id	sid	tid	token	lemma	pos
ejpam-4422	1	1	european	european	PROPN
ejpam-4422	1	2	journal	journal	PROPN
ejpam-4422	1	3	of	of	ADP
ejpam-4422	1	4	pure	pure	ADJ
ejpam-4422	1	5	and	and	CCONJ
ejpam-4422	1	6	applied	apply	VERB
ejpam-4422	1	7	mathematics	mathematic	NOUN
ejpam-4422	1	8	vol	vol	NOUN
ejpam-4422	1	9	.	.	PROPN
ejpam-4422	2	1	15	15	NUM
ejpam-4422	2	2	,	,	PUNCT
ejpam-4422	2	3	no	no	INTJ
ejpam-4422	2	4	.	.	NOUN
ejpam-4422	2	5	3	3	NUM
ejpam-4422	2	6	,	,	PUNCT
ejpam-4422	2	7	2022	2022	NUM
ejpam-4422	2	8	,	,	PUNCT
ejpam-4422	2	9	1090	1090	NUM
ejpam-4422	2	10	-	-	SYM
ejpam-4422	2	11	1097	1097	NUM
ejpam-4422	2	12	issn	issn	PROPN
ejpam-4422	2	13	1307	1307	NUM
ejpam-4422	2	14	-	-	SYM
ejpam-4422	2	15	5543	5543	NUM
ejpam-4422	2	16	–	–	PUNCT
ejpam-4422	2	17	ejpam.com	ejpam.com	X
ejpam-4422	2	18	published	publish	VERB
ejpam-4422	2	19	by	by	ADP
ejpam-4422	2	20	new	new	PROPN
ejpam-4422	2	21	york	york	PROPN
ejpam-4422	2	22	business	business	PROPN
ejpam-4422	2	23	global	global	PROPN
ejpam-4422	2	24	on	on	ADP
ejpam-4422	2	25	the	the	DET
ejpam-4422	2	26	cospectrality	cospectrality	NOUN
ejpam-4422	2	27	of	of	ADP
ejpam-4422	2	28	hermitian	hermitian	ADJ
ejpam-4422	2	29	adjacency	adjacency	NOUN
ejpam-4422	2	30	matrices	matrix	NOUN
ejpam-4422	2	31	of	of	ADP
ejpam-4422	2	32	mixed	mixed	ADJ
ejpam-4422	2	33	graphs	graph	NOUN
ejpam-4422	2	34	omar	omar	PROPN
ejpam-4422	2	35	alomari1,∗	alomari1,∗	PROPN
ejpam-4422	2	36	,	,	PUNCT
ejpam-4422	2	37	mohammad	mohammad	PROPN
ejpam-4422	2	38	abudayah1	abudayah1	PROPN
ejpam-4422	2	39	,	,	PUNCT
ejpam-4422	2	40	manal	manal	ADJ
ejpam-4422	2	41	ghanem2	ghanem2	NOUN
ejpam-4422	2	42	1	1	NUM
ejpam-4422	2	43	school	school	NOUN
ejpam-4422	2	44	of	of	ADP
ejpam-4422	2	45	basic	basic	ADJ
ejpam-4422	2	46	sciences	science	NOUN
ejpam-4422	2	47	and	and	CCONJ
ejpam-4422	2	48	humanities	humanity	NOUN
ejpam-4422	2	49	,	,	PUNCT
ejpam-4422	2	50	german	german	ADJ
ejpam-4422	2	51	jordanian	jordanian	ADJ
ejpam-4422	2	52	university	university	NOUN
ejpam-4422	2	53	,	,	PUNCT
ejpam-4422	2	54	amman	amman	PROPN
ejpam-4422	2	55	,	,	PUNCT
ejpam-4422	2	56	jordan	jordan	PROPN
ejpam-4422	2	57	2	2	NUM
ejpam-4422	2	58	department	department	NOUN
ejpam-4422	2	59	of	of	ADP
ejpam-4422	2	60	mathematics	mathematic	NOUN
ejpam-4422	2	61	,	,	PUNCT
ejpam-4422	2	62	school	school	NOUN
ejpam-4422	2	63	of	of	ADP
ejpam-4422	2	64	science	science	NOUN
ejpam-4422	2	65	,	,	PUNCT
ejpam-4422	2	66	the	the	DET
ejpam-4422	2	67	university	university	PROPN
ejpam-4422	2	68	of	of	ADP
ejpam-4422	2	69	jordan	jordan	PROPN
ejpam-4422	2	70	,	,	PUNCT
ejpam-4422	2	71	amman	amman	PROPN
ejpam-4422	2	72	,	,	PUNCT
ejpam-4422	2	73	11942	11942	NUM
ejpam-4422	2	74	,	,	PUNCT
ejpam-4422	2	75	jordan	jordan	PROPN
ejpam-4422	2	76	abstract	abstract	PROPN
ejpam-4422	2	77	.	.	PUNCT
ejpam-4422	3	1	a	a	DET
ejpam-4422	3	2	mixed	mixed	ADJ
ejpam-4422	3	3	graph	graph	NOUN
ejpam-4422	3	4	d	d	NOUN
ejpam-4422	3	5	is	be	AUX
ejpam-4422	3	6	a	a	DET
ejpam-4422	3	7	graph	graph	NOUN
ejpam-4422	3	8	that	that	PRON
ejpam-4422	3	9	can	can	AUX
ejpam-4422	3	10	be	be	AUX
ejpam-4422	3	11	obtained	obtain	VERB
ejpam-4422	3	12	from	from	ADP
ejpam-4422	3	13	a	a	DET
ejpam-4422	3	14	graph	graph	NOUN
ejpam-4422	3	15	by	by	ADP
ejpam-4422	3	16	orienting	orient	VERB
ejpam-4422	3	17	some	some	PRON
ejpam-4422	3	18	of	of	ADP
ejpam-4422	3	19	its	its	PRON
ejpam-4422	3	20	edges	edge	NOUN
ejpam-4422	3	21	.	.	PUNCT
ejpam-4422	4	1	let	let	VERB
ejpam-4422	4	2	α	α	PRON
ejpam-4422	4	3	be	be	AUX
ejpam-4422	4	4	a	a	DET
ejpam-4422	4	5	primitive	primitive	ADJ
ejpam-4422	4	6	nth	nth	NOUN
ejpam-4422	4	7	root	root	NOUN
ejpam-4422	4	8	of	of	ADP
ejpam-4422	4	9	unity	unity	NOUN
ejpam-4422	4	10	,	,	PUNCT
ejpam-4422	4	11	then	then	ADV
ejpam-4422	4	12	the	the	DET
ejpam-4422	4	13	α−hermitian	α−hermitian	ADJ
ejpam-4422	4	14	adjacency	adjacency	NOUN
ejpam-4422	4	15	matrix	matrix	NOUN
ejpam-4422	4	16	of	of	ADP
ejpam-4422	4	17	a	a	DET
ejpam-4422	4	18	mixed	mixed	ADJ
ejpam-4422	4	19	graph	graph	NOUN
ejpam-4422	4	20	is	be	AUX
ejpam-4422	4	21	defined	define	VERB
ejpam-4422	4	22	to	to	PART
ejpam-4422	4	23	be	be	AUX
ejpam-4422	4	24	the	the	DET
ejpam-4422	4	25	matrix	matrix	NOUN
ejpam-4422	4	26	hα	hα	ADP
ejpam-4422	4	27	=	=	PUNCT
ejpam-4422	5	1	[	[	X
ejpam-4422	5	2	hrs	hrs	X
ejpam-4422	5	3	]	]	X
ejpam-4422	5	4	where	where	SCONJ
ejpam-4422	5	5	hrs	hrs	NOUN
ejpam-4422	5	6	=	=	SYM
ejpam-4422	5	7	α	α	NOUN
ejpam-4422	5	8	if	if	SCONJ
ejpam-4422	5	9	rs	rs	ADV
ejpam-4422	5	10	is	be	AUX
ejpam-4422	5	11	an	an	DET
ejpam-4422	5	12	arc	arc	NOUN
ejpam-4422	5	13	in	in	ADP
ejpam-4422	5	14	d	d	NOUN
ejpam-4422	5	15	,	,	PUNCT
ejpam-4422	5	16	hrs	hrs	NOUN
ejpam-4422	5	17	=	=	SYM
ejpam-4422	5	18	α	α	PROPN
ejpam-4422	5	19	if	if	SCONJ
ejpam-4422	5	20	sr	sr	PROPN
ejpam-4422	5	21	is	be	AUX
ejpam-4422	5	22	an	an	DET
ejpam-4422	5	23	arc	arc	NOUN
ejpam-4422	5	24	in	in	ADP
ejpam-4422	5	25	d	d	NOUN
ejpam-4422	5	26	,	,	PUNCT
ejpam-4422	5	27	hrs	hrs	NOUN
ejpam-4422	5	28	=	=	SYM
ejpam-4422	5	29	1	1	NUM
ejpam-4422	5	30	if	if	SCONJ
ejpam-4422	5	31	sr	sr	PROPN
ejpam-4422	5	32	is	be	AUX
ejpam-4422	5	33	a	a	DET
ejpam-4422	5	34	digon	digon	NOUN
ejpam-4422	5	35	in	in	ADP
ejpam-4422	5	36	d	d	PROPN
ejpam-4422	5	37	and	and	CCONJ
ejpam-4422	5	38	hrs	hrs	NOUN
ejpam-4422	6	1	=	=	SYM
ejpam-4422	6	2	0	0	PUNCT
ejpam-4422	6	3	otherwise	otherwise	ADV
ejpam-4422	6	4	.	.	PUNCT
ejpam-4422	7	1	in	in	ADP
ejpam-4422	7	2	this	this	DET
ejpam-4422	7	3	paper	paper	NOUN
ejpam-4422	7	4	we	we	PRON
ejpam-4422	7	5	study	study	VERB
ejpam-4422	7	6	the	the	DET
ejpam-4422	7	7	cospectrality	cospectrality	NOUN
ejpam-4422	7	8	of	of	ADP
ejpam-4422	7	9	the	the	DET
ejpam-4422	7	10	hermitian	hermitian	ADJ
ejpam-4422	7	11	adjacency	adjacency	NOUN
ejpam-4422	7	12	matrix	matrix	NOUN
ejpam-4422	7	13	of	of	ADP
ejpam-4422	7	14	a	a	DET
ejpam-4422	7	15	mixed	mixed	ADJ
ejpam-4422	7	16	graph	graph	NOUN
ejpam-4422	7	17	.	.	PUNCT
ejpam-4422	8	1	2020	2020	NUM
ejpam-4422	8	2	mathematics	mathematic	NOUN
ejpam-4422	8	3	subject	subject	NOUN
ejpam-4422	8	4	classifications	classification	NOUN
ejpam-4422	8	5	:	:	PUNCT
ejpam-4422	8	6	05c20	05c20	NUM
ejpam-4422	8	7	,	,	PUNCT
ejpam-4422	8	8	05c50	05c50	NUM
ejpam-4422	8	9	,	,	PUNCT
ejpam-4422	8	10	15a30	15a30	NUM
ejpam-4422	8	11	key	key	ADJ
ejpam-4422	8	12	words	word	NOUN
ejpam-4422	8	13	and	and	CCONJ
ejpam-4422	8	14	phrases	phrase	NOUN
ejpam-4422	8	15	:	:	PUNCT
ejpam-4422	8	16	adjacency	adjacency	PROPN
ejpam-4422	8	17	matrix	matrix	NOUN
ejpam-4422	8	18	,	,	PUNCT
ejpam-4422	8	19	mixed	mixed	ADJ
ejpam-4422	8	20	graphs	graph	NOUN
ejpam-4422	8	21	,	,	PUNCT
ejpam-4422	8	22	hermitian	hermitian	ADJ
ejpam-4422	8	23	matrix	matrix	NOUN
ejpam-4422	8	24	,	,	PUNCT
ejpam-4422	8	25	spectrum	spectrum	NOUN
ejpam-4422	8	26	,	,	PUNCT
ejpam-4422	8	27	cospectrality	cospectrality	NOUN
ejpam-4422	8	28	1	1	NUM
ejpam-4422	8	29	.	.	PUNCT
ejpam-4422	9	1	introduction	introduction	NOUN
ejpam-4422	9	2	in	in	ADP
ejpam-4422	9	3	this	this	DET
ejpam-4422	9	4	paper	paper	NOUN
ejpam-4422	9	5	we	we	PRON
ejpam-4422	9	6	consider	consider	VERB
ejpam-4422	9	7	graphs	graph	NOUN
ejpam-4422	9	8	without	without	ADP
ejpam-4422	9	9	loops	loop	NOUN
ejpam-4422	9	10	or	or	CCONJ
ejpam-4422	9	11	multiple	multiple	ADJ
ejpam-4422	9	12	edges	edge	NOUN
ejpam-4422	9	13	.	.	PUNCT
ejpam-4422	10	1	a	a	DET
ejpam-4422	10	2	mixed	mixed	ADJ
ejpam-4422	10	3	graph	graph	NOUN
ejpam-4422	10	4	d	d	NOUN
ejpam-4422	10	5	is	be	AUX
ejpam-4422	10	6	a	a	DET
ejpam-4422	10	7	set	set	NOUN
ejpam-4422	10	8	of	of	ADP
ejpam-4422	10	9	vertices	vertex	NOUN
ejpam-4422	10	10	v	v	X
ejpam-4422	10	11	(	(	PUNCT
ejpam-4422	10	12	d	d	NOUN
ejpam-4422	10	13	)	)	PUNCT
ejpam-4422	10	14	together	together	ADV
ejpam-4422	10	15	with	with	ADP
ejpam-4422	10	16	a	a	DET
ejpam-4422	10	17	set	set	NOUN
ejpam-4422	10	18	of	of	ADP
ejpam-4422	10	19	edges	edge	NOUN
ejpam-4422	10	20	e(d	e(d	PROPN
ejpam-4422	10	21	)	)	PUNCT
ejpam-4422	11	1	⊂	⊂	PROPN
ejpam-4422	11	2	v	v	X
ejpam-4422	11	3	(	(	PUNCT
ejpam-4422	11	4	d	d	NOUN
ejpam-4422	11	5	)	)	PUNCT
ejpam-4422	11	6	×	×	NOUN
ejpam-4422	11	7	v	v	NOUN
ejpam-4422	11	8	(	(	PUNCT
ejpam-4422	11	9	d	d	NOUN
ejpam-4422	11	10	)	)	PUNCT
ejpam-4422	11	11	where	where	SCONJ
ejpam-4422	11	12	,	,	PUNCT
ejpam-4422	11	13	(	(	PUNCT
ejpam-4422	11	14	u	u	NOUN
ejpam-4422	11	15	,	,	PUNCT
ejpam-4422	11	16	v	v	NOUN
ejpam-4422	11	17	)	)	PUNCT
ejpam-4422	11	18	∈	∈	PROPN
ejpam-4422	11	19	e(d	e(d	PROPN
ejpam-4422	11	20	)	)	PUNCT
ejpam-4422	11	21	does	do	AUX
ejpam-4422	11	22	not	not	PART
ejpam-4422	11	23	always	always	ADV
ejpam-4422	11	24	imply	imply	VERB
ejpam-4422	11	25	(	(	PUNCT
ejpam-4422	11	26	v	v	NOUN
ejpam-4422	11	27	,	,	PUNCT
ejpam-4422	11	28	u	u	NOUN
ejpam-4422	11	29	)	)	PUNCT
ejpam-4422	11	30	∈	∈	PROPN
ejpam-4422	11	31	e(d	e(d	PROPN
ejpam-4422	11	32	)	)	PUNCT
ejpam-4422	11	33	.	.	PUNCT
ejpam-4422	12	1	an	an	DET
ejpam-4422	12	2	edge	edge	NOUN
ejpam-4422	12	3	(	(	PUNCT
ejpam-4422	12	4	u	u	NOUN
ejpam-4422	12	5	,	,	PUNCT
ejpam-4422	12	6	v	v	NOUN
ejpam-4422	12	7	)	)	PUNCT
ejpam-4422	12	8	of	of	ADP
ejpam-4422	12	9	a	a	DET
ejpam-4422	12	10	mixed	mixed	ADJ
ejpam-4422	12	11	graph	graph	NOUN
ejpam-4422	12	12	d	d	NOUN
ejpam-4422	12	13	is	be	AUX
ejpam-4422	12	14	called	call	VERB
ejpam-4422	12	15	oriented	oriented	ADJ
ejpam-4422	12	16	(	(	PUNCT
ejpam-4422	12	17	resp	resp	NOUN
ejpam-4422	12	18	.	.	PUNCT
ejpam-4422	13	1	digon	digon	PROPN
ejpam-4422	13	2	)	)	PUNCT
ejpam-4422	14	1	if	if	SCONJ
ejpam-4422	14	2	only	only	ADV
ejpam-4422	14	3	one	one	NUM
ejpam-4422	14	4	of	of	ADP
ejpam-4422	14	5	(	(	PUNCT
ejpam-4422	14	6	u	u	NOUN
ejpam-4422	14	7	,	,	PUNCT
ejpam-4422	14	8	v	v	NOUN
ejpam-4422	14	9	)	)	PUNCT
ejpam-4422	14	10	and	and	CCONJ
ejpam-4422	14	11	(	(	PUNCT
ejpam-4422	14	12	v	v	NOUN
ejpam-4422	14	13	,	,	PUNCT
ejpam-4422	14	14	u	u	NOUN
ejpam-4422	14	15	)	)	PUNCT
ejpam-4422	14	16	belongs	belong	VERB
ejpam-4422	14	17	to	to	ADP
ejpam-4422	14	18	e(d	e(d	PROPN
ejpam-4422	14	19	)	)	PUNCT
ejpam-4422	14	20	(	(	PUNCT
ejpam-4422	14	21	resp	resp	NOUN
ejpam-4422	14	22	.	.	PUNCT
ejpam-4422	15	1	both	both	PRON
ejpam-4422	15	2	of	of	ADP
ejpam-4422	15	3	(	(	PUNCT
ejpam-4422	15	4	u	u	NOUN
ejpam-4422	15	5	,	,	PUNCT
ejpam-4422	15	6	v	v	NOUN
ejpam-4422	15	7	)	)	PUNCT
ejpam-4422	15	8	and	and	CCONJ
ejpam-4422	15	9	(	(	PUNCT
ejpam-4422	15	10	v	v	NOUN
ejpam-4422	15	11	,	,	PUNCT
ejpam-4422	15	12	u	u	NOUN
ejpam-4422	15	13	)	)	PUNCT
ejpam-4422	15	14	belong	belong	VERB
ejpam-4422	15	15	to	to	ADP
ejpam-4422	15	16	e(d	e(d	PROPN
ejpam-4422	15	17	)	)	PUNCT
ejpam-4422	15	18	)	)	PUNCT
ejpam-4422	15	19	.	.	PUNCT
ejpam-4422	16	1	for	for	ADP
ejpam-4422	16	2	simplicity	simplicity	NOUN
ejpam-4422	16	3	,	,	PUNCT
ejpam-4422	16	4	through	through	ADP
ejpam-4422	16	5	this	this	DET
ejpam-4422	16	6	paper	paper	NOUN
ejpam-4422	16	7	arcs	arcs	NOUN
ejpam-4422	16	8	and	and	CCONJ
ejpam-4422	16	9	digon	digon	NOUN
ejpam-4422	16	10	will	will	AUX
ejpam-4422	16	11	be	be	AUX
ejpam-4422	16	12	denoted	denote	VERB
ejpam-4422	16	13	by	by	ADP
ejpam-4422	16	14	uv	uv	NOUN
ejpam-4422	16	15	instead	instead	ADV
ejpam-4422	16	16	of	of	ADP
ejpam-4422	16	17	(	(	PUNCT
ejpam-4422	16	18	u	u	NOUN
ejpam-4422	16	19	,	,	PUNCT
ejpam-4422	16	20	v	v	NOUN
ejpam-4422	16	21	)	)	PUNCT
ejpam-4422	16	22	.	.	PUNCT
ejpam-4422	17	1	the	the	DET
ejpam-4422	17	2	underlying	underlie	VERB
ejpam-4422	17	3	graph	graph	NOUN
ejpam-4422	17	4	of	of	ADP
ejpam-4422	17	5	a	a	DET
ejpam-4422	17	6	mixed	mixed	ADJ
ejpam-4422	17	7	graph	graph	NOUN
ejpam-4422	17	8	d	d	NOUN
ejpam-4422	17	9	,	,	PUNCT
ejpam-4422	17	10	denoted	denote	VERB
ejpam-4422	17	11	by	by	ADP
ejpam-4422	17	12	γ(d	γ(d	NOUN
ejpam-4422	17	13	)	)	PUNCT
ejpam-4422	17	14	,	,	PUNCT
ejpam-4422	17	15	is	be	AUX
ejpam-4422	17	16	the	the	DET
ejpam-4422	17	17	graph	graph	NOUN
ejpam-4422	17	18	obtained	obtain	VERB
ejpam-4422	17	19	from	from	ADP
ejpam-4422	17	20	d	d	PROPN
ejpam-4422	17	21	after	after	ADP
ejpam-4422	17	22	unorienting	unoriente	VERB
ejpam-4422	17	23	all	all	PRON
ejpam-4422	17	24	of	of	ADP
ejpam-4422	17	25	its	its	PRON
ejpam-4422	17	26	edges	edge	NOUN
ejpam-4422	17	27	.	.	PUNCT
ejpam-4422	18	1	a	a	DET
ejpam-4422	18	2	cycle	cycle	NOUN
ejpam-4422	18	3	,	,	PUNCT
ejpam-4422	18	4	(	(	PUNCT
ejpam-4422	18	5	resp	resp	NOUN
ejpam-4422	18	6	.	.	PUNCT
ejpam-4422	19	1	a	a	DET
ejpam-4422	19	2	walk	walk	NOUN
ejpam-4422	19	3	,	,	PUNCT
ejpam-4422	19	4	a	a	DET
ejpam-4422	19	5	path	path	NOUN
ejpam-4422	19	6	)	)	PUNCT
ejpam-4422	19	7	of	of	ADP
ejpam-4422	19	8	a	a	DET
ejpam-4422	19	9	mixed	mixed	ADJ
ejpam-4422	19	10	graph	graph	NOUN
ejpam-4422	19	11	d	d	NOUN
ejpam-4422	19	12	is	be	AUX
ejpam-4422	19	13	just	just	ADV
ejpam-4422	19	14	a	a	DET
ejpam-4422	19	15	cycle	cycle	NOUN
ejpam-4422	19	16	(	(	PUNCT
ejpam-4422	19	17	resp	resp	NOUN
ejpam-4422	19	18	.	.	PUNCT
ejpam-4422	20	1	a	a	DET
ejpam-4422	20	2	walk	walk	NOUN
ejpam-4422	20	3	,	,	PUNCT
ejpam-4422	20	4	a	a	DET
ejpam-4422	20	5	path	path	NOUN
ejpam-4422	20	6	)	)	PUNCT
ejpam-4422	20	7	of	of	ADP
ejpam-4422	20	8	the	the	DET
ejpam-4422	20	9	underlying	underlie	VERB
ejpam-4422	20	10	graph	graph	NOUN
ejpam-4422	20	11	of	of	ADP
ejpam-4422	20	12	d.	d.	PROPN
ejpam-4422	20	13	a	a	DET
ejpam-4422	20	14	mixed	mixed	ADJ
ejpam-4422	20	15	graph	graph	NOUN
ejpam-4422	20	16	d	d	NOUN
ejpam-4422	20	17	is	be	AUX
ejpam-4422	20	18	called	call	VERB
ejpam-4422	20	19	weakly	weakly	ADV
