id	sid	tid	token	lemma	pos
ejpam-5943	1	1	european	european	PROPN
ejpam-5943	1	2	journal	journal	PROPN
ejpam-5943	1	3	of	of	ADP
ejpam-5943	1	4	pure	pure	ADJ
ejpam-5943	1	5	and	and	CCONJ
ejpam-5943	1	6	applied	applied	ADJ
ejpam-5943	1	7	mathematics	mathematic	NOUN
ejpam-5943	1	8	2025	2025	NUM
ejpam-5943	1	9	,	,	PUNCT
ejpam-5943	1	10	vol	vol	NOUN
ejpam-5943	1	11	.	.	PROPN
ejpam-5943	1	12	18	18	NUM
ejpam-5943	1	13	,	,	PUNCT
ejpam-5943	1	14	issue	issue	NOUN
ejpam-5943	1	15	2	2	NUM
ejpam-5943	1	16	,	,	PUNCT
ejpam-5943	1	17	article	article	NOUN
ejpam-5943	1	18	number	number	NOUN
ejpam-5943	1	19	5943	5943	NUM
ejpam-5943	1	20	issn	issn	PROPN
ejpam-5943	1	21	1307	1307	NUM
ejpam-5943	1	22	-	-	SYM
ejpam-5943	1	23	5543	5543	NUM
ejpam-5943	1	24	–	–	PUNCT
ejpam-5943	1	25	ejpam.com	ejpam.com	X
ejpam-5943	1	26	published	publish	VERB
ejpam-5943	1	27	by	by	ADP
ejpam-5943	1	28	new	new	PROPN
ejpam-5943	1	29	york	york	PROPN
ejpam-5943	1	30	business	business	PROPN
ejpam-5943	1	31	global	global	ADJ
ejpam-5943	1	32	proximity	proximity	NOUN
ejpam-5943	1	33	prestige	prestige	NOUN
ejpam-5943	1	34	of	of	ADP
ejpam-5943	1	35	a	a	DET
ejpam-5943	1	36	vertex	vertex	NOUN
ejpam-5943	1	37	in	in	ADP
ejpam-5943	1	38	some	some	DET
ejpam-5943	1	39	graph	graph	NOUN
ejpam-5943	1	40	families	family	NOUN
ejpam-5943	1	41	lysandra	lysandra	VERB
ejpam-5943	1	42	a.	a.	NOUN
ejpam-5943	1	43	toladro1,∗	toladro1,∗	NOUN
ejpam-5943	1	44	,	,	PUNCT
ejpam-5943	1	45	isagani	isagani	PROPN
ejpam-5943	1	46	s.	s.	PROPN
ejpam-5943	1	47	cabahug	cabahug	PROPN
ejpam-5943	1	48	,	,	PUNCT
ejpam-5943	1	49	jr.2	jr.2	PROPN
ejpam-5943	1	50	1	1	NUM
ejpam-5943	1	51	department	department	NOUN
ejpam-5943	1	52	of	of	ADP
ejpam-5943	1	53	mathematics	mathematic	NOUN
ejpam-5943	1	54	,	,	PUNCT
ejpam-5943	1	55	college	college	NOUN
ejpam-5943	1	56	of	of	ADP
ejpam-5943	1	57	arts	art	NOUN
ejpam-5943	1	58	and	and	CCONJ
ejpam-5943	1	59	sciences	science	NOUN
ejpam-5943	1	60	,	,	PUNCT
ejpam-5943	1	61	central	central	ADJ
ejpam-5943	1	62	mindanao	mindanao	PROPN
ejpam-5943	1	63	university	university	PROPN
ejpam-5943	1	64	,	,	PUNCT
ejpam-5943	1	65	musuan	musuan	PROPN
ejpam-5943	1	66	,	,	PUNCT
ejpam-5943	1	67	maramag	maramag	NOUN
ejpam-5943	1	68	,	,	PUNCT
ejpam-5943	1	69	bukidnon	bukidnon	NOUN
ejpam-5943	1	70	,	,	PUNCT
ejpam-5943	1	71	8710	8710	NUM
ejpam-5943	1	72	philippines	philippine	NOUN
ejpam-5943	1	73	abstract	abstract	ADJ
ejpam-5943	1	74	.	.	PUNCT
ejpam-5943	2	1	let	let	VERB
ejpam-5943	2	2	g	g	PROPN
ejpam-5943	2	3	=	=	SYM
ejpam-5943	2	4	(	(	PUNCT
ejpam-5943	2	5	v	v	NOUN
ejpam-5943	2	6	,	,	PUNCT
ejpam-5943	2	7	e	e	NOUN
ejpam-5943	2	8	)	)	PUNCT
ejpam-5943	2	9	be	be	AUX
ejpam-5943	2	10	an	an	DET
ejpam-5943	2	11	undirected	undirected	ADJ
ejpam-5943	2	12	graph	graph	NOUN
ejpam-5943	2	13	where	where	SCONJ
ejpam-5943	2	14	v	v	NOUN
ejpam-5943	2	15	,	,	PUNCT
ejpam-5943	2	16	e	e	X
ejpam-5943	2	17	are	be	AUX
ejpam-5943	2	18	the	the	DET
ejpam-5943	2	19	set	set	NOUN
ejpam-5943	2	20	of	of	ADP
ejpam-5943	2	21	vertices	vertex	NOUN
ejpam-5943	2	22	and	and	CCONJ
ejpam-5943	2	23	edges	edge	NOUN
ejpam-5943	2	24	respectively	respectively	ADV
ejpam-5943	2	25	.	.	PUNCT
ejpam-5943	3	1	the	the	DET
ejpam-5943	3	2	proximity	proximity	NOUN
ejpam-5943	3	3	prestige	prestige	NOUN
ejpam-5943	3	4	(	(	PUNCT
ejpam-5943	3	5	pp	pp	ADV
ejpam-5943	3	6	)	)	PUNCT
ejpam-5943	3	7	of	of	ADP
ejpam-5943	3	8	a	a	DET
ejpam-5943	3	9	vertex	vertex	NOUN
ejpam-5943	3	10	vi	vi	PROPN
ejpam-5943	3	11	is	be	AUX
ejpam-5943	3	12	the	the	DET
ejpam-5943	3	13	sum	sum	NOUN
ejpam-5943	3	14	of	of	ADP
ejpam-5943	3	15	the	the	DET
ejpam-5943	3	16	shortest	short	ADJ
ejpam-5943	3	17	path	path	NOUN
ejpam-5943	3	18	distance	distance	NOUN
ejpam-5943	3	19	between	between	ADP
ejpam-5943	3	20	vertex	vertex	PROPN
ejpam-5943	3	21	vi	vi	PROPN
ejpam-5943	3	22	and	and	CCONJ
ejpam-5943	3	23	vj	vj	PROPN
ejpam-5943	3	24	all	all	ADV
ejpam-5943	3	25	over	over	ADP
ejpam-5943	3	26	the	the	DET
ejpam-5943	3	27	number	number	NOUN
ejpam-5943	3	28	of	of	ADP
ejpam-5943	3	29	vertices	vertex	NOUN
ejpam-5943	3	30	in	in	ADP
ejpam-5943	3	31	the	the	DET
ejpam-5943	3	32	graph	graph	NOUN
ejpam-5943	3	33	.	.	PUNCT
ejpam-5943	4	1	proximity	proximity	NOUN
ejpam-5943	4	2	prestige	prestige	NOUN
ejpam-5943	4	3	(	(	PUNCT
ejpam-5943	4	4	pp	pp	ADV
ejpam-5943	4	5	)	)	PUNCT
ejpam-5943	4	6	emphasizes	emphasize	VERB
ejpam-5943	4	7	the	the	DET
ejpam-5943	4	8	importance	importance	NOUN
ejpam-5943	4	9	of	of	ADP
ejpam-5943	4	10	both	both	CCONJ
ejpam-5943	4	11	reachability	reachability	NOUN
ejpam-5943	4	12	and	and	CCONJ
ejpam-5943	4	13	distance	distance	NOUN
ejpam-5943	4	14	.	.	PUNCT
ejpam-5943	5	1	here	here	ADV
ejpam-5943	5	2	,	,	PUNCT
ejpam-5943	5	3	general	general	ADJ
ejpam-5943	5	4	properties	property	NOUN
ejpam-5943	5	5	of	of	ADP
ejpam-5943	5	6	proximity	proximity	NOUN
ejpam-5943	5	7	prestige	prestige	NOUN
ejpam-5943	5	8	in	in	ADP
ejpam-5943	5	9	some	some	DET
ejpam-5943	5	10	classes	class	NOUN
ejpam-5943	5	11	of	of	ADP
ejpam-5943	5	12	graph	graph	NOUN
ejpam-5943	5	13	,	,	PUNCT
ejpam-5943	5	14	including	include	VERB
ejpam-5943	5	15	path	path	NOUN
ejpam-5943	5	16	,	,	PUNCT
ejpam-5943	5	17	cycle	cycle	NOUN
ejpam-5943	5	18	,	,	PUNCT
ejpam-5943	5	19	complete	complete	ADJ
ejpam-5943	5	20	,	,	PUNCT
ejpam-5943	5	21	friendship	friendship	NOUN
ejpam-5943	5	22	,	,	PUNCT
ejpam-5943	5	23	complete	complete	ADJ
ejpam-5943	5	24	bipartite	bipartite	PROPN
ejpam-5943	5	25	,	,	PUNCT
ejpam-5943	5	26	star	star	NOUN
ejpam-5943	5	27	,	,	PUNCT
ejpam-5943	5	28	fan	fan	PROPN
ejpam-5943	5	29	and	and	CCONJ
ejpam-5943	5	30	wheel	wheel	NOUN
ejpam-5943	5	31	were	be	AUX
ejpam-5943	5	32	determined	determine	VERB
ejpam-5943	5	33	.	.	PUNCT
ejpam-5943	6	1	2020	2020	NUM
ejpam-5943	6	2	mathematics	mathematic	NOUN
ejpam-5943	6	3	subject	subject	NOUN
ejpam-5943	6	4	classifications	classification	NOUN
ejpam-5943	6	5	:	:	PUNCT
ejpam-5943	6	6	05c12	05c12	NUM
ejpam-5943	6	7	,	,	PUNCT
ejpam-5943	6	8	91d30	91d30	NUM
ejpam-5943	6	9	key	key	ADJ
ejpam-5943	6	10	words	word	NOUN
ejpam-5943	6	11	and	and	CCONJ
ejpam-5943	6	12	phrases	phrase	NOUN
ejpam-5943	6	13	:	:	PUNCT
ejpam-5943	6	14	proximity	proximity	NOUN
ejpam-5943	6	15	prestige	prestige	NOUN
ejpam-5943	6	16	,	,	PUNCT
ejpam-5943	6	17	distance	distance	NOUN
ejpam-5943	6	18	,	,	PUNCT
ejpam-5943	6	19	graph	graph	NOUN
ejpam-5943	6	20	families	family	NOUN
ejpam-5943	6	21	1	1	NUM
ejpam-5943	6	22	.	.	PUNCT
ejpam-5943	7	1	introduction	introduction	NOUN
ejpam-5943	7	2	graph	graph	NOUN
ejpam-5943	7	3	theory	theory	NOUN
ejpam-5943	7	4	has	have	AUX
ejpam-5943	7	5	become	become	VERB
ejpam-5943	7	6	an	an	DET
ejpam-5943	7	7	essential	essential	ADJ
ejpam-5943	7	8	tool	tool	NOUN
ejpam-5943	7	9	for	for	ADP
ejpam-5943	7	10	analyzing	analyze	VERB
ejpam-5943	7	11	complex	complex	ADJ
ejpam-5943	7	12	systems	system	NOUN
ejpam-5943	7	13	and	and	CCONJ
ejpam-5943	7	14	networks	network	NOUN
ejpam-5943	7	15	,	,	PUNCT
ejpam-5943	7	16	providing	provide	VERB
ejpam-5943	7	17	insights	insight	NOUN
ejpam-5943	7	18	into	into	ADP
ejpam-5943	7	19	the	the	DET
ejpam-5943	7	20	structure	structure	NOUN
ejpam-5943	7	21	and	and	CCONJ
ejpam-5943	7	22	dynamics	dynamic	NOUN
ejpam-5943	7	23	of	of	ADP
ejpam-5943	7	24	various	various	ADJ
ejpam-5943	7	25	real	real	ADJ
ejpam-5943	7	26	-	-	PUNCT
ejpam-5943	7	27	world	world	NOUN
ejpam-5943	7	28	systems	system	NOUN
ejpam-5943	7	29	,	,	PUNCT
ejpam-5943	7	30	from	from	ADP
ejpam-5943	7	31	social	social	ADJ
ejpam-5943	7	32	networks	network	NOUN
ejpam-5943	7	33	to	to	ADP
ejpam-5943	7	34	biological	biological	ADJ
ejpam-5943	7	35	systems	system	NOUN
ejpam-5943	7	36	.	.	PUNCT
ejpam-5943	8	1	one	one	NUM
ejpam-5943	8	2	of	of	ADP
ejpam-5943	8	3	the	the	DET
ejpam-5943	8	4	key	key	ADJ
ejpam-5943	8	5	aspects	aspect	NOUN
ejpam-5943	8	6	of	of	ADP
ejpam-5943	8	7	graph	graph	NOUN
ejpam-5943	8	8	analysis	analysis	NOUN
ejpam-5943	8	9	is	be	AUX
ejpam-5943	8	10	centrality	centrality	NOUN
ejpam-5943	8	11	,	,	PUNCT
ejpam-5943	8	12	which	which	PRON
ejpam-5943	8	13	aims	aim	VERB
ejpam-5943	8	14	to	to	PART
ejpam-5943	8	15	identify	identify	VERB
ejpam-5943	8	16	the	the	DET
ejpam-5943	8	17	most	most	ADV
ejpam-5943	8	18	important	important	ADJ
ejpam-5943	8	19	or	or	CCONJ
ejpam-5943	8	20	influential	influential	ADJ
ejpam-5943	8	21	nodes	node	NOUN
ejpam-5943	8	22	in	in	ADP
ejpam-5943	8	23	a	a	DET
ejpam-5943	8	24	network	network	NOUN
ejpam-5943	8	25	.	.	PUNCT
ejpam-5943	9	1	traditional	traditional	ADJ
ejpam-5943	9	2	centrality	centrality	NOUN
ejpam-5943	9	3	measures	measure	NOUN
ejpam-5943	9	4	,	,	PUNCT
ejpam-5943	9	5	such	such	ADJ
ejpam-5943	9	6	as	as	ADP
ejpam-5943	9	7	degree	degree	NOUN
ejpam-5943	9	8	centrality	centrality	NOUN
ejpam-5943	9	9	,	,	PUNCT
ejpam-5943	9	10	betweenness	betweenness	NOUN
ejpam-5943	9	11	centrality	centrality	NOUN
ejpam-5943	9	12	,	,	PUNCT
ejpam-5943	9	13	and	and	CCONJ
ejpam-5943	9	14	closeness	closeness	NOUN
ejpam-5943	9	15	centrality	centrality	NOUN
ejpam-5943	9	16	,	,	PUNCT
ejpam-5943	9	17	have	have	AUX
ejpam-5943	9	18	been	be	AUX
ejpam-5943	9	19	widely	widely	ADV
ejpam-5943	9	20	used	use	VERB
ejpam-5943	9	21	to	to	PART
ejpam-5943	9	22	capture	capture	VERB
ejpam-5943	9	23	different	different	ADJ
ejpam-5943	9	24	aspects	aspect	NOUN
ejpam-5943	9	25	of	of	ADP
ejpam-5943	9	26	node	node	ADJ
ejpam-5943	9	27	importance	importance	NOUN
ejpam-5943	9	28	based	base	VERB
ejpam-5943	9	29	on	on	ADP
ejpam-5943	9	30	direct	direct	ADJ
ejpam-5943	9	31	and	and	CCONJ
ejpam-5943	9	32	indirect	indirect	ADJ
ejpam-5943	9	33	connections	connection	NOUN
ejpam-5943	9	34	within	within	ADP
ejpam-5943	9	35	a	a	DET
ejpam-5943	9	36	network	network	NOUN
ejpam-5943	9	37	.	.	PUNCT
ejpam-5943	10	1	however	however	ADV
ejpam-5943	10	2	,	,	PUNCT
ejpam-5943	10	3	as	as	SCONJ
ejpam-5943	10	4	networks	network	NOUN
ejpam-5943	10	5	grow	grow	VERB
ejpam-5943	10	6	increasingly	increasingly	ADV
ejpam-5943	10	7	complex	complex	ADJ
ejpam-5943	10	8	,	,	PUNCT
ejpam-5943	10	9	these	these	DET
ejpam-5943	10	10	conventional	conventional	ADJ
ejpam-5943	10	11	measures	measure	NOUN
ejpam-5943	10	12	may	may	AUX
ejpam-5943	10	13	fail	fail	VERB
ejpam-5943	10	14	to	to	PART
ejpam-5943	10	15	fully	fully	ADV
ejpam-5943	10	16	capture	capture	VERB
ejpam-5943	10	17	the	the	DET
ejpam-5943	10	18	nuanced	nuanced	ADJ
ejpam-5943	10	19	roles	role	NOUN
ejpam-5943	10	20	that	that	PRON
ejpam-5943	10	21	certain	certain	ADJ
ejpam-5943	10	22	nodes	node	NOUN
ejpam-5943	10	23	play	play	VERB
ejpam-5943	10	24	in	in	ADP
ejpam-5943	10	25	facilitating	facilitate	VERB
ejpam-5943	10	26	information	information	NOUN
ejpam-5943	10	27	flow	flow	NOUN
ejpam-5943	10	28	and	and	CCONJ
ejpam-5943	10	29	influencing	influence	VERB
ejpam-5943	10	30	others	other	NOUN
ejpam-5943	10	31	.	.	PUNCT
ejpam-5943	11	1	a	a	DET
ejpam-5943	11	2	critical	critical	ADJ
ejpam-5943	11	3	aspect	aspect	NOUN
ejpam-5943	11	4	of	of	ADP
ejpam-5943	11	5	network	network	NOUN
ejpam-5943	11	6	analysis	analysis	NOUN
ejpam-5943	11	7	is	be	AUX
ejpam-5943	11	8	centrality	centrality	NOUN
ejpam-5943	11	9	,	,	PUNCT
ejpam-5943	11	10	which	which	PRON
ejpam-5943	11	11	represents	represent	VERB
ejpam-5943	11	12	the	the	DET
ejpam-5943	11	13	importance	importance	NOUN
ejpam-5943	11	14	of	of	ADP
ejpam-5943	11	15	a	a	DET
ejpam-5943	11	16	node	node	NOUN
ejpam-5943	11	17	by	by	ADP
ejpam-5943	11	18	its	its	PRON
ejpam-5943	11	19	position	position	NOUN
ejpam-5943	11	20	in	in	ADP
ejpam-5943	11	21	the	the	DET
ejpam-5943	11	22	network	network	NOUN
ejpam-5943	11	23	.	.	PUNCT
ejpam-5943	12	1	using	use	VERB
ejpam-5943	12	2	this	this	DET
ejpam-5943	12	3	type	type	NOUN
ejpam-5943	12	4	of	of	ADP
ejpam-5943	12	5	information	information	NOUN
ejpam-5943	12	6	about	about	ADP
ejpam-5943	12	7	social	social	ADJ
ejpam-5943	12	8	network	network	NOUN
ejpam-5943	12	9	,	,	PUNCT
ejpam-5943	12	10	linton	linton	PROPN
ejpam-5943	12	11	freeman	freeman	PROPN
ejpam-5943	12	12	in	in	ADP
ejpam-5943	12	13	1976	1976	NUM
ejpam-5943	12	14	[	[	X
ejpam-5943	12	15	1	1	X
ejpam-5943	12	16	]	]	PUNCT
ejpam-5943	12	17	first	first	ADV
ejpam-5943	12	18	proposed	propose	VERB
ejpam-5943	12	19	a	a	DET
ejpam-5943	12	20	measure	measure	NOUN
ejpam-5943	12	21	of	of	ADP
ejpam-5943	12	22	prestige	prestige	NOUN
ejpam-5943	12	23	called	call	VERB
ejpam-5943	12	24	proximity	proximity	NOUN
ejpam-5943	12	25	prestige	prestige	NOUN
ejpam-5943	12	26	.	.	PUNCT
ejpam-5943	13	1	this	this	DET
ejpam-5943	13	2	measure	measure	NOUN
ejpam-5943	13	3	,	,	PUNCT
ejpam-5943	13	4	introduced	introduce	VERB
ejpam-5943	13	5	by	by	ADP
ejpam-5943	13	6	freeman	freeman	PROPN
ejpam-5943	13	7	in	in	ADP
ejpam-5943	13	8	1970	1970	NUM
ejpam-5943	13	9	’s	’s	PART
ejpam-5943	13	10	,	,	PUNCT
ejpam-5943	13	11	considers	consider	VERB
ejpam-5943	13	12	not	not	PART
ejpam-5943	13	13	only	only	ADV
ejpam-5943	13	14	the	the	DET
ejpam-5943	13	15	number	number	NOUN
ejpam-5943	13	16	of	of	ADP
ejpam-5943	13	17	connections	connection	NOUN
ejpam-5943	13	18	a	a	DET
ejpam-5943	13	19	node	node	NOUN
ejpam-5943	13	20	has	have	VERB
ejpam-5943	13	21	but	but	CCONJ
ejpam-5943	13	22	also	also	ADV
ejpam-5943	13	23	how	how	SCONJ
ejpam-5943	13	24	accessible	accessible	ADJ
ejpam-5943	13	25	it	it	PRON
ejpam-5943	13	26	is	be	AUX
ejpam-5943	13	27	to	to	ADP
ejpam-5943	13	28	others	other	NOUN
ejpam-5943	13	29	in	in	ADP
ejpam-5943	13	30	the	the	DET
ejpam-5943	13	31	network	network	NOUN
ejpam-5943	13	32	.	.	PUNCT
ejpam-5943	14	1	proximity	proximity	NOUN
ejpam-5943	14	2	prestige	prestige	NOUN
ejpam-5943	14	3	emphasizes	emphasize	VERB
ejpam-5943	14	4	strategically	strategically	ADV
ejpam-5943	14	5	positioned	position	VERB
ejpam-5943	14	6	nodes	node	NOUN
ejpam-5943	14	7	,	,	PUNCT
ejpam-5943	14	8	by	by	ADP
ejpam-5943	14	9	providing	provide	VERB
ejpam-5943	14	10	a	a	DET
ejpam-5943	14	11	perspective	perspective	NOUN
ejpam-5943	14	12	on	on	ADP
ejpam-5943	14	13	influence	influence	NOUN
ejpam-5943	14	14	and	and	CCONJ
ejpam-5943	14	15	importance	importance	NOUN
ejpam-5943	14	16	that	that	PRON
ejpam-5943	14	17	goes	go	VERB
ejpam-5943	14	18	beyond	beyond	ADP
ejpam-5943	14	19	connectivity	connectivity	NOUN
ejpam-5943	14	20	.	.	PUNCT
ejpam-5943	15	1	this	this	PRON
ejpam-5943	15	2	focuses	focus	VERB
ejpam-5943	15	3	on	on	ADP
ejpam-5943	15	4	reach	reach	NOUN
ejpam-5943	15	5	offers	offer	VERB
ejpam-5943	15	6	a	a	DET
ejpam-5943	15	7	more	more	ADJ
ejpam-5943	15	8	∗corresponding	∗corresponding	NOUN
ejpam-5943	15	9	author	author	NOUN
ejpam-5943	15	10	.	.	PUNCT
ejpam-5943	16	1	doi	doi	NOUN
ejpam-5943	16	2	:	:	PUNCT
ejpam-5943	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5943	https://doi.org/10.29020/nybg.ejpam.v18i2.5943	ADJ
ejpam-5943	16	4	email	email	NOUN
ejpam-5943	16	5	addresses	address	VERB
ejpam-5943	16	6	:	:	PUNCT
ejpam-5943	16	7	lysatoladro@gmail.com	lysatoladro@gmail.com	X
ejpam-5943	16	8	(	(	PUNCT
ejpam-5943	16	9	l.	l.	PROPN
ejpam-5943	16	10	toladro	toladro	PROPN
ejpam-5943	16	11	)	)	PUNCT
ejpam-5943	16	12	,	,	PUNCT
ejpam-5943	16	13	isaganicabahugjr@cmu.edu.ph	isaganicabahugjr@cmu.edu.ph	PROPN
ejpam-5943	16	14	(	(	PUNCT
ejpam-5943	16	15	i.	i.	PROPN
ejpam-5943	16	16	cabahug	cabahug	PROPN
ejpam-5943	16	17	,	,	PUNCT
ejpam-5943	16	18	jr	jr	PROPN
ejpam-5943	16	19	.	.	PUNCT
ejpam-5943	16	20	)	)	PUNCT
ejpam-5943	16	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5943	17	1	1	1	NUM
ejpam-5943	17	2	copyright	copyright	NOUN
ejpam-5943	17	3	:	:	PUNCT
ejpam-5943	17	4	©	©	PROPN
ejpam-5943	17	5	2025	2025	NUM
ejpam-5943	17	6	the	the	DET
ejpam-5943	17	7	author(s	author(s	NOUN
ejpam-5943	17	8	)	)	PUNCT
ejpam-5943	17	9	.	.	PUNCT
ejpam-5943	18	1	(	(	PUNCT
ejpam-5943	18	2	cc	cc	NOUN
ejpam-5943	18	3	by	by	ADP
ejpam-5943	18	4	-	-	PUNCT
ejpam-5943	18	5	nc	nc	PROPN
ejpam-5943	18	6	4.0	4.0	NUM
ejpam-5943	18	7	)	)	PUNCT
ejpam-5943	18	8	l.	l.	PROPN
ejpam-5943	18	9	toladro	toladro	PROPN
ejpam-5943	18	10	,	,	PUNCT
ejpam-5943	18	11	i.	i.	PROPN
ejpam-5943	18	12	cabahug	cabahug	PROPN
ejpam-5943	18	13	/	/	SYM
ejpam-5943	18	14	eur	eur	PROPN
ejpam-5943	18	15	.	.	PUNCT
ejpam-5943	19	1	j.	j.	PROPN
ejpam-5943	19	2	pure	pure	PROPN
ejpam-5943	19	3	appl	appl	PROPN
ejpam-5943	19	4	.	.	PROPN
ejpam-5943	19	5	math	math	PROPN
ejpam-5943	19	6	,	,	PUNCT
ejpam-5943	19	7	18	18	NUM
ejpam-5943	19	8	(	(	PUNCT
ejpam-5943	19	9	2	2	NUM
ejpam-5943	19	10	)	)	PUNCT
ejpam-5943	19	11	(	(	PUNCT
ejpam-5943	19	12	2025	2025	NUM
ejpam-5943	19	13	)	)	PUNCT
ejpam-5943	19	14	,	,	PUNCT
ejpam-5943	19	15	5943	5943	NUM
ejpam-5943	19	16	2	2	NUM
ejpam-5943	19	17	of	of	ADP
ejpam-5943	19	18	13	13	NUM
ejpam-5943	19	19	complex	complex	ADJ
ejpam-5943	19	20	conception	conception	NOUN
ejpam-5943	19	21	of	of	ADP
ejpam-5943	19	22	influence	influence	NOUN
ejpam-5943	19	23	than	than	SCONJ
ejpam-5943	19	24	is	be	AUX
ejpam-5943	19	25	commonly	commonly	ADV
ejpam-5943	19	26	used	use	VERB
ejpam-5943	19	27	in	in	ADP
ejpam-5943	19	28	disciplines	discipline	NOUN
ejpam-5943	19	29	like	like	ADP
ejpam-5943	19	30	sociology	sociology	NOUN
ejpam-5943	19	31	and	and	CCONJ
ejpam-5943	19	32	organizational	organizational	ADJ
ejpam-5943	19	33	studies	study	NOUN
ejpam-5943	19	34	.	.	PUNCT
ejpam-5943	20	1	in	in	ADP
ejpam-5943	20	2	2015	2015	NUM
ejpam-5943	20	3	,	,	PUNCT
ejpam-5943	20	4	these	these	DET
ejpam-5943	20	5	foundational	foundational	ADJ
ejpam-5943	20	6	studies	study	NOUN
ejpam-5943	20	7	by	by	ADP
ejpam-5943	20	8	freeman	freeman	PROPN
ejpam-5943	21	1	[	[	X
ejpam-5943	21	2	1	1	NUM
ejpam-5943	21	3	]	]	PUNCT
ejpam-5943	21	4	and	and	CCONJ
ejpam-5943	21	5	zhao	zhao	X
ejpam-5943	21	6	[	[	X
ejpam-5943	21	7	2	2	X
ejpam-5943	21	8	]	]	PUNCT
ejpam-5943	21	9	motivated	motivate	VERB
ejpam-5943	21	10	the	the	DET
ejpam-5943	21	11	current	current	ADJ
ejpam-5943	21	12	investigation	investigation	NOUN
ejpam-5943	21	13	into	into	ADP
ejpam-5943	21	14	proximity	proximity	NOUN
ejpam-5943	21	15	prestige	prestige	NOUN
ejpam-5943	21	16	.	.	PUNCT
ejpam-5943	22	1	in	in	ADP
ejpam-5943	22	2	this	this	DET
ejpam-5943	22	3	paper	paper	NOUN
ejpam-5943	22	4	,	,	PUNCT
ejpam-5943	22	5	the	the	DET
ejpam-5943	22	6	researcher	researcher	NOUN
ejpam-5943	22	7	’s	’s	PART
ejpam-5943	22	8	employed	employ	VERB
ejpam-5943	22	9	the	the	DET
ejpam-5943	22	10	concept	concept	NOUN
ejpam-5943	22	11	of	of	ADP
ejpam-5943	22	12	proximity	proximity	NOUN
ejpam-5943	22	13	prestige	prestige	NOUN
ejpam-5943	22	14	to	to	PART
ejpam-5943	22	15	study	study	VERB
ejpam-5943	22	16	the	the	DET
ejpam-5943	22	17	prestige	prestige	NOUN
ejpam-5943	22	18	of	of	ADP
ejpam-5943	22	19	vertices	vertex	NOUN
ejpam-5943	22	20	in	in	ADP
ejpam-5943	22	21	nontrivial	nontrivial	NOUN
ejpam-5943	22	22	,	,	PUNCT
ejpam-5943	22	23	connected	connect	VERB
ejpam-5943	22	24	,	,	PUNCT
ejpam-5943	22	25	and	and	CCONJ
ejpam-5943	22	26	undirected	undirected	ADJ
ejpam-5943	22	27	graphs	graph	NOUN
ejpam-5943	22	28	utilizing	utilize	VERB
ejpam-5943	22	29	the	the	DET
ejpam-5943	22	30	results	result	NOUN
ejpam-5943	22	31	established	establish	VERB
ejpam-5943	22	32	by	by	ADP
ejpam-5943	22	33	zhao	zhao	PROPN
ejpam-5943	22	34	et	et	PROPN
ejpam-5943	22	35	al	al	PROPN
ejpam-5943	22	36	.	.	PUNCT
ejpam-5943	23	1	[	[	X
ejpam-5943	23	2	2	2	NUM
ejpam-5943	23	3	]	]	PUNCT
ejpam-5943	23	4	.	.	PUNCT
ejpam-5943	24	1	by	by	ADP
ejpam-5943	24	2	extending	extend	VERB
ejpam-5943	24	3	their	their	PRON
ejpam-5943	24	4	work	work	NOUN
ejpam-5943	24	5	,	,	PUNCT
ejpam-5943	24	6	this	this	DET
ejpam-5943	24	7	study	study	NOUN
ejpam-5943	24	8	contributes	contribute	VERB
ejpam-5943	24	9	to	to	ADP
ejpam-5943	24	10	a	a	DET
ejpam-5943	24	11	deeper	deep	ADJ
ejpam-5943	24	12	understanding	understanding	NOUN
ejpam-5943	24	13	of	of	ADP
ejpam-5943	24	14	how	how	SCONJ
ejpam-5943	24	15	proximity	proximity	NOUN
ejpam-5943	24	16	prestige	prestige	NOUN
ejpam-5943	24	17	can	can	AUX
ejpam-5943	24	18	be	be	AUX
ejpam-5943	24	19	used	use	VERB
ejpam-5943	24	20	to	to	PART
ejpam-5943	24	21	evaluate	evaluate	VERB
ejpam-5943	24	22	node	node	ADJ
ejpam-5943	24	23	importance	importance	NOUN
ejpam-5943	24	24	in	in	ADP
ejpam-5943	24	25	various	various	ADJ
ejpam-5943	24	26	types	type	NOUN
ejpam-5943	24	27	of	of	ADP
ejpam-5943	24	28	networks	network	NOUN
ejpam-5943	24	29	,	,	PUNCT
ejpam-5943	24	30	particularly	particularly	ADV
ejpam-5943	24	31	in	in	ADP
ejpam-5943	24	32	settings	setting	NOUN
ejpam-5943	24	33	where	where	SCONJ
