id	sid	tid	token	lemma	pos
ejpam-3052	1	1	european	european	PROPN
ejpam-3052	1	2	journal	journal	PROPN
ejpam-3052	1	3	of	of	ADP
ejpam-3052	1	4	pure	pure	ADJ
ejpam-3052	1	5	and	and	CCONJ
ejpam-3052	1	6	applied	apply	VERB
ejpam-3052	1	7	mathematics	mathematic	NOUN
ejpam-3052	1	8	vol	vol	NOUN
ejpam-3052	1	9	.	.	PROPN
ejpam-3052	2	1	10	10	NUM
ejpam-3052	2	2	,	,	PUNCT
ejpam-3052	2	3	no	no	INTJ
ejpam-3052	2	4	.	.	NOUN
ejpam-3052	2	5	5	5	NUM
ejpam-3052	2	6	,	,	PUNCT
ejpam-3052	2	7	2017	2017	NUM
ejpam-3052	2	8	,	,	PUNCT
ejpam-3052	2	9	1050	1050	NUM
ejpam-3052	2	10	-	-	SYM
ejpam-3052	2	11	1057	1057	NUM
ejpam-3052	2	12	issn	issn	PROPN
ejpam-3052	2	13	1307	1307	NUM
ejpam-3052	2	14	-	-	SYM
ejpam-3052	2	15	5543	5543	NUM
ejpam-3052	2	16	–	–	PUNCT
ejpam-3052	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3052	2	18	published	publish	VERB
ejpam-3052	2	19	by	by	ADP
ejpam-3052	2	20	new	new	PROPN
ejpam-3052	2	21	york	york	PROPN
ejpam-3052	2	22	business	business	PROPN
ejpam-3052	2	23	global	global	ADJ
ejpam-3052	2	24	nullity	nullity	NOUN
ejpam-3052	2	25	of	of	ADP
ejpam-3052	2	26	corona	corona	NOUN
ejpam-3052	2	27	of	of	ADP
ejpam-3052	2	28	a	a	DET
ejpam-3052	2	29	path	path	NOUN
ejpam-3052	2	30	with	with	ADP
ejpam-3052	2	31	smith	smith	PROPN
ejpam-3052	2	32	graphs	graphs	PROPN
ejpam-3052	2	33	usha	usha	PROPN
ejpam-3052	2	34	sharma1	sharma1	PROPN
ejpam-3052	2	35	,	,	PUNCT
ejpam-3052	2	36	renu	renu	PROPN
ejpam-3052	2	37	naresh1,∗	naresh1,∗	PROPN
ejpam-3052	2	38	1	1	NUM
ejpam-3052	2	39	department	department	NOUN
ejpam-3052	2	40	of	of	ADP
ejpam-3052	2	41	mathematics	mathematic	NOUN
ejpam-3052	2	42	and	and	CCONJ
ejpam-3052	2	43	statistics	statistic	NOUN
ejpam-3052	2	44	,	,	PUNCT
ejpam-3052	2	45	banasthali	banasthali	PROPN
ejpam-3052	2	46	university	university	NOUN
ejpam-3052	2	47	,	,	PUNCT
ejpam-3052	2	48	rajasthan	rajasthan	PROPN
ejpam-3052	2	49	304022	304022	NUM
ejpam-3052	2	50	,	,	PUNCT
ejpam-3052	2	51	india	india	PROPN
ejpam-3052	2	52	abstract	abstract	NOUN
ejpam-3052	2	53	.	.	PUNCT
ejpam-3052	3	1	let	let	VERB
ejpam-3052	3	2	g	g	PRON
ejpam-3052	3	3	be	be	AUX
ejpam-3052	3	4	a	a	DET
ejpam-3052	3	5	graph	graph	NOUN
ejpam-3052	3	6	and	and	CCONJ
ejpam-3052	3	7	a(g	a(g	PROPN
ejpam-3052	3	8	)	)	PUNCT
ejpam-3052	3	9	be	be	AUX
ejpam-3052	3	10	its	its	PRON
ejpam-3052	3	11	adjacency	adjacency	NOUN
ejpam-3052	3	12	matrix	matrix	NOUN
ejpam-3052	3	13	.	.	PUNCT
ejpam-3052	4	1	the	the	DET
ejpam-3052	4	2	nullity	nullity	NOUN
ejpam-3052	4	3	of	of	ADP
ejpam-3052	4	4	graph	graph	NOUN
ejpam-3052	4	5	is	be	AUX
ejpam-3052	4	6	the	the	DET
ejpam-3052	4	7	presence	presence	NOUN
ejpam-3052	4	8	of	of	ADP
ejpam-3052	4	9	zero	zero	NUM
ejpam-3052	4	10	as	as	ADP
ejpam-3052	4	11	an	an	DET
ejpam-3052	4	12	eigenvalue	eigenvalue	NOUN
ejpam-3052	4	13	in	in	ADP
ejpam-3052	4	14	the	the	DET
ejpam-3052	4	15	spectrum	spectrum	NOUN
ejpam-3052	4	16	of	of	ADP
ejpam-3052	4	17	g.	g.	PROPN
ejpam-3052	4	18	in	in	ADP
ejpam-3052	4	19	this	this	DET
ejpam-3052	4	20	paper	paper	NOUN
ejpam-3052	4	21	,	,	PUNCT
ejpam-3052	4	22	we	we	PRON
ejpam-3052	4	23	have	have	AUX
ejpam-3052	4	24	established	establish	VERB
ejpam-3052	4	25	the	the	DET
ejpam-3052	4	26	results	result	NOUN
ejpam-3052	4	27	on	on	ADP
ejpam-3052	4	28	nullity	nullity	NOUN
ejpam-3052	4	29	of	of	ADP
ejpam-3052	4	30	(	(	PUNCT
ejpam-3052	4	31	pn	pn	PROPN
ejpam-3052	4	32	�	�	PROPN
ejpam-3052	4	33	sm	sm	PROPN
ejpam-3052	4	34	)	)	PUNCT
ejpam-3052	4	35	where	where	SCONJ
ejpam-3052	4	36	sm	sm	PROPN
ejpam-3052	4	37	is	be	AUX
ejpam-3052	4	38	smith	smith	PROPN
ejpam-3052	4	39	graph	graph	NOUN
ejpam-3052	4	40	and	and	CCONJ
ejpam-3052	4	41	�	�	PROPN
ejpam-3052	4	42	is	be	AUX
ejpam-3052	4	43	corona	corona	NOUN
ejpam-3052	4	44	product	product	NOUN
ejpam-3052	4	45	.	.	PUNCT
ejpam-3052	5	1	moreover	moreover	ADV
ejpam-3052	5	2	we	we	PRON
ejpam-3052	5	3	have	have	AUX
ejpam-3052	5	4	shown	show	VERB
ejpam-3052	5	5	that	that	DET
ejpam-3052	5	6	nullity	nullity	NOUN
ejpam-3052	5	7	of	of	ADP
ejpam-3052	5	8	(	(	PUNCT
ejpam-3052	5	9	pn	pn	PROPN
ejpam-3052	5	10	�	�	PROPN
ejpam-3052	5	11	sm	sm	PROPN
ejpam-3052	5	12	)	)	PUNCT
ejpam-3052	5	13	depends	depend	VERB
ejpam-3052	5	14	upon	upon	SCONJ
ejpam-3052	5	15	the	the	DET
ejpam-3052	5	16	nullity	nullity	NOUN
ejpam-3052	5	17	of	of	ADP
ejpam-3052	5	18	sm	sm	PROPN
ejpam-3052	5	19	,	,	PUNCT
ejpam-3052	5	20	which	which	PRON
ejpam-3052	5	21	comes	come	VERB
ejpam-3052	5	22	out	out	ADP
ejpam-3052	5	23	to	to	PART
ejpam-3052	5	24	be	be	AUX
ejpam-3052	5	25	a	a	DET
ejpam-3052	5	26	multiple	multiple	NOUN
ejpam-3052	5	27	of	of	ADP
ejpam-3052	5	28	nullity	nullity	NOUN
ejpam-3052	5	29	of	of	ADP
ejpam-3052	5	30	sm	sm	PROPN
ejpam-3052	5	31	.	.	PROPN
ejpam-3052	5	32	2010	2010	NUM
ejpam-3052	5	33	mathematics	mathematic	NOUN
ejpam-3052	5	34	subject	subject	NOUN
ejpam-3052	5	35	classifications	classification	NOUN
ejpam-3052	5	36	:	:	PUNCT
ejpam-3052	5	37	05c50	05c50	NUM
ejpam-3052	5	38	key	key	ADJ
ejpam-3052	5	39	words	word	NOUN
ejpam-3052	5	40	and	and	CCONJ
ejpam-3052	5	41	phrases	phrase	NOUN
ejpam-3052	5	42	:	:	PUNCT
ejpam-3052	5	43	smith	smith	NOUN
ejpam-3052	5	44	graphs	graph	NOUN
ejpam-3052	5	45	,	,	PUNCT
ejpam-3052	5	46	eigenvalue	eigenvalue	NOUN
ejpam-3052	5	47	,	,	PUNCT
ejpam-3052	5	48	nullity	nullity	NOUN
ejpam-3052	5	49	,	,	PUNCT
ejpam-3052	5	50	corona	corona	NOUN
ejpam-3052	5	51	product	product	NOUN
ejpam-3052	5	52	1	1	NUM
ejpam-3052	5	53	.	.	PUNCT
ejpam-3052	5	54	introduction	introduction	NOUN
ejpam-3052	5	55	and	and	CCONJ
ejpam-3052	5	56	preliminaries	preliminary	NOUN
ejpam-3052	5	57	for	for	ADP
ejpam-3052	5	58	all	all	DET
ejpam-3052	5	59	terminology	terminology	NOUN
ejpam-3052	5	60	and	and	CCONJ
ejpam-3052	5	61	notations	notation	NOUN
ejpam-3052	5	62	in	in	ADP
ejpam-3052	5	63	graph	graph	NOUN
ejpam-3052	5	64	theory	theory	NOUN
ejpam-3052	5	65	and	and	CCONJ
ejpam-3052	5	66	spectral	spectral	ADJ
ejpam-3052	5	67	graph	graph	NOUN
ejpam-3052	5	68	theory	theory	NOUN
ejpam-3052	5	69	not	not	PART
ejpam-3052	5	70	especially	especially	ADV
ejpam-3052	5	71	defined	define	VERB
ejpam-3052	5	72	in	in	ADP
ejpam-3052	5	73	this	this	DET
ejpam-3052	5	74	paper	paper	NOUN
ejpam-3052	5	75	,	,	PUNCT
ejpam-3052	5	76	we	we	PRON
ejpam-3052	5	77	refer	refer	VERB
ejpam-3052	5	78	the	the	DET
ejpam-3052	5	79	reader	reader	NOUN
ejpam-3052	5	80	to	to	ADP
ejpam-3052	5	81	the	the	DET
ejpam-3052	5	82	standard	standard	ADJ
ejpam-3052	5	83	text	text	NOUN
ejpam-3052	5	84	books	book	NOUN
ejpam-3052	5	85	[	[	X
ejpam-3052	5	86	4	4	NUM
ejpam-3052	5	87	]	]	PUNCT
ejpam-3052	5	88	and	and	CCONJ
ejpam-3052	5	89	[	[	X
ejpam-3052	5	90	1	1	X
ejpam-3052	5	91	]	]	PUNCT
ejpam-3052	5	92	respectively	respectively	ADV
ejpam-3052	5	93	.	.	PUNCT
ejpam-3052	6	1	by	by	ADP
ejpam-3052	6	2	a	a	DET
ejpam-3052	6	3	graph	graph	NOUN
ejpam-3052	6	4	we	we	PRON
ejpam-3052	6	5	mean	mean	VERB
ejpam-3052	6	6	finite	finite	PROPN
ejpam-3052	6	7	,	,	PUNCT
ejpam-3052	6	8	simple	simple	ADJ
ejpam-3052	6	9	,	,	PUNCT
ejpam-3052	6	10	connected	connected	ADJ
ejpam-3052	6	11	and	and	CCONJ
ejpam-3052	6	12	undirected	undirected	ADJ
ejpam-3052	6	13	graph	graph	NOUN
ejpam-3052	6	14	.	.	PUNCT
ejpam-3052	7	1	the	the	DET
ejpam-3052	7	2	eigenvalues	eigenvalue	NOUN
ejpam-3052	7	3	of	of	ADP
ejpam-3052	7	4	a	a	DET
ejpam-3052	7	5	graph	graph	NOUN
ejpam-3052	7	6	g	g	NOUN
ejpam-3052	7	7	is	be	AUX
ejpam-3052	7	8	the	the	DET
ejpam-3052	7	9	eigenvalues	eigenvalue	NOUN
ejpam-3052	7	10	of	of	ADP
ejpam-3052	7	11	its	its	PRON
ejpam-3052	7	12	adjacency	adjacency	NOUN
ejpam-3052	7	13	matrix	matrix	NOUN
ejpam-3052	7	14	.	.	PUNCT
ejpam-3052	8	1	the	the	DET
ejpam-3052	8	2	nullity	nullity	NOUN
ejpam-3052	8	3	of	of	ADP
ejpam-3052	8	4	a	a	DET
ejpam-3052	8	5	graph	graph	NOUN
ejpam-3052	8	6	g	g	NOUN
ejpam-3052	8	7	is	be	AUX
ejpam-3052	8	8	the	the	DET
ejpam-3052	8	9	presence	presence	NOUN
ejpam-3052	8	10	of	of	ADP
ejpam-3052	8	11	zero	zero	NUM
ejpam-3052	8	12	as	as	ADP
ejpam-3052	8	13	an	an	DET
ejpam-3052	8	14	eigenvalue	eigenvalue	NOUN
ejpam-3052	8	15	in	in	ADP
ejpam-3052	8	16	the	the	DET
ejpam-3052	8	17	spectrum	spectrum	NOUN
ejpam-3052	8	18	of	of	ADP
ejpam-3052	8	19	a	a	DET
ejpam-3052	8	20	graph	graph	NOUN
ejpam-3052	8	21	g.	g.	NOUN
ejpam-3052	9	1	it	it	PRON
ejpam-3052	9	2	is	be	AUX
ejpam-3052	9	3	denoted	denote	VERB
ejpam-3052	9	4	by	by	ADP
ejpam-3052	9	5	η(g	η(g	PROPN
ejpam-3052	9	6	)	)	PUNCT
ejpam-3052	9	7	.	.	PUNCT
ejpam-3052	10	1	firstly	firstly	ADV
ejpam-3052	10	2	we	we	PRON
ejpam-3052	10	3	recall	recall	VERB
ejpam-3052	10	4	some	some	DET
ejpam-3052	10	5	basic	basic	ADJ
ejpam-3052	10	6	definitions	definition	NOUN
ejpam-3052	10	7	and	and	CCONJ
ejpam-3052	10	8	existing	exist	VERB
ejpam-3052	10	9	results	result	NOUN
ejpam-3052	10	10	from	from	ADP
ejpam-3052	10	11	[	[	X
ejpam-3052	10	12	5	5	NUM
ejpam-3052	10	13	]	]	PUNCT
ejpam-3052	10	14	.	.	PUNCT
ejpam-3052	11	1	a	a	DET
ejpam-3052	11	2	function	function	NOUN
ejpam-3052	11	3	f	f	NOUN
ejpam-3052	11	4	:	:	PUNCT
ejpam-3052	11	5	v	v	X
ejpam-3052	11	6	(	(	PUNCT
ejpam-3052	11	7	g	g	NOUN
ejpam-3052	11	8	)	)	PUNCT
ejpam-3052	11	9	→	→	SYM
ejpam-3052	12	1	r	r	NOUN
ejpam-3052	12	2	where	where	SCONJ
ejpam-3052	12	3	r	r	NOUN
ejpam-3052	12	4	is	be	AUX
ejpam-3052	12	5	the	the	DET
ejpam-3052	12	6	set	set	NOUN
ejpam-3052	12	7	of	of	ADP
ejpam-3052	12	8	real	real	ADJ
ejpam-3052	12	9	numbers	number	NOUN
ejpam-3052	12	10	,	,	PUNCT
ejpam-3052	12	11	which	which	PRON
ejpam-3052	12	12	assigns	assign	VERB
ejpam-3052	12	13	a	a	DET
ejpam-3052	12	14	weight	weight	NOUN
ejpam-3052	12	15	(	(	PUNCT
ejpam-3052	12	16	real	real	ADJ
ejpam-3052	12	17	number	number	NOUN
ejpam-3052	12	18	)	)	PUNCT
ejpam-3052	12	19	to	to	ADP
ejpam-3052	12	20	each	each	DET
ejpam-3052	12	21	vertex	vertex	NOUN
ejpam-3052	12	22	of	of	ADP
ejpam-3052	12	23	g	g	PROPN
ejpam-3052	12	24	is	be	AUX
ejpam-3052	12	25	called	call	VERB
ejpam-3052	12	26	a	a	DET
ejpam-3052	12	27	vertex	vertex	NOUN
ejpam-3052	12	28	weighting	weighting	NOUN
ejpam-3052	12	29	of	of	ADP
ejpam-3052	12	30	graph	graph	NOUN
ejpam-3052	12	31	g.	g.	PROPN
ejpam-3052	12	32	if	if	SCONJ
ejpam-3052	12	33	there	there	PRON
ejpam-3052	12	34	exist	exist	VERB
ejpam-3052	12	35	at	at	ADV
ejpam-3052	12	36	least	least	ADV
ejpam-3052	12	37	one	one	NUM
ejpam-3052	12	38	vertex	vertex	NOUN
ejpam-3052	12	39	v	v	ADP
ejpam-3052	12	40	∈	∈	NOUN
ejpam-3052	12	41	v	v	NOUN
ejpam-3052	12	42	(	(	PUNCT
ejpam-3052	12	43	g	g	NOUN
ejpam-3052	12	44	)	)	PUNCT
ejpam-3052	12	45	for	for	ADP
ejpam-3052	12	46	which	which	PRON
ejpam-3052	12	47	f(v	f(v	NOUN
ejpam-3052	12	48	)	)	PUNCT
ejpam-3052	12	49	6=	6=	ADP
ejpam-3052	12	50	0	0	NUM
ejpam-3052	12	51	,	,	PUNCT
ejpam-3052	12	52	then	then	ADV
ejpam-3052	12	53	it	it	PRON
ejpam-3052	12	54	is	be	AUX
ejpam-3052	12	55	called	call	VERB
ejpam-3052	12	56	non	non	ADJ
ejpam-3052	12	57	trivial	trivial	ADJ
ejpam-3052	12	58	weighting	weighting	NOUN
ejpam-3052	12	59	.	.	PUNCT
ejpam-3052	13	1	a	a	DET
ejpam-3052	13	2	non	non	ADJ
ejpam-3052	13	3	-	-	ADJ
ejpam-3052	13	4	trivial	trivial	ADJ
ejpam-3052	13	5	vertex	vertex	NOUN
ejpam-3052	13	6	weighting	weighting	NOUN
ejpam-3052	13	7	of	of	ADP
ejpam-3052	13	8	a	a	DET
ejpam-3052	13	9	graph	graph	NOUN
ejpam-3052	13	10	g	g	NOUN
ejpam-3052	13	11	is	be	AUX
ejpam-3052	13	12	called	call	VERB
ejpam-3052	13	13	a	a	DET
ejpam-3052	13	14	zero	zero	NUM
ejpam-3052	13	15	-	-	PUNCT
ejpam-3052	13	16	sum	sum	NOUN
ejpam-3052	13	17	weighting	weighting	NOUN
ejpam-3052	13	18	of	of	ADP
ejpam-3052	13	19	a	a	DET
ejpam-3052	13	20	graph	graph	NOUN
ejpam-3052	13	21	g	g	NOUN
ejpam-3052	13	22	if	if	SCONJ
ejpam-3052	13	23	for	for	ADP
ejpam-3052	13	24	each	each	DET
ejpam-3052	13	25	v	v	NUM
ejpam-3052	13	26	∈	∈	PROPN
ejpam-3052	13	27	v	v	NOUN
ejpam-3052	13	28	(	(	PUNCT
ejpam-3052	13	29	g	g	NOUN
ejpam-3052	13	30	)	)	PUNCT
ejpam-3052	13	31	,	,	PUNCT
ejpam-3052	13	32	∑	∑	PUNCT
ejpam-3052	13	33	f(u	f(u	PROPN
ejpam-3052	13	34	)	)	PUNCT
ejpam-3052	13	35	=	=	SYM
ejpam-3052	13	36	0	0	NUM
ejpam-3052	13	37	,	,	PUNCT
ejpam-3052	13	38	where	where	SCONJ
ejpam-3052	13	39	∑	∑	PUNCT
ejpam-3052	13	40	is	be	AUX
ejpam-3052	13	41	taken	take	VERB
ejpam-3052	13	42	to	to	ADP
ejpam-3052	13	43	all	all	DET
ejpam-3052	13	44	neighbor	neighbor	NOUN
ejpam-3052	13	45	v.	v.	ADV
ejpam-3052	13	46	for	for	ADP
ejpam-3052	13	47	any	any	DET
ejpam-3052	13	48	two	two	NUM
ejpam-3052	13	49	non	non	ADJ
ejpam-3052	13	50	zero	zero	NUM
ejpam-3052	13	51	real	real	ADJ
ejpam-3052	13	52	number	number	NOUN
ejpam-3052	13	53	a	a	PRON
ejpam-3052	13	54	and	and	CCONJ
ejpam-3052	13	55	b	b	NOUN
ejpam-3052	13	56	the	the	DET
ejpam-3052	13	57	zero	zero	NUM
ejpam-3052	13	58	-	-	PUNCT
ejpam-3052	13	59	sum	sum	NOUN
ejpam-3052	13	60	weighting	weighting	NOUN
ejpam-3052	13	61	of	of	ADP
ejpam-3052	13	62	a	a	DET
ejpam-3052	13	63	graph	graph	NOUN
ejpam-3052	13	64	g	g	NOUN
ejpam-3052	13	65	is	be	AUX
ejpam-3052	13	66	shown	show	VERB
ejpam-3052	13	67	in	in	ADP
ejpam-3052	13	68	figure	figure	NOUN
ejpam-3052	13	69	1	1	NUM
ejpam-3052	13	70	.	.	PUNCT
ejpam-3052	14	1	the	the	DET
ejpam-3052	14	2	maximum	maximum	ADJ
ejpam-3052	14	3	number	number	NOUN
ejpam-3052	14	4	of	of	ADP
ejpam-3052	14	5	non	non	ADJ
ejpam-3052	14	6	-	-	ADJ
ejpam-3052	14	7	zero	zero	ADJ
ejpam-3052	14	8	independent	independent	ADJ
ejpam-3052	14	9	variables	variable	NOUN
ejpam-3052	14	10	used	use	VERB
