PUNCT
ejpam-6307	204	17	and	and	CCONJ
ejpam-6307	204	18	consequently	consequently	ADV
ejpam-6307	204	19	,	,	PUNCT
ejpam-6307	204	20	their	their	PRON
ejpam-6307	204	21	energies	energy	NOUN
ejpam-6307	204	22	are	be	AUX
ejpam-6307	204	23	equal	equal	ADJ
ejpam-6307	204	24	.	.	PUNCT
ejpam-6307	205	1	proof	proof	NOUN
ejpam-6307	205	2	.	.	PUNCT
ejpam-6307	206	1	assume	assume	VERB
ejpam-6307	206	2	g	g	PROPN
ejpam-6307	206	3	is	be	AUX
ejpam-6307	206	4	an	an	DET
ejpam-6307	206	5	fgb	fgb	NOUN
ejpam-6307	206	6	.	.	PUNCT
ejpam-6307	207	1	by	by	ADP
ejpam-6307	207	2	definition	definition	NOUN
ejpam-6307	207	3	,	,	PUNCT
ejpam-6307	207	4	the	the	DET
ejpam-6307	207	5	pair	pair	NOUN
ejpam-6307	207	6	{	{	PUNCT
ejpam-6307	207	7	vi	vi	PROPN
ejpam-6307	207	8	,	,	PUNCT
ejpam-6307	207	9	vj	vj	ADJ
ejpam-6307	207	10	}	}	PUNCT
ejpam-6307	207	11	is	be	AUX
ejpam-6307	207	12	fuzzy	fuzzy	ADJ
ejpam-6307	207	13	geodetic	geodetic	ADJ
ejpam-6307	207	14	convex	convex	NOUN
ejpam-6307	207	15	for	for	ADP
ejpam-6307	207	16	any	any	DET
ejpam-6307	207	17	two	two	NUM
ejpam-6307	207	18	vertices	vertex	NOUN
ejpam-6307	207	19	vi	vi	NOUN
ejpam-6307	207	20	and	and	CCONJ
ejpam-6307	207	21	vj	vj	INTJ
ejpam-6307	207	22	.	.	PUNCT
ejpam-6307	208	1	thus	thus	ADV
ejpam-6307	208	2	,	,	PUNCT
ejpam-6307	208	3	every	every	DET
ejpam-6307	208	4	edge	edge	NOUN
ejpam-6307	208	5	corresponds	correspond	VERB
ejpam-6307	208	6	to	to	ADP
ejpam-6307	208	7	a	a	DET
ejpam-6307	208	8	unique	unique	ADJ
ejpam-6307	208	9	fuzzy	fuzzy	ADJ
ejpam-6307	208	10	geodesic	geodesic	NOUN
ejpam-6307	208	11	,	,	PUNCT
ejpam-6307	208	12	implying	imply	VERB
ejpam-6307	208	13	that	that	SCONJ
ejpam-6307	208	14	all	all	DET
ejpam-6307	208	15	vertex	vertex	NOUN
ejpam-6307	208	16	pairs	pair	NOUN
ejpam-6307	208	17	are	be	AUX
ejpam-6307	208	18	adjacent	adjacent	ADJ
ejpam-6307	208	19	.	.	PUNCT
ejpam-6307	209	1	therefore	therefore	ADV
ejpam-6307	209	2	,	,	PUNCT
ejpam-6307	209	3	the	the	DET
ejpam-6307	209	4	adjacency	adjacency	NOUN
ejpam-6307	209	5	matrix	matrix	NOUN
ejpam-6307	209	6	a	a	PRON
ejpam-6307	209	7	and	and	CCONJ
ejpam-6307	209	8	the	the	DET
ejpam-6307	209	9	fuzzy	fuzzy	ADJ
ejpam-6307	209	10	geodetic	geodetic	ADJ
ejpam-6307	209	11	distance	distance	NOUN
ejpam-6307	209	12	matrix	matrix	NOUN
ejpam-6307	209	13	mfgd	mfgd	ADJ
ejpam-6307	209	14	coincide	coincide	NOUN
ejpam-6307	209	15	.	.	PUNCT
ejpam-6307	210	1	this	this	PRON
ejpam-6307	210	2	establishes	establish	VERB
ejpam-6307	210	3	the	the	DET
ejpam-6307	210	4	equivalence	equivalence	NOUN
ejpam-6307	210	5	of	of	ADP
ejpam-6307	210	6	their	their	PRON
ejpam-6307	210	7	spectra	spectra	NOUN
ejpam-6307	210	8	and	and	CCONJ
ejpam-6307	210	9	hence	hence	ADV
ejpam-6307	210	10	their	their	PRON
ejpam-6307	210	11	energies	energy	NOUN
ejpam-6307	210	12	.	.	PUNCT
ejpam-6307	211	1	3.1	3.1	NUM
ejpam-6307	211	2	.	.	PUNCT
ejpam-6307	211	3	geodesic	geodesic	ADJ
ejpam-6307	211	4	path	path	NOUN
ejpam-6307	211	5	identification	identification	NOUN
ejpam-6307	211	6	and	and	CCONJ
ejpam-6307	211	7	fuzzy	fuzzy	ADJ
ejpam-6307	211	8	geodetic	geodetic	ADJ
ejpam-6307	211	9	energy	energy	NOUN
ejpam-6307	211	10	algorithm	algorithm	NOUN
ejpam-6307	211	11	the	the	DET
ejpam-6307	211	12	pseudocode	pseudocode	PROPN
ejpam-6307	211	13	presented	present	VERB
ejpam-6307	211	14	below	below	ADP
ejpam-6307	211	15	offers	offer	VERB
ejpam-6307	211	16	a	a	DET
ejpam-6307	211	17	clear	clear	ADJ
ejpam-6307	211	18	and	and	CCONJ
ejpam-6307	211	19	systematic	systematic	ADJ
ejpam-6307	211	20	description	description	NOUN
ejpam-6307	211	21	of	of	ADP
ejpam-6307	211	22	the	the	DET
ejpam-6307	211	23	geodesic	geodesic	ADJ
ejpam-6307	211	24	path	path	NOUN
ejpam-6307	211	25	identification	identification	NOUN
ejpam-6307	211	26	process	process	NOUN
ejpam-6307	211	27	,	,	PUNCT
ejpam-6307	211	28	along	along	ADP
ejpam-6307	211	29	with	with	ADP
ejpam-6307	211	30	its	its	PRON
ejpam-6307	211	31	application	application	NOUN
ejpam-6307	211	32	in	in	ADP
ejpam-6307	211	33	constructing	construct	VERB
ejpam-6307	211	34	the	the	DET
ejpam-6307	211	35	fuzzy	fuzzy	ADJ
ejpam-6307	211	36	geodetic	geodetic	ADJ
ejpam-6307	211	37	distance	distance	NOUN
ejpam-6307	211	38	matrix	matrix	NOUN
ejpam-6307	211	39	,	,	PUNCT
ejpam-6307	211	40	spectrum	spectrum	NOUN
ejpam-6307	211	41	,	,	PUNCT
ejpam-6307	211	42	and	and	CCONJ
ejpam-6307	211	43	energy	energy	NOUN
ejpam-6307	211	44	.	.	PUNCT
ejpam-6307	212	1	input	input	NOUN
ejpam-6307	212	2	:	:	PUNCT
ejpam-6307	212	3	a	a	DET
ejpam-6307	212	4	fuzzy	fuzzy	ADJ
ejpam-6307	212	5	graph	graph	NOUN
ejpam-6307	212	6	g	g	PROPN
ejpam-6307	212	7	=	=	SYM
ejpam-6307	212	8	(	(	PUNCT
ejpam-6307	212	9	v	v	NOUN
ejpam-6307	212	10	,	,	PUNCT
ejpam-6307	212	11	σ	σ	PROPN
ejpam-6307	212	12	,	,	PUNCT
ejpam-6307	212	13	µ	µ	NOUN
ejpam-6307	212	14	)	)	PUNCT
ejpam-6307	212	15	with	with	ADP
ejpam-6307	212	16	vertex	vertex	NOUN
ejpam-6307	212	17	set	set	VERB
ejpam-6307	212	18	v	v	NOUN
ejpam-6307	212	19	=	=	SYM
ejpam-6307	212	20	{	{	PUNCT
ejpam-6307	212	21	v1	v1	PROPN
ejpam-6307	212	22	,	,	PUNCT
ejpam-6307	212	23	v2	v2	PROPN
ejpam-6307	212	24	,	,	PUNCT
ejpam-6307	212	25	.	.	PUNCT
ejpam-6307	212	26	.	.	PUNCT
ejpam-6307	212	27	.	.	PUNCT
ejpam-6307	213	1	,	,	PUNCT
ejpam-6307	213	2	vn	vn	NOUN
ejpam-6307	213	3	}	}	PUNCT
ejpam-6307	213	4	and	and	CCONJ
ejpam-6307	213	5	fuzzy	fuzzy	ADJ
ejpam-6307	213	6	edge	edge	NOUN
ejpam-6307	213	7	weights	weight	NOUN
ejpam-6307	213	8	µ	µ	PRON
ejpam-6307	213	9	output	output	NOUN
ejpam-6307	213	10	:	:	PUNCT
ejpam-6307	213	11	fuzzy	fuzzy	ADJ
ejpam-6307	213	12	geodesic	geodesic	ADJ
ejpam-6307	213	13	paths	path	NOUN
ejpam-6307	213	14	,	,	PUNCT
ejpam-6307	213	15	fuzzy	fuzzy	ADJ
ejpam-6307	213	16	geodetic	geodetic	ADJ
ejpam-6307	213	17	distance	distance	NOUN
ejpam-6307	213	18	matrix	matrix	NOUN
ejpam-6307	213	19	mfgd	mfgd	ADJ
ejpam-6307	213	20	,	,	PUNCT
ejpam-6307	213	21	fuzzy	fuzzy	ADJ
ejpam-6307	213	22	geodetic	geodetic	ADJ
ejpam-6307	213	23	spectrum	spectrum	NOUN
ejpam-6307	213	24	,	,	PUNCT
ejpam-6307	213	25	and	and	CCONJ
ejpam-6307	213	26	fuzzy	fuzzy	ADJ
ejpam-6307	213	27	geodetic	geodetic	ADJ
ejpam-6307	213	28	energy	energy	NOUN
ejpam-6307	213	29	(	(	PUNCT
ejpam-6307	213	30	i	i	NOUN
ejpam-6307	213	31	)	)	PUNCT
ejpam-6307	213	32	initialize	initialize	VERB
ejpam-6307	213	33	an	an	DET
ejpam-6307	213	34	n×	n×	PROPN
ejpam-6307	213	35	n	n	ADV
ejpam-6307	213	36	matrixmfgd	matrixmfgd	ADJ
ejpam-6307	213	37	with	with	ADP
ejpam-6307	213	38	zeros	zero	NOUN
ejpam-6307	213	39	.	.	PUNCT
ejpam-6307	214	1	(	(	PUNCT
ejpam-6307	214	2	ii	ii	NOUN
ejpam-6307	214	3	)	)	PUNCT
ejpam-6307	214	4	for	for	ADP
ejpam-6307	214	5	each	each	DET
ejpam-6307	214	6	unique	unique	ADJ
ejpam-6307	214	7	unordered	unordered	ADJ
ejpam-6307	214	8	vertex	vertex	NOUN
ejpam-6307	214	9	pair	pair	NOUN
ejpam-6307	214	10	(	(	PUNCT
ejpam-6307	214	11	vi	vi	PROPN
ejpam-6307	214	12	,	,	PUNCT
ejpam-6307	214	13	vj	vj	PROPN
ejpam-6307	214	14	):	):	PUNCT
ejpam-6307	214	15	(	(	PUNCT
ejpam-6307	214	16	a	a	X
ejpam-6307	214	17	)	)	PUNCT
ejpam-6307	214	18	generate	generate	VERB
ejpam-6307	214	19	all	all	DET
ejpam-6307	214	20	possible	possible	ADJ
ejpam-6307	214	21	paths	path	NOUN
ejpam-6307	214	22	p	p	NOUN
ejpam-6307	214	23	between	between	ADP
ejpam-6307	214	24	vi	vi	PROPN
ejpam-6307	214	25	and	and	CCONJ
ejpam-6307	214	26	vj	vj	INTJ
ejpam-6307	214	27	.	.	PUNCT
ejpam-6307	215	1	(	(	PUNCT
ejpam-6307	215	2	b	b	X
ejpam-6307	215	3	)	)	PUNCT
ejpam-6307	215	4	for	for	ADP
ejpam-6307	215	5	each	each	DET
ejpam-6307	215	6	path	path	NOUN
ejpam-6307	215	7	p	p	X
ejpam-6307	215	8	:	:	PUNCT
ejpam-6307	215	9	i.	i.	PROPN
ejpam-6307	215	10	compute	compute	VERB
ejpam-6307	215	11	the	the	DET
ejpam-6307	215	12	path	path	NOUN
ejpam-6307	215	13	length	length	NOUN
ejpam-6307	215	14	l(p	l(p	NOUN
ejpam-6307	215	15	)	)	PUNCT
ejpam-6307	216	1	=	=	NOUN
ejpam-6307	216	2	number	number	NOUN
ejpam-6307	216	3	of	of	ADP
ejpam-6307	216	4	edges	edge	NOUN
ejpam-6307	216	5	in	in	ADP
ejpam-6307	216	6	p.	p.	PROPN
ejpam-6307	216	7	ii	ii	PROPN
ejpam-6307	216	8	.	.	PUNCT
ejpam-6307	217	1	compute	compute	VERB
ejpam-6307	217	2	the	the	DET
ejpam-6307	217	3	path	path	NOUN
ejpam-6307	217	4	strength	strength	NOUN
ejpam-6307	217	5	s(p	s(p	PROPN
ejpam-6307	217	6	)	)	PUNCT
ejpam-6307	218	1	=	=	SYM
ejpam-6307	218	2	min{µ(e	min{µ(e	PROPN
ejpam-6307	218	3	)	)	PUNCT
ejpam-6307	218	4	:	:	PUNCT
ejpam-6307	219	1	e	e	X
ejpam-6307	219	2	∈	∈	PROPN
ejpam-6307	219	3	p	p	X
ejpam-6307	219	4	}	}	PUNCT
ejpam-6307	219	5	.	.	PUNCT
ejpam-6307	220	1	(	(	PUNCT
ejpam-6307	220	2	c	c	X
ejpam-6307	220	3	)	)	PUNCT
ejpam-6307	220	4	determine	determine	VERB
ejpam-6307	220	5	the	the	DET
ejpam-6307	220	6	fuzzy	fuzzy	ADJ
ejpam-6307	220	7	geodetic	geodetic	ADJ
ejpam-6307	220	8	distance	distance	NOUN
ejpam-6307	220	9	:	:	PUNCT
ejpam-6307	220	10	df	df	PROPN
ejpam-6307	220	11	(	(	PUNCT
ejpam-6307	220	12	vi	vi	PROPN
ejpam-6307	220	13	,	,	PUNCT
ejpam-6307	220	14	vj	vj	ADJ
ejpam-6307	220	15	)	)	PUNCT
ejpam-6307	220	16	=	=	SYM
ejpam-6307	220	17	min	min	NOUN
ejpam-6307	220	18	p	p	NOUN
ejpam-6307	220	19	{	{	PUNCT
ejpam-6307	220	20	l(p)×	l(p)×	PROPN
ejpam-6307	220	21	s(p	s(p	PROPN
ejpam-6307	220	22	)	)	PUNCT
ejpam-6307	220	23	}	}	PUNCT
ejpam-6307	220	24	.	.	PUNCT
ejpam-6307	221	1	(	(	PUNCT
ejpam-6307	221	2	d	d	X
ejpam-6307	221	3	)	)	PUNCT
ejpam-6307	221	4	assignmfgd	assignmfgd	VERB
ejpam-6307	221	5	[	[	X
ejpam-6307	221	6	i][j]←	i][j]←	X
ejpam-6307	221	7	df	df	PROPN
ejpam-6307	221	8	(	(	PUNCT
ejpam-6307	221	9	vi	vi	PROPN
ejpam-6307	221	10	,	,	PUNCT
ejpam-6307	221	11	vj	vj	NOUN
ejpam-6307	221	12	)	)	PUNCT
ejpam-6307	221	13	.	.	PUNCT
ejpam-6307	222	1	(	(	PUNCT
ejpam-6307	222	2	iii	iii	NOUN
ejpam-6307	222	3	)	)	PUNCT
ejpam-6307	222	4	after	after	ADP
ejpam-6307	222	5	processing	process	VERB
ejpam-6307	222	6	every	every	DET
ejpam-6307	222	7	pair	pair	NOUN
ejpam-6307	222	8	,	,	PUNCT
ejpam-6307	222	9	mfgd	mfgd	PROPN
ejpam-6307	222	10	represents	represent	VERB
ejpam-6307	222	11	the	the	DET
ejpam-6307	222	12	fuzzy	fuzzy	ADJ
ejpam-6307	222	13	geodetic	geodetic	ADJ
ejpam-6307	222	14	distance	distance	NOUN
ejpam-6307	222	15	matrix	matrix	NOUN
ejpam-6307	222	16	.	.	PUNCT
ejpam-6307	223	1	(	(	PUNCT
ejpam-6307	223	2	iv	iv	X
ejpam-6307	223	3	)	)	PUNCT
ejpam-6307	223	4	evaluate	evaluate	VERB
ejpam-6307	223	5	the	the	DET
ejpam-6307	223	6	eigenvalues	eigenvalue	NOUN
ejpam-6307	223	7	{	{	PUNCT
ejpam-6307	223	8	λ1	λ1	ADJ
ejpam-6307	223	9	,	,	PUNCT
ejpam-6307	223	10	λ2	λ2	NOUN
ejpam-6307	223	11	,	,	PUNCT
ejpam-6307	223	12	.	.	PUNCT
ejpam-6307	223	13	.	.	PUNCT
ejpam-6307	224	1	.	.	PUNCT
ejpam-6307	225	1	,	,	PUNCT
ejpam-6307	225	2	λn	λn	NOUN
ejpam-6307	225	3	}	}	PUNCT
ejpam-6307	225	4	ofmfgd	ofmfgd	ADJ
ejpam-6307	225	5	.	.	PUNCT
ejpam-6307	226	1	(	(	PUNCT
ejpam-6307	226	2	v	v	NOUN
ejpam-6307	226	3	)	)	PUNCT
ejpam-6307	226	4	define	define	VERB
ejpam-6307	226	5	the	the	DET
ejpam-6307	226	6	fuzzy	fuzzy	ADJ
ejpam-6307	226	7	geodetic	geodetic	ADJ
ejpam-6307	226	8	spectrum	spectrum	NOUN
ejpam-6307	226	9	as	as	ADP
ejpam-6307	226	10	:	:	PUNCT
ejpam-6307	226	11	fg	fg	ADJ
ejpam-6307	226	12	-	-	NOUN
ejpam-6307	226	13	spectrum	spectrum	NOUN
ejpam-6307	226	14	=	=	SYM
ejpam-6307	226	15	{	{	PUNCT
ejpam-6307	226	16	λ1	λ1	ADJ
ejpam-6307	226	17	,	,	PUNCT
ejpam-6307	226	18	λ2	λ2	NOUN
ejpam-6307	226	19	,	,	PUNCT
ejpam-6307	226	20	.	.	PUNCT
ejpam-6307	226	21	.	.	PUNCT
ejpam-6307	227	1	.	.	PUNCT
ejpam-6307	228	1	,	,	PUNCT
ejpam-6307	228	2	λn	λn	NOUN
ejpam-6307	228	3	}	}	PUNCT
ejpam-6307	228	4	.	.	PUNCT
ejpam-6307	229	1	r.	r.	PROPN
ejpam-6307	229	2	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	229	3	,	,	PUNCT
ejpam-6307	229	4	a.	a.	NOUN
ejpam-6307	229	5	m.	m.	PROPN
ejpam-6307	229	6	anto	anto	PROPN
ejpam-6307	229	7	,	,	PUNCT
ejpam-6307	229	8	v.	v.	PROPN
ejpam-6307	229	9	mary	mary	PROPN
ejpam-6307	229	10	mettilda	mettilda	PROPN
ejpam-6307	229	11	rose	rise	VERB
ejpam-6307	229	12	/	/	SYM
ejpam-6307	229	13	eur	eur	PROPN
ejpam-6307	229	14	.	.	PUNCT
ejpam-6307	230	1	j.	j.	PROPN
ejpam-6307	230	2	pure	pure	PROPN
ejpam-6307	230	3	appl	appl	PROPN
ejpam-6307	230	4	.	.	PROPN
ejpam-6307	230	5	math	math	PROPN
ejpam-6307	230	6	,	,	PUNCT
ejpam-6307	230	7	18	18	NUM
ejpam-6307	230	8	(	(	PUNCT
ejpam-6307	230	9	4	4	NUM
ejpam-6307	230	10	)	)	PUNCT
ejpam-6307	230	11	(	(	PUNCT
ejpam-6307	230	12	2025	2025	NUM
ejpam-6307	230	13	)	)	PUNCT
ejpam-6307	230	14	,	,	PUNCT
ejpam-6307	230	15	6307	6307	NUM
ejpam-6307	230	16	10	10	NUM
ejpam-6307	230	17	of	of	ADP
ejpam-6307	230	18	25	25	NUM
ejpam-6307	230	19	(	(	PUNCT
ejpam-6307	230	20	vi	vi	NOUN
ejpam-6307	230	21	)	)	PUNCT
ejpam-6307	230	22	determine	determine	VERB
ejpam-6307	230	23	the	the	DET
ejpam-6307	230	24	fuzzy	fuzzy	ADJ
ejpam-6307	230	25	geodetic	geodetic	ADJ
ejpam-6307	230	26	energy	energy	NOUN
ejpam-6307	230	27	:	:	PUNCT
ejpam-6307	230	28	fge(g	fge(g	PROPN
ejpam-6307	230	29	)	)	PUNCT
ejpam-6307	231	1	=	=	SYM
ejpam-6307	232	1	n∑	n∑	PROPN
ejpam-6307	232	2	i=1	i=1	PROPN
ejpam-6307	232	3	|λi|	|λi|	PROPN
ejpam-6307	232	4	.	.	PUNCT
ejpam-6307	233	1	(	(	PUNCT
ejpam-6307	233	2	vii	vii	PROPN
ejpam-6307	233	3	)	)	PUNCT
ejpam-6307	233	4	display	display	NOUN
ejpam-6307	233	5	the	the	DET
ejpam-6307	233	6	identified	identify	VERB
ejpam-6307	233	7	geodesic	geodesic	NOUN
ejpam-6307	233	8	paths	path	NOUN
ejpam-6307	233	9	,	,	PUNCT
ejpam-6307	233	10	the	the	DET
ejpam-6307	233	11	constructed	constructed	ADJ
ejpam-6307	233	12	fg	fg	NOUN
ejpam-6307	233	13	-	-	NOUN
ejpam-6307	233	14	matrix	matrix	NOUN
ejpam-6307	233	15	,	,	PUNCT
ejpam-6307	233	16	its	its	PRON
ejpam-6307	233	17	spectrum	spectrum	NOUN
ejpam-6307	233	18	,	,	PUNCT
ejpam-6307	233	19	and	and	CCONJ
ejpam-6307	233	20	the	the	DET
ejpam-6307	233	21	computed	computed	ADJ
ejpam-6307	233	22	energy	energy	NOUN
ejpam-6307	233	23	.	.	PUNCT
ejpam-6307	234	1	4	4	X
ejpam-6307	234	2	.	.	X
ejpam-6307	234	3	fuzzy	fuzzy	ADJ
ejpam-6307	234	4	detour	detour	NOUN
ejpam-6307	234	5	spectrum	spectrum	NOUN
ejpam-6307	234	6	in	in	ADP
ejpam-6307	234	7	fuzzy	fuzzy	ADJ
ejpam-6307	234	8	graph	graph	NOUN
ejpam-6307	234	9	theory	theory	NOUN
ejpam-6307	234	10	,	,	PUNCT
ejpam-6307	234	11	nagoorgani	nagoorgani	PROPN
ejpam-6307	234	12	and	and	CCONJ
ejpam-6307	234	13	umamaheswari	umamaheswari	PROPN
ejpam-6307	234	14	introduced	introduce	VERB
ejpam-6307	234	15	the	the	DET
ejpam-6307	234	16	fuzzy	fuzzy	ADJ
ejpam-6307	234	17	detour	detour	NOUN
ejpam-6307	234	18	µ-distance	µ-distance	NOUN
ejpam-6307	234	19	and	and	CCONJ
ejpam-6307	234	20	examined	examine	VERB
ejpam-6307	234	21	its	its	PRON
ejpam-6307	234	22	fundamental	fundamental	ADJ
ejpam-6307	234	23	properties	property	NOUN
ejpam-6307	234	24	.	.	PUNCT
ejpam-6307	235	1	later	later	ADV
ejpam-6307	235	2	,	,	PUNCT
ejpam-6307	235	3	rajesh	rajesh	PROPN
ejpam-6307	235	4	and	and	CCONJ
ejpam-6307	235	5	anto	anto	PROPN
ejpam-6307	235	6	explored	explore	VERB
ejpam-6307	235	7	detour	detour	PRON
ejpam-6307	235	8	convexity	convexity	NOUN
ejpam-6307	235	9	properties	property	NOUN
ejpam-6307	235	10	.	.	PUNCT
ejpam-6307	236	1	extending	extend	VERB
ejpam-6307	236	2	this	this	DET
ejpam-6307	236	3	framework	framework	NOUN
ejpam-6307	236	4	,	,	PUNCT
ejpam-6307	236	5	we	we	PRON
ejpam-6307	236	6	investigate	investigate	VERB
ejpam-6307	236	7	the	the	DET
ejpam-6307	236	8	fuzzy	fuzzy	ADJ
ejpam-6307	236	9	detour	detour	NOUN
ejpam-6307	236	10	energy	energy	NOUN
ejpam-6307	236	11	derived	derive	VERB
ejpam-6307	236	12	from	from	ADP
ejpam-6307	236	13	the	the	DET
ejpam-6307	236	14	spectrum	spectrum	NOUN
ejpam-6307	236	15	of	of	ADP
ejpam-6307	236	16	the	the	DET
ejpam-6307	236	17	fuzzy	fuzzy	ADJ
ejpam-6307	236	18	detour	detour	NOUN
ejpam-6307	236	19	distance	distance	NOUN
ejpam-6307	236	20	matrix	matrix	NOUN
ejpam-6307	236	21	.	.	PUNCT
ejpam-6307	237	1	this	this	DET
ejpam-6307	237	2	development	development	NOUN
ejpam-6307	237	3	enriches	enrich	VERB
ejpam-6307	237	4	the	the	DET
ejpam-6307	237	5	spectral	spectral	ADJ
ejpam-6307	237	6	analysis	analysis	NOUN
ejpam-6307	237	7	of	of	ADP
ejpam-6307	237	8	fuzzy	fuzzy	ADJ
ejpam-6307	237	9	graphs	graph	NOUN
ejpam-6307	237	10	by	by	ADP
ejpam-6307	237	11	incorporating	incorporate	VERB
ejpam-6307	237	12	long	long	ADJ
ejpam-6307	237	13	-	-	PUNCT
ejpam-6307	237	14	path	path	NOUN
ejpam-6307	237	15	distance	distance	NOUN
ejpam-6307	237	16	measures	measure	NOUN
ejpam-6307	237	17	under	under	ADP
ejpam-6307	237	18	fuzziness	fuzziness	NOUN
ejpam-6307	237	19	,	,	PUNCT
ejpam-6307	237	20	leading	lead	VERB
ejpam-6307	237	21	to	to	ADP
ejpam-6307	237	22	new	new	ADJ
ejpam-6307	237	23	bounds	bound	NOUN
ejpam-6307	237	24	and	and	CCONJ
ejpam-6307	237	25	structural	structural	ADJ
ejpam-6307	237	26	insights	insight	NOUN
ejpam-6307	237	27	.	.	PUNCT
ejpam-6307	238	1	definition	definition	NOUN
ejpam-6307	238	2	16	16	NUM
ejpam-6307	238	3	.	.	PUNCT
ejpam-6307	239	1	the	the	DET
ejpam-6307	239	2	fuzzy	fuzzy	ADJ
ejpam-6307	239	3	detour	detour	NOUN
ejpam-6307	239	4	distance	distance	NOUN
ejpam-6307	239	5	matrix	matrix	NOUN
ejpam-6307	239	6	(	(	PUNCT
ejpam-6307	239	7	fd	fd	X
ejpam-6307	239	8	matrix	matrix	NOUN
ejpam-6307	239	9	)	)	PUNCT
ejpam-6307	239	10	of	of	ADP
ejpam-6307	239	11	g	g	NOUN
ejpam-6307	239	12	with	with	ADP
ejpam-6307	239	13	σ∗	σ∗	NOUN
ejpam-6307	239	14	=	=	SYM
ejpam-6307	239	15	{	{	PUNCT
ejpam-6307	239	16	v1	v1	PROPN
ejpam-6307	239	17	,	,	PUNCT
ejpam-6307	239	18	v2	v2	PROPN
ejpam-6307	239	19	,	,	PUNCT
ejpam-6307	239	20	...	...	PUNCT
ejpam-6307	239	21	..	..	PUNCT
ejpam-6307	240	1	vm	vm	X
ejpam-6307	240	2	}	}	PUNCT
ejpam-6307	240	3	is	be	AUX
ejpam-6307	240	4	an	an	DET
ejpam-6307	240	5	m×m	m×m	ADJ
ejpam-6307	240	6	matrix	matrix	NOUN
ejpam-6307	240	7	mfdd	mfdd	NOUN
ejpam-6307	240	8	=	=	PUNCT
ejpam-6307	241	1	[	[	X
ejpam-6307	241	2	cij	cij	PROPN
ejpam-6307	241	3	]	]	PUNCT
ejpam-6307	241	4	where	where	SCONJ
ejpam-6307	241	5	cij	cij	PROPN
ejpam-6307	241	6	=	=	SYM
ejpam-6307	241	7	∆(vi	∆(vi	PROPN
ejpam-6307	241	8	,	,	PUNCT
ejpam-6307	241	9	vj	vj	NOUN
ejpam-6307	241	10	)	)	PUNCT
ejpam-6307	241	11	.	.	PUNCT
ejpam-6307	242	1	the	the	DET
ejpam-6307	242	2	fuzzy	fuzzy	ADJ
ejpam-6307	242	3	detour	detour	NOUN
ejpam-6307	242	4	energy	energy	NOUN
ejpam-6307	242	5	(	(	PUNCT
ejpam-6307	242	6	fd	fd	NOUN
ejpam-6307	242	7	-	-	PUNCT
ejpam-6307	242	8	energy	energy	NOUN
ejpam-6307	242	9	)	)	PUNCT
ejpam-6307	242	10	is	be	AUX
ejpam-6307	242	11	the	the	DET
ejpam-6307	242	12	sum	sum	NOUN
ejpam-6307	242	13	of	of	ADP
ejpam-6307	242	14	the	the	DET
ejpam-6307	242	15	absolute	absolute	ADJ
ejpam-6307	242	16	values	value	NOUN
ejpam-6307	242	17	of	of	ADP
ejpam-6307	242	18	its	its	PRON
ejpam-6307	242	19	fdeigenvalues	fdeigenvalue	NOUN
ejpam-6307	242	20	of	of	ADP
ejpam-6307	242	21	mfdd	mfdd	NOUN
ejpam-6307	242	22	.	.	PUNCT
ejpam-6307	243	1	the	the	DET
ejpam-6307	243	2	set	set	NOUN
ejpam-6307	243	3	of	of	ADP
ejpam-6307	243	4	fdeigenvalues	fdeigenvalue	NOUN
ejpam-6307	243	5	is	be	AUX
ejpam-6307	243	6	called	call	VERB
ejpam-6307	243	7	the	the	DET
ejpam-6307	243	8	fuzzy	fuzzy	ADJ
ejpam-6307	243	9	detour	detour	NOUN
ejpam-6307	243	10	-	-	PUNCT
ejpam-6307	243	11	spectrum	spectrum	NOUN
ejpam-6307	243	12	(	(	PUNCT
ejpam-6307	243	13	fd	fd	PROPN
ejpam-6307	243	14	−	−	PROPN
ejpam-6307	243	15	spectrum	spectrum	NOUN
ejpam-6307	243	16	)	)	PUNCT
ejpam-6307	243	17	of	of	ADP
ejpam-6307	243	18	g.	g.	PROPN
ejpam-6307	243	19	the	the	DET
ejpam-6307	243	20	fuzzy	fuzzy	ADJ
ejpam-6307	243	21	detour	detour	NOUN
ejpam-6307	243	22	-	-	ADJ
ejpam-6307	243	23	spectral	spectral	ADJ
ejpam-6307	243	24	radius	radius	NOUN
ejpam-6307	243	25	(	(	PUNCT
ejpam-6307	243	26	fdsr	fdsr	NOUN
ejpam-6307	243	27	)	)	PUNCT
ejpam-6307	243	28	ofm	ofm	PROPN
ejpam-6307	243	29	is	be	AUX
ejpam-6307	243	30	the	the	DET
ejpam-6307	243	31	maximum	maximum	NOUN
ejpam-6307	243	32	of	of	ADP
ejpam-6307	243	33	its	its	PRON
ejpam-6307	243	34	fdeigenvalues	fdeigenvalue	NOUN
ejpam-6307	243	35	.	.	PUNCT
ejpam-6307	244	1	example	example	NOUN
ejpam-6307	244	2	2	2	NUM
ejpam-6307	244	3	.	.	X
ejpam-6307	244	4	for	for	ADP
ejpam-6307	244	5	instance	instance	NOUN
ejpam-6307	244	6	,	,	PUNCT
ejpam-6307	244	7	consider	consider	VERB
ejpam-6307	244	8	the	the	DET
ejpam-6307	244	9	fd	fd	NOUN
ejpam-6307	244	10	-	-	PUNCT
ejpam-6307	244	11	matrix	matrix	NOUN
ejpam-6307	244	12	(	(	PUNCT
ejpam-6307	244	13	distance	distance	NOUN
ejpam-6307	244	14	has	have	AUX
ejpam-6307	244	15	been	be	AUX
ejpam-6307	244	16	corrected	correct	VERB
ejpam-6307	244	17	to	to	ADP
ejpam-6307	244	18	two	two	NUM
ejpam-6307	244	19	decimal	decimal	ADJ
ejpam-6307	244	20	places	place	NOUN
ejpam-6307	244	21	)	)	PUNCT
ejpam-6307	244	22	of	of	ADP
ejpam-6307	244	23	g	g	PROPN
ejpam-6307	244	24	in	in	ADP
ejpam-6307	244	25	figure	figure	NOUN
ejpam-6307	244	26	2	2	NUM
ejpam-6307	244	27	with	with	ADP
ejpam-6307	244	28	σ∗	σ∗	NOUN
ejpam-6307	244	29	=	=	SYM
ejpam-6307	244	30	{	{	PUNCT
ejpam-6307	244	31	v1	v1	PROPN
ejpam-6307	244	32	,	,	PUNCT
ejpam-6307	244	33	v2	v2	PROPN
ejpam-6307	244	34	,	,	PUNCT
ejpam-6307	244	35	v3	v3	PROPN
ejpam-6307	244	36	,	,	PUNCT
ejpam-6307	244	37	v4	v4	PROPN
ejpam-6307	244	38	}	}	PUNCT
ejpam-6307	244	39	.	.	PUNCT
ejpam-6307	245	1	figure	figure	VERB
ejpam-6307	245	2	2	2	NUM
ejpam-6307	245	3	:	:	PUNCT
ejpam-6307	245	4	a	a	DET
ejpam-6307	245	5	fuzzy	fuzzy	ADJ
ejpam-6307	245	6	graph	graph	NOUN
ejpam-6307	245	7	with	with	ADP
ejpam-6307	245	8	fuzzy	fuzzy	ADJ
ejpam-6307	245	9	detour	detour	NOUN
ejpam-6307	245	10	-	-	PUNCT
ejpam-6307	245	11	spectral	spectral	ADJ
ejpam-6307	245	12	radius	radius	NOUN
ejpam-6307	245	13	36.9236	36.9236	NUM
ejpam-6307	245	14	.	.	PUNCT
ejpam-6307	246	1	r.	r.	PROPN
ejpam-6307	246	2	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	246	3	,	,	PUNCT
ejpam-6307	246	4	a.	a.	NOUN
ejpam-6307	246	5	m.	m.	PROPN
ejpam-6307	246	6	anto	anto	PROPN
ejpam-6307	246	7	,	,	PUNCT
ejpam-6307	246	8	v.	v.	PROPN
ejpam-6307	246	9	mary	mary	PROPN
ejpam-6307	246	10	mettilda	mettilda	PROPN
ejpam-6307	246	11	rose	rise	VERB
ejpam-6307	246	12	/	/	SYM
ejpam-6307	246	13	eur	eur	PROPN
ejpam-6307	246	14	.	.	PUNCT
ejpam-6307	247	1	j.	j.	PROPN
ejpam-6307	247	2	pure	pure	PROPN
ejpam-6307	247	3	appl	appl	PROPN
ejpam-6307	247	4	.	.	PROPN
ejpam-6307	247	5	math	math	PROPN
ejpam-6307	247	6	,	,	PUNCT
ejpam-6307	247	7	18	18	NUM
ejpam-6307	247	8	(	(	PUNCT
ejpam-6307	247	9	4	4	NUM
ejpam-6307	247	10	)	)	PUNCT
ejpam-6307	247	11	(	(	PUNCT
ejpam-6307	247	12	2025	2025	NUM
ejpam-6307	247	13	)	)	PUNCT
ejpam-6307	247	14	,	,	PUNCT
ejpam-6307	247	15	6307	6307	NUM
ejpam-6307	247	16	11	11	NUM
ejpam-6307	247	17	of	of	ADP
ejpam-6307	247	18	25	25	NOUN
ejpam-6307	248	1	0.00	0.00	NUM
ejpam-6307	248	2	11.66	11.66	NUM
ejpam-6307	248	3	10.00	10.00	NUM
ejpam-6307	248	4	13.33	13.33	NUM
ejpam-6307	248	5	11.66	11.66	NUM
ejpam-6307	248	6	0.00	0.00	NUM
ejpam-6307	248	7	12.00	12.00	NUM
ejpam-6307	248	8	14.66	14.66	NUM
ejpam-6307	248	9	10.00	10.00	NUM
ejpam-6307	248	10	12.00	12.00	NUM
ejpam-6307	248	11	0.00	0.00	NUM
ejpam-6307	248	12	12.50	12.50	NUM
ejpam-6307	248	13	13.33	13.33	NUM
ejpam-6307	248	14	14.16	14.16	NUM
ejpam-6307	248	15	12.50	12.50	NUM
ejpam-6307	248	16	0.00	0.00	NUM
ejpam-6307	248	17	.	.	NOUN
ejpam-6307	248	18	here	here	ADV
ejpam-6307	248	19	,	,	PUNCT
ejpam-6307	248	20	the	the	DET
ejpam-6307	248	21	fd	fd	NOUN
ejpam-6307	248	22	-	-	PUNCT
ejpam-6307	248	23	spectrum	spectrum	NOUN
ejpam-6307	248	24	is	be	AUX
ejpam-6307	248	25	{	{	PUNCT
ejpam-6307	248	26	36.9236	36.9236	NUM
ejpam-6307	248	27	,	,	PUNCT
ejpam-6307	248	28	−14.6074	−14.6074	PROPN
ejpam-6307	248	29	,	,	PUNCT
ejpam-6307	248	30	−12.3964	−12.3964	PROPN
ejpam-6307	248	31	,	,	PUNCT
ejpam-6307	248	32	−9.91979	−9.91979	NOUN
ejpam-6307	248	33	}	}	PUNCT
ejpam-6307	248	34	,	,	PUNCT
ejpam-6307	248	35	and	and	CCONJ
ejpam-6307	248	36	thus	thus	ADV
ejpam-6307	248	37	the	the	DET
ejpam-6307	248	38	fde(g	fde(g	NOUN
ejpam-6307	248	39	)	)	PUNCT
ejpam-6307	248	40	=	=	SYM
ejpam-6307	248	41	73.84719	73.84719	NUM
ejpam-6307	248	42	.	.	PUNCT
ejpam-6307	249	1	the	the	DET
ejpam-6307	249	2	fdsr	fdsr	NOUN
ejpam-6307	249	3	=	=	SYM
ejpam-6307	249	4	36.9236	36.9236	NUM
ejpam-6307	249	5	.	.	PUNCT
ejpam-6307	249	6	theorem	theorem	VERB
ejpam-6307	249	7	7	7	NUM
ejpam-6307	249	8	.	.	PUNCT
ejpam-6307	250	1	let	let	VERB
ejpam-6307	250	2	g	g	PRON
ejpam-6307	250	3	be	be	AUX
ejpam-6307	250	4	an	an	DET
ejpam-6307	250	5	fg	fg	NOUN
ejpam-6307	250	6	.	.	PUNCT
ejpam-6307	251	1	then	then	ADV
ejpam-6307	251	2	,	,	PUNCT
ejpam-6307	251	3	fde(g	fde(g	PROPN
ejpam-6307	251	4	)	)	PUNCT
ejpam-6307	251	5	≤	≤	NOUN
ejpam-6307	251	6	2	2	NUM
ejpam-6307	251	7	∑	∑	PROPN
ejpam-6307	251	8	i	i	PROPN
ejpam-6307	251	9	,	,	PUNCT
ejpam-6307	251	10	j	j	PROPN
ejpam-6307	251	11	∆(vi	∆(vi	PROPN
ejpam-6307	251	12	,	,	PUNCT
ejpam-6307	251	13	vj	vj	NOUN
ejpam-6307	251	14	)	)	PUNCT
ejpam-6307	251	15	,	,	PUNCT
