id	sid	tid	token	lemma	pos
ejpam-4848	1	1	european	european	PROPN
ejpam-4848	1	2	journal	journal	PROPN
ejpam-4848	1	3	of	of	ADP
ejpam-4848	1	4	pure	pure	ADJ
ejpam-4848	1	5	and	and	CCONJ
ejpam-4848	1	6	applied	apply	VERB
ejpam-4848	1	7	mathematics	mathematic	NOUN
ejpam-4848	1	8	vol	vol	NOUN
ejpam-4848	1	9	.	.	PUNCT
ejpam-4848	2	1	16	16	NUM
ejpam-4848	2	2	,	,	PUNCT
ejpam-4848	2	3	no	no	INTJ
ejpam-4848	2	4	.	.	NOUN
ejpam-4848	2	5	3	3	NUM
ejpam-4848	2	6	,	,	PUNCT
ejpam-4848	2	7	2023	2023	NUM
ejpam-4848	2	8	,	,	PUNCT
ejpam-4848	2	9	1406	1406	NUM
ejpam-4848	2	10	-	-	SYM
ejpam-4848	2	11	1420	1420	NUM
ejpam-4848	2	12	issn	issn	PROPN
ejpam-4848	2	13	1307	1307	NUM
ejpam-4848	2	14	-	-	SYM
ejpam-4848	2	15	5543	5543	NUM
ejpam-4848	2	16	–	–	PUNCT
ejpam-4848	2	17	ejpam.com	ejpam.com	X
ejpam-4848	2	18	published	publish	VERB
ejpam-4848	2	19	by	by	ADP
ejpam-4848	2	20	new	new	PROPN
ejpam-4848	2	21	york	york	PROPN
ejpam-4848	2	22	business	business	PROPN
ejpam-4848	2	23	global	global	ADJ
ejpam-4848	2	24	closeness	closeness	NOUN
ejpam-4848	2	25	centrality	centrality	NOUN
ejpam-4848	2	26	of	of	ADP
ejpam-4848	2	27	vertices	vertex	NOUN
ejpam-4848	2	28	in	in	ADP
ejpam-4848	2	29	graphs	graph	NOUN
ejpam-4848	2	30	under	under	ADP
ejpam-4848	2	31	some	some	DET
ejpam-4848	2	32	operations	operation	NOUN
ejpam-4848	2	33	farene	farene	VERB
ejpam-4848	2	34	loida	loida	PROPN
ejpam-4848	2	35	alfeche1	alfeche1	PROPN
ejpam-4848	2	36	,	,	PUNCT
ejpam-4848	2	37	victor	victor	PROPN
ejpam-4848	2	38	barraza2,∗	barraza2,∗	PROPN
ejpam-4848	2	39	,	,	PUNCT
ejpam-4848	2	40	sergio	sergio	PROPN
ejpam-4848	2	41	canoy	canoy	PROPN
ejpam-4848	2	42	,	,	PUNCT
ejpam-4848	2	43	jr.1,3	jr.1,3	PROPN
ejpam-4848	2	44	1	1	NUM
ejpam-4848	2	45	department	department	NOUN
ejpam-4848	2	46	of	of	ADP
ejpam-4848	2	47	mathematics	mathematic	NOUN
ejpam-4848	2	48	and	and	CCONJ
ejpam-4848	2	49	statistics	statistic	NOUN
ejpam-4848	2	50	,	,	PUNCT
ejpam-4848	2	51	college	college	NOUN
ejpam-4848	2	52	of	of	ADP
ejpam-4848	2	53	science	science	NOUN
ejpam-4848	2	54	and	and	CCONJ
ejpam-4848	2	55	mathematics	mathematic	NOUN
ejpam-4848	2	56	,	,	PUNCT
ejpam-4848	2	57	msuiligan	msuiligan	PROPN
ejpam-4848	2	58	institute	institute	PROPN
ejpam-4848	2	59	of	of	ADP
ejpam-4848	2	60	technology	technology	PROPN
ejpam-4848	2	61	,	,	PUNCT
ejpam-4848	2	62	9200	9200	NUM
ejpam-4848	2	63	iligan	iligan	ADJ
ejpam-4848	2	64	city	city	NOUN
ejpam-4848	2	65	,	,	PUNCT
ejpam-4848	2	66	philippines	philippines	PROPN
ejpam-4848	2	67	2	2	NUM
ejpam-4848	2	68	department	department	NOUN
ejpam-4848	2	69	of	of	ADP
ejpam-4848	2	70	arts	art	NOUN
ejpam-4848	2	71	and	and	CCONJ
ejpam-4848	2	72	sciences	science	NOUN
ejpam-4848	2	73	,	,	PUNCT
ejpam-4848	2	74	college	college	NOUN
ejpam-4848	2	75	of	of	ADP
ejpam-4848	2	76	teacher	teacher	NOUN
ejpam-4848	2	77	education	education	NOUN
ejpam-4848	2	78	arts	art	NOUN
ejpam-4848	2	79	and	and	CCONJ
ejpam-4848	2	80	sciences	science	NOUN
ejpam-4848	2	81	,	,	PUNCT
ejpam-4848	2	82	visayas	visayas	PROPN
ejpam-4848	2	83	state	state	PROPN
ejpam-4848	2	84	university	university	PROPN
ejpam-4848	2	85	alangalang	alangalang	PROPN
ejpam-4848	2	86	,	,	PUNCT
ejpam-4848	2	87	alangalang	alangalang	PROPN
ejpam-4848	2	88	,	,	PUNCT
ejpam-4848	2	89	leyte	leyte	PROPN
ejpam-4848	2	90	,	,	PUNCT
ejpam-4848	2	91	philippines	philippine	NOUN
ejpam-4848	2	92	3	3	NUM
ejpam-4848	2	93	center	center	NOUN
ejpam-4848	2	94	for	for	ADP
ejpam-4848	2	95	mathematical	mathematical	ADJ
ejpam-4848	2	96	and	and	CCONJ
ejpam-4848	2	97	theoretical	theoretical	ADJ
ejpam-4848	2	98	physical	physical	ADJ
ejpam-4848	2	99	sciences	science	NOUN
ejpam-4848	2	100	-	-	PUNCT
ejpam-4848	2	101	prism	prism	NOUN
ejpam-4848	2	102	,	,	PUNCT
ejpam-4848	2	103	msu	msu	PROPN
ejpam-4848	2	104	-	-	PUNCT
ejpam-4848	2	105	iligan	iligan	PROPN
ejpam-4848	2	106	institute	institute	PROPN
ejpam-4848	2	107	of	of	ADP
ejpam-4848	2	108	technology	technology	PROPN
ejpam-4848	2	109	,	,	PUNCT
ejpam-4848	2	110	9200	9200	NUM
ejpam-4848	2	111	iligan	iligan	ADJ
ejpam-4848	2	112	city	city	NOUN
ejpam-4848	2	113	,	,	PUNCT
ejpam-4848	2	114	philippines	philippine	NOUN
ejpam-4848	2	115	abstract	abstract	ADJ
ejpam-4848	2	116	.	.	PUNCT
ejpam-4848	3	1	in	in	ADP
ejpam-4848	3	2	this	this	DET
ejpam-4848	3	3	paper	paper	NOUN
ejpam-4848	3	4	,	,	PUNCT
ejpam-4848	3	5	we	we	PRON
ejpam-4848	3	6	revisit	revisit	VERB
ejpam-4848	3	7	the	the	DET
ejpam-4848	3	8	concept	concept	NOUN
ejpam-4848	3	9	of	of	ADP
ejpam-4848	3	10	(	(	PUNCT
ejpam-4848	3	11	normalized	normalize	VERB
ejpam-4848	3	12	)	)	PUNCT
ejpam-4848	3	13	closeness	closeness	NOUN
ejpam-4848	3	14	centrality	centrality	NOUN
ejpam-4848	3	15	of	of	ADP
ejpam-4848	3	16	a	a	DET
ejpam-4848	3	17	vertex	vertex	NOUN
ejpam-4848	3	18	in	in	ADP
ejpam-4848	3	19	a	a	DET
ejpam-4848	3	20	graph	graph	NOUN
ejpam-4848	3	21	and	and	CCONJ
ejpam-4848	3	22	investigate	investigate	VERB
ejpam-4848	3	23	it	it	PRON
ejpam-4848	3	24	in	in	ADP
ejpam-4848	3	25	some	some	DET
ejpam-4848	3	26	graphs	graph	NOUN
ejpam-4848	3	27	under	under	ADP
ejpam-4848	3	28	some	some	DET
ejpam-4848	3	29	operations	operation	NOUN
ejpam-4848	3	30	.	.	PUNCT
ejpam-4848	4	1	specifically	specifically	ADV
ejpam-4848	4	2	,	,	PUNCT
ejpam-4848	4	3	we	we	PRON
ejpam-4848	4	4	derive	derive	VERB
ejpam-4848	4	5	formulas	formula	NOUN
ejpam-4848	4	6	to	to	PART
ejpam-4848	4	7	compute	compute	VERB
ejpam-4848	4	8	the	the	DET
ejpam-4848	4	9	closeness	closeness	NOUN
ejpam-4848	4	10	centrality	centrality	NOUN
ejpam-4848	4	11	of	of	ADP
ejpam-4848	4	12	vertices	vertex	NOUN
ejpam-4848	4	13	in	in	ADP
ejpam-4848	4	14	the	the	DET
ejpam-4848	4	15	shadow	shadow	NOUN
ejpam-4848	4	16	graph	graph	NOUN
ejpam-4848	4	17	,	,	PUNCT
ejpam-4848	4	18	complementary	complementary	ADJ
ejpam-4848	4	19	prism	prism	NOUN
ejpam-4848	4	20	,	,	PUNCT
ejpam-4848	4	21	edge	edge	NOUN
ejpam-4848	4	22	corona	corona	NOUN
ejpam-4848	4	23	,	,	PUNCT
ejpam-4848	4	24	and	and	CCONJ
ejpam-4848	4	25	disjunction	disjunction	NOUN
ejpam-4848	4	26	of	of	ADP
ejpam-4848	4	27	graphs	graph	NOUN
ejpam-4848	4	28	.	.	PUNCT
ejpam-4848	5	1	2020	2020	NUM
ejpam-4848	5	2	mathematics	mathematic	NOUN
ejpam-4848	5	3	subject	subject	NOUN
ejpam-4848	5	4	classifications	classification	NOUN
ejpam-4848	5	5	:	:	PUNCT
ejpam-4848	5	6	05c69	05c69	X
ejpam-4848	5	7	key	key	ADJ
ejpam-4848	5	8	words	word	NOUN
ejpam-4848	5	9	and	and	CCONJ
ejpam-4848	5	10	phrases	phrase	NOUN
ejpam-4848	5	11	:	:	PUNCT
ejpam-4848	5	12	closeness	closeness	NOUN
ejpam-4848	5	13	centrality	centrality	NOUN
ejpam-4848	5	14	,	,	PUNCT
ejpam-4848	5	15	shadow	shadow	NOUN
ejpam-4848	5	16	graph	graph	NOUN
ejpam-4848	5	17	,	,	PUNCT
ejpam-4848	5	18	edge	edge	NOUN
ejpam-4848	5	19	corona	corona	NOUN
ejpam-4848	5	20	,	,	PUNCT
ejpam-4848	5	21	complementary	complementary	ADJ
ejpam-4848	5	22	prism	prism	NOUN
ejpam-4848	5	23	,	,	PUNCT
ejpam-4848	5	24	disjunction	disjunction	NOUN
ejpam-4848	5	25	1	1	NUM
ejpam-4848	5	26	.	.	PUNCT
ejpam-4848	6	1	introduction	introduction	NOUN
ejpam-4848	6	2	according	accord	VERB
ejpam-4848	6	3	to	to	ADP
ejpam-4848	6	4	a	a	DET
ejpam-4848	6	5	study	study	NOUN
ejpam-4848	6	6	in	in	ADP
ejpam-4848	6	7	[	[	X
ejpam-4848	6	8	7	7	NUM
ejpam-4848	6	9	]	]	PUNCT
ejpam-4848	6	10	,	,	PUNCT
ejpam-4848	6	11	centrality	centrality	NOUN
ejpam-4848	6	12	is	be	AUX
ejpam-4848	6	13	one	one	NUM
ejpam-4848	6	14	of	of	ADP
ejpam-4848	6	15	the	the	DET
ejpam-4848	6	16	most	most	ADV
ejpam-4848	6	17	studied	study	VERB
ejpam-4848	6	18	subjects	subject	NOUN
ejpam-4848	6	19	in	in	ADP
ejpam-4848	6	20	the	the	DET
ejpam-4848	6	21	analysis	analysis	NOUN
ejpam-4848	6	22	of	of	ADP
ejpam-4848	6	23	social	social	ADJ
ejpam-4848	6	24	networks	network	NOUN
ejpam-4848	6	25	.	.	PUNCT
ejpam-4848	7	1	as	as	SCONJ
ejpam-4848	7	2	mentioned	mention	VERB
ejpam-4848	7	3	in	in	ADP
ejpam-4848	7	4	[	[	X
ejpam-4848	7	5	4	4	NUM
ejpam-4848	7	6	]	]	PUNCT
ejpam-4848	7	7	,	,	PUNCT
ejpam-4848	7	8	the	the	DET
ejpam-4848	7	9	concept	concept	NOUN
ejpam-4848	7	10	was	be	AUX
ejpam-4848	7	11	developed	develop	VERB
ejpam-4848	7	12	by	by	ADP
ejpam-4848	7	13	social	social	ADJ
ejpam-4848	7	14	scientists	scientist	NOUN
ejpam-4848	7	15	some	some	DET
ejpam-4848	7	16	decades	decade	NOUN
ejpam-4848	7	17	ago	ago	ADV
ejpam-4848	7	18	with	with	ADP
ejpam-4848	7	19	the	the	DET
ejpam-4848	7	20	aim	aim	NOUN
ejpam-4848	7	21	of	of	ADP
ejpam-4848	7	22	quantifying	quantify	VERB
ejpam-4848	7	23	an	an	DET
ejpam-4848	7	24	intuitive	intuitive	ADJ
ejpam-4848	7	25	perception	perception	NOUN
ejpam-4848	7	26	that	that	SCONJ
ejpam-4848	7	27	some	some	DET
ejpam-4848	7	28	nodes	node	NOUN
ejpam-4848	7	29	or	or	CCONJ
ejpam-4848	7	30	linkages	linkage	NOUN
ejpam-4848	7	31	are	be	AUX
ejpam-4848	7	32	regarded	regard	VERB
ejpam-4848	7	33	central	central	ADJ
ejpam-4848	7	34	according	accord	VERB
ejpam-4848	7	35	to	to	ADP
ejpam-4848	7	36	some	some	DET
ejpam-4848	7	37	criteria	criterion	NOUN
ejpam-4848	7	38	in	in	ADP
ejpam-4848	7	39	many	many	ADJ
ejpam-4848	7	40	particular	particular	ADJ
ejpam-4848	7	41	networks	network	NOUN
ejpam-4848	7	42	or	or	CCONJ
ejpam-4848	7	43	graphs	graph	NOUN
ejpam-4848	7	44	.	.	PUNCT
ejpam-4848	8	1	for	for	ADP
ejpam-4848	8	2	example	example	NOUN
ejpam-4848	8	3	,	,	PUNCT
ejpam-4848	8	4	in	in	ADP
ejpam-4848	8	5	a	a	DET
ejpam-4848	8	6	social	social	ADJ
ejpam-4848	8	7	network	network	NOUN
ejpam-4848	8	8	which	which	PRON
ejpam-4848	8	9	is	be	AUX
ejpam-4848	8	10	often	often	ADV
ejpam-4848	8	11	represented	represent	VERB
ejpam-4848	8	12	as	as	ADP
ejpam-4848	8	13	a	a	DET
ejpam-4848	8	14	graph	graph	NOUN
ejpam-4848	8	15	,	,	PUNCT
ejpam-4848	8	16	where	where	SCONJ
ejpam-4848	8	17	each	each	DET
ejpam-4848	8	18	individual	individual	NOUN
ejpam-4848	8	19	is	be	AUX
ejpam-4848	8	20	represented	represent	VERB
ejpam-4848	8	21	as	as	ADP
ejpam-4848	8	22	a	a	DET
ejpam-4848	8	23	vertex	vertex	NOUN
ejpam-4848	8	24	,	,	PUNCT
ejpam-4848	8	25	the	the	DET
ejpam-4848	8	26	relationship	relationship	NOUN
ejpam-4848	8	27	between	between	ADP
ejpam-4848	8	28	pairs	pair	NOUN
ejpam-4848	8	29	of	of	ADP
ejpam-4848	8	30	individuals	individual	NOUN
ejpam-4848	8	31	are	be	AUX
ejpam-4848	8	32	connected	connect	VERB
ejpam-4848	8	33	by	by	ADP
ejpam-4848	8	34	edges	edge	NOUN
ejpam-4848	8	35	,	,	PUNCT
ejpam-4848	8	36	and	and	CCONJ
ejpam-4848	8	37	the	the	DET
ejpam-4848	8	38	weights	weight	NOUN
ejpam-4848	8	39	on	on	ADP
ejpam-4848	8	40	the	the	DET
ejpam-4848	8	41	edges	edge	NOUN
ejpam-4848	8	42	indicate	indicate	VERB
ejpam-4848	8	43	the	the	DET
ejpam-4848	8	44	strength	strength	NOUN
ejpam-4848	8	45	of	of	ADP
ejpam-4848	8	46	the	the	DET
ejpam-4848	8	47	relationships	relationship	NOUN
ejpam-4848	8	48	,	,	PUNCT
ejpam-4848	8	49	centrality	centrality	NOUN
ejpam-4848	8	50	gives	give	VERB
ejpam-4848	8	51	a	a	DET
ejpam-4848	8	52	way	way	NOUN
ejpam-4848	8	53	of	of	ADP
ejpam-4848	8	54	determining	determine	VERB
ejpam-4848	8	55	how	how	SCONJ
ejpam-4848	8	56	central	central	ADJ
ejpam-4848	8	57	an	an	DET
ejpam-4848	8	58	individual	individual	NOUN
ejpam-4848	8	59	is	be	AUX
ejpam-4848	8	60	located	locate	VERB
ejpam-4848	8	61	in	in	ADP
ejpam-4848	8	62	this	this	DET
ejpam-4848	8	63	network	network	NOUN
ejpam-4848	8	64	(	(	PUNCT
ejpam-4848	8	65	see	see	VERB
ejpam-4848	8	66	[	[	X
ejpam-4848	8	67	6	6	NUM
ejpam-4848	8	68	]	]	NUM
ejpam-4848	8	69	)	)	PUNCT
ejpam-4848	8	70	.	.	PUNCT
ejpam-4848	9	1	within	within	ADP
ejpam-4848	9	2	graph	graph	NOUN
ejpam-4848	9	3	theory	theory	NOUN
ejpam-4848	9	4	and	and	CCONJ
ejpam-4848	9	5	network	network	NOUN
ejpam-4848	9	6	analysis	analysis	NOUN
ejpam-4848	9	7	,	,	PUNCT
ejpam-4848	9	8	some	some	PRON
ejpam-4848	9	9	of	of	ADP
ejpam-4848	9	10	the	the	DET
ejpam-4848	9	11	common	common	ADJ
ejpam-4848	9	12	measurements	measurement	NOUN
ejpam-4848	9	13	of	of	ADP
ejpam-4848	9	14	centrality	centrality	NOUN
ejpam-4848	9	15	pointed	point	VERB
ejpam-4848	9	16	out	out	ADP
ejpam-4848	9	17	in	in	ADP
ejpam-4848	9	18	[	[	X
ejpam-4848	9	19	8	8	NUM
ejpam-4848	9	20	]	]	PUNCT
ejpam-4848	9	21	are	be	AUX
ejpam-4848	9	22	degree	degree	NOUN
ejpam-4848	9	23	centrality	centrality	NOUN
ejpam-4848	9	24	,	,	PUNCT
ejpam-4848	9	25	closeness	closeness	NOUN
ejpam-4848	9	26	centrality	centrality	NOUN
ejpam-4848	9	27	,	,	PUNCT
ejpam-4848	9	28	eigen	eigen	PROPN
ejpam-4848	9	29	vector	vector	NOUN
ejpam-4848	9	30	centrality	centrality	NOUN
ejpam-4848	9	31	,	,	PUNCT
ejpam-4848	9	32	and	and	CCONJ
ejpam-4848	9	33	betweeness	betweeness	NOUN
ejpam-4848	9	34	centrality	centrality	NOUN
ejpam-4848	9	35	.	.	PUNCT
ejpam-4848	10	1	one	one	PRON
ejpam-4848	10	2	may	may	AUX
ejpam-4848	10	3	also	also	ADV
ejpam-4848	10	4	refer	refer	VERB
ejpam-4848	10	5	to	to	ADP
ejpam-4848	10	6	[	[	X
ejpam-4848	10	7	1	1	NUM
ejpam-4848	10	8	]	]	PUNCT
ejpam-4848	10	9	,	,	PUNCT
ejpam-4848	10	10	[	[	X
ejpam-4848	10	11	2	2	NUM
ejpam-4848	10	12	]	]	PUNCT
ejpam-4848	10	13	,	,	PUNCT
ejpam-4848	10	14	and	and	CCONJ
ejpam-4848	10	15	[	[	X
ejpam-4848	10	16	5	5	NUM
ejpam-4848	10	17	]	]	PUNCT
ejpam-4848	10	18	for	for	ADP
ejpam-4848	10	19	some	some	DET
ejpam-4848	10	20	studies	study	NOUN
ejpam-4848	10	21	in	in	ADP
ejpam-4848	10	22	measure	measure	NOUN
ejpam-4848	10	23	of	of	ADP
ejpam-4848	10	24	centrality	centrality	NOUN
ejpam-4848	10	25	.	.	PUNCT
ejpam-4848	11	1	∗corresponding	∗corresponde	VERB
ejpam-4848	11	2	author	author	NOUN
ejpam-4848	11	3	.	.	PUNCT
ejpam-4848	12	1	doi	doi	NOUN
ejpam-4848	12	2	:	:	PUNCT
ejpam-4848	12	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4848	https://doi.org/10.29020/nybg.ejpam.v16i3.4848	ADP
ejpam-4848	12	4	email	email	NOUN
ejpam-4848	12	5	addresses	address	NOUN
ejpam-4848	12	6	:	:	PUNCT
ejpam-4848	12	7	fareneloida.alfeche@g.msuiit.edu.ph	fareneloida.alfeche@g.msuiit.edu.ph	PROPN
ejpam-4848	12	8	(	(	PUNCT
ejpam-4848	12	9	f.	f.	PROPN
ejpam-4848	12	10	alfeche	alfeche	PROPN
ejpam-4848	12	11	)	)	PUNCT
ejpam-4848	12	12	,	,	PUNCT
ejpam-4848	12	13	victor.barraza@vsu.edu.ph	victor.barraza@vsu.edu.ph	PROPN
ejpam-4848	12	14	(	(	PUNCT
ejpam-4848	12	15	v.	v.	ADP
ejpam-4848	12	16	barraza	barraza	PROPN
ejpam-4848	12	17	)	)	PUNCT
ejpam-4848	12	18	,	,	PUNCT
ejpam-4848	12	19	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4848	12	20	(	(	PUNCT
ejpam-4848	12	21	s.	s.	PROPN
ejpam-4848	12	22	canoy	canoy	PROPN
ejpam-4848	12	23	)	)	PUNCT
ejpam-4848	12	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4848	12	25	1406	1406	NUM
ejpam-4848	13	1	©	©	PROPN
ejpam-4848	13	2	2023	2023	NUM
ejpam-4848	13	3	ejpam	ejpam	NOUN
ejpam-4848	13	4	all	all	DET
ejpam-4848	13	5	rights	right	NOUN
ejpam-4848	13	6	reserved	reserve	VERB
ejpam-4848	13	7	.	.	PUNCT
ejpam-4848	14	1	f.	f.	PROPN
ejpam-4848	14	2	alfeche	alfeche	PROPN
ejpam-4848	14	3	,	,	PUNCT
ejpam-4848	14	4	v.	v.	PROPN
ejpam-4848	14	5	barraza	barraza	PROPN
ejpam-4848	14	6	,	,	PUNCT
ejpam-4848	14	7	s.	s.	PROPN
ejpam-4848	14	8	canoy	canoy	PROPN
ejpam-4848	14	9	,	,	PUNCT
ejpam-4848	14	10	jr	jr	PROPN
ejpam-4848	14	11	.	.	PROPN
ejpam-4848	14	12	/	/	SYM
ejpam-4848	14	13	eur	eur	PROPN
ejpam-4848	14	14	.	.	PUNCT
ejpam-4848	15	1	j.	j.	PROPN
ejpam-4848	15	2	pure	pure	PROPN
ejpam-4848	15	3	appl	appl	PROPN
ejpam-4848	15	4	.	.	PROPN
ejpam-4848	15	5	math	math	PROPN
ejpam-4848	15	6	,	,	PUNCT
ejpam-4848	15	7	16	16	NUM
ejpam-4848	15	8	(	(	PUNCT
ejpam-4848	15	9	3	3	NUM
ejpam-4848	15	10	)	)	PUNCT
ejpam-4848	15	11	(	(	PUNCT
ejpam-4848	15	12	2023	2023	NUM
ejpam-4848	15	13	)	)	PUNCT
ejpam-4848	15	14	,	,	PUNCT
ejpam-4848	15	15	1406	1406	NUM
ejpam-4848	15	16	-	-	SYM
ejpam-4848	15	17	1420	1420	NUM
ejpam-4848	15	18	1407	1407	NUM
ejpam-4848	15	19	closeness	closeness	NOUN
ejpam-4848	15	20	centrality	centrality	NOUN
ejpam-4848	15	21	measures	measure	NOUN
ejpam-4848	15	22	how	how	SCONJ
ejpam-4848	15	23	close	close	ADJ
ejpam-4848	15	24	a	a	DET
ejpam-4848	15	25	vertex	vertex	NOUN
ejpam-4848	15	26	is	be	AUX
ejpam-4848	15	27	to	to	ADP
ejpam-4848	15	28	all	all	DET
ejpam-4848	15	29	other	other	ADJ
ejpam-4848	15	30	vertices	vertex	NOUN
ejpam-4848	15	31	in	in	ADP
ejpam-4848	15	32	a	a	DET
ejpam-4848	15	33	graph	graph	NOUN
ejpam-4848	15	34	.	.	PUNCT
ejpam-4848	16	1	the	the	DET
ejpam-4848	16	2	closeness	closeness	NOUN
ejpam-4848	16	3	centrality	centrality	NOUN
ejpam-4848	16	4	of	of	ADP
ejpam-4848	16	5	a	a	DET
ejpam-4848	16	6	vertex	vertex	NOUN
ejpam-4848	16	7	in	in	ADP
ejpam-4848	16	8	a	a	DET
ejpam-4848	16	9	graph	graph	NOUN
ejpam-4848	16	10	is	be	AUX
ejpam-4848	16	11	the	the	DET
ejpam-4848	16	12	inverse	inverse	NOUN
ejpam-4848	16	13	of	of	ADP
ejpam-4848	16	14	the	the	DET
ejpam-4848	16	15	average	average	ADJ
ejpam-4848	16	16	geodesic	geodesic	ADJ
ejpam-4848	16	17	distance	distance	NOUN
ejpam-4848	16	18	from	from	ADP
ejpam-4848	16	19	the	the	DET
ejpam-4848	16	20	vertex	vertex	NOUN
ejpam-4848	16	21	to	to	ADP
ejpam-4848	16	22	any	any	DET
ejpam-4848	16	23	other	other	ADJ
ejpam-4848	16	24	vertex	vertex	NOUN
ejpam-4848	16	25	in	in	ADP
ejpam-4848	16	26	the	the	DET
ejpam-4848	16	27	graph	graph	NOUN
ejpam-4848	16	28	.	.	PUNCT
ejpam-4848	17	1	the	the	DET
ejpam-4848	17	2	greater	great	ADJ
ejpam-4848	17	3	value	value	NOUN
ejpam-4848	17	4	of	of	ADP
ejpam-4848	17	5	closeness	closeness	NOUN
ejpam-4848	17	6	centrality	centrality	NOUN
ejpam-4848	17	7	of	of	ADP
ejpam-4848	17	8	a	a	DET
ejpam-4848	17	9	vertex	vertex	NOUN
ejpam-4848	17	10	would	would	AUX
ejpam-4848	17	11	mean	mean	VERB
ejpam-4848	17	12	a	a	DET
ejpam-4848	17	13	better	well	ADJ
ejpam-4848	17	14	position	position	NOUN
ejpam-4848	17	15	of	of	ADP
ejpam-4848	17	16	a	a	DET
ejpam-4848	17	17	vertex	vertex	NOUN
ejpam-4848	17	18	in	in	ADP
ejpam-4848	17	19	spreading	spread	VERB
ejpam-4848	17	20	information	information	NOUN
ejpam-4848	17	21	to	to	ADP
ejpam-4848	17	22	other	other	ADJ
ejpam-4848	17	23	vertices	vertex	NOUN
ejpam-4848	17	24	(	(	PUNCT
ejpam-4848	17	25	see	see	VERB
ejpam-4848	17	26	[	[	X
ejpam-4848	17	27	6	6	NUM
ejpam-4848	17	28	]	]	NUM
ejpam-4848	17	29	)	)	PUNCT
ejpam-4848	17	30	.	.	PUNCT
ejpam-4848	18	1	a	a	DET
ejpam-4848	18	2	study	study	NOUN
ejpam-4848	18	3	on	on	ADP
ejpam-4848	18	4	closeness	closeness	NOUN
ejpam-4848	18	5	centrality	centrality	NOUN
ejpam-4848	18	6	can	can	AUX
ejpam-4848	18	7	be	be	AUX
ejpam-4848	18	8	found	find	VERB
ejpam-4848	18	9	in	in	ADP
ejpam-4848	18	10	[	[	X
ejpam-4848	18	11	4	4	X
ejpam-4848	18	12	]	]	PUNCT
ejpam-4848	18	13	where	where	SCONJ
ejpam-4848	18	14	the	the	DET
ejpam-4848	18	15	authors	author	NOUN
ejpam-4848	18	16	derived	derive	VERB
ejpam-4848	18	17	the	the	DET
ejpam-4848	18	18	closeness	closeness	NOUN
ejpam-4848	18	19	centrality	centrality	NOUN
ejpam-4848	18	20	of	of	ADP
ejpam-4848	18	21	vertices	vertex	NOUN
ejpam-4848	18	22	of	of	ADP
ejpam-4848	18	23	some	some	DET
ejpam-4848	18	24	families	family	NOUN
ejpam-4848	18	25	of	of	ADP
ejpam-4848	18	26	graphs	graph	NOUN
ejpam-4848	18	27	such	such	ADJ
ejpam-4848	18	28	as	as	ADP
ejpam-4848	18	29	paths	path	NOUN
ejpam-4848	18	30	,	,	PUNCT
ejpam-4848	18	31	cycles	cycle	NOUN
ejpam-4848	18	32	,	,	PUNCT
ejpam-4848	18	33	fans	fan	NOUN
ejpam-4848	18	34	,	,	PUNCT
ejpam-4848	18	35	wheels	wheel	NOUN
ejpam-4848	18	36	,	,	PUNCT
ejpam-4848	18	37	complete	complete	ADJ
ejpam-4848	18	38	bipartite	bipartite	NOUN
ejpam-4848	18	39	graphs	graph	NOUN
ejpam-4848	18	40	,	,	PUNCT
ejpam-4848	18	41	and	and	CCONJ
ejpam-4848	18	42	complete	complete	ADJ
ejpam-4848	18	43	split	split	ADJ
ejpam-4848	18	44	graphs	graph	NOUN
ejpam-4848	18	45	.	.	PUNCT
ejpam-4848	19	1	in	in	ADP
ejpam-4848	19	2	a	a	DET
ejpam-4848	19	3	more	more	ADV
ejpam-4848	19	4	recent	recent	ADJ
ejpam-4848	19	5	study	study	NOUN
ejpam-4848	19	6	,	,	PUNCT
ejpam-4848	19	7	eballe	eballe	PROPN
ejpam-4848	19	8	et	et	PROPN
ejpam-4848	19	9	al	al	PROPN
ejpam-4848	19	10	.	.	PUNCT
ejpam-4848	20	1	in	in	ADP
ejpam-4848	20	2	[	[	X
ejpam-4848	20	3	3	3	NUM
ejpam-4848	20	4	]	]	PUNCT
ejpam-4848	20	5	presented	present	VERB
ejpam-4848	20	6	the	the	DET
ejpam-4848	20	7	closeness	closeness	NOUN
ejpam-4848	20	8	centrality	centrality	NOUN
ejpam-4848	20	9	of	of	ADP
ejpam-4848	20	10	the	the	DET
ejpam-4848	20	11	vertices	vertex	NOUN
ejpam-4848	20	12	in	in	ADP
ejpam-4848	20	13	the	the	DET
ejpam-4848	20	14	corona	corona	NOUN
ejpam-4848	20	15	,	,	PUNCT
ejpam-4848	20	16	cartesian	cartesian	ADJ
ejpam-4848	20	17	product	product	NOUN
ejpam-4848	20	18	and	and	CCONJ
ejpam-4848	20	19	lexicographic	lexicographic	ADJ
ejpam-4848	20	20	product	product	NOUN
ejpam-4848	20	21	of	of	ADP
ejpam-4848	20	22	graphs	graph	NOUN
ejpam-4848	20	23	.	.	PUNCT
ejpam-4848	21	1	in	in	ADP
ejpam-4848	21	2	this	this	DET
ejpam-4848	21	3	paper	paper	NOUN
ejpam-4848	21	4	,	,	PUNCT
ejpam-4848	21	5	we	we	PRON
ejpam-4848	21	6	derive	derive	VERB
ejpam-4848	21	7	formulas	formula	NOUN
ejpam-4848	21	8	of	of	ADP
ejpam-4848	21	9	the	the	DET
ejpam-4848	21	10	closeness	closeness	NOUN
ejpam-4848	21	11	centrality	centrality	NOUN
ejpam-4848	21	12	of	of	ADP
ejpam-4848	21	13	a	a	DET
ejpam-4848	21	14	vertex	vertex	NOUN
ejpam-4848	21	15	in	in	ADP
ejpam-4848	21	16	the	the	DET
ejpam-4848	21	17	shadow	shadow	NOUN
ejpam-4848	21	18	graph	graph	NOUN
ejpam-4848	21	19	,	,	PUNCT
ejpam-4848	21	20	edge	edge	NOUN
ejpam-4848	21	21	corona	corona	NOUN
ejpam-4848	21	22	of	of	ADP
ejpam-4848	21	23	graphs	graph	NOUN
ejpam-4848	21	24	,	,	PUNCT
ejpam-4848	21	25	complementary	complementary	ADJ
ejpam-4848	21	26	prism	prism	NOUN
ejpam-4848	21	27	,	,	PUNCT
ejpam-4848	21	28	and	and	CCONJ
ejpam-4848	21	29	disjunction	disjunction	NOUN
ejpam-4848	21	30	of	of	ADP
ejpam-4848	21	31	graphs	graph	NOUN
ejpam-4848	21	32	.	.	PUNCT
ejpam-4848	22	1	2	2	X
ejpam-4848	22	2	.	.	X
ejpam-4848	22	3	terminology	terminology	NOUN
ejpam-4848	22	4	definition	definition	NOUN
ejpam-4848	22	5	1	1	NUM
ejpam-4848	22	6	.	.	PUNCT
ejpam-4848	23	1	let	let	VERB
ejpam-4848	23	2	g	g	PRON
ejpam-4848	23	3	be	be	AUX
ejpam-4848	23	4	a	a	DET
ejpam-4848	23	5	connected	connected	ADJ
ejpam-4848	23	6	graph	graph	NOUN
ejpam-4848	23	7	and	and	CCONJ
ejpam-4848	23	8	let	let	VERB
ejpam-4848	23	9	u	u	NOUN
ejpam-4848	23	10	,	,	PUNCT
ejpam-4848	23	11	v	v	PROPN
ejpam-4848	23	12	∈	∈	PROPN
ejpam-4848	23	13	v	v	NOUN
ejpam-4848	23	14	(	(	PUNCT
ejpam-4848	23	15	g	g	NOUN
ejpam-4848	23	16	)	)	PUNCT
ejpam-4848	23	17	.	.	PUNCT
ejpam-4848	24	1	the	the	DET
ejpam-4848	24	2	distance	distance	NOUN
ejpam-4848	24	3	between	between	ADP
ejpam-4848	24	4	u	u	NOUN
ejpam-4848	24	5	and	and	CCONJ
ejpam-4848	24	6	v	v	NOUN
ejpam-4848	24	7	,	,	PUNCT
ejpam-4848	24	8	denoted	denote	VERB
ejpam-4848	24	9	by	by	ADP
ejpam-4848	24	10	dg(u	dg(u	NOUN
ejpam-4848	24	11	,	,	PUNCT
ejpam-4848	24	12	v	v	NOUN
ejpam-4848	24	13	)	)	PUNCT
ejpam-4848	24	14	,	,	PUNCT
ejpam-4848	24	15	is	be	AUX
ejpam-4848	24	16	the	the	DET
ejpam-4848	24	17	length	length	NOUN
ejpam-4848	24	18	of	of	ADP
ejpam-4848	24	19	a	a	DET
ejpam-4848	24	20	shortest	short	ADJ
ejpam-4848	24	21	path	path	NOUN
ejpam-4848	24	22	(	(	PUNCT
ejpam-4848	24	23	called	call	VERB
ejpam-4848	24	24	u	u	NOUN
ejpam-4848	24	25	-	-	NOUN
ejpam-4848	24	26	v	v	NOUN
ejpam-4848	24	27	geodesic	geodesic	NOUN
ejpam-4848	24	28	)	)	PUNCT
ejpam-4848	24	29	connecting	connect	VERB
ejpam-4848	24	30	u	u	NOUN
ejpam-4848	24	31	and	and	CCONJ
ejpam-4848	24	32	v.	v.	ADP
ejpam-4848	24	33	vertices	vertice	VERB
ejpam-4848	24	34	u	u	NOUN
ejpam-4848	24	35	and	and	CCONJ
ejpam-4848	24	36	v	v	NOUN
ejpam-4848	24	37	are	be	AUX
ejpam-4848	24	38	adjacent	adjacent	ADJ
ejpam-4848	24	39	or	or	CCONJ
ejpam-4848	24	40	neighbors	neighbor	NOUN
ejpam-4848	24	41	(	(	PUNCT
ejpam-4848	24	42	i.e.	i.e.	X
ejpam-4848	24	43	uv	uv	PROPN
ejpam-4848	24	44	∈	∈	PROPN
ejpam-4848	24	45	e(g	e(g	PROPN
ejpam-4848	24	46	)	)	PUNCT
ejpam-4848	24	47	)	)	PUNCT
ejpam-4848	25	1	if	if	SCONJ
ejpam-4848	25	2	and	and	CCONJ
ejpam-4848	25	3	only	only	ADV
ejpam-4848	25	4	if	if	SCONJ
ejpam-4848	25	5	dg(u	dg(u	X
ejpam-4848	25	6	,	,	PUNCT
ejpam-4848	25	7	v	v	NOUN
ejpam-4848	25	8	)	)	PUNCT
ejpam-4848	25	9	=	=	SYM
ejpam-4848	25	10	1	1	X
ejpam-4848	25	11	.	.	PUNCT
ejpam-4848	26	1	the	the	DET
ejpam-4848	26	2	open	open	ADJ
ejpam-4848	26	3	neighborhood	neighborhood	NOUN
ejpam-4848	26	4	of	of	ADP
ejpam-4848	26	5	v	v	NOUN
ejpam-4848	26	6	is	be	AUX
ejpam-4848	26	7	the	the	DET
ejpam-4848	26	8	set	set	NOUN
ejpam-4848	26	9	ng(v	ng(v	PUNCT
ejpam-4848	26	10	)	)	PUNCT
ejpam-4848	26	11	=	=	PRON
ejpam-4848	27	1	{	{	PUNCT
ejpam-4848	27	2	w	w	NOUN
ejpam-4848	27	3	∈	∈	PROPN
ejpam-4848	27	4	v	v	ADP
ejpam-4848	27	5	(	(	PUNCT
ejpam-4848	27	6	g	g	NOUN
ejpam-4848	27	7	)	)	PUNCT
ejpam-4848	27	8	:	:	PUNCT
ejpam-4848	27	9	dg(v	dg(v	X
ejpam-4848	27	10	,	,	PUNCT
ejpam-4848	27	11	w	w	NOUN
ejpam-4848	27	12	)	)	PUNCT
ejpam-4848	27	13	=	=	SYM
ejpam-4848	27	14	1	1	X
ejpam-4848	27	15	}	}	PUNCT
ejpam-4848	27	16	and	and	CCONJ
ejpam-4848	27	17	its	its	PRON
ejpam-4848	27	18	closed	closed	ADJ
ejpam-4848	27	19	neighborhood	neighborhood	NOUN
ejpam-4848	27	20	is	be	AUX
ejpam-4848	27	21	the	the	DET
ejpam-4848	27	22	set	set	NOUN
ejpam-4848	27	23	ng[v	ng[v	NOUN
ejpam-4848	27	24	]	]	X
ejpam-4848	27	25	=	=	SYM
ejpam-4848	27	26	ng(v	ng(v	X
ejpam-4848	27	27	)	)	PUNCT
ejpam-4848	27	28	∪	∪	ADP
ejpam-4848	27	29	{	{	PUNCT
ejpam-4848	27	30	v	v	NOUN
ejpam-4848	27	31	}	}	PUNCT
ejpam-4848	27	32	.	.	PUNCT
ejpam-4848	28	1	definition	definition	NOUN
ejpam-4848	28	2	2	2	NUM
ejpam-4848	28	3	.	.	PUNCT
ejpam-4848	29	1	let	let	VERB
ejpam-4848	29	2	g	g	PRON
ejpam-4848	29	3	be	be	AUX
ejpam-4848	29	4	a	a	DET
ejpam-4848	29	5	connected	connected	ADJ
ejpam-4848	29	6	graph	graph	NOUN
ejpam-4848	29	7	.	.	PUNCT
ejpam-4848	30	1	if	if	SCONJ
ejpam-4848	30	2	v	v	NUM
ejpam-4848	30	3	∈	∈	PROPN
ejpam-4848	30	4	v	v	NOUN
ejpam-4848	30	5	(	(	PUNCT
ejpam-4848	30	6	g	g	NOUN
ejpam-4848	30	7	)	)	PUNCT
ejpam-4848	30	8	and	and	CCONJ
ejpam-4848	30	9	e	e	PROPN
ejpam-4848	30	10	∈	∈	PROPN
ejpam-4848	30	11	e(g	e(g	PROPN
ejpam-4848	30	12	)	)	PUNCT
ejpam-4848	30	13	,	,	PUNCT
ejpam-4848	30	14	then	then	ADV
ejpam-4848	30	15	the	the	DET
ejpam-4848	30	16	distance	distance	NOUN
ejpam-4848	30	17	dg(v	dg(v	PUNCT
ejpam-4848	30	18	,	,	PUNCT
ejpam-4848	30	19	e	e	NOUN
ejpam-4848	30	20	)	)	PUNCT
ejpam-4848	30	21	between	between	ADP
ejpam-4848	30	22	v	v	NOUN
ejpam-4848	30	23	and	and	CCONJ
ejpam-4848	30	24	e	e	NOUN
ejpam-4848	30	25	,	,	PUNCT
ejpam-4848	30	26	is	be	AUX
ejpam-4848	30	27	given	give	VERB
ejpam-4848	30	28	by	by	ADP
ejpam-4848	30	29	dg(v	dg(v	NOUN
ejpam-4848	30	30	,	,	PUNCT
ejpam-4848	30	31	e	e	NOUN
ejpam-4848	30	32	)	)	PUNCT
ejpam-4848	30	33	=	=	SYM
ejpam-4848	30	34	min	min	NOUN
ejpam-4848	30	35	x∈v	x∈v	PROPN
ejpam-4848	30	36	(	(	PUNCT
ejpam-4848	30	37	g	g	NOUN
ejpam-4848	30	38	)	)	PUNCT
ejpam-4848	30	39	{	{	PUNCT
ejpam-4848	30	40	dg(v	dg(v	X
ejpam-4848	30	41	,	,	PUNCT
ejpam-4848	30	42	x	x	NOUN
ejpam-4848	30	43	)	)	PUNCT
ejpam-4848	30	44	,	,	PUNCT
ejpam-4848	30	45	dg(v	dg(v	X
ejpam-4848	30	46	,	,	PUNCT
ejpam-4848	30	47	x	x	NOUN
ejpam-4848	30	48	)	)	PUNCT
ejpam-4848	30	49	}	}	PUNCT
ejpam-4848	30	50	.	.	PUNCT
ejpam-4848	31	1	definition	definition	NOUN
ejpam-4848	31	2	3	3	X
ejpam-4848	31	3	.	.	PUNCT
ejpam-4848	32	1	let	let	VERB
ejpam-4848	32	2	g	g	PROPN
ejpam-4848	32	3	=	=	SYM
ejpam-4848	32	4	(	(	PUNCT
ejpam-4848	32	5	v	v	NOUN
ejpam-4848	32	6	(	(	PUNCT
ejpam-4848	32	7	g	g	NOUN
ejpam-4848	32	8	)	)	PUNCT
ejpam-4848	32	9	,	,	PUNCT
ejpam-4848	32	10	e(g	e(g	PROPN
ejpam-4848	32	11	)	)	PUNCT
ejpam-4848	32	12	)	)	PUNCT
ejpam-4848	33	1	be	be	AUX
ejpam-4848	33	2	a	a	DET
ejpam-4848	33	3	nontrivial	nontrivial	ADJ
ejpam-4848	33	4	connected	connect	VERB
ejpam-4848	33	5	graph	graph	NOUN
ejpam-4848	33	6	of	of	ADP
ejpam-4848	33	7	order	order	NOUN
ejpam-4848	33	8	m.	m.	NOUN
ejpam-4848	33	9	if	if	SCONJ
ejpam-4848	33	10	u	u	PROPN
ejpam-4848	33	11	∈	∈	PROPN
ejpam-4848	33	12	v	v	X
ejpam-4848	33	13	(	(	PUNCT
ejpam-4848	33	14	g	g	NOUN
ejpam-4848	33	15	)	)	PUNCT
ejpam-4848	33	16	,	,	PUNCT
ejpam-4848	33	17	then	then	ADV
ejpam-4848	33	18	the	the	DET
ejpam-4848	33	19	closeness	closeness	NOUN
ejpam-4848	33	20	centrality	centrality	NOUN
ejpam-4848	33	21	of	of	ADP
ejpam-4848	33	22	vertex	vertex	NOUN
ejpam-4848	33	23	u	u	NOUN
ejpam-4848	33	24	is	be	AUX
ejpam-4848	33	25	given	give	VERB
ejpam-4848	33	26	by	by	ADP
ejpam-4848	33	27	cg(u	cg(u	NOUN
ejpam-4848	33	28	)	)	PUNCT
ejpam-4848	34	1	=	=	SYM
ejpam-4848	34	2	m−	m−	PROPN
ejpam-4848	34	3	1	1	NUM
ejpam-4848	34	4	tg(u	tg(u	NUM
ejpam-4848	34	5	)	)	PUNCT
ejpam-4848	34	6	,	,	PUNCT
ejpam-4848	34	7	where	where	SCONJ
ejpam-4848	34	8	tg(u	tg(u	NUM
ejpam-4848	34	9	)	)	PUNCT
ejpam-4848	34	10	=	=	SYM
ejpam-4848	34	11	∑	∑	PUNCT
ejpam-4848	34	12	x∈v(g	x∈v(g	PROPN
ejpam-4848	34	13	)	)	PUNCT
ejpam-4848	34	14	dg(u	dg(u	PUNCT
ejpam-4848	34	15	,	,	PUNCT
ejpam-4848	34	16	x	x	X
ejpam-4848	34	17	)	)	PUNCT
ejpam-4848	34	18	.	.	PUNCT
ejpam-4848	35	1	definition	definition	NOUN
ejpam-4848	35	2	4	4	NUM
ejpam-4848	35	3	.	.	PUNCT
ejpam-4848	36	1	the	the	DET
ejpam-4848	36	2	shadow	shadow	NOUN
ejpam-4848	36	3	graph	graph	NOUN
ejpam-4848	36	4	s(g	s(g	PROPN
ejpam-4848	36	5	)	)	PUNCT
ejpam-4848	36	6	of	of	ADP
ejpam-4848	36	7	g	g	PROPN
ejpam-4848	36	8	is	be	AUX
ejpam-4848	36	9	the	the	DET
ejpam-4848	36	10	graph	graph	NOUN
ejpam-4848	36	11	obtained	obtain	VERB
ejpam-4848	36	12	by	by	ADP
ejpam-4848	36	13	taking	take	VERB
ejpam-4848	36	14	two	two	NUM
ejpam-4848	36	15	copies	copy	NOUN
ejpam-4848	36	16	of	of	ADP
ejpam-4848	36	17	g	g	NOUN
ejpam-4848	36	18	,	,	PUNCT
ejpam-4848	36	19	say	say	VERB
ejpam-4848	36	20	g1	g1	PROPN
ejpam-4848	36	21	and	and	CCONJ
ejpam-4848	36	22	g2	g2	PROPN
ejpam-4848	36	23	,	,	PUNCT
ejpam-4848	36	24	and	and	CCONJ
ejpam-4848	36	25	then	then	ADV
ejpam-4848	36	26	joining	join	VERB
ejpam-4848	36	27	each	each	DET
ejpam-4848	36	28	vertex	vertex	NOUN
ejpam-4848	36	29	v	v	ADP
ejpam-4848	36	30	∈	∈	PROPN
ejpam-4848	36	31	v	v	NOUN
ejpam-4848	36	32	(	(	PUNCT
ejpam-4848	36	33	g1	g1	PROPN
ejpam-4848	36	34	)	)	PUNCT
ejpam-4848	36	35	to	to	ADP
ejpam-4848	36	36	the	the	DET
ejpam-4848	36	37	neighbors	neighbor	NOUN
ejpam-4848	36	38	of	of	ADP
ejpam-4848	36	39	v′	v′	PROPN
ejpam-4848	36	40	∈	∈	PROPN
ejpam-4848	36	41	v	v	PROPN
ejpam-4848	36	42	(	(	PUNCT
ejpam-4848	36	43	g2	g2	PROPN
ejpam-4848	36	44	)	)	PUNCT
ejpam-4848	36	45	,	,	PUNCT
ejpam-4848	36	46	where	where	SCONJ
ejpam-4848	36	47	v′	v′	NOUN
ejpam-4848	36	48	is	be	AUX
ejpam-4848	36	49	the	the	DET
ejpam-4848	36	50	vertex	vertex	NOUN
ejpam-4848	36	51	in	in	ADP
ejpam-4848	36	52	v	v	PROPN
ejpam-4848	36	53	(	(	PUNCT
ejpam-4848	36	54	g2	g2	PROPN
ejpam-4848	36	55	)	)	PUNCT
ejpam-4848	36	56	corresponding	correspond	VERB
ejpam-4848	36	57	to	to	ADP
ejpam-4848	36	58	v	v	NUM
ejpam-4848	36	59	,	,	PUNCT
ejpam-4848	36	60	i.e.	i.e.	X
ejpam-4848	36	61	,	,	PUNCT
ejpam-4848	36	62	v	v	NOUN
ejpam-4848	36	63	and	and	CCONJ
ejpam-4848	36	64	v′	v′	PROPN
ejpam-4848	36	65	represent	represent	VERB
ejpam-4848	36	66	the	the	DET
ejpam-4848	36	67	same	same	ADJ
ejpam-4848	36	68	vertex	vertex	NOUN
ejpam-4848	36	69	in	in	ADP
ejpam-4848	36	70	g.	g.	PROPN
ejpam-4848	36	71	f.	f.	PROPN
ejpam-4848	36	72	alfeche	alfeche	PROPN
ejpam-4848	36	73	,	,	PUNCT
ejpam-4848	36	74	v.	v.	PROPN
ejpam-4848	36	75	barraza	barraza	PROPN
ejpam-4848	36	76	,	,	PUNCT
ejpam-4848	36	77	s.	s.	PROPN
ejpam-4848	36	78	canoy	canoy	PROPN
ejpam-4848	36	79	,	,	PUNCT
ejpam-4848	36	80	jr	jr	PROPN
