id	sid	tid	token	lemma	pos
ejpam-3884	1	1	european	european	PROPN
ejpam-3884	1	2	journal	journal	PROPN
ejpam-3884	1	3	of	of	ADP
ejpam-3884	1	4	pure	pure	ADJ
ejpam-3884	1	5	and	and	CCONJ
ejpam-3884	1	6	applied	apply	VERB
ejpam-3884	1	7	mathematics	mathematic	NOUN
ejpam-3884	1	8	vol	vol	NOUN
ejpam-3884	1	9	.	.	PUNCT
ejpam-3884	2	1	14	14	NUM
ejpam-3884	2	2	,	,	PUNCT
ejpam-3884	2	3	no	no	INTJ
ejpam-3884	2	4	.	.	NOUN
ejpam-3884	2	5	1	1	NUM
ejpam-3884	2	6	,	,	PUNCT
ejpam-3884	2	7	2021	2021	NUM
ejpam-3884	2	8	,	,	PUNCT
ejpam-3884	2	9	248	248	NUM
ejpam-3884	2	10	-	-	SYM
ejpam-3884	2	11	264	264	NUM
ejpam-3884	2	12	issn	issn	PROPN
ejpam-3884	2	13	1307	1307	NUM
ejpam-3884	2	14	-	-	SYM
ejpam-3884	2	15	5543	5543	NUM
ejpam-3884	2	16	–	–	PUNCT
ejpam-3884	3	1	ejpam.com	ejpam.com	X
ejpam-3884	3	2	published	publish	VERB
ejpam-3884	3	3	by	by	ADP
ejpam-3884	3	4	new	new	PROPN
ejpam-3884	3	5	york	york	PROPN
ejpam-3884	3	6	business	business	PROPN
ejpam-3884	3	7	global	global	PROPN
ejpam-3884	3	8	a	a	DET
ejpam-3884	3	9	breadth	breadth	NOUN
ejpam-3884	3	10	-	-	PUNCT
ejpam-3884	3	11	first	first	ADJ
ejpam-3884	3	12	search	search	NOUN
ejpam-3884	3	13	tree	tree	NOUN
ejpam-3884	3	14	construction	construction	NOUN
ejpam-3884	3	15	for	for	ADP
ejpam-3884	3	16	multiplicative	multiplicative	ADJ
ejpam-3884	3	17	circulant	circulant	NOUN
ejpam-3884	3	18	graphs	graph	NOUN
ejpam-3884	3	19	john	john	PROPN
ejpam-3884	3	20	rafael	rafael	PROPN
ejpam-3884	3	21	m.	m.	PROPN
ejpam-3884	3	22	antalan1,2,∗	antalan1,2,∗	PROPN
ejpam-3884	3	23	,	,	PUNCT
ejpam-3884	3	24	francis	francis	PROPN
ejpam-3884	3	25	joseph	joseph	PROPN
ejpam-3884	3	26	h.	h.	PROPN
ejpam-3884	3	27	campeña2	campeña2	PROPN
ejpam-3884	3	28	1	1	NUM
ejpam-3884	3	29	department	department	NOUN
ejpam-3884	3	30	of	of	ADP
ejpam-3884	3	31	mathematics	mathematics	PROPN
ejpam-3884	3	32	and	and	CCONJ
ejpam-3884	3	33	physics	physics	PROPN
ejpam-3884	3	34	,	,	PUNCT
ejpam-3884	3	35	college	college	NOUN
ejpam-3884	3	36	of	of	ADP
ejpam-3884	3	37	science	science	NOUN
ejpam-3884	3	38	,	,	PUNCT
ejpam-3884	3	39	central	central	ADJ
ejpam-3884	3	40	luzon	luzon	PROPN
ejpam-3884	3	41	state	state	PROPN
ejpam-3884	3	42	university	university	PROPN
ejpam-3884	3	43	,	,	PUNCT
ejpam-3884	3	44	science	science	NOUN
ejpam-3884	3	45	city	city	NOUN
ejpam-3884	3	46	of	of	ADP
ejpam-3884	3	47	muñoz	muñoz	PROPN
ejpam-3884	3	48	,	,	PUNCT
ejpam-3884	3	49	3120	3120	NUM
ejpam-3884	3	50	nueva	nueva	NOUN
ejpam-3884	3	51	ecija	ecija	NOUN
ejpam-3884	3	52	,	,	PUNCT
ejpam-3884	3	53	philippines	philippine	NOUN
ejpam-3884	3	54	2	2	NUM
ejpam-3884	3	55	mathematics	mathematic	NOUN
ejpam-3884	3	56	and	and	CCONJ
ejpam-3884	3	57	statistics	statistics	PROPN
ejpam-3884	3	58	department	department	PROPN
ejpam-3884	3	59	,	,	PUNCT
ejpam-3884	3	60	college	college	NOUN
ejpam-3884	3	61	of	of	ADP
ejpam-3884	3	62	science	science	NOUN
ejpam-3884	3	63	,	,	PUNCT
ejpam-3884	3	64	de	de	X
ejpam-3884	3	65	la	la	X
ejpam-3884	3	66	salle	salle	PROPN
ejpam-3884	3	67	university	university	PROPN
ejpam-3884	3	68	,	,	PUNCT
ejpam-3884	3	69	2401	2401	NUM
ejpam-3884	3	70	taft	taft	PROPN
ejpam-3884	3	71	avenue	avenue	PROPN
ejpam-3884	3	72	,	,	PUNCT
ejpam-3884	3	73	malate	malate	NOUN
ejpam-3884	3	74	,	,	PUNCT
ejpam-3884	3	75	manila	manila	PROPN
ejpam-3884	3	76	,	,	PUNCT
ejpam-3884	3	77	1004	1004	NUM
ejpam-3884	3	78	metro	metro	PROPN
ejpam-3884	3	79	manila	manila	PROPN
ejpam-3884	3	80	,	,	PUNCT
ejpam-3884	3	81	philippines	philippine	NOUN
ejpam-3884	3	82	abstract	abstract	ADJ
ejpam-3884	3	83	.	.	PUNCT
ejpam-3884	4	1	in	in	ADP
ejpam-3884	4	2	this	this	DET
ejpam-3884	4	3	paper	paper	NOUN
ejpam-3884	4	4	,	,	PUNCT
ejpam-3884	4	5	we	we	PRON
ejpam-3884	4	6	give	give	VERB
ejpam-3884	4	7	a	a	DET
ejpam-3884	4	8	recursive	recursive	ADJ
ejpam-3884	4	9	method	method	NOUN
ejpam-3884	4	10	in	in	ADP
ejpam-3884	4	11	constructing	construct	VERB
ejpam-3884	4	12	a	a	DET
ejpam-3884	4	13	breadth	breadth	NOUN
ejpam-3884	4	14	-	-	PUNCT
ejpam-3884	4	15	first	first	ADJ
ejpam-3884	4	16	search	search	NOUN
ejpam-3884	4	17	tree	tree	NOUN
ejpam-3884	4	18	for	for	ADP
ejpam-3884	4	19	multiplicative	multiplicative	ADJ
ejpam-3884	4	20	circulant	circulant	ADJ
ejpam-3884	4	21	graphs	graph	NOUN
ejpam-3884	4	22	of	of	ADP
ejpam-3884	4	23	order	order	NOUN
ejpam-3884	4	24	power	power	NOUN
ejpam-3884	4	25	of	of	ADP
ejpam-3884	4	26	odd	odd	ADJ
ejpam-3884	4	27	.	.	PUNCT
ejpam-3884	5	1	we	we	PRON
ejpam-3884	5	2	then	then	ADV
ejpam-3884	5	3	use	use	VERB
ejpam-3884	5	4	the	the	DET
ejpam-3884	5	5	proposed	propose	VERB
ejpam-3884	5	6	construction	construction	NOUN
ejpam-3884	5	7	in	in	ADP
ejpam-3884	5	8	reproving	reprove	VERB
ejpam-3884	5	9	some	some	DET
ejpam-3884	5	10	results	result	NOUN
ejpam-3884	5	11	concerning	concern	VERB
ejpam-3884	5	12	multiplicative	multiplicative	ADJ
ejpam-3884	5	13	circulant	circulant	NOUN
ejpam-3884	5	14	graph	graph	NOUN
ejpam-3884	5	15	’s	’s	PART
ejpam-3884	5	16	diameter	diameter	NOUN
ejpam-3884	5	17	,	,	PUNCT
ejpam-3884	5	18	average	average	ADJ
ejpam-3884	5	19	distance	distance	NOUN
ejpam-3884	5	20	and	and	CCONJ
ejpam-3884	5	21	distance	distance	NOUN
ejpam-3884	5	22	spectral	spectral	ADJ
ejpam-3884	5	23	radius	radius	NOUN
ejpam-3884	5	24	.	.	PUNCT
ejpam-3884	6	1	we	we	PRON
ejpam-3884	6	2	also	also	ADV
ejpam-3884	6	3	determine	determine	VERB
ejpam-3884	6	4	the	the	DET
ejpam-3884	6	5	graph	graph	NOUN
ejpam-3884	6	6	’s	’s	PART
ejpam-3884	6	7	wiener	wiener	NOUN
ejpam-3884	6	8	index	index	NOUN
ejpam-3884	6	9	,	,	PUNCT
ejpam-3884	6	10	vertex	vertex	NOUN
ejpam-3884	6	11	-	-	PUNCT
ejpam-3884	6	12	forwarding	forward	VERB
ejpam-3884	6	13	index	index	NOUN
ejpam-3884	6	14	,	,	PUNCT
ejpam-3884	6	15	and	and	CCONJ
ejpam-3884	6	16	a	a	DET
ejpam-3884	6	17	bound	bind	VERB
ejpam-3884	6	18	for	for	ADP
ejpam-3884	6	19	its	its	PRON
ejpam-3884	6	20	edge	edge	NOUN
ejpam-3884	6	21	-	-	PUNCT
ejpam-3884	6	22	forwarding	forward	VERB
ejpam-3884	6	23	index	index	NOUN
ejpam-3884	6	24	.	.	PUNCT
ejpam-3884	7	1	finally	finally	ADV
ejpam-3884	7	2	,	,	PUNCT
ejpam-3884	7	3	we	we	PRON
ejpam-3884	7	4	discuss	discuss	VERB
ejpam-3884	7	5	some	some	DET
ejpam-3884	7	6	possible	possible	ADJ
ejpam-3884	7	7	research	research	NOUN
ejpam-3884	7	8	works	work	NOUN
ejpam-3884	7	9	in	in	ADP
ejpam-3884	7	10	which	which	PRON
ejpam-3884	7	11	the	the	DET
ejpam-3884	7	12	proposed	propose	VERB
ejpam-3884	7	13	construction	construction	NOUN
ejpam-3884	7	14	can	can	AUX
ejpam-3884	7	15	be	be	AUX
ejpam-3884	7	16	applied	apply	VERB
ejpam-3884	7	17	.	.	PUNCT
ejpam-3884	8	1	2020	2020	NUM
ejpam-3884	8	2	mathematics	mathematic	NOUN
ejpam-3884	8	3	subject	subject	NOUN
ejpam-3884	8	4	classifications	classification	NOUN
ejpam-3884	8	5	:	:	PUNCT
ejpam-3884	8	6	05c09	05c09	NUM
ejpam-3884	8	7	,	,	PUNCT
ejpam-3884	8	8	05c12	05c12	NOUN
ejpam-3884	8	9	,	,	PUNCT
ejpam-3884	8	10	05c25	05c25	NUM
ejpam-3884	8	11	,	,	PUNCT
ejpam-3884	8	12	05c50	05c50	NUM
ejpam-3884	8	13	,	,	PUNCT
ejpam-3884	8	14	05c85	05c85	DET
ejpam-3884	8	15	key	key	ADJ
ejpam-3884	8	16	words	word	NOUN
ejpam-3884	8	17	and	and	CCONJ
ejpam-3884	8	18	phrases	phrase	NOUN
ejpam-3884	8	19	:	:	PUNCT
ejpam-3884	8	20	breadth	breadth	NOUN
ejpam-3884	8	21	-	-	PUNCT
ejpam-3884	8	22	first	first	ADJ
ejpam-3884	8	23	search	search	NOUN
ejpam-3884	8	24	tree	tree	NOUN
ejpam-3884	8	25	,	,	PUNCT
ejpam-3884	8	26	multiplicative	multiplicative	ADJ
ejpam-3884	8	27	circulant	circulant	NOUN
ejpam-3884	8	28	graph	graph	NOUN
ejpam-3884	8	29	,	,	PUNCT
ejpam-3884	8	30	graph	graph	NOUN
ejpam-3884	8	31	distance	distance	NOUN
ejpam-3884	8	32	matrix	matrix	NOUN
ejpam-3884	8	33	,	,	PUNCT
ejpam-3884	8	34	graph	graph	NOUN
ejpam-3884	8	35	diameter	diameter	NOUN
ejpam-3884	8	36	,	,	PUNCT
ejpam-3884	8	37	graph	graph	NOUN
ejpam-3884	8	38	distance	distance	NOUN
ejpam-3884	8	39	spectral	spectral	ADJ
ejpam-3884	8	40	radius	radius	NOUN
ejpam-3884	8	41	,	,	PUNCT
ejpam-3884	8	42	graph	graph	NOUN
ejpam-3884	8	43	average	average	ADJ
ejpam-3884	8	44	distance	distance	NOUN
ejpam-3884	8	45	,	,	PUNCT
ejpam-3884	8	46	wiener	wiener	NOUN
ejpam-3884	8	47	index	index	NOUN
ejpam-3884	8	48	,	,	PUNCT
ejpam-3884	8	49	graph	graph	NOUN
ejpam-3884	8	50	edge	edge	NOUN
ejpam-3884	8	51	-	-	PUNCT
ejpam-3884	8	52	forwarding	forward	VERB
ejpam-3884	8	53	index	index	NOUN
ejpam-3884	8	54	,	,	PUNCT
ejpam-3884	8	55	graph	graph	NOUN
ejpam-3884	8	56	vertex	vertex	NOUN
ejpam-3884	8	57	-	-	PUNCT
ejpam-3884	8	58	forwarding	forward	VERB
ejpam-3884	8	59	index	index	NOUN
ejpam-3884	8	60	1	1	NUM
ejpam-3884	8	61	.	.	PUNCT
ejpam-3884	9	1	introduction	introduction	NOUN
ejpam-3884	9	2	let	let	VERB
ejpam-3884	9	3	γ	γ	NOUN
ejpam-3884	9	4	be	be	AUX
ejpam-3884	9	5	a	a	DET
ejpam-3884	9	6	simple	simple	ADJ
ejpam-3884	9	7	connected	connected	ADJ
ejpam-3884	9	8	graph	graph	NOUN
ejpam-3884	9	9	with	with	ADP
ejpam-3884	9	10	vertex	vertex	NOUN
ejpam-3884	9	11	set	set	VERB
ejpam-3884	9	12	v	v	NOUN
ejpam-3884	9	13	(	(	PUNCT
ejpam-3884	9	14	γ	γ	NOUN
ejpam-3884	9	15	)	)	PUNCT
ejpam-3884	9	16	and	and	CCONJ
ejpam-3884	9	17	edge	edge	NOUN
ejpam-3884	9	18	set	set	VERB
ejpam-3884	9	19	e(γ	e(γ	NOUN
ejpam-3884	9	20	)	)	PUNCT
ejpam-3884	9	21	.	.	PUNCT
ejpam-3884	10	1	the	the	DET
ejpam-3884	10	2	number	number	NOUN
ejpam-3884	10	3	dγ(vi	dγ(vi	PROPN
ejpam-3884	10	4	,	,	PUNCT
ejpam-3884	10	5	vj	vj	NOUN
ejpam-3884	10	6	)	)	PUNCT
ejpam-3884	10	7	denotes	denote	VERB
ejpam-3884	10	8	the	the	DET
ejpam-3884	10	9	distance	distance	NOUN
ejpam-3884	10	10	between	between	ADP
ejpam-3884	10	11	two	two	NUM
ejpam-3884	10	12	vertices	vertex	NOUN
ejpam-3884	10	13	vi	vi	NOUN
ejpam-3884	10	14	and	and	CCONJ
ejpam-3884	10	15	vj	vj	PROPN
ejpam-3884	10	16	of	of	ADP
ejpam-3884	10	17	γ	γ	PROPN
ejpam-3884	10	18	,	,	PUNCT
ejpam-3884	10	19	which	which	PRON
ejpam-3884	10	20	is	be	AUX
ejpam-3884	10	21	the	the	DET
ejpam-3884	10	22	number	number	NOUN
ejpam-3884	10	23	of	of	ADP
ejpam-3884	10	24	edges	edge	NOUN
ejpam-3884	10	25	in	in	ADP
ejpam-3884	10	26	a	a	DET
ejpam-3884	10	27	shortest	short	ADJ
ejpam-3884	10	28	path	path	NOUN
ejpam-3884	10	29	between	between	ADP
ejpam-3884	10	30	the	the	DET
ejpam-3884	10	31	vertices	vertex	NOUN
ejpam-3884	10	32	.	.	PUNCT
ejpam-3884	11	1	for	for	ADP
ejpam-3884	11	2	a	a	DET
ejpam-3884	11	3	fix	fix	NOUN
ejpam-3884	11	4	vi	vi	X
ejpam-3884	11	5	∈	∈	NOUN
ejpam-3884	11	6	v	v	NOUN
ejpam-3884	11	7	(	(	PUNCT
ejpam-3884	11	8	γ	γ	NOUN
ejpam-3884	11	9	)	)	PUNCT
ejpam-3884	11	10	and	and	CCONJ
ejpam-3884	11	11	for	for	ADP
ejpam-3884	11	12	any	any	PRON
ejpam-3884	11	13	vj	vj	PROPN
ejpam-3884	11	14	∈	∈	PROPN
ejpam-3884	11	15	v	v	NOUN
ejpam-3884	11	16	(	(	PUNCT
ejpam-3884	11	17	γ	γ	NOUN
ejpam-3884	11	18	)	)	PUNCT
ejpam-3884	11	19	,	,	PUNCT
ejpam-3884	11	20	dγ(vi	dγ(vi	PROPN
ejpam-3884	11	21	,	,	PUNCT
ejpam-3884	11	22	vj	vj	NOUN
ejpam-3884	11	23	)	)	PUNCT
ejpam-3884	11	24	can	can	AUX
ejpam-3884	11	25	be	be	AUX
ejpam-3884	11	26	determined	determine	VERB
ejpam-3884	11	27	using	use	VERB
ejpam-3884	11	28	the	the	DET
ejpam-3884	11	29	breadth	breadth	NOUN
ejpam-3884	11	30	-	-	PUNCT
ejpam-3884	11	31	first	first	ADJ
ejpam-3884	11	32	search	search	NOUN
ejpam-3884	11	33	method	method	NOUN
ejpam-3884	11	34	or	or	CCONJ
ejpam-3884	11	35	simply	simply	ADV
ejpam-3884	11	36	called	call	VERB
ejpam-3884	11	37	bfs	bfs	NOUN
ejpam-3884	11	38	method	method	NOUN
ejpam-3884	11	39	.	.	PUNCT
ejpam-3884	12	1	the	the	DET
ejpam-3884	12	2	pseudo	pseudo	NOUN
ejpam-3884	12	3	-	-	NOUN
ejpam-3884	12	4	code	code	NOUN
ejpam-3884	12	5	for	for	ADP
ejpam-3884	12	6	bfs	bfs	NOUN
ejpam-3884	12	7	method	method	NOUN
ejpam-3884	12	8	is	be	AUX
ejpam-3884	12	9	given	give	VERB
ejpam-3884	12	10	in	in	ADP
ejpam-3884	12	11	the	the	DET
ejpam-3884	12	12	next	next	ADJ
ejpam-3884	12	13	page	page	NOUN
ejpam-3884	12	14	.	.	PUNCT
ejpam-3884	13	1	when	when	SCONJ
ejpam-3884	13	2	bfs	bfs	NOUN
ejpam-3884	13	3	method	method	NOUN
ejpam-3884	13	4	is	be	AUX
ejpam-3884	13	5	applied	apply	VERB
ejpam-3884	13	6	to	to	ADP
ejpam-3884	13	7	a	a	DET
ejpam-3884	13	8	particular	particular	ADJ
ejpam-3884	13	9	vertex	vertex	NOUN
ejpam-3884	13	10	vi	vi	NOUN
ejpam-3884	13	11	∈	∈	PROPN
ejpam-3884	13	12	v	v	NOUN
ejpam-3884	13	13	(	(	PUNCT
ejpam-3884	13	14	γ	γ	NOUN
ejpam-3884	13	15	)	)	PUNCT
ejpam-3884	13	16	of	of	ADP
ejpam-3884	13	17	the	the	DET
ejpam-3884	13	18	graph	graph	NOUN
ejpam-3884	13	19	γ	γ	PROPN
ejpam-3884	13	20	,	,	PUNCT
ejpam-3884	13	21	the	the	DET
ejpam-3884	13	22	result	result	NOUN
ejpam-3884	13	23	is	be	AUX
ejpam-3884	13	24	a	a	DET
ejpam-3884	13	25	rooted	rooted	ADJ
ejpam-3884	13	26	tree	tree	NOUN
ejpam-3884	13	27	with	with	ADP
ejpam-3884	13	28	vertex	vertex	NOUN
ejpam-3884	13	29	vi	vi	PROPN
ejpam-3884	13	30	as	as	ADP
ejpam-3884	13	31	the	the	DET
ejpam-3884	13	32	root	root	NOUN
ejpam-3884	13	33	.	.	PUNCT
ejpam-3884	14	1	this	this	DET
ejpam-3884	14	2	tree	tree	NOUN
ejpam-3884	14	3	is	be	AUX
ejpam-3884	14	4	called	call	VERB
ejpam-3884	14	5	a	a	DET
ejpam-3884	14	6	bfs	bfs	NOUN
ejpam-3884	14	7	tree	tree	NOUN
ejpam-3884	14	8	with	with	ADP
ejpam-3884	14	9	root	root	PROPN
ejpam-3884	14	10	vi	vi	PROPN
ejpam-3884	14	11	and	and	CCONJ
ejpam-3884	14	12	is	be	AUX
ejpam-3884	14	13	denoted	denote	VERB
ejpam-3884	14	14	by	by	ADP
ejpam-3884	14	15	bfsvi(γ	bfsvi(γ	NOUN
ejpam-3884	14	16	)	)	PUNCT
ejpam-3884	14	17	.	.	PUNCT
ejpam-3884	15	1	the	the	DET
ejpam-3884	15	2	rooted	root	VERB
ejpam-3884	15	3	tree	tree	NOUN
ejpam-3884	15	4	bfs0(c5	bfs0(c5	PROPN
ejpam-3884	15	5	)	)	PUNCT
ejpam-3884	15	6	is	be	AUX
ejpam-3884	15	7	shown	show	VERB
ejpam-3884	15	8	in	in	ADP
ejpam-3884	15	9	the	the	DET
ejpam-3884	15	10	right	right	ADJ
ejpam-3884	15	11	part	part	NOUN
ejpam-3884	15	12	of	of	ADP
ejpam-3884	15	13	figure	figure	NOUN
ejpam-3884	15	14	1	1	NUM
ejpam-3884	15	15	.	.	PUNCT
ejpam-3884	16	1	in	in	ADP
ejpam-3884	16	2	a	a	DET
ejpam-3884	16	3	rooted	rooted	ADJ
ejpam-3884	16	4	tree	tree	NOUN
ejpam-3884	16	5	,	,	PUNCT
ejpam-3884	16	6	we	we	PRON
ejpam-3884	16	7	call	call	VERB
ejpam-3884	16	8	a	a	DET
ejpam-3884	16	9	vertex	vertex	NOUN
ejpam-3884	16	10	vi	vi	NOUN
ejpam-3884	16	11	the	the	DET
ejpam-3884	16	12	parent	parent	NOUN
ejpam-3884	16	13	of	of	ADP
ejpam-3884	16	14	vertex	vertex	NOUN
ejpam-3884	16	15	vj	vj	PROPN
ejpam-3884	16	16	and	and	CCONJ
ejpam-3884	16	17	vertex	vertex	PROPN
ejpam-3884	16	18	vj	vj	INTJ
ejpam-3884	16	19	a	a	DET
ejpam-3884	16	20	child	child	NOUN
ejpam-3884	16	21	of	of	ADP
ejpam-3884	16	22	vertex	vertex	NOUN
ejpam-3884	16	23	vi	vi	PROPN
ejpam-3884	16	24	if	if	SCONJ
ejpam-3884	16	25	the	the	DET
ejpam-3884	16	26	edge	edge	NOUN
ejpam-3884	16	27	(	(	PUNCT
ejpam-3884	16	28	vi	vi	PROPN
ejpam-3884	16	29	,	,	PUNCT
ejpam-3884	16	30	vj	vj	NOUN
ejpam-3884	16	31	)	)	PUNCT
ejpam-3884	16	32	is	be	AUX
ejpam-3884	16	33	an	an	DET
ejpam-3884	16	34	edge	edge	NOUN
ejpam-3884	16	35	in	in	ADP
ejpam-3884	16	36	a	a	DET
ejpam-3884	16	37	rooted	rooted	ADJ
ejpam-3884	16	38	tree	tree	NOUN
ejpam-3884	16	39	;	;	PUNCT
ejpam-3884	16	40	where	where	SCONJ
ejpam-3884	16	41	the	the	DET
ejpam-3884	16	42	naming	naming	NOUN
ejpam-3884	16	43	of	of	ADP
ejpam-3884	16	44	an	an	DET
ejpam-3884	16	45	edge	edge	NOUN
ejpam-3884	16	46	(	(	PUNCT
ejpam-3884	16	47	vi	vi	NOUN
ejpam-3884	16	48	,	,	PUNCT
ejpam-3884	16	49	vj	vj	NOUN
ejpam-3884	16	50	)	)	PUNCT
ejpam-3884	16	51	is	be	AUX
ejpam-3884	16	52	with	with	ADP
ejpam-3884	16	53	respect	respect	NOUN
ejpam-3884	16	54	to	to	ADP
ejpam-3884	16	55	their	their	PRON
ejpam-3884	16	56	level	level	NOUN
ejpam-3884	16	57	relative	relative	ADJ
ejpam-3884	16	58	to	to	ADP
ejpam-3884	16	59	the	the	DET
ejpam-3884	16	60	root	root	NOUN
ejpam-3884	16	61	.	.	PUNCT
ejpam-3884	17	1	also	also	ADV
ejpam-3884	17	2	,	,	PUNCT
ejpam-3884	17	3	a	a	DET
ejpam-3884	17	4	vertex	vertex	NOUN
ejpam-3884	17	5	vi	vi	PROPN
ejpam-3884	17	6	is	be	AUX
ejpam-3884	17	7	said	say	VERB
ejpam-3884	17	8	to	to	PART
ejpam-3884	17	9	be	be	AUX
ejpam-3884	17	10	an	an	DET
ejpam-3884	17	11	ancestor	ancestor	NOUN
ejpam-3884	17	12	of	of	ADP
ejpam-3884	17	13	vertex	vertex	NOUN
ejpam-3884	17	14	vj	vj	PROPN
ejpam-3884	17	15	and	and	CCONJ
ejpam-3884	17	16	vertex	vertex	PROPN
ejpam-3884	17	17	vj	vj	X
ejpam-3884	17	18	is	be	AUX
ejpam-3884	17	19	a	a	DET
ejpam-3884	17	20	descendant	descendant	NOUN
ejpam-3884	17	21	of	of	ADP
ejpam-3884	17	22	vertex	vertex	NOUN
ejpam-3884	17	23	vi	vi	PROPN
ejpam-3884	17	24	if	if	SCONJ
ejpam-3884	17	25	there	there	PRON
ejpam-3884	17	26	is	be	VERB
ejpam-3884	17	27	a	a	DET
ejpam-3884	17	28	path	path	NOUN
ejpam-3884	17	29	from	from	ADP
ejpam-3884	17	30	vi	vi	PROPN
ejpam-3884	17	31	to	to	ADP
ejpam-3884	17	32	vj	vj	NUM
ejpam-3884	17	33	whose	whose	DET
ejpam-3884	17	34	edges	edge	NOUN
ejpam-3884	17	35	all	all	PRON
ejpam-3884	17	36	go	go	VERB
ejpam-3884	17	37	from	from	ADP
ejpam-3884	17	38	parent	parent	NOUN
ejpam-3884	17	39	to	to	ADP
ejpam-3884	17	40	child	child	NOUN
ejpam-3884	17	41	.	.	PUNCT
ejpam-3884	18	1	∗corresponding	∗corresponde	VERB
ejpam-3884	18	2	author	author	NOUN
ejpam-3884	18	3	.	.	PUNCT
ejpam-3884	19	1	doi	doi	NOUN
ejpam-3884	19	2	:	:	PUNCT
ejpam-3884	19	3	https://doi.org/10.29020/nybg.ejpam.v14i1.3884	https://doi.org/10.29020/nybg.ejpam.v14i1.3884	ADJ
ejpam-3884	19	4	email	email	NOUN
ejpam-3884	19	5	addresses	address	NOUN
ejpam-3884	19	6	:	:	PUNCT
ejpam-3884	19	7	jrantalan@clsu.edu.ph	jrantalan@clsu.edu.ph	PROPN
ejpam-3884	19	8	(	(	PUNCT
ejpam-3884	19	9	j.	j.	PROPN
ejpam-3884	19	10	antalan	antalan	PROPN
ejpam-3884	19	11	)	)	PUNCT
ejpam-3884	19	12	,	,	PUNCT
ejpam-3884	19	13	francis.campena@dlsu.edu.ph	francis.campena@dlsu.edu.ph	PROPN
ejpam-3884	19	14	(	(	PUNCT
ejpam-3884	19	15	f.	f.	PROPN
ejpam-3884	19	16	campeña	campeña	PROPN
ejpam-3884	19	17	)	)	PUNCT
ejpam-3884	19	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3884	20	1	248	248	NUM
ejpam-3884	20	2	c	c	AUX
ejpam-3884	20	3	©	©	PROPN
ejpam-3884	20	4	2021	2021	NUM
ejpam-3884	20	5	ejpam	ejpam	VERB
ejpam-3884	20	6	all	all	DET
ejpam-3884	20	7	rights	right	NOUN
ejpam-3884	20	8	reserved	reserve	VERB
ejpam-3884	20	9	.	.	PUNCT
ejpam-3884	21	1	j.	j.	PROPN
ejpam-3884	21	2	antalan	antalan	PROPN
ejpam-3884	21	3	,	,	PUNCT
ejpam-3884	21	4	f.	f.	PROPN
ejpam-3884	21	5	campeña	campeña	PROPN
ejpam-3884	21	6	/	/	SYM
ejpam-3884	21	7	eur	eur	PROPN
ejpam-3884	21	8	.	.	PUNCT
ejpam-3884	22	1	j.	j.	PROPN
ejpam-3884	22	2	pure	pure	PROPN
ejpam-3884	22	3	appl	appl	PROPN
ejpam-3884	22	4	.	.	PROPN
ejpam-3884	22	5	math	math	PROPN
ejpam-3884	22	6	,	,	PUNCT
ejpam-3884	22	7	14	14	NUM
ejpam-3884	22	8	(	(	PUNCT
ejpam-3884	22	9	1	1	NUM
ejpam-3884	22	10	)	)	PUNCT
ejpam-3884	22	11	(	(	PUNCT
ejpam-3884	22	12	2021	2021	NUM
ejpam-3884	22	13	)	)	PUNCT
ejpam-3884	22	14	,	,	PUNCT
ejpam-3884	22	15	248	248	NUM
ejpam-3884	22	16	-	-	SYM
ejpam-3884	22	17	264	264	NUM
ejpam-3884	22	18	249	249	NUM
ejpam-3884	22	19	breadth	breadth	NOUN
ejpam-3884	22	20	-	-	PUNCT
ejpam-3884	22	21	first	first	ADJ
ejpam-3884	22	22	search	search	NOUN
ejpam-3884	22	23	algorithm	algorithm	NOUN
ejpam-3884	22	24	[	[	X
ejpam-3884	22	25	5	5	NUM
ejpam-3884	22	26	]	]	PUNCT
ejpam-3884	22	27	input	input	NOUN
ejpam-3884	22	28	:	:	PUNCT
ejpam-3884	22	29	undirected	undirected	ADJ
ejpam-3884	22	30	graph	graph	NOUN
ejpam-3884	22	31	γ	γ	X
ejpam-3884	22	32	=	=	SYM
ejpam-3884	22	33	(	(	PUNCT
ejpam-3884	22	34	v	v	X
ejpam-3884	22	35	(	(	PUNCT
ejpam-3884	22	36	γ	γ	NOUN
ejpam-3884	22	37	)	)	PUNCT
ejpam-3884	22	38	,	,	PUNCT
ejpam-3884	22	39	e(γ	e(γ	PROPN
ejpam-3884	22	40	)	)	PUNCT
ejpam-3884	22	41	)	)	PUNCT
ejpam-3884	22	42	and	and	CCONJ
ejpam-3884	22	43	a	a	DET
ejpam-3884	22	44	vertex	vertex	NOUN
ejpam-3884	22	45	s	s	NOUN
ejpam-3884	22	46	∈	∈	NOUN
ejpam-3884	22	47	v	v	NOUN
ejpam-3884	22	48	(	(	PUNCT
ejpam-3884	22	49	γ	γ	NOUN
ejpam-3884	22	50	)	)	PUNCT
ejpam-3884	22	51	output	output	NOUN
ejpam-3884	22	52	:	:	PUNCT
ejpam-3884	22	53	breadth	breadth	NOUN
ejpam-3884	22	54	-	-	PUNCT
ejpam-3884	22	55	first	first	ADV
ejpam-3884	22	56	tree	tree	NOUN
ejpam-3884	22	57	t	t	NOUN
ejpam-3884	22	58	from	from	ADP
ejpam-3884	22	59	s.	s.	PROPN
ejpam-3884	22	60	vi	vi	PROPN
ejpam-3884	22	61	=	=	PUNCT
ejpam-3884	22	62	{	{	PUNCT
ejpam-3884	22	63	all	all	DET
ejpam-3884	22	64	vertices	vertice	VERB
ejpam-3884	22	65	at	at	ADP
ejpam-3884	22	66	distance	distance	NOUN
ejpam-3884	22	67	i	i	PRON
ejpam-3884	22	68	from	from	ADP
ejpam-3884	22	69	s	s	PROPN
ejpam-3884	22	70	}	}	PUNCT
ejpam-3884	22	71	v0	v0	NOUN
ejpam-3884	22	72	=	=	SYM
ejpam-3884	22	73	{	{	PUNCT
ejpam-3884	22	74	s	s	PART
ejpam-3884	22	75	}	}	PUNCT
ejpam-3884	22	76	make	make	VERB
ejpam-3884	22	77	s	s	PRON
ejpam-3884	22	78	the	the	DET
ejpam-3884	22	79	root	root	NOUN
ejpam-3884	22	80	of	of	ADP
ejpam-3884	22	81	t	t	PROPN
ejpam-3884	23	1	i	i	NOUN
ejpam-3884	23	2	=	=	NOUN
ejpam-3884	23	3	0	0	PUNCT
ejpam-3884	23	4	while	while	SCONJ
ejpam-3884	23	5	vi	vi	PROPN
ejpam-3884	23	6	6=	6=	PROPN
ejpam-3884	23	7	∅	∅	NOUN
ejpam-3884	23	8	do	do	AUX
ejpam-3884	23	9	construct	construct	VERB
ejpam-3884	23	10	vi+1	vi+1	ADV
ejpam-3884	23	11	vi+1	vi+1	NOUN
ejpam-3884	23	12	=	=	NOUN
ejpam-3884	23	13	∅	∅	NOUN
ejpam-3884	23	14	for	for	ADP
ejpam-3884	23	15	each	each	DET
ejpam-3884	23	16	vertex	vertex	NOUN
ejpam-3884	23	17	v	v	ADP
ejpam-3884	23	18	∈	∈	PROPN
ejpam-3884	23	19	vi	vi	NOUN
ejpam-3884	23	20	do	do	AUX
ejpam-3884	23	21	“	"	PUNCT
ejpam-3884	23	22	scan	scan	NOUN
ejpam-3884	23	23	v	v	NOUN
ejpam-3884	23	24	”	"	PUNCT
ejpam-3884	23	25	for	for	ADP
ejpam-3884	23	26	each	each	DET
ejpam-3884	23	27	edge	edge	NOUN
ejpam-3884	23	28	(	(	PUNCT
ejpam-3884	23	29	v	v	NOUN
ejpam-3884	23	30	,	,	PUNCT
ejpam-3884	23	31	w	w	NOUN
ejpam-3884	23	32	)	)	PUNCT
ejpam-3884	23	33	do	do	AUX
ejpam-3884	23	34	if	if	SCONJ
ejpam-3884	23	35	w	w	PROPN
ejpam-3884	23	36	/∈	/∈	PUNCT
ejpam-3884	23	37	⋃	⋃	PROPN
ejpam-3884	23	38	j	j	PROPN
ejpam-3884	23	39	vj	vj	INTJ
ejpam-3884	23	40	then	then	ADV
ejpam-3884	23	41	make	make	VERB
ejpam-3884	23	42	w	w	ADP
ejpam-3884	23	43	the	the	DET
ejpam-3884	23	44	next	next	ADJ
ejpam-3884	23	45	child	child	NOUN
ejpam-3884	23	46	of	of	ADP
ejpam-3884	23	47	v	v	NOUN
ejpam-3884	23	48	in	in	ADP
ejpam-3884	23	49	t	t	NOUN
ejpam-3884	23	50	add	add	VERB
ejpam-3884	23	51	w	w	ADP
ejpam-3884	23	52	to	to	PART
ejpam-3884	23	53	vi+1	vi+1	NOUN
ejpam-3884	24	1	i	i	PRON
ejpam-3884	24	2	=	=	PUNCT
ejpam-3884	24	3	i+	i+	NUM
ejpam-3884	24	4	1	1	NUM
ejpam-3884	24	5	figure	figure	NOUN
ejpam-3884	24	6	1	1	NUM
ejpam-3884	24	7	:	:	PUNCT
ejpam-3884	24	8	the	the	DET
ejpam-3884	24	9	graph	graph	NOUN
ejpam-3884	24	10	c5	c5	PROPN
ejpam-3884	24	11	and	and	CCONJ
ejpam-3884	24	12	its	its	PRON
ejpam-3884	24	13	corresponding	corresponding	ADJ
ejpam-3884	24	14	bfs	bfs	NOUN
ejpam-3884	24	15	tree	tree	NOUN
ejpam-3884	24	16	for	for	ADP
ejpam-3884	24	17	vertex	vertex	NOUN
ejpam-3884	24	18	0	0	NUM
ejpam-3884	24	19	.	.	PUNCT
ejpam-3884	25	1	in	in	ADP
ejpam-3884	25	2	the	the	DET
ejpam-3884	25	3	rooted	rooted	ADJ
ejpam-3884	25	4	tree	tree	NOUN
ejpam-3884	25	5	of	of	ADP
ejpam-3884	25	6	figure	figure	NOUN
ejpam-3884	25	7	1	1	NUM
ejpam-3884	25	8	,	,	PUNCT
ejpam-3884	25	9	vertex	vertex	NOUN
ejpam-3884	25	10	1	1	NUM
ejpam-3884	25	11	is	be	AUX
ejpam-3884	25	12	the	the	DET
ejpam-3884	25	13	parent	parent	NOUN
ejpam-3884	25	14	of	of	ADP
ejpam-3884	25	15	vertex	vertex	NOUN
ejpam-3884	25	16	2	2	NUM
ejpam-3884	25	17	and	and	CCONJ
ejpam-3884	25	18	hence	hence	ADV
ejpam-3884	25	19	,	,	PUNCT
ejpam-3884	25	20	vertex	vertex	NOUN
ejpam-3884	25	21	2	2	NUM
ejpam-3884	25	22	is	be	AUX
ejpam-3884	25	23	a	a	DET
ejpam-3884	25	24	child	child	NOUN
ejpam-3884	25	25	of	of	ADP
ejpam-3884	25	26	vertex	vertex	NOUN
ejpam-3884	25	27	1	1	NUM
ejpam-3884	25	28	.	.	PUNCT
ejpam-3884	26	1	also	also	ADV
ejpam-3884	26	2	,	,	PUNCT
ejpam-3884	26	3	the	the	DET
ejpam-3884	26	4	vertices	vertex	NOUN
ejpam-3884	26	5	1,2,3	1,2,3	NUM
ejpam-3884	26	6	,	,	PUNCT
ejpam-3884	26	7	and	and	CCONJ
ejpam-3884	26	8	4	4	NUM
ejpam-3884	26	9	are	be	AUX
ejpam-3884	26	10	descendants	descendant	NOUN
ejpam-3884	26	11	of	of	ADP
ejpam-3884	26	12	the	the	DET
ejpam-3884	26	13	root	root	NOUN
ejpam-3884	26	14	vertex	vertex	NOUN
ejpam-3884	26	15	0	0	NUM
ejpam-3884	26	16	.	.	PUNCT
ejpam-3884	27	1	the	the	DET
ejpam-3884	27	2	bfs	bfs	NOUN
ejpam-3884	27	3	tree	tree	NOUN
ejpam-3884	27	4	contains	contain	VERB
ejpam-3884	27	5	the	the	DET
ejpam-3884	27	6	distance	distance	NOUN
ejpam-3884	27	7	information	information	NOUN
ejpam-3884	27	8	between	between	ADP
ejpam-3884	27	9	the	the	DET
ejpam-3884	27	10	root	root	NOUN
ejpam-3884	27	11	and	and	CCONJ
ejpam-3884	27	12	all	all	DET
ejpam-3884	27	13	the	the	DET
ejpam-3884	27	14	other	other	ADJ
ejpam-3884	27	15	vertices	vertex	NOUN
ejpam-3884	27	16	in	in	ADP
ejpam-3884	27	17	v	v	NUM
ejpam-3884	27	18	(	(	PUNCT
ejpam-3884	27	19	γ	γ	NOUN
ejpam-3884	27	20	)	)	PUNCT
ejpam-3884	27	21	.	.	PUNCT
ejpam-3884	28	1	for	for	ADP
ejpam-3884	28	2	instance	instance	NOUN
ejpam-3884	28	3	,	,	PUNCT
ejpam-3884	28	4	for	for	ADP
ejpam-3884	28	5	the	the	DET
ejpam-3884	28	6	graph	graph	NOUN
ejpam-3884	28	7	c5	c5	PROPN
ejpam-3884	28	8	in	in	ADP
ejpam-3884	28	9	the	the	DET
ejpam-3884	28	10	left	left	ADJ
ejpam-3884	28	11	part	part	NOUN
ejpam-3884	28	12	of	of	ADP
ejpam-3884	28	13	figure	figure	NOUN
ejpam-3884	28	14	1	1	NUM
ejpam-3884	28	15	,	,	PUNCT
ejpam-3884	28	16	its	its	PRON
ejpam-3884	28	17	corresponding	corresponding	ADJ
ejpam-3884	28	18	bfs	bfs	NOUN
ejpam-3884	28	19	tree	tree	NOUN
ejpam-3884	28	20	rooted	root	VERB
ejpam-3884	28	21	from	from	ADP
ejpam-3884	28	22	0	0	NUM
ejpam-3884	28	23	-	-	PUNCT
ejpam-3884	28	24	vertex	vertex	NOUN
ejpam-3884	28	25	shown	show	VERB
ejpam-3884	28	26	in	in	ADP
ejpam-3884	28	27	the	the	DET
ejpam-3884	28	28	right	right	ADJ
ejpam-3884	28	29	part	part	NOUN
ejpam-3884	28	30	of	of	ADP
ejpam-3884	28	31	figure	figure	NOUN
ejpam-3884	28	32	1	1	NUM
ejpam-3884	28	33	reveals	reveal	VERB
ejpam-3884	28	34	that	that	SCONJ
ejpam-3884	28	35	dc5(0	dc5(0	VERB
ejpam-3884	28	36	,	,	PUNCT
ejpam-3884	28	37	v	v	NOUN
ejpam-3884	28	38	)	)	PUNCT
ejpam-3884	28	39	=	=	SYM
ejpam-3884	28	40	1	1	NUM
ejpam-3884	28	41	if	if	SCONJ
ejpam-3884	28	42	v	v	NOUN
ejpam-3884	28	43	=	=	SYM
ejpam-3884	28	44	1	1	NUM
ejpam-3884	28	45	,	,	PUNCT
ejpam-3884	28	46	4	4	NUM
ejpam-3884	28	47	and	and	CCONJ
ejpam-3884	28	48	dc5(0	dc5(0	NOUN
ejpam-3884	28	49	,	,	PUNCT
ejpam-3884	28	50	v	v	NOUN
ejpam-3884	28	51	)	)	PUNCT
ejpam-3884	28	52	=	=	SYM
ejpam-3884	28	53	2	2	NUM
ejpam-3884	28	54	if	if	SCONJ
ejpam-3884	28	55	v	v	VERB
ejpam-3884	28	56	=	=	SYM
ejpam-3884	28	57	2	2	NUM
ejpam-3884	28	58	,	,	PUNCT
ejpam-3884	28	59	3	3	NUM
ejpam-3884	28	60	.	.	X
ejpam-3884	29	1	for	for	ADP
ejpam-3884	29	2	a	a	DET
ejpam-3884	29	3	tree	tree	NOUN
ejpam-3884	29	4	with	with	ADP
ejpam-3884	29	5	vertical	vertical	ADJ
ejpam-3884	29	6	axial	axial	ADJ
ejpam-3884	29	7	symmetry	symmetry	NOUN
ejpam-3884	29	8	such	such	ADJ
ejpam-3884	29	9	as	as	ADP
ejpam-3884	29	10	the	the	DET
ejpam-3884	29	11	tree	tree	NOUN
ejpam-3884	29	12	in	in	ADP
ejpam-3884	29	13	figure	figure	NOUN
ejpam-3884	29	14	1	1	NUM
ejpam-3884	29	15	,	,	PUNCT
ejpam-3884	29	16	we	we	PRON
ejpam-3884	29	17	classify	classify	VERB
ejpam-3884	29	18	its	its	PRON
ejpam-3884	29	19	vertices	vertex	NOUN
ejpam-3884	29	20	as	as	ADP
ejpam-3884	29	21	to	to	ADP
ejpam-3884	29	22	whether	whether	SCONJ
ejpam-3884	29	23	it	it	PRON
ejpam-3884	29	24	is	be	AUX
ejpam-3884	29	25	located	locate	VERB
ejpam-3884	29	26	on	on	ADP
ejpam-3884	29	27	the	the	DET
ejpam-3884	29	28	left	left	ADJ
ejpam-3884	29	29	part	part	NOUN
ejpam-3884	29	30	or	or	CCONJ
ejpam-3884	29	31	on	on	ADP
ejpam-3884	29	32	the	the	DET
ejpam-3884	29	33	right	right	ADJ
ejpam-3884	29	34	part	part	NOUN
ejpam-3884	29	35	of	of	ADP
ejpam-3884	29	36	the	the	DET
ejpam-3884	29	37	tree	tree	NOUN
ejpam-3884	29	38	.	.	PUNCT
ejpam-3884	30	1	for	for	ADP
ejpam-3884	30	2	instance	instance	NOUN
ejpam-3884	30	3	,	,	PUNCT
ejpam-3884	30	4	the	the	DET
ejpam-3884	30	5	left	left	ADJ
ejpam-3884	30	6	part	part	NOUN
ejpam-3884	30	7	of	of	ADP
ejpam-3884	30	8	the	the	DET
ejpam-3884	30	9	bfs	bfs	NOUN
ejpam-3884	30	10	tree	tree	NOUN
ejpam-3884	30	11	of	of	ADP
ejpam-3884	30	12	c5	c5	PROPN
ejpam-3884	30	13	with	with	ADP
ejpam-3884	30	14	root	root	NOUN
ejpam-3884	30	15	vertex	vertex	NOUN
ejpam-3884	30	16	0	0	NUM
ejpam-3884	30	17	denoted	denote	VERB
ejpam-3884	30	18	by	by	ADP
ejpam-3884	30	19	l[bfs0(c5	l[bfs0(c5	PROPN
ejpam-3884	30	20	)	)	PUNCT
ejpam-3884	30	21	]	]	PUNCT
ejpam-3884	30	22	contains	contain	VERB
ejpam-3884	30	23	the	the	DET
ejpam-3884	30	24	vertices	vertex	NOUN
ejpam-3884	30	25	1	1	NUM
ejpam-3884	30	26	and	and	CCONJ
ejpam-3884	30	27	2	2	NUM
ejpam-3884	30	28	;	;	PUNCT
ejpam-3884	30	29	while	while	SCONJ
ejpam-3884	30	30	the	the	DET
ejpam-3884	30	31	right	right	ADJ
ejpam-3884	30	32	part	part	NOUN
ejpam-3884	30	33	of	of	ADP
ejpam-3884	30	34	the	the	DET
ejpam-3884	30	35	bfs	bfs	NOUN
ejpam-3884	30	36	tree	tree	NOUN
ejpam-3884	30	37	ofc5	ofc5	PROPN
ejpam-3884	30	38	with	with	ADP
ejpam-3884	30	39	root	root	NOUN
ejpam-3884	30	40	vertex	vertex	NOUN
ejpam-3884	30	41	0	0	NUM
ejpam-3884	30	42	denoted	denote	VERB
ejpam-3884	30	43	by	by	ADP
ejpam-3884	30	44	r[bfs0(c5	r[bfs0(c5	PROPN
ejpam-3884	30	45	)	)	PUNCT
ejpam-3884	30	46	]	]	PUNCT
ejpam-3884	30	47	contains	contain	VERB
ejpam-3884	30	48	the	the	DET
ejpam-3884	30	49	vertices	vertex	NOUN
ejpam-3884	30	50	3	3	NUM
ejpam-3884	30	51	and	and	CCONJ
ejpam-3884	30	52	4	4	NUM
ejpam-3884	30	53	.	.	PUNCT
ejpam-3884	30	54	the	the	DET
ejpam-3884	30	55	main	main	ADJ
ejpam-3884	30	56	goal	goal	NOUN
ejpam-3884	30	57	of	of	ADP
ejpam-3884	30	58	this	this	DET
ejpam-3884	30	59	paper	paper	NOUN
ejpam-3884	30	60	is	be	AUX
ejpam-3884	30	61	to	to	PART
ejpam-3884	30	62	present	present	VERB
ejpam-3884	30	63	a	a	DET
ejpam-3884	30	64	method	method	NOUN
ejpam-3884	30	65	on	on	ADP
ejpam-3884	30	66	constructing	construct	VERB
ejpam-3884	30	67	a	a	DET
ejpam-3884	30	68	bfs	bfs	NOUN
ejpam-3884	30	69	tree	tree	NOUN
ejpam-3884	30	70	for	for	ADP
ejpam-3884	30	71	multiplicative	multiplicative	ADJ
ejpam-3884	30	72	circulant	circulant	ADJ
ejpam-3884	30	73	graphs	graph	NOUN
ejpam-3884	30	74	of	of	ADP
ejpam-3884	30	75	order	order	NOUN
ejpam-3884	30	76	power	power	NOUN
ejpam-3884	30	77	of	of	ADP
ejpam-3884	30	78	odd	odd	ADJ
ejpam-3884	30	79	.	.	PUNCT
ejpam-3884	31	1	we	we	PRON
ejpam-3884	31	2	formally	formally	ADV
ejpam-3884	31	3	define	define	VERB
ejpam-3884	31	4	multiplicative	multiplicative	ADJ
ejpam-3884	31	5	j.	j.	PROPN
ejpam-3884	31	6	antalan	antalan	PROPN
ejpam-3884	31	7	,	,	PUNCT
ejpam-3884	31	8	f.	f.	PROPN
ejpam-3884	31	9	campeña	campeña	PROPN
ejpam-3884	31	10	/	/	SYM
ejpam-3884	31	11	eur	eur	PROPN
ejpam-3884	31	12	.	.	PUNCT
ejpam-3884	32	1	j.	j.	PROPN
ejpam-3884	32	2	pure	pure	PROPN
ejpam-3884	32	3	appl	appl	PROPN
ejpam-3884	32	4	.	.	PROPN
ejpam-3884	32	5	math	math	PROPN
ejpam-3884	32	6	,	,	PUNCT
ejpam-3884	32	7	14	14	NUM
ejpam-3884	32	8	(	(	PUNCT
ejpam-3884	32	9	1	1	NUM
ejpam-3884	32	10	)	)	PUNCT
ejpam-3884	32	11	(	(	PUNCT
ejpam-3884	32	12	2021	2021	NUM
ejpam-3884	32	13	)	)	PUNCT
ejpam-3884	32	14	,	,	PUNCT
ejpam-3884	32	15	248	248	NUM
ejpam-3884	32	16	-	-	SYM
ejpam-3884	32	17	264	264	NUM
ejpam-3884	32	18	250	250	NUM
ejpam-3884	32	19	circulant	circulant	ADJ
ejpam-3884	32	20	graph	graph	NOUN
ejpam-3884	32	21	in	in	ADP
ejpam-3884	32	22	the	the	DET
ejpam-3884	32	23	next	next	ADJ
ejpam-3884	32	24	paragraph	paragraph	NOUN
ejpam-3884	32	25	.	.	PUNCT
ejpam-3884	33	1	multiplicative	multiplicative	ADJ
ejpam-3884	33	2	circulant	circulant	ADJ
ejpam-3884	33	3	graphs	graph	NOUN
ejpam-3884	33	4	are	be	AUX
ejpam-3884	33	5	special	special	ADJ
ejpam-3884	33	6	type	type	NOUN
ejpam-3884	33	7	of	of	ADP
ejpam-3884	33	8	cayley	cayley	ADJ
ejpam-3884	33	9	graphs	graph	NOUN
ejpam-3884	33	10	.	.	PUNCT
ejpam-3884	34	1	by	by	ADP
ejpam-3884	34	2	definition	definition	NOUN
ejpam-3884	34	3	,	,	PUNCT
ejpam-3884	34	4	given	give	VERB
ejpam-3884	34	5	a	a	DET
ejpam-3884	34	6	group	group	NOUN
ejpam-3884	34	7	g	g	NOUN
ejpam-3884	34	8	and	and	CCONJ
ejpam-3884	34	9	a	a	DET
ejpam-3884	34	10	subset	subset	NOUN
ejpam-3884	34	11	s	s	NOUN
ejpam-3884	34	12	of	of	ADP
ejpam-3884	34	13	g−{e	g−{e	PROPN
ejpam-3884	34	14	}	}	PUNCT
