id	sid	tid	token	lemma	pos
ejpam-4798	1	1	european	european	PROPN
ejpam-4798	1	2	journal	journal	PROPN
ejpam-4798	1	3	of	of	ADP
ejpam-4798	1	4	pure	pure	ADJ
ejpam-4798	1	5	and	and	CCONJ
ejpam-4798	1	6	applied	apply	VERB
ejpam-4798	1	7	mathematics	mathematic	NOUN
ejpam-4798	1	8	vol	vol	NOUN
ejpam-4798	1	9	.	.	PROPN
ejpam-4798	2	1	17	17	NUM
ejpam-4798	2	2	,	,	PUNCT
ejpam-4798	2	3	no	no	INTJ
ejpam-4798	2	4	.	.	NOUN
ejpam-4798	2	5	1	1	NUM
ejpam-4798	2	6	,	,	PUNCT
ejpam-4798	2	7	2024	2024	NUM
ejpam-4798	2	8	,	,	PUNCT
ejpam-4798	2	9	504	504	NUM
ejpam-4798	2	10	-	-	SYM
ejpam-4798	2	11	518	518	NUM
ejpam-4798	2	12	issn	issn	PROPN
ejpam-4798	2	13	1307	1307	NUM
ejpam-4798	2	14	-	-	SYM
ejpam-4798	2	15	5543	5543	NUM
ejpam-4798	2	16	–	–	PUNCT
ejpam-4798	2	17	ejpam.com	ejpam.com	X
ejpam-4798	2	18	published	publish	VERB
ejpam-4798	2	19	by	by	ADP
ejpam-4798	2	20	new	new	PROPN
ejpam-4798	2	21	york	york	PROPN
ejpam-4798	2	22	business	business	PROPN
ejpam-4798	2	23	global	global	ADJ
ejpam-4798	2	24	spectral	spectral	ADJ
ejpam-4798	2	25	analysis	analysis	NOUN
ejpam-4798	2	26	of	of	ADP
ejpam-4798	2	27	splitting	split	VERB
ejpam-4798	2	28	signed	sign	VERB
ejpam-4798	2	29	graph	graph	NOUN
ejpam-4798	2	30	sandeep	sandeep	PROPN
ejpam-4798	2	31	kumar1	kumar1	PROPN
ejpam-4798	2	32	,	,	PUNCT
ejpam-4798	2	33	deepa	deepa	PROPN
ejpam-4798	2	34	sinha1,∗	sinha1,∗	PROPN
ejpam-4798	2	35	1	1	PROPN
ejpam-4798	2	36	department	department	NOUN
ejpam-4798	2	37	of	of	ADP
ejpam-4798	2	38	mathematics	mathematic	NOUN
ejpam-4798	2	39	,	,	PUNCT
ejpam-4798	2	40	south	south	ADJ
ejpam-4798	2	41	asian	asian	PROPN
ejpam-4798	2	42	university	university	PROPN
ejpam-4798	2	43	,	,	PUNCT
ejpam-4798	2	44	new	new	ADJ
ejpam-4798	2	45	delhi-110068	delhi-110068	ADJ
ejpam-4798	2	46	,	,	PUNCT
ejpam-4798	2	47	india	india	PROPN
ejpam-4798	2	48	abstract	abstract	NOUN
ejpam-4798	2	49	.	.	PUNCT
ejpam-4798	3	1	an	an	DET
ejpam-4798	3	2	ordered	order	VERB
ejpam-4798	3	3	pair	pair	NOUN
ejpam-4798	3	4	σ	σ	NOUN
ejpam-4798	3	5	=	=	SYM
ejpam-4798	3	6	(	(	PUNCT
ejpam-4798	3	7	σu	σu	INTJ
ejpam-4798	3	8	,	,	PUNCT
ejpam-4798	3	9	σ	σ	PROPN
ejpam-4798	3	10	)	)	PUNCT
ejpam-4798	3	11	is	be	AUX
ejpam-4798	3	12	called	call	VERB
ejpam-4798	3	13	the	the	DET
ejpam-4798	3	14	signed	sign	VERB
ejpam-4798	3	15	graph	graph	NOUN
ejpam-4798	3	16	,	,	PUNCT
ejpam-4798	3	17	where	where	SCONJ
ejpam-4798	3	18	σu	σu	ADV
ejpam-4798	3	19	=	=	SYM
ejpam-4798	3	20	(	(	PUNCT
ejpam-4798	3	21	v	v	NOUN
ejpam-4798	3	22	,	,	PUNCT
ejpam-4798	3	23	e	e	NOUN
ejpam-4798	3	24	)	)	PUNCT
ejpam-4798	3	25	is	be	AUX
ejpam-4798	3	26	a	a	DET
ejpam-4798	3	27	underlying	underlie	VERB
ejpam-4798	3	28	graph	graph	NOUN
ejpam-4798	3	29	and	and	CCONJ
ejpam-4798	3	30	σ	σ	PROPN
ejpam-4798	3	31	is	be	AUX
ejpam-4798	3	32	a	a	DET
ejpam-4798	3	33	signed	sign	VERB
ejpam-4798	3	34	mapping	mapping	NOUN
ejpam-4798	3	35	,	,	PUNCT
ejpam-4798	3	36	called	call	VERB
ejpam-4798	3	37	signature	signature	NOUN
ejpam-4798	3	38	,	,	PUNCT
ejpam-4798	3	39	from	from	ADP
ejpam-4798	3	40	e	e	PRON
ejpam-4798	3	41	to	to	ADP
ejpam-4798	3	42	the	the	DET
ejpam-4798	3	43	sign	sign	NOUN
ejpam-4798	3	44	set	set	VERB
ejpam-4798	3	45	{	{	PUNCT
ejpam-4798	3	46	+	+	NOUN
ejpam-4798	3	47	,	,	PUNCT
ejpam-4798	3	48	−	−	NOUN
ejpam-4798	3	49	}	}	PUNCT
ejpam-4798	3	50	.	.	PUNCT
ejpam-4798	4	1	the	the	DET
ejpam-4798	4	2	splitting	splitting	NOUN
ejpam-4798	4	3	signed	sign	VERB
ejpam-4798	4	4	graph	graph	NOUN
ejpam-4798	4	5	γ(σ	γ(σ	PROPN
ejpam-4798	4	6	)	)	PUNCT
ejpam-4798	4	7	of	of	ADP
ejpam-4798	4	8	a	a	DET
ejpam-4798	4	9	signed	sign	VERB
ejpam-4798	4	10	graph	graph	NOUN
ejpam-4798	4	11	σ	σ	NOUN
ejpam-4798	4	12	is	be	AUX
ejpam-4798	4	13	defined	define	VERB
ejpam-4798	4	14	as	as	ADP
ejpam-4798	4	15	,	,	PUNCT
ejpam-4798	4	16	for	for	ADP
ejpam-4798	4	17	every	every	DET
ejpam-4798	4	18	vertex	vertex	NOUN
ejpam-4798	4	19	u	u	NOUN
ejpam-4798	4	20	∈	∈	PROPN
ejpam-4798	4	21	v	v	PROPN
ejpam-4798	4	22	(	(	PUNCT
ejpam-4798	4	23	σ	σ	PROPN
ejpam-4798	4	24	)	)	PUNCT
ejpam-4798	4	25	,	,	PUNCT
ejpam-4798	4	26	take	take	VERB
ejpam-4798	4	27	a	a	DET
ejpam-4798	4	28	new	new	ADJ
ejpam-4798	4	29	vertex	vertex	NOUN
ejpam-4798	4	30	u′.	u′.	AUX
ejpam-4798	4	31	join	join	VERB
ejpam-4798	4	32	u′	u′	PROPN
ejpam-4798	4	33	to	to	ADP
ejpam-4798	4	34	all	all	DET
ejpam-4798	4	35	the	the	DET
ejpam-4798	4	36	vertices	vertex	NOUN
ejpam-4798	4	37	of	of	ADP
ejpam-4798	4	38	σ	σ	NOUN
ejpam-4798	4	39	adjacent	adjacent	ADJ
ejpam-4798	4	40	to	to	ADP
ejpam-4798	4	41	u	u	PRON
ejpam-4798	4	42	such	such	ADJ
ejpam-4798	4	43	that	that	SCONJ
ejpam-4798	4	44	σγ(u	σγ(u	ADJ
ejpam-4798	4	45	′v	′v	NOUN
ejpam-4798	4	46	)	)	PUNCT
ejpam-4798	4	47	=	=	SYM
ejpam-4798	4	48	σ(u′v	σ(u′v	PROPN
ejpam-4798	4	49	)	)	PUNCT
ejpam-4798	4	50	,	,	PUNCT
ejpam-4798	4	51	u	u	PROPN
ejpam-4798	4	52	∈	∈	PROPN
ejpam-4798	4	53	n(v	n(v	PROPN
ejpam-4798	4	54	)	)	PUNCT
ejpam-4798	4	55	.	.	PUNCT
ejpam-4798	5	1	the	the	DET
ejpam-4798	5	2	objective	objective	NOUN
ejpam-4798	5	3	of	of	ADP
ejpam-4798	5	4	this	this	DET
ejpam-4798	5	5	paper	paper	NOUN
ejpam-4798	5	6	is	be	AUX
ejpam-4798	5	7	to	to	PART
ejpam-4798	5	8	propose	propose	VERB
ejpam-4798	5	9	an	an	DET
ejpam-4798	5	10	algorithm	algorithm	NOUN
ejpam-4798	5	11	for	for	ADP
ejpam-4798	5	12	the	the	DET
ejpam-4798	5	13	generation	generation	NOUN
ejpam-4798	5	14	of	of	ADP
ejpam-4798	5	15	a	a	DET
ejpam-4798	5	16	splitting	splitting	NOUN
ejpam-4798	5	17	signed	sign	VERB
ejpam-4798	5	18	graph	graph	NOUN
ejpam-4798	5	19	,	,	PUNCT
ejpam-4798	5	20	a	a	DET
ejpam-4798	5	21	splitting	splitting	NOUN
ejpam-4798	5	22	root	root	NOUN
ejpam-4798	5	23	signed	sign	VERB
ejpam-4798	5	24	graph	graph	NOUN
ejpam-4798	5	25	from	from	ADP
ejpam-4798	5	26	a	a	DET
ejpam-4798	5	27	given	give	VERB
ejpam-4798	5	28	signed	sign	VERB
ejpam-4798	5	29	graph	graph	NOUN
ejpam-4798	5	30	using	use	VERB
ejpam-4798	5	31	matlab	matlab	PROPN
ejpam-4798	5	32	.	.	PUNCT
ejpam-4798	6	1	additionally	additionally	ADV
ejpam-4798	6	2	,	,	PUNCT
ejpam-4798	6	3	we	we	PRON
ejpam-4798	6	4	conduct	conduct	VERB
ejpam-4798	6	5	a	a	DET
ejpam-4798	6	6	spectral	spectral	ADJ
ejpam-4798	6	7	analysis	analysis	NOUN
ejpam-4798	6	8	of	of	ADP
ejpam-4798	6	9	the	the	DET
ejpam-4798	6	10	resulting	result	VERB
ejpam-4798	6	11	graph	graph	NOUN
ejpam-4798	6	12	.	.	PUNCT
ejpam-4798	7	1	spectral	spectral	ADJ
ejpam-4798	7	2	analysis	analysis	NOUN
ejpam-4798	7	3	is	be	AUX
ejpam-4798	7	4	performed	perform	VERB
ejpam-4798	7	5	on	on	ADP
ejpam-4798	7	6	the	the	DET
ejpam-4798	7	7	adjacency	adjacency	NOUN
ejpam-4798	7	8	and	and	CCONJ
ejpam-4798	7	9	laplacian	laplacian	ADJ
ejpam-4798	7	10	matrices	matrix	NOUN
ejpam-4798	7	11	of	of	ADP
ejpam-4798	7	12	the	the	DET
ejpam-4798	7	13	splitting	splitting	NOUN
ejpam-4798	7	14	signed	sign	VERB
ejpam-4798	7	15	graph	graph	NOUN
ejpam-4798	7	16	to	to	PART
ejpam-4798	7	17	study	study	VERB
ejpam-4798	7	18	its	its	PRON
ejpam-4798	7	19	eigenvalues	eigenvalue	NOUN
ejpam-4798	7	20	and	and	CCONJ
ejpam-4798	7	21	eigenvectors	eigenvector	NOUN
ejpam-4798	7	22	.	.	PUNCT
ejpam-4798	8	1	a	a	DET
ejpam-4798	8	2	relationship	relationship	NOUN
ejpam-4798	8	3	between	between	ADP
ejpam-4798	8	4	the	the	DET
ejpam-4798	8	5	energy	energy	NOUN
ejpam-4798	8	6	of	of	ADP
ejpam-4798	8	7	the	the	DET
ejpam-4798	8	8	original	original	ADJ
ejpam-4798	8	9	signed	sign	VERB
ejpam-4798	8	10	graph	graph	NOUN
ejpam-4798	8	11	σ	σ	PROPN
ejpam-4798	8	12	and	and	CCONJ
ejpam-4798	8	13	the	the	DET
ejpam-4798	8	14	energy	energy	NOUN
ejpam-4798	8	15	of	of	ADP
ejpam-4798	8	16	the	the	DET
ejpam-4798	8	17	splitting	splitting	NOUN
ejpam-4798	8	18	signed	sign	VERB
ejpam-4798	8	19	graph	graph	NOUN
ejpam-4798	8	20	γ(σ	γ(σ	PROPN
ejpam-4798	8	21	)	)	PUNCT
ejpam-4798	8	22	is	be	AUX
ejpam-4798	8	23	established	establish	VERB
ejpam-4798	8	24	.	.	PUNCT
ejpam-4798	9	1	2020	2020	NUM
ejpam-4798	9	2	mathematics	mathematics	PROPN
ejpam-4798	9	3	subject	subject	NOUN
ejpam-4798	9	4	classifications	classification	NOUN
ejpam-4798	9	5	:	:	PUNCT
ejpam-4798	9	6	05c22	05c22	NOUN
ejpam-4798	9	7	,	,	PUNCT
ejpam-4798	9	8	05c50	05c50	NUM
ejpam-4798	9	9	,	,	PUNCT
ejpam-4798	9	10	05c90	05c90	PRON
ejpam-4798	9	11	key	key	ADJ
ejpam-4798	9	12	words	word	NOUN
ejpam-4798	9	13	and	and	CCONJ
ejpam-4798	9	14	phrases	phrase	NOUN
ejpam-4798	9	15	:	:	PUNCT
ejpam-4798	9	16	signed	sign	VERB
ejpam-4798	9	17	graph	graph	NOUN
ejpam-4798	9	18	,	,	PUNCT
ejpam-4798	9	19	splitting	split	VERB
ejpam-4798	9	20	signed	sign	VERB
ejpam-4798	9	21	graph	graph	NOUN
ejpam-4798	9	22	,	,	PUNCT
ejpam-4798	9	23	spectrum	spectrum	NOUN
ejpam-4798	9	24	,	,	PUNCT
ejpam-4798	9	25	energy	energy	NOUN
ejpam-4798	9	26	1	1	NUM
ejpam-4798	9	27	.	.	PUNCT
ejpam-4798	10	1	introduction	introduction	NOUN
ejpam-4798	10	2	the	the	DET
ejpam-4798	10	3	initial	initial	ADJ
ejpam-4798	10	4	notation	notation	NOUN
ejpam-4798	10	5	and	and	CCONJ
ejpam-4798	10	6	terminology	terminology	NOUN
ejpam-4798	10	7	used	use	VERB
ejpam-4798	10	8	in	in	ADP
ejpam-4798	10	9	this	this	DET
ejpam-4798	10	10	paper	paper	NOUN
ejpam-4798	10	11	have	have	AUX
ejpam-4798	10	12	been	be	AUX
ejpam-4798	10	13	sourced	source	VERB
ejpam-4798	10	14	from	from	ADP
ejpam-4798	10	15	harary	harary	NOUN
ejpam-4798	10	16	[	[	X
ejpam-4798	10	17	10	10	NUM
ejpam-4798	10	18	]	]	PUNCT
ejpam-4798	10	19	,	,	PUNCT
ejpam-4798	10	20	zaslavsky	zaslavsky	NOUN
ejpam-4798	11	1	[	[	X
ejpam-4798	11	2	20	20	NUM
ejpam-4798	11	3	]	]	PUNCT
ejpam-4798	11	4	and	and	CCONJ
ejpam-4798	11	5	west	west	NOUN
ejpam-4798	12	1	[	[	X
ejpam-4798	12	2	19	19	NUM
ejpam-4798	12	3	]	]	PUNCT
ejpam-4798	12	4	.	.	PUNCT
ejpam-4798	13	1	the	the	DET
ejpam-4798	13	2	graphs	graph	NOUN
ejpam-4798	13	3	examined	examine	VERB
ejpam-4798	13	4	in	in	ADP
ejpam-4798	13	5	this	this	DET
ejpam-4798	13	6	paper	paper	NOUN
ejpam-4798	13	7	are	be	AUX
ejpam-4798	13	8	finite	finite	ADJ
ejpam-4798	13	9	and	and	CCONJ
ejpam-4798	13	10	simple	simple	ADJ
ejpam-4798	13	11	.	.	PUNCT
ejpam-4798	14	1	a	a	DET
ejpam-4798	14	2	signed	sign	VERB
ejpam-4798	14	3	graph	graph	NOUN
ejpam-4798	14	4	,	,	PUNCT
ejpam-4798	14	5	σ	σ	X
ejpam-4798	14	6	=	=	SYM
ejpam-4798	14	7	(	(	PUNCT
ejpam-4798	14	8	σu	σu	INTJ
ejpam-4798	14	9	,	,	PUNCT
ejpam-4798	14	10	σ	σ	PROPN
ejpam-4798	14	11	)	)	PUNCT
ejpam-4798	14	12	,	,	PUNCT
ejpam-4798	14	13	is	be	AUX
ejpam-4798	14	14	composed	compose	VERB
ejpam-4798	14	15	of	of	ADP
ejpam-4798	14	16	an	an	DET
ejpam-4798	14	17	underlying	underlie	VERB
ejpam-4798	14	18	graph	graph	NOUN
ejpam-4798	14	19	,	,	PUNCT
ejpam-4798	14	20	σu	σu	X
ejpam-4798	14	21	=	=	SYM
ejpam-4798	14	22	(	(	PUNCT
ejpam-4798	14	23	v	v	NOUN
ejpam-4798	14	24	,	,	PUNCT
ejpam-4798	14	25	e	e	NOUN
ejpam-4798	14	26	)	)	PUNCT
ejpam-4798	14	27	,	,	PUNCT
ejpam-4798	14	28	where	where	SCONJ
ejpam-4798	14	29	|v	|v	PROPN
ejpam-4798	14	30	|	|	NOUN
ejpam-4798	14	31	=	=	SYM
ejpam-4798	14	32	n	n	PROPN
ejpam-4798	14	33	&	&	CCONJ
ejpam-4798	14	34	|e|	|e|	PRON
ejpam-4798	14	35	=	=	PROPN
ejpam-4798	14	36	m	m	PROPN
ejpam-4798	14	37	,	,	PUNCT
ejpam-4798	14	38	and	and	CCONJ
ejpam-4798	14	39	a	a	DET
ejpam-4798	14	40	signature	signature	NOUN
ejpam-4798	14	41	,	,	PUNCT
ejpam-4798	14	42	σ	σ	PROPN
ejpam-4798	14	43	:	:	PUNCT
ejpam-4798	14	44	e	e	X
ejpam-4798	14	45	→	→	PUNCT
ejpam-4798	14	46	{	{	PUNCT
ejpam-4798	14	47	+	+	ADJ
ejpam-4798	14	48	,	,	PUNCT
ejpam-4798	14	49	−	−	PROPN
ejpam-4798	14	50	}	}	PUNCT
ejpam-4798	14	51	,	,	PUNCT
ejpam-4798	14	52	which	which	PRON
ejpam-4798	14	53	labels	label	VERB
ejpam-4798	14	54	each	each	DET
ejpam-4798	14	55	edge	edge	NOUN
ejpam-4798	14	56	of	of	ADP
ejpam-4798	14	57	σu	σu	INTJ
ejpam-4798	14	58	as	as	ADP
ejpam-4798	14	59	either	either	CCONJ
ejpam-4798	14	60	‘	'	PUNCT
ejpam-4798	14	61	+	+	NOUN
ejpam-4798	14	62	’	'	PUNCT
ejpam-4798	14	63	or	or	CCONJ
ejpam-4798	14	64	‘	'	PUNCT
ejpam-4798	14	65	−	−	NOUN
ejpam-4798	14	66	’	'	PUNCT
ejpam-4798	14	67	.	.	PUNCT
ejpam-4798	15	1	in	in	ADP
ejpam-4798	15	2	this	this	DET
ejpam-4798	15	3	paper	paper	NOUN
ejpam-4798	15	4	,	,	PUNCT
ejpam-4798	15	5	edges	edge	NOUN
ejpam-4798	15	6	labeled	label	VERB
ejpam-4798	15	7	with	with	ADP
ejpam-4798	15	8	‘	'	PUNCT
ejpam-4798	15	9	+	+	NOUN
ejpam-4798	15	10	’	'	PUNCT
ejpam-4798	15	11	are	be	AUX
ejpam-4798	15	12	considered	consider	VERB
ejpam-4798	15	13	positive	positive	ADJ
ejpam-4798	15	14	and	and	CCONJ
ejpam-4798	15	15	are	be	AUX
ejpam-4798	15	16	depicted	depict	VERB
ejpam-4798	15	17	using	use	VERB
ejpam-4798	15	18	solid	solid	ADJ
ejpam-4798	15	19	lines	line	NOUN
ejpam-4798	15	20	,	,	PUNCT
ejpam-4798	15	21	while	while	SCONJ
ejpam-4798	15	22	edges	edge	NOUN
ejpam-4798	15	23	labeled	label	VERB
ejpam-4798	15	24	with	with	ADP
ejpam-4798	15	25	‘	'	PUNCT
ejpam-4798	15	26	−	−	NOUN
ejpam-4798	15	27	’	'	PUNCT
ejpam-4798	15	28	are	be	AUX
ejpam-4798	15	29	considered	consider	VERB
ejpam-4798	15	30	negative	negative	ADJ
ejpam-4798	15	31	and	and	CCONJ
ejpam-4798	15	32	are	be	AUX
ejpam-4798	15	33	depicted	depict	VERB
ejpam-4798	15	34	using	use	VERB
ejpam-4798	15	35	dashed	dash	VERB
ejpam-4798	15	36	lines	line	NOUN
ejpam-4798	15	37	.	.	PUNCT
ejpam-4798	16	1	if	if	SCONJ
ejpam-4798	16	2	all	all	DET
ejpam-4798	16	3	edges	edge	NOUN
ejpam-4798	16	4	in	in	ADP
ejpam-4798	16	5	σ	σ	PROPN
ejpam-4798	16	6	are	be	AUX
ejpam-4798	16	7	signed	sign	VERB
ejpam-4798	16	8	‘	'	PUNCT
ejpam-4798	16	9	+	+	ADJ
ejpam-4798	16	10	’	'	PUNCT
ejpam-4798	16	11	or	or	CCONJ
ejpam-4798	16	12	‘	'	PUNCT
ejpam-4798	16	13	−	−	NOUN
ejpam-4798	16	14	’	'	PUNCT
ejpam-4798	16	15	,	,	PUNCT
ejpam-4798	16	16	the	the	DET
ejpam-4798	16	17	signed	sign	VERB
ejpam-4798	16	18	graph	graph	NOUN
ejpam-4798	16	19	is	be	AUX
ejpam-4798	16	20	referred	refer	VERB
ejpam-4798	16	21	to	to	ADP
ejpam-4798	16	22	as	as	ADP
ejpam-4798	16	23	homogeneous	homogeneous	ADJ
ejpam-4798	16	24	,	,	PUNCT
ejpam-4798	16	25	otherwise	otherwise	ADV
ejpam-4798	16	26	,	,	PUNCT
ejpam-4798	16	27	it	it	PRON
ejpam-4798	16	28	is	be	AUX
ejpam-4798	16	29	heterogeneous	heterogeneous	ADJ
ejpam-4798	16	30	.	.	PUNCT
ejpam-4798	17	1	graphs	graph	NOUN
ejpam-4798	17	2	can	can	AUX
ejpam-4798	17	3	be	be	AUX
ejpam-4798	17	4	thought	think	VERB
ejpam-4798	17	5	of	of	ADP
ejpam-4798	17	6	as	as	ADP
ejpam-4798	17	7	homogeneous	homogeneous	ADJ
ejpam-4798	17	8	signed	sign	VERB
ejpam-4798	17	9	graphs	graph	NOUN
ejpam-4798	17	10	with	with	ADP
ejpam-4798	17	11	each	each	DET
ejpam-4798	17	12	edge	edge	NOUN
ejpam-4798	17	13	being	be	AUX
ejpam-4798	17	14	labeled	label	VERB
ejpam-4798	17	15	as	as	ADP
ejpam-4798	17	16	‘	'	PUNCT
ejpam-4798	17	17	+	+	NOUN
ejpam-4798	17	18	’	'	PUNCT
ejpam-4798	17	19	.	.	PUNCT
ejpam-4798	18	1	a	a	DET
ejpam-4798	18	2	cycle	cycle	NOUN
ejpam-4798	18	3	in	in	ADP
ejpam-4798	18	4	a	a	DET
ejpam-4798	18	5	signed	sign	VERB
ejpam-4798	18	6	graph	graph	NOUN
ejpam-4798	18	7	σ	σ	NOUN
ejpam-4798	18	8	is	be	AUX
ejpam-4798	18	9	considered	consider	VERB
ejpam-4798	18	10	positive	positive	ADJ
ejpam-4798	18	11	if	if	SCONJ
ejpam-4798	18	12	it	it	PRON
ejpam-4798	18	13	includes	include	VERB
ejpam-4798	18	14	an	an	DET
ejpam-4798	18	15	even	even	ADJ
ejpam-4798	18	16	number	number	NOUN
ejpam-4798	18	17	of	of	ADP
ejpam-4798	18	18	negative	negative	ADJ
ejpam-4798	18	19	edges	edge	NOUN
ejpam-4798	18	20	.	.	PUNCT
ejpam-4798	19	1	if	if	SCONJ
ejpam-4798	19	2	every	every	DET
ejpam-4798	19	3	cycle	cycle	NOUN
ejpam-4798	19	4	in	in	ADP
ejpam-4798	19	5	σ	σ	PROPN
ejpam-4798	19	6	is	be	AUX
ejpam-4798	19	7	positive	positive	ADJ
ejpam-4798	19	8	,	,	PUNCT
ejpam-4798	19	9	then	then	ADV
ejpam-4798	19	10	σ	σ	PROPN
ejpam-4798	19	11	is	be	AUX
ejpam-4798	19	12	defined	define	VERB
ejpam-4798	19	13	as	as	ADP
ejpam-4798	19	14	balanced	balanced	ADJ
ejpam-4798	19	15	signed	sign	VERB
ejpam-4798	19	16	graph	graph	NOUN
ejpam-4798	19	17	.	.	PUNCT
ejpam-4798	20	1	an	an	DET
ejpam-4798	20	2	ordered	order	VERB
ejpam-4798	20	3	pair	pair	NOUN
ejpam-4798	20	4	(	(	PUNCT
ejpam-4798	20	5	σ	σ	PROPN
ejpam-4798	20	6	,	,	PUNCT
ejpam-4798	20	7	µ	µ	NOUN
ejpam-4798	20	8	)	)	PUNCT
ejpam-4798	20	9	is	be	AUX
ejpam-4798	20	10	known	know	VERB
ejpam-4798	20	11	as	as	ADP
ejpam-4798	20	12	a	a	DET
ejpam-4798	20	13	marked	mark	VERB
ejpam-4798	20	14	signed	sign	VERB
ejpam-4798	20	15	graph	graph	NOUN
ejpam-4798	20	16	where	where	SCONJ
ejpam-4798	20	17	σ	σ	NOUN
ejpam-4798	20	18	=	=	SYM
ejpam-4798	20	19	(	(	PUNCT
ejpam-4798	20	20	σu	σu	INTJ
ejpam-4798	20	21	,	,	PUNCT
ejpam-4798	20	22	σ	σ	PROPN
ejpam-4798	20	23	)	)	PUNCT
ejpam-4798	20	24	is	be	AUX
ejpam-4798	20	25	a	a	DET
ejpam-4798	20	26	signed	sign	VERB
ejpam-4798	20	27	graph	graph	NOUN
ejpam-4798	20	28	,	,	PUNCT
ejpam-4798	20	29	and	and	CCONJ
ejpam-4798	20	30	µ	µ	X
ejpam-4798	20	31	:	:	PUNCT
ejpam-4798	20	32	v	v	NOUN
ejpam-4798	20	33	(	(	PUNCT
ejpam-4798	20	34	σu	σu	INTJ
ejpam-4798	20	35	)	)	PUNCT
ejpam-4798	20	36	→	→	PUNCT
ejpam-4798	20	37	{	{	PUNCT
ejpam-4798	20	38	+	+	ADJ
ejpam-4798	20	39	,	,	PUNCT
ejpam-4798	20	40	−	−	NOUN
ejpam-4798	20	41	}	}	PUNCT
ejpam-4798	20	42	is	be	AUX
ejpam-4798	20	43	a	a	DET
ejpam-4798	20	44	function	function	NOUN
ejpam-4798	20	45	defined	define	VERB
ejpam-4798	20	46	on	on	ADP
ejpam-4798	20	47	the	the	DET
ejpam-4798	20	48	vertex	vertex	NOUN
ejpam-4798	20	49	set	set	VERB
ejpam-4798	20	50	v	v	NOUN
ejpam-4798	20	51	(	(	PUNCT
ejpam-4798	20	52	σu	σu	NOUN
ejpam-4798	20	53	)	)	PUNCT
ejpam-4798	20	54	of	of	ADP
ejpam-4798	20	55	σu	σu	X
ejpam-4798	20	56	.	.	PUNCT
ejpam-4798	21	1	the	the	DET
ejpam-4798	21	2	function	function	NOUN
ejpam-4798	21	3	µ	µ	X
ejpam-4798	21	4	assigns	assign	NOUN
ejpam-4798	21	5	each	each	DET
ejpam-4798	21	6	vertex	vertex	NOUN
ejpam-4798	21	7	of	of	ADP
ejpam-4798	21	8	σu	σu	INTJ
ejpam-4798	21	9	to	to	ADP
ejpam-4798	21	10	either	either	CCONJ
ejpam-4798	21	11	the	the	DET
ejpam-4798	21	12	positive	positive	ADJ
ejpam-4798	21	13	or	or	CCONJ
ejpam-4798	21	14	negative	negative	ADJ
ejpam-4798	21	15	sign	sign	NOUN
ejpam-4798	21	16	from	from	ADP
ejpam-4798	21	17	the	the	DET
ejpam-4798	21	18	set	set	NOUN
ejpam-4798	21	19	∗corresponding	∗corresponde	VERB
ejpam-4798	21	20	author	author	NOUN
ejpam-4798	21	21	.	.	PUNCT
ejpam-4798	22	1	doi	doi	NOUN
ejpam-4798	22	2	:	:	PUNCT
ejpam-4798	22	3	https://doi.org/10.29020/nybg.ejpam.v17i1.4798	https://doi.org/10.29020/nybg.ejpam.v17i1.4798	VERB
ejpam-4798	22	4	email	email	NOUN
ejpam-4798	22	5	addresses	address	NOUN
ejpam-4798	22	6	:	:	PUNCT
ejpam-4798	22	7	ssulakh.94@gmail.com	ssulakh.94@gmail.com	PROPN
ejpam-4798	22	8	(	(	PUNCT
ejpam-4798	22	9	s.	s.	PROPN
ejpam-4798	22	10	kumar	kumar	PROPN
ejpam-4798	22	11	)	)	PUNCT
ejpam-4798	22	12	,	,	PUNCT
ejpam-4798	22	13	deepasinha@sau.ac.in	deepasinha@sau.ac.in	NOUN
ejpam-4798	22	14	(	(	PUNCT
ejpam-4798	22	15	d.	d.	PROPN
ejpam-4798	22	16	sinha	sinha	PROPN
ejpam-4798	22	17	)	)	PUNCT
ejpam-4798	22	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4798	23	1	504	504	NUM
ejpam-4798	23	2	©	©	ADP
ejpam-4798	23	3	2024	2024	NUM
ejpam-4798	23	4	ejpam	ejpam	NOUN
ejpam-4798	23	5	all	all	DET
ejpam-4798	23	6	rights	right	NOUN
ejpam-4798	23	7	reserved	reserve	VERB
ejpam-4798	23	8	.	.	PUNCT
ejpam-4798	24	1	s.	s.	PROPN
ejpam-4798	24	2	kumar	kumar	PROPN
ejpam-4798	24	3	,	,	PUNCT
ejpam-4798	24	4	d.	d.	PROPN
ejpam-4798	24	5	sinha	sinha	PROPN
ejpam-4798	24	6	/	/	SYM
ejpam-4798	24	7	eur	eur	PROPN
ejpam-4798	24	8	.	.	PUNCT
ejpam-4798	25	1	j.	j.	PROPN
ejpam-4798	25	2	pure	pure	PROPN
ejpam-4798	25	3	appl	appl	PROPN
ejpam-4798	25	4	.	.	PROPN
ejpam-4798	25	5	math	math	PROPN
ejpam-4798	25	6	,	,	PUNCT
ejpam-4798	25	7	17	17	NUM
ejpam-4798	25	8	(	(	PUNCT
ejpam-4798	25	9	1	1	NUM
ejpam-4798	25	10	)	)	PUNCT
ejpam-4798	25	11	(	(	PUNCT
ejpam-4798	25	12	2024	2024	NUM
ejpam-4798	25	13	)	)	PUNCT
ejpam-4798	25	14	,	,	PUNCT
ejpam-4798	25	15	504	504	NUM
ejpam-4798	25	16	-	-	SYM
ejpam-4798	25	17	518	518	NUM
ejpam-4798	25	18	505	505	NUM
ejpam-4798	25	19	{	{	PUNCT
ejpam-4798	25	20	+	+	NOUN
ejpam-4798	25	21	,	,	PUNCT
ejpam-4798	25	22	−	−	NOUN
ejpam-4798	25	23	}	}	PUNCT
ejpam-4798	25	24	,	,	PUNCT
ejpam-4798	25	25	and	and	CCONJ
ejpam-4798	25	26	is	be	AUX
ejpam-4798	25	27	called	call	VERB
ejpam-4798	25	28	the	the	DET
ejpam-4798	25	29	marking	marking	NOUN
ejpam-4798	25	30	of	of	ADP
ejpam-4798	25	31	σ	σ	PROPN
ejpam-4798	25	32	.	.	PUNCT
ejpam-4798	26	1	the	the	DET
ejpam-4798	26	2	adjacency	adjacency	PROPN
ejpam-4798	26	3	matrix	matrix	NOUN
ejpam-4798	26	4	of	of	ADP
ejpam-4798	26	5	σ	σ	PROPN
ejpam-4798	26	6	,	,	PUNCT
ejpam-4798	26	7	whose	whose	DET
ejpam-4798	26	8	vertices	vertex	NOUN
ejpam-4798	26	9	are	be	AUX
ejpam-4798	26	10	v1	v1	NOUN
ejpam-4798	26	11	,	,	PUNCT
ejpam-4798	26	12	v2	v2	PROPN
ejpam-4798	26	13	,	,	PUNCT
ejpam-4798	26	14	...	...	PUNCT
ejpam-4798	26	15	,	,	PUNCT
ejpam-4798	26	16	vn	vn	PROPN
ejpam-4798	26	17	is	be	AUX
ejpam-4798	26	18	the	the	PRON
ejpam-4798	26	19	n	n	NUM
ejpam-4798	26	20	×	×	NOUN
ejpam-4798	26	21	n	n	NOUN
ejpam-4798	26	22	matrix	matrix	NOUN
ejpam-4798	26	23	a(σ	a(σ	NOUN
ejpam-4798	26	24	)	)	PUNCT
ejpam-4798	27	1	=	=	PUNCT
ejpam-4798	28	1	[	[	X
ejpam-4798	28	2	ai	ai	VERB
ejpam-4798	28	3	,	,	PUNCT
ejpam-4798	28	4	j	j	PROPN
ejpam-4798	28	5	]	]	PUNCT
ejpam-4798	28	6	where	where	SCONJ
ejpam-4798	28	7	ai	ai	VERB
ejpam-4798	28	8	,	,	PUNCT
ejpam-4798	28	9	j	j	PROPN
ejpam-4798	28	10	=	=	PUNCT
ejpam-4798	28	11			PROPN
ejpam-4798	28	12	0	0	NUM
ejpam-4798	28	13	if	if	SCONJ
ejpam-4798	28	14	vi	vi	PROPN
ejpam-4798	28	15	and	and	CCONJ
ejpam-4798	28	16	vj	vj	NOUN
ejpam-4798	28	17	are	be	AUX
ejpam-4798	28	18	not	not	PART
ejpam-4798	28	19	adjacent	adjacent	ADJ
ejpam-4798	28	20	1	1	NUM
ejpam-4798	28	21	if	if	SCONJ
ejpam-4798	28	22	σ(vi	σ(vi	NOUN
ejpam-4798	28	23	,	,	PUNCT
ejpam-4798	28	24	vj	vj	INTJ
ejpam-4798	28	25	)	)	PUNCT
ejpam-4798	28	26	is	be	AUX
ejpam-4798	28	27	positive	positive	ADJ
ejpam-4798	28	28	−1	−1	NOUN
ejpam-4798	28	29	if	if	SCONJ
ejpam-4798	28	30	σ(vi	σ(vi	NOUN
ejpam-4798	28	31	,	,	PUNCT
ejpam-4798	28	32	vj	vj	INTJ
ejpam-4798	28	33	)	)	PUNCT
ejpam-4798	28	34	is	be	AUX
ejpam-4798	28	35	negative	negative	ADJ
ejpam-4798	28	36	(	(	PUNCT
ejpam-4798	28	37	1	1	X
ejpam-4798	28	38	)	)	PUNCT
ejpam-4798	28	39	the	the	DET
ejpam-4798	28	40	spectrum	spectrum	NOUN
ejpam-4798	28	41	of	of	ADP
ejpam-4798	28	42	a	a	DET
ejpam-4798	28	43	matrix	matrix	NOUN
ejpam-4798	28	44	is	be	AUX
ejpam-4798	28	45	a	a	DET
ejpam-4798	28	46	list	list	NOUN
ejpam-4798	28	47	of	of	ADP
ejpam-4798	28	48	its	its	PRON
ejpam-4798	28	49	eigenvalues	eigenvalue	NOUN
ejpam-4798	28	50	along	along	ADV
ejpam-4798	28	51	with	with	ADP
ejpam-4798	28	52	their	their	PRON
ejpam-4798	28	53	multiplicities	multiplicity	NOUN
ejpam-4798	28	54	.	.	PUNCT
ejpam-4798	29	1	since	since	SCONJ
ejpam-4798	29	2	,	,	PUNCT
ejpam-4798	29	3	a(σ	a(σ	PROPN
ejpam-4798	29	4	)	)	PUNCT
ejpam-4798	29	5	is	be	AUX
ejpam-4798	29	6	a	a	DET
ejpam-4798	29	7	symmetric	symmetric	ADJ
ejpam-4798	29	8	matrix	matrix	NOUN
ejpam-4798	29	9	with	with	ADP
ejpam-4798	29	10	real	real	ADJ
ejpam-4798	29	11	entries	entry	NOUN
ejpam-4798	29	12	so	so	SCONJ
ejpam-4798	29	13	all	all	DET
ejpam-4798	29	14	its	its	PRON
ejpam-4798	29	15	eigenvalues	eigenvalue	NOUN
ejpam-4798	29	16	are	be	AUX
ejpam-4798	29	17	real	real	ADJ
ejpam-4798	29	18	.	.	PUNCT
ejpam-4798	30	1	let	let	VERB
ejpam-4798	30	2	λ1(σ	λ1(σ	VERB
ejpam-4798	30	3	)	)	PUNCT
ejpam-4798	30	4	>	>	X
ejpam-4798	31	1	λ2(σ	λ2(σ	X
ejpam-4798	31	2	)	)	PUNCT
ejpam-4798	31	3	>	>	X
ejpam-4798	31	4	...	...	PUNCT
ejpam-4798	31	5	>	>	X
ejpam-4798	31	6	λk(σ	λk(σ	NOUN
ejpam-4798	31	7	)	)	PUNCT
ejpam-4798	31	8	are	be	AUX
ejpam-4798	31	9	distinct	distinct	ADJ
ejpam-4798	31	10	eigenvalues	eigenvalue	NOUN
ejpam-4798	31	11	of	of	ADP
ejpam-4798	31	12	a(σ	a(σ	NOUN
ejpam-4798	31	13	)	)	PUNCT
ejpam-4798	31	14	along	along	ADP
ejpam-4798	31	15	with	with	ADP
ejpam-4798	31	16	their	their	PRON
ejpam-4798	31	17	multiplicities	multiplicity	NOUN
ejpam-4798	31	18	m1,m2	m1,m2	PROPN
ejpam-4798	31	19	,	,	PUNCT
ejpam-4798	31	20	...	...	PUNCT
ejpam-4798	31	21	,	,	PUNCT
ejpam-4798	31	22	mk	mk	PROPN
ejpam-4798	31	23	,	,	PUNCT
ejpam-4798	31	24	1	1	NUM
ejpam-4798	31	25	≤	≤	NUM
ejpam-4798	31	26	k	k	NOUN
ejpam-4798	31	27	≤	≤	PROPN
ejpam-4798	31	28	n	n	CCONJ
ejpam-4798	31	29	,	,	PUNCT
ejpam-4798	31	30	then	then	ADV
ejpam-4798	31	31	the	the	DET
ejpam-4798	31	32	list	list	NOUN
ejpam-4798	31	33	of	of	ADP
ejpam-4798	31	34	eigenvalues	eigenvalue	NOUN
ejpam-4798	31	35	of	of	ADP
ejpam-4798	31	36	adjacency	adjacency	NOUN
ejpam-4798	31	37	matrix	matrix	NOUN
ejpam-4798	31	38	is	be	AUX
ejpam-4798	31	39	called	call	VERB
ejpam-4798	31	40	adjacency	adjacency	PROPN
ejpam-4798	31	41	spectrum	spectrum	NOUN
ejpam-4798	31	42	of	of	ADP
ejpam-4798	31	43	the	the	DET
ejpam-4798	31	44	signed	sign	VERB
ejpam-4798	31	45	graph	graph	NOUN
ejpam-4798	31	46	σ	σ	PROPN
ejpam-4798	31	47	and	and	CCONJ
ejpam-4798	31	48	usually	usually	ADV
ejpam-4798	31	49	denoted	denote	VERB
ejpam-4798	31	50	as	as	ADP
ejpam-4798	31	51	:	:	PUNCT
ejpam-4798	31	52	sp(σ	sp(σ	X
ejpam-4798	31	53	)	)	PUNCT
ejpam-4798	31	54	=	=	SYM
ejpam-4798	31	55	(	(	PUNCT
ejpam-4798	31	56	λ1	λ1	PROPN
ejpam-4798	31	57	λ2	λ2	PROPN
ejpam-4798	31	58	·	·	PUNCT
ejpam-4798	31	59	·	·	PUNCT
ejpam-4798	31	60	·	·	PUNCT
ejpam-4798	32	1	λk	λk	PRON
ejpam-4798	32	2	m1	m1	PROPN
ejpam-4798	32	3	m2	m2	PROPN
ejpam-4798	32	4	·	·	PUNCT
ejpam-4798	32	5	·	·	PUNCT
ejpam-4798	32	6	·	·	PUNCT
ejpam-4798	32	7	mk	mk	NOUN
ejpam-4798	32	8	)	)	PUNCT
ejpam-4798	32	9	let	let	VERB
ejpam-4798	32	10	d(σ	d(σ	NOUN
ejpam-4798	32	11	)	)	PUNCT
ejpam-4798	32	12	=	=	PUNCT
ejpam-4798	33	1	[	[	X
ejpam-4798	33	2	di	di	X
ejpam-4798	33	3	,	,	PUNCT
ejpam-4798	33	4	j	j	PROPN
ejpam-4798	33	5	]	]	PUNCT
ejpam-4798	33	6	be	be	AUX
ejpam-4798	33	7	a	a	DET
ejpam-4798	33	8	diagonal	diagonal	ADJ
ejpam-4798	33	9	matrix	matrix	NOUN
ejpam-4798	33	10	of	of	ADP
ejpam-4798	33	11	order	order	NOUN
ejpam-4798	33	12	n	n	PRON
ejpam-4798	33	13	such	such	ADJ
ejpam-4798	33	14	that	that	SCONJ
ejpam-4798	33	15	the	the	DET
ejpam-4798	33	16	entry	entry	NOUN
ejpam-4798	33	17	(	(	PUNCT
ejpam-4798	33	18	i	i	PROPN
ejpam-4798	33	19	,	,	PUNCT
ejpam-4798	33	20	j	j	PROPN
ejpam-4798	33	21	)	)	PUNCT
ejpam-4798	33	22	is	be	AUX
ejpam-4798	33	23	deg(ui	deg(ui	NOUN
ejpam-4798	33	24	)	)	PUNCT
ejpam-4798	33	25	if	if	SCONJ
ejpam-4798	33	26	i	i	PRON
ejpam-4798	33	27	=	=	SYM
ejpam-4798	33	28	j	j	PROPN
ejpam-4798	33	29	and	and	CCONJ
ejpam-4798	33	30	0	0	NUM
ejpam-4798	33	31	otherwise	otherwise	ADV
ejpam-4798	33	32	,	,	PUNCT
ejpam-4798	33	33	where	where	SCONJ
ejpam-4798	33	34	deg(ui	deg(ui	X
ejpam-4798	33	35	)	)	PUNCT
ejpam-4798	33	36	denotes	denote	VERB
ejpam-4798	33	37	the	the	DET
ejpam-4798	33	38	degree	degree	NOUN
ejpam-4798	33	39	of	of	ADP
ejpam-4798	33	40	the	the	DET
ejpam-4798	33	41	vertex	vertex	NOUN
ejpam-4798	33	42	ui	ui	PROPN
ejpam-4798	33	43	.	.	PUNCT
ejpam-4798	34	1	d(σ	d(σ	PROPN
ejpam-4798	34	2	)	)	PUNCT
ejpam-4798	34	3	is	be	AUX
ejpam-4798	34	4	called	call	VERB
ejpam-4798	34	5	degree	degree	NOUN
ejpam-4798	34	6	matrix	matrix	NOUN
ejpam-4798	34	7	of	of	ADP
ejpam-4798	34	8	the	the	DET
ejpam-4798	34	9	signed	sign	VERB
ejpam-4798	34	10	graph	graph	NOUN
ejpam-4798	34	11	σ	σ	PROPN
ejpam-4798	34	12	.	.	PUNCT
ejpam-4798	35	1	the	the	DET
ejpam-4798	35	2	laplacian	laplacian	ADJ
ejpam-4798	35	3	matrix	matrix	NOUN
ejpam-4798	35	4	l(σ	l(σ	NOUN
ejpam-4798	35	5	)	)	PUNCT
ejpam-4798	36	1	=	=	PUNCT
ejpam-4798	37	1	[	[	X
ejpam-4798	37	2	li	li	X
ejpam-4798	37	3	,	,	PUNCT
ejpam-4798	37	4	j	j	PROPN
ejpam-4798	37	5	]	]	PUNCT
ejpam-4798	37	6	of	of	ADP
ejpam-4798	37	7	a	a	DET
ejpam-4798	37	8	signed	sign	VERB
ejpam-4798	37	9	graph	graph	NOUN
ejpam-4798	37	10	σ	σ	PROPN
ejpam-4798	37	11	is	be	AUX
ejpam-4798	37	12	a	a	DET
ejpam-4798	37	13	square	square	ADJ
ejpam-4798	37	14	matrix	matrix	NOUN
ejpam-4798	37	15	of	of	ADP
ejpam-4798	37	16	order	order	NOUN
ejpam-4798	37	17	n	n	PRON
ejpam-4798	37	18	such	such	ADJ
ejpam-4798	37	19	that	that	SCONJ
ejpam-4798	37	20	li	li	PROPN
ejpam-4798	37	21	,	,	PUNCT
ejpam-4798	37	22	j	j	PROPN
ejpam-4798	37	23	=	=	SYM
ejpam-4798	37	24	di	di	PROPN
ejpam-4798	37	25	,	,	PUNCT
ejpam-4798	37	26	j	j	PROPN
ejpam-4798	37	27	−	−	PROPN
ejpam-4798	37	28	ai	ai	VERB
ejpam-4798	37	29	,	,	PUNCT