ejpam-4848	36	81	.	.	PROPN
ejpam-4848	36	82	/	/	SYM
ejpam-4848	36	83	eur	eur	PROPN
ejpam-4848	36	84	.	.	PUNCT
ejpam-4848	37	1	j.	j.	PROPN
ejpam-4848	37	2	pure	pure	PROPN
ejpam-4848	37	3	appl	appl	PROPN
ejpam-4848	37	4	.	.	PROPN
ejpam-4848	37	5	math	math	PROPN
ejpam-4848	37	6	,	,	PUNCT
ejpam-4848	37	7	16	16	NUM
ejpam-4848	37	8	(	(	PUNCT
ejpam-4848	37	9	3	3	NUM
ejpam-4848	37	10	)	)	PUNCT
ejpam-4848	37	11	(	(	PUNCT
ejpam-4848	37	12	2023	2023	NUM
ejpam-4848	37	13	)	)	PUNCT
ejpam-4848	37	14	,	,	PUNCT
ejpam-4848	37	15	1406	1406	NUM
ejpam-4848	37	16	-	-	SYM
ejpam-4848	37	17	1420	1420	NUM
ejpam-4848	37	18	1408	1408	NUM
ejpam-4848	37	19	....................................	....................................	PUNCT
ejpam-4848	37	20	....................................	....................................	PUNCT
ejpam-4848	38	1	....................................	....................................	PUNCT
ejpam-4848	38	2	....................................	....................................	PUNCT
ejpam-4848	39	1	....................................	....................................	PUNCT
ejpam-4848	39	2	....................................	....................................	PUNCT
ejpam-4848	40	1	....................................	....................................	PUNCT
ejpam-4848	40	2	....................................	....................................	PUNCT
ejpam-4848	40	3	............	............	PUNCT
ejpam-4848	40	4	...........	...........	PUNCT
ejpam-4848	40	5	...........	...........	PUNCT
ejpam-4848	40	6	...........	...........	PUNCT
ejpam-4848	40	7	...........	...........	PUNCT
ejpam-4848	40	8	...........	...........	PUNCT
ejpam-4848	40	9	...........	...........	PUNCT
ejpam-4848	40	10	...........	...........	PUNCT
ejpam-4848	40	11	...........	...........	PUNCT
ejpam-4848	40	12	...........	...........	PUNCT
ejpam-4848	40	13	...........	...........	PUNCT
ejpam-4848	40	14	...........	...........	PUNCT
ejpam-4848	40	15	...........	...........	PUNCT
ejpam-4848	40	16	...........	...........	PUNCT
ejpam-4848	40	17	...........	...........	PUNCT
ejpam-4848	40	18	...........	...........	PUNCT
ejpam-4848	40	19	...........	...........	PUNCT
ejpam-4848	41	1	.....	.....	PUNCT
ejpam-4848	41	2	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4848	41	3	............	............	PUNCT
ejpam-4848	41	4	...........	...........	PUNCT
ejpam-4848	41	5	...........	...........	PUNCT
ejpam-4848	41	6	...........	...........	PUNCT
ejpam-4848	41	7	...........	...........	PUNCT
ejpam-4848	41	8	...........	...........	PUNCT
ejpam-4848	41	9	...........	...........	PUNCT
ejpam-4848	41	10	...........	...........	PUNCT
ejpam-4848	41	11	...........	...........	PUNCT
ejpam-4848	41	12	...........	...........	PUNCT
ejpam-4848	41	13	...........	...........	PUNCT
ejpam-4848	41	14	...........	...........	PUNCT
ejpam-4848	41	15	...........	...........	PUNCT
ejpam-4848	41	16	...........	...........	PUNCT
ejpam-4848	41	17	...........	...........	PUNCT
ejpam-4848	41	18	...........	...........	PUNCT
ejpam-4848	41	19	...........	...........	PUNCT
ejpam-4848	41	20	.....	.....	PUNCT
ejpam-4848	41	21	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4848	41	22	............	............	PUNCT
ejpam-4848	41	23	...........	...........	PUNCT
ejpam-4848	41	24	...........	...........	PUNCT
ejpam-4848	41	25	...........	...........	PUNCT
ejpam-4848	41	26	...........	...........	PUNCT
ejpam-4848	41	27	...........	...........	PUNCT
ejpam-4848	41	28	...........	...........	PUNCT
ejpam-4848	41	29	...........	...........	PUNCT
ejpam-4848	41	30	...........	...........	PUNCT
ejpam-4848	41	31	...........	...........	PUNCT
ejpam-4848	41	32	...........	...........	PUNCT
ejpam-4848	41	33	...........	...........	PUNCT
ejpam-4848	41	34	...........	...........	PUNCT
ejpam-4848	41	35	...........	...........	PUNCT
ejpam-4848	41	36	...........	...........	PUNCT
ejpam-4848	41	37	...........	...........	PUNCT
ejpam-4848	41	38	...........	...........	PUNCT
ejpam-4848	41	39	.....	.....	PUNCT
ejpam-4848	41	40	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4848	41	41	............	............	PUNCT
ejpam-4848	41	42	...........	...........	PUNCT
ejpam-4848	41	43	...........	...........	PUNCT
ejpam-4848	41	44	...........	...........	PUNCT
ejpam-4848	41	45	...........	...........	PUNCT
ejpam-4848	41	46	...........	...........	PUNCT
ejpam-4848	41	47	...........	...........	PUNCT
ejpam-4848	41	48	...........	...........	PUNCT
ejpam-4848	41	49	...........	...........	PUNCT
ejpam-4848	41	50	...........	...........	PUNCT
ejpam-4848	41	51	...........	...........	PUNCT
ejpam-4848	41	52	...........	...........	PUNCT
ejpam-4848	41	53	...........	...........	PUNCT
ejpam-4848	41	54	...........	...........	PUNCT
ejpam-4848	41	55	...........	...........	PUNCT
ejpam-4848	41	56	...........	...........	PUNCT
ejpam-4848	41	57	...........	...........	PUNCT
ejpam-4848	42	1	.....	.....	PUNCT
ejpam-4848	42	2	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4848	42	3	.......................................................................................................................................................................................................................................................................................................................	.......................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4848	43	1	.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4848	43	2	.................................	.................................	PUNCT
ejpam-4848	43	3	.................................	.................................	PUNCT
ejpam-4848	43	4	.................................	.................................	PUNCT
ejpam-4848	43	5	.................................	.................................	PUNCT
ejpam-4848	43	6	.................................	.................................	PUNCT
ejpam-4848	43	7	.................................	.................................	PUNCT
ejpam-4848	43	8	.................................	.................................	PUNCT
ejpam-4848	43	9	.................................	.................................	PUNCT
ejpam-4848	43	10	.................................	.................................	PUNCT
ejpam-4848	43	11	.................................	.................................	PUNCT
ejpam-4848	43	12	.................................	.................................	PUNCT
ejpam-4848	43	13	.................................	.................................	PUNCT
ejpam-4848	43	14	.................................	.................................	PUNCT
ejpam-4848	43	15	.................................	.................................	PUNCT
ejpam-4848	43	16	.................................	.................................	PUNCT
ejpam-4848	43	17	.................................	.................................	PUNCT
ejpam-4848	44	1	.........................	.........................	PUNCT
ejpam-4848	44	2	..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4848	44	3	..................	..................	PUNCT
ejpam-4848	44	4	..................	..................	PUNCT
ejpam-4848	44	5	..................	..................	PUNCT
ejpam-4848	44	6	..................	..................	PUNCT
ejpam-4848	45	1	..................	..................	PUNCT
ejpam-4848	45	2	..................	..................	PUNCT
ejpam-4848	46	1	..................	..................	PUNCT
ejpam-4848	46	2	..................	..................	PUNCT
ejpam-4848	47	1	..................	..................	PUNCT
ejpam-4848	47	2	..................	..................	PUNCT
ejpam-4848	48	1	..................	..................	PUNCT
ejpam-4848	48	2	..................	..................	PUNCT
ejpam-4848	49	1	..................	..................	PUNCT
ejpam-4848	49	2	..................	..................	PUNCT
ejpam-4848	50	1	..................	..................	PUNCT
ejpam-4848	50	2	..................	..................	PUNCT
ejpam-4848	51	1	....	....	PUNCT
ejpam-4848	51	2	..................................	..................................	PUNCT
ejpam-4848	51	3	.................................	.................................	PUNCT
ejpam-4848	51	4	.................................	.................................	PUNCT
ejpam-4848	51	5	.................................	.................................	PUNCT
ejpam-4848	51	6	.................................	.................................	PUNCT
ejpam-4848	51	7	.................................	.................................	PUNCT
ejpam-4848	51	8	.................................	.................................	PUNCT
ejpam-4848	51	9	.................................	.................................	PUNCT
ejpam-4848	51	10	.................................	.................................	PUNCT
ejpam-4848	51	11	.................................	.................................	PUNCT
ejpam-4848	51	12	.................................	.................................	PUNCT
ejpam-4848	51	13	.................................	.................................	PUNCT
ejpam-4848	51	14	.................................	.................................	PUNCT
ejpam-4848	51	15	.................................	.................................	PUNCT
ejpam-4848	51	16	.................................	.................................	PUNCT
ejpam-4848	51	17	.................................	.................................	PUNCT
ejpam-4848	51	18	.................................	.................................	PUNCT
ejpam-4848	51	19	.........................	.........................	PUNCT
ejpam-4848	51	20	...................	...................	PUNCT
ejpam-4848	51	21	..................	..................	PUNCT
ejpam-4848	51	22	..................	..................	PUNCT
ejpam-4848	51	23	..................	..................	PUNCT
ejpam-4848	51	24	..................	..................	PUNCT
ejpam-4848	51	25	..................	..................	PUNCT
ejpam-4848	51	26	..................	..................	PUNCT
ejpam-4848	51	27	..................	..................	PUNCT
ejpam-4848	51	28	..................	..................	PUNCT
ejpam-4848	51	29	..................	..................	PUNCT
ejpam-4848	51	30	..................	..................	PUNCT
ejpam-4848	51	31	..................	..................	PUNCT
ejpam-4848	51	32	..................	..................	PUNCT
ejpam-4848	51	33	..................	..................	PUNCT
ejpam-4848	51	34	..................	..................	PUNCT
ejpam-4848	51	35	..................	..................	PUNCT
ejpam-4848	52	1	..................	..................	PUNCT
ejpam-4848	52	2	....	....	PUNCT
ejpam-4848	53	1	.......................................................................................................................................................................................................................................................................................................................	.......................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4848	54	1	v1	v1	PROPN
ejpam-4848	54	2	v2	v2	PROPN
ejpam-4848	54	3	v3	v3	PROPN
ejpam-4848	54	4	v4	v4	PROPN
ejpam-4848	54	5	v′1	v′1	PROPN
ejpam-4848	54	6	v′2	v′2	PROPN
ejpam-4848	54	7	v′3	v′3	PROPN
ejpam-4848	54	8	v′4	v′4	NOUN
ejpam-4848	54	9	g1	g1	PROPN
ejpam-4848	54	10	=	=	SYM
ejpam-4848	54	11	c4	c4	NOUN
ejpam-4848	54	12	g2	g2	PROPN
ejpam-4848	54	13	=	=	PROPN
ejpam-4848	54	14	c4	c4	NOUN
ejpam-4848	54	15	figure	figure	NOUN
ejpam-4848	54	16	1	1	NUM
ejpam-4848	54	17	:	:	PUNCT
ejpam-4848	54	18	the	the	DET
ejpam-4848	54	19	shadow	shadow	NOUN
ejpam-4848	54	20	graph	graph	VERB
ejpam-4848	54	21	s(c4	s(c4	NOUN
ejpam-4848	54	22	)	)	PUNCT
ejpam-4848	54	23	of	of	ADP
ejpam-4848	54	24	c4	c4	NOUN
ejpam-4848	54	25	definition	definition	NOUN
ejpam-4848	54	26	5	5	NUM
ejpam-4848	54	27	.	.	PUNCT
ejpam-4848	55	1	let	let	VERB
ejpam-4848	55	2	g	g	NOUN
ejpam-4848	55	3	and	and	CCONJ
ejpam-4848	55	4	h	h	NOUN
ejpam-4848	55	5	be	be	VERB
ejpam-4848	55	6	two	two	NUM
ejpam-4848	55	7	graphs	graph	NOUN
ejpam-4848	55	8	.	.	PUNCT
ejpam-4848	56	1	the	the	DET
ejpam-4848	56	2	edge	edge	NOUN
ejpam-4848	56	3	corona	corona	PROPN
ejpam-4848	56	4	g	g	PROPN
ejpam-4848	56	5	⋄	⋄	PROPN
ejpam-4848	56	6	h	h	NOUN
ejpam-4848	56	7	of	of	ADP
ejpam-4848	56	8	g	g	PROPN
ejpam-4848	56	9	and	and	CCONJ
ejpam-4848	56	10	h	h	NOUN
ejpam-4848	56	11	is	be	AUX
ejpam-4848	56	12	the	the	DET
ejpam-4848	56	13	graph	graph	NOUN
ejpam-4848	56	14	obtained	obtain	VERB
ejpam-4848	56	15	by	by	ADP
ejpam-4848	56	16	taking	take	VERB
ejpam-4848	56	17	one	one	NUM
ejpam-4848	56	18	copy	copy	NOUN
ejpam-4848	56	19	of	of	ADP
ejpam-4848	56	20	g	g	PROPN
ejpam-4848	56	21	and	and	CCONJ
ejpam-4848	56	22	|e(g)|	|e(g)|	ADJ
ejpam-4848	56	23	copies	copy	NOUN
ejpam-4848	56	24	of	of	ADP
ejpam-4848	56	25	h	h	NOUN
ejpam-4848	56	26	,	,	PUNCT
ejpam-4848	56	27	and	and	CCONJ
ejpam-4848	56	28	then	then	ADV
ejpam-4848	56	29	joining	join	VERB
ejpam-4848	56	30	two	two	NUM
ejpam-4848	56	31	end	end	NOUN
ejpam-4848	56	32	-	-	PUNCT
ejpam-4848	56	33	vertices	vertex	NOUN
ejpam-4848	56	34	of	of	ADP
ejpam-4848	56	35	the	the	DET
ejpam-4848	56	36	i	i	PROPN
ejpam-4848	56	37	-	-	PUNCT
ejpam-4848	56	38	th	th	X
ejpam-4848	56	39	edge	edge	NOUN
ejpam-4848	56	40	of	of	ADP
ejpam-4848	56	41	g	g	NOUN
ejpam-4848	56	42	to	to	ADP
ejpam-4848	56	43	every	every	DET
ejpam-4848	56	44	vertex	vertex	NOUN
ejpam-4848	56	45	in	in	ADP
ejpam-4848	56	46	the	the	DET
ejpam-4848	56	47	i	i	PROPN
ejpam-4848	56	48	-	-	PUNCT
ejpam-4848	56	49	th	th	PROPN
ejpam-4848	56	50	copy	copy	NOUN
ejpam-4848	56	51	of	of	ADP
ejpam-4848	56	52	h.	h.	PROPN
ejpam-4848	56	53	for	for	ADP
ejpam-4848	56	54	every	every	DET
ejpam-4848	56	55	edge	edge	NOUN
ejpam-4848	56	56	e	e	NOUN
ejpam-4848	57	1	=	=	NOUN
ejpam-4848	57	2	uv	uv	NOUN
ejpam-4848	57	3	of	of	ADP
ejpam-4848	57	4	g	g	NOUN
ejpam-4848	57	5	,	,	PUNCT
ejpam-4848	57	6	denote	denote	VERB
ejpam-4848	57	7	by	by	ADP
ejpam-4848	57	8	he	he	PRON
ejpam-4848	57	9	=	=	PUNCT
ejpam-4848	57	10	huv	huv	PROPN
ejpam-4848	57	11	the	the	DET
ejpam-4848	57	12	copy	copy	NOUN
ejpam-4848	57	13	of	of	ADP
ejpam-4848	57	14	h	h	NOUN
ejpam-4848	57	15	where	where	SCONJ
ejpam-4848	57	16	vertices	vertex	NOUN
ejpam-4848	57	17	are	be	AUX
ejpam-4848	57	18	joined	join	VERB
ejpam-4848	57	19	to	to	ADP
ejpam-4848	57	20	the	the	DET
ejpam-4848	57	21	vertices	vertex	NOUN
ejpam-4848	57	22	u	u	NOUN
ejpam-4848	57	23	and	and	CCONJ
ejpam-4848	57	24	v.	v.	ADP
ejpam-4848	57	25	....................................	....................................	PUNCT
ejpam-4848	58	1	....................................	....................................	PUNCT
ejpam-4848	58	2	....................................	....................................	PUNCT
ejpam-4848	59	1	....................................	....................................	PUNCT
ejpam-4848	59	2	....................................	....................................	PUNCT
ejpam-4848	60	1	..............	..............	PUNCT
ejpam-4848	60	2	.............	.............	PUNCT
ejpam-4848	60	3	.............	.............	PUNCT
ejpam-4848	60	4	.............	.............	PUNCT
ejpam-4848	60	5	.............	.............	PUNCT
ejpam-4848	60	6	.............	.............	PUNCT
ejpam-4848	60	7	.............	.............	PUNCT
ejpam-4848	61	1	..........	..........	PUNCT
ejpam-4848	61	2	......................................................................................	......................................................................................	PUNCT
ejpam-4848	61	3	............................................................................	............................................................................	PUNCT
ejpam-4848	62	1	....	....	PUNCT
ejpam-4848	62	2	.........	.........	PUNCT
ejpam-4848	63	1	.........	.........	PUNCT
ejpam-4848	63	2	.........	.........	PUNCT
ejpam-4848	64	1	.........	.........	PUNCT
ejpam-4848	64	2	.........	.........	PUNCT
ejpam-4848	65	1	.........	.........	PUNCT
ejpam-4848	65	2	.........	.........	PUNCT
ejpam-4848	66	1	.........	.........	PUNCT
ejpam-4848	66	2	.........	.........	PUNCT
ejpam-4848	66	3	.	.	PUNCT
ejpam-4848	67	1	......................................................................................................	......................................................................................................	PUNCT
ejpam-4848	67	2	..............	..............	PUNCT
ejpam-4848	68	1	.............	.............	PUNCT
ejpam-4848	68	2	.............	.............	PUNCT
ejpam-4848	68	3	.............	.............	PUNCT
ejpam-4848	69	1	.........	.........	PUNCT
ejpam-4848	69	2	....................................	....................................	PUNCT
ejpam-4848	69	3	....................................	....................................	PUNCT
ejpam-4848	70	1	..............................................................	..............................................................	PUNCT
ejpam-4848	70	2	....................................	....................................	PUNCT
ejpam-4848	71	1	....................................	....................................	PUNCT
ejpam-4848	71	2	...................................................................................	...................................................................................	PUNCT
ejpam-4848	72	1	....................................	....................................	PUNCT
ejpam-4848	72	2	.................................................	.................................................	PUNCT
ejpam-4848	73	1	....................................	....................................	PUNCT
ejpam-4848	73	2	....................................	....................................	PUNCT
ejpam-4848	74	1	..........	..........	PUNCT
ejpam-4848	74	2	.........	.........	PUNCT
ejpam-4848	75	1	.........	.........	PUNCT
ejpam-4848	75	2	.........	.........	PUNCT
ejpam-4848	76	1	.........	.........	PUNCT
ejpam-4848	76	2	...	...	PUNCT
ejpam-4848	76	3	.	.	PUNCT
ejpam-4848	76	4	...................................	...................................	PUNCT
ejpam-4848	77	1	....................................	....................................	PUNCT
ejpam-4848	77	2	.................................	.................................	PUNCT
ejpam-4848	78	1	................................	................................	PUNCT
ejpam-4848	78	2	................................	................................	PUNCT
ejpam-4848	78	3	...........	...........	PUNCT
ejpam-4848	78	4	.................................................	.................................................	PUNCT
ejpam-4848	79	1	............................................................................................................	............................................................................................................	PUNCT
ejpam-4848	79	2	.................................	.................................	PUNCT
ejpam-4848	80	1	................	................	PUNCT
ejpam-4848	80	2	...................................................	...................................................	PUNCT
ejpam-4848	81	1	.........	.........	PUNCT
ejpam-4848	81	2	.........	.........	PUNCT
ejpam-4848	82	1	.........	.........	PUNCT
ejpam-4848	82	2	.........	.........	PUNCT
ejpam-4848	83	1	.........	.........	PUNCT
ejpam-4848	83	2	.........	.........	PUNCT
ejpam-4848	83	3	.........	.........	PUNCT
ejpam-4848	83	4	........	........	PUNCT
ejpam-4848	83	5	...............	...............	PUNCT
ejpam-4848	83	6	..............	..............	PUNCT
ejpam-4848	83	7	.............	.............	PUNCT
ejpam-4848	83	8	.........	.........	PUNCT
ejpam-4848	83	9	........	........	PUNCT
ejpam-4848	83	10	........	........	PUNCT
ejpam-4848	83	11	........	........	PUNCT
ejpam-4848	83	12	........	........	PUNCT
ejpam-4848	83	13	........	........	PUNCT
ejpam-4848	83	14	........	........	PUNCT
ejpam-4848	84	1	........	........	PUNCT
ejpam-4848	84	2	......	......	PUNCT
ejpam-4848	84	3	.............................................................................................................................................	.............................................................................................................................................	PUNCT
ejpam-4848	84	4	...................................	...................................	PUNCT
ejpam-4848	84	5	..........................................................................................	..........................................................................................	PUNCT
ejpam-4848	85	1	................	................	PUNCT
ejpam-4848	85	2	................	................	PUNCT
ejpam-4848	85	3	................	................	PUNCT
ejpam-4848	85	4	........	........	PUNCT
ejpam-4848	86	1	..........	..........	PUNCT
ejpam-4848	86	2	.........	.........	PUNCT
ejpam-4848	87	1	.........	.........	PUNCT
ejpam-4848	87	2	.......	.......	PUNCT
ejpam-4848	87	3	...............	...............	PUNCT
ejpam-4848	87	4	..............	..............	PUNCT
ejpam-4848	88	1	..............	..............	PUNCT
ejpam-4848	88	2	..............	..............	PUNCT
ejpam-4848	89	1	..............	..............	PUNCT
ejpam-4848	89	2	..............	..............	PUNCT
ejpam-4848	90	1	........	........	PUNCT
ejpam-4848	90	2	................................................	................................................	PUNCT
ejpam-4848	90	3	..........................................	..........................................	PUNCT
ejpam-4848	90	4	.......................................................................	.......................................................................	PUNCT
ejpam-4848	91	1	...........	...........	PUNCT
ejpam-4848	91	2	..........	..........	PUNCT
ejpam-4848	92	1	..........	..........	PUNCT
ejpam-4848	92	2	..........	..........	PUNCT
ejpam-4848	92	3	.	.	PUNCT
ejpam-4848	93	1	................................................................................	................................................................................	PUNCT
ejpam-4848	94	1	figure	figure	NOUN
ejpam-4848	94	2	2	2	NUM
ejpam-4848	94	3	:	:	PUNCT
ejpam-4848	94	4	the	the	DET
ejpam-4848	94	5	edge	edge	NOUN
ejpam-4848	94	6	corona	corona	NOUN
ejpam-4848	94	7	c5	c5	PROPN
ejpam-4848	94	8	⋄	⋄	PROPN
ejpam-4848	94	9	p2	p2	VERB
ejpam-4848	94	10	definition	definition	NOUN
ejpam-4848	94	11	6	6	NUM
ejpam-4848	94	12	.	.	PUNCT
ejpam-4848	95	1	the	the	DET
ejpam-4848	95	2	complementary	complementary	ADJ
ejpam-4848	95	3	prism	prism	NOUN
ejpam-4848	95	4	of	of	ADP
ejpam-4848	95	5	graph	graph	NOUN
ejpam-4848	95	6	g	g	NOUN
ejpam-4848	95	7	,	,	PUNCT
ejpam-4848	95	8	denoted	denote	VERB
ejpam-4848	95	9	by	by	ADP
ejpam-4848	95	10	gg	gg	PROPN
ejpam-4848	95	11	,	,	PUNCT
ejpam-4848	95	12	is	be	AUX
ejpam-4848	95	13	the	the	DET
ejpam-4848	95	14	graph	graph	NOUN
ejpam-4848	95	15	obtained	obtain	VERB
ejpam-4848	95	16	from	from	ADP
ejpam-4848	95	17	the	the	DET
ejpam-4848	95	18	disjoint	disjoint	PROPN
ejpam-4848	95	19	union	union	NOUN
ejpam-4848	95	20	of	of	ADP
ejpam-4848	95	21	g	g	PROPN
ejpam-4848	95	22	and	and	CCONJ
ejpam-4848	95	23	g	g	NOUN
ejpam-4848	95	24	by	by	ADP
ejpam-4848	95	25	adding	add	VERB
ejpam-4848	95	26	the	the	DET
ejpam-4848	95	27	edges	edge	NOUN
ejpam-4848	95	28	vv	vv	ADP
ejpam-4848	95	29	,	,	PUNCT
ejpam-4848	95	30	where	where	SCONJ
ejpam-4848	95	31	v	v	X
ejpam-4848	95	32	∈	∈	PROPN
ejpam-4848	95	33	v	v	NOUN
ejpam-4848	95	34	(	(	PUNCT
ejpam-4848	95	35	g	g	NOUN
ejpam-4848	95	36	)	)	PUNCT
ejpam-4848	95	37	and	and	CCONJ
ejpam-4848	95	38	v	v	NOUN
ejpam-4848	95	39	is	be	AUX
ejpam-4848	95	40	the	the	DET
ejpam-4848	95	41	vertex	vertex	NOUN
ejpam-4848	95	42	of	of	ADP
ejpam-4848	95	43	g	g	PROPN
ejpam-4848	95	44	corresponding	correspond	VERB
ejpam-4848	95	45	to	to	ADP
ejpam-4848	95	46	vertex	vertex	NOUN
ejpam-4848	95	47	v.	v.	ADP
ejpam-4848	95	48	figure	figure	NOUN
ejpam-4848	95	49	3	3	NUM
ejpam-4848	95	50	:	:	PUNCT
ejpam-4848	95	51	the	the	DET
ejpam-4848	95	52	complementary	complementary	ADJ
ejpam-4848	95	53	prism	prism	NOUN
ejpam-4848	95	54	c5c5	c5c5	PROPN
ejpam-4848	95	55	f.	f.	PROPN
ejpam-4848	95	56	alfeche	alfeche	PROPN
ejpam-4848	95	57	,	,	PUNCT
ejpam-4848	95	58	v.	v.	PROPN
ejpam-4848	95	59	barraza	barraza	PROPN
ejpam-4848	95	60	,	,	PUNCT
ejpam-4848	95	61	s.	s.	PROPN
ejpam-4848	95	62	canoy	canoy	PROPN
ejpam-4848	95	63	,	,	PUNCT
ejpam-4848	95	64	jr	jr	PROPN
ejpam-4848	95	65	.	.	PROPN
ejpam-4848	95	66	/	/	SYM
ejpam-4848	95	67	eur	eur	PROPN
ejpam-4848	95	68	.	.	PUNCT
ejpam-4848	96	1	j.	j.	PROPN
ejpam-4848	96	2	pure	pure	PROPN
ejpam-4848	96	3	appl	appl	PROPN
ejpam-4848	96	4	.	.	PROPN
ejpam-4848	96	5	math	math	PROPN
ejpam-4848	96	6	,	,	PUNCT
ejpam-4848	96	7	16	16	NUM
ejpam-4848	96	8	(	(	PUNCT
ejpam-4848	96	9	3	3	NUM
ejpam-4848	96	10	)	)	PUNCT
ejpam-4848	96	11	(	(	PUNCT
ejpam-4848	96	12	2023	2023	NUM
ejpam-4848	96	13	)	)	PUNCT
ejpam-4848	96	14	,	,	PUNCT
ejpam-4848	96	15	1406	1406	NUM
ejpam-4848	96	16	-	-	SYM
ejpam-4848	96	17	1420	1420	NUM
ejpam-4848	96	18	1409	1409	NUM
ejpam-4848	96	19	definition	definition	NOUN
ejpam-4848	96	20	7	7	NUM
ejpam-4848	96	21	.	.	PUNCT
ejpam-4848	97	1	the	the	DET
ejpam-4848	97	2	disjunction	disjunction	NOUN
ejpam-4848	97	3	of	of	ADP
ejpam-4848	97	4	graphs	graph	NOUN
ejpam-4848	97	5	g	g	PROPN
ejpam-4848	97	6	and	and	CCONJ
ejpam-4848	97	7	h	h	NOUN
ejpam-4848	97	8	,	,	PUNCT
ejpam-4848	97	9	denoted	denote	VERB
ejpam-4848	97	10	by	by	ADP
ejpam-4848	97	11	g	g	PROPN
ejpam-4848	97	12	∨h	∨h	NOUN
ejpam-4848	97	13	,	,	PUNCT
ejpam-4848	97	14	is	be	AUX
ejpam-4848	97	15	the	the	DET
ejpam-4848	97	16	graph	graph	NOUN
ejpam-4848	97	17	with	with	ADP
ejpam-4848	97	18	v	v	NOUN
ejpam-4848	97	19	(	(	PUNCT
ejpam-4848	97	20	g	g	PROPN
ejpam-4848	97	21	∨	∨	NUM
ejpam-4848	97	22	h	h	NOUN
ejpam-4848	97	23	)	)	PUNCT
ejpam-4848	97	24	=	=	NOUN
ejpam-4848	97	25	v	v	X
ejpam-4848	97	26	(	(	PUNCT
ejpam-4848	97	27	g	g	NOUN
ejpam-4848	97	28	)	)	PUNCT
ejpam-4848	97	29	×	×	NOUN
ejpam-4848	97	30	v	v	NOUN
ejpam-4848	97	31	(	(	PUNCT
ejpam-4848	97	32	h	h	NOUN
ejpam-4848	97	33	)	)	PUNCT
ejpam-4848	97	34	and	and	CCONJ
ejpam-4848	97	35	(	(	PUNCT
ejpam-4848	97	36	x	x	X
ejpam-4848	97	37	,	,	PUNCT
ejpam-4848	97	38	p)(y	p)(y	PROPN
ejpam-4848	97	39	,	,	PUNCT
ejpam-4848	97	40	q	q	X
ejpam-4848	97	41	)	)	PUNCT
ejpam-4848	97	42	∈	∈	PROPN
ejpam-4848	97	43	e(g	e(g	PROPN
ejpam-4848	97	44	∨	∨	NUM
ejpam-4848	97	45	h	h	NOUN
ejpam-4848	97	46	)	)	PUNCT
ejpam-4848	97	47	if	if	SCONJ
ejpam-4848	97	48	and	and	CCONJ
ejpam-4848	97	49	only	only	ADV
ejpam-4848	97	50	if	if	SCONJ
ejpam-4848	97	51	xy	xy	PROPN
ejpam-4848	97	52	∈	∈	PROPN
ejpam-4848	97	53	e(g	e(g	PROPN
ejpam-4848	97	54	)	)	PUNCT
ejpam-4848	97	55	or	or	CCONJ
ejpam-4848	97	56	pq	pq	NOUN
ejpam-4848	97	57	∈	∈	PROPN
ejpam-4848	97	58	e(h	e(h	PROPN
ejpam-4848	97	59	)	)	PUNCT
ejpam-4848	97	60	.	.	PUNCT
ejpam-4848	98	1	3	3	X
ejpam-4848	98	2	.	.	X
ejpam-4848	98	3	main	main	ADJ
ejpam-4848	98	4	results	result	NOUN
ejpam-4848	98	5	in	in	ADP
ejpam-4848	98	6	what	what	PRON
ejpam-4848	98	7	follows	follow	VERB
ejpam-4848	98	8	,	,	PUNCT
ejpam-4848	98	9	g1	g1	PROPN
ejpam-4848	98	10	and	and	CCONJ
ejpam-4848	98	11	g2	g2	PROPN
ejpam-4848	98	12	are	be	AUX
ejpam-4848	98	13	the	the	DET
ejpam-4848	98	14	copies	copy	NOUN
ejpam-4848	98	15	of	of	ADP
ejpam-4848	98	16	g	g	NOUN
ejpam-4848	98	17	in	in	ADP
ejpam-4848	98	18	the	the	DET
ejpam-4848	98	19	shadow	shadow	NOUN
ejpam-4848	98	20	graph	graph	NOUN
ejpam-4848	98	21	s(g	s(g	PROPN
ejpam-4848	98	22	)	)	PUNCT
ejpam-4848	98	23	.	.	PUNCT
ejpam-4848	99	1	remark	remark	PROPN
ejpam-4848	99	2	1	1	NUM
ejpam-4848	99	3	.	.	PUNCT
ejpam-4848	100	1	let	let	VERB
ejpam-4848	100	2	g	g	PRON
ejpam-4848	100	3	be	be	AUX
ejpam-4848	100	4	a	a	DET
ejpam-4848	100	5	graph	graph	NOUN
ejpam-4848	100	6	and	and	CCONJ
ejpam-4848	100	7	let	let	VERB
ejpam-4848	100	8	v	v	NOUN
ejpam-4848	100	9	,	,	PUNCT
ejpam-4848	100	10	w	w	PROPN
ejpam-4848	100	11	∈	∈	PROPN
ejpam-4848	100	12	v	v	X
ejpam-4848	100	13	(	(	PUNCT
ejpam-4848	100	14	g1	g1	PROPN
ejpam-4848	100	15	)	)	PUNCT
ejpam-4848	100	16	.	.	PUNCT
ejpam-4848	101	1	then	then	ADV
ejpam-4848	101	2	ds(g)(v	ds(g)(v	NOUN
ejpam-4848	101	3	,	,	PUNCT
ejpam-4848	101	4	w	w	NOUN
ejpam-4848	101	5	)	)	PUNCT
ejpam-4848	101	6	=	=	SYM
ejpam-4848	101	7	dg1(v	dg1(v	PROPN
ejpam-4848	101	8	,	,	PUNCT
ejpam-4848	101	9	w	w	NOUN
ejpam-4848	101	10	)	)	PUNCT
ejpam-4848	101	11	=	=	SYM
ejpam-4848	101	12	dg2(v	dg2(v	PROPN
ejpam-4848	101	13	′	′	NOUN
ejpam-4848	101	14	,	,	PUNCT
ejpam-4848	101	15	w′	w′	PROPN
ejpam-4848	101	16	)	)	PUNCT
ejpam-4848	101	17	=	=	SYM
ejpam-4848	101	18	ds(g)(v	ds(g)(v	NOUN
ejpam-4848	101	19	′	′	NOUN
ejpam-4848	101	20	,	,	PUNCT
ejpam-4848	101	21	w′	w′	PROPN
ejpam-4848	101	22	)	)	PUNCT
ejpam-4848	101	23	.	.	PUNCT
ejpam-4848	102	1	lemma	lemma	PROPN
ejpam-4848	102	2	1	1	X
ejpam-4848	102	3	.	.	PUNCT
ejpam-4848	103	1	let	let	VERB
ejpam-4848	103	2	g	g	PRON
ejpam-4848	103	3	be	be	AUX
ejpam-4848	103	4	a	a	DET
ejpam-4848	103	5	nontrivial	nontrivial	ADJ
ejpam-4848	103	6	connected	connect	VERB
ejpam-4848	103	7	graph	graph	NOUN
ejpam-4848	103	8	.	.	PUNCT
ejpam-4848	104	1	for	for	ADP
ejpam-4848	104	2	each	each	DET
ejpam-4848	104	3	p	p	PROPN
ejpam-4848	104	4	∈	∈	PROPN
ejpam-4848	104	5	v	v	NOUN
ejpam-4848	104	6	(	(	PUNCT
ejpam-4848	104	7	g1	g1	PROPN
ejpam-4848	104	8	)	)	PUNCT
ejpam-4848	104	9	and	and	CCONJ
ejpam-4848	104	10	v′	v′	PROPN
ejpam-4848	104	11	∈	∈	PROPN
ejpam-4848	104	12	v	v	NOUN
ejpam-4848	104	13	(	(	PUNCT
ejpam-4848	104	14	g2	g2	PROPN
ejpam-4848	104	15	)	)	PUNCT
ejpam-4848	104	16	,	,	PUNCT
ejpam-4848	104	17	ds(g)(p	ds(g)(p	PROPN
ejpam-4848	104	18	,	,	PUNCT
ejpam-4848	104	19	v	v	NOUN
ejpam-4848	104	20	′	′	NOUN
ejpam-4848	104	21	)	)	PUNCT
ejpam-4848	104	22	=	=	SYM
ejpam-4848	104	23	ds(g)(p	ds(g)(p	NUM
ejpam-4848	104	24	′	′	NUM
ejpam-4848	104	25	,	,	PUNCT
ejpam-4848	104	26	v	v	NOUN
ejpam-4848	104	27	)	)	PUNCT
ejpam-4848	104	28	=	=	NOUN
ejpam-4848	104	29	{	{	PUNCT
ejpam-4848	104	30	2	2	NUM
ejpam-4848	104	31	if	if	SCONJ
ejpam-4848	104	32	p	p	NOUN
ejpam-4848	104	33	=	=	X
ejpam-4848	104	34	v	v	ADP
ejpam-4848	104	35	dg1(p	dg1(p	PROPN
ejpam-4848	104	36	,	,	PUNCT
ejpam-4848	104	37	v	v	NOUN
ejpam-4848	104	38	)	)	PUNCT
ejpam-4848	104	39	if	if	SCONJ
ejpam-4848	104	40	p	p	PRON
ejpam-4848	104	41	̸=	̸=	PROPN
ejpam-4848	104	42	v.	v.	ADP
ejpam-4848	104	43	proof	proof	NOUN
ejpam-4848	104	44	.	.	PUNCT
ejpam-4848	105	1	if	if	SCONJ
ejpam-4848	105	2	p	p	PROPN
ejpam-4848	105	3	=	=	SYM
ejpam-4848	105	4	v	v	NOUN
ejpam-4848	105	5	,	,	PUNCT
ejpam-4848	105	6	then	then	ADV
ejpam-4848	105	7	p′	p′	NOUN
ejpam-4848	105	8	=	=	SYM
ejpam-4848	105	9	v′	v′	NOUN