ejpam-4422	20	20	connected	connected	ADJ
ejpam-4422	20	21	if	if	SCONJ
ejpam-4422	20	22	its	its	PRON
ejpam-4422	20	23	underlying	underlie	VERB
ejpam-4422	20	24	graph	graph	NOUN
ejpam-4422	20	25	is	be	AUX
ejpam-4422	20	26	connected	connect	VERB
ejpam-4422	20	27	.	.	PUNCT
ejpam-4422	21	1	one	one	NUM
ejpam-4422	21	2	of	of	ADP
ejpam-4422	21	3	the	the	DET
ejpam-4422	21	4	important	important	ADJ
ejpam-4422	21	5	branches	branch	NOUN
ejpam-4422	21	6	of	of	ADP
ejpam-4422	21	7	algebraic	algebraic	ADJ
ejpam-4422	21	8	graph	graph	NOUN
ejpam-4422	21	9	theory	theory	NOUN
ejpam-4422	21	10	is	be	AUX
ejpam-4422	21	11	the	the	DET
ejpam-4422	21	12	study	study	NOUN
ejpam-4422	21	13	of	of	ADP
ejpam-4422	21	14	graphs	graph	NOUN
ejpam-4422	21	15	and	and	CCONJ
ejpam-4422	21	16	digraphs	digraph	VERB
ejpam-4422	21	17	with	with	ADP
ejpam-4422	21	18	respect	respect	NOUN
ejpam-4422	21	19	to	to	ADP
ejpam-4422	21	20	some	some	DET
ejpam-4422	21	21	graph	graph	NOUN
ejpam-4422	21	22	matrix	matrix	NOUN
ejpam-4422	21	23	and	and	CCONJ
ejpam-4422	21	24	its	its	PRON
ejpam-4422	21	25	spectrum	spectrum	NOUN
ejpam-4422	21	26	.	.	PUNCT
ejpam-4422	22	1	for	for	ADP
ejpam-4422	22	2	undirected	undirected	ADJ
ejpam-4422	22	3	graphs	graph	NOUN
ejpam-4422	22	4	researchers	researcher	NOUN
ejpam-4422	22	5	focused	focus	VERB
ejpam-4422	22	6	on	on	ADP
ejpam-4422	22	7	two	two	NUM
ejpam-4422	22	8	kinds	kind	NOUN
ejpam-4422	22	9	of	of	ADP
ejpam-4422	22	10	adjacency	adjacency	NOUN
ejpam-4422	22	11	matrices	matrix	NOUN
ejpam-4422	22	12	,	,	PUNCT
ejpam-4422	22	13	the	the	DET
ejpam-4422	22	14	traditional	traditional	ADJ
ejpam-4422	22	15	adjacency	adjacency	NOUN
ejpam-4422	22	16	matrix	matrix	NOUN
ejpam-4422	22	17	and	and	CCONJ
ejpam-4422	22	18	the	the	DET
ejpam-4422	22	19	laplacian	laplacian	ADJ
ejpam-4422	22	20	adjacency	adjacency	NOUN
ejpam-4422	22	21	matrix	matrix	NOUN
ejpam-4422	22	22	.	.	PUNCT
ejpam-4422	23	1	on	on	ADP
ejpam-4422	23	2	the	the	DET
ejpam-4422	23	3	other	other	ADJ
ejpam-4422	23	4	hand	hand	NOUN
ejpam-4422	23	5	for	for	ADP
ejpam-4422	23	6	directed	direct	VERB
ejpam-4422	23	7	graphs	graph	NOUN
ejpam-4422	23	8	(	(	PUNCT
ejpam-4422	23	9	digraphs	digraphs	ADJ
ejpam-4422	23	10	∗corresponding	∗corresponde	VERB
ejpam-4422	23	11	author	author	NOUN
ejpam-4422	23	12	.	.	PUNCT
ejpam-4422	24	1	doi	doi	NOUN
ejpam-4422	24	2	:	:	PUNCT
ejpam-4422	24	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4422	https://doi.org/10.29020/nybg.ejpam.v15i3.4422	VERB
ejpam-4422	24	4	email	email	NOUN
ejpam-4422	24	5	addresses	address	NOUN
ejpam-4422	24	6	:	:	PUNCT
ejpam-4422	24	7	omar.alomari@gju.edu.jo	omar.alomari@gju.edu.jo	NUM
ejpam-4422	24	8	(	(	PUNCT
ejpam-4422	24	9	omar	omar	PROPN
ejpam-4422	24	10	alomari	alomari	PROPN
ejpam-4422	24	11	)	)	PUNCT
ejpam-4422	24	12	,	,	PUNCT
ejpam-4422	24	13	mohammad.abudayah@gju.edu.jo	mohammad.abudayah@gju.edu.jo	PROPN
ejpam-4422	24	14	(	(	PUNCT
ejpam-4422	24	15	mohammad	mohammad	PROPN
ejpam-4422	24	16	abudayah	abudayah	PROPN
ejpam-4422	24	17	)	)	PUNCT
ejpam-4422	24	18	,	,	PUNCT
ejpam-4422	24	19	m.ghanem@ju.edu.jo	m.ghanem@ju.edu.jo	PROPN
ejpam-4422	24	20	(	(	PUNCT
ejpam-4422	24	21	manal	manal	ADJ
ejpam-4422	24	22	ghanem	ghanem	PROPN
ejpam-4422	24	23	)	)	PUNCT
ejpam-4422	24	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4422	24	25	1090	1090	NUM
ejpam-4422	24	26	©	©	PROPN
ejpam-4422	24	27	2022	2022	NUM
ejpam-4422	24	28	ejpam	ejpam	VERB
ejpam-4422	24	29	all	all	DET
ejpam-4422	24	30	rights	right	NOUN
ejpam-4422	24	31	reserved	reserve	VERB
ejpam-4422	24	32	.	.	PUNCT
ejpam-4422	25	1	o.	o.	PROPN
ejpam-4422	25	2	alomari	alomari	PROPN
ejpam-4422	25	3	,	,	PUNCT
ejpam-4422	25	4	m.	m.	NOUN
ejpam-4422	25	5	abudayah	abudayah	PROPN
ejpam-4422	25	6	,	,	PUNCT
ejpam-4422	25	7	m.	m.	NOUN
ejpam-4422	25	8	ghanem	ghanem	PROPN
ejpam-4422	25	9	/	/	SYM
ejpam-4422	25	10	eur	eur	PROPN
ejpam-4422	25	11	.	.	PUNCT
ejpam-4422	26	1	j.	j.	PROPN
ejpam-4422	26	2	pure	pure	PROPN
ejpam-4422	26	3	appl	appl	PROPN
ejpam-4422	26	4	.	.	PROPN
ejpam-4422	26	5	math	math	PROPN
ejpam-4422	26	6	,	,	PUNCT
ejpam-4422	26	7	15	15	NUM
ejpam-4422	26	8	(	(	PUNCT
ejpam-4422	26	9	3	3	NUM
ejpam-4422	26	10	)	)	PUNCT
ejpam-4422	26	11	(	(	PUNCT
ejpam-4422	26	12	2022	2022	NUM
ejpam-4422	26	13	)	)	PUNCT
ejpam-4422	26	14	,	,	PUNCT
ejpam-4422	26	15	1090	1090	NUM
ejpam-4422	26	16	-	-	SYM
ejpam-4422	26	17	1097	1097	NUM
ejpam-4422	26	18	1091	1091	NUM
ejpam-4422	26	19	)	)	PUNCT
ejpam-4422	26	20	the	the	DET
ejpam-4422	26	21	traditional	traditional	ADJ
ejpam-4422	26	22	adjacency	adjacency	NOUN
ejpam-4422	26	23	matrix	matrix	NOUN
ejpam-4422	26	24	is	be	AUX
ejpam-4422	26	25	not	not	PART
ejpam-4422	26	26	symmetric	symmetric	ADJ
ejpam-4422	26	27	in	in	ADP
ejpam-4422	26	28	general	general	ADJ
ejpam-4422	26	29	.	.	PUNCT
ejpam-4422	27	1	therefore	therefore	ADV
ejpam-4422	27	2	,	,	PUNCT
ejpam-4422	27	3	it	it	PRON
ejpam-4422	27	4	is	be	AUX
ejpam-4422	27	5	very	very	ADV
ejpam-4422	27	6	challenging	challenging	ADJ
ejpam-4422	27	7	to	to	PART
ejpam-4422	27	8	deal	deal	VERB
ejpam-4422	27	9	with	with	ADP
ejpam-4422	27	10	such	such	ADJ
ejpam-4422	27	11	matrix	matrix	NOUN
ejpam-4422	27	12	.	.	PUNCT
ejpam-4422	28	1	recently	recently	ADV
ejpam-4422	28	2	,	,	PUNCT
ejpam-4422	28	3	many	many	ADJ
ejpam-4422	28	4	researchers	researcher	NOUN
ejpam-4422	28	5	have	have	AUX
ejpam-4422	28	6	proposed	propose	VERB
ejpam-4422	28	7	other	other	ADJ
ejpam-4422	28	8	hermitian	hermitian	ADJ
ejpam-4422	28	9	adjacency	adjacency	NOUN
ejpam-4422	28	10	matrices	matrix	NOUN
ejpam-4422	28	11	of	of	ADP
ejpam-4422	28	12	mixed	mixed	ADJ
ejpam-4422	28	13	graphs	graph	NOUN
ejpam-4422	28	14	.	.	PUNCT
ejpam-4422	29	1	for	for	ADP
ejpam-4422	29	2	example	example	NOUN
ejpam-4422	29	3	in	in	ADP
ejpam-4422	29	4	[	[	X
ejpam-4422	29	5	2	2	NUM
ejpam-4422	29	6	]	]	PUNCT
ejpam-4422	29	7	and	and	CCONJ
ejpam-4422	29	8	in	in	ADP
ejpam-4422	29	9	[	[	X
ejpam-4422	29	10	1	1	X
ejpam-4422	29	11	]	]	PUNCT
ejpam-4422	29	12	authors	author	NOUN
ejpam-4422	29	13	studied	study	VERB
ejpam-4422	29	14	the	the	DET
ejpam-4422	29	15	singular	singular	ADJ
ejpam-4422	29	16	values	value	NOUN
ejpam-4422	29	17	of	of	ADP
ejpam-4422	29	18	the	the	DET
ejpam-4422	29	19	traditional	traditional	ADJ
ejpam-4422	29	20	adjacency	adjacency	NOUN
ejpam-4422	29	21	matrix	matrix	NOUN
ejpam-4422	29	22	of	of	ADP
ejpam-4422	29	23	a	a	DET
ejpam-4422	29	24	mixed	mixed	ADJ
ejpam-4422	29	25	graph	graph	NOUN
ejpam-4422	29	26	d	d	NOUN
ejpam-4422	29	27	,	,	PUNCT
ejpam-4422	29	28	in	in	ADP
ejpam-4422	29	29	these	these	DET
ejpam-4422	29	30	papers	paper	NOUN
ejpam-4422	29	31	it	it	PRON
ejpam-4422	29	32	was	be	AUX
ejpam-4422	29	33	very	very	ADV
ejpam-4422	29	34	clear	clear	ADJ
ejpam-4422	29	35	that	that	SCONJ
ejpam-4422	29	36	the	the	DET
ejpam-4422	29	37	singular	singular	ADJ
ejpam-4422	29	38	values	value	NOUN
ejpam-4422	29	39	of	of	ADP
ejpam-4422	29	40	a	a	DET
ejpam-4422	29	41	mixed	mixed	ADJ
ejpam-4422	29	42	graph	graph	NOUN
ejpam-4422	29	43	are	be	AUX
ejpam-4422	29	44	related	relate	VERB
ejpam-4422	29	45	to	to	ADP
ejpam-4422	29	46	the	the	DET
ejpam-4422	29	47	common	common	ADJ
ejpam-4422	29	48	out	out	ADP
ejpam-4422	29	49	neighbors	neighbor	NOUN
ejpam-4422	29	50	between	between	ADP
ejpam-4422	29	51	vertices	vertex	NOUN
ejpam-4422	29	52	.	.	PUNCT
ejpam-4422	30	1	coincidentally	coincidentally	ADV
ejpam-4422	30	2	,	,	PUNCT
ejpam-4422	30	3	guo	guo	PROPN
ejpam-4422	30	4	and	and	CCONJ
ejpam-4422	30	5	mohar	mohar	NOUN
ejpam-4422	30	6	in	in	ADP
ejpam-4422	30	7	[	[	X
ejpam-4422	30	8	3	3	NUM
ejpam-4422	30	9	]	]	PUNCT
ejpam-4422	30	10	defined	define	VERB
ejpam-4422	30	11	an	an	DET
ejpam-4422	30	12	interesting	interesting	ADJ
ejpam-4422	30	13	hermitian	hermitian	ADJ
ejpam-4422	30	14	adjacency	adjacency	NOUN
ejpam-4422	30	15	matrix	matrix	NOUN
ejpam-4422	30	16	of	of	ADP
ejpam-4422	30	17	mixed	mixed	ADJ
ejpam-4422	30	18	graphs	graph	NOUN
ejpam-4422	30	19	as	as	SCONJ
ejpam-4422	30	20	follows	follow	VERB
ejpam-4422	30	21	:	:	PUNCT
ejpam-4422	30	22	for	for	ADP
ejpam-4422	30	23	a	a	DET
ejpam-4422	30	24	mixed	mixed	ADJ
ejpam-4422	30	25	graph	graph	NOUN
ejpam-4422	30	26	d	d	NOUN
ejpam-4422	30	27	,	,	PUNCT
ejpam-4422	30	28	the	the	DET
ejpam-4422	30	29	i−hermitian	i−hermitian	ADJ
ejpam-4422	30	30	adjacency	adjacency	NOUN
ejpam-4422	30	31	matrix	matrix	NOUN
ejpam-4422	30	32	of	of	ADP
ejpam-4422	30	33	d	d	PROPN
ejpam-4422	30	34	is	be	AUX
ejpam-4422	30	35	a	a	DET
ejpam-4422	30	36	|v	|v	ADJ
ejpam-4422	31	1	|	|	NOUN
ejpam-4422	31	2	×	×	NOUN
ejpam-4422	31	3	|v	|v	NOUN
ejpam-4422	31	4	|	|	NOUN
ejpam-4422	31	5	matrix	matrix	NOUN
ejpam-4422	31	6	hi(d	hi(d	NOUN
ejpam-4422	31	7	)	)	PUNCT
ejpam-4422	31	8	=	=	PUNCT
ejpam-4422	32	1	[	[	X
ejpam-4422	32	2	huv	huv	X
ejpam-4422	32	3	]	]	X
ejpam-4422	32	4	,	,	PUNCT
ejpam-4422	32	5	where	where	SCONJ
ejpam-4422	32	6	huv	huv	PROPN
ejpam-4422	32	7	=	=	SYM
ejpam-4422	32	8			NUM
ejpam-4422	32	9	1	1	NUM
ejpam-4422	32	10	if	if	SCONJ
ejpam-4422	32	11	uv	uv	NOUN
ejpam-4422	32	12	is	be	AUX
ejpam-4422	32	13	a	a	DET
ejpam-4422	32	14	digon	digon	NOUN
ejpam-4422	32	15	in	in	ADP
ejpam-4422	32	16	d	d	PROPN
ejpam-4422	32	17	,	,	PUNCT
ejpam-4422	32	18	i	i	PRON
ejpam-4422	32	19	if	if	SCONJ
ejpam-4422	32	20	uv	uv	NOUN
ejpam-4422	32	21	is	be	AUX
ejpam-4422	32	22	an	an	DET
ejpam-4422	32	23	arc	arc	NOUN
ejpam-4422	32	24	in	in	ADP
ejpam-4422	32	25	d	d	PROPN
ejpam-4422	32	26	,	,	PUNCT
ejpam-4422	32	27	−i	−i	PROPN
ejpam-4422	32	28	if	if	SCONJ
ejpam-4422	32	29	vu	vu	X
ejpam-4422	32	30	is	be	AUX
ejpam-4422	32	31	an	an	DET
ejpam-4422	32	32	arc	arc	NOUN
ejpam-4422	32	33	in	in	ADP
ejpam-4422	32	34	d	d	PROPN
ejpam-4422	32	35	,	,	PUNCT
ejpam-4422	32	36	0	0	NUM
ejpam-4422	32	37	otherwise	otherwise	ADV
ejpam-4422	32	38	.	.	PUNCT
ejpam-4422	33	1	in	in	ADP
ejpam-4422	33	2	[	[	X
ejpam-4422	33	3	3	3	X
ejpam-4422	33	4	]	]	X
ejpam-4422	33	5	many	many	ADJ
ejpam-4422	33	6	interesting	interesting	ADJ
ejpam-4422	33	7	spectral	spectral	ADJ
ejpam-4422	33	8	properties	property	NOUN
ejpam-4422	33	9	of	of	ADP
ejpam-4422	33	10	hi(d	hi(d	NOUN
ejpam-4422	33	11	)	)	PUNCT
ejpam-4422	33	12	have	have	AUX
ejpam-4422	33	13	been	be	AUX
ejpam-4422	33	14	demonstrated	demonstrate	VERB
ejpam-4422	33	15	.	.	PUNCT
ejpam-4422	34	1	mohar	mohar	NOUN
ejpam-4422	34	2	in	in	ADP
ejpam-4422	34	3	[	[	X
ejpam-4422	34	4	5	5	NUM
ejpam-4422	34	5	]	]	PUNCT
ejpam-4422	34	6	extended	extend	VERB
ejpam-4422	34	7	the	the	DET
ejpam-4422	34	8	previously	previously	ADV
ejpam-4422	34	9	proposed	propose	VERB
ejpam-4422	34	10	adjacency	adjacency	NOUN
ejpam-4422	34	11	matrix	matrix	NOUN
ejpam-4422	34	12	.	.	PUNCT
ejpam-4422	35	1	in	in	ADP
ejpam-4422	35	2	the	the	DET
ejpam-4422	35	3	new	new	ADJ
ejpam-4422	35	4	kind	kind	NOUN
ejpam-4422	35	5	of	of	ADP
ejpam-4422	35	6	hermitian	hermitian	ADJ
ejpam-4422	35	7	adjacency	adjacency	NOUN
ejpam-4422	35	8	matrices	matrice	VERB
ejpam-4422	35	9	the	the	DET
ejpam-4422	35	10	complex	complex	ADJ
ejpam-4422	35	11	number	number	NOUN
ejpam-4422	35	12	i	i	PRON
ejpam-4422	35	13	is	be	AUX
ejpam-4422	35	14	replaced	replace	VERB
ejpam-4422	35	15	with	with	ADP
ejpam-4422	35	16	the	the	DET
ejpam-4422	35	17	sixth	sixth	ADJ
ejpam-4422	35	18	root	root	NOUN
ejpam-4422	35	19	of	of	ADP
ejpam-4422	35	20	unity	unity	NOUN
ejpam-4422	35	21	ω	ω	NOUN
ejpam-4422	35	22	=	=	PUNCT
ejpam-4422	35	23	e	e	PROPN
ejpam-4422	35	24	π	π	PROPN
ejpam-4422	35	25	3	3	NUM
ejpam-4422	35	26	i.	i.	NOUN
ejpam-4422	35	27	the	the	DET
ejpam-4422	35	28	new	new	ADJ
ejpam-4422	35	29	kind	kind	NOUN
ejpam-4422	35	30	of	of	ADP
ejpam-4422	35	31	hermitian	hermitian	ADJ
ejpam-4422	35	32	adjacency	adjacency	NOUN
ejpam-4422	35	33	matrices	matrix	NOUN
ejpam-4422	35	34	is	be	AUX
ejpam-4422	35	35	calledω−hermitian	calledω−hermitian	ADJ
ejpam-4422	35	36	adjacency	adjacency	NOUN
ejpam-4422	35	37	matrices	matrix	NOUN
ejpam-4422	35	38	.	.	PUNCT
ejpam-4422	36	1	in	in	ADP
ejpam-4422	36	2	this	this	DET
ejpam-4422	36	3	paper	paper	NOUN
ejpam-4422	36	4	mohar	mohar	NOUN
ejpam-4422	36	5	discussed	discuss	VERB
ejpam-4422	36	6	many	many	ADJ
ejpam-4422	36	7	cases	case	NOUN
ejpam-4422	36	8	with	with	ADP
ejpam-4422	36	9	general	general	ADJ
ejpam-4422	36	10	complex	complex	ADJ
ejpam-4422	36	11	unit	unit	NOUN
ejpam-4422	36	12	number	number	NOUN
ejpam-4422	36	13	eiθ	eiθ	PROPN
ejpam-4422	36	14	instead	instead	ADV
ejpam-4422	36	15	of	of	ADP
ejpam-4422	36	16	ω	ω	PROPN
ejpam-4422	36	17	.	.	PUNCT
ejpam-4422	36	18	to	to	PART
ejpam-4422	36	19	be	be	AUX
ejpam-4422	36	20	more	more	ADV
ejpam-4422	36	21	precise	precise	ADJ
ejpam-4422	36	22	,	,	PUNCT
ejpam-4422	36	23	the	the	DET
ejpam-4422	36	24	definition	definition	NOUN
ejpam-4422	36	25	of	of	ADP
ejpam-4422	36	26	the	the	DET
ejpam-4422	36	27	general	general	ADJ
ejpam-4422	36	28	hermitian	hermitian	ADJ
ejpam-4422	36	29	adjacency	adjacency	NOUN
ejpam-4422	36	30	matrix	matrix	NOUN
ejpam-4422	36	31	of	of	ADP
ejpam-4422	36	32	a	a	DET
ejpam-4422	36	33	mixed	mixed	ADJ
ejpam-4422	36	34	graph	graph	NOUN
ejpam-4422	36	35	,	,	PUNCT
ejpam-4422	36	36	some	some	DET
ejpam-4422	36	37	times	time	NOUN
ejpam-4422	36	38	called	call	VERB
ejpam-4422	36	39	α	α	PRON
ejpam-4422	36	40	-	-	ADJ
ejpam-4422	36	41	hermitian	hermitian	ADJ
ejpam-4422	36	42	adjacency	adjacency	NOUN
ejpam-4422	36	43	matrix	matrix	NOUN
ejpam-4422	36	44	,	,	PUNCT
ejpam-4422	36	45	was	be	AUX
ejpam-4422	36	46	as	as	SCONJ