ejpam-3052	14	11	in	in	ADP
ejpam-3052	14	12	a	a	DET
ejpam-3052	14	13	zero	zero	NUM
ejpam-3052	14	14	-	-	PUNCT
ejpam-3052	14	15	sum	sum	NOUN
ejpam-3052	14	16	weighting	weighting	NOUN
ejpam-3052	14	17	is	be	AUX
ejpam-3052	14	18	called	call	VERB
ejpam-3052	14	19	a	a	DET
ejpam-3052	14	20	high	high	ADJ
ejpam-3052	14	21	zero	zero	NUM
ejpam-3052	14	22	-	-	PUNCT
ejpam-3052	14	23	sum	sum	NOUN
ejpam-3052	14	24	weighting	weighting	NOUN
ejpam-3052	14	25	of	of	ADP
ejpam-3052	14	26	the	the	DET
ejpam-3052	14	27	graph	graph	NOUN
ejpam-3052	14	28	.	.	PUNCT
ejpam-3052	15	1	∗corresponding	∗corresponde	VERB
ejpam-3052	15	2	author	author	NOUN
ejpam-3052	15	3	.	.	PUNCT
ejpam-3052	16	1	email	email	NOUN
ejpam-3052	16	2	addresses	address	NOUN
ejpam-3052	16	3	:	:	PUNCT
ejpam-3052	16	4	usha.shrma94@yahoo.com	usha.shrma94@yahoo.com	X
ejpam-3052	16	5	(	(	PUNCT
ejpam-3052	16	6	u.	u.	PROPN
ejpam-3052	16	7	sharma	sharma	PROPN
ejpam-3052	16	8	)	)	PUNCT
ejpam-3052	16	9	,	,	PUNCT
ejpam-3052	16	10	renunaresh1@gmail.com	renunaresh1@gmail.com	X
ejpam-3052	16	11	(	(	PUNCT
ejpam-3052	16	12	r.	r.	PROPN
ejpam-3052	16	13	naresh	naresh	PROPN
ejpam-3052	16	14	)	)	PUNCT
ejpam-3052	16	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3052	17	1	1050	1050	NUM
ejpam-3052	18	1	c	c	X
ejpam-3052	18	2	©	©	PROPN
ejpam-3052	18	3	2017	2017	NUM
ejpam-3052	18	4	ejpam	ejpam	VERB
ejpam-3052	18	5	all	all	DET
ejpam-3052	18	6	rights	right	NOUN
ejpam-3052	18	7	reserved	reserve	VERB
ejpam-3052	18	8	.	.	PUNCT
ejpam-3052	19	1	u.	u.	PROPN
ejpam-3052	19	2	sharma	sharma	PROPN
ejpam-3052	19	3	,	,	PUNCT
ejpam-3052	19	4	r.	r.	PROPN
ejpam-3052	19	5	naresh	naresh	PROPN
ejpam-3052	19	6	/	/	SYM
ejpam-3052	19	7	eur	eur	PROPN
ejpam-3052	19	8	.	.	PUNCT
ejpam-3052	20	1	j.	j.	PROPN
ejpam-3052	20	2	pure	pure	PROPN
ejpam-3052	20	3	appl	appl	PROPN
ejpam-3052	20	4	.	.	PROPN
ejpam-3052	20	5	math	math	PROPN
ejpam-3052	20	6	,	,	PUNCT
ejpam-3052	20	7	10	10	NUM
ejpam-3052	20	8	(	(	PUNCT
ejpam-3052	20	9	5	5	NUM
ejpam-3052	20	10	)	)	PUNCT
ejpam-3052	20	11	(	(	PUNCT
ejpam-3052	20	12	2017	2017	NUM
ejpam-3052	20	13	)	)	PUNCT
ejpam-3052	20	14	,	,	PUNCT
ejpam-3052	20	15	1050	1050	NUM
ejpam-3052	20	16	-	-	SYM
ejpam-3052	20	17	1057	1057	NUM
ejpam-3052	20	18	1051	1051	NUM
ejpam-3052	20	19	0	0	NUM
ejpam-3052	21	1	a	a	DET
ejpam-3052	21	2	b	b	NOUN
ejpam-3052	21	3	-b	-b	PUNCT
ejpam-3052	21	4	-a	-a	PROPN
ejpam-3052	21	5	-b	-b	PUNCT
ejpam-3052	21	6	a	a	PRON
ejpam-3052	21	7	b	b	X
ejpam-3052	21	8	-a	-a	X
ejpam-3052	21	9	figure	figure	NOUN
ejpam-3052	21	10	1	1	NUM
ejpam-3052	21	11	:	:	PUNCT
ejpam-3052	21	12	g.	g.	NOUN
ejpam-3052	21	13	in	in	ADP
ejpam-3052	21	14	a	a	DET
ejpam-3052	21	15	high	high	ADJ
ejpam-3052	21	16	zero	zero	NUM
ejpam-3052	21	17	-	-	PUNCT
ejpam-3052	21	18	sum	sum	NOUN
ejpam-3052	21	19	weighting	weighting	NOUN
ejpam-3052	21	20	of	of	ADP
ejpam-3052	21	21	g	g	NOUN
ejpam-3052	21	22	,	,	PUNCT
ejpam-3052	21	23	the	the	DET
ejpam-3052	21	24	maximum	maximum	ADJ
ejpam-3052	21	25	number	number	NOUN
ejpam-3052	21	26	of	of	ADP
ejpam-3052	21	27	non	non	ADJ
ejpam-3052	21	28	-	-	ADJ
ejpam-3052	21	29	zero	zero	ADJ
ejpam-3052	21	30	independent	independent	ADJ
ejpam-3052	21	31	variables	variable	NOUN
ejpam-3052	21	32	is	be	AUX
ejpam-3052	21	33	equal	equal	ADJ
ejpam-3052	21	34	to	to	ADP
ejpam-3052	21	35	the	the	DET
ejpam-3052	21	36	nullity	nullity	NOUN
ejpam-3052	21	37	of	of	ADP
ejpam-3052	21	38	g.	g.	PROPN
ejpam-3052	21	39	for	for	ADP
ejpam-3052	21	40	a	a	DET
ejpam-3052	21	41	graph	graph	NOUN
ejpam-3052	21	42	g	g	NOUN
ejpam-3052	21	43	,	,	PUNCT
ejpam-3052	21	44	shown	show	VERB
ejpam-3052	21	45	in	in	ADP
ejpam-3052	21	46	figure	figure	NOUN
ejpam-3052	21	47	1	1	NUM
ejpam-3052	21	48	,	,	PUNCT
ejpam-3052	21	49	we	we	PRON
ejpam-3052	21	50	have	have	AUX
ejpam-3052	21	51	used	use	VERB
ejpam-3052	21	52	two	two	NUM
ejpam-3052	21	53	non	non	ADJ
ejpam-3052	21	54	-	-	ADJ
ejpam-3052	21	55	zero	zero	ADJ
ejpam-3052	21	56	independent	independent	ADJ
ejpam-3052	21	57	variables	variable	NOUN
ejpam-3052	21	58	a	a	PRON
ejpam-3052	21	59	and	and	CCONJ
ejpam-3052	21	60	b	b	NOUN
ejpam-3052	21	61	for	for	ADP
ejpam-3052	21	62	high	high	ADJ
ejpam-3052	21	63	zero	zero	NUM
ejpam-3052	21	64	-	-	PUNCT
ejpam-3052	21	65	sum	sum	NOUN
ejpam-3052	21	66	weighting	weighting	NOUN
ejpam-3052	21	67	of	of	ADP
ejpam-3052	21	68	g.	g.	PROPN
ejpam-3052	21	69	in	in	ADP
ejpam-3052	21	70	view	view	NOUN
ejpam-3052	21	71	of	of	ADP
ejpam-3052	21	72	the	the	DET
ejpam-3052	21	73	above	above	ADJ
ejpam-3052	21	74	definition	definition	NOUN
ejpam-3052	21	75	,	,	PUNCT
ejpam-3052	21	76	we	we	PRON
ejpam-3052	21	77	conclude	conclude	VERB
ejpam-3052	21	78	that	that	SCONJ
ejpam-3052	21	79	η(g	η(g	PROPN
ejpam-3052	21	80	)	)	PUNCT
ejpam-3052	21	81	=	=	SYM
ejpam-3052	21	82	2	2	X
ejpam-3052	21	83	.	.	X
ejpam-3052	21	84	for	for	ADP
ejpam-3052	21	85	a	a	DET
ejpam-3052	21	86	connected	connected	ADJ
ejpam-3052	21	87	graph	graph	NOUN
ejpam-3052	21	88	,	,	PUNCT
ejpam-3052	21	89	two	two	NUM
ejpam-3052	21	90	non	non	ADJ
ejpam-3052	21	91	-	-	ADJ
ejpam-3052	21	92	adjacent	adjacent	ADJ
ejpam-3052	21	93	vertices	vertex	NOUN
ejpam-3052	21	94	are	be	AUX
ejpam-3052	21	95	said	say	VERB
ejpam-3052	21	96	to	to	PART
ejpam-3052	21	97	be	be	AUX
ejpam-3052	21	98	co	co	NOUN
ejpam-3052	21	99	-	-	NOUN
ejpam-3052	21	100	neighbor	neighbor	NOUN
ejpam-3052	21	101	vertices	vertice	VERB
ejpam-3052	21	102	if	if	SCONJ
ejpam-3052	21	103	they	they	PRON
ejpam-3052	21	104	have	have	VERB
ejpam-3052	21	105	same	same	ADJ
ejpam-3052	21	106	set	set	NOUN
ejpam-3052	21	107	of	of	ADP
ejpam-3052	21	108	neighbors	neighbor	NOUN
ejpam-3052	21	109	.	.	PUNCT
ejpam-3052	22	1	let	let	VERB
ejpam-3052	22	2	g1	g1	PROPN
ejpam-3052	22	3	and	and	CCONJ
ejpam-3052	22	4	g2	g2	PROPN
ejpam-3052	22	5	be	be	VERB
ejpam-3052	22	6	two	two	NUM
ejpam-3052	22	7	graphs	graph	NOUN
ejpam-3052	22	8	with	with	ADP
ejpam-3052	22	9	vertex	vertex	NOUN
ejpam-3052	22	10	set	set	VERB
ejpam-3052	22	11	v	v	NOUN
ejpam-3052	22	12	(	(	PUNCT
ejpam-3052	22	13	g1	g1	PROPN
ejpam-3052	22	14	)	)	PUNCT
ejpam-3052	22	15	=	=	SYM
ejpam-3052	22	16	{	{	PUNCT
ejpam-3052	22	17	v1	v1	PROPN
ejpam-3052	22	18	,	,	PUNCT
ejpam-3052	22	19	v2	v2	PROPN
ejpam-3052	22	20	,	,	PUNCT
ejpam-3052	22	21	.	.	PUNCT
ejpam-3052	22	22	.	.	PUNCT
ejpam-3052	23	1	.	.	PUNCT
ejpam-3052	24	1	,	,	PUNCT
ejpam-3052	24	2	vp1	vp1	CCONJ
ejpam-3052	24	3	}	}	PUNCT
ejpam-3052	24	4	and	and	CCONJ
ejpam-3052	24	5	v	v	X
ejpam-3052	24	6	(	(	PUNCT
ejpam-3052	24	7	g2	g2	PROPN
ejpam-3052	24	8	)	)	PUNCT
ejpam-3052	24	9	=	=	PRON
ejpam-3052	24	10	{	{	PUNCT
ejpam-3052	24	11	u1	u1	NOUN
ejpam-3052	24	12	,	,	PUNCT
ejpam-3052	24	13	u2	u2	NOUN
ejpam-3052	24	14	,	,	PUNCT
ejpam-3052	24	15	.	.	PUNCT
ejpam-3052	24	16	.	.	PUNCT
ejpam-3052	25	1	.	.	PUNCT
ejpam-3052	26	1	,	,	PUNCT
ejpam-3052	26	2	up2	up2	PROPN
ejpam-3052	26	3	}	}	PUNCT
ejpam-3052	26	4	,	,	PUNCT
ejpam-3052	26	5	respectively	respectively	ADV
ejpam-3052	26	6	.	.	PUNCT
ejpam-3052	27	1	then	then	ADV
ejpam-3052	27	2	,	,	PUNCT
ejpam-3052	27	3	the	the	DET
ejpam-3052	27	4	corona	corona	NOUN
ejpam-3052	27	5	of	of	ADP
ejpam-3052	27	6	g1	g1	PROPN
ejpam-3052	27	7	and	and	CCONJ
ejpam-3052	27	8	g2	g2	PROPN
ejpam-3052	27	9	,	,	PUNCT
ejpam-3052	27	10	denoted	denote	VERB
ejpam-3052	27	11	by	by	ADP
ejpam-3052	27	12	g1	g1	PROPN
ejpam-3052	27	13	�	�	PROPN
ejpam-3052	27	14	g2	g2	PROPN
ejpam-3052	27	15	is	be	AUX
ejpam-3052	27	16	defined	define	VERB
ejpam-3052	27	17	as	as	SCONJ
ejpam-3052	27	18	take	take	VERB
ejpam-3052	27	19	one	one	NUM
ejpam-3052	27	20	copy	copy	NOUN
ejpam-3052	27	21	of	of	ADP
ejpam-3052	27	22	g1	g1	PROPN
ejpam-3052	27	23	and	and	CCONJ
ejpam-3052	27	24	p1	p1	PROPN
ejpam-3052	27	25	copies	copy	NOUN
ejpam-3052	27	26	of	of	ADP
ejpam-3052	27	27	g2	g2	PROPN
ejpam-3052	27	28	by	by	ADP
ejpam-3052	27	29	adjoining	adjoin	VERB
ejpam-3052	27	30	ith	ith	PROPN
ejpam-3052	27	31	vertex	vertex	NOUN
ejpam-3052	27	32	of	of	ADP
ejpam-3052	27	33	g1	g1	PROPN
ejpam-3052	27	34	to	to	ADP
ejpam-3052	27	35	each	each	DET
ejpam-3052	27	36	vertex	vertex	NOUN
ejpam-3052	27	37	of	of	ADP
ejpam-3052	27	38	g2	g2	PROPN
ejpam-3052	27	39	in	in	ADP
ejpam-3052	27	40	ith	ith	PROPN
ejpam-3052	27	41	copy	copy	NOUN
ejpam-3052	27	42	.	.	PUNCT
ejpam-3052	28	1	the	the	DET
ejpam-3052	28	2	following	follow	VERB
ejpam-3052	28	3	lemma	lemma	PROPN
ejpam-3052	28	4	is	be	AUX
ejpam-3052	28	5	important	important	ADJ
ejpam-3052	28	6	in	in	ADP
ejpam-3052	28	7	the	the	DET
ejpam-3052	28	8	study	study	NOUN
ejpam-3052	28	9	of	of	ADP
ejpam-3052	28	10	nullity	nullity	NOUN
ejpam-3052	28	11	of	of	ADP
ejpam-3052	28	12	a	a	DET
ejpam-3052	28	13	graph	graph	NOUN
ejpam-3052	28	14	g	g	NOUN
ejpam-3052	28	15	and	and	CCONJ
ejpam-3052	28	16	is	be	AUX
ejpam-3052	28	17	known	know	VERB
ejpam-3052	28	18	as	as	ADP
ejpam-3052	28	19	co	co	NOUN
ejpam-3052	28	20	-	-	NOUN
ejpam-3052	28	21	neighbor	neighbor	ADJ
ejpam-3052	28	22	lemma	lemma	PROPN
ejpam-3052	28	23	.	.	PUNCT
ejpam-3052	29	1	lemma	lemma	PROPN
ejpam-3052	29	2	1	1	X
ejpam-3052	29	3	.	.	PUNCT
ejpam-3052	30	1	let	let	VERB
ejpam-3052	30	2	g	g	PRON
ejpam-3052	30	3	be	be	AUX
ejpam-3052	30	4	a	a	DET
ejpam-3052	30	5	connected	connected	ADJ
ejpam-3052	30	6	graph	graph	NOUN
ejpam-3052	30	7	and	and	CCONJ
ejpam-3052	30	8	vi	vi	PROPN
ejpam-3052	30	9	and	and	CCONJ
ejpam-3052	30	10	vj	vj	INTJ
ejpam-3052	30	11	be	be	AUX
ejpam-3052	30	12	two	two	NUM
ejpam-3052	30	13	co	co	ADJ
ejpam-3052	30	14	-	-	NOUN
ejpam-3052	30	15	neighbor	neighbor	ADJ
ejpam-3052	30	16	vertices	vertex	NOUN
ejpam-3052	30	17	of	of	ADP
ejpam-3052	30	18	g.	g.	PROPN
ejpam-3052	30	19	then	then	ADV
ejpam-3052	30	20	,	,	PUNCT
ejpam-3052	30	21	η(g	η(g	PROPN
ejpam-3052	30	22	)	)	PUNCT
ejpam-3052	30	23	=	=	PUNCT
ejpam-3052	30	24	η(g−	η(g−	NOUN
ejpam-3052	30	25	vi	vi	PROPN
ejpam-3052	30	26	)	)	PUNCT
ejpam-3052	30	27	+	+	CCONJ
ejpam-3052	30	28	1	1	X
ejpam-3052	30	29	=	=	SYM
ejpam-3052	30	30	η(g−	η(g−	NOUN
ejpam-3052	30	31	vj	vj	NOUN
ejpam-3052	30	32	)	)	PUNCT
ejpam-3052	30	33	+	+	NOUN
ejpam-3052	30	34	1	1	X
ejpam-3052	30	35	.	.	X
ejpam-3052	30	36	a	a	DET
ejpam-3052	30	37	graph	graph	NOUN
ejpam-3052	30	38	is	be	AUX
ejpam-3052	30	39	called	call	VERB
ejpam-3052	30	40	smith	smith	PROPN
ejpam-3052	30	41	if	if	SCONJ
ejpam-3052	30	42	one	one	NUM
ejpam-3052	30	43	of	of	ADP
ejpam-3052	30	44	its	its	PRON
ejpam-3052	30	45	eigenvalue	eigenvalue	NOUN
ejpam-3052	30	46	is	be	AUX
ejpam-3052	30	47	2	2	NUM
ejpam-3052	30	48	and	and	CCONJ
ejpam-3052	30	49	a	a	DET
ejpam-3052	30	50	smith	smith	NOUN
ejpam-3052	30	51	graph	graph	NOUN
ejpam-3052	30	52	on	on	ADP
ejpam-3052	30	53	m	m	NOUN
ejpam-3052	30	54	vertices	vertex	NOUN
ejpam-3052	30	55	is	be	AUX
ejpam-3052	30	56	denoted	denote	VERB
ejpam-3052	30	57	by	by	ADP
ejpam-3052	30	58	sm	sm	PROPN
ejpam-3052	30	59	.	.	PROPN
ejpam-3052	30	60	upto	upto	PROPN
ejpam-3052	30	61	isomorphic	isomorphic	NOUN
ejpam-3052	30	62	,	,	PUNCT
ejpam-3052	30	63	there	there	PRON
ejpam-3052	30	64	are	be	VERB
ejpam-3052	30	65	precisely	precisely	ADV
ejpam-3052	30	66	6	6	NUM
ejpam-3052	30	67	kinds	kind	NOUN
ejpam-3052	30	68	of	of	ADP
ejpam-3052	30	69	smith	smith	NOUN
ejpam-3052	30	70	graphs	graph	NOUN
ejpam-3052	30	71	namely	namely	ADV
ejpam-3052	30	72	wm;m	wm;m	PUNCT
ejpam-3052	30	73	≥	≥	NUM
ejpam-3052	30	74	6	6	NUM
ejpam-3052	30	75	(	(	PUNCT
ejpam-3052	30	76	double	double	ADJ
ejpam-3052	30	77	head	head	NOUN
ejpam-3052	30	78	snake	snake	NOUN
ejpam-3052	30	79	graph	graph	NOUN
ejpam-3052	30	80	)	)	PUNCT
ejpam-3052	30	81	,	,	PUNCT
ejpam-3052	30	82	cm;m	cm;m	NUM
ejpam-3052	30	83	≥	≥	NUM
ejpam-3052	30	84	3	3	NUM
ejpam-3052	30	85	(	(	PUNCT
ejpam-3052	30	86	cycle	cycle	NOUN
ejpam-3052	30	87	graph	graph	NOUN
ejpam-3052	30	88	)	)	PUNCT
ejpam-3052	30	89	,	,	PUNCT
ejpam-3052	30	90	h7	h7	PROPN
ejpam-3052	30	91	,	,	PUNCT
ejpam-3052	30	92	h8	h8	PROPN
ejpam-3052	30	93	,	,	PUNCT
ejpam-3052	30	94	h9	h9	NOUN
ejpam-3052	30	95	and	and	CCONJ
ejpam-3052	30	96	k1,4	k1,4	PROPN
ejpam-3052	30	97	.	.	PUNCT
ejpam-3052	31	1	from	from	ADP
ejpam-3052	31	2	[	[	X
ejpam-3052	31	3	2	2	NUM
ejpam-3052	31	4	]	]	PUNCT
ejpam-3052	31	5	except	except	SCONJ
ejpam-3052	31	6	k1,4	k1,4	PROPN
ejpam-3052	31	7	other	other	ADJ
ejpam-3052	31	8	smith	smith	PROPN
ejpam-3052	31	9	graphs	graph	NOUN
ejpam-3052	31	10	(	(	PUNCT
ejpam-3052	31	11	wm;m	wm;m	X
ejpam-3052	31	12	≥	≥	NOUN
ejpam-3052	31	13	6	6	NUM
ejpam-3052	31	14	,	,	PUNCT
ejpam-3052	31	15	cm;m	cm;m	PRON
ejpam-3052	31	16	≥	≥	NOUN
ejpam-3052	31	17	3	3	NUM
ejpam-3052	31	18	,	,	PUNCT
ejpam-3052	31	19	h7	h7	PROPN
ejpam-3052	31	20	,	,	PUNCT
ejpam-3052	31	21	h9	h9	NOUN
ejpam-3052	31	22	)	)	PUNCT
ejpam-3052	31	23	are	be	AUX
ejpam-3052	31	24	extended	extend	VERB
ejpam-3052	31	25	form	form	NOUN
ejpam-3052	31	26	of	of	ADP
ejpam-3052	31	27	dynkin	dynkin	ADJ
ejpam-3052	31	28	graphs	graph	NOUN
ejpam-3052	31	29	(	(	PUNCT
ejpam-3052	31	30	d̃m	d̃m	PROPN
ejpam-3052	31	31	,	,	PUNCT
ejpam-3052	31	32	ãm	ãm	NOUN
ejpam-3052	31	33	,	,	PUNCT
ejpam-3052	31	34	ẽ6	ẽ6	PROPN
ejpam-3052	31	35	,	,	PUNCT
ejpam-3052	31	36	ẽ7	ẽ7	NUM
ejpam-3052	31	37	)	)	PUNCT
ejpam-3052	31	38	and	and	CCONJ
ejpam-3052	31	39	h8	h8	PROPN
ejpam-3052	31	40	is	be	AUX
ejpam-3052	31	41	dynkin	dynkin	ADJ
ejpam-3052	31	42	graph	graph	NOUN
ejpam-3052	31	43	e8	e8	PROPN
ejpam-3052	31	44	.	.	PUNCT
ejpam-3052	32	1	the	the	DET