ejpam-4848	105	10	and	and	CCONJ
ejpam-4848	105	11	pp′	pp′	NOUN
ejpam-4848	105	12	/∈	/∈	PUNCT
ejpam-4848	105	13	e(s(g	e(s(g	PROPN
ejpam-4848	105	14	)	)	PUNCT
ejpam-4848	105	15	)	)	PUNCT
ejpam-4848	105	16	.	.	PUNCT
ejpam-4848	106	1	let	let	VERB
ejpam-4848	106	2	w	w	PROPN
ejpam-4848	106	3	∈	∈	PROPN
ejpam-4848	106	4	ng1(p	ng1(p	PROPN
ejpam-4848	106	5	)	)	PUNCT
ejpam-4848	106	6	.	.	PUNCT
ejpam-4848	107	1	then	then	ADV
ejpam-4848	107	2	wp′	wp′	PROPN
ejpam-4848	107	3	∈	∈	PROPN
ejpam-4848	107	4	e(s(g	e(s(g	PROPN
ejpam-4848	107	5	)	)	PUNCT
ejpam-4848	107	6	)	)	PUNCT
ejpam-4848	107	7	.	.	PUNCT
ejpam-4848	108	1	hence	hence	ADV
ejpam-4848	108	2	,	,	PUNCT
ejpam-4848	108	3	[	[	X
ejpam-4848	108	4	p	p	X
ejpam-4848	108	5	,	,	PUNCT
ejpam-4848	108	6	w	w	PROPN
ejpam-4848	108	7	,	,	PUNCT
ejpam-4848	108	8	v′	v′	PROPN
ejpam-4848	108	9	]	]	PUNCT
ejpam-4848	108	10	is	be	AUX
ejpam-4848	108	11	a	a	DET
ejpam-4848	108	12	p−	p−	NOUN
ejpam-4848	108	13	v′	v′	NOUN
ejpam-4848	108	14	geodesic	geodesic	NOUN
ejpam-4848	108	15	in	in	ADP
ejpam-4848	108	16	s(g	s(g	PROPN
ejpam-4848	108	17	)	)	PUNCT
ejpam-4848	108	18	.	.	PUNCT
ejpam-4848	109	1	this	this	PRON
ejpam-4848	109	2	implies	imply	VERB
ejpam-4848	109	3	that	that	SCONJ
ejpam-4848	109	4	ds(g)(p	ds(g)(p	NOUN
ejpam-4848	109	5	,	,	PUNCT
ejpam-4848	109	6	v	v	NOUN
ejpam-4848	109	7	′	′	NOUN
ejpam-4848	109	8	)	)	PUNCT
ejpam-4848	109	9	=	=	SYM
ejpam-4848	110	1	2	2	X
ejpam-4848	110	2	.	.	PUNCT
ejpam-4848	111	1	next	next	ADV
ejpam-4848	111	2	,	,	PUNCT
ejpam-4848	111	3	suppose	suppose	VERB
ejpam-4848	111	4	that	that	SCONJ
ejpam-4848	111	5	p	p	PROPN
ejpam-4848	111	6	̸=	̸=	PROPN
ejpam-4848	111	7	v	v	ADP
ejpam-4848	111	8	,	,	PUNCT
ejpam-4848	111	9	that	that	ADV
ejpam-4848	111	10	is	is	ADV
ejpam-4848	111	11	,	,	PUNCT
ejpam-4848	111	12	p′	p′	PROPN
ejpam-4848	111	13	̸=	̸=	PROPN
ejpam-4848	111	14	v′.	v′.	ADV
ejpam-4848	111	15	let	let	VERB
ejpam-4848	111	16	[	[	X
ejpam-4848	111	17	p1	p1	NOUN
ejpam-4848	111	18	,	,	PUNCT
ejpam-4848	111	19	p2	p2	NOUN
ejpam-4848	111	20	,	,	PUNCT
ejpam-4848	111	21	...	...	PUNCT
ejpam-4848	111	22	,	,	PUNCT
ejpam-4848	111	23	pk	pk	NOUN
ejpam-4848	111	24	]	]	X
ejpam-4848	111	25	,	,	PUNCT
ejpam-4848	111	26	where	where	SCONJ
ejpam-4848	111	27	p	p	PROPN
ejpam-4848	111	28	=	=	PROPN
ejpam-4848	111	29	p1	p1	PROPN
ejpam-4848	111	30	and	and	CCONJ
ejpam-4848	111	31	v	v	NOUN
ejpam-4848	111	32	=	=	SYM
ejpam-4848	111	33	pk	pk	NOUN
ejpam-4848	111	34	,	,	PUNCT
ejpam-4848	111	35	be	be	AUX
ejpam-4848	111	36	a	a	DET
ejpam-4848	111	37	p	p	NOUN
ejpam-4848	111	38	-	-	PUNCT
ejpam-4848	111	39	v	v	NOUN
ejpam-4848	111	40	geodesic	geodesic	NOUN
ejpam-4848	111	41	in	in	ADP
ejpam-4848	111	42	g1	g1	PROPN
ejpam-4848	111	43	.	.	PUNCT
ejpam-4848	112	1	then	then	ADV
ejpam-4848	112	2	[	[	X
ejpam-4848	112	3	p′1	p′1	X
ejpam-4848	112	4	,	,	PUNCT
ejpam-4848	112	5	p	p	NOUN
ejpam-4848	112	6	′	′	NOUN
ejpam-4848	112	7	2	2	NUM
ejpam-4848	112	8	,	,	PUNCT
ejpam-4848	112	9	...	...	PUNCT
ejpam-4848	112	10	,	,	PUNCT
ejpam-4848	112	11	p	p	NOUN
ejpam-4848	112	12	′	′	NUM
ejpam-4848	113	1	k	k	X
ejpam-4848	113	2	]	]	X
ejpam-4848	113	3	is	be	AUX
ejpam-4848	113	4	a	a	DET
ejpam-4848	113	5	p′-v′	p′-v′	NOUN
ejpam-4848	113	6	geodesic	geodesic	NOUN
ejpam-4848	113	7	in	in	ADP
ejpam-4848	113	8	g2	g2	PROPN
ejpam-4848	113	9	.	.	PUNCT
ejpam-4848	114	1	also	also	ADV
ejpam-4848	114	2	,	,	PUNCT
ejpam-4848	114	3	by	by	ADP
ejpam-4848	114	4	definition	definition	NOUN
ejpam-4848	114	5	of	of	ADP
ejpam-4848	114	6	s(g	s(g	PROPN
ejpam-4848	114	7	)	)	PUNCT
ejpam-4848	114	8	,	,	PUNCT
ejpam-4848	115	1	[	[	X
ejpam-4848	115	2	p1	p1	NOUN
ejpam-4848	115	3	,	,	PUNCT
ejpam-4848	115	4	p	p	NOUN
ejpam-4848	115	5	′	′	NOUN
ejpam-4848	115	6	2	2	NUM
ejpam-4848	115	7	,	,	PUNCT
ejpam-4848	115	8	p	p	NOUN
ejpam-4848	115	9	′	′	NOUN
ejpam-4848	115	10	3	3	NUM
ejpam-4848	115	11	...	...	PUNCT
ejpam-4848	115	12	,	,	PUNCT
ejpam-4848	115	13	p	p	NOUN
ejpam-4848	115	14	′	′	NUM
ejpam-4848	116	1	k	k	X
ejpam-4848	116	2	]	]	X
ejpam-4848	116	3	is	be	AUX
ejpam-4848	116	4	a	a	DET
ejpam-4848	116	5	p	p	ADJ
ejpam-4848	116	6	-	-	PUNCT
ejpam-4848	116	7	v′	v′	NOUN
ejpam-4848	116	8	geodesic	geodesic	NOUN
ejpam-4848	116	9	in	in	ADP
ejpam-4848	116	10	s(g	s(g	PROPN
ejpam-4848	116	11	)	)	PUNCT
ejpam-4848	116	12	.	.	PUNCT
ejpam-4848	117	1	hence	hence	ADV
ejpam-4848	117	2	,	,	PUNCT
ejpam-4848	117	3	ds(g)(p	ds(g)(p	AUX
ejpam-4848	117	4	,	,	PUNCT
ejpam-4848	117	5	v	v	NOUN
ejpam-4848	117	6	′	′	NOUN
ejpam-4848	117	7	)	)	PUNCT
ejpam-4848	117	8	=	=	SYM
ejpam-4848	117	9	dg1(p	dg1(p	PROPN
ejpam-4848	117	10	,	,	PUNCT
ejpam-4848	117	11	v	v	NOUN
ejpam-4848	117	12	)	)	PUNCT
ejpam-4848	117	13	.	.	PUNCT
ejpam-4848	118	1	since	since	SCONJ
ejpam-4848	118	2	dg1(p	dg1(p	PROPN
ejpam-4848	118	3	,	,	PUNCT
ejpam-4848	118	4	v	v	NOUN
ejpam-4848	118	5	)	)	PUNCT
ejpam-4848	118	6	=	=	SYM
ejpam-4848	118	7	dg2(p	dg2(p	PROPN
ejpam-4848	118	8	′	′	NUM
ejpam-4848	118	9	,	,	PUNCT
ejpam-4848	118	10	v′	v′	PROPN
ejpam-4848	118	11	)	)	PUNCT
ejpam-4848	118	12	,	,	PUNCT
ejpam-4848	118	13	it	it	PRON
ejpam-4848	118	14	follows	follow	VERB
ejpam-4848	118	15	that	that	SCONJ
ejpam-4848	118	16	ds(g)(p	ds(g)(p	NOUN
ejpam-4848	118	17	,	,	PUNCT
ejpam-4848	118	18	v	v	NOUN
ejpam-4848	118	19	′	′	NOUN
ejpam-4848	118	20	)	)	PUNCT
ejpam-4848	118	21	=	=	SYM
ejpam-4848	118	22	ds(g)(p	ds(g)(p	NUM
ejpam-4848	118	23	′	′	NUM
ejpam-4848	118	24	,	,	PUNCT
ejpam-4848	118	25	v	v	NOUN
ejpam-4848	118	26	)	)	PUNCT
ejpam-4848	118	27	.	.	PUNCT
ejpam-4848	119	1	consider	consider	VERB
ejpam-4848	119	2	the	the	DET
ejpam-4848	119	3	shadow	shadow	NOUN
ejpam-4848	119	4	graph	graph	VERB
ejpam-4848	119	5	s(p5	s(p5	PROPN
ejpam-4848	119	6	)	)	PUNCT
ejpam-4848	119	7	in	in	ADP
ejpam-4848	119	8	figure	figure	NOUN
ejpam-4848	119	9	4	4	NUM
ejpam-4848	119	10	.	.	PUNCT
ejpam-4848	119	11	....................................	....................................	PUNCT
ejpam-4848	120	1	....................................	....................................	PUNCT
ejpam-4848	120	2	....................................	....................................	PUNCT
ejpam-4848	121	1	....................................	....................................	PUNCT
ejpam-4848	121	2	....................................	....................................	PUNCT
ejpam-4848	122	1	....................................	....................................	PUNCT
ejpam-4848	122	2	....................................	....................................	PUNCT
ejpam-4848	123	1	....................................	....................................	PUNCT
ejpam-4848	123	2	....................................	....................................	PUNCT
ejpam-4848	124	1	....................................	....................................	PUNCT
ejpam-4848	124	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	125	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	125	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	126	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	126	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	127	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	127	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	128	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	128	2	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4848	129	1	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4848	129	2	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4848	130	1	.............................................................................................................................................................................................................	.............................................................................................................................................................................................................	PUNCT
ejpam-4848	130	2	...........	...........	PUNCT
ejpam-4848	130	3	...........	...........	PUNCT
ejpam-4848	130	4	...........	...........	PUNCT
ejpam-4848	130	5	...........	...........	PUNCT
ejpam-4848	130	6	...........	...........	PUNCT
ejpam-4848	130	7	...........	...........	PUNCT
ejpam-4848	130	8	...........	...........	PUNCT
ejpam-4848	130	9	...........	...........	PUNCT
ejpam-4848	130	10	...........	...........	PUNCT
ejpam-4848	130	11	...........	...........	PUNCT
ejpam-4848	130	12	...........	...........	PUNCT
ejpam-4848	130	13	...........	...........	PUNCT
ejpam-4848	130	14	...........	...........	PUNCT
ejpam-4848	130	15	...........	...........	PUNCT
ejpam-4848	130	16	...........	...........	PUNCT
ejpam-4848	130	17	...........	...........	PUNCT
ejpam-4848	130	18	.....	.....	PUNCT
ejpam-4848	130	19	............	............	PUNCT
ejpam-4848	130	20	...........	...........	PUNCT
ejpam-4848	130	21	...........	...........	PUNCT
ejpam-4848	130	22	...........	...........	PUNCT
ejpam-4848	130	23	...........	...........	PUNCT
ejpam-4848	130	24	...........	...........	PUNCT
ejpam-4848	130	25	...........	...........	PUNCT
ejpam-4848	130	26	...........	...........	PUNCT
ejpam-4848	130	27	...........	...........	PUNCT
ejpam-4848	130	28	...........	...........	PUNCT
ejpam-4848	130	29	...........	...........	PUNCT
ejpam-4848	130	30	...........	...........	PUNCT
ejpam-4848	130	31	...........	...........	PUNCT
ejpam-4848	130	32	...........	...........	PUNCT
ejpam-4848	130	33	...........	...........	PUNCT
ejpam-4848	130	34	...........	...........	PUNCT
ejpam-4848	130	35	...........	...........	PUNCT
ejpam-4848	130	36	.....	.....	PUNCT
ejpam-4848	130	37	............	............	PUNCT
ejpam-4848	130	38	...........	...........	PUNCT
ejpam-4848	130	39	...........	...........	PUNCT
ejpam-4848	130	40	...........	...........	PUNCT
ejpam-4848	130	41	...........	...........	PUNCT
ejpam-4848	130	42	...........	...........	PUNCT
ejpam-4848	130	43	...........	...........	PUNCT
ejpam-4848	130	44	...........	...........	PUNCT
ejpam-4848	130	45	...........	...........	PUNCT
ejpam-4848	130	46	...........	...........	PUNCT
ejpam-4848	130	47	...........	...........	PUNCT
ejpam-4848	130	48	...........	...........	PUNCT
ejpam-4848	130	49	...........	...........	PUNCT
ejpam-4848	130	50	...........	...........	PUNCT
ejpam-4848	130	51	...........	...........	PUNCT
ejpam-4848	130	52	...........	...........	PUNCT
ejpam-4848	130	53	...........	...........	PUNCT
ejpam-4848	130	54	.....	.....	PUNCT
ejpam-4848	130	55	............	............	PUNCT
ejpam-4848	130	56	...........	...........	PUNCT
ejpam-4848	130	57	...........	...........	PUNCT
ejpam-4848	130	58	...........	...........	PUNCT
ejpam-4848	130	59	...........	...........	PUNCT
ejpam-4848	130	60	...........	...........	PUNCT
ejpam-4848	130	61	...........	...........	PUNCT
ejpam-4848	130	62	...........	...........	PUNCT
ejpam-4848	130	63	...........	...........	PUNCT
ejpam-4848	130	64	...........	...........	PUNCT
ejpam-4848	130	65	...........	...........	PUNCT
ejpam-4848	130	66	...........	...........	PUNCT
ejpam-4848	130	67	...........	...........	PUNCT
ejpam-4848	130	68	...........	...........	PUNCT
ejpam-4848	130	69	...........	...........	PUNCT
ejpam-4848	130	70	...........	...........	PUNCT
ejpam-4848	130	71	...........	...........	PUNCT
ejpam-4848	131	1	.....	.....	PUNCT
ejpam-4848	131	2	p′	p′	NOUN
ejpam-4848	132	1	p	p	NOUN
ejpam-4848	132	2	v′	v′	NOUN
ejpam-4848	132	3	v	v	ADP
ejpam-4848	132	4	g2	g2	PROPN
ejpam-4848	132	5	g1	g1	PROPN
ejpam-4848	132	6	figure	figure	VERB
ejpam-4848	132	7	4	4	NUM
ejpam-4848	132	8	:	:	PUNCT
ejpam-4848	132	9	the	the	DET
ejpam-4848	132	10	shadow	shadow	NOUN
ejpam-4848	132	11	graph	graph	VERB
ejpam-4848	132	12	s(p5	s(p5	NOUN
ejpam-4848	132	13	)	)	PUNCT
ejpam-4848	132	14	clearly	clearly	ADV
ejpam-4848	132	15	,	,	PUNCT
ejpam-4848	132	16	ds(g)(p	ds(g)(p	NUM
ejpam-4848	132	17	,	,	PUNCT
ejpam-4848	132	18	p	p	NOUN
ejpam-4848	132	19	′	′	NOUN
ejpam-4848	132	20	)	)	PUNCT
ejpam-4848	132	21	=	=	SYM
ejpam-4848	132	22	2	2	NUM
ejpam-4848	132	23	,	,	PUNCT
ejpam-4848	132	24	and	and	CCONJ
ejpam-4848	132	25	ds(g)(p	ds(g)(p	NOUN
ejpam-4848	132	26	,	,	PUNCT
ejpam-4848	132	27	v	v	NOUN
ejpam-4848	132	28	)	)	PUNCT
ejpam-4848	132	29	=	=	SYM
ejpam-4848	133	1	ds(g)(p	ds(g)(p	X
ejpam-4848	133	2	,	,	PUNCT
ejpam-4848	133	3	v	v	NOUN
ejpam-4848	133	4	′	′	NOUN
ejpam-4848	133	5	)	)	PUNCT
ejpam-4848	133	6	=	=	SYM
ejpam-4848	133	7	ds(g)(p	ds(g)(p	NUM
ejpam-4848	133	8	′	′	NUM
ejpam-4848	133	9	,	,	PUNCT
ejpam-4848	133	10	v′	v′	NOUN
ejpam-4848	133	11	)	)	PUNCT
ejpam-4848	133	12	=	=	SYM
ejpam-4848	134	1	3	3	X
ejpam-4848	134	2	.	.	X
ejpam-4848	134	3	theorem	theorem	NOUN
ejpam-4848	134	4	1	1	NUM
ejpam-4848	134	5	.	.	PUNCT
ejpam-4848	135	1	let	let	VERB
ejpam-4848	135	2	g	g	PRON
ejpam-4848	135	3	be	be	AUX
ejpam-4848	135	4	a	a	DET
ejpam-4848	135	5	non	non	ADJ
ejpam-4848	135	6	-	-	ADJ
ejpam-4848	135	7	trivial	trivial	ADJ
ejpam-4848	135	8	connected	connected	ADJ
ejpam-4848	135	9	graph	graph	NOUN
ejpam-4848	135	10	.	.	PUNCT
ejpam-4848	136	1	for	for	ADP
ejpam-4848	136	2	each	each	DET
ejpam-4848	136	3	p	p	PROPN
ejpam-4848	136	4	∈	∈	PROPN
ejpam-4848	136	5	v	v	NOUN
ejpam-4848	136	6	(	(	PUNCT
ejpam-4848	136	7	g1	g1	PROPN
ejpam-4848	136	8	)	)	PUNCT
ejpam-4848	136	9	,	,	PUNCT
ejpam-4848	136	10	τs(g)(p	τs(g)(p	NUM
ejpam-4848	136	11	)	)	PUNCT
ejpam-4848	136	12	=	=	SYM
ejpam-4848	136	13	2(τg1(p	2(τg1(p	X
ejpam-4848	136	14	)	)	PUNCT
ejpam-4848	136	15	)	)	PUNCT
ejpam-4848	137	1	+	+	CCONJ
ejpam-4848	137	2	2	2	NUM
ejpam-4848	137	3	and	and	CCONJ
ejpam-4848	137	4	τs(g)(p	τs(g)(p	NUM
ejpam-4848	137	5	′	′	NOUN
ejpam-4848	137	6	)	)	PUNCT
ejpam-4848	137	7	=	=	SYM
ejpam-4848	137	8	2(τg2(p	2(τg2(p	NUM
ejpam-4848	137	9	′	′	NUM
ejpam-4848	137	10	)	)	PUNCT
ejpam-4848	137	11	)	)	PUNCT
ejpam-4848	138	1	+	+	CCONJ
ejpam-4848	138	2	2	2	X
ejpam-4848	138	3	.	.	X
ejpam-4848	138	4	f.	f.	PROPN
ejpam-4848	138	5	alfeche	alfeche	PROPN
ejpam-4848	138	6	,	,	PUNCT
ejpam-4848	138	7	v.	v.	PROPN
ejpam-4848	138	8	barraza	barraza	PROPN
ejpam-4848	138	9	,	,	PUNCT
ejpam-4848	138	10	s.	s.	PROPN
ejpam-4848	138	11	canoy	canoy	PROPN
ejpam-4848	138	12	,	,	PUNCT
ejpam-4848	138	13	jr	jr	PROPN
ejpam-4848	138	14	.	.	PROPN
ejpam-4848	138	15	/	/	SYM
ejpam-4848	138	16	eur	eur	PROPN
ejpam-4848	138	17	.	.	PUNCT
ejpam-4848	139	1	j.	j.	PROPN
ejpam-4848	139	2	pure	pure	PROPN
ejpam-4848	139	3	appl	appl	PROPN
ejpam-4848	139	4	.	.	PROPN
ejpam-4848	139	5	math	math	PROPN
ejpam-4848	139	6	,	,	PUNCT
ejpam-4848	139	7	16	16	NUM
ejpam-4848	139	8	(	(	PUNCT
ejpam-4848	139	9	3	3	NUM
ejpam-4848	139	10	)	)	PUNCT
ejpam-4848	139	11	(	(	PUNCT
ejpam-4848	139	12	2023	2023	NUM
ejpam-4848	139	13	)	)	PUNCT
ejpam-4848	139	14	,	,	PUNCT
ejpam-4848	139	15	1406	1406	NUM
ejpam-4848	139	16	-	-	SYM
ejpam-4848	139	17	1420	1420	NUM
ejpam-4848	139	18	1410	1410	NUM
ejpam-4848	139	19	proof	proof	NOUN
ejpam-4848	139	20	.	.	PUNCT
ejpam-4848	140	1	let	let	VERB
ejpam-4848	140	2	p	p	PRON
ejpam-4848	140	3	∈	∈	PROPN
ejpam-4848	140	4	v	v	NOUN
ejpam-4848	140	5	(	(	PUNCT
ejpam-4848	140	6	g1	g1	PROPN
ejpam-4848	140	7	)	)	PUNCT
ejpam-4848	140	8	.	.	PUNCT
ejpam-4848	141	1	then	then	ADV
ejpam-4848	141	2	τs(g)(p	τs(g)(p	NUM
ejpam-4848	141	3	)	)	PUNCT
ejpam-4848	141	4	=	=	PUNCT
ejpam-4848	142	1	∑	∑	PUNCT
ejpam-4848	142	2	q∈v	q∈v	ADV
ejpam-4848	142	3	(	(	PUNCT
ejpam-4848	142	4	s(g	s(g	PROPN
ejpam-4848	142	5	)	)	PUNCT
ejpam-4848	142	6	)	)	PUNCT
ejpam-4848	143	1	ds(g)(p	ds(g)(p	NUM
ejpam-4848	143	2	,	,	PUNCT
ejpam-4848	143	3	q	q	X
ejpam-4848	143	4	)	)	PUNCT
ejpam-4848	143	5	=	=	SYM
ejpam-4848	143	6	∑	∑	PUNCT
ejpam-4848	143	7	q∈v	q∈v	ADV
ejpam-4848	143	8	(	(	PUNCT
ejpam-4848	143	9	g1	g1	PROPN
ejpam-4848	143	10	)	)	PUNCT
ejpam-4848	143	11	ds(g)(p	ds(g)(p	NUM
ejpam-4848	143	12	,	,	PUNCT
ejpam-4848	143	13	q	q	NOUN
ejpam-4848	143	14	)	)	PUNCT
ejpam-4848	143	15	+	+	CCONJ
ejpam-4848	143	16	∑	∑	PROPN
ejpam-4848	143	17	v′∈v	v′∈v	PROPN
ejpam-4848	143	18	(	(	PUNCT
ejpam-4848	143	19	g2	g2	PROPN
ejpam-4848	143	20	)	)	PUNCT
ejpam-4848	143	21	ds(g)(p	ds(g)(p	NUM
ejpam-4848	143	22	,	,	PUNCT
ejpam-4848	143	23	v	v	NOUN
ejpam-4848	143	24	′	′	NOUN
ejpam-4848	143	25	)	)	PUNCT
ejpam-4848	143	26	=	=	PUNCT
ejpam-4848	144	1	∑	∑	PUNCT
ejpam-4848	144	2	q∈v	q∈v	ADV
ejpam-4848	144	3	(	(	PUNCT
ejpam-4848	144	4	g1	g1	PROPN
ejpam-4848	144	5	)	)	PUNCT
ejpam-4848	144	6	dg1(p	dg1(p	PROPN
ejpam-4848	144	7	,	,	PUNCT
ejpam-4848	144	8	q	q	NOUN
ejpam-4848	144	9	)	)	PUNCT
ejpam-4848	145	1	+	+	CCONJ
ejpam-4848	145	2	∑	∑	PROPN
ejpam-4848	145	3	v′∈v	v′∈v	PROPN
ejpam-4848	145	4	(	(	PUNCT
ejpam-4848	145	5	g2)−{p′	g2)−{p′	PROPN
ejpam-4848	145	6	}	}	PUNCT
ejpam-4848	145	7	ds(g)(p	ds(g)(p	NUM
ejpam-4848	145	8	,	,	PUNCT
ejpam-4848	145	9	v	v	NOUN
ejpam-4848	145	10	′	′	NOUN
ejpam-4848	145	11	)	)	PUNCT
ejpam-4848	145	12	+	+	CCONJ
ejpam-4848	145	13	ds(g)(p	ds(g)(p	X
ejpam-4848	145	14	,	,	PUNCT
ejpam-4848	145	15	p	p	NOUN
ejpam-4848	145	16	′	′	NOUN
ejpam-4848	145	17	)	)	PUNCT
ejpam-4848	145	18	=	=	SYM
ejpam-4848	145	19	τg1(p	τg1(p	VERB
ejpam-4848	145	20	)	)	PUNCT
ejpam-4848	145	21	+	+	CCONJ
ejpam-4848	145	22	∑	∑	PUNCT
ejpam-4848	145	23	v∈v	v∈v	PROPN
ejpam-4848	145	24	(	(	PUNCT
ejpam-4848	145	25	g1)−{p	g1)−{p	NOUN
ejpam-4848	145	26	}	}	PUNCT
ejpam-4848	145	27	dg1(p	dg1(p	PROPN
ejpam-4848	145	28	,	,	PUNCT
ejpam-4848	145	29	v	v	NOUN
ejpam-4848	145	30	)	)	PUNCT
ejpam-4848	145	31	+	+	CCONJ
ejpam-4848	145	32	2	2	NUM
ejpam-4848	145	33	=	=	SYM
ejpam-4848	145	34	2τg1(p	2τg1(p	NUM
ejpam-4848	145	35	)	)	PUNCT
ejpam-4848	145	36	+	+	CCONJ
ejpam-4848	145	37	2	2	X
ejpam-4848	145	38	.	.	X
ejpam-4848	145	39	similarly	similarly	ADV
ejpam-4848	145	40	,	,	PUNCT
ejpam-4848	145	41	τs(g)(p	τs(g)(p	NUM
ejpam-4848	145	42	′	′	NOUN
ejpam-4848	145	43	)	)	PUNCT
ejpam-4848	145	44	=	=	SYM
ejpam-4848	146	1	2τg2(p	2τg2(p	NUM
ejpam-4848	146	2	′	′	NOUN
ejpam-4848	146	3	)	)	PUNCT
ejpam-4848	147	1	+	+	CCONJ
ejpam-4848	147	2	2	2	X
ejpam-4848	147	3	.	.	X
ejpam-4848	147	4	the	the	DET
ejpam-4848	147	5	next	next	ADJ
ejpam-4848	147	6	result	result	NOUN
ejpam-4848	147	7	follows	follow	VERB
ejpam-4848	147	8	from	from	ADP
ejpam-4848	147	9	theorem	theorem	ADJ
ejpam-4848	147	10	1	1	NUM
ejpam-4848	147	11	and	and	CCONJ
ejpam-4848	147	12	definition	definition	NOUN
ejpam-4848	147	13	3	3	NUM
ejpam-4848	147	14	.	.	PUNCT
ejpam-4848	147	15	corollary	corollary	ADJ
ejpam-4848	147	16	1	1	NUM
ejpam-4848	147	17	.	.	PUNCT
ejpam-4848	148	1	let	let	VERB
ejpam-4848	148	2	g	g	PRON
ejpam-4848	148	3	be	be	AUX
ejpam-4848	148	4	a	a	DET
ejpam-4848	148	5	non	non	ADJ
ejpam-4848	148	6	-	-	ADJ
ejpam-4848	148	7	trivial	trivial	ADJ
ejpam-4848	148	8	connected	connected	ADJ
ejpam-4848	148	9	graph	graph	NOUN
ejpam-4848	148	10	of	of	ADP
ejpam-4848	148	11	order	order	NOUN
ejpam-4848	148	12	m	m	VERB
ejpam-4848	148	13	and	and	CCONJ
ejpam-4848	148	14	let	let	VERB
ejpam-4848	148	15	p	p	PRON
ejpam-4848	148	16	∈	∈	PROPN
ejpam-4848	148	17	v	v	NOUN
ejpam-4848	148	18	(	(	PUNCT
ejpam-4848	148	19	g1	g1	PROPN
ejpam-4848	148	20	)	)	PUNCT
ejpam-4848	148	21	.	.	PUNCT
ejpam-4848	149	1	then	then	ADV
ejpam-4848	149	2	cs(g)(p	cs(g)(p	NOUN
ejpam-4848	149	3	)	)	PUNCT
ejpam-4848	150	1	=	=	PUNCT
ejpam-4848	151	1	2m−	2m−	NUM
ejpam-4848	151	2	1	1	NUM
ejpam-4848	151	3	2(τg1(p	2(τg1(p	NUM
ejpam-4848	151	4	)	)	PUNCT
ejpam-4848	151	5	)	)	PUNCT
ejpam-4848	152	1	+	+	CCONJ
ejpam-4848	152	2	2	2	NUM
ejpam-4848	152	3	and	and	CCONJ
ejpam-4848	152	4	cs(g)(p	cs(g)(p	ADJ
ejpam-4848	152	5	′	′	NOUN
ejpam-4848	152	6	)	)	PUNCT
ejpam-4848	153	1	=	=	PUNCT
ejpam-4848	154	1	2m−	2m−	NUM
ejpam-4848	154	2	1	1	NUM
ejpam-4848	154	3	2(τg2(p	2(τg2(p	NUM
ejpam-4848	154	4	′	′	NUM
ejpam-4848	154	5	)	)	PUNCT
ejpam-4848	154	6	)	)	PUNCT
ejpam-4848	155	1	+	+	CCONJ
ejpam-4848	155	2	2	2	X
ejpam-4848	155	3	.	.	PUNCT
ejpam-4848	155	4	example	example	NOUN
ejpam-4848	156	1	1	1	NUM
ejpam-4848	156	2	.	.	X
ejpam-4848	156	3	consider	consider	VERB
ejpam-4848	156	4	the	the	DET
ejpam-4848	156	5	shadow	shadow	NOUN
ejpam-4848	156	6	graph	graph	VERB
ejpam-4848	156	7	s(p5	s(p5	PROPN
ejpam-4848	156	8	)	)	PUNCT
ejpam-4848	156	9	in	in	ADP
ejpam-4848	156	10	figure	figure	NOUN
ejpam-4848	156	11	5	5	NUM
ejpam-4848	156	12	,	,	PUNCT
ejpam-4848	156	13	where	where	SCONJ
ejpam-4848	156	14	g	g	NOUN
ejpam-4848	156	15	=	=	SYM
ejpam-4848	156	16	p5	p5	PROPN
ejpam-4848	156	17	.	.	PUNCT
ejpam-4848	156	18	....................................	....................................	PUNCT
ejpam-4848	157	1	....................................	....................................	PUNCT
ejpam-4848	157	2	....................................	....................................	PUNCT
ejpam-4848	158	1	....................................	....................................	PUNCT
ejpam-4848	158	2	....................................	....................................	PUNCT
ejpam-4848	159	1	....................................	....................................	PUNCT
ejpam-4848	159	2	....................................	....................................	PUNCT
ejpam-4848	160	1	....................................	....................................	PUNCT
ejpam-4848	160	2	....................................	....................................	PUNCT
ejpam-4848	161	1	....................................	....................................	PUNCT
ejpam-4848	161	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	162	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	162	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	163	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	163	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	164	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	164	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	165	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4848	165	2	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4848	166	1	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4848	166	2	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4848	167	1	.............................................................................................................................................................................................................	.............................................................................................................................................................................................................	PUNCT
ejpam-4848	167	2	...........	...........	PUNCT
ejpam-4848	167	3	...........	...........	PUNCT
ejpam-4848	167	4	...........	...........	PUNCT
ejpam-4848	167	5	...........	...........	PUNCT
ejpam-4848	167	6	...........	...........	PUNCT
ejpam-4848	167	7	...........	...........	PUNCT
ejpam-4848	167	8	...........	...........	PUNCT
ejpam-4848	167	9	...........	...........	PUNCT
ejpam-4848	167	10	...........	...........	PUNCT
ejpam-4848	167	11	...........	...........	PUNCT
ejpam-4848	167	12	...........	...........	PUNCT
ejpam-4848	167	13	...........	...........	PUNCT
ejpam-4848	167	14	...........	...........	PUNCT
ejpam-4848	167	15	...........	...........	PUNCT
ejpam-4848	167	16	...........	...........	PUNCT
ejpam-4848	167	17	...........	...........	PUNCT
ejpam-4848	167	18	.....	.....	PUNCT
ejpam-4848	167	19	............	............	PUNCT
ejpam-4848	167	20	...........	...........	PUNCT
ejpam-4848	167	21	...........	...........	PUNCT
ejpam-4848	167	22	...........	...........	PUNCT
ejpam-4848	167	23	...........	...........	PUNCT
ejpam-4848	167	24	...........	...........	PUNCT
ejpam-4848	167	25	...........	...........	PUNCT
ejpam-4848	167	26	...........	...........	PUNCT
ejpam-4848	167	27	...........	...........	PUNCT
ejpam-4848	167	28	...........	...........	PUNCT
ejpam-4848	167	29	...........	...........	PUNCT
ejpam-4848	167	30	...........	...........	PUNCT
ejpam-4848	167	31	...........	...........	PUNCT
ejpam-4848	167	32	...........	...........	PUNCT
ejpam-4848	167	33	...........	...........	PUNCT
ejpam-4848	167	34	...........	...........	PUNCT
ejpam-4848	167	35	...........	...........	PUNCT
ejpam-4848	167	36	.....	.....	PUNCT
ejpam-4848	167	37	............	............	PUNCT
ejpam-4848	167	38	...........	...........	PUNCT
ejpam-4848	167	39	...........	...........	PUNCT
ejpam-4848	167	40	...........	...........	PUNCT
ejpam-4848	167	41	...........	...........	PUNCT
ejpam-4848	167	42	...........	...........	PUNCT
ejpam-4848	167	43	...........	...........	PUNCT
ejpam-4848	167	44	...........	...........	PUNCT
ejpam-4848	167	45	...........	...........	PUNCT
ejpam-4848	167	46	...........	...........	PUNCT
ejpam-4848	167	47	...........	...........	PUNCT
ejpam-4848	167	48	...........	...........	PUNCT
ejpam-4848	167	49	...........	...........	PUNCT
ejpam-4848	167	50	...........	...........	PUNCT
ejpam-4848	167	51	...........	...........	PUNCT
ejpam-4848	167	52	...........	...........	PUNCT
ejpam-4848	167	53	...........	...........	PUNCT
ejpam-4848	167	54	.....	.....	PUNCT
ejpam-4848	167	55	............	............	PUNCT
ejpam-4848	167	56	...........	...........	PUNCT
ejpam-4848	167	57	...........	...........	PUNCT
ejpam-4848	167	58	...........	...........	PUNCT
ejpam-4848	167	59	...........	...........	PUNCT
ejpam-4848	167	60	...........	...........	PUNCT
ejpam-4848	167	61	...........	...........	PUNCT
ejpam-4848	167	62	...........	...........	PUNCT
ejpam-4848	167	63	...........	...........	PUNCT
ejpam-4848	167	64	...........	...........	PUNCT
ejpam-4848	167	65	...........	...........	PUNCT
ejpam-4848	167	66	...........	...........	PUNCT
ejpam-4848	167	67	...........	...........	PUNCT
ejpam-4848	167	68	...........	...........	PUNCT
ejpam-4848	167	69	...........	...........	PUNCT
ejpam-4848	167	70	...........	...........	PUNCT
ejpam-4848	167	71	...........	...........	PUNCT
ejpam-4848	168	1	.....	.....	PUNCT
ejpam-4848	168	2	•	•	NUM
ejpam-4848	168	3	p′	p′	PROPN
ejpam-4848	168	4	g2	g2	PROPN
ejpam-4848	168	5	g1	g1	PROPN
ejpam-4848	168	6	figure	figure	VERB
ejpam-4848	168	7	5	5	NUM
ejpam-4848	168	8	:	:	PUNCT
ejpam-4848	168	9	the	the	DET
ejpam-4848	168	10	shadow	shadow	NOUN
ejpam-4848	168	11	graph	graph	VERB
ejpam-4848	168	12	s(p5	s(p5	PROPN
ejpam-4848	168	13	)	)	PUNCT
ejpam-4848	168	14	and	and	CCONJ
ejpam-4848	168	15	p′	p′	NOUN
ejpam-4848	168	16	∈	∈	NOUN
ejpam-4848	168	17	v	v	X
ejpam-4848	168	18	(	(	PUNCT
ejpam-4848	168	19	g2	g2	PROPN
ejpam-4848	168	20	)	)	PUNCT
ejpam-4848	168	21	then	then	ADV
ejpam-4848	168	22	m	m	VERB
ejpam-4848	168	23	=	=	SYM
ejpam-4848	168	24	5	5	NUM
ejpam-4848	168	25	and	and	CCONJ
ejpam-4848	168	26	τg2(p	τg2(p	NUM
ejpam-4848	168	27	′	′	NUM
ejpam-4848	168	28	)	)	PUNCT
ejpam-4848	169	1	=	=	SYM
ejpam-4848	169	2	7	7	X
ejpam-4848	169	3	.	.	X
ejpam-4848	169	4	using	use	VERB
ejpam-4848	169	5	corollary	corollary	ADJ
ejpam-4848	169	6	1	1	NUM
ejpam-4848	169	7	,	,	PUNCT
ejpam-4848	169	8	the	the	DET
ejpam-4848	169	9	closeness	closeness	NOUN
ejpam-4848	169	10	centrality	centrality	NOUN
ejpam-4848	169	11	of	of	ADP
ejpam-4848	169	12	p′	p′	NOUN
ejpam-4848	169	13	is	be	AUX
ejpam-4848	169	14	cs(g)(p	cs(g)(p	NOUN
ejpam-4848	169	15	′	′	NUM
ejpam-4848	169	16	)	)	PUNCT
ejpam-4848	170	1	=	=	PUNCT
ejpam-4848	171	1	2m−	2m−	NUM
ejpam-4848	171	2	1	1	NUM
ejpam-4848	171	3	2τg2(p	2τg2(p	NUM
ejpam-4848	171	4	′	′	NUM
ejpam-4848	171	5	)	)	PUNCT
ejpam-4848	172	1	+	+	CCONJ
ejpam-4848	172	2	2	2	NUM
ejpam-4848	172	3	=	=	SYM
ejpam-4848	172	4	2(5)−	2(5)−	NUM
ejpam-4848	172	5	1	1	NUM
ejpam-4848	172	6	2(7	2(7	NUM
ejpam-4848	172	7	)	)	PUNCT
ejpam-4848	172	8	+	+	CCONJ
ejpam-4848	172	9	2	2	NUM
ejpam-4848	172	10	=	=	SYM
ejpam-4848	172	11	10−	10−	NUM
ejpam-4848	172	12	1	1	NUM
ejpam-4848	172	13	14	14	NUM
ejpam-4848	172	14	+	+	SYM
ejpam-4848	172	15	2	2	NUM
ejpam-4848	172	16	f.	f.	PROPN
ejpam-4848	172	17	alfeche	alfeche	PROPN
ejpam-4848	172	18	,	,	PUNCT
ejpam-4848	172	19	v.	v.	PROPN
ejpam-4848	172	20	barraza	barraza	PROPN
ejpam-4848	172	21	,	,	PUNCT
ejpam-4848	172	22	s.	s.	PROPN
ejpam-4848	172	23	canoy	canoy	PROPN
ejpam-4848	172	24	,	,	PUNCT
ejpam-4848	172	25	jr	jr	PROPN
ejpam-4848	172	26	.	.	PROPN
ejpam-4848	172	27	/	/	SYM
ejpam-4848	172	28	eur	eur	PROPN
ejpam-4848	172	29	.	.	PUNCT
ejpam-4848	173	1	j.	j.	PROPN
ejpam-4848	173	2	pure	pure	PROPN
ejpam-4848	173	3	appl	appl	PROPN
ejpam-4848	173	4	.	.	PROPN
ejpam-4848	173	5	math	math	PROPN
ejpam-4848	173	6	,	,	PUNCT
ejpam-4848	173	7	16	16	NUM
ejpam-4848	173	8	(	(	PUNCT
ejpam-4848	173	9	3	3	NUM
ejpam-4848	173	10	)	)	PUNCT
ejpam-4848	173	11	(	(	PUNCT
ejpam-4848	173	12	2023	2023	NUM
ejpam-4848	173	13	)	)	PUNCT
ejpam-4848	173	14	,	,	PUNCT
ejpam-4848	173	15	1406	1406	NUM
ejpam-4848	173	16	-	-	SYM
ejpam-4848	173	17	1420	1420	NUM
ejpam-4848	173	18	1411	1411	NUM
ejpam-4848	173	19	=	=	SYM
ejpam-4848	173	20	9	9	NUM
ejpam-4848	173	21	16	16	NUM
ejpam-4848	173	22	.	.	PUNCT
ejpam-4848	174	1	for	for	ADP
ejpam-4848	174	2	a	a	DET
ejpam-4848	174	3	non	non	ADJ
ejpam-4848	174	4	-	-	ADJ
ejpam-4848	174	5	trivial	trivial	ADJ
ejpam-4848	174	6	connected	connected	ADJ
ejpam-4848	174	7	graph	graph	NOUN
ejpam-4848	174	8	g	g	NOUN
ejpam-4848	174	9	and	and	CCONJ
ejpam-4848	174	10	v	v	ADP
ejpam-4848	174	11	∈	∈	PROPN
ejpam-4848	174	12	v	v	NOUN
ejpam-4848	174	13	(	(	PUNCT
ejpam-4848	174	14	g	g	NOUN
ejpam-4848	174	15	)	)	PUNCT
ejpam-4848	174	16	,	,	PUNCT
ejpam-4848	174	17	the	the	DET
ejpam-4848	174	18	set	set	NOUN
ejpam-4848	174	19	ev	ev	X
ejpam-4848	174	20	is	be	AUX
ejpam-4848	174	21	given	give	VERB
ejpam-4848	174	22	by	by	ADP
ejpam-4848	174	23	ev	ev	X
ejpam-4848	174	24	=	=	SYM
ejpam-4848	174	25	{	{	PUNCT
ejpam-4848	174	26	xv	xv	PROPN
ejpam-4848	174	27	∈	∈	PROPN
ejpam-4848	174	28	e(g	e(g	PROPN
ejpam-4848	174	29	)	)	PUNCT
ejpam-4848	174	30	:	:	PUNCT
ejpam-4848	175	1	x	x	X
ejpam-4848	175	2	∈	∈	NOUN
ejpam-4848	175	3	v	v	ADP
ejpam-4848	175	4	(	(	PUNCT
ejpam-4848	175	5	g	g	NOUN
ejpam-4848	175	6	)	)	PUNCT
ejpam-4848	175	7	\	\	NOUN
ejpam-4848	175	8	{	{	PUNCT
ejpam-4848	175	9	v	v	NOUN
ejpam-4848	175	10	}	}	PUNCT
ejpam-4848	175	11	}	}	PUNCT
ejpam-4848	175	12	.	.	PUNCT
ejpam-4848	176	1	theorem	theorem	NOUN
ejpam-4848	176	2	2	2	NUM
ejpam-4848	176	3	.	.	PUNCT
ejpam-4848	177	1	let	let	VERB
ejpam-4848	177	2	g	g	NOUN
ejpam-4848	177	3	and	and	CCONJ
ejpam-4848	177	4	h	h	PROPN
ejpam-4848	177	5	be	be	VERB
ejpam-4848	177	6	non	non	ADJ
ejpam-4848	177	7	-	-	ADJ
ejpam-4848	177	8	trivial	trivial	ADJ
ejpam-4848	177	9	connected	connected	ADJ
ejpam-4848	177	10	graphs	graph	NOUN
ejpam-4848	177	11	.	.	PUNCT
ejpam-4848	178	1	if	if	SCONJ
ejpam-4848	178	2	v	v	NUM
ejpam-4848	178	3	∈	∈	PROPN
ejpam-4848	178	4	v	v	NOUN
ejpam-4848	178	5	(	(	PUNCT
ejpam-4848	178	6	g	g	NOUN
ejpam-4848	178	7	)	)	PUNCT
ejpam-4848	178	8	,	,	PUNCT
ejpam-4848	178	9	then	then	ADV
ejpam-4848	178	10	τg⋄h(v	τg⋄h(v	NOUN
ejpam-4848	178	11	)	)	PUNCT
ejpam-4848	178	12	=	=	PUNCT
ejpam-4848	178	13	τg(v	τg(v	X
ejpam-4848	178	14	)	)	PUNCT
ejpam-4848	179	1	+	+	CCONJ
ejpam-4848	179	2	|v	|v	X
ejpam-4848	179	3	(	(	PUNCT
ejpam-4848	179	4	h)||e(g)|+	h)||e(g)|+	PROPN
ejpam-4848	179	5	|v	|v	PROPN
ejpam-4848	179	6	(	(	PUNCT
ejpam-4848	179	7	h)|	h)|	VERB
ejpam-4848	179	8	∑	∑	PROPN
ejpam-4848	179	9	e∈e(g)\ev	e∈e(g)\ev	NOUN
ejpam-4848	179	10	dg(v	dg(v	NOUN