ejpam-5943	24	34	indirect	indirect	ADJ
ejpam-5943	24	35	influence	influence	NOUN
ejpam-5943	24	36	is	be	AUX
ejpam-5943	24	37	a	a	DET
ejpam-5943	24	38	critical	critical	ADJ
ejpam-5943	24	39	factor	factor	NOUN
ejpam-5943	24	40	.	.	PUNCT
ejpam-5943	25	1	this	this	DET
ejpam-5943	25	2	paper	paper	NOUN
ejpam-5943	25	3	explores	explore	VERB
ejpam-5943	25	4	the	the	DET
ejpam-5943	25	5	formal	formal	ADJ
ejpam-5943	25	6	definition	definition	NOUN
ejpam-5943	25	7	of	of	ADP
ejpam-5943	25	8	proximity	proximity	NOUN
ejpam-5943	25	9	prestige	prestige	NOUN
ejpam-5943	25	10	as	as	SCONJ
ejpam-5943	25	11	it	it	PRON
ejpam-5943	25	12	applies	apply	VERB
ejpam-5943	25	13	to	to	ADP
ejpam-5943	25	14	vertices	vertex	NOUN
ejpam-5943	25	15	in	in	ADP
ejpam-5943	25	16	a	a	DET
ejpam-5943	25	17	graph	graph	NOUN
ejpam-5943	25	18	,	,	PUNCT
ejpam-5943	25	19	providing	provide	VERB
ejpam-5943	25	20	a	a	DET
ejpam-5943	25	21	mathematical	mathematical	ADJ
ejpam-5943	25	22	framework	framework	NOUN
ejpam-5943	25	23	for	for	ADP
ejpam-5943	25	24	calculating	calculate	VERB
ejpam-5943	25	25	node	node	ADJ
ejpam-5943	25	26	importance	importance	NOUN
ejpam-5943	25	27	based	base	VERB
ejpam-5943	25	28	on	on	ADP
ejpam-5943	25	29	their	their	PRON
ejpam-5943	25	30	indirect	indirect	ADJ
ejpam-5943	25	31	connections	connection	NOUN
ejpam-5943	25	32	.	.	PUNCT
ejpam-5943	26	1	other	other	ADJ
ejpam-5943	26	2	studies	study	NOUN
ejpam-5943	26	3	that	that	PRON
ejpam-5943	26	4	deal	deal	VERB
ejpam-5943	26	5	with	with	ADP
ejpam-5943	26	6	the	the	DET
ejpam-5943	26	7	concept	concept	NOUN
ejpam-5943	26	8	of	of	ADP
ejpam-5943	26	9	centralities	centrality	NOUN
ejpam-5943	26	10	are	be	AUX
ejpam-5943	26	11	located	locate	VERB
ejpam-5943	26	12	in	in	ADP
ejpam-5943	26	13	[	[	X
ejpam-5943	26	14	3	3	NUM
ejpam-5943	26	15	]	]	PUNCT
ejpam-5943	26	16	and	and	CCONJ
ejpam-5943	26	17	[	[	X
ejpam-5943	26	18	4	4	NUM
ejpam-5943	26	19	]	]	PUNCT
ejpam-5943	26	20	.	.	PUNCT
ejpam-5943	27	1	for	for	ADP
ejpam-5943	27	2	graph	graph	NOUN
ejpam-5943	27	3	-	-	PUNCT
ejpam-5943	27	4	theoretic	theoretic	NOUN
ejpam-5943	27	5	terminologies	terminology	NOUN
ejpam-5943	27	6	not	not	PART
ejpam-5943	27	7	specifically	specifically	ADV
ejpam-5943	27	8	defined	define	VERB
ejpam-5943	27	9	nor	nor	CCONJ
ejpam-5943	27	10	described	describe	VERB
ejpam-5943	27	11	in	in	ADP
ejpam-5943	27	12	this	this	DET
ejpam-5943	27	13	study	study	NOUN
ejpam-5943	27	14	,	,	PUNCT
ejpam-5943	27	15	please	please	INTJ
ejpam-5943	27	16	refer	refer	VERB
ejpam-5943	27	17	to	to	ADP
ejpam-5943	27	18	either	either	CCONJ
ejpam-5943	27	19	[	[	X
ejpam-5943	27	20	5	5	NUM
ejpam-5943	27	21	]	]	PUNCT
ejpam-5943	27	22	or	or	CCONJ
ejpam-5943	27	23	[	[	X
ejpam-5943	27	24	6	6	NUM
ejpam-5943	27	25	]	]	PUNCT
ejpam-5943	27	26	.	.	PUNCT
ejpam-5943	28	1	therefore	therefore	ADV
ejpam-5943	28	2	,	,	PUNCT
ejpam-5943	28	3	all	all	DET
ejpam-5943	28	4	graphs	graph	NOUN
ejpam-5943	28	5	considered	consider	VERB
ejpam-5943	28	6	in	in	ADP
ejpam-5943	28	7	this	this	DET
ejpam-5943	28	8	study	study	NOUN
ejpam-5943	28	9	are	be	AUX
ejpam-5943	28	10	nontrivial	nontrivial	ADJ
ejpam-5943	28	11	,	,	PUNCT
ejpam-5943	28	12	connected	connected	ADJ
ejpam-5943	28	13	and	and	CCONJ
ejpam-5943	28	14	undirected	undirected	ADJ
ejpam-5943	28	15	.	.	PUNCT
ejpam-5943	29	1	2	2	X
ejpam-5943	29	2	.	.	X
ejpam-5943	29	3	terminology	terminology	NOUN
ejpam-5943	29	4	and	and	CCONJ
ejpam-5943	29	5	notation	notation	NOUN
ejpam-5943	29	6	2.1	2.1	NUM
ejpam-5943	29	7	.	.	PUNCT
ejpam-5943	30	1	preliminary	preliminary	ADJ
ejpam-5943	30	2	concepts	concept	NOUN
ejpam-5943	30	3	a	a	DET
ejpam-5943	30	4	graph	graph	NOUN
ejpam-5943	30	5	g	g	NOUN
ejpam-5943	30	6	is	be	AUX
ejpam-5943	30	7	a	a	DET
ejpam-5943	30	8	finite	finite	NOUN
ejpam-5943	30	9	nonempty	nonempty	ADV
ejpam-5943	30	10	set	set	VERB
ejpam-5943	30	11	v	v	NOUN
ejpam-5943	30	12	of	of	ADP
ejpam-5943	30	13	objects	object	NOUN
ejpam-5943	30	14	called	call	VERB
ejpam-5943	30	15	vertices	vertex	NOUN
ejpam-5943	30	16	together	together	ADV
ejpam-5943	30	17	with	with	ADP
ejpam-5943	30	18	a	a	DET
ejpam-5943	30	19	possibly	possibly	ADV
ejpam-5943	30	20	empty	empty	ADJ
ejpam-5943	30	21	set	set	ADJ
ejpam-5943	30	22	e	e	NOUN
ejpam-5943	30	23	of	of	ADP
ejpam-5943	30	24	2	2	NUM
ejpam-5943	30	25	-	-	PUNCT
ejpam-5943	30	26	element	element	NOUN
ejpam-5943	30	27	sets	set	NOUN
ejpam-5943	30	28	of	of	ADP
ejpam-5943	30	29	v	v	NOUN
ejpam-5943	30	30	called	call	VERB
ejpam-5943	30	31	edges	edge	NOUN
ejpam-5943	30	32	.	.	PUNCT
ejpam-5943	31	1	to	to	PART
ejpam-5943	31	2	indicate	indicate	VERB
ejpam-5943	31	3	that	that	SCONJ
ejpam-5943	31	4	a	a	DET
ejpam-5943	31	5	graph	graph	NOUN
ejpam-5943	31	6	g	g	NOUN
ejpam-5943	31	7	has	have	VERB
ejpam-5943	31	8	vertex	vertex	NOUN
ejpam-5943	31	9	set	set	VERB
ejpam-5943	31	10	v	v	NOUN
ejpam-5943	31	11	and	and	CCONJ
ejpam-5943	31	12	edge	edge	NOUN
ejpam-5943	31	13	set	set	ADJ
ejpam-5943	31	14	e	e	NOUN
ejpam-5943	31	15	,	,	PUNCT
ejpam-5943	31	16	we	we	PRON
ejpam-5943	31	17	write	write	VERB
ejpam-5943	31	18	g	g	PROPN
ejpam-5943	31	19	=	=	SYM
ejpam-5943	31	20	(	(	PUNCT
ejpam-5943	31	21	v	v	NOUN
ejpam-5943	31	22	,	,	PUNCT
ejpam-5943	31	23	e	e	NOUN
ejpam-5943	31	24	)	)	PUNCT
ejpam-5943	31	25	.	.	PUNCT
ejpam-5943	32	1	to	to	PART
ejpam-5943	32	2	emphasize	emphasize	VERB
ejpam-5943	32	3	that	that	DET
ejpam-5943	32	4	v	v	NOUN
ejpam-5943	32	5	and	and	CCONJ
ejpam-5943	32	6	e	e	NOUN
ejpam-5943	32	7	are	be	AUX
ejpam-5943	32	8	the	the	DET
ejpam-5943	32	9	vertex	vertex	NOUN
ejpam-5943	32	10	set	set	NOUN
ejpam-5943	32	11	and	and	CCONJ
ejpam-5943	32	12	edge	edge	NOUN
ejpam-5943	32	13	set	set	NOUN
ejpam-5943	32	14	of	of	ADP
ejpam-5943	32	15	a	a	DET
ejpam-5943	32	16	graph	graph	NOUN
ejpam-5943	32	17	g	g	NOUN
ejpam-5943	32	18	,	,	PUNCT
ejpam-5943	32	19	we	we	PRON
ejpam-5943	32	20	often	often	ADV
ejpam-5943	32	21	write	write	VERB
ejpam-5943	32	22	v	v	NOUN
ejpam-5943	32	23	as	as	ADP
ejpam-5943	32	24	v	v	NOUN
ejpam-5943	32	25	(	(	PUNCT
ejpam-5943	32	26	g	g	NOUN
ejpam-5943	32	27	)	)	PUNCT
ejpam-5943	32	28	and	and	CCONJ
ejpam-5943	32	29	e	e	NOUN
ejpam-5943	32	30	as	as	ADP
ejpam-5943	32	31	e(g	e(g	PROPN
ejpam-5943	32	32	)	)	PUNCT
ejpam-5943	32	33	.	.	PUNCT
ejpam-5943	33	1	each	each	DET
ejpam-5943	33	2	edge	edge	NOUN
ejpam-5943	33	3	{	{	PUNCT
ejpam-5943	33	4	u	u	NOUN
ejpam-5943	33	5	,	,	PUNCT
ejpam-5943	33	6	v	v	NOUN
ejpam-5943	33	7	}	}	PUNCT
ejpam-5943	33	8	of	of	ADP
ejpam-5943	33	9	g	g	PROPN
ejpam-5943	33	10	is	be	AUX
ejpam-5943	33	11	usually	usually	ADV
ejpam-5943	33	12	denoted	denote	VERB
ejpam-5943	33	13	by	by	ADP
ejpam-5943	33	14	uv	uv	NOUN
ejpam-5943	33	15	or	or	CCONJ
ejpam-5943	33	16	vu	vu	NOUN
ejpam-5943	33	17	.	.	PUNCT
ejpam-5943	34	1	the	the	DET
ejpam-5943	34	2	number	number	NOUN
ejpam-5943	34	3	of	of	ADP
ejpam-5943	34	4	vertices	vertex	NOUN
ejpam-5943	34	5	in	in	ADP
ejpam-5943	34	6	a	a	DET
ejpam-5943	34	7	graph	graph	NOUN
ejpam-5943	34	8	g	g	NOUN
ejpam-5943	34	9	is	be	AUX
ejpam-5943	34	10	the	the	DET
ejpam-5943	34	11	order	order	NOUN
ejpam-5943	34	12	of	of	ADP
ejpam-5943	34	13	g	g	NOUN
ejpam-5943	34	14	and	and	CCONJ
ejpam-5943	34	15	the	the	DET
ejpam-5943	34	16	number	number	NOUN
ejpam-5943	34	17	of	of	ADP
ejpam-5943	34	18	edges	edge	NOUN
ejpam-5943	34	19	is	be	AUX
ejpam-5943	34	20	the	the	DET
ejpam-5943	34	21	sizeof	sizeof	ADJ
ejpam-5943	34	22	g.	g.	NOUN
ejpam-5943	35	1	the	the	DET
ejpam-5943	35	2	degree	degree	NOUN
ejpam-5943	35	3	of	of	ADP
ejpam-5943	35	4	a	a	DET
ejpam-5943	35	5	vertex	vertex	NOUN
ejpam-5943	35	6	v	v	NOUN
ejpam-5943	35	7	in	in	ADP
ejpam-5943	35	8	a	a	DET
ejpam-5943	35	9	graph	graph	NOUN
ejpam-5943	35	10	g	g	NOUN
ejpam-5943	35	11	is	be	AUX
ejpam-5943	35	12	the	the	DET
ejpam-5943	35	13	number	number	NOUN
ejpam-5943	35	14	of	of	ADP
ejpam-5943	35	15	edges	edge	NOUN
ejpam-5943	35	16	incident	incident	NOUN
ejpam-5943	35	17	with	with	ADP
ejpam-5943	35	18	v	v	NOUN
ejpam-5943	35	19	and	and	CCONJ
ejpam-5943	35	20	is	be	AUX
ejpam-5943	35	21	denoted	denote	VERB
ejpam-5943	35	22	by	by	ADP
ejpam-5943	35	23	deg	deg	PROPN
ejpam-5943	35	24	v	v	NOUN
ejpam-5943	35	25	or	or	CCONJ
ejpam-5943	35	26	simply	simply	ADV
ejpam-5943	35	27	by	by	ADP
ejpam-5943	35	28	deg	deg	PROPN
ejpam-5943	35	29	v.	v.	CCONJ
ejpam-5943	35	30	the	the	DET
ejpam-5943	35	31	degree	degree	NOUN
ejpam-5943	35	32	of	of	ADP
ejpam-5943	35	33	a	a	DET
ejpam-5943	35	34	vertex	vertex	NOUN
ejpam-5943	35	35	v	v	NOUN
ejpam-5943	35	36	is	be	AUX
ejpam-5943	35	37	denoted	denote	VERB
ejpam-5943	35	38	by	by	ADP
ejpam-5943	35	39	deg(v	deg(v	PROPN
ejpam-5943	35	40	)	)	PUNCT
ejpam-5943	35	41	and	and	CCONJ
ejpam-5943	35	42	the	the	DET
ejpam-5943	35	43	minimum	minimum	NOUN
ejpam-5943	35	44	degree	degree	NOUN
ejpam-5943	35	45	of	of	ADP
ejpam-5943	35	46	g	g	PROPN
ejpam-5943	35	47	is	be	AUX
ejpam-5943	35	48	denoted	denote	VERB
ejpam-5943	35	49	by	by	ADP
ejpam-5943	35	50	δ(g	δ(g	NOUN
ejpam-5943	35	51	)	)	PUNCT
ejpam-5943	35	52	and	and	CCONJ
ejpam-5943	35	53	the	the	DET
ejpam-5943	35	54	maximum	maximum	ADJ
ejpam-5943	35	55	degree	degree	NOUN
ejpam-5943	35	56	of	of	ADP
ejpam-5943	35	57	g	g	PROPN
ejpam-5943	35	58	is	be	AUX
ejpam-5943	35	59	denoted	denote	VERB
ejpam-5943	35	60	by	by	ADP
ejpam-5943	35	61	∆(g	∆(g	PROPN
ejpam-5943	35	62	)	)	PUNCT
ejpam-5943	36	1	[	[	X
ejpam-5943	36	2	7	7	NUM
ejpam-5943	36	3	]	]	PUNCT
ejpam-5943	36	4	.	.	PUNCT
ejpam-5943	37	1	if	if	SCONJ
ejpam-5943	37	2	uv	uv	NOUN
ejpam-5943	37	3	is	be	AUX
ejpam-5943	37	4	an	an	DET
ejpam-5943	37	5	edge	edge	NOUN
ejpam-5943	37	6	of	of	ADP
ejpam-5943	37	7	g	g	NOUN
ejpam-5943	37	8	,	,	PUNCT
ejpam-5943	37	9	then	then	ADV
ejpam-5943	37	10	u	u	NOUN
ejpam-5943	37	11	and	and	CCONJ
ejpam-5943	37	12	v	v	NOUN
ejpam-5943	37	13	are	be	AUX
ejpam-5943	37	14	adjacent	adjacent	ADJ
ejpam-5943	37	15	vertices	vertex	NOUN
ejpam-5943	37	16	.	.	PUNCT
ejpam-5943	38	1	two	two	NUM
ejpam-5943	38	2	adjacent	adjacent	ADJ
ejpam-5943	38	3	vertices	vertex	NOUN
ejpam-5943	38	4	are	be	AUX
ejpam-5943	38	5	referred	refer	VERB
ejpam-5943	38	6	to	to	ADP
ejpam-5943	38	7	as	as	ADP
ejpam-5943	38	8	neighbors	neighbor	NOUN
ejpam-5943	38	9	of	of	ADP
ejpam-5943	38	10	each	each	DET
ejpam-5943	38	11	other	other	ADJ
ejpam-5943	38	12	.	.	PUNCT
ejpam-5943	39	1	the	the	DET
ejpam-5943	39	2	set	set	NOUN
ejpam-5943	39	3	of	of	ADP
ejpam-5943	39	4	neighbors	neighbor	NOUN
ejpam-5943	39	5	of	of	ADP
ejpam-5943	39	6	a	a	DET
ejpam-5943	39	7	vertex	vertex	NOUN
ejpam-5943	39	8	v	v	NOUN
ejpam-5943	39	9	is	be	AUX
ejpam-5943	39	10	called	call	VERB
ejpam-5943	39	11	the	the	DET
ejpam-5943	39	12	open	open	ADJ
ejpam-5943	39	13	neighborhood	neighborhood	NOUN
ejpam-5943	39	14	of	of	ADP
ejpam-5943	39	15	v	v	NOUN
ejpam-5943	39	16	(	(	PUNCT
ejpam-5943	39	17	or	or	CCONJ
ejpam-5943	39	18	simply	simply	ADV
ejpam-5943	39	19	the	the	DET
ejpam-5943	39	20	neighborhood	neighborhood	NOUN
ejpam-5943	39	21	of	of	ADP
ejpam-5943	39	22	v	v	NOUN
ejpam-5943	39	23	)	)	PUNCT
ejpam-5943	39	24	and	and	CCONJ
ejpam-5943	39	25	is	be	AUX
ejpam-5943	39	26	denoted	denote	VERB
ejpam-5943	39	27	by	by	ADP
ejpam-5943	39	28	ng(v	ng(v	NOUN
ejpam-5943	39	29	)	)	PUNCT
ejpam-5943	39	30	or	or	CCONJ
ejpam-5943	39	31	n(v	n(v	PROPN
ejpam-5943	39	32	)	)	PUNCT
ejpam-5943	39	33	if	if	SCONJ
ejpam-5943	39	34	the	the	DET
ejpam-5943	39	35	graph	graph	NOUN
ejpam-5943	39	36	is	be	AUX
ejpam-5943	39	37	understood	understand	VERB
ejpam-5943	39	38	.	.	PUNCT
ejpam-5943	40	1	the	the	DET
ejpam-5943	40	2	set	set	ADJ
ejpam-5943	40	3	n	n	PROPN
ejpam-5943	40	4	[	[	X
ejpam-5943	40	5	v	v	X
ejpam-5943	40	6	]	]	X
ejpam-5943	40	7	=	=	PUNCT
ejpam-5943	40	8	n(v	n(v	PROPN
ejpam-5943	40	9	)	)	PUNCT
ejpam-5943	40	10	∪	∪	NOUN
ejpam-5943	40	11	{	{	PUNCT
ejpam-5943	40	12	v	v	NOUN
ejpam-5943	40	13	}	}	PUNCT
ejpam-5943	40	14	is	be	AUX
ejpam-5943	40	15	called	call	VERB
ejpam-5943	40	16	the	the	DET
ejpam-5943	40	17	closed	closed	ADJ
ejpam-5943	40	18	neighborhood	neighborhood	NOUN
ejpam-5943	40	19	of	of	ADP
ejpam-5943	40	20	v.	v.	ADV
ejpam-5943	40	21	if	if	SCONJ
ejpam-5943	40	22	uv	uv	PROPN
ejpam-5943	40	23	and	and	CCONJ
ejpam-5943	40	24	vw	vw	PROPN
ejpam-5943	40	25	are	be	AUX
ejpam-5943	40	26	distinct	distinct	ADJ
ejpam-5943	40	27	edges	edge	NOUN
ejpam-5943	40	28	in	in	ADP
ejpam-5943	40	29	g	g	NOUN
ejpam-5943	40	30	,	,	PUNCT
ejpam-5943	40	31	then	then	ADV
ejpam-5943	40	32	uv	uv	PROPN
ejpam-5943	40	33	and	and	CCONJ
ejpam-5943	40	34	vw	vw	PROPN
ejpam-5943	40	35	are	be	AUX
ejpam-5943	40	36	adjacent	adjacent	ADJ
ejpam-5943	40	37	edges	edge	NOUN
ejpam-5943	40	38	.	.	PUNCT
ejpam-5943	41	1	the	the	DET
ejpam-5943	41	2	vertex	vertex	NOUN
ejpam-5943	41	3	u	u	NOUN
ejpam-5943	41	4	and	and	CCONJ
ejpam-5943	41	5	the	the	DET
ejpam-5943	41	6	edge	edge	NOUN
ejpam-5943	41	7	uv	uv	NOUN
ejpam-5943	41	8	are	be	AUX
ejpam-5943	41	9	said	say	VERB
ejpam-5943	41	10	to	to	PART
ejpam-5943	41	11	be	be	AUX
ejpam-5943	41	12	incident	incident	NOUN
ejpam-5943	41	13	with	with	ADP
ejpam-5943	41	14	each	each	DET
ejpam-5943	41	15	other	other	ADJ
ejpam-5943	41	16	.	.	PUNCT
ejpam-5943	42	1	similarly	similarly	ADV
ejpam-5943	42	2	,	,	PUNCT
ejpam-5943	42	3	v	v	NOUN
ejpam-5943	42	4	and	and	CCONJ
ejpam-5943	42	5	uv	uv	NOUN
ejpam-5943	42	6	are	be	AUX
ejpam-5943	42	7	incident	incident	NOUN
ejpam-5943	42	8	[	[	X
ejpam-5943	42	9	7	7	NUM
ejpam-5943	42	10	]	]	PUNCT
ejpam-5943	42	11	.	.	PUNCT
ejpam-5943	43	1	a	a	DET
ejpam-5943	43	2	graph	graph	NOUN
ejpam-5943	43	3	of	of	ADP
ejpam-5943	43	4	order	order	NOUN
ejpam-5943	43	5	1	1	NUM
ejpam-5943	43	6	is	be	AUX
ejpam-5943	43	7	called	call	VERB
ejpam-5943	43	8	a	a	DET
ejpam-5943	43	9	trivial	trivial	ADJ
ejpam-5943	43	10	graph	graph	NOUN
ejpam-5943	43	11	.	.	PUNCT
ejpam-5943	44	1	a	a	DET
ejpam-5943	44	2	nontrivial	nontrivial	ADJ
ejpam-5943	44	3	graph	graph	NOUN
ejpam-5943	44	4	therefore	therefore	ADV
ejpam-5943	44	5	has	have	VERB
ejpam-5943	44	6	two	two	NUM
ejpam-5943	44	7	or	or	CCONJ
ejpam-5943	44	8	more	more	ADJ
ejpam-5943	44	9	vertices	vertex	NOUN
ejpam-5943	44	10	.	.	PUNCT
ejpam-5943	45	1	a	a	DET
ejpam-5943	45	2	graph	graph	NOUN
ejpam-5943	45	3	of	of	ADP
ejpam-5943	45	4	size	size	NOUN
ejpam-5943	45	5	0	0	NUM
ejpam-5943	45	6	is	be	AUX
ejpam-5943	45	7	called	call	VERB
ejpam-5943	45	8	an	an	DET
ejpam-5943	45	9	empty	empty	ADJ
ejpam-5943	45	10	graph	graph	NOUN
ejpam-5943	45	11	.	.	PUNCT
ejpam-5943	46	1	a	a	DET
ejpam-5943	46	2	nonempty	nonempty	ADJ
ejpam-5943	46	3	graph	graph	NOUN
ejpam-5943	46	4	then	then	ADV
ejpam-5943	46	5	has	have	VERB
ejpam-5943	46	6	one	one	NUM
ejpam-5943	46	7	or	or	CCONJ
ejpam-5943	46	8	more	more	ADJ
ejpam-5943	46	9	edges	edge	NOUN
ejpam-5943	46	10	.	.	PUNCT
ejpam-5943	47	1	in	in	ADP
ejpam-5943	47	2	any	any	DET
ejpam-5943	47	3	empty	empty	ADJ
ejpam-5943	47	4	graph	graph	NOUN
ejpam-5943	47	5	,	,	PUNCT
ejpam-5943	47	6	no	no	DET
ejpam-5943	47	7	two	two	NUM
ejpam-5943	47	8	vertices	vertex	NOUN
ejpam-5943	47	9	are	be	AUX
ejpam-5943	47	10	adjacent	adjacent	ADJ
ejpam-5943	47	11	[	[	X
ejpam-5943	47	12	7	7	NUM
ejpam-5943	47	13	]	]	PUNCT
ejpam-5943	47	14	.	.	PUNCT
ejpam-5943	48	1	a	a	DET
ejpam-5943	48	2	u−	u−	PROPN
ejpam-5943	48	3	v	v	NUM
ejpam-5943	48	4	walk	walk	NOUN
ejpam-5943	48	5	w	w	NOUN
ejpam-5943	48	6	in	in	ADP
ejpam-5943	48	7	g	g	PROPN
ejpam-5943	48	8	is	be	AUX
ejpam-5943	48	9	a	a	DET
ejpam-5943	48	10	sequence	sequence	NOUN
ejpam-5943	48	11	of	of	ADP
ejpam-5943	48	12	vertices	vertex	NOUN
ejpam-5943	48	13	in	in	ADP
ejpam-5943	48	14	g	g	NOUN
ejpam-5943	48	15	,	,	PUNCT
ejpam-5943	48	16	beginning	begin	VERB
ejpam-5943	48	17	with	with	ADP
ejpam-5943	48	18	u	u	NOUN
ejpam-5943	48	19	and	and	CCONJ
ejpam-5943	48	20	ending	end	VERB
ejpam-5943	48	21	at	at	ADP
ejpam-5943	48	22	v	v	ADP
ejpam-5943	48	23	such	such	DET
ejpam-5943	48	24	that	that	DET
ejpam-5943	48	25	consecutive	consecutive	ADJ
ejpam-5943	48	26	vertices	vertex	NOUN
ejpam-5943	48	27	in	in	ADP
ejpam-5943	48	28	the	the	DET
ejpam-5943	48	29	sequence	sequence	NOUN
ejpam-5943	48	30	are	be	AUX
ejpam-5943	48	31	adjacent	adjacent	ADJ
ejpam-5943	48	32	.	.	PUNCT
ejpam-5943	49	1	a	a	DET
ejpam-5943	49	2	u−	u−	PROPN
ejpam-5943	49	3	v	v	ADJ
ejpam-5943	49	4	walk	walk	NOUN
ejpam-5943	49	5	in	in	ADP
ejpam-5943	49	6	a	a	DET
ejpam-5943	49	7	graph	graph	NOUN
ejpam-5943	49	8	in	in	ADP
ejpam-5943	49	9	which	which	PRON
ejpam-5943	49	10	no	no	DET
ejpam-5943	49	11	vertices	vertex	NOUN
ejpam-5943	49	12	are	be	AUX
ejpam-5943	49	13	repeated	repeat	VERB
ejpam-5943	49	14	is	be	AUX
ejpam-5943	49	15	a	a	DET
ejpam-5943	49	16	u−	u−	PROPN
ejpam-5943	49	17	v	v	NUM
ejpam-5943	49	18	path	path	NOUN
ejpam-5943	49	19	.	.	PUNCT
ejpam-5943	50	1	the	the	DET
ejpam-5943	50	2	distance	distance	NOUN
ejpam-5943	50	3	dg(u	dg(u	NOUN
ejpam-5943	50	4	,	,	PUNCT
ejpam-5943	50	5	v	v	NOUN
ejpam-5943	50	6	)	)	PUNCT
ejpam-5943	50	7	from	from	ADP
ejpam-5943	50	8	a	a	DET
ejpam-5943	50	9	vertex	vertex	NOUN
ejpam-5943	50	10	u	u	NOUN
ejpam-5943	50	11	to	to	ADP
ejpam-5943	50	12	a	a	DET
ejpam-5943	50	13	vertex	vertex	NOUN
ejpam-5943	50	14	v	v	NOUN
ejpam-5943	50	15	in	in	ADP
ejpam-5943	50	16	a	a	DET
ejpam-5943	50	17	connected	connected	ADJ
ejpam-5943	50	18	graph	graph	NOUN
ejpam-5943	50	19	g	g	PROPN
ejpam-5943	50	20	is	be	AUX
ejpam-5943	50	21	the	the	DET
ejpam-5943	50	22	length	length	NOUN
ejpam-5943	50	23	of	of	ADP
ejpam-5943	50	24	a	a	DET
ejpam-5943	50	25	shortest	short	ADJ
ejpam-5943	50	26	u−	u−	NOUN
ejpam-5943	50	27	v	v	ADJ
ejpam-5943	50	28	path	path	NOUN
ejpam-5943	50	29	in	in	ADP
ejpam-5943	50	30	g.	g.	PROPN
ejpam-5943	51	1	if	if	SCONJ
ejpam-5943	51	2	the	the	DET
ejpam-5943	51	3	graph	graph	NOUN
ejpam-5943	51	4	l.	l.	PROPN
ejpam-5943	51	5	toladro	toladro	PROPN
ejpam-5943	51	6	,	,	PUNCT
ejpam-5943	51	7	i.	i.	PROPN
ejpam-5943	51	8	cabahug	cabahug	PROPN
ejpam-5943	51	9	/	/	SYM
ejpam-5943	51	10	eur	eur	PROPN
ejpam-5943	51	11	.	.	PUNCT
ejpam-5943	52	1	j.	j.	PROPN
ejpam-5943	52	2	pure	pure	PROPN
ejpam-5943	52	3	appl	appl	PROPN
ejpam-5943	52	4	.	.	PROPN
ejpam-5943	52	5	math	math	PROPN
ejpam-5943	52	6	,	,	PUNCT
ejpam-5943	52	7	18	18	NUM
ejpam-5943	52	8	(	(	PUNCT
ejpam-5943	52	9	2	2	NUM
ejpam-5943	52	10	)	)	PUNCT
ejpam-5943	52	11	(	(	PUNCT
ejpam-5943	52	12	2025	2025	NUM
ejpam-5943	52	13	)	)	PUNCT
ejpam-5943	52	14	,	,	PUNCT
ejpam-5943	52	15	5943	5943	NUM
ejpam-5943	52	16	3	3	NUM
ejpam-5943	52	17	of	of	ADP
ejpam-5943	52	18	13	13	NUM
ejpam-5943	52	19	g	g	NOUN
ejpam-5943	52	20	being	be	AUX
ejpam-5943	52	21	considered	consider	VERB
ejpam-5943	52	22	is	be	AUX
ejpam-5943	52	23	understood	understand	VERB
ejpam-5943	52	24	,	,	PUNCT
ejpam-5943	52	25	then	then	ADV
ejpam-5943	52	26	this	this	DET
ejpam-5943	52	27	distance	distance	NOUN
ejpam-5943	52	28	is	be	AUX
ejpam-5943	52	29	written	write	VERB
ejpam-5943	52	30	more	more	ADV
ejpam-5943	52	31	simply	simply	ADV
ejpam-5943	52	32	as	as	ADP
ejpam-5943	52	33	d(u	d(u	PROPN
ejpam-5943	52	34	,	,	PUNCT
ejpam-5943	52	35	v	v	NOUN
ejpam-5943	52	36	)	)	PUNCT
ejpam-5943	52	37	.	.	PUNCT
ejpam-5943	53	1	a	a	DET
ejpam-5943	53	2	u−	u−	PROPN
ejpam-5943	53	3	v	v	ADP
ejpam-5943	53	4	path	path	NOUN
ejpam-5943	53	5	of	of	ADP
ejpam-5943	53	6	length	length	NOUN
ejpam-5943	53	7	d(u	d(u	PROPN
ejpam-5943	53	8	,	,	PUNCT
ejpam-5943	53	9	v	v	NOUN
ejpam-5943	53	10	)	)	PUNCT
ejpam-5943	53	11	is	be	AUX
ejpam-5943	53	12	called	call	VERB
ejpam-5943	53	13	a	a	DET
ejpam-5943	53	14	u−	u−	PROPN
ejpam-5943	53	15	v	v	ADJ
ejpam-5943	53	16	geodesic	geodesic	NOUN
ejpam-5943	53	17	[	[	X
ejpam-5943	53	18	7	7	NUM
ejpam-5943	53	19	]	]	PUNCT
ejpam-5943	53	20	.	.	PUNCT
ejpam-5943	54	1	for	for	ADP
ejpam-5943	54	2	an	an	DET
ejpam-5943	54	3	integer	integer	NOUN
ejpam-5943	54	4	n	n	PRON
ejpam-5943	54	5	≥	≥	NOUN
ejpam-5943	54	6	1	1	NUM
ejpam-5943	54	7	,	,	PUNCT
ejpam-5943	54	8	the	the	DET
ejpam-5943	54	9	path	path	NOUN
ejpam-5943	54	10	pn	pn	PROPN
ejpam-5943	54	11	is	be	AUX
ejpam-5943	54	12	a	a	DET
ejpam-5943	54	13	graph	graph	NOUN
ejpam-5943	54	14	of	of	ADP
ejpam-5943	54	15	order	order	NOUN
ejpam-5943	54	16	n	n	NOUN
ejpam-5943	54	17	and	and	CCONJ
ejpam-5943	54	18	size	size	NOUN
ejpam-5943	54	19	n−	n−	PROPN
ejpam-5943	54	20	1	1	NUM
ejpam-5943	54	21	whose	whose	DET
ejpam-5943	54	22	vertices	vertex	NOUN
ejpam-5943	54	23	can	can	AUX
ejpam-5943	54	24	be	be	AUX
ejpam-5943	54	25	labeled	label	VERB
ejpam-5943	54	26	by	by	ADP
ejpam-5943	54	27	v1	v1	NOUN
ejpam-5943	54	28	,	,	PUNCT
ejpam-5943	54	29	v2	v2	PROPN
ejpam-5943	54	30	,	,	PUNCT