ejpam-3052	32	2	concept	concept	NOUN
ejpam-3052	32	3	of	of	ADP
ejpam-3052	32	4	nullity	nullity	NOUN
ejpam-3052	32	5	is	be	AUX
ejpam-3052	32	6	very	very	ADV
ejpam-3052	32	7	much	much	ADV
ejpam-3052	32	8	applicable	applicable	ADJ
ejpam-3052	32	9	for	for	ADP
ejpam-3052	32	10	the	the	DET
ejpam-3052	32	11	stability	stability	NOUN
ejpam-3052	32	12	of	of	ADP
ejpam-3052	32	13	unsaturated	unsaturated	ADJ
ejpam-3052	32	14	conjugate	conjugate	ADJ
ejpam-3052	32	15	hydrocarbons	hydrocarbon	NOUN
ejpam-3052	32	16	molecules	molecule	NOUN
ejpam-3052	32	17	by	by	ADP
ejpam-3052	32	18	huckel	huckel	NOUN
ejpam-3052	32	19	molecular	molecular	ADJ
ejpam-3052	32	20	orbital	orbital	ADJ
ejpam-3052	32	21	theory	theory	NOUN
ejpam-3052	32	22	(	(	PUNCT
ejpam-3052	32	23	hmo	hmo	NOUN
ejpam-3052	32	24	)	)	PUNCT
ejpam-3052	33	1	[	[	X
ejpam-3052	33	2	3	3	NUM
ejpam-3052	33	3	]	]	PUNCT
ejpam-3052	33	4	.	.	PUNCT
ejpam-3052	34	1	according	accord	VERB
ejpam-3052	34	2	to	to	ADP
ejpam-3052	34	3	hmo	hmo	PROPN
ejpam-3052	34	4	theory	theory	NOUN
ejpam-3052	34	5	,	,	PUNCT
ejpam-3052	34	6	following	follow	VERB
ejpam-3052	34	7	two	two	NUM
ejpam-3052	34	8	cases	case	NOUN
ejpam-3052	34	9	occurs	occur	VERB
ejpam-3052	34	10	:	:	PUNCT
ejpam-3052	34	11	(	(	PUNCT
ejpam-3052	34	12	i	i	NOUN
ejpam-3052	34	13	)	)	PUNCT
ejpam-3052	34	14	if	if	SCONJ
ejpam-3052	34	15	η(g	η(g	PROPN
ejpam-3052	34	16	)	)	PUNCT
ejpam-3052	34	17	>	>	X
ejpam-3052	35	1	0	0	NUM
ejpam-3052	35	2	,	,	PUNCT
ejpam-3052	35	3	then	then	ADV
ejpam-3052	35	4	the	the	DET
ejpam-3052	35	5	isomorphic	isomorphic	ADJ
ejpam-3052	35	6	chemical	chemical	NOUN
ejpam-3052	35	7	molecule	molecule	NOUN
ejpam-3052	35	8	is	be	AUX
ejpam-3052	35	9	more	more	ADV
ejpam-3052	35	10	reactive	reactive	ADJ
ejpam-3052	35	11	and	and	CCONJ
ejpam-3052	35	12	unstable	unstable	ADJ
ejpam-3052	35	13	.	.	PUNCT
ejpam-3052	36	1	u.	u.	PROPN
ejpam-3052	36	2	sharma	sharma	PROPN
ejpam-3052	36	3	,	,	PUNCT
ejpam-3052	36	4	r.	r.	PROPN
ejpam-3052	36	5	naresh	naresh	PROPN
ejpam-3052	36	6	/	/	SYM
ejpam-3052	36	7	eur	eur	PROPN
ejpam-3052	36	8	.	.	PUNCT
ejpam-3052	37	1	j.	j.	PROPN
ejpam-3052	37	2	pure	pure	PROPN
ejpam-3052	37	3	appl	appl	PROPN
ejpam-3052	37	4	.	.	PROPN
ejpam-3052	37	5	math	math	PROPN
ejpam-3052	37	6	,	,	PUNCT
ejpam-3052	37	7	10	10	NUM
ejpam-3052	37	8	(	(	PUNCT
ejpam-3052	37	9	5	5	NUM
ejpam-3052	37	10	)	)	PUNCT
ejpam-3052	37	11	(	(	PUNCT
ejpam-3052	37	12	2017	2017	NUM
ejpam-3052	37	13	)	)	PUNCT
ejpam-3052	37	14	,	,	PUNCT
ejpam-3052	37	15	1050	1050	NUM
ejpam-3052	37	16	-	-	SYM
ejpam-3052	37	17	1057	1057	NUM
ejpam-3052	37	18	1052	1052	NUM
ejpam-3052	37	19	(	(	PUNCT
ejpam-3052	37	20	ii	ii	NOUN
ejpam-3052	37	21	)	)	PUNCT
ejpam-3052	37	22	if	if	SCONJ
ejpam-3052	37	23	η(g	η(g	NUM
ejpam-3052	37	24	)	)	PUNCT
ejpam-3052	37	25	=	=	SYM
ejpam-3052	37	26	0	0	NUM
ejpam-3052	37	27	,	,	PUNCT
ejpam-3052	37	28	then	then	ADV
ejpam-3052	37	29	the	the	DET
ejpam-3052	37	30	isomorphic	isomorphic	ADJ
ejpam-3052	37	31	chemical	chemical	NOUN
ejpam-3052	37	32	molecule	molecule	NOUN
ejpam-3052	37	33	is	be	AUX
ejpam-3052	37	34	stable	stable	ADJ
ejpam-3052	37	35	and	and	CCONJ
ejpam-3052	37	36	less	less	ADV
ejpam-3052	37	37	reactive	reactive	ADJ
ejpam-3052	37	38	.	.	PUNCT
ejpam-3052	38	1	motivated	motivate	VERB
ejpam-3052	38	2	by	by	ADP
ejpam-3052	38	3	the	the	DET
ejpam-3052	38	4	earlier	early	ADJ
ejpam-3052	38	5	study	study	NOUN
ejpam-3052	38	6	on	on	ADP
ejpam-3052	38	7	the	the	DET
ejpam-3052	38	8	nullity	nullity	NOUN
ejpam-3052	38	9	of	of	ADP
ejpam-3052	38	10	a	a	DET
ejpam-3052	38	11	graph	graph	NOUN
ejpam-3052	38	12	.	.	PUNCT
ejpam-3052	39	1	here	here	ADV
ejpam-3052	39	2	,	,	PUNCT
ejpam-3052	39	3	we	we	PRON
ejpam-3052	39	4	have	have	AUX
ejpam-3052	39	5	determined	determine	VERB
ejpam-3052	39	6	the	the	DET
ejpam-3052	39	7	nullity	nullity	NOUN
ejpam-3052	39	8	of	of	ADP
ejpam-3052	39	9	corona	corona	NOUN
ejpam-3052	39	10	of	of	ADP
ejpam-3052	39	11	a	a	DET
ejpam-3052	39	12	path	path	NOUN
ejpam-3052	39	13	with	with	ADP
ejpam-3052	39	14	smith	smith	NOUN
ejpam-3052	39	15	graphs	graph	NOUN
ejpam-3052	39	16	.	.	PUNCT
ejpam-3052	40	1	2	2	X
ejpam-3052	40	2	.	.	X
ejpam-3052	40	3	main	main	ADJ
ejpam-3052	40	4	results	result	NOUN
ejpam-3052	40	5	in	in	ADP
ejpam-3052	40	6	this	this	DET
ejpam-3052	40	7	section	section	NOUN
ejpam-3052	40	8	,	,	PUNCT
ejpam-3052	40	9	we	we	PRON
ejpam-3052	40	10	study	study	VERB
ejpam-3052	40	11	the	the	DET
ejpam-3052	40	12	nullity	nullity	NOUN
ejpam-3052	40	13	of	of	ADP
ejpam-3052	40	14	corona	corona	NOUN
ejpam-3052	40	15	of	of	ADP
ejpam-3052	40	16	a	a	DET
ejpam-3052	40	17	path	path	NOUN
ejpam-3052	40	18	with	with	ADP
ejpam-3052	40	19	smith	smith	PROPN
ejpam-3052	40	20	graphs	graph	NOUN
ejpam-3052	40	21	.	.	PUNCT
ejpam-3052	41	1	lemma	lemma	PROPN
ejpam-3052	41	2	2	2	NUM
ejpam-3052	41	3	.	.	PUNCT
ejpam-3052	42	1	for	for	ADP
ejpam-3052	42	2	a	a	DET
ejpam-3052	42	3	smith	smith	PROPN
ejpam-3052	42	4	graphs	graphs	PROPN
ejpam-3052	42	5	sm	sm	PROPN
ejpam-3052	42	6	,	,	PUNCT
ejpam-3052	42	7	nullity	nullity	NOUN
ejpam-3052	42	8	is	be	AUX
ejpam-3052	42	9	given	give	VERB
ejpam-3052	42	10	by	by	ADP
ejpam-3052	42	11	(	(	PUNCT
ejpam-3052	42	12	i	i	NOUN
ejpam-3052	42	13	)	)	PUNCT
ejpam-3052	42	14	η(cm	η(cm	NOUN
ejpam-3052	42	15	)	)	PUNCT
ejpam-3052	42	16	=	=	PRON
ejpam-3052	42	17	{	{	PUNCT
ejpam-3052	42	18	2	2	NUM
ejpam-3052	42	19	,	,	PUNCT
ejpam-3052	42	20	m	m	VERB
ejpam-3052	42	21	≡	≡	PROPN
ejpam-3052	42	22	0	0	PUNCT
ejpam-3052	43	1	(	(	PUNCT
ejpam-3052	43	2	mod	mod	NOUN
ejpam-3052	43	3	4	4	NUM
ejpam-3052	43	4	)	)	PUNCT
ejpam-3052	43	5	0	0	NUM
ejpam-3052	43	6	,	,	PUNCT
ejpam-3052	43	7	otherwise	otherwise	ADV
ejpam-3052	43	8	(	(	PUNCT
ejpam-3052	43	9	ii	ii	NOUN
ejpam-3052	43	10	)	)	PUNCT
ejpam-3052	43	11	η(wm	η(wm	NOUN
ejpam-3052	43	12	)	)	PUNCT
ejpam-3052	43	13	=	=	PUNCT
ejpam-3052	43	14	{	{	PUNCT
ejpam-3052	43	15	3	3	NUM
ejpam-3052	43	16	,	,	PUNCT
ejpam-3052	43	17	if	if	SCONJ
ejpam-3052	43	18	m	m	PROPN
ejpam-3052	43	19	is	be	AUX
ejpam-3052	43	20	odd	odd	ADJ
ejpam-3052	43	21	2	2	NUM
ejpam-3052	43	22	,	,	PUNCT
ejpam-3052	43	23	otherwise	otherwise	ADV
ejpam-3052	43	24	(	(	PUNCT
ejpam-3052	43	25	iii	iii	NOUN
ejpam-3052	43	26	)	)	PUNCT
ejpam-3052	43	27	η(k1,4	η(k1,4	NOUN
ejpam-3052	43	28	)	)	PUNCT
ejpam-3052	43	29	=	=	SYM
ejpam-3052	43	30	3	3	NUM
ejpam-3052	43	31	(	(	PUNCT
ejpam-3052	43	32	iv	iv	NOUN
ejpam-3052	43	33	)	)	PUNCT
ejpam-3052	43	34	η(h7	η(h7	NOUN
ejpam-3052	43	35	)	)	PUNCT
ejpam-3052	44	1	=	=	SYM
ejpam-3052	44	2	1	1	NUM
ejpam-3052	44	3	(	(	PUNCT
ejpam-3052	44	4	v	v	NOUN
ejpam-3052	44	5	)	)	PUNCT
ejpam-3052	44	6	η(h8	η(h8	NOUN
ejpam-3052	44	7	)	)	PUNCT
ejpam-3052	45	1	=	=	SYM
ejpam-3052	45	2	0	0	NUM
ejpam-3052	45	3	(	(	PUNCT
ejpam-3052	45	4	vi	vi	NOUN
ejpam-3052	45	5	)	)	PUNCT
ejpam-3052	45	6	η(h9	η(h9	NOUN
ejpam-3052	45	7	)	)	PUNCT
ejpam-3052	45	8	=	=	SYM
ejpam-3052	45	9	1	1	X
ejpam-3052	45	10	.	.	PUNCT
ejpam-3052	45	11	proof	proof	NOUN
ejpam-3052	45	12	.	.	PUNCT
ejpam-3052	46	1	we	we	PRON
ejpam-3052	46	2	will	will	AUX
ejpam-3052	46	3	prove	prove	VERB
ejpam-3052	46	4	the	the	DET
ejpam-3052	46	5	entire	entire	ADJ
ejpam-3052	46	6	result	result	NOUN
ejpam-3052	46	7	by	by	ADP
ejpam-3052	46	8	weighting	weight	VERB
ejpam-3052	46	9	technique	technique	NOUN
ejpam-3052	46	10	.	.	PUNCT
ejpam-3052	47	1	(	(	PUNCT
ejpam-3052	47	2	i	i	NOUN
ejpam-3052	47	3	)	)	PUNCT
ejpam-3052	47	4	firstly	firstly	ADV
ejpam-3052	47	5	we	we	PRON
ejpam-3052	47	6	assume	assume	VERB
ejpam-3052	47	7	that	that	SCONJ
ejpam-3052	47	8	sm	sm	PROPN
ejpam-3052	47	9	be	be	AUX
ejpam-3052	47	10	cm	cm	NUM
ejpam-3052	47	11	;	;	PUNCT
ejpam-3052	48	1	m	m	VERB
ejpam-3052	48	2	≥	≥	NOUN
ejpam-3052	48	3	3	3	X
ejpam-3052	48	4	.	.	PUNCT
ejpam-3052	49	1	there	there	PRON
ejpam-3052	49	2	are	be	VERB
ejpam-3052	49	3	two	two	NUM
ejpam-3052	49	4	cases	case	NOUN
ejpam-3052	49	5	viz	viz	VERB
ejpam-3052	49	6	.	.	PUNCT
ejpam-3052	50	1	m	m	PROPN
ejpam-3052	51	1	≡	≡	PROPN
ejpam-3052	51	2	0	0	PUNCT
ejpam-3052	52	1	(	(	PUNCT
ejpam-3052	52	2	mod	mod	NOUN
ejpam-3052	52	3	4	4	NUM
ejpam-3052	52	4	)	)	PUNCT
ejpam-3052	52	5	and	and	CCONJ
ejpam-3052	52	6	m	m	PROPN
ejpam-3052	52	7	6≡	6≡	NUM
ejpam-3052	52	8	0	0	NUM
ejpam-3052	52	9	(	(	PUNCT
ejpam-3052	52	10	mod	mod	PROPN
ejpam-3052	52	11	4	4	NUM
ejpam-3052	52	12	)	)	PUNCT
ejpam-3052	52	13	.	.	PUNCT
ejpam-3052	53	1	for	for	ADP
ejpam-3052	53	2	m	m	PROPN
ejpam-3052	53	3	≡	≡	PROPN
ejpam-3052	53	4	0	0	PUNCT
ejpam-3052	54	1	(	(	PUNCT
ejpam-3052	54	2	mod	mod	PROPN
ejpam-3052	54	3	4	4	NUM
ejpam-3052	54	4	)	)	PUNCT
ejpam-3052	54	5	,	,	PUNCT
ejpam-3052	54	6	let	let	VERB
ejpam-3052	54	7	xi	xi	PRON
ejpam-3052	54	8	be	be	AUX
ejpam-3052	54	9	the	the	DET
ejpam-3052	54	10	weights	weight	NOUN
ejpam-3052	54	11	of	of	ADP
ejpam-3052	54	12	vertices	vertex	NOUN
ejpam-3052	54	13	of	of	ADP
ejpam-3052	54	14	cm	cm	NOUN
ejpam-3052	54	15	.	.	PUNCT
ejpam-3052	55	1	we	we	PRON
ejpam-3052	55	2	have	have	VERB
ejpam-3052	55	3	the	the	DET
ejpam-3052	55	4	following	follow	VERB
ejpam-3052	55	5	conditions	condition	NOUN
ejpam-3052	55	6	∑	∑	PUNCT
ejpam-3052	55	7	w∈ncm	w∈ncm	PROPN
ejpam-3052	55	8	(	(	PUNCT
ejpam-3052	55	9	v	v	NOUN
ejpam-3052	55	10	)	)	PUNCT
ejpam-3052	55	11	f(w	f(w	PROPN
ejpam-3052	55	12	)	)	PUNCT
ejpam-3052	55	13	=	=	SYM
ejpam-3052	56	1	0	0	NUM
ejpam-3052	56	2	,	,	PUNCT
ejpam-3052	56	3	∀	∀	X
ejpam-3052	56	4	v	v	ADP
ejpam-3052	56	5	∈	∈	PROPN
ejpam-3052	56	6	v	v	NOUN
ejpam-3052	56	7	(	(	PUNCT
ejpam-3052	56	8	cm	cm	NOUN
ejpam-3052	56	9	)	)	PUNCT
ejpam-3052	56	10	.	.	PUNCT
ejpam-3052	57	1	u.	u.	PROPN
ejpam-3052	57	2	sharma	sharma	PROPN
ejpam-3052	57	3	,	,	PUNCT
ejpam-3052	57	4	r.	r.	PROPN
ejpam-3052	57	5	naresh	naresh	PROPN
ejpam-3052	57	6	/	/	SYM
ejpam-3052	57	7	eur	eur	PROPN
ejpam-3052	57	8	.	.	PUNCT
ejpam-3052	58	1	j.	j.	PROPN
ejpam-3052	58	2	pure	pure	PROPN
ejpam-3052	58	3	appl	appl	PROPN
ejpam-3052	58	4	.	.	PROPN
ejpam-3052	58	5	math	math	PROPN
ejpam-3052	58	6	,	,	PUNCT
ejpam-3052	58	7	10	10	NUM
ejpam-3052	58	8	(	(	PUNCT
ejpam-3052	58	9	5	5	NUM
ejpam-3052	58	10	)	)	PUNCT
ejpam-3052	58	11	(	(	PUNCT
ejpam-3052	58	12	2017	2017	NUM
ejpam-3052	58	13	)	)	PUNCT
ejpam-3052	58	14	,	,	PUNCT
ejpam-3052	58	15	1050	1050	NUM
ejpam-3052	58	16	-	-	SYM
ejpam-3052	58	17	1057	1057	NUM
ejpam-3052	58	18	1053	1053	NUM
ejpam-3052	58	19	on	on	ADP
ejpam-3052	58	20	solving	solve	VERB
ejpam-3052	58	21	the	the	DET
ejpam-3052	58	22	equation	equation	NOUN
ejpam-3052	58	23	we	we	PRON
ejpam-3052	58	24	get	get	VERB
ejpam-3052	58	25	x1	x1	NOUN
ejpam-3052	58	26	=	=	SYM
ejpam-3052	58	27	x5	x5	PROPN
ejpam-3052	58	28	=	=	PUNCT
ejpam-3052	58	29	.	.	PUNCT
ejpam-3052	58	30	.	.	PUNCT
ejpam-3052	58	31	.	.	PUNCT
ejpam-3052	59	1	xm−3	xm−3	PROPN
ejpam-3052	59	2	=	=	PUNCT
ejpam-3052	59	3	a1(say	a1(say	ADJ
ejpam-3052	59	4	)	)	PUNCT
ejpam-3052	59	5	x3	x3	NOUN
ejpam-3052	59	6	=	=	SYM
ejpam-3052	60	1	x7	x7	NOUN
ejpam-3052	60	2	=	=	SYM
ejpam-3052	60	3	·	·	PUNCT
ejpam-3052	60	4	·	·	PUNCT
ejpam-3052	60	5	·	·	PUNCT
ejpam-3052	61	1	=	=	SYM
ejpam-3052	61	2	xm−1	xm−1	PROPN
ejpam-3052	61	3	=	=	PRON
ejpam-3052	61	4	−a1	−a1	PROPN
ejpam-3052	61	5	and	and	CCONJ
ejpam-3052	61	6	x2	x2	NOUN
ejpam-3052	61	7	=	=	SYM
ejpam-3052	61	8	x6	x6	PROPN
ejpam-3052	61	9	=	=	PUNCT
ejpam-3052	61	10	.	.	PUNCT
ejpam-3052	61	11	.	.	PUNCT
ejpam-3052	61	12	.	.	PUNCT
ejpam-3052	62	1	xm−2	xm−2	NOUN
ejpam-3052	62	2	=	=	SYM
ejpam-3052	62	3	a2(say	a2(say	PROPN
ejpam-3052	62	4	)	)	PUNCT
ejpam-3052	62	5	x4	x4	PROPN
ejpam-3052	63	1	=	=	SYM
ejpam-3052	63	2	x8	x8	PROPN
ejpam-3052	63	3	=	=	PRON
ejpam-3052	63	4	.	.	PUNCT
ejpam-3052	63	5	.	.	PUNCT
ejpam-3052	63	6	.	.	PUNCT
ejpam-3052	64	1	xm	xm	PROPN
ejpam-3052	64	2	=	=	PROPN
ejpam-3052	64	3	−a2	−a2	PROPN
ejpam-3052	64	4	.	.	PUNCT
ejpam-3052	65	1	we	we	PRON
ejpam-3052	65	2	have	have	AUX
ejpam-3052	65	3	used	use	VERB
ejpam-3052	65	4	two	two	NUM
ejpam-3052	65	5	non	non	ADJ
ejpam-3052	65	6	-	-	ADJ
ejpam-3052	65	7	zero	zero	ADJ
ejpam-3052	65	8	independent	independent	ADJ
ejpam-3052	65	9	variables	variable	NOUN
ejpam-3052	65	10	a1	a1	NOUN
ejpam-3052	65	11	and	and	CCONJ
ejpam-3052	65	12	a2	a2	PROPN
ejpam-3052	65	13	in	in	ADP
ejpam-3052	65	14	a	a	DET
ejpam-3052	65	15	zero	zero	NUM
ejpam-3052	65	16	-	-	PUNCT
ejpam-3052	65	17	sum	sum	NOUN
ejpam-3052	65	18	weighting	weighting	NOUN
ejpam-3052	65	19	of	of	ADP
ejpam-3052	65	20	cm	cm	PROPN
ejpam-3052	65	21	.	.	PUNCT
ejpam-3052	66	1	therefore	therefore	ADV
ejpam-3052	66	2	,	,	PUNCT
ejpam-3052	66	3	η(cm	η(cm	NOUN
ejpam-3052	66	4	)	)	PUNCT
ejpam-3052	66	5	=	=	SYM
ejpam-3052	66	6	2	2	X
ejpam-3052	66	7	.	.	X
ejpam-3052	66	8	for	for	ADP
ejpam-3052	66	9	m	m	PROPN
ejpam-3052	66	10	6≡	6≡	NUM
ejpam-3052	66	11	0	0	NUM
ejpam-3052	66	12	(	(	PUNCT
ejpam-3052	66	13	mod	mod	PROPN
ejpam-3052	66	14	4	4	NUM
ejpam-3052	66	15	)	)	PUNCT
ejpam-3052	66	16	,	,	PUNCT
ejpam-3052	66	17	we	we	PRON
ejpam-3052	66	18	have	have	AUX
ejpam-3052	66	19	used	use	VERB
ejpam-3052	66	20	same	same	ADJ
ejpam-3052	66	21	procedure	procedure	NOUN
ejpam-3052	66	22	as	as	ADP
ejpam-3052	66	23	above	above	ADV
ejpam-3052	66	24	.	.	PUNCT
ejpam-3052	67	1	after	after	SCONJ
ejpam-3052	67	2	solving	solve	VERB
ejpam-3052	67	3	we	we	PRON
ejpam-3052	67	4	get	get	VERB
ejpam-3052	67	5	solution	solution	NOUN
ejpam-3052	67	6	x1	x1	NOUN
ejpam-3052	67	7	=	=	PUNCT
ejpam-3052	67	8	x2	x2	PROPN
ejpam-3052	67	9	=	=	X