ejpam-4798	37	30	j	j	PROPN
ejpam-4798	37	31	for	for	ADP
ejpam-4798	37	32	0	0	NUM
ejpam-4798	37	33	≤	≤	NOUN
ejpam-4798	37	34	i	i	PRON
ejpam-4798	37	35	,	,	PUNCT
ejpam-4798	37	36	j	j	PROPN
ejpam-4798	37	37	≤	≤	PROPN
ejpam-4798	37	38	n.	n.	VERB
ejpam-4798	37	39	the	the	DET
ejpam-4798	37	40	eigenvalues	eigenvalue	NOUN
ejpam-4798	37	41	of	of	ADP
ejpam-4798	37	42	the	the	DET
ejpam-4798	37	43	laplacian	laplacian	ADJ
ejpam-4798	37	44	matrix	matrix	NOUN
ejpam-4798	37	45	is	be	AUX
ejpam-4798	37	46	called	call	VERB
ejpam-4798	37	47	laplacian	laplacian	ADJ
ejpam-4798	37	48	spectrum	spectrum	NOUN
ejpam-4798	37	49	and	and	CCONJ
ejpam-4798	37	50	is	be	AUX
ejpam-4798	37	51	denoted	denote	VERB
ejpam-4798	37	52	by	by	ADP
ejpam-4798	37	53	slp(σ	slp(σ	PROPN
ejpam-4798	37	54	)	)	PUNCT
ejpam-4798	37	55	.	.	PUNCT
ejpam-4798	38	1	two	two	NUM
ejpam-4798	38	2	signed	sign	VERB
ejpam-4798	38	3	graphs	graph	NOUN
ejpam-4798	38	4	are	be	AUX
ejpam-4798	38	5	said	say	VERB
ejpam-4798	38	6	to	to	PART
ejpam-4798	38	7	be	be	AUX
ejpam-4798	38	8	co	co	NOUN
ejpam-4798	38	9	-	-	ADJ
ejpam-4798	38	10	spectral	spectral	ADJ
ejpam-4798	38	11	if	if	SCONJ
ejpam-4798	38	12	they	they	PRON
ejpam-4798	38	13	have	have	VERB
ejpam-4798	38	14	same	same	ADJ
ejpam-4798	38	15	spectrum	spectrum	NOUN
ejpam-4798	38	16	.	.	PUNCT
ejpam-4798	39	1	the	the	DET
ejpam-4798	39	2	largest	large	ADJ
ejpam-4798	39	3	eigenvalue	eigenvalue	NOUN
ejpam-4798	39	4	λ1(σ	λ1(σ	NOUN
ejpam-4798	39	5	)	)	PUNCT
ejpam-4798	39	6	is	be	AUX
ejpam-4798	39	7	called	call	VERB
ejpam-4798	39	8	the	the	DET
ejpam-4798	39	9	index	index	NOUN
ejpam-4798	39	10	of	of	ADP
ejpam-4798	39	11	σ	σ	PROPN
ejpam-4798	39	12	,	,	PUNCT
ejpam-4798	39	13	whereas	whereas	SCONJ
ejpam-4798	39	14	the	the	DET
ejpam-4798	39	15	largest	large	ADJ
ejpam-4798	39	16	absolute	absolute	ADJ
ejpam-4798	39	17	eigenvalue	eigenvalue	NOUN
ejpam-4798	39	18	is	be	AUX
ejpam-4798	39	19	called	call	VERB
ejpam-4798	39	20	spectral	spectral	ADJ
ejpam-4798	39	21	radius	radius	NOUN
ejpam-4798	39	22	ρ(σ	ρ(σ	PROPN
ejpam-4798	39	23	)	)	PUNCT
ejpam-4798	39	24	,	,	PUNCT
ejpam-4798	39	25	i.e.	i.e.	X
ejpam-4798	39	26	ρ	ρ	X
ejpam-4798	39	27	=	=	SYM
ejpam-4798	39	28	max{λ1(σ),−λk(σ	max{λ1(σ),−λk(σ	NOUN
ejpam-4798	39	29	)	)	PUNCT
ejpam-4798	39	30	}	}	PUNCT
ejpam-4798	39	31	.	.	PUNCT
ejpam-4798	40	1	(	(	PUNCT
ejpam-4798	40	2	2	2	X
ejpam-4798	40	3	)	)	PUNCT
ejpam-4798	40	4	the	the	DET
ejpam-4798	40	5	study	study	NOUN
ejpam-4798	40	6	of	of	ADP
ejpam-4798	40	7	graph	graph	NOUN
ejpam-4798	40	8	spectrum	spectrum	NOUN
ejpam-4798	40	9	is	be	AUX
ejpam-4798	40	10	of	of	ADP
ejpam-4798	40	11	significant	significant	ADJ
ejpam-4798	40	12	importance	importance	NOUN
ejpam-4798	40	13	in	in	ADP
ejpam-4798	40	14	the	the	DET
ejpam-4798	40	15	field	field	NOUN
ejpam-4798	40	16	of	of	ADP
ejpam-4798	40	17	graph	graph	NOUN
ejpam-4798	40	18	theory	theory	NOUN
ejpam-4798	40	19	,	,	PUNCT
ejpam-4798	40	20	and	and	CCONJ
ejpam-4798	40	21	spectral	spectral	ADJ
ejpam-4798	40	22	graph	graph	NOUN
ejpam-4798	40	23	-	-	PUNCT
ejpam-4798	40	24	theoretic	theoretic	NOUN
ejpam-4798	40	25	techniques	technique	NOUN
ejpam-4798	40	26	have	have	AUX
ejpam-4798	40	27	been	be	AUX
ejpam-4798	40	28	applied	apply	VERB
ejpam-4798	40	29	in	in	ADP
ejpam-4798	40	30	a	a	DET
ejpam-4798	40	31	range	range	NOUN
ejpam-4798	40	32	of	of	ADP
ejpam-4798	40	33	fields	field	NOUN
ejpam-4798	40	34	including	include	VERB
ejpam-4798	40	35	quantum	quantum	NOUN
ejpam-4798	40	36	physics	physics	NOUN
ejpam-4798	40	37	,	,	PUNCT
ejpam-4798	40	38	chemistry	chemistry	NOUN
ejpam-4798	40	39	,	,	PUNCT
ejpam-4798	40	40	computer	computer	NOUN
ejpam-4798	40	41	science	science	NOUN
ejpam-4798	40	42	,	,	PUNCT
ejpam-4798	40	43	and	and	CCONJ
ejpam-4798	40	44	more	more	ADJ
ejpam-4798	40	45	.	.	PUNCT
ejpam-4798	41	1	in	in	ADP
ejpam-4798	41	2	recent	recent	ADJ
ejpam-4798	41	3	years	year	NOUN
ejpam-4798	41	4	,	,	PUNCT
ejpam-4798	41	5	researchers	researcher	NOUN
ejpam-4798	41	6	have	have	AUX
ejpam-4798	41	7	explored	explore	VERB
ejpam-4798	41	8	the	the	DET
ejpam-4798	41	9	spectral	spectral	ADJ
ejpam-4798	41	10	properties	property	NOUN
ejpam-4798	41	11	of	of	ADP
ejpam-4798	41	12	graphs	graph	NOUN
ejpam-4798	41	13	constructed	construct	VERB
ejpam-4798	41	14	through	through	ADP
ejpam-4798	41	15	graph	graph	NOUN
ejpam-4798	41	16	operations	operation	NOUN
ejpam-4798	41	17	such	such	ADJ
ejpam-4798	41	18	as	as	ADP
ejpam-4798	41	19	disjoint	disjoint	NOUN
ejpam-4798	41	20	union	union	NOUN
ejpam-4798	41	21	,	,	PUNCT
ejpam-4798	41	22	cartesian	cartesian	ADJ
ejpam-4798	41	23	product	product	NOUN
ejpam-4798	41	24	,	,	PUNCT
ejpam-4798	41	25	kronecker	kronecker	NOUN
ejpam-4798	41	26	product	product	NOUN
ejpam-4798	41	27	,	,	PUNCT
ejpam-4798	41	28	strong	strong	ADJ
ejpam-4798	41	29	product	product	NOUN
ejpam-4798	41	30	,	,	PUNCT
ejpam-4798	41	31	lexicographic	lexicographic	ADJ
ejpam-4798	41	32	product	product	NOUN
ejpam-4798	41	33	,	,	PUNCT
ejpam-4798	41	34	corona	corona	PROPN
ejpam-4798	41	35	,	,	PUNCT
ejpam-4798	41	36	edge	edge	NOUN
ejpam-4798	41	37	corona	corona	NOUN
ejpam-4798	41	38	,	,	PUNCT
ejpam-4798	41	39	and	and	CCONJ
ejpam-4798	41	40	neighbourhood	neighbourhood	NOUN
ejpam-4798	41	41	corona	corona	NOUN
ejpam-4798	41	42	.	.	PUNCT
ejpam-4798	42	1	a	a	DET
ejpam-4798	42	2	comprehensive	comprehensive	ADJ
ejpam-4798	42	3	overview	overview	NOUN
ejpam-4798	42	4	of	of	ADP
ejpam-4798	42	5	results	result	NOUN
ejpam-4798	42	6	on	on	ADP
ejpam-4798	42	7	the	the	DET
ejpam-4798	42	8	spectra	spectra	NOUN
ejpam-4798	42	9	of	of	ADP
ejpam-4798	42	10	these	these	DET
ejpam-4798	42	11	graphs	graph	NOUN
ejpam-4798	42	12	can	can	AUX
ejpam-4798	42	13	be	be	AUX
ejpam-4798	42	14	found	find	VERB
ejpam-4798	42	15	in	in	ADP
ejpam-4798	42	16	the	the	DET
ejpam-4798	42	17	literature	literature	NOUN
ejpam-4798	43	1	[	[	X
ejpam-4798	43	2	4–7	4–7	NOUN
ejpam-4798	43	3	,	,	PUNCT
ejpam-4798	43	4	9	9	NUM
ejpam-4798	43	5	,	,	PUNCT
ejpam-4798	43	6	14–16	14–16	NUM
ejpam-4798	43	7	]	]	PUNCT
ejpam-4798	43	8	.	.	PUNCT
ejpam-4798	44	1	in	in	ADP
ejpam-4798	44	2	[	[	X
ejpam-4798	44	3	?	?	PUNCT
ejpam-4798	44	4	]	]	PUNCT
ejpam-4798	45	1	authors	author	NOUN
ejpam-4798	45	2	presented	present	VERB
ejpam-4798	45	3	the	the	DET
ejpam-4798	45	4	idea	idea	NOUN
ejpam-4798	45	5	of	of	ADP
ejpam-4798	45	6	the	the	DET
ejpam-4798	45	7	splitting	splitting	NOUN
ejpam-4798	45	8	graph	graph	NOUN
ejpam-4798	45	9	γ(σu	γ(σu	NOUN
ejpam-4798	45	10	)	)	PUNCT
ejpam-4798	45	11	for	for	ADP
ejpam-4798	45	12	a	a	DET
ejpam-4798	45	13	given	give	VERB
ejpam-4798	45	14	graph	graph	NOUN
ejpam-4798	45	15	σu	σu	NOUN
ejpam-4798	45	16	.	.	PUNCT
ejpam-4798	46	1	the	the	DET
ejpam-4798	46	2	process	process	NOUN
ejpam-4798	46	3	of	of	ADP
ejpam-4798	46	4	creating	create	VERB
ejpam-4798	46	5	the	the	DET
ejpam-4798	46	6	splitting	splitting	NOUN
ejpam-4798	46	7	graph	graph	NOUN
ejpam-4798	46	8	γ(σu	γ(σu	NOUN
ejpam-4798	46	9	)	)	PUNCT
ejpam-4798	46	10	involves	involve	VERB
ejpam-4798	46	11	taking	take	VERB
ejpam-4798	46	12	a	a	DET
ejpam-4798	46	13	new	new	ADJ
ejpam-4798	46	14	vertex	vertex	NOUN
ejpam-4798	46	15	v′	v′	NOUN
ejpam-4798	46	16	for	for	ADP
ejpam-4798	46	17	each	each	DET
ejpam-4798	46	18	vertex	vertex	NOUN
ejpam-4798	46	19	v	v	NOUN
ejpam-4798	46	20	in	in	ADP
ejpam-4798	46	21	graph	graph	NOUN
ejpam-4798	46	22	σu	σu	NOUN
ejpam-4798	46	23	.	.	PUNCT
ejpam-4798	47	1	the	the	DET
ejpam-4798	47	2	new	new	ADJ
ejpam-4798	47	3	vertex	vertex	NOUN
ejpam-4798	47	4	v′	v′	NOUN
ejpam-4798	47	5	is	be	AUX
ejpam-4798	47	6	then	then	ADV
ejpam-4798	47	7	connected	connect	VERB
ejpam-4798	47	8	to	to	ADP
ejpam-4798	47	9	all	all	DET
ejpam-4798	47	10	vertices	vertex	NOUN
ejpam-4798	47	11	in	in	ADP
ejpam-4798	47	12	σu	σu	PROPN
ejpam-4798	47	13	that	that	PRON
ejpam-4798	47	14	are	be	AUX
ejpam-4798	47	15	adjacent	adjacent	ADJ
ejpam-4798	47	16	to	to	ADP
ejpam-4798	47	17	v.	v.	ADP
ejpam-4798	47	18	the	the	DET
ejpam-4798	47	19	resulting	result	VERB
ejpam-4798	47	20	graph	graph	NOUN
ejpam-4798	47	21	is	be	AUX
ejpam-4798	47	22	referred	refer	VERB
ejpam-4798	47	23	to	to	ADP
ejpam-4798	47	24	as	as	ADP
ejpam-4798	47	25	the	the	DET
ejpam-4798	47	26	splitting	splitting	NOUN
ejpam-4798	47	27	graph	graph	NOUN
ejpam-4798	47	28	γ(σu	γ(σu	NOUN
ejpam-4798	47	29	)	)	PUNCT
ejpam-4798	47	30	of	of	ADP
ejpam-4798	47	31	graph	graph	NOUN
ejpam-4798	47	32	σu	σu	INTJ
ejpam-4798	47	33	.	.	PUNCT
ejpam-4798	48	1	recently	recently	ADV
ejpam-4798	48	2	,	,	PUNCT
ejpam-4798	48	3	a	a	DET
ejpam-4798	48	4	variation	variation	NOUN
ejpam-4798	48	5	of	of	ADP
ejpam-4798	48	6	this	this	DET
ejpam-4798	48	7	concept	concept	NOUN
ejpam-4798	48	8	has	have	AUX
ejpam-4798	48	9	been	be	AUX
ejpam-4798	48	10	applied	apply	VERB
ejpam-4798	48	11	in	in	ADP
ejpam-4798	48	12	the	the	DET
ejpam-4798	48	13	analysis	analysis	NOUN
ejpam-4798	48	14	of	of	ADP
ejpam-4798	48	15	online	online	ADJ
ejpam-4798	48	16	social	social	ADJ
ejpam-4798	48	17	networks	network	NOUN
ejpam-4798	48	18	(	(	PUNCT
ejpam-4798	48	19	osns	osns	NOUN
ejpam-4798	48	20	)	)	PUNCT
ejpam-4798	48	21	,	,	PUNCT
ejpam-4798	48	22	where	where	SCONJ
ejpam-4798	48	23	v′	v′	NOUN
ejpam-4798	48	24	is	be	AUX
ejpam-4798	48	25	also	also	ADV
ejpam-4798	48	26	connected	connect	VERB
ejpam-4798	48	27	to	to	ADP
ejpam-4798	48	28	v.	v.	ADP
ejpam-4798	48	29	this	this	DET
ejpam-4798	48	30	variation	variation	NOUN
ejpam-4798	48	31	of	of	ADP
ejpam-4798	48	32	the	the	DET
ejpam-4798	48	33	concept	concept	NOUN
ejpam-4798	48	34	is	be	AUX
ejpam-4798	48	35	referred	refer	VERB
ejpam-4798	48	36	to	to	ADP
ejpam-4798	48	37	as	as	ADP
ejpam-4798	48	38	the	the	DET
ejpam-4798	48	39	“	"	PUNCT
ejpam-4798	48	40	clone	clone	NOUN
ejpam-4798	48	41	”	"	PUNCT
ejpam-4798	48	42	of	of	ADP
ejpam-4798	48	43	v.	v.	CCONJ
ejpam-4798	48	44	for	for	ADP
ejpam-4798	48	45	the	the	DET
ejpam-4798	48	46	purpose	purpose	NOUN
ejpam-4798	48	47	of	of	ADP
ejpam-4798	48	48	convenience	convenience	NOUN
ejpam-4798	48	49	,	,	PUNCT
ejpam-4798	48	50	the	the	DET
ejpam-4798	48	51	term	term	NOUN
ejpam-4798	48	52	“	"	PUNCT
ejpam-4798	48	53	clone	clone	NOUN
ejpam-4798	48	54	”	"	PUNCT
ejpam-4798	48	55	is	be	AUX
ejpam-4798	48	56	adopted	adopt	VERB
ejpam-4798	48	57	for	for	ADP
ejpam-4798	48	58	v′	v′	NOUN
ejpam-4798	48	59	in	in	ADP
ejpam-4798	48	60	the	the	DET
ejpam-4798	48	61	splitting	splitting	NOUN
ejpam-4798	48	62	graph	graph	NOUN
ejpam-4798	48	63	γ(σu	γ(σu	NOUN
ejpam-4798	48	64	)	)	PUNCT
ejpam-4798	48	65	as	as	ADV
ejpam-4798	48	66	well	well	ADV
ejpam-4798	48	67	.	.	PUNCT
ejpam-4798	49	1	gutman	gutman	NOUN
ejpam-4798	50	1	[	[	X
ejpam-4798	50	2	11	11	NUM
ejpam-4798	50	3	]	]	PUNCT
ejpam-4798	50	4	introduced	introduce	VERB
ejpam-4798	50	5	the	the	DET
ejpam-4798	50	6	concept	concept	NOUN
ejpam-4798	50	7	of	of	ADP
ejpam-4798	50	8	energy	energy	NOUN
ejpam-4798	50	9	of	of	ADP
ejpam-4798	50	10	a	a	DET
ejpam-4798	50	11	graph	graph	NOUN
ejpam-4798	50	12	σu	σu	NOUN
ejpam-4798	50	13	in	in	ADP
ejpam-4798	50	14	1978	1978	NUM
ejpam-4798	50	15	as	as	ADP
ejpam-4798	50	16	the	the	DET
ejpam-4798	50	17	sum	sum	NOUN
ejpam-4798	50	18	of	of	ADP
ejpam-4798	50	19	the	the	DET
ejpam-4798	50	20	s.	s.	PROPN
ejpam-4798	50	21	kumar	kumar	PROPN
ejpam-4798	50	22	,	,	PUNCT
ejpam-4798	50	23	d.	d.	PROPN
ejpam-4798	50	24	sinha	sinha	PROPN
ejpam-4798	50	25	/	/	SYM
ejpam-4798	50	26	eur	eur	PROPN
ejpam-4798	50	27	.	.	PUNCT
ejpam-4798	51	1	j.	j.	PROPN
ejpam-4798	51	2	pure	pure	PROPN
ejpam-4798	51	3	appl	appl	PROPN
ejpam-4798	51	4	.	.	PROPN
ejpam-4798	51	5	math	math	PROPN
ejpam-4798	51	6	,	,	PUNCT
ejpam-4798	51	7	17	17	NUM
ejpam-4798	51	8	(	(	PUNCT
ejpam-4798	51	9	1	1	NUM
ejpam-4798	51	10	)	)	PUNCT
ejpam-4798	51	11	(	(	PUNCT
ejpam-4798	51	12	2024	2024	NUM
ejpam-4798	51	13	)	)	PUNCT
ejpam-4798	51	14	,	,	PUNCT
ejpam-4798	51	15	504	504	NUM
ejpam-4798	51	16	-	-	SYM
ejpam-4798	51	17	518	518	NUM
ejpam-4798	51	18	506	506	NUM
ejpam-4798	51	19	absolute	absolute	ADJ
ejpam-4798	51	20	values	value	NOUN
ejpam-4798	51	21	of	of	ADP
ejpam-4798	51	22	its	its	PRON
ejpam-4798	51	23	eigenvalues	eigenvalue	NOUN
ejpam-4798	51	24	,	,	PUNCT
ejpam-4798	51	25	denoted	denote	VERB
ejpam-4798	51	26	by	by	ADP
ejpam-4798	51	27	e(σu	e(σu	NOUN
ejpam-4798	51	28	)	)	PUNCT
ejpam-4798	51	29	,	,	PUNCT
ejpam-4798	51	30	i.e.	i.e.	X
ejpam-4798	51	31	,	,	PUNCT
ejpam-4798	51	32	e(σu	e(σu	ADJ
ejpam-4798	51	33	)	)	PUNCT
ejpam-4798	51	34	=	=	SYM
ejpam-4798	52	1	n∑	n∑	NOUN
ejpam-4798	52	2	i=1	i=1	PROPN
ejpam-4798	52	3	|λi|	|λi|	NOUN
ejpam-4798	52	4	later	later	ADV
ejpam-4798	52	5	,	,	PUNCT
ejpam-4798	52	6	in	in	ADP
ejpam-4798	52	7	2004	2004	NUM
ejpam-4798	52	8	,	,	PUNCT
ejpam-4798	52	9	bapat	bapat	X
ejpam-4798	52	10	et.al	et.al	NOUN
ejpam-4798	52	11	[	[	X
ejpam-4798	52	12	3	3	NUM
ejpam-4798	52	13	]	]	PUNCT
ejpam-4798	52	14	proved	prove	VERB
ejpam-4798	52	15	that	that	SCONJ
ejpam-4798	52	16	the	the	DET
ejpam-4798	52	17	energy	energy	NOUN
ejpam-4798	52	18	of	of	ADP
ejpam-4798	52	19	a	a	DET
ejpam-4798	52	20	graph	graph	NOUN
ejpam-4798	52	21	can	can	AUX
ejpam-4798	52	22	only	only	ADV
ejpam-4798	52	23	be	be	AUX
ejpam-4798	52	24	an	an	DET
ejpam-4798	52	25	even	even	ADV
ejpam-4798	52	26	integer	integer	NOUN
ejpam-4798	52	27	if	if	SCONJ
ejpam-4798	52	28	it	it	PRON
ejpam-4798	52	29	is	be	AUX
ejpam-4798	52	30	a	a	DET
ejpam-4798	52	31	rational	rational	ADJ
ejpam-4798	52	32	number	number	NOUN
ejpam-4798	52	33	.	.	PUNCT
ejpam-4798	53	1	pirzada	pirzada	PROPN
ejpam-4798	53	2	et.al	et.al	PROPN
ejpam-4798	54	1	[	[	X
ejpam-4798	54	2	12	12	NUM
ejpam-4798	54	3	]	]	PUNCT
ejpam-4798	54	4	,	,	PUNCT
ejpam-4798	54	5	on	on	ADP
ejpam-4798	54	6	the	the	DET
ejpam-4798	54	7	other	other	ADJ
ejpam-4798	54	8	hand	hand	NOUN
ejpam-4798	54	9	,	,	PUNCT
ejpam-4798	54	10	demonstrated	demonstrate	VERB
ejpam-4798	54	11	that	that	SCONJ
ejpam-4798	54	12	the	the	DET
ejpam-4798	54	13	energy	energy	NOUN
ejpam-4798	54	14	of	of	ADP
ejpam-4798	54	15	a	a	DET
ejpam-4798	54	16	given	give	VERB
ejpam-4798	54	17	graph	graph	NOUN
ejpam-4798	54	18	can	can	AUX
ejpam-4798	54	19	never	never	ADV
ejpam-4798	54	20	be	be	AUX
ejpam-4798	54	21	the	the	DET
ejpam-4798	54	22	square	square	ADJ
ejpam-4798	54	23	root	root	NOUN
ejpam-4798	54	24	of	of	ADP
ejpam-4798	54	25	an	an	DET
ejpam-4798	54	26	odd	odd	ADJ
ejpam-4798	54	27	integer	integer	NOUN
ejpam-4798	54	28	.	.	PUNCT
ejpam-4798	55	1	graph	graph	NOUN
ejpam-4798	55	2	energy	energy	NOUN
ejpam-4798	55	3	is	be	AUX
ejpam-4798	55	4	briefly	briefly	ADV
ejpam-4798	55	5	discussed	discuss	VERB
ejpam-4798	55	6	in	in	ADP
ejpam-4798	55	7	[	[	X
ejpam-4798	55	8	2	2	NUM
ejpam-4798	55	9	]	]	PUNCT
ejpam-4798	55	10	,	,	PUNCT
ejpam-4798	55	11	while	while	SCONJ
ejpam-4798	55	12	in	in	ADP
ejpam-4798	55	13	[	[	PUNCT
ejpam-4798	55	14	18	18	NUM
ejpam-4798	55	15	]	]	PUNCT
ejpam-4798	55	16	authors	author	NOUN
ejpam-4798	55	17	established	establish	VERB
ejpam-4798	55	18	a	a	DET
ejpam-4798	55	19	relationship	relationship	NOUN
ejpam-4798	55	20	between	between	ADP
ejpam-4798	55	21	the	the	DET
ejpam-4798	55	22	energy	energy	NOUN
ejpam-4798	55	23	of	of	ADP
ejpam-4798	55	24	a	a	DET
ejpam-4798	55	25	graph	graph	NOUN
ejpam-4798	55	26	and	and	CCONJ
ejpam-4798	55	27	its	its	PRON
ejpam-4798	55	28	splitting	splitting	NOUN
ejpam-4798	55	29	graph	graph	NOUN
ejpam-4798	55	30	.	.	PUNCT
ejpam-4798	56	1	the	the	DET
ejpam-4798	56	2	concept	concept	NOUN
ejpam-4798	56	3	of	of	ADP
ejpam-4798	56	4	graph	graph	NOUN
ejpam-4798	56	5	energy	energy	NOUN
ejpam-4798	56	6	has	have	AUX
ejpam-4798	56	7	been	be	AUX
ejpam-4798	56	8	widely	widely	ADV
ejpam-4798	56	9	studied	study	VERB
ejpam-4798	56	10	in	in	ADP
ejpam-4798	56	11	graph	graph	NOUN
ejpam-4798	56	12	theory	theory	NOUN
ejpam-4798	56	13	and	and	CCONJ
ejpam-4798	56	14	has	have	VERB
ejpam-4798	56	15	significant	significant	ADJ
ejpam-4798	56	16	applications	application	NOUN
ejpam-4798	56	17	in	in	ADP
ejpam-4798	56	18	various	various	ADJ
ejpam-4798	56	19	fields	field	NOUN
ejpam-4798	56	20	.	.	PUNCT
ejpam-4798	57	1	the	the	DET
ejpam-4798	57	2	study	study	NOUN
ejpam-4798	57	3	of	of	ADP
ejpam-4798	57	4	graph	graph	NOUN
ejpam-4798	57	5	energy	energy	NOUN
ejpam-4798	57	6	can	can	AUX
ejpam-4798	57	7	provide	provide	VERB
ejpam-4798	57	8	insights	insight	NOUN
ejpam-4798	57	9	into	into	ADP
ejpam-4798	57	10	the	the	DET
ejpam-4798	57	11	structural	structural	ADJ
ejpam-4798	57	12	properties	property	NOUN
ejpam-4798	57	13	of	of	ADP
ejpam-4798	57	14	the	the	DET
ejpam-4798	57	15	graph	graph	NOUN
ejpam-4798	57	16	and	and	CCONJ
ejpam-4798	57	17	is	be	AUX
ejpam-4798	57	18	often	often	ADV
ejpam-4798	57	19	used	use	VERB
ejpam-4798	57	20	in	in	ADP
ejpam-4798	57	21	the	the	DET
ejpam-4798	57	22	design	design	NOUN
ejpam-4798	57	23	and	and	CCONJ
ejpam-4798	57	24	analysis	analysis	NOUN
ejpam-4798	57	25	of	of	ADP
ejpam-4798	57	26	communication	communication	NOUN
ejpam-4798	57	27	networks	network	NOUN
ejpam-4798	57	28	,	,	PUNCT
ejpam-4798	57	29	molecular	molecular	ADJ
ejpam-4798	57	30	chemistry	chemistry	NOUN
ejpam-4798	57	31	,	,	PUNCT
ejpam-4798	57	32	and	and	CCONJ
ejpam-4798	57	33	social	social	ADJ
ejpam-4798	57	34	networks	network	NOUN
ejpam-4798	57	35	.	.	PUNCT
ejpam-4798	58	1	additionally	additionally	ADV
ejpam-4798	58	2	,	,	PUNCT
ejpam-4798	58	3	the	the	DET
ejpam-4798	58	4	energy	energy	NOUN
ejpam-4798	58	5	of	of	ADP
ejpam-4798	58	6	a	a	DET
ejpam-4798	58	7	graph	graph	NOUN
ejpam-4798	58	8	is	be	AUX
ejpam-4798	58	9	closely	closely	ADV
ejpam-4798	58	10	related	relate	VERB
ejpam-4798	58	11	to	to	ADP
ejpam-4798	58	12	its	its	PRON
ejpam-4798	58	13	spectrum	spectrum	NOUN
ejpam-4798	58	14	and	and	CCONJ
ejpam-4798	58	15	can	can	AUX
ejpam-4798	58	16	be	be	AUX
ejpam-4798	58	17	used	use	VERB
ejpam-4798	58	18	to	to	PART
ejpam-4798	58	19	investigate	investigate	VERB
ejpam-4798	58	20	various	various	ADJ
ejpam-4798	58	21	graph	graph	NOUN
ejpam-4798	58	22	invariants	invariant	NOUN
ejpam-4798	58	23	,	,	PUNCT
ejpam-4798	58	24	such	such	ADJ
ejpam-4798	58	25	as	as	ADP
ejpam-4798	58	26	chromatic	chromatic	ADJ
ejpam-4798	58	27	number	number	NOUN
ejpam-4798	58	28	,	,	PUNCT
ejpam-4798	58	29	clique	clique	ADJ
ejpam-4798	58	30	number	number	NOUN
ejpam-4798	58	31	,	,	PUNCT
ejpam-4798	58	32	and	and	CCONJ
ejpam-4798	58	33	independence	independence	NOUN
ejpam-4798	58	34	number	number	NOUN
ejpam-4798	59	1	[	[	X
ejpam-4798	59	2	5	5	NUM
ejpam-4798	59	3	,	,	PUNCT
ejpam-4798	59	4	7	7	NUM
ejpam-4798	59	5	,	,	PUNCT
ejpam-4798	59	6	8	8	NUM
ejpam-4798	59	7	,	,	PUNCT
ejpam-4798	59	8	12	12	NUM
ejpam-4798	59	9	,	,	PUNCT
ejpam-4798	59	10	16	16	NUM
ejpam-4798	59	11	]	]	PUNCT
ejpam-4798	59	12	.	.	PUNCT
ejpam-4798	60	1	sinha	sinha	NOUN
ejpam-4798	60	2	et.al	et.al	PROPN
ejpam-4798	60	3	[	[	X
ejpam-4798	60	4	13	13	NUM
ejpam-4798	60	5	]	]	PUNCT
ejpam-4798	60	6	introduced	introduce	VERB
ejpam-4798	60	7	the	the	DET
ejpam-4798	60	8	splitting	splitting	NOUN
ejpam-4798	60	9	signed	sign	VERB
ejpam-4798	60	10	graphs	graph	NOUN
ejpam-4798	60	11	as	as	ADP
ejpam-4798	60	12	an	an	DET
ejpam-4798	60	13	extension	extension	NOUN
ejpam-4798	60	14	of	of	ADP
ejpam-4798	60	15	the	the	DET
ejpam-4798	60	16	splitting	splitting	NOUN
ejpam-4798	60	17	graph	graph	NOUN
ejpam-4798	60	18	concept	concept	NOUN
ejpam-4798	60	19	.	.	PUNCT
ejpam-4798	61	1	the	the	DET
ejpam-4798	61	2	splitting	splitting	NOUN
ejpam-4798	61	3	signed	sign	VERB
ejpam-4798	61	4	graph	graph	NOUN
ejpam-4798	61	5	of	of	ADP
ejpam-4798	61	6	a	a	DET
ejpam-4798	61	7	signed	sign	VERB
ejpam-4798	61	8	graph	graph	NOUN
ejpam-4798	61	9	σ	σ	NOUN
ejpam-4798	61	10	=	=	SYM
ejpam-4798	61	11	(	(	PUNCT
ejpam-4798	61	12	v	v	NOUN
ejpam-4798	61	13	,	,	PUNCT
ejpam-4798	61	14	e	e	NOUN
ejpam-4798	61	15	,	,	PUNCT
ejpam-4798	61	16	σ	σ	PROPN
ejpam-4798	61	17	)	)	PUNCT
ejpam-4798	61	18	,	,	PUNCT
ejpam-4798	61	19	denoted	denote	VERB
ejpam-4798	61	20	as	as	ADP
ejpam-4798	61	21	γ(σ	γ(σ	ADJ
ejpam-4798	61	22	)	)	PUNCT
ejpam-4798	61	23	=	=	SYM
ejpam-4798	61	24	(	(	PUNCT
ejpam-4798	61	25	vγ	vγ	NOUN
ejpam-4798	61	26	,	,	PUNCT
ejpam-4798	61	27	eγ	eγ	ADP
ejpam-4798	61	28	,	,	PUNCT
ejpam-4798	61	29	σγ	σγ	NOUN
ejpam-4798	61	30	)	)	PUNCT
ejpam-4798	61	31	,	,	PUNCT
ejpam-4798	61	32	is	be	AUX
ejpam-4798	61	33	obtained	obtain	VERB
ejpam-4798	61	34	by	by	ADP
ejpam-4798	61	35	creating	create	VERB
ejpam-4798	61	36	a	a	DET
ejpam-4798	61	37	new	new	ADJ
ejpam-4798	61	38	vertex	vertex	NOUN
ejpam-4798	61	39	v′	v′	NOUN
ejpam-4798	61	40	for	for	ADP
ejpam-4798	61	41	each	each	DET
ejpam-4798	61	42	vertex	vertex	NOUN
ejpam-4798	61	43	v	v	ADP
ejpam-4798	61	44	∈	∈	PROPN
ejpam-4798	61	45	v	v	NOUN
ejpam-4798	61	46	(	(	PUNCT
ejpam-4798	61	47	σ	σ	NOUN
ejpam-4798	61	48	)	)	PUNCT
ejpam-4798	61	49	,	,	PUNCT
ejpam-4798	61	50	and	and	CCONJ
ejpam-4798	61	51	connecting	connect	VERB
ejpam-4798	61	52	v′	v′	NOUN
ejpam-4798	61	53	to	to	ADP
ejpam-4798	61	54	all	all	DET
ejpam-4798	61	55	vertices	vertex	NOUN
ejpam-4798	61	56	in	in	ADP
ejpam-4798	61	57	σ	σ	NOUN
ejpam-4798	61	58	adjacent	adjacent	ADJ
ejpam-4798	61	59	to	to	ADP
ejpam-4798	61	60	v	v	NOUN
ejpam-4798	61	61	such	such	ADJ
ejpam-4798	61	62	that	that	SCONJ
ejpam-4798	61	63	the	the	DET
ejpam-4798	61	64	sign	sign	NOUN
ejpam-4798	61	65	of	of	ADP
ejpam-4798	61	66	the	the	DET
ejpam-4798	61	67	corresponding	corresponding	ADJ
ejpam-4798	61	68	edges	edge	NOUN
ejpam-4798	61	69	is	be	AUX
ejpam-4798	61	70	preserved	preserve	VERB
ejpam-4798	61	71	,	,	PUNCT
ejpam-4798	61	72	i.e.	i.e.	X
ejpam-4798	61	73	,	,	PUNCT
ejpam-4798	61	74	σγ(v	σγ(v	PUNCT
ejpam-4798	61	75	′u	′u	NOUN
ejpam-4798	61	76	)	)	PUNCT
ejpam-4798	61	77	=	=	SYM
ejpam-4798	61	78	σ(vu	σ(vu	PROPN
ejpam-4798	61	79	)	)	PUNCT
ejpam-4798	61	80	for	for	ADP
ejpam-4798	61	81	all	all	DET
ejpam-4798	61	82	u	u	PROPN
ejpam-4798	61	83	∈	∈	PROPN
ejpam-4798	61	84	n(v	n(v	PROPN
ejpam-4798	61	85	)	)	PUNCT
ejpam-4798	61	86	.	.	PUNCT
ejpam-4798	62	1	this	this	DET
ejpam-4798	62	2	construction	construction	NOUN
ejpam-4798	62	3	is	be	AUX
ejpam-4798	62	4	depicted	depict	VERB
ejpam-4798	62	5	in	in	ADP
ejpam-4798	62	6	figure	figure	NOUN
ejpam-4798	62	7	1	1	NUM
ejpam-4798	62	8	.	.	PUNCT
ejpam-4798	63	1	a	a	DET
ejpam-4798	63	2	signed	sign	VERB
ejpam-4798	63	3	graph	graph	NOUN
ejpam-4798	63	4	σ	σ	PROPN
ejpam-4798	63	5	is	be	AUX
ejpam-4798	63	6	called	call	VERB
ejpam-4798	63	7	a	a	DET
ejpam-4798	63	8	splitting	splitting	NOUN
ejpam-4798	63	9	signed	sign	VERB
ejpam-4798	63	10	graph	graph	NOUN
ejpam-4798	63	11	if	if	SCONJ
ejpam-4798	63	12	it	it	PRON
ejpam-4798	63	13	is	be	AUX
ejpam-4798	63	14	isomorphic	isomorphic	ADJ
ejpam-4798	63	15	to	to	ADP
ejpam-4798	63	16	the	the	DET
ejpam-4798	63	17	splitting	splitting	NOUN
ejpam-4798	63	18	signed	sign	VERB
ejpam-4798	63	19	graph	graph	NOUN
ejpam-4798	63	20	γ(u	γ(u	NOUN
ejpam-4798	63	21	)	)	PUNCT
ejpam-4798	63	22	of	of	ADP
ejpam-4798	63	23	some	some	DET
ejpam-4798	63	24	signed	sign	VERB
ejpam-4798	63	25	graph	graph	NOUN
ejpam-4798	63	26	u	u	PROPN
ejpam-4798	63	27	,	,	PUNCT
ejpam-4798	63	28	where	where	SCONJ
ejpam-4798	63	29	u	u	NOUN
ejpam-4798	63	30	is	be	AUX
ejpam-4798	63	31	referred	refer	VERB
ejpam-4798	63	32	to	to	ADP
ejpam-4798	63	33	as	as	ADP
ejpam-4798	63	34	the	the	DET
ejpam-4798	63	35	splitting	splitting	NOUN
ejpam-4798	63	36	root	root	NOUN
ejpam-4798	63	37	signed	sign	VERB
ejpam-4798	63	38	graph	graph	NOUN
ejpam-4798	63	39	of	of	ADP
ejpam-4798	63	40	σ	σ	PROPN
ejpam-4798	63	41	.	.	PROPN
ejpam-4798	63	42	1	1	NUM
ejpam-4798	63	43	2	2	NUM
ejpam-4798	63	44	3	3	NUM
ejpam-4798	63	45	4	4	NUM
ejpam-4798	63	46	5	5	NUM
ejpam-4798	63	47	1	1	NUM
ejpam-4798	63	48	2	2	NUM
ejpam-4798	63	49	1	1	NUM
ejpam-4798	63	50	'	'	NUM
ejpam-4798	64	1	2	2	NUM
ejpam-4798	64	2	'	'	NUM
ejpam-4798	64	3	3	3	NUM
ejpam-4798	64	4	'	'	NUM
ejpam-4798	64	5	4	4	NUM
ejpam-4798	64	6	'	'	NUM
ejpam-4798	64	7	5	5	NUM
ejpam-4798	64	8	'	'	NUM
ejpam-4798	64	9	35	35	NUM
ejpam-4798	64	10	4	4	NUM
ejpam-4798	64	11	figure	figure	NOUN
ejpam-4798	64	12	1	1	NUM
ejpam-4798	64	13	:	:	PUNCT
ejpam-4798	64	14	signed	sign	VERB
ejpam-4798	64	15	graph	graph	NOUN
ejpam-4798	64	16	σ	σ	PROPN
ejpam-4798	64	17	and	and	CCONJ
ejpam-4798	64	18	its	its	PRON
ejpam-4798	64	19	splitting	splitting	NOUN
ejpam-4798	64	20	signed	sign	VERB
ejpam-4798	64	21	graph	graph	NOUN
ejpam-4798	64	22	γ(σ	γ(σ	ADJ
ejpam-4798	64	23	)	)	PUNCT
ejpam-4798	64	24	algorithmic	algorithmic	ADJ
ejpam-4798	64	25	characterization	characterization	NOUN
ejpam-4798	64	26	of	of	ADP
ejpam-4798	64	27	splitting	split	VERB
ejpam-4798	64	28	signed	sign	VERB
ejpam-4798	64	29	graph	graph	NOUN
ejpam-4798	64	30	by	by	ADP
ejpam-4798	64	31	sinha	sinha	NOUN
ejpam-4798	64	32	et.al	et.al	PROPN
ejpam-4798	64	33	appears	appear	VERB
ejpam-4798	64	34	in	in	ADP
ejpam-4798	64	35	the	the	DET
ejpam-4798	64	36	proceedings	proceeding	NOUN
ejpam-4798	64	37	of	of	ADP
ejpam-4798	64	38	the	the	DET
ejpam-4798	64	39	international	international	ADJ
ejpam-4798	64	40	conference	conference	NOUN
ejpam-4798	64	41	on	on	ADP
ejpam-4798	64	42	current	current	ADJ
ejpam-4798	64	43	trends	trend	NOUN
ejpam-4798	64	44	in	in	ADP
ejpam-4798	64	45	graph	graph	NOUN
ejpam-4798	64	46	theory	theory	NOUN
ejpam-4798	64	47	and	and	CCONJ
ejpam-4798	64	48	computation	computation	NOUN
ejpam-4798	64	49	in	in	ADP
ejpam-4798	64	50	[	[	X
ejpam-4798	64	51	17	17	NUM
ejpam-4798	64	52	]	]	PUNCT
ejpam-4798	64	53	.	.	PUNCT
ejpam-4798	65	1	here	here	ADV
ejpam-4798	65	2	,	,	PUNCT
ejpam-4798	65	3	in	in	ADP
ejpam-4798	65	4	this	this	DET
ejpam-4798	65	5	research	research	NOUN
ejpam-4798	65	6	paper	paper	NOUN
ejpam-4798	65	7	,	,	PUNCT
ejpam-4798	65	8	we	we	PRON
ejpam-4798	65	9	give	give	VERB
ejpam-4798	65	10	an	an	DET
ejpam-4798	65	11	algorithm	algorithm	NOUN
ejpam-4798	65	12	to	to	PART
ejpam-4798	65	13	generate	generate	VERB
ejpam-4798	65	14	the	the	DET
ejpam-4798	65	15	splitting	splitting	NOUN
ejpam-4798	65	16	signed	sign	VERB
ejpam-4798	65	17	graph	graph	NOUN
ejpam-4798	65	18	and	and	CCONJ
ejpam-4798	65	19	its	its	PRON
ejpam-4798	65	20	variant	variant	NOUN
ejpam-4798	65	21	,	,	PUNCT
ejpam-4798	65	22	the	the	DET
ejpam-4798	65	23	splitting	splitting	NOUN
ejpam-4798	65	24	root	root	NOUN
ejpam-4798	65	25	signed	sign	VERB
ejpam-4798	65	26	graph	graph	NOUN
ejpam-4798	65	27	,	,	PUNCT
ejpam-4798	65	28	from	from	ADP
ejpam-4798	65	29	a	a	DET
ejpam-4798	65	30	given	give	VERB
ejpam-4798	65	31	signed	sign	VERB
ejpam-4798	65	32	graph	graph	NOUN
ejpam-4798	65	33	by	by	ADP
ejpam-4798	65	34	using	use	VERB
ejpam-4798	65	35	matlab	matlab	PROPN
ejpam-4798	65	36	.	.	PUNCT
ejpam-4798	66	1	we	we	PRON
ejpam-4798	66	2	also	also	ADV
ejpam-4798	66	3	perform	perform	VERB
ejpam-4798	66	4	spectral	spectral	ADJ
ejpam-4798	66	5	analysis	analysis	NOUN
ejpam-4798	66	6	on	on	ADP
ejpam-4798	66	7	the	the	DET
ejpam-4798	66	8	adjacency	adjacency	NOUN
ejpam-4798	66	9	and	and	CCONJ
ejpam-4798	66	10	laplacian	laplacian	ADJ
ejpam-4798	66	11	matrices	matrix	NOUN
ejpam-4798	66	12	of	of	ADP
ejpam-4798	66	13	the	the	DET
ejpam-4798	66	14	splitting	splitting	NOUN
ejpam-4798	66	15	signed	sign	VERB
ejpam-4798	66	16	graph	graph	NOUN
ejpam-4798	66	17	to	to	PART
ejpam-4798	66	18	investigate	investigate	VERB
ejpam-4798	66	19	its	its	PRON
ejpam-4798	66	20	eigenvalues	eigenvalue	NOUN
ejpam-4798	66	21	and	and	CCONJ
ejpam-4798	66	22	eigenvectors	eigenvector	NOUN
ejpam-4798	66	23	.	.	PUNCT
ejpam-4798	67	1	furthermore	furthermore	ADV
ejpam-4798	67	2	,	,	PUNCT
ejpam-4798	67	3	we	we	PRON
ejpam-4798	67	4	establish	establish	VERB
ejpam-4798	67	5	a	a	DET
ejpam-4798	67	6	relationship	relationship	NOUN
ejpam-4798	67	7	between	between	ADP
ejpam-4798	67	8	the	the	DET
ejpam-4798	67	9	energy	energy	NOUN
ejpam-4798	67	10	of	of	ADP
ejpam-4798	67	11	the	the	DET
ejpam-4798	67	12	original	original	ADJ
ejpam-4798	67	13	signed	sign	VERB
ejpam-4798	67	14	graph	graph	NOUN
ejpam-4798	67	15	and	and	CCONJ
ejpam-4798	67	16	the	the	DET
ejpam-4798	67	17	energy	energy	NOUN
ejpam-4798	67	18	of	of	ADP
ejpam-4798	67	19	the	the	DET
ejpam-4798	67	20	splitting	splitting	NOUN
ejpam-4798	67	21	signed	sign	VERB
ejpam-4798	67	22	graph	graph	NOUN
ejpam-4798	67	23	.	.	PUNCT
ejpam-4798	68	1	our	our	PRON
ejpam-4798	68	2	study	study	NOUN