ejpam-4422	36	47	follows	follow	VERB
ejpam-4422	36	48	:	:	PUNCT
ejpam-4422	36	49	let	let	VERB
ejpam-4422	36	50	α	α	NOUN
ejpam-4422	36	51	=	=	PUNCT
ejpam-4422	36	52	eiθ	eiθ	PROPN
ejpam-4422	37	1	and	and	CCONJ
ejpam-4422	37	2	d	d	AUX
ejpam-4422	37	3	be	be	AUX
ejpam-4422	37	4	a	a	DET
ejpam-4422	37	5	mixed	mixed	ADJ
ejpam-4422	37	6	graph	graph	NOUN
ejpam-4422	37	7	.	.	PUNCT
ejpam-4422	38	1	then	then	ADV
ejpam-4422	38	2	,	,	PUNCT
ejpam-4422	38	3	the	the	DET
ejpam-4422	38	4	α	α	NOUN
ejpam-4422	38	5	-	-	ADJ
ejpam-4422	38	6	hermitian	hermitian	ADJ
ejpam-4422	38	7	adjacency	adjacency	NOUN
ejpam-4422	38	8	matrix	matrix	NOUN
ejpam-4422	38	9	of	of	ADP
ejpam-4422	38	10	d	d	PROPN
ejpam-4422	38	11	is	be	AUX
ejpam-4422	38	12	a	a	DET
ejpam-4422	38	13	|v	|v	ADJ
ejpam-4422	39	1	|	|	NOUN
ejpam-4422	39	2	×	×	NOUN
ejpam-4422	39	3	|v	|v	NOUN
ejpam-4422	39	4	|	|	NOUN
ejpam-4422	39	5	matrix	matrix	NOUN
ejpam-4422	39	6	hα(d	hα(d	PRON
ejpam-4422	39	7	)	)	PUNCT
ejpam-4422	39	8	=	=	PUNCT
ejpam-4422	40	1	[	[	X
ejpam-4422	40	2	huv	huv	X
ejpam-4422	40	3	]	]	X
ejpam-4422	40	4	,	,	PUNCT
ejpam-4422	40	5	where	where	SCONJ
ejpam-4422	40	6	huv	huv	PROPN
ejpam-4422	40	7	=	=	SYM
ejpam-4422	40	8			NUM
ejpam-4422	40	9	1	1	NUM
ejpam-4422	40	10	if	if	SCONJ
ejpam-4422	40	11	uv	uv	NOUN
ejpam-4422	40	12	is	be	AUX
ejpam-4422	40	13	a	a	DET
ejpam-4422	40	14	digon	digon	NOUN
ejpam-4422	40	15	in	in	ADP
ejpam-4422	40	16	d	d	PROPN
ejpam-4422	40	17	,	,	PUNCT
ejpam-4422	40	18	α	α	PRON
ejpam-4422	40	19	if	if	SCONJ
ejpam-4422	40	20	uv	uv	NOUN
ejpam-4422	40	21	is	be	AUX
ejpam-4422	40	22	an	an	DET
ejpam-4422	40	23	arc	arc	NOUN
ejpam-4422	40	24	in	in	ADP
ejpam-4422	40	25	d	d	PROPN
ejpam-4422	40	26	,	,	PUNCT
ejpam-4422	40	27	α	α	PROPN
ejpam-4422	40	28	if	if	SCONJ
ejpam-4422	40	29	vu	vu	PROPN
ejpam-4422	40	30	is	be	AUX
ejpam-4422	40	31	an	an	DET
ejpam-4422	40	32	arc	arc	NOUN
ejpam-4422	40	33	in	in	ADP
ejpam-4422	40	34	d	d	PROPN
ejpam-4422	40	35	,	,	PUNCT
ejpam-4422	40	36	0	0	NUM
ejpam-4422	40	37	otherwise	otherwise	ADV
ejpam-4422	40	38	.	.	PUNCT
ejpam-4422	41	1	in	in	ADP
ejpam-4422	41	2	fact	fact	NOUN
ejpam-4422	41	3	,	,	PUNCT
ejpam-4422	41	4	these	these	DET
ejpam-4422	41	5	definitions	definition	NOUN
ejpam-4422	41	6	can	can	AUX
ejpam-4422	41	7	be	be	AUX
ejpam-4422	41	8	considered	consider	VERB
ejpam-4422	41	9	as	as	ADP
ejpam-4422	41	10	special	special	ADJ
ejpam-4422	41	11	cases	case	NOUN
ejpam-4422	41	12	of	of	ADP
ejpam-4422	41	13	the	the	DET
ejpam-4422	41	14	complex	complex	ADJ
ejpam-4422	41	15	unit	unit	NOUN
ejpam-4422	41	16	gain	gain	VERB
ejpam-4422	41	17	graphs	graph	NOUN
ejpam-4422	41	18	which	which	PRON
ejpam-4422	41	19	was	be	AUX
ejpam-4422	41	20	defined	define	VERB
ejpam-4422	41	21	in	in	ADP
ejpam-4422	41	22	[	[	X
ejpam-4422	41	23	4	4	NUM
ejpam-4422	41	24	]	]	PUNCT
ejpam-4422	41	25	.	.	PUNCT
ejpam-4422	42	1	the	the	DET
ejpam-4422	42	2	fact	fact	NOUN
ejpam-4422	42	3	that	that	SCONJ
ejpam-4422	42	4	these	these	DET
ejpam-4422	42	5	adjacency	adjacency	NOUN
ejpam-4422	42	6	matrices	matrix	NOUN
ejpam-4422	42	7	(	(	PUNCT
ejpam-4422	42	8	hi	hi	INTJ
ejpam-4422	42	9	and	and	CCONJ
ejpam-4422	42	10	hα	hα	NOUN
ejpam-4422	42	11	)	)	PUNCT
ejpam-4422	42	12	are	be	AUX
ejpam-4422	42	13	hermitian	hermitian	ADJ
ejpam-4422	42	14	has	have	AUX
ejpam-4422	42	15	opened	open	VERB
ejpam-4422	42	16	a	a	DET
ejpam-4422	42	17	hot	hot	ADJ
ejpam-4422	42	18	research	research	NOUN
ejpam-4422	42	19	topic	topic	NOUN
ejpam-4422	42	20	nowadays	nowadays	ADV
ejpam-4422	42	21	.	.	PUNCT
ejpam-4422	43	1	finally	finally	ADV
ejpam-4422	43	2	,	,	PUNCT
ejpam-4422	43	3	let	let	VERB
ejpam-4422	43	4	d	d	PRON
ejpam-4422	43	5	be	be	AUX
ejpam-4422	43	6	a	a	DET
ejpam-4422	43	7	mixed	mixed	ADJ
ejpam-4422	43	8	graph	graph	NOUN
ejpam-4422	43	9	,	,	PUNCT
ejpam-4422	43	10	hα	hα	AUX
ejpam-4422	43	11	be	be	AUX
ejpam-4422	43	12	its	its	PRON
ejpam-4422	43	13	α	α	NOUN
ejpam-4422	43	14	-	-	ADJ
ejpam-4422	43	15	hermitian	hermitian	ADJ
ejpam-4422	43	16	adjacency	adjacency	NOUN
ejpam-4422	43	17	matrix	matrix	NOUN
ejpam-4422	43	18	of	of	ADP
ejpam-4422	43	19	d	d	PROPN
ejpam-4422	43	20	and	and	CCONJ
ejpam-4422	43	21	u	u	NOUN
ejpam-4422	43	22	,	,	PUNCT
ejpam-4422	43	23	v	v	NOUN
ejpam-4422	43	24	,	,	PUNCT
ejpam-4422	43	25	r	r	NOUN
ejpam-4422	43	26	be	be	VERB
ejpam-4422	43	27	three	three	NUM
ejpam-4422	43	28	vertices	vertex	NOUN
ejpam-4422	43	29	of	of	ADP
ejpam-4422	43	30	d.	d.	PROPN
ejpam-4422	43	31	then	then	ADV
ejpam-4422	43	32	the	the	DET
ejpam-4422	43	33	α	α	NOUN
ejpam-4422	43	34	-	-	PUNCT
ejpam-4422	43	35	weight	weight	NOUN
ejpam-4422	43	36	of	of	ADP
ejpam-4422	43	37	a	a	DET
ejpam-4422	43	38	walk	walk	NOUN
ejpam-4422	43	39	w	w	NOUN
ejpam-4422	43	40	in	in	ADP
ejpam-4422	43	41	d	d	PROPN
ejpam-4422	43	42	,	,	PUNCT
ejpam-4422	43	43	say	say	VERB
ejpam-4422	43	44	w	w	PROPN
ejpam-4422	43	45	=	=	SYM
ejpam-4422	43	46	r1	r1	PROPN
ejpam-4422	43	47	,	,	PUNCT
ejpam-4422	43	48	r2	r2	PROPN
ejpam-4422	43	49	,	,	PUNCT
ejpam-4422	43	50	...	...	PUNCT
ejpam-4422	43	51	,	,	PUNCT
ejpam-4422	43	52	rk	rk	NOUN
ejpam-4422	43	53	,	,	PUNCT
ejpam-4422	43	54	is	be	AUX
ejpam-4422	43	55	defined	define	VERB
ejpam-4422	43	56	to	to	PART
ejpam-4422	43	57	be	be	AUX
ejpam-4422	43	58	the	the	DET
ejpam-4422	43	59	product	product	NOUN
ejpam-4422	43	60	of	of	ADP
ejpam-4422	43	61	the	the	DET
ejpam-4422	43	62	entries	entry	NOUN
ejpam-4422	43	63	of	of	ADP
ejpam-4422	43	64	hα	hα	ADP
ejpam-4422	43	65	corresponds	correspond	NOUN
ejpam-4422	43	66	to	to	ADP
ejpam-4422	43	67	the	the	DET
ejpam-4422	43	68	values	value	NOUN
ejpam-4422	43	69	of	of	ADP
ejpam-4422	43	70	the	the	DET
ejpam-4422	43	71	arcs	arc	NOUN
ejpam-4422	43	72	and	and	CCONJ
ejpam-4422	43	73	digons	digon	NOUN
ejpam-4422	43	74	in	in	ADP
ejpam-4422	43	75	w	w	PROPN
ejpam-4422	43	76	.	.	PUNCT
ejpam-4422	44	1	to	to	PART
ejpam-4422	44	2	be	be	AUX
ejpam-4422	44	3	more	more	ADV
ejpam-4422	44	4	formal	formal	ADJ
ejpam-4422	44	5	,	,	PUNCT
ejpam-4422	44	6	hα(w	hα(w	NOUN
ejpam-4422	44	7	)	)	PUNCT
ejpam-4422	45	1	=	=	PUNCT
ejpam-4422	45	2	hr1r2hr2r3	hr1r2hr2r3	PROPN
ejpam-4422	45	3	.	.	PUNCT
ejpam-4422	45	4	.	.	PUNCT
ejpam-4422	45	5	.	.	PUNCT
ejpam-4422	46	1	hrk−1rk	hrk−1rk	PROPN
ejpam-4422	46	2	.	.	PUNCT
ejpam-4422	47	1	furthermore	furthermore	ADV
ejpam-4422	47	2	,	,	PUNCT
ejpam-4422	47	3	if	if	SCONJ
ejpam-4422	47	4	wuv	wuv	PROPN
ejpam-4422	47	5	is	be	AUX
ejpam-4422	47	6	a	a	DET
ejpam-4422	47	7	walk	walk	NOUN
ejpam-4422	47	8	from	from	ADP
ejpam-4422	47	9	the	the	DET
ejpam-4422	47	10	vertex	vertex	NOUN
ejpam-4422	47	11	u	u	NOUN
ejpam-4422	47	12	to	to	ADP
ejpam-4422	47	13	the	the	DET
ejpam-4422	47	14	vertex	vertex	NOUN
ejpam-4422	47	15	v	v	NOUN
ejpam-4422	47	16	and	and	CCONJ
ejpam-4422	47	17	wvr	wvr	NOUN
ejpam-4422	47	18	is	be	AUX
ejpam-4422	47	19	a	a	DET
ejpam-4422	47	20	walk	walk	NOUN
ejpam-4422	47	21	from	from	ADP
ejpam-4422	47	22	the	the	DET
ejpam-4422	47	23	vertex	vertex	NOUN
ejpam-4422	47	24	v	v	NOUN
ejpam-4422	47	25	to	to	ADP
ejpam-4422	47	26	the	the	DET
ejpam-4422	47	27	vertex	vertex	NOUN
ejpam-4422	47	28	r	r	NOUN
ejpam-4422	47	29	,	,	PUNCT
ejpam-4422	47	30	then	then	ADV
ejpam-4422	47	31	by	by	ADP
ejpam-4422	47	32	the	the	DET
ejpam-4422	47	33	walk	walk	NOUN
ejpam-4422	47	34	wuvwvr	wuvwvr	NOUN
ejpam-4422	47	35	we	we	PRON
ejpam-4422	47	36	mean	mean	VERB
ejpam-4422	47	37	the	the	DET
ejpam-4422	47	38	walk	walk	NOUN
ejpam-4422	47	39	from	from	ADP
ejpam-4422	47	40	the	the	DET
ejpam-4422	47	41	vertex	vertex	NOUN
ejpam-4422	47	42	v	v	NOUN
ejpam-4422	47	43	to	to	ADP
ejpam-4422	47	44	the	the	DET
ejpam-4422	47	45	vertex	vertex	NOUN
ejpam-4422	47	46	r	r	NOUN
ejpam-4422	47	47	through	through	ADP
ejpam-4422	47	48	the	the	DET
ejpam-4422	47	49	walk	walk	NOUN
ejpam-4422	47	50	wuv	wuv	NOUN
ejpam-4422	47	51	then	then	ADV
ejpam-4422	47	52	the	the	DET
ejpam-4422	47	53	walk	walk	NOUN
ejpam-4422	47	54	wvr	wvr	NOUN
ejpam-4422	47	55	.	.	PUNCT
ejpam-4422	48	1	by	by	ADP
ejpam-4422	48	2	rev(wuv	rev(wuv	NOUN
ejpam-4422	48	3	)	)	PUNCT
ejpam-4422	49	1	we	we	PRON
ejpam-4422	49	2	mean	mean	VERB
ejpam-4422	49	3	the	the	DET
ejpam-4422	49	4	walk	walk	NOUN
ejpam-4422	49	5	from	from	ADP
ejpam-4422	49	6	the	the	DET
ejpam-4422	49	7	vertex	vertex	NOUN
ejpam-4422	49	8	v	v	NOUN
ejpam-4422	49	9	to	to	ADP
ejpam-4422	49	10	the	the	DET
ejpam-4422	49	11	vertex	vertex	NOUN
ejpam-4422	49	12	u	u	NOUN
ejpam-4422	49	13	through	through	ADP
ejpam-4422	49	14	the	the	DET
ejpam-4422	49	15	walk	walk	NOUN
ejpam-4422	49	16	wuv	wuv	NOUN
ejpam-4422	49	17	.	.	PUNCT
ejpam-4422	50	1	o.	o.	PROPN
ejpam-4422	50	2	alomari	alomari	PROPN
ejpam-4422	50	3	,	,	PUNCT
ejpam-4422	50	4	m.	m.	NOUN
ejpam-4422	50	5	abudayah	abudayah	PROPN
ejpam-4422	50	6	,	,	PUNCT
ejpam-4422	50	7	m.	m.	NOUN
ejpam-4422	50	8	ghanem	ghanem	PROPN
ejpam-4422	50	9	/	/	SYM
ejpam-4422	50	10	eur	eur	PROPN
ejpam-4422	50	11	.	.	PUNCT
ejpam-4422	51	1	j.	j.	PROPN
ejpam-4422	51	2	pure	pure	PROPN
ejpam-4422	51	3	appl	appl	PROPN
ejpam-4422	51	4	.	.	PROPN
ejpam-4422	51	5	math	math	PROPN
ejpam-4422	51	6	,	,	PUNCT
ejpam-4422	51	7	15	15	NUM
ejpam-4422	51	8	(	(	PUNCT
ejpam-4422	51	9	3	3	NUM
ejpam-4422	51	10	)	)	PUNCT
ejpam-4422	51	11	(	(	PUNCT
ejpam-4422	51	12	2022	2022	NUM
ejpam-4422	51	13	)	)	PUNCT
ejpam-4422	51	14	,	,	PUNCT
ejpam-4422	51	15	1090	1090	NUM
ejpam-4422	51	16	-	-	SYM
ejpam-4422	51	17	1097	1097	NUM
ejpam-4422	51	18	1092	1092	NUM
ejpam-4422	51	19	2	2	NUM
ejpam-4422	51	20	.	.	PUNCT
ejpam-4422	52	1	cospectrality	cospectrality	NOUN
ejpam-4422	52	2	of	of	ADP
ejpam-4422	52	3	hermitian	hermitian	ADJ
ejpam-4422	52	4	adjacency	adjacency	NOUN
ejpam-4422	52	5	matrices	matrix	NOUN
ejpam-4422	52	6	of	of	ADP
ejpam-4422	52	7	mixed	mixed	ADJ
ejpam-4422	52	8	graphs	graph	NOUN
ejpam-4422	52	9	studying	study	VERB
ejpam-4422	52	10	cospectrality	cospectrality	NOUN
ejpam-4422	52	11	of	of	ADP
ejpam-4422	52	12	two	two	NUM
ejpam-4422	52	13	graphs	graph	NOUN
ejpam-4422	52	14	is	be	AUX
ejpam-4422	52	15	one	one	NUM
ejpam-4422	52	16	of	of	ADP
ejpam-4422	52	17	the	the	DET
ejpam-4422	52	18	classical	classical	ADJ
ejpam-4422	52	19	field	field	NOUN
ejpam-4422	52	20	of	of	ADP
ejpam-4422	52	21	algebraic	algebraic	ADJ
ejpam-4422	52	22	graph	graph	NOUN
ejpam-4422	52	23	theory	theory	NOUN
ejpam-4422	52	24	.	.	PUNCT
ejpam-4422	53	1	however	however	ADV
ejpam-4422	53	2	,	,	PUNCT
ejpam-4422	53	3	the	the	DET
ejpam-4422	53	4	cospectrality	cospectrality	NOUN
ejpam-4422	53	5	of	of	ADP
ejpam-4422	53	6	mixed	mixed	ADJ
ejpam-4422	53	7	graphs	graph	NOUN
ejpam-4422	53	8	can	can	AUX
ejpam-4422	53	9	be	be	AUX
ejpam-4422	53	10	divided	divide	VERB
ejpam-4422	53	11	into	into	ADP
ejpam-4422	53	12	two	two	NUM
ejpam-4422	53	13	studies	study	NOUN
ejpam-4422	53	14	:	:	PUNCT
ejpam-4422	53	15	the	the	DET
ejpam-4422	53	16	first	first	ADJ
ejpam-4422	53	17	one	one	NOUN
ejpam-4422	53	18	is	be	AUX
ejpam-4422	53	19	studying	study	VERB
ejpam-4422	53	20	the	the	DET
ejpam-4422	53	21	cospectrality	cospectrality	NOUN
ejpam-4422	53	22	of	of	ADP
ejpam-4422	53	23	two	two	NUM
ejpam-4422	53	24	different	different	ADJ
ejpam-4422	53	25	mixed	mixed	ADJ
ejpam-4422	53	26	graphs	graph	NOUN
ejpam-4422	53	27	with	with	ADP
ejpam-4422	53	28	same	same	ADJ
ejpam-4422	53	29	unit	unit	NOUN
ejpam-4422	53	30	complex	complex	ADJ
ejpam-4422	53	31	number	number	NOUN
ejpam-4422	53	32	α	α	NOUN
ejpam-4422	53	33	(	(	PUNCT
ejpam-4422	53	34	α	α	NOUN
ejpam-4422	53	35	-	-	NOUN
ejpam-4422	53	36	cospectrality	cospectrality	NOUN
ejpam-4422	53	37	)	)	PUNCT
ejpam-4422	53	38	,	,	PUNCT
ejpam-4422	53	39	and	and	CCONJ
ejpam-4422	53	40	the	the	DET
ejpam-4422	53	41	second	second	ADJ
ejpam-4422	53	42	one	one	NOUN
ejpam-4422	53	43	is	be	AUX
ejpam-4422	53	44	studying	study	VERB
ejpam-4422	53	45	cospectrality	cospectrality	NOUN
ejpam-4422	53	46	of	of	ADP
ejpam-4422	53	47	same	same	ADJ
ejpam-4422	53	48	mixed	mixed	ADJ
ejpam-4422	53	49	graphs	graph	NOUN
ejpam-4422	53	50	but	but	CCONJ
ejpam-4422	53	51	with	with	ADP
ejpam-4422	53	52	different	different	ADJ
ejpam-4422	53	53	values	value	NOUN
ejpam-4422	53	54	of	of	ADP
ejpam-4422	53	55	α	α	NOUN
ejpam-4422	53	56	.	.	PUNCT
ejpam-4422	54	1	in	in	ADP
ejpam-4422	54	2	this	this	DET
ejpam-4422	54	3	section	section	NOUN
ejpam-4422	54	4	we	we	PRON
ejpam-4422	54	5	study	study	VERB
ejpam-4422	54	6	when	when	SCONJ
ejpam-4422	54	7	the	the	DET
ejpam-4422	54	8	hermitian	hermitian	ADJ
ejpam-4422	54	9	adjacency	adjacency	NOUN
ejpam-4422	54	10	matrices	matrix	NOUN
ejpam-4422	54	11	(	(	PUNCT
ejpam-4422	54	12	with	with	ADP
ejpam-4422	54	13	respect	respect	NOUN
ejpam-4422	54	14	to	to	ADP
ejpam-4422	54	15	different	different	ADJ
ejpam-4422	54	16	values	value	NOUN
ejpam-4422	54	17	of	of	ADP
ejpam-4422	54	18	α	α	NOUN
ejpam-4422	54	19	)	)	PUNCT
ejpam-4422	54	20	of	of	ADP
ejpam-4422	54	21	a	a	DET
ejpam-4422	54	22	weakly	weakly	ADV
ejpam-4422	54	23	connected	connected	ADJ
ejpam-4422	54	24	mixed	mixed	ADJ
ejpam-4422	54	25	graph	graph	NOUN
ejpam-4422	54	26	are	be	AUX
ejpam-4422	54	27	cospectral	cospectral	ADJ
ejpam-4422	54	28	.	.	PUNCT
ejpam-4422	55	1	also	also	ADV
ejpam-4422	55	2	we	we	PRON
ejpam-4422	55	3	study	study	VERB
ejpam-4422	55	4	when	when	SCONJ
ejpam-4422	55	5	αspectrum	αspectrum	NOUN
ejpam-4422	55	6	of	of	ADP
ejpam-4422	55	7	a	a	DET
ejpam-4422	55	8	weakly	weakly	ADV
ejpam-4422	55	9	connected	connected	ADJ
ejpam-4422	55	10	mixed	mixed	ADJ
ejpam-4422	55	11	graphd	graphd	NOUN
ejpam-4422	55	12	is	be	AUX