ejpam-3052	67	10	.	.	PUNCT
ejpam-3052	67	11	.	.	PUNCT
ejpam-3052	67	12	.	.	PUNCT
ejpam-3052	68	1	xm	xm	PROPN
ejpam-3052	68	2	=	=	PUNCT
ejpam-3052	69	1	0	0	X
ejpam-3052	69	2	.	.	PUNCT
ejpam-3052	70	1	therefore	therefore	ADV
ejpam-3052	70	2	,	,	PUNCT
ejpam-3052	70	3	η(cm	η(cm	NOUN
ejpam-3052	70	4	)	)	PUNCT
ejpam-3052	70	5	=	=	SYM
ejpam-3052	71	1	0	0	X
ejpam-3052	71	2	.	.	PUNCT
ejpam-3052	72	1	hence	hence	ADV
ejpam-3052	72	2	,	,	PUNCT
ejpam-3052	72	3	by	by	ADP
ejpam-3052	72	4	the	the	DET
ejpam-3052	72	5	above	above	ADJ
ejpam-3052	72	6	two	two	NUM
ejpam-3052	72	7	cases	case	NOUN
ejpam-3052	72	8	η(cm	η(cm	NOUN
ejpam-3052	72	9	)	)	PUNCT
ejpam-3052	72	10	=	=	SYM
ejpam-3052	72	11	{	{	PUNCT
ejpam-3052	72	12	2	2	NUM
ejpam-3052	72	13	,	,	PUNCT
ejpam-3052	72	14	m	m	VERB
ejpam-3052	72	15	≡	≡	PROPN
ejpam-3052	72	16	0	0	PUNCT
ejpam-3052	72	17	(	(	PUNCT
ejpam-3052	72	18	mod	mod	NOUN
ejpam-3052	72	19	4	4	NUM
ejpam-3052	72	20	)	)	PUNCT
ejpam-3052	72	21	0	0	NUM
ejpam-3052	72	22	,	,	PUNCT
ejpam-3052	72	23	otherwise	otherwise	ADV
ejpam-3052	72	24	(	(	PUNCT
ejpam-3052	72	25	ii	ii	NOUN
ejpam-3052	72	26	)	)	PUNCT
ejpam-3052	72	27	let	let	VERB
ejpam-3052	72	28	sm	sm	NOUN
ejpam-3052	72	29	to	to	PART
ejpam-3052	72	30	be	be	AUX
ejpam-3052	72	31	wm	wm	PROPN
ejpam-3052	72	32	;	;	PUNCT
ejpam-3052	72	33	m	m	VERB
ejpam-3052	72	34	≥	≥	NOUN
ejpam-3052	72	35	6	6	NUM
ejpam-3052	72	36	.	.	PUNCT
ejpam-3052	73	1	we	we	PRON
ejpam-3052	73	2	tackle	tackle	VERB
ejpam-3052	73	3	following	follow	VERB
ejpam-3052	73	4	cases	case	NOUN
ejpam-3052	73	5	:	:	PUNCT
ejpam-3052	73	6	case	case	NOUN
ejpam-3052	73	7	(	(	PUNCT
ejpam-3052	73	8	i	i	NOUN
ejpam-3052	73	9	)	)	PUNCT
ejpam-3052	73	10	if	if	SCONJ
ejpam-3052	73	11	m	m	NOUN
ejpam-3052	73	12	is	be	AUX
ejpam-3052	73	13	even	even	ADV
ejpam-3052	73	14	,	,	PUNCT
ejpam-3052	73	15	then	then	ADV
ejpam-3052	73	16	we	we	PRON
ejpam-3052	73	17	have	have	AUX
ejpam-3052	73	18	used	use	VERB
ejpam-3052	73	19	two	two	NUM
ejpam-3052	73	20	independent	independent	ADJ
ejpam-3052	73	21	variables	variable	NOUN
ejpam-3052	73	22	a1	a1	PROPN
ejpam-3052	73	23	6=	6=	ADP
ejpam-3052	73	24	0	0	NUM
ejpam-3052	73	25	,	,	PUNCT
ejpam-3052	73	26	a2	a2	PROPN
ejpam-3052	73	27	6=	6=	ADP
ejpam-3052	73	28	0	0	NUM
ejpam-3052	73	29	in	in	ADP
ejpam-3052	73	30	a	a	DET
ejpam-3052	73	31	zero	zero	NUM
ejpam-3052	73	32	-	-	PUNCT
ejpam-3052	73	33	sum	sum	NOUN
ejpam-3052	73	34	weighting	weighting	NOUN
ejpam-3052	73	35	of	of	ADP
ejpam-3052	73	36	wm	wm	PROPN
ejpam-3052	73	37	.	.	PROPN
ejpam-3052	73	38	therefore	therefore	ADV
ejpam-3052	73	39	,	,	PUNCT
ejpam-3052	73	40	η(wm	η(wm	NOUN
ejpam-3052	73	41	)	)	PUNCT
ejpam-3052	73	42	=	=	SYM
ejpam-3052	73	43	2	2	X
ejpam-3052	73	44	.	.	X
ejpam-3052	73	45	case	case	NOUN
ejpam-3052	73	46	(	(	PUNCT
ejpam-3052	73	47	ii	ii	NOUN
ejpam-3052	73	48	)	)	PUNCT
ejpam-3052	73	49	if	if	SCONJ
ejpam-3052	73	50	m	m	PROPN
ejpam-3052	73	51	is	be	AUX
ejpam-3052	73	52	odd	odd	ADJ
ejpam-3052	73	53	,	,	PUNCT
ejpam-3052	73	54	then	then	ADV
ejpam-3052	73	55	we	we	PRON
ejpam-3052	73	56	have	have	AUX
ejpam-3052	73	57	used	use	VERB
ejpam-3052	73	58	three	three	NUM
ejpam-3052	73	59	non	non	ADJ
ejpam-3052	73	60	-	-	ADJ
ejpam-3052	73	61	zero	zero	ADJ
ejpam-3052	73	62	independent	independent	ADJ
ejpam-3052	73	63	variables	variable	NOUN
ejpam-3052	73	64	in	in	ADP
ejpam-3052	73	65	a	a	DET
ejpam-3052	73	66	zero	zero	NUM
ejpam-3052	73	67	-	-	PUNCT
ejpam-3052	73	68	sum	sum	NOUN
ejpam-3052	73	69	weighting	weighting	NOUN
ejpam-3052	73	70	of	of	ADP
ejpam-3052	73	71	wm	wm	PROPN
ejpam-3052	73	72	.	.	PROPN
ejpam-3052	74	1	therefore	therefore	ADV
ejpam-3052	74	2	,	,	PUNCT
ejpam-3052	74	3	η(wm	η(wm	NOUN
ejpam-3052	74	4	)	)	PUNCT
ejpam-3052	74	5	=	=	SYM
ejpam-3052	75	1	3	3	X
ejpam-3052	75	2	.	.	X
ejpam-3052	75	3	hence	hence	ADV
ejpam-3052	75	4	,	,	PUNCT
ejpam-3052	75	5	η(wm	η(wm	NOUN
ejpam-3052	75	6	)	)	PUNCT
ejpam-3052	75	7	=	=	PUNCT
ejpam-3052	75	8	{	{	PUNCT
ejpam-3052	75	9	3	3	NUM
ejpam-3052	75	10	,	,	PUNCT
ejpam-3052	75	11	if	if	SCONJ
ejpam-3052	75	12	m	m	PROPN
ejpam-3052	75	13	is	be	AUX
ejpam-3052	75	14	odd	odd	ADJ
ejpam-3052	75	15	2	2	NUM
ejpam-3052	75	16	,	,	PUNCT
ejpam-3052	75	17	otherwise	otherwise	ADV
ejpam-3052	75	18	(	(	PUNCT
ejpam-3052	75	19	iii	iii	NOUN
ejpam-3052	75	20	)	)	PUNCT
ejpam-3052	75	21	let	let	VERB
ejpam-3052	75	22	sm	sm	NOUN
ejpam-3052	75	23	to	to	PART
ejpam-3052	75	24	be	be	AUX
ejpam-3052	75	25	isomorphic	isomorphic	ADJ
ejpam-3052	75	26	to	to	ADP
ejpam-3052	75	27	k1,4	k1,4	PROPN
ejpam-3052	75	28	.	.	PUNCT
ejpam-3052	76	1	let	let	VERB
ejpam-3052	76	2	xi	xi	NOUN
ejpam-3052	76	3	,	,	PUNCT
ejpam-3052	76	4	∀	∀	VERB
ejpam-3052	77	1	i	i	NOUN
ejpam-3052	77	2	=	=	NOUN
ejpam-3052	77	3	1	1	NUM
ejpam-3052	77	4	,	,	PUNCT
ejpam-3052	77	5	2	2	NUM
ejpam-3052	77	6	,	,	PUNCT
ejpam-3052	77	7	.	.	PUNCT
ejpam-3052	77	8	.	.	PUNCT
ejpam-3052	78	1	.	.	PUNCT
ejpam-3052	79	1	,	,	PUNCT
ejpam-3052	79	2	5	5	NUM
ejpam-3052	79	3	be	be	AUX
ejpam-3052	79	4	the	the	DET
ejpam-3052	79	5	weights	weight	NOUN
ejpam-3052	79	6	of	of	ADP
ejpam-3052	79	7	vertices	vertex	NOUN
ejpam-3052	79	8	respectively	respectively	ADV
ejpam-3052	79	9	.	.	PUNCT
ejpam-3052	80	1	then	then	ADV
ejpam-3052	80	2	,	,	PUNCT
ejpam-3052	80	3	we	we	PRON
ejpam-3052	80	4	have	have	AUX
ejpam-3052	80	5	following	follow	VERB
ejpam-3052	80	6	conditions∑	conditions∑	PROPN
ejpam-3052	80	7	w∈nk1,4	w∈nk1,4	PROPN
ejpam-3052	80	8	(	(	PUNCT
ejpam-3052	80	9	v	v	NOUN
ejpam-3052	80	10	)	)	PUNCT
ejpam-3052	80	11	f(w	f(w	PROPN
ejpam-3052	80	12	)	)	PUNCT
ejpam-3052	81	1	=	=	SYM
ejpam-3052	81	2	0	0	NUM
ejpam-3052	81	3	,	,	PUNCT
ejpam-3052	81	4	∀	∀	X
ejpam-3052	81	5	v	v	ADP
ejpam-3052	81	6	∈	∈	PROPN
ejpam-3052	81	7	v	v	NOUN
ejpam-3052	81	8	(	(	PUNCT
ejpam-3052	81	9	k1,4	k1,4	PROPN
ejpam-3052	81	10	)	)	PUNCT
ejpam-3052	81	11	.	.	PUNCT
ejpam-3052	82	1	5∑	5∑	ADJ
ejpam-3052	82	2	i=2	i=2	PROPN
ejpam-3052	82	3	xi	xi	ADP
ejpam-3052	82	4	=	=	SYM
ejpam-3052	82	5	0	0	NUM
ejpam-3052	82	6	and	and	CCONJ
ejpam-3052	82	7	x1	x1	NUM
ejpam-3052	82	8	=	=	SYM
ejpam-3052	82	9	0	0	NUM
ejpam-3052	82	10	,	,	PUNCT
ejpam-3052	82	11	∀	∀	X
ejpam-3052	82	12	xi	xi	NOUN
ejpam-3052	82	13	;	;	PUNCT
ejpam-3052	82	14	i	i	NOUN
ejpam-3052	82	15	=	=	NOUN
ejpam-3052	82	16	2	2	NUM
ejpam-3052	82	17	,	,	PUNCT
ejpam-3052	82	18	3	3	NUM
ejpam-3052	82	19	,	,	PUNCT
ejpam-3052	82	20	4	4	NUM
ejpam-3052	82	21	,	,	PUNCT
ejpam-3052	82	22	5	5	NUM
ejpam-3052	82	23	.	.	PUNCT
ejpam-3052	83	1	after	after	ADP
ejpam-3052	83	2	solving	solve	VERB
ejpam-3052	83	3	these	these	DET
ejpam-3052	83	4	equations	equation	NOUN
ejpam-3052	83	5	,	,	PUNCT
ejpam-3052	83	6	we	we	PRON
ejpam-3052	83	7	get	get	VERB
ejpam-3052	83	8	x2	x2	PROPN
ejpam-3052	83	9	=	=	NOUN
ejpam-3052	83	10	a1	a1	NOUN
ejpam-3052	83	11	,	,	PUNCT
ejpam-3052	83	12	x3	x3	NOUN
ejpam-3052	83	13	=	=	SYM
ejpam-3052	83	14	a2	a2	PROPN
ejpam-3052	83	15	,	,	PUNCT
ejpam-3052	83	16	x4	x4	PROPN
ejpam-3052	83	17	=	=	PROPN
ejpam-3052	83	18	a3	a3	NOUN
ejpam-3052	83	19	and	and	CCONJ
ejpam-3052	83	20	x5	x5	NOUN
ejpam-3052	83	21	=	=	SYM
ejpam-3052	83	22	−(a1	−(a1	X
ejpam-3052	83	23	+	+	NOUN
ejpam-3052	83	24	a2	a2	PROPN
ejpam-3052	83	25	+	+	CCONJ
ejpam-3052	83	26	a3	a3	NOUN
ejpam-3052	83	27	)	)	PUNCT
ejpam-3052	83	28	.	.	PUNCT
ejpam-3052	84	1	here	here	ADV
ejpam-3052	84	2	,	,	PUNCT
ejpam-3052	84	3	we	we	PRON
ejpam-3052	84	4	have	have	AUX
ejpam-3052	84	5	used	use	VERB
ejpam-3052	84	6	three	three	NUM
ejpam-3052	84	7	non	non	ADJ
ejpam-3052	84	8	-	-	ADJ
ejpam-3052	84	9	zero	zero	ADJ
ejpam-3052	84	10	independent	independent	ADJ
ejpam-3052	84	11	variables	variable	NOUN
ejpam-3052	84	12	in	in	ADP
ejpam-3052	84	13	a	a	DET
ejpam-3052	84	14	zero	zero	NUM
ejpam-3052	84	15	-	-	PUNCT
ejpam-3052	84	16	sum	sum	NOUN
ejpam-3052	84	17	weighting	weighting	NOUN
ejpam-3052	84	18	of	of	ADP
ejpam-3052	84	19	k1,4	k1,4	PROPN
ejpam-3052	84	20	.	.	PUNCT
ejpam-3052	85	1	therefore	therefore	ADV
ejpam-3052	85	2	,	,	PUNCT
ejpam-3052	85	3	η(k1,4	η(k1,4	ADV
ejpam-3052	85	4	)	)	PUNCT
ejpam-3052	85	5	=	=	SYM
ejpam-3052	85	6	3	3	X
ejpam-3052	85	7	.	.	PUNCT
ejpam-3052	85	8	u.	u.	PROPN
ejpam-3052	85	9	sharma	sharma	PROPN
ejpam-3052	85	10	,	,	PUNCT
ejpam-3052	85	11	r.	r.	PROPN
ejpam-3052	85	12	naresh	naresh	PROPN
ejpam-3052	85	13	/	/	SYM
ejpam-3052	85	14	eur	eur	PROPN
ejpam-3052	85	15	.	.	PUNCT
ejpam-3052	86	1	j.	j.	PROPN
ejpam-3052	86	2	pure	pure	PROPN
ejpam-3052	86	3	appl	appl	PROPN
ejpam-3052	86	4	.	.	PROPN
ejpam-3052	86	5	math	math	PROPN
ejpam-3052	86	6	,	,	PUNCT
ejpam-3052	86	7	10	10	NUM
ejpam-3052	86	8	(	(	PUNCT
ejpam-3052	86	9	5	5	NUM
ejpam-3052	86	10	)	)	PUNCT
ejpam-3052	86	11	(	(	PUNCT
ejpam-3052	86	12	2017	2017	NUM
ejpam-3052	86	13	)	)	PUNCT
ejpam-3052	86	14	,	,	PUNCT
ejpam-3052	86	15	1050	1050	NUM
ejpam-3052	86	16	-	-	SYM
ejpam-3052	86	17	1057	1057	NUM
ejpam-3052	86	18	1054	1054	NUM
ejpam-3052	86	19	(	(	PUNCT
ejpam-3052	86	20	iv	iv	X
ejpam-3052	86	21	)	)	PUNCT
ejpam-3052	86	22	let	let	VERB
ejpam-3052	86	23	us	we	PRON
ejpam-3052	86	24	take	take	VERB
ejpam-3052	86	25	sm	sm	ADV
ejpam-3052	86	26	to	to	PART
ejpam-3052	86	27	be	be	AUX
ejpam-3052	86	28	h7	h7	PROPN
ejpam-3052	86	29	.	.	PUNCT
ejpam-3052	87	1	in	in	ADP
ejpam-3052	87	2	zero	zero	NUM
ejpam-3052	87	3	-	-	PUNCT
ejpam-3052	87	4	sum	sum	NOUN
ejpam-3052	87	5	weighting	weighting	NOUN
ejpam-3052	87	6	of	of	ADP
ejpam-3052	87	7	h7	h7	PROPN
ejpam-3052	87	8	,	,	PUNCT
ejpam-3052	87	9	we	we	PRON
ejpam-3052	87	10	have	have	AUX
ejpam-3052	87	11	used	use	VERB
ejpam-3052	87	12	only	only	ADV
ejpam-3052	87	13	one	one	NUM
ejpam-3052	87	14	non	non	ADJ
ejpam-3052	87	15	-	-	ADJ
ejpam-3052	87	16	zero	zero	ADJ
ejpam-3052	87	17	independent	independent	ADJ
ejpam-3052	87	18	variables	variable	NOUN
ejpam-3052	87	19	.	.	PUNCT
ejpam-3052	88	1	therefore	therefore	ADV
ejpam-3052	88	2	,	,	PUNCT
ejpam-3052	88	3	η(h7	η(h7	NOUN
ejpam-3052	88	4	)	)	PUNCT
ejpam-3052	88	5	=	=	SYM
ejpam-3052	89	1	1	1	X
ejpam-3052	89	2	.	.	PUNCT
ejpam-3052	89	3	(	(	PUNCT
ejpam-3052	89	4	v	v	X
ejpam-3052	89	5	)	)	PUNCT
ejpam-3052	89	6	we	we	PRON
ejpam-3052	89	7	suppose	suppose	VERB
ejpam-3052	89	8	that	that	SCONJ
ejpam-3052	89	9	sm	sm	PROPN
ejpam-3052	89	10	be	be	VERB
ejpam-3052	89	11	h8	h8	PROPN
ejpam-3052	89	12	.	.	PUNCT
ejpam-3052	90	1	we	we	PRON
ejpam-3052	90	2	have	have	AUX
ejpam-3052	90	3	not	not	PART
ejpam-3052	90	4	found	find	VERB
ejpam-3052	90	5	the	the	DET
ejpam-3052	90	6	non	non	ADJ
ejpam-3052	90	7	-	-	ADJ
ejpam-3052	90	8	zero	zero	ADJ
ejpam-3052	90	9	independent	independent	ADJ
ejpam-3052	90	10	variables	variable	NOUN
ejpam-3052	90	11	for	for	ADP
ejpam-3052	90	12	zero	zero	NUM
ejpam-3052	90	13	-	-	PUNCT
ejpam-3052	90	14	sum	sum	NOUN
ejpam-3052	90	15	weighting	weighting	NOUN
ejpam-3052	90	16	of	of	ADP
ejpam-3052	90	17	h8	h8	PROPN
ejpam-3052	90	18	.	.	PUNCT
ejpam-3052	91	1	hence	hence	ADV
ejpam-3052	91	2	,	,	PUNCT
ejpam-3052	91	3	η(h8	η(h8	NOUN
ejpam-3052	91	4	)	)	PUNCT
ejpam-3052	91	5	=	=	SYM
ejpam-3052	92	1	0	0	X
ejpam-3052	92	2	.	.	PUNCT
ejpam-3052	92	3	(	(	PUNCT
ejpam-3052	92	4	vi	vi	X
ejpam-3052	92	5	)	)	PUNCT
ejpam-3052	92	6	if	if	SCONJ
ejpam-3052	92	7	we	we	PRON
ejpam-3052	92	8	take	take	VERB
ejpam-3052	92	9	sm	sm	PROPN
ejpam-3052	92	10	be	be	AUX
ejpam-3052	92	11	h9	h9	NOUN
ejpam-3052	92	12	,	,	PUNCT
ejpam-3052	92	13	then	then	ADV
ejpam-3052	92	14	we	we	PRON
ejpam-3052	92	15	have	have	AUX
ejpam-3052	92	16	used	use	VERB
ejpam-3052	92	17	one	one	NUM
ejpam-3052	92	18	non	non	ADJ
ejpam-3052	92	19	-	-	ADJ
ejpam-3052	92	20	zero	zero	ADJ
ejpam-3052	92	21	independent	independent	ADJ
ejpam-3052	92	22	variable	variable	NOUN
ejpam-3052	92	23	in	in	ADP
ejpam-3052	92	24	zerosum	zerosum	PROPN
ejpam-3052	92	25	weighting	weighting	NOUN
ejpam-3052	92	26	of	of	ADP
ejpam-3052	92	27	h9	h9	NOUN
ejpam-3052	92	28	.	.	PUNCT
ejpam-3052	93	1	hence	hence	ADV
ejpam-3052	93	2	,	,	PUNCT
ejpam-3052	93	3	η(h9	η(h9	NOUN
ejpam-3052	93	4	)	)	PUNCT
ejpam-3052	93	5	=	=	SYM
ejpam-3052	93	6	1	1	X
ejpam-3052	93	7	.	.	X
ejpam-3052	93	8	�	�	PROPN
ejpam-3052	93	9	theorem	theorem	VERB
ejpam-3052	93	10	1	1	NUM
ejpam-3052	93	11	.	.	PUNCT
ejpam-3052	94	1	let	let	VERB
ejpam-3052	94	2	sm	sm	PRON
ejpam-3052	94	3	be	be	AUX
ejpam-3052	94	4	any	any	DET
ejpam-3052	94	5	smith	smith	NOUN
ejpam-3052	94	6	graph	graph	NOUN
ejpam-3052	94	7	with	with	ADP
ejpam-3052	94	8	m	m	PROPN
ejpam-3052	94	9	vertices	vertex	NOUN
ejpam-3052	94	10	and	and	CCONJ
ejpam-3052	94	11	let	let	VERB
ejpam-3052	94	12	η(sm	η(sm	NOUN
ejpam-3052	94	13	)	)	PUNCT
ejpam-3052	94	14	denote	denote	VERB
ejpam-3052	94	15	the	the	DET
ejpam-3052	94	16	nullity	nullity	NOUN
ejpam-3052	94	17	of	of	ADP
ejpam-3052	94	18	sm	sm	PROPN
ejpam-3052	94	19	.	.	PUNCT
ejpam-3052	95	1	then	then	ADV
ejpam-3052	95	2	the	the	DET
ejpam-3052	95	3	nullity	nullity	NOUN
ejpam-3052	95	4	of	of	ADP
ejpam-3052	95	5	smith	smith	PROPN
ejpam-3052	95	6	graph	graph	PROPN
ejpam-3052	95	7	sm	sm	PROPN
ejpam-3052	95	8	belongs	belong	VERB
ejpam-3052	95	9	to	to	ADP
ejpam-3052	95	10	the	the	DET
ejpam-3052	95	11	set	set	NOUN
ejpam-3052	95	12	{	{	PUNCT
ejpam-3052	95	13	0	0	NUM
ejpam-3052	95	14	,	,	PUNCT
ejpam-3052	95	15	1	1	NUM
ejpam-3052	95	16	,	,	PUNCT
ejpam-3052	95	17	2	2	NUM
ejpam-3052	95	18	,	,	PUNCT
ejpam-3052	95	19	3	3	NUM
ejpam-3052	95	20	}	}	PUNCT
ejpam-3052	95	21	.	.	PUNCT
ejpam-3052	96	1	proof	proof	NOUN