ejpam-5943	54	31	...	...	PUNCT
ejpam-5943	54	32	,	,	PUNCT
ejpam-5943	54	33	vn	vn	PROPN
ejpam-5943	54	34	and	and	CCONJ
ejpam-5943	54	35	whose	whose	DET
ejpam-5943	54	36	edges	edge	NOUN
ejpam-5943	54	37	are	be	AUX
ejpam-5943	54	38	vivi+1	vivi+1	ADJ
ejpam-5943	54	39	for	for	ADP
ejpam-5943	54	40	i	i	PRON
ejpam-5943	54	41	=	=	NOUN
ejpam-5943	54	42	1	1	NUM
ejpam-5943	54	43	,	,	PUNCT
ejpam-5943	54	44	2	2	NUM
ejpam-5943	54	45	,	,	PUNCT
ejpam-5943	54	46	...	...	PUNCT
ejpam-5943	54	47	,	,	PUNCT
ejpam-5943	54	48	n−	n−	NOUN
ejpam-5943	54	49	1	1	NUM
ejpam-5943	54	50	[	[	X
ejpam-5943	54	51	7	7	NUM
ejpam-5943	54	52	]	]	PUNCT
ejpam-5943	54	53	.	.	PUNCT
ejpam-5943	55	1	for	for	ADP
ejpam-5943	55	2	an	an	DET
ejpam-5943	55	3	integer	integer	NOUN
ejpam-5943	55	4	n	n	PRON
ejpam-5943	55	5	≥	≥	NOUN
ejpam-5943	55	6	3	3	NUM
ejpam-5943	55	7	,	,	PUNCT
ejpam-5943	55	8	the	the	DET
ejpam-5943	55	9	cycle	cycle	NOUN
ejpam-5943	55	10	cn	cn	PROPN
ejpam-5943	55	11	is	be	AUX
ejpam-5943	55	12	a	a	DET
ejpam-5943	55	13	graph	graph	NOUN
ejpam-5943	55	14	of	of	ADP
ejpam-5943	55	15	order	order	NOUN
ejpam-5943	55	16	n	n	NOUN
ejpam-5943	55	17	and	and	CCONJ
ejpam-5943	55	18	size	size	NOUN
ejpam-5943	55	19	n	n	CCONJ
ejpam-5943	55	20	whose	whose	DET
ejpam-5943	55	21	vertices	vertex	NOUN
ejpam-5943	55	22	can	can	AUX
ejpam-5943	55	23	be	be	AUX
ejpam-5943	55	24	labeled	label	VERB
ejpam-5943	55	25	by	by	ADP
ejpam-5943	55	26	v1	v1	NOUN
ejpam-5943	55	27	,	,	PUNCT
ejpam-5943	55	28	v2	v2	PROPN
ejpam-5943	55	29	,	,	PUNCT
ejpam-5943	55	30	...	...	PUNCT
ejpam-5943	55	31	,	,	PUNCT
ejpam-5943	55	32	vn	vn	PROPN
ejpam-5943	55	33	and	and	CCONJ
ejpam-5943	55	34	whose	whose	DET
ejpam-5943	55	35	edges	edge	NOUN
ejpam-5943	55	36	are	be	AUX
ejpam-5943	55	37	v1vn	v1vn	NUM
ejpam-5943	55	38	and	and	CCONJ
ejpam-5943	55	39	vivi+1	vivi+1	NOUN
ejpam-5943	55	40	for	for	ADP
ejpam-5943	55	41	i	i	PRON
ejpam-5943	55	42	=	=	NOUN
ejpam-5943	55	43	1	1	NUM
ejpam-5943	55	44	,	,	PUNCT
ejpam-5943	55	45	2	2	NUM
ejpam-5943	55	46	,	,	PUNCT
ejpam-5943	55	47	...	...	PUNCT
ejpam-5943	55	48	,	,	PUNCT
ejpam-5943	55	49	n−	n−	NOUN
ejpam-5943	55	50	1	1	NUM
ejpam-5943	55	51	.	.	PUNCT
ejpam-5943	56	1	the	the	DET
ejpam-5943	56	2	cycle	cycle	NOUN
ejpam-5943	56	3	cn	cn	PROPN
ejpam-5943	56	4	is	be	AUX
ejpam-5943	56	5	also	also	ADV
ejpam-5943	56	6	referred	refer	VERB
ejpam-5943	56	7	to	to	ADP
ejpam-5943	56	8	as	as	ADP
ejpam-5943	56	9	an	an	DET
ejpam-5943	56	10	n−cycle	n−cycle	NOUN
ejpam-5943	57	1	[	[	X
ejpam-5943	57	2	7	7	NUM
ejpam-5943	57	3	]	]	PUNCT
ejpam-5943	57	4	.	.	PUNCT
ejpam-5943	58	1	a	a	DET
ejpam-5943	58	2	complete	complete	ADJ
ejpam-5943	58	3	graph	graph	NOUN
ejpam-5943	58	4	of	of	ADP
ejpam-5943	58	5	order	order	NOUN
ejpam-5943	58	6	n	n	PRON
ejpam-5943	58	7	≥	≥	NOUN
ejpam-5943	58	8	2	2	NUM
ejpam-5943	58	9	,	,	PUNCT
ejpam-5943	58	10	denoted	denote	VERB
ejpam-5943	58	11	by	by	ADP
ejpam-5943	58	12	kn	kn	PROPN
ejpam-5943	58	13	,	,	PUNCT
ejpam-5943	58	14	is	be	AUX
ejpam-5943	58	15	a	a	DET
ejpam-5943	58	16	graph	graph	NOUN
ejpam-5943	58	17	with	with	ADP
ejpam-5943	58	18	n	n	ADP
ejpam-5943	58	19	vertices	vertex	NOUN
ejpam-5943	58	20	where	where	SCONJ
ejpam-5943	58	21	in	in	ADP
ejpam-5943	58	22	every	every	DET
ejpam-5943	58	23	pair	pair	NOUN
ejpam-5943	58	24	of	of	ADP
ejpam-5943	58	25	distinct	distinct	ADJ
ejpam-5943	58	26	vertices	vertex	NOUN
ejpam-5943	58	27	are	be	AUX
ejpam-5943	58	28	adjacent	adjacent	ADJ
ejpam-5943	58	29	[	[	X
ejpam-5943	58	30	7	7	NUM
ejpam-5943	58	31	]	]	PUNCT
ejpam-5943	58	32	.	.	PUNCT
ejpam-5943	59	1	the	the	DET
ejpam-5943	59	2	friendship	friendship	NOUN
ejpam-5943	59	3	graph	graph	NOUN
ejpam-5943	59	4	denoted	denote	VERB
ejpam-5943	59	5	by	by	ADP
ejpam-5943	59	6	frn	frn	PROPN
ejpam-5943	59	7	is	be	AUX
ejpam-5943	59	8	a	a	DET
ejpam-5943	59	9	set	set	NOUN
ejpam-5943	59	10	of	of	ADP
ejpam-5943	59	11	n	n	PRON
ejpam-5943	59	12	triangles	triangle	NOUN
ejpam-5943	59	13	having	have	VERB
ejpam-5943	59	14	a	a	DET
ejpam-5943	59	15	common	common	ADJ
ejpam-5943	59	16	central	central	ADJ
ejpam-5943	59	17	vertex	vertex	NOUN
ejpam-5943	59	18	[	[	X
ejpam-5943	59	19	8	8	NUM
ejpam-5943	59	20	]	]	PUNCT
ejpam-5943	59	21	.	.	PUNCT
ejpam-5943	60	1	a	a	DET
ejpam-5943	60	2	graph	graph	NOUN
ejpam-5943	60	3	g	g	NOUN
ejpam-5943	60	4	is	be	AUX
ejpam-5943	60	5	a	a	DET
ejpam-5943	60	6	complete	complete	ADJ
ejpam-5943	60	7	bipartite	bipartite	NOUN
ejpam-5943	60	8	graph	graph	NOUN
ejpam-5943	60	9	denoted	denote	VERB
ejpam-5943	60	10	by	by	ADP
ejpam-5943	60	11	km	km	PROPN
ejpam-5943	60	12	,	,	PUNCT
ejpam-5943	60	13	n	n	CCONJ
ejpam-5943	60	14	if	if	SCONJ
ejpam-5943	60	15	its	its	PRON
ejpam-5943	60	16	vertices	vertex	NOUN
ejpam-5943	60	17	can	can	AUX
ejpam-5943	60	18	be	be	AUX
ejpam-5943	60	19	partitioned	partition	VERB
ejpam-5943	60	20	into	into	ADP
ejpam-5943	60	21	two	two	NUM
ejpam-5943	60	22	disjoint	disjoint	NOUN
ejpam-5943	60	23	nonempty	nonempty	NOUN
ejpam-5943	60	24	sets	set	VERB
ejpam-5943	60	25	v1	v1	NOUN
ejpam-5943	60	26	and	and	CCONJ
ejpam-5943	60	27	v2	v2	VERB
ejpam-5943	60	28	such	such	ADJ
ejpam-5943	60	29	that	that	SCONJ
ejpam-5943	60	30	two	two	NUM
ejpam-5943	60	31	vertices	vertex	NOUN
ejpam-5943	60	32	u	u	NOUN
ejpam-5943	60	33	and	and	CCONJ
ejpam-5943	60	34	v	v	NOUN
ejpam-5943	60	35	are	be	AUX
ejpam-5943	60	36	adjacent	adjacent	ADJ
ejpam-5943	60	37	if	if	SCONJ
ejpam-5943	60	38	and	and	CCONJ
ejpam-5943	60	39	only	only	ADV
ejpam-5943	60	40	if	if	SCONJ
ejpam-5943	60	41	u	u	PROPN
ejpam-5943	60	42	∈	∈	NOUN
ejpam-5943	60	43	v1	v1	NOUN
ejpam-5943	60	44	and	and	CCONJ
ejpam-5943	60	45	v	v	ADP
ejpam-5943	60	46	∈	∈	PROPN
ejpam-5943	60	47	v2	v2	NOUN
ejpam-5943	60	48	.	.	PUNCT
ejpam-5943	61	1	if	if	SCONJ
ejpam-5943	61	2	|v1|	|v1|	NUM
ejpam-5943	61	3	=	=	SYM
ejpam-5943	61	4	m	m	NOUN
ejpam-5943	61	5	and	and	CCONJ
ejpam-5943	61	6	|v2|	|v2|	NOUN
ejpam-5943	61	7	=	=	SYM
ejpam-5943	62	1	n	n	PROPN
ejpam-5943	63	1	[	[	X
ejpam-5943	63	2	9	9	NUM
ejpam-5943	63	3	]	]	PUNCT
ejpam-5943	63	4	.	.	PUNCT
ejpam-5943	64	1	a	a	DET
ejpam-5943	64	2	star	star	NOUN
ejpam-5943	64	3	graph	graph	NOUN
ejpam-5943	64	4	denoted	denote	VERB
ejpam-5943	64	5	by	by	ADP
ejpam-5943	64	6	k1,n	k1,n	PROPN
ejpam-5943	64	7	is	be	AUX
ejpam-5943	64	8	a	a	DET
ejpam-5943	64	9	graph	graph	NOUN
ejpam-5943	64	10	of	of	ADP
ejpam-5943	64	11	order	order	NOUN
ejpam-5943	64	12	n+	n+	ADP
ejpam-5943	64	13	1	1	NUM
ejpam-5943	64	14	whose	whose	DET
ejpam-5943	64	15	one	one	NUM
ejpam-5943	64	16	vertex	vertex	NOUN
ejpam-5943	64	17	has	have	AUX
ejpam-5943	64	18	degree	degree	NOUN
ejpam-5943	64	19	n	n	PRON
ejpam-5943	64	20	which	which	PRON
ejpam-5943	64	21	is	be	AUX
ejpam-5943	64	22	called	call	VERB
ejpam-5943	64	23	the	the	DET
ejpam-5943	64	24	apex	apex	NOUN
ejpam-5943	64	25	u	u	NOUN
ejpam-5943	64	26	and	and	CCONJ
ejpam-5943	64	27	the	the	DET
ejpam-5943	64	28	remaining	remain	VERB
ejpam-5943	64	29	n	n	PRON
ejpam-5943	64	30	vertices	vertex	NOUN
ejpam-5943	64	31	have	have	VERB
ejpam-5943	64	32	a	a	DET
ejpam-5943	64	33	degree	degree	NOUN
ejpam-5943	64	34	equal	equal	ADJ
ejpam-5943	64	35	to	to	ADP
ejpam-5943	64	36	1	1	NUM
ejpam-5943	64	37	[	[	X
ejpam-5943	64	38	6	6	NUM
ejpam-5943	64	39	]	]	PUNCT
ejpam-5943	64	40	.	.	PUNCT
ejpam-5943	65	1	for	for	ADP
ejpam-5943	65	2	n	n	PRON
ejpam-5943	65	3	≥	≥	NUM
ejpam-5943	65	4	2	2	NUM
ejpam-5943	65	5	,	,	PUNCT
ejpam-5943	65	6	the	the	DET
ejpam-5943	65	7	fan	fan	NOUN
ejpam-5943	65	8	graph	graph	NOUN
ejpam-5943	65	9	fn	fn	NOUN
ejpam-5943	65	10	of	of	ADP
ejpam-5943	65	11	order	order	NOUN
ejpam-5943	65	12	n+	n+	ADP
ejpam-5943	65	13	1	1	NUM
ejpam-5943	65	14	is	be	AUX
ejpam-5943	65	15	a	a	DET
ejpam-5943	65	16	graph	graph	NOUN
ejpam-5943	65	17	obtained	obtain	VERB
ejpam-5943	65	18	by	by	ADP
ejpam-5943	65	19	connecting	connect	VERB
ejpam-5943	65	20	a	a	DET
ejpam-5943	65	21	new	new	ADJ
ejpam-5943	65	22	vertex	vertex	NOUN
ejpam-5943	65	23	v	v	NOUN
ejpam-5943	65	24	to	to	ADP
ejpam-5943	65	25	each	each	DET
ejpam-5943	65	26	vertex	vertex	NOUN
ejpam-5943	65	27	of	of	ADP
ejpam-5943	65	28	the	the	DET
ejpam-5943	65	29	path	path	NOUN
ejpam-5943	65	30	pn	pn	PROPN
ejpam-5943	66	1	[	[	X
ejpam-5943	66	2	6	6	NUM
ejpam-5943	66	3	]	]	PUNCT
ejpam-5943	66	4	.	.	PUNCT
ejpam-5943	67	1	a	a	DET
ejpam-5943	67	2	wheel	wheel	NOUN
ejpam-5943	67	3	graph	graph	NOUN
ejpam-5943	67	4	wn	wn	PROPN
ejpam-5943	67	5	is	be	AUX
ejpam-5943	67	6	a	a	DET
ejpam-5943	67	7	graph	graph	NOUN
ejpam-5943	67	8	of	of	ADP
ejpam-5943	67	9	order	order	NOUN
ejpam-5943	67	10	n	n	X
ejpam-5943	67	11	+	+	NOUN
ejpam-5943	67	12	1	1	NUM
ejpam-5943	67	13	,	,	PUNCT
ejpam-5943	67	14	where	where	SCONJ
ejpam-5943	67	15	n	n	PRON
ejpam-5943	67	16	≥	≥	NOUN
ejpam-5943	67	17	3	3	NUM
ejpam-5943	67	18	,	,	PUNCT
ejpam-5943	67	19	which	which	PRON
ejpam-5943	67	20	is	be	AUX
ejpam-5943	67	21	obtained	obtain	VERB
ejpam-5943	67	22	by	by	ADP
ejpam-5943	67	23	joining	join	VERB
ejpam-5943	67	24	a	a	DET
ejpam-5943	67	25	new	new	ADJ
ejpam-5943	67	26	vertex	vertex	NOUN
ejpam-5943	67	27	called	call	VERB
ejpam-5943	67	28	the	the	DET
ejpam-5943	67	29	root	root	NOUN
ejpam-5943	67	30	vertex	vertex	NOUN
ejpam-5943	67	31	of	of	ADP
ejpam-5943	67	32	wn	wn	PROPN
ejpam-5943	67	33	to	to	ADP
ejpam-5943	67	34	each	each	PRON
ejpam-5943	67	35	of	of	ADP
ejpam-5943	67	36	the	the	DET
ejpam-5943	67	37	vertices	vertex	NOUN
ejpam-5943	67	38	of	of	ADP
ejpam-5943	67	39	the	the	DET
ejpam-5943	67	40	cycle	cycle	NOUN
ejpam-5943	67	41	cn	cn	PROPN
ejpam-5943	67	42	produced	produce	VERB
ejpam-5943	67	43	from	from	ADP
ejpam-5943	67	44	the	the	DET
ejpam-5943	67	45	complete	complete	ADJ
ejpam-5943	67	46	product	product	NOUN
ejpam-5943	67	47	of	of	ADP
ejpam-5943	67	48	an	an	DET
ejpam-5943	67	49	isolated	isolated	ADJ
ejpam-5943	67	50	vertex	vertex	NOUN
ejpam-5943	67	51	and	and	CCONJ
ejpam-5943	67	52	a	a	DET
ejpam-5943	67	53	cycle	cycle	NOUN
ejpam-5943	67	54	cn	cn	PROPN
ejpam-5943	68	1	[	[	X
ejpam-5943	68	2	6	6	NUM
ejpam-5943	68	3	]	]	PUNCT
ejpam-5943	68	4	.	.	PUNCT
ejpam-5943	69	1	3	3	X
ejpam-5943	69	2	.	.	X
ejpam-5943	69	3	results	result	VERB
ejpam-5943	69	4	this	this	DET
ejpam-5943	69	5	paper	paper	NOUN
ejpam-5943	69	6	employs	employ	VERB
ejpam-5943	69	7	the	the	DET
ejpam-5943	69	8	term	term	NOUN
ejpam-5943	69	9	proximity	proximity	NOUN
ejpam-5943	69	10	prestige	prestige	NOUN
ejpam-5943	69	11	in	in	ADP
ejpam-5943	69	12	social	social	ADJ
ejpam-5943	69	13	network	network	NOUN
ejpam-5943	69	14	analysis	analysis	NOUN
ejpam-5943	69	15	to	to	PART
ejpam-5943	69	16	represent	represent	VERB
ejpam-5943	69	17	specific	specific	ADJ
ejpam-5943	69	18	concepts	concept	NOUN
ejpam-5943	69	19	in	in	ADP
ejpam-5943	69	20	graph	graph	NOUN
ejpam-5943	69	21	.	.	PUNCT
ejpam-5943	70	1	furthermore	furthermore	ADV
ejpam-5943	70	2	,	,	PUNCT
ejpam-5943	70	3	for	for	ADP
ejpam-5943	70	4	a	a	DET
ejpam-5943	70	5	graph	graph	NOUN
ejpam-5943	70	6	g	g	NOUN
ejpam-5943	70	7	,	,	PUNCT
ejpam-5943	70	8	the	the	DET
ejpam-5943	70	9	vertex	vertex	NOUN
ejpam-5943	70	10	set	set	NOUN
ejpam-5943	70	11	is	be	AUX
ejpam-5943	70	12	denoted	denote	VERB
ejpam-5943	70	13	asv	asv	PROPN
ejpam-5943	70	14	(	(	PUNCT
ejpam-5943	70	15	g	g	NOUN
ejpam-5943	70	16	)	)	PUNCT
ejpam-5943	70	17	and	and	CCONJ
ejpam-5943	70	18	the	the	DET
ejpam-5943	70	19	edge	edge	NOUN
ejpam-5943	70	20	set	set	VERB
ejpam-5943	70	21	as	as	ADP
ejpam-5943	70	22	e(g	e(g	PROPN
ejpam-5943	70	23	)	)	PUNCT
ejpam-5943	70	24	,	,	PUNCT
ejpam-5943	70	25	abbreviated	abbreviate	VERB
ejpam-5943	70	26	to	to	ADP
ejpam-5943	70	27	v	v	NOUN
ejpam-5943	70	28	and	and	CCONJ
ejpam-5943	70	29	e	e	NOUN
ejpam-5943	70	30	,	,	PUNCT
ejpam-5943	70	31	respectively	respectively	ADV
ejpam-5943	70	32	.	.	PUNCT
ejpam-5943	71	1	definition	definition	NOUN
ejpam-5943	71	2	1	1	NUM
ejpam-5943	71	3	.	.	PUNCT
ejpam-5943	72	1	let	let	VERB
ejpam-5943	72	2	g	g	PROPN
ejpam-5943	72	3	=	=	SYM
ejpam-5943	72	4	(	(	PUNCT
ejpam-5943	72	5	v	v	NOUN
ejpam-5943	72	6	,	,	PUNCT
ejpam-5943	72	7	e	e	NOUN
ejpam-5943	72	8	)	)	PUNCT
ejpam-5943	72	9	be	be	AUX
ejpam-5943	72	10	a	a	DET
ejpam-5943	72	11	graph	graph	NOUN
ejpam-5943	72	12	where	where	SCONJ
ejpam-5943	72	13	v	v	NOUN
ejpam-5943	72	14	represents	represent	VERB
ejpam-5943	72	15	the	the	DET
ejpam-5943	72	16	set	set	NOUN
ejpam-5943	72	17	of	of	ADP
ejpam-5943	72	18	vertices	vertex	NOUN
ejpam-5943	72	19	and	and	CCONJ
ejpam-5943	72	20	e	e	NOUN
ejpam-5943	72	21	represents	represent	VERB
ejpam-5943	72	22	the	the	DET
ejpam-5943	72	23	set	set	NOUN
ejpam-5943	72	24	of	of	ADP
ejpam-5943	72	25	edges	edge	NOUN
ejpam-5943	72	26	.	.	PUNCT
ejpam-5943	73	1	the	the	DET
ejpam-5943	73	2	proximity	proximity	NOUN
ejpam-5943	73	3	prestige	prestige	NOUN
ejpam-5943	73	4	of	of	ADP
ejpam-5943	73	5	a	a	DET
ejpam-5943	73	6	vertex	vertex	NOUN
ejpam-5943	73	7	vi	vi	NOUN
ejpam-5943	73	8	∈	∈	PROPN
ejpam-5943	73	9	v	v	NOUN
ejpam-5943	73	10	is	be	AUX
ejpam-5943	73	11	defined	define	VERB
ejpam-5943	73	12	as	as	ADP
ejpam-5943	73	13	:	:	PUNCT
ejpam-5943	73	14	ppg(vi	ppg(vi	NUM
ejpam-5943	73	15	)	)	PUNCT
ejpam-5943	73	16	=	=	SYM
ejpam-5943	73	17	∑	∑	PUNCT
ejpam-5943	73	18	dg(vi	dg(vi	PROPN
ejpam-5943	73	19	,	,	PUNCT
ejpam-5943	73	20	vj	vj	PROPN
ejpam-5943	73	21	)	)	PUNCT
ejpam-5943	73	22	|v	|v	PROPN
ejpam-5943	73	23	(	(	PUNCT
ejpam-5943	73	24	g)|	g)|	VERB
ejpam-5943	73	25	where	where	SCONJ
ejpam-5943	73	26	,	,	PUNCT
ejpam-5943	73	27	•	•	NOUN
ejpam-5943	73	28	ppg(vi	ppg(vi	NUM
ejpam-5943	73	29	)	)	PUNCT
ejpam-5943	73	30	:	:	PUNCT
ejpam-5943	73	31	proximity	proximity	NOUN
ejpam-5943	73	32	prestige	prestige	NOUN
ejpam-5943	73	33	of	of	ADP
ejpam-5943	73	34	vertex	vertex	NOUN
ejpam-5943	73	35	vi	vi	NOUN
ejpam-5943	73	36	;	;	PUNCT
ejpam-5943	73	37	•	•	NUM
ejpam-5943	73	38	dg(vi	dg(vi	NOUN
ejpam-5943	73	39	,	,	PUNCT
ejpam-5943	73	40	vj	vj	INTJ
ejpam-5943	73	41	):	):	PUNCT
ejpam-5943	73	42	length	length	NOUN
ejpam-5943	73	43	of	of	ADP
ejpam-5943	73	44	the	the	DET
ejpam-5943	73	45	shortest	short	ADJ
ejpam-5943	73	46	path	path	NOUN
ejpam-5943	73	47	from	from	ADP
ejpam-5943	73	48	vi	vi	PROPN
ejpam-5943	73	49	to	to	ADP
ejpam-5943	73	50	any	any	DET
ejpam-5943	73	51	vj	vj	NOUN
ejpam-5943	73	52	;	;	PUNCT
ejpam-5943	73	53	and	and	CCONJ
ejpam-5943	73	54	•	•	NUM
ejpam-5943	73	55	|v	|v	X
ejpam-5943	73	56	(	(	PUNCT
ejpam-5943	73	57	g)|	g)|	NOUN
ejpam-5943	73	58	:	:	PUNCT
ejpam-5943	73	59	number	number	NOUN
ejpam-5943	73	60	of	of	ADP
ejpam-5943	73	61	vertices	vertex	NOUN
ejpam-5943	73	62	in	in	ADP
ejpam-5943	73	63	the	the	DET
ejpam-5943	73	64	graph	graph	NOUN
ejpam-5943	73	65	.	.	PUNCT
ejpam-5943	74	1	l.	l.	PROPN
ejpam-5943	74	2	toladro	toladro	PROPN
ejpam-5943	74	3	,	,	PUNCT
ejpam-5943	74	4	i.	i.	PROPN
ejpam-5943	74	5	cabahug	cabahug	PROPN
ejpam-5943	74	6	/	/	SYM
ejpam-5943	74	7	eur	eur	PROPN
ejpam-5943	74	8	.	.	PUNCT
ejpam-5943	75	1	j.	j.	PROPN
ejpam-5943	75	2	pure	pure	PROPN
ejpam-5943	75	3	appl	appl	PROPN
ejpam-5943	75	4	.	.	PROPN
ejpam-5943	75	5	math	math	PROPN
ejpam-5943	75	6	,	,	PUNCT
ejpam-5943	75	7	18	18	NUM
ejpam-5943	75	8	(	(	PUNCT
ejpam-5943	75	9	2	2	NUM
ejpam-5943	75	10	)	)	PUNCT
ejpam-5943	75	11	(	(	PUNCT
ejpam-5943	75	12	2025	2025	NUM
ejpam-5943	75	13	)	)	PUNCT
ejpam-5943	75	14	,	,	PUNCT
ejpam-5943	75	15	5943	5943	NUM
ejpam-5943	75	16	4	4	NUM
ejpam-5943	75	17	of	of	ADP
ejpam-5943	75	18	13	13	NUM
ejpam-5943	75	19	example	example	NOUN
ejpam-5943	75	20	1	1	NUM
ejpam-5943	75	21	.	.	X
ejpam-5943	75	22	consider	consider	VERB
ejpam-5943	75	23	the	the	DET
ejpam-5943	75	24	example	example	NOUN
ejpam-5943	75	25	below	below	ADV
ejpam-5943	75	26	.	.	PUNCT
ejpam-5943	76	1	by	by	ADP
ejpam-5943	76	2	definition	definition	NOUN
ejpam-5943	76	3	,	,	PUNCT
ejpam-5943	76	4	if	if	SCONJ
ejpam-5943	76	5	we	we	PRON
ejpam-5943	76	6	choose	choose	VERB
ejpam-5943	76	7	v4	v4	PROPN
ejpam-5943	76	8	,	,	PUNCT
ejpam-5943	76	9	we	we	PRON
ejpam-5943	76	10	have	have	VERB
ejpam-5943	76	11	,	,	PUNCT
ejpam-5943	76	12	ppg(v4	ppg(v4	PROPN
ejpam-5943	76	13	)	)	PUNCT
ejpam-5943	76	14	=	=	SYM
ejpam-5943	76	15	∑	∑	PUNCT
ejpam-5943	76	16	dg(v4	dg(v4	X
ejpam-5943	76	17	,	,	PUNCT
ejpam-5943	76	18	vj	vj	PROPN
ejpam-5943	76	19	)	)	PUNCT
ejpam-5943	76	20	|v	|v	PROPN
ejpam-5943	76	21	(	(	PUNCT
ejpam-5943	76	22	g)|	g)|	NOUN
ejpam-5943	76	23	=	=	SYM
ejpam-5943	76	24	1	1	NUM
ejpam-5943	76	25	+	+	NUM
ejpam-5943	76	26	1	1	NUM
ejpam-5943	76	27	+	+	NUM
ejpam-5943	76	28	1	1	NUM
ejpam-5943	77	1	+	+	CCONJ
ejpam-5943	77	2	2	2	NUM
ejpam-5943	77	3	5	5	NUM
ejpam-5943	77	4	=	=	SYM
ejpam-5943	77	5	5	5	NUM
ejpam-5943	77	6	5	5	NUM
ejpam-5943	77	7	=	=	SYM
ejpam-5943	77	8	1	1	X
ejpam-5943	77	9	.	.	X
ejpam-5943	77	10	figure	figure	NOUN
ejpam-5943	77	11	3.1	3.1	NUM
ejpam-5943	77	12	:	:	PUNCT
ejpam-5943	77	13	the	the	DET
ejpam-5943	77	14	proximity	proximity	NOUN
ejpam-5943	77	15	prestige	prestige	NOUN
ejpam-5943	77	16	of	of	ADP
ejpam-5943	77	17	v4	v4	NOUN
ejpam-5943	77	18	v4	v4	NOUN
ejpam-5943	77	19	v1	v1	PROPN
ejpam-5943	77	20	v2	v2	PROPN
ejpam-5943	77	21	v3	v3	PROPN
ejpam-5943	77	22	v5	v5	PROPN
ejpam-5943	77	23	d(1	d(1	PROPN
ejpam-5943	77	24	)	)	PUNCT
ejpam-5943	77	25	d(2	d(2	PROPN
ejpam-5943	77	26	)	)	PUNCT
ejpam-5943	77	27	d(1	d(1	NOUN
ejpam-5943	77	28	)	)	PUNCT
ejpam-5943	77	29	d(1	d(1	NOUN
ejpam-5943	77	30	)	)	PUNCT
ejpam-5943	77	31	special	special	ADJ
ejpam-5943	77	32	graph	graph	NOUN
ejpam-5943	77	33	families	family	NOUN
ejpam-5943	77	34	considered	consider	VERB
ejpam-5943	77	35	in	in	ADP
ejpam-5943	77	36	this	this	DET
ejpam-5943	77	37	paper	paper	NOUN
ejpam-5943	77	38	are	be	AUX
ejpam-5943	77	39	path	path	NOUN
ejpam-5943	77	40	pn	pn	PROPN
ejpam-5943	77	41	,	,	PUNCT
ejpam-5943	77	42	cycle	cycle	NOUN
ejpam-5943	77	43	cn	cn	PROPN
ejpam-5943	77	44	,	,	PUNCT
ejpam-5943	77	45	complete	complete	PROPN
ejpam-5943	77	46	kn	kn	PROPN
ejpam-5943	77	47	,	,	PUNCT
ejpam-5943	77	48	friendship	friendship	PROPN
ejpam-5943	77	49	frn	frn	PROPN
ejpam-5943	77	50	,	,	PUNCT
ejpam-5943	77	51	complete	complete	ADJ
ejpam-5943	77	52	bipartite	bipartite	PROPN
ejpam-5943	77	53	km	km	PROPN
ejpam-5943	77	54	,	,	PUNCT
ejpam-5943	77	55	n	n	CCONJ
ejpam-5943	77	56	,	,	PUNCT
ejpam-5943	77	57	star	star	PROPN
ejpam-5943	77	58	k1,n	k1,n	PROPN
ejpam-5943	77	59	,	,	PUNCT
ejpam-5943	77	60	fan	fan	NOUN
ejpam-5943	77	61	fn	fn	NOUN
ejpam-5943	77	62	,	,	PUNCT
ejpam-5943	77	63	and	and	CCONJ
ejpam-5943	77	64	wheel	wheel	PROPN
ejpam-5943	78	1	wn	wn	PROPN
ejpam-5943	78	2	.	.	PROPN
ejpam-5943	78	3	theorem	theorem	PROPN
ejpam-5943	78	4	1	1	NUM
ejpam-5943	78	5	.	.	PUNCT
ejpam-5943	79	1	let	let	VERB
ejpam-5943	79	2	g	g	PROPN
ejpam-5943	79	3	=	=	SYM
ejpam-5943	79	4	(	(	PUNCT
ejpam-5943	79	5	v	v	NOUN
ejpam-5943	79	6	,	,	PUNCT
ejpam-5943	79	7	e	e	NOUN
ejpam-5943	79	8	)	)	PUNCT
ejpam-5943	79	9	be	be	AUX
ejpam-5943	79	10	a	a	DET
ejpam-5943	79	11	path	path	NOUN
ejpam-5943	79	12	graph	graph	NOUN
ejpam-5943	80	1	pn	pn	NOUN
ejpam-5943	80	2	=	=	PUNCT
ejpam-5943	81	1	[	[	X
ejpam-5943	81	2	v1	v1	NOUN
ejpam-5943	81	3	,	,	PUNCT
ejpam-5943	81	4	v2	v2	NOUN
ejpam-5943	81	5	,	,	PUNCT
ejpam-5943	81	6	.	.	PUNCT
ejpam-5943	81	7	.	.	PUNCT
ejpam-5943	81	8	.	.	PUNCT
ejpam-5943	82	1	vn	vn	INTJ
ejpam-5943	82	2	]	]	X
ejpam-5943	82	3	of	of	ADP
ejpam-5943	82	4	order	order	NOUN
ejpam-5943	82	5	n	n	PRON
ejpam-5943	82	6	≥	≥	NOUN
ejpam-5943	82	7	2	2	NUM
ejpam-5943	82	8	,	,	PUNCT
ejpam-5943	82	9	then	then	ADV
ejpam-5943	82	10	the	the	DET
ejpam-5943	82	11	proximity	proximity	NOUN
ejpam-5943	82	12	prestige	prestige	NOUN
ejpam-5943	82	13	of	of	ADP
ejpam-5943	82	14	any	any	DET
ejpam-5943	82	15	vertex	vertex	NOUN
ejpam-5943	82	16	vi	vi	NOUN
ejpam-5943	82	17	where	where	SCONJ
ejpam-5943	82	18	1	1	NUM
ejpam-5943	82	19	≤	≤	NUM
ejpam-5943	82	20	i	i	NOUN
ejpam-5943	82	21	≤	≤	NOUN
ejpam-5943	82	22	n	n	CCONJ
ejpam-5943	82	23	is	be	AUX
ejpam-5943	82	24	given	give	VERB
ejpam-5943	82	25	by	by	ADP
ejpam-5943	82	26	,	,	PUNCT
ejpam-5943	82	27	ppp	ppp	PROPN
ejpam-5943	82	28	n(vi	n(vi	NUM
ejpam-5943	82	29	)	)	PUNCT
ejpam-5943	82	30	=	=	PUNCT
ejpam-5943	82	31			NOUN
ejpam-5943	82	32	(	(	PUNCT
ejpam-5943	82	33	n	n	ADV
ejpam-5943	82	34	2	2	NUM
ejpam-5943	82	35	)	)	PUNCT
ejpam-5943	82	36	n	n	CCONJ
ejpam-5943	82	37	,	,	PUNCT
ejpam-5943	82	38	if	if	SCONJ
ejpam-5943	82	39	i	i	PRON
ejpam-5943	82	40	=	=	VERB
ejpam-5943	82	41	1	1	NUM
ejpam-5943	82	42	or	or	CCONJ
ejpam-5943	82	43	i	i	PRON
ejpam-5943	82	44	=	=	SYM
ejpam-5943	82	45	n	n	CCONJ
ejpam-5943	82	46	;	;	PUNCT
ejpam-5943	82	47	(	(	PUNCT