ejpam-4798	68	3	sheds	shed	VERB
ejpam-4798	68	4	light	light	NOUN
ejpam-4798	68	5	on	on	ADP
ejpam-4798	68	6	the	the	DET
ejpam-4798	68	7	properties	property	NOUN
ejpam-4798	68	8	of	of	ADP
ejpam-4798	68	9	s.	s.	PROPN
ejpam-4798	68	10	kumar	kumar	PROPN
ejpam-4798	68	11	,	,	PUNCT
ejpam-4798	68	12	d.	d.	PROPN
ejpam-4798	68	13	sinha	sinha	PROPN
ejpam-4798	68	14	/	/	SYM
ejpam-4798	68	15	eur	eur	PROPN
ejpam-4798	68	16	.	.	PUNCT
ejpam-4798	69	1	j.	j.	PROPN
ejpam-4798	69	2	pure	pure	PROPN
ejpam-4798	69	3	appl	appl	PROPN
ejpam-4798	69	4	.	.	PROPN
ejpam-4798	69	5	math	math	PROPN
ejpam-4798	69	6	,	,	PUNCT
ejpam-4798	69	7	17	17	NUM
ejpam-4798	69	8	(	(	PUNCT
ejpam-4798	69	9	1	1	NUM
ejpam-4798	69	10	)	)	PUNCT
ejpam-4798	69	11	(	(	PUNCT
ejpam-4798	69	12	2024	2024	NUM
ejpam-4798	69	13	)	)	PUNCT
ejpam-4798	69	14	,	,	PUNCT
ejpam-4798	69	15	504	504	NUM
ejpam-4798	69	16	-	-	SYM
ejpam-4798	69	17	518	518	NUM
ejpam-4798	69	18	507	507	NUM
ejpam-4798	69	19	the	the	DET
ejpam-4798	69	20	splitting	splitting	NOUN
ejpam-4798	69	21	signed	sign	VERB
ejpam-4798	69	22	graph	graph	NOUN
ejpam-4798	69	23	,	,	PUNCT
ejpam-4798	69	24	and	and	CCONJ
ejpam-4798	69	25	its	its	PRON
ejpam-4798	69	26	potential	potential	ADJ
ejpam-4798	69	27	applications	application	NOUN
ejpam-4798	69	28	in	in	ADP
ejpam-4798	69	29	various	various	ADJ
ejpam-4798	69	30	domains	domain	NOUN
ejpam-4798	69	31	.	.	PUNCT
ejpam-4798	70	1	the	the	DET
ejpam-4798	70	2	kronecker	kronecker	NOUN
ejpam-4798	70	3	product	product	NOUN
ejpam-4798	70	4	(	(	PUNCT
ejpam-4798	70	5	or	or	CCONJ
ejpam-4798	70	6	tensor	tensor	NOUN
ejpam-4798	70	7	product	product	NOUN
ejpam-4798	70	8	)	)	PUNCT
ejpam-4798	70	9	of	of	ADP
ejpam-4798	70	10	matrices	matrix	NOUN
ejpam-4798	70	11	u	u	NOUN
ejpam-4798	70	12	and	and	CCONJ
ejpam-4798	70	13	w	w	PROPN
ejpam-4798	70	14	is	be	AUX
ejpam-4798	70	15	a	a	DET
ejpam-4798	70	16	matrix	matrix	NOUN
ejpam-4798	70	17	defined	define	VERB
ejpam-4798	70	18	as	as	SCONJ
ejpam-4798	70	19	follows	follow	VERB
ejpam-4798	70	20	:	:	PUNCT
ejpam-4798	70	21	u	u	NOUN
ejpam-4798	70	22	⊗w	⊗w	NOUN
ejpam-4798	70	23	=	=	NOUN
ejpam-4798	70	24			PROPN
ejpam-4798	70	25	a11w	a11w	VERB
ejpam-4798	70	26	a12w	a12w	PROPN
ejpam-4798	70	27	·	·	PUNCT
ejpam-4798	70	28	·	·	PUNCT
ejpam-4798	70	29	·	·	PUNCT
ejpam-4798	71	1	a1,nw	a1,nw	NOUN
ejpam-4798	71	2	a21w	a21w	VERB
ejpam-4798	71	3	a22w	a22w	NOUN
ejpam-4798	71	4	·	·	PUNCT
ejpam-4798	71	5	·	·	PUNCT
ejpam-4798	71	6	·	·	PUNCT
ejpam-4798	72	1	a2,nw	a2,nw	PROPN
ejpam-4798	72	2	...	...	PUNCT
ejpam-4798	72	3	...	...	PUNCT
ejpam-4798	72	4	.	.	PUNCT
ejpam-4798	72	5	.	.	PUNCT
ejpam-4798	72	6	.	.	PUNCT
ejpam-4798	72	7	...	...	PUNCT
ejpam-4798	73	1	am1w	am1w	VERB
ejpam-4798	73	2	am2w	am2w	ADV
ejpam-4798	73	3	·	·	PUNCT
ejpam-4798	73	4	·	·	PUNCT
ejpam-4798	73	5	·	·	PUNCT
ejpam-4798	73	6	am	be	AUX
ejpam-4798	73	7	,	,	PUNCT
ejpam-4798	73	8	nw	nw	PROPN
ejpam-4798	73	9			VERB
ejpam-4798	73	10	where	where	SCONJ
ejpam-4798	73	11	,	,	PUNCT
ejpam-4798	73	12	u	u	PROPN
ejpam-4798	73	13	∈	∈	PROPN
ejpam-4798	73	14	rm×n	rm×n	ADJ
ejpam-4798	73	15	and	and	CCONJ
ejpam-4798	73	16	w	w	PROPN
ejpam-4798	73	17	∈	∈	PROPN
ejpam-4798	73	18	rp×q	rp×q	PROPN
ejpam-4798	73	19	.	.	PUNCT
ejpam-4798	74	1	theorem	theorem	NOUN
ejpam-4798	74	2	1	1	NUM
ejpam-4798	74	3	.	.	PUNCT
ejpam-4798	75	1	[	[	X
ejpam-4798	75	2	8	8	NUM
ejpam-4798	75	3	]	]	PUNCT
ejpam-4798	75	4	let	let	VERB
ejpam-4798	75	5	u	u	PRON
ejpam-4798	75	6	and	and	CCONJ
ejpam-4798	75	7	w	w	NOUN
ejpam-4798	75	8	are	be	AUX
ejpam-4798	75	9	two	two	NUM
ejpam-4798	75	10	square	square	ADJ
ejpam-4798	75	11	matrices	matrix	NOUN
ejpam-4798	75	12	such	such	ADJ
ejpam-4798	75	13	that	that	SCONJ
ejpam-4798	75	14	u	u	PROPN
ejpam-4798	75	15	∈	∈	PROPN
ejpam-4798	75	16	mm	mm	PROPN
ejpam-4798	75	17	and	and	CCONJ
ejpam-4798	75	18	w	w	PROPN
ejpam-4798	75	19	∈	∈	PROPN
ejpam-4798	75	20	mn	mn	PROPN
ejpam-4798	75	21	.	.	PUNCT
ejpam-4798	76	1	if	if	SCONJ
ejpam-4798	76	2	µi	µi	PROPN
ejpam-4798	76	3	is	be	AUX
ejpam-4798	76	4	an	an	DET
ejpam-4798	76	5	eigenvalue	eigenvalue	NOUN
ejpam-4798	76	6	of	of	ADP
ejpam-4798	76	7	u	u	NOUN
ejpam-4798	76	8	with	with	ADP
ejpam-4798	76	9	its	its	PRON
ejpam-4798	76	10	corresponding	correspond	VERB
ejpam-4798	76	11	eigenvector	eigenvector	NOUN
ejpam-4798	76	12	yi	yi	PROPN
ejpam-4798	76	13	,	,	PUNCT
ejpam-4798	76	14	and	and	CCONJ
ejpam-4798	76	15	λj	λj	PROPN
ejpam-4798	76	16	is	be	AUX
ejpam-4798	76	17	an	an	DET
ejpam-4798	76	18	eigenvalue	eigenvalue	NOUN
ejpam-4798	76	19	of	of	ADP
ejpam-4798	76	20	w	w	PROPN
ejpam-4798	76	21	with	with	ADP
ejpam-4798	76	22	its	its	PRON
ejpam-4798	76	23	corresponding	correspond	VERB
ejpam-4798	76	24	eigenvector	eigenvector	NOUN
ejpam-4798	76	25	xi	xi	PROPN
ejpam-4798	76	26	,	,	PUNCT
ejpam-4798	76	27	then	then	ADV
ejpam-4798	76	28	µiλj	µiλj	PROPN
ejpam-4798	76	29	is	be	AUX
ejpam-4798	76	30	an	an	DET
ejpam-4798	76	31	eigenvalue	eigenvalue	NOUN
ejpam-4798	76	32	of	of	ADP
ejpam-4798	76	33	the	the	DET
ejpam-4798	76	34	kronecker	kronecker	NOUN
ejpam-4798	76	35	product	product	NOUN
ejpam-4798	76	36	u	u	PROPN
ejpam-4798	76	37	⊗w	⊗w	NOUN
ejpam-4798	76	38	,	,	PUNCT
ejpam-4798	76	39	with	with	ADP
ejpam-4798	76	40	the	the	DET
ejpam-4798	76	41	corresponding	correspond	VERB
ejpam-4798	76	42	eigenvector	eigenvector	PROPN
ejpam-4798	76	43	yi	yi	PROPN
ejpam-4798	76	44	⊗	⊗	PROPN
ejpam-4798	76	45	xj	xj	PROPN
ejpam-4798	76	46	.	.	PROPN
ejpam-4798	77	1	2	2	X
ejpam-4798	77	2	.	.	X
ejpam-4798	77	3	generating	generate	VERB
ejpam-4798	77	4	splitting	splitting	NOUN
ejpam-4798	77	5	signed	sign	VERB
ejpam-4798	77	6	graph	graph	NOUN
ejpam-4798	77	7	the	the	DET
ejpam-4798	77	8	procedure	procedure	NOUN
ejpam-4798	77	9	for	for	ADP
ejpam-4798	77	10	generating	generate	VERB
ejpam-4798	77	11	a	a	DET
ejpam-4798	77	12	splitting	splitting	NOUN
ejpam-4798	77	13	signed	sign	VERB
ejpam-4798	77	14	graph	graph	NOUN
ejpam-4798	78	1	can	can	AUX
ejpam-4798	78	2	be	be	AUX
ejpam-4798	78	3	described	describe	VERB
ejpam-4798	78	4	as	as	ADP
ejpam-4798	78	5	follows	follow	VERB
ejpam-4798	78	6	:	:	PUNCT
ejpam-4798	78	7	given	give	VERB
ejpam-4798	78	8	a	a	DET
ejpam-4798	78	9	graph	graph	NOUN
ejpam-4798	78	10	with	with	ADP
ejpam-4798	78	11	n	n	ADP
ejpam-4798	78	12	vertices	vertex	NOUN
ejpam-4798	78	13	,	,	PUNCT
ejpam-4798	78	14	the	the	DET
ejpam-4798	78	15	first	first	ADJ
ejpam-4798	78	16	step	step	NOUN
ejpam-4798	78	17	is	be	AUX
ejpam-4798	78	18	to	to	PART
ejpam-4798	78	19	encode	encode	VERB
ejpam-4798	78	20	an	an	DET
ejpam-4798	78	21	n	n	NUM
ejpam-4798	78	22	×	×	NOUN
ejpam-4798	78	23	n	n	CCONJ
ejpam-4798	78	24	symmetric	symmetric	ADJ
ejpam-4798	78	25	adjacency	adjacency	NOUN
ejpam-4798	78	26	matrix	matrix	NOUN
ejpam-4798	78	27	for	for	ADP
ejpam-4798	78	28	the	the	DET
ejpam-4798	78	29	graph	graph	NOUN
ejpam-4798	78	30	.	.	PUNCT
ejpam-4798	79	1	since	since	SCONJ
ejpam-4798	79	2	a	a	DET
ejpam-4798	79	3	new	new	ADJ
ejpam-4798	79	4	vertex	vertex	NOUN
ejpam-4798	79	5	is	be	AUX
ejpam-4798	79	6	created	create	VERB
ejpam-4798	79	7	for	for	ADP
ejpam-4798	79	8	each	each	DET
ejpam-4798	79	9	vertex	vertex	NOUN
ejpam-4798	79	10	in	in	ADP
ejpam-4798	79	11	the	the	DET
ejpam-4798	79	12	original	original	ADJ
ejpam-4798	79	13	graph	graph	NOUN
ejpam-4798	79	14	,	,	PUNCT
ejpam-4798	79	15	the	the	DET
ejpam-4798	79	16	splitting	splitting	NOUN
ejpam-4798	79	17	graph	graph	NOUN
ejpam-4798	79	18	will	will	AUX
ejpam-4798	79	19	have	have	VERB
ejpam-4798	79	20	a	a	DET
ejpam-4798	79	21	total	total	NOUN
ejpam-4798	79	22	of	of	ADP
ejpam-4798	79	23	2n	2n	NUM
ejpam-4798	79	24	vertices	vertex	NOUN
ejpam-4798	79	25	.	.	PUNCT
ejpam-4798	80	1	the	the	DET
ejpam-4798	80	2	non	non	ADJ
ejpam-4798	80	3	-	-	ADJ
ejpam-4798	80	4	zero	zero	NUM
ejpam-4798	80	5	entries	entry	NOUN
ejpam-4798	80	6	in	in	ADP
ejpam-4798	80	7	the	the	DET
ejpam-4798	80	8	first	first	ADJ
ejpam-4798	80	9	row	row	NOUN
ejpam-4798	80	10	of	of	ADP
ejpam-4798	80	11	the	the	DET
ejpam-4798	80	12	adjacency	adjacency	NOUN
ejpam-4798	80	13	matrix	matrix	NOUN
ejpam-4798	80	14	indicate	indicate	VERB
ejpam-4798	80	15	the	the	DET
ejpam-4798	80	16	vertices	vertex	NOUN
ejpam-4798	80	17	which	which	PRON
ejpam-4798	80	18	are	be	AUX
ejpam-4798	80	19	adjacent	adjacent	ADJ
ejpam-4798	80	20	to	to	ADP
ejpam-4798	80	21	the	the	DET
ejpam-4798	80	22	first	first	ADJ
ejpam-4798	80	23	vertex	vertex	NOUN
ejpam-4798	80	24	i.e.	i.e.	X
ejpam-4798	80	25	v1	v1	NOUN
ejpam-4798	80	26	.	.	PUNCT
ejpam-4798	81	1	these	these	DET
ejpam-4798	81	2	entries	entry	NOUN
ejpam-4798	81	3	in	in	ADP
ejpam-4798	81	4	first	first	ADJ
ejpam-4798	81	5	row	row	NOUN
ejpam-4798	81	6	are	be	AUX
ejpam-4798	81	7	also	also	ADV
ejpam-4798	81	8	considered	consider	VERB
ejpam-4798	81	9	adjacent	adjacent	ADJ
ejpam-4798	81	10	to	to	ADP
ejpam-4798	81	11	vertex	vertex	PROPN
ejpam-4798	81	12	vn+1	vn+1	PROPN
ejpam-4798	81	13	and	and	CCONJ
ejpam-4798	81	14	are	be	AUX
ejpam-4798	81	15	updated	update	VERB
ejpam-4798	81	16	in	in	ADP
ejpam-4798	81	17	the	the	DET
ejpam-4798	81	18	output	output	NOUN
ejpam-4798	81	19	matrix	matrix	NOUN
ejpam-4798	81	20	.	.	PUNCT
ejpam-4798	82	1	this	this	DET
ejpam-4798	82	2	process	process	NOUN
ejpam-4798	82	3	is	be	AUX
ejpam-4798	82	4	repeated	repeat	VERB
ejpam-4798	82	5	for	for	ADP
ejpam-4798	82	6	each	each	DET
ejpam-4798	82	7	row	row	NOUN
ejpam-4798	82	8	until	until	SCONJ
ejpam-4798	82	9	all	all	DET
ejpam-4798	82	10	rows	row	NOUN
ejpam-4798	82	11	have	have	AUX
ejpam-4798	82	12	been	be	AUX
ejpam-4798	82	13	processed	process	VERB
ejpam-4798	82	14	.	.	PUNCT
ejpam-4798	83	1	as	as	ADP
ejpam-4798	83	2	a	a	DET
ejpam-4798	83	3	result	result	NOUN
ejpam-4798	83	4	,	,	PUNCT
ejpam-4798	83	5	a	a	DET
ejpam-4798	83	6	2n	2n	NUM
ejpam-4798	83	7	×	×	PROPN
ejpam-4798	83	8	2n	2n	NUM
ejpam-4798	83	9	output	output	NOUN
ejpam-4798	83	10	matrix	matrix	NOUN
ejpam-4798	83	11	is	be	AUX
ejpam-4798	83	12	generated	generate	VERB
ejpam-4798	83	13	.	.	PUNCT
ejpam-4798	84	1	the	the	DET
ejpam-4798	84	2	adjacency	adjacency	NOUN
ejpam-4798	84	3	matrices	matrix	NOUN
ejpam-4798	84	4	of	of	ADP
ejpam-4798	84	5	the	the	DET
ejpam-4798	84	6	original	original	ADJ
ejpam-4798	84	7	signed	sign	VERB
ejpam-4798	84	8	graph	graph	NOUN
ejpam-4798	84	9	σ	σ	PROPN
ejpam-4798	84	10	and	and	CCONJ
ejpam-4798	84	11	its	its	PRON
ejpam-4798	84	12	splitting	splitting	NOUN
ejpam-4798	84	13	signed	sign	VERB
ejpam-4798	84	14	graph	graph	NOUN
ejpam-4798	84	15	γ(σ	γ(σ	PROPN
ejpam-4798	84	16	)	)	PUNCT
ejpam-4798	84	17	can	can	AUX
ejpam-4798	84	18	be	be	AUX
ejpam-4798	84	19	represented	represent	VERB
ejpam-4798	84	20	as	as	SCONJ
ejpam-4798	84	21	follows	follow	VERB
ejpam-4798	84	22	:	:	PUNCT
ejpam-4798	84	23	a(σ	a(σ	ADJ
ejpam-4798	84	24	)	)	PUNCT
ejpam-4798	84	25	=	=	NOUN
ejpam-4798	85	1			NOUN
ejpam-4798	85	2	0	0	NUM
ejpam-4798	86	1	1	1	NUM
ejpam-4798	86	2	0	0	NUM
ejpam-4798	86	3	0	0	NUM
ejpam-4798	86	4	0	0	NUM
ejpam-4798	86	5	1	1	NUM
ejpam-4798	86	6	0	0	NUM
ejpam-4798	86	7	1	1	NUM
ejpam-4798	86	8	0	0	NUM
ejpam-4798	86	9	−1	−1	NOUN
ejpam-4798	86	10	0	0	NUM
ejpam-4798	86	11	1	1	NUM
ejpam-4798	86	12	0	0	NUM
ejpam-4798	86	13	1	1	NUM
ejpam-4798	86	14	0	0	NUM
ejpam-4798	86	15	0	0	NUM
ejpam-4798	86	16	0	0	NUM
ejpam-4798	86	17	1	1	NUM
ejpam-4798	86	18	0	0	NUM
ejpam-4798	86	19	−1	−1	NOUN
ejpam-4798	86	20	0	0	NUM
ejpam-4798	86	21	−1	−1	NOUN
ejpam-4798	86	22	0	0	NUM
ejpam-4798	86	23	−1	−1	NOUN
ejpam-4798	86	24	0	0	NUM
ejpam-4798	86	25			NOUN
ejpam-4798	86	26	and	and	CCONJ
ejpam-4798	86	27	a(γ(σ	a(γ(σ	NOUN
ejpam-4798	86	28	)	)	PUNCT
ejpam-4798	86	29	)	)	PUNCT
ejpam-4798	87	1	=	=	SYM
ejpam-4798	87	2			NOUN
ejpam-4798	87	3	0	0	NUM
ejpam-4798	87	4	1	1	NUM
ejpam-4798	87	5	0	0	NUM
ejpam-4798	87	6	0	0	NUM
ejpam-4798	87	7	0	0	NUM
ejpam-4798	87	8	0	0	NUM
ejpam-4798	87	9	1	1	NUM
ejpam-4798	87	10	0	0	NUM
ejpam-4798	87	11	0	0	NUM
ejpam-4798	87	12	0	0	NUM
ejpam-4798	87	13	1	1	NUM
ejpam-4798	87	14	0	0	NUM
ejpam-4798	87	15	1	1	NUM
ejpam-4798	87	16	0	0	NUM
ejpam-4798	87	17	−1	−1	NOUN
ejpam-4798	87	18	1	1	NUM
ejpam-4798	87	19	0	0	NUM
ejpam-4798	87	20	1	1	NUM
ejpam-4798	87	21	0	0	NUM
ejpam-4798	87	22	−1	−1	NOUN
ejpam-4798	87	23	0	0	NUM
ejpam-4798	87	24	1	1	NUM
ejpam-4798	87	25	0	0	NUM
ejpam-4798	87	26	1	1	NUM
ejpam-4798	87	27	0	0	NUM
ejpam-4798	87	28	0	0	NUM
ejpam-4798	87	29	1	1	NUM
ejpam-4798	87	30	0	0	NUM
ejpam-4798	87	31	1	1	NUM
ejpam-4798	87	32	0	0	NUM
ejpam-4798	87	33	0	0	NUM
ejpam-4798	87	34	0	0	NUM
ejpam-4798	87	35	1	1	NUM
ejpam-4798	87	36	0	0	NUM
ejpam-4798	87	37	−1	−1	NOUN
ejpam-4798	87	38	0	0	NUM
ejpam-4798	87	39	0	0	NUM
ejpam-4798	87	40	1	1	NUM
ejpam-4798	87	41	0	0	NUM
ejpam-4798	87	42	−1	−1	NOUN
ejpam-4798	87	43	0	0	NUM
ejpam-4798	87	44	−1	−1	NOUN
ejpam-4798	87	45	0	0	NUM
ejpam-4798	87	46	−1	−1	NOUN
ejpam-4798	87	47	0	0	NUM
ejpam-4798	87	48	0	0	NUM
ejpam-4798	87	49	−1	−1	NOUN
ejpam-4798	87	50	0	0	NUM
ejpam-4798	87	51	−1	−1	NOUN
ejpam-4798	87	52	0	0	NUM
ejpam-4798	87	53	0	0	NUM
ejpam-4798	87	54	1	1	NUM
ejpam-4798	87	55	0	0	NUM
ejpam-4798	87	56	0	0	NUM
ejpam-4798	87	57	0	0	NUM
ejpam-4798	87	58	0	0	NUM
ejpam-4798	87	59	0	0	NUM
ejpam-4798	87	60	0	0	NUM
ejpam-4798	87	61	0	0	NUM
ejpam-4798	87	62	0	0	NUM
ejpam-4798	87	63	1	1	NUM
ejpam-4798	87	64	0	0	NUM
ejpam-4798	87	65	1	1	NUM
ejpam-4798	87	66	0	0	NUM
ejpam-4798	87	67	−1	−1	NOUN
ejpam-4798	87	68	0	0	NUM
ejpam-4798	87	69	0	0	NUM
ejpam-4798	87	70	0	0	NUM
ejpam-4798	87	71	0	0	NUM
ejpam-4798	87	72	0	0	NUM
ejpam-4798	87	73	0	0	NUM
ejpam-4798	87	74	1	1	NUM
ejpam-4798	87	75	0	0	NUM
ejpam-4798	87	76	1	1	NUM
ejpam-4798	87	77	0	0	NUM
ejpam-4798	87	78	0	0	NUM
ejpam-4798	87	79	0	0	NUM
ejpam-4798	87	80	0	0	NUM
ejpam-4798	87	81	0	0	NUM
ejpam-4798	87	82	0	0	NUM
ejpam-4798	87	83	0	0	NUM
ejpam-4798	87	84	0	0	NUM
ejpam-4798	87	85	1	1	NUM
ejpam-4798	87	86	0	0	NUM
ejpam-4798	87	87	−1	−1	NOUN
ejpam-4798	87	88	0	0	NUM
ejpam-4798	87	89	0	0	NUM
ejpam-4798	87	90	0	0	NUM
ejpam-4798	87	91	0	0	NUM
ejpam-4798	87	92	0	0	NUM
ejpam-4798	87	93	0	0	NUM
ejpam-4798	87	94	−1	−1	NOUN
ejpam-4798	87	95	0	0	NUM
ejpam-4798	87	96	−1	−1	NOUN
ejpam-4798	87	97	0	0	NUM
ejpam-4798	87	98	0	0	NUM
ejpam-4798	87	99	0	0	NUM
ejpam-4798	87	100	0	0	NUM
ejpam-4798	87	101	0	0	NUM
ejpam-4798	87	102	0	0	NUM
ejpam-4798	87	103			PART
ejpam-4798	87	104	s.	s.	PROPN
ejpam-4798	87	105	kumar	kumar	PROPN
ejpam-4798	87	106	,	,	PUNCT
ejpam-4798	87	107	d.	d.	PROPN
ejpam-4798	87	108	sinha	sinha	PROPN
ejpam-4798	87	109	/	/	SYM
ejpam-4798	87	110	eur	eur	PROPN
ejpam-4798	87	111	.	.	PUNCT
ejpam-4798	88	1	j.	j.	PROPN
ejpam-4798	88	2	pure	pure	PROPN
ejpam-4798	88	3	appl	appl	PROPN
ejpam-4798	88	4	.	.	PROPN
ejpam-4798	88	5	math	math	PROPN
ejpam-4798	88	6	,	,	PUNCT
ejpam-4798	88	7	17	17	NUM
ejpam-4798	88	8	(	(	PUNCT
ejpam-4798	88	9	1	1	NUM
ejpam-4798	88	10	)	)	PUNCT
ejpam-4798	88	11	(	(	PUNCT
ejpam-4798	88	12	2024	2024	NUM
ejpam-4798	88	13	)	)	PUNCT
ejpam-4798	88	14	,	,	PUNCT
ejpam-4798	88	15	504	504	NUM
ejpam-4798	88	16	-	-	SYM
ejpam-4798	88	17	518	518	NUM
ejpam-4798	88	18	508	508	NUM
ejpam-4798	88	19	it	it	PRON
ejpam-4798	88	20	has	have	AUX
ejpam-4798	88	21	been	be	AUX
ejpam-4798	88	22	observed	observe	VERB
ejpam-4798	88	23	that	that	SCONJ
ejpam-4798	88	24	the	the	DET
ejpam-4798	88	25	adjacency	adjacency	NOUN
ejpam-4798	88	26	matrix	matrix	NOUN
ejpam-4798	88	27	,	,	PUNCT
ejpam-4798	88	28	of	of	ADP
ejpam-4798	88	29	order	order	NOUN
ejpam-4798	88	30	2n	2n	NUM
ejpam-4798	88	31	,	,	PUNCT
ejpam-4798	88	32	of	of	ADP
ejpam-4798	88	33	the	the	DET
ejpam-4798	88	34	splitting	splitting	NOUN
ejpam-4798	88	35	signed	sign	VERB
ejpam-4798	88	36	graph	graph	NOUN
ejpam-4798	88	37	γ(σ	γ(σ	PROPN
ejpam-4798	88	38	)	)	PUNCT
ejpam-4798	88	39	can	can	AUX
ejpam-4798	88	40	be	be	AUX
ejpam-4798	88	41	partitioned	partition	VERB
ejpam-4798	88	42	into	into	ADP
ejpam-4798	88	43	four	four	NUM
ejpam-4798	88	44	equal	equal	ADJ
ejpam-4798	88	45	matrices	matrix	NOUN
ejpam-4798	88	46	each	each	PRON
ejpam-4798	88	47	of	of	ADP
ejpam-4798	88	48	order	order	NOUN
ejpam-4798	88	49	n	n	CCONJ
ejpam-4798	88	50	,	,	PUNCT
ejpam-4798	88	51	where	where	SCONJ
ejpam-4798	88	52	the	the	DET
ejpam-4798	88	53	initial	initial	ADJ
ejpam-4798	88	54	three	three	NUM
ejpam-4798	88	55	matrices	matrix	NOUN
ejpam-4798	88	56	are	be	AUX
ejpam-4798	88	57	identical	identical	ADJ
ejpam-4798	88	58	and	and	CCONJ
ejpam-4798	88	59	the	the	DET
ejpam-4798	88	60	fourth	fourth	ADJ
ejpam-4798	88	61	is	be	AUX
ejpam-4798	88	62	always	always	ADV
ejpam-4798	88	63	zero	zero	NUM
ejpam-4798	88	64	.	.	PUNCT
ejpam-4798	89	1	additionally	additionally	ADV
ejpam-4798	89	2	,	,	PUNCT
ejpam-4798	89	3	it	it	PRON
ejpam-4798	89	4	has	have	AUX
ejpam-4798	89	5	been	be	AUX
ejpam-4798	89	6	discovered	discover	VERB
ejpam-4798	89	7	that	that	SCONJ
ejpam-4798	89	8	the	the	DET
ejpam-4798	89	9	original	original	ADJ
ejpam-4798	89	10	signed	sign	VERB
ejpam-4798	89	11	graph	graph	NOUN
ejpam-4798	89	12	σ	σ	PROPN
ejpam-4798	89	13	is	be	AUX
ejpam-4798	89	14	an	an	DET
ejpam-4798	89	15	induced	induced	ADJ
ejpam-4798	89	16	subgraph	subgraph	NOUN
ejpam-4798	89	17	of	of	ADP
ejpam-4798	89	18	its	its	PRON
ejpam-4798	89	19	splitting	splitting	NOUN
ejpam-4798	89	20	signed	sign	VERB
ejpam-4798	89	21	graph	graph	NOUN
ejpam-4798	89	22	γ(σ	γ(σ	PROPN
ejpam-4798	89	23	)	)	PUNCT
ejpam-4798	89	24	.	.	PUNCT
ejpam-4798	90	1	algorithm	algorithm	NOUN
ejpam-4798	90	2	1	1	NUM
ejpam-4798	90	3	algorithm	algorithm	NOUN
ejpam-4798	90	4	to	to	PART
ejpam-4798	90	5	derive	derive	VERB
ejpam-4798	90	6	the	the	DET
ejpam-4798	90	7	splitting	splitting	NOUN
ejpam-4798	90	8	signed	sign	VERB
ejpam-4798	90	9	graph	graph	NOUN
ejpam-4798	90	10	γ(σ	γ(σ	PROPN
ejpam-4798	90	11	)	)	PUNCT
ejpam-4798	90	12	of	of	ADP
ejpam-4798	90	13	a	a	DET
ejpam-4798	90	14	signed	sign	VERB
ejpam-4798	90	15	graph	graph	NOUN
ejpam-4798	90	16	σ	σ	PROPN
ejpam-4798	90	17	1	1	NUM
ejpam-4798	90	18	:	:	PUNCT
ejpam-4798	90	19	input	input	NOUN
ejpam-4798	90	20	:	:	PUNCT
ejpam-4798	90	21	number	number	NOUN
ejpam-4798	90	22	of	of	ADP
ejpam-4798	90	23	vertices	vertex	NOUN
ejpam-4798	90	24	(	(	PUNCT
ejpam-4798	90	25	n	n	CCONJ
ejpam-4798	90	26	)	)	PUNCT
ejpam-4798	90	27	2	2	NUM
ejpam-4798	90	28	:	:	PUNCT
ejpam-4798	90	29	input	input	NOUN
ejpam-4798	90	30	:	:	PUNCT
ejpam-4798	90	31	adjacency	adjacency	NOUN
ejpam-4798	90	32	matrix	matrix	NOUN
ejpam-4798	90	33	of	of	ADP
ejpam-4798	90	34	the	the	DET
ejpam-4798	90	35	signed	sign	VERB
ejpam-4798	90	36	graph	graph	NOUN
ejpam-4798	90	37	a(σ	a(σ	PROPN
ejpam-4798	90	38	)	)	PUNCT
ejpam-4798	91	1	=	=	PUNCT
ejpam-4798	91	2	a(i	a(i	PROPN
ejpam-4798	91	3	,	,	PUNCT
ejpam-4798	91	4	j	j	NOUN
ejpam-4798	91	5	)	)	PUNCT
ejpam-4798	91	6	3	3	NUM
ejpam-4798	91	7	:	:	PUNCT
ejpam-4798	91	8	for	for	ADP
ejpam-4798	91	9	i	i	PRON
ejpam-4798	91	10	=	=	NOUN
ejpam-4798	91	11	1	1	NUM
ejpam-4798	91	12	:	:	SYM
ejpam-4798	91	13	2n	2n	NUM
ejpam-4798	91	14	do	do	VERB
ejpam-4798	91	15	4	4	NUM
ejpam-4798	91	16	:	:	PUNCT
ejpam-4798	91	17	for	for	ADP
ejpam-4798	91	18	j	j	PROPN
ejpam-4798	91	19	=	=	SYM
ejpam-4798	91	20	1	1	NUM
ejpam-4798	91	21	:	:	SYM
ejpam-4798	91	22	2n	2n	NUM
ejpam-4798	91	23	do	do	VERB
ejpam-4798	91	24	5	5	NUM
ejpam-4798	91	25	:	:	PUNCT
ejpam-4798	91	26	check	check	VERB
ejpam-4798	91	27	6	6	NUM
ejpam-4798	91	28	:	:	PUNCT
ejpam-4798	91	29	if	if	SCONJ
ejpam-4798	91	30	i	i	PRON
ejpam-4798	91	31	>	>	X
ejpam-4798	91	32	n&&j	n&&j	PROPN
ejpam-4798	91	33	>	>	X
ejpam-4798	91	34	n	n	CCONJ
ejpam-4798	91	35	then	then	ADV
ejpam-4798	91	36	7	7	NUM
ejpam-4798	91	37	:	:	PUNCT
ejpam-4798	91	38	assign	assign	NOUN
ejpam-4798	91	39	a(i	a(i	PROPN
ejpam-4798	91	40	,	,	PUNCT
ejpam-4798	91	41	j)=0	j)=0	PROPN
ejpam-4798	91	42	;	;	PUNCT
ejpam-4798	91	43	8	8	NUM
ejpam-4798	91	44	:	:	PUNCT
ejpam-4798	91	45	else	else	ADV
ejpam-4798	91	46	9	9	NUM
ejpam-4798	91	47	:	:	PUNCT
ejpam-4798	91	48	check	check	VERB
ejpam-4798	91	49	10	10	NUM
ejpam-4798	91	50	:	:	PUNCT
ejpam-4798	91	51	if	if	SCONJ
ejpam-4798	91	52	i	i	PRON
ejpam-4798	91	53	>	>	X
ejpam-4798	91	54	n&&j	n&&j	PROPN
ejpam-4798	91	55	≤	≤	NOUN
ejpam-4798	92	1	n	n	CCONJ
ejpam-4798	92	2	then	then	ADV
ejpam-4798	92	3	11	11	NUM
ejpam-4798	92	4	:	:	PUNCT
ejpam-4798	92	5	assign	assign	NOUN
ejpam-4798	92	6	a(i	a(i	PROPN
ejpam-4798	92	7	,	,	PUNCT
ejpam-4798	92	8	j	j	NOUN
ejpam-4798	92	9	)	)	PUNCT
ejpam-4798	92	10	=	=	PUNCT
ejpam-4798	92	11	a(i	a(i	VERB
ejpam-4798	92	12	-	-	PUNCT
ejpam-4798	92	13	n	n	CCONJ
ejpam-4798	92	14	,	,	PUNCT
ejpam-4798	92	15	j	j	PROPN
ejpam-4798	92	16	)	)	PUNCT
ejpam-4798	92	17	;	;	PUNCT
ejpam-4798	92	18	12	12	NUM
ejpam-4798	92	19	:	:	PUNCT
ejpam-4798	92	20	else	else	ADV
ejpam-4798	92	21	13	13	NUM
ejpam-4798	92	22	:	:	PUNCT
ejpam-4798	92	23	check	check	VERB
ejpam-4798	92	24	14	14	NUM
ejpam-4798	92	25	:	:	PUNCT
ejpam-4798	92	26	if	if	SCONJ
ejpam-4798	92	27	i	i	PRON
ejpam-4798	92	28	≤	≤	PUNCT
ejpam-4798	92	29	n&&j	n&&j	PROPN
ejpam-4798	92	30	>	>	X
ejpam-4798	92	31	n	n	PROPN
ejpam-4798	92	32	then	then	ADV
ejpam-4798	92	33	15	15	NUM
ejpam-4798	92	34	:	:	PUNCT
ejpam-4798	92	35	assign	assign	NOUN
ejpam-4798	92	36	a(i	a(i	PROPN
ejpam-4798	92	37	,	,	PUNCT
ejpam-4798	92	38	j	j	NOUN
ejpam-4798	92	39	)	)	PUNCT
ejpam-4798	92	40	=	=	PUNCT
ejpam-4798	92	41	a(i	a(i	PROPN
ejpam-4798	92	42	,	,	PUNCT
ejpam-4798	92	43	j	j	PROPN
ejpam-4798	92	44	-	-	PUNCT
ejpam-4798	92	45	n	n	CCONJ
ejpam-4798	92	46	)	)	PUNCT
ejpam-4798	92	47	;	;	PUNCT
ejpam-4798	92	48	16	16	NUM
ejpam-4798	92	49	:	:	PUNCT
ejpam-4798	92	50	else	else	ADV
ejpam-4798	92	51	17	17	NUM
ejpam-4798	92	52	:	:	PUNCT
ejpam-4798	92	53	assign	assign	NOUN
ejpam-4798	92	54	a(i	a(i	PROPN
ejpam-4798	92	55	,	,	PUNCT
ejpam-4798	92	56	j	j	NOUN
ejpam-4798	92	57	)	)	PUNCT
ejpam-4798	92	58	=	=	PUNCT
ejpam-4798	92	59	a(i	a(i	PROPN
ejpam-4798	92	60	,	,	PUNCT
ejpam-4798	92	61	j	j	PROPN
ejpam-4798	92	62	)	)	PUNCT
ejpam-4798	92	63	;	;	PUNCT
ejpam-4798	92	64	18	18	NUM
ejpam-4798	92	65	:	:	PUNCT
ejpam-4798	92	66	end	end	VERB
ejpam-4798	92	67	if	if	SCONJ
ejpam-4798	92	68	19	19	NUM
ejpam-4798	92	69	:	:	PUNCT
ejpam-4798	92	70	end	end	VERB
ejpam-4798	92	71	if	if	SCONJ
ejpam-4798	92	72	20	20	NUM
ejpam-4798	92	73	:	:	PUNCT
ejpam-4798	92	74	end	end	VERB
ejpam-4798	92	75	if	if	SCONJ
ejpam-4798	92	76	21	21	NUM
ejpam-4798	92	77	:	:	PUNCT
ejpam-4798	92	78	end	end	VERB
ejpam-4798	92	79	for	for	ADP
ejpam-4798	92	80	22	22	NUM
ejpam-4798	92	81	:	:	PUNCT
ejpam-4798	92	82	end	end	VERB
ejpam-4798	92	83	for	for	ADP
ejpam-4798	92	84	23	23	NUM
ejpam-4798	92	85	:	:	PUNCT
ejpam-4798	92	86	output	output	NOUN
ejpam-4798	92	87	generate	generate	VERB
ejpam-4798	92	88	2n	2n	NUM
ejpam-4798	92	89	×	×	NOUN
ejpam-4798	92	90	2n	2n	NUM
ejpam-4798	92	91	matrix	matrix	NOUN
ejpam-4798	92	92	i.e.	i.e.	X
ejpam-4798	92	93	adjacency	adjacency	NOUN
ejpam-4798	92	94	matrix	matrix	NOUN
ejpam-4798	92	95	of	of	ADP
ejpam-4798	92	96	signed	sign	VERB
ejpam-4798	92	97	split	split	NOUN
ejpam-4798	92	98	graph	graph	NOUN
ejpam-4798	92	99	computational	computational	ADJ
ejpam-4798	92	100	complexity	complexity	NOUN
ejpam-4798	92	101	:	:	PUNCT
ejpam-4798	92	102	computational	computational	ADJ
ejpam-4798	92	103	complexity	complexity	NOUN
ejpam-4798	92	104	analysis	analysis	NOUN
ejpam-4798	92	105	is	be	AUX
ejpam-4798	92	106	an	an	DET
ejpam-4798	92	107	essential	essential	ADJ
ejpam-4798	92	108	aspect	aspect	NOUN
ejpam-4798	92	109	of	of	ADP
ejpam-4798	92	110	evaluating	evaluate	VERB
ejpam-4798	92	111	the	the	DET
ejpam-4798	92	112	performance	performance	NOUN
ejpam-4798	92	113	of	of	ADP
ejpam-4798	92	114	an	an	DET
ejpam-4798	92	115	algorithm	algorithm	NOUN
ejpam-4798	92	116	.	.	PUNCT
ejpam-4798	93	1	in	in	ADP
ejpam-4798	93	2	this	this	DET
ejpam-4798	93	3	regard	regard	NOUN
ejpam-4798	93	4	,	,	PUNCT
ejpam-4798	93	5	we	we	PRON
ejpam-4798	93	6	analyze	analyze	VERB
ejpam-4798	93	7	the	the	DET
ejpam-4798	93	8	complexity	complexity	NOUN
ejpam-4798	93	9	involved	involve	VERB
ejpam-4798	93	10	in	in	ADP
ejpam-4798	93	11	steps	step	NOUN
ejpam-4798	93	12	3	3	NUM
ejpam-4798	93	13	and	and	CCONJ
ejpam-4798	93	14	4	4	NUM
ejpam-4798	93	15	of	of	ADP
ejpam-4798	93	16	our	our	PRON
ejpam-4798	93	17	algorithm	algorithm	NOUN
ejpam-4798	93	18	.	.	PUNCT
ejpam-4798	94	1	in	in	ADP
ejpam-4798	94	2	these	these	DET
ejpam-4798	94	3	steps	step	NOUN
ejpam-4798	94	4	,	,	PUNCT
ejpam-4798	94	5	we	we	PRON
ejpam-4798	94	6	traverse	traverse	VERB
ejpam-4798	94	7	each	each	DET
ejpam-4798	94	8	vertex	vertex	NOUN
ejpam-4798	94	9	of	of	ADP
ejpam-4798	94	10	the	the	DET
ejpam-4798	94	11	signed	sign	VERB
ejpam-4798	94	12	graph	graph	NOUN
ejpam-4798	94	13	and	and	CCONJ
ejpam-4798	94	14	examine	examine	VERB
ejpam-4798	94	15	its	its	PRON
ejpam-4798	94	16	adjacency	adjacency	NOUN
ejpam-4798	94	17	with	with	ADP
ejpam-4798	94	18	all	all	DET
ejpam-4798	94	19	other	other	ADJ
ejpam-4798	94	20	vertices	vertex	NOUN
ejpam-4798	94	21	.	.	PUNCT
ejpam-4798	95	1	as	as	ADP
ejpam-4798	95	2	a	a	DET
ejpam-4798	95	3	result	result	NOUN
ejpam-4798	95	4	,	,	PUNCT
ejpam-4798	95	5	the	the	DET
ejpam-4798	95	6	complexity	complexity	NOUN
ejpam-4798	95	7	involved	involve	VERB
ejpam-4798	95	8	in	in	ADP
ejpam-4798	95	9	these	these	DET
ejpam-4798	95	10	steps	step	NOUN
ejpam-4798	95	11	is	be	AUX
ejpam-4798	95	12	o(n2	o(n2	ADJ
ejpam-4798	95	13	)	)	PUNCT
ejpam-4798	95	14	.	.	PUNCT
ejpam-4798	96	1	considering	consider	VERB
ejpam-4798	96	2	the	the	DET
ejpam-4798	96	3	overall	overall	ADJ
ejpam-4798	96	4	algorithm	algorithm	NOUN
ejpam-4798	96	5	,	,	PUNCT
ejpam-4798	96	6	the	the	DET
ejpam-4798	96	7	total	total	ADJ
ejpam-4798	96	8	complexity	complexity	NOUN
ejpam-4798	96	9	involved	involve	VERB
ejpam-4798	96	10	is	be	AUX
ejpam-4798	96	11	the	the	DET
ejpam-4798	96	12	sum	sum	NOUN
ejpam-4798	96	13	of	of	ADP
ejpam-4798	96	14	the	the	DET
ejpam-4798	96	15	complexities	complexity	NOUN
ejpam-4798	96	16	of	of	ADP
ejpam-4798	96	17	all	all	DET
ejpam-4798	96	18	the	the	DET
ejpam-4798	96	19	steps	step	NOUN
ejpam-4798	96	20	.	.	PUNCT
ejpam-4798	97	1	as	as	SCONJ
ejpam-4798	97	2	the	the	DET
ejpam-4798	97	3	complexity	complexity	NOUN
ejpam-4798	97	4	in	in	ADP
ejpam-4798	97	5	steps	step	NOUN
ejpam-4798	97	6	3	3	NUM
ejpam-4798	97	7	and	and	CCONJ
ejpam-4798	97	8	4	4	NUM
ejpam-4798	97	9	is	be	AUX
ejpam-4798	97	10	the	the	DET
ejpam-4798	97	11	highest	high	ADJ
ejpam-4798	97	12	,	,	PUNCT
ejpam-4798	97	13	the	the	DET
ejpam-4798	97	14	total	total	ADJ
ejpam-4798	97	15	complexity	complexity	NOUN
ejpam-4798	97	16	is	be	AUX
ejpam-4798	97	17	also	also	ADV
ejpam-4798	97	18	o(n2	o(n2	ADJ
ejpam-4798	97	19	)	)	PUNCT
ejpam-4798	97	20	.	.	PUNCT
ejpam-4798	98	1	therefore	therefore	ADV
ejpam-4798	98	2	,	,	PUNCT
ejpam-4798	98	3	the	the	DET
ejpam-4798	98	4	complexity	complexity	NOUN
ejpam-4798	98	5	of	of	ADP
ejpam-4798	98	6	the	the	DET
ejpam-4798	98	7	proposed	propose	VERB
ejpam-4798	98	8	algorithm	algorithm	NOUN
ejpam-4798	98	9	for	for	ADP
ejpam-4798	98	10	finding	find	VERB
ejpam-4798	98	11	a	a	DET
ejpam-4798	98	12	signed	sign	VERB
ejpam-4798	98	13	split	split	NOUN
ejpam-4798	98	14	graph	graph	NOUN
ejpam-4798	98	15	with	with	ADP
ejpam-4798	98	16	a	a	DET
ejpam-4798	98	17	given	give	VERB
ejpam-4798	98	18	adjacency	adjacency	NOUN
ejpam-4798	98	19	matrix	matrix	NOUN
ejpam-4798	98	20	is	be	AUX
ejpam-4798	98	21	o(n2	o(n2	ADJ
ejpam-4798	98	22	)	)	PUNCT
ejpam-4798	98	23	,	,	PUNCT
ejpam-4798	98	24	where	where	SCONJ
ejpam-4798	98	25	n	n	PRON
ejpam-4798	98	26	represents	represent	VERB
ejpam-4798	98	27	the	the	DET
ejpam-4798	98	28	number	number	NOUN
ejpam-4798	98	29	of	of	ADP
ejpam-4798	98	30	vertices	vertex	NOUN
ejpam-4798	98	31	in	in	ADP
ejpam-4798	98	32	the	the	DET
ejpam-4798	98	33	signed	sign	VERB
ejpam-4798	98	34	graph	graph	NOUN
ejpam-4798	98	35	.	.	PUNCT
ejpam-4798	99	1	s.	s.	PROPN
ejpam-4798	99	2	kumar	kumar	PROPN
ejpam-4798	99	3	,	,	PUNCT
ejpam-4798	99	4	d.	d.	PROPN
ejpam-4798	99	5	sinha	sinha	PROPN
ejpam-4798	99	6	/	/	SYM
ejpam-4798	99	7	eur	eur	PROPN
ejpam-4798	99	8	.	.	PUNCT
ejpam-4798	100	1	j.	j.	PROPN
ejpam-4798	100	2	pure	pure	PROPN
ejpam-4798	100	3	appl	appl	PROPN
ejpam-4798	100	4	.	.	PROPN
ejpam-4798	100	5	math	math	PROPN
ejpam-4798	100	6	,	,	PUNCT
ejpam-4798	100	7	17	17	NUM