ejpam-3884	34	15	,	,	PUNCT
ejpam-3884	34	16	a	a	DET
ejpam-3884	34	17	graph	graph	NOUN
ejpam-3884	34	18	γ	γ	PROPN
ejpam-3884	34	19	is	be	AUX
ejpam-3884	34	20	a	a	DET
ejpam-3884	34	21	cayley	cayley	ADJ
ejpam-3884	34	22	graph	graph	NOUN
ejpam-3884	34	23	of	of	ADP
ejpam-3884	34	24	g	g	NOUN
ejpam-3884	34	25	with	with	ADP
ejpam-3884	34	26	connection	connection	NOUN
ejpam-3884	34	27	(	(	PUNCT
ejpam-3884	34	28	or	or	CCONJ
ejpam-3884	34	29	jump	jump	NOUN
ejpam-3884	34	30	)	)	PUNCT
ejpam-3884	34	31	set	set	VERB
ejpam-3884	34	32	s	s	PROPN
ejpam-3884	34	33	,	,	PUNCT
ejpam-3884	34	34	written	write	VERB
ejpam-3884	34	35	γ	γ	NOUN
ejpam-3884	34	36	=	=	SYM
ejpam-3884	34	37	cay(g	cay(g	PROPN
ejpam-3884	34	38	,	,	PUNCT
ejpam-3884	34	39	s	s	PART
ejpam-3884	34	40	)	)	PUNCT
ejpam-3884	34	41	if	if	SCONJ
ejpam-3884	34	42	v	v	X
ejpam-3884	34	43	(	(	PUNCT
ejpam-3884	34	44	γ	γ	NOUN
ejpam-3884	34	45	)	)	PUNCT
ejpam-3884	34	46	=	=	SYM
ejpam-3884	34	47	g	g	NOUN
ejpam-3884	34	48	and	and	CCONJ
ejpam-3884	34	49	e(γ	e(γ	NOUN
ejpam-3884	34	50	)	)	PUNCT
ejpam-3884	35	1	=	=	PRON
ejpam-3884	35	2	{	{	PUNCT
ejpam-3884	35	3	{	{	PUNCT
ejpam-3884	35	4	g	g	PROPN
ejpam-3884	35	5	,	,	PUNCT
ejpam-3884	35	6	sg	sg	ADP
ejpam-3884	35	7	}	}	PUNCT
ejpam-3884	35	8	:	:	PUNCT
ejpam-3884	35	9	g	g	PROPN
ejpam-3884	35	10	∈	∈	PROPN
ejpam-3884	35	11	g	g	PROPN
ejpam-3884	35	12	,	,	PUNCT
ejpam-3884	35	13	s	s	PART
ejpam-3884	35	14	∈	∈	PROPN
ejpam-3884	35	15	s	s	PART
ejpam-3884	35	16	}	}	PUNCT
ejpam-3884	35	17	.	.	PUNCT
ejpam-3884	36	1	if	if	SCONJ
ejpam-3884	36	2	g	g	PROPN
ejpam-3884	36	3	=	=	SYM
ejpam-3884	36	4	〈	〈	PROPN
ejpam-3884	36	5	zn,+n	zn,+n	NOUN
ejpam-3884	36	6	〉	〉	NOUN
ejpam-3884	36	7	,	,	PUNCT
ejpam-3884	36	8	then	then	ADV
ejpam-3884	36	9	the	the	DET
ejpam-3884	36	10	graph	graph	NOUN
ejpam-3884	36	11	γ	γ	X
ejpam-3884	36	12	=	=	SYM
ejpam-3884	36	13	cay(g	cay(g	PROPN
ejpam-3884	36	14	,	,	PUNCT
ejpam-3884	36	15	s	s	PART
ejpam-3884	36	16	)	)	PUNCT
ejpam-3884	36	17	is	be	AUX
ejpam-3884	36	18	called	call	VERB
ejpam-3884	36	19	the	the	DET
ejpam-3884	36	20	circulant	circulant	ADJ
ejpam-3884	36	21	graph	graph	NOUN
ejpam-3884	36	22	with	with	ADP
ejpam-3884	36	23	connection	connection	NOUN
ejpam-3884	36	24	set	set	VERB
ejpam-3884	36	25	s.	s.	PROPN
ejpam-3884	36	26	if	if	SCONJ
ejpam-3884	36	27	a	a	DET
ejpam-3884	36	28	circulant	circulant	ADJ
ejpam-3884	36	29	graph	graph	NOUN
ejpam-3884	36	30	cay(zn	cay(zn	PROPN
ejpam-3884	36	31	,	,	PUNCT
ejpam-3884	36	32	s	s	PART
ejpam-3884	36	33	)	)	PUNCT
ejpam-3884	36	34	is	be	AUX
ejpam-3884	36	35	such	such	ADJ
ejpam-3884	36	36	that	that	SCONJ
ejpam-3884	36	37	n	n	NOUN
ejpam-3884	36	38	=	=	SYM
ejpam-3884	36	39	mh	mh	PROPN
ejpam-3884	36	40	and	and	CCONJ
ejpam-3884	36	41	s	s	PART
ejpam-3884	36	42	=	=	SYM
ejpam-3884	36	43	{	{	PUNCT
ejpam-3884	36	44	m0,m1	m0,m1	PROPN
ejpam-3884	36	45	,	,	PUNCT
ejpam-3884	36	46	.	.	PUNCT
ejpam-3884	36	47	.	.	PUNCT
ejpam-3884	37	1	.	.	PUNCT
ejpam-3884	38	1	,	,	PUNCT
ejpam-3884	38	2	mh−1	mh−1	NOUN
ejpam-3884	38	3	}	}	PUNCT
ejpam-3884	38	4	where	where	SCONJ
ejpam-3884	38	5	m	m	VERB
ejpam-3884	38	6	and	and	CCONJ
ejpam-3884	38	7	h	h	PROPN
ejpam-3884	38	8	are	be	AUX
ejpam-3884	38	9	integers	integer	NOUN
ejpam-3884	38	10	with	with	ADP
ejpam-3884	38	11	bounds	bound	NOUN
ejpam-3884	38	12	m	m	VERB
ejpam-3884	38	13	>	>	X
ejpam-3884	38	14	1	1	NUM
ejpam-3884	38	15	and	and	CCONJ
ejpam-3884	38	16	h	h	PROPN
ejpam-3884	38	17	≥	≥	PROPN
ejpam-3884	38	18	0	0	NUM
ejpam-3884	38	19	,	,	PUNCT
ejpam-3884	38	20	then	then	ADV
ejpam-3884	38	21	cay(zn	cay(zn	PROPN
ejpam-3884	38	22	,	,	PUNCT
ejpam-3884	38	23	s	s	PART
ejpam-3884	38	24	)	)	PUNCT
ejpam-3884	38	25	is	be	AUX
ejpam-3884	38	26	called	call	VERB
ejpam-3884	38	27	a	a	DET
ejpam-3884	38	28	multiplicative	multiplicative	ADJ
ejpam-3884	38	29	circulant	circulant	NOUN
ejpam-3884	38	30	graph	graph	NOUN
ejpam-3884	38	31	or	or	CCONJ
ejpam-3884	38	32	mc	mc	PROPN
ejpam-3884	38	33	graph	graph	NOUN
ejpam-3884	38	34	for	for	ADP
ejpam-3884	38	35	short	short	ADJ
ejpam-3884	38	36	.	.	PUNCT
ejpam-3884	39	1	mc	mc	PROPN
ejpam-3884	39	2	graphs	graph	NOUN
ejpam-3884	39	3	will	will	AUX
ejpam-3884	39	4	be	be	AUX
ejpam-3884	39	5	denoted	denote	VERB
ejpam-3884	39	6	by	by	ADP
ejpam-3884	39	7	mc(mh	mc(mh	PROPN
ejpam-3884	39	8	)	)	PUNCT
ejpam-3884	39	9	or	or	CCONJ
ejpam-3884	39	10	γ(m	γ(m	PROPN
ejpam-3884	39	11	h	h	PROPN
ejpam-3884	39	12	)	)	PUNCT
ejpam-3884	39	13	.	.	PUNCT
ejpam-3884	40	1	mc	mc	PROPN
ejpam-3884	40	2	graphs	graphs	PROPN
ejpam-3884	40	3	was	be	AUX
ejpam-3884	40	4	originally	originally	ADV
ejpam-3884	40	5	defined	define	VERB
ejpam-3884	40	6	by	by	ADP
ejpam-3884	40	7	stojmenovic	stojmenovic	NOUN
ejpam-3884	40	8	[	[	X
ejpam-3884	40	9	12	12	NUM
ejpam-3884	40	10	]	]	PUNCT
ejpam-3884	40	11	in	in	ADP
ejpam-3884	40	12	1997	1997	NUM
ejpam-3884	40	13	when	when	SCONJ
ejpam-3884	40	14	he	he	PRON
ejpam-3884	40	15	studied	study	VERB
ejpam-3884	40	16	a	a	DET
ejpam-3884	40	17	particular	particular	ADJ
ejpam-3884	40	18	class	class	NOUN
ejpam-3884	40	19	of	of	ADP
ejpam-3884	40	20	circulant	circulant	ADJ
ejpam-3884	40	21	graph	graph	NOUN
ejpam-3884	40	22	called	call	VERB
ejpam-3884	40	23	recursive	recursive	ADJ
ejpam-3884	40	24	circulant	circulant	NOUN
ejpam-3884	40	25	graph	graph	NOUN
ejpam-3884	40	26	or	or	CCONJ
ejpam-3884	40	27	rc	rc	PROPN
ejpam-3884	40	28	graph	graph	NOUN
ejpam-3884	40	29	that	that	PRON
ejpam-3884	40	30	was	be	AUX
ejpam-3884	40	31	introduced	introduce	VERB
ejpam-3884	40	32	by	by	ADP
ejpam-3884	40	33	park	park	NOUN
ejpam-3884	40	34	and	and	CCONJ
ejpam-3884	40	35	chwa	chwa	NOUN
ejpam-3884	41	1	[	[	X
ejpam-3884	41	2	11	11	NUM
ejpam-3884	41	3	]	]	PUNCT
ejpam-3884	41	4	in	in	ADP
ejpam-3884	41	5	1994	1994	NUM
ejpam-3884	41	6	.	.	PUNCT
ejpam-3884	42	1	both	both	DET
ejpam-3884	42	2	mc	mc	PROPN
ejpam-3884	42	3	and	and	CCONJ
ejpam-3884	42	4	rc	rc	PROPN
ejpam-3884	42	5	graphs	graph	NOUN
ejpam-3884	42	6	are	be	AUX
ejpam-3884	42	7	a	a	DET
ejpam-3884	42	8	special	special	ADJ
ejpam-3884	42	9	class	class	NOUN
ejpam-3884	42	10	of	of	ADP
ejpam-3884	42	11	generalized	generalized	ADJ
ejpam-3884	42	12	recursive	recursive	ADJ
ejpam-3884	42	13	circulant	circulant	NOUN
ejpam-3884	42	14	graph	graph	NOUN
ejpam-3884	42	15	or	or	CCONJ
ejpam-3884	42	16	grc	grc	NOUN
ejpam-3884	42	17	graph	graph	NOUN
ejpam-3884	42	18	defined	define	VERB
ejpam-3884	42	19	by	by	ADP
ejpam-3884	42	20	tang	tang	PROPN
ejpam-3884	42	21	et	et	PROPN
ejpam-3884	42	22	al	al	PROPN
ejpam-3884	42	23	.	.	PUNCT
ejpam-3884	43	1	[	[	X
ejpam-3884	43	2	14	14	NUM
ejpam-3884	43	3	]	]	PUNCT
ejpam-3884	43	4	in	in	ADP
ejpam-3884	43	5	2012	2012	NUM
ejpam-3884	43	6	.	.	PUNCT
ejpam-3884	44	1	in	in	ADP
ejpam-3884	44	2	particular	particular	ADJ
ejpam-3884	44	3	,	,	PUNCT
ejpam-3884	44	4	mc	mc	PROPN
ejpam-3884	44	5	graphs	graph	NOUN
ejpam-3884	44	6	are	be	AUX
ejpam-3884	44	7	grc	grc	NOUN
ejpam-3884	44	8	graphs	graph	NOUN
ejpam-3884	44	9	in	in	ADP
ejpam-3884	44	10	which	which	PRON
ejpam-3884	44	11	each	each	DET
ejpam-3884	44	12	dimensions	dimension	NOUN
ejpam-3884	44	13	have	have	VERB
ejpam-3884	44	14	identical	identical	ADJ
ejpam-3884	44	15	bases	basis	NOUN
ejpam-3884	44	16	.	.	PUNCT
ejpam-3884	45	1	figure	figure	NOUN
ejpam-3884	45	2	2	2	NUM
ejpam-3884	45	3	shows	show	VERB
ejpam-3884	45	4	some	some	DET
ejpam-3884	45	5	examples	example	NOUN
ejpam-3884	45	6	of	of	ADP
ejpam-3884	45	7	mc	mc	PROPN
ejpam-3884	45	8	graphs	graph	NOUN
ejpam-3884	45	9	.	.	PUNCT
ejpam-3884	46	1	figure	figure	VERB
ejpam-3884	46	2	2	2	NUM
ejpam-3884	46	3	:	:	PUNCT
ejpam-3884	46	4	the	the	DET
ejpam-3884	46	5	graphs	graph	NOUN
ejpam-3884	46	6	mc(52	mc(52	PROPN
ejpam-3884	46	7	)	)	PUNCT
ejpam-3884	46	8	,	,	PUNCT
ejpam-3884	46	9	mc(72	mc(72	PROPN
ejpam-3884	46	10	)	)	PUNCT
ejpam-3884	46	11	and	and	CCONJ
ejpam-3884	46	12	mc(73	mc(73	NOUN
ejpam-3884	46	13	)	)	PUNCT
ejpam-3884	46	14	mc	mc	PROPN
ejpam-3884	46	15	graphs	graph	NOUN
ejpam-3884	46	16	and	and	CCONJ
ejpam-3884	46	17	in	in	ADP
ejpam-3884	46	18	general	general	ADJ
ejpam-3884	46	19	circulant	circulant	ADJ
ejpam-3884	46	20	graphs	graph	NOUN
ejpam-3884	46	21	have	have	VERB
ejpam-3884	46	22	vast	vast	ADJ
ejpam-3884	46	23	applications	application	NOUN
ejpam-3884	46	24	in	in	ADP
ejpam-3884	46	25	different	different	ADJ
ejpam-3884	46	26	fields	field	NOUN
ejpam-3884	46	27	of	of	ADP
ejpam-3884	46	28	study	study	NOUN
ejpam-3884	46	29	;	;	PUNCT
ejpam-3884	46	30	some	some	PRON
ejpam-3884	46	31	of	of	ADP
ejpam-3884	46	32	these	these	DET
ejpam-3884	46	33	fields	field	NOUN
ejpam-3884	46	34	include	include	VERB
ejpam-3884	46	35	telecommunication	telecommunication	NOUN
ejpam-3884	46	36	networking	networking	NOUN
ejpam-3884	46	37	[	[	X
ejpam-3884	46	38	4	4	NUM
ejpam-3884	46	39	]	]	PUNCT
ejpam-3884	46	40	,	,	PUNCT
ejpam-3884	46	41	vlsi	vlsi	PROPN
ejpam-3884	46	42	(	(	PUNCT
ejpam-3884	46	43	very	very	ADV
ejpam-3884	46	44	-	-	PUNCT
ejpam-3884	46	45	largescale	largescale	ADJ
ejpam-3884	46	46	integration	integration	NOUN
ejpam-3884	46	47	)	)	PUNCT
ejpam-3884	46	48	design	design	NOUN
ejpam-3884	46	49	[	[	X
ejpam-3884	46	50	8	8	NUM
ejpam-3884	46	51	]	]	PUNCT
ejpam-3884	46	52	,	,	PUNCT
ejpam-3884	46	53	and	and	CCONJ
ejpam-3884	46	54	distributed	distribute	VERB
ejpam-3884	46	55	computing	computing	NOUN
ejpam-3884	47	1	[	[	X
ejpam-3884	47	2	10	10	NUM
ejpam-3884	47	3	]	]	PUNCT
ejpam-3884	47	4	.	.	PUNCT
ejpam-3884	48	1	in	in	ADP
ejpam-3884	48	2	the	the	DET
ejpam-3884	48	3	definition	definition	NOUN
ejpam-3884	48	4	of	of	ADP
ejpam-3884	48	5	multiplicative	multiplicative	ADJ
ejpam-3884	48	6	circulant	circulant	NOUN
ejpam-3884	48	7	graph	graph	NOUN
ejpam-3884	48	8	,	,	PUNCT
ejpam-3884	48	9	let	let	VERB
ejpam-3884	48	10	m	m	PRON
ejpam-3884	48	11	be	be	AUX
ejpam-3884	48	12	odd	odd	ADJ
ejpam-3884	48	13	.	.	PUNCT
ejpam-3884	49	1	the	the	DET
ejpam-3884	49	2	following	follow	VERB
ejpam-3884	49	3	are	be	AUX
ejpam-3884	49	4	important	important	ADJ
ejpam-3884	49	5	observable	observable	ADJ
ejpam-3884	49	6	properties	property	NOUN
ejpam-3884	49	7	of	of	ADP
ejpam-3884	49	8	γmh	γmh	NOUN
ejpam-3884	49	9	whose	whose	DET
ejpam-3884	49	10	proofs	proof	NOUN
ejpam-3884	49	11	follow	follow	VERB
ejpam-3884	49	12	from	from	ADP
ejpam-3884	49	13	the	the	DET
ejpam-3884	49	14	definition	definition	NOUN
ejpam-3884	49	15	of	of	ADP
ejpam-3884	49	16	mc	mc	PROPN
ejpam-3884	49	17	graph	graph	NOUN
ejpam-3884	49	18	and	and	CCONJ
ejpam-3884	49	19	the	the	DET
ejpam-3884	49	20	bfs	bfs	NOUN
ejpam-3884	49	21	method	method	NOUN
ejpam-3884	49	22	:	:	PUNCT
ejpam-3884	49	23	(	(	PUNCT
ejpam-3884	49	24	i	i	NOUN
ejpam-3884	49	25	)	)	PUNCT
ejpam-3884	49	26	dγ	dγ	ADP
ejpam-3884	49	27	mh	mh	PROPN
ejpam-3884	49	28	(	(	PUNCT
ejpam-3884	49	29	0	0	PROPN
ejpam-3884	49	30	,	,	PUNCT
ejpam-3884	49	31	i	i	NOUN
ejpam-3884	49	32	)	)	PUNCT
ejpam-3884	50	1	=	=	PUNCT
ejpam-3884	50	2	dγ	dγ	ADP
ejpam-3884	50	3	mh	mh	PROPN
ejpam-3884	50	4	(	(	PUNCT
ejpam-3884	50	5	0,mh	0,mh	PROPN
ejpam-3884	50	6	−	−	PROPN
ejpam-3884	50	7	i	i	NOUN
ejpam-3884	50	8	)	)	PUNCT
ejpam-3884	50	9	for	for	ADP
ejpam-3884	50	10	all	all	DET
ejpam-3884	50	11	non	non	ADJ
ejpam-3884	50	12	-	-	ADJ
ejpam-3884	50	13	zero	zero	NUM
ejpam-3884	50	14	i	i	NOUN
ejpam-3884	50	15	∈	∈	PROPN
ejpam-3884	50	16	v	v	ADP
ejpam-3884	50	17	(	(	PUNCT
ejpam-3884	50	18	γmh	γmh	NOUN
ejpam-3884	50	19	)	)	PUNCT
ejpam-3884	50	20	.	.	PUNCT
ejpam-3884	51	1	(	(	PUNCT
ejpam-3884	51	2	ii	ii	NOUN
ejpam-3884	51	3	)	)	PUNCT
ejpam-3884	51	4	let	let	VERB
ejpam-3884	51	5	a	a	DET
ejpam-3884	51	6	=	=	X
ejpam-3884	51	7	{	{	PUNCT
ejpam-3884	51	8	mh−1	mh−1	NOUN
ejpam-3884	51	9	−mh−2,mh−1	−mh−2,mh−1	PROPN
ejpam-3884	51	10	−mh−3	−mh−3	NUM
ejpam-3884	51	11	,	,	PUNCT
ejpam-3884	51	12	.	.	PUNCT
ejpam-3884	51	13	.	.	PUNCT
ejpam-3884	52	1	.	.	PUNCT
ejpam-3884	53	1	,	,	PUNCT
ejpam-3884	53	2	mh−1	mh−1	NOUN
ejpam-3884	53	3	−mh−h	−mh−h	NOUN
ejpam-3884	53	4	}	}	PUNCT
ejpam-3884	53	5	.	.	PUNCT
ejpam-3884	54	1	for	for	ADP
ejpam-3884	54	2	each	each	PRON
ejpam-3884	54	3	a	a	DET
ejpam-3884	54	4	∈	∈	PROPN
ejpam-3884	54	5	a	a	X
ejpam-3884	54	6	,	,	PUNCT
ejpam-3884	54	7	we	we	PRON
ejpam-3884	54	8	have	have	VERB
ejpam-3884	54	9	dγ	dγ	ADP
ejpam-3884	54	10	mh	mh	PROPN
ejpam-3884	54	11	(	(	PUNCT
ejpam-3884	54	12	0	0	NUM
ejpam-3884	54	13	,	,	PUNCT
ejpam-3884	54	14	a	a	PRON
ejpam-3884	54	15	)	)	PUNCT
ejpam-3884	55	1	=	=	NOUN
ejpam-3884	55	2	dγ	dγ	ADP
ejpam-3884	55	3	mh−1	mh−1	PROPN
ejpam-3884	55	4	(	(	PUNCT
ejpam-3884	55	5	0	0	NUM
ejpam-3884	55	6	,	,	PUNCT
ejpam-3884	55	7	a	a	NOUN
ejpam-3884	55	8	)	)	PUNCT
ejpam-3884	55	9	+	+	NOUN
ejpam-3884	55	10	1	1	X
ejpam-3884	55	11	.	.	X
ejpam-3884	55	12	(	(	PUNCT
ejpam-3884	55	13	iii	iii	X
ejpam-3884	55	14	)	)	PUNCT
ejpam-3884	55	15	γmh	γmh	NOUN
ejpam-3884	55	16	is	be	AUX
ejpam-3884	55	17	ancestor	ancestor	NOUN
ejpam-3884	55	18	-	-	PUNCT
ejpam-3884	55	19	preserving	preserve	VERB
ejpam-3884	55	20	for	for	ADP
ejpam-3884	55	21	parents	parent	NOUN
ejpam-3884	55	22	m0,m1	m0,m1	PROPN
ejpam-3884	55	23	,	,	PUNCT
ejpam-3884	55	24	.	.	PUNCT
ejpam-3884	55	25	.	.	PUNCT
ejpam-3884	55	26	.	.	PUNCT
ejpam-3884	56	1	,	,	PUNCT
ejpam-3884	56	2	mh−2	mh−2	NOUN
ejpam-3884	56	3	in	in	ADP
ejpam-3884	56	4	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	56	5	)	)	PUNCT
ejpam-3884	56	6	.	.	PUNCT
ejpam-3884	57	1	that	that	PRON
ejpam-3884	57	2	is	be	AUX
ejpam-3884	57	3	,	,	PUNCT
ejpam-3884	57	4	for	for	ADP
ejpam-3884	57	5	parents	parent	NOUN
ejpam-3884	57	6	m0,m1	m0,m1	PROPN
ejpam-3884	57	7	,	,	PUNCT
ejpam-3884	57	8	.	.	PUNCT
ejpam-3884	57	9	.	.	PUNCT
ejpam-3884	57	10	.	.	PUNCT
ejpam-3884	58	1	,	,	PUNCT
ejpam-3884	58	2	mh−2	mh−2	PROPN
ejpam-3884	58	3	,	,	PUNCT
ejpam-3884	58	4	the	the	DET
ejpam-3884	58	5	ancestor	ancestor	NOUN
ejpam-3884	58	6	-	-	PUNCT
ejpam-3884	58	7	descendant	descendant	ADJ
ejpam-3884	58	8	relationship	relationship	NOUN
ejpam-3884	58	9	is	be	AUX
ejpam-3884	58	10	the	the	DET
ejpam-3884	58	11	same	same	ADJ
ejpam-3884	58	12	for	for	ADP
ejpam-3884	58	13	bfs0(γmh−1	bfs0(γmh−1	PROPN
ejpam-3884	58	14	)	)	PUNCT
ejpam-3884	58	15	and	and	CCONJ
ejpam-3884	58	16	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	58	17	)	)	PUNCT
ejpam-3884	58	18	.	.	PUNCT
ejpam-3884	59	1	j.	j.	PROPN
ejpam-3884	59	2	antalan	antalan	PROPN
ejpam-3884	59	3	,	,	PUNCT
ejpam-3884	59	4	f.	f.	PROPN
ejpam-3884	59	5	campeña	campeña	PROPN
ejpam-3884	59	6	/	/	SYM
ejpam-3884	59	7	eur	eur	PROPN
ejpam-3884	59	8	.	.	PUNCT
ejpam-3884	60	1	j.	j.	PROPN
ejpam-3884	60	2	pure	pure	PROPN
ejpam-3884	60	3	appl	appl	PROPN
ejpam-3884	60	4	.	.	PROPN
ejpam-3884	60	5	math	math	PROPN
ejpam-3884	60	6	,	,	PUNCT
ejpam-3884	60	7	14	14	NUM
ejpam-3884	60	8	(	(	PUNCT
ejpam-3884	60	9	1	1	NUM
ejpam-3884	60	10	)	)	PUNCT
ejpam-3884	60	11	(	(	PUNCT
ejpam-3884	60	12	2021	2021	NUM
ejpam-3884	60	13	)	)	PUNCT
ejpam-3884	60	14	,	,	PUNCT
ejpam-3884	60	15	248	248	NUM
ejpam-3884	60	16	-	-	SYM
ejpam-3884	60	17	264	264	NUM
ejpam-3884	60	18	251	251	NUM
ejpam-3884	60	19	(	(	PUNCT
ejpam-3884	60	20	iv	iv	X
ejpam-3884	60	21	)	)	PUNCT
ejpam-3884	60	22	for	for	ADP
ejpam-3884	60	23	b	b	NOUN
ejpam-3884	60	24	=	=	SYM
ejpam-3884	60	25	1	1	NUM
ejpam-3884	60	26	,	,	PUNCT
ejpam-3884	60	27	2	2	NUM
ejpam-3884	60	28	,	,	PUNCT
ejpam-3884	60	29	.	.	PUNCT
ejpam-3884	60	30	.	.	PUNCT
ejpam-3884	61	1	.	.	PUNCT
ejpam-3884	62	1	,	,	PUNCT
ejpam-3884	62	2	m	m	VERB
ejpam-3884	62	3	h−1−1	h−1−1	ADJ
ejpam-3884	62	4	2	2	NUM
ejpam-3884	62	5	,	,	PUNCT
ejpam-3884	62	6	we	we	PRON
ejpam-3884	62	7	have	have	VERB
ejpam-3884	62	8	dγ	dγ	ADP
ejpam-3884	62	9	mh−1	mh−1	PROPN
ejpam-3884	62	10	(	(	PUNCT
ejpam-3884	62	11	0	0	NUM
ejpam-3884	62	12	,	,	PUNCT
ejpam-3884	62	13	b	b	NOUN
ejpam-3884	62	14	)	)	PUNCT
ejpam-3884	62	15	=	=	PUNCT
ejpam-3884	62	16	dγ	dγ	ADP
ejpam-3884	62	17	mh	mh	PROPN
ejpam-3884	62	18	(	(	PUNCT
ejpam-3884	62	19	mh−1,mh−1	mh−1,mh−1	PROPN
ejpam-3884	62	20	+	+	CCONJ
ejpam-3884	62	21	b	b	NOUN
ejpam-3884	62	22	)	)	PUNCT
ejpam-3884	62	23	.	.	PUNCT
ejpam-3884	63	1	(	(	PUNCT
ejpam-3884	63	2	v	v	NOUN
ejpam-3884	63	3	)	)	PUNCT
ejpam-3884	63	4	for	for	ADP
ejpam-3884	63	5	b	b	NOUN
ejpam-3884	63	6	=	=	SYM
ejpam-3884	63	7	1	1	NUM
ejpam-3884	63	8	,	,	PUNCT
ejpam-3884	63	9	2	2	NUM
ejpam-3884	63	10	,	,	PUNCT
ejpam-3884	63	11	.	.	PUNCT
ejpam-3884	63	12	.	.	PUNCT
ejpam-3884	63	13	.	.	PUNCT
ejpam-3884	64	1	,	,	PUNCT
ejpam-3884	64	2	m	m	VERB
ejpam-3884	64	3	h−1−1	h−1−1	ADJ
ejpam-3884	64	4	2	2	NUM
ejpam-3884	64	5	,	,	PUNCT
ejpam-3884	64	6	we	we	PRON
ejpam-3884	64	7	have	have	VERB
ejpam-3884	64	8	dγ	dγ	ADP
ejpam-3884	64	9	mh	mh	PROPN
ejpam-3884	64	10	(	(	PUNCT
ejpam-3884	64	11	mh−1,mh−1	mh−1,mh−1	PROPN
ejpam-3884	64	12	±	±	NUM
ejpam-3884	64	13	b	b	NOUN
ejpam-3884	64	14	)	)	PUNCT
ejpam-3884	64	15	=	=	PUNCT
ejpam-3884	64	16	dγ	dγ	ADP
ejpam-3884	64	17	mh	mh	PROPN
ejpam-3884	64	18	(	(	PUNCT
ejpam-3884	64	19	2(mh−1	2(mh−1	NUM
ejpam-3884	64	20	)	)	PUNCT
ejpam-3884	64	21	,	,	PUNCT
ejpam-3884	64	22	2(mh−1)±	2(mh−1)±	NUM
ejpam-3884	64	23	b	b	X
ejpam-3884	64	24	)	)	PUNCT
ejpam-3884	65	1	=	=	PUNCT
ejpam-3884	65	2	dγ	dγ	ADP
ejpam-3884	65	3	mh	mh	PROPN
ejpam-3884	65	4	(	(	PUNCT
ejpam-3884	65	5	3(mh−1	3(mh−1	PROPN
ejpam-3884	65	6	)	)	PUNCT
ejpam-3884	65	7	,	,	PUNCT
ejpam-3884	65	8	3(mh−1)±	3(mh−1)±	NUM
ejpam-3884	65	9	b	b	X
ejpam-3884	65	10	)	)	PUNCT
ejpam-3884	65	11	...	...	PUNCT
ejpam-3884	66	1	=	=	PUNCT
ejpam-3884	66	2	dγ	dγ	ADP
ejpam-3884	66	3	mh	mh	PROPN
ejpam-3884	66	4	(	(	PUNCT
ejpam-3884	66	5	m−	m−	PROPN
ejpam-3884	66	6	1	1	NUM
ejpam-3884	66	7	2	2	NUM
ejpam-3884	66	8	(	(	PUNCT
ejpam-3884	66	9	mh−1	mh−1	PROPN
ejpam-3884	66	10	)	)	PUNCT
ejpam-3884	66	11	,	,	PUNCT
ejpam-3884	66	12	m−	m−	PROPN
ejpam-3884	66	13	1	1	NUM
ejpam-3884	66	14	2	2	NUM
ejpam-3884	66	15	(	(	PUNCT
ejpam-3884	66	16	mh−1)±	mh−1)±	PROPN
ejpam-3884	66	17	b	b	PROPN
ejpam-3884	66	18	)	)	PUNCT
ejpam-3884	66	19	.	.	PUNCT
ejpam-3884	67	1	in	in	ADP
ejpam-3884	67	2	this	this	DET
ejpam-3884	67	3	paper	paper	NOUN
ejpam-3884	67	4	,	,	PUNCT
ejpam-3884	67	5	we	we	PRON
ejpam-3884	67	6	give	give	VERB
ejpam-3884	67	7	a	a	DET
ejpam-3884	67	8	recursive	recursive	ADJ
ejpam-3884	67	9	method	method	NOUN
ejpam-3884	67	10	on	on	ADP
ejpam-3884	67	11	constructing	construct	VERB
ejpam-3884	67	12	the	the	DET
ejpam-3884	67	13	bfs	bfs	NOUN
ejpam-3884	67	14	tree	tree	NOUN
ejpam-3884	67	15	for	for	ADP
ejpam-3884	67	16	γmh	γmh	NOUN
ejpam-3884	67	17	using	use	VERB
ejpam-3884	67	18	the	the	DET
ejpam-3884	67	19	listed	list	VERB
ejpam-3884	67	20	properties	property	NOUN
ejpam-3884	67	21	above	above	ADV
ejpam-3884	67	22	.	.	PUNCT
ejpam-3884	68	1	we	we	PRON
ejpam-3884	68	2	then	then	ADV
ejpam-3884	68	3	use	use	VERB
ejpam-3884	68	4	the	the	DET
ejpam-3884	68	5	construction	construction	NOUN
ejpam-3884	68	6	to	to	PART
ejpam-3884	68	7	reprove	reprove	VERB
ejpam-3884	68	8	some	some	DET
ejpam-3884	68	9	known	know	VERB
ejpam-3884	68	10	results	result	NOUN
ejpam-3884	68	11	about	about	ADP
ejpam-3884	68	12	γmh	γmh	PROPN
ejpam-3884	68	13	’s	’s	PART
ejpam-3884	68	14	diameter	diameter	NOUN
ejpam-3884	68	15	,	,	PUNCT
ejpam-3884	68	16	average	average	ADJ
ejpam-3884	68	17	distance	distance	NOUN
ejpam-3884	68	18	and	and	CCONJ
ejpam-3884	68	19	distance	distance	NOUN
ejpam-3884	68	20	spectral	spectral	ADJ
ejpam-3884	68	21	radius	radius	NOUN
ejpam-3884	68	22	.	.	PUNCT
ejpam-3884	69	1	we	we	PRON
ejpam-3884	69	2	also	also	ADV
ejpam-3884	69	3	determine	determine	VERB
ejpam-3884	69	4	the	the	DET
ejpam-3884	69	5	following	follow	VERB
ejpam-3884	69	6	graph	graph	NOUN
ejpam-3884	69	7	-	-	PUNCT
ejpam-3884	69	8	related	relate	VERB
ejpam-3884	69	9	properties	property	NOUN
ejpam-3884	69	10	for	for	ADP
ejpam-3884	69	11	γmh	γmh	NOUN
ejpam-3884	69	12	:	:	PUNCT
ejpam-3884	69	13	wiener	wiener	NOUN
ejpam-3884	69	14	index	index	NOUN
ejpam-3884	69	15	,	,	PUNCT
ejpam-3884	69	16	vertex	vertex	NOUN
ejpam-3884	69	17	-	-	PUNCT
ejpam-3884	69	18	forwarding	forward	VERB
ejpam-3884	69	19	index	index	NOUN
ejpam-3884	69	20	,	,	PUNCT
ejpam-3884	69	21	and	and	CCONJ
ejpam-3884	69	22	bounds	bound	VERB
ejpam-3884	69	23	for	for	ADP
ejpam-3884	69	24	its	its	PRON
ejpam-3884	69	25	edge	edge	NOUN
ejpam-3884	69	26	-	-	PUNCT
ejpam-3884	69	27	forwarding	forward	VERB
ejpam-3884	69	28	index	index	NOUN
ejpam-3884	69	29	.	.	PUNCT
ejpam-3884	70	1	finally	finally	ADV
ejpam-3884	70	2	,	,	PUNCT
ejpam-3884	70	3	we	we	PRON
ejpam-3884	70	4	discuss	discuss	VERB
ejpam-3884	70	5	some	some	DET
ejpam-3884	70	6	possible	possible	ADJ
ejpam-3884	70	7	research	research	NOUN
ejpam-3884	70	8	works	work	NOUN
ejpam-3884	70	9	in	in	ADP
ejpam-3884	70	10	which	which	PRON
ejpam-3884	70	11	the	the	DET
ejpam-3884	70	12	proposed	propose	VERB
ejpam-3884	70	13	construction	construction	NOUN
ejpam-3884	70	14	can	can	AUX
ejpam-3884	70	15	be	be	AUX
ejpam-3884	70	16	applied	apply	VERB
ejpam-3884	70	17	.	.	PUNCT
ejpam-3884	71	1	2	2	X
ejpam-3884	71	2	.	.	X
ejpam-3884	71	3	preliminaries	preliminary	NOUN
ejpam-3884	71	4	in	in	ADP
ejpam-3884	71	5	this	this	DET
ejpam-3884	71	6	section	section	NOUN
ejpam-3884	71	7	,	,	PUNCT
ejpam-3884	71	8	we	we	PRON
ejpam-3884	71	9	discuss	discuss	VERB
ejpam-3884	71	10	in	in	ADP
ejpam-3884	71	11	a	a	DET
ejpam-3884	71	12	brief	brief	NOUN
ejpam-3884	71	13	,	,	PUNCT
ejpam-3884	71	14	the	the	DET
ejpam-3884	71	15	necessary	necessary	ADJ
ejpam-3884	71	16	concepts	concept	NOUN
ejpam-3884	71	17	and	and	CCONJ
ejpam-3884	71	18	results	result	NOUN
ejpam-3884	71	19	that	that	PRON
ejpam-3884	71	20	will	will	AUX
ejpam-3884	71	21	be	be	AUX
ejpam-3884	71	22	used	use	VERB
ejpam-3884	71	23	in	in	ADP
ejpam-3884	71	24	the	the	DET
ejpam-3884	71	25	discussion	discussion	NOUN
ejpam-3884	71	26	of	of	ADP
ejpam-3884	71	27	our	our	PRON
ejpam-3884	71	28	main	main	ADJ
ejpam-3884	71	29	results	result	NOUN
ejpam-3884	71	30	.	.	PUNCT
ejpam-3884	72	1	the	the	DET
ejpam-3884	72	2	discussion	discussion	NOUN
ejpam-3884	72	3	includes	include	VERB
ejpam-3884	72	4	graphs	graph	NOUN
ejpam-3884	72	5	’	'	PUNCT
ejpam-3884	72	6	distance	distance	NOUN
ejpam-3884	72	7	matrix	matrix	NOUN
ejpam-3884	72	8	,	,	PUNCT
ejpam-3884	72	9	distance	distance	NOUN
ejpam-3884	72	10	spectral	spectral	ADJ
ejpam-3884	72	11	radius	radius	NOUN
ejpam-3884	72	12	,	,	PUNCT
ejpam-3884	72	13	vertex	vertex	NOUN
ejpam-3884	72	14	and	and	CCONJ
ejpam-3884	72	15	edge	edge	NOUN
ejpam-3884	72	16	forwarding	forwarding	NOUN
ejpam-3884	72	17	index	index	NOUN
ejpam-3884	72	18	,	,	PUNCT
ejpam-3884	72	19	and	and	CCONJ
ejpam-3884	72	20	wiener	wiener	NOUN
ejpam-3884	72	21	index	index	NOUN
ejpam-3884	72	22	.	.	PUNCT
ejpam-3884	73	1	in	in	ADP
ejpam-3884	73	2	the	the	DET
ejpam-3884	73	3	following	follow	VERB
ejpam-3884	73	4	definitions	definition	NOUN
ejpam-3884	73	5	and	and	CCONJ
ejpam-3884	73	6	discussion	discussion	NOUN
ejpam-3884	73	7	,	,	PUNCT
ejpam-3884	73	8	we	we	PRON
ejpam-3884	73	9	assume	assume	VERB
ejpam-3884	73	10	that	that	SCONJ
ejpam-3884	73	11	our	our	PRON
ejpam-3884	73	12	graph	graph	NOUN
ejpam-3884	73	13	γ	γ	X
ejpam-3884	73	14	is	be	AUX
ejpam-3884	73	15	of	of	ADP
ejpam-3884	73	16	n	n	PRON
ejpam-3884	73	17	number	number	NOUN
ejpam-3884	73	18	of	of	ADP
ejpam-3884	73	19	vertices	vertex	NOUN
ejpam-3884	73	20	.	.	PUNCT
ejpam-3884	74	1	we	we	PRON
ejpam-3884	74	2	begin	begin	VERB
ejpam-3884	74	3	by	by	ADP
ejpam-3884	74	4	defining	define	VERB
ejpam-3884	74	5	the	the	DET
ejpam-3884	74	6	concept	concept	NOUN
ejpam-3884	74	7	of	of	ADP
ejpam-3884	74	8	distance	distance	NOUN
ejpam-3884	74	9	matrix	matrix	NOUN
ejpam-3884	74	10	of	of	ADP
ejpam-3884	74	11	a	a	DET
ejpam-3884	74	12	graph	graph	NOUN
ejpam-3884	74	13	.	.	PUNCT
ejpam-3884	75	1	definition	definition	NOUN
ejpam-3884	75	2	1	1	NUM
ejpam-3884	75	3	.	.	PUNCT
ejpam-3884	76	1	the	the	DET
ejpam-3884	76	2	distance	distance	NOUN
ejpam-3884	76	3	matrix	matrix	NOUN
ejpam-3884	76	4	of	of	ADP
ejpam-3884	76	5	γ	γ	PRON
ejpam-3884	76	6	denoted	denote	VERB
ejpam-3884	76	7	by	by	ADP
ejpam-3884	76	8	d(γ	d(γ	NOUN
ejpam-3884	76	9	)	)	PUNCT
ejpam-3884	76	10	=	=	PUNCT
ejpam-3884	77	1	[	[	X
ejpam-3884	77	2	dij	dij	X
ejpam-3884	77	3	]	]	X
ejpam-3884	77	4	where	where	SCONJ
ejpam-3884	77	5	dij	dij	NOUN
ejpam-3884	77	6	=	=	SYM
ejpam-3884	77	7	{	{	PUNCT
ejpam-3884	77	8	dγ(vi	dγ(vi	PROPN
ejpam-3884	77	9	,	,	PUNCT
ejpam-3884	77	10	vj	vj	INTJ
ejpam-3884	77	11	)	)	PUNCT
ejpam-3884	77	12	if	if	SCONJ
ejpam-3884	77	13	vi	vi	PROPN
ejpam-3884	77	14	6=	6=	SYM
ejpam-3884	77	15	vj	vj	PROPN
ejpam-3884	77	16	0	0	NUM
ejpam-3884	77	17	otherwise	otherwise	ADV
ejpam-3884	77	18	.	.	PUNCT
ejpam-3884	78	1	remark	remark	PROPN
ejpam-3884	78	2	1	1	NUM
ejpam-3884	78	3	.	.	PUNCT
ejpam-3884	79	1	circulant	circulant	ADJ
ejpam-3884	79	2	graphs	graph	NOUN
ejpam-3884	79	3	have	have	VERB
ejpam-3884	79	4	circulant	circulant	ADJ
ejpam-3884	79	5	distance	distance	NOUN
ejpam-3884	79	6	matrix	matrix	NOUN
ejpam-3884	79	7	[	[	X
ejpam-3884	79	8	9	9	NUM
ejpam-3884	79	9	]	]	PUNCT
ejpam-3884	79	10	.	.	PUNCT
ejpam-3884	80	1	the	the	DET
ejpam-3884	80	2	next	next	ADJ
ejpam-3884	80	3	series	series	NOUN
ejpam-3884	80	4	of	of	ADP
ejpam-3884	80	5	graph	graph	NOUN
ejpam-3884	80	6	concepts	concept	NOUN
ejpam-3884	80	7	for	for	ADP
ejpam-3884	80	8	γ	γ	X
ejpam-3884	80	9	can	can	AUX
ejpam-3884	80	10	be	be	AUX
ejpam-3884	80	11	calculated	calculate	VERB
ejpam-3884	80	12	once	once	ADV
ejpam-3884	80	13	d(γ	d(γ	PROPN
ejpam-3884	80	14	)	)	PUNCT
ejpam-3884	80	15	is	be	AUX
ejpam-3884	80	16	known	know	VERB
ejpam-3884	80	17	.	.	PUNCT
ejpam-3884	81	1	definition	definition	NOUN
ejpam-3884	81	2	2	2	NUM
ejpam-3884	81	3	.	.	PUNCT
ejpam-3884	82	1	the	the	DET
ejpam-3884	82	2	diameter	diameter	NOUN
ejpam-3884	82	3	of	of	ADP
ejpam-3884	82	4	γ	γ	PROPN
ejpam-3884	82	5	,	,	PUNCT
ejpam-3884	82	6	denoted	denote	VERB
ejpam-3884	82	7	by	by	ADP
ejpam-3884	82	8	diam(γ	diam(γ	NOUN
ejpam-3884	82	9	)	)	PUNCT
ejpam-3884	82	10	,	,	PUNCT
ejpam-3884	82	11	is	be	AUX
ejpam-3884	82	12	the	the	DET
ejpam-3884	82	13	maximum	maximum	ADJ
ejpam-3884	82	14	distance	distance	NOUN
ejpam-3884	82	15	between	between	ADP
ejpam-3884	82	16	any	any	DET
ejpam-3884	82	17	pair	pair	NOUN
ejpam-3884	82	18	of	of	ADP
ejpam-3884	82	19	vertices	vertex	NOUN
ejpam-3884	82	20	in	in	ADP
ejpam-3884	82	21	γ	γ	PROPN
ejpam-3884	82	22	.	.	PROPN
ejpam-3884	82	23	remark	remark	PROPN
ejpam-3884	82	24	2	2	NUM
ejpam-3884	82	25	.	.	PUNCT
ejpam-3884	83	1	diam(γ	diam(γ	NOUN
ejpam-3884	83	2	)	)	PUNCT
ejpam-3884	83	3	is	be	AUX
ejpam-3884	83	4	the	the	DET
ejpam-3884	83	5	maximum	maximum	ADJ
ejpam-3884	83	6	entry	entry	NOUN
ejpam-3884	83	7	in	in	ADP
ejpam-3884	83	8	d(γ	d(γ	PROPN
ejpam-3884	83	9	)	)	PUNCT
ejpam-3884	83	10	.	.	PUNCT
ejpam-3884	84	1	definition	definition	NOUN
ejpam-3884	84	2	3	3	NUM
ejpam-3884	84	3	.	.	PUNCT
ejpam-3884	85	1	the	the	DET
ejpam-3884	85	2	transmission	transmission	NOUN
ejpam-3884	85	3	of	of	ADP
ejpam-3884	85	4	vi	vi	NOUN
ejpam-3884	85	5	in	in	ADP
ejpam-3884	85	6	γ	γ	NOUN
ejpam-3884	85	7	denoted	denote	VERB
ejpam-3884	85	8	by	by	ADP
ejpam-3884	85	9	trγ(vi	trγ(vi	NOUN
ejpam-3884	85	10	)	)	PUNCT
ejpam-3884	85	11	,	,	PUNCT
ejpam-3884	85	12	is	be	AUX
ejpam-3884	85	13	the	the	DET
ejpam-3884	85	14	sum	sum	NOUN
ejpam-3884	85	15	of	of	ADP
ejpam-3884	85	16	distances	distance	NOUN
ejpam-3884	85	17	from	from	ADP
ejpam-3884	85	18	vi	vi	PROPN
ejpam-3884	85	19	to	to	ADP
ejpam-3884	85	20	all	all	DET
ejpam-3884	85	21	other	other	ADJ
ejpam-3884	85	22	vertices	vertex	NOUN
ejpam-3884	85	23	of	of	ADP
ejpam-3884	85	24	γ	γ	NOUN
ejpam-3884	85	25	,	,	PUNCT
ejpam-3884	85	26	that	that	PRON
ejpam-3884	85	27	is	be	AUX
ejpam-3884	85	28	trγ(vi	trγ(vi	X
ejpam-3884	85	29	)	)	PUNCT
ejpam-3884	85	30	=	=	SYM
ejpam-3884	85	31	∑	∑	PUNCT
ejpam-3884	85	32	vj∈v	vj∈v	X
ejpam-3884	85	33	(	(	PUNCT
ejpam-3884	85	34	γ	γ	NOUN
ejpam-3884	85	35	)	)	PUNCT
ejpam-3884	85	36	dγ(vi	dγ(vi	PROPN
ejpam-3884	85	37	,	,	PUNCT
ejpam-3884	85	38	vj	vj	PROPN
ejpam-3884	85	39	)	)	PUNCT
ejpam-3884	85	40	.	.	PUNCT
ejpam-3884	86	1	j.	j.	PROPN
ejpam-3884	86	2	antalan	antalan	PROPN
ejpam-3884	86	3	,	,	PUNCT
ejpam-3884	86	4	f.	f.	PROPN
ejpam-3884	86	5	campeña	campeña	PROPN
ejpam-3884	86	6	/	/	SYM
ejpam-3884	86	7	eur	eur	PROPN
ejpam-3884	86	8	.	.	PUNCT
ejpam-3884	87	1	j.	j.	PROPN
ejpam-3884	87	2	pure	pure	PROPN
ejpam-3884	87	3	appl	appl	PROPN
ejpam-3884	87	4	.	.	PROPN
ejpam-3884	87	5	math	math	PROPN
ejpam-3884	87	6	,	,	PUNCT
ejpam-3884	87	7	14	14	NUM
ejpam-3884	87	8	(	(	PUNCT
ejpam-3884	87	9	1	1	NUM
ejpam-3884	87	10	)	)	PUNCT
ejpam-3884	87	11	(	(	PUNCT
ejpam-3884	87	12	2021	2021	NUM
ejpam-3884	87	13	)	)	PUNCT
ejpam-3884	87	14	,	,	PUNCT
ejpam-3884	87	15	248	248	NUM
ejpam-3884	87	16	-	-	SYM
ejpam-3884	87	17	264	264	NUM
ejpam-3884	87	18	252	252	NUM
ejpam-3884	87	19	remark	remark	NOUN
ejpam-3884	87	20	3	3	NUM
ejpam-3884	87	21	.	.	NOUN
ejpam-3884	87	22	trγ(vi	trγ(vi	NOUN
ejpam-3884	87	23	)	)	PUNCT
ejpam-3884	87	24	is	be	AUX
ejpam-3884	87	25	the	the	DET
ejpam-3884	87	26	sum	sum	NOUN
ejpam-3884	87	27	of	of	ADP
ejpam-3884	87	28	the	the	DET
ejpam-3884	87	29	entries	entry	NOUN
ejpam-3884	87	30	in	in	ADP
ejpam-3884	87	31	the	the	DET
ejpam-3884	87	32	ith	ith	NOUN
ejpam-3884	87	33	row	row	NOUN
ejpam-3884	87	34	of	of	ADP
ejpam-3884	87	35	d(γ	d(γ	PROPN
ejpam-3884	87	36	)	)	PUNCT
ejpam-3884	87	37	.	.	PUNCT
ejpam-3884	88	1	definition	definition	NOUN
ejpam-3884	88	2	4	4	NUM
ejpam-3884	88	3	.	.	PUNCT
ejpam-3884	89	1	the	the	DET
ejpam-3884	89	2	wiener	wiener	NOUN
ejpam-3884	89	3	index	index	NOUN
ejpam-3884	89	4	of	of	ADP
ejpam-3884	89	5	γ	γ	PROPN
ejpam-3884	89	6	denoted	denote	VERB
ejpam-3884	89	7	by	by	ADP
ejpam-3884	89	8	w	w	PROPN
ejpam-3884	89	9	(	(	PUNCT
ejpam-3884	89	10	γ	γ	X
ejpam-3884	89	11	)	)	PUNCT
ejpam-3884	89	12	is	be	AUX
ejpam-3884	89	13	defined	define	VERB
ejpam-3884	89	14	by	by	ADP
ejpam-3884	89	15	w	w	PROPN
ejpam-3884	89	16	(	(	PUNCT
ejpam-3884	89	17	γ	γ	NOUN
ejpam-3884	89	18	)	)	PUNCT
ejpam-3884	89	19	=	=	SYM
ejpam-3884	89	20	∑	∑	PROPN
ejpam-3884	89	21	{	{	PUNCT
ejpam-3884	89	22	vi	vi	PROPN
ejpam-3884	89	23	,	,	PUNCT
ejpam-3884	89	24	vj}⊆v	vj}⊆v	NOUN
ejpam-3884	89	25	(	(	PUNCT
ejpam-3884	89	26	γ	γ	NOUN
ejpam-3884	89	27	)	)	PUNCT
ejpam-3884	89	28	dγ(vi	dγ(vi	PROPN
ejpam-3884	89	29	,	,	PUNCT
ejpam-3884	89	30	vj	vj	NOUN
ejpam-3884	89	31	)	)	PUNCT
ejpam-3884	89	32	.	.	PUNCT
ejpam-3884	90	1	remark	remark	PROPN
ejpam-3884	90	2	4	4	NUM
ejpam-3884	90	3	.	.	PUNCT
ejpam-3884	91	1	w	w	PROPN
ejpam-3884	91	2	(	(	PUNCT
ejpam-3884	91	3	γ	γ	X
ejpam-3884	91	4	)	)	PUNCT
ejpam-3884	91	5	is	be	AUX
ejpam-3884	91	6	the	the	DET
ejpam-3884	91	7	sum	sum	NOUN
ejpam-3884	91	8	of	of	ADP
ejpam-3884	91	9	all	all	DET
ejpam-3884	91	10	the	the	DET
ejpam-3884	91	11	entries	entry	NOUN
ejpam-3884	91	12	in	in	ADP
ejpam-3884	91	13	d(γ	d(γ	PROPN
ejpam-3884	91	14	)	)	PUNCT
ejpam-3884	91	15	divided	divide	VERB
ejpam-3884	91	16	by	by	ADP
ejpam-3884	91	17	2	2	NUM
ejpam-3884	91	18	.	.	PUNCT
ejpam-3884	91	19	definition	definition	NOUN
ejpam-3884	91	20	5	5	NUM
ejpam-3884	91	21	.	.	PUNCT
ejpam-3884	92	1	the	the	DET
ejpam-3884	92	2	average	average	ADJ
ejpam-3884	92	3	distance	distance	NOUN
ejpam-3884	92	4	of	of	ADP
ejpam-3884	92	5	γ	γ	PRON
ejpam-3884	92	6	denoted	denote	VERB
ejpam-3884	92	7	by	by	ADP
ejpam-3884	92	8	µ(γ	µ(γ	NOUN
ejpam-3884	92	9	)	)	PUNCT
ejpam-3884	92	10	is	be	AUX
ejpam-3884	92	11	the	the	DET
ejpam-3884	92	12	average	average	NOUN
ejpam-3884	92	13	of	of	ADP
ejpam-3884	92	14	all	all	DET
ejpam-3884	92	15	distances	distance	NOUN
ejpam-3884	92	16	in	in	ADP
ejpam-3884	92	17	γ	γ	PROPN
ejpam-3884	92	18	.	.	PROPN
ejpam-3884	92	19	in	in	ADP
ejpam-3884	92	20	symbol	symbol	NOUN
ejpam-3884	92	21	µ(γ	µ(γ	NOUN
ejpam-3884	92	22	)	)	PUNCT
ejpam-3884	92	23	=	=	PUNCT
ejpam-3884	92	24	∑	∑	PUNCT
ejpam-3884	92	25	{	{	PUNCT
ejpam-3884	92	26	vi	vi	PROPN
ejpam-3884	92	27	,	,	PUNCT
ejpam-3884	92	28	vj}⊆v	vj}⊆v	NOUN
ejpam-3884	92	29	(	(	PUNCT
ejpam-3884	92	30	γ	γ	NOUN
ejpam-3884	92	31	)	)	PUNCT
ejpam-3884	92	32	dγ(vi	dγ(vi	PROPN
ejpam-3884	92	33	,	,	PUNCT
ejpam-3884	92	34	vj	vj	NOUN
ejpam-3884	92	35	)	)	PUNCT
ejpam-3884	92	36	(	(	PUNCT
ejpam-3884	92	37	n	n	PROPN
ejpam-3884	92	38	2	2	NUM
ejpam-3884	92	39	)	)	PUNCT
ejpam-3884	92	40	.	.	PUNCT
ejpam-3884	93	1	remark	remark	VERB