ejpam-5943	82	48	i2	i2	PROPN
ejpam-5943	82	49	−	−	PROPN
ejpam-5943	82	50	i	i	PROPN
ejpam-5943	82	51	)	)	PUNCT
ejpam-5943	82	52	2n	2n	NUM
ejpam-5943	83	1	+	+	CCONJ
ejpam-5943	83	2	(	(	PUNCT
ejpam-5943	83	3	n−	n−	NOUN
ejpam-5943	83	4	i)(n−	i)(n−	NOUN
ejpam-5943	83	5	i+	i+	PUNCT
ejpam-5943	83	6	1	1	NUM
ejpam-5943	83	7	)	)	PUNCT
ejpam-5943	83	8	2n	2n	NUM
ejpam-5943	83	9	,	,	PUNCT
ejpam-5943	83	10	if	if	SCONJ
ejpam-5943	83	11	2	2	NUM
ejpam-5943	83	12	≤	≤	NUM
ejpam-5943	83	13	i	i	PRON
ejpam-5943	83	14	≤	≤	ADJ
ejpam-5943	83	15	n−	n−	PROPN
ejpam-5943	83	16	i.	i.	NOUN
ejpam-5943	83	17	proof	proof	NOUN
ejpam-5943	83	18	.	.	PUNCT
ejpam-5943	84	1	considering	consider	VERB
ejpam-5943	84	2	the	the	DET
ejpam-5943	84	3	structure	structure	NOUN
ejpam-5943	84	4	of	of	ADP
ejpam-5943	84	5	path	path	NOUN
ejpam-5943	84	6	graph	graph	NOUN
ejpam-5943	84	7	pn	pn	NOUN
ejpam-5943	84	8	=	=	PUNCT
ejpam-5943	85	1	[	[	X
ejpam-5943	85	2	v1	v1	NOUN
ejpam-5943	85	3	,	,	PUNCT
ejpam-5943	85	4	v2	v2	NOUN
ejpam-5943	85	5	,	,	PUNCT
ejpam-5943	85	6	.	.	PUNCT
ejpam-5943	85	7	.	.	PUNCT
ejpam-5943	85	8	.	.	PUNCT
ejpam-5943	86	1	,	,	PUNCT
ejpam-5943	86	2	vn	vn	X
ejpam-5943	86	3	]	]	PUNCT
ejpam-5943	86	4	of	of	ADP
ejpam-5943	86	5	order	order	NOUN
ejpam-5943	86	6	n	n	PRON
ejpam-5943	86	7	≥	≥	NOUN
ejpam-5943	86	8	2	2	NUM
ejpam-5943	86	9	,	,	PUNCT
ejpam-5943	86	10	ppp	ppp	NOUN
ejpam-5943	86	11	n(v1	n(v1	NOUN
ejpam-5943	86	12	)	)	PUNCT
ejpam-5943	87	1	=	=	SYM
ejpam-5943	87	2	ppp	ppp	PROPN
ejpam-5943	87	3	n(vn	n(vn	PROPN
ejpam-5943	87	4	)	)	PUNCT
ejpam-5943	87	5	=	=	SYM
ejpam-5943	88	1	1	1	NUM
ejpam-5943	88	2	+	+	NUM
ejpam-5943	88	3	2	2	NUM
ejpam-5943	88	4	+	+	NUM
ejpam-5943	88	5	3	3	NUM
ejpam-5943	88	6	+	+	NUM
ejpam-5943	88	7	.	.	PUNCT
ejpam-5943	88	8	.	.	PUNCT
ejpam-5943	89	1	.+	.+	NOUN
ejpam-5943	89	2	n−	n−	VERB
ejpam-5943	89	3	1	1	NUM
ejpam-5943	89	4	n	n	NOUN
ejpam-5943	89	5	=	=	PUNCT
ejpam-5943	89	6	(	(	PUNCT
ejpam-5943	89	7	n	n	ADV
ejpam-5943	89	8	2	2	NUM
ejpam-5943	89	9	)	)	PUNCT
ejpam-5943	89	10	n	n	NOUN
ejpam-5943	89	11	.	.	PUNCT
ejpam-5943	90	1	but	but	CCONJ
ejpam-5943	90	2	for	for	ADP
ejpam-5943	90	3	2	2	NUM
ejpam-5943	90	4	≤	≤	NUM
ejpam-5943	90	5	i	i	PRON
ejpam-5943	90	6	≤	≤	ADJ
ejpam-5943	90	7	n−	n−	NOUN
ejpam-5943	90	8	1	1	NUM
ejpam-5943	90	9	,	,	PUNCT
ejpam-5943	90	10	n−1∑	n−1∑	NUM
ejpam-5943	90	11	i=2	i=2	PROPN
ejpam-5943	90	12	dp	dp	NOUN
ejpam-5943	90	13	n(vi	n(vi	NOUN
ejpam-5943	90	14	,	,	PUNCT
ejpam-5943	90	15	vj	vj	ADJ
ejpam-5943	90	16	)	)	PUNCT
ejpam-5943	90	17	=	=	NOUN
ejpam-5943	90	18	i−1∑	i−1∑	NUM
ejpam-5943	90	19	i=2	i=2	PROPN
ejpam-5943	90	20	dp	dp	NOUN
ejpam-5943	90	21	n(vi	n(vi	NOUN
ejpam-5943	90	22	,	,	PUNCT
ejpam-5943	90	23	vj	vj	PROPN
ejpam-5943	90	24	)	)	PUNCT
ejpam-5943	91	1	+	+	CCONJ
ejpam-5943	91	2	n−1∑	n−1∑	NUM
ejpam-5943	91	3	i=2	i=2	PROPN
ejpam-5943	91	4	dp	dp	NOUN
ejpam-5943	91	5	n(vi	n(vi	NOUN
ejpam-5943	91	6	,	,	PUNCT
ejpam-5943	91	7	vj	vj	INTJ
ejpam-5943	91	8	)	)	PUNCT
ejpam-5943	91	9	=	=	NOUN
ejpam-5943	92	1	[	[	X
ejpam-5943	92	2	1	1	NUM
ejpam-5943	92	3	+	+	NUM
ejpam-5943	92	4	2	2	NUM
ejpam-5943	92	5	+	+	CCONJ
ejpam-5943	92	6	.	.	PUNCT
ejpam-5943	92	7	.	.	PUNCT
ejpam-5943	93	1	.+	.+	NOUN
ejpam-5943	93	2	(	(	PUNCT
ejpam-5943	93	3	i−	i−	PROPN
ejpam-5943	93	4	1	1	NUM
ejpam-5943	93	5	)	)	PUNCT
ejpam-5943	93	6	]	]	PUNCT
ejpam-5943	94	1	+	+	CCONJ
ejpam-5943	94	2	[	[	X
ejpam-5943	94	3	1	1	NUM
ejpam-5943	94	4	+	+	NUM
ejpam-5943	94	5	2	2	NUM
ejpam-5943	94	6	+	+	CCONJ
ejpam-5943	94	7	.	.	PUNCT
ejpam-5943	94	8	.	.	PUNCT
ejpam-5943	95	1	.+	.+	NOUN
ejpam-5943	95	2	(	(	PUNCT
ejpam-5943	95	3	n−	n−	NOUN
ejpam-5943	95	4	i	i	NOUN
ejpam-5943	95	5	)	)	PUNCT
ejpam-5943	95	6	]	]	PUNCT
ejpam-5943	96	1	=	=	PUNCT
ejpam-5943	96	2	(	(	PUNCT
ejpam-5943	96	3	i2	i2	PROPN
ejpam-5943	96	4	−	−	PROPN
ejpam-5943	96	5	1	1	NUM
ejpam-5943	96	6	)	)	PUNCT
ejpam-5943	96	7	2	2	NUM
ejpam-5943	96	8	+	+	CCONJ
ejpam-5943	96	9	(	(	PUNCT
ejpam-5943	96	10	n−	n−	NOUN
ejpam-5943	96	11	i)(n−	i)(n−	NOUN
ejpam-5943	96	12	i+	i+	PRON
ejpam-5943	96	13	1	1	NUM
ejpam-5943	96	14	)	)	PUNCT
ejpam-5943	96	15	2	2	NUM
ejpam-5943	96	16	thus	thus	ADV
ejpam-5943	96	17	,	,	PUNCT
ejpam-5943	96	18	ppp	ppp	NOUN
ejpam-5943	96	19	n(vi	n(vi	NUM
ejpam-5943	96	20	)	)	PUNCT
ejpam-5943	96	21	=	=	SYM
ejpam-5943	96	22	(	(	PUNCT
ejpam-5943	96	23	i2	i2	PROPN
ejpam-5943	96	24	−	−	PROPN
ejpam-5943	96	25	1	1	NUM
ejpam-5943	96	26	)	)	PUNCT
ejpam-5943	96	27	2n	2n	NUM
ejpam-5943	97	1	+	+	CCONJ
ejpam-5943	97	2	(	(	PUNCT
ejpam-5943	97	3	n−	n−	NOUN
ejpam-5943	97	4	i)(n−	i)(n−	NOUN
ejpam-5943	97	5	i+	i+	PUNCT
ejpam-5943	97	6	1	1	NUM
ejpam-5943	97	7	)	)	PUNCT
ejpam-5943	97	8	2n	2n	NUM
ejpam-5943	97	9	.	.	PUNCT
ejpam-5943	98	1	l.	l.	PROPN
ejpam-5943	98	2	toladro	toladro	PROPN
ejpam-5943	98	3	,	,	PUNCT
ejpam-5943	98	4	i.	i.	PROPN
ejpam-5943	98	5	cabahug	cabahug	PROPN
ejpam-5943	98	6	/	/	SYM
ejpam-5943	98	7	eur	eur	PROPN
ejpam-5943	98	8	.	.	PUNCT
ejpam-5943	99	1	j.	j.	PROPN
ejpam-5943	99	2	pure	pure	PROPN
ejpam-5943	99	3	appl	appl	PROPN
ejpam-5943	99	4	.	.	PROPN
ejpam-5943	99	5	math	math	PROPN
ejpam-5943	99	6	,	,	PUNCT
ejpam-5943	99	7	18	18	NUM
ejpam-5943	99	8	(	(	PUNCT
ejpam-5943	99	9	2	2	NUM
ejpam-5943	99	10	)	)	PUNCT
ejpam-5943	99	11	(	(	PUNCT
ejpam-5943	99	12	2025	2025	NUM
ejpam-5943	99	13	)	)	PUNCT
ejpam-5943	99	14	,	,	PUNCT
ejpam-5943	99	15	5943	5943	NUM
ejpam-5943	99	16	5	5	NUM
ejpam-5943	99	17	of	of	ADP
ejpam-5943	99	18	13	13	NUM
ejpam-5943	99	19	therefore	therefore	ADV
ejpam-5943	99	20	,	,	PUNCT
ejpam-5943	99	21	we	we	PRON
ejpam-5943	99	22	have	have	AUX
ejpam-5943	99	23	ppp	ppp	NOUN
ejpam-5943	99	24	n(vi	n(vi	PRON
ejpam-5943	99	25	)	)	PUNCT
ejpam-5943	99	26	=	=	PUNCT
ejpam-5943	99	27			NOUN
ejpam-5943	99	28	(	(	PUNCT
ejpam-5943	99	29	n	n	ADV
ejpam-5943	99	30	2	2	NUM
ejpam-5943	99	31	)	)	PUNCT
ejpam-5943	99	32	n	n	CCONJ
ejpam-5943	99	33	,	,	PUNCT
ejpam-5943	99	34	if	if	SCONJ
ejpam-5943	99	35	i	i	PRON
ejpam-5943	99	36	=	=	VERB
ejpam-5943	99	37	1	1	NUM
ejpam-5943	99	38	or	or	CCONJ
ejpam-5943	99	39	i	i	PRON
ejpam-5943	99	40	=	=	SYM
ejpam-5943	99	41	n	n	CCONJ
ejpam-5943	99	42	;	;	PUNCT
ejpam-5943	99	43	(	(	PUNCT
ejpam-5943	99	44	i2	i2	PROPN
ejpam-5943	99	45	−	−	PROPN
ejpam-5943	99	46	i	i	PROPN
ejpam-5943	99	47	)	)	PUNCT
ejpam-5943	99	48	2n	2n	NUM
ejpam-5943	100	1	+	+	CCONJ
ejpam-5943	100	2	(	(	PUNCT
ejpam-5943	100	3	n−	n−	NOUN
ejpam-5943	100	4	i)(n−	i)(n−	NOUN
ejpam-5943	100	5	i+	i+	PUNCT
ejpam-5943	100	6	1	1	NUM
ejpam-5943	100	7	)	)	PUNCT
ejpam-5943	100	8	2n	2n	NUM
ejpam-5943	100	9	,	,	PUNCT
ejpam-5943	100	10	if	if	SCONJ
ejpam-5943	100	11	2	2	NUM
ejpam-5943	100	12	≤	≤	NUM
ejpam-5943	100	13	i	i	PRON
ejpam-5943	100	14	≤	≤	ADJ
ejpam-5943	100	15	n−	n−	AUX
ejpam-5943	100	16	i.	i.	NOUN
ejpam-5943	100	17	■	■	PUNCT
ejpam-5943	100	18	theorem	theorem	ADJ
ejpam-5943	100	19	2	2	NUM
ejpam-5943	100	20	.	.	PUNCT
ejpam-5943	101	1	let	let	VERB
ejpam-5943	101	2	g	g	PROPN
ejpam-5943	101	3	=	=	SYM
ejpam-5943	101	4	(	(	PUNCT
ejpam-5943	101	5	v	v	NOUN
ejpam-5943	101	6	,	,	PUNCT
ejpam-5943	101	7	e	e	NOUN
ejpam-5943	101	8	)	)	PUNCT
ejpam-5943	101	9	be	be	AUX
ejpam-5943	101	10	a	a	DET
ejpam-5943	101	11	cycle	cycle	NOUN
ejpam-5943	101	12	graph	graph	NOUN
ejpam-5943	102	1	cn	cn	NOUN
ejpam-5943	103	1	=	=	PUNCT
ejpam-5943	104	1	[	[	X
ejpam-5943	104	2	v1	v1	NOUN
ejpam-5943	104	3	,	,	PUNCT
ejpam-5943	104	4	v2	v2	NOUN
ejpam-5943	104	5	,	,	PUNCT
ejpam-5943	104	6	.	.	PUNCT
ejpam-5943	104	7	.	.	PUNCT
ejpam-5943	105	1	.	.	PUNCT
ejpam-5943	106	1	,	,	PUNCT
ejpam-5943	106	2	vn	vn	X
ejpam-5943	106	3	,	,	PUNCT
ejpam-5943	106	4	v1	v1	PROPN
ejpam-5943	106	5	]	]	PUNCT
ejpam-5943	106	6	of	of	ADP
ejpam-5943	106	7	order	order	NOUN
ejpam-5943	106	8	n	n	PRON
ejpam-5943	106	9	≥	≥	NOUN
ejpam-5943	106	10	3	3	NUM
ejpam-5943	106	11	,	,	PUNCT
ejpam-5943	106	12	then	then	ADV
ejpam-5943	106	13	the	the	DET
ejpam-5943	106	14	proximity	proximity	NOUN
ejpam-5943	106	15	prestige	prestige	NOUN
ejpam-5943	106	16	of	of	ADP
ejpam-5943	106	17	any	any	DET
ejpam-5943	106	18	vertex	vertex	NOUN
ejpam-5943	106	19	vi	vi	NOUN
ejpam-5943	106	20	where	where	SCONJ
ejpam-5943	106	21	1	1	NUM
ejpam-5943	106	22	≤	≤	NUM
ejpam-5943	106	23	i	i	NOUN
ejpam-5943	106	24	≤	≤	NOUN
ejpam-5943	106	25	n	n	CCONJ
ejpam-5943	106	26	is	be	AUX
ejpam-5943	106	27	given	give	VERB
ejpam-5943	106	28	by	by	ADP
ejpam-5943	106	29	,	,	PUNCT
ejpam-5943	106	30	ppcn(vi	ppcn(vi	PROPN
ejpam-5943	106	31	)	)	PUNCT
ejpam-5943	106	32	=	=	PUNCT
ejpam-5943	107	1			PROPN
ejpam-5943	107	2	n	n	PRON
ejpam-5943	107	3	4	4	NUM
ejpam-5943	107	4	if	if	SCONJ
ejpam-5943	107	5	n	n	PRON
ejpam-5943	107	6	is	be	AUX
ejpam-5943	107	7	even	even	ADV
ejpam-5943	107	8	;	;	PUNCT
ejpam-5943	107	9	n2	n2	ADJ
ejpam-5943	107	10	−	−	PROPN
ejpam-5943	107	11	1	1	NUM
ejpam-5943	107	12	4n	4n	NOUN
ejpam-5943	107	13	if	if	SCONJ
ejpam-5943	107	14	n	n	PRON
ejpam-5943	107	15	is	be	AUX
ejpam-5943	107	16	odd	odd	ADJ
ejpam-5943	107	17	.	.	PUNCT
ejpam-5943	108	1	proof	proof	NOUN
ejpam-5943	108	2	.	.	PUNCT
ejpam-5943	109	1	suppose	suppose	VERB
ejpam-5943	109	2	first	first	ADV
ejpam-5943	109	3	that	that	SCONJ
ejpam-5943	109	4	n	n	X
ejpam-5943	109	5	is	be	AUX
ejpam-5943	109	6	even	even	ADV
ejpam-5943	109	7	.	.	PUNCT
ejpam-5943	110	1	by	by	ADP
ejpam-5943	110	2	the	the	DET
ejpam-5943	110	3	structure	structure	NOUN
ejpam-5943	110	4	of	of	ADP
ejpam-5943	110	5	cycle	cycle	NOUN
ejpam-5943	110	6	cn	cn	NOUN
ejpam-5943	111	1	=	=	PUNCT
ejpam-5943	112	1	[	[	X
ejpam-5943	112	2	v1	v1	NOUN
ejpam-5943	112	3	,	,	PUNCT
ejpam-5943	112	4	v2	v2	NOUN
ejpam-5943	112	5	,	,	PUNCT
ejpam-5943	112	6	.	.	PUNCT
ejpam-5943	112	7	.	.	PUNCT
ejpam-5943	112	8	.	.	PUNCT
ejpam-5943	113	1	,	,	PUNCT
ejpam-5943	113	2	vn	vn	X
ejpam-5943	113	3	,	,	PUNCT
ejpam-5943	113	4	v1	v1	PROPN
ejpam-5943	113	5	]	]	PUNCT
ejpam-5943	113	6	,	,	PUNCT
ejpam-5943	113	7	the	the	DET
ejpam-5943	113	8	sum	sum	NOUN
ejpam-5943	113	9	of	of	ADP
ejpam-5943	113	10	the	the	DET
ejpam-5943	113	11	distance	distance	NOUN
ejpam-5943	113	12	of	of	ADP
ejpam-5943	113	13	vi	vi	NOUN
ejpam-5943	113	14	and	and	CCONJ
ejpam-5943	113	15	vj	vj	INTJ
ejpam-5943	113	16	where	where	SCONJ
ejpam-5943	113	17	i	i	PRON
ejpam-5943	113	18	̸=	̸=	PROPN
ejpam-5943	113	19	j	j	PROPN
ejpam-5943	113	20	can	can	AUX
ejpam-5943	113	21	be	be	AUX
ejpam-5943	113	22	derived	derive	VERB
ejpam-5943	113	23	as	as	SCONJ
ejpam-5943	113	24	follows	follow	VERB
ejpam-5943	113	25	.	.	PUNCT
ejpam-5943	114	1	for	for	ADP
ejpam-5943	114	2	each	each	DET
ejpam-5943	114	3	i	i	PRON
ejpam-5943	114	4	,	,	PUNCT
ejpam-5943	114	5	we	we	PRON
ejpam-5943	114	6	have	have	VERB
ejpam-5943	114	7	distance	distance	NOUN
ejpam-5943	114	8	d(vi	d(vi	NOUN
ejpam-5943	114	9	,	,	PUNCT
ejpam-5943	114	10	vj	vj	ADJ
ejpam-5943	114	11	)	)	PUNCT
ejpam-5943	114	12	=	=	SYM
ejpam-5943	115	1	1	1	NUM
ejpam-5943	115	2	+	+	NUM
ejpam-5943	115	3	1	1	NUM
ejpam-5943	115	4	+	+	NUM
ejpam-5943	115	5	2	2	NUM
ejpam-5943	115	6	+	+	SYM
ejpam-5943	115	7	2	2	NUM
ejpam-5943	115	8	+	+	NUM
ejpam-5943	115	9	.	.	PUNCT
ejpam-5943	115	10	.	.	PUNCT
ejpam-5943	116	1	.+	.+	NOUN
ejpam-5943	116	2	2	2	NUM
ejpam-5943	116	3	(	(	PUNCT
ejpam-5943	116	4	n	n	ADV
ejpam-5943	116	5	2	2	NUM
ejpam-5943	116	6	−	−	NOUN
ejpam-5943	116	7	1	1	NUM
ejpam-5943	116	8	)	)	PUNCT
ejpam-5943	116	9	+	+	CCONJ
ejpam-5943	116	10	n	n	DET
ejpam-5943	116	11	2	2	NUM
ejpam-5943	116	12	.	.	PUNCT
ejpam-5943	117	1	thus	thus	ADV
ejpam-5943	117	2	,	,	PUNCT
ejpam-5943	117	3	∑	∑	ADP
ejpam-5943	117	4	i	i	PRON
ejpam-5943	117	5	̸=j	̸=j	VERB
ejpam-5943	117	6	dcn(vi	dcn(vi	NOUN
ejpam-5943	117	7	,	,	PUNCT
ejpam-5943	117	8	vj	vj	INTJ
ejpam-5943	117	9	)	)	PUNCT
ejpam-5943	117	10	=	=	SYM
ejpam-5943	117	11	2	2	NUM
ejpam-5943	117	12	(	(	PUNCT
ejpam-5943	117	13	1	1	NUM
ejpam-5943	117	14	+	+	NUM
ejpam-5943	117	15	2	2	NUM
ejpam-5943	117	16	+	+	CCONJ
ejpam-5943	117	17	.	.	PUNCT
ejpam-5943	117	18	.	.	PUNCT
ejpam-5943	118	1	.+	.+	NOUN
ejpam-5943	118	2	(	(	PUNCT
ejpam-5943	118	3	n	n	CCONJ
ejpam-5943	118	4	2	2	NUM
ejpam-5943	118	5	−	−	NOUN
ejpam-5943	118	6	1	1	NUM
ejpam-5943	118	7	)	)	PUNCT
ejpam-5943	118	8	)	)	PUNCT
ejpam-5943	119	1	+	+	CCONJ
ejpam-5943	119	2	n	n	PRON
ejpam-5943	119	3	2	2	NUM
ejpam-5943	119	4	=	=	SYM
ejpam-5943	119	5	n2	n2	NOUN
ejpam-5943	119	6	4	4	NUM
ejpam-5943	119	7	.	.	PUNCT
ejpam-5943	120	1	hence	hence	ADV
ejpam-5943	120	2	,	,	PUNCT
ejpam-5943	120	3	ppcn(vi	ppcn(vi	PROPN
ejpam-5943	120	4	)	)	PUNCT
ejpam-5943	120	5	=	=	SYM
ejpam-5943	120	6	n2	n2	ADJ
ejpam-5943	120	7	4	4	NUM
ejpam-5943	120	8	n	n	NOUN
ejpam-5943	120	9	=	=	SYM
ejpam-5943	120	10	n	n	PRON
ejpam-5943	120	11	4	4	NUM
ejpam-5943	120	12	.	.	PUNCT
ejpam-5943	121	1	on	on	ADP
ejpam-5943	121	2	the	the	DET
ejpam-5943	121	3	other	other	ADJ
ejpam-5943	121	4	hand	hand	NOUN
ejpam-5943	121	5	,	,	PUNCT
ejpam-5943	121	6	if	if	SCONJ
ejpam-5943	121	7	n	n	PRON
ejpam-5943	121	8	is	be	AUX
ejpam-5943	121	9	odd	odd	ADJ
ejpam-5943	121	10	,	,	PUNCT
ejpam-5943	121	11	where	where	SCONJ
ejpam-5943	121	12	i	i	PRON
ejpam-5943	121	13	̸=	̸=	PROPN
ejpam-5943	121	14	j.	j.	PROPN
ejpam-5943	121	15	for	for	ADP
ejpam-5943	121	16	each	each	DET
ejpam-5943	121	17	i	i	PRON
ejpam-5943	121	18	,	,	PUNCT
ejpam-5943	121	19	we	we	PRON
ejpam-5943	121	20	have	have	VERB
ejpam-5943	121	21	distance	distance	NOUN
ejpam-5943	121	22	d(vi	d(vi	NOUN
ejpam-5943	121	23	,	,	PUNCT
ejpam-5943	121	24	vj	vj	ADJ
ejpam-5943	121	25	)	)	PUNCT
ejpam-5943	121	26	=	=	SYM
ejpam-5943	122	1	1	1	NUM
ejpam-5943	122	2	+	+	NUM
ejpam-5943	122	3	1	1	NUM
ejpam-5943	122	4	+	+	NUM
ejpam-5943	122	5	2	2	NUM
ejpam-5943	122	6	+	+	SYM
ejpam-5943	122	7	2	2	NUM
ejpam-5943	122	8	+	+	NUM
ejpam-5943	122	9	.	.	PUNCT
ejpam-5943	122	10	.	.	PUNCT
ejpam-5943	123	1	.+	.+	NOUN
ejpam-5943	123	2	2	2	NUM
ejpam-5943	123	3	(	(	PUNCT
ejpam-5943	123	4	n−	n−	NOUN
ejpam-5943	123	5	1	1	NUM
ejpam-5943	123	6	2	2	NUM
ejpam-5943	123	7	)	)	PUNCT
ejpam-5943	123	8	.	.	PUNCT
ejpam-5943	124	1	thus	thus	ADV
ejpam-5943	124	2	,	,	PUNCT
ejpam-5943	124	3	∑	∑	ADP
ejpam-5943	124	4	i	i	PRON
ejpam-5943	124	5	̸=j	̸=j	VERB
ejpam-5943	124	6	dcn(vi	dcn(vi	NOUN
ejpam-5943	124	7	,	,	PUNCT
ejpam-5943	124	8	vj	vj	INTJ
ejpam-5943	124	9	)	)	PUNCT
ejpam-5943	124	10	=	=	SYM
ejpam-5943	124	11	2	2	NUM
ejpam-5943	124	12	[	[	PUNCT
ejpam-5943	124	13	1	1	NUM
ejpam-5943	124	14	+	+	SYM
ejpam-5943	124	15	2	2	NUM
ejpam-5943	124	16	+	+	CCONJ
ejpam-5943	124	17	.	.	PUNCT
ejpam-5943	124	18	.	.	PUNCT
ejpam-5943	125	1	.+	.+	NOUN
ejpam-5943	125	2	n−	n−	NOUN
ejpam-5943	125	3	1	1	NUM
ejpam-5943	125	4	2	2	NUM
ejpam-5943	125	5	]	]	PUNCT
ejpam-5943	125	6	=	=	SYM
ejpam-5943	125	7	n2	n2	NOUN
ejpam-5943	125	8	−	−	PROPN
ejpam-5943	125	9	1	1	NUM
ejpam-5943	125	10	4	4	NUM
ejpam-5943	125	11	.	.	PUNCT
ejpam-5943	126	1	hence	hence	ADV
ejpam-5943	126	2	,	,	PUNCT
ejpam-5943	126	3	ppcn(vi	ppcn(vi	PROPN
ejpam-5943	126	4	)	)	PUNCT
ejpam-5943	126	5	=	=	SYM
ejpam-5943	126	6	n2	n2	NOUN
ejpam-5943	126	7	−	−	PROPN
ejpam-5943	126	8	1	1	NUM
ejpam-5943	126	9	4	4	NUM
ejpam-5943	126	10	n	n	NOUN
ejpam-5943	126	11	=	=	PUNCT
ejpam-5943	126	12	n2	n2	NOUN
ejpam-5943	126	13	−	−	PROPN
ejpam-5943	126	14	1	1	NUM
ejpam-5943	126	15	4n	4n	X
ejpam-5943	126	16	.	.	PUNCT
ejpam-5943	127	1	l.	l.	PROPN
ejpam-5943	127	2	toladro	toladro	PROPN
ejpam-5943	127	3	,	,	PUNCT
ejpam-5943	127	4	i.	i.	PROPN
ejpam-5943	127	5	cabahug	cabahug	PROPN
ejpam-5943	127	6	/	/	SYM
ejpam-5943	127	7	eur	eur	PROPN
ejpam-5943	127	8	.	.	PUNCT
ejpam-5943	128	1	j.	j.	PROPN
ejpam-5943	128	2	pure	pure	PROPN
ejpam-5943	128	3	appl	appl	PROPN
ejpam-5943	128	4	.	.	PROPN
ejpam-5943	128	5	math	math	PROPN
ejpam-5943	128	6	,	,	PUNCT
ejpam-5943	128	7	18	18	NUM
ejpam-5943	128	8	(	(	PUNCT
ejpam-5943	128	9	2	2	NUM
ejpam-5943	128	10	)	)	PUNCT
ejpam-5943	128	11	(	(	PUNCT
ejpam-5943	128	12	2025	2025	NUM
ejpam-5943	128	13	)	)	PUNCT
ejpam-5943	128	14	,	,	PUNCT
ejpam-5943	128	15	5943	5943	NUM
ejpam-5943	128	16	6	6	NUM
ejpam-5943	128	17	of	of	ADP
ejpam-5943	128	18	13	13	NUM
ejpam-5943	128	19	therefore	therefore	ADV
ejpam-5943	128	20	,	,	PUNCT
ejpam-5943	128	21	we	we	PRON
ejpam-5943	128	22	have	have	AUX
ejpam-5943	128	23	ppcn(vi	ppcn(vi	NOUN
ejpam-5943	128	24	)	)	PUNCT
ejpam-5943	128	25	=	=	PUNCT
ejpam-5943	129	1			PROPN
ejpam-5943	129	2	n	n	PRON
ejpam-5943	129	3	4	4	NUM
ejpam-5943	129	4	if	if	SCONJ
ejpam-5943	129	5	n	n	PRON
ejpam-5943	129	6	is	be	AUX
ejpam-5943	129	7	even	even	ADV
ejpam-5943	129	8	;	;	PUNCT
ejpam-5943	129	9	n2	n2	ADJ
ejpam-5943	129	10	−	−	PROPN
ejpam-5943	129	11	1	1	NUM
ejpam-5943	129	12	4n	4n	NOUN
ejpam-5943	129	13	if	if	SCONJ
ejpam-5943	129	14	n	n	PRON
ejpam-5943	129	15	is	be	AUX
ejpam-5943	129	16	odd	odd	ADJ
ejpam-5943	129	17	.	.	PUNCT
ejpam-5943	130	1	■	■	PUNCT
ejpam-5943	130	2	theorem	theorem	ADJ
ejpam-5943	130	3	3	3	X
ejpam-5943	130	4	.	.	PUNCT
ejpam-5943	131	1	let	let	VERB
ejpam-5943	131	2	g	g	PRON
ejpam-5943	131	3	be	be	AUX
ejpam-5943	131	4	a	a	DET
ejpam-5943	131	5	complete	complete	ADJ
ejpam-5943	131	6	graph	graph	NOUN
ejpam-5943	131	7	kn	kn	NOUN
ejpam-5943	131	8	of	of	ADP
ejpam-5943	131	9	order	order	NOUN
ejpam-5943	131	10	n	n	PRON
ejpam-5943	131	11	≥	≥	NOUN
ejpam-5943	131	12	3	3	NUM
ejpam-5943	131	13	,	,	PUNCT
ejpam-5943	131	14	then	then	ADV
ejpam-5943	131	15	the	the	DET
ejpam-5943	131	16	proximity	proximity	NOUN
ejpam-5943	131	17	prestige	prestige	NOUN
ejpam-5943	131	18	of	of	ADP
ejpam-5943	131	19	any	any	DET
ejpam-5943	131	20	vertex	vertex	NOUN
ejpam-5943	131	21	vi	vi	NOUN
ejpam-5943	131	22	where	where	SCONJ
ejpam-5943	131	23	1	1	NUM
ejpam-5943	131	24	≤	≤	NUM
ejpam-5943	131	25	i	i	NOUN
ejpam-5943	131	26	≤	≤	NOUN
ejpam-5943	131	27	n	n	CCONJ
ejpam-5943	131	28	is	be	AUX
ejpam-5943	131	29	given	give	VERB
ejpam-5943	131	30	by	by	ADP
ejpam-5943	131	31	,	,	PUNCT
ejpam-5943	131	32	ppkn(vi	ppkn(vi	ADJ
ejpam-5943	131	33	)	)	PUNCT
ejpam-5943	131	34	=	=	SYM
ejpam-5943	131	35	n−	n−	NOUN
ejpam-5943	131	36	1	1	NUM
ejpam-5943	131	37	n	n	NOUN
ejpam-5943	131	38	.	.	PUNCT
ejpam-5943	132	1	proof	proof	NOUN
ejpam-5943	132	2	.	.	PUNCT
ejpam-5943	133	1	for	for	ADP
ejpam-5943	133	2	each	each	DET
ejpam-5943	133	3	i	i	PROPN
ejpam-5943	133	4	,	,	PUNCT
ejpam-5943	133	5	∑	∑	ADP
ejpam-5943	133	6	i	i	PRON
ejpam-5943	133	7	̸=j	̸=j	NOUN
ejpam-5943	133	8	dkn(vi	dkn(vi	NOUN
ejpam-5943	133	9	,	,	PUNCT
ejpam-5943	133	10	vj	vj	ADJ
ejpam-5943	133	11	)	)	PUNCT
ejpam-5943	133	12	=	=	SYM
ejpam-5943	133	13	1	1	NUM
ejpam-5943	133	14	+	+	NUM
ejpam-5943	133	15	1	1	NUM
ejpam-5943	133	16	+	+	CCONJ
ejpam-5943	133	17	.	.	PUNCT
ejpam-5943	133	18	.	.	PUNCT
ejpam-5943	134	1	.+	.+	NOUN
ejpam-5943	135	1	1︸	1︸	NUM
ejpam-5943	135	2	︷︷	︷︷	NOUN
ejpam-5943	135	3	︸	︸	X
ejpam-5943	135	4	n-1	n-1	NOUN
ejpam-5943	135	5	addends	addend	VERB
ejpam-5943	135	6	=	=	PUNCT
ejpam-5943	135	7	n−	n−	NOUN
ejpam-5943	135	8	1	1	NUM
ejpam-5943	135	9	.	.	PUNCT
ejpam-5943	136	1	therefore	therefore	ADV
ejpam-5943	136	2	,	,	PUNCT
ejpam-5943	136	3	ppkn(vi	ppkn(vi	ADJ
ejpam-5943	136	4	)	)	PUNCT
ejpam-5943	136	5	=	=	SYM
ejpam-5943	136	6	n−	n−	NOUN
ejpam-5943	136	7	1	1	NUM
ejpam-5943	136	8	n	n	NOUN
ejpam-5943	136	9	.	.	PUNCT
ejpam-5943	137	1	■	■	PUNCT
ejpam-5943	137	2	theorem	theorem	ADJ
ejpam-5943	137	3	4	4	NUM
ejpam-5943	137	4	.	.	PUNCT
ejpam-5943	138	1	let	let	VERB
ejpam-5943	138	2	g	g	PRON
ejpam-5943	138	3	be	be	AUX
ejpam-5943	138	4	a	a	DET
ejpam-5943	138	5	friendship	friendship	NOUN
ejpam-5943	138	6	graph	graph	NOUN
ejpam-5943	138	7	frn	frn	PROPN
ejpam-5943	138	8	=	=	PUNCT
ejpam-5943	139	1	[	[	X
ejpam-5943	139	2	v1	v1	NOUN
ejpam-5943	139	3	,	,	PUNCT
ejpam-5943	139	4	v2	v2	NOUN
ejpam-5943	139	5	,	,	PUNCT
ejpam-5943	139	6	.	.	PUNCT
ejpam-5943	139	7	.	.	PUNCT
ejpam-5943	140	1	.	.	PUNCT
ejpam-5943	141	1	,	,	PUNCT
ejpam-5943	141	2	v2n	v2n	NOUN
ejpam-5943	141	3	,	,	PUNCT
ejpam-5943	141	4	,	,	PUNCT
ejpam-5943	141	5	v2n+1	v2n+1	PROPN
ejpam-5943	141	6	]	]	PUNCT
ejpam-5943	141	7	where	where	SCONJ
ejpam-5943	141	8	deg(v2n+1	deg(v2n+1	VERB
ejpam-5943	141	9	)	)	PUNCT
ejpam-5943	142	1	=	=	SYM
ejpam-5943	142	2	2n	2n	NUM
ejpam-5943	142	3	,	,	PUNCT
ejpam-5943	142	4	then	then	ADV
ejpam-5943	142	5	the	the	DET
ejpam-5943	142	6	proximity	proximity	NOUN
ejpam-5943	142	7	prestige	prestige	NOUN
ejpam-5943	142	8	of	of	ADP
ejpam-5943	142	9	any	any	DET
ejpam-5943	142	10	vertex	vertex	NOUN
ejpam-5943	142	11	vi	vi	NOUN
ejpam-5943	142	12	where	where	SCONJ
ejpam-5943	142	13	1	1	NUM
ejpam-5943	142	14	≤	≤	NUM
ejpam-5943	142	15	i	i	PRON
ejpam-5943	142	16	≤	≤	NOUN