ejpam-4422	55	13	completely	completely	ADV
ejpam-4422	55	14	determined	determine	VERB
ejpam-4422	55	15	by	by	ADP
ejpam-4422	55	16	the	the	DET
ejpam-4422	55	17	underlying	underlie	VERB
ejpam-4422	55	18	graph	graph	NOUN
ejpam-4422	55	19	of	of	ADP
ejpam-4422	55	20	the	the	DET
ejpam-4422	55	21	mixed	mixed	ADJ
ejpam-4422	55	22	graph	graph	NOUN
ejpam-4422	55	23	d.	d.	NOUN
ejpam-4422	55	24	to	to	ADP
ejpam-4422	55	25	this	this	DET
ejpam-4422	55	26	end	end	NOUN
ejpam-4422	55	27	,	,	PUNCT
ejpam-4422	55	28	fix	fix	VERB
ejpam-4422	55	29	a	a	DET
ejpam-4422	55	30	weakly	weakly	ADV
ejpam-4422	55	31	connected	connected	ADJ
ejpam-4422	55	32	mixed	mixed	ADJ
ejpam-4422	55	33	graph	graph	NOUN
ejpam-4422	55	34	d	d	NOUN
ejpam-4422	55	35	and	and	CCONJ
ejpam-4422	55	36	a	a	DET
ejpam-4422	55	37	unit	unit	NOUN
ejpam-4422	55	38	complex	complex	ADJ
ejpam-4422	55	39	number	number	NOUN
ejpam-4422	55	40	α	α	NOUN
ejpam-4422	55	41	.	.	PUNCT
ejpam-4422	56	1	let	let	VERB
ejpam-4422	56	2	u	u	NOUN
ejpam-4422	56	3	,	,	PUNCT
ejpam-4422	56	4	v	v	PROPN
ejpam-4422	56	5	∈	∈	PROPN
ejpam-4422	56	6	v	v	NOUN
ejpam-4422	56	7	(	(	PUNCT
ejpam-4422	56	8	d	d	NOUN
ejpam-4422	56	9	)	)	PUNCT
ejpam-4422	56	10	and	and	CCONJ
ejpam-4422	56	11	let	let	VERB
ejpam-4422	56	12	w	w	NOUN
ejpam-4422	56	13	be	be	AUX
ejpam-4422	56	14	a	a	DET
ejpam-4422	56	15	walk	walk	NOUN
ejpam-4422	56	16	in	in	ADP
ejpam-4422	56	17	d	d	PROPN
ejpam-4422	56	18	,	,	PUNCT
ejpam-4422	56	19	say	say	VERB
ejpam-4422	56	20	w	w	NOUN
ejpam-4422	56	21	=	=	SYM
ejpam-4422	56	22	(	(	PUNCT
ejpam-4422	56	23	u	u	NOUN
ejpam-4422	56	24	=	=	PROPN
ejpam-4422	56	25	r1	r1	PROPN
ejpam-4422	56	26	,	,	PUNCT
ejpam-4422	56	27	...	...	PUNCT
ejpam-4422	56	28	,	,	PUNCT
ejpam-4422	56	29	rk	rk	NOUN
ejpam-4422	56	30	=	=	SYM
ejpam-4422	56	31	v	v	NOUN
ejpam-4422	56	32	)	)	PUNCT
ejpam-4422	56	33	.	.	PUNCT
ejpam-4422	57	1	we	we	PRON
ejpam-4422	57	2	now	now	ADV
ejpam-4422	57	3	recursively	recursively	ADV
ejpam-4422	57	4	define	define	VERB
ejpam-4422	57	5	a	a	DET
ejpam-4422	57	6	function	function	NOUN
ejpam-4422	57	7	that	that	PRON
ejpam-4422	57	8	assigns	assign	VERB
ejpam-4422	57	9	a	a	DET
ejpam-4422	57	10	value	value	NOUN
ejpam-4422	57	11	fα	fα	ADP
ejpam-4422	57	12	w	w	PROPN
ejpam-4422	57	13	(	(	PUNCT
ejpam-4422	57	14	j	j	NOUN
ejpam-4422	57	15	)	)	PUNCT
ejpam-4422	57	16	to	to	ADP
ejpam-4422	57	17	the	the	DET
ejpam-4422	57	18	jth	jth	PROPN
ejpam-4422	57	19	vertex	vertex	NOUN
ejpam-4422	57	20	(	(	PUNCT
ejpam-4422	57	21	i.e.	i.e.	X
ejpam-4422	57	22	to	to	ADP
ejpam-4422	57	23	rj	rj	PROPN
ejpam-4422	57	24	)	)	PUNCT
ejpam-4422	57	25	along	along	ADP
ejpam-4422	57	26	w	w	NOUN
ejpam-4422	57	27	by	by	ADP
ejpam-4422	57	28	fα	fα	ADV
ejpam-4422	57	29	w	w	NOUN
ejpam-4422	57	30	(	(	PUNCT
ejpam-4422	57	31	1	1	NUM
ejpam-4422	57	32	)	)	PUNCT
ejpam-4422	57	33	=	=	SYM
ejpam-4422	57	34	1	1	NUM
ejpam-4422	57	35	,	,	PUNCT
ejpam-4422	57	36	fα	fα	ADP
ejpam-4422	57	37	w	w	NOUN
ejpam-4422	57	38	(	(	PUNCT
ejpam-4422	57	39	j	j	PROPN
ejpam-4422	58	1	+	+	CCONJ
ejpam-4422	58	2	1	1	X
ejpam-4422	58	3	)	)	PUNCT
ejpam-4422	58	4	=	=	PUNCT
ejpam-4422	58	5			PUNCT
ejpam-4422	58	6	fα	fα	ADP
ejpam-4422	58	7	w	w	NOUN
ejpam-4422	58	8	(	(	PUNCT
ejpam-4422	58	9	j	j	NOUN
ejpam-4422	58	10	)	)	PUNCT
ejpam-4422	58	11	if	if	SCONJ
ejpam-4422	58	12	rjrj+1	rjrj+1	PRON
ejpam-4422	58	13	is	be	AUX
ejpam-4422	58	14	a	a	DET
ejpam-4422	58	15	digon	digon	NOUN
ejpam-4422	58	16	in	in	ADP
ejpam-4422	58	17	d	d	PROPN
ejpam-4422	58	18	αfα	αfα	NUM
ejpam-4422	58	19	w	w	PROPN
ejpam-4422	58	20	(	(	PUNCT
ejpam-4422	58	21	j	j	NOUN
ejpam-4422	58	22	)	)	PUNCT
ejpam-4422	58	23	if	if	SCONJ
ejpam-4422	58	24	rjrj+1	rjrj+1	PRON
ejpam-4422	58	25	is	be	AUX
ejpam-4422	58	26	an	an	DET
ejpam-4422	58	27	arc	arc	NOUN
ejpam-4422	58	28	in	in	ADP
ejpam-4422	58	29	d	d	PROPN
ejpam-4422	58	30	ᾱfα	ᾱfα	PROPN
ejpam-4422	58	31	w	w	PROPN
ejpam-4422	58	32	(	(	PUNCT
ejpam-4422	58	33	j	j	NOUN
ejpam-4422	58	34	)	)	PUNCT
ejpam-4422	58	35	if	if	SCONJ
ejpam-4422	58	36	rj+1rj	rj+1rj	PROPN
ejpam-4422	58	37	is	be	AUX
ejpam-4422	58	38	an	an	DET
ejpam-4422	58	39	arc	arc	NOUN
ejpam-4422	58	40	in	in	ADP
ejpam-4422	58	41	d	d	PROPN
ejpam-4422	58	42			NOUN
ejpam-4422	58	43	for	for	ADP
ejpam-4422	58	44	j	j	PROPN
ejpam-4422	58	45	=	=	SYM
ejpam-4422	58	46	1	1	NUM
ejpam-4422	58	47	,	,	PUNCT
ejpam-4422	58	48	...	...	PUNCT
ejpam-4422	58	49	,	,	PUNCT
ejpam-4422	58	50	k.	k.	PROPN
ejpam-4422	59	1	we	we	PRON
ejpam-4422	59	2	shall	shall	AUX
ejpam-4422	59	3	write	write	VERB
ejpam-4422	59	4	fα	fα	ADP
ejpam-4422	59	5	w	w	PROPN
ejpam-4422	59	6	(	(	PUNCT
ejpam-4422	59	7	∗	∗	NOUN
ejpam-4422	59	8	)	)	PUNCT
ejpam-4422	59	9	for	for	ADP
ejpam-4422	59	10	the	the	DET
ejpam-4422	59	11	final	final	ADJ
ejpam-4422	59	12	value	value	NOUN
ejpam-4422	59	13	fα	fα	ADP
ejpam-4422	59	14	w	w	NOUN
ejpam-4422	59	15	(	(	PUNCT
ejpam-4422	59	16	k	k	NOUN
ejpam-4422	59	17	)	)	PUNCT
ejpam-4422	59	18	,	,	PUNCT
ejpam-4422	59	19	see	see	VERB
ejpam-4422	59	20	figure	figure	NOUN
ejpam-4422	59	21	1	1	NUM
ejpam-4422	59	22	figure	figure	NOUN
ejpam-4422	59	23	1	1	NUM
ejpam-4422	59	24	:	:	PUNCT
ejpam-4422	59	25	the	the	DET
ejpam-4422	59	26	values	value	NOUN
ejpam-4422	59	27	of	of	ADP
ejpam-4422	59	28	the	the	DET
ejpam-4422	59	29	function	function	NOUN
ejpam-4422	59	30	fα	fα	ADP
ejpam-4422	59	31	w	w	PROPN
ejpam-4422	59	32	(	(	PUNCT
ejpam-4422	59	33	j	j	NOUN
ejpam-4422	59	34	)	)	PUNCT
ejpam-4422	59	35	along	along	ADP
ejpam-4422	59	36	the	the	DET
ejpam-4422	59	37	walk	walk	NOUN
ejpam-4422	59	38	w	w	PROPN
ejpam-4422	59	39	=	=	NOUN
ejpam-4422	59	40	1234567	1234567	NUM
ejpam-4422	59	41	let	let	VERB
ejpam-4422	59	42	d	d	PRON
ejpam-4422	59	43	be	be	AUX
ejpam-4422	59	44	a	a	DET
ejpam-4422	59	45	mixed	mixed	ADJ
ejpam-4422	59	46	graph	graph	NOUN
ejpam-4422	59	47	,	,	PUNCT
ejpam-4422	59	48	u	u	NOUN
ejpam-4422	59	49	∈	∈	PROPN
ejpam-4422	59	50	v	v	NOUN
ejpam-4422	59	51	(	(	PUNCT
ejpam-4422	59	52	d	d	NOUN
ejpam-4422	59	53	)	)	PUNCT
ejpam-4422	59	54	,	,	PUNCT
ejpam-4422	59	55	then	then	ADV
ejpam-4422	59	56	for	for	ADP
ejpam-4422	59	57	a	a	DET
ejpam-4422	59	58	vertex	vertex	NOUN
ejpam-4422	59	59	v	v	ADP
ejpam-4422	59	60	∈	∈	PROPN
ejpam-4422	59	61	v	v	NOUN
ejpam-4422	59	62	(	(	PUNCT
ejpam-4422	59	63	d	d	NOUN
ejpam-4422	59	64	)	)	PUNCT
ejpam-4422	59	65	define	define	VERB
ejpam-4422	59	66	the	the	DET
ejpam-4422	59	67	α	α	NOUN
ejpam-4422	59	68	-	-	NOUN
ejpam-4422	59	69	store	store	NOUN
ejpam-4422	59	70	of	of	ADP
ejpam-4422	59	71	the	the	DET
ejpam-4422	59	72	vertex	vertex	NOUN
ejpam-4422	59	73	v	v	NOUN
ejpam-4422	59	74	with	with	ADP
ejpam-4422	59	75	respect	respect	NOUN
ejpam-4422	59	76	to	to	ADP
ejpam-4422	59	77	the	the	DET
ejpam-4422	59	78	vertex	vertex	NOUN
ejpam-4422	59	79	u	u	NOUN
ejpam-4422	59	80	by	by	ADP
ejpam-4422	59	81	:	:	PUNCT
ejpam-4422	59	82	tα	tα	PROPN
ejpam-4422	59	83	u(v	u(v	PROPN
ejpam-4422	59	84	)	)	PUNCT
ejpam-4422	59	85	=	=	PRON
ejpam-4422	59	86	{	{	PUNCT
ejpam-4422	59	87	fα	fα	ADP
ejpam-4422	59	88	w	w	PROPN
ejpam-4422	59	89	(	(	PUNCT
ejpam-4422	59	90	∗	∗	PROPN
ejpam-4422	59	91	)	)	PUNCT
ejpam-4422	59	92	:	:	PUNCT
ejpam-4422	60	1	w	w	NOUN
ejpam-4422	60	2	is	be	AUX
ejpam-4422	60	3	a	a	DET
ejpam-4422	60	4	walk	walk	NOUN
ejpam-4422	60	5	from	from	ADP
ejpam-4422	60	6	u	u	NOUN
ejpam-4422	60	7	to	to	ADP
ejpam-4422	60	8	v	v	NOUN
ejpam-4422	60	9	}	}	PUNCT
ejpam-4422	60	10	,	,	PUNCT
ejpam-4422	60	11	and	and	CCONJ
ejpam-4422	60	12	the	the	DET
ejpam-4422	60	13	store	store	NOUN
ejpam-4422	60	14	size	size	NOUN
ejpam-4422	60	15	of	of	ADP
ejpam-4422	60	16	the	the	DET
ejpam-4422	60	17	vertex	vertex	NOUN
ejpam-4422	60	18	v	v	NOUN
ejpam-4422	60	19	with	with	ADP
ejpam-4422	60	20	respect	respect	NOUN
ejpam-4422	60	21	to	to	ADP
ejpam-4422	60	22	the	the	DET
ejpam-4422	60	23	vertex	vertex	NOUN
ejpam-4422	60	24	u	u	NOUN
ejpam-4422	60	25	by	by	ADP
ejpam-4422	60	26	tαu(v	tαu(v	NOUN
ejpam-4422	60	27	)	)	PUNCT
ejpam-4422	60	28	=	=	SYM
ejpam-4422	60	29	|tα	|tα	NUM
ejpam-4422	60	30	u(v)|	u(v)|	NOUN
ejpam-4422	60	31	.	.	PUNCT
ejpam-4422	61	1	clearly	clearly	ADV
ejpam-4422	61	2	1	1	NUM
ejpam-4422	61	3	∈	∈	NOUN
ejpam-4422	61	4	tα	tα	PROPN
ejpam-4422	61	5	u(u	u(u	NOUN
ejpam-4422	61	6	)	)	PUNCT
ejpam-4422	61	7	and	and	CCONJ
ejpam-4422	61	8	if	if	SCONJ
ejpam-4422	61	9	d	d	PROPN
ejpam-4422	61	10	contains	contain	VERB
ejpam-4422	61	11	a	a	DET
ejpam-4422	61	12	cycle	cycle	NOUN
ejpam-4422	61	13	c	c	NOUN
ejpam-4422	61	14	of	of	ADP
ejpam-4422	61	15	weight	weight	NOUN
ejpam-4422	61	16	other	other	ADJ
ejpam-4422	61	17	than	than	ADP
ejpam-4422	61	18	1	1	NUM
ejpam-4422	61	19	,	,	PUNCT
ejpam-4422	61	20	then	then	ADV
ejpam-4422	61	21	along	along	ADP
ejpam-4422	61	22	any	any	DET
ejpam-4422	61	23	walk	walk	NOUN
ejpam-4422	61	24	w	w	ADP
ejpam-4422	61	25	that	that	DET
ejpam-4422	61	26	o.	o.	PROPN
ejpam-4422	61	27	alomari	alomari	PROPN
ejpam-4422	61	28	,	,	PUNCT
ejpam-4422	61	29	m.	m.	NOUN
ejpam-4422	61	30	abudayah	abudayah	PROPN
ejpam-4422	61	31	,	,	PUNCT
ejpam-4422	61	32	m.	m.	NOUN
ejpam-4422	61	33	ghanem	ghanem	PROPN
ejpam-4422	61	34	/	/	SYM
ejpam-4422	61	35	eur	eur	PROPN
ejpam-4422	61	36	.	.	PUNCT
ejpam-4422	62	1	j.	j.	PROPN
ejpam-4422	62	2	pure	pure	PROPN
ejpam-4422	62	3	appl	appl	PROPN
ejpam-4422	62	4	.	.	PROPN
ejpam-4422	62	5	math	math	PROPN
ejpam-4422	62	6	,	,	PUNCT
ejpam-4422	62	7	15	15	NUM
ejpam-4422	62	8	(	(	PUNCT
ejpam-4422	62	9	3	3	NUM
ejpam-4422	62	10	)	)	PUNCT
ejpam-4422	62	11	(	(	PUNCT
ejpam-4422	62	12	2022	2022	NUM
ejpam-4422	62	13	)	)	PUNCT
ejpam-4422	62	14	,	,	PUNCT
ejpam-4422	62	15	1090	1090	NUM
ejpam-4422	62	16	-	-	SYM
ejpam-4422	62	17	1097	1097	NUM
ejpam-4422	62	18	1093	1093	NUM
ejpam-4422	62	19	contains	contain	VERB
ejpam-4422	62	20	c	c	PROPN
ejpam-4422	62	21	,	,	PUNCT
ejpam-4422	62	22	the	the	DET
ejpam-4422	62	23	store	store	NOUN
ejpam-4422	62	24	of	of	ADP
ejpam-4422	62	25	u	u	NOUN
ejpam-4422	62	26	will	will	AUX
ejpam-4422	62	27	contain	contain	VERB
ejpam-4422	62	28	values	value	NOUN
ejpam-4422	62	29	other	other	ADJ
ejpam-4422	62	30	than	than	ADP
ejpam-4422	62	31	1	1	NUM
ejpam-4422	62	32	.	.	PUNCT
ejpam-4422	63	1	in	in	ADP
ejpam-4422	63	2	fact	fact	NOUN
ejpam-4422	63	3	,	,	PUNCT
ejpam-4422	63	4	if	if	SCONJ
ejpam-4422	63	5	α	α	PRON
ejpam-4422	63	6	is	be	AUX
ejpam-4422	63	7	the	the	DET
ejpam-4422	63	8	primitive	primitive	ADJ
ejpam-4422	63	9	nth	nth	NOUN
ejpam-4422	63	10	root	root	NOUN
ejpam-4422	63	11	of	of	ADP
ejpam-4422	63	12	unity	unity	NOUN
ejpam-4422	63	13	,	,	PUNCT
ejpam-4422	63	14	the	the	DET
ejpam-4422	63	15	weight	weight	NOUN
ejpam-4422	63	16	of	of	ADP
ejpam-4422	63	17	the	the	DET
ejpam-4422	63	18	cycle	cycle	NOUN
ejpam-4422	63	19	c	c	NOUN
ejpam-4422	63	20	is	be	AUX
ejpam-4422	63	21	αr	αr	ADP
ejpam-4422	63	22	,	,	PUNCT
ejpam-4422	63	23	and	and	CCONJ
ejpam-4422	63	24	gcd(n	gcd(n	NOUN
ejpam-4422	63	25	,	,	PUNCT
ejpam-4422	63	26	r	r	NOUN
ejpam-4422	63	27	)	)	PUNCT
ejpam-4422	63	28	=	=	SYM
ejpam-4422	63	29	1	1	NUM
ejpam-4422	63	30	then	then	ADV
ejpam-4422	63	31	the	the	DET
ejpam-4422	63	32	store	store	NOUN
ejpam-4422	63	33	of	of	ADP
ejpam-4422	63	34	the	the	DET
ejpam-4422	63	35	vertex	vertex	NOUN
ejpam-4422	63	36	u	u	NOUN
ejpam-4422	63	37	will	will	AUX
ejpam-4422	63	38	contain	contain	VERB
ejpam-4422	63	39	all	all	DET
ejpam-4422	63	40	powers	power	NOUN
ejpam-4422	63	41	of	of	ADP
ejpam-4422	63	42	α	α	PROPN
ejpam-4422	63	43	.	.	PUNCT
ejpam-4422	64	1	theorem	theorem	NOUN
ejpam-4422	64	2	1	1	NUM
ejpam-4422	64	3	.	.	PUNCT
ejpam-4422	65	1	let	let	VERB
ejpam-4422	65	2	d	d	PRON
ejpam-4422	65	3	be	be	AUX
ejpam-4422	65	4	a	a	DET
ejpam-4422	65	5	weakly	weakly	ADV
ejpam-4422	65	6	connected	connected	ADJ
ejpam-4422	65	7	mixed	mixed	ADJ
ejpam-4422	65	8	graph	graph	NOUN
ejpam-4422	65	9	,	,	PUNCT
ejpam-4422	65	10	u	u	NOUN
ejpam-4422	65	11	∈	∈	PROPN
ejpam-4422	65	12	v	v	NOUN
ejpam-4422	65	13	(	(	PUNCT
ejpam-4422	65	14	d	d	NOUN
ejpam-4422	65	15	)	)	PUNCT
ejpam-4422	65	16	and	and	CCONJ
ejpam-4422	65	17	hα	hα	X
ejpam-4422	65	18	=	=	PUNCT
ejpam-4422	66	1	[	[	X
ejpam-4422	66	2	hij	hij	NOUN
ejpam-4422	66	3	]	]	PUNCT
ejpam-4422	66	4	be	be	AUX
ejpam-4422	66	5	its	its	PRON
ejpam-4422	66	6	α	α	NOUN
ejpam-4422	66	7	-	-	ADJ
ejpam-4422	66	8	hermitian	hermitian	ADJ
ejpam-4422	66	9	adjacency	adjacency	NOUN
ejpam-4422	66	10	matrix	matrix	NOUN
ejpam-4422	66	11	.	.	PUNCT
ejpam-4422	67	1	then	then	ADV
ejpam-4422	67	2	the	the	DET
ejpam-4422	67	3	following	follow	VERB
ejpam-4422	67	4	statements	statement	NOUN
ejpam-4422	67	5	are	be	AUX
ejpam-4422	67	6	equivalent	equivalent	ADJ
ejpam-4422	67	7	:	:	PUNCT
ejpam-4422	67	8	(	(	PUNCT
ejpam-4422	67	9	1	1	X
ejpam-4422	67	10	)	)	PUNCT
ejpam-4422	67	11	tαu(v	tαu(v	NOUN
ejpam-4422	67	12	)	)	PUNCT
ejpam-4422	67	13	=	=	SYM
ejpam-4422	67	14	1	1	NUM
ejpam-4422	67	15	for	for	ADP
ejpam-4422	67	16	a	a	DET
ejpam-4422	67	17	vertex	vertex	NOUN
ejpam-4422	67	18	v	v	NOUN
ejpam-4422	67	19	of	of	ADP
ejpam-4422	67	20	d.	d.	PROPN
ejpam-4422	67	21	(	(	PUNCT
ejpam-4422	67	22	2	2	NUM
ejpam-4422	67	23	)	)	PUNCT
ejpam-4422	67	24	tαu(m	tαu(m	NOUN
ejpam-4422	67	25	)	)	PUNCT
ejpam-4422	67	26	=	=	SYM
ejpam-4422	67	27	1	1	NUM
ejpam-4422	67	28	for	for	ADP
ejpam-4422	67	29	every	every	DET
ejpam-4422	67	30	vertex	vertex	NOUN
ejpam-4422	67	31	m	m	PROPN
ejpam-4422	67	32	of	of	ADP
ejpam-4422	67	33	d.	d.	PROPN
ejpam-4422	67	34	(	(	PUNCT
ejpam-4422	67	35	3	3	NUM
ejpam-4422	67	36	)	)	PUNCT
ejpam-4422	67	37	for	for	ADP