ejpam-4798	100	8	(	(	PUNCT
ejpam-4798	100	9	1	1	NUM
ejpam-4798	100	10	)	)	PUNCT
ejpam-4798	100	11	(	(	PUNCT
ejpam-4798	100	12	2024	2024	NUM
ejpam-4798	100	13	)	)	PUNCT
ejpam-4798	100	14	,	,	PUNCT
ejpam-4798	100	15	504	504	NUM
ejpam-4798	100	16	-	-	SYM
ejpam-4798	100	17	518	518	NUM
ejpam-4798	100	18	509	509	NUM
ejpam-4798	100	19	3	3	NUM
ejpam-4798	100	20	.	.	PUNCT
ejpam-4798	100	21	structural	structural	ADJ
ejpam-4798	100	22	characterization	characterization	NOUN
ejpam-4798	100	23	to	to	PART
ejpam-4798	100	24	derive	derive	VERB
ejpam-4798	100	25	splitting	splitting	NOUN
ejpam-4798	100	26	root	root	NOUN
ejpam-4798	100	27	signed	sign	VERB
ejpam-4798	100	28	graph	graph	NOUN
ejpam-4798	100	29	sampathkumar	sampathkumar	NOUN
ejpam-4798	100	30	and	and	CCONJ
ejpam-4798	100	31	walikar	walikar	NOUN
ejpam-4798	101	1	[	[	X
ejpam-4798	101	2	?	?	X
ejpam-4798	101	3	]	]	PUNCT
ejpam-4798	101	4	presented	present	VERB
ejpam-4798	101	5	the	the	DET
ejpam-4798	101	6	following	follow	VERB
ejpam-4798	101	7	characterization	characterization	NOUN
ejpam-4798	101	8	of	of	ADP
ejpam-4798	101	9	splitting	splitting	NOUN
ejpam-4798	101	10	graphs	graph	NOUN
ejpam-4798	101	11	,	,	PUNCT
ejpam-4798	101	12	which	which	PRON
ejpam-4798	101	13	is	be	AUX
ejpam-4798	101	14	utilized	utilize	VERB
ejpam-4798	101	15	to	to	PART
ejpam-4798	101	16	derive	derive	VERB
ejpam-4798	101	17	the	the	DET
ejpam-4798	101	18	splitting	splitting	NOUN
ejpam-4798	101	19	root	root	NOUN
ejpam-4798	101	20	graph	graph	NOUN
ejpam-4798	101	21	.	.	PUNCT
ejpam-4798	102	1	theorem	theorem	NOUN
ejpam-4798	102	2	2	2	NUM
ejpam-4798	102	3	.	.	PUNCT
ejpam-4798	103	1	[	[	X
ejpam-4798	103	2	?	?	X
ejpam-4798	103	3	]	]	X
ejpam-4798	103	4	a	a	DET
ejpam-4798	103	5	graph	graph	NOUN
ejpam-4798	103	6	σu	σu	INTJ
ejpam-4798	103	7	can	can	AUX
ejpam-4798	103	8	be	be	AUX
ejpam-4798	103	9	characterized	characterize	VERB
ejpam-4798	103	10	as	as	ADP
ejpam-4798	103	11	a	a	DET
ejpam-4798	103	12	splitting	splitting	NOUN
ejpam-4798	103	13	graph	graph	NOUN
ejpam-4798	103	14	if	if	SCONJ
ejpam-4798	103	15	and	and	CCONJ
ejpam-4798	103	16	only	only	ADV
ejpam-4798	103	17	if	if	SCONJ
ejpam-4798	103	18	its	its	PRON
ejpam-4798	103	19	vertex	vertex	NOUN
ejpam-4798	103	20	set	set	NOUN
ejpam-4798	103	21	,	,	PUNCT
ejpam-4798	103	22	v	v	PROPN
ejpam-4798	103	23	(	(	PUNCT
ejpam-4798	103	24	σu	σu	INTJ
ejpam-4798	103	25	)	)	PUNCT
ejpam-4798	103	26	,	,	PUNCT
ejpam-4798	103	27	can	can	AUX
ejpam-4798	103	28	be	be	AUX
ejpam-4798	103	29	divided	divide	VERB
ejpam-4798	103	30	into	into	ADP
ejpam-4798	103	31	two	two	NUM
ejpam-4798	103	32	sets	set	NOUN
ejpam-4798	103	33	,	,	PUNCT
ejpam-4798	103	34	v1	v1	NOUN
ejpam-4798	103	35	and	and	CCONJ
ejpam-4798	103	36	v2	v2	NOUN
ejpam-4798	103	37	,	,	PUNCT
ejpam-4798	103	38	such	such	ADJ
ejpam-4798	103	39	that	that	SCONJ
ejpam-4798	103	40	:	:	PUNCT
ejpam-4798	103	41	(	(	PUNCT
ejpam-4798	103	42	a	a	X
ejpam-4798	103	43	)	)	PUNCT
ejpam-4798	103	44	there	there	PRON
ejpam-4798	103	45	exists	exist	VERB
ejpam-4798	103	46	a	a	DET
ejpam-4798	103	47	bijective	bijective	ADJ
ejpam-4798	103	48	mapping	mapping	NOUN
ejpam-4798	103	49	between	between	ADP
ejpam-4798	103	50	v1	v1	NOUN
ejpam-4798	103	51	and	and	CCONJ
ejpam-4798	103	52	v2	v2	NOUN
ejpam-4798	103	53	,	,	PUNCT
ejpam-4798	103	54	with	with	ADP
ejpam-4798	103	55	v	v	ADP
ejpam-4798	103	56	mapping	mapping	NOUN
ejpam-4798	103	57	to	to	ADP
ejpam-4798	103	58	v′	v′	PROPN
ejpam-4798	103	59	,	,	PUNCT
ejpam-4798	103	60	and	and	CCONJ
ejpam-4798	103	61	(	(	PUNCT
ejpam-4798	103	62	b	b	X
ejpam-4798	103	63	)	)	PUNCT
ejpam-4798	103	64	the	the	DET
ejpam-4798	103	65	neighbours	neighbour	NOUN
ejpam-4798	103	66	of	of	ADP
ejpam-4798	103	67	v′	v′	PROPN
ejpam-4798	103	68	,	,	PUNCT
ejpam-4798	103	69	n(v′	n(v′	NUM
ejpam-4798	103	70	)	)	PUNCT
ejpam-4798	103	71	,	,	PUNCT
ejpam-4798	103	72	are	be	AUX
ejpam-4798	103	73	equal	equal	ADJ
ejpam-4798	103	74	to	to	ADP
ejpam-4798	103	75	the	the	DET
ejpam-4798	103	76	intersection	intersection	NOUN
ejpam-4798	103	77	of	of	ADP
ejpam-4798	103	78	the	the	DET
ejpam-4798	103	79	neighbours	neighbour	NOUN
ejpam-4798	103	80	of	of	ADP
ejpam-4798	103	81	v	v	NOUN
ejpam-4798	103	82	,	,	PUNCT
ejpam-4798	103	83	n(v	n(v	PROPN
ejpam-4798	103	84	)	)	PUNCT
ejpam-4798	103	85	,	,	PUNCT
ejpam-4798	103	86	and	and	CCONJ
ejpam-4798	103	87	the	the	DET
ejpam-4798	103	88	set	set	VERB
ejpam-4798	103	89	v1	v1	NOUN
ejpam-4798	103	90	.	.	PUNCT
ejpam-4798	104	1	in	in	ADP
ejpam-4798	104	2	[	[	X
ejpam-4798	104	3	17	17	NUM
ejpam-4798	104	4	]	]	PUNCT
ejpam-4798	104	5	authors	author	NOUN
ejpam-4798	104	6	presented	present	VERB
ejpam-4798	104	7	a	a	DET
ejpam-4798	104	8	structural	structural	ADJ
ejpam-4798	104	9	characterization	characterization	NOUN
ejpam-4798	104	10	of	of	ADP
ejpam-4798	104	11	a	a	DET
ejpam-4798	104	12	splitting	splitting	NOUN
ejpam-4798	104	13	signed	sign	VERB
ejpam-4798	104	14	graph	graph	NOUN
ejpam-4798	104	15	that	that	PRON
ejpam-4798	104	16	can	can	AUX
ejpam-4798	104	17	be	be	AUX
ejpam-4798	104	18	used	use	VERB
ejpam-4798	104	19	to	to	PART
ejpam-4798	104	20	derive	derive	VERB
ejpam-4798	104	21	the	the	DET
ejpam-4798	104	22	splitting	splitting	NOUN
ejpam-4798	104	23	root	root	NOUN
ejpam-4798	104	24	signed	sign	VERB
ejpam-4798	104	25	graph	graph	NOUN
ejpam-4798	104	26	.	.	PUNCT
ejpam-4798	105	1	theorem	theorem	NOUN
ejpam-4798	105	2	3	3	NUM
ejpam-4798	105	3	.	.	PUNCT
ejpam-4798	106	1	[	[	X
ejpam-4798	106	2	17	17	NUM
ejpam-4798	106	3	]	]	PUNCT
ejpam-4798	106	4	let	let	VERB
ejpam-4798	106	5	σ	σ	NOUN
ejpam-4798	106	6	be	be	AUX
ejpam-4798	106	7	a	a	DET
ejpam-4798	106	8	connected	connected	ADJ
ejpam-4798	106	9	signed	sign	VERB
ejpam-4798	106	10	graph	graph	NOUN
ejpam-4798	106	11	,	,	PUNCT
ejpam-4798	106	12	then	then	ADV
ejpam-4798	106	13	σ	σ	PROPN
ejpam-4798	106	14	is	be	AUX
ejpam-4798	106	15	splitting	split	VERB
ejpam-4798	106	16	signed	sign	VERB
ejpam-4798	106	17	graph	graph	NOUN
ejpam-4798	106	18	if	if	SCONJ
ejpam-4798	107	1	and	and	CCONJ
ejpam-4798	107	2	only	only	ADV
ejpam-4798	107	3	if	if	SCONJ
ejpam-4798	107	4	the	the	DET
ejpam-4798	107	5	following	follow	VERB
ejpam-4798	107	6	two	two	NUM
ejpam-4798	107	7	conditions	condition	NOUN
ejpam-4798	107	8	hold	hold	VERB
ejpam-4798	107	9	:	:	PUNCT
ejpam-4798	107	10	(	(	PUNCT
ejpam-4798	107	11	a	a	X
ejpam-4798	107	12	)	)	PUNCT
ejpam-4798	107	13	the	the	DET
ejpam-4798	107	14	underlying	underlie	VERB
ejpam-4798	107	15	graph	graph	NOUN
ejpam-4798	107	16	σu	σu	ADP
ejpam-4798	107	17	is	be	AUX
ejpam-4798	107	18	splitting	split	VERB
ejpam-4798	107	19	graph	graph	NOUN
ejpam-4798	107	20	(	(	PUNCT
ejpam-4798	107	21	b	b	NOUN
ejpam-4798	107	22	)	)	PUNCT
ejpam-4798	107	23	the	the	DET
ejpam-4798	107	24	vertex	vertex	NOUN
ejpam-4798	107	25	set	set	NOUN
ejpam-4798	107	26	of	of	ADP
ejpam-4798	107	27	σ	σ	PROPN
ejpam-4798	107	28	can	can	AUX
ejpam-4798	107	29	be	be	AUX
ejpam-4798	107	30	divided	divide	VERB
ejpam-4798	107	31	into	into	ADP
ejpam-4798	107	32	two	two	NUM
ejpam-4798	107	33	sets	set	NOUN
ejpam-4798	107	34	,	,	PUNCT
ejpam-4798	107	35	v1	v1	NOUN
ejpam-4798	107	36	and	and	CCONJ
ejpam-4798	107	37	v2	v2	NOUN
ejpam-4798	107	38	,	,	PUNCT
ejpam-4798	107	39	such	such	ADJ
ejpam-4798	107	40	that	that	PRON
ejpam-4798	107	41	for	for	ADP
ejpam-4798	107	42	each	each	DET
ejpam-4798	107	43	u′	u′	PROPN
ejpam-4798	107	44	∈	∈	PROPN
ejpam-4798	107	45	v2	v2	PROPN
ejpam-4798	107	46	there	there	PRON
ejpam-4798	107	47	exist	exist	VERB
ejpam-4798	107	48	a	a	DET
ejpam-4798	107	49	vertex	vertex	NOUN
ejpam-4798	107	50	u	u	NOUN
ejpam-4798	107	51	∈	∈	NOUN
ejpam-4798	107	52	v1	v1	NOUN
ejpam-4798	107	53	that	that	PRON
ejpam-4798	107	54	holds	hold	VERB
ejpam-4798	107	55	the	the	DET
ejpam-4798	107	56	condition	condition	NOUN
ejpam-4798	107	57	σ(u′v	σ(u′v	PROPN
ejpam-4798	107	58	)	)	PUNCT
ejpam-4798	107	59	=	=	SYM
ejpam-4798	107	60	σ(uv	σ(uv	NUM
ejpam-4798	107	61	)	)	PUNCT
ejpam-4798	107	62	for	for	ADP
ejpam-4798	107	63	every	every	DET
ejpam-4798	107	64	v	v	NUM
ejpam-4798	107	65	∈	∈	NOUN
ejpam-4798	107	66	v1	v1	NOUN
ejpam-4798	107	67	∩n(v	∩n(v	NOUN
ejpam-4798	107	68	)	)	PUNCT
ejpam-4798	107	69	.	.	PUNCT
ejpam-4798	108	1	generating	generate	VERB
ejpam-4798	108	2	splitting	splitting	NOUN
ejpam-4798	108	3	root	root	NOUN
ejpam-4798	108	4	signed	sign	VERB
ejpam-4798	108	5	graph	graph	NOUN
ejpam-4798	108	6	using	use	VERB
ejpam-4798	108	7	theorem	theorem	NOUN
ejpam-4798	108	8	3	3	NUM
ejpam-4798	108	9	the	the	DET
ejpam-4798	108	10	process	process	NOUN
ejpam-4798	108	11	for	for	ADP
ejpam-4798	108	12	deriving	derive	VERB
ejpam-4798	108	13	the	the	DET
ejpam-4798	108	14	splitting	splitting	NOUN
ejpam-4798	108	15	root	root	NOUN
ejpam-4798	108	16	signed	sign	VERB
ejpam-4798	108	17	graph	graph	NOUN
ejpam-4798	108	18	involves	involve	VERB
ejpam-4798	108	19	several	several	ADJ
ejpam-4798	108	20	steps	step	NOUN
ejpam-4798	108	21	.	.	PUNCT
ejpam-4798	109	1	firstly	firstly	ADV
ejpam-4798	109	2	,	,	PUNCT
ejpam-4798	109	3	it	it	PRON
ejpam-4798	109	4	is	be	AUX
ejpam-4798	109	5	necessary	necessary	ADJ
ejpam-4798	109	6	for	for	SCONJ
ejpam-4798	109	7	the	the	DET
ejpam-4798	109	8	number	number	NOUN
ejpam-4798	109	9	of	of	ADP
ejpam-4798	109	10	vertices	vertex	NOUN
ejpam-4798	109	11	,	,	PUNCT
ejpam-4798	109	12	denoted	denote	VERB
ejpam-4798	109	13	as	as	ADP
ejpam-4798	109	14	“	"	PUNCT
ejpam-4798	109	15	n	n	CCONJ
ejpam-4798	109	16	”	"	PUNCT
ejpam-4798	109	17	,	,	PUNCT
ejpam-4798	109	18	to	to	PART
ejpam-4798	109	19	be	be	AUX
ejpam-4798	109	20	even	even	ADV
ejpam-4798	109	21	in	in	ADP
ejpam-4798	109	22	order	order	NOUN
ejpam-4798	109	23	for	for	ADP
ejpam-4798	109	24	a	a	DET
ejpam-4798	109	25	splitting	splitting	NOUN
ejpam-4798	109	26	root	root	NOUN
ejpam-4798	109	27	signed	sign	VERB
ejpam-4798	109	28	graph	graph	NOUN
ejpam-4798	109	29	to	to	PART
ejpam-4798	109	30	exist	exist	VERB
ejpam-4798	109	31	.	.	PUNCT
ejpam-4798	110	1	if	if	SCONJ
ejpam-4798	110	2	“	"	PUNCT
ejpam-4798	110	3	n	n	CCONJ
ejpam-4798	110	4	”	"	PUNCT
ejpam-4798	110	5	is	be	AUX
ejpam-4798	110	6	odd	odd	ADJ
ejpam-4798	110	7	,	,	PUNCT
ejpam-4798	110	8	then	then	ADV
ejpam-4798	110	9	it	it	PRON
ejpam-4798	110	10	is	be	AUX
ejpam-4798	110	11	impossible	impossible	ADJ
ejpam-4798	110	12	to	to	PART
ejpam-4798	110	13	construct	construct	VERB
ejpam-4798	110	14	a	a	DET
ejpam-4798	110	15	splitting	splitting	NOUN
ejpam-4798	110	16	root	root	NOUN
ejpam-4798	110	17	signed	sign	VERB
ejpam-4798	110	18	graph	graph	NOUN
ejpam-4798	110	19	.	.	PUNCT
ejpam-4798	111	1	once	once	SCONJ
ejpam-4798	111	2	it	it	PRON
ejpam-4798	111	3	has	have	AUX
ejpam-4798	111	4	been	be	AUX
ejpam-4798	111	5	established	establish	VERB
ejpam-4798	111	6	that	that	SCONJ
ejpam-4798	111	7	“	"	PUNCT
ejpam-4798	111	8	n	n	CCONJ
ejpam-4798	111	9	”	"	PUNCT
ejpam-4798	111	10	is	be	AUX
ejpam-4798	111	11	even	even	ADV
ejpam-4798	111	12	,	,	PUNCT
ejpam-4798	111	13	an	an	DET
ejpam-4798	111	14	n	n	CCONJ
ejpam-4798	111	15	dimensional	dimensional	ADJ
ejpam-4798	111	16	matrix	matrix	NOUN
ejpam-4798	111	17	is	be	AUX
ejpam-4798	111	18	generated	generate	VERB
ejpam-4798	111	19	to	to	PART
ejpam-4798	111	20	represent	represent	VERB
ejpam-4798	111	21	the	the	DET
ejpam-4798	111	22	given	give	VERB
ejpam-4798	111	23	signed	sign	VERB
ejpam-4798	111	24	graph	graph	NOUN
ejpam-4798	111	25	.	.	PUNCT
ejpam-4798	112	1	the	the	DET
ejpam-4798	112	2	matrix	matrix	NOUN
ejpam-4798	112	3	is	be	AUX
ejpam-4798	112	4	examined	examine	VERB
ejpam-4798	112	5	to	to	PART
ejpam-4798	112	6	count	count	VERB
ejpam-4798	112	7	the	the	DET
ejpam-4798	112	8	number	number	NOUN
ejpam-4798	112	9	of	of	ADP
ejpam-4798	112	10	positive	positive	ADJ
ejpam-4798	112	11	and	and	CCONJ
ejpam-4798	112	12	negative	negative	ADJ
ejpam-4798	112	13	edges	edge	NOUN
ejpam-4798	112	14	,	,	PUNCT
ejpam-4798	112	15	and	and	CCONJ
ejpam-4798	112	16	it	it	PRON
ejpam-4798	112	17	is	be	AUX
ejpam-4798	112	18	determined	determine	VERB
ejpam-4798	112	19	whether	whether	SCONJ
ejpam-4798	112	20	both	both	DET
ejpam-4798	112	21	counts	count	NOUN
ejpam-4798	112	22	are	be	AUX
ejpam-4798	112	23	divisible	divisible	ADJ
ejpam-4798	112	24	by	by	ADP
ejpam-4798	112	25	3	3	NUM
ejpam-4798	112	26	.	.	PUNCT
ejpam-4798	113	1	if	if	SCONJ
ejpam-4798	113	2	this	this	DET
ejpam-4798	113	3	condition	condition	NOUN
ejpam-4798	113	4	is	be	AUX
ejpam-4798	113	5	met	meet	VERB
ejpam-4798	113	6	,	,	PUNCT
ejpam-4798	113	7	a	a	DET
ejpam-4798	113	8	splitting	splitting	NOUN
ejpam-4798	113	9	root	root	NOUN
ejpam-4798	113	10	signed	sign	VERB
ejpam-4798	113	11	graph	graph	NOUN
ejpam-4798	113	12	can	can	AUX
ejpam-4798	113	13	be	be	AUX
ejpam-4798	113	14	created	create	VERB
ejpam-4798	113	15	;	;	PUNCT
ejpam-4798	113	16	otherwise	otherwise	ADV
ejpam-4798	113	17	,	,	PUNCT
ejpam-4798	113	18	it	it	PRON
ejpam-4798	113	19	can	can	AUX
ejpam-4798	113	20	not	not	PART
ejpam-4798	113	21	.	.	PUNCT
ejpam-4798	114	1	the	the	DET
ejpam-4798	114	2	next	next	ADJ
ejpam-4798	114	3	step	step	NOUN
ejpam-4798	114	4	involves	involve	VERB
ejpam-4798	114	5	calculating	calculate	VERB
ejpam-4798	114	6	the	the	DET
ejpam-4798	114	7	number	number	NOUN
ejpam-4798	114	8	of	of	ADP
ejpam-4798	114	9	negative	negative	ADJ
ejpam-4798	114	10	and	and	CCONJ
ejpam-4798	114	11	positive	positive	ADJ
ejpam-4798	114	12	edges	edge	NOUN
ejpam-4798	114	13	for	for	ADP
ejpam-4798	114	14	each	each	DET
ejpam-4798	114	15	vertex	vertex	NOUN
ejpam-4798	114	16	by	by	ADP
ejpam-4798	114	17	counting	count	VERB
ejpam-4798	114	18	the	the	DET
ejpam-4798	114	19	number	number	NOUN
ejpam-4798	114	20	of	of	ADP
ejpam-4798	114	21	−1s	−1s	X
ejpam-4798	114	22	and	and	CCONJ
ejpam-4798	114	23	1s	1	NOUN
ejpam-4798	114	24	in	in	ADP
ejpam-4798	114	25	each	each	DET
ejpam-4798	114	26	row	row	NOUN
ejpam-4798	114	27	.	.	PUNCT
ejpam-4798	115	1	if	if	SCONJ
ejpam-4798	115	2	it	it	PRON
ejpam-4798	115	3	is	be	AUX
ejpam-4798	115	4	possible	possible	ADJ
ejpam-4798	115	5	to	to	PART
ejpam-4798	115	6	partition	partition	VERB
ejpam-4798	115	7	the	the	DET
ejpam-4798	115	8	vertex	vertex	NOUN
ejpam-4798	115	9	set	set	VERB
ejpam-4798	115	10	v	v	PROPN
ejpam-4798	115	11	(	(	PUNCT
ejpam-4798	115	12	σ	σ	NOUN
ejpam-4798	115	13	)	)	PUNCT
ejpam-4798	115	14	into	into	ADP
ejpam-4798	115	15	two	two	NUM
ejpam-4798	115	16	sets	set	NOUN
ejpam-4798	115	17	,	,	PUNCT
ejpam-4798	115	18	such	such	ADJ
ejpam-4798	115	19	that	that	SCONJ
ejpam-4798	115	20	the	the	DET
ejpam-4798	115	21	number	number	NOUN
ejpam-4798	115	22	of	of	ADP
ejpam-4798	115	23	negative	negative	ADJ
ejpam-4798	115	24	and	and	CCONJ
ejpam-4798	115	25	positive	positive	ADJ
ejpam-4798	115	26	edges	edge	NOUN
ejpam-4798	115	27	in	in	ADP
ejpam-4798	115	28	one	one	NUM
ejpam-4798	115	29	set	set	NOUN
ejpam-4798	115	30	is	be	AUX
ejpam-4798	115	31	exactly	exactly	ADV
ejpam-4798	115	32	double	double	ADJ
ejpam-4798	115	33	of	of	ADP
ejpam-4798	115	34	the	the	DET
ejpam-4798	115	35	other	other	ADJ
ejpam-4798	115	36	set	set	NOUN
ejpam-4798	115	37	,	,	PUNCT
ejpam-4798	115	38	then	then	ADV
ejpam-4798	115	39	a	a	DET
ejpam-4798	115	40	splitting	splitting	NOUN
ejpam-4798	115	41	root	root	NOUN
ejpam-4798	115	42	signed	sign	VERB
ejpam-4798	115	43	graph	graph	NOUN
ejpam-4798	115	44	can	can	AUX
ejpam-4798	115	45	be	be	AUX
ejpam-4798	115	46	constructed	construct	VERB
ejpam-4798	115	47	.	.	PUNCT
ejpam-4798	116	1	if	if	SCONJ
ejpam-4798	116	2	a	a	DET
ejpam-4798	116	3	splitting	splitting	NOUN
ejpam-4798	116	4	root	root	NOUN
ejpam-4798	116	5	signed	sign	VERB
ejpam-4798	116	6	graph	graph	NOUN
ejpam-4798	116	7	exists	exist	VERB
ejpam-4798	116	8	,	,	PUNCT
ejpam-4798	116	9	it	it	PRON
ejpam-4798	116	10	’s	’	VERB
ejpam-4798	116	11	adjacency	adjacency	NOUN
ejpam-4798	116	12	matrix	matrix	NOUN
ejpam-4798	116	13	of	of	ADP
ejpam-4798	116	14	order	order	NOUN
ejpam-4798	116	15	n	n	PRON
ejpam-4798	116	16	can	can	AUX
ejpam-4798	116	17	be	be	AUX
ejpam-4798	116	18	partitioned	partition	VERB
ejpam-4798	116	19	into	into	ADP
ejpam-4798	116	20	four	four	NUM
ejpam-4798	116	21	matrices	matrix	NOUN
ejpam-4798	116	22	of	of	ADP
ejpam-4798	116	23	equal	equal	ADJ
ejpam-4798	116	24	order	order	NOUN
ejpam-4798	116	25	n	n	PRON
ejpam-4798	116	26	2	2	NUM
ejpam-4798	116	27	.	.	PUNCT
ejpam-4798	117	1	let	let	VERB
ejpam-4798	117	2	[	[	X
ejpam-4798	117	3	ai	ai	VERB
ejpam-4798	117	4	,	,	PUNCT
ejpam-4798	117	5	j	j	PROPN
ejpam-4798	117	6	]	]	X
ejpam-4798	117	7	,	,	PUNCT
ejpam-4798	117	8	[	[	X
ejpam-4798	117	9	bi	bi	NOUN
ejpam-4798	117	10	,	,	PUNCT
ejpam-4798	117	11	j	j	PROPN
ejpam-4798	117	12	]	]	X
ejpam-4798	117	13	,	,	PUNCT
ejpam-4798	117	14	[	[	X
ejpam-4798	117	15	ci	ci	NOUN
ejpam-4798	117	16	,	,	PUNCT
ejpam-4798	117	17	j	j	PROPN
ejpam-4798	117	18	]	]	PUNCT
ejpam-4798	117	19	and	and	CCONJ
ejpam-4798	117	20	[	[	X
ejpam-4798	117	21	di	di	X
ejpam-4798	117	22	,	,	PUNCT
ejpam-4798	117	23	j	j	PROPN
ejpam-4798	117	24	]	]	X
ejpam-4798	117	25	are	be	AUX
ejpam-4798	117	26	the	the	DET
ejpam-4798	117	27	four	four	NUM
ejpam-4798	117	28	matrices	matrix	NOUN
ejpam-4798	117	29	of	of	ADP
ejpam-4798	117	30	order	order	NOUN
ejpam-4798	117	31	n	n	PRON
ejpam-4798	117	32	2	2	NUM
ejpam-4798	117	33	,	,	PUNCT
ejpam-4798	117	34	then	then	ADV
ejpam-4798	117	35	ai	ai	VERB
ejpam-4798	117	36	,	,	PUNCT
ejpam-4798	117	37	j	j	PROPN
ejpam-4798	117	38	=	=	SYM
ejpam-4798	117	39	bi	bi	PROPN
ejpam-4798	117	40	,	,	PUNCT
ejpam-4798	117	41	j	j	PROPN
ejpam-4798	117	42	=	=	SYM
ejpam-4798	117	43	ci	ci	PROPN
ejpam-4798	117	44	,	,	PUNCT
ejpam-4798	117	45	j	j	PROPN
ejpam-4798	117	46	for	for	ADP
ejpam-4798	117	47	0	0	NUM
ejpam-4798	117	48	≤	≤	NOUN
ejpam-4798	118	1	i	i	PRON
ejpam-4798	118	2	,	,	PUNCT
ejpam-4798	118	3	j	j	PROPN
ejpam-4798	118	4	≤	≤	PROPN
ejpam-4798	118	5	n	n	PRON
ejpam-4798	118	6	2	2	NUM
ejpam-4798	118	7	and	and	CCONJ
ejpam-4798	118	8	di	di	NOUN
ejpam-4798	118	9	,	,	PUNCT
ejpam-4798	118	10	j	j	PROPN
ejpam-4798	118	11	=	=	PUNCT
ejpam-4798	118	12	0	0	PROPN
ejpam-4798	118	13	for	for	ADP
ejpam-4798	118	14	0	0	NUM
ejpam-4798	118	15	≤	≤	NOUN
ejpam-4798	118	16	i	i	PROPN
ejpam-4798	118	17	,	,	PUNCT
ejpam-4798	118	18	j	j	PROPN
ejpam-4798	118	19	≤	≤	PROPN
ejpam-4798	118	20	n	n	PRON
ejpam-4798	118	21	2	2	NUM
ejpam-4798	118	22	i.e.	i.e.	X
ejpam-4798	118	23	[	[	X
ejpam-4798	118	24	di	di	X
ejpam-4798	118	25	,	,	PUNCT
ejpam-4798	118	26	j	j	PROPN
ejpam-4798	118	27	]	]	PUNCT
ejpam-4798	118	28	is	be	AUX
ejpam-4798	118	29	zero	zero	NUM
ejpam-4798	118	30	matrix	matrix	NOUN
ejpam-4798	118	31	.	.	PUNCT
ejpam-4798	119	1	to	to	PART
ejpam-4798	119	2	make	make	VERB
ejpam-4798	119	3	the	the	DET
ejpam-4798	119	4	matrix	matrix	NOUN
ejpam-4798	119	5	identical	identical	ADJ
ejpam-4798	119	6	and	and	CCONJ
ejpam-4798	119	7	zero	zero	NUM
ejpam-4798	119	8	,	,	PUNCT
ejpam-4798	119	9	it	it	PRON
ejpam-4798	119	10	is	be	AUX
ejpam-4798	119	11	necessary	necessary	ADJ
ejpam-4798	119	12	to	to	PART
ejpam-4798	119	13	interchange	interchange	VERB
ejpam-4798	119	14	rows	row	NOUN
ejpam-4798	119	15	and	and	CCONJ
ejpam-4798	119	16	columns	column	NOUN
ejpam-4798	119	17	.	.	PUNCT
ejpam-4798	120	1	this	this	PRON
ejpam-4798	120	2	will	will	AUX
ejpam-4798	120	3	result	result	VERB
ejpam-4798	120	4	in	in	ADP
ejpam-4798	120	5	a	a	DET
ejpam-4798	120	6	matrix	matrix	NOUN
ejpam-4798	120	7	of	of	ADP
ejpam-4798	120	8	size	size	NOUN
ejpam-4798	120	9	n	n	CCONJ
ejpam-4798	120	10	2	2	NUM
ejpam-4798	120	11	×	×	NOUN
ejpam-4798	120	12	n	n	PRON
ejpam-4798	120	13	2	2	NUM
ejpam-4798	120	14	.	.	PUNCT
ejpam-4798	121	1	an	an	DET
ejpam-4798	121	2	example	example	NOUN
ejpam-4798	121	3	of	of	ADP
ejpam-4798	121	4	the	the	DET
ejpam-4798	121	5	computation	computation	NOUN
ejpam-4798	121	6	of	of	ADP
ejpam-4798	121	7	a	a	DET
ejpam-4798	121	8	splitting	splitting	NOUN
ejpam-4798	121	9	root	root	NOUN
ejpam-4798	121	10	signed	sign	VERB
ejpam-4798	121	11	graph	graph	NOUN
ejpam-4798	121	12	from	from	ADP
ejpam-4798	121	13	a	a	DET
ejpam-4798	121	14	given	give	VERB
ejpam-4798	121	15	signed	sign	VERB
ejpam-4798	121	16	graph	graph	NOUN
ejpam-4798	121	17	will	will	AUX
ejpam-4798	121	18	be	be	AUX
ejpam-4798	121	19	provided	provide	VERB
ejpam-4798	121	20	in	in	ADP
ejpam-4798	121	21	the	the	DET
ejpam-4798	121	22	following	follow	VERB
ejpam-4798	121	23	section	section	NOUN
ejpam-4798	121	24	.	.	PUNCT
ejpam-4798	122	1	s.	s.	PROPN
ejpam-4798	122	2	kumar	kumar	PROPN
ejpam-4798	122	3	,	,	PUNCT
ejpam-4798	122	4	d.	d.	PROPN
ejpam-4798	122	5	sinha	sinha	PROPN
ejpam-4798	122	6	/	/	SYM
ejpam-4798	122	7	eur	eur	PROPN
ejpam-4798	122	8	.	.	PUNCT
ejpam-4798	123	1	j.	j.	PROPN
ejpam-4798	123	2	pure	pure	PROPN
ejpam-4798	123	3	appl	appl	PROPN
ejpam-4798	123	4	.	.	PROPN
ejpam-4798	123	5	math	math	PROPN
ejpam-4798	123	6	,	,	PUNCT
ejpam-4798	123	7	17	17	NUM
ejpam-4798	123	8	(	(	PUNCT
ejpam-4798	123	9	1	1	NUM
ejpam-4798	123	10	)	)	PUNCT
ejpam-4798	123	11	(	(	PUNCT
ejpam-4798	123	12	2024	2024	NUM
ejpam-4798	123	13	)	)	PUNCT
ejpam-4798	123	14	,	,	PUNCT
ejpam-4798	123	15	504	504	NUM
ejpam-4798	123	16	-	-	SYM
ejpam-4798	123	17	518	518	NUM
ejpam-4798	123	18	510	510	NUM
ejpam-4798	123	19	a(σ1	a(σ1	NOUN
ejpam-4798	123	20	)	)	PUNCT
ejpam-4798	124	1	=	=	X
ejpam-4798	124	2			NOUN
ejpam-4798	124	3	0	0	NUM
ejpam-4798	124	4	−1	−1	NOUN
ejpam-4798	124	5	0	0	NUM
ejpam-4798	124	6	−1	−1	NOUN
ejpam-4798	124	7	−1	−1	NOUN
ejpam-4798	124	8	0	0	NUM
ejpam-4798	124	9	−1	−1	NOUN
ejpam-4798	124	10	0	0	NUM
ejpam-4798	124	11	−1	−1	NOUN
ejpam-4798	124	12	0	0	NUM
ejpam-4798	124	13	1	1	NUM
ejpam-4798	124	14	0	0	NUM
ejpam-4798	124	15	0	0	NUM
ejpam-4798	124	16	0	0	NUM
ejpam-4798	124	17	0	0	NUM
ejpam-4798	124	18	0	0	NUM
ejpam-4798	124	19	0	0	NUM
ejpam-4798	124	20	1	1	NUM
ejpam-4798	124	21	0	0	NUM
ejpam-4798	124	22	1	1	NUM
ejpam-4798	124	23	1	1	NUM
ejpam-4798	124	24	0	0	NUM
ejpam-4798	124	25	1	1	NUM
ejpam-4798	124	26	0	0	NUM
ejpam-4798	124	27	−1	−1	NOUN
ejpam-4798	124	28	0	0	NUM
ejpam-4798	124	29	1	1	NUM
ejpam-4798	124	30	0	0	NUM
ejpam-4798	124	31	0	0	NUM
ejpam-4798	124	32	0	0	NUM
ejpam-4798	124	33	0	0	NUM
ejpam-4798	124	34	0	0	NUM
ejpam-4798	124	35	−1	−1	NOUN
ejpam-4798	124	36	0	0	NUM
ejpam-4798	124	37	1	1	NUM
ejpam-4798	124	38	0	0	NUM
ejpam-4798	124	39	0	0	NUM
ejpam-4798	124	40	1	1	NUM
ejpam-4798	124	41	0	0	NUM
ejpam-4798	124	42	−1	−1	NOUN
ejpam-4798	124	43	0	0	NUM
ejpam-4798	124	44	0	0	NUM
ejpam-4798	124	45	0	0	NUM
ejpam-4798	124	46	0	0	NUM
ejpam-4798	124	47	1	1	NUM
ejpam-4798	124	48	0	0	NUM
ejpam-4798	124	49	1	1	NUM
ejpam-4798	124	50	0	0	NUM
ejpam-4798	124	51	−1	−1	NOUN
ejpam-4798	124	52	0	0	NUM
ejpam-4798	124	53	1	1	NUM
ejpam-4798	124	54	0	0	NUM
ejpam-4798	124	55	0	0	NUM
ejpam-4798	124	56	1	1	NUM
ejpam-4798	124	57	0	0	NUM
ejpam-4798	124	58	−1	−1	NOUN
ejpam-4798	124	59	0	0	NUM
ejpam-4798	124	60	0	0	NUM
ejpam-4798	124	61	0	0	NUM
ejpam-4798	124	62	0	0	NUM
ejpam-4798	124	63	−1	−1	NOUN
ejpam-4798	124	64	0	0	NUM
ejpam-4798	124	65	−1	−1	NOUN
ejpam-4798	124	66	0	0	PUNCT
ejpam-4798	124	67			NOUN
ejpam-4798	124	68	the	the	DET
ejpam-4798	124	69	adjacency	adjacency	NOUN
ejpam-4798	124	70	matrix	matrix	NOUN
ejpam-4798	124	71	of	of	ADP
ejpam-4798	124	72	this	this	DET
ejpam-4798	124	73	signed	sign	VERB
ejpam-4798	124	74	graph	graph	NOUN
ejpam-4798	124	75	,	,	PUNCT
ejpam-4798	124	76	a(σ1	a(σ1	NOUN
ejpam-4798	124	77	)	)	PUNCT
ejpam-4798	124	78	is	be	AUX
ejpam-4798	124	79	a	a	DET
ejpam-4798	124	80	8×	8×	NUM
ejpam-4798	124	81	8	8	NUM
ejpam-4798	124	82	matrix	matrix	NOUN
ejpam-4798	124	83	.	.	PUNCT
ejpam-4798	125	1	here	here	ADV
ejpam-4798	125	2	the	the	DET
ejpam-4798	125	3	number	number	NOUN
ejpam-4798	125	4	of	of	ADP
ejpam-4798	125	5	vertices	vertex	NOUN
ejpam-4798	125	6	in	in	ADP
ejpam-4798	125	7	a	a	DET
ejpam-4798	125	8	signed	sign	VERB
ejpam-4798	125	9	graph	graph	NOUN
ejpam-4798	125	10	is	be	AUX
ejpam-4798	125	11	even	even	ADV
ejpam-4798	125	12	,	,	PUNCT
ejpam-4798	125	13	so	so	SCONJ
ejpam-4798	125	14	we	we	PRON
ejpam-4798	125	15	can	can	AUX
ejpam-4798	125	16	find	find	VERB
ejpam-4798	125	17	its	its	PRON
ejpam-4798	125	18	splitting	splitting	NOUN
ejpam-4798	125	19	root	root	NOUN
ejpam-4798	125	20	signed	sign	VERB
ejpam-4798	125	21	graph	graph	NOUN
ejpam-4798	125	22	.	.	PUNCT
ejpam-4798	126	1	however	however	ADV
ejpam-4798	126	2	,	,	PUNCT
ejpam-4798	126	3	if	if	SCONJ
ejpam-4798	126	4	the	the	DET
ejpam-4798	126	5	vertices	vertex	NOUN
ejpam-4798	126	6	are	be	AUX
ejpam-4798	126	7	odd	odd	ADJ
ejpam-4798	126	8	in	in	ADP
ejpam-4798	126	9	numbers	number	NOUN
ejpam-4798	126	10	,	,	PUNCT
ejpam-4798	126	11	then	then	ADV
ejpam-4798	126	12	splitting	split	VERB
ejpam-4798	126	13	root	root	NOUN
ejpam-4798	126	14	signed	sign	VERB
ejpam-4798	126	15	graph	graph	NOUN
ejpam-4798	126	16	of	of	ADP
ejpam-4798	126	17	the	the	DET
ejpam-4798	126	18	given	give	VERB
ejpam-4798	126	19	signed	sign	VERB
ejpam-4798	126	20	graph	graph	NOUN
ejpam-4798	126	21	will	will	AUX
ejpam-4798	126	22	not	not	PART
ejpam-4798	126	23	exist	exist	VERB
ejpam-4798	126	24	.	.	PUNCT
ejpam-4798	127	1	in	in	ADP
ejpam-4798	127	2	this	this	DET
ejpam-4798	127	3	case	case	NOUN
ejpam-4798	127	4	,	,	PUNCT
ejpam-4798	127	5	there	there	PRON
ejpam-4798	127	6	are	be	VERB
ejpam-4798	127	7	12	12	NUM
ejpam-4798	127	8	occurrences	occurrence	NOUN
ejpam-4798	127	9	of	of	ADP
ejpam-4798	127	10	the	the	DET
ejpam-4798	127	11	value	value	NOUN
ejpam-4798	127	12	−1	−1	NOUN
ejpam-4798	127	13	and	and	CCONJ
ejpam-4798	127	14	12	12	NUM
ejpam-4798	127	15	occurrences	occurrence	NOUN
ejpam-4798	127	16	of	of	ADP
ejpam-4798	127	17	the	the	DET
ejpam-4798	127	18	value	value	NOUN
ejpam-4798	127	19	1	1	NUM
ejpam-4798	127	20	in	in	ADP
ejpam-4798	127	21	the	the	DET
ejpam-4798	127	22	adjacency	adjacency	NOUN
ejpam-4798	127	23	matrix	matrix	NOUN
ejpam-4798	127	24	.	.	PUNCT
ejpam-4798	128	1	clearly	clearly	ADV
ejpam-4798	128	2	,	,	PUNCT
ejpam-4798	128	3	here	here	ADV
ejpam-4798	128	4	both	both	CCONJ
ejpam-4798	128	5	the	the	DET
ejpam-4798	128	6	values	value	NOUN
ejpam-4798	128	7	are	be	AUX
ejpam-4798	128	8	divisible	divisible	ADJ
ejpam-4798	128	9	by	by	ADP
ejpam-4798	128	10	3	3	NUM
ejpam-4798	128	11	,	,	PUNCT
ejpam-4798	128	12	so	so	ADV
ejpam-4798	128	13	the	the	DET
ejpam-4798	128	14	splitting	splitting	NOUN
ejpam-4798	128	15	root	root	NOUN
ejpam-4798	128	16	signed	sign	VERB
ejpam-4798	128	17	graph	graph	NOUN
ejpam-4798	128	18	can	can	AUX
ejpam-4798	128	19	be	be	AUX
ejpam-4798	128	20	computed	compute	VERB
ejpam-4798	128	21	.	.	PUNCT
ejpam-4798	129	1	the	the	DET
ejpam-4798	129	2	next	next	ADJ
ejpam-4798	129	3	step	step	NOUN
ejpam-4798	129	4	is	be	AUX
ejpam-4798	129	5	to	to	PART
ejpam-4798	129	6	count	count	VERB
ejpam-4798	129	7	the	the	DET
ejpam-4798	129	8	number	number	NOUN
ejpam-4798	129	9	of	of	ADP
ejpam-4798	129	10	1s	1s	NUM
ejpam-4798	129	11	and	and	CCONJ
ejpam-4798	129	12	−1s	−1s	PROPN
ejpam-4798	129	13	in	in	ADP
ejpam-4798	129	14	each	each	DET
ejpam-4798	129	15	row	row	NOUN
ejpam-4798	129	16	of	of	ADP
ejpam-4798	129	17	the	the	DET
ejpam-4798	129	18	matrix	matrix	NOUN
ejpam-4798	129	19	:	:	PUNCT
ejpam-4798	129	20	vertex	vertex	NOUN
ejpam-4798	129	21	vi	vi	NOUN
ejpam-4798	130	1	no	no	INTJ
ejpam-4798	130	2	.	.	PUNCT
ejpam-4798	131	1	of	of	ADP
ejpam-4798	131	2	1s	1s	NUM
ejpam-4798	131	3	no	no	INTJ
ejpam-4798	131	4	.	.	PUNCT
ejpam-4798	132	1	of	of	ADP
ejpam-4798	132	2	−1s	−1s	PROPN
ejpam-4798	132	3	1	1	NUM
ejpam-4798	132	4	0	0	NUM
ejpam-4798	132	5	4	4	NUM
ejpam-4798	132	6	2	2	NUM
ejpam-4798	132	7	1	1	NUM
ejpam-4798	132	8	1	1	NUM
ejpam-4798	132	9	3	3	NUM
ejpam-4798	132	10	4	4	NUM
ejpam-4798	132	11	0	0	NUM
ejpam-4798	132	12	4	4	NUM
ejpam-4798	132	13	1	1	NUM
ejpam-4798	132	14	1	1	NUM
ejpam-4798	132	15	5	5	NUM
ejpam-4798	132	16	2	2	NUM
ejpam-4798	132	17	2	2	NUM
ejpam-4798	132	18	6	6	NUM
ejpam-4798	132	19	2	2	NUM
ejpam-4798	132	20	0	0	NUM
ejpam-4798	132	21	7	7	NUM
ejpam-4798	132	22	2	2	NUM
ejpam-4798	132	23	2	2	NUM
ejpam-4798	132	24	8	8	NUM
ejpam-4798	132	25	0	0	NUM
ejpam-4798	132	26	2	2	NUM
ejpam-4798	132	27	with	with	ADP
ejpam-4798	132	28	this	this	DET
ejpam-4798	132	29	knowledge	knowledge	NOUN
ejpam-4798	132	30	,	,	PUNCT
ejpam-4798	132	31	the	the	DET
ejpam-4798	132	32	vertex	vertex	NOUN
ejpam-4798	132	33	set	set	NOUN