ejpam-6307	251	16	∀	∀	PUNCT
ejpam-6307	252	1	i	i	NOUN
ejpam-6307	252	2	,	,	PUNCT
ejpam-6307	252	3	j.	j.	PROPN
ejpam-6307	252	4	proof	proof	PROPN
ejpam-6307	252	5	.	.	PUNCT
ejpam-6307	253	1	consider	consider	VERB
ejpam-6307	253	2	the	the	DET
ejpam-6307	253	3	fuzzy	fuzzy	ADJ
ejpam-6307	253	4	detour	detour	NOUN
ejpam-6307	253	5	distance	distance	NOUN
ejpam-6307	253	6	matrix	matrix	NOUN
ejpam-6307	253	7	mfdd	mfdd	NOUN
ejpam-6307	253	8	,	,	PUNCT
ejpam-6307	253	9	which	which	PRON
ejpam-6307	253	10	is	be	AUX
ejpam-6307	253	11	a	a	DET
ejpam-6307	253	12	non	non	ADJ
ejpam-6307	253	13	-	-	ADJ
ejpam-6307	253	14	negative	negative	ADJ
ejpam-6307	253	15	,	,	PUNCT
ejpam-6307	253	16	symmetric	symmetric	ADJ
ejpam-6307	253	17	square	square	ADJ
ejpam-6307	253	18	matrix	matrix	NOUN
ejpam-6307	253	19	.	.	PUNCT
ejpam-6307	254	1	the	the	DET
ejpam-6307	254	2	trace	trace	NOUN
ejpam-6307	254	3	ofm2	ofm2	PROPN
ejpam-6307	254	4	fdd	fdd	PROPN
ejpam-6307	254	5	is	be	AUX
ejpam-6307	254	6	given	give	VERB
ejpam-6307	254	7	by	by	ADP
ejpam-6307	254	8	tr(m2	tr(m2	X
ejpam-6307	254	9	fdd	fdd	PROPN
ejpam-6307	254	10	)	)	PUNCT
ejpam-6307	255	1	=	=	PUNCT
ejpam-6307	255	2	m∑	m∑	ADP
ejpam-6307	255	3	i=1	i=1	PROPN
ejpam-6307	255	4	m∑	m∑	PROPN
ejpam-6307	256	1	j=1	j=1	ADJ
ejpam-6307	256	2	∆(vi	∆(vi	PROPN
ejpam-6307	256	3	,	,	PUNCT
ejpam-6307	256	4	vj)∆(vj	vj)∆(vj	NOUN
ejpam-6307	256	5	,	,	PUNCT
ejpam-6307	256	6	vi	vi	NOUN
ejpam-6307	256	7	)	)	PUNCT
ejpam-6307	256	8	.	.	PUNCT
ejpam-6307	257	1	sincemfdd	sincemfdd	NOUN
ejpam-6307	257	2	is	be	AUX
ejpam-6307	257	3	symmetric	symmetric	ADJ
ejpam-6307	257	4	,	,	PUNCT
ejpam-6307	257	5	we	we	PRON
ejpam-6307	257	6	have	have	VERB
ejpam-6307	257	7	∆(vi	∆(vi	NOUN
ejpam-6307	257	8	,	,	PUNCT
ejpam-6307	257	9	vj	vj	ADJ
ejpam-6307	257	10	)	)	PUNCT
ejpam-6307	257	11	=	=	PUNCT
ejpam-6307	258	1	∆(vj	∆(vj	ADJ
ejpam-6307	258	2	,	,	PUNCT
ejpam-6307	258	3	vi	vi	NOUN
ejpam-6307	258	4	)	)	PUNCT
ejpam-6307	258	5	,	,	PUNCT
ejpam-6307	258	6	and	and	CCONJ
ejpam-6307	258	7	thus	thus	ADV
ejpam-6307	258	8	tr(m2	tr(m2	NOUN
ejpam-6307	258	9	fdd	fdd	PROPN
ejpam-6307	258	10	)	)	PUNCT
ejpam-6307	259	1	=	=	PUNCT
ejpam-6307	259	2	m∑	m∑	ADP
ejpam-6307	259	3	i=1	i=1	PROPN
ejpam-6307	259	4	m∑	m∑	PROPN
ejpam-6307	260	1	j=1	j=1	PROPN
ejpam-6307	260	2	∆(vi	∆(vi	PROPN
ejpam-6307	260	3	,	,	PUNCT
ejpam-6307	260	4	vj	vj	NOUN
ejpam-6307	260	5	)	)	PUNCT
ejpam-6307	260	6	2	2	NUM
ejpam-6307	260	7	.	.	X
ejpam-6307	260	8	using	use	VERB
ejpam-6307	260	9	theorem	theorem	ADJ
ejpam-6307	260	10	1	1	NUM
ejpam-6307	260	11	and	and	CCONJ
ejpam-6307	260	12	properties	property	NOUN
ejpam-6307	260	13	of	of	ADP
ejpam-6307	260	14	symmetric	symmetric	ADJ
ejpam-6307	260	15	matrices	matrix	NOUN
ejpam-6307	260	16	,	,	PUNCT
ejpam-6307	260	17	it	it	PRON
ejpam-6307	260	18	follows	follow	VERB
ejpam-6307	260	19	that	that	SCONJ
ejpam-6307	260	20	fde(g	fde(g	NOUN
ejpam-6307	260	21	)	)	PUNCT
ejpam-6307	260	22	≤	≤	NOUN
ejpam-6307	260	23	2	2	NUM
ejpam-6307	260	24	∑	∑	PROPN
ejpam-6307	260	25	i	i	PROPN
ejpam-6307	260	26	,	,	PUNCT
ejpam-6307	260	27	j	j	PROPN
ejpam-6307	260	28	∆(vi	∆(vi	PROPN
ejpam-6307	260	29	,	,	PUNCT
ejpam-6307	260	30	vj	vj	NOUN
ejpam-6307	260	31	)	)	PUNCT
ejpam-6307	260	32	,	,	PUNCT
ejpam-6307	260	33	∀	∀	PUNCT
ejpam-6307	261	1	i	i	PRON
ejpam-6307	261	2	,	,	PUNCT
ejpam-6307	261	3	j	j	PROPN
ejpam-6307	261	4	,	,	PUNCT
ejpam-6307	261	5	as	as	SCONJ
ejpam-6307	261	6	required	require	VERB
ejpam-6307	261	7	.	.	PUNCT
ejpam-6307	262	1	theorem	theorem	ADJ
ejpam-6307	262	2	8	8	NUM
ejpam-6307	262	3	.	.	PUNCT
ejpam-6307	263	1	let	let	VERB
ejpam-6307	263	2	g	g	PRON
ejpam-6307	263	3	be	be	AUX
ejpam-6307	263	4	a	a	DET
ejpam-6307	263	5	fuzzy	fuzzy	ADJ
ejpam-6307	263	6	graph	graph	NOUN
ejpam-6307	263	7	,	,	PUNCT
ejpam-6307	263	8	and	and	CCONJ
ejpam-6307	263	9	let	let	VERB
ejpam-6307	263	10	ri	ri	PRON
ejpam-6307	263	11	denote	denote	VERB
ejpam-6307	263	12	the	the	DET
ejpam-6307	263	13	sum	sum	NOUN
ejpam-6307	263	14	of	of	ADP
ejpam-6307	263	15	the	the	DET
ejpam-6307	263	16	entries	entry	NOUN
ejpam-6307	263	17	in	in	ADP
ejpam-6307	263	18	the	the	DET
ejpam-6307	263	19	ith	ith	PROPN
ejpam-6307	263	20	row	row	NOUN
ejpam-6307	263	21	of	of	ADP
ejpam-6307	263	22	the	the	DET
ejpam-6307	263	23	fd	fd	NOUN
ejpam-6307	263	24	-	-	PUNCT
ejpam-6307	263	25	matrix	matrix	NOUN
ejpam-6307	263	26	.	.	PUNCT
ejpam-6307	264	1	then	then	ADV
ejpam-6307	264	2	,	,	PUNCT
ejpam-6307	264	3	fde(g	fde(g	PROPN
ejpam-6307	264	4	)	)	PUNCT
ejpam-6307	264	5	≤	≤	NOUN
ejpam-6307	265	1	n	n	PRON
ejpam-6307	265	2	max	max	PROPN
ejpam-6307	265	3	1≤i≤n	1≤i≤n	NUM
ejpam-6307	265	4	ri	ri	PROPN
ejpam-6307	265	5	.	.	PUNCT
ejpam-6307	265	6	proof	proof	NOUN
ejpam-6307	265	7	.	.	PUNCT
ejpam-6307	266	1	the	the	DET
ejpam-6307	266	2	fd	fd	NOUN
ejpam-6307	266	3	-	-	PUNCT
ejpam-6307	266	4	matrix	matrix	NOUN
ejpam-6307	266	5	is	be	AUX
ejpam-6307	266	6	a	a	DET
ejpam-6307	266	7	non	non	ADJ
ejpam-6307	266	8	-	-	ADJ
ejpam-6307	266	9	negative	negative	ADJ
ejpam-6307	266	10	square	square	ADJ
ejpam-6307	266	11	matrix	matrix	NOUN
ejpam-6307	266	12	with	with	ADP
ejpam-6307	266	13	zero	zero	NUM
ejpam-6307	266	14	diagonal	diagonal	ADJ
ejpam-6307	266	15	entries	entry	NOUN
ejpam-6307	266	16	.	.	PUNCT
ejpam-6307	267	1	thus	thus	ADV
ejpam-6307	267	2	,	,	PUNCT
ejpam-6307	267	3	the	the	DET
ejpam-6307	267	4	spectral	spectral	ADJ
ejpam-6307	267	5	radius	radius	NOUN
ejpam-6307	267	6	fdsr	fdsr	NOUN
ejpam-6307	267	7	satisfies	satisfie	NOUN
ejpam-6307	267	8	min	min	PROPN
ejpam-6307	267	9	1≤i≤n	1≤i≤n	NUM
ejpam-6307	267	10	ri	ri	PROPN
ejpam-6307	267	11	≤	≤	PROPN
ejpam-6307	267	12	fdsr	fdsr	NOUN
ejpam-6307	267	13	≤	≤	NUM
ejpam-6307	267	14	max	max	PROPN
ejpam-6307	267	15	1≤i≤n	1≤i≤n	NUM
ejpam-6307	267	16	ri	ri	PROPN
ejpam-6307	267	17	.	.	PUNCT
ejpam-6307	268	1	hence	hence	ADV
ejpam-6307	268	2	,	,	PUNCT
ejpam-6307	268	3	fdsr	fdsr	VERB
ejpam-6307	268	4	≤	≤	NUM
ejpam-6307	268	5	max	max	PROPN
ejpam-6307	268	6	1≤i≤n	1≤i≤n	NUM
ejpam-6307	268	7	ri	ri	PROPN
ejpam-6307	268	8	.	.	PUNCT
ejpam-6307	269	1	since	since	SCONJ
ejpam-6307	269	2	the	the	DET
ejpam-6307	269	3	fuzzy	fuzzy	ADJ
ejpam-6307	269	4	detour	detour	NOUN
ejpam-6307	269	5	energy	energy	NOUN
ejpam-6307	269	6	fde(g	fde(g	NOUN
ejpam-6307	269	7	)	)	PUNCT
ejpam-6307	269	8	is	be	AUX
ejpam-6307	269	9	the	the	DET
ejpam-6307	269	10	sum	sum	NOUN
ejpam-6307	269	11	of	of	ADP
ejpam-6307	269	12	the	the	DET
ejpam-6307	269	13	absolute	absolute	ADJ
ejpam-6307	269	14	values	value	NOUN
ejpam-6307	269	15	of	of	ADP
ejpam-6307	269	16	the	the	DET
ejpam-6307	269	17	eigenvalues	eigenvalue	NOUN
ejpam-6307	269	18	,	,	PUNCT
ejpam-6307	269	19	we	we	PRON
ejpam-6307	269	20	have	have	VERB
ejpam-6307	269	21	fde(g	fde(g	NOUN
ejpam-6307	269	22	)	)	PUNCT
ejpam-6307	269	23	≤	≤	NOUN
ejpam-6307	269	24	n	n	PRON
ejpam-6307	269	25	·	·	PUNCT
ejpam-6307	269	26	max	max	PROPN
ejpam-6307	269	27	1≤i≤n	1≤i≤n	NUM
ejpam-6307	269	28	ri	ri	PROPN
ejpam-6307	269	29	,	,	PUNCT
ejpam-6307	269	30	as	as	SCONJ
ejpam-6307	269	31	required	require	VERB
ejpam-6307	269	32	.	.	PUNCT
ejpam-6307	270	1	to	to	PART
ejpam-6307	270	2	derive	derive	VERB
ejpam-6307	270	3	the	the	DET
ejpam-6307	270	4	lower	low	ADJ
ejpam-6307	270	5	bound	bind	VERB
ejpam-6307	270	6	for	for	ADP
ejpam-6307	270	7	fde(g	fde(g	PROPN
ejpam-6307	270	8	)	)	PUNCT
ejpam-6307	270	9	,	,	PUNCT
ejpam-6307	270	10	a	a	DET
ejpam-6307	270	11	similar	similar	ADJ
ejpam-6307	270	12	proof	proof	NOUN
ejpam-6307	270	13	is	be	AUX
ejpam-6307	270	14	possible	possible	ADJ
ejpam-6307	270	15	.	.	PUNCT
ejpam-6307	271	1	r.	r.	PROPN
ejpam-6307	271	2	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	271	3	,	,	PUNCT
ejpam-6307	271	4	a.	a.	NOUN
ejpam-6307	271	5	m.	m.	PROPN
ejpam-6307	271	6	anto	anto	PROPN
ejpam-6307	271	7	,	,	PUNCT
ejpam-6307	271	8	v.	v.	PROPN
ejpam-6307	271	9	mary	mary	PROPN
ejpam-6307	271	10	mettilda	mettilda	PROPN
ejpam-6307	271	11	rose	rise	VERB
ejpam-6307	271	12	/	/	SYM
ejpam-6307	271	13	eur	eur	PROPN
ejpam-6307	271	14	.	.	PUNCT
ejpam-6307	272	1	j.	j.	PROPN
ejpam-6307	272	2	pure	pure	PROPN
ejpam-6307	272	3	appl	appl	PROPN
ejpam-6307	272	4	.	.	PROPN
ejpam-6307	272	5	math	math	PROPN
ejpam-6307	272	6	,	,	PUNCT
ejpam-6307	272	7	18	18	NUM
ejpam-6307	272	8	(	(	PUNCT
ejpam-6307	272	9	4	4	NUM
ejpam-6307	272	10	)	)	PUNCT
ejpam-6307	272	11	(	(	PUNCT
ejpam-6307	272	12	2025	2025	NUM
ejpam-6307	272	13	)	)	PUNCT
ejpam-6307	272	14	,	,	PUNCT
ejpam-6307	272	15	6307	6307	NUM
ejpam-6307	272	16	12	12	NUM
ejpam-6307	272	17	of	of	ADP
ejpam-6307	272	18	25	25	NUM
ejpam-6307	272	19	theorem	theorem	NOUN
ejpam-6307	272	20	9	9	NUM
ejpam-6307	272	21	.	.	PUNCT
ejpam-6307	273	1	let	let	VERB
ejpam-6307	273	2	g	g	PRON
ejpam-6307	273	3	be	be	AUX
ejpam-6307	273	4	a	a	DET
ejpam-6307	273	5	fg	fg	NOUN
ejpam-6307	273	6	with	with	ADP
ejpam-6307	273	7	|v|	|v|	NOUN
ejpam-6307	273	8	=	=	NOUN
ejpam-6307	273	9	m	m	NOUN
ejpam-6307	273	10	and	and	CCONJ
ejpam-6307	273	11	|e|	|e|	ADJ
ejpam-6307	273	12	=	=	PUNCT
ejpam-6307	273	13	n.	n.	NOUN
ejpam-6307	273	14	if	if	SCONJ
ejpam-6307	273	15	cij	cij	PROPN
ejpam-6307	273	16	=	=	SYM
ejpam-6307	273	17	∆(vi	∆(vi	PROPN
ejpam-6307	273	18	,	,	PUNCT
ejpam-6307	273	19	vj	vj	NOUN
ejpam-6307	273	20	)	)	PUNCT
ejpam-6307	273	21	denotes	denote	VERB
ejpam-6307	273	22	the	the	DET
ejpam-6307	273	23	fuzzy	fuzzy	ADJ
ejpam-6307	273	24	detour	detour	NOUN
ejpam-6307	273	25	distance	distance	NOUN
ejpam-6307	273	26	andmfdd	andmfdd	NOUN
ejpam-6307	273	27	is	be	AUX
ejpam-6307	273	28	the	the	DET
ejpam-6307	273	29	fuzzy	fuzzy	ADJ
ejpam-6307	273	30	detour	detour	NOUN
ejpam-6307	273	31	distance	distance	NOUN
ejpam-6307	273	32	matrix	matrix	NOUN
ejpam-6307	273	33	,	,	PUNCT
ejpam-6307	273	34	then	then	ADV
ejpam-6307	273	35	fde(g	fde(g	PROPN
ejpam-6307	273	36	)	)	PUNCT
ejpam-6307	273	37	≤	≤	NUM
ejpam-6307	274	1	√	√	NUM
ejpam-6307	275	1	(	(	PUNCT
ejpam-6307	275	2	m−	m−	PROPN
ejpam-6307	275	3	1	1	NUM
ejpam-6307	275	4	)	)	PUNCT
ejpam-6307	275	5	[	[	PUNCT
ejpam-6307	275	6	κ−	κ−	X
ejpam-6307	275	7	θ2i	θ2i	PROPN
ejpam-6307	275	8	]	]	PUNCT
ejpam-6307	275	9	,	,	PUNCT
ejpam-6307	275	10	where	where	SCONJ
ejpam-6307	275	11	κ	κ	NOUN
ejpam-6307	275	12	=	=	PUNCT
ejpam-6307	275	13	∑	∑	PUNCT
ejpam-6307	275	14	i	i	PROPN
ejpam-6307	275	15	<	<	X
ejpam-6307	275	16	j	j	X
ejpam-6307	275	17	c2ij	c2ij	X
ejpam-6307	275	18	.	.	PUNCT
ejpam-6307	276	1	proof	proof	NOUN
ejpam-6307	276	2	.	.	PUNCT
ejpam-6307	277	1	by	by	ADP
ejpam-6307	277	2	the	the	DET
ejpam-6307	277	3	cauchy	cauchy	PROPN
ejpam-6307	277	4	–	–	PUNCT
ejpam-6307	277	5	schwarz	schwarz	NOUN
ejpam-6307	277	6	inequality	inequality	NOUN
ejpam-6307	277	7	,	,	PUNCT
ejpam-6307	277	8	we	we	PRON
ejpam-6307	277	9	have	have	VERB
ejpam-6307	277	10	:	:	PUNCT
ejpam-6307	277	11	m∑	m∑	CCONJ
ejpam-6307	278	1	i=2	i=2	PROPN
ejpam-6307	278	2	|θi|	|θi|	PROPN
ejpam-6307	278	3	≤	≤	PUNCT
ejpam-6307	278	4	√√√√(m−	√√√√(m−	PROPN
ejpam-6307	278	5	1	1	NUM
ejpam-6307	278	6	)	)	PUNCT
ejpam-6307	278	7	m∑	m∑	ADP
ejpam-6307	278	8	i=2	i=2	PROPN
ejpam-6307	278	9	θ2i	θ2i	PROPN
ejpam-6307	278	10	.	.	PUNCT
ejpam-6307	279	1	(	(	PUNCT
ejpam-6307	279	2	6	6	X
ejpam-6307	279	3	)	)	PUNCT
ejpam-6307	279	4	suppose	suppose	VERB
ejpam-6307	279	5	that	that	SCONJ
ejpam-6307	279	6	the	the	DET
ejpam-6307	279	7	total	total	ADJ
ejpam-6307	279	8	sum	sum	NOUN
ejpam-6307	279	9	of	of	ADP
ejpam-6307	279	10	squared	square	VERB
ejpam-6307	279	11	eigenvalues	eigenvalue	NOUN
ejpam-6307	279	12	satisfies	satisfie	NOUN
ejpam-6307	279	13	:	:	PUNCT
ejpam-6307	279	14	m∑	m∑	ADP
ejpam-6307	279	15	i=1	i=1	PROPN
ejpam-6307	279	16	θ2i	θ2i	PROPN
ejpam-6307	279	17	≤	≤	PROPN
ejpam-6307	279	18	κ	κ	X
ejpam-6307	279	19	=	=	PUNCT
ejpam-6307	279	20	∑	∑	PUNCT
ejpam-6307	279	21	i	i	PROPN
ejpam-6307	279	22	<	<	X
ejpam-6307	279	23	j	j	X
ejpam-6307	279	24	c2ij	c2ij	X
ejpam-6307	279	25	.	.	PUNCT
ejpam-6307	280	1	then	then	ADV
ejpam-6307	280	2	,	,	PUNCT
ejpam-6307	280	3	θ21	θ21	NOUN
ejpam-6307	280	4	+	+	CCONJ
ejpam-6307	280	5	m∑	m∑	ADV
ejpam-6307	280	6	i=2	i=2	PROPN
ejpam-6307	280	7	θ2i	θ2i	PROPN
ejpam-6307	280	8	≤	≤	PROPN
ejpam-6307	280	9	κ	κ	ADP
ejpam-6307	280	10	⇒	⇒	NOUN
ejpam-6307	280	11	m∑	m∑	VERB
ejpam-6307	280	12	i=2	i=2	PROPN
ejpam-6307	280	13	θ2i	θ2i	PROPN
ejpam-6307	280	14	≤	≤	PROPN
ejpam-6307	280	15	κ−	κ−	PROPN
ejpam-6307	280	16	θ21	θ21	NOUN
ejpam-6307	280	17	.	.	PUNCT
ejpam-6307	281	1	substituting	substitute	VERB
ejpam-6307	281	2	into	into	ADP
ejpam-6307	281	3	(	(	PUNCT
ejpam-6307	281	4	6	6	NUM
ejpam-6307	281	5	)	)	PUNCT
ejpam-6307	281	6	,	,	PUNCT
ejpam-6307	281	7	we	we	PRON
ejpam-6307	281	8	get	get	VERB
ejpam-6307	281	9	:	:	PUNCT
ejpam-6307	281	10	m∑	m∑	CCONJ
ejpam-6307	281	11	i=2	i=2	PROPN
ejpam-6307	281	12	|θi|	|θi|	PROPN
ejpam-6307	281	13	≤	≤	NOUN
ejpam-6307	282	1	√	√	NUM
ejpam-6307	283	1	(	(	PUNCT
ejpam-6307	283	2	m−	m−	PROPN
ejpam-6307	283	3	1)(κ−	1)(κ−	NUM
ejpam-6307	283	4	θ21	θ21	NOUN
ejpam-6307	283	5	)	)	PUNCT
ejpam-6307	283	6	.	.	PUNCT
ejpam-6307	284	1	therefore	therefore	ADV
ejpam-6307	284	2	,	,	PUNCT
ejpam-6307	284	3	the	the	DET
ejpam-6307	284	4	fuzzy	fuzzy	ADJ
ejpam-6307	284	5	detour	detour	NOUN
ejpam-6307	284	6	energy	energy	NOUN
ejpam-6307	284	7	satisfies	satisfie	NOUN
ejpam-6307	284	8	:	:	PUNCT
ejpam-6307	284	9	fde(g	fde(g	NOUN
ejpam-6307	284	10	)	)	PUNCT
ejpam-6307	284	11	=	=	PUNCT
ejpam-6307	285	1	m∑	m∑	CCONJ
ejpam-6307	285	2	i=1	i=1	PRON
ejpam-6307	285	3	|θi|	|θi|	PROPN
ejpam-6307	285	4	≤	≤	ADJ
ejpam-6307	285	5	θ1	θ1	NOUN
ejpam-6307	285	6	+	+	CCONJ
ejpam-6307	285	7	√	√	PROPN
ejpam-6307	285	8	(	(	PUNCT
ejpam-6307	285	9	m−	m−	PROPN
ejpam-6307	285	10	1)(κ−	1)(κ−	NUM
ejpam-6307	285	11	θ21	θ21	NOUN
ejpam-6307	285	12	)	)	PUNCT
ejpam-6307	285	13	,	,	PUNCT
ejpam-6307	285	14	as	as	SCONJ
ejpam-6307	285	15	required	require	VERB
ejpam-6307	285	16	.	.	PUNCT
ejpam-6307	286	1	another	another	PRON
ejpam-6307	286	2	,	,	PUNCT
ejpam-6307	286	3	potentially	potentially	ADV
ejpam-6307	286	4	more	more	ADV
ejpam-6307	286	5	satisfying	satisfying	ADJ
ejpam-6307	286	6	,	,	PUNCT
ejpam-6307	286	7	upper	upper	ADJ
ejpam-6307	286	8	and	and	CCONJ
ejpam-6307	286	9	lower	low	ADJ
ejpam-6307	286	10	bound	bind	VERB
ejpam-6307	286	11	is	be	AUX
ejpam-6307	286	12	established	establish	VERB
ejpam-6307	286	13	in	in	ADP
ejpam-6307	286	14	the	the	DET
ejpam-6307	286	15	next	next	ADJ
ejpam-6307	286	16	theorem	theorem	PROPN
ejpam-6307	286	17	.	.	PUNCT
ejpam-6307	287	1	theorem	theorem	PROPN
ejpam-6307	287	2	10	10	NUM
ejpam-6307	287	3	.	.	PUNCT
ejpam-6307	288	1	let	let	VERB
ejpam-6307	288	2	g	g	PRON
ejpam-6307	288	3	be	be	AUX
ejpam-6307	288	4	a	a	DET
ejpam-6307	288	5	fg	fg	NOUN
ejpam-6307	288	6	with	with	ADP
ejpam-6307	288	7	|v|	|v|	NOUN
ejpam-6307	288	8	=	=	NOUN
ejpam-6307	288	9	m	m	NOUN
ejpam-6307	288	10	and	and	CCONJ
ejpam-6307	288	11	|e|	|e|	ADJ
ejpam-6307	288	12	=	=	PUNCT
ejpam-6307	288	13	n.	n.	NOUN
ejpam-6307	288	14	if	if	SCONJ
ejpam-6307	288	15	cij	cij	PROPN
ejpam-6307	288	16	=	=	SYM
ejpam-6307	288	17	∆(vi	∆(vi	PROPN
ejpam-6307	288	18	,	,	PUNCT
ejpam-6307	288	19	vj	vj	NOUN
ejpam-6307	288	20	)	)	PUNCT
ejpam-6307	288	21	denotes	denote	VERB
ejpam-6307	288	22	the	the	DET
ejpam-6307	288	23	fuzzy	fuzzy	ADJ
ejpam-6307	288	24	detour	detour	NOUN
ejpam-6307	288	25	distance	distance	NOUN
ejpam-6307	288	26	andmfdd	andmfdd	NOUN
ejpam-6307	288	27	is	be	AUX
ejpam-6307	288	28	the	the	DET
ejpam-6307	288	29	fuzzy	fuzzy	ADJ
ejpam-6307	288	30	detour	detour	NOUN
ejpam-6307	288	31	distance	distance	NOUN
ejpam-6307	288	32	matrix	matrix	NOUN
ejpam-6307	288	33	,	,	PUNCT
ejpam-6307	288	34	then	then	ADV
ejpam-6307	288	35	√	√	PROPN
ejpam-6307	288	36	2	2	NUM
ejpam-6307	288	37	∑	∑	PROPN
ejpam-6307	288	38	i	i	PRON
ejpam-6307	288	39	<	<	X
ejpam-6307	288	40	j	j	X
ejpam-6307	288	41	(	(	PUNCT
ejpam-6307	289	1	cij)2	cij)2	PROPN
ejpam-6307	289	2	+	+	PROPN
ejpam-6307	289	3	m(m−	m(m−	PROPN
ejpam-6307	289	4	1)|mfdd	1)|mfdd	NUM
ejpam-6307	289	5	|	|	ADV
ejpam-6307	289	6	2	2	NUM
ejpam-6307	289	7	m	m	NOUN
ejpam-6307	289	8	≤	≤	NUM
ejpam-6307	289	9	fde(g	fde(g	NOUN
ejpam-6307	289	10	)	)	PUNCT
ejpam-6307	289	11	≤	≤	NOUN
ejpam-6307	289	12	√√√√√2	√√√√√2	ADV
ejpam-6307	289	13	∑	∑	VERB
ejpam-6307	289	14	i	i	X
ejpam-6307	289	15	<	<	X
ejpam-6307	289	16	j	j	X
ejpam-6307	289	17	(	(	PUNCT
ejpam-6307	289	18	cij)2	cij)2	PROPN
ejpam-6307	289	19	m	m	PROPN
ejpam-6307	289	20	.	.	PUNCT
ejpam-6307	290	1	proof	proof	NOUN
ejpam-6307	290	2	.	.	PUNCT
ejpam-6307	291	1	the	the	DET
ejpam-6307	291	2	proof	proof	NOUN
ejpam-6307	291	3	follows	follow	VERB
ejpam-6307	291	4	similarly	similarly	ADV
ejpam-6307	291	5	to	to	ADP
ejpam-6307	291	6	that	that	PRON
ejpam-6307	291	7	of	of	ADP
ejpam-6307	291	8	theorem	theorem	ADJ
ejpam-6307	291	9	4	4	NUM
ejpam-6307	291	10	.	.	PUNCT
ejpam-6307	291	11	r.	r.	PROPN
ejpam-6307	291	12	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	291	13	,	,	PUNCT
ejpam-6307	291	14	a.	a.	NOUN
ejpam-6307	291	15	m.	m.	PROPN
ejpam-6307	291	16	anto	anto	PROPN
ejpam-6307	291	17	,	,	PUNCT
ejpam-6307	291	18	v.	v.	PROPN
ejpam-6307	291	19	mary	mary	PROPN
ejpam-6307	291	20	mettilda	mettilda	PROPN
ejpam-6307	291	21	rose	rise	VERB
ejpam-6307	291	22	/	/	SYM
ejpam-6307	291	23	eur	eur	PROPN
ejpam-6307	291	24	.	.	PUNCT
ejpam-6307	292	1	j.	j.	PROPN
ejpam-6307	292	2	pure	pure	PROPN
ejpam-6307	292	3	appl	appl	PROPN
ejpam-6307	292	4	.	.	PROPN
ejpam-6307	292	5	math	math	PROPN
ejpam-6307	292	6	,	,	PUNCT
ejpam-6307	292	7	18	18	NUM
ejpam-6307	292	8	(	(	PUNCT
ejpam-6307	292	9	4	4	NUM
ejpam-6307	292	10	)	)	PUNCT
ejpam-6307	292	11	(	(	PUNCT
ejpam-6307	292	12	2025	2025	NUM
ejpam-6307	292	13	)	)	PUNCT
ejpam-6307	292	14	,	,	PUNCT
ejpam-6307	292	15	6307	6307	NUM
ejpam-6307	292	16	13	13	NUM
ejpam-6307	292	17	of	of	ADP
ejpam-6307	292	18	25	25	NUM
ejpam-6307	292	19	5	5	NUM
ejpam-6307	292	20	.	.	PUNCT
ejpam-6307	292	21	fuzzy	fuzzy	ADJ
ejpam-6307	292	22	geodetic	geodetic	ADJ
ejpam-6307	292	23	-	-	PUNCT
ejpam-6307	292	24	laplacian	laplacian	ADJ
ejpam-6307	292	25	energy	energy	NOUN
ejpam-6307	292	26	in	in	ADP
ejpam-6307	292	27	classical	classical	ADJ
ejpam-6307	292	28	graph	graph	NOUN
ejpam-6307	292	29	theory	theory	NOUN
ejpam-6307	292	30	,	,	PUNCT
ejpam-6307	292	31	distance	distance	NOUN
ejpam-6307	292	32	laplacian	laplacian	ADJ
ejpam-6307	292	33	spectra	spectra	NOUN
ejpam-6307	292	34	were	be	AUX
ejpam-6307	292	35	introduced	introduce	VERB
ejpam-6307	292	36	by	by	ADP
ejpam-6307	292	37	milan	milan	PROPN
ejpam-6307	292	38	nath	nath	PROPN
ejpam-6307	292	39	and	and	CCONJ
ejpam-6307	292	40	somnath	somnath	PROPN
ejpam-6307	292	41	paul	paul	PROPN
ejpam-6307	292	42	.	.	PUNCT
ejpam-6307	293	1	in	in	ADP
ejpam-6307	293	2	fuzzy	fuzzy	ADJ
ejpam-6307	293	3	graphs	graph	NOUN
ejpam-6307	293	4	,	,	PUNCT
ejpam-6307	293	5	the	the	DET
ejpam-6307	293	6	ordinary	ordinary	ADJ
ejpam-6307	293	7	and	and	CCONJ
ejpam-6307	293	8	laplacian	laplacian	ADJ
ejpam-6307	293	9	energies	energy	NOUN
ejpam-6307	293	10	,	,	PUNCT
ejpam-6307	293	11	studied	study	VERB
ejpam-6307	293	12	in	in	ADP
ejpam-6307	293	13	[	[	X
ejpam-6307	293	14	19	19	NUM
ejpam-6307	293	15	]	]	PUNCT
ejpam-6307	293	16	and	and	CCONJ
ejpam-6307	293	17	[	[	X
ejpam-6307	293	18	21	21	NUM
ejpam-6307	293	19	]	]	PUNCT
ejpam-6307	293	20	,	,	PUNCT
ejpam-6307	293	21	share	share	VERB
ejpam-6307	293	22	several	several	ADJ
ejpam-6307	293	23	spectral	spectral	ADJ
ejpam-6307	293	24	similarities	similarity	NOUN
ejpam-6307	293	25	with	with	ADP
ejpam-6307	293	26	their	their	PRON
ejpam-6307	293	27	crisp	crisp	ADJ
ejpam-6307	293	28	counterparts	counterpart	NOUN
ejpam-6307	293	29	.	.	PUNCT
ejpam-6307	294	1	however	however	ADV
ejpam-6307	294	2	,	,	PUNCT
ejpam-6307	294	3	to	to	PART
ejpam-6307	294	4	extend	extend	VERB
ejpam-6307	294	5	laplacian	laplacian	NOUN
ejpam-6307	294	6	-	-	PUNCT
ejpam-6307	294	7	based	base	VERB
ejpam-6307	294	8	energy	energy	NOUN
ejpam-6307	294	9	to	to	ADP
ejpam-6307	294	10	geodetic	geodetic	ADJ
ejpam-6307	294	11	frameworks	framework	NOUN
ejpam-6307	294	12	,	,	PUNCT
ejpam-6307	294	13	we	we	PRON
ejpam-6307	294	14	define	define	VERB
ejpam-6307	294	15	the	the	DET
ejpam-6307	294	16	fuzzy	fuzzy	ADJ
ejpam-6307	294	17	geodeticlaplacian	geodeticlaplacian	ADJ
ejpam-6307	294	18	energy	energy	NOUN
ejpam-6307	294	19	,	,	PUNCT
ejpam-6307	294	20	derived	derive	VERB
ejpam-6307	294	21	from	from	ADP
ejpam-6307	294	22	the	the	DET
ejpam-6307	294	23	spectrum	spectrum	NOUN
ejpam-6307	294	24	of	of	ADP
ejpam-6307	294	25	the	the	DET
ejpam-6307	294	26	fuzzy	fuzzy	ADJ
ejpam-6307	294	27	geodetic	geodetic	ADJ
ejpam-6307	294	28	-	-	PUNCT
ejpam-6307	294	29	distance	distance	NOUN
ejpam-6307	294	30	matrix	matrix	NOUN
ejpam-6307	294	31	,	,	PUNCT
ejpam-6307	294	32	offering	offer	VERB
ejpam-6307	294	33	a	a	DET
ejpam-6307	294	34	novel	novel	ADJ
ejpam-6307	294	35	spectral	spectral	ADJ
ejpam-6307	294	36	invariant	invariant	NOUN
ejpam-6307	294	37	for	for	ADP
ejpam-6307	294	38	fuzzy	fuzzy	ADJ
ejpam-6307	294	39	graphs	graph	NOUN
ejpam-6307	294	40	.	.	PUNCT
ejpam-6307	295	1	definition	definition	NOUN
ejpam-6307	295	2	17	17	NUM
ejpam-6307	295	3	.	.	PUNCT
ejpam-6307	296	1	for	for	ADP
ejpam-6307	296	2	a	a	DET
ejpam-6307	296	3	connected	connected	ADJ
ejpam-6307	296	4	fg	fg	NOUN
ejpam-6307	296	5	g	g	PROPN
ejpam-6307	296	6	=	=	SYM
ejpam-6307	296	7	(	(	PUNCT
ejpam-6307	296	8	v	v	NOUN
ejpam-6307	296	9	,	,	PUNCT
ejpam-6307	296	10	σ	σ	PROPN
ejpam-6307	296	11	,	,	PUNCT
ejpam-6307	296	12	µ	µ	NOUN
ejpam-6307	296	13	)	)	PUNCT
ejpam-6307	296	14	with	with	ADP
ejpam-6307	296	15	|v|	|v|	NOUN
ejpam-6307	296	16	=	=	SYM
ejpam-6307	296	17	n	n	CCONJ
ejpam-6307	296	18	,	,	PUNCT
ejpam-6307	296	19	let	let	VERB
ejpam-6307	296	20	mfgd	mfgd	PROPN
ejpam-6307	296	21	denote	denote	VERB
ejpam-6307	296	22	the	the	DET
ejpam-6307	296	23	fg	fg	NOUN
ejpam-6307	296	24	-	-	NOUN
ejpam-6307	296	25	matrix	matrix	NOUN
ejpam-6307	296	26	.	.	PUNCT
ejpam-6307	297	1	then	then	ADV
ejpam-6307	297	2	the	the	DET
ejpam-6307	297	3	fuzzy	fuzzy	ADJ
ejpam-6307	297	4	geodetic	geodetic	ADJ
ejpam-6307	297	5	transmission	transmission	NOUN
ejpam-6307	297	6	matrix	matrix	NOUN
ejpam-6307	297	7	,	,	PUNCT
ejpam-6307	297	8	tfgd	tfgd	ADJ
ejpam-6307	297	9	,	,	PUNCT
ejpam-6307	297	10	is	be	AUX
ejpam-6307	297	11	an	an	DET
ejpam-6307	297	12	n×n	n×n	PROPN
ejpam-6307	297	13	diagonal	diagonal	ADJ
ejpam-6307	297	14	matrix	matrix	NOUN
ejpam-6307	297	15	,	,	PUNCT
ejpam-6307	297	16	where	where	SCONJ
ejpam-6307	297	17	each	each	DET
ejpam-6307	297	18	diagonal	diagonal	ADJ
ejpam-6307	297	19	entry	entry	NOUN
ejpam-6307	297	20	tii	tii	PROPN
ejpam-6307	297	21	is	be	AUX
ejpam-6307	297	22	defined	define	VERB
ejpam-6307	297	23	as	as	ADP
ejpam-6307	297	24	tii	tii	PROPN
ejpam-6307	297	25	=	=	PROPN
ejpam-6307	297	26	n∑	n∑	PROPN
ejpam-6307	297	27	j=1	j=1	PROPN
ejpam-6307	297	28	df	df	PROPN
ejpam-6307	297	29	(	(	PUNCT
ejpam-6307	297	30	vi	vi	PROPN
ejpam-6307	297	31	,	,	PUNCT
ejpam-6307	297	32	vj	vj	NOUN
ejpam-6307	297	33	)	)	PUNCT
ejpam-6307	297	34	.	.	PUNCT
ejpam-6307	298	1	definition	definition	NOUN
ejpam-6307	298	2	18	18	NUM
ejpam-6307	298	3	.	.	PUNCT
ejpam-6307	299	1	letmfgd	letmfgd	PROPN
ejpam-6307	299	2	and	and	CCONJ
ejpam-6307	299	3	tfgd	tfgd	ADJ
ejpam-6307	299	4	be	be	AUX
ejpam-6307	299	5	the	the	DET
ejpam-6307	299	6	fg	fg	NOUN
ejpam-6307	299	7	-	-	NOUN
ejpam-6307	299	8	matrix	matrix	NOUN
ejpam-6307	299	9	and	and	CCONJ
ejpam-6307	299	10	the	the	DET
ejpam-6307	299	11	fuzzy	fuzzy	ADJ
ejpam-6307	299	12	geodetic	geodetic	ADJ
ejpam-6307	299	13	transmission	transmission	NOUN
ejpam-6307	299	14	matrix	matrix	NOUN
ejpam-6307	299	15	,	,	PUNCT
ejpam-6307	299	16	respectively	respectively	ADV
ejpam-6307	299	17	,	,	PUNCT
ejpam-6307	299	18	of	of	ADP
ejpam-6307	299	19	an	an	DET
ejpam-6307	299	20	fg	fg	PROPN
ejpam-6307	299	21	g	g	PROPN
ejpam-6307	299	22	=	=	SYM
ejpam-6307	299	23	(	(	PUNCT
ejpam-6307	299	24	v	v	NOUN
ejpam-6307	299	25	,	,	PUNCT
ejpam-6307	299	26	σ	σ	PROPN
ejpam-6307	299	27	,	,	PUNCT
ejpam-6307	299	28	µ	µ	NOUN
ejpam-6307	299	29	)	)	PUNCT
ejpam-6307	299	30	.	.	PUNCT
ejpam-6307	300	1	their	their	PRON
ejpam-6307	300	2	difference	difference	NOUN
ejpam-6307	300	3	is	be	AUX
ejpam-6307	300	4	called	call	VERB
ejpam-6307	300	5	the	the	DET
ejpam-6307	300	6	fuzzy	fuzzy	ADJ
ejpam-6307	300	7	geodeticlaplacian	geodeticlaplacian	ADJ
ejpam-6307	300	8	matrix	matrix	NOUN
ejpam-6307	300	9	,	,	PUNCT
ejpam-6307	300	10	represented	represent	VERB
ejpam-6307	300	11	bymfgld	bymfgld	NOUN
ejpam-6307	300	12	,	,	PUNCT
ejpam-6307	300	13	and	and	CCONJ
ejpam-6307	300	14	is	be	AUX
ejpam-6307	300	15	defined	define	VERB
ejpam-6307	300	16	as	as	ADP
ejpam-6307	300	17	mfgld	mfgld	ADJ
ejpam-6307	300	18	=	=	SYM
ejpam-6307	300	19	tfgd	tfgd	ADJ
ejpam-6307	300	20	−mfgd	−mfgd	NOUN
ejpam-6307	300	21	.	.	PUNCT
ejpam-6307	301	1	definition	definition	NOUN
ejpam-6307	301	2	19	19	NUM
ejpam-6307	301	3	.	.	PUNCT
ejpam-6307	302	1	let	let	VERB