ejpam-4848	179	11	,	,	PUNCT
ejpam-4848	179	12	e	e	NOUN
ejpam-4848	179	13	)	)	PUNCT
ejpam-4848	179	14	.	.	PUNCT
ejpam-4848	180	1	proof	proof	NOUN
ejpam-4848	180	2	.	.	PUNCT
ejpam-4848	181	1	let	let	VERB
ejpam-4848	181	2	v	v	NUM
ejpam-4848	181	3	∈	∈	PROPN
ejpam-4848	181	4	v	v	NOUN
ejpam-4848	181	5	(	(	PUNCT
ejpam-4848	181	6	g	g	NOUN
ejpam-4848	181	7	)	)	PUNCT
ejpam-4848	181	8	.	.	PUNCT
ejpam-4848	182	1	then	then	ADV
ejpam-4848	182	2	|ev|	|ev|	NUM
ejpam-4848	182	3	=	=	PUNCT
ejpam-4848	182	4	|ng(v)|	|ng(v)|	NOUN
ejpam-4848	182	5	and	and	CCONJ
ejpam-4848	182	6	dg⋄h(v	dg⋄h(v	PROPN
ejpam-4848	182	7	,	,	PUNCT
ejpam-4848	182	8	a	a	PRON
ejpam-4848	182	9	)	)	PUNCT
ejpam-4848	182	10	=	=	SYM
ejpam-4848	182	11	dg(v	dg(v	X
ejpam-4848	182	12	,	,	PUNCT
ejpam-4848	182	13	e	e	NOUN
ejpam-4848	182	14	)	)	PUNCT
ejpam-4848	182	15	+	+	CCONJ
ejpam-4848	182	16	1	1	NUM
ejpam-4848	182	17	for	for	ADP
ejpam-4848	182	18	every	every	DET
ejpam-4848	182	19	a	a	DET
ejpam-4848	182	20	∈	∈	PROPN
ejpam-4848	182	21	v	v	NOUN
ejpam-4848	182	22	(	(	PUNCT
ejpam-4848	182	23	he	he	PRON
ejpam-4848	182	24	)	)	PUNCT
ejpam-4848	182	25	where	where	SCONJ
ejpam-4848	182	26	e	e	PROPN
ejpam-4848	182	27	∈	∈	PROPN
ejpam-4848	182	28	e(g	e(g	PROPN
ejpam-4848	182	29	)	)	PUNCT
ejpam-4848	182	30	\	\	PROPN
ejpam-4848	183	1	ev	ev	PROPN
ejpam-4848	183	2	.	.	PROPN
ejpam-4848	183	3	hence	hence	ADV
ejpam-4848	183	4	,	,	PUNCT
ejpam-4848	183	5	τg⋄h(v	τg⋄h(v	NOUN
ejpam-4848	183	6	)	)	PUNCT
ejpam-4848	183	7	=	=	PUNCT
ejpam-4848	183	8	∑	∑	PUNCT
ejpam-4848	183	9	x∈v	x∈v	PROPN
ejpam-4848	183	10	(	(	PUNCT
ejpam-4848	183	11	g	g	NOUN
ejpam-4848	183	12	)	)	PUNCT
ejpam-4848	183	13	(	(	PUNCT
ejpam-4848	183	14	dg(v	dg(v	X
ejpam-4848	183	15	,	,	PUNCT
ejpam-4848	183	16	x	x	NOUN
ejpam-4848	183	17	)	)	PUNCT
ejpam-4848	183	18	)	)	PUNCT
ejpam-4848	184	1	+	+	CCONJ
ejpam-4848	184	2	∑	∑	PROPN
ejpam-4848	184	3	e∈ev	e∈ev	PROPN
ejpam-4848	184	4	∑	∑	PART
ejpam-4848	184	5	a∈v	a∈v	PROPN
ejpam-4848	184	6	(	(	PUNCT
ejpam-4848	184	7	he	he	PRON
ejpam-4848	184	8	)	)	PUNCT
ejpam-4848	185	1	dg⋄h(v	dg⋄h(v	PROPN
ejpam-4848	185	2	,	,	PUNCT
ejpam-4848	185	3	a	a	PRON
ejpam-4848	185	4	)	)	PUNCT
ejpam-4848	185	5	+	+	CCONJ
ejpam-4848	185	6	∑	∑	PART
ejpam-4848	185	7	e∈e(g)\ev	e∈e(g)\ev	X
ejpam-4848	185	8	∑	∑	PUNCT
ejpam-4848	185	9	a∈v	a∈v	PROPN
ejpam-4848	185	10	(	(	PUNCT
ejpam-4848	185	11	he	he	PRON
ejpam-4848	185	12	)	)	PUNCT
ejpam-4848	186	1	dg⋄h(v	dg⋄h(v	PROPN
ejpam-4848	186	2	,	,	PUNCT
ejpam-4848	186	3	a	a	PRON
ejpam-4848	186	4	)	)	PUNCT
ejpam-4848	186	5	=	=	NOUN
ejpam-4848	186	6	τg(v	τg(v	X
ejpam-4848	186	7	)	)	PUNCT
ejpam-4848	187	1	+	+	CCONJ
ejpam-4848	187	2	|ev||v	|ev||v	PROPN
ejpam-4848	187	3	(	(	PUNCT
ejpam-4848	187	4	h)|+	h)|+	ADJ
ejpam-4848	187	5	∑	∑	PART
ejpam-4848	187	6	e∈e(g)\ev	e∈e(g)\ev	X
ejpam-4848	187	7	[	[	X
ejpam-4848	187	8	(	(	PUNCT
ejpam-4848	187	9	dg(v	dg(v	X
ejpam-4848	187	10	,	,	PUNCT
ejpam-4848	187	11	e	e	NOUN
ejpam-4848	187	12	)	)	PUNCT
ejpam-4848	187	13	+	+	CCONJ
ejpam-4848	187	14	1)|v	1)|v	NUM
ejpam-4848	187	15	(	(	PUNCT
ejpam-4848	187	16	h)|	h)|	PROPN
ejpam-4848	187	17	]	]	X
ejpam-4848	187	18	=	=	PUNCT
ejpam-4848	187	19	τg(v	τg(v	X
ejpam-4848	187	20	)	)	PUNCT
ejpam-4848	188	1	+	+	CCONJ
ejpam-4848	188	2	|ev||v	|ev||v	PROPN
ejpam-4848	188	3	(	(	PUNCT
ejpam-4848	188	4	h)|+	h)|+	ADJ
ejpam-4848	188	5	|v	|v	NOUN
ejpam-4848	188	6	(	(	PUNCT
ejpam-4848	188	7	h)|	h)|	NOUN
ejpam-4848	188	8	∑	∑	PROPN
ejpam-4848	188	9	e∈e(g)\ev	e∈e(g)\ev	NOUN
ejpam-4848	188	10	dg(v	dg(v	NOUN
ejpam-4848	188	11	,	,	PUNCT
ejpam-4848	188	12	e	e	NOUN
ejpam-4848	188	13	)	)	PUNCT
ejpam-4848	189	1	+	+	CCONJ
ejpam-4848	189	2	|v	|v	X
ejpam-4848	189	3	(	(	PUNCT
ejpam-4848	189	4	h)||e(g)|	h)||e(g)|	NOUN
ejpam-4848	189	5	−	−	PROPN
ejpam-4848	189	6	|ev||v	|ev||v	PROPN
ejpam-4848	189	7	(	(	PUNCT
ejpam-4848	189	8	h)|	h)|	NOUN
ejpam-4848	189	9	=	=	PUNCT
ejpam-4848	189	10	τg(v	τg(v	X
ejpam-4848	189	11	)	)	PUNCT
ejpam-4848	190	1	+	+	CCONJ
ejpam-4848	190	2	|v	|v	X
ejpam-4848	190	3	(	(	PUNCT
ejpam-4848	190	4	h)||e(g)|+	h)||e(g)|+	PROPN
ejpam-4848	190	5	|v	|v	PROPN
ejpam-4848	190	6	(	(	PUNCT
ejpam-4848	190	7	h)|	h)|	VERB
ejpam-4848	190	8	∑	∑	PROPN
ejpam-4848	190	9	e∈e(g)\ev	e∈e(g)\ev	NOUN
ejpam-4848	190	10	dg(v	dg(v	NOUN
ejpam-4848	190	11	,	,	PUNCT
ejpam-4848	190	12	e	e	NOUN
ejpam-4848	190	13	)	)	PUNCT
ejpam-4848	190	14	.	.	PUNCT
ejpam-4848	191	1	the	the	DET
ejpam-4848	191	2	next	next	ADJ
ejpam-4848	191	3	result	result	NOUN
ejpam-4848	191	4	is	be	AUX
ejpam-4848	191	5	immediate	immediate	ADJ
ejpam-4848	191	6	from	from	ADP
ejpam-4848	191	7	theorem	theorem	ADJ
ejpam-4848	191	8	2	2	NUM
ejpam-4848	191	9	.	.	PUNCT
ejpam-4848	191	10	corollary	corollary	ADJ
ejpam-4848	191	11	2	2	NUM
ejpam-4848	191	12	.	.	PUNCT
ejpam-4848	192	1	let	let	VERB
ejpam-4848	192	2	g	g	NOUN
ejpam-4848	192	3	and	and	CCONJ
ejpam-4848	192	4	h	h	NOUN
ejpam-4848	192	5	be	be	AUX
ejpam-4848	192	6	connected	connect	VERB
ejpam-4848	192	7	non	non	ADJ
ejpam-4848	192	8	-	-	ADJ
ejpam-4848	192	9	trivial	trivial	ADJ
ejpam-4848	192	10	graphs	graph	NOUN
ejpam-4848	192	11	with	with	ADP
ejpam-4848	192	12	m	m	NOUN
ejpam-4848	192	13	=	=	SYM
ejpam-4848	192	14	|v	|v	X
ejpam-4848	192	15	(	(	PUNCT
ejpam-4848	192	16	g)|	g)|	NOUN
ejpam-4848	192	17	,	,	PUNCT
ejpam-4848	192	18	r	r	NOUN
ejpam-4848	192	19	=	=	SYM
ejpam-4848	192	20	|e(g)|	|e(g)|	NOUN
ejpam-4848	192	21	,	,	PUNCT
ejpam-4848	192	22	and	and	CCONJ
ejpam-4848	192	23	n	n	PROPN
ejpam-4848	192	24	=	=	SYM
ejpam-4848	192	25	|v	|v	PROPN
ejpam-4848	192	26	(	(	PUNCT
ejpam-4848	192	27	h)|	h)|	PROPN
ejpam-4848	192	28	.	.	PUNCT
ejpam-4848	193	1	if	if	SCONJ
ejpam-4848	193	2	v	v	NUM
ejpam-4848	193	3	∈	∈	PROPN
ejpam-4848	193	4	v	v	NOUN
ejpam-4848	193	5	(	(	PUNCT
ejpam-4848	193	6	g	g	NOUN
ejpam-4848	193	7	)	)	PUNCT
ejpam-4848	193	8	,	,	PUNCT
ejpam-4848	193	9	then	then	ADV
ejpam-4848	193	10	cg⋄h(v	cg⋄h(v	PROPN
ejpam-4848	193	11	)	)	PUNCT
ejpam-4848	193	12	=	=	SYM
ejpam-4848	193	13	m+	m+	NUM
ejpam-4848	193	14	rn−	rn−	NOUN
ejpam-4848	193	15	1	1	NUM
ejpam-4848	193	16	τg(v	τg(v	PUNCT
ejpam-4848	193	17	)	)	PUNCT
ejpam-4848	194	1	+	+	CCONJ
ejpam-4848	194	2	rn+	rn+	NOUN
ejpam-4848	194	3	n	n	PRON
ejpam-4848	194	4	∑	∑	ADV
ejpam-4848	194	5	e∈e(g)\ev	e∈e(g)\ev	NOUN
ejpam-4848	194	6	dg(v	dg(v	NOUN
ejpam-4848	194	7	,	,	PUNCT
ejpam-4848	194	8	e	e	NOUN
ejpam-4848	194	9	)	)	PUNCT
ejpam-4848	194	10	.	.	PUNCT
ejpam-4848	195	1	example	example	NOUN
ejpam-4848	196	1	2	2	NUM
ejpam-4848	196	2	.	.	X
ejpam-4848	196	3	consider	consider	VERB
ejpam-4848	196	4	the	the	DET
ejpam-4848	196	5	edge	edge	NOUN
ejpam-4848	196	6	corona	corona	NOUN
ejpam-4848	196	7	of	of	ADP
ejpam-4848	196	8	g	g	PROPN
ejpam-4848	196	9	=	=	SYM
ejpam-4848	196	10	c4	c4	NOUN
ejpam-4848	196	11	,	,	PUNCT
ejpam-4848	196	12	h	h	NOUN
ejpam-4848	196	13	=	=	PUNCT
ejpam-4848	196	14	p5	p5	PROPN
ejpam-4848	196	15	,	,	PUNCT
ejpam-4848	196	16	and	and	CCONJ
ejpam-4848	196	17	v	v	ADP
ejpam-4848	196	18	∈	∈	NOUN
ejpam-4848	196	19	v	v	NOUN
ejpam-4848	196	20	(	(	PUNCT
ejpam-4848	196	21	g	g	NOUN
ejpam-4848	196	22	)	)	PUNCT
ejpam-4848	196	23	in	in	ADP
ejpam-4848	196	24	figure	figure	NOUN
ejpam-4848	196	25	6	6	NUM
ejpam-4848	196	26	.	.	PUNCT
ejpam-4848	197	1	then	then	ADV
ejpam-4848	197	2	m	m	VERB
ejpam-4848	197	3	=	=	ADJ
ejpam-4848	197	4	|v	|v	X
ejpam-4848	197	5	(	(	PUNCT
ejpam-4848	197	6	g)|	g)|	NOUN
ejpam-4848	197	7	=	=	PUNCT
ejpam-4848	197	8	|e(g)|	|e(g)|	PROPN
ejpam-4848	197	9	=	=	SYM
ejpam-4848	197	10	r	r	NOUN
ejpam-4848	197	11	=	=	SYM
ejpam-4848	197	12	4	4	NUM
ejpam-4848	197	13	,	,	PUNCT
ejpam-4848	197	14	n	n	NOUN
ejpam-4848	197	15	=	=	PRON
ejpam-4848	197	16	|v	|v	X
ejpam-4848	197	17	(	(	PUNCT
ejpam-4848	197	18	h)|	h)|	NOUN
ejpam-4848	197	19	=	=	SYM
ejpam-4848	197	20	5	5	NUM
ejpam-4848	197	21	,	,	PUNCT
ejpam-4848	197	22	τg(v	τg(v	PUNCT
ejpam-4848	197	23	)	)	PUNCT
ejpam-4848	197	24	=	=	SYM
ejpam-4848	197	25	4	4	NUM
ejpam-4848	197	26	,	,	PUNCT
ejpam-4848	197	27	|ev|	|ev|	NUM
ejpam-4848	197	28	=	=	SYM
ejpam-4848	197	29	|e(g	|e(g	PROPN
ejpam-4848	197	30	)	)	PUNCT
ejpam-4848	197	31	\	\	PROPN
ejpam-4848	198	1	ev|	ev|	PROPN
ejpam-4848	198	2	=	=	SYM
ejpam-4848	198	3	2	2	NUM
ejpam-4848	198	4	and	and	CCONJ
ejpam-4848	198	5	∑	∑	ADP
ejpam-4848	198	6	e∈e(g)\ev	e∈e(g)\ev	NOUN
ejpam-4848	198	7	dg(v	dg(v	NOUN
ejpam-4848	198	8	,	,	PUNCT
ejpam-4848	198	9	e	e	NOUN
ejpam-4848	198	10	)	)	PUNCT
ejpam-4848	198	11	=	=	SYM
ejpam-4848	198	12	2	2	X
ejpam-4848	198	13	.	.	X
ejpam-4848	198	14	using	use	VERB
ejpam-4848	198	15	corollary	corollary	ADJ
ejpam-4848	198	16	2	2	NUM
ejpam-4848	198	17	,	,	PUNCT
ejpam-4848	198	18	the	the	DET
ejpam-4848	198	19	closeness	closeness	NOUN
ejpam-4848	198	20	centrality	centrality	NOUN
ejpam-4848	198	21	of	of	ADP
ejpam-4848	198	22	v	v	NUM
ejpam-4848	198	23	∈	∈	NOUN
ejpam-4848	198	24	v	v	NOUN
ejpam-4848	198	25	(	(	PUNCT
ejpam-4848	198	26	g	g	NOUN
ejpam-4848	198	27	)	)	PUNCT
ejpam-4848	198	28	is	be	AUX
ejpam-4848	198	29	cg⋄h	cg⋄h	PROPN
ejpam-4848	198	30	=	=	PUNCT
ejpam-4848	198	31	m+	m+	NUM
ejpam-4848	198	32	qn−	qn−	VERB
ejpam-4848	198	33	1	1	NUM
ejpam-4848	198	34	τg(v	τg(v	NOUN
ejpam-4848	198	35	)	)	PUNCT
ejpam-4848	199	1	+	+	CCONJ
ejpam-4848	199	2	nq	nq	PROPN
ejpam-4848	199	3	+	+	CCONJ
ejpam-4848	199	4	n	n	CCONJ
ejpam-4848	199	5	∑	∑	ADV
ejpam-4848	199	6	e∈e(g)\ev	e∈e(g)\ev	NOUN
ejpam-4848	199	7	dg(v	dg(v	NOUN
ejpam-4848	199	8	,	,	PUNCT
ejpam-4848	199	9	e	e	NOUN
ejpam-4848	199	10	)	)	PUNCT
ejpam-4848	199	11	=	=	SYM
ejpam-4848	199	12	24−	24−	NUM
ejpam-4848	199	13	1	1	NUM
ejpam-4848	199	14	4	4	NUM
ejpam-4848	199	15	+	+	CCONJ
ejpam-4848	199	16	(	(	PUNCT
ejpam-4848	199	17	5)(4	5)(4	NUM
ejpam-4848	199	18	)	)	PUNCT
ejpam-4848	200	1	+	+	CCONJ
ejpam-4848	200	2	(	(	PUNCT
ejpam-4848	200	3	5)(2	5)(2	NUM
ejpam-4848	200	4	)	)	PUNCT
ejpam-4848	200	5	f.	f.	PROPN
ejpam-4848	200	6	alfeche	alfeche	PROPN
ejpam-4848	200	7	,	,	PUNCT
ejpam-4848	200	8	v.	v.	PROPN
ejpam-4848	200	9	barraza	barraza	PROPN
ejpam-4848	200	10	,	,	PUNCT
ejpam-4848	200	11	s.	s.	PROPN
ejpam-4848	200	12	canoy	canoy	PROPN
ejpam-4848	200	13	,	,	PUNCT
ejpam-4848	200	14	jr	jr	PROPN
ejpam-4848	200	15	.	.	PROPN
ejpam-4848	200	16	/	/	SYM
ejpam-4848	200	17	eur	eur	PROPN
ejpam-4848	200	18	.	.	PUNCT
ejpam-4848	201	1	j.	j.	PROPN
ejpam-4848	201	2	pure	pure	PROPN
ejpam-4848	201	3	appl	appl	PROPN
ejpam-4848	201	4	.	.	PROPN
ejpam-4848	201	5	math	math	PROPN
ejpam-4848	201	6	,	,	PUNCT
ejpam-4848	201	7	16	16	NUM
ejpam-4848	201	8	(	(	PUNCT
ejpam-4848	201	9	3	3	NUM
ejpam-4848	201	10	)	)	PUNCT
ejpam-4848	201	11	(	(	PUNCT
ejpam-4848	201	12	2023	2023	NUM
ejpam-4848	201	13	)	)	PUNCT
ejpam-4848	201	14	,	,	PUNCT
ejpam-4848	201	15	1406	1406	NUM
ejpam-4848	201	16	-	-	SYM
ejpam-4848	201	17	1420	1420	NUM
ejpam-4848	201	18	1412	1412	NUM
ejpam-4848	201	19	....................................	....................................	PUNCT
ejpam-4848	201	20	....................................	....................................	PUNCT
ejpam-4848	202	1	....................................	....................................	PUNCT
ejpam-4848	202	2	....................................	....................................	PUNCT
ejpam-4848	203	1	....................................	....................................	PUNCT
ejpam-4848	203	2	....................................	....................................	PUNCT
ejpam-4848	204	1	....................................	....................................	PUNCT
ejpam-4848	204	2	....................................	....................................	PUNCT
ejpam-4848	205	1	....................................	....................................	PUNCT
ejpam-4848	205	2	....................................	....................................	PUNCT
ejpam-4848	206	1	....................................	....................................	PUNCT
ejpam-4848	206	2	....................................	....................................	PUNCT
ejpam-4848	207	1	....................................	....................................	PUNCT
ejpam-4848	207	2	....................................	....................................	PUNCT
ejpam-4848	208	1	....................................	....................................	PUNCT
ejpam-4848	208	2	....................................	....................................	PUNCT
ejpam-4848	209	1	....................................	....................................	PUNCT
ejpam-4848	209	2	....................................	....................................	PUNCT
ejpam-4848	210	1	....................................	....................................	PUNCT
ejpam-4848	210	2	....................................	....................................	PUNCT
ejpam-4848	211	1	....................................	....................................	PUNCT
ejpam-4848	211	2	....................................	....................................	PUNCT
ejpam-4848	212	1	....................................	....................................	PUNCT
ejpam-4848	212	2	....................................	....................................	PUNCT
ejpam-4848	213	1	.........	.........	PUNCT
ejpam-4848	213	2	........	........	PUNCT
ejpam-4848	213	3	........	........	PUNCT
ejpam-4848	213	4	........	........	PUNCT
ejpam-4848	213	5	........	........	PUNCT
ejpam-4848	213	6	........	........	PUNCT
ejpam-4848	213	7	........	........	PUNCT
ejpam-4848	213	8	........	........	PUNCT
ejpam-4848	213	9	........	........	PUNCT
ejpam-4848	213	10	........	........	PUNCT
ejpam-4848	213	11	........	........	PUNCT
ejpam-4848	213	12	........	........	PUNCT
ejpam-4848	213	13	........	........	PUNCT
ejpam-4848	213	14	........	........	PUNCT
ejpam-4848	213	15	........	........	PUNCT
ejpam-4848	213	16	........	........	PUNCT
ejpam-4848	213	17	........	........	PUNCT
ejpam-4848	213	18	........	........	PUNCT
ejpam-4848	213	19	........	........	PUNCT
ejpam-4848	213	20	........	........	PUNCT
ejpam-4848	213	21	.	.	PUNCT
ejpam-4848	214	1	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4848	214	2	....	....	PUNCT
ejpam-4848	215	1	........	........	PUNCT
ejpam-4848	215	2	........	........	PUNCT
ejpam-4848	215	3	........	........	PUNCT
ejpam-4848	215	4	........	........	PUNCT
ejpam-4848	215	5	........	........	PUNCT
ejpam-4848	215	6	........	........	PUNCT
ejpam-4848	215	7	........	........	PUNCT
ejpam-4848	215	8	........	........	PUNCT
ejpam-4848	215	9	........	........	PUNCT
ejpam-4848	215	10	........	........	PUNCT
ejpam-4848	215	11	........	........	PUNCT
ejpam-4848	215	12	........	........	PUNCT
ejpam-4848	215	13	........	........	PUNCT
ejpam-4848	215	14	........	........	PUNCT
ejpam-4848	215	15	........	........	PUNCT
ejpam-4848	215	16	........	........	PUNCT
ejpam-4848	215	17	........	........	PUNCT
ejpam-4848	215	18	........	........	PUNCT
ejpam-4848	215	19	........	........	PUNCT
ejpam-4848	216	1	......	......	PUNCT
ejpam-4848	216	2	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4848	217	1	..........................................	..........................................	PUNCT
ejpam-4848	217	2	...........	...........	PUNCT
ejpam-4848	218	1	..........	..........	PUNCT
ejpam-4848	218	2	..........	..........	PUNCT
ejpam-4848	219	1	..........	..........	PUNCT
ejpam-4848	219	2	.	.	PUNCT
ejpam-4848	220	1	..........................................	..........................................	PUNCT
ejpam-4848	220	2	...........	...........	PUNCT
ejpam-4848	221	1	..........	..........	PUNCT
ejpam-4848	221	2	..........	..........	PUNCT
ejpam-4848	222	1	..........	..........	PUNCT
ejpam-4848	222	2	.	.	PUNCT
ejpam-4848	223	1	..........	..........	PUNCT
ejpam-4848	223	2	.........	.........	PUNCT
ejpam-4848	224	1	.........	.........	PUNCT
ejpam-4848	224	2	.........	.........	PUNCT
ejpam-4848	225	1	.........	.........	PUNCT
ejpam-4848	225	2	.........	.........	PUNCT
ejpam-4848	226	1	.........	.........	PUNCT
ejpam-4848	226	2	.........	.........	PUNCT
ejpam-4848	226	3	.......	.......	PUNCT
ejpam-4848	226	4	..............	..............	PUNCT
ejpam-4848	226	5	.............	.............	PUNCT
ejpam-4848	226	6	.............	.............	PUNCT
ejpam-4848	226	7	.............	.............	PUNCT
ejpam-4848	226	8	.........	.........	PUNCT
ejpam-4848	226	9	............	............	PUNCT
ejpam-4848	226	10	...........	...........	PUNCT
ejpam-4848	226	11	...........	...........	PUNCT
ejpam-4848	226	12	...........	...........	PUNCT
ejpam-4848	226	13	...........	...........	PUNCT
ejpam-4848	226	14	...........	...........	PUNCT
ejpam-4848	226	15	...........	...........	PUNCT
ejpam-4848	226	16	...........	...........	PUNCT
ejpam-4848	226	17	...........	...........	PUNCT
ejpam-4848	226	18	...........	...........	PUNCT
ejpam-4848	226	19	........................	........................	PUNCT
ejpam-4848	226	20	.......................	.......................	PUNCT
ejpam-4848	226	21	.......................	.......................	PUNCT
ejpam-4848	226	22	.......................	.......................	PUNCT
ejpam-4848	227	1	...................	...................	PUNCT
ejpam-4848	227	2	.................	.................	PUNCT
ejpam-4848	228	1	................	................	PUNCT
ejpam-4848	228	2	................	................	PUNCT
ejpam-4848	229	1	................	................	PUNCT
ejpam-4848	229	2	................	................	PUNCT
ejpam-4848	230	1	................	................	PUNCT
ejpam-4848	230	2	................	................	PUNCT
ejpam-4848	231	1	................	................	PUNCT
ejpam-4848	231	2	................	................	PUNCT
ejpam-4848	232	1	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-4848	232	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4848	232	3	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4848	233	1	..............................................................	..............................................................	PUNCT
ejpam-4848	233	2	................................................................................	................................................................................	PUNCT
ejpam-4848	234	1	...........	...........	PUNCT
ejpam-4848	234	2	..........	..........	PUNCT
ejpam-4848	235	1	..........	..........	PUNCT
ejpam-4848	235	2	..........	..........	PUNCT
ejpam-4848	235	3	.	.	PUNCT
ejpam-4848	236	1	..........................................	..........................................	PUNCT
ejpam-4848	236	2	...........	...........	PUNCT
ejpam-4848	237	1	..........	..........	PUNCT
ejpam-4848	237	2	..........	..........	PUNCT
ejpam-4848	238	1	..........	..........	PUNCT
ejpam-4848	238	2	.	.	PUNCT
ejpam-4848	239	1	..........................................	..........................................	PUNCT
ejpam-4848	239	2	................................................................................	................................................................................	PUNCT
ejpam-4848	240	1	..............................................................	..............................................................	PUNCT
ejpam-4848	240	2	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4848	241	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4848	241	2	..............................................................................................................................................................................	..............................................................................................................................................................................	PUNCT
ejpam-4848	242	1	................	................	PUNCT
ejpam-4848	242	2	................	................	PUNCT
ejpam-4848	243	1	................	................	PUNCT
ejpam-4848	243	2	................	................	PUNCT
ejpam-4848	244	1	................	................	PUNCT
ejpam-4848	244	2	................	................	PUNCT
ejpam-4848	245	1	................	................	PUNCT
ejpam-4848	245	2	................	................	PUNCT
ejpam-4848	245	3	............	............	PUNCT
ejpam-4848	245	4	........................	........................	PUNCT
ejpam-4848	245	5	.......................	.......................	PUNCT
ejpam-4848	246	1	.......................	.......................	PUNCT
ejpam-4848	246	2	.......................	.......................	PUNCT
ejpam-4848	247	1	...................	...................	PUNCT
ejpam-4848	247	2	............	............	PUNCT
ejpam-4848	247	3	...........	...........	PUNCT
ejpam-4848	247	4	...........	...........	PUNCT
ejpam-4848	247	5	...........	...........	PUNCT
ejpam-4848	247	6	...........	...........	PUNCT
ejpam-4848	247	7	...........	...........	PUNCT
ejpam-4848	247	8	...........	...........	PUNCT
ejpam-4848	247	9	...........	...........	PUNCT
ejpam-4848	247	10	...........	...........	PUNCT
ejpam-4848	247	11	...........	...........	PUNCT
ejpam-4848	247	12	..............	..............	PUNCT
ejpam-4848	247	13	.............	.............	PUNCT
ejpam-4848	247	14	.............	.............	PUNCT
ejpam-4848	247	15	.............	.............	PUNCT
ejpam-4848	248	1	.........	.........	PUNCT
ejpam-4848	248	2	..........	..........	PUNCT
ejpam-4848	249	1	.........	.........	PUNCT
ejpam-4848	249	2	.........	.........	PUNCT
ejpam-4848	250	1	.........	.........	PUNCT
ejpam-4848	250	2	.........	.........	PUNCT
ejpam-4848	251	1	.........	.........	PUNCT
ejpam-4848	251	2	.........	.........	PUNCT
ejpam-4848	252	1	.........	.........	PUNCT
ejpam-4848	252	2	.......	.......	PUNCT
ejpam-4848	252	3	...............	...............	PUNCT
ejpam-4848	253	1	..............	..............	PUNCT
ejpam-4848	253	2	.............	.............	PUNCT
ejpam-4848	253	3	..........................................	..........................................	PUNCT
ejpam-4848	253	4	...............	...............	PUNCT
ejpam-4848	254	1	..............	..............	PUNCT
ejpam-4848	254	2	.............	.............	PUNCT
ejpam-4848	254	3	..........................................	..........................................	PUNCT
ejpam-4848	254	4	...........	...........	PUNCT
ejpam-4848	255	1	..........	..........	PUNCT
ejpam-4848	255	2	..........	..........	PUNCT
ejpam-4848	256	1	..........	..........	PUNCT
ejpam-4848	256	2	..........	..........	PUNCT
ejpam-4848	257	1	..........	..........	PUNCT
ejpam-4848	257	2	..........	..........	PUNCT
ejpam-4848	258	1	..........	..........	PUNCT
ejpam-4848	258	2	..........	..........	PUNCT
ejpam-4848	259	1	..........	..........	PUNCT
ejpam-4848	259	2	..........	..........	PUNCT
ejpam-4848	260	1	..........	..........	PUNCT
ejpam-4848	260	2	..........	..........	PUNCT
ejpam-4848	261	1	..........	..........	PUNCT
ejpam-4848	261	2	..........	..........	PUNCT
ejpam-4848	262	1	......	......	PUNCT
ejpam-4848	262	2	..........	..........	PUNCT
ejpam-4848	263	1	.........	.........	PUNCT
ejpam-4848	263	2	.........	.........	PUNCT
ejpam-4848	264	1	.........	.........	PUNCT
ejpam-4848	264	2	.........	.........	PUNCT
ejpam-4848	265	1	.........	.........	PUNCT
ejpam-4848	265	2	.........	.........	PUNCT
ejpam-4848	266	1	.........	.........	PUNCT
ejpam-4848	266	2	.........	.........	PUNCT
ejpam-4848	267	1	.........	.........	PUNCT
ejpam-4848	267	2	.........	.........	PUNCT
ejpam-4848	268	1	.........	.........	PUNCT
ejpam-4848	268	2	...	...	PUNCT
ejpam-4848	268	3	............	............	PUNCT
ejpam-4848	268	4	...........	...........	PUNCT
ejpam-4848	268	5	...........	...........	PUNCT
ejpam-4848	268	6	...........	...........	PUNCT
ejpam-4848	268	7	...........	...........	PUNCT
ejpam-4848	268	8	...........	...........	PUNCT
ejpam-4848	268	9	...........	...........	PUNCT
ejpam-4848	268	10	...........	...........	PUNCT
ejpam-4848	268	11	...........	...........	PUNCT
ejpam-4848	268	12	...........	...........	PUNCT
ejpam-4848	268	13	...........	...........	PUNCT
ejpam-4848	268	14	..........	..........	PUNCT
ejpam-4848	269	1	..........	..........	PUNCT
ejpam-4848	269	2	..........	..........	PUNCT
ejpam-4848	270	1	..........	..........	PUNCT
ejpam-4848	270	2	..........	..........	PUNCT
ejpam-4848	270	3	.	.	PUNCT
ejpam-4848	271	1	..........................	..........................	PUNCT
ejpam-4848	271	2	.........................	.........................	PUNCT
ejpam-4848	272	1	.........................	.........................	PUNCT
ejpam-4848	272	2	....	....	PUNCT
ejpam-4848	273	1	................................................................................	................................................................................	PUNCT
ejpam-4848	273	2	..............................................................	..............................................................	PUNCT
ejpam-4848	274	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4848	274	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4848	274	3	.............................................................................................................................................................	.............................................................................................................................................................	PUNCT
ejpam-4848	274	4	...............	...............	PUNCT
ejpam-4848	275	1	..............	..............	PUNCT
ejpam-4848	275	2	.............	.............	PUNCT
ejpam-4848	275	3	..........................................	..........................................	PUNCT
ejpam-4848	275	4	...............	...............	PUNCT
ejpam-4848	276	1	..............	..............	PUNCT
ejpam-4848	276	2	.............	.............	PUNCT
ejpam-4848	276	3	..........................................	..........................................	PUNCT
ejpam-4848	276	4	................................................................................	................................................................................	PUNCT
ejpam-4848	277	1	..............................................................	..............................................................	PUNCT
ejpam-4848	277	2	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4848	278	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4848	278	2	.............................................................................................................................................................	.............................................................................................................................................................	PUNCT
ejpam-4848	279	1	...........	...........	PUNCT
ejpam-4848	279	2	..........	..........	PUNCT
ejpam-4848	280	1	..........	..........	PUNCT
ejpam-4848	280	2	..........	..........	PUNCT
ejpam-4848	281	1	..........	..........	PUNCT
ejpam-4848	281	2	..........	..........	PUNCT
ejpam-4848	282	1	..........	..........	PUNCT
ejpam-4848	282	2	..........	..........	PUNCT
ejpam-4848	283	1	..........	..........	PUNCT
ejpam-4848	283	2	..........	..........	PUNCT
ejpam-4848	284	1	..........	..........	PUNCT
ejpam-4848	284	2	..........	..........	PUNCT
ejpam-4848	285	1	..........	..........	PUNCT
ejpam-4848	285	2	..........	..........	PUNCT
ejpam-4848	286	1	..........	..........	PUNCT
ejpam-4848	286	2	......	......	PUNCT
ejpam-4848	287	1	..........	..........	PUNCT
ejpam-4848	287	2	.........	.........	PUNCT
ejpam-4848	288	1	.........	.........	PUNCT
ejpam-4848	288	2	.........	.........	PUNCT
ejpam-4848	289	1	.........	.........	PUNCT
ejpam-4848	289	2	.........	.........	PUNCT
ejpam-4848	290	1	.........	.........	PUNCT
ejpam-4848	290	2	.........	.........	PUNCT
ejpam-4848	291	1	.........	.........	PUNCT
ejpam-4848	291	2	.........	.........	PUNCT
ejpam-4848	292	1	.........	.........	PUNCT
ejpam-4848	292	2	.........	.........	PUNCT
ejpam-4848	292	3	...	...	PUNCT
ejpam-4848	292	4	............	............	PUNCT
ejpam-4848	292	5	...........	...........	PUNCT
ejpam-4848	292	6	...........	...........	PUNCT
ejpam-4848	292	7	...........	...........	PUNCT
ejpam-4848	292	8	...........	...........	PUNCT
ejpam-4848	292	9	...........	...........	PUNCT
ejpam-4848	292	10	...........	...........	PUNCT
ejpam-4848	292	11	...........	...........	PUNCT
ejpam-4848	292	12	...........	...........	PUNCT
ejpam-4848	292	13	...........	...........	PUNCT
ejpam-4848	292	14	...........	...........	PUNCT
ejpam-4848	292	15	..........	..........	PUNCT
ejpam-4848	293	1	..........	..........	PUNCT
ejpam-4848	293	2	..........	..........	PUNCT
ejpam-4848	294	1	..........	..........	PUNCT
ejpam-4848	294	2	..........	..........	PUNCT
ejpam-4848	294	3	.	.	PUNCT
ejpam-4848	295	1	..........................	..........................	PUNCT
ejpam-4848	295	2	.........................	.........................	PUNCT
ejpam-4848	296	1	.........................	.........................	PUNCT
ejpam-4848	296	2	....	....	PUNCT
ejpam-4848	297	1	•v	•v	ADJ
ejpam-4848	297	2	figure	figure	NOUN
ejpam-4848	297	3	6	6	NUM
ejpam-4848	297	4	:	:	PUNCT
ejpam-4848	297	5	the	the	DET
ejpam-4848	297	6	edge	edge	NOUN
ejpam-4848	297	7	corona	corona	NOUN
ejpam-4848	297	8	graph	graph	NOUN
ejpam-4848	297	9	c4	c4	PROPN
ejpam-4848	297	10	⋄	⋄	PROPN
ejpam-4848	297	11	p5	p5	PROPN
ejpam-4848	297	12	and	and	CCONJ
ejpam-4848	297	13	v	v	ADP
ejpam-4848	297	14	∈	∈	PROPN
ejpam-4848	297	15	v	v	NOUN
ejpam-4848	297	16	(	(	PUNCT
ejpam-4848	297	17	c4	c4	NOUN
ejpam-4848	297	18	)	)	PUNCT
ejpam-4848	297	19	=	=	PUNCT
ejpam-4848	298	1	23	23	NUM
ejpam-4848	298	2	34	34	NUM
ejpam-4848	298	3	.	.	PUNCT
ejpam-4848	299	1	for	for	ADP
ejpam-4848	299	2	a	a	DET
ejpam-4848	299	3	non	non	ADJ
ejpam-4848	299	4	-	-	ADJ
ejpam-4848	299	5	trivial	trivial	ADJ
ejpam-4848	299	6	connected	connected	ADJ
ejpam-4848	299	7	graphg	graphg	NOUN
ejpam-4848	299	8	and	and	CCONJ
ejpam-4848	299	9	e	e	NOUN
ejpam-4848	299	10	=	=	NOUN
ejpam-4848	299	11	uv	uv	PROPN
ejpam-4848	299	12	∈	∈	PROPN
ejpam-4848	299	13	e(g	e(g	PROPN
ejpam-4848	299	14	)	)	PUNCT
ejpam-4848	299	15	,	,	PUNCT
ejpam-4848	299	16	the	the	DET
ejpam-4848	299	17	sets	set	NOUN
ejpam-4848	299	18	vu≤v	vu≤v	NOUN
ejpam-4848	299	19	,	,	PUNCT
ejpam-4848	299	20	vv	vv	ADP
ejpam-4848	299	21	<	<	X
ejpam-4848	299	22	u	u	NOUN
ejpam-4848	299	23	,	,	PUNCT
ejpam-4848	299	24	eu≤v	eu≤v	NOUN
ejpam-4848	299	25	,	,	PUNCT
ejpam-4848	299	26	ev	ev	ADP
ejpam-4848	299	27	<	<	X
ejpam-4848	299	28	u	u	NOUN
ejpam-4848	299	29	are	be	AUX
ejpam-4848	299	30	given	give	VERB
ejpam-4848	299	31	by	by	ADP
ejpam-4848	299	32	:	:	PUNCT
ejpam-4848	299	33	vu≤v	vu≤v	PROPN
ejpam-4848	299	34	=	=	SYM
ejpam-4848	299	35	{	{	PUNCT
ejpam-4848	299	36	z	z	NOUN
ejpam-4848	299	37	∈	∈	PROPN
ejpam-4848	299	38	v	v	ADP
ejpam-4848	299	39	(	(	PUNCT
ejpam-4848	299	40	g	g	NOUN
ejpam-4848	299	41	)	)	PUNCT
ejpam-4848	299	42	\	\	NOUN
ejpam-4848	299	43	{	{	PUNCT
ejpam-4848	299	44	u	u	NOUN
ejpam-4848	299	45	}	}	PUNCT
ejpam-4848	299	46	:	:	PUNCT
ejpam-4848	299	47	dg(z	dg(z	NUM
ejpam-4848	299	48	,	,	PUNCT