ejpam-4798	132	34	is	be	AUX
ejpam-4798	132	35	splitted	splitte	VERB
ejpam-4798	132	36	into	into	ADP
ejpam-4798	132	37	two	two	NUM
ejpam-4798	132	38	sets	set	NOUN
ejpam-4798	132	39	,	,	PUNCT
ejpam-4798	132	40	v1	v1	NOUN
ejpam-4798	132	41	and	and	CCONJ
ejpam-4798	132	42	v2	v2	NOUN
ejpam-4798	132	43	,	,	PUNCT
ejpam-4798	132	44	where	where	SCONJ
ejpam-4798	132	45	the	the	DET
ejpam-4798	132	46	number	number	NOUN
ejpam-4798	132	47	of	of	ADP
ejpam-4798	132	48	1s	1s	NUM
ejpam-4798	132	49	and	and	CCONJ
ejpam-4798	132	50	−1s	−1s	PROPN
ejpam-4798	132	51	in	in	ADP
ejpam-4798	132	52	v1	v1	NOUN
ejpam-4798	132	53	is	be	AUX
ejpam-4798	132	54	double	double	DET
ejpam-4798	132	55	that	that	PRON
ejpam-4798	132	56	of	of	ADP
ejpam-4798	132	57	in	in	ADP
ejpam-4798	132	58	v2	v2	PROPN
ejpam-4798	132	59	.	.	PUNCT
ejpam-4798	133	1	in	in	ADP
ejpam-4798	133	2	this	this	DET
ejpam-4798	133	3	example	example	NOUN
ejpam-4798	133	4	,	,	PUNCT
ejpam-4798	133	5	v1	v1	PROPN
ejpam-4798	133	6	is	be	AUX
ejpam-4798	133	7	{	{	PUNCT
ejpam-4798	133	8	1	1	NUM
ejpam-4798	133	9	,	,	PUNCT
ejpam-4798	133	10	3	3	NUM
ejpam-4798	133	11	,	,	PUNCT
ejpam-4798	133	12	5	5	NUM
ejpam-4798	133	13	,	,	PUNCT
ejpam-4798	133	14	7	7	NUM
ejpam-4798	133	15	}	}	PUNCT
ejpam-4798	133	16	and	and	CCONJ
ejpam-4798	133	17	v2	v2	PROPN
ejpam-4798	133	18	is	be	AUX
ejpam-4798	133	19	{	{	PUNCT
ejpam-4798	133	20	2	2	NUM
ejpam-4798	133	21	,	,	PUNCT
ejpam-4798	133	22	4	4	NUM
ejpam-4798	133	23	,	,	PUNCT
ejpam-4798	133	24	6	6	NUM
ejpam-4798	133	25	,	,	PUNCT
ejpam-4798	133	26	8	8	NUM
ejpam-4798	133	27	}	}	PUNCT
ejpam-4798	133	28	.	.	PUNCT
ejpam-4798	134	1	if	if	SCONJ
ejpam-4798	134	2	the	the	DET
ejpam-4798	134	3	partition	partition	NOUN
ejpam-4798	134	4	is	be	AUX
ejpam-4798	134	5	successful	successful	ADJ
ejpam-4798	134	6	,	,	PUNCT
ejpam-4798	134	7	the	the	DET
ejpam-4798	134	8	splitting	splitting	NOUN
ejpam-4798	134	9	root	root	NOUN
ejpam-4798	134	10	signed	sign	VERB
ejpam-4798	134	11	graph	graph	NOUN
ejpam-4798	134	12	exists	exist	VERB
ejpam-4798	134	13	,	,	PUNCT
ejpam-4798	134	14	otherwise	otherwise	ADV
ejpam-4798	134	15	it	it	PRON
ejpam-4798	134	16	does	do	VERB
ejpam-4798	134	17	not	not	PART
ejpam-4798	134	18	.	.	PUNCT
ejpam-4798	135	1	next	next	ADV
ejpam-4798	135	2	,	,	PUNCT
ejpam-4798	135	3	the	the	DET
ejpam-4798	135	4	splitting	splitting	NOUN
ejpam-4798	135	5	root	root	NOUN
ejpam-4798	135	6	graph	graph	NOUN
ejpam-4798	135	7	is	be	AUX
ejpam-4798	135	8	computed	compute	VERB
ejpam-4798	135	9	.	.	PUNCT
ejpam-4798	136	1	the	the	DET
ejpam-4798	136	2	adjacency	adjacency	PROPN
ejpam-4798	136	3	matrix	matrix	NOUN
ejpam-4798	136	4	a(γ(σ	a(γ(σ	PROPN
ejpam-4798	136	5	)	)	PUNCT
ejpam-4798	136	6	)	)	PUNCT
ejpam-4798	136	7	,	,	PUNCT
ejpam-4798	136	8	of	of	ADP
ejpam-4798	136	9	order	order	NOUN
ejpam-4798	136	10	2n	2n	NUM
ejpam-4798	136	11	,	,	PUNCT
ejpam-4798	136	12	of	of	ADP
ejpam-4798	136	13	the	the	DET
ejpam-4798	136	14	splitting	splitting	NOUN
ejpam-4798	136	15	signed	sign	VERB
ejpam-4798	136	16	graph	graph	NOUN
ejpam-4798	136	17	can	can	AUX
ejpam-4798	136	18	be	be	AUX
ejpam-4798	136	19	partitioned	partition	VERB
ejpam-4798	136	20	into	into	ADP
ejpam-4798	136	21	four	four	NUM
ejpam-4798	136	22	equal	equal	ADJ
ejpam-4798	136	23	matrices	matrix	NOUN
ejpam-4798	136	24	of	of	ADP
ejpam-4798	136	25	the	the	DET
ejpam-4798	136	26	order	order	NOUN
ejpam-4798	136	27	n.	n.	NOUN
ejpam-4798	136	28	let	let	VERB
ejpam-4798	137	1	[	[	X
ejpam-4798	137	2	ai	ai	VERB
ejpam-4798	137	3	,	,	PUNCT
ejpam-4798	137	4	j	j	PROPN
ejpam-4798	137	5	]	]	X
ejpam-4798	137	6	,	,	PUNCT
ejpam-4798	138	1	[	[	X
ejpam-4798	138	2	bi	bi	NOUN
ejpam-4798	138	3	,	,	PUNCT
ejpam-4798	138	4	j	j	PROPN
ejpam-4798	138	5	]	]	X
ejpam-4798	138	6	,	,	PUNCT
ejpam-4798	138	7	[	[	X
ejpam-4798	138	8	ci	ci	NOUN
ejpam-4798	138	9	,	,	PUNCT
ejpam-4798	138	10	j	j	PROPN
ejpam-4798	138	11	]	]	PUNCT
ejpam-4798	138	12	and	and	CCONJ
ejpam-4798	138	13	[	[	X
ejpam-4798	138	14	di	di	X
ejpam-4798	138	15	,	,	PUNCT
ejpam-4798	138	16	j	j	PROPN
ejpam-4798	138	17	]	]	X
ejpam-4798	138	18	are	be	AUX
ejpam-4798	138	19	the	the	DET
ejpam-4798	138	20	four	four	NUM
ejpam-4798	138	21	matrices	matrix	NOUN
ejpam-4798	138	22	of	of	ADP
ejpam-4798	138	23	order	order	NOUN
ejpam-4798	138	24	n	n	CCONJ
ejpam-4798	138	25	,	,	PUNCT
ejpam-4798	138	26	then	then	ADV
ejpam-4798	138	27	ai	ai	VERB
ejpam-4798	138	28	,	,	PUNCT
ejpam-4798	138	29	j	j	PROPN
ejpam-4798	138	30	=	=	SYM
ejpam-4798	138	31	bi	bi	PROPN
ejpam-4798	138	32	,	,	PUNCT
ejpam-4798	138	33	j	j	PROPN
ejpam-4798	138	34	=	=	SYM
ejpam-4798	138	35	ci	ci	PROPN
ejpam-4798	138	36	,	,	PUNCT
ejpam-4798	138	37	j	j	PROPN
ejpam-4798	138	38	for	for	ADP
ejpam-4798	138	39	0	0	NUM
ejpam-4798	138	40	≤	≤	NOUN
ejpam-4798	138	41	i	i	PRON
ejpam-4798	138	42	,	,	PUNCT
ejpam-4798	138	43	j	j	PROPN
ejpam-4798	138	44	≤	≤	PROPN
ejpam-4798	138	45	n	n	CCONJ
ejpam-4798	138	46	and	and	CCONJ
ejpam-4798	138	47	di	di	NOUN
ejpam-4798	138	48	,	,	PUNCT
ejpam-4798	138	49	j	j	PROPN
ejpam-4798	139	1	=	=	PUNCT
ejpam-4798	139	2	0	0	PROPN
ejpam-4798	140	1	for	for	ADP
ejpam-4798	140	2	0	0	NUM
ejpam-4798	140	3	≤	≤	NOUN
ejpam-4798	140	4	i	i	PROPN
ejpam-4798	140	5	,	,	PUNCT
ejpam-4798	140	6	j	j	PROPN
ejpam-4798	140	7	≤	≤	PROPN
ejpam-4798	140	8	n	n	CCONJ
ejpam-4798	140	9	i.e.	i.e.	X
ejpam-4798	140	10	[	[	X
ejpam-4798	140	11	di	di	X
ejpam-4798	140	12	,	,	PUNCT
ejpam-4798	140	13	j	j	PROPN
ejpam-4798	140	14	]	]	PUNCT
ejpam-4798	140	15	is	be	AUX
ejpam-4798	140	16	zero	zero	NUM
ejpam-4798	140	17	matrix	matrix	NOUN
ejpam-4798	140	18	.	.	PUNCT
ejpam-4798	141	1	in	in	ADP
ejpam-4798	141	2	this	this	DET
ejpam-4798	141	3	example	example	NOUN
ejpam-4798	141	4	,	,	PUNCT
ejpam-4798	141	5	the	the	DET
ejpam-4798	141	6	8	8	NUM
ejpam-4798	141	7	×	×	NOUN
ejpam-4798	141	8	8	8	NUM
ejpam-4798	141	9	input	input	NOUN
ejpam-4798	141	10	matrix	matrix	NOUN
ejpam-4798	141	11	is	be	AUX
ejpam-4798	141	12	divided	divide	VERB
ejpam-4798	141	13	into	into	ADP
ejpam-4798	141	14	four	four	NUM
ejpam-4798	141	15	equal	equal	ADJ
ejpam-4798	141	16	matrices	matrix	NOUN
ejpam-4798	141	17	of	of	ADP
ejpam-4798	141	18	size	size	NOUN
ejpam-4798	141	19	4×	4×	NOUN
ejpam-4798	141	20	4	4	NUM
ejpam-4798	141	21	.	.	PUNCT
ejpam-4798	142	1	the	the	DET
ejpam-4798	142	2	fourth	fourth	ADJ
ejpam-4798	142	3	matrix	matrix	NOUN
ejpam-4798	142	4	is	be	AUX
ejpam-4798	142	5	made	make	VERB
ejpam-4798	142	6	zero	zero	NUM
ejpam-4798	142	7	and	and	CCONJ
ejpam-4798	142	8	the	the	DET
ejpam-4798	142	9	first	first	ADJ
ejpam-4798	142	10	,	,	PUNCT
ejpam-4798	142	11	second	second	ADJ
ejpam-4798	142	12	,	,	PUNCT
ejpam-4798	142	13	and	and	CCONJ
ejpam-4798	142	14	third	third	ADJ
ejpam-4798	142	15	matrices	matrix	NOUN
ejpam-4798	142	16	are	be	AUX
ejpam-4798	142	17	made	make	VERB
ejpam-4798	142	18	identical	identical	ADJ
ejpam-4798	142	19	through	through	ADP
ejpam-4798	142	20	row	row	NOUN
ejpam-4798	142	21	and	and	CCONJ
ejpam-4798	142	22	column	column	NOUN
ejpam-4798	142	23	transformations	transformation	NOUN
ejpam-4798	142	24	.	.	PUNCT
ejpam-4798	143	1	the	the	DET
ejpam-4798	143	2	output	output	NOUN
ejpam-4798	143	3	matrix	matrix	NOUN
ejpam-4798	143	4	is	be	AUX
ejpam-4798	143	5	4×	4×	NOUN
ejpam-4798	143	6	4	4	NUM
ejpam-4798	143	7	.	.	PUNCT
ejpam-4798	144	1	after	after	ADP
ejpam-4798	144	2	applying	apply	VERB
ejpam-4798	144	3	transformations	transformation	NOUN
ejpam-4798	144	4	such	such	ADJ
ejpam-4798	144	5	that	that	DET
ejpam-4798	144	6	r2	r2	PROPN
ejpam-4798	144	7	⇔	⇔	PROPN
ejpam-4798	144	8	r7	r7	PROPN
ejpam-4798	144	9	and	and	CCONJ
ejpam-4798	144	10	c2	c2	PROPN
ejpam-4798	144	11	⇔	⇔	PROPN
ejpam-4798	144	12	c7	c7	PROPN
ejpam-4798	144	13	,	,	PUNCT
ejpam-4798	144	14	we	we	PRON
ejpam-4798	144	15	get	get	VERB
ejpam-4798	144	16	:	:	PUNCT
ejpam-4798	144	17	s.	s.	PROPN
ejpam-4798	144	18	kumar	kumar	PROPN
ejpam-4798	144	19	,	,	PUNCT
ejpam-4798	144	20	d.	d.	PROPN
ejpam-4798	144	21	sinha	sinha	PROPN
ejpam-4798	144	22	/	/	SYM
ejpam-4798	144	23	eur	eur	PROPN
ejpam-4798	144	24	.	.	PUNCT
ejpam-4798	145	1	j.	j.	PROPN
ejpam-4798	145	2	pure	pure	PROPN
ejpam-4798	145	3	appl	appl	PROPN
ejpam-4798	145	4	.	.	PROPN
ejpam-4798	145	5	math	math	PROPN
ejpam-4798	145	6	,	,	PUNCT
ejpam-4798	145	7	17	17	NUM
ejpam-4798	145	8	(	(	PUNCT
ejpam-4798	145	9	1	1	NUM
ejpam-4798	145	10	)	)	PUNCT
ejpam-4798	145	11	(	(	PUNCT
ejpam-4798	145	12	2024	2024	NUM
ejpam-4798	145	13	)	)	PUNCT
ejpam-4798	145	14	,	,	PUNCT
ejpam-4798	145	15	504	504	NUM
ejpam-4798	145	16	-	-	SYM
ejpam-4798	145	17	518	518	NUM
ejpam-4798	145	18	511	511	NUM
ejpam-4798	145	19	vertex	vertex	NOUN
ejpam-4798	145	20	vi	vi	NOUN
ejpam-4798	145	21	1	1	NUM
ejpam-4798	145	22	7	7	NUM
ejpam-4798	145	23	3	3	NUM
ejpam-4798	145	24	4	4	NUM
ejpam-4798	145	25	5	5	NUM
ejpam-4798	145	26	6	6	NUM
ejpam-4798	145	27	2	2	NUM
ejpam-4798	145	28	8	8	NUM
ejpam-4798	145	29	1	1	NUM
ejpam-4798	145	30	0	0	NUM
ejpam-4798	145	31	-1	-1	SYM
ejpam-4798	145	32	0	0	NUM
ejpam-4798	146	1	-1	-1	NUM
ejpam-4798	147	1	-1	-1	NOUN
ejpam-4798	147	2	0	0	NUM
ejpam-4798	148	1	-1	-1	SYM
ejpam-4798	148	2	0	0	NUM
ejpam-4798	148	3	7	7	NUM
ejpam-4798	148	4	-1	-1	SYM
ejpam-4798	148	5	0	0	NUM
ejpam-4798	149	1	1	1	NUM
ejpam-4798	149	2	0	0	NUM
ejpam-4798	149	3	0	0	NUM
ejpam-4798	149	4	1	1	NUM
ejpam-4798	149	5	0	0	NUM
ejpam-4798	149	6	-1	-1	SYM
ejpam-4798	149	7	3	3	NUM
ejpam-4798	149	8	0	0	NUM
ejpam-4798	149	9	1	1	NUM
ejpam-4798	149	10	0	0	NUM
ejpam-4798	149	11	1	1	NUM
ejpam-4798	149	12	1	1	NUM
ejpam-4798	149	13	0	0	NUM
ejpam-4798	149	14	1	1	NUM
ejpam-4798	149	15	0	0	NUM
ejpam-4798	149	16	4	4	NUM
ejpam-4798	149	17	-1	-1	SYM
ejpam-4798	149	18	0	0	NUM
ejpam-4798	149	19	1	1	NUM
ejpam-4798	149	20	0	0	NUM
ejpam-4798	149	21	0	0	NUM
ejpam-4798	149	22	0	0	NUM
ejpam-4798	149	23	0	0	NUM
ejpam-4798	149	24	0	0	NUM
ejpam-4798	149	25	5	5	NUM
ejpam-4798	149	26	-1	-1	SYM
ejpam-4798	149	27	0	0	NUM
ejpam-4798	150	1	1	1	NUM
ejpam-4798	150	2	0	0	NUM
ejpam-4798	150	3	0	0	NUM
ejpam-4798	150	4	1	1	NUM
ejpam-4798	150	5	0	0	NUM
ejpam-4798	150	6	-1	-1	SYM
ejpam-4798	150	7	6	6	NUM
ejpam-4798	150	8	0	0	NUM
ejpam-4798	150	9	1	1	NUM
ejpam-4798	150	10	0	0	NUM
ejpam-4798	150	11	0	0	NUM
ejpam-4798	150	12	1	1	NUM
ejpam-4798	150	13	0	0	NUM
ejpam-4798	150	14	0	0	NUM
ejpam-4798	150	15	0	0	NUM
ejpam-4798	150	16	2	2	NUM
ejpam-4798	150	17	-1	-1	SYM
ejpam-4798	150	18	0	0	NUM
ejpam-4798	151	1	1	1	NUM
ejpam-4798	151	2	0	0	NUM
ejpam-4798	151	3	0	0	NUM
ejpam-4798	151	4	0	0	NUM
ejpam-4798	151	5	0	0	NUM
ejpam-4798	151	6	0	0	NUM
ejpam-4798	151	7	8	8	NUM
ejpam-4798	151	8	0	0	NUM
ejpam-4798	151	9	-1	-1	SYM
ejpam-4798	151	10	0	0	NUM
ejpam-4798	151	11	0	0	NUM
ejpam-4798	152	1	-1	-1	SYM
ejpam-4798	152	2	0	0	NUM
ejpam-4798	152	3	0	0	NUM
ejpam-4798	152	4	0	0	NUM
ejpam-4798	153	1	and	and	CCONJ
ejpam-4798	153	2	then	then	ADV
ejpam-4798	153	3	r4	r4	VERB
ejpam-4798	153	4	⇔	⇔	PROPN
ejpam-4798	153	5	r5	r5	PROPN
ejpam-4798	153	6	and	and	CCONJ
ejpam-4798	153	7	c4	c4	PROPN
ejpam-4798	153	8	⇔	⇔	PROPN
ejpam-4798	153	9	c5	c5	PROPN
ejpam-4798	153	10	,	,	PUNCT
ejpam-4798	153	11	we	we	PRON
ejpam-4798	153	12	get	get	VERB
ejpam-4798	153	13	:	:	PUNCT
ejpam-4798	153	14	vertex	vertex	NOUN
ejpam-4798	153	15	vi	vi	NOUN
ejpam-4798	153	16	1	1	NUM
ejpam-4798	153	17	7	7	NUM
ejpam-4798	153	18	3	3	NUM
ejpam-4798	153	19	4	4	NUM
ejpam-4798	153	20	5	5	NUM
ejpam-4798	153	21	6	6	NUM
ejpam-4798	153	22	2	2	NUM
ejpam-4798	153	23	8	8	NUM
ejpam-4798	153	24	1	1	NUM
ejpam-4798	153	25	0	0	NUM
ejpam-4798	153	26	-1	-1	SYM
ejpam-4798	153	27	0	0	NUM
ejpam-4798	154	1	-1	-1	NUM
ejpam-4798	155	1	-1	-1	NOUN
ejpam-4798	155	2	0	0	NUM
ejpam-4798	156	1	-1	-1	SYM
ejpam-4798	156	2	0	0	NUM
ejpam-4798	156	3	7	7	NUM
ejpam-4798	156	4	-1	-1	SYM
ejpam-4798	156	5	0	0	NUM
ejpam-4798	157	1	1	1	NUM
ejpam-4798	157	2	0	0	NUM
ejpam-4798	157	3	0	0	NUM
ejpam-4798	157	4	1	1	NUM
ejpam-4798	157	5	0	0	NUM
ejpam-4798	157	6	-1	-1	SYM
ejpam-4798	157	7	3	3	NUM
ejpam-4798	157	8	0	0	NUM
ejpam-4798	157	9	1	1	NUM
ejpam-4798	157	10	0	0	NUM
ejpam-4798	157	11	1	1	NUM
ejpam-4798	157	12	1	1	NUM
ejpam-4798	157	13	0	0	NUM
ejpam-4798	157	14	1	1	NUM
ejpam-4798	157	15	0	0	NUM
ejpam-4798	157	16	4	4	NUM
ejpam-4798	157	17	-1	-1	SYM
ejpam-4798	157	18	0	0	NUM
ejpam-4798	158	1	1	1	NUM
ejpam-4798	158	2	0	0	NUM
ejpam-4798	158	3	0	0	NUM
ejpam-4798	158	4	1	1	NUM
ejpam-4798	158	5	0	0	NUM
ejpam-4798	158	6	-1	-1	SYM
ejpam-4798	158	7	5	5	NUM
ejpam-4798	158	8	-1	-1	SYM
ejpam-4798	158	9	0	0	NUM
ejpam-4798	158	10	1	1	NUM
ejpam-4798	158	11	0	0	NUM
ejpam-4798	158	12	0	0	NUM
ejpam-4798	158	13	0	0	NUM
ejpam-4798	158	14	0	0	NUM
ejpam-4798	158	15	0	0	NUM
ejpam-4798	158	16	6	6	NUM
ejpam-4798	158	17	0	0	NUM
ejpam-4798	158	18	1	1	NUM
ejpam-4798	158	19	0	0	NUM
ejpam-4798	158	20	1	1	NUM
ejpam-4798	158	21	0	0	NUM
ejpam-4798	158	22	0	0	NUM
ejpam-4798	158	23	0	0	NUM
ejpam-4798	158	24	0	0	NUM
ejpam-4798	158	25	2	2	NUM
ejpam-4798	158	26	-1	-1	SYM
ejpam-4798	158	27	0	0	NUM
ejpam-4798	159	1	1	1	NUM
ejpam-4798	159	2	0	0	NUM
ejpam-4798	159	3	0	0	NUM
ejpam-4798	159	4	0	0	NUM
ejpam-4798	159	5	0	0	NUM
ejpam-4798	159	6	0	0	NUM
ejpam-4798	159	7	8	8	NUM
ejpam-4798	159	8	0	0	NUM
ejpam-4798	159	9	-1	-1	SYM
ejpam-4798	159	10	0	0	NUM
ejpam-4798	160	1	-1	-1	SYM
ejpam-4798	160	2	0	0	NUM
ejpam-4798	160	3	0	0	NUM
ejpam-4798	161	1	0	0	NUM
ejpam-4798	161	2	0	0	NUM
ejpam-4798	162	1	the	the	DET
ejpam-4798	162	2	first	first	ADJ
ejpam-4798	162	3	,	,	PUNCT
ejpam-4798	162	4	second	second	ADJ
ejpam-4798	162	5	,	,	PUNCT
ejpam-4798	162	6	and	and	CCONJ
ejpam-4798	162	7	third	third	ADJ
ejpam-4798	162	8	matrices	matrix	NOUN
ejpam-4798	162	9	can	can	AUX
ejpam-4798	162	10	be	be	AUX
ejpam-4798	162	11	seen	see	VERB
ejpam-4798	162	12	to	to	PART
ejpam-4798	162	13	be	be	AUX
ejpam-4798	162	14	the	the	DET
ejpam-4798	162	15	same	same	ADJ
ejpam-4798	162	16	,	,	PUNCT
ejpam-4798	162	17	and	and	CCONJ
ejpam-4798	162	18	the	the	DET
ejpam-4798	162	19	fourth	fourth	ADJ
ejpam-4798	162	20	matrix	matrix	NOUN
ejpam-4798	162	21	is	be	AUX
ejpam-4798	162	22	zero	zero	NUM
ejpam-4798	162	23	,	,	PUNCT
ejpam-4798	162	24	which	which	PRON
ejpam-4798	162	25	satisfies	satisfy	VERB
ejpam-4798	162	26	the	the	DET
ejpam-4798	162	27	requirements	requirement	NOUN
ejpam-4798	162	28	for	for	ADP
ejpam-4798	162	29	a	a	DET
ejpam-4798	162	30	splitting	splitting	NOUN
ejpam-4798	162	31	root	root	NOUN
ejpam-4798	162	32	signed	sign	VERB
ejpam-4798	162	33	graph	graph	NOUN
ejpam-4798	162	34	.	.	PUNCT
ejpam-4798	163	1	the	the	DET
ejpam-4798	163	2	final	final	ADJ
ejpam-4798	163	3	output	output	NOUN
ejpam-4798	163	4	matrix	matrix	NOUN
ejpam-4798	163	5	is	be	AUX
ejpam-4798	163	6	the	the	DET
ejpam-4798	163	7	splitting	splitting	NOUN
ejpam-4798	163	8	root	root	NOUN
ejpam-4798	163	9	signed	sign	VERB
ejpam-4798	163	10	graph	graph	NOUN
ejpam-4798	163	11	:	:	PUNCT
ejpam-4798	163	12	vertex	vertex	NOUN
ejpam-4798	163	13	vi	vi	NOUN
ejpam-4798	163	14	1	1	NUM
ejpam-4798	163	15	7	7	NUM
ejpam-4798	163	16	3	3	NUM
ejpam-4798	163	17	5	5	NUM
ejpam-4798	163	18	1	1	NUM
ejpam-4798	163	19	0	0	NUM
ejpam-4798	163	20	-1	-1	SYM
ejpam-4798	163	21	0	0	NUM
ejpam-4798	164	1	-1	-1	SYM
ejpam-4798	164	2	7	7	NUM
ejpam-4798	164	3	-1	-1	SYM
ejpam-4798	164	4	0	0	NUM
ejpam-4798	164	5	1	1	NUM
ejpam-4798	164	6	0	0	NUM
ejpam-4798	164	7	3	3	NUM
ejpam-4798	164	8	0	0	NUM
ejpam-4798	164	9	1	1	NUM
ejpam-4798	164	10	0	0	NUM
ejpam-4798	164	11	1	1	NUM
ejpam-4798	164	12	5	5	NUM
ejpam-4798	164	13	-1	-1	SYM
ejpam-4798	164	14	0	0	NUM
ejpam-4798	164	15	1	1	NUM
ejpam-4798	164	16	0	0	NUM
ejpam-4798	164	17	the	the	DET
ejpam-4798	164	18	splitting	splitting	NOUN
ejpam-4798	164	19	signed	sign	VERB
ejpam-4798	164	20	graph	graph	NOUN
ejpam-4798	164	21	s1	s1	NOUN
ejpam-4798	164	22	and	and	CCONJ
ejpam-4798	164	23	its	its	PRON
ejpam-4798	164	24	corresponding	corresponding	ADJ
ejpam-4798	164	25	splitting	splitting	NOUN
ejpam-4798	164	26	root	root	NOUN
ejpam-4798	164	27	signed	sign	VERB
ejpam-4798	164	28	graph	graph	NOUN
ejpam-4798	164	29	s	s	NOUN
ejpam-4798	164	30	are	be	AUX
ejpam-4798	164	31	depicted	depict	VERB
ejpam-4798	164	32	in	in	ADP
ejpam-4798	164	33	the	the	DET
ejpam-4798	164	34	figure	figure	NOUN
ejpam-4798	164	35	2	2	NUM
ejpam-4798	164	36	.	.	NOUN
ejpam-4798	164	37	4	4	NUM
ejpam-4798	164	38	2	2	NUM
ejpam-4798	164	39	s1	s1	NOUN
ejpam-4798	164	40	7	7	NUM
ejpam-4798	164	41	8	8	NUM
ejpam-4798	164	42	6	6	NUM
ejpam-4798	164	43	5	5	NUM
ejpam-4798	164	44	3	3	NUM
ejpam-4798	164	45	1	1	NUM
ejpam-4798	164	46	s	s	NOUN
ejpam-4798	164	47	figure	figure	NOUN
ejpam-4798	164	48	2	2	NUM
ejpam-4798	164	49	:	:	PUNCT
ejpam-4798	164	50	signed	sign	VERB
ejpam-4798	164	51	graph	graph	NOUN
ejpam-4798	164	52	s1	s1	NOUN
ejpam-4798	164	53	and	and	CCONJ
ejpam-4798	164	54	s	s	NOUN
ejpam-4798	164	55	is	be	AUX
ejpam-4798	164	56	its	its	PRON
ejpam-4798	164	57	splitting	splitting	NOUN
ejpam-4798	164	58	root	root	NOUN
ejpam-4798	164	59	signed	sign	VERB
ejpam-4798	164	60	graph	graph	NOUN
ejpam-4798	164	61	s.	s.	PROPN
ejpam-4798	164	62	kumar	kumar	PROPN
ejpam-4798	164	63	,	,	PUNCT
ejpam-4798	164	64	d.	d.	PROPN
ejpam-4798	164	65	sinha	sinha	PROPN
ejpam-4798	164	66	/	/	SYM
ejpam-4798	164	67	eur	eur	PROPN
ejpam-4798	164	68	.	.	PUNCT
ejpam-4798	165	1	j.	j.	PROPN
ejpam-4798	165	2	pure	pure	PROPN
ejpam-4798	165	3	appl	appl	PROPN
ejpam-4798	165	4	.	.	PROPN
ejpam-4798	165	5	math	math	PROPN
ejpam-4798	165	6	,	,	PUNCT
ejpam-4798	165	7	17	17	NUM
ejpam-4798	165	8	(	(	PUNCT
ejpam-4798	165	9	1	1	NUM
ejpam-4798	165	10	)	)	PUNCT
ejpam-4798	165	11	(	(	PUNCT
ejpam-4798	165	12	2024	2024	NUM
ejpam-4798	165	13	)	)	PUNCT
ejpam-4798	165	14	,	,	PUNCT
ejpam-4798	165	15	504	504	NUM
ejpam-4798	165	16	-	-	SYM
ejpam-4798	165	17	518	518	NUM
ejpam-4798	165	18	512	512	NUM
ejpam-4798	165	19	algorithm	algorithm	NOUN
ejpam-4798	165	20	2	2	NUM
ejpam-4798	165	21	algorithm	algorithm	NOUN
ejpam-4798	165	22	to	to	PART
ejpam-4798	165	23	derive	derive	VERB
ejpam-4798	165	24	the	the	DET
ejpam-4798	165	25	splitting	splitting	NOUN
ejpam-4798	165	26	root	root	NOUN
ejpam-4798	165	27	signed	sign	VERB
ejpam-4798	165	28	graph	graph	NOUN
ejpam-4798	165	29	of	of	ADP
ejpam-4798	165	30	a	a	DET
ejpam-4798	165	31	given	give	VERB
ejpam-4798	165	32	signed	sign	VERB
ejpam-4798	165	33	graph	graph	NOUN
ejpam-4798	165	34	1	1	NUM
ejpam-4798	165	35	:	:	PUNCT
ejpam-4798	165	36	input	input	NOUN
ejpam-4798	165	37	:	:	PUNCT
ejpam-4798	165	38	number	number	NOUN
ejpam-4798	165	39	of	of	ADP
ejpam-4798	165	40	vertices	vertex	NOUN
ejpam-4798	165	41	(	(	PUNCT
ejpam-4798	165	42	n	n	CCONJ
ejpam-4798	165	43	)	)	PUNCT
ejpam-4798	165	44	2	2	NUM
ejpam-4798	165	45	:	:	PUNCT
ejpam-4798	165	46	input	input	NOUN
ejpam-4798	165	47	:	:	PUNCT
ejpam-4798	165	48	adjacency	adjacency	NOUN
ejpam-4798	165	49	matrix	matrix	NOUN
ejpam-4798	165	50	of	of	ADP
ejpam-4798	165	51	the	the	DET
ejpam-4798	165	52	signed	sign	VERB
ejpam-4798	165	53	graph	graph	NOUN
ejpam-4798	165	54	a(σ	a(σ	PROPN
ejpam-4798	165	55	)	)	PUNCT
ejpam-4798	165	56	=	=	PUNCT
ejpam-4798	165	57	a(i	a(i	PROPN
ejpam-4798	165	58	,	,	PUNCT
ejpam-4798	165	59	j	j	NOUN
ejpam-4798	165	60	)	)	PUNCT
ejpam-4798	165	61	3	3	NUM
ejpam-4798	165	62	:	:	PUNCT
ejpam-4798	165	63	check	check	VERB
ejpam-4798	165	64	4	4	NUM
ejpam-4798	165	65	:	:	PUNCT
ejpam-4798	165	66	if	if	SCONJ
ejpam-4798	165	67	n	n	CCONJ
ejpam-4798	165	68	mod	mod	NOUN
ejpam-4798	165	69	2	2	NUM
ejpam-4798	165	70	=	=	SYM
ejpam-4798	165	71	1	1	NUM
ejpam-4798	165	72	then	then	ADV
ejpam-4798	165	73	5	5	NUM
ejpam-4798	165	74	:	:	PUNCT
ejpam-4798	165	75	print	print	NOUN
ejpam-4798	165	76	:	:	PUNCT
ejpam-4798	165	77	matrix	matrix	NOUN
ejpam-4798	165	78	is	be	AUX
ejpam-4798	165	79	of	of	ADP
ejpam-4798	165	80	odd	odd	ADJ
ejpam-4798	165	81	order	order	NOUN
ejpam-4798	165	82	,	,	PUNCT
ejpam-4798	165	83	splitting	split	VERB
ejpam-4798	165	84	root	root	NOUN
ejpam-4798	165	85	signed	sign	VERB
ejpam-4798	165	86	graph	graph	NOUN
ejpam-4798	165	87	dose	dose	VERB
ejpam-4798	165	88	not	not	PART
ejpam-4798	165	89	exist	exist	VERB
ejpam-4798	165	90	6	6	NUM
ejpam-4798	165	91	:	:	PUNCT
ejpam-4798	165	92	terminate	terminate	VERB
ejpam-4798	165	93	7	7	NUM
ejpam-4798	165	94	:	:	PUNCT
ejpam-4798	165	95	else	else	ADV
ejpam-4798	165	96	8	8	NUM
ejpam-4798	165	97	:	:	PUNCT
ejpam-4798	165	98	for	for	ADP
ejpam-4798	165	99	i	i	PRON
ejpam-4798	165	100	=	=	NOUN
ejpam-4798	165	101	1	1	NUM
ejpam-4798	165	102	:	:	PUNCT
ejpam-4798	165	103	n	n	PRON
ejpam-4798	165	104	do	do	VERB
ejpam-4798	165	105	9	9	NUM
ejpam-4798	165	106	:	:	PUNCT
ejpam-4798	165	107	for	for	ADP
ejpam-4798	165	108	j	j	PROPN
ejpam-4798	165	109	=	=	SYM
ejpam-4798	165	110	1	1	NUM
ejpam-4798	165	111	:	:	PUNCT
ejpam-4798	165	112	n	n	PRON
ejpam-4798	165	113	do	do	VERB
ejpam-4798	165	114	10	10	NUM
ejpam-4798	165	115	:	:	PUNCT
ejpam-4798	165	116	check	check	VERB
ejpam-4798	165	117	11	11	NUM
ejpam-4798	165	118	:	:	PUNCT
ejpam-4798	165	119	if	if	SCONJ
ejpam-4798	165	120	a(i	a(i	NOUN
ejpam-4798	165	121	,	,	PUNCT
ejpam-4798	165	122	j)==1	j)==1	NOUN
ejpam-4798	165	123	then	then	ADV
ejpam-4798	165	124	12	12	NUM
ejpam-4798	165	125	:	:	PUNCT
ejpam-4798	165	126	countp	countp	NOUN
ejpam-4798	165	127	=	=	SYM
ejpam-4798	165	128	countp	countp	NOUN
ejpam-4798	166	1	+	+	CCONJ
ejpam-4798	166	2	1	1	NUM
ejpam-4798	166	3	13	13	NUM
ejpam-4798	166	4	:	:	PUNCT
ejpam-4798	166	5	else	else	ADV
ejpam-4798	166	6	14	14	NUM
ejpam-4798	166	7	:	:	PUNCT
ejpam-4798	166	8	if	if	SCONJ
ejpam-4798	166	9	a(i	a(i	VERB
ejpam-4798	166	10	,	,	PUNCT
ejpam-4798	166	11	j)==	j)==	PROPN
ejpam-4798	166	12	-1	-1	PUNCT
ejpam-4798	166	13	then	then	ADV
ejpam-4798	166	14	15	15	NUM
ejpam-4798	166	15	:	:	PUNCT
ejpam-4798	166	16	countq	countq	NOUN
ejpam-4798	166	17	=	=	PUNCT
ejpam-4798	166	18	countq	countq	NOUN
ejpam-4798	166	19	+	+	CCONJ
ejpam-4798	166	20	1	1	NUM
ejpam-4798	166	21	16	16	NUM
ejpam-4798	166	22	:	:	PUNCT
ejpam-4798	166	23	end	end	VERB
ejpam-4798	166	24	if	if	SCONJ
ejpam-4798	166	25	17	17	NUM
ejpam-4798	166	26	:	:	PUNCT
ejpam-4798	166	27	end	end	VERB
ejpam-4798	166	28	if	if	SCONJ
ejpam-4798	166	29	18	18	NUM
ejpam-4798	166	30	:	:	PUNCT
ejpam-4798	166	31	end	end	VERB
ejpam-4798	166	32	for	for	ADP
ejpam-4798	166	33	19	19	NUM
ejpam-4798	166	34	:	:	PUNCT
ejpam-4798	166	35	end	end	VERB
ejpam-4798	166	36	for	for	ADP
ejpam-4798	166	37	20	20	NUM
ejpam-4798	166	38	:	:	PUNCT
ejpam-4798	166	39	end	end	VERB
ejpam-4798	166	40	if	if	SCONJ
ejpam-4798	166	41	21	21	NUM
ejpam-4798	166	42	:	:	PUNCT
ejpam-4798	166	43	check	check	VERB
ejpam-4798	166	44	22	22	NUM
ejpam-4798	166	45	:	:	PUNCT
ejpam-4798	166	46	if	if	SCONJ
ejpam-4798	166	47	countp	countp	NOUN
ejpam-4798	166	48	mod	mod	NOUN
ejpam-4798	166	49	3	3	NUM
ejpam-4798	166	50	=	=	NOUN
ejpam-4798	166	51	=	=	SYM
ejpam-4798	166	52	0	0	PROPN
ejpam-4798	166	53	&	&	CCONJ
ejpam-4798	166	54	&	&	CCONJ
ejpam-4798	166	55	countq	countq	PROPN
ejpam-4798	166	56	mod	mod	PROPN
ejpam-4798	166	57	3	3	NUM
ejpam-4798	167	1	=	=	SYM
ejpam-4798	167	2	=	=	SYM
ejpam-4798	167	3	0	0	NUM
ejpam-4798	167	4	then	then	ADV
ejpam-4798	167	5	23	23	NUM
ejpam-4798	167	6	:	:	PUNCT
ejpam-4798	167	7	print	print	NOUN
ejpam-4798	167	8	:	:	PUNCT
ejpam-4798	167	9	splitting	split	VERB
ejpam-4798	167	10	root	root	NOUN
ejpam-4798	167	11	signed	sign	VERB
ejpam-4798	167	12	graph	graph	NOUN
ejpam-4798	167	13	is	be	AUX
ejpam-4798	167	14	possible	possible	ADJ
ejpam-4798	167	15	24	24	NUM
ejpam-4798	167	16	:	:	PUNCT
ejpam-4798	167	17	else	else	ADV
ejpam-4798	167	18	25	25	NUM
ejpam-4798	167	19	:	:	PUNCT
ejpam-4798	167	20	print	print	NOUN
ejpam-4798	167	21	:	:	PUNCT
ejpam-4798	167	22	splitting	split	VERB
ejpam-4798	167	23	root	root	NOUN
ejpam-4798	167	24	signed	sign	VERB
ejpam-4798	167	25	graph	graph	NOUN
ejpam-4798	167	26	is	be	AUX
ejpam-4798	167	27	not	not	PART
ejpam-4798	167	28	possible	possible	ADJ
ejpam-4798	167	29	and	and	CCONJ
ejpam-4798	167	30	terminate	terminate	VERB
ejpam-4798	167	31	26	26	NUM
ejpam-4798	167	32	:	:	PUNCT
ejpam-4798	167	33	end	end	VERB
ejpam-4798	167	34	if	if	SCONJ
ejpam-4798	167	35	27	27	NUM
ejpam-4798	167	36	:	:	PUNCT
ejpam-4798	167	37	assign	assign	VERB
ejpam-4798	167	38	:	:	PUNCT
ejpam-4798	167	39	positive[i	positive[i	NOUN
ejpam-4798	167	40	]	]	PUNCT
ejpam-4798	167	41	=	=	SYM
ejpam-4798	167	42	countp	countp	NOUN
ejpam-4798	167	43	28	28	NUM
ejpam-4798	167	44	:	:	PUNCT
ejpam-4798	167	45	negative[i	negative[i	NOUN
ejpam-4798	167	46	]	]	X
ejpam-4798	167	47	=	=	SYM
ejpam-4798	167	48	countq	countq	NOUN
ejpam-4798	167	49	29	29	NUM
ejpam-4798	167	50	:	:	PUNCT
ejpam-4798	167	51	boole[i	boole[i	PROPN
ejpam-4798	167	52	]	]	X
ejpam-4798	167	53	=	=	SYM
ejpam-4798	167	54	f	f	PROPN
ejpam-4798	167	55	30	30	NUM
ejpam-4798	167	56	:	:	PUNCT
ejpam-4798	167	57	for	for	ADP
ejpam-4798	167	58	i	i	PRON
ejpam-4798	167	59	=	=	NOUN
ejpam-4798	167	60	1	1	NUM
ejpam-4798	167	61	:	:	PUNCT
ejpam-4798	167	62	n	n	PRON
ejpam-4798	167	63	do	do	AUX
ejpam-4798	167	64	31	31	NUM
ejpam-4798	167	65	:	:	PUNCT
ejpam-4798	167	66	for	for	ADP
ejpam-4798	167	67	j	j	PROPN
ejpam-4798	168	1	=	=	PRON
ejpam-4798	168	2	i+	i+	PROPN
ejpam-4798	168	3	1	1	NUM
ejpam-4798	168	4	:	:	PUNCT
ejpam-4798	168	5	n	n	PRON
ejpam-4798	168	6	do	do	AUX
ejpam-4798	168	7	32	32	NUM
ejpam-4798	168	8	:	:	PUNCT
ejpam-4798	168	9	assign	assign	VERB
ejpam-4798	168	10	:	:	PUNCT
ejpam-4798	168	11	k	k	X
ejpam-4798	169	1	=	=	PUNCT
ejpam-4798	169	2	i	i	PRON
ejpam-4798	169	3	33	33	NUM
ejpam-4798	169	4	:	:	PUNCT
ejpam-4798	169	5	if	if	SCONJ
ejpam-4798	169	6	boole[i	boole[i	PROPN
ejpam-4798	169	7	]	]	X
ejpam-4798	170	1	=	=	PUNCT
ejpam-4798	170	2	=	=	SYM
ejpam-4798	170	3	t	t	PROPN
ejpam-4798	170	4	then	then	ADV
ejpam-4798	170	5	34	34	NUM
ejpam-4798	170	6	:	:	PUNCT
ejpam-4798	170	7	no	no	PRON
ejpam-4798	170	8	-	-	PUNCT
ejpam-4798	170	9	found	find	VERB
ejpam-4798	170	10	=	=	NOUN
ejpam-4798	170	11	1	1	NUM
ejpam-4798	170	12	35	35	NUM
ejpam-4798	170	13	:	:	PUNCT
ejpam-4798	170	14	if	if	SCONJ
ejpam-4798	170	15	positive[i	positive[i	NOUN
ejpam-4798	170	16	]	]	X
ejpam-4798	171	1	=	=	NOUN
ejpam-4798	171	2	=	=	SYM
ejpam-4798	171	3	2	2	NUM
ejpam-4798	171	4	positive[j	positive[j	NOUN
ejpam-4798	171	5	]	]	PUNCT
ejpam-4798	171	6	&	&	CCONJ
ejpam-4798	171	7	&	&	CCONJ
ejpam-4798	171	8	negative[i	negative[i	PROPN
ejpam-4798	171	9	]	]	X
ejpam-4798	171	10	=	=	NOUN
ejpam-4798	171	11	=	=	SYM
ejpam-4798	171	12	2	2	NUM
ejpam-4798	171	13	negative[j	negative[j	NOUN
ejpam-4798	171	14	]	]	PUNCT
ejpam-4798	171	15	&	&	CCONJ
ejpam-4798	171	16	&	&	CCONJ
ejpam-4798	171	17	boole[i	boole[i	PROPN
ejpam-4798	171	18	]	]	PUNCT
ejpam-4798	172	1	=	=	PUNCT
ejpam-4798	172	2	=	=	SYM
ejpam-4798	172	3	t	t	PROPN
ejpam-4798	172	4	then	then	ADV
ejpam-4798	172	5	s.	s.	PROPN
ejpam-4798	172	6	kumar	kumar	PROPN
ejpam-4798	172	7	,	,	PUNCT
ejpam-4798	172	8	d.	d.	PROPN
ejpam-4798	172	9	sinha	sinha	PROPN
ejpam-4798	172	10	/	/	SYM
ejpam-4798	172	11	eur	eur	PROPN
ejpam-4798	172	12	.	.	PUNCT
ejpam-4798	173	1	j.	j.	PROPN
ejpam-4798	173	2	pure	pure	PROPN
ejpam-4798	173	3	appl	appl	PROPN
ejpam-4798	173	4	.	.	PROPN
ejpam-4798	173	5	math	math	PROPN
ejpam-4798	173	6	,	,	PUNCT
ejpam-4798	173	7	17	17	NUM
ejpam-4798	173	8	(	(	PUNCT
ejpam-4798	173	9	1	1	NUM
ejpam-4798	173	10	)	)	PUNCT
ejpam-4798	173	11	(	(	PUNCT
ejpam-4798	173	12	2024	2024	NUM
ejpam-4798	173	13	)	)	PUNCT
ejpam-4798	173	14	,	,	PUNCT
ejpam-4798	173	15	504	504	NUM
ejpam-4798	173	16	-	-	SYM
ejpam-4798	173	17	518	518	NUM
ejpam-4798	173	18	513	513	NUM
ejpam-4798	173	19	36	36	NUM
ejpam-4798	173	20	:	:	PUNCT
ejpam-4798	173	21	assign	assign	VERB
ejpam-4798	173	22	:	:	PUNCT
ejpam-4798	173	23	vertex[i	vertex[i	NOUN
ejpam-4798	173	24	]	]	PUNCT
ejpam-4798	173	25	=	=	SYM
ejpam-4798	174	1	2	2	NUM
ejpam-4798	174	2	37	37	NUM
ejpam-4798	174	3	:	:	PUNCT
ejpam-4798	174	4	vertex[j	vertex[j	X
ejpam-4798	174	5	]	]	PUNCT
ejpam-4798	174	6	=	=	PUNCT
ejpam-4798	175	1	1	1	NUM
ejpam-4798	175	2	38	38	NUM
ejpam-4798	175	3	:	:	PUNCT
ejpam-4798	175	4	boole[i	boole[i	PROPN
ejpam-4798	175	5	]	]	X
ejpam-4798	175	6	=	=	SYM
ejpam-4798	175	7	t	t	PROPN
ejpam-4798	175	8	39	39	NUM
ejpam-4798	175	9	:	:	PUNCT
ejpam-4798	175	10	boole[i	boole[i	PROPN
ejpam-4798	175	11	]	]	X
ejpam-4798	175	12	=	=	SYM