ejpam-6307	302	2	g	g	PROPN
ejpam-6307	302	3	=	=	SYM
ejpam-6307	302	4	(	(	PUNCT
ejpam-6307	302	5	v	v	NOUN
ejpam-6307	302	6	,	,	PUNCT
ejpam-6307	302	7	σ	σ	PROPN
ejpam-6307	302	8	,	,	PUNCT
ejpam-6307	302	9	µ	µ	NOUN
ejpam-6307	302	10	)	)	PUNCT
ejpam-6307	302	11	be	be	VERB
ejpam-6307	302	12	an	an	DET
ejpam-6307	302	13	fg	fg	NOUN
ejpam-6307	302	14	with	with	ADP
ejpam-6307	302	15	|v|	|v|	PROPN
ejpam-6307	302	16	=	=	SYM
ejpam-6307	302	17	n	n	CCONJ
ejpam-6307	302	18	,	,	PUNCT
ejpam-6307	302	19	and	and	CCONJ
ejpam-6307	302	20	let	let	VERB
ejpam-6307	302	21	γgl1	γgl1	PROPN
ejpam-6307	302	22	≥	≥	PRON
ejpam-6307	302	23	γgl2	γgl2	PROPN
ejpam-6307	302	24	≥	≥	X
ejpam-6307	302	25	·	·	PUNCT
ejpam-6307	302	26	·	·	PUNCT
ejpam-6307	302	27	·	·	PUNCT
ejpam-6307	302	28	≥	≥	NUM
ejpam-6307	302	29	γgln	γgln	NOUN
ejpam-6307	302	30	be	be	VERB
ejpam-6307	302	31	the	the	DET
ejpam-6307	302	32	fuzzy	fuzzy	ADJ
ejpam-6307	302	33	geodetic	geodetic	ADJ
ejpam-6307	302	34	-	-	PUNCT
ejpam-6307	302	35	laplacian	laplacian	NOUN
ejpam-6307	302	36	eigenvalues	eigenvalue	NOUN
ejpam-6307	302	37	.	.	PUNCT
ejpam-6307	303	1	then	then	ADV
ejpam-6307	303	2	,	,	PUNCT
ejpam-6307	303	3	the	the	DET
ejpam-6307	303	4	geodetic	geodetic	ADJ
ejpam-6307	303	5	-	-	PUNCT
ejpam-6307	303	6	laplacian	laplacian	ADJ
ejpam-6307	303	7	energy	energy	NOUN
ejpam-6307	303	8	is	be	AUX
ejpam-6307	303	9	defined	define	VERB
ejpam-6307	303	10	as	as	ADP
ejpam-6307	303	11	gle(g	gle(g	X
ejpam-6307	303	12	)	)	PUNCT
ejpam-6307	304	1	=	=	PUNCT
ejpam-6307	305	1	n∑	n∑	PROPN
ejpam-6307	305	2	i=1	i=1	PROPN
ejpam-6307	305	3	|ψi|	|ψi|	PROPN
ejpam-6307	305	4	,	,	PUNCT
ejpam-6307	305	5	where	where	SCONJ
ejpam-6307	305	6	|ψi|	|ψi|	NOUN
ejpam-6307	305	7	=	=	AUX
ejpam-6307	305	8	∣∣∣∣γgli	∣∣∣∣γgli	NOUN
ejpam-6307	305	9	−	−	NOUN
ejpam-6307	305	10	2	2	NUM
ejpam-6307	305	11	∑	∑	PUNCT
ejpam-6307	305	12	1≤i	1≤i	PROPN
ejpam-6307	305	13	<	<	X
ejpam-6307	305	14	j≤n	j≤n	NOUN
ejpam-6307	305	15	df	df	NOUN
ejpam-6307	305	16	(	(	PUNCT
ejpam-6307	305	17	vi	vi	PROPN
ejpam-6307	305	18	,	,	PUNCT
ejpam-6307	305	19	vj	vj	NOUN
ejpam-6307	305	20	)	)	PUNCT
ejpam-6307	305	21	n	n	PRON
ejpam-6307	305	22	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6307	305	23	.	.	PUNCT
ejpam-6307	305	24	example	example	NOUN
ejpam-6307	306	1	3	3	NUM
ejpam-6307	306	2	.	.	X
ejpam-6307	306	3	figure	figure	NOUN
ejpam-6307	306	4	3	3	NUM
ejpam-6307	306	5	illustrates	illustrate	VERB
ejpam-6307	306	6	the	the	DET
ejpam-6307	306	7	fuzzy	fuzzy	ADJ
ejpam-6307	306	8	geodetic	geodetic	ADJ
ejpam-6307	306	9	-	-	PUNCT
ejpam-6307	306	10	laplacian	laplacian	NOUN
ejpam-6307	306	11	matrix	matrix	NOUN
ejpam-6307	306	12	and	and	CCONJ
ejpam-6307	306	13	its	its	PRON
ejpam-6307	306	14	eigenvalues	eigenvalue	NOUN
ejpam-6307	306	15	for	for	ADP
ejpam-6307	306	16	the	the	DET
ejpam-6307	306	17	fg	fg	PROPN
ejpam-6307	306	18	g.	g.	PROPN
ejpam-6307	306	19	the	the	DET
ejpam-6307	306	20	associated	associate	VERB
ejpam-6307	306	21	fuzzy	fuzzy	ADJ
ejpam-6307	306	22	geodetic	geodetic	ADJ
ejpam-6307	306	23	-	-	PUNCT
ejpam-6307	306	24	laplacian	laplacian	ADJ
ejpam-6307	306	25	matrix	matrix	NOUN
ejpam-6307	306	26	is:	is:	NUM
ejpam-6307	306	27	1.4	1.4	NUM
ejpam-6307	306	28	−0.6	−0.6	X
ejpam-6307	306	29	−0.5	−0.5	NUM
ejpam-6307	307	1	−0.3	−0.3	PROPN
ejpam-6307	307	2	−0.6	−0.6	PROPN
ejpam-6307	307	3	1.7	1.7	NUM
ejpam-6307	307	4	−0.5	−0.5	NOUN
ejpam-6307	307	5	−0.6	−0.6	X
ejpam-6307	307	6	−0.5	−0.5	PUNCT
ejpam-6307	308	1	−0.5	−0.5	NUM
ejpam-6307	308	2	1.3	1.3	NUM
ejpam-6307	308	3	−0.3	−0.3	PROPN
ejpam-6307	308	4	−0.3	−0.3	PROPN
ejpam-6307	308	5	−0.6	−0.6	PROPN
ejpam-6307	308	6	−0.3	−0.3	PROPN
ejpam-6307	308	7	1.2	1.2	NUM
ejpam-6307	308	8	.	.	NOUN
ejpam-6307	308	9	here	here	ADV
ejpam-6307	308	10	,	,	PUNCT
ejpam-6307	308	11	γgl1	γgl1	PROPN
ejpam-6307	308	12	=	=	PROPN
ejpam-6307	308	13	2.2842	2.2842	NUM
ejpam-6307	308	14	,	,	PUNCT
ejpam-6307	308	15	γgl2	γgl2	PROPN
ejpam-6307	308	16	=	=	PROPN
ejpam-6307	308	17	1.8384	1.8384	NUM
ejpam-6307	308	18	,	,	PUNCT
ejpam-6307	308	19	γgl3	γgl3	PROPN
ejpam-6307	308	20	=	=	SYM
ejpam-6307	308	21	1.4774	1.4774	NUM
ejpam-6307	308	22	,	,	PUNCT
ejpam-6307	308	23	and	and	CCONJ
ejpam-6307	308	24	γgl4	γgl4	PROPN
ejpam-6307	308	25	=	=	SYM
ejpam-6307	308	26	0.0	0.0	NUM
ejpam-6307	308	27	,	,	PUNCT
ejpam-6307	308	28	then	then	ADV
ejpam-6307	308	29	gle(g	gle(g	NUM
ejpam-6307	308	30	)	)	PUNCT
ejpam-6307	308	31	=	=	NOUN
ejpam-6307	309	1	2.8	2.8	NUM
ejpam-6307	309	2	.	.	PUNCT
ejpam-6307	310	1	the	the	DET
ejpam-6307	310	2	following	follow	VERB
ejpam-6307	310	3	theorems	theorem	NOUN
ejpam-6307	310	4	establish	establish	VERB
ejpam-6307	310	5	the	the	DET
ejpam-6307	310	6	upper	upper	ADJ
ejpam-6307	310	7	and	and	CCONJ
ejpam-6307	310	8	lower	low	ADJ
ejpam-6307	310	9	bounds	bound	NOUN
ejpam-6307	310	10	for	for	ADP
ejpam-6307	310	11	the	the	DET
ejpam-6307	310	12	geodetic	geodetic	ADJ
ejpam-6307	310	13	-	-	PUNCT
ejpam-6307	310	14	laplacian	laplacian	ADJ
ejpam-6307	310	15	energy	energy	NOUN
ejpam-6307	310	16	.	.	PUNCT
ejpam-6307	311	1	r.	r.	PROPN
ejpam-6307	311	2	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	311	3	,	,	PUNCT
ejpam-6307	311	4	a.	a.	NOUN
ejpam-6307	311	5	m.	m.	PROPN
ejpam-6307	311	6	anto	anto	PROPN
ejpam-6307	311	7	,	,	PUNCT
ejpam-6307	311	8	v.	v.	PROPN
ejpam-6307	311	9	mary	mary	PROPN
ejpam-6307	311	10	mettilda	mettilda	PROPN
ejpam-6307	311	11	rose	rise	VERB
ejpam-6307	311	12	/	/	SYM
ejpam-6307	311	13	eur	eur	PROPN
ejpam-6307	311	14	.	.	PUNCT
ejpam-6307	312	1	j.	j.	PROPN
ejpam-6307	312	2	pure	pure	PROPN
ejpam-6307	312	3	appl	appl	PROPN
ejpam-6307	312	4	.	.	PROPN
ejpam-6307	312	5	math	math	PROPN
ejpam-6307	312	6	,	,	PUNCT
ejpam-6307	312	7	18	18	NUM
ejpam-6307	312	8	(	(	PUNCT
ejpam-6307	312	9	4	4	NUM
ejpam-6307	312	10	)	)	PUNCT
ejpam-6307	312	11	(	(	PUNCT
ejpam-6307	312	12	2025	2025	NUM
ejpam-6307	312	13	)	)	PUNCT
ejpam-6307	312	14	,	,	PUNCT
ejpam-6307	312	15	6307	6307	NUM
ejpam-6307	312	16	14	14	NUM
ejpam-6307	312	17	of	of	ADP
ejpam-6307	312	18	25	25	NUM
ejpam-6307	312	19	figure	figure	NOUN
ejpam-6307	312	20	3	3	NUM
ejpam-6307	312	21	:	:	PUNCT
ejpam-6307	312	22	illustration	illustration	NOUN
ejpam-6307	312	23	of	of	ADP
ejpam-6307	312	24	the	the	DET
ejpam-6307	312	25	fuzzy	fuzzy	ADJ
ejpam-6307	312	26	geodetic	geodetic	ADJ
ejpam-6307	312	27	–	–	PUNCT
ejpam-6307	312	28	laplacian	laplacian	ADJ
ejpam-6307	312	29	matrix	matrix	NOUN
ejpam-6307	312	30	theorem	theorem	VERB
ejpam-6307	312	31	11	11	NUM
ejpam-6307	312	32	.	.	PUNCT
ejpam-6307	313	1	let	let	VERB
ejpam-6307	313	2	g	g	PROPN
ejpam-6307	313	3	=	=	SYM
ejpam-6307	313	4	(	(	PUNCT
ejpam-6307	313	5	v	v	NOUN
ejpam-6307	313	6	,	,	PUNCT
ejpam-6307	313	7	σ	σ	PROPN
ejpam-6307	313	8	,	,	PUNCT
ejpam-6307	313	9	µ	µ	NOUN
ejpam-6307	313	10	)	)	PUNCT
ejpam-6307	313	11	be	be	VERB
ejpam-6307	313	12	an	an	DET
ejpam-6307	313	13	fg	fg	NOUN
ejpam-6307	313	14	with	with	ADP
ejpam-6307	313	15	fuzzy	fuzzy	ADJ
ejpam-6307	313	16	geodetic	geodetic	ADJ
ejpam-6307	313	17	-	-	PUNCT
ejpam-6307	313	18	laplacian	laplacian	ADJ
ejpam-6307	313	19	matrix	matrix	NOUN
ejpam-6307	314	1	mfgld	mfgld	NOUN
ejpam-6307	314	2	whose	whose	DET
ejpam-6307	314	3	diagonal	diagonal	ADJ
ejpam-6307	314	4	entries	entry	NOUN
ejpam-6307	314	5	are	be	AUX
ejpam-6307	314	6	denoted	denote	VERB
ejpam-6307	314	7	as	as	ADP
ejpam-6307	314	8	dmfgld	dmfgld	ADJ
ejpam-6307	314	9	(	(	PUNCT
ejpam-6307	314	10	ti	ti	NOUN
ejpam-6307	314	11	)	)	PUNCT
ejpam-6307	314	12	.	.	PUNCT
ejpam-6307	315	1	then	then	ADV
ejpam-6307	315	2	,	,	PUNCT
ejpam-6307	315	3	the	the	DET
ejpam-6307	315	4	geodetic	geodetic	ADJ
ejpam-6307	315	5	-	-	PUNCT
ejpam-6307	315	6	laplacian	laplacian	NOUN
ejpam-6307	315	7	energy	energy	NOUN
ejpam-6307	315	8	satisfies	satisfie	NOUN
ejpam-6307	315	9	:	:	PUNCT
ejpam-6307	315	10	gle(g	gle(g	NUM
ejpam-6307	315	11	)	)	PUNCT
ejpam-6307	315	12	≤	≤	NUM
ejpam-6307	315	13	√√√√√n	√√√√√n	NOUN
ejpam-6307	315	14	2	2	ADP
ejpam-6307	315	15	∑	∑	PUNCT
ejpam-6307	315	16	1≤i	1≤i	PROPN
ejpam-6307	315	17	<	<	X
ejpam-6307	315	18	j≤n	j≤n	NOUN
ejpam-6307	315	19	d2ij	d2ij	VERB
ejpam-6307	316	1	+	+	CCONJ
ejpam-6307	316	2	n∑	n∑	X
ejpam-6307	316	3	i=1	i=1	PROPN
ejpam-6307	316	4	(	(	PUNCT
ejpam-6307	316	5	dmfgld	dmfgld	ADJ
ejpam-6307	316	6	(	(	PUNCT
ejpam-6307	316	7	ti)−	ti)−	NOUN
ejpam-6307	316	8	2	2	NUM
ejpam-6307	316	9	∑	∑	PUNCT
ejpam-6307	316	10	dij	dij	VERB
ejpam-6307	316	11	n	n	CCONJ
ejpam-6307	316	12	)	)	PUNCT
ejpam-6307	316	13	2	2	NUM
ejpam-6307	316	14	.	.	ADJ
ejpam-6307	316	15	proof	proof	NOUN
ejpam-6307	316	16	.	.	PUNCT
ejpam-6307	317	1	applying	apply	VERB
ejpam-6307	317	2	the	the	DET
ejpam-6307	317	3	cauchy	cauchy	NOUN
ejpam-6307	317	4	–	–	PUNCT
ejpam-6307	317	5	schwarz	schwarz	PROPN
ejpam-6307	317	6	inequality	inequality	NOUN
ejpam-6307	317	7	to	to	ADP
ejpam-6307	317	8	the	the	DET
ejpam-6307	317	9	vector	vector	NOUN
ejpam-6307	317	10	(	(	PUNCT
ejpam-6307	317	11	|ψ1|	|ψ1|	NOUN
ejpam-6307	317	12	,	,	PUNCT
ejpam-6307	317	13	|ψ2|	|ψ2|	NOUN
ejpam-6307	317	14	,	,	PUNCT
ejpam-6307	317	15	.	.	PUNCT
ejpam-6307	317	16	.	.	PUNCT
ejpam-6307	318	1	.	.	PUNCT
ejpam-6307	319	1	,	,	PUNCT
ejpam-6307	319	2	|ψn|	|ψn|	NUM
ejpam-6307	319	3	)	)	PUNCT
ejpam-6307	319	4	,	,	PUNCT
ejpam-6307	319	5	we	we	PRON
ejpam-6307	319	6	have	have	VERB
ejpam-6307	319	7	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6307	319	8	n∑	n∑	PROPN
ejpam-6307	319	9	i=1	i=1	PROPN
ejpam-6307	319	10	ψi	ψi	ADP
ejpam-6307	319	11	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-6307	319	12	2	2	NUM
ejpam-6307	319	13	≤	≤	NOUN
ejpam-6307	320	1	n	n	PRON
ejpam-6307	320	2	n∑	n∑	NOUN
ejpam-6307	320	3	i=1	i=1	PROPN
ejpam-6307	321	1	|ψi|2	|ψi|2	PROPN
ejpam-6307	321	2	,	,	PUNCT
ejpam-6307	321	3	where	where	SCONJ
ejpam-6307	321	4	ψi	ψi	ADP
ejpam-6307	321	5	=	=	SYM
ejpam-6307	321	6	γgli	γgli	NOUN
ejpam-6307	321	7	−	−	PROPN
ejpam-6307	321	8	2	2	NUM
ejpam-6307	321	9	∑	∑	PUNCT
ejpam-6307	321	10	1≤i	1≤i	PROPN
ejpam-6307	321	11	<	<	X
ejpam-6307	321	12	j≤n	j≤n	NOUN
ejpam-6307	321	13	df	df	NOUN
ejpam-6307	321	14	(	(	PUNCT
ejpam-6307	321	15	vi	vi	PROPN
ejpam-6307	321	16	,	,	PUNCT
ejpam-6307	321	17	vj	vj	NOUN
ejpam-6307	321	18	)	)	PUNCT
ejpam-6307	321	19	n	n	NOUN
ejpam-6307	321	20	.	.	PUNCT
ejpam-6307	322	1	by	by	ADP
ejpam-6307	322	2	definition	definition	NOUN
ejpam-6307	322	3	19	19	NUM
ejpam-6307	322	4	,	,	PUNCT
ejpam-6307	322	5	gle(g	gle(g	X
ejpam-6307	322	6	)	)	PUNCT
ejpam-6307	322	7	=	=	PUNCT
ejpam-6307	323	1	n∑	n∑	PROPN
ejpam-6307	323	2	i=1	i=1	PROPN
ejpam-6307	324	1	|ψi|	|ψi|	PROPN
ejpam-6307	324	2	≤	≤	NUM
ejpam-6307	325	1	√√√√n	√√√√n	PROPN
ejpam-6307	325	2	n∑	n∑	PROPN
ejpam-6307	325	3	i=1	i=1	PROPN
ejpam-6307	325	4	|ψi|2	|ψi|2	PUNCT
ejpam-6307	325	5	=	=	PUNCT
ejpam-6307	325	6	√	√	NUM
ejpam-6307	325	7	2mn	2mn	PROPN
ejpam-6307	325	8	,	,	PUNCT
ejpam-6307	325	9	where	where	SCONJ
ejpam-6307	325	10	m	m	VERB
ejpam-6307	325	11	=	=	PUNCT
ejpam-6307	325	12	∑	∑	PUNCT
ejpam-6307	325	13	1≤i	1≤i	X
ejpam-6307	325	14	<	<	X
ejpam-6307	325	15	j≤n	j≤n	NOUN
ejpam-6307	325	16	d2ij	d2ij	VERB
ejpam-6307	325	17	+	+	CCONJ
ejpam-6307	325	18	1	1	NUM
ejpam-6307	325	19	2	2	NUM
ejpam-6307	325	20	n∑	n∑	NOUN
ejpam-6307	325	21	i=1	i=1	PROPN
ejpam-6307	326	1	(	(	PUNCT
ejpam-6307	326	2	dmfgld	dmfgld	ADJ
ejpam-6307	326	3	(	(	PUNCT
ejpam-6307	326	4	ti)−	ti)−	NOUN
ejpam-6307	326	5	2	2	NUM
ejpam-6307	326	6	∑	∑	PUNCT
ejpam-6307	326	7	dij	dij	VERB
ejpam-6307	326	8	n	n	CCONJ
ejpam-6307	326	9	)	)	PUNCT
ejpam-6307	326	10	2	2	NUM
ejpam-6307	326	11	.	.	PUNCT
ejpam-6307	327	1	r.	r.	PROPN
ejpam-6307	327	2	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	327	3	,	,	PUNCT
ejpam-6307	327	4	a.	a.	NOUN
ejpam-6307	327	5	m.	m.	PROPN
ejpam-6307	327	6	anto	anto	PROPN
ejpam-6307	327	7	,	,	PUNCT
ejpam-6307	327	8	v.	v.	PROPN
ejpam-6307	327	9	mary	mary	PROPN
ejpam-6307	327	10	mettilda	mettilda	PROPN
ejpam-6307	327	11	rose	rise	VERB
ejpam-6307	327	12	/	/	SYM
ejpam-6307	327	13	eur	eur	PROPN
ejpam-6307	327	14	.	.	PUNCT
ejpam-6307	328	1	j.	j.	PROPN
ejpam-6307	328	2	pure	pure	PROPN
ejpam-6307	328	3	appl	appl	PROPN
ejpam-6307	328	4	.	.	PROPN
ejpam-6307	328	5	math	math	PROPN
ejpam-6307	328	6	,	,	PUNCT
ejpam-6307	328	7	18	18	NUM
ejpam-6307	328	8	(	(	PUNCT
ejpam-6307	328	9	4	4	NUM
ejpam-6307	328	10	)	)	PUNCT
ejpam-6307	328	11	(	(	PUNCT
ejpam-6307	328	12	2025	2025	NUM
ejpam-6307	328	13	)	)	PUNCT
ejpam-6307	328	14	,	,	PUNCT
ejpam-6307	328	15	6307	6307	NUM
ejpam-6307	328	16	15	15	NUM
ejpam-6307	328	17	of	of	ADP
ejpam-6307	328	18	25	25	NUM
ejpam-6307	328	19	thus	thus	ADV
ejpam-6307	328	20	,	,	PUNCT
ejpam-6307	328	21	gle(g	gle(g	PROPN
ejpam-6307	328	22	)	)	PUNCT
ejpam-6307	328	23	≤	≤	NUM
ejpam-6307	328	24	√√√√√n	√√√√√n	NOUN
ejpam-6307	328	25	2	2	ADP
ejpam-6307	328	26	∑	∑	PUNCT
ejpam-6307	328	27	1≤i	1≤i	PROPN
ejpam-6307	328	28	<	<	X
ejpam-6307	328	29	j≤n	j≤n	NOUN
ejpam-6307	328	30	d2ij	d2ij	VERB
ejpam-6307	329	1	+	+	CCONJ
ejpam-6307	329	2	n∑	n∑	X
ejpam-6307	329	3	i=1	i=1	PROPN
ejpam-6307	329	4	(	(	PUNCT
ejpam-6307	329	5	dmfgld	dmfgld	ADJ
ejpam-6307	329	6	(	(	PUNCT
ejpam-6307	329	7	ti)−	ti)−	NOUN
ejpam-6307	329	8	2	2	NUM
ejpam-6307	329	9	∑	∑	PUNCT
ejpam-6307	329	10	dij	dij	VERB
ejpam-6307	329	11	n	n	CCONJ
ejpam-6307	329	12	)	)	SYM
ejpam-6307	329	13	2	2	NUM
ejpam-6307	329	14	.	.	NOUN
ejpam-6307	329	15	theorem	theorem	NOUN
ejpam-6307	329	16	12	12	NUM
ejpam-6307	329	17	.	.	PUNCT
ejpam-6307	330	1	let	let	VERB
ejpam-6307	330	2	g	g	PROPN
ejpam-6307	330	3	=	=	SYM
ejpam-6307	330	4	(	(	PUNCT
ejpam-6307	330	5	v	v	NOUN
ejpam-6307	330	6	,	,	PUNCT
ejpam-6307	330	7	σ	σ	PROPN
ejpam-6307	330	8	,	,	PUNCT
ejpam-6307	330	9	µ	µ	NOUN
ejpam-6307	330	10	)	)	PUNCT
ejpam-6307	330	11	be	be	VERB
ejpam-6307	330	12	an	an	DET
ejpam-6307	330	13	fg	fg	NOUN
ejpam-6307	330	14	with	with	ADP
ejpam-6307	330	15	fuzzy	fuzzy	ADJ
ejpam-6307	330	16	geodetic	geodetic	ADJ
ejpam-6307	330	17	-	-	PUNCT
ejpam-6307	330	18	laplacian	laplacian	ADJ
ejpam-6307	330	19	matrix	matrix	NOUN
ejpam-6307	330	20	mfgld	mfgld	ADV
ejpam-6307	330	21	,	,	PUNCT
ejpam-6307	330	22	and	and	CCONJ
ejpam-6307	330	23	let	let	VERB
ejpam-6307	330	24	its	its	PRON
ejpam-6307	330	25	diagonal	diagonal	ADJ
ejpam-6307	330	26	entries	entry	NOUN
ejpam-6307	330	27	be	be	AUX
ejpam-6307	330	28	represented	represent	VERB
ejpam-6307	330	29	by	by	ADP
ejpam-6307	330	30	dmfgld	dmfgld	PROPN
ejpam-6307	330	31	(	(	PUNCT
ejpam-6307	330	32	ti	ti	NOUN
ejpam-6307	330	33	)	)	PUNCT
ejpam-6307	330	34	.	.	PUNCT
ejpam-6307	331	1	then	then	ADV
ejpam-6307	331	2	,	,	PUNCT
ejpam-6307	331	3	the	the	DET
ejpam-6307	331	4	geodetic	geodetic	ADJ
ejpam-6307	331	5	-	-	PUNCT
ejpam-6307	331	6	laplacian	laplacian	NOUN
ejpam-6307	331	7	energy	energy	NOUN
ejpam-6307	331	8	satisfies	satisfy	VERB
ejpam-6307	331	9	the	the	DET
ejpam-6307	331	10	inequality	inequality	NOUN
ejpam-6307	331	11	:	:	PUNCT
ejpam-6307	331	12	gle(g	gle(g	NUM
ejpam-6307	331	13	)	)	PUNCT
ejpam-6307	331	14	≥	≥	NOUN
ejpam-6307	331	15	2	2	NUM
ejpam-6307	331	16	√(∑	√(∑	PROPN
ejpam-6307	331	17	1≤i	1≤i	NUM
ejpam-6307	331	18	<	<	X
ejpam-6307	331	19	j≤n	j≤n	NOUN
ejpam-6307	331	20	d	d	NOUN
ejpam-6307	331	21	2	2	NUM
ejpam-6307	331	22	ij	ij	NOUN
ejpam-6307	331	23	+	+	NOUN
ejpam-6307	331	24	1	1	NUM
ejpam-6307	331	25	2	2	NUM
ejpam-6307	331	26	∑n	∑n	PROPN
ejpam-6307	331	27	i=1	i=1	PROPN
ejpam-6307	331	28	(	(	PUNCT
ejpam-6307	331	29	dmfgld	dmfgld	ADJ
ejpam-6307	331	30	(	(	PUNCT
ejpam-6307	331	31	ti)−	ti)−	NOUN
ejpam-6307	331	32	2	2	NUM
ejpam-6307	331	33	∑	∑	PUNCT
ejpam-6307	331	34	dij	dij	VERB
ejpam-6307	331	35	n	n	CCONJ
ejpam-6307	331	36	)	)	PUNCT
ejpam-6307	331	37	2	2	NUM
ejpam-6307	331	38	)	)	PUNCT
ejpam-6307	331	39	.	.	PUNCT
ejpam-6307	332	1	proof	proof	NOUN
ejpam-6307	332	2	.	.	PUNCT
ejpam-6307	333	1	by	by	ADP
ejpam-6307	333	2	definition	definition	NOUN
ejpam-6307	333	3	19	19	NUM
ejpam-6307	333	4	,	,	PUNCT
ejpam-6307	333	5	we	we	PRON
ejpam-6307	333	6	have	have	VERB
ejpam-6307	333	7	(	(	PUNCT
ejpam-6307	333	8	gle(g))2	gle(g))2	NOUN
ejpam-6307	333	9	=	=	SYM
ejpam-6307	333	10	(	(	PUNCT
ejpam-6307	333	11	∑n	∑n	PROPN
ejpam-6307	333	12	i=1	i=1	PROPN
ejpam-6307	333	13	|ψi|)2	|ψi|)2	PROPN
ejpam-6307	333	14	=	=	SYM
ejpam-6307	333	15	∑n	∑n	PROPN
ejpam-6307	333	16	i=1	i=1	X
ejpam-6307	333	17	|ψi|2	|ψi|2	PUNCT
ejpam-6307	334	1	+	+	NUM
ejpam-6307	334	2	2	2	NUM
ejpam-6307	334	3	∑	∑	SYM
ejpam-6307	334	4	1≤i	1≤i	NUM
ejpam-6307	334	5	<	<	X
ejpam-6307	334	6	j≤n	j≤n	NOUN
ejpam-6307	334	7	|ψi||ψj	|ψi||ψj	PROPN
ejpam-6307	334	8	|	|	ADV
ejpam-6307	334	9	≥	≥	NUM
ejpam-6307	334	10	4	4	NUM
ejpam-6307	334	11	m	m	NOUN
ejpam-6307	334	12	.	.	PUNCT
ejpam-6307	335	1	thus	thus	ADV
ejpam-6307	335	2	we	we	PRON
ejpam-6307	335	3	get	get	VERB
ejpam-6307	335	4	,	,	PUNCT
ejpam-6307	335	5	gle(g	gle(g	PROPN
ejpam-6307	335	6	)	)	PUNCT
ejpam-6307	335	7	≥	≥	NOUN
ejpam-6307	335	8	2	2	NUM
ejpam-6307	335	9	√(∑	√(∑	PROPN
ejpam-6307	335	10	1≤i	1≤i	NUM
ejpam-6307	335	11	<	<	X
ejpam-6307	335	12	j≤n	j≤n	NOUN
ejpam-6307	335	13	d	d	NOUN
ejpam-6307	335	14	2	2	NUM
ejpam-6307	335	15	ij	ij	NOUN
ejpam-6307	335	16	+	+	NOUN
ejpam-6307	335	17	1	1	NUM
ejpam-6307	335	18	2	2	NUM
ejpam-6307	335	19	∑n	∑n	PROPN
ejpam-6307	335	20	i=1	i=1	PROPN
ejpam-6307	335	21	(	(	PUNCT
ejpam-6307	335	22	dmfgld	dmfgld	ADJ
ejpam-6307	335	23	(	(	PUNCT
ejpam-6307	335	24	ti)−	ti)−	NOUN
ejpam-6307	335	25	2	2	NUM
ejpam-6307	335	26	∑	∑	PUNCT
ejpam-6307	335	27	dij	dij	VERB
ejpam-6307	335	28	n	n	CCONJ
ejpam-6307	335	29	)	)	PUNCT
ejpam-6307	335	30	2	2	NUM
ejpam-6307	335	31	)	)	PUNCT
ejpam-6307	335	32	.	.	PUNCT
ejpam-6307	336	1	theorem	theorem	VERB
ejpam-6307	336	2	13	13	NUM
ejpam-6307	336	3	.	.	PUNCT
ejpam-6307	337	1	let	let	VERB
ejpam-6307	337	2	g	g	PROPN
ejpam-6307	337	3	=	=	SYM
ejpam-6307	337	4	(	(	PUNCT
ejpam-6307	337	5	v	v	NOUN
ejpam-6307	337	6	,	,	PUNCT
ejpam-6307	337	7	σ	σ	PROPN
ejpam-6307	337	8	,	,	PUNCT
ejpam-6307	337	9	µ	µ	NOUN
ejpam-6307	337	10	)	)	PUNCT
ejpam-6307	337	11	be	be	AUX
ejpam-6307	337	12	an	an	DET
ejpam-6307	337	13	fg	fg	NOUN
ejpam-6307	337	14	.	.	PUNCT
ejpam-6307	338	1	if	if	SCONJ
ejpam-6307	338	2	g	g	PROPN
ejpam-6307	338	3	is	be	AUX
ejpam-6307	338	4	a	a	DET
ejpam-6307	338	5	geodetic	geodetic	ADJ
ejpam-6307	338	6	block	block	NOUN
ejpam-6307	338	7	,	,	PUNCT
ejpam-6307	338	8	then	then	ADV
ejpam-6307	338	9	le(g	le(g	NUM
ejpam-6307	338	10	)	)	PUNCT
ejpam-6307	338	11	=	=	SYM
ejpam-6307	338	12	gle(g	gle(g	PROPN
ejpam-6307	338	13	)	)	PUNCT
ejpam-6307	338	14	.	.	PUNCT
ejpam-6307	339	1	proof	proof	NOUN
ejpam-6307	339	2	.	.	PUNCT
ejpam-6307	340	1	since	since	SCONJ
ejpam-6307	340	2	g	g	PROPN
ejpam-6307	340	3	is	be	AUX
ejpam-6307	340	4	a	a	DET
ejpam-6307	340	5	geodetic	geodetic	ADJ
ejpam-6307	340	6	block	block	NOUN
ejpam-6307	340	7	,	,	PUNCT
ejpam-6307	340	8	every	every	DET
ejpam-6307	340	9	edge	edge	NOUN
ejpam-6307	340	10	corresponds	correspond	VERB
ejpam-6307	340	11	to	to	ADP
ejpam-6307	340	12	a	a	DET
ejpam-6307	340	13	distinct	distinct	ADJ
ejpam-6307	340	14	fuzzy	fuzzy	ADJ
ejpam-6307	340	15	geodesic	geodesic	NOUN
ejpam-6307	340	16	.	.	PUNCT
ejpam-6307	341	1	consequently	consequently	ADV
ejpam-6307	341	2	,	,	PUNCT
ejpam-6307	341	3	the	the	DET
ejpam-6307	341	4	fuzzy	fuzzy	ADJ
ejpam-6307	341	5	geodetic	geodetic	ADJ
ejpam-6307	341	6	-	-	PUNCT
ejpam-6307	341	7	laplacian	laplacian	ADJ
ejpam-6307	341	8	matrix	matrix	NOUN
ejpam-6307	341	9	mfgld	mfgld	NOUN
ejpam-6307	341	10	is	be	AUX
ejpam-6307	341	11	identical	identical	ADJ
ejpam-6307	341	12	to	to	ADP
ejpam-6307	341	13	the	the	DET
ejpam-6307	341	14	standard	standard	ADJ
ejpam-6307	341	15	laplacian	laplacian	ADJ
ejpam-6307	341	16	matrix	matrix	NOUN
ejpam-6307	341	17	.	.	PUNCT
ejpam-6307	342	1	hence	hence	ADV
ejpam-6307	342	2	,	,	PUNCT
ejpam-6307	342	3	the	the	DET
ejpam-6307	342	4	spectra	spectra	NOUN
ejpam-6307	342	5	of	of	ADP
ejpam-6307	342	6	both	both	DET
ejpam-6307	342	7	matrices	matrix	NOUN
ejpam-6307	342	8	are	be	AUX
ejpam-6307	342	9	the	the	DET
ejpam-6307	342	10	same	same	ADJ
ejpam-6307	342	11	,	,	PUNCT
ejpam-6307	342	12	and	and	CCONJ
ejpam-6307	342	13	it	it	PRON
ejpam-6307	342	14	follows	follow	VERB
ejpam-6307	342	15	that	that	PRON
ejpam-6307	342	16	le(g	le(g	PUNCT
ejpam-6307	342	17	)	)	PUNCT
ejpam-6307	342	18	=	=	SYM
ejpam-6307	342	19	gle(g	gle(g	PROPN
ejpam-6307	342	20	)	)	PUNCT
ejpam-6307	342	21	.	.	PUNCT
ejpam-6307	343	1	6	6	X
ejpam-6307	343	2	.	.	X
ejpam-6307	343	3	fuzzy	fuzzy	ADJ
ejpam-6307	343	4	detour	detour	NOUN
ejpam-6307	343	5	-	-	PUNCT
ejpam-6307	343	6	laplacian	laplacian	ADJ
ejpam-6307	343	7	energy	energy	NOUN
ejpam-6307	343	8	in	in	ADP
ejpam-6307	343	9	fuzzy	fuzzy	ADJ
ejpam-6307	343	10	graph	graph	NOUN
ejpam-6307	343	11	theory	theory	NOUN
ejpam-6307	343	12	,	,	PUNCT
ejpam-6307	343	13	detour	detour	PRON
ejpam-6307	343	14	distance	distance	NOUN
ejpam-6307	343	15	has	have	AUX
ejpam-6307	343	16	been	be	AUX
ejpam-6307	343	17	studied	study	VERB
ejpam-6307	343	18	for	for	ADP
ejpam-6307	343	19	its	its	PRON
ejpam-6307	343	20	role	role	NOUN
ejpam-6307	343	21	in	in	ADP
ejpam-6307	343	22	path	path	NOUN
ejpam-6307	343	23	analysis	analysis	NOUN
ejpam-6307	343	24	,	,	PUNCT
ejpam-6307	343	25	although	although	SCONJ
ejpam-6307	343	26	detour	detour	NOUN
ejpam-6307	343	27	-	-	PUNCT
ejpam-6307	343	28	based	base	VERB
ejpam-6307	343	29	spectral	spectral	ADJ
ejpam-6307	343	30	properties	property	NOUN
ejpam-6307	343	31	have	have	AUX
ejpam-6307	343	32	been	be	AUX
ejpam-6307	343	33	explored	explore	VERB
ejpam-6307	343	34	in	in	ADP
ejpam-6307	343	35	earlier	early	ADJ
ejpam-6307	343	36	sections	section	NOUN
ejpam-6307	343	37	,	,	PUNCT
ejpam-6307	343	38	the	the	DET
ejpam-6307	343	39	extension	extension	NOUN
ejpam-6307	343	40	of	of	ADP
ejpam-6307	343	41	laplacian	laplacian	ADJ
ejpam-6307	343	42	energy	energy	NOUN
ejpam-6307	343	43	concepts	concept	NOUN
ejpam-6307	343	44	to	to	ADP
ejpam-6307	343	45	detour	detour	NOUN
ejpam-6307	343	46	-	-	PUNCT
ejpam-6307	343	47	based	base	VERB
ejpam-6307	343	48	frameworks	framework	NOUN
ejpam-6307	343	49	remains	remains	AUX
ejpam-6307	343	50	largely	largely	ADV
ejpam-6307	343	51	unaddressed	unaddresse	VERB
ejpam-6307	343	52	.	.	PUNCT
ejpam-6307	344	1	in	in	ADP
ejpam-6307	344	2	this	this	DET
ejpam-6307	344	3	section	section	NOUN
ejpam-6307	344	4	,	,	PUNCT
ejpam-6307	344	5	we	we	PRON
ejpam-6307	344	6	define	define	VERB
ejpam-6307	344	7	the	the	DET
ejpam-6307	344	8	fuzzy	fuzzy	ADJ
ejpam-6307	344	9	detour	detour	NOUN
ejpam-6307	344	10	-	-	PUNCT
ejpam-6307	344	11	laplacian	laplacian	ADJ
ejpam-6307	344	12	energy	energy	NOUN
ejpam-6307	344	13	by	by	ADP
ejpam-6307	344	14	employing	employ	VERB
ejpam-6307	344	15	the	the	DET
ejpam-6307	344	16	spectrum	spectrum	NOUN
ejpam-6307	344	17	of	of	ADP
ejpam-6307	344	18	the	the	DET
ejpam-6307	344	19	fuzzy	fuzzy	ADJ
ejpam-6307	344	20	detour	detour	NOUN
ejpam-6307	344	21	-	-	PUNCT
ejpam-6307	344	22	distance	distance	NOUN
ejpam-6307	344	23	laplacian	laplacian	ADJ
ejpam-6307	344	24	matrix	matrix	NOUN
ejpam-6307	344	25	.	.	PUNCT
ejpam-6307	345	1	this	this	DET
ejpam-6307	345	2	formulation	formulation	NOUN
ejpam-6307	345	3	offers	offer	VERB
ejpam-6307	345	4	a	a	DET
ejpam-6307	345	5	new	new	ADJ
ejpam-6307	345	6	spectral	spectral	ADJ
ejpam-6307	345	7	invariant	invariant	ADJ
ejpam-6307	345	8	and	and	CCONJ
ejpam-6307	345	9	bridges	bridge	NOUN
ejpam-6307	345	10	the	the	DET
ejpam-6307	345	11	gap	gap	NOUN
ejpam-6307	345	12	between	between	ADP
ejpam-6307	345	13	classical	classical	ADJ
ejpam-6307	345	14	laplacian	laplacian	ADJ
ejpam-6307	345	15	energy	energy	NOUN
ejpam-6307	345	16	and	and	CCONJ
ejpam-6307	345	17	detour	detour	NOUN
ejpam-6307	345	18	-	-	PUNCT
ejpam-6307	345	19	based	base	VERB
ejpam-6307	345	20	distance	distance	NOUN
ejpam-6307	345	21	measures	measure	NOUN
ejpam-6307	345	22	in	in	ADP
ejpam-6307	345	23	fuzzy	fuzzy	ADJ
ejpam-6307	345	24	graphs	graph	NOUN
ejpam-6307	345	25	.	.	PUNCT
ejpam-6307	346	1	definition	definition	NOUN
ejpam-6307	346	2	20	20	NUM
ejpam-6307	346	3	.	.	PUNCT
ejpam-6307	347	1	let	let	VERB
ejpam-6307	347	2	g	g	PROPN
ejpam-6307	347	3	=	=	SYM
ejpam-6307	347	4	(	(	PUNCT
ejpam-6307	347	5	v	v	NOUN
ejpam-6307	347	6	,	,	PUNCT
ejpam-6307	347	7	σ	σ	PROPN
ejpam-6307	347	8	,	,	PUNCT
ejpam-6307	347	9	µ	µ	NOUN
ejpam-6307	347	10	)	)	PUNCT
ejpam-6307	347	11	be	be	VERB
ejpam-6307	347	12	a	a	DET
ejpam-6307	347	13	connected	connected	ADJ
ejpam-6307	347	14	fg	fg	NOUN
ejpam-6307	347	15	with	with	ADP
ejpam-6307	347	16	|v|	|v|	PROPN
ejpam-6307	347	17	=	=	SYM
ejpam-6307	347	18	n	n	CCONJ
ejpam-6307	347	19	,	,	PUNCT
ejpam-6307	347	20	and	and	CCONJ
ejpam-6307	347	21	let	let	VERB
ejpam-6307	347	22	mfdd	mfdd	NOUN
ejpam-6307	347	23	denote	denote	VERB
ejpam-6307	347	24	the	the	DET
ejpam-6307	347	25	fd	fd	NOUN
ejpam-6307	347	26	-	-	PUNCT
ejpam-6307	347	27	matrix	matrix	NOUN
ejpam-6307	347	28	.	.	PUNCT
ejpam-6307	348	1	then	then	ADV
ejpam-6307	348	2	,	,	PUNCT