ejpam-5943	142	17	2n+	2n+	NUM
ejpam-5943	142	18	1	1	NUM
ejpam-5943	142	19	is	be	AUX
ejpam-5943	142	20	given	give	VERB
ejpam-5943	142	21	by	by	ADP
ejpam-5943	142	22	,	,	PUNCT
ejpam-5943	142	23	ppfrn(vi	ppfrn(vi	ADJ
ejpam-5943	142	24	)	)	PUNCT
ejpam-5943	142	25	=	=	PUNCT
ejpam-5943	142	26			NUM
ejpam-5943	142	27	2n	2n	NUM
ejpam-5943	142	28	2n+	2n+	NUM
ejpam-5943	142	29	1	1	NUM
ejpam-5943	142	30	if	if	SCONJ
ejpam-5943	142	31	deg(vi	deg(vi	NOUN
ejpam-5943	142	32	)	)	PUNCT
ejpam-5943	142	33	=	=	SYM
ejpam-5943	142	34	2n	2n	NUM
ejpam-5943	142	35	;	;	PUNCT
ejpam-5943	143	1	4n−	4n−	NUM
ejpam-5943	143	2	2	2	NUM
ejpam-5943	143	3	2n+	2n+	NUM
ejpam-5943	143	4	1	1	NUM
ejpam-5943	143	5	if	if	SCONJ
ejpam-5943	143	6	deg(vi	deg(vi	NOUN
ejpam-5943	143	7	)	)	PUNCT
ejpam-5943	143	8	=	=	SYM
ejpam-5943	143	9	2	2	X
ejpam-5943	143	10	.	.	PUNCT
ejpam-5943	143	11	proof	proof	NOUN
ejpam-5943	143	12	.	.	PUNCT
ejpam-5943	144	1	consider	consider	VERB
ejpam-5943	144	2	the	the	DET
ejpam-5943	144	3	structure	structure	NOUN
ejpam-5943	144	4	of	of	ADP
ejpam-5943	144	5	a	a	DET
ejpam-5943	144	6	friendship	friendship	NOUN
ejpam-5943	144	7	graph	graph	NOUN
ejpam-5943	144	8	which	which	PRON
ejpam-5943	144	9	consists	consist	VERB
ejpam-5943	144	10	of	of	ADP
ejpam-5943	144	11	n	n	NOUN
ejpam-5943	144	12	triangles	triangle	NOUN
ejpam-5943	144	13	sharing	share	VERB
ejpam-5943	144	14	a	a	DET
ejpam-5943	144	15	common	common	ADJ
ejpam-5943	144	16	vertex	vertex	NOUN
ejpam-5943	144	17	often	often	ADV
ejpam-5943	144	18	called	call	VERB
ejpam-5943	144	19	the	the	DET
ejpam-5943	144	20	center	center	ADJ
ejpam-5943	144	21	vertex	vertex	NOUN
ejpam-5943	144	22	v2n+1	v2n+1	PROPN
ejpam-5943	144	23	.	.	PUNCT
ejpam-5943	145	1	thus	thus	ADV
ejpam-5943	145	2	the	the	DET
ejpam-5943	145	3	total	total	ADJ
ejpam-5943	145	4	number	number	NOUN
ejpam-5943	145	5	of	of	ADP
ejpam-5943	145	6	vertices	vertex	NOUN
ejpam-5943	145	7	in	in	ADP
ejpam-5943	145	8	frn	frn	PROPN
ejpam-5943	145	9	is	be	AUX
ejpam-5943	145	10	2n+	2n+	NUM
ejpam-5943	145	11	1	1	NUM
ejpam-5943	145	12	,	,	PUNCT
ejpam-5943	145	13	with	with	ADP
ejpam-5943	145	14	one	one	NUM
ejpam-5943	145	15	center	center	NOUN
ejpam-5943	145	16	vertex	vertex	NOUN
ejpam-5943	145	17	of	of	ADP
ejpam-5943	145	18	degree	degree	NOUN
ejpam-5943	145	19	2n	2n	NUM
ejpam-5943	145	20	and	and	CCONJ
ejpam-5943	145	21	outer	outer	ADJ
ejpam-5943	145	22	vertices	vertex	NOUN
ejpam-5943	145	23	each	each	PRON
ejpam-5943	145	24	of	of	ADP
ejpam-5943	145	25	degree	degree	NOUN
ejpam-5943	145	26	2	2	NUM
ejpam-5943	145	27	.	.	PUNCT
ejpam-5943	145	28	case	case	NOUN
ejpam-5943	145	29	1	1	NUM
ejpam-5943	145	30	:	:	PUNCT
ejpam-5943	145	31	deg(vi	deg(vi	X
ejpam-5943	145	32	)	)	PUNCT
ejpam-5943	145	33	=	=	SYM
ejpam-5943	145	34	2n	2n	NUM
ejpam-5943	145	35	.	.	PUNCT
ejpam-5943	146	1	there	there	PRON
ejpam-5943	146	2	is	be	VERB
ejpam-5943	146	3	only	only	ADV
ejpam-5943	146	4	one	one	NUM
ejpam-5943	146	5	vertex	vertex	NOUN
ejpam-5943	146	6	with	with	ADP
ejpam-5943	146	7	a	a	DET
ejpam-5943	146	8	degree	degree	NOUN
ejpam-5943	146	9	of	of	ADP
ejpam-5943	146	10	2n	2n	NUM
ejpam-5943	146	11	,	,	PUNCT
ejpam-5943	146	12	which	which	PRON
ejpam-5943	146	13	is	be	AUX
ejpam-5943	146	14	v2n+1	v2n+1	ADJ
ejpam-5943	146	15	and	and	CCONJ
ejpam-5943	146	16	for	for	ADP
ejpam-5943	146	17	any	any	DET
ejpam-5943	146	18	i	i	NOUN
ejpam-5943	146	19	=	=	PUNCT
ejpam-5943	146	20	2n	2n	NUM
ejpam-5943	147	1	+	+	CCONJ
ejpam-5943	147	2	1	1	NUM
ejpam-5943	147	3	̸=	̸=	PROPN
ejpam-5943	147	4	j	j	PROPN
ejpam-5943	147	5	the	the	DET
ejpam-5943	147	6	distance	distance	NOUN
ejpam-5943	147	7	d(vi	d(vi	PROPN
ejpam-5943	147	8	,	,	PUNCT
ejpam-5943	147	9	vj	vj	INTJ
ejpam-5943	147	10	)	)	PUNCT
ejpam-5943	147	11	=	=	SYM
ejpam-5943	147	12	1	1	X
ejpam-5943	147	13	.	.	PUNCT
ejpam-5943	148	1	thus,∑	thus,∑	PROPN
ejpam-5943	148	2	dfrn(vi	dfrn(vi	PROPN
ejpam-5943	148	3	,	,	PUNCT
ejpam-5943	148	4	vj	vj	PROPN
ejpam-5943	148	5	)	)	PUNCT
ejpam-5943	148	6	=	=	SYM
ejpam-5943	148	7	1	1	NUM
ejpam-5943	148	8	+	+	NUM
ejpam-5943	148	9	1	1	NUM
ejpam-5943	148	10	+	+	CCONJ
ejpam-5943	148	11	.	.	PUNCT
ejpam-5943	148	12	.	.	PUNCT
ejpam-5943	149	1	.+	.+	NOUN
ejpam-5943	150	1	1︸	1︸	NUM
ejpam-5943	150	2	︷︷	︷︷	NOUN
ejpam-5943	150	3	︸	︸	ADP
ejpam-5943	150	4	2n	2n	NUM
ejpam-5943	150	5	addends	addend	NOUN
ejpam-5943	150	6	=	=	SYM
ejpam-5943	150	7	2n	2n	NUM
ejpam-5943	150	8	.	.	PUNCT
ejpam-5943	151	1	hence	hence	ADV
ejpam-5943	151	2	,	,	PUNCT
ejpam-5943	151	3	ppfrn(vi	ppfrn(vi	ADJ
ejpam-5943	151	4	)	)	PUNCT
ejpam-5943	151	5	=	=	SYM
ejpam-5943	151	6	2n	2n	NUM
ejpam-5943	151	7	2n+	2n+	NUM
ejpam-5943	151	8	1	1	NUM
ejpam-5943	151	9	.	.	PUNCT
ejpam-5943	152	1	l.	l.	PROPN
ejpam-5943	152	2	toladro	toladro	PROPN
ejpam-5943	152	3	,	,	PUNCT
ejpam-5943	152	4	i.	i.	PROPN
ejpam-5943	152	5	cabahug	cabahug	PROPN
ejpam-5943	152	6	/	/	SYM
ejpam-5943	152	7	eur	eur	PROPN
ejpam-5943	152	8	.	.	PUNCT
ejpam-5943	153	1	j.	j.	PROPN
ejpam-5943	153	2	pure	pure	PROPN
ejpam-5943	153	3	appl	appl	PROPN
ejpam-5943	153	4	.	.	PROPN
ejpam-5943	153	5	math	math	PROPN
ejpam-5943	153	6	,	,	PUNCT
ejpam-5943	153	7	18	18	NUM
ejpam-5943	153	8	(	(	PUNCT
ejpam-5943	153	9	2	2	NUM
ejpam-5943	153	10	)	)	PUNCT
ejpam-5943	153	11	(	(	PUNCT
ejpam-5943	153	12	2025	2025	NUM
ejpam-5943	153	13	)	)	PUNCT
ejpam-5943	153	14	,	,	PUNCT
ejpam-5943	153	15	5943	5943	NUM
ejpam-5943	153	16	7	7	NUM
ejpam-5943	153	17	of	of	ADP
ejpam-5943	153	18	13	13	NUM
ejpam-5943	153	19	case	case	NOUN
ejpam-5943	153	20	2	2	NUM
ejpam-5943	153	21	:	:	PUNCT
ejpam-5943	153	22	deg	deg	X
ejpam-5943	153	23	(	(	PUNCT
ejpam-5943	153	24	vi	vi	NOUN
ejpam-5943	153	25	)	)	PUNCT
ejpam-5943	153	26	=	=	SYM
ejpam-5943	154	1	2	2	X
ejpam-5943	154	2	.	.	X
ejpam-5943	154	3	choose	choose	VERB
ejpam-5943	154	4	v1	v1	PROPN
ejpam-5943	154	5	∈	∈	PROPN
ejpam-5943	154	6	v	v	NOUN
ejpam-5943	154	7	(	(	PUNCT
ejpam-5943	154	8	frn	frn	PROPN
ejpam-5943	154	9	)	)	PUNCT
ejpam-5943	154	10	,	,	PUNCT
ejpam-5943	154	11	observe	observe	VERB
ejpam-5943	154	12	that	that	SCONJ
ejpam-5943	154	13	the	the	DET
ejpam-5943	154	14	distance	distance	NOUN
ejpam-5943	154	15	d(v1	d(v1	NOUN
ejpam-5943	154	16	,	,	PUNCT
ejpam-5943	154	17	vj	vj	INTJ
ejpam-5943	154	18	)	)	PUNCT
ejpam-5943	154	19	=	=	SYM
ejpam-5943	154	20	d(v1	d(v1	X
ejpam-5943	154	21	,	,	PUNCT
ejpam-5943	154	22	v2n+1	v2n+1	ADJ
ejpam-5943	154	23	)	)	PUNCT
ejpam-5943	155	1	+	+	CCONJ
ejpam-5943	155	2	d(v1	d(v1	NOUN
ejpam-5943	155	3	,	,	PUNCT
ejpam-5943	155	4	v2	v2	PROPN
ejpam-5943	155	5	)	)	PUNCT
ejpam-5943	156	1	+	+	CCONJ
ejpam-5943	156	2	∑	∑	PROPN
ejpam-5943	156	3	j	j	PROPN
ejpam-5943	156	4	/∈{2,2n+1	/∈{2,2n+1	SYM
ejpam-5943	156	5	}	}	PUNCT
ejpam-5943	156	6	d(v1	d(v1	PROPN
ejpam-5943	156	7	,	,	PUNCT
ejpam-5943	156	8	vj	vj	NOUN
ejpam-5943	156	9	)	)	PUNCT
ejpam-5943	156	10	.	.	PUNCT
ejpam-5943	157	1	now	now	ADV
ejpam-5943	157	2	,	,	PUNCT
ejpam-5943	157	3	the	the	DET
ejpam-5943	157	4	distance	distance	NOUN
ejpam-5943	157	5	d(v1	d(v1	NOUN
ejpam-5943	157	6	,	,	PUNCT
ejpam-5943	157	7	v2n+1	v2n+1	NOUN
ejpam-5943	157	8	)	)	PUNCT
ejpam-5943	157	9	=	=	SYM
ejpam-5943	157	10	1	1	NUM
ejpam-5943	157	11	=	=	SYM
ejpam-5943	157	12	d(v1	d(v1	X
ejpam-5943	157	13	,	,	PUNCT
ejpam-5943	157	14	v2	v2	PROPN
ejpam-5943	157	15	)	)	PUNCT
ejpam-5943	157	16	and	and	CCONJ
ejpam-5943	157	17	d(v1	d(v1	PROPN
ejpam-5943	157	18	,	,	PUNCT
ejpam-5943	157	19	vj	vj	PROPN
ejpam-5943	157	20	)	)	PUNCT
ejpam-5943	157	21	=	=	SYM
ejpam-5943	157	22	2	2	NUM
ejpam-5943	157	23	for	for	ADP
ejpam-5943	157	24	j	j	PROPN
ejpam-5943	157	25	/∈	/∈	PUNCT
ejpam-5943	157	26	{	{	PUNCT
ejpam-5943	157	27	2	2	NUM
ejpam-5943	157	28	,	,	PUNCT
ejpam-5943	157	29	2n+	2n+	NUM
ejpam-5943	157	30	1	1	NUM
ejpam-5943	157	31	}	}	PUNCT
ejpam-5943	157	32	.	.	PUNCT
ejpam-5943	158	1	thus,∑	thus,∑	PROPN
ejpam-5943	158	2	j	j	PROPN
ejpam-5943	158	3	/∈{2,2n+1	/∈{2,2n+1	PROPN
ejpam-5943	158	4	}	}	PUNCT
ejpam-5943	158	5	d(v1	d(v1	PROPN
ejpam-5943	158	6	,	,	PUNCT
ejpam-5943	158	7	vj	vj	PROPN
ejpam-5943	158	8	)	)	PUNCT
ejpam-5943	158	9	=	=	SYM
ejpam-5943	158	10	2	2	NUM
ejpam-5943	158	11	+	+	NUM
ejpam-5943	158	12	2	2	NUM
ejpam-5943	158	13	+	+	NUM
ejpam-5943	158	14	.	.	PUNCT
ejpam-5943	158	15	.	.	PUNCT
ejpam-5943	159	1	.+	.+	NOUN
ejpam-5943	159	2	2︸	2︸	NUM
ejpam-5943	159	3	︷︷	︷︷	PROPN
ejpam-5943	159	4	︸	︸	ADP
ejpam-5943	159	5	2n-2	2n-2	NUM
ejpam-5943	159	6	addends	addend	VERB
ejpam-5943	159	7	=	=	SYM
ejpam-5943	159	8	2(2n−	2(2n−	NUM
ejpam-5943	159	9	2	2	NUM
ejpam-5943	159	10	)	)	PUNCT
ejpam-5943	159	11	=	=	PUNCT
ejpam-5943	160	1	4n−	4n−	NUM
ejpam-5943	160	2	4	4	NUM
ejpam-5943	160	3	thus	thus	ADV
ejpam-5943	160	4	,	,	PUNCT
ejpam-5943	160	5	∑	∑	PUNCT
ejpam-5943	160	6	dfrn(v1	dfrn(v1	NOUN
ejpam-5943	160	7	,	,	PUNCT
ejpam-5943	160	8	vj	vj	INTJ
ejpam-5943	160	9	)	)	PUNCT
ejpam-5943	160	10	=	=	SYM
ejpam-5943	160	11	1	1	NUM
ejpam-5943	160	12	+	+	NUM
ejpam-5943	160	13	1	1	NUM
ejpam-5943	160	14	+	+	NUM
ejpam-5943	160	15	2	2	NUM
ejpam-5943	160	16	+	+	SYM
ejpam-5943	160	17	2	2	NUM
ejpam-5943	160	18	+	+	NUM
ejpam-5943	160	19	.	.	PUNCT
ejpam-5943	160	20	.	.	PUNCT
ejpam-5943	161	1	.+	.+	NOUN
ejpam-5943	161	2	2︸	2︸	NUM
ejpam-5943	161	3	︷︷	︷︷	PROPN
ejpam-5943	161	4	︸	︸	ADP
ejpam-5943	161	5	2n-2	2n-2	NUM
ejpam-5943	161	6	addends	addend	VERB
ejpam-5943	161	7	=	=	SYM
ejpam-5943	161	8	2	2	NUM
ejpam-5943	161	9	+	+	CCONJ
ejpam-5943	161	10	(	(	PUNCT
ejpam-5943	161	11	4n−	4n−	NUM
ejpam-5943	161	12	4	4	NUM
ejpam-5943	161	13	)	)	PUNCT
ejpam-5943	161	14	=	=	PUNCT
ejpam-5943	162	1	4n−	4n−	NUM
ejpam-5943	162	2	2	2	NUM
ejpam-5943	162	3	hence	hence	ADV
ejpam-5943	162	4	,	,	PUNCT
ejpam-5943	162	5	ppfrn(vi	ppfrn(vi	ADJ
ejpam-5943	162	6	)	)	PUNCT
ejpam-5943	162	7	=	=	PUNCT
ejpam-5943	163	1	4n−	4n−	NUM
ejpam-5943	163	2	2	2	NUM
ejpam-5943	163	3	2n+	2n+	NUM
ejpam-5943	163	4	1	1	NUM
ejpam-5943	163	5	.	.	PUNCT
ejpam-5943	164	1	therefore	therefore	ADV
ejpam-5943	164	2	,	,	PUNCT
ejpam-5943	164	3	we	we	PRON
ejpam-5943	164	4	have	have	VERB
ejpam-5943	164	5	ppfrn(vi	ppfrn(vi	NOUN
ejpam-5943	164	6	)	)	PUNCT
ejpam-5943	164	7	=	=	PUNCT
ejpam-5943	165	1			NUM
ejpam-5943	165	2	2n	2n	NUM
ejpam-5943	165	3	2n+	2n+	NUM
ejpam-5943	165	4	1	1	NUM
ejpam-5943	165	5	if	if	SCONJ
ejpam-5943	165	6	deg(vi	deg(vi	NOUN
ejpam-5943	165	7	)	)	PUNCT
ejpam-5943	165	8	=	=	SYM
ejpam-5943	165	9	2n	2n	NUM
ejpam-5943	165	10	;	;	PUNCT
ejpam-5943	166	1	4n−	4n−	NUM
ejpam-5943	166	2	2	2	NUM
ejpam-5943	166	3	2n+	2n+	NUM
ejpam-5943	166	4	1	1	NUM
ejpam-5943	166	5	if	if	SCONJ
ejpam-5943	166	6	deg(vi	deg(vi	NOUN
ejpam-5943	166	7	)	)	PUNCT
ejpam-5943	166	8	=	=	SYM
ejpam-5943	166	9	2	2	X
ejpam-5943	166	10	.	.	X
ejpam-5943	166	11	■	■	PUNCT
ejpam-5943	166	12	theorem	theorem	ADJ
ejpam-5943	166	13	5	5	NUM
ejpam-5943	166	14	.	.	PUNCT
ejpam-5943	166	15	let	let	VERB
ejpam-5943	166	16	g	g	PROPN
ejpam-5943	166	17	=	=	SYM
ejpam-5943	166	18	(	(	PUNCT
ejpam-5943	166	19	v	v	NOUN
ejpam-5943	166	20	,	,	PUNCT
ejpam-5943	166	21	e	e	NOUN
ejpam-5943	166	22	)	)	PUNCT
ejpam-5943	166	23	be	be	AUX
ejpam-5943	166	24	a	a	DET
ejpam-5943	166	25	fan	fan	NOUN
ejpam-5943	166	26	graph	graph	NOUN
ejpam-5943	166	27	fn	fn	NOUN
ejpam-5943	167	1	=	=	PUNCT
ejpam-5943	168	1	[	[	X
ejpam-5943	168	2	v1	v1	NOUN
ejpam-5943	168	3	,	,	PUNCT
ejpam-5943	168	4	.	.	PUNCT
ejpam-5943	168	5	.	.	PUNCT
ejpam-5943	169	1	.	.	PUNCT
ejpam-5943	170	1	,	,	PUNCT
ejpam-5943	170	2	vn	vn	X
ejpam-5943	170	3	,	,	PUNCT
ejpam-5943	170	4	vn+1	vn+1	PROPN
ejpam-5943	170	5	]	]	PUNCT
ejpam-5943	170	6	where	where	SCONJ
ejpam-5943	170	7	deg(vn+1	deg(vn+1	NOUN
ejpam-5943	170	8	)	)	PUNCT
ejpam-5943	170	9	=	=	SYM
ejpam-5943	171	1	n	n	X
ejpam-5943	171	2	,	,	PUNCT
ejpam-5943	171	3	then	then	ADV
ejpam-5943	171	4	the	the	DET
ejpam-5943	171	5	proximity	proximity	NOUN
ejpam-5943	171	6	prestige	prestige	NOUN
ejpam-5943	171	7	of	of	ADP
ejpam-5943	171	8	any	any	DET
ejpam-5943	171	9	vertex	vertex	NOUN
ejpam-5943	171	10	vi	vi	NOUN
ejpam-5943	171	11	where	where	SCONJ
ejpam-5943	171	12	1	1	NUM
ejpam-5943	171	13	≤	≤	NUM
ejpam-5943	171	14	i	i	PRON
ejpam-5943	171	15	≤	≤	NOUN
ejpam-5943	171	16	n+	n+	PUNCT
ejpam-5943	171	17	1	1	NUM
ejpam-5943	171	18	is	be	AUX
ejpam-5943	171	19	given	give	VERB
ejpam-5943	171	20	by	by	ADP
ejpam-5943	171	21	,	,	PUNCT
ejpam-5943	171	22	ppf	ppf	PROPN
ejpam-5943	171	23	n(vi	n(vi	PROPN
ejpam-5943	171	24	)	)	PUNCT
ejpam-5943	171	25	=	=	SYM
ejpam-5943	171	26			PROPN
ejpam-5943	171	27	n	n	X
ejpam-5943	171	28	n+	n+	NUM
ejpam-5943	171	29	1	1	NUM
ejpam-5943	171	30	,	,	PUNCT
ejpam-5943	171	31	if	if	SCONJ
ejpam-5943	171	32	deg(vi	deg(vi	NOUN
ejpam-5943	171	33	)	)	PUNCT
ejpam-5943	171	34	=	=	SYM
ejpam-5943	171	35	n	n	CCONJ
ejpam-5943	171	36	;	;	PUNCT
ejpam-5943	171	37	2n−	2n−	PROPN
ejpam-5943	171	38	2	2	NUM
ejpam-5943	171	39	n+	n+	NUM
ejpam-5943	171	40	1	1	NUM
ejpam-5943	171	41	,	,	PUNCT
ejpam-5943	171	42	if	if	SCONJ
ejpam-5943	171	43	deg(vi	deg(vi	NOUN
ejpam-5943	171	44	)	)	PUNCT
ejpam-5943	171	45	=	=	SYM
ejpam-5943	171	46	2	2	NUM
ejpam-5943	171	47	;	;	PUNCT
ejpam-5943	171	48	2n−	2n−	PROPN
ejpam-5943	171	49	3	3	NUM
ejpam-5943	171	50	n+	n+	NUM
ejpam-5943	171	51	1	1	NUM
ejpam-5943	171	52	,	,	PUNCT
ejpam-5943	171	53	if	if	SCONJ
ejpam-5943	171	54	deg(vi	deg(vi	NOUN
ejpam-5943	171	55	)	)	PUNCT
ejpam-5943	171	56	=	=	SYM
ejpam-5943	171	57	3	3	X
ejpam-5943	171	58	.	.	PUNCT
ejpam-5943	172	1	proof	proof	NOUN
ejpam-5943	172	2	.	.	PUNCT
ejpam-5943	173	1	using	use	VERB
ejpam-5943	173	2	the	the	DET
ejpam-5943	173	3	structure	structure	NOUN
ejpam-5943	173	4	of	of	ADP
ejpam-5943	173	5	fan	fan	NOUN
ejpam-5943	173	6	graph	graph	NOUN
ejpam-5943	173	7	fn	fn	NOUN
ejpam-5943	173	8	of	of	ADP
ejpam-5943	173	9	order	order	NOUN
ejpam-5943	173	10	n	n	PRON
ejpam-5943	173	11	≥	≥	NOUN
ejpam-5943	173	12	3	3	NUM
ejpam-5943	173	13	,	,	PUNCT
ejpam-5943	173	14	obtained	obtain	VERB
ejpam-5943	173	15	by	by	ADP
ejpam-5943	173	16	connecting	connect	VERB
ejpam-5943	173	17	a	a	DET
ejpam-5943	173	18	single	single	ADJ
ejpam-5943	173	19	vertex	vertex	NOUN
ejpam-5943	173	20	vn+1	vn+1	NOUN
ejpam-5943	173	21	to	to	ADP
ejpam-5943	173	22	each	each	DET
ejpam-5943	173	23	vertex	vertex	NOUN
ejpam-5943	173	24	of	of	ADP
ejpam-5943	173	25	the	the	DET
ejpam-5943	173	26	path	path	NOUN
ejpam-5943	173	27	.	.	PUNCT
ejpam-5943	174	1	here	here	ADV
ejpam-5943	174	2	,	,	PUNCT
ejpam-5943	174	3	we	we	PRON
ejpam-5943	174	4	need	need	VERB
ejpam-5943	174	5	to	to	PART
ejpam-5943	174	6	consider	consider	VERB
ejpam-5943	174	7	three	three	NUM
ejpam-5943	174	8	cases	case	NOUN
ejpam-5943	174	9	separately	separately	ADV
ejpam-5943	174	10	.	.	PUNCT
ejpam-5943	175	1	case	case	NOUN
ejpam-5943	175	2	1	1	NUM
ejpam-5943	175	3	:	:	PUNCT
ejpam-5943	175	4	deg(vi	deg(vi	X
ejpam-5943	175	5	)	)	PUNCT
ejpam-5943	175	6	=	=	SYM
ejpam-5943	175	7	n.	n.	PROPN
ejpam-5943	175	8	l.	l.	PROPN
ejpam-5943	175	9	toladro	toladro	PROPN
ejpam-5943	175	10	,	,	PUNCT
ejpam-5943	175	11	i.	i.	PROPN
ejpam-5943	175	12	cabahug	cabahug	PROPN
ejpam-5943	175	13	/	/	SYM
ejpam-5943	175	14	eur	eur	PROPN
ejpam-5943	175	15	.	.	PUNCT
ejpam-5943	176	1	j.	j.	PROPN
ejpam-5943	176	2	pure	pure	PROPN
ejpam-5943	176	3	appl	appl	PROPN
ejpam-5943	176	4	.	.	PROPN
ejpam-5943	176	5	math	math	PROPN
ejpam-5943	176	6	,	,	PUNCT
ejpam-5943	176	7	18	18	NUM
ejpam-5943	176	8	(	(	PUNCT
ejpam-5943	176	9	2	2	NUM
ejpam-5943	176	10	)	)	PUNCT
ejpam-5943	176	11	(	(	PUNCT
ejpam-5943	176	12	2025	2025	NUM
ejpam-5943	176	13	)	)	PUNCT
ejpam-5943	176	14	,	,	PUNCT
ejpam-5943	176	15	5943	5943	NUM
ejpam-5943	176	16	8	8	NUM
ejpam-5943	176	17	of	of	ADP
ejpam-5943	176	18	13	13	NUM
ejpam-5943	176	19	there	there	PRON
ejpam-5943	176	20	is	be	VERB
ejpam-5943	176	21	only	only	ADV
ejpam-5943	176	22	one	one	NUM
ejpam-5943	176	23	vertex	vertex	NOUN
ejpam-5943	176	24	with	with	ADP
ejpam-5943	176	25	a	a	DET
ejpam-5943	176	26	degree	degree	NOUN
ejpam-5943	176	27	n	n	CCONJ
ejpam-5943	176	28	,	,	PUNCT
ejpam-5943	176	29	which	which	PRON
ejpam-5943	176	30	is	be	AUX
ejpam-5943	176	31	vn+1	vn+1	PROPN
ejpam-5943	176	32	and	and	CCONJ
ejpam-5943	176	33	for	for	ADP
ejpam-5943	176	34	i	i	PRON
ejpam-5943	176	35	=	=	SYM
ejpam-5943	177	1	n+1	n+1	PROPN
ejpam-5943	177	2	̸=	̸=	PROPN
ejpam-5943	177	3	j	j	NOUN
ejpam-5943	177	4	the	the	DET
ejpam-5943	177	5	distance	distance	NOUN
ejpam-5943	177	6	d(vi	d(vi	PROPN
ejpam-5943	177	7	,	,	PUNCT
ejpam-5943	177	8	vj	vj	INTJ
ejpam-5943	177	9	)	)	PUNCT
ejpam-5943	177	10	=	=	SYM
ejpam-5943	177	11	1	1	X
ejpam-5943	177	12	.	.	PUNCT
ejpam-5943	178	1	thus	thus	ADV
ejpam-5943	178	2	,	,	PUNCT
ejpam-5943	178	3	∑	∑	ADP
ejpam-5943	178	4	i	i	PRON
ejpam-5943	178	5	̸=j	̸=j	X
ejpam-5943	178	6	df	df	PROPN
ejpam-5943	178	7	n(vi	n(vi	NOUN
ejpam-5943	178	8	,	,	PUNCT
ejpam-5943	178	9	vj	vj	ADJ
ejpam-5943	178	10	)	)	PUNCT
ejpam-5943	178	11	=	=	SYM
ejpam-5943	178	12	1	1	NUM
ejpam-5943	178	13	+	+	NUM
ejpam-5943	178	14	1	1	NUM
ejpam-5943	178	15	+	+	CCONJ
ejpam-5943	178	16	.	.	PUNCT
ejpam-5943	178	17	.	.	PUNCT
ejpam-5943	179	1	.+	.+	NOUN
ejpam-5943	180	1	1︸	1︸	NUM
ejpam-5943	180	2	︷︷	︷︷	NOUN
ejpam-5943	180	3	︸	︸	ADP
ejpam-5943	180	4	n	n	PROPN
ejpam-5943	180	5	addends	addend	VERB
ejpam-5943	180	6	=	=	PUNCT
ejpam-5943	180	7	n.	n.	PROPN
ejpam-5943	180	8	hence	hence	ADV
ejpam-5943	180	9	,	,	PUNCT
ejpam-5943	180	10	ppf	ppf	PROPN
ejpam-5943	180	11	n(vi	n(vi	PROPN
ejpam-5943	180	12	)	)	PUNCT
ejpam-5943	180	13	=	=	SYM
ejpam-5943	180	14	n	n	X
ejpam-5943	180	15	n+	n+	NUM
ejpam-5943	180	16	1	1	NUM
ejpam-5943	180	17	.	.	PUNCT
ejpam-5943	180	18	case	case	NOUN
ejpam-5943	180	19	2	2	NUM
ejpam-5943	180	20	:	:	PUNCT
ejpam-5943	180	21	deg(vi	deg(vi	NUM
ejpam-5943	180	22	)	)	PUNCT
ejpam-5943	180	23	=	=	SYM
ejpam-5943	180	24	2	2	X
ejpam-5943	180	25	.	.	X
ejpam-5943	180	26	if	if	SCONJ
ejpam-5943	180	27	deg(vi	deg(vi	NOUN
ejpam-5943	180	28	)	)	PUNCT
ejpam-5943	180	29	=	=	SYM
ejpam-5943	180	30	2	2	NUM
ejpam-5943	180	31	,	,	PUNCT
ejpam-5943	180	32	then	then	ADV
ejpam-5943	180	33	there	there	PRON
ejpam-5943	180	34	are	be	VERB
ejpam-5943	180	35	only	only	ADV
ejpam-5943	180	36	two	two	NUM
ejpam-5943	180	37	vertices	vertex	NOUN
ejpam-5943	180	38	with	with	ADP
ejpam-5943	180	39	a	a	DET
ejpam-5943	180	40	degree	degree	NOUN
ejpam-5943	180	41	of	of	ADP
ejpam-5943	180	42	2	2	NUM
ejpam-5943	180	43	in	in	ADP
ejpam-5943	180	44	fn	fn	NOUN
ejpam-5943	180	45	,	,	PUNCT
ejpam-5943	180	46	that	that	PRON
ejpam-5943	180	47	is	be	AUX
ejpam-5943	180	48	v1	v1	ADJ
ejpam-5943	180	49	and	and	CCONJ
ejpam-5943	180	50	vn	vn	X
ejpam-5943	180	51	i.e.	i.e.	X
ejpam-5943	180	52	,	,	PUNCT
ejpam-5943	180	53	i	i	PRON
ejpam-5943	180	54	∈	∈	PROPN
ejpam-5943	180	55	{	{	PUNCT
ejpam-5943	180	56	1	1	NUM
ejpam-5943	180	57	,	,	PUNCT
ejpam-5943	180	58	n	n	CCONJ
ejpam-5943	180	59	}	}	PUNCT
ejpam-5943	180	60	.	.	PUNCT
ejpam-5943	181	1	choose	choose	VERB
ejpam-5943	181	2	v1	v1	PROPN
ejpam-5943	181	3	,	,	PUNCT
ejpam-5943	181	4	thus	thus	ADV
ejpam-5943	181	5	the	the	DET
ejpam-5943	181	6	distance	distance	NOUN
ejpam-5943	181	7	d(v1	d(v1	NOUN
ejpam-5943	181	8	,	,	PUNCT
ejpam-5943	181	9	vj	vj	INTJ
ejpam-5943	181	10	)	)	PUNCT
ejpam-5943	182	1	=	=	SYM
ejpam-5943	182	2	d(v1	d(v1	X
ejpam-5943	182	3	,	,	PUNCT
ejpam-5943	182	4	v2	v2	PROPN
ejpam-5943	182	5	)	)	PUNCT
ejpam-5943	182	6	+	+	CCONJ
ejpam-5943	182	7	d(v1	d(v1	NOUN
ejpam-5943	182	8	,	,	PUNCT
ejpam-5943	182	9	vn+1	vn+1	PROPN
ejpam-5943	182	10	)	)	PUNCT
ejpam-5943	183	1	+	+	CCONJ
ejpam-5943	183	2	∑	∑	PROPN
ejpam-5943	183	3	j	j	PROPN
ejpam-5943	183	4	/∈{2,n+1	/∈{2,n+1	PROPN
ejpam-5943	183	5	}	}	PUNCT
ejpam-5943	183	6	d(v1	d(v1	PROPN
ejpam-5943	183	7	,	,	PUNCT
ejpam-5943	183	8	vj	vj	NOUN
ejpam-5943	183	9	)	)	PUNCT
ejpam-5943	183	10	.	.	PUNCT
ejpam-5943	184	1	now	now	ADV
ejpam-5943	184	2	,	,	PUNCT
ejpam-5943	184	3	d(v1	d(v1	NOUN
ejpam-5943	184	4	,	,	PUNCT
ejpam-5943	184	5	v2	v2	PROPN
ejpam-5943	184	6	)	)	PUNCT
ejpam-5943	184	7	=	=	SYM
ejpam-5943	184	8	1	1	NUM
ejpam-5943	184	9	=	=	SYM
ejpam-5943	184	10	d(v1	d(v1	X
ejpam-5943	184	11	,	,	PUNCT
ejpam-5943	184	12	vn+1	vn+1	PROPN
ejpam-5943	184	13	)	)	PUNCT
ejpam-5943	184	14	and	and	CCONJ
ejpam-5943	184	15	d(v1	d(v1	PROPN
ejpam-5943	184	16	,	,	PUNCT
ejpam-5943	184	17	vj	vj	PROPN
ejpam-5943	184	18	)	)	PUNCT
ejpam-5943	184	19	=	=	SYM
ejpam-5943	184	20	2	2	NUM
ejpam-5943	184	21	for	for	ADP
ejpam-5943	184	22	j	j	PROPN
ejpam-5943	184	23	/∈	/∈	PUNCT
ejpam-5943	184	24	{	{	PUNCT
ejpam-5943	184	25	2	2	NUM
ejpam-5943	184	26	,	,	PUNCT