ejpam-3884	93	2	5	5	NUM
ejpam-3884	93	3	.	.	PUNCT
ejpam-3884	93	4	µ(γ	µ(γ	ADV
ejpam-3884	93	5	)	)	PUNCT
ejpam-3884	94	1	=	=	SYM
ejpam-3884	94	2	w	w	PROPN
ejpam-3884	94	3	(	(	PUNCT
ejpam-3884	94	4	γ	γ	X
ejpam-3884	94	5	)	)	PUNCT
ejpam-3884	94	6	(	(	PUNCT
ejpam-3884	94	7	n	n	PRON
ejpam-3884	94	8	2	2	NUM
ejpam-3884	94	9	)	)	PUNCT
ejpam-3884	94	10	.	.	PUNCT
ejpam-3884	95	1	definition	definition	NOUN
ejpam-3884	95	2	6	6	NUM
ejpam-3884	95	3	.	.	PUNCT
ejpam-3884	96	1	the	the	DET
ejpam-3884	96	2	largest	large	ADJ
ejpam-3884	96	3	eigenvalue	eigenvalue	NOUN
ejpam-3884	96	4	of	of	ADP
ejpam-3884	96	5	the	the	DET
ejpam-3884	96	6	distance	distance	NOUN
ejpam-3884	96	7	matrix	matrix	NOUN
ejpam-3884	96	8	of	of	ADP
ejpam-3884	96	9	γ	γ	PROPN
ejpam-3884	96	10	is	be	AUX
ejpam-3884	96	11	called	call	VERB
ejpam-3884	96	12	the	the	DET
ejpam-3884	96	13	distance	distance	NOUN
ejpam-3884	96	14	spectral	spectral	ADJ
ejpam-3884	96	15	radius	radius	NOUN
ejpam-3884	96	16	of	of	ADP
ejpam-3884	96	17	γ	γ	PROPN
ejpam-3884	96	18	and	and	CCONJ
ejpam-3884	96	19	is	be	AUX
ejpam-3884	96	20	denoted	denote	VERB
ejpam-3884	96	21	by	by	ADP
ejpam-3884	96	22	ρ(γ	ρ(γ	NOUN
ejpam-3884	96	23	)	)	PUNCT
ejpam-3884	96	24	.	.	PUNCT
ejpam-3884	97	1	in	in	ADP
ejpam-3884	97	2	terms	term	NOUN
ejpam-3884	97	3	of	of	ADP
ejpam-3884	97	4	vertex	vertex	NOUN
ejpam-3884	97	5	transmission	transmission	NOUN
ejpam-3884	97	6	,	,	PUNCT
ejpam-3884	97	7	a	a	DET
ejpam-3884	97	8	special	special	ADJ
ejpam-3884	97	9	name	name	NOUN
ejpam-3884	97	10	for	for	ADP
ejpam-3884	97	11	a	a	DET
ejpam-3884	97	12	graph	graph	NOUN
ejpam-3884	97	13	γ	γ	X
ejpam-3884	97	14	with	with	ADP
ejpam-3884	97	15	uniform	uniform	ADJ
ejpam-3884	97	16	vertex	vertex	NOUN
ejpam-3884	97	17	transmission	transmission	NOUN
ejpam-3884	97	18	is	be	AUX
ejpam-3884	97	19	given	give	VERB
ejpam-3884	97	20	in	in	ADP
ejpam-3884	97	21	the	the	DET
ejpam-3884	97	22	next	next	ADJ
ejpam-3884	97	23	definition	definition	NOUN
ejpam-3884	97	24	.	.	PUNCT
ejpam-3884	98	1	definition	definition	NOUN
ejpam-3884	98	2	7	7	NUM
ejpam-3884	98	3	.	.	PUNCT
ejpam-3884	99	1	a	a	DET
ejpam-3884	99	2	graph	graph	NOUN
ejpam-3884	99	3	γ	γ	PROPN
ejpam-3884	99	4	is	be	AUX
ejpam-3884	99	5	said	say	VERB
ejpam-3884	99	6	to	to	PART
ejpam-3884	99	7	be	be	AUX
ejpam-3884	99	8	s	s	NOUN
ejpam-3884	99	9	-	-	PUNCT
ejpam-3884	99	10	transmission	transmission	NOUN
ejpam-3884	99	11	regular	regular	ADJ
ejpam-3884	99	12	if	if	SCONJ
ejpam-3884	99	13	trγ(vi	trγ(vi	NOUN
ejpam-3884	99	14	)	)	PUNCT
ejpam-3884	99	15	=	=	SYM
ejpam-3884	99	16	s	s	PROPN
ejpam-3884	99	17	for	for	ADP
ejpam-3884	99	18	every	every	DET
ejpam-3884	99	19	vi	vi	PROPN
ejpam-3884	99	20	∈	∈	PROPN
ejpam-3884	99	21	v	v	NOUN
ejpam-3884	99	22	(	(	PUNCT
ejpam-3884	99	23	γ	γ	NOUN
ejpam-3884	99	24	)	)	PUNCT
ejpam-3884	99	25	.	.	PUNCT
ejpam-3884	100	1	remark	remark	PROPN
ejpam-3884	100	2	6	6	NUM
ejpam-3884	100	3	.	.	PUNCT
ejpam-3884	101	1	since	since	SCONJ
ejpam-3884	101	2	the	the	DET
ejpam-3884	101	3	distance	distance	NOUN
ejpam-3884	101	4	matrix	matrix	NOUN
ejpam-3884	101	5	of	of	ADP
ejpam-3884	101	6	a	a	DET
ejpam-3884	101	7	circulant	circulant	ADJ
ejpam-3884	101	8	graph	graph	NOUN
ejpam-3884	101	9	is	be	AUX
ejpam-3884	101	10	circulant	circulant	ADJ
ejpam-3884	101	11	,	,	PUNCT
ejpam-3884	101	12	it	it	PRON
ejpam-3884	101	13	follows	follow	VERB
ejpam-3884	101	14	that	that	SCONJ
ejpam-3884	101	15	circulant	circulant	ADJ
ejpam-3884	101	16	graphs	graph	NOUN
ejpam-3884	101	17	are	be	AUX
ejpam-3884	101	18	transmission	transmission	NOUN
ejpam-3884	101	19	regular	regular	ADJ
ejpam-3884	101	20	graphs	graph	NOUN
ejpam-3884	101	21	with	with	ADP
ejpam-3884	101	22	transmission	transmission	NOUN
ejpam-3884	101	23	-	-	PUNCT
ejpam-3884	101	24	regularity	regularity	NOUN
ejpam-3884	101	25	trγ(v0	trγ(v0	VERB
ejpam-3884	101	26	)	)	PUNCT
ejpam-3884	101	27	.	.	PUNCT
ejpam-3884	102	1	for	for	ADP
ejpam-3884	102	2	transmission	transmission	NOUN
ejpam-3884	102	3	regular	regular	ADJ
ejpam-3884	102	4	graphs	graph	NOUN
ejpam-3884	102	5	such	such	ADJ
ejpam-3884	102	6	as	as	ADP
ejpam-3884	102	7	circulant	circulant	ADJ
ejpam-3884	102	8	graphs	graph	NOUN
ejpam-3884	102	9	,	,	PUNCT
ejpam-3884	102	10	the	the	DET
ejpam-3884	102	11	calculation	calculation	NOUN
ejpam-3884	102	12	of	of	ADP
ejpam-3884	102	13	distance	distance	NOUN
ejpam-3884	102	14	spectral	spectral	ADJ
ejpam-3884	102	15	radius	radius	NOUN
ejpam-3884	102	16	is	be	AUX
ejpam-3884	102	17	simpler	simple	ADJ
ejpam-3884	102	18	.	.	PUNCT
ejpam-3884	103	1	lemma	lemma	PROPN
ejpam-3884	103	2	1	1	NUM
ejpam-3884	103	3	(	(	PUNCT
ejpam-3884	103	4	[	[	X
ejpam-3884	103	5	9	9	NUM
ejpam-3884	103	6	]	]	PUNCT
ejpam-3884	103	7	)	)	PUNCT
ejpam-3884	103	8	.	.	PUNCT
ejpam-3884	104	1	let	let	VERB
ejpam-3884	104	2	γ	γ	NOUN
ejpam-3884	104	3	be	be	AUX
ejpam-3884	104	4	a	a	DET
ejpam-3884	104	5	circulant	circulant	ADJ
ejpam-3884	104	6	graph	graph	NOUN
ejpam-3884	104	7	.	.	PUNCT
ejpam-3884	105	1	then	then	ADV
ejpam-3884	105	2	ρ(γ	ρ(γ	NOUN
ejpam-3884	105	3	)	)	PUNCT
ejpam-3884	105	4	=	=	SYM
ejpam-3884	105	5	trγ(v0	trγ(v0	VERB
ejpam-3884	105	6	)	)	PUNCT
ejpam-3884	105	7	.	.	PUNCT
ejpam-3884	106	1	we	we	PRON
ejpam-3884	106	2	now	now	ADV
ejpam-3884	106	3	define	define	VERB
ejpam-3884	106	4	the	the	DET
ejpam-3884	106	5	concept	concept	NOUN
ejpam-3884	106	6	of	of	ADP
ejpam-3884	106	7	graph	graph	NOUN
ejpam-3884	106	8	’s	’s	PART
ejpam-3884	106	9	vertex	vertex	NOUN
ejpam-3884	106	10	and	and	CCONJ
ejpam-3884	106	11	edge	edge	NOUN
ejpam-3884	106	12	forwarding	forwarding	NOUN
ejpam-3884	106	13	index	index	NOUN
ejpam-3884	106	14	.	.	PUNCT
ejpam-3884	107	1	to	to	PART
ejpam-3884	107	2	define	define	VERB
ejpam-3884	107	3	them	they	PRON
ejpam-3884	107	4	we	we	PRON
ejpam-3884	107	5	need	need	VERB
ejpam-3884	107	6	to	to	PART
ejpam-3884	107	7	define	define	VERB
ejpam-3884	107	8	a	a	DET
ejpam-3884	107	9	series	series	NOUN
ejpam-3884	107	10	of	of	ADP
ejpam-3884	107	11	interrelated	interrelated	ADJ
ejpam-3884	107	12	concepts	concept	NOUN
ejpam-3884	107	13	.	.	PUNCT
ejpam-3884	108	1	definition	definition	NOUN
ejpam-3884	108	2	8	8	NUM
ejpam-3884	108	3	.	.	PUNCT
ejpam-3884	109	1	a	a	DET
ejpam-3884	109	2	routing	routing	NOUN
ejpam-3884	109	3	r	r	NOUN
ejpam-3884	109	4	of	of	ADP
ejpam-3884	109	5	γ	γ	PROPN
ejpam-3884	109	6	is	be	AUX
ejpam-3884	109	7	a	a	DET
ejpam-3884	109	8	set	set	NOUN
ejpam-3884	109	9	of	of	ADP
ejpam-3884	109	10	n(n−	n(n−	PROPN
ejpam-3884	109	11	1	1	NUM
ejpam-3884	109	12	)	)	PUNCT
ejpam-3884	109	13	elementary	elementary	ADJ
ejpam-3884	109	14	paths	path	NOUN
ejpam-3884	109	15	(	(	PUNCT
ejpam-3884	109	16	i.e.	i.e.	X
ejpam-3884	109	17	paths	path	NOUN
ejpam-3884	109	18	where	where	SCONJ
ejpam-3884	109	19	no	no	DET
ejpam-3884	109	20	vertices	vertex	NOUN
ejpam-3884	109	21	appear	appear	VERB
ejpam-3884	109	22	more	more	ADV
ejpam-3884	109	23	than	than	ADP
ejpam-3884	109	24	once	once	ADV
ejpam-3884	109	25	)	)	PUNCT
ejpam-3884	109	26	r(x	r(x	PROPN
ejpam-3884	109	27	,	,	PUNCT
ejpam-3884	109	28	y	y	NOUN
ejpam-3884	109	29	)	)	PUNCT
ejpam-3884	109	30	specified	specify	VERB
ejpam-3884	109	31	for	for	ADP
ejpam-3884	109	32	all	all	DET
ejpam-3884	109	33	ordered	order	VERB
ejpam-3884	109	34	pairs	pair	NOUN
ejpam-3884	109	35	(	(	PUNCT
ejpam-3884	109	36	x	x	NOUN
ejpam-3884	109	37	,	,	PUNCT
ejpam-3884	109	38	y	y	NOUN
ejpam-3884	109	39	)	)	PUNCT
ejpam-3884	109	40	of	of	ADP
ejpam-3884	109	41	vertices	vertex	NOUN
ejpam-3884	109	42	of	of	ADP
ejpam-3884	109	43	γ	γ	PROPN
ejpam-3884	109	44	.	.	PROPN
ejpam-3884	109	45	remark	remark	PROPN
ejpam-3884	109	46	7	7	NUM
ejpam-3884	109	47	.	.	PUNCT
ejpam-3884	110	1	the	the	DET
ejpam-3884	110	2	set	set	NOUN
ejpam-3884	110	3	of	of	ADP
ejpam-3884	110	4	all	all	DET
ejpam-3884	110	5	possible	possible	ADJ
ejpam-3884	110	6	routing	routing	NOUN
ejpam-3884	110	7	in	in	ADP
ejpam-3884	110	8	a	a	DET
ejpam-3884	110	9	graph	graph	NOUN
ejpam-3884	110	10	γ	γ	X
ejpam-3884	110	11	is	be	AUX
ejpam-3884	110	12	denoted	denote	VERB
ejpam-3884	110	13	by	by	ADP
ejpam-3884	110	14	r(γ	r(γ	NOUN
ejpam-3884	110	15	)	)	PUNCT
ejpam-3884	110	16	.	.	PUNCT
ejpam-3884	111	1	for	for	ADP
ejpam-3884	111	2	vertex	vertex	NOUN
ejpam-3884	111	3	-	-	PUNCT
ejpam-3884	111	4	forwarding	forward	VERB
ejpam-3884	111	5	index	index	NOUN
ejpam-3884	111	6	we	we	PRON
ejpam-3884	111	7	have	have	VERB
ejpam-3884	111	8	definition	definition	NOUN
ejpam-3884	111	9	9	9	NUM
ejpam-3884	111	10	.	.	PUNCT
ejpam-3884	112	1	let	let	VERB
ejpam-3884	112	2	r	r	NOUN
ejpam-3884	112	3	∈	∈	PROPN
ejpam-3884	112	4	r(γ	r(γ	NOUN
ejpam-3884	112	5	)	)	PUNCT
ejpam-3884	112	6	and	and	CCONJ
ejpam-3884	112	7	x	x	PUNCT
ejpam-3884	112	8	∈	∈	NOUN
ejpam-3884	112	9	v	v	NOUN
ejpam-3884	112	10	(	(	PUNCT
ejpam-3884	112	11	γ	γ	NOUN
ejpam-3884	112	12	)	)	PUNCT
ejpam-3884	112	13	.	.	PUNCT
ejpam-3884	113	1	the	the	DET
ejpam-3884	113	2	load	load	NOUN
ejpam-3884	113	3	of	of	ADP
ejpam-3884	113	4	a	a	DET
ejpam-3884	113	5	vertex	vertex	NOUN
ejpam-3884	113	6	x	x	PUNCT
ejpam-3884	113	7	in	in	ADP
ejpam-3884	113	8	r	r	NOUN
ejpam-3884	113	9	of	of	ADP
ejpam-3884	113	10	γ	γ	NOUN
ejpam-3884	113	11	denoted	denote	VERB
ejpam-3884	113	12	by	by	ADP
ejpam-3884	113	13	ξx(γ	ξx(γ	NOUN
ejpam-3884	113	14	,	,	PUNCT
ejpam-3884	113	15	r	r	NOUN
ejpam-3884	113	16	)	)	PUNCT
ejpam-3884	113	17	is	be	AUX
ejpam-3884	113	18	the	the	DET
ejpam-3884	113	19	number	number	NOUN
ejpam-3884	113	20	of	of	ADP
ejpam-3884	113	21	paths	path	NOUN
ejpam-3884	113	22	specified	specify	VERB
ejpam-3884	113	23	by	by	ADP
ejpam-3884	113	24	r	r	NOUN
ejpam-3884	113	25	passing	pass	VERB
ejpam-3884	113	26	through	through	ADP
ejpam-3884	113	27	x	x	PUNCT
ejpam-3884	113	28	and	and	CCONJ
ejpam-3884	113	29	admitting	admit	VERB
ejpam-3884	113	30	x	x	PRON
ejpam-3884	113	31	as	as	ADP
ejpam-3884	113	32	an	an	DET
ejpam-3884	113	33	inner	inner	ADJ
ejpam-3884	113	34	vertex	vertex	NOUN
ejpam-3884	113	35	.	.	PUNCT
ejpam-3884	114	1	j.	j.	PROPN
ejpam-3884	114	2	antalan	antalan	PROPN
ejpam-3884	114	3	,	,	PUNCT
ejpam-3884	114	4	f.	f.	PROPN
ejpam-3884	114	5	campeña	campeña	PROPN
ejpam-3884	114	6	/	/	SYM
ejpam-3884	114	7	eur	eur	PROPN
ejpam-3884	114	8	.	.	PUNCT
ejpam-3884	115	1	j.	j.	PROPN
ejpam-3884	115	2	pure	pure	PROPN
ejpam-3884	115	3	appl	appl	PROPN
ejpam-3884	115	4	.	.	PROPN
ejpam-3884	115	5	math	math	PROPN
ejpam-3884	115	6	,	,	PUNCT
ejpam-3884	115	7	14	14	NUM
ejpam-3884	115	8	(	(	PUNCT
ejpam-3884	115	9	1	1	NUM
ejpam-3884	115	10	)	)	PUNCT
ejpam-3884	115	11	(	(	PUNCT
ejpam-3884	115	12	2021	2021	NUM
ejpam-3884	115	13	)	)	PUNCT
ejpam-3884	115	14	,	,	PUNCT
ejpam-3884	115	15	248	248	NUM
ejpam-3884	115	16	-	-	SYM
ejpam-3884	115	17	264	264	NUM
ejpam-3884	115	18	253	253	NUM
ejpam-3884	115	19	definition	definition	NOUN
ejpam-3884	115	20	10	10	NUM
ejpam-3884	115	21	.	.	PUNCT
ejpam-3884	116	1	the	the	DET
ejpam-3884	116	2	vertex	vertex	NOUN
ejpam-3884	116	3	-	-	PUNCT
ejpam-3884	116	4	forwarding	forward	VERB
ejpam-3884	116	5	index	index	NOUN
ejpam-3884	116	6	of	of	ADP
ejpam-3884	116	7	γ	γ	NOUN
ejpam-3884	116	8	with	with	ADP
ejpam-3884	116	9	respect	respect	NOUN
ejpam-3884	116	10	to	to	ADP
ejpam-3884	116	11	a	a	DET
ejpam-3884	116	12	routing	routing	NOUN
ejpam-3884	116	13	r	r	NOUN
ejpam-3884	116	14	,	,	PUNCT
ejpam-3884	116	15	denoted	denote	VERB
ejpam-3884	116	16	by	by	ADP
ejpam-3884	116	17	ξ(γ	ξ(γ	PROPN
ejpam-3884	116	18	,	,	PUNCT
ejpam-3884	116	19	r	r	NOUN
ejpam-3884	116	20	)	)	PUNCT
ejpam-3884	116	21	is	be	AUX
ejpam-3884	116	22	the	the	DET
ejpam-3884	116	23	maximum	maximum	ADJ
ejpam-3884	116	24	number	number	NOUN
ejpam-3884	116	25	of	of	ADP
ejpam-3884	116	26	paths	path	NOUN
ejpam-3884	116	27	of	of	ADP
ejpam-3884	116	28	r	r	NOUN
ejpam-3884	116	29	going	go	VERB
ejpam-3884	116	30	through	through	ADP
ejpam-3884	116	31	any	any	DET
ejpam-3884	116	32	vertex	vertex	NOUN
ejpam-3884	116	33	x	x	PUNCT
ejpam-3884	116	34	in	in	ADP
ejpam-3884	116	35	γ	γ	X
ejpam-3884	116	36	.	.	PROPN
ejpam-3884	116	37	hence	hence	ADV
ejpam-3884	116	38	ξ(γ	ξ(γ	PROPN
ejpam-3884	116	39	,	,	PUNCT
ejpam-3884	116	40	r	r	NOUN
ejpam-3884	116	41	)	)	PUNCT
ejpam-3884	116	42	=	=	PUNCT
ejpam-3884	116	43	max{ξx(γ	max{ξx(γ	PROPN
ejpam-3884	116	44	,	,	PUNCT
ejpam-3884	116	45	r	r	NOUN
ejpam-3884	116	46	)	)	PUNCT
ejpam-3884	116	47	:	:	PUNCT
ejpam-3884	116	48	x	x	X
ejpam-3884	116	49	∈	∈	NOUN
ejpam-3884	116	50	v	v	ADP
ejpam-3884	116	51	(	(	PUNCT
ejpam-3884	116	52	γ	γ	NOUN
ejpam-3884	116	53	)	)	PUNCT
ejpam-3884	116	54	}	}	PUNCT
ejpam-3884	116	55	.	.	PUNCT
ejpam-3884	117	1	definition	definition	NOUN
ejpam-3884	117	2	11	11	NUM
ejpam-3884	117	3	.	.	PUNCT
ejpam-3884	118	1	the	the	DET
ejpam-3884	118	2	vertex	vertex	NOUN
ejpam-3884	118	3	-	-	PUNCT
ejpam-3884	118	4	forwarding	forward	VERB
ejpam-3884	118	5	index	index	NOUN
ejpam-3884	118	6	of	of	ADP
ejpam-3884	118	7	γ	γ	PROPN
ejpam-3884	118	8	,	,	PUNCT
ejpam-3884	118	9	denoted	denote	VERB
ejpam-3884	118	10	by	by	ADP
ejpam-3884	118	11	ξ(γ	ξ(γ	PROPN
ejpam-3884	118	12	)	)	PUNCT
ejpam-3884	118	13	is	be	AUX
ejpam-3884	118	14	the	the	DET
ejpam-3884	118	15	minimum	minimum	ADJ
ejpam-3884	118	16	forwarding	forwarding	NOUN
ejpam-3884	118	17	index	index	NOUN
ejpam-3884	118	18	over	over	ADP
ejpam-3884	118	19	all	all	DET
ejpam-3884	118	20	possible	possible	ADJ
ejpam-3884	118	21	routing	routing	NOUN
ejpam-3884	118	22	of	of	ADP
ejpam-3884	118	23	γ	γ	PROPN
ejpam-3884	118	24	.	.	PROPN
ejpam-3884	118	25	in	in	ADP
ejpam-3884	118	26	symbol	symbol	NOUN
ejpam-3884	118	27	,	,	PUNCT
ejpam-3884	118	28	ξ(γ	ξ(γ	PROPN
ejpam-3884	118	29	)	)	PUNCT
ejpam-3884	118	30	=	=	SYM
ejpam-3884	118	31	min{ξ(γ	min{ξ(γ	NOUN
ejpam-3884	118	32	,	,	PUNCT
ejpam-3884	118	33	r	r	NOUN
ejpam-3884	118	34	)	)	PUNCT
ejpam-3884	118	35	:	:	PUNCT
ejpam-3884	118	36	r	r	NOUN
ejpam-3884	118	37	∈	∈	PROPN
ejpam-3884	118	38	r(γ	r(γ	NOUN
ejpam-3884	118	39	)	)	PUNCT
ejpam-3884	118	40	}	}	PUNCT
ejpam-3884	118	41	.	.	PUNCT
ejpam-3884	119	1	for	for	ADP
ejpam-3884	119	2	edge	edge	NOUN
ejpam-3884	119	3	-	-	PUNCT
ejpam-3884	119	4	forwarding	forward	VERB
ejpam-3884	119	5	index	index	NOUN
ejpam-3884	119	6	we	we	PRON
ejpam-3884	119	7	have	have	VERB
ejpam-3884	119	8	definition	definition	NOUN
ejpam-3884	119	9	12	12	NUM
ejpam-3884	119	10	.	.	PUNCT
ejpam-3884	120	1	the	the	DET
ejpam-3884	120	2	load	load	NOUN
ejpam-3884	120	3	of	of	ADP
ejpam-3884	120	4	an	an	DET
ejpam-3884	120	5	edge	edge	NOUN
ejpam-3884	120	6	e	e	NOUN
ejpam-3884	120	7	with	with	ADP
ejpam-3884	120	8	respect	respect	NOUN
ejpam-3884	120	9	to	to	ADP
ejpam-3884	120	10	r	r	NOUN
ejpam-3884	120	11	,	,	PUNCT
ejpam-3884	120	12	denoted	denote	VERB
ejpam-3884	120	13	by	by	ADP
ejpam-3884	120	14	πe(γ	πe(γ	NOUN
ejpam-3884	120	15	,	,	PUNCT
ejpam-3884	120	16	r	r	NOUN
ejpam-3884	120	17	)	)	PUNCT
ejpam-3884	120	18	,	,	PUNCT
ejpam-3884	120	19	is	be	AUX
ejpam-3884	120	20	the	the	DET
ejpam-3884	120	21	number	number	NOUN
ejpam-3884	120	22	of	of	ADP
ejpam-3884	120	23	the	the	DET
ejpam-3884	120	24	paths	path	NOUN
ejpam-3884	120	25	specified	specify	VERB
ejpam-3884	120	26	by	by	ADP
ejpam-3884	120	27	r	r	NOUN
ejpam-3884	120	28	going	go	VERB
ejpam-3884	120	29	through	through	ADP
ejpam-3884	120	30	it	it	PRON
ejpam-3884	120	31	.	.	PUNCT
ejpam-3884	121	1	definition	definition	NOUN
ejpam-3884	121	2	13	13	NUM
ejpam-3884	121	3	.	.	PUNCT
ejpam-3884	122	1	the	the	DET
ejpam-3884	122	2	edge	edge	NOUN
ejpam-3884	122	3	forwarding	forward	VERB
ejpam-3884	122	4	index	index	NOUN
ejpam-3884	122	5	of	of	ADP
ejpam-3884	122	6	a	a	DET
ejpam-3884	122	7	graph	graph	NOUN
ejpam-3884	122	8	γ	γ	NOUN
ejpam-3884	122	9	with	with	ADP
ejpam-3884	122	10	respect	respect	NOUN
ejpam-3884	122	11	to	to	ADP
ejpam-3884	122	12	a	a	DET
ejpam-3884	122	13	routing	routing	NOUN
ejpam-3884	122	14	r	r	NOUN
ejpam-3884	122	15	,	,	PUNCT
ejpam-3884	122	16	denoted	denote	VERB
ejpam-3884	122	17	by	by	ADP
ejpam-3884	122	18	π(γ	π(γ	PROPN
ejpam-3884	122	19	,	,	PUNCT
ejpam-3884	122	20	r	r	NOUN
ejpam-3884	122	21	)	)	PUNCT
ejpam-3884	122	22	is	be	AUX
ejpam-3884	122	23	the	the	DET
ejpam-3884	122	24	maximum	maximum	ADJ
ejpam-3884	122	25	number	number	NOUN
ejpam-3884	122	26	of	of	ADP
ejpam-3884	122	27	paths	path	NOUN
ejpam-3884	122	28	specified	specify	VERB
ejpam-3884	122	29	by	by	ADP
ejpam-3884	122	30	r	r	NOUN
ejpam-3884	122	31	going	go	VERB
ejpam-3884	122	32	through	through	ADP
ejpam-3884	122	33	any	any	DET
ejpam-3884	122	34	edge	edge	NOUN
ejpam-3884	122	35	of	of	ADP
ejpam-3884	122	36	γ	γ	PROPN
ejpam-3884	122	37	.	.	PROPN
ejpam-3884	122	38	hence	hence	ADV
ejpam-3884	122	39	π(γ	π(γ	PROPN
ejpam-3884	122	40	,	,	PUNCT
ejpam-3884	122	41	r	r	NOUN
ejpam-3884	122	42	)	)	PUNCT
ejpam-3884	122	43	=	=	SYM
ejpam-3884	122	44	max{πe(γ	max{πe(γ	NOUN
ejpam-3884	122	45	,	,	PUNCT
ejpam-3884	122	46	r	r	NOUN
ejpam-3884	122	47	)	)	PUNCT
ejpam-3884	122	48	:	:	PUNCT
ejpam-3884	123	1	e	e	X
ejpam-3884	123	2	∈	∈	PROPN
ejpam-3884	123	3	e(γ	e(γ	PROPN
ejpam-3884	123	4	)	)	PUNCT
ejpam-3884	123	5	}	}	PUNCT
ejpam-3884	123	6	.	.	PUNCT
ejpam-3884	124	1	definition	definition	NOUN
ejpam-3884	124	2	14	14	NUM
ejpam-3884	124	3	.	.	PUNCT
ejpam-3884	125	1	the	the	DET
ejpam-3884	125	2	edge	edge	NOUN
ejpam-3884	125	3	-	-	PUNCT
ejpam-3884	125	4	forwarding	forward	VERB
ejpam-3884	125	5	index	index	NOUN
ejpam-3884	125	6	of	of	ADP
ejpam-3884	125	7	a	a	DET
ejpam-3884	125	8	graph	graph	NOUN
ejpam-3884	125	9	γ	γ	NOUN
ejpam-3884	125	10	,	,	PUNCT
ejpam-3884	125	11	denoted	denote	VERB
ejpam-3884	125	12	by	by	ADP
ejpam-3884	125	13	π(γ	π(γ	PROPN
ejpam-3884	125	14	)	)	PUNCT
ejpam-3884	125	15	is	be	AUX
ejpam-3884	125	16	defined	define	VERB
ejpam-3884	125	17	by	by	ADP
ejpam-3884	125	18	π(γ	π(γ	PROPN
ejpam-3884	125	19	)	)	PUNCT
ejpam-3884	125	20	=	=	PUNCT
ejpam-3884	126	1	min{π(γ	min{π(γ	PROPN
ejpam-3884	126	2	,	,	PUNCT
ejpam-3884	126	3	r	r	NOUN
ejpam-3884	126	4	)	)	PUNCT
ejpam-3884	126	5	:	:	PUNCT
ejpam-3884	126	6	r	r	NOUN
ejpam-3884	126	7	∈	∈	PROPN
ejpam-3884	126	8	r(γ	r(γ	NOUN
ejpam-3884	126	9	)	)	PUNCT
ejpam-3884	126	10	}	}	PUNCT
ejpam-3884	126	11	.	.	PUNCT
ejpam-3884	127	1	we	we	PRON
ejpam-3884	127	2	end	end	VERB
ejpam-3884	127	3	this	this	DET
ejpam-3884	127	4	section	section	NOUN
ejpam-3884	127	5	by	by	ADP
ejpam-3884	127	6	giving	give	VERB
ejpam-3884	127	7	the	the	DET
ejpam-3884	127	8	exact	exact	ADJ
ejpam-3884	127	9	value	value	NOUN
ejpam-3884	127	10	of	of	ADP
ejpam-3884	127	11	vertex	vertex	NOUN
ejpam-3884	127	12	-	-	PUNCT
ejpam-3884	127	13	forwarding	forward	VERB
ejpam-3884	127	14	index	index	NOUN
ejpam-3884	127	15	and	and	CCONJ
ejpam-3884	127	16	a	a	DET
ejpam-3884	127	17	bound	bind	VERB
ejpam-3884	127	18	for	for	ADP
ejpam-3884	127	19	the	the	DET
ejpam-3884	127	20	edge	edge	NOUN
ejpam-3884	127	21	-	-	PUNCT
ejpam-3884	127	22	forwarding	forward	VERB
ejpam-3884	127	23	index	index	NOUN
ejpam-3884	127	24	of	of	ADP
ejpam-3884	127	25	a	a	DET
ejpam-3884	127	26	graph	graph	NOUN
ejpam-3884	127	27	γ	γ	X
ejpam-3884	127	28	.	.	PUNCT
ejpam-3884	128	1	they	they	PRON
ejpam-3884	128	2	are	be	AUX
ejpam-3884	128	3	given	give	VERB
ejpam-3884	128	4	in	in	ADP
ejpam-3884	128	5	the	the	DET
ejpam-3884	128	6	last	last	ADJ
ejpam-3884	128	7	two	two	NUM
ejpam-3884	128	8	results	result	NOUN
ejpam-3884	128	9	for	for	ADP
ejpam-3884	128	10	this	this	DET
ejpam-3884	128	11	section	section	NOUN
ejpam-3884	128	12	.	.	PUNCT
ejpam-3884	129	1	lemma	lemma	PROPN
ejpam-3884	129	2	2	2	PROPN
ejpam-3884	129	3	(	(	PUNCT
ejpam-3884	129	4	lemma	lemma	PROPN
ejpam-3884	129	5	4.2	4.2	NUM
ejpam-3884	129	6	[	[	X
ejpam-3884	129	7	9	9	NUM
ejpam-3884	129	8	]	]	PUNCT
ejpam-3884	129	9	)	)	PUNCT
ejpam-3884	129	10	.	.	PUNCT
ejpam-3884	130	1	if	if	SCONJ
ejpam-3884	130	2	γ	γ	X
ejpam-3884	130	3	is	be	AUX
ejpam-3884	130	4	a	a	DET
ejpam-3884	130	5	connected	connected	ADJ
ejpam-3884	130	6	circulant	circulant	ADJ
ejpam-3884	130	7	graph	graph	NOUN
ejpam-3884	130	8	of	of	ADP
ejpam-3884	130	9	order	order	NOUN
ejpam-3884	130	10	n	n	CCONJ
ejpam-3884	130	11	,	,	PUNCT
ejpam-3884	130	12	then	then	ADV
ejpam-3884	130	13	ξ(γ	ξ(γ	NUM
ejpam-3884	130	14	)	)	PUNCT
ejpam-3884	131	1	=	=	SYM
ejpam-3884	131	2	ρ(γ)−	ρ(γ)−	PROPN
ejpam-3884	131	3	(	(	PUNCT
ejpam-3884	131	4	n−	n−	NOUN
ejpam-3884	131	5	1	1	NUM
ejpam-3884	131	6	)	)	PUNCT
ejpam-3884	131	7	.	.	PUNCT
ejpam-3884	132	1	lemma	lemma	PROPN
ejpam-3884	132	2	3	3	NUM
ejpam-3884	132	3	(	(	PUNCT
ejpam-3884	132	4	lemma	lemma	PROPN
ejpam-3884	132	5	4.5	4.5	NUM
ejpam-3884	133	1	[	[	X
ejpam-3884	133	2	9	9	NUM
ejpam-3884	133	3	]	]	PUNCT
ejpam-3884	133	4	)	)	PUNCT
ejpam-3884	133	5	.	.	PUNCT
ejpam-3884	134	1	if	if	SCONJ
ejpam-3884	134	2	γ	γ	X
ejpam-3884	134	3	is	be	AUX
ejpam-3884	134	4	a	a	DET
ejpam-3884	134	5	connected	connected	ADJ
ejpam-3884	134	6	r−regular	r−regular	ADJ
ejpam-3884	134	7	circulant	circulant	ADJ
ejpam-3884	134	8	graph	graph	NOUN
ejpam-3884	134	9	of	of	ADP
ejpam-3884	134	10	order	order	NOUN
ejpam-3884	134	11	n	n	CCONJ
ejpam-3884	134	12	,	,	PUNCT
ejpam-3884	134	13	then	then	ADV
ejpam-3884	134	14	2ρ(γ	2ρ(γ	NUM
ejpam-3884	134	15	)	)	PUNCT
ejpam-3884	134	16	r	r	NOUN
ejpam-3884	134	17	≤	≤	NUM
ejpam-3884	134	18	π(γ	π(γ	PROPN
ejpam-3884	134	19	)	)	PUNCT
ejpam-3884	134	20	≤	≤	NOUN
ejpam-3884	134	21	n+	n+	PUNCT
ejpam-3884	135	1	ρ(γ)−	ρ(γ)−	PROPN
ejpam-3884	135	2	(	(	PUNCT
ejpam-3884	135	3	2r	2r	NUM
ejpam-3884	135	4	−	−	NOUN
ejpam-3884	135	5	1	1	NUM
ejpam-3884	135	6	)	)	PUNCT
ejpam-3884	135	7	.	.	PUNCT
ejpam-3884	136	1	3	3	X
ejpam-3884	136	2	.	.	X
ejpam-3884	136	3	a	a	DET
ejpam-3884	136	4	bfs	bfs	NOUN
ejpam-3884	136	5	tree	tree	NOUN
ejpam-3884	136	6	construction	construction	NOUN
ejpam-3884	136	7	for	for	ADP
ejpam-3884	136	8	γmh	γmh	NOUN
ejpam-3884	137	1	it	it	PRON
ejpam-3884	137	2	is	be	AUX
ejpam-3884	137	3	evident	evident	ADJ
ejpam-3884	137	4	from	from	ADP
ejpam-3884	137	5	properties	property	NOUN
ejpam-3884	137	6	(	(	PUNCT
ejpam-3884	137	7	i)-(v	i)-(v	PROPN
ejpam-3884	137	8	)	)	PUNCT
ejpam-3884	137	9	that	that	SCONJ
ejpam-3884	137	10	the	the	DET
ejpam-3884	137	11	construction	construction	NOUN
ejpam-3884	137	12	of	of	ADP
ejpam-3884	137	13	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	137	14	)	)	PUNCT
ejpam-3884	137	15	will	will	AUX
ejpam-3884	137	16	be	be	AUX
ejpam-3884	137	17	based	base	VERB
ejpam-3884	137	18	on	on	ADP
ejpam-3884	137	19	bfs0(γmh−1	bfs0(γmh−1	PROPN
ejpam-3884	137	20	)	)	PUNCT
ejpam-3884	137	21	.	.	PUNCT
ejpam-3884	138	1	also	also	ADV
ejpam-3884	138	2	,	,	PUNCT
ejpam-3884	138	3	from	from	ADP
ejpam-3884	138	4	property	property	NOUN
ejpam-3884	138	5	(	(	PUNCT
ejpam-3884	138	6	i	i	NOUN
ejpam-3884	138	7	)	)	PUNCT
ejpam-3884	138	8	and	and	CCONJ
ejpam-3884	138	9	the	the	DET
ejpam-3884	138	10	fact	fact	NOUN
ejpam-3884	138	11	that	that	SCONJ
ejpam-3884	138	12	for	for	ADP
ejpam-3884	138	13	any	any	DET
ejpam-3884	138	14	x	x	NOUN
ejpam-3884	138	15	,	,	PUNCT
ejpam-3884	138	16	y	y	PROPN
ejpam-3884	138	17	∈	∈	PROPN
ejpam-3884	138	18	zn	zn	PROPN
ejpam-3884	138	19	and	and	CCONJ
ejpam-3884	138	20	s	s	PROPN
ejpam-3884	138	21	∈	∈	PROPN
ejpam-3884	138	22	s	s	X
ejpam-3884	138	23	,	,	PUNCT
ejpam-3884	138	24	we	we	PRON
ejpam-3884	138	25	have	have	AUX
ejpam-3884	138	26	if	if	SCONJ
ejpam-3884	138	27	x	x	X
ejpam-3884	138	28	+	+	NUM
ejpam-3884	138	29	y	y	NOUN
ejpam-3884	138	30	=	=	SYM
ejpam-3884	138	31	0	0	PUNCT
ejpam-3884	139	1	then	then	ADV
ejpam-3884	139	2	(	(	PUNCT
ejpam-3884	139	3	x	x	X
ejpam-3884	139	4	+	+	NUM
ejpam-3884	139	5	s	s	X
ejpam-3884	139	6	)	)	PUNCT
ejpam-3884	140	1	+	+	CCONJ
ejpam-3884	140	2	(	(	PUNCT
ejpam-3884	140	3	y	y	PROPN
ejpam-3884	140	4	−	−	PROPN
ejpam-3884	140	5	s	s	PART
ejpam-3884	140	6	)	)	PUNCT
ejpam-3884	140	7	=	=	SYM
ejpam-3884	140	8	0	0	PUNCT
ejpam-3884	141	1	and	and	CCONJ
ejpam-3884	141	2	(	(	PUNCT
ejpam-3884	141	3	x	x	X
ejpam-3884	141	4	−	−	NOUN
ejpam-3884	141	5	s	s	PART
ejpam-3884	141	6	)	)	PUNCT
ejpam-3884	142	1	+	+	CCONJ
ejpam-3884	142	2	(	(	PUNCT
ejpam-3884	142	3	y	y	PROPN
ejpam-3884	142	4	+	+	PROPN
ejpam-3884	142	5	s	s	X
ejpam-3884	142	6	)	)	PUNCT
ejpam-3884	142	7	=	=	SYM
ejpam-3884	142	8	0	0	NUM
ejpam-3884	142	9	,	,	PUNCT
ejpam-3884	142	10	we	we	PRON
ejpam-3884	142	11	know	know	VERB
ejpam-3884	142	12	that	that	DET
ejpam-3884	142	13	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	142	14	)	)	PUNCT
ejpam-3884	142	15	has	have	VERB
ejpam-3884	142	16	a	a	DET
ejpam-3884	142	17	vertical	vertical	ADJ
ejpam-3884	142	18	axial	axial	ADJ
ejpam-3884	142	19	-	-	PUNCT
ejpam-3884	142	20	symmetry	symmetry	NOUN
ejpam-3884	142	21	with	with	ADP
ejpam-3884	142	22	respect	respect	NOUN
ejpam-3884	142	23	to	to	ADP
ejpam-3884	142	24	the	the	DET
ejpam-3884	142	25	0	0	NUM
ejpam-3884	142	26	-	-	PUNCT
ejpam-3884	142	27	vertex	vertex	NOUN
ejpam-3884	142	28	.	.	PUNCT
ejpam-3884	143	1	so	so	ADV
ejpam-3884	143	2	we	we	PRON
ejpam-3884	143	3	have	have	VERB
ejpam-3884	143	4	a	a	DET
ejpam-3884	143	5	definition	definition	NOUN
ejpam-3884	143	6	and	and	CCONJ
ejpam-3884	143	7	a	a	DET
ejpam-3884	143	8	remark	remark	NOUN
ejpam-3884	143	9	.	.	PUNCT
ejpam-3884	144	1	j.	j.	PROPN
ejpam-3884	144	2	antalan	antalan	PROPN
ejpam-3884	144	3	,	,	PUNCT
ejpam-3884	144	4	f.	f.	PROPN
ejpam-3884	144	5	campeña	campeña	PROPN
ejpam-3884	144	6	/	/	SYM
ejpam-3884	144	7	eur	eur	PROPN
ejpam-3884	144	8	.	.	PUNCT
ejpam-3884	145	1	j.	j.	PROPN
ejpam-3884	145	2	pure	pure	PROPN
ejpam-3884	145	3	appl	appl	PROPN
ejpam-3884	145	4	.	.	PROPN
ejpam-3884	145	5	math	math	PROPN
ejpam-3884	145	6	,	,	PUNCT
ejpam-3884	145	7	14	14	NUM
ejpam-3884	145	8	(	(	PUNCT
ejpam-3884	145	9	1	1	NUM
ejpam-3884	145	10	)	)	PUNCT
ejpam-3884	145	11	(	(	PUNCT
ejpam-3884	145	12	2021	2021	NUM
ejpam-3884	145	13	)	)	PUNCT
ejpam-3884	145	14	,	,	PUNCT
ejpam-3884	145	15	248	248	NUM
ejpam-3884	145	16	-	-	SYM
ejpam-3884	145	17	264	264	NUM
ejpam-3884	145	18	254	254	NUM
ejpam-3884	145	19	definition	definition	NOUN
ejpam-3884	145	20	15	15	NUM
ejpam-3884	145	21	.	.	PUNCT
ejpam-3884	146	1	the	the	DET
ejpam-3884	146	2	left	left	ADJ
ejpam-3884	146	3	part	part	NOUN
ejpam-3884	146	4	of	of	ADP
ejpam-3884	146	5	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	146	6	)	)	PUNCT
ejpam-3884	146	7	denoted	denote	VERB
ejpam-3884	146	8	by	by	ADP
ejpam-3884	146	9	l[bfs0(γmh	l[bfs0(γmh	PROPN
ejpam-3884	146	10	)	)	PUNCT
ejpam-3884	146	11	]	]	PUNCT
ejpam-3884	146	12	refers	refer	VERB
ejpam-3884	146	13	to	to	ADP
ejpam-3884	146	14	the	the	DET
ejpam-3884	146	15	vertices	vertex	NOUN
ejpam-3884	146	16	m0,m1	m0,m1	PROPN
ejpam-3884	146	17	,	,	PUNCT
ejpam-3884	146	18	.	.	PUNCT
ejpam-3884	146	19	.	.	PUNCT
ejpam-3884	147	1	.	.	PUNCT
ejpam-3884	148	1	,	,	PUNCT
ejpam-3884	148	2	mh−1	mh−1	PROPN
ejpam-3884	148	3	,	,	PUNCT
ejpam-3884	148	4	and	and	CCONJ
ejpam-3884	148	5	their	their	PRON
ejpam-3884	148	6	descendants	descendant	NOUN
ejpam-3884	148	7	.	.	PUNCT
ejpam-3884	149	1	while	while	SCONJ
ejpam-3884	149	2	the	the	DET
ejpam-3884	149	3	right	right	ADJ
ejpam-3884	149	4	part	part	NOUN
ejpam-3884	149	5	of	of	ADP
ejpam-3884	149	6	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	149	7	)	)	PUNCT
ejpam-3884	149	8	denoted	denote	VERB
ejpam-3884	149	9	by	by	ADP
ejpam-3884	149	10	r[bfs0(γmh	r[bfs0(γmh	PROPN
ejpam-3884	149	11	)	)	PUNCT
ejpam-3884	149	12	]	]	PUNCT
ejpam-3884	149	13	refers	refer	VERB
ejpam-3884	149	14	to	to	ADP
ejpam-3884	149	15	the	the	DET
ejpam-3884	149	16	vertices	vertex	NOUN
ejpam-3884	149	17	mh	mh	PROPN
ejpam-3884	149	18	−mh−1,mh	−mh−1,mh	ADJ
ejpam-3884	149	19	−mh−2	−mh−2	PROPN
ejpam-3884	149	20	,	,	PUNCT
ejpam-3884	149	21	.	.	PUNCT
ejpam-3884	149	22	.	.	PUNCT
ejpam-3884	150	1	.	.	PUNCT
ejpam-3884	151	1	,	,	PUNCT
ejpam-3884	151	2	mh	mh	PROPN
ejpam-3884	151	3	−mh−h	−mh−h	NOUN
ejpam-3884	151	4	,	,	PUNCT
ejpam-3884	151	5	and	and	CCONJ
ejpam-3884	151	6	their	their	PRON
ejpam-3884	151	7	descendants	descendant	NOUN
ejpam-3884	151	8	.	.	PUNCT
ejpam-3884	152	1	remark	remark	VERB
ejpam-3884	152	2	8	8	NUM
ejpam-3884	152	3	.	.	PUNCT
ejpam-3884	153	1	for	for	ADP
ejpam-3884	153	2	odd	odd	ADJ
ejpam-3884	153	3	intger	intger	NOUN
ejpam-3884	153	4	m	m	NOUN
ejpam-3884	153	5	and	and	CCONJ
ejpam-3884	153	6	positive	positive	ADJ
ejpam-3884	153	7	integer	integer	NOUN
ejpam-3884	153	8	h	h	NOUN
ejpam-3884	153	9	we	we	PRON
ejpam-3884	153	10	have	have	VERB
ejpam-3884	153	11	l[bfs0(γmh	l[bfs0(γmh	PROPN
ejpam-3884	153	12	)	)	PUNCT
ejpam-3884	153	13	]	]	PUNCT
ejpam-3884	154	1	=	=	PUNCT
ejpam-3884	154	2	{	{	PUNCT
ejpam-3884	154	3	1	1	NUM
ejpam-3884	154	4	,	,	PUNCT
ejpam-3884	154	5	2	2	NUM
ejpam-3884	154	6	,	,	PUNCT
ejpam-3884	154	7	.	.	PUNCT
ejpam-3884	154	8	.	.	PUNCT
ejpam-3884	155	1	.	.	PUNCT
ejpam-3884	156	1	,	,	PUNCT
ejpam-3884	156	2	mh−1	mh−1	NOUN
ejpam-3884	156	3	2	2	X
ejpam-3884	156	4	}	}	PUNCT
ejpam-3884	156	5	while	while	SCONJ
ejpam-3884	156	6	r[bfs0(γmh	r[bfs0(γmh	PROPN
ejpam-3884	156	7	)	)	PUNCT
ejpam-3884	156	8	]	]	PUNCT
ejpam-3884	157	1	=	=	PRON
ejpam-3884	157	2	{	{	PUNCT
ejpam-3884	157	3	mh−1	mh−1	NOUN
ejpam-3884	157	4	2	2	NUM
ejpam-3884	157	5	+	+	NUM
ejpam-3884	157	6	1	1	NUM
ejpam-3884	157	7	,	,	PUNCT
ejpam-3884	157	8	m	m	VERB
ejpam-3884	157	9	h−1	h−1	NOUN
ejpam-3884	157	10	2	2	NUM
ejpam-3884	157	11	+	+	CCONJ
ejpam-3884	157	12	2	2	NUM
ejpam-3884	157	13	,	,	PUNCT
ejpam-3884	157	14	.	.	PUNCT
ejpam-3884	157	15	.	.	PUNCT
ejpam-3884	157	16	.	.	PUNCT
ejpam-3884	158	1	,	,	PUNCT
ejpam-3884	158	2	mh	mh	PROPN
ejpam-3884	158	3	−	−	PROPN
ejpam-3884	158	4	1	1	NUM
ejpam-3884	158	5	}	}	PUNCT
ejpam-3884	158	6	.	.	PUNCT
ejpam-3884	159	1	using	use	VERB
ejpam-3884	159	2	the	the	DET
ejpam-3884	159	3	five	five	NUM
ejpam-3884	159	4	properties	property	NOUN
ejpam-3884	159	5	of	of	ADP
ejpam-3884	159	6	γmh	γmh	NOUN
ejpam-3884	159	7	presented	present	VERB
ejpam-3884	159	8	in	in	ADP
ejpam-3884	159	9	the	the	DET
ejpam-3884	159	10	introduction	introduction	NOUN
ejpam-3884	159	11	,	,	PUNCT
ejpam-3884	159	12	a	a	DET
ejpam-3884	159	13	method	method	NOUN
ejpam-3884	159	14	for	for	ADP
ejpam-3884	159	15	constructing	construct	VERB
ejpam-3884	159	16	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	159	17	)	)	PUNCT
ejpam-3884	159	18	based	base	VERB
ejpam-3884	159	19	from	from	ADP
ejpam-3884	159	20	bfs0(γmh−1	bfs0(γmh−1	PROPN
ejpam-3884	159	21	)	)	PUNCT
ejpam-3884	159	22	is	be	AUX
ejpam-3884	159	23	as	as	SCONJ
ejpam-3884	159	24	follows	follow	VERB
ejpam-3884	159	25	:	:	PUNCT
ejpam-3884	159	26	method	method	NOUN
ejpam-3884	159	27	on	on	ADP
ejpam-3884	159	28	constructing	construct	VERB
ejpam-3884	159	29	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	159	30	)	)	PUNCT
ejpam-3884	159	31	given	give	VERB
ejpam-3884	159	32	bfs0(γmh−1	bfs0(γmh−1	PROPN
ejpam-3884	159	33	)	)	PUNCT
ejpam-3884	159	34	,	,	PUNCT
ejpam-3884	159	35	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	159	36	)	)	PUNCT
ejpam-3884	159	37	can	can	AUX
ejpam-3884	159	38	be	be	AUX
ejpam-3884	159	39	constructed	construct	VERB
ejpam-3884	159	40	as	as	SCONJ
ejpam-3884	159	41	follows	follow	VERB
ejpam-3884	159	42	:	:	PUNCT
ejpam-3884	159	43	step	step	NOUN
ejpam-3884	159	44	1	1	NUM
ejpam-3884	159	45	.	.	PUNCT
ejpam-3884	160	1	in	in	ADP
ejpam-3884	160	2	bfs0(γmh−1	bfs0(γmh−1	PROPN
ejpam-3884	160	3	)	)	PUNCT
ejpam-3884	160	4	,	,	PUNCT
ejpam-3884	160	5	replace	replace	VERB
ejpam-3884	160	6	the	the	DET
ejpam-3884	160	7	0	0	NUM
ejpam-3884	160	8	-	-	PUNCT
ejpam-3884	160	9	vertex	vertex	NOUN
ejpam-3884	160	10	by	by	ADP
ejpam-3884	160	11	mh−1	mh−1	PROPN
ejpam-3884	160	12	.	.	PUNCT
ejpam-3884	161	1	step	step	NOUN
ejpam-3884	161	2	2	2	NUM
ejpam-3884	161	3	.	.	PUNCT
ejpam-3884	162	1	(	(	PUNCT
ejpam-3884	162	2	properties	property	NOUN
ejpam-3884	162	3	(	(	PUNCT
ejpam-3884	162	4	ii	ii	NOUN
ejpam-3884	162	5	)	)	PUNCT
ejpam-3884	162	6	and	and	CCONJ
ejpam-3884	162	7	(	(	PUNCT
ejpam-3884	162	8	iii	iii	NOUN
ejpam-3884	162	9	)	)	PUNCT
ejpam-3884	162	10	)	)	PUNCT
ejpam-3884	162	11	descend	descend	VERB
ejpam-3884	162	12	the	the	DET
ejpam-3884	162	13	vertex	vertex	NOUN
ejpam-3884	162	14	mh−1	mh−1	NOUN
ejpam-3884	162	15	and	and	CCONJ
ejpam-3884	162	16	the	the	DET
ejpam-3884	162	17	right	right	ADJ
ejpam-3884	162	18	part	part	NOUN
ejpam-3884	162	19	of	of	ADP
ejpam-3884	162	20	bfs0(γmh−1	bfs0(γmh−1	PROPN
ejpam-3884	162	21	)	)	PUNCT
ejpam-3884	162	22	by	by	ADP
ejpam-3884	162	23	a	a	DET