ejpam-6307	348	3	the	the	DET
ejpam-6307	348	4	detour	detour	NOUN
ejpam-6307	348	5	transmission	transmission	NOUN
ejpam-6307	348	6	matrix	matrix	NOUN
ejpam-6307	348	7	tfdd	tfdd	NOUN
ejpam-6307	348	8	is	be	AUX
ejpam-6307	348	9	an	an	DET
ejpam-6307	348	10	n	n	NUM
ejpam-6307	348	11	×	×	NOUN
ejpam-6307	348	12	n	n	CCONJ
ejpam-6307	348	13	diagonal	diagonal	ADJ
ejpam-6307	348	14	matrix	matrix	NOUN
ejpam-6307	348	15	whose	whose	DET
ejpam-6307	348	16	diagonal	diagonal	ADJ
ejpam-6307	348	17	entries	entry	NOUN
ejpam-6307	348	18	are	be	AUX
ejpam-6307	348	19	given	give	VERB
ejpam-6307	348	20	by	by	ADP
ejpam-6307	348	21	tii	tii	PROPN
ejpam-6307	348	22	=	=	SYM
ejpam-6307	348	23	n∑	n∑	PROPN
ejpam-6307	348	24	j=1	j=1	PROPN
ejpam-6307	348	25	∆(vi	∆(vi	PROPN
ejpam-6307	348	26	,	,	PUNCT
ejpam-6307	348	27	vj	vj	NOUN
ejpam-6307	348	28	)	)	PUNCT
ejpam-6307	348	29	,	,	PUNCT
ejpam-6307	348	30	where	where	SCONJ
ejpam-6307	348	31	∆(vi	∆(vi	NOUN
ejpam-6307	348	32	,	,	PUNCT
ejpam-6307	348	33	vj	vj	NOUN
ejpam-6307	348	34	)	)	PUNCT
ejpam-6307	348	35	denotes	denote	VERB
ejpam-6307	348	36	the	the	DET
ejpam-6307	348	37	fuzzy	fuzzy	ADJ
ejpam-6307	348	38	detour	detour	NOUN
ejpam-6307	348	39	distance	distance	NOUN
ejpam-6307	348	40	between	between	ADP
ejpam-6307	348	41	vertices	vertex	NOUN
ejpam-6307	348	42	vi	vi	PROPN
ejpam-6307	348	43	and	and	CCONJ
ejpam-6307	348	44	vj	vj	PROPN
ejpam-6307	348	45	.	.	PROPN
ejpam-6307	348	46	r.	r.	PROPN
ejpam-6307	348	47	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	348	48	,	,	PUNCT
ejpam-6307	348	49	a.	a.	NOUN
ejpam-6307	348	50	m.	m.	PROPN
ejpam-6307	348	51	anto	anto	PROPN
ejpam-6307	348	52	,	,	PUNCT
ejpam-6307	348	53	v.	v.	PROPN
ejpam-6307	348	54	mary	mary	PROPN
ejpam-6307	348	55	mettilda	mettilda	PROPN
ejpam-6307	348	56	rose	rise	VERB
ejpam-6307	348	57	/	/	SYM
ejpam-6307	348	58	eur	eur	PROPN
ejpam-6307	348	59	.	.	PUNCT
ejpam-6307	349	1	j.	j.	PROPN
ejpam-6307	349	2	pure	pure	PROPN
ejpam-6307	349	3	appl	appl	PROPN
ejpam-6307	349	4	.	.	PROPN
ejpam-6307	349	5	math	math	PROPN
ejpam-6307	349	6	,	,	PUNCT
ejpam-6307	349	7	18	18	NUM
ejpam-6307	349	8	(	(	PUNCT
ejpam-6307	349	9	4	4	NUM
ejpam-6307	349	10	)	)	PUNCT
ejpam-6307	349	11	(	(	PUNCT
ejpam-6307	349	12	2025	2025	NUM
ejpam-6307	349	13	)	)	PUNCT
ejpam-6307	349	14	,	,	PUNCT
ejpam-6307	349	15	6307	6307	NUM
ejpam-6307	349	16	16	16	NUM
ejpam-6307	349	17	of	of	ADP
ejpam-6307	349	18	25	25	NUM
ejpam-6307	349	19	definition	definition	NOUN
ejpam-6307	349	20	21	21	NUM
ejpam-6307	349	21	.	.	PUNCT
ejpam-6307	350	1	let	let	VERB
ejpam-6307	350	2	g	g	PROPN
ejpam-6307	350	3	=	=	SYM
ejpam-6307	350	4	(	(	PUNCT
ejpam-6307	350	5	v	v	NOUN
ejpam-6307	350	6	,	,	PUNCT
ejpam-6307	350	7	σ	σ	PROPN
ejpam-6307	350	8	,	,	PUNCT
ejpam-6307	350	9	µ	µ	NOUN
ejpam-6307	350	10	)	)	PUNCT
ejpam-6307	350	11	be	be	AUX
ejpam-6307	350	12	an	an	DET
ejpam-6307	350	13	fg	fg	PROPN
ejpam-6307	350	14	.	.	PROPN
ejpam-6307	350	15	ifmfdd	ifmfdd	PROPN
ejpam-6307	350	16	and	and	CCONJ
ejpam-6307	350	17	tfdd	tfdd	PROPN
ejpam-6307	350	18	denote	denote	VERB
ejpam-6307	350	19	the	the	DET
ejpam-6307	350	20	fd	fd	NOUN
ejpam-6307	350	21	-	-	PUNCT
ejpam-6307	350	22	matrix	matrix	NOUN
ejpam-6307	350	23	and	and	CCONJ
ejpam-6307	350	24	the	the	DET
ejpam-6307	350	25	detour	detour	NOUN
ejpam-6307	350	26	transmission	transmission	NOUN
ejpam-6307	350	27	matrix	matrix	NOUN
ejpam-6307	350	28	of	of	ADP
ejpam-6307	350	29	g	g	NOUN
ejpam-6307	350	30	,	,	PUNCT
ejpam-6307	350	31	respectively	respectively	ADV
ejpam-6307	350	32	,	,	PUNCT
ejpam-6307	350	33	then	then	ADV
ejpam-6307	350	34	their	their	PRON
ejpam-6307	350	35	difference	difference	NOUN
ejpam-6307	350	36	is	be	AUX
ejpam-6307	350	37	defined	define	VERB
ejpam-6307	350	38	as	as	ADP
ejpam-6307	350	39	the	the	DET
ejpam-6307	350	40	fuzzy	fuzzy	ADJ
ejpam-6307	350	41	detour	detour	NOUN
ejpam-6307	350	42	-	-	PUNCT
ejpam-6307	350	43	laplacian	laplacian	ADJ
ejpam-6307	350	44	matrixmfdld	matrixmfdld	NOUN
ejpam-6307	350	45	,	,	PUNCT
ejpam-6307	350	46	given	give	VERB
ejpam-6307	350	47	by	by	ADP
ejpam-6307	350	48	mfdld	mfdld	NOUN
ejpam-6307	350	49	=	=	SYM
ejpam-6307	350	50	tfdd	tfdd	PROPN
ejpam-6307	350	51	−mfdd	−mfdd	PROPN
ejpam-6307	350	52	.	.	PUNCT
ejpam-6307	351	1	definition	definition	NOUN
ejpam-6307	351	2	22	22	NUM
ejpam-6307	351	3	.	.	PUNCT
ejpam-6307	352	1	let	let	VERB
ejpam-6307	352	2	g	g	PROPN
ejpam-6307	352	3	=	=	SYM
ejpam-6307	352	4	(	(	PUNCT
ejpam-6307	352	5	v	v	NOUN
ejpam-6307	352	6	,	,	PUNCT
ejpam-6307	352	7	σ	σ	PROPN
ejpam-6307	352	8	,	,	PUNCT
ejpam-6307	352	9	µ	µ	NOUN
ejpam-6307	352	10	)	)	PUNCT
ejpam-6307	352	11	be	be	VERB
ejpam-6307	352	12	an	an	DET
ejpam-6307	352	13	fg	fg	NOUN
ejpam-6307	352	14	with	with	ADP
ejpam-6307	352	15	|v|	|v|	PROPN
ejpam-6307	352	16	=	=	SYM
ejpam-6307	352	17	n	n	CCONJ
ejpam-6307	352	18	,	,	PUNCT
ejpam-6307	352	19	and	and	CCONJ
ejpam-6307	352	20	let	let	VERB
ejpam-6307	352	21	γdl1	γdl1	PROPN
ejpam-6307	352	22	≥	≥	PROPN
ejpam-6307	352	23	γdl2	γdl2	PROPN
ejpam-6307	352	24	≥	≥	NUM
ejpam-6307	352	25	·	·	PUNCT
ejpam-6307	352	26	·	·	PUNCT
ejpam-6307	352	27	·	·	PUNCT
ejpam-6307	352	28	≥	≥	PRON
ejpam-6307	352	29	γdln	γdln	AUX
ejpam-6307	352	30	denote	denote	VERB
ejpam-6307	352	31	the	the	DET
ejpam-6307	352	32	fuzzy	fuzzy	ADJ
ejpam-6307	352	33	detour	detour	NOUN
ejpam-6307	352	34	-	-	PUNCT
ejpam-6307	352	35	laplacian	laplacian	ADJ
ejpam-6307	352	36	eigenvalues	eigenvalue	NOUN
ejpam-6307	352	37	of	of	ADP
ejpam-6307	352	38	g.	g.	PROPN
ejpam-6307	352	39	then	then	ADV
ejpam-6307	352	40	the	the	DET
ejpam-6307	352	41	fuzzy	fuzzy	ADJ
ejpam-6307	352	42	detour	detour	NOUN
ejpam-6307	352	43	-	-	PUNCT
ejpam-6307	352	44	laplacian	laplacian	ADJ
ejpam-6307	352	45	energy	energy	NOUN
ejpam-6307	352	46	is	be	AUX
ejpam-6307	352	47	defined	define	VERB
ejpam-6307	352	48	as	as	ADP
ejpam-6307	352	49	dle(g	dle(g	PROPN
ejpam-6307	352	50	)	)	PUNCT
ejpam-6307	353	1	=	=	SYM
ejpam-6307	353	2	n∑	n∑	PROPN
ejpam-6307	353	3	i=1	i=1	PROPN
ejpam-6307	353	4	|χi|	|χi|	PROPN
ejpam-6307	353	5	,	,	PUNCT
ejpam-6307	353	6	where	where	SCONJ
ejpam-6307	353	7	χi	χi	NOUN
ejpam-6307	353	8	=	=	SYM
ejpam-6307	353	9	γdli	γdli	NOUN
ejpam-6307	353	10	−	−	PROPN
ejpam-6307	353	11	2	2	NUM
ejpam-6307	353	12	n	n	PROPN
ejpam-6307	353	13	∑	∑	ADV
ejpam-6307	353	14	1≤i	1≤i	PROPN
ejpam-6307	353	15	<	<	X
ejpam-6307	353	16	j≤n	j≤n	NOUN
ejpam-6307	353	17	∆(vi	∆(vi	NOUN
ejpam-6307	353	18	,	,	PUNCT
ejpam-6307	353	19	vj	vj	NOUN
ejpam-6307	353	20	)	)	PUNCT
ejpam-6307	353	21	.	.	PUNCT
ejpam-6307	354	1	example	example	NOUN
ejpam-6307	355	1	4	4	NUM
ejpam-6307	355	2	.	.	PUNCT
ejpam-6307	355	3	to	to	PART
ejpam-6307	355	4	comprehend	comprehend	VERB
ejpam-6307	355	5	the	the	DET
ejpam-6307	355	6	fuzzy	fuzzy	ADJ
ejpam-6307	355	7	detour	detour	NOUN
ejpam-6307	355	8	-	-	PUNCT
ejpam-6307	355	9	laplacian	laplacian	ADJ
ejpam-6307	355	10	matrix	matrix	NOUN
ejpam-6307	355	11	and	and	CCONJ
ejpam-6307	355	12	its	its	PRON
ejpam-6307	355	13	eigenvalues	eigenvalue	NOUN
ejpam-6307	355	14	,	,	PUNCT
ejpam-6307	355	15	consider	consider	VERB
ejpam-6307	355	16	the	the	DET
ejpam-6307	355	17	graph	graph	NOUN
ejpam-6307	355	18	g	g	NOUN
ejpam-6307	355	19	shown	show	VERB
ejpam-6307	355	20	in	in	ADP
ejpam-6307	355	21	figure	figure	NOUN
ejpam-6307	355	22	2	2	NUM
ejpam-6307	355	23	.	.	PUNCT
ejpam-6307	356	1	the	the	DET
ejpam-6307	356	2	associated	associated	ADJ
ejpam-6307	356	3	fuzzy	fuzzy	ADJ
ejpam-6307	356	4	detour	detour	NOUN
ejpam-6307	356	5	-	-	PUNCT
ejpam-6307	356	6	laplacian	laplacian	ADJ
ejpam-6307	356	7	matrixmfdld	matrixmfdld	PROPN
ejpam-6307	356	8	is	be	AUX
ejpam-6307	356	9	given	give	VERB
ejpam-6307	356	10	by	by	ADP
ejpam-6307	356	11	:	:	PUNCT
ejpam-6307	356	12			PROPN
ejpam-6307	356	13	34.99	34.99	NUM
ejpam-6307	356	14	−11.66	−11.66	X
ejpam-6307	356	15	−10.00	−10.00	CCONJ
ejpam-6307	357	1	−13.33	−13.33	X
ejpam-6307	357	2	−11.66	−11.66	VERB
ejpam-6307	357	3	38.32	38.32	NUM
ejpam-6307	357	4	−12.00	−12.00	NOUN
ejpam-6307	357	5	−14.66	−14.66	PROPN
ejpam-6307	357	6	−10.00	−10.00	CCONJ
ejpam-6307	358	1	−12.00	−12.00	ADP
ejpam-6307	358	2	34.5	34.5	NUM
ejpam-6307	358	3	−12.50	−12.50	NOUN
ejpam-6307	359	1	−13.33	−13.33	NOUN
ejpam-6307	360	1	−14.16	−14.16	NOUN
ejpam-6307	361	1	−12.50	−12.50	NOUN
ejpam-6307	361	2	39.99	39.99	NUM
ejpam-6307	361	3	.	.	NOUN
ejpam-6307	361	4	here	here	ADV
ejpam-6307	361	5	,	,	PUNCT
ejpam-6307	361	6	γdl1	γdl1	PROPN
ejpam-6307	361	7	=	=	PUNCT
ejpam-6307	361	8	54.0166	54.0166	NUM
ejpam-6307	361	9	,	,	PUNCT
ejpam-6307	361	10	γdl2	γdl2	PROPN
ejpam-6307	361	11	=	=	PUNCT
ejpam-6307	361	12	49.0913	49.0913	NUM
ejpam-6307	361	13	,	,	PUNCT
ejpam-6307	361	14	γdl3	γdl3	NOUN
ejpam-6307	361	15	=	=	SYM
ejpam-6307	361	16	44.6921	44.6921	NUM
ejpam-6307	361	17	and	and	CCONJ
ejpam-6307	361	18	γdl4	γdl4	NOUN
ejpam-6307	361	19	=	=	SYM
ejpam-6307	361	20	0.0000	0.0000	NUM
ejpam-6307	361	21	,	,	PUNCT
ejpam-6307	361	22	dle(g	dle(g	PROPN
ejpam-6307	361	23	)	)	PUNCT
ejpam-6307	361	24	=	=	PROPN
ejpam-6307	362	1	148.8	148.8	NUM
ejpam-6307	362	2	.	.	PUNCT
ejpam-6307	363	1	the	the	DET
ejpam-6307	363	2	following	follow	VERB
ejpam-6307	363	3	theorems	theorem	NOUN
ejpam-6307	363	4	establish	establish	VERB
ejpam-6307	363	5	upper	upper	ADJ
ejpam-6307	363	6	and	and	CCONJ
ejpam-6307	363	7	lower	low	ADJ
ejpam-6307	363	8	bounds	bound	NOUN
ejpam-6307	363	9	for	for	ADP
ejpam-6307	363	10	the	the	DET
ejpam-6307	363	11	detour	detour	NOUN
ejpam-6307	363	12	-	-	PUNCT
ejpam-6307	363	13	laplacian	laplacian	ADJ
ejpam-6307	363	14	energy	energy	NOUN
ejpam-6307	363	15	.	.	PUNCT
ejpam-6307	364	1	theorem	theorem	VERB
ejpam-6307	364	2	14	14	NUM
ejpam-6307	364	3	.	.	PUNCT
ejpam-6307	365	1	let	let	VERB
ejpam-6307	365	2	g	g	NOUN
ejpam-6307	365	3	:	:	PUNCT
ejpam-6307	365	4	(	(	PUNCT
ejpam-6307	365	5	v	v	NOUN
ejpam-6307	365	6	,	,	PUNCT
ejpam-6307	365	7	σ	σ	PROPN
ejpam-6307	365	8	,	,	PUNCT
ejpam-6307	365	9	µ	µ	NOUN
ejpam-6307	365	10	)	)	PUNCT
ejpam-6307	365	11	be	be	VERB
ejpam-6307	365	12	an	an	DET
ejpam-6307	365	13	fg	fg	NOUN
ejpam-6307	365	14	with	with	ADP
ejpam-6307	365	15	fuzzy	fuzzy	ADJ
ejpam-6307	365	16	detour	detour	NOUN
ejpam-6307	365	17	-	-	PUNCT
ejpam-6307	365	18	laplacian	laplacian	ADJ
ejpam-6307	365	19	matrix	matrix	NOUN
ejpam-6307	365	20	mfdld	mfdld	NOUN
ejpam-6307	365	21	,	,	PUNCT
ejpam-6307	365	22	and	and	CCONJ
ejpam-6307	365	23	let	let	VERB
ejpam-6307	365	24	its	its	PRON
ejpam-6307	365	25	diagonal	diagonal	ADJ
ejpam-6307	365	26	entries	entry	NOUN
ejpam-6307	365	27	be	be	AUX
ejpam-6307	365	28	denoted	denote	VERB
ejpam-6307	365	29	as	as	ADP
ejpam-6307	365	30	dmfdld	dmfdld	NOUN
ejpam-6307	365	31	(	(	PUNCT
ejpam-6307	365	32	ti	ti	NOUN
ejpam-6307	365	33	)	)	PUNCT
ejpam-6307	365	34	.	.	PUNCT
ejpam-6307	366	1	then	then	ADV
ejpam-6307	366	2	,	,	PUNCT
ejpam-6307	366	3	dle(g	dle(g	PROPN
ejpam-6307	366	4	)	)	PUNCT
ejpam-6307	366	5	≤	≤	NOUN
ejpam-6307	367	1	√√√√√	√√√√√	ADP
ejpam-6307	367	2	2	2	ADP
ejpam-6307	367	3	∑	∑	PROPN
ejpam-6307	367	4	1≤i	1≤i	PROPN
ejpam-6307	367	5	<	<	X
ejpam-6307	367	6	j≤n	j≤n	NOUN
ejpam-6307	367	7	c2ij	c2ij	X
ejpam-6307	368	1	+	+	CCONJ
ejpam-6307	368	2	n∑	n∑	ADJ
ejpam-6307	368	3	i=1	i=1	PROPN
ejpam-6307	368	4	(	(	PUNCT
ejpam-6307	368	5	dmfdld	dmfdld	ADJ
ejpam-6307	368	6	(	(	PUNCT
ejpam-6307	368	7	ti)−	ti)−	NOUN
ejpam-6307	368	8	2	2	NUM
ejpam-6307	368	9	∑	∑	PROPN
ejpam-6307	368	10	cij	cij	PROPN
ejpam-6307	368	11	n	n	CCONJ
ejpam-6307	368	12	)	)	PUNCT
ejpam-6307	368	13	2	2	NUM
ejpam-6307	368	14	n	n	NOUN
ejpam-6307	368	15	.	.	PUNCT
ejpam-6307	369	1	proof	proof	NOUN
ejpam-6307	369	2	.	.	PUNCT
ejpam-6307	370	1	applying	apply	VERB
ejpam-6307	370	2	the	the	DET
ejpam-6307	370	3	cauchy	cauchy	NOUN
ejpam-6307	370	4	–	–	PUNCT
ejpam-6307	370	5	schwarz	schwarz	PROPN
ejpam-6307	370	6	inequality	inequality	NOUN
ejpam-6307	370	7	to	to	ADP
ejpam-6307	370	8	the	the	DET
ejpam-6307	370	9	vector	vector	NOUN
ejpam-6307	370	10	(	(	PUNCT
ejpam-6307	370	11	|χ1|	|χ1|	ADJ
ejpam-6307	370	12	,	,	PUNCT
ejpam-6307	370	13	|χ2|	|χ2|	NOUN
ejpam-6307	370	14	,	,	PUNCT
ejpam-6307	370	15	.	.	PUNCT
ejpam-6307	370	16	.	.	PUNCT
ejpam-6307	371	1	.	.	PUNCT
ejpam-6307	372	1	,	,	PUNCT
ejpam-6307	372	2	|χn|	|χn|	PROPN
ejpam-6307	372	3	)	)	PUNCT
ejpam-6307	372	4	yields	yield	VERB
ejpam-6307	372	5	the	the	DET
ejpam-6307	372	6	result	result	NOUN
ejpam-6307	372	7	.	.	PUNCT
ejpam-6307	373	1	the	the	DET
ejpam-6307	373	2	argument	argument	NOUN
ejpam-6307	373	3	proceeds	proceed	VERB
ejpam-6307	373	4	analogously	analogously	ADV
ejpam-6307	373	5	to	to	AUX
ejpam-6307	373	6	theorem	theorem	VERB
ejpam-6307	373	7	11	11	NUM
ejpam-6307	373	8	and	and	CCONJ
ejpam-6307	373	9	is	be	AUX
ejpam-6307	373	10	thus	thus	ADV
ejpam-6307	373	11	omitted	omit	VERB
ejpam-6307	373	12	for	for	ADP
ejpam-6307	373	13	brevity	brevity	NOUN
ejpam-6307	373	14	.	.	PUNCT
ejpam-6307	374	1	theorem	theorem	NOUN
ejpam-6307	374	2	15	15	NUM
ejpam-6307	374	3	.	.	PUNCT
ejpam-6307	375	1	let	let	VERB
ejpam-6307	375	2	g	g	NOUN
ejpam-6307	375	3	:	:	PUNCT
ejpam-6307	375	4	(	(	PUNCT
ejpam-6307	375	5	v	v	NOUN
ejpam-6307	375	6	,	,	PUNCT
ejpam-6307	375	7	σ	σ	PROPN
ejpam-6307	375	8	,	,	PUNCT
ejpam-6307	375	9	µ	µ	NOUN
ejpam-6307	375	10	)	)	PUNCT
ejpam-6307	375	11	be	be	VERB
ejpam-6307	375	12	an	an	DET
ejpam-6307	375	13	fg	fg	NOUN
ejpam-6307	375	14	with	with	ADP
ejpam-6307	375	15	fuzzy	fuzzy	ADJ
ejpam-6307	375	16	detour	detour	NOUN
ejpam-6307	375	17	-	-	PUNCT
ejpam-6307	375	18	laplacian	laplacian	ADJ
ejpam-6307	375	19	matrix	matrix	NOUN
ejpam-6307	375	20	mfdld	mfdld	NOUN
ejpam-6307	375	21	,	,	PUNCT
ejpam-6307	375	22	and	and	CCONJ
ejpam-6307	375	23	let	let	VERB
ejpam-6307	375	24	its	its	PRON
ejpam-6307	375	25	diagonal	diagonal	ADJ
ejpam-6307	375	26	entries	entry	NOUN
ejpam-6307	375	27	be	be	AUX
ejpam-6307	375	28	denoted	denote	VERB
ejpam-6307	375	29	as	as	ADP
ejpam-6307	375	30	dmfdld	dmfdld	NOUN
ejpam-6307	375	31	(	(	PUNCT
ejpam-6307	375	32	ti	ti	NOUN
ejpam-6307	375	33	)	)	PUNCT
ejpam-6307	375	34	.	.	PUNCT
ejpam-6307	376	1	then	then	ADV
ejpam-6307	376	2	,	,	PUNCT
ejpam-6307	376	3	dle(g	dle(g	PROPN
ejpam-6307	376	4	)	)	PUNCT
ejpam-6307	376	5	≥	≥	NOUN
ejpam-6307	376	6	2	2	NUM
ejpam-6307	376	7	√√√√√	√√√√√	ADP
ejpam-6307	376	8			PROPN
ejpam-6307	376	9	∑	∑	PUNCT
ejpam-6307	376	10	1≤i	1≤i	PROPN
ejpam-6307	376	11	<	<	X
ejpam-6307	376	12	j≤n	j≤n	NOUN
ejpam-6307	376	13	c2ij	c2ij	X
ejpam-6307	377	1	+	+	CCONJ
ejpam-6307	377	2	1	1	NUM
ejpam-6307	377	3	2	2	NUM
ejpam-6307	377	4	n∑	n∑	NOUN
ejpam-6307	377	5	i=1	i=1	PROPN
ejpam-6307	377	6	(	(	PUNCT
ejpam-6307	377	7	dmfdld	dmfdld	ADJ
ejpam-6307	377	8	(	(	PUNCT
ejpam-6307	377	9	ti)−	ti)−	NOUN
ejpam-6307	377	10	2	2	NUM
ejpam-6307	377	11	∑	∑	PROPN
ejpam-6307	377	12	cij	cij	PROPN
ejpam-6307	377	13	n	n	PART
ejpam-6307	377	14	)	)	SYM
ejpam-6307	377	15	2	2	NUM
ejpam-6307	377	16			PROPN
ejpam-6307	377	17	,	,	PUNCT
ejpam-6307	377	18	where	where	SCONJ
ejpam-6307	377	19	cij	cij	PROPN
ejpam-6307	377	20	=	=	SYM
ejpam-6307	377	21	∆(vi	∆(vi	PROPN
ejpam-6307	377	22	,	,	PUNCT
ejpam-6307	377	23	vj	vj	NOUN
ejpam-6307	377	24	)	)	PUNCT
ejpam-6307	377	25	.	.	PUNCT
ejpam-6307	378	1	r.	r.	PROPN
ejpam-6307	378	2	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	378	3	,	,	PUNCT
ejpam-6307	378	4	a.	a.	NOUN
ejpam-6307	378	5	m.	m.	PROPN
ejpam-6307	378	6	anto	anto	PROPN
ejpam-6307	378	7	,	,	PUNCT
ejpam-6307	378	8	v.	v.	PROPN
ejpam-6307	378	9	mary	mary	PROPN
ejpam-6307	378	10	mettilda	mettilda	PROPN
ejpam-6307	378	11	rose	rise	VERB
ejpam-6307	378	12	/	/	SYM
ejpam-6307	378	13	eur	eur	PROPN
ejpam-6307	378	14	.	.	PUNCT
ejpam-6307	379	1	j.	j.	PROPN
ejpam-6307	379	2	pure	pure	PROPN
ejpam-6307	379	3	appl	appl	PROPN
ejpam-6307	379	4	.	.	PROPN
ejpam-6307	379	5	math	math	PROPN
ejpam-6307	379	6	,	,	PUNCT
ejpam-6307	379	7	18	18	NUM
ejpam-6307	379	8	(	(	PUNCT
ejpam-6307	379	9	4	4	NUM
ejpam-6307	379	10	)	)	PUNCT
ejpam-6307	379	11	(	(	PUNCT
ejpam-6307	379	12	2025	2025	NUM
ejpam-6307	379	13	)	)	PUNCT
ejpam-6307	379	14	,	,	PUNCT
ejpam-6307	379	15	6307	6307	NUM
ejpam-6307	379	16	17	17	NUM
ejpam-6307	379	17	of	of	ADP
ejpam-6307	379	18	25	25	NUM
ejpam-6307	379	19	proof	proof	NOUN
ejpam-6307	379	20	.	.	PUNCT
ejpam-6307	380	1	by	by	ADP
ejpam-6307	380	2	definition	definition	NOUN
ejpam-6307	380	3	22	22	NUM
ejpam-6307	380	4	,	,	PUNCT
ejpam-6307	380	5	we	we	PRON
ejpam-6307	380	6	have	have	VERB
ejpam-6307	380	7	(	(	PUNCT
ejpam-6307	380	8	dle(g))2	dle(g))2	X
ejpam-6307	380	9	=	=	SYM
ejpam-6307	380	10	(	(	PUNCT
ejpam-6307	380	11	n∑	n∑	NOUN
ejpam-6307	380	12	i=1	i=1	PROPN
ejpam-6307	380	13	|χi|	|χi|	PROPN
ejpam-6307	380	14	)	)	PUNCT
ejpam-6307	380	15	2	2	NUM
ejpam-6307	381	1	=	=	SYM
ejpam-6307	381	2	n∑	n∑	NOUN
ejpam-6307	381	3	i=1	i=1	PROPN
ejpam-6307	381	4	|χi|2	|χi|2	PROPN
ejpam-6307	382	1	+	+	CCONJ
ejpam-6307	382	2	2	2	NUM
ejpam-6307	382	3	∑	∑	SYM
ejpam-6307	382	4	1≤i	1≤i	NUM
ejpam-6307	382	5	<	<	X
ejpam-6307	382	6	j≤n	j≤n	PROPN
ejpam-6307	382	7	|χi||χj	|χi||χj	PROPN
ejpam-6307	382	8	|	|	NOUN
ejpam-6307	382	9	.	.	PUNCT
ejpam-6307	383	1	since	since	SCONJ
ejpam-6307	383	2	both	both	DET
ejpam-6307	383	3	terms	term	NOUN
ejpam-6307	383	4	are	be	AUX
ejpam-6307	383	5	non	non	ADJ
ejpam-6307	383	6	-	-	ADJ
ejpam-6307	383	7	negative	negative	ADJ
ejpam-6307	383	8	,	,	PUNCT
ejpam-6307	383	9	it	it	PRON
ejpam-6307	383	10	follows	follow	VERB
ejpam-6307	383	11	that	that	SCONJ
ejpam-6307	383	12	(	(	PUNCT
ejpam-6307	383	13	dle(g))2	dle(g))2	X
ejpam-6307	383	14	≥	≥	NUM
ejpam-6307	383	15	4	4	NUM
ejpam-6307	383	16	m	m	NOUN
ejpam-6307	383	17	,	,	PUNCT
ejpam-6307	383	18	where	where	SCONJ
ejpam-6307	383	19	m	m	VERB
ejpam-6307	383	20	=	=	PUNCT
ejpam-6307	383	21	∑	∑	PUNCT
ejpam-6307	383	22	1≤i	1≤i	X
ejpam-6307	383	23	<	<	X
ejpam-6307	383	24	j≤n	j≤n	X
ejpam-6307	383	25	c2ij	c2ij	X
ejpam-6307	384	1	+	+	CCONJ
ejpam-6307	384	2	1	1	NUM
ejpam-6307	384	3	2	2	NUM
ejpam-6307	384	4	n∑	n∑	NOUN
ejpam-6307	384	5	i=1	i=1	PROPN
ejpam-6307	384	6	(	(	PUNCT
ejpam-6307	384	7	dmfdld	dmfdld	ADJ
ejpam-6307	384	8	(	(	PUNCT
ejpam-6307	384	9	ti)−	ti)−	NOUN
ejpam-6307	384	10	2	2	NUM
ejpam-6307	384	11	∑	∑	PROPN
ejpam-6307	384	12	cij	cij	PROPN
ejpam-6307	384	13	n	n	CCONJ
ejpam-6307	384	14	)	)	PUNCT
ejpam-6307	384	15	2	2	NUM
ejpam-6307	384	16	.	.	PUNCT
ejpam-6307	384	17	taking	take	VERB
ejpam-6307	384	18	square	square	ADJ
ejpam-6307	384	19	roots	root	NOUN
ejpam-6307	384	20	on	on	ADP
ejpam-6307	384	21	both	both	DET
ejpam-6307	384	22	sides	side	NOUN
ejpam-6307	384	23	yields	yield	VERB
ejpam-6307	384	24	the	the	DET
ejpam-6307	384	25	desired	desire	VERB
ejpam-6307	384	26	inequality	inequality	NOUN
ejpam-6307	384	27	.	.	PUNCT
ejpam-6307	385	1	7	7	X
ejpam-6307	385	2	.	.	X
ejpam-6307	385	3	applications	application	NOUN
ejpam-6307	385	4	of	of	ADP
ejpam-6307	385	5	fuzzy	fuzzy	ADJ
ejpam-6307	385	6	geodetic	geodetic	ADJ
ejpam-6307	385	7	-	-	PUNCT
ejpam-6307	385	8	laplacian	laplacian	ADJ
ejpam-6307	385	9	energy	energy	NOUN
ejpam-6307	385	10	this	this	DET
ejpam-6307	385	11	section	section	NOUN
ejpam-6307	385	12	explores	explore	VERB
ejpam-6307	385	13	the	the	DET
ejpam-6307	385	14	use	use	NOUN
ejpam-6307	385	15	of	of	ADP
ejpam-6307	385	16	geodetic	geodetic	ADJ
ejpam-6307	385	17	-	-	PUNCT
ejpam-6307	385	18	laplacian	laplacian	ADJ
ejpam-6307	385	19	energy	energy	NOUN
ejpam-6307	385	20	in	in	ADP
ejpam-6307	385	21	decision	decision	NOUN
ejpam-6307	385	22	-	-	PUNCT
ejpam-6307	385	23	making	make	VERB
ejpam-6307	385	24	processes	process	NOUN
ejpam-6307	385	25	aimed	aim	VERB
ejpam-6307	385	26	at	at	ADP
ejpam-6307	385	27	addressing	address	VERB
ejpam-6307	385	28	modern	modern	ADJ
ejpam-6307	385	29	-	-	PUNCT
ejpam-6307	385	30	day	day	NOUN
ejpam-6307	385	31	slavery	slavery	NOUN
ejpam-6307	385	32	.	.	PUNCT
ejpam-6307	386	1	additionally	additionally	ADV
ejpam-6307	386	2	,	,	PUNCT
ejpam-6307	386	3	the	the	DET
ejpam-6307	386	4	study	study	NOUN
ejpam-6307	386	5	highlights	highlight	VERB
ejpam-6307	386	6	an	an	DET
ejpam-6307	386	7	effective	effective	ADJ
ejpam-6307	386	8	mathematical	mathematical	ADJ
ejpam-6307	386	9	model	model	NOUN
ejpam-6307	386	10	for	for	ADP
ejpam-6307	386	11	its	its	PRON
ejpam-6307	386	12	application	application	NOUN
ejpam-6307	386	13	in	in	ADP
ejpam-6307	386	14	modern	modern	ADJ
ejpam-6307	386	15	law	law	NOUN
ejpam-6307	386	16	enforcement	enforcement	NOUN
ejpam-6307	386	17	,	,	PUNCT
ejpam-6307	386	18	particularly	particularly	ADV
ejpam-6307	386	19	in	in	ADP
ejpam-6307	386	20	the	the	DET
ejpam-6307	386	21	areas	area	NOUN
ejpam-6307	386	22	of	of	ADP
ejpam-6307	386	23	efficient	efficient	ADJ
ejpam-6307	386	24	crime	crime	NOUN
ejpam-6307	386	25	detection	detection	NOUN
ejpam-6307	386	26	and	and	CCONJ
ejpam-6307	386	27	combating	combat	VERB
ejpam-6307	386	28	illegal	illegal	ADJ
ejpam-6307	386	29	activities	activity	NOUN
ejpam-6307	386	30	.	.	PUNCT
ejpam-6307	387	1	7.1	7.1	NUM
ejpam-6307	387	2	.	.	PUNCT
ejpam-6307	387	3	analyzing	analyze	VERB
ejpam-6307	387	4	the	the	DET
ejpam-6307	387	5	illicit	illicit	ADJ
ejpam-6307	387	6	routes	route	NOUN
ejpam-6307	387	7	of	of	ADP
ejpam-6307	387	8	human	human	ADJ
ejpam-6307	387	9	trading	trading	NOUN
ejpam-6307	387	10	networks	network	NOUN
ejpam-6307	387	11	human	human	ADJ
ejpam-6307	387	12	trafficking	trafficking	NOUN
ejpam-6307	387	13	often	often	ADV
ejpam-6307	387	14	operates	operate	VERB
ejpam-6307	387	15	through	through	ADP
ejpam-6307	387	16	complex	complex	ADJ
ejpam-6307	387	17	networks	network	NOUN
ejpam-6307	387	18	of	of	ADP
ejpam-6307	387	19	individuals	individual	NOUN
ejpam-6307	387	20	and	and	CCONJ
ejpam-6307	387	21	organizations	organization	NOUN
ejpam-6307	387	22	.	.	PUNCT
ejpam-6307	388	1	given	give	VERB
ejpam-6307	388	2	the	the	DET
ejpam-6307	388	3	inherent	inherent	ADJ
ejpam-6307	388	4	ambiguity	ambiguity	NOUN
ejpam-6307	388	5	and	and	CCONJ
ejpam-6307	388	6	uncertainty	uncertainty	NOUN
ejpam-6307	388	7	in	in	ADP
ejpam-6307	388	8	these	these	DET
ejpam-6307	388	9	connections	connection	NOUN
ejpam-6307	388	10	,	,	PUNCT
ejpam-6307	388	11	fuzzy	fuzzy	ADJ
ejpam-6307	388	12	graph	graph	NOUN
ejpam-6307	388	13	(	(	PUNCT
ejpam-6307	388	14	fg	fg	NOUN
ejpam-6307	388	15	)	)	PUNCT
ejpam-6307	388	16	theory	theory	NOUN
ejpam-6307	388	17	provides	provide	VERB
ejpam-6307	388	18	a	a	DET
ejpam-6307	388	19	valuable	valuable	ADJ
ejpam-6307	388	20	framework	framework	NOUN
ejpam-6307	388	21	for	for	ADP
ejpam-6307	388	22	examining	examine	VERB
ejpam-6307	388	23	and	and	CCONJ
ejpam-6307	388	24	visualizing	visualize	VERB
ejpam-6307	388	25	these	these	DET
ejpam-6307	388	26	networks	network	NOUN
ejpam-6307	388	27	.	.	PUNCT
ejpam-6307	389	1	this	this	DET
ejpam-6307	389	2	strategy	strategy	NOUN
ejpam-6307	389	3	could	could	AUX
ejpam-6307	389	4	be	be	AUX
ejpam-6307	389	5	helpful	helpful	ADJ
ejpam-6307	389	6	to	to	PART
ejpam-6307	389	7	law	law	VERB
ejpam-6307	389	8	enforcement	enforcement	NOUN
ejpam-6307	389	9	and	and	CCONJ
ejpam-6307	389	10	governments	government	NOUN
ejpam-6307	389	11	in	in	ADP
ejpam-6307	389	12	identifying	identify	VERB
ejpam-6307	389	13	the	the	DET
ejpam-6307	389	14	structure	structure	NOUN
ejpam-6307	389	15	and	and	CCONJ
ejpam-6307	389	16	dynamics	dynamic	NOUN
ejpam-6307	389	17	of	of	ADP
ejpam-6307	389	18	trafficking	traffic	VERB
ejpam-6307	389	19	routes	route	NOUN
ejpam-6307	389	20	.	.	PUNCT
ejpam-6307	390	1	in	in	ADP
ejpam-6307	390	2	this	this	DET
ejpam-6307	390	3	study	study	NOUN
ejpam-6307	390	4	,	,	PUNCT
ejpam-6307	390	5	we	we	PRON
ejpam-6307	390	6	focus	focus	VERB
ejpam-6307	390	7	on	on	ADP
ejpam-6307	390	8	the	the	DET
ejpam-6307	390	9	major	major	ADJ
ejpam-6307	390	10	illicit	illicit	ADJ
ejpam-6307	390	11	human	human	ADJ
ejpam-6307	390	12	trafficking	trafficking	NOUN
ejpam-6307	390	13	routes	route	NOUN
ejpam-6307	390	14	into	into	ADP
ejpam-6307	390	15	the	the	DET
ejpam-6307	390	16	united	united	PROPN
ejpam-6307	390	17	states	states	PROPN
ejpam-6307	390	18	,	,	PUNCT
ejpam-6307	390	19	as	as	SCONJ
ejpam-6307	390	20	outlined	outline	VERB
ejpam-6307	390	21	in	in	ADP
ejpam-6307	390	22	studies	study	NOUN
ejpam-6307	390	23	[	[	X
ejpam-6307	390	24	23	23	NUM
ejpam-6307	390	25	]	]	PUNCT
ejpam-6307	390	26	.	.	PUNCT
ejpam-6307	391	1	our	our	PRON
ejpam-6307	391	2	primary	primary	ADJ
ejpam-6307	391	3	aim	aim	NOUN
ejpam-6307	391	4	is	be	AUX
ejpam-6307	391	5	to	to	PART
ejpam-6307	391	6	evaluate	evaluate	VERB
ejpam-6307	391	7	the	the	DET
ejpam-6307	391	8	fuzzy	fuzzy	ADJ
ejpam-6307	391	9	geodetic	geodetic	ADJ
ejpam-6307	391	10	laplacian	laplacian	ADJ
ejpam-6307	391	11	energy	energy	NOUN
ejpam-6307	391	12	as	as	ADP
ejpam-6307	391	13	a	a	DET
ejpam-6307	391	14	comparative	comparative	ADJ
ejpam-6307	391	15	measure	measure	NOUN
ejpam-6307	391	16	,	,	PUNCT
ejpam-6307	391	17	in	in	ADP
ejpam-6307	391	18	contrast	contrast	NOUN
ejpam-6307	391	19	to	to	ADP
ejpam-6307	391	20	the	the	DET