ejpam-3052	96	2	.	.	PUNCT
ejpam-3052	97	1	the	the	DET
ejpam-3052	97	2	proof	proof	NOUN
ejpam-3052	97	3	of	of	ADP
ejpam-3052	97	4	the	the	DET
ejpam-3052	97	5	result	result	NOUN
ejpam-3052	97	6	can	can	AUX
ejpam-3052	97	7	be	be	AUX
ejpam-3052	97	8	given	give	VERB
ejpam-3052	97	9	by	by	ADP
ejpam-3052	97	10	lemma	lemma	PROPN
ejpam-3052	97	11	2	2	PROPN
ejpam-3052	97	12	.	.	PUNCT
ejpam-3052	97	13	�	�	PROPN
ejpam-3052	97	14	corollary	corollary	NOUN
ejpam-3052	97	15	1	1	NUM
ejpam-3052	97	16	.	.	PUNCT
ejpam-3052	98	1	the	the	DET
ejpam-3052	98	2	converse	converse	NOUN
ejpam-3052	98	3	of	of	ADP
ejpam-3052	98	4	theorem	theorem	NOUN
ejpam-3052	98	5	2	2	NUM
ejpam-3052	98	6	.	.	PUNCT
ejpam-3052	98	7	does	do	AUX
ejpam-3052	98	8	not	not	PART
ejpam-3052	98	9	hold	hold	VERB
ejpam-3052	98	10	in	in	ADP
ejpam-3052	98	11	general	general	ADJ
ejpam-3052	98	12	,	,	PUNCT
ejpam-3052	98	13	i.e.	i.e.	X
ejpam-3052	98	14	η(g	η(g	PROPN
ejpam-3052	98	15	)	)	PUNCT
ejpam-3052	98	16	∈	∈	PROPN
ejpam-3052	98	17	{	{	PUNCT
ejpam-3052	98	18	0	0	NUM
ejpam-3052	98	19	,	,	PUNCT
ejpam-3052	98	20	1	1	NUM
ejpam-3052	98	21	,	,	PUNCT
ejpam-3052	98	22	2	2	NUM
ejpam-3052	98	23	,	,	PUNCT
ejpam-3052	98	24	3	3	NUM
ejpam-3052	98	25	}	}	PUNCT
ejpam-3052	98	26	then	then	ADV
ejpam-3052	98	27	g	g	PROPN
ejpam-3052	98	28	need	need	AUX
ejpam-3052	98	29	not	not	PART
ejpam-3052	98	30	be	be	AUX
ejpam-3052	98	31	a	a	DET
ejpam-3052	98	32	smith	smith	NOUN
ejpam-3052	98	33	graph	graph	NOUN
ejpam-3052	98	34	.	.	PUNCT
ejpam-3052	99	1	as	as	ADP
ejpam-3052	99	2	for	for	ADP
ejpam-3052	99	3	instance	instance	NOUN
ejpam-3052	99	4	,	,	PUNCT
ejpam-3052	99	5	the	the	DET
ejpam-3052	99	6	nullity	nullity	NOUN
ejpam-3052	99	7	of	of	ADP
ejpam-3052	99	8	both	both	DET
ejpam-3052	99	9	pn	pn	PROPN
ejpam-3052	99	10	and	and	CCONJ
ejpam-3052	99	11	kn	kn	PROPN
ejpam-3052	99	12	∈	∈	PROPN
ejpam-3052	99	13	(	(	PUNCT
ejpam-3052	99	14	0	0	NUM
ejpam-3052	99	15	,	,	PUNCT
ejpam-3052	99	16	1	1	NUM
ejpam-3052	99	17	)	)	PUNCT
ejpam-3052	99	18	however	however	ADV
ejpam-3052	99	19	none	none	NOUN
ejpam-3052	99	20	of	of	ADP
ejpam-3052	99	21	them	they	PRON
ejpam-3052	99	22	is	be	AUX
ejpam-3052	99	23	smith	smith	PROPN
ejpam-3052	99	24	.	.	PROPN
ejpam-3052	99	25	remark	remark	PROPN
ejpam-3052	99	26	.	.	PUNCT
ejpam-3052	100	1	it	it	PRON
ejpam-3052	100	2	is	be	AUX
ejpam-3052	100	3	interesting	interesting	ADJ
ejpam-3052	100	4	to	to	PART
ejpam-3052	100	5	note	note	VERB
ejpam-3052	100	6	here	here	ADV
ejpam-3052	100	7	that	that	SCONJ
ejpam-3052	100	8	we	we	PRON
ejpam-3052	100	9	can	can	AUX
ejpam-3052	100	10	not	not	PART
ejpam-3052	100	11	have	have	VERB
ejpam-3052	100	12	a	a	DET
ejpam-3052	100	13	graph	graph	NOUN
ejpam-3052	100	14	as	as	ADP
ejpam-3052	100	15	from	from	ADP
ejpam-3052	100	16	[	[	X
ejpam-3052	100	17	3	3	NUM
ejpam-3052	100	18	]	]	X
ejpam-3052	100	19	η(g	η(g	NUM
ejpam-3052	100	20	)	)	PUNCT
ejpam-3052	100	21	=	=	SYM
ejpam-3052	101	1	n	n	NOUN
ejpam-3052	101	2	if	if	SCONJ
ejpam-3052	102	1	and	and	CCONJ
ejpam-3052	102	2	only	only	ADV
ejpam-3052	102	3	if	if	SCONJ
ejpam-3052	102	4	g	g	PROPN
ejpam-3052	102	5	is	be	AUX
ejpam-3052	102	6	a	a	DET
ejpam-3052	102	7	null	null	ADJ
ejpam-3052	102	8	graph	graph	NOUN
ejpam-3052	102	9	.	.	PUNCT
ejpam-3052	103	1	thus	thus	ADV
ejpam-3052	103	2	the	the	DET
ejpam-3052	103	3	following	follow	VERB
ejpam-3052	103	4	problem	problem	NOUN
ejpam-3052	103	5	arises	arise	VERB
ejpam-3052	103	6	.	.	PUNCT
ejpam-3052	104	1	problem	problem	NOUN
ejpam-3052	104	2	:	:	PUNCT
ejpam-3052	104	3	for	for	ADP
ejpam-3052	104	4	a	a	DET
ejpam-3052	104	5	given	give	VERB
ejpam-3052	104	6	n	n	CCONJ
ejpam-3052	104	7	,	,	PUNCT
ejpam-3052	104	8	does	do	AUX
ejpam-3052	104	9	there	there	PRON
ejpam-3052	104	10	exist	exist	VERB
ejpam-3052	104	11	a	a	DET
ejpam-3052	104	12	graph	graph	NOUN
ejpam-3052	104	13	of	of	ADP
ejpam-3052	104	14	order	order	NOUN
ejpam-3052	104	15	p	p	NOUN
ejpam-3052	104	16	>	>	X
ejpam-3052	104	17	n	n	CCONJ
ejpam-3052	104	18	,	,	PUNCT
ejpam-3052	104	19	such	such	ADJ
ejpam-3052	104	20	that	that	SCONJ
ejpam-3052	104	21	η(g	η(g	PROPN
ejpam-3052	104	22	)	)	PUNCT
ejpam-3052	104	23	=	=	VERB
ejpam-3052	105	1	n.	n.	NOUN
ejpam-3052	105	2	we	we	PRON
ejpam-3052	105	3	answer	answer	VERB
ejpam-3052	105	4	to	to	ADP
ejpam-3052	105	5	this	this	DET
ejpam-3052	105	6	problem	problem	NOUN
ejpam-3052	105	7	in	in	ADP
ejpam-3052	105	8	affirmative	affirmative	ADJ
ejpam-3052	105	9	due	due	ADP
ejpam-3052	105	10	to	to	ADP
ejpam-3052	105	11	the	the	DET
ejpam-3052	105	12	following	follow	VERB
ejpam-3052	105	13	theorem	theorem	NOUN
ejpam-3052	105	14	:	:	PUNCT
ejpam-3052	105	15	theorem	theorem	NOUN
ejpam-3052	105	16	2	2	NUM
ejpam-3052	105	17	.	.	PUNCT
ejpam-3052	106	1	let	let	AUX
ejpam-3052	106	2	(	(	PUNCT
ejpam-3052	106	3	pn	pn	PROPN
ejpam-3052	106	4	�	�	PROPN
ejpam-3052	106	5	sm	sm	PROPN
ejpam-3052	106	6	)	)	PUNCT
ejpam-3052	106	7	be	be	VERB
ejpam-3052	106	8	the	the	DET
ejpam-3052	106	9	corona	corona	NOUN
ejpam-3052	106	10	of	of	ADP
ejpam-3052	106	11	a	a	DET
ejpam-3052	106	12	path	path	NOUN
ejpam-3052	106	13	with	with	ADP
ejpam-3052	106	14	sm	sm	PROPN
ejpam-3052	106	15	,	,	PUNCT
ejpam-3052	106	16	where	where	SCONJ
ejpam-3052	106	17	sm	sm	PROPN
ejpam-3052	106	18	is	be	AUX
ejpam-3052	106	19	h9	h9	NOUN
ejpam-3052	106	20	.	.	PUNCT
ejpam-3052	107	1	then	then	ADV
ejpam-3052	107	2	η(pn	η(pn	PROPN
ejpam-3052	107	3	�	�	PROPN
ejpam-3052	107	4	sm	sm	PROPN
ejpam-3052	107	5	)	)	PUNCT
ejpam-3052	107	6	=	=	SYM
ejpam-3052	107	7	n.	n.	NOUN
ejpam-3052	107	8	proof	proof	NOUN
ejpam-3052	107	9	.	.	PUNCT
ejpam-3052	108	1	let	let	VERB
ejpam-3052	108	2	us	we	PRON
ejpam-3052	108	3	consider	consider	VERB
ejpam-3052	108	4	smith	smith	NOUN
ejpam-3052	108	5	graph	graph	NOUN
ejpam-3052	108	6	sm	sm	INTJ
ejpam-3052	108	7	to	to	ADP
ejpam-3052	108	8	beh9	beh9	VERB
ejpam-3052	108	9	and	and	CCONJ
ejpam-3052	108	10	let	let	VERB
ejpam-3052	108	11	the	the	DET
ejpam-3052	108	12	vertices	vertex	NOUN
ejpam-3052	108	13	of	of	ADP
ejpam-3052	108	14	pn	pn	PROPN
ejpam-3052	108	15	are	be	AUX
ejpam-3052	108	16	v1	v1	NOUN
ejpam-3052	108	17	,	,	PUNCT
ejpam-3052	108	18	v2	v2	PROPN
ejpam-3052	108	19	,	,	PUNCT
ejpam-3052	108	20	v3	v3	PROPN
ejpam-3052	108	21	,	,	PUNCT
ejpam-3052	108	22	.	.	PUNCT
ejpam-3052	108	23	.	.	PUNCT
ejpam-3052	109	1	.	.	PUNCT
ejpam-3052	110	1	vn	vn	NOUN
ejpam-3052	110	2	and	and	CCONJ
ejpam-3052	110	3	vertices	vertex	NOUN
ejpam-3052	110	4	of	of	ADP
ejpam-3052	110	5	h9	h9	NOUN
ejpam-3052	110	6	are	be	AUX
ejpam-3052	110	7	u1	u1	NOUN
ejpam-3052	110	8	,	,	PUNCT
ejpam-3052	110	9	u2	u2	NOUN
ejpam-3052	110	10	,	,	PUNCT
ejpam-3052	110	11	u3	u3	NOUN
ejpam-3052	110	12	,	,	PUNCT
ejpam-3052	110	13	.	.	PUNCT
ejpam-3052	110	14	.	.	PUNCT
ejpam-3052	110	15	.	.	PUNCT
ejpam-3052	111	1	u9	u9	PROPN
ejpam-3052	111	2	in	in	ADP
ejpam-3052	111	3	a	a	DET
ejpam-3052	111	4	usual	usual	ADJ
ejpam-3052	111	5	manner	manner	NOUN
ejpam-3052	111	6	as	as	SCONJ
ejpam-3052	111	7	shown	show	VERB
ejpam-3052	111	8	in	in	ADP
ejpam-3052	111	9	figure	figure	NOUN
ejpam-3052	111	10	2	2	NUM
ejpam-3052	111	11	.	.	PUNCT
ejpam-3052	112	1	the	the	DET
ejpam-3052	112	2	corona	corona	NOUN
ejpam-3052	112	3	of	of	ADP
ejpam-3052	112	4	pn	pn	PROPN
ejpam-3052	112	5	withh9	withh9	PROPN
ejpam-3052	112	6	has	have	VERB
ejpam-3052	112	7	vertex	vertex	NOUN
ejpam-3052	112	8	set	set	VERB
ejpam-3052	112	9	v	v	ADP
ejpam-3052	112	10	i(g	i(g	NOUN
ejpam-3052	112	11	)	)	PUNCT
ejpam-3052	113	1	=	=	PRON
ejpam-3052	113	2	{	{	PUNCT
ejpam-3052	113	3	uij	uij	PROPN
ejpam-3052	113	4	,	,	PUNCT
ejpam-3052	113	5	vi	vi	PROPN
ejpam-3052	113	6	:	:	PUNCT
ejpam-3052	113	7	i	i	NOUN
ejpam-3052	113	8	=	=	NOUN
ejpam-3052	113	9	1	1	NUM
ejpam-3052	113	10	,	,	PUNCT
ejpam-3052	113	11	2	2	NUM
ejpam-3052	113	12	,	,	PUNCT
ejpam-3052	113	13	.	.	PUNCT
ejpam-3052	113	14	.	.	PUNCT
ejpam-3052	114	1	.	.	PUNCT
ejpam-3052	115	1	,	,	PUNCT
ejpam-3052	115	2	n	n	CCONJ
ejpam-3052	115	3	,	,	PUNCT
ejpam-3052	115	4	j	j	PROPN
ejpam-3052	115	5	=	=	SYM
ejpam-3052	115	6	1	1	NUM
ejpam-3052	115	7	,	,	PUNCT
ejpam-3052	115	8	2	2	NUM
ejpam-3052	115	9	,	,	PUNCT
ejpam-3052	115	10	.	.	PUNCT
ejpam-3052	115	11	.	.	PUNCT
ejpam-3052	116	1	.	.	PUNCT
ejpam-3052	117	1	,	,	PUNCT
ejpam-3052	117	2	9	9	NUM
ejpam-3052	117	3	}	}	PUNCT
ejpam-3052	117	4	.	.	PUNCT
ejpam-3052	118	1	v	v	X
ejpam-3052	118	2	v	v	NUM
ejpam-3052	118	3	v	v	NOUN
ejpam-3052	118	4	u	u	NOUN
ejpam-3052	118	5	u	u	NOUN
ejpam-3052	118	6	u	u	NOUN
ejpam-3052	118	7	u	u	NOUN
ejpam-3052	118	8	u	u	NOUN
ejpam-3052	118	9	u	u	NOUN
ejpam-3052	118	10	14	14	NUM
ejpam-3052	118	11	u15	u15	NOUN
ejpam-3052	118	12	u17	u17	NOUN
ejpam-3052	119	1	u1911	u1911	ADV
ejpam-3052	119	2	12	12	NUM
ejpam-3052	119	3	181613	181613	NUM
ejpam-3052	119	4	u	u	NOUN
ejpam-3052	119	5	u	u	PROPN
ejpam-3052	119	6	u	u	NOUN
ejpam-3052	119	7	u	u	X
ejpam-3052	119	8	u	u	NOUN
ejpam-3052	119	9	u	u	NOUN
ejpam-3052	119	10	24	24	NUM
ejpam-3052	119	11	u	u	NOUN
ejpam-3052	119	12	u	u	NOUN
ejpam-3052	119	13	u2921	u2921	ADP
ejpam-3052	119	14	2622	2622	NUM
ejpam-3052	119	15	23	23	NUM
ejpam-3052	119	16	25	25	NUM
ejpam-3052	119	17	27	27	NUM
ejpam-3052	119	18	28	28	NUM
ejpam-3052	119	19	u	u	NOUN
ejpam-3052	119	20	u	u	NOUN
ejpam-3052	119	21	u	u	NOUN
ejpam-3052	119	22	u	u	NOUN
ejpam-3052	119	23	u	u	NOUN
ejpam-3052	119	24	u	u	NOUN
ejpam-3052	119	25	n4	n4	PROPN
ejpam-3052	119	26	u	u	PROPN
ejpam-3052	119	27	u	u	PROPN
ejpam-3052	119	28	un1	un1	PROPN
ejpam-3052	119	29	n2	n2	PROPN
ejpam-3052	119	30	n3	n3	PROPN
ejpam-3052	119	31	n5	n5	PROPN
ejpam-3052	119	32	n6	n6	PROPN
ejpam-3052	119	33	n7	n7	PROPN
ejpam-3052	119	34	n8	n8	PROPN
ejpam-3052	119	35	n9	n9	PROPN
ejpam-3052	119	36	1	1	NUM
ejpam-3052	119	37	2	2	NUM
ejpam-3052	119	38	n	n	PRON
ejpam-3052	119	39	figure	figure	NOUN
ejpam-3052	119	40	2	2	NUM
ejpam-3052	119	41	:	:	PUNCT
ejpam-3052	119	42	(	(	PUNCT
ejpam-3052	119	43	pn	pn	PROPN
ejpam-3052	119	44	�	�	PROPN
ejpam-3052	119	45	h9	h9	NOUN
ejpam-3052	119	46	)	)	PUNCT
ejpam-3052	119	47	let	let	VERB
ejpam-3052	119	48	xij	xij	PRON
ejpam-3052	119	49	and	and	CCONJ
ejpam-3052	119	50	yi	yi	PROPN
ejpam-3052	119	51	be	be	AUX
ejpam-3052	119	52	weights	weight	NOUN
ejpam-3052	119	53	of	of	ADP
ejpam-3052	119	54	the	the	DET
ejpam-3052	119	55	vertices	vertex	NOUN
ejpam-3052	119	56	of	of	ADP
ejpam-3052	119	57	(	(	PUNCT
ejpam-3052	119	58	pn	pn	PROPN
ejpam-3052	119	59	�	�	PROPN
ejpam-3052	119	60	h9	h9	PROPN
ejpam-3052	119	61	)	)	PUNCT
ejpam-3052	119	62	as	as	SCONJ
ejpam-3052	119	63	indicated	indicate	VERB
ejpam-3052	119	64	in	in	ADP
ejpam-3052	119	65	figure	figure	NOUN
ejpam-3052	119	66	3	3	NUM
ejpam-3052	119	67	.	.	PUNCT
ejpam-3052	120	1	then	then	ADV
ejpam-3052	120	2	,	,	PUNCT
ejpam-3052	120	3	∑	∑	PROPN
ejpam-3052	120	4	w∈n(pn	w∈n(pn	NOUN
ejpam-3052	120	5	�	�	PROPN
ejpam-3052	120	6	h9	h9	NOUN
ejpam-3052	120	7	)	)	PUNCT
ejpam-3052	120	8	(	(	PUNCT
ejpam-3052	120	9	v	v	NOUN
ejpam-3052	120	10	)	)	PUNCT
ejpam-3052	120	11	f(w	f(w	PROPN
ejpam-3052	120	12	)	)	PUNCT
ejpam-3052	120	13	=	=	SYM
ejpam-3052	120	14	0	0	NUM
ejpam-3052	120	15	,	,	PUNCT
ejpam-3052	120	16	∀	∀	X
ejpam-3052	120	17	v	v	ADP
ejpam-3052	120	18	∈	∈	PROPN
ejpam-3052	120	19	v	v	NOUN
ejpam-3052	120	20	(	(	PUNCT
ejpam-3052	120	21	pn	pn	PROPN
ejpam-3052	120	22	�	�	PROPN
ejpam-3052	120	23	h9	h9	PROPN
ejpam-3052	120	24	)	)	PUNCT
ejpam-3052	120	25	.	.	PUNCT
ejpam-3052	121	1	u.	u.	PROPN
ejpam-3052	121	2	sharma	sharma	PROPN
ejpam-3052	121	3	,	,	PUNCT
ejpam-3052	121	4	r.	r.	PROPN
ejpam-3052	121	5	naresh	naresh	PROPN
ejpam-3052	121	6	/	/	SYM
ejpam-3052	121	7	eur	eur	PROPN
ejpam-3052	121	8	.	.	PUNCT
ejpam-3052	122	1	j.	j.	PROPN
ejpam-3052	122	2	pure	pure	PROPN
ejpam-3052	122	3	appl	appl	PROPN
ejpam-3052	122	4	.	.	PROPN
ejpam-3052	122	5	math	math	PROPN
ejpam-3052	122	6	,	,	PUNCT
ejpam-3052	122	7	10	10	NUM
ejpam-3052	122	8	(	(	PUNCT
ejpam-3052	122	9	5	5	NUM
ejpam-3052	122	10	)	)	PUNCT
ejpam-3052	122	11	(	(	PUNCT
ejpam-3052	122	12	2017	2017	NUM
ejpam-3052	122	13	)	)	PUNCT
ejpam-3052	122	14	,	,	PUNCT
ejpam-3052	122	15	1050	1050	NUM
ejpam-3052	122	16	-	-	SYM
ejpam-3052	122	17	1057	1057	NUM
ejpam-3052	122	18	1055	1055	NUM
ejpam-3052	122	19	x	x	SYM
ejpam-3052	122	20	x	x	PUNCT
ejpam-3052	122	21	x	x	PUNCT
ejpam-3052	122	22	x	x	PUNCT
ejpam-3052	122	23	x	x	PUNCT
ejpam-3052	122	24	x	x	PUNCT
ejpam-3052	122	25	x	x	PUNCT
ejpam-3052	122	26	x	x	PUNCT
ejpam-3052	122	27	x	x	PUNCT
ejpam-3052	122	28	x	x	PUNCT
ejpam-3052	122	29	x	x	PUNCT
ejpam-3052	122	30	x	x	PUNCT
ejpam-3052	122	31	x	x	PUNCT
ejpam-3052	122	32	x	x	PUNCT
ejpam-3052	122	33	x	x	PUNCT
ejpam-3052	122	34	x	x	PUNCT
ejpam-3052	122	35	x	x	PUNCT
ejpam-3052	122	36	x	x	PUNCT
ejpam-3052	122	37	x	x	PUNCT
ejpam-3052	122	38	x	x	PUNCT
ejpam-3052	122	39	x	x	PUNCT
ejpam-3052	122	40	x	x	PUNCT
ejpam-3052	122	41	x	x	PUNCT
ejpam-3052	122	42	x	x	PUNCT
ejpam-3052	122	43	x	x	PUNCT
ejpam-3052	122	44	x	x	PUNCT
ejpam-3052	122	45	x	x	PUNCT
ejpam-3052	122	46	y	y	VERB
ejpam-3052	122	47	y	y	PROPN
ejpam-3052	122	48	y	y	PROPN
ejpam-3052	122	49	11	11	NUM
ejpam-3052	122	50	12	12	NUM
ejpam-3052	122	51	13	13	NUM
ejpam-3052	122	52	14	14	NUM
ejpam-3052	122	53	15	15	NUM
ejpam-3052	122	54	16	16	NUM
ejpam-3052	122	55	17	17	NUM
ejpam-3052	122	56	18	18	NUM
ejpam-3052	122	57	19	19	NUM
ejpam-3052	122	58	21	21	NUM
ejpam-3052	122	59	22	22	NUM
ejpam-3052	122	60	23	23	NUM
ejpam-3052	122	61	24	24	NUM