ejpam-5943	184	27	n+	n+	NUM
ejpam-5943	185	1	1	1	NUM
ejpam-5943	185	2	}	}	PUNCT
ejpam-5943	185	3	.	.	PUNCT
ejpam-5943	186	1	thus,∑	thus,∑	PROPN
ejpam-5943	186	2	j	j	PROPN
ejpam-5943	186	3	/∈{2,n+1	/∈{2,n+1	PROPN
ejpam-5943	186	4	}	}	PUNCT
ejpam-5943	186	5	d(v1	d(v1	PROPN
ejpam-5943	186	6	,	,	PUNCT
ejpam-5943	186	7	vj	vj	PROPN
ejpam-5943	186	8	)	)	PUNCT
ejpam-5943	186	9	=	=	SYM
ejpam-5943	186	10	2	2	NUM
ejpam-5943	186	11	+	+	NUM
ejpam-5943	186	12	2	2	NUM
ejpam-5943	186	13	+	+	NUM
ejpam-5943	186	14	.	.	PUNCT
ejpam-5943	186	15	.	.	PUNCT
ejpam-5943	187	1	.+	.+	NOUN
ejpam-5943	187	2	2︸	2︸	NUM
ejpam-5943	187	3	︷︷	︷︷	PROPN
ejpam-5943	187	4	︸	︸	PRON
ejpam-5943	187	5	n-2	n-2	PROPN
ejpam-5943	187	6	addends	addend	VERB
ejpam-5943	187	7	=	=	PUNCT
ejpam-5943	187	8	2(n−	2(n−	NUM
ejpam-5943	187	9	2	2	NUM
ejpam-5943	187	10	)	)	PUNCT
ejpam-5943	187	11	=	=	PUNCT
ejpam-5943	188	1	2n−	2n−	NUM
ejpam-5943	188	2	4	4	NUM
ejpam-5943	188	3	.	.	PUNCT
ejpam-5943	189	1	thus	thus	ADV
ejpam-5943	189	2	,	,	PUNCT
ejpam-5943	189	3	∑	∑	ADP
ejpam-5943	189	4	dfn(v1	dfn(v1	NOUN
ejpam-5943	189	5	,	,	PUNCT
ejpam-5943	189	6	vj	vj	NOUN
ejpam-5943	189	7	)	)	PUNCT
ejpam-5943	189	8	=	=	SYM
ejpam-5943	190	1	1	1	NUM
ejpam-5943	190	2	+	+	NUM
ejpam-5943	190	3	1	1	NUM
ejpam-5943	190	4	+	+	CCONJ
ejpam-5943	190	5	(	(	PUNCT
ejpam-5943	190	6	2n−	2n−	NUM
ejpam-5943	190	7	4	4	NUM
ejpam-5943	190	8	)	)	PUNCT
ejpam-5943	190	9	=	=	SYM
ejpam-5943	190	10	2	2	NUM
ejpam-5943	190	11	+	+	CCONJ
ejpam-5943	190	12	(	(	PUNCT
ejpam-5943	190	13	2n−	2n−	NUM
ejpam-5943	190	14	4	4	NUM
ejpam-5943	190	15	)	)	PUNCT
ejpam-5943	190	16	=	=	PUNCT
ejpam-5943	191	1	2n−	2n−	PROPN
ejpam-5943	191	2	2	2	NUM
ejpam-5943	191	3	.	.	PUNCT
ejpam-5943	192	1	hence	hence	ADV
ejpam-5943	192	2	,	,	PUNCT
ejpam-5943	192	3	ppf	ppf	PROPN
ejpam-5943	192	4	n(vi	n(vi	PRON
ejpam-5943	192	5	)	)	PUNCT
ejpam-5943	192	6	=	=	PUNCT
ejpam-5943	193	1	2n−	2n−	NUM
ejpam-5943	193	2	2	2	NUM
ejpam-5943	193	3	n+	n+	SYM
ejpam-5943	193	4	1	1	NUM
ejpam-5943	193	5	.	.	PUNCT
ejpam-5943	193	6	case	case	NOUN
ejpam-5943	193	7	3	3	NUM
ejpam-5943	193	8	:	:	PUNCT
ejpam-5943	193	9	deg(vi	deg(vi	NOUN
ejpam-5943	193	10	)	)	PUNCT
ejpam-5943	193	11	=	=	SYM
ejpam-5943	193	12	3	3	X
ejpam-5943	193	13	.	.	X
ejpam-5943	193	14	choose	choose	VERB
ejpam-5943	193	15	v2	v2	PROPN
ejpam-5943	193	16	∈	∈	PROPN
ejpam-5943	193	17	v	v	NOUN
ejpam-5943	193	18	(	(	PUNCT
ejpam-5943	193	19	fn	fn	NOUN
ejpam-5943	193	20	)	)	PUNCT
ejpam-5943	193	21	.	.	PUNCT
ejpam-5943	194	1	then	then	ADV
ejpam-5943	194	2	the	the	DET
ejpam-5943	194	3	distance	distance	NOUN
ejpam-5943	194	4	d(v2	d(v2	NOUN
ejpam-5943	194	5	,	,	PUNCT
ejpam-5943	194	6	vj	vj	PROPN
ejpam-5943	194	7	)	)	PUNCT
ejpam-5943	194	8	=	=	SYM
ejpam-5943	194	9	d(v2	d(v2	NOUN
ejpam-5943	194	10	,	,	PUNCT
ejpam-5943	194	11	v1	v1	NOUN
ejpam-5943	194	12	)	)	PUNCT
ejpam-5943	194	13	+	+	NUM
ejpam-5943	194	14	d(v2	d(v2	NOUN
ejpam-5943	194	15	,	,	PUNCT
ejpam-5943	194	16	v3	v3	PROPN
ejpam-5943	194	17	)	)	PUNCT
ejpam-5943	195	1	+	+	NUM
ejpam-5943	195	2	d(v2	d(v2	NOUN
ejpam-5943	195	3	,	,	PUNCT
ejpam-5943	195	4	vn+1	vn+1	PROPN
ejpam-5943	195	5	)	)	PUNCT
ejpam-5943	196	1	+	+	CCONJ
ejpam-5943	196	2	∑	∑	PROPN
ejpam-5943	196	3	j	j	PROPN
ejpam-5943	196	4	/∈{1,3,n+1	/∈{1,3,n+1	SYM
ejpam-5943	196	5	}	}	PUNCT
ejpam-5943	196	6	d(v2	d(v2	NOUN
ejpam-5943	196	7	,	,	PUNCT
ejpam-5943	196	8	vj	vj	PROPN
ejpam-5943	196	9	)	)	PUNCT
ejpam-5943	196	10	.	.	PUNCT
ejpam-5943	197	1	now	now	ADV
ejpam-5943	197	2	,	,	PUNCT
ejpam-5943	197	3	d(v2	d(v2	NOUN
ejpam-5943	197	4	,	,	PUNCT
ejpam-5943	197	5	v1	v1	NOUN
ejpam-5943	197	6	)	)	PUNCT
ejpam-5943	197	7	=	=	SYM
ejpam-5943	197	8	d(v2	d(v2	NOUN
ejpam-5943	197	9	,	,	PUNCT
ejpam-5943	197	10	v3	v3	PROPN
ejpam-5943	197	11	)	)	PUNCT
ejpam-5943	198	1	=	=	SYM
ejpam-5943	198	2	d(v2	d(v2	NOUN
ejpam-5943	198	3	,	,	PUNCT
ejpam-5943	198	4	vn+1	vn+1	PROPN
ejpam-5943	198	5	)	)	PUNCT
ejpam-5943	198	6	=	=	SYM
ejpam-5943	198	7	1	1	NUM
ejpam-5943	198	8	and	and	CCONJ
ejpam-5943	198	9	d(v2	d(v2	NOUN
ejpam-5943	198	10	,	,	PUNCT
ejpam-5943	198	11	vj	vj	PROPN
ejpam-5943	198	12	)	)	PUNCT
ejpam-5943	198	13	=	=	SYM
ejpam-5943	198	14	2	2	NUM
ejpam-5943	198	15	,	,	PUNCT
ejpam-5943	198	16	j	j	NOUN
ejpam-5943	198	17	/∈	/∈	PUNCT
ejpam-5943	198	18	{	{	PUNCT
ejpam-5943	198	19	1	1	NUM
ejpam-5943	198	20	,	,	PUNCT
ejpam-5943	198	21	3	3	NUM
ejpam-5943	198	22	,	,	PUNCT
ejpam-5943	198	23	n+	n+	NUM
ejpam-5943	198	24	1	1	NUM
ejpam-5943	198	25	}	}	PUNCT
ejpam-5943	198	26	.	.	PUNCT
ejpam-5943	199	1	thus,∑	thus,∑	PROPN
ejpam-5943	199	2	j	j	PROPN
ejpam-5943	199	3	/∈{1,3,n+1	/∈{1,3,n+1	SYM
ejpam-5943	199	4	}	}	PUNCT
ejpam-5943	199	5	d(v2	d(v2	NOUN
ejpam-5943	199	6	,	,	PUNCT
ejpam-5943	199	7	vj	vj	PROPN
ejpam-5943	199	8	)	)	PUNCT
ejpam-5943	199	9	=	=	SYM
ejpam-5943	199	10	2	2	NUM
ejpam-5943	199	11	+	+	NUM
ejpam-5943	199	12	2	2	NUM
ejpam-5943	199	13	+	+	NUM
ejpam-5943	199	14	.	.	PUNCT
ejpam-5943	199	15	.	.	PUNCT
ejpam-5943	200	1	.+	.+	NOUN
ejpam-5943	200	2	2︸	2︸	NUM
ejpam-5943	200	3	︷︷	︷︷	PROPN
ejpam-5943	200	4	︸	︸	ADP
ejpam-5943	200	5	n-3	n-3	ADJ
ejpam-5943	200	6	addends	addend	VERB
ejpam-5943	200	7	=	=	PUNCT
ejpam-5943	200	8	2(n−	2(n−	NUM
ejpam-5943	200	9	3	3	NUM
ejpam-5943	200	10	)	)	PUNCT
ejpam-5943	200	11	=	=	PUNCT
ejpam-5943	201	1	2n−	2n−	NUM
ejpam-5943	201	2	6	6	NUM
ejpam-5943	201	3	thus	thus	ADV
ejpam-5943	201	4	,	,	PUNCT
ejpam-5943	201	5	∑	∑	PROPN
ejpam-5943	201	6	df	df	PROPN
ejpam-5943	201	7	n(v2	n(v2	NOUN
ejpam-5943	201	8	,	,	PUNCT
ejpam-5943	201	9	vj	vj	INTJ
ejpam-5943	201	10	)	)	PUNCT
ejpam-5943	201	11	=	=	SYM
ejpam-5943	201	12	1	1	NUM
ejpam-5943	202	1	+	+	NUM
ejpam-5943	202	2	1	1	NUM
ejpam-5943	203	1	+	+	NUM
ejpam-5943	203	2	1	1	NUM
ejpam-5943	203	3	+	+	NUM
ejpam-5943	203	4	2	2	NUM
ejpam-5943	203	5	+	+	SYM
ejpam-5943	203	6	2	2	NUM
ejpam-5943	203	7	+	+	NUM
ejpam-5943	203	8	.	.	PUNCT
ejpam-5943	203	9	.	.	PUNCT
ejpam-5943	204	1	.+	.+	NOUN
ejpam-5943	204	2	2︸	2︸	NUM
ejpam-5943	204	3	︷︷	︷︷	PROPN
ejpam-5943	204	4	︸	︸	ADP
ejpam-5943	204	5	n-3	n-3	ADJ
ejpam-5943	204	6	addends	addend	NOUN
ejpam-5943	204	7	=	=	SYM
ejpam-5943	204	8	3	3	NUM
ejpam-5943	204	9	+	+	CCONJ
ejpam-5943	204	10	(	(	PUNCT
ejpam-5943	204	11	2n−	2n−	NUM
ejpam-5943	204	12	6	6	NUM
ejpam-5943	204	13	)	)	PUNCT
ejpam-5943	204	14	=	=	PUNCT
ejpam-5943	205	1	2n−	2n−	NUM
ejpam-5943	205	2	3	3	NUM
ejpam-5943	205	3	.	.	PUNCT
ejpam-5943	205	4	l.	l.	PROPN
ejpam-5943	205	5	toladro	toladro	PROPN
ejpam-5943	205	6	,	,	PUNCT
ejpam-5943	205	7	i.	i.	PROPN
ejpam-5943	205	8	cabahug	cabahug	PROPN
ejpam-5943	205	9	/	/	SYM
ejpam-5943	205	10	eur	eur	PROPN
ejpam-5943	205	11	.	.	PUNCT
ejpam-5943	206	1	j.	j.	PROPN
ejpam-5943	206	2	pure	pure	PROPN
ejpam-5943	206	3	appl	appl	PROPN
ejpam-5943	206	4	.	.	PROPN
ejpam-5943	206	5	math	math	PROPN
ejpam-5943	206	6	,	,	PUNCT
ejpam-5943	206	7	18	18	NUM
ejpam-5943	206	8	(	(	PUNCT
ejpam-5943	206	9	2	2	NUM
ejpam-5943	206	10	)	)	PUNCT
ejpam-5943	206	11	(	(	PUNCT
ejpam-5943	206	12	2025	2025	NUM
ejpam-5943	206	13	)	)	PUNCT
ejpam-5943	206	14	,	,	PUNCT
ejpam-5943	206	15	5943	5943	NUM
ejpam-5943	206	16	9	9	NUM
ejpam-5943	206	17	of	of	ADP
ejpam-5943	206	18	13	13	NUM
ejpam-5943	206	19	hence	hence	ADV
ejpam-5943	206	20	,	,	PUNCT
ejpam-5943	206	21	ppf	ppf	PROPN
ejpam-5943	206	22	n(vi	n(vi	PRON
ejpam-5943	206	23	)	)	PUNCT
ejpam-5943	206	24	=	=	PUNCT
ejpam-5943	207	1	2n−	2n−	NUM
ejpam-5943	207	2	3	3	NUM
ejpam-5943	207	3	n+	n+	SYM
ejpam-5943	207	4	1	1	NUM
ejpam-5943	207	5	.	.	PUNCT
ejpam-5943	208	1	therefore	therefore	ADV
ejpam-5943	208	2	,	,	PUNCT
ejpam-5943	208	3	we	we	PRON
ejpam-5943	208	4	have	have	VERB
ejpam-5943	208	5	ppf	ppf	PROPN
ejpam-5943	208	6	n(vi	n(vi	PROPN
ejpam-5943	208	7	)	)	PUNCT
ejpam-5943	208	8	=	=	SYM
ejpam-5943	208	9			PROPN
ejpam-5943	208	10	n	n	X
ejpam-5943	208	11	n+	n+	NUM
ejpam-5943	208	12	1	1	NUM
ejpam-5943	208	13	,	,	PUNCT
ejpam-5943	208	14	if	if	SCONJ
ejpam-5943	208	15	deg(vi	deg(vi	NOUN
ejpam-5943	208	16	)	)	PUNCT
ejpam-5943	208	17	=	=	SYM
ejpam-5943	208	18	n	n	CCONJ
ejpam-5943	208	19	;	;	PUNCT
ejpam-5943	208	20	2n−	2n−	PROPN
ejpam-5943	208	21	2	2	NUM
ejpam-5943	208	22	n+	n+	NUM
ejpam-5943	208	23	1	1	NUM
ejpam-5943	208	24	,	,	PUNCT
ejpam-5943	208	25	if	if	SCONJ
ejpam-5943	208	26	deg(vi	deg(vi	NOUN
ejpam-5943	208	27	)	)	PUNCT
ejpam-5943	208	28	=	=	SYM
ejpam-5943	208	29	2	2	NUM
ejpam-5943	208	30	;	;	PUNCT
ejpam-5943	208	31	2n−	2n−	PROPN
ejpam-5943	208	32	3	3	NUM
ejpam-5943	208	33	n+	n+	NUM
ejpam-5943	208	34	1	1	NUM
ejpam-5943	208	35	,	,	PUNCT
ejpam-5943	208	36	if	if	SCONJ
ejpam-5943	208	37	deg(vi	deg(vi	NOUN
ejpam-5943	208	38	)	)	PUNCT
ejpam-5943	208	39	=	=	SYM
ejpam-5943	208	40	3	3	X
ejpam-5943	208	41	.	.	X
ejpam-5943	209	1	■	■	PUNCT
ejpam-5943	209	2	theorem	theorem	ADJ
ejpam-5943	209	3	6	6	NUM
ejpam-5943	209	4	.	.	PUNCT
ejpam-5943	210	1	let	let	VERB
ejpam-5943	210	2	g	g	PROPN
ejpam-5943	210	3	=	=	SYM
ejpam-5943	210	4	(	(	PUNCT
ejpam-5943	210	5	v	v	NOUN
ejpam-5943	210	6	,	,	PUNCT
ejpam-5943	210	7	e	e	NOUN
ejpam-5943	210	8	)	)	PUNCT
ejpam-5943	210	9	be	be	VERB
ejpam-5943	210	10	a	a	DET
ejpam-5943	210	11	wheel	wheel	NOUN
ejpam-5943	210	12	graph	graph	NOUN
ejpam-5943	211	1	wn	wn	NOUN
ejpam-5943	211	2	=	=	PROPN
ejpam-5943	212	1	[	[	X
ejpam-5943	212	2	v1	v1	NOUN
ejpam-5943	212	3	,	,	PUNCT
ejpam-5943	212	4	v2	v2	NOUN
ejpam-5943	212	5	,	,	PUNCT
ejpam-5943	212	6	.	.	PUNCT
ejpam-5943	212	7	.	.	PUNCT
ejpam-5943	212	8	.	.	PUNCT
ejpam-5943	213	1	,	,	PUNCT
ejpam-5943	213	2	vn	vn	X
ejpam-5943	213	3	,	,	PUNCT
ejpam-5943	213	4	vn+1	vn+1	PROPN
ejpam-5943	213	5	]	]	PUNCT
ejpam-5943	213	6	where	where	SCONJ
ejpam-5943	213	7	deg(vn+1	deg(vn+1	NOUN
ejpam-5943	213	8	)	)	PUNCT
ejpam-5943	213	9	=	=	SYM
ejpam-5943	214	1	n	n	CCONJ
ejpam-5943	214	2	,	,	PUNCT
ejpam-5943	214	3	then	then	ADV
ejpam-5943	214	4	the	the	DET
ejpam-5943	214	5	proximity	proximity	NOUN
ejpam-5943	214	6	prestige	prestige	NOUN
ejpam-5943	214	7	of	of	ADP
ejpam-5943	214	8	any	any	DET
ejpam-5943	214	9	vertex	vertex	NOUN
ejpam-5943	214	10	vi	vi	NOUN
ejpam-5943	214	11	where	where	SCONJ
ejpam-5943	214	12	1	1	NUM
ejpam-5943	214	13	≤	≤	NUM
ejpam-5943	214	14	i	i	PRON
ejpam-5943	214	15	≤	≤	NOUN
ejpam-5943	214	16	n+	n+	PUNCT
ejpam-5943	214	17	1	1	NUM
ejpam-5943	214	18	is	be	AUX
ejpam-5943	214	19	given	give	VERB
ejpam-5943	214	20	by	by	ADP
ejpam-5943	214	21	,	,	PUNCT
ejpam-5943	214	22	ppwn(vi	ppwn(vi	NOUN
ejpam-5943	214	23	)	)	PUNCT
ejpam-5943	214	24	=	=	PUNCT
ejpam-5943	215	1			PROPN
ejpam-5943	215	2	n	n	NUM
ejpam-5943	215	3	n+	n+	NUM
ejpam-5943	215	4	1	1	NUM
ejpam-5943	215	5	,	,	PUNCT
ejpam-5943	215	6	if	if	SCONJ
ejpam-5943	215	7	deg(vvi	deg(vvi	NOUN
ejpam-5943	215	8	)	)	PUNCT
ejpam-5943	215	9	=	=	SYM
ejpam-5943	215	10	n	n	CCONJ
ejpam-5943	215	11	;	;	PUNCT
ejpam-5943	215	12	2n−	2n−	PROPN
ejpam-5943	215	13	3	3	NUM
ejpam-5943	215	14	n+	n+	NUM
ejpam-5943	215	15	1	1	NUM
ejpam-5943	215	16	,	,	PUNCT
ejpam-5943	215	17	if	if	SCONJ
ejpam-5943	215	18	deg(vi	deg(vi	NOUN
ejpam-5943	215	19	)	)	PUNCT
ejpam-5943	215	20	=	=	SYM
ejpam-5943	215	21	3	3	X
ejpam-5943	215	22	.	.	PUNCT
ejpam-5943	215	23	proof	proof	NOUN
ejpam-5943	215	24	.	.	PUNCT
ejpam-5943	216	1	using	use	VERB
ejpam-5943	216	2	the	the	DET
ejpam-5943	216	3	structure	structure	NOUN
ejpam-5943	216	4	of	of	ADP
ejpam-5943	216	5	a	a	DET
ejpam-5943	216	6	wheel	wheel	NOUN
ejpam-5943	216	7	graph	graph	NOUN
ejpam-5943	216	8	,	,	PUNCT
ejpam-5943	216	9	formed	form	VERB
ejpam-5943	216	10	by	by	ADP
ejpam-5943	216	11	adjoining	adjoin	VERB
ejpam-5943	216	12	central	central	ADJ
ejpam-5943	216	13	vertex	vertex	NOUN
ejpam-5943	216	14	(	(	PUNCT
ejpam-5943	216	15	vn+1	vn+1	NOUN
ejpam-5943	216	16	)	)	PUNCT
ejpam-5943	216	17	to	to	ADP
ejpam-5943	216	18	each	each	DET
ejpam-5943	216	19	vertex	vertex	NOUN
ejpam-5943	216	20	of	of	ADP
ejpam-5943	216	21	the	the	DET
ejpam-5943	216	22	cycle	cycle	NOUN
ejpam-5943	216	23	cn	cn	NOUN
ejpam-5943	217	1	=	=	PUNCT
ejpam-5943	218	1	[	[	X
ejpam-5943	218	2	v1	v1	NOUN
ejpam-5943	218	3	,	,	PUNCT
ejpam-5943	218	4	v2	v2	NOUN
ejpam-5943	218	5	,	,	PUNCT
ejpam-5943	218	6	.	.	PUNCT
ejpam-5943	218	7	.	.	PUNCT
ejpam-5943	218	8	.	.	PUNCT
ejpam-5943	219	1	,	,	PUNCT
ejpam-5943	219	2	vn	vn	X
ejpam-5943	219	3	,	,	PUNCT
ejpam-5943	219	4	v1	v1	PROPN
ejpam-5943	219	5	]	]	PUNCT
ejpam-5943	219	6	the	the	DET
ejpam-5943	219	7	following	follow	VERB
ejpam-5943	219	8	cases	case	NOUN
ejpam-5943	219	9	are	be	AUX
ejpam-5943	219	10	need	need	ADJ
ejpam-5943	219	11	to	to	PART
ejpam-5943	219	12	be	be	AUX
ejpam-5943	219	13	considered	consider	VERB
ejpam-5943	219	14	.	.	PUNCT
ejpam-5943	220	1	case	case	NOUN
ejpam-5943	220	2	1	1	NUM
ejpam-5943	220	3	:	:	PUNCT
ejpam-5943	220	4	deg(vi	deg(vi	X
ejpam-5943	220	5	)	)	PUNCT
ejpam-5943	220	6	=	=	VERB
ejpam-5943	221	1	n.	n.	NOUN
ejpam-5943	221	2	in	in	ADP
ejpam-5943	221	3	this	this	DET
ejpam-5943	221	4	case	case	NOUN
ejpam-5943	221	5	,	,	PUNCT
ejpam-5943	221	6	vi	vi	NOUN
ejpam-5943	221	7	=	=	SYM
ejpam-5943	221	8	vn+1	vn+1	PROPN
ejpam-5943	221	9	,	,	PUNCT
ejpam-5943	221	10	that	that	PRON
ejpam-5943	221	11	is	be	AUX
ejpam-5943	221	12	the	the	DET
ejpam-5943	221	13	central	central	ADJ
ejpam-5943	221	14	vertex	vertex	NOUN
ejpam-5943	221	15	of	of	ADP
ejpam-5943	221	16	a	a	DET
ejpam-5943	221	17	wheel	wheel	NOUN
ejpam-5943	221	18	graph	graph	NOUN
ejpam-5943	221	19	.	.	PUNCT
ejpam-5943	222	1	there	there	PRON
ejpam-5943	222	2	is	be	VERB
ejpam-5943	222	3	only	only	ADV
ejpam-5943	222	4	one	one	NUM
ejpam-5943	222	5	vertex	vertex	NOUN
ejpam-5943	222	6	with	with	ADP
ejpam-5943	222	7	a	a	DET
ejpam-5943	222	8	degree	degree	NOUN
ejpam-5943	222	9	n	n	CCONJ
ejpam-5943	222	10	,	,	PUNCT
ejpam-5943	222	11	that	that	PRON
ejpam-5943	222	12	is	be	AUX
ejpam-5943	222	13	vn+1	vn+1	NUM
ejpam-5943	222	14	and	and	CCONJ
ejpam-5943	222	15	distance	distance	NOUN
ejpam-5943	222	16	d(vn+1	d(vn+1	NOUN
ejpam-5943	222	17	,	,	PUNCT
ejpam-5943	222	18	vj	vj	INTJ
ejpam-5943	222	19	)	)	PUNCT
ejpam-5943	222	20	=	=	SYM
ejpam-5943	222	21	1	1	NUM
ejpam-5943	222	22	for	for	ADP
ejpam-5943	222	23	j	j	PROPN
ejpam-5943	222	24	̸=	̸=	PROPN
ejpam-5943	222	25	n+	n+	PUNCT
ejpam-5943	222	26	1	1	NUM
ejpam-5943	222	27	since	since	SCONJ
ejpam-5943	222	28	each	each	DET
ejpam-5943	222	29	vertex	vertex	NOUN
ejpam-5943	222	30	{	{	PUNCT
ejpam-5943	222	31	v1	v1	NOUN
ejpam-5943	222	32	,	,	PUNCT
ejpam-5943	222	33	v2	v2	NOUN
ejpam-5943	222	34	,	,	PUNCT
ejpam-5943	222	35	.	.	PUNCT
ejpam-5943	222	36	.	.	PUNCT
ejpam-5943	222	37	.	.	PUNCT
ejpam-5943	223	1	,	,	PUNCT
ejpam-5943	223	2	vn	vn	AUX
ejpam-5943	223	3	}	}	PUNCT
ejpam-5943	223	4	is	be	AUX
ejpam-5943	223	5	directly	directly	ADV
ejpam-5943	223	6	connected	connect	VERB
ejpam-5943	223	7	to	to	ADP
ejpam-5943	223	8	the	the	DET
ejpam-5943	223	9	central	central	ADJ
ejpam-5943	223	10	vertex	vertex	NOUN
ejpam-5943	223	11	.	.	PUNCT
ejpam-5943	224	1	thus,∑	thus,∑	NOUN
ejpam-5943	224	2	dwn(vi	dwn(vi	NOUN
ejpam-5943	224	3	,	,	PUNCT
ejpam-5943	224	4	vj	vj	INTJ
ejpam-5943	224	5	)	)	PUNCT
ejpam-5943	224	6	=	=	SYM
ejpam-5943	225	1	1	1	NUM
ejpam-5943	225	2	+	+	NUM
ejpam-5943	225	3	1	1	NUM
ejpam-5943	225	4	+	+	CCONJ
ejpam-5943	225	5	.	.	PUNCT
ejpam-5943	225	6	.	.	PUNCT
ejpam-5943	226	1	.+	.+	NOUN
ejpam-5943	227	1	1︸	1︸	NUM
ejpam-5943	227	2	︷︷	︷︷	NOUN
ejpam-5943	227	3	︸	︸	ADP
ejpam-5943	227	4	n	n	PROPN
ejpam-5943	227	5	addends	addend	VERB
ejpam-5943	227	6	=	=	PUNCT
ejpam-5943	227	7	n.	n.	PROPN
ejpam-5943	227	8	hence	hence	ADV
ejpam-5943	227	9	,	,	PUNCT
ejpam-5943	227	10	ppwn(vi	ppwn(vi	PROPN
ejpam-5943	227	11	)	)	PUNCT
ejpam-5943	227	12	=	=	SYM
ejpam-5943	227	13	n	n	NUM
ejpam-5943	227	14	2n+	2n+	NUM
ejpam-5943	227	15	1	1	NUM
ejpam-5943	227	16	.	.	PUNCT
ejpam-5943	228	1	case	case	NOUN
ejpam-5943	228	2	2	2	NUM
ejpam-5943	228	3	:	:	PUNCT
ejpam-5943	228	4	deg(vi	deg(vi	NUM
ejpam-5943	228	5	)	)	PUNCT
ejpam-5943	228	6	=	=	SYM
ejpam-5943	228	7	3	3	X
ejpam-5943	228	8	.	.	X
ejpam-5943	229	1	in	in	ADP
ejpam-5943	229	2	this	this	DET
ejpam-5943	229	3	case	case	NOUN
ejpam-5943	229	4	,	,	PUNCT
ejpam-5943	229	5	vi	vi	PROPN
ejpam-5943	229	6	is	be	AUX
ejpam-5943	229	7	any	any	PRON
ejpam-5943	229	8	of	of	ADP
ejpam-5943	229	9	the	the	DET
ejpam-5943	229	10	vertices	vertex	NOUN
ejpam-5943	229	11	{	{	PUNCT
ejpam-5943	229	12	v1	v1	NOUN
ejpam-5943	229	13	,	,	PUNCT
ejpam-5943	229	14	v2	v2	NOUN
ejpam-5943	229	15	,	,	PUNCT
ejpam-5943	229	16	.	.	PUNCT
ejpam-5943	229	17	.	.	PUNCT
ejpam-5943	229	18	.	.	PUNCT
ejpam-5943	230	1	,	,	PUNCT
ejpam-5943	230	2	vn	vn	PROPN
ejpam-5943	230	3	}	}	PUNCT
ejpam-5943	230	4	.	.	PUNCT
ejpam-5943	231	1	the	the	DET
ejpam-5943	231	2	distance	distance	NOUN
ejpam-5943	231	3	from	from	ADP
ejpam-5943	231	4	any	any	DET
ejpam-5943	231	5	vertex	vertex	NOUN
ejpam-5943	231	6	vi	vi	NOUN
ejpam-5943	231	7	where	where	SCONJ
ejpam-5943	231	8	1	1	NUM
ejpam-5943	231	9	≤	≤	NUM
ejpam-5943	231	10	i	i	PRON
ejpam-5943	231	11	≤	≤	NOUN
ejpam-5943	231	12	n	n	CCONJ
ejpam-5943	231	13	to	to	ADP
ejpam-5943	231	14	the	the	DET
ejpam-5943	231	15	central	central	ADJ
ejpam-5943	231	16	vertex	vertex	NOUN
ejpam-5943	231	17	vn+1	vn+1	PROPN
ejpam-5943	231	18	is	be	AUX
ejpam-5943	231	19	1	1	NUM
ejpam-5943	231	20	since	since	SCONJ
ejpam-5943	231	21	each	each	DET
ejpam-5943	231	22	vi	vi	NOUN
ejpam-5943	231	23	is	be	AUX
ejpam-5943	231	24	adjacent	adjacent	ADJ
ejpam-5943	231	25	to	to	PART
ejpam-5943	231	26	vn+1	vn+1	VERB
ejpam-5943	231	27	and	and	CCONJ
ejpam-5943	231	28	also	also	ADV
ejpam-5943	231	29	the	the	DET
ejpam-5943	231	30	distance	distance	NOUN
ejpam-5943	231	31	from	from	ADP
ejpam-5943	231	32	vi	vi	NOUN
ejpam-5943	231	33	to	to	ADP
ejpam-5943	231	34	its	its	PRON
ejpam-5943	231	35	two	two	NUM
ejpam-5943	231	36	adjacent	adjacent	ADJ
ejpam-5943	231	37	vertices	vertex	NOUN
ejpam-5943	231	38	vi−1	vi−1	PROPN
ejpam-5943	231	39	and	and	CCONJ
ejpam-5943	231	40	vi+1	vi+1	ADV
ejpam-5943	231	41	in	in	ADP
ejpam-5943	231	42	the	the	DET
ejpam-5943	231	43	cycle	cycle	NOUN
ejpam-5943	231	44	cn	cn	PROPN
ejpam-5943	231	45	is	be	AUX
ejpam-5943	231	46	1	1	NUM
ejpam-5943	231	47	.	.	PUNCT
ejpam-5943	232	1	then	then	ADV
ejpam-5943	232	2	l.	l.	PROPN
ejpam-5943	232	3	toladro	toladro	PROPN
ejpam-5943	232	4	,	,	PUNCT
ejpam-5943	232	5	i.	i.	PROPN
ejpam-5943	232	6	cabahug	cabahug	PROPN
ejpam-5943	232	7	/	/	SYM
ejpam-5943	232	8	eur	eur	PROPN
ejpam-5943	232	9	.	.	PUNCT
ejpam-5943	233	1	j.	j.	PROPN
ejpam-5943	233	2	pure	pure	PROPN
ejpam-5943	233	3	appl	appl	PROPN
ejpam-5943	233	4	.	.	PROPN
ejpam-5943	233	5	math	math	PROPN
ejpam-5943	233	6	,	,	PUNCT
ejpam-5943	233	7	18	18	NUM
ejpam-5943	233	8	(	(	PUNCT
ejpam-5943	233	9	2	2	NUM
ejpam-5943	233	10	)	)	PUNCT
ejpam-5943	233	11	(	(	PUNCT
ejpam-5943	233	12	2025	2025	NUM
ejpam-5943	233	13	)	)	PUNCT
ejpam-5943	233	14	,	,	PUNCT
ejpam-5943	233	15	5943	5943	NUM
ejpam-5943	233	16	10	10	NUM
ejpam-5943	233	17	of	of	ADP
ejpam-5943	233	18	13	13	NUM
ejpam-5943	233	19	the	the	DET
ejpam-5943	233	20	distance	distance	NOUN
ejpam-5943	233	21	from	from	ADP
ejpam-5943	233	22	vi	vi	NOUN
ejpam-5943	233	23	to	to	ADP
ejpam-5943	233	24	any	any	DET
ejpam-5943	233	25	other	other	ADJ
ejpam-5943	233	26	vertex	vertex	NOUN
ejpam-5943	233	27	vj	vj	NOUN
ejpam-5943	233	28	in	in	ADP
ejpam-5943	233	29	the	the	DET
ejpam-5943	233	30	cycle	cycle	NOUN
ejpam-5943	233	31	where	where	SCONJ
ejpam-5943	233	32	j	j	PROPN
ejpam-5943	233	33	/∈	/∈	PUNCT
ejpam-5943	233	34	{	{	PUNCT
ejpam-5943	233	35	i	i	NOUN
ejpam-5943	233	36	,	,	PUNCT
ejpam-5943	233	37	i−	i−	PROPN
ejpam-5943	233	38	1	1	NUM
ejpam-5943	233	39	,	,	PUNCT
ejpam-5943	233	40	i+	i+	NOUN
ejpam-5943	233	41	1	1	X
ejpam-5943	233	42	}	}	PUNCT
ejpam-5943	233	43	is	be	AUX
ejpam-5943	233	44	2	2	NUM
ejpam-5943	233	45	.	.	PUNCT
ejpam-5943	234	1	thus	thus	ADV
ejpam-5943	234	2	the	the	DET
ejpam-5943	234	3	distance	distance	NOUN
ejpam-5943	234	4	d(vi	d(vi	PROPN
ejpam-5943	234	5	,	,	PUNCT
ejpam-5943	234	6	vj	vj	ADJ
ejpam-5943	234	7	)	)	PUNCT
ejpam-5943	234	8	=	=	SYM
ejpam-5943	234	9	d(vi	d(vi	PROPN
ejpam-5943	234	10	,	,	PUNCT
ejpam-5943	234	11	vi−1	vi−1	PROPN
ejpam-5943	234	12	)	)	PUNCT
ejpam-5943	234	13	+	+	CCONJ
ejpam-5943	234	14	d(vi	d(vi	PROPN
ejpam-5943	234	15	,	,	PUNCT
ejpam-5943	234	16	vi+1	vi+1	NOUN
ejpam-5943	234	17	)	)	PUNCT
ejpam-5943	234	18	+	+	CCONJ
ejpam-5943	234	19	d(vi	d(vi	PROPN
ejpam-5943	234	20	,	,	PUNCT
ejpam-5943	234	21	vn+1	vn+1	NOUN
ejpam-5943	234	22	)	)	PUNCT
ejpam-5943	235	1	+	+	CCONJ
ejpam-5943	235	2	∑	∑	PROPN