ejpam-4798	175	13	t	t	PROPN
ejpam-4798	175	14	40	40	NUM
ejpam-4798	175	15	:	:	PUNCT
ejpam-4798	175	16	no	no	PRON
ejpam-4798	175	17	-	-	PUNCT
ejpam-4798	175	18	found	find	VERB
ejpam-4798	175	19	=	=	NOUN
ejpam-4798	175	20	0	0	NUM
ejpam-4798	175	21	41	41	NUM
ejpam-4798	175	22	:	:	PUNCT
ejpam-4798	175	23	end	end	VERB
ejpam-4798	175	24	if	if	SCONJ
ejpam-4798	175	25	42	42	NUM
ejpam-4798	175	26	:	:	PUNCT
ejpam-4798	175	27	if	if	SCONJ
ejpam-4798	175	28	positive[i	positive[i	NOUN
ejpam-4798	175	29	]	]	X
ejpam-4798	175	30	=	=	PUNCT
ejpam-4798	175	31	=	=	SYM
ejpam-4798	175	32	positive[j	positive[j	X
ejpam-4798	175	33	]	]	PUNCT
ejpam-4798	175	34	2	2	NUM
ejpam-4798	175	35	&	&	CCONJ
ejpam-4798	175	36	&	&	CCONJ
ejpam-4798	175	37	negative[i	negative[i	PROPN
ejpam-4798	175	38	]	]	X
ejpam-4798	175	39	=	=	SYM
ejpam-4798	175	40	=	=	SYM
ejpam-4798	175	41	negative[j	negative[j	NOUN
ejpam-4798	175	42	]	]	X
ejpam-4798	175	43	2	2	NUM
ejpam-4798	175	44	&	&	CCONJ
ejpam-4798	175	45	&	&	CCONJ
ejpam-4798	175	46	boole[i	boole[i	PROPN
ejpam-4798	175	47	]	]	PUNCT
ejpam-4798	176	1	=	=	PUNCT
ejpam-4798	176	2	=	=	SYM
ejpam-4798	176	3	t	t	PROPN
ejpam-4798	176	4	then	then	ADV
ejpam-4798	176	5	43	43	NUM
ejpam-4798	176	6	:	:	PUNCT
ejpam-4798	176	7	assign	assign	VERB
ejpam-4798	176	8	:	:	PUNCT
ejpam-4798	176	9	vertex[i	vertex[i	NOUN
ejpam-4798	176	10	]	]	PUNCT
ejpam-4798	176	11	=	=	SYM
ejpam-4798	177	1	1	1	NUM
ejpam-4798	177	2	44	44	NUM
ejpam-4798	177	3	:	:	PUNCT
ejpam-4798	177	4	vertex[j	vertex[j	PROPN
ejpam-4798	177	5	]	]	PUNCT
ejpam-4798	177	6	=	=	SYM
ejpam-4798	177	7	2	2	NUM
ejpam-4798	177	8	45	45	NUM
ejpam-4798	177	9	:	:	PUNCT
ejpam-4798	177	10	boole[i	boole[i	PROPN
ejpam-4798	177	11	]	]	X
ejpam-4798	177	12	=	=	SYM
ejpam-4798	177	13	t	t	PROPN
ejpam-4798	177	14	46	46	NUM
ejpam-4798	177	15	:	:	PUNCT
ejpam-4798	177	16	boole[i	boole[i	PROPN
ejpam-4798	177	17	]	]	X
ejpam-4798	177	18	=	=	SYM
ejpam-4798	177	19	t	t	PROPN
ejpam-4798	177	20	47	47	NUM
ejpam-4798	177	21	:	:	PUNCT
ejpam-4798	177	22	no	no	PRON
ejpam-4798	177	23	-	-	PUNCT
ejpam-4798	177	24	found	find	VERB
ejpam-4798	177	25	=	=	NOUN
ejpam-4798	177	26	0	0	NUM
ejpam-4798	177	27	48	48	NUM
ejpam-4798	177	28	:	:	PUNCT
ejpam-4798	177	29	end	end	VERB
ejpam-4798	177	30	if	if	SCONJ
ejpam-4798	177	31	49	49	NUM
ejpam-4798	177	32	:	:	PUNCT
ejpam-4798	177	33	if	if	SCONJ
ejpam-4798	177	34	no	no	ADV
ejpam-4798	177	35	-	-	PUNCT
ejpam-4798	177	36	found	find	VERB
ejpam-4798	177	37	=	=	NOUN
ejpam-4798	177	38	=	=	SYM
ejpam-4798	177	39	0	0	NUM
ejpam-4798	177	40	then	then	ADV
ejpam-4798	177	41	50	50	NUM
ejpam-4798	177	42	:	:	PUNCT
ejpam-4798	177	43	assign	assign	VERB
ejpam-4798	177	44	:	:	PUNCT
ejpam-4798	177	45	j	j	PROPN
ejpam-4798	177	46	=	=	PROPN
ejpam-4798	177	47	n	n	PROPN
ejpam-4798	177	48	51	51	NUM
ejpam-4798	177	49	:	:	PUNCT
ejpam-4798	177	50	if	if	SCONJ
ejpam-4798	177	51	no	no	ADV
ejpam-4798	177	52	-	-	PUNCT
ejpam-4798	177	53	found	find	VERB
ejpam-4798	177	54	=	=	NOUN
ejpam-4798	177	55	=	=	SYM
ejpam-4798	177	56	0	0	NUM
ejpam-4798	177	57	then	then	ADV
ejpam-4798	177	58	52	52	NUM
ejpam-4798	177	59	:	:	PUNCT
ejpam-4798	177	60	print	print	NOUN
ejpam-4798	177	61	:	:	PUNCT
ejpam-4798	177	62	splitting	splitting	NOUN
ejpam-4798	177	63	graph	graph	NOUN
ejpam-4798	177	64	is	be	AUX
ejpam-4798	177	65	not	not	PART
ejpam-4798	177	66	possible	possible	ADJ
ejpam-4798	177	67	as	as	SCONJ
ejpam-4798	177	68	vertex	vertex	NOUN
ejpam-4798	177	69	division	division	NOUN
ejpam-4798	177	70	is	be	AUX
ejpam-4798	177	71	not	not	PART
ejpam-4798	177	72	proper	proper	ADJ
ejpam-4798	177	73	and	and	CCONJ
ejpam-4798	177	74	terminate	terminate	VERB
ejpam-4798	177	75	53	53	NUM
ejpam-4798	177	76	:	:	PUNCT
ejpam-4798	177	77	end	end	VERB
ejpam-4798	177	78	if	if	SCONJ
ejpam-4798	177	79	54	54	NUM
ejpam-4798	177	80	:	:	PUNCT
ejpam-4798	177	81	end	end	VERB
ejpam-4798	177	82	if	if	SCONJ
ejpam-4798	177	83	55	55	NUM
ejpam-4798	177	84	:	:	PUNCT
ejpam-4798	177	85	for	for	ADP
ejpam-4798	177	86	i	i	PRON
ejpam-4798	177	87	=	=	NOUN
ejpam-4798	177	88	1	1	NUM
ejpam-4798	177	89	:	:	PUNCT
ejpam-4798	177	90	n	n	PRON
ejpam-4798	177	91	do	do	VERB
ejpam-4798	177	92	56	56	NUM
ejpam-4798	177	93	:	:	PUNCT
ejpam-4798	177	94	if	if	SCONJ
ejpam-4798	177	95	vertex[i	vertex[i	VERB
ejpam-4798	177	96	]	]	X
ejpam-4798	178	1	=	=	SYM
ejpam-4798	178	2	=	=	SYM
ejpam-4798	178	3	2	2	NUM
ejpam-4798	178	4	then	then	ADV
ejpam-4798	178	5	57	57	NUM
ejpam-4798	178	6	:	:	PUNCT
ejpam-4798	178	7	assign	assign	VERB
ejpam-4798	178	8	:	:	PUNCT
ejpam-4798	178	9	arrayhigh[o1	arrayhigh[o1	PROPN
ejpam-4798	178	10	]	]	X
ejpam-4798	178	11	=	=	PUNCT
ejpam-4798	178	12	i	i	PRON
ejpam-4798	178	13	58	58	NUM
ejpam-4798	178	14	:	:	PUNCT
ejpam-4798	178	15	count	count	NOUN
ejpam-4798	178	16	o1	o1	NOUN
ejpam-4798	178	17	=	=	SYM
ejpam-4798	178	18	o1	o1	NOUN
ejpam-4798	178	19	+	+	ADP
ejpam-4798	178	20	1	1	NUM
ejpam-4798	178	21	59	59	NUM
ejpam-4798	178	22	:	:	PUNCT
ejpam-4798	178	23	else	else	ADV
ejpam-4798	178	24	60	60	NUM
ejpam-4798	178	25	:	:	PUNCT
ejpam-4798	178	26	if	if	SCONJ
ejpam-4798	178	27	vertex[i	vertex[i	VERB
ejpam-4798	178	28	]	]	X
ejpam-4798	179	1	=	=	SYM
ejpam-4798	179	2	=	=	SYM
ejpam-4798	179	3	1	1	NUM
ejpam-4798	179	4	then	then	ADV
ejpam-4798	179	5	61	61	NUM
ejpam-4798	179	6	:	:	PUNCT
ejpam-4798	179	7	assign	assign	VERB
ejpam-4798	179	8	:	:	PUNCT
ejpam-4798	179	9	arrayhigh[o2	arrayhigh[o2	PROPN
ejpam-4798	179	10	]	]	X
ejpam-4798	180	1	=	=	PUNCT
ejpam-4798	180	2	i	i	PRON
ejpam-4798	180	3	62	62	NUM
ejpam-4798	180	4	:	:	PUNCT
ejpam-4798	180	5	count	count	VERB
ejpam-4798	180	6	o2	o2	PROPN
ejpam-4798	180	7	=	=	SYM
ejpam-4798	180	8	o2	o2	PROPN
ejpam-4798	180	9	+	+	PROPN
ejpam-4798	180	10	1	1	NUM
ejpam-4798	180	11	63	63	NUM
ejpam-4798	180	12	:	:	PUNCT
ejpam-4798	180	13	end	end	VERB
ejpam-4798	180	14	if	if	SCONJ
ejpam-4798	180	15	64	64	NUM
ejpam-4798	180	16	:	:	PUNCT
ejpam-4798	180	17	end	end	VERB
ejpam-4798	180	18	if	if	SCONJ
ejpam-4798	180	19	65	65	NUM
ejpam-4798	180	20	:	:	PUNCT
ejpam-4798	180	21	end	end	VERB
ejpam-4798	180	22	for	for	ADP
ejpam-4798	180	23	66	66	NUM
ejpam-4798	180	24	:	:	PUNCT
ejpam-4798	180	25	end	end	VERB
ejpam-4798	180	26	if	if	SCONJ
ejpam-4798	180	27	67	67	NUM
ejpam-4798	180	28	:	:	PUNCT
ejpam-4798	180	29	assign	assign	VERB
ejpam-4798	180	30	:	:	PUNCT
ejpam-4798	181	1	j	j	PROPN
ejpam-4798	181	2	=	=	SYM
ejpam-4798	181	3	1	1	NUM
ejpam-4798	181	4	68	68	NUM
ejpam-4798	181	5	:	:	PUNCT
ejpam-4798	181	6	for	for	ADP
ejpam-4798	181	7	i	i	PRON
ejpam-4798	181	8	=	=	NOUN
ejpam-4798	181	9	1	1	NUM
ejpam-4798	181	10	:	:	PUNCT
ejpam-4798	181	11	n	n	PRON
ejpam-4798	181	12	2	2	NUM
ejpam-4798	181	13	do	do	AUX
ejpam-4798	181	14	69	69	NUM
ejpam-4798	181	15	:	:	PUNCT
ejpam-4798	181	16	assign	assign	VERB
ejpam-4798	181	17	:	:	PUNCT
ejpam-4798	181	18	val	val	NOUN
ejpam-4798	182	1	=	=	PUNCT
ejpam-4798	183	1	arrayhigh[i	arrayhigh[i	PROPN
ejpam-4798	183	2	]	]	PUNCT
ejpam-4798	184	1	70	70	NUM
ejpam-4798	184	2	:	:	PUNCT
ejpam-4798	184	3	if	if	SCONJ
ejpam-4798	184	4	val	val	PROPN
ejpam-4798	184	5	>	>	X
ejpam-4798	184	6	n	n	CCONJ
ejpam-4798	184	7	2	2	NUM
ejpam-4798	184	8	then	then	ADV
ejpam-4798	184	9	71	71	NUM
ejpam-4798	184	10	:	:	PUNCT
ejpam-4798	184	11	assign	assign	VERB
ejpam-4798	184	12	:	:	PUNCT
ejpam-4798	184	13	val	val	ADJ
ejpam-4798	184	14	-	-	PUNCT
ejpam-4798	184	15	low	low	NOUN
ejpam-4798	184	16	=	=	SYM
ejpam-4798	184	17	arraylow[j	arraylow[j	NOUN
ejpam-4798	184	18	]	]	X
ejpam-4798	184	19	72	72	NUM
ejpam-4798	184	20	:	:	PUNCT
ejpam-4798	184	21	if	if	SCONJ
ejpam-4798	184	22	val	val	ADJ
ejpam-4798	184	23	−	−	PROPN
ejpam-4798	184	24	low	low	ADJ
ejpam-4798	184	25	≤	≤	NOUN
ejpam-4798	184	26	n	n	PRON
ejpam-4798	184	27	2	2	NUM
ejpam-4798	184	28	then	then	ADV
ejpam-4798	184	29	73	73	NUM
ejpam-4798	184	30	:	:	PUNCT
ejpam-4798	184	31	apply	apply	VERB
ejpam-4798	184	32	row	row	NOUN
ejpam-4798	184	33	transformation	transformation	NOUN
ejpam-4798	184	34	74	74	NUM
ejpam-4798	184	35	:	:	PUNCT
ejpam-4798	184	36	end	end	VERB
ejpam-4798	184	37	if	if	SCONJ
ejpam-4798	184	38	75	75	NUM
ejpam-4798	184	39	:	:	PUNCT
ejpam-4798	184	40	end	end	VERB
ejpam-4798	184	41	if	if	SCONJ
ejpam-4798	184	42	76	76	NUM
ejpam-4798	184	43	:	:	PUNCT
ejpam-4798	184	44	end	end	VERB
ejpam-4798	184	45	for	for	ADP
ejpam-4798	184	46	77	77	NUM
ejpam-4798	184	47	:	:	PUNCT
ejpam-4798	184	48	assign	assign	VERB
ejpam-4798	184	49	:	:	PUNCT
ejpam-4798	185	1	j	j	X
ejpam-4798	185	2	=	=	SYM
ejpam-4798	186	1	j+1	j+1	ADJ
ejpam-4798	186	2	78	78	NUM
ejpam-4798	186	3	:	:	PUNCT
ejpam-4798	186	4	for	for	ADP
ejpam-4798	186	5	i	i	PRON
ejpam-4798	186	6	=	=	NOUN
ejpam-4798	186	7	1	1	NUM
ejpam-4798	186	8	:	:	SYM
ejpam-4798	186	9	2n	2n	NUM
ejpam-4798	186	10	do	do	VERB
ejpam-4798	186	11	79	79	NUM
ejpam-4798	186	12	:	:	PUNCT
ejpam-4798	186	13	for	for	ADP
ejpam-4798	186	14	j	j	PROPN
ejpam-4798	186	15	=	=	SYM
ejpam-4798	186	16	1	1	NUM
ejpam-4798	186	17	:	:	SYM
ejpam-4798	186	18	2n	2n	NUM
ejpam-4798	186	19	do	do	AUX
ejpam-4798	186	20	s.	s.	PROPN
ejpam-4798	186	21	kumar	kumar	PROPN
ejpam-4798	186	22	,	,	PUNCT
ejpam-4798	186	23	d.	d.	PROPN
ejpam-4798	186	24	sinha	sinha	PROPN
ejpam-4798	186	25	/	/	SYM
ejpam-4798	186	26	eur	eur	PROPN
ejpam-4798	186	27	.	.	PUNCT
ejpam-4798	187	1	j.	j.	PROPN
ejpam-4798	187	2	pure	pure	PROPN
ejpam-4798	187	3	appl	appl	PROPN
ejpam-4798	187	4	.	.	PROPN
ejpam-4798	187	5	math	math	PROPN
ejpam-4798	187	6	,	,	PUNCT
ejpam-4798	187	7	17	17	NUM
ejpam-4798	187	8	(	(	PUNCT
ejpam-4798	187	9	1	1	NUM
ejpam-4798	187	10	)	)	PUNCT
ejpam-4798	187	11	(	(	PUNCT
ejpam-4798	187	12	2024	2024	NUM
ejpam-4798	187	13	)	)	PUNCT
ejpam-4798	187	14	,	,	PUNCT
ejpam-4798	187	15	504	504	NUM
ejpam-4798	187	16	-	-	SYM
ejpam-4798	187	17	518	518	NUM
ejpam-4798	187	18	514	514	NUM
ejpam-4798	187	19	80	80	NUM
ejpam-4798	187	20	:	:	PUNCT
ejpam-4798	187	21	assign	assign	VERB
ejpam-4798	187	22	:	:	PUNCT
ejpam-4798	187	23	b(i	b(i	NOUN
ejpam-4798	187	24	,	,	PUNCT
ejpam-4798	187	25	j	j	NOUN
ejpam-4798	187	26	)	)	PUNCT
ejpam-4798	187	27	=	=	PUNCT
ejpam-4798	187	28	a(i	a(i	PROPN
ejpam-4798	187	29	,	,	PUNCT
ejpam-4798	187	30	j	j	NOUN
ejpam-4798	187	31	)	)	PUNCT
ejpam-4798	187	32	81	81	NUM
ejpam-4798	187	33	:	:	PUNCT
ejpam-4798	187	34	divide	divide	VERB
ejpam-4798	187	35	the	the	DET
ejpam-4798	187	36	matrix	matrix	NOUN
ejpam-4798	187	37	into	into	ADP
ejpam-4798	187	38	four	four	NUM
ejpam-4798	187	39	equal	equal	ADJ
ejpam-4798	187	40	blocks	block	NOUN
ejpam-4798	187	41	82	82	NUM
ejpam-4798	187	42	:	:	PUNCT
ejpam-4798	187	43	set	set	NOUN
ejpam-4798	187	44	:	:	PUNCT
ejpam-4798	187	45	val	val	ADJ
ejpam-4798	187	46	-	-	PUNCT
ejpam-4798	187	47	ret	ret	NOUN
ejpam-4798	187	48	=	=	PUNCT
ejpam-4798	187	49	above	above	ADP
ejpam-4798	187	50	divided	divided	ADJ
ejpam-4798	187	51	matrix	matrix	NOUN
ejpam-4798	187	52	83	83	NUM
ejpam-4798	187	53	:	:	PUNCT
ejpam-4798	187	54	if	if	SCONJ
ejpam-4798	187	55	val	val	ADJ
ejpam-4798	187	56	-	-	PUNCT
ejpam-4798	187	57	ret	ret	NOUN
ejpam-4798	187	58	=	=	NOUN
ejpam-4798	187	59	=	=	SYM
ejpam-4798	187	60	0	0	NUM
ejpam-4798	187	61	then	then	ADV
ejpam-4798	187	62	84	84	NUM
ejpam-4798	187	63	:	:	PUNCT
ejpam-4798	187	64	assign	assign	VERB
ejpam-4798	187	65	:	:	PUNCT
ejpam-4798	187	66	j	j	X
ejpam-4798	187	67	=	=	VERB
ejpam-4798	187	68	n+1	n+1	PROPN
ejpam-4798	187	69	and	and	CCONJ
ejpam-4798	187	70	terminate	terminate	VERB
ejpam-4798	187	71	85	85	NUM
ejpam-4798	187	72	:	:	PUNCT
ejpam-4798	187	73	else	else	ADV
ejpam-4798	187	74	86	86	NUM
ejpam-4798	187	75	:	:	PUNCT
ejpam-4798	187	76	assign	assign	VERB
ejpam-4798	187	77	:	:	PUNCT
ejpam-4798	187	78	a(i	a(i	VERB
ejpam-4798	187	79	,	,	PUNCT
ejpam-4798	187	80	j	j	NOUN
ejpam-4798	187	81	)	)	PUNCT
ejpam-4798	187	82	=	=	PUNCT
ejpam-4798	188	1	b(i	b(i	PROPN
ejpam-4798	188	2	,	,	PUNCT
ejpam-4798	188	3	j	j	NOUN
ejpam-4798	188	4	)	)	PUNCT
ejpam-4798	188	5	87	87	NUM
ejpam-4798	188	6	:	:	PUNCT
ejpam-4798	188	7	end	end	VERB
ejpam-4798	188	8	if	if	SCONJ
ejpam-4798	188	9	88	88	NUM
ejpam-4798	188	10	:	:	PUNCT
ejpam-4798	188	11	end	end	VERB
ejpam-4798	188	12	for	for	ADP
ejpam-4798	188	13	89	89	NUM
ejpam-4798	188	14	:	:	PUNCT
ejpam-4798	188	15	end	end	VERB
ejpam-4798	188	16	for	for	ADP
ejpam-4798	188	17	90	90	NUM
ejpam-4798	188	18	:	:	PUNCT
ejpam-4798	188	19	end	end	VERB
ejpam-4798	188	20	for	for	ADP
ejpam-4798	188	21	91	91	NUM
ejpam-4798	188	22	:	:	PUNCT
ejpam-4798	188	23	end	end	VERB
ejpam-4798	188	24	for	for	ADP
ejpam-4798	188	25	92	92	NUM
ejpam-4798	188	26	:	:	PUNCT
ejpam-4798	188	27	output	output	NOUN
ejpam-4798	188	28	:	:	PUNCT
ejpam-4798	188	29	generate	generate	VERB
ejpam-4798	188	30	[	[	X
ejpam-4798	188	31	ai	ai	NOUN
ejpam-4798	188	32	,	,	PUNCT
ejpam-4798	188	33	j	j	NOUN
ejpam-4798	188	34	]	]	X
ejpam-4798	188	35	matrix	matrix	NOUN
ejpam-4798	188	36	of	of	ADP
ejpam-4798	188	37	order	order	NOUN
ejpam-4798	188	38	n	n	DET
ejpam-4798	188	39	2	2	NUM
ejpam-4798	188	40	computational	computational	ADJ
ejpam-4798	188	41	complexity	complexity	NOUN
ejpam-4798	188	42	:	:	PUNCT
ejpam-4798	188	43	the	the	DET
ejpam-4798	188	44	algorithm	algorithm	NOUN
ejpam-4798	188	45	calculates	calculate	VERB
ejpam-4798	188	46	the	the	DET
ejpam-4798	188	47	total	total	ADJ
ejpam-4798	188	48	number	number	NOUN
ejpam-4798	188	49	of	of	ADP
ejpam-4798	188	50	positive	positive	ADJ
ejpam-4798	188	51	and	and	CCONJ
ejpam-4798	188	52	negative	negative	ADJ
ejpam-4798	188	53	edges	edge	NOUN
ejpam-4798	188	54	and	and	CCONJ
ejpam-4798	188	55	traverses	traverse	NOUN
ejpam-4798	188	56	every	every	DET
ejpam-4798	188	57	entry	entry	NOUN
ejpam-4798	188	58	of	of	ADP
ejpam-4798	188	59	the	the	DET
ejpam-4798	188	60	matrix	matrix	NOUN
ejpam-4798	188	61	.	.	PUNCT
ejpam-4798	189	1	as	as	ADP
ejpam-4798	189	2	a	a	DET
ejpam-4798	189	3	result	result	NOUN
ejpam-4798	189	4	,	,	PUNCT
ejpam-4798	189	5	the	the	DET
ejpam-4798	189	6	complexity	complexity	NOUN
ejpam-4798	189	7	to	to	PART
ejpam-4798	189	8	count	count	VERB
ejpam-4798	189	9	the	the	DET
ejpam-4798	189	10	edges	edge	NOUN
ejpam-4798	189	11	is	be	AUX
ejpam-4798	189	12	o(n2	o(n2	ADJ
ejpam-4798	189	13	)	)	PUNCT
ejpam-4798	189	14	.	.	PUNCT
ejpam-4798	190	1	in	in	ADP
ejpam-4798	190	2	steps	step	NOUN
ejpam-4798	190	3	30	30	NUM
ejpam-4798	190	4	to	to	ADP
ejpam-4798	190	5	52	52	NUM
ejpam-4798	190	6	,	,	PUNCT
ejpam-4798	190	7	the	the	DET
ejpam-4798	190	8	vertex	vertex	NOUN
ejpam-4798	190	9	set	set	NOUN
ejpam-4798	190	10	is	be	AUX
ejpam-4798	190	11	partitioned	partition	VERB
ejpam-4798	190	12	into	into	ADP
ejpam-4798	190	13	two	two	NUM
ejpam-4798	190	14	sets	set	NOUN
ejpam-4798	190	15	such	such	ADJ
ejpam-4798	190	16	that	that	DET
ejpam-4798	190	17	number	number	NOUN
ejpam-4798	190	18	of	of	ADP
ejpam-4798	190	19	positive	positive	ADJ
ejpam-4798	190	20	and	and	CCONJ
ejpam-4798	190	21	negative	negative	ADJ
ejpam-4798	190	22	edges	edge	NOUN
ejpam-4798	190	23	in	in	ADP
ejpam-4798	190	24	one	one	NUM
ejpam-4798	190	25	set	set	NOUN
ejpam-4798	190	26	is	be	AUX
ejpam-4798	190	27	exactly	exactly	ADV
ejpam-4798	190	28	double	double	ADJ
ejpam-4798	190	29	of	of	ADP
ejpam-4798	190	30	the	the	DET
ejpam-4798	190	31	other	other	ADJ
ejpam-4798	190	32	.	.	PUNCT
ejpam-4798	191	1	as	as	ADP
ejpam-4798	191	2	a	a	DET
ejpam-4798	191	3	result	result	NOUN
ejpam-4798	191	4	,	,	PUNCT
ejpam-4798	191	5	the	the	DET
ejpam-4798	191	6	complexity	complexity	NOUN
ejpam-4798	191	7	is	be	AUX
ejpam-4798	191	8	o(n2	o(n2	ADJ
ejpam-4798	191	9	)	)	PUNCT
ejpam-4798	191	10	.	.	PUNCT
ejpam-4798	192	1	if	if	SCONJ
ejpam-4798	192	2	the	the	DET
ejpam-4798	192	3	function	function	NOUN
ejpam-4798	192	4	is	be	AUX
ejpam-4798	192	5	denoted	denote	VERB
ejpam-4798	192	6	by	by	ADP
ejpam-4798	192	7	fun	fun	NOUN
ejpam-4798	192	8	then	then	ADV
ejpam-4798	192	9	the	the	DET
ejpam-4798	192	10	complexity	complexity	NOUN
ejpam-4798	192	11	required	require	VERB
ejpam-4798	192	12	for	for	ADP
ejpam-4798	192	13	the	the	DET
ejpam-4798	192	14	row	row	NOUN
ejpam-4798	192	15	and	and	CCONJ
ejpam-4798	192	16	column	column	NOUN
ejpam-4798	192	17	transformations	transformation	NOUN
ejpam-4798	192	18	from	from	ADP
ejpam-4798	192	19	step	step	NOUN
ejpam-4798	192	20	67	67	NUM
ejpam-4798	192	21	to	to	PART
ejpam-4798	192	22	step	step	VERB
ejpam-4798	192	23	77	77	NUM
ejpam-4798	192	24	to	to	PART
ejpam-4798	192	25	make	make	VERB
ejpam-4798	192	26	all	all	DET
ejpam-4798	192	27	the	the	DET
ejpam-4798	192	28	three	three	NUM
ejpam-4798	192	29	matrices	matrix	NOUN
ejpam-4798	192	30	identical	identical	ADJ
ejpam-4798	192	31	is	be	AUX
ejpam-4798	192	32	o(n3	o(n3	NOUN
ejpam-4798	192	33	)	)	PUNCT
ejpam-4798	192	34	.	.	PUNCT
ejpam-4798	193	1	if	if	SCONJ
ejpam-4798	193	2	the	the	DET
ejpam-4798	193	3	fourth	fourth	ADJ
ejpam-4798	193	4	submatrix	submatrix	NOUN
ejpam-4798	193	5	is	be	AUX
ejpam-4798	193	6	already	already	ADV
ejpam-4798	193	7	zero	zero	NUM
ejpam-4798	193	8	in	in	ADP
ejpam-4798	193	9	the	the	DET
ejpam-4798	193	10	steps	step	NOUN
ejpam-4798	193	11	78	78	NUM
ejpam-4798	193	12	to	to	PART
ejpam-4798	193	13	91	91	NUM
ejpam-4798	193	14	then	then	ADV
ejpam-4798	193	15	we	we	PRON
ejpam-4798	193	16	apply	apply	VERB
ejpam-4798	193	17	row	row	NOUN
ejpam-4798	193	18	operation	operation	NOUN
ejpam-4798	193	19	to	to	PART
ejpam-4798	193	20	make	make	VERB
ejpam-4798	193	21	all	all	DET
ejpam-4798	193	22	other	other	ADJ
ejpam-4798	193	23	sub	sub	NOUN
ejpam-4798	193	24	matrices	matrix	NOUN
ejpam-4798	193	25	identical	identical	ADJ
ejpam-4798	193	26	.	.	PUNCT
ejpam-4798	194	1	we	we	PRON
ejpam-4798	194	2	traverse	traverse	VERB
ejpam-4798	194	3	each	each	DET
ejpam-4798	194	4	vertex	vertex	NOUN
ejpam-4798	194	5	of	of	ADP
ejpam-4798	194	6	the	the	DET
ejpam-4798	194	7	signed	sign	VERB
ejpam-4798	194	8	graph	graph	NOUN
ejpam-4798	194	9	and	and	CCONJ
ejpam-4798	194	10	examine	examine	VERB
ejpam-4798	194	11	every	every	DET
ejpam-4798	194	12	entry	entry	NOUN
ejpam-4798	194	13	if	if	SCONJ
ejpam-4798	194	14	it	it	PRON
ejpam-4798	194	15	is	be	AUX
ejpam-4798	194	16	identical	identical	ADJ
ejpam-4798	194	17	.	.	PUNCT
ejpam-4798	195	1	as	as	ADP
ejpam-4798	195	2	a	a	DET
ejpam-4798	195	3	result	result	NOUN
ejpam-4798	195	4	,	,	PUNCT
ejpam-4798	195	5	the	the	DET
ejpam-4798	195	6	complexity	complexity	NOUN
ejpam-4798	195	7	involved	involve	VERB
ejpam-4798	195	8	in	in	ADP
ejpam-4798	195	9	these	these	DET
ejpam-4798	195	10	steps	step	NOUN
ejpam-4798	195	11	is	be	AUX
ejpam-4798	195	12	o(n2×n×n	o(n2×n×n	NOUN
ejpam-4798	195	13	)	)	PUNCT
ejpam-4798	195	14	=	=	SYM
ejpam-4798	195	15	o(n4	o(n4	NOUN
ejpam-4798	195	16	)	)	PUNCT
ejpam-4798	195	17	.	.	PUNCT
ejpam-4798	196	1	therefore	therefore	ADV
ejpam-4798	196	2	,	,	PUNCT
ejpam-4798	196	3	the	the	DET
ejpam-4798	196	4	complexity	complexity	NOUN
ejpam-4798	196	5	of	of	ADP
ejpam-4798	196	6	the	the	DET
ejpam-4798	196	7	proposed	propose	VERB
ejpam-4798	196	8	algorithm	algorithm	NOUN
ejpam-4798	196	9	for	for	ADP
ejpam-4798	196	10	finding	find	VERB
ejpam-4798	196	11	a	a	DET
ejpam-4798	196	12	root	root	NOUN
ejpam-4798	196	13	signed	sign	VERB
ejpam-4798	196	14	split	split	NOUN
ejpam-4798	196	15	graph	graph	NOUN
ejpam-4798	196	16	with	with	ADP
ejpam-4798	196	17	a	a	DET
ejpam-4798	196	18	given	give	VERB
ejpam-4798	196	19	adjacency	adjacency	NOUN
ejpam-4798	196	20	matrix	matrix	NOUN
ejpam-4798	196	21	is	be	AUX
ejpam-4798	196	22	o(n2)+o(n3)+o(n4)+o(n2	o(n2)+o(n3)+o(n4)+o(n2	ADJ
ejpam-4798	196	23	)	)	PUNCT
ejpam-4798	196	24	=	=	SYM
ejpam-4798	196	25	o(n4	o(n4	NOUN
ejpam-4798	196	26	)	)	PUNCT
ejpam-4798	196	27	.	.	PUNCT
ejpam-4798	197	1	,	,	PUNCT
ejpam-4798	197	2	where	where	SCONJ
ejpam-4798	197	3	n	n	PRON
ejpam-4798	197	4	represents	represent	VERB
ejpam-4798	197	5	the	the	DET
ejpam-4798	197	6	number	number	NOUN
ejpam-4798	197	7	of	of	ADP
ejpam-4798	197	8	vertices	vertex	NOUN
ejpam-4798	197	9	in	in	ADP
ejpam-4798	197	10	the	the	DET
ejpam-4798	197	11	signed	sign	VERB
ejpam-4798	197	12	graph	graph	NOUN
ejpam-4798	197	13	.	.	PUNCT
ejpam-4798	198	1	4	4	X
ejpam-4798	198	2	.	.	X
ejpam-4798	198	3	spectrum	spectrum	NOUN
ejpam-4798	198	4	of	of	ADP
ejpam-4798	198	5	splitting	splitting	NOUN
ejpam-4798	198	6	signed	sign	VERB
ejpam-4798	198	7	graph	graph	NOUN
ejpam-4798	198	8	in	in	ADP
ejpam-4798	198	9	this	this	DET
ejpam-4798	198	10	section	section	NOUN
ejpam-4798	198	11	,	,	PUNCT
ejpam-4798	198	12	we	we	PRON
ejpam-4798	198	13	aim	aim	VERB
ejpam-4798	198	14	to	to	PART
ejpam-4798	198	15	find	find	VERB
ejpam-4798	198	16	out	out	ADP
ejpam-4798	198	17	the	the	DET
ejpam-4798	198	18	spectrum	spectrum	NOUN
ejpam-4798	198	19	of	of	ADP
ejpam-4798	198	20	the	the	DET
ejpam-4798	198	21	adjacency	adjacency	NOUN
ejpam-4798	198	22	matrix	matrix	NOUN
ejpam-4798	198	23	and	and	CCONJ
ejpam-4798	198	24	laplacian	laplacian	ADJ
ejpam-4798	198	25	matrix	matrix	NOUN
ejpam-4798	198	26	of	of	ADP
ejpam-4798	198	27	a	a	DET
ejpam-4798	198	28	splitting	splitting	NOUN
ejpam-4798	198	29	signed	sign	VERB
ejpam-4798	198	30	graph	graph	NOUN
ejpam-4798	198	31	γ(σ	γ(σ	PROPN
ejpam-4798	198	32	)	)	PUNCT
ejpam-4798	198	33	.	.	PUNCT
ejpam-4798	199	1	let	let	VERB
ejpam-4798	199	2	a(σ	a(σ	PROPN
ejpam-4798	199	3	)	)	PUNCT
ejpam-4798	199	4	be	be	VERB
ejpam-4798	199	5	the	the	DET
ejpam-4798	199	6	adjacency	adjacency	NOUN
ejpam-4798	199	7	matrix	matrix	NOUN
ejpam-4798	199	8	of	of	ADP
ejpam-4798	199	9	the	the	DET
ejpam-4798	199	10	signed	sign	VERB
ejpam-4798	199	11	graph	graph	NOUN
ejpam-4798	199	12	σ	σ	NOUN
ejpam-4798	199	13	on	on	ADP
ejpam-4798	199	14	n	n	DET
ejpam-4798	199	15	vertices	vertex	NOUN
ejpam-4798	199	16	,	,	PUNCT
ejpam-4798	199	17	and	and	CCONJ
ejpam-4798	199	18	is	be	AUX
ejpam-4798	199	19	given	give	VERB
ejpam-4798	199	20	as	as	ADP
ejpam-4798	199	21	follow	follow	VERB
ejpam-4798	199	22	a(σ	a(σ	NOUN
ejpam-4798	199	23	)	)	PUNCT
ejpam-4798	200	1	=	=	PUNCT
ejpam-4798	200	2			NOUN
ejpam-4798	200	3	0	0	PUNCT
ejpam-4798	200	4	a1,2	a1,2	PROPN
ejpam-4798	200	5	·	·	PUNCT
ejpam-4798	200	6	·	·	PUNCT
ejpam-4798	200	7	·	·	PUNCT
ejpam-4798	201	1	a1,n	a1,n	PROPN
ejpam-4798	201	2	a2,1	a2,1	PROPN
ejpam-4798	201	3	0	0	NUM
ejpam-4798	201	4	·	·	PUNCT
ejpam-4798	201	5	·	·	PUNCT
ejpam-4798	201	6	·	·	PUNCT
ejpam-4798	202	1	a2,n	a2,n	ADV
ejpam-4798	202	2	...	...	PUNCT
ejpam-4798	202	3	...	...	PUNCT
ejpam-4798	202	4	.	.	PUNCT
ejpam-4798	202	5	.	.	PUNCT
ejpam-4798	202	6	.	.	PUNCT
ejpam-4798	203	1	...	...	PUNCT
ejpam-4798	204	1	an,1	an,1	PROPN
ejpam-4798	204	2	an,2	an,2	PROPN
ejpam-4798	204	3	·	·	PUNCT
ejpam-4798	204	4	·	·	PUNCT
ejpam-4798	204	5	·	·	PUNCT
ejpam-4798	204	6	0	0	NUM
ejpam-4798	204	7			ADJ
ejpam-4798	204	8	let	let	VERB
ejpam-4798	204	9	v′i	v′i	ADV
ejpam-4798	204	10	be	be	AUX
ejpam-4798	204	11	the	the	DET
ejpam-4798	204	12	vertex	vertex	NOUN
ejpam-4798	204	13	corresponding	correspond	VERB
ejpam-4798	204	14	to	to	ADP
ejpam-4798	204	15	vi	vi	PROPN
ejpam-4798	204	16	,	,	PUNCT
ejpam-4798	204	17	1	1	NUM
ejpam-4798	204	18	≤	≤	NUM
ejpam-4798	204	19	i	i	PRON
ejpam-4798	204	20	≤	≤	PROPN
ejpam-4798	204	21	n	n	CCONJ
ejpam-4798	204	22	,	,	PUNCT
ejpam-4798	204	23	which	which	PRON
ejpam-4798	204	24	is	be	AUX
ejpam-4798	204	25	added	add	VERB
ejpam-4798	204	26	in	in	ADP
ejpam-4798	204	27	σ	σ	PROPN
ejpam-4798	204	28	to	to	PART
ejpam-4798	204	29	construct	construct	VERB
ejpam-4798	204	30	γ(σ	γ(σ	NOUN
ejpam-4798	204	31	)	)	PUNCT
ejpam-4798	204	32	,	,	PUNCT
ejpam-4798	204	33	such	such	ADJ
ejpam-4798	204	34	that	that	SCONJ
ejpam-4798	204	35	n(v′i	n(v′i	ADJ
ejpam-4798	204	36	)	)	PUNCT
ejpam-4798	204	37	=	=	SYM
ejpam-4798	204	38	n(vi	n(vi	NUM
ejpam-4798	204	39	)	)	PUNCT
ejpam-4798	204	40	,	,	PUNCT
ejpam-4798	204	41	for	for	ADP
ejpam-4798	204	42	1	1	NUM
ejpam-4798	204	43	≤	≤	NUM
ejpam-4798	204	44	i	i	PRON
ejpam-4798	204	45	≤	≤	PROPN
ejpam-4798	205	1	n.	n.	NOUN
ejpam-4798	205	2	then	then	ADV
ejpam-4798	205	3	the	the	DET
ejpam-4798	205	4	adjacency	adjacency	NOUN
ejpam-4798	205	5	matrix	matrix	NOUN
ejpam-4798	205	6	of	of	ADP
ejpam-4798	205	7	γ(σ	γ(σ	PROPN
ejpam-4798	205	8	)	)	PUNCT
ejpam-4798	205	9	,	,	PUNCT
ejpam-4798	205	10	a(γ(σ	a(γ(σ	PROPN
ejpam-4798	205	11	)	)	PUNCT
ejpam-4798	205	12	)	)	PUNCT
ejpam-4798	205	13	,	,	PUNCT
ejpam-4798	205	14	s.	s.	PROPN
ejpam-4798	205	15	kumar	kumar	PROPN
ejpam-4798	205	16	,	,	PUNCT
ejpam-4798	205	17	d.	d.	PROPN
ejpam-4798	205	18	sinha	sinha	PROPN
ejpam-4798	205	19	/	/	SYM
ejpam-4798	205	20	eur	eur	PROPN
ejpam-4798	205	21	.	.	PUNCT
ejpam-4798	206	1	j.	j.	PROPN
ejpam-4798	206	2	pure	pure	PROPN
ejpam-4798	206	3	appl	appl	PROPN
ejpam-4798	206	4	.	.	PROPN
ejpam-4798	206	5	math	math	PROPN
ejpam-4798	206	6	,	,	PUNCT
ejpam-4798	206	7	17	17	NUM
ejpam-4798	206	8	(	(	PUNCT
ejpam-4798	206	9	1	1	NUM
ejpam-4798	206	10	)	)	PUNCT
ejpam-4798	206	11	(	(	PUNCT
ejpam-4798	206	12	2024	2024	NUM
ejpam-4798	206	13	)	)	PUNCT
ejpam-4798	206	14	,	,	PUNCT
ejpam-4798	206	15	504	504	NUM
ejpam-4798	206	16	-	-	SYM
ejpam-4798	206	17	518	518	NUM
ejpam-4798	206	18	515	515	NUM
ejpam-4798	206	19	can	can	AUX
ejpam-4798	206	20	be	be	AUX
ejpam-4798	206	21	expressed	express	VERB
ejpam-4798	206	22	as	as	ADP
ejpam-4798	206	23	a	a	DET
ejpam-4798	206	24	block	block	NOUN
ejpam-4798	206	25	matrix	matrix	NOUN
ejpam-4798	206	26	with	with	ADP
ejpam-4798	206	27	blocks	block	NOUN
ejpam-4798	206	28	as	as	SCONJ
ejpam-4798	206	29	follows	follow	VERB
ejpam-4798	206	30	a(γ(σ	a(γ(σ	NOUN
ejpam-4798	206	31	)	)	PUNCT
ejpam-4798	206	32	)	)	PUNCT
ejpam-4798	207	1	=	=	SYM
ejpam-4798	207	2			ADJ
ejpam-4798	207	3	0	0	PROPN
ejpam-4798	207	4	a1,2	a1,2	PROPN
ejpam-4798	207	5	·	·	PUNCT
ejpam-4798	207	6	·	·	PUNCT
ejpam-4798	207	7	·	·	PUNCT
ejpam-4798	208	1	a1,n	a1,n	PROPN
ejpam-4798	208	2	0	0	PUNCT
ejpam-4798	208	3	a1,2	a1,2	PROPN
ejpam-4798	208	4	·	·	PUNCT
ejpam-4798	208	5	·	·	PUNCT
ejpam-4798	208	6	·	·	PUNCT
ejpam-4798	209	1	a1,n	a1,n	PROPN
ejpam-4798	209	2	a2,1	a2,1	PROPN
ejpam-4798	209	3	0	0	NUM
ejpam-4798	209	4	·	·	PUNCT
ejpam-4798	209	5	·	·	PUNCT
ejpam-4798	209	6	·	·	PUNCT
ejpam-4798	210	1	a2,n	a2,n	ADV
ejpam-4798	210	2	a2,1	a2,1	PROPN
ejpam-4798	210	3	0	0	PUNCT
ejpam-4798	210	4	·	·	PUNCT
ejpam-4798	210	5	·	·	PUNCT
ejpam-4798	210	6	·	·	PUNCT
ejpam-4798	211	1	a2,n	a2,n	ADV
ejpam-4798	211	2	...	...	PUNCT
ejpam-4798	211	3	...	...	PUNCT
ejpam-4798	211	4	.	.	PUNCT
ejpam-4798	211	5	.	.	PUNCT
ejpam-4798	211	6	.	.	PUNCT
ejpam-4798	212	1	...	...	PUNCT
ejpam-4798	212	2	...	...	PUNCT
ejpam-4798	212	3	...	...	PUNCT
ejpam-4798	212	4	.	.	PUNCT
ejpam-4798	212	5	.	.	PUNCT
ejpam-4798	213	1	.	.	PUNCT
ejpam-4798	214	1	...	...	PUNCT
ejpam-4798	215	1	an,1	an,1	PROPN
ejpam-4798	215	2	an,2	an,2	PROPN
ejpam-4798	215	3	·	·	PUNCT
ejpam-4798	215	4	·	·	PUNCT
ejpam-4798	215	5	·	·	PUNCT
ejpam-4798	215	6	0	0	NUM
ejpam-4798	216	1	an,1	an,1	PROPN
ejpam-4798	216	2	an,2	an,2	PROPN
ejpam-4798	216	3	·	·	PUNCT
ejpam-4798	216	4	·	·	PUNCT
ejpam-4798	216	5	·	·	PUNCT
ejpam-4798	216	6	0	0	NUM
ejpam-4798	217	1	0	0	NUM
ejpam-4798	217	2	a1,2	a1,2	PROPN
ejpam-4798	217	3	·	·	PUNCT
ejpam-4798	217	4	·	·	PUNCT
ejpam-4798	217	5	·	·	PUNCT
ejpam-4798	218	1	a1,n	a1,n	PROPN
ejpam-4798	218	2	0	0	NUM
ejpam-4798	218	3	0	0	NUM
ejpam-4798	218	4	·	·	PUNCT
ejpam-4798	218	5	·	·	PUNCT
ejpam-4798	218	6	·	·	PUNCT
ejpam-4798	218	7	0	0	PUNCT
ejpam-4798	219	1	a2,1	a2,1	NOUN
ejpam-4798	219	2	0	0	NUM
ejpam-4798	219	3	·	·	PUNCT
ejpam-4798	219	4	·	·	PUNCT
ejpam-4798	219	5	·	·	PUNCT
ejpam-4798	220	1	a2,n	a2,n	ADV
ejpam-4798	220	2	0	0	NUM
ejpam-4798	220	3	0	0	NUM
ejpam-4798	220	4	·	·	PUNCT
ejpam-4798	220	5	·	·	PUNCT
ejpam-4798	220	6	·	·	PUNCT
ejpam-4798	220	7	0	0	NUM
ejpam-4798	220	8	...	...	PUNCT
ejpam-4798	220	9	...	...	PUNCT
ejpam-4798	220	10	.	.	PUNCT
ejpam-4798	220	11	.	.	PUNCT
ejpam-4798	220	12	.	.	PUNCT
ejpam-4798	221	1	...	...	PUNCT
ejpam-4798	221	2	...	...	PUNCT
ejpam-4798	221	3	...	...	PUNCT
ejpam-4798	221	4	.	.	PUNCT
ejpam-4798	221	5	.	.	PUNCT
ejpam-4798	222	1	.	.	PUNCT
ejpam-4798	223	1	...	...	PUNCT
ejpam-4798	224	1	an,1	an,1	PROPN
ejpam-4798	224	2	an,2	an,2	PROPN
ejpam-4798	224	3	·	·	PUNCT
ejpam-4798	224	4	·	·	PUNCT
ejpam-4798	224	5	·	·	PUNCT
ejpam-4798	224	6	0	0	NUM
ejpam-4798	224	7	0	0	NUM
ejpam-4798	224	8	0	0	NUM
ejpam-4798	224	9	·	·	PUNCT
ejpam-4798	224	10	·	·	PUNCT