ejpam-4422	67	38	every	every	DET
ejpam-4422	67	39	cycle	cycle	NOUN
ejpam-4422	67	40	c	c	NOUN
ejpam-4422	67	41	=	=	SYM
ejpam-4422	67	42	(	(	PUNCT
ejpam-4422	67	43	r1	r1	PROPN
ejpam-4422	67	44	,	,	PUNCT
ejpam-4422	67	45	r2	r2	PROPN
ejpam-4422	67	46	,	,	PUNCT
ejpam-4422	67	47	.	.	PUNCT
ejpam-4422	67	48	.	.	PUNCT
ejpam-4422	68	1	.	.	PUNCT
ejpam-4422	69	1	,	,	PUNCT
ejpam-4422	69	2	rk−1	rk−1	PROPN
ejpam-4422	69	3	,	,	PUNCT
ejpam-4422	69	4	r1	r1	NOUN
ejpam-4422	69	5	)	)	PUNCT
ejpam-4422	69	6	in	in	ADP
ejpam-4422	69	7	d	d	PROPN
ejpam-4422	69	8	,	,	PUNCT
ejpam-4422	69	9	the	the	DET
ejpam-4422	69	10	weight	weight	NOUN
ejpam-4422	69	11	of	of	ADP
ejpam-4422	69	12	c	c	NOUN
ejpam-4422	69	13	hα(c	hα(c	NOUN
ejpam-4422	69	14	)	)	PUNCT
ejpam-4422	69	15	=	=	PUNCT
ejpam-4422	70	1	hr1r2hr2r3	hr1r2hr2r3	PROPN
ejpam-4422	70	2	.	.	PUNCT
ejpam-4422	70	3	.	.	PUNCT
ejpam-4422	70	4	.	.	PUNCT
ejpam-4422	71	1	hrk−1r1	hrk−1r1	PROPN
ejpam-4422	71	2	in	in	ADP
ejpam-4422	71	3	hα	hα	X
ejpam-4422	71	4	equals	equal	VERB
ejpam-4422	71	5	one	one	NUM
ejpam-4422	71	6	.	.	PUNCT
ejpam-4422	72	1	proof	proof	NOUN
ejpam-4422	72	2	.	.	PUNCT
ejpam-4422	73	1	(	(	PUNCT
ejpam-4422	73	2	(	(	PUNCT
ejpam-4422	73	3	1	1	NUM
ejpam-4422	73	4	)	)	PUNCT
ejpam-4422	73	5	)	)	PUNCT
ejpam-4422	73	6	→	→	PUNCT
ejpam-4422	73	7	(	(	PUNCT
ejpam-4422	73	8	(	(	PUNCT
ejpam-4422	73	9	2	2	NUM
ejpam-4422	73	10	)	)	PUNCT
ejpam-4422	73	11	)	)	PUNCT
ejpam-4422	73	12	suppose	suppose	VERB
ejpam-4422	73	13	that	that	SCONJ
ejpam-4422	73	14	tαu(v	tαu(v	NOUN
ejpam-4422	73	15	)	)	PUNCT
ejpam-4422	73	16	=	=	SYM
ejpam-4422	73	17	1	1	NUM
ejpam-4422	73	18	for	for	ADP
ejpam-4422	73	19	a	a	DET
ejpam-4422	73	20	vertex	vertex	NOUN
ejpam-4422	73	21	v	v	NOUN
ejpam-4422	73	22	of	of	ADP
ejpam-4422	73	23	d	d	NOUN
ejpam-4422	73	24	and	and	CCONJ
ejpam-4422	73	25	let	let	VERB
ejpam-4422	73	26	m	m	PRON
ejpam-4422	73	27	be	be	AUX
ejpam-4422	73	28	a	a	DET
ejpam-4422	73	29	vertex	vertex	NOUN
ejpam-4422	73	30	of	of	ADP
ejpam-4422	73	31	d	d	PROPN
ejpam-4422	73	32	with	with	ADP
ejpam-4422	73	33	tαu(m	tαu(m	PROPN
ejpam-4422	73	34	)	)	PUNCT
ejpam-4422	73	35	>	>	X
ejpam-4422	74	1	1	1	X
ejpam-4422	74	2	.	.	PUNCT
ejpam-4422	74	3	suppose	suppose	VERB
ejpam-4422	74	4	further	further	ADJ
ejpam-4422	74	5	wuv	wuv	PROPN
ejpam-4422	74	6	is	be	AUX
ejpam-4422	74	7	a	a	DET
ejpam-4422	74	8	walk	walk	NOUN
ejpam-4422	74	9	from	from	ADP
ejpam-4422	74	10	u	u	PRON
ejpam-4422	74	11	to	to	ADP
ejpam-4422	74	12	v.	v.	ADP
ejpam-4422	74	13	then	then	ADV
ejpam-4422	74	14	,	,	PUNCT
ejpam-4422	74	15	since	since	SCONJ
ejpam-4422	74	16	tαu(m	tαu(m	PROPN
ejpam-4422	74	17	)	)	PUNCT
ejpam-4422	74	18	>	>	X
ejpam-4422	75	1	1	1	NUM
ejpam-4422	75	2	,	,	PUNCT
ejpam-4422	75	3	there	there	PRON
ejpam-4422	75	4	are	be	VERB
ejpam-4422	75	5	two	two	NUM
ejpam-4422	75	6	walks	walk	NOUN
ejpam-4422	75	7	wum	wum	NOUN
ejpam-4422	75	8	and	and	CCONJ
ejpam-4422	75	9	w	w	PROPN
ejpam-4422	75	10	′	′	NUM
ejpam-4422	75	11	um	um	INTJ
ejpam-4422	75	12	from	from	ADP
ejpam-4422	75	13	u	u	PRON
ejpam-4422	75	14	to	to	ADP
ejpam-4422	75	15	m	m	PROPN
ejpam-4422	75	16	with	with	ADP
ejpam-4422	75	17	fα	fα	ADP
ejpam-4422	75	18	wum	wum	NOUN
ejpam-4422	75	19	(	(	PUNCT
ejpam-4422	75	20	∗	∗	NOUN
ejpam-4422	75	21	)	)	PUNCT
ejpam-4422	75	22	̸=	̸=	PROPN
ejpam-4422	75	23	fα	fα	PART
ejpam-4422	75	24	w	w	NOUN
ejpam-4422	75	25	′	′	NUM
ejpam-4422	75	26	um	um	INTJ
ejpam-4422	75	27	(	(	PUNCT
ejpam-4422	75	28	∗	∗	NOUN
ejpam-4422	75	29	)	)	PUNCT
ejpam-4422	75	30	.	.	PUNCT
ejpam-4422	76	1	now	now	ADV
ejpam-4422	76	2	,	,	PUNCT
ejpam-4422	76	3	consider	consider	VERB
ejpam-4422	76	4	the	the	DET
ejpam-4422	76	5	walk	walk	NOUN
ejpam-4422	76	6	w	w	NOUN
ejpam-4422	76	7	=	=	NOUN
ejpam-4422	76	8	wumrev(w	wumrev(w	PRON
ejpam-4422	76	9	′	′	NUM
ejpam-4422	76	10	um)wuv	um)wuv	NOUN
ejpam-4422	76	11	,	,	PUNCT
ejpam-4422	76	12	where	where	SCONJ
ejpam-4422	76	13	rev(w	rev(w	X
ejpam-4422	76	14	′	′	NOUN
ejpam-4422	76	15	um	um	INTJ
ejpam-4422	76	16	)	)	PUNCT
ejpam-4422	76	17	is	be	AUX
ejpam-4422	76	18	the	the	DET
ejpam-4422	76	19	walk	walk	NOUN
ejpam-4422	76	20	from	from	ADP
ejpam-4422	76	21	m	m	PROPN
ejpam-4422	76	22	to	to	ADP
ejpam-4422	76	23	u	u	NOUN
ejpam-4422	76	24	through	through	ADP
ejpam-4422	76	25	the	the	DET
ejpam-4422	76	26	walk	walk	NOUN
ejpam-4422	76	27	w	w	PROPN
ejpam-4422	76	28	′	′	NUM
ejpam-4422	76	29	um	um	INTJ
ejpam-4422	76	30	.	.	PUNCT
ejpam-4422	77	1	since	since	SCONJ
ejpam-4422	77	2	fα	fα	ADP
ejpam-4422	77	3	wum	wum	NOUN
ejpam-4422	77	4	(	(	PUNCT
ejpam-4422	77	5	∗	∗	NOUN
ejpam-4422	77	6	)	)	PUNCT
ejpam-4422	77	7	̸=	̸=	PROPN
ejpam-4422	77	8	fα	fα	PART
ejpam-4422	77	9	w	w	NOUN
ejpam-4422	77	10	′	′	NUM
ejpam-4422	77	11	um	um	INTJ
ejpam-4422	77	12	(	(	PUNCT
ejpam-4422	77	13	∗	∗	NOUN
ejpam-4422	77	14	)	)	PUNCT
ejpam-4422	77	15	we	we	PRON
ejpam-4422	77	16	have	have	VERB
ejpam-4422	77	17	:	:	PUNCT
ejpam-4422	77	18	fα	fα	ADP
ejpam-4422	77	19	w(∗	w(∗	PROPN
ejpam-4422	77	20	)	)	PUNCT
ejpam-4422	77	21	=	=	SYM
ejpam-4422	78	1	fwum(∗)frev(w	fwum(∗)frev(w	NOUN
ejpam-4422	78	2	′	′	NUM
ejpam-4422	78	3	um	um	INTJ
ejpam-4422	78	4	(	(	PUNCT
ejpam-4422	78	5	∗)fwuv(∗	∗)fwuv(∗	PROPN
ejpam-4422	78	6	)	)	PUNCT
ejpam-4422	78	7	(	(	PUNCT
ejpam-4422	78	8	1	1	X
ejpam-4422	78	9	)	)	PUNCT
ejpam-4422	78	10	̸=	̸=	PROPN
ejpam-4422	78	11	fwuv(∗	fwuv(∗	NOUN
ejpam-4422	78	12	)	)	PUNCT
ejpam-4422	78	13	.	.	PUNCT
ejpam-4422	79	1	(	(	PUNCT
ejpam-4422	79	2	2	2	X
ejpam-4422	79	3	)	)	PUNCT
ejpam-4422	79	4	therefore	therefore	ADV
ejpam-4422	79	5	,	,	PUNCT
ejpam-4422	79	6	tαu(v	tαu(v	PROPN
ejpam-4422	79	7	)	)	PUNCT
ejpam-4422	79	8	>	>	X
ejpam-4422	80	1	1	1	NUM
ejpam-4422	80	2	,	,	PUNCT
ejpam-4422	80	3	which	which	PRON
ejpam-4422	80	4	is	be	AUX
ejpam-4422	80	5	a	a	DET
ejpam-4422	80	6	contradiction	contradiction	NOUN
ejpam-4422	80	7	.	.	PUNCT
ejpam-4422	81	1	(	(	PUNCT
ejpam-4422	81	2	(	(	PUNCT
ejpam-4422	81	3	2	2	NUM
ejpam-4422	81	4	)	)	PUNCT
ejpam-4422	81	5	)	)	PUNCT
ejpam-4422	81	6	→	→	PUNCT
ejpam-4422	81	7	(	(	PUNCT
ejpam-4422	81	8	(	(	PUNCT
ejpam-4422	81	9	3	3	NUM
ejpam-4422	81	10	)	)	PUNCT
ejpam-4422	81	11	)	)	PUNCT
ejpam-4422	81	12	suppose	suppose	VERB
ejpam-4422	81	13	that	that	SCONJ
ejpam-4422	81	14	c	c	PROPN
ejpam-4422	81	15	is	be	AUX
ejpam-4422	81	16	a	a	DET
ejpam-4422	81	17	cycle	cycle	NOUN
ejpam-4422	81	18	in	in	ADP
ejpam-4422	81	19	d	d	NOUN
ejpam-4422	81	20	and	and	CCONJ
ejpam-4422	81	21	let	let	VERB
ejpam-4422	81	22	v	v	PART
ejpam-4422	81	23	be	be	AUX
ejpam-4422	81	24	a	a	DET
ejpam-4422	81	25	vertex	vertex	NOUN
ejpam-4422	81	26	of	of	ADP
ejpam-4422	81	27	the	the	DET
ejpam-4422	81	28	cycle	cycle	NOUN
ejpam-4422	81	29	c.	c.	NOUN
ejpam-4422	81	30	then	then	ADV
ejpam-4422	81	31	consider	consider	VERB
ejpam-4422	81	32	the	the	DET
ejpam-4422	81	33	closed	closed	ADJ
ejpam-4422	81	34	walk	walk	NOUN
ejpam-4422	81	35	w	w	NOUN
ejpam-4422	81	36	=	=	SYM
ejpam-4422	81	37	puvcvrev(puv	puvcvrev(puv	PROPN
ejpam-4422	81	38	)	)	PUNCT
ejpam-4422	81	39	,	,	PUNCT
ejpam-4422	81	40	where	where	SCONJ
ejpam-4422	81	41	puv	puv	NOUN
ejpam-4422	81	42	is	be	AUX
ejpam-4422	81	43	a	a	DET
ejpam-4422	81	44	path	path	NOUN
ejpam-4422	81	45	from	from	ADP
ejpam-4422	81	46	u	u	NOUN
ejpam-4422	81	47	to	to	ADP
ejpam-4422	81	48	v	v	NOUN
ejpam-4422	81	49	and	and	CCONJ
ejpam-4422	81	50	cv	cv	PROPN
ejpam-4422	81	51	is	be	AUX
ejpam-4422	81	52	the	the	DET
ejpam-4422	81	53	closed	closed	ADJ
ejpam-4422	81	54	path	path	NOUN
ejpam-4422	81	55	from	from	ADP
ejpam-4422	81	56	v	v	NUM
ejpam-4422	81	57	to	to	ADP
ejpam-4422	81	58	v	v	NOUN
ejpam-4422	81	59	along	along	ADP
ejpam-4422	81	60	the	the	DET
ejpam-4422	81	61	cycle	cycle	NOUN
ejpam-4422	81	62	c.	c.	NOUN
ejpam-4422	81	63	then	then	ADV
ejpam-4422	81	64	,	,	PUNCT
ejpam-4422	81	65	using	use	VERB
ejpam-4422	81	66	the	the	DET
ejpam-4422	81	67	definition	definition	NOUN
ejpam-4422	81	68	of	of	ADP
ejpam-4422	81	69	fα	fα	ADP
ejpam-4422	81	70	w	w	PROPN
ejpam-4422	81	71	(	(	PUNCT
ejpam-4422	81	72	∗	∗	NOUN
ejpam-4422	81	73	)	)	PUNCT
ejpam-4422	81	74	we	we	PRON
ejpam-4422	81	75	have	have	VERB
ejpam-4422	81	76	,	,	PUNCT
ejpam-4422	81	77	fα	fα	ADP
ejpam-4422	81	78	w(∗	w(∗	NUM
ejpam-4422	81	79	)	)	PUNCT
ejpam-4422	81	80	=	=	SYM
ejpam-4422	81	81	hα(puv)hα(c)hα(rev(puv	hα(puv)hα(c)hα(rev(puv	NOUN
ejpam-4422	81	82	)	)	PUNCT
ejpam-4422	81	83	)	)	PUNCT
ejpam-4422	82	1	(	(	PUNCT
ejpam-4422	82	2	3	3	X
ejpam-4422	82	3	)	)	PUNCT
ejpam-4422	82	4	=	=	NOUN
ejpam-4422	82	5	hα(c	hα(c	NOUN
ejpam-4422	82	6	)	)	PUNCT
ejpam-4422	82	7	.	.	PUNCT
ejpam-4422	83	1	(	(	PUNCT
ejpam-4422	83	2	4	4	X
ejpam-4422	83	3	)	)	PUNCT
ejpam-4422	83	4	finally	finally	ADV
ejpam-4422	83	5	,	,	PUNCT
ejpam-4422	83	6	using	use	VERB
ejpam-4422	83	7	the	the	DET
ejpam-4422	83	8	definition	definition	NOUN
ejpam-4422	83	9	of	of	ADP
ejpam-4422	83	10	fα	fα	ADP
ejpam-4422	83	11	w	w	PROPN
ejpam-4422	83	12	(	(	PUNCT
ejpam-4422	83	13	∗	∗	NOUN
ejpam-4422	83	14	)	)	PUNCT
ejpam-4422	83	15	and	and	CCONJ
ejpam-4422	83	16	the	the	DET
ejpam-4422	83	17	assumption	assumption	NOUN
ejpam-4422	83	18	that	that	SCONJ
ejpam-4422	83	19	tαu(v	tαu(v	NOUN
ejpam-4422	83	20	)	)	PUNCT
ejpam-4422	83	21	=	=	SYM
ejpam-4422	83	22	1	1	NUM
ejpam-4422	83	23	for	for	ADP
ejpam-4422	83	24	every	every	DET
ejpam-4422	83	25	vertex	vertex	NOUN
ejpam-4422	83	26	v	v	NOUN
ejpam-4422	83	27	of	of	ADP
ejpam-4422	83	28	d	d	PROPN
ejpam-4422	83	29	,	,	PUNCT
ejpam-4422	83	30	we	we	PRON
ejpam-4422	83	31	have	have	VERB
ejpam-4422	83	32	hα(c	hα(c	NOUN
ejpam-4422	83	33	)	)	PUNCT
ejpam-4422	83	34	equals	equal	VERB
ejpam-4422	83	35	to	to	ADP
ejpam-4422	83	36	1	1	NUM
ejpam-4422	83	37	.	.	PUNCT
ejpam-4422	84	1	(	(	PUNCT
ejpam-4422	84	2	(	(	PUNCT
ejpam-4422	84	3	3	3	NUM
ejpam-4422	84	4	)	)	PUNCT
ejpam-4422	84	5	)	)	PUNCT
ejpam-4422	85	1	→	→	PUNCT
ejpam-4422	85	2	(	(	PUNCT
ejpam-4422	85	3	(	(	PUNCT
ejpam-4422	85	4	1	1	NUM
ejpam-4422	85	5	)	)	PUNCT
ejpam-4422	85	6	)	)	PUNCT
ejpam-4422	85	7	let	let	VERB
ejpam-4422	85	8	w	w	NOUN
ejpam-4422	85	9	be	be	AUX
ejpam-4422	85	10	a	a	DET
ejpam-4422	85	11	closed	closed	ADJ
ejpam-4422	85	12	walk	walk	NOUN
ejpam-4422	85	13	start	start	NOUN
ejpam-4422	85	14	from	from	ADP
ejpam-4422	85	15	the	the	DET
ejpam-4422	85	16	initial	initial	ADJ
ejpam-4422	85	17	vertex	vertex	NOUN
ejpam-4422	86	1	u.	u.	NOUN
ejpam-4422	86	2	then	then	ADV
ejpam-4422	86	3	,	,	PUNCT
ejpam-4422	86	4	w	w	NOUN
ejpam-4422	86	5	consists	consist	NOUN
ejpam-4422	86	6	of	of	ADP
ejpam-4422	86	7	a	a	DET
ejpam-4422	86	8	sequence	sequence	NOUN
ejpam-4422	86	9	of	of	ADP
ejpam-4422	86	10	cycles	cycle	NOUN
ejpam-4422	86	11	{	{	PUNCT
ejpam-4422	86	12	ci}ni=1	ci}ni=1	NOUN
ejpam-4422	86	13	and	and	CCONJ
ejpam-4422	86	14	sequence	sequence	NOUN
ejpam-4422	86	15	of	of	ADP
ejpam-4422	86	16	paths	path	NOUN
ejpam-4422	86	17	{	{	PUNCT
ejpam-4422	86	18	pj}mj=1	pj}mj=1	NOUN
ejpam-4422	86	19	.	.	PUNCT
ejpam-4422	87	1	further	far	ADV
ejpam-4422	87	2	,	,	PUNCT
ejpam-4422	87	3	using	use	VERB
ejpam-4422	87	4	the	the	DET
ejpam-4422	87	5	assumption	assumption	NOUN
ejpam-4422	87	6	in	in	ADP
ejpam-4422	87	7	(	(	PUNCT
ejpam-4422	87	8	3	3	X
ejpam-4422	87	9	)	)	PUNCT
ejpam-4422	87	10	we	we	PRON
ejpam-4422	87	11	have	have	AUX
ejpam-4422	87	12	o.	o.	NOUN
ejpam-4422	87	13	alomari	alomari	PROPN
ejpam-4422	87	14	,	,	PUNCT
ejpam-4422	87	15	m.	m.	NOUN
ejpam-4422	87	16	abudayah	abudayah	PROPN
ejpam-4422	87	17	,	,	PUNCT
ejpam-4422	87	18	m.	m.	NOUN
ejpam-4422	87	19	ghanem	ghanem	PROPN
ejpam-4422	87	20	/	/	SYM
ejpam-4422	87	21	eur	eur	PROPN
ejpam-4422	87	22	.	.	PUNCT
ejpam-4422	88	1	j.	j.	PROPN
ejpam-4422	88	2	pure	pure	PROPN
ejpam-4422	88	3	appl	appl	PROPN
ejpam-4422	88	4	.	.	PROPN
ejpam-4422	88	5	math	math	PROPN
ejpam-4422	88	6	,	,	PUNCT
ejpam-4422	88	7	15	15	NUM
ejpam-4422	88	8	(	(	PUNCT
ejpam-4422	88	9	3	3	NUM
ejpam-4422	88	10	)	)	PUNCT
ejpam-4422	88	11	(	(	PUNCT
ejpam-4422	88	12	2022	2022	NUM
ejpam-4422	88	13	)	)	PUNCT
ejpam-4422	88	14	,	,	PUNCT
ejpam-4422	88	15	1090	1090	NUM
ejpam-4422	88	16	-	-	SYM
ejpam-4422	88	17	1097	1097	NUM
ejpam-4422	88	18	1094	1094	NUM
ejpam-4422	88	19	fα	fα	ADP
ejpam-4422	88	20	w(∗	w(∗	PROPN
ejpam-4422	88	21	)	)	PUNCT
ejpam-4422	88	22	=	=	PUNCT
ejpam-4422	88	23	n∏	n∏	PROPN
ejpam-4422	88	24	i=1	i=1	X
ejpam-4422	88	25	hα(ci	hα(ci	ADJ
ejpam-4422	88	26	)	)	PUNCT
ejpam-4422	88	27	m∏	m∏	PROPN
ejpam-4422	88	28	j=1	j=1	ADJ
ejpam-4422	88	29	hα(pj	hα(pj	NOUN
ejpam-4422	88	30	)	)	PUNCT
ejpam-4422	88	31	m∏	m∏	PROPN
ejpam-4422	88	32	j=1	j=1	PROPN
ejpam-4422	88	33	hα(rev(pj	hα(rev(pj	PROPN
ejpam-4422	88	34	)	)	PUNCT
ejpam-4422	88	35	)	)	PUNCT
ejpam-4422	88	36	(	(	PUNCT
ejpam-4422	88	37	5	5	X
ejpam-4422	88	38	)	)	PUNCT
ejpam-4422	88	39	=	=	PUNCT
ejpam-4422	88	40	n∏	n∏	PROPN
ejpam-4422	88	41	i=1	i=1	X
ejpam-4422	88	42	hα(ci	hα(ci	PROPN
ejpam-4422	88	43	)	)	PUNCT
ejpam-4422	88	44	(	(	PUNCT
ejpam-4422	88	45	6	6	NUM
ejpam-4422	88	46	)	)	PUNCT
ejpam-4422	88	47	=	=	SYM
ejpam-4422	89	1	1	1	X
ejpam-4422	89	2	.	.	PUNCT
ejpam-4422	89	3	(	(	PUNCT
ejpam-4422	89	4	7	7	NUM
ejpam-4422	89	5	)	)	PUNCT
ejpam-4422	89	6	therefore	therefore	ADV
ejpam-4422	89	7	,	,	PUNCT
ejpam-4422	89	8	tαu(u	tαu(u	PROPN
ejpam-4422	89	9	)	)	PUNCT
ejpam-4422	89	10	=	=	SYM
ejpam-4422	90	1	1	1	X
ejpam-4422	90	2	.	.	PUNCT
ejpam-4422	91	1	the	the	DET
ejpam-4422	91	2	above	above	ADJ
ejpam-4422	91	3	theorem	theorem	NOUN
ejpam-4422	91	4	paved	pave	VERB
ejpam-4422	91	5	the	the	DET
ejpam-4422	91	6	way	way	NOUN