ejpam-3052	122	62	25	25	NUM
ejpam-3052	122	63	26	26	NUM
ejpam-3052	122	64	27	27	NUM
ejpam-3052	122	65	28	28	NUM
ejpam-3052	122	66	29	29	NUM
ejpam-3052	122	67	n1	n1	PROPN
ejpam-3052	122	68	n2	n2	NOUN
ejpam-3052	122	69	n3	n3	PROPN
ejpam-3052	122	70	n5	n5	PROPN
ejpam-3052	122	71	n4	n4	PROPN
ejpam-3052	122	72	n6	n6	PROPN
ejpam-3052	122	73	n7	n7	PROPN
ejpam-3052	122	74	n8	n8	PROPN
ejpam-3052	122	75	n9	n9	PROPN
ejpam-3052	122	76	1	1	NUM
ejpam-3052	122	77	2	2	NUM
ejpam-3052	122	78	n	n	PRON
ejpam-3052	122	79	figure	figure	VERB
ejpam-3052	122	80	3	3	NUM
ejpam-3052	122	81	:	:	PUNCT
ejpam-3052	122	82	(	(	PUNCT
ejpam-3052	122	83	pn	pn	PROPN
ejpam-3052	122	84	�	�	PROPN
ejpam-3052	122	85	h9	h9	PROPN
ejpam-3052	122	86	)	)	PUNCT
ejpam-3052	122	87	these	these	DET
ejpam-3052	122	88	equations	equation	NOUN
ejpam-3052	122	89	possess	possess	VERB
ejpam-3052	122	90	solution	solution	NOUN
ejpam-3052	122	91	if	if	SCONJ
ejpam-3052	122	92	and	and	CCONJ
ejpam-3052	122	93	only	only	ADV
ejpam-3052	122	94	if	if	SCONJ
ejpam-3052	122	95	xnj	xnj	PROPN
ejpam-3052	122	96	=	=	SYM
ejpam-3052	122	97	0	0	NUM
ejpam-3052	122	98	;	;	PUNCT
ejpam-3052	122	99	j	j	PROPN
ejpam-3052	122	100	=	=	SYM
ejpam-3052	122	101	1	1	NUM
ejpam-3052	122	102	,	,	PUNCT
ejpam-3052	122	103	2	2	NUM
ejpam-3052	122	104	,	,	PUNCT
ejpam-3052	122	105	3	3	NUM
ejpam-3052	122	106	,	,	PUNCT
ejpam-3052	122	107	6	6	NUM
ejpam-3052	122	108	,	,	PUNCT
ejpam-3052	122	109	8	8	NUM
ejpam-3052	122	110	and	and	CCONJ
ejpam-3052	122	111	xn4	xn4	X
ejpam-3052	123	1	=	=	SYM
ejpam-3052	123	2	xn7	xn7	NOUN
ejpam-3052	124	1	=	=	PUNCT
ejpam-3052	124	2	a1;xn5	a1;xn5	PROPN
ejpam-3052	124	3	=	=	PUNCT
ejpam-3052	125	1	xn9	xn9	NOUN
ejpam-3052	125	2	=	=	PUNCT
ejpam-3052	126	1	−a1	−a1	PROPN
ejpam-3052	126	2	.	.	PUNCT
ejpam-3052	127	1	clearly	clearly	ADV
ejpam-3052	127	2	,	,	PUNCT
ejpam-3052	127	3	we	we	PRON
ejpam-3052	127	4	have	have	AUX
ejpam-3052	127	5	used	use	VERB
ejpam-3052	127	6	n	n	PRON
ejpam-3052	127	7	independent	independent	ADJ
ejpam-3052	127	8	variable	variable	NOUN
ejpam-3052	127	9	in	in	ADP
ejpam-3052	127	10	a	a	DET
ejpam-3052	127	11	zero	zero	NUM
ejpam-3052	127	12	-	-	PUNCT
ejpam-3052	127	13	sum	sum	NOUN
ejpam-3052	127	14	weighting	weighting	NOUN
ejpam-3052	127	15	of	of	ADP
ejpam-3052	127	16	(	(	PUNCT
ejpam-3052	127	17	pn	pn	PROPN
ejpam-3052	127	18	�	�	PROPN
ejpam-3052	127	19	h9	h9	NOUN
ejpam-3052	127	20	)	)	PUNCT
ejpam-3052	127	21	.	.	PUNCT
ejpam-3052	128	1	therefore	therefore	ADV
ejpam-3052	128	2	,	,	PUNCT
ejpam-3052	128	3	η(pn	η(pn	PROPN
ejpam-3052	128	4	�	�	NOUN
ejpam-3052	128	5	h9	h9	NOUN
ejpam-3052	128	6	)	)	PUNCT
ejpam-3052	128	7	=	=	VERB
ejpam-3052	128	8	n.	n.	NOUN
ejpam-3052	128	9	hence	hence	ADV
ejpam-3052	128	10	from	from	ADP
ejpam-3052	128	11	the	the	DET
ejpam-3052	128	12	above	above	ADJ
ejpam-3052	128	13	discussion	discussion	NOUN
ejpam-3052	128	14	it	it	PRON
ejpam-3052	128	15	is	be	AUX
ejpam-3052	128	16	clear	clear	ADJ
ejpam-3052	128	17	that	that	SCONJ
ejpam-3052	128	18	η(pn	η(pn	PROPN
ejpam-3052	128	19	�	�	PROPN
ejpam-3052	128	20	sm	sm	PROPN
ejpam-3052	128	21	)	)	PUNCT
ejpam-3052	128	22	=	=	SYM
ejpam-3052	128	23	n	n	CCONJ
ejpam-3052	128	24	,	,	PUNCT
ejpam-3052	128	25	where	where	SCONJ
ejpam-3052	128	26	sm	sm	PROPN
ejpam-3052	128	27	is	be	AUX
ejpam-3052	128	28	h9	h9	NOUN
ejpam-3052	128	29	.	.	PUNCT
ejpam-3052	129	1	�	�	PROPN
ejpam-3052	129	2	theorem	theorem	VERB
ejpam-3052	129	3	3	3	X
ejpam-3052	129	4	.	.	PUNCT
ejpam-3052	130	1	let	let	AUX
ejpam-3052	130	2	(	(	PUNCT
ejpam-3052	130	3	pn	pn	PROPN
ejpam-3052	130	4	�	�	PROPN
ejpam-3052	130	5	sm	sm	PROPN
ejpam-3052	130	6	)	)	PUNCT
ejpam-3052	130	7	denotes	denote	VERB
ejpam-3052	130	8	the	the	DET
ejpam-3052	130	9	corona	corona	NOUN
ejpam-3052	130	10	of	of	ADP
ejpam-3052	130	11	a	a	DET
ejpam-3052	130	12	path	path	NOUN
ejpam-3052	130	13	with	with	ADP
ejpam-3052	130	14	sm	sm	PROPN
ejpam-3052	130	15	.	.	PROPN
ejpam-3052	131	1	then	then	ADV
ejpam-3052	131	2	η(pn	η(pn	PROPN
ejpam-3052	131	3	�	�	PROPN
ejpam-3052	131	4	sm	sm	PROPN
ejpam-3052	131	5	)	)	PUNCT
ejpam-3052	131	6	∈	∈	PROPN
ejpam-3052	131	7	{	{	PUNCT
ejpam-3052	131	8	0	0	NUM
ejpam-3052	131	9	,	,	PUNCT
ejpam-3052	131	10	2n	2n	NUM
ejpam-3052	131	11	,	,	PUNCT
ejpam-3052	131	12	3n	3n	NUM
ejpam-3052	131	13	}	}	PUNCT
ejpam-3052	131	14	,	,	PUNCT
ejpam-3052	131	15	where	where	SCONJ
ejpam-3052	131	16	sm	sm	PROPN
ejpam-3052	131	17	is	be	AUX
ejpam-3052	131	18	either	either	CCONJ
ejpam-3052	131	19	wm	wm	PROPN
ejpam-3052	131	20	or	or	CCONJ
ejpam-3052	131	21	k1,4	k1,4	PROPN
ejpam-3052	131	22	or	or	CCONJ
ejpam-3052	131	23	cm	cm	PROPN
ejpam-3052	131	24	or	or	CCONJ
ejpam-3052	131	25	h7	h7	PROPN
ejpam-3052	131	26	or	or	CCONJ
ejpam-3052	131	27	h8	h8	PROPN
ejpam-3052	131	28	.	.	PUNCT
ejpam-3052	132	1	proof	proof	NOUN
ejpam-3052	132	2	.	.	PUNCT
ejpam-3052	133	1	we	we	PRON
ejpam-3052	133	2	will	will	AUX
ejpam-3052	133	3	prove	prove	VERB
ejpam-3052	133	4	the	the	DET
ejpam-3052	133	5	entire	entire	ADJ
ejpam-3052	133	6	result	result	NOUN
ejpam-3052	133	7	for	for	ADP
ejpam-3052	133	8	each	each	PRON
ejpam-3052	133	9	of	of	ADP
ejpam-3052	133	10	the	the	DET
ejpam-3052	133	11	smith	smith	PROPN
ejpam-3052	133	12	graph	graph	NOUN
ejpam-3052	133	13	separately	separately	ADV
ejpam-3052	133	14	.	.	PUNCT
ejpam-3052	134	1	first	first	ADV
ejpam-3052	134	2	consider	consider	VERB
ejpam-3052	134	3	sm	sm	PRON
ejpam-3052	134	4	to	to	PART
ejpam-3052	134	5	be	be	AUX
ejpam-3052	134	6	wm;m	wm;m	PROPN
ejpam-3052	134	7	≥	≥	NOUN
ejpam-3052	134	8	6	6	NUM
ejpam-3052	134	9	to	to	ADP
ejpam-3052	134	10	the	the	DET
ejpam-3052	134	11	vertices	vertex	NOUN
ejpam-3052	134	12	of	of	ADP
ejpam-3052	134	13	(	(	PUNCT
ejpam-3052	134	14	pn	pn	PROPN
ejpam-3052	134	15	�	�	PROPN
ejpam-3052	134	16	sm	sm	PROPN
ejpam-3052	134	17	)	)	PUNCT
ejpam-3052	134	18	.	.	PUNCT
ejpam-3052	135	1	we	we	PRON
ejpam-3052	135	2	need	need	VERB
ejpam-3052	135	3	to	to	PART
ejpam-3052	135	4	tackle	tackle	VERB
ejpam-3052	135	5	two	two	NUM
ejpam-3052	135	6	cases	case	NOUN
ejpam-3052	135	7	for	for	ADP
ejpam-3052	135	8	m	m	PROPN
ejpam-3052	135	9	,	,	PUNCT
ejpam-3052	135	10	viz	viz	PROPN
ejpam-3052	135	11	.	.	PROPN
ejpam-3052	135	12	,	,	PUNCT
ejpam-3052	135	13	m	m	VERB
ejpam-3052	135	14	=	=	PUNCT
ejpam-3052	135	15	4k	4k	NOUN
ejpam-3052	135	16	+	+	CCONJ
ejpam-3052	135	17	1	1	NUM
ejpam-3052	135	18	and	and	CCONJ
ejpam-3052	135	19	m	m	PROPN
ejpam-3052	135	20	6=	6=	NUM
ejpam-3052	135	21	4k	4k	NOUN
ejpam-3052	135	22	+	+	CCONJ
ejpam-3052	135	23	1	1	NUM
ejpam-3052	135	24	where	where	SCONJ
ejpam-3052	135	25	k	k	PROPN
ejpam-3052	135	26	=	=	SYM
ejpam-3052	135	27	2	2	NUM
ejpam-3052	135	28	,	,	PUNCT
ejpam-3052	135	29	3	3	NUM
ejpam-3052	135	30	,	,	PUNCT
ejpam-3052	135	31	.	.	PUNCT
ejpam-3052	135	32	.	.	PUNCT
ejpam-3052	135	33	.	.	PUNCT
ejpam-3052	136	1	.	.	PUNCT
ejpam-3052	137	1	let	let	VERB
ejpam-3052	137	2	m	m	NOUN
ejpam-3052	137	3	=	=	SYM
ejpam-3052	137	4	4k+1	4k+1	PROPN
ejpam-3052	137	5	on	on	ADP
ejpam-3052	137	6	applying	apply	VERB
ejpam-3052	137	7	co	co	NOUN
ejpam-3052	137	8	-	-	NOUN
ejpam-3052	137	9	neighbor	neighbor	NOUN
ejpam-3052	137	10	lemma	lemma	PROPN
ejpam-3052	137	11	.	.	PUNCT
ejpam-3052	138	1	in	in	ADP
ejpam-3052	138	2	this	this	DET
ejpam-3052	138	3	case	case	NOUN
ejpam-3052	138	4	,	,	PUNCT
ejpam-3052	138	5	we	we	PRON
ejpam-3052	138	6	have	have	VERB
ejpam-3052	138	7	2	2	NUM
ejpam-3052	138	8	pairs	pair	NOUN
ejpam-3052	138	9	of	of	ADP
ejpam-3052	138	10	co	co	NOUN
ejpam-3052	138	11	-	-	NOUN
ejpam-3052	138	12	neighbor	neighbor	NOUN
ejpam-3052	138	13	vertices	vertice	VERB
ejpam-3052	138	14	in	in	ADP
ejpam-3052	138	15	each	each	DET
ejpam-3052	138	16	copy	copy	NOUN
ejpam-3052	138	17	of	of	ADP
ejpam-3052	138	18	wm	wm	PROPN
ejpam-3052	138	19	,	,	PUNCT
ejpam-3052	138	20	it	it	PRON
ejpam-3052	138	21	means	mean	VERB
ejpam-3052	138	22	that	that	SCONJ
ejpam-3052	138	23	we	we	PRON
ejpam-3052	138	24	have	have	VERB
ejpam-3052	138	25	to	to	PART
ejpam-3052	138	26	remove	remove	VERB
ejpam-3052	138	27	2	2	NUM
ejpam-3052	138	28	vertices	vertex	NOUN
ejpam-3052	138	29	in	in	ADP
ejpam-3052	138	30	each	each	DET
ejpam-3052	138	31	copy	copy	NOUN
ejpam-3052	138	32	of	of	ADP
ejpam-3052	138	33	wm	wm	PROPN
ejpam-3052	138	34	.	.	PUNCT
ejpam-3052	139	1	it	it	PRON
ejpam-3052	139	2	implies	imply	VERB
ejpam-3052	139	3	that	that	SCONJ
ejpam-3052	139	4	total	total	ADJ
ejpam-3052	139	5	2n	2n	NUM
ejpam-3052	139	6	vertices	vertex	NOUN
ejpam-3052	139	7	have	have	AUX
ejpam-3052	139	8	been	be	AUX
ejpam-3052	139	9	removed	remove	VERB
ejpam-3052	139	10	from	from	ADP
ejpam-3052	139	11	(	(	PUNCT
ejpam-3052	139	12	pn	pn	PROPN
ejpam-3052	139	13	�	�	PROPN
ejpam-3052	139	14	wm	wm	PROPN
ejpam-3052	139	15	)	)	PUNCT
ejpam-3052	139	16	.	.	PUNCT
ejpam-3052	140	1	thus	thus	ADV
ejpam-3052	140	2	we	we	PRON
ejpam-3052	140	3	get	get	VERB
ejpam-3052	140	4	η(pn	η(pn	PROPN
ejpam-3052	140	5	�	�	NOUN
ejpam-3052	140	6	wm	wm	PROPN
ejpam-3052	140	7	)	)	PUNCT
ejpam-3052	140	8	=	=	SYM
ejpam-3052	140	9	η(pn	η(pn	PROPN
ejpam-3052	140	10	�	�	PROPN
ejpam-3052	140	11	w	w	PROPN
ejpam-3052	140	12	′m	′m	PROPN
ejpam-3052	140	13	)	)	PUNCT
ejpam-3052	140	14	+	+	X
ejpam-3052	141	1	2n	2n	NUM
ejpam-3052	141	2	,	,	PUNCT
ejpam-3052	141	3	where	where	SCONJ
ejpam-3052	141	4	w	w	PROPN
ejpam-3052	141	5	′m	′m	PROPN
ejpam-3052	141	6	=	=	VERB
ejpam-3052	142	1	pm−2;m	pm−2;m	ADP
ejpam-3052	142	2	−	−	NUM
ejpam-3052	142	3	2	2	NUM
ejpam-3052	142	4	=	=	SYM
ejpam-3052	142	5	4k	4k	NOUN
ejpam-3052	142	6	−	−	NOUN
ejpam-3052	142	7	1	1	NUM
ejpam-3052	142	8	and	and	CCONJ
ejpam-3052	142	9	k	k	NOUN
ejpam-3052	142	10	=	=	SYM
ejpam-3052	142	11	2	2	NUM
ejpam-3052	142	12	,	,	PUNCT
ejpam-3052	142	13	3	3	NUM
ejpam-3052	142	14	,	,	PUNCT
ejpam-3052	142	15	.	.	PUNCT
ejpam-3052	142	16	.	.	PUNCT
ejpam-3052	142	17	.	.	PUNCT
ejpam-3052	142	18	.	.	PUNCT
ejpam-3052	143	1	therefore	therefore	ADV
ejpam-3052	143	2	,	,	PUNCT
ejpam-3052	143	3	we	we	PRON
ejpam-3052	143	4	conclude	conclude	VERB
ejpam-3052	143	5	that	that	SCONJ
ejpam-3052	143	6	η(pn	η(pn	PROPN
ejpam-3052	143	7	�	�	PROPN
ejpam-3052	143	8	wm	wm	PROPN
ejpam-3052	143	9	)	)	PUNCT
ejpam-3052	143	10	=	=	SYM
ejpam-3052	144	1	3n	3n	NUM
ejpam-3052	144	2	.	.	PUNCT
ejpam-3052	145	1	next	next	ADV
ejpam-3052	145	2	,	,	PUNCT
ejpam-3052	145	3	let	let	VERB
ejpam-3052	145	4	m	m	PRON
ejpam-3052	145	5	6=	6=	NUM
ejpam-3052	145	6	4k+	4k+	NUM
ejpam-3052	145	7	1	1	NUM
ejpam-3052	145	8	,	,	PUNCT
ejpam-3052	145	9	using	use	VERB
ejpam-3052	145	10	the	the	DET
ejpam-3052	145	11	same	same	ADJ
ejpam-3052	145	12	procedure	procedure	NOUN
ejpam-3052	145	13	as	as	ADP
ejpam-3052	145	14	above	above	ADV
ejpam-3052	145	15	,	,	PUNCT
ejpam-3052	145	16	we	we	PRON
ejpam-3052	145	17	conclude	conclude	VERB
ejpam-3052	145	18	that	that	SCONJ
ejpam-3052	145	19	η(pn	η(pn	PROPN
ejpam-3052	145	20	�	�	NOUN
ejpam-3052	145	21	wm	wm	PROPN
ejpam-3052	145	22	)	)	PUNCT
ejpam-3052	145	23	=	=	SYM
ejpam-3052	145	24	2n	2n	NUM
ejpam-3052	145	25	.	.	PUNCT
ejpam-3052	146	1	hence	hence	ADV
ejpam-3052	146	2	.	.	PUNCT
ejpam-3052	147	1	we	we	PRON
ejpam-3052	147	2	get	get	VERB
ejpam-3052	147	3	η(pn	η(pn	PROPN
ejpam-3052	147	4	�	�	NOUN
ejpam-3052	147	5	wm	wm	PROPN
ejpam-3052	147	6	)	)	PUNCT
ejpam-3052	147	7	=	=	NOUN
ejpam-3052	147	8	{	{	PUNCT
ejpam-3052	147	9	3n	3n	NUM
ejpam-3052	147	10	,	,	PUNCT
ejpam-3052	147	11	m	m	VERB
ejpam-3052	147	12	=	=	X
ejpam-3052	147	13	4k	4k	NOUN
ejpam-3052	147	14	+	+	NOUN
ejpam-3052	147	15	1	1	NUM
ejpam-3052	147	16	,	,	PUNCT
ejpam-3052	147	17	where	where	SCONJ
ejpam-3052	147	18	k	k	PROPN
ejpam-3052	147	19	=	=	SYM
ejpam-3052	147	20	2	2	NUM
ejpam-3052	147	21	,	,	PUNCT
ejpam-3052	147	22	3	3	NUM
ejpam-3052	147	23	,	,	PUNCT
ejpam-3052	147	24	.	.	PUNCT
ejpam-3052	147	25	.	.	PUNCT
ejpam-3052	148	1	.	.	PUNCT
ejpam-3052	149	1	2n	2n	NUM
ejpam-3052	149	2	,	,	PUNCT
ejpam-3052	149	3	otherwise	otherwise	ADV
ejpam-3052	149	4	consider	consider	VERB
ejpam-3052	149	5	sm	sm	PRON
ejpam-3052	149	6	to	to	PART
ejpam-3052	149	7	be	be	AUX
ejpam-3052	149	8	k1,4	k1,4	PROPN
ejpam-3052	149	9	.	.	PUNCT
ejpam-3052	150	1	the	the	DET
ejpam-3052	150	2	co	co	NOUN
ejpam-3052	150	3	-	-	NOUN
ejpam-3052	150	4	neighbor	neighbor	ADJ
ejpam-3052	150	5	vertices	vertex	NOUN
ejpam-3052	150	6	of	of	ADP
ejpam-3052	150	7	(	(	PUNCT
ejpam-3052	150	8	pn	pn	PROPN
ejpam-3052	150	9	�	�	PROPN
ejpam-3052	150	10	k1,4	k1,4	PROPN
ejpam-3052	150	11	)	)	PUNCT
ejpam-3052	150	12	are	be	AUX
ejpam-3052	150	13	(	(	PUNCT
ejpam-3052	150	14	u2	u2	NOUN
ejpam-3052	150	15	,	,	PUNCT
ejpam-3052	150	16	u3	u3	NOUN
ejpam-3052	150	17	)	)	PUNCT
ejpam-3052	150	18	,	,	PUNCT
ejpam-3052	150	19	(	(	PUNCT
ejpam-3052	150	20	u3	u3	PROPN
ejpam-3052	150	21	,	,	PUNCT
ejpam-3052	150	22	u4	u4	PROPN
ejpam-3052	150	23	)	)	PUNCT
ejpam-3052	150	24	,	,	PUNCT
ejpam-3052	150	25	(	(	PUNCT
ejpam-3052	150	26	u4	u4	PROPN
ejpam-3052	150	27	,	,	PUNCT
ejpam-3052	150	28	u5	u5	PROPN
ejpam-3052	150	29	)	)	PUNCT
ejpam-3052	150	30	in	in	ADP
ejpam-3052	150	31	each	each	DET
ejpam-3052	150	32	copy	copy	NOUN
ejpam-3052	150	33	.	.	PUNCT
ejpam-3052	151	1	on	on	ADP
ejpam-3052	151	2	applying	apply	VERB
ejpam-3052	151	3	co	co	NOUN
ejpam-3052	151	4	-	-	NOUN
ejpam-3052	151	5	neighbor	neighbor	NOUN
ejpam-3052	151	6	lemma	lemma	PROPN
ejpam-3052	151	7	,	,	PUNCT
ejpam-3052	151	8	we	we	PRON
ejpam-3052	151	9	remove	remove	VERB
ejpam-3052	151	10	three	three	NUM