ejpam-4798	224	11	·	·	PUNCT
ejpam-4798	224	12	0	0	NUM
ejpam-4798	225	1			VERB
ejpam-4798	225	2	let	let	VERB
ejpam-4798	225	3	λ1(σ	λ1(σ	VERB
ejpam-4798	225	4	)	)	PUNCT
ejpam-4798	225	5	,	,	PUNCT
ejpam-4798	225	6	λ2(σ	λ2(σ	NOUN
ejpam-4798	225	7	)	)	PUNCT
ejpam-4798	225	8	,	,	PUNCT
ejpam-4798	225	9	...	...	PUNCT
ejpam-4798	225	10	,	,	PUNCT
ejpam-4798	225	11	λn(σ	λn(σ	NUM
ejpam-4798	225	12	)	)	PUNCT
ejpam-4798	225	13	are	be	AUX
ejpam-4798	225	14	the	the	DET
ejpam-4798	225	15	eigenvalues	eigenvalue	NOUN
ejpam-4798	225	16	of	of	ADP
ejpam-4798	225	17	the	the	DET
ejpam-4798	225	18	signed	sign	VERB
ejpam-4798	225	19	graph	graph	NOUN
ejpam-4798	225	20	σ	σ	PROPN
ejpam-4798	225	21	.	.	PUNCT
ejpam-4798	226	1	we	we	PRON
ejpam-4798	226	2	can	can	AUX
ejpam-4798	226	3	write	write	VERB
ejpam-4798	226	4	above	above	ADP
ejpam-4798	226	5	adjacency	adjacency	NOUN
ejpam-4798	226	6	matrix	matrix	NOUN
ejpam-4798	226	7	as	as	ADP
ejpam-4798	226	8	,	,	PUNCT
ejpam-4798	226	9	a(γ(σ	a(γ(σ	NOUN
ejpam-4798	226	10	)	)	PUNCT
ejpam-4798	226	11	)	)	PUNCT
ejpam-4798	227	1	=	=	PUNCT
ejpam-4798	227	2	[	[	PUNCT
ejpam-4798	227	3	a(σ	a(σ	ADJ
ejpam-4798	227	4	)	)	PUNCT
ejpam-4798	227	5	a(σ	a(σ	ADJ
ejpam-4798	227	6	)	)	PUNCT
ejpam-4798	227	7	a(σ	a(σ	PROPN
ejpam-4798	227	8	)	)	PUNCT
ejpam-4798	227	9	0	0	PUNCT
ejpam-4798	227	10	]	]	PUNCT
ejpam-4798	228	1	=	=	PUNCT
ejpam-4798	228	2	[	[	PUNCT
ejpam-4798	228	3	1	1	NUM
ejpam-4798	228	4	1	1	NUM
ejpam-4798	228	5	1	1	NUM
ejpam-4798	228	6	0	0	NUM
ejpam-4798	228	7	]	]	PUNCT
ejpam-4798	228	8	⊗a(σ	⊗a(σ	NOUN
ejpam-4798	228	9	)	)	PUNCT
ejpam-4798	228	10	from	from	ADP
ejpam-4798	228	11	here	here	ADV
ejpam-4798	228	12	we	we	PRON
ejpam-4798	228	13	can	can	AUX
ejpam-4798	228	14	see	see	VERB
ejpam-4798	228	15	that	that	DET
ejpam-4798	228	16	adjacency	adjacency	PROPN
ejpam-4798	228	17	matrix	matrix	NOUN
ejpam-4798	228	18	a(λ(σ	a(λ(σ	PROPN
ejpam-4798	228	19	)	)	PUNCT
ejpam-4798	228	20	)	)	PUNCT
ejpam-4798	228	21	is	be	AUX
ejpam-4798	228	22	a	a	DET
ejpam-4798	228	23	kronecker	kronecker	NOUN
ejpam-4798	228	24	product	product	NOUN
ejpam-4798	228	25	of	of	ADP
ejpam-4798	228	26	the	the	DET
ejpam-4798	228	27	matrices	matrix	NOUN
ejpam-4798	228	28	m	m	VERB
ejpam-4798	228	29	and	and	CCONJ
ejpam-4798	228	30	a(σ	a(σ	NOUN
ejpam-4798	228	31	)	)	PUNCT
ejpam-4798	228	32	,	,	PUNCT
ejpam-4798	228	33	where	where	SCONJ
ejpam-4798	228	34	m	m	VERB
ejpam-4798	228	35	=	=	X
ejpam-4798	228	36	[	[	PUNCT
ejpam-4798	228	37	1	1	NUM
ejpam-4798	228	38	1	1	NUM
ejpam-4798	228	39	1	1	NUM
ejpam-4798	228	40	0	0	NUM
ejpam-4798	228	41	]	]	PUNCT
ejpam-4798	228	42	.	.	PUNCT
ejpam-4798	229	1	easily	easily	ADV
ejpam-4798	229	2	we	we	PRON
ejpam-4798	229	3	can	can	AUX
ejpam-4798	229	4	see	see	VERB
ejpam-4798	229	5	that	that	SCONJ
ejpam-4798	229	6	{	{	PUNCT
ejpam-4798	229	7	1	1	NUM
ejpam-4798	229	8	+	+	NUM
ejpam-4798	229	9	√	√	NUM
ejpam-4798	229	10	5	5	NUM
ejpam-4798	229	11	2	2	NUM
ejpam-4798	229	12	,	,	PUNCT
ejpam-4798	229	13	1−	1−	NUM
ejpam-4798	229	14	√	√	NOUN
ejpam-4798	229	15	5	5	NUM
ejpam-4798	229	16	2	2	NUM
ejpam-4798	229	17	}	}	PUNCT
ejpam-4798	229	18	are	be	AUX
ejpam-4798	229	19	the	the	DET
ejpam-4798	229	20	eigenvalues	eigenvalue	NOUN
ejpam-4798	229	21	of	of	ADP
ejpam-4798	229	22	the	the	DET
ejpam-4798	229	23	matrix	matrix	NOUN
ejpam-4798	229	24	m	m	VERB
ejpam-4798	229	25	.	.	PUNCT
ejpam-4798	230	1	so	so	ADV
ejpam-4798	230	2	the	the	DET
ejpam-4798	230	3	adjacency	adjacency	PROPN
ejpam-4798	230	4	spectrum	spectrum	NOUN
ejpam-4798	230	5	of	of	ADP
ejpam-4798	230	6	the	the	DET
ejpam-4798	230	7	splitting	splitting	NOUN
ejpam-4798	230	8	signed	sign	VERB
ejpam-4798	230	9	graph	graph	NOUN
ejpam-4798	230	10	λ(σ	λ(σ	NOUN
ejpam-4798	230	11	)	)	PUNCT
ejpam-4798	230	12	is	be	AUX
ejpam-4798	230	13	given	give	VERB
ejpam-4798	230	14	as	as	ADP
ejpam-4798	230	15	{	{	PUNCT
ejpam-4798	230	16	(	(	PUNCT
ejpam-4798	230	17	1	1	NUM
ejpam-4798	230	18	+	+	NUM
ejpam-4798	230	19	√	√	NUM
ejpam-4798	230	20	5	5	NUM
ejpam-4798	230	21	2	2	NUM
ejpam-4798	230	22	)	)	PUNCT
ejpam-4798	230	23	λi	λi	NOUN
ejpam-4798	230	24	,	,	PUNCT
ejpam-4798	230	25	(	(	PUNCT
ejpam-4798	230	26	1−	1−	NUM
ejpam-4798	230	27	√	√	NUM
ejpam-4798	230	28	5	5	NUM
ejpam-4798	230	29	2	2	NUM
ejpam-4798	230	30	)	)	PUNCT
ejpam-4798	230	31	λi	λi	ADP
ejpam-4798	230	32	}	}	PUNCT
ejpam-4798	230	33	,	,	PUNCT
ejpam-4798	230	34	where	where	SCONJ
ejpam-4798	230	35	1	1	NUM
ejpam-4798	230	36	≤	≤	NUM
ejpam-4798	230	37	i	i	PRON
ejpam-4798	230	38	≤	≤	PROPN
ejpam-4798	230	39	n.	n.	NOUN
ejpam-4798	230	40	now	now	ADV
ejpam-4798	230	41	consider	consider	VERB
ejpam-4798	230	42	l(σ	l(σ	X
ejpam-4798	230	43	)	)	PUNCT
ejpam-4798	230	44	be	be	AUX
ejpam-4798	230	45	the	the	DET
ejpam-4798	230	46	laplacian	laplacian	ADJ
ejpam-4798	230	47	matrix	matrix	NOUN
ejpam-4798	230	48	of	of	ADP
ejpam-4798	230	49	the	the	DET
ejpam-4798	230	50	signed	sign	VERB
ejpam-4798	230	51	graph	graph	NOUN
ejpam-4798	230	52	σ	σ	NOUN
ejpam-4798	230	53	and	and	CCONJ
ejpam-4798	230	54	ψ1	ψ1	NOUN
ejpam-4798	230	55	,	,	PUNCT
ejpam-4798	230	56	ψ2	ψ2	NOUN
ejpam-4798	230	57	,	,	PUNCT
ejpam-4798	230	58	...	...	PUNCT
ejpam-4798	230	59	,	,	PUNCT
ejpam-4798	230	60	ψi	ψi	ADV
ejpam-4798	230	61	are	be	AUX
ejpam-4798	230	62	the	the	DET
ejpam-4798	230	63	eigenvalues	eigenvalue	NOUN
ejpam-4798	230	64	of	of	ADP
ejpam-4798	230	65	the	the	DET
ejpam-4798	230	66	laplacian	laplacian	ADJ
ejpam-4798	230	67	matrix	matrix	NOUN
ejpam-4798	230	68	l(σ	l(σ	PROPN
ejpam-4798	230	69	)	)	PUNCT
ejpam-4798	230	70	.	.	PUNCT
ejpam-4798	231	1	by	by	ADP
ejpam-4798	231	2	some	some	DET
ejpam-4798	231	3	easy	easy	ADJ
ejpam-4798	231	4	calculations	calculation	NOUN
ejpam-4798	231	5	we	we	PRON
ejpam-4798	231	6	can	can	AUX
ejpam-4798	231	7	find	find	VERB
ejpam-4798	231	8	that	that	SCONJ
ejpam-4798	231	9	the	the	DET
ejpam-4798	231	10	laplacian	laplacian	ADJ
ejpam-4798	231	11	matrix	matrix	NOUN
ejpam-4798	231	12	l(γ(σ	l(γ(σ	PROPN
ejpam-4798	231	13	)	)	PUNCT
ejpam-4798	231	14	)	)	PUNCT
ejpam-4798	231	15	of	of	ADP
ejpam-4798	231	16	the	the	DET
ejpam-4798	231	17	splitting	splitting	NOUN
ejpam-4798	231	18	signed	sign	VERB
ejpam-4798	231	19	graph	graph	NOUN
ejpam-4798	231	20	is	be	AUX
ejpam-4798	231	21	a	a	DET
ejpam-4798	231	22	kronecker	kronecker	NOUN
ejpam-4798	231	23	product	product	NOUN
ejpam-4798	231	24	of	of	ADP
ejpam-4798	231	25	the	the	DET
ejpam-4798	231	26	matrices	matrix	NOUN
ejpam-4798	231	27	m	m	VERB
ejpam-4798	231	28	and	and	CCONJ
ejpam-4798	231	29	l(σ	l(σ	PROPN
ejpam-4798	231	30	)	)	PUNCT
ejpam-4798	231	31	,	,	PUNCT
ejpam-4798	231	32	where	where	SCONJ
ejpam-4798	231	33	m	m	VERB
ejpam-4798	231	34	=	=	X
ejpam-4798	231	35	[	[	PUNCT
ejpam-4798	231	36	1	1	NUM
ejpam-4798	231	37	1	1	NUM
ejpam-4798	231	38	1	1	NUM
ejpam-4798	231	39	0	0	NUM
ejpam-4798	231	40	]	]	PUNCT
ejpam-4798	231	41	.	.	PUNCT
ejpam-4798	232	1	so	so	ADV
ejpam-4798	232	2	the	the	DET
ejpam-4798	232	3	laplacian	laplacian	ADJ
ejpam-4798	232	4	spectrum	spectrum	NOUN
ejpam-4798	232	5	of	of	ADP
ejpam-4798	232	6	the	the	DET
ejpam-4798	232	7	splitting	splitting	NOUN
ejpam-4798	232	8	signed	sign	VERB
ejpam-4798	232	9	graph	graph	NOUN
ejpam-4798	232	10	λ(σ	λ(σ	NOUN
ejpam-4798	232	11	)	)	PUNCT
ejpam-4798	232	12	is	be	AUX
ejpam-4798	232	13	given	give	VERB
ejpam-4798	232	14	as	as	ADP
ejpam-4798	232	15	{	{	PUNCT
ejpam-4798	232	16	(	(	PUNCT
ejpam-4798	232	17	1	1	NUM
ejpam-4798	232	18	+	+	NUM
ejpam-4798	232	19	√	√	NUM
ejpam-4798	232	20	5	5	NUM
ejpam-4798	232	21	2	2	NUM
ejpam-4798	232	22	)	)	PUNCT
ejpam-4798	232	23	ψi	ψi	NOUN
ejpam-4798	232	24	,	,	PUNCT
ejpam-4798	232	25	(	(	PUNCT
ejpam-4798	232	26	1−	1−	NUM
ejpam-4798	232	27	√	√	NUM
ejpam-4798	232	28	5	5	NUM
ejpam-4798	232	29	2	2	NUM
ejpam-4798	232	30	)	)	PUNCT
ejpam-4798	232	31	ψi	ψi	ADP
ejpam-4798	232	32	}	}	PUNCT
ejpam-4798	232	33	,	,	PUNCT
ejpam-4798	232	34	where	where	SCONJ
ejpam-4798	232	35	1	1	NUM
ejpam-4798	232	36	≤	≤	NUM
ejpam-4798	232	37	i	i	PRON
ejpam-4798	232	38	≤	≤	ADJ
ejpam-4798	232	39	n.	n.	NOUN
ejpam-4798	232	40	from	from	ADP
ejpam-4798	232	41	equation	equation	NOUN
ejpam-4798	232	42	2	2	NUM
ejpam-4798	232	43	,	,	PUNCT
ejpam-4798	232	44	we	we	PRON
ejpam-4798	232	45	can	can	AUX
ejpam-4798	232	46	see	see	VERB
ejpam-4798	232	47	that	that	PRON
ejpam-4798	232	48	spectral	spectral	ADJ
ejpam-4798	232	49	radius	radius	NOUN
ejpam-4798	232	50	of	of	ADP
ejpam-4798	232	51	σ	σ	PROPN
ejpam-4798	232	52	will	will	AUX
ejpam-4798	232	53	always	always	ADV
ejpam-4798	232	54	be	be	AUX
ejpam-4798	232	55	greater	great	ADJ
ejpam-4798	232	56	than	than	ADP
ejpam-4798	232	57	equal	equal	ADJ
ejpam-4798	232	58	to	to	ADP
ejpam-4798	232	59	the	the	DET
ejpam-4798	232	60	index	index	NOUN
ejpam-4798	232	61	,	,	PUNCT
ejpam-4798	232	62	i.e.	i.e.	X
ejpam-4798	232	63	ρ(σ	ρ(σ	NOUN
ejpam-4798	232	64	)	)	PUNCT
ejpam-4798	232	65	≥	≥	X
ejpam-4798	233	1	λ1(σ	λ1(σ	VERB
ejpam-4798	233	2	)	)	PUNCT
ejpam-4798	233	3	in	in	ADP
ejpam-4798	233	4	[	[	X
ejpam-4798	233	5	1	1	X
ejpam-4798	233	6	]	]	PUNCT
ejpam-4798	233	7	acharya	acharya	NOUN
ejpam-4798	233	8	provided	provide	VERB
ejpam-4798	233	9	the	the	DET
ejpam-4798	233	10	spectral	spectral	ADJ
ejpam-4798	233	11	criterion	criterion	NOUN
ejpam-4798	233	12	for	for	ADP
ejpam-4798	233	13	balance	balance	NOUN
ejpam-4798	233	14	in	in	ADP
ejpam-4798	233	15	σ	σ	NOUN
ejpam-4798	233	16	as	as	ADP
ejpam-4798	233	17	,	,	PUNCT
ejpam-4798	233	18	theorem	theorem	ADJ
ejpam-4798	233	19	4	4	NUM
ejpam-4798	233	20	.	.	PUNCT
ejpam-4798	234	1	[	[	X
ejpam-4798	234	2	1	1	X
ejpam-4798	234	3	]	]	PUNCT
ejpam-4798	234	4	a	a	DET
ejpam-4798	234	5	signed	sign	VERB
ejpam-4798	234	6	graph	graph	NOUN
ejpam-4798	234	7	σ	σ	PROPN
ejpam-4798	234	8	is	be	AUX
ejpam-4798	234	9	balanced	balance	VERB
ejpam-4798	234	10	if	if	SCONJ
ejpam-4798	234	11	and	and	CCONJ
ejpam-4798	234	12	only	only	ADV
ejpam-4798	234	13	if	if	SCONJ
ejpam-4798	234	14	it	it	PRON
ejpam-4798	234	15	is	be	AUX
ejpam-4798	234	16	cospectral	cospectral	ADJ
ejpam-4798	234	17	to	to	ADP
ejpam-4798	234	18	it	it	PRON
ejpam-4798	234	19	’s	’	VERB
ejpam-4798	234	20	underlying	underlie	VERB
ejpam-4798	234	21	graph	graph	NOUN
ejpam-4798	234	22	.	.	PUNCT
ejpam-4798	235	1	it	it	PRON
ejpam-4798	235	2	provides	provide	VERB
ejpam-4798	235	3	that	that	SCONJ
ejpam-4798	235	4	the	the	DET
ejpam-4798	235	5	balanced	balanced	ADJ
ejpam-4798	235	6	signed	sign	VERB
ejpam-4798	235	7	graphs	graph	NOUN
ejpam-4798	235	8	have	have	VERB
ejpam-4798	235	9	the	the	DET
ejpam-4798	235	10	spectral	spectral	ADJ
ejpam-4798	235	11	radius	radius	NOUN
ejpam-4798	235	12	equal	equal	ADJ
ejpam-4798	235	13	to	to	ADP
ejpam-4798	235	14	the	the	DET
ejpam-4798	235	15	index	index	NOUN
ejpam-4798	235	16	.	.	PUNCT
ejpam-4798	236	1	so	so	ADV
ejpam-4798	236	2	,	,	PUNCT
ejpam-4798	236	3	here	here	ADV
ejpam-4798	236	4	in	in	ADP
ejpam-4798	236	5	this	this	DET
ejpam-4798	236	6	section	section	NOUN
ejpam-4798	236	7	we	we	PRON
ejpam-4798	236	8	characterize	characterize	VERB
ejpam-4798	236	9	the	the	DET
ejpam-4798	236	10	balanced	balanced	ADJ
ejpam-4798	236	11	splitting	splitting	NOUN
ejpam-4798	236	12	signed	sign	VERB
ejpam-4798	236	13	graphs	graph	NOUN
ejpam-4798	236	14	.	.	PUNCT
ejpam-4798	237	1	sampathkumar	sampathkumar	PROPN
ejpam-4798	237	2	provided	provide	VERB
ejpam-4798	237	3	an	an	DET
ejpam-4798	237	4	important	important	ADJ
ejpam-4798	237	5	characterization	characterization	NOUN
ejpam-4798	237	6	of	of	ADP
ejpam-4798	237	7	balanced	balanced	ADJ
ejpam-4798	237	8	signed	sign	VERB
ejpam-4798	237	9	graphs	graph	NOUN
ejpam-4798	237	10	based	base	VERB
ejpam-4798	237	11	on	on	ADP
ejpam-4798	237	12	marking	mark	VERB
ejpam-4798	237	13	:	:	PUNCT
ejpam-4798	237	14	s.	s.	PROPN
ejpam-4798	237	15	kumar	kumar	PROPN
ejpam-4798	237	16	,	,	PUNCT
ejpam-4798	237	17	d.	d.	PROPN
ejpam-4798	237	18	sinha	sinha	PROPN
ejpam-4798	237	19	/	/	SYM
ejpam-4798	237	20	eur	eur	PROPN
ejpam-4798	237	21	.	.	PUNCT
ejpam-4798	238	1	j.	j.	PROPN
ejpam-4798	238	2	pure	pure	PROPN
ejpam-4798	238	3	appl	appl	PROPN
ejpam-4798	238	4	.	.	PROPN
ejpam-4798	238	5	math	math	PROPN
ejpam-4798	238	6	,	,	PUNCT
ejpam-4798	238	7	17	17	NUM
ejpam-4798	238	8	(	(	PUNCT
ejpam-4798	238	9	1	1	NUM
ejpam-4798	238	10	)	)	PUNCT
ejpam-4798	238	11	(	(	PUNCT
ejpam-4798	238	12	2024	2024	NUM
ejpam-4798	238	13	)	)	PUNCT
ejpam-4798	238	14	,	,	PUNCT
ejpam-4798	238	15	504	504	NUM
ejpam-4798	238	16	-	-	SYM
ejpam-4798	238	17	518	518	NUM
ejpam-4798	238	18	516	516	NUM
ejpam-4798	238	19	theorem	theorem	NOUN
ejpam-4798	238	20	5	5	NUM
ejpam-4798	238	21	.	.	PUNCT
ejpam-4798	239	1	[	[	X
ejpam-4798	239	2	?	?	PUNCT
ejpam-4798	239	3	]	]	X
ejpam-4798	239	4	the	the	DET
ejpam-4798	239	5	balance	balance	NOUN
ejpam-4798	239	6	of	of	ADP
ejpam-4798	239	7	a	a	DET
ejpam-4798	239	8	signed	sign	VERB
ejpam-4798	239	9	graph	graph	NOUN
ejpam-4798	239	10	σ	σ	NOUN
ejpam-4798	239	11	=	=	SYM
ejpam-4798	239	12	(	(	PUNCT
ejpam-4798	239	13	σu	σu	INTJ
ejpam-4798	239	14	,	,	PUNCT
ejpam-4798	239	15	σ	σ	PROPN
ejpam-4798	239	16	)	)	PUNCT
ejpam-4798	239	17	can	can	AUX
ejpam-4798	239	18	be	be	AUX
ejpam-4798	239	19	determined	determine	VERB
ejpam-4798	239	20	if	if	SCONJ
ejpam-4798	239	21	and	and	CCONJ
ejpam-4798	239	22	only	only	ADV
ejpam-4798	239	23	if	if	SCONJ
ejpam-4798	239	24	there	there	PRON
ejpam-4798	239	25	is	be	VERB
ejpam-4798	239	26	a	a	DET
ejpam-4798	239	27	marking	marking	NOUN
ejpam-4798	239	28	µ	µ	NOUN
ejpam-4798	239	29	of	of	ADP
ejpam-4798	239	30	its	its	PRON
ejpam-4798	239	31	vertices	vertex	NOUN
ejpam-4798	239	32	such	such	ADJ
ejpam-4798	239	33	that	that	SCONJ
ejpam-4798	239	34	the	the	DET
ejpam-4798	239	35	sign	sign	NOUN
ejpam-4798	239	36	of	of	ADP
ejpam-4798	239	37	each	each	DET
ejpam-4798	239	38	edge	edge	NOUN
ejpam-4798	239	39	vu	vu	NOUN
ejpam-4798	239	40	in	in	ADP
ejpam-4798	239	41	σ	σ	PROPN
ejpam-4798	239	42	satisfies	satisfie	NOUN
ejpam-4798	239	43	the	the	DET
ejpam-4798	239	44	condition	condition	NOUN
ejpam-4798	239	45	σ(vu	σ(vu	PROPN
ejpam-4798	239	46	)	)	PUNCT
ejpam-4798	240	1	=	=	SYM
ejpam-4798	240	2	µ(v)µ(u	µ(v)µ(u	NOUN
ejpam-4798	240	3	)	)	PUNCT
ejpam-4798	240	4	.	.	PUNCT
ejpam-4798	241	1	the	the	DET
ejpam-4798	241	2	operation	operation	NOUN
ejpam-4798	241	3	of	of	ADP
ejpam-4798	241	4	changing	change	VERB
ejpam-4798	241	5	the	the	DET
ejpam-4798	241	6	sign	sign	NOUN
ejpam-4798	241	7	of	of	ADP
ejpam-4798	241	8	every	every	DET
ejpam-4798	241	9	edge	edge	NOUN
ejpam-4798	241	10	in	in	ADP
ejpam-4798	241	11	a	a	DET
ejpam-4798	241	12	signed	sign	VERB
ejpam-4798	241	13	graph	graph	NOUN
ejpam-4798	241	14	σ	σ	NOUN
ejpam-4798	241	15	to	to	ADP
ejpam-4798	241	16	its	its	PRON
ejpam-4798	241	17	opposite	opposite	NOUN
ejpam-4798	241	18	,	,	PUNCT
ejpam-4798	241	19	based	base	VERB
ejpam-4798	241	20	on	on	ADP
ejpam-4798	241	21	the	the	DET
ejpam-4798	241	22	marking	mark	VERB
ejpam-4798	241	23	µ	µ	NOUN
ejpam-4798	241	24	of	of	ADP
ejpam-4798	241	25	its	its	PRON
ejpam-4798	241	26	vertices	vertex	NOUN
ejpam-4798	241	27	,	,	PUNCT
ejpam-4798	241	28	is	be	AUX
ejpam-4798	241	29	called	call	VERB
ejpam-4798	241	30	switching	switch	VERB
ejpam-4798	241	31	σ	σ	NOUN
ejpam-4798	241	32	with	with	ADP
ejpam-4798	241	33	respect	respect	NOUN
ejpam-4798	241	34	to	to	AUX
ejpam-4798	241	35	µ.	µ.	VERB
ejpam-4798	241	36	this	this	DET
ejpam-4798	241	37	operation	operation	NOUN
ejpam-4798	241	38	is	be	AUX
ejpam-4798	241	39	performed	perform	VERB
ejpam-4798	241	40	whenever	whenever	SCONJ
ejpam-4798	241	41	the	the	DET
ejpam-4798	241	42	end	end	NOUN
ejpam-4798	241	43	vertices	vertex	NOUN
ejpam-4798	241	44	of	of	ADP
ejpam-4798	241	45	an	an	DET
ejpam-4798	241	46	edge	edge	NOUN
ejpam-4798	241	47	have	have	VERB
ejpam-4798	241	48	opposite	opposite	ADJ
ejpam-4798	241	49	signs	sign	NOUN
ejpam-4798	241	50	in	in	ADP
ejpam-4798	241	51	σµ.	σµ.	NOUN
ejpam-4798	241	52	the	the	DET
ejpam-4798	241	53	concept	concept	NOUN
ejpam-4798	241	54	of	of	ADP
ejpam-4798	241	55	switching	switch	VERB
ejpam-4798	241	56	signed	sign	VERB
ejpam-4798	241	57	graphs	graph	NOUN
ejpam-4798	241	58	is	be	AUX
ejpam-4798	241	59	closely	closely	ADV
ejpam-4798	241	60	connected	connect	VERB
ejpam-4798	241	61	to	to	ADP
ejpam-4798	241	62	the	the	DET
ejpam-4798	241	63	concept	concept	NOUN
ejpam-4798	241	64	of	of	ADP
ejpam-4798	241	65	balance	balance	NOUN
ejpam-4798	241	66	,	,	PUNCT
ejpam-4798	241	67	as	as	SCONJ
ejpam-4798	241	68	indicated	indicate	VERB
ejpam-4798	241	69	by	by	ADP
ejpam-4798	241	70	the	the	DET
ejpam-4798	241	71	following	follow	VERB
ejpam-4798	241	72	theorem	theorem	NOUN
ejpam-4798	241	73	:	:	PUNCT
ejpam-4798	241	74	theorem	theorem	NOUN
ejpam-4798	241	75	6	6	NUM
ejpam-4798	241	76	.	.	PUNCT
ejpam-4798	242	1	[	[	X
ejpam-4798	242	2	20	20	NUM
ejpam-4798	242	3	]	]	PUNCT
ejpam-4798	242	4	a	a	DET
ejpam-4798	242	5	signed	sign	VERB
ejpam-4798	242	6	graph	graph	NOUN
ejpam-4798	242	7	σ	σ	NOUN
ejpam-4798	242	8	=	=	SYM
ejpam-4798	242	9	(	(	PUNCT
ejpam-4798	242	10	σu	σu	INTJ
ejpam-4798	242	11	,	,	PUNCT
ejpam-4798	242	12	σ	σ	PROPN
ejpam-4798	242	13	)	)	PUNCT
ejpam-4798	242	14	is	be	AUX
ejpam-4798	242	15	considered	consider	VERB
ejpam-4798	242	16	balanced	balanced	ADJ
ejpam-4798	242	17	if	if	SCONJ
ejpam-4798	242	18	and	and	CCONJ
ejpam-4798	242	19	only	only	ADV
ejpam-4798	242	20	if	if	SCONJ
ejpam-4798	242	21	it	it	PRON
ejpam-4798	242	22	is	be	AUX
ejpam-4798	242	23	equivalent	equivalent	ADJ
ejpam-4798	242	24	under	under	ADP
ejpam-4798	242	25	switching	switch	VERB
ejpam-4798	242	26	to	to	ADP
ejpam-4798	242	27	its	its	PRON
ejpam-4798	242	28	underlying	underlie	VERB
ejpam-4798	242	29	graph	graph	NOUN
ejpam-4798	242	30	σu	σu	NOUN
ejpam-4798	242	31	.	.	PUNCT
ejpam-4798	243	1	theorem	theorem	ADJ
ejpam-4798	243	2	7	7	NUM
ejpam-4798	243	3	.	.	PUNCT
ejpam-4798	244	1	[	[	X
ejpam-4798	244	2	13	13	NUM
ejpam-4798	244	3	]	]	PUNCT
ejpam-4798	244	4	the	the	DET
ejpam-4798	244	5	splitting	splitting	NOUN
ejpam-4798	244	6	signed	sign	VERB
ejpam-4798	244	7	graph	graph	NOUN
ejpam-4798	244	8	γ(σ	γ(σ	PROPN
ejpam-4798	244	9	)	)	PUNCT
ejpam-4798	244	10	is	be	AUX
ejpam-4798	244	11	balanced	balance	VERB
ejpam-4798	244	12	if	if	SCONJ
ejpam-4798	244	13	and	and	CCONJ
ejpam-4798	244	14	only	only	ADV
ejpam-4798	244	15	if	if	SCONJ
ejpam-4798	244	16	the	the	DET
ejpam-4798	244	17	signed	sign	VERB
ejpam-4798	244	18	graph	graph	NOUN
ejpam-4798	244	19	σ	σ	PROPN
ejpam-4798	244	20	is	be	AUX
ejpam-4798	244	21	balanced	balanced	ADJ
ejpam-4798	244	22	.	.	PUNCT
ejpam-4798	245	1	remark	remark	PROPN
ejpam-4798	245	2	1	1	NUM
ejpam-4798	245	3	.	.	PUNCT
ejpam-4798	246	1	the	the	DET
ejpam-4798	246	2	splitting	splitting	NOUN
ejpam-4798	246	3	signed	sign	VERB
ejpam-4798	246	4	graph	graph	NOUN
ejpam-4798	246	5	γ(σ	γ(σ	PROPN
ejpam-4798	246	6	)	)	PUNCT
ejpam-4798	246	7	is	be	AUX
ejpam-4798	246	8	cospectral	cospectral	ADJ
ejpam-4798	246	9	to	to	ADP
ejpam-4798	246	10	it	it	PRON
ejpam-4798	246	11	’s	’	VERB
ejpam-4798	246	12	underlying	underlie	VERB
ejpam-4798	246	13	graph	graph	NOUN
ejpam-4798	246	14	γ(σu	γ(σu	NOUN
ejpam-4798	246	15	)	)	PUNCT
ejpam-4798	246	16	if	if	SCONJ
ejpam-4798	247	1	and	and	CCONJ
ejpam-4798	247	2	only	only	ADV
ejpam-4798	247	3	if	if	SCONJ
ejpam-4798	247	4	σ	σ	PROPN
ejpam-4798	247	5	is	be	AUX
ejpam-4798	247	6	balanced	balanced	ADJ
ejpam-4798	247	7	.	.	PUNCT
ejpam-4798	248	1	5	5	X
ejpam-4798	248	2	.	.	X
ejpam-4798	248	3	energy	energy	NOUN
ejpam-4798	248	4	of	of	ADP
ejpam-4798	248	5	splitting	split	VERB
ejpam-4798	248	6	signed	sign	VERB
ejpam-4798	248	7	graph	graph	NOUN
ejpam-4798	248	8	in	in	ADP
ejpam-4798	248	9	this	this	DET
ejpam-4798	248	10	section	section	NOUN
ejpam-4798	248	11	,	,	PUNCT
ejpam-4798	248	12	we	we	PRON
ejpam-4798	248	13	explore	explore	VERB
ejpam-4798	248	14	the	the	DET
ejpam-4798	248	15	connection	connection	NOUN
ejpam-4798	248	16	between	between	ADP
ejpam-4798	248	17	the	the	DET
ejpam-4798	248	18	energy	energy	NOUN
ejpam-4798	248	19	of	of	ADP
ejpam-4798	248	20	a	a	DET
ejpam-4798	248	21	signed	sign	VERB
ejpam-4798	248	22	graph	graph	NOUN
ejpam-4798	248	23	σ	σ	NOUN
ejpam-4798	248	24	and	and	CCONJ
ejpam-4798	248	25	its	its	PRON
ejpam-4798	248	26	splitting	splitting	NOUN
ejpam-4798	248	27	signed	sign	VERB
ejpam-4798	248	28	graph	graph	NOUN
ejpam-4798	248	29	γ(σ	γ(σ	PROPN
ejpam-4798	248	30	)	)	PUNCT
ejpam-4798	248	31	.	.	PUNCT
ejpam-4798	249	1	theorem	theorem	ADJ
ejpam-4798	249	2	8	8	NUM
ejpam-4798	249	3	.	.	PUNCT
ejpam-4798	250	1	let	let	AUX
ejpam-4798	250	2	e(σ	e(σ	PROPN
ejpam-4798	250	3	)	)	PUNCT
ejpam-4798	250	4	be	be	AUX
ejpam-4798	250	5	the	the	DET
ejpam-4798	250	6	energy	energy	NOUN
ejpam-4798	250	7	of	of	ADP
ejpam-4798	250	8	signed	sign	VERB
ejpam-4798	250	9	graph	graph	NOUN
ejpam-4798	250	10	σ	σ	PROPN
ejpam-4798	250	11	and	and	CCONJ
ejpam-4798	250	12	e(γ(σ	e(γ(σ	PROPN
ejpam-4798	250	13	)	)	PUNCT
ejpam-4798	250	14	)	)	PUNCT
ejpam-4798	251	1	be	be	AUX
ejpam-4798	251	2	the	the	DET
ejpam-4798	251	3	energy	energy	NOUN
ejpam-4798	251	4	of	of	ADP
ejpam-4798	251	5	splitting	splitting	NOUN
ejpam-4798	251	6	signed	sign	VERB
ejpam-4798	251	7	graph	graph	NOUN
ejpam-4798	251	8	γ(σ	γ(σ	PROPN
ejpam-4798	251	9	)	)	PUNCT
ejpam-4798	251	10	,	,	PUNCT
ejpam-4798	251	11	then	then	ADV
ejpam-4798	251	12	e(γ(σ	e(γ(σ	PROPN
ejpam-4798	251	13	)	)	PUNCT
ejpam-4798	251	14	)	)	PUNCT
ejpam-4798	252	1	=	=	PUNCT
ejpam-4798	253	1	√	√	NUM
ejpam-4798	253	2	5e(σ	5e(σ	NUM
ejpam-4798	253	3	)	)	PUNCT
ejpam-4798	253	4	.	.	PUNCT
ejpam-4798	254	1	proof	proof	NOUN
ejpam-4798	254	2	.	.	PUNCT
ejpam-4798	255	1	let	let	VERB
ejpam-4798	255	2	v	v	VERB
ejpam-4798	255	3	=	=	SYM
ejpam-4798	255	4	{	{	PUNCT
ejpam-4798	255	5	v1	v1	PROPN
ejpam-4798	255	6	,	,	PUNCT
ejpam-4798	255	7	v2	v2	PROPN
ejpam-4798	255	8	,	,	PUNCT
ejpam-4798	255	9	...	...	PUNCT
ejpam-4798	255	10	,	,	PUNCT
ejpam-4798	255	11	vn	vn	AUX
ejpam-4798	255	12	}	}	PUNCT
ejpam-4798	255	13	be	be	AUX
ejpam-4798	255	14	the	the	DET
ejpam-4798	255	15	vertex	vertex	NOUN
ejpam-4798	255	16	set	set	NOUN
ejpam-4798	255	17	of	of	ADP
ejpam-4798	255	18	the	the	DET
ejpam-4798	255	19	signed	sign	VERB
ejpam-4798	255	20	graph	graph	NOUN
ejpam-4798	255	21	σ	σ	PROPN
ejpam-4798	255	22	.	.	PUNCT
ejpam-4798	256	1	then	then	ADV
ejpam-4798	256	2	adjacency	adjacency	PROPN
ejpam-4798	256	3	matrix	matrix	NOUN
ejpam-4798	256	4	of	of	ADP
ejpam-4798	256	5	σ	σ	PROPN
ejpam-4798	256	6	is	be	AUX
ejpam-4798	256	7	given	give	VERB
ejpam-4798	256	8	by	by	ADP
ejpam-4798	256	9	,	,	PUNCT
ejpam-4798	256	10	a(σ	a(σ	ADJ
ejpam-4798	256	11	)	)	PUNCT
ejpam-4798	256	12	=	=	PUNCT
ejpam-4798	256	13			NOUN
ejpam-4798	256	14	0	0	PUNCT
ejpam-4798	256	15	a1,2	a1,2	PROPN
ejpam-4798	256	16	·	·	PUNCT
ejpam-4798	256	17	·	·	PUNCT
ejpam-4798	256	18	·	·	PUNCT
ejpam-4798	257	1	a1,n	a1,n	PROPN
ejpam-4798	257	2	a2,1	a2,1	PROPN
ejpam-4798	257	3	0	0	NUM
ejpam-4798	257	4	·	·	PUNCT
ejpam-4798	257	5	·	·	PUNCT
ejpam-4798	257	6	·	·	PUNCT
ejpam-4798	258	1	a2,n	a2,n	ADV
ejpam-4798	258	2	...	...	PUNCT
ejpam-4798	258	3	...	...	PUNCT
ejpam-4798	258	4	.	.	PUNCT
ejpam-4798	258	5	.	.	PUNCT
ejpam-4798	258	6	.	.	PUNCT
ejpam-4798	259	1	...	...	PUNCT
ejpam-4798	260	1	am,1	am,1	PROPN
ejpam-4798	260	2	am,2	am,2	PROPN
ejpam-4798	260	3	·	·	PUNCT
ejpam-4798	260	4	·	·	PUNCT
ejpam-4798	260	5	·	·	PUNCT
ejpam-4798	260	6	0	0	NUM
ejpam-4798	261	1			ADJ
ejpam-4798	261	2	let	let	VERB
ejpam-4798	261	3	v′i	v′i	ADV
ejpam-4798	261	4	be	be	AUX
ejpam-4798	261	5	the	the	DET
ejpam-4798	261	6	vertex	vertex	NOUN
ejpam-4798	261	7	corresponding	correspond	VERB
ejpam-4798	261	8	to	to	ADP
ejpam-4798	261	9	vi	vi	PROPN
ejpam-4798	261	10	,	,	PUNCT
ejpam-4798	261	11	1	1	NUM
ejpam-4798	261	12	≤	≤	NUM
ejpam-4798	261	13	i	i	PRON
ejpam-4798	261	14	≤	≤	PROPN
ejpam-4798	261	15	n	n	CCONJ
ejpam-4798	261	16	,	,	PUNCT
ejpam-4798	261	17	which	which	PRON
ejpam-4798	261	18	is	be	AUX
ejpam-4798	261	19	added	add	VERB
ejpam-4798	261	20	in	in	ADP
ejpam-4798	261	21	σ	σ	PROPN
ejpam-4798	261	22	to	to	PART
ejpam-4798	261	23	construct	construct	VERB
ejpam-4798	261	24	γ(σ	γ(σ	NOUN
ejpam-4798	261	25	)	)	PUNCT
ejpam-4798	261	26	,	,	PUNCT
ejpam-4798	261	27	such	such	ADJ
ejpam-4798	261	28	that	that	SCONJ
ejpam-4798	261	29	n(v′i	n(v′i	ADJ
ejpam-4798	261	30	)	)	PUNCT
ejpam-4798	261	31	=	=	SYM
ejpam-4798	261	32	n(vi	n(vi	NUM
ejpam-4798	261	33	)	)	PUNCT
ejpam-4798	261	34	,	,	PUNCT
ejpam-4798	261	35	for	for	ADP
ejpam-4798	261	36	1	1	NUM
ejpam-4798	261	37	≤	≤	NUM
ejpam-4798	261	38	i	i	PRON
ejpam-4798	261	39	≤	≤	PROPN
ejpam-4798	262	1	n.	n.	NOUN
ejpam-4798	262	2	then	then	ADV
ejpam-4798	262	3	the	the	DET
ejpam-4798	262	4	adjacency	adjacency	NOUN
ejpam-4798	262	5	matrix	matrix	NOUN
ejpam-4798	262	6	of	of	ADP
ejpam-4798	262	7	γ(σ	γ(σ	PROPN
ejpam-4798	262	8	)	)	PUNCT
ejpam-4798	262	9	,	,	PUNCT
ejpam-4798	262	10	a(γ(σ	a(γ(σ	NOUN
ejpam-4798	262	11	)	)	PUNCT
ejpam-4798	262	12	)	)	PUNCT
ejpam-4798	262	13	,	,	PUNCT
ejpam-4798	262	14	can	can	AUX
ejpam-4798	262	15	be	be	AUX
ejpam-4798	262	16	expressed	express	VERB
ejpam-4798	262	17	as	as	ADP
ejpam-4798	262	18	a	a	DET
ejpam-4798	262	19	block	block	NOUN
ejpam-4798	262	20	matrix	matrix	NOUN
ejpam-4798	262	21	with	with	ADP
ejpam-4798	262	22	blocks	block	NOUN
ejpam-4798	262	23	as	as	SCONJ
ejpam-4798	262	24	follows	follow	VERB
ejpam-4798	262	25	a(γ(σ	a(γ(σ	NOUN
ejpam-4798	262	26	)	)	PUNCT
ejpam-4798	262	27	)	)	PUNCT
ejpam-4798	263	1	=	=	SYM
ejpam-4798	263	2			ADJ
ejpam-4798	263	3	0	0	PROPN
ejpam-4798	263	4	a1,2	a1,2	PROPN
ejpam-4798	263	5	·	·	PUNCT
ejpam-4798	263	6	·	·	PUNCT
ejpam-4798	263	7	·	·	PUNCT
ejpam-4798	264	1	a1,n	a1,n	PROPN
ejpam-4798	264	2	0	0	PUNCT
ejpam-4798	264	3	a1,2	a1,2	PROPN
ejpam-4798	264	4	·	·	PUNCT
ejpam-4798	264	5	·	·	PUNCT
ejpam-4798	264	6	·	·	PUNCT
ejpam-4798	265	1	a1,n	a1,n	PROPN
ejpam-4798	265	2	a2,1	a2,1	PROPN
ejpam-4798	265	3	0	0	NUM
ejpam-4798	265	4	·	·	PUNCT
ejpam-4798	265	5	·	·	PUNCT
ejpam-4798	265	6	·	·	PUNCT
ejpam-4798	266	1	a2,n	a2,n	ADV
ejpam-4798	266	2	a2,1	a2,1	PROPN
ejpam-4798	266	3	0	0	PUNCT
ejpam-4798	266	4	·	·	PUNCT
ejpam-4798	266	5	·	·	PUNCT
ejpam-4798	266	6	·	·	PUNCT
ejpam-4798	267	1	a2,n	a2,n	ADV
ejpam-4798	267	2	...	...	PUNCT
ejpam-4798	267	3	...	...	PUNCT
ejpam-4798	267	4	.	.	PUNCT
ejpam-4798	267	5	.	.	PUNCT
ejpam-4798	267	6	.	.	PUNCT
ejpam-4798	268	1	...	...	PUNCT
ejpam-4798	268	2	...	...	PUNCT
ejpam-4798	268	3	...	...	PUNCT
ejpam-4798	268	4	.	.	PUNCT
ejpam-4798	268	5	.	.	PUNCT
ejpam-4798	269	1	.	.	PUNCT
ejpam-4798	270	1	...	...	PUNCT
ejpam-4798	271	1	an,1	an,1	PROPN
ejpam-4798	271	2	an,2	an,2	PROPN
ejpam-4798	271	3	·	·	PUNCT
ejpam-4798	271	4	·	·	PUNCT
ejpam-4798	271	5	·	·	PUNCT
ejpam-4798	271	6	0	0	NUM
ejpam-4798	272	1	an,1	an,1	PROPN
ejpam-4798	272	2	an,2	an,2	PROPN
ejpam-4798	272	3	·	·	PUNCT
ejpam-4798	272	4	·	·	PUNCT
ejpam-4798	272	5	·	·	PUNCT
ejpam-4798	272	6	0	0	NUM
ejpam-4798	273	1	0	0	NUM
ejpam-4798	273	2	a1,2	a1,2	PROPN
ejpam-4798	273	3	·	·	PUNCT
ejpam-4798	273	4	·	·	PUNCT
ejpam-4798	273	5	·	·	PUNCT
ejpam-4798	274	1	a1,n	a1,n	PROPN
ejpam-4798	274	2	0	0	NUM
ejpam-4798	274	3	0	0	NUM
ejpam-4798	274	4	·	·	PUNCT
ejpam-4798	274	5	·	·	PUNCT
ejpam-4798	274	6	·	·	PUNCT
ejpam-4798	274	7	0	0	PUNCT
ejpam-4798	275	1	a2,1	a2,1	NOUN
ejpam-4798	275	2	0	0	NUM
ejpam-4798	275	3	·	·	PUNCT
ejpam-4798	275	4	·	·	PUNCT
ejpam-4798	275	5	·	·	PUNCT
ejpam-4798	276	1	a2,n	a2,n	ADV
ejpam-4798	276	2	0	0	NUM
ejpam-4798	276	3	0	0	NUM
ejpam-4798	276	4	·	·	PUNCT
ejpam-4798	276	5	·	·	PUNCT
ejpam-4798	276	6	·	·	PUNCT
ejpam-4798	276	7	0	0	NUM
ejpam-4798	276	8	...	...	PUNCT
ejpam-4798	276	9	...	...	PUNCT
ejpam-4798	276	10	.	.	PUNCT
ejpam-4798	276	11	.	.	PUNCT
ejpam-4798	276	12	.	.	PUNCT
ejpam-4798	277	1	...	...	PUNCT
ejpam-4798	277	2	...	...	PUNCT
ejpam-4798	277	3	...	...	PUNCT
ejpam-4798	277	4	.	.	PUNCT
ejpam-4798	277	5	.	.	PUNCT
ejpam-4798	278	1	.	.	PUNCT
ejpam-4798	279	1	...	...	PUNCT
ejpam-4798	280	1	an,1	an,1	PROPN
ejpam-4798	280	2	an,2	an,2	PROPN
ejpam-4798	280	3	·	·	PUNCT
ejpam-4798	280	4	·	·	PUNCT
ejpam-4798	280	5	·	·	PUNCT
ejpam-4798	280	6	0	0	NUM
ejpam-4798	280	7	0	0	NUM
ejpam-4798	280	8	0	0	NUM
ejpam-4798	280	9	·	·	PUNCT
ejpam-4798	280	10	·	·	PUNCT
ejpam-4798	280	11	·	·	PUNCT
ejpam-4798	280	12	0	0	NUM
ejpam-4798	281	1			NOUN