ejpam-3884	162	24	unit	unit	NOUN
ejpam-3884	162	25	and	and	CCONJ
ejpam-3884	162	26	introduce	introduce	VERB
ejpam-3884	162	27	the	the	DET
ejpam-3884	162	28	new	new	ADJ
ejpam-3884	162	29	0	0	NUM
ejpam-3884	162	30	-	-	PUNCT
ejpam-3884	162	31	vertex	vertex	NOUN
ejpam-3884	162	32	.	.	PUNCT
ejpam-3884	163	1	step	step	NOUN
ejpam-3884	163	2	3	3	NUM
ejpam-3884	163	3	.	.	PUNCT
ejpam-3884	164	1	(	(	PUNCT
ejpam-3884	164	2	property	property	NOUN
ejpam-3884	164	3	(	(	PUNCT
ejpam-3884	164	4	iv	iv	NOUN
ejpam-3884	164	5	)	)	PUNCT
ejpam-3884	164	6	)	)	PUNCT
ejpam-3884	164	7	reproduce	reproduce	VERB
ejpam-3884	164	8	the	the	DET
ejpam-3884	164	9	left	left	ADJ
ejpam-3884	164	10	part	part	NOUN
ejpam-3884	164	11	of	of	ADP
ejpam-3884	164	12	bfs0(γmh−1	bfs0(γmh−1	PROPN
ejpam-3884	164	13	)	)	PUNCT
ejpam-3884	164	14	with	with	ADP
ejpam-3884	164	15	the	the	DET
ejpam-3884	164	16	substitution	substitution	NOUN
ejpam-3884	164	17	0	0	NUM
ejpam-3884	165	1	:	:	PUNCT
ejpam-3884	165	2	=	=	PUNCT
ejpam-3884	165	3	mh−1	mh−1	NOUN
ejpam-3884	165	4	.	.	PUNCT
ejpam-3884	166	1	step	step	NOUN
ejpam-3884	166	2	4	4	NUM
ejpam-3884	166	3	.	.	PUNCT
ejpam-3884	167	1	(	(	PUNCT
ejpam-3884	167	2	property	property	NOUN
ejpam-3884	167	3	(	(	PUNCT
ejpam-3884	167	4	v	v	NOUN
ejpam-3884	167	5	)	)	PUNCT
ejpam-3884	167	6	)	)	PUNCT
ejpam-3884	167	7	let	let	VERB
ejpam-3884	167	8	r	r	NOUN
ejpam-3884	167	9	=	=	SYM
ejpam-3884	167	10	2	2	X
ejpam-3884	167	11	.	.	X
ejpam-3884	167	12	introduce	introduce	VERB
ejpam-3884	167	13	the	the	DET
ejpam-3884	167	14	vertex	vertex	NOUN
ejpam-3884	167	15	r(mh−1	r(mh−1	NOUN
ejpam-3884	167	16	)	)	PUNCT
ejpam-3884	167	17	as	as	ADP
ejpam-3884	167	18	a	a	DET
ejpam-3884	167	19	child	child	NOUN
ejpam-3884	167	20	of	of	ADP
ejpam-3884	167	21	vertex	vertex	NOUN
ejpam-3884	167	22	(	(	PUNCT
ejpam-3884	167	23	r−1)(mh−1	r−1)(mh−1	PROPN
ejpam-3884	167	24	)	)	PUNCT
ejpam-3884	167	25	and	and	CCONJ
ejpam-3884	167	26	reproduce	reproduce	VERB
ejpam-3884	167	27	the	the	DET
ejpam-3884	167	28	genealogy	genealogy	NOUN
ejpam-3884	167	29	of	of	ADP
ejpam-3884	167	30	vertex	vertex	NOUN
ejpam-3884	167	31	(	(	PUNCT
ejpam-3884	167	32	r	r	NOUN
ejpam-3884	167	33	−	−	NOUN
ejpam-3884	167	34	1)(mh−1	1)(mh−1	NUM
ejpam-3884	167	35	)	)	PUNCT
ejpam-3884	167	36	with	with	ADP
ejpam-3884	167	37	the	the	DET
ejpam-3884	167	38	substitution	substitution	NOUN
ejpam-3884	167	39	(	(	PUNCT
ejpam-3884	167	40	r	r	NOUN
ejpam-3884	167	41	−	−	NOUN
ejpam-3884	167	42	1)(mh−1	1)(mh−1	NUM
ejpam-3884	167	43	)	)	PUNCT
ejpam-3884	167	44	:	:	PUNCT
ejpam-3884	168	1	=	=	PUNCT
ejpam-3884	168	2	r(mh−1	r(mh−1	NOUN
ejpam-3884	168	3	)	)	PUNCT
ejpam-3884	168	4	.	.	PUNCT
ejpam-3884	169	1	step	step	NOUN
ejpam-3884	169	2	5	5	NUM
ejpam-3884	169	3	.	.	PUNCT
ejpam-3884	170	1	(	(	PUNCT
ejpam-3884	170	2	property	property	NOUN
ejpam-3884	170	3	(	(	PUNCT
ejpam-3884	170	4	v	v	NOUN
ejpam-3884	170	5	)	)	PUNCT
ejpam-3884	170	6	)	)	PUNCT
ejpam-3884	171	1	repeat	repeat	NOUN
ejpam-3884	171	2	step	step	NOUN
ejpam-3884	171	3	4	4	NUM
ejpam-3884	171	4	for	for	ADP
ejpam-3884	171	5	r	r	NOUN
ejpam-3884	171	6	=	=	SYM
ejpam-3884	171	7	3	3	NUM
ejpam-3884	171	8	,	,	PUNCT
ejpam-3884	171	9	4	4	NUM
ejpam-3884	171	10	,	,	PUNCT
ejpam-3884	171	11	.	.	PUNCT
ejpam-3884	171	12	.	.	PUNCT
ejpam-3884	172	1	.	.	PUNCT
ejpam-3884	173	1	,	,	PUNCT
ejpam-3884	173	2	m−1	m−1	PROPN
ejpam-3884	173	3	2	2	NUM
ejpam-3884	173	4	step	step	NOUN
ejpam-3884	173	5	6	6	NUM
ejpam-3884	173	6	.	.	PUNCT
ejpam-3884	173	7	complete	complete	ADJ
ejpam-3884	173	8	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	173	9	)	)	PUNCT
ejpam-3884	173	10	using	use	VERB
ejpam-3884	173	11	property	property	NOUN
ejpam-3884	173	12	(	(	PUNCT
ejpam-3884	173	13	i	i	NOUN
ejpam-3884	173	14	)	)	PUNCT
ejpam-3884	173	15	.	.	PUNCT
ejpam-3884	173	16	remark	remark	PROPN
ejpam-3884	173	17	9	9	NUM
ejpam-3884	173	18	.	.	PUNCT
ejpam-3884	174	1	the	the	DET
ejpam-3884	174	2	method	method	NOUN
ejpam-3884	174	3	just	just	ADV
ejpam-3884	174	4	presented	present	VERB
ejpam-3884	174	5	is	be	AUX
ejpam-3884	174	6	an	an	DET
ejpam-3884	174	7	extension	extension	NOUN
ejpam-3884	174	8	of	of	ADP
ejpam-3884	174	9	a	a	DET
ejpam-3884	174	10	method	method	NOUN
ejpam-3884	174	11	presented	present	VERB
ejpam-3884	174	12	in	in	ADP
ejpam-3884	174	13	[	[	X
ejpam-3884	174	14	3	3	NUM
ejpam-3884	174	15	]	]	PUNCT
ejpam-3884	174	16	for	for	ADP
ejpam-3884	174	17	constructing	construct	VERB
ejpam-3884	174	18	bfs0(γ3h	bfs0(γ3h	NOUN
ejpam-3884	174	19	)	)	PUNCT
ejpam-3884	174	20	.	.	PUNCT
ejpam-3884	175	1	example	example	NOUN
ejpam-3884	176	1	1	1	X
ejpam-3884	176	2	.	.	PUNCT
ejpam-3884	176	3	we	we	PRON
ejpam-3884	176	4	illustrate	illustrate	VERB
ejpam-3884	176	5	the	the	DET
ejpam-3884	176	6	method	method	NOUN
ejpam-3884	176	7	by	by	ADP
ejpam-3884	176	8	constructing	construct	VERB
ejpam-3884	176	9	a	a	DET
ejpam-3884	176	10	bfs	bfs	NOUN
ejpam-3884	176	11	tree	tree	NOUN
ejpam-3884	176	12	rooted	root	VERB
ejpam-3884	176	13	at	at	ADP
ejpam-3884	176	14	0	0	NUM
ejpam-3884	176	15	-	-	PUNCT
ejpam-3884	176	16	vertex	vertex	NOUN
ejpam-3884	176	17	for	for	ADP
ejpam-3884	176	18	the	the	DET
ejpam-3884	176	19	graph	graph	NOUN
ejpam-3884	176	20	γ52	γ52	NOUN
ejpam-3884	176	21	using	use	VERB
ejpam-3884	176	22	bfs0(γ51	bfs0(γ51	NOUN
ejpam-3884	176	23	)	)	PUNCT
ejpam-3884	176	24	in	in	ADP
ejpam-3884	176	25	figure	figure	NOUN
ejpam-3884	176	26	1	1	NUM
ejpam-3884	176	27	as	as	ADP
ejpam-3884	176	28	an	an	DET
ejpam-3884	176	29	input	input	NOUN
ejpam-3884	176	30	.	.	PUNCT
ejpam-3884	177	1	using	use	VERB
ejpam-3884	177	2	the	the	DET
ejpam-3884	177	3	propose	propose	ADJ
ejpam-3884	177	4	method	method	NOUN
ejpam-3884	177	5	,	,	PUNCT
ejpam-3884	177	6	we	we	PRON
ejpam-3884	177	7	have	have	VERB
ejpam-3884	177	8	a	a	DET
ejpam-3884	177	9	bfs	bfs	NOUN
ejpam-3884	177	10	tree	tree	NOUN
ejpam-3884	177	11	rooted	root	VERB
ejpam-3884	177	12	at	at	ADP
ejpam-3884	177	13	0	0	NUM
ejpam-3884	177	14	-	-	PUNCT
ejpam-3884	177	15	vertex	vertex	NOUN
ejpam-3884	177	16	for	for	ADP
ejpam-3884	177	17	γ52	γ52	NOUN
ejpam-3884	177	18	as	as	SCONJ
ejpam-3884	177	19	shown	show	VERB
ejpam-3884	177	20	in	in	ADP
ejpam-3884	177	21	figure	figure	NOUN
ejpam-3884	177	22	3	3	NUM
ejpam-3884	177	23	.	.	PUNCT
ejpam-3884	177	24	j.	j.	PROPN
ejpam-3884	177	25	antalan	antalan	PROPN
ejpam-3884	177	26	,	,	PUNCT
ejpam-3884	177	27	f.	f.	PROPN
ejpam-3884	177	28	campeña	campeña	PROPN
ejpam-3884	177	29	/	/	SYM
ejpam-3884	177	30	eur	eur	PROPN
ejpam-3884	177	31	.	.	PUNCT
ejpam-3884	178	1	j.	j.	PROPN
ejpam-3884	178	2	pure	pure	PROPN
ejpam-3884	178	3	appl	appl	PROPN
ejpam-3884	178	4	.	.	PROPN
ejpam-3884	178	5	math	math	PROPN
ejpam-3884	178	6	,	,	PUNCT
ejpam-3884	178	7	14	14	NUM
ejpam-3884	178	8	(	(	PUNCT
ejpam-3884	178	9	1	1	NUM
ejpam-3884	178	10	)	)	PUNCT
ejpam-3884	178	11	(	(	PUNCT
ejpam-3884	178	12	2021	2021	NUM
ejpam-3884	178	13	)	)	PUNCT
ejpam-3884	178	14	,	,	PUNCT
ejpam-3884	178	15	248	248	NUM
ejpam-3884	178	16	-	-	SYM
ejpam-3884	178	17	264	264	NUM
ejpam-3884	178	18	255	255	NUM
ejpam-3884	178	19	figure	figure	NOUN
ejpam-3884	178	20	3	3	NUM
ejpam-3884	178	21	:	:	PUNCT
ejpam-3884	178	22	a	a	DET
ejpam-3884	178	23	bfs	bfs	NOUN
ejpam-3884	178	24	tree	tree	NOUN
ejpam-3884	178	25	of	of	ADP
ejpam-3884	178	26	the	the	DET
ejpam-3884	178	27	graph	graph	NOUN
ejpam-3884	178	28	γ52	γ52	NOUN
ejpam-3884	178	29	with	with	ADP
ejpam-3884	178	30	root	root	NOUN
ejpam-3884	178	31	0	0	NUM
ejpam-3884	178	32	.	.	PUNCT
ejpam-3884	179	1	the	the	DET
ejpam-3884	179	2	green	green	ADJ
ejpam-3884	179	3	-	-	PUNCT
ejpam-3884	179	4	colored	color	VERB
ejpam-3884	179	5	vertices	vertex	NOUN
ejpam-3884	179	6	refer	refer	VERB
ejpam-3884	179	7	to	to	ADP
ejpam-3884	179	8	the	the	DET
ejpam-3884	179	9	vertices	vertex	NOUN
ejpam-3884	179	10	that	that	PRON
ejpam-3884	179	11	originally	originally	ADV
ejpam-3884	179	12	appeared	appear	VERB
ejpam-3884	179	13	in	in	ADP
ejpam-3884	179	14	bfs0(γ51	bfs0(γ51	NOUN
ejpam-3884	179	15	)	)	PUNCT
ejpam-3884	179	16	.	.	PUNCT
ejpam-3884	180	1	while	while	SCONJ
ejpam-3884	180	2	the	the	DET
ejpam-3884	180	3	green	green	ADJ
ejpam-3884	180	4	-	-	PUNCT
ejpam-3884	180	5	colored	color	VERB
ejpam-3884	180	6	vertices	vertex	NOUN
ejpam-3884	180	7	with	with	ADP
ejpam-3884	180	8	red	red	ADJ
ejpam-3884	180	9	edges	edge	NOUN
ejpam-3884	180	10	refer	refer	VERB
ejpam-3884	180	11	to	to	ADP
ejpam-3884	180	12	the	the	DET
ejpam-3884	180	13	descended	descend	VERB
ejpam-3884	180	14	vertices	vertex	NOUN
ejpam-3884	180	15	in	in	ADP
ejpam-3884	180	16	bfs0(γ51	bfs0(γ51	NOUN
ejpam-3884	180	17	)	)	PUNCT
ejpam-3884	180	18	.	.	PUNCT
ejpam-3884	181	1	the	the	DET
ejpam-3884	181	2	yellow	yellow	ADJ
ejpam-3884	181	3	-	-	PUNCT
ejpam-3884	181	4	colored	color	VERB
ejpam-3884	181	5	vertices	vertex	NOUN
ejpam-3884	181	6	refer	refer	VERB
ejpam-3884	181	7	to	to	ADP
ejpam-3884	181	8	the	the	DET
ejpam-3884	181	9	resulting	result	VERB
ejpam-3884	181	10	vertices	vertex	NOUN
ejpam-3884	181	11	as	as	ADP
ejpam-3884	181	12	a	a	DET
ejpam-3884	181	13	result	result	NOUN
ejpam-3884	181	14	of	of	ADP
ejpam-3884	181	15	reproducing	reproduce	VERB
ejpam-3884	181	16	the	the	DET
ejpam-3884	181	17	left	left	ADJ
ejpam-3884	181	18	part	part	NOUN
ejpam-3884	181	19	of	of	ADP
ejpam-3884	181	20	bfs0(γ51	bfs0(γ51	NOUN
ejpam-3884	181	21	)	)	PUNCT
ejpam-3884	181	22	with	with	ADP
ejpam-3884	181	23	the	the	DET
ejpam-3884	181	24	substitution	substitution	NOUN
ejpam-3884	181	25	0	0	NUM
ejpam-3884	182	1	:	:	PUNCT
ejpam-3884	182	2	=	=	SYM
ejpam-3884	182	3	5	5	X
ejpam-3884	182	4	.	.	PUNCT
ejpam-3884	183	1	the	the	DET
ejpam-3884	183	2	violet	violet	NOUN
ejpam-3884	183	3	-	-	PUNCT
ejpam-3884	183	4	colored	color	VERB
ejpam-3884	183	5	vertices	vertex	NOUN
ejpam-3884	183	6	refer	refer	VERB
ejpam-3884	183	7	to	to	ADP
ejpam-3884	183	8	the	the	DET
ejpam-3884	183	9	resulting	result	VERB
ejpam-3884	183	10	vertices	vertex	NOUN
ejpam-3884	183	11	as	as	ADP
ejpam-3884	183	12	a	a	DET
ejpam-3884	183	13	result	result	NOUN
ejpam-3884	183	14	of	of	ADP
ejpam-3884	183	15	introducing	introduce	VERB
ejpam-3884	183	16	the	the	DET
ejpam-3884	183	17	vertex	vertex	NOUN
ejpam-3884	183	18	5	5	NUM
ejpam-3884	183	19	+	+	SYM
ejpam-3884	183	20	5	5	NUM
ejpam-3884	183	21	as	as	ADP
ejpam-3884	183	22	a	a	DET
ejpam-3884	183	23	child	child	NOUN
ejpam-3884	183	24	of	of	ADP
ejpam-3884	183	25	vertex	vertex	NOUN
ejpam-3884	183	26	5	5	NUM
ejpam-3884	183	27	and	and	CCONJ
ejpam-3884	183	28	reproducing	reproduce	VERB
ejpam-3884	183	29	the	the	DET
ejpam-3884	183	30	genealogy	genealogy	NOUN
ejpam-3884	183	31	of	of	ADP
ejpam-3884	183	32	vertex	vertex	NOUN
ejpam-3884	183	33	5	5	NUM
ejpam-3884	183	34	with	with	ADP
ejpam-3884	183	35	the	the	DET
ejpam-3884	183	36	substitution	substitution	NOUN
ejpam-3884	183	37	5	5	NUM
ejpam-3884	183	38	=	=	NOUN
ejpam-3884	183	39	:	:	PUNCT
ejpam-3884	183	40	5	5	NUM
ejpam-3884	183	41	+	+	SYM
ejpam-3884	183	42	5	5	X
ejpam-3884	183	43	.	.	PUNCT
ejpam-3884	184	1	finally	finally	ADV
ejpam-3884	184	2	,	,	PUNCT
ejpam-3884	184	3	the	the	DET
ejpam-3884	184	4	blue	blue	ADJ
ejpam-3884	184	5	-	-	PUNCT
ejpam-3884	184	6	colored	color	VERB
ejpam-3884	184	7	vertices	vertex	NOUN
ejpam-3884	184	8	are	be	AUX
ejpam-3884	184	9	the	the	DET
ejpam-3884	184	10	vertices	vertex	NOUN
ejpam-3884	184	11	obtained	obtain	VERB
ejpam-3884	184	12	using	use	VERB
ejpam-3884	184	13	property	property	NOUN
ejpam-3884	184	14	(	(	PUNCT
ejpam-3884	184	15	i	i	NOUN
ejpam-3884	184	16	)	)	PUNCT
ejpam-3884	184	17	.	.	PUNCT
ejpam-3884	185	1	example	example	NOUN
ejpam-3884	186	1	2	2	NUM
ejpam-3884	186	2	.	.	X
ejpam-3884	186	3	in	in	ADP
ejpam-3884	186	4	this	this	DET
ejpam-3884	186	5	example	example	NOUN
ejpam-3884	186	6	,	,	PUNCT
ejpam-3884	186	7	we	we	PRON
ejpam-3884	186	8	illustrate	illustrate	VERB
ejpam-3884	186	9	the	the	DET
ejpam-3884	186	10	method	method	NOUN
ejpam-3884	186	11	by	by	ADP
ejpam-3884	186	12	constructing	construct	VERB
ejpam-3884	186	13	a	a	DET
ejpam-3884	186	14	bfs	bfs	NOUN
ejpam-3884	186	15	tree	tree	NOUN
ejpam-3884	186	16	for	for	ADP
ejpam-3884	186	17	the	the	DET
ejpam-3884	186	18	graph	graph	NOUN
ejpam-3884	186	19	γ72	γ72	NOUN
ejpam-3884	186	20	with	with	ADP
ejpam-3884	186	21	root	root	NOUN
ejpam-3884	186	22	0	0	PUNCT
ejpam-3884	186	23	using	use	VERB
ejpam-3884	186	24	bfs0(γ71	bfs0(γ71	NOUN
ejpam-3884	186	25	)	)	PUNCT
ejpam-3884	186	26	shown	show	VERB
ejpam-3884	186	27	in	in	ADP
ejpam-3884	186	28	figure	figure	NOUN
ejpam-3884	186	29	4	4	NUM
ejpam-3884	186	30	as	as	ADP
ejpam-3884	186	31	an	an	DET
ejpam-3884	186	32	input	input	NOUN
ejpam-3884	186	33	.	.	PUNCT
ejpam-3884	187	1	using	use	VERB
ejpam-3884	187	2	the	the	DET
ejpam-3884	187	3	propose	propose	ADJ
ejpam-3884	187	4	method	method	NOUN
ejpam-3884	187	5	,	,	PUNCT
ejpam-3884	187	6	we	we	PRON
ejpam-3884	187	7	have	have	VERB
ejpam-3884	187	8	a	a	DET
ejpam-3884	187	9	bfs	bfs	NOUN
ejpam-3884	187	10	tree	tree	NOUN
ejpam-3884	187	11	for	for	ADP
ejpam-3884	187	12	γ72	γ72	NOUN
ejpam-3884	187	13	with	with	ADP
ejpam-3884	187	14	root	root	NOUN
ejpam-3884	187	15	0	0	PUNCT
ejpam-3884	187	16	as	as	SCONJ
ejpam-3884	187	17	shown	show	VERB
ejpam-3884	187	18	in	in	ADP
ejpam-3884	187	19	figure	figure	NOUN
ejpam-3884	187	20	5	5	NUM
ejpam-3884	187	21	.	.	PUNCT
ejpam-3884	187	22	figure	figure	VERB
ejpam-3884	187	23	4	4	NUM
ejpam-3884	187	24	:	:	PUNCT
ejpam-3884	187	25	the	the	DET
ejpam-3884	187	26	bfs	bfs	NOUN
ejpam-3884	187	27	tree	tree	NOUN
ejpam-3884	187	28	of	of	ADP
ejpam-3884	187	29	γ71	γ71	NOUN
ejpam-3884	187	30	with	with	ADP
ejpam-3884	187	31	0	0	NUM
ejpam-3884	187	32	-	-	PUNCT
ejpam-3884	187	33	vertex	vertex	NOUN
ejpam-3884	187	34	as	as	ADP
ejpam-3884	187	35	the	the	DET
ejpam-3884	187	36	root	root	NOUN
ejpam-3884	187	37	.	.	PUNCT
ejpam-3884	188	1	based	base	VERB
ejpam-3884	188	2	on	on	ADP
ejpam-3884	188	3	the	the	DET
ejpam-3884	188	4	bfs	bfs	NOUN
ejpam-3884	188	5	tree	tree	NOUN
ejpam-3884	188	6	construction	construction	NOUN
ejpam-3884	188	7	for	for	ADP
ejpam-3884	188	8	γmh	γmh	NOUN
ejpam-3884	188	9	with	with	ADP
ejpam-3884	188	10	0	0	NUM
ejpam-3884	188	11	as	as	ADP
ejpam-3884	188	12	the	the	DET
ejpam-3884	188	13	root	root	NOUN
ejpam-3884	188	14	vertex	vertex	NOUN
ejpam-3884	188	15	,	,	PUNCT
ejpam-3884	188	16	we	we	PRON
ejpam-3884	188	17	have	have	AUX
ejpam-3884	188	18	theorem	theorem	VERB
ejpam-3884	188	19	1	1	NUM
ejpam-3884	188	20	.	.	PUNCT
ejpam-3884	189	1	let	let	VERB
ejpam-3884	189	2	h	h	PRON
ejpam-3884	189	3	be	be	AUX
ejpam-3884	189	4	a	a	DET
ejpam-3884	189	5	positive	positive	ADJ
ejpam-3884	189	6	integer	integer	NOUN
ejpam-3884	189	7	.	.	PUNCT
ejpam-3884	190	1	then	then	ADV
ejpam-3884	190	2	dγ	dγ	ADP
ejpam-3884	190	3	mh	mh	PROPN
ejpam-3884	190	4	(	(	PUNCT
ejpam-3884	190	5	0	0	PROPN
ejpam-3884	190	6	,	,	PUNCT
ejpam-3884	190	7	j	j	NOUN
ejpam-3884	190	8	)	)	PUNCT
ejpam-3884	190	9	=	=	PRON
ejpam-3884	190	10	{	{	PUNCT
ejpam-3884	190	11	dγ	dγ	ADP
ejpam-3884	190	12	mh−1	mh−1	PROPN
ejpam-3884	190	13	(	(	PUNCT
ejpam-3884	190	14	0	0	NUM
ejpam-3884	190	15	,	,	PUNCT
ejpam-3884	190	16	j	j	NOUN
ejpam-3884	190	17	)	)	PUNCT
ejpam-3884	190	18	if	if	SCONJ
ejpam-3884	190	19	j	j	PROPN
ejpam-3884	190	20	=	=	SYM
ejpam-3884	190	21	0	0	NUM
ejpam-3884	190	22	,	,	PUNCT
ejpam-3884	190	23	1	1	NUM
ejpam-3884	190	24	,	,	PUNCT
ejpam-3884	190	25	2	2	NUM
ejpam-3884	190	26	,	,	PUNCT
ejpam-3884	190	27	.	.	PUNCT
ejpam-3884	190	28	.	.	PUNCT
ejpam-3884	191	1	.	.	PUNCT
ejpam-3884	192	1	,	,	PUNCT
ejpam-3884	192	2	m	m	VERB
ejpam-3884	192	3	h−1−1	h−1−1	VERB
ejpam-3884	192	4	2	2	NUM
ejpam-3884	192	5	dγ	dγ	ADP
ejpam-3884	192	6	mh−1	mh−1	PROPN
ejpam-3884	192	7	(	(	PUNCT
ejpam-3884	192	8	0	0	NUM
ejpam-3884	192	9	,	,	PUNCT
ejpam-3884	192	10	j	j	NOUN
ejpam-3884	192	11	)	)	PUNCT
ejpam-3884	193	1	+	+	CCONJ
ejpam-3884	193	2	1	1	NUM
ejpam-3884	193	3	if	if	SCONJ
ejpam-3884	193	4	j	j	PROPN
ejpam-3884	193	5	=	=	NOUN
ejpam-3884	193	6	,	,	PUNCT
ejpam-3884	193	7	m	m	VERB
ejpam-3884	193	8	h−1−1	h−1−1	ADJ
ejpam-3884	193	9	2	2	NUM
ejpam-3884	193	10	+	+	CCONJ
ejpam-3884	193	11	1	1	NUM
ejpam-3884	193	12	.	.	PUNCT
ejpam-3884	193	13	.	.	PUNCT
ejpam-3884	193	14	.	.	PUNCT
ejpam-3884	194	1	,	,	PUNCT
ejpam-3884	194	2	mh−1	mh−1	NOUN
ejpam-3884	194	3	−	−	NOUN
ejpam-3884	195	1	1	1	X
ejpam-3884	195	2	.	.	PUNCT
ejpam-3884	195	3	(	(	PUNCT
ejpam-3884	195	4	1	1	X
ejpam-3884	195	5	)	)	PUNCT
ejpam-3884	195	6	moreover	moreover	ADV
ejpam-3884	195	7	,	,	PUNCT
ejpam-3884	195	8	if	if	SCONJ
ejpam-3884	195	9	kj	kj	PROPN
ejpam-3884	195	10	,	,	PUNCT
ejpam-3884	195	11	lij+	lij+	PROPN
ejpam-3884	195	12	,	,	PUNCT
ejpam-3884	195	13	and	and	CCONJ
ejpam-3884	195	14	lij−	lij−	PROPN
ejpam-3884	195	15	∈	∈	PROPN
ejpam-3884	195	16	v	v	ADP
ejpam-3884	195	17	(	(	PUNCT
ejpam-3884	195	18	γmh	γmh	NOUN
ejpam-3884	195	19	)	)	PUNCT
ejpam-3884	195	20	such	such	ADJ
ejpam-3884	195	21	that	that	SCONJ
ejpam-3884	195	22	kj	kj	PROPN
ejpam-3884	195	23	=	=	PUNCT
ejpam-3884	195	24	mh−1	mh−1	PROPN
ejpam-3884	195	25	+	+	CCONJ
ejpam-3884	195	26	j	j	PROPN
ejpam-3884	195	27	,	,	PUNCT
ejpam-3884	195	28	lij+	lij+	PROPN
ejpam-3884	195	29	=	=	PUNCT
ejpam-3884	195	30	(	(	PUNCT
ejpam-3884	195	31	i+	i+	NUM
ejpam-3884	195	32	1)(mh−1	1)(mh−1	NUM
ejpam-3884	195	33	)	)	PUNCT
ejpam-3884	196	1	+	+	CCONJ
ejpam-3884	196	2	j	j	PROPN
ejpam-3884	196	3	and	and	CCONJ
ejpam-3884	196	4	lij−	lij−	PROPN
ejpam-3884	196	5	=	=	SYM
ejpam-3884	196	6	(	(	PUNCT
ejpam-3884	196	7	i+	i+	NUM
ejpam-3884	196	8	1)(mh−1)−	1)(mh−1)−	NOUN
ejpam-3884	196	9	j	j	PROPN
ejpam-3884	196	10	where	where	SCONJ
ejpam-3884	196	11	i	i	PRON
ejpam-3884	196	12	=	=	NOUN
ejpam-3884	196	13	1	1	NUM
ejpam-3884	196	14	,	,	PUNCT
ejpam-3884	196	15	2	2	NUM
ejpam-3884	196	16	,	,	PUNCT
ejpam-3884	196	17	.	.	PUNCT
ejpam-3884	196	18	.	.	PUNCT
ejpam-3884	197	1	.	.	PUNCT
ejpam-3884	198	1	,	,	PUNCT
ejpam-3884	198	2	m−1	m−1	PROPN
ejpam-3884	198	3	2	2	NUM
ejpam-3884	198	4	−	−	NOUN
ejpam-3884	198	5	1	1	NUM
ejpam-3884	198	6	and	and	CCONJ
ejpam-3884	198	7	j	j	PROPN
ejpam-3884	198	8	=	=	SYM
ejpam-3884	198	9	0	0	PROPN
ejpam-3884	198	10	,	,	PUNCT
ejpam-3884	198	11	1	1	NUM
ejpam-3884	198	12	,	,	PUNCT
ejpam-3884	198	13	.	.	PUNCT
ejpam-3884	198	14	.	.	PUNCT
ejpam-3884	198	15	.	.	PUNCT
ejpam-3884	199	1	,	,	PUNCT
ejpam-3884	199	2	m	m	VERB
ejpam-3884	199	3	h−1−1	h−1−1	VERB
ejpam-3884	199	4	2	2	NUM
ejpam-3884	199	5	then	then	ADV
ejpam-3884	199	6	dγ	dγ	ADP
ejpam-3884	199	7	mh	mh	PROPN
ejpam-3884	199	8	(	(	PUNCT
ejpam-3884	199	9	0	0	PROPN
ejpam-3884	199	10	,	,	PUNCT
ejpam-3884	199	11	kj	kj	PROPN
ejpam-3884	199	12	)	)	PUNCT
ejpam-3884	200	1	=	=	PUNCT
ejpam-3884	200	2	dγ	dγ	ADP
ejpam-3884	200	3	mh−1	mh−1	PROPN
ejpam-3884	200	4	(	(	PUNCT
ejpam-3884	200	5	0	0	NUM
ejpam-3884	200	6	,	,	PUNCT
ejpam-3884	200	7	j	j	NOUN
ejpam-3884	200	8	)	)	PUNCT
ejpam-3884	201	1	+	+	CCONJ
ejpam-3884	201	2	1	1	NUM
ejpam-3884	201	3	,	,	PUNCT
ejpam-3884	201	4	(	(	PUNCT
ejpam-3884	201	5	2	2	NUM
ejpam-3884	201	6	)	)	PUNCT
ejpam-3884	201	7	and	and	CCONJ
ejpam-3884	201	8	dγ	dγ	ADP
ejpam-3884	201	9	mh	mh	PROPN
ejpam-3884	201	10	(	(	PUNCT
ejpam-3884	201	11	0	0	PROPN
ejpam-3884	201	12	,	,	PUNCT
ejpam-3884	201	13	lij+	lij+	PROPN
ejpam-3884	201	14	)	)	PUNCT
ejpam-3884	202	1	=	=	PRON
ejpam-3884	202	2	dγ	dγ	ADP
ejpam-3884	202	3	mh	mh	PROPN
ejpam-3884	202	4	(	(	PUNCT
ejpam-3884	202	5	0	0	PROPN
ejpam-3884	202	6	,	,	PUNCT
ejpam-3884	202	7	lij−	lij−	NOUN
ejpam-3884	202	8	)	)	PUNCT
ejpam-3884	203	1	=	=	PUNCT
ejpam-3884	203	2	dγ	dγ	ADP
ejpam-3884	203	3	mh−1	mh−1	PROPN
ejpam-3884	203	4	(	(	PUNCT
ejpam-3884	203	5	0	0	NUM
ejpam-3884	203	6	,	,	PUNCT
ejpam-3884	203	7	j	j	NOUN
ejpam-3884	203	8	)	)	PUNCT
ejpam-3884	204	1	+	+	CCONJ
ejpam-3884	204	2	(	(	PUNCT
ejpam-3884	204	3	i+	i+	NOUN
ejpam-3884	204	4	1	1	NUM
ejpam-3884	204	5	)	)	PUNCT
ejpam-3884	204	6	(	(	PUNCT
ejpam-3884	204	7	3	3	X
ejpam-3884	204	8	)	)	PUNCT
ejpam-3884	204	9	j.	j.	PROPN
ejpam-3884	204	10	antalan	antalan	PROPN
ejpam-3884	204	11	,	,	PUNCT
ejpam-3884	204	12	f.	f.	PROPN
ejpam-3884	204	13	campeña	campeña	PROPN
ejpam-3884	204	14	/	/	SYM
ejpam-3884	204	15	eur	eur	PROPN
ejpam-3884	204	16	.	.	PUNCT
ejpam-3884	205	1	j.	j.	PROPN
ejpam-3884	205	2	pure	pure	PROPN
ejpam-3884	205	3	appl	appl	PROPN
ejpam-3884	205	4	.	.	PROPN
ejpam-3884	205	5	math	math	PROPN
ejpam-3884	205	6	,	,	PUNCT
ejpam-3884	205	7	14	14	NUM
ejpam-3884	205	8	(	(	PUNCT
ejpam-3884	205	9	1	1	NUM
ejpam-3884	205	10	)	)	PUNCT
ejpam-3884	205	11	(	(	PUNCT
ejpam-3884	205	12	2021	2021	NUM
ejpam-3884	205	13	)	)	PUNCT
ejpam-3884	205	14	,	,	PUNCT
ejpam-3884	205	15	248	248	NUM
ejpam-3884	205	16	-	-	SYM
ejpam-3884	205	17	264	264	NUM
ejpam-3884	205	18	256	256	NUM
ejpam-3884	205	19	figure	figure	NOUN
ejpam-3884	205	20	5	5	NUM
ejpam-3884	205	21	:	:	PUNCT
ejpam-3884	205	22	a	a	DET
ejpam-3884	205	23	bfs	bfs	NOUN
ejpam-3884	205	24	tree	tree	NOUN
ejpam-3884	205	25	of	of	ADP
ejpam-3884	205	26	the	the	DET
ejpam-3884	205	27	graph	graph	NOUN
ejpam-3884	205	28	γ72	γ72	NOUN
ejpam-3884	205	29	.	.	PUNCT
ejpam-3884	206	1	the	the	DET
ejpam-3884	206	2	green	green	ADJ
ejpam-3884	206	3	-	-	PUNCT
ejpam-3884	206	4	colored	color	VERB
ejpam-3884	206	5	vertices	vertex	NOUN
ejpam-3884	206	6	refer	refer	VERB
ejpam-3884	206	7	to	to	ADP
ejpam-3884	206	8	the	the	DET
ejpam-3884	206	9	vertices	vertex	NOUN
ejpam-3884	206	10	that	that	PRON
ejpam-3884	206	11	originally	originally	ADV
ejpam-3884	206	12	appeared	appear	VERB
ejpam-3884	206	13	in	in	ADP
ejpam-3884	206	14	bfs0(γ71	bfs0(γ71	NUM
ejpam-3884	206	15	)	)	PUNCT
ejpam-3884	206	16	.	.	PUNCT
ejpam-3884	207	1	while	while	SCONJ
ejpam-3884	207	2	the	the	DET
ejpam-3884	207	3	green	green	ADJ
ejpam-3884	207	4	-	-	PUNCT
ejpam-3884	207	5	colored	color	VERB
ejpam-3884	207	6	vertices	vertex	NOUN
ejpam-3884	207	7	with	with	ADP
ejpam-3884	207	8	red	red	ADJ
ejpam-3884	207	9	edges	edge	NOUN
ejpam-3884	207	10	refer	refer	VERB
ejpam-3884	207	11	to	to	ADP
ejpam-3884	207	12	the	the	DET
ejpam-3884	207	13	descended	descend	VERB
ejpam-3884	207	14	vertices	vertex	NOUN
ejpam-3884	207	15	in	in	ADP
ejpam-3884	207	16	bfs0(γ71	bfs0(γ71	NUM
ejpam-3884	207	17	)	)	PUNCT
ejpam-3884	207	18	.	.	PUNCT
ejpam-3884	208	1	the	the	DET
ejpam-3884	208	2	yellow	yellow	ADJ
ejpam-3884	208	3	-	-	PUNCT
ejpam-3884	208	4	colored	color	VERB
ejpam-3884	208	5	vertices	vertex	NOUN
ejpam-3884	208	6	refer	refer	VERB
ejpam-3884	208	7	to	to	ADP
ejpam-3884	208	8	the	the	DET
ejpam-3884	208	9	resulting	result	VERB
ejpam-3884	208	10	vertices	vertex	NOUN
ejpam-3884	208	11	as	as	ADP
ejpam-3884	208	12	a	a	DET
ejpam-3884	208	13	result	result	NOUN
ejpam-3884	208	14	of	of	ADP
ejpam-3884	208	15	reproducing	reproduce	VERB
ejpam-3884	208	16	the	the	DET
ejpam-3884	208	17	left	left	ADJ
ejpam-3884	208	18	part	part	NOUN
ejpam-3884	208	19	of	of	ADP
ejpam-3884	208	20	bfs0(γ71	bfs0(γ71	NOUN
ejpam-3884	208	21	)	)	PUNCT
ejpam-3884	208	22	with	with	ADP
ejpam-3884	208	23	the	the	DET
ejpam-3884	208	24	substitution	substitution	NOUN
ejpam-3884	208	25	0	0	NUM
ejpam-3884	209	1	:	:	PUNCT
ejpam-3884	209	2	=	=	SYM
ejpam-3884	209	3	7	7	X
ejpam-3884	209	4	.	.	PUNCT
ejpam-3884	210	1	the	the	DET
ejpam-3884	210	2	violet	violet	NOUN
ejpam-3884	210	3	-	-	PUNCT
ejpam-3884	210	4	colored	color	VERB
ejpam-3884	210	5	vertices	vertex	NOUN
ejpam-3884	210	6	refer	refer	VERB
ejpam-3884	210	7	to	to	ADP
ejpam-3884	210	8	the	the	DET
ejpam-3884	210	9	resulting	result	VERB
ejpam-3884	210	10	vertices	vertex	NOUN
ejpam-3884	210	11	as	as	ADP
ejpam-3884	210	12	a	a	DET
ejpam-3884	210	13	result	result	NOUN
ejpam-3884	210	14	of	of	ADP
ejpam-3884	210	15	introducing	introduce	VERB
ejpam-3884	210	16	the	the	DET
ejpam-3884	210	17	vertex	vertex	NOUN
ejpam-3884	210	18	7	7	NUM
ejpam-3884	210	19	+	+	SYM
ejpam-3884	210	20	7	7	NUM
ejpam-3884	210	21	as	as	ADP
ejpam-3884	210	22	a	a	DET
ejpam-3884	210	23	child	child	NOUN
ejpam-3884	210	24	of	of	ADP
ejpam-3884	210	25	vertex	vertex	NOUN
ejpam-3884	210	26	7	7	NUM
ejpam-3884	210	27	and	and	CCONJ
ejpam-3884	210	28	reproducing	reproduce	VERB
ejpam-3884	210	29	the	the	DET
ejpam-3884	210	30	genealogy	genealogy	NOUN
ejpam-3884	210	31	of	of	ADP
ejpam-3884	210	32	vertex	vertex	NOUN
ejpam-3884	210	33	7	7	NUM
ejpam-3884	210	34	with	with	ADP
ejpam-3884	210	35	the	the	DET
ejpam-3884	210	36	substitution	substitution	NOUN
ejpam-3884	210	37	7	7	NUM
ejpam-3884	210	38	=	=	NOUN
ejpam-3884	210	39	:	:	PUNCT
ejpam-3884	210	40	7	7	NUM
ejpam-3884	210	41	+	+	SYM
ejpam-3884	210	42	7	7	X
ejpam-3884	210	43	.	.	PUNCT
ejpam-3884	211	1	the	the	DET
ejpam-3884	211	2	beige	beige	NOUN
ejpam-3884	211	3	-	-	PUNCT
ejpam-3884	211	4	colored	color	VERB
ejpam-3884	211	5	vertices	vertex	NOUN
ejpam-3884	211	6	refer	refer	VERB
ejpam-3884	211	7	to	to	ADP
ejpam-3884	211	8	the	the	DET
ejpam-3884	211	9	resulting	result	VERB
ejpam-3884	211	10	vertices	vertex	NOUN
ejpam-3884	211	11	as	as	ADP
ejpam-3884	211	12	a	a	DET
ejpam-3884	211	13	result	result	NOUN
ejpam-3884	211	14	of	of	ADP
ejpam-3884	211	15	introducing	introduce	VERB
ejpam-3884	211	16	the	the	DET
ejpam-3884	211	17	vertex	vertex	NOUN
ejpam-3884	211	18	7	7	NUM
ejpam-3884	211	19	+	+	CCONJ
ejpam-3884	211	20	7	7	NUM
ejpam-3884	211	21	+	+	SYM
ejpam-3884	211	22	7	7	NUM
ejpam-3884	211	23	as	as	ADP
ejpam-3884	211	24	a	a	DET
ejpam-3884	211	25	child	child	NOUN
ejpam-3884	211	26	of	of	ADP
ejpam-3884	211	27	vertex	vertex	NOUN
ejpam-3884	211	28	7	7	NUM
ejpam-3884	211	29	+	+	SYM
ejpam-3884	211	30	7	7	NUM
ejpam-3884	211	31	and	and	CCONJ
ejpam-3884	211	32	reproducing	reproduce	VERB
ejpam-3884	211	33	the	the	DET
ejpam-3884	211	34	genealogy	genealogy	NOUN
ejpam-3884	211	35	of	of	ADP
ejpam-3884	211	36	vertex	vertex	NOUN
ejpam-3884	211	37	7	7	NUM
ejpam-3884	211	38	+	+	CCONJ
ejpam-3884	211	39	7	7	NUM
ejpam-3884	211	40	with	with	ADP
ejpam-3884	211	41	the	the	DET
ejpam-3884	211	42	substitution	substitution	NOUN
ejpam-3884	211	43	7	7	NUM
ejpam-3884	211	44	+	+	CCONJ
ejpam-3884	211	45	7	7	NUM
ejpam-3884	211	46	=	=	NOUN
ejpam-3884	211	47	:	:	PUNCT
ejpam-3884	211	48	7	7	NUM
ejpam-3884	212	1	+	+	CCONJ
ejpam-3884	212	2	7	7	NUM
ejpam-3884	212	3	+	+	SYM
ejpam-3884	212	4	7	7	NUM
ejpam-3884	212	5	.	.	PUNCT
ejpam-3884	213	1	the	the	DET
ejpam-3884	213	2	blue	blue	ADJ
ejpam-3884	213	3	-	-	PUNCT
ejpam-3884	213	4	colored	color	VERB
ejpam-3884	213	5	vertices	vertex	NOUN
ejpam-3884	213	6	are	be	AUX
ejpam-3884	213	7	the	the	DET
ejpam-3884	213	8	vertices	vertex	NOUN
ejpam-3884	213	9	obtained	obtain	VERB
ejpam-3884	213	10	using	use	VERB
ejpam-3884	213	11	property	property	NOUN
ejpam-3884	213	12	(	(	PUNCT
ejpam-3884	213	13	i	i	NOUN
ejpam-3884	213	14	)	)	PUNCT
ejpam-3884	213	15	.	.	PUNCT
ejpam-3884	214	1	proof	proof	NOUN
ejpam-3884	214	2	.	.	PUNCT
ejpam-3884	215	1	steps	step	NOUN
ejpam-3884	215	2	1	1	NUM
ejpam-3884	215	3	and	and	CCONJ
ejpam-3884	215	4	2	2	NUM
ejpam-3884	215	5	imply	imply	VERB
ejpam-3884	215	6	that	that	SCONJ
ejpam-3884	215	7	if	if	SCONJ
ejpam-3884	215	8	j	j	PROPN
ejpam-3884	215	9	=	=	SYM
ejpam-3884	215	10	mh−1	mh−1	PROPN
ejpam-3884	215	11	,	,	PUNCT
ejpam-3884	215	12	then	then	ADV
ejpam-3884	215	13	dγ	dγ	ADP
ejpam-3884	215	14	mh	mh	PROPN
ejpam-3884	215	15	(	(	PUNCT
ejpam-3884	215	16	0	0	PROPN
ejpam-3884	215	17	,	,	PUNCT
ejpam-3884	215	18	j	j	NOUN
ejpam-3884	215	19	)	)	PUNCT
ejpam-3884	215	20	=	=	SYM
ejpam-3884	216	1	1	1	NUM
ejpam-3884	216	2	=	=	SYM
ejpam-3884	216	3	dγ	dγ	ADP
ejpam-3884	216	4	mh−1	mh−1	PROPN
ejpam-3884	216	5	(	(	PUNCT
ejpam-3884	216	6	0	0	NUM
ejpam-3884	216	7	,	,	PUNCT
ejpam-3884	216	8	0	0	NUM
ejpam-3884	216	9	)	)	PUNCT
ejpam-3884	217	1	+	+	CCONJ
ejpam-3884	217	2	1	1	X
ejpam-3884	217	3	.	.	PUNCT
ejpam-3884	217	4	and	and	CCONJ
ejpam-3884	217	5	that	that	SCONJ
ejpam-3884	217	6	dγ	dγ	ADP
ejpam-3884	217	7	mh	mh	PROPN
ejpam-3884	217	8	(	(	PUNCT
ejpam-3884	217	9	0	0	PROPN
ejpam-3884	217	10	,	,	PUNCT
ejpam-3884	217	11	j	j	NOUN
ejpam-3884	217	12	)	)	PUNCT
ejpam-3884	217	13	=	=	PRON
ejpam-3884	217	14	{	{	PUNCT
ejpam-3884	217	15	dγ	dγ	ADP
ejpam-3884	217	16	mh−1	mh−1	PROPN
ejpam-3884	217	17	(	(	PUNCT
ejpam-3884	217	18	0	0	NUM
ejpam-3884	217	19	,	,	PUNCT
ejpam-3884	217	20	j	j	NOUN
ejpam-3884	217	21	)	)	PUNCT
ejpam-3884	217	22	if	if	SCONJ
ejpam-3884	217	23	j	j	PROPN
ejpam-3884	217	24	∈	∈	PROPN
ejpam-3884	217	25	l[bfs0(γmh−1	l[bfs0(γmh−1	X
ejpam-3884	217	26	)	)	PUNCT
ejpam-3884	217	27	]	]	PUNCT
ejpam-3884	217	28	dγ	dγ	ADP
ejpam-3884	217	29	mh−1	mh−1	PROPN
ejpam-3884	217	30	(	(	PUNCT
ejpam-3884	217	31	0	0	NUM
ejpam-3884	217	32	,	,	PUNCT
ejpam-3884	217	33	j	j	NOUN
ejpam-3884	217	34	)	)	PUNCT
ejpam-3884	217	35	+	+	CCONJ
ejpam-3884	217	36	1	1	NUM
ejpam-3884	217	37	if	if	SCONJ
ejpam-3884	217	38	j	j	PROPN
ejpam-3884	217	39	∈	∈	PROPN
ejpam-3884	217	40	r[bfs0(γmh−1	r[bfs0(γmh−1	VERB
ejpam-3884	217	41	)	)	PUNCT
ejpam-3884	217	42	]	]	PUNCT
ejpam-3884	217	43	.	.	PUNCT
ejpam-3884	218	1	by	by	ADP
ejpam-3884	218	2	referring	refer	VERB
ejpam-3884	218	3	to	to	ADP
ejpam-3884	218	4	remark	remark	NOUN
ejpam-3884	218	5	8	8	NUM
ejpam-3884	218	6	we	we	PRON
ejpam-3884	218	7	verified	verify	VERB
ejpam-3884	218	8	equation	equation	NOUN
ejpam-3884	218	9	(	(	PUNCT
ejpam-3884	218	10	1	1	NUM
ejpam-3884	218	11	)	)	PUNCT
ejpam-3884	218	12	.	.	PUNCT
ejpam-3884	219	1	next	next	ADV
ejpam-3884	219	2	,	,	PUNCT
ejpam-3884	219	3	we	we	PRON
ejpam-3884	219	4	consider	consider	VERB
ejpam-3884	219	5	the	the	DET
ejpam-3884	219	6	implication	implication	NOUN
ejpam-3884	219	7	of	of	ADP
ejpam-3884	219	8	step	step	NOUN
ejpam-3884	219	9	3	3	NUM
ejpam-3884	219	10	.	.	NOUN
ejpam-3884	219	11	step	step	NOUN
ejpam-3884	219	12	3	3	NUM
ejpam-3884	219	13	implies	imply	VERB
ejpam-3884	219	14	that	that	SCONJ
ejpam-3884	219	15	if	if	SCONJ
ejpam-3884	219	16	kj	kj	PROPN
ejpam-3884	219	17	=	=	PUNCT
ejpam-3884	219	18	mh−1	mh−1	PROPN
ejpam-3884	220	1	+	+	CCONJ
ejpam-3884	220	2	j	j	PROPN
ejpam-3884	220	3	where	where	SCONJ
ejpam-3884	220	4	j	j	PROPN
ejpam-3884	220	5	=	=	SYM
ejpam-3884	220	6	1	1	NUM
ejpam-3884	220	7	,	,	PUNCT
ejpam-3884	220	8	2	2	NUM
ejpam-3884	220	9	,	,	PUNCT
ejpam-3884	220	10	.	.	PUNCT
ejpam-3884	220	11	.	.	PUNCT
ejpam-3884	221	1	.	.	PUNCT
ejpam-3884	222	1	,	,	PUNCT
ejpam-3884	222	2	m	m	VERB
ejpam-3884	222	3	h−1−1	h−1−1	ADJ
ejpam-3884	222	4	2	2	NUM
ejpam-3884	222	5	,	,	PUNCT
ejpam-3884	222	6	we	we	PRON
ejpam-3884	222	7	have	have	VERB
ejpam-3884	222	8	dγ	dγ	ADP
ejpam-3884	222	9	mh	mh	PROPN
ejpam-3884	222	10	(	(	PUNCT
ejpam-3884	222	11	0	0	PROPN
ejpam-3884	222	12	,	,	PUNCT
ejpam-3884	222	13	kj	kj	PROPN
ejpam-3884	222	14	)	)	PUNCT
ejpam-3884	223	1	=	=	PUNCT
ejpam-3884	223	2	dγ	dγ	ADP
ejpam-3884	223	3	mh−1	mh−1	PROPN
ejpam-3884	223	4	(	(	PUNCT
ejpam-3884	223	5	0	0	NUM
ejpam-3884	223	6	,	,	PUNCT
ejpam-3884	223	7	j	j	NOUN
ejpam-3884	223	8	)	)	PUNCT
ejpam-3884	224	1	+	+	NOUN
ejpam-3884	224	2	1	1	X
ejpam-3884	224	3	.	.	X
ejpam-3884	224	4	combining	combine	VERB
ejpam-3884	224	5	this	this	PRON
ejpam-3884	224	6	with	with	ADP
ejpam-3884	224	7	the	the	DET
ejpam-3884	224	8	fact	fact	NOUN
ejpam-3884	224	9	that	that	SCONJ
ejpam-3884	224	10	for	for	ADP
ejpam-3884	224	11	j	j	PROPN
ejpam-3884	224	12	=	=	SYM
ejpam-3884	224	13	mh−1	mh−1	PROPN
ejpam-3884	224	14	,	,	PUNCT
ejpam-3884	224	15	we	we	PRON
ejpam-3884	224	16	have	have	AUX
ejpam-3884	224	17	dγ	dγ	ADP
ejpam-3884	224	18	mh	mh	PROPN
ejpam-3884	224	19	(	(	PUNCT
ejpam-3884	224	20	0	0	PROPN
ejpam-3884	224	21	,	,	PUNCT
ejpam-3884	224	22	j	j	NOUN
ejpam-3884	224	23	)	)	PUNCT
ejpam-3884	224	24	=	=	SYM
ejpam-3884	224	25	1	1	NUM
ejpam-3884	224	26	=	=	SYM
ejpam-3884	224	27	dγ	dγ	ADP
ejpam-3884	224	28	mh−1	mh−1	PROPN
ejpam-3884	224	29	(	(	PUNCT
ejpam-3884	224	30	0	0	NUM
ejpam-3884	224	31	,	,	PUNCT
ejpam-3884	224	32	0	0	NUM
ejpam-3884	224	33	)	)	PUNCT
ejpam-3884	224	34	+	+	CCONJ
ejpam-3884	224	35	1	1	NUM
ejpam-3884	224	36	proves	prove	VERB
ejpam-3884	224	37	equation	equation	NOUN
ejpam-3884	224	38	(	(	PUNCT
ejpam-3884	224	39	2	2	NUM
ejpam-3884	224	40	)	)	PUNCT
ejpam-3884	224	41	.	.	PUNCT
ejpam-3884	225	1	the	the	DET
ejpam-3884	225	2	substitution	substitution	NOUN
ejpam-3884	225	3	part	part	NOUN
ejpam-3884	225	4	of	of	ADP
ejpam-3884	225	5	step	step	NOUN
ejpam-3884	225	6	4	4	NUM
ejpam-3884	225	7	implies	imply	VERB
ejpam-3884	225	8	that	that	SCONJ
ejpam-3884	225	9	for	for	ADP