ejpam-5943	235	3	j	j	PROPN
ejpam-5943	235	4	/∈{i−1,i+1,n+1	/∈{i−1,i+1,n+1	PROPN
ejpam-5943	235	5	}	}	PUNCT
ejpam-5943	235	6	d(vi	d(vi	PROPN
ejpam-5943	235	7	,	,	PUNCT
ejpam-5943	235	8	vj	vj	NOUN
ejpam-5943	235	9	)	)	PUNCT
ejpam-5943	235	10	.	.	PUNCT
ejpam-5943	236	1	now	now	ADV
ejpam-5943	236	2	,	,	PUNCT
ejpam-5943	236	3	from	from	ADP
ejpam-5943	236	4	vi	vi	PROPN
ejpam-5943	236	5	there	there	PRON
ejpam-5943	236	6	are	be	VERB
ejpam-5943	236	7	3	3	NUM
ejpam-5943	236	8	vertices	vertex	NOUN
ejpam-5943	236	9	that	that	PRON
ejpam-5943	236	10	have	have	VERB
ejpam-5943	236	11	distance	distance	NOUN
ejpam-5943	236	12	1	1	NUM
ejpam-5943	236	13	,	,	PUNCT
ejpam-5943	236	14	that	that	PRON
ejpam-5943	236	15	is	be	AUX
ejpam-5943	236	16	d(vi	d(vi	PROPN
ejpam-5943	236	17	,	,	PUNCT
ejpam-5943	236	18	vi−1	vi−1	PROPN
ejpam-5943	236	19	)	)	PUNCT
ejpam-5943	236	20	,	,	PUNCT
ejpam-5943	236	21	d(vi	d(vi	PROPN
ejpam-5943	236	22	,	,	PUNCT
ejpam-5943	236	23	vi+1)and	vi+1)and	CCONJ
ejpam-5943	236	24	d(vi	d(vi	PROPN
ejpam-5943	236	25	,	,	PUNCT
ejpam-5943	236	26	vn+1	vn+1	PROPN
ejpam-5943	236	27	)	)	PUNCT
ejpam-5943	236	28	.	.	PUNCT
ejpam-5943	237	1	also	also	ADV
ejpam-5943	237	2	,	,	PUNCT
ejpam-5943	237	3	the	the	DET
ejpam-5943	237	4	remaining	remain	VERB
ejpam-5943	237	5	n−	n−	NOUN
ejpam-5943	237	6	3	3	NUM
ejpam-5943	237	7	vertices	vertex	NOUN
ejpam-5943	237	8	has	have	VERB
ejpam-5943	237	9	distance	distance	NOUN
ejpam-5943	237	10	2	2	NUM
ejpam-5943	237	11	from	from	ADP
ejpam-5943	237	12	vi	vi	PROPN
ejpam-5943	237	13	.	.	PUNCT
ejpam-5943	237	14	thus,∑	thus,∑	NOUN
ejpam-5943	237	15	dfn(vi	dfn(vi	NOUN
ejpam-5943	237	16	,	,	PUNCT
ejpam-5943	237	17	vj	vj	PROPN
ejpam-5943	237	18	)	)	PUNCT
ejpam-5943	237	19	=	=	SYM
ejpam-5943	238	1	1	1	NUM
ejpam-5943	238	2	+	+	NUM
ejpam-5943	238	3	1	1	NUM
ejpam-5943	238	4	+	+	NUM
ejpam-5943	238	5	1	1	NUM
ejpam-5943	238	6	+	+	NUM
ejpam-5943	238	7	2	2	NUM
ejpam-5943	238	8	+	+	SYM
ejpam-5943	238	9	2	2	NUM
ejpam-5943	238	10	+	+	NUM
ejpam-5943	238	11	.	.	PUNCT
ejpam-5943	238	12	.	.	PUNCT
ejpam-5943	239	1	.+	.+	NOUN
ejpam-5943	239	2	2︸	2︸	NUM
ejpam-5943	239	3	︷︷	︷︷	PROPN
ejpam-5943	239	4	︸	︸	ADP
ejpam-5943	239	5	n-3	n-3	ADJ
ejpam-5943	239	6	addends	addend	NOUN
ejpam-5943	239	7	=	=	PUNCT
ejpam-5943	239	8	3	3	NUM
ejpam-5943	239	9	+	+	CCONJ
ejpam-5943	240	1	2n−	2n−	NUM
ejpam-5943	240	2	6	6	NUM
ejpam-5943	240	3	=	=	SYM
ejpam-5943	240	4	2n−	2n−	NUM
ejpam-5943	240	5	3	3	NUM
ejpam-5943	240	6	hence	hence	ADV
ejpam-5943	240	7	,	,	PUNCT
ejpam-5943	240	8	ppwn(vi	ppwn(vi	NOUN
ejpam-5943	240	9	)	)	PUNCT
ejpam-5943	240	10	=	=	PUNCT
ejpam-5943	241	1	2n−	2n−	NUM
ejpam-5943	241	2	3	3	NUM
ejpam-5943	241	3	n+	n+	SYM
ejpam-5943	241	4	1	1	NUM
ejpam-5943	241	5	.	.	PUNCT
ejpam-5943	242	1	therefore	therefore	ADV
ejpam-5943	242	2	,	,	PUNCT
ejpam-5943	242	3	we	we	PRON
ejpam-5943	242	4	have	have	AUX
ejpam-5943	242	5	ppwn(vi	ppwn(vi	VERB
ejpam-5943	242	6	)	)	PUNCT
ejpam-5943	242	7	=	=	PUNCT
ejpam-5943	243	1			PROPN
ejpam-5943	243	2	n	n	NUM
ejpam-5943	243	3	n+	n+	NUM
ejpam-5943	243	4	1	1	NUM
ejpam-5943	243	5	,	,	PUNCT
ejpam-5943	243	6	if	if	SCONJ
ejpam-5943	243	7	deg(vi	deg(vi	NOUN
ejpam-5943	243	8	)	)	PUNCT
ejpam-5943	243	9	=	=	SYM
ejpam-5943	243	10	n	n	CCONJ
ejpam-5943	243	11	;	;	PUNCT
ejpam-5943	243	12	2n−	2n−	PROPN
ejpam-5943	243	13	3	3	NUM
ejpam-5943	243	14	n+	n+	NUM
ejpam-5943	243	15	1	1	NUM
ejpam-5943	243	16	,	,	PUNCT
ejpam-5943	243	17	if	if	SCONJ
ejpam-5943	243	18	deg(vi	deg(vi	NOUN
ejpam-5943	243	19	)	)	PUNCT
ejpam-5943	243	20	=	=	SYM
ejpam-5943	243	21	3	3	X
ejpam-5943	243	22	.	.	X
ejpam-5943	243	23	■	■	PUNCT
ejpam-5943	243	24	theorem	theorem	ADJ
ejpam-5943	243	25	7	7	NUM
ejpam-5943	243	26	.	.	PUNCT
ejpam-5943	244	1	let	let	VERB
ejpam-5943	244	2	g	g	PROPN
ejpam-5943	244	3	=	=	SYM
ejpam-5943	244	4	(	(	PUNCT
ejpam-5943	244	5	v	v	NOUN
ejpam-5943	244	6	,	,	PUNCT
ejpam-5943	244	7	e	e	NOUN
ejpam-5943	244	8	)	)	PUNCT
ejpam-5943	244	9	be	be	AUX
ejpam-5943	244	10	a	a	DET
ejpam-5943	244	11	complete	complete	ADJ
ejpam-5943	244	12	bipartite	bipartite	ADJ
ejpam-5943	244	13	km	km	PROPN
ejpam-5943	244	14	,	,	PUNCT
ejpam-5943	244	15	n	n	CCONJ
ejpam-5943	244	16	,	,	PUNCT
ejpam-5943	244	17	then	then	ADV
ejpam-5943	244	18	the	the	DET
ejpam-5943	244	19	proximity	proximity	NOUN
ejpam-5943	244	20	prestige	prestige	NOUN
ejpam-5943	244	21	of	of	ADP
ejpam-5943	244	22	any	any	DET
ejpam-5943	244	23	vertex	vertex	NOUN
ejpam-5943	244	24	vi	vi	NOUN
ejpam-5943	244	25	where	where	SCONJ
ejpam-5943	244	26	1	1	NUM
ejpam-5943	244	27	≤	≤	NUM
ejpam-5943	244	28	i	i	PRON
ejpam-5943	244	29	≤	≤	NUM
ejpam-5943	245	1	m+	m+	NUM
ejpam-5943	245	2	n	n	PRON
ejpam-5943	245	3	is	be	AUX
ejpam-5943	245	4	given	give	VERB
ejpam-5943	245	5	by	by	ADP
ejpam-5943	245	6	,	,	PUNCT
ejpam-5943	245	7	ppkm	ppkm	PROPN
ejpam-5943	245	8	,	,	PUNCT
ejpam-5943	245	9	n(vi	n(vi	NUM
ejpam-5943	245	10	)	)	PUNCT
ejpam-5943	245	11	=	=	PUNCT
ejpam-5943	245	12			X
ejpam-5943	245	13	n+	n+	PUNCT
ejpam-5943	245	14	(	(	PUNCT
ejpam-5943	245	15	2m−	2m−	NOUN
ejpam-5943	245	16	2	2	NUM
ejpam-5943	245	17	)	)	PUNCT
ejpam-5943	245	18	m+	m+	NUM
ejpam-5943	245	19	n	n	CCONJ
ejpam-5943	245	20	,	,	PUNCT
ejpam-5943	245	21	if	if	SCONJ
ejpam-5943	245	22	deg(vi	deg(vi	NOUN
ejpam-5943	245	23	)	)	PUNCT
ejpam-5943	245	24	=	=	SYM
ejpam-5943	245	25	n	n	CCONJ
ejpam-5943	245	26	;	;	PUNCT
ejpam-5943	245	27	m+	m+	NUM
ejpam-5943	245	28	(	(	PUNCT
ejpam-5943	245	29	2n−	2n−	PROPN
ejpam-5943	245	30	2	2	NUM
ejpam-5943	245	31	)	)	PUNCT
ejpam-5943	245	32	m+	m+	NUM
ejpam-5943	245	33	n	n	CCONJ
ejpam-5943	245	34	,	,	PUNCT
ejpam-5943	245	35	if	if	SCONJ
ejpam-5943	245	36	deg(vi	deg(vi	NOUN
ejpam-5943	245	37	)	)	PUNCT
ejpam-5943	245	38	=	=	SYM
ejpam-5943	245	39	m.	m.	NOUN
ejpam-5943	245	40	proof	proof	NOUN
ejpam-5943	245	41	.	.	PUNCT
ejpam-5943	246	1	using	use	VERB
ejpam-5943	246	2	the	the	DET
ejpam-5943	246	3	structure	structure	NOUN
ejpam-5943	246	4	of	of	ADP
ejpam-5943	246	5	complete	complete	ADJ
ejpam-5943	246	6	bipartite	bipartite	NOUN
ejpam-5943	246	7	graph	graph	NOUN
ejpam-5943	246	8	,	,	PUNCT
ejpam-5943	246	9	formed	form	VERB
ejpam-5943	246	10	if	if	SCONJ
ejpam-5943	246	11	its	its	PRON
ejpam-5943	246	12	vertices	vertex	NOUN
ejpam-5943	246	13	can	can	AUX
ejpam-5943	246	14	be	be	AUX
ejpam-5943	246	15	partitioned	partition	VERB
ejpam-5943	246	16	into	into	ADP
ejpam-5943	246	17	two	two	NUM
ejpam-5943	246	18	disjoint	disjoint	NOUN
ejpam-5943	246	19	nonempty	nonempty	NOUN
ejpam-5943	246	20	sets	set	VERB
ejpam-5943	246	21	v1	v1	NOUN
ejpam-5943	246	22	and	and	CCONJ
ejpam-5943	246	23	v2	v2	VERB
ejpam-5943	246	24	such	such	ADJ
ejpam-5943	246	25	that	that	SCONJ
ejpam-5943	246	26	two	two	NUM
ejpam-5943	246	27	vertices	vertex	NOUN
ejpam-5943	246	28	u	u	NOUN
ejpam-5943	246	29	and	and	CCONJ
ejpam-5943	246	30	v	v	NOUN
ejpam-5943	246	31	are	be	AUX
ejpam-5943	246	32	adjacent	adjacent	ADJ
ejpam-5943	246	33	if	if	SCONJ
ejpam-5943	246	34	and	and	CCONJ
ejpam-5943	246	35	only	only	ADV
ejpam-5943	246	36	if	if	SCONJ
ejpam-5943	246	37	u	u	PROPN
ejpam-5943	246	38	∈	∈	NOUN
ejpam-5943	246	39	v1	v1	NOUN
ejpam-5943	246	40	and	and	CCONJ
ejpam-5943	246	41	v	v	ADP
ejpam-5943	246	42	∈	∈	PROPN
ejpam-5943	246	43	v2	v2	NOUN
ejpam-5943	246	44	then	then	ADV
ejpam-5943	246	45	the	the	DET
ejpam-5943	246	46	following	follow	VERB
ejpam-5943	246	47	cases	case	NOUN
ejpam-5943	246	48	are	be	AUX
ejpam-5943	246	49	needed	need	VERB
ejpam-5943	246	50	to	to	PART
ejpam-5943	246	51	be	be	AUX
ejpam-5943	246	52	consider	consider	VERB
ejpam-5943	246	53	.	.	PUNCT
ejpam-5943	247	1	case	case	NOUN
ejpam-5943	247	2	1	1	NUM
ejpam-5943	247	3	:	:	PUNCT
ejpam-5943	247	4	deg(vi	deg(vi	X
ejpam-5943	247	5	)	)	PUNCT
ejpam-5943	247	6	=	=	SYM
ejpam-5943	247	7	n.	n.	NOUN
ejpam-5943	247	8	then	then	ADV
ejpam-5943	247	9	,	,	PUNCT
ejpam-5943	247	10	∑	∑	PROPN
ejpam-5943	247	11	i	i	PRON
ejpam-5943	247	12	̸=j	̸=j	VERB
ejpam-5943	247	13	dkm	dkm	PROPN
ejpam-5943	247	14	,	,	PUNCT
ejpam-5943	247	15	n(vi	n(vi	PROPN
ejpam-5943	247	16	,	,	PUNCT
ejpam-5943	247	17	vj	vj	ADJ
ejpam-5943	247	18	)	)	PUNCT
ejpam-5943	247	19	=	=	PUNCT
ejpam-5943	247	20	∑	∑	PUNCT
ejpam-5943	247	21	1≤q≤n	1≤q≤n	NUM
ejpam-5943	247	22	d(vi	d(vi	PROPN
ejpam-5943	247	23	,	,	PUNCT
ejpam-5943	247	24	vq	vq	NOUN
ejpam-5943	247	25	)	)	PUNCT
ejpam-5943	247	26	+	+	CCONJ
ejpam-5943	247	27	∑	∑	PROPN
ejpam-5943	247	28	k	k	PROPN
ejpam-5943	247	29	̸=i,1≤k≤m	̸=i,1≤k≤m	PROPN
ejpam-5943	247	30	d(vi	d(vi	PROPN
ejpam-5943	247	31	,	,	PUNCT
ejpam-5943	247	32	vk	vk	PROPN
ejpam-5943	247	33	)	)	PUNCT
ejpam-5943	247	34	.	.	PUNCT
ejpam-5943	248	1	l.	l.	PROPN
ejpam-5943	248	2	toladro	toladro	PROPN
ejpam-5943	248	3	,	,	PUNCT
ejpam-5943	248	4	i.	i.	PROPN
ejpam-5943	248	5	cabahug	cabahug	PROPN
ejpam-5943	248	6	/	/	SYM
ejpam-5943	248	7	eur	eur	PROPN
ejpam-5943	248	8	.	.	PUNCT
ejpam-5943	249	1	j.	j.	PROPN
ejpam-5943	249	2	pure	pure	PROPN
ejpam-5943	249	3	appl	appl	PROPN
ejpam-5943	249	4	.	.	PROPN
ejpam-5943	249	5	math	math	PROPN
ejpam-5943	249	6	,	,	PUNCT
ejpam-5943	249	7	18	18	NUM
ejpam-5943	249	8	(	(	PUNCT
ejpam-5943	249	9	2	2	NUM
ejpam-5943	249	10	)	)	PUNCT
ejpam-5943	249	11	(	(	PUNCT
ejpam-5943	249	12	2025	2025	NUM
ejpam-5943	249	13	)	)	PUNCT
ejpam-5943	249	14	,	,	PUNCT
ejpam-5943	249	15	5943	5943	NUM
ejpam-5943	249	16	11	11	NUM
ejpam-5943	249	17	of	of	ADP
ejpam-5943	249	18	13	13	NUM
ejpam-5943	249	19	now	now	ADV
ejpam-5943	249	20	,	,	PUNCT
ejpam-5943	249	21	∑	∑	PROPN
ejpam-5943	249	22	1≤q≤n	1≤q≤n	NUM
ejpam-5943	249	23	d(vi	d(vi	PROPN
ejpam-5943	249	24	,	,	PUNCT
ejpam-5943	249	25	vq	vq	NOUN
ejpam-5943	249	26	)	)	PUNCT
ejpam-5943	249	27	=	=	SYM
ejpam-5943	249	28	1	1	NUM
ejpam-5943	249	29	+	+	NUM
ejpam-5943	249	30	1	1	NUM
ejpam-5943	249	31	+	+	CCONJ
ejpam-5943	249	32	.	.	PUNCT
ejpam-5943	249	33	.	.	PUNCT
ejpam-5943	250	1	.+	.+	NOUN
ejpam-5943	251	1	1︸	1︸	NUM
ejpam-5943	251	2	︷︷	︷︷	NOUN
ejpam-5943	251	3	︸	︸	ADP
ejpam-5943	251	4	n	n	PROPN
ejpam-5943	251	5	addends	addend	VERB
ejpam-5943	251	6	=	=	SYM
ejpam-5943	251	7	n	n	PROPN
ejpam-5943	251	8	and	and	CCONJ
ejpam-5943	251	9	∑	∑	PROPN
ejpam-5943	251	10	k	k	PROPN
ejpam-5943	251	11	̸=i,1≤k≤m	̸=i,1≤k≤m	PROPN
ejpam-5943	251	12	d(vi	d(vi	PROPN
ejpam-5943	251	13	,	,	PUNCT
ejpam-5943	251	14	vk	vk	NOUN
ejpam-5943	251	15	)	)	PUNCT
ejpam-5943	251	16	=	=	SYM
ejpam-5943	251	17	2	2	NUM
ejpam-5943	251	18	+	+	NUM
ejpam-5943	251	19	2	2	NUM
ejpam-5943	251	20	+	+	NUM
ejpam-5943	251	21	.	.	PUNCT
ejpam-5943	251	22	.	.	PUNCT
ejpam-5943	252	1	.+	.+	NOUN
ejpam-5943	252	2	2︸	2︸	NUM
ejpam-5943	252	3	︷︷	︷︷	PROPN
ejpam-5943	252	4	︸	︸	ADP
ejpam-5943	252	5	m-1	m-1	PROPN
ejpam-5943	252	6	addends	addend	VERB
ejpam-5943	252	7	=	=	SYM
ejpam-5943	252	8	2(m−	2(m−	NUM
ejpam-5943	252	9	1	1	NUM
ejpam-5943	252	10	)	)	PUNCT
ejpam-5943	252	11	=	=	SYM
ejpam-5943	253	1	2m−	2m−	NUM
ejpam-5943	253	2	2	2	NUM
ejpam-5943	253	3	.	.	PUNCT
ejpam-5943	254	1	thus	thus	ADV
ejpam-5943	254	2	,	,	PUNCT
ejpam-5943	254	3	∑	∑	PROPN
ejpam-5943	254	4	i	i	PRON
ejpam-5943	254	5	̸=j	̸=j	VERB
ejpam-5943	254	6	dkm	dkm	PROPN
ejpam-5943	254	7	,	,	PUNCT
ejpam-5943	254	8	n(vi	n(vi	PROPN
ejpam-5943	254	9	,	,	PUNCT
ejpam-5943	254	10	vj	vj	ADJ
ejpam-5943	254	11	)	)	PUNCT
ejpam-5943	254	12	=	=	SYM
ejpam-5943	255	1	n+	n+	PROPN
ejpam-5943	256	1	2m−	2m−	NUM
ejpam-5943	256	2	2	2	NUM
ejpam-5943	256	3	.	.	PUNCT
ejpam-5943	257	1	hence	hence	ADV
ejpam-5943	257	2	,	,	PUNCT
ejpam-5943	257	3	ppkm	ppkm	PROPN
ejpam-5943	257	4	,	,	PUNCT
ejpam-5943	257	5	n(vm	n(vm	X
ejpam-5943	257	6	)	)	PUNCT
ejpam-5943	257	7	=	=	SYM
ejpam-5943	258	1	n+	n+	PROPN
ejpam-5943	259	1	2m−	2m−	NUM
ejpam-5943	259	2	2	2	NUM
ejpam-5943	259	3	m+	m+	NUM
ejpam-5943	259	4	n	n	NOUN
ejpam-5943	259	5	.	.	PUNCT
ejpam-5943	260	1	case	case	NOUN
ejpam-5943	260	2	2	2	NUM
ejpam-5943	260	3	:	:	PUNCT
ejpam-5943	260	4	deg(vi	deg(vi	NUM
ejpam-5943	260	5	)	)	PUNCT
ejpam-5943	260	6	=	=	SYM
ejpam-5943	260	7	m.	m.	NOUN
ejpam-5943	260	8	then	then	ADV
ejpam-5943	260	9	,	,	PUNCT
ejpam-5943	260	10	∑	∑	PROPN
ejpam-5943	260	11	i	i	PRON
ejpam-5943	260	12	̸=j	̸=j	VERB
ejpam-5943	260	13	dkm	dkm	PROPN
ejpam-5943	260	14	,	,	PUNCT
ejpam-5943	260	15	n(vi	n(vi	PROPN
ejpam-5943	260	16	,	,	PUNCT
ejpam-5943	260	17	vj	vj	ADJ
ejpam-5943	260	18	)	)	PUNCT
ejpam-5943	260	19	=	=	PUNCT
ejpam-5943	260	20	∑	∑	PROPN
ejpam-5943	260	21	1≤k≤m	1≤k≤m	NUM
ejpam-5943	260	22	d(vi	d(vi	NOUN
ejpam-5943	260	23	,	,	PUNCT
ejpam-5943	260	24	vk	vk	NOUN
ejpam-5943	260	25	)	)	PUNCT
ejpam-5943	260	26	+	+	CCONJ
ejpam-5943	260	27	∑	∑	PUNCT
ejpam-5943	260	28	q	q	PROPN
ejpam-5943	260	29	̸=i,1≤q≤n	̸=i,1≤q≤n	PROPN
ejpam-5943	260	30	d(vi	d(vi	PROPN
ejpam-5943	260	31	,	,	PUNCT
ejpam-5943	260	32	vq	vq	PROPN
ejpam-5943	260	33	)	)	PUNCT
ejpam-5943	260	34	.	.	PUNCT
ejpam-5943	261	1	now	now	ADV
ejpam-5943	261	2	,	,	PUNCT
ejpam-5943	261	3	∑	∑	PROPN
ejpam-5943	261	4	1≤k≤m	1≤k≤m	NUM
ejpam-5943	261	5	d(vi	d(vi	NOUN
ejpam-5943	261	6	,	,	PUNCT
ejpam-5943	261	7	vk	vk	NOUN
ejpam-5943	261	8	)	)	PUNCT
ejpam-5943	261	9	=	=	SYM
ejpam-5943	261	10	1	1	NUM
ejpam-5943	261	11	+	+	NUM
ejpam-5943	261	12	1	1	NUM
ejpam-5943	261	13	+	+	CCONJ
ejpam-5943	261	14	.	.	PUNCT
ejpam-5943	261	15	.	.	PUNCT
ejpam-5943	262	1	.+	.+	NOUN
ejpam-5943	263	1	1︸	1︸	NUM
ejpam-5943	263	2	︷︷	︷︷	NOUN
ejpam-5943	263	3	︸	︸	X
ejpam-5943	263	4	m	m	AUX
ejpam-5943	263	5	addends	addend	VERB
ejpam-5943	263	6	=	=	PUNCT
ejpam-5943	263	7	m	m	PROPN
ejpam-5943	263	8	and	and	CCONJ
ejpam-5943	263	9	∑	∑	PROPN
ejpam-5943	263	10	l	l	PROPN
ejpam-5943	263	11	̸=i,1≤q≤n	̸=i,1≤q≤n	PROPN
ejpam-5943	263	12	d(vi	d(vi	PROPN
ejpam-5943	263	13	,	,	PUNCT
ejpam-5943	263	14	vq	vq	NOUN
ejpam-5943	263	15	)	)	PUNCT
ejpam-5943	263	16	=	=	SYM
ejpam-5943	263	17	2	2	NUM
ejpam-5943	263	18	+	+	NUM
ejpam-5943	263	19	2	2	NUM
ejpam-5943	263	20	+	+	NUM
ejpam-5943	263	21	.	.	PUNCT
ejpam-5943	263	22	.	.	PUNCT
ejpam-5943	264	1	.+	.+	NOUN
ejpam-5943	264	2	2︸	2︸	NUM
ejpam-5943	264	3	︷︷	︷︷	PROPN
ejpam-5943	264	4	︸	︸	X
ejpam-5943	264	5	n-1	n-1	PROPN
ejpam-5943	264	6	addends	addend	VERB
ejpam-5943	264	7	=	=	PUNCT
ejpam-5943	264	8	2(n−	2(n−	NUM
ejpam-5943	264	9	1	1	NUM
ejpam-5943	264	10	)	)	PUNCT
ejpam-5943	264	11	=	=	PUNCT
ejpam-5943	265	1	2n−	2n−	NUM
ejpam-5943	265	2	2	2	NUM
ejpam-5943	265	3	.	.	PUNCT
ejpam-5943	266	1	thus	thus	ADV
ejpam-5943	266	2	,	,	PUNCT
ejpam-5943	266	3	∑	∑	PROPN
ejpam-5943	266	4	i	i	PRON
ejpam-5943	266	5	̸=j	̸=j	VERB
ejpam-5943	266	6	dkm	dkm	PROPN
ejpam-5943	266	7	,	,	PUNCT
ejpam-5943	266	8	n(vi	n(vi	PROPN
ejpam-5943	266	9	,	,	PUNCT
ejpam-5943	266	10	vj	vj	INTJ
ejpam-5943	266	11	)	)	PUNCT
ejpam-5943	266	12	=	=	SYM
ejpam-5943	266	13	m+	m+	NUM
ejpam-5943	266	14	(	(	PUNCT
ejpam-5943	266	15	2n−	2n−	PROPN
ejpam-5943	266	16	2	2	NUM
ejpam-5943	266	17	)	)	PUNCT
ejpam-5943	266	18	.	.	PUNCT
ejpam-5943	267	1	l.	l.	PROPN
ejpam-5943	267	2	toladro	toladro	PROPN
ejpam-5943	267	3	,	,	PUNCT
ejpam-5943	267	4	i.	i.	PROPN
ejpam-5943	267	5	cabahug	cabahug	PROPN
ejpam-5943	267	6	/	/	SYM
ejpam-5943	267	7	eur	eur	PROPN
ejpam-5943	267	8	.	.	PUNCT
ejpam-5943	268	1	j.	j.	PROPN
ejpam-5943	268	2	pure	pure	PROPN
ejpam-5943	268	3	appl	appl	PROPN
ejpam-5943	268	4	.	.	PROPN
ejpam-5943	268	5	math	math	PROPN
ejpam-5943	268	6	,	,	PUNCT
ejpam-5943	268	7	18	18	NUM
ejpam-5943	268	8	(	(	PUNCT
ejpam-5943	268	9	2	2	NUM
ejpam-5943	268	10	)	)	PUNCT
ejpam-5943	268	11	(	(	PUNCT
ejpam-5943	268	12	2025	2025	NUM
ejpam-5943	268	13	)	)	PUNCT
ejpam-5943	268	14	,	,	PUNCT
ejpam-5943	268	15	5943	5943	NUM
ejpam-5943	268	16	12	12	NUM
ejpam-5943	268	17	of	of	ADP
ejpam-5943	268	18	13	13	NUM
ejpam-5943	268	19	hence	hence	ADV
ejpam-5943	268	20	,	,	PUNCT
ejpam-5943	268	21	ppkm	ppkm	PROPN
ejpam-5943	268	22	,	,	PUNCT
ejpam-5943	268	23	n(vn	n(vn	PROPN
ejpam-5943	268	24	)	)	PUNCT
ejpam-5943	268	25	=	=	SYM
ejpam-5943	269	1	m+	m+	NUM
ejpam-5943	269	2	(	(	PUNCT
ejpam-5943	269	3	2n−	2n−	PROPN
ejpam-5943	269	4	2	2	NUM
ejpam-5943	269	5	)	)	PUNCT
ejpam-5943	269	6	m+	m+	NUM
ejpam-5943	269	7	n	n	PROPN
ejpam-5943	269	8	.	.	PUNCT
ejpam-5943	270	1	therefore	therefore	ADV
ejpam-5943	270	2	,	,	PUNCT
ejpam-5943	270	3	we	we	PRON
ejpam-5943	270	4	have	have	VERB
ejpam-5943	270	5	ppkm	ppkm	NOUN
ejpam-5943	270	6	,	,	PUNCT
ejpam-5943	270	7	n(vi	n(vi	NUM
ejpam-5943	270	8	)	)	PUNCT
ejpam-5943	270	9	=	=	PUNCT
ejpam-5943	270	10			X
ejpam-5943	270	11	n+	n+	PUNCT
ejpam-5943	271	1	(	(	PUNCT
ejpam-5943	271	2	2m−	2m−	NOUN
ejpam-5943	271	3	2	2	NUM
ejpam-5943	271	4	)	)	PUNCT
ejpam-5943	271	5	m+	m+	NUM
ejpam-5943	271	6	n	n	CCONJ
ejpam-5943	271	7	,	,	PUNCT
ejpam-5943	271	8	if	if	SCONJ
ejpam-5943	271	9	deg(vi	deg(vi	NOUN
ejpam-5943	271	10	)	)	PUNCT
ejpam-5943	271	11	=	=	SYM
ejpam-5943	271	12	n	n	CCONJ
ejpam-5943	271	13	;	;	PUNCT
ejpam-5943	271	14	m+	m+	NUM
ejpam-5943	271	15	(	(	PUNCT
ejpam-5943	271	16	2n−	2n−	PROPN
ejpam-5943	271	17	2	2	NUM
ejpam-5943	271	18	)	)	PUNCT
ejpam-5943	271	19	m+	m+	NUM
ejpam-5943	271	20	n	n	CCONJ
ejpam-5943	271	21	,	,	PUNCT
ejpam-5943	271	22	if	if	SCONJ
ejpam-5943	271	23	deg(vi	deg(vi	NOUN
ejpam-5943	271	24	)	)	PUNCT
ejpam-5943	271	25	=	=	SYM
ejpam-5943	271	26	m.	m.	NOUN
ejpam-5943	271	27	■	■	PUNCT
ejpam-5943	271	28	theorem	theorem	ADJ
ejpam-5943	271	29	8	8	NUM
ejpam-5943	271	30	.	.	PUNCT
ejpam-5943	272	1	let	let	VERB
ejpam-5943	272	2	g	g	PROPN
ejpam-5943	272	3	=	=	SYM
ejpam-5943	272	4	(	(	PUNCT
ejpam-5943	272	5	v	v	NOUN
ejpam-5943	272	6	,	,	PUNCT
ejpam-5943	272	7	e	e	NOUN
ejpam-5943	272	8	)	)	PUNCT
ejpam-5943	272	9	be	be	AUX
ejpam-5943	272	10	a	a	DET
ejpam-5943	272	11	star	star	NOUN
ejpam-5943	272	12	k1,n	k1,n	PROPN
ejpam-5943	272	13	=	=	PUNCT
ejpam-5943	273	1	[	[	X
ejpam-5943	273	2	v1	v1	NOUN
ejpam-5943	273	3	,	,	PUNCT
ejpam-5943	273	4	v2	v2	NOUN
ejpam-5943	273	5	,	,	PUNCT
ejpam-5943	273	6	.	.	PUNCT
ejpam-5943	273	7	.	.	PUNCT
ejpam-5943	273	8	.	.	PUNCT
ejpam-5943	274	1	,	,	PUNCT
ejpam-5943	274	2	vn	vn	X
ejpam-5943	274	3	,	,	PUNCT
ejpam-5943	274	4	vn+1	vn+1	PROPN
ejpam-5943	274	5	]	]	PUNCT
ejpam-5943	274	6	where	where	SCONJ
ejpam-5943	274	7	deg(vn+1	deg(vn+1	NOUN
ejpam-5943	274	8	)	)	PUNCT
ejpam-5943	274	9	=	=	SYM
ejpam-5943	275	1	n	n	CCONJ
ejpam-5943	275	2	,	,	PUNCT
ejpam-5943	275	3	then	then	ADV
ejpam-5943	275	4	the	the	DET
ejpam-5943	275	5	proximity	proximity	NOUN
ejpam-5943	275	6	prestige	prestige	NOUN
ejpam-5943	275	7	of	of	ADP
ejpam-5943	275	8	any	any	DET
ejpam-5943	275	9	vertex	vertex	NOUN
ejpam-5943	275	10	vi	vi	NOUN
ejpam-5943	275	11	where	where	SCONJ
ejpam-5943	275	12	1	1	NUM
ejpam-5943	275	13	≤	≤	NUM
ejpam-5943	275	14	i	i	PRON
ejpam-5943	275	15	≤	≤	NOUN
ejpam-5943	275	16	n+	n+	PUNCT
ejpam-5943	275	17	1	1	NUM
ejpam-5943	275	18	is	be	AUX
ejpam-5943	275	19	given	give	VERB
ejpam-5943	275	20	by	by	ADP
ejpam-5943	275	21	,	,	PUNCT
ejpam-5943	275	22	pp	pp	CCONJ
ejpam-5943	275	23	(	(	PUNCT
ejpam-5943	275	24	vi	vi	NOUN
ejpam-5943	275	25	)	)	PUNCT
ejpam-5943	275	26	=	=	SYM
ejpam-5943	276	1			PROPN
ejpam-5943	276	2	n	n	NUM
ejpam-5943	276	3	n+	n+	NUM
ejpam-5943	276	4	1	1	NUM
ejpam-5943	276	5	,	,	PUNCT
ejpam-5943	276	6	if	if	SCONJ
ejpam-5943	276	7	deg(vi	deg(vi	NOUN
ejpam-5943	276	8	)	)	PUNCT
ejpam-5943	276	9	=	=	SYM
ejpam-5943	276	10	n	n	CCONJ
ejpam-5943	276	11	;	;	PUNCT
ejpam-5943	276	12	2n−	2n−	PROPN
ejpam-5943	276	13	1	1	NUM
ejpam-5943	276	14	n+	n+	NUM
ejpam-5943	276	15	1	1	NUM
ejpam-5943	276	16	,	,	PUNCT
ejpam-5943	276	17	if	if	SCONJ
ejpam-5943	276	18	deg(vi	deg(vi	NOUN
ejpam-5943	276	19	)	)	PUNCT
ejpam-5943	276	20	=	=	SYM
ejpam-5943	276	21	1	1	X
ejpam-5943	276	22	.	.	PUNCT
ejpam-5943	276	23	proof	proof	NOUN
ejpam-5943	276	24	.	.	PUNCT
ejpam-5943	277	1	suppose	suppose	VERB
ejpam-5943	277	2	first	first	ADV
ejpam-5943	277	3	that	that	SCONJ
ejpam-5943	277	4	deg(vi	deg(vi	NOUN
ejpam-5943	277	5	)	)	PUNCT
ejpam-5943	277	6	=	=	VERB
ejpam-5943	277	7	n.	n.	NOUN
ejpam-5943	277	8	there	there	PRON
ejpam-5943	277	9	is	be	VERB
ejpam-5943	277	10	only	only	ADV
ejpam-5943	277	11	one	one	NUM
ejpam-5943	277	12	vertex	vertex	NOUN
ejpam-5943	277	13	with	with	ADP
ejpam-5943	277	14	a	a	DET
ejpam-5943	277	15	degree	degree	NOUN
ejpam-5943	277	16	n	n	NOUN
ejpam-5943	277	17	in	in	ADP
ejpam-5943	277	18	k1,n	k1,n	PROPN
ejpam-5943	277	19	,	,	PUNCT
ejpam-5943	277	20	that	that	PRON
ejpam-5943	277	21	is	be	AUX
ejpam-5943	277	22	vn+1	vn+1	PROPN
ejpam-5943	277	23	,	,	PUNCT
ejpam-5943	277	24	and	and	CCONJ
ejpam-5943	277	25	the	the	DET
ejpam-5943	277	26	distance	distance	NOUN
ejpam-5943	277	27	d(vi	d(vi	PROPN
ejpam-5943	277	28	,	,	PUNCT