ejpam-6307	391	21	various	various	ADJ
ejpam-6307	391	22	fuzzy	fuzzy	ADJ
ejpam-6307	391	23	graph	graph	NOUN
ejpam-6307	391	24	metrics	metric	NOUN
ejpam-6307	391	25	discussed	discuss	VERB
ejpam-6307	391	26	in	in	ADP
ejpam-6307	391	27	previous	previous	ADJ
ejpam-6307	391	28	researches	research	NOUN
ejpam-6307	391	29	[	[	X
ejpam-6307	391	30	23–25	23–25	NUM
ejpam-6307	391	31	]	]	PUNCT
ejpam-6307	391	32	.	.	PUNCT
ejpam-6307	392	1	the	the	DET
ejpam-6307	392	2	global	global	ADJ
ejpam-6307	392	3	slavery	slavery	PROPN
ejpam-6307	392	4	index	index	NOUN
ejpam-6307	392	5	,	,	PUNCT
ejpam-6307	392	6	as	as	SCONJ
ejpam-6307	392	7	referenced	reference	VERB
ejpam-6307	392	8	in	in	ADP
ejpam-6307	392	9	[	[	X
ejpam-6307	392	10	28	28	NUM
ejpam-6307	392	11	]	]	PUNCT
ejpam-6307	392	12	,	,	PUNCT
ejpam-6307	392	13	offers	offer	VERB
ejpam-6307	392	14	a	a	DET
ejpam-6307	392	15	detailed	detailed	ADJ
ejpam-6307	392	16	assessment	assessment	NOUN
ejpam-6307	392	17	of	of	ADP
ejpam-6307	392	18	the	the	DET
ejpam-6307	392	19	susceptibility	susceptibility	NOUN
ejpam-6307	392	20	to	to	ADP
ejpam-6307	392	21	modern	modern	ADJ
ejpam-6307	392	22	slavery	slavery	NOUN
ejpam-6307	392	23	across	across	ADP
ejpam-6307	392	24	150	150	NUM
ejpam-6307	392	25	+	+	NUM
ejpam-6307	392	26	countries	country	NOUN
ejpam-6307	392	27	.	.	PUNCT
ejpam-6307	393	1	over	over	ADP
ejpam-6307	393	2	the	the	DET
ejpam-6307	393	3	past	past	ADJ
ejpam-6307	393	4	two	two	NUM
ejpam-6307	393	5	decades	decade	NOUN
ejpam-6307	393	6	,	,	PUNCT
ejpam-6307	393	7	global	global	ADJ
ejpam-6307	393	8	institutions	institution	NOUN
ejpam-6307	393	9	like	like	ADP
ejpam-6307	393	10	the	the	DET
ejpam-6307	393	11	united	united	PROPN
ejpam-6307	393	12	nations	nations	PROPN
ejpam-6307	393	13	office	office	NOUN
ejpam-6307	393	14	on	on	ADP
ejpam-6307	393	15	drugs	drug	NOUN
ejpam-6307	393	16	and	and	CCONJ
ejpam-6307	393	17	crime	crime	NOUN
ejpam-6307	393	18	(	(	PUNCT
ejpam-6307	393	19	unodc	unodc	ADJ
ejpam-6307	393	20	)	)	PUNCT
ejpam-6307	393	21	and	and	CCONJ
ejpam-6307	393	22	the	the	DET
ejpam-6307	393	23	international	international	ADJ
ejpam-6307	393	24	labour	labour	PROPN
ejpam-6307	393	25	organization	organization	NOUN
ejpam-6307	393	26	(	(	PUNCT
ejpam-6307	393	27	ilo	ilo	PROPN
ejpam-6307	393	28	)	)	PUNCT
ejpam-6307	393	29	have	have	VERB
ejpam-6307	393	30	significantly	significantly	ADV
ejpam-6307	393	31	advanced	advanced	ADJ
ejpam-6307	393	32	efforts	effort	NOUN
ejpam-6307	393	33	to	to	PART
ejpam-6307	393	34	quantify	quantify	VERB
ejpam-6307	393	35	the	the	DET
ejpam-6307	393	36	scale	scale	NOUN
ejpam-6307	393	37	of	of	ADP
ejpam-6307	393	38	modern	modern	ADJ
ejpam-6307	393	39	slavery	slavery	NOUN
ejpam-6307	393	40	worldwide	worldwide	ADV
ejpam-6307	393	41	.	.	PUNCT
ejpam-6307	394	1	various	various	ADJ
ejpam-6307	394	2	methods	method	NOUN
ejpam-6307	394	3	have	have	AUX
ejpam-6307	394	4	been	be	AUX
ejpam-6307	394	5	applied	apply	VERB
ejpam-6307	394	6	to	to	ADP
ejpam-6307	394	7	fuzzy	fuzzy	ADJ
ejpam-6307	394	8	graphs	graph	NOUN
ejpam-6307	394	9	in	in	ADP
ejpam-6307	394	10	order	order	NOUN
ejpam-6307	394	11	to	to	PART
ejpam-6307	394	12	assess	assess	VERB
ejpam-6307	394	13	the	the	DET
ejpam-6307	394	14	likelihood	likelihood	NOUN
ejpam-6307	394	15	of	of	ADP
ejpam-6307	394	16	illegal	illegal	ADJ
ejpam-6307	394	17	immigration	immigration	NOUN
ejpam-6307	394	18	along	along	ADP
ejpam-6307	394	19	different	different	ADJ
ejpam-6307	394	20	routes	route	NOUN
ejpam-6307	394	21	from	from	ADP
ejpam-6307	394	22	countries	country	NOUN
ejpam-6307	394	23	of	of	ADP
ejpam-6307	394	24	origin	origin	NOUN
ejpam-6307	394	25	to	to	ADP
ejpam-6307	394	26	the	the	DET
ejpam-6307	394	27	united	united	PROPN
ejpam-6307	394	28	states	states	PROPN
ejpam-6307	394	29	.	.	PUNCT
ejpam-6307	395	1	notably	notably	ADV
ejpam-6307	395	2	,	,	PUNCT
ejpam-6307	395	3	binu	binu	NOUN
ejpam-6307	395	4	et	et	NOUN
ejpam-6307	395	5	al	al	PROPN
ejpam-6307	395	6	.	.	PUNCT
ejpam-6307	396	1	[	[	X
ejpam-6307	396	2	23	23	NUM
ejpam-6307	396	3	]	]	PUNCT
ejpam-6307	396	4	explored	explore	VERB
ejpam-6307	396	5	the	the	DET
ejpam-6307	396	6	use	use	NOUN
ejpam-6307	396	7	of	of	ADP
ejpam-6307	396	8	the	the	DET
ejpam-6307	396	9	wiener	wiener	NOUN
ejpam-6307	396	10	index	index	NOUN
ejpam-6307	396	11	on	on	ADP
ejpam-6307	396	12	fuzzy	fuzzy	ADJ
ejpam-6307	396	13	graphs	graph	NOUN
ejpam-6307	396	14	to	to	PART
ejpam-6307	396	15	examine	examine	VERB
ejpam-6307	396	16	pathways	pathway	NOUN
ejpam-6307	396	17	of	of	ADP
ejpam-6307	396	18	illegal	illegal	ADJ
ejpam-6307	396	19	immigration	immigration	NOUN
ejpam-6307	396	20	,	,	PUNCT
ejpam-6307	396	21	providing	provide	VERB
ejpam-6307	396	22	a	a	DET
ejpam-6307	396	23	novel	novel	ADJ
ejpam-6307	396	24	approach	approach	NOUN
ejpam-6307	396	25	to	to	ADP
ejpam-6307	396	26	studying	study	VERB
ejpam-6307	396	27	human	human	ADJ
ejpam-6307	396	28	trafficking	trafficking	NOUN
ejpam-6307	396	29	networks	network	NOUN
ejpam-6307	396	30	.	.	PUNCT
ejpam-6307	397	1	additionally	additionally	ADV
ejpam-6307	397	2	,	,	PUNCT
ejpam-6307	397	3	studies	study	NOUN
ejpam-6307	397	4	referenced	reference	VERB
ejpam-6307	397	5	in	in	ADP
ejpam-6307	397	6	[	[	X
ejpam-6307	397	7	24	24	NUM
ejpam-6307	397	8	]	]	PUNCT
ejpam-6307	397	9	have	have	AUX
ejpam-6307	397	10	introduced	introduce	VERB
ejpam-6307	397	11	the	the	DET
ejpam-6307	397	12	use	use	NOUN
ejpam-6307	397	13	of	of	ADP
ejpam-6307	397	14	r.	r.	PROPN
ejpam-6307	397	15	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	397	16	,	,	PUNCT
ejpam-6307	397	17	a.	a.	NOUN
ejpam-6307	397	18	m.	m.	PROPN
ejpam-6307	397	19	anto	anto	PROPN
ejpam-6307	397	20	,	,	PUNCT
ejpam-6307	397	21	v.	v.	PROPN
ejpam-6307	397	22	mary	mary	PROPN
ejpam-6307	397	23	mettilda	mettilda	PROPN
ejpam-6307	397	24	rose	rise	VERB
ejpam-6307	397	25	/	/	SYM
ejpam-6307	397	26	eur	eur	PROPN
ejpam-6307	397	27	.	.	PUNCT
ejpam-6307	398	1	j.	j.	PROPN
ejpam-6307	398	2	pure	pure	PROPN
ejpam-6307	398	3	appl	appl	PROPN
ejpam-6307	398	4	.	.	PROPN
ejpam-6307	398	5	math	math	PROPN
ejpam-6307	398	6	,	,	PUNCT
ejpam-6307	398	7	18	18	NUM
ejpam-6307	398	8	(	(	PUNCT
ejpam-6307	398	9	4	4	NUM
ejpam-6307	398	10	)	)	PUNCT
ejpam-6307	398	11	(	(	PUNCT
ejpam-6307	398	12	2025	2025	NUM
ejpam-6307	398	13	)	)	PUNCT
ejpam-6307	398	14	,	,	PUNCT
ejpam-6307	398	15	6307	6307	NUM
ejpam-6307	398	16	18	18	NUM
ejpam-6307	398	17	of	of	ADP
ejpam-6307	398	18	25	25	NUM
ejpam-6307	398	19	the	the	DET
ejpam-6307	398	20	intuitionistic	intuitionistic	ADJ
ejpam-6307	398	21	fuzzy	fuzzy	ADJ
ejpam-6307	398	22	geodetic	geodetic	ADJ
ejpam-6307	398	23	wiener	wiener	NOUN
ejpam-6307	398	24	index	index	NOUN
ejpam-6307	398	25	,	,	PUNCT
ejpam-6307	398	26	a	a	DET
ejpam-6307	398	27	method	method	NOUN
ejpam-6307	398	28	that	that	PRON
ejpam-6307	398	29	proves	prove	VERB
ejpam-6307	398	30	effective	effective	ADJ
ejpam-6307	398	31	in	in	ADP
ejpam-6307	398	32	modeling	model	VERB
ejpam-6307	398	33	illicit	illicit	ADJ
ejpam-6307	398	34	trafficking	trafficking	NOUN
ejpam-6307	398	35	by	by	ADP
ejpam-6307	398	36	capturing	capture	VERB
ejpam-6307	398	37	migration	migration	NOUN
ejpam-6307	398	38	flows	flow	NOUN
ejpam-6307	398	39	and	and	CCONJ
ejpam-6307	398	40	network	network	NOUN
ejpam-6307	398	41	centralities	centrality	NOUN
ejpam-6307	398	42	within	within	ADP
ejpam-6307	398	43	fuzzy	fuzzy	ADJ
ejpam-6307	398	44	relational	relational	ADJ
ejpam-6307	398	45	frameworks	framework	NOUN
ejpam-6307	398	46	.	.	PUNCT
ejpam-6307	399	1	building	build	VERB
ejpam-6307	399	2	upon	upon	SCONJ
ejpam-6307	399	3	these	these	DET
ejpam-6307	399	4	earlier	early	ADJ
ejpam-6307	399	5	works	work	NOUN
ejpam-6307	399	6	,	,	PUNCT
ejpam-6307	399	7	this	this	DET
ejpam-6307	399	8	paper	paper	NOUN
ejpam-6307	399	9	adopts	adopt	VERB
ejpam-6307	399	10	the	the	DET
ejpam-6307	399	11	fuzzy	fuzzy	ADJ
ejpam-6307	399	12	graph	graph	NOUN
ejpam-6307	399	13	structure	structure	NOUN
ejpam-6307	399	14	employed	employ	VERB
ejpam-6307	399	15	by	by	ADP
ejpam-6307	399	16	binu	binu	NOUN
ejpam-6307	399	17	et	et	PROPN
ejpam-6307	399	18	al.[23	al.[23	PROPN
ejpam-6307	399	19	]	]	PUNCT
ejpam-6307	399	20	to	to	PART
ejpam-6307	399	21	test	test	VERB
ejpam-6307	399	22	the	the	DET
ejpam-6307	399	23	applicability	applicability	NOUN
ejpam-6307	399	24	and	and	CCONJ
ejpam-6307	399	25	accuracy	accuracy	NOUN
ejpam-6307	399	26	of	of	ADP
ejpam-6307	399	27	the	the	DET
ejpam-6307	399	28	fuzzy	fuzzy	ADJ
ejpam-6307	399	29	geodetic	geodetic	ADJ
ejpam-6307	399	30	laplacian	laplacian	ADJ
ejpam-6307	399	31	energy	energy	NOUN
ejpam-6307	399	32	as	as	ADP
ejpam-6307	399	33	a	a	DET
ejpam-6307	399	34	metric	metric	NOUN
ejpam-6307	399	35	for	for	ADP
ejpam-6307	399	36	analyzing	analyze	VERB
ejpam-6307	399	37	human	human	ADJ
ejpam-6307	399	38	trafficking	trafficking	NOUN
ejpam-6307	399	39	networks	network	NOUN
ejpam-6307	399	40	.	.	PUNCT
ejpam-6307	400	1	by	by	ADP
ejpam-6307	400	2	comparing	compare	VERB
ejpam-6307	400	3	this	this	DET
ejpam-6307	400	4	approach	approach	NOUN
ejpam-6307	400	5	with	with	ADP
ejpam-6307	400	6	existing	exist	VERB
ejpam-6307	400	7	fuzzy	fuzzy	ADJ
ejpam-6307	400	8	graph	graph	NOUN
ejpam-6307	400	9	measures	measure	NOUN
ejpam-6307	400	10	,	,	PUNCT
ejpam-6307	400	11	we	we	PRON
ejpam-6307	400	12	aim	aim	VERB
ejpam-6307	400	13	to	to	PART
ejpam-6307	400	14	enhance	enhance	VERB
ejpam-6307	400	15	our	our	PRON
ejpam-6307	400	16	understanding	understanding	NOUN
ejpam-6307	400	17	of	of	ADP
ejpam-6307	400	18	the	the	DET
ejpam-6307	400	19	dynamics	dynamic	NOUN
ejpam-6307	400	20	and	and	CCONJ
ejpam-6307	400	21	complexities	complexity	NOUN
ejpam-6307	400	22	of	of	ADP
ejpam-6307	400	23	trafficking	traffic	VERB
ejpam-6307	400	24	networks	network	NOUN
ejpam-6307	400	25	,	,	PUNCT
ejpam-6307	400	26	ultimately	ultimately	ADV
ejpam-6307	400	27	contributing	contribute	VERB
ejpam-6307	400	28	to	to	ADP
ejpam-6307	400	29	more	more	ADV
ejpam-6307	400	30	effective	effective	ADJ
ejpam-6307	400	31	measures	measure	NOUN
ejpam-6307	400	32	for	for	ADP
ejpam-6307	400	33	combating	combat	VERB
ejpam-6307	400	34	human	human	ADJ
ejpam-6307	400	35	exploitation	exploitation	NOUN
ejpam-6307	400	36	.	.	PUNCT
ejpam-6307	401	1	let	let	VERB
ejpam-6307	401	2	df	df	PROPN
ejpam-6307	401	3	(	(	PUNCT
ejpam-6307	401	4	pu→v	pu→v	PROPN
ejpam-6307	401	5	)	)	PUNCT
ejpam-6307	401	6	represent	represent	VERB
ejpam-6307	401	7	the	the	DET
ejpam-6307	401	8	fuzzy	fuzzy	ADJ
ejpam-6307	401	9	geodetic	geodetic	ADJ
ejpam-6307	401	10	distance	distance	NOUN
ejpam-6307	401	11	relation	relation	NOUN
ejpam-6307	401	12	matrix	matrix	NOUN
ejpam-6307	401	13	for	for	ADP
ejpam-6307	401	14	various	various	ADJ
ejpam-6307	401	15	path	path	NOUN
ejpam-6307	401	16	relations	relation	NOUN
ejpam-6307	401	17	pu→v	pu→v	PROPN
ejpam-6307	401	18	,	,	PUNCT
ejpam-6307	401	19	and	and	CCONJ
ejpam-6307	401	20	let	let	AUX
ejpam-6307	401	21	fdg(pu→v	fdg(pu→v	VERB
ejpam-6307	401	22	)	)	PUNCT
ejpam-6307	401	23	denote	denote	VERB
ejpam-6307	401	24	the	the	DET
ejpam-6307	401	25	relation	relation	NOUN
ejpam-6307	401	26	degree	degree	NOUN
ejpam-6307	401	27	matrix	matrix	NOUN
ejpam-6307	401	28	.	.	PUNCT
ejpam-6307	402	1	figure	figure	VERB
ejpam-6307	402	2	4	4	NUM
ejpam-6307	402	3	:	:	PUNCT
ejpam-6307	402	4	main	main	ADJ
ejpam-6307	402	5	routes	route	NOUN
ejpam-6307	402	6	of	of	ADP
ejpam-6307	402	7	illicit	illicit	ADJ
ejpam-6307	402	8	trade	trade	NOUN
ejpam-6307	402	9	in	in	ADP
ejpam-6307	402	10	humans	human	NOUN
ejpam-6307	402	11	to	to	ADP
ejpam-6307	402	12	the	the	DET
ejpam-6307	402	13	u.s	u.s	PROPN
ejpam-6307	402	14	.	.	PROPN
ejpam-6307	402	15	in	in	ADP
ejpam-6307	402	16	figure	figure	NOUN
ejpam-6307	402	17	4	4	NUM
ejpam-6307	402	18	,	,	PUNCT
ejpam-6307	402	19	consider	consider	VERB
ejpam-6307	402	20	the	the	DET
ejpam-6307	402	21	different	different	ADJ
ejpam-6307	402	22	paths	path	NOUN
ejpam-6307	402	23	to	to	ADP
ejpam-6307	402	24	the	the	DET
ejpam-6307	402	25	united	united	PROPN
ejpam-6307	402	26	states	states	PROPN
ejpam-6307	402	27	.	.	PUNCT
ejpam-6307	403	1	first	first	ADV
ejpam-6307	403	2	,	,	PUNCT
ejpam-6307	403	3	we	we	PRON
ejpam-6307	403	4	evaluate	evaluate	VERB
ejpam-6307	403	5	df	df	NOUN
ejpam-6307	403	6	(	(	PUNCT
ejpam-6307	403	7	pu→v	pu→v	PROPN
ejpam-6307	403	8	)	)	PUNCT
ejpam-6307	403	9	for	for	ADP
ejpam-6307	403	10	any	any	DET
ejpam-6307	403	11	one	one	NUM
ejpam-6307	403	12	of	of	ADP
ejpam-6307	403	13	the	the	DET
ejpam-6307	403	14	paths	path	NOUN
ejpam-6307	403	15	—	—	PUNCT
ejpam-6307	403	16	specifically	specifically	ADV
ejpam-6307	403	17	,	,	PUNCT
ejpam-6307	403	18	say	say	VERB
ejpam-6307	403	19	df	df	PROPN
ejpam-6307	403	20	(	(	PUNCT
ejpam-6307	403	21	pchina→u	pchina→u	X
ejpam-6307	403	22	.	.	PUNCT
ejpam-6307	404	1	s.	s.	PROPN
ejpam-6307	404	2	)	)	PUNCT
ejpam-6307	404	3	.	.	PUNCT
ejpam-6307	405	1	now	now	ADV
ejpam-6307	405	2	we	we	PRON
ejpam-6307	405	3	have	have	VERB
ejpam-6307	405	4	df	df	PROPN
ejpam-6307	405	5	(	(	PUNCT
ejpam-6307	405	6	pchina→u	pchina→u	X
ejpam-6307	405	7	.	.	PUNCT
ejpam-6307	406	1	s.	s.	PROPN
ejpam-6307	406	2	)	)	PUNCT
ejpam-6307	407	1	=	=	NOUN
ejpam-6307	407	2			NOUN
ejpam-6307	407	3	0.0	0.0	NUM
ejpam-6307	407	4	0.19	0.19	NUM
ejpam-6307	407	5	0.38	0.38	NUM
ejpam-6307	407	6	0.38	0.38	NUM
ejpam-6307	407	7	0.57	0.57	NUM
ejpam-6307	407	8	0.19	0.19	NUM
ejpam-6307	407	9	0.0	0.0	NUM
ejpam-6307	407	10	0.3	0.3	NUM
ejpam-6307	407	11	0.3	0.3	NUM
ejpam-6307	407	12	0.6	0.6	NUM
ejpam-6307	407	13	0.38	0.38	NUM
ejpam-6307	407	14	0.3	0.3	NUM
ejpam-6307	407	15	0.0	0.0	NUM
ejpam-6307	407	16	0.32	0.32	NUM
ejpam-6307	407	17	0.64	0.64	NUM
ejpam-6307	407	18	0.38	0.38	NUM
ejpam-6307	407	19	0.3	0.3	NUM
ejpam-6307	407	20	0.32	0.32	NUM
ejpam-6307	407	21	0.0	0.0	NUM
ejpam-6307	407	22	0.47	0.47	NUM
ejpam-6307	407	23	0.57	0.57	NUM
ejpam-6307	407	24	0.6	0.6	NUM
ejpam-6307	407	25	0.64	0.64	NUM
ejpam-6307	407	26	0.47	0.47	NUM
ejpam-6307	407	27	0.0	0.0	NUM
ejpam-6307	407	28	.	.	NOUN
ejpam-6307	407	29	also	also	ADV
ejpam-6307	407	30	,	,	PUNCT
ejpam-6307	407	31	we	we	PRON
ejpam-6307	407	32	have	have	AUX
ejpam-6307	407	33	r.	r.	PROPN
ejpam-6307	407	34	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	407	35	,	,	PUNCT
ejpam-6307	407	36	a.	a.	NOUN
ejpam-6307	407	37	m.	m.	PROPN
ejpam-6307	407	38	anto	anto	PROPN
ejpam-6307	407	39	,	,	PUNCT
ejpam-6307	407	40	v.	v.	PROPN
ejpam-6307	407	41	mary	mary	PROPN
ejpam-6307	407	42	mettilda	mettilda	PROPN
ejpam-6307	407	43	rose	rise	VERB
ejpam-6307	407	44	/	/	SYM
ejpam-6307	407	45	eur	eur	PROPN
ejpam-6307	407	46	.	.	PUNCT
ejpam-6307	408	1	j.	j.	PROPN
ejpam-6307	408	2	pure	pure	PROPN
ejpam-6307	408	3	appl	appl	PROPN
ejpam-6307	408	4	.	.	PROPN
ejpam-6307	408	5	math	math	PROPN
ejpam-6307	408	6	,	,	PUNCT
ejpam-6307	408	7	18	18	NUM
ejpam-6307	408	8	(	(	PUNCT
ejpam-6307	408	9	4	4	NUM
ejpam-6307	408	10	)	)	PUNCT
ejpam-6307	408	11	(	(	PUNCT
ejpam-6307	408	12	2025	2025	NUM
ejpam-6307	408	13	)	)	PUNCT
ejpam-6307	408	14	,	,	PUNCT
ejpam-6307	408	15	6307	6307	NUM
ejpam-6307	408	16	19	19	NUM
ejpam-6307	408	17	of	of	ADP
ejpam-6307	408	18	25	25	NUM
ejpam-6307	408	19	tf	tf	PROPN
ejpam-6307	408	20	gd(pchina→u	gd(pchina→u	PROPN
ejpam-6307	408	21	.	.	PUNCT
ejpam-6307	408	22	s.	s.	PROPN
ejpam-6307	408	23	)	)	PUNCT
ejpam-6307	409	1	=	=	X
ejpam-6307	409	2			NOUN
ejpam-6307	409	3	1.52	1.52	NUM
ejpam-6307	409	4	0.0	0.0	NUM
ejpam-6307	409	5	0.0	0.0	NUM
ejpam-6307	409	6	0.0	0.0	NUM
ejpam-6307	409	7	0.0	0.0	NUM
ejpam-6307	409	8	0.0	0.0	NUM
ejpam-6307	409	9	1.39	1.39	NUM
ejpam-6307	409	10	0.0	0.0	NUM
ejpam-6307	409	11	0.0	0.0	NUM
ejpam-6307	409	12	0.0	0.0	NUM
ejpam-6307	409	13	0.0	0.0	NUM
ejpam-6307	409	14	0.0	0.0	NUM
ejpam-6307	409	15	1.64	1.64	NUM
ejpam-6307	409	16	0.0	0.0	NUM
ejpam-6307	409	17	0.0	0.0	NUM
ejpam-6307	409	18	0.0	0.0	NUM
ejpam-6307	409	19	0.0	0.0	NUM
ejpam-6307	409	20	0.0	0.0	NUM
ejpam-6307	409	21	1.47	1.47	NUM
ejpam-6307	409	22	0.0	0.0	NUM
ejpam-6307	409	23	0.0	0.0	NUM
ejpam-6307	409	24	0.0	0.0	NUM
ejpam-6307	409	25	0.0	0.0	NUM
ejpam-6307	409	26	0.0	0.0	NUM
ejpam-6307	409	27	2.28	2.28	NUM
ejpam-6307	409	28	.	.	NOUN
ejpam-6307	409	29	thus	thus	ADV
ejpam-6307	409	30	,	,	PUNCT
ejpam-6307	409	31	the	the	DET
ejpam-6307	409	32	corresponding	corresponding	ADJ
ejpam-6307	409	33	fuzzy	fuzzy	ADJ
ejpam-6307	409	34	geodetic	geodetic	ADJ
ejpam-6307	409	35	-	-	PUNCT
ejpam-6307	409	36	laplacian	laplacian	ADJ
ejpam-6307	409	37	matrix	matrix	NOUN
ejpam-6307	409	38	,	,	PUNCT
ejpam-6307	409	39	mfgld	mfgld	ADJ
ejpam-6307	409	40	(	(	PUNCT
ejpam-6307	409	41	pchina→u	pchina→u	X
ejpam-6307	409	42	.	.	PUNCT
ejpam-6307	410	1	s.	s.	PROPN
ejpam-6307	410	2	)	)	PUNCT
ejpam-6307	410	3	is	be	AUX
ejpam-6307	410	4	as	as	SCONJ
ejpam-6307	410	5	follows	follow	VERB
ejpam-6307	410	6	:	:	PUNCT
ejpam-6307	410	7	mfgld	mfgld	ADJ
ejpam-6307	410	8	(	(	PUNCT
ejpam-6307	410	9	pchina→u	pchina→u	X
ejpam-6307	410	10	.	.	PUNCT
ejpam-6307	411	1	s.	s.	PROPN
ejpam-6307	411	2	)	)	PUNCT
ejpam-6307	412	1	=	=	X
ejpam-6307	412	2			NOUN
ejpam-6307	412	3	1.52	1.52	NUM
ejpam-6307	413	1	−0.19	−0.19	PROPN
ejpam-6307	414	1	−0.38	−0.38	X
ejpam-6307	414	2	−0.38	−0.38	X
ejpam-6307	414	3	−0.57	−0.57	X
ejpam-6307	415	1	−0.19	−0.19	NUM
ejpam-6307	415	2	1.39	1.39	NUM
ejpam-6307	415	3	−0.3	−0.3	PROPN
ejpam-6307	415	4	−0.3	−0.3	PROPN
ejpam-6307	416	1	−0.6	−0.6	PROPN
ejpam-6307	416	2	−0.38	−0.38	ADP
ejpam-6307	416	3	−0.3	−0.3	PROPN
ejpam-6307	417	1	1.64	1.64	NUM
ejpam-6307	417	2	−0.32	−0.32	NOUN
ejpam-6307	417	3	−0.64	−0.64	X
ejpam-6307	417	4	−0.38	−0.38	PRON
ejpam-6307	417	5	−0.3	−0.3	PROPN
ejpam-6307	417	6	−0.32	−0.32	X
ejpam-6307	417	7	1.47	1.47	NUM
ejpam-6307	417	8	−0.47	−0.47	X
ejpam-6307	417	9	−0.57	−0.57	CCONJ
ejpam-6307	417	10	−0.6	−0.6	PROPN
ejpam-6307	417	11	−0.64	−0.64	X
ejpam-6307	417	12	−0.47	−0.47	SYM
ejpam-6307	417	13	2.28	2.28	NUM
ejpam-6307	417	14	.	.	NOUN
ejpam-6307	417	15	the	the	DET
ejpam-6307	417	16	eigenvalues	eigenvalue	NOUN
ejpam-6307	417	17	are	be	AUX
ejpam-6307	417	18	γgl1	γgl1	PROPN
ejpam-6307	417	19	=	=	SYM
ejpam-6307	417	20	2.8692	2.8692	NUM
ejpam-6307	417	21	,	,	PUNCT
ejpam-6307	417	22	γgl2	γgl2	PROPN
ejpam-6307	417	23	=	=	SYM
ejpam-6307	417	24	1.9900	1.9900	NUM
ejpam-6307	417	25	,	,	PUNCT
ejpam-6307	417	26	γgl3	γgl3	PROPN
ejpam-6307	417	27	=	=	SYM
ejpam-6307	418	1	1.8317	1.8317	NUM
ejpam-6307	418	2	,	,	PUNCT
ejpam-6307	418	3	γgl4	γgl4	PROPN
ejpam-6307	418	4	=	=	PROPN
ejpam-6307	418	5	1.6090	1.6090	NUM
ejpam-6307	418	6	,	,	PUNCT
ejpam-6307	418	7	and	and	CCONJ
ejpam-6307	419	1	γgl5	γgl5	NOUN
ejpam-6307	419	2	=	=	SYM
ejpam-6307	419	3	0.0000	0.0000	NUM
ejpam-6307	419	4	.	.	PUNCT
ejpam-6307	420	1	then	then	ADV
ejpam-6307	420	2	,	,	PUNCT
ejpam-6307	420	3	gle(pchina→u	gle(pchina→u	PROPN
ejpam-6307	420	4	.	.	PUNCT
ejpam-6307	420	5	s.	s.	PROPN
ejpam-6307	420	6	)	)	PUNCT
ejpam-6307	421	1	=	=	PUNCT
ejpam-6307	421	2	∣∣∣γgli	∣∣∣γgli	NOUN
ejpam-6307	421	3	−	−	NOUN
ejpam-6307	421	4	2	2	NUM
ejpam-6307	421	5	∑	∑	PUNCT
ejpam-6307	421	6	1≤i	1≤i	PROPN
ejpam-6307	421	7	<	<	X
ejpam-6307	421	8	j≤n	j≤n	NOUN
ejpam-6307	421	9	df	df	NOUN
ejpam-6307	421	10	(	(	PUNCT
ejpam-6307	421	11	pchina→u	pchina→u	X
ejpam-6307	421	12	.	.	PUNCT
ejpam-6307	422	1	s.	s.	PROPN
ejpam-6307	422	2	)	)	PUNCT
ejpam-6307	423	1	n	n	PROPN
ejpam-6307	423	2	∣∣∣.	∣∣∣.	PROPN
ejpam-6307	423	3	gle(pchina→u	gle(pchina→u	PROPN
ejpam-6307	423	4	.	.	PUNCT
ejpam-6307	424	1	s.	s.	PROPN
ejpam-6307	424	2	)	)	PUNCT
ejpam-6307	425	1	=	=	SYM
ejpam-6307	425	2	|2.8692−	|2.8692−	PROPN
ejpam-6307	425	3	1.66|+	1.66|+	NUM
ejpam-6307	425	4	|1.9900−	|1.9900−	PROPN
ejpam-6307	425	5	1.66|	1.66|	NUM
ejpam-6307	426	1	+	+	CCONJ
ejpam-6307	426	2	|1.8317−	|1.8317−	PROPN
ejpam-6307	426	3	1.66|+	1.66|+	NUM
ejpam-6307	426	4	|1.6090−	|1.6090−	PROPN
ejpam-6307	426	5	1.66|	1.66|	PROPN
ejpam-6307	426	6	+	+	CCONJ
ejpam-6307	426	7	|0.0000−	|0.0000−	PROPN
ejpam-6307	426	8	1.66|	1.66|	NUM
ejpam-6307	426	9	=	=	SYM
ejpam-6307	426	10	3.4219	3.4219	NUM
ejpam-6307	426	11	.	.	PUNCT
ejpam-6307	427	1	likewise	likewise	ADV
ejpam-6307	427	2	,	,	PUNCT
ejpam-6307	427	3	along	along	ADP
ejpam-6307	427	4	the	the	DET
ejpam-6307	427	5	pindia→u	pindia→u	PROPN
ejpam-6307	427	6	.	.	PUNCT
ejpam-6307	428	1	s.	s.	PROPN
ejpam-6307	428	2	route	route	PROPN
ejpam-6307	428	3	,	,	PUNCT
ejpam-6307	428	4	we	we	PRON
ejpam-6307	428	5	have	have	VERB
ejpam-6307	428	6	:	:	PUNCT
ejpam-6307	428	7	df	df	PROPN
ejpam-6307	428	8	(	(	PUNCT
ejpam-6307	428	9	pindia→u	pindia→u	PROPN
ejpam-6307	428	10	.	.	PUNCT
ejpam-6307	429	1	s.	s.	PROPN
ejpam-6307	429	2	)	)	PUNCT
ejpam-6307	430	1	=	=	PRON
ejpam-6307	430	2			ADJ
ejpam-6307	430	3	0.0	0.0	NUM
ejpam-6307	430	4	0.26	0.26	NUM
ejpam-6307	430	5	0.52	0.52	NUM
ejpam-6307	430	6	0.78	0.78	NUM
ejpam-6307	430	7	0.26	0.26	NUM
ejpam-6307	430	8	0.0	0.0	NUM
ejpam-6307	430	9	0.32	0.32	NUM
ejpam-6307	430	10	0.64	0.64	NUM
ejpam-6307	430	11	0.52	0.52	NUM
ejpam-6307	430	12	0.32	0.32	NUM
ejpam-6307	430	13	0.0	0.0	NUM
ejpam-6307	430	14	0.47	0.47	NUM
ejpam-6307	430	15	0.78	0.78	NUM
ejpam-6307	430	16	0.64	0.64	NUM
ejpam-6307	430	17	0.47	0.47	NUM
ejpam-6307	430	18	0.0	0.0	NUM
ejpam-6307	430	19			NOUN
ejpam-6307	430	20	and	and	CCONJ
ejpam-6307	430	21	tf	tf	PROPN
ejpam-6307	430	22	gd(pindia→u	gd(pindia→u	PROPN
ejpam-6307	430	23	.	.	PUNCT
ejpam-6307	431	1	s.	s.	PROPN
ejpam-6307	431	2	)	)	PUNCT
ejpam-6307	432	1	=	=	PRON
ejpam-6307	432	2			PROPN
ejpam-6307	432	3	1.56	1.56	NUM
ejpam-6307	432	4	0.0	0.0	NUM
ejpam-6307	432	5	0.0	0.0	NUM
ejpam-6307	432	6	0.0	0.0	NUM
ejpam-6307	432	7	0.0	0.0	NUM
ejpam-6307	432	8	1.22	1.22	NUM
ejpam-6307	432	9	0.0	0.0	NUM
ejpam-6307	432	10	0.0	0.0	NUM
ejpam-6307	432	11	0.0	0.0	NUM
ejpam-6307	432	12	0.0	0.0	NUM
ejpam-6307	432	13	1.31	1.31	NUM
ejpam-6307	432	14	0.0	0.0	NUM
ejpam-6307	432	15	0.0	0.0	NUM
ejpam-6307	432	16	0.0	0.0	NUM
ejpam-6307	432	17	0.0	0.0	NUM
ejpam-6307	432	18	1.89	1.89	NUM
ejpam-6307	432	19	.	.	NOUN
ejpam-6307	432	20	thus	thus	ADV
ejpam-6307	432	21	mfgld	mfgld	ADV
ejpam-6307	432	22	(	(	PUNCT
ejpam-6307	432	23	pindia→u	pindia→u	PROPN
ejpam-6307	432	24	.	.	PUNCT
ejpam-6307	433	1	s.	s.	PROPN
ejpam-6307	433	2	)	)	PUNCT
ejpam-6307	434	1	=	=	PRON
ejpam-6307	434	2			PROPN
ejpam-6307	434	3	1.56	1.56	NUM
ejpam-6307	434	4	−0.26	−0.26	NOUN
ejpam-6307	434	5	−0.52	−0.52	ADP
ejpam-6307	434	6	−0.78	−0.78	NOUN
ejpam-6307	434	7	−0.26	−0.26	INTJ
ejpam-6307	434	8	1.22	1.22	NUM
ejpam-6307	434	9	−0.32	−0.32	NOUN
ejpam-6307	434	10	−0.64	−0.64	X
ejpam-6307	434	11	−0.52	−0.52	ADV
ejpam-6307	434	12	−0.32	−0.32	NOUN
ejpam-6307	434	13	1.31	1.31	NUM
ejpam-6307	434	14	−0.47	−0.47	NOUN
ejpam-6307	434	15	−0.78	−0.78	X
ejpam-6307	434	16	−0.64	−0.64	X
ejpam-6307	434	17	−0.47	−0.47	ADP
ejpam-6307	434	18	1.89	1.89	NUM
ejpam-6307	434	19	.	.	NOUN
ejpam-6307	434	20	r.	r.	PROPN
ejpam-6307	434	21	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	434	22	,	,	PUNCT
ejpam-6307	434	23	a.	a.	NOUN
ejpam-6307	434	24	m.	m.	PROPN
ejpam-6307	434	25	anto	anto	PROPN
ejpam-6307	434	26	,	,	PUNCT
ejpam-6307	434	27	v.	v.	PROPN
ejpam-6307	434	28	mary	mary	PROPN
ejpam-6307	434	29	mettilda	mettilda	PROPN
ejpam-6307	434	30	rose	rise	VERB
ejpam-6307	434	31	/	/	SYM
ejpam-6307	434	32	eur	eur	PROPN
ejpam-6307	434	33	.	.	PUNCT
ejpam-6307	435	1	j.	j.	PROPN
ejpam-6307	435	2	pure	pure	PROPN
ejpam-6307	435	3	appl	appl	PROPN
ejpam-6307	435	4	.	.	PROPN
ejpam-6307	435	5	math	math	PROPN
ejpam-6307	435	6	,	,	PUNCT
ejpam-6307	435	7	18	18	NUM
ejpam-6307	435	8	(	(	PUNCT
ejpam-6307	435	9	4	4	NUM
ejpam-6307	435	10	)	)	PUNCT
ejpam-6307	435	11	(	(	PUNCT
ejpam-6307	435	12	2025	2025	NUM
ejpam-6307	435	13	)	)	PUNCT
ejpam-6307	435	14	,	,	PUNCT
ejpam-6307	435	15	6307	6307	NUM
ejpam-6307	435	16	20	20	NUM
ejpam-6307	435	17	of	of	ADP
ejpam-6307	435	18	25	25	NUM
ejpam-6307	435	19	then	then	ADV
ejpam-6307	435	20	we	we	PRON
ejpam-6307	435	21	obtain	obtain	VERB
ejpam-6307	435	22	,	,	PUNCT
ejpam-6307	435	23	gle(pindia→u	gle(pindia→u	PROPN
ejpam-6307	435	24	.	.	PUNCT
ejpam-6307	436	1	s.	s.	PROPN
ejpam-6307	436	2	)	)	PUNCT
ejpam-6307	437	1	=	=	PUNCT
ejpam-6307	438	1	2.9789	2.9789	NUM
ejpam-6307	438	2	.	.	PUNCT
ejpam-6307	439	1	using	use	VERB
ejpam-6307	439	2	similar	similar	ADJ
ejpam-6307	439	3	computations	computation	NOUN
ejpam-6307	439	4	for	for	ADP
ejpam-6307	439	5	the	the	DET
ejpam-6307	439	6	pethiopia→u	pethiopia→u	NOUN
ejpam-6307	439	7	.	.	PUNCT
ejpam-6307	440	1	s.	s.	PROPN
ejpam-6307	440	2	,	,	PUNCT
ejpam-6307	440	3	we	we	PRON
ejpam-6307	440	4	obtaingle(pethiopia→u	obtaingle(pethiopia→u	AUX
ejpam-6307	440	5	.	.	PUNCT
ejpam-6307	441	1	s.	s.	PROPN
ejpam-6307	441	2	)	)	PUNCT
ejpam-6307	442	1	=	=	PUNCT
ejpam-6307	443	1	5.026	5.026	NUM
ejpam-6307	443	2	.	.	PUNCT
ejpam-6307	444	1	along	along	ADP
ejpam-6307	444	2	psomalia→u	psomalia→u	X
ejpam-6307	444	3	.	.	PUNCT
ejpam-6307	445	1	s.	s.	PROPN
ejpam-6307	445	2	route	route	PROPN