ejpam-4422	91	7	to	to	ADP
ejpam-4422	91	8	the	the	DET
ejpam-4422	91	9	following	follow	VERB
ejpam-4422	91	10	definition	definition	NOUN
ejpam-4422	91	11	.	.	PUNCT
ejpam-4422	92	1	definition	definition	NOUN
ejpam-4422	92	2	1	1	NUM
ejpam-4422	92	3	.	.	PUNCT
ejpam-4422	93	1	let	let	VERB
ejpam-4422	93	2	d	d	PRON
ejpam-4422	93	3	be	be	AUX
ejpam-4422	93	4	a	a	DET
ejpam-4422	93	5	weakly	weakly	ADV
ejpam-4422	93	6	connected	connected	ADJ
ejpam-4422	93	7	mixed	mixed	ADJ
ejpam-4422	93	8	graph	graph	NOUN
ejpam-4422	93	9	and	and	CCONJ
ejpam-4422	93	10	u	u	NOUN
ejpam-4422	93	11	be	be	VERB
ejpam-4422	93	12	a	a	DET
ejpam-4422	93	13	vertex	vertex	NOUN
ejpam-4422	93	14	of	of	ADP
ejpam-4422	93	15	d.	d.	PROPN
ejpam-4422	93	16	then	then	ADV
ejpam-4422	93	17	,	,	PUNCT
ejpam-4422	93	18	d	d	PROPN
ejpam-4422	93	19	is	be	AUX
ejpam-4422	93	20	called	call	VERB
ejpam-4422	93	21	an	an	DET
ejpam-4422	93	22	α	α	NOUN
ejpam-4422	93	23	-	-	PUNCT
ejpam-4422	93	24	monostore	monostore	ADJ
ejpam-4422	93	25	graph	graph	NOUN
ejpam-4422	93	26	if	if	SCONJ
ejpam-4422	93	27	tαu(v	tαu(v	NUM
ejpam-4422	93	28	)	)	PUNCT
ejpam-4422	93	29	=	=	SYM
ejpam-4422	93	30	1	1	NUM
ejpam-4422	93	31	for	for	ADP
ejpam-4422	93	32	a	a	DET
ejpam-4422	93	33	vertex	vertex	NOUN
ejpam-4422	93	34	v	v	NOUN
ejpam-4422	93	35	in	in	ADP
ejpam-4422	93	36	d.	d.	PROPN
ejpam-4422	93	37	obviously	obviously	ADV
ejpam-4422	93	38	,	,	PUNCT
ejpam-4422	93	39	changing	change	VERB
ejpam-4422	93	40	the	the	DET
ejpam-4422	93	41	initial	initial	ADJ
ejpam-4422	93	42	vertex	vertex	NOUN
ejpam-4422	93	43	u	u	NOUN
ejpam-4422	93	44	of	of	ADP
ejpam-4422	93	45	a	a	DET
ejpam-4422	93	46	mixed	mixed	ADJ
ejpam-4422	93	47	graph	graph	NOUN
ejpam-4422	93	48	d	d	NOUN
ejpam-4422	93	49	will	will	AUX
ejpam-4422	93	50	not	not	PART
ejpam-4422	93	51	change	change	VERB
ejpam-4422	93	52	the	the	DET
ejpam-4422	93	53	store	store	NOUN
ejpam-4422	93	54	size	size	NOUN
ejpam-4422	93	55	of	of	ADP
ejpam-4422	93	56	the	the	DET
ejpam-4422	93	57	vertices	vertex	NOUN
ejpam-4422	93	58	of	of	ADP
ejpam-4422	93	59	d	d	NOUN
ejpam-4422	93	60	,	,	PUNCT
ejpam-4422	93	61	but	but	CCONJ
ejpam-4422	93	62	it	it	PRON
ejpam-4422	93	63	may	may	AUX
ejpam-4422	93	64	change	change	VERB
ejpam-4422	93	65	the	the	DET
ejpam-4422	93	66	values	value	NOUN
ejpam-4422	93	67	in	in	ADP
ejpam-4422	93	68	the	the	DET
ejpam-4422	93	69	store	store	NOUN
ejpam-4422	93	70	set	set	NOUN
ejpam-4422	93	71	of	of	ADP
ejpam-4422	93	72	the	the	DET
ejpam-4422	93	73	vertices	vertex	NOUN
ejpam-4422	93	74	.	.	PUNCT
ejpam-4422	94	1	theorem	theorem	NOUN
ejpam-4422	94	2	2	2	NUM
ejpam-4422	94	3	.	.	PUNCT
ejpam-4422	95	1	let	let	VERB
ejpam-4422	95	2	d	d	PRON
ejpam-4422	95	3	be	be	AUX
ejpam-4422	95	4	an	an	DET
ejpam-4422	95	5	α	α	NOUN
ejpam-4422	95	6	-	-	PUNCT
ejpam-4422	95	7	monostore	monostore	ADJ
ejpam-4422	95	8	graph	graph	NOUN
ejpam-4422	95	9	,	,	PUNCT
ejpam-4422	95	10	hα	hα	ADP
ejpam-4422	95	11	=	=	PUNCT
ejpam-4422	96	1	[	[	X
ejpam-4422	96	2	hst	hst	X
ejpam-4422	96	3	]	]	X
ejpam-4422	96	4	be	be	AUX
ejpam-4422	96	5	its	its	PRON
ejpam-4422	96	6	α	α	NOUN
ejpam-4422	96	7	-	-	ADJ
ejpam-4422	96	8	hermitian	hermitian	ADJ
ejpam-4422	96	9	adjacency	adjacency	NOUN
ejpam-4422	96	10	matrix	matrix	NOUN
ejpam-4422	96	11	and	and	CCONJ
ejpam-4422	96	12	for	for	ADP
ejpam-4422	96	13	a	a	DET
ejpam-4422	96	14	vertex	vertex	NOUN
ejpam-4422	96	15	u	u	NOUN
ejpam-4422	96	16	in	in	ADP
ejpam-4422	96	17	d	d	PROPN
ejpam-4422	96	18	,	,	PUNCT
ejpam-4422	96	19	∆α	∆α	PROPN
ejpam-4422	96	20	=	=	PUNCT
ejpam-4422	97	1	diag{tv	diag{tv	PROPN
ejpam-4422	97	2	:	:	PUNCT
ejpam-4422	97	3	tv	tv	PROPN
ejpam-4422	97	4	∈	∈	PROPN
ejpam-4422	97	5	tα	tα	PROPN
ejpam-4422	97	6	u(v	u(v	PROPN
ejpam-4422	97	7	)	)	PUNCT
ejpam-4422	97	8	and	and	CCONJ
ejpam-4422	97	9	v	v	ADP
ejpam-4422	97	10	∈	∈	PROPN
ejpam-4422	97	11	v	v	NOUN
ejpam-4422	97	12	(	(	PUNCT
ejpam-4422	97	13	d	d	NOUN
ejpam-4422	97	14	)	)	PUNCT
ejpam-4422	97	15	}	}	PUNCT
ejpam-4422	97	16	.	.	PUNCT
ejpam-4422	98	1	then	then	ADV
ejpam-4422	98	2	,	,	PUNCT
ejpam-4422	98	3	∆αhα∆	∆αhα∆	PROPN
ejpam-4422	98	4	∗	∗	VERB
ejpam-4422	98	5	α	α	NOUN
ejpam-4422	98	6	=	=	SYM
ejpam-4422	98	7	a(γ(d	a(γ(d	PROPN
ejpam-4422	98	8	)	)	PUNCT
ejpam-4422	98	9	)	)	PUNCT
ejpam-4422	98	10	where	where	SCONJ
ejpam-4422	98	11	a(γ(d	a(γ(d	PROPN
ejpam-4422	98	12	)	)	PUNCT
ejpam-4422	98	13	)	)	PUNCT
ejpam-4422	98	14	is	be	AUX
ejpam-4422	98	15	the	the	DET
ejpam-4422	98	16	traditional	traditional	ADJ
ejpam-4422	98	17	adjacency	adjacency	NOUN
ejpam-4422	98	18	matrix	matrix	NOUN
ejpam-4422	98	19	of	of	ADP
ejpam-4422	98	20	the	the	DET
ejpam-4422	98	21	graph	graph	NOUN
ejpam-4422	98	22	γ(d	γ(d	PROPN
ejpam-4422	98	23	)	)	PUNCT
ejpam-4422	98	24	.	.	PUNCT
ejpam-4422	99	1	proof	proof	NOUN
ejpam-4422	99	2	.	.	PUNCT
ejpam-4422	100	1	since	since	SCONJ
ejpam-4422	100	2	the	the	DET
ejpam-4422	100	3	matrix	matrix	NOUN
ejpam-4422	100	4	∆α	∆α	PROPN
ejpam-4422	100	5	is	be	AUX
ejpam-4422	100	6	a	a	DET
ejpam-4422	100	7	diagonal	diagonal	ADJ
ejpam-4422	100	8	matrix	matrix	NOUN
ejpam-4422	100	9	,	,	PUNCT
ejpam-4422	100	10	it	it	PRON
ejpam-4422	100	11	is	be	AUX
ejpam-4422	100	12	enough	enough	ADJ
ejpam-4422	100	13	to	to	PART
ejpam-4422	100	14	prove	prove	VERB
ejpam-4422	100	15	that	that	SCONJ
ejpam-4422	100	16	∆αhα∆	∆αhα∆	PROPN
ejpam-4422	100	17	∗	∗	VERB
ejpam-4422	100	18	α	α	PROPN
ejpam-4422	100	19	is	be	AUX
ejpam-4422	100	20	a	a	DET
ejpam-4422	100	21	{	{	PUNCT
ejpam-4422	100	22	0	0	NUM
ejpam-4422	100	23	,	,	PUNCT
ejpam-4422	100	24	1}-matrix	1}-matrix	NUM
ejpam-4422	100	25	.	.	PUNCT
ejpam-4422	101	1	to	to	PART
ejpam-4422	101	2	do	do	VERB
ejpam-4422	101	3	this	this	PRON
ejpam-4422	101	4	,	,	PUNCT
ejpam-4422	101	5	suppose	suppose	VERB
ejpam-4422	101	6	that	that	SCONJ
ejpam-4422	101	7	rs	rs	PROPN
ejpam-4422	101	8	is	be	AUX
ejpam-4422	101	9	an	an	DET
ejpam-4422	101	10	arc	arc	NOUN
ejpam-4422	101	11	in	in	ADP
ejpam-4422	101	12	d	d	PROPN
ejpam-4422	101	13	,	,	PUNCT
ejpam-4422	101	14	then	then	ADV
ejpam-4422	101	15	(	(	PUNCT
ejpam-4422	101	16	∆αhα∆	∆αhα∆	PROPN
ejpam-4422	101	17	∗	∗	VERB
ejpam-4422	101	18	α)rs	α)rs	PROPN
ejpam-4422	101	19	=	=	NOUN
ejpam-4422	101	20	trhrsts	trhrst	NOUN
ejpam-4422	101	21	.	.	PUNCT
ejpam-4422	102	1	since	since	SCONJ
ejpam-4422	102	2	rs	rs	PROPN
ejpam-4422	102	3	is	be	VERB
ejpam-4422	102	4	an	an	DET
ejpam-4422	102	5	arc	arc	NOUN
ejpam-4422	102	6	in	in	ADP
ejpam-4422	102	7	d	d	PROPN
ejpam-4422	102	8	and	and	CCONJ
ejpam-4422	102	9	d	d	PROPN
ejpam-4422	102	10	is	be	AUX
ejpam-4422	102	11	α	α	DET
ejpam-4422	102	12	-	-	ADJ
ejpam-4422	102	13	monostore	monostore	ADJ
ejpam-4422	102	14	mixed	mixed	ADJ
ejpam-4422	102	15	graph	graph	NOUN
ejpam-4422	102	16	,	,	PUNCT
ejpam-4422	102	17	ts	ts	ADP
ejpam-4422	102	18	=	=	PUNCT
ejpam-4422	102	19	hrstr	hrstr	PROPN
ejpam-4422	102	20	.	.	PUNCT
ejpam-4422	103	1	therefore	therefore	ADV
ejpam-4422	103	2	,	,	PUNCT
ejpam-4422	103	3	(	(	PUNCT
ejpam-4422	103	4	∆αhα∆	∆αhα∆	PROPN
ejpam-4422	103	5	∗	∗	VERB
ejpam-4422	103	6	α)rs	α)rs	PROPN
ejpam-4422	103	7	=	=	SYM
ejpam-4422	103	8	1	1	X
ejpam-4422	103	9	.	.	PUNCT
ejpam-4422	103	10	using	use	VERB
ejpam-4422	103	11	the	the	DET
ejpam-4422	103	12	definition	definition	NOUN
ejpam-4422	103	13	of	of	ADP
ejpam-4422	103	14	fα	fα	ADP
ejpam-4422	103	15	w	w	PROPN
ejpam-4422	103	16	(	(	PUNCT
ejpam-4422	103	17	∗	∗	PROPN
ejpam-4422	103	18	)	)	PUNCT
ejpam-4422	103	19	,	,	PUNCT
ejpam-4422	103	20	theorem	theorem	VERB
ejpam-4422	103	21	1	1	NUM
ejpam-4422	103	22	and	and	CCONJ
ejpam-4422	103	23	theorem	theorem	VERB
ejpam-4422	103	24	2	2	NUM
ejpam-4422	103	25	,	,	PUNCT
ejpam-4422	103	26	any	any	DET
ejpam-4422	103	27	vertex	vertex	NOUN
ejpam-4422	103	28	of	of	ADP
ejpam-4422	103	29	an	an	DET
ejpam-4422	103	30	α	α	NOUN
ejpam-4422	103	31	-	-	PUNCT
ejpam-4422	103	32	monostore	monostore	ADJ
ejpam-4422	103	33	graph	graph	NOUN
ejpam-4422	103	34	d	d	NOUN
ejpam-4422	103	35	can	can	AUX
ejpam-4422	103	36	be	be	AUX
ejpam-4422	103	37	used	use	VERB
ejpam-4422	103	38	to	to	PART
ejpam-4422	103	39	construct	construct	VERB
ejpam-4422	103	40	∆α	∆α	PROPN
ejpam-4422	103	41	.	.	PUNCT
ejpam-4422	104	1	also	also	ADV
ejpam-4422	104	2	,	,	PUNCT
ejpam-4422	104	3	theorem	theorem	ADJ
ejpam-4422	104	4	2	2	NUM
ejpam-4422	104	5	indicates	indicate	VERB
ejpam-4422	104	6	that	that	SCONJ
ejpam-4422	104	7	if	if	SCONJ
ejpam-4422	104	8	d	d	NOUN
ejpam-4422	104	9	is	be	AUX
ejpam-4422	104	10	an	an	DET
ejpam-4422	104	11	αmonostore	αmonostore	ADV
ejpam-4422	104	12	mixed	mixed	ADJ
ejpam-4422	104	13	graph	graph	NOUN
ejpam-4422	104	14	,	,	PUNCT
ejpam-4422	104	15	then	then	ADV
ejpam-4422	104	16	the	the	DET
ejpam-4422	104	17	orientation	orientation	NOUN
ejpam-4422	104	18	of	of	ADP
ejpam-4422	104	19	d	d	NOUN
ejpam-4422	104	20	can	can	AUX
ejpam-4422	104	21	be	be	AUX
ejpam-4422	104	22	stored	store	VERB
ejpam-4422	104	23	in	in	ADP
ejpam-4422	104	24	a	a	DET
ejpam-4422	104	25	diagonal	diagonal	ADJ
ejpam-4422	104	26	matrix	matrix	NOUN
ejpam-4422	104	27	∆α	∆α	PROPN
ejpam-4422	104	28	.	.	PUNCT
ejpam-4422	105	1	definition	definition	NOUN
ejpam-4422	105	2	2	2	NUM
ejpam-4422	105	3	.	.	PUNCT
ejpam-4422	106	1	if	if	SCONJ
ejpam-4422	106	2	d	d	PROPN
ejpam-4422	106	3	is	be	AUX
ejpam-4422	106	4	an	an	DET
ejpam-4422	106	5	α	α	NOUN
ejpam-4422	106	6	-	-	PUNCT
ejpam-4422	106	7	monostore	monostore	ADJ
ejpam-4422	106	8	graph	graph	NOUN
ejpam-4422	106	9	,	,	PUNCT
ejpam-4422	106	10	then	then	ADV
ejpam-4422	106	11	a	a	DET
ejpam-4422	106	12	diagonal	diagonal	ADJ
ejpam-4422	106	13	matrix	matrix	NOUN
ejpam-4422	106	14	∆α	∆α	PROPN
ejpam-4422	106	15	that	that	PRON
ejpam-4422	106	16	satisfies	satisfy	VERB
ejpam-4422	106	17	∆αhα∆	∆αhα∆	PROPN
ejpam-4422	106	18	∗	∗	VERB
ejpam-4422	106	19	α	α	NOUN
ejpam-4422	106	20	=	=	SYM
ejpam-4422	106	21	a(γ(d	a(γ(d	PROPN
ejpam-4422	106	22	)	)	PUNCT
ejpam-4422	106	23	)	)	PUNCT
ejpam-4422	106	24	is	be	AUX
ejpam-4422	106	25	called	call	VERB
ejpam-4422	106	26	an	an	DET
ejpam-4422	106	27	orienting	orient	VERB
ejpam-4422	106	28	matrix	matrix	NOUN
ejpam-4422	106	29	of	of	ADP
ejpam-4422	106	30	d.	d.	PROPN
ejpam-4422	106	31	corollary	corollary	PROPN
ejpam-4422	106	32	1	1	NUM
ejpam-4422	106	33	.	.	PUNCT
ejpam-4422	107	1	if	if	SCONJ
ejpam-4422	107	2	d	d	PROPN
ejpam-4422	107	3	is	be	AUX
ejpam-4422	107	4	an	an	DET
ejpam-4422	107	5	α	α	NOUN
ejpam-4422	107	6	-	-	ADJ
ejpam-4422	107	7	monostore	monostore	ADJ
ejpam-4422	107	8	mixed	mixed	ADJ
ejpam-4422	107	9	graph	graph	NOUN
ejpam-4422	107	10	then	then	ADV
ejpam-4422	107	11	d	d	NOUN
ejpam-4422	107	12	is	be	AUX
ejpam-4422	107	13	cospectral	cospectral	ADJ
ejpam-4422	107	14	with	with	ADP
ejpam-4422	107	15	its	its	PRON
ejpam-4422	107	16	underlying	underlie	VERB
ejpam-4422	107	17	graph	graph	NOUN
ejpam-4422	107	18	.	.	PUNCT
ejpam-4422	108	1	corollary	corollary	ADJ
ejpam-4422	108	2	2	2	NUM
ejpam-4422	108	3	.	.	PUNCT
ejpam-4422	109	1	if	if	SCONJ
ejpam-4422	109	2	d	d	PROPN
ejpam-4422	109	3	is	be	AUX
ejpam-4422	109	4	a	a	DET
ejpam-4422	109	5	tree	tree	NOUN
ejpam-4422	109	6	mixed	mixed	ADJ
ejpam-4422	109	7	graph	graph	NOUN
ejpam-4422	109	8	then	then	ADV
ejpam-4422	109	9	the	the	DET
ejpam-4422	109	10	spectrum	spectrum	NOUN
ejpam-4422	109	11	of	of	ADP
ejpam-4422	109	12	d	d	PROPN
ejpam-4422	109	13	is	be	AUX
ejpam-4422	109	14	completely	completely	ADV
ejpam-4422	109	15	determined	determine	VERB
ejpam-4422	109	16	by	by	ADP
ejpam-4422	109	17	its	its	PRON
ejpam-4422	109	18	underlying	underlie	VERB
ejpam-4422	109	19	graph	graph	NOUN
ejpam-4422	109	20	γ(d	γ(d	NOUN
ejpam-4422	109	21	)	)	PUNCT
ejpam-4422	109	22	.	.	PUNCT
ejpam-4422	110	1	o.	o.	PROPN
ejpam-4422	110	2	alomari	alomari	PROPN
ejpam-4422	110	3	,	,	PUNCT
ejpam-4422	110	4	m.	m.	NOUN
ejpam-4422	110	5	abudayah	abudayah	PROPN
ejpam-4422	110	6	,	,	PUNCT
ejpam-4422	110	7	m.	m.	NOUN
ejpam-4422	110	8	ghanem	ghanem	PROPN
ejpam-4422	110	9	/	/	SYM
ejpam-4422	110	10	eur	eur	PROPN
ejpam-4422	110	11	.	.	PUNCT
ejpam-4422	111	1	j.	j.	PROPN
ejpam-4422	111	2	pure	pure	PROPN
ejpam-4422	111	3	appl	appl	PROPN
ejpam-4422	111	4	.	.	PROPN
ejpam-4422	111	5	math	math	PROPN
ejpam-4422	111	6	,	,	PUNCT
ejpam-4422	111	7	15	15	NUM
ejpam-4422	111	8	(	(	PUNCT
ejpam-4422	111	9	3	3	NUM
ejpam-4422	111	10	)	)	PUNCT
ejpam-4422	111	11	(	(	PUNCT
ejpam-4422	111	12	2022	2022	NUM
ejpam-4422	111	13	)	)	PUNCT
ejpam-4422	111	14	,	,	PUNCT
ejpam-4422	111	15	1090	1090	NUM
ejpam-4422	111	16	-	-	SYM
ejpam-4422	111	17	1097	1097	NUM
ejpam-4422	111	18	1095	1095	NUM
ejpam-4422	111	19	lemma	lemma	PROPN
ejpam-4422	111	20	1	1	NUM
ejpam-4422	111	21	.	.	PUNCT
ejpam-4422	112	1	let	let	VERB
ejpam-4422	112	2	hα	hα	PART
ejpam-4422	112	3	be	be	AUX
ejpam-4422	112	4	the	the	DET
ejpam-4422	112	5	α	α	NOUN
ejpam-4422	112	6	-	-	ADJ
ejpam-4422	112	7	hermitian	hermitian	ADJ
ejpam-4422	112	8	adjacency	adjacency	NOUN
ejpam-4422	112	9	matrix	matrix	NOUN
ejpam-4422	112	10	of	of	ADP
ejpam-4422	112	11	a	a	DET
ejpam-4422	112	12	mixed	mixed	ADJ
ejpam-4422	112	13	graph	graph	NOUN
ejpam-4422	112	14	d	d	NOUN
ejpam-4422	112	15	,	,	PUNCT
ejpam-4422	112	16	∆	∆	X
ejpam-4422	113	1	=	=	PUNCT
ejpam-4422	113	2	diag(du	diag(du	NOUN
ejpam-4422	113	3	:	:	PUNCT
ejpam-4422	113	4	du	du	PROPN
ejpam-4422	113	5	∈	∈	PROPN
ejpam-4422	113	6	c	c	AUX
ejpam-4422	113	7	,	,	PUNCT
ejpam-4422	113	8	u	u	PROPN
ejpam-4422	113	9	∈	∈	PROPN
ejpam-4422	113	10	v	v	NOUN
ejpam-4422	113	11	(	(	PUNCT
ejpam-4422	113	12	d	d	NOUN