ejpam-3052	151	11	vertices	vertex	NOUN
ejpam-3052	151	12	from	from	ADP
ejpam-3052	151	13	each	each	DET
ejpam-3052	151	14	copy	copy	NOUN
ejpam-3052	151	15	.	.	PUNCT
ejpam-3052	152	1	then	then	ADV
ejpam-3052	152	2	the	the	DET
ejpam-3052	152	3	nullity	nullity	NOUN
ejpam-3052	152	4	of	of	ADP
ejpam-3052	152	5	(	(	PUNCT
ejpam-3052	152	6	pn	pn	PROPN
ejpam-3052	152	7	�	�	PROPN
ejpam-3052	152	8	k1,4	k1,4	PROPN
ejpam-3052	152	9	)	)	PUNCT
ejpam-3052	152	10	=	=	SYM
ejpam-3052	152	11	η(pn	η(pn	PROPN
ejpam-3052	152	12	�	�	NOUN
ejpam-3052	152	13	k2	k2	NOUN
ejpam-3052	152	14	)	)	PUNCT
ejpam-3052	152	15	+	+	NUM
ejpam-3052	152	16	3n	3n	NUM
ejpam-3052	152	17	.	.	PUNCT
ejpam-3052	153	1	hence	hence	ADV
ejpam-3052	153	2	,	,	PUNCT
ejpam-3052	153	3	we	we	PRON
ejpam-3052	153	4	conclude	conclude	VERB
ejpam-3052	153	5	that	that	SCONJ
ejpam-3052	153	6	η(pn	η(pn	PROPN
ejpam-3052	153	7	�	�	PROPN
ejpam-3052	153	8	k1,4	k1,4	NOUN
ejpam-3052	153	9	)	)	PUNCT
ejpam-3052	154	1	=	=	SYM
ejpam-3052	155	1	3n	3n	NUM
ejpam-3052	155	2	.	.	PUNCT
ejpam-3052	156	1	let	let	VERB
ejpam-3052	156	2	sm	sm	PRON
ejpam-3052	156	3	to	to	PART
ejpam-3052	156	4	be	be	AUX
ejpam-3052	156	5	cm	cm	NOUN
ejpam-3052	156	6	.	.	PUNCT
ejpam-3052	157	1	here	here	ADV
ejpam-3052	157	2	we	we	PRON
ejpam-3052	157	3	need	need	VERB
ejpam-3052	157	4	to	to	PART
ejpam-3052	157	5	tackle	tackle	VERB
ejpam-3052	157	6	two	two	NUM
ejpam-3052	157	7	cases	case	NOUN
ejpam-3052	157	8	for	for	ADP
ejpam-3052	157	9	m	m	PROPN
ejpam-3052	157	10	,	,	PUNCT
ejpam-3052	157	11	viz	viz	PROPN
ejpam-3052	157	12	.	.	PUNCT
ejpam-3052	158	1	m	m	PROPN
ejpam-3052	159	1	≡	≡	PROPN
ejpam-3052	159	2	0	0	PUNCT
ejpam-3052	160	1	(	(	PUNCT
ejpam-3052	160	2	mod	mod	NOUN
ejpam-3052	160	3	4	4	NUM
ejpam-3052	160	4	)	)	PUNCT
ejpam-3052	160	5	and	and	CCONJ
ejpam-3052	160	6	m	m	PROPN
ejpam-3052	160	7	6≡	6≡	NUM
ejpam-3052	160	8	0	0	NUM
ejpam-3052	160	9	(	(	PUNCT
ejpam-3052	160	10	mod	mod	PROPN
ejpam-3052	160	11	4	4	NUM
ejpam-3052	160	12	)	)	PUNCT
ejpam-3052	160	13	.	.	PUNCT
ejpam-3052	161	1	case	case	NOUN
ejpam-3052	161	2	(	(	PUNCT
ejpam-3052	161	3	i	i	NOUN
ejpam-3052	161	4	)	)	PUNCT
ejpam-3052	161	5	.	.	PUNCT
ejpam-3052	162	1	for	for	ADP
ejpam-3052	162	2	m	m	PROPN
ejpam-3052	162	3	≡	≡	PROPN
ejpam-3052	162	4	0	0	PUNCT
ejpam-3052	163	1	(	(	PUNCT
ejpam-3052	163	2	mod	mod	PROPN
ejpam-3052	163	3	4	4	X
ejpam-3052	163	4	)	)	PUNCT
ejpam-3052	163	5	we	we	PRON
ejpam-3052	163	6	will	will	AUX
ejpam-3052	163	7	find	find	VERB
ejpam-3052	163	8	the	the	DET
ejpam-3052	163	9	nullity	nullity	NOUN
ejpam-3052	163	10	of	of	ADP
ejpam-3052	163	11	(	(	PUNCT
ejpam-3052	163	12	pn	pn	PROPN
ejpam-3052	163	13	�	�	PROPN
ejpam-3052	163	14	cm	cm	PROPN
ejpam-3052	163	15	)	)	PUNCT
ejpam-3052	163	16	.	.	PUNCT
ejpam-3052	164	1	we	we	PRON
ejpam-3052	164	2	assume	assume	VERB
ejpam-3052	164	3	that	that	SCONJ
ejpam-3052	164	4	u.	u.	PROPN
ejpam-3052	164	5	sharma	sharma	PROPN
ejpam-3052	164	6	,	,	PUNCT
ejpam-3052	164	7	r.	r.	PROPN
ejpam-3052	164	8	naresh	naresh	PROPN
ejpam-3052	164	9	/	/	SYM
ejpam-3052	164	10	eur	eur	PROPN
ejpam-3052	164	11	.	.	PUNCT
ejpam-3052	165	1	j.	j.	PROPN
ejpam-3052	165	2	pure	pure	PROPN
ejpam-3052	165	3	appl	appl	PROPN
ejpam-3052	165	4	.	.	PROPN
ejpam-3052	165	5	math	math	PROPN
ejpam-3052	165	6	,	,	PUNCT
ejpam-3052	165	7	10	10	NUM
ejpam-3052	165	8	(	(	PUNCT
ejpam-3052	165	9	5	5	NUM
ejpam-3052	165	10	)	)	PUNCT
ejpam-3052	165	11	(	(	PUNCT
ejpam-3052	165	12	2017	2017	NUM
ejpam-3052	165	13	)	)	PUNCT
ejpam-3052	165	14	,	,	PUNCT
ejpam-3052	165	15	1050	1050	NUM
ejpam-3052	165	16	-	-	SYM
ejpam-3052	165	17	1057	1057	NUM
ejpam-3052	165	18	1056	1056	NUM
ejpam-3052	165	19	v	v	ADP
ejpam-3052	165	20	v	v	ADP
ejpam-3052	165	21	v	v	NOUN
ejpam-3052	165	22	u	u	PROPN
ejpam-3052	165	23	u	u	NOUN
ejpam-3052	165	24	u	u	NOUN
ejpam-3052	165	25	u	u	NOUN
ejpam-3052	165	26	u	u	X
ejpam-3052	165	27	u	u	X
ejpam-3052	165	28	u	u	X
ejpam-3052	165	29	u	u	X
ejpam-3052	165	30	u	u	NOUN
ejpam-3052	165	31	u	u	NOUN
ejpam-3052	165	32	u	u	NOUN
ejpam-3052	165	33	12	12	NUM
ejpam-3052	165	34	13	13	NUM
ejpam-3052	165	35	14	14	NUM
ejpam-3052	165	36	15	15	NUM
ejpam-3052	165	37	22	22	NUM
ejpam-3052	165	38	23	23	NUM
ejpam-3052	165	39	24	24	NUM
ejpam-3052	165	40	n2	n2	PROPN
ejpam-3052	165	41	n3	n3	PROPN
ejpam-3052	165	42	n4	n4	PROPN
ejpam-3052	165	43	u25	u25	PROPN
ejpam-3052	166	1	un5	un5	NOUN
ejpam-3052	166	2	1	1	NUM
ejpam-3052	166	3	2	2	NUM
ejpam-3052	166	4	n	n	NUM
ejpam-3052	166	5	11	11	NUM
ejpam-3052	166	6	u21	u21	NOUN
ejpam-3052	166	7	un1	un1	NOUN
ejpam-3052	166	8	figure	figure	NOUN
ejpam-3052	166	9	4	4	NUM
ejpam-3052	166	10	:	:	PUNCT
ejpam-3052	166	11	(	(	PUNCT
ejpam-3052	166	12	pn	pn	PROPN
ejpam-3052	166	13	�	�	PROPN
ejpam-3052	166	14	k1,4	k1,4	PROPN
ejpam-3052	166	15	)	)	PUNCT
ejpam-3052	166	16	uij	uij	PRON
ejpam-3052	166	17	=	=	PUNCT
ejpam-3052	166	18	xij	xij	PROPN
ejpam-3052	166	19	and	and	CCONJ
ejpam-3052	166	20	vi	vi	PROPN
ejpam-3052	166	21	=	=	NOUN
ejpam-3052	166	22	yi	yi	PROPN
ejpam-3052	166	23	be	be	AUX
ejpam-3052	166	24	weighting	weight	VERB
ejpam-3052	166	25	of	of	ADP
ejpam-3052	166	26	graph	graph	NOUN
ejpam-3052	166	27	(	(	PUNCT
ejpam-3052	166	28	pn	pn	PROPN
ejpam-3052	166	29	�	�	PROPN
ejpam-3052	166	30	cm	cm	PROPN
ejpam-3052	166	31	)	)	PUNCT
ejpam-3052	166	32	,	,	PUNCT
ejpam-3052	167	1	where	where	SCONJ
ejpam-3052	167	2	;	;	PUNCT
ejpam-3052	167	3	i	i	PRON
ejpam-3052	167	4	=	=	NOUN
ejpam-3052	167	5	1	1	NUM
ejpam-3052	167	6	,	,	PUNCT
ejpam-3052	167	7	2	2	NUM
ejpam-3052	167	8	,	,	PUNCT
ejpam-3052	167	9	.	.	PUNCT
ejpam-3052	167	10	.	.	PUNCT
ejpam-3052	168	1	.	.	PUNCT
ejpam-3052	169	1	,	,	PUNCT
ejpam-3052	169	2	n	n	PROPN
ejpam-3052	169	3	and	and	CCONJ
ejpam-3052	169	4	j	j	PROPN
ejpam-3052	169	5	=	=	SYM
ejpam-3052	169	6	1	1	NUM
ejpam-3052	169	7	,	,	PUNCT
ejpam-3052	169	8	2	2	NUM
ejpam-3052	169	9	,	,	PUNCT
ejpam-3052	169	10	.	.	PUNCT
ejpam-3052	169	11	.	.	PUNCT
ejpam-3052	170	1	.	.	PUNCT
ejpam-3052	171	1	,	,	PUNCT
ejpam-3052	171	2	m.	m.	NOUN
ejpam-3052	171	3	then	then	ADV
ejpam-3052	171	4	from	from	ADP
ejpam-3052	171	5	∑	∑	PROPN
ejpam-3052	171	6	w∈n(pn	w∈n(pn	PROPN
ejpam-3052	171	7	�	�	PROPN
ejpam-3052	171	8	cm)(v	cm)(v	NOUN
ejpam-3052	171	9	)	)	PUNCT
ejpam-3052	171	10	f(w	f(w	PROPN
ejpam-3052	171	11	)	)	PUNCT
ejpam-3052	172	1	=	=	SYM
ejpam-3052	172	2	0	0	NUM
ejpam-3052	172	3	,	,	PUNCT
ejpam-3052	172	4	∀	∀	X
ejpam-3052	172	5	v	v	ADP
ejpam-3052	172	6	∈	∈	PROPN
ejpam-3052	172	7	v	v	NOUN
ejpam-3052	172	8	(	(	PUNCT
ejpam-3052	172	9	pn	pn	PROPN
ejpam-3052	172	10	�	�	PROPN
ejpam-3052	172	11	cm	cm	PROPN
ejpam-3052	172	12	)	)	PUNCT
ejpam-3052	172	13	.	.	PUNCT
ejpam-3052	173	1	we	we	PRON
ejpam-3052	173	2	get	get	VERB
ejpam-3052	173	3	equations	equation	NOUN
ejpam-3052	173	4	,	,	PUNCT
ejpam-3052	173	5	and	and	CCONJ
ejpam-3052	173	6	after	after	ADP
ejpam-3052	173	7	solving	solve	VERB
ejpam-3052	173	8	these	these	DET
ejpam-3052	173	9	equations	equation	NOUN
ejpam-3052	173	10	,	,	PUNCT
ejpam-3052	173	11	we	we	PRON
ejpam-3052	173	12	have	have	AUX
ejpam-3052	173	13	used	use	VERB
ejpam-3052	173	14	2	2	NUM
ejpam-3052	173	15	non	non	ADJ
ejpam-3052	173	16	-	-	ADJ
ejpam-3052	173	17	zero	zero	ADJ
ejpam-3052	173	18	variables	variable	NOUN
ejpam-3052	173	19	in	in	ADP
ejpam-3052	173	20	each	each	DET
ejpam-3052	173	21	copy	copy	NOUN
ejpam-3052	173	22	of	of	ADP
ejpam-3052	173	23	cm	cm	PROPN
ejpam-3052	173	24	.	.	PUNCT
ejpam-3052	174	1	it	it	PRON
ejpam-3052	174	2	means	mean	VERB
ejpam-3052	174	3	that	that	SCONJ
ejpam-3052	174	4	we	we	PRON
ejpam-3052	174	5	have	have	VERB
ejpam-3052	174	6	to	to	PART
ejpam-3052	174	7	use	use	VERB
ejpam-3052	174	8	2n	2n	NUM
ejpam-3052	174	9	independent	independent	ADJ
ejpam-3052	174	10	variables	variable	NOUN
ejpam-3052	174	11	,	,	PUNCT
ejpam-3052	174	12	for	for	ADP
ejpam-3052	174	13	a	a	DET
ejpam-3052	174	14	zerosum	zerosum	NOUN
ejpam-3052	174	15	weighting	weighting	NOUN
ejpam-3052	174	16	of	of	ADP
ejpam-3052	174	17	(	(	PUNCT
ejpam-3052	174	18	pn	pn	PROPN
ejpam-3052	174	19	�	�	PROPN
ejpam-3052	174	20	cm	cm	PROPN
ejpam-3052	174	21	)	)	PUNCT
ejpam-3052	174	22	.	.	PUNCT
ejpam-3052	175	1	case	case	NOUN
ejpam-3052	175	2	(	(	PUNCT
ejpam-3052	175	3	ii	ii	NOUN
ejpam-3052	175	4	)	)	PUNCT
ejpam-3052	175	5	.	.	PUNCT
ejpam-3052	176	1	for	for	ADP
ejpam-3052	176	2	m	m	PROPN
ejpam-3052	176	3	6≡	6≡	NUM
ejpam-3052	176	4	0	0	NUM
ejpam-3052	176	5	(	(	PUNCT
ejpam-3052	176	6	mod	mod	PROPN
ejpam-3052	176	7	4	4	NUM
ejpam-3052	176	8	)	)	PUNCT
ejpam-3052	176	9	.	.	PUNCT
ejpam-3052	177	1	we	we	PRON
ejpam-3052	177	2	found	find	VERB
ejpam-3052	177	3	that	that	SCONJ
ejpam-3052	177	4	no	no	DET
ejpam-3052	177	5	non	non	ADJ
ejpam-3052	177	6	-	-	ADJ
ejpam-3052	177	7	zero	zero	ADJ
ejpam-3052	177	8	independent	independent	ADJ
ejpam-3052	177	9	variables	variable	NOUN
ejpam-3052	177	10	in	in	ADP
ejpam-3052	177	11	a	a	DET
ejpam-3052	177	12	zero	zero	NUM
ejpam-3052	177	13	-	-	PUNCT
ejpam-3052	177	14	sum	sum	NOUN
ejpam-3052	177	15	weighting	weighting	NOUN
ejpam-3052	177	16	of	of	ADP
ejpam-3052	177	17	(	(	PUNCT
ejpam-3052	177	18	pn	pn	PROPN
ejpam-3052	177	19	�	�	PROPN
ejpam-3052	177	20	cm	cm	PROPN
ejpam-3052	177	21	)	)	PUNCT
ejpam-3052	177	22	.	.	PUNCT
ejpam-3052	178	1	from	from	ADP
ejpam-3052	178	2	the	the	DET
ejpam-3052	178	3	above	above	ADJ
ejpam-3052	178	4	cases	case	NOUN
ejpam-3052	178	5	,	,	PUNCT
ejpam-3052	178	6	we	we	PRON
ejpam-3052	178	7	conclude	conclude	VERB
ejpam-3052	178	8	that	that	SCONJ
ejpam-3052	178	9	η(pn	η(pn	PROPN
ejpam-3052	178	10	�	�	PROPN
ejpam-3052	178	11	cm	cm	NOUN
ejpam-3052	178	12	)	)	PUNCT
ejpam-3052	179	1	=	=	PRON
ejpam-3052	179	2	{	{	PUNCT
ejpam-3052	179	3	2n	2n	NUM
ejpam-3052	179	4	,	,	PUNCT
ejpam-3052	179	5	m	m	PROPN
ejpam-3052	179	6	≡	≡	PROPN
ejpam-3052	179	7	0	0	PUNCT
ejpam-3052	179	8	(	(	PUNCT
ejpam-3052	179	9	mod	mod	NOUN
ejpam-3052	179	10	4	4	NUM
ejpam-3052	179	11	)	)	PUNCT
ejpam-3052	179	12	0	0	NUM
ejpam-3052	179	13	,	,	PUNCT
ejpam-3052	179	14	m	m	VERB
ejpam-3052	179	15	6≡	6≡	NUM
ejpam-3052	179	16	0	0	NUM
ejpam-3052	179	17	(	(	PUNCT
ejpam-3052	179	18	mod	mod	PROPN
ejpam-3052	179	19	4	4	NUM
ejpam-3052	179	20	)	)	PUNCT
ejpam-3052	179	21	finally	finally	ADV
ejpam-3052	179	22	,	,	PUNCT
ejpam-3052	179	23	let	let	VERB
ejpam-3052	179	24	sm	sm	PRON
ejpam-3052	179	25	to	to	PART
ejpam-3052	179	26	be	be	AUX
ejpam-3052	179	27	either	either	CCONJ
ejpam-3052	179	28	h7	h7	PROPN
ejpam-3052	179	29	or	or	CCONJ
ejpam-3052	179	30	h8	h8	PROPN
ejpam-3052	179	31	respectively	respectively	ADV
ejpam-3052	179	32	.	.	PUNCT
ejpam-3052	180	1	using	use	VERB
ejpam-3052	180	2	the	the	DET
ejpam-3052	180	3	procedure	procedure	NOUN
ejpam-3052	180	4	analogues	analogue	NOUN
ejpam-3052	180	5	as	as	SCONJ
ejpam-3052	180	6	done	do	VERB
ejpam-3052	180	7	in	in	ADP
ejpam-3052	180	8	theorem	theorem	NOUN
ejpam-3052	180	9	2	2	NUM
ejpam-3052	180	10	,	,	PUNCT
ejpam-3052	180	11	we	we	PRON
ejpam-3052	180	12	have	have	AUX
ejpam-3052	180	13	used	use	VERB
ejpam-3052	180	14	no	no	DET
ejpam-3052	180	15	independent	independent	ADJ
ejpam-3052	180	16	variables	variable	NOUN
ejpam-3052	180	17	in	in	ADP
ejpam-3052	180	18	zero	zero	NUM
ejpam-3052	180	19	-	-	PUNCT
ejpam-3052	180	20	sum	sum	NOUN
ejpam-3052	180	21	weighting	weighting	NOUN
ejpam-3052	180	22	of	of	ADP
ejpam-3052	180	23	(	(	PUNCT
ejpam-3052	180	24	pn	pn	PROPN
ejpam-3052	180	25	�	�	PROPN
ejpam-3052	180	26	h7	h7	PROPN
ejpam-3052	180	27	)	)	PUNCT
ejpam-3052	180	28	and	and	CCONJ
ejpam-3052	180	29	(	(	PUNCT
ejpam-3052	180	30	pn	pn	PROPN
ejpam-3052	180	31	�	�	PROPN
ejpam-3052	180	32	h8	h8	PROPN
ejpam-3052	180	33	)	)	PUNCT
ejpam-3052	180	34	.	.	PUNCT
ejpam-3052	181	1	therefore	therefore	ADV
ejpam-3052	181	2	,	,	PUNCT
ejpam-3052	181	3	nullity	nullity	NOUN
ejpam-3052	181	4	of	of	ADP
ejpam-3052	181	5	both	both	CCONJ
ejpam-3052	181	6	the	the	DET
ejpam-3052	181	7	graphs	graph	NOUN
ejpam-3052	181	8	is	be	AUX
ejpam-3052	181	9	zero	zero	NUM
ejpam-3052	181	10	.	.	PUNCT
ejpam-3052	182	1	therefore	therefore	ADV
ejpam-3052	182	2	,	,	PUNCT
ejpam-3052	182	3	η(pn	η(pn	PROPN
ejpam-3052	182	4	�	�	PROPN
ejpam-3052	182	5	h7	h7	PROPN
ejpam-3052	182	6	)	)	PUNCT
ejpam-3052	182	7	=	=	SYM
ejpam-3052	182	8	0	0	NUM
ejpam-3052	182	9	or	or	CCONJ
ejpam-3052	182	10	η(pn	η(pn	PROPN
ejpam-3052	182	11	�	�	NOUN
ejpam-3052	182	12	h8	h8	NOUN
ejpam-3052	182	13	)	)	PUNCT
ejpam-3052	182	14	=	=	SYM
ejpam-3052	183	1	0	0	X
ejpam-3052	183	2	.	.	PUNCT
ejpam-3052	184	1	from	from	ADP
ejpam-3052	184	2	the	the	DET
ejpam-3052	184	3	above	above	ADJ
ejpam-3052	184	4	analysis	analysis	NOUN
ejpam-3052	184	5	,	,	PUNCT
ejpam-3052	184	6	it	it	PRON
ejpam-3052	184	7	is	be	AUX
ejpam-3052	184	8	clear	clear	ADJ
ejpam-3052	185	1	that	that	SCONJ
ejpam-3052	185	2	,	,	PUNCT
ejpam-3052	185	3	η(pn	η(pn	PROPN
ejpam-3052	185	4	�	�	PROPN
ejpam-3052	185	5	sm	sm	PROPN
ejpam-3052	185	6	)	)	PUNCT
ejpam-3052	185	7	∈	∈	PROPN
ejpam-3052	185	8	{	{	PUNCT
ejpam-3052	185	9	0	0	NUM
ejpam-3052	185	10	,	,	PUNCT
ejpam-3052	185	11	2n	2n	NUM
ejpam-3052	185	12	,	,	PUNCT
ejpam-3052	185	13	3n	3n	NUM
ejpam-3052	185	14	}	}	PUNCT
ejpam-3052	185	15	.	.	PUNCT
ejpam-3052	185	16	�	�	PROPN
ejpam-3052	185	17	theorem	theorem	VERB
ejpam-3052	185	18	4	4	NUM
ejpam-3052	185	19	.	.	PUNCT
ejpam-3052	186	1	let	let	AUX
ejpam-3052	186	2	(	(	PUNCT
ejpam-3052	186	3	pn	pn	PROPN
ejpam-3052	186	4	�	�	PROPN