ejpam-6307	445	3	,	,	PUNCT
ejpam-6307	445	4	gle(psomalia→u	gle(psomalia→u	PROPN
ejpam-6307	445	5	.	.	PUNCT
ejpam-6307	446	1	s.	s.	PROPN
ejpam-6307	446	2	)	)	PUNCT
ejpam-6307	447	1	=	=	PUNCT
ejpam-6307	448	1	5.855	5.855	NUM
ejpam-6307	448	2	.	.	PUNCT
ejpam-6307	449	1	in	in	ADP
ejpam-6307	449	2	the	the	DET
ejpam-6307	449	3	route	route	NOUN
ejpam-6307	449	4	pnigeria→u	pnigeria→u	X
ejpam-6307	449	5	.	.	PUNCT
ejpam-6307	450	1	s.	s.	PROPN
ejpam-6307	450	2	,	,	PUNCT
ejpam-6307	450	3	gle(pnigeria→u	gle(pnigeria→u	PROPN
ejpam-6307	450	4	.	.	PUNCT
ejpam-6307	450	5	s.	s.	PROPN
ejpam-6307	450	6	)	)	PUNCT
ejpam-6307	451	1	=	=	PUNCT
ejpam-6307	452	1	5.518	5.518	NUM
ejpam-6307	452	2	.	.	PUNCT
ejpam-6307	453	1	now	now	ADV
ejpam-6307	453	2	we	we	PRON
ejpam-6307	453	3	analyze	analyze	VERB
ejpam-6307	453	4	the	the	DET
ejpam-6307	453	5	human	human	ADJ
ejpam-6307	453	6	trafficking	trafficking	NOUN
ejpam-6307	453	7	from	from	ADP
ejpam-6307	453	8	the	the	DET
ejpam-6307	453	9	continents	continent	NOUN
ejpam-6307	453	10	of	of	ADP
ejpam-6307	453	11	africa	africa	PROPN
ejpam-6307	453	12	and	and	CCONJ
ejpam-6307	453	13	asia	asia	PROPN
ejpam-6307	453	14	to	to	PART
ejpam-6307	453	15	enter	enter	VERB
ejpam-6307	453	16	the	the	DET
ejpam-6307	453	17	u.s	u.s	PROPN
ejpam-6307	453	18	.	.	PROPN
ejpam-6307	453	19	illegally	illegally	ADV
ejpam-6307	453	20	over	over	ADP
ejpam-6307	453	21	the	the	DET
ejpam-6307	453	22	mexican	mexican	ADJ
ejpam-6307	453	23	border	border	NOUN
ejpam-6307	453	24	.	.	PUNCT
ejpam-6307	454	1	let	let	VERB
ejpam-6307	454	2	’s	’s	NOUN
ejpam-6307	454	3	first	first	ADV
ejpam-6307	454	4	evaluatemfgld	evaluatemfgld	PROPN
ejpam-6307	454	5	(	(	PUNCT
ejpam-6307	454	6	pasia→u	pasia→u	X
ejpam-6307	454	7	.	.	PUNCT
ejpam-6307	455	1	s.	s.	PROPN
ejpam-6307	455	2	)	)	PUNCT
ejpam-6307	455	3	.	.	PUNCT
ejpam-6307	456	1	thus	thus	ADV
ejpam-6307	456	2	mfgld	mfgld	ADV
ejpam-6307	456	3	(	(	PUNCT
ejpam-6307	456	4	pasia→u	pasia→u	X
ejpam-6307	456	5	.	.	PUNCT
ejpam-6307	456	6	s.	s.	PROPN
ejpam-6307	456	7	)	)	PUNCT
ejpam-6307	457	1	=	=	NOUN
ejpam-6307	457	2			NOUN
ejpam-6307	457	3	0.78	0.78	NUM
ejpam-6307	457	4	0.0	0.0	NUM
ejpam-6307	457	5	0.0	0.0	NUM
ejpam-6307	457	6	0.0	0.0	NUM
ejpam-6307	457	7	−0.78	−0.78	VERB
ejpam-6307	457	8	0.0	0.0	NUM
ejpam-6307	457	9	0	0	NUM
ejpam-6307	457	10	..	..	SYM
ejpam-6307	457	11	57	57	NUM
ejpam-6307	457	12	0.0	0.0	NUM
ejpam-6307	457	13	0.0	0.0	NUM
ejpam-6307	458	1	−0.57	−0.57	CCONJ
ejpam-6307	458	2	0.0	0.0	NUM
ejpam-6307	458	3	0.0	0.0	NUM
ejpam-6307	458	4	0.47	0.47	NUM
ejpam-6307	458	5	−0.17	−0.17	X
ejpam-6307	458	6	−0.3	−0.3	PROPN
ejpam-6307	458	7	0.0	0.0	NUM
ejpam-6307	458	8	0.0	0.0	NUM
ejpam-6307	458	9	−0.17	−0.17	INTJ
ejpam-6307	458	10	0.41	0.41	NUM
ejpam-6307	458	11	−0.24	−0.24	NOUN
ejpam-6307	458	12	−0.78	−0.78	VERB
ejpam-6307	458	13	−0.57	−0.57	SYM
ejpam-6307	458	14	−0.3	−0.3	PROPN
ejpam-6307	458	15	−0.24	−0.24	NOUN
ejpam-6307	458	16	1.89	1.89	NUM
ejpam-6307	458	17	.	.	NOUN
ejpam-6307	458	18	the	the	DET
ejpam-6307	458	19	eigenvalues	eigenvalue	NOUN
ejpam-6307	458	20	are	be	AUX
ejpam-6307	458	21	γgl1	γgl1	PROPN
ejpam-6307	458	22	=	=	PUNCT
ejpam-6307	458	23	1.545	1.545	NUM
ejpam-6307	458	24	,	,	PUNCT
ejpam-6307	458	25	γgl2	γgl2	PROPN
ejpam-6307	458	26	=	=	PROPN
ejpam-6307	458	27	1.281	1.281	NUM
ejpam-6307	458	28	,	,	PUNCT
ejpam-6307	458	29	γgl3	γgl3	PROPN
ejpam-6307	458	30	=	=	SYM
ejpam-6307	458	31	0.612	0.612	NUM
ejpam-6307	458	32	,	,	PUNCT
ejpam-6307	458	33	γgl4	γgl4	PROPN
ejpam-6307	458	34	=	=	NOUN
ejpam-6307	458	35	0.491	0.491	NUM
ejpam-6307	458	36	,	,	PUNCT
ejpam-6307	458	37	and	and	CCONJ
ejpam-6307	458	38	γgl5	γgl5	NOUN
ejpam-6307	458	39	=	=	SYM
ejpam-6307	458	40	0.191	0.191	NUM
ejpam-6307	458	41	.	.	PUNCT
ejpam-6307	459	1	therefore	therefore	ADV
ejpam-6307	459	2	,	,	PUNCT
ejpam-6307	459	3	we	we	PRON
ejpam-6307	459	4	have	have	VERB
ejpam-6307	459	5	gle(pasia→u	gle(pasia→u	PROPN
ejpam-6307	459	6	.	.	PUNCT
ejpam-6307	460	1	s.	s.	PROPN
ejpam-6307	460	2	)	)	PUNCT
ejpam-6307	461	1	=	=	PUNCT
ejpam-6307	461	2	2.356	2.356	NUM
ejpam-6307	461	3	.	.	PUNCT
ejpam-6307	462	1	similarly	similarly	ADV
ejpam-6307	462	2	,	,	PUNCT
ejpam-6307	462	3	along	along	ADP
ejpam-6307	462	4	the	the	DET
ejpam-6307	462	5	pafrica→u	pafrica→u	PROPN
ejpam-6307	462	6	.	.	PUNCT
ejpam-6307	463	1	s.	s.	PROPN
ejpam-6307	463	2	route	route	PROPN
ejpam-6307	463	3	,	,	PUNCT
ejpam-6307	463	4	we	we	PRON
ejpam-6307	463	5	have	have	AUX
ejpam-6307	463	6	mfgld	mfgld	ADV
ejpam-6307	463	7	(	(	PUNCT
ejpam-6307	463	8	pafrica→u	pafrica→u	X
ejpam-6307	463	9	.	.	PUNCT
ejpam-6307	464	1	s.	s.	PROPN
ejpam-6307	464	2	)	)	PUNCT
ejpam-6307	465	1	=	=	PRON
ejpam-6307	465	2			PROPN
ejpam-6307	465	3	1.05	1.05	NUM
ejpam-6307	465	4	0.00	0.00	NUM
ejpam-6307	465	5	0.00	0.00	NUM
ejpam-6307	465	6	−1.05	−1.05	PRON
ejpam-6307	465	7	0.00	0.00	NUM
ejpam-6307	465	8	0.36	0.36	NUM
ejpam-6307	465	9	0.00	0.00	NUM
ejpam-6307	465	10	−0.36	−0.36	ADP
ejpam-6307	465	11	0.00	0.00	NUM
ejpam-6307	465	12	0.00	0.00	NUM
ejpam-6307	465	13	0.55	0.55	NUM
ejpam-6307	465	14	−0.55	−0.55	NOUN
ejpam-6307	465	15	−1.05	−1.05	NOUN
ejpam-6307	465	16	−0.36	−0.36	NUM
ejpam-6307	465	17	−0.55	−0.55	NOUN
ejpam-6307	465	18	1.96	1.96	NUM
ejpam-6307	465	19			NOUN
ejpam-6307	465	20	.	.	PUNCT
ejpam-6307	466	1	then	then	ADV
ejpam-6307	466	2	we	we	PRON
ejpam-6307	466	3	obtain	obtain	VERB
ejpam-6307	466	4	:	:	PUNCT
ejpam-6307	466	5	gle(pafrica→u	gle(pafrica→u	PROPN
ejpam-6307	466	6	.	.	PUNCT
ejpam-6307	466	7	s.	s.	PROPN
ejpam-6307	466	8	)	)	PUNCT
ejpam-6307	467	1	=	=	PUNCT
ejpam-6307	468	1	3.608	3.608	NUM
ejpam-6307	468	2	.	.	PUNCT
ejpam-6307	469	1	based	base	VERB
ejpam-6307	469	2	on	on	ADP
ejpam-6307	469	3	the	the	DET
ejpam-6307	469	4	methodology	methodology	NOUN
ejpam-6307	469	5	employed	employ	VERB
ejpam-6307	469	6	in	in	ADP
ejpam-6307	469	7	[	[	X
ejpam-6307	469	8	23	23	NUM
ejpam-6307	469	9	]	]	PUNCT
ejpam-6307	469	10	to	to	PART
ejpam-6307	469	11	assess	assess	VERB
ejpam-6307	469	12	the	the	DET
ejpam-6307	469	13	likelihood	likelihood	NOUN
ejpam-6307	469	14	of	of	ADP
ejpam-6307	469	15	illegal	illegal	ADJ
ejpam-6307	469	16	immigration	immigration	NOUN
ejpam-6307	469	17	from	from	ADP
ejpam-6307	469	18	countries	country	NOUN
ejpam-6307	469	19	of	of	ADP
ejpam-6307	469	20	origin	origin	NOUN
ejpam-6307	469	21	to	to	ADP
ejpam-6307	469	22	the	the	DET
ejpam-6307	469	23	united	united	PROPN
ejpam-6307	469	24	states	states	PROPN
ejpam-6307	469	25	,	,	PUNCT
ejpam-6307	469	26	as	as	ADV
ejpam-6307	469	27	well	well	ADV
ejpam-6307	469	28	as	as	ADP
ejpam-6307	469	29	the	the	DET
ejpam-6307	469	30	approach	approach	NOUN
ejpam-6307	469	31	used	use	VERB
ejpam-6307	469	32	in	in	ADP
ejpam-6307	469	33	this	this	DET
ejpam-6307	469	34	study	study	NOUN
ejpam-6307	469	35	,	,	PUNCT
ejpam-6307	469	36	somalia	somalia	PROPN
ejpam-6307	469	37	emerges	emerge	VERB
ejpam-6307	469	38	as	as	ADP
ejpam-6307	469	39	the	the	DET
ejpam-6307	469	40	most	most	ADV
ejpam-6307	469	41	vulnerable	vulnerable	ADJ
ejpam-6307	469	42	country	country	NOUN
ejpam-6307	469	43	of	of	ADP
ejpam-6307	469	44	origin	origin	NOUN
ejpam-6307	469	45	for	for	ADP
ejpam-6307	469	46	migration	migration	NOUN
ejpam-6307	469	47	routes	route	NOUN
ejpam-6307	469	48	leading	lead	VERB
ejpam-6307	469	49	to	to	ADP
ejpam-6307	469	50	the	the	DET
ejpam-6307	469	51	united	united	PROPN
ejpam-6307	469	52	states	states	PROPN
ejpam-6307	469	53	.	.	PUNCT
ejpam-6307	470	1	similar	similar	ADJ
ejpam-6307	470	2	findings	finding	NOUN
ejpam-6307	470	3	regarding	regard	VERB
ejpam-6307	470	4	somalia	somalia	PROPN
ejpam-6307	470	5	’s	’s	PART
ejpam-6307	470	6	high	high	ADJ
ejpam-6307	470	7	vulnerability	vulnerability	NOUN
ejpam-6307	470	8	are	be	AUX
ejpam-6307	470	9	reported	report	VERB
ejpam-6307	470	10	in	in	ADP
ejpam-6307	470	11	[	[	X
ejpam-6307	470	12	23–25	23–25	NUM
ejpam-6307	470	13	]	]	PUNCT
ejpam-6307	470	14	.	.	PUNCT
ejpam-6307	471	1	moreover	moreover	ADV
ejpam-6307	471	2	,	,	PUNCT
ejpam-6307	471	3	our	our	PRON
ejpam-6307	471	4	results	result	NOUN
ejpam-6307	471	5	indicate	indicate	VERB
ejpam-6307	471	6	that	that	SCONJ
ejpam-6307	471	7	the	the	DET
ejpam-6307	471	8	continent	continent	NOUN
ejpam-6307	471	9	of	of	ADP
ejpam-6307	471	10	africa	africa	PROPN
ejpam-6307	471	11	exhibits	exhibit	VERB
ejpam-6307	471	12	a	a	DET
ejpam-6307	471	13	higher	high	ADJ
ejpam-6307	471	14	level	level	NOUN
ejpam-6307	471	15	of	of	ADP
ejpam-6307	471	16	vulnerability	vulnerability	NOUN
ejpam-6307	471	17	compared	compare	VERB
ejpam-6307	471	18	to	to	ADP
ejpam-6307	471	19	asia	asia	PROPN
ejpam-6307	471	20	.	.	PUNCT
ejpam-6307	472	1	to	to	PART
ejpam-6307	472	2	quantify	quantify	VERB
ejpam-6307	472	3	such	such	ADJ
ejpam-6307	472	4	vulnerability	vulnerability	NOUN
ejpam-6307	472	5	,	,	PUNCT
ejpam-6307	472	6	this	this	DET
ejpam-6307	472	7	study	study	NOUN
ejpam-6307	472	8	introduces	introduce	VERB
ejpam-6307	472	9	the	the	DET
ejpam-6307	472	10	concept	concept	NOUN
ejpam-6307	472	11	of	of	ADP
ejpam-6307	472	12	fuzzy	fuzzy	ADJ
ejpam-6307	472	13	geodetic	geodetic	ADJ
ejpam-6307	472	14	-	-	PUNCT
ejpam-6307	472	15	laplacian	laplacian	ADJ
ejpam-6307	472	16	energy	energy	NOUN
ejpam-6307	472	17	as	as	ADP
ejpam-6307	472	18	a	a	DET
ejpam-6307	472	19	potential	potential	ADJ
ejpam-6307	472	20	metric	metric	NOUN
ejpam-6307	472	21	.	.	PUNCT
ejpam-6307	473	1	this	this	DET
ejpam-6307	473	2	work	work	NOUN
ejpam-6307	473	3	demonstrates	demonstrate	VERB
ejpam-6307	473	4	that	that	PRON
ejpam-6307	473	5	fuzzy	fuzzy	ADJ
ejpam-6307	473	6	geodetic	geodetic	ADJ
ejpam-6307	473	7	-	-	PUNCT
ejpam-6307	473	8	laplacian	laplacian	ADJ
ejpam-6307	473	9	energy	energy	NOUN
ejpam-6307	473	10	can	can	AUX
ejpam-6307	473	11	effectively	effectively	ADV
ejpam-6307	473	12	analyze	analyze	VERB
ejpam-6307	473	13	complex	complex	ADJ
ejpam-6307	473	14	relational	relational	ADJ
ejpam-6307	473	15	structures	structure	NOUN
ejpam-6307	473	16	,	,	PUNCT
ejpam-6307	473	17	providing	provide	VERB
ejpam-6307	473	18	a	a	DET
ejpam-6307	473	19	valuable	valuable	ADJ
ejpam-6307	473	20	tool	tool	NOUN
ejpam-6307	473	21	for	for	ADP
ejpam-6307	473	22	identifying	identify	VERB
ejpam-6307	473	23	patterns	pattern	NOUN
ejpam-6307	473	24	of	of	ADP
ejpam-6307	473	25	migratory	migratory	ADJ
ejpam-6307	473	26	risk	risk	NOUN
ejpam-6307	473	27	.	.	PUNCT
ejpam-6307	474	1	the	the	DET
ejpam-6307	474	2	results	result	NOUN
ejpam-6307	474	3	validate	validate	VERB
ejpam-6307	474	4	the	the	DET
ejpam-6307	474	5	applicability	applicability	NOUN
ejpam-6307	474	6	of	of	ADP
ejpam-6307	474	7	this	this	DET
ejpam-6307	474	8	approach	approach	NOUN
ejpam-6307	474	9	,	,	PUNCT
ejpam-6307	474	10	suggesting	suggest	VERB
ejpam-6307	474	11	that	that	SCONJ
ejpam-6307	474	12	it	it	PRON
ejpam-6307	474	13	offers	offer	VERB
ejpam-6307	474	14	enhanced	enhanced	ADJ
ejpam-6307	474	15	insights	insight	NOUN
ejpam-6307	474	16	into	into	ADP
ejpam-6307	474	17	regional	regional	ADJ
ejpam-6307	474	18	vulnerability	vulnerability	NOUN
ejpam-6307	474	19	assessments	assessment	NOUN
ejpam-6307	474	20	and	and	CCONJ
ejpam-6307	474	21	supports	support	VERB
ejpam-6307	474	22	informed	informed	ADJ
ejpam-6307	474	23	decision	decision	NOUN
ejpam-6307	474	24	-	-	PUNCT
ejpam-6307	474	25	making	making	NOUN
ejpam-6307	474	26	.	.	PUNCT
ejpam-6307	475	1	7.2	7.2	NUM
ejpam-6307	475	2	.	.	PUNCT
ejpam-6307	475	3	role	role	NOUN
ejpam-6307	475	4	of	of	ADP
ejpam-6307	475	5	different	different	ADJ
ejpam-6307	475	6	agencies	agency	NOUN
ejpam-6307	475	7	in	in	ADP
ejpam-6307	475	8	decision	decision	NOUN
ejpam-6307	475	9	making	make	VERB
ejpam-6307	475	10	for	for	ADP
ejpam-6307	475	11	combating	combat	VERB
ejpam-6307	475	12	crimes	crime	NOUN
ejpam-6307	475	13	in	in	ADP
ejpam-6307	475	14	contemporary	contemporary	ADJ
ejpam-6307	475	15	law	law	NOUN
ejpam-6307	475	16	enforcement	enforcement	NOUN
ejpam-6307	475	17	,	,	PUNCT
ejpam-6307	475	18	effective	effective	ADJ
ejpam-6307	475	19	crime	crime	NOUN
ejpam-6307	475	20	detection	detection	NOUN
ejpam-6307	475	21	and	and	CCONJ
ejpam-6307	475	22	prevention	prevention	NOUN
ejpam-6307	475	23	require	require	VERB
ejpam-6307	475	24	coordinated	coordinate	VERB
ejpam-6307	475	25	collaboration	collaboration	NOUN
ejpam-6307	475	26	across	across	ADP
ejpam-6307	475	27	multiple	multiple	ADJ
ejpam-6307	475	28	agencies	agency	NOUN
ejpam-6307	475	29	.	.	PUNCT
ejpam-6307	476	1	in	in	ADP
ejpam-6307	476	2	this	this	DET
ejpam-6307	476	3	study	study	NOUN
ejpam-6307	476	4	,	,	PUNCT
ejpam-6307	476	5	we	we	PRON
ejpam-6307	476	6	propose	propose	VERB
ejpam-6307	476	7	a	a	DET
ejpam-6307	476	8	mathematical	mathematical	ADJ
ejpam-6307	476	9	model	model	NOUN
ejpam-6307	476	10	that	that	PRON
ejpam-6307	476	11	employs	employ	VERB
ejpam-6307	476	12	fuzzy	fuzzy	ADJ
ejpam-6307	476	13	geodetic	geodetic	ADJ
ejpam-6307	476	14	-	-	PUNCT
ejpam-6307	476	15	laplacian	laplacian	ADJ
ejpam-6307	476	16	energy	energy	NOUN
ejpam-6307	476	17	to	to	PART
ejpam-6307	476	18	facilitate	facilitate	VERB
ejpam-6307	476	19	informed	informed	ADJ
ejpam-6307	476	20	decisionmaking	decisionmaking	NOUN
ejpam-6307	476	21	.	.	PUNCT
ejpam-6307	477	1	we	we	PRON
ejpam-6307	477	2	consider	consider	VERB
ejpam-6307	477	3	a	a	DET
ejpam-6307	477	4	hypothetical	hypothetical	ADJ
ejpam-6307	477	5	team	team	NOUN
ejpam-6307	477	6	formation	formation	NOUN
ejpam-6307	477	7	comprising	comprise	VERB
ejpam-6307	477	8	four	four	NUM
ejpam-6307	477	9	police	police	NOUN
ejpam-6307	477	10	departments	department	NOUN
ejpam-6307	477	11	—	—	PUNCT
ejpam-6307	477	12	alpha	alpha	NOUN
ejpam-6307	477	13	(	(	PUNCT
ejpam-6307	477	14	a	a	NOUN
ejpam-6307	477	15	)	)	PUNCT
ejpam-6307	477	16	,	,	PUNCT
ejpam-6307	477	17	bravo	bravo	PROPN
ejpam-6307	477	18	(	(	PUNCT
ejpam-6307	477	19	b	b	NOUN
ejpam-6307	477	20	)	)	PUNCT
ejpam-6307	477	21	,	,	PUNCT
ejpam-6307	477	22	charlie	charlie	PROPN
ejpam-6307	477	23	(	(	PUNCT
ejpam-6307	477	24	c	c	NOUN
ejpam-6307	477	25	)	)	PUNCT
ejpam-6307	477	26	,	,	PUNCT
ejpam-6307	477	27	and	and	CCONJ
ejpam-6307	477	28	delta	delta	NOUN
ejpam-6307	477	29	(	(	PUNCT
ejpam-6307	477	30	d)—each	d)—each	ADV
ejpam-6307	477	31	authorized	authorize	VERB
ejpam-6307	477	32	to	to	PART
ejpam-6307	477	33	detect	detect	VERB
ejpam-6307	477	34	,	,	PUNCT
ejpam-6307	477	35	investigate	investigate	VERB
ejpam-6307	477	36	,	,	PUNCT
ejpam-6307	477	37	and	and	CCONJ
ejpam-6307	477	38	r.	r.	PROPN
ejpam-6307	477	39	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	477	40	,	,	PUNCT
ejpam-6307	477	41	a.	a.	NOUN
ejpam-6307	477	42	m.	m.	PROPN
ejpam-6307	477	43	anto	anto	PROPN
ejpam-6307	477	44	,	,	PUNCT
ejpam-6307	477	45	v.	v.	PROPN
ejpam-6307	477	46	mary	mary	PROPN
ejpam-6307	477	47	mettilda	mettilda	PROPN
ejpam-6307	477	48	rose	rise	VERB
ejpam-6307	477	49	/	/	SYM
ejpam-6307	477	50	eur	eur	PROPN
ejpam-6307	477	51	.	.	PUNCT
ejpam-6307	478	1	j.	j.	PROPN
ejpam-6307	478	2	pure	pure	PROPN
ejpam-6307	478	3	appl	appl	PROPN
ejpam-6307	478	4	.	.	PROPN
ejpam-6307	478	5	math	math	PROPN
ejpam-6307	478	6	,	,	PUNCT
ejpam-6307	478	7	18	18	NUM
ejpam-6307	478	8	(	(	PUNCT
ejpam-6307	478	9	4	4	NUM
ejpam-6307	478	10	)	)	PUNCT
ejpam-6307	478	11	(	(	PUNCT
ejpam-6307	478	12	2025	2025	NUM
ejpam-6307	478	13	)	)	PUNCT
ejpam-6307	478	14	,	,	PUNCT
ejpam-6307	478	15	6307	6307	NUM
ejpam-6307	478	16	21	21	NUM
ejpam-6307	478	17	of	of	ADP
ejpam-6307	478	18	25	25	NUM
ejpam-6307	478	19	take	take	VERB
ejpam-6307	478	20	remedial	remedial	ADJ
ejpam-6307	478	21	action	action	NOUN
ejpam-6307	478	22	against	against	ADP
ejpam-6307	478	23	reported	report	VERB
ejpam-6307	478	24	crimes	crime	NOUN
ejpam-6307	478	25	.	.	PUNCT
ejpam-6307	479	1	these	these	DET
ejpam-6307	479	2	departments	department	NOUN
ejpam-6307	479	3	interact	interact	VERB
ejpam-6307	479	4	across	across	ADP
ejpam-6307	479	5	three	three	NUM
ejpam-6307	479	6	key	key	ADJ
ejpam-6307	479	7	relational	relational	ADJ
ejpam-6307	479	8	dimensions	dimension	NOUN
ejpam-6307	479	9	:	:	PUNCT
ejpam-6307	479	10	law	law	NOUN
ejpam-6307	479	11	enforcement	enforcement	NOUN
ejpam-6307	479	12	coordination	coordination	NOUN
ejpam-6307	479	13	(	(	PUNCT
ejpam-6307	479	14	ψ1	ψ1	NOUN
ejpam-6307	479	15	)	)	PUNCT
ejpam-6307	479	16	,	,	PUNCT
ejpam-6307	479	17	joint	joint	ADJ
ejpam-6307	479	18	investigative	investigative	ADJ
ejpam-6307	479	19	involvement	involvement	NOUN
ejpam-6307	479	20	(	(	PUNCT
ejpam-6307	479	21	ψ2	ψ2	NOUN
ejpam-6307	479	22	)	)	PUNCT
ejpam-6307	479	23	,	,	PUNCT
ejpam-6307	479	24	and	and	CCONJ
ejpam-6307	479	25	engagement	engagement	NOUN
ejpam-6307	479	26	with	with	ADP
ejpam-6307	479	27	external	external	ADJ
ejpam-6307	479	28	agencies	agency	NOUN
ejpam-6307	479	29	(	(	PUNCT
ejpam-6307	479	30	ψ3	ψ3	NOUN
ejpam-6307	479	31	)	)	PUNCT
ejpam-6307	479	32	.	.	PUNCT
ejpam-6307	480	1	as	as	SCONJ
ejpam-6307	480	2	illustrated	illustrate	VERB
ejpam-6307	480	3	in	in	ADP
ejpam-6307	480	4	figure	figure	NOUN
ejpam-6307	480	5	5	5	NUM
ejpam-6307	480	6	,	,	PUNCT
ejpam-6307	480	7	the	the	DET
ejpam-6307	480	8	relationships	relationship	NOUN
ejpam-6307	480	9	among	among	ADP
ejpam-6307	480	10	alpha	alpha	PROPN
ejpam-6307	480	11	,	,	PUNCT
ejpam-6307	480	12	bravo	bravo	PROPN
ejpam-6307	480	13	,	,	PUNCT
ejpam-6307	480	14	charlie	charlie	PROPN
ejpam-6307	480	15	,	,	PUNCT
ejpam-6307	480	16	and	and	CCONJ
ejpam-6307	480	17	delta	delta	NOUN
ejpam-6307	480	18	are	be	AUX
ejpam-6307	480	19	clearly	clearly	ADV
ejpam-6307	480	20	depicted	depict	VERB
ejpam-6307	480	21	.	.	PUNCT
ejpam-6307	481	1	to	to	PART
ejpam-6307	481	2	analyze	analyze	VERB
ejpam-6307	481	3	these	these	DET
ejpam-6307	481	4	interactions	interaction	NOUN
ejpam-6307	481	5	,	,	PUNCT
ejpam-6307	481	6	we	we	PRON
ejpam-6307	481	7	first	first	ADV
ejpam-6307	481	8	compute	compute	VERB
ejpam-6307	481	9	the	the	DET
ejpam-6307	481	10	geodetic	geodetic	ADJ
ejpam-6307	481	11	-	-	PUNCT
ejpam-6307	481	12	laplacian	laplacian	ADJ
ejpam-6307	481	13	energies	energy	NOUN
ejpam-6307	481	14	for	for	ADP
ejpam-6307	481	15	each	each	DET
ejpam-6307	481	16	relational	relational	ADJ
ejpam-6307	481	17	aspect	aspect	NOUN
ejpam-6307	481	18	ψi	ψi	NOUN
ejpam-6307	481	19	.	.	PUNCT
ejpam-6307	482	1	let	let	VERB
ejpam-6307	482	2	df	df	PROPN
ejpam-6307	482	3	(	(	PUNCT
ejpam-6307	482	4	ψi	ψi	NOUN
ejpam-6307	482	5	)	)	PUNCT
ejpam-6307	482	6	denote	denote	VERB
ejpam-6307	482	7	the	the	DET
ejpam-6307	482	8	fuzzy	fuzzy	ADJ
ejpam-6307	482	9	geodetic	geodetic	ADJ
ejpam-6307	482	10	distance	distance	NOUN
ejpam-6307	482	11	relation	relation	NOUN
ejpam-6307	482	12	matrix	matrix	NOUN
ejpam-6307	482	13	corresponding	correspond	VERB
ejpam-6307	482	14	to	to	ADP
ejpam-6307	482	15	the	the	DET
ejpam-6307	482	16	relations	relation	NOUN
ejpam-6307	482	17	ψi	ψi	NOUN
ejpam-6307	482	18	,	,	PUNCT
ejpam-6307	482	19	and	and	CCONJ
ejpam-6307	482	20	fdg(ψi	fdg(ψi	NOUN
ejpam-6307	482	21	)	)	PUNCT
ejpam-6307	482	22	represent	represent	VERB
ejpam-6307	482	23	the	the	DET
ejpam-6307	482	24	relation	relation	NOUN
ejpam-6307	482	25	degree	degree	NOUN
ejpam-6307	482	26	matrix	matrix	NOUN
ejpam-6307	482	27	.	.	PUNCT
ejpam-6307	483	1	figure	figure	NOUN
ejpam-6307	483	2	5	5	NUM
ejpam-6307	483	3	:	:	PUNCT
ejpam-6307	483	4	relational	relational	ADJ
ejpam-6307	483	5	aspects	aspect	NOUN
ejpam-6307	483	6	of	of	ADP
ejpam-6307	483	7	different	different	ADJ
ejpam-6307	483	8	agencies	agency	NOUN
ejpam-6307	483	9	.	.	PUNCT
ejpam-6307	484	1	now	now	ADV
ejpam-6307	484	2	we	we	PRON
ejpam-6307	484	3	evaluate	evaluate	VERB
ejpam-6307	484	4	gle	gle	NOUN
ejpam-6307	484	5	for	for	ADP
ejpam-6307	484	6	all	all	DET
ejpam-6307	484	7	ψi	ψi	NOUN
ejpam-6307	484	8	;	;	PUNCT
ejpam-6307	484	9	from	from	ADP
ejpam-6307	484	10	figure	figure	NOUN
ejpam-6307	484	11	5	5	NUM
ejpam-6307	484	12	we	we	PRON
ejpam-6307	484	13	have	have	VERB
ejpam-6307	484	14	df	df	PROPN
ejpam-6307	484	15	(	(	PUNCT
ejpam-6307	484	16	ψ1	ψ1	NOUN
ejpam-6307	484	17	)	)	PUNCT
ejpam-6307	484	18	=	=	PUNCT
ejpam-6307	485	1			ADJ
ejpam-6307	485	2	0.0	0.0	NUM
ejpam-6307	485	3	0.1	0.1	NUM
ejpam-6307	485	4	0.0	0.0	NUM
ejpam-6307	485	5	0.2	0.2	NUM
ejpam-6307	485	6	0.1	0.1	NUM
ejpam-6307	485	7	0.0	0.0	NUM
ejpam-6307	485	8	0.0	0.0	NUM
ejpam-6307	485	9	0.2	0.2	NUM
ejpam-6307	485	10	0.0	0.0	NUM
ejpam-6307	485	11	0.0	0.0	NUM
ejpam-6307	485	12	0.0	0.0	NUM
ejpam-6307	485	13	0.0	0.0	NUM
ejpam-6307	485	14	0.2	0.2	NUM
ejpam-6307	485	15	0.2	0.2	NUM
ejpam-6307	485	16	0.0	0.0	NUM
ejpam-6307	485	17	0.0	0.0	NUM
ejpam-6307	485	18			NOUN
ejpam-6307	485	19	.	.	PUNCT
ejpam-6307	486	1	tfgd	tfgd	ADJ
ejpam-6307	486	2	(	(	PUNCT
ejpam-6307	486	3	ψ1	ψ1	NOUN
ejpam-6307	486	4	)	)	PUNCT
ejpam-6307	486	5	=	=	PUNCT
ejpam-6307	486	6			ADJ
ejpam-6307	486	7	0.3	0.3	NUM
ejpam-6307	486	8	0.0	0.0	NUM
ejpam-6307	486	9	0.0	0.0	NUM
ejpam-6307	486	10	0.0	0.0	NUM
ejpam-6307	486	11	0.0	0.0	NUM
ejpam-6307	486	12	0.3	0.3	NUM
ejpam-6307	486	13	0.0	0.0	NUM
ejpam-6307	486	14	0.0	0.0	NUM
ejpam-6307	486	15	0.0	0.0	NUM
ejpam-6307	486	16	0.0	0.0	NUM
ejpam-6307	486	17	0.0	0.0	NUM
ejpam-6307	486	18	0.0	0.0	NUM
ejpam-6307	486	19	0.0	0.0	NUM
ejpam-6307	486	20	0.0	0.0	NUM
ejpam-6307	486	21	0.0	0.0	NUM
ejpam-6307	486	22	0.4	0.4	NUM
ejpam-6307	486	23			NOUN
ejpam-6307	486	24	.	.	PUNCT
ejpam-6307	487	1	thus	thus	ADV
ejpam-6307	487	2	,	,	PUNCT
ejpam-6307	487	3	the	the	DET
ejpam-6307	487	4	corresponding	corresponding	ADJ
ejpam-6307	487	5	fuzzy	fuzzy	ADJ
ejpam-6307	487	6	geodetic	geodetic	ADJ
ejpam-6307	487	7	-	-	PUNCT
ejpam-6307	487	8	laplacian	laplacian	ADJ
ejpam-6307	487	9	matrix	matrix	NOUN
ejpam-6307	487	10	for	for	ADP
ejpam-6307	487	11	ψ1	ψ1	NOUN
ejpam-6307	487	12	,	,	PUNCT
ejpam-6307	487	13	denotedmfgld	denotedmfgld	ADJ
ejpam-6307	487	14	(	(	PUNCT
ejpam-6307	487	15	ψ1	ψ1	NOUN
ejpam-6307	487	16	)	)	PUNCT
ejpam-6307	487	17	,	,	PUNCT
ejpam-6307	487	18	is	be	AUX
ejpam-6307	487	19	r.	r.	PROPN
ejpam-6307	487	20	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	487	21	,	,	PUNCT
ejpam-6307	487	22	a.	a.	NOUN
ejpam-6307	487	23	m.	m.	PROPN
ejpam-6307	487	24	anto	anto	PROPN
ejpam-6307	487	25	,	,	PUNCT
ejpam-6307	487	26	v.	v.	PROPN
ejpam-6307	487	27	mary	mary	PROPN
ejpam-6307	487	28	mettilda	mettilda	PROPN
ejpam-6307	487	29	rose	rise	VERB
ejpam-6307	487	30	/	/	SYM
ejpam-6307	487	31	eur	eur	PROPN
ejpam-6307	487	32	.	.	PUNCT
ejpam-6307	488	1	j.	j.	PROPN
ejpam-6307	488	2	pure	pure	PROPN
ejpam-6307	488	3	appl	appl	PROPN
ejpam-6307	488	4	.	.	PROPN
ejpam-6307	488	5	math	math	PROPN
ejpam-6307	488	6	,	,	PUNCT
ejpam-6307	488	7	18	18	NUM
ejpam-6307	488	8	(	(	PUNCT
ejpam-6307	488	9	4	4	NUM
ejpam-6307	488	10	)	)	PUNCT
ejpam-6307	488	11	(	(	PUNCT
ejpam-6307	488	12	2025	2025	NUM
ejpam-6307	488	13	)	)	PUNCT
ejpam-6307	488	14	,	,	PUNCT
ejpam-6307	488	15	6307	6307	NUM
ejpam-6307	488	16	22	22	NUM
ejpam-6307	488	17	of	of	ADP
ejpam-6307	488	18	25	25	NUM
ejpam-6307	488	19	mfgld	mfgld	ADJ
ejpam-6307	488	20	(	(	PUNCT
ejpam-6307	488	21	ψ1	ψ1	NOUN
ejpam-6307	488	22	)	)	PUNCT
ejpam-6307	488	23	=	=	PUNCT
ejpam-6307	488	24			NOUN
ejpam-6307	488	25	0.3	0.3	NUM
ejpam-6307	488	26	−0.1	−0.1	PROPN
ejpam-6307	488	27	0.0	0.0	NUM
ejpam-6307	488	28	−0.2	−0.2	PROPN
ejpam-6307	488	29	−0.1	−0.1	NOUN
ejpam-6307	488	30	0.1	0.1	NUM
ejpam-6307	488	31	0.0	0.0	NUM
ejpam-6307	488	32	−0.2	−0.2	PROPN
ejpam-6307	488	33	0.0	0.0	NUM
ejpam-6307	488	34	0.0	0.0	NUM
ejpam-6307	488	35	0.0	0.0	NUM
ejpam-6307	488	36	0.0	0.0	NUM
ejpam-6307	488	37	−0.2	−0.2	PROPN
ejpam-6307	488	38	−0.2	−0.2	PROPN
ejpam-6307	488	39	0.0	0.0	NUM
ejpam-6307	488	40	0.2	0.2	NUM
ejpam-6307	488	41			NOUN
ejpam-6307	488	42	.	.	PUNCT
ejpam-6307	489	1	the	the	DET
ejpam-6307	489	2	eigenvalues	eigenvalue	NOUN
ejpam-6307	489	3	are	be	AUX
ejpam-6307	489	4	γgl1(ψ1	γgl1(ψ1	NOUN
ejpam-6307	489	5	)	)	PUNCT
ejpam-6307	489	6	=	=	SYM
ejpam-6307	489	7	0.6	0.6	NUM
ejpam-6307	489	8	,	,	PUNCT
ejpam-6307	489	9	γgl2(ψ1	γgl2(ψ1	PROPN
ejpam-6307	489	10	)	)	PUNCT
ejpam-6307	489	11	=	=	SYM
ejpam-6307	489	12	0.4	0.4	NUM
ejpam-6307	489	13	,	,	PUNCT
ejpam-6307	489	14	γgl3(ψ1	γgl3(ψ1	PROPN
ejpam-6307	489	15	)	)	PUNCT
ejpam-6307	489	16	=	=	SYM
ejpam-6307	489	17	0	0	NUM
ejpam-6307	489	18	,	,	PUNCT
ejpam-6307	489	19	and	and	CCONJ
ejpam-6307	489	20	γgl4(ψ1	γgl4(ψ1	PROPN
ejpam-6307	489	21	)	)	PUNCT
ejpam-6307	490	1	=	=	SYM
ejpam-6307	490	2	0	0	NUM
ejpam-6307	490	3	,	,	PUNCT
ejpam-6307	490	4	yielding	yield	VERB
ejpam-6307	490	5	gle(ψ1	gle(ψ1	X
ejpam-6307	490	6	)	)	PUNCT
ejpam-6307	490	7	=	=	SYM
ejpam-6307	491	1	1	1	X
ejpam-6307	491	2	.	.	PUNCT
ejpam-6307	491	3	now	now	ADV
ejpam-6307	491	4	,	,	PUNCT
ejpam-6307	491	5	according	accord	VERB
ejpam-6307	491	6	to	to	ADP
ejpam-6307	491	7	the	the	DET
ejpam-6307	491	8	relationship	relationship	NOUN
ejpam-6307	491	9	ψ2	ψ2	NOUN
ejpam-6307	491	10	,	,	PUNCT
ejpam-6307	491	11	we	we	PRON
ejpam-6307	491	12	have	have	VERB
ejpam-6307	491	13	df	df	NOUN
ejpam-6307	491	14	(	(	PUNCT