ejpam-4422	113	13	)	)	PUNCT
ejpam-4422	113	14	and	and	CCONJ
ejpam-4422	113	15	|du|	|du|	NOUN
ejpam-4422	113	16	=	=	SYM
ejpam-4422	113	17	1	1	NUM
ejpam-4422	113	18	)	)	PUNCT
ejpam-4422	113	19	and	and	CCONJ
ejpam-4422	113	20	k	k	NOUN
ejpam-4422	113	21	=	=	PUNCT
ejpam-4422	114	1	[	[	X
ejpam-4422	114	2	kuv	kuv	X
ejpam-4422	114	3	]	]	X
ejpam-4422	114	4	=	=	PUNCT
ejpam-4422	114	5	∆hα∆	∆hα∆	PROPN
ejpam-4422	114	6	∗.	∗.	PUNCT
ejpam-4422	114	7	then	then	ADV
ejpam-4422	114	8	,	,	PUNCT
ejpam-4422	114	9	for	for	ADP
ejpam-4422	114	10	every	every	DET
ejpam-4422	114	11	cycle	cycle	NOUN
ejpam-4422	114	12	c	c	NOUN
ejpam-4422	114	13	in	in	ADP
ejpam-4422	114	14	d	d	PROPN
ejpam-4422	114	15	the	the	DET
ejpam-4422	114	16	weight	weight	NOUN
ejpam-4422	114	17	of	of	ADP
ejpam-4422	114	18	the	the	DET
ejpam-4422	114	19	cycle	cycle	NOUN
ejpam-4422	114	20	c	c	NOUN
ejpam-4422	114	21	in	in	ADP
ejpam-4422	114	22	hα	hα	ADP
ejpam-4422	114	23	and	and	CCONJ
ejpam-4422	114	24	in	in	ADP
ejpam-4422	114	25	k	k	PROPN
ejpam-4422	114	26	are	be	AUX
ejpam-4422	114	27	equal	equal	ADJ
ejpam-4422	114	28	.	.	PUNCT
ejpam-4422	115	1	proof	proof	NOUN
ejpam-4422	115	2	.	.	PUNCT
ejpam-4422	116	1	suppose	suppose	VERB
ejpam-4422	116	2	that	that	SCONJ
ejpam-4422	116	3	c	c	PROPN
ejpam-4422	116	4	=	=	X
ejpam-4422	116	5	u1u2	u1u2	PROPN
ejpam-4422	116	6	.	.	PUNCT
ejpam-4422	116	7	.	.	PUNCT
ejpam-4422	116	8	.	.	PUNCT
ejpam-4422	117	1	unu1	unu1	PROPN
ejpam-4422	117	2	is	be	AUX
ejpam-4422	117	3	a	a	DET
ejpam-4422	117	4	cycle	cycle	NOUN
ejpam-4422	117	5	ind	ind	NOUN
ejpam-4422	117	6	.	.	PUNCT
ejpam-4422	118	1	then	then	ADV
ejpam-4422	118	2	,	,	PUNCT
ejpam-4422	118	3	observing	observe	VERB
ejpam-4422	118	4	that	that	SCONJ
ejpam-4422	118	5	(	(	PUNCT
ejpam-4422	118	6	∆hα∆	∆hα∆	PROPN
ejpam-4422	118	7	∗)uv	∗)uv	PROPN
ejpam-4422	118	8	=	=	PUNCT
ejpam-4422	118	9	duhuvdv	duhuvdv	NOUN
ejpam-4422	118	10	,	,	PUNCT
ejpam-4422	118	11	we	we	PRON
ejpam-4422	118	12	have	have	VERB
ejpam-4422	118	13	hα(c	hα(c	NOUN
ejpam-4422	118	14	)	)	PUNCT
ejpam-4422	118	15	=	=	SYM
ejpam-4422	118	16	hα(u1u2)hα(u2u3	hα(u1u2)hα(u2u3	X
ejpam-4422	118	17	)	)	PUNCT
ejpam-4422	118	18	.	.	PUNCT
ejpam-4422	118	19	.	.	PUNCT
ejpam-4422	118	20	.	.	PUNCT
ejpam-4422	119	1	hα(unu1	hα(unu1	NOUN
ejpam-4422	119	2	)	)	PUNCT
ejpam-4422	119	3	(	(	PUNCT
ejpam-4422	119	4	8)	8)	NUM
ejpam-4422	119	5	=	=	PUNCT
ejpam-4422	119	6	du1hα(u1u2)du2du2hα(u2u3)du3	du1hα(u1u2)du2du2hα(u2u3)du3	PROPN
ejpam-4422	119	7	.	.	PUNCT
ejpam-4422	119	8	.	.	PUNCT
ejpam-4422	119	9	.	.	PUNCT
ejpam-4422	120	1	dunhα(unu1)du1	dunhα(unu1)du1	INTJ
ejpam-4422	120	2	(	(	PUNCT
ejpam-4422	120	3	9	9	NUM
ejpam-4422	120	4	)	)	PUNCT
ejpam-4422	120	5	=	=	SYM
ejpam-4422	121	1	k(c	k(c	PROPN
ejpam-4422	121	2	)	)	PUNCT
ejpam-4422	121	3	.	.	PUNCT
ejpam-4422	122	1	(	(	PUNCT
ejpam-4422	122	2	10	10	NUM
ejpam-4422	122	3	)	)	PUNCT
ejpam-4422	122	4	example	example	NOUN
ejpam-4422	123	1	1	1	NUM
ejpam-4422	123	2	.	.	PUNCT
ejpam-4422	124	1	let	let	VERB
ejpam-4422	124	2	d	d	PRON
ejpam-4422	124	3	be	be	AUX
ejpam-4422	124	4	the	the	DET
ejpam-4422	124	5	mixed	mixed	ADJ
ejpam-4422	124	6	graph	graph	NOUN
ejpam-4422	124	7	shown	show	VERB
ejpam-4422	124	8	in	in	ADP
ejpam-4422	124	9	figure	figure	NOUN
ejpam-4422	124	10	2a	2a	NUM
ejpam-4422	124	11	,	,	PUNCT
ejpam-4422	124	12	α	α	PROPN
ejpam-4422	124	13	is	be	AUX
ejpam-4422	124	14	the	the	DET
ejpam-4422	124	15	primitive	primitive	ADJ
ejpam-4422	124	16	third	third	ADJ
ejpam-4422	124	17	root	root	NOUN
ejpam-4422	124	18	of	of	ADP
ejpam-4422	124	19	unity	unity	NOUN
ejpam-4422	124	20	e	e	NOUN
ejpam-4422	124	21	2π	2π	NOUN
ejpam-4422	124	22	3	3	NUM
ejpam-4422	124	23	i	i	NOUN
ejpam-4422	124	24	and	and	CCONJ
ejpam-4422	124	25	hα	hα	ADP
ejpam-4422	124	26	its	its	PRON
ejpam-4422	124	27	α	α	NOUN
ejpam-4422	124	28	-	-	ADJ
ejpam-4422	124	29	hermitian	hermitian	ADJ
ejpam-4422	124	30	adjacency	adjacency	NOUN
ejpam-4422	124	31	matrix	matrix	NOUN
ejpam-4422	124	32	.	.	PUNCT
ejpam-4422	125	1	obviously	obviously	ADV
ejpam-4422	125	2	,	,	PUNCT
ejpam-4422	125	3	the	the	DET
ejpam-4422	125	4	tree	tree	NOUN
ejpam-4422	125	5	mixed	mix	VERB
ejpam-4422	125	6	subgraph	subgraph	NOUN
ejpam-4422	125	7	t	t	PROPN
ejpam-4422	125	8	illustrated	illustrate	VERB
ejpam-4422	125	9	in	in	ADP
ejpam-4422	125	10	the	the	DET
ejpam-4422	125	11	solid	solid	ADJ
ejpam-4422	125	12	lines	line	NOUN
ejpam-4422	125	13	is	be	AUX
ejpam-4422	125	14	α	α	NOUN
ejpam-4422	125	15	-	-	NOUN
ejpam-4422	125	16	monograph	monograph	NOUN
ejpam-4422	125	17	with	with	ADP
ejpam-4422	125	18	the	the	DET
ejpam-4422	125	19	orienting	orient	VERB
ejpam-4422	125	20	matrix	matrix	NOUN
ejpam-4422	125	21	∆α	∆α	NOUN
ejpam-4422	125	22	=	=	SYM
ejpam-4422	126	1	diag(tv	diag(tv	NOUN
ejpam-4422	126	2	:	:	PUNCT
ejpam-4422	126	3	tv	tv	PROPN
ejpam-4422	126	4	∈	∈	PROPN
ejpam-4422	126	5	t	t	PROPN
ejpam-4422	126	6	and	and	CCONJ
ejpam-4422	126	7	v	v	ADP
ejpam-4422	126	8	∈	∈	PROPN
ejpam-4422	126	9	v	v	NOUN
ejpam-4422	126	10	(	(	PUNCT
ejpam-4422	126	11	d	d	NOUN
ejpam-4422	126	12	)	)	PUNCT
ejpam-4422	126	13	)	)	PUNCT
ejpam-4422	126	14	.	.	PUNCT
ejpam-4422	127	1	then	then	ADV
ejpam-4422	127	2	,	,	PUNCT
ejpam-4422	127	3	the	the	DET
ejpam-4422	127	4	matrix	matrix	NOUN
ejpam-4422	127	5	k	k	NOUN
ejpam-4422	127	6	=	=	PUNCT
ejpam-4422	127	7	∆αhα∆	∆αhα∆	PROPN
ejpam-4422	127	8	∗	∗	VERB
ejpam-4422	127	9	α	α	PRON
ejpam-4422	127	10	can	can	AUX
ejpam-4422	127	11	be	be	AUX
ejpam-4422	127	12	considered	consider	VERB
ejpam-4422	127	13	as	as	SCONJ
ejpam-4422	127	14	the	the	DET
ejpam-4422	127	15	adjacency	adjacency	NOUN
ejpam-4422	127	16	matrix	matrix	NOUN
ejpam-4422	127	17	of	of	ADP
ejpam-4422	127	18	the	the	DET
ejpam-4422	127	19	complex	complex	ADJ
ejpam-4422	127	20	weighted	weight	VERB
ejpam-4422	127	21	graph	graph	NOUN
ejpam-4422	127	22	dα	dα	X
ejpam-4422	127	23	(	(	PUNCT
ejpam-4422	127	24	or	or	CCONJ
ejpam-4422	127	25	the	the	DET
ejpam-4422	127	26	unit	unit	NOUN
ejpam-4422	127	27	gain	gain	NOUN
ejpam-4422	127	28	graph	graph	NOUN
ejpam-4422	127	29	dα	dα	NOUN
ejpam-4422	127	30	,	,	PUNCT
ejpam-4422	127	31	see[4	see[4	NOUN
ejpam-4422	127	32	]	]	PUNCT
ejpam-4422	127	33	)	)	PUNCT
ejpam-4422	127	34	shown	show	VERB
ejpam-4422	127	35	in	in	ADP
ejpam-4422	127	36	figure	figure	NOUN
ejpam-4422	127	37	2b	2b	NOUN
ejpam-4422	127	38	with	with	ADP
ejpam-4422	127	39	weight	weight	NOUN
ejpam-4422	127	40	1	1	NUM
ejpam-4422	127	41	for	for	ADP
ejpam-4422	127	42	each	each	DET
ejpam-4422	127	43	edge	edge	NOUN
ejpam-4422	127	44	of	of	ADP
ejpam-4422	127	45	the	the	DET
ejpam-4422	127	46	tree	tree	NOUN
ejpam-4422	127	47	γ(t	γ(t	PUNCT
ejpam-4422	127	48	)	)	PUNCT
ejpam-4422	127	49	.	.	PUNCT
ejpam-4422	128	1	furthermore	furthermore	ADV
ejpam-4422	128	2	according	accord	VERB
ejpam-4422	128	3	to	to	ADP
ejpam-4422	128	4	lemma	lemma	PROPN
ejpam-4422	128	5	1	1	NUM
ejpam-4422	128	6	,	,	PUNCT
ejpam-4422	128	7	the	the	DET
ejpam-4422	128	8	weight	weight	NOUN
ejpam-4422	128	9	of	of	ADP
ejpam-4422	128	10	the	the	DET
ejpam-4422	128	11	edge	edge	NOUN
ejpam-4422	128	12	53	53	NUM
ejpam-4422	128	13	in	in	ADP
ejpam-4422	128	14	dα	dα	NOUN
ejpam-4422	128	15	,	,	PUNCT
ejpam-4422	128	16	say	say	VERB
ejpam-4422	128	17	k(53	k(53	NOUN
ejpam-4422	128	18	)	)	PUNCT
ejpam-4422	128	19	,	,	PUNCT
ejpam-4422	128	20	equals	equal	VERB
ejpam-4422	128	21	to	to	ADP
ejpam-4422	128	22	the	the	DET
ejpam-4422	128	23	weight	weight	NOUN
ejpam-4422	128	24	of	of	ADP
ejpam-4422	128	25	the	the	DET
ejpam-4422	128	26	fundamental	fundamental	ADJ
ejpam-4422	128	27	cycle	cycle	NOUN
ejpam-4422	128	28	c53	c53	NOUN
ejpam-4422	128	29	=	=	SYM
ejpam-4422	128	30	32453	32453	NUM
ejpam-4422	128	31	in	in	ADP
ejpam-4422	128	32	hα	hα	NOUN
ejpam-4422	128	33	.	.	PROPN
ejpam-4422	128	34	to	to	PART
ejpam-4422	128	35	be	be	AUX
ejpam-4422	128	36	more	more	ADV
ejpam-4422	128	37	formal	formal	ADJ
ejpam-4422	128	38	,	,	PUNCT
ejpam-4422	128	39	k(53	k(53	NOUN
ejpam-4422	128	40	)	)	PUNCT
ejpam-4422	128	41	=	=	SYM
ejpam-4422	128	42	t5h53t3	t5h53t3	NOUN
ejpam-4422	128	43	.	.	PUNCT
ejpam-4422	129	1	but	but	CCONJ
ejpam-4422	129	2	,	,	PUNCT
ejpam-4422	129	3	t5	t5	PROPN
ejpam-4422	129	4	=	=	SYM
ejpam-4422	129	5	t3h32h24h45	t3h32h24h45	PROPN
ejpam-4422	129	6	therefore	therefore	ADV
ejpam-4422	129	7	,	,	PUNCT
ejpam-4422	129	8	k(53	k(53	NOUN
ejpam-4422	129	9	)	)	PUNCT
ejpam-4422	130	1	=	=	SYM
ejpam-4422	130	2	α2	α2	ADJ
ejpam-4422	130	3	=	=	SYM
ejpam-4422	130	4	k(35	k(35	PROPN
ejpam-4422	130	5	)	)	PUNCT
ejpam-4422	130	6	similar	similar	ADJ
ejpam-4422	130	7	calculations	calculation	NOUN
ejpam-4422	130	8	can	can	AUX
ejpam-4422	130	9	be	be	AUX
ejpam-4422	130	10	done	do	VERB
ejpam-4422	130	11	to	to	PART
ejpam-4422	130	12	get	get	VERB
ejpam-4422	130	13	,	,	PUNCT
ejpam-4422	130	14	k(89	k(89	PROPN
ejpam-4422	130	15	)	)	PUNCT
ejpam-4422	130	16	=	=	SYM
ejpam-4422	130	17	α2	α2	ADJ
ejpam-4422	130	18	.	.	PUNCT
ejpam-4422	131	1	therefore	therefore	ADV
ejpam-4422	131	2	,	,	PUNCT
ejpam-4422	131	3	the	the	DET
ejpam-4422	131	4	matrix	matrix	NOUN
ejpam-4422	131	5	k	k	NOUN
ejpam-4422	131	6	=	=	SYM
ejpam-4422	131	7	∆αhα∆	∆αhα∆	PROPN
ejpam-4422	131	8	∗	∗	VERB
ejpam-4422	131	9	α	α	PROPN
ejpam-4422	131	10	is	be	AUX
ejpam-4422	131	11	the	the	DET
ejpam-4422	131	12	adjacency	adjacency	NOUN
ejpam-4422	131	13	matrix	matrix	NOUN
ejpam-4422	131	14	of	of	ADP
ejpam-4422	131	15	the	the	DET
ejpam-4422	131	16	complex	complex	ADJ
ejpam-4422	131	17	weighted	weight	VERB
ejpam-4422	131	18	graph	graph	NOUN
ejpam-4422	131	19	dα	dα	NOUN
ejpam-4422	131	20	.	.	PUNCT
ejpam-4422	132	1	the	the	DET
ejpam-4422	132	2	above	above	ADJ
ejpam-4422	132	3	example	example	NOUN
ejpam-4422	132	4	illustrates	illustrate	VERB
ejpam-4422	132	5	that	that	SCONJ
ejpam-4422	132	6	,	,	PUNCT
ejpam-4422	132	7	for	for	ADP
ejpam-4422	132	8	every	every	DET
ejpam-4422	132	9	mixed	mixed	ADJ
ejpam-4422	132	10	graphd	graphd	NOUN
ejpam-4422	132	11	and	and	CCONJ
ejpam-4422	132	12	a	a	DET
ejpam-4422	132	13	spanning	span	VERB
ejpam-4422	132	14	mixed	mixed	ADJ
ejpam-4422	132	15	tree	tree	NOUN
ejpam-4422	132	16	t	t	PROPN
ejpam-4422	132	17	of	of	ADP
ejpam-4422	132	18	d	d	PROPN
ejpam-4422	132	19	,	,	PUNCT
ejpam-4422	132	20	there	there	PRON
ejpam-4422	132	21	is	be	VERB
ejpam-4422	132	22	a	a	DET
ejpam-4422	132	23	complex	complex	ADJ
ejpam-4422	132	24	weighted	weight	VERB
ejpam-4422	132	25	mixed	mixed	ADJ
ejpam-4422	132	26	graph	graph	NOUN
ejpam-4422	132	27	d	d	NOUN
ejpam-4422	132	28	that	that	PRON
ejpam-4422	132	29	is	be	AUX
ejpam-4422	132	30	cospectral	cospectral	ADJ
ejpam-4422	132	31	with	with	ADP
ejpam-4422	132	32	the	the	DET
ejpam-4422	132	33	α	α	NOUN
ejpam-4422	132	34	-	-	ADJ
ejpam-4422	132	35	hermitian	hermitian	ADJ
ejpam-4422	132	36	adjacency	adjacency	NOUN
ejpam-4422	132	37	matrix	matrix	NOUN
ejpam-4422	132	38	of	of	ADP
ejpam-4422	132	39	d.	d.	PROPN
ejpam-4422	132	40	this	this	DET
ejpam-4422	132	41	idea	idea	NOUN
ejpam-4422	132	42	will	will	AUX
ejpam-4422	132	43	be	be	AUX
ejpam-4422	132	44	used	use	VERB
ejpam-4422	132	45	to	to	PART
ejpam-4422	132	46	prove	prove	VERB
ejpam-4422	132	47	some	some	DET
ejpam-4422	132	48	further	further	ADJ
ejpam-4422	132	49	results	result	NOUN
ejpam-4422	132	50	.	.	PUNCT
ejpam-4422	133	1	definition	definition	NOUN
ejpam-4422	133	2	3	3	X
ejpam-4422	133	3	.	.	PUNCT
ejpam-4422	134	1	let	let	VERB
ejpam-4422	134	2	d	d	PRON
ejpam-4422	134	3	be	be	AUX
ejpam-4422	134	4	a	a	DET
ejpam-4422	134	5	graph	graph	NOUN
ejpam-4422	134	6	and	and	CCONJ
ejpam-4422	134	7	α	α	NOUN
ejpam-4422	134	8	,	,	PUNCT
ejpam-4422	134	9	γ	γ	NOUN
ejpam-4422	134	10	are	be	AUX
ejpam-4422	134	11	two	two	NUM
ejpam-4422	134	12	unit	unit	NOUN
ejpam-4422	134	13	complex	complex	ADJ
ejpam-4422	134	14	numbers	number	NOUN
ejpam-4422	134	15	.	.	PUNCT
ejpam-4422	135	1	if	if	SCONJ
ejpam-4422	135	2	the	the	DET
ejpam-4422	135	3	αhermitian	αhermitian	ADJ
ejpam-4422	135	4	adjacency	adjacency	NOUN
ejpam-4422	135	5	matrix	matrix	NOUN
ejpam-4422	135	6	and	and	CCONJ
ejpam-4422	135	7	the	the	DET
ejpam-4422	135	8	γ	γ	PROPN
ejpam-4422	135	9	-	-	ADJ
ejpam-4422	135	10	hermitian	hermitian	ADJ
ejpam-4422	135	11	adjacency	adjacency	NOUN
ejpam-4422	135	12	matrix	matrix	NOUN
ejpam-4422	135	13	of	of	ADP
ejpam-4422	135	14	d	d	PROPN
ejpam-4422	135	15	are	be	AUX
ejpam-4422	135	16	cospectral	cospectral	ADJ
ejpam-4422	135	17	,	,	PUNCT
ejpam-4422	135	18	then	then	ADV
ejpam-4422	135	19	d	d	PROPN
ejpam-4422	135	20	is	be	AUX
ejpam-4422	135	21	called	call	VERB
ejpam-4422	135	22	α−	α−	ADP
ejpam-4422	135	23	γ	γ	PROPN
ejpam-4422	135	24	cospectral	cospectral	PROPN
ejpam-4422	135	25	.	.	PUNCT
ejpam-4422	136	1	theorem	theorem	NOUN
ejpam-4422	136	2	3	3	X
ejpam-4422	136	3	.	.	PUNCT
ejpam-4422	137	1	let	let	VERB
ejpam-4422	137	2	d	d	PRON
ejpam-4422	137	3	be	be	AUX
ejpam-4422	137	4	a	a	DET
ejpam-4422	137	5	mixed	mixed	ADJ
ejpam-4422	137	6	graph	graph	NOUN
ejpam-4422	137	7	and	and	CCONJ
ejpam-4422	137	8	α	α	NOUN
ejpam-4422	137	9	,	,	PUNCT
ejpam-4422	137	10	γ	γ	X
ejpam-4422	137	11	be	be	VERB
ejpam-4422	137	12	two	two	NUM
ejpam-4422	137	13	unit	unit	NOUN
ejpam-4422	137	14	complex	complex	ADJ
ejpam-4422	137	15	numbers	number	NOUN
ejpam-4422	137	16	.	.	PUNCT
ejpam-4422	138	1	if	if	SCONJ
ejpam-4422	138	2	for	for	ADP
ejpam-4422	138	3	all	all	DET
ejpam-4422	138	4	cycles	cycle	NOUN
ejpam-4422	138	5	c	c	VERB
ejpam-4422	138	6	in	in	ADP
ejpam-4422	138	7	d	d	PROPN
ejpam-4422	138	8	one	one	NUM