ejpam-3884	225	10	i	i	PRON
ejpam-3884	225	11	=	=	SYM
ejpam-3884	225	12	1	1	NUM
ejpam-3884	225	13	and	and	CCONJ
ejpam-3884	225	14	j	j	PROPN
ejpam-3884	225	15	=	=	SYM
ejpam-3884	225	16	0	0	PROPN
ejpam-3884	225	17	,	,	PUNCT
ejpam-3884	225	18	we	we	PRON
ejpam-3884	225	19	have	have	VERB
ejpam-3884	225	20	dγ	dγ	ADP
ejpam-3884	225	21	mh	mh	PROPN
ejpam-3884	225	22	(	(	PUNCT
ejpam-3884	225	23	0	0	PROPN
ejpam-3884	225	24	,	,	PUNCT
ejpam-3884	225	25	lij	lij	PROPN
ejpam-3884	225	26	)	)	PUNCT
ejpam-3884	226	1	=	=	PUNCT
ejpam-3884	226	2	dγ	dγ	ADP
ejpam-3884	226	3	mh	mh	PROPN
ejpam-3884	226	4	(	(	PUNCT
ejpam-3884	226	5	0	0	NUM
ejpam-3884	226	6	,	,	PUNCT
ejpam-3884	226	7	l0j	l0j	PROPN
ejpam-3884	226	8	)	)	PUNCT
ejpam-3884	227	1	+	+	CCONJ
ejpam-3884	227	2	1	1	NUM
ejpam-3884	227	3	where	where	SCONJ
ejpam-3884	227	4	l0j	l0j	VERB
ejpam-3884	227	5	=	=	SYM
ejpam-3884	227	6	mh−1	mh−1	PROPN
ejpam-3884	227	7	.	.	PUNCT
ejpam-3884	228	1	while	while	SCONJ
ejpam-3884	228	2	the	the	DET
ejpam-3884	228	3	part	part	NOUN
ejpam-3884	228	4	involving	involve	VERB
ejpam-3884	228	5	reproduction	reproduction	NOUN
ejpam-3884	228	6	of	of	ADP
ejpam-3884	228	7	genealogy	genealogy	NOUN
ejpam-3884	228	8	implies	imply	VERB
ejpam-3884	228	9	that	that	SCONJ
ejpam-3884	228	10	for	for	ADP
ejpam-3884	228	11	i	i	PRON
ejpam-3884	228	12	=	=	SYM
ejpam-3884	228	13	1	1	NUM
ejpam-3884	228	14	and	and	CCONJ
ejpam-3884	228	15	j	j	NOUN
ejpam-3884	228	16	=	=	SYM
ejpam-3884	228	17	1	1	NUM
ejpam-3884	228	18	,	,	PUNCT
ejpam-3884	228	19	2	2	NUM
ejpam-3884	228	20	,	,	PUNCT
ejpam-3884	228	21	.	.	PUNCT
ejpam-3884	228	22	.	.	PUNCT
ejpam-3884	229	1	.	.	PUNCT
ejpam-3884	230	1	,	,	PUNCT
ejpam-3884	230	2	m	m	VERB
ejpam-3884	230	3	h−1−1	h−1−1	ADJ
ejpam-3884	230	4	2	2	NUM
ejpam-3884	230	5	we	we	PRON
ejpam-3884	230	6	have	have	VERB
ejpam-3884	230	7	dγ	dγ	ADP
ejpam-3884	230	8	mh	mh	PROPN
ejpam-3884	230	9	(	(	PUNCT
ejpam-3884	230	10	0	0	PROPN
ejpam-3884	230	11	,	,	PUNCT
ejpam-3884	230	12	lij+	lij+	PROPN
ejpam-3884	230	13	)	)	PUNCT
ejpam-3884	230	14	=	=	PRON
ejpam-3884	231	1	dγ	dγ	ADP
ejpam-3884	231	2	mh	mh	PROPN
ejpam-3884	231	3	(	(	PUNCT
ejpam-3884	231	4	0	0	PROPN
ejpam-3884	231	5	,	,	PUNCT
ejpam-3884	231	6	lij−	lij−	NOUN
ejpam-3884	231	7	)	)	PUNCT
ejpam-3884	231	8	=	=	PUNCT
ejpam-3884	232	1	dγ	dγ	ADP
ejpam-3884	232	2	mh	mh	PROPN
ejpam-3884	232	3	(	(	PUNCT
ejpam-3884	232	4	0	0	PROPN
ejpam-3884	232	5	,	,	PUNCT
ejpam-3884	232	6	kj	kj	PROPN
ejpam-3884	232	7	)	)	PUNCT
ejpam-3884	233	1	+	+	CCONJ
ejpam-3884	233	2	1	1	X
ejpam-3884	233	3	.	.	X
ejpam-3884	233	4	using	use	VERB
ejpam-3884	233	5	equation	equation	NOUN
ejpam-3884	233	6	(	(	PUNCT
ejpam-3884	233	7	2	2	X
ejpam-3884	233	8	)	)	PUNCT
ejpam-3884	233	9	we	we	PRON
ejpam-3884	233	10	get	get	VERB
ejpam-3884	233	11	dγ	dγ	ADP
ejpam-3884	233	12	mh	mh	PROPN
ejpam-3884	233	13	(	(	PUNCT
ejpam-3884	233	14	0	0	PROPN
ejpam-3884	233	15	,	,	PUNCT
ejpam-3884	233	16	lij+	lij+	PROPN
ejpam-3884	233	17	)	)	PUNCT
ejpam-3884	233	18	=	=	PRON
ejpam-3884	234	1	dγ	dγ	ADP
ejpam-3884	234	2	mh	mh	PROPN
ejpam-3884	234	3	(	(	PUNCT
ejpam-3884	234	4	0	0	PROPN
ejpam-3884	234	5	,	,	PUNCT
ejpam-3884	234	6	lij−	lij−	NOUN
ejpam-3884	234	7	)	)	PUNCT
ejpam-3884	234	8	=	=	PUNCT
ejpam-3884	234	9	dγ	dγ	ADP
ejpam-3884	234	10	mh−1	mh−1	PROPN
ejpam-3884	234	11	(	(	PUNCT
ejpam-3884	234	12	0	0	NUM
ejpam-3884	234	13	,	,	PUNCT
ejpam-3884	234	14	j	j	NOUN
ejpam-3884	234	15	)	)	PUNCT
ejpam-3884	235	1	+	+	CCONJ
ejpam-3884	235	2	1	1	NUM
ejpam-3884	235	3	+	+	NUM
ejpam-3884	235	4	1	1	NUM
ejpam-3884	235	5	.	.	PUNCT
ejpam-3884	236	1	this	this	PRON
ejpam-3884	236	2	proves	prove	VERB
ejpam-3884	236	3	the	the	DET
ejpam-3884	236	4	i	i	NOUN
ejpam-3884	236	5	=	=	SYM
ejpam-3884	236	6	1	1	NUM
ejpam-3884	236	7	case	case	NOUN
ejpam-3884	236	8	of	of	ADP
ejpam-3884	236	9	equation	equation	NOUN
ejpam-3884	236	10	(	(	PUNCT
ejpam-3884	236	11	3	3	NUM
ejpam-3884	236	12	)	)	PUNCT
ejpam-3884	236	13	.	.	PUNCT
ejpam-3884	237	1	finally	finally	ADV
ejpam-3884	237	2	,	,	PUNCT
ejpam-3884	237	3	step	step	NOUN
ejpam-3884	237	4	5	5	NUM
ejpam-3884	237	5	implies	imply	VERB
ejpam-3884	237	6	the	the	DET
ejpam-3884	237	7	validity	validity	NOUN
ejpam-3884	237	8	of	of	ADP
ejpam-3884	237	9	equation	equation	NOUN
ejpam-3884	237	10	(	(	PUNCT
ejpam-3884	237	11	3	3	NUM
ejpam-3884	237	12	)	)	PUNCT
ejpam-3884	237	13	for	for	ADP
ejpam-3884	237	14	i	i	PRON
ejpam-3884	237	15	=	=	SYM
ejpam-3884	237	16	2	2	NUM
ejpam-3884	237	17	,	,	PUNCT
ejpam-3884	237	18	3	3	NUM
ejpam-3884	237	19	,	,	PUNCT
ejpam-3884	237	20	.	.	PUNCT
ejpam-3884	237	21	.	.	PUNCT
ejpam-3884	238	1	.	.	PUNCT
ejpam-3884	239	1	,	,	PUNCT
ejpam-3884	239	2	m−1	m−1	PROPN
ejpam-3884	239	3	2	2	NUM
ejpam-3884	239	4	−	−	NOUN
ejpam-3884	239	5	1	1	NUM
ejpam-3884	239	6	.	.	PUNCT
ejpam-3884	240	1	this	this	PRON
ejpam-3884	240	2	completes	complete	VERB
ejpam-3884	240	3	the	the	DET
ejpam-3884	240	4	proof	proof	NOUN
ejpam-3884	240	5	of	of	ADP
ejpam-3884	240	6	the	the	DET
ejpam-3884	240	7	theorem	theorem	PROPN
ejpam-3884	240	8	.	.	PROPN
ejpam-3884	240	9	example	example	NOUN
ejpam-3884	240	10	3	3	NUM
ejpam-3884	240	11	.	.	PUNCT
ejpam-3884	240	12	using	use	VERB
ejpam-3884	240	13	the	the	DET
ejpam-3884	240	14	constructed	construct	VERB
ejpam-3884	240	15	bfs	bfs	NOUN
ejpam-3884	240	16	tree	tree	NOUN
ejpam-3884	240	17	for	for	ADP
ejpam-3884	240	18	γ72	γ72	NOUN
ejpam-3884	240	19	in	in	ADP
ejpam-3884	240	20	figure	figure	NOUN
ejpam-3884	240	21	5	5	NUM
ejpam-3884	240	22	we	we	PRON
ejpam-3884	240	23	have	have	VERB
ejpam-3884	240	24	{	{	PUNCT
ejpam-3884	240	25	0	0	NUM
ejpam-3884	240	26	,	,	PUNCT
ejpam-3884	240	27	1	1	NUM
ejpam-3884	240	28	,	,	PUNCT
ejpam-3884	240	29	2	2	NUM
ejpam-3884	240	30	,	,	PUNCT
ejpam-3884	240	31	3	3	NUM
ejpam-3884	240	32	,	,	PUNCT
ejpam-3884	240	33	4	4	NUM
ejpam-3884	240	34	,	,	PUNCT
ejpam-3884	240	35	3	3	NUM
ejpam-3884	240	36	,	,	PUNCT
ejpam-3884	240	37	2	2	NUM
ejpam-3884	240	38	,	,	PUNCT
ejpam-3884	240	39	1	1	NUM
ejpam-3884	240	40	,	,	PUNCT
ejpam-3884	240	41	2	2	NUM
ejpam-3884	240	42	,	,	PUNCT
ejpam-3884	240	43	3	3	NUM
ejpam-3884	240	44	,	,	PUNCT
ejpam-3884	240	45	4	4	NUM
ejpam-3884	240	46	,	,	PUNCT
ejpam-3884	240	47	5	5	NUM
ejpam-3884	240	48	,	,	PUNCT
ejpam-3884	240	49	4	4	NUM
ejpam-3884	240	50	,	,	PUNCT
ejpam-3884	240	51	3	3	NUM
ejpam-3884	240	52	,	,	PUNCT
ejpam-3884	240	53	2	2	NUM
ejpam-3884	240	54	,	,	PUNCT
ejpam-3884	240	55	3	3	NUM
ejpam-3884	240	56	,	,	PUNCT
ejpam-3884	240	57	4	4	NUM
ejpam-3884	240	58	,	,	PUNCT
ejpam-3884	240	59	5	5	NUM
ejpam-3884	240	60	,	,	PUNCT
ejpam-3884	240	61	6	6	NUM
ejpam-3884	240	62	,	,	PUNCT
ejpam-3884	240	63	5	5	NUM
ejpam-3884	240	64	,	,	PUNCT
ejpam-3884	240	65	4	4	NUM
ejpam-3884	240	66	,	,	PUNCT
ejpam-3884	240	67	3	3	NUM
ejpam-3884	240	68	,	,	PUNCT
ejpam-3884	240	69	4	4	NUM
ejpam-3884	240	70	,	,	PUNCT
ejpam-3884	240	71	5	5	NUM
ejpam-3884	240	72	,	,	PUNCT
ejpam-3884	240	73	6	6	NUM
ejpam-3884	240	74	,	,	PUNCT
ejpam-3884	240	75	6	6	NUM
ejpam-3884	240	76	,	,	PUNCT
ejpam-3884	240	77	5	5	NUM
ejpam-3884	240	78	,	,	PUNCT
ejpam-3884	240	79	4	4	NUM
ejpam-3884	240	80	,	,	PUNCT
ejpam-3884	240	81	3	3	NUM
ejpam-3884	240	82	,	,	PUNCT
ejpam-3884	240	83	4	4	NUM
ejpam-3884	240	84	,	,	PUNCT
ejpam-3884	240	85	5	5	NUM
ejpam-3884	240	86	,	,	PUNCT
ejpam-3884	240	87	6	6	NUM
ejpam-3884	240	88	,	,	PUNCT
ejpam-3884	240	89	5	5	NUM
ejpam-3884	240	90	,	,	PUNCT
ejpam-3884	240	91	4	4	NUM
ejpam-3884	240	92	,	,	PUNCT
ejpam-3884	240	93	3	3	NUM
ejpam-3884	240	94	,	,	PUNCT
ejpam-3884	240	95	2	2	NUM
ejpam-3884	240	96	,	,	PUNCT
ejpam-3884	240	97	3	3	NUM
ejpam-3884	240	98	,	,	PUNCT
ejpam-3884	240	99	4	4	NUM
ejpam-3884	240	100	,	,	PUNCT
ejpam-3884	240	101	5	5	NUM
ejpam-3884	240	102	,	,	PUNCT
ejpam-3884	240	103	4	4	NUM
ejpam-3884	240	104	,	,	PUNCT
ejpam-3884	240	105	3	3	NUM
ejpam-3884	240	106	,	,	PUNCT
ejpam-3884	240	107	2	2	NUM
ejpam-3884	240	108	,	,	PUNCT
ejpam-3884	240	109	1	1	NUM
ejpam-3884	240	110	,	,	PUNCT
ejpam-3884	240	111	2	2	NUM
ejpam-3884	240	112	,	,	PUNCT
ejpam-3884	240	113	3	3	NUM
ejpam-3884	240	114	,	,	PUNCT
ejpam-3884	240	115	4	4	NUM
ejpam-3884	240	116	,	,	PUNCT
ejpam-3884	240	117	3	3	NUM
ejpam-3884	240	118	,	,	PUNCT
ejpam-3884	240	119	2	2	NUM
ejpam-3884	240	120	,	,	PUNCT
ejpam-3884	240	121	1	1	NUM
ejpam-3884	240	122	}	}	PUNCT
ejpam-3884	240	123	as	as	ADP
ejpam-3884	240	124	the	the	DET
ejpam-3884	240	125	first	first	ADJ
ejpam-3884	240	126	row	row	NOUN
ejpam-3884	240	127	entries	entry	NOUN
ejpam-3884	240	128	of	of	ADP
ejpam-3884	240	129	d(γ72	d(γ72	NOUN
ejpam-3884	240	130	)	)	PUNCT
ejpam-3884	240	131	.	.	PUNCT
ejpam-3884	241	1	using	use	VERB
ejpam-3884	241	2	theorem	theorem	NOUN
ejpam-3884	241	3	1	1	NUM
ejpam-3884	241	4	,	,	PUNCT
ejpam-3884	241	5	given	give	VERB
ejpam-3884	241	6	the	the	DET
ejpam-3884	241	7	first	first	ADJ
ejpam-3884	241	8	row	row	NOUN
ejpam-3884	241	9	of	of	ADP
ejpam-3884	241	10	the	the	DET
ejpam-3884	241	11	distance	distance	NOUN
ejpam-3884	241	12	matrix	matrix	NOUN
ejpam-3884	241	13	of	of	ADP
ejpam-3884	241	14	the	the	DET
ejpam-3884	241	15	graph	graph	NOUN
ejpam-3884	241	16	γ72	γ72	NOUN
ejpam-3884	241	17	,	,	PUNCT
ejpam-3884	241	18	we	we	PRON
ejpam-3884	241	19	can	can	AUX
ejpam-3884	241	20	determine	determine	VERB
ejpam-3884	241	21	the	the	DET
ejpam-3884	241	22	first	first	ADJ
ejpam-3884	241	23	row	row	NOUN
ejpam-3884	241	24	of	of	ADP
ejpam-3884	241	25	the	the	DET
ejpam-3884	241	26	distance	distance	NOUN
ejpam-3884	241	27	matrix	matrix	NOUN
ejpam-3884	241	28	of	of	ADP
ejpam-3884	241	29	the	the	DET
ejpam-3884	241	30	graph	graph	NOUN
ejpam-3884	241	31	γ73	γ73	NOUN
ejpam-3884	241	32	.	.	PUNCT
ejpam-3884	242	1	the	the	DET
ejpam-3884	242	2	first	first	ADJ
ejpam-3884	242	3	row	row	NOUN
ejpam-3884	242	4	of	of	ADP
ejpam-3884	242	5	the	the	DET
ejpam-3884	242	6	distance	distance	NOUN
ejpam-3884	242	7	matrix	matrix	NOUN
ejpam-3884	242	8	of	of	ADP
ejpam-3884	242	9	the	the	DET
ejpam-3884	242	10	graph	graph	NOUN
ejpam-3884	242	11	γ73	γ73	NOUN
ejpam-3884	242	12	is	be	AUX
ejpam-3884	242	13	given	give	VERB
ejpam-3884	242	14	by	by	ADP
ejpam-3884	242	15	j.	j.	PROPN
ejpam-3884	242	16	antalan	antalan	PROPN
ejpam-3884	242	17	,	,	PUNCT
ejpam-3884	242	18	f.	f.	PROPN
ejpam-3884	242	19	campeña	campeña	PROPN
ejpam-3884	242	20	/	/	SYM
ejpam-3884	242	21	eur	eur	PROPN
ejpam-3884	242	22	.	.	PUNCT
ejpam-3884	243	1	j.	j.	PROPN
ejpam-3884	243	2	pure	pure	PROPN
ejpam-3884	243	3	appl	appl	PROPN
ejpam-3884	243	4	.	.	PROPN
ejpam-3884	243	5	math	math	PROPN
ejpam-3884	243	6	,	,	PUNCT
ejpam-3884	243	7	14	14	NUM
ejpam-3884	243	8	(	(	PUNCT
ejpam-3884	243	9	1	1	NUM
ejpam-3884	243	10	)	)	PUNCT
ejpam-3884	243	11	(	(	PUNCT
ejpam-3884	243	12	2021	2021	NUM
ejpam-3884	243	13	)	)	PUNCT
ejpam-3884	243	14	,	,	PUNCT
ejpam-3884	243	15	248	248	NUM
ejpam-3884	243	16	-	-	SYM
ejpam-3884	243	17	264	264	NUM
ejpam-3884	243	18	257	257	NUM
ejpam-3884	243	19	{	{	PUNCT
ejpam-3884	243	20	0	0	NUM
ejpam-3884	243	21	,	,	PUNCT
ejpam-3884	243	22	1	1	NUM
ejpam-3884	243	23	,	,	PUNCT
ejpam-3884	243	24	2	2	NUM
ejpam-3884	243	25	,	,	PUNCT
ejpam-3884	243	26	3	3	NUM
ejpam-3884	243	27	,	,	PUNCT
ejpam-3884	243	28	4	4	NUM
ejpam-3884	243	29	,	,	PUNCT
ejpam-3884	243	30	3	3	NUM
ejpam-3884	243	31	,	,	PUNCT
ejpam-3884	243	32	2	2	NUM
ejpam-3884	243	33	,	,	PUNCT
ejpam-3884	243	34	1	1	NUM
ejpam-3884	243	35	,	,	PUNCT
ejpam-3884	243	36	2	2	NUM
ejpam-3884	243	37	,	,	PUNCT
ejpam-3884	243	38	3	3	NUM
ejpam-3884	243	39	,	,	PUNCT
ejpam-3884	243	40	4	4	NUM
ejpam-3884	243	41	,	,	PUNCT
ejpam-3884	243	42	5	5	NUM
ejpam-3884	243	43	,	,	PUNCT
ejpam-3884	243	44	4	4	NUM
ejpam-3884	243	45	,	,	PUNCT
ejpam-3884	243	46	3	3	NUM
ejpam-3884	243	47	,	,	PUNCT
ejpam-3884	243	48	2	2	NUM
ejpam-3884	243	49	,	,	PUNCT
ejpam-3884	243	50	3	3	NUM
ejpam-3884	243	51	,	,	PUNCT
ejpam-3884	243	52	4	4	NUM
ejpam-3884	243	53	,	,	PUNCT
ejpam-3884	243	54	5	5	NUM
ejpam-3884	243	55	,	,	PUNCT
ejpam-3884	243	56	6	6	NUM
ejpam-3884	243	57	,	,	PUNCT
ejpam-3884	243	58	5	5	NUM
ejpam-3884	243	59	,	,	PUNCT
ejpam-3884	243	60	4	4	NUM
ejpam-3884	243	61	,	,	PUNCT
ejpam-3884	243	62	3	3	NUM
ejpam-3884	243	63	,	,	PUNCT
ejpam-3884	243	64	4	4	NUM
ejpam-3884	243	65	,	,	PUNCT
ejpam-3884	243	66	5	5	NUM
ejpam-3884	243	67	,	,	PUNCT
ejpam-3884	243	68	6	6	NUM
ejpam-3884	243	69	,	,	PUNCT
ejpam-3884	243	70	7	7	NUM
ejpam-3884	243	71	,	,	PUNCT
ejpam-3884	243	72	6	6	NUM
ejpam-3884	243	73	,	,	PUNCT
ejpam-3884	243	74	5	5	NUM
ejpam-3884	243	75	,	,	PUNCT
ejpam-3884	243	76	4	4	NUM
ejpam-3884	243	77	,	,	PUNCT
ejpam-3884	243	78	5	5	NUM
ejpam-3884	243	79	,	,	PUNCT
ejpam-3884	243	80	6	6	NUM
ejpam-3884	243	81	,	,	PUNCT
ejpam-3884	243	82	7	7	NUM
ejpam-3884	243	83	,	,	PUNCT
ejpam-3884	243	84	6	6	NUM
ejpam-3884	243	85	,	,	PUNCT
ejpam-3884	243	86	5	5	NUM
ejpam-3884	243	87	,	,	PUNCT
ejpam-3884	243	88	4	4	NUM
ejpam-3884	243	89	,	,	PUNCT
ejpam-3884	243	90	3	3	NUM
ejpam-3884	243	91	,	,	PUNCT
ejpam-3884	243	92	4	4	NUM
ejpam-3884	243	93	,	,	PUNCT
ejpam-3884	243	94	5	5	NUM
ejpam-3884	243	95	,	,	PUNCT
ejpam-3884	243	96	6	6	NUM
ejpam-3884	243	97	,	,	PUNCT
ejpam-3884	243	98	5	5	NUM
ejpam-3884	243	99	,	,	PUNCT
ejpam-3884	243	100	4	4	NUM
ejpam-3884	243	101	,	,	PUNCT
ejpam-3884	243	102	3	3	NUM
ejpam-3884	243	103	,	,	PUNCT
ejpam-3884	243	104	2	2	NUM
ejpam-3884	243	105	,	,	PUNCT
ejpam-3884	243	106	3	3	NUM
ejpam-3884	243	107	,	,	PUNCT
ejpam-3884	243	108	4	4	NUM
ejpam-3884	243	109	,	,	PUNCT
ejpam-3884	243	110	5	5	NUM
ejpam-3884	243	111	,	,	PUNCT
ejpam-3884	243	112	4	4	NUM
ejpam-3884	243	113	,	,	PUNCT
ejpam-3884	243	114	3	3	NUM
ejpam-3884	243	115	,	,	PUNCT
ejpam-3884	243	116	2	2	NUM
ejpam-3884	243	117	,	,	PUNCT
ejpam-3884	243	118	1	1	NUM
ejpam-3884	243	119	,	,	PUNCT
ejpam-3884	243	120	2	2	NUM
ejpam-3884	243	121	,	,	PUNCT
ejpam-3884	243	122	3	3	NUM
ejpam-3884	243	123	,	,	PUNCT
ejpam-3884	243	124	4	4	NUM
ejpam-3884	243	125	,	,	PUNCT
ejpam-3884	243	126	5	5	NUM
ejpam-3884	243	127	,	,	PUNCT
ejpam-3884	243	128	4	4	NUM
ejpam-3884	243	129	,	,	PUNCT
ejpam-3884	243	130	3	3	NUM
ejpam-3884	243	131	,	,	PUNCT
ejpam-3884	243	132	2	2	NUM
ejpam-3884	243	133	,	,	PUNCT
ejpam-3884	243	134	3	3	NUM
ejpam-3884	243	135	,	,	PUNCT
ejpam-3884	243	136	4	4	NUM
ejpam-3884	243	137	,	,	PUNCT
ejpam-3884	243	138	5	5	NUM
ejpam-3884	243	139	,	,	PUNCT
ejpam-3884	243	140	6	6	NUM
ejpam-3884	243	141	,	,	PUNCT
ejpam-3884	243	142	5	5	NUM
ejpam-3884	243	143	,	,	PUNCT
ejpam-3884	243	144	4	4	NUM
ejpam-3884	243	145	,	,	PUNCT
ejpam-3884	243	146	3	3	NUM
ejpam-3884	243	147	,	,	PUNCT
ejpam-3884	243	148	4	4	NUM
ejpam-3884	243	149	,	,	PUNCT
ejpam-3884	243	150	5	5	NUM
ejpam-3884	243	151	,	,	PUNCT
ejpam-3884	243	152	6	6	NUM
ejpam-3884	243	153	,	,	PUNCT
ejpam-3884	243	154	7	7	NUM
ejpam-3884	243	155	,	,	PUNCT
ejpam-3884	243	156	6	6	NUM
ejpam-3884	243	157	,	,	PUNCT
ejpam-3884	243	158	5	5	NUM
ejpam-3884	243	159	,	,	PUNCT
ejpam-3884	243	160	4	4	NUM
ejpam-3884	243	161	,	,	PUNCT
ejpam-3884	243	162	5	5	NUM
ejpam-3884	243	163	,	,	PUNCT
ejpam-3884	243	164	6	6	NUM
ejpam-3884	243	165	,	,	PUNCT
ejpam-3884	243	166	7	7	NUM
ejpam-3884	243	167	,	,	PUNCT
ejpam-3884	243	168	8	8	NUM
ejpam-3884	243	169	,	,	PUNCT
ejpam-3884	243	170	7	7	NUM
ejpam-3884	243	171	,	,	PUNCT
ejpam-3884	243	172	6	6	NUM
ejpam-3884	243	173	,	,	PUNCT
ejpam-3884	243	174	5	5	NUM
ejpam-3884	243	175	,	,	PUNCT
ejpam-3884	243	176	6	6	NUM
ejpam-3884	243	177	,	,	PUNCT
ejpam-3884	243	178	7	7	NUM
ejpam-3884	243	179	,	,	PUNCT
ejpam-3884	243	180	8	8	NUM
ejpam-3884	243	181	,	,	PUNCT
ejpam-3884	243	182	7	7	NUM
ejpam-3884	243	183	,	,	PUNCT
ejpam-3884	243	184	6	6	NUM
ejpam-3884	243	185	,	,	PUNCT
ejpam-3884	243	186	5	5	NUM
ejpam-3884	243	187	,	,	PUNCT
ejpam-3884	243	188	4	4	NUM
ejpam-3884	243	189	,	,	PUNCT
ejpam-3884	243	190	5	5	NUM
ejpam-3884	243	191	,	,	PUNCT
ejpam-3884	243	192	6	6	NUM
ejpam-3884	243	193	,	,	PUNCT
ejpam-3884	243	194	7	7	NUM
ejpam-3884	243	195	,	,	PUNCT
ejpam-3884	243	196	6	6	NUM
ejpam-3884	243	197	,	,	PUNCT
ejpam-3884	243	198	5	5	NUM
ejpam-3884	243	199	,	,	PUNCT
ejpam-3884	243	200	4	4	NUM
ejpam-3884	243	201	,	,	PUNCT
ejpam-3884	243	202	3	3	NUM
ejpam-3884	243	203	,	,	PUNCT
ejpam-3884	243	204	4	4	NUM
ejpam-3884	243	205	,	,	PUNCT
ejpam-3884	243	206	5	5	NUM
ejpam-3884	243	207	,	,	PUNCT
ejpam-3884	243	208	6	6	NUM
ejpam-3884	243	209	,	,	PUNCT
ejpam-3884	243	210	5	5	NUM
ejpam-3884	243	211	,	,	PUNCT
ejpam-3884	243	212	4	4	NUM
ejpam-3884	243	213	,	,	PUNCT
ejpam-3884	243	214	3	3	NUM
ejpam-3884	243	215	,	,	PUNCT
ejpam-3884	243	216	2	2	NUM
ejpam-3884	243	217	,	,	PUNCT
ejpam-3884	243	218	3	3	NUM
ejpam-3884	243	219	,	,	PUNCT
ejpam-3884	243	220	4	4	NUM
ejpam-3884	243	221	,	,	PUNCT
ejpam-3884	243	222	5	5	NUM
ejpam-3884	243	223	,	,	PUNCT
ejpam-3884	243	224	6	6	NUM
ejpam-3884	243	225	,	,	PUNCT
ejpam-3884	243	226	5	5	NUM
ejpam-3884	243	227	,	,	PUNCT
ejpam-3884	243	228	4	4	NUM
ejpam-3884	243	229	,	,	PUNCT
ejpam-3884	243	230	3	3	NUM
ejpam-3884	243	231	,	,	PUNCT
ejpam-3884	243	232	4	4	NUM
ejpam-3884	243	233	,	,	PUNCT
ejpam-3884	243	234	5	5	NUM
ejpam-3884	243	235	,	,	PUNCT
ejpam-3884	243	236	6	6	NUM
ejpam-3884	243	237	,	,	PUNCT
ejpam-3884	243	238	7	7	NUM
ejpam-3884	243	239	,	,	PUNCT
ejpam-3884	243	240	6	6	NUM
ejpam-3884	243	241	,	,	PUNCT
ejpam-3884	243	242	5	5	NUM
ejpam-3884	243	243	,	,	PUNCT
ejpam-3884	243	244	4	4	NUM
ejpam-3884	243	245	,	,	PUNCT
ejpam-3884	243	246	5	5	NUM
ejpam-3884	243	247	,	,	PUNCT
ejpam-3884	243	248	6	6	NUM
ejpam-3884	243	249	,	,	PUNCT
ejpam-3884	243	250	7	7	NUM
ejpam-3884	243	251	,	,	PUNCT
ejpam-3884	243	252	8	8	NUM
ejpam-3884	243	253	,	,	PUNCT
ejpam-3884	243	254	7	7	NUM
ejpam-3884	243	255	,	,	PUNCT
ejpam-3884	243	256	6	6	NUM
ejpam-3884	243	257	,	,	PUNCT
ejpam-3884	243	258	5	5	NUM
ejpam-3884	243	259	,	,	PUNCT
ejpam-3884	243	260	6	6	NUM
ejpam-3884	243	261	,	,	PUNCT
ejpam-3884	243	262	7	7	NUM
ejpam-3884	243	263	,	,	PUNCT
ejpam-3884	243	264	8	8	NUM
ejpam-3884	243	265	,	,	PUNCT
ejpam-3884	243	266	9	9	NUM
ejpam-3884	243	267	,	,	PUNCT
ejpam-3884	243	268	8	8	NUM
ejpam-3884	243	269	,	,	PUNCT
ejpam-3884	243	270	7	7	NUM
ejpam-3884	243	271	,	,	PUNCT
ejpam-3884	243	272	6	6	NUM
ejpam-3884	243	273	,	,	PUNCT
ejpam-3884	243	274	7	7	NUM
ejpam-3884	243	275	,	,	PUNCT
ejpam-3884	243	276	8	8	NUM
ejpam-3884	243	277	,	,	PUNCT
ejpam-3884	243	278	9	9	NUM
ejpam-3884	243	279	,	,	PUNCT
ejpam-3884	243	280	8	8	NUM
ejpam-3884	243	281	,	,	PUNCT
ejpam-3884	243	282	7	7	NUM
ejpam-3884	243	283	,	,	PUNCT
ejpam-3884	243	284	6	6	NUM
ejpam-3884	243	285	,	,	PUNCT
ejpam-3884	243	286	5	5	NUM
ejpam-3884	243	287	,	,	PUNCT
ejpam-3884	243	288	6	6	NUM
ejpam-3884	243	289	,	,	PUNCT
ejpam-3884	243	290	7	7	NUM
ejpam-3884	243	291	,	,	PUNCT
ejpam-3884	243	292	8	8	NUM
ejpam-3884	243	293	,	,	PUNCT
ejpam-3884	243	294	7	7	NUM
ejpam-3884	243	295	,	,	PUNCT
ejpam-3884	243	296	6	6	NUM
ejpam-3884	243	297	,	,	PUNCT
ejpam-3884	243	298	5	5	NUM
ejpam-3884	243	299	,	,	PUNCT
ejpam-3884	243	300	4	4	NUM
ejpam-3884	243	301	,	,	PUNCT
ejpam-3884	243	302	5	5	NUM
ejpam-3884	243	303	,	,	PUNCT
ejpam-3884	243	304	6	6	NUM
ejpam-3884	243	305	,	,	PUNCT
ejpam-3884	243	306	7	7	NUM
ejpam-3884	243	307	,	,	PUNCT
ejpam-3884	243	308	6	6	NUM
ejpam-3884	243	309	,	,	PUNCT
ejpam-3884	243	310	5	5	NUM
ejpam-3884	243	311	,	,	PUNCT
ejpam-3884	243	312	4	4	NUM
ejpam-3884	243	313	,	,	PUNCT
ejpam-3884	243	314	3	3	NUM
ejpam-3884	243	315	,	,	PUNCT
ejpam-3884	243	316	4	4	NUM
ejpam-3884	243	317	,	,	PUNCT
ejpam-3884	243	318	5	5	NUM
ejpam-3884	243	319	,	,	PUNCT
ejpam-3884	243	320	6	6	NUM
ejpam-3884	243	321	,	,	PUNCT
ejpam-3884	243	322	7	7	NUM
ejpam-3884	243	323	,	,	PUNCT
ejpam-3884	243	324	6	6	NUM
ejpam-3884	243	325	,	,	PUNCT
ejpam-3884	243	326	5	5	NUM
ejpam-3884	243	327	,	,	PUNCT
ejpam-3884	243	328	4	4	NUM
ejpam-3884	243	329	,	,	PUNCT
ejpam-3884	243	330	5	5	NUM
ejpam-3884	243	331	,	,	PUNCT
ejpam-3884	243	332	6	6	NUM
ejpam-3884	243	333	,	,	PUNCT
ejpam-3884	243	334	7	7	NUM
ejpam-3884	243	335	,	,	PUNCT
ejpam-3884	243	336	8	8	NUM
ejpam-3884	243	337	,	,	PUNCT
ejpam-3884	243	338	7	7	NUM
ejpam-3884	243	339	,	,	PUNCT
ejpam-3884	243	340	6	6	NUM
ejpam-3884	243	341	,	,	PUNCT
ejpam-3884	243	342	5	5	NUM
ejpam-3884	243	343	,	,	PUNCT
ejpam-3884	243	344	6	6	NUM
ejpam-3884	243	345	,	,	PUNCT
ejpam-3884	243	346	7	7	NUM
ejpam-3884	243	347	,	,	PUNCT
ejpam-3884	243	348	8	8	NUM
ejpam-3884	243	349	,	,	PUNCT
ejpam-3884	243	350	9	9	NUM
ejpam-3884	243	351	,	,	PUNCT
ejpam-3884	243	352	8	8	NUM
ejpam-3884	243	353	,	,	PUNCT
ejpam-3884	243	354	7	7	NUM
ejpam-3884	243	355	,	,	PUNCT
ejpam-3884	243	356	6	6	NUM
ejpam-3884	243	357	,	,	PUNCT
ejpam-3884	243	358	7	7	NUM
ejpam-3884	243	359	,	,	PUNCT
ejpam-3884	243	360	8	8	NUM
ejpam-3884	243	361	,	,	PUNCT
ejpam-3884	243	362	9	9	NUM
ejpam-3884	243	363	,	,	PUNCT
ejpam-3884	243	364	9	9	NUM
ejpam-3884	243	365	,	,	PUNCT
ejpam-3884	243	366	8	8	NUM
ejpam-3884	243	367	,	,	PUNCT
ejpam-3884	243	368	7	7	NUM
ejpam-3884	243	369	,	,	PUNCT
ejpam-3884	243	370	6	6	NUM
ejpam-3884	243	371	,	,	PUNCT
ejpam-3884	243	372	7	7	NUM
ejpam-3884	243	373	,	,	PUNCT
ejpam-3884	243	374	8	8	NUM
ejpam-3884	243	375	,	,	PUNCT
ejpam-3884	243	376	9	9	NUM
ejpam-3884	243	377	,	,	PUNCT
ejpam-3884	243	378	8	8	NUM
ejpam-3884	243	379	,	,	PUNCT
ejpam-3884	243	380	7	7	NUM
ejpam-3884	243	381	,	,	PUNCT
ejpam-3884	243	382	6	6	NUM
ejpam-3884	243	383	,	,	PUNCT
ejpam-3884	243	384	5	5	NUM
ejpam-3884	243	385	,	,	PUNCT
ejpam-3884	243	386	6	6	NUM
ejpam-3884	243	387	,	,	PUNCT
ejpam-3884	243	388	7	7	NUM
ejpam-3884	243	389	,	,	PUNCT
ejpam-3884	243	390	8	8	NUM
ejpam-3884	243	391	,	,	PUNCT
ejpam-3884	243	392	7	7	NUM
ejpam-3884	243	393	,	,	PUNCT
ejpam-3884	243	394	6	6	NUM
ejpam-3884	243	395	,	,	PUNCT
ejpam-3884	243	396	5	5	NUM
ejpam-3884	243	397	,	,	PUNCT
ejpam-3884	243	398	4	4	NUM
ejpam-3884	243	399	,	,	PUNCT
ejpam-3884	243	400	5	5	NUM
ejpam-3884	243	401	,	,	PUNCT
ejpam-3884	243	402	6	6	NUM
ejpam-3884	243	403	,	,	PUNCT
ejpam-3884	243	404	7	7	NUM
ejpam-3884	243	405	,	,	PUNCT
ejpam-3884	243	406	6	6	NUM
ejpam-3884	243	407	,	,	PUNCT
ejpam-3884	243	408	5	5	NUM
ejpam-3884	243	409	,	,	PUNCT
ejpam-3884	243	410	4	4	NUM
ejpam-3884	243	411	,	,	PUNCT
ejpam-3884	243	412	3	3	NUM
ejpam-3884	243	413	,	,	PUNCT
ejpam-3884	243	414	4	4	NUM
ejpam-3884	243	415	,	,	PUNCT
ejpam-3884	243	416	5	5	NUM
ejpam-3884	243	417	,	,	PUNCT
ejpam-3884	243	418	6	6	NUM
ejpam-3884	243	419	,	,	PUNCT
ejpam-3884	243	420	7	7	NUM
ejpam-3884	243	421	,	,	PUNCT
ejpam-3884	243	422	6	6	NUM
ejpam-3884	243	423	,	,	PUNCT
ejpam-3884	243	424	5	5	NUM
ejpam-3884	243	425	,	,	PUNCT
ejpam-3884	243	426	4	4	NUM
ejpam-3884	243	427	,	,	PUNCT
ejpam-3884	243	428	5	5	NUM
ejpam-3884	243	429	,	,	PUNCT
ejpam-3884	243	430	6	6	NUM
ejpam-3884	243	431	,	,	PUNCT
ejpam-3884	243	432	7	7	NUM
ejpam-3884	243	433	,	,	PUNCT
ejpam-3884	243	434	8	8	NUM
ejpam-3884	243	435	,	,	PUNCT
ejpam-3884	243	436	7	7	NUM
ejpam-3884	243	437	,	,	PUNCT
ejpam-3884	243	438	6	6	NUM
ejpam-3884	243	439	,	,	PUNCT
ejpam-3884	243	440	5	5	NUM
ejpam-3884	243	441	,	,	PUNCT
ejpam-3884	243	442	6	6	NUM
ejpam-3884	243	443	,	,	PUNCT
ejpam-3884	243	444	7	7	NUM
ejpam-3884	243	445	,	,	PUNCT
ejpam-3884	243	446	8	8	NUM
ejpam-3884	243	447	,	,	PUNCT
ejpam-3884	243	448	9	9	NUM
ejpam-3884	243	449	,	,	PUNCT
ejpam-3884	243	450	8	8	NUM
ejpam-3884	243	451	,	,	PUNCT
ejpam-3884	243	452	7	7	NUM
ejpam-3884	243	453	,	,	PUNCT
ejpam-3884	243	454	6	6	NUM
ejpam-3884	243	455	,	,	PUNCT
ejpam-3884	243	456	7	7	NUM
ejpam-3884	243	457	,	,	PUNCT
ejpam-3884	243	458	8	8	NUM
ejpam-3884	243	459	,	,	PUNCT
ejpam-3884	243	460	9	9	NUM
ejpam-3884	243	461	,	,	PUNCT
ejpam-3884	243	462	8	8	NUM
ejpam-3884	243	463	,	,	PUNCT
ejpam-3884	243	464	7	7	NUM
ejpam-3884	243	465	,	,	PUNCT
ejpam-3884	243	466	6	6	NUM
ejpam-3884	243	467	,	,	PUNCT
ejpam-3884	243	468	5	5	NUM
ejpam-3884	243	469	,	,	PUNCT
ejpam-3884	243	470	6	6	NUM
ejpam-3884	243	471	,	,	PUNCT
ejpam-3884	243	472	7	7	NUM
ejpam-3884	243	473	,	,	PUNCT
ejpam-3884	243	474	8	8	NUM
ejpam-3884	243	475	,	,	PUNCT
ejpam-3884	243	476	7	7	NUM
ejpam-3884	243	477	,	,	PUNCT
ejpam-3884	243	478	6	6	NUM
ejpam-3884	243	479	,	,	PUNCT
ejpam-3884	243	480	5	5	NUM
ejpam-3884	243	481	,	,	PUNCT
ejpam-3884	243	482	4	4	NUM
ejpam-3884	243	483	,	,	PUNCT
ejpam-3884	243	484	5	5	NUM
ejpam-3884	243	485	,	,	PUNCT
ejpam-3884	243	486	6	6	NUM
ejpam-3884	243	487	,	,	PUNCT
ejpam-3884	243	488	7	7	NUM
ejpam-3884	243	489	,	,	PUNCT
ejpam-3884	243	490	6	6	NUM
ejpam-3884	243	491	,	,	PUNCT
ejpam-3884	243	492	5	5	NUM
ejpam-3884	243	493	,	,	PUNCT
ejpam-3884	243	494	4	4	NUM
ejpam-3884	243	495	,	,	PUNCT
ejpam-3884	243	496	3	3	NUM
ejpam-3884	243	497	,	,	PUNCT
ejpam-3884	243	498	4	4	NUM
ejpam-3884	243	499	,	,	PUNCT
ejpam-3884	243	500	5	5	NUM
ejpam-3884	243	501	,	,	PUNCT
ejpam-3884	243	502	6	6	NUM
ejpam-3884	243	503	,	,	PUNCT
ejpam-3884	243	504	5	5	NUM
ejpam-3884	243	505	,	,	PUNCT
ejpam-3884	243	506	4	4	NUM
ejpam-3884	243	507	,	,	PUNCT
ejpam-3884	243	508	3	3	NUM
ejpam-3884	243	509	,	,	PUNCT
ejpam-3884	243	510	2	2	NUM
ejpam-3884	243	511	,	,	PUNCT
ejpam-3884	243	512	3	3	NUM
ejpam-3884	243	513	,	,	PUNCT
ejpam-3884	243	514	4	4	NUM
ejpam-3884	243	515	,	,	PUNCT
ejpam-3884	243	516	5	5	NUM
ejpam-3884	243	517	,	,	PUNCT
ejpam-3884	243	518	6	6	NUM
ejpam-3884	243	519	,	,	PUNCT
ejpam-3884	243	520	5	5	NUM
ejpam-3884	243	521	,	,	PUNCT
ejpam-3884	243	522	4	4	NUM
ejpam-3884	243	523	,	,	PUNCT
ejpam-3884	243	524	3	3	NUM
ejpam-3884	243	525	,	,	PUNCT
ejpam-3884	243	526	4	4	NUM
ejpam-3884	243	527	,	,	PUNCT
ejpam-3884	243	528	5	5	NUM
ejpam-3884	243	529	,	,	PUNCT
ejpam-3884	243	530	6	6	NUM
ejpam-3884	243	531	,	,	PUNCT
ejpam-3884	243	532	7	7	NUM
ejpam-3884	243	533	,	,	PUNCT
ejpam-3884	243	534	6	6	NUM
ejpam-3884	243	535	,	,	PUNCT
ejpam-3884	243	536	5	5	NUM
ejpam-3884	243	537	,	,	PUNCT
ejpam-3884	243	538	4	4	NUM
ejpam-3884	243	539	,	,	PUNCT
ejpam-3884	243	540	5	5	NUM
ejpam-3884	243	541	,	,	PUNCT
ejpam-3884	243	542	6	6	NUM
ejpam-3884	243	543	,	,	PUNCT
ejpam-3884	243	544	7	7	NUM
ejpam-3884	243	545	,	,	PUNCT
ejpam-3884	243	546	8	8	NUM
ejpam-3884	243	547	,	,	PUNCT
ejpam-3884	243	548	7	7	NUM
ejpam-3884	243	549	,	,	PUNCT
ejpam-3884	243	550	6	6	NUM
ejpam-3884	243	551	,	,	PUNCT
ejpam-3884	243	552	5	5	NUM
ejpam-3884	243	553	,	,	PUNCT
ejpam-3884	243	554	6	6	NUM
ejpam-3884	243	555	,	,	PUNCT
ejpam-3884	243	556	7	7	NUM
ejpam-3884	243	557	,	,	PUNCT
ejpam-3884	243	558	8	8	NUM
ejpam-3884	243	559	,	,	PUNCT
ejpam-3884	243	560	7	7	NUM
ejpam-3884	243	561	,	,	PUNCT
ejpam-3884	243	562	6	6	NUM
ejpam-3884	243	563	,	,	PUNCT
ejpam-3884	243	564	5	5	NUM
ejpam-3884	243	565	,	,	PUNCT
ejpam-3884	243	566	4	4	NUM
ejpam-3884	243	567	,	,	PUNCT
ejpam-3884	243	568	5	5	NUM
ejpam-3884	243	569	,	,	PUNCT
ejpam-3884	243	570	6	6	NUM
ejpam-3884	243	571	,	,	PUNCT
ejpam-3884	243	572	7	7	NUM
ejpam-3884	243	573	,	,	PUNCT
ejpam-3884	243	574	6	6	NUM
ejpam-3884	243	575	,	,	PUNCT
ejpam-3884	243	576	5	5	NUM
ejpam-3884	243	577	,	,	PUNCT
ejpam-3884	243	578	4	4	NUM
ejpam-3884	243	579	,	,	PUNCT
ejpam-3884	243	580	3	3	NUM
ejpam-3884	243	581	,	,	PUNCT
ejpam-3884	243	582	4	4	NUM
ejpam-3884	243	583	,	,	PUNCT
ejpam-3884	243	584	5	5	NUM
ejpam-3884	243	585	,	,	PUNCT
ejpam-3884	243	586	6	6	NUM
ejpam-3884	243	587	,	,	PUNCT
ejpam-3884	243	588	5	5	NUM
ejpam-3884	243	589	,	,	PUNCT
ejpam-3884	243	590	4	4	NUM
ejpam-3884	243	591	,	,	PUNCT
ejpam-3884	243	592	3	3	NUM
ejpam-3884	243	593	,	,	PUNCT
ejpam-3884	243	594	2	2	NUM
ejpam-3884	243	595	,	,	PUNCT
ejpam-3884	243	596	3	3	NUM
ejpam-3884	243	597	,	,	PUNCT
ejpam-3884	243	598	4	4	NUM
ejpam-3884	243	599	,	,	PUNCT
ejpam-3884	243	600	5	5	NUM
ejpam-3884	243	601	,	,	PUNCT
ejpam-3884	243	602	4	4	NUM
ejpam-3884	243	603	,	,	PUNCT
ejpam-3884	243	604	3	3	NUM
ejpam-3884	243	605	,	,	PUNCT
ejpam-3884	243	606	2	2	NUM
ejpam-3884	243	607	,	,	PUNCT
ejpam-3884	243	608	1	1	NUM
ejpam-3884	243	609	,	,	PUNCT
ejpam-3884	243	610	2	2	NUM
ejpam-3884	243	611	,	,	PUNCT
ejpam-3884	243	612	3	3	NUM
ejpam-3884	243	613	,	,	PUNCT
ejpam-3884	243	614	4	4	NUM
ejpam-3884	243	615	,	,	PUNCT
ejpam-3884	243	616	5	5	NUM
ejpam-3884	243	617	,	,	PUNCT
ejpam-3884	243	618	4	4	NUM
ejpam-3884	243	619	,	,	PUNCT
ejpam-3884	243	620	3	3	NUM
ejpam-3884	243	621	,	,	PUNCT
ejpam-3884	243	622	2	2	NUM
ejpam-3884	243	623	,	,	PUNCT
ejpam-3884	243	624	3	3	NUM
ejpam-3884	243	625	,	,	PUNCT
ejpam-3884	243	626	4	4	NUM
ejpam-3884	243	627	,	,	PUNCT
ejpam-3884	243	628	5	5	NUM
ejpam-3884	243	629	,	,	PUNCT
ejpam-3884	243	630	6	6	NUM
ejpam-3884	243	631	,	,	PUNCT
ejpam-3884	243	632	5	5	NUM
ejpam-3884	243	633	,	,	PUNCT
ejpam-3884	243	634	4	4	NUM
ejpam-3884	243	635	,	,	PUNCT
ejpam-3884	243	636	3	3	NUM
ejpam-3884	243	637	,	,	PUNCT
ejpam-3884	243	638	4	4	NUM
ejpam-3884	243	639	,	,	PUNCT
ejpam-3884	243	640	5	5	NUM
ejpam-3884	243	641	,	,	PUNCT
ejpam-3884	243	642	6	6	NUM
ejpam-3884	243	643	,	,	PUNCT
ejpam-3884	243	644	7	7	NUM
ejpam-3884	243	645	,	,	PUNCT
ejpam-3884	243	646	6	6	NUM
ejpam-3884	243	647	,	,	PUNCT
ejpam-3884	243	648	5	5	NUM
ejpam-3884	243	649	,	,	PUNCT
ejpam-3884	243	650	4	4	NUM
ejpam-3884	243	651	,	,	PUNCT
ejpam-3884	243	652	5	5	NUM
ejpam-3884	243	653	,	,	PUNCT
ejpam-3884	243	654	6	6	NUM
ejpam-3884	243	655	,	,	PUNCT
ejpam-3884	243	656	7	7	NUM
ejpam-3884	243	657	,	,	PUNCT
ejpam-3884	243	658	6	6	NUM
ejpam-3884	243	659	,	,	PUNCT
ejpam-3884	243	660	5	5	NUM
ejpam-3884	243	661	,	,	PUNCT
ejpam-3884	243	662	4	4	NUM
ejpam-3884	243	663	,	,	PUNCT
ejpam-3884	243	664	3	3	NUM
ejpam-3884	243	665	,	,	PUNCT
ejpam-3884	243	666	4	4	NUM
ejpam-3884	243	667	,	,	PUNCT
ejpam-3884	243	668	5	5	NUM
ejpam-3884	243	669	,	,	PUNCT
ejpam-3884	243	670	6	6	NUM
ejpam-3884	243	671	,	,	PUNCT
ejpam-3884	243	672	5	5	NUM
ejpam-3884	243	673	,	,	PUNCT
ejpam-3884	243	674	4	4	NUM
ejpam-3884	243	675	,	,	PUNCT
ejpam-3884	243	676	3	3	NUM
ejpam-3884	243	677	,	,	PUNCT
ejpam-3884	243	678	2	2	NUM
ejpam-3884	243	679	,	,	PUNCT
ejpam-3884	243	680	3	3	NUM
ejpam-3884	243	681	,	,	PUNCT
ejpam-3884	243	682	4	4	NUM
ejpam-3884	243	683	,	,	PUNCT
ejpam-3884	243	684	5	5	NUM
ejpam-3884	243	685	,	,	PUNCT
ejpam-3884	243	686	4	4	NUM
ejpam-3884	243	687	,	,	PUNCT
ejpam-3884	243	688	3	3	NUM
ejpam-3884	243	689	,	,	PUNCT
ejpam-3884	243	690	2	2	NUM
ejpam-3884	243	691	,	,	PUNCT
ejpam-3884	243	692	1	1	NUM
ejpam-3884	243	693	,	,	PUNCT
ejpam-3884	243	694	2	2	NUM
ejpam-3884	243	695	,	,	PUNCT
ejpam-3884	243	696	3	3	NUM
ejpam-3884	243	697	,	,	PUNCT
ejpam-3884	243	698	4	4	NUM
ejpam-3884	243	699	,	,	PUNCT
ejpam-3884	243	700	3	3	NUM
ejpam-3884	243	701	,	,	PUNCT
ejpam-3884	243	702	2	2	NUM
ejpam-3884	243	703	,	,	PUNCT
ejpam-3884	243	704	1	1	NUM
ejpam-3884	243	705	}	}	PUNCT
ejpam-3884	243	706	in	in	ADP
ejpam-3884	243	707	the	the	DET
ejpam-3884	243	708	above	above	ADJ
ejpam-3884	243	709	set	set	NOUN
ejpam-3884	244	1	,	,	PUNCT
ejpam-3884	244	2	we	we	PRON
ejpam-3884	244	3	use	use	VERB
ejpam-3884	244	4	six	six	NUM
ejpam-3884	244	5	colors	color	NOUN
ejpam-3884	244	6	to	to	PART
ejpam-3884	244	7	represent	represent	VERB
ejpam-3884	244	8	the	the	DET
ejpam-3884	244	9	distances	distance	NOUN
ejpam-3884	244	10	of	of	ADP
ejpam-3884	244	11	each	each	DET
ejpam-3884	244	12	vertices	vertex	NOUN
ejpam-3884	244	13	per	per	ADP
ejpam-3884	244	14	group	group	NOUN
ejpam-3884	244	15	.	.	PUNCT
ejpam-3884	245	1	we	we	PRON
ejpam-3884	245	2	use	use	VERB
ejpam-3884	245	3	color	color	NOUN
ejpam-3884	245	4	green	green	NOUN
ejpam-3884	245	5	for	for	ADP
ejpam-3884	245	6	the	the	DET
ejpam-3884	245	7	group	group	NOUN
ejpam-3884	245	8	of	of	ADP
ejpam-3884	245	9	vertices	vertex	NOUN
ejpam-3884	245	10	covered	cover	VERB
ejpam-3884	245	11	by	by	ADP
ejpam-3884	245	12	the	the	DET
ejpam-3884	245	13	first	first	ADJ
ejpam-3884	245	14	part	part	NOUN
ejpam-3884	245	15	of	of	ADP
ejpam-3884	245	16	equation	equation	NOUN
ejpam-3884	245	17	(	(	PUNCT
ejpam-3884	245	18	1	1	X
ejpam-3884	245	19	)	)	PUNCT
ejpam-3884	245	20	while	while	SCONJ
ejpam-3884	245	21	red	red	ADJ
ejpam-3884	245	22	for	for	ADP
ejpam-3884	245	23	the	the	DET
ejpam-3884	245	24	group	group	NOUN
ejpam-3884	245	25	of	of	ADP
ejpam-3884	245	26	vertices	vertex	NOUN
ejpam-3884	245	27	covered	cover	VERB
ejpam-3884	245	28	by	by	ADP
ejpam-3884	245	29	second	second	ADJ
ejpam-3884	245	30	part	part	NOUN
ejpam-3884	245	31	.	.	PUNCT
ejpam-3884	246	1	color	color	NOUN
ejpam-3884	246	2	yellow	yellow	PROPN
ejpam-3884	246	3	were	be	AUX
ejpam-3884	246	4	used	use	VERB