ejpam-4798	281	2	references	reference	NOUN
ejpam-4798	281	3	517	517	NUM
ejpam-4798	281	4	we	we	PRON
ejpam-4798	281	5	can	can	AUX
ejpam-4798	281	6	write	write	VERB
ejpam-4798	281	7	it	it	PRON
ejpam-4798	281	8	as	as	ADP
ejpam-4798	281	9	,	,	PUNCT
ejpam-4798	281	10	a(γ(σ	a(γ(σ	NOUN
ejpam-4798	281	11	)	)	PUNCT
ejpam-4798	281	12	)	)	PUNCT
ejpam-4798	282	1	=	=	PUNCT
ejpam-4798	282	2	[	[	PUNCT
ejpam-4798	282	3	a(σ	a(σ	ADJ
ejpam-4798	282	4	)	)	PUNCT
ejpam-4798	282	5	a(σ	a(σ	ADJ
ejpam-4798	282	6	)	)	PUNCT
ejpam-4798	282	7	a(σ	a(σ	PROPN
ejpam-4798	282	8	)	)	PUNCT
ejpam-4798	282	9	0	0	PUNCT
ejpam-4798	282	10	]	]	PUNCT
ejpam-4798	283	1	=	=	PUNCT
ejpam-4798	283	2	[	[	PUNCT
ejpam-4798	283	3	1	1	NUM
ejpam-4798	283	4	1	1	NUM
ejpam-4798	283	5	1	1	NUM
ejpam-4798	283	6	0	0	NUM
ejpam-4798	283	7	]	]	PUNCT
ejpam-4798	283	8	⊗a(σ	⊗a(σ	NOUN
ejpam-4798	283	9	)	)	PUNCT
ejpam-4798	283	10	let	let	VERB
ejpam-4798	283	11	λ1	λ1	ADJ
ejpam-4798	283	12	,	,	PUNCT
ejpam-4798	283	13	λ2	λ2	NOUN
ejpam-4798	283	14	,	,	PUNCT
ejpam-4798	283	15	...	...	PUNCT
ejpam-4798	283	16	,	,	PUNCT
ejpam-4798	283	17	λn	λn	PROPN
ejpam-4798	283	18	are	be	AUX
ejpam-4798	283	19	the	the	DET
ejpam-4798	283	20	eigenvalues	eigenvalue	NOUN
ejpam-4798	283	21	of	of	ADP
ejpam-4798	283	22	the	the	DET
ejpam-4798	283	23	signed	sign	VERB
ejpam-4798	283	24	graph	graph	NOUN
ejpam-4798	283	25	σ	σ	NOUN
ejpam-4798	283	26	and	and	CCONJ
ejpam-4798	283	27	we	we	PRON
ejpam-4798	283	28	can	can	AUX
ejpam-4798	283	29	observe	observe	VERB
ejpam-4798	283	30	that	that	SCONJ
ejpam-4798	283	31	the	the	DET
ejpam-4798	283	32	eigenvalues	eigenvalue	NOUN
ejpam-4798	283	33	of	of	ADP
ejpam-4798	283	34	[	[	PUNCT
ejpam-4798	283	35	1	1	NUM
ejpam-4798	283	36	1	1	NUM
ejpam-4798	283	37	1	1	NUM
ejpam-4798	283	38	0	0	NUM
ejpam-4798	283	39	]	]	PUNCT
ejpam-4798	283	40	are	be	AUX
ejpam-4798	283	41	{	{	PUNCT
ejpam-4798	283	42	1	1	NUM
ejpam-4798	283	43	+	+	NUM
ejpam-4798	283	44	√	√	NUM
ejpam-4798	283	45	5	5	NUM
ejpam-4798	283	46	2	2	NUM
ejpam-4798	283	47	,	,	PUNCT
ejpam-4798	283	48	1−	1−	NUM
ejpam-4798	283	49	√	√	NUM
ejpam-4798	283	50	5	5	NUM
ejpam-4798	283	51	2	2	NUM
ejpam-4798	283	52	}	}	PUNCT
ejpam-4798	283	53	.	.	PUNCT
ejpam-4798	284	1	therefore	therefore	ADV
ejpam-4798	284	2	,	,	PUNCT
ejpam-4798	284	3	spec(γ(σ	spec(γ(σ	PROPN
ejpam-4798	284	4	)	)	PUNCT
ejpam-4798	284	5	)	)	PUNCT
ejpam-4798	285	1	=	=	PUNCT
ejpam-4798	285	2	(	(	PUNCT
ejpam-4798	285	3	(	(	PUNCT
ejpam-4798	285	4	1	1	NUM
ejpam-4798	285	5	+	+	NUM
ejpam-4798	285	6	√	√	NUM
ejpam-4798	285	7	5	5	NUM
ejpam-4798	285	8	2	2	NUM
ejpam-4798	285	9	)	)	PUNCT
ejpam-4798	285	10	λi	λi	NOUN
ejpam-4798	285	11	(	(	PUNCT
ejpam-4798	285	12	1−	1−	NUM
ejpam-4798	285	13	√	√	NUM
ejpam-4798	285	14	5	5	NUM
ejpam-4798	285	15	2	2	NUM
ejpam-4798	285	16	)	)	PUNCT
ejpam-4798	285	17	λi	λi	CCONJ
ejpam-4798	285	18	n	n	CCONJ
ejpam-4798	285	19	n	n	CCONJ
ejpam-4798	285	20	)	)	PUNCT
ejpam-4798	285	21	e(γ(σ	e(γ(σ	PROPN
ejpam-4798	285	22	)	)	PUNCT
ejpam-4798	285	23	)	)	PUNCT
ejpam-4798	286	1	=	=	PUNCT
ejpam-4798	287	1	n∑	n∑	NUM
ejpam-4798	287	2	i=1	i=1	PROPN
ejpam-4798	287	3	|(1±	|(1±	NOUN
ejpam-4798	287	4	√	√	NUM
ejpam-4798	287	5	5	5	NUM
ejpam-4798	287	6	2	2	NUM
ejpam-4798	287	7	)	)	PUNCT
ejpam-4798	288	1	λi|	λi|	NOUN
ejpam-4798	288	2	=	=	SYM
ejpam-4798	288	3	n∑	n∑	PROPN
ejpam-4798	288	4	i=1	i=1	PROPN
ejpam-4798	288	5	|λi|	|λi|	PROPN
ejpam-4798	288	6	[	[	PUNCT
ejpam-4798	288	7	1	1	NUM
ejpam-4798	288	8	+	+	CCONJ
ejpam-4798	288	9	√	√	NUM
ejpam-4798	288	10	5	5	NUM
ejpam-4798	288	11	2	2	NUM
ejpam-4798	288	12	+	+	SYM
ejpam-4798	288	13	1−	1−	NUM
ejpam-4798	288	14	√	√	NUM
ejpam-4798	288	15	5	5	NUM
ejpam-4798	288	16	2	2	NUM
ejpam-4798	288	17	]	]	PUNCT
ejpam-4798	288	18	=	=	PUNCT
ejpam-4798	288	19	√	√	NUM
ejpam-4798	288	20	5	5	NUM
ejpam-4798	288	21	n∑	n∑	NOUN
ejpam-4798	288	22	i=1	i=1	PROPN
ejpam-4798	288	23	|λi|	|λi|	NOUN
ejpam-4798	288	24	hence	hence	ADV
ejpam-4798	288	25	,	,	PUNCT
ejpam-4798	288	26	e(γ(σ	e(γ(σ	PROPN
ejpam-4798	288	27	)	)	PUNCT
ejpam-4798	288	28	)	)	PUNCT
ejpam-4798	289	1	=	=	PUNCT
ejpam-4798	290	1	√	√	NUM
ejpam-4798	290	2	5e(σ	5e(σ	NUM
ejpam-4798	290	3	)	)	PUNCT
ejpam-4798	290	4	6	6	NUM
ejpam-4798	290	5	.	.	PUNCT
ejpam-4798	290	6	conclusion	conclusion	NOUN
ejpam-4798	290	7	and	and	CCONJ
ejpam-4798	290	8	scope	scope	NOUN
ejpam-4798	290	9	in	in	ADP
ejpam-4798	290	10	conclusion	conclusion	NOUN
ejpam-4798	290	11	,	,	PUNCT
ejpam-4798	290	12	this	this	DET
ejpam-4798	290	13	research	research	NOUN
ejpam-4798	290	14	gives	give	VERB
ejpam-4798	290	15	an	an	DET
ejpam-4798	290	16	algorithm	algorithm	NOUN
ejpam-4798	290	17	for	for	ADP
ejpam-4798	290	18	generating	generate	VERB
ejpam-4798	290	19	a	a	DET
ejpam-4798	290	20	splitting	splitting	NOUN
ejpam-4798	290	21	signed	sign	VERB
ejpam-4798	290	22	graph	graph	NOUN
ejpam-4798	290	23	and	and	CCONJ
ejpam-4798	290	24	a	a	DET
ejpam-4798	290	25	splitting	splitting	NOUN
ejpam-4798	290	26	root	root	NOUN
ejpam-4798	290	27	signed	sign	VERB
ejpam-4798	290	28	graph	graph	NOUN
ejpam-4798	290	29	from	from	ADP
ejpam-4798	290	30	a	a	DET
ejpam-4798	290	31	given	give	VERB
ejpam-4798	290	32	signed	sign	VERB
ejpam-4798	290	33	graph	graph	NOUN
ejpam-4798	290	34	,	,	PUNCT
ejpam-4798	290	35	provided	provide	VERB
ejpam-4798	290	36	it	it	PRON
ejpam-4798	290	37	exists	exist	VERB
ejpam-4798	290	38	.	.	PUNCT
ejpam-4798	291	1	additionally	additionally	ADV
ejpam-4798	291	2	,	,	PUNCT
ejpam-4798	291	3	a	a	DET
ejpam-4798	291	4	spectral	spectral	ADJ
ejpam-4798	291	5	analysis	analysis	NOUN
ejpam-4798	291	6	of	of	ADP
ejpam-4798	291	7	the	the	DET
ejpam-4798	291	8	resulting	result	VERB
ejpam-4798	291	9	graph	graph	NOUN
ejpam-4798	291	10	is	be	AUX
ejpam-4798	291	11	conducted	conduct	VERB
ejpam-4798	291	12	by	by	ADP
ejpam-4798	291	13	studying	study	VERB
ejpam-4798	291	14	its	its	PRON
ejpam-4798	291	15	eigenvalues	eigenvalue	NOUN
ejpam-4798	291	16	and	and	CCONJ
ejpam-4798	291	17	eigenvectors	eigenvector	NOUN
ejpam-4798	291	18	through	through	ADP
ejpam-4798	291	19	the	the	DET
ejpam-4798	291	20	adjacency	adjacency	NOUN
ejpam-4798	291	21	and	and	CCONJ
ejpam-4798	291	22	laplacian	laplacian	ADJ
ejpam-4798	291	23	matrices	matrix	NOUN
ejpam-4798	291	24	.	.	PUNCT
ejpam-4798	292	1	the	the	DET
ejpam-4798	292	2	research	research	NOUN
ejpam-4798	292	3	also	also	ADV
ejpam-4798	292	4	establishes	establish	VERB
ejpam-4798	292	5	a	a	DET
ejpam-4798	292	6	relationship	relationship	NOUN
ejpam-4798	292	7	between	between	ADP
ejpam-4798	292	8	the	the	DET
ejpam-4798	292	9	energy	energy	NOUN
ejpam-4798	292	10	of	of	ADP
ejpam-4798	292	11	the	the	DET
ejpam-4798	292	12	original	original	ADJ
ejpam-4798	292	13	signed	sign	VERB
ejpam-4798	292	14	graph	graph	NOUN
ejpam-4798	292	15	σ	σ	PROPN
ejpam-4798	292	16	and	and	CCONJ
ejpam-4798	292	17	the	the	DET
ejpam-4798	292	18	energy	energy	NOUN
ejpam-4798	292	19	of	of	ADP
ejpam-4798	292	20	the	the	DET
ejpam-4798	292	21	splitting	splitting	NOUN
ejpam-4798	292	22	signed	sign	VERB
ejpam-4798	292	23	graph	graph	NOUN
ejpam-4798	292	24	γ(σ	γ(σ	PROPN
ejpam-4798	292	25	)	)	PUNCT
ejpam-4798	292	26	.	.	PUNCT
ejpam-4798	293	1	the	the	DET
ejpam-4798	293	2	scope	scope	NOUN
ejpam-4798	293	3	of	of	ADP
ejpam-4798	293	4	this	this	DET
ejpam-4798	293	5	research	research	NOUN
ejpam-4798	293	6	could	could	AUX
ejpam-4798	293	7	be	be	AUX
ejpam-4798	293	8	extended	extend	VERB
ejpam-4798	293	9	by	by	ADP
ejpam-4798	293	10	exploring	explore	VERB
ejpam-4798	293	11	further	further	ADJ
ejpam-4798	293	12	applications	application	NOUN
ejpam-4798	293	13	of	of	ADP
ejpam-4798	293	14	the	the	DET
ejpam-4798	293	15	proposed	propose	VERB
ejpam-4798	293	16	algorithm	algorithm	NOUN
ejpam-4798	293	17	and	and	CCONJ
ejpam-4798	293	18	studying	study	VERB
ejpam-4798	293	19	the	the	DET
ejpam-4798	293	20	properties	property	NOUN
ejpam-4798	293	21	of	of	ADP
ejpam-4798	293	22	splitting	split	VERB
ejpam-4798	293	23	signed	sign	VERB
ejpam-4798	293	24	graphs	graph	NOUN
ejpam-4798	293	25	in	in	ADP
ejpam-4798	293	26	more	more	ADJ
ejpam-4798	293	27	detail	detail	NOUN
ejpam-4798	293	28	.	.	PUNCT
ejpam-4798	294	1	conflicts	conflict	NOUN
ejpam-4798	294	2	of	of	ADP
ejpam-4798	294	3	interest	interest	NOUN
ejpam-4798	294	4	:	:	PUNCT
ejpam-4798	294	5	all	all	DET
ejpam-4798	294	6	the	the	DET
ejpam-4798	294	7	authors	author	NOUN
ejpam-4798	294	8	declare	declare	VERB
ejpam-4798	294	9	that	that	SCONJ
ejpam-4798	294	10	they	they	PRON
ejpam-4798	294	11	have	have	VERB
ejpam-4798	294	12	no	no	DET
ejpam-4798	294	13	conflicts	conflict	NOUN
ejpam-4798	294	14	of	of	ADP
ejpam-4798	294	15	interest	interest	NOUN
ejpam-4798	294	16	regarding	regard	VERB
ejpam-4798	294	17	the	the	DET
ejpam-4798	294	18	publication	publication	NOUN
ejpam-4798	294	19	of	of	ADP
ejpam-4798	294	20	this	this	DET
ejpam-4798	294	21	paper	paper	NOUN
ejpam-4798	294	22	.	.	PUNCT
ejpam-4798	295	1	references	reference	NOUN
ejpam-4798	295	2	[	[	X
ejpam-4798	295	3	1	1	NUM
ejpam-4798	295	4	]	]	SYM
ejpam-4798	295	5	b	b	PROPN
ejpam-4798	295	6	devadas	devadas	PROPN
ejpam-4798	295	7	acharya	acharya	NOUN
ejpam-4798	295	8	.	.	PUNCT
ejpam-4798	296	1	spectral	spectral	ADJ
ejpam-4798	296	2	criterion	criterion	NOUN
ejpam-4798	296	3	for	for	ADP
ejpam-4798	296	4	cycle	cycle	NOUN
ejpam-4798	296	5	balance	balance	NOUN
ejpam-4798	296	6	in	in	ADP
ejpam-4798	296	7	networks	network	NOUN
ejpam-4798	296	8	.	.	PUNCT
ejpam-4798	297	1	journal	journal	NOUN
ejpam-4798	297	2	of	of	ADP
ejpam-4798	297	3	graph	graph	NOUN
ejpam-4798	297	4	theory	theory	NOUN
ejpam-4798	297	5	,	,	PUNCT
ejpam-4798	297	6	4(1):1–11	4(1):1–11	PROPN
ejpam-4798	297	7	,	,	PUNCT
ejpam-4798	297	8	1980	1980	NUM
ejpam-4798	297	9	.	.	PUNCT
ejpam-4798	298	1	[	[	X
ejpam-4798	298	2	2	2	NUM
ejpam-4798	298	3	]	]	X
ejpam-4798	298	4	r	r	NOUN
ejpam-4798	298	5	balakrishnan	balakrishnan	PROPN
ejpam-4798	298	6	.	.	PUNCT
ejpam-4798	299	1	the	the	DET
ejpam-4798	299	2	energy	energy	NOUN
ejpam-4798	299	3	of	of	ADP
ejpam-4798	299	4	a	a	DET
ejpam-4798	299	5	graph	graph	NOUN
ejpam-4798	299	6	.	.	PUNCT
ejpam-4798	300	1	linear	linear	ADJ
ejpam-4798	300	2	algebra	algebra	NOUN
ejpam-4798	300	3	and	and	CCONJ
ejpam-4798	300	4	its	its	PRON
ejpam-4798	300	5	applications	application	NOUN
ejpam-4798	300	6	,	,	PUNCT
ejpam-4798	300	7	387:287	387:287	PROPN
ejpam-4798	300	8	–	–	PUNCT
ejpam-4798	300	9	295	295	NUM
ejpam-4798	300	10	,	,	PUNCT
ejpam-4798	300	11	2004	2004	NUM
ejpam-4798	300	12	.	.	PUNCT
ejpam-4798	301	1	[	[	X
ejpam-4798	301	2	3	3	X
ejpam-4798	301	3	]	]	X
ejpam-4798	301	4	rb	rb	X
ejpam-4798	301	5	bapat	bapat	NOUN
ejpam-4798	301	6	and	and	CCONJ
ejpam-4798	301	7	suganta	suganta	PROPN
ejpam-4798	301	8	pati	pati	NOUN
ejpam-4798	301	9	.	.	PUNCT
ejpam-4798	302	1	energy	energy	NOUN
ejpam-4798	302	2	of	of	ADP
ejpam-4798	302	3	a	a	DET
ejpam-4798	302	4	graph	graph	NOUN
ejpam-4798	302	5	is	be	AUX
ejpam-4798	302	6	never	never	ADV
ejpam-4798	302	7	an	an	DET
ejpam-4798	302	8	odd	odd	ADJ
ejpam-4798	302	9	integer	integer	NOUN
ejpam-4798	302	10	.	.	PUNCT
ejpam-4798	303	1	2004	2004	NUM
ejpam-4798	303	2	.	.	PUNCT
ejpam-4798	304	1	[	[	X
ejpam-4798	304	2	4	4	NUM
ejpam-4798	304	3	]	]	X
ejpam-4798	304	4	sasmita	sasmita	PROPN
ejpam-4798	304	5	barik	barik	PROPN
ejpam-4798	304	6	,	,	PUNCT
ejpam-4798	304	7	ravindra	ravindra	PROPN
ejpam-4798	304	8	b	b	PROPN
ejpam-4798	304	9	bapat	bapat	PROPN
ejpam-4798	304	10	,	,	PUNCT
ejpam-4798	304	11	and	and	CCONJ
ejpam-4798	304	12	sukanta	sukanta	PROPN
ejpam-4798	304	13	pati	pati	PROPN
ejpam-4798	304	14	.	.	PUNCT
ejpam-4798	305	1	on	on	ADP
ejpam-4798	305	2	the	the	DET
ejpam-4798	305	3	laplacian	laplacian	ADJ
ejpam-4798	305	4	spectra	spectra	NOUN
ejpam-4798	305	5	of	of	ADP
ejpam-4798	305	6	product	product	NOUN
ejpam-4798	305	7	graphs	graph	NOUN
ejpam-4798	305	8	.	.	PUNCT
ejpam-4798	306	1	applicable	applicable	ADJ
ejpam-4798	306	2	analysis	analysis	NOUN
ejpam-4798	306	3	and	and	CCONJ
ejpam-4798	306	4	discrete	discrete	ADJ
ejpam-4798	306	5	mathematics	mathematic	NOUN
ejpam-4798	306	6	,	,	PUNCT
ejpam-4798	306	7	pages	page	NOUN
ejpam-4798	306	8	39–58	39–58	NUM
ejpam-4798	306	9	,	,	PUNCT
ejpam-4798	306	10	2015	2015	NUM
ejpam-4798	306	11	.	.	PUNCT
ejpam-4798	307	1	references	reference	NOUN
ejpam-4798	307	2	518	518	NUM
ejpam-4798	307	3	[	[	X
ejpam-4798	307	4	5	5	NUM
ejpam-4798	307	5	]	]	PUNCT
ejpam-4798	307	6	sasmita	sasmita	PROPN
ejpam-4798	307	7	barik	barik	PROPN
ejpam-4798	307	8	,	,	PUNCT
ejpam-4798	307	9	deabajit	deabajit	PROPN
ejpam-4798	307	10	kalita	kalita	PROPN
ejpam-4798	307	11	,	,	PUNCT
ejpam-4798	307	12	sukanta	sukanta	PROPN
ejpam-4798	307	13	pati	pati	PROPN
ejpam-4798	307	14	,	,	PUNCT
ejpam-4798	307	15	and	and	CCONJ
ejpam-4798	307	16	gopinath	gopinath	PROPN
ejpam-4798	307	17	sahoo	sahoo	PROPN
ejpam-4798	307	18	.	.	PUNCT
ejpam-4798	307	19	spectra	spectra	PROPN
ejpam-4798	307	20	of	of	ADP
ejpam-4798	307	21	graphs	graph	NOUN
ejpam-4798	307	22	resulting	result	VERB
ejpam-4798	307	23	from	from	ADP
ejpam-4798	307	24	various	various	ADJ
ejpam-4798	307	25	graph	graph	NOUN
ejpam-4798	307	26	operations	operation	NOUN
ejpam-4798	307	27	and	and	CCONJ
ejpam-4798	307	28	products	product	NOUN
ejpam-4798	307	29	:	:	PUNCT
ejpam-4798	307	30	a	a	DET
ejpam-4798	307	31	survey	survey	NOUN
ejpam-4798	307	32	.	.	PUNCT
ejpam-4798	308	1	special	special	ADJ
ejpam-4798	308	2	matrices	matrix	NOUN
ejpam-4798	308	3	,	,	PUNCT
ejpam-4798	308	4	6(1):323–342	6(1):323–342	NOUN
ejpam-4798	308	5	,	,	PUNCT
ejpam-4798	308	6	2018	2018	NUM
ejpam-4798	308	7	.	.	PUNCT
ejpam-4798	309	1	[	[	X
ejpam-4798	309	2	6	6	NUM
ejpam-4798	309	3	]	]	X
ejpam-4798	309	4	sasmita	sasmita	PROPN
ejpam-4798	309	5	barik	barik	PROPN
ejpam-4798	309	6	,	,	PUNCT
ejpam-4798	309	7	sukanta	sukanta	PROPN
ejpam-4798	309	8	pati	pati	PROPN
ejpam-4798	309	9	,	,	PUNCT
ejpam-4798	309	10	and	and	CCONJ
ejpam-4798	309	11	bk	bk	ADP
ejpam-4798	309	12	sarma	sarma	PROPN
ejpam-4798	309	13	.	.	PUNCT
ejpam-4798	310	1	the	the	DET
ejpam-4798	310	2	spectrum	spectrum	NOUN
ejpam-4798	310	3	of	of	ADP
ejpam-4798	310	4	the	the	DET
ejpam-4798	310	5	corona	corona	NOUN
ejpam-4798	310	6	of	of	ADP
ejpam-4798	310	7	two	two	NUM
ejpam-4798	310	8	graphs	graph	NOUN
ejpam-4798	310	9	.	.	PUNCT
ejpam-4798	311	1	siam	siam	PROPN
ejpam-4798	311	2	journal	journal	PROPN
ejpam-4798	311	3	on	on	ADP
ejpam-4798	311	4	discrete	discrete	ADJ
ejpam-4798	311	5	mathematics	mathematic	NOUN
ejpam-4798	311	6	,	,	PUNCT
ejpam-4798	311	7	21(1):47–56	21(1):47–56	NUM
ejpam-4798	311	8	,	,	PUNCT
ejpam-4798	311	9	2007	2007	NUM
ejpam-4798	311	10	.	.	PUNCT
ejpam-4798	312	1	[	[	X
ejpam-4798	312	2	7	7	X
ejpam-4798	312	3	]	]	X
ejpam-4798	312	4	a	a	DET
ejpam-4798	312	5	das	das	PROPN
ejpam-4798	312	6	and	and	CCONJ
ejpam-4798	312	7	p	p	NOUN
ejpam-4798	312	8	panigrahi	panigrahi	NOUN
ejpam-4798	312	9	.	.	PUNCT
ejpam-4798	313	1	new	new	ADJ
ejpam-4798	313	2	classes	class	NOUN
ejpam-4798	313	3	of	of	ADP
ejpam-4798	313	4	simultaneous	simultaneous	ADJ
ejpam-4798	313	5	cospectral	cospectral	ADJ
ejpam-4798	313	6	graphs	graph	NOUN
ejpam-4798	313	7	for	for	ADP
ejpam-4798	313	8	adjacency	adjacency	NOUN
ejpam-4798	313	9	,	,	PUNCT
ejpam-4798	313	10	laplacian	laplacian	ADJ
ejpam-4798	313	11	and	and	CCONJ
ejpam-4798	313	12	normalized	normalize	VERB
ejpam-4798	313	13	laplacian	laplacian	ADJ
ejpam-4798	313	14	matrices	matrix	NOUN
ejpam-4798	313	15	.	.	PUNCT
ejpam-4798	314	1	kragujevac	kragujevac	PROPN
ejpam-4798	314	2	journal	journal	PROPN
ejpam-4798	314	3	of	of	ADP
ejpam-4798	314	4	mathematics	mathematics	PROPN
ejpam-4798	314	5	,	,	PUNCT
ejpam-4798	314	6	43(2):303–323	43(2):303–323	PROPN
ejpam-4798	314	7	,	,	PUNCT
ejpam-4798	314	8	2019	2019	NUM
ejpam-4798	314	9	.	.	PUNCT
ejpam-4798	315	1	[	[	X
ejpam-4798	315	2	8	8	NUM
ejpam-4798	315	3	]	]	X
ejpam-4798	315	4	roger	roger	NOUN
ejpam-4798	315	5	a	a	DET
ejpam-4798	315	6	horn	horn	NOUN
ejpam-4798	315	7	and	and	CCONJ
ejpam-4798	315	8	charles	charles	PROPN
ejpam-4798	315	9	r	r	PROPN
ejpam-4798	315	10	johnson	johnson	PROPN
ejpam-4798	315	11	.	.	PROPN
ejpam-4798	316	1	matrix	matrix	NOUN
ejpam-4798	316	2	analysis	analysis	NOUN
ejpam-4798	316	3	.	.	PUNCT
ejpam-4798	317	1	cambridge	cambridge	PROPN
ejpam-4798	317	2	university	university	PROPN
ejpam-4798	317	3	press	press	NOUN
ejpam-4798	317	4	,	,	PUNCT
ejpam-4798	317	5	2012	2012	NUM
ejpam-4798	317	6	.	.	PUNCT
ejpam-4798	318	1	[	[	X
ejpam-4798	318	2	9	9	NUM
ejpam-4798	318	3	]	]	X
ejpam-4798	318	4	zhiqin	zhiqin	PROPN
ejpam-4798	318	5	lu	lu	PROPN
ejpam-4798	318	6	,	,	PUNCT
ejpam-4798	318	7	xiaoling	xiaoling	PROPN
ejpam-4798	318	8	ma	ma	PROPN
ejpam-4798	318	9	,	,	PUNCT
ejpam-4798	318	10	and	and	CCONJ
ejpam-4798	318	11	minshao	minshao	PROPN
ejpam-4798	318	12	zhang	zhang	PROPN
ejpam-4798	318	13	.	.	PUNCT
ejpam-4798	318	14	spectra	spectra	PROPN
ejpam-4798	318	15	of	of	ADP
ejpam-4798	318	16	graph	graph	NOUN
ejpam-4798	318	17	operations	operation	NOUN
ejpam-4798	318	18	based	base	VERB
ejpam-4798	318	19	on	on	ADP
ejpam-4798	318	20	splitting	splitting	NOUN
ejpam-4798	318	21	graph	graph	NOUN
ejpam-4798	318	22	.	.	PUNCT
ejpam-4798	318	23	journal	journal	PROPN
ejpam-4798	318	24	of	of	ADP
ejpam-4798	318	25	applied	apply	VERB
ejpam-4798	318	26	analysis	analysis	NOUN
ejpam-4798	318	27	&	&	CCONJ
ejpam-4798	318	28	computation	computation	NOUN
ejpam-4798	318	29	,	,	PUNCT
ejpam-4798	318	30	13(1):133–155	13(1):133–155	PROPN
ejpam-4798	318	31	,	,	PUNCT
ejpam-4798	318	32	2023	2023	NUM
ejpam-4798	318	33	.	.	PUNCT
ejpam-4798	319	1	[	[	X
ejpam-4798	319	2	10	10	NUM
ejpam-4798	319	3	]	]	PUNCT
ejpam-4798	319	4	rb	rb	PRON
ejpam-4798	319	5	mallion	mallion	NOUN
ejpam-4798	319	6	.	.	PUNCT
ejpam-4798	320	1	some	some	DET
ejpam-4798	320	2	graph	graph	NOUN
ejpam-4798	320	3	-	-	PUNCT
ejpam-4798	320	4	theoretical	theoretical	ADJ
ejpam-4798	320	5	aspects	aspect	NOUN
ejpam-4798	320	6	of	of	ADP
ejpam-4798	320	7	simple	simple	ADJ
ejpam-4798	320	8	ring	ring	NOUN
ejpam-4798	320	9	current	current	ADJ
ejpam-4798	320	10	calculations	calculation	NOUN
ejpam-4798	320	11	on	on	ADP
ejpam-4798	320	12	conjugated	conjugated	ADJ
ejpam-4798	320	13	systems	system	NOUN
ejpam-4798	320	14	.	.	PUNCT
ejpam-4798	321	1	proceedings	proceeding	NOUN
ejpam-4798	321	2	of	of	ADP
ejpam-4798	321	3	the	the	DET
ejpam-4798	321	4	royal	royal	ADJ
ejpam-4798	321	5	society	society	NOUN
ejpam-4798	321	6	of	of	ADP
ejpam-4798	321	7	london	london	PROPN
ejpam-4798	321	8	.	.	PUNCT
ejpam-4798	322	1	a.	a.	PROPN
ejpam-4798	322	2	mathematical	mathematical	PROPN
ejpam-4798	322	3	and	and	CCONJ
ejpam-4798	322	4	physical	physical	ADJ
ejpam-4798	322	5	sciences	science	NOUN
ejpam-4798	322	6	,	,	PUNCT
ejpam-4798	322	7	341(1627):429–449	341(1627):429–449	NUM
ejpam-4798	322	8	,	,	PUNCT
ejpam-4798	322	9	1975	1975	NUM
ejpam-4798	322	10	.	.	PUNCT
ejpam-4798	323	1	[	[	X
ejpam-4798	323	2	11	11	NUM
ejpam-4798	323	3	]	]	PUNCT
ejpam-4798	323	4	vladimir	vladimir	NOUN
ejpam-4798	323	5	nikiforov	nikiforov	PROPN
ejpam-4798	323	6	.	.	PUNCT
ejpam-4798	324	1	the	the	DET
ejpam-4798	324	2	energy	energy	NOUN
ejpam-4798	324	3	of	of	ADP
ejpam-4798	324	4	graphs	graph	NOUN
ejpam-4798	324	5	and	and	CCONJ
ejpam-4798	324	6	matrices	matrix	NOUN
ejpam-4798	324	7	.	.	PUNCT
ejpam-4798	325	1	journal	journal	PROPN
ejpam-4798	325	2	of	of	ADP
ejpam-4798	325	3	mathematical	mathematical	ADJ
ejpam-4798	325	4	analysis	analysis	NOUN
ejpam-4798	325	5	and	and	CCONJ
ejpam-4798	325	6	applications	application	NOUN
ejpam-4798	325	7	,	,	PUNCT
ejpam-4798	325	8	326(2):1472–1475	326(2):1472–1475	PROPN
ejpam-4798	325	9	,	,	PUNCT
ejpam-4798	325	10	2007	2007	NUM
ejpam-4798	325	11	.	.	PUNCT
ejpam-4798	326	1	[	[	X
ejpam-4798	326	2	12	12	NUM
ejpam-4798	326	3	]	]	X
ejpam-4798	326	4	s	s	X
ejpam-4798	326	5	pirzada	pirzada	NOUN
ejpam-4798	326	6	and	and	CCONJ
ejpam-4798	326	7	i	i	PROPN
ejpam-4798	326	8	gutman	gutman	PROPN
ejpam-4798	326	9	.	.	PUNCT
ejpam-4798	327	1	energy	energy	NOUN
ejpam-4798	327	2	of	of	ADP
ejpam-4798	327	3	a	a	DET
ejpam-4798	327	4	graph	graph	NOUN
ejpam-4798	327	5	is	be	AUX
ejpam-4798	327	6	never	never	ADV
ejpam-4798	327	7	the	the	DET
ejpam-4798	327	8	square	square	ADJ
ejpam-4798	327	9	root	root	NOUN
ejpam-4798	327	10	of	of	ADP
ejpam-4798	327	11	an	an	DET
ejpam-4798	327	12	odd	odd	ADJ
ejpam-4798	327	13	integer	integer	NOUN
ejpam-4798	327	14	.	.	PUNCT
ejpam-4798	328	1	applicable	applicable	ADJ
ejpam-4798	328	2	analysis	analysis	NOUN
ejpam-4798	328	3	and	and	CCONJ
ejpam-4798	328	4	discrete	discrete	ADJ
ejpam-4798	328	5	mathematics	mathematic	NOUN
ejpam-4798	328	6	,	,	PUNCT
ejpam-4798	328	7	pages	page	NOUN
ejpam-4798	328	8	118–121	118–121	NUM
ejpam-4798	328	9	,	,	PUNCT
ejpam-4798	328	10	2008	2008	NUM
ejpam-4798	328	11	.	.	PUNCT
ejpam-4798	329	1	[	[	X
ejpam-4798	329	2	13	13	NUM
ejpam-4798	329	3	]	]	X
ejpam-4798	329	4	deepa	deepa	PROPN
ejpam-4798	329	5	sinha	sinha	PROPN
ejpam-4798	329	6	,	,	PUNCT
ejpam-4798	329	7	pravin	pravin	PROPN
ejpam-4798	329	8	garg	garg	PROPN
ejpam-4798	329	9	,	,	PUNCT
ejpam-4798	329	10	and	and	CCONJ
ejpam-4798	329	11	hina	hina	NOUN
ejpam-4798	329	12	saraswat	saraswat	NOUN
ejpam-4798	329	13	.	.	PUNCT
ejpam-4798	330	1	on	on	ADP
ejpam-4798	330	2	the	the	DET
ejpam-4798	330	3	splitting	splitting	NOUN
ejpam-4798	330	4	signed	sign	VERB
ejpam-4798	330	5	graphs	graph	NOUN
ejpam-4798	330	6	.	.	PUNCT
ejpam-4798	331	1	journal	journal	PROPN
ejpam-4798	331	2	of	of	ADP
ejpam-4798	331	3	combinatorics	combinatoric	NOUN
ejpam-4798	331	4	&	&	CCONJ
ejpam-4798	331	5	system	system	PROPN
ejpam-4798	331	6	sciences	sciences	PROPN
ejpam-4798	331	7	,	,	PUNCT
ejpam-4798	331	8	38	38	NUM
ejpam-4798	331	9	,	,	PUNCT
ejpam-4798	331	10	2013	2013	NUM
ejpam-4798	331	11	.	.	PUNCT
ejpam-4798	332	1	[	[	X
ejpam-4798	332	2	14	14	NUM
ejpam-4798	332	3	]	]	X
ejpam-4798	332	4	deepa	deepa	PROPN
ejpam-4798	332	5	sinha	sinha	PROPN
ejpam-4798	332	6	and	and	CCONJ
ejpam-4798	332	7	sandeep	sandeep	PROPN
ejpam-4798	332	8	kumar	kumar	PROPN
ejpam-4798	332	9	.	.	PUNCT
ejpam-4798	333	1	an	an	DET
ejpam-4798	333	2	algorithmic	algorithmic	ADJ
ejpam-4798	333	3	characterization	characterization	NOUN
ejpam-4798	333	4	and	and	CCONJ
ejpam-4798	333	5	spectral	spectral	ADJ
ejpam-4798	333	6	analysis	analysis	NOUN
ejpam-4798	333	7	of	of	ADP
ejpam-4798	333	8	canonical	canonical	ADJ
ejpam-4798	333	9	splitting	splitting	NOUN
ejpam-4798	333	10	signed	sign	VERB
ejpam-4798	333	11	graph	graph	NOUN
ejpam-4798	333	12	ξ	ξ	PROPN
ejpam-4798	333	13	(	(	PUNCT
ejpam-4798	333	14	σ	σ	PROPN
ejpam-4798	333	15	)	)	PUNCT
ejpam-4798	333	16	.	.	PUNCT
ejpam-4798	334	1	methodsx	methodsx	PROPN
ejpam-4798	334	2	,	,	PUNCT
ejpam-4798	334	3	12:102517	12:102517	NUM
ejpam-4798	334	4	,	,	PUNCT
ejpam-4798	334	5	2024	2024	NUM
ejpam-4798	334	6	.	.	PUNCT
ejpam-4798	335	1	[	[	X
ejpam-4798	335	2	15	15	NUM
ejpam-4798	335	3	]	]	X
ejpam-4798	335	4	deepa	deepa	PROPN
ejpam-4798	335	5	sinha	sinha	PROPN
ejpam-4798	335	6	and	and	CCONJ
ejpam-4798	335	7	anita	anita	PROPN
ejpam-4798	335	8	kumari	kumari	PROPN
ejpam-4798	335	9	rao	rao	PROPN
ejpam-4798	335	10	.	.	PUNCT
ejpam-4798	336	1	embedding	embed	VERB
ejpam-4798	336	2	of	of	ADP
ejpam-4798	336	3	sign	sign	NOUN
ejpam-4798	336	4	-	-	PUNCT
ejpam-4798	336	5	regular	regular	ADJ
ejpam-4798	336	6	signed	sign	VERB
ejpam-4798	336	7	graphs	graph	NOUN
ejpam-4798	336	8	and	and	CCONJ
ejpam-4798	336	9	its	its	PRON
ejpam-4798	336	10	spectral	spectral	ADJ
ejpam-4798	336	11	analysis	analysis	NOUN
ejpam-4798	336	12	.	.	PUNCT
ejpam-4798	337	1	linear	linear	ADJ
ejpam-4798	337	2	and	and	CCONJ
ejpam-4798	337	3	multilinear	multilinear	PROPN
ejpam-4798	337	4	algebra	algebra	PROPN
ejpam-4798	337	5	,	,	PUNCT
ejpam-4798	337	6	70(8):1496–1512	70(8):1496–1512	NUM
ejpam-4798	337	7	,	,	PUNCT
ejpam-4798	337	8	2022	2022	NUM
ejpam-4798	337	9	.	.	PUNCT
ejpam-4798	338	1	[	[	X
ejpam-4798	338	2	16	16	NUM
ejpam-4798	338	3	]	]	X
ejpam-4798	338	4	deepa	deepa	PROPN
ejpam-4798	338	5	sinha	sinha	PROPN
ejpam-4798	338	6	,	,	PUNCT
ejpam-4798	338	7	anita	anita	PROPN
ejpam-4798	338	8	kumari	kumari	PROPN
ejpam-4798	338	9	rao	rao	PROPN
ejpam-4798	338	10	,	,	PUNCT
ejpam-4798	338	11	and	and	CCONJ
ejpam-4798	338	12	ayushi	ayushi	PROPN
ejpam-4798	338	13	dhama	dhama	PROPN
ejpam-4798	338	14	.	.	PUNCT
ejpam-4798	339	1	spectral	spectral	ADJ
ejpam-4798	339	2	analysis	analysis	NOUN
ejpam-4798	339	3	of	of	ADP
ejpam-4798	339	4	t	t	PROPN
ejpam-4798	339	5	-	-	PUNCT
ejpam-4798	339	6	path	path	NOUN
ejpam-4798	339	7	signed	sign	VERB
ejpam-4798	339	8	graphs	graph	NOUN
ejpam-4798	339	9	.	.	PUNCT
ejpam-4798	340	1	linear	linear	ADJ
ejpam-4798	340	2	and	and	CCONJ
ejpam-4798	340	3	multilinear	multilinear	PROPN
ejpam-4798	340	4	algebra	algebra	PROPN
ejpam-4798	340	5	,	,	PUNCT
ejpam-4798	340	6	67(9):1879–1897	67(9):1879–1897	NUM
ejpam-4798	340	7	,	,	PUNCT
ejpam-4798	340	8	2019	2019	NUM
ejpam-4798	340	9	.	.	PUNCT
ejpam-4798	341	1	[	[	X
ejpam-4798	341	2	17	17	NUM
ejpam-4798	341	3	]	]	X
ejpam-4798	341	4	deepa	deepa	PROPN
ejpam-4798	341	5	sinha	sinha	PROPN
ejpam-4798	341	6	and	and	CCONJ
ejpam-4798	341	7	anshu	anshu	PROPN
ejpam-4798	341	8	sethi	sethi	PROPN
ejpam-4798	341	9	.	.	PUNCT
ejpam-4798	342	1	an	an	DET
ejpam-4798	342	2	algorithmic	algorithmic	ADJ
ejpam-4798	342	3	characterization	characterization	NOUN
ejpam-4798	342	4	of	of	ADP
ejpam-4798	342	5	splitting	split	VERB
ejpam-4798	342	6	signed	sign	VERB
ejpam-4798	342	7	graph	graph	NOUN
ejpam-4798	342	8	.	.	PUNCT
ejpam-4798	343	1	electronic	electronic	ADJ
ejpam-4798	343	2	notes	note	NOUN
ejpam-4798	343	3	in	in	ADP
ejpam-4798	343	4	discrete	discrete	ADJ
ejpam-4798	343	5	mathematics	mathematic	NOUN
ejpam-4798	343	6	,	,	PUNCT
ejpam-4798	343	7	63:323–332	63:323–332	PROPN
ejpam-4798	343	8	,	,	PUNCT
ejpam-4798	343	9	2017	2017	NUM
ejpam-4798	343	10	.	.	PUNCT
ejpam-4798	344	1	[	[	X
ejpam-4798	344	2	18	18	NUM
ejpam-4798	344	3	]	]	X
ejpam-4798	344	4	samir	samir	PROPN
ejpam-4798	344	5	k	k	PROPN
ejpam-4798	344	6	vaidya	vaidya	PROPN
ejpam-4798	344	7	and	and	CCONJ
ejpam-4798	344	8	kalpesh	kalpesh	PROPN
ejpam-4798	344	9	m	m	PROPN
ejpam-4798	344	10	popat	popat	PROPN
ejpam-4798	344	11	.	.	PUNCT
ejpam-4798	345	1	some	some	DET
ejpam-4798	345	2	new	new	ADJ
ejpam-4798	345	3	results	result	NOUN
ejpam-4798	345	4	on	on	ADP
ejpam-4798	345	5	energy	energy	NOUN
ejpam-4798	345	6	of	of	ADP
ejpam-4798	345	7	graphs	graph	NOUN
ejpam-4798	345	8	.	.	PUNCT
ejpam-4798	346	1	match	match	PROPN
ejpam-4798	346	2	commun	commun	PROPN
ejpam-4798	346	3	.	.	PUNCT
ejpam-4798	346	4	math	math	PROPN
ejpam-4798	346	5	.	.	PUNCT
ejpam-4798	347	1	comput	comput	NOUN
ejpam-4798	347	2	.	.	PUNCT
ejpam-4798	348	1	chem	chem	PROPN
ejpam-4798	348	2	,	,	PUNCT
ejpam-4798	348	3	77:589–594	77:589–594	NOUN
ejpam-4798	348	4	,	,	PUNCT
ejpam-4798	348	5	2017	2017	NUM
ejpam-4798	348	6	.	.	PUNCT
ejpam-4798	349	1	[	[	X
ejpam-4798	349	2	19	19	NUM
ejpam-4798	349	3	]	]	X
ejpam-4798	349	4	douglas	douglas	PROPN
ejpam-4798	349	5	brent	brent	PROPN
ejpam-4798	349	6	west	west	PROPN
ejpam-4798	349	7	et	et	PROPN
ejpam-4798	349	8	al	al	PROPN
ejpam-4798	349	9	.	.	PROPN
ejpam-4798	349	10	introduction	introduction	NOUN
ejpam-4798	349	11	to	to	AUX
ejpam-4798	349	12	graph	graph	NOUN
ejpam-4798	349	13	theory	theory	NOUN
ejpam-4798	349	14	,	,	PUNCT
ejpam-4798	349	15	volume	volume	NOUN
ejpam-4798	349	16	2	2	NUM
ejpam-4798	349	17	.	.	PUNCT
ejpam-4798	349	18	prentice	prentice	PROPN
ejpam-4798	349	19	hall	hall	PROPN
ejpam-4798	349	20	upper	upper	PROPN
ejpam-4798	349	21	saddle	saddle	PROPN
ejpam-4798	349	22	river	river	NOUN
ejpam-4798	349	23	,	,	PUNCT
ejpam-4798	349	24	2001	2001	NUM
ejpam-4798	349	25	.	.	PUNCT
ejpam-4798	350	1	[	[	X
ejpam-4798	350	2	20	20	NUM
ejpam-4798	350	3	]	]	PUNCT
ejpam-4798	350	4	thomas	thomas	PROPN
ejpam-4798	350	5	zaslavsky	zaslavsky	PROPN
ejpam-4798	350	6	.	.	PUNCT
ejpam-4798	351	1	signed	sign	VERB
ejpam-4798	351	2	graphs	graph	NOUN
ejpam-4798	351	3	.	.	PUNCT
ejpam-4798	352	1	discrete	discrete	ADJ
ejpam-4798	352	2	applied	apply	VERB
ejpam-4798	352	3	mathematics	mathematic	NOUN
ejpam-4798	352	4	,	,	PUNCT
ejpam-4798	352	5	4(1):47–74	4(1):47–74	NUM
ejpam-4798	352	6	,	,	PUNCT
ejpam-4798	352	7	1982	1982	NUM
ejpam-4798	352	8	.	.	PUNCT