ejpam-4422	138	9	of	of	ADP
ejpam-4422	138	10	hα(c	hα(c	NOUN
ejpam-4422	138	11	)	)	PUNCT
ejpam-4422	138	12	=	=	SYM
ejpam-4422	138	13	hγ(c	hγ(c	X
ejpam-4422	138	14	)	)	PUNCT
ejpam-4422	138	15	or	or	CCONJ
ejpam-4422	138	16	hα(c	hα(c	NOUN
ejpam-4422	138	17	)	)	PUNCT
ejpam-4422	138	18	=	=	SYM
ejpam-4422	138	19	hγ(c	hγ(c	X
ejpam-4422	138	20	)	)	PUNCT
ejpam-4422	138	21	is	be	AUX
ejpam-4422	138	22	hold	hold	VERB
ejpam-4422	138	23	then	then	ADV
ejpam-4422	138	24	d	d	PROPN
ejpam-4422	138	25	is	be	AUX
ejpam-4422	138	26	α−γ	α−γ	NOUN
ejpam-4422	138	27	cospectral	cospectral	ADJ
ejpam-4422	138	28	.	.	PUNCT
ejpam-4422	139	1	proof	proof	NOUN
ejpam-4422	139	2	.	.	PUNCT
ejpam-4422	140	1	suppose	suppose	VERB
ejpam-4422	140	2	that	that	SCONJ
ejpam-4422	140	3	t	t	PROPN
ejpam-4422	140	4	is	be	AUX
ejpam-4422	140	5	a	a	DET
ejpam-4422	140	6	spanning	span	VERB
ejpam-4422	140	7	tree	tree	NOUN
ejpam-4422	140	8	of	of	ADP
ejpam-4422	140	9	d	d	PROPN
ejpam-4422	140	10	,	,	PUNCT
ejpam-4422	140	11	u	u	NOUN
ejpam-4422	140	12	is	be	AUX
ejpam-4422	140	13	a	a	DET
ejpam-4422	140	14	vertex	vertex	NOUN
ejpam-4422	140	15	of	of	ADP
ejpam-4422	140	16	d	d	PROPN
ejpam-4422	140	17	and	and	CCONJ
ejpam-4422	140	18	∆α	∆α	PROPN
ejpam-4422	140	19	(	(	PUNCT
ejpam-4422	140	20	resp	resp	NOUN
ejpam-4422	140	21	.	.	PUNCT
ejpam-4422	141	1	∆γ	∆γ	NOUN
ejpam-4422	141	2	)	)	PUNCT
ejpam-4422	141	3	is	be	AUX
ejpam-4422	141	4	the	the	DET
ejpam-4422	141	5	α	α	NOUN
ejpam-4422	141	6	-	-	ADJ
ejpam-4422	141	7	orienting	orienting	ADJ
ejpam-4422	141	8	(	(	PUNCT
ejpam-4422	141	9	resp	resp	NOUN
ejpam-4422	141	10	.	.	PUNCT
ejpam-4422	142	1	the	the	DET
ejpam-4422	142	2	γ	γ	PROPN
ejpam-4422	142	3	-	-	ADJ
ejpam-4422	142	4	orienting	orienting	ADJ
ejpam-4422	142	5	)	)	PUNCT
ejpam-4422	142	6	matrix	matrix	NOUN
ejpam-4422	142	7	of	of	ADP
ejpam-4422	142	8	t	t	PROPN
ejpam-4422	142	9	.	.	PUNCT
ejpam-4422	143	1	then	then	ADV
ejpam-4422	143	2	,	,	PUNCT
ejpam-4422	143	3	∆αhα(t	∆αhα(t	ADJ
ejpam-4422	143	4	)	)	PUNCT
ejpam-4422	143	5	∆	∆	PROPN
ejpam-4422	143	6	∗	∗	NOUN
ejpam-4422	143	7	α	α	NOUN
ejpam-4422	143	8	=	=	X
ejpam-4422	143	9	∆γhγ(t	∆γhγ(t	NOUN
ejpam-4422	143	10	)	)	PUNCT
ejpam-4422	143	11	∆	∆	PROPN
ejpam-4422	143	12	∗	∗	NOUN
ejpam-4422	143	13	γ	γ	X
ejpam-4422	143	14	=	=	VERB
ejpam-4422	143	15	a(γ(t	a(γ(t	PROPN
ejpam-4422	143	16	)	)	PUNCT
ejpam-4422	143	17	)	)	PUNCT
ejpam-4422	143	18	references	reference	NOUN
ejpam-4422	143	19	1096	1096	NUM
ejpam-4422	143	20	(	(	PUNCT
ejpam-4422	143	21	a	a	X
ejpam-4422	143	22	)	)	PUNCT
ejpam-4422	143	23	the	the	DET
ejpam-4422	143	24	mixed	mixed	ADJ
ejpam-4422	143	25	graph	graph	NOUN
ejpam-4422	143	26	d	d	NOUN
ejpam-4422	143	27	with	with	ADP
ejpam-4422	143	28	the	the	DET
ejpam-4422	143	29	values	value	NOUN
ejpam-4422	143	30	of	of	ADP
ejpam-4422	143	31	tv	tv	NOUN
ejpam-4422	143	32	in	in	ADP
ejpam-4422	143	33	the	the	DET
ejpam-4422	143	34	spanning	span	VERB
ejpam-4422	143	35	tree	tree	NOUN
ejpam-4422	143	36	t.	t.	NOUN
ejpam-4422	143	37	(	(	PUNCT
ejpam-4422	143	38	b	b	X
ejpam-4422	143	39	)	)	PUNCT
ejpam-4422	143	40	the	the	DET
ejpam-4422	143	41	complex	complex	ADJ
ejpam-4422	143	42	weighted	weight	VERB
ejpam-4422	143	43	graph	graph	NOUN
ejpam-4422	143	44	dα	dα	NOUN
ejpam-4422	143	45	with	with	ADP
ejpam-4422	143	46	the	the	DET
ejpam-4422	143	47	weight	weight	NOUN
ejpam-4422	143	48	of	of	ADP
ejpam-4422	143	49	the	the	DET
ejpam-4422	143	50	edges	edge	NOUN
ejpam-4422	143	51	figure	figure	NOUN
ejpam-4422	143	52	2	2	NUM
ejpam-4422	143	53	which	which	PRON
ejpam-4422	143	54	means	mean	VERB
ejpam-4422	143	55	that	that	SCONJ
ejpam-4422	143	56	the	the	DET
ejpam-4422	143	57	matrices	matrix	NOUN
ejpam-4422	143	58	∆αhα(d)∆∗	∆αhα(d)∆∗	VERB
ejpam-4422	143	59	α	α	PROPN
ejpam-4422	143	60	(	(	PUNCT
ejpam-4422	143	61	resp	resp	NOUN
ejpam-4422	143	62	.	.	PUNCT
ejpam-4422	144	1	∆γhγ(d)∆∗	∆γhγ(d)∆∗	PROPN
ejpam-4422	144	2	γ	γ	PROPN
ejpam-4422	144	3	)	)	PUNCT
ejpam-4422	144	4	can	can	AUX
ejpam-4422	144	5	be	be	AUX
ejpam-4422	144	6	considered	consider	VERB
ejpam-4422	144	7	as	as	ADP
ejpam-4422	144	8	a	a	DET
ejpam-4422	144	9	hermitian	hermitian	ADJ
ejpam-4422	144	10	adjacency	adjacency	NOUN
ejpam-4422	144	11	matrices	matrix	NOUN
ejpam-4422	144	12	of	of	ADP
ejpam-4422	144	13	the	the	DET
ejpam-4422	144	14	weight	weight	NOUN
ejpam-4422	144	15	mixed	mix	VERB
ejpam-4422	144	16	graph	graph	NOUN
ejpam-4422	144	17	dα	dα	X
ejpam-4422	144	18	(	(	PUNCT
ejpam-4422	144	19	resp	resp	NOUN
ejpam-4422	144	20	.	.	PUNCT
ejpam-4422	145	1	dγ	dγ	PROPN
ejpam-4422	145	2	)	)	PUNCT
ejpam-4422	145	3	with	with	ADP
ejpam-4422	145	4	underlying	underlie	VERB
ejpam-4422	145	5	graph	graph	NOUN
ejpam-4422	145	6	γ(d	γ(d	NOUN
ejpam-4422	145	7	)	)	PUNCT
ejpam-4422	145	8	,	,	PUNCT
ejpam-4422	145	9	all	all	DET
ejpam-4422	145	10	edges	edge	NOUN
ejpam-4422	145	11	of	of	ADP
ejpam-4422	145	12	the	the	DET
ejpam-4422	145	13	tree	tree	NOUN
ejpam-4422	145	14	t	t	PROPN
ejpam-4422	145	15	have	have	VERB
ejpam-4422	145	16	weight	weight	NOUN
ejpam-4422	145	17	1	1	NUM
ejpam-4422	145	18	.	.	PUNCT
ejpam-4422	146	1	furthermore	furthermore	ADV
ejpam-4422	146	2	,	,	PUNCT
ejpam-4422	146	3	suppose	suppose	VERB
ejpam-4422	146	4	that	that	SCONJ
ejpam-4422	146	5	rs	rs	NOUN
ejpam-4422	146	6	is	be	AUX
ejpam-4422	146	7	an	an	DET
ejpam-4422	146	8	edge	edge	NOUN
ejpam-4422	146	9	in	in	ADP
ejpam-4422	146	10	d	d	PROPN
ejpam-4422	146	11	that	that	PRON
ejpam-4422	146	12	is	be	AUX
ejpam-4422	146	13	not	not	PART
ejpam-4422	146	14	in	in	ADP
ejpam-4422	146	15	t	t	NOUN
ejpam-4422	146	16	,	,	PUNCT
ejpam-4422	146	17	and	and	CCONJ
ejpam-4422	146	18	crs	crs	PROPN
ejpam-4422	146	19	be	be	AUX
ejpam-4422	146	20	the	the	DET
ejpam-4422	146	21	fundamental	fundamental	ADJ
ejpam-4422	146	22	cycle	cycle	NOUN
ejpam-4422	146	23	of	of	ADP
ejpam-4422	146	24	d	d	PROPN
ejpam-4422	146	25	corresponding	correspond	VERB
ejpam-4422	146	26	to	to	PART
ejpam-4422	146	27	rs	rs	VERB
ejpam-4422	146	28	.	.	PUNCT
ejpam-4422	147	1	then	then	ADV
ejpam-4422	147	2	,	,	PUNCT
ejpam-4422	147	3	using	use	VERB
ejpam-4422	147	4	lemma	lemma	PROPN
ejpam-4422	147	5	1	1	NUM
ejpam-4422	147	6	we	we	PRON
ejpam-4422	147	7	get	get	VERB
ejpam-4422	147	8	that	that	PRON
ejpam-4422	147	9	,	,	PUNCT
ejpam-4422	147	10	the	the	DET
ejpam-4422	147	11	weight	weight	NOUN
ejpam-4422	147	12	of	of	ADP
ejpam-4422	147	13	rs	r	NOUN
ejpam-4422	147	14	in	in	ADP
ejpam-4422	147	15	dα	dα	X
ejpam-4422	147	16	(	(	PUNCT
ejpam-4422	147	17	resp	resp	NOUN
ejpam-4422	147	18	.	.	PUNCT
ejpam-4422	148	1	dγ	dγ	PROPN
ejpam-4422	148	2	)	)	PUNCT
ejpam-4422	148	3	equals	equal	VERB
ejpam-4422	148	4	hα(crs	hα(crs	PROPN
ejpam-4422	148	5	)	)	PUNCT
ejpam-4422	148	6	(	(	PUNCT
ejpam-4422	148	7	resp	resp	NOUN
ejpam-4422	148	8	.	.	PUNCT
ejpam-4422	149	1	hγ(crs	hγ(cr	NOUN
ejpam-4422	149	2	)	)	PUNCT
ejpam-4422	149	3	)	)	PUNCT
ejpam-4422	149	4	.	.	PUNCT
ejpam-4422	150	1	therefore	therefore	ADV
ejpam-4422	150	2	,	,	PUNCT
ejpam-4422	150	3	either	either	CCONJ
ejpam-4422	150	4	∆αhα(d)∆∗	∆αhα(d)∆∗	PROPN
ejpam-4422	150	5	α	α	NOUN
ejpam-4422	150	6	=	=	PUNCT
ejpam-4422	150	7	∆γhγ(d)∆∗	∆γhγ(d)∆∗	VERB
ejpam-4422	150	8	γ	γ	NOUN
ejpam-4422	150	9	or	or	CCONJ
ejpam-4422	150	10	∆αhα(d)∆∗	∆αhα(d)∆∗	VERB
ejpam-4422	150	11	α	α	NOUN
ejpam-4422	150	12	=	=	PUNCT
ejpam-4422	150	13	∆γhγ(d)∆∗	∆γhγ(d)∆∗	PROPN
ejpam-4422	150	14	γ	γ	NOUN
ejpam-4422	150	15	,	,	PUNCT
ejpam-4422	150	16	which	which	PRON
ejpam-4422	150	17	means	mean	VERB
ejpam-4422	150	18	hα(d	hα(d	PRON
ejpam-4422	150	19	)	)	PUNCT
ejpam-4422	150	20	and	and	CCONJ
ejpam-4422	150	21	hγ(d	hγ(d	NOUN
ejpam-4422	150	22	)	)	PUNCT
ejpam-4422	150	23	are	be	AUX
ejpam-4422	150	24	cospectral	cospectral	ADJ
ejpam-4422	150	25	.	.	PUNCT
ejpam-4422	151	1	corollary	corollary	ADJ
ejpam-4422	151	2	3	3	X
ejpam-4422	151	3	.	.	PUNCT
ejpam-4422	152	1	let	let	VERB
ejpam-4422	152	2	d	d	PRON
ejpam-4422	152	3	be	be	AUX
ejpam-4422	152	4	a	a	DET
ejpam-4422	152	5	mixed	mixed	ADJ
ejpam-4422	152	6	graph	graph	NOUN
ejpam-4422	152	7	and	and	CCONJ
ejpam-4422	152	8	α	α	NOUN
ejpam-4422	152	9	,	,	PUNCT
ejpam-4422	152	10	γ	γ	PROPN
ejpam-4422	152	11	are	be	AUX
ejpam-4422	152	12	unit	unit	NOUN
ejpam-4422	152	13	complex	complex	ADJ
ejpam-4422	152	14	numbers	number	NOUN
ejpam-4422	152	15	.	.	PUNCT
ejpam-4422	153	1	if	if	SCONJ
ejpam-4422	153	2	d	d	NOUN
ejpam-4422	153	3	is	be	AUX
ejpam-4422	153	4	αmonostore	αmonostore	ADV
ejpam-4422	153	5	mixed	mixed	ADJ
ejpam-4422	153	6	graph	graph	NOUN
ejpam-4422	153	7	then	then	ADV
ejpam-4422	153	8	d	d	PROPN
ejpam-4422	153	9	is	be	AUX
ejpam-4422	153	10	γ	γ	X
ejpam-4422	153	11	−	−	PROPN
ejpam-4422	153	12	αγ	αγ	PROPN
ejpam-4422	153	13	cospectral	cospectral	NOUN
ejpam-4422	153	14	.	.	PUNCT
ejpam-4422	154	1	references	reference	NOUN
ejpam-4422	154	2	[	[	X
ejpam-4422	154	3	1	1	NUM
ejpam-4422	154	4	]	]	X
ejpam-4422	154	5	mohammad	mohammad	PROPN
ejpam-4422	154	6	abudayah	abudayah	PROPN
ejpam-4422	154	7	,	,	PUNCT
ejpam-4422	154	8	omar	omar	PROPN
ejpam-4422	154	9	alomari	alomari	PROPN
ejpam-4422	154	10	,	,	PUNCT
ejpam-4422	154	11	and	and	CCONJ
ejpam-4422	154	12	torsten	torsten	PROPN
ejpam-4422	154	13	sander	sander	PROPN
ejpam-4422	154	14	.	.	PUNCT
ejpam-4422	155	1	on	on	ADP
ejpam-4422	155	2	the	the	DET
ejpam-4422	155	3	n	n	NOUN
ejpam-4422	155	4	-	-	PUNCT
ejpam-4422	155	5	spectrum	spectrum	NOUN
ejpam-4422	155	6	of	of	ADP
ejpam-4422	155	7	oriented	orient	VERB
ejpam-4422	155	8	graphs	graph	NOUN
ejpam-4422	155	9	.	.	PUNCT
ejpam-4422	156	1	open	open	ADJ
ejpam-4422	156	2	mathematics	mathematic	NOUN
ejpam-4422	156	3	,	,	PUNCT
ejpam-4422	156	4	18(1):486–495	18(1):486–495	NUM
ejpam-4422	156	5	,	,	PUNCT
ejpam-4422	156	6	2020	2020	NUM
ejpam-4422	156	7	.	.	PUNCT
ejpam-4422	157	1	[	[	X
ejpam-4422	157	2	2	2	NUM
ejpam-4422	157	3	]	]	X
ejpam-4422	157	4	omar	omar	PROPN
ejpam-4422	157	5	alomari	alomari	PROPN
ejpam-4422	157	6	,	,	PUNCT
ejpam-4422	157	7	mohammad	mohammad	PROPN
ejpam-4422	157	8	abudayah	abudayah	PROPN
ejpam-4422	157	9	,	,	PUNCT
ejpam-4422	157	10	and	and	CCONJ
ejpam-4422	157	11	torsten	torsten	PROPN
ejpam-4422	157	12	sander	sander	PROPN
ejpam-4422	157	13	.	.	PUNCT
ejpam-4422	158	1	the	the	DET
ejpam-4422	158	2	non	non	ADJ
ejpam-4422	158	3	-	-	ADJ
ejpam-4422	158	4	negative	negative	ADJ
ejpam-4422	158	5	spectrum	spectrum	NOUN
ejpam-4422	158	6	of	of	ADP
ejpam-4422	158	7	a	a	DET
ejpam-4422	158	8	digraph	digraph	NOUN
ejpam-4422	158	9	.	.	PUNCT
ejpam-4422	159	1	open	open	ADJ
ejpam-4422	159	2	mathematics	mathematic	NOUN
ejpam-4422	159	3	,	,	PUNCT
ejpam-4422	159	4	18(1):22–35	18(1):22–35	NUM
ejpam-4422	159	5	,	,	PUNCT
ejpam-4422	159	6	2020	2020	NUM
ejpam-4422	159	7	.	.	PUNCT
ejpam-4422	160	1	[	[	X
ejpam-4422	160	2	3	3	X
ejpam-4422	160	3	]	]	X
ejpam-4422	160	4	krystal	krystal	ADJ
ejpam-4422	160	5	guo	guo	PROPN
ejpam-4422	160	6	and	and	CCONJ
ejpam-4422	160	7	bojan	bojan	PROPN
ejpam-4422	160	8	mohar	mohar	PROPN
ejpam-4422	160	9	.	.	PUNCT
ejpam-4422	161	1	hermitian	hermitian	ADJ
ejpam-4422	161	2	adjacency	adjacency	PROPN
ejpam-4422	161	3	matrix	matrix	NOUN
ejpam-4422	161	4	of	of	ADP
ejpam-4422	161	5	digraphs	digraph	NOUN
ejpam-4422	161	6	and	and	CCONJ
ejpam-4422	161	7	mixed	mixed	ADJ
ejpam-4422	161	8	graphs	graph	NOUN
ejpam-4422	161	9	.	.	PUNCT
ejpam-4422	162	1	journal	journal	NOUN
ejpam-4422	162	2	of	of	ADP
ejpam-4422	162	3	graph	graph	NOUN
ejpam-4422	162	4	theory	theory	NOUN
ejpam-4422	162	5	,	,	PUNCT
ejpam-4422	162	6	85(1):217–248	85(1):217–248	PROPN
ejpam-4422	162	7	,	,	PUNCT
ejpam-4422	162	8	2017	2017	NUM
ejpam-4422	162	9	.	.	PUNCT
ejpam-4422	163	1	references	reference	NOUN
ejpam-4422	163	2	1097	1097	NUM
ejpam-4422	163	3	[	[	X
ejpam-4422	163	4	4	4	NUM
ejpam-4422	163	5	]	]	PUNCT
ejpam-4422	163	6	ranjit	ranjit	NOUN
ejpam-4422	163	7	mehatari	mehatari	PROPN
ejpam-4422	163	8	,	,	PUNCT
ejpam-4422	163	9	m.	m.	PROPN
ejpam-4422	163	10	rajesh	rajesh	PROPN
ejpam-4422	163	11	kannan	kannan	PROPN
ejpam-4422	163	12	,	,	PUNCT
ejpam-4422	163	13	and	and	CCONJ
ejpam-4422	163	14	aniruddha	aniruddha	PROPN
ejpam-4422	163	15	samanta	samanta	PROPN
ejpam-4422	163	16	.	.	PUNCT
ejpam-4422	164	1	on	on	ADP
ejpam-4422	164	2	the	the	DET
ejpam-4422	164	3	adjacency	adjacency	NOUN
ejpam-4422	164	4	matrix	matrix	NOUN
ejpam-4422	164	5	of	of	ADP
ejpam-4422	164	6	a	a	DET
ejpam-4422	164	7	complex	complex	ADJ
ejpam-4422	164	8	unit	unit	NOUN
ejpam-4422	164	9	gain	gain	NOUN
ejpam-4422	164	10	graph	graph	NOUN
ejpam-4422	164	11	.	.	PUNCT
ejpam-4422	165	1	linear	linear	ADJ
ejpam-4422	165	2	and	and	CCONJ
ejpam-4422	165	3	multilinear	multilinear	PROPN
ejpam-4422	165	4	algebra	algebra	NOUN
ejpam-4422	165	5	,	,	PUNCT
ejpam-4422	165	6	0(0):1–16	0(0):1–16	NUM
ejpam-4422	165	7	,	,	PUNCT
ejpam-4422	165	8	2020	2020	NUM
ejpam-4422	165	9	.	.	PUNCT
ejpam-4422	166	1	[	[	X
ejpam-4422	166	2	5	5	X
ejpam-4422	166	3	]	]	PUNCT
ejpam-4422	166	4	b.	b.	PROPN
ejpam-4422	166	5	mohar	mohar	PROPN
ejpam-4422	166	6	.	.	PUNCT
ejpam-4422	167	1	a	a	DET
ejpam-4422	167	2	new	new	ADJ
ejpam-4422	167	3	kind	kind	NOUN
ejpam-4422	167	4	of	of	ADP
ejpam-4422	167	5	hermitian	hermitian	ADJ
ejpam-4422	167	6	matrices	matrix	NOUN
ejpam-4422	167	7	for	for	ADP
ejpam-4422	167	8	digraphs	digraph	NOUN
ejpam-4422	167	9	.	.	PUNCT
ejpam-4422	168	1	arxiv	arxiv	NOUN
ejpam-4422	168	2	:	:	PUNCT
ejpam-4422	168	3	combinatorics	combinatoric	NOUN
ejpam-4422	168	4	,	,	PUNCT
ejpam-4422	168	5	2019	2019	NUM
ejpam-4422	168	6	.	.	PUNCT