ejpam-6307	491	15	ψ2	ψ2	NOUN
ejpam-6307	491	16	)	)	PUNCT
ejpam-6307	491	17	=	=	PUNCT
ejpam-6307	491	18			ADJ
ejpam-6307	491	19	0.0	0.0	NUM
ejpam-6307	491	20	0.1	0.1	NUM
ejpam-6307	491	21	0.2	0.2	NUM
ejpam-6307	491	22	0.2	0.2	NUM
ejpam-6307	491	23	0.1	0.1	NUM
ejpam-6307	491	24	0.0	0.0	NUM
ejpam-6307	491	25	0.1	0.1	NUM
ejpam-6307	491	26	0.2	0.2	NUM
ejpam-6307	491	27	0.2	0.2	NUM
ejpam-6307	491	28	0.1	0.1	NUM
ejpam-6307	491	29	0.0	0.0	NUM
ejpam-6307	491	30	0.2	0.2	NUM
ejpam-6307	491	31	0.2	0.2	NUM
ejpam-6307	491	32	0.2	0.2	NUM
ejpam-6307	491	33	0.2	0.2	NUM
ejpam-6307	491	34	0.0	0.0	NUM
ejpam-6307	491	35			NOUN
ejpam-6307	491	36	.	.	PUNCT
ejpam-6307	492	1	and	and	CCONJ
ejpam-6307	492	2	tfgd	tfgd	ADJ
ejpam-6307	492	3	(	(	PUNCT
ejpam-6307	492	4	ψ2	ψ2	NOUN
ejpam-6307	492	5	)	)	PUNCT
ejpam-6307	492	6	=	=	SYM
ejpam-6307	492	7			ADJ
ejpam-6307	492	8	0.5	0.5	NUM
ejpam-6307	492	9	0.0	0.0	NUM
ejpam-6307	492	10	0.0	0.0	NUM
ejpam-6307	492	11	0.0	0.0	NUM
ejpam-6307	492	12	0.0	0.0	NUM
ejpam-6307	492	13	0.4	0.4	NUM
ejpam-6307	492	14	0.0	0.0	NUM
ejpam-6307	492	15	0.0	0.0	NUM
ejpam-6307	492	16	0.0	0.0	NUM
ejpam-6307	492	17	0.0	0.0	NUM
ejpam-6307	492	18	0.5	0.5	NUM
ejpam-6307	492	19	0.0	0.0	NUM
ejpam-6307	492	20	0.0	0.0	NUM
ejpam-6307	492	21	0.0	0.0	NUM
ejpam-6307	492	22	0.0	0.0	NUM
ejpam-6307	492	23	0.6	0.6	NUM
ejpam-6307	492	24			NOUN
ejpam-6307	492	25	.	.	PUNCT
ejpam-6307	493	1	then	then	ADV
ejpam-6307	493	2	,	,	PUNCT
ejpam-6307	493	3	mfgld	mfgld	ADV
ejpam-6307	493	4	(	(	PUNCT
ejpam-6307	493	5	ψ2	ψ2	NOUN
ejpam-6307	493	6	)	)	PUNCT
ejpam-6307	493	7	=	=	SYM
ejpam-6307	493	8			NOUN
ejpam-6307	493	9	0.5	0.5	NUM
ejpam-6307	493	10	−0.1	−0.1	PROPN
ejpam-6307	493	11	−0.2	−0.2	PROPN
ejpam-6307	494	1	−0.2	−0.2	PROPN
ejpam-6307	495	1	−0.1	−0.1	PROPN
ejpam-6307	495	2	0.4	0.4	NUM
ejpam-6307	496	1	−0.1	−0.1	PROPN
ejpam-6307	496	2	−0.2	−0.2	PROPN
ejpam-6307	497	1	−0.2	−0.2	PROPN
ejpam-6307	497	2	−0.1	−0.1	PROPN
ejpam-6307	497	3	0.5	0.5	NUM
ejpam-6307	497	4	−0.2	−0.2	PROPN
ejpam-6307	497	5	−0.2	−0.2	PROPN
ejpam-6307	498	1	−0.2	−0.2	PROPN
ejpam-6307	498	2	−0.2	−0.2	PROPN
ejpam-6307	498	3	0.6	0.6	NUM
ejpam-6307	498	4			NOUN
ejpam-6307	498	5	.	.	PUNCT
ejpam-6307	499	1	after	after	ADP
ejpam-6307	499	2	computing	compute	VERB
ejpam-6307	499	3	the	the	DET
ejpam-6307	499	4	eigenvalues	eigenvalue	NOUN
ejpam-6307	499	5	,	,	PUNCT
ejpam-6307	499	6	gle(ψ2	gle(ψ2	NOUN
ejpam-6307	499	7	)	)	PUNCT
ejpam-6307	499	8	=	=	SYM
ejpam-6307	499	9	1	1	X
ejpam-6307	499	10	.	.	PUNCT
ejpam-6307	500	1	in	in	ADP
ejpam-6307	500	2	a	a	DET
ejpam-6307	500	3	similar	similar	ADJ
ejpam-6307	500	4	fashion	fashion	NOUN
ejpam-6307	500	5	,	,	PUNCT
ejpam-6307	500	6	for	for	ADP
ejpam-6307	500	7	the	the	DET
ejpam-6307	500	8	relationship	relationship	NOUN
ejpam-6307	500	9	ψ3	ψ3	NOUN
ejpam-6307	500	10	,	,	PUNCT
ejpam-6307	500	11	mfgld	mfgld	ADJ
ejpam-6307	500	12	(	(	PUNCT
ejpam-6307	500	13	ψ3	ψ3	NOUN
ejpam-6307	500	14	)	)	PUNCT
ejpam-6307	500	15	=	=	SYM
ejpam-6307	500	16			ADJ
ejpam-6307	500	17	0.0	0.0	NUM
ejpam-6307	500	18	0.0	0.0	NUM
ejpam-6307	500	19	0.0	0.0	NUM
ejpam-6307	500	20	0.0	0.0	NUM
ejpam-6307	500	21	0.0	0.0	NUM
ejpam-6307	500	22	0.7	0.7	NUM
ejpam-6307	500	23	−0.3	−0.3	NUM
ejpam-6307	501	1	−0.4	−0.4	NUM
ejpam-6307	501	2	0.0	0.0	NUM
ejpam-6307	501	3	−0.3	−0.3	PROPN
ejpam-6307	501	4	0.9	0.9	NUM
ejpam-6307	501	5	−0.6	−0.6	PROPN
ejpam-6307	501	6	0.0	0.0	NUM
ejpam-6307	501	7	−0.4	−0.4	NUM
ejpam-6307	502	1	−0.6	−0.6	PROPN
ejpam-6307	502	2	1.0	1.0	NUM
ejpam-6307	502	3			NOUN
ejpam-6307	502	4	.	.	PUNCT
ejpam-6307	503	1	r.	r.	PROPN
ejpam-6307	503	2	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	503	3	,	,	PUNCT
ejpam-6307	503	4	a.	a.	NOUN
ejpam-6307	503	5	m.	m.	PROPN
ejpam-6307	503	6	anto	anto	PROPN
ejpam-6307	503	7	,	,	PUNCT
ejpam-6307	503	8	v.	v.	PROPN
ejpam-6307	503	9	mary	mary	PROPN
ejpam-6307	503	10	mettilda	mettilda	PROPN
ejpam-6307	503	11	rose	rise	VERB
ejpam-6307	503	12	/	/	SYM
ejpam-6307	503	13	eur	eur	PROPN
ejpam-6307	503	14	.	.	PUNCT
ejpam-6307	504	1	j.	j.	PROPN
ejpam-6307	504	2	pure	pure	PROPN
ejpam-6307	504	3	appl	appl	PROPN
ejpam-6307	504	4	.	.	PROPN
ejpam-6307	504	5	math	math	PROPN
ejpam-6307	504	6	,	,	PUNCT
ejpam-6307	504	7	18	18	NUM
ejpam-6307	504	8	(	(	PUNCT
ejpam-6307	504	9	4	4	NUM
ejpam-6307	504	10	)	)	PUNCT
ejpam-6307	504	11	(	(	PUNCT
ejpam-6307	504	12	2025	2025	NUM
ejpam-6307	504	13	)	)	PUNCT
ejpam-6307	504	14	,	,	PUNCT
ejpam-6307	504	15	6307	6307	NUM
ejpam-6307	504	16	23	23	NUM
ejpam-6307	504	17	of	of	ADP
ejpam-6307	504	18	25	25	NUM
ejpam-6307	504	19	thus	thus	ADV
ejpam-6307	504	20	,	,	PUNCT
ejpam-6307	504	21	gle(ψ3	gle(ψ3	VERB
ejpam-6307	504	22	)	)	PUNCT
ejpam-6307	504	23	=	=	SYM
ejpam-6307	504	24	2.599	2.599	NUM
ejpam-6307	504	25	.	.	PUNCT
ejpam-6307	505	1	therefore	therefore	ADV
ejpam-6307	505	2	,	,	PUNCT
ejpam-6307	505	3	gle(g	gle(g	PROPN
ejpam-6307	505	4	)	)	PUNCT
ejpam-6307	505	5	=	=	PUNCT
ejpam-6307	505	6	{	{	PUNCT
ejpam-6307	505	7	1.000	1.000	NUM
ejpam-6307	505	8	,	,	PUNCT
ejpam-6307	505	9	1.000	1.000	NUM
ejpam-6307	505	10	,	,	PUNCT
ejpam-6307	505	11	2.599	2.599	NUM
ejpam-6307	505	12	}	}	PUNCT
ejpam-6307	505	13	.	.	PUNCT
ejpam-6307	506	1	key	key	ADJ
ejpam-6307	506	2	findings	finding	NOUN
ejpam-6307	506	3	:	:	PUNCT
ejpam-6307	506	4	•	•	ADP
ejpam-6307	506	5	the	the	DET
ejpam-6307	506	6	highest	high	ADJ
ejpam-6307	506	7	fuzzy	fuzzy	ADJ
ejpam-6307	506	8	geodetic	geodetic	ADJ
ejpam-6307	506	9	-	-	PUNCT
ejpam-6307	506	10	laplacian	laplacian	ADJ
ejpam-6307	506	11	energy	energy	NOUN
ejpam-6307	506	12	is	be	AUX
ejpam-6307	506	13	associated	associate	VERB
ejpam-6307	506	14	with	with	ADP
ejpam-6307	506	15	maintaining	maintain	VERB
ejpam-6307	506	16	relationships	relationship	NOUN
ejpam-6307	506	17	with	with	ADP
ejpam-6307	506	18	external	external	ADJ
ejpam-6307	506	19	agencies	agency	NOUN
ejpam-6307	506	20	(	(	PUNCT
ejpam-6307	506	21	ψ3	ψ3	NOUN
ejpam-6307	506	22	)	)	PUNCT
ejpam-6307	506	23	.	.	PUNCT
ejpam-6307	507	1	this	this	PRON
ejpam-6307	507	2	indicates	indicate	VERB
ejpam-6307	507	3	that	that	SCONJ
ejpam-6307	507	4	bravo	bravo	PROPN
ejpam-6307	507	5	(	(	PUNCT
ejpam-6307	507	6	b	b	NOUN
ejpam-6307	507	7	)	)	PUNCT
ejpam-6307	507	8	,	,	PUNCT
ejpam-6307	507	9	charlie	charlie	PROPN
ejpam-6307	507	10	(	(	PUNCT
ejpam-6307	507	11	c	c	NOUN
ejpam-6307	507	12	)	)	PUNCT
ejpam-6307	507	13	,	,	PUNCT
ejpam-6307	507	14	and	and	CCONJ
ejpam-6307	507	15	delta	delta	NOUN
ejpam-6307	507	16	(	(	PUNCT
ejpam-6307	507	17	d	d	X
ejpam-6307	507	18	)	)	PUNCT
ejpam-6307	507	19	are	be	AUX
ejpam-6307	507	20	primarily	primarily	ADV
ejpam-6307	507	21	responsible	responsible	ADJ
ejpam-6307	507	22	for	for	ADP
ejpam-6307	507	23	the	the	DET
ejpam-6307	507	24	complex	complex	ADJ
ejpam-6307	507	25	task	task	NOUN
ejpam-6307	507	26	of	of	ADP
ejpam-6307	507	27	coordinating	coordinate	VERB
ejpam-6307	507	28	and	and	CCONJ
ejpam-6307	507	29	leveraging	leverage	VERB
ejpam-6307	507	30	support	support	NOUN
ejpam-6307	507	31	from	from	ADP
ejpam-6307	507	32	outside	outside	ADJ
ejpam-6307	507	33	organizations	organization	NOUN
ejpam-6307	507	34	.	.	PUNCT
ejpam-6307	508	1	the	the	DET
ejpam-6307	508	2	significant	significant	ADJ
ejpam-6307	508	3	energy	energy	NOUN
ejpam-6307	508	4	allocation	allocation	NOUN
ejpam-6307	508	5	underscores	underscore	VERB
ejpam-6307	508	6	the	the	DET
ejpam-6307	508	7	critical	critical	ADJ
ejpam-6307	508	8	role	role	NOUN
ejpam-6307	508	9	these	these	DET
ejpam-6307	508	10	external	external	ADJ
ejpam-6307	508	11	collaborations	collaboration	NOUN
ejpam-6307	508	12	play	play	VERB
ejpam-6307	508	13	in	in	ADP
ejpam-6307	508	14	enhancing	enhance	VERB
ejpam-6307	508	15	the	the	DET
ejpam-6307	508	16	overall	overall	ADJ
ejpam-6307	508	17	effectiveness	effectiveness	NOUN
ejpam-6307	508	18	of	of	ADP
ejpam-6307	508	19	crime	crime	NOUN
ejpam-6307	508	20	prevention	prevention	NOUN
ejpam-6307	508	21	and	and	CCONJ
ejpam-6307	508	22	control	control	NOUN
ejpam-6307	508	23	.	.	PUNCT
ejpam-6307	509	1	•	•	NUM
ejpam-6307	509	2	the	the	DET
ejpam-6307	509	3	energy	energy	NOUN
ejpam-6307	509	4	related	relate	VERB
ejpam-6307	509	5	to	to	ADP
ejpam-6307	509	6	mutual	mutual	ADJ
ejpam-6307	509	7	involvement	involvement	NOUN
ejpam-6307	509	8	in	in	ADP
ejpam-6307	509	9	investigations	investigation	NOUN
ejpam-6307	509	10	(	(	PUNCT
ejpam-6307	509	11	ψ2	ψ2	NOUN
ejpam-6307	509	12	)	)	PUNCT
ejpam-6307	509	13	ranks	rank	VERB
ejpam-6307	509	14	second	second	ADV
ejpam-6307	509	15	.	.	PUNCT
ejpam-6307	510	1	this	this	PRON
ejpam-6307	510	2	reflects	reflect	VERB
ejpam-6307	510	3	a	a	DET
ejpam-6307	510	4	strong	strong	ADJ
ejpam-6307	510	5	cooperative	cooperative	ADJ
ejpam-6307	510	6	dynamic	dynamic	NOUN
ejpam-6307	510	7	among	among	ADP
ejpam-6307	510	8	alpha	alpha	NOUN
ejpam-6307	510	9	(	(	PUNCT
ejpam-6307	510	10	a	a	NOUN
ejpam-6307	510	11	)	)	PUNCT
ejpam-6307	510	12	,	,	PUNCT
ejpam-6307	510	13	bravo	bravo	PROPN
ejpam-6307	510	14	(	(	PUNCT
ejpam-6307	510	15	b	b	NOUN
ejpam-6307	510	16	)	)	PUNCT
ejpam-6307	510	17	,	,	PUNCT
ejpam-6307	510	18	charlie	charlie	PROPN
ejpam-6307	510	19	(	(	PUNCT
ejpam-6307	510	20	c	c	NOUN
ejpam-6307	510	21	)	)	PUNCT
ejpam-6307	510	22	,	,	PUNCT
ejpam-6307	510	23	and	and	CCONJ
ejpam-6307	510	24	delta	delta	NOUN
ejpam-6307	510	25	(	(	PUNCT
ejpam-6307	510	26	d	d	X
ejpam-6307	510	27	)	)	PUNCT
ejpam-6307	510	28	in	in	ADP
ejpam-6307	510	29	investigative	investigative	ADJ
ejpam-6307	510	30	activities	activity	NOUN
ejpam-6307	510	31	,	,	PUNCT
ejpam-6307	510	32	demonstrating	demonstrate	VERB
ejpam-6307	510	33	effective	effective	ADJ
ejpam-6307	510	34	teamwork	teamwork	NOUN
ejpam-6307	510	35	in	in	ADP
ejpam-6307	510	36	pursuing	pursue	VERB
ejpam-6307	510	37	criminal	criminal	ADJ
ejpam-6307	510	38	cases	case	NOUN
ejpam-6307	510	39	.	.	PUNCT
ejpam-6307	511	1	•	•	NUM
ejpam-6307	511	2	the	the	DET
ejpam-6307	511	3	energy	energy	NOUN
ejpam-6307	511	4	devoted	devote	VERB
ejpam-6307	511	5	to	to	ADP
ejpam-6307	511	6	enforcing	enforce	VERB
ejpam-6307	511	7	law	law	NOUN
ejpam-6307	511	8	and	and	CCONJ
ejpam-6307	511	9	order	order	NOUN
ejpam-6307	511	10	(	(	PUNCT
ejpam-6307	511	11	ψ1	ψ1	NOUN
ejpam-6307	511	12	)	)	PUNCT
ejpam-6307	511	13	is	be	AUX
ejpam-6307	511	14	comparable	comparable	ADJ
ejpam-6307	511	15	to	to	ADP
ejpam-6307	511	16	that	that	PRON
ejpam-6307	511	17	of	of	ADP
ejpam-6307	511	18	mutual	mutual	ADJ
ejpam-6307	511	19	investigations	investigation	NOUN
ejpam-6307	511	20	(	(	PUNCT
ejpam-6307	511	21	ψ2	ψ2	NOUN
ejpam-6307	511	22	)	)	PUNCT
ejpam-6307	511	23	.	.	PUNCT
ejpam-6307	512	1	this	this	PRON
ejpam-6307	512	2	suggests	suggest	VERB
ejpam-6307	512	3	that	that	SCONJ
ejpam-6307	512	4	the	the	DET
ejpam-6307	512	5	foundational	foundational	ADJ
ejpam-6307	512	6	collaboration	collaboration	NOUN
ejpam-6307	512	7	between	between	ADP
ejpam-6307	512	8	departments	department	NOUN
ejpam-6307	512	9	is	be	AUX
ejpam-6307	512	10	well	well	ADV
ejpam-6307	512	11	established	establish	VERB
ejpam-6307	512	12	,	,	PUNCT
ejpam-6307	512	13	facilitating	facilitate	VERB
ejpam-6307	512	14	smoother	smooth	ADJ
ejpam-6307	512	15	and	and	CCONJ
ejpam-6307	512	16	more	more	ADV
ejpam-6307	512	17	efficient	efficient	ADJ
ejpam-6307	512	18	investigative	investigative	ADJ
ejpam-6307	512	19	processes	process	NOUN
ejpam-6307	512	20	.	.	PUNCT
ejpam-6307	513	1	overall	overall	ADJ
ejpam-6307	513	2	,	,	PUNCT
ejpam-6307	513	3	to	to	PART
ejpam-6307	513	4	further	far	ADV
ejpam-6307	513	5	enhance	enhance	VERB
ejpam-6307	513	6	crime	crime	NOUN
ejpam-6307	513	7	prevention	prevention	NOUN
ejpam-6307	513	8	and	and	CCONJ
ejpam-6307	513	9	resolution	resolution	NOUN
ejpam-6307	513	10	outcomes	outcome	NOUN
ejpam-6307	513	11	,	,	PUNCT
ejpam-6307	513	12	these	these	DET
ejpam-6307	513	13	departments	department	NOUN
ejpam-6307	513	14	should	should	AUX
ejpam-6307	513	15	prioritize	prioritize	VERB
ejpam-6307	513	16	strengthening	strengthen	VERB
ejpam-6307	513	17	their	their	PRON
ejpam-6307	513	18	partnerships	partnership	NOUN
ejpam-6307	513	19	with	with	ADP
ejpam-6307	513	20	external	external	ADJ
ejpam-6307	513	21	agencies	agency	NOUN
ejpam-6307	513	22	.	.	PUNCT
ejpam-6307	514	1	8	8	X
ejpam-6307	514	2	.	.	X
ejpam-6307	514	3	conclusion	conclusion	NOUN
ejpam-6307	514	4	this	this	DET
ejpam-6307	514	5	study	study	NOUN
ejpam-6307	514	6	introduced	introduce	VERB
ejpam-6307	514	7	and	and	CCONJ
ejpam-6307	514	8	examined	examine	VERB
ejpam-6307	514	9	the	the	DET
ejpam-6307	514	10	fuzzy	fuzzy	ADJ
ejpam-6307	514	11	geodetic	geodetic	ADJ
ejpam-6307	514	12	spectrum	spectrum	NOUN
ejpam-6307	514	13	and	and	CCONJ
ejpam-6307	514	14	fuzzy	fuzzy	ADJ
ejpam-6307	514	15	detour	detour	NOUN
ejpam-6307	514	16	spectrum	spectrum	NOUN
ejpam-6307	514	17	as	as	ADP
ejpam-6307	514	18	novel	novel	ADJ
ejpam-6307	514	19	extensions	extension	NOUN
ejpam-6307	514	20	of	of	ADP
ejpam-6307	514	21	classical	classical	ADJ
ejpam-6307	514	22	spectral	spectral	ADJ
ejpam-6307	514	23	graph	graph	NOUN
ejpam-6307	514	24	theory	theory	NOUN
ejpam-6307	514	25	to	to	ADP
ejpam-6307	514	26	the	the	DET
ejpam-6307	514	27	fuzzy	fuzzy	ADJ
ejpam-6307	514	28	domain	domain	NOUN
ejpam-6307	514	29	.	.	PUNCT
ejpam-6307	515	1	we	we	PRON
ejpam-6307	515	2	defined	define	VERB
ejpam-6307	515	3	the	the	DET
ejpam-6307	515	4	fuzzy	fuzzy	ADJ
ejpam-6307	515	5	geodetic	geodetic	ADJ
ejpam-6307	515	6	-	-	PUNCT
ejpam-6307	515	7	laplacian	laplacian	ADJ
ejpam-6307	515	8	energy	energy	NOUN
ejpam-6307	515	9	and	and	CCONJ
ejpam-6307	515	10	detour	detour	NOUN
ejpam-6307	515	11	-	-	PUNCT
ejpam-6307	515	12	laplacian	laplacian	ADJ
ejpam-6307	515	13	energy	energy	NOUN
ejpam-6307	515	14	,	,	PUNCT
ejpam-6307	515	15	derived	derive	VERB
ejpam-6307	515	16	their	their	PRON
ejpam-6307	515	17	respective	respective	ADJ
ejpam-6307	515	18	expressions	expression	NOUN
ejpam-6307	515	19	,	,	PUNCT
ejpam-6307	515	20	and	and	CCONJ
ejpam-6307	515	21	established	establish	VERB
ejpam-6307	515	22	upper	upper	ADJ
ejpam-6307	515	23	and	and	CCONJ
ejpam-6307	515	24	lower	low	ADJ
ejpam-6307	515	25	bounds	bound	NOUN
ejpam-6307	515	26	.	.	PUNCT
ejpam-6307	516	1	notably	notably	ADV
ejpam-6307	516	2	,	,	PUNCT
ejpam-6307	516	3	it	it	PRON
ejpam-6307	516	4	was	be	AUX
ejpam-6307	516	5	shown	show	VERB
ejpam-6307	516	6	that	that	SCONJ
ejpam-6307	516	7	for	for	ADP
ejpam-6307	516	8	geodetic	geodetic	ADJ
ejpam-6307	516	9	blocks	block	NOUN
ejpam-6307	516	10	,	,	PUNCT
ejpam-6307	516	11	the	the	DET
ejpam-6307	516	12	geodetic	geodetic	ADJ
ejpam-6307	516	13	-	-	PUNCT
ejpam-6307	516	14	laplacian	laplacian	ADJ
ejpam-6307	516	15	energy	energy	NOUN
ejpam-6307	516	16	coincides	coincide	VERB
ejpam-6307	516	17	with	with	ADP
ejpam-6307	516	18	the	the	DET
ejpam-6307	516	19	standard	standard	ADJ
ejpam-6307	516	20	laplacian	laplacian	ADJ
ejpam-6307	516	21	energy	energy	NOUN
ejpam-6307	516	22	,	,	PUNCT
ejpam-6307	516	23	highlighting	highlight	VERB
ejpam-6307	516	24	a	a	DET
ejpam-6307	516	25	structural	structural	ADJ
ejpam-6307	516	26	consistency	consistency	NOUN
ejpam-6307	516	27	within	within	ADP
ejpam-6307	516	28	fuzzy	fuzzy	ADJ
ejpam-6307	516	29	graph	graph	NOUN
ejpam-6307	516	30	frameworks	framework	NOUN
ejpam-6307	516	31	.	.	PUNCT
ejpam-6307	517	1	the	the	DET
ejpam-6307	517	2	practical	practical	ADJ
ejpam-6307	517	3	applicability	applicability	NOUN
ejpam-6307	517	4	of	of	ADP
ejpam-6307	517	5	fuzzy	fuzzy	ADJ
ejpam-6307	517	6	geodetic	geodetic	ADJ
ejpam-6307	517	7	-	-	PUNCT
ejpam-6307	517	8	laplacian	laplacian	ADJ
ejpam-6307	517	9	energy	energy	NOUN
ejpam-6307	517	10	was	be	AUX
ejpam-6307	517	11	illustrated	illustrate	VERB
ejpam-6307	517	12	through	through	ADP
ejpam-6307	517	13	a	a	DET
ejpam-6307	517	14	case	case	NOUN
ejpam-6307	517	15	analysis	analysis	NOUN
ejpam-6307	517	16	of	of	ADP
ejpam-6307	517	17	trafficking	traffic	VERB
ejpam-6307	517	18	channels	channel	NOUN
ejpam-6307	517	19	,	,	PUNCT
ejpam-6307	517	20	demonstrating	demonstrate	VERB
ejpam-6307	517	21	its	its	PRON
ejpam-6307	517	22	potential	potential	NOUN
ejpam-6307	517	23	in	in	ADP
ejpam-6307	517	24	decision	decision	NOUN
ejpam-6307	517	25	-	-	PUNCT
ejpam-6307	517	26	making	make	VERB
ejpam-6307	517	27	contexts	context	NOUN
ejpam-6307	517	28	such	such	ADJ
ejpam-6307	517	29	as	as	ADP
ejpam-6307	517	30	crime	crime	NOUN
ejpam-6307	517	31	detection	detection	NOUN
ejpam-6307	517	32	and	and	CCONJ
ejpam-6307	517	33	prevention	prevention	NOUN
ejpam-6307	517	34	.	.	PUNCT
ejpam-6307	518	1	the	the	DET
ejpam-6307	518	2	findings	finding	NOUN
ejpam-6307	518	3	are	be	AUX
ejpam-6307	518	4	consistent	consistent	ADJ
ejpam-6307	518	5	with	with	ADP
ejpam-6307	518	6	results	result	NOUN
ejpam-6307	518	7	reported	report	VERB
ejpam-6307	518	8	in	in	ADP
ejpam-6307	518	9	the	the	DET
ejpam-6307	518	10	existing	exist	VERB
ejpam-6307	518	11	literature	literature	NOUN
ejpam-6307	518	12	,	,	PUNCT
ejpam-6307	518	13	supporting	support	VERB
ejpam-6307	518	14	the	the	DET
ejpam-6307	518	15	validity	validity	NOUN
ejpam-6307	518	16	and	and	CCONJ
ejpam-6307	518	17	relevance	relevance	NOUN
ejpam-6307	518	18	of	of	ADP
ejpam-6307	518	19	the	the	DET
ejpam-6307	518	20	proposed	propose	VERB
ejpam-6307	518	21	spectral	spectral	ADJ
ejpam-6307	518	22	measures	measure	NOUN
ejpam-6307	518	23	.	.	PUNCT
ejpam-6307	519	1	future	future	ADJ
ejpam-6307	519	2	research	research	NOUN
ejpam-6307	519	3	may	may	AUX
ejpam-6307	519	4	focus	focus	VERB
ejpam-6307	519	5	on	on	ADP
ejpam-6307	519	6	extending	extend	VERB
ejpam-6307	519	7	these	these	DET
ejpam-6307	519	8	spectral	spectral	ADJ
ejpam-6307	519	9	invariants	invariant	NOUN
ejpam-6307	519	10	to	to	PART
ejpam-6307	519	11	directed	direct	VERB
ejpam-6307	519	12	or	or	CCONJ
ejpam-6307	519	13	weighted	weight	VERB
ejpam-6307	519	14	fuzzy	fuzzy	ADJ
ejpam-6307	519	15	graphs	graph	NOUN
ejpam-6307	519	16	,	,	PUNCT
ejpam-6307	519	17	enhancing	enhance	VERB
ejpam-6307	519	18	robustness	robustness	NOUN
ejpam-6307	519	19	under	under	ADP
ejpam-6307	519	20	data	datum	NOUN
ejpam-6307	519	21	uncertainty	uncertainty	NOUN
ejpam-6307	519	22	,	,	PUNCT
ejpam-6307	519	23	and	and	CCONJ
ejpam-6307	519	24	applying	apply	VERB
ejpam-6307	519	25	the	the	DET
ejpam-6307	519	26	proposed	propose	VERB
ejpam-6307	519	27	energies	energy	NOUN
ejpam-6307	519	28	to	to	ADP
ejpam-6307	519	29	infrastructure	infrastructure	NOUN
ejpam-6307	519	30	domains	domain	NOUN
ejpam-6307	519	31	such	such	ADJ
ejpam-6307	519	32	as	as	ADP
ejpam-6307	519	33	water	water	NOUN
ejpam-6307	519	34	distribution	distribution	NOUN
ejpam-6307	519	35	systems	system	NOUN
ejpam-6307	519	36	and	and	CCONJ
ejpam-6307	519	37	wireless	wireless	ADJ
ejpam-6307	519	38	communication	communication	NOUN
ejpam-6307	519	39	networks	network	NOUN
ejpam-6307	519	40	.	.	PUNCT
ejpam-6307	520	1	algorithmic	algorithmic	ADJ
ejpam-6307	520	2	development	development	NOUN
ejpam-6307	520	3	for	for	ADP
ejpam-6307	520	4	efficient	efficient	ADJ
ejpam-6307	520	5	spectral	spectral	ADJ
ejpam-6307	520	6	computation	computation	NOUN
ejpam-6307	520	7	in	in	ADP
ejpam-6307	520	8	large	large	ADJ
ejpam-6307	520	9	fuzzy	fuzzy	ADJ
ejpam-6307	520	10	systems	system	NOUN
ejpam-6307	520	11	also	also	ADV
ejpam-6307	520	12	represents	represent	VERB
ejpam-6307	520	13	a	a	DET
ejpam-6307	520	14	promising	promising	ADJ
ejpam-6307	520	15	direction	direction	NOUN
ejpam-6307	520	16	.	.	PUNCT
ejpam-6307	521	1	r.	r.	PROPN
ejpam-6307	521	2	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	521	3	,	,	PUNCT
ejpam-6307	521	4	a.	a.	NOUN
ejpam-6307	521	5	m.	m.	PROPN
ejpam-6307	521	6	anto	anto	PROPN
ejpam-6307	521	7	,	,	PUNCT
ejpam-6307	521	8	v.	v.	PROPN
ejpam-6307	521	9	mary	mary	PROPN
ejpam-6307	521	10	mettilda	mettilda	PROPN
ejpam-6307	521	11	rose	rise	VERB
ejpam-6307	521	12	/	/	SYM
ejpam-6307	521	13	eur	eur	PROPN
ejpam-6307	521	14	.	.	PUNCT
ejpam-6307	522	1	j.	j.	PROPN
ejpam-6307	522	2	pure	pure	PROPN
ejpam-6307	522	3	appl	appl	PROPN
ejpam-6307	522	4	.	.	PROPN
ejpam-6307	522	5	math	math	PROPN
ejpam-6307	522	6	,	,	PUNCT
ejpam-6307	522	7	18	18	NUM
ejpam-6307	522	8	(	(	PUNCT
ejpam-6307	522	9	4	4	NUM
ejpam-6307	522	10	)	)	PUNCT
ejpam-6307	522	11	(	(	PUNCT
ejpam-6307	522	12	2025	2025	NUM
ejpam-6307	522	13	)	)	PUNCT
ejpam-6307	522	14	,	,	PUNCT
ejpam-6307	522	15	6307	6307	NUM
ejpam-6307	522	16	24	24	NUM
ejpam-6307	522	17	of	of	ADP
ejpam-6307	522	18	25	25	NUM
ejpam-6307	522	19	references	reference	NOUN
ejpam-6307	522	20	[	[	X
ejpam-6307	522	21	1	1	NUM
ejpam-6307	522	22	]	]	PUNCT
ejpam-6307	522	23	l.	l.	PROPN
ejpam-6307	522	24	a.	a.	PROPN
ejpam-6307	522	25	zadeh	zadeh	PROPN
ejpam-6307	522	26	.	.	PUNCT
ejpam-6307	523	1	fuzzy	fuzzy	ADJ
ejpam-6307	523	2	sets	set	NOUN
ejpam-6307	523	3	.	.	PUNCT
ejpam-6307	524	1	information	information	NOUN
ejpam-6307	524	2	and	and	CCONJ
ejpam-6307	524	3	control	control	NOUN
ejpam-6307	524	4	,	,	PUNCT
ejpam-6307	524	5	8(3):338–353	8(3):338–353	NUM
ejpam-6307	524	6	,	,	PUNCT
ejpam-6307	524	7	1965	1965	NUM
ejpam-6307	524	8	.	.	PUNCT
ejpam-6307	525	1	[	[	X
ejpam-6307	525	2	2	2	NUM
ejpam-6307	525	3	]	]	PUNCT
ejpam-6307	525	4	l.	l.	PROPN
ejpam-6307	525	5	a.	a.	PROPN
ejpam-6307	525	6	zadeh	zadeh	PROPN
ejpam-6307	525	7	,	,	PUNCT
ejpam-6307	525	8	k.	k.	PROPN
ejpam-6307	525	9	s.	s.	PROPN
ejpam-6307	525	10	fu	fu	PROPN
ejpam-6307	525	11	,	,	PUNCT
ejpam-6307	525	12	and	and	CCONJ
ejpam-6307	525	13	m.	m.	PROPN
ejpam-6307	525	14	shimura	shimura	PROPN
ejpam-6307	525	15	.	.	PUNCT
ejpam-6307	526	1	fuzzy	fuzzy	ADJ
ejpam-6307	526	2	sets	set	NOUN
ejpam-6307	526	3	and	and	CCONJ
ejpam-6307	526	4	their	their	PRON
ejpam-6307	526	5	applications	application	NOUN
ejpam-6307	526	6	.	.	PUNCT
ejpam-6307	527	1	academic	academic	ADJ
ejpam-6307	527	2	press	press	PROPN
ejpam-6307	527	3	,	,	PUNCT
ejpam-6307	527	4	cambridge	cambridge	PROPN
ejpam-6307	527	5	,	,	PUNCT
ejpam-6307	527	6	ma	ma	PROPN
ejpam-6307	527	7	,	,	PUNCT
ejpam-6307	527	8	usa	usa	PROPN
ejpam-6307	527	9	,	,	PUNCT
ejpam-6307	527	10	1975	1975	NUM
ejpam-6307	527	11	.	.	PUNCT
ejpam-6307	528	1	[	[	X
ejpam-6307	528	2	3	3	NUM
ejpam-6307	528	3	]	]	PUNCT
ejpam-6307	528	4	a.	a.	NOUN
ejpam-6307	528	5	rosenfeld	rosenfeld	PROPN
ejpam-6307	528	6	.	.	PUNCT
ejpam-6307	529	1	fuzzy	fuzzy	ADJ
ejpam-6307	529	2	sets	set	NOUN
ejpam-6307	529	3	and	and	CCONJ
ejpam-6307	529	4	their	their	PRON
ejpam-6307	529	5	applications	application	NOUN
ejpam-6307	529	6	.	.	PUNCT
ejpam-6307	530	1	academic	academic	ADJ
ejpam-6307	530	2	press	press	NOUN
ejpam-6307	530	3	,	,	PUNCT
ejpam-6307	530	4	new	new	PROPN
ejpam-6307	530	5	york	york	PROPN
ejpam-6307	530	6	,	,	PUNCT
ejpam-6307	530	7	usa	usa	PROPN
ejpam-6307	530	8	,	,	PUNCT
ejpam-6307	530	9	1975	1975	NUM
ejpam-6307	530	10	.	.	PUNCT
ejpam-6307	531	1	[	[	X
ejpam-6307	531	2	4	4	NUM
ejpam-6307	531	3	]	]	X
ejpam-6307	531	4	l.	l.	PROPN
ejpam-6307	531	5	platil	platil	PROPN
ejpam-6307	531	6	and	and	CCONJ
ejpam-6307	531	7	t.	t.	PROPN
ejpam-6307	531	8	tanaka	tanaka	PROPN
ejpam-6307	531	9	.	.	PUNCT
ejpam-6307	532	1	multi	multi	ADJ
ejpam-6307	532	2	-	-	ADJ
ejpam-6307	532	3	criteria	criteria	ADJ
ejpam-6307	532	4	evaluation	evaluation	NOUN
ejpam-6307	532	5	for	for	ADP
ejpam-6307	532	6	intuitionistic	intuitionistic	ADJ
ejpam-6307	532	7	fuzzy	fuzzy	ADJ
ejpam-6307	532	8	sets	set	NOUN
ejpam-6307	532	9	based	base	VERB
ejpam-6307	532	10	on	on	ADP
ejpam-6307	532	11	set	set	NOUN
ejpam-6307	532	12	-	-	PUNCT
ejpam-6307	532	13	relations	relation	NOUN
ejpam-6307	532	14	.	.	PUNCT
ejpam-6307	533	1	nihonkai	nihonkai	PROPN
ejpam-6307	533	2	mathematical	mathematical	PROPN
ejpam-6307	533	3	journal	journal	PROPN
ejpam-6307	533	4	,	,	PUNCT
ejpam-6307	533	5	34:1–18	34:1–18	NUM
ejpam-6307	533	6	,	,	PUNCT
ejpam-6307	533	7	2023	2023	NUM
ejpam-6307	533	8	.	.	PUNCT
ejpam-6307	534	1	[	[	X
ejpam-6307	534	2	5	5	X
ejpam-6307	534	3	]	]	PUNCT
ejpam-6307	534	4	g.	g.	PROPN
ejpam-6307	534	5	chartrand	chartrand	PROPN
ejpam-6307	534	6	,	,	PUNCT
ejpam-6307	534	7	g.	g.	PROPN
ejpam-6307	534	8	l.	l.	PROPN
ejpam-6307	534	9	johns	johns	PROPN
ejpam-6307	534	10	,	,	PUNCT
ejpam-6307	534	11	and	and	CCONJ
ejpam-6307	534	12	songlin	songlin	PROPN
ejpam-6307	534	13	tian	tian	PROPN
ejpam-6307	534	14	.	.	PUNCT
ejpam-6307	535	1	detour	detour	NOUN
ejpam-6307	535	2	distance	distance	NOUN
ejpam-6307	535	3	in	in	ADP
ejpam-6307	535	4	graphs	graph	NOUN
ejpam-6307	535	5	.	.	PUNCT
ejpam-6307	536	1	annals	annal	NOUN
ejpam-6307	536	2	of	of	ADP
ejpam-6307	536	3	discrete	discrete	ADJ
ejpam-6307	536	4	mathematics	mathematic	NOUN
ejpam-6307	536	5	,	,	PUNCT
ejpam-6307	536	6	55:127–136	55:127–136	NUM
ejpam-6307	536	7	,	,	PUNCT
ejpam-6307	536	8	1993	1993	NUM
ejpam-6307	536	9	.	.	PUNCT
ejpam-6307	537	1	[	[	X
ejpam-6307	537	2	6	6	NUM
ejpam-6307	537	3	]	]	PUNCT
ejpam-6307	537	4	j.	j.	PROPN
ejpam-6307	537	5	n.	n.	PROPN
ejpam-6307	537	6	mordeson	mordeson	PROPN
ejpam-6307	537	7	and	and	CCONJ