ejpam-3884	246	5	for	for	ADP
ejpam-3884	246	6	the	the	DET
ejpam-3884	246	7	group	group	NOUN
ejpam-3884	246	8	of	of	ADP
ejpam-3884	246	9	vertices	vertex	NOUN
ejpam-3884	246	10	covered	cover	VERB
ejpam-3884	246	11	by	by	ADP
ejpam-3884	246	12	equation	equation	NOUN
ejpam-3884	246	13	(	(	PUNCT
ejpam-3884	246	14	2	2	NUM
ejpam-3884	246	15	)	)	PUNCT
ejpam-3884	246	16	,	,	PUNCT
ejpam-3884	246	17	color	color	NOUN
ejpam-3884	246	18	violet	violet	NOUN
ejpam-3884	246	19	were	be	AUX
ejpam-3884	246	20	used	use	VERB
ejpam-3884	246	21	for	for	ADP
ejpam-3884	246	22	the	the	DET
ejpam-3884	246	23	group	group	NOUN
ejpam-3884	246	24	of	of	ADP
ejpam-3884	246	25	vertices	vertex	NOUN
ejpam-3884	246	26	covered	cover	VERB
ejpam-3884	246	27	by	by	ADP
ejpam-3884	246	28	equation	equation	NOUN
ejpam-3884	246	29	(	(	PUNCT
ejpam-3884	246	30	3	3	NUM
ejpam-3884	246	31	)	)	PUNCT
ejpam-3884	246	32	in	in	ADP
ejpam-3884	246	33	the	the	DET
ejpam-3884	246	34	first	first	ADJ
ejpam-3884	246	35	implementation	implementation	NOUN
ejpam-3884	246	36	while	while	SCONJ
ejpam-3884	246	37	color	color	NOUN
ejpam-3884	246	38	orange	orange	NOUN
ejpam-3884	246	39	were	be	AUX
ejpam-3884	246	40	used	use	VERB
ejpam-3884	246	41	for	for	ADP
ejpam-3884	246	42	the	the	DET
ejpam-3884	246	43	group	group	NOUN
ejpam-3884	246	44	of	of	ADP
ejpam-3884	246	45	vertices	vertex	NOUN
ejpam-3884	246	46	covered	cover	VERB
ejpam-3884	246	47	by	by	ADP
ejpam-3884	246	48	equation	equation	NOUN
ejpam-3884	246	49	(	(	PUNCT
ejpam-3884	246	50	3	3	NUM
ejpam-3884	246	51	)	)	PUNCT
ejpam-3884	246	52	in	in	ADP
ejpam-3884	246	53	the	the	DET
ejpam-3884	246	54	second	second	ADJ
ejpam-3884	246	55	/	/	SYM
ejpam-3884	246	56	final	final	ADJ
ejpam-3884	246	57	implementation	implementation	NOUN
ejpam-3884	246	58	.	.	PUNCT
ejpam-3884	247	1	finally	finally	ADV
ejpam-3884	247	2	,	,	PUNCT
ejpam-3884	247	3	we	we	PRON
ejpam-3884	247	4	used	use	VERB
ejpam-3884	247	5	color	color	NOUN
ejpam-3884	247	6	blue	blue	NOUN
ejpam-3884	247	7	for	for	ADP
ejpam-3884	247	8	the	the	DET
ejpam-3884	247	9	group	group	NOUN
ejpam-3884	247	10	of	of	ADP
ejpam-3884	247	11	vertices	vertex	NOUN
ejpam-3884	247	12	covered	cover	VERB
ejpam-3884	247	13	by	by	ADP
ejpam-3884	247	14	property	property	NOUN
ejpam-3884	247	15	(	(	PUNCT
ejpam-3884	247	16	i	i	NOUN
ejpam-3884	247	17	)	)	PUNCT
ejpam-3884	247	18	.	.	PUNCT
ejpam-3884	248	1	remark	remark	PROPN
ejpam-3884	248	2	10	10	NUM
ejpam-3884	248	3	.	.	PUNCT
ejpam-3884	249	1	the	the	DET
ejpam-3884	249	2	first	first	ADJ
ejpam-3884	249	3	row	row	NOUN
ejpam-3884	249	4	of	of	ADP
ejpam-3884	249	5	the	the	DET
ejpam-3884	249	6	distance	distance	NOUN
ejpam-3884	249	7	matrix	matrix	NOUN
ejpam-3884	249	8	of	of	ADP
ejpam-3884	249	9	γ72	γ72	NOUN
ejpam-3884	249	10	and	and	CCONJ
ejpam-3884	249	11	γ73	γ73	NOUN
ejpam-3884	249	12	are	be	AUX
ejpam-3884	249	13	verified	verify	VERB
ejpam-3884	249	14	to	to	PART
ejpam-3884	249	15	be	be	AUX
ejpam-3884	249	16	correct	correct	ADJ
ejpam-3884	249	17	using	use	VERB
ejpam-3884	249	18	wolfram	wolfram	PROPN
ejpam-3884	249	19	mathematica	mathematica	PROPN
ejpam-3884	250	1	[	[	X
ejpam-3884	250	2	7	7	NUM
ejpam-3884	250	3	]	]	PUNCT
ejpam-3884	250	4	with	with	ADP
ejpam-3884	250	5	the	the	DET
ejpam-3884	250	6	inputs	input	NOUN
ejpam-3884	250	7	d	d	X
ejpam-3884	250	8	=	=	SYM
ejpam-3884	250	9	graphdistancematrix[circulantgraph[49	graphdistancematrix[circulantgraph[49	NOUN
ejpam-3884	250	10	,	,	PUNCT
ejpam-3884	250	11	{	{	PUNCT
ejpam-3884	250	12	1,7	1,7	NUM
ejpam-3884	250	13	}	}	PUNCT
ejpam-3884	250	14	]	]	PUNCT
ejpam-3884	250	15	]	]	X
ejpam-3884	250	16	;	;	PUNCT
ejpam-3884	250	17	d[[1	d[[1	NOUN
ejpam-3884	250	18	]	]	X
ejpam-3884	250	19	]	]	PUNCT
ejpam-3884	250	20	and	and	CCONJ
ejpam-3884	250	21	d	d	X
ejpam-3884	250	22	=	=	SYM
ejpam-3884	250	23	graphdistancematrix[circulantgraph[343	graphdistancematrix[circulantgraph[343	PROPN
ejpam-3884	250	24	,	,	PUNCT
ejpam-3884	250	25	{	{	PUNCT
ejpam-3884	250	26	1,7,49	1,7,49	NUM
ejpam-3884	250	27	}	}	PUNCT
ejpam-3884	250	28	]	]	X
ejpam-3884	250	29	]	]	X
ejpam-3884	250	30	;	;	PUNCT
ejpam-3884	250	31	d[[1	d[[1	NOUN
ejpam-3884	250	32	]	]	X
ejpam-3884	250	33	]	]	PUNCT
ejpam-3884	250	34	.	.	PUNCT
ejpam-3884	251	1	once	once	SCONJ
ejpam-3884	251	2	the	the	DET
ejpam-3884	251	3	distance	distance	NOUN
ejpam-3884	251	4	of	of	ADP
ejpam-3884	251	5	all	all	DET
ejpam-3884	251	6	the	the	DET
ejpam-3884	251	7	vertices	vertex	NOUN
ejpam-3884	251	8	in	in	ADP
ejpam-3884	251	9	v	v	ADP
ejpam-3884	251	10	(	(	PUNCT
ejpam-3884	251	11	γmh	γmh	NOUN
ejpam-3884	251	12	)	)	PUNCT
ejpam-3884	251	13	from	from	ADP
ejpam-3884	251	14	the	the	DET
ejpam-3884	251	15	0	0	NUM
ejpam-3884	251	16	-	-	PUNCT
ejpam-3884	251	17	vertex	vertex	NOUN
ejpam-3884	251	18	is	be	AUX
ejpam-3884	251	19	known	know	VERB
ejpam-3884	251	20	,	,	PUNCT
ejpam-3884	251	21	the	the	DET
ejpam-3884	251	22	distance	distance	NOUN
ejpam-3884	251	23	matrix	matrix	NOUN
ejpam-3884	251	24	of	of	ADP
ejpam-3884	251	25	γmh	γmh	NOUN
ejpam-3884	251	26	can	can	AUX
ejpam-3884	251	27	be	be	AUX
ejpam-3884	251	28	easily	easily	ADV
ejpam-3884	251	29	determined	determine	VERB
ejpam-3884	251	30	using	use	VERB
ejpam-3884	251	31	remark	remark	NOUN
ejpam-3884	251	32	1	1	NUM
ejpam-3884	251	33	.	.	PUNCT
ejpam-3884	252	1	in	in	ADP
ejpam-3884	252	2	the	the	DET
ejpam-3884	252	3	next	next	ADJ
ejpam-3884	252	4	section	section	NOUN
ejpam-3884	252	5	,	,	PUNCT
ejpam-3884	252	6	we	we	PRON
ejpam-3884	252	7	discuss	discuss	VERB
ejpam-3884	252	8	some	some	PRON
ejpam-3884	252	9	of	of	ADP
ejpam-3884	252	10	the	the	DET
ejpam-3884	252	11	many	many	ADJ
ejpam-3884	252	12	graph	graph	NOUN
ejpam-3884	252	13	properties	property	NOUN
ejpam-3884	252	14	of	of	ADP
ejpam-3884	252	15	γmh	γmh	NOUN
ejpam-3884	252	16	that	that	PRON
ejpam-3884	252	17	can	can	AUX
ejpam-3884	252	18	be	be	AUX
ejpam-3884	252	19	determined	determine	VERB
ejpam-3884	252	20	using	use	VERB
ejpam-3884	252	21	its	its	PRON
ejpam-3884	252	22	distance	distance	NOUN
ejpam-3884	252	23	matrix	matrix	NOUN
ejpam-3884	252	24	.	.	PUNCT
ejpam-3884	253	1	4	4	X
ejpam-3884	253	2	.	.	X
ejpam-3884	254	1	some	some	DET
ejpam-3884	254	2	consequences	consequence	NOUN
ejpam-3884	254	3	of	of	ADP
ejpam-3884	254	4	the	the	DET
ejpam-3884	254	5	bfs	bfs	NOUN
ejpam-3884	254	6	tree	tree	NOUN
ejpam-3884	254	7	construction	construction	NOUN
ejpam-3884	254	8	for	for	ADP
ejpam-3884	254	9	γmh	γmh	NOUN
ejpam-3884	254	10	in	in	ADP
ejpam-3884	254	11	this	this	DET
ejpam-3884	254	12	section	section	NOUN
ejpam-3884	254	13	,	,	PUNCT
ejpam-3884	254	14	we	we	PRON
ejpam-3884	254	15	use	use	VERB
ejpam-3884	254	16	our	our	PRON
ejpam-3884	254	17	proposed	propose	VERB
ejpam-3884	254	18	construction	construction	NOUN
ejpam-3884	254	19	to	to	PART
ejpam-3884	254	20	reprove	reprove	VERB
ejpam-3884	254	21	some	some	DET
ejpam-3884	254	22	known	know	VERB
ejpam-3884	254	23	results	result	NOUN
ejpam-3884	254	24	involving	involve	VERB
ejpam-3884	254	25	the	the	DET
ejpam-3884	254	26	diameter	diameter	NOUN
ejpam-3884	254	27	,	,	PUNCT
ejpam-3884	254	28	average	average	ADJ
ejpam-3884	254	29	distance	distance	NOUN
ejpam-3884	254	30	and	and	CCONJ
ejpam-3884	254	31	distance	distance	NOUN
ejpam-3884	254	32	spectral	spectral	ADJ
ejpam-3884	254	33	radius	radius	NOUN
ejpam-3884	254	34	of	of	ADP
ejpam-3884	254	35	γmh	γmh	NOUN
ejpam-3884	254	36	.	.	PUNCT
ejpam-3884	255	1	we	we	PRON
ejpam-3884	255	2	also	also	ADV
ejpam-3884	255	3	determine	determine	VERB
ejpam-3884	255	4	the	the	DET
ejpam-3884	255	5	following	follow	VERB
ejpam-3884	255	6	graph	graph	NOUN
ejpam-3884	255	7	-	-	PUNCT
ejpam-3884	255	8	related	relate	VERB
ejpam-3884	255	9	properties	property	NOUN
ejpam-3884	255	10	for	for	ADP
ejpam-3884	255	11	γmh	γmh	NOUN
ejpam-3884	255	12	:	:	PUNCT
ejpam-3884	255	13	wiener	wiener	NOUN
ejpam-3884	255	14	index	index	NOUN
ejpam-3884	255	15	,	,	PUNCT
ejpam-3884	255	16	vertex	vertex	NOUN
ejpam-3884	255	17	-	-	PUNCT
ejpam-3884	255	18	forwarding	forward	VERB
ejpam-3884	255	19	index	index	NOUN
ejpam-3884	255	20	,	,	PUNCT
ejpam-3884	255	21	and	and	CCONJ
ejpam-3884	255	22	bounds	bound	VERB
ejpam-3884	255	23	for	for	ADP
ejpam-3884	255	24	its	its	PRON
ejpam-3884	255	25	edge	edge	NOUN
ejpam-3884	255	26	-	-	PUNCT
ejpam-3884	255	27	forwarding	forward	VERB
ejpam-3884	255	28	index	index	NOUN
ejpam-3884	255	29	.	.	PUNCT
ejpam-3884	256	1	except	except	SCONJ
ejpam-3884	256	2	for	for	ADP
ejpam-3884	256	3	the	the	DET
ejpam-3884	256	4	diameter	diameter	NOUN
ejpam-3884	256	5	and	and	CCONJ
ejpam-3884	256	6	average	average	ADJ
ejpam-3884	256	7	distance	distance	NOUN
ejpam-3884	256	8	,	,	PUNCT
ejpam-3884	256	9	the	the	DET
ejpam-3884	256	10	results	result	NOUN
ejpam-3884	256	11	in	in	ADP
ejpam-3884	256	12	this	this	DET
ejpam-3884	256	13	section	section	NOUN
ejpam-3884	256	14	is	be	AUX
ejpam-3884	256	15	a	a	DET
ejpam-3884	256	16	generalization	generalization	NOUN
ejpam-3884	256	17	of	of	ADP
ejpam-3884	256	18	the	the	DET
ejpam-3884	256	19	results	result	NOUN
ejpam-3884	256	20	presented	present	VERB
ejpam-3884	256	21	in	in	ADP
ejpam-3884	256	22	[	[	X
ejpam-3884	256	23	3	3	NUM
ejpam-3884	256	24	]	]	PUNCT
ejpam-3884	256	25	for	for	ADP
ejpam-3884	256	26	γ3h	γ3h	PROPN
ejpam-3884	256	27	.	.	PUNCT
ejpam-3884	257	1	j.	j.	PROPN
ejpam-3884	257	2	antalan	antalan	PROPN
ejpam-3884	257	3	,	,	PUNCT
ejpam-3884	257	4	f.	f.	PROPN
ejpam-3884	257	5	campeña	campeña	PROPN
ejpam-3884	257	6	/	/	SYM
ejpam-3884	257	7	eur	eur	PROPN
ejpam-3884	257	8	.	.	PUNCT
ejpam-3884	258	1	j.	j.	PROPN
ejpam-3884	258	2	pure	pure	PROPN
ejpam-3884	258	3	appl	appl	PROPN
ejpam-3884	258	4	.	.	PROPN
ejpam-3884	258	5	math	math	PROPN
ejpam-3884	258	6	,	,	PUNCT
ejpam-3884	258	7	14	14	NUM
ejpam-3884	258	8	(	(	PUNCT
ejpam-3884	258	9	1	1	NUM
ejpam-3884	258	10	)	)	PUNCT
ejpam-3884	258	11	(	(	PUNCT
ejpam-3884	258	12	2021	2021	NUM
ejpam-3884	258	13	)	)	PUNCT
ejpam-3884	258	14	,	,	PUNCT
ejpam-3884	258	15	248	248	NUM
ejpam-3884	258	16	-	-	SYM
ejpam-3884	258	17	264	264	NUM
ejpam-3884	258	18	258	258	NUM
ejpam-3884	258	19	on	on	ADP
ejpam-3884	258	20	the	the	DET
ejpam-3884	258	21	diameter	diameter	NOUN
ejpam-3884	258	22	,	,	PUNCT
ejpam-3884	258	23	average	average	ADJ
ejpam-3884	258	24	distance	distance	NOUN
ejpam-3884	258	25	and	and	CCONJ
ejpam-3884	258	26	distance	distance	NOUN
ejpam-3884	258	27	spectral	spectral	ADJ
ejpam-3884	258	28	radius	radius	NOUN
ejpam-3884	258	29	of	of	ADP
ejpam-3884	258	30	γmh	γmh	NOUN
ejpam-3884	258	31	in	in	ADP
ejpam-3884	258	32	1974	1974	NUM
ejpam-3884	258	33	,	,	PUNCT
ejpam-3884	258	34	wong	wong	PROPN
ejpam-3884	258	35	and	and	CCONJ
ejpam-3884	258	36	coppersmith	coppersmith	PROPN
ejpam-3884	259	1	[	[	X
ejpam-3884	259	2	15	15	NUM
ejpam-3884	259	3	]	]	PUNCT
ejpam-3884	259	4	introduced	introduce	VERB
ejpam-3884	259	5	a	a	DET
ejpam-3884	259	6	combinatorial	combinatorial	ADJ
ejpam-3884	259	7	problem	problem	NOUN
ejpam-3884	259	8	related	relate	VERB
ejpam-3884	259	9	to	to	ADP
ejpam-3884	259	10	multimodule	multimodule	ADJ
ejpam-3884	259	11	memory	memory	NOUN
ejpam-3884	259	12	organizations	organization	NOUN
ejpam-3884	259	13	which	which	PRON
ejpam-3884	259	14	involves	involve	VERB
ejpam-3884	259	15	“	"	PUNCT
ejpam-3884	259	16	memory	memory	NOUN
ejpam-3884	259	17	circulator	circulator	NOUN
ejpam-3884	259	18	”	"	PUNCT
ejpam-3884	259	19	,	,	PUNCT
ejpam-3884	259	20	a	a	DET
ejpam-3884	259	21	bank	bank	NOUN
ejpam-3884	259	22	of	of	ADP
ejpam-3884	259	23	interconnected	interconnected	ADJ
ejpam-3884	259	24	registers	register	NOUN
ejpam-3884	259	25	and	and	CCONJ
ejpam-3884	259	26	control	control	NOUN
ejpam-3884	259	27	circuitry	circuitry	NOUN
ejpam-3884	259	28	.	.	PUNCT
ejpam-3884	260	1	one	one	NUM
ejpam-3884	260	2	model	model	NOUN
ejpam-3884	260	3	of	of	ADP
ejpam-3884	260	4	a	a	DET
ejpam-3884	260	5	memory	memory	NOUN
ejpam-3884	260	6	circulator	circulator	NOUN
ejpam-3884	260	7	that	that	PRON
ejpam-3884	260	8	was	be	AUX
ejpam-3884	260	9	considered	consider	VERB
ejpam-3884	260	10	in	in	ADP
ejpam-3884	260	11	[	[	X
ejpam-3884	260	12	15	15	NUM
ejpam-3884	260	13	]	]	PUNCT
ejpam-3884	260	14	is	be	AUX
ejpam-3884	260	15	actually	actually	ADV
ejpam-3884	260	16	the	the	DET
ejpam-3884	260	17	graph	graph	NOUN
ejpam-3884	260	18	γmh	γmh	NOUN
ejpam-3884	260	19	.	.	PUNCT
ejpam-3884	261	1	they	they	PRON
ejpam-3884	261	2	determined	determine	VERB
ejpam-3884	261	3	its	its	PRON
ejpam-3884	261	4	diameter	diameter	NOUN
ejpam-3884	261	5	as	as	ADV
ejpam-3884	261	6	well	well	ADV
ejpam-3884	261	7	as	as	ADP
ejpam-3884	261	8	its	its	PRON
ejpam-3884	261	9	average	average	ADJ
ejpam-3884	261	10	distance	distance	NOUN
ejpam-3884	261	11	by	by	ADP
ejpam-3884	261	12	calculating	calculate	VERB
ejpam-3884	261	13	the	the	DET
ejpam-3884	261	14	points	point	NOUN
ejpam-3884	261	15	(	(	PUNCT
ejpam-3884	261	16	with	with	ADP
ejpam-3884	261	17	integral	integral	ADJ
ejpam-3884	261	18	coordinate	coordinate	NOUN
ejpam-3884	261	19	)	)	PUNCT
ejpam-3884	261	20	which	which	PRON
ejpam-3884	261	21	can	can	AUX
ejpam-3884	261	22	be	be	AUX
ejpam-3884	261	23	reached	reach	VERB
ejpam-3884	261	24	from	from	ADP
ejpam-3884	261	25	0	0	NUM
ejpam-3884	261	26	in	in	ADP
ejpam-3884	261	27	a	a	DET
ejpam-3884	261	28	given	give	VERB
ejpam-3884	261	29	number	number	NOUN
ejpam-3884	261	30	of	of	ADP
ejpam-3884	261	31	steps	step	NOUN
ejpam-3884	261	32	displayed	display	VERB
ejpam-3884	261	33	in	in	ADP
ejpam-3884	261	34	the	the	DET
ejpam-3884	261	35	cartesian	cartesian	ADJ
ejpam-3884	261	36	coordinate	coordinate	NOUN
ejpam-3884	261	37	plane	plane	NOUN
ejpam-3884	261	38	showing	show	VERB
ejpam-3884	261	39	a	a	DET
ejpam-3884	261	40	uniform	uniform	ADJ
ejpam-3884	261	41	filled	fill	VERB
ejpam-3884	261	42	pattern	pattern	NOUN
ejpam-3884	261	43	.	.	PUNCT
ejpam-3884	262	1	wong	wong	PROPN
ejpam-3884	262	2	and	and	CCONJ
ejpam-3884	262	3	coppersmith	coppersmith	PROPN
ejpam-3884	262	4	found	find	VERB
ejpam-3884	262	5	out	out	ADP
ejpam-3884	262	6	that	that	SCONJ
ejpam-3884	262	7	the	the	DET
ejpam-3884	262	8	diameter	diameter	NOUN
ejpam-3884	262	9	of	of	ADP
ejpam-3884	262	10	γmh	γmh	NOUN
ejpam-3884	262	11	for	for	ADP
ejpam-3884	262	12	odd	odd	ADJ
ejpam-3884	262	13	base	base	NOUN
ejpam-3884	262	14	m	m	VERB
ejpam-3884	262	15	is	be	AUX
ejpam-3884	262	16	given	give	VERB
ejpam-3884	262	17	by	by	ADP
ejpam-3884	262	18	h	h	PROPN
ejpam-3884	262	19	(	(	PUNCT
ejpam-3884	262	20	m−1	m−1	PROPN
ejpam-3884	262	21	2	2	NUM
ejpam-3884	262	22	)	)	PUNCT
ejpam-3884	262	23	.	.	PUNCT
ejpam-3884	263	1	they	they	PRON
ejpam-3884	263	2	also	also	ADV
ejpam-3884	263	3	found	find	VERB
ejpam-3884	263	4	out	out	ADP
ejpam-3884	263	5	that	that	SCONJ
ejpam-3884	263	6	the	the	DET
ejpam-3884	263	7	average	average	ADJ
ejpam-3884	263	8	distance	distance	NOUN
ejpam-3884	263	9	of	of	ADP
ejpam-3884	263	10	γmh	γmh	NOUN
ejpam-3884	263	11	where	where	SCONJ
ejpam-3884	263	12	the	the	DET
ejpam-3884	263	13	“	"	PUNCT
ejpam-3884	263	14	average	average	ADJ
ejpam-3884	263	15	distance	distance	NOUN
ejpam-3884	263	16	”	"	PUNCT
ejpam-3884	263	17	refers	refer	VERB
ejpam-3884	263	18	to	to	ADP
ejpam-3884	263	19	the	the	DET
ejpam-3884	263	20	sum	sum	NOUN
ejpam-3884	263	21	of	of	ADP
ejpam-3884	263	22	all	all	DET
ejpam-3884	263	23	entries	entry	NOUN
ejpam-3884	263	24	in	in	ADP
ejpam-3884	263	25	d	d	PROPN
ejpam-3884	263	26	(	(	PUNCT
ejpam-3884	263	27	γmh	γmh	NOUN
ejpam-3884	263	28	)	)	PUNCT
ejpam-3884	263	29	divided	divide	VERB
ejpam-3884	263	30	by	by	ADP
ejpam-3884	263	31	the	the	DET
ejpam-3884	263	32	number	number	NOUN
ejpam-3884	263	33	of	of	ADP
ejpam-3884	263	34	entries	entry	NOUN
ejpam-3884	263	35	is	be	AUX
ejpam-3884	263	36	given	give	VERB
ejpam-3884	263	37	by	by	ADP
ejpam-3884	263	38	h	h	NOUN
ejpam-3884	263	39	m	m	VERB
ejpam-3884	263	40	(	(	PUNCT
ejpam-3884	263	41	m2−1	m2−1	PRON
ejpam-3884	263	42	4	4	NUM
ejpam-3884	263	43	)	)	PUNCT
ejpam-3884	263	44	.	.	PUNCT
ejpam-3884	264	1	as	as	ADP
ejpam-3884	264	2	a	a	DET
ejpam-3884	264	3	consequence	consequence	NOUN
ejpam-3884	264	4	,	,	PUNCT
ejpam-3884	264	5	since	since	SCONJ
ejpam-3884	264	6	the	the	DET
ejpam-3884	264	7	distance	distance	NOUN
ejpam-3884	264	8	matrix	matrix	NOUN
ejpam-3884	264	9	of	of	ADP
ejpam-3884	264	10	γmh	γmh	NOUN
ejpam-3884	264	11	is	be	AUX
ejpam-3884	264	12	circulant	circulant	ADJ
ejpam-3884	264	13	,	,	PUNCT
ejpam-3884	264	14	the	the	DET
ejpam-3884	264	15	distance	distance	NOUN
ejpam-3884	264	16	spectral	spectral	ADJ
ejpam-3884	264	17	radius	radius	NOUN
ejpam-3884	264	18	of	of	ADP
ejpam-3884	264	19	γmh	γmh	NOUN
ejpam-3884	264	20	is	be	AUX
ejpam-3884	264	21	then	then	ADV
ejpam-3884	264	22	given	give	VERB
ejpam-3884	264	23	by	by	ADP
ejpam-3884	264	24	(	(	PUNCT
ejpam-3884	264	25	m2−1	m2−1	PRON
ejpam-3884	264	26	4	4	NUM
ejpam-3884	264	27	)	)	PUNCT
ejpam-3884	264	28	h(mh−1	h(mh−1	NOUN
ejpam-3884	264	29	)	)	PUNCT
ejpam-3884	264	30	.	.	PUNCT
ejpam-3884	265	1	we	we	PRON
ejpam-3884	265	2	reprove	reprove	VERB
ejpam-3884	265	3	the	the	DET
ejpam-3884	265	4	results	result	NOUN
ejpam-3884	265	5	involving	involve	VERB
ejpam-3884	265	6	γmh	γmh	NOUN
ejpam-3884	265	7	’s	’s	PART
ejpam-3884	265	8	diameter	diameter	NOUN
ejpam-3884	265	9	and	and	CCONJ
ejpam-3884	265	10	distance	distance	NOUN
ejpam-3884	265	11	spectral	spectral	ADJ
ejpam-3884	265	12	radius	radius	NOUN
ejpam-3884	265	13	using	use	VERB
ejpam-3884	265	14	our	our	PRON
ejpam-3884	265	15	proposed	propose	VERB
ejpam-3884	265	16	bfs	bfs	NOUN
ejpam-3884	265	17	tree	tree	NOUN
ejpam-3884	265	18	construction	construction	NOUN
ejpam-3884	265	19	in	in	ADP
ejpam-3884	265	20	this	this	DET
ejpam-3884	265	21	subsection	subsection	NOUN
ejpam-3884	265	22	.	.	PUNCT
ejpam-3884	266	1	this	this	DET
ejpam-3884	266	2	subsection	subsection	NOUN
ejpam-3884	266	3	is	be	AUX
ejpam-3884	266	4	motivated	motivate	VERB
ejpam-3884	266	5	by	by	ADP
ejpam-3884	266	6	the	the	DET
ejpam-3884	266	7	work	work	NOUN
ejpam-3884	266	8	of	of	ADP
ejpam-3884	266	9	liu	liu	PROPN
ejpam-3884	266	10	et	et	PROPN
ejpam-3884	266	11	al	al	PROPN
ejpam-3884	266	12	.	.	PUNCT
ejpam-3884	267	1	[	[	X
ejpam-3884	267	2	9	9	NUM
ejpam-3884	267	3	]	]	PUNCT
ejpam-3884	267	4	where	where	SCONJ
ejpam-3884	267	5	they	they	PRON
ejpam-3884	267	6	determined	determine	VERB
ejpam-3884	267	7	the	the	DET
ejpam-3884	267	8	distance	distance	NOUN
ejpam-3884	267	9	spectral	spectral	ADJ
ejpam-3884	267	10	radius	radius	NOUN
ejpam-3884	267	11	of	of	ADP
ejpam-3884	267	12	certain	certain	ADJ
ejpam-3884	267	13	class	class	NOUN
ejpam-3884	267	14	of	of	ADP
ejpam-3884	267	15	circulant	circulant	ADJ
ejpam-3884	267	16	graphs	graph	NOUN
ejpam-3884	267	17	.	.	PUNCT
ejpam-3884	268	1	to	to	PART
ejpam-3884	268	2	determine	determine	VERB
ejpam-3884	268	3	the	the	DET
ejpam-3884	268	4	diameter	diameter	NOUN
ejpam-3884	268	5	of	of	ADP
ejpam-3884	268	6	γmh	γmh	NOUN
ejpam-3884	268	7	,	,	PUNCT
ejpam-3884	268	8	we	we	PRON
ejpam-3884	268	9	begin	begin	VERB
ejpam-3884	268	10	by	by	ADP
ejpam-3884	268	11	proving	prove	VERB
ejpam-3884	268	12	a	a	DET
ejpam-3884	268	13	relationship	relationship	NOUN
ejpam-3884	268	14	between	between	ADP
ejpam-3884	268	15	the	the	DET
ejpam-3884	268	16	diameters	diameter	NOUN
ejpam-3884	268	17	of	of	ADP
ejpam-3884	268	18	γmh	γmh	NOUN
ejpam-3884	268	19	and	and	CCONJ
ejpam-3884	268	20	γmh−1	γmh−1	INTJ
ejpam-3884	268	21	.	.	PUNCT
ejpam-3884	269	1	theorem	theorem	NOUN
ejpam-3884	269	2	2	2	NUM
ejpam-3884	269	3	.	.	PUNCT
ejpam-3884	270	1	the	the	DET
ejpam-3884	270	2	two	two	NUM
ejpam-3884	270	3	diameters	diameter	NOUN
ejpam-3884	270	4	diam(γmh	diam(γmh	PROPN
ejpam-3884	270	5	)	)	PUNCT
ejpam-3884	270	6	and	and	CCONJ
ejpam-3884	270	7	diam(γmh−1	diam(γmh−1	NOUN
ejpam-3884	270	8	)	)	PUNCT
ejpam-3884	270	9	are	be	AUX
ejpam-3884	270	10	related	relate	VERB
ejpam-3884	270	11	by	by	ADP
ejpam-3884	270	12	diam(γmh	diam(γmh	PROPN
ejpam-3884	270	13	)	)	PUNCT
ejpam-3884	271	1	=	=	SYM
ejpam-3884	271	2	diam(γmh−1	diam(γmh−1	NOUN
ejpam-3884	271	3	)	)	PUNCT
ejpam-3884	272	1	+	+	CCONJ
ejpam-3884	272	2	m−	m−	PROPN
ejpam-3884	272	3	1	1	NUM
ejpam-3884	272	4	2	2	NUM
ejpam-3884	272	5	.	.	PUNCT
ejpam-3884	273	1	(	(	PUNCT
ejpam-3884	273	2	4	4	X
ejpam-3884	273	3	)	)	PUNCT
ejpam-3884	273	4	proof	proof	NOUN
ejpam-3884	273	5	.	.	PUNCT
ejpam-3884	274	1	we	we	PRON
ejpam-3884	274	2	start	start	VERB
ejpam-3884	274	3	by	by	ADP
ejpam-3884	274	4	initially	initially	ADV
ejpam-3884	274	5	assuming	assume	VERB
ejpam-3884	274	6	that	that	SCONJ
ejpam-3884	274	7	diam(γmh)=diam(γmh−1	diam(γmh)=diam(γmh−1	VERB
ejpam-3884	274	8	)	)	PUNCT
ejpam-3884	274	9	.	.	PUNCT
ejpam-3884	275	1	performing	perform	VERB
ejpam-3884	275	2	the	the	DET
ejpam-3884	275	3	steps	step	NOUN
ejpam-3884	275	4	necessary	necessary	ADJ
ejpam-3884	275	5	to	to	PART
ejpam-3884	275	6	construct	construct	VERB
ejpam-3884	275	7	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	275	8	)	)	PUNCT
ejpam-3884	275	9	from	from	ADP
ejpam-3884	275	10	bfs0(γmh−1	bfs0(γmh−1	PROPN
ejpam-3884	275	11	)	)	PUNCT
ejpam-3884	275	12	gives	give	VERB
ejpam-3884	275	13	the	the	DET
ejpam-3884	275	14	following	follow	VERB
ejpam-3884	275	15	update	update	NOUN
ejpam-3884	275	16	in	in	ADP
ejpam-3884	275	17	the	the	DET
ejpam-3884	275	18	initial	initial	ADJ
ejpam-3884	275	19	diameter	diameter	NOUN
ejpam-3884	275	20	of	of	ADP
ejpam-3884	275	21	γmh	γmh	NOUN
ejpam-3884	275	22	step	step	NOUN
ejpam-3884	275	23	1	1	NUM
ejpam-3884	275	24	:	:	PUNCT
ejpam-3884	275	25	diam(γmh)=diam(γmh−1	diam(γmh)=diam(γmh−1	NOUN
ejpam-3884	275	26	)	)	PUNCT
ejpam-3884	275	27	step	step	NOUN
ejpam-3884	275	28	2	2	NUM
ejpam-3884	275	29	:	:	PUNCT
ejpam-3884	275	30	diam(γmh)=diam(γmh−1	diam(γmh)=diam(γmh−1	NOUN
ejpam-3884	275	31	)	)	PUNCT
ejpam-3884	276	1	+	+	CCONJ
ejpam-3884	276	2	1	1	NUM
ejpam-3884	276	3	step	step	NOUN
ejpam-3884	276	4	3	3	NUM
ejpam-3884	276	5	:	:	PUNCT
ejpam-3884	276	6	diam(γmh)=diam(γmh−1	diam(γmh)=diam(γmh−1	NOUN
ejpam-3884	276	7	)	)	PUNCT
ejpam-3884	277	1	+	+	CCONJ
ejpam-3884	277	2	1	1	NUM
ejpam-3884	277	3	step	step	NOUN
ejpam-3884	277	4	4	4	NUM
ejpam-3884	277	5	:	:	PUNCT
ejpam-3884	277	6	diam(γmh)=diam(γmh−1	diam(γmh)=diam(γmh−1	NOUN
ejpam-3884	277	7	)	)	PUNCT
ejpam-3884	278	1	+	+	CCONJ
ejpam-3884	278	2	1	1	NUM
ejpam-3884	278	3	+	+	SYM
ejpam-3884	278	4	1	1	NUM
ejpam-3884	278	5	step	step	NOUN
ejpam-3884	278	6	5	5	NUM
ejpam-3884	278	7	:	:	PUNCT
ejpam-3884	278	8	diam(γmh)=diam(γmh−1	diam(γmh)=diam(γmh−1	NOUN
ejpam-3884	278	9	)	)	PUNCT
ejpam-3884	279	1	+	+	CCONJ
ejpam-3884	279	2	1	1	NUM
ejpam-3884	279	3	+	+	SYM
ejpam-3884	279	4	1	1	NUM
ejpam-3884	279	5	+	+	NUM
ejpam-3884	279	6	1	1	NUM
ejpam-3884	279	7	+	+	NUM
ejpam-3884	279	8	1	1	NUM
ejpam-3884	279	9	+	+	NUM
ejpam-3884	279	10	.	.	PUNCT
ejpam-3884	279	11	.	.	PUNCT
ejpam-3884	280	1	.+	.+	NOUN
ejpam-3884	281	1	1︸	1︸	NUM
ejpam-3884	281	2	︷︷	︷︷	NOUN
ejpam-3884	281	3	︸	︸	X
ejpam-3884	282	1	m−1	m−1	PROPN
ejpam-3884	282	2	2	2	NUM
ejpam-3884	282	3	−	−	NOUN
ejpam-3884	282	4	2	2	NUM
ejpam-3884	282	5	.	.	PUNCT
ejpam-3884	282	6	step	step	NOUN
ejpam-3884	282	7	6	6	NUM
ejpam-3884	282	8	:	:	PUNCT
ejpam-3884	282	9	diam(γmh)=diam(γmh−1	diam(γmh)=diam(γmh−1	NOUN
ejpam-3884	282	10	)	)	PUNCT
ejpam-3884	283	1	+	+	CCONJ
ejpam-3884	283	2	1	1	NUM
ejpam-3884	283	3	+	+	SYM
ejpam-3884	283	4	1	1	NUM
ejpam-3884	283	5	+	+	NUM
ejpam-3884	283	6	1	1	NUM
ejpam-3884	283	7	+	+	NUM
ejpam-3884	283	8	1	1	NUM
ejpam-3884	283	9	+	+	NUM
ejpam-3884	283	10	.	.	PUNCT
ejpam-3884	283	11	.	.	PUNCT
ejpam-3884	284	1	.+	.+	NOUN
ejpam-3884	285	1	1︸	1︸	NUM
ejpam-3884	285	2	︷︷	︷︷	NOUN
ejpam-3884	285	3	︸	︸	X
ejpam-3884	285	4	m−1	m−1	PROPN
ejpam-3884	285	5	2	2	NUM
ejpam-3884	285	6	−	−	NOUN
ejpam-3884	285	7	2	2	NUM
ejpam-3884	285	8	.	.	PUNCT
ejpam-3884	286	1	hence	hence	ADV
ejpam-3884	286	2	diam(γmh	diam(γmh	PROPN
ejpam-3884	286	3	)	)	PUNCT
ejpam-3884	287	1	=	=	PUNCT
ejpam-3884	287	2	diam(γmh−1	diam(γmh−1	NOUN
ejpam-3884	287	3	)	)	PUNCT
ejpam-3884	288	1	+	+	CCONJ
ejpam-3884	288	2	m−1	m−1	PROPN
ejpam-3884	288	3	2	2	NUM
ejpam-3884	288	4	.	.	PUNCT
ejpam-3884	288	5	corollary	corollary	ADJ
ejpam-3884	288	6	1	1	NUM
ejpam-3884	288	7	.	.	PUNCT
ejpam-3884	289	1	the	the	DET
ejpam-3884	289	2	diameter	diameter	NOUN
ejpam-3884	289	3	of	of	ADP
ejpam-3884	289	4	γmh	γmh	NOUN
ejpam-3884	289	5	is	be	AUX
ejpam-3884	289	6	h	h	NOUN
ejpam-3884	289	7	(	(	PUNCT
ejpam-3884	289	8	m−1	m−1	PROPN
ejpam-3884	289	9	2	2	NUM
ejpam-3884	289	10	)	)	PUNCT
ejpam-3884	289	11	.	.	PUNCT
ejpam-3884	290	1	j.	j.	PROPN
ejpam-3884	290	2	antalan	antalan	PROPN
ejpam-3884	290	3	,	,	PUNCT
ejpam-3884	290	4	f.	f.	PROPN
ejpam-3884	290	5	campeña	campeña	PROPN
ejpam-3884	290	6	/	/	SYM
ejpam-3884	290	7	eur	eur	PROPN
ejpam-3884	290	8	.	.	PUNCT
ejpam-3884	291	1	j.	j.	PROPN
ejpam-3884	291	2	pure	pure	PROPN
ejpam-3884	291	3	appl	appl	PROPN
ejpam-3884	291	4	.	.	PROPN
ejpam-3884	291	5	math	math	PROPN
ejpam-3884	291	6	,	,	PUNCT
ejpam-3884	291	7	14	14	NUM
ejpam-3884	291	8	(	(	PUNCT
ejpam-3884	291	9	1	1	NUM
ejpam-3884	291	10	)	)	PUNCT
ejpam-3884	291	11	(	(	PUNCT
ejpam-3884	291	12	2021	2021	NUM
ejpam-3884	291	13	)	)	PUNCT
ejpam-3884	291	14	,	,	PUNCT
ejpam-3884	291	15	248	248	NUM
ejpam-3884	291	16	-	-	SYM
ejpam-3884	291	17	264	264	NUM
ejpam-3884	291	18	259	259	NUM
ejpam-3884	291	19	proof	proof	NOUN
ejpam-3884	291	20	.	.	PUNCT
ejpam-3884	292	1	note	note	VERB
ejpam-3884	292	2	that	that	SCONJ
ejpam-3884	292	3	for	for	ADP
ejpam-3884	292	4	all	all	DET
ejpam-3884	292	5	odd	odd	ADJ
ejpam-3884	292	6	integer	integer	NOUN
ejpam-3884	292	7	m	m	PROPN
ejpam-3884	292	8	>	>	X
ejpam-3884	292	9	1	1	NUM
ejpam-3884	292	10	,	,	PUNCT
ejpam-3884	292	11	we	we	PRON
ejpam-3884	292	12	have	have	VERB
ejpam-3884	292	13	diam(γm1	diam(γm1	ADJ
ejpam-3884	292	14	)	)	PUNCT
ejpam-3884	292	15	=	=	SYM
ejpam-3884	293	1	m−1	m−1	PROPN
ejpam-3884	293	2	2	2	NUM
ejpam-3884	293	3	.	.	PUNCT
ejpam-3884	293	4	using	use	VERB
ejpam-3884	293	5	theorem	theorem	NOUN
ejpam-3884	293	6	2	2	NUM
ejpam-3884	293	7	,	,	PUNCT
ejpam-3884	293	8	we	we	PRON
ejpam-3884	293	9	have	have	AUX
ejpam-3884	293	10	diam(γm2	diam(γm2	PROPN
ejpam-3884	293	11	)	)	PUNCT
ejpam-3884	293	12	=	=	SYM
ejpam-3884	293	13	diam(γm1	diam(γm1	NOUN
ejpam-3884	293	14	)	)	PUNCT
ejpam-3884	293	15	+	+	CCONJ
ejpam-3884	293	16	(	(	PUNCT
ejpam-3884	293	17	m−	m−	PROPN
ejpam-3884	293	18	1	1	NUM
ejpam-3884	293	19	)	)	PUNCT
ejpam-3884	293	20	2	2	NUM
ejpam-3884	293	21	=	=	SYM
ejpam-3884	293	22	2	2	NUM
ejpam-3884	293	23	(	(	PUNCT
ejpam-3884	293	24	m−	m−	PROPN
ejpam-3884	293	25	1	1	NUM
ejpam-3884	293	26	2	2	NUM
ejpam-3884	293	27	)	)	PUNCT
ejpam-3884	293	28	.	.	PUNCT
ejpam-3884	294	1	diam(γm3	diam(γm3	PROPN
ejpam-3884	294	2	)	)	PUNCT
ejpam-3884	294	3	=	=	SYM
ejpam-3884	294	4	diam(γm2	diam(γm2	PROPN
ejpam-3884	294	5	)	)	PUNCT
ejpam-3884	295	1	+	+	CCONJ
ejpam-3884	295	2	(	(	PUNCT
ejpam-3884	295	3	m−	m−	PROPN
ejpam-3884	295	4	1	1	NUM
ejpam-3884	295	5	)	)	PUNCT
ejpam-3884	295	6	2	2	NUM
ejpam-3884	295	7	=	=	SYM
ejpam-3884	295	8	3	3	NUM
ejpam-3884	295	9	(	(	PUNCT
ejpam-3884	295	10	m−	m−	PROPN
ejpam-3884	295	11	1	1	NUM
ejpam-3884	295	12	2	2	NUM
ejpam-3884	295	13	)	)	PUNCT
ejpam-3884	295	14	.	.	PUNCT
ejpam-3884	296	1	...	...	PUNCT
ejpam-3884	296	2	diam(γmh	diam(γmh	PROPN
ejpam-3884	296	3	)	)	PUNCT
ejpam-3884	297	1	=	=	PUNCT
ejpam-3884	297	2	diam(γmh−1	diam(γmh−1	NOUN
ejpam-3884	297	3	)	)	PUNCT
ejpam-3884	298	1	+	+	CCONJ
ejpam-3884	298	2	(	(	PUNCT
ejpam-3884	298	3	m−	m−	PROPN
ejpam-3884	298	4	1	1	NUM
ejpam-3884	298	5	)	)	PUNCT
ejpam-3884	298	6	2	2	NUM
ejpam-3884	298	7	=	=	SYM
ejpam-3884	298	8	(	(	PUNCT
ejpam-3884	298	9	h−	h−	NOUN
ejpam-3884	298	10	1	1	NUM
ejpam-3884	298	11	)	)	PUNCT
ejpam-3884	298	12	(	(	PUNCT
ejpam-3884	298	13	m−	m−	PROPN
ejpam-3884	298	14	1	1	NUM
ejpam-3884	298	15	2	2	NUM
ejpam-3884	298	16	)	)	PUNCT
ejpam-3884	298	17	+	+	CCONJ
ejpam-3884	298	18	(	(	PUNCT
ejpam-3884	298	19	m−	m−	PROPN
ejpam-3884	298	20	1	1	NUM
ejpam-3884	298	21	)	)	PUNCT
ejpam-3884	298	22	2	2	NUM
ejpam-3884	298	23	.	.	PUNCT
ejpam-3884	299	1	=	=	PRON
ejpam-3884	299	2	h	h	PROPN
ejpam-3884	299	3	(	(	PUNCT
ejpam-3884	299	4	m−	m−	PROPN
ejpam-3884	299	5	1	1	NUM
ejpam-3884	299	6	2	2	NUM
ejpam-3884	299	7	)	)	PUNCT
ejpam-3884	299	8	.	.	PUNCT
ejpam-3884	300	1	the	the	DET
ejpam-3884	300	2	next	next	ADJ
ejpam-3884	300	3	result	result	NOUN
ejpam-3884	300	4	gives	give	VERB
ejpam-3884	300	5	the	the	DET
ejpam-3884	300	6	relationship	relationship	NOUN
ejpam-3884	300	7	between	between	ADP
ejpam-3884	300	8	the	the	DET
ejpam-3884	300	9	two	two	NUM
ejpam-3884	300	10	distance	distance	NOUN
ejpam-3884	300	11	spectral	spectral	ADJ
ejpam-3884	300	12	radii	radius	NOUN
ejpam-3884	300	13	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	300	14	)	)	PUNCT
ejpam-3884	300	15	and	and	CCONJ
ejpam-3884	300	16	ρ(γmh−1	ρ(γmh−1	PROPN
ejpam-3884	300	17	)	)	PUNCT
ejpam-3884	300	18	.	.	PUNCT
ejpam-3884	301	1	theorem	theorem	NOUN
ejpam-3884	301	2	3	3	NUM
ejpam-3884	301	3	.	.	PUNCT
ejpam-3884	302	1	the	the	DET
ejpam-3884	302	2	two	two	NUM
ejpam-3884	302	3	distance	distance	NOUN
ejpam-3884	302	4	spectral	spectral	ADJ
ejpam-3884	302	5	radii	radius	NOUN
ejpam-3884	302	6	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	302	7	)	)	PUNCT
ejpam-3884	302	8	and	and	CCONJ
ejpam-3884	302	9	ρ(γmh−1	ρ(γmh−1	PROPN
ejpam-3884	302	10	)	)	PUNCT
ejpam-3884	302	11	are	be	AUX
ejpam-3884	302	12	related	relate	VERB
ejpam-3884	302	13	by	by	ADP
ejpam-3884	302	14	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	302	15	)	)	PUNCT
ejpam-3884	303	1	=	=	SYM
ejpam-3884	303	2	mρ(γmh−1	mρ(γmh−1	PROPN
ejpam-3884	303	3	)	)	PUNCT
ejpam-3884	304	1	+	+	CCONJ
ejpam-3884	304	2	(	(	PUNCT
ejpam-3884	304	3	m−	m−	PROPN
ejpam-3884	304	4	1)(m+	1)(m+	NUM
ejpam-3884	304	5	1	1	NUM
ejpam-3884	304	6	)	)	PUNCT
ejpam-3884	304	7	2	2	NUM
ejpam-3884	304	8	mh−1	mh−1	NOUN
ejpam-3884	304	9	.	.	PUNCT
ejpam-3884	305	1	(	(	PUNCT
ejpam-3884	305	2	5	5	X
ejpam-3884	305	3	)	)	PUNCT
ejpam-3884	305	4	proof	proof	NOUN
ejpam-3884	305	5	.	.	PUNCT
ejpam-3884	306	1	note	note	VERB
ejpam-3884	306	2	that	that	SCONJ
ejpam-3884	306	3	the	the	DET
ejpam-3884	306	4	distance	distance	NOUN
ejpam-3884	306	5	spectral	spectral	ADJ
ejpam-3884	306	6	radius	radius	NOUN
ejpam-3884	306	7	of	of	ADP
ejpam-3884	306	8	γmh	γmh	NOUN
ejpam-3884	306	9	corresponds	correspond	VERB
ejpam-3884	306	10	to	to	ADP
ejpam-3884	306	11	the	the	DET
ejpam-3884	306	12	sum	sum	NOUN
ejpam-3884	306	13	of	of	ADP
ejpam-3884	306	14	all	all	DET
ejpam-3884	306	15	distances	distance	NOUN
ejpam-3884	306	16	in	in	ADP
ejpam-3884	306	17	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	306	18	)	)	PUNCT
ejpam-3884	306	19	.	.	PUNCT
ejpam-3884	307	1	initially	initially	ADV
ejpam-3884	307	2	,	,	PUNCT
ejpam-3884	307	3	we	we	PRON
ejpam-3884	307	4	have	have	VERB
ejpam-3884	307	5	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	307	6	)	)	PUNCT
ejpam-3884	308	1	=	=	SYM
ejpam-3884	308	2	ρ(γmh−1	ρ(γmh−1	X
ejpam-3884	308	3	)	)	PUNCT
ejpam-3884	308	4	.	.	PUNCT
ejpam-3884	309	1	as	as	SCONJ
ejpam-3884	309	2	we	we	PRON
ejpam-3884	309	3	go	go	VERB
ejpam-3884	309	4	over	over	ADP
ejpam-3884	309	5	the	the	DET
ejpam-3884	309	6	steps	step	NOUN
ejpam-3884	309	7	of	of	ADP
ejpam-3884	309	8	constructing	construct	VERB
ejpam-3884	309	9	bfs0(γmh	bfs0(γmh	NOUN
ejpam-3884	309	10	)	)	PUNCT
ejpam-3884	309	11	from	from	ADP
ejpam-3884	309	12	bfs0(γmh−1	bfs0(γmh−1	PROPN
ejpam-3884	309	13	)	)	PUNCT
ejpam-3884	309	14	,	,	PUNCT
ejpam-3884	309	15	the	the	DET
ejpam-3884	309	16	value	value	NOUN
ejpam-3884	309	17	of	of	ADP
ejpam-3884	309	18	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	309	19	)	)	PUNCT
ejpam-3884	309	20	will	will	AUX
ejpam-3884	309	21	be	be	AUX
ejpam-3884	309	22	updated	update	VERB
ejpam-3884	309	23	.	.	PUNCT
ejpam-3884	310	1	after	after	ADP
ejpam-3884	310	2	performing	perform	VERB
ejpam-3884	310	3	step	step	NOUN
ejpam-3884	310	4	2	2	NUM
ejpam-3884	310	5	,	,	PUNCT
ejpam-3884	310	6	the	the	DET
ejpam-3884	310	7	initial	initial	ADJ
ejpam-3884	310	8	value	value	NOUN
ejpam-3884	310	9	of	of	ADP
ejpam-3884	310	10	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	310	11	)	)	PUNCT
ejpam-3884	310	12	will	will	AUX
ejpam-3884	310	13	be	be	AUX
ejpam-3884	310	14	added	add	VERB