ejpam-3052	186	5	sm	sm	PART
ejpam-3052	186	6	)	)	PUNCT
ejpam-3052	186	7	denotes	denote	VERB
ejpam-3052	186	8	the	the	DET
ejpam-3052	186	9	corona	corona	NOUN
ejpam-3052	186	10	of	of	ADP
ejpam-3052	186	11	a	a	DET
ejpam-3052	186	12	path	path	NOUN
ejpam-3052	186	13	with	with	ADP
ejpam-3052	186	14	any	any	DET
ejpam-3052	186	15	smith	smith	NOUN
ejpam-3052	186	16	graph	graph	NOUN
ejpam-3052	186	17	sm	sm	PROPN
ejpam-3052	186	18	.	.	PUNCT
ejpam-3052	187	1	then	then	ADV
ejpam-3052	187	2	η(pn	η(pn	PROPN
ejpam-3052	187	3	�	�	PROPN
ejpam-3052	187	4	sm	sm	PROPN
ejpam-3052	187	5	)	)	PUNCT
ejpam-3052	187	6	∈	∈	PROPN
ejpam-3052	187	7	{	{	PUNCT
ejpam-3052	187	8	0	0	NUM
ejpam-3052	187	9	,	,	PUNCT
ejpam-3052	187	10	n	n	CCONJ
ejpam-3052	187	11	,	,	PUNCT
ejpam-3052	187	12	2n	2n	NUM
ejpam-3052	187	13	,	,	PUNCT
ejpam-3052	187	14	3n	3n	NUM
ejpam-3052	187	15	}	}	PUNCT
ejpam-3052	187	16	.	.	PUNCT
ejpam-3052	188	1	proof	proof	NOUN
ejpam-3052	188	2	.	.	PUNCT
ejpam-3052	189	1	the	the	DET
ejpam-3052	189	2	proof	proof	NOUN
ejpam-3052	189	3	of	of	ADP
ejpam-3052	189	4	the	the	DET
ejpam-3052	189	5	result	result	NOUN
ejpam-3052	189	6	can	can	AUX
ejpam-3052	189	7	be	be	AUX
ejpam-3052	189	8	given	give	VERB
ejpam-3052	189	9	by	by	ADP
ejpam-3052	189	10	theorem	theorem	ADJ
ejpam-3052	189	11	2	2	NUM
ejpam-3052	189	12	and	and	CCONJ
ejpam-3052	189	13	theorem	theorem	VERB
ejpam-3052	189	14	3	3	NUM
ejpam-3052	189	15	.	.	X
ejpam-3052	189	16	�	�	PROPN
ejpam-3052	189	17	now	now	ADV
ejpam-3052	189	18	we	we	PRON
ejpam-3052	189	19	give	give	VERB
ejpam-3052	189	20	the	the	DET
ejpam-3052	189	21	following	following	ADJ
ejpam-3052	189	22	result	result	NOUN
ejpam-3052	189	23	which	which	PRON
ejpam-3052	189	24	established	establish	VERB
ejpam-3052	189	25	the	the	DET
ejpam-3052	189	26	connection	connection	NOUN
ejpam-3052	189	27	between	between	ADP
ejpam-3052	189	28	nullity	nullity	NOUN
ejpam-3052	189	29	of	of	ADP
ejpam-3052	189	30	corona	corona	NOUN
ejpam-3052	189	31	of	of	ADP
ejpam-3052	189	32	pn	pn	PROPN
ejpam-3052	189	33	with	with	ADP
ejpam-3052	189	34	sm	sm	PROPN
ejpam-3052	189	35	and	and	CCONJ
ejpam-3052	189	36	nullity	nullity	NOUN
ejpam-3052	189	37	of	of	ADP
ejpam-3052	189	38	sm	sm	PROPN
ejpam-3052	189	39	.	.	PROPN
ejpam-3052	189	40	references	reference	NOUN
ejpam-3052	189	41	1057	1057	NUM
ejpam-3052	189	42	theorem	theorem	VERB
ejpam-3052	189	43	5	5	NUM
ejpam-3052	189	44	.	.	PUNCT
ejpam-3052	190	1	let	let	AUX
ejpam-3052	190	2	(	(	PUNCT
ejpam-3052	190	3	pn	pn	PROPN
ejpam-3052	190	4	�	�	PROPN
ejpam-3052	190	5	sm	sm	PART
ejpam-3052	190	6	)	)	PUNCT
ejpam-3052	190	7	denotes	denote	VERB
ejpam-3052	190	8	the	the	DET
ejpam-3052	190	9	corona	corona	NOUN
ejpam-3052	190	10	of	of	ADP
ejpam-3052	190	11	a	a	DET
ejpam-3052	190	12	path	path	NOUN
ejpam-3052	190	13	with	with	ADP
ejpam-3052	190	14	smith	smith	PROPN
ejpam-3052	190	15	graph	graph	PROPN
ejpam-3052	190	16	sm	sm	PROPN
ejpam-3052	190	17	,	,	PUNCT
ejpam-3052	190	18	where	where	SCONJ
ejpam-3052	190	19	sm	sm	PROPN
ejpam-3052	190	20	is	be	AUX
ejpam-3052	190	21	either	either	CCONJ
ejpam-3052	190	22	k1,4	k1,4	PROPN
ejpam-3052	190	23	or	or	CCONJ
ejpam-3052	190	24	cm;m	cm;m	NUM
ejpam-3052	190	25	≥	≥	NUM
ejpam-3052	190	26	3	3	NUM
ejpam-3052	190	27	or	or	CCONJ
ejpam-3052	190	28	h8	h8	PROPN
ejpam-3052	190	29	or	or	CCONJ
ejpam-3052	190	30	h9	h9	PROPN
ejpam-3052	190	31	or	or	CCONJ
ejpam-3052	190	32	wm	wm	PROPN
ejpam-3052	190	33	,	,	PUNCT
ejpam-3052	190	34	m	m	VERB
ejpam-3052	190	35	=	=	ADJ
ejpam-3052	190	36	4k+	4k+	NUM
ejpam-3052	190	37	5	5	NUM
ejpam-3052	190	38	or	or	CCONJ
ejpam-3052	190	39	m	m	PROPN
ejpam-3052	190	40	=	=	ADJ
ejpam-3052	191	1	2k+	2k+	NUM
ejpam-3052	191	2	4	4	NUM
ejpam-3052	191	3	,	,	PUNCT
ejpam-3052	191	4	k	k	NOUN
ejpam-3052	191	5	=	=	SYM
ejpam-3052	191	6	1	1	NUM
ejpam-3052	191	7	,	,	PUNCT
ejpam-3052	191	8	2	2	NUM
ejpam-3052	191	9	,	,	PUNCT
ejpam-3052	191	10	3	3	NUM
ejpam-3052	191	11	,	,	PUNCT
ejpam-3052	191	12	.	.	PUNCT
ejpam-3052	191	13	.	.	PUNCT
ejpam-3052	191	14	.	.	PUNCT
ejpam-3052	191	15	.	.	PUNCT
ejpam-3052	192	1	then	then	ADV
ejpam-3052	192	2	η(pn	η(pn	PROPN
ejpam-3052	192	3	�	�	PROPN
ejpam-3052	192	4	sm	sm	PROPN
ejpam-3052	192	5	)	)	PUNCT
ejpam-3052	192	6	=	=	SYM
ejpam-3052	192	7	n.η(sm	n.η(sm	NOUN
ejpam-3052	192	8	)	)	PUNCT
ejpam-3052	192	9	,	,	PUNCT
ejpam-3052	192	10	where	where	SCONJ
ejpam-3052	192	11	n	n	X
ejpam-3052	192	12	is	be	AUX
ejpam-3052	192	13	the	the	DET
ejpam-3052	192	14	order	order	NOUN
ejpam-3052	192	15	of	of	ADP
ejpam-3052	192	16	path	path	NOUN
ejpam-3052	192	17	.	.	PUNCT
ejpam-3052	193	1	theorem	theorem	ADJ
ejpam-3052	193	2	6	6	NUM
ejpam-3052	193	3	.	.	PUNCT
ejpam-3052	194	1	let	let	AUX
ejpam-3052	194	2	(	(	PUNCT
ejpam-3052	194	3	pn	pn	PROPN
ejpam-3052	194	4	�	�	PROPN
ejpam-3052	194	5	sm	sm	PROPN
ejpam-3052	194	6	)	)	PUNCT
ejpam-3052	194	7	denotes	denote	VERB
ejpam-3052	194	8	the	the	DET
ejpam-3052	194	9	corona	corona	NOUN
ejpam-3052	194	10	of	of	ADP
ejpam-3052	194	11	a	a	DET
ejpam-3052	194	12	path	path	NOUN
ejpam-3052	194	13	with	with	ADP
ejpam-3052	194	14	smith	smith	PROPN
ejpam-3052	194	15	graph	graph	PROPN
ejpam-3052	194	16	sm	sm	PROPN
ejpam-3052	194	17	,	,	PUNCT
ejpam-3052	194	18	where	where	SCONJ
ejpam-3052	194	19	sm	sm	PROPN
ejpam-3052	194	20	is	be	AUX
ejpam-3052	194	21	either	either	CCONJ
ejpam-3052	194	22	h7	h7	PROPN
ejpam-3052	194	23	or	or	CCONJ
ejpam-3052	194	24	wm	wm	PROPN
ejpam-3052	194	25	,	,	PUNCT
ejpam-3052	194	26	m	m	PROPN
ejpam-3052	194	27	=	=	NOUN
ejpam-3052	194	28	2k	2k	NUM
ejpam-3052	195	1	+	+	CCONJ
ejpam-3052	195	2	5	5	NUM
ejpam-3052	195	3	,	,	PUNCT
ejpam-3052	195	4	k	k	NOUN
ejpam-3052	195	5	=	=	SYM
ejpam-3052	195	6	1	1	NUM
ejpam-3052	195	7	,	,	PUNCT
ejpam-3052	195	8	3	3	NUM
ejpam-3052	195	9	,	,	PUNCT
ejpam-3052	195	10	5	5	NUM
ejpam-3052	195	11	,	,	PUNCT
ejpam-3052	195	12	.	.	PUNCT
ejpam-3052	195	13	.	.	PUNCT
ejpam-3052	195	14	.	.	PUNCT
ejpam-3052	195	15	.	.	PUNCT
ejpam-3052	196	1	then	then	ADV
ejpam-3052	196	2	η(pn	η(pn	PROPN
ejpam-3052	196	3	�	�	PROPN
ejpam-3052	196	4	sm	sm	PROPN
ejpam-3052	196	5	)	)	PUNCT
ejpam-3052	196	6	=	=	SYM
ejpam-3052	196	7	n.(η(sm	n.(η(sm	NOUN
ejpam-3052	196	8	)	)	PUNCT
ejpam-3052	196	9	−	−	PROPN
ejpam-3052	197	1	1	1	NUM
ejpam-3052	197	2	)	)	PUNCT
ejpam-3052	197	3	,	,	PUNCT
ejpam-3052	197	4	where	where	SCONJ
ejpam-3052	197	5	n	n	X
ejpam-3052	197	6	is	be	AUX
ejpam-3052	197	7	the	the	DET
ejpam-3052	197	8	order	order	NOUN
ejpam-3052	197	9	of	of	ADP
ejpam-3052	197	10	path	path	NOUN
ejpam-3052	197	11	.	.	PUNCT
ejpam-3052	198	1	acknowledgements	acknowledgement	NOUN
ejpam-3052	198	2	the	the	DET
ejpam-3052	198	3	authors	author	NOUN
ejpam-3052	198	4	would	would	AUX
ejpam-3052	198	5	like	like	VERB
ejpam-3052	198	6	to	to	PART
ejpam-3052	198	7	thank	thank	VERB
ejpam-3052	198	8	dr	dr	PROPN
ejpam-3052	198	9	.	.	PROPN
ejpam-3052	198	10	pranjali	pranjali	PROPN
ejpam-3052	198	11	(	(	PUNCT
ejpam-3052	198	12	banasthali	banasthali	PROPN
ejpam-3052	198	13	university	university	PROPN
ejpam-3052	198	14	rajasthan	rajasthan	PROPN
ejpam-3052	198	15	)	)	PUNCT
ejpam-3052	198	16	for	for	SCONJ
ejpam-3052	198	17	her	her	PRON
ejpam-3052	198	18	thought	thought	NOUN
ejpam-3052	198	19	suggestions	suggestion	NOUN
ejpam-3052	198	20	to	to	PART
ejpam-3052	198	21	improve	improve	VERB
ejpam-3052	198	22	the	the	DET
ejpam-3052	198	23	provoking	provoking	ADJ
ejpam-3052	198	24	presentation	presentation	NOUN
ejpam-3052	198	25	of	of	ADP
ejpam-3052	198	26	the	the	DET
ejpam-3052	198	27	paper	paper	NOUN
ejpam-3052	198	28	.	.	PUNCT
ejpam-3052	199	1	the	the	DET
ejpam-3052	199	2	authors	author	NOUN
ejpam-3052	199	3	are	be	AUX
ejpam-3052	199	4	also	also	ADV
ejpam-3052	199	5	thankful	thankful	ADJ
ejpam-3052	199	6	to	to	ADP
ejpam-3052	199	7	anonymous	anonymous	ADJ
ejpam-3052	199	8	referee	referee	NOUN
ejpam-3052	199	9	for	for	ADP
ejpam-3052	199	10	giving	give	VERB
ejpam-3052	199	11	valuable	valuable	ADJ
ejpam-3052	199	12	comments	comment	NOUN
ejpam-3052	199	13	.	.	PUNCT
ejpam-3052	200	1	references	reference	NOUN
ejpam-3052	200	2	[	[	X
ejpam-3052	200	3	1	1	NUM
ejpam-3052	200	4	]	]	X
ejpam-3052	200	5	cvetkovic	cvetkovic	ADJ
ejpam-3052	200	6	,	,	PUNCT
ejpam-3052	200	7	d.	d.	PROPN
ejpam-3052	200	8	m.	m.	PROPN
ejpam-3052	200	9	,	,	PUNCT
ejpam-3052	200	10	doob	doob	PROPN
ejpam-3052	200	11	,	,	PUNCT
ejpam-3052	200	12	m.	m.	NOUN
ejpam-3052	200	13	,	,	PUNCT
ejpam-3052	200	14	sachs	sachs	PROPN
ejpam-3052	200	15	,	,	PUNCT
ejpam-3052	200	16	h.	h.	PROPN
ejpam-3052	200	17	,	,	PUNCT
ejpam-3052	200	18	spectra	spectra	NOUN
ejpam-3052	200	19	of	of	ADP
ejpam-3052	200	20	graphs	graph	NOUN
ejpam-3052	200	21	.	.	PUNCT
ejpam-3052	201	1	theory	theory	NOUN
ejpam-3052	201	2	and	and	CCONJ
ejpam-3052	201	3	applications	application	NOUN
ejpam-3052	201	4	,	,	PUNCT
ejpam-3052	201	5	1995	1995	NUM
ejpam-3052	201	6	.	.	PUNCT
ejpam-3052	202	1	[	[	X
ejpam-3052	202	2	2	2	NUM
ejpam-3052	202	3	]	]	SYM
ejpam-3052	202	4	dokuchaev	dokuchaev	PROPN
ejpam-3052	202	5	,	,	PUNCT
ejpam-3052	202	6	michael	michael	PROPN
ejpam-3052	202	7	a.	a.	PROPN
ejpam-3052	202	8	,	,	PUNCT
ejpam-3052	202	9	gubareni	gubareni	PROPN
ejpam-3052	202	10	,	,	PUNCT
ejpam-3052	202	11	nadiya	nadiya	PROPN
ejpam-3052	202	12	m.	m.	PROPN
ejpam-3052	202	13	,	,	PUNCT
ejpam-3052	202	14	futorny	futorny	NOUN
ejpam-3052	202	15	,	,	PUNCT
ejpam-3052	202	16	vyacheslav	vyacheslav	NOUN
ejpam-3052	202	17	m.	m.	NOUN
ejpam-3052	202	18	,	,	PUNCT
ejpam-3052	202	19	khibina	khibina	PROPN
ejpam-3052	202	20	,	,	PUNCT
ejpam-3052	202	21	marina	marina	PROPN
ejpam-3052	202	22	a.	a.	PROPN
ejpam-3052	202	23	,	,	PUNCT
ejpam-3052	202	24	kirichenko	kirichenko	PROPN
ejpam-3052	202	25	,	,	PUNCT
ejpam-3052	202	26	vladimir	vladimir	PROPN
ejpam-3052	202	27	,	,	PUNCT
ejpam-3052	202	28	v.	v.	ADV
ejpam-3052	202	29	,	,	PUNCT
ejpam-3052	202	30	dynkin	dynkin	ADJ
ejpam-3052	202	31	diagrams	diagram	NOUN
ejpam-3052	202	32	and	and	CCONJ
ejpam-3052	202	33	spectra	spectra	NOUN
ejpam-3052	202	34	of	of	ADP
ejpam-3052	202	35	graphs	graph	NOUN
ejpam-3052	202	36	,	,	PUNCT
ejpam-3052	202	37	sao	sao	PROPN
ejpam-3052	202	38	paulo	paulo	PROPN
ejpam-3052	202	39	journal	journal	PROPN
ejpam-3052	202	40	of	of	ADP
ejpam-3052	202	41	mathematical	mathematical	ADJ
ejpam-3052	202	42	sciences	science	NOUN
ejpam-3052	202	43	,	,	PUNCT
ejpam-3052	202	44	7	7	NUM
ejpam-3052	202	45	(	(	PUNCT
ejpam-3052	202	46	1),83	1),83	NUM
ejpam-3052	202	47	-	-	SYM
ejpam-3052	202	48	104	104	NUM
ejpam-3052	202	49	,	,	PUNCT
ejpam-3052	202	50	2013	2013	NUM
ejpam-3052	202	51	.	.	PUNCT
ejpam-3052	203	1	[	[	X
ejpam-3052	203	2	3	3	X
ejpam-3052	203	3	]	]	X
ejpam-3052	203	4	gutman	gutman	NOUN
ejpam-3052	203	5	,	,	PUNCT
ejpam-3052	203	6	i.	i.	NOUN
ejpam-3052	203	7	and	and	CCONJ
ejpam-3052	203	8	borovicanin	borovicanin	PROPN
ejpam-3052	203	9	,	,	PUNCT
ejpam-3052	203	10	b.	b.	PROPN
ejpam-3052	203	11	,	,	PUNCT
ejpam-3052	203	12	nullity	nullity	NOUN
ejpam-3052	203	13	of	of	ADP
ejpam-3052	203	14	graphs	graph	NOUN
ejpam-3052	203	15	:	:	PUNCT
ejpam-3052	203	16	an	an	DET
ejpam-3052	203	17	updated	update	VERB
ejpam-3052	203	18	survey	survey	NOUN
ejpam-3052	203	19	.	.	PUNCT
ejpam-3052	204	1	zbornik	zbornik	PROPN
ejpam-3052	204	2	radona	radona	PROPN
ejpam-3052	204	3	(	(	PUNCT
ejpam-3052	204	4	beograd	beograd	PROPN
ejpam-3052	204	5	)	)	PUNCT
ejpam-3052	204	6	,	,	PUNCT
ejpam-3052	204	7	14	14	NUM
ejpam-3052	204	8	(	(	PUNCT
ejpam-3052	204	9	22	22	NUM
ejpam-3052	204	10	)	)	PUNCT
ejpam-3052	204	11	,	,	PUNCT
ejpam-3052	204	12	137	137	NUM
ejpam-3052	204	13	-	-	SYM
ejpam-3052	204	14	154	154	NUM
ejpam-3052	204	15	,	,	PUNCT
ejpam-3052	204	16	2011	2011	NUM
ejpam-3052	204	17	.	.	PUNCT
ejpam-3052	205	1	[	[	X
ejpam-3052	205	2	4	4	NUM
ejpam-3052	205	3	]	]	X
ejpam-3052	205	4	harary	harary	NOUN
ejpam-3052	205	5	,	,	PUNCT
ejpam-3052	205	6	f.	f.	PROPN
ejpam-3052	205	7	,	,	PUNCT
ejpam-3052	205	8	graph	graph	NOUN
ejpam-3052	205	9	theory	theory	NOUN
ejpam-3052	205	10	,	,	PUNCT
ejpam-3052	205	11	addison	addison	PROPN
ejpam-3052	205	12	-	-	PUNCT
ejpam-3052	205	13	wesley	wesley	PROPN
ejpam-3052	205	14	publ	publ	PROPN
ejpam-3052	205	15	.	.	PUNCT
ejpam-3052	206	1	comp	comp	NOUN
ejpam-3052	206	2	.	.	PUNCT
ejpam-3052	207	1	reading	read	VERB
ejpam-3052	207	2	m.	m.	NOUN
ejpam-3052	207	3	a.	a.	PROPN
ejpam-3052	207	4	,(1969	,(1969	PUNCT
ejpam-3052	207	5	)	)	PUNCT
ejpam-3052	208	1	[	[	X
ejpam-3052	208	2	5	5	NUM
ejpam-3052	208	3	]	]	SYM
ejpam-3052	208	4	sharaf	sharaf	NOUN
ejpam-3052	208	5	,	,	PUNCT
ejpam-3052	208	6	k.	k.	PROPN
ejpam-3052	208	7	r.	r.	PROPN
ejpam-3052	208	8	and	and	CCONJ
ejpam-3052	208	9	rasul	rasul	PROPN
ejpam-3052	208	10	,	,	PUNCT
ejpam-3052	208	11	k.	k.	PROPN
ejpam-3052	208	12	b.	b.	PROPN
ejpam-3052	208	13	,	,	PUNCT
ejpam-3052	208	14	on	on	ADP
ejpam-3052	208	15	the	the	DET
ejpam-3052	208	16	nullity	nullity	NOUN
ejpam-3052	208	17	of	of	ADP
ejpam-3052	208	18	expanded	expand	VERB
ejpam-3052	208	19	graphs	graph	NOUN
ejpam-3052	208	20	,	,	PUNCT
ejpam-3052	208	21	gen	gen	PROPN
ejpam-3052	208	22	.	.	PROPN
ejpam-3052	208	23	math	math	PROPN
ejpam-3052	208	24	.	.	PUNCT
ejpam-3052	209	1	notes	note	NOUN
ejpam-3052	209	2	,	,	PUNCT
ejpam-3052	209	3	21(1	21(1	NUM
ejpam-3052	209	4	)	)	PUNCT
ejpam-3052	209	5	,	,	PUNCT
ejpam-3052	209	6	97117	97117	NUM
ejpam-3052	209	7	,	,	PUNCT
ejpam-3052	209	8	2014	2014	NUM
ejpam-3052	209	9	.	.	PUNCT