ejpam-6307	537	8	p.	p.	PROPN
ejpam-6307	537	9	s.	s.	PROPN
ejpam-6307	537	10	nair	nair	PROPN
ejpam-6307	537	11	.	.	PUNCT
ejpam-6307	538	1	applications	application	NOUN
ejpam-6307	538	2	of	of	ADP
ejpam-6307	538	3	fuzzy	fuzzy	ADJ
ejpam-6307	538	4	graphs	graph	NOUN
ejpam-6307	538	5	.	.	PUNCT
ejpam-6307	539	1	physica	physica	NOUN
ejpam-6307	539	2	-	-	PUNCT
ejpam-6307	539	3	verlag	verlag	PROPN
ejpam-6307	539	4	,	,	PUNCT
ejpam-6307	539	5	heidelberg	heidelberg	PROPN
ejpam-6307	539	6	,	,	PUNCT
ejpam-6307	539	7	germany	germany	PROPN
ejpam-6307	539	8	,	,	PUNCT
ejpam-6307	539	9	2012	2012	NUM
ejpam-6307	539	10	.	.	PUNCT
ejpam-6307	540	1	[	[	X
ejpam-6307	540	2	7	7	NUM
ejpam-6307	540	3	]	]	X
ejpam-6307	540	4	sunil	sunil	PROPN
ejpam-6307	540	5	mathew	mathew	PROPN
ejpam-6307	540	6	,	,	PUNCT
ejpam-6307	540	7	john	john	PROPN
ejpam-6307	540	8	n.	n.	PROPN
ejpam-6307	540	9	mordeson	mordeson	PROPN
ejpam-6307	540	10	,	,	PUNCT
ejpam-6307	540	11	and	and	CCONJ
ejpam-6307	540	12	davender	davender	PROPN
ejpam-6307	540	13	s.	s.	PROPN
ejpam-6307	540	14	malik	malik	PROPN
ejpam-6307	540	15	.	.	PUNCT
ejpam-6307	541	1	connectivity	connectivity	NOUN
ejpam-6307	541	2	in	in	ADP
ejpam-6307	541	3	fuzzy	fuzzy	ADJ
ejpam-6307	541	4	graphs	graph	NOUN
ejpam-6307	541	5	theory	theory	NOUN
ejpam-6307	541	6	.	.	PUNCT
ejpam-6307	542	1	springer	springer	NOUN
ejpam-6307	542	2	international	international	ADJ
ejpam-6307	542	3	publishing	publishing	NOUN
ejpam-6307	542	4	,	,	PUNCT
ejpam-6307	542	5	cham	cham	PROPN
ejpam-6307	542	6	,	,	PUNCT
ejpam-6307	542	7	switzerland	switzerland	PROPN
ejpam-6307	542	8	,	,	PUNCT
ejpam-6307	542	9	2018	2018	NUM
ejpam-6307	542	10	.	.	PUNCT
ejpam-6307	543	1	[	[	X
ejpam-6307	543	2	8	8	X
ejpam-6307	543	3	]	]	PUNCT
ejpam-6307	543	4	j.	j.	PROPN
ejpam-6307	543	5	n.	n.	PROPN
ejpam-6307	543	6	mordeson	mordeson	PROPN
ejpam-6307	543	7	and	and	CCONJ
ejpam-6307	543	8	sunil	sunil	PROPN
ejpam-6307	543	9	mathew	mathew	PROPN
ejpam-6307	543	10	.	.	PUNCT
ejpam-6307	544	1	distances	distance	NOUN
ejpam-6307	544	2	and	and	CCONJ
ejpam-6307	544	3	convexity	convexity	NOUN
ejpam-6307	544	4	in	in	ADP
ejpam-6307	544	5	fuzzy	fuzzy	ADJ
ejpam-6307	544	6	graphs	graph	NOUN
ejpam-6307	544	7	.	.	PUNCT
ejpam-6307	545	1	springer	springer	PROPN
ejpam-6307	545	2	cham	cham	PROPN
ejpam-6307	545	3	,	,	PUNCT
ejpam-6307	545	4	cham	cham	PROPN
ejpam-6307	545	5	,	,	PUNCT
ejpam-6307	545	6	switzerland	switzerland	PROPN
ejpam-6307	545	7	,	,	PUNCT
ejpam-6307	545	8	2019	2019	NUM
ejpam-6307	545	9	.	.	PUNCT
ejpam-6307	546	1	[	[	X
ejpam-6307	546	2	9	9	NUM
ejpam-6307	546	3	]	]	PUNCT
ejpam-6307	546	4	m.	m.	NOUN
ejpam-6307	546	5	s.	s.	PROPN
ejpam-6307	546	6	sunitha	sunitha	PROPN
ejpam-6307	546	7	and	and	CCONJ
ejpam-6307	546	8	a.	a.	PROPN
ejpam-6307	546	9	vijayakumar	vijayakumar	PROPN
ejpam-6307	546	10	.	.	PUNCT
ejpam-6307	547	1	complement	complement	NOUN
ejpam-6307	547	2	of	of	ADP
ejpam-6307	547	3	a	a	DET
ejpam-6307	547	4	fuzzy	fuzzy	ADJ
ejpam-6307	547	5	graph	graph	NOUN
ejpam-6307	547	6	.	.	PUNCT
ejpam-6307	548	1	indian	indian	PROPN
ejpam-6307	548	2	journal	journal	PROPN
ejpam-6307	548	3	of	of	ADP
ejpam-6307	548	4	pure	pure	ADJ
ejpam-6307	548	5	and	and	CCONJ
ejpam-6307	548	6	applied	applied	ADJ
ejpam-6307	548	7	mathematics	mathematic	NOUN
ejpam-6307	548	8	,	,	PUNCT
ejpam-6307	548	9	33:1451–1464	33:1451–1464	NUM
ejpam-6307	548	10	,	,	PUNCT
ejpam-6307	548	11	2002	2002	NUM
ejpam-6307	548	12	.	.	PUNCT
ejpam-6307	549	1	[	[	X
ejpam-6307	549	2	10	10	NUM
ejpam-6307	549	3	]	]	X
ejpam-6307	549	4	r.	r.	PROPN
ejpam-6307	549	5	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	549	6	and	and	CCONJ
ejpam-6307	549	7	a.	a.	NOUN
ejpam-6307	549	8	m.	m.	PROPN
ejpam-6307	549	9	anto	anto	PROPN
ejpam-6307	549	10	.	.	PUNCT
ejpam-6307	549	11	fuzzy	fuzzy	PROPN
ejpam-6307	549	12	detour	detour	PRON
ejpam-6307	549	13	convexity	convexity	NOUN
ejpam-6307	549	14	and	and	CCONJ
ejpam-6307	549	15	fuzzy	fuzzy	ADJ
ejpam-6307	549	16	detour	detour	NOUN
ejpam-6307	549	17	covering	cover	VERB
ejpam-6307	549	18	in	in	ADP
ejpam-6307	549	19	fuzzy	fuzzy	ADJ
ejpam-6307	549	20	graphs	graph	NOUN
ejpam-6307	549	21	.	.	PUNCT
ejpam-6307	550	1	turkish	turkish	ADJ
ejpam-6307	550	2	journal	journal	NOUN
ejpam-6307	550	3	of	of	ADP
ejpam-6307	550	4	computer	computer	NOUN
ejpam-6307	550	5	and	and	CCONJ
ejpam-6307	550	6	mathematics	mathematics	PROPN
ejpam-6307	550	7	education	education	NOUN
ejpam-6307	550	8	(	(	PUNCT
ejpam-6307	550	9	turcomat	turcomat	NOUN
ejpam-6307	550	10	)	)	PUNCT
ejpam-6307	550	11	,	,	PUNCT
ejpam-6307	550	12	12:2170–2175	12:2170–2175	PROPN
ejpam-6307	550	13	,	,	PUNCT
ejpam-6307	550	14	2021	2021	NUM
ejpam-6307	550	15	.	.	PUNCT
ejpam-6307	551	1	[	[	X
ejpam-6307	551	2	11	11	NUM
ejpam-6307	551	3	]	]	X
ejpam-6307	551	4	r.	r.	PROPN
ejpam-6307	551	5	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	551	6	and	and	CCONJ
ejpam-6307	551	7	a.	a.	NOUN
ejpam-6307	551	8	m.	m.	PROPN
ejpam-6307	551	9	anto	anto	PROPN
ejpam-6307	551	10	.	.	PUNCT
ejpam-6307	552	1	some	some	DET
ejpam-6307	552	2	domination	domination	NOUN
ejpam-6307	552	3	parameters	parameter	NOUN
ejpam-6307	552	4	in	in	ADP
ejpam-6307	552	5	intuitionistic	intuitionistic	ADJ
ejpam-6307	552	6	fuzzy	fuzzy	ADJ
ejpam-6307	552	7	graphs	graph	NOUN
ejpam-6307	552	8	.	.	PUNCT
ejpam-6307	553	1	aip	aip	PROPN
ejpam-6307	553	2	conference	conference	NOUN
ejpam-6307	553	3	proceedings	proceeding	NOUN
ejpam-6307	553	4	,	,	PUNCT
ejpam-6307	553	5	2516:200016	2516:200016	NUM
ejpam-6307	553	6	,	,	PUNCT
ejpam-6307	553	7	2022	2022	NUM
ejpam-6307	553	8	.	.	PUNCT
ejpam-6307	554	1	[	[	X
ejpam-6307	554	2	12	12	NUM
ejpam-6307	554	3	]	]	PUNCT
ejpam-6307	554	4	a.	a.	NOUN
ejpam-6307	554	5	nagoor	nagoor	PROPN
ejpam-6307	554	6	gani	gani	PROPN
ejpam-6307	554	7	and	and	CCONJ
ejpam-6307	554	8	j.	j.	PROPN
ejpam-6307	554	9	umamaheswari	umamaheswari	PROPN
ejpam-6307	554	10	.	.	PUNCT
ejpam-6307	555	1	fuzzy	fuzzy	ADJ
ejpam-6307	555	2	detour	detour	NOUN
ejpam-6307	555	3	µ-distance	µ-distance	NOUN
ejpam-6307	555	4	in	in	ADP
ejpam-6307	555	5	fuzzy	fuzzy	ADJ
ejpam-6307	555	6	graphs	graph	NOUN
ejpam-6307	555	7	.	.	PUNCT
ejpam-6307	556	1	in	in	ADP
ejpam-6307	556	2	proceedings	proceeding	NOUN
ejpam-6307	556	3	of	of	ADP
ejpam-6307	556	4	the	the	DET
ejpam-6307	556	5	international	international	ADJ
ejpam-6307	556	6	conference	conference	NOUN
ejpam-6307	556	7	on	on	ADP
ejpam-6307	556	8	mathematical	mathematical	ADJ
ejpam-6307	556	9	methods	method	NOUN
ejpam-6307	556	10	and	and	CCONJ
ejpam-6307	556	11	computations	computation	NOUN
ejpam-6307	556	12	,	,	PUNCT
ejpam-6307	556	13	pages	page	NOUN
ejpam-6307	556	14	184–187	184–187	NUM
ejpam-6307	556	15	.	.	PUNCT
ejpam-6307	557	1	allied	ally	VERB
ejpam-6307	557	2	publications	publication	NOUN
ejpam-6307	557	3	,	,	PUNCT
ejpam-6307	557	4	2009	2009	NUM
ejpam-6307	557	5	.	.	PUNCT
ejpam-6307	558	1	[	[	X
ejpam-6307	558	2	13	13	NUM
ejpam-6307	558	3	]	]	SYM
ejpam-6307	558	4	i.	i.	PROPN
ejpam-6307	558	5	gutman	gutman	PROPN
ejpam-6307	558	6	.	.	PUNCT
ejpam-6307	559	1	the	the	DET
ejpam-6307	559	2	energy	energy	NOUN
ejpam-6307	559	3	of	of	ADP
ejpam-6307	559	4	a	a	DET
ejpam-6307	559	5	graph	graph	NOUN
ejpam-6307	559	6	.	.	PUNCT
ejpam-6307	560	1	berichte	berichte	NOUN
ejpam-6307	560	2	der	der	ADJ
ejpam-6307	560	3	mathematisch	mathematisch	PROPN
ejpam-6307	560	4	-	-	PUNCT
ejpam-6307	560	5	statistischen	statistischen	NOUN
ejpam-6307	560	6	sektion	sektion	NOUN
ejpam-6307	561	1	i	i	PRON
ejpam-6307	561	2	m	m	VERB
ejpam-6307	561	3	forschungszentrum	forschungszentrum	PROPN
ejpam-6307	561	4	graz	graz	PROPN
ejpam-6307	561	5	,	,	PUNCT
ejpam-6307	561	6	103:1–22	103:1–22	NUM
ejpam-6307	561	7	,	,	PUNCT
ejpam-6307	561	8	1978	1978	NUM
ejpam-6307	561	9	.	.	PUNCT
ejpam-6307	562	1	[	[	X
ejpam-6307	562	2	14	14	NUM
ejpam-6307	562	3	]	]	X
ejpam-6307	562	4	g.	g.	PROPN
ejpam-6307	562	5	indulal	indulal	PROPN
ejpam-6307	562	6	and	and	CCONJ
ejpam-6307	562	7	a.	a.	NOUN
ejpam-6307	562	8	vijayakumar	vijayakumar	PROPN
ejpam-6307	562	9	.	.	PUNCT
ejpam-6307	563	1	energies	energy	NOUN
ejpam-6307	563	2	of	of	ADP
ejpam-6307	563	3	some	some	DET
ejpam-6307	563	4	non	non	ADJ
ejpam-6307	563	5	-	-	ADJ
ejpam-6307	563	6	regular	regular	ADJ
ejpam-6307	563	7	graphs	graph	NOUN
ejpam-6307	563	8	.	.	PUNCT
ejpam-6307	564	1	journal	journal	NOUN
ejpam-6307	564	2	of	of	ADP
ejpam-6307	564	3	mathematical	mathematical	ADJ
ejpam-6307	564	4	chemistry	chemistry	NOUN
ejpam-6307	564	5	,	,	PUNCT
ejpam-6307	564	6	42:377–386	42:377–386	NUM
ejpam-6307	564	7	,	,	PUNCT
ejpam-6307	564	8	2007	2007	NUM
ejpam-6307	564	9	.	.	PUNCT
ejpam-6307	565	1	[	[	X
ejpam-6307	565	2	15	15	NUM
ejpam-6307	565	3	]	]	X
ejpam-6307	565	4	w.	w.	PROPN
ejpam-6307	565	5	du	du	PROPN
ejpam-6307	565	6	,	,	PUNCT
ejpam-6307	565	7	x.	x.	PROPN
ejpam-6307	565	8	li	li	PROPN
ejpam-6307	565	9	,	,	PUNCT
ejpam-6307	565	10	and	and	CCONJ
ejpam-6307	565	11	y.	y.	PROPN
ejpam-6307	565	12	li	li	PROPN
ejpam-6307	565	13	.	.	PUNCT
ejpam-6307	566	1	various	various	ADJ
ejpam-6307	566	2	energies	energy	NOUN
ejpam-6307	566	3	of	of	ADP
ejpam-6307	566	4	random	random	ADJ
ejpam-6307	566	5	graphs	graph	NOUN
ejpam-6307	566	6	.	.	PUNCT
ejpam-6307	567	1	match	match	VERB
ejpam-6307	567	2	communications	communication	NOUN
ejpam-6307	567	3	in	in	ADP
ejpam-6307	567	4	mathematical	mathematical	ADJ
ejpam-6307	567	5	and	and	CCONJ
ejpam-6307	567	6	in	in	ADP
ejpam-6307	567	7	computer	computer	NOUN
ejpam-6307	567	8	chemistry	chemistry	NOUN
ejpam-6307	567	9	,	,	PUNCT
ejpam-6307	567	10	64:251–260	64:251–260	NOUN
ejpam-6307	567	11	,	,	PUNCT
ejpam-6307	567	12	2010	2010	NUM
ejpam-6307	567	13	.	.	PUNCT
ejpam-6307	568	1	[	[	X
ejpam-6307	568	2	16	16	NUM
ejpam-6307	568	3	]	]	PUNCT
ejpam-6307	568	4	r.	r.	PROPN
ejpam-6307	568	5	balakrishnan	balakrishnan	PROPN
ejpam-6307	568	6	.	.	PUNCT
ejpam-6307	569	1	the	the	DET
ejpam-6307	569	2	energy	energy	NOUN
ejpam-6307	569	3	of	of	ADP
ejpam-6307	569	4	a	a	DET
ejpam-6307	569	5	graph	graph	NOUN
ejpam-6307	569	6	.	.	PUNCT
ejpam-6307	570	1	linear	linear	ADJ
ejpam-6307	570	2	algebra	algebra	NOUN
ejpam-6307	570	3	and	and	CCONJ
ejpam-6307	570	4	its	its	PRON
ejpam-6307	570	5	applications	application	NOUN
ejpam-6307	570	6	,	,	PUNCT
ejpam-6307	570	7	387:287	387:287	PROPN
ejpam-6307	570	8	–	–	PUNCT
ejpam-6307	570	9	295	295	NUM
ejpam-6307	570	10	,	,	PUNCT
ejpam-6307	570	11	2004	2004	NUM
ejpam-6307	570	12	.	.	PUNCT
ejpam-6307	571	1	[	[	X
ejpam-6307	571	2	17	17	NUM
ejpam-6307	571	3	]	]	PUNCT
ejpam-6307	571	4	h.	h.	PROPN
ejpam-6307	571	5	s.	s.	PROPN
ejpam-6307	571	6	ramane	ramane	PROPN
ejpam-6307	571	7	and	and	CCONJ
ejpam-6307	571	8	r.	r.	PROPN
ejpam-6307	571	9	b.	b.	PROPN
ejpam-6307	571	10	jummannaver	jummannaver	PROPN
ejpam-6307	571	11	.	.	PUNCT
ejpam-6307	572	1	harary	harary	PROPN
ejpam-6307	572	2	spectra	spectra	PROPN
ejpam-6307	572	3	and	and	CCONJ
ejpam-6307	572	4	harary	harary	ADJ
ejpam-6307	572	5	energy	energy	NOUN
ejpam-6307	572	6	of	of	ADP
ejpam-6307	572	7	line	line	NOUN
ejpam-6307	572	8	graphs	graph	NOUN
ejpam-6307	572	9	of	of	ADP
ejpam-6307	572	10	regular	regular	ADJ
ejpam-6307	572	11	graphs	graph	NOUN
ejpam-6307	572	12	.	.	PUNCT
ejpam-6307	573	1	gulf	gulf	PROPN
ejpam-6307	573	2	journal	journal	PROPN
ejpam-6307	573	3	of	of	ADP
ejpam-6307	573	4	mathematics	mathematic	NOUN
ejpam-6307	573	5	,	,	PUNCT
ejpam-6307	573	6	4:39–46	4:39–46	NUM
ejpam-6307	573	7	,	,	PUNCT
ejpam-6307	573	8	2016	2016	NUM
ejpam-6307	573	9	.	.	PUNCT
ejpam-6307	574	1	[	[	X
ejpam-6307	574	2	18	18	NUM
ejpam-6307	574	3	]	]	X
ejpam-6307	574	4	j.	j.	PROPN
ejpam-6307	574	5	shao	shao	PROPN
ejpam-6307	574	6	,	,	PUNCT
ejpam-6307	574	7	f.	f.	PROPN
ejpam-6307	574	8	gong	gong	PROPN
ejpam-6307	574	9	,	,	PUNCT
ejpam-6307	574	10	and	and	CCONJ
ejpam-6307	574	11	z.	z.	PROPN
ejpam-6307	574	12	du	du	PROPN
ejpam-6307	574	13	.	.	PROPN
ejpam-6307	574	14	extremal	extremal	ADJ
ejpam-6307	574	15	energies	energy	NOUN
ejpam-6307	574	16	of	of	ADP
ejpam-6307	574	17	weighted	weight	VERB
ejpam-6307	574	18	trees	tree	NOUN
ejpam-6307	574	19	and	and	CCONJ
ejpam-6307	574	20	forests	forest	NOUN
ejpam-6307	574	21	with	with	ADP
ejpam-6307	574	22	fixed	fix	VERB
ejpam-6307	574	23	total	total	ADJ
ejpam-6307	574	24	weight	weight	NOUN
ejpam-6307	574	25	sum	sum	NOUN
ejpam-6307	574	26	.	.	PUNCT
ejpam-6307	575	1	match	match	VERB
ejpam-6307	575	2	communications	communication	NOUN
ejpam-6307	575	3	in	in	ADP
ejpam-6307	575	4	mathematical	mathematical	ADJ
ejpam-6307	575	5	and	and	CCONJ
ejpam-6307	575	6	in	in	ADP
ejpam-6307	575	7	computer	computer	NOUN
ejpam-6307	575	8	chemistry	chemistry	NOUN
ejpam-6307	575	9	,	,	PUNCT
ejpam-6307	575	10	66:879–890	66:879–890	PROPN
ejpam-6307	575	11	,	,	PUNCT
ejpam-6307	575	12	2011	2011	NUM
ejpam-6307	575	13	.	.	PUNCT
ejpam-6307	576	1	[	[	X
ejpam-6307	576	2	19	19	NUM
ejpam-6307	576	3	]	]	X
ejpam-6307	576	4	anjali	anjali	PROPN
ejpam-6307	576	5	narayanan	narayanan	PROPN
ejpam-6307	576	6	and	and	CCONJ
ejpam-6307	576	7	sunil	sunil	PROPN
ejpam-6307	576	8	mathew	mathew	PROPN
ejpam-6307	576	9	.	.	PUNCT
ejpam-6307	577	1	energy	energy	NOUN
ejpam-6307	577	2	of	of	ADP
ejpam-6307	577	3	a	a	DET
ejpam-6307	577	4	fuzzy	fuzzy	ADJ
ejpam-6307	577	5	graph	graph	NOUN
ejpam-6307	577	6	.	.	PUNCT
ejpam-6307	578	1	annals	annal	NOUN
ejpam-6307	578	2	of	of	ADP
ejpam-6307	578	3	fuzzy	fuzzy	ADJ
ejpam-6307	578	4	mathematics	mathematic	NOUN
ejpam-6307	578	5	and	and	CCONJ
ejpam-6307	578	6	informatics	informatic	NOUN
ejpam-6307	578	7	,	,	PUNCT
ejpam-6307	578	8	6:455–465	6:455–465	NOUN
ejpam-6307	578	9	,	,	PUNCT
ejpam-6307	578	10	2013	2013	NUM
ejpam-6307	578	11	.	.	PUNCT
ejpam-6307	579	1	[	[	X
ejpam-6307	579	2	20	20	NUM
ejpam-6307	579	3	]	]	PUNCT
ejpam-6307	579	4	i.	i.	PROPN
ejpam-6307	579	5	gutman	gutman	PROPN
ejpam-6307	579	6	and	and	CCONJ
ejpam-6307	579	7	bo	bo	PROPN
ejpam-6307	579	8	zhou	zhou	PROPN
ejpam-6307	579	9	.	.	PUNCT
ejpam-6307	580	1	laplacian	laplacian	ADJ
ejpam-6307	580	2	energy	energy	NOUN
ejpam-6307	580	3	of	of	ADP
ejpam-6307	580	4	a	a	DET
ejpam-6307	580	5	graph	graph	NOUN
ejpam-6307	580	6	.	.	PUNCT
ejpam-6307	581	1	linear	linear	ADJ
ejpam-6307	581	2	algebra	algebra	NOUN
ejpam-6307	581	3	and	and	CCONJ
ejpam-6307	581	4	its	its	PRON
ejpam-6307	581	5	applir	applir	NOUN
ejpam-6307	581	6	.	.	PUNCT
ejpam-6307	582	1	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	582	2	,	,	PUNCT
ejpam-6307	582	3	a.	a.	NOUN
ejpam-6307	582	4	m.	m.	PROPN
ejpam-6307	582	5	anto	anto	PROPN
ejpam-6307	582	6	,	,	PUNCT
ejpam-6307	582	7	v.	v.	PROPN
ejpam-6307	582	8	mary	mary	PROPN
ejpam-6307	582	9	mettilda	mettilda	PROPN
ejpam-6307	582	10	rose	rise	VERB
ejpam-6307	582	11	/	/	SYM
ejpam-6307	582	12	eur	eur	PROPN
ejpam-6307	582	13	.	.	PUNCT
ejpam-6307	583	1	j.	j.	PROPN
ejpam-6307	583	2	pure	pure	PROPN
ejpam-6307	583	3	appl	appl	PROPN
ejpam-6307	583	4	.	.	PROPN
ejpam-6307	583	5	math	math	PROPN
ejpam-6307	583	6	,	,	PUNCT
ejpam-6307	583	7	18	18	NUM
ejpam-6307	583	8	(	(	PUNCT
ejpam-6307	583	9	4	4	NUM
ejpam-6307	583	10	)	)	PUNCT
ejpam-6307	583	11	(	(	PUNCT
ejpam-6307	583	12	2025	2025	NUM
ejpam-6307	583	13	)	)	PUNCT
ejpam-6307	583	14	,	,	PUNCT
ejpam-6307	583	15	6307	6307	NUM
ejpam-6307	583	16	25	25	NUM
ejpam-6307	583	17	of	of	ADP
ejpam-6307	583	18	25	25	NUM
ejpam-6307	583	19	cations	cation	NOUN
ejpam-6307	583	20	,	,	PUNCT
ejpam-6307	583	21	414:29–37	414:29–37	NUM
ejpam-6307	583	22	,	,	PUNCT
ejpam-6307	583	23	2006	2006	NUM
ejpam-6307	583	24	.	.	PUNCT
ejpam-6307	584	1	[	[	X
ejpam-6307	584	2	21	21	NUM
ejpam-6307	584	3	]	]	X
ejpam-6307	584	4	s.	s.	PROPN
ejpam-6307	584	5	rahimi	rahimi	PROPN
ejpam-6307	584	6	sharbaf	sharbaf	PROPN
ejpam-6307	584	7	and	and	CCONJ
ejpam-6307	584	8	f.	f.	PROPN
ejpam-6307	584	9	fayazi	fayazi	PROPN
ejpam-6307	584	10	.	.	PUNCT
ejpam-6307	585	1	laplacian	laplacian	ADJ
ejpam-6307	585	2	energy	energy	NOUN
ejpam-6307	585	3	of	of	ADP
ejpam-6307	585	4	a	a	DET
ejpam-6307	585	5	fuzzy	fuzzy	ADJ
ejpam-6307	585	6	graph	graph	NOUN
ejpam-6307	585	7	.	.	PUNCT
ejpam-6307	586	1	iranian	iranian	ADJ
ejpam-6307	586	2	journal	journal	PROPN
ejpam-6307	586	3	of	of	ADP
ejpam-6307	586	4	mathematical	mathematical	ADJ
ejpam-6307	586	5	chemistry	chemistry	NOUN
ejpam-6307	586	6	,	,	PUNCT
ejpam-6307	586	7	5:1–10	5:1–10	NUM
ejpam-6307	586	8	,	,	PUNCT
ejpam-6307	586	9	2014	2014	NUM
ejpam-6307	586	10	.	.	PUNCT
ejpam-6307	587	1	[	[	X
ejpam-6307	587	2	22	22	NUM
ejpam-6307	587	3	]	]	X
ejpam-6307	587	4	milan	milan	PROPN
ejpam-6307	587	5	nath	nath	PROPN
ejpam-6307	587	6	and	and	CCONJ
ejpam-6307	587	7	somnath	somnath	PROPN
ejpam-6307	587	8	paul	paul	PROPN
ejpam-6307	587	9	.	.	PUNCT
ejpam-6307	588	1	on	on	ADP
ejpam-6307	588	2	the	the	DET
ejpam-6307	588	3	distance	distance	NOUN
ejpam-6307	588	4	laplacian	laplacian	ADJ
ejpam-6307	588	5	spectra	spectra	NOUN
ejpam-6307	588	6	of	of	ADP
ejpam-6307	588	7	graphs	graph	NOUN
ejpam-6307	588	8	.	.	PUNCT
ejpam-6307	589	1	linear	linear	ADJ
ejpam-6307	589	2	algebra	algebra	NOUN
ejpam-6307	589	3	and	and	CCONJ
ejpam-6307	589	4	its	its	PRON
ejpam-6307	589	5	applications	application	NOUN
ejpam-6307	589	6	,	,	PUNCT
ejpam-6307	589	7	460:97–110	460:97–110	NUM
ejpam-6307	589	8	,	,	PUNCT
ejpam-6307	589	9	2014	2014	NUM
ejpam-6307	589	10	.	.	PUNCT
ejpam-6307	590	1	[	[	X
ejpam-6307	590	2	23	23	NUM
ejpam-6307	590	3	]	]	PUNCT
ejpam-6307	590	4	m.	m.	NOUN
ejpam-6307	590	5	binu	binu	NOUN
ejpam-6307	590	6	,	,	PUNCT
ejpam-6307	590	7	sunil	sunil	PROPN
ejpam-6307	590	8	mathew	mathew	PROPN
ejpam-6307	590	9	,	,	PUNCT
ejpam-6307	590	10	and	and	CCONJ
ejpam-6307	590	11	j.	j.	PROPN
ejpam-6307	590	12	n.	n.	PROPN
ejpam-6307	590	13	mordeson	mordeson	PROPN
ejpam-6307	590	14	.	.	PUNCT
ejpam-6307	591	1	wiener	wiener	NOUN
ejpam-6307	591	2	index	index	NOUN
ejpam-6307	591	3	of	of	ADP
ejpam-6307	591	4	a	a	DET
ejpam-6307	591	5	fuzzy	fuzzy	ADJ
ejpam-6307	591	6	graph	graph	NOUN
ejpam-6307	591	7	and	and	CCONJ
ejpam-6307	591	8	application	application	NOUN
ejpam-6307	591	9	to	to	ADP
ejpam-6307	591	10	illegal	illegal	ADJ
ejpam-6307	591	11	immigration	immigration	NOUN
ejpam-6307	591	12	networks	network	NOUN
ejpam-6307	591	13	.	.	PUNCT
ejpam-6307	592	1	fuzzy	fuzzy	ADJ
ejpam-6307	592	2	sets	set	NOUN
ejpam-6307	592	3	and	and	CCONJ
ejpam-6307	592	4	systems	system	NOUN
ejpam-6307	592	5	,	,	PUNCT
ejpam-6307	592	6	384:132–147	384:132–147	NUM
ejpam-6307	592	7	,	,	PUNCT
ejpam-6307	592	8	2020	2020	NUM
ejpam-6307	592	9	.	.	PUNCT
ejpam-6307	593	1	[	[	X
ejpam-6307	593	2	24	24	NUM
ejpam-6307	593	3	]	]	PUNCT
ejpam-6307	593	4	a.	a.	NOUN
ejpam-6307	593	5	m.	m.	PROPN
ejpam-6307	593	6	anto	anto	PROPN
ejpam-6307	593	7	,	,	PUNCT
ejpam-6307	593	8	r.	r.	PROPN
ejpam-6307	593	9	rajeshkumar	rajeshkumar	PROPN
ejpam-6307	593	10	,	,	PUNCT
ejpam-6307	593	11	l.	l.	PROPN
ejpam-6307	593	12	e.	e.	PROPN
ejpam-6307	593	13	preshiba	preshiba	PROPN
ejpam-6307	593	14	,	,	PUNCT
ejpam-6307	593	15	and	and	CCONJ
ejpam-6307	593	16	v.	v.	ADP
ejpam-6307	593	17	mary	mary	PROPN
ejpam-6307	593	18	mettilda	mettilda	PROPN
ejpam-6307	593	19	rose	rise	VERB
ejpam-6307	593	20	.	.	PUNCT
ejpam-6307	594	1	insights	insight	NOUN
ejpam-6307	594	2	into	into	ADP
ejpam-6307	594	3	if	if	SCONJ
ejpam-6307	594	4	-	-	PUNCT
ejpam-6307	594	5	geodetic	geodetic	ADJ
ejpam-6307	594	6	convexity	convexity	NOUN
ejpam-6307	594	7	in	in	ADP
ejpam-6307	594	8	intuitionistic	intuitionistic	ADJ
ejpam-6307	594	9	fuzzy	fuzzy	ADJ
ejpam-6307	594	10	graphs	graph	NOUN
ejpam-6307	594	11	:	:	PUNCT
ejpam-6307	594	12	harnessing	harness	VERB
ejpam-6307	594	13	the	the	DET
ejpam-6307	594	14	if	if	ADV
ejpam-6307	594	15	-	-	PUNCT
ejpam-6307	594	16	geodetic	geodetic	ADJ
ejpam-6307	594	17	wiener	wiener	NOUN
ejpam-6307	594	18	index	index	NOUN
ejpam-6307	594	19	for	for	ADP
ejpam-6307	594	20	global	global	ADJ
ejpam-6307	594	21	human	human	ADJ
ejpam-6307	594	22	trading	trading	NOUN
ejpam-6307	594	23	analysis	analysis	NOUN
ejpam-6307	594	24	and	and	CCONJ
ejpam-6307	594	25	if	if	ADV
ejpam-6307	594	26	-	-	PUNCT
ejpam-6307	594	27	geodetic	geodetic	ADJ
ejpam-6307	594	28	cover	cover	NOUN
ejpam-6307	594	29	for	for	ADP
ejpam-6307	594	30	gateway	gateway	NOUN
ejpam-6307	594	31	node	node	NOUN
ejpam-6307	594	32	identification	identification	NOUN
ejpam-6307	594	33	.	.	PUNCT
ejpam-6307	595	1	symmetry	symmetry	NOUN
ejpam-6307	595	2	,	,	PUNCT
ejpam-6307	595	3	17:1277	17:1277	NUM
ejpam-6307	595	4	,	,	PUNCT
ejpam-6307	595	5	2025	2025	NUM
ejpam-6307	595	6	.	.	PUNCT
ejpam-6307	596	1	[	[	X
ejpam-6307	596	2	25	25	NUM
ejpam-6307	596	3	]	]	PUNCT
ejpam-6307	596	4	j.	j.	PROPN
ejpam-6307	596	5	n.	n.	PROPN
ejpam-6307	596	6	mordeson	mordeson	PROPN
ejpam-6307	596	7	and	and	CCONJ
ejpam-6307	596	8	sunil	sunil	PROPN
ejpam-6307	596	9	mathew	mathew	PROPN
ejpam-6307	596	10	.	.	PUNCT
ejpam-6307	597	1	t	t	PROPN
ejpam-6307	597	2	-	-	PUNCT
ejpam-6307	597	3	norm	norm	NOUN
ejpam-6307	597	4	fuzzy	fuzzy	ADJ
ejpam-6307	597	5	graphs	graph	NOUN
ejpam-6307	597	6	.	.	PUNCT
ejpam-6307	598	1	new	new	ADJ
ejpam-6307	598	2	mathematics	mathematic	NOUN
ejpam-6307	598	3	and	and	CCONJ
ejpam-6307	598	4	natural	natural	ADJ
ejpam-6307	598	5	computation	computation	NOUN
ejpam-6307	598	6	,	,	PUNCT
ejpam-6307	598	7	14:129–143	14:129–143	PROPN
ejpam-6307	598	8	,	,	PUNCT
ejpam-6307	598	9	2018	2018	NUM
ejpam-6307	598	10	.	.	PUNCT
ejpam-6307	599	1	[	[	X
ejpam-6307	599	2	26	26	NUM
ejpam-6307	599	3	]	]	X
ejpam-6307	599	4	e.	e.	PROPN
ejpam-6307	599	5	darabian	darabian	PROPN
ejpam-6307	599	6	and	and	CCONJ
ejpam-6307	599	7	r.	r.	PROPN
ejpam-6307	599	8	a.	a.	PROPN
ejpam-6307	599	9	borzooei	borzooei	PROPN
ejpam-6307	599	10	.	.	PUNCT
ejpam-6307	600	1	results	result	NOUN
ejpam-6307	600	2	on	on	ADP
ejpam-6307	600	3	vague	vague	ADJ
ejpam-6307	600	4	graphs	graph	NOUN
ejpam-6307	600	5	with	with	ADP
ejpam-6307	600	6	applications	application	NOUN
ejpam-6307	600	7	to	to	ADP
ejpam-6307	600	8	human	human	ADJ
ejpam-6307	600	9	trafficking	trafficking	NOUN
ejpam-6307	600	10	.	.	PUNCT
ejpam-6307	601	1	new	new	ADJ
ejpam-6307	601	2	mathematics	mathematic	NOUN
ejpam-6307	601	3	and	and	CCONJ
ejpam-6307	601	4	natural	natural	ADJ
ejpam-6307	601	5	computation	computation	NOUN
ejpam-6307	601	6	,	,	PUNCT
ejpam-6307	601	7	14:37–52	14:37–52	NUM
ejpam-6307	601	8	,	,	PUNCT
ejpam-6307	601	9	2018	2018	NUM
ejpam-6307	601	10	.	.	PUNCT
ejpam-6307	602	1	[	[	X
ejpam-6307	602	2	27	27	NUM
ejpam-6307	602	3	]	]	X
ejpam-6307	602	4	s.	s.	PROPN
ejpam-6307	602	5	sharief	sharief	PROPN
ejpam-6307	602	6	basha	basha	PROPN
ejpam-6307	602	7	and	and	CCONJ
ejpam-6307	602	8	e.	e.	PROPN
ejpam-6307	602	9	kartheek	kartheek	PROPN
ejpam-6307	602	10	.	.	PUNCT
ejpam-6307	603	1	laplacian	laplacian	ADJ
ejpam-6307	603	2	energy	energy	NOUN
ejpam-6307	603	3	of	of	ADP
ejpam-6307	603	4	an	an	DET
ejpam-6307	603	5	intuitionistic	intuitionistic	ADJ
ejpam-6307	603	6	fuzzy	fuzzy	ADJ
ejpam-6307	603	7	graph	graph	NOUN
ejpam-6307	603	8	.	.	PUNCT
ejpam-6307	604	1	indian	indian	PROPN
ejpam-6307	604	2	journal	journal	PROPN
ejpam-6307	604	3	of	of	ADP
ejpam-6307	604	4	science	science	NOUN
ejpam-6307	604	5	and	and	CCONJ
ejpam-6307	604	6	technology	technology	NOUN
ejpam-6307	604	7	,	,	PUNCT
ejpam-6307	604	8	8:1–9	8:1–9	NUM
ejpam-6307	604	9	,	,	PUNCT
ejpam-6307	604	10	2015	2015	NUM
ejpam-6307	604	11	.	.	PUNCT
ejpam-6307	605	1	[	[	X
ejpam-6307	605	2	28	28	NUM
ejpam-6307	605	3	]	]	X
ejpam-6307	605	4	global	global	ADJ
ejpam-6307	605	5	slavery	slavery	NOUN
ejpam-6307	605	6	index	index	NOUN
ejpam-6307	605	7	.	.	PUNCT
ejpam-6307	606	1	http://www.globalslaveryindex.org/findings	http://www.globalslaveryindex.org/finding	NOUN
ejpam-6307	606	2	,	,	PUNCT
ejpam-6307	606	3	2016	2016	NUM
ejpam-6307	606	4	.	.	PUNCT
ejpam-6307	606	5	accessed	access	VERB
ejpam-6307	606	6	:	:	PUNCT
ejpam-6307	606	7	2025	2025	NUM
ejpam-6307	606	8	-	-	SYM
ejpam-6307	606	9	08	08	NUM
ejpam-6307	606	10	-	-	PUNCT
ejpam-6307	606	11	08	08	NUM
ejpam-6307	606	12	.	.	PUNCT
ejpam-6307	607	1	[	[	X
ejpam-6307	607	2	29	29	NUM
ejpam-6307	607	3	]	]	X
ejpam-6307	607	4	l.	l.	PROPN
ejpam-6307	607	5	c.	c.	PROPN
ejpam-6307	607	6	platil	platil	PROPN
ejpam-6307	607	7	and	and	CCONJ
ejpam-6307	607	8	g.	g.	PROPN
ejpam-6307	607	9	c.	c.	PROPN
ejpam-6307	607	10	petalcorin	petalcorin	PROPN
ejpam-6307	607	11	.	.	PUNCT
ejpam-6307	608	1	fuzzy	fuzzy	ADJ
ejpam-6307	608	2	γ	γ	NOUN
ejpam-6307	608	3	-	-	NOUN
ejpam-6307	608	4	semimodules	semimodule	NOUN
ejpam-6307	608	5	over	over	ADP
ejpam-6307	608	6	γ	γ	NOUN
ejpam-6307	608	7	-	-	PUNCT
ejpam-6307	608	8	semirings	semiring	NOUN
ejpam-6307	608	9	.	.	PUNCT
ejpam-6307	609	1	journal	journal	PROPN
ejpam-6307	609	2	of	of	ADP
ejpam-6307	609	3	analysis	analysis	NOUN
ejpam-6307	609	4	and	and	CCONJ
ejpam-6307	609	5	applications	application	NOUN
ejpam-6307	609	6	,	,	PUNCT
ejpam-6307	609	7	15(1):71–83	15(1):71–83	NUM
ejpam-6307	609	8	,	,	PUNCT
ejpam-6307	609	9	2017	2017	NUM
ejpam-6307	609	10	.	.	PUNCT