ejpam-3884	310	15	by	by	ADP
ejpam-3884	310	16	the	the	DET
ejpam-3884	310	17	number	number	NOUN
ejpam-3884	310	18	of	of	ADP
ejpam-3884	310	19	distance	distance	NOUN
ejpam-3884	310	20	created	create	VERB
ejpam-3884	310	21	as	as	ADP
ejpam-3884	310	22	a	a	DET
ejpam-3884	310	23	result	result	NOUN
ejpam-3884	310	24	of	of	ADP
ejpam-3884	310	25	descending	descend	VERB
ejpam-3884	310	26	the	the	DET
ejpam-3884	310	27	vertices	vertex	NOUN
ejpam-3884	310	28	mh−1	mh−1	PROPN
ejpam-3884	310	29	and	and	CCONJ
ejpam-3884	310	30	the	the	DET
ejpam-3884	310	31	right	right	ADJ
ejpam-3884	310	32	part	part	NOUN
ejpam-3884	310	33	of	of	ADP
ejpam-3884	310	34	bfs0(γmh−1	bfs0(γmh−1	PROPN
ejpam-3884	310	35	)	)	PUNCT
ejpam-3884	310	36	by	by	ADP
ejpam-3884	310	37	a	a	DET
ejpam-3884	310	38	unit	unit	NOUN
ejpam-3884	310	39	.	.	PUNCT
ejpam-3884	311	1	the	the	DET
ejpam-3884	311	2	number	number	NOUN
ejpam-3884	311	3	of	of	ADP
ejpam-3884	311	4	created	create	VERB
ejpam-3884	311	5	distance	distance	NOUN
ejpam-3884	311	6	of	of	ADP
ejpam-3884	311	7	the	the	DET
ejpam-3884	311	8	just	just	ADV
ejpam-3884	311	9	stated	state	VERB
ejpam-3884	311	10	action	action	NOUN
ejpam-3884	311	11	is	be	AUX
ejpam-3884	311	12	exacty	exacty	ADJ
ejpam-3884	311	13	|r[bfs0(γmh−1)]|+	|r[bfs0(γmh−1)]|+	NOUN
ejpam-3884	311	14	1	1	NUM
ejpam-3884	311	15	.	.	PUNCT
ejpam-3884	312	1	so	so	ADV
ejpam-3884	312	2	we	we	PRON
ejpam-3884	312	3	have	have	VERB
ejpam-3884	312	4	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	312	5	)	)	PUNCT
ejpam-3884	313	1	=	=	SYM
ejpam-3884	313	2	ρ(γmh−1	ρ(γmh−1	X
ejpam-3884	313	3	)	)	PUNCT
ejpam-3884	314	1	+	+	CCONJ
ejpam-3884	314	2	|r[bfs0(γmh−1)]|+	|r[bfs0(γmh−1)]|+	NOUN
ejpam-3884	314	3	1	1	NUM
ejpam-3884	314	4	after	after	ADP
ejpam-3884	314	5	step	step	NOUN
ejpam-3884	314	6	2	2	NUM
ejpam-3884	314	7	.	.	PUNCT
ejpam-3884	315	1	for	for	ADP
ejpam-3884	315	2	step	step	NOUN
ejpam-3884	315	3	3	3	NUM
ejpam-3884	315	4	,	,	PUNCT
ejpam-3884	315	5	reproducing	reproduce	VERB
ejpam-3884	315	6	the	the	DET
ejpam-3884	315	7	left	left	ADJ
ejpam-3884	315	8	part	part	NOUN
ejpam-3884	315	9	of	of	ADP
ejpam-3884	315	10	bfs0(γmh−1	bfs0(γmh−1	PROPN
ejpam-3884	315	11	)	)	PUNCT
ejpam-3884	315	12	will	will	AUX
ejpam-3884	315	13	create	create	VERB
ejpam-3884	315	14	a	a	DET
ejpam-3884	315	15	distance	distance	NOUN
ejpam-3884	315	16	of	of	ADP
ejpam-3884	315	17	ρ(γ	ρ(γ	PROPN
ejpam-3884	315	18	mh−1	mh−1	PROPN
ejpam-3884	315	19	)	)	PUNCT
ejpam-3884	315	20	2	2	X
ejpam-3884	315	21	.	.	PUNCT
ejpam-3884	316	1	since	since	SCONJ
ejpam-3884	316	2	the	the	DET
ejpam-3884	316	3	reproduction	reproduction	NOUN
ejpam-3884	316	4	starts	start	VERB
ejpam-3884	316	5	at	at	ADP
ejpam-3884	316	6	vertex	vertex	NOUN
ejpam-3884	316	7	mh−1	mh−1	NOUN
ejpam-3884	316	8	which	which	PRON
ejpam-3884	316	9	is	be	AUX
ejpam-3884	316	10	of	of	ADP
ejpam-3884	316	11	distance	distance	NOUN
ejpam-3884	316	12	1	1	NUM
ejpam-3884	316	13	to	to	ADP
ejpam-3884	316	14	the	the	DET
ejpam-3884	316	15	0−vertex	0−vertex	NOUN
ejpam-3884	316	16	,	,	PUNCT
ejpam-3884	316	17	we	we	PRON
ejpam-3884	316	18	need	need	VERB
ejpam-3884	316	19	to	to	PART
ejpam-3884	316	20	add	add	VERB
ejpam-3884	316	21	another	another	DET
ejpam-3884	316	22	|l[bfs0(γmh−1)]|	|l[bfs0(γmh−1)]|	NOUN
ejpam-3884	316	23	.	.	PUNCT
ejpam-3884	317	1	so	so	ADV
ejpam-3884	317	2	,	,	PUNCT
ejpam-3884	317	3	after	after	ADP
ejpam-3884	317	4	step	step	NOUN
ejpam-3884	317	5	3	3	NUM
ejpam-3884	317	6	,	,	PUNCT
ejpam-3884	317	7	we	we	PRON
ejpam-3884	317	8	have	have	VERB
ejpam-3884	317	9	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	317	10	)	)	PUNCT
ejpam-3884	318	1	=	=	SYM
ejpam-3884	318	2	ρ(γmh−1	ρ(γmh−1	X
ejpam-3884	318	3	)	)	PUNCT
ejpam-3884	319	1	+	+	CCONJ
ejpam-3884	319	2	|r[bfs0(γmh−1)]|+	|r[bfs0(γmh−1)]|+	NOUN
ejpam-3884	319	3	1	1	NUM
ejpam-3884	319	4	+	+	NUM
ejpam-3884	319	5	ρ(γ	ρ(γ	PROPN
ejpam-3884	319	6	mh−1	mh−1	NOUN
ejpam-3884	319	7	)	)	PUNCT
ejpam-3884	319	8	2	2	NUM
ejpam-3884	319	9	+	+	CCONJ
ejpam-3884	319	10	|l[bfs0(γmh−1)]|	|l[bfs0(γmh−1)]|	PROPN
ejpam-3884	319	11	.	.	PUNCT
ejpam-3884	319	12	j.	j.	PROPN
ejpam-3884	319	13	antalan	antalan	PROPN
ejpam-3884	319	14	,	,	PUNCT
ejpam-3884	319	15	f.	f.	PROPN
ejpam-3884	319	16	campeña	campeña	PROPN
ejpam-3884	319	17	/	/	SYM
ejpam-3884	319	18	eur	eur	PROPN
ejpam-3884	319	19	.	.	PUNCT
ejpam-3884	320	1	j.	j.	PROPN
ejpam-3884	320	2	pure	pure	PROPN
ejpam-3884	320	3	appl	appl	PROPN
ejpam-3884	320	4	.	.	PROPN
ejpam-3884	320	5	math	math	PROPN
ejpam-3884	320	6	,	,	PUNCT
ejpam-3884	320	7	14	14	NUM
ejpam-3884	320	8	(	(	PUNCT
ejpam-3884	320	9	1	1	NUM
ejpam-3884	320	10	)	)	PUNCT
ejpam-3884	320	11	(	(	PUNCT
ejpam-3884	320	12	2021	2021	NUM
ejpam-3884	320	13	)	)	PUNCT
ejpam-3884	320	14	,	,	PUNCT
ejpam-3884	320	15	248	248	NUM
ejpam-3884	320	16	-	-	SYM
ejpam-3884	320	17	264	264	NUM
ejpam-3884	320	18	260	260	NUM
ejpam-3884	320	19	the	the	DET
ejpam-3884	320	20	action	action	NOUN
ejpam-3884	320	21	reproduce	reproduce	VERB
ejpam-3884	320	22	the	the	DET
ejpam-3884	320	23	genealogy	genealogy	NOUN
ejpam-3884	320	24	ofmh−1	ofmh−1	NOUN
ejpam-3884	320	25	in	in	ADP
ejpam-3884	320	26	step	step	NOUN
ejpam-3884	320	27	4	4	NUM
ejpam-3884	320	28	will	will	AUX
ejpam-3884	320	29	create	create	VERB
ejpam-3884	320	30	a	a	DET
ejpam-3884	320	31	distance	distance	NOUN
ejpam-3884	320	32	of	of	ADP
ejpam-3884	320	33	ρ(γmh−1	ρ(γmh−1	NOUN
ejpam-3884	320	34	)	)	PUNCT
ejpam-3884	320	35	.	.	PUNCT
ejpam-3884	321	1	moreover	moreover	ADV
ejpam-3884	321	2	,	,	PUNCT
ejpam-3884	321	3	since	since	SCONJ
ejpam-3884	321	4	the	the	DET
ejpam-3884	321	5	reproduction	reproduction	NOUN
ejpam-3884	321	6	starts	start	VERB
ejpam-3884	321	7	at	at	ADP
ejpam-3884	321	8	vertex	vertex	NOUN
ejpam-3884	321	9	2mh−1	2mh−1	NUM
ejpam-3884	321	10	which	which	PRON
ejpam-3884	321	11	is	be	AUX
ejpam-3884	321	12	of	of	ADP
ejpam-3884	321	13	distance	distance	NOUN
ejpam-3884	321	14	2	2	NUM
ejpam-3884	321	15	to	to	ADP
ejpam-3884	321	16	the	the	DET
ejpam-3884	321	17	0−vertex	0−vertex	NOUN
ejpam-3884	321	18	,	,	PUNCT
ejpam-3884	321	19	we	we	PRON
ejpam-3884	321	20	need	need	VERB
ejpam-3884	321	21	to	to	PART
ejpam-3884	321	22	add	add	VERB
ejpam-3884	321	23	another	another	DET
ejpam-3884	321	24	2(mh−1	2(mh−1	NUM
ejpam-3884	321	25	)	)	PUNCT
ejpam-3884	321	26	.	.	PUNCT
ejpam-3884	322	1	as	as	ADP
ejpam-3884	322	2	a	a	DET
ejpam-3884	322	3	result	result	NOUN
ejpam-3884	322	4	,	,	PUNCT
ejpam-3884	322	5	we	we	PRON
ejpam-3884	322	6	have	have	VERB
ejpam-3884	322	7	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	322	8	)	)	PUNCT
ejpam-3884	323	1	=	=	SYM
ejpam-3884	323	2	ρ(γmh−1	ρ(γmh−1	X
ejpam-3884	323	3	)	)	PUNCT
ejpam-3884	324	1	+	+	CCONJ
ejpam-3884	324	2	|r[bfs0(γmh−1)]|+	|r[bfs0(γmh−1)]|+	NOUN
ejpam-3884	324	3	1	1	NUM
ejpam-3884	324	4	+	+	NUM
ejpam-3884	324	5	ρ(γ	ρ(γ	PROPN
ejpam-3884	324	6	mh−1	mh−1	NOUN
ejpam-3884	324	7	)	)	PUNCT
ejpam-3884	324	8	2	2	NUM
ejpam-3884	325	1	+	+	NUM
ejpam-3884	325	2	|l[bfs0(γmh−1)]|+	|l[bfs0(γmh−1)]|+	NOUN
ejpam-3884	325	3	ρ(γmh−1	ρ(γmh−1	PROPN
ejpam-3884	325	4	)	)	PUNCT
ejpam-3884	325	5	+	+	CCONJ
ejpam-3884	326	1	2(mh−1	2(mh−1	NUM
ejpam-3884	326	2	)	)	PUNCT
ejpam-3884	326	3	.	.	PUNCT
ejpam-3884	327	1	the	the	DET
ejpam-3884	327	2	principle	principle	NOUN
ejpam-3884	327	3	that	that	PRON
ejpam-3884	327	4	holds	hold	VERB
ejpam-3884	327	5	in	in	ADP
ejpam-3884	327	6	step	step	NOUN
ejpam-3884	327	7	4	4	NUM
ejpam-3884	327	8	is	be	AUX
ejpam-3884	327	9	the	the	DET
ejpam-3884	327	10	same	same	ADJ
ejpam-3884	327	11	principle	principle	NOUN
ejpam-3884	327	12	that	that	PRON
ejpam-3884	327	13	holds	hold	VERB
ejpam-3884	327	14	for	for	ADP
ejpam-3884	327	15	step	step	NOUN
ejpam-3884	327	16	5	5	NUM
ejpam-3884	327	17	.	.	PUNCT
ejpam-3884	328	1	in	in	ADP
ejpam-3884	328	2	general	general	ADJ
ejpam-3884	328	3	,	,	PUNCT
ejpam-3884	328	4	for	for	ADP
ejpam-3884	328	5	r	r	PROPN
ejpam-3884	328	6	∈	∈	PROPN
ejpam-3884	328	7	{	{	PUNCT
ejpam-3884	328	8	3	3	NUM
ejpam-3884	328	9	,	,	PUNCT
ejpam-3884	328	10	4	4	NUM
ejpam-3884	328	11	,	,	PUNCT
ejpam-3884	328	12	.	.	PUNCT
ejpam-3884	328	13	.	.	PUNCT
ejpam-3884	328	14	.	.	PUNCT
ejpam-3884	329	1	,	,	PUNCT
ejpam-3884	329	2	m−1	m−1	PROPN
ejpam-3884	329	3	2	2	X
ejpam-3884	329	4	}	}	PUNCT
ejpam-3884	329	5	we	we	PRON
ejpam-3884	329	6	have	have	VERB
ejpam-3884	329	7	an	an	DET
ejpam-3884	329	8	additional	additional	ADJ
ejpam-3884	329	9	distance	distance	NOUN
ejpam-3884	329	10	ρ(γmh−1	ρ(γmh−1	NOUN
ejpam-3884	329	11	)	)	PUNCT
ejpam-3884	330	1	+	+	CCONJ
ejpam-3884	330	2	r(mh−1	r(mh−1	NOUN
ejpam-3884	330	3	)	)	PUNCT
ejpam-3884	330	4	.	.	PUNCT
ejpam-3884	331	1	so	so	ADV
ejpam-3884	331	2	after	after	ADP
ejpam-3884	331	3	step	step	NOUN
ejpam-3884	331	4	5	5	NUM
ejpam-3884	331	5	,	,	PUNCT
ejpam-3884	331	6	we	we	PRON
ejpam-3884	331	7	have	have	VERB
ejpam-3884	331	8	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	331	9	)	)	PUNCT
ejpam-3884	332	1	=	=	SYM
ejpam-3884	332	2	ρ(γmh−1	ρ(γmh−1	X
ejpam-3884	332	3	)	)	PUNCT
ejpam-3884	333	1	+	+	CCONJ
ejpam-3884	333	2	|r[bfs0(γmh−1)]|+	|r[bfs0(γmh−1)]|+	NOUN
ejpam-3884	333	3	1	1	NUM
ejpam-3884	333	4	+	+	CCONJ
ejpam-3884	333	5	ρ(γmh−1	ρ(γmh−1	NOUN
ejpam-3884	333	6	)	)	PUNCT
ejpam-3884	333	7	2	2	NUM
ejpam-3884	333	8	+	+	CCONJ
ejpam-3884	333	9	|l[bfs0(γmh−1)]|	|l[bfs0(γmh−1)]|	PROPN
ejpam-3884	333	10	+	+	CCONJ
ejpam-3884	333	11	m−1	m−1	PROPN
ejpam-3884	333	12	2∑	2∑	NUM
ejpam-3884	333	13	r=2	r=2	X
ejpam-3884	333	14	[	[	PUNCT
ejpam-3884	333	15	ρ(γmh−1	ρ(γmh−1	PROPN
ejpam-3884	333	16	)	)	PUNCT
ejpam-3884	333	17	+	+	ADJ
ejpam-3884	333	18	r(mh−1	r(mh−1	NOUN
ejpam-3884	333	19	)	)	PUNCT
ejpam-3884	333	20	]	]	PUNCT
ejpam-3884	334	1	=	=	PUNCT
ejpam-3884	334	2	ρ(γmh−1	ρ(γmh−1	X
ejpam-3884	334	3	)	)	PUNCT
ejpam-3884	335	1	+	+	CCONJ
ejpam-3884	335	2	ρ(γmh−1	ρ(γmh−1	X
ejpam-3884	335	3	)	)	PUNCT
ejpam-3884	335	4	2	2	NUM
ejpam-3884	336	1	+	+	NOUN
ejpam-3884	336	2	mh−1	mh−1	NOUN
ejpam-3884	336	3	+	+	CCONJ
ejpam-3884	336	4	(	(	PUNCT
ejpam-3884	336	5	m−	m−	PROPN
ejpam-3884	336	6	1	1	NUM
ejpam-3884	336	7	2	2	NUM
ejpam-3884	336	8	−	−	NUM
ejpam-3884	336	9	1	1	NUM
ejpam-3884	336	10	)	)	PUNCT
ejpam-3884	336	11	ρ(γmh−1	ρ(γmh−1	PROPN
ejpam-3884	336	12	)	)	PUNCT
ejpam-3884	337	1	+	+	CCONJ
ejpam-3884	338	1	m−1	m−1	PROPN
ejpam-3884	338	2	2∑	2∑	NUM
ejpam-3884	338	3	r=2	r=2	X
ejpam-3884	338	4	r(mh−1	r(mh−1	NOUN
ejpam-3884	338	5	)	)	PUNCT
ejpam-3884	338	6	=	=	PUNCT
ejpam-3884	338	7	(	(	PUNCT
ejpam-3884	338	8	1	1	NUM
ejpam-3884	338	9	+	+	CCONJ
ejpam-3884	338	10	1	1	NUM
ejpam-3884	338	11	2	2	NUM
ejpam-3884	338	12	+	+	CCONJ
ejpam-3884	338	13	m−	m−	PROPN
ejpam-3884	338	14	1	1	NUM
ejpam-3884	338	15	2	2	NUM
ejpam-3884	338	16	−	−	NUM
ejpam-3884	338	17	1	1	NUM
ejpam-3884	338	18	)	)	PUNCT
ejpam-3884	338	19	ρ(γmh−1	ρ(γmh−1	PROPN
ejpam-3884	338	20	)	)	PUNCT
ejpam-3884	339	1	+	+	CCONJ
ejpam-3884	340	1	m−1	m−1	PROPN
ejpam-3884	340	2	2∑	2∑	NUM
ejpam-3884	340	3	r=1	r=1	ADJ
ejpam-3884	340	4	r(mh−1	r(mh−1	NOUN
ejpam-3884	340	5	)	)	PUNCT
ejpam-3884	340	6	=	=	SYM
ejpam-3884	340	7	m	m	VERB
ejpam-3884	340	8	2	2	NUM
ejpam-3884	340	9	ρ(γmh−1	ρ(γmh−1	NOUN
ejpam-3884	340	10	)	)	PUNCT
ejpam-3884	341	1	+	+	CCONJ
ejpam-3884	341	2	(	(	PUNCT
ejpam-3884	341	3	m−	m−	PROPN
ejpam-3884	341	4	1)(m+	1)(m+	NUM
ejpam-3884	341	5	1	1	NUM
ejpam-3884	341	6	)	)	PUNCT
ejpam-3884	341	7	4	4	NUM
ejpam-3884	341	8	(	(	PUNCT
ejpam-3884	341	9	mh−1	mh−1	PROPN
ejpam-3884	341	10	)	)	PUNCT
ejpam-3884	341	11	.	.	PUNCT
ejpam-3884	342	1	finally	finally	ADV
ejpam-3884	342	2	,	,	PUNCT
ejpam-3884	342	3	performing	perform	VERB
ejpam-3884	342	4	step	step	NOUN
ejpam-3884	342	5	6	6	NUM
ejpam-3884	342	6	doubles	double	VERB
ejpam-3884	342	7	the	the	DET
ejpam-3884	342	8	current	current	ADJ
ejpam-3884	342	9	value	value	NOUN
ejpam-3884	342	10	of	of	ADP
ejpam-3884	342	11	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	342	12	)	)	PUNCT
ejpam-3884	342	13	.	.	PUNCT
ejpam-3884	343	1	as	as	ADP
ejpam-3884	343	2	a	a	DET
ejpam-3884	343	3	result	result	NOUN
ejpam-3884	343	4	,	,	PUNCT
ejpam-3884	343	5	we	we	PRON
ejpam-3884	343	6	have	have	VERB
ejpam-3884	343	7	the	the	DET
ejpam-3884	343	8	final	final	ADJ
ejpam-3884	343	9	value	value	NOUN
ejpam-3884	343	10	of	of	ADP
ejpam-3884	343	11	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	343	12	)	)	PUNCT
ejpam-3884	344	1	=	=	SYM
ejpam-3884	344	2	2	2	NUM
ejpam-3884	344	3	[	[	PUNCT
ejpam-3884	344	4	m	m	NOUN
ejpam-3884	344	5	2	2	NUM
ejpam-3884	344	6	ρ(γmh−1	ρ(γmh−1	NOUN
ejpam-3884	344	7	)	)	PUNCT
ejpam-3884	345	1	+	+	CCONJ
ejpam-3884	345	2	(	(	PUNCT
ejpam-3884	345	3	m−	m−	PROPN
ejpam-3884	345	4	1)(m+	1)(m+	NUM
ejpam-3884	345	5	1	1	NUM
ejpam-3884	345	6	)	)	PUNCT
ejpam-3884	345	7	4	4	NUM
ejpam-3884	345	8	(	(	PUNCT
ejpam-3884	345	9	mh−1	mh−1	NOUN
ejpam-3884	345	10	)	)	PUNCT
ejpam-3884	345	11	]	]	PUNCT
ejpam-3884	345	12	=	=	SYM
ejpam-3884	345	13	mρ(γmh−1	mρ(γmh−1	PROPN
ejpam-3884	345	14	)	)	PUNCT
ejpam-3884	346	1	+	+	CCONJ
ejpam-3884	346	2	(	(	PUNCT
ejpam-3884	346	3	m−	m−	PROPN
ejpam-3884	346	4	1)(m+	1)(m+	NUM
ejpam-3884	346	5	1	1	NUM
ejpam-3884	346	6	)	)	PUNCT
ejpam-3884	346	7	2	2	NUM
ejpam-3884	346	8	mh−1	mh−1	NOUN
ejpam-3884	346	9	.	.	PUNCT
ejpam-3884	347	1	an	an	DET
ejpam-3884	347	2	explicit	explicit	ADJ
ejpam-3884	347	3	formula	formula	NOUN
ejpam-3884	347	4	for	for	ADP
ejpam-3884	347	5	the	the	DET
ejpam-3884	347	6	distance	distance	NOUN
ejpam-3884	347	7	spectral	spectral	ADJ
ejpam-3884	347	8	radius	radius	NOUN
ejpam-3884	347	9	of	of	ADP
ejpam-3884	347	10	the	the	DET
ejpam-3884	347	11	graph	graph	NOUN
ejpam-3884	347	12	γmh	γmh	NOUN
ejpam-3884	347	13	for	for	ADP
ejpam-3884	347	14	any	any	DET
ejpam-3884	347	15	positive	positive	ADJ
ejpam-3884	347	16	integer	integer	NOUN
ejpam-3884	347	17	h	h	NOUN
ejpam-3884	347	18	is	be	AUX
ejpam-3884	347	19	given	give	VERB
ejpam-3884	347	20	in	in	ADP
ejpam-3884	347	21	the	the	DET
ejpam-3884	347	22	next	next	ADJ
ejpam-3884	347	23	result	result	NOUN
ejpam-3884	347	24	.	.	PUNCT
ejpam-3884	348	1	corollary	corollary	ADJ
ejpam-3884	348	2	2	2	NUM
ejpam-3884	348	3	.	.	PUNCT
ejpam-3884	349	1	for	for	ADP
ejpam-3884	349	2	all	all	DET
ejpam-3884	349	3	positive	positive	ADJ
ejpam-3884	349	4	integer	integer	NOUN
ejpam-3884	349	5	h	h	NOUN
ejpam-3884	349	6	,	,	PUNCT
ejpam-3884	349	7	we	we	PRON
ejpam-3884	349	8	have	have	VERB
ejpam-3884	349	9	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	349	10	)	)	PUNCT
ejpam-3884	350	1	=	=	PUNCT
ejpam-3884	350	2	(	(	PUNCT
ejpam-3884	350	3	m2	m2	PROPN
ejpam-3884	350	4	−	−	PROPN
ejpam-3884	350	5	1	1	NUM
ejpam-3884	350	6	4	4	NUM
ejpam-3884	350	7	)	)	PUNCT
ejpam-3884	350	8	h(mh−1	h(mh−1	NOUN
ejpam-3884	350	9	)	)	PUNCT
ejpam-3884	350	10	.	.	PUNCT
ejpam-3884	351	1	proof	proof	NOUN
ejpam-3884	351	2	.	.	PUNCT
ejpam-3884	352	1	for	for	ADP
ejpam-3884	352	2	h	h	NOUN
ejpam-3884	352	3	=	=	SYM
ejpam-3884	352	4	1	1	NUM
ejpam-3884	352	5	,	,	PUNCT
ejpam-3884	352	6	we	we	PRON
ejpam-3884	352	7	have	have	VERB
ejpam-3884	352	8	ρ(γm1	ρ(γm1	NUM
ejpam-3884	352	9	)	)	PUNCT
ejpam-3884	352	10	=	=	SYM
ejpam-3884	353	1	m−1	m−1	PROPN
ejpam-3884	353	2	2∑	2∑	NUM
ejpam-3884	354	1	i=1	i=1	PROPN
ejpam-3884	354	2	2i	2i	NUM
ejpam-3884	354	3	=	=	SYM
ejpam-3884	354	4	(	(	PUNCT
ejpam-3884	354	5	m2	m2	PROPN
ejpam-3884	354	6	−	−	PROPN
ejpam-3884	354	7	1	1	NUM
ejpam-3884	354	8	4	4	NUM
ejpam-3884	354	9	)	)	PUNCT
ejpam-3884	354	10	(	(	PUNCT
ejpam-3884	354	11	1)(m1−1	1)(m1−1	NUM
ejpam-3884	354	12	)	)	PUNCT
ejpam-3884	354	13	.	.	PUNCT
ejpam-3884	355	1	now	now	ADV
ejpam-3884	355	2	,	,	PUNCT
ejpam-3884	355	3	let	let	VERB
ejpam-3884	356	1	h	h	PRON
ejpam-3884	356	2	>	>	X
ejpam-3884	356	3	1	1	NUM
ejpam-3884	356	4	be	be	AUX
ejpam-3884	356	5	an	an	DET
ejpam-3884	356	6	integer	integer	NOUN
ejpam-3884	356	7	and	and	CCONJ
ejpam-3884	356	8	suppose	suppose	VERB
ejpam-3884	356	9	that	that	SCONJ
ejpam-3884	356	10	for	for	ADP
ejpam-3884	356	11	all	all	PRON
ejpam-3884	356	12	k	k	PROPN
ejpam-3884	356	13	<	<	X
ejpam-3884	356	14	h	h	NOUN
ejpam-3884	356	15	we	we	PRON
ejpam-3884	356	16	have	have	VERB
ejpam-3884	356	17	ρ(γmk	ρ(γmk	PRON
ejpam-3884	356	18	)	)	PUNCT
ejpam-3884	357	1	=	=	PRON
ejpam-3884	357	2	(	(	PUNCT
ejpam-3884	357	3	m2−1	m2−1	DET
ejpam-3884	357	4	4	4	NUM
ejpam-3884	357	5	)	)	PUNCT
ejpam-3884	357	6	k(mk−1	k(mk−1	NOUN
ejpam-3884	357	7	)	)	PUNCT
ejpam-3884	357	8	.	.	PUNCT
ejpam-3884	358	1	we	we	PRON
ejpam-3884	358	2	show	show	VERB
ejpam-3884	358	3	that	that	SCONJ
ejpam-3884	358	4	for	for	ADP
ejpam-3884	358	5	h	h	NOUN
ejpam-3884	358	6	we	we	PRON
ejpam-3884	358	7	have	have	VERB
ejpam-3884	358	8	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	358	9	)	)	PUNCT
ejpam-3884	359	1	=	=	PRON
ejpam-3884	359	2	(	(	PUNCT
ejpam-3884	359	3	m2−1	m2−1	PRON
ejpam-3884	359	4	4	4	NUM
ejpam-3884	359	5	)	)	PUNCT
ejpam-3884	359	6	h(mh−1	h(mh−1	NOUN
ejpam-3884	359	7	)	)	PUNCT
ejpam-3884	359	8	.	.	PUNCT
ejpam-3884	360	1	j.	j.	PROPN
ejpam-3884	360	2	antalan	antalan	PROPN
ejpam-3884	360	3	,	,	PUNCT
ejpam-3884	360	4	f.	f.	PROPN
ejpam-3884	360	5	campeña	campeña	PROPN
ejpam-3884	360	6	/	/	SYM
ejpam-3884	360	7	eur	eur	PROPN
ejpam-3884	360	8	.	.	PUNCT
ejpam-3884	361	1	j.	j.	PROPN
ejpam-3884	361	2	pure	pure	PROPN
ejpam-3884	361	3	appl	appl	PROPN
ejpam-3884	361	4	.	.	PROPN
ejpam-3884	361	5	math	math	PROPN
ejpam-3884	361	6	,	,	PUNCT
ejpam-3884	361	7	14	14	NUM
ejpam-3884	361	8	(	(	PUNCT
ejpam-3884	361	9	1	1	NUM
ejpam-3884	361	10	)	)	PUNCT
ejpam-3884	361	11	(	(	PUNCT
ejpam-3884	361	12	2021	2021	NUM
ejpam-3884	361	13	)	)	PUNCT
ejpam-3884	361	14	,	,	PUNCT
ejpam-3884	361	15	248	248	NUM
ejpam-3884	361	16	-	-	SYM
ejpam-3884	361	17	264	264	NUM
ejpam-3884	361	18	261	261	NUM
ejpam-3884	361	19	by	by	ADP
ejpam-3884	361	20	theorem	theorem	NOUN
ejpam-3884	361	21	3	3	NUM
ejpam-3884	361	22	we	we	PRON
ejpam-3884	361	23	have	have	VERB
ejpam-3884	361	24	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	361	25	)	)	PUNCT
ejpam-3884	362	1	=	=	SYM
ejpam-3884	362	2	mρ(γmh−1	mρ(γmh−1	PROPN
ejpam-3884	362	3	)	)	PUNCT
ejpam-3884	363	1	+	+	CCONJ
ejpam-3884	363	2	(	(	PUNCT
ejpam-3884	363	3	m−	m−	PROPN
ejpam-3884	363	4	1)(m+	1)(m+	NUM
ejpam-3884	363	5	1	1	NUM
ejpam-3884	363	6	)	)	PUNCT
ejpam-3884	363	7	2	2	NUM
ejpam-3884	363	8	mh−1	mh−1	NOUN
ejpam-3884	363	9	.	.	PUNCT
ejpam-3884	364	1	now	now	ADV
ejpam-3884	364	2	since	since	SCONJ
ejpam-3884	364	3	h−	h−	PROPN
ejpam-3884	364	4	1	1	NUM
ejpam-3884	364	5	<	<	NOUN
ejpam-3884	364	6	h	h	NOUN
ejpam-3884	364	7	,	,	PUNCT
ejpam-3884	364	8	using	use	VERB
ejpam-3884	364	9	our	our	PRON
ejpam-3884	364	10	induction	induction	NOUN
ejpam-3884	364	11	hypothesis	hypothesis	NOUN
ejpam-3884	364	12	yields	yield	NOUN
ejpam-3884	364	13	ρ(γmh	ρ(γmh	PROPN
ejpam-3884	364	14	)	)	PUNCT
ejpam-3884	365	1	=	=	PUNCT
ejpam-3884	365	2	m	m	VERB
ejpam-3884	366	1	[	[	X
ejpam-3884	366	2	(	(	PUNCT
ejpam-3884	366	3	m2	m2	PROPN
ejpam-3884	366	4	−	−	PROPN
ejpam-3884	366	5	1	1	NUM
ejpam-3884	366	6	4	4	NUM
ejpam-3884	366	7	)	)	PUNCT
ejpam-3884	366	8	(	(	PUNCT
ejpam-3884	366	9	h−	h−	NOUN
ejpam-3884	366	10	1)(mh−2	1)(mh−2	NUM
ejpam-3884	366	11	)	)	PUNCT
ejpam-3884	366	12	]	]	PUNCT
ejpam-3884	367	1	+	+	CCONJ
ejpam-3884	367	2	(	(	PUNCT
ejpam-3884	367	3	m2	m2	PROPN
ejpam-3884	367	4	−	−	PROPN
ejpam-3884	367	5	1	1	NUM
ejpam-3884	367	6	2	2	NUM
ejpam-3884	367	7	)	)	PUNCT
ejpam-3884	367	8	mh−1	mh−1	NOUN
ejpam-3884	367	9	=	=	PUNCT
ejpam-3884	367	10	(	(	PUNCT
ejpam-3884	367	11	m2	m2	PROPN
ejpam-3884	367	12	−	−	PROPN
ejpam-3884	367	13	1	1	NUM
ejpam-3884	367	14	4	4	NUM
ejpam-3884	367	15	)	)	PUNCT
ejpam-3884	367	16	(	(	PUNCT
ejpam-3884	367	17	h−	h−	PROPN
ejpam-3884	367	18	1)(mh−1	1)(mh−1	NUM
ejpam-3884	367	19	)	)	PUNCT
ejpam-3884	368	1	+	+	CCONJ
ejpam-3884	368	2	(	(	PUNCT
ejpam-3884	368	3	m2	m2	PROPN
ejpam-3884	368	4	−	−	PROPN
ejpam-3884	368	5	1	1	NUM
ejpam-3884	368	6	2	2	NUM
ejpam-3884	368	7	)	)	PUNCT
ejpam-3884	368	8	mh−1	mh−1	NOUN
ejpam-3884	368	9	=	=	PUNCT
ejpam-3884	368	10	(	(	PUNCT
ejpam-3884	368	11	m2	m2	PROPN
ejpam-3884	368	12	−	−	PROPN
ejpam-3884	368	13	1	1	NUM
ejpam-3884	368	14	4	4	NUM
ejpam-3884	368	15	)	)	PUNCT
ejpam-3884	368	16	(	(	PUNCT
ejpam-3884	368	17	h−	h−	NOUN
ejpam-3884	368	18	1	1	NUM
ejpam-3884	368	19	+	+	CCONJ
ejpam-3884	368	20	1)(mh−1	1)(mh−1	NUM
ejpam-3884	368	21	)	)	PUNCT
ejpam-3884	368	22	=	=	PUNCT
ejpam-3884	368	23	(	(	PUNCT
ejpam-3884	368	24	m2	m2	PROPN
ejpam-3884	368	25	−	−	PROPN
ejpam-3884	368	26	1	1	NUM
ejpam-3884	368	27	4	4	NUM
ejpam-3884	368	28	)	)	PUNCT
ejpam-3884	368	29	h(mh−1	h(mh−1	NOUN
ejpam-3884	368	30	)	)	PUNCT
ejpam-3884	368	31	.	.	PUNCT
ejpam-3884	369	1	remark	remark	PROPN
ejpam-3884	369	2	11	11	NUM
ejpam-3884	369	3	.	.	PUNCT
ejpam-3884	370	1	for	for	ADP
ejpam-3884	370	2	h	h	NOUN
ejpam-3884	370	3	=	=	SYM
ejpam-3884	370	4	1	1	NUM
ejpam-3884	370	5	,	,	PUNCT
ejpam-3884	370	6	2	2	NUM
ejpam-3884	370	7	,	,	PUNCT
ejpam-3884	370	8	.	.	PUNCT
ejpam-3884	370	9	.	.	PUNCT
ejpam-3884	371	1	.	.	PUNCT
ejpam-3884	371	2	,	,	PUNCT
ejpam-3884	371	3	the	the	DET
ejpam-3884	371	4	sequence	sequence	NOUN
ejpam-3884	371	5	(	(	PUNCT
ejpam-3884	371	6	m2−1	m2−1	PRON
ejpam-3884	371	7	4	4	NUM
ejpam-3884	371	8	)	)	PUNCT
ejpam-3884	371	9	h(mh−1	h(mh−1	NOUN
ejpam-3884	371	10	)	)	PUNCT
ejpam-3884	371	11	denotes	denote	VERB
ejpam-3884	371	12	the	the	DET
ejpam-3884	371	13	distance	distance	NOUN
ejpam-3884	371	14	spectral	spectral	ADJ
ejpam-3884	371	15	radius	radius	NOUN
ejpam-3884	371	16	of	of	ADP
ejpam-3884	371	17	γmh	γmh	PROPN
ejpam-3884	371	18	.	.	PUNCT
ejpam-3884	372	1	for	for	ADP
ejpam-3884	372	2	m	m	PROPN
ejpam-3884	372	3	=	=	SYM
ejpam-3884	372	4	3	3	NUM
ejpam-3884	372	5	,	,	PUNCT
ejpam-3884	372	6	the	the	DET
ejpam-3884	372	7	sequence	sequence	NOUN
ejpam-3884	372	8	generated	generate	VERB
ejpam-3884	372	9	is	be	AUX
ejpam-3884	372	10	the	the	DET
ejpam-3884	372	11	sequence	sequence	NOUN
ejpam-3884	373	1	a212697	a212697	ADV
ejpam-3884	374	1	[	[	X
ejpam-3884	374	2	13	13	NUM
ejpam-3884	374	3	]	]	PUNCT
ejpam-3884	374	4	in	in	ADP
ejpam-3884	374	5	the	the	DET
ejpam-3884	374	6	on	on	ADP
ejpam-3884	374	7	-	-	PUNCT
ejpam-3884	374	8	line	line	NOUN
ejpam-3884	374	9	encyclopedia	encyclopedia	NOUN
ejpam-3884	374	10	of	of	ADP
ejpam-3884	374	11	integer	integer	NOUN
ejpam-3884	374	12	sequence	sequence	NOUN
ejpam-3884	374	13	(	(	PUNCT
ejpam-3884	374	14	oeis	oeis	PROPN
ejpam-3884	374	15	)	)	PUNCT
ejpam-3884	374	16	.	.	PUNCT
ejpam-3884	375	1	for	for	ADP
ejpam-3884	375	2	m	m	PROPN
ejpam-3884	375	3	=	=	SYM
ejpam-3884	375	4	5	5	NUM
ejpam-3884	375	5	,	,	PUNCT
ejpam-3884	375	6	the	the	DET
ejpam-3884	375	7	sequence	sequence	NOUN
ejpam-3884	375	8	generated	generate	VERB
ejpam-3884	375	9	is	be	AUX
ejpam-3884	375	10	the	the	DET
ejpam-3884	375	11	sequence	sequence	NOUN
ejpam-3884	375	12	a269760	a269760	PROPN
ejpam-3884	376	1	[	[	X
ejpam-3884	376	2	6	6	NUM
ejpam-3884	376	3	]	]	PUNCT
ejpam-3884	376	4	in	in	ADP
ejpam-3884	376	5	the	the	DET
ejpam-3884	376	6	oeis	oeis	NOUN
ejpam-3884	376	7	.	.	PUNCT
ejpam-3884	377	1	the	the	DET
ejpam-3884	377	2	wiener	wiener	NOUN
ejpam-3884	377	3	index	index	NOUN
ejpam-3884	377	4	and	and	CCONJ
ejpam-3884	377	5	average	average	ADJ
ejpam-3884	377	6	distance	distance	NOUN
ejpam-3884	377	7	of	of	ADP
ejpam-3884	377	8	γmh	γmh	NOUN
ejpam-3884	377	9	this	this	DET
ejpam-3884	377	10	subsection	subsection	NOUN
ejpam-3884	377	11	is	be	AUX
ejpam-3884	377	12	motivated	motivate	VERB
ejpam-3884	377	13	by	by	ADP
ejpam-3884	377	14	the	the	DET
ejpam-3884	377	15	works	work	NOUN
ejpam-3884	377	16	of	of	ADP
ejpam-3884	377	17	ali	ali	PROPN
ejpam-3884	377	18	et	et	PROPN
ejpam-3884	377	19	al	al	PROPN
ejpam-3884	377	20	.	.	PUNCT
ejpam-3884	378	1	[	[	X
ejpam-3884	378	2	1	1	NUM
ejpam-3884	378	3	,	,	PUNCT
ejpam-3884	378	4	2	2	NUM
ejpam-3884	378	5	]	]	PUNCT
ejpam-3884	378	6	,	,	PUNCT
ejpam-3884	378	7	where	where	SCONJ
ejpam-3884	378	8	they	they	PRON
ejpam-3884	378	9	determined	determine	VERB
ejpam-3884	378	10	some	some	DET
ejpam-3884	378	11	distance	distance	NOUN
ejpam-3884	378	12	-	-	PUNCT
ejpam-3884	378	13	based	base	VERB
ejpam-3884	378	14	topological	topological	ADJ
ejpam-3884	378	15	indices	index	NOUN
ejpam-3884	378	16	for	for	ADP
ejpam-3884	378	17	certain	certain	ADJ
ejpam-3884	378	18	class	class	NOUN
ejpam-3884	378	19	of	of	ADP
ejpam-3884	378	20	circulant	circulant	ADJ
ejpam-3884	378	21	graphs	graph	NOUN
ejpam-3884	378	22	.	.	PUNCT
ejpam-3884	379	1	the	the	DET
ejpam-3884	379	2	computation	computation	NOUN
ejpam-3884	379	3	of	of	ADP
ejpam-3884	379	4	the	the	DET
ejpam-3884	379	5	wiener	wiener	NOUN
ejpam-3884	379	6	index	index	NOUN
ejpam-3884	379	7	of	of	ADP
ejpam-3884	379	8	the	the	DET
ejpam-3884	379	9	graph	graph	NOUN
ejpam-3884	379	10	γmh	γmh	NOUN
ejpam-3884	379	11	follows	follow	VERB
ejpam-3884	379	12	immediately	immediately	ADV
ejpam-3884	379	13	from	from	ADP
ejpam-3884	379	14	corollary	corollary	ADJ
ejpam-3884	379	15	2	2	NUM
ejpam-3884	379	16	,	,	PUNCT
ejpam-3884	379	17	remark	remark	NOUN
ejpam-3884	379	18	4	4	NUM
ejpam-3884	379	19	,	,	PUNCT
ejpam-3884	379	20	and	and	CCONJ
ejpam-3884	379	21	remark	remark	NOUN
ejpam-3884	379	22	1	1	NUM
ejpam-3884	379	23	.	.	PUNCT
ejpam-3884	379	24	theorem	theorem	NOUN
ejpam-3884	379	25	4	4	NUM
ejpam-3884	379	26	.	.	PUNCT
ejpam-3884	380	1	the	the	DET
ejpam-3884	380	2	wiener	wiener	NOUN
ejpam-3884	380	3	index	index	NOUN
ejpam-3884	380	4	of	of	ADP
ejpam-3884	380	5	γmh	γmh	NOUN
ejpam-3884	380	6	is	be	AUX
ejpam-3884	380	7	h	h	PRON
ejpam-3884	380	8	8	8	NUM
ejpam-3884	380	9	(	(	PUNCT
ejpam-3884	380	10	m2h−1)(m2	m2h−1)(m2	NOUN
ejpam-3884	380	11	−	−	NOUN
ejpam-3884	380	12	1	1	NUM
ejpam-3884	380	13	)	)	PUNCT
ejpam-3884	380	14	.	.	PUNCT
ejpam-3884	381	1	the	the	DET
ejpam-3884	381	2	next	next	ADJ
ejpam-3884	381	3	result	result	NOUN
ejpam-3884	381	4	about	about	ADP
ejpam-3884	381	5	the	the	DET
ejpam-3884	381	6	average	average	ADJ
ejpam-3884	381	7	distance	distance	NOUN
ejpam-3884	381	8	of	of	ADP
ejpam-3884	381	9	mc(mh	mc(mh	NOUN
ejpam-3884	381	10	)	)	PUNCT
ejpam-3884	381	11	follows	follow	VERB
ejpam-3884	381	12	immediately	immediately	ADV
ejpam-3884	381	13	from	from	ADP
ejpam-3884	381	14	theorem	theorem	ADJ
ejpam-3884	381	15	4	4	NUM
ejpam-3884	381	16	and	and	CCONJ
ejpam-3884	381	17	remark	remark	NOUN
ejpam-3884	381	18	5	5	NUM
ejpam-3884	381	19	.	.	PUNCT
ejpam-3884	381	20	theorem	theorem	NOUN
ejpam-3884	381	21	5	5	NUM
ejpam-3884	381	22	.	.	PUNCT
ejpam-3884	382	1	the	the	DET
ejpam-3884	382	2	average	average	ADJ
ejpam-3884	382	3	distance	distance	NOUN
ejpam-3884	382	4	of	of	ADP
ejpam-3884	382	5	γmh	γmh	NOUN
ejpam-3884	382	6	is	be	AUX
ejpam-3884	382	7	h	h	PRON
ejpam-3884	382	8	4	4	NUM
ejpam-3884	382	9	(	(	PUNCT
ejpam-3884	382	10	m2−1)(mh−1	m2−1)(mh−1	NOUN
ejpam-3884	382	11	)	)	PUNCT
ejpam-3884	382	12	mh−1	mh−1	NOUN
ejpam-3884	382	13	.	.	PUNCT
ejpam-3884	383	1	exact	exact	ADJ
ejpam-3884	383	2	value	value	NOUN
ejpam-3884	383	3	of	of	ADP
ejpam-3884	383	4	γ′	γ′	PROPN
ejpam-3884	383	5	mhs	mhs	NOUN
ejpam-3884	383	6	vertex	vertex	NOUN
ejpam-3884	383	7	-	-	PUNCT
ejpam-3884	383	8	forwarding	forward	VERB
ejpam-3884	383	9	index	index	NOUN
ejpam-3884	383	10	this	this	DET
ejpam-3884	383	11	subsection	subsection	NOUN
ejpam-3884	383	12	and	and	CCONJ
ejpam-3884	383	13	the	the	DET
ejpam-3884	383	14	last	last	ADJ
ejpam-3884	383	15	is	be	AUX
ejpam-3884	383	16	motivated	motivate	VERB
ejpam-3884	383	17	by	by	ADP
ejpam-3884	383	18	the	the	DET
ejpam-3884	383	19	work	work	NOUN
ejpam-3884	383	20	of	of	ADP
ejpam-3884	383	21	liu	liu	PROPN
ejpam-3884	383	22	et	et	PROPN
ejpam-3884	383	23	al	al	PROPN
ejpam-3884	383	24	.	.	PUNCT
ejpam-3884	384	1	[	[	X
ejpam-3884	384	2	9	9	NUM
ejpam-3884	384	3	]	]	PUNCT
ejpam-3884	384	4	where	where	SCONJ
ejpam-3884	384	5	they	they	PRON
ejpam-3884	384	6	determined	determine	VERB
ejpam-3884	384	7	the	the	DET
ejpam-3884	384	8	exact	exact	ADJ
ejpam-3884	384	9	values	value	NOUN
ejpam-3884	384	10	of	of	ADP
ejpam-3884	384	11	vertex	vertex	NOUN
ejpam-3884	384	12	-	-	PUNCT
ejpam-3884	384	13	forwarding	forward	VERB
ejpam-3884	384	14	index	index	NOUN
ejpam-3884	384	15	and	and	CCONJ
ejpam-3884	384	16	bounds	bound	NOUN
ejpam-3884	384	17	for	for	ADP
ejpam-3884	384	18	the	the	DET
ejpam-3884	384	19	edge	edge	NOUN
ejpam-3884	384	20	-	-	PUNCT
ejpam-3884	384	21	forwarding	forward	VERB
ejpam-3884	384	22	index	index	NOUN
ejpam-3884	384	23	of	of	ADP
ejpam-3884	384	24	some	some	DET
ejpam-3884	384	25	class	class	NOUN
ejpam-3884	384	26	of	of	ADP
ejpam-3884	384	27	circulant	circulant	ADJ
ejpam-3884	384	28	graphs	graph	NOUN
ejpam-3884	384	29	.	.	PUNCT
ejpam-3884	385	1	the	the	DET
ejpam-3884	385	2	exact	exact	ADJ
ejpam-3884	385	3	value	value	NOUN
ejpam-3884	385	4	of	of	ADP
ejpam-3884	385	5	the	the	DET
ejpam-3884	385	6	vertex	vertex	NOUN
ejpam-3884	385	7	-	-	PUNCT
ejpam-3884	385	8	forwarding	forward	VERB
ejpam-3884	385	9	index	index	NOUN
ejpam-3884	385	10	of	of	ADP
ejpam-3884	385	11	γmh	γmh	NOUN
ejpam-3884	385	12	is	be	AUX
ejpam-3884	385	13	given	give	VERB
ejpam-3884	385	14	in	in	ADP
ejpam-3884	385	15	the	the	DET
ejpam-3884	385	16	next	next	ADJ
ejpam-3884	385	17	result	result	NOUN
ejpam-3884	385	18	.	.	PUNCT
ejpam-3884	386	1	j.	j.	PROPN
ejpam-3884	386	2	antalan	antalan	PROPN
ejpam-3884	386	3	,	,	PUNCT
ejpam-3884	386	4	f.	f.	PROPN
ejpam-3884	386	5	campeña	campeña	PROPN
ejpam-3884	386	6	/	/	SYM
ejpam-3884	386	7	eur	eur	PROPN
ejpam-3884	386	8	.	.	PUNCT
ejpam-3884	387	1	j.	j.	PROPN
ejpam-3884	387	2	pure	pure	PROPN
ejpam-3884	387	3	appl	appl	PROPN
ejpam-3884	387	4	.	.	PROPN
ejpam-3884	387	5	math	math	PROPN
ejpam-3884	387	6	,	,	PUNCT
ejpam-3884	387	7	14	14	NUM
ejpam-3884	387	8	(	(	PUNCT
ejpam-3884	387	9	1	1	NUM
ejpam-3884	387	10	)	)	PUNCT
ejpam-3884	387	11	(	(	PUNCT
ejpam-3884	387	12	2021	2021	NUM
ejpam-3884	387	13	)	)	PUNCT
ejpam-3884	387	14	,	,	PUNCT
ejpam-3884	387	15	248	248	NUM
ejpam-3884	387	16	-	-	SYM
ejpam-3884	387	17	264	264	NUM
ejpam-3884	387	18	262	262	NUM
ejpam-3884	387	19	theorem	theorem	NOUN
ejpam-3884	387	20	6	6	NUM
ejpam-3884	387	21	.	.	PUNCT
ejpam-3884	388	1	let	let	VERB
ejpam-3884	388	2	m	m	PRON
ejpam-3884	388	3	>	>	X
ejpam-3884	388	4	1	1	NUM
ejpam-3884	388	5	be	be	AUX
ejpam-3884	388	6	odd	odd	ADJ
ejpam-3884	388	7	and	and	CCONJ
ejpam-3884	388	8	h	h	NOUN
ejpam-3884	388	9	be	be	AUX
ejpam-3884	388	10	a	a	DET
ejpam-3884	388	11	positive	positive	ADJ
ejpam-3884	388	12	integer	integer	NOUN
ejpam-3884	388	13	.	.	PUNCT
ejpam-3884	389	1	then	then	ADV
ejpam-3884	389	2	ξ(γmh	ξ(γmh	PROPN
ejpam-3884	389	3	)	)	PUNCT
ejpam-3884	389	4	=	=	PUNCT
ejpam-3884	390	1	(	(	PUNCT
ejpam-3884	390	2	m2	m2	PROPN
ejpam-3884	390	3	−	−	PROPN
ejpam-3884	390	4	1	1	NUM
ejpam-3884	390	5	4	4	NUM
ejpam-3884	390	6	)	)	PUNCT
ejpam-3884	390	7	h(mh−1)−	h(mh−1)−	NOUN
ejpam-3884	390	8	(	(	PUNCT
ejpam-3884	390	9	mh	mh	PROPN
ejpam-3884	390	10	−	−	PROPN
ejpam-3884	390	11	1	1	NUM
ejpam-3884	390	12	)	)	PUNCT
ejpam-3884	390	13	.	.	PUNCT
ejpam-3884	391	1	proof	proof	NOUN
ejpam-3884	391	2	.	.	PUNCT
ejpam-3884	392	1	follows	follow	VERB
ejpam-3884	392	2	from	from	ADP
ejpam-3884	392	3	theorem	theorem	ADJ
ejpam-3884	392	4	2	2	NUM
ejpam-3884	392	5	and	and	CCONJ
ejpam-3884	392	6	lemma	lemma	PROPN
ejpam-3884	392	7	2	2	PROPN
ejpam-3884	392	8	.	.	NOUN
ejpam-3884	392	9	bounds	bound	NOUN
ejpam-3884	392	10	for	for	ADP
ejpam-3884	392	11	mc(mh)′s	mc(mh)′s	ADJ
ejpam-3884	392	12	edge	edge	NOUN
ejpam-3884	392	13	-	-	PUNCT
ejpam-3884	392	14	forwarding	forward	VERB
ejpam-3884	392	15	index	index	NOUN
ejpam-3884	392	16	our	our	PRON
ejpam-3884	392	17	final	final	ADJ
ejpam-3884	392	18	result	result	NOUN
ejpam-3884	392	19	in	in	ADP
ejpam-3884	392	20	this	this	DET
ejpam-3884	392	21	section	section	NOUN
ejpam-3884	392	22	gives	give	VERB
ejpam-3884	392	23	an	an	DET
ejpam-3884	392	24	upper	upper	ADJ
ejpam-3884	392	25	and	and	CCONJ
ejpam-3884	392	26	lower	low	ADJ
ejpam-3884	392	27	bounds	bound	NOUN
ejpam-3884	392	28	for	for	ADP
ejpam-3884	392	29	γ′	γ′	PROPN
ejpam-3884	392	30	mhs	mhs	PROPN
ejpam-3884	392	31	edgeforwarding	edgeforwarde	VERB
ejpam-3884	392	32	index	index	NOUN
ejpam-3884	392	33	.	.	PUNCT
ejpam-3884	393	1	the	the	DET
ejpam-3884	393	2	result	result	NOUN
ejpam-3884	393	3	follows	follow	VERB
ejpam-3884	393	4	from	from	ADP
ejpam-3884	393	5	theorem	theorem	ADJ