ejpam-5943	277	29	vj	vj	ADJ
ejpam-5943	277	30	)	)	PUNCT
ejpam-5943	277	31	=	=	SYM
ejpam-5943	277	32	1	1	NUM
ejpam-5943	277	33	,	,	PUNCT
ejpam-5943	277	34	for	for	ADP
ejpam-5943	277	35	j	j	PROPN
ejpam-5943	277	36	̸=	̸=	PROPN
ejpam-5943	277	37	n+	n+	PUNCT
ejpam-5943	277	38	1	1	NUM
ejpam-5943	277	39	.	.	PUNCT
ejpam-5943	278	1	thus,∑	thus,∑	PROPN
ejpam-5943	278	2	j	j	PROPN
ejpam-5943	278	3	̸=n+1	̸=n+1	PROPN
ejpam-5943	278	4	dk1,n(vi	dk1,n(vi	PROPN
ejpam-5943	278	5	,	,	PUNCT
ejpam-5943	278	6	vj	vj	ADJ
ejpam-5943	278	7	)	)	PUNCT
ejpam-5943	278	8	=	=	SYM
ejpam-5943	278	9	1	1	NUM
ejpam-5943	279	1	+	+	NUM
ejpam-5943	279	2	1	1	NUM
ejpam-5943	280	1	+	+	CCONJ
ejpam-5943	280	2	.	.	PUNCT
ejpam-5943	281	1	.	.	PUNCT
ejpam-5943	282	1	.+	.+	NOUN
ejpam-5943	283	1	1︸	1︸	NUM
ejpam-5943	283	2	︷︷	︷︷	NOUN
ejpam-5943	283	3	︸	︸	ADP
ejpam-5943	283	4	n	n	PROPN
ejpam-5943	283	5	addends	addend	VERB
ejpam-5943	283	6	=	=	PUNCT
ejpam-5943	283	7	n.	n.	PROPN
ejpam-5943	283	8	hence	hence	ADV
ejpam-5943	283	9	,	,	PUNCT
ejpam-5943	283	10	ppk1,n(vi	ppk1,n(vi	ADP
ejpam-5943	283	11	)	)	PUNCT
ejpam-5943	283	12	=	=	SYM
ejpam-5943	283	13	n	n	X
ejpam-5943	283	14	n+	n+	NUM
ejpam-5943	283	15	1	1	NUM
ejpam-5943	283	16	.	.	PUNCT
ejpam-5943	284	1	on	on	ADP
ejpam-5943	284	2	the	the	DET
ejpam-5943	284	3	other	other	ADJ
ejpam-5943	284	4	hand	hand	NOUN
ejpam-5943	284	5	,	,	PUNCT
ejpam-5943	284	6	if	if	SCONJ
ejpam-5943	284	7	deg(vi	deg(vi	NOUN
ejpam-5943	284	8	)	)	PUNCT
ejpam-5943	284	9	=	=	SYM
ejpam-5943	284	10	1	1	X
ejpam-5943	284	11	.	.	X
ejpam-5943	285	1	then,∑	then,∑	X
ejpam-5943	285	2	i	i	PRON
ejpam-5943	285	3	̸=j	̸=j	PROPN
ejpam-5943	285	4	dk1,n(vi	dk1,n(vi	SYM
ejpam-5943	285	5	,	,	PUNCT
ejpam-5943	285	6	vj	vj	ADJ
ejpam-5943	285	7	)	)	PUNCT
ejpam-5943	285	8	=	=	SYM
ejpam-5943	285	9	1	1	NUM
ejpam-5943	285	10	+	+	NUM
ejpam-5943	285	11	2	2	NUM
ejpam-5943	285	12	+	+	SYM
ejpam-5943	285	13	2	2	NUM
ejpam-5943	285	14	+	+	NUM
ejpam-5943	285	15	.	.	PUNCT
ejpam-5943	285	16	.	.	PUNCT
ejpam-5943	286	1	.+	.+	NOUN
ejpam-5943	286	2	2︸	2︸	NUM
ejpam-5943	286	3	︷︷	︷︷	PROPN
ejpam-5943	286	4	︸	︸	X
ejpam-5943	286	5	n-1	n-1	PROPN
ejpam-5943	286	6	addends	addend	VERB
ejpam-5943	286	7	=	=	SYM
ejpam-5943	286	8	1	1	NUM
ejpam-5943	286	9	+	+	NUM
ejpam-5943	286	10	2(n−	2(n−	NUM
ejpam-5943	286	11	1	1	NUM
ejpam-5943	286	12	)	)	PUNCT
ejpam-5943	286	13	=	=	PUNCT
ejpam-5943	287	1	2n−	2n−	NUM
ejpam-5943	287	2	1	1	NUM
ejpam-5943	287	3	hence	hence	ADV
ejpam-5943	287	4	,	,	PUNCT
ejpam-5943	287	5	ppk1,n(vi	ppk1,n(vi	ADP
ejpam-5943	287	6	)	)	PUNCT
ejpam-5943	287	7	=	=	SYM
ejpam-5943	288	1	2n−	2n−	NUM
ejpam-5943	288	2	1	1	NUM
ejpam-5943	288	3	n+	n+	NUM
ejpam-5943	288	4	1	1	NUM
ejpam-5943	288	5	.	.	PUNCT
ejpam-5943	289	1	therefore	therefore	ADV
ejpam-5943	289	2	,	,	PUNCT
ejpam-5943	289	3	we	we	PRON
ejpam-5943	289	4	have	have	VERB
ejpam-5943	289	5	ppk1,n(vi	ppk1,n(vi	ADP
ejpam-5943	289	6	)	)	PUNCT
ejpam-5943	289	7	=	=	SYM
ejpam-5943	290	1			PROPN
ejpam-5943	290	2	n	n	PROPN
ejpam-5943	290	3	n+	n+	NUM
ejpam-5943	290	4	1	1	NUM
ejpam-5943	290	5	,	,	PUNCT
ejpam-5943	290	6	if	if	SCONJ
ejpam-5943	290	7	deg(vi	deg(vi	NOUN
ejpam-5943	290	8	)	)	PUNCT
ejpam-5943	290	9	=	=	SYM
ejpam-5943	290	10	n	n	CCONJ
ejpam-5943	290	11	;	;	PUNCT
ejpam-5943	290	12	2n−	2n−	PROPN
ejpam-5943	290	13	1	1	NUM
ejpam-5943	290	14	n+	n+	NUM
ejpam-5943	290	15	1	1	NUM
ejpam-5943	290	16	,	,	PUNCT
ejpam-5943	290	17	if	if	SCONJ
ejpam-5943	290	18	deg(vi	deg(vi	NOUN
ejpam-5943	290	19	)	)	PUNCT
ejpam-5943	290	20	=	=	SYM
ejpam-5943	290	21	1	1	X
ejpam-5943	290	22	.	.	X
ejpam-5943	290	23	■	■	PUNCT
ejpam-5943	290	24	l.	l.	PROPN
ejpam-5943	290	25	toladro	toladro	PROPN
ejpam-5943	290	26	,	,	PUNCT
ejpam-5943	290	27	i.	i.	PROPN
ejpam-5943	290	28	cabahug	cabahug	PROPN
ejpam-5943	290	29	/	/	SYM
ejpam-5943	290	30	eur	eur	PROPN
ejpam-5943	290	31	.	.	PUNCT
ejpam-5943	291	1	j.	j.	PROPN
ejpam-5943	291	2	pure	pure	PROPN
ejpam-5943	291	3	appl	appl	PROPN
ejpam-5943	291	4	.	.	PROPN
ejpam-5943	291	5	math	math	PROPN
ejpam-5943	291	6	,	,	PUNCT
ejpam-5943	291	7	18	18	NUM
ejpam-5943	291	8	(	(	PUNCT
ejpam-5943	291	9	2	2	NUM
ejpam-5943	291	10	)	)	PUNCT
ejpam-5943	291	11	(	(	PUNCT
ejpam-5943	291	12	2025	2025	NUM
ejpam-5943	291	13	)	)	PUNCT
ejpam-5943	291	14	,	,	PUNCT
ejpam-5943	291	15	5943	5943	NUM
ejpam-5943	291	16	13	13	NUM
ejpam-5943	291	17	of	of	ADP
ejpam-5943	291	18	13	13	NUM
ejpam-5943	291	19	4	4	NUM
ejpam-5943	291	20	.	.	PUNCT
ejpam-5943	291	21	conclusion	conclusion	VERB
ejpam-5943	291	22	this	this	DET
ejpam-5943	291	23	paper	paper	NOUN
ejpam-5943	291	24	introduced	introduce	VERB
ejpam-5943	291	25	proximity	proximity	NOUN
ejpam-5943	291	26	prestige	prestige	NOUN
ejpam-5943	291	27	(	(	PUNCT
ejpam-5943	291	28	pp	pp	ADV
ejpam-5943	291	29	)	)	PUNCT
ejpam-5943	291	30	as	as	ADP
ejpam-5943	291	31	a	a	DET
ejpam-5943	291	32	centrality	centrality	NOUN
ejpam-5943	291	33	measure	measure	NOUN
ejpam-5943	291	34	in	in	ADP
ejpam-5943	291	35	fixed	fix	VERB
ejpam-5943	291	36	graphs	graph	NOUN
ejpam-5943	291	37	,	,	PUNCT
ejpam-5943	291	38	defined	define	VERB
ejpam-5943	291	39	by	by	ADP
ejpam-5943	291	40	the	the	DET
ejpam-5943	291	41	average	average	ADJ
ejpam-5943	291	42	shortest	short	ADJ
ejpam-5943	291	43	path	path	NOUN
ejpam-5943	291	44	distance	distance	NOUN
ejpam-5943	291	45	from	from	ADP
ejpam-5943	291	46	a	a	DET
ejpam-5943	291	47	vertex	vertex	NOUN
ejpam-5943	291	48	to	to	ADP
ejpam-5943	291	49	all	all	DET
ejpam-5943	291	50	other	other	ADJ
ejpam-5943	291	51	vertices	vertex	NOUN
ejpam-5943	291	52	,	,	PUNCT
ejpam-5943	291	53	focusing	focus	VERB
ejpam-5943	291	54	on	on	ADP
ejpam-5943	291	55	indirect	indirect	ADJ
ejpam-5943	291	56	connections	connection	NOUN
ejpam-5943	291	57	.	.	PUNCT
ejpam-5943	292	1	proximity	proximity	NOUN
ejpam-5943	292	2	prestige	prestige	NOUN
ejpam-5943	292	3	(	(	PUNCT
ejpam-5943	292	4	pp	pp	ADV
ejpam-5943	292	5	)	)	PUNCT
ejpam-5943	292	6	offers	offer	VERB
ejpam-5943	292	7	a	a	DET
ejpam-5943	292	8	valuable	valuable	ADJ
ejpam-5943	292	9	approach	approach	NOUN
ejpam-5943	292	10	for	for	ADP
ejpam-5943	292	11	quantifying	quantify	VERB
ejpam-5943	292	12	vertex	vertex	NOUN
ejpam-5943	292	13	importance	importance	NOUN
ejpam-5943	292	14	based	base	VERB
ejpam-5943	292	15	on	on	ADP
ejpam-5943	292	16	its	its	PRON
ejpam-5943	292	17	reach	reach	NOUN
ejpam-5943	292	18	within	within	ADP
ejpam-5943	292	19	the	the	DET
ejpam-5943	292	20	network	network	NOUN
ejpam-5943	292	21	.	.	PUNCT
ejpam-5943	293	1	future	future	ADJ
ejpam-5943	293	2	research	research	NOUN
ejpam-5943	293	3	could	could	AUX
ejpam-5943	293	4	explore	explore	VERB
ejpam-5943	293	5	the	the	DET
ejpam-5943	293	6	application	application	NOUN
ejpam-5943	293	7	of	of	ADP
ejpam-5943	293	8	proximity	proximity	NOUN
ejpam-5943	293	9	prestige	prestige	NOUN
ejpam-5943	293	10	(	(	PUNCT
ejpam-5943	293	11	pp	pp	ADV
ejpam-5943	293	12	)	)	PUNCT
ejpam-5943	293	13	to	to	ADP
ejpam-5943	293	14	random	random	ADJ
ejpam-5943	293	15	and	and	CCONJ
ejpam-5943	293	16	dynamic	dynamic	ADJ
ejpam-5943	293	17	graphs	graph	NOUN
ejpam-5943	293	18	,	,	PUNCT
ejpam-5943	293	19	as	as	ADV
ejpam-5943	293	20	well	well	ADV
ejpam-5943	293	21	as	as	ADP
ejpam-5943	293	22	its	its	PRON
ejpam-5943	293	23	integration	integration	NOUN
ejpam-5943	293	24	with	with	ADP
ejpam-5943	293	25	other	other	ADJ
ejpam-5943	293	26	centrality	centrality	NOUN
ejpam-5943	293	27	measures	measure	NOUN
ejpam-5943	293	28	,	,	PUNCT
ejpam-5943	293	29	to	to	PART
ejpam-5943	293	30	enhance	enhance	VERB
ejpam-5943	293	31	understanding	understanding	NOUN
ejpam-5943	293	32	of	of	ADP
ejpam-5943	293	33	vertex	vertex	NOUN
ejpam-5943	293	34	influence	influence	NOUN
ejpam-5943	293	35	in	in	ADP
ejpam-5943	293	36	evolving	evolve	VERB
ejpam-5943	293	37	network	network	NOUN
ejpam-5943	293	38	structures	structure	NOUN
ejpam-5943	293	39	and	and	CCONJ
ejpam-5943	293	40	real	real	ADJ
ejpam-5943	293	41	-	-	PUNCT
ejpam-5943	293	42	world	world	NOUN
ejpam-5943	293	43	,	,	PUNCT
ejpam-5943	293	44	complex	complex	ADJ
ejpam-5943	293	45	networks	network	NOUN
ejpam-5943	293	46	.	.	PUNCT
ejpam-5943	294	1	acknowledgements	acknowledgement	NOUN
ejpam-5943	294	2	the	the	DET
ejpam-5943	294	3	authors	author	NOUN
ejpam-5943	294	4	would	would	AUX
ejpam-5943	294	5	like	like	VERB
ejpam-5943	294	6	to	to	PART
ejpam-5943	294	7	express	express	VERB
ejpam-5943	294	8	their	their	PRON
ejpam-5943	294	9	sincere	sincere	ADJ
ejpam-5943	294	10	thanks	thank	NOUN
ejpam-5943	294	11	to	to	ADP
ejpam-5943	294	12	everyone	everyone	PRON
ejpam-5943	294	13	who	who	PRON
ejpam-5943	294	14	contributed	contribute	VERB
ejpam-5943	294	15	to	to	ADP
ejpam-5943	294	16	the	the	DET
ejpam-5943	294	17	successful	successful	ADJ
ejpam-5943	294	18	completion	completion	NOUN
ejpam-5943	294	19	of	of	ADP
ejpam-5943	294	20	this	this	DET
ejpam-5943	294	21	research	research	NOUN
ejpam-5943	294	22	.	.	PUNCT
ejpam-5943	295	1	in	in	ADP
ejpam-5943	295	2	particular	particular	ADJ
ejpam-5943	295	3	,	,	PUNCT
ejpam-5943	295	4	they	they	PRON
ejpam-5943	295	5	gratefully	gratefully	ADV
ejpam-5943	295	6	acknowledge	acknowledge	VERB
ejpam-5943	295	7	the	the	DET
ejpam-5943	295	8	invaluable	invaluable	ADJ
ejpam-5943	295	9	support	support	NOUN
ejpam-5943	295	10	provided	provide	VERB
ejpam-5943	295	11	by	by	ADP
ejpam-5943	295	12	the	the	DET
ejpam-5943	295	13	department	department	PROPN
ejpam-5943	295	14	of	of	ADP
ejpam-5943	295	15	science	science	NOUN
ejpam-5943	295	16	and	and	CCONJ
ejpam-5943	295	17	technology	technology	NOUN
ejpam-5943	295	18	-	-	PUNCT
ejpam-5943	295	19	science	science	NOUN
ejpam-5943	295	20	education	education	PROPN
ejpam-5943	295	21	institute	institute	PROPN
ejpam-5943	295	22	science	science	PROPN
ejpam-5943	295	23	and	and	CCONJ
ejpam-5943	295	24	technology	technology	NOUN
ejpam-5943	295	25	regional	regional	ADJ
ejpam-5943	295	26	alliance	alliance	NOUN
ejpam-5943	295	27	of	of	ADP
ejpam-5943	295	28	universities	university	NOUN
ejpam-5943	295	29	for	for	ADP
ejpam-5943	295	30	inclusive	inclusive	ADJ
ejpam-5943	295	31	national	national	ADJ
ejpam-5943	295	32	development	development	NOUN
ejpam-5943	295	33	(	(	PUNCT
ejpam-5943	295	34	dost	dost	NOUN
ejpam-5943	295	35	-	-	PUNCT
ejpam-5943	295	36	sei	sei	ADJ
ejpam-5943	295	37	strand	strand	NOUN
ejpam-5943	295	38	)	)	PUNCT
ejpam-5943	295	39	throughout	throughout	ADP
ejpam-5943	295	40	the	the	DET
ejpam-5943	295	41	study	study	NOUN
ejpam-5943	295	42	.	.	PUNCT
ejpam-5943	296	1	the	the	DET
ejpam-5943	296	2	authors	author	NOUN
ejpam-5943	296	3	also	also	ADV
ejpam-5943	296	4	wish	wish	VERB
ejpam-5943	296	5	to	to	PART
ejpam-5943	296	6	extend	extend	VERB
ejpam-5943	296	7	their	their	PRON
ejpam-5943	296	8	heartfelt	heartfelt	ADJ
ejpam-5943	296	9	appreciation	appreciation	NOUN
ejpam-5943	296	10	to	to	ADP
ejpam-5943	296	11	the	the	DET
ejpam-5943	296	12	referees	referee	NOUN
ejpam-5943	296	13	for	for	ADP
ejpam-5943	296	14	their	their	PRON
ejpam-5943	296	15	constructive	constructive	ADJ
ejpam-5943	296	16	feedback	feedback	NOUN
ejpam-5943	296	17	and	and	CCONJ
ejpam-5943	296	18	insightful	insightful	ADJ
ejpam-5943	296	19	suggestions	suggestion	NOUN
ejpam-5943	296	20	,	,	PUNCT
ejpam-5943	296	21	which	which	PRON
ejpam-5943	296	22	greatly	greatly	ADV
ejpam-5943	296	23	enhanced	enhance	VERB
ejpam-5943	296	24	the	the	DET
ejpam-5943	296	25	quality	quality	NOUN
ejpam-5943	296	26	of	of	ADP
ejpam-5943	296	27	this	this	DET
ejpam-5943	296	28	work	work	NOUN
ejpam-5943	296	29	.	.	PUNCT
ejpam-5943	297	1	references	reference	NOUN
ejpam-5943	297	2	[	[	X
ejpam-5943	297	3	1	1	NUM
ejpam-5943	297	4	]	]	PUNCT
ejpam-5943	297	5	l	l	NOUN
ejpam-5943	297	6	freeman	freeman	PROPN
ejpam-5943	297	7	.	.	PUNCT
ejpam-5943	298	1	centrality	centrality	NOUN
ejpam-5943	298	2	in	in	ADP
ejpam-5943	298	3	social	social	ADJ
ejpam-5943	298	4	networks	network	NOUN
ejpam-5943	298	5	:	:	PUNCT
ejpam-5943	298	6	conceptual	conceptual	ADJ
ejpam-5943	298	7	clarification	clarification	NOUN
ejpam-5943	298	8	.	.	PUNCT
ejpam-5943	299	1	social	social	ADJ
ejpam-5943	299	2	networks	network	NOUN
ejpam-5943	299	3	,	,	PUNCT
ejpam-5943	299	4	1(3):215–239	1(3):215–239	NUM
ejpam-5943	299	5	,	,	PUNCT
ejpam-5943	299	6	1979	1979	NUM
ejpam-5943	299	7	.	.	PUNCT
ejpam-5943	300	1	[	[	X
ejpam-5943	300	2	2	2	NUM
ejpam-5943	300	3	]	]	X
ejpam-5943	300	4	h	h	PROPN
ejpam-5943	300	5	yu	yu	PROPN
ejpam-5943	300	6	and	and	CCONJ
ejpam-5943	300	7	y	y	PROPN
ejpam-5943	300	8	zhao	zhao	PROPN
ejpam-5943	300	9	.	.	PUNCT
ejpam-5943	301	1	a	a	DET
ejpam-5943	301	2	social	social	ADJ
ejpam-5943	301	3	network	network	NOUN
ejpam-5943	301	4	model	model	NOUN
ejpam-5943	301	5	with	with	ADP
ejpam-5943	301	6	proximity	proximity	NOUN
ejpam-5943	301	7	prestige	prestige	NOUN
ejpam-5943	301	8	property	property	NOUN
ejpam-5943	301	9	.	.	PUNCT
ejpam-5943	302	1	journal	journal	PROPN
ejpam-5943	302	2	of	of	ADP
ejpam-5943	302	3	applied	apply	VERB
ejpam-5943	302	4	analysis	analysis	NOUN
ejpam-5943	302	5	and	and	CCONJ
ejpam-5943	302	6	computation	computation	NOUN
ejpam-5943	302	7	,	,	PUNCT
ejpam-5943	302	8	5(2):177–188	5(2):177–188	NUM
ejpam-5943	302	9	,	,	PUNCT
ejpam-5943	302	10	2015	2015	NUM
ejpam-5943	302	11	.	.	PUNCT
ejpam-5943	303	1	[	[	X
ejpam-5943	303	2	3	3	NUM
ejpam-5943	303	3	]	]	X
ejpam-5943	303	4	r	r	NOUN
ejpam-5943	303	5	eballe	eballe	NOUN
ejpam-5943	303	6	and	and	CCONJ
ejpam-5943	303	7	i	i	PRON
ejpam-5943	303	8	cabahug	cabahug	VERB
ejpam-5943	303	9	jr	jr	PROPN
ejpam-5943	303	10	.	.	PROPN
ejpam-5943	303	11	closeness	closeness	NOUN
ejpam-5943	303	12	centrality	centrality	NOUN
ejpam-5943	303	13	of	of	ADP
ejpam-5943	303	14	some	some	DET
ejpam-5943	303	15	graph	graph	NOUN
ejpam-5943	303	16	families	family	NOUN
ejpam-5943	303	17	.	.	PUNCT
ejpam-5943	304	1	international	international	ADJ
ejpam-5943	304	2	journal	journal	PROPN
ejpam-5943	304	3	of	of	ADP
ejpam-5943	304	4	mathematics	mathematics	PROPN
ejpam-5943	304	5	and	and	CCONJ
ejpam-5943	304	6	statistics	statistic	NOUN
ejpam-5943	304	7	invention	invention	NOUN
ejpam-5943	304	8	(	(	PUNCT
ejpam-5943	304	9	ijmsi	ijmsi	NOUN
ejpam-5943	304	10	)	)	PUNCT
ejpam-5943	304	11	,	,	PUNCT
ejpam-5943	304	12	16(4):127–134	16(4):127–134	NUM
ejpam-5943	304	13	,	,	PUNCT
ejpam-5943	304	14	2021	2021	NUM
ejpam-5943	304	15	.	.	PUNCT
ejpam-5943	305	1	[	[	X
ejpam-5943	305	2	4	4	NUM
ejpam-5943	305	3	]	]	X
ejpam-5943	305	4	r	r	NOUN
ejpam-5943	305	5	eballe	eballe	NOUN
ejpam-5943	305	6	,	,	PUNCT
ejpam-5943	305	7	cm	cm	NOUN
ejpam-5943	305	8	balingit	balingit	ADJ
ejpam-5943	305	9	,	,	PUNCT
ejpam-5943	305	10	i	i	PRON
ejpam-5943	305	11	cabahug	cabahug	VERB
ejpam-5943	305	12	jr	jr	PROPN
ejpam-5943	305	13	,	,	PUNCT
ejpam-5943	305	14	al	al	PROPN
ejpam-5943	305	15	flores	flores	PROPN
ejpam-5943	305	16	,	,	PUNCT
ejpam-5943	305	17	sm	sm	PROPN
ejpam-5943	305	18	lumpayao	lumpayao	PROPN
ejpam-5943	305	19	,	,	PUNCT
ejpam-5943	305	20	b	b	PROPN
ejpam-5943	305	21	pe	pe	PROPN
ejpam-5943	305	22	nalosa	nalosa	PROPN
ejpam-5943	305	23	,	,	PUNCT
ejpam-5943	305	24	ga	ga	PROPN
ejpam-5943	305	25	tampipi	tampipi	NOUN
ejpam-5943	305	26	,	,	PUNCT
ejpam-5943	305	27	and	and	CCONJ
ejpam-5943	305	28	c	c	PROPN
ejpam-5943	305	29	villarta	villarta	NOUN
ejpam-5943	305	30	.	.	PUNCT
ejpam-5943	306	1	closeness	closeness	NOUN
ejpam-5943	306	2	centrality	centrality	NOUN
ejpam-5943	306	3	in	in	ADP
ejpam-5943	306	4	graph	graph	NOUN
ejpam-5943	306	5	products	product	NOUN
ejpam-5943	306	6	.	.	PUNCT
ejpam-5943	307	1	advances	advance	NOUN
ejpam-5943	307	2	and	and	CCONJ
ejpam-5943	307	3	applications	application	NOUN
ejpam-5943	307	4	in	in	ADP
ejpam-5943	307	5	discrete	discrete	ADJ
ejpam-5943	307	6	mathematics	mathematic	NOUN
ejpam-5943	307	7	,	,	PUNCT
ejpam-5943	307	8	39(1):29–41	39(1):29–41	NUM
ejpam-5943	307	9	,	,	PUNCT
ejpam-5943	307	10	2023	2023	NUM
ejpam-5943	307	11	.	.	PUNCT
ejpam-5943	308	1	[	[	X
ejpam-5943	308	2	5	5	NUM
ejpam-5943	308	3	]	]	SYM
ejpam-5943	308	4	f	f	PROPN
ejpam-5943	308	5	buckley	buckley	PROPN
ejpam-5943	308	6	and	and	CCONJ
ejpam-5943	308	7	f	f	PROPN
ejpam-5943	308	8	harary	harary	NOUN
ejpam-5943	308	9	.	.	PUNCT
ejpam-5943	309	1	distance	distance	NOUN
ejpam-5943	309	2	in	in	ADP
ejpam-5943	309	3	graphs	graph	NOUN
ejpam-5943	309	4	.	.	PUNCT
ejpam-5943	310	1	addison	addison	PROPN
ejpam-5943	310	2	-	-	PUNCT
ejpam-5943	310	3	wesley	wesley	PROPN
ejpam-5943	310	4	publishing	publishing	PROPN
ejpam-5943	310	5	company	company	NOUN
ejpam-5943	310	6	,	,	PUNCT
ejpam-5943	310	7	redwood	redwood	NOUN
ejpam-5943	310	8	city	city	NOUN
ejpam-5943	310	9	,	,	PUNCT
ejpam-5943	310	10	ca	ca	NOUN
ejpam-5943	310	11	,	,	PUNCT
ejpam-5943	310	12	1990	1990	NUM
ejpam-5943	310	13	.	.	PUNCT
ejpam-5943	311	1	[	[	X
ejpam-5943	311	2	6	6	NUM
ejpam-5943	311	3	]	]	SYM
ejpam-5943	311	4	f	f	PROPN
ejpam-5943	311	5	harary	harary	NOUN
ejpam-5943	311	6	.	.	PUNCT
ejpam-5943	312	1	graph	graph	NOUN
ejpam-5943	312	2	theory	theory	NOUN
ejpam-5943	312	3	.	.	PUNCT
ejpam-5943	313	1	addison	addison	PROPN
ejpam-5943	313	2	-	-	PUNCT
ejpam-5943	313	3	wesly	wesly	ADV
ejpam-5943	313	4	publiching	publiche	VERB
ejpam-5943	313	5	company	company	PROPN
ejpam-5943	313	6	inc	inc	PROPN
ejpam-5943	313	7	.	.	PROPN
ejpam-5943	313	8	,	,	PUNCT
ejpam-5943	313	9	united	united	PROPN
ejpam-5943	313	10	states	states	PROPN
ejpam-5943	313	11	of	of	ADP
ejpam-5943	313	12	america	america	PROPN
ejpam-5943	313	13	,	,	PUNCT
ejpam-5943	313	14	1969	1969	NUM
ejpam-5943	313	15	.	.	PUNCT
ejpam-5943	314	1	[	[	X
ejpam-5943	314	2	7	7	X
ejpam-5943	314	3	]	]	X
ejpam-5943	314	4	g	g	PROPN
ejpam-5943	314	5	chartrand	chartrand	NOUN
ejpam-5943	314	6	,	,	PUNCT
ejpam-5943	314	7	l	l	PROPN
ejpam-5943	314	8	lesniak	lesniak	PROPN
ejpam-5943	314	9	,	,	PUNCT
ejpam-5943	314	10	and	and	CCONJ
ejpam-5943	314	11	p	p	PROPN
ejpam-5943	314	12	zhang	zhang	PROPN
ejpam-5943	314	13	.	.	PUNCT
ejpam-5943	314	14	graphs	graph	NOUN
ejpam-5943	314	15	and	and	CCONJ
ejpam-5943	314	16	digraphs	digraph	NOUN
ejpam-5943	314	17	.	.	PUNCT
ejpam-5943	315	1	chapman	chapman	NOUN
ejpam-5943	315	2	and	and	CCONJ
ejpam-5943	315	3	hall	hall	PROPN
ejpam-5943	315	4	/	/	SYM
ejpam-5943	315	5	crc	crc	PROPN
ejpam-5943	315	6	,	,	PUNCT
ejpam-5943	315	7	new	new	PROPN
ejpam-5943	315	8	york	york	PROPN
ejpam-5943	315	9	,	,	PUNCT
ejpam-5943	315	10	6th	6th	ADJ
ejpam-5943	315	11	edition	edition	NOUN
ejpam-5943	315	12	,	,	PUNCT
ejpam-5943	315	13	2015	2015	NUM
ejpam-5943	315	14	.	.	PUNCT
ejpam-5943	316	1	[	[	X
ejpam-5943	316	2	8	8	NUM
ejpam-5943	316	3	]	]	X
ejpam-5943	316	4	k	k	PROPN
ejpam-5943	316	5	vaithilingan	vaithilingan	PROPN
ejpam-5943	316	6	.	.	PUNCT
ejpam-5943	317	1	difference	difference	NOUN
ejpam-5943	317	2	labeling	labeling	NOUN
ejpam-5943	317	3	of	of	ADP
ejpam-5943	317	4	some	some	DET
ejpam-5943	317	5	graph	graph	NOUN
ejpam-5943	317	6	families	family	NOUN
ejpam-5943	317	7	.	.	PUNCT
ejpam-5943	318	1	international	international	ADJ
ejpam-5943	318	2	journal	journal	PROPN
ejpam-5943	318	3	of	of	ADP
ejpam-5943	318	4	mathematics	mathematics	PROPN
ejpam-5943	318	5	and	and	CCONJ
ejpam-5943	318	6	statistics	statistic	NOUN
ejpam-5943	318	7	invention	invention	NOUN
ejpam-5943	318	8	(	(	PUNCT
ejpam-5943	318	9	ijmsi	ijmsi	NOUN
ejpam-5943	318	10	)	)	PUNCT
ejpam-5943	318	11	,	,	PUNCT
ejpam-5943	318	12	2(6):37–43	2(6):37–43	NUM
ejpam-5943	318	13	,	,	PUNCT
ejpam-5943	318	14	2014	2014	NUM
ejpam-5943	318	15	.	.	PUNCT
ejpam-5943	319	1	[	[	X
ejpam-5943	319	2	9	9	NUM
ejpam-5943	319	3	]	]	X
ejpam-5943	319	4	r	r	NOUN
ejpam-5943	319	5	kumar	kumar	PROPN
ejpam-5943	319	6	,	,	PUNCT
ejpam-5943	319	7	b	b	PROPN
ejpam-5943	319	8	kannan	kannan	PROPN
ejpam-5943	319	9	,	,	PUNCT
ejpam-5943	319	10	and	and	CCONJ
ejpam-5943	319	11	m	m	PROPN
ejpam-5943	319	12	jathavedan	jathavedan	PROPN
ejpam-5943	319	13	.	.	PUNCT
ejpam-5943	320	1	betweenness	betweenness	ADJ
ejpam-5943	320	2	centrality	centrality	NOUN
ejpam-5943	320	3	in	in	ADP
ejpam-5943	320	4	some	some	DET
ejpam-5943	320	5	classes	class	NOUN
ejpam-5943	320	6	of	of	ADP
ejpam-5943	320	7	graphs	graph	NOUN
ejpam-5943	320	8	.	.	PUNCT
ejpam-5943	321	1	international	international	ADJ
ejpam-5943	321	2	journal	journal	PROPN
ejpam-5943	321	3	of	of	ADP
ejpam-5943	321	4	combinatorics	combinatoric	NOUN
ejpam-5943	321	5	,	,	PUNCT
ejpam-5943	321	6	pages	page	NOUN
ejpam-5943	321	7	1–12	1–12	PROPN
ejpam-5943	321	8	,	,	PUNCT
ejpam-5943	321	9	2014	2014	NUM
ejpam-5943	321	10	.	.	PUNCT