ejpam-4848	299	49	u	u	NOUN
ejpam-4848	299	50	)	)	PUNCT
ejpam-4848	299	51	≤	≤	NOUN
ejpam-4848	299	52	dg(z	dg(z	NUM
ejpam-4848	299	53	,	,	PUNCT
ejpam-4848	299	54	v	v	NOUN
ejpam-4848	299	55	)	)	PUNCT
ejpam-4848	299	56	}	}	PUNCT
ejpam-4848	299	57	vv	vv	ADP
ejpam-4848	299	58	<	<	X
ejpam-4848	299	59	u	u	X
ejpam-4848	299	60	=	=	PUNCT
ejpam-4848	299	61	{	{	PUNCT
ejpam-4848	299	62	y	y	PROPN
ejpam-4848	299	63	∈	∈	PROPN
ejpam-4848	299	64	v	v	NOUN
ejpam-4848	299	65	(	(	PUNCT
ejpam-4848	299	66	g	g	NOUN
ejpam-4848	299	67	)	)	PUNCT
ejpam-4848	299	68	\	\	NOUN
ejpam-4848	299	69	{	{	PUNCT
ejpam-4848	299	70	v	v	NOUN
ejpam-4848	299	71	}	}	PUNCT
ejpam-4848	299	72	:	:	PUNCT
ejpam-4848	299	73	dg(v	dg(v	X
ejpam-4848	299	74	,	,	PUNCT
ejpam-4848	299	75	y	y	NOUN
ejpam-4848	299	76	)	)	PUNCT
ejpam-4848	299	77	<	<	X
ejpam-4848	299	78	dg(u	dg(u	X
ejpam-4848	299	79	,	,	PUNCT
ejpam-4848	299	80	y	y	NOUN
ejpam-4848	299	81	)	)	PUNCT
ejpam-4848	299	82	}	}	PUNCT
ejpam-4848	299	83	eu≤v	eu≤v	NOUN
ejpam-4848	299	84	=	=	PRON
ejpam-4848	299	85	{	{	PUNCT
ejpam-4848	299	86	e′	e′	PROPN
ejpam-4848	299	87	∈	∈	PROPN
ejpam-4848	299	88	e(g	e(g	PROPN
ejpam-4848	299	89	)	)	PUNCT
ejpam-4848	299	90	\	\	PUNCT
ejpam-4848	300	1	{	{	PUNCT
ejpam-4848	300	2	e	e	NOUN
ejpam-4848	300	3	}	}	PUNCT
ejpam-4848	300	4	:	:	PUNCT
ejpam-4848	300	5	dg(u	dg(u	X
ejpam-4848	300	6	,	,	PUNCT
ejpam-4848	300	7	e	e	NOUN
ejpam-4848	300	8	′	′	NOUN
ejpam-4848	300	9	)	)	PUNCT
ejpam-4848	300	10	≤	≤	NOUN
ejpam-4848	300	11	dg(v	dg(v	PUNCT
ejpam-4848	300	12	,	,	PUNCT
ejpam-4848	300	13	e	e	NOUN
ejpam-4848	300	14	′	′	NUM
ejpam-4848	300	15	)	)	PUNCT
ejpam-4848	300	16	}	}	PUNCT
ejpam-4848	300	17	ev	ev	ADP
ejpam-4848	300	18	<	<	X
ejpam-4848	300	19	u	u	X
ejpam-4848	300	20	=	=	PUNCT
ejpam-4848	300	21	{	{	PUNCT
ejpam-4848	300	22	e′	e′	PROPN
ejpam-4848	300	23	∈	∈	PROPN
ejpam-4848	300	24	e(g	e(g	PROPN
ejpam-4848	300	25	)	)	PUNCT
ejpam-4848	300	26	:	:	PUNCT
ejpam-4848	300	27	dg(v	dg(v	X
ejpam-4848	300	28	,	,	PUNCT
ejpam-4848	300	29	e	e	NOUN
ejpam-4848	300	30	′	′	NOUN
ejpam-4848	300	31	)	)	PUNCT
ejpam-4848	300	32	<	<	X
ejpam-4848	300	33	dg(u	dg(u	X
ejpam-4848	300	34	,	,	PUNCT
ejpam-4848	300	35	e	e	NOUN
ejpam-4848	300	36	′	′	NUM
ejpam-4848	300	37	)	)	PUNCT
ejpam-4848	300	38	}	}	PUNCT
ejpam-4848	300	39	note	note	VERB
ejpam-4848	300	40	that	that	SCONJ
ejpam-4848	300	41	|eu≤v|+	|eu≤v|+	PROPN
ejpam-4848	300	42	|ev	|ev	X
ejpam-4848	300	43	<	<	X
ejpam-4848	300	44	u|	u|	ADJ
ejpam-4848	300	45	=	=	SYM
ejpam-4848	300	46	|e(g)|	|e(g)|	ADJ
ejpam-4848	300	47	−	−	PROPN
ejpam-4848	300	48	1	1	NUM
ejpam-4848	300	49	and	and	CCONJ
ejpam-4848	300	50	|vu≤v|+	|vu≤v|+	ADJ
ejpam-4848	300	51	|vv	|vv	ADJ
ejpam-4848	300	52	<	<	X
ejpam-4848	300	53	u|	u|	PROPN
ejpam-4848	300	54	=	=	SYM
ejpam-4848	300	55	|v	|v	X
ejpam-4848	300	56	(	(	PUNCT
ejpam-4848	300	57	g)|	g)|	INTJ
ejpam-4848	300	58	−	−	NOUN
ejpam-4848	300	59	2	2	NUM
ejpam-4848	300	60	.	.	PUNCT
ejpam-4848	300	61	theorem	theorem	NOUN
ejpam-4848	300	62	3	3	X
ejpam-4848	300	63	.	.	PUNCT
ejpam-4848	301	1	let	let	VERB
ejpam-4848	301	2	g	g	NOUN
ejpam-4848	302	1	and	and	CCONJ
ejpam-4848	302	2	h	h	NOUN
ejpam-4848	302	3	be	be	AUX
ejpam-4848	302	4	connected	connect	VERB
ejpam-4848	302	5	non	non	ADJ
ejpam-4848	302	6	-	-	ADJ
ejpam-4848	302	7	trivial	trivial	ADJ
ejpam-4848	302	8	graphs	graph	NOUN
ejpam-4848	302	9	and	and	CCONJ
ejpam-4848	302	10	let	let	VERB
ejpam-4848	302	11	e	e	NOUN
ejpam-4848	302	12	=	=	VERB
ejpam-4848	302	13	uv	uv	PROPN
ejpam-4848	302	14	∈	∈	PROPN
ejpam-4848	302	15	e(g	e(g	PROPN
ejpam-4848	302	16	)	)	PUNCT
ejpam-4848	302	17	.	.	PUNCT
ejpam-4848	303	1	if	if	SCONJ
ejpam-4848	303	2	p	p	PROPN
ejpam-4848	303	3	∈	∈	PROPN
ejpam-4848	303	4	v	v	X
ejpam-4848	303	5	(	(	PUNCT
ejpam-4848	303	6	he	he	PRON
ejpam-4848	303	7	)	)	PUNCT
ejpam-4848	303	8	,	,	PUNCT
ejpam-4848	303	9	then	then	ADV
ejpam-4848	303	10	τg⋄h(p	τg⋄h(p	PROPN
ejpam-4848	303	11	)	)	PUNCT
ejpam-4848	304	1	=	=	SYM
ejpam-4848	304	2	|v	|v	PROPN
ejpam-4848	304	3	(	(	PUNCT
ejpam-4848	304	4	g)|	g)|	NOUN
ejpam-4848	304	5	−	−	PROPN
ejpam-4848	304	6	degh(p	degh(p	PROPN
ejpam-4848	304	7	)	)	PUNCT
ejpam-4848	304	8	+	+	NUM
ejpam-4848	304	9	2|v	2|v	NUM
ejpam-4848	304	10	(	(	PUNCT
ejpam-4848	304	11	h)||e(g)|	h)||e(g)|	NOUN
ejpam-4848	304	12	−	−	NOUN
ejpam-4848	304	13	2	2	NUM
ejpam-4848	304	14	+	+	CCONJ
ejpam-4848	304	15	∑	∑	PROPN
ejpam-4848	304	16	x∈vu≤v	x∈vu≤v	PROPN
ejpam-4848	304	17	dg(u	dg(u	X
ejpam-4848	304	18	,	,	PUNCT
ejpam-4848	304	19	x	x	X
ejpam-4848	304	20	)	)	PUNCT
ejpam-4848	304	21	+	+	CCONJ
ejpam-4848	304	22	∑	∑	PROPN
ejpam-4848	304	23	x∈vv	x∈vv	PROPN
ejpam-4848	304	24	<	<	X
ejpam-4848	304	25	u	u	NOUN
ejpam-4848	304	26	dg(v	dg(v	NOUN
ejpam-4848	304	27	,	,	PUNCT
ejpam-4848	304	28	x	x	X
ejpam-4848	304	29	)	)	PUNCT
ejpam-4848	305	1	+	+	CCONJ
ejpam-4848	305	2	|v	|v	X
ejpam-4848	305	3	(	(	PUNCT
ejpam-4848	305	4	h)|	h)|	PROPN
ejpam-4848	305	5	∑	∑	PROPN
ejpam-4848	305	6	e′∈eu≤v	e′∈eu≤v	PROPN
ejpam-4848	305	7	dg(u	dg(u	X
ejpam-4848	305	8	,	,	PUNCT
ejpam-4848	305	9	e	e	NOUN
ejpam-4848	305	10	′	′	NOUN
ejpam-4848	305	11	)	)	PUNCT
ejpam-4848	306	1	+	+	CCONJ
ejpam-4848	306	2	|v	|v	PROPN
ejpam-4848	306	3	(	(	PUNCT
ejpam-4848	306	4	h)|	h)|	PROPN
ejpam-4848	306	5	∑	∑	PROPN
ejpam-4848	306	6	e′∈ev	e′∈ev	PROPN
ejpam-4848	306	7	<	<	X
ejpam-4848	306	8	u	u	NOUN
ejpam-4848	306	9	dg(v	dg(v	X
ejpam-4848	306	10	,	,	PUNCT
ejpam-4848	306	11	e	e	NOUN
ejpam-4848	306	12	′	′	NUM
ejpam-4848	306	13	)	)	PUNCT
ejpam-4848	306	14	.	.	PUNCT
ejpam-4848	307	1	proof	proof	NOUN
ejpam-4848	307	2	.	.	PUNCT
ejpam-4848	308	1	let	let	VERB
ejpam-4848	308	2	e	e	NOUN
ejpam-4848	308	3	=	=	PUNCT
ejpam-4848	308	4	uv	uv	PROPN
ejpam-4848	308	5	∈	∈	PROPN
ejpam-4848	308	6	e(g	e(g	PROPN
ejpam-4848	308	7	)	)	PUNCT
ejpam-4848	308	8	and	and	CCONJ
ejpam-4848	308	9	let	let	VERB
ejpam-4848	308	10	p	p	PRON
ejpam-4848	308	11	∈	∈	PROPN
ejpam-4848	308	12	v	v	NOUN
ejpam-4848	308	13	(	(	PUNCT
ejpam-4848	308	14	he	he	PRON
ejpam-4848	308	15	)	)	PUNCT
ejpam-4848	308	16	.	.	PUNCT
ejpam-4848	309	1	then	then	ADV
ejpam-4848	309	2	τg⋄h(p	τg⋄h(p	PROPN
ejpam-4848	309	3	)	)	PUNCT
ejpam-4848	309	4	=	=	PUNCT
ejpam-4848	310	1	∑	∑	PUNCT
ejpam-4848	310	2	q∈v	q∈v	ADV
ejpam-4848	310	3	(	(	PUNCT
ejpam-4848	310	4	g⋄h	g⋄h	X
ejpam-4848	310	5	)	)	PUNCT
ejpam-4848	310	6	dg⋄h(p	dg⋄h(p	NOUN
ejpam-4848	310	7	,	,	PUNCT
ejpam-4848	310	8	q	q	NOUN
ejpam-4848	310	9	)	)	PUNCT
ejpam-4848	310	10	=	=	SYM
ejpam-4848	310	11	∑	∑	NOUN
ejpam-4848	310	12	e′∈e(g	e′∈e(g	NOUN
ejpam-4848	310	13	)	)	PUNCT
ejpam-4848	310	14	∑	∑	PUNCT
ejpam-4848	310	15	q∈v	q∈v	ADV
ejpam-4848	310	16	(	(	PUNCT
ejpam-4848	310	17	he′	he′	NOUN
ejpam-4848	310	18	)	)	PUNCT
ejpam-4848	310	19	dg⋄h(p	dg⋄h(p	NOUN
ejpam-4848	310	20	,	,	PUNCT
ejpam-4848	310	21	q	q	NOUN
ejpam-4848	310	22	)	)	PUNCT
ejpam-4848	311	1	+	+	CCONJ
ejpam-4848	311	2	∑	∑	PUNCT
ejpam-4848	311	3	q∈v	q∈v	ADV
ejpam-4848	311	4	(	(	PUNCT
ejpam-4848	311	5	g	g	NOUN
ejpam-4848	311	6	)	)	PUNCT
ejpam-4848	311	7	dg⋄h(p	dg⋄h(p	NOUN
ejpam-4848	311	8	,	,	PUNCT
ejpam-4848	311	9	q	q	NOUN
ejpam-4848	311	10	)	)	PUNCT
ejpam-4848	311	11	=	=	SYM
ejpam-4848	311	12	∑	∑	PUNCT
ejpam-4848	311	13	q∈v	q∈v	ADV
ejpam-4848	311	14	(	(	PUNCT
ejpam-4848	311	15	he	he	PRON
ejpam-4848	311	16	)	)	PUNCT
ejpam-4848	311	17	dg⋄h(p	dg⋄h(p	PROPN
ejpam-4848	311	18	,	,	PUNCT
ejpam-4848	311	19	q	q	NOUN
ejpam-4848	311	20	)	)	PUNCT
ejpam-4848	311	21	+	+	CCONJ
ejpam-4848	311	22	∑	∑	PUNCT
ejpam-4848	311	23	e′	e′	ADJ
ejpam-4848	311	24	̸=e	̸=e	VERB
ejpam-4848	311	25	∑	∑	PROPN
ejpam-4848	311	26	q∈v	q∈v	ADV
ejpam-4848	311	27	(	(	PUNCT
ejpam-4848	311	28	he′	he′	NOUN
ejpam-4848	311	29	)	)	PUNCT
ejpam-4848	311	30	dg⋄h(p	dg⋄h(p	NOUN
ejpam-4848	311	31	,	,	PUNCT
ejpam-4848	311	32	q	q	NOUN
ejpam-4848	311	33	)	)	PUNCT
ejpam-4848	311	34	+	+	CCONJ
ejpam-4848	311	35	∑	∑	PROPN
ejpam-4848	311	36	x∈vu≤v	x∈vu≤v	PROPN
ejpam-4848	311	37	(	(	PUNCT
ejpam-4848	311	38	1	1	NUM
ejpam-4848	311	39	+	+	CCONJ
ejpam-4848	311	40	dg(u	dg(u	ADJ
ejpam-4848	311	41	,	,	PUNCT
ejpam-4848	311	42	x	x	NOUN
ejpam-4848	311	43	)	)	PUNCT
ejpam-4848	311	44	)	)	PUNCT
ejpam-4848	312	1	+	+	CCONJ
ejpam-4848	312	2	∑	∑	PUNCT
ejpam-4848	312	3	x∈vv	x∈vv	PROPN
ejpam-4848	312	4	<	<	X
ejpam-4848	312	5	u	u	X
ejpam-4848	312	6	(	(	PUNCT
ejpam-4848	312	7	1	1	NUM
ejpam-4848	312	8	+	+	CCONJ
ejpam-4848	312	9	dg(v	dg(v	NOUN
ejpam-4848	312	10	,	,	PUNCT
ejpam-4848	312	11	x	x	NOUN
ejpam-4848	312	12	)	)	PUNCT
ejpam-4848	312	13	)	)	PUNCT
ejpam-4848	313	1	+	+	CCONJ
ejpam-4848	313	2	dg⋄h(p	dg⋄h(p	NOUN
ejpam-4848	313	3	,	,	PUNCT
ejpam-4848	313	4	u	u	NOUN
ejpam-4848	313	5	)	)	PUNCT
ejpam-4848	313	6	+	+	X
ejpam-4848	313	7	dg⋄h(p	dg⋄h(p	NOUN
ejpam-4848	313	8	,	,	PUNCT
ejpam-4848	313	9	v	v	NOUN
ejpam-4848	313	10	)	)	PUNCT
ejpam-4848	313	11	f.	f.	PROPN
ejpam-4848	313	12	alfeche	alfeche	PROPN
ejpam-4848	313	13	,	,	PUNCT
ejpam-4848	313	14	v.	v.	PROPN
ejpam-4848	313	15	barraza	barraza	PROPN
ejpam-4848	313	16	,	,	PUNCT
ejpam-4848	313	17	s.	s.	PROPN
ejpam-4848	313	18	canoy	canoy	PROPN
ejpam-4848	313	19	,	,	PUNCT
ejpam-4848	313	20	jr	jr	PROPN
ejpam-4848	313	21	.	.	PROPN
ejpam-4848	313	22	/	/	SYM
ejpam-4848	313	23	eur	eur	PROPN
ejpam-4848	313	24	.	.	PUNCT
ejpam-4848	314	1	j.	j.	PROPN
ejpam-4848	314	2	pure	pure	PROPN
ejpam-4848	314	3	appl	appl	PROPN
ejpam-4848	314	4	.	.	PROPN
ejpam-4848	314	5	math	math	PROPN
ejpam-4848	314	6	,	,	PUNCT
ejpam-4848	314	7	16	16	NUM
ejpam-4848	314	8	(	(	PUNCT
ejpam-4848	314	9	3	3	NUM
ejpam-4848	314	10	)	)	PUNCT
ejpam-4848	314	11	(	(	PUNCT
ejpam-4848	314	12	2023	2023	NUM
ejpam-4848	314	13	)	)	PUNCT
ejpam-4848	314	14	,	,	PUNCT
ejpam-4848	314	15	1406	1406	NUM
ejpam-4848	314	16	-	-	SYM
ejpam-4848	314	17	1420	1420	NUM
ejpam-4848	314	18	1413	1413	NUM
ejpam-4848	314	19	=	=	PUNCT
ejpam-4848	314	20	∑	∑	PUNCT
ejpam-4848	314	21	q∈nhe	q∈nhe	PROPN
ejpam-4848	314	22	(	(	PUNCT
ejpam-4848	314	23	p	p	NOUN
ejpam-4848	314	24	)	)	PUNCT
ejpam-4848	314	25	dg⋄h(p	dg⋄h(p	NOUN
ejpam-4848	314	26	,	,	PUNCT
ejpam-4848	314	27	q	q	NOUN
ejpam-4848	314	28	)	)	PUNCT
ejpam-4848	315	1	+	+	CCONJ
ejpam-4848	315	2	∑	∑	PUNCT
ejpam-4848	315	3	q∈v	q∈v	PROPN
ejpam-4848	315	4	(	(	PUNCT
ejpam-4848	315	5	he)\nhe	he)\nhe	PROPN
ejpam-4848	315	6	[	[	X
ejpam-4848	315	7	p	p	X
ejpam-4848	315	8	]	]	PUNCT
ejpam-4848	315	9	dg⋄h(p	dg⋄h(p	NOUN
ejpam-4848	315	10	,	,	PUNCT
ejpam-4848	315	11	q	q	NOUN
ejpam-4848	315	12	)	)	PUNCT
ejpam-4848	315	13	+	+	CCONJ
ejpam-4848	315	14	∑	∑	ADP
ejpam-4848	315	15	e′∈eu≤v	e′∈eu≤v	PROPN
ejpam-4848	315	16	∑	∑	PUNCT
ejpam-4848	315	17	q∈v	q∈v	ADV
ejpam-4848	315	18	(	(	PUNCT
ejpam-4848	315	19	he′	he′	NOUN
ejpam-4848	315	20	)	)	PUNCT
ejpam-4848	315	21	dg⋄h(p	dg⋄h(p	NOUN
ejpam-4848	315	22	,	,	PUNCT
ejpam-4848	315	23	q	q	NOUN
ejpam-4848	315	24	)	)	PUNCT
ejpam-4848	315	25	+	+	CCONJ
ejpam-4848	315	26	∑	∑	PROPN
ejpam-4848	315	27	e′∈ev	e′∈ev	PROPN
ejpam-4848	315	28	<	<	X
ejpam-4848	315	29	u	u	X
ejpam-4848	315	30	∑	∑	PROPN
ejpam-4848	315	31	q∈v	q∈v	ADV
ejpam-4848	315	32	(	(	PUNCT
ejpam-4848	315	33	he′	he′	NOUN
ejpam-4848	315	34	)	)	PUNCT
ejpam-4848	315	35	dg⋄h(p	dg⋄h(p	NOUN
ejpam-4848	315	36	,	,	PUNCT
ejpam-4848	315	37	q	q	NOUN
ejpam-4848	315	38	)	)	PUNCT
ejpam-4848	316	1	+	+	CCONJ
ejpam-4848	316	2	∑	∑	PROPN
ejpam-4848	316	3	x∈vu≤v	x∈vu≤v	PROPN
ejpam-4848	316	4	(	(	PUNCT
ejpam-4848	316	5	1	1	NUM
ejpam-4848	316	6	+	+	CCONJ
ejpam-4848	316	7	dg(u	dg(u	ADJ
ejpam-4848	316	8	,	,	PUNCT
ejpam-4848	316	9	x	x	NOUN
ejpam-4848	316	10	)	)	PUNCT
ejpam-4848	316	11	)	)	PUNCT
ejpam-4848	317	1	+	+	CCONJ
ejpam-4848	317	2	∑	∑	PUNCT
ejpam-4848	317	3	x∈vv	x∈vv	PROPN
ejpam-4848	317	4	<	<	X
ejpam-4848	317	5	u	u	X
ejpam-4848	317	6	(	(	PUNCT
ejpam-4848	317	7	1	1	NUM
ejpam-4848	317	8	+	+	CCONJ
ejpam-4848	317	9	dg(v	dg(v	NOUN
ejpam-4848	317	10	,	,	PUNCT
ejpam-4848	317	11	x	x	NOUN
ejpam-4848	317	12	)	)	PUNCT
ejpam-4848	317	13	)	)	PUNCT
ejpam-4848	318	1	+	+	CCONJ
ejpam-4848	318	2	2	2	NUM
ejpam-4848	318	3	=	=	SYM
ejpam-4848	318	4	|nh(p)|+	|nh(p)|+	NOUN
ejpam-4848	318	5	2(|v	2(|v	NUM
ejpam-4848	318	6	(	(	PUNCT
ejpam-4848	318	7	h)|	h)|	NOUN
ejpam-4848	318	8	−	−	PROPN
ejpam-4848	318	9	|nh	|nh	NUM
ejpam-4848	319	1	[	[	X
ejpam-4848	319	2	p]|	p]|	PROPN
ejpam-4848	319	3	)	)	PUNCT
ejpam-4848	320	1	+	+	CCONJ
ejpam-4848	320	2	|v	|v	X
ejpam-4848	320	3	(	(	PUNCT
ejpam-4848	320	4	h)|	h)|	NOUN
ejpam-4848	320	5	∑	∑	ADV
ejpam-4848	320	6	e′∈eu≤v	e′∈eu≤v	PROPN
ejpam-4848	320	7	(	(	PUNCT
ejpam-4848	320	8	2	2	NUM
ejpam-4848	320	9	+	+	CCONJ
ejpam-4848	320	10	dg(u	dg(u	X
ejpam-4848	320	11	,	,	PUNCT
ejpam-4848	320	12	e	e	NOUN
ejpam-4848	320	13	′	′	NUM
ejpam-4848	320	14	)	)	PUNCT
ejpam-4848	320	15	)	)	PUNCT
ejpam-4848	321	1	+	+	CCONJ
ejpam-4848	321	2	|v	|v	PROPN
ejpam-4848	321	3	(	(	PUNCT
ejpam-4848	321	4	h)|	h)|	PROPN
ejpam-4848	321	5	∑	∑	PROPN
ejpam-4848	321	6	e′∈ev	e′∈ev	PROPN
ejpam-4848	321	7	<	<	X
ejpam-4848	321	8	u	u	X
ejpam-4848	321	9	(	(	PUNCT
ejpam-4848	321	10	2	2	NUM
ejpam-4848	321	11	+	+	CCONJ
ejpam-4848	321	12	dg(v	dg(v	X
ejpam-4848	321	13	,	,	PUNCT
ejpam-4848	321	14	e	e	NOUN
ejpam-4848	321	15	′	′	NUM
ejpam-4848	321	16	)	)	PUNCT
ejpam-4848	321	17	)	)	PUNCT
ejpam-4848	322	1	+	+	CCONJ
ejpam-4848	322	2	∑	∑	PUNCT
ejpam-4848	322	3	x∈vu≤v	x∈vu≤v	PROPN
ejpam-4848	322	4	(	(	PUNCT
ejpam-4848	322	5	1	1	NUM
ejpam-4848	322	6	+	+	CCONJ
ejpam-4848	322	7	dg(u	dg(u	ADJ
ejpam-4848	322	8	,	,	PUNCT
ejpam-4848	322	9	x	x	NOUN
ejpam-4848	322	10	)	)	PUNCT
ejpam-4848	322	11	)	)	PUNCT
ejpam-4848	323	1	+	+	CCONJ
ejpam-4848	323	2	∑	∑	PUNCT
ejpam-4848	323	3	x∈vv	x∈vv	PROPN
ejpam-4848	323	4	<	<	X
ejpam-4848	323	5	u	u	X
ejpam-4848	323	6	(	(	PUNCT
ejpam-4848	323	7	1	1	NUM
ejpam-4848	323	8	+	+	CCONJ
ejpam-4848	323	9	dg(v	dg(v	NOUN
ejpam-4848	323	10	,	,	PUNCT
ejpam-4848	323	11	x	x	NOUN
ejpam-4848	323	12	)	)	PUNCT
ejpam-4848	323	13	)	)	PUNCT
ejpam-4848	324	1	+	+	CCONJ
ejpam-4848	324	2	2	2	X
ejpam-4848	324	3	.	.	PUNCT
ejpam-4848	324	4	now	now	ADV
ejpam-4848	324	5	,	,	PUNCT
ejpam-4848	324	6	|v	|v	PROPN
ejpam-4848	324	7	(	(	PUNCT
ejpam-4848	324	8	h)|	h)|	PROPN
ejpam-4848	324	9	∑	∑	ADV
ejpam-4848	324	10	e′∈eu≤v	e′∈eu≤v	PROPN
ejpam-4848	324	11	(	(	PUNCT
ejpam-4848	324	12	2	2	NUM
ejpam-4848	324	13	+	+	CCONJ
ejpam-4848	324	14	dg(u	dg(u	X
ejpam-4848	324	15	,	,	PUNCT
ejpam-4848	324	16	e	e	NOUN
ejpam-4848	324	17	′	′	NUM
ejpam-4848	324	18	)	)	PUNCT
ejpam-4848	324	19	)	)	PUNCT
ejpam-4848	324	20	=	=	SYM
ejpam-4848	325	1	2|v	2|v	NOUN
ejpam-4848	325	2	(	(	PUNCT
ejpam-4848	325	3	h)||eu≤v|+	h)||eu≤v|+	ADJ
ejpam-4848	325	4	|v	|v	X
ejpam-4848	325	5	(	(	PUNCT
ejpam-4848	325	6	h)|	h)|	NOUN
ejpam-4848	325	7	∑	∑	PROPN
ejpam-4848	325	8	e′∈eu≤v	e′∈eu≤v	PROPN
ejpam-4848	325	9	dg(u	dg(u	X
ejpam-4848	325	10	,	,	PUNCT
ejpam-4848	325	11	e	e	NOUN
ejpam-4848	325	12	′	′	NOUN
ejpam-4848	325	13	)	)	PUNCT
ejpam-4848	325	14	,	,	PUNCT
ejpam-4848	325	15	|v	|v	PROPN
ejpam-4848	325	16	(	(	PUNCT
ejpam-4848	325	17	h)|	h)|	PROPN
ejpam-4848	325	18	∑	∑	PROPN
ejpam-4848	325	19	e′∈ev	e′∈ev	PROPN
ejpam-4848	325	20	<	<	X
ejpam-4848	325	21	v	v	X
ejpam-4848	325	22	(	(	PUNCT
ejpam-4848	325	23	2	2	NUM
ejpam-4848	325	24	+	+	CCONJ
ejpam-4848	325	25	dg(v	dg(v	X
ejpam-4848	325	26	,	,	PUNCT
ejpam-4848	325	27	e	e	NOUN
ejpam-4848	325	28	′	′	NUM
ejpam-4848	325	29	)	)	PUNCT
ejpam-4848	325	30	)	)	PUNCT
ejpam-4848	326	1	=	=	SYM
ejpam-4848	326	2	2|v	2|v	PROPN
ejpam-4848	326	3	(	(	PUNCT
ejpam-4848	326	4	h)||ev	h)||ev	PROPN
ejpam-4848	326	5	<	<	X
ejpam-4848	326	6	u|+	u|+	PROPN
ejpam-4848	326	7	|v	|v	NOUN
ejpam-4848	326	8	(	(	PUNCT
ejpam-4848	326	9	h)|	h)|	PROPN
ejpam-4848	326	10	∑	∑	PROPN
ejpam-4848	326	11	e′∈ev	e′∈ev	PROPN
ejpam-4848	326	12	<	<	X
ejpam-4848	326	13	u	u	NOUN
ejpam-4848	326	14	dg(v	dg(v	X
ejpam-4848	326	15	,	,	PUNCT
ejpam-4848	326	16	e	e	NOUN
ejpam-4848	326	17	′	′	NUM
ejpam-4848	326	18	)	)	PUNCT
ejpam-4848	326	19	,	,	PUNCT
ejpam-4848	326	20	∑	∑	PUNCT
ejpam-4848	326	21	x∈vu≤v	x∈vu≤v	PROPN
ejpam-4848	326	22	(	(	PUNCT
ejpam-4848	326	23	1	1	NUM
ejpam-4848	326	24	+	+	CCONJ
ejpam-4848	326	25	dg(u	dg(u	ADJ
ejpam-4848	326	26	,	,	PUNCT
ejpam-4848	326	27	x	x	NOUN
ejpam-4848	326	28	)	)	PUNCT
ejpam-4848	326	29	)	)	PUNCT
ejpam-4848	327	1	=	=	PUNCT
ejpam-4848	327	2	|vu≤v|+	|vu≤v|+	VERB
ejpam-4848	327	3	∑	∑	PUNCT
ejpam-4848	327	4	x∈vu≤v	x∈vu≤v	PROPN
ejpam-4848	327	5	dg(u	dg(u	X
ejpam-4848	327	6	,	,	PUNCT
ejpam-4848	327	7	x	x	NOUN
ejpam-4848	327	8	)	)	PUNCT
ejpam-4848	327	9	,	,	PUNCT
ejpam-4848	327	10	and	and	CCONJ
ejpam-4848	327	11	∑	∑	ADP
ejpam-4848	327	12	x∈vv	x∈vv	PROPN
ejpam-4848	327	13	<	<	X
ejpam-4848	327	14	u	u	X
ejpam-4848	327	15	(	(	PUNCT
ejpam-4848	327	16	1	1	NUM
ejpam-4848	327	17	+	+	CCONJ
ejpam-4848	327	18	dg(v	dg(v	NOUN
ejpam-4848	327	19	,	,	PUNCT
ejpam-4848	327	20	x	x	NOUN
ejpam-4848	327	21	)	)	PUNCT
ejpam-4848	327	22	)	)	PUNCT
ejpam-4848	327	23	=	=	PUNCT
ejpam-4848	327	24	|vv	|vv	NOUN
ejpam-4848	327	25	<	<	X
ejpam-4848	327	26	u|+	u|+	PROPN
ejpam-4848	327	27	∑	∑	PART
ejpam-4848	327	28	x∈vv	x∈vv	PROPN
ejpam-4848	327	29	<	<	X
ejpam-4848	327	30	u	u	NOUN
ejpam-4848	327	31	dg(u	dg(u	X
ejpam-4848	327	32	,	,	PUNCT
ejpam-4848	327	33	x	x	NOUN
ejpam-4848	327	34	)	)	PUNCT
ejpam-4848	327	35	.	.	PUNCT
ejpam-4848	328	1	hence	hence	ADV
ejpam-4848	328	2	,	,	PUNCT
ejpam-4848	328	3	τg⋄h(p	τg⋄h(p	PROPN
ejpam-4848	328	4	)	)	PUNCT
ejpam-4848	328	5	=	=	PUNCT
ejpam-4848	329	1	|nh(p)|+	|nh(p)|+	NOUN
ejpam-4848	330	1	2|v	2|v	NUM
ejpam-4848	330	2	(	(	PUNCT
ejpam-4848	330	3	h)|	h)|	NOUN
ejpam-4848	330	4	−	−	PROPN
ejpam-4848	330	5	2|nh(p)|	2|nh(p)|	NUM
ejpam-4848	330	6	−	−	NOUN
ejpam-4848	330	7	2	2	NUM
ejpam-4848	331	1	+	+	CCONJ
ejpam-4848	331	2	2	2	NUM
ejpam-4848	331	3	+	+	NUM
ejpam-4848	331	4	2|v	2|v	NOUN
ejpam-4848	331	5	(	(	PUNCT
ejpam-4848	331	6	h)||eu≤v|	h)||eu≤v|	PROPN
ejpam-4848	331	7	+	+	CCONJ
ejpam-4848	331	8	|v	|v	PROPN
ejpam-4848	331	9	(	(	PUNCT
ejpam-4848	331	10	h)|	h)|	PROPN
ejpam-4848	331	11	∑	∑	PROPN
ejpam-4848	331	12	e′∈eu≤v	e′∈eu≤v	PROPN
ejpam-4848	331	13	dg(u	dg(u	X
ejpam-4848	331	14	,	,	PUNCT
ejpam-4848	331	15	e	e	NOUN
ejpam-4848	331	16	′	′	NOUN
ejpam-4848	331	17	)	)	PUNCT
ejpam-4848	332	1	+	+	CCONJ
ejpam-4848	332	2	2|v	2|v	NUM
ejpam-4848	332	3	(	(	PUNCT
ejpam-4848	332	4	h)||ev	h)||ev	PROPN
ejpam-4848	332	5	<	<	X
ejpam-4848	332	6	u|+	u|+	PROPN
ejpam-4848	332	7	|v	|v	NOUN
ejpam-4848	332	8	(	(	PUNCT
ejpam-4848	332	9	h)|	h)|	PROPN
ejpam-4848	332	10	∑	∑	PROPN
ejpam-4848	332	11	e′∈ev	e′∈ev	PROPN
ejpam-4848	332	12	<	<	X
ejpam-4848	332	13	u	u	NOUN
ejpam-4848	332	14	dg(v	dg(v	X
ejpam-4848	332	15	,	,	PUNCT
ejpam-4848	332	16	e	e	NOUN
ejpam-4848	332	17	′	′	NUM
ejpam-4848	332	18	)	)	PUNCT
ejpam-4848	333	1	+	+	CCONJ
ejpam-4848	333	2	|vu≤v|+	|vu≤v|+	ADJ
ejpam-4848	333	3	∑	∑	PUNCT
ejpam-4848	333	4	x∈vu≤v	x∈vu≤v	PROPN
ejpam-4848	333	5	dg(u	dg(u	AUX
ejpam-4848	333	6	,	,	PUNCT
ejpam-4848	333	7	x	x	X
ejpam-4848	333	8	)	)	PUNCT
ejpam-4848	333	9	+	+	CCONJ
ejpam-4848	333	10	|vv	|vv	ADJ
ejpam-4848	333	11	<	<	X
ejpam-4848	333	12	u|+	u|+	PROPN
ejpam-4848	333	13	∑	∑	PART
ejpam-4848	333	14	x∈vv	x∈vv	PROPN
ejpam-4848	333	15	<	<	X
ejpam-4848	333	16	u	u	NOUN
ejpam-4848	333	17	dg(u	dg(u	X
ejpam-4848	333	18	,	,	PUNCT
ejpam-4848	333	19	x	x	X
ejpam-4848	333	20	)	)	PUNCT
ejpam-4848	333	21	=	=	SYM
ejpam-4848	333	22	2|v	2|v	PROPN
ejpam-4848	333	23	(	(	PUNCT
ejpam-4848	333	24	h)|	h)|	NOUN
ejpam-4848	333	25	−	−	PROPN
ejpam-4848	333	26	|nh(p)|+	|nh(p)|+	NOUN
ejpam-4848	333	27	2|v	2|v	PROPN
ejpam-4848	333	28	(	(	PUNCT
ejpam-4848	333	29	h)|(|eu≤v|+	h)|(|eu≤v|+	PROPN
ejpam-4848	333	30	|ev	|ev	NOUN
ejpam-4848	333	31	<	<	X
ejpam-4848	333	32	u|	u|	NOUN
ejpam-4848	333	33	)	)	PUNCT
ejpam-4848	333	34	+	+	CCONJ
ejpam-4848	333	35	(	(	PUNCT
ejpam-4848	333	36	|vu≤v|+	|vu≤v|+	ADP
ejpam-4848	333	37	|vv	|vv	ADJ
ejpam-4848	333	38	<	<	X
ejpam-4848	333	39	u|	u|	NOUN
ejpam-4848	333	40	)	)	PUNCT
ejpam-4848	333	41	+	+	CCONJ
ejpam-4848	333	42	∑	∑	PROPN
ejpam-4848	333	43	x∈vu≤v	x∈vu≤v	PROPN
ejpam-4848	333	44	dg(u	dg(u	X
ejpam-4848	333	45	,	,	PUNCT
ejpam-4848	333	46	x	x	X
ejpam-4848	333	47	)	)	PUNCT
ejpam-4848	333	48	+	+	CCONJ
ejpam-4848	333	49	∑	∑	PROPN
ejpam-4848	333	50	x∈vv	x∈vv	PROPN
ejpam-4848	333	51	<	<	X
ejpam-4848	333	52	u	u	NOUN
ejpam-4848	333	53	dg(v	dg(v	NOUN
ejpam-4848	333	54	,	,	PUNCT
ejpam-4848	333	55	x	x	X
ejpam-4848	333	56	)	)	PUNCT
ejpam-4848	334	1	+	+	CCONJ
ejpam-4848	334	2	|v	|v	X
ejpam-4848	334	3	(	(	PUNCT
ejpam-4848	334	4	h)|	h)|	PROPN
ejpam-4848	334	5	∑	∑	PROPN
ejpam-4848	334	6	e′∈eu≤v	e′∈eu≤v	PROPN
ejpam-4848	334	7	dg(u	dg(u	X
ejpam-4848	334	8	,	,	PUNCT
ejpam-4848	334	9	e	e	NOUN
ejpam-4848	334	10	′	′	NOUN
ejpam-4848	334	11	)	)	PUNCT
ejpam-4848	335	1	+	+	CCONJ
ejpam-4848	335	2	|v	|v	PROPN
ejpam-4848	335	3	(	(	PUNCT
ejpam-4848	335	4	h)|	h)|	PROPN
ejpam-4848	335	5	∑	∑	PROPN
ejpam-4848	335	6	e′∈ev	e′∈ev	PROPN
ejpam-4848	335	7	<	<	X
ejpam-4848	335	8	u	u	NOUN
ejpam-4848	335	9	dg(v	dg(v	X
ejpam-4848	335	10	,	,	PUNCT
ejpam-4848	335	11	e	e	NOUN
ejpam-4848	335	12	′	′	NOUN
ejpam-4848	335	13	)	)	PUNCT
ejpam-4848	335	14	=	=	SYM
ejpam-4848	336	1	2|v	2|v	PROPN
ejpam-4848	336	2	(	(	PUNCT
ejpam-4848	336	3	h)|	h)|	NOUN
ejpam-4848	336	4	−	−	PROPN
ejpam-4848	336	5	|nh(p)|+	|nh(p)|+	NOUN
ejpam-4848	337	1	2|v	2|v	PROPN
ejpam-4848	337	2	(	(	PUNCT
ejpam-4848	337	3	h)|(|e(g)|	h)|(|e(g)|	NOUN
ejpam-4848	337	4	−	−	NOUN
ejpam-4848	337	5	1	1	X
ejpam-4848	337	6	)	)	PUNCT
ejpam-4848	338	1	+	+	CCONJ
ejpam-4848	338	2	|v	|v	X
ejpam-4848	338	3	(	(	PUNCT
ejpam-4848	338	4	g)|	g)|	NOUN
ejpam-4848	338	5	−	−	PROPN
ejpam-4848	338	6	2	2	NUM
ejpam-4848	338	7	f.	f.	PROPN
ejpam-4848	338	8	alfeche	alfeche	PROPN
ejpam-4848	338	9	,	,	PUNCT
ejpam-4848	338	10	v.	v.	PROPN
ejpam-4848	338	11	barraza	barraza	PROPN
ejpam-4848	338	12	,	,	PUNCT
ejpam-4848	338	13	s.	s.	PROPN
ejpam-4848	338	14	canoy	canoy	PROPN
ejpam-4848	338	15	,	,	PUNCT
ejpam-4848	338	16	jr	jr	PROPN
ejpam-4848	338	17	.	.	PROPN
ejpam-4848	338	18	/	/	SYM
ejpam-4848	338	19	eur	eur	PROPN
ejpam-4848	338	20	.	.	PUNCT
ejpam-4848	339	1	j.	j.	PROPN
ejpam-4848	339	2	pure	pure	PROPN
ejpam-4848	339	3	appl	appl	PROPN
ejpam-4848	339	4	.	.	PROPN
ejpam-4848	339	5	math	math	PROPN
ejpam-4848	339	6	,	,	PUNCT
ejpam-4848	339	7	16	16	NUM
ejpam-4848	339	8	(	(	PUNCT
ejpam-4848	339	9	3	3	NUM
ejpam-4848	339	10	)	)	PUNCT
ejpam-4848	339	11	(	(	PUNCT
ejpam-4848	339	12	2023	2023	NUM
ejpam-4848	339	13	)	)	PUNCT
ejpam-4848	339	14	,	,	PUNCT
ejpam-4848	339	15	1406	1406	NUM
ejpam-4848	339	16	-	-	SYM
ejpam-4848	339	17	1420	1420	NUM
ejpam-4848	339	18	1414	1414	NUM
ejpam-4848	340	1	+	+	CCONJ
ejpam-4848	340	2	∑	∑	PROPN
ejpam-4848	340	3	x∈vu≤v	x∈vu≤v	PROPN
ejpam-4848	340	4	dg(u	dg(u	X
ejpam-4848	340	5	,	,	PUNCT
ejpam-4848	340	6	x	x	X
ejpam-4848	340	7	)	)	PUNCT
ejpam-4848	340	8	+	+	CCONJ
ejpam-4848	340	9	∑	∑	PROPN
ejpam-4848	340	10	x∈vv	x∈vv	PROPN
ejpam-4848	340	11	<	<	X
ejpam-4848	340	12	u	u	NOUN
ejpam-4848	340	13	dg(v	dg(v	NOUN
ejpam-4848	340	14	,	,	PUNCT
ejpam-4848	340	15	x	x	X
ejpam-4848	340	16	)	)	PUNCT
ejpam-4848	341	1	+	+	CCONJ
ejpam-4848	341	2	|v	|v	X
ejpam-4848	341	3	(	(	PUNCT
ejpam-4848	341	4	h)|	h)|	PROPN
ejpam-4848	341	5	∑	∑	PROPN
ejpam-4848	341	6	e′∈eu≤v	e′∈eu≤v	PROPN
ejpam-4848	341	7	dg(u	dg(u	X
ejpam-4848	341	8	,	,	PUNCT
ejpam-4848	341	9	e	e	NOUN
ejpam-4848	341	10	′	′	NOUN
ejpam-4848	341	11	)	)	PUNCT
ejpam-4848	342	1	+	+	CCONJ
ejpam-4848	342	2	|v	|v	PROPN
ejpam-4848	342	3	(	(	PUNCT
ejpam-4848	342	4	h)|	h)|	PROPN
ejpam-4848	342	5	∑	∑	PROPN
ejpam-4848	342	6	e′∈ev	e′∈ev	PROPN
ejpam-4848	342	7	<	<	X
ejpam-4848	342	8	u	u	NOUN
ejpam-4848	342	9	dg(v	dg(v	X
ejpam-4848	342	10	,	,	PUNCT
ejpam-4848	342	11	e	e	NOUN
ejpam-4848	342	12	′	′	NOUN
ejpam-4848	342	13	)	)	PUNCT
ejpam-4848	343	1	=	=	SYM
ejpam-4848	343	2	|v	|v	PROPN
ejpam-4848	343	3	(	(	PUNCT
ejpam-4848	343	4	g)|	g)|	NOUN
ejpam-4848	343	5	−	−	PROPN
ejpam-4848	343	6	degh(p	degh(p	PROPN
ejpam-4848	343	7	)	)	PUNCT
ejpam-4848	343	8	+	+	NUM
ejpam-4848	344	1	2|v	2|v	NUM
ejpam-4848	345	1	(	(	PUNCT
ejpam-4848	345	2	h)||e(g)|	h)||e(g)|	NOUN
ejpam-4848	345	3	−	−	NOUN
ejpam-4848	345	4	2	2	NUM
ejpam-4848	346	1	+	+	CCONJ
ejpam-4848	346	2	∑	∑	PROPN
ejpam-4848	346	3	x∈vu≤v	x∈vu≤v	PROPN
ejpam-4848	346	4	dg(u	dg(u	X
ejpam-4848	346	5	,	,	PUNCT
ejpam-4848	346	6	x	x	X
ejpam-4848	346	7	)	)	PUNCT
ejpam-4848	346	8	+	+	CCONJ
ejpam-4848	346	9	∑	∑	PROPN
ejpam-4848	346	10	x∈vv	x∈vv	PROPN
ejpam-4848	346	11	<	<	X
ejpam-4848	346	12	u	u	NOUN
ejpam-4848	346	13	dg(v	dg(v	NOUN
ejpam-4848	346	14	,	,	PUNCT
ejpam-4848	346	15	x	x	X
ejpam-4848	346	16	)	)	PUNCT
ejpam-4848	346	17	+	+	CCONJ
ejpam-4848	346	18	|v	|v	X
ejpam-4848	346	19	(	(	PUNCT
ejpam-4848	346	20	h)|	h)|	PROPN
ejpam-4848	346	21	∑	∑	PROPN
ejpam-4848	346	22	e′∈eu≤v	e′∈eu≤v	PROPN
ejpam-4848	346	23	dg(u	dg(u	X
ejpam-4848	346	24	,	,	PUNCT
ejpam-4848	346	25	e	e	NOUN
ejpam-4848	346	26	′	′	NOUN
ejpam-4848	346	27	)	)	PUNCT
ejpam-4848	347	1	+	+	CCONJ
ejpam-4848	347	2	|v	|v	PROPN
ejpam-4848	347	3	(	(	PUNCT
ejpam-4848	347	4	h)|	h)|	PROPN
ejpam-4848	347	5	∑	∑	PROPN
ejpam-4848	347	6	e′∈ev	e′∈ev	PROPN
ejpam-4848	347	7	<	<	X
ejpam-4848	347	8	u	u	NOUN
ejpam-4848	347	9	dg(v	dg(v	X
ejpam-4848	347	10	,	,	PUNCT
ejpam-4848	347	11	e	e	NOUN
ejpam-4848	347	12	′	′	NUM
ejpam-4848	347	13	)	)	PUNCT
ejpam-4848	347	14	.	.	PUNCT
ejpam-4848	348	1	the	the	DET
ejpam-4848	348	2	next	next	ADJ
ejpam-4848	348	3	result	result	NOUN
ejpam-4848	348	4	is	be	AUX
ejpam-4848	348	5	a	a	DET
ejpam-4848	348	6	direct	direct	ADJ
ejpam-4848	348	7	consequence	consequence	NOUN
ejpam-4848	348	8	of	of	ADP
ejpam-4848	348	9	theorem	theorem	ADJ
ejpam-4848	348	10	3	3	NUM
ejpam-4848	348	11	.	.	PUNCT
ejpam-4848	348	12	corollary	corollary	ADJ
ejpam-4848	348	13	3	3	NUM
ejpam-4848	348	14	.	.	PUNCT
ejpam-4848	348	15	letg	letg	NOUN
ejpam-4848	348	16	andh	andh	NOUN
ejpam-4848	348	17	be	be	AUX
ejpam-4848	348	18	connected	connect	VERB
ejpam-4848	348	19	non	non	ADJ
ejpam-4848	348	20	-	-	ADJ
ejpam-4848	348	21	trivial	trivial	ADJ
ejpam-4848	348	22	graphs	graph	NOUN
ejpam-4848	348	23	of	of	ADP
ejpam-4848	348	24	ordersm	ordersm	NOUN
ejpam-4848	348	25	and	and	CCONJ
ejpam-4848	348	26	n	n	CCONJ
ejpam-4848	348	27	,	,	PUNCT
ejpam-4848	348	28	respectively	respectively	ADV
ejpam-4848	348	29	,	,	PUNCT
ejpam-4848	348	30	and	and	CCONJ
ejpam-4848	348	31	let	let	VERB
ejpam-4848	348	32	r	r	NOUN
ejpam-4848	348	33	=	=	SYM
ejpam-4848	348	34	|e(g)|	|e(g)|	PROPN
ejpam-4848	348	35	and	and	CCONJ
ejpam-4848	348	36	e	e	NOUN
ejpam-4848	348	37	=	=	NOUN
ejpam-4848	348	38	uv	uv	PROPN
ejpam-4848	348	39	∈	∈	PROPN
ejpam-4848	348	40	e(g	e(g	PROPN
ejpam-4848	348	41	)	)	PUNCT
ejpam-4848	348	42	.	.	PUNCT
ejpam-4848	349	1	if	if	SCONJ
ejpam-4848	349	2	p	p	PROPN
ejpam-4848	349	3	∈	∈	PROPN
ejpam-4848	349	4	v	v	X
ejpam-4848	349	5	(	(	PUNCT
ejpam-4848	349	6	he	he	PRON
ejpam-4848	349	7	)	)	PUNCT
ejpam-4848	349	8	,	,	PUNCT
ejpam-4848	349	9	then	then	ADV
ejpam-4848	349	10	cg⋄h(p	cg⋄h(p	PROPN
ejpam-4848	349	11	)	)	PUNCT
ejpam-4848	349	12	=	=	SYM
ejpam-4848	349	13	m+	m+	NUM
ejpam-4848	349	14	rn−	rn−	NOUN
ejpam-4848	349	15	1	1	NUM
ejpam-4848	349	16	τg⋄h(p	τg⋄h(p	NOUN
ejpam-4848	349	17	)	)	PUNCT
ejpam-4848	349	18	,	,	PUNCT
ejpam-4848	349	19	where	where	SCONJ
ejpam-4848	349	20	τg⋄h(p	τg⋄h(p	NOUN
ejpam-4848	349	21	)	)	PUNCT
ejpam-4848	349	22	is	be	AUX
ejpam-4848	349	23	given	give	VERB
ejpam-4848	349	24	in	in	ADP
ejpam-4848	349	25	theorem	theorem	ADJ
ejpam-4848	349	26	3	3	NUM
ejpam-4848	349	27	.	.	NOUN
ejpam-4848	349	28	example	example	NOUN
ejpam-4848	350	1	3	3	X
ejpam-4848	350	2	.	.	X
ejpam-4848	350	3	consider	consider	VERB
ejpam-4848	350	4	p	p	PRON
ejpam-4848	350	5	∈	∈	PROPN
ejpam-4848	350	6	v	v	NOUN
ejpam-4848	350	7	(	(	PUNCT
ejpam-4848	350	8	he	he	PRON
ejpam-4848	350	9	)	)	PUNCT
ejpam-4848	350	10	,	,	PUNCT
ejpam-4848	350	11	where	where	SCONJ
ejpam-4848	350	12	e	e	NOUN
ejpam-4848	350	13	=	=	NOUN
ejpam-4848	350	14	uv	uv	PROPN
ejpam-4848	350	15	,	,	PUNCT
ejpam-4848	350	16	in	in	ADP
ejpam-4848	350	17	figure	figure	NOUN
ejpam-4848	350	18	7	7	NUM
ejpam-4848	350	19	,	,	PUNCT
ejpam-4848	350	20	where	where	SCONJ
ejpam-4848	350	21	g	g	NOUN
ejpam-4848	350	22	=	=	SYM
ejpam-4848	350	23	p4	p4	ADJ
ejpam-4848	350	24	and	and	CCONJ
ejpam-4848	350	25	h	h	NOUN
ejpam-4848	350	26	=	=	NOUN
ejpam-4848	350	27	p5	p5	PROPN
ejpam-4848	350	28	.	.	PUNCT
ejpam-4848	351	1	then	then	ADV
ejpam-4848	351	2	m	m	VERB
ejpam-4848	351	3	=	=	ADJ
ejpam-4848	351	4	4	4	NUM
ejpam-4848	351	5	,	,	PUNCT
ejpam-4848	351	6	r	r	NOUN
ejpam-4848	351	7	=	=	SYM
ejpam-4848	351	8	4	4	NUM
ejpam-4848	351	9	,	,	PUNCT
ejpam-4848	351	10	n	n	NOUN
ejpam-4848	351	11	=	=	SYM
ejpam-4848	351	12	5	5	NUM
ejpam-4848	351	13	,	,	PUNCT
ejpam-4848	351	14	degh(p	degh(p	PROPN
ejpam-4848	351	15	)	)	PUNCT
ejpam-4848	351	16	=	=	SYM
ejpam-4848	351	17	1	1	NUM
ejpam-4848	351	18	,	,	PUNCT
ejpam-4848	351	19	∑	∑	ADP
ejpam-4848	351	20	x∈vu≤v	x∈vu≤v	PROPN
ejpam-4848	351	21	dg(u	dg(u	X
ejpam-4848	351	22	,	,	PUNCT
ejpam-4848	351	23	x	x	X
ejpam-4848	351	24	)	)	PUNCT
ejpam-4848	351	25	=	=	SYM
ejpam-4848	351	26	1	1	NUM
ejpam-4848	351	27	,	,	PUNCT
ejpam-4848	351	28	∑	∑	INTJ
ejpam-4848	351	29	x∈vv	x∈vv	PROPN
ejpam-4848	351	30	<	<	X
ejpam-4848	351	31	u	u	NOUN
ejpam-4848	351	32	dg(v	dg(v	X
ejpam-4848	351	33	,	,	PUNCT
ejpam-4848	351	34	x	x	X
ejpam-4848	351	35	)	)	PUNCT
ejpam-4848	351	36	=	=	SYM
ejpam-4848	351	37	1,∑	1,∑	NUM
ejpam-4848	351	38	e′∈eu≤v	e′∈eu≤v	NOUN
ejpam-4848	351	39	dg(u	dg(u	X
ejpam-4848	351	40	,	,	PUNCT
ejpam-4848	351	41	e	e	NOUN
ejpam-4848	351	42	′	′	NOUN
ejpam-4848	351	43	)	)	PUNCT
ejpam-4848	351	44	=	=	SYM
ejpam-4848	351	45	1	1	NUM
ejpam-4848	351	46	,	,	PUNCT
ejpam-4848	351	47	and	and	CCONJ
ejpam-4848	351	48	∑	∑	ADV
ejpam-4848	351	49	e′∈ev	e′∈ev	PROPN
ejpam-4848	351	50	<	<	X
ejpam-4848	351	51	u	u	NOUN
ejpam-4848	351	52	dg(v	dg(v	X
ejpam-4848	351	53	,	,	PUNCT
ejpam-4848	351	54	e	e	NOUN
ejpam-4848	351	55	′	′	NOUN
ejpam-4848	351	56	)	)	PUNCT
ejpam-4848	351	57	=	=	SYM
ejpam-4848	352	1	0	0	X
ejpam-4848	352	2	.	.	PUNCT
ejpam-4848	352	3	by	by	ADP
ejpam-4848	352	4	corollary	corollary	ADJ
ejpam-4848	352	5	3	3	NUM
ejpam-4848	352	6	,	,	PUNCT
ejpam-4848	352	7	the	the	DET
ejpam-4848	352	8	closeness	closeness	NOUN
ejpam-4848	352	9	centrality	centrality	NOUN
ejpam-4848	352	10	of	of	ADP
ejpam-4848	352	11	p	p	PROPN
ejpam-4848	352	12	∈	∈	PROPN
ejpam-4848	352	13	hv	hv	PROPN
ejpam-4848	352	14	is	be	AUX
ejpam-4848	352	15	cg⋄h(p	cg⋄h(p	NOUN
ejpam-4848	352	16	)	)	PUNCT
ejpam-4848	352	17	=	=	PUNCT
ejpam-4848	352	18	23	23	NUM
ejpam-4848	352	19	48	48	NUM
ejpam-4848	352	20	.	.	PUNCT
ejpam-4848	353	1	....................................	....................................	PUNCT
ejpam-4848	353	2	....................................	....................................	PUNCT
ejpam-4848	354	1	....................................	....................................	PUNCT
ejpam-4848	354	2	....................................	....................................	PUNCT
ejpam-4848	355	1	....................................	....................................	PUNCT
ejpam-4848	355	2	....................................	....................................	PUNCT
ejpam-4848	356	1	....................................	....................................	PUNCT
ejpam-4848	356	2	....................................	....................................	PUNCT