ejpam-3884	393	6	2	2	NUM
ejpam-3884	393	7	,	,	PUNCT
ejpam-3884	393	8	lemma	lemma	PROPN
ejpam-3884	393	9	3	3	NUM
ejpam-3884	393	10	and	and	CCONJ
ejpam-3884	393	11	the	the	DET
ejpam-3884	393	12	fact	fact	NOUN
ejpam-3884	393	13	that	that	SCONJ
ejpam-3884	393	14	γmh	γmh	NOUN
ejpam-3884	393	15	is	be	AUX
ejpam-3884	393	16	a	a	DET
ejpam-3884	393	17	2h	2h	NUM
ejpam-3884	393	18	-	-	PUNCT
ejpam-3884	393	19	regular	regular	ADJ
ejpam-3884	393	20	graph	graph	NOUN
ejpam-3884	393	21	.	.	PUNCT
ejpam-3884	394	1	theorem	theorem	NOUN
ejpam-3884	394	2	7	7	NUM
ejpam-3884	394	3	.	.	PUNCT
ejpam-3884	395	1	let	let	VERB
ejpam-3884	395	2	m	m	PRON
ejpam-3884	395	3	>	>	X
ejpam-3884	395	4	1	1	NUM
ejpam-3884	395	5	be	be	AUX
ejpam-3884	395	6	odd	odd	ADJ
ejpam-3884	395	7	and	and	CCONJ
ejpam-3884	395	8	h	h	NOUN
ejpam-3884	395	9	be	be	AUX
ejpam-3884	395	10	a	a	DET
ejpam-3884	395	11	positive	positive	ADJ
ejpam-3884	395	12	integer	integer	NOUN
ejpam-3884	395	13	.	.	PUNCT
ejpam-3884	396	1	then	then	ADV
ejpam-3884	396	2	(	(	PUNCT
ejpam-3884	396	3	m2	m2	PROPN
ejpam-3884	396	4	−	−	PROPN
ejpam-3884	396	5	1	1	NUM
ejpam-3884	396	6	4	4	NUM
ejpam-3884	396	7	)	)	PUNCT
ejpam-3884	396	8	(	(	PUNCT
ejpam-3884	396	9	mh−1	mh−1	NOUN
ejpam-3884	396	10	)	)	PUNCT
ejpam-3884	396	11	≤	≤	NUM
ejpam-3884	396	12	π(γmh	π(γmh	NOUN
ejpam-3884	396	13	)	)	PUNCT
ejpam-3884	396	14	≤	≤	NUM
ejpam-3884	397	1	mh−1	mh−1	NOUN
ejpam-3884	397	2	(	(	PUNCT
ejpam-3884	397	3	m+	m+	NUM
ejpam-3884	397	4	m2	m2	PROPN
ejpam-3884	397	5	−	−	PROPN
ejpam-3884	397	6	1	1	NUM
ejpam-3884	397	7	4	4	NUM
ejpam-3884	397	8	h	h	NOUN
ejpam-3884	397	9	)	)	PUNCT
ejpam-3884	397	10	−	−	PROPN
ejpam-3884	398	1	4h+	4h+	NUM
ejpam-3884	398	2	1	1	NUM
ejpam-3884	398	3	.	.	NOUN
ejpam-3884	398	4	5	5	NUM
ejpam-3884	398	5	.	.	PUNCT
ejpam-3884	398	6	future	future	ADJ
ejpam-3884	398	7	applications	application	NOUN
ejpam-3884	398	8	of	of	ADP
ejpam-3884	398	9	the	the	DET
ejpam-3884	398	10	bfs	bfs	NOUN
ejpam-3884	398	11	tree	tree	NOUN
ejpam-3884	398	12	construction	construction	NOUN
ejpam-3884	398	13	for	for	ADP
ejpam-3884	398	14	γmh	γmh	NOUN
ejpam-3884	398	15	in	in	ADP
ejpam-3884	398	16	this	this	DET
ejpam-3884	398	17	short	short	ADJ
ejpam-3884	398	18	section	section	NOUN
ejpam-3884	398	19	,	,	PUNCT
ejpam-3884	398	20	we	we	PRON
ejpam-3884	398	21	state	state	VERB
ejpam-3884	398	22	some	some	DET
ejpam-3884	398	23	particular	particular	ADJ
ejpam-3884	398	24	research	research	NOUN
ejpam-3884	398	25	works	work	NOUN
ejpam-3884	398	26	in	in	ADP
ejpam-3884	398	27	which	which	PRON
ejpam-3884	398	28	the	the	DET
ejpam-3884	398	29	proposed	propose	VERB
ejpam-3884	398	30	bfs	bfs	NOUN
ejpam-3884	398	31	tree	tree	NOUN
ejpam-3884	398	32	construction	construction	NOUN
ejpam-3884	398	33	can	can	AUX
ejpam-3884	398	34	be	be	AUX
ejpam-3884	398	35	applied	apply	VERB
ejpam-3884	398	36	.	.	PUNCT
ejpam-3884	399	1	as	as	SCONJ
ejpam-3884	399	2	stated	state	VERB
ejpam-3884	399	3	earlier	early	ADV
ejpam-3884	399	4	,	,	PUNCT
ejpam-3884	399	5	ali	ali	PROPN
ejpam-3884	399	6	et	et	PROPN
ejpam-3884	399	7	al	al	PROPN
ejpam-3884	399	8	.	.	PUNCT
ejpam-3884	400	1	[	[	X
ejpam-3884	400	2	1	1	NUM
ejpam-3884	400	3	,	,	PUNCT
ejpam-3884	400	4	2]computed	2]computed	NUM
ejpam-3884	400	5	some	some	DET
ejpam-3884	400	6	distance	distance	NOUN
ejpam-3884	400	7	-	-	PUNCT
ejpam-3884	400	8	based	base	VERB
ejpam-3884	400	9	topological	topological	ADJ
ejpam-3884	400	10	indices	index	NOUN
ejpam-3884	400	11	for	for	ADP
ejpam-3884	400	12	some	some	DET
ejpam-3884	400	13	class	class	NOUN
ejpam-3884	400	14	of	of	ADP
ejpam-3884	400	15	circulant	circulant	ADJ
ejpam-3884	400	16	graphs	graph	NOUN
ejpam-3884	400	17	.	.	PUNCT
ejpam-3884	401	1	in	in	ADP
ejpam-3884	401	2	particular	particular	ADJ
ejpam-3884	401	3	,	,	PUNCT
ejpam-3884	401	4	they	they	PRON
ejpam-3884	401	5	determined	determine	VERB
ejpam-3884	401	6	the	the	DET
ejpam-3884	401	7	wiener	wiener	NOUN
ejpam-3884	401	8	index	index	NOUN
ejpam-3884	401	9	,	,	PUNCT
ejpam-3884	401	10	hyper	hyper	NOUN
ejpam-3884	401	11	-	-	ADJ
ejpam-3884	401	12	wiener	wiener	NOUN
ejpam-3884	401	13	index	index	NOUN
ejpam-3884	401	14	,	,	PUNCT
ejpam-3884	401	15	and	and	CCONJ
ejpam-3884	401	16	schultz	schultz	PROPN
ejpam-3884	401	17	molecular	molecular	PROPN
ejpam-3884	401	18	topological	topological	ADJ
ejpam-3884	401	19	index	index	NOUN
ejpam-3884	401	20	of	of	ADP
ejpam-3884	401	21	circulant	circulant	ADJ
ejpam-3884	401	22	graph	graph	NOUN
ejpam-3884	401	23	class	class	NOUN
ejpam-3884	401	24	cay(zn	cay(zn	NOUN
ejpam-3884	401	25	,	,	PUNCT
ejpam-3884	401	26	{	{	PUNCT
ejpam-3884	401	27	1	1	NUM
ejpam-3884	401	28	,	,	PUNCT
ejpam-3884	401	29	a	a	PRON
ejpam-3884	401	30	}	}	PUNCT
ejpam-3884	401	31	)	)	PUNCT
ejpam-3884	401	32	where	where	SCONJ
ejpam-3884	401	33	a	a	DET
ejpam-3884	401	34	=	=	SYM
ejpam-3884	401	35	2	2	NUM
ejpam-3884	401	36	,	,	PUNCT
ejpam-3884	401	37	3	3	NUM
ejpam-3884	401	38	,	,	PUNCT
ejpam-3884	401	39	4	4	NUM
ejpam-3884	401	40	,	,	PUNCT
ejpam-3884	401	41	5	5	NUM
ejpam-3884	401	42	.	.	PUNCT
ejpam-3884	401	43	since	since	SCONJ
ejpam-3884	401	44	the	the	DET
ejpam-3884	401	45	proposed	propose	VERB
ejpam-3884	401	46	construction	construction	NOUN
ejpam-3884	401	47	presented	present	VERB
ejpam-3884	401	48	in	in	ADP
ejpam-3884	401	49	this	this	DET
ejpam-3884	401	50	paper	paper	NOUN
ejpam-3884	401	51	determines	determine	VERB
ejpam-3884	401	52	the	the	DET
ejpam-3884	401	53	distance	distance	NOUN
ejpam-3884	401	54	of	of	ADP
ejpam-3884	401	55	0	0	NUM
ejpam-3884	401	56	-	-	PUNCT
ejpam-3884	401	57	vertex	vertex	NOUN
ejpam-3884	401	58	to	to	ADP
ejpam-3884	401	59	all	all	DET
ejpam-3884	401	60	the	the	DET
ejpam-3884	401	61	other	other	ADJ
ejpam-3884	401	62	vertices	vertex	NOUN
ejpam-3884	401	63	of	of	ADP
ejpam-3884	401	64	the	the	DET
ejpam-3884	401	65	graph	graph	NOUN
ejpam-3884	401	66	γmh	γmh	NOUN
ejpam-3884	401	67	,	,	PUNCT
ejpam-3884	401	68	and	and	CCONJ
ejpam-3884	401	69	the	the	DET
ejpam-3884	401	70	distance	distance	NOUN
ejpam-3884	401	71	matrix	matrix	NOUN
ejpam-3884	401	72	of	of	ADP
ejpam-3884	401	73	γmh	γmh	NOUN
ejpam-3884	401	74	is	be	AUX
ejpam-3884	401	75	circulant	circulant	ADJ
ejpam-3884	401	76	,	,	PUNCT
ejpam-3884	401	77	we	we	PRON
ejpam-3884	401	78	can	can	AUX
ejpam-3884	401	79	use	use	VERB
ejpam-3884	401	80	the	the	DET
ejpam-3884	401	81	proposed	propose	VERB
ejpam-3884	401	82	construction	construction	NOUN
ejpam-3884	401	83	to	to	PART
ejpam-3884	401	84	obtain	obtain	VERB
ejpam-3884	401	85	γmh	γmh	NOUN
ejpam-3884	401	86	’s	’s	PART
ejpam-3884	401	87	distance	distance	NOUN
ejpam-3884	401	88	matrix	matrix	NOUN
ejpam-3884	401	89	.	.	PUNCT
ejpam-3884	402	1	once	once	SCONJ
ejpam-3884	402	2	the	the	DET
ejpam-3884	402	3	distance	distance	NOUN
ejpam-3884	402	4	matrix	matrix	NOUN
ejpam-3884	402	5	of	of	ADP
ejpam-3884	402	6	γmh	γmh	NOUN
ejpam-3884	402	7	is	be	AUX
ejpam-3884	402	8	known	know	VERB
ejpam-3884	402	9	,	,	PUNCT
ejpam-3884	402	10	the	the	DET
ejpam-3884	402	11	computation	computation	NOUN
ejpam-3884	402	12	for	for	ADP
ejpam-3884	402	13	some	some	DET
ejpam-3884	402	14	distance	distance	NOUN
ejpam-3884	402	15	-	-	PUNCT
ejpam-3884	402	16	based	base	VERB
ejpam-3884	402	17	topological	topological	ADJ
ejpam-3884	402	18	indices	index	NOUN
ejpam-3884	402	19	can	can	AUX
ejpam-3884	402	20	be	be	AUX
ejpam-3884	402	21	performed	perform	VERB
ejpam-3884	402	22	.	.	PUNCT
ejpam-3884	403	1	the	the	DET
ejpam-3884	403	2	distance	distance	NOUN
ejpam-3884	403	3	matrix	matrix	NOUN
ejpam-3884	403	4	of	of	ADP
ejpam-3884	403	5	γmh	γmh	NOUN
ejpam-3884	403	6	can	can	AUX
ejpam-3884	403	7	also	also	ADV
ejpam-3884	403	8	be	be	AUX
ejpam-3884	403	9	used	use	VERB
ejpam-3884	403	10	to	to	PART
ejpam-3884	403	11	aid	aid	VERB
ejpam-3884	403	12	in	in	ADP
ejpam-3884	403	13	the	the	DET
ejpam-3884	403	14	study	study	NOUN
ejpam-3884	403	15	of	of	ADP
ejpam-3884	403	16	various	various	ADJ
ejpam-3884	403	17	distancebased	distancebased	ADJ
ejpam-3884	403	18	coloring	coloring	NOUN
ejpam-3884	403	19	problem	problem	NOUN
ejpam-3884	403	20	related	relate	VERB
ejpam-3884	403	21	to	to	ADP
ejpam-3884	403	22	multiplicative	multiplicative	ADJ
ejpam-3884	403	23	circulant	circulant	ADJ
ejpam-3884	403	24	graphs	graph	NOUN
ejpam-3884	403	25	.	.	PUNCT
ejpam-3884	404	1	for	for	ADP
ejpam-3884	404	2	instance	instance	NOUN
ejpam-3884	404	3	,	,	PUNCT
ejpam-3884	404	4	the	the	DET
ejpam-3884	404	5	l(h	l(h	PROPN
ejpam-3884	404	6	,	,	PUNCT
ejpam-3884	404	7	k)-coloring	k)-coloring	NOUN
ejpam-3884	404	8	problem	problem	NOUN
ejpam-3884	404	9	.	.	PUNCT
ejpam-3884	405	1	6	6	X
ejpam-3884	405	2	.	.	X
ejpam-3884	405	3	conclusion	conclusion	NOUN
ejpam-3884	405	4	in	in	ADP
ejpam-3884	405	5	this	this	DET
ejpam-3884	405	6	paper	paper	NOUN
ejpam-3884	405	7	,	,	PUNCT
ejpam-3884	405	8	we	we	PRON
ejpam-3884	405	9	successfully	successfully	ADV
ejpam-3884	405	10	presented	present	VERB
ejpam-3884	405	11	a	a	DET
ejpam-3884	405	12	method	method	NOUN
ejpam-3884	405	13	in	in	ADP
ejpam-3884	405	14	constructing	construct	VERB
ejpam-3884	405	15	a	a	DET
ejpam-3884	405	16	breadth	breadth	NOUN
ejpam-3884	405	17	-	-	PUNCT
ejpam-3884	405	18	first	first	ADJ
ejpam-3884	405	19	search	search	NOUN
ejpam-3884	405	20	tree	tree	NOUN
ejpam-3884	405	21	for	for	ADP
ejpam-3884	405	22	multiplicative	multiplicative	ADJ
ejpam-3884	405	23	circulant	circulant	ADJ
ejpam-3884	405	24	graphs	graph	NOUN
ejpam-3884	405	25	of	of	ADP
ejpam-3884	405	26	order	order	NOUN
ejpam-3884	405	27	power	power	NOUN
ejpam-3884	405	28	of	of	ADP
ejpam-3884	405	29	odd	odd	ADJ
ejpam-3884	405	30	with	with	ADP
ejpam-3884	405	31	0	0	NUM
ejpam-3884	405	32	-	-	PUNCT
ejpam-3884	405	33	vertex	vertex	NOUN
ejpam-3884	405	34	as	as	ADP
ejpam-3884	405	35	the	the	DET
ejpam-3884	405	36	root	root	NOUN
ejpam-3884	405	37	.	.	PUNCT
ejpam-3884	406	1	as	as	ADP
ejpam-3884	406	2	a	a	DET
ejpam-3884	406	3	consequence	consequence	NOUN
ejpam-3884	406	4	,	,	PUNCT
ejpam-3884	406	5	we	we	PRON
ejpam-3884	406	6	were	be	AUX
ejpam-3884	406	7	able	able	ADJ
ejpam-3884	406	8	to	to	PART
ejpam-3884	406	9	reprove	reprove	VERB
ejpam-3884	406	10	some	some	DET
ejpam-3884	406	11	known	know	VERB
ejpam-3884	406	12	results	result	NOUN
ejpam-3884	406	13	about	about	ADP
ejpam-3884	406	14	multiplicative	multiplicative	ADJ
ejpam-3884	406	15	circulant	circulant	NOUN
ejpam-3884	406	16	graph	graph	NOUN
ejpam-3884	406	17	’s	’s	PART
ejpam-3884	406	18	diameter	diameter	NOUN
ejpam-3884	406	19	,	,	PUNCT
ejpam-3884	406	20	average	average	ADJ
ejpam-3884	406	21	distance	distance	NOUN
ejpam-3884	406	22	,	,	PUNCT
ejpam-3884	406	23	and	and	CCONJ
ejpam-3884	406	24	distance	distance	NOUN
ejpam-3884	406	25	spectral	spectral	ADJ
ejpam-3884	406	26	radius	radius	NOUN
ejpam-3884	406	27	.	.	PUNCT
ejpam-3884	407	1	we	we	PRON
ejpam-3884	407	2	also	also	ADV
ejpam-3884	407	3	determined	determine	VERB
ejpam-3884	407	4	the	the	DET
ejpam-3884	407	5	wiener	wiener	NOUN
ejpam-3884	407	6	index	index	NOUN
ejpam-3884	407	7	,	,	PUNCT
ejpam-3884	407	8	vertex	vertex	NOUN
ejpam-3884	407	9	-	-	PUNCT
ejpam-3884	407	10	forwarding	forward	VERB
ejpam-3884	407	11	index	index	NOUN
ejpam-3884	407	12	,	,	PUNCT
ejpam-3884	407	13	and	and	CCONJ
ejpam-3884	407	14	bounds	bound	VERB
ejpam-3884	407	15	for	for	ADP
ejpam-3884	407	16	the	the	DET
ejpam-3884	407	17	edge	edge	NOUN
ejpam-3884	407	18	-	-	PUNCT
ejpam-3884	407	19	forwarding	forward	VERB
ejpam-3884	407	20	index	index	NOUN
ejpam-3884	407	21	of	of	ADP
ejpam-3884	407	22	the	the	DET
ejpam-3884	407	23	studied	study	VERB
ejpam-3884	407	24	multiplicative	multiplicative	ADJ
ejpam-3884	407	25	circulant	circulant	NOUN
ejpam-3884	407	26	graph	graph	NOUN
ejpam-3884	407	27	.	.	PUNCT
ejpam-3884	408	1	new	new	ADJ
ejpam-3884	408	2	integer	integer	NOUN
ejpam-3884	408	3	sequences	sequence	NOUN
ejpam-3884	408	4	were	be	AUX
ejpam-3884	408	5	also	also	ADV
ejpam-3884	408	6	generated	generate	VERB
ejpam-3884	408	7	.	.	PUNCT
ejpam-3884	409	1	finally	finally	ADV
ejpam-3884	409	2	,	,	PUNCT
ejpam-3884	409	3	we	we	PRON
ejpam-3884	409	4	stated	state	VERB
ejpam-3884	409	5	some	some	DET
ejpam-3884	409	6	particular	particular	ADJ
ejpam-3884	409	7	research	research	NOUN
ejpam-3884	409	8	works	work	NOUN
ejpam-3884	409	9	in	in	ADP
ejpam-3884	409	10	which	which	PRON
ejpam-3884	409	11	the	the	DET
ejpam-3884	409	12	proposed	propose	VERB
ejpam-3884	409	13	bfs	bfs	NOUN
ejpam-3884	409	14	tree	tree	NOUN
ejpam-3884	409	15	construction	construction	NOUN
ejpam-3884	409	16	can	can	AUX
ejpam-3884	409	17	be	be	AUX
ejpam-3884	409	18	applied	apply	VERB
ejpam-3884	409	19	.	.	PUNCT
ejpam-3884	410	1	references	reference	NOUN
ejpam-3884	410	2	263	263	NUM
ejpam-3884	410	3	in	in	ADP
ejpam-3884	410	4	our	our	PRON
ejpam-3884	410	5	next	next	ADJ
ejpam-3884	410	6	paper	paper	NOUN
ejpam-3884	410	7	,	,	PUNCT
ejpam-3884	410	8	we	we	PRON
ejpam-3884	410	9	wish	wish	VERB
ejpam-3884	410	10	to	to	PART
ejpam-3884	410	11	determine	determine	VERB
ejpam-3884	410	12	some	some	DET
ejpam-3884	410	13	distance	distance	NOUN
ejpam-3884	410	14	-	-	PUNCT
ejpam-3884	410	15	based	base	VERB
ejpam-3884	410	16	topological	topological	ADJ
ejpam-3884	410	17	indices	index	NOUN
ejpam-3884	410	18	for	for	ADP
ejpam-3884	410	19	multiplicative	multiplicative	ADJ
ejpam-3884	410	20	circulant	circulant	ADJ
ejpam-3884	410	21	graphs	graph	NOUN
ejpam-3884	410	22	that	that	PRON
ejpam-3884	410	23	utilizes	utilize	VERB
ejpam-3884	410	24	our	our	PRON
ejpam-3884	410	25	bfs	bfs	NOUN
ejpam-3884	410	26	tree	tree	NOUN
ejpam-3884	410	27	construction	construction	NOUN
ejpam-3884	410	28	.	.	PUNCT
ejpam-3884	411	1	acknowledgements	acknowledgement	VERB
ejpam-3884	411	2	the	the	DET
ejpam-3884	411	3	creation	creation	NOUN
ejpam-3884	411	4	of	of	ADP
ejpam-3884	411	5	this	this	DET
ejpam-3884	411	6	paper	paper	NOUN
ejpam-3884	411	7	and	and	CCONJ
ejpam-3884	411	8	the	the	DET
ejpam-3884	411	9	research	research	NOUN
ejpam-3884	411	10	behind	behind	ADP
ejpam-3884	411	11	it	it	PRON
ejpam-3884	411	12	would	would	AUX
ejpam-3884	411	13	not	not	PART
ejpam-3884	411	14	have	have	AUX
ejpam-3884	411	15	been	be	AUX
ejpam-3884	411	16	possible	possible	ADJ
ejpam-3884	411	17	without	without	ADP
ejpam-3884	411	18	the	the	DET
ejpam-3884	411	19	support	support	NOUN
ejpam-3884	411	20	of	of	ADP
ejpam-3884	411	21	the	the	DET
ejpam-3884	411	22	philippines	philippine	NOUN
ejpam-3884	411	23	’	'	PUNCT
ejpam-3884	411	24	department	department	NOUN
ejpam-3884	411	25	of	of	ADP
ejpam-3884	411	26	science	science	NOUN
ejpam-3884	411	27	and	and	CCONJ
ejpam-3884	411	28	technology	technology	NOUN
ejpam-3884	411	29	asthrdpnsc	asthrdpnsc	NOUN
ejpam-3884	411	30	,	,	PUNCT
ejpam-3884	411	31	central	central	ADJ
ejpam-3884	411	32	luzon	luzon	PROPN
ejpam-3884	411	33	state	state	PROPN
ejpam-3884	411	34	university	university	PROPN
ejpam-3884	411	35	,	,	PUNCT
ejpam-3884	411	36	and	and	CCONJ
ejpam-3884	411	37	de	de	ADP
ejpam-3884	411	38	la	la	X
ejpam-3884	411	39	salle	salle	PROPN
ejpam-3884	411	40	university	university	PROPN
ejpam-3884	411	41	.	.	PUNCT
ejpam-3884	412	1	the	the	DET
ejpam-3884	412	2	authors	author	NOUN
ejpam-3884	412	3	are	be	AUX
ejpam-3884	412	4	also	also	ADV
ejpam-3884	412	5	thankful	thankful	ADJ
ejpam-3884	412	6	to	to	ADP
ejpam-3884	412	7	the	the	DET
ejpam-3884	412	8	referees	referee	NOUN
ejpam-3884	412	9	for	for	ADP
ejpam-3884	412	10	their	their	PRON
ejpam-3884	412	11	valuable	valuable	ADJ
ejpam-3884	412	12	comments	comment	NOUN
ejpam-3884	412	13	and	and	CCONJ
ejpam-3884	412	14	suggestions	suggestion	NOUN
ejpam-3884	412	15	that	that	PRON
ejpam-3884	412	16	helped	help	VERB
ejpam-3884	412	17	improve	improve	VERB
ejpam-3884	412	18	the	the	DET
ejpam-3884	412	19	content	content	NOUN
ejpam-3884	412	20	of	of	ADP
ejpam-3884	412	21	this	this	DET
ejpam-3884	412	22	paper	paper	NOUN
ejpam-3884	412	23	.	.	PUNCT
ejpam-3884	413	1	references	reference	NOUN
ejpam-3884	413	2	[	[	X
ejpam-3884	413	3	1	1	NUM
ejpam-3884	413	4	]	]	PUNCT
ejpam-3884	413	5	f.	f.	PROPN
ejpam-3884	413	6	ali	ali	PROPN
ejpam-3884	413	7	,	,	PUNCT
ejpam-3884	413	8	a.	a.	PROPN
ejpam-3884	413	9	hafeez	hafeez	PROPN
ejpam-3884	413	10	,	,	PUNCT
ejpam-3884	413	11	m.	m.	PROPN
ejpam-3884	413	12	salman	salman	PROPN
ejpam-3884	413	13	,	,	PUNCT
ejpam-3884	413	14	and	and	CCONJ
ejpam-3884	413	15	s.	s.	PROPN
ejpam-3884	413	16	huang	huang	PROPN
ejpam-3884	413	17	.	.	PUNCT
ejpam-3884	414	1	on	on	ADP
ejpam-3884	414	2	computation	computation	NOUN
ejpam-3884	414	3	of	of	ADP
ejpam-3884	414	4	some	some	DET
ejpam-3884	414	5	distancebased	distancebase	VERB
ejpam-3884	414	6	topological	topological	ADJ
ejpam-3884	414	7	indices	index	NOUN
ejpam-3884	414	8	of	of	ADP
ejpam-3884	414	9	circulant	circulant	ADJ
ejpam-3884	414	10	networks	network	NOUN
ejpam-3884	414	11	.	.	PUNCT
ejpam-3884	415	1	hacettepe	hacettepe	PROPN
ejpam-3884	415	2	journal	journal	PROPN
ejpam-3884	415	3	of	of	ADP
ejpam-3884	415	4	mathematics	mathematic	NOUN
ejpam-3884	415	5	and	and	CCONJ
ejpam-3884	415	6	statistics	statistic	NOUN
ejpam-3884	415	7	,	,	PUNCT
ejpam-3884	415	8	47:1427–1437	47:1427–1437	NUM
ejpam-3884	415	9	,	,	PUNCT
ejpam-3884	415	10	2018	2018	NUM
ejpam-3884	415	11	.	.	PUNCT
ejpam-3884	416	1	[	[	X
ejpam-3884	416	2	2	2	NUM
ejpam-3884	416	3	]	]	PUNCT
ejpam-3884	416	4	f.	f.	PROPN
ejpam-3884	416	5	ali	ali	PROPN
ejpam-3884	416	6	,	,	PUNCT
ejpam-3884	416	7	a.	a.	PROPN
ejpam-3884	416	8	hafeez	hafeez	PROPN
ejpam-3884	416	9	,	,	PUNCT
ejpam-3884	416	10	m.	m.	PROPN
ejpam-3884	416	11	salman	salman	PROPN
ejpam-3884	416	12	,	,	PUNCT
ejpam-3884	416	13	and	and	CCONJ
ejpam-3884	416	14	s.	s.	PROPN
ejpam-3884	416	15	huang	huang	PROPN
ejpam-3884	416	16	.	.	PUNCT
ejpam-3884	417	1	on	on	ADP
ejpam-3884	417	2	computation	computation	NOUN
ejpam-3884	417	3	of	of	ADP
ejpam-3884	417	4	some	some	DET
ejpam-3884	417	5	distance	distance	NOUN
ejpam-3884	417	6	-	-	PUNCT
ejpam-3884	417	7	based	base	VERB
ejpam-3884	417	8	topological	topological	ADJ
ejpam-3884	417	9	indices	index	NOUN
ejpam-3884	417	10	of	of	ADP
ejpam-3884	417	11	circulant	circulant	ADJ
ejpam-3884	417	12	networks	network	NOUN
ejpam-3884	417	13	-	-	PUNCT
ejpam-3884	417	14	ii	ii	NOUN
ejpam-3884	417	15	.	.	PUNCT
ejpam-3884	417	16	journal	journal	PROPN
ejpam-3884	417	17	of	of	ADP
ejpam-3884	417	18	information	information	NOUN
ejpam-3884	417	19	and	and	CCONJ
ejpam-3884	417	20	optimization	optimization	NOUN
ejpam-3884	417	21	sciences	science	NOUN
ejpam-3884	417	22	,	,	PUNCT
ejpam-3884	417	23	39:759–782	39:759–782	NUM
ejpam-3884	417	24	,	,	PUNCT
ejpam-3884	417	25	2018	2018	NUM
ejpam-3884	417	26	.	.	PUNCT
ejpam-3884	418	1	[	[	X
ejpam-3884	418	2	3	3	NUM
ejpam-3884	418	3	]	]	X
ejpam-3884	418	4	j.r.m	j.r.m	PROPN
ejpam-3884	418	5	.	.	PUNCT
ejpam-3884	419	1	antalan	antalan	PROPN
ejpam-3884	419	2	and	and	CCONJ
ejpam-3884	419	3	f.j.h	f.j.h	ADJ
ejpam-3884	419	4	.	.	PUNCT
ejpam-3884	419	5	campena	campena	NOUN
ejpam-3884	419	6	.	.	PUNCT
ejpam-3884	420	1	distance	distance	NOUN
ejpam-3884	420	2	eigenvalues	eigenvalue	VERB
ejpam-3884	420	3	and	and	CCONJ
ejpam-3884	420	4	forwarding	forward	VERB
ejpam-3884	420	5	indices	index	NOUN
ejpam-3884	420	6	of	of	ADP
ejpam-3884	420	7	multiplicative	multiplicative	ADJ
ejpam-3884	420	8	circulant	circulant	ADJ
ejpam-3884	420	9	graph	graph	NOUN
ejpam-3884	420	10	of	of	ADP
ejpam-3884	420	11	order	order	NOUN
ejpam-3884	420	12	power	power	NOUN
ejpam-3884	420	13	of	of	ADP
ejpam-3884	420	14	two	two	NUM
ejpam-3884	420	15	and	and	CCONJ
ejpam-3884	420	16	three	three	NUM
ejpam-3884	420	17	.	.	PUNCT
ejpam-3884	421	1	arxiv	arxiv	PROPN
ejpam-3884	421	2	e	e	PROPN
ejpam-3884	421	3	-	-	NOUN
ejpam-3884	421	4	prints	print	NOUN
ejpam-3884	421	5	,	,	PUNCT
ejpam-3884	421	6	arxiv:2009.11608	arxiv:2009.11608	PROPN
ejpam-3884	421	7	,	,	PUNCT
ejpam-3884	421	8	arxiv:2009.11608[math.co	arxiv:2009.11608[math.co	ADV
ejpam-3884	421	9	]	]	X
ejpam-3884	421	10	,	,	PUNCT
ejpam-3884	421	11	(	(	PUNCT
ejpam-3884	421	12	submitted	submit	VERB
ejpam-3884	421	13	to	to	ADP
ejpam-3884	421	14	electronic	electronic	ADJ
ejpam-3884	421	15	journal	journal	NOUN
ejpam-3884	421	16	of	of	ADP
ejpam-3884	421	17	graph	graph	NOUN
ejpam-3884	421	18	theory	theory	NOUN
ejpam-3884	421	19	and	and	CCONJ
ejpam-3884	421	20	applications	application	NOUN
ejpam-3884	421	21	,	,	PUNCT
ejpam-3884	421	22	september	september	PROPN
ejpam-3884	421	23	25	25	NUM
ejpam-3884	421	24	,	,	PUNCT
ejpam-3884	421	25	2020	2020	NUM
ejpam-3884	421	26	)	)	PUNCT
ejpam-3884	421	27	,	,	PUNCT
ejpam-3884	421	28	2020	2020	NUM
ejpam-3884	421	29	.	.	PUNCT
ejpam-3884	422	1	[	[	X
ejpam-3884	422	2	4	4	NUM
ejpam-3884	422	3	]	]	X
ejpam-3884	422	4	j.-c	j.-c	PROPN
ejpam-3884	422	5	.	.	PUNCT
ejpam-3884	423	1	bermond	bermond	PROPN
ejpam-3884	423	2	,	,	PUNCT
ejpam-3884	423	3	f.	f.	PROPN
ejpam-3884	423	4	comellas	comellas	PROPN
ejpam-3884	423	5	,	,	PUNCT
ejpam-3884	423	6	and	and	CCONJ
ejpam-3884	423	7	d.-f	d.-f	NOUN
ejpam-3884	423	8	.	.	PUNCT
ejpam-3884	424	1	hsu	hsu	PROPN
ejpam-3884	424	2	.	.	PUNCT
ejpam-3884	424	3	distributed	distribute	VERB
ejpam-3884	424	4	loop	loop	NOUN
ejpam-3884	424	5	computer	computer	NOUN
ejpam-3884	424	6	networks	network	NOUN
ejpam-3884	424	7	:	:	PUNCT
ejpam-3884	424	8	a	a	DET
ejpam-3884	424	9	survey	survey	NOUN
ejpam-3884	424	10	.	.	PUNCT
ejpam-3884	425	1	journal	journal	NOUN
ejpam-3884	425	2	of	of	ADP
ejpam-3884	425	3	parallel	parallel	ADJ
ejpam-3884	425	4	and	and	CCONJ
ejpam-3884	425	5	distributed	distributed	ADJ
ejpam-3884	425	6	computing	computing	NOUN
ejpam-3884	425	7	,	,	PUNCT
ejpam-3884	425	8	24:2–10	24:2–10	NUM
ejpam-3884	425	9	,	,	PUNCT
ejpam-3884	425	10	1995	1995	NUM
ejpam-3884	425	11	.	.	PUNCT
ejpam-3884	426	1	[	[	X
ejpam-3884	426	2	5	5	NUM
ejpam-3884	426	3	]	]	X
ejpam-3884	426	4	j.l	j.l	PROPN
ejpam-3884	426	5	.	.	PROPN
ejpam-3884	426	6	gross	gross	PROPN
ejpam-3884	426	7	,	,	PUNCT
ejpam-3884	426	8	j.	j.	PROPN
ejpam-3884	426	9	yellen	yellen	PROPN
ejpam-3884	426	10	,	,	PUNCT
ejpam-3884	426	11	and	and	CCONJ
ejpam-3884	426	12	p.	p.	PROPN
ejpam-3884	426	13	zhang	zhang	PROPN
ejpam-3884	426	14	.	.	PUNCT
ejpam-3884	427	1	handbook	handbook	NOUN
ejpam-3884	427	2	of	of	ADP
ejpam-3884	427	3	graph	graph	NOUN
ejpam-3884	427	4	theory	theory	PROPN
ejpam-3884	427	5	second	second	PROPN
ejpam-3884	427	6	edition	edition	NOUN
ejpam-3884	427	7	.	.	PUNCT
ejpam-3884	428	1	crc	crc	PROPN
ejpam-3884	428	2	press	press	PROPN
ejpam-3884	428	3	,	,	PUNCT
ejpam-3884	428	4	taylor	taylor	PROPN
ejpam-3884	428	5	and	and	CCONJ
ejpam-3884	428	6	francis	francis	PROPN
ejpam-3884	428	7	group	group	PROPN
ejpam-3884	428	8	,	,	PUNCT
ejpam-3884	428	9	boca	boca	PROPN
ejpam-3884	428	10	raton	raton	PROPN
ejpam-3884	428	11	,	,	PUNCT
ejpam-3884	428	12	fl	fl	PROPN
ejpam-3884	428	13	,	,	PUNCT
ejpam-3884	428	14	2014	2014	NUM
ejpam-3884	428	15	.	.	PUNCT
ejpam-3884	429	1	[	[	X
ejpam-3884	429	2	6	6	NUM
ejpam-3884	429	3	]	]	X
ejpam-3884	429	4	r.h	r.h	PROPN
ejpam-3884	429	5	.	.	PROPN
ejpam-3884	429	6	hardin	hardin	PROPN
ejpam-3884	429	7	.	.	PUNCT
ejpam-3884	429	8	sequence	sequence	NOUN
ejpam-3884	429	9	a269760	a269760	PROPN
ejpam-3884	429	10	in	in	ADP
ejpam-3884	429	11	the	the	DET
ejpam-3884	429	12	on	on	ADP
ejpam-3884	429	13	-	-	PUNCT
ejpam-3884	429	14	line	line	NOUN
ejpam-3884	429	15	encyclopedia	encyclopedia	NOUN
ejpam-3884	429	16	of	of	ADP
ejpam-3884	429	17	integer	integer	NOUN
ejpam-3884	429	18	sequences	sequence	NOUN
ejpam-3884	429	19	.	.	PUNCT
ejpam-3884	429	20	,	,	PUNCT
ejpam-3884	429	21	2016	2016	NUM
ejpam-3884	429	22	.	.	PUNCT
ejpam-3884	430	1	[	[	X
ejpam-3884	430	2	7	7	X
ejpam-3884	430	3	]	]	PUNCT
ejpam-3884	430	4	wolfram	wolfram	PROPN
ejpam-3884	430	5	research	research	PROPN
ejpam-3884	430	6	,	,	PUNCT
ejpam-3884	430	7	inc	inc	PROPN
ejpam-3884	430	8	.	.	PROPN
ejpam-3884	430	9	mathematica	mathematica	PROPN
ejpam-3884	430	10	,	,	PUNCT
ejpam-3884	430	11	version	version	NOUN
ejpam-3884	430	12	9.0.1	9.0.1	NUM
ejpam-3884	430	13	.	.	PUNCT
ejpam-3884	431	1	champaign	champaign	PROPN
ejpam-3884	431	2	,	,	PUNCT
ejpam-3884	431	3	il	il	PROPN
ejpam-3884	431	4	,	,	PUNCT
ejpam-3884	431	5	2020	2020	NUM
ejpam-3884	431	6	.	.	PUNCT
ejpam-3884	432	1	[	[	X
ejpam-3884	432	2	8	8	NUM
ejpam-3884	432	3	]	]	X
ejpam-3884	432	4	f.t	f.t	PROPN
ejpam-3884	432	5	.	.	PUNCT
ejpam-3884	432	6	leighton	leighton	PROPN
ejpam-3884	432	7	.	.	PUNCT
ejpam-3884	433	1	introduction	introduction	NOUN
ejpam-3884	433	2	to	to	ADP
ejpam-3884	433	3	parallel	parallel	ADJ
ejpam-3884	433	4	algorithms	algorithm	NOUN
ejpam-3884	433	5	and	and	CCONJ
ejpam-3884	433	6	architectures	architecture	NOUN
ejpam-3884	433	7	:	:	PUNCT
ejpam-3884	433	8	arrays	array	VERB
ejpam-3884	433	9	,	,	PUNCT
ejpam-3884	433	10	trees	tree	NOUN
ejpam-3884	433	11	,	,	PUNCT
ejpam-3884	433	12	hypercubes	hypercube	NOUN
ejpam-3884	433	13	.	.	PUNCT
ejpam-3884	434	1	morgan	morgan	PROPN
ejpam-3884	434	2	kauffman	kauffman	PROPN
ejpam-3884	434	3	publishers	publishers	PROPN
ejpam-3884	434	4	,	,	PUNCT
ejpam-3884	434	5	1992	1992	NUM
ejpam-3884	434	6	.	.	PUNCT
ejpam-3884	435	1	[	[	X
ejpam-3884	435	2	9	9	NUM
ejpam-3884	435	3	]	]	PUNCT
ejpam-3884	435	4	s.	s.	PROPN
ejpam-3884	435	5	liu	liu	PROPN
ejpam-3884	435	6	,	,	PUNCT
ejpam-3884	435	7	h.	h.	PROPN
ejpam-3884	435	8	lin	lin	PROPN
ejpam-3884	435	9	,	,	PUNCT
ejpam-3884	435	10	and	and	CCONJ
ejpam-3884	435	11	j.	j.	PROPN
ejpam-3884	435	12	shu	shu	PROPN
ejpam-3884	435	13	.	.	PUNCT
ejpam-3884	436	1	distance	distance	NOUN
ejpam-3884	436	2	eigenvalues	eigenvalue	VERB
ejpam-3884	436	3	and	and	CCONJ
ejpam-3884	436	4	forwarding	forward	VERB
ejpam-3884	436	5	indices	index	NOUN
ejpam-3884	436	6	of	of	ADP
ejpam-3884	436	7	circulants	circulant	NOUN
ejpam-3884	436	8	.	.	PUNCT
ejpam-3884	437	1	taiwanese	taiwanese	ADJ
ejpam-3884	437	2	journal	journal	NOUN
ejpam-3884	437	3	of	of	ADP
ejpam-3884	437	4	mathematics	mathematic	NOUN
ejpam-3884	437	5	,	,	PUNCT
ejpam-3884	437	6	22:513–528	22:513–528	NUM
ejpam-3884	437	7	,	,	PUNCT
ejpam-3884	437	8	2018	2018	NUM
ejpam-3884	437	9	.	.	PUNCT
ejpam-3884	438	1	[	[	X
ejpam-3884	438	2	10	10	NUM
ejpam-3884	438	3	]	]	X
ejpam-3884	438	4	b.	b.	PROPN
ejpam-3884	438	5	mans	mans	PROPN
ejpam-3884	438	6	.	.	PUNCT
ejpam-3884	439	1	optimal	optimal	ADJ
ejpam-3884	439	2	distributed	distribute	VERB
ejpam-3884	439	3	algorithms	algorithm	NOUN
ejpam-3884	439	4	in	in	ADP
ejpam-3884	439	5	unlabeled	unlabeled	PROPN
ejpam-3884	439	6	tori	tori	NOUN
ejpam-3884	439	7	and	and	CCONJ
ejpam-3884	439	8	chordal	chordal	NOUN
ejpam-3884	439	9	rings	ring	NOUN
ejpam-3884	439	10	.	.	PUNCT
ejpam-3884	440	1	journal	journal	PROPN
ejpam-3884	440	2	of	of	ADP
ejpam-3884	440	3	parallel	parallel	ADJ
ejpam-3884	440	4	and	and	CCONJ
ejpam-3884	440	5	distributed	distributed	ADJ
ejpam-3884	440	6	computing	computing	NOUN
ejpam-3884	440	7	,	,	PUNCT
ejpam-3884	440	8	46:80–90	46:80–90	PROPN
ejpam-3884	440	9	,	,	PUNCT
ejpam-3884	440	10	1997	1997	NUM
ejpam-3884	440	11	.	.	PUNCT
ejpam-3884	441	1	references	reference	NOUN
ejpam-3884	441	2	264	264	NUM
ejpam-3884	442	1	[	[	X
ejpam-3884	442	2	11	11	NUM
ejpam-3884	442	3	]	]	X
ejpam-3884	442	4	j	j	PROPN
ejpam-3884	442	5	-	-	PROPN
ejpam-3884	442	6	h.	h.	PROPN
ejpam-3884	442	7	park	park	PROPN
ejpam-3884	442	8	and	and	CCONJ
ejpam-3884	442	9	k	k	PROPN
ejpam-3884	442	10	-	-	PROPN
ejpam-3884	442	11	y.	y.	PROPN
ejpam-3884	442	12	chwa	chwa	PROPN
ejpam-3884	442	13	.	.	PUNCT
ejpam-3884	443	1	recursive	recursive	ADJ
ejpam-3884	443	2	circulant	circulant	NOUN
ejpam-3884	443	3	:	:	PUNCT
ejpam-3884	443	4	a	a	DET
ejpam-3884	443	5	new	new	ADJ
ejpam-3884	443	6	topology	topology	NOUN
ejpam-3884	443	7	for	for	ADP
ejpam-3884	443	8	multicomputer	multicomputer	NOUN
ejpam-3884	443	9	networks	network	NOUN
ejpam-3884	443	10	.	.	PUNCT
ejpam-3884	444	1	in	in	ADP
ejpam-3884	444	2	proceedings	proceeding	NOUN
ejpam-3884	444	3	of	of	ADP
ejpam-3884	444	4	international	international	ADJ
ejpam-3884	444	5	symposium	symposium	NOUN
ejpam-3884	444	6	on	on	ADP
ejpam-3884	444	7	parallel	parallel	ADJ
ejpam-3884	444	8	architectures	architecture	NOUN
ejpam-3884	444	9	,	,	PUNCT
ejpam-3884	444	10	algorithms	algorithm	NOUN
ejpam-3884	444	11	and	and	CCONJ
ejpam-3884	444	12	networks	network	NOUN
ejpam-3884	444	13	.	.	PUNCT
ejpam-3884	444	14	,	,	PUNCT
ejpam-3884	444	15	pages	page	NOUN
ejpam-3884	444	16	73–80	73–80	NUM
ejpam-3884	444	17	,	,	PUNCT
ejpam-3884	444	18	1994	1994	NUM
ejpam-3884	444	19	.	.	PUNCT
ejpam-3884	445	1	[	[	X
ejpam-3884	445	2	12	12	NUM
ejpam-3884	445	3	]	]	PUNCT
ejpam-3884	445	4	i.	i.	NOUN
ejpam-3884	445	5	stojmenovic	stojmenovic	PROPN
ejpam-3884	445	6	.	.	PUNCT
ejpam-3884	446	1	multiplicative	multiplicative	ADJ
ejpam-3884	446	2	circulant	circulant	ADJ
ejpam-3884	446	3	networks	network	NOUN
ejpam-3884	446	4	:	:	PUNCT
ejpam-3884	446	5	topological	topological	ADJ
ejpam-3884	446	6	properties	property	NOUN
ejpam-3884	446	7	and	and	CCONJ
ejpam-3884	446	8	communication	communication	NOUN
ejpam-3884	446	9	algorithms	algorithm	NOUN
ejpam-3884	446	10	.	.	PUNCT
ejpam-3884	447	1	discrete	discrete	VERB
ejpam-3884	447	2	applied	apply	VERB
ejpam-3884	447	3	mathematics	mathematic	NOUN
ejpam-3884	447	4	,	,	PUNCT
ejpam-3884	447	5	77:281–305	77:281–305	PROPN
ejpam-3884	447	6	,	,	PUNCT
ejpam-3884	447	7	1997	1997	NUM
ejpam-3884	447	8	.	.	PUNCT
ejpam-3884	448	1	[	[	X
ejpam-3884	448	2	13	13	NUM
ejpam-3884	448	3	]	]	PUNCT
ejpam-3884	448	4	s.	s.	PROPN
ejpam-3884	448	5	sykora	sykora	PROPN
ejpam-3884	448	6	.	.	PUNCT
ejpam-3884	449	1	sequence	sequence	NOUN
ejpam-3884	450	1	a212697	a212697	ADV
ejpam-3884	450	2	in	in	ADP
ejpam-3884	450	3	the	the	DET
ejpam-3884	450	4	on	on	ADP
ejpam-3884	450	5	-	-	PUNCT
ejpam-3884	450	6	line	line	NOUN
ejpam-3884	450	7	encyclopedia	encyclopedia	NOUN
ejpam-3884	450	8	of	of	ADP
ejpam-3884	450	9	integer	integer	NOUN
ejpam-3884	450	10	sequences	sequence	NOUN
ejpam-3884	450	11	.	.	PUNCT
ejpam-3884	450	12	,	,	PUNCT
ejpam-3884	450	13	2012	2012	NUM
ejpam-3884	450	14	.	.	PUNCT
ejpam-3884	451	1	[	[	X
ejpam-3884	451	2	14	14	NUM
ejpam-3884	451	3	]	]	X
ejpam-3884	451	4	s	s	NOUN
ejpam-3884	451	5	-	-	PUNCT
ejpam-3884	451	6	m.	m.	NOUN
ejpam-3884	451	7	tang	tang	PROPN
ejpam-3884	451	8	,	,	PUNCT
ejpam-3884	451	9	y	y	PROPN
ejpam-3884	451	10	-	-	PUNCT
ejpam-3884	451	11	l.	l.	PROPN
ejpam-3884	451	12	wang	wang	PROPN
ejpam-3884	451	13	,	,	PUNCT
ejpam-3884	451	14	and	and	CCONJ
ejpam-3884	451	15	c	c	X
ejpam-3884	451	16	-	-	PUNCT
ejpam-3884	451	17	y.	y.	PROPN
ejpam-3884	451	18	li	li	PROPN
ejpam-3884	451	19	.	.	PUNCT
ejpam-3884	452	1	generalized	generalize	VERB
ejpam-3884	452	2	recursive	recursive	ADJ
ejpam-3884	452	3	circulant	circulant	NOUN
ejpam-3884	452	4	graphs	graph	NOUN
ejpam-3884	452	5	.	.	PUNCT
ejpam-3884	453	1	ieee	ieee	NOUN
ejpam-3884	453	2	transactions	transaction	NOUN
ejpam-3884	453	3	on	on	ADP
ejpam-3884	453	4	parallel	parallel	ADJ
ejpam-3884	453	5	distributed	distribute	VERB
ejpam-3884	453	6	systems	system	NOUN
ejpam-3884	453	7	,	,	PUNCT
ejpam-3884	453	8	23:87–93	23:87–93	NUM
ejpam-3884	453	9	,	,	PUNCT
ejpam-3884	453	10	2012	2012	NUM
ejpam-3884	453	11	.	.	PUNCT
ejpam-3884	454	1	[	[	X
ejpam-3884	454	2	15	15	NUM
ejpam-3884	454	3	]	]	X
ejpam-3884	454	4	c.k	c.k	PROPN
ejpam-3884	454	5	.	.	PROPN
ejpam-3884	454	6	wong	wong	PROPN
ejpam-3884	454	7	and	and	CCONJ
ejpam-3884	454	8	d.	d.	PROPN
ejpam-3884	454	9	coppersmith	coppersmith	PROPN
ejpam-3884	454	10	.	.	PUNCT
ejpam-3884	455	1	a	a	DET
ejpam-3884	455	2	combinatorial	combinatorial	ADJ
ejpam-3884	455	3	problem	problem	NOUN
ejpam-3884	455	4	related	relate	VERB
ejpam-3884	455	5	to	to	ADP
ejpam-3884	455	6	multimodule	multimodule	ADJ
ejpam-3884	455	7	memory	memory	NOUN
ejpam-3884	455	8	organizations	organization	NOUN
ejpam-3884	455	9	.	.	PUNCT
ejpam-3884	456	1	journal	journal	NOUN
ejpam-3884	456	2	of	of	ADP
ejpam-3884	456	3	the	the	DET
ejpam-3884	456	4	association	association	NOUN
ejpam-3884	456	5	for	for	ADP
ejpam-3884	456	6	computing	computing	NOUN
ejpam-3884	456	7	machinery	machinery	NOUN
ejpam-3884	456	8	,	,	PUNCT
ejpam-3884	456	9	21:392	21:392	NUM
ejpam-3884	456	10	–	–	PUNCT
ejpam-3884	456	11	402	402	NUM
ejpam-3884	456	12	,	,	PUNCT
ejpam-3884	456	13	1974	1974	NUM
ejpam-3884	456	14	.	.	PUNCT