ejpam-4848	357	1	....................................	....................................	PUNCT
ejpam-4848	357	2	....................................	....................................	PUNCT
ejpam-4848	358	1	....................................	....................................	PUNCT
ejpam-4848	358	2	....................................	....................................	PUNCT
ejpam-4848	359	1	....................................	....................................	PUNCT
ejpam-4848	359	2	....................................	....................................	PUNCT
ejpam-4848	360	1	....................................	....................................	PUNCT
ejpam-4848	360	2	....................................	....................................	PUNCT
ejpam-4848	361	1	....................................	....................................	PUNCT
ejpam-4848	361	2	....................................	....................................	PUNCT
ejpam-4848	362	1	....................................	....................................	PUNCT
ejpam-4848	362	2	....................................	....................................	PUNCT
ejpam-4848	363	1	....................................	....................................	PUNCT
ejpam-4848	363	2	....................................	....................................	PUNCT
ejpam-4848	364	1	....................................	....................................	PUNCT
ejpam-4848	364	2	....................................	....................................	PUNCT
ejpam-4848	365	1	.........	.........	PUNCT
ejpam-4848	365	2	........	........	PUNCT
ejpam-4848	365	3	........	........	PUNCT
ejpam-4848	365	4	........	........	PUNCT
ejpam-4848	365	5	........	........	PUNCT
ejpam-4848	365	6	........	........	PUNCT
ejpam-4848	365	7	........	........	PUNCT
ejpam-4848	365	8	........	........	PUNCT
ejpam-4848	365	9	........	........	PUNCT
ejpam-4848	365	10	........	........	PUNCT
ejpam-4848	365	11	........	........	PUNCT
ejpam-4848	365	12	........	........	PUNCT
ejpam-4848	365	13	........	........	PUNCT
ejpam-4848	365	14	........	........	PUNCT
ejpam-4848	365	15	........	........	PUNCT
ejpam-4848	365	16	........	........	PUNCT
ejpam-4848	365	17	........	........	PUNCT
ejpam-4848	365	18	........	........	PUNCT
ejpam-4848	365	19	........	........	PUNCT
ejpam-4848	365	20	........	........	PUNCT
ejpam-4848	365	21	.	.	PUNCT
ejpam-4848	366	1	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4848	366	2	....	....	PUNCT
ejpam-4848	367	1	........	........	PUNCT
ejpam-4848	367	2	........	........	PUNCT
ejpam-4848	367	3	........	........	PUNCT
ejpam-4848	367	4	........	........	PUNCT
ejpam-4848	367	5	........	........	PUNCT
ejpam-4848	367	6	........	........	PUNCT
ejpam-4848	367	7	........	........	PUNCT
ejpam-4848	367	8	........	........	PUNCT
ejpam-4848	367	9	........	........	PUNCT
ejpam-4848	367	10	........	........	PUNCT
ejpam-4848	367	11	........	........	PUNCT
ejpam-4848	367	12	........	........	PUNCT
ejpam-4848	367	13	........	........	PUNCT
ejpam-4848	367	14	........	........	PUNCT
ejpam-4848	367	15	........	........	PUNCT
ejpam-4848	367	16	........	........	PUNCT
ejpam-4848	367	17	........	........	PUNCT
ejpam-4848	367	18	........	........	PUNCT
ejpam-4848	367	19	........	........	PUNCT
ejpam-4848	368	1	......	......	PUNCT
ejpam-4848	368	2	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4848	369	1	..........................................	..........................................	PUNCT
ejpam-4848	369	2	...........	...........	PUNCT
ejpam-4848	370	1	..........	..........	PUNCT
ejpam-4848	370	2	..........	..........	PUNCT
ejpam-4848	371	1	..........	..........	PUNCT
ejpam-4848	371	2	.	.	PUNCT
ejpam-4848	372	1	..........................................	..........................................	PUNCT
ejpam-4848	372	2	...........	...........	PUNCT
ejpam-4848	373	1	..........	..........	PUNCT
ejpam-4848	373	2	..........	..........	PUNCT
ejpam-4848	374	1	..........	..........	PUNCT
ejpam-4848	374	2	.	.	PUNCT
ejpam-4848	375	1	..........	..........	PUNCT
ejpam-4848	375	2	.........	.........	PUNCT
ejpam-4848	376	1	.........	.........	PUNCT
ejpam-4848	376	2	.........	.........	PUNCT
ejpam-4848	377	1	.........	.........	PUNCT
ejpam-4848	377	2	.........	.........	PUNCT
ejpam-4848	378	1	.........	.........	PUNCT
ejpam-4848	378	2	.........	.........	PUNCT
ejpam-4848	378	3	.......	.......	PUNCT
ejpam-4848	378	4	..............	..............	PUNCT
ejpam-4848	378	5	.............	.............	PUNCT
ejpam-4848	378	6	.............	.............	PUNCT
ejpam-4848	378	7	.............	.............	PUNCT
ejpam-4848	378	8	.........	.........	PUNCT
ejpam-4848	378	9	............	............	PUNCT
ejpam-4848	378	10	...........	...........	PUNCT
ejpam-4848	378	11	...........	...........	PUNCT
ejpam-4848	378	12	...........	...........	PUNCT
ejpam-4848	378	13	...........	...........	PUNCT
ejpam-4848	378	14	...........	...........	PUNCT
ejpam-4848	378	15	...........	...........	PUNCT
ejpam-4848	378	16	...........	...........	PUNCT
ejpam-4848	378	17	...........	...........	PUNCT
ejpam-4848	378	18	...........	...........	PUNCT
ejpam-4848	378	19	........................	........................	PUNCT
ejpam-4848	378	20	.......................	.......................	PUNCT
ejpam-4848	378	21	.......................	.......................	PUNCT
ejpam-4848	378	22	.......................	.......................	PUNCT
ejpam-4848	379	1	...................	...................	PUNCT
ejpam-4848	379	2	.................	.................	PUNCT
ejpam-4848	380	1	................	................	PUNCT
ejpam-4848	380	2	................	................	PUNCT
ejpam-4848	381	1	................	................	PUNCT
ejpam-4848	381	2	................	................	PUNCT
ejpam-4848	382	1	................	................	PUNCT
ejpam-4848	382	2	................	................	PUNCT
ejpam-4848	383	1	................	................	PUNCT
ejpam-4848	383	2	................	................	PUNCT
ejpam-4848	384	1	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-4848	384	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4848	384	3	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4848	385	1	..............................................................	..............................................................	PUNCT
ejpam-4848	385	2	................................................................................	................................................................................	PUNCT
ejpam-4848	386	1	...........	...........	PUNCT
ejpam-4848	386	2	..........	..........	PUNCT
ejpam-4848	387	1	..........	..........	PUNCT
ejpam-4848	387	2	..........	..........	PUNCT
ejpam-4848	387	3	.	.	PUNCT
ejpam-4848	388	1	..........................................	..........................................	PUNCT
ejpam-4848	388	2	...........	...........	PUNCT
ejpam-4848	389	1	..........	..........	PUNCT
ejpam-4848	389	2	..........	..........	PUNCT
ejpam-4848	390	1	..........	..........	PUNCT
ejpam-4848	390	2	.	.	PUNCT
ejpam-4848	391	1	..........................................	..........................................	PUNCT
ejpam-4848	391	2	................................................................................	................................................................................	PUNCT
ejpam-4848	392	1	..............................................................	..............................................................	PUNCT
ejpam-4848	392	2	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4848	393	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4848	393	2	..............................................................................................................................................................................	..............................................................................................................................................................................	PUNCT
ejpam-4848	394	1	................	................	PUNCT
ejpam-4848	394	2	................	................	PUNCT
ejpam-4848	395	1	................	................	PUNCT
ejpam-4848	395	2	................	................	PUNCT
ejpam-4848	396	1	................	................	PUNCT
ejpam-4848	396	2	................	................	PUNCT
ejpam-4848	397	1	................	................	PUNCT
ejpam-4848	397	2	................	................	PUNCT
ejpam-4848	397	3	............	............	PUNCT
ejpam-4848	397	4	........................	........................	PUNCT
ejpam-4848	397	5	.......................	.......................	PUNCT
ejpam-4848	398	1	.......................	.......................	PUNCT
ejpam-4848	398	2	.......................	.......................	PUNCT
ejpam-4848	399	1	...................	...................	PUNCT
ejpam-4848	399	2	............	............	PUNCT
ejpam-4848	399	3	...........	...........	PUNCT
ejpam-4848	399	4	...........	...........	PUNCT
ejpam-4848	399	5	...........	...........	PUNCT
ejpam-4848	399	6	...........	...........	PUNCT
ejpam-4848	399	7	...........	...........	PUNCT
ejpam-4848	399	8	...........	...........	PUNCT
ejpam-4848	399	9	...........	...........	PUNCT
ejpam-4848	399	10	...........	...........	PUNCT
ejpam-4848	399	11	...........	...........	PUNCT
ejpam-4848	399	12	..............	..............	PUNCT
ejpam-4848	399	13	.............	.............	PUNCT
ejpam-4848	399	14	.............	.............	PUNCT
ejpam-4848	399	15	.............	.............	PUNCT
ejpam-4848	400	1	.........	.........	PUNCT
ejpam-4848	400	2	..........	..........	PUNCT
ejpam-4848	401	1	.........	.........	PUNCT
ejpam-4848	401	2	.........	.........	PUNCT
ejpam-4848	402	1	.........	.........	PUNCT
ejpam-4848	402	2	.........	.........	PUNCT
ejpam-4848	403	1	.........	.........	PUNCT
ejpam-4848	403	2	.........	.........	PUNCT
ejpam-4848	404	1	.........	.........	PUNCT
ejpam-4848	404	2	.......	.......	PUNCT
ejpam-4848	404	3	...............	...............	PUNCT
ejpam-4848	405	1	..............	..............	PUNCT
ejpam-4848	405	2	.............	.............	PUNCT
ejpam-4848	405	3	..........................................	..........................................	PUNCT
ejpam-4848	405	4	...............	...............	PUNCT
ejpam-4848	406	1	..............	..............	PUNCT
ejpam-4848	406	2	.............	.............	PUNCT
ejpam-4848	406	3	..........................................	..........................................	PUNCT
ejpam-4848	406	4	...........	...........	PUNCT
ejpam-4848	407	1	..........	..........	PUNCT
ejpam-4848	407	2	..........	..........	PUNCT
ejpam-4848	408	1	..........	..........	PUNCT
ejpam-4848	408	2	..........	..........	PUNCT
ejpam-4848	409	1	..........	..........	PUNCT
ejpam-4848	409	2	..........	..........	PUNCT
ejpam-4848	410	1	..........	..........	PUNCT
ejpam-4848	410	2	..........	..........	PUNCT
ejpam-4848	411	1	..........	..........	PUNCT
ejpam-4848	411	2	..........	..........	PUNCT
ejpam-4848	412	1	..........	..........	PUNCT
ejpam-4848	412	2	..........	..........	PUNCT
ejpam-4848	413	1	..........	..........	PUNCT
ejpam-4848	413	2	..........	..........	PUNCT
ejpam-4848	414	1	......	......	PUNCT
ejpam-4848	414	2	..........	..........	PUNCT
ejpam-4848	415	1	.........	.........	PUNCT
ejpam-4848	415	2	.........	.........	PUNCT
ejpam-4848	416	1	.........	.........	PUNCT
ejpam-4848	416	2	.........	.........	PUNCT
ejpam-4848	417	1	.........	.........	PUNCT
ejpam-4848	417	2	.........	.........	PUNCT
ejpam-4848	418	1	.........	.........	PUNCT
ejpam-4848	418	2	.........	.........	PUNCT
ejpam-4848	419	1	.........	.........	PUNCT
ejpam-4848	419	2	.........	.........	PUNCT
ejpam-4848	420	1	.........	.........	PUNCT
ejpam-4848	420	2	...	...	PUNCT
ejpam-4848	420	3	............	............	PUNCT
ejpam-4848	420	4	...........	...........	PUNCT
ejpam-4848	420	5	...........	...........	PUNCT
ejpam-4848	420	6	...........	...........	PUNCT
ejpam-4848	420	7	...........	...........	PUNCT
ejpam-4848	420	8	...........	...........	PUNCT
ejpam-4848	420	9	...........	...........	PUNCT
ejpam-4848	420	10	...........	...........	PUNCT
ejpam-4848	420	11	...........	...........	PUNCT
ejpam-4848	420	12	...........	...........	PUNCT
ejpam-4848	420	13	...........	...........	PUNCT
ejpam-4848	420	14	..........	..........	PUNCT
ejpam-4848	421	1	..........	..........	PUNCT
ejpam-4848	421	2	..........	..........	PUNCT
ejpam-4848	422	1	..........	..........	PUNCT
ejpam-4848	422	2	..........	..........	PUNCT
ejpam-4848	422	3	.	.	PUNCT
ejpam-4848	423	1	..........................	..........................	PUNCT
ejpam-4848	423	2	.........................	.........................	PUNCT
ejpam-4848	424	1	.........................	.........................	PUNCT
ejpam-4848	424	2	....	....	PUNCT
ejpam-4848	425	1	................................................................................	................................................................................	PUNCT
ejpam-4848	425	2	..............................................................	..............................................................	PUNCT
ejpam-4848	426	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4848	426	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4848	426	3	.............................................................................................................................................................	.............................................................................................................................................................	PUNCT
ejpam-4848	426	4	...............	...............	PUNCT
ejpam-4848	427	1	..............	..............	PUNCT
ejpam-4848	427	2	.............	.............	PUNCT
ejpam-4848	427	3	..........................................	..........................................	PUNCT
ejpam-4848	427	4	...............	...............	PUNCT
ejpam-4848	428	1	..............	..............	PUNCT
ejpam-4848	428	2	.............	.............	PUNCT
ejpam-4848	428	3	..........................................	..........................................	PUNCT
ejpam-4848	428	4	................................................................................	................................................................................	PUNCT
ejpam-4848	429	1	..............................................................	..............................................................	PUNCT
ejpam-4848	429	2	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4848	430	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4848	430	2	.............................................................................................................................................................	.............................................................................................................................................................	PUNCT
ejpam-4848	431	1	...........	...........	PUNCT
ejpam-4848	431	2	..........	..........	PUNCT
ejpam-4848	432	1	..........	..........	PUNCT
ejpam-4848	432	2	..........	..........	PUNCT
ejpam-4848	433	1	..........	..........	PUNCT
ejpam-4848	433	2	..........	..........	PUNCT
ejpam-4848	434	1	..........	..........	PUNCT
ejpam-4848	434	2	..........	..........	PUNCT
ejpam-4848	435	1	..........	..........	PUNCT
ejpam-4848	435	2	..........	..........	PUNCT
ejpam-4848	436	1	..........	..........	PUNCT
ejpam-4848	436	2	..........	..........	PUNCT
ejpam-4848	437	1	..........	..........	PUNCT
ejpam-4848	437	2	..........	..........	PUNCT
ejpam-4848	438	1	..........	..........	PUNCT
ejpam-4848	438	2	......	......	PUNCT
ejpam-4848	439	1	..........	..........	PUNCT
ejpam-4848	439	2	.........	.........	PUNCT
ejpam-4848	440	1	.........	.........	PUNCT
ejpam-4848	440	2	.........	.........	PUNCT
ejpam-4848	441	1	.........	.........	PUNCT
ejpam-4848	441	2	.........	.........	PUNCT
ejpam-4848	442	1	.........	.........	PUNCT
ejpam-4848	442	2	.........	.........	PUNCT
ejpam-4848	443	1	.........	.........	PUNCT
ejpam-4848	443	2	.........	.........	PUNCT
ejpam-4848	444	1	.........	.........	PUNCT
ejpam-4848	444	2	.........	.........	PUNCT
ejpam-4848	444	3	...	...	PUNCT
ejpam-4848	444	4	............	............	PUNCT
ejpam-4848	444	5	...........	...........	PUNCT
ejpam-4848	444	6	...........	...........	PUNCT
ejpam-4848	444	7	...........	...........	PUNCT
ejpam-4848	444	8	...........	...........	PUNCT
ejpam-4848	444	9	...........	...........	PUNCT
ejpam-4848	444	10	...........	...........	PUNCT
ejpam-4848	444	11	...........	...........	PUNCT
ejpam-4848	444	12	...........	...........	PUNCT
ejpam-4848	444	13	...........	...........	PUNCT
ejpam-4848	444	14	...........	...........	PUNCT
ejpam-4848	444	15	..........	..........	PUNCT
ejpam-4848	445	1	..........	..........	PUNCT
ejpam-4848	445	2	..........	..........	PUNCT
ejpam-4848	446	1	..........	..........	PUNCT
ejpam-4848	446	2	..........	..........	PUNCT
ejpam-4848	446	3	.	.	PUNCT
ejpam-4848	447	1	..........................	..........................	PUNCT
ejpam-4848	447	2	.........................	.........................	PUNCT
ejpam-4848	448	1	.........................	.........................	PUNCT
ejpam-4848	448	2	....	....	PUNCT
ejpam-4848	449	1	•p	•p	NOUN
ejpam-4848	449	2	u	u	NOUN
ejpam-4848	449	3	v	v	NOUN
ejpam-4848	449	4	figure	figure	NOUN
ejpam-4848	449	5	7	7	NUM
ejpam-4848	449	6	:	:	PUNCT
ejpam-4848	449	7	the	the	DET
ejpam-4848	449	8	edge	edge	NOUN
ejpam-4848	449	9	corona	corona	NOUN
ejpam-4848	449	10	graph	graph	NOUN
ejpam-4848	449	11	of	of	ADP
ejpam-4848	449	12	c4	c4	NOUN
ejpam-4848	449	13	⋄	⋄	PROPN
ejpam-4848	449	14	p5	p5	ADJ
ejpam-4848	449	15	with	with	ADP
ejpam-4848	449	16	point	point	NOUN
ejpam-4848	449	17	p	p	NOUN
ejpam-4848	449	18	in	in	ADP
ejpam-4848	449	19	he	he	PRON
ejpam-4848	449	20	lemma	lemma	PROPN
ejpam-4848	449	21	2	2	X
ejpam-4848	449	22	.	.	PUNCT
ejpam-4848	450	1	let	let	VERB
ejpam-4848	450	2	g	g	PRON
ejpam-4848	450	3	be	be	AUX
ejpam-4848	450	4	a	a	DET
ejpam-4848	450	5	non	non	ADJ
ejpam-4848	450	6	-	-	ADJ
ejpam-4848	450	7	trivial	trivial	ADJ
ejpam-4848	450	8	connected	connected	ADJ
ejpam-4848	450	9	graph	graph	NOUN
ejpam-4848	450	10	and	and	CCONJ
ejpam-4848	450	11	let	let	VERB
ejpam-4848	450	12	v	v	NOUN
ejpam-4848	450	13	,	,	PUNCT
ejpam-4848	450	14	x	x	SYM
ejpam-4848	450	15	∈	∈	NOUN
ejpam-4848	450	16	v	v	X
ejpam-4848	450	17	(	(	PUNCT
ejpam-4848	450	18	g	g	NOUN
ejpam-4848	450	19	)	)	PUNCT
ejpam-4848	450	20	.	.	PUNCT
ejpam-4848	451	1	then	then	ADV
ejpam-4848	451	2	dgg(v	dgg(v	PUNCT
ejpam-4848	451	3	,	,	PUNCT
ejpam-4848	451	4	x	x	NOUN
ejpam-4848	451	5	)	)	PUNCT
ejpam-4848	451	6	=	=	PUNCT
ejpam-4848	451	7			NOUN
ejpam-4848	451	8	0	0	PUNCT
ejpam-4848	452	1	if	if	SCONJ
ejpam-4848	452	2	x	x	X
ejpam-4848	452	3	=	=	SYM
ejpam-4848	452	4	v	v	ADP
ejpam-4848	452	5	1	1	NUM
ejpam-4848	452	6	if	if	SCONJ
ejpam-4848	452	7	vx	vx	PROPN
ejpam-4848	452	8	∈	∈	PROPN
ejpam-4848	452	9	e(g	e(g	PROPN
ejpam-4848	452	10	)	)	PUNCT
ejpam-4848	452	11	2	2	NUM
ejpam-4848	452	12	if	if	SCONJ
ejpam-4848	452	13	dg(v	dg(v	NOUN
ejpam-4848	452	14	,	,	PUNCT
ejpam-4848	452	15	x	x	X
ejpam-4848	452	16	)	)	PUNCT
ejpam-4848	452	17	=	=	SYM
ejpam-4848	452	18	2	2	NUM
ejpam-4848	452	19	3	3	NUM
ejpam-4848	452	20	if	if	SCONJ
ejpam-4848	452	21	dg(v	dg(v	NOUN
ejpam-4848	452	22	,	,	PUNCT
ejpam-4848	452	23	x	x	X
ejpam-4848	452	24	)	)	PUNCT
ejpam-4848	452	25	≥	≥	NOUN
ejpam-4848	452	26	3	3	NUM
ejpam-4848	452	27	f.	f.	PROPN
ejpam-4848	452	28	alfeche	alfeche	PROPN
ejpam-4848	452	29	,	,	PUNCT
ejpam-4848	452	30	v.	v.	PROPN
ejpam-4848	452	31	barraza	barraza	PROPN
ejpam-4848	452	32	,	,	PUNCT
ejpam-4848	452	33	s.	s.	PROPN
ejpam-4848	452	34	canoy	canoy	PROPN
ejpam-4848	452	35	,	,	PUNCT
ejpam-4848	452	36	jr	jr	PROPN
ejpam-4848	452	37	.	.	PROPN
ejpam-4848	452	38	/	/	SYM
ejpam-4848	452	39	eur	eur	PROPN
ejpam-4848	452	40	.	.	PUNCT
ejpam-4848	453	1	j.	j.	PROPN
ejpam-4848	453	2	pure	pure	PROPN
ejpam-4848	453	3	appl	appl	PROPN
ejpam-4848	453	4	.	.	PROPN
ejpam-4848	453	5	math	math	PROPN
ejpam-4848	453	6	,	,	PUNCT
ejpam-4848	453	7	16	16	NUM
ejpam-4848	453	8	(	(	PUNCT
ejpam-4848	453	9	3	3	NUM
ejpam-4848	453	10	)	)	PUNCT
ejpam-4848	453	11	(	(	PUNCT
ejpam-4848	453	12	2023	2023	NUM
ejpam-4848	453	13	)	)	PUNCT
ejpam-4848	453	14	,	,	PUNCT
ejpam-4848	453	15	1406	1406	NUM
ejpam-4848	453	16	-	-	SYM
ejpam-4848	453	17	1420	1420	NUM
ejpam-4848	453	18	1415	1415	NUM
ejpam-4848	453	19	proof	proof	NOUN
ejpam-4848	453	20	.	.	PUNCT
ejpam-4848	454	1	clearly	clearly	ADV
ejpam-4848	454	2	,	,	PUNCT
ejpam-4848	454	3	dgg(v	dgg(v	PROPN
ejpam-4848	454	4	,	,	PUNCT
ejpam-4848	454	5	x	x	NOUN
ejpam-4848	454	6	)	)	PUNCT
ejpam-4848	454	7	=	=	SYM
ejpam-4848	454	8	dg(v	dg(v	X
ejpam-4848	454	9	,	,	PUNCT
ejpam-4848	454	10	x	x	X
ejpam-4848	454	11	)	)	PUNCT
ejpam-4848	454	12	if	if	SCONJ
ejpam-4848	454	13	1	1	NUM
ejpam-4848	454	14	≤	≤	X
ejpam-4848	454	15	dg(v	dg(v	NOUN
ejpam-4848	454	16	,	,	PUNCT
ejpam-4848	454	17	x	x	NOUN
ejpam-4848	454	18	)	)	PUNCT
ejpam-4848	454	19	≤	≤	NUM
ejpam-4848	454	20	2	2	NUM
ejpam-4848	454	21	.	.	PUNCT
ejpam-4848	454	22	suppose	suppose	VERB
ejpam-4848	454	23	dg(v	dg(v	NOUN
ejpam-4848	454	24	,	,	PUNCT
ejpam-4848	454	25	x	x	X
ejpam-4848	454	26	)	)	PUNCT
ejpam-4848	454	27	≥	≥	NOUN
ejpam-4848	454	28	3	3	NUM
ejpam-4848	454	29	.	.	PUNCT
ejpam-4848	455	1	then	then	ADV
ejpam-4848	455	2	dgg(v	dgg(v	PROPN
ejpam-4848	455	3	,	,	PUNCT
ejpam-4848	455	4	x	x	X
ejpam-4848	455	5	)	)	PUNCT
ejpam-4848	455	6	≥	≥	NOUN
ejpam-4848	455	7	3	3	NUM
ejpam-4848	455	8	.	.	PUNCT
ejpam-4848	456	1	since	since	SCONJ
ejpam-4848	456	2	v	v	NUM
ejpam-4848	456	3	x	x	SYM
ejpam-4848	456	4	∈	∈	PROPN
ejpam-4848	456	5	e(g	e(g	PROPN
ejpam-4848	456	6	)	)	PUNCT
ejpam-4848	456	7	,	,	PUNCT
ejpam-4848	456	8	it	it	PRON
ejpam-4848	456	9	follows	follow	VERB
ejpam-4848	456	10	that	that	SCONJ
ejpam-4848	456	11	[	[	X
ejpam-4848	456	12	v	v	NOUN
ejpam-4848	456	13	,	,	PUNCT
ejpam-4848	456	14	v	v	NOUN
ejpam-4848	456	15	,	,	PUNCT
ejpam-4848	456	16	x	x	X
ejpam-4848	456	17	,	,	PUNCT
ejpam-4848	456	18	x	x	X
ejpam-4848	456	19	]	]	X
ejpam-4848	456	20	is	be	AUX
ejpam-4848	456	21	a	a	DET
ejpam-4848	456	22	v	v	NOUN
ejpam-4848	456	23	-	-	PUNCT
ejpam-4848	456	24	x	x	NOUN
ejpam-4848	456	25	geodesic	geodesic	NOUN
ejpam-4848	456	26	in	in	ADP
ejpam-4848	456	27	gg	gg	PROPN
ejpam-4848	456	28	.	.	PUNCT
ejpam-4848	457	1	hence	hence	ADV
ejpam-4848	457	2	,	,	PUNCT
ejpam-4848	457	3	dgg(v	dgg(v	PROPN
ejpam-4848	457	4	,	,	PUNCT
ejpam-4848	457	5	x	x	NOUN
ejpam-4848	457	6	)	)	PUNCT
ejpam-4848	457	7	=	=	SYM
ejpam-4848	458	1	3	3	X
ejpam-4848	458	2	.	.	X
ejpam-4848	458	3	lemma	lemma	PROPN
ejpam-4848	458	4	3	3	X
ejpam-4848	458	5	.	.	PUNCT
ejpam-4848	459	1	let	let	VERB
ejpam-4848	459	2	g	g	PRON
ejpam-4848	459	3	be	be	AUX
ejpam-4848	459	4	a	a	DET
ejpam-4848	459	5	non	non	ADJ
ejpam-4848	459	6	-	-	ADJ
ejpam-4848	459	7	trivial	trivial	ADJ
ejpam-4848	459	8	connected	connected	ADJ
ejpam-4848	459	9	graph	graph	NOUN
ejpam-4848	459	10	and	and	CCONJ
ejpam-4848	459	11	let	let	VERB
ejpam-4848	459	12	v	v	NOUN
ejpam-4848	459	13	,	,	PUNCT
ejpam-4848	459	14	x	x	SYM
ejpam-4848	459	15	∈	∈	NOUN
ejpam-4848	459	16	v	v	X
ejpam-4848	459	17	(	(	PUNCT
ejpam-4848	459	18	g	g	NOUN
ejpam-4848	459	19	)	)	PUNCT
ejpam-4848	459	20	.	.	PUNCT
ejpam-4848	460	1	then	then	ADV
ejpam-4848	460	2	dgg(v	dgg(v	PUNCT
ejpam-4848	460	3	,	,	PUNCT
ejpam-4848	460	4	x	x	NOUN
ejpam-4848	460	5	)	)	PUNCT
ejpam-4848	460	6	=	=	SYM
ejpam-4848	460	7	{	{	PUNCT
ejpam-4848	460	8	1	1	NUM
ejpam-4848	460	9	if	if	SCONJ
ejpam-4848	460	10	x	x	X
ejpam-4848	460	11	=	=	SYM
ejpam-4848	460	12	v	v	NUM
ejpam-4848	460	13	2	2	NUM
ejpam-4848	460	14	otherwise	otherwise	ADV
ejpam-4848	460	15	proof	proof	NOUN
ejpam-4848	460	16	.	.	PUNCT
ejpam-4848	461	1	if	if	SCONJ
ejpam-4848	461	2	x	x	X
ejpam-4848	461	3	=	=	SYM
ejpam-4848	461	4	v	v	NOUN
ejpam-4848	461	5	,	,	PUNCT
ejpam-4848	461	6	then	then	ADV
ejpam-4848	461	7	dgg(v	dgg(v	PROPN
ejpam-4848	461	8	,	,	PUNCT
ejpam-4848	461	9	v	v	NOUN
ejpam-4848	461	10	)	)	PUNCT
ejpam-4848	461	11	=	=	SYM
ejpam-4848	461	12	1	1	NUM
ejpam-4848	461	13	by	by	ADP
ejpam-4848	461	14	definition	definition	NOUN
ejpam-4848	461	15	of	of	ADP
ejpam-4848	461	16	gg	gg	PROPN
ejpam-4848	461	17	.	.	PUNCT
ejpam-4848	461	18	suppose	suppose	VERB
ejpam-4848	461	19	x	x	X
ejpam-4848	461	20	̸=	̸=	PROPN
ejpam-4848	461	21	v	v	ADP
ejpam-4848	461	22	,	,	PUNCT
ejpam-4848	461	23	i.e.	i.e.	X
ejpam-4848	461	24	,	,	PUNCT
ejpam-4848	461	25	x	x	PUNCT
ejpam-4848	461	26	̸=	̸=	PROPN
ejpam-4848	461	27	v.	v.	ADP
ejpam-4848	461	28	if	if	SCONJ
ejpam-4848	461	29	xv	xv	PROPN
ejpam-4848	461	30	∈	∈	PROPN
ejpam-4848	461	31	e(g	e(g	PROPN
ejpam-4848	461	32	)	)	PUNCT
ejpam-4848	461	33	,	,	PUNCT
ejpam-4848	461	34	then	then	ADV
ejpam-4848	461	35	xv	xv	PROPN
ejpam-4848	461	36	/∈	/∈	PUNCT
ejpam-4848	461	37	e(gg	e(gg	NUM
ejpam-4848	461	38	)	)	PUNCT
ejpam-4848	461	39	and	and	CCONJ
ejpam-4848	461	40	[	[	X
ejpam-4848	461	41	v	v	NOUN
ejpam-4848	461	42	,	,	PUNCT
ejpam-4848	461	43	x	x	X
ejpam-4848	461	44	,	,	PUNCT
ejpam-4848	461	45	x	x	X
ejpam-4848	461	46	]	]	X
ejpam-4848	461	47	is	be	AUX
ejpam-4848	461	48	a	a	DET
ejpam-4848	461	49	v	v	NOUN
ejpam-4848	461	50	−	−	NOUN
ejpam-4848	461	51	x	x	PUNCT
ejpam-4848	461	52	geodesic	geodesic	NOUN
ejpam-4848	461	53	in	in	ADP
ejpam-4848	461	54	gg	gg	PROPN
ejpam-4848	461	55	.	.	PUNCT
ejpam-4848	462	1	if	if	SCONJ
ejpam-4848	462	2	xv	xv	PROPN
ejpam-4848	462	3	/∈	/∈	PROPN
ejpam-4848	462	4	e(g	e(g	PROPN
ejpam-4848	462	5	)	)	PUNCT
ejpam-4848	462	6	,	,	PUNCT
ejpam-4848	462	7	then	then	ADV
ejpam-4848	462	8	xv	xv	PROPN
ejpam-4848	462	9	∈	∈	PROPN
ejpam-4848	462	10	e(g	e(g	PROPN
ejpam-4848	462	11	)	)	PUNCT
ejpam-4848	462	12	.	.	PUNCT
ejpam-4848	463	1	hence	hence	ADV
ejpam-4848	463	2	,	,	PUNCT
ejpam-4848	463	3	[	[	X
ejpam-4848	463	4	v	v	NOUN
ejpam-4848	463	5	,	,	PUNCT
ejpam-4848	463	6	v	v	NOUN
ejpam-4848	463	7	,	,	PUNCT
ejpam-4848	463	8	x	x	X
ejpam-4848	463	9	]	]	X
ejpam-4848	463	10	is	be	AUX
ejpam-4848	463	11	a	a	DET
ejpam-4848	463	12	v	v	NOUN
ejpam-4848	463	13	-	-	PUNCT
ejpam-4848	463	14	x	x	NOUN
ejpam-4848	463	15	geodesic	geodesic	NOUN
ejpam-4848	463	16	in	in	ADP
ejpam-4848	463	17	gg	gg	PROPN
ejpam-4848	463	18	.	.	PUNCT
ejpam-4848	464	1	thus	thus	ADV
ejpam-4848	464	2	dgg(v	dgg(v	PROPN
ejpam-4848	464	3	,	,	PUNCT
ejpam-4848	464	4	x	x	NOUN
ejpam-4848	464	5	)	)	PUNCT
ejpam-4848	464	6	=	=	SYM
ejpam-4848	465	1	2	2	X
ejpam-4848	465	2	.	.	X
ejpam-4848	465	3	lemma	lemma	PROPN
ejpam-4848	465	4	4	4	X
ejpam-4848	465	5	.	.	PUNCT
ejpam-4848	466	1	let	let	VERB
ejpam-4848	466	2	g	g	PRON
ejpam-4848	466	3	be	be	AUX
ejpam-4848	466	4	a	a	DET
ejpam-4848	466	5	non	non	ADJ
ejpam-4848	466	6	-	-	ADJ
ejpam-4848	466	7	trivial	trivial	ADJ
ejpam-4848	466	8	connected	connected	ADJ
ejpam-4848	466	9	graph	graph	NOUN
ejpam-4848	466	10	and	and	CCONJ
ejpam-4848	466	11	let	let	VERB
ejpam-4848	466	12	v	v	NOUN
ejpam-4848	466	13	,	,	PUNCT
ejpam-4848	466	14	x	x	SYM
ejpam-4848	466	15	∈	∈	NOUN
ejpam-4848	466	16	v	v	X
ejpam-4848	466	17	(	(	PUNCT
ejpam-4848	466	18	g	g	NOUN
ejpam-4848	466	19	)	)	PUNCT
ejpam-4848	466	20	.	.	PUNCT
ejpam-4848	467	1	then	then	ADV
ejpam-4848	467	2	dgg(v	dgg(v	PUNCT
ejpam-4848	467	3	,	,	PUNCT
ejpam-4848	467	4	x	x	NOUN
ejpam-4848	467	5	)	)	PUNCT
ejpam-4848	467	6	=	=	PUNCT
ejpam-4848	467	7			NOUN
ejpam-4848	467	8	0	0	PUNCT
ejpam-4848	468	1	x	x	X
ejpam-4848	468	2	=	=	SYM
ejpam-4848	468	3	v	v	NUM
ejpam-4848	468	4	1	1	NUM
ejpam-4848	468	5	if	if	SCONJ
ejpam-4848	468	6	xv	xv	PROPN
ejpam-4848	468	7	/∈	/∈	PUNCT
ejpam-4848	468	8	e(g	e(g	PROPN
ejpam-4848	468	9	)	)	PUNCT
ejpam-4848	468	10	,	,	PUNCT
ejpam-4848	468	11	x	x	X
ejpam-4848	468	12	̸=	̸=	PROPN
ejpam-4848	468	13	v	v	ADP
ejpam-4848	468	14	2	2	NUM
ejpam-4848	468	15	if	if	SCONJ
ejpam-4848	468	16	xv	xv	PROPN
ejpam-4848	468	17	∈	∈	PROPN
ejpam-4848	468	18	e(g	e(g	PROPN
ejpam-4848	468	19	)	)	PUNCT
ejpam-4848	468	20	and	and	CCONJ
ejpam-4848	468	21	(	(	PUNCT
ejpam-4848	468	22	v	v	NOUN
ejpam-4848	468	23	(	(	PUNCT
ejpam-4848	468	24	g	g	NOUN
ejpam-4848	468	25	)	)	PUNCT
ejpam-4848	468	26	\ng[x	\ng[x	PROPN
ejpam-4848	468	27	]	]	PUNCT
ejpam-4848	468	28	)	)	PUNCT
ejpam-4848	468	29	∩	∩	NOUN
ejpam-4848	468	30	(	(	PUNCT
ejpam-4848	468	31	v	v	NOUN
ejpam-4848	468	32	(	(	PUNCT
ejpam-4848	468	33	g	g	NOUN
ejpam-4848	468	34	)	)	PUNCT
ejpam-4848	468	35	\ng[v	\ng[v	NOUN
ejpam-4848	468	36	]	]	PUNCT
ejpam-4848	468	37	)	)	PUNCT
ejpam-4848	469	1	̸=	̸=	PROPN
ejpam-4848	469	2	ø	ø	PROPN
ejpam-4848	469	3	,	,	PUNCT
ejpam-4848	469	4	x	x	PROPN
ejpam-4848	469	5	̸=	̸=	PROPN
ejpam-4848	469	6	v	v	ADP
ejpam-4848	469	7	3	3	NUM
ejpam-4848	469	8	if	if	SCONJ
ejpam-4848	469	9	xv	xv	PROPN
ejpam-4848	469	10	∈	∈	PROPN
ejpam-4848	469	11	e(g	e(g	PROPN
ejpam-4848	469	12	)	)	PUNCT
ejpam-4848	469	13	and	and	CCONJ
ejpam-4848	469	14	(	(	PUNCT
ejpam-4848	469	15	v	v	NOUN
ejpam-4848	469	16	(	(	PUNCT
ejpam-4848	469	17	g	g	NOUN
ejpam-4848	469	18	)	)	PUNCT
ejpam-4848	469	19	\ng[x	\ng[x	PROPN
ejpam-4848	469	20	]	]	PUNCT
ejpam-4848	469	21	)	)	PUNCT
ejpam-4848	469	22	∩	∩	NOUN
ejpam-4848	469	23	(	(	PUNCT
ejpam-4848	469	24	v	v	NOUN
ejpam-4848	469	25	(	(	PUNCT
ejpam-4848	469	26	g	g	NOUN
ejpam-4848	469	27	)	)	PUNCT
ejpam-4848	469	28	\ng[v	\ng[v	NOUN
ejpam-4848	469	29	]	]	PUNCT
ejpam-4848	469	30	)	)	PUNCT
ejpam-4848	469	31	=	=	SYM
ejpam-4848	469	32	ø	ø	PROPN
ejpam-4848	469	33	,	,	PUNCT
ejpam-4848	469	34	x	x	PART
ejpam-4848	469	35	̸=	̸=	PROPN
ejpam-4848	469	36	v	v	ADP
ejpam-4848	469	37	proof	proof	NOUN
ejpam-4848	469	38	.	.	PUNCT
ejpam-4848	470	1	clearly	clearly	ADV
ejpam-4848	470	2	,	,	PUNCT
ejpam-4848	470	3	dgg(v	dgg(v	PROPN
ejpam-4848	470	4	,	,	PUNCT
ejpam-4848	470	5	v	v	NOUN
ejpam-4848	470	6	)	)	PUNCT
ejpam-4848	470	7	=	=	SYM
ejpam-4848	470	8	0	0	NUM
ejpam-4848	470	9	and	and	CCONJ
ejpam-4848	470	10	dgg(v	dgg(v	PROPN
ejpam-4848	470	11	,	,	PUNCT
ejpam-4848	470	12	x	x	NOUN
ejpam-4848	470	13	)	)	PUNCT
ejpam-4848	470	14	=	=	SYM
ejpam-4848	470	15	1	1	NUM
ejpam-4848	470	16	if	if	SCONJ
ejpam-4848	470	17	xv	xv	PROPN
ejpam-4848	470	18	/∈	/∈	PUNCT
ejpam-4848	470	19	e(g	e(g	PROPN
ejpam-4848	470	20	)	)	PUNCT
ejpam-4848	470	21	.	.	PUNCT
ejpam-4848	471	1	next	next	ADV
ejpam-4848	471	2	,	,	PUNCT
ejpam-4848	471	3	suppose	suppose	VERB
ejpam-4848	471	4	that	that	SCONJ
ejpam-4848	471	5	xv	xv	PROPN
ejpam-4848	471	6	∈	∈	PROPN
ejpam-4848	471	7	e(g	e(g	PROPN
ejpam-4848	471	8	)	)	PUNCT
ejpam-4848	471	9	.	.	PUNCT
ejpam-4848	472	1	then	then	ADV
ejpam-4848	472	2	dgg(v	dgg(v	PUNCT
ejpam-4848	472	3	,	,	PUNCT
ejpam-4848	472	4	x	x	X
ejpam-4848	472	5	)	)	PUNCT
ejpam-4848	472	6	≥	≥	NOUN
ejpam-4848	472	7	2	2	NUM
ejpam-4848	472	8	.	.	PUNCT
ejpam-4848	472	9	suppose	suppose	VERB
ejpam-4848	472	10	there	there	PRON
ejpam-4848	472	11	exists	exist	VERB
ejpam-4848	472	12	z	z	PROPN
ejpam-4848	472	13	∈	∈	PROPN
ejpam-4848	472	14	(	(	PUNCT
ejpam-4848	472	15	v	v	NOUN
ejpam-4848	472	16	(	(	PUNCT
ejpam-4848	472	17	g)\ng[x])∩(v	g)\ng[x])∩(v	PROPN
ejpam-4848	472	18	(	(	PUNCT
ejpam-4848	472	19	g)\ng[v	g)\ng[v	PROPN
ejpam-4848	472	20	]	]	PUNCT
ejpam-4848	472	21	)	)	PUNCT
ejpam-4848	472	22	.	.	PUNCT
ejpam-4848	473	1	then	then	ADV
ejpam-4848	473	2	x̄z̄	x̄z̄	PROPN
ejpam-4848	473	3	,	,	PUNCT
ejpam-4848	473	4	z̄v̄	z̄v̄	PROPN
ejpam-4848	473	5	∈	∈	PROPN
ejpam-4848	473	6	e(g	e(g	PROPN
ejpam-4848	473	7	)	)	PUNCT
ejpam-4848	473	8	.	.	PUNCT
ejpam-4848	474	1	hence	hence	ADV
ejpam-4848	474	2	,	,	PUNCT
ejpam-4848	474	3	[	[	X
ejpam-4848	474	4	v̄	v̄	ADJ
ejpam-4848	474	5	,	,	PUNCT
ejpam-4848	474	6	z̄	z̄	X
ejpam-4848	474	7	,	,	PUNCT
ejpam-4848	474	8	x	x	X
ejpam-4848	474	9	]	]	X
ejpam-4848	474	10	is	be	AUX
ejpam-4848	474	11	a	a	DET
ejpam-4848	474	12	v	v	NOUN
ejpam-4848	474	13	x	x	NOUN
ejpam-4848	474	14	geodesic	geodesic	NOUN
ejpam-4848	474	15	on	on	ADP
ejpam-4848	474	16	gg	gg	PROPN
ejpam-4848	474	17	.	.	PUNCT
ejpam-4848	475	1	thus	thus	ADV
ejpam-4848	475	2	,	,	PUNCT
ejpam-4848	475	3	dg(v	dg(v	X
ejpam-4848	475	4	,	,	PUNCT
ejpam-4848	475	5	x	x	X
ejpam-4848	475	6	)	)	PUNCT
ejpam-4848	475	7	=	=	SYM
ejpam-4848	476	1	2	2	X
ejpam-4848	476	2	.	.	PUNCT
ejpam-4848	477	1	next	next	ADV
ejpam-4848	477	2	,	,	PUNCT
ejpam-4848	477	3	suppose	suppose	VERB
ejpam-4848	477	4	that	that	SCONJ
ejpam-4848	477	5	(	(	PUNCT
ejpam-4848	477	6	v	v	X
ejpam-4848	477	7	(	(	PUNCT
ejpam-4848	477	8	g	g	NOUN
ejpam-4848	477	9	)	)	PUNCT
ejpam-4848	477	10	\	\	PUNCT
ejpam-4848	477	11	ng[x	ng[x	PROPN
ejpam-4848	477	12	]	]	PUNCT
ejpam-4848	477	13	)	)	PUNCT
ejpam-4848	477	14	∩	∩	NOUN
ejpam-4848	477	15	(	(	PUNCT
ejpam-4848	477	16	v	v	NOUN
ejpam-4848	477	17	(	(	PUNCT
ejpam-4848	477	18	g	g	NOUN
ejpam-4848	477	19	)	)	PUNCT
ejpam-4848	477	20	\	\	PUNCT
ejpam-4848	478	1	ng[v	ng[v	ADV
ejpam-4848	478	2	]	]	X
ejpam-4848	478	3	)	)	PUNCT
ejpam-4848	478	4	=	=	VERB
ejpam-4848	478	5	∅.	∅.	ADV
ejpam-4848	478	6	suppose	suppose	VERB
ejpam-4848	478	7	[	[	X
ejpam-4848	478	8	v	v	NOUN
ejpam-4848	478	9	,	,	PUNCT
ejpam-4848	478	10	p	p	X
ejpam-4848	478	11	,	,	PUNCT
ejpam-4848	478	12	x	x	X
ejpam-4848	478	13	]	]	X
ejpam-4848	478	14	is	be	AUX
ejpam-4848	478	15	a	a	DET
ejpam-4848	478	16	v	v	NOUN
ejpam-4848	478	17	x	x	SYM
ejpam-4848	478	18	geodesic	geodesic	NOUN
ejpam-4848	478	19	in	in	ADP
ejpam-4848	478	20	gg	gg	PROPN
ejpam-4848	478	21	.	.	PUNCT
ejpam-4848	478	22	suppose	suppose	VERB
ejpam-4848	478	23	first	first	ADV
ejpam-4848	478	24	that	that	SCONJ
ejpam-4848	478	25	p	p	PROPN
ejpam-4848	478	26	∈	∈	PROPN
ejpam-4848	478	27	v	v	ADP
ejpam-4848	478	28	(	(	PUNCT
ejpam-4848	478	29	g	g	NOUN
ejpam-4848	478	30	)	)	PUNCT
ejpam-4848	478	31	.	.	PUNCT
ejpam-4848	479	1	then	then	ADV
ejpam-4848	479	2	p	p	X
ejpam-4848	479	3	=	=	SYM
ejpam-4848	479	4	v	v	NOUN
ejpam-4848	479	5	by	by	ADP
ejpam-4848	479	6	definition	definition	NOUN
ejpam-4848	479	7	of	of	ADP
ejpam-4848	479	8	gg	gg	PROPN
ejpam-4848	479	9	.	.	PUNCT
ejpam-4848	480	1	similarly	similarly	ADV
ejpam-4848	480	2	,	,	PUNCT
ejpam-4848	480	3	p	p	X
ejpam-4848	480	4	=	=	PUNCT
ejpam-4848	480	5	x.	x.	NOUN
ejpam-4848	481	1	this	this	PRON
ejpam-4848	481	2	is	be	AUX
ejpam-4848	481	3	a	a	DET
ejpam-4848	481	4	contradiction	contradiction	NOUN
ejpam-4848	481	5	because	because	SCONJ
ejpam-4848	481	6	x	x	PROPN
ejpam-4848	481	7	̸=	̸=	PROPN
ejpam-4848	481	8	v.	v.	ADP
ejpam-4848	481	9	hence	hence	ADV
ejpam-4848	481	10	,	,	PUNCT
ejpam-4848	481	11	p	p	PROPN
ejpam-4848	481	12	∈	∈	PROPN
ejpam-4848	481	13	v	v	NOUN
ejpam-4848	481	14	(	(	PUNCT
ejpam-4848	481	15	g	g	NOUN
ejpam-4848	481	16	)	)	PUNCT
ejpam-4848	481	17	,	,	PUNCT
ejpam-4848	481	18	say	say	VERB
ejpam-4848	481	19	p	p	PROPN
ejpam-4848	481	20	=	=	PROPN
ejpam-4848	481	21	q.	q.	PROPN
ejpam-4848	481	22	however	however	ADV
ejpam-4848	481	23	,	,	PUNCT
ejpam-4848	481	24	since	since	SCONJ
ejpam-4848	481	25	v̄q̄	v̄q̄	NOUN
ejpam-4848	481	26	,	,	PUNCT
ejpam-4848	481	27	q̄x̄	q̄x̄	PROPN
ejpam-4848	481	28	∈	∈	PROPN
ejpam-4848	481	29	e(g	e(g	PROPN
ejpam-4848	481	30	)	)	PUNCT
ejpam-4848	481	31	,	,	PUNCT
ejpam-4848	481	32	q	q	PROPN
ejpam-4848	481	33	∈	∈	PROPN
ejpam-4848	481	34	(	(	PUNCT
ejpam-4848	481	35	v	v	NOUN
ejpam-4848	481	36	(	(	PUNCT
ejpam-4848	481	37	g)\ng[v])∩	g)\ng[v])∩	PROPN
ejpam-4848	481	38	(	(	PUNCT
ejpam-4848	481	39	v	v	NOUN
ejpam-4848	481	40	(	(	PUNCT
ejpam-4848	481	41	g)\ng[x	g)\ng[x	PROPN
ejpam-4848	481	42	]	]	PUNCT
ejpam-4848	481	43	)	)	PUNCT
ejpam-4848	481	44	,	,	PUNCT
ejpam-4848	481	45	a	a	DET
ejpam-4848	481	46	contradiction	contradiction	NOUN
ejpam-4848	481	47	.	.	PUNCT
ejpam-4848	482	1	thus	thus	ADV
ejpam-4848	482	2	,	,	PUNCT
ejpam-4848	482	3	dgg(v	dgg(v	PROPN
ejpam-4848	482	4	,	,	PUNCT
ejpam-4848	482	5	x	x	NOUN
ejpam-4848	482	6	)	)	PUNCT
ejpam-4848	482	7	≥	≥	NOUN
ejpam-4848	482	8	3	3	NUM
ejpam-4848	482	9	.	.	PUNCT
ejpam-4848	483	1	since	since	SCONJ
ejpam-4848	483	2	[	[	X
ejpam-4848	483	3	v	v	ADP
ejpam-4848	483	4	,	,	PUNCT
ejpam-4848	483	5	v	v	NOUN
ejpam-4848	483	6	,	,	PUNCT
ejpam-4848	483	7	x	x	X
ejpam-4848	483	8	,	,	PUNCT
ejpam-4848	483	9	x	x	X
ejpam-4848	483	10	]	]	X
ejpam-4848	483	11	is	be	AUX
ejpam-4848	483	12	a	a	DET
ejpam-4848	483	13	v	v	NOUN
ejpam-4848	483	14	x	x	SYM
ejpam-4848	483	15	geodesic	geodesic	NOUN
ejpam-4848	483	16	in	in	ADP
ejpam-4848	483	17	gg	gg	PROPN
ejpam-4848	483	18	,	,	PUNCT
ejpam-4848	483	19	it	it	PRON
ejpam-4848	483	20	follows	follow	VERB
ejpam-4848	483	21	that	that	SCONJ
ejpam-4848	483	22	dgg(v	dgg(v	PROPN
ejpam-4848	483	23	,	,	PUNCT
ejpam-4848	483	24	x	x	X
ejpam-4848	483	25	)	)	PUNCT
ejpam-4848	483	26	=	=	SYM
ejpam-4848	484	1	3	3	X
ejpam-4848	484	2	.	.	PUNCT
ejpam-4848	485	1	in	in	ADP
ejpam-4848	485	2	what	what	PRON
ejpam-4848	485	3	follows	follow	VERB
ejpam-4848	485	4	,	,	PUNCT
ejpam-4848	485	5	n2	n2	ADJ
ejpam-4848	485	6	g(v	g(v	X
ejpam-4848	485	7	)	)	PUNCT
ejpam-4848	485	8	=	=	PRON
ejpam-4848	485	9	{	{	PUNCT
ejpam-4848	485	10	w	w	NOUN
ejpam-4848	485	11	∈	∈	PROPN
ejpam-4848	485	12	v	v	ADP
ejpam-4848	485	13	(	(	PUNCT
ejpam-4848	485	14	g	g	NOUN
ejpam-4848	485	15	)	)	PUNCT
ejpam-4848	485	16	:	:	PUNCT
ejpam-4848	485	17	dg(v	dg(v	X
ejpam-4848	485	18	,	,	PUNCT
ejpam-4848	485	19	w	w	NOUN
ejpam-4848	485	20	)	)	PUNCT
ejpam-4848	485	21	=	=	SYM
ejpam-4848	485	22	2	2	NUM
ejpam-4848	485	23	}	}	PUNCT
ejpam-4848	485	24	.	.	PUNCT
ejpam-4848	486	1	theorem	theorem	ADJ
ejpam-4848	486	2	4	4	NUM
ejpam-4848	486	3	.	.	PUNCT
ejpam-4848	487	1	let	let	VERB
ejpam-4848	487	2	g	g	NOUN
ejpam-4848	487	3	and	and	CCONJ
ejpam-4848	487	4	g	g	PROPN
ejpam-4848	487	5	be	be	VERB
ejpam-4848	487	6	non	non	ADJ
ejpam-4848	487	7	-	-	ADJ
ejpam-4848	487	8	trivial	trivial	ADJ
ejpam-4848	487	9	connected	connected	ADJ
ejpam-4848	487	10	graphs	graph	NOUN
ejpam-4848	487	11	.	.	PUNCT
ejpam-4848	488	1	if	if	SCONJ
ejpam-4848	488	2	v	v	NUM
ejpam-4848	488	3	∈	∈	PROPN
ejpam-4848	488	4	v	v	NOUN
ejpam-4848	488	5	(	(	PUNCT
ejpam-4848	488	6	g	g	NOUN
ejpam-4848	488	7	)	)	PUNCT
ejpam-4848	488	8	,	,	PUNCT
ejpam-4848	488	9	then	then	ADV
ejpam-4848	488	10	τgg(v	τgg(v	X
ejpam-4848	488	11	)	)	PUNCT
ejpam-4848	488	12	=	=	SYM
ejpam-4848	489	1	5|v	5|v	PROPN
ejpam-4848	489	2	(	(	PUNCT
ejpam-4848	489	3	g)|	g)|	NOUN
ejpam-4848	489	4	−	−	PROPN
ejpam-4848	489	5	2	2	NUM
ejpam-4848	489	6	·	·	PUNCT
ejpam-4848	489	7	degg(v)−	degg(v)−	PROPN
ejpam-4848	489	8	|n2	|n2	PROPN
ejpam-4848	489	9	g(v)|	g(v)|	PROPN
ejpam-4848	489	10	−	−	PROPN
ejpam-4848	489	11	4	4	NUM
ejpam-4848	489	12	.	.	PUNCT
ejpam-4848	489	13	f.	f.	PROPN
ejpam-4848	489	14	alfeche	alfeche	PROPN
ejpam-4848	489	15	,	,	PUNCT
ejpam-4848	489	16	v.	v.	PROPN
ejpam-4848	489	17	barraza	barraza	PROPN
ejpam-4848	489	18	,	,	PUNCT
ejpam-4848	489	19	s.	s.	PROPN
ejpam-4848	489	20	canoy	canoy	PROPN
ejpam-4848	489	21	,	,	PUNCT
ejpam-4848	489	22	jr	jr	PROPN
ejpam-4848	489	23	.	.	PROPN
ejpam-4848	489	24	/	/	SYM
ejpam-4848	489	25	eur	eur	PROPN
ejpam-4848	489	26	.	.	PUNCT
ejpam-4848	490	1	j.	j.	PROPN
ejpam-4848	490	2	pure	pure	PROPN
ejpam-4848	490	3	appl	appl	PROPN
ejpam-4848	490	4	.	.	PROPN
ejpam-4848	490	5	math	math	PROPN
ejpam-4848	490	6	,	,	PUNCT
ejpam-4848	490	7	16	16	NUM
ejpam-4848	490	8	(	(	PUNCT
ejpam-4848	490	9	3	3	NUM
ejpam-4848	490	10	)	)	PUNCT
ejpam-4848	490	11	(	(	PUNCT
ejpam-4848	490	12	2023	2023	NUM
ejpam-4848	490	13	)	)	PUNCT
ejpam-4848	490	14	,	,	PUNCT
ejpam-4848	490	15	1406	1406	NUM
ejpam-4848	490	16	-	-	SYM
ejpam-4848	490	17	1420	1420	NUM
ejpam-4848	490	18	1416	1416	NUM
ejpam-4848	490	19	proof	proof	NOUN
ejpam-4848	490	20	.	.	PUNCT
ejpam-4848	491	1	let	let	VERB
ejpam-4848	491	2	v	v	NUM
ejpam-4848	491	3	∈	∈	PROPN
ejpam-4848	491	4	v	v	NOUN
ejpam-4848	491	5	(	(	PUNCT
ejpam-4848	491	6	g	g	NOUN
ejpam-4848	491	7	)	)	PUNCT
ejpam-4848	491	8	.	.	PUNCT
ejpam-4848	492	1	τgg(v	τgg(v	X
ejpam-4848	492	2	)	)	PUNCT
ejpam-4848	493	1	=	=	PUNCT
ejpam-4848	493	2	∑	∑	PUNCT
ejpam-4848	493	3	x∈v	x∈v	PROPN
ejpam-4848	493	4	(	(	PUNCT
ejpam-4848	493	5	g	g	NOUN
ejpam-4848	493	6	)	)	PUNCT
ejpam-4848	493	7	dgg(v	dgg(v	PROPN
ejpam-4848	493	8	,	,	PUNCT
ejpam-4848	493	9	x	x	PRON
ejpam-4848	493	10	)	)	PUNCT
ejpam-4848	494	1	+	+	CCONJ
ejpam-4848	494	2	∑	∑	PUNCT
ejpam-4848	494	3	y∈v	y∈v	NOUN
ejpam-4848	494	4	(	(	PUNCT
ejpam-4848	494	5	g	g	NOUN
ejpam-4848	494	6	)	)	PUNCT
ejpam-4848	494	7	dgg(v	dgg(v	PROPN
ejpam-4848	494	8	,	,	PUNCT
ejpam-4848	494	9	y	y	NOUN
ejpam-4848	494	10	)	)	PUNCT
ejpam-4848	494	11	=	=	SYM
ejpam-4848	494	12	∑	∑	PUNCT
ejpam-4848	494	13	x∈ng(v	x∈ng(v	PROPN
ejpam-4848	494	14	)	)	PUNCT
ejpam-4848	494	15	dgg(v	dgg(v	PROPN
ejpam-4848	494	16	,	,	PUNCT
ejpam-4848	494	17	x	x	PRON
ejpam-4848	494	18	)	)	PUNCT
ejpam-4848	495	1	+	+	CCONJ
ejpam-4848	495	2	∑	∑	PROPN
ejpam-4848	495	3	x∈n2	x∈n2	ADJ
ejpam-4848	495	4	g(v	g(v	PROPN
ejpam-4848	495	5	)	)	PUNCT
ejpam-4848	495	6	dgg(v	dgg(v	PROPN
ejpam-4848	495	7	,	,	PUNCT
ejpam-4848	495	8	x	x	PRON
ejpam-4848	495	9	)	)	PUNCT
ejpam-4848	496	1	+	+	CCONJ
ejpam-4848	496	2	∑	∑	PROPN
ejpam-4848	496	3	x∈v	x∈v	PROPN
ejpam-4848	496	4	(	(	PUNCT
ejpam-4848	496	5	g)−(ng[v]∪n2	g)−(ng[v]∪n2	NOUN
ejpam-4848	496	6	g(v	g(v	PROPN
ejpam-4848	496	7	)	)	PUNCT
ejpam-4848	496	8	)	)	PUNCT
ejpam-4848	497	1	dgg(v	dgg(v	PROPN
ejpam-4848	497	2	,	,	PUNCT
ejpam-4848	497	3	x	x	PRON
ejpam-4848	497	4	)	)	PUNCT
ejpam-4848	498	1	+	+	CCONJ
ejpam-4848	498	2	∑	∑	PUNCT
ejpam-4848	498	3	y∈v	y∈v	NOUN
ejpam-4848	498	4	(	(	PUNCT
ejpam-4848	498	5	g)−{v	g)−{v	NOUN
ejpam-4848	498	6	}	}	SYM
ejpam-4848	498	7	dgg(v	dgg(v	PROPN
ejpam-4848	498	8	,	,	PUNCT
ejpam-4848	498	9	y	y	NOUN
ejpam-4848	498	10	)	)	PUNCT
ejpam-4848	499	1	+	+	CCONJ
ejpam-4848	499	2	dgg(v	dgg(v	PROPN
ejpam-4848	499	3	,	,	PUNCT
ejpam-4848	499	4	v	v	NOUN
ejpam-4848	499	5	)	)	PUNCT
ejpam-4848	499	6	=	=	PUNCT
ejpam-4848	499	7	|ng(v)|+	|ng(v)|+	PROPN
ejpam-4848	499	8	2|n2	2|n2	PROPN
ejpam-4848	499	9	g(v)|+	g(v)|+	VERB
ejpam-4848	499	10	3(|v	3(|v	NUM
ejpam-4848	499	11	(	(	PUNCT
ejpam-4848	499	12	g)|	g)|	NOUN
ejpam-4848	499	13	−	−	PROPN
ejpam-4848	499	14	|ng[v]|	|ng[v]|	PROPN
ejpam-4848	499	15	−	−	PROPN
ejpam-4848	499	16	|n2	|n2	PROPN
ejpam-4848	499	17	g(v)|	g(v)|	NOUN
ejpam-4848	499	18	)	)	PUNCT
ejpam-4848	500	1	+	+	CCONJ
ejpam-4848	500	2	2(|v	2(|v	NUM
ejpam-4848	500	3	(	(	PUNCT
ejpam-4848	500	4	g)|	g)|	NOUN
ejpam-4848	500	5	−	−	NOUN
ejpam-4848	500	6	1	1	NUM
ejpam-4848	500	7	)	)	PUNCT
ejpam-4848	500	8	+	+	CCONJ
ejpam-4848	500	9	1	1	NUM
ejpam-4848	500	10	=	=	SYM
ejpam-4848	500	11	|ng(v)|+	|ng(v)|+	PROPN
ejpam-4848	500	12	2|n2	2|n2	PROPN
ejpam-4848	500	13	g(v)|+	g(v)|+	VERB
ejpam-4848	500	14	3|v	3|v	NUM
ejpam-4848	500	15	(	(	PUNCT
ejpam-4848	500	16	g)|	g)|	NOUN
ejpam-4848	500	17	−	−	PROPN
ejpam-4848	500	18	3ng[v]−	3ng[v]−	NUM
ejpam-4848	500	19	3|n2	3|n2	PROPN
ejpam-4848	500	20	g(v)|+	g(v)|+	NOUN
ejpam-4848	501	1	2|v	2|v	PROPN
ejpam-4848	502	1	(	(	PUNCT
ejpam-4848	502	2	g)|	g)|	NOUN
ejpam-4848	502	3	−	−	PROPN
ejpam-4848	502	4	2	2	NUM
ejpam-4848	502	5	+	+	CCONJ
ejpam-4848	502	6	1	1	NUM
ejpam-4848	502	7	=	=	SYM
ejpam-4848	502	8	|ng(v)|+	|ng(v)|+	PROPN
ejpam-4848	502	9	2|n2	2|n2	PROPN
ejpam-4848	502	10	g(v)|+	g(v)|+	VERB
ejpam-4848	502	11	3|v	3|v	NUM
ejpam-4848	502	12	(	(	PUNCT
ejpam-4848	502	13	g)|	g)|	NOUN
ejpam-4848	502	14	−	−	PROPN
ejpam-4848	502	15	3(|ng(v)|+	3(|ng(v)|+	NUM
ejpam-4848	502	16	1)−	1)−	PROPN
ejpam-4848	502	17	3|n2	3|n2	NUM
ejpam-4848	502	18	g(v)|	g(v)|	NOUN
ejpam-4848	503	1	+	+	CCONJ
ejpam-4848	503	2	2|v	2|v	NUM
ejpam-4848	503	3	(	(	PUNCT
ejpam-4848	503	4	g)|	g)|	NOUN
ejpam-4848	503	5	−	−	PROPN
ejpam-4848	503	6	1	1	NUM
ejpam-4848	503	7	=	=	SYM
ejpam-4848	503	8	|ng(v)|+	|ng(v)|+	PROPN
ejpam-4848	503	9	2|n2	2|n2	PROPN
ejpam-4848	503	10	g(v)|+	g(v)|+	VERB
ejpam-4848	503	11	3|v	3|v	NUM
ejpam-4848	503	12	(	(	PUNCT
ejpam-4848	503	13	g)|	g)|	NOUN
ejpam-4848	503	14	−	−	PROPN
ejpam-4848	503	15	3|ng(v)|	3|ng(v)|	NUM
ejpam-4848	503	16	−	−	PROPN
ejpam-4848	503	17	3−	3−	NUM
ejpam-4848	503	18	3|n2	3|n2	NUM
ejpam-4848	503	19	g(v)|	g(v)|	NOUN
ejpam-4848	504	1	+	+	CCONJ
ejpam-4848	504	2	2|v	2|v	NUM
ejpam-4848	504	3	(	(	PUNCT
ejpam-4848	504	4	g)|	g)|	NOUN
ejpam-4848	504	5	−	−	PROPN
ejpam-4848	504	6	1	1	NUM
ejpam-4848	504	7	=	=	SYM
ejpam-4848	504	8	5|v	5|v	PROPN
ejpam-4848	504	9	(	(	PUNCT
ejpam-4848	504	10	g)|	g)|	NOUN
ejpam-4848	504	11	−	−	PROPN
ejpam-4848	504	12	2	2	NUM
ejpam-4848	504	13	·	·	PUNCT
ejpam-4848	504	14	degg(v)−	degg(v)−	PROPN
ejpam-4848	504	15	|n2	|n2	PROPN
ejpam-4848	504	16	g(v)|	g(v)|	PROPN
ejpam-4848	505	1	−	−	PROPN
ejpam-4848	505	2	4	4	NUM
ejpam-4848	505	3	.	.	PUNCT
ejpam-4848	506	1	this	this	PRON
ejpam-4848	506	2	proves	prove	VERB
ejpam-4848	506	3	the	the	DET
ejpam-4848	506	4	assertion	assertion	NOUN
ejpam-4848	506	5	.	.	PUNCT
ejpam-4848	507	1	corollary	corollary	ADJ
ejpam-4848	507	2	4	4	NUM
ejpam-4848	507	3	.	.	PUNCT
ejpam-4848	508	1	let	let	VERB
ejpam-4848	508	2	g	g	PRON
ejpam-4848	508	3	be	be	AUX
ejpam-4848	508	4	a	a	DET
ejpam-4848	508	5	non	non	ADJ
ejpam-4848	508	6	-	-	ADJ
ejpam-4848	508	7	trivial	trivial	ADJ
ejpam-4848	508	8	connected	connected	ADJ
ejpam-4848	508	9	graph	graph	NOUN
ejpam-4848	508	10	of	of	ADP
ejpam-4848	508	11	order	order	NOUN
ejpam-4848	508	12	m	m	VERB
ejpam-4848	508	13	such	such	ADJ
ejpam-4848	508	14	that	that	SCONJ
ejpam-4848	508	15	g	g	PROPN
ejpam-4848	508	16	is	be	AUX
ejpam-4848	508	17	connected	connect	VERB
ejpam-4848	508	18	and	and	CCONJ
ejpam-4848	508	19	let	let	VERB
ejpam-4848	508	20	v	v	NUM
ejpam-4848	508	21	∈	∈	PROPN
ejpam-4848	508	22	v	v	NOUN
ejpam-4848	508	23	(	(	PUNCT
ejpam-4848	508	24	g	g	NOUN
ejpam-4848	508	25	)	)	PUNCT
ejpam-4848	508	26	.	.	PUNCT
ejpam-4848	509	1	then	then	ADV
ejpam-4848	509	2	cgg(v	cgg(v	X
ejpam-4848	509	3	)	)	PUNCT
ejpam-4848	509	4	=	=	PUNCT
ejpam-4848	510	1	2m−	2m−	NUM
ejpam-4848	510	2	1	1	NUM
ejpam-4848	510	3	5|v	5|v	PROPN
ejpam-4848	510	4	(	(	PUNCT
ejpam-4848	510	5	g)|	g)|	NOUN
ejpam-4848	510	6	−	−	PROPN
ejpam-4848	510	7	2	2	NUM
ejpam-4848	510	8	·	·	PUNCT
ejpam-4848	510	9	degg(v)−	degg(v)−	PROPN
ejpam-4848	510	10	|n2	|n2	PROPN
ejpam-4848	510	11	g(v)|	g(v)|	PROPN
ejpam-4848	511	1	−	−	PROPN
ejpam-4848	511	2	4	4	NUM
ejpam-4848	511	3	.	.	PUNCT
ejpam-4848	511	4	example	example	NOUN
ejpam-4848	512	1	4	4	NUM
ejpam-4848	512	2	.	.	X
ejpam-4848	512	3	consider	consider	VERB
ejpam-4848	512	4	g	g	NOUN
ejpam-4848	512	5	=	=	SYM
ejpam-4848	512	6	p4	p4	ADJ
ejpam-4848	512	7	,	,	PUNCT
ejpam-4848	512	8	gg	gg	PROPN
ejpam-4848	512	9	=	=	SYM
ejpam-4848	512	10	p4p	p4p	PROPN
ejpam-4848	512	11	4	4	NUM
ejpam-4848	512	12	,	,	PUNCT
ejpam-4848	512	13	and	and	CCONJ
ejpam-4848	512	14	v	v	ADP
ejpam-4848	512	15	∈	∈	NOUN
ejpam-4848	512	16	v	v	NOUN
ejpam-4848	512	17	(	(	PUNCT
ejpam-4848	512	18	g	g	NOUN
ejpam-4848	512	19	)	)	PUNCT
ejpam-4848	512	20	in	in	ADP
ejpam-4848	512	21	figure	figure	NOUN
ejpam-4848	512	22	8	8	NUM
ejpam-4848	512	23	.	.	PUNCT
ejpam-4848	513	1	then	then	ADV
ejpam-4848	513	2	|v	|v	PROPN
ejpam-4848	513	3	(	(	PUNCT
ejpam-4848	513	4	g)|	g)|	NOUN
ejpam-4848	513	5	=	=	SYM
ejpam-4848	513	6	4	4	NUM
ejpam-4848	513	7	,	,	PUNCT
ejpam-4848	513	8	m	m	VERB
ejpam-4848	513	9	=	=	NOUN
ejpam-4848	513	10	8	8	NUM
ejpam-4848	513	11	,	,	PUNCT
ejpam-4848	513	12	ng(v	ng(v	PUNCT
ejpam-4848	513	13	)	)	PUNCT
ejpam-4848	513	14	=	=	PRON
ejpam-4848	513	15	{	{	PUNCT
ejpam-4848	513	16	x	x	NOUN
ejpam-4848	513	17	}	}	PUNCT
ejpam-4848	513	18	,	,	PUNCT
ejpam-4848	513	19	and	and	CCONJ
ejpam-4848	513	20	n2	n2	ADJ
ejpam-4848	513	21	g(v	g(v	X
ejpam-4848	513	22	)	)	PUNCT
ejpam-4848	513	23	=	=	PRON
ejpam-4848	513	24	{	{	PUNCT
ejpam-4848	513	25	y	y	NOUN
ejpam-4848	513	26	}	}	PUNCT
ejpam-4848	513	27	.	.	PUNCT
ejpam-4848	514	1	using	use	VERB
ejpam-4848	514	2	corollary	corollary	ADJ
ejpam-4848	514	3	4	4	NUM
ejpam-4848	514	4	,	,	PUNCT
ejpam-4848	514	5	the	the	DET
ejpam-4848	514	6	closeness	closeness	NOUN
ejpam-4848	514	7	centrality	centrality	NOUN
ejpam-4848	514	8	of	of	ADP
ejpam-4848	514	9	v	v	NOUN
ejpam-4848	514	10	is	be	AUX
ejpam-4848	514	11	cgg(v	cgg(v	NOUN
ejpam-4848	514	12	)	)	PUNCT
ejpam-4848	514	13	=	=	PUNCT
ejpam-4848	515	1	2m−	2m−	NUM
ejpam-4848	515	2	1	1	NUM
ejpam-4848	515	3	5|v	5|v	PROPN
ejpam-4848	515	4	(	(	PUNCT
ejpam-4848	515	5	g)|	g)|	NOUN
ejpam-4848	515	6	−	−	PROPN
ejpam-4848	515	7	2	2	NUM
ejpam-4848	515	8	·	·	PUNCT
ejpam-4848	515	9	degg(v)−	degg(v)−	PROPN
ejpam-4848	515	10	|n2	|n2	PROPN
ejpam-4848	515	11	g(v)|	g(v)|	PROPN
ejpam-4848	515	12	−	−	PROPN
ejpam-4848	515	13	4	4	NUM
ejpam-4848	515	14	=	=	SYM
ejpam-4848	515	15	8−	8−	NUM
ejpam-4848	515	16	1	1	NUM
ejpam-4848	515	17	5(4)−	5(4)−	PROPN
ejpam-4848	515	18	2(1)−	2(1)−	PROPN
ejpam-4848	515	19	1−	1−	NUM
ejpam-4848	515	20	4	4	NUM
ejpam-4848	515	21	=	=	SYM
ejpam-4848	515	22	7	7	NUM
ejpam-4848	515	23	20−	20−	NUM
ejpam-4848	515	24	2−	2−	NUM
ejpam-4848	515	25	1−	1−	NUM
ejpam-4848	515	26	4	4	NUM
ejpam-4848	515	27	=	=	SYM
ejpam-4848	515	28	7	7	NUM
ejpam-4848	515	29	13	13	NUM
ejpam-4848	515	30	.	.	PUNCT
ejpam-4848	516	1	for	for	ADP
ejpam-4848	516	2	a	a	DET
ejpam-4848	516	3	non	non	ADJ
ejpam-4848	516	4	-	-	ADJ
ejpam-4848	516	5	trivial	trivial	ADJ
ejpam-4848	516	6	connected	connected	ADJ
ejpam-4848	516	7	graph	graph	NOUN
ejpam-4848	516	8	g	g	NOUN
ejpam-4848	516	9	and	and	CCONJ
ejpam-4848	516	10	v	v	ADP
ejpam-4848	516	11	∈	∈	PROPN
ejpam-4848	516	12	v	v	NOUN
ejpam-4848	516	13	(	(	PUNCT
ejpam-4848	516	14	g	g	NOUN
ejpam-4848	516	15	)	)	PUNCT
ejpam-4848	516	16	,	,	PUNCT
ejpam-4848	516	17	the	the	DET
ejpam-4848	516	18	sets	set	NOUN
ejpam-4848	516	19	n0	n0	X
ejpam-4848	516	20	g(v	g(v	PROPN
ejpam-4848	516	21	)	)	PUNCT
ejpam-4848	516	22	and	and	CCONJ
ejpam-4848	516	23	n1	n1	PROPN
ejpam-4848	516	24	g(v	g(v	NOUN
ejpam-4848	516	25	)	)	PUNCT
ejpam-4848	516	26	are	be	AUX
ejpam-4848	516	27	given	give	VERB
ejpam-4848	516	28	below	below	ADP
ejpam-4848	516	29	:	:	PUNCT
ejpam-4848	516	30	f.	f.	PROPN
ejpam-4848	516	31	alfeche	alfeche	PROPN
ejpam-4848	516	32	,	,	PUNCT
ejpam-4848	516	33	v.	v.	PROPN
ejpam-4848	516	34	barraza	barraza	PROPN
ejpam-4848	516	35	,	,	PUNCT
ejpam-4848	516	36	s.	s.	PROPN
ejpam-4848	516	37	canoy	canoy	PROPN
ejpam-4848	516	38	,	,	PUNCT
ejpam-4848	516	39	jr	jr	PROPN
ejpam-4848	516	40	.	.	PROPN
ejpam-4848	516	41	/	/	SYM
ejpam-4848	516	42	eur	eur	PROPN
ejpam-4848	516	43	.	.	PUNCT
ejpam-4848	517	1	j.	j.	PROPN
ejpam-4848	517	2	pure	pure	PROPN
ejpam-4848	517	3	appl	appl	PROPN
ejpam-4848	517	4	.	.	PROPN
ejpam-4848	517	5	math	math	PROPN
ejpam-4848	517	6	,	,	PUNCT
ejpam-4848	517	7	16	16	NUM
ejpam-4848	517	8	(	(	PUNCT
ejpam-4848	517	9	3	3	NUM
ejpam-4848	517	10	)	)	PUNCT
ejpam-4848	517	11	(	(	PUNCT
ejpam-4848	517	12	2023	2023	NUM
ejpam-4848	517	13	)	)	PUNCT
ejpam-4848	517	14	,	,	PUNCT
ejpam-4848	517	15	1406	1406	NUM
ejpam-4848	517	16	-	-	SYM
ejpam-4848	517	17	1420	1420	NUM
ejpam-4848	517	18	1417	1417	NUM
ejpam-4848	517	19	g	g	NOUN
ejpam-4848	517	20	g	g	PROPN
ejpam-4848	517	21	v	v	NUM
ejpam-4848	517	22	x	x	SYM
ejpam-4848	517	23	y	y	PROPN
ejpam-4848	517	24	z	z	NOUN
ejpam-4848	517	25	figure	figure	NOUN
ejpam-4848	517	26	8	8	NUM
ejpam-4848	517	27	:	:	PUNCT
ejpam-4848	517	28	the	the	DET
ejpam-4848	517	29	complementary	complementary	ADJ
ejpam-4848	517	30	prism	prism	NOUN
ejpam-4848	517	31	p4p	p4p	PROPN
ejpam-4848	517	32	4	4	NUM
ejpam-4848	517	33	and	and	CCONJ
ejpam-4848	517	34	v	v	ADP
ejpam-4848	517	35	∈	∈	PROPN
ejpam-4848	517	36	v	v	NOUN
ejpam-4848	517	37	(	(	PUNCT
ejpam-4848	517	38	p4	p4	ADJ
ejpam-4848	517	39	)	)	PUNCT
ejpam-4848	517	40	n0	n0	X
ejpam-4848	517	41	g(v	g(v	X
ejpam-4848	517	42	)	)	PUNCT
ejpam-4848	517	43	=	=	PRON
ejpam-4848	518	1	{	{	PUNCT
ejpam-4848	518	2	x	x	SYM
ejpam-4848	518	3	∈	∈	NOUN
ejpam-4848	518	4	ng(v	ng(v	PRON
ejpam-4848	518	5	)	)	PUNCT
ejpam-4848	518	6	:	:	PUNCT
ejpam-4848	518	7	(	(	PUNCT
ejpam-4848	518	8	v	v	X
ejpam-4848	518	9	(	(	PUNCT
ejpam-4848	518	10	g	g	NOUN
ejpam-4848	518	11	)	)	PUNCT
ejpam-4848	518	12	\ng[x	\ng[x	PROPN
ejpam-4848	518	13	]	]	PUNCT
ejpam-4848	518	14	)	)	PUNCT
ejpam-4848	518	15	∩	∩	NOUN
ejpam-4848	518	16	(	(	PUNCT
ejpam-4848	518	17	v	v	NOUN
ejpam-4848	518	18	(	(	PUNCT
ejpam-4848	518	19	g	g	NOUN
ejpam-4848	518	20	)	)	PUNCT
ejpam-4848	518	21	\ng[v	\ng[v	NOUN
ejpam-4848	518	22	]	]	PUNCT
ejpam-4848	518	23	)	)	PUNCT
ejpam-4848	518	24	̸=	̸=	PROPN
ejpam-4848	518	25	∅	∅	NOUN
ejpam-4848	518	26	}	}	PUNCT
ejpam-4848	518	27	and	and	CCONJ
ejpam-4848	518	28	n1	n1	ADJ
ejpam-4848	518	29	g(v	g(v	X
ejpam-4848	518	30	)	)	PUNCT
ejpam-4848	518	31	=	=	PRON
ejpam-4848	519	1	{	{	PUNCT
ejpam-4848	519	2	x	x	SYM
ejpam-4848	519	3	∈	∈	NOUN
ejpam-4848	519	4	ng(v	ng(v	PRON
ejpam-4848	519	5	)	)	PUNCT
ejpam-4848	519	6	:	:	PUNCT
ejpam-4848	519	7	(	(	PUNCT
ejpam-4848	519	8	v	v	X
ejpam-4848	519	9	(	(	PUNCT
ejpam-4848	519	10	g	g	NOUN
ejpam-4848	519	11	)	)	PUNCT
ejpam-4848	519	12	\ng[x	\ng[x	PROPN
ejpam-4848	519	13	]	]	PUNCT
ejpam-4848	519	14	)	)	PUNCT
ejpam-4848	519	15	∩	∩	NOUN
ejpam-4848	519	16	(	(	PUNCT
ejpam-4848	519	17	v	v	NOUN
ejpam-4848	519	18	(	(	PUNCT
ejpam-4848	519	19	g	g	NOUN
ejpam-4848	519	20	)	)	PUNCT
ejpam-4848	519	21	\ng[v	\ng[v	NOUN
ejpam-4848	519	22	]	]	PUNCT
ejpam-4848	519	23	)	)	PUNCT
ejpam-4848	519	24	=	=	SYM
ejpam-4848	519	25	∅	∅	NOUN
ejpam-4848	519	26	}	}	PUNCT
ejpam-4848	519	27	.	.	PUNCT
ejpam-4848	520	1	clearly	clearly	ADV
ejpam-4848	520	2	,	,	PUNCT
ejpam-4848	520	3	ng(v	ng(v	PUNCT
ejpam-4848	520	4	)	)	PUNCT
ejpam-4848	520	5	=	=	SYM
ejpam-4848	520	6	n0	n0	NUM
ejpam-4848	520	7	g(v	g(v	PROPN
ejpam-4848	520	8	)	)	PUNCT
ejpam-4848	520	9	∪n1	∪n1	NOUN
ejpam-4848	520	10	g(v	g(v	PROPN
ejpam-4848	520	11	)	)	PUNCT
ejpam-4848	520	12	.	.	PUNCT
ejpam-4848	521	1	theorem	theorem	NOUN
ejpam-4848	521	2	5	5	NUM
ejpam-4848	521	3	.	.	PUNCT
ejpam-4848	522	1	let	let	VERB
ejpam-4848	522	2	g	g	NOUN
ejpam-4848	522	3	and	and	CCONJ
ejpam-4848	522	4	g	g	PROPN
ejpam-4848	522	5	be	be	VERB
ejpam-4848	522	6	non	non	ADJ
ejpam-4848	522	7	-	-	ADJ
ejpam-4848	522	8	trivial	trivial	ADJ
ejpam-4848	522	9	connected	connected	ADJ
ejpam-4848	522	10	graphs	graph	NOUN
ejpam-4848	522	11	and	and	CCONJ
ejpam-4848	522	12	let	let	VERB
ejpam-4848	522	13	v	v	NUM
ejpam-4848	522	14	∈	∈	PROPN
ejpam-4848	522	15	v	v	NOUN
ejpam-4848	522	16	(	(	PUNCT
ejpam-4848	522	17	g	g	NOUN
ejpam-4848	522	18	)	)	PUNCT
ejpam-4848	522	19	.	.	PUNCT
ejpam-4848	523	1	then	then	ADV
ejpam-4848	523	2	τgg(v	τgg(v	PRON
ejpam-4848	523	3	)	)	PUNCT
ejpam-4848	523	4	=	=	SYM
ejpam-4848	524	1	3|v	3|v	NUM
ejpam-4848	524	2	(	(	PUNCT
ejpam-4848	524	3	g	g	NOUN
ejpam-4848	524	4	)	)	PUNCT
ejpam-4848	524	5	+	+	CCONJ
ejpam-4848	524	6	degg(v	degg(v	PROPN
ejpam-4848	524	7	)	)	PUNCT
ejpam-4848	524	8	+	+	NUM
ejpam-4848	524	9	|n1	|n1	VERB
ejpam-4848	524	10	g(v)|	g(v)|	NOUN
ejpam-4848	524	11	−	−	NOUN
ejpam-4848	524	12	2	2	X
ejpam-4848	524	13	.	.	PUNCT
ejpam-4848	524	14	proof	proof	NOUN
ejpam-4848	524	15	.	.	PUNCT
ejpam-4848	525	1	τgg(v	τgg(v	X
ejpam-4848	525	2	)	)	PUNCT
ejpam-4848	526	1	=	=	PUNCT
ejpam-4848	526	2	∑	∑	PUNCT
ejpam-4848	526	3	x∈v	x∈v	PROPN
ejpam-4848	526	4	(	(	PUNCT
ejpam-4848	526	5	g	g	NOUN
ejpam-4848	526	6	)	)	PUNCT
ejpam-4848	526	7	dgg(v	dgg(v	PROPN
ejpam-4848	526	8	,	,	PUNCT
ejpam-4848	526	9	x	x	PRON
ejpam-4848	526	10	)	)	PUNCT
ejpam-4848	527	1	+	+	CCONJ
ejpam-4848	527	2	∑	∑	PROPN
ejpam-4848	527	3	x∈v	x∈v	PROPN
ejpam-4848	527	4	(	(	PUNCT
ejpam-4848	527	5	g)−{v	g)−{v	NOUN
ejpam-4848	527	6	}	}	PUNCT
ejpam-4848	527	7	dgg(v	dgg(v	PROPN
ejpam-4848	527	8	,	,	PUNCT
ejpam-4848	527	9	x	x	NOUN
ejpam-4848	527	10	)	)	PUNCT
ejpam-4848	527	11	=	=	PUNCT
ejpam-4848	527	12	∑	∑	PROPN
ejpam-4848	527	13	x∈v	x∈v	PROPN
ejpam-4848	527	14	(	(	PUNCT
ejpam-4848	527	15	g)−{v	g)−{v	NOUN
ejpam-4848	527	16	}	}	PUNCT
ejpam-4848	527	17	dgg(v	dgg(v	PROPN
ejpam-4848	527	18	,	,	PUNCT
ejpam-4848	527	19	x	x	PRON
ejpam-4848	527	20	)	)	PUNCT
ejpam-4848	528	1	+	+	CCONJ
ejpam-4848	528	2	dgg(v	dgg(v	PROPN
ejpam-4848	528	3	,	,	PUNCT
ejpam-4848	528	4	v	v	NOUN
ejpam-4848	528	5	)	)	PUNCT
ejpam-4848	529	1	+	+	CCONJ
ejpam-4848	529	2	∑	∑	PROPN
ejpam-4848	529	3	x∈v	x∈v	PROPN
ejpam-4848	529	4	(	(	PUNCT
ejpam-4848	529	5	g)−ng[v	g)−ng[v	PROPN
ejpam-4848	529	6	]	]	X
ejpam-4848	529	7	dgg(v	dgg(v	PROPN
ejpam-4848	529	8	,	,	PUNCT
ejpam-4848	529	9	x	x	PRON
ejpam-4848	529	10	)	)	PUNCT
ejpam-4848	530	1	+	+	CCONJ
ejpam-4848	530	2	∑	∑	PROPN
ejpam-4848	530	3	x∈n0	x∈n0	PROPN
ejpam-4848	530	4	g(v	g(v	PROPN
ejpam-4848	530	5	)	)	PUNCT
ejpam-4848	530	6	dgg(v	dgg(v	PROPN
ejpam-4848	530	7	,	,	PUNCT
ejpam-4848	530	8	x	x	PRON
ejpam-4848	530	9	)	)	PUNCT
ejpam-4848	531	1	+	+	CCONJ
ejpam-4848	531	2	∑	∑	PROPN
ejpam-4848	531	3	x∈n1	x∈n1	PROPN
ejpam-4848	531	4	g(v	g(v	PROPN
ejpam-4848	531	5	)	)	PUNCT
ejpam-4848	532	1	dgg(v	dgg(v	PROPN
ejpam-4848	532	2	,	,	PUNCT
ejpam-4848	532	3	x	x	NOUN
ejpam-4848	532	4	)	)	PUNCT
ejpam-4848	532	5	=	=	SYM
ejpam-4848	532	6	2(|v	2(|v	NUM
ejpam-4848	532	7	(	(	PUNCT
ejpam-4848	532	8	g)|	g)|	NOUN
ejpam-4848	532	9	−	−	NOUN
ejpam-4848	532	10	1	1	NUM
ejpam-4848	532	11	)	)	PUNCT
ejpam-4848	532	12	+	+	CCONJ
ejpam-4848	532	13	1	1	NUM
ejpam-4848	532	14	+	+	CCONJ
ejpam-4848	532	15	(	(	PUNCT
ejpam-4848	532	16	|v	|v	X
ejpam-4848	532	17	(	(	PUNCT
ejpam-4848	532	18	g)|	g)|	PROPN
ejpam-4848	532	19	−ng[v	−ng[v	PROPN
ejpam-4848	532	20	]	]	PUNCT
ejpam-4848	532	21	)	)	PUNCT
ejpam-4848	533	1	+	+	CCONJ
ejpam-4848	533	2	2|n0	2|n0	PROPN
ejpam-4848	533	3	g(v)|+	g(v)|+	NOUN
ejpam-4848	533	4	3|n1	3|n1	NUM
ejpam-4848	533	5	g(v)|	g(v)|	NOUN
ejpam-4848	533	6	=	=	SYM
ejpam-4848	533	7	2|v	2|v	PROPN
ejpam-4848	533	8	(	(	PUNCT
ejpam-4848	533	9	g)|	g)|	NOUN
ejpam-4848	533	10	−	−	PROPN
ejpam-4848	533	11	2	2	NUM
ejpam-4848	533	12	+	+	CCONJ
ejpam-4848	533	13	1	1	NUM
ejpam-4848	533	14	+	+	CCONJ
ejpam-4848	533	15	|v	|v	X
ejpam-4848	533	16	(	(	PUNCT
ejpam-4848	533	17	g)|	g)|	NOUN
ejpam-4848	533	18	−	−	NOUN
ejpam-4848	533	19	|ng(v)|	|ng(v)|	NOUN
ejpam-4848	533	20	−	−	PROPN
ejpam-4848	533	21	1	1	NUM
ejpam-4848	533	22	+	+	NUM
ejpam-4848	533	23	2(|n0	2(|n0	NUM
ejpam-4848	533	24	g(v)|+	g(v)|+	NOUN
ejpam-4848	533	25	|n1	|n1	VERB
ejpam-4848	533	26	g(v)|	g(v)|	NOUN
ejpam-4848	533	27	)	)	PUNCT
ejpam-4848	534	1	+	+	PRON
ejpam-4848	534	2	|n1	|n1	VERB
ejpam-4848	534	3	g(v)|	g(v)|	NOUN
ejpam-4848	534	4	=	=	SYM
ejpam-4848	534	5	3|v	3|v	NUM
ejpam-4848	534	6	(	(	PUNCT
ejpam-4848	534	7	g)|+	g)|+	PROPN
ejpam-4848	534	8	|ng(v)|+	|ng(v)|+	PROPN
ejpam-4848	534	9	|n1	|n1	VERB
ejpam-4848	534	10	g(v)|	g(v)|	NOUN
ejpam-4848	534	11	−	−	PROPN
ejpam-4848	534	12	2	2	NUM
ejpam-4848	534	13	=	=	SYM
ejpam-4848	534	14	3|v	3|v	NUM
ejpam-4848	534	15	(	(	PUNCT
ejpam-4848	534	16	g)|+	g)|+	NOUN
ejpam-4848	534	17	degg(v	degg(v	PROPN
ejpam-4848	534	18	)	)	PUNCT
ejpam-4848	534	19	+	+	NUM
ejpam-4848	534	20	|n1	|n1	VERB
ejpam-4848	534	21	g(v)|	g(v)|	NOUN
ejpam-4848	534	22	−	−	PROPN
ejpam-4848	534	23	2	2	X
ejpam-4848	534	24	.	.	PUNCT
ejpam-4848	534	25	corollary	corollary	ADJ
ejpam-4848	534	26	5	5	NUM
ejpam-4848	534	27	.	.	PUNCT
ejpam-4848	535	1	let	let	VERB
ejpam-4848	535	2	g	g	PRON
ejpam-4848	535	3	be	be	AUX
ejpam-4848	535	4	a	a	DET
ejpam-4848	535	5	non	non	ADJ
ejpam-4848	535	6	-	-	ADJ
ejpam-4848	535	7	trivial	trivial	ADJ
ejpam-4848	535	8	connected	connected	ADJ
ejpam-4848	535	9	graph	graph	NOUN
ejpam-4848	535	10	of	of	ADP
ejpam-4848	535	11	order	order	NOUN
ejpam-4848	535	12	m	m	VERB
ejpam-4848	535	13	such	such	ADJ
ejpam-4848	535	14	that	that	SCONJ
ejpam-4848	535	15	g	g	PROPN
ejpam-4848	535	16	is	be	AUX
ejpam-4848	535	17	connected	connect	VERB
ejpam-4848	535	18	and	and	CCONJ
ejpam-4848	535	19	let	let	VERB
ejpam-4848	535	20	v	v	NUM
ejpam-4848	535	21	∈	∈	PROPN
ejpam-4848	535	22	v	v	NOUN
ejpam-4848	535	23	(	(	PUNCT
ejpam-4848	535	24	g	g	NOUN
ejpam-4848	535	25	)	)	PUNCT
ejpam-4848	535	26	.	.	PUNCT
ejpam-4848	536	1	then	then	ADV
ejpam-4848	536	2	cgg(v	cgg(v	X
ejpam-4848	536	3	)	)	PUNCT
ejpam-4848	536	4	=	=	PUNCT
ejpam-4848	537	1	2m−	2m−	NUM
ejpam-4848	537	2	1	1	NUM
ejpam-4848	537	3	3|v	3|v	NUM
ejpam-4848	537	4	(	(	PUNCT
ejpam-4848	537	5	g)|+	g)|+	NOUN
ejpam-4848	537	6	degg(v	degg(v	PROPN
ejpam-4848	537	7	)	)	PUNCT
ejpam-4848	537	8	+	+	NUM
ejpam-4848	537	9	|n1	|n1	VERB
ejpam-4848	537	10	g(v)|	g(v)|	NOUN
ejpam-4848	537	11	−	−	PROPN
ejpam-4848	537	12	2	2	NUM
ejpam-4848	537	13	.	.	PUNCT
ejpam-4848	538	1	f.	f.	PROPN
ejpam-4848	538	2	alfeche	alfeche	PROPN
ejpam-4848	538	3	,	,	PUNCT
ejpam-4848	538	4	v.	v.	PROPN
ejpam-4848	538	5	barraza	barraza	PROPN
ejpam-4848	538	6	,	,	PUNCT
ejpam-4848	538	7	s.	s.	PROPN
ejpam-4848	538	8	canoy	canoy	PROPN
ejpam-4848	538	9	,	,	PUNCT
ejpam-4848	538	10	jr	jr	PROPN
ejpam-4848	538	11	.	.	PROPN
ejpam-4848	538	12	/	/	SYM
ejpam-4848	538	13	eur	eur	PROPN
ejpam-4848	538	14	.	.	PUNCT
ejpam-4848	539	1	j.	j.	PROPN
ejpam-4848	539	2	pure	pure	PROPN
ejpam-4848	539	3	appl	appl	PROPN
ejpam-4848	539	4	.	.	PROPN
ejpam-4848	539	5	math	math	PROPN
ejpam-4848	539	6	,	,	PUNCT
ejpam-4848	539	7	16	16	NUM
ejpam-4848	539	8	(	(	PUNCT
ejpam-4848	539	9	3	3	NUM
ejpam-4848	539	10	)	)	PUNCT
ejpam-4848	539	11	(	(	PUNCT
ejpam-4848	539	12	2023	2023	NUM
ejpam-4848	539	13	)	)	PUNCT
ejpam-4848	539	14	,	,	PUNCT
ejpam-4848	539	15	1406	1406	NUM
ejpam-4848	539	16	-	-	SYM
ejpam-4848	539	17	1420	1420	NUM
ejpam-4848	539	18	1418	1418	NUM
ejpam-4848	539	19	example	example	NOUN
ejpam-4848	539	20	5	5	NUM
ejpam-4848	539	21	.	.	PUNCT
ejpam-4848	540	1	let	let	VERB
ejpam-4848	540	2	g	g	NOUN
ejpam-4848	540	3	=	=	SYM
ejpam-4848	540	4	p4	p4	ADJ
ejpam-4848	540	5	and	and	CCONJ
ejpam-4848	540	6	consider	consider	VERB
ejpam-4848	540	7	gg	gg	NOUN
ejpam-4848	540	8	=	=	SYM
ejpam-4848	540	9	p4p	p4p	PROPN
ejpam-4848	540	10	4	4	NUM
ejpam-4848	540	11	and	and	CCONJ
ejpam-4848	540	12	v	v	ADP
ejpam-4848	540	13	∈	∈	PROPN
ejpam-4848	540	14	v	v	NOUN
ejpam-4848	540	15	(	(	PUNCT
ejpam-4848	540	16	g	g	NOUN
ejpam-4848	540	17	)	)	PUNCT
ejpam-4848	540	18	in	in	ADP
ejpam-4848	540	19	figure	figure	NOUN
ejpam-4848	540	20	9	9	NUM
ejpam-4848	540	21	.	.	PUNCT
ejpam-4848	541	1	then	then	ADV
ejpam-4848	541	2	ng(v	ng(v	PUNCT
ejpam-4848	541	3	)	)	PUNCT
ejpam-4848	542	1	=	=	PRON
ejpam-4848	542	2	{	{	PUNCT
ejpam-4848	542	3	x	x	NOUN
ejpam-4848	542	4	}	}	PUNCT
ejpam-4848	542	5	and	and	CCONJ
ejpam-4848	542	6	n1	n1	ADJ
ejpam-4848	542	7	g(v	g(v	X
ejpam-4848	542	8	)	)	PUNCT
ejpam-4848	543	1	=	=	NOUN
ejpam-4848	543	2	∅.	∅.	VERB
ejpam-4848	543	3	hence	hence	ADV
ejpam-4848	543	4	|v	|v	PROPN
ejpam-4848	543	5	(	(	PUNCT
ejpam-4848	543	6	g)|	g)|	NOUN
ejpam-4848	543	7	=	=	SYM
ejpam-4848	543	8	4	4	NUM
ejpam-4848	543	9	,	,	PUNCT
ejpam-4848	543	10	m	m	VERB
ejpam-4848	543	11	=	=	NOUN
ejpam-4848	543	12	8	8	NUM
ejpam-4848	543	13	,	,	PUNCT
ejpam-4848	543	14	|ng(v)|	|ng(v)|	PROPN
ejpam-4848	543	15	=	=	SYM
ejpam-4848	543	16	degg(v	degg(v	PROPN
ejpam-4848	543	17	)	)	PUNCT
ejpam-4848	543	18	=	=	SYM
ejpam-4848	543	19	1	1	NUM
ejpam-4848	543	20	and	and	CCONJ
ejpam-4848	543	21	|n1	|n1	VERB
ejpam-4848	543	22	g(v)|	g(v)|	NOUN
ejpam-4848	543	23	=	=	X
ejpam-4848	543	24	0	0	X
ejpam-4848	543	25	.	.	PUNCT
ejpam-4848	543	26	using	use	VERB
ejpam-4848	543	27	corollary	corollary	ADJ
ejpam-4848	543	28	5	5	NUM
ejpam-4848	543	29	,	,	PUNCT
ejpam-4848	543	30	we	we	PRON
ejpam-4848	543	31	have	have	VERB
ejpam-4848	543	32	cgg(v	cgg(v	NOUN
ejpam-4848	543	33	)	)	PUNCT
ejpam-4848	543	34	=	=	PUNCT
ejpam-4848	544	1	2m−	2m−	NUM
ejpam-4848	544	2	1	1	NUM
ejpam-4848	544	3	3|v	3|v	NUM
ejpam-4848	544	4	(	(	PUNCT
ejpam-4848	544	5	g)|+	g)|+	NOUN
ejpam-4848	544	6	degg(v	degg(v	PROPN
ejpam-4848	544	7	)	)	PUNCT
ejpam-4848	544	8	+	+	NUM
ejpam-4848	544	9	|n1	|n1	VERB
ejpam-4848	544	10	g(v)|	g(v)|	NOUN
ejpam-4848	544	11	−	−	PROPN
ejpam-4848	544	12	2	2	NUM
ejpam-4848	544	13	=	=	SYM
ejpam-4848	544	14	8−	8−	NUM
ejpam-4848	544	15	1	1	NUM
ejpam-4848	544	16	3(4	3(4	NUM
ejpam-4848	544	17	)	)	PUNCT
ejpam-4848	545	1	+	+	CCONJ
ejpam-4848	545	2	1	1	NUM
ejpam-4848	545	3	+	+	CCONJ
ejpam-4848	545	4	0−	0−	NUM
ejpam-4848	545	5	2	2	NUM
ejpam-4848	545	6	=	=	SYM
ejpam-4848	545	7	7	7	NUM
ejpam-4848	545	8	11	11	NUM
ejpam-4848	545	9	.	.	PUNCT
ejpam-4848	546	1	g	g	NOUN
ejpam-4848	546	2	gv	gv	PROPN
ejpam-4848	546	3	v	v	PROPN
ejpam-4848	546	4	x	x	SYM
ejpam-4848	546	5	y	y	PROPN
ejpam-4848	546	6	z	z	NOUN
ejpam-4848	546	7	figure	figure	NOUN
ejpam-4848	546	8	9	9	NUM
ejpam-4848	546	9	:	:	PUNCT
ejpam-4848	546	10	the	the	DET
ejpam-4848	546	11	complementary	complementary	ADJ
ejpam-4848	546	12	prism	prism	NOUN
ejpam-4848	546	13	p4p	p4p	PROPN
ejpam-4848	546	14	4	4	NUM
ejpam-4848	546	15	and	and	CCONJ
ejpam-4848	546	16	v	v	ADP
ejpam-4848	546	17	∈	∈	PROPN
ejpam-4848	546	18	v	v	NOUN
ejpam-4848	546	19	(	(	PUNCT
ejpam-4848	546	20	p4	p4	ADJ
ejpam-4848	546	21	)	)	PUNCT
ejpam-4848	546	22	lemma	lemma	PROPN
ejpam-4848	546	23	5	5	NUM
ejpam-4848	546	24	.	.	PUNCT
ejpam-4848	546	25	letg	letg	NOUN
ejpam-4848	546	26	andh	andh	NOUN
ejpam-4848	546	27	be	be	VERB
ejpam-4848	546	28	a	a	DET
ejpam-4848	546	29	non	non	ADJ
ejpam-4848	546	30	-	-	ADJ
ejpam-4848	546	31	trivial	trivial	ADJ
ejpam-4848	546	32	connected	connected	ADJ
ejpam-4848	546	33	graphs	graph	NOUN
ejpam-4848	546	34	and	and	CCONJ
ejpam-4848	546	35	let	let	VERB
ejpam-4848	546	36	(	(	PUNCT
ejpam-4848	546	37	x	x	NOUN
ejpam-4848	546	38	,	,	PUNCT
ejpam-4848	546	39	p	p	NOUN
ejpam-4848	546	40	)	)	PUNCT
ejpam-4848	546	41	,	,	PUNCT
ejpam-4848	546	42	(	(	PUNCT
ejpam-4848	546	43	y	y	NOUN
ejpam-4848	546	44	,	,	PUNCT
ejpam-4848	546	45	q	q	X
ejpam-4848	546	46	)	)	PUNCT
ejpam-4848	546	47	∈	∈	NOUN
ejpam-4848	546	48	v	v	NOUN
ejpam-4848	546	49	(	(	PUNCT
ejpam-4848	546	50	g∨h	g∨h	PROPN
ejpam-4848	546	51	)	)	PUNCT
ejpam-4848	546	52	.	.	PUNCT
ejpam-4848	547	1	then	then	ADV
ejpam-4848	547	2	dg∨h((x	dg∨h((x	VERB
ejpam-4848	547	3	,	,	PUNCT
ejpam-4848	547	4	p	p	NOUN
ejpam-4848	547	5	)	)	PUNCT
ejpam-4848	547	6	,	,	PUNCT
ejpam-4848	547	7	(	(	PUNCT
ejpam-4848	547	8	y	y	NOUN
ejpam-4848	547	9	,	,	PUNCT
ejpam-4848	547	10	q	q	NOUN
ejpam-4848	547	11	)	)	PUNCT
ejpam-4848	547	12	)	)	PUNCT
ejpam-4848	548	1	=	=	PUNCT
ejpam-4848	548	2			NOUN
ejpam-4848	548	3	0	0	PUNCT
ejpam-4848	549	1	if	if	SCONJ
ejpam-4848	549	2	x	x	X
ejpam-4848	549	3	=	=	SYM
ejpam-4848	549	4	y	y	PROPN
ejpam-4848	549	5	and	and	CCONJ
ejpam-4848	549	6	p	p	NOUN
ejpam-4848	549	7	=	=	NOUN
ejpam-4848	549	8	q	q	PROPN
ejpam-4848	549	9	1	1	NUM
ejpam-4848	549	10	if	if	SCONJ
ejpam-4848	549	11	xy	xy	PROPN
ejpam-4848	549	12	∈	∈	PROPN
ejpam-4848	549	13	e(g	e(g	PROPN
ejpam-4848	549	14	)	)	PUNCT
ejpam-4848	549	15	or	or	CCONJ
ejpam-4848	549	16	pq	pq	NOUN
ejpam-4848	549	17	∈	∈	PROPN
ejpam-4848	549	18	e(h	e(h	PROPN
ejpam-4848	549	19	)	)	PUNCT
ejpam-4848	549	20	2	2	NUM
ejpam-4848	549	21	otherwise	otherwise	ADV
ejpam-4848	549	22	proof	proof	NOUN
ejpam-4848	549	23	.	.	PUNCT
ejpam-4848	550	1	clearly	clearly	ADV
ejpam-4848	550	2	,	,	PUNCT
ejpam-4848	550	3	dg∨h((x	dg∨h((x	NOUN
ejpam-4848	550	4	,	,	PUNCT
ejpam-4848	550	5	p	p	NOUN
ejpam-4848	550	6	)	)	PUNCT
ejpam-4848	550	7	,	,	PUNCT
ejpam-4848	550	8	(	(	PUNCT
ejpam-4848	550	9	y	y	NOUN
ejpam-4848	550	10	,	,	PUNCT
ejpam-4848	550	11	q	q	NOUN
ejpam-4848	550	12	)	)	PUNCT
ejpam-4848	550	13	)	)	PUNCT
ejpam-4848	551	1	=	=	SYM
ejpam-4848	551	2	0	0	PUNCT
ejpam-4848	552	1	if	if	SCONJ
ejpam-4848	552	2	x	x	NOUN
ejpam-4848	552	3	=	=	SYM
ejpam-4848	552	4	y	y	PROPN
ejpam-4848	552	5	and	and	CCONJ
ejpam-4848	552	6	p	p	NOUN
ejpam-4848	552	7	=	=	NOUN
ejpam-4848	552	8	q.	q.	PROPN
ejpam-4848	552	9	also	also	ADV
ejpam-4848	552	10	,	,	PUNCT
ejpam-4848	552	11	by	by	ADP
ejpam-4848	552	12	definition	definition	NOUN
ejpam-4848	552	13	,	,	PUNCT
ejpam-4848	552	14	dg∨h((x	dg∨h((x	NOUN
ejpam-4848	552	15	,	,	PUNCT
ejpam-4848	552	16	p	p	NOUN
ejpam-4848	552	17	)	)	PUNCT
ejpam-4848	552	18	,	,	PUNCT
ejpam-4848	552	19	(	(	PUNCT
ejpam-4848	552	20	y	y	NOUN
ejpam-4848	552	21	,	,	PUNCT
ejpam-4848	552	22	q	q	NOUN
ejpam-4848	552	23	)	)	PUNCT
ejpam-4848	552	24	)	)	PUNCT
ejpam-4848	553	1	=	=	SYM
ejpam-4848	553	2	1	1	NUM
ejpam-4848	553	3	if	if	SCONJ
ejpam-4848	553	4	xy	xy	PROPN
ejpam-4848	553	5	∈	∈	PROPN
ejpam-4848	553	6	e(g	e(g	PROPN
ejpam-4848	553	7	)	)	PUNCT
ejpam-4848	553	8	pq	pq	PROPN
ejpam-4848	553	9	∈	∈	PROPN
ejpam-4848	553	10	e(h	e(h	PROPN
ejpam-4848	553	11	)	)	PUNCT
ejpam-4848	553	12	.	.	PUNCT
ejpam-4848	554	1	suppose	suppose	VERB
ejpam-4848	554	2	x	x	PUNCT
ejpam-4848	554	3	̸=	̸=	PROPN
ejpam-4848	554	4	y	y	PROPN
ejpam-4848	554	5	,	,	PUNCT
ejpam-4848	554	6	p	p	PROPN
ejpam-4848	554	7	̸=	̸=	PROPN
ejpam-4848	554	8	q	q	PROPN
ejpam-4848	554	9	,	,	PUNCT
ejpam-4848	554	10	xy	xy	PROPN
ejpam-4848	554	11	/∈	/∈	PUNCT
ejpam-4848	554	12	e(g	e(g	PROPN
ejpam-4848	554	13	)	)	PUNCT
ejpam-4848	554	14	,	,	PUNCT
ejpam-4848	554	15	and	and	CCONJ
ejpam-4848	554	16	pq	pq	INTJ
ejpam-4848	554	17	/∈	/∈	PUNCT
ejpam-4848	554	18	e(h	e(h	PROPN
ejpam-4848	554	19	)	)	PUNCT
ejpam-4848	554	20	.	.	PUNCT
ejpam-4848	555	1	let	let	VERB
ejpam-4848	555	2	z	z	NOUN
ejpam-4848	555	3	∈	∈	PROPN
ejpam-4848	555	4	ng(y	ng(y	NOUN
ejpam-4848	555	5	)	)	PUNCT
ejpam-4848	555	6	and	and	CCONJ
ejpam-4848	555	7	r	r	NOUN
ejpam-4848	555	8	∈	∈	PROPN
ejpam-4848	555	9	nh(p	nh(p	NUM
ejpam-4848	555	10	)	)	PUNCT
ejpam-4848	555	11	.	.	PUNCT
ejpam-4848	556	1	then	then	ADV
ejpam-4848	556	2	(	(	PUNCT
ejpam-4848	556	3	x	x	X
ejpam-4848	556	4	,	,	PUNCT
ejpam-4848	556	5	p)(z	p)(z	PROPN
ejpam-4848	556	6	,	,	PUNCT
ejpam-4848	556	7	r	r	NOUN
ejpam-4848	556	8	)	)	PUNCT
ejpam-4848	556	9	,	,	PUNCT
ejpam-4848	556	10	(	(	PUNCT
ejpam-4848	556	11	z	z	NOUN
ejpam-4848	556	12	,	,	PUNCT
ejpam-4848	556	13	r)(y	r)(y	PROPN
ejpam-4848	556	14	,	,	PUNCT
ejpam-4848	556	15	q	q	X
ejpam-4848	556	16	)	)	PUNCT
ejpam-4848	556	17	∈	∈	PROPN
ejpam-4848	556	18	e(g	e(g	PROPN
ejpam-4848	556	19	∨	∨	NUM
ejpam-4848	556	20	h	h	NOUN
ejpam-4848	556	21	)	)	PUNCT
ejpam-4848	556	22	.	.	PUNCT
ejpam-4848	557	1	this	this	PRON
ejpam-4848	557	2	implies	imply	VERB
ejpam-4848	557	3	that	that	SCONJ
ejpam-4848	557	4	[	[	X
ejpam-4848	557	5	(	(	PUNCT
ejpam-4848	557	6	x	x	X
ejpam-4848	557	7	,	,	PUNCT
ejpam-4848	557	8	p	p	NOUN
ejpam-4848	557	9	)	)	PUNCT
ejpam-4848	557	10	,	,	PUNCT
ejpam-4848	557	11	(	(	PUNCT
ejpam-4848	557	12	z	z	X
ejpam-4848	557	13	,	,	PUNCT
ejpam-4848	557	14	r	r	NOUN
ejpam-4848	557	15	)	)	PUNCT
ejpam-4848	557	16	,	,	PUNCT
ejpam-4848	557	17	(	(	PUNCT
ejpam-4848	557	18	y	y	NOUN
ejpam-4848	557	19	,	,	PUNCT
ejpam-4848	557	20	q	q	NOUN
ejpam-4848	557	21	)	)	PUNCT
ejpam-4848	557	22	]	]	PUNCT
ejpam-4848	557	23	is	be	AUX
ejpam-4848	557	24	an	an	DET
ejpam-4848	557	25	(	(	PUNCT
ejpam-4848	557	26	x	x	NOUN
ejpam-4848	557	27	,	,	PUNCT
ejpam-4848	557	28	p)-(y	p)-(y	ADJ
ejpam-4848	557	29	,	,	PUNCT
ejpam-4848	557	30	q	q	ADJ
ejpam-4848	557	31	)	)	PUNCT
ejpam-4848	557	32	geodesic	geodesic	NOUN
ejpam-4848	557	33	in	in	ADP
ejpam-4848	557	34	g	g	PROPN
ejpam-4848	557	35	∨	∨	PROPN
ejpam-4848	557	36	h.	h.	PROPN
ejpam-4848	557	37	thus	thus	ADV
ejpam-4848	557	38	,	,	PUNCT
ejpam-4848	557	39	dg∨h((x	dg∨h((x	NOUN
ejpam-4848	557	40	,	,	PUNCT
ejpam-4848	557	41	p	p	NOUN
ejpam-4848	557	42	)	)	PUNCT
ejpam-4848	557	43	,	,	PUNCT
ejpam-4848	557	44	(	(	PUNCT
ejpam-4848	557	45	y	y	NOUN
ejpam-4848	557	46	,	,	PUNCT
ejpam-4848	557	47	q	q	NOUN
ejpam-4848	557	48	)	)	PUNCT
ejpam-4848	557	49	)	)	PUNCT
ejpam-4848	558	1	=	=	SYM
ejpam-4848	559	1	2	2	X
ejpam-4848	559	2	.	.	X
ejpam-4848	559	3	theorem	theorem	NOUN
ejpam-4848	559	4	6	6	NUM
ejpam-4848	559	5	.	.	PUNCT
ejpam-4848	560	1	let	let	VERB
ejpam-4848	560	2	g	g	NOUN
ejpam-4848	560	3	andh	andh	NOUN
ejpam-4848	560	4	be	be	AUX
ejpam-4848	560	5	connected	connect	VERB
ejpam-4848	560	6	non	non	ADJ
ejpam-4848	560	7	-	-	ADJ
ejpam-4848	560	8	trivial	trivial	ADJ
ejpam-4848	560	9	graphs	graph	NOUN
ejpam-4848	560	10	of	of	ADP
ejpam-4848	560	11	ordersm	ordersm	NOUN
ejpam-4848	560	12	and	and	CCONJ
ejpam-4848	560	13	n	n	CCONJ
ejpam-4848	560	14	,	,	PUNCT
ejpam-4848	560	15	respectively	respectively	ADV
ejpam-4848	560	16	,	,	PUNCT
ejpam-4848	560	17	and	and	CCONJ
ejpam-4848	560	18	let	let	VERB
ejpam-4848	560	19	(	(	PUNCT
ejpam-4848	560	20	x	x	NOUN
ejpam-4848	560	21	,	,	PUNCT
ejpam-4848	560	22	p	p	NOUN
ejpam-4848	560	23	)	)	PUNCT
ejpam-4848	560	24	∈	∈	PROPN
ejpam-4848	560	25	e(g	e(g	PROPN
ejpam-4848	560	26	∨h	∨h	PROPN
ejpam-4848	560	27	)	)	PUNCT
ejpam-4848	560	28	.	.	PUNCT
ejpam-4848	561	1	then	then	ADV
ejpam-4848	561	2	τg∨h((x	τg∨h((x	NUM
ejpam-4848	561	3	,	,	PUNCT
ejpam-4848	561	4	p	p	NOUN
ejpam-4848	561	5	)	)	PUNCT
ejpam-4848	561	6	)	)	PUNCT
ejpam-4848	562	1	=	=	PUNCT
ejpam-4848	562	2	2mn+	2mn+	NUM
ejpam-4848	562	3	degg(x)degh(p)−	degg(x)degh(p)−	NOUN
ejpam-4848	562	4	n	n	CCONJ
ejpam-4848	562	5	·	·	PUNCT
ejpam-4848	562	6	degg(x)−m	degg(x)−m	NOUN
ejpam-4848	562	7	·	·	PUNCT
ejpam-4848	562	8	degh(p)−	degh(p)−	ADJ
ejpam-4848	562	9	2	2	X
ejpam-4848	562	10	.	.	PUNCT
ejpam-4848	563	1	proof	proof	NOUN
ejpam-4848	563	2	.	.	PUNCT
ejpam-4848	564	1	by	by	ADP
ejpam-4848	564	2	definition	definition	NOUN
ejpam-4848	564	3	3	3	NUM
ejpam-4848	564	4	and	and	CCONJ
ejpam-4848	564	5	lemma	lemma	PROPN
ejpam-4848	564	6	5	5	NUM
ejpam-4848	564	7	,	,	PUNCT
ejpam-4848	564	8	τg∨h((x	τg∨h((x	PROPN
ejpam-4848	564	9	,	,	PUNCT
ejpam-4848	564	10	p	p	NOUN
ejpam-4848	564	11	)	)	PUNCT
ejpam-4848	564	12	)	)	PUNCT
ejpam-4848	564	13	=	=	PUNCT
ejpam-4848	565	1	∑	∑	PUNCT
ejpam-4848	565	2	q∈v	q∈v	ADV
ejpam-4848	565	3	(	(	PUNCT
ejpam-4848	565	4	h	h	NOUN
ejpam-4848	565	5	)	)	PUNCT
ejpam-4848	565	6	∑	∑	ADV
ejpam-4848	565	7	y∈ng(x	y∈ng(x	PROPN
ejpam-4848	565	8	)	)	PUNCT
ejpam-4848	565	9	dg∨h(x	dg∨h(x	PROPN
ejpam-4848	565	10	,	,	PUNCT
ejpam-4848	565	11	p)(y	p)(y	PROPN
ejpam-4848	565	12	,	,	PUNCT
ejpam-4848	565	13	q	q	X
ejpam-4848	565	14	)	)	PUNCT
ejpam-4848	565	15	+	+	CCONJ
ejpam-4848	565	16	∑	∑	PUNCT
ejpam-4848	565	17	q∈nh(p	q∈nh(p	PROPN
ejpam-4848	565	18	)	)	PUNCT
ejpam-4848	565	19	∑	∑	ADV
ejpam-4848	565	20	y∈v	y∈v	NOUN
ejpam-4848	565	21	(	(	PUNCT
ejpam-4848	565	22	g)\ng(x	g)\ng(x	NOUN
ejpam-4848	565	23	)	)	PUNCT
ejpam-4848	565	24	dg∨h(x	dg∨h(x	PROPN
ejpam-4848	565	25	,	,	PUNCT
ejpam-4848	565	26	p)(y	p)(y	PROPN
ejpam-4848	565	27	,	,	PUNCT
ejpam-4848	565	28	q	q	X
ejpam-4848	565	29	)	)	PUNCT
ejpam-4848	565	30	references	reference	NOUN
ejpam-4848	565	31	1419	1419	NUM
ejpam-4848	565	32	+	+	CCONJ
ejpam-4848	565	33	∑	∑	PUNCT
ejpam-4848	565	34	q∈v	q∈v	ADV
ejpam-4848	565	35	(	(	PUNCT
ejpam-4848	565	36	h)\nh	h)\nh	PROPN
ejpam-4848	566	1	[	[	X
ejpam-4848	566	2	p	p	X
ejpam-4848	566	3	]	]	X
ejpam-4848	566	4	dg∨h(x	dg∨h(x	PROPN
ejpam-4848	566	5	,	,	PUNCT
ejpam-4848	566	6	p)(x	p)(x	NOUN
ejpam-4848	566	7	,	,	PUNCT
ejpam-4848	566	8	q	q	NOUN
ejpam-4848	566	9	)	)	PUNCT
ejpam-4848	567	1	+	+	CCONJ
ejpam-4848	567	2	∑	∑	PUNCT
ejpam-4848	567	3	q∈v	q∈v	PROPN
ejpam-4848	567	4	(	(	PUNCT
ejpam-4848	567	5	h)\nh(p	h)\nh(p	NOUN
ejpam-4848	567	6	)	)	PUNCT
ejpam-4848	567	7	∑	∑	ADV
ejpam-4848	567	8	y∈v	y∈v	NOUN
ejpam-4848	567	9	(	(	PUNCT
ejpam-4848	567	10	g)\ng[x	g)\ng[x	PROPN
ejpam-4848	567	11	]	]	PUNCT
ejpam-4848	567	12	dg∨h(x	dg∨h(x	PROPN
ejpam-4848	567	13	,	,	PUNCT
ejpam-4848	567	14	p)(y	p)(y	PROPN
ejpam-4848	567	15	,	,	PUNCT
ejpam-4848	567	16	q	q	X
ejpam-4848	567	17	)	)	PUNCT
ejpam-4848	567	18	=	=	SYM
ejpam-4848	567	19	|v	|v	X
ejpam-4848	567	20	(	(	PUNCT
ejpam-4848	567	21	h)||ng(x)|+	h)||ng(x)|+	PROPN
ejpam-4848	567	22	(	(	PUNCT
ejpam-4848	567	23	|v	|v	PROPN
ejpam-4848	567	24	(	(	PUNCT
ejpam-4848	567	25	g)|	g)|	NOUN
ejpam-4848	567	26	−	−	PROPN
ejpam-4848	567	27	|ng(x)|)|nh(p)|+	|ng(x)|)|nh(p)|+	PROPN
ejpam-4848	567	28	2(|v	2(|v	NUM
ejpam-4848	567	29	(	(	PUNCT
ejpam-4848	567	30	h)|	h)|	NOUN
ejpam-4848	567	31	−	−	PROPN
ejpam-4848	567	32	|nh(p)|	|nh(p)|	NOUN
ejpam-4848	567	33	−	−	NOUN
ejpam-4848	567	34	1	1	NUM
ejpam-4848	567	35	)	)	PUNCT
ejpam-4848	567	36	+	+	CCONJ
ejpam-4848	567	37	2(|v	2(|v	NUM
ejpam-4848	567	38	(	(	PUNCT
ejpam-4848	567	39	h)|	h)|	NOUN
ejpam-4848	567	40	−	−	PROPN
ejpam-4848	567	41	|nh(p)|)(|v	|nh(p)|)(|v	X
ejpam-4848	567	42	(	(	PUNCT
ejpam-4848	567	43	g)|	g)|	NOUN
ejpam-4848	567	44	−	−	NOUN
ejpam-4848	567	45	|ng(x)|	|ng(x)|	NOUN
ejpam-4848	567	46	−	−	NOUN
ejpam-4848	567	47	1	1	NUM
ejpam-4848	567	48	)	)	PUNCT
ejpam-4848	567	49	=	=	VERB
ejpam-4848	567	50	n|ng(x)|+	n|ng(x)|+	NUM
ejpam-4848	567	51	(	(	PUNCT
ejpam-4848	567	52	m−	m−	PROPN
ejpam-4848	567	53	|ng(x)|)|nh(p)|+	|ng(x)|)|nh(p)|+	PROPN
ejpam-4848	567	54	2(n−	2(n−	NUM
ejpam-4848	567	55	|nh(p)|	|nh(p)|	NOUN
ejpam-4848	567	56	−	−	NOUN
ejpam-4848	567	57	1	1	NUM
ejpam-4848	567	58	)	)	PUNCT
ejpam-4848	567	59	+	+	CCONJ
ejpam-4848	567	60	2(n−	2(n−	NUM
ejpam-4848	567	61	|nh(p)|)(m−	|nh(p)|)(m−	PROPN
ejpam-4848	567	62	|ng(x)|	|ng(x)|	VERB
ejpam-4848	567	63	−	−	PROPN
ejpam-4848	567	64	1	1	NUM
ejpam-4848	567	65	)	)	PUNCT
ejpam-4848	567	66	=	=	SYM
ejpam-4848	567	67	n|ng(x)|+m|nh(p)|	n|ng(x)|+m|nh(p)|	NOUN
ejpam-4848	567	68	−	−	NOUN
ejpam-4848	567	69	|ng(x)||nh(p)|	|ng(x)||nh(p)|	NOUN
ejpam-4848	567	70	−	−	PROPN
ejpam-4848	567	71	2|nh(p)|	2|nh(p)|	NUM
ejpam-4848	567	72	−	−	PROPN
ejpam-4848	568	1	2n−	2n−	NUM
ejpam-4848	568	2	2	2	NUM
ejpam-4848	568	3	+	+	NUM
ejpam-4848	568	4	2mn−	2mn−	NUM
ejpam-4848	568	5	2n|ng(x)|	2n|ng(x)|	NUM
ejpam-4848	568	6	−	−	NUM
ejpam-4848	568	7	2m|nh(p)|+	2m|nh(p)|+	NUM
ejpam-4848	568	8	2|ng(x)||nh(p)|	2|ng(x)||nh(p)|	NUM
ejpam-4848	568	9	−	−	NOUN
ejpam-4848	568	10	2n+	2n+	NUM
ejpam-4848	568	11	2|nh(p)|	2|nh(p)|	NUM
ejpam-4848	568	12	=	=	SYM
ejpam-4848	568	13	2mn+	2mn+	NUM
ejpam-4848	568	14	|ng(x)||nh(p)|	|ng(x)||nh(p)|	NOUN
ejpam-4848	568	15	−	−	NOUN
ejpam-4848	568	16	n|ng(x)|	n|ng(x)|	VERB
ejpam-4848	568	17	−m|nh(p)|	−m|nh(p)|	NOUN
ejpam-4848	568	18	−	−	PROPN
ejpam-4848	569	1	2	2	NUM
ejpam-4848	569	2	=	=	SYM
ejpam-4848	569	3	2mn+	2mn+	NUM
ejpam-4848	569	4	degg(x)degh(p)−	degg(x)degh(p)−	NOUN
ejpam-4848	569	5	n	n	CCONJ
ejpam-4848	569	6	·	·	PUNCT
ejpam-4848	569	7	degg(x)−m	degg(x)−m	NOUN
ejpam-4848	569	8	·	·	PUNCT
ejpam-4848	569	9	degh(p)−	degh(p)−	ADJ
ejpam-4848	569	10	2	2	X
ejpam-4848	569	11	.	.	PUNCT
ejpam-4848	569	12	corollary	corollary	ADJ
ejpam-4848	569	13	6	6	NUM
ejpam-4848	569	14	.	.	PUNCT
ejpam-4848	569	15	letg	letg	NOUN
ejpam-4848	569	16	andh	andh	NOUN
ejpam-4848	569	17	be	be	AUX
ejpam-4848	569	18	connected	connect	VERB
ejpam-4848	569	19	non	non	ADJ
ejpam-4848	569	20	-	-	ADJ
ejpam-4848	569	21	trivial	trivial	ADJ
ejpam-4848	569	22	graphs	graph	NOUN
ejpam-4848	569	23	of	of	ADP
ejpam-4848	569	24	ordersm	ordersm	NOUN
ejpam-4848	569	25	and	and	CCONJ
ejpam-4848	569	26	n	n	CCONJ
ejpam-4848	569	27	,	,	PUNCT
ejpam-4848	569	28	respectively	respectively	ADV
ejpam-4848	569	29	,	,	PUNCT
ejpam-4848	569	30	and	and	CCONJ
ejpam-4848	569	31	let	let	VERB
ejpam-4848	569	32	(	(	PUNCT
ejpam-4848	569	33	x	x	NOUN
ejpam-4848	569	34	,	,	PUNCT
ejpam-4848	569	35	p	p	NOUN
ejpam-4848	569	36	)	)	PUNCT
ejpam-4848	569	37	∈	∈	PROPN
ejpam-4848	569	38	v	v	NOUN
ejpam-4848	569	39	(	(	PUNCT
ejpam-4848	569	40	g	g	NOUN
ejpam-4848	569	41	∨h	∨h	PROPN
ejpam-4848	569	42	)	)	PUNCT
ejpam-4848	569	43	.	.	PUNCT
ejpam-4848	570	1	then	then	ADV
ejpam-4848	570	2	cg∨h((x	cg∨h((x	VERB
ejpam-4848	570	3	,	,	PUNCT
ejpam-4848	570	4	p	p	NOUN
ejpam-4848	570	5	)	)	PUNCT
ejpam-4848	570	6	)	)	PUNCT
ejpam-4848	571	1	=	=	PUNCT
ejpam-4848	571	2	mn−	mn−	NOUN
ejpam-4848	571	3	1	1	NUM
ejpam-4848	571	4	2mn+	2mn+	NUM
ejpam-4848	571	5	degg(x)degh(p)−	degg(x)degh(p)−	ADJ
ejpam-4848	571	6	n	n	CCONJ
ejpam-4848	571	7	·	·	PUNCT
ejpam-4848	571	8	degg(x)−m	degg(x)−m	NOUN
ejpam-4848	571	9	·	·	PUNCT
ejpam-4848	571	10	degh(p)−	degh(p)−	ADJ
ejpam-4848	571	11	2	2	X
ejpam-4848	571	12	.	.	PUNCT
ejpam-4848	571	13	example	example	NOUN
ejpam-4848	572	1	6	6	NUM
ejpam-4848	572	2	.	.	PUNCT
ejpam-4848	573	1	let	let	VERB
ejpam-4848	573	2	g	g	PROPN
ejpam-4848	573	3	=	=	PROPN
ejpam-4848	573	4	p3	p3	PROPN
ejpam-4848	573	5	=	=	PUNCT
ejpam-4848	574	1	[	[	X
ejpam-4848	574	2	x	x	X
ejpam-4848	574	3	,	,	PUNCT
ejpam-4848	574	4	y	y	PROPN
ejpam-4848	574	5	,	,	PUNCT
ejpam-4848	574	6	z	z	NOUN
ejpam-4848	574	7	]	]	X
ejpam-4848	574	8	,	,	PUNCT
ejpam-4848	574	9	h	h	NOUN
ejpam-4848	574	10	=	=	SYM
ejpam-4848	574	11	p3	p3	PROPN
ejpam-4848	574	12	=	=	PUNCT
ejpam-4848	575	1	[	[	X
ejpam-4848	575	2	q	q	X
ejpam-4848	575	3	,	,	PUNCT
ejpam-4848	575	4	p	p	X
ejpam-4848	575	5	,	,	PUNCT
ejpam-4848	575	6	s	s	PART
ejpam-4848	575	7	]	]	X
ejpam-4848	575	8	,	,	PUNCT
ejpam-4848	575	9	and	and	CCONJ
ejpam-4848	575	10	(	(	PUNCT
ejpam-4848	575	11	x	x	X
ejpam-4848	575	12	,	,	PUNCT
ejpam-4848	575	13	p	p	NOUN
ejpam-4848	575	14	)	)	PUNCT
ejpam-4848	575	15	∈	∈	PROPN
ejpam-4848	575	16	v	v	NOUN
ejpam-4848	575	17	(	(	PUNCT
ejpam-4848	575	18	g	g	PROPN
ejpam-4848	575	19	∨	∨	NUM
ejpam-4848	575	20	h	h	NOUN
ejpam-4848	575	21	)	)	PUNCT
ejpam-4848	575	22	.	.	PUNCT
ejpam-4848	576	1	by	by	ADP
ejpam-4848	576	2	corollary	corollary	ADJ
ejpam-4848	576	3	6	6	NUM
ejpam-4848	576	4	with	with	ADP
ejpam-4848	576	5	mn	mn	PROPN
ejpam-4848	576	6	=	=	SYM
ejpam-4848	576	7	9	9	NUM
ejpam-4848	576	8	,	,	PUNCT
ejpam-4848	576	9	degg(x	degg(x	NOUN
ejpam-4848	576	10	)	)	PUNCT
ejpam-4848	576	11	=	=	SYM
ejpam-4848	576	12	1	1	NUM
ejpam-4848	576	13	,	,	PUNCT
ejpam-4848	576	14	and	and	CCONJ
ejpam-4848	576	15	degh(p	degh(p	PROPN
ejpam-4848	576	16	)	)	PUNCT
ejpam-4848	576	17	=	=	SYM
ejpam-4848	576	18	2	2	NUM
ejpam-4848	576	19	,	,	PUNCT
ejpam-4848	576	20	we	we	PRON
ejpam-4848	576	21	find	find	VERB
ejpam-4848	576	22	that	that	SCONJ
ejpam-4848	576	23	cg∨h((x	cg∨h((x	ADJ
ejpam-4848	576	24	,	,	PUNCT
ejpam-4848	576	25	p	p	NOUN
ejpam-4848	576	26	)	)	PUNCT
ejpam-4848	576	27	)	)	PUNCT
ejpam-4848	577	1	=	=	SYM
ejpam-4848	577	2	8	8	NUM
ejpam-4848	577	3	9	9	NUM
ejpam-4848	577	4	.	.	PUNCT
ejpam-4848	578	1	4	4	X
ejpam-4848	578	2	.	.	X
ejpam-4848	578	3	conclusion	conclusion	NOUN
ejpam-4848	578	4	the	the	DET
ejpam-4848	578	5	study	study	NOUN
ejpam-4848	578	6	revisited	revisit	VERB
ejpam-4848	578	7	the	the	DET
ejpam-4848	578	8	concept	concept	NOUN
ejpam-4848	578	9	of	of	ADP
ejpam-4848	578	10	closeness	closeness	NOUN
ejpam-4848	578	11	centrality	centrality	NOUN
ejpam-4848	578	12	of	of	ADP
ejpam-4848	578	13	a	a	DET
ejpam-4848	578	14	vertex	vertex	NOUN
ejpam-4848	578	15	in	in	ADP
ejpam-4848	578	16	a	a	DET
ejpam-4848	578	17	graph	graph	NOUN
ejpam-4848	578	18	.	.	PUNCT
ejpam-4848	579	1	formulas	formula	NOUN
ejpam-4848	579	2	that	that	PRON
ejpam-4848	579	3	can	can	AUX
ejpam-4848	579	4	be	be	AUX
ejpam-4848	579	5	used	use	VERB
ejpam-4848	579	6	to	to	PART
ejpam-4848	579	7	determine	determine	VERB
ejpam-4848	579	8	the	the	DET
ejpam-4848	579	9	closeness	closeness	NOUN
ejpam-4848	579	10	centrality	centrality	NOUN
ejpam-4848	579	11	of	of	ADP
ejpam-4848	579	12	vertices	vertex	NOUN
ejpam-4848	579	13	in	in	ADP
ejpam-4848	579	14	the	the	DET
ejpam-4848	579	15	shadow	shadow	NOUN
ejpam-4848	579	16	graph	graph	NOUN
ejpam-4848	579	17	,	,	PUNCT
ejpam-4848	579	18	edge	edge	NOUN
ejpam-4848	579	19	corona	corona	NOUN
ejpam-4848	579	20	of	of	ADP
ejpam-4848	579	21	graphs	graph	NOUN
ejpam-4848	579	22	,	,	PUNCT
ejpam-4848	579	23	complementary	complementary	ADJ
ejpam-4848	579	24	prism	prism	NOUN
ejpam-4848	579	25	,	,	PUNCT
ejpam-4848	579	26	and	and	CCONJ
ejpam-4848	579	27	disjunction	disjunction	NOUN
ejpam-4848	579	28	of	of	ADP
ejpam-4848	579	29	graphs	graph	NOUN
ejpam-4848	579	30	were	be	AUX
ejpam-4848	579	31	generated	generate	VERB
ejpam-4848	579	32	.	.	PUNCT
ejpam-4848	580	1	the	the	DET
ejpam-4848	580	2	parameter	parameter	NOUN
ejpam-4848	580	3	can	can	AUX
ejpam-4848	580	4	be	be	AUX
ejpam-4848	580	5	studied	study	VERB
ejpam-4848	580	6	further	far	ADV
ejpam-4848	580	7	for	for	ADP
ejpam-4848	580	8	other	other	ADJ
ejpam-4848	580	9	graphs	graph	NOUN
ejpam-4848	580	10	under	under	ADP
ejpam-4848	580	11	some	some	DET
ejpam-4848	580	12	other	other	ADJ
ejpam-4848	580	13	binary	binary	ADJ
ejpam-4848	580	14	operations	operation	NOUN
ejpam-4848	580	15	.	.	PUNCT
ejpam-4848	581	1	acknowledgements	acknowledgement	NOUN
ejpam-4848	581	2	the	the	DET
ejpam-4848	581	3	authors	author	NOUN
ejpam-4848	581	4	would	would	AUX
ejpam-4848	581	5	like	like	VERB
ejpam-4848	581	6	to	to	PART
ejpam-4848	581	7	thank	thank	VERB
ejpam-4848	581	8	the	the	DET
ejpam-4848	581	9	referees	referee	NOUN
ejpam-4848	581	10	for	for	ADP
ejpam-4848	581	11	the	the	DET
ejpam-4848	581	12	invaluable	invaluable	ADJ
ejpam-4848	581	13	corrections	correction	NOUN
ejpam-4848	581	14	and	and	CCONJ
ejpam-4848	581	15	suggestions	suggestion	NOUN
ejpam-4848	581	16	that	that	PRON
ejpam-4848	581	17	resulted	result	VERB
ejpam-4848	581	18	to	to	ADP
ejpam-4848	581	19	this	this	DET
ejpam-4848	581	20	final	final	ADJ
ejpam-4848	581	21	version	version	NOUN
ejpam-4848	581	22	of	of	ADP
ejpam-4848	581	23	the	the	DET
ejpam-4848	581	24	paper	paper	NOUN
ejpam-4848	581	25	.	.	PUNCT
ejpam-4848	582	1	also	also	ADV
ejpam-4848	582	2	,	,	PUNCT
ejpam-4848	582	3	they	they	PRON
ejpam-4848	582	4	would	would	AUX
ejpam-4848	582	5	like	like	VERB
ejpam-4848	582	6	to	to	PART
ejpam-4848	582	7	convey	convey	VERB
ejpam-4848	582	8	their	their	PRON
ejpam-4848	582	9	gratefulness	gratefulness	NOUN
ejpam-4848	582	10	to	to	ADP
ejpam-4848	582	11	msu	msu	PROPN
ejpam-4848	582	12	-	-	PUNCT
ejpam-4848	582	13	iligan	iligan	PROPN
ejpam-4848	582	14	institute	institute	PROPN
ejpam-4848	582	15	of	of	ADP
ejpam-4848	582	16	technology	technology	PROPN
ejpam-4848	582	17	,	,	PUNCT
ejpam-4848	582	18	philippines	philippine	NOUN
ejpam-4848	582	19	and	and	CCONJ
ejpam-4848	582	20	visayas	visayas	PROPN
ejpam-4848	582	21	state	state	PROPN
ejpam-4848	582	22	university	university	PROPN
ejpam-4848	582	23	,	,	PUNCT
ejpam-4848	582	24	philippines	philippine	NOUN
ejpam-4848	582	25	for	for	ADP
ejpam-4848	582	26	the	the	DET
ejpam-4848	582	27	support	support	NOUN
ejpam-4848	582	28	throughout	throughout	ADP
ejpam-4848	582	29	the	the	DET
ejpam-4848	582	30	study	study	NOUN
ejpam-4848	582	31	.	.	PUNCT
ejpam-4848	583	1	references	reference	NOUN
ejpam-4848	583	2	[	[	X
ejpam-4848	583	3	1	1	NUM
ejpam-4848	583	4	]	]	PUNCT
ejpam-4848	583	5	s	s	AUX
ejpam-4848	583	6	borgatti	borgatti	NOUN
ejpam-4848	583	7	.	.	PUNCT
ejpam-4848	584	1	centrality	centrality	NOUN
ejpam-4848	584	2	and	and	CCONJ
ejpam-4848	584	3	network	network	NOUN
ejpam-4848	584	4	flow	flow	NOUN
ejpam-4848	584	5	.	.	PUNCT
ejpam-4848	585	1	social	social	ADJ
ejpam-4848	585	2	networks	network	NOUN
ejpam-4848	585	3	,	,	PUNCT
ejpam-4848	585	4	27:55–71	27:55–71	NUM
ejpam-4848	585	5	,	,	PUNCT
ejpam-4848	585	6	2005	2005	NUM
ejpam-4848	585	7	.	.	PUNCT
ejpam-4848	586	1	[	[	X
ejpam-4848	586	2	2	2	NUM
ejpam-4848	586	3	]	]	SYM
ejpam-4848	586	4	m	m	PROPN
ejpam-4848	586	5	van	van	PROPN
ejpam-4848	586	6	den	den	PROPN
ejpam-4848	586	7	heuvel	heuvel	PROPN
ejpam-4848	586	8	and	and	CCONJ
ejpam-4848	586	9	o	o	NOUN
ejpam-4848	586	10	sporns	sporn	NOUN
ejpam-4848	586	11	.	.	PUNCT
ejpam-4848	587	1	network	network	NOUN
ejpam-4848	587	2	hubs	hub	NOUN
ejpam-4848	587	3	in	in	ADP
ejpam-4848	587	4	the	the	DET
ejpam-4848	587	5	human	human	ADJ
ejpam-4848	587	6	brain	brain	NOUN
ejpam-4848	587	7	.	.	PUNCT
ejpam-4848	588	1	trends	trend	NOUN
ejpam-4848	588	2	in	in	ADP
ejpam-4848	588	3	the	the	DET
ejpam-4848	588	4	cognitive	cognitive	ADJ
ejpam-4848	588	5	sciences	science	NOUN
ejpam-4848	588	6	,	,	PUNCT
ejpam-4848	588	7	17(12):683–696	17(12):683–696	NUM
ejpam-4848	588	8	,	,	PUNCT
ejpam-4848	588	9	2013	2013	NUM
ejpam-4848	588	10	.	.	PUNCT
ejpam-4848	589	1	references	reference	NOUN
ejpam-4848	589	2	1420	1420	NUM
ejpam-4848	589	3	[	[	X
ejpam-4848	589	4	3	3	NUM
ejpam-4848	589	5	]	]	X
ejpam-4848	589	6	r.	r.	PROPN
ejpam-4848	589	7	eballe	eballe	PROPN
ejpam-4848	589	8	,	,	PUNCT
ejpam-4848	589	9	c.	c.	PROPN
ejpam-4848	589	10	m.	m.	PROPN
ejpam-4848	589	11	balingit	balingit	PROPN
ejpam-4848	589	12	,	,	PUNCT
ejpam-4848	589	13	i.	i.	PROPN
ejpam-4848	589	14	cabahug	cabahug	PROPN
ejpam-4848	589	15	jr	jr	PROPN
ejpam-4848	589	16	.	.	PROPN
ejpam-4848	589	17	,	,	PUNCT
ejpam-4848	589	18	a.	a.	PROPN
ejpam-4848	589	19	flores	flores	PROPN
ejpam-4848	589	20	,	,	PUNCT
ejpam-4848	589	21	s.	s.	PROPN
ejpam-4848	589	22	lumpayao	lumpayao	PROPN
ejpam-4848	589	23	,	,	PUNCT
ejpam-4848	589	24	b.	b.	PROPN
ejpam-4848	589	25	peñalosa	peñalosa	PROPN
ejpam-4848	589	26	,	,	PUNCT
ejpam-4848	589	27	g.	g.	PROPN
ejpam-4848	589	28	tampipi	tampipi	PROPN
ejpam-4848	589	29	,	,	PUNCT
ejpam-4848	589	30	and	and	CCONJ
ejpam-4848	589	31	c.	c.	PROPN
ejpam-4848	589	32	villarta	villarta	PROPN
ejpam-4848	589	33	.	.	PUNCT
ejpam-4848	590	1	closeness	closeness	NOUN
ejpam-4848	590	2	centrality	centrality	NOUN
ejpam-4848	590	3	in	in	ADP
ejpam-4848	590	4	graph	graph	NOUN
ejpam-4848	590	5	products	product	NOUN
ejpam-4848	590	6	.	.	PUNCT
ejpam-4848	591	1	advances	advance	NOUN
ejpam-4848	591	2	and	and	CCONJ
ejpam-4848	591	3	applications	application	NOUN
ejpam-4848	591	4	in	in	ADP
ejpam-4848	591	5	discrete	discrete	ADJ
ejpam-4848	591	6	mathematics	mathematic	NOUN
ejpam-4848	591	7	,	,	PUNCT
ejpam-4848	591	8	39(1):29–41	39(1):29–41	NUM
ejpam-4848	591	9	,	,	PUNCT
ejpam-4848	591	10	2023	2023	NUM
ejpam-4848	591	11	.	.	PUNCT
ejpam-4848	592	1	[	[	X
ejpam-4848	592	2	4	4	NUM
ejpam-4848	592	3	]	]	SYM
ejpam-4848	592	4	r	r	NOUN
ejpam-4848	592	5	eballe	eballe	NOUN
ejpam-4848	592	6	and	and	CCONJ
ejpam-4848	592	7	i	i	PRON
ejpam-4848	592	8	cabahug	cabahug	VERB
ejpam-4848	592	9	.	.	PUNCT
ejpam-4848	593	1	closeness	closeness	NOUN
ejpam-4848	593	2	centrality	centrality	NOUN
ejpam-4848	593	3	of	of	ADP
ejpam-4848	593	4	some	some	DET
ejpam-4848	593	5	graph	graph	NOUN
ejpam-4848	593	6	families	family	NOUN
ejpam-4848	593	7	.	.	PUNCT
ejpam-4848	594	1	international	international	ADJ
ejpam-4848	594	2	journal	journal	PROPN
ejpam-4848	594	3	of	of	ADP
ejpam-4848	594	4	contemporary	contemporary	PROPN
ejpam-4848	594	5	mathematical	mathematical	PROPN
ejpam-4848	594	6	sciences	sciences	PROPN
ejpam-4848	594	7	,	,	PUNCT
ejpam-4848	594	8	16(4):127–134	16(4):127–134	PROPN
ejpam-4848	594	9	,	,	PUNCT
ejpam-4848	594	10	2021	2021	NUM
ejpam-4848	594	11	.	.	PUNCT
ejpam-4848	595	1	[	[	X
ejpam-4848	595	2	5	5	NUM
ejpam-4848	595	3	]	]	PUNCT
ejpam-4848	595	4	j	j	PROPN
ejpam-4848	595	5	golbeck	golbeck	PROPN
ejpam-4848	595	6	.	.	PUNCT
ejpam-4848	595	7	network	network	NOUN
ejpam-4848	595	8	structure	structure	NOUN
ejpam-4848	595	9	and	and	CCONJ
ejpam-4848	595	10	measures	measure	NOUN
ejpam-4848	595	11	.	.	PUNCT
ejpam-4848	596	1	analyzing	analyze	VERB
ejpam-4848	596	2	the	the	DET
ejpam-4848	596	3	social	social	ADJ
ejpam-4848	596	4	web	web	NOUN
ejpam-4848	596	5	,	,	PUNCT
ejpam-4848	596	6	pages	page	NOUN
ejpam-4848	596	7	25–44	25–44	NUM
ejpam-4848	596	8	,	,	PUNCT
ejpam-4848	596	9	2013	2013	NUM
ejpam-4848	596	10	.	.	PUNCT
ejpam-4848	597	1	[	[	X
ejpam-4848	597	2	6	6	NUM
ejpam-4848	597	3	]	]	PUNCT
ejpam-4848	597	4	w	w	PROPN
ejpam-4848	597	5	chen	chen	PROPN
ejpam-4848	597	6	k	k	PROPN
ejpam-4848	597	7	okamoto	okamoto	PROPN
ejpam-4848	597	8	and	and	CCONJ
ejpam-4848	597	9	x	x	PROPN
ejpam-4848	597	10	li	li	PROPN
ejpam-4848	597	11	.	.	PROPN
ejpam-4848	597	12	ranking	ranking	NOUN
ejpam-4848	597	13	of	of	ADP
ejpam-4848	597	14	closeness	closeness	NOUN
ejpam-4848	597	15	centrality	centrality	NOUN
ejpam-4848	597	16	for	for	ADP
ejpam-4848	597	17	large	large	ADJ
ejpam-4848	597	18	-	-	PUNCT
ejpam-4848	597	19	scale	scale	NOUN
ejpam-4848	597	20	social	social	ADJ
ejpam-4848	597	21	networks	network	NOUN
ejpam-4848	597	22	.	.	PUNCT
ejpam-4848	598	1	international	international	ADJ
ejpam-4848	598	2	workshop	workshop	NOUN
ejpam-4848	598	3	on	on	ADP
ejpam-4848	598	4	frontiers	frontier	NOUN
ejpam-4848	598	5	in	in	ADP
ejpam-4848	598	6	algorithmics	algorithmic	NOUN
ejpam-4848	598	7	,	,	PUNCT
ejpam-4848	598	8	pages	page	NOUN
ejpam-4848	598	9	186–195	186–195	NUM
ejpam-4848	598	10	,	,	PUNCT
ejpam-4848	598	11	2008	2008	NUM
ejpam-4848	598	12	.	.	PUNCT
ejpam-4848	599	1	[	[	X
ejpam-4848	599	2	7	7	X
ejpam-4848	599	3	]	]	X
ejpam-4848	599	4	y	y	PROPN
ejpam-4848	599	5	rochat	rochat	PROPN
ejpam-4848	599	6	.	.	PUNCT
ejpam-4848	600	1	closeness	closeness	NOUN
ejpam-4848	600	2	centrality	centrality	NOUN
ejpam-4848	600	3	extended	extend	VERB
ejpam-4848	600	4	to	to	ADP
ejpam-4848	600	5	unconnected	unconnected	ADJ
ejpam-4848	600	6	graphs	graph	NOUN
ejpam-4848	600	7	:	:	PUNCT
ejpam-4848	600	8	the	the	DET
ejpam-4848	600	9	harmonic	harmonic	ADJ
ejpam-4848	600	10	centrality	centrality	NOUN
ejpam-4848	600	11	index	index	NOUN
ejpam-4848	600	12	.	.	PUNCT
ejpam-4848	601	1	2009	2009	NUM
ejpam-4848	601	2	.	.	PUNCT
ejpam-4848	602	1	[	[	X
ejpam-4848	602	2	8	8	NUM
ejpam-4848	602	3	]	]	X
ejpam-4848	602	4	j	j	PROPN
ejpam-4848	602	5	zhang	zhang	PROPN
ejpam-4848	602	6	and	and	CCONJ
ejpam-4848	602	7	y	y	PROPN
ejpam-4848	602	8	luo	luo	PROPN
ejpam-4848	602	9	.	.	PROPN
ejpam-4848	602	10	degree	degree	NOUN
ejpam-4848	602	11	centrality	centrality	NOUN
ejpam-4848	602	12	,	,	PUNCT
ejpam-4848	602	13	betweenness	betweenness	NOUN
ejpam-4848	602	14	centrality	centrality	NOUN
ejpam-4848	602	15	,	,	PUNCT
ejpam-4848	602	16	and	and	CCONJ
ejpam-4848	602	17	closeness	closeness	NOUN
ejpam-4848	602	18	centrality	centrality	NOUN
ejpam-4848	602	19	in	in	ADP
ejpam-4848	602	20	social	social	ADJ
ejpam-4848	602	21	network	network	NOUN
ejpam-4848	602	22	.	.	PUNCT
ejpam-4848	603	1	2nd	2nd	ADJ
ejpam-4848	603	2	international	international	ADJ
ejpam-4848	603	3	conference	conference	NOUN
ejpam-4848	603	4	on	on	ADP
ejpam-4848	603	5	modelling	modelling	NOUN
ejpam-4848	603	6	,	,	PUNCT
ejpam-4848	603	7	simulation	simulation	NOUN
ejpam-4848	603	8	and	and	CCONJ
ejpam-4848	603	9	applied	apply	VERB
ejpam-4848	603	10	mathematics	mathematic	NOUN
ejpam-4848	603	11	,	,	PUNCT
ejpam-4848	603	12	pages	page	NOUN
ejpam-4848	603	13	300–303	300–303	NUM
ejpam-4848	603	14	,	,	PUNCT
ejpam-4848	603	15	2017	2017	NUM
ejpam-4848	603	16	.	.	PUNCT